LMFDB - Embedded newform 315.2.bo.b.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248464 - 0.143451i) q^{2} +(0.701026 - 1.58384i) q^{3} +(-0.958844 - 1.66077i) q^{4} +(2.21083 - 0.335020i) q^{5} +(-0.401384 + 0.292966i) q^{6} +(-2.25543 - 1.38312i) q^{7} +1.12399i q^{8} +(-2.01713 - 2.22063i) q^{9} +O(q^{10})$	\(q+(-0.248464 - 0.143451i) q^{2} +(0.701026 - 1.58384i) q^{3} +(-0.958844 - 1.66077i) q^{4} +(2.21083 - 0.335020i) q^{5} +(-0.401384 + 0.292966i) q^{6} +(-2.25543 - 1.38312i) q^{7} +1.12399i q^{8} +(-2.01713 - 2.22063i) q^{9} +(-0.597370 - 0.233905i) q^{10} +2.24786 q^{11} +(-3.30257 + 0.354419i) q^{12} +(0.740832 + 0.427720i) q^{13} +(0.361985 + 0.667199i) q^{14} +(1.01923 - 3.73647i) q^{15} +(-1.75645 + 3.04226i) q^{16} +(-3.53834 - 2.04286i) q^{17} +(0.182632 + 0.841106i) q^{18} +(2.84162 + 4.92182i) q^{19} +(-2.67623 - 3.35044i) q^{20} +(-3.77176 + 2.60265i) q^{21} +(-0.558513 - 0.322458i) q^{22} -1.00792i q^{23} +(1.78023 + 0.787947i) q^{24} +(4.77552 - 1.48134i) q^{25} +(-0.122713 - 0.212546i) q^{26} +(-4.93119 + 1.63809i) q^{27} +(-0.134430 + 5.07194i) q^{28} +(-3.05734 - 5.29547i) q^{29} +(-0.789241 + 0.782168i) q^{30} +(-0.335102 - 0.580413i) q^{31} +(2.81964 - 1.62792i) q^{32} +(1.57581 - 3.56027i) q^{33} +(0.586100 + 1.01515i) q^{34} +(-5.44975 - 2.30223i) q^{35} +(-1.75384 + 5.47921i) q^{36} +(4.95382 - 2.86009i) q^{37} -1.63053i q^{38} +(1.19678 - 0.873520i) q^{39} +(0.376559 + 2.48495i) q^{40} +(3.29852 - 5.71321i) q^{41} +(1.31050 - 0.105603i) q^{42} +(-0.200024 + 0.115484i) q^{43} +(-2.15535 - 3.73318i) q^{44} +(-5.20347 - 4.23366i) q^{45} +(-0.144587 + 0.250432i) q^{46} +(7.57804 + 4.37518i) q^{47} +(3.58715 + 4.91465i) q^{48} +(3.17396 + 6.23907i) q^{49} +(-1.39905 - 0.316992i) q^{50} +(-5.71604 + 4.17208i) q^{51} -1.64047i q^{52} +(11.1069 + 6.41258i) q^{53} +(1.46021 + 0.300376i) q^{54} +(4.96964 - 0.753079i) q^{55} +(1.55461 - 2.53509i) q^{56} +(9.78745 - 1.05035i) q^{57} +1.75431i q^{58} +(-4.37646 - 7.58026i) q^{59} +(-7.18268 + 1.88999i) q^{60} +(0.995824 - 1.72482i) q^{61} +0.192282i q^{62} +(1.47809 + 7.79841i) q^{63} +6.09169 q^{64} +(1.78115 + 0.697421i) q^{65} +(-0.902255 + 0.658547i) q^{66} +(-12.4267 + 7.17453i) q^{67} +7.83513i q^{68} +(-1.59639 - 0.706578i) q^{69} +(1.02381 + 1.35379i) q^{70} +3.32909 q^{71} +(2.49597 - 2.26723i) q^{72} +(10.1230 + 5.84452i) q^{73} -1.64113 q^{74} +(1.00155 - 8.60215i) q^{75} +(5.44933 - 9.43852i) q^{76} +(-5.06991 - 3.10906i) q^{77} +(-0.422665 + 0.0453588i) q^{78} +(-5.84731 + 10.1278i) q^{79} +(-2.86399 + 7.31436i) q^{80} +(-0.862407 + 8.95859i) q^{81} +(-1.63913 + 0.946352i) q^{82} +(-2.97552 + 1.71792i) q^{83} +(7.93893 + 3.76848i) q^{84} +(-8.50705 - 3.33100i) q^{85} +0.0662650 q^{86} +(-10.5305 + 1.13009i) q^{87} +2.52658i q^{88} +(-2.59402 - 4.49298i) q^{89} +(0.685555 + 1.79835i) q^{90} +(-1.07931 - 1.98935i) q^{91} +(-1.67392 + 0.966438i) q^{92} +(-1.15420 + 0.123864i) q^{93} +(-1.25525 - 2.17415i) q^{94} +(7.93123 + 9.92931i) q^{95} +(-0.601731 - 5.60708i) q^{96} +(15.4265 - 8.90650i) q^{97} +(0.106384 - 2.00549i) q^{98} +(-4.53422 - 4.99168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.248464	−	0.143451i	−0.175691	−	0.101435i	0.409576	−	0.912276i	$-0.365677\pi$
$2$	−0.248464	−	0.143451i	−0.175691	−	0.101435i	−0.585266	+	0.810841i	$0.699010\pi$
$3$	0.701026	−	1.58384i	0.404737	−	0.914433i
$3$	0.701026	−	1.58384i	0.404737	−	0.914433i
$4$	−0.958844	−	1.66077i	−0.479422	−	0.830383i
$5$	2.21083	−	0.335020i	0.988712	−	0.149825i
$5$	2.21083	−	0.335020i	0.988712	−	0.149825i
$6$	−0.401384	+	0.292966i	−0.163864	+	0.119603i
$7$	−2.25543	−	1.38312i	−0.852474	−	0.522770i
$7$	−2.25543	−	1.38312i	−0.852474	−	0.522770i
$8$			1.12399i			0.397391i
$9$	−2.01713	−	2.22063i	−0.672375	−	0.740210i
$10$	−0.597370	−	0.233905i	−0.188905	−	0.0739672i
$11$	2.24786			0.677756			0.338878	−	0.940830i	$-0.389953\pi$
$11$	2.24786			0.677756			0.338878	+	0.940830i	$0.389953\pi$
$12$	−3.30257	+	0.354419i	−0.953370	+	0.102312i
$13$	0.740832	+	0.427720i	0.205470	+	0.118628i	0.599204	−	0.800596i	$-0.295484\pi$
$13$	0.740832	+	0.427720i	0.205470	+	0.118628i	−0.393734	+	0.919224i	$0.628817\pi$
$14$	0.361985	+	0.667199i	0.0967445	+	0.178317i
$15$	1.01923	−	3.73647i	0.263164	−	0.964751i
$16$	−1.75645	+	3.04226i	−0.439113	+	0.760565i
$17$	−3.53834	−	2.04286i	−0.858173	−	0.495466i	0.00522717	−	0.999986i	$-0.498336\pi$
$17$	−3.53834	−	2.04286i	−0.858173	−	0.495466i	−0.863400	+	0.504520i	$0.831669\pi$
$18$	0.182632	+	0.841106i	0.0430468	+	0.198250i
$19$	2.84162	+	4.92182i	0.651911	+	1.12914i	0.982659	+	0.185424i	$0.0593660\pi$
$19$	2.84162	+	4.92182i	0.651911	+	1.12914i	−0.330747	+	0.943719i	$0.607301\pi$
$20$	−2.67623	−	3.35044i	−0.598423	−	0.749180i
$21$	−3.77176	+	2.60265i	−0.823066	+	0.567945i
$22$	−0.558513	−	0.322458i	−0.119075	−	0.0687483i
$23$		−	1.00792i		−	0.210166i	−0.994463	−	0.105083i	$-0.966489\pi$
$23$		−	1.00792i		−	0.210166i	0.994463	−	0.105083i	$-0.0335108\pi$
$24$	1.78023	+	0.787947i	0.363387	+	0.160839i
$25$	4.77552	−	1.48134i	0.955105	−	0.296269i
$26$	−0.122713	−	0.212546i	−0.0240661	−	0.0416837i
$27$	−4.93119	+	1.63809i	−0.949008	+	0.315251i
$28$	−0.134430	+	5.07194i	−0.0254049	+	0.958507i
$29$	−3.05734	−	5.29547i	−0.567734	−	0.983343i	−0.996790	−	0.0800656i	$-0.974487\pi$
$29$	−3.05734	−	5.29547i	−0.567734	−	0.983343i	0.429056	−	0.903278i	$-0.358846\pi$
$30$	−0.789241	+	0.782168i	−0.144095	+	0.142804i
$31$	−0.335102	−	0.580413i	−0.0601860	−	0.104245i	0.834362	−	0.551216i	$-0.185836\pi$
$31$	−0.335102	−	0.580413i	−0.0601860	−	0.104245i	−0.894548	+	0.446971i	$0.852503\pi$
$32$	2.81964	−	1.62792i	0.498446	−	0.287778i
$33$	1.57581	−	3.56027i	0.274313	−	0.619763i
$34$	0.586100	+	1.01515i	0.100515	+	0.174098i
$35$	−5.44975	−	2.30223i	−0.921176	−	0.389147i
$36$	−1.75384	+	5.47921i	−0.292307	+	0.913202i
$37$	4.95382	−	2.86009i	0.814403	−	0.470196i	−0.0340797	−	0.999419i	$-0.510850\pi$
$37$	4.95382	−	2.86009i	0.814403	−	0.470196i	0.848483	+	0.529223i	$0.177517\pi$
$38$		−	1.63053i		−	0.264507i
$39$	1.19678	−	0.873520i	0.191639	−	0.139875i
$40$	0.376559	+	2.48495i	0.0595392	+	0.392905i
$41$	3.29852	−	5.71321i	0.515143	−	0.892254i	−0.484703	−	0.874679i	$-0.661072\pi$
$41$	3.29852	−	5.71321i	0.515143	−	0.892254i	0.999846	−	0.0175747i	$-0.00559447\pi$
$42$	1.31050	−	0.105603i	0.202215	−	0.0162949i
$43$	−0.200024	+	0.115484i	−0.0305033	+	0.0176111i	−0.515174	−	0.857086i	$-0.672273\pi$
$43$	−0.200024	+	0.115484i	−0.0305033	+	0.0176111i	0.484671	+	0.874697i	$0.338939\pi$
$44$	−2.15535	−	3.73318i	−0.324931	−	0.562797i
$45$	−5.20347	−	4.23366i	−0.775688	−	0.631116i
$46$	−0.144587	+	0.250432i	−0.0213182	+	0.0369242i
$47$	7.57804	+	4.37518i	1.10537	+	0.638186i	0.937626	−	0.347644i	$-0.113018\pi$
$47$	7.57804	+	4.37518i	1.10537	+	0.638186i	0.167744	+	0.985831i	$0.446352\pi$
$48$	3.58715	+	4.91465i	0.517761	+	0.709368i
$49$	3.17396	+	6.23907i	0.453423	+	0.891296i
$50$	−1.39905	−	0.316992i	−0.197855	−	0.0448295i
$51$	−5.71604	+	4.17208i	−0.800405	+	0.584208i
$52$		−	1.64047i		−	0.227492i
$53$	11.1069	+	6.41258i	1.52565	+	0.880836i	0.999537	+	0.0304235i	$0.00968561\pi$
$53$	11.1069	+	6.41258i	1.52565	+	0.880836i	0.526116	+	0.850413i	$0.323648\pi$
$54$	1.46021	+	0.300376i	0.198709	+	0.0408760i
$55$	4.96964	−	0.753079i	0.670106	−	0.101545i
$56$	1.55461	−	2.53509i	0.207744	−	0.338765i
$57$	9.78745	−	1.05035i	1.29638	−	0.139123i
$58$			1.75431i			0.230352i
$59$	−4.37646	−	7.58026i	−0.569767	−	0.986866i	−0.996589	−	0.0825298i	$-0.973700\pi$
$59$	−4.37646	−	7.58026i	−0.569767	−	0.986866i	0.426821	−	0.904336i	$-0.359633\pi$
$60$	−7.18268	+	1.88999i	−0.927279	+	0.243996i
$61$	0.995824	−	1.72482i	0.127502	−	0.220840i	−0.795206	−	0.606339i	$-0.792637\pi$
$61$	0.995824	−	1.72482i	0.127502	−	0.220840i	0.922708	+	0.385499i	$0.125971\pi$
$62$			0.192282i			0.0244199i
$63$	1.47809	+	7.79841i	0.186222	+	0.982508i
$64$	6.09169			0.761462
$65$	1.78115	+	0.697421i	0.220924	+	0.0865045i
$66$	−0.902255	+	0.658547i	−0.111060	+	0.0810615i
$67$	−12.4267	+	7.17453i	−1.51816	+	0.876508i	−0.518385	+	0.855147i	$0.673467\pi$
$67$	−12.4267	+	7.17453i	−1.51816	+	0.876508i	−0.999772	+	0.0213612i	$0.993200\pi$
$68$			7.83513i			0.950150i
$69$	−1.59639	−	0.706578i	−0.192183	−	0.0850620i
$70$	1.02381	+	1.35379i	0.122369	+	0.161809i
$71$	3.32909			0.395090			0.197545	−	0.980294i	$-0.436703\pi$
$71$	3.32909			0.395090			0.197545	+	0.980294i	$0.436703\pi$
$72$	2.49597	−	2.26723i	0.294153	−	0.267196i
$73$	10.1230	+	5.84452i	1.18481	+	0.684049i	0.957122	−	0.289685i	$-0.0935506\pi$
$73$	10.1230	+	5.84452i	1.18481	+	0.684049i	0.227686	+	0.973735i	$0.426884\pi$
$74$	−1.64113			−0.190777
$75$	1.00155	−	8.60215i	0.115649	−	0.993290i
$76$	5.44933	−	9.43852i	0.625081	−	1.08267i
$77$	−5.06991	−	3.10906i	−0.577770	−	0.354311i
$78$	−0.422665	+	0.0453588i	−0.0478574	+	0.00513588i
$79$	−5.84731	+	10.1278i	−0.657874	+	1.13947i	0.323291	+	0.946300i	$0.395211\pi$
$79$	−5.84731	+	10.1278i	−0.657874	+	1.13947i	−0.981165	+	0.193172i	$0.938123\pi$
