LMFDB - Embedded newform 360.2.bk.a.229.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (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:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.15
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07641 - 0.917248i) q^{2} +(1.70505 - 0.304648i) q^{3} +(0.317314 + 1.97467i) q^{4} +(-0.596890 + 2.15493i) q^{5} +(-2.11477 - 1.23603i) q^{6} +(-4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 - 1.03888i) q^{9} +O(q^{10})$	\(q+(-1.07641 - 0.917248i) q^{2} +(1.70505 - 0.304648i) q^{3} +(0.317314 + 1.97467i) q^{4} +(-0.596890 + 2.15493i) q^{5} +(-2.11477 - 1.23603i) q^{6} +(-4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 - 1.03888i) q^{9} +(2.61910 - 1.77209i) q^{10} +(-1.89283 + 1.09283i) q^{11} +(1.14261 + 3.27023i) q^{12} +(-1.56540 + 2.71134i) q^{13} +(6.42783 + 1.18385i) q^{14} +(-0.361231 + 3.85610i) q^{15} +(-3.79862 + 1.25318i) q^{16} -2.09803i q^{17} +(-3.98233 - 1.46322i) q^{18} +7.51339i q^{19} +(-4.44467 - 0.494870i) q^{20} +(-6.12035 + 5.15936i) q^{21} +(3.03986 + 0.559867i) q^{22} +(-0.173434 - 0.100132i) q^{23} +(1.76969 - 4.56817i) q^{24} +(-4.28744 - 2.57251i) q^{25} +(4.17198 - 1.48266i) q^{26} +(4.48216 - 2.62873i) q^{27} +(-5.83309 - 7.17021i) q^{28} +(4.48703 - 2.59059i) q^{29} +(3.92583 - 3.81940i) q^{30} +(0.115444 - 0.199954i) q^{31} +(5.23835 + 2.13534i) q^{32} +(-2.89445 + 2.43997i) q^{33} +(-1.92441 + 2.25834i) q^{34} +(-2.59061 - 10.0042i) q^{35} +(2.94448 + 5.22781i) q^{36} -0.0984028 q^{37} +(6.89164 - 8.08748i) q^{38} +(-1.84307 + 5.09987i) q^{39} +(4.33037 + 4.60955i) q^{40} +(-2.10507 + 3.64609i) q^{41} +(11.3204 + 0.0602924i) q^{42} +(4.69577 + 8.13332i) q^{43} +(-2.75860 - 3.39095i) q^{44} +(0.558836 + 6.68489i) q^{45} +(0.0948400 + 0.266865i) q^{46} +(6.70474 - 3.87099i) q^{47} +(-6.09506 + 3.29397i) q^{48} +(7.17962 - 12.4355i) q^{49} +(2.25542 + 6.70172i) q^{50} +(-0.639160 - 3.57724i) q^{51} +(-5.85072 - 2.23079i) q^{52} +7.81882 q^{53} +(-7.23584 - 1.28166i) q^{54} +(-1.22516 - 4.73122i) q^{55} +(-0.298065 + 13.0685i) q^{56} +(2.28894 + 12.8107i) q^{57} +(-7.20609 - 1.32718i) q^{58} +(-0.434562 - 0.250894i) q^{59} +(-7.72914 + 0.510283i) q^{60} +(8.80696 - 5.08470i) q^{61} +(-0.307673 + 0.109342i) q^{62} +(-8.86370 + 10.6615i) q^{63} +(-3.67997 - 7.10337i) q^{64} +(-4.90839 - 4.99169i) q^{65} +(5.35367 + 0.0285136i) q^{66} +(-2.36402 + 4.09460i) q^{67} +(4.14291 - 0.665733i) q^{68} +(-0.326218 - 0.117894i) q^{69} +(-6.38781 + 13.1449i) q^{70} -12.8654 q^{71} +(1.62573 - 8.32809i) q^{72} -4.83099i q^{73} +(0.105922 + 0.0902597i) q^{74} +(-8.09401 - 3.08010i) q^{75} +(-14.8364 + 2.38410i) q^{76} +(5.05062 - 8.74793i) q^{77} +(6.66174 - 3.79899i) q^{78} +(2.14223 + 3.71045i) q^{79} +(-0.433153 - 8.93378i) q^{80} +(6.84146 - 5.84760i) q^{81} +(5.61028 - 1.99381i) q^{82} +(-0.320637 - 0.555359i) q^{83} +(-12.1301 - 10.4485i) q^{84} +(4.52110 + 1.25229i) q^{85} +(2.40569 - 13.0620i) q^{86} +(6.86138 - 5.78404i) q^{87} +(-0.140961 + 6.18036i) q^{88} -0.894402 q^{89} +(5.53016 - 7.70826i) q^{90} -14.4693i q^{91} +(0.142695 - 0.374248i) q^{92} +(0.135921 - 0.376102i) q^{93} +(-10.7677 - 1.98314i) q^{94} +(-16.1908 - 4.48466i) q^{95} +(9.58217 + 2.04501i) q^{96} +(12.2234 - 7.05717i) q^{97} +(-19.1346 + 6.80016i) q^{98} +(-4.19184 + 5.04206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.07641	−	0.917248i	−0.761136	−	0.648592i
$2$	−1.07641	−	0.917248i	−0.761136	−	0.648592i
$3$	1.70505	−	0.304648i	0.984410	−	0.175889i
$3$	1.70505	−	0.304648i	0.984410	−	0.175889i
$4$	0.317314	+	1.97467i	0.158657	+	0.987334i
$5$	−0.596890	+	2.15493i	−0.266937	+	0.963714i
$5$	−0.596890	+	2.15493i	−0.266937	+	0.963714i
$6$	−2.11477	−	1.23603i	−0.863350	−	0.504605i
$7$	−4.00243	+	2.31080i	−1.51278	+	0.873401i	−0.512887	+	0.858456i	$0.671424\pi$
$7$	−4.00243	+	2.31080i	−1.51278	+	0.873401i	−0.999888	+	0.0149451i	$0.995243\pi$
$8$	1.46970	−	2.41661i	0.519617	−	0.854399i
$9$	2.81438	−	1.03888i	0.938126	−	0.346293i
$10$	2.61910	−	1.77209i	0.828233	−	0.560384i
$11$	−1.89283	+	1.09283i	−0.570711	+	0.329500i	−0.757433	−	0.652913i	$-0.773547\pi$
$11$	−1.89283	+	1.09283i	−0.570711	+	0.329500i	0.186722	+	0.982413i	$0.440214\pi$
$12$	1.14261	+	3.27023i	0.329844	+	0.944035i
$13$	−1.56540	+	2.71134i	−0.434162	+	0.751991i	−0.997227	−	0.0744216i	$-0.976289\pi$
$13$	−1.56540	+	2.71134i	−0.434162	+	0.751991i	0.563064	+	0.826413i	$0.309622\pi$
$14$	6.42783	+	1.18385i	1.71791	+	0.316396i
$15$	−0.361231	+	3.85610i	−0.0932695	+	0.995641i
$16$	−3.79862	+	1.25318i	−0.949656	+	0.313295i
$17$		−	2.09803i		−	0.508846i	−0.967093	−	0.254423i	$-0.918114\pi$
$17$		−	2.09803i		−	0.508846i	0.967093	−	0.254423i	$-0.0818856\pi$
$18$	−3.98233	−	1.46322i	−0.938645	−	0.344885i
$19$			7.51339i			1.72369i	0.507172	+	0.861845i	$0.330691\pi$
$19$			7.51339i			1.72369i	−0.507172	+	0.861845i	$0.669309\pi$
$20$	−4.44467	−	0.494870i	−0.993859	−	0.110656i
$21$	−6.12035	+	5.15936i	−1.33557	+	1.12586i
$22$	3.03986	+	0.559867i	0.648100	+	0.119364i
$23$	−0.173434	−	0.100132i	−0.0361635	−	0.0208790i	0.481809	−	0.876276i	$-0.339980\pi$
$23$	−0.173434	−	0.100132i	−0.0361635	−	0.0208790i	−0.517973	+	0.855397i	$0.673313\pi$
$24$	1.76969	−	4.56817i	0.361237	−	0.932474i
$25$	−4.28744	−	2.57251i	−0.857489	−	0.514502i
$26$	4.17198	−	1.48266i	0.818192	−	0.290774i
$27$	4.48216	−	2.62873i	0.862592	−	0.505900i
$28$	−5.83309	−	7.17021i	−1.10235	−	1.35504i
$29$	4.48703	−	2.59059i	0.833220	−	0.481060i	−0.0217339	−	0.999764i	$-0.506919\pi$
$29$	4.48703	−	2.59059i	0.833220	−	0.481060i	0.854954	+	0.518704i	$0.173585\pi$
$30$	3.92583	−	3.81940i	0.716755	−	0.697325i
$31$	0.115444	−	0.199954i	0.0207343	−	0.0359129i	−0.855472	−	0.517849i	$-0.826733\pi$
$31$	0.115444	−	0.199954i	0.0207343	−	0.0359129i	0.876206	+	0.481936i	$0.160066\pi$
$32$	5.23835	+	2.13534i	0.926018	+	0.377479i
$33$	−2.89445	+	2.43997i	−0.503858	+	0.424745i
$34$	−1.92441	+	2.25834i	−0.330034	+	0.387301i
$35$	−2.59061	−	10.0042i	−0.437893	−	1.69103i
$36$	2.94448	+	5.22781i	0.490747	+	0.871302i
$37$	−0.0984028			−0.0161773			−0.00808866	−	0.999967i	$-0.502575\pi$
$37$	−0.0984028			−0.0161773			−0.00808866	+	0.999967i	$0.502575\pi$
$38$	6.89164	−	8.08748i	1.11797	−	1.31196i
$39$	−1.84307	+	5.09987i	−0.295127	+	0.816632i
$40$	4.33037	+	4.60955i	0.684691	+	0.728833i
$41$	−2.10507	+	3.64609i	−0.328757	+	0.569423i	−0.982265	−	0.187496i	$-0.939963\pi$
$41$	−2.10507	+	3.64609i	−0.328757	+	0.569423i	0.653509	+	0.756919i	$0.273296\pi$
$42$	11.3204	+	0.0602924i	1.74678	+	0.00930332i
$43$	4.69577	+	8.13332i	0.716099	+	1.24032i	0.962534	+	0.271160i	$0.0874073\pi$
$43$	4.69577	+	8.13332i	0.716099	+	1.24032i	−0.246436	+	0.969159i	$0.579259\pi$
$44$	−2.75860	−	3.39095i	−0.415874	−	0.511205i
$45$	0.558836	+	6.68489i	0.0833064	+	0.996524i
$46$	0.0948400	+	0.266865i	0.0139834	+	0.0393471i
$47$	6.70474	−	3.87099i	0.977987	−	0.564641i	0.0763255	−	0.997083i	$-0.475681\pi$
$47$	6.70474	−	3.87099i	0.977987	−	0.564641i	0.901662	+	0.432442i	$0.142348\pi$
$48$	−6.09506	+	3.29397i	−0.879746	+	0.475444i
$49$	7.17962	−	12.4355i	1.02566	−	1.77649i
$50$	2.25542	+	6.70172i	0.318964	+	0.947767i
$51$	−0.639160	−	3.57724i	−0.0895003	−	0.500914i
$52$	−5.85072	−	2.23079i	−0.811349	−	0.309355i
$53$	7.81882			1.07400			0.536999	−	0.843583i	$-0.319558\pi$
$53$	7.81882			1.07400			0.536999	+	0.843583i	$0.319558\pi$
$54$	−7.23584	−	1.28166i	−0.984673	−	0.174411i
$55$	−1.22516	−	4.73122i	−0.165200	−	0.637958i
$56$	−0.298065	+	13.0685i	−0.0398306	+	1.74635i
$57$	2.28894	+	12.8107i	0.303177	+	1.69682i
$58$	−7.20609	−	1.32718i	−0.946205	−	0.174268i
$59$	−0.434562	−	0.250894i	−0.0565751	−	0.0326637i	0.471446	−	0.881895i	$-0.343732\pi$
$59$	−0.434562	−	0.250894i	−0.0565751	−	0.0326637i	−0.528021	+	0.849231i	$0.677066\pi$
$60$	−7.72914	+	0.510283i	−0.997828	+	0.0658773i
$61$	8.80696	−	5.08470i	1.12762	−	0.651030i	0.184282	−	0.982873i	$-0.441004\pi$
$61$	8.80696	−	5.08470i	1.12762	−	0.651030i	0.943334	+	0.331844i	$0.107671\pi$
$62$	−0.307673	+	0.109342i	−0.0390744	+	0.0138865i
$63$	−8.86370	+	10.6615i	−1.11672	+	1.34322i
$64$	−3.67997	−	7.10337i	−0.459996	−	0.887921i
$65$	−4.90839	−	4.99169i	−0.608810	−	0.619143i
$66$	5.35367	+	0.0285136i	0.658991	+	0.00350978i
$67$	−2.36402	+	4.09460i	−0.288811	+	0.500235i	−0.973526	−	0.228576i	$-0.926593\pi$
$67$	−2.36402	+	4.09460i	−0.288811	+	0.500235i	0.684715	+	0.728811i	$0.259926\pi$
$68$	4.14291	−	0.665733i	0.502401	−	0.0807320i
$69$	−0.326218	−	0.117894i	−0.0392721	−	0.0141928i
$70$	−6.38781	+	13.1449i	−0.763490	+	1.57111i
$71$	−12.8654			−1.52684			−0.763421	−	0.645902i	$-0.776482\pi$
$71$	−12.8654			−1.52684			−0.763421	+	0.645902i	$0.776482\pi$
$72$	1.62573	−	8.32809i	0.191594	−	0.981474i
$73$		−	4.83099i		−	0.565425i	−0.959205	−	0.282712i	$-0.908766\pi$
$73$		−	4.83099i		−	0.565425i	0.959205	−	0.282712i	$-0.0912342\pi$
$74$	0.105922	+	0.0902597i	0.0123131	+	0.0104925i
$75$	−8.09401	−	3.08010i	−0.934616	−	0.355659i
$76$	−14.8364	+	2.38410i	−1.70186	+	0.273475i
$77$	5.05062	−	8.74793i	0.575572	−	0.996920i
$78$	6.66174	−	3.79899i	0.754293	−	0.430151i
