LMFDB - Embedded newform 540.2.be.a.11.67

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.67
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.67

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36607 + 0.365849i) q^{2} +(1.31530 - 1.12693i) q^{3} +(1.73231 + 0.999552i) q^{4} +(0.342020 - 0.939693i) q^{5} +(2.20909 - 1.05827i) q^{6} +(1.60972 + 0.283837i) q^{7} +(2.00078 + 1.99922i) q^{8} +(0.460037 - 2.96452i) q^{9} +(0.811010 - 1.15856i) q^{10} +(-2.42284 + 0.881840i) q^{11} +(3.40494 - 0.637486i) q^{12} +(-2.45829 + 2.06275i) q^{13} +(2.09515 + 0.976655i) q^{14} +(-0.609113 - 1.62141i) q^{15} +(2.00179 + 3.46307i) q^{16} +(-2.30833 + 1.33272i) q^{17} +(1.71301 - 3.88144i) q^{18} +(-0.766220 - 0.442377i) q^{19} +(1.53176 - 1.28597i) q^{20} +(2.43713 - 1.44072i) q^{21} +(-3.63239 + 0.318266i) q^{22} +(-1.27245 - 7.21642i) q^{23} +(4.88462 + 0.374841i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-4.11287 + 1.91851i) q^{26} +(-2.73573 - 4.41767i) q^{27} +(2.50482 + 2.10069i) q^{28} +(-4.19994 + 5.00529i) q^{29} +(-0.238900 - 2.43781i) q^{30} +(3.65753 - 0.644921i) q^{31} +(1.46763 + 5.46315i) q^{32} +(-2.19298 + 3.89026i) q^{33} +(-3.64092 + 0.976086i) q^{34} +(0.817275 - 1.41556i) q^{35} +(3.76012 - 4.67563i) q^{36} +(4.01739 + 6.95832i) q^{37} +(-0.884869 - 0.884640i) q^{38} +(-0.908810 + 5.48348i) q^{39} +(2.56296 - 1.19634i) q^{40} +(3.67865 + 4.38405i) q^{41} +(3.85638 - 1.07650i) q^{42} +(-1.35117 - 3.71231i) q^{43} +(-5.07855 - 0.894132i) q^{44} +(-2.62839 - 1.44622i) q^{45} +(0.901861 - 10.3237i) q^{46} +(0.825162 - 4.67973i) q^{47} +(6.53561 + 2.29909i) q^{48} +(-4.06722 - 1.48035i) q^{49} +(-0.811309 - 1.15835i) q^{50} +(-1.53427 + 4.35426i) q^{51} +(-6.32036 + 1.11613i) q^{52} +0.903877i q^{53} +(-2.12101 - 7.03572i) q^{54} +2.57833i q^{55} +(2.65323 + 3.78608i) q^{56} +(-1.50634 + 0.281620i) q^{57} +(-7.56860 + 5.30105i) q^{58} +(-4.65700 - 1.69501i) q^{59} +(0.565517 - 3.41763i) q^{60} +(0.652414 - 3.70002i) q^{61} +(5.23239 + 0.457094i) q^{62} +(1.58197 - 4.64146i) q^{63} +(0.00620220 + 8.00000i) q^{64} +(1.09757 + 3.01555i) q^{65} +(-4.41902 + 4.51208i) q^{66} +(10.1814 + 12.1337i) q^{67} +(-5.33086 + 0.00137763i) q^{68} +(-9.80609 - 8.05780i) q^{69} +(1.63434 - 1.63476i) q^{70} +(-7.02717 - 12.1714i) q^{71} +(6.84717 - 5.01162i) q^{72} +(-2.01151 + 3.48404i) q^{73} +(2.94235 + 10.9753i) q^{74} +(-1.73196 + 0.0178224i) q^{75} +(-0.885151 - 1.53221i) q^{76} +(-4.15038 + 0.731824i) q^{77} +(-3.24763 + 7.15835i) q^{78} +(-2.44445 + 2.91319i) q^{79} +(3.93887 - 0.696629i) q^{80} +(-8.57673 - 2.72757i) q^{81} +(3.42141 + 7.33476i) q^{82} +(6.67412 + 5.60025i) q^{83} +(5.66193 - 0.0597265i) q^{84} +(0.462847 + 2.62494i) q^{85} +(-0.487652 - 5.56561i) q^{86} +(0.116451 + 11.3165i) q^{87} +(-6.61055 - 3.07943i) q^{88} +(-2.17066 - 1.25323i) q^{89} +(-3.06148 - 2.93723i) q^{90} +(-4.54264 + 2.62270i) q^{91} +(5.00891 - 13.7729i) q^{92} +(4.08397 - 4.97006i) q^{93} +(2.83930 - 6.09096i) q^{94} +(-0.677761 + 0.568709i) q^{95} +(8.08700 + 5.53177i) q^{96} +(-14.0166 + 5.10161i) q^{97} +(-5.01454 - 3.51025i) q^{98} +(1.49964 + 7.58822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.36607	+	0.365849i	0.965959	+	0.258694i
$2$	1.36607	+	0.365849i	0.965959	+	0.258694i
$3$	1.31530	−	1.12693i	0.759390	−	0.650636i
$3$	1.31530	−	1.12693i	0.759390	−	0.650636i
$4$	1.73231	+	0.999552i	0.866155	+	0.499776i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$	2.20909	−	1.05827i	0.901855	−	0.432038i
$7$	1.60972	+	0.283837i	0.608416	+	0.107280i	0.469364	−	0.883005i	$-0.344483\pi$
$7$	1.60972	+	0.283837i	0.608416	+	0.107280i	0.139052	+	0.990285i	$0.455594\pi$
$8$	2.00078	+	1.99922i	0.707381	+	0.706833i
$9$	0.460037	−	2.96452i	0.153346	−	0.988173i
$10$	0.811010	−	1.15856i	0.256464	−	0.366369i
$11$	−2.42284	+	0.881840i	−0.730513	+	0.265885i	−0.680382	−	0.732858i	$-0.738186\pi$
$11$	−2.42284	+	0.881840i	−0.730513	+	0.265885i	−0.0501308	+	0.998743i	$0.515964\pi$
$12$	3.40494	−	0.637486i	0.982921	−	0.184026i
$13$	−2.45829	+	2.06275i	−0.681808	+	0.572105i	−0.916534	−	0.399957i	$-0.869025\pi$
$13$	−2.45829	+	2.06275i	−0.681808	+	0.572105i	0.234726	+	0.972062i	$0.424581\pi$
$14$	2.09515	+	0.976655i	0.559952	+	0.261022i
$15$	−0.609113	−	1.62141i	−0.157272	−	0.418647i
$16$	2.00179	+	3.46307i	0.500448	+	0.865767i
$17$	−2.30833	+	1.33272i	−0.559853	+	0.323231i	−0.753086	−	0.657922i	$-0.771436\pi$
$17$	−2.30833	+	1.33272i	−0.559853	+	0.323231i	0.193234	+	0.981153i	$0.438102\pi$
$18$	1.71301	−	3.88144i	0.403760	−	0.914865i
$19$	−0.766220	−	0.442377i	−0.175783	−	0.101488i	0.409527	−	0.912298i	$-0.365694\pi$
$19$	−0.766220	−	0.442377i	−0.175783	−	0.101488i	−0.585310	+	0.810810i	$0.699027\pi$
$20$	1.53176	−	1.28597i	0.342511	−	0.287552i
$21$	2.43713	−	1.44072i	0.531825	−	0.314390i
$22$	−3.63239	+	0.318266i	−0.774428	+	0.0678545i
$23$	−1.27245	−	7.21642i	−0.265324	−	1.50473i	−0.768111	−	0.640317i	$-0.778803\pi$
$23$	−1.27245	−	7.21642i	−0.265324	−	1.50473i	0.502787	−	0.864410i	$-0.332308\pi$
$24$	4.88462	+	0.374841i	0.997069	+	0.0765140i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−4.11287	+	1.91851i	−0.806599	+	0.376250i
$27$	−2.73573	−	4.41767i	−0.526492	−	0.850180i
$28$	2.50482	+	2.10069i	0.473366	+	0.396993i
$29$	−4.19994	+	5.00529i	−0.779909	+	0.929459i	−0.998929	−	0.0462613i	$-0.985269\pi$
$29$	−4.19994	+	5.00529i	−0.779909	+	0.929459i	0.219021	+	0.975720i	$0.429714\pi$
$30$	−0.238900	−	2.43781i	−0.0436169	−	0.445082i
$31$	3.65753	−	0.644921i	0.656911	−	0.115831i	0.164750	−	0.986335i	$-0.447318\pi$
$31$	3.65753	−	0.644921i	0.656911	−	0.115831i	0.492161	+	0.870504i	$0.336207\pi$
$32$	1.46763	+	5.46315i	0.259443	+	0.965758i
$33$	−2.19298	+	3.89026i	−0.381750	+	0.677208i
$34$	−3.64092	+	0.976086i	−0.624413	+	0.167397i
$35$	0.817275	−	1.41556i	0.138145	−	0.239274i
$36$	3.76012	−	4.67563i	0.626686	−	0.779272i
$37$	4.01739	+	6.95832i	0.660454	+	1.14394i	0.980496	+	0.196537i	$0.0629697\pi$
$37$	4.01739	+	6.95832i	0.660454	+	1.14394i	−0.320042	+	0.947403i	$0.603697\pi$
$38$	−0.884869	−	0.884640i	−0.143545	−	0.143508i
$39$	−0.908810	+	5.48348i	−0.145526	+	0.878060i
$40$	2.56296	−	1.19634i	0.405240	−	0.189158i
$41$	3.67865	+	4.38405i	0.574509	+	0.684673i	0.972550	−	0.232695i	$-0.0747543\pi$
$41$	3.67865	+	4.38405i	0.574509	+	0.684673i	−0.398041	+	0.917368i	$0.630310\pi$
$42$	3.85638	−	1.07650i	0.595052	−	0.166108i
$43$	−1.35117	−	3.71231i	−0.206051	−	0.566122i	0.793021	−	0.609195i	$-0.208507\pi$
$43$	−1.35117	−	3.71231i	−0.206051	−	0.566122i	−0.999072	+	0.0430734i	$0.986285\pi$
$44$	−5.07855	−	0.894132i	−0.765620	−	0.134795i
$45$	−2.62839	−	1.44622i	−0.391818	−	0.215589i
$46$	0.901861	−	10.3237i	0.132972	−	1.52214i
$47$	0.825162	−	4.67973i	0.120362	−	0.682608i	−0.863593	−	0.504190i	$-0.831791\pi$
$47$	0.825162	−	4.67973i	0.120362	−	0.682608i	0.983955	−	0.178418i	$-0.0570979\pi$
$48$	6.53561	+	2.29909i	0.943334	+	0.331845i
$49$	−4.06722	−	1.48035i	−0.581032	−	0.211478i
$50$	−0.811309	−	1.15835i	−0.114736	−	0.163816i
$51$	−1.53427	+	4.35426i	−0.214841	+	0.609719i
$52$	−6.32036	+	1.11613i	−0.876476	+	0.154780i
$53$			0.903877i			0.124157i	0.998071	+	0.0620785i	$0.0197729\pi$
$53$			0.903877i			0.124157i	−0.998071	+	0.0620785i	$0.980227\pi$
$54$	−2.12101	−	7.03572i	−0.288633	−	0.957440i
$55$			2.57833i			0.347662i
$56$	2.65323	+	3.78608i	0.354553	+	0.505936i
$57$	−1.50634	+	0.281620i	−0.199520	+	0.0373015i
$58$	−7.56860	+	5.30105i	−0.993806	+	0.696062i
$59$	−4.65700	−	1.69501i	−0.606290	−	0.220672i	0.0205892	−	0.999788i	$-0.493446\pi$
$59$	−4.65700	−	1.69501i	−0.606290	−	0.220672i	−0.626879	+	0.779117i	$0.715668\pi$
$60$	0.565517	−	3.41763i	0.0730079	−	0.441214i
$61$	0.652414	−	3.70002i	0.0835331	−	0.473740i	−0.914130	−	0.405420i	$-0.867125\pi$
$61$	0.652414	−	3.70002i	0.0835331	−	0.473740i	0.997664	−	0.0683194i	$-0.0217637\pi$
$62$	5.23239	+	0.457094i	0.664515	+	0.0580510i
$63$	1.58197	−	4.64146i	0.199309	−	0.584769i
$64$	0.00620220	+	8.00000i	0.000775274	+	1.00000i
$65$	1.09757	+	3.01555i	0.136137	+	0.374032i
$66$	−4.41902	+	4.51208i	−0.543944	+	0.555399i
$67$	10.1814	+	12.1337i	1.24386	+	1.48237i	0.815493	+	0.578767i	$0.196466\pi$
$67$	10.1814	+	12.1337i	1.24386	+	1.48237i	0.428365	+	0.903606i	$0.359090\pi$
$68$	−5.33086	+	0.00137763i	−0.646462	+	0.000167062i
$69$	−9.80609	−	8.05780i	−1.18051	−	0.970045i
$70$	1.63434	−	1.63476i	0.195341	−	0.195391i
$71$	−7.02717	−	12.1714i	−0.833972	−	1.44448i	−0.894865	−	0.446337i	$-0.852728\pi$
$71$	−7.02717	−	12.1714i	−0.833972	−	1.44448i	0.0608930	−	0.998144i	$-0.480605\pi$
$72$	6.84717	−	5.01162i	0.806946	−	0.590625i
$73$	−2.01151	+	3.48404i	−0.235430	+	0.407776i	−0.959397	−	0.282058i	$-0.908983\pi$
$73$	−2.01151	+	3.48404i	−0.235430	+	0.407776i	0.723968	+	0.689834i	$0.242316\pi$
$74$	2.94235	+	10.9753i	0.342041	+	1.27586i
$75$	−1.73196	+	0.0178224i	−0.199989	+	0.00205796i
$76$	−0.885151	−	1.53221i	−0.101534	−	0.175757i
$77$	−4.15038	+	0.731824i	−0.472980	+	0.0833991i
$78$	−3.24763	+	7.15835i	−0.367721	+	0.810523i
$79$	−2.44445	+	2.91319i	−0.275023	+	0.327759i	−0.885821	−	0.464027i	$-0.846404\pi$
$79$	−2.44445	+	2.91319i	−0.275023	+	0.327759i	0.610799	+	0.791786i	$0.290849\pi$