$80$	−2.86399	+	7.31436i	−0.320204	+	0.817770i
$81$	−0.862407	+	8.95859i	−0.0958230	+	0.995398i
$82$	−1.63913	+	0.946352i	−0.181012	+	0.104507i
$83$	−2.97552	+	1.71792i	−0.326606	+	0.188566i	−0.654333	−	0.756206i	$-0.727051\pi$
$83$	−2.97552	+	1.71792i	−0.326606	+	0.188566i	0.327727	+	0.944772i	$0.393717\pi$
$84$	7.93893	+	3.76848i	0.866208	+	0.411175i
$85$	−8.50705	−	3.33100i	−0.922720	−	0.361298i
$86$	0.0662650			0.00714553
$87$	−10.5305	+	1.13009i	−1.12898	+	0.121158i
$88$			2.52658i			0.269334i
$89$	−2.59402	−	4.49298i	−0.274966	−	0.476255i	0.695161	−	0.718855i	$-0.255333\pi$
$89$	−2.59402	−	4.49298i	−0.274966	−	0.476255i	−0.970127	+	0.242599i	$0.922000\pi$
$90$	0.685555	+	1.79835i	0.0722638	+	0.189563i
$91$	−1.07931	−	1.98935i	−0.113142	−	0.208541i
$92$	−1.67392	+	0.966438i	−0.174518	+	0.100758i
$93$	−1.15420	+	0.123864i	−0.119685	+	0.0128441i
$94$	−1.25525	−	2.17415i	−0.129469	−	0.224247i
$95$	7.93123	+	9.92931i	0.813727	+	1.01873i
$96$	−0.601731	−	5.60708i	−0.0614139	−	0.572270i
$97$	15.4265	−	8.90650i	1.56632	−	0.904318i	0.569733	−	0.821830i	$-0.307047\pi$
$97$	15.4265	−	8.90650i	1.56632	−	0.904318i	0.996592	−	0.0824881i	$-0.0262866\pi$
$98$	0.106384	−	2.00549i	0.0107464	−	0.202585i
$99$	−4.53422	−	4.99168i	−0.455707	−	0.501682i
$100$	−7.03914	−	6.51065i	−0.703914	−	0.651065i
$101$	9.81787			0.976915			0.488457	−	0.872588i	$-0.337560\pi$
$101$	9.81787			0.976915			0.488457	+	0.872588i	$0.337560\pi$
$102$	2.01872	−	0.216641i	0.199883	−	0.0214507i
$103$		−	3.55278i		−	0.350066i	−0.984563	−	0.175033i	$-0.943997\pi$
$103$		−	3.55278i		−	0.350066i	0.984563	−	0.175033i	$-0.0560032\pi$
$104$	−0.480753	+	0.832689i	−0.0471417	+	0.0816518i
$105$	−7.46678	+	7.01763i	−0.728683	+	0.684851i
$106$	−1.83978	−	3.18659i	−0.178695	−	0.309509i
$107$	1.46307	−	0.844702i	0.141440	−	0.0816605i	−0.427610	−	0.903963i	$-0.640644\pi$
$107$	1.46307	−	0.844702i	0.141440	−	0.0816605i	0.569050	+	0.822303i	$0.307311\pi$
$108$	7.44873	+	6.61888i	0.716755	+	0.636902i
$109$	−6.88901	+	11.9321i	−0.659847	+	1.14289i	0.320808	+	0.947144i	$0.396046\pi$
$109$	−6.88901	+	11.9321i	−0.659847	+	1.14289i	−0.980655	+	0.195745i	$0.937288\pi$
$110$	−1.34281	−	0.525786i	−0.128032	−	0.0501317i
$111$	−1.05718	−	9.85107i	−0.100343	−	0.935023i
$112$	8.16937	−	4.43224i	0.771933	−	0.418807i
$113$	5.81081	+	3.35487i	0.546635	+	0.315600i	0.747764	−	0.663965i	$-0.231128\pi$
$113$	5.81081	+	3.35487i	0.546635	+	0.315600i	−0.201129	+	0.979565i	$0.564461\pi$
$114$	−2.58250	−	1.14304i	−0.241874	−	0.107056i
$115$	−0.337673	−	2.22834i	−0.0314882	−	0.207794i
$116$	−5.86302	+	10.1550i	−0.544368	+	0.942873i
$117$	−0.544544	−	2.50788i	−0.0503431	−	0.231854i
$118$			2.51123i			0.231177i
$119$	5.15496	+	9.50148i	0.472555	+	0.870999i
$120$	4.19975	+	1.14560i	0.383383	+	0.104579i
$121$	−5.94711			−0.540646
$122$	−0.494853	+	0.285704i	−0.0448019	+	0.0258664i
$123$	−6.73649	−	9.22946i	−0.607409	−	0.832192i
$124$	−0.642620	+	1.11305i	−0.0577090	+	0.0999549i
$125$	10.0616	−	4.87489i	0.899935	−	0.436023i
$126$	0.751435	−	2.14966i	0.0669432	−	0.191507i
$127$			14.8859i			1.32091i	0.750865	+	0.660456i	$0.229637\pi$
$127$			14.8859i			1.32091i	−0.750865	+	0.660456i	$0.770363\pi$
$128$	−7.15285	−	4.12970i	−0.632228	−	0.365017i
$129$	0.0426865	+	0.397764i	0.00375834	+	0.0350211i
$130$	−0.342506	−	0.428791i	−0.0300397	−	0.0376075i
$131$	5.18024			0.452600			0.226300	−	0.974058i	$-0.427337\pi$
$131$	5.18024			0.452600			0.226300	+	0.974058i	$0.427337\pi$
$132$	−7.42373	+	0.796687i	−0.646152	+	0.0693427i
$133$	0.398395	−	15.0311i	0.0345452	−	1.30337i
$134$	4.11677			0.355635
$135$	−10.3532	+	5.27359i	−0.891064	+	0.453878i
$136$	2.29616	−	3.97706i	0.196894	−	0.341030i
$137$		−	13.8141i		−	1.18022i	−0.807323	−	0.590110i	$-0.799084\pi$
$137$		−	13.8141i		−	1.18022i	0.807323	−	0.590110i	$-0.200916\pi$
$138$	0.295286	+	0.404563i	0.0251364	+	0.0344387i
$139$	−0.203667	+	0.352762i	−0.0172748	+	0.0299209i	−0.874534	−	0.484965i	$-0.838832\pi$
$139$	−0.203667	+	0.352762i	−0.0172748	+	0.0299209i	0.857259	+	0.514886i	$0.172166\pi$
$140$	1.40200	+	11.2582i	0.118491	+	0.951494i
$141$	12.2420	−	8.93532i	1.03096	−	0.752490i
$142$	−0.827158	−	0.477560i	−0.0694136	−	0.0400760i
$143$	1.66529	+	0.961456i	0.139259	+	0.0804010i
$144$	10.2987	−	2.23619i	0.858227	−	0.186350i
$145$	−8.53334	−	10.6831i	−0.708655	−	0.887183i
$146$	−1.67680	−	2.90431i	−0.138773	−	0.240362i
$147$	12.1067	−	0.653311i	0.998547	−	0.0538842i
$148$	−9.49988	−	5.48476i	−0.780885	−	0.450844i
$149$	−20.0379			−1.64157			−0.820784	−	0.571238i	$-0.806463\pi$
$149$	−20.0379			−1.64157			−0.820784	+	0.571238i	$0.806463\pi$
$150$	−1.48283	+	1.99365i	−0.121073	+	0.162781i
$151$	5.85679			0.476619			0.238309	−	0.971189i	$-0.423407\pi$
$151$	5.85679			0.476619			0.238309	+	0.971189i	$0.423407\pi$
$152$	−5.53209	+	3.19395i	−0.448711	+	0.259064i
$153$	2.60083	+	11.9780i	0.210265	+	0.968368i
$154$	0.813692	+	1.49977i	0.0655692	+	0.120855i
$155$	−0.935302	−	1.17093i	−0.0751253	−	0.0940512i
$156$	−2.59824	−	1.15001i	−0.208026	−	0.0920744i
$157$	−5.57363	+	3.21793i	−0.444824	+	0.256819i	−0.705642	−	0.708569i	$-0.749341\pi$
$157$	−5.57363	+	3.21793i	−0.444824	+	0.256819i	0.260818	+	0.965388i	$0.416008\pi$
$158$	2.90570	−	1.67760i	0.231165	−	0.133463i
$159$	17.9428	−	13.0962i	1.42295	−	1.03860i
$160$	5.68835	−	4.54369i	0.449704	−	0.359210i
$161$	−1.39407	+	2.27330i	−0.109868	+	0.179161i
$162$	1.49939	−	2.10217i	0.117803	−	0.165162i
$163$	−0.578987	+	0.334278i	−0.0453497	+	0.0261827i	−0.522503	−	0.852637i	$-0.675002\pi$
$163$	−0.578987	+	0.334278i	−0.0453497	+	0.0261827i	0.477154	+	0.878820i	$0.341668\pi$
$164$	−12.6511			−0.987883
$165$	2.29109	−	8.39907i	0.178361	−	0.653866i
$166$	0.985747			0.0765088
$167$	−16.3425	−	9.43533i	−1.26462	−	0.730128i	−0.290654	−	0.956828i	$-0.593873\pi$
$167$	−16.3425	−	9.43533i	−1.26462	−	0.730128i	−0.973964	+	0.226701i	$0.927206\pi$
$168$	−2.92536	−	4.23943i	−0.225696	−	0.327079i
$169$	−6.13411	−	10.6246i	−0.471855	−	0.817276i
$170$	1.63586	+	2.04798i	0.125465	+	0.157073i
$171$	5.19766	−	16.2381i	0.397475	−	1.24176i
$172$	0.383583	+	0.221462i	0.0292479	+	0.0168863i
$173$	−8.58780	−	4.95817i	−0.652918	−	0.376963i	0.136655	−	0.990619i	$-0.456365\pi$
$173$	−8.58780	−	4.95817i	−0.652918	−	0.376963i	−0.789573	+	0.613656i	$0.789698\pi$
$174$	2.77856	+	1.22982i	0.210642	+	0.0932322i
$175$	−12.8197	−	3.26405i	−0.969082	−	0.246739i
$176$	−3.94826	+	6.83859i	−0.297611	+	0.515478i
$177$	−15.0740	+	1.61768i	−1.13303	+	0.121592i
$178$			1.48846i			0.111565i
$179$	8.29475	−	14.3669i	0.619979	−	1.07384i	−0.369510	−	0.929227i	$-0.620474\pi$
$179$	8.29475	−	14.3669i	0.619979	−	1.07384i	0.989489	−	0.144608i	$-0.0461922\pi$
$180$	−2.04180	+	12.7012i	−0.152186	+	0.946689i
$181$	−18.2831			−1.35897			−0.679486	−	0.733689i	$-0.737797\pi$
$181$	−18.2831			−1.35897			−0.679486	+	0.733689i	$0.737797\pi$
$182$	−0.0172044	+	0.649111i	−0.00127528	+	0.0481153i
$183$	−2.03374	−	2.78637i	−0.150339	−	0.205975i
$184$	1.13289			0.0835180
$185$	9.99386	−	7.98279i	0.734763	−	0.586907i
$186$	0.304545	+	0.134795i	0.0223304	+	0.00988365i
$187$	−7.95370	−	4.59207i	−0.581632	−	0.335805i
$188$		−	16.7805i		−	1.22384i
$189$	13.3877	+	3.12582i	0.973809	+	0.227370i
$190$	−0.546259	−	3.60482i	−0.0396298	−	0.261521i
$191$	−5.07371	+	8.78792i	−0.367121	+	0.635871i	−0.989114	−	0.147151i	$-0.952990\pi$
$191$	−5.07371	+	8.78792i	−0.367121	+	0.635871i	0.621993	+	0.783022i	$0.286323\pi$
$192$	4.27043	−	9.64830i	0.308192	−	0.696306i
$193$	−5.82527	+	3.36322i	−0.419312	+	0.242090i	−0.694783	−	0.719219i	$-0.744500\pi$
$193$	−5.82527	+	3.36322i	−0.419312	+	0.242090i	0.275471	+	0.961309i	$0.411166\pi$
$194$	−5.11058			−0.366918
$195$	2.35324	−	2.33215i	0.168519	−	0.167009i
$196$	7.31830	−	11.2535i	0.522736	−	0.803821i
$197$			21.3178i			1.51883i	0.650605	+	0.759416i	$0.274515\pi$
$197$			21.3178i			1.51883i	−0.650605	+	0.759416i	$0.725485\pi$
$198$	0.410532	+	1.89069i	0.0291752	+	0.134366i
$199$	−7.94628	+	13.7634i	−0.563297	+	0.975659i	0.433909	+	0.900957i	$0.357134\pi$
$199$	−7.94628	+	13.7634i	−0.563297	+	0.975659i	−0.997206	+	0.0747023i	$0.976199\pi$
$200$	1.66502	+	5.36765i	0.117734	+	0.379550i
$201$	2.65194	+	24.7114i	0.187053	+	1.74301i
$202$	−2.43939	−	1.40838i	−0.171635	−	0.0990934i
$203$	−0.428639	+	16.1722i	−0.0300846	+	1.13507i
$204$	12.4096	+	5.49263i	0.868848	+	0.384561i
$205$	5.37843	−	13.7360i	0.375646	−	0.959364i
$206$	−0.509649	+	0.882738i	−0.0355089	+	0.0615033i
$207$	−2.23822	+	2.03310i	−0.155567	+	0.141310i
$208$	−2.60247	+	1.50254i	−0.180449	+	0.104182i
$209$	6.38757	+	11.0636i	0.441837	+	0.765284i
$210$	2.86191	−	0.672514i	0.197491	−	0.0464079i
$211$	−9.41937	+	16.3148i	−0.648456	+	1.12316i	0.335036	+	0.942205i	$0.391252\pi$
$211$	−9.41937	+	16.3148i	−0.648456	+	1.12316i	−0.983492	+	0.180953i	$0.942082\pi$
$212$		−	24.5947i		−	1.68917i
$213$	2.33378	−	5.27275i	0.159908	−	0.361283i
$214$	−0.484693			−0.0331329
