LMFDB - Embedded newform 740.2.u.a.31.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(31,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.u (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	740.31
Dual form			740.2.u.a.191.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10727 - 0.879744i) q^{2} -0.686367 q^{3} +(0.452103 + 1.94823i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.759995 + 0.603827i) q^{6} +4.62323i q^{7} +(1.21334 - 2.55496i) q^{8} -2.52890 q^{9} +(1.40503 - 0.160887i) q^{10} +0.152447 q^{11} +(-0.310308 - 1.33720i) q^{12} +(-1.77094 + 1.77094i) q^{13} +(4.06726 - 5.11918i) q^{14} +(0.485335 - 0.485335i) q^{15} +(-3.59121 + 1.76160i) q^{16} +(0.944461 - 0.944461i) q^{17} +(2.80018 + 2.22478i) q^{18} +(0.408771 + 0.408771i) q^{19} +(-1.69729 - 1.05792i) q^{20} -3.17323i q^{21} +(-0.168800 - 0.134114i) q^{22} +(-3.65317 - 3.65317i) q^{23} +(-0.832798 + 1.75364i) q^{24} -1.00000i q^{25} +(3.51888 - 0.402939i) q^{26} +3.79485 q^{27} +(-9.00712 + 2.09018i) q^{28} +(-6.45456 - 6.45456i) q^{29} +(-0.964368 + 0.110427i) q^{30} +(7.03825 - 7.03825i) q^{31} +(5.52620 + 1.20877i) q^{32} -0.104634 q^{33} +(-1.87666 + 0.214892i) q^{34} +(-3.26912 - 3.26912i) q^{35} +(-1.14332 - 4.92688i) q^{36} +(-6.00727 - 0.955363i) q^{37} +(-0.0930071 - 0.812235i) q^{38} +(1.21551 - 1.21551i) q^{39} +(0.948664 + 2.66459i) q^{40} -6.64409i q^{41} +(-2.79163 + 3.51363i) q^{42} +(5.74433 + 5.74433i) q^{43} +(0.0689215 + 0.297001i) q^{44} +(1.78820 - 1.78820i) q^{45} +(0.831201 + 7.25891i) q^{46} +3.02588i q^{47} +(2.46489 - 1.20910i) q^{48} -14.3743 q^{49} +(-0.879744 + 1.10727i) q^{50} +(-0.648247 + 0.648247i) q^{51} +(-4.25084 - 2.64955i) q^{52} -8.28283 q^{53} +(-4.20194 - 3.33850i) q^{54} +(-0.107796 + 0.107796i) q^{55} +(11.8122 + 5.60957i) q^{56} +(-0.280567 - 0.280567i) q^{57} +(1.46860 + 12.8253i) q^{58} +(4.48922 + 4.48922i) q^{59} +(1.16497 + 0.726123i) q^{60} +(-0.752780 - 0.752780i) q^{61} +(-13.9851 + 1.60140i) q^{62} -11.6917i q^{63} +(-5.05560 - 6.20007i) q^{64} -2.50449i q^{65} +(0.115859 + 0.0920514i) q^{66} -10.9167 q^{67} +(2.26702 + 1.41303i) q^{68} +(2.50742 + 2.50742i) q^{69} +(0.743818 + 6.49579i) q^{70} -0.151676i q^{71} +(-3.06842 + 6.46123i) q^{72} +8.66157i q^{73} +(5.81121 + 6.34270i) q^{74} +0.686367i q^{75} +(-0.611574 + 0.981188i) q^{76} +0.704797i q^{77} +(-2.41525 + 0.276564i) q^{78} +(-11.0003 - 11.0003i) q^{79} +(1.29373 - 3.78501i) q^{80} +4.98204 q^{81} +(-5.84509 + 7.35681i) q^{82} +11.0767i q^{83} +(6.18219 - 1.43463i) q^{84} +1.33567i q^{85} +(-1.30700 - 11.4141i) q^{86} +(4.43019 + 4.43019i) q^{87} +(0.184970 - 0.389495i) q^{88} +(3.63135 + 3.63135i) q^{89} +(-3.55319 + 0.406867i) q^{90} +(-8.18746 - 8.18746i) q^{91} +(5.46562 - 8.76883i) q^{92} +(-4.83082 + 4.83082i) q^{93} +(2.66200 - 3.35047i) q^{94} -0.578090 q^{95} +(-3.79300 - 0.829660i) q^{96} +(-3.41372 + 3.41372i) q^{97} +(15.9162 + 12.6457i) q^{98} -0.385522 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) $ 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.10727	−	0.879744i	−0.782960	−	0.622073i
$2$	−1.10727	−	0.879744i	−0.782960	−	0.622073i
$3$	−0.686367			−0.396274			−0.198137	−	0.980174i	$-0.563489\pi$
$3$	−0.686367			−0.396274			−0.198137	+	0.980174i	$0.563489\pi$
$4$	0.452103	+	1.94823i	0.226051	+	0.974115i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	0.759995	+	0.603827i	0.310267	+	0.246511i
$7$			4.62323i			1.74742i	0.486449	+	0.873709i	$0.338292\pi$
$7$			4.62323i			1.74742i	−0.486449	+	0.873709i	$0.661708\pi$
$8$	1.21334	−	2.55496i	0.428981	−	0.903313i
$9$	−2.52890			−0.842967
$10$	1.40503	−	0.160887i	0.444310	−	0.0508769i
$11$	0.152447			0.0459644			0.0229822	−	0.999736i	$-0.492684\pi$
$11$	0.152447			0.0459644			0.0229822	+	0.999736i	$0.492684\pi$
$12$	−0.310308	−	1.33720i	−0.0895783	−	0.386017i
$13$	−1.77094	+	1.77094i	−0.491170	+	0.491170i	−0.908675	−	0.417505i	$-0.862905\pi$
$13$	−1.77094	+	1.77094i	−0.491170	+	0.491170i	0.417505	+	0.908675i	$0.362905\pi$
$14$	4.06726	−	5.11918i	1.08702	−	1.36816i
$15$	0.485335	−	0.485335i	0.125313	−	0.125313i
$16$	−3.59121	+	1.76160i	−0.897802	+	0.440400i
$17$	0.944461	−	0.944461i	0.229065	−	0.229065i	−0.583237	−	0.812302i	$-0.698214\pi$
$17$	0.944461	−	0.944461i	0.229065	−	0.229065i	0.812302	+	0.583237i	$0.198214\pi$
$18$	2.80018	+	2.22478i	0.660009	+	0.524387i
$19$	0.408771	+	0.408771i	0.0937786	+	0.0937786i	0.752440	−	0.658661i	$-0.228877\pi$
$19$	0.408771	+	0.408771i	0.0937786	+	0.0937786i	−0.658661	+	0.752440i	$0.728877\pi$
$20$	−1.69729	−	1.05792i	−0.379526	−	0.236559i
$21$		−	3.17323i		−	0.692456i
$22$	−0.168800	−	0.134114i	−0.0359883	−	0.0285932i
$23$	−3.65317	−	3.65317i	−0.761739	−	0.761739i	0.214897	−	0.976637i	$-0.431058\pi$
$23$	−3.65317	−	3.65317i	−0.761739	−	0.761739i	−0.976637	+	0.214897i	$0.931058\pi$
$24$	−0.832798	+	1.75364i	−0.169994	+	0.357960i
$25$		−	1.00000i		−	0.200000i
$26$	3.51888	−	0.402939i	0.690110	−	0.0790228i
$27$	3.79485			0.730320
$28$	−9.00712	+	2.09018i	−1.70219	+	0.395006i
$29$	−6.45456	−	6.45456i	−1.19858	−	1.19858i	−0.974592	−	0.223989i	$-0.928092\pi$
$29$	−6.45456	−	6.45456i	−1.19858	−	1.19858i	−0.223989	−	0.974592i	$-0.571908\pi$
$30$	−0.964368	+	0.110427i	−0.176069	+	0.0201612i
$31$	7.03825	−	7.03825i	1.26411	−	1.26411i	0.315023	−	0.949084i	$-0.397988\pi$
$31$	7.03825	−	7.03825i	1.26411	−	1.26411i	0.949084	−	0.315023i	$-0.102012\pi$
$32$	5.52620	+	1.20877i	0.976903	+	0.213682i
$33$	−0.104634			−0.0182145
$34$	−1.87666	+	0.214892i	−0.321844	+	0.0368536i
$35$	−3.26912	−	3.26912i	−0.552582	−	0.552582i
$36$	−1.14332	−	4.92688i	−0.190554	−	0.821147i
$37$	−6.00727	−	0.955363i	−0.987589	−	0.157061i
$37$	−6.00727	−	0.955363i	−0.987589	−	0.157061i
$38$	−0.0930071	−	0.812235i	−0.0150878	−	0.131762i
$39$	1.21551	−	1.21551i	0.194638	−	0.194638i
$40$	0.948664	+	2.66459i	0.149997	+	0.421309i
$41$		−	6.64409i		−	1.03763i	−0.854886	−	0.518816i	$-0.826373\pi$
$41$		−	6.64409i		−	1.03763i	0.854886	−	0.518816i	$-0.173627\pi$
$42$	−2.79163	+	3.51363i	−0.430758	+	0.542165i
$43$	5.74433	+	5.74433i	0.876003	+	0.876003i	0.993118	−	0.117116i	$-0.0373649\pi$
$43$	5.74433	+	5.74433i	0.876003	+	0.876003i	−0.117116	+	0.993118i	$0.537365\pi$
$44$	0.0689215	+	0.297001i	0.0103903	+	0.0447746i
$45$	1.78820	−	1.78820i	0.266570	−	0.266570i
$46$	0.831201	+	7.25891i	0.122554	+	1.07027i
$47$			3.02588i			0.441370i	0.975345	+	0.220685i	$0.0708292\pi$
$47$			3.02588i			0.441370i	−0.975345	+	0.220685i	$0.929171\pi$
$48$	2.46489	−	1.20910i	0.355776	−	0.174519i
$49$	−14.3743			−2.05347
$50$	−0.879744	+	1.10727i	−0.124415	+	0.156592i
$51$	−0.648247	+	0.648247i	−0.0907727	+	0.0907727i
$52$	−4.25084	−	2.64955i	−0.589486	−	0.367427i
$53$	−8.28283			−1.13773			−0.568867	−	0.822430i	$-0.692618\pi$
$53$	−8.28283			−1.13773			−0.568867	+	0.822430i	$0.692618\pi$
$54$	−4.20194	−	3.33850i	−0.571811	−	0.454312i
$55$	−0.107796	+	0.107796i	−0.0145352	+	0.0145352i
$56$	11.8122	+	5.60957i	1.57847	+	0.749610i
$57$	−0.280567	−	0.280567i	−0.0371620	−	0.0371620i
$58$	1.46860	+	12.8253i	0.192836	+	1.68404i
$59$	4.48922	+	4.48922i	0.584446	+	0.584446i	0.936122	−	0.351676i	$-0.114388\pi$
$59$	4.48922	+	4.48922i	0.584446	+	0.584446i	−0.351676	+	0.936122i	$0.614388\pi$
$60$	1.16497	+	0.726123i	0.150396	+	0.0937421i
$61$	−0.752780	−	0.752780i	−0.0963836	−	0.0963836i	0.657271	−	0.753654i	$-0.271711\pi$
$61$	−0.752780	−	0.752780i	−0.0963836	−	0.0963836i	−0.753654	+	0.657271i	$0.771711\pi$
$62$	−13.9851	+	1.60140i	−1.77611	+	0.203378i
$63$		−	11.6917i		−	1.47302i
$64$	−5.05560	−	6.20007i	−0.631950	−	0.775009i
$65$		−	2.50449i		−	0.310643i
$66$	0.115859	+	0.0920514i	0.0142612	+	0.0113307i
$67$	−10.9167			−1.33369			−0.666847	−	0.745195i	$-0.732356\pi$
$67$	−10.9167			−1.33369			−0.666847	+	0.745195i	$0.732356\pi$
$68$	2.26702	+	1.41303i	0.274917	+	0.171356i
$69$	2.50742	+	2.50742i	0.301858	+	0.301858i
$70$	0.743818	+	6.49579i	0.0889032	+	0.776396i
$71$		−	0.151676i		−	0.0180007i	−0.999959	−	0.00900034i	$-0.997135\pi$
$71$		−	0.151676i		−	0.0180007i	0.999959	−	0.00900034i	$-0.00286494\pi$
$72$	−3.06842	+	6.46123i	−0.361617	+	0.761463i
$73$			8.66157i			1.01376i	0.862017	+	0.506880i	$0.169201\pi$
$73$			8.66157i			1.01376i	−0.862017	+	0.506880i	$0.830799\pi$
$74$	5.81121	+	6.34270i	0.675539	+	0.737324i
$75$			0.686367i			0.0792548i
$76$	−0.611574	+	0.981188i	−0.0701524	+	0.112550i
$77$			0.704797i			0.0803190i
$78$	−2.41525	+	0.276564i	−0.273473	+	0.0313147i
$79$	−11.0003	−	11.0003i	−1.23763	−	1.23763i	−0.960969	−	0.276657i	$-0.910773\pi$
$79$	−11.0003	−	11.0003i	−1.23763	−	1.23763i	−0.276657	−	0.960969i	$-0.589227\pi$
