LMFDB - Embedded newform 540.2.be.a.11.27

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)

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")

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);

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			11.27
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.597507 - 1.28179i) q^{2} +(-1.31530 + 1.12693i) q^{3} +(-1.28597 + 1.53176i) q^{4} +(0.342020 - 0.939693i) q^{5} +(2.23040 + 1.01259i) q^{6} +(-1.60972 - 0.283837i) q^{7} +(2.73177 + 0.733110i) q^{8} +(0.460037 - 2.96452i) q^{9} +(-1.40885 + 0.123075i) q^{10} +(2.42284 - 0.881840i) q^{11} +(-0.0347497 - 3.46393i) q^{12} +(-2.45829 + 2.06275i) q^{13} +(0.597998 + 2.23291i) q^{14} +(0.609113 + 1.62141i) q^{15} +(-0.692557 - 3.93959i) q^{16} +(-2.30833 + 1.33272i) q^{17} +(-4.07476 + 1.18165i) q^{18} +(0.766220 + 0.442377i) q^{19} +(0.999552 + 1.73231i) q^{20} +(2.43713 - 1.44072i) q^{21} +(-2.57800 - 2.57866i) q^{22} +(1.27245 + 7.21642i) q^{23} +(-4.41926 + 2.11426i) 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} +(1.71436 - 1.74956i) q^{30} +(-3.65753 + 0.644921i) q^{31} +(-4.63592 + 3.24164i) q^{32} +(-2.19298 + 3.89026i) q^{33} +(3.08751 + 2.16249i) q^{34} +(-0.817275 + 1.41556i) q^{35} +(3.94933 + 4.51695i) q^{36} +(4.01739 + 6.95832i) q^{37} +(0.109213 - 1.24646i) q^{38} +(0.908810 - 5.48348i) q^{39} +(1.62322 - 2.31628i) q^{40} +(3.67865 + 4.38405i) q^{41} +(-3.30290 - 2.26305i) q^{42} +(1.35117 + 3.71231i) q^{43} +(-1.76493 + 4.84522i) q^{44} +(-2.62839 - 1.44622i) q^{45} +(8.48964 - 5.94287i) q^{46} +(-0.825162 + 4.67973i) q^{47} +(5.35058 + 4.40128i) q^{48} +(-4.06722 - 1.48035i) q^{49} +(-0.366202 + 1.36598i) q^{50} +(1.53427 - 4.35426i) q^{51} +(0.00165861 - 6.41815i) q^{52} +0.903877i q^{53} +(4.02790 - 6.14622i) q^{54} -2.57833i q^{55} +(-4.18929 - 1.95547i) q^{56} +(-1.50634 + 0.281620i) q^{57} +(8.92522 + 2.39274i) q^{58} +(4.65700 + 1.69501i) q^{59} +(-3.26691 - 1.15208i) q^{60} +(0.652414 - 3.70002i) q^{61} +(3.01205 + 4.30284i) q^{62} +(-1.58197 + 4.64146i) q^{63} +(6.92510 + 4.00537i) q^{64} +(1.09757 + 3.01555i) q^{65} +(6.29682 + 0.486486i) q^{66} +(-10.1814 - 12.1337i) q^{67} +(0.927051 - 5.24964i) q^{68} +(-9.80609 - 8.05780i) q^{69} +(2.30278 + 0.201767i) q^{70} +(7.02717 + 12.1714i) q^{71} +(3.43003 - 7.76111i) q^{72} +(-2.01151 + 3.48404i) q^{73} +(6.51869 - 9.30709i) q^{74} +(1.73196 - 0.0178224i) q^{75} +(-1.66295 + 0.604778i) q^{76} +(-4.15038 + 0.731824i) q^{77} +(-7.57169 + 2.11151i) 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} +(-0.927252 + 5.58581i) q^{84} +(0.462847 + 2.62494i) q^{85} +(3.95107 - 3.95004i) q^{86} +(-0.116451 - 11.3165i) q^{87} +(7.26511 - 0.632777i) q^{88} +(-2.17066 - 1.25323i) q^{89} +(-0.283264 + 4.23317i) q^{90} +(4.54264 - 2.62270i) q^{91} +(-12.6901 - 7.33102i) q^{92} +(4.08397 - 4.97006i) q^{93} +(6.49147 - 1.73848i) q^{94} +(0.677761 - 0.568709i) q^{95} +(2.44451 - 9.48812i) q^{96} +(-14.0166 + 5.10161i) q^{97} +(0.532698 + 6.09784i) 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 $

$2$	−0.597507	−	1.28179i	−0.422501	−	0.906362i
$2$	−0.597507	−	1.28179i	−0.422501	−	0.906362i
$3$	−1.31530	+	1.12693i	−0.759390	+	0.650636i
$3$	−1.31530	+	1.12693i	−0.759390	+	0.650636i
$4$	−1.28597	+	1.53176i	−0.642986	+	0.765878i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$	2.23040	+	1.01259i	0.910555	+	0.413388i
$7$	−1.60972	−	0.283837i	−0.608416	−	0.107280i	−0.139052	−	0.990285i	$-0.544406\pi$
$7$	−1.60972	−	0.283837i	−0.608416	−	0.107280i	−0.469364	+	0.883005i	$0.655517\pi$
$8$	2.73177	+	0.733110i	0.965825	+	0.259193i
$9$	0.460037	−	2.96452i	0.153346	−	0.988173i
$10$	−1.40885	+	0.123075i	−0.445517	+	0.0389197i
$11$	2.42284	−	0.881840i	0.730513	−	0.265885i	0.0501308	−	0.998743i	$-0.484036\pi$
$11$	2.42284	−	0.881840i	0.730513	−	0.265885i	0.680382	+	0.732858i	$0.261814\pi$
$12$	−0.0347497	−	3.46393i	−0.0100314	−	0.999950i
$13$	−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	$0.424581\pi$
$14$	0.597998	+	2.23291i	0.159822	+	0.596771i
$15$	0.609113	+	1.62141i	0.157272	+	0.418647i
$16$	−0.692557	−	3.93959i	−0.173139	−	0.984897i
$17$	−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	$0.438102\pi$
$18$	−4.07476	+	1.18165i	−0.960431	+	0.278517i
$19$	0.766220	+	0.442377i	0.175783	+	0.101488i	0.585310	−	0.810810i	$-0.300973\pi$
$19$	0.766220	+	0.442377i	0.175783	+	0.101488i	−0.409527	+	0.912298i	$0.634306\pi$
$20$	0.999552	+	1.73231i	0.223507	+	0.387356i
$21$	2.43713	−	1.44072i	0.531825	−	0.314390i
$22$	−2.57800	−	2.57866i	−0.549630	−	0.549773i
$23$	1.27245	+	7.21642i	0.265324	+	1.50473i	0.768111	+	0.640317i	$0.221197\pi$
$23$	1.27245	+	7.21642i	0.265324	+	1.50473i	−0.502787	+	0.864410i	$0.667692\pi$
$24$	−4.41926	+	2.11426i	−0.902079	+	0.431572i
$25$	−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	$0.429714\pi$
$30$	1.71436	−	1.74956i	0.312998	−	0.319425i
$31$	−3.65753	+	0.644921i	−0.656911	+	0.115831i	−0.492161	−	0.870504i	$-0.663793\pi$
$31$	−3.65753	+	0.644921i	−0.656911	+	0.115831i	−0.164750	+	0.986335i	$0.552682\pi$
$32$	−4.63592	+	3.24164i	−0.819522	+	0.573047i
$33$	−2.19298	+	3.89026i	−0.381750	+	0.677208i
$34$	3.08751	+	2.16249i	0.529503	+	0.370864i
$35$	−0.817275	+	1.41556i	−0.138145	+	0.239274i
$36$	3.94933	+	4.51695i	0.658221	+	0.752825i
$37$	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	$0.603697\pi$
$38$	0.109213	−	1.24646i	0.0177167	−	0.202202i
$39$	0.908810	−	5.48348i	0.145526	−	0.878060i
$40$	1.62322	−	2.31628i	0.256653	−	0.366236i
$41$	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	$0.630310\pi$
$42$	−3.30290	−	2.26305i	−0.509648	−	0.349196i
$43$	1.35117	+	3.71231i	0.206051	+	0.566122i	0.999072	−	0.0430734i	$-0.0137149\pi$
$43$	1.35117	+	3.71231i	0.206051	+	0.566122i	−0.793021	+	0.609195i	$0.791493\pi$
$44$	−1.76493	+	4.84522i	−0.266074	+	0.730444i
$45$	−2.62839	−	1.44622i	−0.391818	−	0.215589i
$46$	8.48964	−	5.94287i	1.25173	−	0.876229i
$47$	−0.825162	+	4.67973i	−0.120362	+	0.682608i	0.863593	+	0.504190i	$0.168209\pi$
$47$	−0.825162	+	4.67973i	−0.120362	+	0.682608i	−0.983955	+	0.178418i	$0.942902\pi$
$48$	5.35058	+	4.40128i	0.772290	+	0.635270i
$49$	−4.06722	−	1.48035i	−0.581032	−	0.211478i
$50$	−0.366202	+	1.36598i	−0.0517888	+	0.193178i
$51$	1.53427	−	4.35426i	0.214841	−	0.609719i
$52$	0.00165861	−	6.41815i	0.000230008	−	0.890038i
$53$			0.903877i			0.124157i	0.998071	+	0.0620785i	$0.0197729\pi$
$53$			0.903877i			0.124157i	−0.998071	+	0.0620785i	$0.980227\pi$
$54$	4.02790	−	6.14622i	0.548128	−	0.836394i
$55$		−	2.57833i		−	0.347662i
$56$	−4.18929	−	1.95547i	−0.559817	−	0.261311i
$57$	−1.50634	+	0.281620i	−0.199520	+	0.0373015i
$58$	8.92522	+	2.39274i	1.17194	+	0.314182i
$59$	4.65700	+	1.69501i	0.606290	+	0.220672i	0.626879	−	0.779117i	$-0.284332\pi$
$59$	4.65700	+	1.69501i	0.606290	+	0.220672i	−0.0205892	+	0.999788i	$0.506554\pi$
$60$	−3.26691	−	1.15208i	−0.421757	−	0.148733i
$61$	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	$-0.0217637\pi$
$62$	3.01205	+	4.30284i	0.382531	+	0.546461i
$63$	−1.58197	+	4.64146i	−0.199309	+	0.584769i
$64$	6.92510	+	4.00537i	0.865638	+	0.500671i
$65$	1.09757	+	3.01555i	0.136137	+	0.374032i
$66$	6.29682	+	0.486486i	0.775086	+	0.0598822i
$67$	−10.1814	−	12.1337i	−1.24386	−	1.48237i	−0.815493	−	0.578767i	$-0.803534\pi$
$67$	−10.1814	−	12.1337i	−1.24386	−	1.48237i	−0.428365	−	0.903606i	$-0.640910\pi$
$68$	0.927051	−	5.24964i	0.112421	−	0.636612i
$69$	−9.80609	−	8.05780i	−1.18051	−	0.970045i
$70$	2.30278	+	0.201767i	0.275235	+	0.0241158i
$71$	7.02717	+	12.1714i	0.833972	+	1.44448i	0.894865	+	0.446337i	$0.147272\pi$
$71$	7.02717	+	12.1714i	0.833972	+	1.44448i	−0.0608930	+	0.998144i	$0.519395\pi$
$72$	3.43003	−	7.76111i	0.404233	−	0.914656i
$73$	−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	$0.242316\pi$
$74$	6.51869	−	9.30709i	0.757782	−	1.08193i