$215$	−0.403529	+	0.322327i	−0.0275204	+	0.0219825i
$216$	−1.84120	−	5.54261i	−0.125278	−	0.377127i
$217$	−0.0469813	+	1.77257i	−0.00318930	+	0.120330i
$218$	3.42334	−	1.97647i	0.231858	−	0.133863i
$219$	16.3533	−	11.9361i	1.10505	−	0.806567i
$220$	−6.01580	−	7.53133i	−0.405585	−	0.507762i
$221$	−1.74754	−	3.02683i	−0.117552	−	0.203607i
$222$	−1.15047	+	2.59929i	−0.0772147	+	0.174453i
$223$	7.54894	−	4.35838i	0.505514	−	0.291859i	−0.225474	−	0.974249i	$-0.572393\pi$
$223$	7.54894	−	4.35838i	0.505514	−	0.291859i	0.730988	+	0.682390i	$0.239060\pi$
$224$	−8.61112	−	0.228234i	−0.575354	−	0.0152496i
$225$	−12.9223	−	7.61662i	−0.861490	−	0.507775i
$226$	−0.962518	−	1.66713i	−0.0640258	−	0.110896i
$227$			11.8384i			0.785744i	0.919593	+	0.392872i	$0.128518\pi$
$227$			11.8384i			0.785744i	−0.919593	+	0.392872i	$0.871482\pi$
$228$	−11.1290	−	15.2475i	−0.737038	−	1.00979i
$229$	11.7956			0.779474			0.389737	−	0.920926i	$-0.372566\pi$
$229$	11.7956			0.779474			0.389737	+	0.920926i	$0.372566\pi$
$230$	−0.235757	+	0.602102i	−0.0155454	+	0.0397014i
$231$	−8.47841	+	5.85041i	−0.557838	+	0.384929i
$232$	5.95206	−	3.43642i	0.390772	−	0.225612i
$233$	−0.870225	+	0.502425i	−0.0570104	+	0.0329150i	−0.528234	−	0.849099i	$-0.677146\pi$
$233$	−0.870225	+	0.502425i	−0.0570104	+	0.0329150i	0.471224	+	0.882014i	$0.343812\pi$
$234$	−0.224458	+	0.701233i	−0.0146733	+	0.0458411i
$235$	18.2195	+	7.13399i	1.18851	+	0.465370i
$236$	−8.39269	+	14.5366i	−0.546318	+	0.946250i
$237$	11.9418	+	16.3611i	0.775704	+	1.06277i
$238$	0.0821713	−	3.10026i	0.00532637	−	0.200960i
$239$	−5.67377	+	9.82725i	−0.367006	+	0.635672i	−0.989096	−	0.147273i	$-0.952950\pi$
$239$	−5.67377	+	9.82725i	−0.367006	+	0.635672i	0.622090	+	0.782945i	$0.286284\pi$
$240$	9.57708	+	9.66367i	0.618198	+	0.623787i
$241$	26.3118			1.69489			0.847445	−	0.530883i	$-0.178140\pi$
$241$	26.3118			1.69489			0.847445	+	0.530883i	$0.178140\pi$
$242$	1.47764	+	0.853118i	0.0949865	+	0.0548405i
$243$	13.5844	+	7.64612i	0.871442	+	0.490499i
$244$	−3.81936			−0.244509
$245$	9.10729	+	12.7302i	0.581844	+	0.813301i
$246$	0.349802	+	3.25954i	0.0223026	+	0.207821i
$247$			4.86166i			0.309340i
$248$	0.652379	−	0.376651i	0.0414261	−	0.0239174i
$249$	0.634998	+	5.91707i	0.0402413	+	0.374979i
$250$	−3.19925	−	0.232107i	−0.202338	−	0.0146798i
$251$	−4.32289			−0.272859			−0.136429	−	0.990650i	$-0.543563\pi$
$251$	−4.32289			−0.272859			−0.136429	+	0.990650i	$0.543563\pi$
$252$	11.5341	−	9.93223i	0.726579	−	0.625672i
$253$		−	2.26567i		−	0.142441i
$254$	2.13540	−	3.69862i	0.133987	−	0.232072i
$255$	−11.2394	+	11.1387i	−0.703842	+	0.697535i
$256$	−4.90688	−	8.49896i	−0.306680	−	0.531185i
$257$			16.4564i			1.02652i	0.858233	+	0.513261i	$0.171563\pi$
$257$			16.4564i			1.02652i	−0.858233	+	0.513261i	$0.828437\pi$
$258$	0.0464534	−	0.104953i	0.00289206	−	0.00653411i
$259$	−15.1289	−	0.400985i	−0.940061	−	0.0249160i
$260$	−0.549588	−	3.62679i	−0.0340840	−	0.224924i
$261$	−5.59224	+	17.4708i	−0.346151	+	1.08142i
$262$	−1.28710	−	0.743110i	−0.0795176	−	0.0459095i
$263$			5.91312i			0.364618i	0.983241	+	0.182309i	$0.0583572\pi$
$263$			5.91312i			0.364618i	−0.983241	+	0.182309i	$0.941643\pi$
$264$	4.00171	+	1.77120i	0.246288	+	0.109010i
$265$	26.7038	+	10.4561i	1.64040	+	0.642312i
$266$	−2.25522	+	3.67755i	−0.138276	+	0.225485i
$267$	−8.93466	+	0.958835i	−0.546792	+	0.0586797i
$268$	23.8304	+	13.7585i	1.45568	+	0.840435i
$269$	5.81929	−	10.0793i	0.354808	−	0.614546i	−0.632277	−	0.774742i	$-0.717880\pi$
$269$	5.81929	−	10.0793i	0.354808	−	0.614546i	0.987085	+	0.160197i	$0.0512129\pi$
$270$	3.32891	+	0.174881i	0.202591	+	0.0106429i
$271$	−6.62163	−	11.4690i	−0.402236	−	0.696692i	0.591760	−	0.806114i	$-0.298433\pi$
$271$	−6.62163	−	11.4690i	−0.402236	−	0.696692i	−0.993995	+	0.109422i	$0.965100\pi$
$272$	12.4298	−	7.17636i	0.753669	−	0.435131i
$273$	−3.90745	+	0.314872i	−0.236490	+	0.0190569i
$274$	−1.98165	+	3.43231i	−0.119716	+	0.207354i
$275$	10.7347	−	3.32986i	0.647328	−	0.200798i
$276$	0.357227	+	3.32873i	0.0215025	+	0.200366i
$277$			24.6189i			1.47920i	0.673045	+	0.739602i	$0.264986\pi$
$277$			24.6189i			1.47920i	−0.673045	+	0.739602i	$0.735014\pi$
$278$	0.101208	−	0.0584325i	0.00607006	−	0.00350455i
$279$	−0.612941	+	1.91490i	−0.0366958	+	0.114642i
$280$	2.58768	−	6.12547i	0.154643	−	0.366067i
$281$	1.56861	+	2.71691i	0.0935752	+	0.162077i	0.909013	−	0.416768i	$-0.136837\pi$
$281$	1.56861	+	2.71691i	0.0935752	+	0.162077i	−0.815438	+	0.578845i	$0.803504\pi$
$282$	−4.32348	+	0.463980i	−0.257459	+	0.0276296i
$283$	−9.73561	+	5.62086i	−0.578722	+	0.334125i	−0.760625	−	0.649191i	$-0.775108\pi$
$283$	−9.73561	+	5.62086i	−0.578722	+	0.334125i	0.181903	+	0.983316i	$0.441774\pi$
$284$	−3.19207	−	5.52883i	−0.189415	−	0.328076i
$285$	21.2865	−	5.60114i	1.26090	−	0.331783i
$286$	−0.275843	−	0.477774i	−0.0163109	−	0.0282514i
$287$	−15.3417	+	8.32351i	−0.905589	+	0.491321i
$288$	−9.30258	−	2.97766i	−0.548159	−	0.175460i
$289$	−0.153447	−	0.265777i	−0.00902627	−	0.0156340i
$290$	0.587729	+	3.87848i	0.0345126	+	0.227752i
$291$	−3.29213	−	30.6769i	−0.192988	−	1.79831i
$292$		−	22.4159i		−	1.31179i
$293$	−21.7078	−	12.5330i	−1.26819	−	0.732187i	−0.293541	−	0.955947i	$-0.594834\pi$
$293$	−21.7078	−	12.5330i	−1.26819	−	0.732187i	−0.974644	+	0.223760i	$0.928167\pi$
$294$	−3.10181	−	1.57440i	−0.180901	−	0.0918207i
$295$	−12.2151	−	15.2924i	−0.711193	−	0.890361i
$296$	3.21471	+	5.56805i	0.186851	+	0.323636i
$297$	−11.0846	+	3.68221i	−0.643196	+	0.213664i
$298$	4.97870	+	2.87445i	0.288408	+	0.166513i
$299$	0.431107	−	0.746700i	0.0249316	−	0.0431828i
$300$	−15.2465	+	6.58477i	−0.880256	+	0.380172i
$301$	0.610868	+	0.0161908i	0.0352098	+	0.000933224i
$302$	−1.45520	−	0.840161i	−0.0837375	−	0.0483459i
$303$	6.88258	−	15.5500i	0.395394	−	0.893323i
$304$	−19.9646			−1.14505
$305$	1.62375	−	4.14690i	0.0929755	−	0.237451i
$306$	1.07205	−	3.34921i	0.0612849	−	0.191461i
$307$		−	5.97619i		−	0.341079i	−0.985351	−	0.170540i	$-0.945449\pi$
$307$		−	5.97619i		−	0.341079i	0.985351	−	0.170540i	$-0.0545511\pi$
$308$	−0.302180	+	11.4010i	−0.0172183	+	0.649634i
$309$	−5.62705	−	2.49059i	−0.320112	−	0.141685i
$310$	0.0644184	+	0.425103i	0.00365872	+	0.0241443i
$311$	10.5910	+	18.3441i	0.600560	+	1.04020i	0.992736	+	0.120311i	$0.0383891\pi$
$311$	10.5910	+	18.3441i	0.600560	+	1.04020i	−0.392176	+	0.919890i	$0.628278\pi$
$312$	0.981829	+	1.34517i	0.0555851	+	0.0761555i
$313$	−28.8388	−	16.6501i	−1.63006	−	0.941117i	−0.984072	−	0.177772i	$-0.943111\pi$
$313$	−28.8388	−	16.6501i	−1.63006	−	0.941117i	−0.645991	−	0.763345i	$-0.723556\pi$
$314$	1.84646			0.104202
$315$	5.88043	+	16.7458i	0.331325	+	0.943517i
$316$	22.4266			1.26160
$317$	28.0029	+	16.1675i	1.57280	+	0.908057i	0.995824	+	0.0912978i	$0.0291015\pi$
$317$	28.0029	+	16.1675i	1.57280	+	0.908057i	0.576978	+	0.816760i	$0.304232\pi$
$318$	−6.33680	+	0.680042i	−0.355350	+	0.0381349i
$319$	−6.87248	−	11.9035i	−0.384785	−	0.666467i
$320$	13.4677	−	2.04084i	0.752867	−	0.114086i
$321$	−0.312229	−	2.90943i	−0.0174269	−	0.162389i
$322$	0.672484	−	0.364852i	0.0374761	−	0.0203324i
$323$		−	23.2201i		−	1.29200i
$324$	15.7050	−	7.15763i	0.872502	−	0.397646i
$325$	4.17146	+	0.945159i	0.231391	+	0.0524280i
$326$	0.191810			0.0106234
$327$	14.0692	+	19.2758i	0.778031	+	1.06596i
$328$	6.42160	+	3.70751i	0.354573	+	0.204713i
$329$	−11.0404	−	20.3493i	−0.608675	−	1.12189i
$330$	−1.77411	+	1.75821i	−0.0976613	+	0.0967862i
$331$	−11.0403	+	19.1223i	−0.606828	+	1.05106i	0.384932	+	0.922945i	$0.374225\pi$
$331$	−11.0403	+	19.1223i	−0.606828	+	1.05106i	−0.991760	+	0.128111i	$0.959109\pi$
$332$	5.70612	+	3.29443i	0.313164	+	0.180805i
$333$	−16.3437	−	5.23145i	−0.895628	−	0.286682i
$334$	2.70701	+	4.68868i	0.148121	+	0.256553i
$335$	−25.0696	+	20.0248i	−1.36970	+	1.09407i
$336$	−1.29304	−	16.0461i	−0.0705409	−	0.875387i
$337$	10.9359	+	6.31384i	0.595716	+	0.343937i	0.767354	−	0.641223i	$-0.221573\pi$
$337$	10.9359	+	6.31384i	0.595716	+	0.343937i	−0.171639	+	0.985160i	$0.554906\pi$
$338$			3.51977i			0.191450i
$339$	9.38712	−	6.85157i	0.509839	−	0.372126i
$340$	2.62493	+	17.3221i	0.142357	+	0.939425i
$341$	−0.753263	−	1.30469i	−0.0407915	−	0.0706529i
$342$	−3.62080	+	3.28898i	−0.195791	+	0.177848i
$343$	1.47072	−	18.4618i	0.0794116	−	0.996842i
$344$	−0.129803	−	0.224825i	−0.00699849	−	0.0121217i
$345$	−3.76606	−	1.02730i	−0.202758	−	0.0553080i
$346$	1.42251	+	2.46385i	0.0764744	+	0.132458i
$347$	20.1579	−	11.6382i	1.08213	−	0.624770i	0.150663	−	0.988585i	$-0.451859\pi$
$347$	20.1579	−	11.6382i	1.08213	−	0.624770i	0.931471	+	0.363815i	$0.118526\pi$
$348$	11.9739	+	16.4051i	0.641868	+	0.879404i
$349$	12.5958	+	21.8166i	0.674238	+	1.16782i	0.976691	+	0.214651i	$0.0688613\pi$
$349$	12.5958	+	21.8166i	0.674238	+	1.16782i	−0.302452	+	0.953164i	$0.597805\pi$
$350$	2.71702	+	2.65000i	0.145231	+	0.141649i
$351$	−4.35383	−	0.895615i	−0.232390	−	0.0478044i
$352$	6.33816	−	3.65934i	0.337825	−	0.195044i
$353$		−	20.8313i		−	1.10874i	−0.832272	−	0.554368i	$-0.812960\pi$