$80$	1.29373	−	3.78501i	0.144643	−	0.423177i
$81$	4.98204			0.553560
$82$	−5.84509	+	7.35681i	−0.645483	+	0.812424i
$83$			11.0767i			1.21583i	0.794002	+	0.607915i	$0.207994\pi$
$83$			11.0767i			1.21583i	−0.794002	+	0.607915i	$0.792006\pi$
$84$	6.18219	−	1.43463i	0.674533	−	0.156531i
$85$			1.33567i			0.144874i
$86$	−1.30700	−	11.4141i	−0.140937	−	1.23081i
$87$	4.43019	+	4.43019i	0.474967	+	0.474967i
$88$	0.184970	−	0.389495i	0.0197179	−	0.0415203i
$89$	3.63135	+	3.63135i	0.384923	+	0.384923i	0.872872	−	0.487949i	$-0.162255\pi$
$89$	3.63135	+	3.63135i	0.384923	+	0.384923i	−0.487949	+	0.872872i	$0.662255\pi$
$90$	−3.55319	+	0.406867i	−0.374539	+	0.0428875i
$91$	−8.18746	−	8.18746i	−0.858279	−	0.858279i
$92$	5.46562	−	8.76883i	0.569830	−	0.914214i
$93$	−4.83082	+	4.83082i	−0.500933	+	0.500933i
$94$	2.66200	−	3.35047i	0.274564	−	0.345575i
$95$	−0.578090			−0.0593108
$96$	−3.79300	−	0.829660i	−0.387121	−	0.0846768i
$97$	−3.41372	+	3.41372i	−0.346610	+	0.346610i	−0.858845	−	0.512235i	$-0.828818\pi$
$97$	−3.41372	+	3.41372i	−0.346610	+	0.346610i	0.512235	+	0.858845i	$0.328818\pi$
$98$	15.9162	+	12.6457i	1.60778	+	1.27741i
$99$	−0.385522			−0.0387465
$100$	1.94823	−	0.452103i	0.194823	−	0.0452103i
$101$		−	16.8134i		−	1.67299i	−0.547971	−	0.836497i	$-0.684600\pi$
$101$		−	16.8134i		−	1.67299i	0.547971	−	0.836497i	$-0.315400\pi$
$102$	1.28808	−	0.147495i	0.127539	−	0.0146041i
$103$	−3.95059	+	3.95059i	−0.389263	+	0.389263i	−0.874425	−	0.485161i	$-0.838761\pi$
$103$	−3.95059	+	3.95059i	−0.389263	+	0.389263i	0.485161	+	0.874425i	$0.338761\pi$
$104$	2.37591	+	6.67343i	0.232978	+	0.654383i
$105$	2.24382	+	2.24382i	0.218974	+	0.218974i
$106$	9.17134	+	7.28677i	0.890800	+	0.707753i
$107$			0.816823i			0.0789652i	0.999220	+	0.0394826i	$0.0125710\pi$
$107$			0.816823i			0.0789652i	−0.999220	+	0.0394826i	$0.987429\pi$
$108$	1.71566	+	7.39325i	0.165090	+	0.711416i
$109$	0.905024	−	0.905024i	0.0866855	−	0.0866855i	−0.662434	−	0.749120i	$-0.730477\pi$
$109$	0.905024	−	0.905024i	0.0866855	−	0.0866855i	0.749120	+	0.662434i	$0.230477\pi$
$110$	0.214192	−	0.0245267i	0.0204225	−	0.00233853i
$111$	4.12319	+	0.655730i	0.391356	+	0.0622391i
$112$	−8.14429	−	16.6030i	−0.769563	−	1.56883i
$113$	0.271189	+	0.271189i	0.0255113	+	0.0255113i	0.719747	−	0.694236i	$-0.244258\pi$
$113$	0.271189	+	0.271189i	0.0255113	+	0.0255113i	−0.694236	+	0.719747i	$0.744258\pi$
$114$	0.0638370	+	0.557491i	0.00597889	+	0.0522139i
$115$	5.16637			0.481766
$116$	9.65684	−	15.4931i	0.896615	−	1.43850i
$117$	4.47853	−	4.47853i	0.414040	−	0.414040i
$118$	−1.02142	−	8.92015i	−0.0940298	−	0.821166i
$119$	4.36646	+	4.36646i	0.400273	+	0.400273i
$120$	−0.651131	−	1.82889i	−0.0594399	−	0.166954i
$121$	−10.9768			−0.997887
$122$	0.171279	+	1.49579i	0.0155069	+	0.135422i
$123$			4.56028i			0.411187i
$124$	16.8941	+	10.5301i	1.51714	+	0.945633i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−10.2857	+	12.9459i	−0.916322	+	1.15331i
$127$		−	11.1505i		−	0.989446i	−0.869051	−	0.494723i	$-0.835270\pi$
$127$		−	11.1505i		−	0.989446i	0.869051	−	0.494723i	$-0.164730\pi$
$128$	0.143447	+	11.3128i	0.0126790	+	0.999920i
$129$	−3.94272	−	3.94272i	−0.347137	−	0.347137i
$130$	−2.20331	+	2.77315i	−0.193243	+	0.243221i
$131$	−6.81609	+	6.81609i	−0.595525	+	0.595525i	−0.939118	−	0.343594i	$-0.888356\pi$
$131$	−6.81609	+	6.81609i	−0.595525	+	0.595525i	0.343594	+	0.939118i	$0.388356\pi$
$132$	−0.0473055	−	0.203852i	−0.00411741	−	0.0177430i
$133$	−1.88985	+	1.88985i	−0.163870	+	0.163870i
$134$	12.0878	+	9.60394i	1.04423	+	0.829654i
$135$	−2.68337	+	2.68337i	−0.230947	+	0.230947i
$136$	−1.26710	−	3.55901i	−0.108653	−	0.305183i
$137$	12.0257			1.02742			0.513712	−	0.857963i	$-0.328270\pi$
$137$	12.0257			1.02742			0.513712	+	0.857963i	$0.328270\pi$
$138$	−0.570509	−	4.98228i	−0.0485649	−	0.424120i
$139$	−10.1241			−0.858718			−0.429359	−	0.903134i	$-0.641260\pi$
$139$	−10.1241			−0.858718			−0.429359	+	0.903134i	$0.641260\pi$
$140$	4.89102	−	7.84698i	0.413367	−	0.663191i
$141$		−	2.07686i		−	0.174903i
$142$	−0.133436	+	0.167947i	−0.0111977	+	0.0140938i
$143$	−0.269974	+	0.269974i	−0.0225763	+	0.0225763i
$144$	9.08180	−	4.45491i	0.756817	−	0.371243i
$145$	9.12812			0.758049
$146$	7.61996	−	9.59072i	0.630633	−	0.793733i
$147$	9.86603			0.813737
$148$	−0.854634	−	12.1355i	−0.0702505	−	0.997529i
$149$	1.68465			0.138012			0.0690058	−	0.997616i	$-0.478017\pi$
$149$	1.68465			0.138012			0.0690058	+	0.997616i	$0.478017\pi$
$150$	0.603827	−	0.759995i	0.0493023	−	0.0620533i
$151$	10.2897			0.837360			0.418680	−	0.908134i	$-0.362493\pi$
$151$	10.2897			0.837360			0.418680	+	0.908134i	$0.362493\pi$
$152$	1.54037	−	0.548413i	0.124941	−	0.0444822i
$153$	−2.38845	+	2.38845i	−0.193095	+	0.193095i
$154$	0.620040	−	0.780401i	0.0499643	−	0.0628865i
$155$			9.95359i			0.799491i
$156$	2.91764	+	1.81856i	0.233598	+	0.145602i
$157$	−0.00716759			−0.000572036			−0.000286018	−	1.00000i	$-0.500091\pi$
$157$	−0.00716759			−0.000572036			−0.000286018		1.00000i	$0.500091\pi$
$158$	2.50287	+	21.8577i	0.199118	+	1.73890i
$159$	5.68506			0.450855
$160$	−4.76234	+	3.05288i	−0.376496	+	0.241352i
$161$	16.8895	−	16.8895i	1.33108	−	1.33108i
$162$	−5.51647	−	4.38292i	−0.433415	−	0.344354i
$163$	6.04855	−	6.04855i	0.473759	−	0.473759i	−0.429370	−	0.903129i	$-0.641264\pi$
$163$	6.04855	−	6.04855i	0.473759	−	0.473759i	0.903129	+	0.429370i	$0.141264\pi$
$164$	12.9442	−	3.00381i	1.01077	−	0.234558i
$165$	0.0739877	−	0.0739877i	0.00575993	−	0.00575993i
$166$	9.74468	−	12.2650i	0.756334	−	0.951945i
$167$	−14.8189	−	14.8189i	−1.14672	−	1.14672i	−0.987193	−	0.159532i	$-0.949002\pi$
$167$	−14.8189	−	14.8189i	−1.14672	−	1.14672i	−0.159532	−	0.987193i	$-0.550998\pi$
$168$	−8.10747	−	3.85022i	−0.625505	−	0.297051i
$169$			6.72755i			0.517504i
$170$	1.17505	−	1.47895i	0.0901220	−	0.113430i
$171$	−1.03374	−	1.03374i	−0.0790522	−	0.0790522i
$172$	−8.59426	+	13.7883i	−0.655306	+	1.05135i
$173$		−	4.56061i		−	0.346737i	−0.984857	−	0.173368i	$-0.944535\pi$
$173$		−	4.56061i		−	0.346737i	0.984857	−	0.173368i	$-0.0554651\pi$
$174$	−1.00800	−	8.80286i	−0.0764159	−	0.667343i
$175$	4.62323			0.349484
$176$	−0.547468	+	0.268550i	−0.0412669	+	0.0202427i
$177$	−3.08125	−	3.08125i	−0.231601	−	0.231601i
$178$	−0.826237	−	7.21556i	−0.0619291	−	0.540829i
$179$	−13.9141	+	13.9141i	−1.03999	+	1.03999i	−0.0408234	+	0.999166i	$0.512998\pi$
$179$	−13.9141	+	13.9141i	−1.03999	+	1.03999i	−0.999166	+	0.0408234i	$0.987002\pi$
$180$	4.29228	+	2.67538i	0.319928	+	0.199411i
$181$	−3.65701			−0.271824			−0.135912	−	0.990721i	$-0.543396\pi$
$181$	−3.65701			−0.271824			−0.135912	+	0.990721i	$0.543396\pi$
$182$	1.86288	+	16.2686i	0.138086	+	1.20591i
$183$	0.516683	+	0.516683i	0.0381943	+	0.0381943i
$184$	−13.7662	+	4.90114i	−1.01486	+	0.361317i
$185$	4.92332	−	3.57224i	0.361970	−	0.262636i
$186$	9.59892	−	1.09915i	0.703827	−	0.0805936i
$187$	0.143980	−	0.143980i	0.0105289	−	0.0105289i
$188$	−5.89511	+	1.36801i	−0.429945	+	0.0997722i
$189$			17.5445i			1.27617i
$190$	0.640103	+	0.508571i	0.0464380	+	0.0368956i
$191$	16.9877	+	16.9877i	1.22918	+	1.22918i	0.964272	+	0.264912i	$0.0853431\pi$
$191$	16.9877	+	16.9877i	1.22918	+	1.22918i	0.264912	+	0.964272i	$0.414657\pi$
$192$	3.47000	+	4.25553i	0.250425	+	0.307116i
$193$	16.9773	−	16.9773i	1.22205	−	1.22205i	0.255149	−	0.966902i	$-0.417875\pi$
$193$	16.9773	−	16.9773i	1.22205	−	1.22205i	0.966902	−	0.255149i	$-0.0821246\pi$
$194$	6.78311	−	0.776718i	0.486999	−	0.0557651i
$195$			1.71900i			0.123100i
$196$	−6.49865	−	28.0044i	−0.464189	−	2.00032i
$197$	−3.46793			−0.247080			−0.123540	−	0.992340i	$-0.539425\pi$
$197$	−3.46793			−0.247080			−0.123540	+	0.992340i	$0.539425\pi$
$198$	0.426878	+	0.339161i	0.0303369	+	0.0241031i
$199$	6.94771	−	6.94771i	0.492510	−	0.492510i	−0.416586	−	0.909096i	$-0.636774\pi$
$199$	6.94771	−	6.94771i	0.492510	−	0.492510i	0.909096	+	0.416586i	$0.136774\pi$
$200$	−2.55496	−	1.21334i	−0.180663	−	0.0857963i
$201$	7.49289			0.528508
$202$	−14.7915	+	18.6170i	−1.04072	+	1.30989i
$203$	29.8409	−	29.8409i	2.09442	−	2.09442i
$204$	−1.55601	−	0.969860i	−0.108942	−	0.0679038i
$205$	4.69808	+	4.69808i	0.328128	+	0.328128i
$206$	7.84989	−	0.898872i	0.546928	−	0.0626274i
$207$	9.23851	+	9.23851i	0.642121	+	0.642121i
$208$	3.24012	−	9.47949i	0.224662	−	0.657285i
$209$	0.0623158	+	0.0623158i	0.00431048	+	0.00431048i
$210$	−0.510532	−	4.45850i	−0.0352300	−	0.307665i
$211$			15.2591i			1.05048i	0.850955	+	0.525238i	$0.176024\pi$
$211$			15.2591i			1.05048i	−0.850955	+	0.525238i	$0.823976\pi$
$212$	−3.74469	−	16.1369i	−0.257186	−	1.10828i
$213$			0.104106i			0.00713321i
$214$	0.718594	−	0.904445i	0.0491221	−	0.0618266i
