LMFDB - Embedded newform 120.2.w.c.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 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("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})$	\(q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +(2.99919 + 1.00243i) q^{10} +3.68607 q^{11} +(-3.18773 + 1.35587i) q^{12} +(-3.88771 + 3.88771i) q^{13} +(0.452626 + 1.07407i) q^{14} +(-3.66213 - 1.26047i) q^{15} +(0.0980619 + 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(3.91883 - 1.62567i) q^{18} +6.32919 q^{19} +(-2.91214 + 3.39403i) q^{20} +(-0.542584 - 1.32036i) q^{21} +(-1.96533 + 4.82821i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(-0.0763660 - 4.89838i) q^{24} +(-4.95909 + 0.638332i) q^{25} +(-3.01950 - 7.16518i) q^{26} +(-4.81715 + 1.94809i) q^{27} +(-1.64820 + 0.0202063i) q^{28} -1.37122i q^{29} +(3.60361 - 4.12481i) q^{30} +3.32075 q^{31} +(-5.29013 - 2.00362i) q^{32} +(2.45973 - 5.89160i) q^{33} +(-1.62206 + 0.683558i) q^{34} +(-1.38380 - 1.21710i) q^{35} +(0.0399575 + 5.99987i) q^{36} +(-2.44147 - 2.44147i) q^{37} +(-3.37458 + 8.29032i) q^{38} +(3.61961 + 8.80819i) q^{39} +(-2.89300 - 5.62410i) q^{40} -0.648104i q^{41} +(2.01877 - 0.00672215i) q^{42} +(-0.819412 + 0.819412i) q^{43} +(-5.27640 - 5.14859i) q^{44} +(-4.45843 + 5.01223i) q^{45} +(-1.60482 - 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(6.45689 + 2.51168i) q^{48} +6.32075i q^{49} +(1.80795 - 6.83603i) q^{50} +(1.99401 - 0.819412i) q^{51} +(10.9953 - 0.134798i) q^{52} +(5.60782 + 5.60782i) q^{53} +(0.0166776 - 7.34845i) q^{54} +(-0.527212 - 8.22542i) q^{55} +(0.852318 - 2.16968i) q^{56} +(4.22349 - 10.1162i) q^{57} +(1.79611 + 0.731106i) q^{58} +6.12026i q^{59} +(3.48154 + 6.91946i) q^{60} -5.13471i q^{61} +(-1.77055 + 4.34971i) q^{62} +(-2.47245 - 0.0138443i) q^{63} +(5.44503 - 5.86102i) q^{64} +(9.23144 + 8.11933i) q^{65} +(6.40568 + 6.36316i) q^{66} +(-4.90636 - 4.90636i) q^{67} +(-0.0305156 - 2.48912i) q^{68} +(1.92377 + 4.68141i) q^{69} +(2.33203 - 1.16365i) q^{70} -4.13251i q^{71} +(-7.88026 - 3.14666i) q^{72} +(4.69820 + 4.69820i) q^{73} +(4.49972 - 1.89624i) q^{74} +(-2.28895 + 8.35229i) q^{75} +(-9.05987 - 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-13.4674 + 0.0448439i) q^{78} -1.10079i q^{79} +(8.90925 - 0.790765i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(0.848922 + 0.345554i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(-1.06756 + 2.64788i) q^{84} +(1.83806 - 2.08982i) q^{85} +(-0.636420 - 1.51020i) q^{86} +(-2.19169 - 0.915024i) q^{87} +(9.55717 - 4.16621i) q^{88} -15.3562 q^{89} +(-4.18816 - 8.51230i) q^{90} +4.53130i q^{91} +(5.84382 - 0.0716428i) q^{92} +(2.21595 - 5.30771i) q^{93} +(-11.5836 + 4.88148i) q^{94} +(-0.905253 - 14.1235i) q^{95} +(-6.73261 + 7.11843i) q^{96} +(-5.42154 + 5.42154i) q^{97} +(-8.27927 - 3.37008i) q^{98} +(-7.77542 - 7.86299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.533177	+	1.30986i	−0.377013	+	0.926208i
$2$	−0.533177	+	1.30986i	−0.377013	+	0.926208i
$3$	0.667305	−	1.59834i	0.385268	−	0.922805i
$3$	0.667305	−	1.59834i	0.385268	−	0.922805i
$4$	−1.43144	−	1.39677i	−0.715722	−	0.698385i
$5$	−0.143028	−	2.23149i	−0.0639642	−	0.997952i
$5$	−0.143028	−	2.23149i	−0.0639642	−	0.997952i
$6$	1.73781	+	1.72627i	0.709457	+	0.704748i
$7$	0.582772	−	0.582772i	0.220267	−	0.220267i	−0.588344	−	0.808611i	$-0.700220\pi$
$7$	0.582772	−	0.582772i	0.220267	−	0.220267i	0.808611	+	0.588344i	$0.200220\pi$
$8$	2.59278	−	1.13026i	0.916687	−	0.399606i
$9$	−2.10941	−	2.13317i	−0.703136	−	0.711055i
$10$	2.99919	+	1.00243i	0.948426	+	0.316997i
$11$	3.68607			1.11139			0.555695	−	0.831386i	$-0.312452\pi$
$11$	3.68607			1.11139			0.555695	+	0.831386i	$0.312452\pi$
$12$	−3.18773	+	1.35587i	−0.920218	+	0.391405i
$13$	−3.88771	+	3.88771i	−1.07826	+	1.07826i	−0.0815911	+	0.996666i	$0.526000\pi$
$13$	−3.88771	+	3.88771i	−1.07826	+	1.07826i	−0.996666	+	0.0815911i	$0.974000\pi$
$14$	0.452626	+	1.07407i	0.120969	+	0.287057i
$15$	−3.66213	−	1.26047i	−0.945558	−	0.325453i
$16$	0.0980619	+	3.99880i	0.0245155	+	0.999699i
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	0.805734	−	0.592277i	$-0.201771\pi$
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	−0.592277	+	0.805734i	$0.701771\pi$
$18$	3.91883	−	1.62567i	0.923677	−	0.383173i
$19$	6.32919			1.45201			0.726007	−	0.687687i	$-0.241374\pi$
$19$	6.32919			1.45201			0.726007	+	0.687687i	$0.241374\pi$
$20$	−2.91214	+	3.39403i	−0.651175	+	0.758928i
$21$	−0.542584	−	1.32036i	−0.118402	−	0.288125i
$22$	−1.96533	+	4.82821i	−0.419009	+	1.02938i
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	−0.888916	−	0.458071i	$-0.848540\pi$
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	0.458071	+	0.888916i	$0.348540\pi$
$24$	−0.0763660	−	4.89838i	−0.0155882	−	0.999878i
$25$	−4.95909	+	0.638332i	−0.991817	+	0.127666i
$26$	−3.01950	−	7.16518i	−0.592173	−	1.40521i
$27$	−4.81715	+	1.94809i	−0.927061	+	0.374910i
$28$	−1.64820	+	0.0202063i	−0.311481	+	0.00381863i
$29$		−	1.37122i		−	0.254630i	−0.991862	−	0.127315i	$-0.959364\pi$
$29$		−	1.37122i		−	0.254630i	0.991862	−	0.127315i	$-0.0406359\pi$
$30$	3.60361	−	4.12481i	0.657925	−	0.753083i
$31$	3.32075			0.596425			0.298212	−	0.954500i	$-0.403610\pi$
$31$	3.32075			0.596425			0.298212	+	0.954500i	$0.403610\pi$
$32$	−5.29013	−	2.00362i	−0.935172	−	0.354194i
$33$	2.45973	−	5.89160i	0.428184	−	1.02560i
$34$	−1.62206	+	0.683558i	−0.278181	+	0.117229i
$35$	−1.38380	−	1.21710i	−0.233905	−	0.205727i
$36$	0.0399575	+	5.99987i	0.00665958	+	0.999978i
$37$	−2.44147	−	2.44147i	−0.401376	−	0.401376i	0.477342	−	0.878718i	$-0.341600\pi$
$37$	−2.44147	−	2.44147i	−0.401376	−	0.401376i	−0.878718	+	0.477342i	$0.841600\pi$
$38$	−3.37458	+	8.29032i	−0.547429	+	1.34487i
$39$	3.61961	+	8.80819i	0.579602	+	1.41044i
$40$	−2.89300	−	5.62410i	−0.457423	−	0.889249i
$41$		−	0.648104i		−	0.101217i	−0.998719	−	0.0506084i	$-0.983884\pi$
$41$		−	0.648104i		−	0.101217i	0.998719	−	0.0506084i	$-0.0161160\pi$
$42$	2.01877	−	0.00672215i	0.311503	−	0.00103725i
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	−0.766821	−	0.641861i	$-0.778162\pi$
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	0.641861	+	0.766821i	$0.278162\pi$
$44$	−5.27640	−	5.14859i	−0.795447	−	0.776179i
$45$	−4.45843	+	5.01223i	−0.664623	+	0.747179i
$46$	−1.60482	−	3.80818i	−0.236617	−	0.561485i
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	0.996793	−	0.0800208i	$-0.0254987\pi$
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	−0.0800208	+	0.996793i	$0.525499\pi$
$48$	6.45689	+	2.51168i	0.931972	+	0.362530i
$49$			6.32075i			0.902965i
$50$	1.80795	−	6.83603i	0.255683	−	0.966761i
$51$	1.99401	−	0.819412i	0.279217	−	0.114741i
$52$	10.9953	−	0.134798i	1.52477	−	0.0186931i
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	0.978158	−	0.207864i	$-0.0666512\pi$
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	−0.207864	+	0.978158i	$0.566651\pi$
$54$	0.0166776	−	7.34845i	0.00226953	−	0.999997i
$55$	−0.527212	−	8.22542i	−0.0710892	−	1.10911i
