LMFDB - Embedded newform 1183.2.e.l.170.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.5
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.l.508.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.883662 + 1.53055i) q^{2} +(1.16401 + 2.01613i) q^{3} +(-0.561718 - 0.972924i) q^{4} +(-2.03380 + 3.52265i) q^{5} -4.11437 q^{6} +(1.79914 + 1.93987i) q^{7} -1.54917 q^{8} +(-1.20985 + 2.09552i) q^{9} +O(q^{10})$	\(q+(-0.883662 + 1.53055i) q^{2} +(1.16401 + 2.01613i) q^{3} +(-0.561718 - 0.972924i) q^{4} +(-2.03380 + 3.52265i) q^{5} -4.11437 q^{6} +(1.79914 + 1.93987i) q^{7} -1.54917 q^{8} +(-1.20985 + 2.09552i) q^{9} +(-3.59438 - 6.22566i) q^{10} +(-1.45338 - 2.51733i) q^{11} +(1.30769 - 2.26499i) q^{12} +(-4.55889 + 1.03949i) q^{14} -9.46947 q^{15} +(2.49238 - 4.31693i) q^{16} +(1.68835 + 2.92430i) q^{17} +(-2.13819 - 3.70346i) q^{18} +(0.593154 - 1.02737i) q^{19} +4.56969 q^{20} +(-1.81680 + 5.88533i) q^{21} +5.13720 q^{22} +(0.00373203 - 0.00646406i) q^{23} +(-1.80326 - 3.12333i) q^{24} +(-5.77269 - 9.99859i) q^{25} +1.35096 q^{27} +(0.876732 - 2.84009i) q^{28} -8.00705 q^{29} +(8.36781 - 14.4935i) q^{30} +(0.339720 + 0.588412i) q^{31} +(2.85567 + 4.94617i) q^{32} +(3.38351 - 5.86041i) q^{33} -5.96771 q^{34} +(-10.4926 + 2.39244i) q^{35} +2.71837 q^{36} +(-1.29493 + 2.24288i) q^{37} +(1.04830 + 1.81570i) q^{38} +(3.15071 - 5.45719i) q^{40} +10.5725 q^{41} +(-7.40235 - 7.98134i) q^{42} +4.33374 q^{43} +(-1.63278 + 2.82806i) q^{44} +(-4.92118 - 8.52373i) q^{45} +(0.00659571 + 0.0114241i) q^{46} +(-5.70745 + 9.88560i) q^{47} +11.6047 q^{48} +(-0.526169 + 6.98020i) q^{49} +20.4044 q^{50} +(-3.93051 + 6.80785i) q^{51} +(3.04864 + 5.28040i) q^{53} +(-1.19379 + 2.06771i) q^{54} +11.8236 q^{55} +(-2.78719 - 3.00519i) q^{56} +2.76175 q^{57} +(7.07553 - 12.2552i) q^{58} +(-1.97815 - 3.42626i) q^{59} +(5.31917 + 9.21307i) q^{60} +(-1.80171 + 3.12065i) q^{61} -1.20079 q^{62} +(-6.24172 + 1.42319i) q^{63} -0.124274 q^{64} +(5.97976 + 10.3572i) q^{66} +(0.838797 + 1.45284i) q^{67} +(1.89675 - 3.28527i) q^{68} +0.0173765 q^{69} +(5.61014 - 18.1735i) q^{70} -7.13225 q^{71} +(1.87427 - 3.24632i) q^{72} +(-5.24721 - 9.08843i) q^{73} +(-2.28856 - 3.96390i) q^{74} +(13.4390 - 23.2769i) q^{75} -1.33274 q^{76} +(2.26845 - 7.34841i) q^{77} +(-5.72103 + 9.90912i) q^{79} +(10.1380 + 17.5596i) q^{80} +(5.20208 + 9.01027i) q^{81} +(-9.34251 + 16.1817i) q^{82} +1.82071 q^{83} +(6.74650 - 1.53829i) q^{84} -13.7350 q^{85} +(-3.82956 + 6.63299i) q^{86} +(-9.32031 - 16.1432i) q^{87} +(2.25154 + 3.89979i) q^{88} +(1.80318 - 3.12320i) q^{89} +17.3946 q^{90} -0.00838539 q^{92} +(-0.790876 + 1.36984i) q^{93} +(-10.0869 - 17.4711i) q^{94} +(2.41271 + 4.17894i) q^{95} +(-6.64808 + 11.5148i) q^{96} +10.1115 q^{97} +(-10.2186 - 6.97346i) q^{98} +7.03349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.883662	+	1.53055i	−0.624844	+	1.08226i	0.363728	+	0.931505i	$0.381504\pi$
$2$	−0.883662	+	1.53055i	−0.624844	+	1.08226i	−0.988571	+	0.150755i	$0.951829\pi$
$3$	1.16401	+	2.01613i	0.672043	+	1.16401i	0.977324	+	0.211750i	$0.0679162\pi$
$3$	1.16401	+	2.01613i	0.672043	+	1.16401i	−0.305281	+	0.952262i	$0.598750\pi$
$4$	−0.561718	−	0.972924i	−0.280859	−	0.486462i
$5$	−2.03380	+	3.52265i	−0.909543	+	1.57537i	−0.0948430	+	0.995492i	$0.530235\pi$
$5$	−2.03380	+	3.52265i	−0.909543	+	1.57537i	−0.814700	+	0.579883i	$0.803098\pi$
$6$	−4.11437			−1.67969
$7$	1.79914	+	1.93987i	0.680012	+	0.733201i
$7$	1.79914	+	1.93987i	0.680012	+	0.733201i
$8$	−1.54917			−0.547716
$9$	−1.20985	+	2.09552i	−0.403283	+	0.698506i
$10$	−3.59438	−	6.22566i	−1.13664	−	1.96873i
$11$	−1.45338	−	2.51733i	−0.438211	−	0.759004i	0.559340	−	0.828938i	$-0.311054\pi$
$11$	−1.45338	−	2.51733i	−0.438211	−	0.759004i	−0.997552	+	0.0699339i	$0.977721\pi$
$12$	1.30769	−	2.26499i	0.377498	−	0.653846i
$13$		0			0
$13$		0			0
$14$	−4.55889	+	1.03949i	−1.21842	+	0.277815i
$15$	−9.46947			−2.44501
$16$	2.49238	−	4.31693i	0.623095	−	1.07923i
$17$	1.68835	+	2.92430i	0.409484	+	0.709248i	0.994832	−	0.101535i	$-0.0323753\pi$
$17$	1.68835	+	2.92430i	0.409484	+	0.709248i	−0.585348	+	0.810782i	$0.699042\pi$
$18$	−2.13819	−	3.70346i	−0.503977	−	0.872914i
$19$	0.593154	−	1.02737i	0.136079	−	0.235696i	−0.789930	−	0.613197i	$-0.789883\pi$
$19$	0.593154	−	1.02737i	0.136079	−	0.235696i	0.926009	+	0.377501i	$0.123217\pi$
$20$	4.56969			1.02181
$21$	−1.81680	+	5.88533i	−0.396458	+	1.28428i
$22$	5.13720			1.09525
$23$	0.00373203	−	0.00646406i	0.000778182	−	0.00134785i	−0.865636	−	0.500674i	$-0.833086\pi$
$23$	0.00373203	−	0.00646406i	0.000778182	−	0.00134785i	0.866414	+	0.499326i	$0.166419\pi$
$24$	−1.80326	−	3.12333i	−0.368088	−	0.637548i
$25$	−5.77269	−	9.99859i	−1.15454	−	1.99972i
$26$		0			0
$27$	1.35096			0.259993
$28$	0.876732	−	2.84009i	0.165687	−	0.536726i
$29$	−8.00705			−1.48687			−0.743436	−	0.668807i	$-0.766805\pi$
$29$	−8.00705			−1.48687			−0.743436	+	0.668807i	$0.766805\pi$
$30$	8.36781	−	14.4935i	1.52775	−	2.64614i
$31$	0.339720	+	0.588412i	0.0610155	+	0.105682i	0.894920	−	0.446227i	$-0.147233\pi$
$31$	0.339720	+	0.588412i	0.0610155	+	0.105682i	−0.833904	+	0.551909i	$0.813899\pi$
$32$	2.85567	+	4.94617i	0.504816	+	0.874368i
$33$	3.38351	−	5.86041i	0.588993	−	1.02017i
$34$	−5.96771			−1.02345
$35$	−10.4926	+	2.39244i	−1.77357	+	0.404396i
$36$	2.71837			0.453062
$37$	−1.29493	+	2.24288i	−0.212885	+	0.368728i	−0.952616	−	0.304175i	$-0.901619\pi$
$37$	−1.29493	+	2.24288i	−0.212885	+	0.368728i	0.739731	+	0.672903i	$0.234953\pi$
$38$	1.04830	+	1.81570i	0.170056	+	0.294546i
$39$		0			0
$40$	3.15071	−	5.45719i	0.498171	−	0.862858i
$41$	10.5725			1.65115			0.825573	−	0.564295i	$-0.190852\pi$
$41$	10.5725			1.65115			0.825573	+	0.564295i	$0.190852\pi$
$42$	−7.40235	−	7.98134i	−1.14221	−	1.23155i
$43$	4.33374			0.660888			0.330444	−	0.943826i	$-0.392801\pi$
$43$	4.33374			0.660888			0.330444	+	0.943826i	$0.392801\pi$
$44$	−1.63278	+	2.82806i	−0.246151	+	0.426346i
$45$	−4.92118	−	8.52373i	−0.733606	−	1.27064i
$46$	0.00659571	+	0.0114241i	0.000972484	+	0.00168439i
$47$	−5.70745	+	9.88560i	−0.832517	+	1.44196i	0.0635186	+	0.997981i	$0.479768\pi$
$47$	−5.70745	+	9.88560i	−0.832517	+	1.44196i	−0.896036	+	0.443982i	$0.853566\pi$
$48$	11.6047			1.67499
$49$	−0.526169	+	6.98020i	−0.0751670	+	0.997171i
$50$	20.4044			2.88562
$51$	−3.93051	+	6.80785i	−0.550382	+	0.953289i
$52$		0			0
$53$	3.04864	+	5.28040i	0.418763	+	0.725319i	0.995815	−	0.0913880i	$-0.0291303\pi$
$53$	3.04864	+	5.28040i	0.418763	+	0.725319i	−0.577052	+	0.816707i	$0.695797\pi$
$54$	−1.19379	+	2.06771i	−0.162455	+	0.281380i
$55$	11.8236			1.59429
$56$	−2.78719	−	3.00519i	−0.372453	−	0.401586i
$57$	2.76175			0.365803
$58$	7.07553	−	12.2552i	0.929062	−	1.60918i
$59$	−1.97815	−	3.42626i	−0.257533	−	0.446061i	0.708047	−	0.706165i	$-0.249576\pi$
$59$	−1.97815	−	3.42626i	−0.257533	−	0.446061i	−0.965581	+	0.260104i	$0.916243\pi$
$60$	5.31917	+	9.21307i	0.686702	+	1.18940i
$61$	−1.80171	+	3.12065i	−0.230685	+	0.399558i	−0.958010	−	0.286735i	$-0.907430\pi$
$61$	−1.80171	+	3.12065i	−0.230685	+	0.399558i	0.727325	+	0.686293i	$0.240763\pi$
$62$	−1.20079			−0.152501
$63$	−6.24172	+	1.42319i	−0.786382	+	0.179305i
$64$	−0.124274			−0.0155343
$65$		0			0
$66$	5.97976	+	10.3572i	0.736057	+	1.27489i
$67$	0.838797	+	1.45284i	0.102475	+	0.177493i	0.912704	−	0.408622i	$-0.133990\pi$
$67$	0.838797	+	1.45284i	0.102475	+	0.177493i	−0.810229	+	0.586114i	$0.800657\pi$
$68$	1.89675	−	3.28527i	0.230015	−	0.398397i
$69$	0.0173765			0.00209189
$70$	5.61014	−	18.1735i	0.670539	−	2.17215i
$71$	−7.13225			−0.846442			−0.423221	−	0.906026i	$-0.639101\pi$
$71$	−7.13225			−0.846442			−0.423221	+	0.906026i	$0.639101\pi$
$72$	1.87427	−	3.24632i	0.220884	−	0.382583i
$73$	−5.24721	−	9.08843i	−0.614139	−	1.06372i	−0.990535	−	0.137262i	$-0.956170\pi$
$73$	−5.24721	−	9.08843i	−0.614139	−	1.06372i	0.376395	−	0.926459i	$-0.377163\pi$
$74$	−2.28856	−	3.96390i	−0.266040	−	0.460794i
$75$	13.4390	−	23.2769i	1.55180	−	2.68779i
$76$	−1.33274			−0.152876
$77$	2.26845	−	7.34841i	0.258514	−	0.837429i
$78$		0			0
