LMFDB - Embedded newform 273.2.bh.a.131.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.12
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987309 - 0.570023i) q^{2} +(1.12414 + 1.31769i) q^{3} +(-0.350147 - 0.606472i) q^{4} +(-0.578962 + 1.00279i) q^{5} +(-0.358764 - 1.94175i) q^{6} +(-2.55265 + 0.695677i) q^{7} +3.07846i q^{8} +(-0.472604 + 2.96254i) q^{9} +O(q^{10})$	\(q+(-0.987309 - 0.570023i) q^{2} +(1.12414 + 1.31769i) q^{3} +(-0.350147 - 0.606472i) q^{4} +(-0.578962 + 1.00279i) q^{5} +(-0.358764 - 1.94175i) q^{6} +(-2.55265 + 0.695677i) q^{7} +3.07846i q^{8} +(-0.472604 + 2.96254i) q^{9} +(1.14323 - 0.660043i) q^{10} +(-2.88243 + 1.66417i) q^{11} +(0.405526 - 1.14315i) q^{12} -1.00000i q^{13} +(2.91681 + 0.768223i) q^{14} +(-1.97220 + 0.364390i) q^{15} +(1.05450 - 1.82645i) q^{16} +(2.80806 + 4.86371i) q^{17} +(2.15532 - 2.65555i) q^{18} +(-0.600609 - 0.346762i) q^{19} +0.810886 q^{20} +(-3.78623 - 2.58156i) q^{21} +3.79447 q^{22} +(-6.42002 - 3.70660i) q^{23} +(-4.05645 + 3.46063i) q^{24} +(1.82961 + 3.16897i) q^{25} +(-0.570023 + 0.987309i) q^{26} +(-4.43498 + 2.70757i) q^{27} +(1.31571 + 1.30452i) q^{28} +3.13574i q^{29} +(2.15488 + 0.764436i) q^{30} +(5.29706 - 3.05826i) q^{31} +(3.24981 - 1.87628i) q^{32} +(-5.43313 - 1.92738i) q^{33} -6.40265i q^{34} +(0.780269 - 2.96255i) q^{35} +(1.96218 - 0.750702i) q^{36} +(-4.98890 + 8.64102i) q^{37} +(0.395325 + 0.684723i) q^{38} +(1.31769 - 1.12414i) q^{39} +(-3.08705 - 1.78231i) q^{40} -5.92904 q^{41} +(2.26663 + 4.70704i) q^{42} +12.1671 q^{43} +(2.01855 + 1.16541i) q^{44} +(-2.69719 - 2.18912i) q^{45} +(4.22569 + 7.31912i) q^{46} +(-1.34842 + 2.33554i) q^{47} +(3.59210 - 0.663687i) q^{48} +(6.03207 - 3.55164i) q^{49} -4.17167i q^{50} +(-3.25219 + 9.16766i) q^{51} +(-0.606472 + 0.350147i) q^{52} +(9.81343 - 5.66579i) q^{53} +(5.92208 - 0.145171i) q^{54} -3.85397i q^{55} +(-2.14162 - 7.85824i) q^{56} +(-0.218247 - 1.18123i) q^{57} +(1.78745 - 3.09595i) q^{58} +(-2.77665 - 4.80929i) q^{59} +(0.911552 + 1.06850i) q^{60} +(-9.38886 - 5.42066i) q^{61} -6.97311 q^{62} +(-0.854577 - 7.89112i) q^{63} -8.49610 q^{64} +(1.00279 + 0.578962i) q^{65} +(4.26553 + 4.99993i) q^{66} +(-0.342963 - 0.594029i) q^{67} +(1.96647 - 3.40602i) q^{68} +(-2.33288 - 12.6263i) q^{69} +(-2.45909 + 2.48018i) q^{70} +0.968922i q^{71} +(-9.12006 - 1.45489i) q^{72} +(1.05102 - 0.606807i) q^{73} +(9.85117 - 5.68758i) q^{74} +(-2.11898 + 5.97323i) q^{75} +0.485670i q^{76} +(6.20012 - 6.25330i) q^{77} +(-1.94175 + 0.358764i) q^{78} +(5.42596 - 9.39803i) q^{79} +(1.22103 + 2.11489i) q^{80} +(-8.55329 - 2.80022i) q^{81} +(5.85380 + 3.37969i) q^{82} +11.6625 q^{83} +(-0.239906 + 3.20017i) q^{84} -6.50305 q^{85} +(-12.0127 - 6.93555i) q^{86} +(-4.13193 + 3.52502i) q^{87} +(-5.12309 - 8.87346i) q^{88} +(-1.09337 + 1.89377i) q^{89} +(1.41511 + 3.69880i) q^{90} +(0.695677 + 2.55265i) q^{91} +5.19141i q^{92} +(9.98448 + 3.54195i) q^{93} +(2.66262 - 1.53727i) q^{94} +(0.695460 - 0.401524i) q^{95} +(6.12561 + 2.17303i) q^{96} +10.5820i q^{97} +(-7.98004 + 0.0681537i) q^{98} +(-3.56793 - 9.32582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.987309	−	0.570023i	−0.698133	−	0.403067i	0.108519	−	0.994094i	$-0.465389\pi$