$75$	1.73196	−	0.0178224i	0.199989	−	0.00205796i
$76$	−1.66295	+	0.604778i	−0.190754	+	0.0693728i
$77$	−4.15038	+	0.731824i	−0.472980	+	0.0833991i
$78$	−7.57169	+	2.11151i	−0.857325	+	0.239082i
$79$	2.44445	−	2.91319i	0.275023	−	0.327759i	−0.610799	−	0.791786i	$-0.709151\pi$
$79$	2.44445	−	2.91319i	0.275023	−	0.327759i	0.885821	+	0.464027i	$0.153596\pi$
$80$	−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	0.198254	−	0.980151i	$-0.436473\pi$
$83$	−6.67412	−	5.60025i	−0.732579	−	0.614707i	−0.930833	+	0.365444i	$0.880917\pi$
$84$	−0.927252	+	5.58581i	−0.101171	+	0.609461i
$85$	0.462847	+	2.62494i	0.0502028	+	0.284714i
$86$	3.95107	−	3.95004i	0.426054	−	0.425944i
$87$	−0.116451	−	11.3165i	−0.0124848	−	1.21326i
$88$	7.26511	−	0.632777i	0.774463	−	0.0674543i
$89$	−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	$0.709077\pi$
$90$	−0.283264	+	4.23317i	−0.0298587	+	0.446216i
$91$	4.54264	−	2.62270i	0.476199	−	0.274933i
$92$	−12.6901	−	7.33102i	−1.32304	−	0.764312i
$93$	4.08397	−	4.97006i	0.423488	−	0.515371i
$94$	6.49147	−	1.73848i	0.669544	−	0.179311i
$95$	0.677761	−	0.568709i	0.0695368	−	0.0583483i
$96$	2.44451	−	9.48812i	0.249492	−	0.968377i
$97$	−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	$0.662347\pi$
$98$	0.532698	+	6.09784i	0.0538106	+	0.615975i
$99$	−1.49964	−	7.58822i	−0.150719	−	0.762645i
$100$	1.96971	−	0.346787i	0.196971	−	0.0346787i
$101$	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	$0.460780\pi$
$102$	−6.49798	+	0.635091i	−0.643396	+	0.0628834i
$103$	−2.88550	+	7.92785i	−0.284317	+	0.781154i	0.712518	+	0.701654i	$0.247555\pi$
$103$	−2.88550	+	7.92785i	−0.284317	+	0.781154i	−0.996835	+	0.0795005i	$0.974667\pi$
$104$	−8.22771	+	3.83276i	−0.806794	+	0.375833i
$105$	−0.520282	−	2.78291i	−0.0507744	−	0.271584i
$106$	1.15858	−	0.540073i	0.112531	−	0.0524565i
$107$	9.38211			0.907003			0.453502	−	0.891255i	$-0.350175\pi$
$107$	9.38211			0.907003			0.453502	+	0.891255i	$0.350175\pi$
$108$	−10.2849	−	1.49052i	−0.989661	−	0.143425i
$109$	16.6485			1.59464			0.797319	−	0.603558i	$-0.206251\pi$
$109$	16.6485			1.59464			0.797319	+	0.603558i	$0.206251\pi$
$110$	−3.30488	+	1.54057i	−0.315108	+	0.146887i
$111$	−13.1256	−	4.62496i	−1.24583	−	0.438981i
$112$	−0.00337927	+	6.53820i	−0.000319311	+	0.617802i
$113$	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	$-0.208021\pi$
$114$	1.26103	+	1.76254i	0.118106	+	0.165077i
$115$	7.21642	+	1.27245i	0.672935	+	0.118657i
$116$	−2.26589	−	12.8699i	−0.210382	−	1.19494i
$117$	4.98417	+	8.23660i	0.460786	+	0.761474i
$118$	−0.609944	−	6.98208i	−0.0561499	−	0.642752i
$119$	4.09403	−	1.49011i	0.375299	−	0.136598i
$120$	0.475279	+	4.87587i	0.0433869	+	0.445104i
$121$	−3.33400	+	2.79755i	−0.303090	+	0.254323i
$122$	−5.13248	+	1.37453i	−0.464673	+	0.124444i
$123$	−9.77907	−	1.62074i	−0.881749	−	0.146137i
$124$	3.71561	−	6.43179i	0.333672	−	0.577592i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	6.89461	−	0.745554i	0.614221	−	0.0664192i
$127$	−1.33068	−	0.768267i	−0.118079	−	0.0681727i	0.439797	−	0.898097i	$-0.355050\pi$
$127$	−1.33068	−	0.768267i	−0.118079	−	0.0681727i	−0.557876	+	0.829924i	$0.688384\pi$
$128$	0.996248	−	11.2698i	0.0880568	−	0.996115i
$129$	−5.96072	−	3.36012i	−0.524812	−	0.295842i
$130$	3.20949	−	3.20866i	0.281491	−	0.281418i
$131$	1.35023	+	7.65753i	0.117970	+	0.669042i	0.985237	+	0.171198i	$0.0547637\pi$
$131$	1.35023	+	7.65753i	0.117970	+	0.669042i	−0.867267	+	0.497844i	$0.834125\pi$
$132$	−3.13882	−	8.36189i	−0.273200	−	0.727809i
$133$	−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	$0.911077\pi$
$138$	−4.46920	+	17.3839i	−0.380444	+	1.47982i
$139$	−19.5792	+	3.45234i	−1.66069	+	0.292824i	−0.923709	−	0.383094i	$-0.874858\pi$
$139$	−19.5792	+	3.45234i	−1.66069	+	0.292824i	−0.736977	+	0.675918i	$0.763747\pi$
$140$	−1.11730	−	3.07224i	−0.0944294	−	0.259651i
$141$	−4.18841	−	7.08516i	−0.352728	−	0.596678i
$142$	11.4024	−	16.2799i	0.956870	−	1.36618i
$143$	−4.13703	+	7.16554i	−0.345956	+	0.599213i
$144$	−11.9976	+	0.240741i	−0.999799	+	0.0200617i
$145$	3.26697	+	5.65856i	0.271307	+	0.469918i
$146$	5.66770	+	0.496597i	0.469062	+	0.0410987i
$147$	7.01788	−	2.63639i	0.578825	−	0.217446i
$148$	−15.8247	−	2.79454i	−1.30078	−	0.229710i
$149$	−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	$0.902215\pi$
$150$	−1.05770	−	2.20936i	−0.0863610	−	0.180393i
$151$	1.06670	+	2.93074i	0.0868069	+	0.238500i	0.975499	−	0.220005i	$-0.0706073\pi$
$151$	1.06670	+	2.93074i	0.0868069	+	0.238500i	−0.888692	+	0.458505i	$0.848385\pi$
$152$	1.76882	+	1.77019i	0.143470	+	0.143582i
$153$	2.88894	+	7.45619i	0.233557	+	0.602797i
$154$	3.41792	+	4.88265i	0.275424	+	0.393455i
$155$	−0.644921	+	3.65753i	−0.0518013	+	0.293780i
$156$	7.23066	+	8.44367i	0.578916	+	0.676035i
$157$	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	$0.541479\pi$
$158$	−5.19467	−	1.39263i	−0.413266	−	0.110791i
$159$	−1.01861	−	1.18887i	−0.0807811	−	0.0942836i
$160$	1.46057	+	5.46505i	0.115468	+	0.432050i
$161$		−	11.9776i		−	0.943964i
$162$	1.62848	+	12.6233i	0.127945	+	0.991781i
$163$		−	18.6426i		−	1.46020i	−0.683338	−	0.730102i	$-0.739472\pi$
$163$		−	18.6426i		−	1.46020i	0.683338	−	0.730102i	$-0.260528\pi$
$164$	−11.4459	−	0.00295791i	−0.893777	−	0.000230974i
$165$	2.90561	+	3.39128i	0.226201	+	0.264011i
$166$	−3.19051	+	11.9010i	−0.247632	+	0.923697i
$167$	5.19275	+	1.89001i	0.401827	+	0.146253i	0.535025	−	0.844836i	$-0.320302\pi$
$167$	5.19275	+	1.89001i	0.401827	+	0.146253i	−0.133198	+	0.991089i	$0.542525\pi$
$168$	7.71387	−	2.14902i	0.595138	−	0.165800i
$169$	−0.469168	+	2.66078i	−0.0360898	+	0.204676i
$170$	3.08806	−	2.16169i	0.236844	−	0.165794i
$171$	1.66392	−	2.06796i	0.127243	−	0.158141i
$172$	−7.42392	−	2.70426i	−0.566068	−	0.206198i
$173$	−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	$-0.357776\pi$
$174$	−14.4358	+	6.91096i	−1.09438	+	0.523919i
$175$	1.05067	+	1.25214i	0.0794231	+	0.0946527i
$176$	−5.15204	−	8.93426i	−0.388350	−	0.673445i
$177$	−8.03553	+	3.01869i	−0.603987	+	0.226898i
$178$	−0.309394	+	3.53114i	−0.0231901	+	0.264670i
$179$	−3.19139	−	5.52764i	−0.238535	−	0.413155i	0.721759	−	0.692145i	$-0.243334\pi$
$179$	−3.19139	−	5.52764i	−0.238535	−	0.413155i	−0.960294	+	0.278989i	$0.910001\pi$
$180$	5.59529	−	2.16627i	0.417048	−	0.161464i
$181$	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	$-0.0779404\pi$
$182$	−6.07601	−	4.25564i	−0.450384	−	0.315449i
$183$	3.31156	+	5.60188i	0.244798	+	0.414103i
$184$	−1.81439	+	20.6464i	−0.133759	+	1.52207i
$185$	7.91271	−	1.39522i	0.581754	−	0.102579i
$186$	−8.81077	−	2.26515i	−0.646037	−	0.166088i
$187$	−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	0.979078	−	0.203486i	$-0.0652270\pi$
$191$	13.1113	+	11.0017i	0.948699	+	0.796053i	−0.0303792	+	0.999538i	$0.509671\pi$
$192$	−13.6224	+	2.53587i	−0.983111	+	0.183010i
$193$	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	$0.918003\pi$
$194$	14.9142	+	14.9180i	1.07078	+	1.07105i
$195$	−4.84196	−	2.72946i	−0.346740	−	0.195461i
$196$	7.49786	−	4.32631i	0.535562	−	0.309022i
$197$	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	$0.400884\pi$
$198$	−8.83046	+	6.45623i	−0.627554	+	0.458825i
$199$	−9.81898	+	5.66899i	−0.696049	+	0.401864i	−0.805874	−	0.592087i	$-0.798304\pi$
$199$	−9.81898	+	5.66899i	−0.696049	+	0.401864i	0.109825	+	0.993951i	$0.464971\pi$
$200$	−1.62142	−	2.31754i	−0.114652	−	0.163875i
$201$	27.0656	+	4.48574i	1.90906	+	0.316400i
$202$	−2.15725	−	8.05514i	−0.151784	−	0.566758i
$203$	8.18139	−	6.86500i	0.574221	−	0.481829i
$204$	4.69664	+	7.94958i	0.328831	+	0.556582i
$205$	5.37783	−	1.95737i	0.375604	−	0.136709i
$206$	11.8859	−	1.03834i	0.828133	−	0.0723444i
$207$	21.9786	−	0.452382i	1.52762	−	0.0314427i
$208$	9.82891	+	8.25610i	0.681513	+	0.572457i
$209$	2.24653	+	0.396124i	0.155396	+	0.0274005i
$210$	−3.25623	+	2.32970i	−0.224701	+	0.160764i