$79$	−5.72103	+	9.90912i	−0.643667	+	1.11486i	0.340941	+	0.940085i	$0.389254\pi$
$79$	−5.72103	+	9.90912i	−0.643667	+	1.11486i	−0.984608	+	0.174779i	$0.944079\pi$
$80$	10.1380	+	17.5596i	1.13346	+	1.96322i
$81$	5.20208	+	9.01027i	0.578009	+	1.00114i
$82$	−9.34251	+	16.1817i	−1.03171	+	1.78697i
$83$	1.82071			0.199849			0.0999246	−	0.994995i	$-0.468140\pi$
$83$	1.82071			0.199849			0.0999246	+	0.994995i	$0.468140\pi$
$84$	6.74650	−	1.53829i	0.736104	−	0.167841i
$85$	−13.7350			−1.48977
$86$	−3.82956	+	6.63299i	−0.412952	+	0.715254i
$87$	−9.32031	−	16.1432i	−0.999242	−	1.73074i
$88$	2.25154	+	3.89979i	0.240015	+	0.415719i
$89$	1.80318	−	3.12320i	0.191137	−	0.331058i	−0.754491	−	0.656311i	$-0.772116\pi$
$89$	1.80318	−	3.12320i	0.191137	−	0.331058i	0.945627	+	0.325253i	$0.105449\pi$
$90$	17.3946			1.83356
$91$		0			0
$92$	−0.00838539			−0.000874237
$93$	−0.790876	+	1.36984i	−0.0820100	+	0.142046i
$94$	−10.0869	−	17.4711i	−1.04039	−	1.80200i
$95$	2.41271	+	4.17894i	0.247539	+	0.428751i
$96$	−6.64808	+	11.5148i	−0.678516	+	1.17522i
$97$	10.1115			1.02667			0.513333	−	0.858189i	$-0.328411\pi$
$97$	10.1115			1.02667			0.513333	+	0.858189i	$0.328411\pi$
$98$	−10.2186	−	6.97346i	−1.03223	−	0.704426i
$99$	7.03349			0.706892
$100$	−6.48524	+	11.2328i	−0.648524	+	1.12328i
$101$	−2.58482	−	4.47703i	−0.257199	−	0.445481i	0.708292	−	0.705920i	$-0.249466\pi$
$101$	−2.58482	−	4.47703i	−0.257199	−	0.445481i	−0.965490	+	0.260439i	$0.916133\pi$
$102$	−6.94649	−	12.0317i	−0.687805	−	1.19131i
$103$	1.90234	−	3.29494i	0.187443	−	0.324660i	−0.756954	−	0.653468i	$-0.773313\pi$
$103$	1.90234	−	3.29494i	0.187443	−	0.324660i	0.944397	+	0.328808i	$0.106647\pi$
$104$		0			0
$105$	−17.0369	−	18.3695i	−1.66263	−	1.79268i
$106$	−10.7759			−1.04665
$107$	−3.95990	+	6.85875i	−0.382818	+	0.663061i	−0.991464	−	0.130381i	$-0.958380\pi$
$107$	−3.95990	+	6.85875i	−0.382818	+	0.663061i	0.608646	+	0.793442i	$0.291713\pi$
$108$	−0.758859	−	1.31438i	−0.0730212	−	0.126476i
$109$	1.16748	+	2.02213i	0.111824	+	0.193685i	0.916506	−	0.400021i	$-0.130997\pi$
$109$	1.16748	+	2.02213i	0.111824	+	0.193685i	−0.804682	+	0.593707i	$0.797664\pi$
$110$	−10.4480	+	18.0965i	−0.996181	+	1.72544i
$111$	−6.02925			−0.572271
$112$	12.8584	−	2.93189i	1.21501	−	0.277037i
$113$	7.22596			0.679761			0.339880	−	0.940469i	$-0.389613\pi$
$113$	7.22596			0.679761			0.339880	+	0.940469i	$0.389613\pi$
$114$	−2.44046	+	4.22700i	−0.228570	+	0.395895i
$115$	0.0151804	+	0.0262932i	0.00141558	+	0.00245186i
$116$	4.49770	+	7.79025i	0.417601	+	0.723307i
$117$		0			0
$118$	6.99207			0.643672
$119$	−2.63518	+	8.53641i	−0.241567	+	0.782531i
$120$	14.6699			1.33917
$121$	1.27536	−	2.20899i	0.115942	−	0.200817i
$122$	−3.18420	−	5.51519i	−0.288284	−	0.499322i
$123$	12.3065	+	21.3155i	1.10964	+	1.92195i
$124$	0.381653	−	0.661043i	0.0342735	−	0.0593634i
$125$	26.6240			2.38132
$126$	3.33731	−	10.8109i	0.297311	−	0.963109i
$127$	3.31802			0.294427			0.147213	−	0.989105i	$-0.452970\pi$
$127$	3.31802			0.294427			0.147213	+	0.989105i	$0.452970\pi$
$128$	−5.60153	+	9.70213i	−0.495110	+	0.857556i
$129$	5.04452	+	8.73737i	0.444145	+	0.769282i
$130$		0			0
$131$	−9.77958	+	16.9387i	−0.854446	+	1.47994i	0.0227123	+	0.999742i	$0.492770\pi$
$131$	−9.77958	+	16.9387i	−0.854446	+	1.47994i	−0.877158	+	0.480202i	$0.840564\pi$
$132$	−7.60231			−0.661696
$133$	3.06014	−	0.697751i	0.265347	−	0.0605027i
$134$	−2.96485			−0.256124
$135$	−2.74758	+	4.75896i	−0.236474	+	0.409586i
$136$	−2.61554	−	4.53025i	−0.224281	−	0.388466i
$137$	−4.09755	−	7.09716i	−0.350077	−	0.606351i	0.636186	−	0.771536i	$-0.280511\pi$
$137$	−4.09755	−	7.09716i	−0.350077	−	0.606351i	−0.986263	+	0.165185i	$0.947178\pi$
$138$	−0.0153550	+	0.0265956i	−0.00130710	+	0.00226397i
$139$	−3.12762			−0.265282			−0.132641	−	0.991164i	$-0.542346\pi$
$139$	−3.12762			−0.265282			−0.132641	+	0.991164i	$0.542346\pi$
$140$	8.22152	+	8.86458i	0.694845	+	0.749194i
$141$	−26.5742			−2.23795
$142$	6.30250	−	10.9162i	0.528894	−	0.916071i
$143$		0			0
$144$	6.03081	+	10.4457i	0.502567	+	0.870472i
$145$	16.2847	−	28.2060i	1.35237	−	2.34238i
$146$	18.5470			1.53496
$147$	−14.6854	+	7.06421i	−1.21123	+	0.582646i
$148$	2.90954			0.239163
$149$	8.89716	−	15.4103i	0.728884	−	1.26246i	−0.228471	−	0.973551i	$-0.573373\pi$
$149$	8.89716	−	15.4103i	0.728884	−	1.26246i	0.957355	−	0.288914i	$-0.0932940\pi$
$150$	23.7510	+	41.1379i	1.93926	+	3.35890i
$151$	−1.75472	−	3.03926i	−0.142797	−	0.247332i	0.785752	−	0.618542i	$-0.212276\pi$
$151$	−1.75472	−	3.03926i	−0.142797	−	0.247332i	−0.928549	+	0.371210i	$0.878943\pi$
$152$	−0.918899	+	1.59158i	−0.0745326	+	0.129094i
$153$	−8.17058			−0.660552
$154$	9.24255	+	9.96548i	0.744786	+	0.803041i
$155$	−2.76369			−0.221985
$156$		0			0
$157$	−1.06319	−	1.84149i	−0.0848515	−	0.146967i	0.820476	−	0.571680i	$-0.193708\pi$
$157$	−1.06319	−	1.84149i	−0.0848515	−	0.146967i	−0.905328	+	0.424713i	$0.860375\pi$
$158$	−10.1109	−	17.5126i	−0.804382	−	1.39323i
$159$	−7.09731	+	12.2929i	−0.562854	+	0.974891i
$160$	−23.2315			−1.83661
$161$	0.0192539	−	0.00439013i	0.00151742	−	0.000345991i
$162$	−18.3875			−1.44466
$163$	9.50862	−	16.4694i	0.744773	−	1.28998i	−0.205528	−	0.978651i	$-0.565891\pi$
$163$	9.50862	−	16.4694i	0.744773	−	1.28998i	0.950301	−	0.311333i	$-0.100775\pi$
$164$	−5.93876	−	10.2862i	−0.463739	−	0.803219i
$165$	13.7628	+	23.8378i	1.07143	+	1.85577i
$166$	−1.60890	+	2.78669i	−0.124875	+	0.216289i
$167$	20.5398			1.58942			0.794711	−	0.606988i	$-0.207623\pi$
$167$	20.5398			1.58942			0.794711	+	0.606988i	$0.207623\pi$
$168$	2.81453	−	9.11740i	0.217146	−	0.703423i
$169$		0			0
$170$	12.1371	−	21.0221i	0.930876	−	1.61232i
$171$	1.43525	+	2.48593i	0.109757	+	0.190104i
$172$	−2.43434	−	4.21639i	−0.185616	−	0.321497i
$173$	2.63399	−	4.56220i	0.200258	−	0.346857i	−0.748353	−	0.663300i	$-0.769155\pi$
$173$	2.63399	−	4.56220i	0.200258	−	0.346857i	0.948612	+	0.316443i	$0.102489\pi$
$174$	32.9440			2.49748
$175$	9.01004	−	29.1871i	0.681095	−	2.20634i
$176$	−14.4895			−1.09219
$177$	4.60518	−	7.97641i	0.346147	−	0.599544i
$178$	3.18680	+	5.51970i	0.238861	+	0.413719i
$179$	−4.38110	−	7.58829i	−0.327459	−	0.567176i	0.654548	−	0.756021i	$-0.272859\pi$
$179$	−4.38110	−	7.58829i	−0.327459	−	0.567176i	−0.982007	+	0.188845i	$0.939526\pi$
$180$	−5.52863	+	9.57586i	−0.412080	+	0.713743i
$181$	−16.9098			−1.25690			−0.628449	−	0.777851i	$-0.716310\pi$
$181$	−16.9098			−1.25690			−0.628449	+	0.777851i	$0.716310\pi$
$182$		0			0
$183$	−8.38883			−0.620120
$184$	−0.00578156	+	0.0100140i	−0.000426222	+	0.000738239i
$185$	−5.26726	−	9.12315i	−0.387256	−	0.670748i
$186$	−1.39773	−	2.42095i	−0.102487	−	0.177512i
$187$	4.90763	−	8.50026i	0.358881	−	0.621601i
$188$	12.8239			0.935279
$189$	2.43057	+	2.62068i	0.176798	+	0.190627i
$190$	−8.52810			−0.618693
$191$	3.24644	−	5.62300i	0.234904	−	0.406866i	−0.724341	−	0.689442i	$-0.757856\pi$
$191$	3.24644	−	5.62300i	0.234904	−	0.406866i	0.959245	+	0.282576i	$0.0911890\pi$
$192$	−0.144657	−	0.250553i	−0.0104397	−	0.0180821i
$193$	3.76191	+	6.51581i	0.270788	+	0.469018i	0.969064	−	0.246810i	$-0.0793825\pi$
$193$	3.76191	+	6.51581i	0.270788	+	0.469018i	−0.698276	+	0.715829i	$0.746049\pi$
$194$	−8.93514	+	15.4761i	−0.641506	+	1.11112i
$195$		0			0
$196$	7.08676	−	3.40898i	0.506197	−	0.243498i
$197$	−21.4727			−1.52987			−0.764933	−	0.644109i	$-0.777228\pi$
$197$	−21.4727			−1.52987			−0.764933	+	0.644109i	$0.777228\pi$
$198$	−6.21523	+	10.7651i	−0.441697	+	0.765042i
$199$	−0.605104	−	1.04807i	−0.0428947	−	0.0742958i	0.843781	−	0.536688i	$-0.180325\pi$
$199$	−0.605104	−	1.04807i	−0.0428947	−	0.0742958i	−0.886676	+	0.462392i	$0.846991\pi$
$200$	8.94290	+	15.4895i	0.632358	+	1.09528i
$201$	−1.95274	+	3.38224i	−0.137736	+	0.238565i
$202$	9.13641			0.642836
$203$	−14.4058	−	15.5326i	−1.01109	−	1.09018i
$204$	8.83136			0.618319
$205$	−21.5023	+	37.2431i	−1.50179	+	2.60117i
$206$	3.36205	+	5.82323i	0.234245	+	0.405724i
$207$	0.00903038	+	0.0156411i	0.000627655	+	0.00108713i
$208$		0			0
$209$	−3.44832			−0.238525
$210$	43.1703	−	9.84339i	2.97903	−	0.679259i