$2$	−0.987309	−	0.570023i	−0.698133	−	0.403067i	−0.806652	+	0.591027i	$0.798723\pi$
$3$	1.12414	+	1.31769i	0.649024	+	0.760768i
$3$	1.12414	+	1.31769i	0.649024	+	0.760768i
$4$	−0.350147	−	0.606472i	−0.175073	−	0.303236i
$5$	−0.578962	+	1.00279i	−0.258920	+	0.448462i	−0.965953	−	0.258719i	$-0.916700\pi$
$5$	−0.578962	+	1.00279i	−0.258920	+	0.448462i	0.707033	+	0.707180i	$0.250033\pi$
$6$	−0.358764	−	1.94175i	−0.146465	−	0.792718i
$7$	−2.55265	+	0.695677i	−0.964812	+	0.262941i
$7$	−2.55265	+	0.695677i	−0.964812	+	0.262941i
$8$			3.07846i			1.08840i
$9$	−0.472604	+	2.96254i	−0.157535	+	0.987513i
$10$	1.14323	−	0.660043i	0.361521	−	0.208724i
$11$	−2.88243	+	1.66417i	−0.869086	+	0.501767i	−0.867045	−	0.498231i	$-0.833983\pi$
$11$	−2.88243	+	1.66417i	−0.869086	+	0.501767i	−0.00204186	+	0.999998i	$0.500650\pi$
$12$	0.405526	−	1.14315i	0.117065	−	0.329998i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.91681	+	0.768223i	0.779550	+	0.205316i
$15$	−1.97220	+	0.364390i	−0.509220	+	0.0940850i
$16$	1.05450	−	1.82645i	0.263625	−	0.456612i
$17$	2.80806	+	4.86371i	0.681056	+	1.17962i	0.974659	+	0.223696i	$0.0718121\pi$
$17$	2.80806	+	4.86371i	0.681056	+	1.17962i	−0.293604	+	0.955927i	$0.594855\pi$
$18$	2.15532	−	2.65555i	0.508015	−	0.625919i
$19$	−0.600609	−	0.346762i	−0.137789	−	0.0795527i	0.429521	−	0.903057i	$-0.358683\pi$
$19$	−0.600609	−	0.346762i	−0.137789	−	0.0795527i	−0.567310	+	0.823504i	$0.692016\pi$
$20$	0.810886			0.181320
$21$	−3.78623	−	2.58156i	−0.826224	−	0.563342i
$22$	3.79447			0.808984
$23$	−6.42002	−	3.70660i	−1.33867	−	0.772879i	−0.352056	−	0.935979i	$-0.614517\pi$
$23$	−6.42002	−	3.70660i	−1.33867	−	0.772879i	−0.986610	+	0.163100i	$0.947851\pi$
$24$	−4.05645	+	3.46063i	−0.828020	+	0.706398i
$25$	1.82961	+	3.16897i	0.365921	+	0.633794i
$26$	−0.570023	+	0.987309i	−0.111791	+	0.193627i
$27$	−4.43498	+	2.70757i	−0.853512	+	0.521073i
$28$	1.31571	+	1.30452i	0.248646	+	0.246532i
$29$			3.13574i			0.582292i	0.956679	+	0.291146i	$0.0940366\pi$
$29$			3.13574i			0.582292i	−0.956679	+	0.291146i	$0.905963\pi$
$30$	2.15488	+	0.764436i	0.393426	+	0.139566i
$31$	5.29706	−	3.05826i	0.951380	−	0.549279i	0.0578705	−	0.998324i	$-0.481569\pi$
$31$	5.29706	−	3.05826i	0.951380	−	0.549279i	0.893509	+	0.449045i	$0.148236\pi$
$32$	3.24981	−	1.87628i	0.574491	−	0.331683i
$33$	−5.43313	−	1.92738i	−0.945787	−	0.335514i
$34$		−	6.40265i		−	1.09805i