$211$	−1.18353	+	3.25171i	−0.0814773	+	0.223857i	−0.973741	−	0.227657i	$-0.926894\pi$
$211$	−1.18353	+	3.25171i	−0.0814773	+	0.223857i	0.892264	+	0.451514i	$0.149116\pi$
$212$	−1.38452	−	1.16236i	−0.0950892	−	0.0798312i
$213$	−22.9592	−	8.08992i	−1.57314	−	0.554312i
$214$	−5.60588	−	12.0259i	−0.383210	−	0.822074i
$215$	3.95055			0.269426
$216$	4.23474	+	14.0736i	0.288138	+	0.957589i
$217$	6.07064			0.412102
$218$	−9.94760	−	21.3399i	−0.673736	−	1.44532i
$219$	−1.28054	−	6.84940i	−0.0865309	−	0.462840i
$220$	3.94937	+	3.31566i	0.266267	+	0.223541i
$221$	2.92549	−	8.03773i	0.196790	−	0.540676i
$222$	1.91444	+	19.5878i	0.128489	+	1.31464i
$223$	−5.32012	−	0.938081i	−0.356262	−	0.0628186i	−0.00734698	−	0.999973i	$-0.502339\pi$
$223$	−5.32012	−	0.938081i	−0.356262	−	0.0628186i	−0.348915	+	0.937154i	$0.613450\pi$
$224$	8.38262	−	3.90229i	0.560087	−	0.260732i
$225$	−2.25796	+	1.97525i	−0.150531	+	0.131683i
$226$	−25.2459	+	2.20544i	−1.67933	+	0.146704i
$227$	9.97850	−	3.63188i	0.662296	−	0.241056i	0.0110688	−	0.999939i	$-0.496477\pi$
$227$	9.97850	−	3.63188i	0.662296	−	0.241056i	0.651227	+	0.758883i	$0.274254\pi$
$228$	1.50574	−	2.66950i	0.0997199	−	0.176792i
$229$	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	$-0.0288390\pi$
$230$	−2.68085	−	10.0102i	−0.176770	−	0.660055i
$231$	4.63428	−	5.63978i	0.304913	−	0.371070i
$232$	−15.1427	+	10.5943i	−0.994165	+	0.695548i
$233$	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	$0.0345813\pi$
$234$	7.57952	−	11.3101i	0.495489	−	0.739363i
$235$	4.11528	+	2.37596i	0.268451	+	0.154991i
$236$	−8.58511	+	4.95366i	−0.558843	+	0.322456i
$237$	0.0677769	+	6.58646i	0.00440258	+	0.427836i
$238$	−4.35622	−	4.35734i	−0.282372	−	0.282445i
$239$	−0.439066	−	2.49007i	−0.0284008	−	0.161069i	0.967309	−	0.253601i	$-0.0816151\pi$
$239$	−0.439066	−	2.49007i	−0.0284008	−	0.161069i	−0.995710	+	0.0925320i	$0.970504\pi$
$240$	5.96586	−	3.52257i	0.385095	−	0.227381i
$241$	−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
$246$	3.76561	+	13.5031i	0.240086	+	0.860927i
$247$	−2.79611	+	0.493030i	−0.177912	+	0.0313707i
$248$	−10.4643	−	0.919596i	−0.664484	−	0.0583944i
$249$	15.0896	−	0.155277i	0.956264	−	0.00984027i
$250$	1.15835	+	0.811309i	0.0732606	+	0.0513117i
$251$	−12.5905	+	21.8074i	−0.794704	+	1.37647i	0.128322	+	0.991733i	$0.459041\pi$
$251$	−12.5905	+	21.8074i	−0.794704	+	1.37647i	−0.923027	+	0.384736i	$0.874293\pi$
$252$	−5.07522	−	8.39197i	−0.319709	−	0.528645i
$253$	9.44667	+	16.3621i	0.593907	+	1.02868i
$254$	−0.189668	+	2.16469i	−0.0119008	+	0.135825i
$255$	−3.56692	−	2.93099i	−0.223369	−	0.183545i
$256$	−15.0407	+	5.45678i	−0.940046	+	0.341049i
$257$	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	$0.696789\pi$
$258$	−0.745401	+	9.64809i	−0.0464066	+	0.600664i
$259$	−4.49183	−	12.3412i	−0.279109	−	0.766845i
$260$	−6.03052	−	2.19670i	−0.373997	−	0.136233i
$261$	12.9061	+	14.7534i	0.798870	+	0.913213i
$262$	9.00858	−	6.30614i	0.556552	−	0.389595i
$263$	2.63157	−	14.9243i	0.162269	−	0.920275i	−0.789566	−	0.613665i	$-0.789694\pi$
$263$	2.63157	−	14.9243i	0.162269	−	0.920275i	0.951835	−	0.306609i	$-0.0991945\pi$
$264$	−8.84271	+	9.01960i	−0.544231	+	0.555118i
$265$	0.849367	+	0.309144i	0.0521762	+	0.0189906i
$266$	−0.529592	+	1.97544i	−0.0324714	+	0.121122i
$267$	4.26738	−	0.797814i	0.261159	−	0.0488254i
$268$	31.6790	+	0.00818663i	1.93510	+	0.000500078i
$269$		−	11.8299i		−	0.721283i	−0.932704	−	0.360642i	$-0.882558\pi$
$269$		−	11.8299i		−	0.721283i	0.932704	−	0.360642i	$-0.117442\pi$
$270$	−4.39793	−	5.88712i	−0.267650	−	0.358279i
$271$			7.57692i			0.460265i	0.973159	+	0.230133i	$0.0739160\pi$
$271$			7.57692i			0.460265i	−0.973159	+	0.230133i	$0.926084\pi$
$272$	6.84900	+	8.17090i	0.415282	+	0.495433i
$273$	−3.01934	+	8.56890i	−0.182739	+	0.518613i
$274$	26.5118	+	7.10749i	1.60164	+	0.429379i
$275$	−2.42284	−	0.881840i	−0.146103	−	0.0531770i
$276$	24.9529	−	4.65844i	1.50199	−	0.280405i
$277$	−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	$0.745557\pi$
$278$	16.1239	+	23.0336i	0.967046	+	1.38147i
$279$	0.229283	+	11.1395i	0.0137268	+	0.666904i
$280$	−3.27037	+	3.26783i	−0.195442	+	0.195290i
$281$	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	$0.775754\pi$
$282$	−6.57908	+	9.60209i	−0.391778	+	0.571796i
$283$	−10.7544	−	12.8166i	−0.639283	−	0.761868i	0.344974	−	0.938612i	$-0.387888\pi$
$283$	−10.7544	−	12.8166i	−0.639283	−	0.761868i	−0.984257	+	0.176744i	$0.943443\pi$
$284$	−27.6804	−	4.88818i	−1.64253	−	0.290060i
$285$	−0.250562	+	1.51182i	−0.0148420	+	0.0895523i
$286$	11.6566	+	1.02134i	0.689270	+	0.0603931i
$287$	−4.67724	−	8.10121i	−0.276088	−	0.478199i
$288$	7.47722	+	15.2345i	0.440599	+	0.897704i
$289$	−4.94774	+	8.56973i	−0.291043	+	0.504102i
$290$	5.30105	−	7.56860i	0.311288	−	0.444443i
$291$	12.6868	−	22.5059i	0.743715	−	1.31932i
$292$	−2.74995	−	7.56152i	−0.160929	−	0.442504i
$293$	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	$0.178804\pi$
$294$	−7.57253	−	7.42019i	−0.441639	−	0.432754i
$295$	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
$300$	−2.19995	+	2.67586i	−0.127014	+	0.154491i
$301$	−1.12131	−	6.35928i	−0.0646313	−	0.366543i
$302$	3.11923	−	3.11842i	0.179491	−	0.179445i
$303$	−8.79184	+	5.19732i	−0.505078	+	0.298578i
$304$	1.21213	−	3.32496i	0.0695207	−	0.190700i
$305$	−3.25375	−	1.87855i	−0.186309	−	0.107566i
$306$	7.83110	−	8.15814i	0.447674	−	0.466370i
$307$	−19.4402	+	11.2238i	−1.10951	+	0.640577i	−0.938703	−	0.344727i	$-0.887972\pi$
$307$	−19.4402	+	11.2238i	−1.10951	+	0.640577i	−0.170809	+	0.985304i	$0.554638\pi$
$308$	4.21629	−	7.29848i	0.240246	−	0.415869i
$309$	−5.13887	−	13.6793i	−0.292340	−	0.778188i
$310$	5.07353	−	1.35874i	0.288157	−	0.0771715i
$311$	−6.28107	+	5.27044i	−0.356167	+	0.298859i	−0.803261	−	0.595628i	$-0.796903\pi$
$311$	−6.28107	+	5.27044i	−0.356167	+	0.298859i	0.447094	+	0.894487i	$0.352459\pi$
$312$	6.50265	−	14.3133i	0.368140	−	0.810333i
$313$	−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	$0.489397\pi$
$314$	−0.669325	−	7.66182i	−0.0377722	−	0.432382i
$315$	3.82048	+	3.07404i	0.215260	+	0.173202i
$316$	1.31880	+	7.49058i	0.0741881	+	0.421378i
$317$	−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	$0.588246\pi$
$318$	−0.915256	+	2.01600i	−0.0513250	+	0.113052i
$319$	−5.76189	+	15.8307i	−0.322604	+	0.886347i
$320$	6.13234	−	5.13755i	0.342808	−	0.287198i
$321$	−12.3403	+	10.5730i	−0.688769	+	0.590129i
$322$	−15.3527	+	7.15668i	−0.855574	+	0.398826i
$323$	−2.35825			−0.131217
$324$	15.2074	−	9.62989i	0.844856	−	0.534994i
$325$	3.20908			0.178008
$326$	−23.8959	+	11.1391i	−1.32347	+	0.616938i
$327$	−21.8978	+	18.7618i	−1.21095	+	1.03753i
$328$	6.83523	+	14.6730i	0.377412	+	0.810183i
$329$	2.65656	−	7.29883i	0.146461	−	0.402397i
$330$	2.61079	−	5.75069i	0.143719	−	0.316565i
$331$	−2.12995	−	0.375567i	−0.117072	−	0.0206430i	0.114805	−	0.993388i	$-0.463376\pi$
$331$	−2.12995	−	0.375567i	−0.117072	−	0.0206430i	−0.231877	+	0.972745i	$0.574487\pi$
$332$	17.1609	−	3.02136i	0.941829	−	0.165819i
$333$	22.4762	−	8.70854i	1.23169	−	0.477225i
$334$	−0.680112	−	7.78531i	−0.0372141	−	0.425993i
$335$	−14.8842	+	5.41742i	−0.813213	+	0.295985i
$336$	−7.36368	−	8.60351i	−0.401721	−	0.469360i
$337$	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	$0.146844\pi$
$338$	3.69090	−	0.988462i	0.200758	−	0.0537652i
$339$	10.9150	+	29.0550i	0.592823	+	1.57805i
$340$	−4.61597	−	2.66662i	−0.250336	−	0.144618i
$341$	−8.29287	+	4.78789i	−0.449084	+	0.259279i
$342$	−3.64490	−	0.897180i	−0.197094	−	0.0485139i
$343$	16.0358	+	9.25829i	0.865853	+	0.499901i
$344$	0.969551	+	11.1317i	0.0522747	+	0.600182i
$345$	−10.9257	+	6.45878i	−0.588222	+	0.347729i
$346$	−18.4076	+	18.4028i	−0.989597	+	0.989341i
$347$	−5.96877	−	33.8506i	−0.320421	−	1.81720i	−0.540074	−	0.841617i	$-0.681604\pi$
$347$	−5.96877	−	33.8506i	−0.320421	−	1.81720i	0.219654	−	0.975578i	$-0.429507\pi$
$348$	17.4839	+	14.3743i	0.937236	+	0.770546i