$215$	−8.12371			−0.554033
$216$	4.60446	−	9.69569i	0.313294	−	0.659708i
$217$	32.5395	+	32.5395i	2.20892	+	2.20892i
$218$	−1.79830	+	0.205919i	−0.121796	+	0.0139466i
$219$		−	5.94502i		−	0.401727i
$220$	−0.258747	−	0.161277i	−0.0174447	−	0.0108733i
$221$			3.34517i			0.225020i
$222$	−3.98862	−	4.35342i	−0.267699	−	0.292183i
$223$			8.82390i			0.590892i	0.955359	+	0.295446i	$0.0954683\pi$
$223$			8.82390i			0.590892i	−0.955359	+	0.295446i	$0.904532\pi$
$224$	−5.58842	+	25.5489i	−0.373392	+	1.70706i
$225$			2.52890i			0.168593i
$226$	−0.0617032	−	0.538857i	−0.00410444	−	0.0358442i
$227$	−13.2169	−	13.2169i	−0.877236	−	0.877236i	0.116012	−	0.993248i	$-0.462989\pi$
$227$	−13.2169	−	13.2169i	−0.877236	−	0.877236i	−0.993248	+	0.116012i	$0.962989\pi$
$228$	0.419764	−	0.673455i	0.0277996	−	0.0446006i
$229$	−26.8629			−1.77515			−0.887574	−	0.460666i	$-0.847611\pi$
$229$	−26.8629			−1.77515			−0.887574	+	0.460666i	$0.847611\pi$
$230$	−5.72057	−	4.54508i	−0.377203	−	0.299694i
$231$		−	0.483749i		−	0.0318284i
$232$	−24.3227	+	8.65952i	−1.59686	+	0.568525i
$233$		−	3.38525i		−	0.221775i	−0.993833	−	0.110888i	$-0.964631\pi$
$233$		−	3.38525i		−	0.221775i	0.993833	−	0.110888i	$-0.0353694\pi$
$234$	−8.89891	+	1.01899i	−0.581740	+	0.0666136i
$235$	−2.13962	−	2.13962i	−0.139573	−	0.139573i
$236$	−6.71645	+	10.7756i	−0.437203	+	0.701433i
$237$	7.55021	+	7.55021i	0.490439	+	0.490439i
$238$	−0.993495	−	8.67623i	−0.0643987	−	0.562397i
$239$	−2.62747	−	2.62747i	−0.169957	−	0.169957i	0.617003	−	0.786960i	$-0.288346\pi$
$239$	−2.62747	−	2.62747i	−0.169957	−	0.169957i	−0.786960	+	0.617003i	$0.788346\pi$
$240$	−0.887971	+	2.59790i	−0.0573183	+	0.167694i
$241$	15.0259	−	15.0259i	0.967906	−	0.967906i	−0.0315943	−	0.999501i	$-0.510058\pi$
$241$	15.0259	−	15.0259i	0.967906	−	0.967906i	0.999501	+	0.0315943i	$0.0100585\pi$
$242$	12.1543	+	9.65673i	0.781305	+	0.620758i
$243$	−14.8041			−0.949682
$244$	1.12626	−	1.80692i	0.0721011	−	0.115676i
$245$	10.1642	−	10.1642i	0.649364	−	0.649364i
$246$	4.01188	−	5.04947i	0.255788	−	0.321943i
$247$	−1.44782			−0.0921225
$248$	−9.44261	−	26.5222i	−0.599606	−	1.68416i
$249$		−	7.60270i		−	0.481802i
$250$	−0.160887	−	1.40503i	−0.0101754	−	0.0888620i
$251$	3.09677	−	3.09677i	0.195467	−	0.195467i	−0.602587	−	0.798053i	$-0.705863\pi$
$251$	3.09677	−	3.09677i	0.195467	−	0.195467i	0.798053	+	0.602587i	$0.205863\pi$
$252$	22.7781	−	5.28585i	1.43489	−	0.332977i
$253$	−0.556914	−	0.556914i	−0.0350129	−	0.0350129i
$254$	−9.80957	+	12.3466i	−0.615507	+	0.774696i
$255$		−	0.916760i		−	0.0574097i
$256$	9.79353	−	12.6525i	0.612095	−	0.790784i
$257$	15.0397	−	15.0397i	0.938151	−	0.938151i	−0.0600447	−	0.998196i	$-0.519124\pi$
$257$	15.0397	−	15.0397i	0.938151	−	0.938151i	0.998196	+	0.0600447i	$0.0191243\pi$
$258$	0.897081	+	7.83425i	0.0558498	+	0.487739i
$259$	4.41687	−	27.7730i	0.274451	−	1.72573i
$260$	4.87932	−	1.13228i	0.302602	−	0.0702213i
$261$	16.3229	+	16.3229i	1.01036	+	1.01036i
$262$	13.5437	−	1.55086i	0.836731	−	0.0958121i
$263$	−13.9167			−0.858142			−0.429071	−	0.903271i	$-0.641159\pi$
$263$	−13.9167			−0.858142			−0.429071	+	0.903271i	$0.641159\pi$
$264$	−0.126957	+	0.267336i	−0.00781369	+	0.0164534i
$265$	5.85684	−	5.85684i	0.359783	−	0.359783i
$266$	3.75515	−	0.429994i	0.230243	−	0.0263646i
$267$	−2.49244	−	2.49244i	−0.152535	−	0.152535i
$268$	−4.93549	−	21.2683i	−0.301483	−	1.29917i
$269$	−6.64469			−0.405134			−0.202567	−	0.979268i	$-0.564928\pi$
$269$	−6.64469			−0.405134			−0.202567	+	0.979268i	$0.564928\pi$
$270$	5.33189	−	0.610542i	0.324489	−	0.0371564i
$271$			19.5052i			1.18486i	0.805622	+	0.592429i	$0.201831\pi$
$271$			19.5052i			1.18486i	−0.805622	+	0.592429i	$0.798169\pi$
$272$	−1.72799	+	5.05552i	−0.104775	+	0.306536i
$273$	5.61960	+	5.61960i	0.340114	+	0.340114i
$274$	−13.3157	−	10.5795i	−0.804431	−	0.639132i
$275$		−	0.152447i		−	0.00919288i
$276$	−3.75142	+	6.01864i	−0.225809	+	0.362279i
$277$	2.25076	+	2.25076i	0.135235	+	0.135235i	0.771484	−	0.636249i	$-0.219515\pi$
$277$	2.25076	+	2.25076i	0.135235	+	0.135235i	−0.636249	+	0.771484i	$0.719515\pi$
$278$	11.2102	+	8.90664i	0.672342	+	0.534185i
$279$	−17.7990	+	17.7990i	−1.06560	+	1.06560i
$280$	−12.3190	+	4.38589i	−0.736202	+	0.262107i
$281$	−18.7599	+	18.7599i	−1.11912	+	1.11912i	−0.127250	+	0.991871i	$0.540615\pi$
$281$	−18.7599	+	18.7599i	−1.11912	+	1.11912i	−0.991871	+	0.127250i	$0.959385\pi$
$282$	−1.82711	+	2.29965i	−0.108803	+	0.136942i
$283$	−18.9527	+	18.9527i	−1.12662	+	1.12662i	−0.135895	+	0.990723i	$0.543391\pi$
$283$	−18.9527	+	18.9527i	−1.12662	+	1.12662i	−0.990723	+	0.135895i	$0.956609\pi$
$284$	0.295501	−	0.0685733i	0.0175347	−	0.00406908i
$285$	0.396782			0.0235033
$286$	0.536442	−	0.0614267i	0.0317205	−	0.00363224i
$287$	30.7172			1.81318
$288$	−13.9752	−	3.05686i	−0.823497	−	0.180127i
$289$			15.2160i			0.895058i
$290$	−10.1073	−	8.03041i	−0.593522	−	0.471562i
$291$	2.34306	−	2.34306i	0.137353	−	0.137353i
$292$	−16.8747	+	3.91592i	−0.987520	+	0.229162i
$293$	−23.9267			−1.39781			−0.698906	−	0.715213i	$-0.746330\pi$
$293$	−23.9267			−1.39781			−0.698906	+	0.715213i	$0.746330\pi$
$294$	−10.9244	−	8.67958i	−0.637123	−	0.506203i
$295$	−6.34871			−0.369636
$296$	−9.72979	+	14.1891i	−0.565532	+	0.824726i
$297$	0.578513			0.0335687
$298$	−1.86536	−	1.48206i	−0.108058	−	0.0858532i
$299$	12.9391			0.748287
$300$	−1.33720	+	0.310308i	−0.0772033	+	0.0179157i
$301$	−26.5574	+	26.5574i	−1.53074	+	1.53074i
$302$	−11.3934	−	9.05226i	−0.655619	−	0.520899i
$303$			11.5402i			0.662964i
$304$	−2.18807	−	0.747891i	−0.125495	−	0.0428945i
$305$	1.06459			0.0609584
$306$	4.74588	−	0.543440i	0.271304	−	0.0310664i
$307$	10.1836			0.581209			0.290605	−	0.956843i	$-0.406144\pi$
$307$	10.1836			0.581209			0.290605	+	0.956843i	$0.406144\pi$
$308$	−1.37311	+	0.318640i	−0.0782400	+	0.0181562i
$309$	2.71156	−	2.71156i	0.154255	−	0.154255i
$310$	8.75661	−	11.0213i	0.497342	−	0.625969i
$311$	−16.6056	+	16.6056i	−0.941615	+	0.941615i	−0.998387	−	0.0567725i	$-0.981919\pi$
$311$	−16.6056	+	16.6056i	−0.941615	+	0.941615i	0.0567725	+	0.998387i	$0.481919\pi$
$312$	−1.63075	−	4.58042i	−0.0923230	−	0.259315i
$313$	−12.2773	+	12.2773i	−0.693952	+	0.693952i	−0.963099	−	0.269147i	$-0.913258\pi$
$313$	−12.2773	+	12.2773i	−0.693952	+	0.693952i	0.269147	+	0.963099i	$0.413258\pi$
$314$	0.00793647	+	0.00630564i	0.000447881	+	0.000355848i
$315$	8.26728	+	8.26728i	0.465808	+	0.465808i
$316$	16.4578	−	26.4043i	0.925823	−	1.48536i
$317$			4.62216i			0.259606i	0.991540	+	0.129803i	$0.0414346\pi$
$317$			4.62216i			0.259606i	−0.991540	+	0.129803i	$0.958565\pi$
$318$	−6.29491	−	5.00139i	−0.353001	−	0.280464i
$319$	−0.983976	−	0.983976i	−0.0550921	−	0.0550921i
$320$	7.95896	+	0.809267i	0.444920	+	0.0452394i
$321$		−	0.560640i		−	0.0312919i
$322$	−33.5596	+	3.84284i	−1.87021	+	0.214153i
$323$	0.772137			0.0429629
$324$	2.25239	+	9.70616i	0.125133	+	0.539231i
$325$	1.77094	+	1.77094i	0.0982340	+	0.0982340i
$326$	−12.0186	+	1.37622i	−0.665646	+	0.0762216i
$327$	−0.621178	+	0.621178i	−0.0343512	+	0.0343512i
$328$	−16.9754	−	8.06156i	−0.937307	−	0.445125i
$329$	−13.9893			−0.771257
$330$	−0.147015	+	0.0168343i	−0.00809289	+	0.000926698i
$331$	1.02604	+	1.02604i	0.0563963	+	0.0563963i	0.734742	−	0.678346i	$-0.237303\pi$
$331$	1.02604	+	1.02604i	0.0563963	+	0.0563963i	−0.678346	+	0.734742i	$0.737303\pi$
$332$	−21.5800	+	5.00782i	−1.18436	+	0.274840i
$333$	15.1918	+	2.41602i	0.832505	+	0.132397i
$334$	3.37173	+	29.4455i	0.184493	+	1.61119i
$335$	7.71931	−	7.71931i	0.421751	−	0.421751i
$336$	5.58997	+	11.3957i	0.304958	+	0.621689i
$337$			11.7073i			0.637735i	0.947799	+	0.318868i	$0.103303\pi$
$337$			11.7073i			0.637735i	−0.947799	+	0.318868i	$0.896697\pi$
$338$	5.91852	−	7.44923i	0.321925	−	0.405185i
$339$	−0.186135	−	0.186135i	−0.0101095	−	0.0101095i
$340$	−2.60219	+	0.603860i	−0.141124	+	0.0327489i
$341$	1.07296	−	1.07296i	0.0581039	−	0.0581039i
$342$	0.235206	+	2.05406i	0.0127185	+	0.111071i
$343$		−	34.0930i		−	1.84085i
$344$	21.6464	−	7.70667i	1.16709	−	0.415516i
$345$	−3.54602			−0.190912
$346$	−4.01217	+	5.04983i	−0.215695	+	0.271481i
$347$	−20.2046	+	20.2046i	−1.08464	+	1.08464i	−0.0885721	+	0.996070i	$0.528230\pi$
$347$	−20.2046	+	20.2046i	−1.08464	+	1.08464i	−0.996070	+	0.0885721i	$0.971770\pi$
$348$	−6.62814	+	10.6339i	−0.355306	+	0.570039i
$349$	−19.0813			−1.02140			−0.510699	−	0.859760i	$-0.670613\pi$
$349$	−19.0813			−1.02140			−0.510699	+	0.859760i	$0.670613\pi$
$350$	−5.11918	−	4.06726i	−0.273631	−	0.217404i
$351$	−6.72046	+	6.72046i	−0.358711	+	0.358711i
$352$	0.842451	+	0.184273i	0.0449028	+	0.00982178i
