LMFDB - Embedded newform 360.2.bm.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.962641 + 1.03601i) q^{2} +(-1.57528 - 0.720074i) q^{3} +(-0.146644 + 1.99462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.770419 - 2.32518i) q^{6} +(1.68164 + 0.970893i) q^{7} +(-2.20761 + 1.76818i) q^{8} +(1.96299 + 2.26863i) q^{9} +O(q^{10})$	\(q+(0.962641 + 1.03601i) q^{2} +(-1.57528 - 0.720074i) q^{3} +(-0.146644 + 1.99462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.770419 - 2.32518i) q^{6} +(1.68164 + 0.970893i) q^{7} +(-2.20761 + 1.76818i) q^{8} +(1.96299 + 2.26863i) q^{9} +(0.415893 - 1.35168i) q^{10} +(4.90205 + 2.83020i) q^{11} +(1.66728 - 3.03648i) q^{12} +(-4.57071 + 2.63890i) q^{13} +(0.612955 + 2.67682i) q^{14} +(0.164035 + 1.72427i) q^{15} +(-3.95699 - 0.584996i) q^{16} +1.68726i q^{17} +(-0.460679 + 4.21756i) q^{18} -1.99138 q^{19} +(1.80071 - 0.870311i) q^{20} +(-1.94992 - 2.74033i) q^{21} +(1.78679 + 7.80305i) q^{22} +(3.68476 + 6.38219i) q^{23} +(4.75082 - 1.19572i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-7.13389 - 2.19500i) q^{26} +(-1.45866 - 4.98721i) q^{27} +(-2.18316 + 3.21184i) q^{28} +(-1.72182 + 2.98228i) q^{29} +(-1.62845 + 1.82979i) q^{30} +(9.12573 - 5.26874i) q^{31} +(-3.20310 - 4.66263i) q^{32} +(-5.68412 - 7.98818i) q^{33} +(-1.74803 + 1.62423i) q^{34} -1.94179i q^{35} +(-4.81291 + 3.58272i) q^{36} -8.70063i q^{37} +(-1.91698 - 2.06309i) q^{38} +(9.10033 - 0.865744i) q^{39} +(2.63509 + 1.02776i) q^{40} +(-0.985576 + 0.569022i) q^{41} +(0.961935 - 4.65810i) q^{42} +(2.18806 - 3.78982i) q^{43} +(-6.36402 + 9.36268i) q^{44} +(0.983199 - 2.83431i) q^{45} +(-3.06493 + 9.96122i) q^{46} +(-1.78578 + 3.09306i) q^{47} +(5.81211 + 3.77086i) q^{48} +(-1.61473 - 2.79680i) q^{49} +(-1.37853 + 0.315665i) q^{50} +(1.21496 - 2.65791i) q^{51} +(-4.59333 - 9.50379i) q^{52} +2.77000 q^{53} +(3.76265 - 6.31209i) q^{54} -5.66040i q^{55} +(-5.42911 + 0.830071i) q^{56} +(3.13697 + 1.43394i) q^{57} +(-4.74717 + 1.08704i) q^{58} +(4.64849 - 2.68381i) q^{59} +(-3.46330 + 0.0743340i) q^{60} +(7.02634 + 4.05666i) q^{61} +(14.2433 + 4.38246i) q^{62} +(1.09843 + 5.72086i) q^{63} +(1.74711 - 7.80689i) q^{64} +(4.57071 + 2.63890i) q^{65} +(2.80409 - 13.5786i) q^{66} +(-2.52195 - 4.36814i) q^{67} +(-3.36545 - 0.247427i) q^{68} +(-1.20886 - 12.7070i) q^{69} +(2.01171 - 1.86924i) q^{70} -3.47345 q^{71} +(-8.34485 - 1.53736i) q^{72} -14.6455 q^{73} +(9.01396 - 8.37558i) q^{74} +(1.41124 - 1.00419i) q^{75} +(0.292023 - 3.97204i) q^{76} +(5.49564 + 9.51873i) q^{77} +(9.65727 + 8.59465i) q^{78} +(2.53359 + 1.46277i) q^{79} +(1.47187 + 3.71935i) q^{80} +(-1.29337 + 8.90658i) q^{81} +(-1.53827 - 0.473304i) q^{82} +(-4.94415 - 2.85451i) q^{83} +(5.75184 - 3.48750i) q^{84} +(1.46121 - 0.843632i) q^{85} +(6.03262 - 1.38139i) q^{86} +(4.85980 - 3.45807i) q^{87} +(-15.8261 + 2.41970i) q^{88} -11.1657i q^{89} +(3.88285 - 1.70982i) q^{90} -10.2484 q^{91} +(-13.2704 + 6.41377i) q^{92} +(-18.1694 + 1.72852i) q^{93} +(-4.92351 + 1.12742i) q^{94} +(0.995689 + 1.72458i) q^{95} +(1.68832 + 9.65140i) q^{96} +(1.57552 - 2.72888i) q^{97} +(1.34311 - 4.36520i) q^{98} +(3.20197 + 16.6766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.962641	+	1.03601i	0.680690	+	0.732571i
$2$	0.962641	+	1.03601i	0.680690	+	0.732571i
$3$	−1.57528	−	0.720074i	−0.909486	−	0.415735i
$3$	−1.57528	−	0.720074i	−0.909486	−	0.415735i
$4$	−0.146644	+	1.99462i	−0.0733219	+	0.997308i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.770419	−	2.32518i	−0.314522	−	0.949250i
$7$	1.68164	+	0.970893i	0.635599	+	0.366963i	0.782917	−	0.622126i	$-0.213731\pi$
$7$	1.68164	+	0.970893i	0.635599	+	0.366963i	−0.147319	+	0.989089i	$0.547064\pi$
$8$	−2.20761	+	1.76818i	−0.780509	+	0.625144i
$9$	1.96299	+	2.26863i	0.654329	+	0.756210i
$10$	0.415893	−	1.35168i	0.131517	−	0.427438i
$11$	4.90205	+	2.83020i	1.47802	+	0.853337i	0.999691	−	0.0248420i	$-0.00790825\pi$
$11$	4.90205	+	2.83020i	1.47802	+	0.853337i	0.478332	+	0.878179i	$0.341242\pi$
$12$	1.66728	−	3.03648i	0.481301	−	0.876555i
$13$	−4.57071	+	2.63890i	−1.26769	+	0.731899i	−0.974550	−	0.224171i	$-0.928032\pi$
$13$	−4.57071	+	2.63890i	−1.26769	+	0.731899i	−0.293137	+	0.956071i	$0.594699\pi$
$14$	0.612955	+	2.67682i	0.163819	+	0.715409i
$15$	0.164035	+	1.72427i	0.0423537	+	0.445204i
$16$	−3.95699	−	0.584996i	−0.989248	−	0.146249i
$17$			1.68726i			0.409222i	0.978843	+	0.204611i	$0.0655929\pi$
$17$			1.68726i			0.409222i	−0.978843	+	0.204611i	$0.934407\pi$
$18$	−0.460679	+	4.21756i	−0.108583	+	0.994087i
$19$	−1.99138			−0.456854			−0.228427	−	0.973561i	$-0.573358\pi$
$19$	−1.99138			−0.456854			−0.228427	+	0.973561i	$0.573358\pi$
$20$	1.80071	−	0.870311i	0.402651	−	0.194607i
$21$	−1.94992	−	2.74033i	−0.425508	−	0.597988i
$22$	1.78679	+	7.80305i	0.380945	+	1.66362i
$23$	3.68476	+	6.38219i	0.768326	+	1.33078i	0.938470	+	0.345360i	$0.112243\pi$
$23$	3.68476	+	6.38219i	0.768326	+	1.33078i	−0.170145	+	0.985419i	$0.554424\pi$
$24$	4.75082	−	1.19572i	0.969756	−	0.244075i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−7.13389	−	2.19500i	−1.39907	−	0.430474i
$27$	−1.45866	−	4.98721i	−0.280719	−	0.959790i
$28$	−2.18316	+	3.21184i	−0.412579	+	0.606981i
$29$	−1.72182	+	2.98228i	−0.319733	+	0.553795i	−0.980432	−	0.196856i	$-0.936927\pi$
$29$	−1.72182	+	2.98228i	−0.319733	+	0.553795i	0.660699	+	0.750651i	$0.270260\pi$
$30$	−1.62845	+	1.82979i	−0.297314	+	0.334073i
$31$	9.12573	−	5.26874i	1.63903	−	0.946294i	0.657862	−	0.753139i	$-0.271461\pi$
$31$	9.12573	−	5.26874i	1.63903	−	0.946294i	0.981168	−	0.193155i	$-0.0618721\pi$
$32$	−3.20310	−	4.66263i	−0.566233	−	0.824245i
$33$	−5.68412	−	7.98818i	−0.989479	−	1.39056i
$34$	−1.74803	+	1.62423i	−0.299784	+	0.278553i
$35$		−	1.94179i		−	0.328222i
$36$	−4.81291	+	3.58272i	−0.802152	+	0.597121i
$37$		−	8.70063i		−	1.43037i	−0.698933	−	0.715187i	$-0.746341\pi$
$37$		−	8.70063i		−	1.43037i	0.698933	−	0.715187i	$-0.253659\pi$
$38$	−1.91698	−	2.06309i	−0.310976	−	0.334678i
$39$	9.10033	−	0.865744i	1.45722	−	0.138630i
$40$	2.63509	+	1.02776i	0.416645	+	0.162503i
$41$	−0.985576	+	0.569022i	−0.153921	+	0.0888664i	−0.574982	−	0.818166i	$-0.694991\pi$
$41$	−0.985576	+	0.569022i	−0.153921	+	0.0888664i	0.421061	+	0.907032i	$0.361658\pi$
$42$	0.961935	−	4.65810i	0.148430	−	0.718760i
$43$	2.18806	−	3.78982i	0.333675	−	0.577943i	−0.649554	−	0.760315i	$-0.725044\pi$
$43$	2.18806	−	3.78982i	0.333675	−	0.577943i	0.983229	+	0.182373i	$0.0583777\pi$
$44$	−6.36402	+	9.36268i	−0.959412	+	1.41148i
$45$	0.983199	−	2.83431i	0.146567	−	0.422514i
$46$	−3.06493	+	9.96122i	−0.451899	+	1.46870i
$47$	−1.78578	+	3.09306i	−0.260482	+	0.451169i	−0.966370	−	0.257155i	$-0.917215\pi$
$47$	−1.78578	+	3.09306i	−0.260482	+	0.451169i	0.705888	+	0.708324i	$0.250548\pi$
$48$	5.81211	+	3.77086i	0.838906	+	0.544277i
$49$	−1.61473	−	2.79680i	−0.230676	−	0.399543i
$50$	−1.37853	+	0.315665i	−0.194954	+	0.0446418i
$51$	1.21496	−	2.65791i	0.170128	−	0.372181i
$52$	−4.59333	−	9.50379i	−0.636980	−	1.31794i
$53$	2.77000			0.380488			0.190244	−	0.981737i	$-0.439072\pi$
$53$	2.77000			0.380488			0.190244	+	0.981737i	$0.439072\pi$
$54$	3.76265	−	6.31209i	0.512032	−	0.858966i
$55$		−	5.66040i		−	0.763248i
$56$	−5.42911	+	0.830071i	−0.725495	+	0.110923i
$57$	3.13697	+	1.43394i	0.415502	+	0.189930i
$58$	−4.74717	+	1.08704i	−0.623334	+	0.142735i
$59$	4.64849	−	2.68381i	0.605181	−	0.349402i	−0.165896	−	0.986143i	$-0.553052\pi$
$59$	4.64849	−	2.68381i	0.605181	−	0.349402i	0.771077	+	0.636742i	$0.219718\pi$
$60$	−3.46330	+	0.0743340i	−0.447111	+	0.00959648i
$61$	7.02634	+	4.05666i	0.899631	+	0.519402i	0.877080	−	0.480344i	$-0.159488\pi$
$61$	7.02634	+	4.05666i	0.899631	+	0.519402i	0.0225502	+	0.999746i	$0.492821\pi$
$62$	14.2433	+	4.38246i	1.80890	+	0.556573i
$63$	1.09843	+	5.72086i	0.138389	+	0.720761i
$64$	1.74711	−	7.80689i	0.218389	−	0.975862i
$65$	4.57071	+	2.63890i	0.566927	+	0.327315i
$66$	2.80409	−	13.5786i	0.345159	−	1.67141i
$67$	−2.52195	−	4.36814i	−0.308105	−	0.533653i	0.669843	−	0.742503i	$-0.266361\pi$
$67$	−2.52195	−	4.36814i	−0.308105	−	0.533653i	−0.977948	+	0.208850i	$0.933028\pi$
$68$	−3.36545	−	0.247427i	−0.408120	−	0.0300049i
$69$	−1.20886	−	12.7070i	−0.145530	−	1.52974i
$70$	2.01171	−	1.86924i	0.240446	−	0.223417i
$71$	−3.47345			−0.412222			−0.206111	−	0.978529i	$-0.566081\pi$
$71$	−3.47345			−0.412222			−0.206111	+	0.978529i	$0.566081\pi$
$72$	−8.34485	−	1.53736i	−0.983450	−	0.181179i
$73$	−14.6455			−1.71412			−0.857062	−	0.515214i	$-0.827712\pi$
$73$	−14.6455			−1.71412			−0.857062	+	0.515214i	$0.827712\pi$
$74$	9.01396	−	8.37558i	1.04785	−	0.973642i
$75$	1.41124	−	1.00419i	0.162956	−	0.115954i
$76$	0.292023	−	3.97204i	0.0334974	−	0.455624i
$77$	5.49564	+	9.51873i	0.626286	+	1.08476i
$78$	9.65727	+	8.59465i	1.09347	+	0.973153i
$79$	2.53359	+	1.46277i	0.285051	+	0.164574i	0.635708	−	0.771930i	$-0.280708\pi$
$79$	2.53359	+	1.46277i	0.285051	+	0.164574i	−0.350657	+	0.936504i	$0.614042\pi$
$80$	1.47187	+	3.71935i	0.164560	+	0.415836i