$80$	3.93887	−	0.696629i	0.440379	−	0.0778854i
$81$	−8.57673	−	2.72757i	−0.952970	−	0.303064i
$82$	3.42141	+	7.33476i	0.377831	+	0.809988i
$83$	6.67412	+	5.60025i	0.732579	+	0.614707i	0.930833	−	0.365444i	$-0.119083\pi$
$83$	6.67412	+	5.60025i	0.732579	+	0.614707i	−0.198254	+	0.980151i	$0.563527\pi$
$84$	5.66193	−	0.0597265i	0.617767	−	0.00651670i
$85$	0.462847	+	2.62494i	0.0502028	+	0.284714i
$86$	−0.487652	−	5.56561i	−0.0525849	−	0.600155i
$87$	0.116451	+	11.3165i	0.0124848	+	1.21326i
$88$	−6.61055	−	3.07943i	−0.704687	−	0.328268i
$89$	−2.17066	−	1.25323i	−0.230089	−	0.132842i	0.380524	−	0.924771i	$-0.375744\pi$
$89$	−2.17066	−	1.25323i	−0.230089	−	0.132842i	−0.610613	+	0.791929i	$0.709077\pi$
$90$	−3.06148	−	2.93723i	−0.322708	−	0.309612i
$91$	−4.54264	+	2.62270i	−0.476199	+	0.274933i
$92$	5.00891	−	13.7729i	0.522215	−	1.43593i
$93$	4.08397	−	4.97006i	0.423488	−	0.515371i
$94$	2.83930	−	6.09096i	0.292852	−	0.628235i
$95$	−0.677761	+	0.568709i	−0.0695368	+	0.0583483i
$96$	8.08700	+	5.53177i	0.825376	+	0.564584i
$97$	−14.0166	+	5.10161i	−1.42317	+	0.517990i	−0.934965	−	0.354741i	$-0.884569\pi$
$97$	−14.0166	+	5.10161i	−1.42317	+	0.517990i	−0.488201	+	0.872731i	$0.662347\pi$
$98$	−5.01454	−	3.51025i	−0.506545	−	0.354589i
$99$	1.49964	+	7.58822i	0.150719	+	0.762645i
$100$	−0.684526	−	1.87921i	−0.0684526	−	0.187921i
$101$	5.80699	+	1.02393i	0.577817	+	0.101885i	0.454916	−	0.890534i	$-0.349669\pi$
$101$	5.80699	+	1.02393i	0.577817	+	0.101885i	0.122901	+	0.992419i	$0.460780\pi$
$102$	−3.68892	+	5.38693i	−0.365258	+	0.533385i
$103$	2.88550	−	7.92785i	0.284317	−	0.781154i	−0.712518	−	0.701654i	$-0.752445\pi$
$103$	2.88550	−	7.92785i	0.284317	−	0.781154i	0.996835	−	0.0795005i	$-0.0253325\pi$
$104$	−9.04240	−	0.787576i	−0.886681	−	0.0772282i
$105$	−0.520282	−	2.78291i	−0.0507744	−	0.271584i
$106$	−0.330683	+	1.23476i	−0.0321187	+	0.119931i
$107$	−9.38211			−0.907003			−0.453502	−	0.891255i	$-0.649825\pi$
$107$	−9.38211			−0.907003			−0.453502	+	0.891255i	$0.649825\pi$
$108$	−0.323443	−	10.3873i	−0.0311233	−	0.999516i
$109$	16.6485			1.59464			0.797319	−	0.603558i	$-0.206251\pi$
$109$	16.6485			1.59464			0.797319	+	0.603558i	$0.206251\pi$
$110$	−0.943279	+	3.52218i	−0.0899381	+	0.335827i
$111$	13.1256	+	4.62496i	1.24583	+	0.438981i
$112$	2.23937	+	6.14274i	0.211601	+	0.580434i
$113$	6.12885	−	16.8389i	0.576553	−	1.58407i	−0.217396	−	0.976083i	$-0.569756\pi$
$113$	6.12885	−	16.8389i	0.576553	−	1.58407i	0.793949	−	0.607984i	$-0.208021\pi$
$114$	−2.16080	−	0.166379i	−0.202378	−	0.0155829i
$115$	−7.21642	−	1.27245i	−0.672935	−	0.118657i
$116$	−12.2786	+	4.47265i	−1.14004	+	0.415275i
$117$	4.98417	+	8.23660i	0.460786	+	0.761474i
$118$	−5.74169	−	4.01927i	−0.528565	−	0.370003i
$119$	−4.09403	+	1.49011i	−0.375299	+	0.136598i
$120$	2.02287	−	4.46184i	0.184662	−	0.407308i
$121$	−3.33400	+	2.79755i	−0.303090	+	0.254323i
$122$	2.24490	−	4.81582i	0.203243	−	0.436004i
$123$	9.77907	+	1.62074i	0.881749	+	0.146137i
$124$	6.98060	+	2.53869i	0.626877	+	0.227981i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	3.85916	−	5.76181i	0.343801	−	0.513303i
$127$	1.33068	+	0.768267i	0.118079	+	0.0681727i	0.557876	−	0.829924i	$-0.311616\pi$
$127$	1.33068	+	0.768267i	0.118079	+	0.0681727i	−0.439797	+	0.898097i	$0.644950\pi$
$128$	−2.91832	+	10.9308i	−0.257945	+	0.966160i
$129$	−5.96072	−	3.36012i	−0.524812	−	0.295842i
$130$	0.396125	+	4.52100i	0.0347424	+	0.396518i
$131$	−1.35023	−	7.65753i	−0.117970	−	0.669042i	−0.985237	−	0.171198i	$-0.945236\pi$
$131$	−1.35023	−	7.65753i	−0.117970	−	0.669042i	0.867267	−	0.497844i	$-0.165875\pi$
$132$	−7.68745	+	4.54714i	−0.669107	+	0.395778i
$133$	−1.10783	−	0.929583i	−0.0960614	−	0.0806051i
$134$	9.46944	+	20.3004i	0.818035	+	1.75369i
$135$	−5.08692	+	1.05982i	−0.437813	+	0.0912144i
$136$	−7.28285	−	1.94841i	−0.624499	−	0.167075i
$137$	−12.4756	+	14.8679i	−1.06587	+	1.27025i	−0.104634	+	0.994511i	$0.533367\pi$
$137$	−12.4756	+	14.8679i	−1.06587	+	1.27025i	−0.961232	+	0.275739i	$0.911077\pi$
$138$	−10.4479	−	14.5951i	−0.889384	−	1.24242i
$139$	19.5792	−	3.45234i	1.66069	−	0.292824i	0.736977	−	0.675918i	$-0.236253\pi$
$139$	19.5792	−	3.45234i	1.66069	−	0.292824i	0.923709	+	0.383094i	$0.125142\pi$
$140$	2.83070	−	1.63528i	0.239238	−	0.138206i
$141$	−4.18841	−	7.08516i	−0.352728	−	0.596678i
$142$	−5.14673	−	19.1979i	−0.431904	−	1.61105i
$143$	4.13703	−	7.16554i	0.345956	−	0.599213i
$144$	11.1872	−	4.34120i	0.932269	−	0.361767i
$145$	3.26697	+	5.65856i	0.271307	+	0.469918i
$146$	−4.02250	+	4.02354i	−0.332905	+	0.332991i
$147$	−7.01788	+	2.63639i	−0.578825	+	0.217446i
$148$	0.00415277	+	16.0696i	0.000341356	+	1.32091i
$149$	−5.97960	−	7.12622i	−0.489868	−	0.583802i	0.463316	−	0.886193i	$-0.346660\pi$
$149$	−5.97960	−	7.12622i	−0.489868	−	0.583802i	−0.953184	+	0.302391i	$0.902215\pi$
$150$	−2.37250	−	0.609289i	−0.193714	−	0.0497482i
$151$	−1.06670	−	2.93074i	−0.0868069	−	0.238500i	0.888692	−	0.458505i	$-0.151615\pi$
$151$	−1.06670	−	2.93074i	−0.0868069	−	0.238500i	−0.975499	+	0.220005i	$0.929393\pi$
$152$	−0.648622	−	2.41694i	−0.0526102	−	0.196040i
$153$	2.88894	+	7.45619i	0.233557	+	0.602797i
$154$	−5.93746	−	0.518687i	−0.478454	−	0.0417970i
$155$	0.644921	−	3.65753i	0.0518013	−	0.293780i
$156$	−7.05537	+	8.59068i	−0.564881	+	0.687805i
$157$	5.11039	+	1.86003i	0.407853	+	0.148446i	0.537796	−	0.843075i	$-0.319257\pi$
$157$	5.11039	+	1.86003i	0.407853	+	0.148446i	−0.129943	+	0.991522i	$0.541479\pi$
$158$	−4.40509	+	3.08532i	−0.350450	+	0.245455i
$159$	1.01861	+	1.18887i	0.0807811	+	0.0942836i
$160$	5.63565	+	0.489386i	0.445537	+	0.0386894i
$161$		−	11.9776i		−	0.943964i
$162$	−10.7186	−	6.86385i	−0.842130	−	0.539275i
$163$			18.6426i			1.46020i	0.683338	+	0.730102i	$0.260528\pi$
$163$			18.6426i			1.46020i	−0.683338	+	0.730102i	$0.739472\pi$
$164$	1.99048	+	11.2715i	0.155430	+	0.880158i
$165$	2.90561	+	3.39128i	0.226201	+	0.264011i
$166$	7.06848	+	10.0921i	0.548621	+	0.783296i
$167$	−5.19275	−	1.89001i	−0.401827	−	0.146253i	0.133198	−	0.991089i	$-0.457475\pi$
$167$	−5.19275	−	1.89001i	−0.401827	−	0.146253i	−0.535025	+	0.844836i	$0.679698\pi$
$168$	7.75646	+	1.98982i	0.598424	+	0.153518i
$169$	−0.469168	+	2.66078i	−0.0360898	+	0.204676i
$170$	−0.328047	+	3.75519i	−0.0251601	+	0.288010i
$171$	−1.66392	+	2.06796i	−0.127243	+	0.158141i
$172$	1.37000	−	7.78143i	0.104462	−	0.593328i
$173$	−6.29494	−	17.2952i	−0.478596	−	1.31493i	−0.910685	−	0.413100i	$-0.864446\pi$
$173$	−6.29494	−	17.2952i	−0.478596	−	1.31493i	0.432090	−	0.901831i	$-0.357776\pi$
$174$	−3.98106	+	15.5018i	−0.301803	+	1.17519i
$175$	−1.05067	−	1.25214i	−0.0794231	−	0.0946527i
$176$	−7.90388	−	6.62519i	−0.595778	−	0.499392i
$177$	−8.03553	+	3.01869i	−0.603987	+	0.226898i
$178$	−2.50678	−	2.50614i	−0.187891	−	0.187843i
$179$	3.19139	+	5.52764i	0.238535	+	0.413155i	0.960294	−	0.278989i	$-0.0899994\pi$
$179$	3.19139	+	5.52764i	0.238535	+	0.413155i	−0.721759	+	0.692145i	$0.756666\pi$
$180$	−3.10762	−	5.13251i	−0.231628	−	0.382555i
$181$	9.35062	−	16.1957i	0.695026	−	1.20382i	−0.275146	−	0.961402i	$-0.588726\pi$
$181$	9.35062	−	16.1957i	0.695026	−	1.20382i	0.970172	−	0.242418i	$-0.0779404\pi$
$182$	−7.16509	+	1.92087i	−0.531112	+	0.142385i
$183$	−3.31156	−	5.60188i	−0.244798	−	0.414103i
$184$	11.8814	−	16.9823i	0.875905	−	1.25196i
$185$	7.91271	−	1.39522i	0.581754	−	0.102579i
$186$	7.39729	−	5.29535i	0.542396	−	0.388274i
$187$	4.41747	−	5.26453i	0.323037	−	0.384981i
$188$	6.10707	−	7.28194i	0.445404	−	0.531090i
$189$	−3.14986	−	7.88769i	−0.229118	−	0.573745i
$190$	−1.13393	+	0.528940i	−0.0822641	+	0.0383733i
$191$	−13.1113	−	11.0017i	−0.948699	−	0.796053i	0.0303792	−	0.999538i	$-0.490329\pi$
$191$	−13.1113	−	11.0017i	−0.948699	−	0.796053i	−0.979078	+	0.203486i	$0.934773\pi$
$192$	9.02363	+	10.5154i	0.651225	+	0.758885i
$193$	0.400322	+	2.27034i	0.0288158	+	0.163422i	0.995820	−	0.0913382i	$-0.0291144\pi$
$193$	0.400322	+	2.27034i	0.0288158	+	0.163422i	−0.967004	+	0.254761i	$0.918003\pi$
$194$	−21.0141	+	1.84123i	−1.50872	+	0.132192i
$195$	4.84196	+	2.72946i	0.346740	+	0.195461i
$196$	−5.56600	−	6.62982i	−0.397572	−	0.473559i
$197$	18.0209	+	10.4044i	1.28394	+	0.741283i	0.977566	−	0.210629i	$-0.0675511\pi$
$197$	18.0209	+	10.4044i	1.28394	+	0.741283i	0.306373	+	0.951911i	$0.400884\pi$
$198$	−0.727528	+	10.9147i	−0.0517031	+	0.775674i
$199$	9.81898	−	5.66899i	0.696049	−	0.401864i	−0.109825	−	0.993951i	$-0.535029\pi$
$199$	9.81898	−	5.66899i	0.696049	−	0.401864i	0.805874	+	0.592087i	$0.201696\pi$
$200$	−0.247606	−	2.81757i	−0.0175084	−	0.199232i
$201$	27.0656	+	4.48574i	1.90906	+	0.316400i
$202$	7.55817	+	3.52324i	0.531791	+	0.247894i
$203$	−8.18139	+	6.86500i	−0.574221	+	0.481829i
$204$	−7.01014	+	6.00935i	−0.490808	+	0.420738i
$205$	5.37783	−	1.95737i	0.375604	−	0.136709i
$206$	6.84220	−	9.77436i	0.476719	−	0.681012i
$207$	−21.9786	+	0.452382i	−1.52762	+	0.0314427i
$208$	−12.0644	−	4.38404i	−0.836519	−	0.303978i
$209$	2.24653	+	0.396124i	0.155396	+	0.0274005i
$210$	0.307379	−	3.99200i	0.0212112	−	0.275474i
$211$	1.18353	−	3.25171i	0.0814773	−	0.223857i	−0.892264	−	0.451514i	$-0.850884\pi$
$211$	1.18353	−	3.25171i	0.0814773	−	0.223857i	0.973741	+	0.227657i	$0.0731064\pi$