$349$	−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	$0.403136\pi$
$354$	8.67061	+	8.49617i	0.460837	+	0.451566i
$355$	13.8408	−	2.44051i	0.734595	−	0.129529i
$356$	4.71105	−	1.71330i	0.249685	−	0.0908048i
$357$	−3.70564	+	6.57365i	−0.196123	+	0.347914i
$358$	−5.17840	+	7.39349i	−0.273687	+	0.390758i
$359$	−11.7376	+	20.3301i	−0.619485	+	1.07298i	0.370095	+	0.928994i	$0.379325\pi$
$359$	−11.7376	+	20.3301i	−0.619485	+	1.07298i	−0.989580	+	0.143985i	$0.954008\pi$
$360$	−6.11992	−	5.87763i	−0.322548	−	0.309778i
$361$	−9.10860	−	15.7766i	−0.479400	−	0.830346i
$362$	−26.3466	−	2.30846i	−1.38475	−	0.121330i
$363$	1.23255	−	7.43682i	0.0646920	−	0.390332i
$364$	−1.82438	+	10.3309i	−0.0956233	+	0.541488i
$365$	2.58595	+	3.08181i	0.135355	+	0.161309i
$366$	5.20175	−	7.59189i	0.271900	−	0.396834i
$367$	10.2341	+	28.1179i	0.534215	+	1.46774i	0.854010	+	0.520257i	$0.174164\pi$
$367$	10.2341	+	28.1179i	0.534215	+	1.46774i	−0.319794	+	0.947487i	$0.603614\pi$
$368$	27.5485	−	10.0107i	1.43606	−	0.521844i
$369$	14.6889	−	8.88860i	0.764673	−	0.462722i
$370$	−6.51628	−	9.30878i	−0.338765	−	0.483940i
$371$	0.256553	−	1.45499i	0.0133196	−	0.0755392i
$372$	2.36106	+	12.6470i	0.122415	+	0.655716i
$373$	−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	$0.805229\pi$
$374$	9.38749	+	2.51667i	0.485416	+	0.130134i
$375$	0.575617	−	1.63360i	0.0297247	−	0.0843590i
$376$	−5.68490	+	12.1790i	−0.293177	+	0.628083i
$377$		−	20.9679i		−	1.07990i
$378$	−8.22831	+	8.75041i	−0.423218	+	0.450072i
$379$			17.8548i			0.917139i	0.888659	+	0.458569i	$0.151638\pi$
$379$			17.8548i			0.917139i	−0.888659	+	0.458569i	$0.848362\pi$
$380$	−0.000457285		1.76951i	−2.34582e−5		0.0907739i
$381$	2.61603	−	0.489084i	0.134023	−	0.0250565i
$382$	6.26775	−	23.3795i	0.320686	−	1.19620i
$383$	−31.7118	−	11.5422i	−1.62040	−	0.589777i	−0.636940	−	0.770914i	$-0.719800\pi$
$383$	−31.7118	−	11.5422i	−1.62040	−	0.589777i	−0.983458	+	0.181137i	$0.942022\pi$
$384$	11.3899	+	15.9458i	0.581239	+	0.813733i
$385$	−0.731824	+	4.15038i	−0.0372972	+	0.211523i
$386$	2.67090	−	1.86967i	0.135945	−	0.0951637i
$387$	11.6268	−	2.29777i	0.591023	−	0.116802i
$388$	10.2105	−	28.0305i	0.518358	−	1.42303i
$389$	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	$0.663169\pi$
$390$	−0.605497	+	7.83724i	−0.0306605	+	0.396854i
$391$	−12.5547	−	14.9621i	−0.634917	−	0.756665i
$392$	−10.0254	−	7.02569i	−0.506361	−	0.354851i
$393$	−10.4055	−	8.55035i	−0.524888	−	0.431308i
$394$	2.56861	−	29.3158i	0.129405	−	1.47691i
$395$	−1.90145	−	3.29340i	−0.0956722	−	0.165709i
$396$	13.5518	+	7.46115i	0.681003	+	0.374937i
$397$	−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	$0.284524\pi$
$398$	13.1334	+	9.19861i	0.658316	+	0.461085i
$399$	2.50472	−	0.0257744i	0.125393	−	0.00129033i
$400$	−2.00179	+	3.46307i	−0.100090	+	0.173153i
$401$	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	$0.350023\pi$
$402$	−10.4221	−	37.3726i	−0.519807	−	1.86398i
$403$	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
$408$	7.38342	−	10.7700i	0.365534	−	0.533196i
$409$	−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	$0.984973\pi$
$410$	−5.72223	−	5.72370i	−0.282601	−	0.282674i
$411$	−0.345910	−	33.6150i	−0.0170625	−	1.65811i
$412$	−8.43287	−	14.6149i	−0.415458	−	0.720023i
$413$	−7.01535	−	4.05031i	−0.345203	−	0.199303i
$414$	−13.7122	−	27.9016i	−0.673918	−	1.37129i
$415$	−7.54519	+	4.35622i	−0.370379	+	0.213838i
$416$	4.70974	−	17.5317i	0.230914	−	0.859561i
$417$	21.8620	−	26.6053i	1.07059	−	1.30287i
$418$	−0.834570	−	3.11627i	−0.0408202	−	0.152422i
$419$	17.6909	−	14.8444i	0.864257	−	0.725198i	−0.0986238	−	0.995125i	$-0.531444\pi$
$419$	17.6909	−	14.8444i	0.864257	−	0.725198i	0.962881	+	0.269927i	$0.0869996\pi$
$420$	4.93180	+	2.78179i	0.240647	+	0.135737i
$421$	−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	$0.467812\pi$
$422$	4.87518	−	0.425888i	0.237320	−	0.0207319i
$423$	13.4935	+	4.59905i	0.656078	+	0.223614i
$424$	−0.662641	+	2.46918i	−0.0321807	+	0.119914i
$425$	2.62494	+	0.462847i	0.127328	+	0.0224514i
$426$	3.34872	+	34.2627i	0.162246	+	1.66003i
$427$	−2.10040	+	5.77081i	−0.101646	+	0.279269i
$428$	−12.0651	+	14.3711i	−0.583190	+	0.694654i
$429$	−2.63366	−	14.0870i	−0.127154	−	0.680127i
$430$	−2.36048	−	5.06378i	−0.113833	−	0.244197i
$431$	−22.1305			−1.06599			−0.532995	−	0.846118i	$-0.678934\pi$
$431$	−22.1305			−1.06599			−0.532995	+	0.846118i	$0.678934\pi$
$432$	15.5091	−	13.8371i	0.746184	−	0.665740i
$433$	13.2571			0.637095			0.318548	−	0.947907i	$-0.396805\pi$
$433$	13.2571			0.637095			0.318548	+	0.947907i	$0.396805\pi$
$434$	−3.62725	−	7.78128i	−0.174113	−	0.373514i
$435$	−10.6739	−	3.76105i	−0.511773	−	0.180329i
$436$	−21.4095	+	25.5015i	−1.02533	+	1.22130i
$437$	−2.21740	+	6.09227i	−0.106073	+	0.291433i
$438$	−8.01436	+	5.73395i	−0.382941	+	0.273979i
$439$	−7.50669	−	1.32363i	−0.358275	−	0.0631735i	−0.00838615	−	0.999965i	$-0.502669\pi$
$439$	−7.50669	−	1.32363i	−0.358275	−	0.0631735i	−0.349889	+	0.936791i	$0.613781\pi$
$440$	1.89020	−	7.04339i	0.0901117	−	0.335781i
$441$	−6.25959	+	11.3763i	−0.298076	+	0.541730i
$442$	−12.0507	+	1.05273i	−0.573192	+	0.0500732i
$443$	11.8766	−	4.32274i	0.564276	−	0.205380i	−0.0441020	−	0.999027i	$-0.514043\pi$
$443$	11.8766	−	4.32274i	0.564276	−	0.205380i	0.608378	+	0.793647i	$0.291820\pi$
$444$	23.9635	−	14.1577i	1.13726	−	0.671897i
$445$	−1.92006	+	1.61112i	−0.0910195	+	0.0763745i
$446$	1.97639	+	7.37979i	0.0935846	+	0.349443i
$447$	15.8958	+	2.63450i	0.751844	+	0.124608i
$448$	−10.0106	−	8.41311i	−0.472956	−	0.397482i
$449$	−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	$0.491713\pi$
$450$	3.88100	+	1.71401i	0.182952	+	0.0807993i
$451$	12.7788	+	7.37784i	0.601730	+	0.347409i
$452$	17.9115	+	31.0422i	0.842487	+	1.46010i
$453$	−4.70578	−	2.65270i	−0.221097	−	0.124635i
$454$	−10.6175	−	10.6203i	−0.498305	−	0.498434i
$455$	−0.910853	−	5.16570i	−0.0427015	−	0.242172i
$456$	−4.32143	−	0.334992i	−0.202369	−	0.0156874i
$457$	−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	$0.909343\pi$
$462$	−9.99802	−	2.57037i	−0.465150	−	0.119585i
$463$	18.6395	−	3.28665i	0.866253	−	0.152744i	0.277174	−	0.960820i	$-0.410602\pi$
$463$	18.6395	−	3.28665i	0.866253	−	0.152744i	0.589078	+	0.808076i	$0.299491\pi$
$464$	22.6275	+	13.0796i	1.05045	+	0.607204i
$465$	−3.27353	−	5.53754i	−0.151806	−	0.256797i
$466$	−28.5275	−	19.9807i	−1.32151	−	0.925586i
$467$	1.35095	−	2.33991i	0.0625143	−	0.108278i	−0.833074	−	0.553161i	$-0.813421\pi$
$467$	1.35095	−	2.33991i	0.0625143	−	0.108278i	0.895589	+	0.444883i	$0.146755\pi$
$468$	−19.0260	−	2.95750i	−0.879475	−	0.136711i
$469$	12.9452	+	22.4218i	0.597754	+	1.03534i
$470$	0.586572	−	6.69458i	0.0270565	−	0.308798i
$471$	−8.81783	+	3.31257i	−0.406304	+	0.152635i
$472$	11.4792	+	8.04447i	0.528374	+	0.370277i
$473$	6.54732	+	7.80280i	0.301046	+	0.358773i
$474$	8.40196	−	4.02233i	0.385915	−	0.184752i
$475$	−0.302604	−	0.831397i	−0.0138844	−	0.0381471i
$476$	−2.98233	+	8.18730i	−0.136695	+	0.375264i
$477$	2.67956	+	0.415817i	0.122689	+	0.0190389i
$478$	−2.92940	+	2.05062i	−0.133988	+	0.0937933i
$479$	−3.97037	+	22.5171i	−0.181411	+	1.02883i	0.749070	+	0.662491i	$0.230501\pi$
$479$	−3.97037	+	22.5171i	−0.181411	+	1.02883i	−0.930481	+	0.366341i	$0.880610\pi$
$480$	−8.07984	−	5.54222i	−0.368793	−	0.252966i
$481$	−24.2292	−	8.81872i	−1.10476	−	0.402099i
$482$	−2.85593	+	10.6530i	−0.130084	+	0.485229i
$483$	13.4979	+	15.7541i	0.614177	+	0.716837i
$484$	0.00224944	−	8.70444i	0.000102247	−	0.395657i
$485$			14.9161i			0.677306i
$486$	−16.3676	−	14.7683i	−0.742449	−	0.669903i
$487$			9.34956i			0.423669i	0.977306	+	0.211834i	$0.0679438\pi$
$487$			9.34956i			0.423669i	−0.977306	+	0.211834i	$0.932056\pi$
$488$	4.49477	−	9.62931i	0.203469	−	0.435899i
$489$	21.0090	+	24.5207i	0.950061	+	1.10886i
$490$	5.91229	+	1.58501i	0.267090	+	0.0716036i