$79$	2.14223	+	3.71045i	0.241020	+	0.417458i	0.961005	−	0.276531i	$-0.0891849\pi$
$79$	2.14223	+	3.71045i	0.241020	+	0.417458i	−0.719985	+	0.693989i	$0.755852\pi$
$80$	−0.433153	−	8.93378i	−0.0484280	−	0.998827i
$81$	6.84146	−	5.84760i	0.760162	−	0.649733i
$82$	5.61028	−	1.99381i	0.619552	−	0.220180i
$83$	−0.320637	−	0.555359i	−0.0351944	−	0.0609586i	0.847892	−	0.530170i	$-0.177872\pi$
$83$	−0.320637	−	0.555359i	−0.0351944	−	0.0609586i	−0.883086	+	0.469211i	$0.844538\pi$
$84$	−12.1301	−	10.4485i	−1.32350	−	1.14003i
$85$	4.52110	+	1.25229i	0.490382	+	0.135830i
$86$	2.40569	−	13.0620i	0.259412	−	1.40851i
$87$	6.86138	−	5.78404i	0.735617	−	0.620114i
$88$	−0.140961	+	6.18036i	−0.0150265	+	0.658829i
$89$	−0.894402			−0.0948064			−0.0474032	−	0.998876i	$-0.515095\pi$
$89$	−0.894402			−0.0948064			−0.0474032	+	0.998876i	$0.515095\pi$
$90$	5.53016	−	7.70826i	0.582930	−	0.812522i
$91$		−	14.4693i		−	1.51679i
$92$	0.142695	−	0.374248i	0.0148769	−	0.0390180i
$93$	0.135921	−	0.376102i	0.0140944	−	0.0389999i
$94$	−10.7677	−	1.98314i	−1.11060	−	0.204546i
$95$	−16.1908	−	4.48466i	−1.66114	−	0.460117i
$96$	9.58217	+	2.04501i	0.977976	+	0.208718i
$97$	12.2234	−	7.05717i	1.24110	−	0.716547i	0.271779	−	0.962360i	$-0.412388\pi$
$97$	12.2234	−	7.05717i	1.24110	−	0.716547i	0.969317	+	0.245813i	$0.0790548\pi$
$98$	−19.1346	+	6.80016i	−1.93289	+	0.686920i
$99$	−4.19184	+	5.04206i	−0.421296	+	0.506746i
$100$	3.71939	−	9.28257i	0.371939	−	0.928257i
$101$	−10.6281	+	6.13613i	−1.05754	+	0.610568i	−0.924749	−	0.380577i	$-0.875726\pi$
$101$	−10.6281	+	6.13613i	−1.05754	+	0.610568i	−0.132786	+	0.991145i	$0.542392\pi$
$102$	−2.59322	+	4.43684i	−0.256767	+	0.439313i
$103$	−7.06779	−	4.08059i	−0.696410	−	0.402073i	0.109599	−	0.993976i	$-0.465043\pi$
$103$	−7.06779	−	4.08059i	−0.696410	−	0.402073i	−0.806009	+	0.591903i	$0.798377\pi$
$104$	4.25159	+	7.76780i	0.416903	+	0.761696i
$105$	−7.46489	−	16.2685i	−0.728498	−	1.58764i
$106$	−8.41626	−	7.17180i	−0.817459	−	0.696587i
$107$	−13.8413			−1.33809			−0.669044	−	0.743223i	$-0.733296\pi$
$107$	−13.8413			−1.33809			−0.669044	+	0.743223i	$0.733296\pi$
$108$	6.61313	+	8.01664i	0.636348	+	0.771402i
$109$			7.69725i			0.737263i	0.929576	+	0.368631i	$0.120174\pi$
$109$			7.69725i			0.737263i	−0.929576	+	0.368631i	$0.879826\pi$
$110$	−3.02094	+	6.21650i	−0.288035	+	0.592720i
$111$	−0.167782	+	0.0299782i	−0.0159251	+	0.00284541i
$112$	12.3079	−	13.7936i	1.16298	−	1.30338i
$113$	13.1424	+	7.58775i	1.23633	+	0.713795i	0.968342	−	0.249627i	$-0.0803080\pi$
$113$	13.1424	+	7.58775i	1.23633	+	0.713795i	0.267988	+	0.963422i	$0.413641\pi$
$114$	9.28674	−	15.8891i	0.869783	−	1.48815i
$115$	0.319299	−	0.313970i	0.0297748	−	0.0292779i
$116$	6.53934	+	8.03836i	0.607163	+	0.746343i
$117$	−1.58886	+	9.25701i	−0.146890	+	0.855810i
$118$	0.237634	+	0.668666i	0.0218760	+	0.0615557i
$119$	4.84813	+	8.39720i	0.444427	+	0.769770i
$120$	8.78777	+	6.54026i	0.802210	+	0.597041i
$121$	−3.11145	+	5.38919i	−0.282859	+	0.489927i
$122$	−14.1438	−	2.60494i	−1.28052	−	0.235841i
$123$	−2.47847	+	6.85806i	−0.223476	+	0.618370i
$124$	0.431476	+	0.164515i	0.0387476	+	0.0147739i
$125$	8.10271	−	7.70364i	0.724729	−	0.689034i
$126$	19.3202	−	3.34594i	1.72118	−	0.298080i
$127$			12.4252i			1.10256i	0.834320	+	0.551280i	$0.185860\pi$
$127$			12.4252i			1.10256i	−0.834320	+	0.551280i	$0.814140\pi$
$128$	−2.55439	+	11.0216i	−0.225779	+	0.974179i
$129$	10.4843	+	12.4371i	0.923093	+	1.09503i
$130$	0.704818	+	9.87531i	0.0618166	+	0.866122i
$131$	−0.00857433	−	0.00495039i	−0.000749143	−	0.000432518i	0.499625	−	0.866242i	$-0.333471\pi$
$131$	−0.00857433	−	0.00495039i	−0.000749143	−	0.000432518i	−0.500375	+	0.865809i	$0.666804\pi$
$132$	−5.73658	−	4.94133i	−0.499306	−	0.430088i
$133$	−17.3620	−	30.0718i	−1.50547	−	2.60755i
$134$	6.30041	−	2.23907i	0.544273	−	0.193427i
$135$	2.98938	+	11.2278i	0.257285	+	0.966336i
$136$	−5.07011	−	3.08347i	−0.434758	−	0.264405i
$137$	−2.21400	+	1.27825i	−0.189155	+	0.109208i	−0.591587	−	0.806241i	$-0.701498\pi$
$137$	−2.21400	+	1.27825i	−0.189155	+	0.109208i	0.402432	+	0.915450i	$0.368165\pi$
$138$	0.243007	+	0.426125i	0.0206861	+	0.0362742i
$139$	−1.74603	−	1.00807i	−0.148096	−	0.0855033i	0.424121	−	0.905606i	$-0.360583\pi$
$139$	−1.74603	−	1.00807i	−0.148096	−	0.0855033i	−0.572217	+	0.820102i	$0.693916\pi$
$140$	18.9330	−	8.29008i	1.60013	−	0.700639i
$141$	10.2526	−	8.64280i	0.863427	−	0.727855i
$142$	13.8484	+	11.8008i	1.16213	+	0.990297i
$143$		−	6.84283i		−	0.572226i
$144$	−9.38887	+	7.47323i	−0.782406	+	0.622769i
$145$	2.90427	+	11.2155i	0.241187	+	0.931398i
$146$	−4.43122	+	5.20012i	−0.366730	+	0.430365i
$147$	8.45315	−	23.3903i	0.697204	−	1.92920i
$148$	−0.0312246	−	0.194313i	−0.00256665	−	0.0159724i
$149$	−2.10492	−	1.21527i	−0.172441	−	0.0995591i	0.411295	−	0.911502i	$-0.365077\pi$
$149$	−2.10492	−	1.21527i	−0.172441	−	0.0995591i	−0.583737	+	0.811943i	$0.698410\pi$
$150$	5.88726	+	10.7397i	0.480693	+	0.876889i
$151$	−7.97044	−	13.8052i	−0.648625	−	1.12345i	−0.983451	−	0.181172i	$-0.942011\pi$
$151$	−7.97044	−	13.8052i	−0.648625	−	1.12345i	0.334826	−	0.942280i	$-0.391322\pi$
$152$	18.1569	+	11.0424i	1.47272	+	0.895659i
$153$	−2.17960	−	5.90464i	−0.176210	−	0.477362i
$154$	−13.4606	+	4.78369i	−1.08468	+	0.385480i
$155$	0.361981	+	0.368124i	0.0290750	+	0.0295684i
$156$	−10.6554	−	2.02119i	−0.853113	−	0.161825i
$157$	−4.41535	+	7.64760i	−0.352383	+	0.610345i	−0.986666	−	0.162755i	$-0.947962\pi$
$157$	−4.41535	+	7.64760i	−0.352383	+	0.610345i	0.634283	+	0.773101i	$0.281295\pi$
$158$	1.09749	−	5.95892i	0.0873113	−	0.474066i
$159$	13.3315	−	2.38199i	1.05725	−	0.188904i
$160$	−7.72824	+	10.0137i	−0.610971	+	0.791653i
$161$	0.925542			0.0729430
$162$	−12.7279	+	0.0190950i	−0.999999	+	0.00150025i
$163$	16.5538			1.29660			0.648298	−	0.761386i	$-0.275481\pi$
$163$	16.5538			1.29660			0.648298	+	0.761386i	$0.275481\pi$
$164$	−7.86778	−	2.99986i	−0.614370	−	0.234250i
$165$	−3.53031	−	7.69372i	−0.274834	−	0.598956i
$166$	−0.164265	+	0.891897i	−0.0127495	+	0.0692246i
$167$	11.3110	+	6.53039i	0.875268	+	0.505336i	0.869095	−	0.494645i	$-0.164702\pi$
$167$	11.3110	+	6.53039i	0.875268	+	0.505336i	0.00617297	+	0.999981i	$0.498035\pi$
$168$	3.47307	+	22.3732i	0.267953	+	1.72613i
$169$	1.59908	+	2.76968i	0.123006	+	0.213052i
$170$	−3.71789	−	5.49495i	−0.285150	−	0.421443i
$171$	7.80550	+	21.1455i	0.596901	+	1.61704i
$172$	−14.5706	+	11.8534i	−1.11100	+	0.903814i
$173$	−4.62414	−	8.00925i	−0.351567	−	0.608932i	0.634957	−	0.772547i	$-0.281018\pi$
$173$	−4.62414	−	8.00925i	−0.351567	−	0.608932i	−0.986524	+	0.163615i	$0.947684\pi$
$174$	−12.6910	−	0.0675924i	−0.962106	−	0.00512417i
$175$	23.1048	+	0.388852i	1.74656	+	0.0293944i
$176$	5.82066	−	6.52331i	0.438748	−	0.491713i
$177$	−0.817384	−	0.295399i	−0.0614383	−	0.0222035i
$178$	0.962743	+	0.820388i	0.0721606	+	0.0614907i
$179$			1.48075i			0.110676i	0.998468	+	0.0553382i	$0.0176237\pi$
$179$			1.48075i			0.110676i	−0.998468	+	0.0553382i	$0.982376\pi$
$180$	−13.0231	+	3.22472i	−0.970685	+	0.240357i
$181$		−	3.16795i		−	0.235472i	−0.993045	−	0.117736i	$-0.962436\pi$
$181$		−	3.16795i		−	0.235472i	0.993045	−	0.117736i	$-0.0375636\pi$
$182$	−13.2719	+	15.5749i	−0.983779	+	1.15449i
$183$	13.4673	−	11.3527i	0.995528	−	0.839215i
$184$	−0.496876	+	0.271957i	−0.0366302	+	0.0200490i
$185$	0.0587356	−	0.212051i	0.00431833	−	0.0155903i
$186$	−0.491286	+	0.280166i	−0.0360228	+	0.0205428i
$187$	2.29278	+	3.97122i	0.167665	+	0.290404i
$188$	9.77142	+	12.0113i	0.712654	+	0.876016i
$189$	−11.8650	+	20.8787i	−0.863054	+	1.51870i
$190$	13.3144	+	19.6783i	0.965928	+	1.42762i
$191$	7.42363	+	12.8581i	0.537155	+	0.930380i	0.999056	+	0.0434484i	$0.0138344\pi$
$191$	7.42363	+	12.8581i	0.537155	+	0.930380i	−0.461900	+	0.886932i	$0.652832\pi$
$192$	−8.43855	−	10.9905i	−0.609000	−	0.793170i
$193$	0.514796	+	0.297218i	0.0370559	+	0.0213942i	0.518413	−	0.855130i	$-0.326523\pi$
$193$	0.514796	+	0.297218i	0.0370559	+	0.0213942i	−0.481358	+	0.876524i	$0.659856\pi$
$194$	−19.6305	−	3.61546i	−1.40939	−	0.259575i
$195$	−9.88974	−	7.01574i	−0.708219	−	0.502408i
$196$	26.8341	+	10.2314i	1.91672	+	0.730815i
$197$	7.77837			0.554186			0.277093	−	0.960843i	$-0.410629\pi$
$197$	7.77837			0.554186			0.277093	+	0.960843i	$0.410629\pi$
$198$	9.13695	−	1.58237i	0.649335	−	0.112454i
$199$	7.20235			0.510561			0.255280	−	0.966867i	$-0.417832\pi$
$199$	7.20235			0.510561			0.255280	+	0.966867i	$0.417832\pi$
$200$	−12.5180	+	6.58025i	−0.885156	+	0.465294i
$201$	−2.78335	+	7.70168i	−0.196323	+	0.543235i
$202$	17.0685	+	3.14360i	1.20094	+	0.221183i
$203$	−11.9727	+	20.7373i	−0.840316	+	1.45547i
$204$	6.86104	−	2.39724i	0.480369	−	0.167840i
$205$	−6.60057	−	6.71259i	−0.461004	−	0.468828i
$206$	3.86492	+	10.8753i	0.269282	+	0.757718i
$207$	−0.592134	−	0.101633i	−0.0411562	−	0.00706398i
$208$	2.54855	−	12.2611i	0.176710	−	0.850154i
$209$	−8.21084	−	14.2216i	−0.567956	−	0.983729i
$210$	−6.88697	+	24.3587i	−0.475246	+	1.68091i
$211$	13.5190	+	7.80519i	0.930686	+	0.537332i	0.887028	−	0.461715i	$-0.152766\pi$