$212$	−0.903473	+	1.56579i	−0.0620508	+	0.107539i
$213$	−22.9592	−	8.08992i	−1.57314	−	0.554312i
$214$	−12.8166	−	3.43244i	−0.876128	−	0.234636i
$215$	−3.95055			−0.269426
$216$	3.35832	−	14.3081i	0.228505	−	0.973543i
$217$	6.07064			0.412102
$218$	22.7431	+	6.09084i	1.54036	+	0.412524i
$219$	1.28054	+	6.84940i	0.0865309	+	0.462840i
$220$	−2.57717	+	4.46646i	−0.173753	+	0.301129i
$221$	2.92549	−	8.03773i	0.196790	−	0.540676i
$222$	16.2386	+	11.1200i	1.08986	+	0.746328i
$223$	5.32012	+	0.938081i	0.356262	+	0.0628186i	0.348915	−	0.937154i	$-0.386550\pi$
$223$	5.32012	+	0.938081i	0.356262	+	0.0628186i	0.00734698	+	0.999973i	$0.497661\pi$
$224$	0.811828	+	9.21070i	0.0542426	+	0.615416i
$225$	−2.25796	+	1.97525i	−0.150531	+	0.131683i
$226$	14.5329	−	20.7609i	0.966716	−	1.38099i
$227$	−9.97850	+	3.63188i	−0.662296	+	0.241056i	−0.651227	−	0.758883i	$-0.725746\pi$
$227$	−9.97850	+	3.63188i	−0.662296	+	0.241056i	−0.0110688	+	0.999939i	$0.503523\pi$
$228$	−2.89094	−	1.01781i	−0.191457	−	0.0674063i
$229$	19.0360	−	15.9731i	1.25794	−	1.05553i	0.262038	−	0.965058i	$-0.415605\pi$
$229$	19.0360	−	15.9731i	1.25794	−	1.05553i	0.995899	−	0.0904764i	$-0.0288390\pi$
$230$	−9.39263	−	4.37838i	−0.619332	−	0.288702i
$231$	−4.63428	+	5.63978i	−0.304913	+	0.371070i
$232$	−18.4098	+	1.61784i	−1.20866	+	0.106217i
$233$	21.3282	−	12.3138i	1.39726	−	0.806706i	0.403152	−	0.915133i	$-0.367915\pi$
$233$	21.3282	−	12.3138i	1.39726	−	0.806706i	0.994104	+	0.108427i	$0.0345813\pi$
$234$	3.79538	+	13.0752i	0.248112	+	0.854756i
$235$	−4.11528	−	2.37596i	−0.268451	−	0.154991i
$236$	−6.37312	−	7.59120i	−0.414854	−	0.494145i
$237$	0.0677769	+	6.58646i	0.00440258	+	0.427836i
$238$	−6.13790	+	0.537796i	−0.397861	+	0.0348601i
$239$	0.439066	+	2.49007i	0.0284008	+	0.161069i	0.995710	−	0.0925320i	$-0.0294961\pi$
$239$	0.439066	+	2.49007i	0.0284008	+	0.161069i	−0.967309	+	0.253601i	$0.918385\pi$
$240$	4.39575	−	5.35513i	0.283744	−	0.345672i
$241$	−5.97421	−	5.01296i	−0.384833	−	0.322913i	0.429763	−	0.902942i	$-0.358597\pi$
$241$	−5.97421	−	5.01296i	−0.384833	−	0.322913i	−0.814596	+	0.580028i	$0.803041\pi$
$242$	−5.57796	+	2.60192i	−0.358565	+	0.167258i
$243$	−14.3548	+	6.07783i	−0.920860	+	0.389893i
$244$	4.82855	−	5.75746i	0.309116	−	0.368584i
$245$	−2.78214	+	3.31563i	−0.177745	+	0.211828i
$246$	12.7660	+	5.79171i	0.813929	+	0.369266i
$247$	2.79611	−	0.493030i	0.177912	−	0.0313707i
$248$	8.60723	+	6.02188i	0.546560	+	0.382390i
$249$	15.0896	−	0.155277i	0.956264	−	0.00984027i
$250$	−1.36598	+	0.366202i	−0.0863920	+	0.0231606i
$251$	12.5905	−	21.8074i	0.794704	−	1.37647i	−0.128322	−	0.991733i	$-0.540959\pi$
$251$	12.5905	−	21.8074i	0.794704	−	1.37647i	0.923027	−	0.384736i	$-0.125707\pi$
$252$	7.37984	−	6.45918i	0.464886	−	0.406890i
$253$	9.44667	+	16.3621i	0.593907	+	1.02868i
$254$	1.53673	+	1.53634i	0.0964232	+	0.0963983i
$255$	3.56692	+	2.93099i	0.223369	+	0.183545i
$256$	−7.98567	+	13.8647i	−0.499105	+	0.866542i
$257$	5.18733	+	6.18201i	0.323577	+	0.385623i	0.903171	−	0.429282i	$-0.141233\pi$
$257$	5.18733	+	6.18201i	0.323577	+	0.385623i	−0.579594	+	0.814905i	$0.696789\pi$
$258$	−6.91348	−	6.77090i	−0.430415	−	0.421538i
$259$	4.49183	+	12.3412i	0.279109	+	0.766845i
$260$	−1.11287	+	6.32093i	−0.0690171	+	0.392008i
$261$	12.9061	+	14.7534i	0.798870	+	0.913213i
$262$	0.956988	−	10.9547i	0.0591229	−	0.676785i
$263$	−2.63157	+	14.9243i	−0.162269	+	0.920275i	0.789566	+	0.613665i	$0.210306\pi$
$263$	−2.63157	+	14.9243i	−0.162269	+	0.920275i	−0.951835	+	0.306609i	$0.900806\pi$
$264$	−12.1652	+	3.39928i	−0.748715	+	0.209211i
$265$	0.849367	+	0.309144i	0.0521762	+	0.0189906i
$266$	−1.17330	−	1.67518i	−0.0719394	−	0.102712i
$267$	−4.26738	+	0.797814i	−0.261159	+	0.0488254i
$268$	5.50905	+	31.1963i	0.336519	+	1.90561i
$269$		−	11.8299i		−	0.721283i	−0.932704	−	0.360642i	$-0.882558\pi$
$269$		−	11.8299i		−	0.721283i	0.932704	−	0.360642i	$-0.117442\pi$
$270$	−7.33684	−	0.413261i	−0.446506	−	0.0251502i
$271$		−	7.57692i		−	0.460265i	−0.973159	−	0.230133i	$-0.926084\pi$
$271$		−	7.57692i		−	0.460265i	0.973159	−	0.230133i	$-0.0739160\pi$
$272$	−9.23608	−	5.32609i	−0.560020	−	0.322942i
$273$	−3.01934	+	8.56890i	−0.182739	+	0.518613i
$274$	−22.4820	+	15.7464i	−1.35819	+	0.951276i
$275$	2.42284	+	0.881840i	0.146103	+	0.0531770i
$276$	−8.93298	−	23.7603i	−0.537702	−	1.43020i
$277$	−4.78065	+	27.1124i	−0.287241	+	1.62903i	0.409926	+	0.912119i	$0.365555\pi$
$277$	−4.78065	+	27.1124i	−0.287241	+	1.62903i	−0.697167	+	0.716909i	$0.745557\pi$
$278$	28.0096	+	2.44688i	1.67991	+	0.146754i
$279$	−0.229283	−	11.1395i	−0.0137268	−	0.666904i
$280$	4.46521	−	1.19830i	0.266847	−	0.0716124i
$281$	3.99023	+	10.9631i	0.238037	+	0.654001i	0.999980	+	0.00635695i	$0.00202349\pi$
$281$	3.99023	+	10.9631i	0.238037	+	0.654001i	−0.761943	+	0.647644i	$0.775754\pi$
$282$	−3.12958	−	11.2112i	−0.186363	−	0.667615i
$283$	10.7544	+	12.8166i	0.639283	+	0.761868i	0.984257	−	0.176744i	$-0.0565566\pi$
$283$	10.7544	+	12.8166i	0.639283	+	0.761868i	−0.344974	+	0.938612i	$0.612112\pi$
$284$	−0.00726398	−	28.1087i	−0.000431038	−	1.66794i
$285$	−0.250562	+	1.51182i	−0.0148420	+	0.0895523i
$286$	8.27298	−	8.27512i	0.489192	−	0.489318i
$287$	4.67724	+	8.10121i	0.276088	+	0.478199i
$288$	16.8708	−	1.83757i	0.994120	−	0.108280i
$289$	−4.94774	+	8.56973i	−0.291043	+	0.504102i
$290$	2.39274	+	8.92522i	0.140507	+	0.524107i
$291$	−12.6868	+	22.5059i	−0.743715	+	1.31932i
$292$	−6.96704	+	4.02482i	−0.407715	+	0.235535i
$293$	24.9818	−	4.40497i	1.45945	−	0.257341i	0.613118	−	0.789991i	$-0.289915\pi$
$293$	24.9818	−	4.40497i	1.45945	−	0.257341i	0.846336	+	0.532650i	$0.178804\pi$
$294$	−10.5515	+	1.03402i	−0.615373	+	0.0603051i
$295$	−3.18558	+	3.79642i	−0.185471	+	0.221036i
$296$	−5.87335	+	21.9537i	−0.341382	+	1.27603i
$297$	10.5239	+	8.29080i	0.610659	+	0.481081i
$298$	−5.56146	−	11.9226i	−0.322167	−	0.690655i
$299$	18.0138	+	15.1153i	1.04176	+	0.874142i
$300$	−3.01810	−	1.70031i	−0.174250	−	0.0981674i
$301$	−1.12131	−	6.35928i	−0.0646313	−	0.366543i
$302$	−0.384984	−	4.39385i	−0.0221534	−	0.252838i
$303$	8.79184	−	5.19732i	0.505078	−	0.298578i
$304$	−0.00182914	−	3.53902i	−0.000104908	−	0.202977i
$305$	−3.25375	−	1.87855i	−0.186309	−	0.107566i
$306$	1.21867	+	11.2426i	0.0696666	+	0.642697i
$307$	19.4402	−	11.2238i	1.10951	−	0.640577i	0.170809	−	0.985304i	$-0.445362\pi$
$307$	19.4402	−	11.2238i	1.10951	−	0.640577i	0.938703	+	0.344727i	$0.112028\pi$
$308$	−7.92124	−	2.88078i	−0.451354	−	0.164147i
$309$	−5.13887	−	13.6793i	−0.292340	−	0.778188i
$310$	2.21911	−	4.76051i	0.126037	−	0.270379i
$311$	6.28107	−	5.27044i	0.356167	−	0.298859i	−0.447094	−	0.894487i	$-0.647541\pi$
$311$	6.28107	−	5.27044i	0.356167	−	0.298859i	0.803261	+	0.595628i	$0.203097\pi$
$312$	−12.7810	+	9.15430i	−0.723584	+	0.518260i
$313$	−10.3252	+	3.75805i	−0.583613	+	0.212418i	−0.616918	−	0.787028i	$-0.711619\pi$
$313$	−10.3252	+	3.75805i	−0.583613	+	0.212418i	0.0333050	+	0.999445i	$0.489397\pi$
$314$	6.30067	+	4.41057i	0.355568	+	0.248903i
$315$	−3.82048	−	3.07404i	−0.215260	−	0.173202i
$316$	−7.14643	+	2.60318i	−0.402018	+	0.146440i
$317$	−3.59517	−	0.633925i	−0.201925	−	0.0356048i	0.0717709	−	0.997421i	$-0.477135\pi$
$317$	−3.59517	−	0.633925i	−0.201925	−	0.0356048i	−0.273696	+	0.961816i	$0.588246\pi$
$318$	0.956549	+	1.99674i	0.0536406	+	0.111972i
$319$	5.76189	−	15.8307i	0.322604	−	0.886347i
$320$	7.51966	+	2.73033i	0.420362	+	0.152630i
$321$	−12.3403	+	10.5730i	−0.688769	+	0.590129i
$322$	4.38198	−	16.3622i	0.244198	−	0.911831i
$323$	2.35825			0.131217
$324$	−12.1312	−	13.2979i	−0.673956	−	0.738772i
$325$	3.20908			0.178008
$326$	−6.82039	+	25.4672i	−0.377746	+	1.41050i
$327$	21.8978	−	18.7618i	1.21095	−	1.03753i
$328$	−1.40454	+	16.1259i	−0.0775526	+	0.890406i
$329$	2.65656	−	7.29883i	0.146461	−	0.402397i
$330$	2.72858	+	5.69575i	0.150203	+	0.313541i
$331$	2.12995	+	0.375567i	0.117072	+	0.0206430i	0.231877	−	0.972745i	$-0.425513\pi$
$331$	2.12995	+	0.375567i	0.117072	+	0.0206430i	−0.114805	+	0.993388i	$0.536624\pi$
$332$	5.96389	+	16.3725i	0.327311	+	0.898557i
$333$	22.4762	−	8.70854i	1.23169	−	0.477225i
$334$	−6.40222	−	4.48165i	−0.350314	−	0.245225i
$335$	14.8842	−	5.41742i	0.813213	−	0.295985i
$336$	9.86791	+	5.55593i	0.538339	+	0.303101i
$337$	11.2457	−	9.43623i	0.612590	−	0.514024i	−0.282875	−	0.959157i	$-0.591288\pi$
$337$	11.2457	−	9.43623i	0.612590	−	0.514024i	0.895464	+	0.445133i	$0.146844\pi$
$338$	−1.61436	+	3.46318i	−0.0878097	+	0.188372i
$339$	−10.9150	−	29.0550i	−0.592823	−	1.57805i
$340$	−1.82197	+	5.00984i	−0.0988101	+	0.271697i
$341$	−8.29287	+	4.78789i	−0.449084	+	0.259279i
$342$	−3.02960	+	2.21624i	−0.163822	+	0.119841i
$343$	−16.0358	−	9.25829i	−0.865853	−	0.499901i
$344$	4.71835	−	10.1288i	0.254396	−	0.546107i
$345$	−10.9257	+	6.45878i	−0.588222	+	0.347729i
$346$	−2.27192	−	25.9295i	−0.122139	−	1.39398i
$347$	5.96877	+	33.8506i	0.320421	+	1.81720i	0.540074	+	0.841617i	$0.318396\pi$
$347$	5.96877	+	33.8506i	0.320421	+	1.81720i	−0.219654	+	0.975578i	$0.570493\pi$
$348$	−11.1097	+	19.7201i	−0.595544	+	1.05711i
$349$	−22.0180	−	18.4753i	−1.17860	−	0.988961i	−0.999987	−	0.00504076i	$-0.998395\pi$