$491$	32.2509	+	11.7384i	1.45546	+	0.529745i	0.944111	−	0.329628i	$-0.106923\pi$
$491$	32.2509	+	11.7384i	1.45546	+	0.529745i	0.511350	+	0.859372i	$0.329146\pi$
$492$	15.0582	−	12.8949i	0.678875	−	0.581348i
$493$	3.02422	−	17.1512i	0.136204	−	0.772451i
$494$	2.30266	+	3.28944i	0.103601	+	0.147999i
$495$	−7.64350	−	1.18613i	−0.343550	−	0.0533124i
$496$	5.07377	+	13.9625i	0.227819	+	0.626935i
$497$	−7.85706	−	21.5871i	−0.352438	−	0.968314i
$498$	−9.21516	−	19.2489i	−0.412941	−	0.862564i
$499$	−1.37303	−	1.63631i	−0.0614653	−	0.0732515i	0.734436	−	0.678678i	$-0.237447\pi$
$499$	−1.37303	−	1.63631i	−0.0614653	−	0.0732515i	−0.795901	+	0.605427i	$0.793002\pi$
$500$	0.347805	−	1.96953i	0.0155543	−	0.0880799i
$501$	−8.95995	+	3.36596i	−0.400301	+	0.150380i
$502$	35.4754	+	3.10831i	1.58334	+	0.138731i
$503$	−14.3984	−	24.9388i	−0.641994	−	1.11197i	−0.984987	−	0.172629i	$-0.944774\pi$
$503$	−14.3984	−	24.9388i	−0.641994	−	1.11197i	0.342993	−	0.939338i	$-0.388559\pi$
$504$	−7.72427	+	11.5196i	−0.344066	+	0.513125i
$505$	2.94829	−	5.10658i	0.131197	−	0.227240i
$506$	15.3283	−	21.8851i	0.681428	−	0.972912i
$507$	−2.38143	−	4.02845i	−0.105763	−	0.178910i
$508$	2.88801	−	1.05031i	0.128135	−	0.0465998i
$509$	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	$0.368917\pi$
$510$	−1.62565	+	6.32332i	−0.0719850	+	0.280001i
$511$	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
$516$	12.8122	−	4.80935i	0.564026	−	0.211720i
$517$	2.12754	+	12.0659i	0.0935691	+	0.530657i
$518$	−13.1349	+	13.1315i	−0.577116	+	0.576967i
$519$	27.7703	+	15.6544i	1.21898	+	0.687153i
$520$	0.787576	+	9.04240i	0.0345375	+	0.396536i
$521$	−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	$0.756040\pi$
$522$	11.1993	−	25.3582i	0.490178	−	1.10990i
$523$	36.5118	−	21.0801i	1.59655	−	0.921769i	0.604406	−	0.796676i	$-0.293410\pi$
$523$	36.5118	−	21.0801i	1.59655	−	0.921769i	0.992145	−	0.125093i	$-0.0399229\pi$
$524$	−13.4658	−	7.77914i	−0.588258	−	0.339833i
$525$	−2.79302	−	0.462904i	−0.121898	−	0.0202028i
$526$	−20.7023	+	5.54429i	−0.902661	+	0.241742i
$527$	7.58329	−	6.36314i	0.330333	−	0.277183i
$528$	16.8448	+	5.94523i	0.733076	+	0.258733i
$529$	−28.8447	+	10.4986i	−1.25412	+	0.456461i
$530$	−0.111245	−	1.27343i	−0.00483215	−	0.0553141i
$531$	7.16728	−	13.0260i	0.311033	−	0.565280i
$532$	2.84854	−	0.501515i	0.123500	−	0.0217434i
$533$	−18.0864	−	3.18912i	−0.783410	−	0.138136i
$534$	−3.57242	−	4.99318i	−0.154594	−	0.216076i
$535$	3.20887	−	8.81630i	0.138732	−	0.381162i
$536$	−18.9179	−	40.6107i	−0.817129	−	1.75411i
$537$	10.4269	+	3.67403i	0.449955	+	0.158546i
$538$	−15.1635	+	7.06846i	−0.653744	+	0.304743i
$539$	−11.1596			−0.480680
$540$	−4.91826	+	9.15482i	−0.211648	+	0.393961i
$541$	−31.9023			−1.37159			−0.685793	−	0.727796i	$-0.740545\pi$
$541$	−31.9023			−1.37159			−0.685793	+	0.727796i	$0.740545\pi$
$542$	9.71202	−	4.52726i	0.417167	−	0.194463i
$543$	5.95266	+	31.8398i	0.255453	+	1.36638i
$544$	6.38105	−	13.6611i	0.273585	−	0.585717i
$545$	5.69413	−	15.6445i	0.243910	−	0.670136i
$546$	12.7876	−	1.24982i	0.547259	−	0.0534873i
$547$	13.8757	+	2.44666i	0.593283	+	0.104612i	0.462225	−	0.886763i	$-0.347051\pi$
$547$	13.8757	+	2.44666i	0.593283	+	0.104612i	0.131058	+	0.991375i	$0.458163\pi$
$548$	−6.73068	−	38.2293i	−0.287520	−	1.63308i
$549$	−10.6687	−	3.63624i	−0.455327	−	0.155191i
$550$	0.317327	+	3.63247i	0.0135309	+	0.154889i
$551$	−5.43230	+	1.97720i	−0.231424	+	0.0842314i
$552$	−20.8807	−	29.2010i	−0.888741	−	1.24288i
$553$	−4.76175	+	3.99558i	−0.202490	+	0.169909i
$554$	37.6089	−	10.0721i	1.59785	−	0.427921i
$555$	−8.83527	+	10.7522i	−0.375036	+	0.456407i
$556$	19.8901	−	34.4302i	0.843530	−	1.46016i
$557$	−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	$0.477615\pi$
$558$	14.1415	−	6.94982i	0.598657	−	0.294209i
$559$	−10.9791	−	6.33882i	−0.464369	−	0.268103i
$560$	6.14274	+	2.23937i	0.259578	+	0.0946307i
$561$	−0.122482	−	11.9026i	−0.00517120	−	0.502530i
$562$	11.6682	−	11.6651i	0.492191	−	0.492064i
$563$	−0.871473	−	4.94237i	−0.0367282	−	0.208296i	0.960921	−	0.276822i	$-0.0892814\pi$
$563$	−0.871473	−	4.94237i	−0.0367282	−	0.208296i	−0.997649	+	0.0685264i	$0.978170\pi$
$564$	16.2389	+	2.69568i	0.683781	+	0.113509i
$565$	−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	$0.0634069\pi$
$570$	2.08754	−	0.582153i	0.0874376	−	0.0243837i
$571$	36.1517	−	6.37452i	1.51290	−	0.266765i	0.645262	−	0.763961i	$-0.276748\pi$
$571$	36.1517	−	6.37452i	1.51290	−	0.266765i	0.867638	+	0.497196i	$0.165637\pi$
$572$	−5.65577	−	15.5516i	−0.236479	−	0.650245i
$573$	−29.6434	+	0.305041i	−1.23837	+	0.0127433i
$574$	−7.58937	+	10.8358i	−0.316774	+	0.452276i
$575$	3.66387	−	6.34601i	0.152794	−	0.264647i
$576$	15.0598	−	18.6870i	0.627491	−	0.778624i
$577$	−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	$0.969035\pi$
$578$	13.9409	+	1.22149i	0.579865	+	0.0508071i
$579$	−3.08507	−	2.53504i	−0.128211	−	0.105353i
$580$	−12.8688	−	2.27254i	−0.534346	−	0.0943621i
$581$	9.15388	+	10.9092i	0.379767	+	0.452589i
$582$	−36.4283	−	2.81441i	−1.51000	−	0.116661i
$583$	0.797075	+	2.18995i	0.0330115	+	0.0906983i
$584$	−8.04916	+	8.04292i	−0.333077	+	0.332819i
$585$	9.44456	−	1.86650i	0.390484	−	0.0771703i
$586$	−20.5731	−	29.3895i	−0.849865	−	1.21407i
$587$	4.22930	−	23.9855i	0.174562	−	0.989989i	−0.764087	−	0.645114i	$-0.776810\pi$
$587$	4.22930	−	23.9855i	0.174562	−	0.989989i	0.938648	−	0.344876i	$-0.112079\pi$
$588$	−4.98648	+	14.1400i	−0.205639	+	0.583124i
$589$	−3.08777	−	1.12386i	−0.127229	−	0.0463077i
$590$	−6.76962	−	1.81485i	−0.278701	−	0.0747163i
$591$	−35.4281	+	6.62351i	−1.45732	+	0.272455i
$592$	24.6307	−	20.6459i	1.01231	−	0.848541i
$593$		−	10.2248i		−	0.419881i	−0.977714	−	0.209941i	$-0.932673\pi$
$593$		−	10.2248i		−	0.419881i	0.977714	−	0.209941i	$-0.0673271\pi$
$594$	4.33897	−	18.4432i	0.178030	−	0.756736i
$595$		−	4.35678i		−	0.178611i
$596$	18.6052	+	0.00480805i	0.762100	+	0.000196945i
$597$	6.52634	−	18.5218i	0.267105	−	0.758046i
$598$	−8.61134	+	32.1214i	−0.352144	+	1.31354i
$599$	17.4081	+	6.33602i	0.711274	+	0.258883i	0.672217	−	0.740354i	$-0.265342\pi$
$599$	17.4081	+	6.33602i	0.711274	+	0.258883i	0.0390575	+	0.999237i	$0.487564\pi$
$600$	4.74437	+	1.22103i	0.193688	+	0.0498483i
$601$	−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	$0.978218\pi$
$602$	−7.48126	+	5.23700i	−0.304914	+	0.213444i
$603$	−40.6545	+	24.6010i	−1.65558	+	1.00183i
$604$	−5.86092	−	2.13492i	−0.238478	−	0.0868685i
$605$	1.48855	+	4.08975i	0.0605181	+	0.166272i
$606$	11.9151	+	8.16386i	0.484016	+	0.331634i
$607$	−5.88832	−	7.01743i	−0.239000	−	0.284829i	0.633190	−	0.773996i	$-0.281745\pi$
$607$	−5.88832	−	7.01743i	−0.239000	−	0.284829i	−0.872190	+	0.489168i	$0.837301\pi$
$608$	−4.98616	+	0.432987i	−0.202216	+	0.0175599i
$609$	−3.02459	+	18.2494i	−0.122563	+	0.739505i
$610$	−0.463773	+	5.29307i	−0.0187776	+	0.214310i
$611$	−7.62464	−	13.2063i	−0.308460	−	0.534268i
$612$	−15.1362	−	5.16328i	−0.611843	−	0.208713i
$613$	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	$0.00639350\pi$
$614$	26.0022	+	18.2120i	1.04937	+	0.734976i
$615$	−4.86764	+	8.63499i	−0.196282	+	0.348196i
$616$	−11.8744	−	1.04351i	−0.478432	−	0.0420443i
$617$	−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	$0.497978\pi$
$618$	−14.4635	+	14.7604i	−0.581806	+	0.593751i
$619$	6.89956	−	8.22257i	0.277317	−	0.330493i	−0.609351	−	0.792901i	$-0.708570\pi$
$619$	6.89956	−	8.22257i	0.277317	−	0.330493i	0.886667	+	0.462408i	$0.153014\pi$
$620$	−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
$624$	−22.2321	+	0.217284i	−0.889995	+	0.00869831i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	10.9864	+	10.9892i	0.439105	+	0.439218i
$627$	−3.40127	+	2.01067i	−0.135834	+	0.0802985i
$628$	−9.42092	+	5.43593i	−0.375936	+	0.216917i
$629$	−18.5469	−	10.7081i	−0.739514	−	0.426959i
$630$	1.65750	−	6.73381i	0.0660366	−	0.268281i