$56$	0.852318	−	2.16968i	0.113896	−	0.289936i
$57$	4.22349	−	10.1162i	0.559415	−	1.33993i
$58$	1.79611	+	0.731106i	0.235840	+	0.0959989i
$59$			6.12026i			0.796790i	0.917214	+	0.398395i	$0.130433\pi$
$59$			6.12026i			0.796790i	−0.917214	+	0.398395i	$0.869567\pi$
$60$	3.48154	+	6.91946i	0.449465	+	0.893298i
$61$		−	5.13471i		−	0.657432i	−0.944429	−	0.328716i	$-0.893384\pi$
$61$		−	5.13471i		−	0.657432i	0.944429	−	0.328716i	$-0.106616\pi$
$62$	−1.77055	+	4.34971i	−0.224860	+	0.552413i
$63$	−2.47245	−	0.0138443i	−0.311500	−	0.00174421i
$64$	5.44503	−	5.86102i	0.680629	−	0.732628i
$65$	9.23144	+	8.11933i	1.14502	+	1.00708i
$66$	6.40568	+	6.36316i	0.788484	+	0.783251i
$67$	−4.90636	−	4.90636i	−0.599408	−	0.599408i	0.340747	−	0.940155i	$-0.389320\pi$
$67$	−4.90636	−	4.90636i	−0.599408	−	0.599408i	−0.940155	+	0.340747i	$0.889320\pi$
$68$	−0.0305156	−	2.48912i	−0.00370056	−	0.301851i
$69$	1.92377	+	4.68141i	0.231594	+	0.563576i
$70$	2.33203	−	1.16365i	0.278731	−	0.139083i
$71$		−	4.13251i		−	0.490439i	−0.969468	−	0.245220i	$-0.921140\pi$
$71$		−	4.13251i		−	0.490439i	0.969468	−	0.245220i	$-0.0788601\pi$
$72$	−7.88026	−	3.14666i	−0.928698	−	0.370837i
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	0.926407	−	0.376524i	$-0.122881\pi$
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	−0.376524	+	0.926407i	$0.622881\pi$
$74$	4.49972	−	1.89624i	0.523082	−	0.220433i
$75$	−2.28895	+	8.35229i	−0.264305	+	0.964439i
$76$	−9.05987	−	8.84042i	−1.03924	−	1.01407i
$77$	2.14814	−	2.14814i	0.244803	−	0.244803i
$78$	−13.4674	+	0.0448439i	−1.52488	+	0.00507757i
$79$		−	1.10079i		−	0.123848i	−0.998081	−	0.0619241i	$-0.980276\pi$
$79$		−	1.10079i		−	0.123848i	0.998081	−	0.0619241i	$-0.0197237\pi$
$80$	8.90925	−	0.790765i	0.996084	−	0.0884103i
$81$	−0.100786	+	8.99944i	−0.0111985	+	0.999937i
$82$	0.848922	+	0.345554i	0.0937478	+	0.0381601i
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	0.273242	−	0.961945i	$-0.411904\pi$
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	−0.961945	+	0.273242i	$0.911904\pi$
$84$	−1.06756	+	2.64788i	−0.116480	+	0.288908i
$85$	1.83806	−	2.08982i	0.199366	−	0.226673i
$86$	−0.636420	−	1.51020i	−0.0686269	−	0.162849i
$87$	−2.19169	−	0.915024i	−0.234974	−	0.0981009i
$88$	9.55717	−	4.16621i	1.01880	−	0.444119i
$89$	−15.3562			−1.62775			−0.813875	−	0.581040i	$-0.802646\pi$
$89$	−15.3562			−1.62775			−0.813875	+	0.581040i	$0.802646\pi$
$90$	−4.18816	−	8.51230i	−0.441471	−	0.897276i
$91$			4.53130i			0.475009i
$92$	5.84382	−	0.0716428i	0.609260	−	0.00746928i
$93$	2.21595	−	5.30771i	0.229784	−	0.550384i
$94$	−11.5836	+	4.88148i	−1.19476	+	0.503486i
$95$	−0.905253	−	14.1235i	−0.0928770	−	1.44904i
$96$	−6.73261	+	7.11843i	−0.687144	+	0.726521i
$97$	−5.42154	+	5.42154i	−0.550474	+	0.550474i	−0.926578	−	0.376104i	$-0.877264\pi$
$97$	−5.42154	+	5.42154i	−0.550474	+	0.550474i	0.376104	+	0.926578i	$0.377264\pi$
$98$	−8.27927	−	3.37008i	−0.836333	−	0.340430i
$99$	−7.77542	−	7.86299i	−0.781459	−	0.790260i
$100$	7.99026	+	6.01297i	0.799026	+	0.601297i
$101$	−9.84442			−0.979556			−0.489778	−	0.871847i	$-0.662922\pi$
$101$	−9.84442			−0.979556			−0.489778	+	0.871847i	$0.662922\pi$
$102$	0.0101518	+	3.04875i	0.00100518	+	0.301872i
$103$	−8.28098	−	8.28098i	−0.815949	−	0.815949i	0.169569	−	0.985518i	$-0.445762\pi$
$103$	−8.28098	−	8.28098i	−0.815949	−	0.815949i	−0.985518	+	0.169569i	$0.945762\pi$
$104$	−5.68587	+	14.4741i	−0.557545	+	1.41930i
$105$	−2.86876	+	1.39962i	−0.279962	+	0.136589i
$106$	−10.3354	+	4.35547i	−1.00386	+	0.423041i
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	−0.365559	−	0.930788i	$-0.619122\pi$
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	0.930788	+	0.365559i	$0.119122\pi$
$108$	9.61652	+	3.93987i	0.925350	+	0.379114i
$109$	11.7033			1.12097			0.560487	−	0.828163i	$-0.310614\pi$
$109$	11.7033			1.12097			0.560487	+	0.828163i	$0.310614\pi$
$110$	11.0552	+	3.69503i	1.05407	+	0.352308i
$111$	−5.53152	+	2.27311i	−0.525029	+	0.215754i
$112$	2.38754	+	2.27324i	0.225601	+	0.214801i
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	−0.176796	−	0.984248i	$-0.556573\pi$
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	0.984248	+	0.176796i	$0.0565731\pi$
$114$	10.9989	+	10.9259i	1.03014	+	1.02330i
$115$	4.90636	+	4.31530i	0.457521	+	0.402403i
$116$	−1.91529	+	1.96283i	−0.177830	+	0.182244i
$117$	16.4939	+	0.0923560i	1.52486	+	0.00853832i
$118$	−8.01666	−	3.26318i	−0.737993	−	0.300400i
$119$	1.02580			0.0940350
$120$	−10.9198	+	0.871018i	−0.996834	+	0.0795127i
$121$	2.58708			0.235189
$122$	6.72573	+	2.73771i	0.608919	+	0.247861i
$123$	−1.03589	−	0.432483i	−0.0934033	−	0.0389956i
$124$	−4.75347	−	4.63833i	−0.426874	−	0.416535i
$125$	2.13372	+	10.9748i	0.190846	+	0.981620i
$126$	1.33639	−	3.23118i	0.119055	−	0.287856i
$127$	−0.0146460	+	0.0146460i	−0.00129962	+	0.00129962i	−0.707756	−	0.706457i	$-0.750293\pi$
$127$	−0.0146460	+	0.0146460i	−0.00129962	+	0.00129962i	0.706457	+	0.707756i	$0.250293\pi$
$128$	4.77393	+	10.2572i	0.421959	+	0.906615i
$129$	0.762905	+	1.85650i	0.0671701	+	0.163456i
$130$	−15.5571	+	7.76281i	−1.36445	+	0.680843i
$131$	−5.23989			−0.457811			−0.228906	−	0.973449i	$-0.573515\pi$
$131$	−5.23989			−0.457811			−0.228906	+	0.973449i	$0.573515\pi$
$132$	−11.7502	+	4.99782i	−1.02272	+	0.435004i
$133$	3.68847	−	3.68847i	0.319831	−	0.319831i
$134$	9.04259	−	3.81066i	0.781161	−	0.329191i
$135$	5.03613	+	10.4708i	0.433441	+	0.901182i
$136$	3.27666	+	1.28717i	0.280972	+	0.110374i
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.972782	−	0.231722i	$-0.925564\pi$
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.231722	−	0.972782i	$-0.574436\pi$
$138$	−7.15768	+	0.0238338i	−0.609302	+	0.00202887i
$139$	−9.22166			−0.782171			−0.391085	−	0.920354i	$-0.627900\pi$
$139$	−9.22166			−0.782171			−0.391085	+	0.920354i	$0.627900\pi$
$140$	0.280830	+	3.67506i	0.0237345	+	0.310599i
$141$	14.2398	−	5.85165i	1.19921	−	0.492798i
$142$	5.41300	+	2.20336i	0.454249	+	0.184902i
$143$	−14.3304	+	14.3304i	−1.19836	+	1.19836i
$144$	8.32324	−	8.64428i	0.693604	−	0.720357i
$145$	−3.05987	+	0.196124i	−0.254109	+	0.0162872i
$146$	−8.65895	+	3.64899i	−0.716619	+	0.301993i
$147$	10.1027	+	4.21787i	0.833260	+	0.347884i
$148$	0.0846526	+	6.90501i	0.00695840	+	0.567589i
$149$		−	14.0054i		−	1.14737i	−0.819076	−	0.573685i	$-0.805513\pi$
$149$		−	14.0054i		−	1.14737i	0.819076	−	0.573685i	$-0.194487\pi$
$150$	−9.71988	−	7.45144i	−0.793625	−	0.608408i
$151$	13.1301			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$151$	13.1301			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$152$	16.4102	−	7.15361i	1.33104	−	0.580234i
$153$	0.0209077	−	3.73391i	0.00169028	−	0.301869i
$154$	1.66841	+	3.95909i	0.134444	+	0.319032i
$155$	−0.474962	−	7.41023i	−0.0381498	−	0.595204i
$156$	7.12175	−	17.6642i	0.570196	−	1.41427i
$157$	−6.36936	−	6.36936i	−0.508330	−	0.508330i	0.405683	−	0.914014i	$-0.367034\pi$
$157$	−6.36936	−	6.36936i	−0.508330	−	0.508330i	−0.914014	+	0.405683i	$0.867034\pi$
$158$	1.44187	+	0.586914i	0.114709	+	0.0466924i