$353$	−4.58965	−	4.58965i	−0.244282	−	0.244282i	0.574337	−	0.818619i	$-0.305260\pi$
$353$	−4.58965	−	4.58965i	−0.244282	−	0.244282i	−0.818619	+	0.574337i	$0.805260\pi$
$354$	0.701072	+	6.12249i	0.0372616	+	0.325407i
$355$	0.107251	+	0.107251i	0.00569232	+	0.00569232i
$356$	−5.43297	+	8.71646i	−0.287947	+	0.461972i
$357$	−2.99700	−	2.99700i	−0.158618	−	0.158618i
$358$	27.6476	−	3.16586i	1.46122	−	0.167321i
$359$			29.7181i			1.56846i	0.620469	+	0.784231i	$0.286942\pi$
$359$			29.7181i			1.56846i	−0.620469	+	0.784231i	$0.713058\pi$
$360$	−2.39908	−	6.73848i	−0.126442	−	0.355149i
$361$		−	18.6658i		−	0.982411i
$362$	4.04931	+	3.21723i	0.212827	+	0.169094i
$363$	7.53409			0.395437
$364$	12.2495	−	19.6526i	0.642048	−	1.03008i
$365$	−6.12466	−	6.12466i	−0.320579	−	0.320579i
$366$	−0.117560	−	1.02666i	−0.00614497	−	0.0536643i
$367$			11.9378i			0.623149i	0.950222	+	0.311574i	$0.100856\pi$
$367$			11.9378i			0.623149i	−0.950222	+	0.311574i	$0.899144\pi$
$368$	19.5547	+	6.68387i	1.01936	+	0.348421i
$369$			16.8022i			0.874690i
$370$	−8.59411	−	0.375825i	−0.446787	−	0.0195382i
$371$		−	38.2934i		−	1.98810i
$372$	−11.5956	−	7.22753i	−0.601203	−	0.374730i
$373$		−	11.7243i		−	0.607062i	−0.952822	−	0.303531i	$-0.901834\pi$
$373$		−	11.7243i		−	0.607062i	0.952822	−	0.303531i	$-0.0981656\pi$
$374$	−0.286090	+	0.0327595i	−0.0147934	+	0.00169396i
$375$	−0.485335	−	0.485335i	−0.0250626	−	0.0250626i
$376$	7.73099	+	3.67143i	0.398695	+	0.189339i
$377$	22.8613			1.17741
$378$	15.4347	−	19.4265i	0.793873	−	0.999193i
$379$		−	7.12135i		−	0.365799i	−0.983132	−	0.182900i	$-0.941452\pi$
$379$		−	7.12135i		−	0.365799i	0.983132	−	0.182900i	$-0.0585483\pi$
$380$	−0.261356	−	1.12625i	−0.0134073	−	0.0577756i
$381$			7.65333i			0.392092i
$382$	−3.86518	−	33.7548i	−0.197760	−	1.72704i
$383$	−16.9237	−	16.9237i	−0.864760	−	0.864760i	0.127127	−	0.991886i	$-0.459424\pi$
$383$	−16.9237	−	16.9237i	−0.864760	−	0.864760i	−0.991886	+	0.127127i	$0.959424\pi$
$384$	−0.0984570	−	7.76473i	−0.00502436	−	0.396242i
$385$	−0.498366	−	0.498366i	−0.0253991	−	0.0253991i
$386$	−33.7341	+	3.86281i	−1.71702	+	0.196612i
$387$	−14.5268	−	14.5268i	−0.738441	−	0.738441i
$388$	−8.19406	−	5.10736i	−0.415990	−	0.259287i
$389$	−0.126189	+	0.126189i	−0.00639804	+	0.00639804i	−0.710299	−	0.703901i	$-0.751440\pi$
$389$	−0.126189	+	0.126189i	−0.00639804	+	0.00639804i	0.703901	+	0.710299i	$0.251440\pi$
$390$	1.51228	−	1.90340i	0.0765771	−	0.0963822i
$391$	−6.90056			−0.348976
$392$	−17.4409	+	36.7257i	−0.880900	+	1.85493i
$393$	4.67834	−	4.67834i	0.235991	−	0.235991i
$394$	3.83994	+	3.05089i	0.193453	+	0.153702i
$395$	15.5567			0.782743
$396$	−0.174296	−	0.751087i	−0.00875869	−	0.0377435i
$397$		−	2.85499i		−	0.143288i	−0.997430	−	0.0716440i	$-0.977175\pi$
$397$		−	2.85499i		−	0.143288i	0.997430	−	0.0716440i	$-0.0228245\pi$
$398$	−13.8052	+	1.58080i	−0.691993	+	0.0792385i
$399$	1.29713	−	1.29713i	0.0649376	−	0.0649376i
$400$	1.76160	+	3.59121i	0.0880800	+	0.179560i
$401$	14.4547	+	14.4547i	0.721834	+	0.721834i	0.968979	−	0.247145i	$-0.0794924\pi$
$401$	14.4547	+	14.4547i	0.721834	+	0.721834i	−0.247145	+	0.968979i	$0.579492\pi$
$402$	−8.29667	−	6.59183i	−0.413800	−	0.328770i
$403$			24.9286i			1.24178i
$404$	32.7564	−	7.60138i	1.62969	−	0.378183i
$405$	−3.52283	+	3.52283i	−0.175051	+	0.175051i
$406$	−59.2944	+	6.78966i	−2.94273	+	0.336965i
$407$	−0.915788	−	0.145642i	−0.0453939	−	0.00721920i
$408$	0.869696	+	2.44279i	0.0430564	+	0.120936i
$409$	9.53133	+	9.53133i	0.471294	+	0.471294i	0.902333	−	0.431039i	$-0.141853\pi$
$409$	9.53133	+	9.53133i	0.471294	+	0.471294i	−0.431039	+	0.902333i	$0.641853\pi$
$410$	−1.06895	−	9.33516i	−0.0527915	−	0.461031i
$411$	−8.25403			−0.407141
$412$	−9.48274	−	5.91059i	−0.467181	−	0.291194i
$413$	−20.7547	+	20.7547i	−1.02127	+	1.02127i
$414$	−2.10202	−	18.3571i	−0.103309	−	0.902201i
$415$	−7.83243	−	7.83243i	−0.384479	−	0.384479i
$416$	−11.9272	+	7.64590i	−0.584780	+	0.374871i
$417$	6.94887			0.340288
$418$	−0.0141786	−	0.123823i	−0.000693499	−	0.00605636i
$419$		−	27.6684i		−	1.35169i	−0.737044	−	0.675845i	$-0.763779\pi$
$419$		−	27.6684i		−	1.35169i	0.737044	−	0.675845i	$-0.236221\pi$
$420$	−3.35704	+	5.38591i	−0.163807	+	0.262805i
$421$	−1.50775	−	1.50775i	−0.0734833	−	0.0734833i	0.669410	−	0.742893i	$-0.266547\pi$
$421$	−1.50775	−	1.50775i	−0.0734833	−	0.0734833i	−0.742893	+	0.669410i	$0.766547\pi$
$422$	13.4241	−	16.8959i	0.653473	−	0.822481i
$423$		−	7.65215i		−	0.372060i
$424$	−10.0499	+	21.1623i	−0.488067	+	1.02773i
$425$	−0.944461	−	0.944461i	−0.0458131	−	0.0458131i
$426$	0.0915863	−	0.115273i	0.00443737	−	0.00558501i
$427$	3.48028	−	3.48028i	0.168422	−	0.168422i
$428$	−1.59136	+	0.369288i	−0.0769212	+	0.0178502i
$429$	0.185301	−	0.185301i	0.00894642	−	0.00894642i
$430$	8.99516	+	7.14678i	0.433785	+	0.344649i
$431$	18.5353	−	18.5353i	0.892813	−	0.892813i	−0.101974	−	0.994787i	$-0.532516\pi$
$431$	18.5353	−	18.5353i	0.892813	−	0.892813i	0.994787	+	0.101974i	$0.0325159\pi$
$432$	−13.6281	+	6.68502i	−0.655683	+	0.321633i
$433$	−22.8633			−1.09874			−0.549371	−	0.835578i	$-0.685133\pi$
$433$	−22.8633			−1.09874			−0.549371	+	0.835578i	$0.685133\pi$
$434$	−7.40366	−	64.6564i	−0.355387	−	3.10361i
$435$	−6.26524			−0.300395
$436$	2.17236	+	1.35403i	0.104037	+	0.0648463i
$437$		−	2.98663i		−	0.142870i
$438$	−5.23009	+	6.58275i	−0.249903	+	0.314536i
$439$	16.8712	−	16.8712i	0.805218	−	0.805218i	−0.178688	−	0.983906i	$-0.557185\pi$
$439$	16.8712	−	16.8712i	0.805218	−	0.805218i	0.983906	+	0.178688i	$0.0571853\pi$
$440$	0.144621	+	0.406208i	0.00689452	+	0.0193652i
$441$	36.3511			1.73101
$442$	2.94289	−	3.70401i	0.139979	−	0.176182i
$443$	22.5835			1.07297			0.536487	−	0.843908i	$-0.319751\pi$
$443$	22.5835			1.07297			0.536487	+	0.843908i	$0.319751\pi$
$444$	0.586592	+	8.32938i	0.0278384	+	0.395295i
$445$	−5.13551			−0.243447
$446$	7.76277	−	9.77046i	0.367578	−	0.462645i
$447$	−1.15629			−0.0546904
$448$	28.6644	−	23.3732i	1.35427	−	1.10428i
$449$	−8.35691	+	8.35691i	−0.394387	+	0.394387i	−0.876248	−	0.481861i	$-0.839961\pi$
$449$	−8.35691	+	8.35691i	−0.394387	+	0.394387i	0.481861	+	0.876248i	$0.339961\pi$
$450$	2.22478	−	2.80018i	0.104877	−	0.132002i
$451$		−	1.01287i		−	0.0476942i
$452$	−0.405734	+	0.650944i	−0.0190841	+	0.0306178i
$453$	−7.06248			−0.331824
$454$	3.00722	+	26.2622i	0.141136	+	1.23254i
$455$	11.5788			0.542824
$456$	−1.05726	+	0.376413i	−0.0495108	+	0.0176271i
$457$	−16.5839	+	16.5839i	−0.775761	+	0.775761i	−0.979107	−	0.203346i	$-0.934818\pi$
$457$	−16.5839	+	16.5839i	−0.775761	+	0.775761i	0.203346	+	0.979107i	$0.434818\pi$
$458$	29.7445	+	23.6324i	1.38987	+	1.10427i
$459$	3.58409	−	3.58409i	0.167291	−	0.167291i
$460$	2.33573	+	10.0653i	0.108904	+	0.469296i
$461$	−9.26246	+	9.26246i	−0.431396	+	0.431396i	−0.889103	−	0.457707i	$-0.848671\pi$
$461$	−9.26246	+	9.26246i	−0.431396	+	0.431396i	0.457707	+	0.889103i	$0.348671\pi$
$462$	−0.425575	+	0.535642i	−0.0197995	+	0.0249203i
$463$	8.94318	+	8.94318i	0.415625	+	0.415625i	0.883693	−	0.468068i	$-0.155050\pi$
$463$	8.94318	+	8.94318i	0.415625	+	0.415625i	−0.468068	+	0.883693i	$0.655050\pi$
$464$	34.5500	+	11.8093i	1.60394	+	0.548233i
$465$		−	6.83181i		−	0.316818i
$466$	−2.97816	+	3.74840i	−0.137960	+	0.173641i
$467$	−8.21792	−	8.21792i	−0.380280	−	0.380280i	0.490923	−	0.871203i	$-0.336660\pi$
$467$	−8.21792	−	8.21792i	−0.380280	−	0.380280i	−0.871203	+	0.490923i	$0.836660\pi$
$468$	10.7500	+	6.70045i	0.496917	+	0.309729i
$469$		−	50.4707i		−	2.33052i
$470$	0.486824	+	4.25146i	0.0224555	+	0.196105i
$471$	0.00491959			0.000226683
$472$	16.9167	−	6.02279i	0.778655	−	0.277222i
$473$	0.875704	+	0.875704i	0.0402649	+	0.0402649i
$474$	−1.71789	−	15.0024i	−0.0789052	−	0.689083i
$475$	0.408771	−	0.408771i	0.0187557	−	0.0187557i
$476$	−6.53279	+	10.4810i	−0.299430	+	0.480394i
$477$	20.9464			0.959072
$478$	0.597825	+	5.22083i	0.0273439	+	0.238795i
$479$	27.2226	+	27.2226i	1.24383	+	1.24383i	0.958398	+	0.285434i	$0.0921378\pi$
$479$	27.2226	+	27.2226i	1.24383	+	1.24383i	0.285434	+	0.958398i	$0.407862\pi$
$480$	3.26871	−	2.09540i	0.149196	−	0.0956414i
$481$	12.3304	−	8.94662i	0.562218	−	0.407931i
$482$	−29.8568	+	3.41883i	−1.35994	+	0.155723i
$483$	−11.5924	+	11.5924i	−0.527471	+	0.527471i
$484$	−4.96262	−	21.3853i	−0.225574	−	0.972057i
$485$		−	4.82772i		−	0.219216i
$486$	16.3921	+	13.0238i	0.743562	+	0.590771i
$487$	11.9920	+	11.9920i	0.543408	+	0.543408i	0.924526	−	0.381118i	$-0.124461\pi$
$487$	11.9920	+	11.9920i	0.543408	+	0.543408i	−0.381118	+	0.924526i	$0.624461\pi$
$488$	−2.83670	+	1.00994i	−0.128411	+	0.0457178i
$489$	−4.15152	+	4.15152i	−0.187738	+	0.187738i
$490$	−20.1963	+	2.31263i	−0.912377	+	0.104474i