$81$	−1.29337	+	8.90658i	−0.143708	+	0.989620i
$82$	−1.53827	−	0.473304i	−0.169873	−	0.0522677i
$83$	−4.94415	−	2.85451i	−0.542691	−	0.313323i	0.203478	−	0.979080i	$-0.434775\pi$
$83$	−4.94415	−	2.85451i	−0.542691	−	0.313323i	−0.746169	+	0.665757i	$0.768109\pi$
$84$	5.75184	−	3.48750i	0.627578	−	0.380517i
$85$	1.46121	−	0.843632i	0.158491	−	0.0915048i
$86$	6.03262	−	1.38139i	0.650514	−	0.148959i
$87$	4.85980	−	3.45807i	0.521025	−	0.370744i
$88$	−15.8261	+	2.41970i	−1.68707	+	0.257941i
$89$		−	11.1657i		−	1.18356i	−0.806100	−	0.591780i	$-0.798425\pi$
$89$		−	11.1657i		−	1.18356i	0.806100	−	0.591780i	$-0.201575\pi$
$90$	3.88285	−	1.70982i	0.409288	−	0.180231i
$91$	−10.2484			−1.07432
$92$	−13.2704	+	6.41377i	−1.38353	+	0.668682i
$93$	−18.1694	+	1.72852i	−1.88408	+	0.179239i
$94$	−4.92351	+	1.12742i	−0.507821	+	0.116284i
$95$	0.995689	+	1.72458i	0.102156	+	0.176939i
$96$	1.68832	+	9.65140i	0.172313	+	0.985042i
$97$	1.57552	−	2.72888i	0.159970	−	0.277076i	−0.774888	−	0.632099i	$-0.782194\pi$
$97$	1.57552	−	2.72888i	0.159970	−	0.277076i	0.934858	+	0.355023i	$0.115527\pi$
$98$	1.34311	−	4.36520i	0.135675	−	0.440952i
$99$	3.20197	+	16.6766i	0.321810	+	1.67606i
$100$	−1.65407	−	1.12431i	−0.165407	−	0.112431i
$101$	1.30429	−	2.25910i	0.129782	−	0.224789i	−0.793810	−	0.608166i	$-0.791906\pi$
$101$	1.30429	−	2.25910i	0.129782	−	0.224789i	0.923592	+	0.383377i	$0.125239\pi$
$102$	3.92319	−	1.29990i	0.388454	−	0.128709i
$103$	0.751411	−	0.433827i	0.0740387	−	0.0427463i	−0.462524	−	0.886607i	$-0.653056\pi$
$103$	0.751411	−	0.433827i	0.0740387	−	0.0427463i	0.536562	+	0.843861i	$0.319723\pi$
$104$	5.42432	−	13.9075i	0.531898	−	1.36374i
$105$	−1.39823	+	3.05885i	−0.136453	+	0.298513i
$106$	2.66651	+	2.86975i	0.258995	+	0.278735i
$107$			13.3577i			1.29134i	0.763618	+	0.645669i	$0.223421\pi$
$107$			13.3577i			1.29134i	−0.763618	+	0.645669i	$0.776579\pi$
$108$	10.1615	−	2.17812i	0.977789	−	0.209590i
$109$			2.18620i			0.209400i	0.994504	+	0.104700i	$0.0333882\pi$
$109$			2.18620i			0.209400i	−0.994504	+	0.104700i	$0.966612\pi$
$110$	5.86424	−	5.44893i	0.559134	−	0.519535i
$111$	−6.26510	+	13.7059i	−0.594657	+	1.30091i
$112$	−6.08625	−	4.82556i	−0.575096	−	0.455973i
$113$	16.0357	−	9.25822i	1.50851	−	0.870940i	0.508562	−	0.861026i	$-0.330177\pi$
$113$	16.0357	−	9.25822i	1.50851	−	0.870940i	0.999951	−	0.00991443i	$-0.00315591\pi$
$114$	1.53420	+	4.63031i	0.143691	+	0.433668i
$115$	3.68476	−	6.38219i	0.343606	−	0.595142i
$116$	−5.69600	−	3.87170i	−0.528860	−	0.359478i
$117$	−14.9589	−	5.18913i	−1.38295	−	0.479735i
$118$	7.25528	+	2.23235i	0.667903	+	0.205504i
$119$	−1.63815	+	2.83736i	−0.150169	+	0.260101i
$120$	−3.41093	−	3.51647i	−0.311374	−	0.321008i
$121$	10.5201	+	18.2213i	0.956369	+	1.65648i
$122$	2.56109	+	11.1845i	0.231871	+	1.01260i
$123$	1.96229	−	0.186679i	0.176934	−	0.0168323i
$124$	9.17089	+	18.9750i	0.823570	+	1.70400i
$125$	1.00000			0.0894427
$126$	−4.86949	+	6.64512i	−0.433809	+	0.591994i
$127$		−	12.5673i		−	1.11517i	−0.830121	−	0.557583i	$-0.811729\pi$
$127$		−	12.5673i		−	1.11517i	0.830121	−	0.557583i	$-0.188271\pi$
$128$	9.76988	−	5.70521i	0.863544	−	0.504274i
$129$	−6.17575	+	4.39445i	−0.543744	+	0.386910i
$130$	1.66602	+	7.27562i	0.146120	+	0.638114i
$131$	14.0493	−	8.11137i	1.22749	−	0.708694i	0.260989	−	0.965342i	$-0.415951\pi$
$131$	14.0493	−	8.11137i	1.22749	−	0.708694i	0.966505	+	0.256648i	$0.0826181\pi$
$132$	16.7669	−	10.1662i	1.45937	−	0.884857i
$133$	−3.34877	−	1.93341i	−0.290375	−	0.167648i
$134$	2.09772	−	6.81772i	0.181215	−	0.588961i
$135$	−3.58972	+	3.75684i	−0.308954	+	0.323338i
$136$	−2.98338	−	3.72483i	−0.255823	−	0.319401i
$137$	−1.05524	−	0.609244i	−0.0901554	−	0.0520513i	0.454244	−	0.890877i	$-0.349909\pi$
$137$	−1.05524	−	0.609244i	−0.0901554	−	0.0520513i	−0.544400	+	0.838826i	$0.683243\pi$
$138$	12.0009	−	13.4847i	1.02159	−	1.14789i
$139$	4.99600	+	8.65332i	0.423755	+	0.733965i	0.996303	−	0.0859060i	$-0.0273785\pi$
$139$	4.99600	+	8.65332i	0.423755	+	0.733965i	−0.572548	+	0.819871i	$0.694045\pi$
$140$	3.87312	+	0.284751i	0.327338	+	0.0240658i
$141$	5.04032	−	3.58652i	0.424472	−	0.302040i
$142$	−3.34368	−	3.59853i	−0.280596	−	0.301982i
$143$	−29.8744			−2.49823
$144$	−6.44038	−	10.1253i	−0.536698	−	0.843774i
$145$	3.44363			0.285978
$146$	−14.0983	−	15.1729i	−1.16679	−	1.25572i
$147$	0.529746	+	5.56846i	0.0436927	+	0.459279i
$148$	17.3544	+	1.27589i	1.42652	+	0.104878i
$149$	1.90503	+	3.29960i	0.156066	+	0.270314i	0.933447	−	0.358716i	$-0.116785\pi$
$149$	1.90503	+	3.29960i	0.156066	+	0.270314i	−0.777381	+	0.629030i	$0.783452\pi$
$150$	2.39887	+	0.495387i	0.195867	+	0.0404482i
$151$	−0.466943	−	0.269590i	−0.0379993	−	0.0219389i	0.480880	−	0.876786i	$-0.340317\pi$
$151$	−0.466943	−	0.269590i	−0.0379993	−	0.0219389i	−0.518879	+	0.854848i	$0.673651\pi$
$152$	4.39619	−	3.52111i	0.356578	−	0.285599i
$153$	−3.82778	+	3.31208i	−0.309458	+	0.267765i
$154$	−4.57119	+	14.8567i	−0.368357	+	1.19718i
$155$	−9.12573	−	5.26874i	−0.732996	−	0.423196i
$156$	0.392320	+	18.2786i	0.0314107	+	1.46346i
$157$	−13.0515	+	7.53531i	−1.04163	+	0.601384i	−0.920294	−	0.391228i	$-0.872050\pi$
$157$	−13.0515	+	7.53531i	−1.04163	+	0.601384i	−0.121333	+	0.992612i	$0.538717\pi$
$158$	0.923490	+	4.03295i	0.0734689	+	0.320844i
$159$	−4.36351	−	1.99460i	−0.346049	−	0.158182i
$160$	−2.43641	+	5.10528i	−0.192615	+	0.403608i
$161$			14.3100i			1.12779i
$162$	−10.4724	+	7.23389i	−0.822788	+	0.568348i
$163$	−12.3848			−0.970052			−0.485026	−	0.874500i	$-0.661190\pi$
$163$	−12.3848			−0.970052			−0.485026	+	0.874500i	$0.661190\pi$
$164$	−0.990453	−	2.04929i	−0.0773414	−	0.160023i
$165$	−4.07591	+	8.91669i	−0.317309	+	0.694163i
$166$	−1.80214	−	7.87006i	−0.139873	−	0.610835i
$167$	6.08840	+	10.5454i	0.471135	+	0.816029i	0.999455	−	0.0330159i	$-0.0105112\pi$
$167$	6.08840	+	10.5454i	0.471135	+	0.816029i	−0.528320	+	0.849045i	$0.677178\pi$
$168$	9.15006	+	2.60177i	0.705942	+	0.200731i
$169$	7.42758	−	12.8650i	0.571353	−	0.989612i
$170$	2.28064	+	0.701721i	0.174917	+	0.0538195i
$171$	−3.90905	−	4.51770i	−0.298932	−	0.345477i
$172$	7.23838	+	4.92009i	0.551922	+	0.375153i
$173$	3.76233	−	6.51655i	0.286045	−	0.495444i	−0.686817	−	0.726830i	$-0.740993\pi$
$173$	3.76233	−	6.51655i	0.286045	−	0.495444i	0.972862	+	0.231386i	$0.0743260\pi$
$174$	8.26084	+	1.70593i	0.626253	+	0.129326i
$175$	−1.68164	+	0.970893i	−0.127120	+	0.0733926i
$176$	−17.7417	−	14.0668i	−1.33733	−	1.06032i
$177$	−9.25519	+	0.880476i	−0.695662	+	0.0661806i
$178$	11.5678	−	10.7485i	0.867042	−	0.805638i
$179$			16.7992i			1.25563i	0.778362	+	0.627816i	$0.216051\pi$
$179$			16.7992i			1.25563i	−0.778362	+	0.627816i	$0.783949\pi$
$180$	5.50918	+	2.37674i	0.410630	+	0.177152i
$181$			1.51254i			0.112426i	0.998419	+	0.0562130i	$0.0179026\pi$
$181$			1.51254i			0.112426i	−0.998419	+	0.0562130i	$0.982097\pi$
$182$	−9.86549	−	10.6174i	−0.731279	−	0.787016i
$183$	−8.14732	−	11.4498i	−0.602267	−	0.846397i
$184$	−19.4194	−	7.57411i	−1.43161	−	0.558371i
$185$	−7.53497	+	4.35031i	−0.553982	+	0.319841i
$186$	−19.2814	−	17.1598i	−1.41378	−	1.25822i
$187$	−4.77529	+	8.27105i	−0.349204	+	0.604839i
$188$	−5.90759	−	4.01552i	−0.430855	−	0.292862i
$189$	2.38912	−	9.80288i	0.173783	−	0.713055i
$190$	−0.828199	+	2.69170i	−0.0600839	+	0.195277i
$191$	0.0785395	−	0.136034i	0.00568292	−	0.00984311i	−0.863170	−	0.504913i	$-0.831524\pi$
$191$	0.0785395	−	0.136034i	0.00568292	−	0.00984311i	0.868853	+	0.495070i	$0.164858\pi$
$192$	−8.37373	+	11.0400i	−0.604322	+	0.796740i
$193$	−8.06998	−	13.9776i	−0.580890	−	1.00613i	−0.995374	−	0.0960746i	$-0.969371\pi$
$193$	−8.06998	−	13.9776i	−0.580890	−	1.00613i	0.414484	−	0.910057i	$-0.363962\pi$
$194$	4.34381	−	0.994674i	0.311868	−	0.0714134i
$195$	−5.29992	−	7.44824i	−0.379535	−	0.533380i
$196$	5.81534	−	2.81064i	0.415381	−	0.200760i
$197$	21.2885			1.51675			0.758373	−	0.651821i	$-0.225995\pi$
$197$	21.2885			1.51675			0.758373	+	0.651821i	$0.225995\pi$
$198$	−14.1948	+	19.3708i	−1.00878	+	1.37663i
$199$		−	24.6139i		−	1.74483i	−0.488764	−	0.872416i	$-0.662552\pi$
$199$		−	24.6139i		−	1.74483i	0.488764	−	0.872416i	$-0.337448\pi$
$200$	−0.427478	−	2.79594i	−0.0302273	−	0.197703i
$201$	0.827375	+	8.69701i	0.0583586	+	0.613440i
$202$	3.59603	−	0.823441i	0.253016	−	0.0579371i
$203$	−5.79094	+	3.34340i	−0.406444	+	0.234661i
$204$	5.12334	+	2.81314i	0.358705	+	0.196959i
$205$	0.985576	+	0.569022i	0.0688356	+	0.0397422i
$206$	1.17279	+	0.360851i	0.0817121	+	0.0251417i
$207$	−7.24571	+	20.8875i	−0.503611	+	1.45178i
$208$	19.6300	−	7.76825i	1.36110	−	0.538632i
$209$	−9.76183	−	5.63600i	−0.675240	−	0.389850i
$210$	−4.51500	+	1.49599i	−0.311564	+	0.103233i
$211$	−4.63277	−	8.02419i	−0.318933	−	0.552408i	0.661333	−	0.750093i	$-0.269991\pi$
$211$	−4.63277	−	8.02419i	−0.318933	−	0.552408i	−0.980266	+	0.197685i	$0.936658\pi$
$212$	−0.406203	+	5.52508i	−0.0278981	+	0.379464i
$213$	5.47163	+	2.50114i	0.374910	+	0.171375i
$214$	−13.8387	+	12.8587i	−0.945997	+	0.879001i
$215$	−4.37611			−0.298448