$211$	13.5190	+	7.80519i	0.930686	+	0.537332i	0.0436573	+	0.999047i	$0.486099\pi$
$212$	2.48102	+	15.4396i	0.170397	+	1.06039i
$213$	−21.9361	+	3.91942i	−1.50304	+	0.268554i
$214$	14.8989	+	12.6959i	1.01847	+	0.867873i
$215$	−20.3296	+	5.26437i	−1.38647	+	0.359027i
$216$	0.234815	−	14.6951i	0.0159771	−	0.999872i
$217$			1.06707i			0.0724375i
$218$	7.06028	−	8.28539i	0.478183	−	0.561157i
$219$	−1.47175	−	8.23707i	−0.0994517	−	0.556610i
$220$	8.95384	−	3.92056i	0.603667	−	0.264324i
$221$	5.68847	+	3.28424i	0.382648	+	0.220922i
$222$	0.208099	+	0.121628i	0.0139667	+	0.00816316i
$223$	15.7400	−	9.08748i	1.05403	−	0.608542i	0.130253	−	0.991481i	$-0.458421\pi$
$223$	15.7400	−	9.08748i	1.05403	−	0.608542i	0.923774	+	0.382938i	$0.125088\pi$
$224$	−25.9005	+	3.55823i	−1.73055	+	0.237744i
$225$	−14.7390	−	2.78589i	−0.982602	−	0.185726i
$226$	−7.18672	−	20.2223i	−0.478054	−	1.34517i
$227$	−9.87001	−	17.0954i	−0.655096	−	1.13466i	−0.981870	−	0.189557i	$-0.939295\pi$
$227$	−9.87001	−	17.0954i	−0.655096	−	1.13466i	0.326774	−	0.945102i	$-0.394038\pi$
$228$	−24.5705	+	8.58490i	−1.62722	+	0.568549i
$229$	15.5917	+	9.00188i	1.03033	+	0.594861i	0.917079	−	0.398705i	$-0.130540\pi$
$229$	15.5917	+	9.00188i	1.03033	+	0.594861i	0.113251	+	0.993566i	$0.463874\pi$
$230$	−0.631684	+	0.0450844i	−0.0416520	+	0.00297278i
$231$	5.94651	−	16.4543i	0.391252	−	1.08261i
$232$	0.334154	−	14.6508i	0.0219383	−	0.961869i
$233$		−	0.450632i		−	0.0295219i	−0.999891	−	0.0147609i	$-0.995301\pi$
$233$		−	0.450632i		−	0.0295219i	0.999891	−	0.0147609i	$-0.00469872\pi$
$234$	10.2012	−	8.50695i	0.666875	−	0.556117i
$235$	4.33971	+	16.7588i	0.283091	+	1.09322i
$236$	0.357541	−	0.937728i	0.0232739	−	0.0610409i
$237$	4.78298	+	5.67387i	0.310688	+	0.368557i
$238$	2.48374	−	13.4858i	0.160997	−	0.874152i
$239$	12.7762	−	22.1290i	0.826422	−	1.43140i	−0.0744065	−	0.997228i	$-0.523706\pi$
$239$	12.7762	−	22.1290i	0.826422	−	1.43140i	0.900828	−	0.434176i	$-0.142960\pi$
$240$	−3.46020	−	15.1006i	−0.223355	−	0.974737i
$241$	3.39288	+	5.87664i	0.218555	+	0.378548i	0.954366	−	0.298639i	$-0.0965325\pi$
$241$	3.39288	+	5.87664i	0.218555	+	0.378548i	−0.735812	+	0.677186i	$0.763199\pi$
$242$	8.29242	−	2.94701i	0.533057	−	0.189441i
$243$	9.88356	−	12.0547i	0.634031	−	0.773308i
$244$	12.8352	+	15.7774i	0.821688	+	1.01004i
$245$	22.5121	+	22.8942i	1.43825	+	1.46265i
$246$	8.95839	−	5.10871i	0.571166	−	0.325719i
$247$	−20.3714	−	11.7614i	−1.29620	−	0.748361i
$248$	−0.313544	−	0.572855i	−0.0199100	−	0.0363763i
$249$	−0.715890	−	0.849232i	−0.0453677	−	0.0538179i
$250$	−15.7880	+	0.860072i	−0.998519	+	0.0543957i
$251$		−	21.1794i		−	1.33683i	−0.743787	−	0.668417i	$-0.766972\pi$
$251$		−	21.1794i		−	1.33683i	0.743787	−	0.668417i	$-0.233028\pi$
$252$	−23.8655	−	14.1198i	−1.50339	−	0.889465i
$253$	0.437709			0.0275185
$254$	11.3970	−	13.3746i	0.715111	−	0.839198i
$255$	8.09020	+	0.757873i	0.506628	+	0.0474598i
$256$	12.8591	−	9.52071i	0.803693	−	0.595045i
$257$	−18.5004	−	10.6812i	−1.15403	−	0.666277i	−0.204160	−	0.978937i	$-0.565446\pi$
$257$	−18.5004	−	10.6812i	−1.15403	−	0.666277i	−0.949865	+	0.312661i	$0.898780\pi$
$258$	0.122520	−	23.0042i	0.00762776	−	1.43218i
$259$	0.393850	−	0.227389i	0.0244727	−	0.0141293i
$260$	8.29943	−	11.2764i	0.514709	−	0.699330i
$261$	9.93689	−	11.9524i	0.615078	−	0.739833i
$262$	0.00468875	+	0.0131934i	0.000289672	+	0.000815093i
$263$	−20.5261	+	11.8507i	−1.26569	+	0.730748i	−0.974170	−	0.225816i	$-0.927495\pi$
$263$	−20.5261	+	11.8507i	−1.26569	+	0.730748i	−0.291523	+	0.956564i	$0.594162\pi$
$264$	1.64249	+	10.5808i	0.101088	+	0.651201i
$265$	−4.66698	+	16.8490i	−0.286690	+	1.03503i
$266$	−8.89470	+	48.2948i	−0.545369	+	2.96114i
$267$	−1.52500	+	0.272478i	−0.0933284	+	0.0166754i
$268$	−8.83561	−	3.36888i	−0.539721	−	0.205787i
$269$			12.2928i			0.749504i	0.927125	+	0.374752i	$0.122272\pi$
$269$			12.2928i			0.749504i	−0.927125	+	0.374752i	$0.877728\pi$
$270$	7.08088	−	14.8277i	0.430929	−	0.902386i
$271$	−7.73588			−0.469921			−0.234961	−	0.972005i	$-0.575496\pi$
$271$	−7.73588			−0.469921			−0.234961	+	0.972005i	$0.575496\pi$
$272$	2.62920	+	7.96962i	0.159419	+	0.483229i
$273$	−4.40803	−	24.6708i	−0.266786	−	1.49315i
$274$	3.55564	+	0.654861i	0.214804	+	0.0395616i
$275$	10.9267	+	0.183896i	0.658907	+	0.0110894i
$276$	0.129288	−	0.681582i	0.00778219	−	0.0410264i
$277$	2.39019	+	4.13992i	0.143612	+	0.248744i	0.928854	−	0.370445i	$-0.120795\pi$
$277$	2.39019	+	4.13992i	0.143612	+	0.248744i	−0.785242	+	0.619189i	$0.787461\pi$
$278$	0.954790	+	2.68663i	0.0572645	+	0.161134i
$279$	0.117174	−	0.682680i	0.00701503	−	0.0408710i
$280$	−27.9837	−	8.44275i	−1.67235	−	0.504551i
$281$	7.28700	+	12.6215i	0.434706	+	0.752933i	0.997272	−	0.0738196i	$-0.0235189\pi$
$281$	7.28700	+	12.6215i	0.434706	+	0.752933i	−0.562565	+	0.826753i	$0.690186\pi$
$282$	−18.9636	−	0.101000i	−1.12927	−	0.00601446i
$283$	−11.9769	+	20.7446i	−0.711953	+	1.23314i	0.252170	+	0.967683i	$0.418856\pi$
$283$	−11.9769	+	20.7446i	−0.711953	+	1.23314i	−0.964123	+	0.265456i	$0.914477\pi$
$284$	−4.08237	−	25.4049i	−0.242244	−	1.50750i
$285$	−28.9724	−	2.71407i	−1.71618	−	0.160768i
$286$	−6.27657	+	7.36569i	−0.371141	+	0.435542i
$287$		−	19.4576i		−	1.14855i
$288$	16.9611	+	0.567659i	0.999440	+	0.0334496i
$289$	12.5983			0.741075
$290$	7.16123	−	14.7364i	0.420522	−	0.865353i
$291$	18.6915	−	15.7566i	1.09571	−	0.923671i
$292$	9.53960	−	1.53294i	0.558263	−	0.0897086i
$293$	4.74433	−	8.21741i	0.277166	−	0.480066i	−0.693513	−	0.720444i	$-0.743938\pi$
$293$	4.74433	−	8.21741i	0.277166	−	0.480066i	0.970679	+	0.240378i	$0.0772713\pi$
$294$	−30.5538	+	17.4239i	−1.78193	+	1.01618i
$295$	0.800046	−	0.786694i	0.0465805	−	0.0458031i
$296$	−0.144623	+	0.237801i	−0.00840601	+	0.0138219i
$297$	−5.61123	+	9.87399i	−0.325597	+	0.572947i
$298$	1.15104	+	3.23886i	0.0666782	+	0.187622i
$299$	0.542985	−	0.313493i	0.0314017	−	0.0181298i
$300$	3.51382	−	16.9603i	0.202871	−	0.979206i
$301$	−37.5890	−	21.7020i	−2.16659	−	1.25088i
$302$	−4.08334	+	22.1709i	−0.234970	+	1.27579i
$303$	−16.2521	+	13.7002i	−0.933656	+	0.787058i
$304$	−9.41562	−	28.5405i	−0.540023	−	1.63691i
$305$	5.70039	+	22.0134i	0.326403	+	1.26048i
$306$	−3.06988	+	8.35504i	−0.175494	+	0.477626i
$307$	12.5350			0.715408			0.357704	−	0.933835i	$-0.383560\pi$
$307$	12.5350			0.715408			0.357704	+	0.933835i	$0.383560\pi$
$308$	18.8769	+	7.19746i	1.07561	+	0.410113i
$309$	−13.2941	−	4.80442i	−0.756273	−	0.273314i
$310$	−0.0519785	−	0.728278i	−0.00295218	−	0.0413634i
$311$	13.4009	−	23.2110i	0.759896	−	1.31618i	−0.183008	−	0.983111i	$-0.558583\pi$
$311$	13.4009	−	23.2110i	0.759896	−	1.31618i	0.942903	−	0.333066i	$-0.108083\pi$
$312$	9.61561	+	11.9492i	0.544377	+	0.676493i
$313$	24.5893	−	14.1966i	1.38987	−	0.802441i	0.396569	−	0.918005i	$-0.370201\pi$
$313$	24.5893	−	14.1966i	1.38987	−	0.802441i	0.993300	+	0.115564i	$0.0368676\pi$
$314$	11.7675	−	4.18199i	0.664076	−	0.236003i
$315$	−17.6842	−	25.4644i	−0.996389	−	1.43476i
$316$	−6.64715	+	5.40757i	−0.373931	+	0.304199i
$317$	−0.294763	−	0.510545i	−0.0165555	−	0.0286750i	0.857629	−	0.514269i	$-0.171937\pi$
$317$	−0.294763	−	0.510545i	−0.0165555	−	0.0286750i	−0.874184	+	0.485594i	$0.838603\pi$
$318$	−16.5350	−	9.66427i	−0.927236	−	0.541945i
$319$	−5.66213	+	9.80710i	−0.317019	+	0.549092i
$320$	17.5038	−	3.69015i	0.978492	−	0.206285i
$321$	−23.6001	+	4.21672i	−1.31723	+	0.235354i
$322$	−0.996262	−	0.848951i	−0.0555195	−	0.0473102i
$323$	15.7633			0.877093
$324$	13.7180	+	11.6541i	0.762109	+	0.647449i
$325$	13.6865	−	7.59774i	0.759191	−	0.421447i
$326$	−17.8187	−	15.1840i	−0.986887	−	0.840962i
$327$	2.34495	+	13.1242i	0.129676	+	0.725769i
$328$	5.71734	+	10.4458i	0.315687	+	0.576771i
$329$	−17.8902	+	30.9867i	−0.986317	+	1.70835i
$330$	−3.25700	+	11.5198i	−0.179292	+	0.634142i
$331$	−20.5118	+	11.8425i	−1.12743	+	0.650923i	−0.943288	−	0.331977i	$-0.892285\pi$
$331$	−20.5118	+	11.8425i	−1.12743	+	0.650923i	−0.184144	+	0.982899i	$0.558951\pi$
$332$	0.994907	−	0.809374i	0.0546026	−	0.0444202i
$333$	−0.276943	+	0.102229i	−0.0151764	+	0.00560209i
$334$	−6.18524	−	17.4043i	−0.338441	−	0.952322i
$335$	−7.41251	−	7.53832i	−0.404989	−	0.411862i
$336$	16.7833	−	27.2684i	0.915604	−	1.48761i
$337$	−24.5827	−	14.1928i	−1.33910	−	0.773132i	−0.352430	−	0.935838i	$-0.614645\pi$
$337$	−24.5827	−	14.1928i	−1.33910	−	0.773132i	−0.986675	+	0.162706i	$0.947978\pi$
$338$	0.819223	−	4.44806i	0.0445599	−	0.241943i
$339$	24.7200	+	8.93368i	1.34260	+	0.485211i
$340$	−1.03825	+	9.32504i	−0.0563070	+	0.505721i
$341$			0.504641i			0.0273278i
$342$	10.9938	−	29.9208i	0.594475	−	1.61793i
$343$			34.0115i			1.83645i
$344$	26.5564	+	0.605697i	1.43183	+	0.0326570i
$345$	0.448769	−	0.632608i	0.0241609	−	0.0340585i
$346$	−2.36899	+	12.8627i	−0.127358	+	0.691504i
$347$	−5.66681	+	9.81520i	−0.304210	+	0.526907i	−0.977085	−	0.212849i	$-0.931726\pi$
$347$	−5.66681	+	9.81520i	−0.304210	+	0.526907i	0.672875	+	0.739756i	$0.265059\pi$
$348$	13.5988	+	11.7136i	0.728970	+	0.627914i
$349$	4.06099	−	2.34461i	0.217380	−	0.125504i	−0.387357	−	0.921930i	$-0.626612\pi$