$211$	17.4646			1.20232			0.601158	−	0.799130i	$-0.294706\pi$
$211$	17.4646			1.20232			0.601158	+	0.799130i	$0.294706\pi$
$212$	3.42495	−	5.93219i	0.235227	−	0.407425i
$213$	−8.30202	−	14.3795i	−0.568845	−	0.985269i
$214$	−6.99843	−	12.1216i	−0.478403	−	0.828619i
$215$	−8.81395	+	15.2662i	−0.601107	+	1.04115i
$216$	−2.09287			−0.142402
$217$	−0.530237	+	1.71765i	−0.0359948	+	0.116602i
$218$	−4.12663			−0.279490
$219$	12.2156	−	21.1581i	0.825456	−	1.42973i
$220$	−6.64150	−	11.5034i	−0.447770	−	0.775560i
$221$		0			0
$222$	5.32782	−	9.22806i	0.357580	−	0.619347i
$223$	12.5328			0.839258			0.419629	−	0.907696i	$-0.362160\pi$
$223$	12.5328			0.839258			0.419629	+	0.907696i	$0.362160\pi$
$224$	−4.45715	+	14.4385i	−0.297806	+	0.964713i
$225$	27.9363			1.86242
$226$	−6.38530	+	11.0597i	−0.424744	+	0.735678i
$227$	11.5960	+	20.0848i	0.769653	+	1.33308i	0.937751	+	0.347308i	$0.112904\pi$
$227$	11.5960	+	20.0848i	0.769653	+	1.33308i	−0.168098	+	0.985770i	$0.553763\pi$
$228$	−1.55133	−	2.68698i	−0.102739	−	0.177949i
$229$	−3.80674	+	6.59347i	−0.251557	+	0.435709i	−0.963955	−	0.266067i	$-0.914276\pi$
$229$	−3.80674	+	6.59347i	−0.251557	+	0.435709i	0.712398	+	0.701776i	$0.247609\pi$
$230$	−0.0536574			−0.00353806
$231$	17.4558	−	3.98016i	1.14851	−	0.261875i
$232$	12.4043			0.814383
$233$	−11.9794	+	20.7489i	−0.784797	+	1.35931i	0.144323	+	0.989531i	$0.453900\pi$
$233$	−11.9794	+	20.7489i	−0.784797	+	1.35931i	−0.929120	+	0.369778i	$0.879434\pi$
$234$		0			0
$235$	−23.2156	−	40.2107i	−1.51442	−	2.62305i
$236$	−2.22233	+	3.84918i	−0.144661	+	0.250560i
$237$	−26.6374			−1.73029
$238$	−10.7368	−	11.5766i	−0.695962	−	0.750398i
$239$	−15.2589			−0.987015			−0.493508	−	0.869741i	$-0.664285\pi$
$239$	−15.2589			−0.987015			−0.493508	+	0.869741i	$0.664285\pi$
$240$	−23.6015	+	40.8791i	−1.52347	+	2.63873i
$241$	5.11356	+	8.85694i	0.329393	+	0.570526i	0.982392	−	0.186834i	$-0.0598225\pi$
$241$	5.11356	+	8.85694i	0.329393	+	0.570526i	−0.652998	+	0.757359i	$0.726489\pi$
$242$	2.25397	+	3.90400i	0.144891	+	0.250958i
$243$	−10.0841	+	17.4662i	−0.646897	+	1.12046i
$244$	4.04820			0.259160
$245$	−23.5186	−	16.0498i	−1.50255	−	1.02539i
$246$	−43.4992			−2.77341
$247$		0			0
$248$	−0.526285	−	0.911553i	−0.0334191	−	0.0578837i
$249$	2.11933	+	3.67079i	0.134307	+	0.232627i
$250$	−23.5266	+	40.7492i	−1.48795	+	2.57721i
$251$	13.0463			0.823473			0.411737	−	0.911303i	$-0.364922\pi$
$251$	13.0463			0.823473			0.411737	+	0.911303i	$0.364922\pi$
$252$	4.89074	+	5.27328i	0.308088	+	0.332186i
$253$	−0.0216963			−0.00136403
$254$	−2.93201	+	5.07839i	−0.183971	+	0.318646i
$255$	−15.9878	−	27.6916i	−1.00119	−	1.73412i
$256$	−10.0240	−	17.3621i	−0.626500	−	1.08513i
$257$	−7.58097	+	13.1306i	−0.472888	+	0.819066i	−0.999519	−	0.0310282i	$-0.990122\pi$
$257$	−7.58097	+	13.1306i	−0.472888	+	0.819066i	0.526630	+	0.850094i	$0.323455\pi$
$258$	−17.8306			−1.11009
$259$	−6.68066	+	1.52328i	−0.415116	+	0.0946518i
$260$		0			0
$261$	9.68732	−	16.7789i	0.599630	−	1.03859i
$262$	−17.2837	−	29.9362i	−1.06779	−	1.84947i
$263$	−0.335858	−	0.581723i	−0.0207099	−	0.0358706i	0.855485	−	0.517828i	$-0.173259\pi$
$263$	−0.335858	−	0.581723i	−0.0207099	−	0.0358706i	−0.876195	+	0.481957i	$0.839926\pi$
$264$	−5.24164	+	9.07879i	−0.322601	+	0.558761i
$265$	−24.8013			−1.52353
$266$	−1.63619	+	5.30026i	−0.100321	+	0.324980i
$267$	8.39569			0.513808
$268$	0.942334	−	1.63217i	0.0575622	−	0.0997007i
$269$	−9.01860	−	15.6207i	−0.549874	−	0.952409i	−0.998283	−	0.0585809i	$-0.981342\pi$
$269$	−9.01860	−	15.6207i	−0.549874	−	0.952409i	0.448409	−	0.893829i	$-0.351991\pi$
$270$	−4.85587	−	8.41062i	−0.295519	−	0.511854i
$271$	−4.75629	+	8.23813i	−0.288924	+	0.500431i	−0.973553	−	0.228461i	$-0.926631\pi$
$271$	−4.75629	+	8.23813i	−0.288924	+	0.500431i	0.684629	+	0.728891i	$0.259964\pi$
$272$	16.8320			1.02059
$273$		0			0
$274$	14.4834			0.874974
$275$	−16.7798	+	29.0635i	−1.01186	+	1.75260i
$276$	−0.00976069	−	0.0169060i	−0.000587525	−	0.00101762i
$277$	−1.74310	−	3.01914i	−0.104733	−	0.181403i	0.808896	−	0.587951i	$-0.200065\pi$
$277$	−1.74310	−	3.01914i	−0.104733	−	0.181403i	−0.913629	+	0.406549i	$0.866732\pi$
$278$	2.76376	−	4.78698i	0.165759	−	0.287104i
$279$	−1.64404			−0.0984260
$280$	16.2548	−	3.70631i	0.971410	−	0.221494i
$281$	13.0611			0.779160			0.389580	−	0.920993i	$-0.372620\pi$
$281$	13.0611			0.779160			0.389580	+	0.920993i	$0.372620\pi$
$282$	23.4826	−	40.6730i	1.39837	−	2.42204i
$283$	−3.68337	−	6.37979i	−0.218954	−	0.379239i	0.735535	−	0.677487i	$-0.236931\pi$
$283$	−3.68337	−	6.37979i	−0.218954	−	0.379239i	−0.954488	+	0.298248i	$0.903598\pi$
$284$	4.00631	+	6.93913i	0.237731	+	0.411762i
$285$	−5.61686	+	9.72868i	−0.332714	+	0.576277i
$286$		0			0
$287$	19.0214	+	20.5092i	1.12280	+	1.21062i
$288$	−13.8197			−0.814335
$289$	2.79897	−	4.84795i	0.164645	−	0.285174i
$290$	28.7804	+	49.8492i	1.69004	+	2.92724i
$291$	11.7699	+	20.3861i	0.689964	+	1.19505i
$292$	−5.89490	+	10.2103i	−0.344973	+	0.597511i
$293$	−23.9996			−1.40207			−0.701035	−	0.713127i	$-0.747278\pi$
$293$	−23.9996			−1.40207			−0.701035	+	0.713127i	$0.747278\pi$
$294$	2.16486	−	28.7191i	0.126257	−	1.67493i
$295$	16.0927			0.936951
$296$	2.00607	−	3.47462i	0.116601	−	0.201958i
$297$	−1.96346	−	3.40082i	−0.113932	−	0.197335i
$298$	15.7242	+	27.2351i	0.910877	+	1.57769i
$299$		0			0
$300$	−30.1956			−1.74334
$301$	7.79701	+	8.40687i	0.449412	+	0.484564i
$302$	6.20232			0.356903
$303$	6.01751	−	10.4226i	0.345697	−	0.598765i
$304$	−2.95673	−	5.12121i	−0.169580	−	0.293722i
$305$	−7.32862	−	12.6935i	−0.419636	−	0.726830i
$306$	7.22003	−	12.5055i	0.412742	−	0.714889i
$307$	−0.871450			−0.0497363			−0.0248681	−	0.999691i	$-0.507917\pi$
$307$	−0.871450			−0.0497363			−0.0248681	+	0.999691i	$0.507917\pi$
$308$	−8.42367	+	1.92071i	−0.479983	+	0.109442i
$309$	8.85737			0.503878
$310$	2.44217	−	4.22996i	0.138706	−	0.240245i
$311$	−8.19208	−	14.1891i	−0.464530	−	0.804590i	0.534650	−	0.845074i	$-0.320443\pi$
$311$	−8.19208	−	14.1891i	−0.464530	−	0.804590i	−0.999180	+	0.0404836i	$0.987110\pi$
$312$		0			0
$313$	−8.61501	+	14.9216i	−0.486949	+	0.843420i	−0.999887	−	0.0150050i	$-0.995224\pi$
$313$	−8.61501	+	14.9216i	−0.486949	+	0.843420i	0.512938	+	0.858425i	$0.328557\pi$
$314$	3.75799			0.212076
$315$	7.68100	−	24.8818i	0.432776	−	1.40193i
$316$	12.8544			0.723118
$317$	4.51988	−	7.82867i	0.253862	−	0.439702i	−0.710724	−	0.703471i	$-0.751632\pi$
$317$	4.51988	−	7.82867i	0.253862	−	0.439702i	0.964586	+	0.263769i	$0.0849658\pi$
$318$	−12.5433	−	21.7256i	−0.703391	−	1.21831i
$319$	11.6373	+	20.1564i	0.651564	+	1.12854i
$320$	0.252749	−	0.437774i	0.0141291	−	0.0244723i
$321$	−18.4375			−1.02908
$322$	−0.0102946	+	0.0333484i	−0.000573696	+	0.00185843i
$323$	4.00580			0.222889
$324$	5.84420	−	10.1225i	0.324678	−	0.562358i
$325$		0			0
$326$	16.8048	+	29.1068i	0.930733	+	1.61208i
$327$	−2.71792	+	4.70757i	−0.150301	+	0.260329i
$328$	−16.3786			−0.904358
$329$	−29.4453	+	6.71390i	−1.62337	+	0.370149i
$330$	−48.6465			−2.67790
$331$	−17.9440	+	31.0799i	−0.986291	+	1.70831i	−0.350239	+	0.936660i	$0.613900\pi$
$331$	−17.9440	+	31.0799i	−0.986291	+	1.70831i	−0.636052	+	0.771646i	$0.719434\pi$
$332$	−1.02273	−	1.77141i	−0.0561294	−	0.0972190i
$333$	−3.13334	−	5.42710i	−0.171706	−	0.297403i
$334$	−18.1503	+	31.4372i	−0.993140	+	1.72017i
$335$	−6.82378			−0.372823
$336$	20.8784	+	22.5115i	1.13901	+	1.22810i
$337$	17.5864			0.957992			0.478996	−	0.877817i	$-0.341001\pi$
$337$	17.5864			0.957992			0.478996	+	0.877817i	$0.341001\pi$
$338$		0			0
$339$	8.41110	+	14.5685i	0.456828	+	0.791250i
$340$	7.71522	+	13.3631i	0.418416	+	0.724718i
$341$	0.987486	−	1.71038i	0.0534754	−	0.0926220i
$342$	−5.07312			−0.274323
$343$	−14.4873	+	11.5377i	−0.782241	+	0.622976i
$344$	−6.71371			−0.361979
$345$	−0.0353403	+	0.0612113i	−0.00190266	+	0.00329550i
$346$	4.65511	+	8.06288i	0.250260	+	0.433463i
$347$	−10.0413	−	17.3920i	−0.539045	−	0.933653i	−0.998956	−	0.0456881i	$-0.985452\pi$
$347$	−10.0413	−	17.3920i	−0.539045	−	0.933653i	0.459911	−	0.887965i	$-0.347881\pi$
$348$	−10.4708	+	18.1359i	−0.561292	+	0.972186i