$216$	12.0384	+	8.43067i	0.819111	+	0.573635i
$217$	20.4615			1.38902
$218$	−2.26493	+	2.10452i	−0.153400	+	0.142536i
$219$	23.0707	+	10.5458i	1.55897	+	0.712621i
$220$	11.2903	+	0.830063i	0.761194	+	0.0559628i
$221$	−4.45252	−	7.71199i	−0.299509	−	0.518765i
$222$	−20.2305	+	6.70313i	−1.35778	+	0.449885i
$223$	20.3660	+	11.7583i	1.36381	+	0.787396i	0.990129	−	0.140161i	$-0.0447619\pi$
$223$	20.3660	+	11.7583i	1.36381	+	0.787396i	0.373682	+	0.927557i	$0.378095\pi$
$224$	−0.859528	−	10.9507i	−0.0574296	−	0.731676i
$225$	−2.94619	+	0.565680i	−0.196412	+	0.0377120i
$226$	25.0283	+	7.70085i	1.66486	+	0.512253i
$227$	10.6659	+	6.15798i	0.707923	+	0.408720i	0.810292	−	0.586027i	$-0.199309\pi$
$227$	10.6659	+	6.15798i	0.707923	+	0.408720i	−0.102369	+	0.994747i	$0.532642\pi$
$228$	−3.32018	+	6.04677i	−0.219884	+	0.400457i
$229$	−13.1327	+	7.58218i	−0.867834	+	0.501044i	−0.866628	−	0.498955i	$-0.833717\pi$
$229$	−13.1327	+	7.58218i	−0.867834	+	0.501044i	−0.00120631	+	0.999999i	$0.500384\pi$
$230$	10.1591	−	2.32630i	0.669873	−	0.153392i
$231$	−1.80295	−	18.9519i	−0.118626	−	1.24694i
$232$	−1.47208	−	9.62818i	−0.0966467	−	0.632121i
$233$		−	3.86454i		−	0.253175i	−0.991955	−	0.126587i	$-0.959598\pi$
$233$		−	3.86454i		−	0.253175i	0.991955	−	0.126587i	$-0.0404024\pi$
$234$	−9.02408	−	20.4929i	−0.589922	−	1.33966i
$235$	3.57155			0.232982
$236$	4.67149	+	9.66551i	0.304088	+	0.629171i
$237$	−2.93780	−	4.12863i	−0.190830	−	0.268184i
$238$	−4.51650	+	1.03422i	−0.292761	+	0.0670383i
$239$	−1.83359	−	3.17587i	−0.118605	−	0.205430i	0.800610	−	0.599186i	$-0.204509\pi$
$239$	−1.83359	−	3.17587i	−0.118605	−	0.205430i	−0.919215	+	0.393756i	$0.871176\pi$
$240$	0.359604	−	6.91886i	0.0232124	−	0.446611i
$241$	−7.70335	+	13.3426i	−0.496217	+	0.859472i	−0.999990	−	0.00436319i	$-0.998611\pi$
$241$	−7.70335	+	13.3426i	−0.496217	+	0.859472i	0.503774	+	0.863836i	$0.331944\pi$
$242$	−8.75042	+	28.4395i	−0.562499	+	1.82816i
$243$	8.45082	−	13.0990i	0.542120	−	0.840301i
$244$	−9.12185	+	13.4200i	−0.583967	+	0.859125i
$245$	−1.61473	+	2.79680i	−0.103162	+	0.178681i
$246$	2.08238	+	1.85325i	0.132768	+	0.118159i
$247$	9.10201	−	5.25505i	0.579147	−	0.334371i
$248$	−10.8300	+	27.7672i	−0.687707	+	1.76322i
$249$	5.73294	+	8.05679i	0.363310	+	0.510578i
$250$	0.962641	+	1.03601i	0.0608828	+	0.0655232i
$251$		−	5.56724i		−	0.351401i	−0.984444	−	0.175701i	$-0.943781\pi$
$251$		−	5.56724i		−	0.351401i	0.984444	−	0.175701i	$-0.0562191\pi$
$252$	−11.5720	+	1.35202i	−0.728967	+	0.0851690i
$253$			41.7144i			2.62256i
$254$	13.0199	−	12.0978i	0.816939	−	0.759082i
$255$	−2.90929	+	0.276770i	−0.182187	+	0.0173320i
$256$	15.3156	+	4.62965i	0.957222	+	0.289353i
$257$	−8.06613	+	4.65698i	−0.503151	+	0.290494i	−0.730014	−	0.683432i	$-0.760486\pi$
$257$	−8.06613	+	4.65698i	−0.503151	+	0.290494i	0.226863	+	0.973927i	$0.427153\pi$
$258$	−10.4977	−	2.16787i	−0.653561	−	0.134966i
$259$	8.44738	−	14.6313i	0.524895	−	0.909144i
$260$	−5.93386	+	8.72983i	−0.368002	+	0.541401i
$261$	−10.1456	+	1.94799i	−0.627996	+	0.120578i
$262$	21.9279	+	6.74692i	1.35471	+	0.416826i
$263$	7.32317	−	12.6841i	0.451566	−	0.782135i	−0.546917	−	0.837187i	$-0.684199\pi$
$263$	7.32317	−	12.6841i	0.451566	−	0.782135i	0.998484	+	0.0550512i	$0.0175322\pi$
$264$	26.6729	+	7.58429i	1.64160	+	0.466781i
$265$	−1.38500	−	2.39889i	−0.0850797	−	0.147362i
$266$	−1.22062	−	5.33056i	−0.0748413	−	0.326837i
$267$	−8.04012	+	17.5890i	−0.492047	+	1.07643i
$268$	9.08259	−	4.38976i	0.554808	−	0.268147i
$269$	−3.38901			−0.206632			−0.103316	−	0.994649i	$-0.532945\pi$
$269$	−3.38901			−0.206632			−0.103316	+	0.994649i	$0.532945\pi$
$270$	−7.34775	−	0.102507i	−0.447170	−	0.00623837i
$271$			10.3581i			0.629209i	0.949223	+	0.314605i	$0.101872\pi$
$271$			10.3581i			0.629209i	−0.949223	+	0.314605i	$0.898128\pi$
$272$	0.987044	−	6.67649i	0.0598483	−	0.404822i
$273$	16.1440	+	7.37958i	0.977078	+	0.446632i
$274$	−0.384635	−	1.67973i	−0.0232366	−	0.101476i
$275$	−4.90205	+	2.83020i	−0.295605	+	0.170667i
$276$	25.5229	−	0.547806i	1.53630	−	0.0329740i
$277$	13.5429	+	7.81902i	0.813717	+	0.469800i	0.848245	−	0.529604i	$-0.177660\pi$
$277$	13.5429	+	7.81902i	0.813717	+	0.469800i	−0.0345283	+	0.999404i	$0.510993\pi$
$278$	−4.15560	+	13.5060i	−0.249236	+	0.810033i
$279$	29.8665	+	10.3605i	1.78806	+	0.620264i
$280$	3.43342	+	4.28671i	0.205186	+	0.256180i
$281$	−3.24900	−	1.87581i	−0.193819	−	0.111901i	0.399950	−	0.916537i	$-0.369027\pi$
$281$	−3.24900	−	1.87581i	−0.193819	−	0.111901i	−0.593769	+	0.804635i	$0.702361\pi$
$282$	8.56770	+	1.76930i	0.510199	+	0.105360i
$283$	6.58457	+	11.4048i	0.391412	+	0.677946i	0.992636	−	0.121135i	$-0.0386533\pi$
$283$	6.58457	+	11.4048i	0.391412	+	0.677946i	−0.601224	+	0.799081i	$0.705320\pi$
$284$	0.509359	−	6.92819i	0.0302249	−	0.411113i
$285$	−0.326656	−	3.43367i	−0.0193494	−	0.203393i
$286$	−28.7584	−	30.9503i	−1.70052	−	1.83013i
$287$	−2.20984			−0.130443
$288$	4.29016	−	16.4193i	0.252800	−	0.967519i
$289$	14.1531			0.832538
$290$	3.31498	+	3.56765i	0.194663	+	0.209500i
$291$	−4.44687	+	3.16425i	−0.260680	+	0.185491i
$292$	2.14767	−	29.2121i	0.125683	−	1.70951i
$293$	−6.21333	−	10.7618i	−0.362987	−	0.628711i	0.625464	−	0.780253i	$-0.284910\pi$
$293$	−6.21333	−	10.7618i	−0.362987	−	0.628711i	−0.988451	+	0.151541i	$0.951576\pi$
$294$	−5.25904	+	5.90926i	−0.306714	+	0.344635i
$295$	−4.64849	−	2.68381i	−0.270645	−	0.156257i
$296$	15.3842	+	19.2076i	0.894191	+	1.11642i
$297$	6.96439	−	28.5759i	0.404115	−	1.65814i
$298$	−1.58457	+	5.14997i	−0.0917918	+	0.298329i
$299$	−33.6839	−	19.4474i	−1.94799	−	1.12467i
$300$	1.79603	+	2.96214i	0.103694	+	0.171019i
$301$	7.35903	−	4.24874i	0.424167	−	0.244893i
$302$	−0.170200	−	0.743278i	−0.00979393	−	0.0427708i
$303$	−3.68134	+	2.61952i	−0.211488	+	0.150488i
$304$	7.87987	+	1.16495i	0.451941	+	0.0668144i
$305$		−	8.11332i		−	0.464567i
$306$	−7.11613	−	0.777288i	−0.406802	−	0.0444346i
$307$	16.6578			0.950708			0.475354	−	0.879795i	$-0.342320\pi$
$307$	16.6578			0.950708			0.475354	+	0.879795i	$0.342320\pi$
$308$	−19.7921	+	9.56583i	−1.12776	+	0.545064i
$309$	−1.49607	+	0.142326i	−0.0851083	+	0.00809663i
$310$	−3.32632	−	14.5263i	−0.188922	−	0.825037i
$311$	−15.4298	−	26.7252i	−0.874944	−	1.51545i	−0.856823	−	0.515611i	$-0.827565\pi$
$311$	−15.4298	−	26.7252i	−0.874944	−	1.51545i	−0.0181208	−	0.999836i	$-0.505768\pi$
$312$	−18.5592	+	18.0022i	−1.05071	+	1.01917i
$313$	3.99823	−	6.92513i	0.225993	−	0.391432i	−0.730624	−	0.682780i	$-0.760771\pi$
$313$	3.99823	−	6.92513i	0.225993	−	0.391432i	0.956617	+	0.291349i	$0.0941040\pi$
$314$	−20.3706	−	6.26776i	−1.14958	−	0.353710i
$315$	4.40520	−	3.81170i	0.248205	−	0.214765i
$316$	−3.28919	+	4.83903i	−0.185032	+	0.272217i
$317$	4.94005	−	8.55641i	0.277461	−	0.480576i	−0.693292	−	0.720656i	$-0.743841\pi$
$317$	4.94005	−	8.55641i	0.277461	−	0.480576i	0.970753	+	0.240081i	$0.0771739\pi$
$318$	−2.13406	−	6.44073i	−0.119672	−	0.361178i
$319$	−16.8809	+	9.74617i	−0.945147	+	0.545681i
$320$	−7.63452	+	2.39040i	−0.426783	+	0.133628i
$321$	9.61854	−	21.0421i	0.536854	−	1.17445i
$322$	−14.8254	+	13.7754i	−0.826185	+	0.767674i
$323$		−	3.35998i		−	0.186954i
$324$	−17.5755	−	3.88588i	−0.976419	−	0.215882i
$325$		−	5.27780i		−	0.292760i
$326$	−11.9221	−	12.8308i	−0.660305	−	0.710633i
$327$	1.57422	−	3.44386i	0.0870548	−	0.190446i
$328$	1.16964	−	2.99885i	0.0645825	−	0.165584i
$329$	−6.00605	+	3.46760i	−0.331124	+	0.191175i
$330$	−13.1614	+	4.36088i	−0.724513	+	0.240058i
$331$	13.5054	−	23.3921i	0.742325	−	1.28574i	−0.209109	−	0.977892i	$-0.567056\pi$
$331$	13.5054	−	23.3921i	0.742325	−	1.28574i	0.951434	−	0.307852i	$-0.0996103\pi$
$332$	6.41867	−	9.44309i	0.352270	−	0.518257i
$333$	19.7385	−	17.0792i	1.08166	−	0.935935i
$334$	−5.06424	+	16.4591i	−0.277103	+	0.900603i
$335$	−2.52195	+	4.36814i	−0.137789	+	0.238657i
$336$	6.11275	+	11.9841i	0.333478	+	0.653789i
$337$	3.46925	+	6.00893i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$337$	3.46925	+	6.00893i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$338$	20.4783	−	4.68926i	1.11388	−	0.255062i
$339$	−31.9273	+	3.03734i	−1.73405	+	0.164966i
$340$	1.46844	+	3.03828i	0.0796376	+	0.164774i
$341$	59.6464			3.23003
$342$	0.917387	−	8.39875i	0.0496066	−	0.454152i
$343$		−	19.8634i		−	1.07252i
$344$	1.87069	+	12.2353i	0.100861	+	0.659685i
$345$	−10.4002	+	7.40041i	−0.559926	+	0.398425i
$346$	10.3730	−	2.37528i	0.557656	−	0.127696i
$347$	−11.1355	+	6.42907i	−0.597784	+	0.345131i	−0.768169	−	0.640247i	$-0.778832\pi$
$347$	−11.1355	+	6.42907i	−0.597784	+	0.345131i	0.170385	+	0.985378i	$0.445499\pi$
$348$	6.18486	+	10.2005i	0.331543	+	0.546806i
$349$	13.3824	+	7.72636i	0.716346	+	0.413582i	0.813406	−	0.581696i	$-0.197611\pi$
$349$	13.3824	+	7.72636i	0.716346	+	0.413582i	−0.0970605	+	0.995278i	$0.530944\pi$
$350$	−2.62467	−	0.807574i	−0.140294	−	0.0431667i
$351$	19.8279	+	18.9458i	1.05833	+	1.01125i
$352$	−2.50556	−	31.9219i	−0.133547	−	1.70144i
$353$	7.55488	+	4.36181i	0.402105	+	0.232156i	0.687392	−	0.726287i	$-0.258755\pi$