$35$	0.780269	−	2.96255i	0.131889	−	0.500762i
$36$	1.96218	−	0.750702i	0.327030	−	0.125117i
$37$	−4.98890	+	8.64102i	−0.820170	+	1.42058i	0.0853860	+	0.996348i	$0.472788\pi$
$37$	−4.98890	+	8.64102i	−0.820170	+	1.42058i	−0.905556	+	0.424228i	$0.860546\pi$
$38$	0.395325	+	0.684723i	0.0641302	+	0.111077i
$39$	1.31769	−	1.12414i	0.210999	−	0.180007i
$40$	−3.08705	−	1.78231i	−0.488106	−	0.281808i
$41$	−5.92904			−0.925961			−0.462980	−	0.886369i	$-0.653220\pi$
$41$	−5.92904			−0.925961			−0.462980	+	0.886369i	$0.653220\pi$
$42$	2.26663	+	4.70704i	0.349749	+	0.726312i
$43$	12.1671			1.85547			0.927735	−	0.373239i	$-0.121753\pi$
$43$	12.1671			1.85547			0.927735	+	0.373239i	$0.121753\pi$
$44$	2.01855	+	1.16541i	0.304308	+	0.175692i
$45$	−2.69719	−	2.18912i	−0.402073	−	0.326335i
$46$	4.22569	+	7.31912i	0.623045	+	1.07914i
$47$	−1.34842	+	2.33554i	−0.196688	+	0.340673i	−0.947452	−	0.319897i	$-0.896352\pi$
$47$	−1.34842	+	2.33554i	−0.196688	+	0.340673i	0.750765	+	0.660570i	$0.229685\pi$
$48$	3.59210	−	0.663687i	0.518475	−	0.0957950i
$49$	6.03207	−	3.55164i	0.861724	−	0.507378i
$50$		−	4.17167i		−	0.589964i
$51$	−3.25219	+	9.16766i	−0.455397	+	1.28373i
$52$	−0.606472	+	0.350147i	−0.0841025	+	0.0485566i
$53$	9.81343	−	5.66579i	1.34798	−	0.778255i	0.360015	−	0.932946i	$-0.382772\pi$
$53$	9.81343	−	5.66579i	1.34798	−	0.778255i	0.987963	+	0.154691i	$0.0494382\pi$
$54$	5.92208	−	0.145171i	0.805893	−	0.0197553i
$55$		−	3.85397i		−	0.519669i
$56$	−2.14162	−	7.85824i	−0.286185	−	1.05010i
$57$	−0.218247	−	1.18123i	−0.0289075	−	0.156457i
$58$	1.78745	−	3.09595i	0.234703	−	0.406518i
$59$	−2.77665	−	4.80929i	−0.361488	−	0.626116i	0.626718	−	0.779246i	$-0.284398\pi$
$59$	−2.77665	−	4.80929i	−0.361488	−	0.626116i	−0.988206	+	0.153130i	$0.951065\pi$
$60$	0.911552	+	1.06850i	0.117681	+	0.137942i
$61$	−9.38886	−	5.42066i	−1.20212	−	0.694044i	−0.241094	−	0.970502i	$-0.577506\pi$
$61$	−9.38886	−	5.42066i	−1.20212	−	0.694044i	−0.961026	+	0.276457i	$0.910840\pi$
$62$	−6.97311			−0.885586
$63$	−0.854577	−	7.89112i	−0.107667	−	0.994187i
$64$	−8.49610			−1.06201
$65$	1.00279	+	0.578962i	0.124381	+	0.0718114i
$66$	4.26553	+	4.99993i	0.525050	+	0.615449i
$67$	−0.342963	−	0.594029i	−0.0418996	−	0.0725722i	0.844315	−	0.535847i	$-0.180008\pi$
$67$	−0.342963	−	0.594029i	−0.0418996	−	0.0725722i	−0.886215	+	0.463275i	$0.846674\pi$
$68$	1.96647	−	3.40602i	0.238469	−	0.413041i
$69$	−2.33288	−	12.6263i	−0.280845	−	1.52003i
$70$	−2.45909	+	2.48018i	−0.293917	+	0.296438i
$71$			0.968922i			0.114990i	0.998346	+	0.0574949i	$0.0183113\pi$
$71$			0.968922i			0.114990i	−0.998346	+	0.0574949i	$0.981689\pi$
$72$	−9.12006	−	1.45489i	−1.07481	−	0.171461i
$73$	1.05102	−	0.606807i	0.123013	−	0.0710214i	−0.437231	−	0.899349i	$-0.644041\pi$
$73$	1.05102	−	0.606807i	0.123013	−	0.0710214i	0.560244	+	0.828328i	$0.310707\pi$