$353$		−	20.8313i		−	1.10874i	0.832272	−	0.554368i	$-0.187040\pi$
$354$	3.97740	+	1.76044i	0.211396	+	0.0935662i
$355$	7.36004	−	1.11531i	0.390630	−	0.0591945i
$356$	−4.97453	+	8.61614i	−0.263649	+	0.456654i
$357$	18.6626	−	1.50388i	0.987731	−	0.0795938i
$358$	−4.12190	+	2.37978i	−0.217849	+	0.125775i
$359$	3.33882	+	5.78301i	0.176216	+	0.305216i	0.940582	−	0.339568i	$-0.110281\pi$
$359$	3.33882	+	5.78301i	0.176216	+	0.305216i	−0.764365	+	0.644784i	$0.776948\pi$
$360$	4.75859	−	5.84866i	0.250800	−	0.308251i
$361$	−6.64957	+	11.5174i	−0.349977	+	0.606178i
$362$	4.54269	+	2.62272i	0.238759	+	0.137847i
$363$	−4.16908	+	9.41929i	−0.218820	+	0.494385i
$364$	−2.26896	+	3.69996i	−0.118926	+	0.193931i
$365$	24.3383	+	9.52982i	1.27392	+	0.498814i
$366$	0.105605	+	0.984056i	0.00552007	+	0.0514374i
$367$		−	0.433617i		−	0.0226346i	−0.999936	−	0.0113173i	$-0.996398\pi$
$367$		−	0.433617i		−	0.0226346i	0.999936	−	0.0113173i	$-0.00360249\pi$
$368$	3.06636	+	1.77036i	0.159845	+	0.0922865i
$369$	−19.3405	+	4.19946i	−1.00682	+	0.218615i
$370$	−3.62825	+	0.549811i	−0.188624	+	0.0285833i
$371$	−16.1816	−	29.8254i	−0.840104	−	1.54846i
$372$	1.31241	+	1.79809i	0.0680451	+	0.0932265i
$373$			22.1191i			1.14528i	0.819806	+	0.572641i	$0.194081\pi$
$373$			22.1191i			1.14528i	−0.819806	+	0.572641i	$0.805919\pi$
$374$	1.31747	+	2.28193i	0.0681249	+	0.117996i
$375$	−0.667637	−	19.3534i	−0.0344766	−	0.999406i
$376$	−4.91767	+	8.51765i	−0.253609	+	0.439264i
$377$		−	5.23074i		−	0.269397i
$378$	−2.87795	−	2.69712i	−0.148026	−	0.138725i
$379$	3.58105			0.183946			0.0919732	−	0.995761i	$-0.470683\pi$
$379$	3.58105			0.183946			0.0919732	+	0.995761i	$0.470683\pi$
$380$	8.88545	−	22.6926i	0.455814	−	1.16410i
$381$	23.5770	+	10.4354i	1.20789	+	0.534622i
$382$	2.52127	−	1.45565i	0.128999	−	0.0744778i
$383$			8.08436i			0.413091i	0.978437	+	0.206546i	$0.0662222\pi$
$383$			8.08436i			0.413091i	−0.978437	+	0.206546i	$0.933778\pi$
$384$	−11.5551	+	8.43397i	−0.589670	+	0.430394i
$385$	−12.2503	−	5.17509i	−0.624333	−	0.263747i
$386$	1.92983			0.0982256
$387$	0.659920	+	0.211234i	0.0335456	+	0.0107376i
$388$	−29.5832	−	17.0799i	−1.50186	−	0.867100i
$389$	−12.1299			−0.615009			−0.307505	−	0.951547i	$-0.599494\pi$
$389$	−12.1299			−0.615009			−0.307505	+	0.951547i	$0.599494\pi$
$390$	−0.919244	+	0.241882i	−0.0465477	+	0.0122482i
$391$	−2.05904	+	3.56636i	−0.104130	+	0.180359i
$392$	−7.01266	+	3.56750i	−0.354193	+	0.180186i
$393$	3.63148	−	8.20470i	0.183184	−	0.413872i
$394$	3.05806	−	5.29672i	0.154063	−	0.266845i
$395$	−9.53438	+	24.3499i	−0.479727	+	1.22518i
$396$	−3.94240	+	12.3165i	−0.198113	+	0.618929i
$397$	12.9868	−	7.49793i	0.651788	−	0.376310i	−0.137353	−	0.990522i	$-0.543859\pi$
$397$	12.9868	−	7.49793i	0.651788	−	0.376310i	0.789141	+	0.614212i	$0.210526\pi$
$398$	3.94873	−	2.27980i	0.197932	−	0.114276i
$399$	−23.5277	−	11.1682i	−1.17786	−	0.559110i
$400$	−3.88134	+	17.1303i	−0.194067	+	0.856515i
$401$	19.5501			0.976286			0.488143	−	0.872764i	$-0.337675\pi$
$401$	19.5501			0.976286			0.488143	+	0.872764i	$0.337675\pi$
$402$	2.88596	−	6.52032i	0.143939	−	0.325204i
$403$		−	0.573318i		−	0.0285590i
$404$	−9.41380	−	16.3052i	−0.468354	−	0.811213i
$405$	1.09467	+	20.0948i	0.0543946	+	0.998520i
$406$	2.42642	−	3.95673i	0.120421	−	0.196369i
$407$	11.1355	−	6.42909i	0.551967	−	0.318678i
$408$	−4.68938	−	6.42477i	−0.232159	−	0.318074i
$409$	6.92782	+	11.9993i	0.342559	+	0.593329i	0.984907	−	0.173084i	$-0.0553731\pi$
$409$	6.92782	+	11.9993i	0.342559	+	0.593329i	−0.642348	+	0.766413i	$0.722040\pi$
$410$	−3.30679	+	2.64136i	−0.163311	+	0.130448i
$411$	−21.8794	−	9.68406i	−1.07923	−	0.477679i
$412$	−5.90033	+	3.40656i	−0.290689	+	0.167829i
$413$	−0.613581	+	23.1499i	−0.0301923	+	1.13913i
$414$	0.847767	−	0.184078i	0.0416655	−	0.00904696i
$415$	−6.00283	+	4.79488i	−0.294667	+	0.235371i
$416$	2.78517			0.136554
$417$	0.415944	+	0.569873i	0.0203689	+	0.0279068i
$418$		−	3.66521i		−	0.179271i
$419$	8.37876	−	14.5124i	0.409329	−	0.708979i	−0.585485	−	0.810683i	$-0.699096\pi$
$419$	8.37876	−	14.5124i	0.409329	−	0.708979i	0.994815	+	0.101704i	$0.0324294\pi$
$420$	18.8141	+	5.67176i	0.918035	+	0.276754i
$421$	−1.12245	−	1.94414i	−0.0547048	−	0.0947514i	0.837376	−	0.546627i	$-0.184088\pi$
$421$	−1.12245	−	1.94414i	−0.0547048	−	0.0947514i	−0.892081	+	0.451876i	$0.850755\pi$
$422$	4.68075	−	2.70243i	0.227855	−	0.131552i
$423$	−5.57019	−	25.6533i	−0.270832	−	1.24731i
$424$	−7.20769	+	12.4841i	−0.350036	+	0.606281i
$425$	−19.9236	−	4.51424i	−0.966436	−	0.218973i
$426$	−1.33624	+	0.975308i	−0.0647411	+	0.0472538i
$427$	−4.63164	+	2.51287i	−0.224141	+	0.121606i
$428$	−2.80571	−	1.61988i	−0.135619	−	0.0782996i
$429$	2.69021	−	1.96355i	0.129884	−	0.0948013i
$430$	0.146500	−	0.0222001i	0.00706488	−	0.00107058i
$431$	−4.24971	+	7.36071i	−0.204701	+	0.354553i	−0.950038	−	0.312136i	$-0.898956\pi$
$431$	−4.24971	+	7.36071i	−0.204701	+	0.354553i	0.745336	+	0.666689i	$0.232289\pi$
$432$	3.67788	−	17.8792i	0.176952	−	0.860213i
$433$		−	8.16372i		−	0.392324i	−0.980572	−	0.196162i	$-0.937152\pi$
$433$		−	8.16372i		−	0.392324i	0.980572	−	0.196162i	$-0.0628478\pi$
$434$	0.265950	−	0.433680i	0.0127660	−	0.0208173i
$435$	−22.9025	+	6.02635i	−1.09809	+	0.288941i
$436$	26.4219			1.26538
$437$	4.96081	−	2.86412i	0.237308	−	0.137010i
$438$	−5.77545	+	0.619800i	−0.275962	+	0.0296152i
$439$	−5.17928	+	8.97077i	−0.247194	+	0.428152i	−0.962746	−	0.270407i	$-0.912842\pi$
$439$	−5.17928	+	8.97077i	−0.247194	+	0.428152i	0.715553	+	0.698559i	$0.246175\pi$
$440$	0.846454	+	5.58583i	0.0403531	+	0.266294i
$441$	7.45240	−	19.6332i	0.354876	−	0.934913i
$442$			1.00275i			0.0476958i
$443$	−15.6249	−	9.02104i	−0.742361	−	0.428602i	0.0805661	−	0.996749i	$-0.474327\pi$
$443$	−15.6249	−	9.02104i	−0.742361	−	0.428602i	−0.822927	+	0.568147i	$0.807661\pi$
$444$	−15.3467	+	11.2014i	−0.728320	+	0.531594i
$445$	−7.24018	−	9.06416i	−0.343217	−	0.429682i
$446$	−2.50085			−0.118419
$447$	−14.0471	+	31.7369i	−0.664404	+	1.50110i
$448$	−13.7394	−	8.42554i	−0.649126	−	0.398069i
$449$	−14.6178			−0.689855			−0.344928	−	0.938629i	$-0.612097\pi$
$449$	−14.6178			−0.689855			−0.344928	+	0.938629i	$0.612097\pi$
$450$	2.11813	+	3.74618i	0.0998495	+	0.176597i
$451$	7.41463	−	12.8425i	0.349141	−	0.604731i
$452$		−	12.8672i		−	0.605222i
$453$	4.10576	−	9.27624i	0.192905	−	0.435836i
$454$	1.69823	−	2.94142i	0.0797020	−	0.138048i
$455$	−3.05264	−	4.03653i	−0.143110	−	0.189235i
$456$	1.18059	+	11.0010i	0.0552860	+	0.515169i
$457$	−20.2914	−	11.7153i	−0.949192	−	0.548017i	−0.0563625	−	0.998410i	$-0.517950\pi$
$457$	−20.2914	−	11.7153i	−0.949192	−	0.548017i	−0.892830	+	0.450394i	$0.851284\pi$
$458$	−2.93078	−	1.69209i	−0.136946	−	0.0790660i
$459$	20.7946	+	4.27761i	0.970609	+	0.199662i
$460$	−3.37697	+	2.69743i	−0.157452	+	0.125768i
$461$	−10.5017	−	18.1895i	−0.489114	−	0.847170i	0.510808	−	0.859695i	$-0.329346\pi$
$461$	−10.5017	−	18.1895i	−0.489114	−	0.847170i	−0.999922	+	0.0125252i	$0.996013\pi$
$462$	2.94583	−	0.237382i	0.137052	−	0.0110440i
$463$	−2.63625	−	1.52204i	−0.122517	−	0.0707352i	0.437489	−	0.899224i	$-0.355868\pi$
$463$	−2.63625	−	1.52204i	−0.122517	−	0.0707352i	−0.560006	+	0.828489i	$0.689201\pi$
$464$	21.4803			0.997196
$465$	−2.51024	+	0.660522i	−0.116410	+	0.0306310i
$466$	0.288293			0.0133549
$467$	−24.8341	+	14.3380i	−1.14919	+	0.663483i	−0.948689	−	0.316212i	$-0.897589\pi$
$467$	−24.8341	+	14.3380i	−1.14919	+	0.663483i	−0.200497	+	0.979694i	$0.564256\pi$
$468$	−3.64287	+	3.30903i	−0.168392	+	0.152960i
$469$	37.9507	+	1.00587i	1.75240	+	0.0464468i
$470$	−3.50352	−	4.38614i	−0.161605	−	0.202318i
$471$	1.18945	+	11.0836i	0.0548070	+	0.510706i
$472$	8.52014	−	4.91911i	0.392171	−	0.226420i
$473$	−0.449626	+	0.259592i	−0.0206738	+	0.0119360i
$474$	−0.620096	−	5.77821i	−0.0284820	−	0.265402i
$475$	20.8611	+	19.2949i	0.957173	+	0.885310i
$476$	10.8369	−	17.6716i	0.496710	−	0.809977i
$477$	−8.16407	−	37.5994i	−0.373807	−	1.72156i
$478$	2.81946	−	1.62781i	0.128959	−	0.0744544i
$479$	15.5755			0.711663			0.355832	−	0.934550i	$-0.384198\pi$
$479$	15.5755			0.711663			0.355832	+	0.934550i	$0.384198\pi$
$480$	−3.20881	−	12.1947i	−0.146461	−	0.556610i
$481$	4.89327			0.223114
$482$	−6.53753	−	3.77445i	−0.297776	−	0.171921i
$483$	2.62327	+	3.80164i	0.119363	+	0.172980i
$484$	5.70235	+	9.87676i	0.259198	+	0.448943i
$485$	31.1215	−	24.8589i	1.41316	−	1.12879i
$486$	−2.27840	−	3.84848i	−0.103350	−	0.174571i
$487$	−23.9807	−	13.8453i	−1.08667	−	0.627389i	−0.153981	−	0.988074i	$-0.549210\pi$
$487$	−23.9807	−	13.8453i	−1.08667	−	0.627389i	−0.932688	+	0.360685i	$0.882543\pi$
$488$	1.93868	+	1.11930i	0.0877599	+	0.0506682i
$489$	0.123560	+	1.15136i	0.00558757	+	0.0520664i
$490$	−0.436682	−	4.46944i	−0.0197273	−	0.201909i
$491$	9.85333	−	17.0665i	0.444674	−	0.770199i	−0.553355	−	0.832945i	$-0.686653\pi$
$491$	9.85333	−	17.0665i	0.444674	−	0.770199i	0.998029	+	0.0627468i	$0.0199861\pi$
$492$	−8.86873	+	20.0373i	−0.399833	+	0.903353i