$353$	7.55488	+	4.36181i	0.402105	+	0.232156i	−0.285287	+	0.958442i	$0.592089\pi$
$354$	−9.82161	−	8.74091i	−0.522013	−	0.464574i
$355$	1.73672	+	3.00809i	0.0921757	+	0.159653i
$356$	22.2713	+	1.63738i	1.18037	+	0.0867809i
$357$	4.62366	−	3.29004i	0.244710	−	0.174127i
$358$	−17.4042	+	16.1716i	−0.919840	+	0.854696i
$359$	−28.9896			−1.53001			−0.765005	−	0.644024i	$-0.777264\pi$
$359$	−28.9896			−1.53001			−0.765005	+	0.644024i	$0.777264\pi$
$360$	2.84103	+	7.99553i	0.149736	+	0.421401i
$361$	−15.0344			−0.791285
$362$	−1.56701	+	1.45603i	−0.0823601	+	0.0765273i
$363$	−3.45131	−	36.2787i	−0.181147	−	1.90414i
$364$	1.50286	−	20.4415i	0.0787712	−	1.07143i
$365$	7.32274	+	12.6834i	0.383290	+	0.663877i
$366$	4.01923	−	19.4628i	0.210089	−	1.01734i
$367$	−12.7828	−	7.38014i	−0.667256	−	0.385240i	0.127780	−	0.991802i	$-0.459215\pi$
$367$	−12.7828	−	7.38014i	−0.667256	−	0.385240i	−0.795036	+	0.606562i	$0.792548\pi$
$368$	−10.8470	−	27.4098i	−0.565439	−	1.42884i
$369$	−3.22557	−	1.11892i	−0.167917	−	0.0582489i
$370$	−11.7604	−	3.61853i	−0.611397	−	0.188118i
$371$	4.65812	+	2.68937i	0.241838	+	0.139625i
$372$	−0.783294	−	36.4945i	−0.0406119	−	1.89215i
$373$	8.40337	−	4.85169i	0.435110	−	0.251211i	−0.266411	−	0.963859i	$-0.585838\pi$
$373$	8.40337	−	4.85169i	0.435110	−	0.251211i	0.701521	+	0.712649i	$0.252505\pi$
$374$	−13.1658	+	3.01479i	−0.680788	+	0.155891i
$375$	−1.57528	−	0.720074i	−0.0813469	−	0.0371845i
$376$	−1.52676	−	9.98584i	−0.0787367	−	0.514980i
$377$		−	18.1748i		−	0.936050i
$378$	12.4558	−	6.96150i	0.640656	−	0.358061i
$379$	−12.6212			−0.648308			−0.324154	−	0.946004i	$-0.605080\pi$
$379$	−12.6212			−0.648308			−0.324154	+	0.946004i	$0.605080\pi$
$380$	−3.58590	+	1.73312i	−0.183953	+	0.0889071i
$381$	−9.04938	+	19.7969i	−0.463614	+	1.01423i
$382$	0.216539	−	0.0495844i	0.0110791	−	0.00253696i
$383$	1.33195	+	2.30701i	0.0680595	+	0.117883i	0.898047	−	0.439899i	$-0.144986\pi$
$383$	1.33195	+	2.30701i	0.0680595	+	0.117883i	−0.829988	+	0.557782i	$0.811653\pi$
$384$	−19.4984	+	1.95223i	−0.995025	+	0.0996244i
$385$	5.49564	−	9.51873i	0.280084	−	0.485119i
$386$	6.71249	−	21.8160i	0.341657	−	1.11041i
$387$	12.8928	−	2.47548i	0.655380	−	0.125836i
$388$	5.21203	+	3.54273i	0.264601	+	0.179855i
$389$	−10.9564	+	18.9770i	−0.555511	+	0.962173i	0.442353	+	0.896841i	$0.354144\pi$
$389$	−10.9564	+	18.9770i	−0.555511	+	0.962173i	−0.997864	+	0.0653320i	$0.979189\pi$
$390$	2.61455	−	12.6608i	0.132393	−	0.641103i
$391$	−10.7684	+	6.21716i	−0.544584	+	0.314416i
$392$	8.50995	+	3.31912i	0.429817	+	0.167641i
$393$	−27.9723	+	2.66110i	−1.41102	+	0.134235i
$394$	20.4932	+	22.0552i	1.03243	+	1.11112i
$395$		−	2.92553i		−	0.147200i
$396$	−33.7329	+	3.94119i	−1.69514	+	0.198052i
$397$		−	14.1456i		−	0.709946i	−0.934877	−	0.354973i	$-0.884490\pi$
$397$		−	14.1456i		−	0.709946i	0.934877	−	0.354973i	$-0.115510\pi$
$398$	25.5003	−	23.6943i	1.27821	−	1.18769i
$399$	3.88304	+	5.45703i	0.194395	+	0.273193i
$400$	2.48512	−	3.13436i	0.124256	−	0.156718i
$401$	−6.82670	+	3.94140i	−0.340909	+	0.196824i	−0.660674	−	0.750673i	$-0.729729\pi$
$401$	−6.82670	+	3.94140i	−0.340909	+	0.196824i	0.319765	+	0.947497i	$0.396396\pi$
$402$	−8.21375	+	9.22928i	−0.409665	+	0.460314i
$403$	−27.8074	+	48.1638i	−1.38518	+	2.39921i
$404$	4.31478	+	2.93285i	0.214668	+	0.145915i
$405$	8.36001	−	3.33320i	0.415412	−	0.165628i
$406$	−9.03840	−	2.78099i	−0.448568	−	0.138018i
$407$	24.6245	−	42.6509i	1.22059	−	2.11413i
$408$	2.01749	+	8.01588i	0.0998807	+	0.396845i
$409$	−5.29441	−	9.17019i	−0.261792	−	0.453437i	0.704926	−	0.709280i	$-0.250980\pi$
$409$	−5.29441	−	9.17019i	−0.261792	−	0.453437i	−0.966718	+	0.255844i	$0.917647\pi$
$410$	0.359241	+	1.56883i	0.0177417	+	0.0774791i
$411$	1.22360	+	1.71958i	0.0603555	+	0.0848207i
$412$	0.755129	+	1.56239i	0.0372025	+	0.0769737i
$413$	10.4227			0.512870
$414$	−28.6147	+	12.6005i	−1.40634	+	0.619283i
$415$			5.70901i			0.280244i
$416$	26.9447	+	12.8589i	1.32107	+	0.630459i
$417$	−1.63904	−	17.2289i	−0.0802640	−	0.843700i
$418$	−3.55818	−	15.5388i	−0.174036	−	0.760029i
$419$	7.56644	−	4.36849i	0.369645	−	0.213414i	−0.303658	−	0.952781i	$-0.598208\pi$
$419$	7.56644	−	4.36849i	0.369645	−	0.213414i	0.673303	+	0.739366i	$0.264875\pi$
$420$	−5.89619	−	3.23749i	−0.287704	−	0.157974i
$421$	−0.00687338	−	0.00396835i	−0.000334988	−	0.000193405i	0.499832	−	0.866122i	$-0.333395\pi$
$421$	−0.00687338	−	0.00396835i	−0.000334988	−	0.000193405i	−0.500167	+	0.865929i	$0.666728\pi$
$422$	3.85347	−	12.5240i	0.187584	−	0.609660i
$423$	−10.5225	+	2.02036i	−0.511619	+	0.0982331i
$424$	−6.11508	+	4.89784i	−0.296974	+	0.237860i
$425$	−1.46121	−	0.843632i	−0.0708793	−	0.0409222i
$426$	2.67601	+	8.07638i	0.129653	+	0.391302i
$427$	7.87716	+	13.6436i	0.381203	+	0.660262i
$428$	−26.6435	−	1.95882i	−1.28786	−	0.0946833i
$429$	47.0605	+	21.5118i	2.27210	+	1.03860i
$430$	−4.21263	−	4.53371i	−0.203151	−	0.218635i
$431$	−14.9660			−0.720885			−0.360442	−	0.932781i	$-0.617374\pi$
$431$	−14.9660			−0.720885			−0.360442	+	0.932781i	$0.617374\pi$
$432$	2.85440	+	20.5877i	0.137332	+	0.990525i
$433$	−7.84296			−0.376909			−0.188454	−	0.982082i	$-0.560348\pi$
$433$	−7.84296			−0.376909			−0.188454	+	0.982082i	$0.560348\pi$
$434$	19.6971	+	21.1984i	0.945492	+	1.01756i
$435$	−5.42467	−	2.47967i	−0.260093	−	0.118891i
$436$	−4.36062	−	0.320592i	−0.208836	−	0.0153536i
$437$	−7.33775	−	12.7094i	−0.351012	−	0.607971i
$438$	11.2832	+	34.0533i	0.539130	+	1.62713i
$439$	2.04075	+	1.17823i	0.0973995	+	0.0562336i	0.547909	−	0.836538i	$-0.315424\pi$
$439$	2.04075	+	1.17823i	0.0973995	+	0.0562336i	−0.450509	+	0.892772i	$0.648757\pi$
$440$	10.0086	+	12.4960i	0.477140	+	0.595722i
$441$	3.17521	−	9.15332i	0.151201	−	0.435872i
$442$	3.70354	−	12.0368i	0.176159	−	0.572530i
$443$	32.2073	+	18.5949i	1.53021	+	0.883469i	0.999351	+	0.0360115i	$0.0114653\pi$
$443$	32.2073	+	18.5949i	1.53021	+	0.883469i	0.530863	+	0.847458i	$0.321868\pi$
$444$	−26.4193	−	14.5064i	−1.25380	−	0.688441i
$445$	−9.66976	+	5.58284i	−0.458391	+	0.264652i
$446$	7.42340	+	32.4185i	0.351508	+	1.53506i
$447$	−0.624982	−	6.56954i	−0.0295606	−	0.310729i
$448$	10.5177	−	11.4321i	0.496913	−	0.540116i
$449$		−	18.3340i		−	0.865235i	−0.901578	−	0.432617i	$-0.857590\pi$
$449$		−	18.3340i		−	0.865235i	0.901578	−	0.432617i	$-0.142410\pi$
$450$	−3.42217	−	2.50774i	−0.161323	−	0.118216i
$451$	−6.44179			−0.303332
$452$	16.1151	+	33.3427i	0.757989	+	1.56831i
$453$	0.541440	+	0.760912i	0.0254391	+	0.0357508i
$454$	3.88772	+	16.9780i	0.182460	+	0.796816i
$455$	5.12418	+	8.87534i	0.240225	+	0.416082i
$456$	−9.46067	+	2.38113i	−0.443037	+	0.111506i
$457$	6.73581	−	11.6668i	0.315088	−	0.545748i	−0.664368	−	0.747405i	$-0.731299\pi$
$457$	6.73581	−	11.6668i	0.315088	−	0.545748i	0.979456	+	0.201657i	$0.0646327\pi$
$458$	−20.4973	−	6.30674i	−0.957777	−	0.294695i
$459$	8.41475	−	2.46115i	0.392767	−	0.114876i
$460$	12.1897	+	8.28559i	0.568347	+	0.386318i
$461$	−11.3561	+	19.6693i	−0.528905	+	0.916090i	0.470527	+	0.882386i	$0.344064\pi$
$461$	−11.3561	+	19.6693i	−0.528905	+	0.916090i	−0.999432	+	0.0337043i	$0.989270\pi$
$462$	17.8988	−	20.1118i	0.832727	−	0.935683i
$463$	−16.3988	+	9.46787i	−0.762119	+	0.440009i	−0.830056	−	0.557680i	$-0.811692\pi$
$463$	−16.3988	+	9.46787i	−0.762119	+	0.440009i	0.0679373	+	0.997690i	$0.478358\pi$
$464$	8.55784	−	10.7936i	0.397288	−	0.501079i
$465$	10.5817	+	14.8709i	0.490712	+	0.689623i
$466$	4.00372	−	3.72017i	0.185469	−	0.172334i
$467$			8.18513i			0.378763i	0.981904	+	0.189381i	$0.0606482\pi$
$467$			8.18513i			0.378763i	−0.981904	+	0.189381i	$0.939352\pi$
$468$	12.5440	−	29.0764i	0.579845	−	1.34406i
$469$		−	9.79416i		−	0.452252i
$470$	3.43812	+	3.70017i	0.158589	+	0.170676i
$471$	25.9858	−	2.47211i	1.19736	−	0.113909i
$472$	−5.51662	+	14.1441i	−0.253923	+	0.651037i
$473$	21.4519	−	12.3853i	0.986360	−	0.569475i
$474$	1.44927	−	7.01799i	0.0665672	−	0.322347i
$475$	0.995689	−	1.72458i	0.0456854	−	0.0791294i
$476$	−5.41923	−	3.68357i	−0.248390	−	0.168836i
$477$	5.43746	+	6.28410i	0.248964	+	0.287729i
$478$	1.52515	−	4.95684i	0.0697588	−	0.226721i
$479$	−9.94391	+	17.2234i	−0.454349	+	0.786955i	−0.998651	−	0.0519342i	$-0.983461\pi$
$479$	−9.94391	+	17.2234i	−0.454349	+	0.786955i	0.544302	+	0.838890i	$0.316795\pi$
$480$	7.51420	−	6.28783i	0.342975	−	0.286999i
$481$	22.9601	+	39.7680i	1.04689	+	1.81327i
$482$	−21.2387	+	4.86337i	−0.967395	+	0.221520i
$483$	10.3043	−	22.5422i	0.468861	−	1.02571i
$484$	−37.8871	+	18.3114i	−1.72214	+	0.832338i
$485$	−3.15104			−0.143081
$486$	21.7058	−	3.85447i	0.984596	−	0.174842i
$487$		−	2.52636i		−	0.114480i	−0.998360	−	0.0572401i	$-0.981770\pi$
$487$		−	2.52636i		−	0.114480i	0.998360	−	0.0572401i	$-0.0182301\pi$
$488$	−22.6843	+	3.46827i	−1.02687	+	0.157001i
$489$	19.5095	+	8.91798i	0.882249	+	0.403285i
$490$	−4.45193	+	1.01943i	−0.201118	+	0.0460532i
$491$	2.49209	−	1.43881i	0.112466	−	0.0649324i	−0.442712	−	0.896664i	$-0.645983\pi$
$491$	2.49209	−	1.43881i	0.112466	−	0.0649324i	0.555178	+	0.831732i	$0.312650\pi$