$349$	−27.3383			−1.46339			−0.731693	−	0.681635i	$-0.761269\pi$
$349$	−27.3383			−1.46339			−0.731693	+	0.681635i	$0.761269\pi$
$350$	36.7105	+	39.5819i	1.96226	+	2.11574i
$351$		0			0
$352$	8.30077	−	14.3774i	0.442433	−	0.766316i
$353$	8.22701	+	14.2496i	0.437879	+	0.758429i	0.997526	−	0.0703023i	$-0.0223964\pi$
$353$	8.22701	+	14.2496i	0.437879	+	0.758429i	−0.559646	+	0.828731i	$0.689063\pi$
$354$	8.13885	+	14.0969i	0.432575	+	0.749242i
$355$	14.5056	−	25.1244i	0.769876	−	1.33346i
$356$	−4.05151			−0.214730
$357$	−20.2779	+	4.62362i	−1.07322	+	0.244708i
$358$	15.4857			0.818443
$359$	−11.0709	+	19.1753i	−0.584299	+	1.01204i	0.410664	+	0.911787i	$0.365297\pi$
$359$	−11.0709	+	19.1753i	−0.584299	+	1.01204i	−0.994962	+	0.100248i	$0.968036\pi$
$360$	7.62376	+	13.2047i	0.401808	+	0.695951i
$361$	8.79634	+	15.2357i	0.462965	+	0.801879i
$362$	14.9426	−	25.8813i	0.785364	−	1.36029i
$363$	5.93813			0.311671
$364$		0			0
$365$	42.6871			2.23434
$366$	7.41289	−	12.8395i	0.387478	−	0.671132i
$367$	5.29985	+	9.17961i	0.276650	+	0.479172i	0.970550	−	0.240899i	$-0.0774424\pi$
$367$	5.29985	+	9.17961i	0.276650	+	0.479172i	−0.693900	+	0.720071i	$0.744109\pi$
$368$	−0.0186033	−	0.0322218i	−0.000969763	−	0.00167968i
$369$	−12.7911	+	22.1549i	−0.665879	+	1.15334i
$370$	18.6179			0.967898
$371$	−4.75834	+	15.4142i	−0.247041	+	0.800264i
$372$	1.77700			0.0921330
$373$	−7.87982	+	13.6483i	−0.408002	+	0.706680i	−0.994666	−	0.103151i	$-0.967108\pi$
$373$	−7.87982	+	13.6483i	−0.408002	+	0.706680i	0.586664	+	0.809830i	$0.300441\pi$
$374$	8.67337	+	15.0227i	0.448489	+	0.776806i
$375$	30.9906	+	53.6773i	1.60035	+	2.77188i
$376$	8.84183	−	15.3145i	0.455983	−	0.789785i
$377$		0			0
$378$	−6.15889	+	1.40431i	−0.316779	+	0.0722297i
$379$	−22.6327			−1.16257			−0.581283	−	0.813702i	$-0.697449\pi$
$379$	−22.6327			−1.16257			−0.581283	+	0.813702i	$0.697449\pi$
$380$	2.71053	−	4.69477i	0.139047	−	0.240837i
$381$	3.86221	+	6.68955i	0.197867	+	0.342716i
$382$	5.73752	+	9.93767i	0.293557	+	0.508455i
$383$	0.139164	−	0.241039i	0.00711095	−	0.0123165i	−0.862448	−	0.506146i	$-0.831070\pi$
$383$	0.139164	−	0.241039i	0.00711095	−	0.0123165i	0.869559	+	0.493829i	$0.164403\pi$
$384$	−26.0810			−1.33094
$385$	21.2723	+	22.9361i	1.08414	+	1.16893i
$386$	−13.2970			−0.676800
$387$	−5.24316	+	9.08142i	−0.266525	+	0.461635i
$388$	−5.67980	−	9.83771i	−0.288348	−	0.499434i
$389$	15.9846	+	27.6862i	0.810453	+	1.40375i	0.912547	+	0.408971i	$0.134112\pi$
$389$	15.9846	+	27.6862i	0.810453	+	1.40375i	−0.102094	+	0.994775i	$0.532554\pi$
$390$		0			0
$391$	0.0252038			0.00127461
$392$	0.815128	−	10.8135i	0.0411702	−	0.546166i
$393$	−45.5342			−2.29690
$394$	18.9746	−	32.8650i	0.955927	−	1.65571i
$395$	−23.2709	−	40.3063i	−1.17088	−	2.02803i
$396$	−3.95083	−	6.84305i	−0.198537	−	0.343876i
$397$	9.11002	−	15.7790i	0.457219	−	0.791926i	−0.541594	−	0.840640i	$-0.682179\pi$
$397$	9.11002	−	15.7790i	0.457219	−	0.791926i	0.998813	+	0.0487140i	$0.0155123\pi$
$398$	2.13883			0.107210
$399$	4.96879	+	5.35744i	0.248751	+	0.268207i
$400$	−57.5510			−2.87755
$401$	−10.3812	+	17.9808i	−0.518414	+	0.897920i	0.481357	+	0.876525i	$0.340144\pi$
$401$	−10.3812	+	17.9808i	−0.518414	+	0.897920i	−0.999771	+	0.0213950i	$0.993189\pi$
$402$	−3.45112	−	5.97752i	−0.172126	−	0.298132i
$403$		0			0
$404$	−2.90387	+	5.02966i	−0.144473	+	0.250235i
$405$	−42.3200			−2.10290
$406$	36.5033	−	8.32323i	1.81163	−	0.413075i
$407$	7.52811			0.373155
$408$	6.08905	−	10.5465i	0.301453	−	0.522132i
$409$	−8.28993	−	14.3586i	−0.409911	−	0.709986i	0.584968	−	0.811056i	$-0.301107\pi$
$409$	−8.28993	−	14.3586i	−0.409911	−	0.709986i	−0.994879	+	0.101070i	$0.967774\pi$
$410$	−38.0016	−	65.8207i	−1.87677	−	3.25065i
$411$	9.53919	−	16.5224i	0.470533	−	0.814988i
$412$	−4.27430			−0.210580
$413$	3.08751	−	10.0017i	0.151926	−	0.492151i
$414$	−0.0319192			−0.00156874
$415$	−3.70297	+	6.41373i	−0.181771	+	0.314837i
$416$		0			0
$417$	−3.64059	−	6.30569i	−0.178281	−	0.308791i
$418$	3.04715	−	5.27782i	0.149041	−	0.258146i
$419$	−4.21062			−0.205702			−0.102851	−	0.994697i	$-0.532797\pi$
$419$	−4.21062			−0.205702			−0.102851	+	0.994697i	$0.532797\pi$
$420$	−8.30219	+	26.8941i	−0.405105	+	1.31230i
$421$	33.9650			1.65535			0.827677	−	0.561205i	$-0.189662\pi$
$421$	33.9650			1.65535			0.827677	+	0.561205i	$0.189662\pi$
$422$	−15.4328	+	26.7305i	−0.751259	+	1.30122i
$423$	−13.8103	−	23.9201i	−0.671480	−	1.16304i
$424$	−4.72288	−	8.18027i	−0.229363	−	0.397269i
$425$	19.4926	−	33.7622i	0.945530	−	1.63771i
$426$	29.3447			1.42176
$427$	−9.29517	+	2.11942i	−0.449825	+	0.102566i
$428$	8.89739			0.430072
$429$		0			0
$430$	−15.5771	−	26.9803i	−0.751195	−	1.30111i
$431$	−12.6570	−	21.9226i	−0.609667	−	1.05597i	−0.991295	−	0.131659i	$-0.957970\pi$
$431$	−12.6570	−	21.9226i	−0.609667	−	1.05597i	0.381628	−	0.924316i	$-0.375364\pi$
$432$	3.36711	−	5.83201i	0.162000	−	0.280593i
$433$	−2.37946			−0.114350			−0.0571749	−	0.998364i	$-0.518209\pi$
$433$	−2.37946			−0.114350			−0.0571749	+	0.998364i	$0.518209\pi$
$434$	−2.16039	−	2.32937i	−0.103702	−	0.111814i
$435$	75.8226			3.63541
$436$	1.31159	−	2.27174i	0.0628136	−	0.108796i
$437$	−0.00442734	−	0.00766837i	−0.000211788	−	0.000366828i
$438$	21.5890	+	37.3932i	1.03156	+	1.78672i
$439$	−8.40861	+	14.5641i	−0.401321	+	0.695108i	−0.993886	−	0.110415i	$-0.964782\pi$
$439$	−8.40861	+	14.5641i	−0.401321	+	0.695108i	0.592565	+	0.805523i	$0.298115\pi$
$440$	−18.3167			−0.873217
$441$	−13.9905	−	9.54758i	−0.666217	−	0.454646i
$442$		0			0
$443$	8.06251	−	13.9647i	0.383061	−	0.663482i	−0.608437	−	0.793602i	$-0.708203\pi$
$443$	8.06251	−	13.9647i	0.383061	−	0.663482i	0.991498	+	0.130121i	$0.0415364\pi$
$444$	3.38674	+	5.86600i	0.160728	+	0.278388i
$445$	7.33461	+	12.7039i	0.347694	+	0.602224i
$446$	−11.0748	+	19.1820i	−0.524405	+	0.908296i
$447$	41.4256			1.95936
$448$	−0.223587	−	0.241076i	−0.0105635	−	0.0113898i
$449$	40.5289			1.91268			0.956339	−	0.292261i	$-0.0944076\pi$
$449$	40.5289			1.91268			0.956339	+	0.292261i	$0.0944076\pi$
$450$	−24.6862	+	42.7578i	−1.16372	+	2.01562i
$451$	−15.3659	−	26.6145i	−0.723551	−	1.25323i
$452$	−4.05895	−	7.03030i	−0.190917	−	0.330678i
$453$	4.08503	−	7.07548i	0.191932	−	0.332435i
$454$	−40.9877			−1.92365
$455$		0			0
$456$	−4.27844			−0.200356
$457$	5.80455	−	10.0538i	0.271526	−	0.470296i	−0.697727	−	0.716364i	$-0.745805\pi$
$457$	5.80455	−	10.0538i	0.271526	−	0.470296i	0.969253	+	0.246068i	$0.0791385\pi$
$458$	−6.72775	−	11.6528i	−0.314367	−	0.544500i
$459$	2.28089	+	3.95062i	0.106463	+	0.184399i
$460$	0.0170542	−	0.0295387i	0.000795156	−	0.00137725i
$461$	26.4282			1.23088			0.615441	−	0.788183i	$-0.288978\pi$
$461$	26.4282			1.23088			0.615441	+	0.788183i	$0.288978\pi$
$462$	−9.33324	+	30.2341i	−0.434222	+	1.40662i
$463$	−15.7251			−0.730810			−0.365405	−	0.930849i	$-0.619069\pi$
$463$	−15.7251			−0.730810			−0.365405	+	0.930849i	$0.619069\pi$
$464$	−19.9566	+	34.5659i	−0.926463	+	1.60468i
$465$	−3.21697	−	5.57195i	−0.149183	−	0.258393i
$466$	−21.1715	−	36.6701i	−0.980751	−	1.69871i
$467$	13.7128	−	23.7513i	0.634553	−	1.09908i	−0.352056	−	0.935979i	$-0.614517\pi$
$467$	13.7128	−	23.7513i	0.634553	−	1.09908i	0.986610	−	0.163100i	$-0.0521493\pi$
$468$		0			0
$469$	−1.30920	+	4.24102i	−0.0604532	+	0.195832i
$470$	82.0591			3.78510
$471$	2.47512	−	4.28704i	0.114048	−	0.197536i
$472$	3.06450	+	5.30787i	0.141055	+	0.244315i
$473$	−6.29857	−	10.9095i	−0.289609	−	0.501617i
$474$	23.5385	−	40.7698i	1.08116	−	1.87262i
$475$	−13.6964			−0.628433
$476$	9.78550	−	2.23122i	0.448518	−	0.102268i
$477$	−14.7536			−0.675520
$478$	13.4837	−	23.3545i	0.616730	−	1.06821i
$479$	8.92302	+	15.4551i	0.407703	+	0.706162i	0.994632	−	0.103476i	$-0.0329965\pi$
$479$	8.92302	+	15.4551i	0.407703	+	0.706162i	−0.586929	+	0.809638i	$0.699663\pi$
$480$	−27.0417	−	46.8376i	−1.23428	−	2.13784i
$481$		0			0
$482$	−18.0746			−0.823277
$483$	0.0312628	+	0.0337081i	0.00142251	+	0.00153377i
$484$	−2.86557			−0.130253
$485$	−20.5648	+	35.6192i	−0.933797	+	1.61738i
$486$	−17.8219	−	30.8685i	−0.808419	−	1.40022i