$493$			24.9829i			1.12517i
$494$	0.697409	−	1.20795i	0.0313779	−	0.0543482i
$495$	−11.6967	−	9.51669i	−0.525728	−	0.427743i
$496$	2.35436			0.105714
$497$	−7.50853	−	4.60452i	−0.336804	−	0.206541i
$498$	0.691034	−	1.56127i	0.0309660	−	0.0699622i
$499$	21.9071			0.980695			0.490348	−	0.871527i	$-0.336870\pi$
$499$	21.9071			0.980695			0.490348	+	0.871527i	$0.336870\pi$
$500$	−17.7435	−	12.0357i	−0.793515	−	0.538252i
$501$	−26.4006	+	19.2695i	−1.17949	+	0.860898i
$502$	1.07408	+	0.620123i	0.0479387	+	0.0276774i
$503$		−	38.2146i		−	1.70391i	−0.523618	−	0.851953i	$-0.675418\pi$
$503$		−	38.2146i		−	1.70391i	0.523618	−	0.851953i	$-0.324582\pi$
$504$	−8.76534	+	1.66136i	−0.390439	+	0.0740030i
$505$	21.7056	−	3.28918i	0.965888	−	0.146367i
$506$	−0.325012	+	0.562937i	−0.0144485	+	0.0250256i
$507$	−21.1279	+	2.26736i	−0.938322	+	0.100697i
$508$	24.7220	−	14.2733i	1.09686	−	0.633274i
$509$	−18.6411			−0.826254			−0.413127	−	0.910673i	$-0.635563\pi$
$509$	−18.6411			−0.826254			−0.413127	+	0.910673i	$0.635563\pi$
$510$	4.39046	−	1.15527i	0.194413	−	0.0511561i
$511$	−14.7481	−	27.1833i	−0.652417	−	1.20252i
$512$			19.3344i			0.854467i
$513$	−22.0750	−	19.6156i	−0.974633	−	0.866051i
$514$	2.36068	−	4.08882i	0.104125	−	0.180350i
$515$	−1.19025	−	7.85458i	−0.0524487	−	0.346114i
$516$	0.619662	−	0.452285i	0.0272791	−	0.0199108i
$517$	17.0344	+	9.83482i	0.749172	+	0.432535i
$518$	3.70146	+	2.26988i	0.162633	+	0.0997327i
$519$	−13.8732	+	10.1259i	−0.608967	+	0.444479i
$520$	−0.783895	+	2.00199i	−0.0343761	+	0.0877932i
$521$	16.2951	−	28.2240i	0.713903	−	1.23652i	−0.249478	−	0.968380i	$-0.580259\pi$
$521$	16.2951	−	28.2240i	0.713903	−	1.23652i	0.963381	−	0.268136i	$-0.0864075\pi$
$522$	3.89568	−	3.53867i	0.170509	−	0.154883i
$523$	−2.01721	+	1.16464i	−0.0882066	+	0.0509261i	−0.543455	−	0.839439i	$-0.682884\pi$
$523$	−2.01721	+	1.16464i	−0.0882066	+	0.0509261i	0.455248	+	0.890365i	$0.349551\pi$
$524$	−4.96704	−	8.60317i	−0.216986	−	0.375831i
$525$	−14.1567	+	18.0163i	−0.617850	+	0.786296i
$526$	0.848241	−	1.46920i	0.0369851	−	0.0640600i
$527$			2.73826i			0.119281i
$528$	8.06343	+	11.0475i	0.350916	+	0.480779i
$529$	21.9841			0.955830
$530$	−5.13501	−	6.42865i	−0.223051	−	0.279243i
$531$	−8.00508	+	25.0089i	−0.347391	+	1.08529i
$532$	−25.3452	+	13.7509i	−1.09885	+	0.596176i
$533$	4.88731	−	2.82169i	0.211693	−	0.122221i
$534$	2.35749	+	1.04345i	0.102019	+	0.0451544i
$535$	2.95160	−	2.35765i	0.127609	−	0.101930i
$536$	−8.06411	−	13.9674i	−0.348316	−	0.603302i
$537$	−16.9402	−	23.2092i	−0.731021	−	1.00155i
$538$	−2.89177	+	1.66956i	−0.124673	+	0.0719800i
$539$	7.13463	+	14.0246i	0.307310	+	0.604081i
$540$	18.6853	+	12.1377i	0.804088	+	0.522325i
$541$	8.29848	+	14.3734i	0.356780	+	0.617961i	0.987421	−	0.158114i	$-0.0505413\pi$
$541$	8.29848	+	14.3734i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$542$			3.79951i			0.163203i
$543$	−12.8169	+	28.9576i	−0.550027	+	1.24269i
$544$	−13.3024			−0.570338
$545$	−11.2329	+	28.6878i	−0.481165	+	1.22885i
$546$	1.01603	+	0.482293i	0.0434821	+	0.0206402i
$547$	−12.0493	+	6.95667i	−0.515191	+	0.297446i	−0.734965	−	0.678105i	$-0.762801\pi$
$547$	−12.0493	+	6.95667i	−0.515191	+	0.297446i	0.219774	+	0.975551i	$0.429468\pi$
$548$	−22.9420	+	13.2456i	−0.980035	+	0.565824i
$549$	−5.83889	+	1.26782i	−0.249198	+	0.0541091i
$550$	−3.14486	−	0.712555i	−0.134097	−	0.0303835i
$551$	17.3756	−	30.0954i	0.740224	−	1.28211i
$552$	0.794187	−	1.79433i	0.0338029	−	0.0763716i
$553$	27.1962	−	14.7551i	1.15650	−	0.627453i
$554$	3.53160	−	6.11690i	0.150043	−	0.259882i
$555$	−5.63755	−	21.4249i	−0.239301	−	0.909435i
$556$	0.781141			0.0331278
$557$	7.68847	+	4.43894i	0.325771	+	0.188084i	0.653962	−	0.756527i	$-0.273106\pi$
$557$	7.68847	+	4.43894i	0.325771	+	0.188084i	−0.328191	+	0.944611i	$0.606439\pi$
$558$	0.426988	−	0.387858i	0.0180759	−	0.0164193i
$559$	−0.197579			−0.00835669
$560$	16.5762	−	12.5358i	0.700471	−	0.529735i
$561$	−12.8489	+	9.37826i	−0.542480	+	0.395951i
$562$		−	0.900071i		−	0.0379672i
$563$	7.06624	−	4.07970i	0.297807	−	0.171939i	−0.343651	−	0.939098i	$-0.611664\pi$
$563$	7.06624	−	4.07970i	0.297807	−	0.171939i	0.641457	+	0.767159i	$0.278330\pi$
$564$	−26.5777	−	11.7635i	−1.11912	−	0.495335i
$565$	13.9707	+	5.47031i	0.587750	+	0.230138i
$566$	3.22527			0.135568
$567$	14.3359	−	19.0127i	0.602051	−	0.798458i
$568$			3.74186i			0.157005i
$569$	3.53575	−	6.12409i	0.148226	−	0.256735i	−0.782346	−	0.622844i	$-0.785977\pi$
$569$	3.53575	−	6.12409i	0.148226	−	0.256735i	0.930572	+	0.366109i	$0.119310\pi$
$570$	−6.09241	−	1.66188i	−0.255183	−	0.0696085i
$571$	−19.9869	−	34.6183i	−0.836425	−	1.44873i	−0.892865	−	0.450325i	$-0.851308\pi$
$571$	−19.9869	−	34.6183i	−0.836425	−	1.44873i	0.0564397	−	0.998406i	$-0.482025\pi$
$572$		−	3.68754i		−	0.154184i
$573$	10.3619	+	14.1965i	0.432874	+	0.593068i
$574$	5.00587	+	0.132679i	0.208941	+	0.00553790i
$575$	−1.49308	−	4.81335i	−0.0622655	−	0.200730i
$576$	−12.2877	−	13.5274i	−0.511988	−	0.563642i
$577$	14.7206	+	8.49894i	0.612826	+	0.353815i	0.774071	−	0.633099i	$-0.218217\pi$
$577$	14.7206	+	8.49894i	0.612826	+	0.353815i	−0.161245	+	0.986914i	$0.551551\pi$
$578$			0.0880482i			0.00366232i
$579$	1.24315	+	11.5840i	0.0516637	+	0.481416i
$580$	−9.55999	+	24.4153i	−0.396957	+	1.01379i
$581$	9.08718	+	0.240852i	0.377000	+	0.00999224i
$582$	−3.58265	+	8.09436i	−0.148506	+	0.335522i
$583$	24.9668	+	14.4146i	1.03402	+	0.596992i
$584$	−6.56919	+	11.3782i	−0.271835	+	0.470832i
$585$	−2.04408	−	5.36206i	−0.0845124	−	0.221694i
$586$	3.59574	+	6.22801i	0.148539	+	0.257277i
$587$	−2.53251	+	1.46215i	−0.104528	+	0.0603493i	−0.551353	−	0.834272i	$-0.685888\pi$
$587$	−2.53251	+	1.46215i	−0.104528	+	0.0603493i	0.446825	+	0.894622i	$0.352555\pi$
$588$	−12.6935	−	19.4800i	−0.523470	−	0.803343i
$589$	1.90446	−	3.29862i	0.0784719	−	0.135917i
$590$	0.841312	+	5.55190i	0.0346363	+	0.228568i
$591$	33.7641	+	14.9443i	1.38887	+	0.614728i
$592$			20.0944i			0.825875i
$593$	10.5920	−	6.11527i	0.434960	−	0.251124i	−0.266498	−	0.963836i	$-0.585866\pi$
$593$	10.5920	−	6.11527i	0.434960	−	0.251124i	0.701457	+	0.712711i	$0.252533\pi$
$594$	3.28235	+	0.675204i	0.134677	+	0.0277040i
$595$	14.5799	+	19.2791i	0.597719	+	0.790367i
$596$	19.2132	+	33.2783i	0.787004	+	1.36313i
$597$	16.2285	+	22.2341i	0.664187	+	0.909983i
$598$	−0.214229	+	0.123685i	−0.00876049	+	0.00505787i
$599$	13.5151	+	23.4089i	0.552213	+	0.956461i	0.998115	+	0.0613793i	$0.0195499\pi$
$599$	13.5151	+	23.4089i	0.552213	+	0.956461i	−0.445901	+	0.895082i	$0.647117\pi$
$600$	9.66873	+	1.12573i	0.394724	+	0.0459578i
$601$	−0.479634	−	0.830750i	−0.0195647	−	0.0338870i	0.856077	−	0.516848i	$-0.172895\pi$
$601$	−0.479634	−	0.830750i	−0.0195647	−	0.0338870i	−0.875642	+	0.482961i	$0.839561\pi$
$602$	−0.149456	−	0.0916524i	−0.00609138	−	0.00373547i
$603$	40.9981	+	13.1231i	1.66957	+	0.534413i
$604$	−5.61575	−	9.72676i	−0.228502	−	0.395776i
$605$	−13.1480	+	1.99240i	−0.534544	+	0.0810025i
$606$	−3.94073	+	2.87630i	−0.160081	+	0.116842i
$607$		−	1.55855i		−	0.0632597i	−0.999500	−	0.0316298i	$-0.989930\pi$
$607$		−	1.55855i		−	0.0632597i	0.999500	−	0.0316298i	$-0.0100698\pi$
$608$	16.0247	+	9.25184i	0.649886	+	0.375212i
$609$	25.3138	+	12.0161i	1.02577	+	0.486915i
$610$	−0.998319	+	0.797427i	−0.0404207	+	0.0322869i
$611$	3.74271	+	6.48256i	0.151414	+	0.262256i
$612$	17.3989	−	15.8045i	0.703311	−	0.638857i
$613$	−14.7756	−	8.53068i	−0.596779	−	0.344551i	0.170994	−	0.985272i	$-0.445302\pi$
$613$	−14.7756	−	8.53068i	−0.596779	−	0.344551i	−0.767774	+	0.640721i	$0.778635\pi$
$614$	−0.857290	+	1.48487i	−0.0345974	+	0.0599244i
$615$	−17.9853	−	18.1479i	−0.725236	−	0.731793i
$616$	3.49456	−	5.69853i	0.140800	−	0.229600i
$617$	−37.5321	−	21.6691i	−1.51098	−	0.872367i	−0.999918	−	0.0128252i	$-0.995917\pi$
$617$	−37.5321	−	21.6691i	−1.51098	−	0.872367i	−0.511066	−	0.859542i	$-0.670749\pi$
$618$	1.04084	+	1.42603i	0.0418688	+	0.0573632i
$619$	−13.6732			−0.549573			−0.274786	−	0.961505i	$-0.588607\pi$
$619$	−13.6732			−0.549573			−0.274786	+	0.961505i	$0.588607\pi$
$620$	−1.04783	+	2.67606i	−0.0420818	+	0.107473i
$621$	1.65107	+	4.97025i	0.0662551	+	0.199449i
$622$		−	6.07715i		−	0.243671i
$623$	−0.363682	+	13.7215i	−0.0145706	+	0.549739i
$624$	0.555386	+	5.17522i	0.0222332	+	0.207175i
$625$	20.6112	−	14.1484i	0.824450	−	0.565935i
$626$	4.77693	+	8.27389i	0.190925	+	0.330691i
$627$	22.0009	−	2.36105i	0.878629	−	0.0942912i
$628$	10.6885	+	6.17099i	0.426516	+	0.246249i
$629$	−23.3710			−0.931865
$630$	0.941116	−	5.00427i	0.0374950	−	0.199375i
$631$	−3.11420			−0.123974			−0.0619872	−	0.998077i	$-0.519744\pi$
$631$	−3.11420			−0.123974			−0.0619872	+	0.998077i	$0.519744\pi$
$632$	−11.3836	−	6.57233i	−0.452816	−	0.261433i
$633$	19.2369	+	26.3559i	0.764599	+	1.04755i
$634$	−4.63848	−	8.03409i	−0.184218	−	0.319074i
$635$	4.98708	+	32.9102i	0.197906	+	1.30600i
$636$	−38.9541	−	17.2415i	−1.54463	−	0.683670i
$637$	−0.317201	+	5.97967i	−0.0125679	+	0.236923i