$492$	0.0845954	+	3.94139i	0.00381386	+	0.177692i
$493$	−5.03189	−	2.90516i	−0.226625	−	0.130842i
$494$	14.2063	+	4.37107i	0.639170	+	0.196664i
$495$	12.8414	−	11.1113i	0.577176	−	0.499415i
$496$	−39.1926	+	15.5099i	−1.75980	+	0.696413i
$497$	−5.84107	−	3.37234i	−0.262008	−	0.151270i
$498$	−2.82817	+	13.6952i	−0.126733	+	0.613696i
$499$	−9.74886	−	16.8855i	−0.436419	−	0.755900i	0.560991	−	0.827822i	$-0.310420\pi$
$499$	−9.74886	−	16.8855i	−0.436419	−	0.755900i	−0.997410	+	0.0719219i	$0.977087\pi$
$500$	−0.146644	+	1.99462i	−0.00655811	+	0.0892020i
$501$	−1.99742	−	20.9961i	−0.0892383	−	0.938034i
$502$	5.76773	−	5.35926i	0.257426	−	0.239195i
$503$	26.6990			1.19045			0.595225	−	0.803559i	$-0.297063\pi$
$503$	26.6990			1.19045			0.595225	+	0.803559i	$0.297063\pi$
$504$	−12.5404	−	10.6872i	−0.558593	−	0.476047i
$505$	−2.60859			−0.116081
$506$	−43.2167	+	40.1560i	−1.92121	+	1.78515i
$507$	−20.9642	+	14.9174i	−0.931053	+	0.662506i
$508$	25.0669	+	1.84291i	1.11216	+	0.0817661i
$509$	−17.0441	−	29.5212i	−0.755465	−	1.30850i	−0.945143	−	0.326657i	$-0.894078\pi$
$509$	−17.0441	−	29.5212i	−0.755465	−	1.30850i	0.189678	−	0.981846i	$-0.439256\pi$
$510$	−3.08734	−	2.74763i	−0.136710	−	0.121667i
$511$	−24.6284	−	14.2192i	−1.08949	−	0.629020i
$512$	9.94701	+	20.3238i	0.439600	+	0.898194i
$513$	2.90474	+	9.93143i	0.128248	+	0.438483i
$514$	−12.5895	−	3.87361i	−0.555298	−	0.170857i
$515$	−0.751411	−	0.433827i	−0.0331111	−	0.0191167i
$516$	−7.85962	−	12.9627i	−0.346000	−	0.570650i
$517$	−17.5079	+	10.1082i	−0.769998	+	0.444558i
$518$	23.2900	−	5.33309i	1.02330	−	0.234323i
$519$	−10.6191	+	7.55621i	−0.466127	+	0.331681i
$520$	−14.7564	+	2.25614i	−0.647111	+	0.0989385i
$521$			27.3159i			1.19673i	0.801223	+	0.598366i	$0.204183\pi$
$521$			27.3159i			1.19673i	−0.801223	+	0.598366i	$0.795817\pi$
$522$	−11.7847	−	8.63573i	−0.515803	−	0.377976i
$523$	24.9239			1.08985			0.544924	−	0.838486i	$-0.316559\pi$
$523$	24.9239			1.08985			0.544924	+	0.838486i	$0.316559\pi$
$524$	14.1188	+	29.2125i	0.616784	+	1.27615i
$525$	3.34815	−	0.318521i	0.146125	−	0.0139014i
$526$	20.1905	−	4.62334i	0.880347	−	0.201587i
$527$	8.88976	+	15.3975i	0.387244	+	0.670727i
$528$	17.8190	+	34.9344i	0.775471	+	1.52032i
$529$	−15.6549	+	27.1151i	−0.680648	+	1.17892i
$530$	1.15202	−	3.74414i	0.0500406	−	0.162635i
$531$	15.2135	+	5.27743i	0.660209	+	0.229021i
$532$	4.34750	−	6.39599i	0.188488	−	0.277302i
$533$	3.00319	−	5.20167i	0.130082	−	0.225309i
$534$	−25.9622	+	8.60225i	−1.12349	+	0.372256i
$535$	11.5681	−	6.67885i	0.500133	−	0.288752i
$536$	13.2911	+	5.18392i	0.574089	+	0.223911i
$537$	12.0967	−	26.4634i	0.522010	−	1.14198i
$538$	−3.26240	−	3.51106i	−0.140652	−	0.151372i
$539$		−	18.2801i		−	0.787379i
$540$	−6.96705	−	7.71104i	−0.299814	−	0.331830i
$541$			13.8058i			0.593560i	0.954946	+	0.296780i	$0.0959127\pi$
$541$			13.8058i			0.593560i	−0.954946	+	0.296780i	$0.904087\pi$
$542$	−10.7311	+	9.97112i	−0.460941	+	0.428296i
$543$	1.08914	−	2.38266i	0.0467395	−	0.102250i
$544$	7.86710	−	5.40448i	0.337299	−	0.231715i
$545$	1.89330	−	1.09310i	0.0811001	−	0.0468232i
$546$	7.89553	+	23.8293i	0.337897	+	1.01980i
$547$	−5.70216	+	9.87644i	−0.243807	+	0.422286i	−0.961795	−	0.273769i	$-0.911730\pi$
$547$	−5.70216	+	9.87644i	−0.243807	+	0.422286i	0.717989	+	0.696055i	$0.245063\pi$
$548$	1.36995	−	2.01546i	0.0585215	−	0.0860963i
$549$	4.58954	+	23.9033i	0.195877	+	1.02017i
$550$	−7.65104	−	2.35412i	−0.326241	−	0.100380i
$551$	3.42879	−	5.93884i	0.146071	−	0.253003i
$552$	25.1369	+	25.9147i	1.06990	+	1.10300i
$553$	2.84038	+	4.91968i	0.120785	+	0.209206i
$554$	4.93639	+	21.5576i	0.209727	+	0.915893i
$555$	15.0022	−	1.42721i	0.636808	−	0.0605816i
$556$	−17.9927	+	8.69614i	−0.763060	+	0.368799i
$557$	−35.3259			−1.49681			−0.748404	−	0.663243i	$-0.769180\pi$
$557$	−35.3259			−1.49681			−0.748404	+	0.663243i	$0.769180\pi$
$558$	18.0172	+	40.9155i	0.762728	+	1.73209i
$559$			23.0962i			0.976867i
$560$	−1.13594	+	7.68363i	−0.0480021	+	0.324693i
$561$	13.4782	−	9.59062i	0.569049	−	0.404916i
$562$	−1.18426	−	5.17173i	−0.0499548	−	0.218156i
$563$	−26.1337	+	15.0883i	−1.10140	+	0.635895i	−0.936589	−	0.350430i	$-0.886036\pi$
$563$	−26.1337	+	15.0883i	−1.10140	+	0.635895i	−0.164813	+	0.986325i	$0.552702\pi$
$564$	6.41461	+	10.5794i	0.270104	+	0.445475i
$565$	−16.0357	−	9.25822i	−0.674627	−	0.389496i
$566$	−5.47695	+	17.8004i	−0.230213	+	0.748209i
$567$	−10.8223	+	13.7219i	−0.454495	+	0.576265i
$568$	7.66802	−	6.14166i	0.321743	−	0.257698i
$569$	−21.8569	−	12.6191i	−0.916290	−	0.529020i	−0.0338402	−	0.999427i	$-0.510774\pi$
$569$	−21.8569	−	12.6191i	−0.916290	−	0.529020i	−0.882450	+	0.470407i	$0.844107\pi$
$570$	3.24287	−	3.64381i	0.135829	−	0.152622i
$571$	−20.7513	−	35.9423i	−0.868415	−	1.50414i	−0.863616	−	0.504150i	$-0.831806\pi$
$571$	−20.7513	−	35.9423i	−0.868415	−	1.50414i	−0.00479825	−	0.999988i	$-0.501527\pi$
$572$	4.38090	−	59.5881i	0.183175	−	2.49150i
$573$	−0.221676	+	0.157737i	−0.00926066	+	0.00658958i
$574$	−2.12728	−	2.28942i	−0.0887910	−	0.0955586i
$575$	−7.36952			−0.307330
$576$	21.1405	−	11.3613i	0.880855	−	0.473386i
$577$	−38.5939			−1.60669			−0.803343	−	0.595517i	$-0.796947\pi$
$577$	−38.5939			−1.60669			−0.803343	+	0.595517i	$0.796947\pi$
$578$	13.6244	+	14.6628i	0.566700	+	0.609893i
$579$	2.64752	+	27.8296i	0.110027	+	1.15656i
$580$	−0.504988	+	6.86873i	−0.0209685	+	0.285209i
$581$	−5.54284	−	9.60048i	−0.229956	−	0.398295i
$582$	−7.55894	−	1.56098i	−0.313328	−	0.0647048i
$583$	13.5787	+	7.83964i	0.562370	+	0.324685i
$584$	32.3315	−	25.8958i	1.33789	−	1.07157i
$585$	2.98555	+	15.5494i	0.123437	+	0.642887i
$586$	5.16816	−	16.7968i	0.213495	−	0.693871i
$587$	21.5190	+	12.4240i	0.888186	+	0.512794i	0.873349	−	0.487096i	$-0.161944\pi$
$587$	21.5190	+	12.4240i	0.888186	+	0.512794i	0.0148372	+	0.999890i	$0.495277\pi$
$588$	−11.1846	+	0.240059i	−0.461246	+	0.00989988i
$589$	−18.1728	+	10.4921i	−0.748797	+	0.432318i
$590$	−1.69437	−	7.39943i	−0.0697561	−	0.304630i
$591$	−33.5353	−	15.3293i	−1.37946	−	0.630564i
$592$	−5.08984	+	34.4283i	−0.209191	+	1.41499i
$593$			24.4900i			1.00569i	0.864378	+	0.502843i	$0.167713\pi$
$593$			24.4900i			1.00569i	−0.864378	+	0.502843i	$0.832287\pi$
$594$	36.3092	−	20.2931i	1.48978	−	0.832637i
$595$	3.27631			0.134315
$596$	−6.86080	+	3.31593i	−0.281029	+	0.135826i
$597$	−17.7238	+	38.7737i	−0.725388	+	1.58690i
$598$	−12.2778	−	53.6179i	−0.502075	−	2.19260i
$599$	6.86374	+	11.8883i	0.280445	+	0.485744i	0.971494	−	0.237063i	$-0.0761848\pi$
$599$	6.86374	+	11.8883i	0.280445	+	0.485744i	−0.691050	+	0.722807i	$0.742851\pi$
$600$	−1.33989	+	4.71219i	−0.0547006	+	0.192374i
$601$	−7.42873	+	12.8669i	−0.303024	+	0.524853i	−0.976819	−	0.214065i	$-0.931330\pi$
$601$	−7.42873	+	12.8669i	−0.303024	+	0.524853i	0.673795	+	0.738918i	$0.264663\pi$
$602$	11.4858	+	3.53404i	0.468128	+	0.144037i
$603$	4.95915	−	14.2960i	0.201952	−	0.582177i
$604$	0.606203	−	0.891839i	0.0246660	−	0.0362884i
$605$	10.5201	−	18.2213i	0.427701	−	0.740800i
$606$	−6.25767	−	1.29226i	−0.254200	−	0.0524945i
$607$	−7.18195	+	4.14650i	−0.291506	+	0.168301i	−0.638621	−	0.769522i	$-0.720495\pi$
$607$	−7.18195	+	4.14650i	−0.291506	+	0.168301i	0.347115	+	0.937823i	$0.387161\pi$
$608$	6.37858	+	9.28507i	0.258686	+	0.376559i
$609$	11.5298	−	1.09687i	0.467212	−	0.0444474i
$610$	8.40550	−	7.81021i	0.340329	−	0.316226i
$611$		−	18.8499i		−	0.762587i
$612$	−6.04500	−	8.12065i	−0.244355	−	0.328258i
$613$		−	43.3001i		−	1.74888i	−0.485137	−	0.874438i	$-0.661230\pi$
$613$		−	43.3001i		−	1.74888i	0.485137	−	0.874438i	$-0.338770\pi$
$614$	16.0354	+	17.2576i	0.647138	+	0.696462i
$615$	−1.14281	−	1.60605i	−0.0460827	−	0.0647624i
$616$	−28.9630	−	11.2964i	−1.16695	−	0.455145i
$617$	−7.21095	+	4.16324i	−0.290302	+	0.167606i	−0.638078	−	0.769972i	$-0.720270\pi$
$617$	−7.21095	+	4.16324i	−0.290302	+	0.167606i	0.347776	+	0.937578i	$0.386937\pi$
$618$	−1.58763	−	1.41294i	−0.0638637	−	0.0568366i
$619$	0.952456	−	1.64970i	0.0382824	−	0.0663071i	−0.846249	−	0.532787i	$-0.821145\pi$
$619$	0.952456	−	1.64970i	0.0382824	−	0.0663071i	0.884532	+	0.466480i	$0.154478\pi$
$620$	11.8474	−	17.4297i	0.475801	−	0.699994i
$621$	26.4545	−	27.6861i	1.06158	−	1.11101i
$622$	12.8343	−	41.7122i	0.514608	−	1.67251i
$623$	10.8407	−	18.7766i	0.434323	−	0.752269i
$624$	−36.5164	−	1.89792i	−1.46183	−	0.0759776i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.0234	−	2.52421i	0.440583	−	0.100888i
$627$	11.3192	+	15.9075i	0.452047	+	0.635284i
$628$	−13.1161	−	27.1378i	−0.523391	−	1.08292i
$629$	14.6803			0.585340
$630$	8.18959	+	0.894540i	0.326281	+	0.0356393i
$631$			2.74380i			0.109229i	0.998508	+	0.0546144i	$0.0173930\pi$
$631$			2.74380i			0.109229i	−0.998508	+	0.0546144i	$0.982607\pi$
$632$	−8.17961	+	1.25060i	−0.325367	+	0.0497463i
$633$	1.51987	+	15.9762i	0.0604095	+	0.634998i
$634$	13.6200	−	3.11880i	0.540921	−	0.123864i
$635$	−10.8836	+	6.28364i	−0.431902	+	0.249359i
$636$	4.61835	−	8.41103i	0.183129	−	0.333519i
$637$	14.7610	+	8.52224i	0.584851	+	0.337664i