$349$	4.06099	−	2.34461i	0.217380	−	0.125504i	0.604736	+	0.796426i	$0.293278\pi$
$350$	−24.5135	−	21.6113i	−1.31030	−	1.15517i
$351$	0.111048	+	16.2677i	0.00592730	+	0.868305i
$352$	−12.2489	+	1.68276i	−0.652868	+	0.0896916i
$353$	−4.10521	+	2.37014i	−0.218498	+	0.126150i	−0.605255	−	0.796032i	$-0.706929\pi$
$353$	−4.10521	+	2.37014i	−0.218498	+	0.126150i	0.386756	+	0.922182i	$0.373595\pi$
$354$	0.608886	+	1.06771i	0.0323619	+	0.0567483i
$355$	7.67922	−	27.7240i	0.407571	−	1.47144i
$356$	−0.283806	−	1.76615i	−0.0150417	−	0.0936056i
$357$	10.8245	+	12.8407i	0.572892	+	0.679600i
$358$	1.35821	−	1.59389i	0.0717838	−	0.0842398i
$359$	26.0996			1.37748			0.688742	−	0.725007i	$-0.258163\pi$
$359$	26.0996			1.37748			0.688742	+	0.725007i	$0.258163\pi$
$360$	16.9761	+	8.47428i	0.894717	+	0.446634i
$361$	−37.4510			−1.97110
$362$	−2.90579	+	3.41001i	−0.152725	+	0.179226i
$363$	−3.66337	+	10.1367i	−0.192277	+	0.532040i
$364$	28.5720	−	4.59130i	1.49758	−	0.240650i
$365$	10.4104	+	2.88357i	0.544908	+	0.150933i
$366$	−24.9095	−	0.132668i	−1.30204	−	0.00693465i
$367$	−5.82958	+	3.36571i	−0.304302	+	0.175689i	−0.644374	−	0.764711i	$-0.722882\pi$
$367$	−5.82958	+	3.36571i	−0.304302	+	0.175689i	0.340072	+	0.940399i	$0.389549\pi$
$368$	0.784294	+	0.163021i	0.0408841	+	0.00849803i
$369$	−2.13662	+	12.4484i	−0.111228	+	0.648037i
$370$	−0.257727	+	0.174379i	−0.0133986	+	0.00906552i
$371$	−31.2943	+	18.0678i	−1.62472	+	0.938031i
$372$	0.785806	+	0.149057i	0.0407421	+	0.00772827i
$373$	7.68104	−	13.3040i	0.397709	−	0.688852i	−0.595734	−	0.803182i	$-0.703139\pi$
$373$	7.68104	−	13.3040i	0.397709	−	0.688852i	0.993443	+	0.114330i	$0.0364720\pi$
$374$	1.17462	−	6.37771i	0.0607380	−	0.329783i
$375$	11.4686	−	15.6035i	0.592237	−	0.805764i
$376$	0.499310	−	21.8919i	0.0257499	−	1.12899i
$377$			16.2212i			0.835432i
$378$	31.9226	−	11.5909i	1.64192	−	0.596169i
$379$			7.88904i			0.405233i	0.979258	+	0.202616i	$0.0649445\pi$
$379$			7.88904i			0.405233i	−0.979258	+	0.202616i	$0.935056\pi$
$380$	3.71815	−	33.3945i	0.190737	−	1.71310i
$381$	3.78532	+	21.1856i	0.193928	+	1.08537i
$382$	3.80320	−	20.6499i	0.194589	−	1.05654i
$383$	7.33495	+	4.23484i	0.374799	+	0.216390i	0.675553	−	0.737312i	$-0.263905\pi$
$383$	7.33495	+	4.23484i	0.374799	+	0.216390i	−0.300754	+	0.953702i	$0.597238\pi$
$384$	−0.997666	+	19.5705i	−0.0509119	+	0.998703i
$385$	15.8365	+	16.1053i	0.807104	+	0.820802i
$386$	−0.281509	−	0.792124i	−0.0143284	−	0.0403180i
$387$	21.6652	+	18.0119i	1.10130	+	0.915596i
$388$	17.8142	+	21.8978i	0.904380	+	1.11169i
$389$	4.38581	−	2.53215i	0.222369	−	0.128385i	−0.384678	−	0.923051i	$-0.625687\pi$
$389$	4.38581	−	2.53215i	0.222369	−	0.128385i	0.607047	+	0.794666i	$0.292354\pi$
$390$	4.21024	+	16.6232i	0.213194	+	0.841746i
$391$	−0.210080	+	0.363869i	−0.0106242	+	0.0184017i
$392$	−19.4997	−	35.6267i	−0.984885	−	1.79942i
$393$	−0.0161278	−	0.00582851i	−0.000813539	−	0.000294009i
$394$	−8.37271	−	7.13469i	−0.421811	−	0.359441i
$395$	−9.27443	+	2.40162i	−0.466647	+	0.120839i
$396$	−11.2865	−	6.67757i	−0.567169	−	0.335561i
$397$	−16.5579			−0.831016			−0.415508	−	0.909589i	$-0.636396\pi$
$397$	−16.5579			−0.831016			−0.415508	+	0.909589i	$0.636396\pi$
$398$	−7.75267	−	6.60633i	−0.388606	−	0.331146i
$399$	−38.7643	−	45.9846i	−1.94064	−	2.30211i
$400$	19.5102	+	4.39907i	0.975510	+	0.219953i
$401$	4.23386	−	7.33326i	0.211429	−	0.366205i	−0.740733	−	0.671799i	$-0.765522\pi$
$401$	4.23386	−	7.33326i	0.211429	−	0.366205i	0.952162	+	0.305594i	$0.0988550\pi$
$402$	10.0604	−	5.73714i	0.501766	−	0.286142i
$403$	0.361430	+	0.626016i	0.0180041	+	0.0311841i
$404$	−15.4893	−	19.0399i	−0.770620	−	0.947269i
$405$	8.51756	+	18.2332i	0.423241	+	0.906017i
$406$	31.9087	−	11.3399i	1.58360	−	0.562789i
$407$	0.186260	−	0.107537i	0.00923258	−	0.00533043i
$408$	−9.58415	−	3.71287i	−0.474486	−	0.183814i
$409$	0.571613	−	0.990063i	0.0282645	−	0.0489555i	−0.851547	−	0.524278i	$-0.824335\pi$
$409$	0.571613	−	0.990063i	0.0282645	−	0.0489555i	0.879812	+	0.475323i	$0.157669\pi$
$410$	0.947806	+	13.2798i	0.0468088	+	0.655845i
$411$	−3.38555	+	2.85397i	−0.166997	+	0.140776i
$412$	5.81510	−	15.2514i	0.286489	−	0.751381i
$413$	2.31907			0.114114
$414$	0.544156	+	0.652532i	0.0267438	+	0.0320702i
$415$	1.38814	−	0.359461i	0.0681413	−	0.0176453i
$416$	−13.9897	+	10.8603i	−0.685903	+	0.532470i
$417$	−3.28416	−	1.18688i	−0.160826	−	0.0581219i
$418$	−4.20650	+	22.8396i	−0.205747	+	1.11712i
$419$	10.0894	+	5.82511i	0.492899	+	0.284575i	0.725776	−	0.687931i	$-0.241481\pi$
$419$	10.0894	+	5.82511i	0.492899	+	0.284575i	−0.232877	+	0.972506i	$0.574814\pi$
$420$	29.7562	−	19.9029i	1.45195	−	0.971161i
$421$	7.47128	−	4.31355i	0.364128	−	0.210229i	−0.306762	−	0.951786i	$-0.599246\pi$
$421$	7.47128	−	4.31355i	0.364128	−	0.210229i	0.670890	+	0.741557i	$0.265912\pi$
$422$	−7.39267	−	20.8018i	−0.359870	−	1.01262i
$423$	14.8482	−	17.8598i	0.721945	−	0.868375i
$424$	11.4913	−	18.8950i	0.558068	−	0.917623i
$425$	−5.39720	+	8.99518i	−0.261803	+	0.436330i
$426$	27.2073	+	15.9020i	1.31820	+	0.770452i
$427$	−23.4995	+	40.7023i	−1.13722	+	1.96972i
$428$	−4.39203	−	27.3319i	−0.212297	−	1.32114i
$429$	−2.08465	−	11.6674i	−0.100648	−	0.563306i
$430$	26.7117	+	12.9807i	1.28815	+	0.625983i
$431$	−2.84066			−0.136830			−0.0684150	−	0.997657i	$-0.521794\pi$
$431$	−2.84066			−0.136830			−0.0684150	+	0.997657i	$0.521794\pi$
$432$	−13.7318	+	15.6025i	−0.660670	+	0.750677i
$433$			31.7616i			1.52637i	0.646183	+	0.763183i	$0.276364\pi$
$433$			31.7616i			1.52637i	−0.646183	+	0.763183i	$0.723636\pi$
$434$	0.978768	−	1.14861i	0.0469824	−	0.0551348i
$435$	8.36871	+	18.2382i	0.401249	+	0.874456i
$436$	−15.1995	+	2.44244i	−0.727924	+	0.116972i
$437$	0.752332	−	1.30308i	0.0359889	−	0.0623346i
$438$	−5.97123	+	10.2164i	−0.285316	+	0.488160i
$439$	11.5938	+	20.0811i	0.553342	+	0.958417i	0.998030	+	0.0627313i	$0.0199811\pi$
$439$	11.5938	+	20.0811i	0.553342	+	0.958417i	−0.444688	+	0.895685i	$0.646686\pi$
$440$	−13.2341	−	3.99276i	−0.630912	−	0.190347i
$441$	7.28723	−	42.4568i	0.347011	−	2.02175i
$442$	−3.11066	−	8.75293i	−0.147959	−	0.416334i
$443$	14.1723	+	24.5472i	0.673347	+	1.16627i	0.976949	+	0.213473i	$0.0684774\pi$
$443$	14.1723	+	24.5472i	0.673347	+	1.16627i	−0.303602	+	0.952799i	$0.598189\pi$
$444$	−0.112436	−	0.321800i	−0.00533600	−	0.0152720i
$445$	0.533860	−	1.92737i	0.0253074	−	0.0913663i
$446$	−25.2781	−	4.65561i	−1.19695	−	0.220449i
$447$	−3.95921	−	1.43084i	−0.187264	−	0.0676765i
$448$	31.1433	+	19.9270i	1.47138	+	0.941464i
$449$	−2.98484			−0.140863			−0.0704317	−	0.997517i	$-0.522438\pi$
$449$	−2.98484			−0.140863			−0.0704317	+	0.997517i	$0.522438\pi$
$450$	13.3099	+	16.5181i	0.627433	+	0.778670i
$451$		−	9.20192i		−	0.433301i
$452$	−10.8130	+	28.3595i	−0.508602	+	1.33392i
$453$	−17.7957	−	21.1104i	−0.836116	−	0.991852i
$454$	−5.05651	+	27.4548i	−0.237314	+	1.28852i
$455$	31.1803	+	8.63656i	1.46175	+	0.404888i
$456$	34.3224	+	13.2964i	1.60730	+	0.622661i
$457$	−30.7880	+	17.7755i	−1.44020	+	0.831502i	−0.997863	−	0.0653453i	$-0.979185\pi$
$457$	−30.7880	+	17.7755i	−1.44020	+	0.831502i	−0.442341	+	0.896847i	$0.645852\pi$
$458$	−8.52612	−	23.9912i	−0.398399	−	1.12103i
$459$	−5.51515	−	9.40370i	−0.257425	−	0.438927i
$460$	0.721305	+	0.530882i	0.0336310	+	0.0247525i
$461$	−10.9739	+	6.33580i	−0.511107	+	0.295088i	−0.733288	−	0.679918i	$-0.762015\pi$
$461$	−10.9739	+	6.33580i	−0.511107	+	0.295088i	0.222182	+	0.975005i	$0.428682\pi$
$462$	−21.4936	+	12.2571i	−0.999971	+	0.570254i
$463$	−15.8157	−	9.13117i	−0.735016	−	0.424362i	0.0852384	−	0.996361i	$-0.472835\pi$
$463$	−15.8157	−	9.13117i	−0.735016	−	0.424362i	−0.820254	+	0.571999i	$0.806168\pi$
$464$	−13.7981	+	15.4637i	−0.640559	+	0.717885i
$465$	0.729343	+	0.517393i	0.0338225	+	0.0239935i
$466$	−0.413341	+	0.485064i	−0.0191477	+	0.0224702i
$467$	−15.3569			−0.710632			−0.355316	−	0.934746i	$-0.615627\pi$
$467$	−15.3569			−0.710632			−0.355316	+	0.934746i	$0.615627\pi$
$468$	−18.7837	−	0.200089i	−0.868276	−	0.00924912i
$469$		−	21.8511i		−	1.00899i
$470$	10.7007	−	22.0199i	0.493585	−	1.01570i
$471$	−5.19855	+	14.3847i	−0.239537	+	0.662810i
$472$	−1.24499	+	0.681426i	−0.0573052	+	0.0313652i
$473$	−17.7766	−	10.2634i	−0.817371	−	0.471909i
$474$	0.0558941	−	10.4946i	0.00256730	−	0.482032i
$475$	19.3283	−	32.2132i	0.886842	−	1.47804i
$476$	−15.0433	+	12.2380i	−0.689509	+	0.560927i
$477$	22.0051	−	8.12281i	1.00755	−	0.371918i
$478$	−34.0501	+	12.1009i	−1.55742	+	0.553483i
$479$	0.968888	+	1.67816i	0.0442696	+	0.0766772i	0.887311	−	0.461171i	$-0.152571\pi$
$479$	0.968888	+	1.67816i	0.0442696	+	0.0766772i	−0.843042	+	0.537848i	$0.819237\pi$
$480$	−10.1264	+	19.4282i	−0.462203	+	0.886774i
$481$	0.154039	−	0.266804i	0.00702359	−	0.0121652i
$482$	1.73821	−	9.43778i	0.0791731	−	0.429879i
$483$	1.57809	−	0.281965i	0.0718058	−	0.0128298i
$484$	−11.6292	−	4.43402i	−0.528599	−	0.201546i
$485$	7.91170	+	30.5529i	0.359252	+	1.38733i
$486$	−21.6959	+	3.91009i	−0.984145	+	0.177365i
$487$		−	22.0666i		−	0.999932i	−0.866045	−	0.499966i	$-0.833346\pi$