$491$		−	43.9468i		−	1.98329i	−0.128995	−	0.991645i	$-0.541175\pi$
$491$		−	43.9468i		−	1.98329i	0.128995	−	0.991645i	$-0.458825\pi$
$492$	−8.88448	+	2.06172i	−0.400543	+	0.0929493i
$493$	−12.1922			−0.549107
$494$	1.60313	+	1.27371i	0.0721282	+	0.0573069i
$495$	0.272606	−	0.272606i	0.0122527	−	0.0122527i
$496$	−12.8772	+	37.6744i	−0.578204	+	1.69163i
$497$	0.701236			0.0314547
$498$	−6.68843	+	8.41826i	−0.299716	+	0.377231i
$499$	−10.0585	+	10.0585i	−0.450279	+	0.450279i	−0.895447	−	0.445168i	$-0.853144\pi$
$499$	−10.0585	+	10.0585i	−0.450279	+	0.450279i	0.445168	+	0.895447i	$0.353144\pi$
$500$	−1.05792	+	1.69729i	−0.0473117	+	0.0759052i
$501$	10.1712	+	10.1712i	0.454417	+	0.454417i
$502$	−6.15334	+	0.704604i	−0.274637	+	0.0314480i
$503$	8.11271	+	8.11271i	0.361728	+	0.361728i	0.864449	−	0.502721i	$-0.167668\pi$
$503$	8.11271	+	8.11271i	0.361728	+	0.361728i	−0.502721	+	0.864449i	$0.667668\pi$
$504$	−29.8718	−	14.1860i	−1.33059	−	0.631896i
$505$	11.8889	+	11.8889i	0.529047	+	0.529047i
$506$	0.126714	+	1.10660i	0.00563312	+	0.0491942i
$507$		−	4.61757i		−	0.205073i
$508$	21.7237	−	5.04116i	0.963834	−	0.223666i
$509$		−	12.4992i		−	0.554017i	−0.960867	−	0.277008i	$-0.910657\pi$
$509$		−	12.4992i		−	0.554017i	0.960867	−	0.277008i	$-0.0893430\pi$
$510$	−0.806513	+	1.01510i	−0.0357130	+	0.0449495i
$511$	−40.0445			−1.77146
$512$	−21.9751	+	5.39401i	−0.971171	+	0.238384i
$513$	1.55123	+	1.55123i	0.0684884	+	0.0684884i
$514$	−29.8841	+	3.42196i	−1.31813	+	0.150936i
$515$		−	5.58698i		−	0.246192i
$516$	5.89881	−	9.46384i	0.259681	−	0.416622i
$517$			0.461285i			0.0202873i
$518$	−29.3238	+	26.8666i	−1.28841	+	1.18045i
$519$			3.13025i			0.137403i
$520$	−6.39885	−	3.03880i	−0.280608	−	0.133260i
$521$			0.853387i			0.0373876i	0.999825	+	0.0186938i	$0.00595076\pi$
$521$			0.853387i			0.0373876i	−0.999825	+	0.0186938i	$0.994049\pi$
$522$	−3.71393	−	32.4339i	−0.162554	−	1.41959i
$523$	13.1095	+	13.1095i	0.573240	+	0.573240i	0.933032	−	0.359792i	$-0.117152\pi$
$523$	13.1095	+	13.1095i	0.573240	+	0.573240i	−0.359792	+	0.933032i	$0.617152\pi$
$524$	−16.3609	−	10.1977i	−0.714729	−	0.445491i
$525$	−3.17323			−0.138491
$526$	15.4096	+	12.2431i	0.671890	+	0.533826i
$527$		−	13.2947i		−	0.579127i
$528$	0.375764	−	0.184324i	0.0163530	−	0.00802167i
$529$			3.69135i			0.160494i
$530$	−11.6376	+	1.33260i	−0.505507	+	0.0578844i
$531$	−11.3528	−	11.3528i	−0.492669	−	0.492669i
$532$	−4.53626	−	2.82745i	−0.196672	−	0.122586i
$533$	11.7663	+	11.7663i	0.509654	+	0.509654i
$534$	0.567102	+	4.95252i	0.0245409	+	0.214317i
$535$	−0.577581	−	0.577581i	−0.0249710	−	0.0249710i
$536$	−13.2458	+	27.8918i	−0.572130	+	1.20474i
$537$	9.55019	−	9.55019i	0.412121	−	0.412121i
$538$	7.35748	+	5.84562i	0.317203	+	0.252023i
$539$	−2.19131			−0.0943865
$540$	−6.44098	−	4.01466i	−0.277175	−	0.172764i
$541$	−30.5123	+	30.5123i	−1.31183	+	1.31183i	−0.391758	+	0.920068i	$0.628133\pi$
$541$	−30.5123	+	30.5123i	−1.31183	+	1.31183i	−0.920068	+	0.391758i	$0.871867\pi$
$542$	17.1596	−	21.5976i	0.737068	−	0.927697i
$543$	2.51005			0.107717
$544$	6.36092	−	4.07764i	0.272722	−	0.174828i
$545$			1.27990i			0.0548247i
$546$	−1.27862	−	11.1662i	−0.0547199	−	0.477871i
$547$	−19.9527	+	19.9527i	−0.853116	+	0.853116i	−0.990516	−	0.137400i	$-0.956126\pi$
$547$	−19.9527	+	19.9527i	−0.853116	+	0.853116i	0.137400	+	0.990516i	$0.456126\pi$
$548$	5.43684	+	23.4288i	0.232250	+	1.00083i
$549$	1.90371	+	1.90371i	0.0812482	+	0.0812482i
$550$	−0.134114	+	0.168800i	−0.00571864	+	0.00719765i
$551$		−	5.27688i		−	0.224802i
$552$	9.44870	−	3.36398i	0.402163	−	0.143181i
$553$	50.8567	−	50.8567i	2.16265	−	2.16265i
$554$	−0.512113	−	4.47230i	−0.0217576	−	0.190010i
$555$	−3.37921	+	2.45187i	−0.143439	+	0.104076i
$556$	−4.57715	−	19.7242i	−0.194114	−	0.836490i
$557$	26.0938	+	26.0938i	1.10563	+	1.10563i	0.993718	+	0.111911i	$0.0356972\pi$
$557$	26.0938	+	26.0938i	1.10563	+	1.10563i	0.111911	+	0.993718i	$0.464303\pi$
$558$	35.3670	−	4.04979i	1.49720	−	0.171441i
$559$	−20.3457			−0.860532
$560$	17.4990	+	5.98120i	0.739466	+	0.252752i
$561$	−0.0988231	+	0.0988231i	−0.00417231	+	0.00417231i
$562$	37.2762	−	4.26841i	1.57240	−	0.180052i
$563$	−5.21056	−	5.21056i	−0.219599	−	0.219599i	0.588730	−	0.808329i	$-0.299628\pi$
$563$	−5.21056	−	5.21056i	−0.219599	−	0.219599i	−0.808329	+	0.588730i	$0.799628\pi$
$564$	4.04621	−	0.938955i	0.170376	−	0.0395371i
$565$	−0.383519			−0.0161348
$566$	37.6592	−	4.31227i	1.58294	−	0.181258i
$567$			23.0331i			0.967300i
$568$	−0.387527	−	0.184036i	−0.0162603	−	0.00772196i
$569$	−10.5402	−	10.5402i	−0.441870	−	0.441870i	0.450770	−	0.892640i	$-0.351149\pi$
$569$	−10.5402	−	10.5402i	−0.441870	−	0.441870i	−0.892640	+	0.450770i	$0.851149\pi$
$570$	−0.439346	−	0.349066i	−0.0184022	−	0.0146208i
$571$			34.0039i			1.42302i	0.702676	+	0.711510i	$0.251988\pi$
$571$			34.0039i			1.42302i	−0.702676	+	0.711510i	$0.748012\pi$
$572$	−0.648027	−	0.403915i	−0.0270954	−	0.0168885i
$573$	−11.6598	−	11.6598i	−0.487094	−	0.487094i
$574$	−34.0123	−	27.0232i	−1.41964	−	1.12793i
$575$	−3.65317	+	3.65317i	−0.152348	+	0.152348i
$576$	12.7851	+	15.6794i	0.532713	+	0.653307i
$577$	8.64631	−	8.64631i	0.359950	−	0.359950i	−0.503844	−	0.863795i	$-0.668081\pi$
$577$	8.64631	−	8.64631i	0.359950	−	0.359950i	0.863795	+	0.503844i	$0.168081\pi$
$578$	13.3862	−	16.8482i	0.556791	−	0.700794i
$579$	−11.6526	+	11.6526i	−0.484267	+	0.484267i
$580$	4.12685	+	17.7837i	0.171358	+	0.738427i
$581$	−51.2103			−2.12456
$582$	−4.65570	+	0.533113i	−0.192985	+	0.0220983i
$583$	−1.26269			−0.0522953
$584$	22.1299	+	10.5095i	0.915743	+	0.434884i
$585$			6.33360i			0.261862i
$586$	26.4934	+	21.0494i	1.09443	+	0.869541i
$587$	−25.5160	+	25.5160i	−1.05316	+	1.05316i	−0.0546531	+	0.998505i	$0.517405\pi$
$587$	−25.5160	+	25.5160i	−1.05316	+	1.05316i	−0.998505	+	0.0546531i	$0.982595\pi$
$588$	4.46046	+	19.2213i	0.183946	+	0.792673i
$589$	5.75407			0.237092
$590$	7.02975	+	5.58524i	0.289410	+	0.229941i
$591$	2.38027			0.0979113
$592$	23.2563	−	7.15150i	0.955829	−	0.293925i
$593$	−5.69861			−0.234014			−0.117007	−	0.993131i	$-0.537330\pi$
$593$	−5.69861			−0.234014			−0.117007	+	0.993131i	$0.537330\pi$
$594$	−0.640571	−	0.508943i	−0.0262830	−	0.0208822i
$595$	−6.17511			−0.253155
$596$	0.761633	+	3.28208i	0.0311977	+	0.134439i
$597$	−4.76868	+	4.76868i	−0.195169	+	0.195169i
$598$	−14.3271	−	11.3831i	−0.585879	−	0.465489i
$599$			1.52611i			0.0623550i	0.999514	+	0.0311775i	$0.00992572\pi$
$599$			1.52611i			0.0623550i	−0.999514	+	0.0311775i	$0.990074\pi$
$600$	1.75364	+	0.832798i	0.0715919	+	0.0339989i
$601$	24.9803			1.01897			0.509483	−	0.860481i	$-0.329837\pi$
$601$	24.9803			1.01897			0.509483	+	0.860481i	$0.329837\pi$
$602$	52.7699	−	6.04256i	2.15074	−	0.246276i
$603$	27.6074			1.12426
$604$	4.65198	+	20.0466i	0.189286	+	0.815685i
$605$	7.76174	−	7.76174i	0.315560	−	0.315560i
$606$	10.1524	−	12.7781i	0.412412	−	0.519074i
$607$	21.7193	−	21.7193i	0.881560	−	0.881560i	−0.112133	−	0.993693i	$-0.535768\pi$
$607$	21.7193	−	21.7193i	0.881560	−	0.881560i	0.993693	+	0.112133i	$0.0357684\pi$
$608$	1.76484	+	2.75306i	0.0715738	+	0.111651i
$609$	−20.4818	+	20.4818i	−0.829965	+	0.829965i
$610$	−1.17879	−	0.936568i	−0.0477279	−	0.0379205i
$611$	−5.35865	−	5.35865i	−0.216788	−	0.216788i
$612$	−5.73307	−	3.57342i	−0.231746	−	0.144447i
$613$		−	15.0790i		−	0.609035i	−0.952507	−	0.304517i	$-0.901505\pi$
$613$		−	15.0790i		−	0.609035i	0.952507	−	0.304517i	$-0.0984952\pi$
$614$	−11.2760	−	8.95896i	−0.455063	−	0.361554i
$615$	−3.22461	−	3.22461i	−0.130029	−	0.130029i
$616$	1.80072	+	0.855160i	0.0725532	+	0.0344554i
$617$		−	41.2273i		−	1.65975i	−0.557952	−	0.829873i	$-0.688413\pi$
$617$		−	41.2273i		−	1.65975i	0.557952	−	0.829873i	$-0.311587\pi$
$618$	−5.38790	+	0.616956i	−0.216733	+	0.0248176i
$619$	29.9401			1.20340			0.601698	−	0.798724i	$-0.294491\pi$
$619$	29.9401			1.20340			0.601698	+	0.798724i	$0.294491\pi$
$620$	−19.3919	+	4.50004i	−0.778797	+	0.180726i
$621$	−13.8633	−	13.8633i	−0.556314	−	0.556314i
$622$	32.9955	−	3.77824i	1.32300	−	0.151493i
$623$	−16.7886	+	16.7886i	−0.672621	+	0.672621i
$624$	−2.22391	+	6.50641i	−0.0890277	+	0.260465i
$625$	−1.00000			−0.0400000
$626$	24.3951	−	2.79343i	0.975025	−	0.111648i
$627$	−0.0427715	−	0.0427715i	−0.00170813	−	0.00170813i
$628$	−0.00324048	−	0.0139641i	−0.000129309	−	0.000557229i
$629$	−6.57594	+	4.77133i	−0.262200	+	0.190245i
$630$	−1.88104	−	16.4272i	−0.0749425	−	0.654476i
$631$	9.78676	−	9.78676i	0.389605	−	0.389605i	−0.484942	−	0.874546i	$-0.661159\pi$
$631$	9.78676	−	9.78676i	0.389605	−	0.389605i	0.874546	+	0.484942i	$0.161159\pi$