$349$	−22.0180	−	18.4753i	−1.17860	−	0.988961i	−0.178610	−	0.983920i	$-0.557160\pi$
$350$	−0.977196	−	2.09490i	−0.0522333	−	0.111977i
$351$	15.8378	+	5.21679i	0.845359	+	0.278451i
$352$	−8.37346	−	11.9421i	−0.446307	−	0.636517i
$353$	−13.0007	+	15.4937i	−0.691960	+	0.824646i	−0.991591	−	0.129409i	$-0.958692\pi$
$353$	−13.0007	+	15.4937i	−0.691960	+	0.824646i	0.299631	+	0.954055i	$0.403136\pi$
$354$	−12.0815	+	1.18396i	−0.642124	+	0.0629266i
$355$	−13.8408	+	2.44051i	−0.734595	+	0.129529i
$356$	−2.50758	−	4.34067i	−0.132902	−	0.230055i
$357$	−3.70564	+	6.57365i	−0.196123	+	0.347914i
$358$	2.33738	+	8.71873i	0.123535	+	0.460799i
$359$	11.7376	−	20.3301i	0.619485	−	1.07298i	−0.370095	−	0.928994i	$-0.620675\pi$
$359$	11.7376	−	20.3301i	0.619485	−	1.07298i	0.989580	−	0.143985i	$-0.0459918\pi$
$360$	−2.36751	−	8.14831i	−0.124779	−	0.429453i
$361$	−9.10860	−	15.7766i	−0.479400	−	0.830346i
$362$	18.6988	−	18.7037i	0.982788	−	0.983042i
$363$	−1.23255	+	7.43682i	−0.0646920	+	0.390332i
$364$	−10.4908	+	0.00271108i	−0.549867	+	0.000142099i
$365$	2.58595	+	3.08181i	0.135355	+	0.161309i
$366$	−2.47440	−	8.86410i	−0.129339	−	0.463334i
$367$	−10.2341	−	28.1179i	−0.534215	−	1.46774i	−0.854010	−	0.520257i	$-0.825836\pi$
$367$	−10.2341	−	28.1179i	−0.534215	−	1.46774i	0.319794	−	0.947487i	$-0.396386\pi$
$368$	22.4438	−	18.8523i	1.16996	−	0.982746i
$369$	14.6889	−	8.88860i	0.764673	−	0.462722i
$370$	11.3198	+	0.988878i	0.588487	+	0.0514093i
$371$	−0.256553	+	1.45499i	−0.0133196	+	0.0755392i
$372$	12.0425	−	4.52754i	0.624376	−	0.234742i
$373$	−20.7885	−	7.56641i	−1.07639	−	0.391774i	−0.257827	−	0.966191i	$-0.583006\pi$
$373$	−20.7885	−	7.56641i	−1.07639	−	0.391774i	−0.818562	+	0.574417i	$0.805229\pi$
$374$	7.96060	−	5.57561i	0.411633	−	0.288308i
$375$	−0.575617	+	1.63360i	−0.0297247	+	0.0843590i
$376$	11.0068	−	7.71340i	0.567632	−	0.397788i
$377$		−	20.9679i		−	1.07990i
$378$	−1.41723	−	11.9275i	−0.0728945	−	0.613486i
$379$		−	17.8548i		−	0.917139i	−0.888659	−	0.458569i	$-0.848362\pi$
$379$		−	17.8548i		−	0.917139i	0.888659	−	0.458569i	$-0.151638\pi$
$380$	−1.74255	+	0.307722i	−0.0893908	+	0.0157858i
$381$	2.61603	−	0.489084i	0.134023	−	0.0250565i
$382$	−13.8860	−	19.8258i	−0.710470	−	1.01438i
$383$	31.7118	+	11.5422i	1.62040	+	0.589777i	0.983458	−	0.181137i	$-0.0579778\pi$
$383$	31.7118	+	11.5422i	1.62040	+	0.589777i	0.636940	+	0.770914i	$0.280200\pi$
$384$	8.47988	+	17.6661i	0.432737	+	0.901520i
$385$	−0.731824	+	4.15038i	−0.0372972	+	0.211523i
$386$	−0.283732	+	3.24790i	−0.0144416	+	0.165314i
$387$	−11.6268	+	2.29777i	−0.591023	+	0.116802i
$388$	−29.3803	−	5.17272i	−1.49156	−	0.262605i
$389$	8.78513	+	24.1370i	0.445424	+	1.22379i	0.935878	+	0.352325i	$0.114609\pi$
$389$	8.78513	+	24.1370i	0.445424	+	1.22379i	−0.490454	+	0.871467i	$0.663169\pi$
$390$	5.61589	+	5.50007i	0.284372	+	0.278507i
$391$	12.5547	+	14.9621i	0.634917	+	0.756665i
$392$	−5.17805	−	11.0931i	−0.261531	−	0.560288i
$393$	−10.4055	−	8.55035i	−0.524888	−	0.431308i
$394$	20.8115	+	20.8061i	1.04847	+	1.04820i
$395$	1.90145	+	3.29340i	0.0956722	+	0.165709i
$396$	−4.98699	+	14.6441i	−0.250606	+	0.735894i
$397$	−7.20997	+	12.4880i	−0.361858	+	0.626756i	−0.988267	−	0.152739i	$-0.951191\pi$
$397$	−7.20997	+	12.4880i	−0.361858	+	0.626756i	0.626409	+	0.779495i	$0.284524\pi$
$398$	15.4874	−	4.15199i	0.776315	−	0.208121i
$399$	−2.50472	+	0.0257744i	−0.125393	+	0.00129033i
$400$	0.692557	−	3.93959i	0.0346278	−	0.196979i
$401$	11.5289	−	2.03285i	0.575724	−	0.101516i	0.121798	−	0.992555i	$-0.461134\pi$
$401$	11.5289	−	2.03285i	0.575724	−	0.101516i	0.453926	+	0.891039i	$0.350023\pi$
$402$	35.3324	+	16.0298i	1.76222	+	0.799491i
$403$	−7.66097	+	9.12999i	−0.381620	+	0.454797i
$404$	9.03603	+	7.57815i	0.449559	+	0.377027i
$405$	−5.49650	+	7.12661i	−0.273123	+	0.354124i
$406$	−13.6879	+	6.38494i	−0.679321	+	0.316879i
$407$	−15.8696	−	13.3162i	−0.786627	−	0.660058i
$408$	−11.7749	+	5.64455i	−0.582943	+	0.279447i
$409$	−0.891863	−	5.05801i	−0.0440998	−	0.250102i	0.954786	−	0.297294i	$-0.0960841\pi$
$409$	−0.891863	−	5.05801i	−0.0440998	−	0.250102i	−0.998886	+	0.0471914i	$0.984973\pi$
$410$	8.06261	−	0.706436i	0.398184	−	0.0348884i
$411$	0.345910	+	33.6150i	0.0170625	+	1.65811i
$412$	12.9229	−	10.8493i	0.636665	−	0.534506i
$413$	−7.01535	−	4.05031i	−0.345203	−	0.199303i
$414$	−30.1898	−	7.42285i	−1.48375	−	0.364813i
$415$	7.54519	−	4.35622i	0.370379	−	0.213838i
$416$	−14.8770	−	10.4027i	−0.729406	−	0.510033i
$417$	21.8620	−	26.6053i	1.07059	−	1.30287i
$418$	2.92400	+	1.36303i	0.143018	+	0.0666678i
$419$	−17.6909	+	14.8444i	−0.864257	+	0.725198i	−0.962881	−	0.269927i	$-0.913000\pi$
$419$	−17.6909	+	14.8444i	−0.864257	+	0.725198i	0.0986238	+	0.995125i	$0.468556\pi$
$420$	1.88037	−	5.34090i	0.0917527	−	0.260609i
$421$	−9.46351	+	3.44444i	−0.461223	+	0.167872i	−0.562173	−	0.827020i	$-0.690034\pi$
$421$	−9.46351	+	3.44444i	−0.461223	+	0.167872i	0.100949	+	0.994892i	$0.467812\pi$
$422$	2.80642	−	4.00908i	0.136614	−	0.195159i
$423$	−13.4935	−	4.59905i	−0.656078	−	0.223614i
$424$	−1.80705	+	1.80846i	−0.0877583	+	0.0878264i
$425$	2.62494	+	0.462847i	0.127328	+	0.0224514i
$426$	−28.4043	−	19.4510i	−1.37619	−	0.942406i
$427$	2.10040	−	5.77081i	0.101646	−	0.279269i
$428$	−16.2527	−	9.37791i	−0.785605	−	0.453299i
$429$	−2.63366	−	14.0870i	−0.127154	−	0.680127i
$430$	−5.39674	−	1.44531i	−0.260254	−	0.0696988i
$431$	22.1305			1.06599			0.532995	−	0.846118i	$-0.321066\pi$
$431$	22.1305			1.06599			0.532995	+	0.846118i	$0.321066\pi$
$432$	9.82232	−	18.3173i	0.472576	−	0.881290i
$433$	13.2571			0.637095			0.318548	−	0.947907i	$-0.396805\pi$
$433$	13.2571			0.637095			0.318548	+	0.947907i	$0.396805\pi$
$434$	8.29293	+	2.22094i	0.398073	+	0.106608i
$435$	10.6739	+	3.76105i	0.511773	+	0.180329i
$436$	28.8404	+	16.6411i	1.38120	+	0.796962i
$437$	−2.21740	+	6.09227i	−0.106073	+	0.291433i
$438$	−0.756535	+	9.82527i	−0.0361486	+	0.469469i
$439$	7.50669	+	1.32363i	0.358275	+	0.0631735i	0.349889	−	0.936791i	$-0.386219\pi$
$439$	7.50669	+	1.32363i	0.358275	+	0.0631735i	0.00838615	+	0.999965i	$0.497331\pi$
$440$	−5.15466	+	5.15866i	−0.245739	+	0.245929i
$441$	−6.25959	+	11.3763i	−0.298076	+	0.541730i
$442$	6.93703	−	9.90983i	0.329961	−	0.471363i
$443$	−11.8766	+	4.32274i	−0.564276	+	0.205380i	−0.608378	−	0.793647i	$-0.708180\pi$
$443$	−11.8766	+	4.32274i	−0.564276	+	0.205380i	0.0441020	+	0.999027i	$0.485957\pi$
$444$	18.1148	+	21.1316i	0.859690	+	1.00286i
$445$	−1.92006	+	1.61112i	−0.0910195	+	0.0763745i
$446$	6.92448	+	3.22785i	0.327884	+	0.152843i
$447$	−15.8958	−	2.63450i	−0.751844	−	0.124608i
$448$	−2.26071	+	12.8795i	−0.106808	+	0.608499i
$449$	−17.5171	+	10.1135i	−0.826683	+	0.477286i	−0.852716	−	0.522375i	$-0.825046\pi$
$449$	−17.5171	+	10.1135i	−0.826683	+	0.477286i	0.0260323	+	0.999661i	$0.491713\pi$
$450$	−3.80718	+	1.87226i	−0.179472	+	0.0882590i
$451$	−12.7788	−	7.37784i	−0.601730	−	0.347409i
$452$	27.4484	−	23.0440i	1.29106	−	1.08390i
$453$	−4.70578	−	2.65270i	−0.221097	−	0.124635i
$454$	−14.9601	+	1.31078i	−0.702111	+	0.0615182i
$455$	0.910853	+	5.16570i	0.0427015	+	0.242172i
$456$	−3.57687	−	2.44805i	−0.167502	−	0.114641i
$457$	−15.1393	−	12.7033i	−0.708184	−	0.594237i	0.215905	−	0.976414i	$-0.430730\pi$
$457$	−15.1393	−	12.7033i	−0.708184	−	0.594237i	−0.924089	+	0.382177i	$0.875174\pi$
$458$	31.8484	−	14.8561i	1.48818	−	0.694182i
$459$	12.2025	+	6.55149i	0.569562	+	0.305797i
$460$	−11.2292	−	9.41746i	−0.523564	−	0.439092i
$461$	−22.9689	+	27.3732i	−1.06977	+	1.27490i	−0.110051	+	0.993926i	$0.535101\pi$
$461$	−22.9689	+	27.3732i	−1.06977	+	1.27490i	−0.959716	+	0.280972i	$0.909343\pi$
$462$	−8.39407	+	6.00890i	−0.390528	+	0.279559i
$463$	−18.6395	+	3.28665i	−0.866253	+	0.152744i	−0.589078	−	0.808076i	$-0.700509\pi$
$463$	−18.6395	+	3.28665i	−0.866253	+	0.152744i	−0.277174	+	0.960820i	$0.589398\pi$
$464$	−25.7410	−	4.52512i	−1.19500	−	0.210074i
$465$	−3.27353	−	5.53754i	−0.151806	−	0.256797i
$466$	33.6409	−	9.01870i	1.55838	−	0.417783i
$467$	−1.35095	+	2.33991i	−0.0625143	+	0.108278i	−0.895589	−	0.444883i	$-0.853245\pi$
$467$	−1.35095	+	2.33991i	−0.0625143	+	0.108278i	0.833074	+	0.553161i	$0.186579\pi$
$468$	0.401202	+	19.2503i	0.0185456	+	0.889844i
$469$	12.9452	+	22.4218i	0.597754	+	1.03534i
$470$	−4.75253	−	4.75131i	−0.219218	−	0.219161i
$471$	8.81783	−	3.31257i	0.406304	−	0.152635i
$472$	−5.92891	−	12.7017i	−0.272900	−	0.584644i
$473$	6.54732	+	7.80280i	0.301046	+	0.358773i
$474$	−2.31706	+	9.02238i	−0.106426	+	0.414412i
$475$	0.302604	+	0.831397i	0.0138844	+	0.0381471i
$476$	−8.58157	−	1.51088i	−0.393336	−	0.0692509i
$477$	2.67956	+	0.415817i	0.122689	+	0.0190389i
$478$	−0.311192	+	3.56224i	−0.0142336	+	0.162933i
$479$	3.97037	−	22.5171i	0.181411	−	1.02883i	−0.749070	−	0.662491i	$-0.769499\pi$
$479$	3.97037	−	22.5171i	0.181411	−	1.02883i	0.930481	−	0.366341i	$-0.119390\pi$
$480$	7.96408	−	5.70731i	0.363509	−	0.260502i
$481$	−24.2292	−	8.81872i	−1.10476	−	0.402099i
$482$	−6.32722	−	9.03373i	−0.288197	−	0.411475i
$483$	−13.4979	−	15.7541i	−0.614177	−	0.716837i
$484$	−8.57181	+	1.51373i	−0.389628	+	0.0688057i
$485$			14.9161i			0.677306i
$486$	−21.8333	+	3.05108i	−0.990376	+	0.138400i