$74$	9.85117	−	5.68758i	1.14518	−	0.661167i
$75$	−2.11898	+	5.97323i	−0.244678	+	0.689729i
$76$			0.485670i			0.0557102i
$77$	6.20012	−	6.25330i	0.706569	−	0.712630i
$78$	−1.94175	+	0.358764i	−0.219860	+	0.0406220i
$79$	5.42596	−	9.39803i	0.610468	−	1.05736i	−0.380694	−	0.924701i	$-0.624315\pi$
$79$	5.42596	−	9.39803i	0.610468	−	1.05736i	0.991162	−	0.132660i	$-0.0423519\pi$
$80$	1.22103	+	2.11489i	0.136515	+	0.236452i
$81$	−8.55329	−	2.80022i	−0.950366	−	0.311136i
$82$	5.85380	+	3.37969i	0.646444	+	0.373224i
$83$	11.6625			1.28012			0.640062	−	0.768323i	$-0.278909\pi$
$83$	11.6625			1.28012			0.640062	+	0.768323i	$0.278909\pi$
$84$	−0.239906	+	3.20017i	−0.0261759	+	0.349167i
$85$	−6.50305			−0.705354
$86$	−12.0127	−	6.93555i	−1.29537	−	0.747880i
$87$	−4.13193	+	3.52502i	−0.442989	+	0.377922i
$88$	−5.12309	−	8.87346i	−0.546124	−	0.945914i
$89$	−1.09337	+	1.89377i	−0.115897	+	0.200739i	−0.918138	−	0.396261i	$-0.870308\pi$
$89$	−1.09337	+	1.89377i	−0.115897	+	0.200739i	0.802241	+	0.597000i	$0.203641\pi$
$90$	1.41511	+	3.69880i	0.149166	+	0.389888i
$91$	0.695677	+	2.55265i	0.0729268	+	0.267591i
$92$			5.19141i			0.541242i
$93$	9.98448	+	3.54195i	1.03534	+	0.367283i
$94$	2.66262	−	1.53727i	0.274628	−	0.158557i
$95$	0.695460	−	0.401524i	0.0713527	−	0.0411955i
$96$	6.12561	+	2.17303i	0.625192	+	0.221784i
$97$			10.5820i			1.07444i	0.843442	+	0.537220i	$0.180526\pi$
$97$			10.5820i			1.07444i	−0.843442	+	0.537220i	$0.819474\pi$
$98$	−7.98004	+	0.0681537i	−0.806105	+	0.00688456i
$99$	−3.56793	−	9.32582i	−0.358591	−	0.937280i
$100$	1.28126	−	2.21921i	0.128126	−	0.221921i
$101$	2.97194	+	5.14756i	0.295719	+	0.512201i	0.975152	−	0.221537i	$-0.0711073\pi$
$101$	2.97194	+	5.14756i	0.295719	+	0.512201i	−0.679433	+	0.733738i	$0.737774\pi$
$102$	8.43669	−	7.19749i	0.835357	−	0.712658i
$103$	0.440177	+	0.254137i	0.0433720	+	0.0250408i	0.521529	−	0.853233i	$-0.325362\pi$
$103$	0.440177	+	0.254137i	0.0433720	+	0.0250408i	−0.478157	+	0.878274i	$0.658695\pi$
$104$	3.07846			0.301868
$105$	4.78085	−	2.30218i	0.466563	−	0.224669i
$106$	−12.9185			−1.25476
$107$	1.61553	+	0.932727i	0.156179	+	0.0901701i	0.576053	−	0.817412i	$-0.304592\pi$
$107$	1.61553	+	0.932727i	0.156179	+	0.0901701i	−0.419874	+	0.907583i	$0.637926\pi$
$108$	3.19496	+	1.74164i	0.307435	+	0.167590i
$109$	6.34844	+	10.9958i	0.608070	+	1.05321i	0.991558	+	0.129663i	$0.0413895\pi$
$109$	6.34844	+	10.9958i	0.608070	+	1.05321i	−0.383488	+	0.923546i	$0.625277\pi$
$110$	−2.19685	+	3.80506i	−0.209462	+	0.362798i
$111$	−16.9944	+	3.13994i	−1.61304	+	0.298030i
$112$	−1.42115	+	5.39588i	−0.134287	+	0.509863i
$113$			11.1298i			1.04700i	0.852025	+	0.523502i	$0.175375\pi$
$113$			11.1298i			1.04700i	−0.852025	+	0.523502i	$0.824625\pi$
$114$	−0.457849	+	1.29064i	−0.0428815	+	0.120880i