$487$	−2.83051	−	4.90258i	−0.128262	−	0.222157i	0.794741	−	0.606949i	$-0.207607\pi$
$487$	−2.83051	−	4.90258i	−0.128262	−	0.222157i	−0.923003	+	0.384792i	$0.874273\pi$
$488$	2.79116	−	4.83442i	0.126350	−	0.218844i
$489$	44.2726			2.00208
$490$	45.3476	−	21.8138i	2.04859	−	0.985445i
$491$	40.2435			1.81616			0.908081	−	0.418795i	$-0.137547\pi$
$491$	40.2435			1.81616			0.908081	+	0.418795i	$0.137547\pi$
$492$	13.8256	−	23.9466i	0.623305	−	1.07960i
$493$	−13.5187	−	23.4150i	−0.608851	−	1.05456i
$494$		0			0
$495$	−14.3047	+	24.7765i	−0.642949	+	1.11362i
$496$	3.38685			0.152074
$497$	−12.8319	−	13.8356i	−0.575591	−	0.620612i
$498$	−7.49109			−0.335684
$499$	−7.02867	+	12.1740i	−0.314647	+	0.544984i	−0.979362	−	0.202112i	$-0.935219\pi$
$499$	−7.02867	+	12.1740i	−0.314647	+	0.544984i	0.664716	+	0.747096i	$0.268553\pi$
$500$	−14.9551	−	25.9031i	−0.668815	−	1.15842i
$501$	23.9086	+	41.4110i	1.06816	+	1.85011i
$502$	−11.5285	+	19.9679i	−0.514542	+	0.891213i
$503$	7.72836			0.344591			0.172295	−	0.985045i	$-0.444882\pi$
$503$	7.72836			0.344591			0.172295	+	0.985045i	$0.444882\pi$
$504$	9.66951	−	2.20477i	0.430714	−	0.0982084i
$505$	21.0280			0.935733
$506$	0.0191722	−	0.0332072i	0.000852307	−	0.00147624i
$507$		0			0
$508$	−1.86379	−	3.22818i	−0.0826923	−	0.143227i
$509$	−3.04300	+	5.27063i	−0.134879	+	0.233617i	−0.925551	−	0.378623i	$-0.876398\pi$
$509$	−3.04300	+	5.27063i	−0.134879	+	0.233617i	0.790672	+	0.612239i	$0.209731\pi$
$510$	56.5111			2.50235
$511$	8.18987	−	26.5303i	0.362299	−	1.17363i
$512$	13.0252			0.575637
$513$	0.801328	−	1.38794i	0.0353795	−	0.0612791i
$514$	−13.3980	−	23.2061i	−0.590962	−	1.02358i
$515$	7.73794	+	13.4025i	0.340975	+	0.590585i
$516$	5.66719	−	9.81587i	0.249484	−	0.432119i
$517$	33.1804			1.45927
$518$	3.57200	−	11.5711i	0.156945	−	0.508406i
$519$	12.2640			0.538328
$520$		0			0
$521$	0.0173552	+	0.0300601i	0.000760344	+	0.00131695i	0.866405	−	0.499341i	$-0.166425\pi$
$521$	0.0173552	+	0.0300601i	0.000760344	+	0.00131695i	−0.865645	+	0.500658i	$0.833091\pi$
$522$	17.1206	+	29.6538i	0.749350	+	1.29791i
$523$	8.79919	−	15.2406i	0.384762	−	0.666427i	−0.606974	−	0.794721i	$-0.707617\pi$
$523$	8.79919	−	15.2406i	0.384762	−	0.666427i	0.991736	+	0.128295i	$0.0409503\pi$
$524$	21.9735			0.959915
$525$	69.3328	−	15.8088i	3.02593	−	0.689952i
$526$	1.18714			0.0517618
$527$	−1.14713	+	1.98689i	−0.0499698	+	0.0865502i
$528$	−16.8660	−	29.2128i	−0.733998	−	1.27132i
$529$	11.5000	+	19.9185i	0.499999	+	0.866023i
$530$	21.9160	−	37.9596i	0.951970	−	1.64886i
$531$	9.57305			0.415435
$532$	−2.39779	−	2.58534i	−0.103957	−	0.112089i
$533$		0			0
$534$	−7.41895	+	12.8500i	−0.321049	+	0.556074i
$535$	−16.1073	−	27.8987i	−0.696380	−	1.20616i
$536$	−1.29944	−	2.25070i	−0.0561274	−	0.0972154i
$537$	10.1993	−	17.6657i	0.440133	−	0.762332i
$538$	31.8776			1.37434
$539$	18.3362	−	8.82035i	0.789796	−	0.379919i
$540$	6.17347			0.265664
$541$	0.289108	−	0.500750i	0.0124297	−	0.0215289i	−0.859744	−	0.510726i	$-0.829377\pi$
$541$	0.289108	−	0.500750i	0.0124297	−	0.0215289i	0.872173	+	0.489197i	$0.162710\pi$
$542$	−8.40590	−	14.5595i	−0.361064	−	0.625382i
$543$	−19.6832	−	34.0924i	−0.844689	−	1.46304i
$544$	−9.64274	+	16.7017i	−0.413429	+	0.716080i
$545$	−9.49767			−0.406836
$546$		0			0
$547$	−13.6270			−0.582650			−0.291325	−	0.956624i	$-0.594096\pi$
$547$	−13.6270			−0.582650			−0.291325	+	0.956624i	$0.594096\pi$
$548$	−4.60333	+	7.97320i	−0.196644	+	0.340598i
$549$	−4.35958	−	7.55102i	−0.186062	−	0.322270i
$550$	−29.6554	−	51.3647i	−1.26451	−	2.19020i
$551$	−4.74942	+	8.22623i	−0.202332	+	0.350449i
$552$	−0.0269192			−0.00114576
$553$	−29.5153	+	6.72988i	−1.25512	+	0.286184i
$554$	6.16125			0.261766
$555$	12.2623	−	21.2389i	0.520506	−	0.901542i
$556$	1.75684	+	3.04294i	0.0745067	+	0.129049i
$557$	−3.23156	−	5.59722i	−0.136925	−	0.237162i	0.789406	−	0.613872i	$-0.210389\pi$
$557$	−3.23156	−	5.59722i	−0.136925	−	0.237162i	−0.926331	+	0.376710i	$0.877055\pi$
$558$	1.45277	−	2.51628i	0.0615008	−	0.106523i
$559$		0			0
$560$	−15.8235	+	51.2585i	−0.668664	+	2.16607i
$561$	22.8502			0.964734
$562$	−11.5416	+	19.9906i	−0.486853	+	0.843254i
$563$	−16.5511	−	28.6674i	−0.697547	−	1.20819i	−0.969314	−	0.245825i	$-0.920941\pi$
$563$	−16.5511	−	28.6674i	−0.697547	−	1.20819i	0.271767	−	0.962363i	$-0.412392\pi$
$564$	14.9272	+	25.8546i	0.628548	+	1.08868i
$565$	−14.6961	+	25.4545i	−0.618272	+	1.07088i
$566$	13.0194			0.547247
$567$	−8.11943	+	26.3021i	−0.340984	+	1.10458i
$568$	11.0491			0.463610
$569$	22.0632	−	38.2145i	0.924936	−	1.60204i	0.133271	−	0.991080i	$-0.457452\pi$
$569$	22.0632	−	38.2145i	0.924936	−	1.60204i	0.791664	−	0.610956i	$-0.209215\pi$
$570$	−9.92681	−	17.1937i	−0.415788	−	0.720166i
$571$	6.07037	+	10.5142i	0.254037	+	0.440005i	0.964633	−	0.263595i	$-0.0849082\pi$
$571$	6.07037	+	10.5142i	0.254037	+	0.440005i	−0.710597	+	0.703600i	$0.751575\pi$
$572$		0			0
$573$	15.1156			0.631463
$574$	−48.1989	+	10.9900i	−2.01178	+	0.458712i
$575$	−0.0861753			−0.00359376
$576$	0.150353	−	0.260419i	0.00626471	−	0.0108508i
$577$	21.1427	+	36.6202i	0.880181	+	1.52452i	0.851139	+	0.524941i	$0.175913\pi$
$577$	21.1427	+	36.6202i	0.880181	+	1.52452i	0.0290428	+	0.999578i	$0.490754\pi$
$578$	4.94668	+	8.56791i	0.205755	+	0.356378i
$579$	−8.75781	+	15.1690i	−0.363962	+	0.630401i
$580$	−36.5897			−1.51931
$581$	3.27572	+	3.53194i	0.135900	+	0.146530i
$582$	−41.6025			−1.72448
$583$	8.86169	−	15.3489i	0.367014	−	0.635686i
$584$	8.12884	+	14.0796i	0.336374	+	0.582616i
$585$		0			0
$586$	21.2075	−	36.7325i	0.876075	−	1.51741i
$587$	34.0219			1.40424			0.702118	−	0.712061i	$-0.252238\pi$
$587$	34.0219			1.40424			0.702118	+	0.712061i	$0.252238\pi$
$588$	15.1220	+	10.3197i	0.623621	+	0.425578i
$589$	0.806025			0.0332117
$590$	−14.2205	+	24.6306i	−0.585448	+	1.01403i
$591$	−24.9945	−	43.2917i	−1.02814	−	1.78078i
$592$	6.45492	+	11.1802i	0.265295	+	0.459505i
$593$	4.64494	−	8.04527i	0.190745	−	0.330379i	−0.754753	−	0.656010i	$-0.772243\pi$
$593$	4.64494	−	8.04527i	0.190745	−	0.330379i	0.945497	+	0.325630i	$0.105576\pi$
$594$	6.94015			0.284758
$595$	−24.7113	−	26.6442i	−1.01306	−	1.09230i
$596$	−19.9908			−0.818854
$597$	1.40870	−	2.43993i	0.0576541	−	0.0998599i
$598$		0			0
$599$	−7.29816	−	12.6408i	−0.298195	−	0.516488i	0.677528	−	0.735497i	$-0.263051\pi$
$599$	−7.29816	−	12.6408i	−0.298195	−	0.516488i	−0.975723	+	0.219008i	$0.929718\pi$
$600$	−20.8193	+	36.0600i	−0.849943	+	1.47215i
$601$	4.28534			0.174803			0.0874013	−	0.996173i	$-0.472144\pi$
$601$	4.28534			0.174803			0.0874013	+	0.996173i	$0.472144\pi$
$602$	−19.7570	+	4.50486i	−0.805237	+	0.183604i
$603$	−4.05927			−0.165306
$604$	−1.97131	+	3.41442i	−0.0802117	+	0.138931i
$605$	5.18765	+	8.98528i	0.210908	+	0.365303i
$606$	10.6349	+	18.4202i	0.432013	+	0.748269i
$607$	−18.3103	+	31.7144i	−0.743192	+	1.28725i	0.207842	+	0.978162i	$0.433356\pi$
$607$	−18.3103	+	31.7144i	−0.743192	+	1.28725i	−0.951035	+	0.309084i	$0.899977\pi$
$608$	6.77542			0.274779
$609$	14.5472	−	47.1242i	0.589482	−	1.90957i
$610$	25.9041			1.04883
$611$		0			0
$612$	4.58956	+	7.94935i	0.185522	+	0.321333i
$613$	21.5483	+	37.3228i	0.870329	+	1.50745i	0.861657	+	0.507492i	$0.169427\pi$
$613$	21.5483	+	37.3228i	0.870329	+	1.50745i	0.00867253	+	0.999962i	$0.497239\pi$
$614$	0.770067	−	1.33380i	0.0310774	−	0.0538276i
$615$	−100.116			−4.03706
$616$	−3.51422	+	11.3840i	−0.141592	+	0.458673i
$617$	−29.5143			−1.18820			−0.594101	−	0.804390i	$-0.702492\pi$
$617$	−29.5143			−1.18820			−0.594101	+	0.804390i	$0.702492\pi$
$618$	−7.82692	+	13.5566i	−0.314845	+	0.545328i
$619$	13.9382	+	24.1418i	0.560225	+	0.970339i	0.997476	+	0.0709994i	$0.0226189\pi$
$619$	13.9382	+	24.1418i	0.560225	+	0.970339i	−0.437251	+	0.899340i	$0.644048\pi$
$620$	1.55241	+	2.68886i	0.0623464	+	0.107987i
$621$	0.00504182	−	0.00873270i	0.000202321	−	0.000350431i
$622$	28.9561			1.16103
$623$	9.30277	−	2.12115i	0.372707	−	0.0849821i
$624$		0			0
$625$	−25.2844	+	43.7938i	−1.01138	+	1.75175i
$626$	−15.2255	−	26.3714i	−0.608534	−	1.05401i
$627$	−4.01389	−	6.95225i	−0.160299	−	0.277646i