$638$	−26.3474	−	8.10672i	−1.04310	−	0.320948i
$639$	−6.81832	−	7.87997i	−0.269729	−	0.311727i
$640$	−9.82580	−	5.60836i	−0.388399	−	0.221690i
$641$	6.58174	+	3.79997i	0.259963	+	0.150090i	0.624318	−	0.781171i	$-0.285377\pi$
$641$	6.58174	+	3.79997i	0.259963	+	0.150090i	−0.364355	+	0.931260i	$0.618710\pi$
$642$	31.0590	−	10.2910i	1.22580	−	0.406154i
$643$	14.3215	+	24.8055i	0.564783	+	0.978233i	0.997070	+	0.0764968i	$0.0243735\pi$
$643$	14.3215	+	24.8055i	0.564783	+	0.978233i	−0.432287	+	0.901736i	$0.642293\pi$
$644$	−28.5430	−	2.09848i	−1.12475	−	0.0826916i
$645$	6.89358	+	3.15113i	0.271435	+	0.124075i
$646$	3.48098	−	3.23446i	0.136957	−	0.127258i
$647$	−22.7326			−0.893711			−0.446856	−	0.894606i	$-0.647456\pi$
$647$	−22.7326			−0.893711			−0.446856	+	0.894606i	$0.647456\pi$
$648$	−12.8931	−	21.9492i	−0.506490	−	0.862246i
$649$	30.3828			1.19263
$650$	5.46787	−	5.08063i	0.214467	−	0.199279i
$651$	−32.2326	−	14.7338i	−1.26329	−	0.577464i
$652$	1.81615	−	24.7029i	0.0711261	−	0.967441i
$653$	−18.5268	−	32.0894i	−0.725010	−	1.25575i	−0.958970	−	0.283508i	$-0.908502\pi$
$653$	−18.5268	−	32.0894i	−0.725010	−	1.25575i	0.233960	−	0.972246i	$-0.424832\pi$
$654$	5.08330	−	1.68429i	0.198773	−	0.0658608i
$655$	−14.0493	−	8.11137i	−0.548952	−	0.316938i
$656$	4.23279	−	1.67506i	0.165263	−	0.0654000i
$657$	−28.7489	−	33.2252i	−1.12160	−	1.29624i
$658$	−9.37414	−	2.88429i	−0.365442	−	0.112441i
$659$	−7.41998	−	4.28392i	−0.289041	−	0.166878i	0.348468	−	0.937321i	$-0.386702\pi$
$659$	−7.41998	−	4.28392i	−0.289041	−	0.166878i	−0.637509	+	0.770443i	$0.720035\pi$
$660$	−17.1877	−	9.43745i	−0.669029	−	0.367352i
$661$	0.666156	−	0.384605i	0.0259105	−	0.0149594i	−0.486989	−	0.873408i	$-0.661905\pi$
$661$	0.666156	−	0.384605i	0.0259105	−	0.0149594i	0.512899	+	0.858449i	$0.328571\pi$
$662$	37.2354	−	8.52639i	1.44719	−	0.331388i
$663$	1.46074	+	15.3547i	0.0567304	+	0.596326i
$664$	15.9620	−	2.44048i	0.619447	−	0.0947089i
$665$			3.86683i			0.149949i
$666$	36.6954	+	4.00820i	1.42192	+	0.155315i
$667$	−25.3779			−0.982638
$668$	−21.9269	+	10.5976i	−0.848377	+	0.410034i
$669$	−23.6152	−	33.1877i	−0.913018	−	1.28311i
$670$	−6.95318	+	1.59218i	−0.268625	+	0.0615114i
$671$	22.9623	+	39.7719i	0.886450	+	1.53538i
$672$	−6.53134	+	17.8693i	−0.251952	+	0.689324i
$673$	−2.74156	+	4.74853i	−0.105679	+	0.183042i	−0.914016	−	0.405679i	$-0.867035\pi$
$673$	−2.74156	+	4.74853i	−0.105679	+	0.183042i	0.808336	+	0.588721i	$0.200368\pi$
$674$	−2.88567	+	9.37863i	−0.111152	+	0.361251i
$675$	5.04838	+	1.23037i	0.194312	+	0.0473570i
$676$	24.5714	+	16.7017i	0.945055	+	0.642375i
$677$	−19.9401	+	34.5373i	−0.766362	+	1.32738i	0.173162	+	0.984893i	$0.444602\pi$
$677$	−19.9401	+	34.5373i	−0.766362	+	1.32738i	−0.939524	+	0.342484i	$0.888732\pi$
$678$	−33.8812	−	30.1532i	−1.30120	−	1.15803i
$679$	5.29890	−	3.05932i	0.203353	−	0.117406i
$680$	−1.73411	+	4.44610i	−0.0664999	+	0.170500i
$681$	−12.3676	−	17.3808i	−0.473927	−	0.666033i
$682$	57.4181	+	61.7944i	2.19865	+	2.36623i
$683$			23.9517i			0.916486i	0.888827	+	0.458243i	$0.151521\pi$
$683$			23.9517i			0.916486i	−0.888827	+	0.458243i	$0.848479\pi$
$684$	9.58432	−	7.13456i	0.366466	−	0.272797i
$685$			1.21849i			0.0465561i
$686$	20.5788	−	19.1214i	0.785701	−	0.730057i
$687$	26.1474	−	2.48748i	0.997585	−	0.0949035i
$688$	−10.8752	+	13.7163i	−0.414611	+	0.522929i
$689$	−12.6608	+	7.30974i	−0.482340	+	0.278479i
$690$	−17.6785	−	3.65076i	−0.673011	−	0.138982i
$691$	3.16453	−	5.48113i	0.120384	−	0.208512i	−0.799535	−	0.600620i	$-0.794921\pi$
$691$	3.16453	−	5.48113i	0.120384	−	0.208512i	0.919919	+	0.392108i	$0.128254\pi$
$692$	12.4463	+	8.46003i	0.473137	+	0.321602i
$693$	−10.8066	+	31.1527i	−0.410510	+	1.18339i
$694$	−17.3801	−	5.34761i	−0.659739	−	0.202992i
$695$	4.99600	−	8.65332i	0.189509	−	0.328239i
$696$	−4.61408	+	16.2270i	−0.174896	+	0.615085i
$697$	−0.960091	−	1.66293i	−0.0363660	−	0.0629878i
$698$	4.87789	+	21.3021i	0.184631	+	0.806296i
$699$	−2.78276	+	6.08772i	−0.105254	+	0.230259i
$700$	−1.68996	−	3.49659i	−0.0638744	−	0.132159i
$701$	−50.6661			−1.91363			−0.956816	−	0.290695i	$-0.906114\pi$
$701$	−50.6661			−1.91363			−0.956816	+	0.290695i	$0.906114\pi$
$702$	−0.541011	+	38.7800i	−0.0204191	+	1.46366i
$703$			17.3262i			0.653472i
$704$	30.6595	−	33.3251i	1.15552	−	1.25599i
$705$	−5.62618	−	2.57178i	−0.211894	−	0.0968590i
$706$	2.75375	+	12.0258i	0.103639	+	0.452597i
$707$	4.38669	−	2.53266i	0.164979	−	0.0952504i
$708$	−0.398996	−	18.5897i	−0.0149952	−	0.698642i
$709$	−42.8358	−	24.7313i	−1.60873	−	0.928802i	−0.989654	−	0.143474i	$-0.954173\pi$
$709$	−42.8358	−	24.7313i	−1.60873	−	0.928802i	−0.619079	−	0.785329i	$-0.712494\pi$
$710$	−1.44458	+	4.69498i	−0.0542141	+	0.176199i
$711$	1.65492	+	8.61917i	0.0620642	+	0.323244i
$712$	19.7429	+	24.6495i	0.739896	+	0.923779i
$713$	67.2523	+	38.8281i	2.51862	+	1.45412i
$714$	7.85944	+	1.62304i	0.294132	+	0.0607407i
$715$	14.9372	+	25.8720i	0.558620	+	0.967559i
$716$	−33.5080	−	2.46350i	−1.25225	−	0.0920653i
$717$	0.601546	+	6.32319i	0.0224651	+	0.236144i
$718$	−27.9065	−	30.0335i	−1.04146	−	1.12084i
$719$	21.7260			0.810244			0.405122	−	0.914263i	$-0.367229\pi$
$719$	21.7260			0.810244			0.405122	+	0.914263i	$0.367229\pi$
$720$	−5.54857	+	10.6402i	−0.206783	+	0.396536i
$721$	1.68480			0.0627452
$722$	−14.4727	−	15.5758i	−0.538620	−	0.579673i
$723$	21.7426	−	15.4713i	0.808615	−	0.575383i
$724$	−3.01693	−	0.221804i	−0.112123	−	0.00824330i
$725$	−1.72182	−	2.98228i	−0.0639467	−	0.110759i
$726$	34.2629	−	38.4990i	1.27161	−	1.42883i
$727$	38.0114	+	21.9459i	1.40977	+	0.813929i	0.995365	−	0.0961659i	$-0.0306579\pi$
$727$	38.0114	+	21.9459i	1.40977	+	0.813929i	0.414401	+	0.910095i	$0.363991\pi$
$728$	22.6244	−	18.1209i	0.838516	−	0.671605i
$729$	−22.7446	+	14.5493i	−0.842393	+	0.538863i
$730$	−6.09094	+	19.7960i	−0.225436	+	0.732682i
$731$	6.39444	+	3.69183i	0.236507	+	0.136547i
$732$	24.0328	−	14.5717i	0.888278	−	0.538587i
$733$	−17.5181	+	10.1141i	−0.647045	+	0.373572i	−0.787323	−	0.616540i	$-0.788534\pi$
$733$	−17.5181	+	10.1141i	−0.647045	+	0.373572i	0.140278	+	0.990112i	$0.455200\pi$
$734$	−4.65931	−	20.3475i	−0.171978	−	0.751042i
$735$	4.55756	−	3.24300i	0.168108	−	0.119620i
$736$	17.9552	−	37.6235i	0.661836	−	1.38682i
$737$		−	28.5505i		−	1.05167i
$738$	−1.94585	−	4.41886i	−0.0716277	−	0.162660i
$739$	44.4840			1.63637			0.818186	−	0.574954i	$-0.194980\pi$
$739$	44.4840			1.63637			0.818186	+	0.574954i	$0.194980\pi$
$740$	−7.57225	−	15.6673i	−0.278362	−	0.575942i
$741$	−18.1222	+	1.72402i	−0.665736	+	0.0633336i
$742$	1.69788	+	7.41477i	0.0623312	+	0.272205i
$743$	−4.59016	−	7.95039i	−0.168397	−	0.291671i	0.769460	−	0.638695i	$-0.220526\pi$
$743$	−4.59016	−	7.95039i	−0.168397	−	0.291671i	−0.937856	+	0.347024i	$0.887192\pi$
$744$	37.0547	−	35.9426i	1.35849	−	1.31772i
$745$	1.90503	−	3.29960i	0.0697948	−	0.120888i
$746$	13.1158	+	4.03556i	0.480205	+	0.147752i
$747$	−3.22947	−	16.8198i	−0.118160	−	0.615404i
$748$	−15.7973	−	10.7378i	−0.577607	−	0.392612i
$749$	−12.9689	+	22.4628i	−0.473873	+	0.820772i
$750$	−0.770419	−	2.32518i	−0.0281317	−	0.0849035i
$751$	−33.1031	+	19.1121i	−1.20795	+	0.697409i	−0.962311	−	0.271952i	$-0.912331\pi$
$751$	−33.1031	+	19.1121i	−1.20795	+	0.697409i	−0.245638	+	0.969362i	$0.578997\pi$
$752$	8.87573	−	11.1945i	0.323665	−	0.408222i
$753$	−4.00883	+	8.76994i	−0.146090	+	0.319594i
$754$	18.8293	−	17.4958i	0.685724	−	0.637160i
$755$			0.539180i			0.0196228i
$756$	19.2026	+	6.20290i	0.698393	+	0.225597i
$757$		−	18.2503i		−	0.663319i	−0.943399	−	0.331660i	$-0.892391\pi$
$757$		−	18.2503i		−	0.663319i	0.943399	−	0.331660i	$-0.107609\pi$
$758$	−12.1497	−	13.0757i	−0.441297	−	0.474932i
$759$	30.0375	−	65.7117i	1.09029	−	2.38518i
$760$	−5.24746	−	2.04666i	−0.190346	−	0.0742402i
$761$	−44.9446	+	25.9488i	−1.62924	+	0.940642i	−0.644920	+	0.764250i	$0.723109\pi$
$761$	−44.9446	+	25.9488i	−1.62924	+	0.940642i	−0.984320	+	0.176392i	$0.943557\pi$
$762$	−29.2212	+	9.68207i	−1.05857	+	0.350744i
$763$	−2.12256	+	3.67638i	−0.0768419	+	0.133094i
$764$	0.259819	+	0.176605i	0.00939993	+	0.00638934i
$765$	4.78223	+	1.65892i	0.172902	+	0.0599783i
$766$	−1.10790	+	3.60074i	−0.0400300	+	0.130100i
$767$	−14.1646	+	24.5338i	−0.511454	+	0.885863i
$768$	−20.7925	−	18.3213i	−0.750286	−	0.661114i
$769$	−7.16847	−	12.4162i	−0.258502	−	0.447738i	0.707339	−	0.706874i	$-0.249895\pi$
$769$	−7.16847	−	12.4162i	−0.258502	−	0.447738i	−0.965841	+	0.259137i	$0.916562\pi$
$770$	15.1518	−	3.46957i	0.546035	−	0.125035i
$771$	16.0597	−	1.52782i	0.578378	−	0.0550229i
$772$	29.0634	−	14.0468i	1.04602	−	0.505555i
$773$	−4.10069			−0.147492			−0.0737458	−	0.997277i	$-0.523495\pi$
$773$	−4.10069			−0.147492			−0.0737458	+	0.997277i	$0.523495\pi$
$774$	14.9758	+	10.9741i	0.538294	+	0.394457i
$775$			10.5375i			0.378518i
$776$	1.34700	+	8.81010i	0.0483545	+	0.316264i
$777$	−23.8426	+	16.9656i	−0.855347	+	0.608636i
$778$	−30.2075	+	6.91711i	−1.08299	+	0.247990i
$779$	1.96265	−	1.13314i	0.0703194	−	0.0405989i