$159$	12.7054	−	5.22110i	1.00760	−	0.414060i
$160$	−3.71442	+	12.0914i	−0.293651	+	0.955913i
$161$			2.40831i			0.189802i
$162$	−11.7342	−	4.93031i	−0.921928	−	0.387362i
$163$	−3.46013	+	3.46013i	−0.271018	+	0.271018i	−0.829510	−	0.558492i	$-0.811380\pi$
$163$	−3.46013	+	3.46013i	−0.271018	+	0.271018i	0.558492	+	0.829510i	$0.311380\pi$
$164$	−0.905253	+	0.927724i	−0.0706884	+	0.0724431i
$165$	−13.4989	−	4.64619i	−1.05088	−	0.361706i
$166$	11.5639	−	4.87318i	0.897533	−	0.378232i
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	0.743060	−	0.669225i	$-0.233374\pi$
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	−0.669225	+	0.743060i	$0.733374\pi$
$168$	−2.89915	−	2.81014i	−0.223674	−	0.216807i
$169$		−	17.2286i		−	1.32528i
$170$	1.75735	+	3.52185i	0.134783	+	0.270113i
$171$	−13.3508	−	13.5012i	−1.02096	−	1.03246i
$172$	2.31747	−	0.0284113i	0.176706	−	0.00216634i
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	0.635262	−	0.772296i	$-0.280892\pi$
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	−0.772296	+	0.635262i	$0.780892\pi$
$174$	2.36711	−	2.38293i	0.179450	−	0.180649i
$175$	−2.51801	+	3.26202i	−0.190344	+	0.246585i
$176$	0.361463	+	14.7398i	0.0272463	+	1.11106i
$177$	9.78228	+	4.08408i	0.735281	+	0.306978i
$178$	8.18756	−	20.1144i	0.613683	−	1.50763i
$179$			24.0166i			1.79508i	0.440930	+	0.897541i	$0.354649\pi$
$179$			24.0166i			1.79508i	−0.440930	+	0.897541i	$0.645351\pi$
$180$	13.3829	−	0.947315i	0.997504	−	0.0706087i
$181$			21.7210i			1.61451i	0.590205	+	0.807253i	$0.299047\pi$
$181$			21.7210i			1.61451i	−0.590205	+	0.807253i	$0.700953\pi$
$182$	−5.93535	−	2.41599i	−0.439957	−	0.179085i
$183$	−8.20703	−	3.42641i	−0.606681	−	0.253288i
$184$	−3.02195	+	7.69276i	−0.222781	+	0.567117i
$185$	−5.09892	+	5.79732i	−0.374880	+	0.426228i
$186$	5.77083	+	5.73253i	0.423138	+	0.420329i
$187$	3.24412	+	3.24412i	0.237234	+	0.237234i
$188$	−0.217921	−	17.7755i	−0.0158935	−	1.29641i
$189$	−1.67201	+	3.94259i	−0.121621	+	0.286781i
$190$	18.9824	+	6.34458i	1.37713	+	0.460285i
$191$		−	12.9839i		−	0.939479i	−0.882805	−	0.469739i	$-0.844348\pi$
$191$		−	12.9839i		−	0.939479i	0.882805	−	0.469739i	$-0.155652\pi$
$192$	−5.73444	−	12.6141i	−0.413847	−	0.910346i
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	0.960639	−	0.277800i	$-0.0896053\pi$
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	−0.277800	+	0.960639i	$0.589605\pi$
$194$	−4.21079	−	9.99208i	−0.302317	−	0.717389i
$195$	19.1377	−	9.33695i	1.37048	−	0.668633i
$196$	8.82864	−	9.04780i	0.630617	−	0.646272i
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	−0.996757	−	0.0804765i	$-0.974356\pi$
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	0.0804765	+	0.996757i	$0.474356\pi$
$198$	14.4451	−	5.99231i	1.02657	−	0.425855i
$199$			0.0463625i			0.00328655i	0.999999	+	0.00164328i	$0.000523071\pi$
$199$			0.0463625i			0.00328655i	−0.999999	+	0.00164328i	$0.999477\pi$
$200$	−12.1363	+	7.26010i	−0.858169	+	0.513367i
$201$	−11.1161	+	4.56802i	−0.784069	+	0.322203i
$202$	5.24882	−	12.8948i	0.369306	−	0.907273i
$203$	−0.799111	−	0.799111i	−0.0560866	−	0.0560866i
$204$	−3.99884	−	1.61223i	−0.279975	−	0.112879i
$205$	−1.44624	+	0.0926972i	−0.101010	+	0.00647425i
$206$	15.2621	−	6.43165i	1.06336	−	0.448115i
$207$	8.76625	+	0.0490858i	0.609296	+	0.00341170i
$208$	−15.9274	−	15.1649i	−1.10437	−	1.05150i
$209$	23.3298			1.61376
$210$	−0.303742	−	4.50390i	−0.0209602	−	0.310799i
$211$			0.591066i			0.0406907i	0.999793	+	0.0203453i	$0.00647657\pi$
$211$			0.591066i			0.0406907i	−0.999793	+	0.0203453i	$0.993523\pi$
$212$	−0.194439	−	15.8601i	−0.0133541	−	1.08928i
$213$	−6.60518	−	2.75765i	−0.452579	−	0.188951i
$214$	4.54107	+	10.7758i	0.310421	+	0.736619i
$215$	1.94571	+	1.71131i	0.132696	+	0.116710i
$216$	−10.2880	+	10.4956i	−0.700008	+	0.714135i
$217$	1.93524	−	1.93524i	0.131373	−	0.131373i
$218$	−6.23994	+	15.3296i	−0.422622	+	1.03825i
$219$	10.6445	−	4.37421i	0.719287	−	0.295582i
$220$	−10.7343	+	12.5106i	−0.723710	+	0.843465i
$221$	−6.84318			−0.460322
$222$	−0.0281619	−	8.45747i	−0.00189010	−	0.567628i
$223$	16.8577	+	16.8577i	1.12888	+	1.12888i	0.990360	+	0.138517i	$0.0442335\pi$
$223$	16.8577	+	16.8577i	1.12888	+	1.12888i	0.138517	+	0.990360i	$0.455767\pi$
$224$	−4.25060	+	1.91529i	−0.284005	+	0.127970i
$225$	11.8224	+	9.23204i	0.788161	+	0.615470i
$226$	6.66649	+	15.8194i	0.443448	+	1.05229i
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	−0.905173	−	0.425043i	$-0.860259\pi$
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	0.425043	+	0.905173i	$0.360259\pi$
$228$	−20.1757	+	8.58154i	−1.33617	+	0.568326i
$229$	−23.0081			−1.52042			−0.760210	−	0.649677i	$-0.774904\pi$
$229$	−23.0081			−1.52042			−0.760210	+	0.649677i	$0.774904\pi$
$230$	−8.26838	+	4.12581i	−0.545201	+	0.272048i
$231$	−2.00000	−	4.86692i	−0.131590	−	0.320220i
$232$	−1.54984	−	3.55529i	−0.101752	−	0.233416i
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	−0.837705	−	0.546122i	$-0.816103\pi$
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	0.546122	+	0.837705i	$0.316103\pi$
$234$	−8.91515	+	21.5554i	−0.582802	+	1.40912i
$235$	13.1261	−	14.9240i	0.856254	−	0.973536i
$236$	8.54860	−	8.76081i	0.556466	−	0.570280i
$237$	−1.75944	−	0.734560i	−0.114288	−	0.0477148i
$238$	−0.546934	+	1.34365i	−0.0354524	+	0.0870959i
$239$	4.03472			0.260984			0.130492	−	0.991449i	$-0.458344\pi$
$239$	4.03472			0.260984			0.130492	+	0.991449i	$0.458344\pi$
$240$	4.68127	−	14.7677i	0.302174	−	0.953253i
$241$	−11.4612			−0.738279			−0.369139	−	0.929374i	$-0.620347\pi$
$241$	−11.4612			−0.738279			−0.369139	+	0.929374i	$0.620347\pi$
$242$	−1.37937	+	3.38871i	−0.0886696	+	0.217834i
$243$	14.3169	+	6.16646i	0.918432	+	0.395578i
$244$	−7.17201	+	7.35005i	−0.459141	+	0.470538i
$245$	14.1047	−	0.904047i	0.901116	−	0.0577574i
$246$	1.11880	−	1.12628i	0.0713324	−	0.0718090i
$247$	−24.6060	+	24.6060i	−1.56564	+	1.56564i
$248$	8.60999	−	3.75331i	0.546735	−	0.238335i
$249$	−14.2156	+	5.84170i	−0.900874	+	0.370203i
$250$	−15.5131	−	3.05667i	−0.981136	−	0.193321i
$251$	17.4804			1.10335			0.551677	−	0.834058i	$-0.313988\pi$
$251$	17.4804			1.10335			0.551677	+	0.834058i	$0.313988\pi$
$252$	3.51984	+	3.47327i	0.221729	+	0.218795i
$253$	−7.61636	+	7.61636i	−0.478836	+	0.478836i
$254$	−0.0113752	−	0.0269930i	−0.000713745	−	0.00169369i
$255$	−2.11371	−	4.33241i	−0.132366	−	0.271306i
$256$	−15.9808	+	0.784260i	−0.998798	+	0.0490162i
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	0.886056	−	0.463578i	$-0.153435\pi$
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	−0.463578	+	0.886056i	$0.653435\pi$
$258$	−2.83851	+	0.00945175i	−0.176718	+	0.000588440i
$259$	−2.84565			−0.176820
$260$	−1.87344	−	24.5166i	−0.116186	−	1.52045i
$261$	−2.92505	+	2.89247i	−0.181056	+	0.179040i
$262$	2.79379	−	6.86350i	0.172601	−	0.424028i
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	−0.0508987	−	0.998704i	$-0.516209\pi$
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	0.998704	+	0.0508987i	$0.0162086\pi$
$264$	−0.281490	−	18.0558i	−0.0173245	−	1.11126i