$632$	−41.4523	+	14.7581i	−1.64888	+	0.587045i
$633$		−	10.4733i		−	0.416277i
$634$	4.06632	−	5.11799i	0.161494	−	0.203261i
$635$	7.88459	+	7.88459i	0.312890	+	0.312890i
$636$	2.57023	+	11.0758i	0.101916	+	0.439184i
$637$	25.4560	−	25.4560i	1.00860	−	1.00860i
$638$	0.223882	+	1.95518i	0.00886359	+	0.0774061i
$639$			0.383575i			0.0151740i
$640$	−8.10079	−	7.89792i	−0.320212	−	0.312193i
$641$	−32.3451			−1.27755			−0.638777	−	0.769392i	$-0.720559\pi$
$641$	−32.3451			−1.27755			−0.638777	+	0.769392i	$0.720559\pi$
$642$	−0.493219	+	0.620781i	−0.0194658	+	0.0245003i
$643$	8.68573	−	8.68573i	0.342532	−	0.342532i	−0.514787	−	0.857318i	$-0.672129\pi$
$643$	8.68573	−	8.68573i	0.342532	−	0.342532i	0.857318	+	0.514787i	$0.172129\pi$
$644$	40.5404	+	25.2688i	1.59751	+	0.995731i
$645$	5.57585			0.219549
$646$	−0.854966	−	0.679283i	−0.0336382	−	0.0267260i
$647$	−16.4116	+	16.4116i	−0.645208	+	0.645208i	−0.951831	−	0.306623i	$-0.900801\pi$
$647$	−16.4116	+	16.4116i	−0.645208	+	0.645208i	0.306623	+	0.951831i	$0.400801\pi$
$648$	6.04492	−	12.7289i	0.237467	−	0.500038i
$649$	0.684366	+	0.684366i	0.0268637	+	0.0268637i
$650$	−0.402939	−	3.51888i	−0.0158046	−	0.138022i
$651$	−22.3340	−	22.3340i	−0.875339	−	0.875339i
$652$	14.5185	+	9.04940i	0.568589	+	0.354402i
$653$	−3.65282	−	3.65282i	−0.142946	−	0.142946i	0.632012	−	0.774958i	$-0.282229\pi$
$653$	−3.65282	−	3.65282i	−0.142946	−	0.142946i	−0.774958	+	0.632012i	$0.782229\pi$
$654$	1.23429	−	0.141336i	0.0482646	−	0.00552666i
$655$		−	9.63941i		−	0.376643i
$656$	11.7042	+	23.8603i	0.456973	+	0.931588i
$657$		−	21.9043i		−	0.854566i
$658$	15.4900	+	12.3070i	0.603863	+	0.479778i
$659$	7.09135			0.276240			0.138120	−	0.990416i	$-0.455894\pi$
$659$	7.09135			0.276240			0.138120	+	0.990416i	$0.455894\pi$
$660$	0.177595	+	0.110695i	0.00691288	+	0.00430880i
$661$	2.01482	+	2.01482i	0.0783674	+	0.0783674i	0.745204	−	0.666837i	$-0.232352\pi$
$661$	2.01482	+	2.01482i	0.0783674	+	0.0783674i	−0.666837	+	0.745204i	$0.732352\pi$
$662$	−0.233454	−	2.03876i	−0.00907343	−	0.0792386i
$663$		−	2.29601i		−	0.0891697i
$664$	28.3006	+	13.4399i	1.09827	+	0.521568i
$665$		−	2.67265i		−	0.103641i
$666$	−14.6960	−	16.0401i	−0.569457	−	0.621540i
$667$			47.1592i			1.82601i
$668$	22.1710	−	35.5704i	0.857824	−	1.37626i
$669$		−	6.05644i		−	0.234155i
$670$	−15.3384	+	1.75636i	−0.592573	+	0.0678542i
$671$	−0.114759	−	0.114759i	−0.00443022	−	0.00443022i
$672$	3.83571	−	17.5359i	0.147966	−	0.676463i
$673$	35.6807			1.37539			0.687694	−	0.726001i	$-0.258623\pi$
$673$	35.6807			1.37539			0.687694	+	0.726001i	$0.258623\pi$
$674$	10.2994	−	12.9631i	0.396718	−	0.499321i
$675$		−	3.79485i		−	0.146064i
$676$	−13.1068	+	3.04154i	−0.504108	+	0.116982i
$677$		−	43.9940i		−	1.69083i	−0.534114	−	0.845413i	$-0.679355\pi$
$677$		−	43.9940i		−	1.69083i	0.534114	−	0.845413i	$-0.320645\pi$
$678$	0.0423511	+	0.369854i	0.00162648	+	0.0142041i
$679$	−15.7824	−	15.7824i	−0.605673	−	0.605673i
$680$	3.41258	+	1.62063i	0.130866	+	0.0621481i
$681$	9.07163	+	9.07163i	0.347626	+	0.347626i
$682$	−2.13198	+	0.244128i	−0.0816379	+	0.00934816i
$683$	−24.8282	−	24.8282i	−0.950024	−	0.950024i	0.0487855	−	0.998809i	$-0.484465\pi$
$683$	−24.8282	−	24.8282i	−0.950024	−	0.950024i	−0.998809	+	0.0487855i	$0.984465\pi$
$684$	1.54661	−	2.48133i	0.0591361	−	0.0948759i
$685$	−8.50344	+	8.50344i	−0.324900	+	0.324900i
$686$	−29.9931	+	37.7503i	−1.14514	+	1.44131i
$687$	18.4378			0.703445
$688$	−30.7483	−	10.5099i	−1.17227	−	0.400685i
$689$	14.6684	−	14.6684i	0.558821	−	0.558821i
$690$	3.92641	+	3.11959i	0.149476	+	0.118761i
$691$	20.4456			0.777788			0.388894	−	0.921283i	$-0.372857\pi$
$691$	20.4456			0.777788			0.388894	+	0.921283i	$0.372857\pi$
$692$	8.88512	−	2.06186i	0.337761	−	0.0783803i
$693$		−	1.78236i		−	0.0677063i
$694$	40.1469	−	4.59713i	1.52396	−	0.174505i
$695$	7.15885	−	7.15885i	0.271550	−	0.271550i
$696$	16.6943	−	5.94361i	0.632796	−	0.225292i
$697$	−6.27508	−	6.27508i	−0.237686	−	0.237686i
$698$	21.1282	+	16.7866i	0.799713	+	0.635383i
$699$			2.32353i			0.0878838i
$700$	2.09018	+	9.00712i	0.0790012	+	0.340437i
$701$	14.3374	−	14.3374i	0.541517	−	0.541517i	−0.382456	−	0.923974i	$-0.624922\pi$
$701$	14.3374	−	14.3374i	0.541517	−	0.541517i	0.923974	+	0.382456i	$0.124922\pi$
$702$	13.3536	−	1.52910i	0.504001	−	0.0577120i
$703$	−2.06507	−	2.84613i	−0.0778858	−	0.107344i
$704$	−0.770709	−	0.945181i	−0.0290472	−	0.0356228i
$705$	1.46856	+	1.46856i	0.0553093	+	0.0553093i
$706$	1.04428	+	9.11970i	0.0393018	+	0.343225i
$707$	77.7322			2.92342
$708$	4.60995	−	7.39603i	0.173252	−	0.277960i
$709$	3.87183	−	3.87183i	0.145409	−	0.145409i	−0.630654	−	0.776064i	$-0.717213\pi$
$709$	3.87183	−	3.87183i	0.145409	−	0.145409i	0.776064	+	0.630654i	$0.217213\pi$
$710$	−0.0244028	−	0.213110i	−0.000915819	−	0.00799789i
$711$	27.8186	+	27.8186i	1.04328	+	1.04328i
$712$	13.6840	−	4.87187i	0.512831	−	0.182581i
$713$	−51.4239			−1.92584
$714$	0.681902	+	5.95508i	0.0255195	+	0.222863i
$715$		−	0.381801i		−	0.0142785i
$716$	−33.3985	−	20.8173i	−1.24816	−	0.777979i
$717$	1.80341	+	1.80341i	0.0673496	+	0.0673496i
$718$	26.1443	−	32.9060i	0.975697	−	1.22804i
$719$		−	34.3550i		−	1.28123i	−0.767864	−	0.640613i	$-0.778680\pi$
$719$		−	34.3550i		−	1.28123i	0.767864	−	0.640613i	$-0.221320\pi$
$720$	−3.27171	+	9.57190i	−0.121929	+	0.356724i
$721$	−18.2645	−	18.2645i	−0.680206	−	0.680206i
$722$	−16.4211	+	20.6681i	−0.611131	+	0.769188i
$723$	−10.3133	+	10.3133i	−0.383556	+	0.383556i
$724$	−1.65335	−	7.12471i	−0.0614461	−	0.264788i
$725$	−6.45456	+	6.45456i	−0.239716	+	0.239716i
$726$	−8.34228	−	6.62806i	−0.309611	−	0.245990i
$727$	−16.9112	+	16.9112i	−0.627203	+	0.627203i	−0.947363	−	0.320160i	$-0.896263\pi$
$727$	−16.9112	+	16.9112i	−0.627203	+	0.627203i	0.320160	+	0.947363i	$0.396263\pi$
$728$	−30.8528	+	10.9844i	−1.14348	+	0.407109i
$729$	−4.78509			−0.177226
$730$	1.39353	+	12.1698i	0.0515770	+	0.450424i
$731$	10.8506			0.401324
$732$	−0.773025	+	1.24021i	−0.0285718	+	0.0458396i
$733$			52.1584i			1.92651i	0.268581	+	0.963257i	$0.413445\pi$
$733$			52.1584i			1.92651i	−0.268581	+	0.963257i	$0.586555\pi$
$734$	10.5022	−	13.2184i	0.387644	−	0.487900i
$735$	−6.97634	+	6.97634i	−0.257326	+	0.257326i
$736$	−15.7723	−	24.6040i	−0.581375	−	0.906916i
$737$	−1.66422			−0.0613024
$738$	14.7817	−	18.6046i	0.544120	−	0.684847i
$739$	39.0581			1.43677			0.718387	−	0.695644i	$-0.244881\pi$
$739$	39.0581			1.43677			0.718387	+	0.695644i	$0.244881\pi$
$740$	9.18539	+	7.97675i	0.337662	+	0.293231i
$741$	0.993735			0.0365058
$742$	−33.6884	+	42.4013i	−1.23674	+	1.55660i
$743$	−36.0235			−1.32157			−0.660786	−	0.750574i	$-0.729777\pi$
$743$	−36.0235			−1.32157			−0.660786	+	0.750574i	$0.729777\pi$
$744$	6.48109	+	18.2040i	0.237608	+	0.667390i
$745$	−1.19122	+	1.19122i	−0.0436431	+	0.0436431i
$746$	−10.3144	+	12.9820i	−0.377637	+	0.475305i
$747$		−	28.0119i		−	1.02490i
$748$	0.345600	+	0.215412i	0.0126364	+	0.00787626i
$749$	−3.77636			−0.137985
$750$	0.110427	+	0.964368i	0.00403224	+	0.0352137i
$751$	−0.429074			−0.0156571			−0.00782856	−	0.999969i	$-0.502492\pi$
$751$	−0.429074			−0.0156571			−0.00782856	+	0.999969i	$0.502492\pi$
$752$	−5.33039	−	10.8666i	−0.194379	−	0.396262i
$753$	−2.12552	+	2.12552i	−0.0774584	+	0.0774584i
$754$	−25.3136	−	20.1120i	−0.921868	−	0.732437i
$755$	−7.27588	+	7.27588i	−0.264796	+	0.264796i
$756$	−34.1807	+	7.93191i	−1.24314	+	0.288481i
$757$	−1.07641	+	1.07641i	−0.0391227	+	0.0391227i	−0.726398	−	0.687275i	$-0.758807\pi$
$757$	−1.07641	+	1.07641i	−0.0391227	+	0.0391227i	0.687275	+	0.726398i	$0.258807\pi$
$758$	−6.26496	+	7.88527i	−0.227554	+	0.286406i
$759$	0.382247	+	0.382247i	0.0138747	+	0.0138747i
$760$	−0.701421	+	1.47699i	−0.0254432	+	0.0535762i
$761$		−	1.67006i		−	0.0605396i	−0.999542	−	0.0302698i	$-0.990363\pi$
$761$		−	1.67006i		−	0.0605396i	0.999542	−	0.0302698i	$-0.00963664\pi$
$762$	6.73296	−	8.47431i	0.243910	−	0.306992i
$763$	4.18413	+	4.18413i	0.151476	+	0.151476i
$764$	−25.4157	+	40.7761i	−0.919509	+	1.47523i
$765$		−	3.37778i		−	0.122124i
$766$	3.85062	+	33.6276i	0.139129	+	1.21502i
$767$	−15.9003			−0.574125
$768$	−6.72195	+	8.68429i	−0.242558	+	0.313367i
$769$	−30.7968	−	30.7968i	−1.11056	−	1.11056i	−0.993075	−	0.117485i	$-0.962517\pi$
$769$	−30.7968	−	30.7968i	−1.11056	−	1.11056i	−0.117485	−	0.993075i	$-0.537483\pi$
$770$	0.113393	+	0.990262i	0.00408638	+	0.0356866i
$771$	−10.3228	+	10.3228i	−0.371765	+	0.371765i
$772$	40.7511	+	25.4002i	1.46666	+	0.914172i
$773$	8.13478			0.292588			0.146294	−	0.989241i	$-0.453266\pi$
$773$	8.13478			0.292588			0.146294	+	0.989241i	$0.453266\pi$
$774$	3.30527	+	28.8651i	0.118806	+	1.03753i