$115$	7.43389	−	4.29196i	0.693213	−	0.400227i
$116$	1.90174	−	1.09797i	0.176572	−	0.101944i
$117$	2.96254	+	0.472604i	0.273887	+	0.0436923i
$118$			6.33101i			0.582817i
$119$	−10.5516	−	10.4619i	−0.967262	−	0.959036i
$120$	−1.12176	−	6.07135i	−0.102402	−	0.554236i
$121$	0.0389485	−	0.0674608i	0.00354078	−	0.00613280i
$122$	6.17981	+	10.7037i	0.559493	+	0.969071i
$123$	−6.66509	−	7.81263i	−0.600971	−	0.704441i
$124$	−3.70950	−	2.14168i	−0.333123	−	0.192328i
$125$	−10.0267			−0.896816
$126$	−3.65439	+	8.27810i	−0.325559	+	0.737472i
$127$	8.97828			0.796694			0.398347	−	0.917235i	$-0.369584\pi$
$127$	8.97828			0.796694			0.398347	+	0.917235i	$0.369584\pi$
$128$	1.88865	+	1.09041i	0.166935	+	0.0963799i
$129$	13.6776	+	16.0325i	1.20425	+	1.41158i
$130$	−0.660043	−	1.14323i	−0.0578896	−	0.100268i
$131$	−3.17912	+	5.50640i	−0.277761	+	0.481096i	−0.970828	−	0.239777i	$-0.922926\pi$
$131$	−3.17912	+	5.50640i	−0.277761	+	0.481096i	0.693067	+	0.720873i	$0.256259\pi$
$132$	0.733491	+	3.96991i	0.0638422	+	0.345536i
$133$	1.77438	+	0.467332i	0.153858	+	0.0405229i
$134$			0.781988i			0.0675535i
$135$	−0.147448	−	6.01494i	−0.0126903	−	0.517684i
$136$	−14.9727	+	8.64451i	−1.28390	+	0.741261i
$137$	1.75177	−	1.01138i	0.149664	−	0.0864084i	−0.423298	−	0.905991i	$-0.639128\pi$
$137$	1.75177	−	1.01138i	0.149664	−	0.0864084i	0.572962	+	0.819582i	$0.305794\pi$
$138$	−4.89403	+	13.7959i	−0.416607	+	1.17438i
$139$			8.15987i			0.692111i	0.938214	+	0.346055i	$0.112479\pi$
$139$			8.15987i			0.692111i	−0.938214	+	0.346055i	$0.887521\pi$
$140$	−2.06991	+	0.564115i	−0.174939	+	0.0476764i
$141$	−4.59333	+	0.848677i	−0.386828	+	0.0714715i
$142$	0.552308	−	0.956625i	0.0463487	−	0.0802782i
$143$	1.66417	+	2.88243i	0.139165	+	0.241041i
$144$	4.91257	+	3.98719i	0.409381	+	0.332266i
$145$	−3.14449	−	1.81547i	−0.261136	−	0.150767i
$146$	−1.38358			−0.114506
$147$	11.4609	+	3.95583i	0.945276	+	0.326271i
$148$	6.98738			0.574359
$149$	−1.82291	−	1.05246i	−0.149339	−	0.0862206i	0.423469	−	0.905911i	$-0.360812\pi$
$149$	−1.82291	−	1.05246i	−0.149339	−	0.0862206i	−0.572807	+	0.819690i	$0.694146\pi$
$150$	5.49697	−	4.68956i	0.448825	−	0.382901i
$151$	4.52532	+	7.83808i	0.368265	+	0.637854i	0.989294	−	0.145933i	$-0.0466185\pi$
$151$	4.52532	+	7.83808i	0.368265	+	0.637854i	−0.621029	+	0.783787i	$0.713285\pi$
$152$	1.06749	−	1.84895i	0.0865851	−	0.149970i
$153$	−15.7360	+	6.02039i	−1.27218	+	0.486720i
$154$	−9.68597	+	2.63973i	−0.780517	+	0.212715i
$155$			7.08246i			0.568877i
$156$	−1.14315	−	0.405526i	−0.0915249	−	0.0324681i
$157$	−9.45875	+	5.46101i	−0.754891	+	0.435836i	−0.827458	−	0.561527i	$-0.810214\pi$
$157$	−9.45875	+	5.46101i	−0.754891	+	0.435836i	0.0725677	+	0.997363i	$0.476881\pi$
$158$	−10.7142	+	6.18584i	−0.852376	+	0.492119i
$159$	18.4974	+	6.56188i	1.46694	+	0.520391i
$160$			4.34518i			0.343516i