$265$	11.7117	−	13.3159i	0.719445	−	0.817987i
$266$	2.86476	+	6.79798i	0.175649	+	0.416811i
$267$	−10.2472	+	24.5444i	−0.627121	+	1.50209i
$268$	0.170117	+	13.8762i	0.0103916	+	0.847627i
$269$		−	9.58859i		−	0.584627i	−0.956323	−	0.292313i	$-0.905575\pi$
$269$		−	9.58859i		−	0.584627i	0.956323	−	0.292313i	$-0.0944250\pi$
$270$	−16.4004	+	1.01382i	−0.998095	+	0.0616992i
$271$	−20.9078			−1.27006			−0.635030	−	0.772487i	$-0.719012\pi$
$271$	−20.9078			−1.27006			−0.635030	+	0.772487i	$0.719012\pi$
$272$	−3.43306	+	3.60567i	−0.208160	+	0.218626i
$273$	7.24257	+	3.02376i	0.438341	+	0.183006i
$274$	25.9837	−	10.9499i	1.56974	−	0.661507i
$275$	−18.2795	+	2.35293i	−1.10230	+	0.141887i
$276$	3.78510	−	9.38824i	0.227836	−	0.565106i
$277$	8.86336	+	8.86336i	0.532547	+	0.532547i	0.921330	−	0.388782i	$-0.127104\pi$
$277$	8.86336	+	8.86336i	0.532547	+	0.532547i	−0.388782	+	0.921330i	$0.627104\pi$
$278$	4.91678	−	12.0790i	0.294889	−	0.724453i
$279$	−7.00483	−	7.08372i	−0.419368	−	0.424091i
$280$	−4.96353	−	1.59161i	−0.296628	−	0.0951170i
$281$		−	12.1925i		−	0.727341i	−0.931528	−	0.363670i	$-0.881523\pi$
$281$		−	12.1925i		−	0.727341i	0.931528	−	0.363670i	$-0.118477\pi$
$282$	0.0724970	+	21.7720i	0.00431713	+	1.29650i
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	−0.268877	−	0.963175i	$-0.586652\pi$
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	0.963175	+	0.268877i	$0.0866525\pi$
$284$	−5.77217	+	5.91546i	−0.342516	+	0.351018i
$285$	−23.1783	−	7.97778i	−1.37296	−	0.472563i
$286$	−11.1301	−	26.4113i	−0.658135	−	1.56173i
$287$	−0.377697	−	0.377697i	−0.0222947	−	0.0222947i
$288$	6.88500	+	15.5112i	0.405702	+	0.914005i
$289$		−	15.4508i		−	0.908872i
$290$	1.37456	−	4.11256i	0.0807170	−	0.241498i
$291$	5.04767	+	12.2833i	0.295900	+	0.720060i
$292$	−0.162900	−	13.2875i	−0.00953298	−	0.777594i
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	0.841680	−	0.539977i	$-0.181567\pi$
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	−0.539977	+	0.841680i	$0.681567\pi$
$294$	−10.9114	+	10.9843i	−0.636363	+	0.640615i
$295$	13.6573	−	0.875370i	0.795158	−	0.0509660i
$296$	−9.08971	−	3.57071i	−0.528328	−	0.207544i
$297$	−17.7563	+	7.18079i	−1.03033	+	0.416672i
$298$	18.3451	+	7.46739i	1.06270	+	0.432574i
$299$		−	16.0660i		−	0.929122i
$300$	14.9427	−	8.75870i	0.862719	−	0.505684i
$301$			0.955061i			0.0550488i
$302$	−7.00066	+	17.1985i	−0.402843	+	0.989663i
$303$	−6.56923	+	15.7348i	−0.377392	+	0.903939i
$304$	0.620652	+	25.3091i	0.0355968	+	1.45158i
$305$	−11.4580	+	0.734409i	−0.656086	+	0.0420521i
$306$	4.87973	+	2.01822i	0.278956	+	0.115374i
$307$	−9.19824	−	9.19824i	−0.524972	−	0.524972i	0.394097	−	0.919069i	$-0.371057\pi$
$307$	−9.19824	−	9.19824i	−0.524972	−	0.524972i	−0.919069	+	0.394097i	$0.871057\pi$
$308$	−6.07539	+	0.0744818i	−0.346177	+	0.00424399i
$309$	−18.7618	+	7.70992i	−1.06732	+	0.438602i
$310$	9.95956	+	3.32883i	0.565665	+	0.189065i
$311$			30.5690i			1.73341i	0.498821	+	0.866705i	$0.333767\pi$
$311$			30.5690i			1.73341i	−0.498821	+	0.866705i	$0.666233\pi$
$312$	19.3404	+	18.7466i	1.09493	+	1.06132i
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	0.0672931	−	0.997733i	$-0.478564\pi$
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	−0.997733	+	0.0672931i	$0.978564\pi$
$314$	11.7389	−	4.94694i	0.662467	−	0.279172i
$315$	0.322737	+	5.51923i	0.0181842	+	0.310974i
$316$	−1.53755	+	1.57571i	−0.0864937	+	0.0886408i
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	−0.707089	−	0.707124i	$-0.749992\pi$
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	0.707124	+	0.707089i	$0.249992\pi$
$318$	0.0646850	+	19.4260i	0.00362736	+	1.08935i
$319$		−	5.05442i		−	0.282993i
$320$	−13.8576	−	11.3122i	−0.774664	−	0.632374i
$321$	−5.44358	−	13.2468i	−0.303831	−	0.739362i
$322$	−3.15454	−	1.28406i	−0.175796	−	0.0715578i
$323$	5.57034	+	5.57034i	0.309942	+	0.309942i
$324$	12.7144	−	12.7414i	0.706357	−	0.707856i
$325$	16.7978	−	21.7611i	0.931777	−	1.20709i
$326$	−2.68740	−	6.37713i	−0.148842	−	0.353196i
$327$	7.80967	−	18.7059i	0.431876	−	1.03444i
$328$	−0.732524	−	1.68039i	−0.0404469	−	0.0927841i
$329$	7.32553			0.403870
$330$	13.2831	−	15.2043i	0.731212	−	0.836970i
$331$			8.28613i			0.455447i	0.973726	+	0.227724i	$0.0731283\pi$
$331$			8.28613i			0.455447i	−0.973726	+	0.227724i	$0.926872\pi$
$332$	0.217550	+	17.7453i	0.0119396	+	0.973901i
$333$	−0.0579994	+	10.3581i	−0.00317835	+	0.567622i
$334$	−1.75853	+	0.741069i	−0.0962226	+	0.0405495i
$335$	−10.2467	+	11.6502i	−0.559839	+	0.636521i
$336$	5.22663	−	2.29916i	0.285136	−	0.125429i
$337$	2.27666	−	2.27666i	0.124018	−	0.124018i	−0.642374	−	0.766392i	$-0.722050\pi$
$337$	2.27666	−	2.27666i	0.124018	−	0.124018i	0.766392	+	0.642374i	$0.222050\pi$
$338$	22.5670	+	9.18590i	1.22748	+	0.499647i
$339$	−7.99142	−	19.4468i	−0.434035	−	1.05621i
$340$	−5.55009	+	0.424111i	−0.300996	+	0.0230006i
$341$	12.2405			0.662861
$342$	24.8030	−	10.2891i	1.34119	−	0.556373i
$343$	7.76296	+	7.76296i	0.419161	+	0.419161i
$344$	−1.19841	+	3.05070i	−0.0646139	+	0.164483i
$345$	10.1714	−	4.96244i	0.547608	−	0.267169i
$346$	3.32189	−	1.39989i	0.178586	−	0.0752584i
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	0.000564305	−	1.00000i	$-0.499820\pi$
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	1.00000		0.000564305i	$-0.000179624\pi$
$348$	1.85920	+	4.37109i	0.0996636	+	0.234315i
$349$	17.7267			0.948889			0.474445	−	0.880285i	$-0.342649\pi$
$349$	17.7267			0.948889			0.474445	+	0.880285i	$0.342649\pi$
$350$	−2.93022	−	5.03747i	−0.156627	−	0.269264i
$351$	11.1541	−	26.3013i	0.595360	−	1.40386i
$352$	−19.4998	−	7.38548i	−1.03934	−	0.393648i
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	−0.930160	−	0.367153i	$-0.880332\pi$
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	0.367153	+	0.930160i	$0.380332\pi$
$354$	−10.5652	+	10.6358i	−0.561536	+	0.565288i
$355$	−9.22166	+	0.591066i	−0.489435	+	0.0313705i
$356$	21.9815	+	21.4490i	1.16502	+	1.13680i
$357$	0.684521	−	1.63958i	0.0362287	−	0.0867759i
$358$	−31.4582	−	12.8051i	−1.66262	−	0.676770i
$359$	−24.7266			−1.30502			−0.652510	−	0.757780i	$-0.726284\pi$
$359$	−24.7266			−1.30502			−0.652510	+	0.757780i	$0.726284\pi$
$360$	−5.89463	+	18.0348i	−0.310674	+	0.950517i
$361$	21.0586			1.10835
$362$	−28.4513	−	11.5811i	−1.49537	−	0.608691i
$363$	1.72637	−	4.13505i	0.0906111	−	0.217034i
$364$	6.32919	−	6.48630i	0.331739	−	0.339974i
$365$	9.81201	−	11.1560i	0.513584	−	0.583930i
$366$	8.86391	−	8.92314i	0.463324	−	0.466420i
$367$	9.33767	−	9.33767i	0.487423	−	0.487423i	−0.420069	−	0.907492i	$-0.637994\pi$
$367$	9.33767	−	9.33767i	0.487423	−	0.487423i	0.907492	+	0.420069i	$0.137994\pi$
$368$	−8.46516	−	8.05992i	−0.441277	−	0.420152i
$369$	−1.38251	+	1.36712i	−0.0719707	+	0.0711692i
$370$	−4.87503	−	9.76985i	−0.253441	−	0.507911i
$371$	6.53616			0.339341
$372$	−10.5857	+	4.50250i	−0.548841	+	0.233444i
$373$	11.9025	−	11.9025i	0.616291	−	0.616291i	−0.328287	−	0.944578i	$-0.606471\pi$
$373$	11.9025	−	11.9025i	0.616291	−	0.616291i	0.944578	+	0.328287i	$0.106471\pi$