$628$	−1.19442	+	2.06880i	−0.0476626	+	0.0825541i
$629$	−8.74516			−0.348692
$630$	31.2954	+	33.7433i	1.24684	+	1.34436i
$631$	30.0124			1.19477			0.597387	−	0.801953i	$-0.296206\pi$
$631$	30.0124			1.19477			0.597387	+	0.801953i	$0.296206\pi$
$632$	8.86288	−	15.3510i	0.352546	−	0.610628i
$633$	20.3291	+	35.2110i	0.808008	+	1.39951i
$634$	7.98810	+	13.8358i	0.317248	+	0.549489i
$635$	−6.74819	+	11.6882i	−0.267794	+	0.463832i
$636$	15.9467			0.632330
$637$		0			0
$638$	−41.1338			−1.62850
$639$	8.62894	−	14.9458i	0.341355	−	0.591245i
$640$	−22.7848	−	39.4644i	−0.900648	−	1.55997i
$641$	4.68832	+	8.12040i	0.185177	+	0.320737i	0.943636	−	0.330984i	$-0.107381\pi$
$641$	4.68832	+	8.12040i	0.185177	+	0.320737i	−0.758459	+	0.651721i	$0.774047\pi$
$642$	16.2925	−	28.2195i	0.643015	−	1.11373i
$643$	−1.78629			−0.0704444			−0.0352222	−	0.999380i	$-0.511214\pi$
$643$	−1.78629			−0.0704444			−0.0352222	+	0.999380i	$0.511214\pi$
$644$	−0.0150865	−	0.0162665i	−0.000594492	−	0.000640991i
$645$	−41.0382			−1.61588
$646$	−3.53977	+	6.13107i	−0.139271	+	0.241224i
$647$	15.8126	+	27.3882i	0.621656	+	1.07674i	0.989177	+	0.146725i	$0.0468731\pi$
$647$	15.8126	+	27.3882i	0.621656	+	1.07674i	−0.367521	+	0.930015i	$0.619794\pi$
$648$	−8.05893	−	13.9585i	−0.316585	−	0.548340i
$649$	−5.75002	+	9.95933i	−0.225708	+	0.390938i
$650$		0			0
$651$	−4.08020	+	0.930339i	−0.159916	+	0.0364629i
$652$	−21.3646			−0.836704
$653$	5.42113	−	9.38968i	0.212145	−	0.367447i	−0.740240	−	0.672342i	$-0.765288\pi$
$653$	5.42113	−	9.38968i	0.212145	−	0.367447i	0.952386	+	0.304896i	$0.0986216\pi$
$654$	−4.80344	−	8.31981i	−0.187830	−	0.325330i
$655$	−39.7794	−	68.9000i	−1.55431	−	2.69214i
$656$	26.3507	−	45.6407i	1.02882	−	1.78197i
$657$	25.3933			0.990687
$658$	15.7437	−	51.0002i	0.613754	−	1.98819i
$659$	−29.4418			−1.14689			−0.573446	−	0.819244i	$-0.694394\pi$
$659$	−29.4418			−1.14689			−0.573446	+	0.819244i	$0.694394\pi$
$660$	15.4616	−	26.7802i	0.601841	−	1.04242i
$661$	9.38631	+	16.2576i	0.365085	+	0.632346i	0.988790	−	0.149314i	$-0.0477066\pi$
$661$	9.38631	+	16.2576i	0.365085	+	0.632346i	−0.623705	+	0.781660i	$0.714373\pi$
$662$	−31.7129	−	54.9283i	−1.23256	−	2.13485i
$663$		0			0
$664$	−2.82060			−0.109461
$665$	−3.76578	+	12.1989i	−0.146031	+	0.473052i
$666$	11.0752			0.429157
$667$	−0.0298826	+	0.0517581i	−0.00115706	+	0.00200408i
$668$	−11.5376	−	19.9837i	−0.446403	−	0.773193i
$669$	14.5883	+	25.2677i	0.564017	+	0.976907i
$670$	6.02992	−	10.4441i	0.232956	−	0.403492i
$671$	10.4743			0.404355
$672$	−34.2980	+	7.82040i	−1.32308	+	0.301678i
$673$	−6.72821			−0.259353			−0.129677	−	0.991556i	$-0.541394\pi$
$673$	−6.72821			−0.259353			−0.129677	+	0.991556i	$0.541394\pi$
$674$	−15.5404	+	26.9168i	−0.598595	+	1.03680i
$675$	−7.79867	−	13.5077i	−0.300171	−	0.519912i
$676$		0			0
$677$	13.8565	−	24.0001i	0.532547	−	0.922399i	−0.466730	−	0.884400i	$-0.654568\pi$
$677$	13.8565	−	24.0001i	0.532547	−	0.922399i	0.999278	−	0.0379995i	$-0.0120985\pi$
$678$	−29.7303			−1.14178
$679$	18.1920	+	19.6149i	0.698146	+	0.752753i
$680$	21.2780			0.815973
$681$	−26.9957	+	46.7580i	−1.03448	+	1.79177i
$682$	1.74521	+	3.02279i	0.0668275	+	0.115749i
$683$	2.30069	+	3.98491i	0.0880335	+	0.152479i	0.906680	−	0.421819i	$-0.138608\pi$
$683$	2.30069	+	3.98491i	0.0880335	+	0.152479i	−0.818646	+	0.574298i	$0.805275\pi$
$684$	1.61241	−	2.79278i	0.0616522	−	0.106785i
$685$	33.3344			1.27364
$686$	−4.85707	−	32.3689i	−0.185444	−	1.23585i
$687$	−17.7244			−0.676227
$688$	10.8013	−	18.7084i	0.411797	−	0.713253i
$689$		0			0
$690$	−0.0624579	−	0.108180i	−0.00237773	−	0.00411835i
$691$	14.6690	−	25.4075i	0.558036	−	0.966547i	−0.439624	−	0.898182i	$-0.644888\pi$
$691$	14.6690	−	25.4075i	0.558036	−	0.966547i	0.997660	−	0.0683649i	$-0.0217782\pi$
$692$	−5.91823			−0.224977
$693$	12.6543	+	13.6440i	0.480695	+	0.518294i
$694$	35.4924			1.34727
$695$	6.36096	−	11.0175i	0.241285	−	0.417918i
$696$	14.4388	+	25.0087i	0.547300	+	0.947952i
$697$	17.8500	+	30.9172i	0.676118	+	1.17107i
$698$	24.1578	−	41.8426i	0.914387	−	1.58376i
$699$	−55.7767			−2.10967
$700$	−33.4579	+	7.62885i	−1.26459	+	0.288343i
$701$	15.1336			0.571588			0.285794	−	0.958291i	$-0.407743\pi$
$701$	15.1336			0.571588			0.285794	+	0.958291i	$0.407743\pi$
$702$		0			0
$703$	1.53619	+	2.66075i	0.0579383	+	0.100352i
$704$	0.180618	+	0.312840i	0.00680730	+	0.0117906i
$705$	54.0465	−	93.6114i	2.03551	−	3.52561i
$706$	−29.0796			−1.09442
$707$	4.03439	−	13.0690i	0.151729	−	0.491511i
$708$	−10.3473			−0.388874
$709$	−10.8913	+	18.8643i	−0.409031	+	0.708462i	−0.994781	−	0.102029i	$-0.967467\pi$
$709$	−10.8913	+	18.8643i	−0.409031	+	0.708462i	0.585750	+	0.810491i	$0.300800\pi$
$710$	25.6360	+	44.4029i	0.962104	+	1.66641i
$711$	−13.8432	−	23.9771i	−0.519159	−	0.899210i
$712$	−2.79344	+	4.83838i	−0.104689	+	0.181326i
$713$	0.00507138			0.000189925
$714$	10.8421	−	35.1220i	0.405756	−	1.31441i
$715$		0			0
$716$	−4.92189	+	8.52496i	−0.183940	+	0.318593i
$717$	−17.7615	−	30.7639i	−0.663316	−	1.14890i
$718$	−19.5658	−	33.8890i	−0.730191	−	1.26473i
$719$	18.8257	−	32.6070i	0.702079	−	1.21604i	−0.265656	−	0.964068i	$-0.585589\pi$
$719$	18.8257	−	32.6070i	0.702079	−	1.21604i	0.967735	−	0.251969i	$-0.0810781\pi$
$720$	−49.0618			−1.82843
$721$	9.81433	−	2.23779i	0.365505	−	0.0833398i
$722$	−31.0920			−1.15712
$723$	−11.9045	+	20.6192i	−0.442733	+	0.766835i
$724$	9.49855	+	16.4520i	0.353011	+	0.611433i
$725$	46.2222	+	80.0592i	1.71665	+	2.97332i
$726$	−5.24730	+	9.08860i	−0.194746	+	0.337309i
$727$	34.5858			1.28272			0.641358	−	0.767242i	$-0.278371\pi$
$727$	34.5858			1.28272			0.641358	+	0.767242i	$0.278371\pi$
$728$		0			0
$729$	−15.7397			−0.582952
$730$	−37.7210	+	65.3346i	−1.39612	+	2.41814i
$731$	7.31685	+	12.6732i	0.270623	+	0.468734i
$732$	4.71215	+	8.16169i	0.174166	+	0.301665i
$733$	−0.586049	+	1.01507i	−0.0216462	+	0.0374924i	−0.876646	−	0.481137i	$-0.840224\pi$
$733$	−0.586049	+	1.01507i	−0.0216462	+	0.0374924i	0.854999	+	0.518629i	$0.173557\pi$
$734$	−18.7331			−0.691452
$735$	4.98255	−	66.0988i	0.183784	−	2.43809i
$736$	0.0426298			0.00157136
$737$	2.43819	−	4.22306i	0.0898117	−	0.155558i
$738$	−22.6060	−	39.1548i	−0.832140	−	1.44131i
$739$	−12.7416	−	22.0690i	−0.468706	−	0.811823i	0.530654	−	0.847588i	$-0.321946\pi$
$739$	−12.7416	−	22.0690i	−0.468706	−	0.811823i	−0.999360	+	0.0357657i	$0.988613\pi$
$740$	−5.91742	+	10.2493i	−0.217529	+	0.376771i
$741$		0			0
$742$	−19.3874	−	20.9038i	−0.711732	−	0.767402i
$743$	18.0403			0.661835			0.330918	−	0.943660i	$-0.392642\pi$
$743$	18.0403			0.661835			0.330918	+	0.943660i	$0.392642\pi$
$744$	1.22520	−	2.12212i	0.0449182	−	0.0778006i
$745$	36.1901	+	62.6831i	1.32590	+	2.29653i
$746$	−13.9262	−	24.1209i	−0.509874	−	0.883128i
$747$	−2.20279	+	3.81534i	−0.0805957	+	0.139596i
$748$	−11.0268			−0.403180
$749$	−20.4295	+	4.65819i	−0.746478	+	0.170207i
$750$	−109.541			−3.99987
$751$	0.369107	−	0.639312i	0.0134689	−	0.0233288i	−0.859212	−	0.511619i	$-0.829046\pi$
$751$	0.369107	−	0.639312i	0.0134689	−	0.0233288i	0.872681	+	0.488290i	$0.162379\pi$
$752$	28.4503	+	49.2774i	1.03748	+	1.79696i
$753$	15.1860	+	26.3029i	0.553409	+	0.958533i
$754$		0			0
$755$	14.2750			0.519521
$756$	1.18443	−	3.83685i	0.0430773	−	0.139545i
$757$	−15.5551			−0.565359			−0.282680	−	0.959214i	$-0.591223\pi$
$757$	−15.5551			−0.565359			−0.282680	+	0.959214i	$0.591223\pi$
$758$	19.9997	−	34.6405i	0.726422	−	1.25820i
$759$	−0.0252547	−	0.0437424i	−0.000916688	−	0.00158775i
$760$	−3.73771	−	6.47391i	−0.135581	−	0.234833i
$761$	17.8466	−	30.9112i	0.646938	−	1.12053i	−0.336913	−	0.941536i	$-0.609383\pi$
$761$	17.8466	−	30.9112i	0.646938	−	1.12053i	0.983850	−	0.178993i	$-0.0572840\pi$
$762$	−13.6516			−0.494544
$763$	−1.82221	+	5.90286i	−0.0659683	+	0.213698i
$764$	−7.29434			−0.263900
$765$	16.6173	−	28.7820i	0.600800	−	1.04062i
$766$	0.245948	+	0.425994i	0.00888646	+	0.0153918i
$767$		0			0
$768$	23.3361	−	40.4193i	0.842069	−	1.45851i
$769$	30.8652			1.11303			0.556514	−	0.830838i	$-0.312139\pi$
$769$	30.8652			1.11303			0.556514	+	0.830838i	$0.312139\pi$