$631$	15.2653	−	8.81341i	0.607701	−	0.350856i	−0.164364	−	0.986400i	$-0.552557\pi$
$631$	15.2653	−	8.81341i	0.607701	−	0.350856i	0.772065	+	0.635543i	$0.219224\pi$
$632$	8.81336	−	6.16609i	0.350577	−	0.245274i
$633$	−2.10777	−	5.61074i	−0.0837765	−	0.223007i
$634$	1.33558	+	4.98702i	0.0530426	+	0.198060i
$635$	−1.17705	+	0.987665i	−0.0467100	+	0.0391943i
$636$	3.13097	−	0.0314095i	0.124151	−	0.00124547i
$637$	13.0520	−	4.75055i	0.517140	−	0.188224i
$638$	23.7344	−	2.07340i	0.939652	−	0.0820866i
$639$	39.3151	−	15.2329i	1.55528	−	0.602603i
$640$	−10.2494	−	4.79065i	−0.405142	−	0.189367i
$641$	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	$0.440510\pi$
$642$	20.9258	+	9.50023i	0.825876	+	0.374944i
$643$	−10.4941	+	28.8323i	−0.413847	+	1.13703i	0.541281	+	0.840842i	$0.317939\pi$
$643$	−10.4941	+	28.8323i	−0.413847	+	1.13703i	−0.955128	+	0.296193i	$0.904283\pi$
$644$	18.3467	+	15.4028i	0.722962	+	0.606955i
$645$	−5.19617	+	4.45202i	−0.204599	+	0.175298i
$646$	1.40907	+	3.02278i	0.0554392	+	0.118930i
$647$	40.7589			1.60240			0.801199	−	0.598399i	$-0.204196\pi$
$647$	40.7589			1.60240			0.801199	+	0.598399i	$0.204196\pi$
$648$	−21.4300	−	13.7388i	−0.841851	−	0.539710i
$649$	12.7779			0.501576
$650$	−1.91744	−	4.11336i	−0.0752084	−	0.161339i
$651$	−7.98472	+	6.84121i	−0.312946	+	0.268128i
$652$	28.5560	+	23.9739i	1.11834	+	0.938890i
$653$	−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	$0.873443\pi$
$654$	37.1328	+	16.8581i	1.45201	+	0.659204i
$655$	7.65753	+	1.35023i	0.299205	+	0.0527578i
$656$	14.7237	−	17.5286i	0.574863	−	0.684376i
$657$	9.40313	+	7.56595i	0.366851	+	0.295176i
$658$	−10.9429	+	0.955952i	−0.426598	+	0.0372669i
$659$	7.80701	−	2.84152i	0.304118	−	0.110690i	−0.185454	−	0.982653i	$-0.559375\pi$
$659$	7.80701	−	2.84152i	0.304118	−	0.110690i	0.489572	+	0.871963i	$0.337153\pi$
$660$	−8.93114	+	0.0895962i	−0.347644	+	0.00348753i
$661$	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	$-0.0767743\pi$
$662$	0.791260	+	2.95455i	0.0307532	+	0.114832i
$663$	5.21009	+	13.8689i	0.202343	+	0.538623i
$664$	−14.1265	−	20.1914i	−0.548216	−	0.783579i
$665$	−1.25242	+	0.723088i	−0.0485669	+	0.0280401i
$666$	−24.5922	−	23.6064i	−0.952929	−	0.914728i
$667$	−41.4645	−	23.9395i	−1.60551	−	0.926942i
$668$	−9.57276	+	5.52354i	−0.370381	+	0.213712i
$669$	8.05472	−	4.76157i	0.311414	−	0.184093i
$670$	15.8374	+	15.8415i	0.611853	+	0.612011i
$671$	−1.68214	−	9.53988i	−0.0649382	−	0.368283i
$672$	−6.62805	+	14.5793i	−0.255682	+	0.562410i
$673$	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	$0.365736\pi$
$678$	30.7206	−	31.3513i	1.17982	−	1.20404i
$679$	24.0107	−	4.23374i	0.921447	−	0.162476i
$680$	−0.659976	+	7.51003i	−0.0253089	+	0.287997i
$681$	−9.03185	+	16.0221i	−0.346101	+	0.613969i
$682$	11.0921	+	7.76892i	0.424739	+	0.297487i
$683$	−20.8007	+	36.0278i	−0.795916	+	1.37857i	0.126340	+	0.991987i	$0.459677\pi$
$683$	−20.8007	+	36.0278i	−0.795916	+	1.37857i	−0.922256	+	0.386580i	$0.873656\pi$
$684$	1.02786	+	5.20807i	0.0393011	+	0.199135i
$685$	9.70433	+	16.8084i	0.370783	+	0.642216i
$686$	2.28567	−	26.0865i	0.0872671	−	0.995986i
$687$	−7.03745	+	42.4618i	−0.268496	+	1.62002i
$688$	13.6892	−	7.89404i	0.521896	−	0.300957i
$689$	−1.86448	−	2.22200i	−0.0710309	−	0.0846513i
$690$	14.8070	+	10.1453i	0.563693	+	0.386226i
$691$	7.60624	+	20.8980i	0.289355	+	0.794996i	0.996157	+	0.0875847i	$0.0279148\pi$
$691$	7.60624	+	20.8980i	0.289355	+	0.794996i	−0.706802	+	0.707411i	$0.749863\pi$
$692$	34.5872	+	12.5988i	1.31481	+	0.478936i
$693$	0.260178	+	12.6405i	0.00988336	+	0.480174i
$694$	−39.8230	+	27.8767i	−1.51166	+	1.05818i
$695$	−3.45234	+	19.5792i	−0.130955	+	0.742681i
$696$	7.97813	−	30.9995i	0.302410	−	1.17503i
$697$	−14.3342	−	5.21723i	−0.542948	−	0.197617i
$698$	−10.5256	+	39.2616i	−0.398398	+	1.48607i
$699$	−14.1761	+	40.2319i	−0.536190	+	1.52171i
$700$	−3.26910		0.000844816i	−0.123560		3.19311e-5i
$701$		−	20.4369i		−	0.771893i	−0.922521	−	0.385946i	$-0.873875\pi$
$701$		−	20.4369i		−	0.771893i	0.922521	−	0.385946i	$-0.126125\pi$
$702$	2.77637	+	23.4178i	0.104787	+	0.883848i
$703$			7.10880i			0.268114i
$704$	20.3105	+	3.59752i	0.765480	+	0.135587i
$705$	−8.09039	+	1.51255i	−0.304702	+	0.0569660i
$706$	27.6277	+	7.40664i	1.03978	+	0.278753i
$707$	−9.05698	−	3.29647i	−0.340623	−	0.123977i
$708$	5.70956	−	16.1904i	0.214578	−	0.608473i
$709$	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	$-0.0310340\pi$
$710$	−11.3982	−	16.2828i	−0.427767	−	0.611083i
$711$	−7.51166	−	8.58680i	−0.281709	−	0.322030i
$712$	−5.01097	−	5.01486i	−0.187794	−	0.187940i
$713$	−9.30804	−	25.5736i	−0.348589	−	0.957740i
$714$	10.6402	+	0.822048i	0.398199	+	0.0307644i
$715$	5.31846	+	6.33829i	0.198899	+	0.237039i
$716$	12.5710	+	2.21996i	0.469802	+	0.0829639i
$717$	3.38365	+	2.78039i	0.126365	+	0.103836i
$718$	33.0721	+	2.89774i	1.23424	+	0.108143i
$719$	−24.6097	−	42.6253i	−0.917788	−	1.58966i	−0.802767	−	0.596292i	$-0.796640\pi$
$719$	−24.6097	−	42.6253i	−0.917788	−	1.58966i	−0.115021	−	0.993363i	$-0.536693\pi$
$720$	−3.87719	+	11.3564i	−0.144494	+	0.423227i
$721$	6.89506	−	11.9426i	0.256785	−	0.444765i
$722$	−14.7798	+	21.1019i	−0.550047	+	0.785332i
$723$	13.5072	−	0.138993i	0.502337	−	0.00516922i
$724$	12.7833	+	35.1501i	0.475088	+	1.30634i
$725$	6.43468	−	1.13461i	0.238978	−	0.0421382i
$726$	−10.2689	+	2.86368i	−0.381115	+	0.106281i
$727$	−18.3844	+	21.9097i	−0.681839	+	0.812584i	−0.990343	−	0.138639i	$-0.955727\pi$
$727$	−18.3844	+	21.9097i	−0.681839	+	0.812584i	0.308504	+	0.951223i	$0.400172\pi$
$728$	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
$732$	−12.8393	−	2.13134i	−0.474554	−	0.0787766i
$733$	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	$0.824462\pi$
$734$	29.9263	−	29.9186i	1.10460	−	1.10432i
$735$	−0.0771399	−	7.49635i	−0.00284535	−	0.276507i
$736$	−29.2920	−	29.3299i	−1.07972	−	1.08111i
$737$	−35.3679	−	20.4197i	−1.30279	−	0.752169i
$738$	−20.1700	−	13.5171i	−0.742469	−	0.497570i
$739$	34.9708	−	20.1904i	1.28642	−	0.742716i	0.308408	−	0.951254i	$-0.400204\pi$
$739$	34.9708	−	20.1904i	1.28642	−	0.742716i	0.978014	+	0.208538i	$0.0668706\pi$
$740$	−8.03837	+	13.9146i	−0.295496	+	0.511509i
$741$	3.12212	−	3.79952i	0.114694	−	0.139579i
$742$	−2.01828	+	0.540517i	−0.0740934	+	0.0198430i
$743$	11.1420	−	9.34928i	0.408762	−	0.342992i	−0.415107	−	0.909773i	$-0.636256\pi$
$743$	11.1420	−	9.34928i	0.408762	−	0.342992i	0.823869	+	0.566781i	$0.191811\pi$
$744$	14.8001	−	10.5830i	0.542596	−	0.387993i
$745$	−8.74160	+	3.18168i	−0.320267	+	0.116568i
$746$	2.72275	+	31.1675i	0.0996868	+	1.14112i
$747$	−19.6724	+	17.2092i	−0.719774	+	0.629652i
$748$	−2.38325	−	13.5365i	−0.0871401	−	0.494944i
$749$	−15.1025	−	2.66299i	−0.551835	−	0.0973034i
$750$	−2.43787	+	0.238270i	−0.0890186	+	0.00870038i
$751$	6.07329	−	16.6862i	0.221618	−	0.608889i	−0.778199	−	0.628017i	$-0.783867\pi$
$751$	6.07329	−	16.6862i	0.221618	−	0.608889i	0.999817	+	0.0191279i	$0.00608896\pi$
$752$	19.0077	+	0.00982411i	0.693139	+	0.000358248i
$753$	−8.01518	−	42.8719i	−0.292090	−	1.56234i
$754$	−26.8765	+	12.5285i	−0.978783	+	0.456260i
$755$	3.11883			0.113506
$756$	16.1327	+	5.31853i	0.586739	+	0.193433i
$757$	44.2100			1.60684			0.803420	−	0.595413i	$-0.203011\pi$
$757$	44.2100			1.60684			0.803420	+	0.595413i	$0.203011\pi$
$758$	22.8861	−	10.6684i	0.831260	−	0.387492i
$759$	−30.8642	−	10.8753i	−1.12030	−	0.394749i
$760$	2.26841	−	1.05671i	0.0822840	−	0.0383308i
$761$	−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	$0.751303\pi$
$762$	−2.19000	−	3.06097i	−0.0793353	−	0.110887i
$763$	−26.7994	−	4.72546i	−0.970203	−	0.171073i
$764$	−33.7126	+	5.93546i	−1.21968	+	0.214737i
$765$	7.99460	−	0.164552i	0.289045	−	0.00594938i
$766$	4.15341	+	47.5444i	0.150069	+	1.71785i
$767$	−14.9447	+	5.43942i	−0.539621	+	0.196406i
$768$	13.6337	−	24.1272i	0.491963	−	0.870616i