$487$		−	22.0666i		−	0.999932i	0.866045	−	0.499966i	$-0.166654\pi$
$488$	0.655864	−	28.7559i	0.0296896	−	1.30172i
$489$	28.2251	−	5.04309i	1.27638	−	0.228056i
$490$	−3.23262	−	45.2927i	−0.146035	−	2.04611i
$491$	18.1933	+	10.5039i	0.821051	+	0.474034i	0.850779	−	0.525524i	$-0.176131\pi$
$491$	18.1933	+	10.5039i	0.821051	+	0.474034i	−0.0297277	+	0.999558i	$0.509464\pi$
$492$	−14.3288	−	2.71800i	−0.645994	−	0.122537i
$493$	−5.43512	−	9.41391i	−0.244786	−	0.423981i
$494$	11.1398	+	31.3457i	0.501204	+	1.41031i
$495$	−8.36322	−	12.0427i	−0.375899	−	0.541278i
$496$	−0.187949	+	0.904224i	−0.00843914	+	0.0406008i
$497$	51.4928	−	29.7294i	2.30977	−	1.33355i
$498$	−0.00836590	+	1.57077i	−0.000374885	+	0.0703879i
$499$	−29.9923	−	17.3160i	−1.34264	−	0.775173i	−0.355444	−	0.934697i	$-0.615670\pi$
$499$	−29.9923	−	17.3160i	−1.34264	−	0.775173i	−0.987194	+	0.159525i	$0.949004\pi$
$500$	17.7832	+	13.5557i	0.795290	+	0.606229i
$501$	21.2752	+	7.68876i	0.950506	+	0.343509i
$502$	−19.4268	+	22.7977i	−0.867060	+	1.01751i
$503$			0.624483i			0.0278443i	0.999903	+	0.0139222i	$0.00443170\pi$
$503$			0.624483i			0.0278443i	−0.999903	+	0.0139222i	$0.995568\pi$
$504$	12.7377	+	37.0893i	0.567382	+	1.65209i
$505$	−6.87914	−	26.5654i	−0.306117	−	1.18214i
$506$	−0.471154	−	0.401488i	−0.0209454	−	0.0178483i
$507$	3.57028	+	4.23529i	0.158562	+	0.188096i
$508$	−24.5357	+	3.94270i	−1.08859	+	0.174929i
$509$	−30.1814	−	17.4252i	−1.33777	−	0.772360i	−0.351291	−	0.936267i	$-0.614257\pi$
$509$	−30.1814	−	17.4252i	−1.33777	−	0.772360i	−0.986476	+	0.163907i	$0.947590\pi$
$510$	−8.01321	−	8.23650i	−0.354831	−	0.364718i
$511$	11.1635	+	19.3357i	0.493843	+	0.855361i
$512$	−22.5745	−	1.54678i	−0.997661	−	0.0683587i
$513$	19.7507	+	33.6762i	0.872014	+	1.48684i
$514$	10.1167	+	28.4668i	0.446229	+	1.25562i
$515$	13.0121	−	12.7949i	0.573381	−	0.563812i
$516$	−21.2324	+	24.6495i	−0.934704	+	1.08513i
$517$	−8.46065	+	14.6543i	−0.372099	+	0.644494i
$518$	−0.632516	−	0.116494i	−0.0277912	−	0.00511845i
$519$	−10.3244	−	12.2474i	−0.453190	−	0.537602i
$520$	−19.2768	+	4.52535i	−0.845344	+	0.198450i
$521$	43.4812			1.90494			0.952472	−	0.304625i	$-0.0985312\pi$
$521$	43.4812			1.90494			0.952472	+	0.304625i	$0.0985312\pi$
$522$	−21.6594	+	3.75105i	−0.948008	+	0.164179i
$523$	20.2848			0.886992			0.443496	−	0.896276i	$-0.353738\pi$
$523$	20.2848			0.886992			0.443496	+	0.896276i	$0.353738\pi$
$524$	0.00705462	−	0.0185023i	0.000308183	−	0.000808276i
$525$	39.5132	−	6.37580i	1.72450	−	0.278263i
$526$	32.9645	+	6.07125i	1.43732	+	0.264719i
$527$	−0.419510	−	0.242204i	−0.0182741	−	0.0105506i
$528$	7.93719	−	12.8958i	0.345422	−	0.561218i
$529$	−11.4799	−	19.8839i	−0.499128	−	0.864515i
$530$	20.4783	−	13.8557i	0.889520	−	0.601852i
$531$	−1.48367	−	0.254655i	−0.0643858	−	0.0110511i
$532$	53.8726	−	43.8263i	2.33567	−	1.90011i
$533$	−6.59053	−	11.4151i	−0.285468	−	0.494444i
$534$	1.89145	+	1.10550i	0.0818512	+	0.0478398i
$535$	8.26172	−	29.8270i	0.357185	−	1.28953i
$536$	6.42064	+	11.7307i	0.277329	+	0.506690i
$537$	0.451107	+	2.52475i	0.0194667	+	0.108951i
$538$	11.2755	−	13.2321i	0.486122	−	0.570474i
$539$			31.3844i			1.35182i
$540$	−21.2226	+	9.46577i	−0.913276	+	0.407342i
$541$			31.5322i			1.35568i	0.735211	+	0.677839i	$0.237083\pi$
$541$			31.5322i			1.35568i	−0.735211	+	0.677839i	$0.762917\pi$
$542$	8.32698	+	7.09572i	0.357674	+	0.304787i
$543$	−0.965109	−	5.40150i	−0.0414168	−	0.231801i
$544$	4.48001	−	10.9902i	0.192079	−	0.471201i
$545$	−16.5870	−	4.59441i	−0.710510	−	0.196803i
$546$	−17.8844	+	30.5991i	−0.765381	+	1.30952i
$547$	−7.90235	−	13.6873i	−0.337880	−	0.585226i	0.646154	−	0.763207i	$-0.276377\pi$
$547$	−7.90235	−	13.6873i	−0.337880	−	0.585226i	−0.984034	+	0.177982i	$0.943043\pi$
$548$	−3.22665	−	3.96630i	−0.137836	−	0.169432i
$549$	19.5037	−	23.4597i	0.832400	−	1.00123i
$550$	−11.5930	−	10.2205i	−0.494326	−	0.435802i
$551$	19.4641	+	33.7128i	0.829198	+	1.43621i
$552$	−0.764346	+	0.615073i	−0.0325327	+	0.0261792i
$553$	−17.1482	−	9.90054i	−0.729217	−	0.421014i
$554$	1.22452	−	6.64864i	0.0520247	−	0.282474i
$555$	0.0355462	−	0.379451i	0.00150885	−	0.0161068i
$556$	1.43656	−	3.76770i	0.0609238	−	0.159786i
$557$	−40.2293			−1.70457			−0.852284	−	0.523079i	$-0.824783\pi$
$557$	−40.2293			−1.70457			−0.852284	+	0.523079i	$0.824783\pi$
$558$	−0.752314	+	0.627365i	−0.0318480	+	0.0265585i
$559$	−29.4030			−1.24361
$560$	22.3779	+	34.7559i	0.945637	+	1.46870i
$561$	5.11913	+	6.07263i	0.216130	+	0.256387i
$562$	3.73320	−	20.2698i	0.157476	−	0.855032i
$563$	2.65347	−	4.59595i	0.111830	−	0.193696i	−0.804678	−	0.593712i	$-0.797662\pi$
$563$	2.65347	−	4.59595i	0.111830	−	0.193696i	0.916508	+	0.400016i	$0.130995\pi$
$564$	20.3200	+	17.5030i	0.855625	+	0.737011i
$565$	−24.1956	+	23.7918i	−1.01792	+	1.00093i
$566$	31.9200	−	11.3439i	1.34170	−	0.476820i
$567$	−13.8698	+	39.2139i	−0.582477	+	1.64683i
$568$	−18.9083	+	31.0906i	−0.793373	+	1.30453i
$569$	−11.7181	−	20.2964i	−0.491250	−	0.850870i	0.508699	−	0.860944i	$-0.330126\pi$
$569$	−11.7181	−	20.2964i	−0.491250	−	0.850870i	−0.999949	+	0.0100746i	$0.996793\pi$
$570$	28.6967	+	29.4963i	1.20197	+	1.23546i
$571$	−30.2311	−	17.4540i	−1.26513	−	0.730425i	−0.291070	−	0.956702i	$-0.594011\pi$
$571$	−30.2311	−	17.4540i	−1.26513	−	0.730425i	−0.974063	+	0.226277i	$0.927345\pi$
$572$	13.5123	−	2.17133i	0.564979	−	0.0907877i
$573$	16.5749	+	19.6621i	0.692424	+	0.821396i
$574$	−17.8474	+	20.9443i	−0.744937	+	0.874200i
$575$	0.485997	+	0.875472i	0.0202675	+	0.0365097i
$576$	−17.7364	−	16.1685i	−0.739015	−	0.673689i
$577$		−	19.4970i		−	0.811673i	−0.913946	−	0.405836i	$-0.866980\pi$
$577$		−	19.4970i		−	0.811673i	0.913946	−	0.405836i	$-0.133020\pi$
$578$	−13.5609	−	11.5557i	−0.564059	−	0.480656i
$579$	0.968299	+	0.349939i	0.0402412	+	0.0145430i
$580$	−21.2254	+	9.29381i	−0.881335	+	0.385904i
$581$	2.56665	+	1.48186i	0.106483	+	0.0614777i
$582$	−34.5724	−	0.184132i	−1.43307	−	0.00763254i
$583$	−14.7997	+	8.54463i	−0.612943	+	0.353883i
$584$	−11.6746	−	7.10010i	−0.483099	−	0.293804i
$585$	−18.9998	−	8.94929i	−0.785546	−	0.370008i
$586$	−12.6442	+	4.49358i	−0.522329	+	0.185628i
$587$	−15.8184	−	27.3982i	−0.652893	−	1.13084i	−0.982417	−	0.186697i	$-0.940222\pi$
$587$	−15.8184	−	27.3982i	−0.652893	−	1.13084i	0.329524	−	0.944147i	$-0.393112\pi$
$588$	48.8704	+	9.27010i	2.01538	+	0.382292i
$589$	1.50234	+	0.867374i	0.0619027	+	0.0357395i
$590$	−1.58277	+	0.112965i	−0.0651616	+	0.00465070i
$591$	13.2625	−	2.36966i	0.545546	−	0.0974750i
$592$	0.373795	−	0.123316i	0.0153629	−	0.00506827i
$593$		−	0.602279i		−	0.0247326i	−0.999924	−	0.0123663i	$-0.996064\pi$
$593$		−	0.602279i		−	0.0247326i	0.999924	−	0.0123663i	$-0.00393642\pi$
$594$	15.0969	−	5.48156i	0.619432	−	0.224911i
$595$	−20.9892	+	5.43517i	−0.860472	+	0.222820i
$596$	1.73184	−	4.54213i	0.0709390	−	0.186053i
$597$	12.2803	−	2.19418i	0.502601	−	0.0898018i
$598$	−0.872025	−	0.160605i	−0.0356597	−	0.00656765i
$599$	4.08597	−	7.07711i	0.166948	−	0.289163i	−0.770397	−	0.637564i	$-0.779942\pi$
$599$	4.08597	−	7.07711i	0.166948	−	0.289163i	0.937345	+	0.348401i	$0.113275\pi$
$600$	−19.3391	+	15.0332i	−0.789517	+	0.613729i
$601$	3.85232	+	6.67241i	0.157139	+	0.272173i	0.933836	−	0.357702i	$-0.116440\pi$
$601$	3.85232	+	6.67241i	0.157139	+	0.272173i	−0.776697	+	0.629875i	$0.783106\pi$
$602$	20.5550	+	57.8386i	0.837760	+	2.35733i
$603$	−2.39945	+	13.9797i	−0.0977132	+	0.569297i
$604$	24.7316	−	20.1196i	1.00631	−	0.818653i
$605$	−9.75614	−	9.92171i	−0.396643	−	0.403375i
$606$	30.0604	+	0.160101i	1.22112	+	0.00650367i
$607$	−9.35464	−	5.40090i	−0.379693	−	0.219216i	0.297992	−	0.954568i	$-0.403683\pi$
$607$	−9.35464	−	5.40090i	−0.379693	−	0.219216i	−0.677685	+	0.735353i	$0.737017\pi$
$608$	−16.0437	+	39.3577i	−0.650657	+	1.59617i
$609$	−14.0964	+	39.0055i	−0.571215	+	1.58058i
$610$	14.0558	−	28.9241i	0.569102	−	1.17110i
$611$			24.2385i			0.980584i
$612$	10.9681	−	6.17760i	0.443359	−	0.249715i
$613$	25.9976			1.05003			0.525016	−	0.851092i	$-0.324059\pi$
$613$	25.9976			1.05003			0.525016	+	0.851092i	$0.324059\pi$
$614$	−13.4928	−	11.4977i	−0.544523	−	0.464008i
$615$	−13.2993	−	9.43444i	−0.536278	−	0.380433i
$616$	−13.7174	−	25.0622i	−0.552690	−	1.00978i
$617$	31.8716	+	18.4011i	1.28310	+	0.740800i	0.977414	−	0.211332i	$-0.0677801\pi$
$617$	31.8716	+	18.4011i	1.28310	+	0.740800i	0.305688	+	0.952132i	$0.401113\pi$
$618$	9.90302	+	17.3655i	0.398358	+	0.698542i
$619$	−3.84060	+	2.21737i	−0.154367	+	0.0891236i	−0.575194	−	0.818017i	$-0.695073\pi$
$619$	−3.84060	+	2.21737i	−0.154367	+	0.0891236i	0.420827	+	0.907141i	$0.361740\pi$
$620$	−0.612061	+	0.831602i	−0.0245810	+	0.0333980i
$621$	−1.04058	+	0.00710330i	−0.0417570	+	0.000285046i
$622$	−35.7151	+	12.6926i	−1.43205	+	0.508929i
$623$	3.57978	−	2.06679i	0.143421	−	0.0828041i
$624$	0.610079	−	21.6822i	0.0244227	−	0.867981i
$625$	11.7644	+	22.0590i	0.470575	+	0.882360i
$626$	−39.4900	−	7.27308i	−1.57834	−	0.290691i
$627$	−18.3325	−	21.7471i	−0.732128	−	0.868495i
$628$	−16.5025	−	6.29215i	−0.658522	−	0.251084i
$629$			0.206452i			0.00823177i