$374$	−5.97903	+	2.51964i	−0.309168	+	0.130288i
$375$	18.9654	+	3.91314i	0.979370	+	0.202074i
$376$	23.3996	+	9.19207i	1.20674	+	0.474045i
$377$	5.33092	+	5.33092i	0.274557	+	0.274557i
$378$	−4.27275	−	4.29219i	−0.219767	−	0.220766i
$379$	2.73341			0.140406			0.0702029	−	0.997533i	$-0.477635\pi$
$379$	2.73341			0.140406			0.0702029	+	0.997533i	$0.477635\pi$
$380$	−18.4315	+	21.4814i	−0.945515	+	1.10197i
$381$	0.0136360	+	0.0331827i	0.000698593	+	0.00170000i
$382$	17.0070	+	6.92270i	0.870153	+	0.354196i
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	−0.0957539	−	0.995405i	$-0.530526\pi$
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	0.995405	+	0.0957539i	$0.0305262\pi$
$384$	19.5802	−	0.785717i	0.999196	−	0.0400960i
$385$	−5.10079	−	4.48630i	−0.259960	−	0.228643i
$386$	−17.4836	+	7.36780i	−0.889890	+	0.375011i
$387$	3.47642	+	0.0194659i	0.176716	+	0.000989506i
$388$	15.3333	−	0.187980i	0.778429	−	0.00954322i
$389$		−	25.1335i		−	1.27432i	−0.770731	−	0.637160i	$-0.780109\pi$
$389$		−	25.1335i		−	1.27432i	0.770731	−	0.637160i	$-0.219891\pi$
$390$	2.02628	+	30.0458i	0.102605	+	1.52143i
$391$	−3.63704			−0.183933
$392$	7.14408	+	16.3883i	0.360831	+	0.827736i
$393$	−3.49660	+	8.37515i	−0.176380	+	0.422470i
$394$	−9.98855	−	23.7025i	−0.503216	−	1.19412i
$395$	−2.45639	+	0.157444i	−0.123594	+	0.00792185i
$396$	0.147286	+	22.1159i	0.00740139	+	1.11137i
$397$	−5.42664	−	5.42664i	−0.272355	−	0.272355i	0.557692	−	0.830048i	$-0.311687\pi$
$397$	−5.42664	−	5.42664i	−0.272355	−	0.272355i	−0.830048	+	0.557692i	$0.811687\pi$
$398$	−0.0607282	−	0.0247195i	−0.00304403	−	0.00123907i
$399$	−3.43411	−	8.35678i	−0.171921	−	0.418362i
$400$	−3.03886	−	19.7678i	−0.151943	−	0.988389i
$401$			5.15831i			0.257594i	0.991671	+	0.128797i	$0.0411115\pi$
$401$			5.15831i			0.257594i	−0.991671	+	0.128797i	$0.958888\pi$
$402$	−0.0565939	−	16.9960i	−0.00282264	−	0.847686i
$403$	−12.9101	+	12.9101i	−0.643099	+	0.643099i
$404$	14.0917	+	13.7504i	0.701090	+	0.684108i
$405$	20.0966	−	1.06227i	0.998606	−	0.0527847i
$406$	1.47279	−	0.620652i	0.0730933	−	0.0308025i
$407$	−8.99944	−	8.99944i	−0.446085	−	0.446085i
$408$	4.24388	−	4.37830i	0.210103	−	0.216758i
$409$			14.1638i			0.700356i	0.936683	+	0.350178i	$0.113879\pi$
$409$			14.1638i			0.700356i	−0.936683	+	0.350178i	$0.886121\pi$
$410$	0.649681	−	1.94379i	0.0320854	−	0.0959967i
$411$	−31.9419	+	13.1261i	−1.57558	+	0.647464i
$412$	0.287124	+	23.4204i	0.0141456	+	1.15384i
$413$	3.56672	+	3.56672i	0.175507	+	0.175507i
$414$	−4.73826	+	11.4563i	−0.232873	+	0.563049i
$415$	−13.1038	+	14.8986i	−0.643241	+	0.731345i
$416$	28.3560	−	12.7770i	1.39027	−	0.626444i
$417$	−6.15365	+	14.7394i	−0.301346	+	0.721791i
$418$	−12.4389	+	30.5587i	−0.608407	+	1.49467i
$419$		−	4.80514i		−	0.234746i	−0.993088	−	0.117373i	$-0.962553\pi$
$419$		−	4.80514i		−	0.234746i	0.993088	−	0.117373i	$-0.0374474\pi$
$420$	6.06141	+	2.00352i	0.295766	+	0.0977618i
$421$		−	15.2187i		−	0.741716i	−0.928690	−	0.370858i	$-0.879064\pi$
$421$		−	15.2187i		−	0.741716i	0.928690	−	0.370858i	$-0.120936\pi$
$422$	−0.774212	−	0.315143i	−0.0376880	−	0.0153409i
$423$	0.149308	−	26.6649i	0.00725958	−	1.29649i
$424$	20.8781	+	8.20157i	1.01393	+	0.398304i
$425$	−4.92631	−	3.80272i	−0.238961	−	0.184459i
$426$	7.13385	−	7.18152i	0.345636	−	0.347946i
$427$	−2.99236	−	2.99236i	−0.144811	−	0.144811i
$428$	−16.5359	+	0.202724i	−0.799295	+	0.00979903i
$429$	13.3421	+	32.4676i	0.644164	+	1.56755i
$430$	−3.27898	+	1.63617i	−0.158126	+	0.0789029i
$431$			27.8760i			1.34274i	0.741122	+	0.671370i	$0.234294\pi$
$431$			27.8760i			1.34274i	−0.741122	+	0.671370i	$0.765706\pi$
$432$	−8.26240	−	19.0718i	−0.397525	−	0.917591i
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	0.637145	−	0.770744i	$-0.280115\pi$
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	−0.770744	+	0.637145i	$0.780115\pi$
$434$	1.50306	+	3.56672i	0.0721492	+	0.171208i
$435$	−1.72839	+	5.02160i	−0.0828701	+	0.240767i
$436$	−16.7526	−	16.3468i	−0.802305	−	0.782872i
$437$	−13.0777	+	13.0777i	−0.625592	+	0.625592i
$438$	0.0541928	+	16.2750i	0.00258943	+	0.777648i
$439$			10.8174i			0.516286i	0.966107	+	0.258143i	$0.0831105\pi$
$439$			10.8174i			0.516286i	−0.966107	+	0.258143i	$0.916889\pi$
$440$	−10.6638	−	20.7308i	−0.508376	−	0.988303i
$441$	13.4832	−	13.3331i	0.642058	−	0.634907i
$442$	3.64863	−	8.96358i	0.173548	−	0.426354i
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	0.557203	−	0.830376i	$-0.311874\pi$
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	−0.830376	+	0.557203i	$0.811874\pi$
$444$	11.0931	+	4.47244i	0.526454	+	0.212253i
$445$	2.19637	+	34.2671i	0.104118	+	1.62442i
$446$	−31.0693	+	13.0930i	−1.47118	+	0.619973i
$447$	−22.3855	−	9.34590i	−1.05880	−	0.442046i
$448$	−0.242427	−	6.58885i	−0.0114536	−	0.311294i
$449$	6.91183			0.326189			0.163095	−	0.986610i	$-0.447852\pi$
$449$	6.91183			0.326189			0.163095	+	0.986610i	$0.447852\pi$
$450$	−18.3961	+	10.5633i	−0.867200	+	0.497960i
$451$		−	2.38895i		−	0.112491i
$452$	−24.2755	+	0.297608i	−1.14182	+	0.0139983i
$453$	8.76176	−	20.9864i	0.411663	−	0.986026i
$454$	−5.61841	−	13.3323i	−0.263685	−	0.625716i
$455$	10.1115	−	0.648104i	0.474036	−	0.0303836i
$456$	−0.483335	−	31.0028i	−0.0226342	−	1.45184i
$457$	−5.15748	+	5.15748i	−0.241257	+	0.241257i	−0.817370	−	0.576113i	$-0.804569\pi$
$457$	−5.15748	+	5.15748i	−0.241257	+	0.241257i	0.576113	+	0.817370i	$0.304569\pi$
$458$	12.2674	−	30.1373i	0.573219	−	1.40823i
$459$	−5.95412	−	2.52507i	−0.277915	−	0.117860i
$460$	−0.995701	−	13.0302i	−0.0464248	−	0.607535i
$461$	−18.4555			−0.859558			−0.429779	−	0.902934i	$-0.641408\pi$
$461$	−18.4555			−0.859558			−0.429779	+	0.902934i	$0.641408\pi$
$462$	7.44132	−	0.0247783i	0.346202	−	0.00115279i
$463$	−19.6899	−	19.6899i	−0.915068	−	0.915068i	0.0815977	−	0.996665i	$-0.473998\pi$
$463$	−19.6899	−	19.6899i	−0.915068	−	0.915068i	−0.996665	+	0.0815977i	$0.973998\pi$
$464$	5.48325	−	0.134465i	0.254553	−	0.00624238i
$465$	−12.1610	−	4.18572i	−0.563955	−	0.194108i
$466$	−3.45685	−	8.20301i	−0.160136	−	0.379997i
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	−0.753581	−	0.657355i	$-0.771675\pi$
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	0.657355	+	0.753581i	$0.271675\pi$
$468$	−23.4811	−	23.1704i	−1.08541	−	1.07105i
$469$	−5.71858			−0.264060
$470$	12.5498	+	25.1505i	0.578877	+	1.16011i
$471$	−14.4307	+	5.93013i	−0.664933	+	0.273246i
$472$	6.91747	+	15.8685i	0.318402	+	0.730407i
$473$	−3.02041	+	3.02041i	−0.138879	+	0.138879i
$474$	1.90026	−	1.91296i	0.0872818	−	0.0878650i
$475$	−31.3870	+	4.04012i	−1.44013	+	0.185374i
$476$	−1.46838	−	1.43281i	−0.0673029	−	0.0656727i
$477$	0.133219	−	23.7916i	0.00609967	−	1.08934i
$478$	−2.15122	+	5.28490i	−0.0983945	+	0.241725i
$479$	19.7088			0.900517			0.450259	−	0.892898i	$-0.351332\pi$
$479$	19.7088			0.900517			0.450259	+	0.892898i	$0.351332\pi$
$480$	16.8476	+	14.0056i	0.768986	+	0.639265i
$481$	18.9835			0.865573
$482$	6.11083	−	15.0125i	0.278341	−	0.683799i
$483$	3.84931	+	1.60708i	0.175150	+	0.0731246i