$769$	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	$0.137671\pi$
$770$	5.75718	−	1.54184i	0.207475	−	0.0555639i
$771$	−13.7896	−	2.28544i	−0.496621	−	0.0823080i
$772$	−3.99241	−	2.30639i	−0.143690	−	0.0830089i
$773$	−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	$0.633296\pi$
$774$	−9.89234	−	13.5302i	−0.355573	−	0.486332i
$775$	3.21638	+	1.85698i	0.115536	+	0.0667045i
$776$	−42.0300	+	3.66073i	−1.50879	+	0.131413i
$777$	19.8158	+	11.1704i	0.710890	+	0.400736i
$778$	25.6893	−	25.6827i	0.921007	−	0.920769i
$779$	0.879254	+	4.98649i	0.0315025	+	0.178660i
$780$	10.4075	−	3.90669i	0.372648	−	0.139882i
$781$	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
$786$	−4.74239	+	18.4466i	−0.169155	+	0.657967i
$787$	11.5406	−	2.03492i	0.411377	−	0.0725369i	0.0358702	−	0.999356i	$-0.488580\pi$
$787$	11.5406	−	2.03492i	0.411377	−	0.0725369i	0.375507	+	0.926820i	$0.377469\pi$
$788$	−39.1114	+	14.2239i	−1.39329	+	0.506707i
$789$	13.3575	+	22.5956i	0.475538	+	0.804425i
$790$	−3.08532	+	4.40509i	−0.109771	+	0.156726i
$791$	−14.6452	+	25.3662i	−0.520723	+	0.901919i
$792$	1.46634	−	21.8286i	0.0521040	−	0.775647i
$793$	6.02842	+	10.4415i	0.214075	+	0.370789i
$794$	20.3150	+	1.77998i	0.720954	+	0.0631691i
$795$	−1.46556	+	0.550563i	−0.0519780	+	0.0195265i
$796$	3.94341	−	22.3305i	0.139771	−	0.791482i
$797$	−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	$0.790097\pi$
$798$	−1.52962	−	3.19512i	−0.0541480	−	0.113106i
$799$	−4.33200	−	11.9021i	−0.153255	−	0.421065i
$800$	5.63501	+	0.496668i	0.199228	+	0.0175599i
$801$	−4.71380	+	5.85842i	−0.166554	+	0.206997i
$802$	−9.49427	−	13.5630i	−0.335254	−	0.478924i
$803$	−1.80120	+	10.2151i	−0.0635628	+	0.360483i
$804$	−41.6766	+	35.6893i	−1.46982	+	1.25867i
$805$	−11.2552	−	4.09657i	−0.396695	−	0.144385i
$806$	−16.2802	−	4.36452i	−0.573446	−	0.153734i
$807$	13.3316	+	15.5599i	0.469293	+	0.547735i
$808$	15.1127	+	7.05430i	0.531662	+	0.248169i
$809$		−	21.0655i		−	0.740624i	−0.928907	−	0.370312i	$-0.879251\pi$
$809$		−	21.0655i		−	0.740624i	0.928907	−	0.370312i	$-0.120749\pi$
$810$	12.4190	+	2.78716i	0.436359	+	0.0979307i
$811$		−	15.8992i		−	0.558297i	−0.960248	−	0.279148i	$-0.909948\pi$
$811$		−	15.8992i		−	0.558297i	0.960248	−	0.279148i	$-0.0900522\pi$
$812$	−0.00551998	+	21.3601i	−0.000193713	+	0.749593i
$813$	−8.53869	−	9.96594i	−0.299465	−	0.349521i
$814$	7.58635	−	28.2980i	0.265901	−	0.991844i
$815$	−17.5184	−	6.37616i	−0.613641	−	0.223347i
$816$	−18.2166	−	3.02881i	−0.637708	−	0.106030i
$817$	−0.606947	+	3.44217i	−0.0212344	+	0.120426i
$818$	−5.95041	+	4.16538i	−0.208051	+	0.145639i
$819$	−5.68525	−	14.6733i	−0.198659	−	0.512726i
$820$	−3.91752	+	10.7546i	−0.136806	+	0.375568i
$821$	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	$0.783824\pi$
$822$	−42.8807	+	20.5286i	−1.49564	+	0.716016i
$823$	−3.30669	−	3.94075i	−0.115264	−	0.137366i	0.705327	−	0.708882i	$-0.250800\pi$
$823$	−3.30669	−	3.94075i	−0.115264	−	0.137366i	−0.820591	+	0.571516i	$0.806356\pi$
$824$	−13.6945	+	19.5417i	−0.477071	+	0.680766i
$825$	4.18054	−	1.57049i	0.145548	−	0.0546775i
$826$	−0.999932	+	11.4123i	−0.0347921	+	0.397085i
$827$	−17.2288	−	29.8411i	−0.599102	−	1.03768i	−0.992954	−	0.118502i	$-0.962191\pi$
$827$	−17.2288	−	29.8411i	−0.599102	−	1.03768i	0.393851	−	0.919174i	$-0.371142\pi$
$828$	−27.5709	+	34.2476i	−0.958154	+	1.19019i
$829$	−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	$0.886355\pi$
$830$	10.0921	+	7.06848i	0.350301	+	0.245351i
$831$	−24.2659	−	41.0485i	−0.841776	−	1.42396i
$832$	−25.2860	+	4.43840i	−0.876635	+	0.153874i
$833$	11.3614	−	2.00332i	0.393648	−	0.0694108i
$834$	−47.1652	−	12.1256i	−1.63320	−	0.419875i
$835$	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	0.732093	−	0.681205i	$-0.238544\pi$
$839$	5.45603	+	4.57815i	0.188363	+	0.158055i	−0.543730	+	0.839260i	$0.682988\pi$
$840$	0.618885	−	7.98367i	0.0213536	−	0.275463i
$841$	−2.37766	−	13.4844i	−0.0819882	−	0.464978i
$842$	10.0696	+	10.0722i	0.347020	+	0.347110i
$843$	−17.6030	−	9.92300i	−0.606280	−	0.341766i
$844$	−3.45885	−	5.99448i	−0.119059	−	0.206339i
$845$	2.33985	+	1.35092i	0.0804934	+	0.0464729i
$846$	−2.16746	−	20.0438i	−0.0745186	−	0.689121i
$847$	6.16084	−	3.55696i	0.211689	−	0.122219i
$848$	3.56091	−	0.625986i	0.122282	−	0.0214965i
$849$	28.5888	+	4.73819i	0.981164	+	0.162614i
$850$	−0.975145	−	3.64117i	−0.0334472	−	0.124891i
$851$	−45.1022	+	37.8453i	−1.54608	+	1.29732i
$852$	41.9167	−	24.7646i	1.43604	−	0.848420i
$853$	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	$0.132430\pi$
$854$	8.65198	−	0.755823i	0.296065	−	0.0258637i
$855$	−1.37415	−	2.27086i	−0.0469951	−	0.0776619i
$856$	25.6297	+	6.87812i	0.876007	+	0.235089i
$857$	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	$0.352600\pi$
$858$	−16.4830	+	11.7929i	−0.562719	+	0.402602i
$859$	−8.57378	+	23.5563i	−0.292534	+	0.803730i	0.703161	+	0.711031i	$0.251771\pi$
$859$	−8.57378	+	23.5563i	−0.292534	+	0.803730i	−0.995694	+	0.0926985i	$0.970451\pi$
$860$	−5.08030	+	6.05129i	−0.173237	+	0.206347i
$861$	15.2815	+	5.38459i	0.520792	+	0.183506i
$862$	13.2232	+	28.3667i	0.450382	+	0.966174i
$863$	45.2113			1.53901			0.769505	−	0.638641i	$-0.220503\pi$
$863$	45.2113			1.53901			0.769505	+	0.638641i	$0.220503\pi$
$864$	−27.0031	−	11.6117i	−0.918665	−	0.395037i
$865$	−18.4052			−0.625795
$866$	−7.92120	−	16.9928i	−0.269173	−	0.577439i
$867$	−3.14976	−	16.8476i	−0.106972	−	0.572173i
$868$	−7.80666	+	9.29874i	−0.264975	+	0.315620i
$869$	3.35355	−	9.21379i	0.113761	−	0.312556i
$870$	1.55684	+	15.9289i	0.0527818	+	0.540041i
$871$	50.0579	+	8.82655i	1.69615	+	0.299076i
$872$	45.4798	+	12.2052i	1.54014	+	0.413320i
$873$	8.67569	+	43.8993i	0.293627	+	1.48577i
$874$	9.13392	−	0.797925i	0.308959	−	0.0269902i
$875$	1.53597	−	0.559049i	0.0519254	−	0.0188993i
$876$	12.1384	+	6.84666i	0.410117	+	0.231327i
$877$	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	$0.0714272\pi$
$878$	2.78868	+	10.4129i	0.0941134	+	0.351418i
$879$	−27.8945	+	33.9468i	−0.940859	+	1.14500i
$880$	−10.1576	+	1.78564i	−0.342411	+	0.0601939i
$881$	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	$0.0686456\pi$
$882$	18.3222	+	1.22604i	0.616941	+	0.0412828i
$883$	35.0060	+	20.2107i	1.17805	+	0.680145i	0.955562	−	0.294792i	$-0.0952502\pi$
$883$	35.0060	+	20.2107i	1.17805	+	0.680145i	0.222484	+	0.974936i	$0.428584\pi$
$884$	8.54974	+	14.8174i	0.287559	+	0.498364i
$885$	0.0883258	+	8.58338i	0.00296904	+	0.288527i
$886$	−12.6372	−	12.6405i	−0.424556	−	0.424665i
$887$	−2.63697	−	14.9550i	−0.0885409	−	0.502140i	−0.996536	−	0.0831601i	$-0.973499\pi$
$887$	−2.63697	−	14.9550i	−0.0885409	−	0.502140i	0.907995	−	0.418980i	$-0.137612\pi$
$888$	−32.4656	−	22.2568i	−1.08947	−	0.746891i
$889$	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
$894$	−6.12095	−	21.9492i	−0.204715	−	0.734090i
$895$	−6.28580	+	1.10836i	−0.210111	+	0.0370483i
$896$	−4.80245	+	17.8584i	−0.160439	+	0.596606i
$897$	40.7275	−	0.419100i	1.35985	−	0.0139933i
$898$	23.4300	+	16.4104i	0.781869	+	0.547621i
$899$	12.1334	−	21.0156i	0.404671	−	0.700910i
$900$	−0.121921	−	5.99876i	−0.00406402	−	0.199959i
$901$	−1.20461	−	2.08645i	−0.0401314	−	0.0695097i
$902$	1.82142	−	20.7880i	0.0606468	−	0.692166i
$903$	8.64135	+	7.10072i	0.287566	+	0.236297i
$904$	29.0873	−	41.5067i	0.967430	−	1.38049i
$905$	−12.0209	−	14.3260i	−0.399589	−	0.476212i
$906$	−0.588468	+	7.61683i	−0.0195505	+	0.253052i
$907$	−8.84222	−	24.2938i	−0.293601	−	0.806662i	−0.995533	−	0.0944180i	$-0.969901\pi$
$907$	−8.84222	−	24.2938i	−0.293601	−	0.806662i	0.701932	−	0.712244i	$-0.252321\pi$
$908$	−7.26891	+	19.9551i	−0.241227	+	0.662234i
$909$	5.70688	−	16.7439i	0.189285	−	0.555359i
$910$	−6.07711	+	4.25407i	−0.201454	+	0.141021i
$911$	−3.92317	+	22.2494i	−0.129980	+	0.737156i	0.848244	+	0.529606i	$0.177660\pi$
$911$	−3.92317	+	22.2494i	−0.129980	+	0.737156i	−0.978224	+	0.207550i	$0.933451\pi$