$775$	−7.03825	−	7.03825i	−0.252821	−	0.252821i
$776$	4.57989	+	12.8639i	0.164408	+	0.461787i
$777$	−3.03159	+	19.0625i	−0.108758	+	0.683862i
$778$	0.250740	−	0.0287116i	0.00898945	−	0.00102936i
$779$	2.71591	−	2.71591i	0.0973077	−	0.0973077i
$780$	−3.34900	+	0.777163i	−0.119913	+	0.0278269i
$781$		−	0.0231226i		−	0.000827391i
$782$	7.64080	+	6.07072i	0.273234	+	0.217089i
$783$	−24.4941	−	24.4941i	−0.875348	−	0.875348i
$784$	51.6210	−	25.3217i	1.84361	−	0.904348i
$785$	0.00506825	−	0.00506825i	0.000180894	−	0.000180894i
$786$	−9.29594	+	1.06446i	−0.331575	+	0.0379679i
$787$			6.01905i			0.214556i	0.994229	+	0.107278i	$0.0342135\pi$
$787$			6.01905i			0.214556i	−0.994229	+	0.107278i	$0.965786\pi$
$788$	−1.56786	−	6.75633i	−0.0558527	−	0.240684i
$789$	9.55198			0.340059
$790$	−17.2255	−	13.6859i	−0.612856	−	0.486923i
$791$	−1.25377	+	1.25377i	−0.0445789	+	0.0445789i
$792$	−0.467771	+	0.984993i	−0.0166215	+	0.0350002i
$793$	2.66626			0.0946815
$794$	−2.51166	+	3.16125i	−0.0891355	+	0.112189i
$795$	−4.01994	+	4.01994i	−0.142573	+	0.142573i
$796$	16.6768	+	10.3947i	0.591095	+	0.368429i
$797$	3.85242	+	3.85242i	0.136460	+	0.136460i	0.772037	−	0.635577i	$-0.219238\pi$
$797$	3.85242	+	3.85242i	0.136460	+	0.136460i	−0.635577	+	0.772037i	$0.719238\pi$
$798$	−2.57741	+	0.295133i	−0.0912394	+	0.0104476i
$799$	2.85782	+	2.85782i	0.101103	+	0.101103i
$800$	1.20877	−	5.52620i	0.0427365	−	0.195381i
$801$	−9.18333	−	9.18333i	−0.324477	−	0.324477i
$802$	−3.28886	−	28.7217i	−0.116134	−	1.01420i
$803$			1.32043i			0.0465969i
$804$	3.38756	+	14.5979i	0.119470	+	0.514828i
$805$			23.8853i			0.841847i
$806$	21.9308	−	27.6028i	0.772479	−	0.972266i
$807$	4.56070			0.160544
$808$	−42.9575	−	20.4004i	−1.51124	−	0.717684i
$809$	14.2189	+	14.2189i	0.499908	+	0.499908i	0.911409	−	0.411501i	$-0.134995\pi$
$809$	14.2189	+	14.2189i	0.499908	+	0.499908i	−0.411501	+	0.911409i	$0.634995\pi$
$810$	6.99992	−	0.801545i	0.245952	−	0.0281634i
$811$			0.906030i			0.0318150i	0.999873	+	0.0159075i	$0.00506373\pi$
$811$			0.906030i			0.0318150i	−0.999873	+	0.0159075i	$0.994936\pi$
$812$	71.6282	+	44.6458i	2.51366	+	1.56676i
$813$		−	13.3878i		−	0.469529i
$814$	0.885899	+	0.966924i	0.0310507	+	0.0338907i
$815$			8.55394i			0.299631i
$816$	1.18604	−	3.46994i	0.0415196	−	0.121472i
$817$			4.69624i			0.164301i
$818$	−2.16865	−	18.9389i	−0.0758250	−	0.662183i
$819$	20.7053	+	20.7053i	0.723501	+	0.723501i
$820$	−7.02893	+	11.2770i	−0.245461	+	0.393808i
$821$	−18.6288			−0.650149			−0.325074	−	0.945688i	$-0.605389\pi$
$821$	−18.6288			−0.650149			−0.325074	+	0.945688i	$0.605389\pi$
$822$	9.13946	+	7.26143i	0.318775	+	0.253271i
$823$		−	4.42361i		−	0.154197i	−0.997023	−	0.0770986i	$-0.975434\pi$
$823$		−	4.42361i		−	0.154197i	0.997023	−	0.0770986i	$-0.0245656\pi$
$824$	5.30017	+	14.8870i	0.184640	+	0.518614i
$825$			0.104634i			0.00364290i
$826$	41.2399	−	4.72229i	1.43492	−	0.164309i
$827$	32.8315	+	32.8315i	1.14166	+	1.14166i	0.988146	+	0.153517i	$0.0490600\pi$
$827$	32.8315	+	32.8315i	1.14166	+	1.14166i	0.153517	+	0.988146i	$0.450940\pi$
$828$	−13.8220	+	22.1755i	−0.480348	+	0.770652i
$829$	16.7696	+	16.7696i	0.582434	+	0.582434i	0.935571	−	0.353138i	$-0.114885\pi$
$829$	16.7696	+	16.7696i	0.582434	+	0.582434i	−0.353138	+	0.935571i	$0.614885\pi$
$830$	1.78210	+	15.5632i	0.0618576	+	0.540205i
$831$	−1.54485	−	1.54485i	−0.0535903	−	0.0535903i
$832$	19.9331	+	2.02680i	0.691056	+	0.0702666i
$833$	−13.5760	+	13.5760i	−0.470379	+	0.470379i
$834$	−7.69429	−	6.11323i	−0.266432	−	0.211684i
$835$	20.9572			0.725252
$836$	−0.0932325	+	0.149579i	−0.00322451	+	0.00517329i
$837$	26.7091	−	26.7091i	0.923203	−	0.923203i
$838$	−24.3411	+	30.6365i	−0.840850	+	1.05832i
$839$	2.82440			0.0975090			0.0487545	−	0.998811i	$-0.484475\pi$
$839$	2.82440			0.0975090			0.0487545	+	0.998811i	$0.484475\pi$
$840$	8.45537	−	3.01033i	0.291738	−	0.103866i
$841$			54.3226i			1.87319i
$842$	0.343056	+	2.99593i	0.0118225	+	0.103246i
$843$	12.8762	−	12.8762i	0.443479	−	0.443479i
$844$	−29.7282	+	6.89866i	−1.02329	+	0.237462i
$845$	−4.75710	−	4.75710i	−0.163649	−	0.163649i
$846$	−6.73193	+	8.47301i	−0.231448	+	0.291308i
$847$		−	50.7481i		−	1.74373i
$848$	29.7453	−	14.5910i	1.02146	−	0.501058i
$849$	13.0085	−	13.0085i	0.446450	−	0.446450i
$850$	0.214892	+	1.87666i	0.00737073	+	0.0643689i
$851$	18.4555	+	25.4357i	0.632646	+	0.871925i
$852$	−0.202822	+	0.0470665i	−0.00694857	+	0.00161247i
$853$	15.6433	+	15.6433i	0.535617	+	0.535617i	0.922239	−	0.386621i	$-0.126358\pi$
$853$	15.6433	+	15.6433i	0.535617	+	0.535617i	−0.386621	+	0.922239i	$0.626358\pi$
$854$	−6.91537	+	0.791862i	−0.236639	+	0.0270970i
$855$	1.46193			0.0499970
$856$	2.08695	+	0.991086i	0.0713303	+	0.0338746i
$857$	−22.6546	+	22.6546i	−0.773866	+	0.773866i	−0.978780	−	0.204914i	$-0.934308\pi$
$857$	−22.6546	+	22.6546i	−0.773866	+	0.773866i	0.204914	+	0.978780i	$0.434308\pi$
$858$	−0.368196	+	0.0421613i	−0.0125700	+	0.00143936i
$859$	8.38884	+	8.38884i	0.286223	+	0.286223i	0.835585	−	0.549361i	$-0.185129\pi$
$859$	8.38884	+	8.38884i	0.286223	+	0.286223i	−0.549361	+	0.835585i	$0.685129\pi$
$860$	−3.67275	−	15.8269i	−0.125240	−	0.539692i
$861$	−21.0833			−0.718515
$862$	−36.8299	+	4.21730i	−1.25443	+	0.143642i
$863$			2.89948i			0.0986996i	0.998782	+	0.0493498i	$0.0157149\pi$
$863$			2.89948i			0.0986996i	−0.998782	+	0.0493498i	$0.984285\pi$
$864$	20.9711	+	4.58711i	0.713452	+	0.156056i
$865$	3.22484	+	3.22484i	0.109648	+	0.109648i
$866$	25.3159	+	20.1139i	0.860271	+	0.683497i
$867$		−	10.4437i		−	0.354688i
$868$	−48.6832	+	78.1056i	−1.65242	+	2.65108i
$869$	−1.67695	−	1.67695i	−0.0568867	−	0.0568867i
$870$	6.93733	+	5.51180i	0.235197	+	0.186868i
$871$	19.3329	−	19.3329i	0.655070	−	0.655070i
$872$	−1.21419	−	3.41040i	−0.0411177	−	0.115491i
$873$	8.63295	−	8.63295i	0.292181	−	0.292181i
$874$	−2.62746	+	3.30701i	−0.0888753	+	0.111861i
$875$	−3.26912	+	3.26912i	−0.110516	+	0.110516i
$876$	11.5823	−	2.68776i	0.391328	−	0.0908109i
$877$	−41.8482			−1.41311			−0.706557	−	0.707656i	$-0.749753\pi$
$877$	−41.8482			−1.41311			−0.706557	+	0.707656i	$0.749753\pi$
$878$	−33.5233	+	3.83867i	−1.13136	+	0.129549i
$879$	16.4225			0.553917
$880$	0.197224	−	0.577012i	0.00664843	−	0.0194511i
$881$			8.78571i			0.295998i	0.988988	+	0.147999i	$0.0472832\pi$
$881$			8.78571i			0.295998i	−0.988988	+	0.147999i	$0.952717\pi$
$882$	−40.2506	−	31.9797i	−1.35531	−	1.07681i
$883$	3.78585	−	3.78585i	0.127404	−	0.127404i	−0.640529	−	0.767934i	$-0.721285\pi$
$883$	3.78585	−	3.78585i	0.127404	−	0.127404i	0.767934	+	0.640529i	$0.221285\pi$
$884$	−6.51716	+	1.51236i	−0.219196	+	0.0508661i
$885$	4.35755			0.146477
$886$	−25.0061	−	19.8677i	−0.840096	−	0.667468i
$887$	−25.0811			−0.842141			−0.421070	−	0.907028i	$-0.638346\pi$
$887$	−25.0811			−0.842141			−0.421070	+	0.907028i	$0.638346\pi$
$888$	6.67820	−	9.73895i	0.224106	−	0.326818i
$889$	51.5513			1.72898
$890$	5.68641	+	4.51793i	0.190609	+	0.151441i
$891$	0.759495			0.0254440
$892$	−17.1910	+	3.98931i	−0.575597	+	0.133572i
$893$	−1.23689	+	1.23689i	−0.0413910	+	0.0413910i
$894$	1.28032	+	1.01723i	0.0428204	+	0.0340214i
$895$		−	19.6775i		−	0.657747i
$896$	−52.3017	+	0.663187i	−1.74728	+	0.0221555i
$897$	−8.88097			−0.296527
$898$	16.6053	−	1.90143i	0.554126	−	0.0634517i
$899$	−90.8576			−3.03027
$900$	−4.92688	+	1.14332i	−0.164229	+	0.0381108i
$901$	−7.82281	+	7.82281i	−0.260616	+	0.260616i
$902$	−0.891065	+	1.12152i	−0.0296692	+	0.0373426i
$903$	18.2281	−	18.2281i	0.606594	−	0.606594i
$904$	1.02192	−	0.363831i	0.0339886	−	0.0121008i
$905$	2.58590	−	2.58590i	0.0859582	−	0.0859582i
$906$	7.82008	+	6.21317i	0.259805	+	0.206419i
$907$	−38.1256	−	38.1256i	−1.26594	−	1.26594i	−0.948166	−	0.317774i	$-0.897065\pi$
$907$	−38.1256	−	38.1256i	−1.26594	−	1.26594i	−0.317774	−	0.948166i	$-0.602935\pi$
$908$	19.7742	−	31.7249i	0.656228	−	1.05283i
$909$			42.5194i			1.41028i
$910$	−12.8209	−	10.1864i	−0.425009	−	0.337676i
$911$	−0.329884	−	0.329884i	−0.0109295	−	0.0109295i	0.701621	−	0.712550i	$-0.252460\pi$
$911$	−0.329884	−	0.329884i	−0.0109295	−	0.0109295i	−0.712550	+	0.701621i	$0.752460\pi$
$912$	1.50182	+	0.513327i	0.0497303	+	0.0169980i
$913$			1.68861i			0.0558849i
$914$	32.9524	−	3.77331i	1.08997	−	0.124810i
$915$	−0.730701			−0.0241562
$916$	−12.1448	−	52.3350i	−0.401274	−	1.72920i
$917$	−31.5124	−	31.5124i	−1.04063	−	1.04063i
$918$	−7.12165	+	0.815483i	−0.235049	+	0.0269150i
$919$	17.8811	−	17.8811i	0.589842	−	0.589842i	−0.347747	−	0.937588i	$-0.613053\pi$
$919$	17.8811	−	17.8811i	0.589842	−	0.589842i	0.937588	+	0.347747i	$0.113053\pi$
$920$	6.26858	−	13.1998i	0.206669	−	0.435186i
$921$	−6.98969			−0.230318