$770$	−53.9023	+	12.2904i	−1.94251	+	0.442917i
$771$	−35.2974			−1.27120
$772$	4.22626	−	7.32009i	0.152106	−	0.263456i
$773$	13.3640	+	23.1471i	0.480669	+	0.832543i	0.999754	−	0.0221798i	$-0.00706064\pi$
$773$	13.3640	+	23.1471i	0.480669	+	0.832543i	−0.519085	+	0.854722i	$0.673727\pi$
$774$	−9.26637	−	16.0498i	−0.333073	−	0.576899i
$775$	3.92219	−	6.79344i	0.140889	−	0.244027i
$776$	−15.6645			−0.562321
$777$	−10.8475	−	11.6960i	−0.389152	−	0.419590i
$778$	−56.5001			−2.02563
$779$	6.27112	−	10.8619i	0.224686	−	0.389168i
$780$		0			0
$781$	10.3659	+	17.9542i	0.370920	+	0.642453i
$782$	−0.0222717	+	0.0385757i	−0.000796434	+	0.00137946i
$783$	−10.8172			−0.386576
$784$	28.8216	+	19.6688i	1.02934	+	0.702455i
$785$	8.64924			0.308704
$786$	40.2368	−	69.6923i	1.43520	−	2.48584i
$787$	−11.9716	−	20.7355i	−0.426742	−	0.739139i	0.569839	−	0.821756i	$-0.307006\pi$
$787$	−11.9716	−	20.7355i	−0.426742	−	0.739139i	−0.996581	+	0.0826170i	$0.973672\pi$
$788$	12.0616	+	20.8913i	0.429677	+	0.744222i
$789$	0.781885	−	1.35427i	0.0278359	−	0.0482131i
$790$	82.2544			2.92648
$791$	13.0005	+	14.0174i	0.462245	+	0.498401i
$792$	−10.8961			−0.387176
$793$		0			0
$794$	16.1004	+	27.8866i	0.571380	+	0.989660i
$795$	−28.8690	−	50.0026i	−1.02388	−	1.77341i
$796$	−0.679795	+	1.17744i	−0.0240947	+	0.0417333i
$797$	41.3242			1.46378			0.731889	−	0.681424i	$-0.238639\pi$
$797$	41.3242			1.46378			0.731889	+	0.681424i	$0.238639\pi$
$798$	−12.5905	+	2.87081i	−0.445700	+	0.101625i
$799$	−38.5446			−1.36361
$800$	32.9698	−	57.1054i	1.16566	−	2.01898i
$801$	4.36315	+	7.55719i	0.154164	+	0.267020i
$802$	−18.3470	−	31.7780i	−0.647855	−	1.12212i
$803$	−15.2524	+	26.4179i	−0.538246	+	0.932269i
$804$	4.38755			0.154737
$805$	−0.0236937	+	0.0767532i	−0.000835092	+	0.00270520i
$806$		0			0
$807$	20.9955	−	36.3653i	0.739077	−	1.28012i
$808$	4.00433	+	6.93570i	0.140872	+	0.243997i
$809$	21.9130	+	37.9545i	0.770421	+	1.33441i	0.937333	+	0.348436i	$0.113287\pi$
$809$	21.9130	+	37.9545i	0.770421	+	1.33441i	−0.166912	+	0.985972i	$0.553380\pi$
$810$	37.3965	−	64.7727i	1.31398	−	2.27588i
$811$	−37.9985			−1.33431			−0.667154	−	0.744920i	$-0.732488\pi$
$811$	−37.9985			−1.33431			−0.667154	+	0.744920i	$0.732488\pi$
$812$	−7.02004	+	22.7407i	−0.246355	+	0.798043i
$813$	−22.1455			−0.776677
$814$	−6.65231	+	11.5221i	−0.233163	+	0.403851i
$815$	38.6773	+	66.9910i	1.35481	+	2.34659i
$816$	19.5927	+	33.9355i	0.685881	+	1.18798i
$817$	2.57057	−	4.45236i	0.0899330	−	0.155768i
$818$	29.3020			1.02452
$819$		0			0
$820$	48.3130			1.68716
$821$	−10.3336	+	17.8983i	−0.360645	+	0.624656i	−0.988067	−	0.154023i	$-0.950777\pi$
$821$	−10.3336	+	17.8983i	−0.360645	+	0.624656i	0.627422	+	0.778680i	$0.284110\pi$
$822$	16.8588	+	29.2004i	0.588020	+	1.01848i
$823$	−3.51444	−	6.08719i	−0.122506	−	0.212186i	0.798250	−	0.602327i	$-0.205760\pi$
$823$	−3.51444	−	6.08719i	−0.122506	−	0.212186i	−0.920755	+	0.390141i	$0.872426\pi$
$824$	−2.94705	+	5.10444i	−0.102665	+	0.177822i
$825$	−78.1277			−2.72006
$826$	12.5797	+	13.5637i	0.437705	+	0.471941i
$827$	−47.5367			−1.65301			−0.826506	−	0.562928i	$-0.809675\pi$
$827$	−47.5367			−1.65301			−0.826506	+	0.562928i	$0.809675\pi$
$828$	0.0101450	−	0.0175717i	0.000352565	−	0.000610660i
$829$	−18.5119	−	32.0635i	−0.642944	−	1.11361i	−0.984772	−	0.173849i	$-0.944379\pi$
$829$	−18.5119	−	32.0635i	−0.642944	−	1.11361i	0.341828	−	0.939762i	$-0.388954\pi$
$830$	−6.54434	−	11.3351i	−0.227157	−	0.393448i
$831$	4.05798	−	7.02863i	0.140770	−	0.243820i
$832$		0			0
$833$	−21.3006	+	10.2463i	−0.738021	+	0.355014i
$834$	12.8682			0.445590
$835$	−41.7739	+	72.3546i	−1.44565	+	2.50393i
$836$	1.93698	+	3.35495i	0.0669919	+	0.116033i
$837$	0.458948	+	0.794922i	0.0158636	+	0.0274765i
$838$	3.72077	−	6.44456i	0.128532	−	0.222624i
$839$	−3.89858			−0.134594			−0.0672970	−	0.997733i	$-0.521437\pi$
$839$	−3.89858			−0.134594			−0.0672970	+	0.997733i	$0.521437\pi$
$840$	26.3932	+	28.4576i	0.910651	+	0.981880i
$841$	35.1129			1.21079
$842$	−30.0136	+	51.9851i	−1.03434	+	1.79152i
$843$	15.2033	+	26.3328i	0.523628	+	0.906951i
$844$	−9.81020	−	16.9918i	−0.337681	−	0.584881i
$845$		0			0
$846$	48.8146			1.67828
$847$	6.57969	−	1.50026i	0.226081	−	0.0515494i
$848$	30.3935			1.04372
$849$	8.57498	−	14.8523i	0.294293	−	0.509730i
$850$	34.4497	+	59.6687i	1.18162	+	2.04662i
$851$	0.00966543	+	0.0167410i	0.000331327	+	0.000573875i
$852$	−9.32679	+	16.1545i	−0.319530	+	0.553443i
$853$	−12.3795			−0.423868			−0.211934	−	0.977284i	$-0.567976\pi$
$853$	−12.3795			−0.423868			−0.211934	+	0.977284i	$0.567976\pi$
$854$	4.96992	−	16.0995i	0.170067	−	0.550915i
$855$	−11.6761			−0.399313
$856$	6.13458	−	10.6254i	0.209676	−	0.363169i
$857$	4.69917	+	8.13921i	0.160521	+	0.278030i	0.935056	−	0.354501i	$-0.115349\pi$
$857$	4.69917	+	8.13921i	0.160521	+	0.278030i	−0.774535	+	0.632531i	$0.782016\pi$
$858$		0			0
$859$	−11.8535	+	20.5309i	−0.404438	+	0.700506i	−0.994256	−	0.107030i	$-0.965866\pi$
$859$	−11.8535	+	20.5309i	−0.404438	+	0.700506i	0.589818	+	0.807536i	$0.299199\pi$
$860$	19.8038			0.675304
$861$	−19.2081	+	62.2226i	−0.654609	+	2.12054i
$862$	44.7381			1.52379
$863$	−9.26438	+	16.0464i	−0.315363	+	0.546225i	−0.979515	−	0.201373i	$-0.935460\pi$
$863$	−9.26438	+	16.0464i	−0.315363	+	0.546225i	0.664152	+	0.747598i	$0.268793\pi$
$864$	3.85790	+	6.68208i	0.131249	+	0.227329i
$865$	10.7140	+	18.5572i	0.364287	+	0.630964i
$866$	2.10264	−	3.64188i	0.0714507	−	0.123756i
$867$	13.0321			0.442594
$868$	1.96898	−	0.448954i	0.0668317	−	0.0152385i
$869$	33.2594			1.12825
$870$	−67.0015	+	116.050i	−2.27156	+	3.93446i
$871$		0			0
$872$	−1.80863	−	3.13264i	−0.0612479	−	0.106084i
$873$	−12.2334	+	21.1888i	−0.414037	+	0.717133i
$874$	0.0156491			0.000529338
$875$	47.9003	+	51.6469i	1.61933	+	1.74599i
$876$	−27.4469			−0.927346
$877$	−3.59542	+	6.22745i	−0.121409	+	0.210286i	−0.920323	−	0.391158i	$-0.872074\pi$
$877$	−3.59542	+	6.22745i	−0.121409	+	0.210286i	0.798915	+	0.601444i	$0.205408\pi$
$878$	−14.8607	−	25.7396i	−0.501526	−	0.868668i
$879$	−27.9358	−	48.3862i	−0.942251	−	1.63203i
$880$	29.4688	−	51.0415i	0.993394	−	1.72061i
$881$	−32.4334			−1.09271			−0.546355	−	0.837554i	$-0.683985\pi$
$881$	−32.4334			−1.09271			−0.546355	+	0.837554i	$0.683985\pi$
$882$	26.9759	−	12.9764i	0.908327	−	0.436937i
$883$	−37.8020			−1.27214			−0.636069	−	0.771632i	$-0.719441\pi$
$883$	−37.8020			−1.27214			−0.636069	+	0.771632i	$0.719441\pi$
$884$		0			0
$885$	18.7320	+	32.4449i	0.629671	+	1.09062i
$886$	14.2491	+	24.6801i	0.478707	+	0.829145i
$887$	22.4809	−	38.9381i	0.754836	−	1.30741i	−0.190619	−	0.981664i	$-0.561050\pi$
$887$	22.4809	−	38.9381i	0.754836	−	1.30741i	0.945456	−	0.325751i	$-0.105617\pi$
$888$	9.34036			0.313442
$889$	5.96959	+	6.43652i	0.200214	+	0.215874i
$890$	−25.9253			−0.869017
$891$	15.1212	−	26.1907i	0.506580	−	0.877422i
$892$	−7.03989	−	12.1935i	−0.235713	−	0.408267i
$893$	6.77080	+	11.7274i	0.226576	+	0.392441i
$894$	−36.6063	+	63.4039i	−1.22430	+	2.12054i
$895$	35.6412			1.19135
$896$	−28.8988	+	6.58930i	−0.965441	+	0.220133i
$897$		0			0
$898$	−35.8139	+	62.0314i	−1.19512	+	2.07002i
$899$	−2.72015	−	4.71145i	−0.0907222	−	0.157136i
$900$	−15.6923	−	27.1799i	−0.523077	−	0.905996i
$901$	−10.2943	+	17.8303i	−0.342954	+	0.594014i
$902$	54.3130			1.80842
$903$	−7.87352	+	25.5055i	−0.262014	+	0.848769i
$904$	−11.1943			−0.372316
$905$	34.3912	−	59.5673i	1.14320	−	1.98008i
$906$	7.21958	+	12.5047i	0.239854	+	0.415440i
$907$	−17.1544	−	29.7124i	−0.569604	−	0.986583i	−0.996605	−	0.0823316i	$-0.973763\pi$
$907$	−17.1544	−	29.7124i	−0.569604	−	0.986583i	0.427001	−	0.904251i	$-0.359570\pi$
$908$	13.0273	−	22.5640i	0.432328	−	0.748813i
$909$	12.5089			0.414895
$910$		0			0
$911$	59.7775			1.98052			0.990258	−	0.139242i	$-0.0444666\pi$
$911$	59.7775			1.98052			0.990258	+	0.139242i	$0.0444666\pi$
$912$	6.88335	−	11.9223i	0.227930	−	0.394787i
$913$	−2.64619	−	4.58334i	−0.0875762	−	0.151686i
$914$	10.2585	+	17.7683i	0.339322	+	0.587723i
$915$	17.0612	−	29.5509i	0.564026	−	0.976922i
$916$	8.55326			0.282608
$917$	−50.4537	+	11.5041i	−1.66613	+	0.379899i