$638$			3.94345i			0.156123i
$639$	−6.71519	−	7.39267i	−0.265649	−	0.292450i
$640$	−17.1972	−	6.73371i	−0.679781	−	0.266173i
$641$	−5.27733			−0.208442			−0.104221	−	0.994554i	$-0.533235\pi$
$641$	−5.27733			−0.208442			−0.104221	+	0.994554i	$0.533235\pi$
$642$	−0.339782	+	0.767678i	−0.0134101	+	0.0302978i
$643$	−19.0370	−	10.9910i	−0.750747	−	0.433444i	0.0752166	−	0.997167i	$-0.476035\pi$
$643$	−19.0370	−	10.9910i	−0.750747	−	0.433444i	−0.825964	+	0.563723i	$0.809369\pi$
$644$	5.11211	+	0.135495i	0.201446	+	0.00533924i
$645$	0.227631	+	0.865086i	0.00896297	+	0.0340627i
$646$	−3.33094	+	5.76936i	−0.131054	+	0.226992i
$647$	19.6891	+	11.3675i	0.774058	+	0.446903i	0.834320	−	0.551280i	$-0.185860\pi$
$647$	19.6891	+	11.3675i	0.774058	+	0.446903i	−0.0602623	+	0.998183i	$0.519194\pi$
$648$	−10.0694	−	0.969338i	−0.395562	−	0.0380792i
$649$	−9.83770	−	17.0394i	−0.386163	−	0.668855i
$650$	−0.900875	−	0.833238i	−0.0353352	−	0.0326823i
$651$	2.77454	+	1.31703i	0.108743	+	0.0516184i
$652$	1.11032	+	0.641041i	0.0434833	+	0.0251051i
$653$		−	0.490659i		−	0.0192010i	−0.999954	−	0.00960049i	$-0.996944\pi$
$653$		−	0.490659i		−	0.0192010i	0.999954	−	0.00960049i	$-0.00305598\pi$
$654$	−0.730566	−	6.80760i	−0.0285674	−	0.266198i
$655$	11.4526	−	1.73548i	0.447491	−	0.0678110i
$656$	11.5874	+	20.0699i	0.452411	+	0.783599i
$657$	−7.44085	−	34.2686i	−0.290295	−	1.33695i
$658$	−0.175986	+	6.63981i	−0.00686064	+	0.258847i
$659$	−11.9122	−	20.6326i	−0.464035	−	0.803731i	0.535123	−	0.844774i	$-0.320265\pi$
$659$	−11.9122	−	20.6326i	−0.464035	−	0.803731i	−0.999157	+	0.0410429i	$0.986932\pi$
$660$	−16.1457	+	4.24843i	−0.628470	+	0.165370i
$661$	5.41989	+	9.38752i	0.210809	+	0.365132i	0.951968	−	0.306197i	$-0.0990568\pi$
$661$	5.41989	+	9.38752i	0.210809	+	0.365132i	−0.741159	+	0.671330i	$0.765723\pi$
$662$	5.48622	−	3.16747i	0.213228	−	0.123107i
$663$	−6.01911	+	0.645948i	−0.233763	+	0.0250865i
$664$	−1.93092	−	3.34446i	−0.0749344	−	0.129790i
$665$	−4.15495	−	33.3647i	−0.161122	−	1.29383i
$666$	3.31036	+	3.64434i	0.128274	+	0.141215i
$667$	−5.33741	+	3.08155i	−0.206665	+	0.119318i
$668$			36.1880i			1.40016i
$669$	−1.61100	−	15.0117i	−0.0622848	−	0.580385i
$670$	9.10147	−	1.37920i	0.351620	−	0.0532831i
$671$	2.23848	−	3.87716i	0.0864154	−	0.149676i
$672$	−6.39810	+	13.4787i	−0.246812	+	0.519951i
$673$	−24.9348	+	14.3961i	−0.961165	+	0.554929i	−0.896531	−	0.442980i	$-0.853921\pi$
$673$	−24.9348	+	14.3961i	−0.961165	+	0.554929i	−0.0646335	+	0.997909i	$0.520588\pi$
$674$	−1.81145	−	3.13752i	−0.0697745	−	0.120853i
$675$	−21.1224	+	15.1275i	−0.813003	+	0.582259i
$676$	−11.7633	+	20.3746i	−0.452435	+	0.783640i
$677$	32.0427	+	18.4998i	1.23150	+	0.711007i	0.967342	−	0.253473i	$-0.0815730\pi$
$677$	32.0427	+	18.4998i	1.23150	+	0.711007i	0.264157	+	0.964480i	$0.414906\pi$
$678$	−3.31523	+	0.355778i	−0.127320	+	0.0136636i
$679$	−47.1122	−	1.24869i	−1.80800	−	0.0479204i
$680$	3.74401	−	9.56185i	0.143576	−	0.366680i
$681$	18.7502	+	8.29904i	0.718510	+	0.318020i
$682$			0.432225i			0.0165507i
$683$	22.8940	+	13.2179i	0.876016	+	0.505768i	0.869343	−	0.494210i	$-0.164543\pi$
$683$	22.8940	+	13.2179i	0.876016	+	0.505768i	0.00667307	+	0.999978i	$0.497876\pi$
$684$	−31.9515	+	6.93772i	−1.22169	+	0.265271i
$685$	−4.62801	−	30.5407i	−0.176827	−	1.16690i
$686$	−3.01378	+	4.37611i	−0.115067	+	0.167081i
$687$	8.26901	−	18.6824i	0.315482	−	0.712777i
$688$		−	0.811366i		−	0.0309330i
$689$	5.48558	+	9.50130i	0.208984	+	0.361971i
$690$	0.788363	+	0.795492i	0.0300125	+	0.0302839i
$691$	−16.1276	+	27.9339i	−0.613524	+	1.06266i	0.377117	+	0.926166i	$0.376915\pi$
$691$	−16.1276	+	27.9339i	−0.613524	+	1.06266i	−0.990641	+	0.136490i	$0.956418\pi$
$692$			19.0164i			0.722896i
$693$	3.32255	+	17.5298i	0.126213	+	0.665901i
$694$	−6.67803			−0.253494
$695$	−0.332091	+	0.848130i	−0.0125969	+	0.0321714i
$696$	−1.27021	−	11.8362i	−0.0481472	−	0.448648i
$697$	−23.3426	+	13.4768i	−0.884163	+	0.510472i
$698$		−	7.22752i		−	0.273566i
$699$	0.185712	+	1.73051i	0.00702429	+	0.0654541i
$700$	6.87131	+	24.4203i	0.259711	+	0.923001i
$701$	−15.4791			−0.584636			−0.292318	−	0.956321i	$-0.594427\pi$
$701$	−15.4791			−0.584636			−0.292318	+	0.956321i	$0.594427\pi$
$702$	0.953294	+	0.847089i	0.0359798	+	0.0319713i
$703$	28.1537	+	16.2546i	1.06184	+	0.613052i
$704$	13.6933			0.516086
$705$	24.0715	−	23.8558i	0.906584	−	0.898461i
$706$	−2.98826	+	5.17582i	−0.112465	+	0.194795i
$707$	−22.1436	−	13.5793i	−0.832794	−	0.510702i
$708$	17.1402	+	23.4832i	0.644167	+	0.882554i
$709$	12.2265	−	21.1769i	0.459175	−	0.795314i	−0.539743	−	0.841830i	$-0.681478\pi$
$709$	12.2265	−	21.1769i	0.459175	−	0.795314i	0.998918	+	0.0465159i	$0.0148118\pi$
$710$	−1.98870	−	0.778689i	−0.0746345	−	0.0292237i
$711$	34.2850	−	7.44441i	1.28579	−	0.279187i
$712$	5.05007	−	2.91566i	0.189259	−	0.109269i
$713$	−0.585010	+	0.337756i	−0.0219088	+	0.0126491i
$714$	−4.85273	−	2.30351i	−0.181609	−	0.0862066i
$715$	4.00378	+	1.56771i	0.149733	+	0.0586290i
$716$	−31.8135			−1.18893
$717$	11.5874	+	15.8755i	0.432739	+	0.592882i
$718$		−	1.91583i		−	0.0714980i
$719$	23.2956	+	40.3492i	0.868779	+	1.50477i	0.863245	+	0.504785i	$0.168428\pi$
$719$	23.2956	+	40.3492i	0.868779	+	1.50477i	0.00553411	+	0.999985i	$0.498238\pi$
$720$	22.0195	−	8.39412i	0.820620	−	0.312830i
$721$	−4.91392	+	8.01306i	−0.183004	+	0.298422i
$722$	3.30436	−	1.90777i	0.122975	−	0.0709999i
$723$	18.4452	−	41.6738i	0.685986	−	1.54986i
$724$	17.5306	+	30.3639i	0.651521	+	1.12847i
$725$	−22.4448	−	20.7597i	−0.833579	−	0.770994i
$726$	2.38707	−	1.74230i	0.0885925	−	0.0646628i
$727$	12.9876	−	7.49840i	0.481684	−	0.278100i	−0.239434	−	0.970913i	$-0.576962\pi$
$727$	12.9876	−	7.49840i	0.481684	−	0.278100i	0.721118	+	0.692812i	$0.243629\pi$
$728$	2.23601	−	1.21314i	0.0828722	−	0.0449618i
$729$	21.6333	−	16.1555i	0.801233	−	0.598352i
$730$	−4.68012	−	5.85916i	−0.173219	−	0.216857i
$731$	0.943668			0.0349028
$732$	−2.67747	+	6.04927i	−0.0989621	+	0.223587i
$733$			18.0699i			0.667429i	0.942674	+	0.333714i	$0.108302\pi$
$733$			18.0699i			0.667429i	−0.942674	+	0.333714i	$0.891698\pi$
$734$	−0.0622027	+	0.107738i	−0.00229594	+	0.00397669i
$735$	26.5471	−	5.50036i	0.979203	−	0.202884i
$736$	−1.64081	−	2.84197i	−0.0604812	−	0.104756i
$737$	−27.9334	+	16.1274i	−1.02894	+	0.594059i
$738$	5.40783	+	1.73099i	0.199065	+	0.0637187i
$739$	3.53515	−	6.12305i	0.130042	−	0.225240i	−0.793650	−	0.608374i	$-0.791822\pi$
$739$	3.53515	−	6.12305i	0.130042	−	0.225240i	0.923693	+	0.383134i	$0.125155\pi$
$740$	−22.8401	−	8.94321i	−0.839619	−	0.328759i
$741$	7.70011	+	3.40815i	0.282871	+	0.125202i
$742$	−0.257937	+	9.73179i	−0.00946918	+	0.357265i
$743$	25.2654	+	14.5870i	0.926899	+	0.535145i	0.885830	−	0.464011i	$-0.153590\pi$
$743$	25.2654	+	14.5870i	0.926899	+	0.535145i	0.0410696	+	0.999156i	$0.486923\pi$
$744$	−0.139222	−	1.29731i	−0.00510414	−	0.0475617i
$745$	−44.3004	+	6.71309i	−1.62304	+	0.245949i
$746$	3.17300	−	5.49579i	0.116172	−	0.201215i
$747$	9.81687	+	3.14228i	0.359180	+	0.114970i
$748$			17.6123i			0.643970i
$749$	−4.46818	−	0.118427i	−0.163264	−	0.00432724i
$750$	−2.61038	+	4.90440i	−0.0953175	+	0.179083i
$751$	−37.4418			−1.36627			−0.683135	−	0.730292i	$-0.739384\pi$
$751$	−37.4418			−1.36627			−0.683135	+	0.730292i	$0.739384\pi$
$752$	−26.6209	+	15.3696i	−0.970764	+	0.560471i
$753$	−3.03046	+	6.84679i	−0.110436	+	0.249511i
$754$	−0.750353	+	1.29965i	−0.0273263	+	0.0473305i
$755$	12.9484	−	1.96214i	0.471239	−	0.0714096i
$756$	−7.64542	−	25.2309i	−0.278061	−	0.917640i
$757$		−	17.2926i		−	0.628511i	−0.949338	−	0.314256i	$-0.898245\pi$
$757$		−	17.2926i		−	0.628511i	0.949338	−	0.314256i	$-0.101755\pi$
$758$	−0.889763	−	0.513705i	−0.0323176	−	0.0186586i
$759$	−3.58846	−	1.58829i	−0.130253	−	0.0576513i
$760$	−11.1605	+	8.91464i	−0.404832	+	0.323368i
$761$	−41.4684			−1.50323			−0.751614	−	0.659603i	$-0.770724\pi$
$761$	−41.4684			−1.50323			−0.751614	+	0.659603i	$0.770724\pi$
$762$	−4.36106	−	5.97496i	−0.157985	−	0.216450i
$763$	32.0412	−	17.3838i	1.15997	−	0.629334i
$764$	19.4596			0.704023
$765$	9.76288	+	25.6101i	0.352978	+	0.925934i
$766$	1.15971	−	2.00867i	0.0419020	−	0.0725763i
$767$		−	7.48760i		−	0.270362i
$768$	−16.9009	+	1.81374i	−0.609858	+	0.0654477i
$769$	7.97753	−	13.8175i	0.287677	−	0.498271i	−0.685578	−	0.727999i	$-0.740450\pi$
$769$	7.97753	−	13.8175i	0.287677	−	0.498271i	0.973255	+	0.229728i	$0.0737836\pi$
$770$	2.30139	+	3.04314i	0.0829362	+	0.109667i
$771$	26.0644	+	11.5364i	0.938685	+	0.415472i
$772$	11.1710	+	6.44961i	0.402055	+	0.232126i
$773$	−27.1920	−	15.6993i	−0.978028	−	0.564665i	−0.0763541	−	0.997081i	$-0.524328\pi$
$773$	−27.1920	−	15.6993i	−0.978028	−	0.564665i	−0.901674	+	0.432416i	$0.857661\pi$
$774$	−0.133665	−	0.147150i	−0.00480448	−	0.00528920i
$775$	−2.46008	−	2.27538i	−0.0883686	−	0.0817339i
$776$	10.0108	+	17.3393i	0.359368	+	0.622443i
$777$	−11.2408	+	23.6807i	−0.403262	+	0.849539i
$778$	3.01384	+	1.74004i	0.108051	+	0.0623835i
$779$	37.4926			1.34331