$780$	15.6336	−	9.47907i	0.559772	−	0.339405i
$781$	−17.0270	−	9.83054i	−0.609274	−	0.351764i
$782$	−16.8072	−	5.17135i	−0.601025	−	0.184927i
$783$	17.3848	+	4.23695i	0.621282	+	0.151416i
$784$	4.75337	+	12.0115i	0.169763	+	0.428983i
$785$	13.0515	+	7.53531i	0.465830	+	0.268947i
$786$	−29.6842	−	26.4180i	−1.05880	−	0.942299i
$787$	−7.77816	−	13.4722i	−0.277262	−	0.480231i	0.693442	−	0.720513i	$-0.256094\pi$
$787$	−7.77816	−	13.4722i	−0.277262	−	0.480231i	−0.970703	+	0.240282i	$0.922760\pi$
$788$	−3.12183	+	42.4625i	−0.111211	+	1.51266i
$789$	−20.6695	+	14.7077i	−0.735854	+	0.523609i
$790$	3.03089	−	2.81624i	0.107834	−	0.100197i
$791$	35.9550			1.27841
$792$	−36.5558	−	31.1538i	−1.29896	−	1.10700i
$793$	−42.8205			−1.52060
$794$	14.6550	−	13.6171i	0.520086	−	0.483253i
$795$	0.454376	+	4.77621i	0.0161151	+	0.169395i
$796$	49.0953	+	3.60948i	1.74014	+	0.127934i
$797$	−18.9543	−	32.8298i	−0.671395	−	1.16289i	−0.977509	−	0.210895i	$-0.932362\pi$
$797$	−18.9543	−	32.8298i	−0.671395	−	1.16289i	0.306113	−	0.951995i	$-0.400971\pi$
$798$	−1.91558	+	9.27603i	−0.0678107	+	0.328368i
$799$	−5.21880	−	3.01308i	−0.184628	−	0.106595i
$800$	5.63951	−	0.442648i	0.199387	−	0.0156500i
$801$	25.3308	−	21.9181i	0.895020	−	0.774437i
$802$	−10.6550	−	3.27839i	−0.376241	−	0.115764i
$803$	−71.7928	−	41.4496i	−2.53351	−	1.46273i
$804$	−17.4685	+	0.374933i	−0.616068	+	0.0132229i
$805$	12.3928	−	7.15501i	0.436790	−	0.252181i
$806$	−76.6668	+	17.5557i	−2.70047	+	0.618372i
$807$	5.33862	+	2.44034i	0.187928	+	0.0859040i
$808$	1.11511	+	7.29345i	0.0392296	+	0.256583i
$809$			34.2344i			1.20362i	0.798641	+	0.601808i	$0.205553\pi$
$809$			34.2344i			1.20362i	−0.798641	+	0.601808i	$0.794447\pi$
$810$	11.5009	+	5.45241i	0.404101	+	0.191578i
$811$	−33.7460			−1.18498			−0.592490	−	0.805578i	$-0.701855\pi$
$811$	−33.7460			−1.18498			−0.592490	+	0.805578i	$0.701855\pi$
$812$	−5.81960	−	12.0410i	−0.204228	−	0.422556i
$813$	7.45860	−	16.3168i	0.261584	−	0.572257i
$814$	67.8914	−	15.5462i	2.37959	−	0.544895i
$815$	6.19240	+	10.7255i	0.216910	+	0.375700i
$816$	−6.36244	+	9.80657i	−0.222730	+	0.343299i
$817$	−4.35725	+	7.54698i	−0.152441	+	0.264035i
$818$	4.40381	−	14.3127i	0.153976	−	0.500431i
$819$	−20.1174	−	23.2497i	−0.702958	−	0.812412i
$820$	−1.27951	+	1.88240i	−0.0446824	+	0.0657363i
$821$	−20.6598	+	35.7839i	−0.721033	+	1.24887i	0.239552	+	0.970883i	$0.422999\pi$
$821$	−20.6598	+	35.7839i	−0.721033	+	1.24887i	−0.960586	+	0.277983i	$0.910334\pi$
$822$	−0.603623	+	2.92300i	−0.0210538	+	0.101951i
$823$	16.0103	−	9.24353i	0.558082	−	0.322209i	−0.194293	−	0.980944i	$-0.562241\pi$
$823$	16.0103	−	9.24353i	0.558082	−	0.322209i	0.752376	+	0.658734i	$0.228908\pi$
$824$	−0.891742	+	2.28635i	−0.0310653	+	0.0796487i
$825$	9.76003	−	0.928503i	0.339801	−	0.0323263i
$826$	10.0334	+	10.7981i	0.349105	+	0.375714i
$827$		−	46.4472i		−	1.61513i	−0.589781	−	0.807563i	$-0.700786\pi$
$827$		−	46.4472i		−	1.61513i	0.589781	−	0.807563i	$-0.299214\pi$
$828$	−40.6000	−	17.5154i	−1.41095	−	0.608703i
$829$		−	48.4837i		−	1.68391i	−0.539549	−	0.841954i	$-0.681405\pi$
$829$		−	48.4837i		−	1.68391i	0.539549	−	0.841954i	$-0.318595\pi$
$830$	−5.91461	+	5.49573i	−0.205299	+	0.190760i
$831$	−15.7036	−	22.0690i	−0.544751	−	0.765567i
$832$	12.6161	+	40.2935i	0.437384	+	1.39693i
$833$	4.71895	−	2.72448i	0.163502	−	0.0943978i
$834$	16.2715	−	18.2833i	0.563436	−	0.633098i
$835$	6.08840	−	10.5454i	0.210698	−	0.364939i
$836$	12.6732	−	18.6446i	0.438311	−	0.644838i
$837$	−39.5877	−	37.8267i	−1.36835	−	1.30748i
$838$	11.8096	+	3.63364i	0.407955	+	0.125522i
$839$	10.1031	−	17.4992i	0.348799	−	0.604138i	−0.637237	−	0.770668i	$-0.719923\pi$
$839$	10.1031	−	17.4992i	0.348799	−	0.604138i	0.986036	+	0.166530i	$0.0532562\pi$
$840$	−2.32183	−	9.22507i	−0.0801106	−	0.318295i
$841$	8.57069	+	14.8449i	0.295541	+	0.511892i
$842$	−0.00250534	−	0.0109410i	−8.63397e−5	−	0.000377052i
$843$	3.76734	+	5.29443i	0.129754	+	0.182350i
$844$	16.6845	−	8.06389i	0.574306	−	0.277571i
$845$	−14.8552			−0.511033
$846$	−12.2225	−	8.95652i	−0.420217	−	0.307931i
$847$			40.8554i			1.40381i
$848$	−10.9608	−	1.62044i	−0.376397	−	0.0556461i
$849$	−2.16020	−	22.7071i	−0.0741379	−	0.779306i
$850$	−0.532611	−	2.32595i	−0.0182684	−	0.0797795i
$851$	55.5291	−	32.0597i	1.90351	−	1.09899i
$852$	−5.79120	+	10.5470i	−0.198403	+	0.361335i
$853$	40.1057	+	23.1550i	1.37319	+	0.792813i	0.991329	−	0.131406i	$-0.0419493\pi$
$853$	40.1057	+	23.1550i	1.37319	+	0.792813i	0.381863	+	0.924219i	$0.375283\pi$
$854$	−6.55211	+	21.2948i	−0.224208	+	0.728692i
$855$	−1.95792	+	5.64419i	−0.0669595	+	0.193027i
$856$	−23.6188	−	29.4886i	−0.807272	−	1.00790i
$857$	18.1647	+	10.4874i	0.620496	+	0.358243i	0.777062	−	0.629424i	$-0.216709\pi$
$857$	18.1647	+	10.4874i	0.620496	+	0.358243i	−0.156566	+	0.987667i	$0.550042\pi$
$858$	23.0158	+	69.4634i	0.785748	+	2.37144i
$859$	17.9466	+	31.0844i	0.612330	+	1.06059i	0.990847	+	0.134992i	$0.0431008\pi$
$859$	17.9466	+	31.0844i	0.612330	+	1.06059i	−0.378517	+	0.925594i	$0.623566\pi$
$860$	0.641730	−	8.72867i	0.0218828	−	0.297645i
$861$	3.48110	+	1.59125i	0.118636	+	0.0542296i
$862$	−14.4068	−	15.5049i	−0.490699	−	0.528100i
$863$	43.6978			1.48749			0.743746	−	0.668463i	$-0.233047\pi$
$863$	43.6978			1.48749			0.743746	+	0.668463i	$0.233047\pi$
$864$	−18.5813	+	22.7757i	−0.632150	+	0.774846i
$865$	−7.52467			−0.255846
$866$	−7.54996	−	8.12540i	−0.256558	−	0.276112i
$867$	−22.2951	−	10.1913i	−0.757181	−	0.346115i
$868$	−3.00056	+	40.8129i	−0.101846	+	1.38528i
$869$	8.27985	+	14.3411i	0.280875	+	0.486489i
$870$	−2.65304	−	8.00706i	−0.0899465	−	0.271465i
$871$	23.0542	+	13.3103i	0.781161	+	0.451003i
$872$	−3.86558	−	4.82627i	−0.130905	−	0.163438i
$873$	9.28354	−	1.78248i	0.314200	−	0.0603278i
$874$	6.10343	−	19.8366i	0.206452	−	0.670981i
$875$	1.68164	+	0.970893i	0.0568497	+	0.0328222i
$876$	−24.4181	+	44.4706i	−0.825010	+	1.50252i
$877$	36.4994	−	21.0729i	1.23250	−	0.711582i	0.264947	−	0.964263i	$-0.414646\pi$
$877$	36.4994	−	21.0729i	1.23250	−	0.711582i	0.967550	+	0.252681i	$0.0813123\pi$
$878$	0.743850	+	3.24845i	0.0251037	+	0.109630i
$879$	2.03841	+	21.4269i	0.0687538	+	0.722710i
$880$	−3.31131	+	22.3981i	−0.111624	+	0.755041i
$881$		−	50.1763i		−	1.69048i	−0.534385	−	0.845241i	$-0.679457\pi$
$881$		−	50.1763i		−	1.69048i	0.534385	−	0.845241i	$-0.320543\pi$
$882$	12.5395	−	5.52180i	0.422228	−	0.185929i
$883$	23.9242			0.805113			0.402556	−	0.915395i	$-0.368122\pi$
$883$	23.9242			0.805113			0.402556	+	0.915395i	$0.368122\pi$
$884$	16.0354	−	7.75016i	0.539329	−	0.260666i
$885$	5.39011	+	7.57499i	0.181186	+	0.254630i
$886$	11.7395	+	51.2673i	0.394397	+	1.72236i
$887$	−16.9349	−	29.3322i	−0.568620	−	0.984879i	−0.996703	−	0.0811391i	$-0.974144\pi$
$887$	−16.9349	−	29.3322i	−0.568620	−	0.984879i	0.428083	−	0.903740i	$-0.359189\pi$
$888$	−10.4035	−	41.3351i	−0.349118	−	1.38711i
$889$	12.2015	−	21.1336i	0.409225	−	0.708798i
$890$	−15.0924	−	4.64372i	−0.505899	−	0.155658i
$891$	−31.5476	+	40.0000i	−1.05688	+	1.34005i
$892$	−26.4399	+	38.8981i	−0.885274	+	1.30241i
$893$	3.55616	−	6.15944i	0.119002	−	0.206118i
$894$	6.20450	−	6.97160i	0.207509	−	0.233165i
$895$	14.5485	−	8.39960i	0.486304	−	0.280768i
$896$	21.9685	−	0.108573i	0.733917	−	0.00362718i
$897$	39.0579	+	54.8900i	1.30410	+	1.83272i
$898$	18.9943	−	17.6491i	0.633846	−	0.588957i
$899$			36.2873i			1.21025i
$900$	−0.696275	−	5.95946i	−0.0232092	−	0.198649i
$901$			4.67372i			0.155704i
$902$	−6.20113	−	6.67377i	−0.206475	−	0.222212i
$903$	−14.6519	+	1.39388i	−0.487585	+	0.0463855i
$904$	−19.0305	+	48.7925i	−0.632944	+	1.62281i
$905$	1.30990	−	0.756269i	0.0435424	−	0.0251392i
$906$	−0.267103	+	1.29342i	−0.00887389	+	0.0429711i
$907$	9.37960	−	16.2459i	0.311445	−	0.539438i	−0.667231	−	0.744851i	$-0.732521\pi$
$907$	9.37960	−	16.2459i	0.311445	−	0.539438i	0.978675	+	0.205413i	$0.0658538\pi$
$908$	−13.8469	+	20.3714i	−0.459526	+	0.676049i
$909$	7.68538	−	1.47563i	0.254908	−	0.0489434i
$910$	−4.26221	+	13.8525i	−0.141291	+	0.459205i
$911$	22.4115	−	38.8179i	0.742527	−	1.28609i	−0.208815	−	0.977955i	$-0.566961\pi$
$911$	22.4115	−	38.8179i	0.742527	−	1.28609i	0.951341	−	0.308139i	$-0.0997061\pi$
$912$	−11.5741	−	7.50921i	−0.383257	−	0.248655i
$913$	−16.1576	−	27.9859i	−0.534740	−	0.926197i
$914$	18.5711	−	4.25252i	0.614277	−	0.140661i
$915$	−5.84219	+	12.7807i	−0.193137	+	0.422517i
$916$	−13.1977	−	27.3066i	−0.436064	−	0.902236i
$917$	31.5011			1.04026
$918$	10.6502	+	6.34859i	0.351508	+	0.209535i
$919$		−	10.5162i		−	0.346897i	−0.984843	−	0.173449i	$-0.944509\pi$
$919$		−	10.5162i		−	0.346897i	0.984843	−	0.173449i	$-0.0554911\pi$
$920$	3.15031	+	20.6047i	0.103863	+	0.679317i
$921$	−26.2406	−	11.9948i	−0.864656	−	0.395243i
$922$	−31.3094	+	7.16944i	−1.03112	+	0.236113i
$923$	15.8761	−	9.16607i	0.522568	−	0.301705i
$924$	38.0661	−	0.817026i	1.25228	−	0.0268782i
$925$	7.53497	+	4.35031i	0.247748	+	0.143037i
$926$	−25.5950	−	7.87524i	−0.841105	−	0.258796i
$927$	2.45920	+	0.853077i	0.0807708	+	0.0280187i