$630$	−4.32178	+	43.6309i	−0.172184	+	1.73830i
$631$	16.2943			0.648666			0.324333	−	0.945943i	$-0.394860\pi$
$631$	16.2943			0.648666			0.324333	+	0.945943i	$0.394860\pi$
$632$	12.1151	+	0.276321i	0.481914	+	0.0109915i
$633$	25.4284	+	9.18970i	1.01069	+	0.365258i
$634$	−0.151010	+	0.819926i	−0.00599738	+	0.0325634i
$635$	−26.7755	−	7.41649i	−1.06255	−	0.294314i
$636$	8.93390	+	25.5694i	0.354252	+	1.01389i
$637$	22.4779	+	38.9328i	0.890606	+	1.54257i
$638$	15.0903	−	5.36288i	0.597431	−	0.212318i
$639$	−36.2081	+	13.3656i	−1.43237	+	0.528734i
$640$	−22.2260	−	12.0832i	−0.878561	−	0.477631i
$641$	−17.5690	−	30.4303i	−0.693932	−	1.20193i	−0.970539	−	0.240943i	$-0.922543\pi$
$641$	−17.5690	−	30.4303i	−0.693932	−	1.20193i	0.276607	−	0.960983i	$-0.410790\pi$
$642$	29.2711	+	17.1082i	1.15524	+	0.675206i
$643$	13.5973	−	23.5512i	0.536225	−	0.928768i	−0.462878	−	0.886422i	$-0.653183\pi$
$643$	13.5973	−	23.5512i	0.536225	−	0.928768i	0.999103	−	0.0423464i	$-0.0134833\pi$
$644$	0.293688	+	1.82764i	0.0115729	+	0.0720190i
$645$	−33.0592	+	15.1694i	−1.30170	+	0.597293i
$646$	−16.9678	−	14.4588i	−0.667587	−	0.568876i
$647$		−	21.8547i		−	0.859197i	−0.903020	−	0.429598i	$-0.858655\pi$
$647$		−	21.8547i		−	0.859197i	0.903020	−	0.429598i	$-0.141345\pi$
$648$	−4.07645	−	25.1273i	−0.160138	−	0.987095i
$649$	1.09674			0.0430508
$650$	−21.7013	−	4.37564i	−0.851195	−	0.171627i
$651$	0.325081	+	1.81941i	0.0127409	+	0.0713082i
$652$	5.25276	+	32.6883i	0.205714	+	1.28017i
$653$	−1.48294	+	2.56853i	−0.0580321	+	0.100515i	−0.893582	−	0.448900i	$-0.851816\pi$
$653$	−1.48294	+	2.56853i	−0.0580321	+	0.100515i	0.835550	+	0.549415i	$0.185149\pi$
$654$	9.51399	−	16.2779i	0.372027	−	0.636516i
$655$	0.0157857	−	0.0155222i	0.000616797	−	0.000606504i
$656$	3.42717	−	16.4881i	0.133808	−	0.643754i
$657$	−5.01881	−	13.5962i	−0.195803	−	0.530440i
$658$	47.6796	−	16.9446i	1.85874	−	0.660571i
$659$	28.3724	−	16.3808i	1.10523	−	0.638107i	0.167643	−	0.985848i	$-0.446384\pi$
$659$	28.3724	−	16.3808i	1.10523	−	0.638107i	0.937591	+	0.347741i	$0.113051\pi$
$660$	14.0723	−	9.41251i	0.547765	−	0.366381i
$661$	19.5382	+	11.2804i	0.759950	+	0.438757i	0.829278	−	0.558837i	$-0.188752\pi$
$661$	19.5382	+	11.2804i	0.759950	+	0.438757i	−0.0693281	+	0.997594i	$0.522086\pi$
$662$	32.9416	+	6.06703i	1.28031	+	0.235802i
$663$	10.6997	+	3.86681i	0.415540	+	0.150174i
$664$	−1.81332	−	0.0413582i	−0.0703706	−	0.00160501i
$665$	75.1658	−	19.4642i	2.91480	−	0.754791i
$666$	0.391873	+	0.143985i	0.0151848	+	0.00557932i
$667$	−1.03760			−0.0401762
$668$	−9.30622	+	24.4076i	−0.360068	+	0.944357i
$669$	24.0689	−	20.2897i	0.930559	−	0.784446i
$670$	1.06440	+	14.9134i	0.0411213	+	0.576156i
$671$	−11.1134	+	19.2490i	−0.429029	+	0.743100i
$672$	−43.0775	+	13.9575i	−1.66175	+	0.538421i
$673$	16.9745	−	9.80026i	0.654321	−	0.377772i	−0.135789	−	0.990738i	$-0.543357\pi$
$673$	16.9745	−	9.80026i	0.654321	−	0.377772i	0.790110	+	0.612966i	$0.210024\pi$
$674$	13.4427	+	37.8257i	0.517794	+	1.45699i
$675$	−25.9795	−	0.259860i	−0.999950	−	0.0100020i
$676$	−4.96179	+	4.03650i	−0.190838	+	0.155250i
$677$	−8.73705	−	15.1330i	−0.335792	−	0.581609i	0.647845	−	0.761773i	$-0.275671\pi$
$677$	−8.73705	−	15.1330i	−0.335792	−	0.581609i	−0.983637	+	0.180164i	$0.942337\pi$
$678$	−18.4144	−	32.2906i	−0.707201	−	1.24011i
$679$	−32.6155	+	56.4916i	−1.25167	+	2.16795i
$680$	9.67095	−	9.08523i	0.370864	−	0.348403i
$681$	−22.0369	−	26.1415i	−0.844456	−	1.00175i
$682$	0.462881	−	0.543200i	0.0177246	−	0.0208002i
$683$	−6.62592			−0.253534			−0.126767	−	0.991933i	$-0.540460\pi$
$683$	−6.62592			−0.253534			−0.126767	+	0.991933i	$0.540460\pi$
$684$	−39.2786	+	22.1230i	−1.50185	+	0.845895i
$685$	−1.43303	−	5.53398i	−0.0547533	−	0.211443i
$686$	31.1969	−	36.6103i	1.19110	−	1.39779i
$687$	29.3270	+	10.5987i	1.11890	+	0.404364i
$688$	−28.0300	−	25.0108i	−1.06863	−	0.953527i
$689$	−12.2395	+	21.1995i	−0.466290	+	0.807637i
$690$	−1.06332	+	0.269312i	−0.0404798	+	0.0102526i
$691$	18.4808	−	10.6699i	0.703042	−	0.405901i	−0.105438	−	0.994426i	$-0.533624\pi$
$691$	18.4808	−	10.6699i	0.703042	−	0.405901i	0.808479	+	0.588525i	$0.200291\pi$
$692$	14.3483	−	11.6726i	0.545441	−	0.443725i
$693$	5.12632	−	29.8670i	0.194733	−	1.13455i
$694$	15.1028	−	5.36730i	0.573293	−	0.203740i
$695$	3.21450	−	3.16086i	0.121933	−	0.119898i
$696$	−3.89357	−	25.0820i	−0.147586	−	0.950733i
$697$	7.64959	+	4.41649i	0.289749	+	0.167287i
$698$	−6.52188	−	1.20117i	−0.246857	−	0.0454649i
$699$	−0.137284	−	0.768349i	−0.00519256	−	0.0290616i
$700$	6.56361	+	45.7476i	0.248081	+	1.72910i
$701$			7.84565i			0.296326i	0.988963	+	0.148163i	$0.0473360\pi$
$701$			7.84565i			0.296326i	−0.988963	+	0.148163i	$0.952664\pi$
$702$	14.8020	−	17.6125i	0.558664	−	0.664743i
$703$		−	0.739339i		−	0.0278847i
$704$	14.7283	+	9.42393i	0.555095	+	0.355178i
$705$	12.5049	+	27.2525i	0.470964	+	1.02639i
$706$	6.59289	+	1.21425i	0.248127	+	0.0456988i
$707$	28.3588	−	49.1189i	1.06654	−	1.84730i
$708$	0.323947	−	1.70780i	0.0121747	−	0.0641829i
$709$	−27.1860	+	15.6959i	−1.02099	+	0.589471i	−0.914392	−	0.404831i	$-0.867330\pi$
$709$	−27.1860	+	15.6959i	−1.02099	+	0.589471i	−0.106602	+	0.994302i	$0.533997\pi$
$710$	−33.6958	+	22.7986i	−1.26458	+	0.855618i
$711$	9.88375	+	8.21710i	0.370670	+	0.308165i
$712$	−1.31450	+	2.16142i	−0.0492630	+	0.0810025i
$713$	−0.0400437	+	0.0231193i	−0.00149965	+	0.000865823i
$714$	0.126495	−	23.7505i	0.00473396	−	0.888841i
$715$	14.7458	+	4.08442i	0.551463	+	0.152749i
$716$	−2.92399	+	0.469862i	−0.109274	+	0.0175596i
$717$	15.0424	−	41.6232i	0.561770	−	1.55445i
$718$	−28.0938	−	23.9398i	−1.04845	−	0.893425i
$719$	6.09017			0.227125			0.113562	−	0.993531i	$-0.463774\pi$
$719$	6.09017			0.227125			0.113562	+	0.993531i	$0.463774\pi$
$720$	−10.5002	−	24.6930i	−0.391318	−	0.920255i
$721$	37.7178			1.40468
$722$	40.3126	+	34.3518i	1.50028	+	1.27844i
$723$	7.57533	+	8.98632i	0.281729	+	0.334205i
$724$	6.25564	−	1.00523i	0.232489	−	0.0373592i
$725$	−25.9022	−	0.435933i	−0.961983	−	0.0161901i
$726$	13.2412	−	7.55105i	0.491426	−	0.280246i
$727$	39.1849	−	22.6234i	1.45329	−	0.839056i	0.454620	−	0.890685i	$-0.349775\pi$
$727$	39.1849	−	22.6234i	1.45329	−	0.839056i	0.998666	+	0.0516297i	$0.0164416\pi$
$728$	−34.9665	−	21.2655i	−1.29595	−	0.788151i
$729$	13.1795	−	23.5648i	0.488130	−	0.872771i
$730$	−8.56096	−	12.6529i	−0.316855	−	0.468303i
$731$	17.0639	−	9.85186i	0.631132	−	0.364384i
$732$	26.6911	+	22.9910i	0.986533	+	0.849771i
$733$	−12.3105	+	21.3224i	−0.454699	+	0.787562i	−0.998671	−	0.0515413i	$-0.983587\pi$
$733$	−12.3105	+	21.3224i	−0.454699	+	0.787562i	0.543971	+	0.839104i	$0.316920\pi$
$734$	9.36221	+	1.72429i	0.345565	+	0.0636446i
$735$	45.3589	+	32.1774i	1.67309	+	1.18688i
$736$	−0.694691	−	0.894868i	−0.0256067	−	0.0329853i
$737$		−	10.3339i		−	0.380653i
$738$	13.7181	−	11.4397i	0.504971	−	0.421103i
$739$		−	18.4734i		−	0.679557i	−0.940506	−	0.339778i	$-0.889648\pi$
$739$		−	18.4734i		−	0.679557i	0.940506	−	0.339778i	$-0.110352\pi$
$740$	0.437368	+	0.0486966i	0.0160780	+	0.00179012i
$741$	−38.3173	−	13.8477i	−1.40762	−	0.508708i
$742$	50.2581	+	9.25629i	1.84503	+	0.339809i
$743$	−18.9414	−	10.9358i	−0.694893	−	0.401197i	0.110549	−	0.993871i	$-0.464739\pi$
$743$	−18.9414	−	10.9358i	−0.694893	−	0.401197i	−0.805442	+	0.592674i	$0.798072\pi$
$744$	−0.709126	−	0.881225i	−0.0259978	−	0.0323073i
$745$	3.87523	−	3.81056i	0.141978	−	0.139608i
$746$	−20.4710	+	7.27508i	−0.749495	+	0.266360i
$747$	−1.47934	−	1.22989i	−0.0541264	−	0.0449992i
$748$	−7.11430	+	5.78761i	−0.260125	+	0.211616i
$749$	55.3987	−	31.9845i	2.02423	−	1.16869i
$750$	−26.6572	+	6.27624i	−0.973385	+	0.229176i
$751$	2.23341	−	3.86839i	0.0814984	−	0.141159i	−0.822395	−	0.568916i	$-0.807363\pi$
$751$	2.23341	−	3.86839i	0.0814984	−	0.141159i	0.903894	+	0.427757i	$0.140696\pi$
$752$	−20.6178	+	23.1067i	−0.751852	+	0.842613i
$753$	−6.45227	−	36.1120i	−0.235134	−	1.31599i
$754$	14.8788	−	17.4606i	0.541855	−	0.635878i
$755$	34.5067	−	8.93555i	1.25583	−	0.325198i
$756$	−44.9934	−	16.8044i	−1.63640	−	0.611170i
$757$	−28.1070			−1.02157			−0.510784	−	0.859709i	$-0.670645\pi$
$757$	−28.1070			−1.02157			−0.510784	+	0.859709i	$0.670645\pi$
$758$	7.23620	−	8.49184i	0.262831	−	0.308437i
$759$	0.746315	−	0.133347i	0.0270895	−	0.00484020i
$760$	−34.6333	+	32.5357i	−1.25628	+	1.18019i
$761$	7.55724	−	13.0895i	0.273950	−	0.474495i	−0.695920	−	0.718119i	$-0.745003\pi$
$761$	7.55724	−	13.0895i	0.273950	−	0.474495i	0.969870	+	0.243624i	$0.0783364\pi$
$762$	15.3579	−	26.2764i	0.556357	−	0.951895i
$763$	−17.7868	−	30.8077i	−0.643926	−	1.11531i
$764$	−23.0349	+	18.7393i	−0.833372	+	0.677963i
$765$	14.0251	−	1.17245i	0.507078	−	0.0423902i
$766$	−4.01102	−	11.2864i	−0.144924	−	0.407794i
$767$	1.36052	−	0.785498i	0.0491256	−	0.0283627i
$768$	19.0249	−	20.1508i	0.686502	−	0.727128i
$769$	18.2248	−	31.5663i	0.657203	−	1.13831i	−0.324134	−	0.946011i	$-0.605073\pi$
$769$	18.2248	−	31.5663i	0.657203	−	1.13831i	0.981337	−	0.192298i	$-0.0615939\pi$
$770$	−2.27404	−	31.8619i	−0.0819507	−	1.14822i
$771$	−34.7981	−	12.5759i	−1.25322	−	0.452910i