$487$		−	9.34956i		−	0.423669i	−0.977306	−	0.211834i	$-0.932056\pi$
$487$		−	9.34956i		−	0.423669i	0.977306	−	0.211834i	$-0.0679438\pi$
$488$	8.70251	−	6.09859i	0.393944	−	0.276070i
$489$	21.0090	+	24.5207i	0.950061	+	1.10886i
$490$	−5.01363	+	3.51155i	−0.226493	+	0.158636i
$491$	−32.2509	−	11.7384i	−1.45546	−	0.529745i	−0.511350	−	0.859372i	$-0.670854\pi$
$491$	−32.2509	−	11.7384i	−1.45546	−	0.529745i	−0.944111	+	0.329628i	$0.893077\pi$
$492$	15.3204	+	12.5823i	0.690695	+	0.567255i
$493$	3.02422	−	17.1512i	0.136204	−	0.772451i
$494$	4.00006	+	0.349439i	0.179971	+	0.0157220i
$495$	7.64350	+	1.18613i	0.343550	+	0.0533124i
$496$	9.55501	+	11.3753i	0.429033	+	0.510765i
$497$	−7.85706	−	21.5871i	−0.352438	−	0.968314i
$498$	20.6703	+	5.30839i	0.926257	+	0.237875i
$499$	1.37303	+	1.63631i	0.0614653	+	0.0732515i	0.795901	−	0.605427i	$-0.206998\pi$
$499$	1.37303	+	1.63631i	0.0614653	+	0.0732515i	−0.734436	+	0.678678i	$0.762553\pi$
$500$	−2.00000		0.000516850i	−0.0894427		2.31142e-5i
$501$	−8.95995	+	3.36596i	−0.400301	+	0.150380i
$502$	25.1777	−	25.1842i	1.12374	−	1.12403i
$503$	14.3984	+	24.9388i	0.641994	+	1.11197i	0.984987	+	0.172629i	$0.0552261\pi$
$503$	14.3984	+	24.9388i	0.641994	+	1.11197i	−0.342993	+	0.939338i	$0.611441\pi$
$504$	12.4445	−	6.12381i	0.554321	−	0.272776i
$505$	2.94829	−	5.10658i	0.131197	−	0.227240i
$506$	6.91877	+	25.8079i	0.307577	+	1.14730i
$507$	2.38143	+	4.02845i	0.105763	+	0.178910i
$508$	1.53722	+	2.66096i	0.0682032	+	0.118061i
$509$	10.4450	−	1.84174i	0.462968	−	0.0816338i	0.0627012	−	0.998032i	$-0.480028\pi$
$509$	10.4450	−	1.84174i	0.462968	−	0.0816338i	0.400267	+	0.916399i	$0.368917\pi$
$510$	3.80037	+	5.30889i	0.168283	+	0.235082i
$511$	−4.22686	+	5.03738i	−0.186985	+	0.222840i
$512$	−15.9814	+	16.0186i	−0.706284	+	0.707929i
$513$	0.141896	+	4.59513i	0.00626488	+	0.202880i
$514$	4.82458	+	10.3429i	0.212803	+	0.456204i
$515$	−6.46284	−	5.42297i	−0.284787	−	0.238965i
$516$	−6.96719	−	11.7788i	−0.306714	−	0.518534i
$517$	2.12754	+	12.0659i	0.0935691	+	0.530657i
$518$	1.62115	+	18.5023i	0.0712293	+	0.812945i
$519$	−27.7703	−	15.6544i	−1.21898	−	0.687153i
$520$	−3.83276	+	8.22771i	−0.168078	+	0.360809i
$521$	−10.9551	−	6.32495i	−0.479953	−	0.277101i	0.240444	−	0.970663i	$-0.422707\pi$
$521$	−10.9551	−	6.32495i	−0.479953	−	0.277101i	−0.720397	+	0.693562i	$0.756040\pi$
$522$	12.2332	+	24.8759i	0.535433	+	1.08879i
$523$	−36.5118	+	21.0801i	−1.59655	+	0.921769i	−0.604406	+	0.796676i	$0.706590\pi$
$523$	−36.5118	+	21.0801i	−1.59655	+	0.921769i	−0.992145	+	0.125093i	$0.960077\pi$
$524$	5.31509	−	14.6148i	0.232191	−	0.638452i
$525$	−2.79302	−	0.462904i	−0.121898	−	0.0202028i
$526$	−9.05496	+	19.4250i	−0.394815	+	0.846970i
$527$	−7.58329	+	6.36314i	−0.330333	+	0.277183i
$528$	−17.8621	+	0.193040i	−0.777350	+	0.00840101i
$529$	−28.8447	+	10.4986i	−1.25412	+	0.456461i
$530$	1.04720	+	0.733053i	0.0454873	+	0.0318418i
$531$	−7.16728	+	13.0260i	−0.311033	+	0.565280i
$532$	−0.989944	−	2.71766i	−0.0429195	−	0.117826i
$533$	−18.0864	−	3.18912i	−0.783410	−	0.138136i
$534$	−6.12143	−	0.471343i	−0.264900	−	0.0203970i
$535$	−3.20887	+	8.81630i	−0.138732	+	0.381162i
$536$	−3.88735	+	44.6318i	−0.167908	+	1.92780i
$537$	10.4269	+	3.67403i	0.449955	+	0.158546i
$538$	4.32797	−	16.1605i	0.186592	−	0.696730i
$539$	11.1596			0.480680
$540$	−9.87147	−	3.24872i	−0.424800	−	0.139803i
$541$	−31.9023			−1.37159			−0.685793	−	0.727796i	$-0.740545\pi$
$541$	−31.9023			−1.37159			−0.685793	+	0.727796i	$0.740545\pi$
$542$	2.77201	−	10.3506i	0.119068	−	0.444597i
$543$	−5.95266	−	31.8398i	−0.255453	−	1.36638i
$544$	−10.6686	−	10.6548i	−0.457413	−	0.456822i
$545$	5.69413	−	15.6445i	0.243910	−	0.670136i
$546$	−7.25956	+	10.6011i	−0.310680	+	0.453686i
$547$	−13.8757	−	2.44666i	−0.593283	−	0.104612i	−0.131058	−	0.991375i	$-0.541837\pi$
$547$	−13.8757	−	2.44666i	−0.593283	−	0.104612i	−0.462225	+	0.886763i	$0.652949\pi$
$548$	−36.4729	+	13.2857i	−1.55805	+	0.567538i
$549$	−10.6687	−	3.63624i	−0.455327	−	0.155191i
$550$	2.98715	+	2.09105i	0.127373	+	0.0891627i
$551$	5.43230	−	1.97720i	0.231424	−	0.0842314i
$552$	−3.51042	−	35.7264i	−0.149414	−	1.52062i
$553$	−4.76175	+	3.99558i	−0.202490	+	0.169909i
$554$	−16.4498	+	35.2885i	−0.698884	+	1.49927i
$555$	8.83527	−	10.7522i	0.375036	−	0.456407i
$556$	37.3680	+	13.5899i	1.58476	+	0.576341i
$557$	−17.9009	+	10.3351i	−0.758486	+	0.437912i	−0.828752	−	0.559616i	$-0.810949\pi$
$557$	−17.9009	+	10.3351i	−0.758486	+	0.437912i	0.0702660	+	0.997528i	$0.477615\pi$
$558$	3.76216	−	15.3012i	0.159265	−	0.647753i
$559$	10.9791	+	6.33882i	0.464369	+	0.268103i
$560$	6.53820	−	0.00337927i	0.276289	−	0.000142800i
$561$	−0.122482	−	11.9026i	−0.00517120	−	0.502530i
$562$	1.44012	+	16.4362i	0.0607477	+	0.693317i
$563$	0.871473	+	4.94237i	0.0367282	+	0.208296i	0.997649	−	0.0685264i	$-0.0218297\pi$
$563$	0.871473	+	4.94237i	0.0367282	+	0.208296i	−0.960921	+	0.276822i	$0.910719\pi$
$564$	−0.173635	−	16.4602i	−0.00731137	−	0.693100i
$565$	−13.7272	−	11.5185i	−0.577506	−	0.484585i
$566$	10.0024	+	21.4429i	0.420431	+	0.901312i
$567$	−13.0319	−	6.82501i	−0.547290	−	0.286624i
$568$	10.2736	−	38.4012i	0.431071	−	1.61128i
$569$	14.6732	−	17.4869i	0.615133	−	0.733087i	−0.365092	−	0.930971i	$-0.618962\pi$
$569$	14.6732	−	17.4869i	0.615133	−	0.733087i	0.980225	+	0.197884i	$0.0634069\pi$
$570$	−0.895383	+	1.97358i	−0.0375035	+	0.0826643i
$571$	−36.1517	+	6.37452i	−1.51290	+	0.266765i	−0.867638	−	0.497196i	$-0.834363\pi$
$571$	−36.1517	+	6.37452i	−1.51290	+	0.266765i	−0.645262	+	0.763961i	$0.723252\pi$
$572$	14.3289	−	8.27776i	0.599123	−	0.346110i
$573$	−29.6434	+	0.305041i	−1.23837	+	0.0127433i
$574$	3.42562	+	12.7780i	0.142983	+	0.533343i
$575$	−3.66387	+	6.34601i	−0.152794	+	0.264647i
$576$	23.7190	+	3.66191i	0.988291	+	0.152579i
$577$	−9.93312	−	17.2047i	−0.413521	−	0.716239i	0.581751	−	0.813367i	$-0.302368\pi$
$577$	−9.93312	−	17.2047i	−0.413521	−	0.716239i	−0.995272	+	0.0971276i	$0.969035\pi$
$578$	−9.89420	+	9.89675i	−0.411544	+	0.411651i
$579$	3.08507	+	2.53504i	0.128211	+	0.105353i
$580$	0.00337707	+	13.0679i	0.000140225	+	0.542614i
$581$	9.15388	+	10.9092i	0.379767	+	0.452589i
$582$	−25.5649	+	26.1032i	−1.05970	+	1.08201i
$583$	−0.797075	−	2.18995i	−0.0330115	−	0.0906983i
$584$	−10.9900	+	2.94932i	−0.454768	+	0.122044i
$585$	9.44456	−	1.86650i	0.390484	−	0.0771703i
$586$	35.7385	+	3.12206i	1.47635	+	0.128971i
$587$	−4.22930	+	23.9855i	−0.174562	+	0.989989i	0.764087	+	0.645114i	$0.223190\pi$
$587$	−4.22930	+	23.9855i	−0.174562	+	0.989989i	−0.938648	+	0.344876i	$0.887921\pi$
$588$	−14.7923	−	2.44770i	−0.610026	−	0.100941i
$589$	−3.08777	−	1.12386i	−0.127229	−	0.0463077i
$590$	−5.74065	+	4.02075i	−0.236339	+	0.165532i
$591$	35.4281	−	6.62351i	1.45732	−	0.272455i
$592$	−16.0552	+	27.8416i	−0.659863	+	1.14428i
$593$		−	10.2248i		−	0.419881i	−0.977714	−	0.209941i	$-0.932673\pi$
$593$		−	10.2248i		−	0.419881i	0.977714	−	0.209941i	$-0.0673271\pi$
$594$	11.3432	+	15.1760i	0.465419	+	0.622679i
$595$			4.35678i			0.178611i
$596$	−3.23550	−	18.3217i	−0.132531	−	0.750488i
$597$	6.52634	−	18.5218i	0.267105	−	0.758046i
$598$	19.0782	+	27.2390i	0.780164	+	1.11388i
$599$	−17.4081	−	6.33602i	−0.711274	−	0.258883i	−0.0390575	−	0.999237i	$-0.512436\pi$
$599$	−17.4081	−	6.33602i	−0.711274	−	0.258883i	−0.672217	+	0.740354i	$0.734658\pi$
$600$	−3.50089	−	3.42692i	−0.142923	−	0.139903i
$601$	−2.04830	+	11.6165i	−0.0835520	+	0.473847i	0.914108	+	0.405472i	$0.132893\pi$
$601$	−2.04830	+	11.6165i	−0.0835520	+	0.473847i	−0.997660	+	0.0683754i	$0.978218\pi$
$602$	0.794740	−	9.09746i	0.0323912	−	0.370785i
$603$	40.6545	−	24.6010i	1.65558	−	1.00183i
$604$	1.08157	−	6.14317i	0.0440084	−	0.249962i
$605$	1.48855	+	4.08975i	0.0605181	+	0.166272i
$606$	13.9117	−	3.88343i	0.565125	−	0.157754i
$607$	5.88832	+	7.01743i	0.239000	+	0.284829i	0.872190	−	0.489168i	$-0.162699\pi$
$607$	5.88832	+	7.01743i	0.239000	+	0.284829i	−0.633190	+	0.773996i	$0.718255\pi$
$608$	1.29225	−	4.83522i	0.0524075	−	0.196094i
$609$	−3.02459	+	18.2494i	−0.122563	+	0.739505i
$610$	−3.75759	−	3.75662i	−0.152140	−	0.152101i
$611$	7.62464	+	13.2063i	0.308460	+	0.534268i
$612$	−2.44831	+	15.8041i	−0.0989670	+	0.638842i
$613$	11.9463	−	20.6916i	0.482506	−	0.835724i	−0.517293	−	0.855809i	$-0.673060\pi$
$613$	11.9463	−	20.6916i	0.482506	−	0.835724i	0.999798	+	0.0200844i	$0.00639350\pi$
$614$	30.6630	−	8.22037i	1.23746	−	0.331747i
$615$	4.86764	−	8.63499i	0.196282	−	0.348196i
$616$	−9.76706	−	6.83333i	−0.393526	−	0.275323i
$617$	−8.18944	+	1.44402i	−0.329694	+	0.0581340i	−0.336045	−	0.941846i	$-0.609090\pi$
$617$	−8.18944	+	1.44402i	−0.329694	+	0.0581340i	0.00635095	+	0.999980i	$0.497978\pi$
$618$	−2.01551	−	20.5670i	−0.0810757	−	0.827324i
$619$	−6.89956	+	8.22257i	−0.277317	+	0.330493i	−0.886667	−	0.462408i	$-0.846986\pi$
$619$	−6.89956	+	8.22257i	−0.277317	+	0.330493i	0.609351	+	0.792901i	$0.291430\pi$
$620$	4.77309	−	5.69134i	0.191692	−	0.228570i
$621$	−28.3987	+	25.3634i	−1.13960	+	1.01780i
$622$	10.5086	−	4.90189i	0.421356	−	0.196548i
$623$	−3.13843	−	2.63346i	−0.125739	−	0.105507i
$624$	−20.8089	+	7.82951i	−0.833023	+	0.313431i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−15.4798	+	1.35632i	−0.618697	+	0.0542096i