$918$	−8.06215			−0.266091
$919$	−11.7374	+	20.3297i	−0.387180	+	0.670615i	−0.992069	−	0.125695i	$-0.959884\pi$
$919$	−11.7374	+	20.3297i	−0.387180	+	0.670615i	0.604889	+	0.796310i	$0.293217\pi$
$920$	−0.0235171	−	0.0407328i	−0.000775335	−	0.00134292i
$921$	−1.01438	−	1.75695i	−0.0334249	−	0.0578936i
$922$	−23.3536	+	40.4496i	−0.769109	+	1.33214i
$923$		0			0
$924$	−13.6776	−	14.7475i	−0.449961	−	0.485156i
$925$	29.9009			0.983135
$926$	13.8957	−	24.0681i	0.456642	−	0.790926i
$927$	4.60308	+	7.97276i	0.151185	+	0.261860i
$928$	−22.8655	−	39.6042i	−0.750598	−	1.30007i
$929$	−2.48447	+	4.30322i	−0.0815127	+	0.141184i	−0.903900	−	0.427744i	$-0.859308\pi$
$929$	−2.48447	+	4.30322i	−0.0815127	+	0.141184i	0.822387	+	0.568928i	$0.192642\pi$
$930$	11.3709			0.372865
$931$	6.85917	+	4.68091i	0.224800	+	0.153410i
$932$	26.9162			0.881669
$933$	19.0714	−	33.0326i	0.624368	−	1.08144i
$934$	24.2350	+	41.9762i	0.792993	+	1.37350i
$935$	19.9623	+	34.5757i	0.652836	+	1.13075i
$936$		0			0
$937$	−22.1788			−0.724550			−0.362275	−	0.932071i	$-0.618000\pi$
$937$	−22.1788			−0.724550			−0.362275	+	0.932071i	$0.618000\pi$
$938$	−5.33419	−	5.75142i	−0.174168	−	0.187791i
$939$	−40.1119			−1.30900
$940$	−26.0813	+	45.1741i	−0.850677	+	1.47342i
$941$	7.59141	+	13.1487i	0.247473	+	0.428635i	0.962824	−	0.270130i	$-0.0870666\pi$
$941$	7.59141	+	13.1487i	0.247473	+	0.428635i	−0.715351	+	0.698765i	$0.753733\pi$
$942$	4.37435	+	7.57659i	0.142524	+	0.246859i
$943$	0.0394568	−	0.0683413i	0.00128489	−	0.00222550i
$944$	−19.7212			−0.641872
$945$	−14.1750	+	3.23209i	−0.461114	+	0.105140i
$946$	22.2632			0.723841
$947$	−21.4460	+	37.1456i	−0.696902	+	1.20707i	0.272633	+	0.962118i	$0.412106\pi$
$947$	−21.4460	+	37.1456i	−0.696902	+	1.20707i	−0.969535	+	0.244952i	$0.921228\pi$
$948$	14.9627	+	25.9162i	0.485966	+	0.841718i
$949$		0			0
$950$	12.1030	−	20.9630i	0.392672	−	0.680128i
$951$	21.0448			0.682424
$952$	4.08235	−	13.2244i	0.132310	−	0.428605i
$953$	−8.91446			−0.288768			−0.144384	−	0.989522i	$-0.546120\pi$
$953$	−8.91446			−0.288768			−0.144384	+	0.989522i	$0.546120\pi$
$954$	13.0372	−	22.5811i	0.422094	−	0.731089i
$955$	13.2052	+	22.8721i	0.427311	+	0.740125i
$956$	8.57119	+	14.8457i	0.277212	+	0.480145i
$957$	−27.0919	+	46.9246i	−0.875758	+	1.51686i
$958$	−31.5397			−1.01900
$959$	6.39547	−	20.7175i	0.206521	−	0.669003i
$960$	1.17681			0.0379814
$961$	15.2692	−	26.4470i	0.492554	−	0.853129i
$962$		0			0
$963$	−9.58176	−	16.5961i	−0.308768	−	0.534802i
$964$	5.74475	−	9.95020i	0.185026	−	0.320474i
$965$	−30.6039			−0.985173
$966$	−0.0792177	+	0.0180627i	−0.00254879	+	0.000581156i
$967$	−13.8676			−0.445952			−0.222976	−	0.974824i	$-0.571577\pi$
$967$	−13.8676			−0.445952			−0.222976	+	0.974824i	$0.571577\pi$
$968$	−1.97575	+	3.42210i	−0.0635031	+	0.109991i
$969$	4.66280	+	8.07621i	0.149791	+	0.259445i
$970$	−36.3446	−	62.9507i	−1.16695	−	2.02122i
$971$	24.9974	−	43.2967i	0.802203	−	1.38946i	−0.115960	−	0.993254i	$-0.536994\pi$
$971$	24.9974	−	43.2967i	0.802203	−	1.38946i	0.918163	−	0.396203i	$-0.129672\pi$
$972$	22.6577			0.726747
$973$	−5.62704	−	6.06718i	−0.180395	−	0.194505i
$974$	10.0048			0.320576
$975$		0			0
$976$	8.98108	+	15.5557i	0.287477	+	0.497925i
$977$	9.79844	+	16.9714i	0.313480	+	0.542963i	0.979113	−	0.203316i	$-0.0651719\pi$
$977$	9.79844	+	16.9714i	0.313480	+	0.542963i	−0.665633	+	0.746279i	$0.731839\pi$
$978$	−39.1220	+	67.7613i	−1.25098	+	2.16677i
$979$	−10.4828			−0.335033
$980$	−2.40443	+	31.8973i	−0.0768067	+	1.01892i
$981$	−5.64989			−0.180387
$982$	−35.5616	+	61.5945i	−1.13482	+	1.96556i
$983$	−21.6047	−	37.4204i	−0.689081	−	1.19352i	−0.972135	−	0.234420i	$-0.924681\pi$
$983$	−21.6047	−	37.4204i	−0.689081	−	1.19352i	0.283054	−	0.959104i	$-0.408652\pi$
$984$	−19.0649	−	33.0214i	−0.607768	−	1.05268i
$985$	43.6712	−	75.6407i	1.39148	−	2.41011i
$986$	47.7838			1.52175
$987$	−47.8107	−	51.5504i	−1.52183	−	1.64087i
$988$		0			0
$989$	0.0161736	−	0.0280135i	0.000514291	−	0.000890779i
$990$	−25.2811	−	43.7881i	−0.803485	−	1.39168i
$991$	−14.9550	−	25.9029i	−0.475063	−	0.822833i	0.524529	−	0.851392i	$-0.324241\pi$
$991$	−14.9550	−	25.9029i	−0.475063	−	0.822833i	−0.999592	+	0.0285595i	$0.990908\pi$
$992$	−1.94026	+	3.36063i	−0.0616032	+	0.106700i
$993$	−83.5481			−2.65132
$994$	32.5152	−	7.41388i	1.03132	−	0.235154i
$995$	4.92264			0.156058
$996$	2.38093	−	4.12390i	0.0754427	−	0.130671i
$997$	−4.68153	−	8.10865i	−0.148266	−	0.256803i	0.782321	−	0.622876i	$-0.214036\pi$
$997$	−4.68153	−	8.10865i	−0.148266	−	0.256803i	−0.930587	+	0.366072i	$0.880702\pi$
$998$	−12.4219	−	21.5154i	−0.393210	−	0.681059i
$999$	−1.74940	+	3.03005i	−0.0553485	+	0.0958665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.170.5	yes	48
7.2	even	3		8281.2.a.cu.1.20		24
7.4	even	3	inner	1183.2.e.l.508.5	yes	48
7.5	odd	6		8281.2.a.ct.1.20		24
13.12	even	2		1183.2.e.k.170.20	✓	48
91.12	odd	6		8281.2.a.cw.1.5		24
91.25	even	6		1183.2.e.k.508.20	yes	48
91.51	even	6		8281.2.a.cv.1.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.20	✓	48	13.12	even	2
1183.2.e.k.508.20	yes	48	91.25	even	6
1183.2.e.l.170.5	yes	48	1.1	even	1	trivial
1183.2.e.l.508.5	yes	48	7.4	even	3	inner
8281.2.a.ct.1.20		24	7.5	odd	6
8281.2.a.cu.1.20		24	7.2	even	3
8281.2.a.cv.1.5		24	91.51	even	6
8281.2.a.cw.1.5		24	91.12	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.883662 + 1.53055i) q^{2} +(1.16401 + 2.01613i) q^{3} +(-0.561718 - 0.972924i) q^{4} +(-2.03380 + 3.52265i) q^{5} -4.11437 q^{6} +(1.79914 + 1.93987i) q^{7} -1.54917 q^{8} +(-1.20985 + 2.09552i) q^{9} +O(q^{10})\)	\(q+(-0.883662 + 1.53055i) q^{2} +(1.16401 + 2.01613i) q^{3} +(-0.561718 - 0.972924i) q^{4} +(-2.03380 + 3.52265i) q^{5} -4.11437 q^{6} +(1.79914 + 1.93987i) q^{7} -1.54917 q^{8} +(-1.20985 + 2.09552i) q^{9} +(-3.59438 - 6.22566i) q^{10} +(-1.45338 - 2.51733i) q^{11} +(1.30769 - 2.26499i) q^{12} +(-4.55889 + 1.03949i) q^{14} -9.46947 q^{15} +(2.49238 - 4.31693i) q^{16} +(1.68835 + 2.92430i) q^{17} +(-2.13819 - 3.70346i) q^{18} +(0.593154 - 1.02737i) q^{19} +4.56969 q^{20} +(-1.81680 + 5.88533i) q^{21} +5.13720 q^{22} +(0.00373203 - 0.00646406i) q^{23} +(-1.80326 - 3.12333i) q^{24} +(-5.77269 - 9.99859i) q^{25} +1.35096 q^{27} +(0.876732 - 2.84009i) q^{28} -8.00705 q^{29} +(8.36781 - 14.4935i) q^{30} +(0.339720 + 0.588412i) q^{31} +(2.85567 + 4.94617i) q^{32} +(3.38351 - 5.86041i) q^{33} -5.96771 q^{34} +(-10.4926 + 2.39244i) q^{35} +2.71837 q^{36} +(-1.29493 + 2.24288i) q^{37} +(1.04830 + 1.81570i) q^{38} +(3.15071 - 5.45719i) q^{40} +10.5725 q^{41} +(-7.40235 - 7.98134i) q^{42} +4.33374 q^{43} +(-1.63278 + 2.82806i) q^{44} +(-4.92118 - 8.52373i) q^{45} +(0.00659571 + 0.0114241i) q^{46} +(-5.70745 + 9.88560i) q^{47} +11.6047 q^{48} +(-0.526169 + 6.98020i) q^{49} +20.4044 q^{50} +(-3.93051 + 6.80785i) q^{51} +(3.04864 + 5.28040i) q^{53} +(-1.19379 + 2.06771i) q^{54} +11.8236 q^{55} +(-2.78719 - 3.00519i) q^{56} +2.76175 q^{57} +(7.07553 - 12.2552i) q^{58} +(-1.97815 - 3.42626i) q^{59} +(5.31917 + 9.21307i) q^{60} +(-1.80171 + 3.12065i) q^{61} -1.20079 q^{62} +(-6.24172 + 1.42319i) q^{63} -0.124274 q^{64} +(5.97976 + 10.3572i) q^{66} +(0.838797 + 1.45284i) q^{67} +(1.89675 - 3.28527i) q^{68} +0.0173765 q^{69} +(5.61014 - 18.1735i) q^{70} -7.13225 q^{71} +(1.87427 - 3.24632i) q^{72} +(-5.24721 - 9.08843i) q^{73} +(-2.28856 - 3.96390i) q^{74} +(13.4390 - 23.2769i) q^{75} -1.33274 q^{76} +(2.26845 - 7.34841i) q^{77} +(-5.72103 + 9.90912i) q^{79} +(10.1380 + 17.5596i) q^{80} +(5.20208 + 9.01027i) q^{81} +(-9.34251 + 16.1817i) q^{82} +1.82071 q^{83} +(6.74650 - 1.53829i) q^{84} -13.7350 q^{85} +(-3.82956 + 6.63299i) q^{86} +(-9.32031 - 16.1432i) q^{87} +(2.25154 + 3.89979i) q^{88} +(1.80318 - 3.12320i) q^{89} +17.3946 q^{90} -0.00838539 q^{92} +(-0.790876 + 1.36984i) q^{93} +(-10.0869 - 17.4711i) q^{94} +(2.41271 + 4.17894i) q^{95} +(-6.64808 + 11.5148i) q^{96} +10.1115 q^{97} +(-10.2186 - 6.97346i) q^{98} +7.03349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

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