$161$	18.9667	+	4.99539i	1.49478	+	0.393692i
$162$	6.84855	+	7.64026i	0.538073	+	0.600275i
$163$	1.33302	−	2.30887i	0.104410	−	0.180844i	−0.809087	−	0.587689i	$-0.800038\pi$
$163$	1.33302	−	2.30887i	0.104410	−	0.180844i	0.913497	+	0.406845i	$0.133371\pi$
$164$	2.07603	+	3.59580i	0.162111	+	0.280785i
$165$	5.07833	−	4.33242i	0.395348	−	0.337278i
$166$	−11.5145	−	6.64789i	−0.893697	−	0.515976i
$167$	4.34535			0.336253			0.168127	−	0.985765i	$-0.446228\pi$
$167$	4.34535			0.336253			0.168127	+	0.985765i	$0.446228\pi$
$168$	7.94723	−	11.6558i	0.613142	−	0.899262i
$169$	−1.00000			−0.0769231
$170$	6.42052	+	3.70689i	0.492431	+	0.284305i
$171$	1.31115	−	1.61545i	0.100266	−	0.123536i
$172$	−4.26028	−	7.37903i	−0.324843	−	0.562645i
$173$	−0.0472049	+	0.0817613i	−0.00358892	+	0.00621619i	−0.867814	−	0.496889i	$-0.834476\pi$
$173$	−0.0472049	+	0.0817613i	−0.00358892	+	0.00621619i	0.864225	+	0.503105i	$0.167809\pi$
$174$	6.08884	−	1.12499i	0.461593	−	0.0852853i
$175$	−6.87493	−	6.81647i	−0.519696	−	0.515276i
$176$			7.01949i			0.529114i
$177$	3.21580	−	9.06508i	0.241714	−	0.681373i
$178$	2.15898	−	1.24649i	0.161823	−	0.0934284i
$179$	−16.3356	+	9.43137i	−1.22098	+	0.704934i	−0.965127	−	0.261782i	$-0.915690\pi$
$179$	−16.3356	+	9.43137i	−1.22098	+	0.704934i	−0.255854	+	0.966715i	$0.582357\pi$
$180$	−0.383228	+	2.40228i	−0.0285642	+	0.179056i
$181$			4.05663i			0.301527i	0.988570	+	0.150763i	$0.0481732\pi$
$181$			4.05663i			0.301527i	−0.988570	+	0.150763i	$0.951827\pi$
$182$	0.768223	−	2.91681i	0.0569444	−	0.216208i
$183$	−3.41168	−	18.4652i	−0.252199	−	1.36499i
$184$	11.4106	−	19.7638i	0.841202	−	1.45700i
$185$	−5.77676	−	10.0056i	−0.424716	−	0.735630i
$186$	−7.83878	−	9.18839i	−0.574767	−	0.673725i
$187$	−16.1881	−	9.34621i	−1.18379	−	0.683463i
$188$	1.88858			0.137739
$189$	9.43736	−	9.99681i	0.686467	−	0.727161i
$190$	−0.915512			−0.0664182
$191$	13.9069	+	8.02913i	1.00626	+	0.580967i	0.910096	−	0.414398i	$-0.136008\pi$
$191$	13.9069	+	8.02913i	1.00626	+	0.580967i	0.0961691	+	0.995365i	$0.469341\pi$
$192$	−9.55083	−	11.1952i	−0.689272	−	0.807945i
$193$	7.34283	+	12.7182i	0.528549	+	0.915473i	0.999446	+	0.0332851i	$0.0105969\pi$
$193$	7.34283	+	12.7182i	0.528549	+	0.915473i	−0.470897	+	0.882188i	$0.656070\pi$
$194$	6.03199	−	10.4477i	0.433072	−	0.750102i
$195$	0.364390	+	1.97220i	0.0260945	+	0.141232i
$196$	−4.26608	−	2.41468i	−0.304720	−	0.172477i
$197$		−	7.74004i		−	0.551455i	−0.961236	−	0.275728i	$-0.911081\pi$
$197$		−	7.74004i		−	0.551455i	0.961236	−	0.275728i	$-0.0889188\pi$
$198$	−1.79328	+	11.2413i	−0.127443	+	0.798883i
$199$	−18.5731	+	10.7232i	−1.31661	+	0.760145i	−0.983182	−	0.182631i	$-0.941539\pi$
$199$	−18.5731	+	10.7232i	−1.31661	+	0.760145i	−0.333428	+	0.942776i	$0.608205\pi$
$200$	−9.75555	+	5.63237i	−0.689822	+	0.398269i