$627$	3.40127	−	2.01067i	0.135834	−	0.0802985i
$628$	6.99358	+	8.33025i	0.279074	+	0.332413i
$629$	−18.5469	−	10.7081i	−0.739514	−	0.426959i
$630$	−4.09442	−	5.59708i	−0.163126	−	0.222993i
$631$	−15.2653	+	8.81341i	−0.607701	+	0.350856i	−0.772065	−	0.635543i	$-0.780776\pi$
$631$	−15.2653	+	8.81341i	−0.607701	+	0.350856i	0.164364	+	0.986400i	$0.447443\pi$
$632$	−10.7149	+	0.941619i	−0.426217	+	0.0374556i
$633$	−2.10777	−	5.61074i	−0.0837765	−	0.223007i
$634$	−4.67934	−	2.18128i	−0.185840	−	0.0866295i
$635$	1.17705	−	0.987665i	0.0467100	−	0.0391943i
$636$	0.576209	+	3.07765i	0.0228482	+	0.122037i
$637$	13.0520	−	4.75055i	0.517140	−	0.188224i
$638$	13.6628	−	19.5179i	0.540915	−	0.772720i
$639$	−39.3151	+	15.2329i	−1.55528	+	0.602603i
$640$	9.27351	+	6.48089i	0.366568	+	0.256180i
$641$	17.6334	+	3.10924i	0.696476	+	0.122807i	0.510667	−	0.859778i	$-0.329398\pi$
$641$	17.6334	+	3.10924i	0.696476	+	0.122807i	0.185809	+	0.982586i	$0.440510\pi$
$642$	−20.7259	+	9.92884i	−0.817986	+	0.391860i
$643$	10.4941	−	28.8323i	0.413847	−	1.13703i	−0.541281	−	0.840842i	$-0.682061\pi$
$643$	10.4941	−	28.8323i	0.413847	−	1.13703i	0.955128	−	0.296193i	$-0.0957172\pi$
$644$	11.9722	−	20.7488i	0.471771	−	0.817619i
$645$	−5.19617	+	4.45202i	−0.204599	+	0.175298i
$646$	3.22154	+	0.862764i	0.126750	+	0.0339450i
$647$	−40.7589			−1.60240			−0.801199	−	0.598399i	$-0.795804\pi$
$647$	−40.7589			−1.60240			−0.801199	+	0.598399i	$0.795804\pi$
$648$	−11.7071	−	22.6041i	−0.459898	−	0.887972i
$649$	12.7779			0.501576
$650$	4.38383	+	1.17404i	0.171948	+	0.0460495i
$651$	7.98472	−	6.84121i	0.312946	−	0.268128i
$652$	−18.6343	+	32.2948i	−0.729775	+	1.26476i
$653$	−11.8721	+	32.6184i	−0.464592	+	1.27645i	0.457406	+	0.889258i	$0.348779\pi$
$653$	−11.8721	+	32.6184i	−0.464592	+	1.27645i	−0.921997	+	0.387197i	$0.873443\pi$
$654$	36.7780	−	17.6187i	1.43813	−	0.688944i
$655$	−7.65753	−	1.35023i	−0.299205	−	0.0527578i
$656$	−7.81836	+	21.5154i	−0.305256	+	0.840034i
$657$	9.40313	+	7.56595i	0.366851	+	0.295176i
$658$	6.29931	−	8.99883i	0.245573	−	0.350811i
$659$	−7.80701	+	2.84152i	−0.304118	+	0.110690i	−0.489572	−	0.871963i	$-0.662847\pi$
$659$	−7.80701	+	2.84152i	−0.304118	+	0.110690i	0.185454	+	0.982653i	$0.440625\pi$
$660$	1.64365	+	8.77905i	0.0639790	+	0.341724i
$661$	35.3488	−	29.6611i	1.37491	−	1.15369i	0.403855	−	0.914823i	$-0.367670\pi$
$661$	35.3488	−	29.6611i	1.37491	−	1.15369i	0.971054	−	0.238862i	$-0.0767743\pi$
$662$	2.77226	+	1.29229i	0.107747	+	0.0502263i
$663$	−5.21009	−	13.8689i	−0.202343	−	0.538623i
$664$	2.15725	+	24.5479i	0.0837176	+	0.952643i
$665$	−1.25242	+	0.723088i	−0.0485669	+	0.0280401i
$666$	33.8901	−	3.67360i	1.31322	−	0.142349i
$667$	41.4645	+	23.9395i	1.60551	+	0.926942i
$668$	−7.10629	−	8.46450i	−0.274951	−	0.327501i
$669$	8.05472	−	4.76157i	0.311414	−	0.184093i
$670$	22.3149	−	1.95521i	0.862100	−	0.0755362i
$671$	1.68214	+	9.53988i	0.0649382	+	0.368283i
$672$	11.4477	+	11.2000i	0.441603	+	0.432048i
$673$	35.8868	+	30.1126i	1.38333	+	1.16075i	0.967961	+	0.251102i	$0.0807930\pi$
$673$	35.8868	+	30.1126i	1.38333	+	1.16075i	0.415372	+	0.909652i	$0.363651\pi$
$674$	18.8146	−	8.77636i	0.724712	−	0.338053i
$675$	−0.743930	+	5.14262i	−0.0286339	+	0.197940i
$676$	−3.47234	+	4.14034i	−0.133551	+	0.159244i
$677$	−14.5754	+	17.3702i	−0.560177	+	0.667593i	−0.969584	−	0.244759i	$-0.921291\pi$
$677$	−14.5754	+	17.3702i	−0.560177	+	0.667593i	0.409407	+	0.912352i	$0.365736\pi$
$678$	−4.28097	−	43.6845i	−0.164410	−	1.67769i
$679$	−24.0107	+	4.23374i	−0.921447	+	0.162476i
$680$	−4.32179	+	6.17725i	−0.165733	+	0.236887i
$681$	−9.03185	+	16.0221i	−0.346101	+	0.613969i
$682$	−13.0803	+	3.50667i	−0.500871	+	0.134277i
$683$	20.8007	−	36.0278i	0.795916	−	1.37857i	−0.126340	−	0.991987i	$-0.540323\pi$
$683$	20.8007	−	36.0278i	0.795916	−	1.37857i	0.922256	−	0.386580i	$-0.126344\pi$
$684$	−4.94947	+	1.91917i	−0.189248	+	0.0733813i
$685$	9.70433	+	16.8084i	0.370783	+	0.642216i
$686$	−18.5190	−	18.5142i	−0.707058	−	0.706875i
$687$	7.03745	−	42.4618i	0.268496	−	1.62002i
$688$	10.1512	−	12.1105i	0.387011	−	0.461707i
$689$	−1.86448	−	2.22200i	−0.0710309	−	0.0846513i
$690$	−17.2883	+	4.82599i	−0.658154	+	0.183722i
$691$	−7.60624	−	20.8980i	−0.289355	−	0.794996i	−0.996157	−	0.0875847i	$-0.972085\pi$
$691$	−7.60624	−	20.8980i	−0.289355	−	0.794996i	0.706802	−	0.707411i	$-0.250137\pi$
$692$	6.38269	−	36.2528i	0.242633	−	1.37812i
$693$	0.260178	+	12.6405i	0.00988336	+	0.480174i
$694$	−4.23042	+	48.4260i	−0.160585	+	1.83823i
$695$	3.45234	−	19.5792i	0.130955	−	0.742681i
$696$	−22.3913	+	22.8746i	−0.848739	+	0.867060i
$697$	−14.3342	−	5.21723i	−0.542948	−	0.197617i
$698$	−23.3190	−	33.2939i	−0.882639	−	1.26019i
$699$	14.1761	−	40.2319i	0.536190	−	1.52171i
$700$	−0.568505	−	3.21929i	−0.0214875	−	0.121678i
$701$		−	20.4369i		−	0.771893i	−0.922521	−	0.385946i	$-0.873875\pi$
$701$		−	20.4369i		−	0.771893i	0.922521	−	0.385946i	$-0.126125\pi$
$702$	19.7270	+	12.9207i	0.744548	+	0.487662i
$703$		−	7.10880i		−	0.268114i
$704$	−7.06975	−	19.3772i	−0.266451	−	0.730306i
$705$	−8.09039	+	1.51255i	−0.304702	+	0.0569660i
$706$	−23.4283	+	16.4092i	−0.881736	+	0.617568i
$707$	9.05698	+	3.29647i	0.340623	+	0.123977i
$708$	−16.9374	−	2.80263i	−0.636545	−	0.105329i
$709$	2.48467	−	14.0913i	0.0933139	−	0.529209i	−0.901937	−	0.431867i	$-0.857855\pi$
$709$	2.48467	−	14.0913i	0.0933139	−	0.529209i	0.995251	−	0.0973419i	$-0.0310340\pi$
$710$	−19.8004	−	1.72974i	−0.743097	−	0.0649158i
$711$	7.51166	+	8.58680i	0.281709	+	0.322030i
$712$	−1.83751	−	6.84706i	−0.0688636	−	0.256604i
$713$	−9.30804	−	25.5736i	−0.348589	−	0.957740i
$714$	−7.46713	+	7.62438i	−0.279450	+	0.285335i
$715$	−5.31846	−	6.33829i	−0.198899	−	0.237039i
$716$	0.00329893	+	12.7655i	0.000123287	+	0.477071i
$717$	3.38365	+	2.78039i	0.126365	+	0.103836i
$718$	23.4721	−	23.4782i	0.875971	−	0.876197i
$719$	24.6097	+	42.6253i	0.917788	+	1.58966i	0.802767	+	0.596292i	$0.203360\pi$
$719$	24.6097	+	42.6253i	0.917788	+	1.58966i	0.115021	+	0.993363i	$0.463307\pi$
$720$	−0.253143	−	11.9973i	−0.00943407	−	0.447114i
$721$	6.89506	−	11.9426i	0.256785	−	0.444765i
$722$	−6.67118	−	24.8843i	−0.248275	−	0.926098i
$723$	−13.5072	+	0.138993i	−0.502337	+	0.00516922i
$724$	32.3867	−	18.7096i	1.20364	−	0.695337i
$725$	6.43468	−	1.13461i	0.238978	−	0.0421382i
$726$	−4.40450	+	9.70831i	−0.163466	+	0.360309i
$727$	18.3844	−	21.9097i	0.681839	−	0.812584i	−0.308504	−	0.951223i	$-0.599828\pi$
$727$	18.3844	−	21.9097i	0.681839	−	0.812584i	0.990343	+	0.138639i	$0.0442728\pi$
$728$	−14.3322	−	3.83434i	−0.531186	−	0.142110i
$729$	−12.0316	+	24.1711i	−0.445613	+	0.895226i
$730$	2.40512	+	5.15605i	0.0890173	+	0.190834i
$731$	8.06640	+	6.76851i	0.298346	+	0.250342i
$732$	−0.137285	−	13.0143i	−0.00507419	−	0.481021i
$733$	3.46089	+	19.6277i	0.127831	+	0.724964i	0.979586	+	0.201025i	$0.0644271\pi$
$733$	3.46089	+	19.6277i	0.127831	+	0.724964i	−0.851755	+	0.523940i	$0.824462\pi$
$734$	−3.69360	−	42.1553i	−0.136333	−	1.55598i
$735$	0.0771399	+	7.49635i	0.00284535	+	0.276507i
$736$	37.5569	−	17.5426i	1.38437	−	0.646630i
$737$	−35.3679	−	20.4197i	−1.30279	−	0.752169i
$738$	23.3180	−	6.76856i	0.858347	−	0.249154i
$739$	−34.9708	+	20.1904i	−1.28642	+	0.742716i	−0.978014	−	0.208538i	$-0.933129\pi$
$739$	−34.9708	+	20.1904i	−1.28642	+	0.742716i	−0.308408	+	0.951254i	$0.599796\pi$
$740$	15.1019	+	5.49221i	0.555155	+	0.201898i
$741$	3.12212	−	3.79952i	0.114694	−	0.139579i
$742$	−0.882776	+	1.89376i	−0.0324077	+	0.0695220i
$743$	−11.1420	+	9.34928i	−0.408762	+	0.342992i	−0.823869	−	0.566781i	$-0.808189\pi$
$743$	−11.1420	+	9.34928i	−0.408762	+	0.342992i	0.415107	+	0.909773i	$0.363744\pi$
$744$	18.1074	−	1.77920i	0.663848	−	0.0652287i
$745$	−8.74160	+	3.18168i	−0.320267	+	0.116568i
$746$	−25.6305	−	17.9417i	−0.938399	−	0.656893i
$747$	19.6724	−	17.2092i	0.719774	−	0.629652i
$748$	12.9146	−	4.70431i	0.472204	−	0.172007i
$749$	−15.1025	−	2.66299i	−0.551835	−	0.0973034i
$750$	−1.38399	+	2.02103i	−0.0505361	+	0.0737977i
$751$	−6.07329	+	16.6862i	−0.221618	+	0.608889i	−0.999817	−	0.0191279i	$-0.993911\pi$
$751$	−6.07329	+	16.6862i	−0.221618	+	0.608889i	0.778199	+	0.628017i	$0.216133\pi$
$752$	17.8580	−	6.51024i	0.651215	−	0.237404i
$753$	−8.01518	−	42.8719i	−0.292090	−	1.56234i
$754$	7.67109	−	28.6437i	0.279365	−	1.04314i
$755$	−3.11883			−0.113506
$756$	2.42764	−	16.8124i	0.0882922	−	0.611460i
$757$	44.2100			1.60684			0.803420	−	0.595413i	$-0.203011\pi$
$757$	44.2100			1.60684			0.803420	+	0.595413i	$0.203011\pi$
$758$	6.53215	−	24.3909i	0.237258	−	0.885919i
$759$	30.8642	+	10.8753i	1.12030	+	0.394749i
$760$	−2.49303	−	0.217138i	−0.0904315	−	0.00787641i
$761$	−17.0693	+	46.8976i	−0.618762	+	1.70004i	0.0912331	+	0.995830i	$0.470919\pi$
$761$	−17.0693	+	46.8976i	−0.618762	+	1.70004i	−0.709995	+	0.704206i	$0.751303\pi$
$762$	3.75262	+	0.288947i	0.135943	+	0.0104675i
$763$	26.7994	+	4.72546i	0.970203	+	0.171073i
$764$	−11.7160	−	32.1637i	−0.423872	−	1.16364i
$765$	7.99460	−	0.164552i	0.289045	−	0.00594938i
$766$	39.0979	+	27.3692i	1.41267	+	0.988888i
$767$	14.9447	−	5.43942i	0.539621	−	0.196406i