$780$	−6.12954	−	1.67201i	−0.219473	−	0.0598675i
$781$	7.48333			0.267775
$782$	1.02320	−	0.590742i	0.0365894	−	0.0211249i
$783$	23.7508	+	21.1048i	0.848784	+	0.754222i
$784$	−24.5558	−	1.30260i	−0.876992	−	0.0465214i
$785$	−11.2443	+	8.98158i	−0.401325	+	0.320566i
$786$	−2.07926	+	1.51763i	−0.0741649	+	0.0541322i
$787$	34.3103	−	19.8091i	1.22303	−	0.706118i	0.257468	−	0.966287i	$-0.417112\pi$
$787$	34.3103	−	19.8091i	1.22303	−	0.706118i	0.965563	+	0.260169i	$0.0837783\pi$
$788$	35.4039	−	20.4405i	1.26121	−	0.728162i
$789$	9.36546	+	4.14525i	0.333419	+	0.147575i
$790$	5.86196	−	4.68236i	0.208559	−	0.166591i
$791$	−8.46570	−	15.6037i	−0.301006	−	0.554805i
$792$	5.61060	−	5.09643i	0.199364	−	0.181094i
$793$	1.47548	−	0.851867i	0.0523957	−	0.0302507i
$794$	−4.30234			−0.152684
$795$	35.2809	−	34.9647i	1.25128	−	1.24007i
$796$	30.4770			1.08023
$797$	16.7794	+	9.68757i	0.594355	+	0.343151i	0.766818	−	0.641865i	$-0.221839\pi$
$797$	16.7794	+	9.68757i	0.594355	+	0.343151i	−0.172462	+	0.985016i	$0.555172\pi$
$798$	4.24370	+	6.14997i	0.150225	+	0.217707i
$799$	−17.8758	−	30.9618i	−0.632400	−	1.09535i
$800$	11.0537	−	11.9510i	0.390809	−	0.422532i
$801$	−4.74478	+	14.8233i	−0.167649	+	0.523755i
$802$	−4.85750	−	2.80448i	−0.171524	−	0.0990296i
$803$	22.7551	+	13.1377i	0.803011	+	0.463619i
$804$	38.4971	−	28.0986i	1.35769	−	0.990962i
$805$	−2.32046	+	5.49291i	−0.0817855	+	0.193600i
$806$	−0.0822430	+	0.142449i	−0.00289689	+	0.00501755i
$807$	−11.8846	−	16.2827i	−0.418357	−	0.573178i
$808$			11.0352i			0.388217i
$809$	−9.48196	+	16.4232i	−0.333368	+	0.577410i	−0.983170	−	0.182693i	$-0.941518\pi$
$809$	−9.48196	+	16.4232i	−0.333368	+	0.577410i	0.649802	+	0.760104i	$0.274852\pi$
$810$	2.61063	−	5.14987i	0.0917283	−	0.180948i
$811$	−1.71293			−0.0601489			−0.0300745	−	0.999548i	$-0.509574\pi$
$811$	−1.71293			−0.0601489			−0.0300745	+	0.999548i	$0.509574\pi$
$812$	27.2693	−	14.7948i	0.956965	−	0.519195i
$813$	−22.8071	+	2.44757i	−0.799878	+	0.0858400i
$814$	−3.68903			−0.129301
$815$	−1.16805	+	0.933004i	−0.0409150	+	0.0326817i
$816$	−2.65261	−	24.7177i	−0.0928601	−	0.865293i
$817$	−1.13678	−	0.656321i	−0.0397709	−	0.0229618i
$818$		−	3.97521i		−	0.138990i
$819$	−2.24052	+	6.40953i	−0.0782899	+	0.223967i
$820$	−27.9694	+	4.23836i	−0.976732	+	0.148010i
$821$	−21.7541	+	37.6792i	−0.759223	+	1.31501i	0.184025	+	0.982922i	$0.441087\pi$
$821$	−21.7541	+	37.6792i	−0.759223	+	1.31501i	−0.943248	+	0.332090i	$0.892246\pi$
$822$	4.04707	+	5.54476i	0.141158	+	0.193396i
$823$	42.3390	−	24.4444i	1.47585	−	0.852080i	0.476217	−	0.879328i	$-0.342008\pi$
$823$	42.3390	−	24.4444i	1.47585	−	0.852080i	0.999629	+	0.0272483i	$0.00867449\pi$
$824$	3.99329			0.139113
$825$	2.25135	−	19.3365i	0.0783818	−	0.673209i
$826$	3.47333	−	5.66391i	0.120853	−	0.197073i
$827$		−	31.7125i		−	1.10275i	−0.834257	−	0.551376i	$-0.814103\pi$
$827$		−	31.7125i		−	1.10275i	0.834257	−	0.551376i	$-0.185897\pi$
$828$	5.52261	+	1.76773i	0.191924	+	0.0614329i
$829$	23.0695	−	39.9576i	0.801238	−	1.38778i	−0.117564	−	0.993065i	$-0.537509\pi$
$829$	23.0695	−	39.9576i	0.801238	−	1.38778i	0.918802	−	0.394719i	$-0.129158\pi$
$830$	2.17932	−	0.330245i	0.0756452	−	0.0114630i
$831$	38.9924	+	17.2585i	1.35263	+	0.598689i
$832$	4.51292	+	2.60554i	0.156457	+	0.0903308i
$833$	1.51500	−	28.5599i	0.0524917	−	0.989541i
$834$	−0.0215985	−	0.201261i	−0.000747896	−	0.00696908i
$835$	−39.2914	−	15.3848i	−1.35974	−	0.532414i
$836$	12.2494	−	21.2165i	0.423653	−	0.733788i
$837$	2.60322	+	2.31320i	0.0899805	+	0.0799559i
$838$	−4.16364	+	2.40388i	−0.143831	+	0.0830407i
$839$	23.0638	+	39.9477i	0.796251	+	1.37915i	0.922042	+	0.387090i	$0.126520\pi$
$839$	23.0638	+	39.9477i	0.796251	+	1.37915i	−0.125791	+	0.992057i	$0.540147\pi$
$840$	−7.88776	−	8.39259i	−0.272153	−	0.289572i
$841$	−4.19464	+	7.26534i	−0.144643	+	0.250529i
$842$			0.644064i			0.0221959i
$843$	5.40279	−	0.579807i	0.186082	−	0.0199696i
$844$	36.1268			1.24354
$845$	−17.1209	−	21.4341i	−0.588977	−	0.737356i
$846$	−2.29600	+	7.17298i	−0.0789381	+	0.246612i
$847$	13.4133	+	8.22556i	0.460887	+	0.282634i
$848$	−39.0175	+	22.5268i	−1.33987	+	0.773572i
$849$	2.07765	+	19.3601i	0.0713047	+	0.664435i
$850$	4.30273	+	3.97968i	0.147582	+	0.136502i
$851$	−2.88274	−	4.99306i	−0.0988191	−	0.171160i
$852$	−10.9945	+	1.17989i	−0.376667	+	0.0404225i
$853$	−49.2271	+	28.4213i	−1.68550	+	0.973125i	−0.727613	+	0.685987i	$0.759371\pi$
$853$	−49.2271	+	28.4213i	−1.68550	+	0.973125i	−0.957889	+	0.287138i	$0.907296\pi$
$854$	1.51127	+	0.0400557i	0.0517146	+	0.00137068i
$855$	6.05104	−	37.6410i	0.206941	−	1.28730i
$856$	0.949438	+	1.64447i	0.0324511	+	0.0562070i
$857$		−	45.5047i		−	1.55441i	−0.629248	−	0.777205i	$-0.716637\pi$
$857$		−	45.5047i		−	1.55441i	0.629248	−	0.777205i	$-0.283363\pi$
$858$	−0.950094	+	0.101960i	−0.0324357	+	0.00348087i
$859$	27.8744			0.951062			0.475531	−	0.879699i	$-0.342256\pi$
$859$	27.8744			0.951062			0.475531	+	0.879699i	$0.342256\pi$
$860$	0.922230	+	0.361106i	0.0314478	+	0.0123136i
$861$	2.42825	+	30.1338i	0.0827547	+	1.02696i
$862$	2.11180	−	1.21925i	0.0719282	−	0.0415278i
$863$	−30.9522	+	17.8703i	−1.05363	+	0.608311i	−0.923662	−	0.383208i	$-0.874819\pi$
$863$	−30.9522	+	17.8703i	−1.05363	+	0.608311i	−0.129963	+	0.991519i	$0.541486\pi$
$864$	−11.2375	+	12.6464i	−0.382307	+	0.430240i
$865$	−20.6472	−	8.08457i	−0.702027	−	0.274884i
$866$	−1.17109	+	2.02839i	−0.0397954	+	0.0689276i
$867$	−0.528520	+	0.0567188i	−0.0179495	+	0.00192627i
$868$	2.98887	−	1.62159i	0.101449	−	0.0550404i
$869$	−13.1440	+	22.7660i	−0.445878	+	0.772284i
$870$	6.55492	+	1.78804i	0.222233	+	0.0606204i
$871$	−12.2748			−0.415914
$872$	−13.4116	−	7.74318i	−0.454174	−	0.262217i
$873$	−50.8953	−	16.2911i	−1.72254	−	0.551369i
$874$	−1.64344			−0.0555903
$875$	−29.4358	−	2.92139i	−0.995111	−	0.0987609i
$876$	−35.5033	−	15.7141i	−1.19955	−	0.530932i
$877$		−	6.14942i		−	0.207651i	−0.994596	−	0.103826i	$-0.966892\pi$
$877$		−	6.14942i		−	0.207651i	0.994596	−	0.103826i	$-0.0331084\pi$
$878$	2.57373	−	1.48594i	0.0868592	−	0.0501482i
$879$	−35.0681	+	25.5959i	−1.18282	+	0.863327i
$880$	−6.43786	+	16.4417i	−0.217020	+	0.554249i
$881$	−27.3869			−0.922687			−0.461343	−	0.887222i	$-0.652632\pi$
$881$	−27.3869			−0.922687			−0.461343	+	0.887222i	$0.652632\pi$
$882$	−4.66805	+	3.80909i	−0.157181	+	0.128259i
$883$		−	2.88643i		−	0.0971362i	−0.998820	−	0.0485681i	$-0.984534\pi$
$883$		−	2.88643i		−	0.0971362i	0.998820	−	0.0485681i	$-0.0154658\pi$
$884$	−3.35124	+	5.80452i	−0.112714	+	0.195227i
$885$	−32.7840	+	8.62649i	−1.10202	+	0.289976i
$886$	2.58815	+	4.48281i	0.0869506	+	0.150603i
$887$		−	46.3047i		−	1.55476i	−0.629032	−	0.777379i	$-0.716549\pi$
$887$		−	46.3047i		−	1.55476i	0.629032	−	0.777379i	$-0.283451\pi$
$888$	11.0725	−	1.18826i	0.371569	−	0.0398754i
$889$	20.5890	−	33.5742i	0.690533	−	1.12604i
$890$	0.498663	+	3.29073i	0.0167152	+	0.110305i
$891$	−1.93857	+	20.1377i	−0.0649447	+	0.674638i
$892$	−14.4765	−	8.35801i	−0.484709	−	0.279847i
$893$			49.7304i			1.66416i
$894$	8.04288	−	5.87042i	0.268994	−	0.196336i
$895$	13.5251	−	34.5417i	0.452093	−	1.15460i
$896$	10.4209	+	19.2075i	0.348138	+	0.641677i
$897$	−0.880439	−	1.20626i	−0.0293970	−	0.0402759i
$898$	3.63199	+	2.09693i	0.121201	+	0.0699755i
$899$	−2.04904	+	3.54904i	−0.0683393	+	0.118367i
$900$	−0.258917	+	28.7641i	−0.00863057	+	0.958805i
$901$	−26.2000	−	45.3798i	−0.872849	−	1.51182i
$902$	−3.68454	+	2.12727i	−0.122682	+	0.0708303i
$903$	0.453878	−	0.956170i	0.0151041	−	0.0318193i
$904$	−3.77085	+	6.53130i	−0.125416	+	0.217228i
$905$	−40.4208	+	6.12520i	−1.34363	+	0.203608i
$906$	−2.35082	+	1.71584i	−0.0781007	+	0.0570049i
$907$		−	23.7311i		−	0.787978i	−0.919115	−	0.393989i	$-0.871095\pi$
$907$		−	23.7311i		−	0.787978i	0.919115	−	0.393989i	$-0.128905\pi$
$908$	19.6609	−	11.3512i	0.652469	−	0.376703i
$909$	−19.8039	−	21.8019i	−0.656853	−	0.723122i
$910$	0.179429	+	1.44084i	0.00594801	+	0.0477633i
$911$	8.92590	+	15.4601i	0.295728	+	0.512216i	0.975154	−	0.221528i	$-0.0711044\pi$
$911$	8.92590	+	15.4601i	0.295728	+	0.512216i	−0.679426	+	0.733744i	$0.737771\pi$
$912$	−13.9957	+	31.6209i	−0.463445	+	1.04707i
$913$	−6.68857	+	3.86165i	−0.221359	+	0.127802i
$914$	3.36113	+	5.82164i	0.111176	+	0.192563i
$915$	−5.42975	−	5.47884i	−0.179502	−	0.181125i
$916$	−11.3101	−	19.5897i	−0.373697	−	0.647262i
$917$	−11.6837	−	7.16490i	−0.385829	−	0.236606i
$918$	−4.55309	−	4.04584i	−0.150274	−	0.133532i
$919$	−15.1019	−	26.1573i	−0.498166	−	0.862850i	0.501831	−	0.864966i	$-0.332660\pi$
$919$	−15.1019	−	26.1573i	−0.498166	−	0.862850i	−0.999998	+	0.00211592i	$0.999326\pi$
$920$	2.50463	−	0.379542i	0.0825753	−	0.0125131i
$921$	−9.46536	−	4.18946i	−0.311894	−	0.138048i
$922$			6.02592i			0.198453i
$923$	2.46629	+	1.42392i	0.0811791	+	0.0468688i
$924$	17.8456	+	8.47103i	0.587078	+	0.278676i
$925$	19.4203	−	20.9967i	0.638536	−	0.690368i
$926$	0.436676	+	0.756344i	0.0143501	+	0.0248550i
$927$	−7.88941	+	7.16640i	−0.259122	+	0.235375i