$912$	2.15269	+	5.73933i	0.0712828	+	0.190048i
$913$	−21.1088	−	7.68298i	−0.698600	−	0.254270i
$914$	−7.23721	+	26.9957i	−0.239386	+	0.892938i
$915$	6.39666	−	1.19590i	0.211467	−	0.0395352i
$916$	−0.0128436	+	49.6996i	−0.000424364	+	1.64212i
$917$		−	12.7097i		−	0.419712i
$918$	−1.10657	+	19.5556i	−0.0365223	+	0.645430i
$919$		−	17.2549i		−	0.569187i	−0.958648	−	0.284594i	$-0.908141\pi$
$919$		−	17.2549i		−	0.569187i	0.958648	−	0.284594i	$-0.0918586\pi$
$920$	18.7807	+	8.76646i	0.619182	+	0.289022i
$921$	12.9212	−	36.6706i	0.425770	−	1.20834i
$922$	48.8108	+	13.0856i	1.60750	+	0.430950i
$923$	−42.3815	−	15.4256i	−1.39500	−	0.507740i
$924$	2.67921	+	14.3512i	0.0881395	+	0.472119i
$925$	1.39522	−	7.91271i	0.0458747	−	0.260168i
$926$	−15.3500	−	21.9282i	−0.504434	−	0.720604i
$927$	22.1748	+	12.2012i	0.728317	+	0.400741i
$928$	3.24520	−	36.8188i	0.106529	−	1.20864i
$929$	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	$0.672241\pi$
$930$	−5.14200	+	7.50469i	−0.168613	+	0.246089i
$931$	−2.46151	−	2.93352i	−0.0806729	−	0.0961422i
$932$	−8.56564	+	48.5048i	−0.280577	+	1.58883i
$933$	2.32206	−	14.0106i	0.0760207	−	0.458686i
$934$	−3.80647	−	0.333519i	−0.124552	−	0.0109131i
$935$	3.43618	+	5.95164i	0.112375	+	0.194639i
$936$	7.57725	+	26.1544i	0.247670	+	0.854884i
$937$	−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	$0.218013\pi$
$938$	21.0051	−	29.9902i	0.685842	−	0.979214i
$939$	9.34563	−	16.5788i	0.304983	−	0.541027i
$940$	−8.93153	+	3.24820i	−0.291314	+	0.105944i
$941$	−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	$0.692110\pi$
$942$	9.51474	+	9.32332i	0.310007	+	0.303770i
$943$	−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	0.694743	−	0.719258i	$-0.255518\pi$
$947$	3.29440	+	2.76433i	0.107054	+	0.0898287i	−0.587690	+	0.809086i	$0.699962\pi$
$948$	−10.1760	−	8.36618i	−0.330501	−	0.271721i
$949$	−2.24183	−	12.7140i	−0.0727729	−	0.412715i
$950$	−0.884869	+	0.884640i	−0.0287089	+	0.0287015i
$951$	5.44312	−	3.21772i	0.176505	−	0.104342i
$952$	12.2764	−	1.06925i	0.397879	−	0.0346545i
$953$	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	$0.268631\pi$
$954$	−1.06807	−	3.68309i	−0.0345799	−	0.119244i
$955$	14.8225	−	8.55778i	0.479645	−	0.276923i
$956$	4.37880	+	2.52961i	0.141621	+	0.0818135i
$957$	−10.2615	−	27.3154i	−0.331707	−	0.882981i
$958$	31.2345	−	8.36493i	1.00914	−	0.270259i
$959$	24.3023	−	20.3921i	0.784763	−	0.658494i
$960$	−2.27620	+	13.6682i	−0.0734639	+	0.441138i
$961$	−16.1689	+	5.88499i	−0.521577	+	0.189838i
$962$	3.17339	+	36.3260i	0.102314	+	1.17120i
$963$	4.31612	−	27.8134i	0.139085	−	0.896276i
$964$	15.3613	−	2.70452i	0.494754	−	0.0871067i
$965$	2.27034	+	0.400322i	0.0730847	+	0.0128868i
$966$	12.1283	−	26.7147i	0.390223	−	0.859531i
$967$	6.96169	−	19.1271i	0.223873	−	0.615085i	−0.776005	−	0.630727i	$-0.782757\pi$
$967$	6.96169	−	19.1271i	0.223873	−	0.615085i	0.999878	+	0.0156416i	$0.00497908\pi$
$968$	−11.1586	+	5.19808i	−0.358651	+	0.167073i
$969$	3.10181	−	2.65760i	0.0996446	−	0.0853743i
$970$	19.1193	−	8.91248i	0.613884	−	0.286162i
$971$	40.1453			1.28833			0.644163	−	0.764889i	$-0.277206\pi$
$971$	40.1453			1.28833			0.644163	+	0.764889i	$0.277206\pi$
$972$	−9.15008	+	29.8040i	−0.293489	+	0.955962i
$973$	32.4969			1.04180
$974$	11.9842	−	5.58642i	0.383998	−	0.179001i
$975$	−4.22090	+	3.61642i	−0.135177	+	0.115818i
$976$	−15.0284	−	0.00776743i	−0.481048	−	0.000248629i
$977$	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	$0.0183646\pi$
$978$	18.8773	−	41.5805i	0.603631	−	1.32960i
$979$	−6.36430	−	1.12220i	−0.203404	−	0.0358656i
$980$	−1.50098	−	8.52537i	−0.0479471	−	0.272333i
$981$	7.65892	−	49.3548i	0.244531	−	1.57578i
$982$	−4.22401	−	48.3526i	−0.134793	−	1.54299i
$983$	−3.04741	+	1.10916i	−0.0971971	+	0.0353769i	−0.390161	−	0.920747i	$-0.627581\pi$
$983$	−3.04741	+	1.10916i	−0.0971971	+	0.0353769i	0.292964	+	0.956124i	$0.405358\pi$
$984$	−25.5260	−	11.5966i	−0.813738	−	0.369687i
$985$	15.9405	−	13.3756i	0.507905	−	0.426183i
$986$	−23.7912	+	6.37154i	−0.757666	+	0.202911i
$987$	4.73113	+	12.5939i	0.150593	+	0.400869i
$988$	2.84052	−	4.91698i	0.0903688	−	0.156430i
$989$	−25.0703	+	14.4743i	−0.797188	+	0.460257i
$990$	3.04668	+	10.5061i	0.0968299	+	0.333905i
$991$	−15.0803	−	8.70660i	−0.479041	−	0.276574i	0.240976	−	0.970531i	$-0.422533\pi$
$991$	−15.0803	−	8.70660i	−0.479041	−	0.276574i	−0.720017	+	0.693957i	$0.755866\pi$
$992$	14.8654	−	14.8462i	0.471977	−	0.471367i
$993$	3.22476	−	1.90633i	0.102335	−	0.0604954i
$994$	−22.9755	+	22.9696i	−0.728738	+	0.728550i
$995$	1.96882	+	11.1657i	0.0624158	+	0.353978i
$996$	−19.1669	+	23.3133i	−0.607327	+	0.738709i
$997$	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.11.27	✓	432
4.3	odd	2	inner	540.2.be.a.11.67	yes	432
27.5	odd	18	inner	540.2.be.a.491.67	yes	432
108.59	even	18	inner	540.2.be.a.491.27	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.27	✓	432	1.1	even	1	trivial
540.2.be.a.11.67	yes	432	4.3	odd	2	inner
540.2.be.a.491.27	yes	432	108.59	even	18	inner
540.2.be.a.491.67	yes	432	27.5	odd	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+(-0.597507 - 1.28179i) q^{2} +(-1.31530 + 1.12693i) q^{3} +(-1.28597 + 1.53176i) q^{4} +(0.342020 - 0.939693i) q^{5} +(2.23040 + 1.01259i) q^{6} +(-1.60972 - 0.283837i) q^{7} +(2.73177 + 0.733110i) q^{8} +(0.460037 - 2.96452i) q^{9} +(-1.40885 + 0.123075i) q^{10} +(2.42284 - 0.881840i) q^{11} +(-0.0347497 - 3.46393i) q^{12} +(-2.45829 + 2.06275i) q^{13} +(0.597998 + 2.23291i) q^{14} +(0.609113 + 1.62141i) q^{15} +(-0.692557 - 3.93959i) q^{16} +(-2.30833 + 1.33272i) q^{17} +(-4.07476 + 1.18165i) q^{18} +(0.766220 + 0.442377i) q^{19} +(0.999552 + 1.73231i) q^{20} +(2.43713 - 1.44072i) q^{21} +(-2.57800 - 2.57866i) q^{22} +(1.27245 + 7.21642i) q^{23} +(-4.41926 + 2.11426i) 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} +(1.71436 - 1.74956i) q^{30} +(-3.65753 + 0.644921i) q^{31} +(-4.63592 + 3.24164i) q^{32} +(-2.19298 + 3.89026i) q^{33} +(3.08751 + 2.16249i) q^{34} +(-0.817275 + 1.41556i) q^{35} +(3.94933 + 4.51695i) q^{36} +(4.01739 + 6.95832i) q^{37} +(0.109213 - 1.24646i) q^{38} +(0.908810 - 5.48348i) q^{39} +(1.62322 - 2.31628i) q^{40} +(3.67865 + 4.38405i) q^{41} +(-3.30290 - 2.26305i) q^{42} +(1.35117 + 3.71231i) q^{43} +(-1.76493 + 4.84522i) q^{44} +(-2.62839 - 1.44622i) q^{45} +(8.48964 - 5.94287i) q^{46} +(-0.825162 + 4.67973i) q^{47} +(5.35058 + 4.40128i) q^{48} +(-4.06722 - 1.48035i) q^{49} +(-0.366202 + 1.36598i) q^{50} +(1.53427 - 4.35426i) q^{51} +(0.00165861 - 6.41815i) q^{52} +0.903877i q^{53} +(4.02790 - 6.14622i) q^{54} -2.57833i q^{55} +(-4.18929 - 1.95547i) q^{56} +(-1.50634 + 0.281620i) q^{57} +(8.92522 + 2.39274i) q^{58} +(4.65700 + 1.69501i) q^{59} +(-3.26691 - 1.15208i) q^{60} +(0.652414 - 3.70002i) q^{61} +(3.01205 + 4.30284i) q^{62} +(-1.58197 + 4.64146i) q^{63} +(6.92510 + 4.00537i) q^{64} +(1.09757 + 3.01555i) q^{65} +(6.29682 + 0.486486i) q^{66} +(-10.1814 - 12.1337i) q^{67} +(0.927051 - 5.24964i) q^{68} +(-9.80609 - 8.05780i) q^{69} +(2.30278 + 0.201767i) q^{70} +(7.02717 + 12.1714i) q^{71} +(3.43003 - 7.76111i) q^{72} +(-2.01151 + 3.48404i) q^{73} +(6.51869 - 9.30709i) q^{74} +(1.73196 - 0.0178224i) q^{75} +(-1.66295 + 0.604778i) q^{76} +(-4.15038 + 0.731824i) q^{77} +(-7.57169 + 2.11151i) 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} +(-0.927252 + 5.58581i) q^{84} +(0.462847 + 2.62494i) q^{85} +(3.95107 - 3.95004i) q^{86} +(-0.116451 - 11.3165i) q^{87} +(7.26511 - 0.632777i) q^{88} +(-2.17066 - 1.25323i) q^{89} +(-0.283264 + 4.23317i) q^{90} +(4.54264 - 2.62270i) q^{91} +(-12.6901 - 7.33102i) q^{92} +(4.08397 - 4.97006i) q^{93} +(6.49147 - 1.73848i) q^{94} +(0.677761 - 0.568709i) q^{95} +(2.44451 - 9.48812i) q^{96} +(-14.0166 + 5.10161i) q^{97} +(0.532698 + 6.09784i) 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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