$768$	5.12101	+	27.2356i	0.184788	+	0.982778i
$769$	18.1026	−	15.1899i	0.652798	−	0.547762i	−0.255121	−	0.966909i	$-0.582115\pi$
$769$	18.1026	−	15.1899i	0.652798	−	0.547762i	0.907918	+	0.419147i	$0.137671\pi$
$770$	−2.51814	+	5.40198i	−0.0907473	+	0.194674i
$771$	13.7896	+	2.28544i	0.496621	+	0.0823080i
$772$	−1.57584	+	4.33307i	−0.0567157	+	0.155951i
$773$	−38.9557	+	22.4911i	−1.40114	+	0.808947i	−0.994510	−	0.104646i	$-0.966629\pi$
$773$	−38.9557	+	22.4911i	−1.40114	+	0.808947i	−0.406629	+	0.913594i	$0.633296\pi$
$774$	−16.7237	−	1.11473i	−0.601120	−	0.0400681i
$775$	−3.21638	−	1.85698i	−0.115536	−	0.0667045i
$776$	−38.2433	−	17.8151i	−1.37285	−	0.639524i
$777$	19.8158	+	11.1704i	0.710890	+	0.400736i
$778$	3.17065	+	36.1869i	0.113673	+	1.29736i
$779$	−0.879254	−	4.98649i	−0.0315025	−	0.178660i
$780$	5.65952	+	9.56806i	0.202643	+	0.342592i
$781$	27.7589	+	23.2925i	0.993293	+	0.833472i
$782$	11.6767	+	25.0324i	0.417559	+	0.895156i
$783$	33.6016	+	4.86079i	1.20082	+	0.173711i
$784$	−3.01518	−	17.0484i	−0.107685	−	0.608872i
$785$	3.49571	−	4.16603i	0.124767	−	0.148692i
$786$	−11.0865	−	15.4872i	−0.395444	−	0.552411i
$787$	−11.5406	+	2.03492i	−0.411377	+	0.0725369i	−0.375507	−	0.926820i	$-0.622531\pi$
$787$	−11.5406	+	2.03492i	−0.411377	+	0.0725369i	−0.0358702	+	0.999356i	$0.511420\pi$
$788$	20.8181	+	36.0365i	0.741615	+	1.28375i
$789$	13.3575	+	22.5956i	0.475538	+	0.804425i
$790$	1.39263	+	5.19467i	0.0495475	+	0.184818i
$791$	14.6452	−	25.3662i	0.520723	−	0.901919i
$792$	−12.1701	+	18.1804i	−0.432446	+	0.646014i
$793$	6.02842	+	10.4415i	0.214075	+	0.370789i
$794$	−14.4181	+	14.4218i	−0.511678	+	0.511810i
$795$	1.46556	−	0.550563i	0.0519780	−	0.0195265i
$796$	22.6760	−	0.00586003i	0.803729	−	0.000207703i
$797$	−1.40422	−	1.67348i	−0.0497400	−	0.0592778i	0.740601	−	0.671945i	$-0.234541\pi$
$797$	−1.40422	−	1.67348i	−0.0497400	−	0.0592778i	−0.790341	+	0.612667i	$0.790097\pi$
$798$	−3.43105	−	0.881138i	−0.121458	−	0.0311919i
$799$	4.33200	+	11.9021i	0.153255	+	0.421065i
$800$	2.38738	−	5.12839i	0.0844065	−	0.181316i
$801$	−4.71380	+	5.85842i	−0.166554	+	0.206997i
$802$	16.4930	+	1.44080i	0.582388	+	0.0508765i
$803$	1.80120	−	10.2151i	0.0635628	−	0.360483i
$804$	42.4022	+	34.8241i	1.49541	+	1.22815i
$805$	−11.2552	−	4.09657i	−0.396695	−	0.144385i
$806$	−13.8056	+	9.66947i	−0.486283	+	0.340593i
$807$	−13.3316	−	15.5599i	−0.469293	−	0.547735i
$808$	9.57142	+	13.6581i	0.336721	+	0.480491i
$809$		−	21.0655i		−	0.740624i	−0.928907	−	0.370312i	$-0.879251\pi$
$809$		−	21.0655i		−	0.740624i	0.928907	−	0.370312i	$-0.120749\pi$
$810$	−10.1159	+	7.72458i	−0.355436	+	0.271414i
$811$			15.8992i			0.558297i	0.960248	+	0.279148i	$0.0900522\pi$
$811$			15.8992i			0.558297i	−0.960248	+	0.279148i	$0.909948\pi$
$812$	−21.0346	+	3.71458i	−0.738171	+	0.130356i
$813$	−8.53869	−	9.96594i	−0.299465	−	0.349521i
$814$	−16.8073	−	23.9967i	−0.589096	−	0.841085i
$815$	17.5184	+	6.37616i	0.613641	+	0.223347i
$816$	−18.1504	+	3.40304i	−0.635391	+	0.119130i
$817$	−0.606947	+	3.44217i	−0.0212344	+	0.120426i
$818$	0.632116	−	7.23589i	0.0221014	−	0.252997i
$819$	5.68525	+	14.6733i	0.198659	+	0.512726i
$820$	11.2726	+	1.98465i	0.393655	+	0.0693070i
$821$	6.35252	+	17.4534i	0.221704	+	0.609128i	0.999820	−	0.0189939i	$-0.00604631\pi$
$821$	6.35252	+	17.4534i	0.221704	+	0.609128i	−0.778115	+	0.628121i	$0.783824\pi$
$822$	−11.8255	+	46.0471i	−0.412461	+	1.60608i
$823$	3.30669	+	3.94075i	0.115264	+	0.137366i	0.820591	−	0.571516i	$-0.193644\pi$
$823$	3.30669	+	3.94075i	0.115264	+	0.137366i	−0.705327	+	0.708882i	$0.749200\pi$
$824$	21.6228	−	10.0931i	0.753266	−	0.351609i
$825$	4.18054	−	1.57049i	0.145548	−	0.0546775i
$826$	−8.10167	−	8.09958i	−0.281893	−	0.281820i
$827$	17.2288	+	29.8411i	0.599102	+	1.03768i	0.992954	+	0.118502i	$0.0378091\pi$
$827$	17.2288	+	29.8411i	0.599102	+	1.03768i	−0.393851	+	0.919174i	$0.628858\pi$
$828$	−38.5259	−	21.1851i	−1.33887	−	0.736232i
$829$	−22.2028	+	38.4565i	−0.771137	+	1.33565i	0.165804	+	0.986159i	$0.446978\pi$
$829$	−22.2028	+	38.4565i	−0.771137	+	1.33565i	−0.936940	+	0.349489i	$0.886355\pi$
$830$	11.9010	−	3.19051i	0.413090	−	0.110744i
$831$	24.2659	+	41.0485i	0.841776	+	1.42396i
$832$	−16.5173	−	19.6536i	−0.572634	−	0.681365i
$833$	11.3614	−	2.00332i	0.393648	−	0.0694108i
$834$	39.5986	−	28.3467i	1.37119	−	0.981564i
$835$	−3.55205	+	4.23317i	−0.122924	+	0.146495i
$836$	3.49574	+	2.93174i	0.120903	+	0.101396i
$837$	−12.8551	−	14.3934i	−0.444336	−	0.497509i
$838$	−29.5979	+	13.8064i	−1.02244	+	0.476933i
$839$	−5.45603	−	4.57815i	−0.188363	−	0.158055i	0.543730	−	0.839260i	$-0.317012\pi$
$839$	−5.45603	−	4.57815i	−0.188363	−	0.158055i	−0.732093	+	0.681205i	$0.761456\pi$
$840$	4.52269	−	6.60813i	0.156047	−	0.228002i
$841$	−2.37766	−	13.4844i	−0.0819882	−	0.464978i
$842$	−14.1880	+	1.24314i	−0.488951	+	0.0428413i
$843$	17.6030	+	9.92300i	0.606280	+	0.341766i
$844$	5.30049	−	4.44997i	0.182450	−	0.153174i
$845$	2.33985	+	1.35092i	0.0804934	+	0.0464729i
$846$	−16.7506	−	11.2192i	−0.575897	−	0.385725i
$847$	−6.16084	+	3.55696i	−0.211689	+	0.122219i
$848$	−3.13019	+	1.80937i	−0.107491	+	0.0621341i
$849$	28.5888	+	4.73819i	0.981164	+	0.162614i
$850$	3.41652	+	1.59261i	0.117186	+	0.0546262i
$851$	45.1022	−	37.8453i	1.54608	−	1.29732i
$852$	−31.6862	−	36.9632i	−1.08555	−	1.26634i
$853$	39.5923	−	14.4104i	1.35562	−	0.493404i	0.440920	−	0.897546i	$-0.354652\pi$
$853$	39.5923	−	14.4104i	1.35562	−	0.493404i	0.914696	+	0.404143i	$0.132430\pi$
$854$	4.98055	−	7.11492i	0.170431	−	0.243468i
$855$	1.37415	+	2.27086i	0.0469951	+	0.0776619i
$856$	−18.7715	−	18.7570i	−0.641597	−	0.641099i
$857$	34.3231	+	6.05210i	1.17246	+	0.206736i	0.725759	−	0.687949i	$-0.241489\pi$
$857$	34.3231	+	6.05210i	1.17246	+	0.206736i	0.446697	+	0.894685i	$0.352600\pi$
$858$	1.55595	−	20.2074i	0.0531192	−	0.689869i
$859$	8.57378	−	23.5563i	0.292534	−	0.803730i	−0.703161	−	0.711031i	$-0.748229\pi$
$859$	8.57378	−	23.5563i	0.292534	−	0.803730i	0.995694	−	0.0926985i	$-0.0295493\pi$
$860$	−6.84358	−	3.94879i	−0.233364	−	0.134652i
$861$	15.2815	+	5.38459i	0.520792	+	0.183506i
$862$	30.2319	+	8.09644i	1.02970	+	0.275766i
$863$	−45.2113			−1.53901			−0.769505	−	0.638641i	$-0.779497\pi$
$863$	−45.2113			−1.53901			−0.769505	+	0.638641i	$0.779497\pi$
$864$	20.1193	−	21.4292i	0.684474	−	0.729037i
$865$	−18.4052			−0.625795
$866$	18.1101	+	4.85009i	0.615408	+	0.164813i
$867$	3.14976	+	16.8476i	0.106972	+	0.572173i
$868$	10.5162	+	6.06792i	0.356944	+	0.205959i
$869$	3.35355	−	9.21379i	0.113761	−	0.312556i
$870$	13.2053	+	9.04289i	0.447702	+	0.306583i
$871$	−50.0579	−	8.82655i	−1.69615	−	0.299076i
$872$	33.3099	+	33.2841i	1.12802	+	1.12714i
$873$	8.67569	+	43.8993i	0.293627	+	1.48577i
$874$	−5.25798	+	7.51124i	−0.177854	+	0.254072i
$875$	−1.53597	+	0.559049i	−0.0519254	+	0.0188993i
$876$	−4.62804	+	13.1453i	−0.156367	+	0.444137i
$877$	27.3957	−	22.9877i	0.925087	−	0.776241i	−0.0498415	−	0.998757i	$-0.515872\pi$
$877$	27.3957	−	22.9877i	0.925087	−	0.776241i	0.974929	+	0.222517i	$0.0714272\pi$
$878$	9.77043	+	4.55449i	0.329736	+	0.153707i
$879$	27.8945	−	33.9468i	0.940859	−	1.14500i
$880$	−8.92893	+	5.16127i	−0.300994	+	0.173986i
$881$	37.9906	−	21.9339i	1.27993	−	0.738970i	0.303098	−	0.952959i	$-0.401979\pi$
$881$	37.9906	−	21.9339i	1.27993	−	0.738970i	0.976836	+	0.213989i	$0.0686456\pi$
$882$	−12.7131	+	13.2508i	−0.428071	+	0.446179i
$883$	−35.0060	−	20.2107i	−1.17805	−	0.680145i	−0.222484	−	0.974936i	$-0.571416\pi$
$883$	−35.0060	−	20.2107i	−1.17805	−	0.680145i	−0.955562	+	0.294792i	$0.904750\pi$
$884$	13.1020	−	10.9996i	0.440668	−	0.369958i
$885$	0.0883258	+	8.58338i	0.00296904	+	0.288527i
$886$	−17.8058	+	1.56013i	−0.598198	+	0.0524135i
$887$	2.63697	+	14.9550i	0.0885409	+	0.502140i	0.996536	+	0.0831601i	$0.0265013\pi$
$887$	2.63697	+	14.9550i	0.0885409	+	0.502140i	−0.907995	+	0.418980i	$0.862388\pi$
$888$	17.0151	+	35.4946i	0.570991	+	1.19112i
$889$	1.92395	+	1.61439i	0.0645273	+	0.0541448i
$890$	−3.21237	+	1.49846i	−0.107679	+	0.0502284i
$891$	23.1853	−	0.954844i	0.776737	−	0.0319885i
$892$	8.27844	+	6.94279i	0.277183	+	0.232462i
$893$	−2.70246	+	3.22067i	−0.0904344	+	0.107776i
$894$	−20.7509	−	9.41436i	−0.694015	−	0.314863i
$895$	6.28580	−	1.10836i	0.210111	−	0.0370483i
$896$	−7.80024	+	16.7672i	−0.260588	+	0.560154i
$897$	40.7275	−	0.419100i	1.35985	−	0.0139933i
$898$	−27.6297	+	7.40717i	−0.922014	+	0.247181i
$899$	−12.1334	+	21.0156i	−0.404671	+	0.700910i
$900$	−5.88585	+	1.16478i	−0.196195	+	0.0388262i
$901$	−1.20461	−	2.08645i	−0.0401314	−	0.0695097i
$902$	−14.7576	−	14.7538i	−0.491374	−	0.491247i
$903$	−8.64135	−	7.10072i	−0.287566	−	0.236297i
$904$	45.9271	−	21.4378i	1.52751	−	0.713012i
$905$	−12.0209	−	14.3260i	−0.399589	−	0.476212i
$906$	−5.45795	−	5.34539i	−0.181328	−	0.177589i
$907$	8.84222	+	24.2938i	0.293601	+	0.806662i	0.995533	+	0.0944180i	$0.0300990\pi$
$907$	8.84222	+	24.2938i	0.293601	+	0.806662i	−0.701932	+	0.712244i	$0.747679\pi$
$908$	−20.9161	−	3.68250i	−0.694125	−	0.122208i
$909$	5.70688	−	16.7439i	0.189285	−	0.555359i
$910$	−0.645576	+	7.38996i	−0.0214006	+	0.244975i
$911$	3.92317	−	22.2494i	0.129980	−	0.737156i	−0.848244	−	0.529606i	$-0.822340\pi$