$928$	−17.2412	−	9.95420i	−0.565970	−	0.326763i
$929$	8.27855	−	14.3389i	0.271610	−	0.470443i	−0.697664	−	0.716425i	$-0.745777\pi$
$929$	8.27855	−	14.3389i	0.271610	−	0.470443i	0.969274	+	0.245982i	$0.0791105\pi$
$930$	0.718457	+	0.195980i	0.0235591	+	0.00642643i
$931$	−21.6884	+	33.3507i	−0.710809	+	1.09303i
$932$	1.66882	+	0.963494i	0.0546640	+	0.0315603i
$933$	36.4788	−	3.91477i	1.19426	−	0.128164i
$934$	8.22718			0.269202
$935$	−19.1227	−	7.48763i	−0.625379	−	0.244872i
$936$	2.81883	−	0.612063i	0.0921365	−	0.0200059i
$937$		−	33.2418i		−	1.08596i	−0.839745	−	0.542981i	$-0.817296\pi$
$937$		−	33.2418i		−	1.08596i	0.839745	−	0.542981i	$-0.182704\pi$
$938$	−9.28510	−	5.69398i	−0.303169	−	0.185915i
$939$	−46.5878	+	34.0040i	−1.52034	+	1.10968i
$940$	−5.62179	−	37.0987i	−0.183363	−	1.21003i
$941$	−5.35031	−	9.26700i	−0.174415	−	0.302096i	0.765544	−	0.643384i	$-0.222470\pi$
$941$	−5.35031	−	9.26700i	−0.174415	−	0.302096i	−0.939959	+	0.341288i	$0.889137\pi$
$942$	1.29442	−	2.92451i	0.0421744	−	0.0952856i
$943$	−5.75846	−	3.32465i	−0.187521	−	0.108265i
$944$	30.7482			1.00077
$945$	30.6450	+	2.42552i	0.996882	+	0.0789020i
$946$	0.148955			0.00484293
$947$	37.1772	+	21.4643i	1.20810	+	0.697495i	0.962343	−	0.271837i	$-0.0876312\pi$
$947$	37.1772	+	21.4643i	1.20810	+	0.697495i	0.245754	+	0.969332i	$0.420965\pi$
$948$	15.7217	−	35.5203i	0.510616	−	1.15365i
$949$	4.99963	+	8.65962i	0.162295	+	0.281103i
$950$	−2.41537	−	7.78663i	−0.0783650	−	0.252632i
$951$	45.2376	−	33.0185i	1.46693	−	1.07070i
$952$	−10.6796	+	5.79413i	−0.346127	+	0.187789i
$953$			41.7181i			1.35138i	0.737186	+	0.675690i	$0.236154\pi$
$953$			41.7181i			1.35138i	−0.737186	+	0.675690i	$0.763846\pi$
$954$	−3.36518	+	10.5132i	−0.108952	+	0.340379i
$955$	−8.27297	+	21.1284i	−0.267707	+	0.683698i
$956$	21.7610			0.703802
$957$	−23.6711	+	2.54029i	−0.765177	+	0.0821159i
$958$	−3.86995	−	2.23432i	−0.125033	−	0.0721876i
$959$	−19.1066	+	31.1568i	−0.616984	+	1.00611i
$960$	6.20883	−	22.7614i	0.200389	−	0.734621i
$961$	15.2754	−	26.4578i	0.492755	−	0.853477i
$962$	−1.21580	−	0.701943i	−0.0391990	−	0.0226315i
$963$	−4.82696	−	1.54506i	−0.155547	−	0.0497889i
$964$	−25.2289	−	43.6977i	−0.812567	−	1.40741i
$965$	−11.7519	+	9.38708i	−0.378308	+	0.302181i
$966$	−0.106440	−	1.32088i	−0.00342464	−	0.0424986i
$967$	−18.8207	−	10.8662i	−0.605235	−	0.349432i	0.165864	−	0.986149i	$-0.446959\pi$
$967$	−18.8207	−	10.8662i	−0.605235	−	0.349432i	−0.771098	+	0.636716i	$0.780292\pi$
$968$		−	6.68450i		−	0.214848i
$969$	−36.7770	−	16.2779i	−1.18145	−	0.522921i
$970$	−11.2986	+	1.71215i	−0.362777	+	0.0549737i
$971$	16.7253	+	28.9691i	0.536741	+	0.929662i	0.999077	+	0.0429577i	$0.0136781\pi$
$971$	16.7253	+	28.9691i	0.536741	+	0.929662i	−0.462336	+	0.886705i	$0.652989\pi$
$972$	−0.326937	−	29.8920i	−0.0104865	−	0.958786i
$973$	0.947271	−	0.513936i	0.0303681	−	0.0164760i
$974$	3.97223	+	6.88010i	0.127278	+	0.220453i
$975$	4.42129	−	5.94436i	0.141594	−	0.190372i
$976$	3.49823	+	6.05911i	0.111976	+	0.193947i
$977$	−30.6946	+	17.7215i	−0.982007	+	0.566962i	−0.902875	−	0.429902i	$-0.858548\pi$
$977$	−30.6946	+	17.7215i	−0.982007	+	0.566962i	−0.0791312	+	0.996864i	$0.525215\pi$
$978$	0.134464	−	0.303797i	0.00429967	−	0.00971436i
$979$	−5.83101	−	10.0996i	−0.186360	−	0.322785i
$980$	12.4094	−	27.3313i	0.396403	−	0.873067i
$981$	40.3928	−	8.77062i	1.28964	−	0.280024i
$982$	−4.89640	+	2.82694i	−0.156250	+	0.0902111i
$983$		−	42.8993i		−	1.36827i	−0.729353	−	0.684137i	$-0.760179\pi$
$983$		−	42.8993i		−	1.36827i	0.729353	−	0.684137i	$-0.239821\pi$
$984$	10.3738	−	7.57175i	0.330705	−	0.241379i
$985$	7.14190	+	47.1301i	0.227560	+	1.50169i
$986$	3.58381	−	6.20734i	0.114132	−	0.197682i
$987$	−39.9697	+	3.22085i	−1.27225	+	0.102521i
$988$	8.07408	−	4.66157i	0.256871	−	0.148304i
$989$	0.116398	+	0.201608i	0.00370125	+	0.00641076i
$990$	1.54103	+	4.04246i	0.0489773	+	0.128478i
$991$	−12.0151	+	20.8107i	−0.381672	+	0.661075i	−0.991301	−	0.131611i	$-0.957985\pi$
$991$	−12.0151	+	20.8107i	−0.381672	+	0.661075i	0.609629	+	0.792687i	$0.291318\pi$
$992$	−1.88973	−	1.09104i	−0.0599990	−	0.0346405i
$993$	22.5472	+	30.8913i	0.715515	+	0.980305i
$994$	1.20508	+	2.22116i	0.0382227	+	0.0704510i
$995$	−12.9569	+	33.0906i	−0.410760	+	1.04904i
$996$	9.21800	−	6.72813i	0.292084	−	0.213189i
$997$		−	0.413115i		−	0.0130835i	−0.999979	−	0.00654175i	$-0.997918\pi$
$997$		−	0.413115i		−	0.0130835i	0.999979	−	0.00654175i	$-0.00208232\pi$
$998$	−5.44312	−	3.14259i	−0.172299	−	0.0994769i
$999$	−19.7431	+	22.2185i	−0.624645	+	0.702961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.19	yes	84
3.2	odd	2		945.2.bo.b.739.24		84
5.4	even	2	inner	315.2.bo.b.4.24	yes	84
7.2	even	3		315.2.r.b.184.24	yes	84
9.2	odd	6		945.2.r.b.424.19		84
9.7	even	3		315.2.r.b.214.24	yes	84
15.14	odd	2		945.2.bo.b.739.19		84
21.2	odd	6		945.2.r.b.604.19		84
35.9	even	6		315.2.r.b.184.19	✓	84
45.29	odd	6		945.2.r.b.424.24		84
45.34	even	6		315.2.r.b.214.19	yes	84
63.2	odd	6		945.2.bo.b.289.19		84
63.16	even	3	inner	315.2.bo.b.79.24	yes	84
105.44	odd	6		945.2.r.b.604.24		84
315.79	even	6	inner	315.2.bo.b.79.19	yes	84
315.254	odd	6		945.2.bo.b.289.24		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.19	✓	84	35.9	even	6
315.2.r.b.184.24	yes	84	7.2	even	3
315.2.r.b.214.19	yes	84	45.34	even	6
315.2.r.b.214.24	yes	84	9.7	even	3
315.2.bo.b.4.19	yes	84	1.1	even	1	trivial
315.2.bo.b.4.24	yes	84	5.4	even	2	inner
315.2.bo.b.79.19	yes	84	315.79	even	6	inner
315.2.bo.b.79.24	yes	84	63.16	even	3	inner
945.2.r.b.424.19		84	9.2	odd	6
945.2.r.b.424.24		84	45.29	odd	6
945.2.r.b.604.19		84	21.2	odd	6
945.2.r.b.604.24		84	105.44	odd	6
945.2.bo.b.289.19		84	63.2	odd	6
945.2.bo.b.289.24		84	315.254	odd	6
945.2.bo.b.739.19		84	15.14	odd	2
945.2.bo.b.739.24		84	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248464 - 0.143451i) q^{2} +(0.701026 - 1.58384i) q^{3} +(-0.958844 - 1.66077i) q^{4} +(2.21083 - 0.335020i) q^{5} +(-0.401384 + 0.292966i) q^{6} +(-2.25543 - 1.38312i) q^{7} +1.12399i q^{8} +(-2.01713 - 2.22063i) q^{9} +O(q^{10})\)	\(q+(-0.248464 - 0.143451i) q^{2} +(0.701026 - 1.58384i) q^{3} +(-0.958844 - 1.66077i) q^{4} +(2.21083 - 0.335020i) q^{5} +(-0.401384 + 0.292966i) q^{6} +(-2.25543 - 1.38312i) q^{7} +1.12399i q^{8} +(-2.01713 - 2.22063i) q^{9} +(-0.597370 - 0.233905i) q^{10} +2.24786 q^{11} +(-3.30257 + 0.354419i) q^{12} +(0.740832 + 0.427720i) q^{13} +(0.361985 + 0.667199i) q^{14} +(1.01923 - 3.73647i) q^{15} +(-1.75645 + 3.04226i) q^{16} +(-3.53834 - 2.04286i) q^{17} +(0.182632 + 0.841106i) q^{18} +(2.84162 + 4.92182i) q^{19} +(-2.67623 - 3.35044i) q^{20} +(-3.77176 + 2.60265i) q^{21} +(-0.558513 - 0.322458i) q^{22} -1.00792i q^{23} +(1.78023 + 0.787947i) q^{24} +(4.77552 - 1.48134i) q^{25} +(-0.122713 - 0.212546i) q^{26} +(-4.93119 + 1.63809i) q^{27} +(-0.134430 + 5.07194i) q^{28} +(-3.05734 - 5.29547i) q^{29} +(-0.789241 + 0.782168i) q^{30} +(-0.335102 - 0.580413i) q^{31} +(2.81964 - 1.62792i) q^{32} +(1.57581 - 3.56027i) q^{33} +(0.586100 + 1.01515i) q^{34} +(-5.44975 - 2.30223i) q^{35} +(-1.75384 + 5.47921i) q^{36} +(4.95382 - 2.86009i) q^{37} -1.63053i q^{38} +(1.19678 - 0.873520i) q^{39} +(0.376559 + 2.48495i) q^{40} +(3.29852 - 5.71321i) q^{41} +(1.31050 - 0.105603i) q^{42} +(-0.200024 + 0.115484i) q^{43} +(-2.15535 - 3.73318i) q^{44} +(-5.20347 - 4.23366i) q^{45} +(-0.144587 + 0.250432i) q^{46} +(7.57804 + 4.37518i) q^{47} +(3.58715 + 4.91465i) q^{48} +(3.17396 + 6.23907i) q^{49} +(-1.39905 - 0.316992i) q^{50} +(-5.71604 + 4.17208i) q^{51} -1.64047i q^{52} +(11.1069 + 6.41258i) q^{53} +(1.46021 + 0.300376i) q^{54} +(4.96964 - 0.753079i) q^{55} +(1.55461 - 2.53509i) q^{56} +(9.78745 - 1.05035i) q^{57} +1.75431i q^{58} +(-4.37646 - 7.58026i) q^{59} +(-7.18268 + 1.88999i) q^{60} +(0.995824 - 1.72482i) q^{61} +0.192282i q^{62} +(1.47809 + 7.79841i) q^{63} +6.09169 q^{64} +(1.78115 + 0.697421i) q^{65} +(-0.902255 + 0.658547i) q^{66} +(-12.4267 + 7.17453i) q^{67} +7.83513i q^{68} +(-1.59639 - 0.706578i) q^{69} +(1.02381 + 1.35379i) q^{70} +3.32909 q^{71} +(2.49597 - 2.26723i) q^{72} +(10.1230 + 5.84452i) q^{73} -1.64113 q^{74} +(1.00155 - 8.60215i) q^{75} +(5.44933 - 9.43852i) q^{76} +(-5.06991 - 3.10906i) q^{77} +(-0.422665 + 0.0453588i) q^{78} +(-5.84731 + 10.1278i) q^{79} +(-2.86399 + 7.31436i) q^{80} +(-0.862407 + 8.95859i) q^{81} +(-1.63913 + 0.946352i) q^{82} +(-2.97552 + 1.71792i) q^{83} +(7.93893 + 3.76848i) q^{84} +(-8.50705 - 3.33100i) q^{85} +0.0662650 q^{86} +(-10.5305 + 1.13009i) q^{87} +2.52658i q^{88} +(-2.59402 - 4.49298i) q^{89} +(0.685555 + 1.79835i) q^{90} +(-1.07931 - 1.98935i) q^{91} +(-1.67392 + 0.966438i) q^{92} +(-1.15420 + 0.123864i) q^{93} +(-1.25525 - 2.17415i) q^{94} +(7.93123 + 9.92931i) q^{95} +(-0.601731 - 5.60708i) q^{96} +(15.4265 - 8.90650i) q^{97} +(0.106384 - 2.00549i) q^{98} +(-4.53422 - 4.99168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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