$772$	−0.423554	+	1.11086i	−0.0152441	+	0.0399808i
$773$	−45.0468			−1.62022			−0.810110	−	0.586278i	$-0.800593\pi$
$773$	−45.0468			−1.62022			−0.810110	+	0.586278i	$0.800593\pi$
$774$	−6.79927	−	39.2605i	−0.244395	−	1.41119i
$775$	−1.00934	+	0.560313i	−0.0362567	+	0.0201271i
$776$	0.910288	−	39.9110i	0.0326774	−	1.43272i
$777$	0.602260	−	0.507696i	0.0216059	−	0.0182135i
$778$	−7.04353	−	1.29725i	−0.252523	−	0.0465085i
$779$	−27.3945	−	15.8162i	−0.981509	−	0.566674i
$780$	10.7156	−	21.7552i	0.383680	−	0.778959i
$781$	24.3521	−	14.0597i	0.871385	−	0.503095i
$782$	0.559890	−	0.198977i	0.0200216	−	0.00711540i
$783$	13.3016	−	23.4066i	0.475361	−	0.836484i
$784$	−11.6888	+	56.2350i	−0.417457	+	2.00839i
$785$	−13.8446	−	14.0795i	−0.494134	−	0.502520i
$786$	0.0120139	+	0.0210670i	0.000428522	+	0.000751436i
$787$	3.98574	−	6.90350i	0.142076	−	0.246083i	−0.786202	−	0.617969i	$-0.787956\pi$
$787$	3.98574	−	6.90350i	0.142076	−	0.246083i	0.928278	+	0.371886i	$0.121289\pi$
$788$	2.46819	+	15.3597i	0.0879255	+	0.547166i
$789$	−31.3877	+	26.4593i	−1.11743	+	0.941977i
$790$	12.1860	+	5.92182i	0.433557	+	0.210689i
$791$	−70.1352			−2.49372
$792$	6.02393	+	17.5403i	0.214051	+	0.623269i
$793$			31.8383i			1.13061i
$794$	17.8231	+	15.1877i	0.632517	+	0.538991i
$795$	−2.82440	+	30.1502i	−0.100171	+	1.06932i
$796$	2.28540	+	14.2222i	0.0810040	+	0.504094i
$797$	−11.4728	+	19.8714i	−0.406386	+	0.703881i	−0.994482	−	0.104910i	$-0.966545\pi$
$797$	−11.4728	+	19.8714i	−0.406386	+	0.703881i	0.588096	+	0.808791i	$0.299878\pi$
$798$	−0.453000	+	85.0547i	−0.0160360	+	3.01090i
$799$	−8.12143	−	14.0667i	−0.287316	−	0.497645i
$800$	−16.9659	−	22.6309i	−0.599836	−	0.800123i
$801$	−2.51719	+	0.929175i	−0.0889404	+	0.0328308i
$802$	−11.2838	+	4.01009i	−0.398444	+	0.141601i
$803$	5.27945	+	9.14427i	0.186308	+	0.322694i
$804$	−16.0915	−	3.05235i	−0.567502	−	0.107648i
$805$	−0.552447	+	1.99448i	−0.0194712	+	0.0702961i
$806$	0.185164	−	1.00537i	0.00652214	−	0.0354126i
$807$	3.74497	+	20.9598i	0.131829	+	0.737819i
$808$	−0.791486	+	34.7022i	−0.0278444	+	1.22082i
$809$	−7.09601			−0.249482			−0.124741	−	0.992189i	$-0.539810\pi$
$809$	−7.09601			−0.249482			−0.124741	+	0.992189i	$0.539810\pi$
$810$	7.55601	−	27.4391i	0.265491	−	0.964113i
$811$			3.76265i			0.132125i	0.997816	+	0.0660623i	$0.0210436\pi$
$811$			3.76265i			0.132125i	−0.997816	+	0.0660623i	$0.978956\pi$
$812$	−44.7483	−	17.0618i	−1.57036	−	0.598752i
$813$	−13.1901	+	2.35672i	−0.462595	+	0.0826538i
$814$	−0.299131	−	0.0550925i	−0.0104845	−	0.00193099i
$815$	−9.88082	+	35.6724i	−0.346110	+	1.24955i
$816$	6.91085	+	12.7876i	0.241928	+	0.447656i
$817$	−61.1088	+	35.2812i	−2.13793	+	1.23433i
$818$	−1.52342	+	0.541402i	−0.0532652	+	0.0189297i
$819$	−15.0318	−	40.7220i	−0.525254	−	1.42294i
$820$	11.1607	−	15.1639i	0.389748	−	0.529547i
$821$	28.6223	−	16.5251i	0.998925	−	0.576730i	0.0909949	−	0.995851i	$-0.470995\pi$
$821$	28.6223	−	16.5251i	0.998925	−	0.576730i	0.907930	+	0.419122i	$0.137662\pi$
$822$	6.26204	+	0.0333516i	0.218414	+	0.00116327i
$823$	37.3901	+	21.5872i	1.30334	+	0.752482i	0.980975	−	0.194134i	$-0.0621898\pi$
$823$	37.3901	+	21.5872i	1.30334	+	0.752482i	0.322362	+	0.946616i	$0.395523\pi$
$824$	−20.2487	+	11.0828i	−0.705397	+	0.386088i
$825$	18.6866	−	3.01526i	0.650585	−	0.104978i
$826$	−2.49627	−	2.12716i	−0.0868563	−	0.0740134i
$827$	39.5272			1.37450			0.687249	−	0.726422i	$-0.258818\pi$
$827$	39.5272			1.37450			0.687249	+	0.726422i	$0.258818\pi$
$828$	0.0127989	−	1.20152i	0.000444793	−	0.0417556i
$829$			4.39738i			0.152727i	0.997080	+	0.0763636i	$0.0243310\pi$
$829$			4.39738i			0.152727i	−0.997080	+	0.0763636i	$0.975669\pi$
$830$	−1.82393	−	0.886344i	−0.0633094	−	0.0307655i
$831$	5.33660	+	6.33060i	0.185125	+	0.219606i
$832$	25.0203	+	1.14192i	0.867422	+	0.0395888i
$833$	−26.0899	−	15.0630i	−0.903963	−	0.521903i
$834$	2.44644	+	4.28996i	0.0847133	+	0.148549i
$835$	−20.8239	+	20.4764i	−0.720641	+	0.708615i
$836$	25.4775	−	20.7264i	0.881158	−	0.716838i
$837$	−0.00818950	−	1.19970i	−0.000283070	−	0.0414677i
$838$	−5.51724	−	15.5247i	−0.190590	−	0.536291i
$839$	15.1864	+	26.3036i	0.524292	+	0.908101i	0.999600	+	0.0282811i	$0.00900335\pi$
$839$	15.1864	+	26.3036i	0.524292	+	0.908101i	−0.475308	+	0.879820i	$0.657663\pi$
$840$	−50.2857	−	5.87011i	−1.73502	−	0.202538i
$841$	−1.07773	+	1.86668i	−0.0371630	+	0.0643682i
$842$	−11.9987	−	2.20987i	−0.413504	−	0.0761573i
$843$	16.2698	+	19.3002i	0.560361	+	0.664735i
$844$	−11.1229	+	29.1722i	−0.382866	+	1.00415i
$845$	−6.92294	+	1.79270i	−0.238157	+	0.0616709i
$846$	−32.3646	+	5.60501i	−1.11272	+	0.192704i
$847$		−	28.7598i		−	0.988198i
$848$	−29.7008	+	9.79839i	−1.01993	+	0.336478i
$849$	−14.1014	+	39.0193i	−0.483959	+	1.33914i
$850$	14.0604	−	4.73192i	0.482268	−	0.162304i
$851$	0.0170664	+	0.00985329i	0.000585028	+	0.000337766i
$852$	−14.7002	−	42.0729i	−0.503620	−	1.44139i
$853$	8.09875	+	14.0274i	0.277296	+	0.480290i	0.970712	−	0.240247i	$-0.0772285\pi$
$853$	8.09875	+	14.0274i	0.277296	+	0.480290i	−0.693416	+	0.720537i	$0.743895\pi$
$854$	62.6292	−	22.2575i	2.14313	−	0.761636i
$855$	−50.2261	+	4.19875i	−1.71770	+	0.143594i
$856$	−20.3425	+	33.4489i	−0.695293	+	1.14326i
$857$	−10.6451	+	6.14596i	−0.363630	+	0.209942i	−0.670672	−	0.741754i	$-0.733994\pi$
$857$	−10.6451	+	6.14596i	−0.363630	+	0.209942i	0.307042	+	0.951696i	$0.400661\pi$
$858$	−8.45792	+	14.4710i	−0.288749	+	0.494032i
$859$	6.43114	+	3.71302i	0.219428	+	0.126687i	0.605685	−	0.795704i	$-0.292899\pi$
$859$	6.43114	+	3.71302i	0.219428	+	0.126687i	−0.386258	+	0.922391i	$0.626232\pi$
$860$	−16.8462	−	38.4737i	−0.574452	−	1.31194i
$861$	−5.92772	−	33.1761i	−0.202016	−	1.13064i
$862$	3.05772	+	2.60559i	0.104146	+	0.0887468i
$863$			47.7746i			1.62626i	0.582079	+	0.813132i	$0.302240\pi$
$863$			47.7746i			1.62626i	−0.582079	+	0.813132i	$0.697760\pi$
$864$	29.0924	−	4.19927i	0.989743	−	0.142862i
$865$	20.0195	−	5.18406i	0.680683	−	0.176263i
$866$	29.1333	−	34.1885i	0.989988	−	1.16177i
$867$	21.4807	−	3.83804i	0.729522	−	0.130347i
$868$	−2.10711	+	0.338597i	−0.0715200	+	0.0114927i
$869$	−8.10977	−	4.68218i	−0.275105	−	0.158832i
$870$	7.72081	−	27.3080i	0.261760	−	0.925827i
$871$	−7.40124	−	12.8193i	−0.250782	−	0.434366i
$872$	18.6012	+	11.3126i	0.629917	+	0.383094i
$873$	27.0697	−	32.5602i	0.916170	−	1.10199i
$874$	−2.00506	+	0.712569i	−0.0678222	+	0.0241030i
$875$	−14.6289	+	49.5570i	−0.494548	+	1.67533i
$876$	15.7985	−	5.51996i	0.533781	−	0.186502i
$877$	25.6334	−	44.3984i	0.865580	−	1.49923i	−0.000891102	−	1.00000i	$-0.500284\pi$
$877$	25.6334	−	44.3984i	0.865580	−	1.49923i	0.866471	−	0.499228i	$-0.166383\pi$
$878$	5.93962	−	32.2498i	0.200453	−	1.08838i
$879$	5.58589	−	15.4564i	0.188407	−	0.521333i
$880$	10.5830	+	16.4368i	0.356752	+	0.554084i
$881$	−29.4991			−0.993851			−0.496925	−	0.867793i	$-0.665538\pi$
$881$	−29.4991			−0.993851			−0.496925	+	0.867793i	$0.665538\pi$
$882$	−46.7875	+	39.0168i	−1.57542	+	1.31376i
$883$	−29.1137			−0.979753			−0.489876	−	0.871792i	$-0.662958\pi$
$883$	−29.1137			−0.979753			−0.489876	+	0.871792i	$0.662958\pi$
$884$	−4.68025	+	12.2750i	−0.157414	+	0.412852i
$885$	1.12445	−	1.58508i	0.0377980	−	0.0532820i
$886$	7.26062	−	39.4223i	0.243925	−	1.32442i
$887$	−27.8025	−	16.0518i	−0.933517	−	0.538966i	−0.0455948	−	0.998960i	$-0.514518\pi$
$887$	−27.8025	−	16.0518i	−0.933517	−	0.538966i	−0.887922	+	0.459994i	$0.847852\pi$
$888$	−0.174143	+	0.449521i	−0.00584385	+	0.0150849i
$889$	−28.7122	−	49.7310i	−0.962977	−	1.66793i
$890$	−2.34253	+	1.58496i	−0.0785218	+	0.0531280i
$891$	−6.55933	+	18.5451i	−0.219746	+	0.621284i
$892$	22.9393	+	28.1976i	0.768063	+	0.944126i
$893$	29.0842	+	50.3753i	0.973266	+	1.68575i
$894$	2.94930	+	5.17175i	0.0986393	+	0.172969i
$895$	−3.19091	−	0.883844i	−0.106660	−	0.0295436i
$896$	−15.2449	−	50.0157i	−0.509296	−	1.67091i
$897$	0.830311	−	0.699940i	0.0277233	−	0.0233703i
$898$	3.21291	+	2.73784i	0.107216	+	0.0913628i
$899$		−	1.19627i		−	0.0398978i
$900$	0.824303	−	29.9887i	0.0274768	−	0.999622i
$901$		−	16.4041i		−	0.546500i
$902$	−8.44044	+	9.90503i	−0.281036	+	0.329801i
$903$	−70.7025	−	25.5516i	−2.35283	−	0.850303i
$904$	37.6519	−	20.6082i	1.25228	−	0.685419i
$905$	6.82671	+	1.89092i	0.226927	+	0.0628562i
$906$	−0.207961	+	39.0465i	−0.00690905	+	1.29723i
$907$	−10.3985	−	18.0107i	−0.345276	−	0.598035i	0.640128	−	0.768268i	$-0.278881\pi$
$907$	−10.3985	−	18.0107i	−0.345276	−	0.598035i	−0.985404	+	0.170233i	$0.945548\pi$
$908$	30.6258	−	24.9146i	1.01635	−	0.826820i
$909$	−23.5368	+	28.3107i	−0.780666	+	0.939007i
$910$	−25.6409	−	37.8965i	−0.849986	−	1.25626i
$911$	−11.0811	−	19.1930i	−0.367132	−	0.635891i	0.621984	−	0.783030i	$-0.286327\pi$
$911$	−11.0811	−	19.1930i	−0.367132	−	0.635891i	−0.989116	+	0.147139i	$0.952994\pi$
$912$	−24.7489	−	45.7945i	−0.819518	−	1.51641i
$913$	1.21382	+	0.700802i	0.0401717	+	0.0231932i
$914$	49.4450	+	9.10656i	1.63550	+	0.301218i
$915$	16.4258	+	35.7973i	0.543019	+	1.18342i
$916$	−12.8283	+	33.6449i	−0.423858	+	1.11166i
$917$	0.0457575			0.00151105