$484$	−3.70326	−	3.61356i	−0.168330	−	0.164253i
$485$	12.8735	+	11.3227i	0.584557	+	0.514136i
$486$	−15.7106	+	15.4653i	−0.712649	+	0.701521i
$487$	4.21395	−	4.21395i	0.190952	−	0.190952i	−0.605155	−	0.796107i	$-0.706889\pi$
$487$	4.21395	−	4.21395i	0.190952	−	0.190952i	0.796107	+	0.605155i	$0.206889\pi$
$488$	−5.80354	−	13.3132i	−0.262714	−	0.602659i
$489$	3.22151	+	7.83943i	0.145682	+	0.354511i
$490$	−6.33613	+	18.9571i	−0.286237	+	0.856396i
$491$	27.7215			1.25105			0.625527	−	0.780203i	$-0.284884\pi$
$491$	27.7215			1.25105			0.625527	+	0.780203i	$0.284884\pi$
$492$	0.878743	+	2.06598i	0.0396168	+	0.0931416i
$493$	1.20682	−	1.20682i	0.0543525	−	0.0543525i
$494$	−19.1110	−	45.3497i	−0.859843	−	2.04038i
$495$	−16.4341	+	18.4754i	−0.738656	+	0.830407i
$496$	0.325640	+	13.2790i	0.0146216	+	0.596246i
$497$	−2.40831	−	2.40831i	−0.108028	−	0.108028i
$498$	−0.0723737	−	21.7350i	−0.00324314	−	0.973968i
$499$	5.14705			0.230414			0.115207	−	0.993342i	$-0.463247\pi$
$499$	5.14705			0.230414			0.115207	+	0.993342i	$0.463247\pi$
$500$	12.2750	−	18.6902i	0.548957	−	0.835851i
$501$	2.16177	−	0.888353i	0.0965809	−	0.0396887i
$502$	−9.32016	+	22.8968i	−0.415979	+	1.02193i
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	−0.379832	−	0.925056i	$-0.624018\pi$
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	0.925056	+	0.379832i	$0.124018\pi$
$504$	−6.42618	+	2.75861i	−0.286245	+	0.122878i
$505$	1.40803	+	21.9677i	0.0626565	+	0.977550i
$506$	−5.91546	−	14.0372i	−0.262974	−	0.624030i
$507$	−27.5372	−	11.4967i	−1.22297	−	0.510587i
$508$	0.0414220		0.000507817i	0.00183780		2.25307e-5i
$509$			35.8361i			1.58841i	0.607651	+	0.794204i	$0.292112\pi$
$509$			35.8361i			1.58841i	−0.607651	+	0.794204i	$0.707888\pi$
$510$	6.80181	−	0.458712i	0.301189	−	0.0203121i
$511$	5.47596			0.242242
$512$	7.49332	−	21.3506i	0.331161	−	0.943574i
$513$	−30.4886	+	12.3298i	−1.34611	+	0.544375i
$514$	−12.4825	+	5.26031i	−0.550581	+	0.232022i
$515$	−17.2945	+	19.6633i	−0.762086	+	0.866469i
$516$	1.50105	−	3.72308i	0.0660800	−	0.163899i
$517$	23.1672	+	23.1672i	1.01889	+	1.01889i
$518$	1.51723	−	3.72738i	0.0666634	−	0.163772i
$519$	−4.08361	+	1.67811i	−0.179251	+	0.0736608i
$520$	33.1120	+	10.6177i	1.45206	+	0.465619i
$521$			18.1715i			0.796107i	0.917362	+	0.398054i	$0.130314\pi$
$521$			18.1715i			0.796107i	−0.917362	+	0.398054i	$0.869686\pi$
$522$	−2.22915	−	5.37359i	−0.0975674	−	0.235196i
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	−0.998846	−	0.0480305i	$-0.984706\pi$
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	0.0480305	+	0.998846i	$0.484706\pi$
$524$	7.50061	+	7.31893i	0.327666	+	0.319729i
$525$	3.53355	+	6.20141i	0.154217	+	0.270652i
$526$	11.9382	+	28.3289i	0.520529	+	1.23520i
$527$	2.92261	+	2.92261i	0.127311	+	0.127311i
$528$	23.8005	+	9.25822i	1.03579	+	0.402912i
$529$			14.4612i			0.628746i
$530$	11.1974	+	22.4404i	0.486386	+	0.974748i
$531$	13.0555	−	12.9101i	0.566561	−	0.560252i
$532$	−10.4318	+	0.127889i	−0.452275	+	0.00554471i
$533$	2.51964	+	2.51964i	0.109138	+	0.109138i
$534$	−26.6861	−	26.5089i	−1.15482	−	1.14715i
$535$	−13.8833	−	12.2108i	−0.600227	−	0.527918i
$536$	−18.2666	−	7.17567i	−0.788996	−	0.309942i
$537$	38.3867	+	16.0264i	1.65651	+	0.691589i
$538$	12.5597	+	5.11242i	0.541486	+	0.220412i
$539$			23.2987i			1.00355i
$540$	7.41635	−	22.0227i	0.319149	−	0.947705i
$541$		−	26.6843i		−	1.14725i	−0.819119	−	0.573623i	$-0.805537\pi$
$541$		−	26.6843i		−	1.14725i	0.819119	−	0.573623i	$-0.194463\pi$
$542$	11.1476	−	27.3862i	0.478830	−	1.17634i
$543$	34.7176	+	14.4945i	1.48987	+	0.622019i
$544$	−2.89247	−	6.41927i	−0.124014	−	0.275224i
$545$	−1.67390	−	26.1158i	−0.0717022	−	1.11868i
$546$	−7.82226	+	7.87453i	−0.334762	+	0.336999i
$547$	22.2551	+	22.2551i	0.951559	+	0.951559i	0.998880	−	0.0473207i	$-0.0150683\pi$
$547$	22.2551	+	22.2551i	0.951559	+	0.951559i	−0.0473207	+	0.998880i	$0.515068\pi$
$548$	0.488829	+	39.8732i	0.0208817	+	1.70330i
$549$	−10.9532	+	10.8312i	−0.467470	+	0.462264i
$550$	6.66422	−	25.1981i	0.284163	−	1.07445i
$551$		−	8.67873i		−	0.369726i
$552$	10.2791	+	9.96353i	0.437508	+	0.424076i
$553$	−0.641507	−	0.641507i	−0.0272797	−	0.0272797i
$554$	−16.3355	+	6.88398i	−0.694027	+	0.292472i
$555$	5.86358	+	12.0184i	0.248895	+	0.510153i
$556$	13.2003	+	12.8805i	0.559817	+	0.546257i
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	−0.535172	−	0.844743i	$-0.679753\pi$
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	0.844743	+	0.535172i	$0.179753\pi$
$558$	13.0135	−	5.39844i	0.550904	−	0.228534i
$559$		−	6.37128i		−	0.269476i
$560$	4.73122	−	5.65290i	0.199931	−	0.238878i
$561$	7.35005	−	3.02041i	0.310319	−	0.127522i
$562$	15.9704	+	6.50074i	0.673669	+	0.274217i
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	0.0957856	−	0.995402i	$-0.469464\pi$
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	−0.995402	+	0.0957856i	$0.969464\pi$
$564$	−28.5569	−	11.5134i	−1.20246	−	0.484801i
$565$	−20.3813	−	17.9260i	−0.857447	−	0.754150i
$566$	9.07152	+	21.5264i	0.381304	+	0.904823i
$567$	5.18588	+	5.30335i	0.217787	+	0.222720i
$568$	−4.67081	−	10.7147i	−0.195983	−	0.449579i
$569$	35.6410			1.49415			0.747075	−	0.664740i	$-0.231458\pi$
$569$	35.6410			1.49415			0.747075	+	0.664740i	$0.231458\pi$
$570$	22.8079	−	26.1067i	0.955317	−	1.09349i
$571$		−	9.49296i		−	0.397268i	−0.980074	−	0.198634i	$-0.936350\pi$
$571$		−	9.49296i		−	0.397268i	0.980074	−	0.198634i	$-0.0636505\pi$
$572$	40.5293	−	0.496873i	1.69462	−	0.0207753i
$573$	−20.7527	−	8.66419i	−0.866955	−	0.361952i
$574$	0.696108	−	0.293349i	0.0290550	−	0.0122441i
$575$	8.92779	−	11.5657i	0.372314	−	0.482323i
$576$	−23.9883	+	0.748140i	−0.999514	+	0.0311725i
$577$	10.6312	−	10.6312i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$577$	10.6312	−	10.6312i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$578$	20.2384	+	8.23803i	0.841805	+	0.342657i
$579$	21.4926	−	8.83212i	0.893203	−	0.367050i
$580$	4.65397	+	3.99320i	0.193246	+	0.165809i
$581$	−7.31307			−0.303397
$582$	−18.7807	+	0.0625363i	−0.778483	+	0.00259221i
$583$	20.6708	+	20.6708i	0.856097	+	0.856097i
$584$	17.4916	+	6.87124i	0.723808	+	0.284334i
$585$	−2.15300	−	36.8192i	−0.0890157	−	1.52229i
$586$	−9.51801	+	4.01102i	−0.393186	+	0.165694i
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	−0.256891	−	0.966441i	$-0.582698\pi$
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	0.966441	+	0.256891i	$0.0826980\pi$
$588$	−8.57011	−	20.1489i	−0.353425	−	0.830925i
$589$	21.0177			0.866018
$590$	−6.13515	+	18.3558i	−0.252580	+	0.755697i
$591$	11.9737	+	29.1376i	0.492534	+	1.19856i
$592$	9.52355	−	10.0024i	0.391415	−	0.411095i
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	−0.877578	−	0.479434i	$-0.840842\pi$
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	0.479434	+	0.877578i	$0.340842\pi$
$594$	0.0614747	−	27.0869i	0.00252234	−	1.11139i
$595$	−0.146719	−	2.28906i	−0.00601487	−	0.0938424i
$596$	−19.5624	+	20.0480i	−0.801307	+	0.821198i
$597$	0.0741033	+	0.0309379i	0.00303285	+	0.00126621i