$201$	0.397206	−	1.11969i	0.0280168	−	0.0789770i
$202$		−	6.77631i		−	0.476779i
$203$	−2.18146	−	8.00446i	−0.153109	−	0.561803i
$204$	6.69867	−	1.23767i	0.469001	−	0.0866539i
$205$	3.43269	−	5.94559i	0.239749	−	0.415258i
$206$	−0.289727	−	0.501823i	−0.0201863	−	0.0349636i
$207$	14.0151	−	17.2678i	0.974115	−	1.20019i
$208$	−1.82645	−	1.05450i	−0.126641	−	0.0731165i
$209$	2.30829			0.159668
$210$	−6.03247	−	0.452234i	−0.416280	−	0.0312071i
$211$	−18.2972			−1.25963			−0.629816	−	0.776744i	$-0.716870\pi$
$211$	−18.2972			−1.25963			−0.629816	+	0.776744i	$0.716870\pi$
$212$	−6.87228	−	3.96771i	−0.471990	−	0.272504i
$213$	−1.27674	+	1.08921i	−0.0874806	+	0.0746312i
$214$	−1.06335	−	1.84178i	−0.0726893	−	0.125902i
$215$	−7.04430	+	12.2011i	−0.480418	+	0.832108i
$216$	−8.33516	−	13.6529i	−0.567136	−	0.928963i
$217$	−11.3940	+	11.4917i	−0.773474	+	0.780108i
$218$		−	14.4750i		−	0.980373i
$219$	1.98108	+	0.702779i	0.133869	+	0.0474894i
$220$	−2.33733	+	1.34946i	−0.157582	+	0.0909803i
$221$	4.86371	−	2.80806i	0.327168	−	0.188891i
$222$	18.5686	+	6.58712i	1.24624	+	0.442099i
$223$		−	11.0508i		−	0.740016i	−0.929029	−	0.370008i	$-0.879355\pi$
$223$		−	11.0508i		−	0.740016i	0.929029	−	0.370008i	$-0.120645\pi$
$224$	−6.99036	+	7.05031i	−0.467063	+	0.471069i
$225$	−10.2529	+	3.92261i	−0.683526	+	0.261508i
$226$	6.34425	−	10.9886i	0.422013	−	0.730948i
$227$	−10.6054	−	18.3691i	−0.703907	−	1.21920i	−0.967084	−	0.254456i	$-0.918104\pi$
$227$	−10.6054	−	18.3691i	−0.703907	−	1.21920i	0.263177	−	0.964748i	$-0.415230\pi$
$228$	−0.639962	+	0.545963i	−0.0423825	+	0.0361573i
$229$	0.389713	+	0.225001i	0.0257530	+	0.0148685i	0.512821	−	0.858495i	$-0.328600\pi$
$229$	0.389713	+	0.225001i	0.0257530	+	0.0148685i	−0.487068	+	0.873364i	$0.661934\pi$
$230$	−9.78606			−0.645274
$231$	15.2097	+	1.14022i	1.00073	+	0.0750212i
$232$	−9.65325			−0.633767
$233$	11.2355	+	6.48683i	0.736063	+	0.424966i	0.820636	−	0.571451i	$-0.193619\pi$
$233$	11.2355	+	6.48683i	0.736063	+	0.424966i	−0.0845729	+	0.996417i	$0.526953\pi$
$234$	−2.65555	−	2.15532i	−0.173599	−	0.140898i
$235$	−1.56137	−	2.70437i	−0.101853	−	0.176414i
$236$	−1.94447	+	3.36792i	−0.126574	+	0.219233i
$237$	18.4832	−	3.41501i	1.20061	−	0.221829i
$238$	4.45418	+	16.3437i	0.288721	+	1.05941i
$239$		−	17.6489i		−	1.14161i	−0.821086	−	0.570805i	$-0.806631\pi$
$239$		−	17.6489i		−	1.14161i	0.821086	−	0.570805i	$-0.193369\pi$
$240$	−1.41415	+	3.98638i	−0.0912830	+	0.257319i
$241$	16.6059	−	9.58745i	1.06968	−	0.617582i	0.141588	−	0.989926i	$-0.454779\pi$
$241$	16.6059	−	9.58745i	1.06968	−	0.617582i	0.928095	+	0.372344i	$0.121446\pi$
$242$	−0.0769085	+	0.0444031i	−0.00494387	+	0.00285434i
$243$	−5.92531	−	14.4184i	−0.380109	−	0.924942i
$244$			7.59211i			0.486035i
$245$	0.0692224	+	8.10517i	0.00442245	+	0.517820i