$928$	19.4204	−	1.52432i	0.637506	−	0.0500382i
$929$	−4.46459	−	2.57763i	−0.146478	−	0.0845694i	0.424970	−	0.905208i	$-0.360285\pi$
$929$	−4.46459	−	2.57763i	−0.146478	−	0.0845694i	−0.571448	+	0.820638i	$0.693618\pi$
$930$	−5.22013	+	25.2781i	−0.171175	+	0.828901i
$931$	3.21555	+	5.56949i	0.105385	+	0.182533i
$932$	7.70829	+	0.566712i	0.252493	+	0.0185633i
$933$	5.06205	+	53.2101i	0.165724	+	1.74202i
$934$	−8.47990	+	7.87935i	−0.277471	+	0.257820i
$935$	9.55059			0.312338
$936$	42.1988	−	14.9944i	1.37931	−	0.490108i
$937$	24.9751			0.815902			0.407951	−	0.913004i	$-0.366243\pi$
$937$	24.9751			0.815902			0.407951	+	0.913004i	$0.366243\pi$
$938$	10.1469	−	9.42826i	0.331307	−	0.307844i
$939$	−11.2849	+	8.02997i	−0.368270	+	0.262048i
$940$	−0.523746	+	7.12388i	−0.0170827	+	0.232355i
$941$	−6.04469	−	10.4697i	−0.197051	−	0.341303i	0.750520	−	0.660848i	$-0.229803\pi$
$941$	−6.04469	−	10.4697i	−0.197051	−	0.341303i	−0.947571	+	0.319545i	$0.896470\pi$
$942$	27.5761	+	24.5418i	0.898478	+	0.799616i
$943$	−7.26322	−	4.19342i	−0.236523	−	0.136557i
$944$	−19.9640	+	7.90044i	−0.649774	+	0.257138i
$945$	−9.68410	+	2.83240i	−0.315024	+	0.0921381i
$946$	33.4818	+	10.3019i	1.08859	+	0.334943i
$947$	14.4548	+	8.34547i	0.469717	+	0.271191i	0.716121	−	0.697976i	$-0.245916\pi$
$947$	14.4548	+	8.34547i	0.469717	+	0.271191i	−0.246404	+	0.969167i	$0.579249\pi$
$948$	8.66585	−	5.25434i	0.281454	−	0.170653i
$949$	66.9402	−	38.6479i	2.17297	−	1.25457i
$950$	2.74518	−	0.628609i	0.0890655	−	0.0203948i
$951$	−13.9432	+	9.92150i	−0.452139	+	0.321727i
$952$	−1.40055	−	9.16034i	−0.0453921	−	0.296888i
$953$		−	15.7672i		−	0.510749i	−0.966842	−	0.255374i	$-0.917801\pi$
$953$		−	15.7672i		−	0.510749i	0.966842	−	0.255374i	$-0.0821987\pi$
$954$	−1.27608	+	11.6826i	−0.0413146	+	0.378238i
$955$	−0.157079			−0.00508296
$956$	6.60353	−	3.19159i	0.213573	−	0.103223i
$957$	33.6100	−	3.19743i	1.08646	−	0.103358i
$958$	−27.4160	+	6.27790i	−0.885772	+	0.202830i
$959$	−1.18302	−	2.04905i	−0.0382018	−	0.0661674i
$960$	13.7477	+	1.73188i	0.443707	+	0.0558962i
$961$	40.0193	−	69.3155i	1.29095	−	2.23598i
$962$	−19.0979	+	62.0693i	−0.615740	+	2.00119i
$963$	−30.3037	+	26.2210i	−0.976523	+	0.844959i
$964$	−25.4837	−	17.3218i	−0.820775	−	0.557899i
$965$	−8.06998	+	13.9776i	−0.259782	+	0.449956i
$966$	33.2734	−	11.0247i	1.07055	−	0.354714i
$967$	−39.3412	+	22.7137i	−1.26513	+	0.730422i	−0.974062	−	0.226281i	$-0.927343\pi$
$967$	−39.3412	+	22.7137i	−1.26513	+	0.730422i	−0.291066	+	0.956703i	$0.594010\pi$
$968$	−55.4426	−	21.6242i	−1.78199	−	0.695029i
$969$	−2.41944	+	5.29290i	−0.0777235	+	0.170032i
$970$	−3.03332	−	3.26451i	−0.0973940	−	0.104817i
$971$			19.1708i			0.615222i	0.951512	+	0.307611i	$0.0995295\pi$
$971$			19.1708i			0.615222i	−0.951512	+	0.307611i	$0.900471\pi$
$972$	24.8882	+	18.7770i	0.798290	+	0.602274i
$973$			19.4023i			0.622009i
$974$	2.61734	−	2.43198i	0.0838649	−	0.0779255i
$975$	−3.80041	+	8.31399i	−0.121710	+	0.266261i
$976$	−25.4300	−	20.1625i	−0.813995	−	0.645387i
$977$	−49.6018	+	28.6376i	−1.58690	+	0.916198i	−0.593088	+	0.805138i	$0.702091\pi$
$977$	−49.6018	+	28.6376i	−1.58690	+	0.916198i	−0.993814	+	0.111060i	$0.964575\pi$
$978$	9.54148	+	28.7969i	0.305103	+	0.920822i
$979$	31.6011	−	54.7347i	1.00998	−	1.74933i
$980$	−5.34176	−	3.63091i	−0.170636	−	0.115985i
$981$	−4.95967	+	4.29147i	−0.158350	+	0.137016i
$982$	3.88961	+	1.19678i	0.124122	+	0.0381907i
$983$	−13.4716	+	23.3334i	−0.429676	+	0.744221i	−0.996844	−	0.0793808i	$-0.974706\pi$
$983$	−13.4716	+	23.3334i	−0.429676	+	0.744221i	0.567168	+	0.823602i	$0.308039\pi$
$984$	−4.00190	+	3.88179i	−0.127576	+	0.123747i
$985$	−10.6443	−	18.4364i	−0.339155	−	0.587433i
$986$	−1.83412	−	8.00973i	−0.0584102	−	0.255082i
$987$	11.9581	−	1.13761i	0.380631	−	0.0362107i
$988$	9.14705	+	18.9256i	0.291006	+	0.602105i
$989$	32.2499			1.02549
$990$	23.8730	+	2.60763i	0.758735	+	0.0828759i
$991$			40.3125i			1.28057i	0.768138	+	0.640284i	$0.221183\pi$
$991$			40.3125i			1.28057i	−0.768138	+	0.640284i	$0.778817\pi$
$992$	−53.7968	−	25.6736i	−1.70805	−	0.815139i
$993$	−38.1188	+	27.1241i	−1.20966	+	0.860756i
$994$	−2.12906	−	9.29778i	−0.0675298	−	0.294908i
$995$	−21.3163	+	12.3069i	−0.675771	+	0.390156i
$996$	−16.9109	+	10.2535i	−0.535842	+	0.324896i
$997$	−28.0699	−	16.2062i	−0.888984	−	0.513255i	−0.0153740	−	0.999882i	$-0.504894\pi$
$997$	−28.0699	−	16.2062i	−0.888984	−	0.513255i	−0.873610	+	0.486627i	$0.838227\pi$
$998$	8.10896	−	26.3546i	0.256685	−	0.834242i
$999$	−43.3919	+	12.6913i	−1.37286	+	0.401534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.19	✓	48
3.2	odd	2		1080.2.bm.b.251.6		48
4.3	odd	2		1440.2.cc.a.911.22		48
8.3	odd	2		360.2.bm.b.11.22	yes	48
8.5	even	2		1440.2.cc.b.911.22		48
9.4	even	3		1080.2.bm.a.611.3		48
9.5	odd	6		360.2.bm.b.131.22	yes	48
12.11	even	2		4320.2.cc.b.1871.8		48
24.5	odd	2		4320.2.cc.a.1871.17		48
24.11	even	2		1080.2.bm.a.251.3		48
36.23	even	6		1440.2.cc.b.1391.22		48
36.31	odd	6		4320.2.cc.a.3311.17		48
72.5	odd	6		1440.2.cc.a.1391.22		48
72.13	even	6		4320.2.cc.b.3311.8		48
72.59	even	6	inner	360.2.bm.a.131.19	yes	48
72.67	odd	6		1080.2.bm.b.611.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.19	✓	48	1.1	even	1	trivial
360.2.bm.a.131.19	yes	48	72.59	even	6	inner
360.2.bm.b.11.22	yes	48	8.3	odd	2
360.2.bm.b.131.22	yes	48	9.5	odd	6
1080.2.bm.a.251.3		48	24.11	even	2
1080.2.bm.a.611.3		48	9.4	even	3
1080.2.bm.b.251.6		48	3.2	odd	2
1080.2.bm.b.611.6		48	72.67	odd	6
1440.2.cc.a.911.22		48	4.3	odd	2
1440.2.cc.a.1391.22		48	72.5	odd	6
1440.2.cc.b.911.22		48	8.5	even	2
1440.2.cc.b.1391.22		48	36.23	even	6
4320.2.cc.a.1871.17		48	24.5	odd	2
4320.2.cc.a.3311.17		48	36.31	odd	6
4320.2.cc.b.1871.8		48	12.11	even	2
4320.2.cc.b.3311.8		48	72.13	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.962641 + 1.03601i) q^{2} +(-1.57528 - 0.720074i) q^{3} +(-0.146644 + 1.99462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.770419 - 2.32518i) q^{6} +(1.68164 + 0.970893i) q^{7} +(-2.20761 + 1.76818i) q^{8} +(1.96299 + 2.26863i) q^{9} +O(q^{10})\)	\(q+(0.962641 + 1.03601i) q^{2} +(-1.57528 - 0.720074i) q^{3} +(-0.146644 + 1.99462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.770419 - 2.32518i) q^{6} +(1.68164 + 0.970893i) q^{7} +(-2.20761 + 1.76818i) q^{8} +(1.96299 + 2.26863i) q^{9} +(0.415893 - 1.35168i) q^{10} +(4.90205 + 2.83020i) q^{11} +(1.66728 - 3.03648i) q^{12} +(-4.57071 + 2.63890i) q^{13} +(0.612955 + 2.67682i) q^{14} +(0.164035 + 1.72427i) q^{15} +(-3.95699 - 0.584996i) q^{16} +1.68726i q^{17} +(-0.460679 + 4.21756i) q^{18} -1.99138 q^{19} +(1.80071 - 0.870311i) q^{20} +(-1.94992 - 2.74033i) q^{21} +(1.78679 + 7.80305i) q^{22} +(3.68476 + 6.38219i) q^{23} +(4.75082 - 1.19572i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-7.13389 - 2.19500i) q^{26} +(-1.45866 - 4.98721i) q^{27} +(-2.18316 + 3.21184i) q^{28} +(-1.72182 + 2.98228i) q^{29} +(-1.62845 + 1.82979i) q^{30} +(9.12573 - 5.26874i) q^{31} +(-3.20310 - 4.66263i) q^{32} +(-5.68412 - 7.98818i) q^{33} +(-1.74803 + 1.62423i) q^{34} -1.94179i q^{35} +(-4.81291 + 3.58272i) q^{36} -8.70063i q^{37} +(-1.91698 - 2.06309i) q^{38} +(9.10033 - 0.865744i) q^{39} +(2.63509 + 1.02776i) q^{40} +(-0.985576 + 0.569022i) q^{41} +(0.961935 - 4.65810i) q^{42} +(2.18806 - 3.78982i) q^{43} +(-6.36402 + 9.36268i) q^{44} +(0.983199 - 2.83431i) q^{45} +(-3.06493 + 9.96122i) q^{46} +(-1.78578 + 3.09306i) q^{47} +(5.81211 + 3.77086i) q^{48} +(-1.61473 - 2.79680i) q^{49} +(-1.37853 + 0.315665i) q^{50} +(1.21496 - 2.65791i) q^{51} +(-4.59333 - 9.50379i) q^{52} +2.77000 q^{53} +(3.76265 - 6.31209i) q^{54} -5.66040i q^{55} +(-5.42911 + 0.830071i) q^{56} +(3.13697 + 1.43394i) q^{57} +(-4.74717 + 1.08704i) q^{58} +(4.64849 - 2.68381i) q^{59} +(-3.46330 + 0.0743340i) q^{60} +(7.02634 + 4.05666i) q^{61} +(14.2433 + 4.38246i) q^{62} +(1.09843 + 5.72086i) q^{63} +(1.74711 - 7.80689i) q^{64} +(4.57071 + 2.63890i) q^{65} +(2.80409 - 13.5786i) q^{66} +(-2.52195 - 4.36814i) q^{67} +(-3.36545 - 0.247427i) q^{68} +(-1.20886 - 12.7070i) q^{69} +(2.01171 - 1.86924i) q^{70} -3.47345 q^{71} +(-8.34485 - 1.53736i) q^{72} -14.6455 q^{73} +(9.01396 - 8.37558i) q^{74} +(1.41124 - 1.00419i) q^{75} +(0.292023 - 3.97204i) q^{76} +(5.49564 + 9.51873i) q^{77} +(9.65727 + 8.59465i) q^{78} +(2.53359 + 1.46277i) q^{79} +(1.47187 + 3.71935i) q^{80} +(-1.29337 + 8.90658i) q^{81} +(-1.53827 - 0.473304i) q^{82} +(-4.94415 - 2.85451i) q^{83} +(5.75184 - 3.48750i) q^{84} +(1.46121 - 0.843632i) q^{85} +(6.03262 - 1.38139i) q^{86} +(4.85980 - 3.45807i) q^{87} +(-15.8261 + 2.41970i) q^{88} -11.1657i q^{89} +(3.88285 - 1.70982i) q^{90} -10.2484 q^{91} +(-13.2704 + 6.41377i) q^{92} +(-18.1694 + 1.72852i) q^{93} +(-4.92351 + 1.12742i) q^{94} +(0.995689 + 1.72458i) q^{95} +(1.68832 + 9.65140i) q^{96} +(1.57552 - 2.72888i) q^{97} +(1.34311 - 4.36520i) q^{98} +(3.20197 + 16.6766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

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