$598$	21.0442	+	8.56604i	0.860560	+	0.350291i
$599$	−26.8502			−1.09707			−0.548535	−	0.836128i	$-0.684814\pi$
$599$	−26.8502			−1.09707			−0.548535	+	0.836128i	$0.684814\pi$
$600$	3.50550	+	24.2428i	0.143112	+	0.989707i
$601$	−42.9566			−1.75224			−0.876119	−	0.482095i	$-0.839876\pi$
$601$	−42.9566			−1.75224			−0.876119	+	0.482095i	$0.839876\pi$
$602$	−1.25099	−	0.509217i	−0.0509866	−	0.0207541i
$603$	−0.116555	+	20.8156i	−0.00474649	+	0.847677i
$604$	−18.7950	−	18.3397i	−0.764756	−	0.746232i
$605$	−0.370026	−	5.77305i	−0.0150437	−	0.234708i
$606$	−17.1077	−	16.9942i	−0.694953	−	0.690341i
$607$	32.0417	−	32.0417i	1.30053	−	1.30053i	0.372498	−	0.928033i	$-0.378501\pi$
$607$	32.0417	−	32.0417i	1.30053	−	1.30053i	0.928033	−	0.372498i	$-0.121499\pi$
$608$	−33.4822	−	12.6813i	−1.35788	−	0.514294i
$609$	−1.81051	+	0.744004i	−0.0733654	+	0.0301486i
$610$	5.14720	−	15.4000i	0.208404	−	0.623526i
$611$	−48.8691			−1.97703
$612$	−5.24534	+	5.31568i	−0.212030	+	0.214874i
$613$	−20.1419	+	20.1419i	−0.813522	+	0.813522i	−0.985160	−	0.171638i	$-0.945094\pi$
$613$	−20.1419	+	20.1419i	−0.813522	+	0.813522i	0.171638	+	0.985160i	$0.445094\pi$
$614$	16.9527	−	7.14408i	0.684154	−	0.288311i
$615$	−0.816918	+	2.37344i	−0.0329413	+	0.0957064i
$616$	3.14170	−	7.99760i	0.126583	−	0.322232i
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	0.839162	−	0.543881i	$-0.183046\pi$
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	−0.543881	+	0.839162i	$0.683046\pi$
$618$	−0.0955193	−	28.6860i	−0.00384235	−	1.15392i
$619$	11.9287			0.479456			0.239728	−	0.970840i	$-0.422942\pi$
$619$	11.9287			0.479456			0.239728	+	0.970840i	$0.422942\pi$
$620$	−9.67051	+	11.2707i	−0.388377	+	0.452644i
$621$	5.92821	−	13.9787i	0.237891	−	0.560947i
$622$	−40.0410	−	16.2987i	−1.60550	−	0.653519i
$623$	−8.94914	+	8.94914i	−0.358540	+	0.358540i
$624$	−34.8672	+	15.3378i	−1.39581	+	0.614005i
$625$	24.1851	−	6.33109i	0.967403	−	0.253244i
$626$	30.3385	−	12.7850i	1.21257	−	0.510993i
$627$	15.5681	−	37.2890i	0.621729	−	1.48918i
$628$	0.220843	+	18.0139i	0.00881260	+	0.718834i
$629$		−	4.29751i		−	0.171353i
$630$	−7.40147	−	2.51999i	−0.294882	−	0.100399i
$631$	7.13985			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$631$	7.13985			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$632$	−1.24417	−	2.85410i	−0.0494905	−	0.113530i
$633$	0.944728	+	0.394421i	0.0375496	+	0.0156768i
$634$	0.000478978		0.00113660i	1.90227e−5		4.51402e-5i
$635$	0.0347772	+	0.0305876i	0.00138009	+	0.00121383i
$636$	−25.4797	−	10.2728i	−1.01034	−	0.407341i
$637$	−24.5733	−	24.5733i	−0.973628	−	0.973628i
$638$	6.62057	+	2.69490i	0.262111	+	0.106692i
$639$	−8.81533	+	8.71716i	−0.348729	+	0.344846i
$640$	22.2060	−	12.1200i	0.877768	−	0.479086i
$641$		−	30.0187i		−	1.18567i	−0.805325	−	0.592834i	$-0.798009\pi$
$641$		−	30.0187i		−	1.18567i	0.805325	−	0.592834i	$-0.201991\pi$
$642$	20.2537	−	0.0674414i	0.799351	−	0.00266170i
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.354812	−	0.934938i	$-0.384545\pi$
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.934938	−	0.354812i	$-0.115455\pi$
$644$	3.36386	−	3.44736i	0.132555	−	0.135845i
$645$	4.03364	−	1.96795i	0.158825	−	0.0774878i
$646$	−10.2663	+	4.32637i	−0.403923	+	0.170219i
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	0.655618	−	0.755093i	$-0.272408\pi$
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	−0.755093	+	0.655618i	$0.772408\pi$
$648$	9.91037	+	23.4475i	0.389316	+	0.921104i
$649$			22.5597i			0.885545i
$650$	19.5477	+	33.6053i	0.766725	+	1.31811i
$651$	−1.80179	−	4.38458i	−0.0706176	−	0.171845i
$652$	9.78598	−	0.119972i	0.383248	−	0.00469847i
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	0.0662023	−	0.997806i	$-0.478912\pi$
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	−0.997806	+	0.0662023i	$0.978912\pi$
$654$	20.3381	+	20.2031i	0.795283	+	0.790004i
$655$	0.749453	+	11.6928i	0.0292835	+	0.456874i
$656$	2.59164	−	0.0635543i	0.101186	−	0.00248138i
$657$	0.111610	−	19.9325i	0.00435432	−	0.777640i
$658$	−3.90581	+	9.59539i	−0.152264	+	0.374067i
$659$			15.7130i			0.612093i	0.952017	+	0.306047i	$0.0990063\pi$
$659$			15.7130i			0.612093i	−0.952017	+	0.306047i	$0.900994\pi$
$660$	12.8332	+	25.5056i	0.499531	+	0.992803i
$661$			25.2637i			0.982643i	0.870978	+	0.491322i	$0.163486\pi$
$661$			25.2637i			0.982643i	−0.870978	+	0.491322i	$0.836514\pi$
$662$	−10.8536	−	4.41798i	−0.421839	−	0.171710i
$663$	−4.56649	+	10.9378i	−0.177348	+	0.424788i
$664$	−23.3598	−	9.17644i	−0.906536	−	0.356115i
$665$	−8.75834	−	7.70323i	−0.339634	−	0.298718i
$666$	−13.5367	−	5.59869i	−0.524538	−	0.216945i
$667$	2.83330	+	2.83330i	0.109706	+	0.109706i
$668$	−0.0330830	−	2.69854i	−0.00128002	−	0.104410i
$669$	38.1937	−	15.6952i	1.47665	−	0.606812i
$670$	−9.79680	−	19.6334i	−0.378483	−	0.758505i
$671$		−	18.9269i		−	0.730664i
$672$	0.224845	+	8.07199i	0.00867359	+	0.311384i
$673$	−15.4486	−	15.4486i	−0.595498	−	0.595498i	0.343613	−	0.939111i	$-0.388349\pi$
$673$	−15.4486	−	15.4486i	−0.595498	−	0.595498i	−0.939111	+	0.343613i	$0.888349\pi$
$674$	1.76824	+	4.19597i	0.0681099	+	0.161623i
$675$	22.6451	−	12.7357i	0.871612	−	0.490197i
$676$	−24.0644	+	24.6618i	−0.925554	+	0.948529i
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	−0.777382	−	0.629029i	$-0.783453\pi$
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	0.629029	+	0.777382i	$0.283453\pi$
$678$	29.7334	−	0.0990069i	1.14190	−	0.00380234i
$679$			6.31904i			0.242503i
$680$	2.40366	−	7.49594i	0.0921761	−	0.287456i
$681$	6.73505	+	16.3895i	0.258088	+	0.628046i
$682$	−6.52637	+	16.0333i	−0.249908	+	0.613947i
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	0.983400	−	0.181451i	$-0.0580793\pi$
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	−0.181451	+	0.983400i	$0.558079\pi$
$684$	0.252898	+	37.9743i	0.00966980	+	1.45198i
$685$	−29.4439	+	33.4768i	−1.12499	+	1.27908i
$686$	−14.3074	+	6.02932i	−0.546259	+	0.230201i
$687$	−15.3534	+	36.7749i	−0.585770	+	1.40305i
$688$	−3.35702	−	3.19631i	−0.127985	−	0.121858i
$689$	−43.6032			−1.66115
$690$	1.07694	+	15.9689i	0.0409983	+	0.607925i
$691$		−	26.8902i		−	1.02295i	−0.859298	−	0.511475i	$-0.829099\pi$
$691$		−	26.8902i		−	1.02295i	0.859298	−	0.511475i	$-0.170901\pi$
$692$	0.0624943	+	5.09759i	0.00237568	+	0.193781i
$693$	−9.11363	−	0.0510309i	−0.346198	−	0.00193850i
$694$	14.4761	+	34.3513i	0.549504	+	1.30396i
$695$	1.31896	+	20.5780i	0.0500309	+	0.780569i
$696$	−6.71678	+	0.104715i	−0.254599	+	0.00396921i
$697$	0.570399	−	0.570399i	0.0216054	−	0.0216054i
$698$	−9.45148	+	23.2194i	−0.357744	+	0.878869i
$699$	4.14389	+	10.0840i	0.156736	+	0.381412i
$700$	8.16069	−	1.15231i	0.308445	−	0.0435531i
$701$	35.7956			1.35198			0.675990	−	0.736911i	$-0.263716\pi$
$701$	35.7956			1.35198			0.675990	+	0.736911i	$0.263716\pi$
$702$	28.5038	+	28.6335i	1.07581	+	1.08070i
$703$	−15.4525	−	15.4525i	−0.582804	−	0.582804i
$704$	20.0708	−	21.6041i	0.756445	−	0.814236i
$705$	−15.0946	−	30.9389i	−0.568495	−	1.16523i
$706$	−8.21566	−	19.4955i	−0.309200	−	0.733723i