$922$	18.4046	−	2.10747i	0.606125	−	0.0694059i
$923$	0.268610	+	0.268610i	0.00884140	+	0.00884140i
$924$	0.942455	−	0.218704i	0.0310045	−	0.00719484i
$925$	−0.955363	+	6.00727i	−0.0314122	+	0.197518i
$926$	−2.03483	−	17.7702i	−0.0668686	−	0.583966i
$927$	9.99066	−	9.99066i	0.328136	−	0.328136i
$928$	−27.8671	−	43.4712i	−0.914782	−	1.42701i
$929$		−	36.1963i		−	1.18756i	−0.804627	−	0.593781i	$-0.797635\pi$
$929$		−	36.1963i		−	1.18756i	0.804627	−	0.593781i	$-0.202365\pi$
$930$	−6.01024	+	7.56468i	−0.197084	+	0.248056i
$931$	−5.87580	−	5.87580i	−0.192571	−	0.192571i
$932$	6.59526	−	1.53048i	0.216035	−	0.0501326i
$933$	11.3975	−	11.3975i	0.373138	−	0.373138i
$934$	1.86981	+	16.3291i	0.0611821	+	0.534306i
$935$			0.203618i			0.00665903i
$936$	−6.00845	−	16.8764i	−0.196392	−	0.551623i
$937$	−12.4988			−0.408318			−0.204159	−	0.978938i	$-0.565446\pi$
$937$	−12.4988			−0.408318			−0.204159	+	0.978938i	$0.565446\pi$
$938$	−44.4012	+	55.8848i	−1.44975	+	1.82470i
$939$	8.42671	−	8.42671i	0.274995	−	0.274995i
$940$	3.20114	−	5.13580i	0.104410	−	0.167511i
$941$	−52.1295			−1.69937			−0.849687	−	0.527288i	$-0.823209\pi$
$941$	−52.1295			−1.69937			−0.849687	+	0.527288i	$0.823209\pi$
$942$	−0.00544733	−	0.00432798i	−0.000177484	−	0.000141013i
$943$	−24.2720	+	24.2720i	−0.790405	+	0.790405i
$944$	−24.0299	−	8.21350i	−0.782107	−	0.267327i
$945$	−12.4058	−	12.4058i	−0.403562	−	0.403562i
$946$	−0.199248	−	1.74004i	−0.00647810	−	0.0565735i
$947$	−18.0288	−	18.0288i	−0.585857	−	0.585857i	0.350650	−	0.936507i	$-0.385961\pi$
$947$	−18.0288	−	18.0288i	−0.585857	−	0.585857i	−0.936507	+	0.350650i	$0.885961\pi$
$948$	−11.2961	+	18.1230i	−0.366880	+	0.588609i
$949$	−15.3391	−	15.3391i	−0.497929	−	0.497929i
$950$	−0.812235	+	0.0930071i	−0.0263524	+	0.00301755i
$951$		−	3.17250i		−	0.102875i
$952$	16.4541	−	5.85810i	0.533282	−	0.189862i
$953$			52.2217i			1.69163i	0.533479	+	0.845814i	$0.320884\pi$
$953$			52.2217i			1.69163i	−0.533479	+	0.845814i	$0.679116\pi$
$954$	−23.1934	−	18.4275i	−0.750915	−	0.596612i
$955$	−24.0242			−0.777405
$956$	3.93104	−	6.30681i	0.127139	−	0.203977i
$957$	0.675368	+	0.675368i	0.0218316	+	0.0218316i
$958$	−6.19392	−	54.0917i	−0.200116	−	1.74762i
$959$			55.5975i			1.79534i
$960$	−5.46277	−	0.555454i	−0.176310	−	0.0179272i
$961$		−	68.0739i		−	2.19593i
$962$	−21.5238	−	0.941249i	−0.693956	−	0.0303471i
$963$		−	2.06566i		−	0.0665651i
$964$	36.0673	+	22.4807i	1.16165	+	0.724056i
$965$			24.0095i			0.772893i
$966$	23.0342	−	2.63760i	0.741114	−	0.0848632i
$967$	−37.8841	−	37.8841i	−1.21827	−	1.21827i	−0.968237	−	0.250034i	$-0.919558\pi$
$967$	−37.8841	−	37.8841i	−1.21827	−	1.21827i	−0.250034	−	0.968237i	$-0.580442\pi$
$968$	−13.3186	+	28.0451i	−0.428075	+	0.901405i
$969$	−0.529970			−0.0170251
$970$	−4.24716	+	5.34560i	−0.136368	+	0.171637i
$971$			55.7027i			1.78758i	0.448483	+	0.893792i	$0.351965\pi$
$971$			55.7027i			1.78758i	−0.448483	+	0.893792i	$0.648035\pi$
$972$	−6.69296	−	28.8417i	−0.214677	−	0.925099i
$973$		−	46.8062i		−	1.50054i
$974$	−2.72851	−	23.8282i	−0.0874273	−	0.763506i
$975$	−1.21551	−	1.21551i	−0.0389276	−	0.0389276i
$976$	4.02949	+	1.37729i	0.128981	+	0.0440860i
$977$	−3.50878	−	3.50878i	−0.112256	−	0.112256i	0.648748	−	0.761004i	$-0.275293\pi$
$977$	−3.50878	−	3.50878i	−0.112256	−	0.112256i	−0.761004	+	0.648748i	$0.775293\pi$
$978$	8.24914	−	0.944589i	0.263778	−	0.0302046i
$979$	0.553588	+	0.553588i	0.0176927	+	0.0176927i
$980$	24.3974	+	15.2069i	0.779345	+	0.485766i
$981$	−2.28871	+	2.28871i	−0.0730730	+	0.0730730i
$982$	−38.6619	+	48.6610i	−1.23375	+	1.55284i
$983$	27.9129			0.890284			0.445142	−	0.895460i	$-0.353153\pi$
$983$	27.9129			0.890284			0.445142	+	0.895460i	$0.353153\pi$
$984$	11.6513	+	5.53319i	0.371431	+	0.176392i
$985$	2.45220	−	2.45220i	0.0781335	−	0.0781335i
$986$	13.5000	+	10.7260i	0.429929	+	0.341584i
$987$	9.60182			0.305629
$988$	−0.654563	−	2.82068i	−0.0208244	−	0.0897379i
$989$		−	41.9701i		−	1.33457i
$990$	−0.541671	+	0.0620255i	−0.0172155	+	0.00197130i
$991$	31.2584	−	31.2584i	0.992957	−	0.992957i	−0.00701847	−	0.999975i	$-0.502234\pi$
$991$	31.2584	−	31.2584i	0.992957	−	0.992957i	0.999975	+	0.00701847i	$0.00223407\pi$
$992$	47.4024	−	30.3871i	1.50503	−	0.964793i
$993$	−0.704241	−	0.704241i	−0.0223484	−	0.0223484i
$994$	−0.776459	−	0.616908i	−0.0246278	−	0.0195671i
$995$			9.82555i			0.311491i
$996$	14.8118	−	3.43720i	0.469330	−	0.108912i
$997$	21.8909	−	21.8909i	0.693293	−	0.693293i	−0.269662	−	0.962955i	$-0.586912\pi$
$997$	21.8909	−	21.8909i	0.693293	−	0.693293i	0.962955	+	0.269662i	$0.0869119\pi$
$998$	19.9864	−	2.28859i	0.632657	−	0.0724441i
$999$	−22.7967	−	3.62547i	−0.721256	−	0.114705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.u.a.31.15	✓	152
4.3	odd	2	inner	740.2.u.a.31.24	yes	152
37.6	odd	4	inner	740.2.u.a.191.24	yes	152
148.43	even	4	inner	740.2.u.a.191.15	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.u.a.31.15	✓	152	1.1	even	1	trivial
740.2.u.a.31.24	yes	152	4.3	odd	2	inner
740.2.u.a.191.15	yes	152	148.43	even	4	inner
740.2.u.a.191.24	yes	152	37.6	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10727 - 0.879744i) q^{2} -0.686367 q^{3} +(0.452103 + 1.94823i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(0.759995 + 0.603827i) q^{6} +4.62323i q^{7} +(1.21334 - 2.55496i) q^{8} -2.52890 q^{9} +(1.40503 - 0.160887i) q^{10} +0.152447 q^{11} +(-0.310308 - 1.33720i) q^{12} +(-1.77094 + 1.77094i) q^{13} +(4.06726 - 5.11918i) q^{14} +(0.485335 - 0.485335i) q^{15} +(-3.59121 + 1.76160i) q^{16} +(0.944461 - 0.944461i) q^{17} +(2.80018 + 2.22478i) q^{18} +(0.408771 + 0.408771i) q^{19} +(-1.69729 - 1.05792i) q^{20} -3.17323i q^{21} +(-0.168800 - 0.134114i) q^{22} +(-3.65317 - 3.65317i) q^{23} +(-0.832798 + 1.75364i) q^{24} -1.00000i q^{25} +(3.51888 - 0.402939i) q^{26} +3.79485 q^{27} +(-9.00712 + 2.09018i) q^{28} +(-6.45456 - 6.45456i) q^{29} +(-0.964368 + 0.110427i) q^{30} +(7.03825 - 7.03825i) q^{31} +(5.52620 + 1.20877i) q^{32} -0.104634 q^{33} +(-1.87666 + 0.214892i) q^{34} +(-3.26912 - 3.26912i) q^{35} +(-1.14332 - 4.92688i) q^{36} +(-6.00727 - 0.955363i) q^{37} +(-0.0930071 - 0.812235i) q^{38} +(1.21551 - 1.21551i) q^{39} +(0.948664 + 2.66459i) q^{40} -6.64409i q^{41} +(-2.79163 + 3.51363i) q^{42} +(5.74433 + 5.74433i) q^{43} +(0.0689215 + 0.297001i) q^{44} +(1.78820 - 1.78820i) q^{45} +(0.831201 + 7.25891i) q^{46} +3.02588i q^{47} +(2.46489 - 1.20910i) q^{48} -14.3743 q^{49} +(-0.879744 + 1.10727i) q^{50} +(-0.648247 + 0.648247i) q^{51} +(-4.25084 - 2.64955i) q^{52} -8.28283 q^{53} +(-4.20194 - 3.33850i) q^{54} +(-0.107796 + 0.107796i) q^{55} +(11.8122 + 5.60957i) q^{56} +(-0.280567 - 0.280567i) q^{57} +(1.46860 + 12.8253i) q^{58} +(4.48922 + 4.48922i) q^{59} +(1.16497 + 0.726123i) q^{60} +(-0.752780 - 0.752780i) q^{61} +(-13.9851 + 1.60140i) q^{62} -11.6917i q^{63} +(-5.05560 - 6.20007i) q^{64} -2.50449i q^{65} +(0.115859 + 0.0920514i) q^{66} -10.9167 q^{67} +(2.26702 + 1.41303i) q^{68} +(2.50742 + 2.50742i) q^{69} +(0.743818 + 6.49579i) q^{70} -0.151676i q^{71} +(-3.06842 + 6.46123i) q^{72} +8.66157i q^{73} +(5.81121 + 6.34270i) q^{74} +0.686367i q^{75} +(-0.611574 + 0.981188i) q^{76} +0.704797i q^{77} +(-2.41525 + 0.276564i) q^{78} +(-11.0003 - 11.0003i) q^{79} +(1.29373 - 3.78501i) q^{80} +4.98204 q^{81} +(-5.84509 + 7.35681i) q^{82} +11.0767i q^{83} +(6.18219 - 1.43463i) q^{84} +1.33567i q^{85} +(-1.30700 - 11.4141i) q^{86} +(4.43019 + 4.43019i) q^{87} +(0.184970 - 0.389495i) q^{88} +(3.63135 + 3.63135i) q^{89} +(-3.55319 + 0.406867i) q^{90} +(-8.18746 - 8.18746i) q^{91} +(5.46562 - 8.76883i) q^{92} +(-4.83082 + 4.83082i) q^{93} +(2.66200 - 3.35047i) q^{94} -0.578090 q^{95} +(-3.79300 - 0.829660i) q^{96} +(-3.41372 + 3.41372i) q^{97} +(15.9162 + 12.6457i) q^{98} -0.385522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} - 4 q^{8} + 152 q^{9} - 16 q^{13} + 24 q^{14} + 40 q^{16} + 16 q^{22} - 36 q^{24} + 32 q^{29} - 4 q^{32} - 16 q^{37} - 40 q^{38} - 20 q^{42} - 72 q^{44} + 8 q^{46} - 248 q^{49} - 4 q^{50}+ \cdots + 24 q^{98}+O(q^{100}) \) 152 * q - 4 * q^2 - 4 * q^8 + 152 * q^9 - 16 * q^13 + 24 * q^14 + 40 * q^16 + 16 * q^22 - 36 * q^24 + 32 * q^29 - 4 * q^32 - 16 * q^37 - 40 * q^38 - 20 * q^42 - 72 * q^44 + 8 * q^46 - 248 * q^49 - 4 * q^50 - 20 * q^52 + 8 * q^54 - 4 * q^56 + 48 * q^57 + 28 * q^60 + 16 * q^61 + 16 * q^66 - 28 * q^68 - 128 * q^72 - 80 * q^74 + 76 * q^76 + 152 * q^81 + 16 * q^82 - 56 * q^84 - 96 * q^86 - 72 * q^88 + 8 * q^89 - 152 * q^92 + 16 * q^93 + 28 * q^94 + 48 * q^96 - 48 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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