$918$	−2.68895	+	15.1810i	−0.0887487	+	0.501047i
$919$	−25.2546			−0.833071			−0.416536	−	0.909119i	$-0.636756\pi$
$919$	−25.2546			−0.833071			−0.416536	+	0.909119i	$0.636756\pi$
$920$	−0.289469	−	1.23306i	−0.00954351	−	0.0406528i
$921$	21.3727	−	3.81875i	0.704255	−	0.125832i
$922$	17.6239	+	3.24589i	0.580413	+	0.106898i
$923$	20.1394	−	34.8825i	0.662897	−	1.14817i
$924$	34.3787	+	6.52121i	1.13098	+	0.214532i
$925$	0.421897	+	0.253142i	0.0138719	+	0.00832327i
$926$	8.64857	+	24.3358i	0.284210	+	0.799723i
$927$	−24.1307	−	4.14175i	−0.792556	−	0.136033i
$928$	29.0364	−	3.98905i	0.953167	−	0.130947i
$929$	−29.9716	−	51.9124i	−0.983337	−	1.70319i	−0.649104	−	0.760700i	$-0.724856\pi$
$929$	−29.9716	−	51.9124i	−0.983337	−	1.70319i	−0.334233	−	0.942490i	$-0.608477\pi$
$930$	−0.310494	−	1.22591i	−0.0101815	−	0.0401993i
$931$	93.4324	+	53.9432i	3.06212	+	1.76792i
$932$	0.889848	−	0.142992i	0.0291480	−	0.00468385i
$933$	15.7780	−	43.6585i	0.516548	−	1.42932i
$934$	16.5303	+	14.0861i	0.540888	+	0.460910i
$935$	−9.92624	+	2.57041i	−0.324623	+	0.0840614i
$936$	20.0354	+	17.4447i	0.654877	+	0.570196i
$937$		−	12.5525i		−	0.410071i	−0.978755	−	0.205035i	$-0.934269\pi$
$937$		−	12.5525i		−	0.410071i	0.978755	−	0.205035i	$-0.0657309\pi$
$938$	−20.0429	+	23.5207i	−0.654423	+	0.767979i
$939$	37.6009	−	31.6970i	1.22706	−	1.03439i
$940$	−31.7160	+	13.8873i	−1.03446	+	0.452953i
$941$	17.5803	+	10.1500i	0.573101	+	0.330880i	0.758387	−	0.651805i	$-0.225988\pi$
$941$	17.5803	+	10.1500i	0.573101	+	0.330880i	−0.185286	+	0.982685i	$0.559321\pi$
$942$	18.7901	−	10.7154i	0.612213	−	0.349127i
$943$	0.730181	−	0.421570i	0.0237780	−	0.0137282i
$944$	1.96515	+	0.408470i	0.0639603	+	0.0132946i
$945$	−37.9100	−	38.0306i	−1.23321	−	1.23714i
$946$	9.72091	+	27.3531i	0.316054	+	0.889328i
$947$	12.5564	+	21.7483i	0.408029	+	0.706726i	0.994669	−	0.103121i	$-0.0328830\pi$
$947$	12.5564	+	21.7483i	0.408029	+	0.706726i	−0.586640	+	0.809848i	$0.699550\pi$
$948$	−9.68630	+	11.2452i	−0.314596	+	0.365227i
$949$	13.0985	+	7.56241i	0.425195	+	0.245486i
$950$	−50.3526	+	16.9458i	−1.63366	+	0.549795i
$951$	−0.658122	−	0.780704i	−0.0213411	−	0.0253161i
$952$	27.4180	+	0.625349i	0.888623	+	0.0202677i
$953$			25.4825i			0.825459i	0.910854	+	0.412729i	$0.135424\pi$
$953$			25.4825i			0.825459i	−0.910854	+	0.412729i	$0.864576\pi$
$954$	−31.1372	−	11.4407i	−1.00810	−	0.370406i
$955$	−32.1394	+	8.32253i	−1.04001	+	0.269311i
$956$	47.7514	+	18.2069i	1.54439	+	0.588852i
$957$	−6.66650	+	18.4465i	−0.215497	+	0.596292i
$958$	0.496371	−	2.69510i	0.0160370	−	0.0870747i
$959$	5.90757	−	10.2322i	0.190766	−	0.330416i
$960$	28.7206	−	11.6244i	0.926954	−	0.375175i
$961$	15.4733	+	26.8006i	0.499140	+	0.864536i
$962$	−0.410535	+	0.145898i	−0.0132362	+	0.00470394i
$963$	−38.9546	+	14.3794i	−1.25530	+	0.463370i
$964$	−10.5278	+	8.56455i	−0.339078	+	0.275846i
$965$	−0.947760	+	0.931944i	−0.0305095	+	0.0300003i
$966$	−1.95731	−	1.14399i	−0.0629753	−	0.0368074i
$967$	39.8470	+	23.0056i	1.28139	+	0.739812i	0.977103	−	0.212768i	$-0.0682479\pi$
$967$	39.8470	+	23.0056i	1.28139	+	0.739812i	0.304289	+	0.952580i	$0.401581\pi$
$968$	8.45066	+	15.4396i	0.271614	+	0.496249i
$969$	26.8772	−	4.80225i	0.863419	−	0.154271i
$970$	19.5083	−	40.1444i	0.626375	−	1.28896i
$971$		−	60.4962i		−	1.94142i	−0.240264	−	0.970708i	$-0.577234\pi$
$971$		−	60.4962i		−	1.94142i	0.240264	−	0.970708i	$-0.422766\pi$
$972$	26.9402	+	15.6916i	0.864106	+	0.503309i
$973$	9.31779			0.298715
$974$	−20.2405	+	23.7527i	−0.648548	+	0.761085i
$975$	21.0215	−	17.1241i	0.673227	−	0.548409i
$976$	−27.0823	+	30.3516i	−0.866883	+	0.971530i
$977$	35.2401	+	20.3459i	1.12743	+	0.650923i	0.943288	−	0.331976i	$-0.107715\pi$
$977$	35.2401	+	20.3459i	1.12743	+	0.650923i	0.184144	+	0.982899i	$0.441049\pi$
$978$	−35.0075	−	20.4610i	−1.11942	−	0.654269i
$979$	1.69296	−	0.977428i	0.0541071	−	0.0312387i
$980$	−38.0650	+	51.7186i	−1.21594	+	1.65209i
$981$	7.99651	+	21.6630i	0.255309	+	0.691646i
$982$	−9.94874	−	27.9942i	−0.317477	−	0.893332i
$983$	19.7592	−	11.4080i	0.630221	−	0.363858i	−0.150617	−	0.988592i	$-0.548126\pi$
$983$	19.7592	−	11.4080i	0.630221	−	0.363858i	0.780838	+	0.624734i	$0.214793\pi$
$984$	12.9306	+	16.0688i	0.412213	+	0.512254i
$985$	−4.64283	+	16.7618i	−0.147933	+	0.534077i
$986$	−2.78447	+	15.1186i	−0.0886755	+	0.481473i
$987$	−21.0636	+	58.2840i	−0.670461	+	1.85520i
$988$	16.7608	−	43.9588i	0.533231	−	1.39851i
$989$		−	1.88079i		−	0.0598057i
$990$	−2.04386	+	20.6340i	−0.0649582	+	0.655791i
$991$	35.6989			1.13401			0.567006	−	0.823713i	$-0.308101\pi$
$991$	35.6989			1.13401			0.567006	+	0.823713i	$0.308101\pi$
$992$	1.03171	−	0.800919i	0.0327567	−	0.0254292i
$993$	−31.3658	+	26.4409i	−0.995365	+	0.839077i
$994$	−82.6965	−	15.2307i	−2.62297	−	0.483087i
$995$	−4.29901	+	15.5205i	−0.136288	+	0.492034i
$996$	1.44979	−	1.68312i	0.0459384	−	0.0533316i
$997$	18.2978	+	31.6926i	0.579496	+	1.00372i	0.995537	+	0.0943704i	$0.0300838\pi$
$997$	18.2978	+	31.6926i	0.579496	+	1.00372i	−0.416041	+	0.909346i	$0.636583\pi$
$998$	16.4009	+	46.1495i	0.519160	+	1.46084i
$999$	−0.441057	+	0.258675i	−0.0139544	+	0.00818411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.15	✓	136
5.4	even	2	inner	360.2.bk.a.229.54	yes	136
8.5	even	2	inner	360.2.bk.a.229.37	yes	136
9.7	even	3	inner	360.2.bk.a.349.32	yes	136
40.29	even	2	inner	360.2.bk.a.229.32	yes	136
45.34	even	6	inner	360.2.bk.a.349.37	yes	136
72.61	even	6	inner	360.2.bk.a.349.54	yes	136
360.349	even	6	inner	360.2.bk.a.349.15	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.15	✓	136	1.1	even	1	trivial
360.2.bk.a.229.32	yes	136	40.29	even	2	inner
360.2.bk.a.229.37	yes	136	8.5	even	2	inner
360.2.bk.a.229.54	yes	136	5.4	even	2	inner
360.2.bk.a.349.15	yes	136	360.349	even	6	inner
360.2.bk.a.349.32	yes	136	9.7	even	3	inner
360.2.bk.a.349.37	yes	136	45.34	even	6	inner
360.2.bk.a.349.54	yes	136	72.61	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07641 - 0.917248i) q^{2} +(1.70505 - 0.304648i) q^{3} +(0.317314 + 1.97467i) q^{4} +(-0.596890 + 2.15493i) q^{5} +(-2.11477 - 1.23603i) q^{6} +(-4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 - 1.03888i) q^{9} +O(q^{10})\)	\(q+(-1.07641 - 0.917248i) q^{2} +(1.70505 - 0.304648i) q^{3} +(0.317314 + 1.97467i) q^{4} +(-0.596890 + 2.15493i) q^{5} +(-2.11477 - 1.23603i) q^{6} +(-4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 - 1.03888i) q^{9} +(2.61910 - 1.77209i) q^{10} +(-1.89283 + 1.09283i) q^{11} +(1.14261 + 3.27023i) q^{12} +(-1.56540 + 2.71134i) q^{13} +(6.42783 + 1.18385i) q^{14} +(-0.361231 + 3.85610i) q^{15} +(-3.79862 + 1.25318i) q^{16} -2.09803i q^{17} +(-3.98233 - 1.46322i) q^{18} +7.51339i q^{19} +(-4.44467 - 0.494870i) q^{20} +(-6.12035 + 5.15936i) q^{21} +(3.03986 + 0.559867i) q^{22} +(-0.173434 - 0.100132i) q^{23} +(1.76969 - 4.56817i) q^{24} +(-4.28744 - 2.57251i) q^{25} +(4.17198 - 1.48266i) q^{26} +(4.48216 - 2.62873i) q^{27} +(-5.83309 - 7.17021i) q^{28} +(4.48703 - 2.59059i) q^{29} +(3.92583 - 3.81940i) q^{30} +(0.115444 - 0.199954i) q^{31} +(5.23835 + 2.13534i) q^{32} +(-2.89445 + 2.43997i) q^{33} +(-1.92441 + 2.25834i) q^{34} +(-2.59061 - 10.0042i) q^{35} +(2.94448 + 5.22781i) q^{36} -0.0984028 q^{37} +(6.89164 - 8.08748i) q^{38} +(-1.84307 + 5.09987i) q^{39} +(4.33037 + 4.60955i) q^{40} +(-2.10507 + 3.64609i) q^{41} +(11.3204 + 0.0602924i) q^{42} +(4.69577 + 8.13332i) q^{43} +(-2.75860 - 3.39095i) q^{44} +(0.558836 + 6.68489i) q^{45} +(0.0948400 + 0.266865i) q^{46} +(6.70474 - 3.87099i) q^{47} +(-6.09506 + 3.29397i) q^{48} +(7.17962 - 12.4355i) q^{49} +(2.25542 + 6.70172i) q^{50} +(-0.639160 - 3.57724i) q^{51} +(-5.85072 - 2.23079i) q^{52} +7.81882 q^{53} +(-7.23584 - 1.28166i) q^{54} +(-1.22516 - 4.73122i) q^{55} +(-0.298065 + 13.0685i) q^{56} +(2.28894 + 12.8107i) q^{57} +(-7.20609 - 1.32718i) q^{58} +(-0.434562 - 0.250894i) q^{59} +(-7.72914 + 0.510283i) q^{60} +(8.80696 - 5.08470i) q^{61} +(-0.307673 + 0.109342i) q^{62} +(-8.86370 + 10.6615i) q^{63} +(-3.67997 - 7.10337i) q^{64} +(-4.90839 - 4.99169i) q^{65} +(5.35367 + 0.0285136i) q^{66} +(-2.36402 + 4.09460i) q^{67} +(4.14291 - 0.665733i) q^{68} +(-0.326218 - 0.117894i) q^{69} +(-6.38781 + 13.1449i) q^{70} -12.8654 q^{71} +(1.62573 - 8.32809i) q^{72} -4.83099i q^{73} +(0.105922 + 0.0902597i) q^{74} +(-8.09401 - 3.08010i) q^{75} +(-14.8364 + 2.38410i) q^{76} +(5.05062 - 8.74793i) q^{77} +(6.66174 - 3.79899i) q^{78} +(2.14223 + 3.71045i) q^{79} +(-0.433153 - 8.93378i) q^{80} +(6.84146 - 5.84760i) q^{81} +(5.61028 - 1.99381i) q^{82} +(-0.320637 - 0.555359i) q^{83} +(-12.1301 - 10.4485i) q^{84} +(4.52110 + 1.25229i) q^{85} +(2.40569 - 13.0620i) q^{86} +(6.86138 - 5.78404i) q^{87} +(-0.140961 + 6.18036i) q^{88} -0.894402 q^{89} +(5.53016 - 7.70826i) q^{90} -14.4693i q^{91} +(0.142695 - 0.374248i) q^{92} +(0.135921 - 0.376102i) q^{93} +(-10.7677 - 1.98314i) q^{94} +(-16.1908 - 4.48466i) q^{95} +(9.58217 + 2.04501i) q^{96} +(12.2234 - 7.05717i) q^{97} +(-19.1346 + 6.80016i) q^{98} +(-4.19184 + 5.04206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more