$707$	−5.73705	+	5.73705i	−0.215764	+	0.215764i
$708$	−8.29826	−	19.5097i	−0.311868	−	0.733221i
$709$	−31.6856			−1.18998			−0.594988	−	0.803735i	$-0.702843\pi$
$709$	−31.6856			−1.18998			−0.594988	+	0.803735i	$0.702843\pi$
$710$	4.14257	−	12.3942i	0.155468	−	0.465145i
$711$	−2.34816	+	2.32201i	−0.0880628	+	0.0870821i
$712$	−39.8152	+	17.3564i	−1.49214	+	0.650459i
$713$	−6.86153	+	6.86153i	−0.256966	+	0.256966i
$714$	1.78265	+	1.77081i	0.0667138	+	0.0662710i
$715$	34.0277	+	29.9284i	1.27256	+	1.11926i
$716$	33.5456	−	34.3784i	1.25366	−	1.28478i
$717$	2.69238	−	6.44887i	0.100549	−	0.240837i
$718$	13.1837	−	32.3883i	0.492010	−	1.20872i
$719$	−47.9558			−1.78845			−0.894225	−	0.447618i	$-0.852272\pi$
$719$	−47.9558			−1.78845			−0.894225	+	0.447618i	$0.852272\pi$
$720$	−20.4801	−	17.3368i	−0.763248	−	0.646106i
$721$	−9.65184			−0.359453
$722$	−11.2280	+	27.5837i	−0.417861	+	1.02656i
$723$	−7.64809	+	18.3189i	−0.284435	+	0.681287i
$724$	30.3392	−	31.0923i	1.12755	−	1.15554i
$725$	0.875297	+	6.80002i	0.0325077	+	0.252546i
$726$	4.49586	+	4.46601i	0.166857	+	0.165749i
$727$	20.8052	−	20.8052i	0.771622	−	0.771622i	−0.206768	−	0.978390i	$-0.566295\pi$
$727$	20.8052	−	20.8052i	0.771622	−	0.771622i	0.978390	+	0.206768i	$0.0662946\pi$
$728$	5.12153	+	11.7487i	0.189817	+	0.435435i
$729$	19.4099	−	18.7685i	0.718884	−	0.695130i
$730$	9.38116	+	18.8004i	0.347212	+	0.695835i
$731$	−1.44234			−0.0533468
$732$	6.96199	+	16.3681i	0.257322	+	0.604981i
$733$	11.3990	−	11.3990i	0.421033	−	0.421033i	−0.464526	−	0.885559i	$-0.653775\pi$
$733$	11.3990	−	11.3990i	0.421033	−	0.421033i	0.885559	+	0.464526i	$0.153775\pi$
$734$	7.25237	+	17.2096i	0.267690	+	0.635219i
$735$	7.96715	−	23.1474i	0.293873	−	0.853806i
$736$	15.0708	−	6.79077i	0.555516	−	0.250311i
$737$	−18.0852	−	18.0852i	−0.666176	−	0.666176i
$738$	−1.05360	−	2.53981i	−0.0387836	−	0.0934916i
$739$	9.60683			0.353393			0.176697	−	0.984265i	$-0.443459\pi$
$739$	9.60683			0.353393			0.176697	+	0.984265i	$0.443459\pi$
$740$	15.3964	−	1.17651i	0.565981	−	0.0432495i
$741$	22.9092	+	55.7487i	0.841591	+	2.04798i
$742$	−3.48493	+	8.56143i	−0.127936	+	0.314300i
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	−0.655562	−	0.755142i	$-0.727568\pi$
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	0.755142	+	0.655562i	$0.227568\pi$
$744$	−0.253593	−	16.2663i	−0.00929716	−	0.596352i
$745$	−31.2530	+	2.00318i	−1.14502	+	0.0733907i
$746$	9.24445	+	21.9368i	0.338463	+	0.803163i
$747$	−0.149054	+	26.6196i	−0.00545359	+	0.973958i
$748$	−0.112483	−	9.17508i	−0.00411277	−	0.335474i
$749$		−	6.81468i		−	0.249003i
$750$	−15.2376	+	22.7556i	−0.556398	+	0.830916i
$751$	−18.9690			−0.692189			−0.346094	−	0.938200i	$-0.612492\pi$
$751$	−18.9690			−0.692189			−0.346094	+	0.938200i	$0.612492\pi$
$752$	−24.5164	+	25.7491i	−0.894022	+	0.938972i
$753$	11.6648	−	27.9397i	0.425087	−	1.01818i
$754$	−9.82507	+	4.14041i	−0.357808	+	0.150785i
$755$	−1.87797	−	29.2996i	−0.0683464	−	1.06632i
$756$	7.90028	−	3.30819i	0.287331	−	0.120318i
$757$	0.279592	+	0.279592i	0.0101620	+	0.0101620i	0.712170	−	0.702008i	$-0.247713\pi$
$757$	0.279592	+	0.279592i	0.0101620	+	0.0101620i	−0.702008	+	0.712170i	$0.747713\pi$
$758$	−1.45739	+	3.58037i	−0.0529349	+	0.130045i
$759$	7.09113	+	17.2560i	0.257392	+	0.626353i
$760$	−18.3103	−	35.5960i	−0.664185	−	1.29120i
$761$		−	20.3237i		−	0.736733i	−0.929681	−	0.368366i	$-0.879917\pi$
$761$		−	20.3237i		−	0.736733i	0.929681	−	0.368366i	$-0.120083\pi$
$762$	−0.0507349		0.000168938i	−0.00183793		6.11999e-6i
$763$	6.82036	−	6.82036i	0.246914	−	0.246914i
$764$	−18.1355	+	18.5857i	−0.656118	+	0.672406i
$765$	−8.33517	+	0.487399i	−0.301359	+	0.0176220i
$766$	13.6746	+	32.4494i	0.494083	+	1.17244i
$767$	−23.7938	−	23.7938i	−0.859144	−	0.859144i
$768$	−9.41052	+	26.0661i	−0.339573	+	0.940580i
$769$			25.1716i			0.907711i	0.891075	+	0.453855i	$0.149952\pi$
$769$			25.1716i			0.907711i	−0.891075	+	0.453855i	$0.850048\pi$
$770$	8.59603	−	4.28930i	0.309779	−

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})\)	\(q+(-0.533177 + 1.30986i) q^{2} +(0.667305 - 1.59834i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.143028 - 2.23149i) q^{5} +(1.73781 + 1.72627i) q^{6} +(0.582772 - 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(-2.10941 - 2.13317i) q^{9} +(2.99919 + 1.00243i) q^{10} +3.68607 q^{11} +(-3.18773 + 1.35587i) q^{12} +(-3.88771 + 3.88771i) q^{13} +(0.452626 + 1.07407i) q^{14} +(-3.66213 - 1.26047i) q^{15} +(0.0980619 + 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(3.91883 - 1.62567i) q^{18} +6.32919 q^{19} +(-2.91214 + 3.39403i) q^{20} +(-0.542584 - 1.32036i) q^{21} +(-1.96533 + 4.82821i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(-0.0763660 - 4.89838i) q^{24} +(-4.95909 + 0.638332i) q^{25} +(-3.01950 - 7.16518i) q^{26} +(-4.81715 + 1.94809i) q^{27} +(-1.64820 + 0.0202063i) q^{28} -1.37122i q^{29} +(3.60361 - 4.12481i) q^{30} +3.32075 q^{31} +(-5.29013 - 2.00362i) q^{32} +(2.45973 - 5.89160i) q^{33} +(-1.62206 + 0.683558i) q^{34} +(-1.38380 - 1.21710i) q^{35} +(0.0399575 + 5.99987i) q^{36} +(-2.44147 - 2.44147i) q^{37} +(-3.37458 + 8.29032i) q^{38} +(3.61961 + 8.80819i) q^{39} +(-2.89300 - 5.62410i) q^{40} -0.648104i q^{41} +(2.01877 - 0.00672215i) q^{42} +(-0.819412 + 0.819412i) q^{43} +(-5.27640 - 5.14859i) q^{44} +(-4.45843 + 5.01223i) q^{45} +(-1.60482 - 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(6.45689 + 2.51168i) q^{48} +6.32075i q^{49} +(1.80795 - 6.83603i) q^{50} +(1.99401 - 0.819412i) q^{51} +(10.9953 - 0.134798i) q^{52} +(5.60782 + 5.60782i) q^{53} +(0.0166776 - 7.34845i) q^{54} +(-0.527212 - 8.22542i) q^{55} +(0.852318 - 2.16968i) q^{56} +(4.22349 - 10.1162i) q^{57} +(1.79611 + 0.731106i) q^{58} +6.12026i q^{59} +(3.48154 + 6.91946i) q^{60} -5.13471i q^{61} +(-1.77055 + 4.34971i) q^{62} +(-2.47245 - 0.0138443i) q^{63} +(5.44503 - 5.86102i) q^{64} +(9.23144 + 8.11933i) q^{65} +(6.40568 + 6.36316i) q^{66} +(-4.90636 - 4.90636i) q^{67} +(-0.0305156 - 2.48912i) q^{68} +(1.92377 + 4.68141i) q^{69} +(2.33203 - 1.16365i) q^{70} -4.13251i q^{71} +(-7.88026 - 3.14666i) q^{72} +(4.69820 + 4.69820i) q^{73} +(4.49972 - 1.89624i) q^{74} +(-2.28895 + 8.35229i) q^{75} +(-9.05987 - 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-13.4674 + 0.0448439i) q^{78} -1.10079i q^{79} +(8.90925 - 0.790765i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(0.848922 + 0.345554i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(-1.06756 + 2.64788i) q^{84} +(1.83806 - 2.08982i) q^{85} +(-0.636420 - 1.51020i) q^{86} +(-2.19169 - 0.915024i) q^{87} +(9.55717 - 4.16621i) q^{88} -15.3562 q^{89} +(-4.18816 - 8.51230i) q^{90} +4.53130i q^{91} +(5.84382 - 0.0716428i) q^{92} +(2.21595 - 5.30771i) q^{93} +(-11.5836 + 4.88148i) q^{94} +(-0.905253 - 14.1235i) q^{95} +(-6.73261 + 7.11843i) q^{96} +(-5.42154 + 5.42154i) q^{97} +(-8.27927 - 3.37008i) q^{98} +(-7.77542 - 7.86299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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