$911$	3.92317	−	22.2494i	0.129980	−	0.737156i	0.978224	−	0.207550i	$-0.0665490\pi$
$912$	−3.99065	−	4.65281i	−0.132144	−	0.154070i
$913$	−21.1088	−	7.68298i	−0.698600	−	0.254270i
$914$	−16.0338	−	22.8924i	−0.530352	−	0.757212i
$915$	−6.39666	+	1.19590i	−0.211467	+	0.0395352i
$916$	48.9423	−	8.64288i	1.61710	−	0.285569i
$917$		−	12.7097i		−	0.419712i
$918$	14.2726	+	13.4141i	0.471066	+	0.442730i
$919$			17.2549i			0.569187i	0.958648	+	0.284594i	$0.0918586\pi$
$919$			17.2549i			0.569187i	−0.958648	+	0.284594i	$0.908141\pi$
$920$	−11.8945	−	16.9731i	−0.392151	−	0.559587i
$921$	12.9212	−	36.6706i	0.425770	−	1.20834i
$922$	−41.3916	+	28.9907i	−1.36316	+	0.954757i
$923$	42.3815	+	15.4256i	1.39500	+	0.507740i
$924$	−13.6653	+	5.13763i	−0.449554	+	0.169015i
$925$	1.39522	−	7.91271i	0.0458747	−	0.260168i
$926$	−26.6654	−	2.32945i	−0.876279	−	0.0765504i
$927$	−22.1748	−	12.2012i	−0.728317	−	0.400741i
$928$	−33.5086	−	15.5990i	−1.09997	−	0.512062i
$929$	13.1199	+	36.0466i	0.430450	+	1.18265i	0.945537	+	0.325513i	$0.105537\pi$
$929$	13.1199	+	36.0466i	0.430450	+	1.18265i	−0.515088	+	0.857137i	$0.672241\pi$
$930$	−2.44598	−	8.76229i	−0.0802068	−	0.287327i
$931$	2.46151	+	2.93352i	0.0806729	+	0.0961422i
$932$	49.2553	−	0.0127288i	1.61341	−	0.000416946i
$933$	2.32206	−	14.0106i	0.0760207	−	0.458686i
$934$	−2.70154	+	2.70224i	−0.0883972	+	0.0884201i
$935$	−3.43618	−	5.95164i	−0.112375	−	0.194639i
$936$	−6.49462	+	26.4441i	−0.212283	+	0.864351i
$937$	−4.91641	+	8.51547i	−0.160612	+	0.278188i	−0.935088	−	0.354415i	$-0.884680\pi$
$937$	−4.91641	+	8.51547i	−0.160612	+	0.278188i	0.774476	+	0.632603i	$0.218013\pi$
$938$	9.48112	+	35.3657i	0.309569	+	1.15473i
$939$	−9.34563	+	16.5788i	−0.304983	+	0.541027i
$940$	−4.75405	−	8.22934i	−0.155060	−	0.268411i
$941$	−42.4085	+	7.47776i	−1.38248	+	0.243768i	−0.814924	−	0.579568i	$-0.803221\pi$
$941$	−42.4085	+	7.47776i	−1.38248	+	0.243768i	−0.567554	+	0.823336i	$0.692110\pi$
$942$	13.2577	−	1.29922i	0.431959	−	0.0423310i
$943$	26.9562	−	32.1252i	0.877815	−	1.04614i
$944$	−3.45241	−	19.5206i	−0.112366	−	0.635340i
$945$	−8.48932	+	0.262148i	−0.276158	+	0.00852767i
$946$	6.08948	+	13.0545i	0.197986	+	0.424439i
$947$	−3.29440	−	2.76433i	−0.107054	−	0.0898287i	0.587690	−	0.809086i	$-0.300038\pi$
$947$	−3.29440	−	2.76433i	−0.107054	−	0.0898287i	−0.694743	+	0.719258i	$0.744482\pi$
$948$	−6.46610	+	11.4775i	−0.210009	+	0.372773i
$949$	−2.24183	−	12.7140i	−0.0727729	−	0.412715i
$950$	0.109213	+	1.24646i	0.00354334	+	0.0404404i
$951$	−5.44312	+	3.21772i	−0.176505	+	0.104342i
$952$	−11.1703	−	5.20352i	−0.362031	−	0.168647i
$953$	50.7497	+	29.3003i	1.64394	+	0.949131i	0.979412	+	0.201871i	$0.0647022\pi$
$953$	50.7497	+	29.3003i	1.64394	+	0.949131i	0.664532	+	0.747260i	$0.268631\pi$
$954$	3.50835	+	1.54835i	0.113587	+	0.0501297i
$955$	−14.8225	+	8.55778i	−0.479645	+	0.276923i
$956$	−1.72835	+	4.75244i	−0.0558990	+	0.153705i
$957$	−10.2615	−	27.3154i	−0.331707	−	0.882981i
$958$	13.6617	−	29.3074i	0.441388	−	0.946880i
$959$	−24.3023	+	20.3921i	−0.784763	+	0.658494i
$960$	12.9675	−	4.88295i	0.418525	−	0.157597i
$961$	−16.1689	+	5.88499i	−0.521577	+	0.189838i
$962$	−29.8726	−	20.9112i	−0.963130	−	0.674206i
$963$	−4.31612	+	27.8134i	−0.139085	+	0.896276i
$964$	−5.33847	−	14.6555i	−0.171941	−	0.472023i
$965$	2.27034	+	0.400322i	0.0730847	+	0.0128868i
$966$	−12.6755	−	26.4595i	−0.407828	−	0.851319i
$967$	−6.96169	+	19.1271i	−0.223873	+	0.615085i	−0.999878	−	0.0156416i	$-0.995021\pi$
$967$	−6.96169	+	19.1271i	−0.223873	+	0.615085i	0.776005	+	0.630727i	$0.217243\pi$
$968$	−12.2635	−	1.06813i	−0.394164	−	0.0343309i
$969$	3.10181	−	2.65760i	0.0996446	−	0.0853743i
$970$	−5.45704	+	20.3765i	−0.175215	+	0.654250i
$971$	−40.1453			−1.28833			−0.644163	−	0.764889i	$-0.722794\pi$
$971$	−40.1453			−1.28833			−0.644163	+	0.764889i	$0.722794\pi$
$972$	−30.9420	−	3.81967i	−0.992467	−	0.122516i
$973$	32.4969			1.04180
$974$	3.42053	−	12.7722i	0.109601	−	0.409247i
$975$	4.22090	−	3.61642i	0.135177	−	0.115818i
$976$	14.1194	−	5.14732i	0.451952	−	0.164762i
$977$	6.14206	−	16.8752i	0.196502	−	0.539885i	−0.801834	−	0.597547i	$-0.796142\pi$
$977$	6.14206	−	16.8752i	0.196502	−	0.539885i	0.998336	+	0.0576619i	$0.0183646\pi$
$978$	19.7290	+	41.1832i	0.630864	+	1.31689i
$979$	6.36430	+	1.12220i	0.203404	+	0.0358656i
$980$	−8.13368	+	2.96280i	−0.259821	+	0.0946431i
$981$	7.65892	−	49.3548i	0.244531	−	1.57578i
$982$	−39.7626	−	27.8344i	−1.26887	−	0.888231i
$983$	3.04741	−	1.10916i	0.0971971	−	0.0353769i	−0.292964	−	0.956124i	$-0.594642\pi$
$983$	3.04741	−	1.10916i	0.0971971	−	0.0353769i	0.390161	+	0.920747i	$0.372419\pi$
$984$	16.3255	+	22.7933i	0.520438	+	0.726624i
$985$	15.9405	−	13.3756i	0.507905	−	0.426183i
$986$	10.4060	−	22.3234i	0.331396	−	0.710921i
$987$	−4.73113	−	12.5939i	−0.150593	−	0.400869i
$988$	5.33654	+	1.94078i	0.169778	+	0.0617444i
$989$	−25.0703	+	14.4743i	−0.797188	+	0.460257i
$990$	10.0076	+	4.41670i	0.318064	+	0.140372i
$991$	15.0803	+	8.70660i	0.479041	+	0.276574i	0.720017	−	0.693957i	$-0.244134\pi$
$991$	15.0803	+	8.70660i	0.479041	+	0.276574i	−0.240976	+	0.970531i	$0.577467\pi$
$992$	8.89121	+	19.0351i	0.282296	+	0.604366i
$993$	3.22476	−	1.90633i	0.102335	−	0.0604954i
$994$	−2.83570	−	32.3641i	−0.0899430	−	1.02653i
$995$	−1.96882	−	11.1657i	−0.0624158	−	0.353978i
$996$	26.2950	+	14.8138i	0.833190	+	0.469395i
$997$	18.7555	+	15.7377i	0.593992	+	0.498419i	0.889508	−	0.456919i	$-0.151047\pi$
$997$	18.7555	+	15.7377i	0.593992	+	0.498419i	−0.295516	+	0.955338i	$0.595492\pi$
$998$	1.27702	+	2.73765i	0.0404232	+	0.0866587i
$999$	19.7490	−	36.7836i	0.624832	−	1.16378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.67	yes	432
4.3	odd	2	inner	540.2.be.a.11.27	✓	432
27.5	odd	18	inner	540.2.be.a.491.27	yes	432
108.59	even	18	inner	540.2.be.a.491.67	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.27	✓	432	4.3	odd	2	inner
540.2.be.a.11.67	yes	432	1.1	even	1	trivial
540.2.be.a.491.27	yes	432	27.5	odd	18	inner
540.2.be.a.491.67	yes	432	108.59	even	18	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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36607 + 0.365849i) q^{2} +(1.31530 - 1.12693i) q^{3} +(1.73231 + 0.999552i) q^{4} +(0.342020 - 0.939693i) q^{5} +(2.20909 - 1.05827i) q^{6} +(1.60972 + 0.283837i) q^{7} +(2.00078 + 1.99922i) q^{8} +(0.460037 - 2.96452i) q^{9} +(0.811010 - 1.15856i) q^{10} +(-2.42284 + 0.881840i) q^{11} +(3.40494 - 0.637486i) q^{12} +(-2.45829 + 2.06275i) q^{13} +(2.09515 + 0.976655i) q^{14} +(-0.609113 - 1.62141i) q^{15} +(2.00179 + 3.46307i) q^{16} +(-2.30833 + 1.33272i) q^{17} +(1.71301 - 3.88144i) q^{18} +(-0.766220 - 0.442377i) q^{19} +(1.53176 - 1.28597i) q^{20} +(2.43713 - 1.44072i) q^{21} +(-3.63239 + 0.318266i) q^{22} +(-1.27245 - 7.21642i) q^{23} +(4.88462 + 0.374841i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-4.11287 + 1.91851i) q^{26} +(-2.73573 - 4.41767i) q^{27} +(2.50482 + 2.10069i) q^{28} +(-4.19994 + 5.00529i) q^{29} +(-0.238900 - 2.43781i) q^{30} +(3.65753 - 0.644921i) q^{31} +(1.46763 + 5.46315i) q^{32} +(-2.19298 + 3.89026i) q^{33} +(-3.64092 + 0.976086i) q^{34} +(0.817275 - 1.41556i) q^{35} +(3.76012 - 4.67563i) q^{36} +(4.01739 + 6.95832i) q^{37} +(-0.884869 - 0.884640i) q^{38} +(-0.908810 + 5.48348i) q^{39} +(2.56296 - 1.19634i) q^{40} +(3.67865 + 4.38405i) q^{41} +(3.85638 - 1.07650i) q^{42} +(-1.35117 - 3.71231i) q^{43} +(-5.07855 - 0.894132i) q^{44} +(-2.62839 - 1.44622i) q^{45} +(0.901861 - 10.3237i) q^{46} +(0.825162 - 4.67973i) q^{47} +(6.53561 + 2.29909i) q^{48} +(-4.06722 - 1.48035i) q^{49} +(-0.811309 - 1.15835i) q^{50} +(-1.53427 + 4.35426i) q^{51} +(-6.32036 + 1.11613i) q^{52} +0.903877i q^{53} +(-2.12101 - 7.03572i) q^{54} +2.57833i q^{55} +(2.65323 + 3.78608i) q^{56} +(-1.50634 + 0.281620i) q^{57} +(-7.56860 + 5.30105i) q^{58} +(-4.65700 - 1.69501i) q^{59} +(0.565517 - 3.41763i) q^{60} +(0.652414 - 3.70002i) q^{61} +(5.23239 + 0.457094i) q^{62} +(1.58197 - 4.64146i) q^{63} +(0.00620220 + 8.00000i) q^{64} +(1.09757 + 3.01555i) q^{65} +(-4.41902 + 4.51208i) q^{66} +(10.1814 + 12.1337i) q^{67} +(-5.33086 + 0.00137763i) q^{68} +(-9.80609 - 8.05780i) q^{69} +(1.63434 - 1.63476i) q^{70} +(-7.02717 - 12.1714i) q^{71} +(6.84717 - 5.01162i) q^{72} +(-2.01151 + 3.48404i) q^{73} +(2.94235 + 10.9753i) q^{74} +(-1.73196 + 0.0178224i) q^{75} +(-0.885151 - 1.53221i) q^{76} +(-4.15038 + 0.731824i) q^{77} +(-3.24763 + 7.15835i) q^{78} +(-2.44445 + 2.91319i) q^{79} +(3.93887 - 0.696629i) q^{80} +(-8.57673 - 2.72757i) q^{81} +(3.42141 + 7.33476i) q^{82} +(6.67412 + 5.60025i) q^{83} +(5.66193 - 0.0597265i) q^{84} +(0.462847 + 2.62494i) q^{85} +(-0.487652 - 5.56561i) q^{86} +(0.116451 + 11.3165i) q^{87} +(-6.61055 - 3.07943i) q^{88} +(-2.17066 - 1.25323i) q^{89} +(-3.06148 - 2.93723i) q^{90} +(-4.54264 + 2.62270i) q^{91} +(5.00891 - 13.7729i) q^{92} +(4.08397 - 4.97006i) q^{93} +(2.83930 - 6.09096i) q^{94} +(-0.677761 + 0.568709i) q^{95} +(8.08700 + 5.53177i) q^{96} +(-14.0166 + 5.10161i) q^{97} +(-5.01454 - 3.51025i) q^{98} +(1.49964 + 7.58822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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