$246$	2.12713	+	11.5127i	0.135621	+	0.734025i
$247$	−0.346762	+	0.600609i	−0.0220639	+	0.0382159i
$248$	9.41473	+	16.3068i	0.597836	+	1.03548i
$249$	13.1103	+	15.3675i	0.830832	+	0.973877i
$250$	9.89946	+	5.71546i	0.626097	+	0.361477i
$251$	−5.89768			−0.372258			−0.186129	−	0.982525i	$-0.559594\pi$
$251$	−5.89768			−0.372258			−0.186129	+	0.982525i	$0.559594\pi$
$252$	−4.48651	+	3.28133i	−0.282624	+	0.206704i
$253$	24.6737			1.55122
$254$	−8.86434	−	5.11783i	−0.556198	−	0.321121i
$255$	−7.31035	−	8.56899i	−0.457792	−	0.536611i
$256$	7.25298	+	12.5625i	0.453311	+	0.785158i
$257$	5.66163	−	9.80623i	0.353163	−	0.611696i	−0.633639	−	0.773629i	$-0.718439\pi$
$257$	5.66163	−	9.80623i	0.353163	−	0.611696i	0.986802	+	0.161933i	$0.0517728\pi$
$258$	−4.36513	−	23.6256i	−0.271761	−	1.47086i
$259$	6.72355	−	25.5282i	0.417781	−	1.58624i
$260$		−	0.810886i		−	0.0502890i
$261$	−9.28976	−	1.48197i	−0.575022	−	0.0917313i
$262$	6.27755	−	3.62435i	0.387829	−	0.223913i
$263$	2.11608	−	1.22172i	0.130483	−	0.0753344i	−0.433338	−	0.901232i	$-0.642664\pi$
$263$	2.11608	−	1.22172i	0.130483	−	0.0753344i	0.563821	+	0.825897i	$0.309331\pi$
$264$	5.93336	−	16.7257i	0.365173	−	1.02939i
$265$			13.1211i			0.806022i
$266$	−1.48547	−	1.47284i	−0.0910802	−	0.0903056i
$267$	−3.72450	+	0.688149i	−0.227936	+	0.0421140i
$268$	−0.240175	+	0.415995i	−0.0146710	+	0.0254109i
$269$	−1.66585	−	2.88533i	−0.101568	−	0.175922i	0.810763	−	0.585375i	$-0.199053\pi$
$269$	−1.66585	−	2.88533i	−0.101568	−	0.175922i	−0.912331	+	0.409453i	$0.865719\pi$
$270$	−3.28308	+	6.02266i	−0.199802	+	0.366527i
$271$	26.1725	+	15.1107i	1.58987	+	0.917910i	0.993328	+	0.115325i	$0.0367911\pi$
$271$	26.1725	+	15.1107i	1.58987	+	0.917910i	0.596539	+	0.802584i	$0.296542\pi$
$272$	11.8444			0.718174
$273$	−2.58156	+	3.78623i	−0.156243	+	0.229153i
$274$	−2.30605			−0.139314
$275$	−10.5474	−	6.08957i	−0.636035	−	0.367215i
$276$	−6.84066	+	5.83589i	−0.411760	+	0.351279i
$277$	6.34839	+	10.9957i	0.381437	+	0.660669i	0.991268	−	0.131863i	$-0.0420958\pi$
$277$	6.34839	+	10.9957i	0.381437	+	0.660669i	−0.609830	+	0.792532i	$0.708762\pi$
$278$	4.65131	−	8.05631i	0.278967	−	0.483186i
$279$	6.55680	+	17.1381i	0.392545	+	1.02603i
$280$	9.12009	+	2.40203i	0.545029	+	0.143549i
$281$			18.8766i			1.12608i	0.826428	+	0.563042i	$0.190369\pi$
$281$			18.8766i			1.12608i	−0.826428	+	0.563042i	$0.809631\pi$
$282$	5.01880	+	1.78040i	0.298865	+	0.106021i
$283$	−8.18888	+	4.72785i	−0.486778	+	0.281042i	−0.723237	−	0.690600i	$-0.757347\pi$
$283$	−8.18888	+	4.72785i	−0.486778	+	0.281042i	0.236459	+	0.971642i	$0.424013\pi$
$284$	0.587624	−	0.339265i	0.0348691	−	0.0201317i
$285$	1.31088	+	0.465029i	0.0776498	+	0.0275459i
$286$		−	3.79447i		−	0.224372i
$287$	15.1348	−	4.12470i	0.893378	−	0.243473i
$288$	4.02268	+	10.5144i	0.237039	+	0.619569i
$289$	−7.27045	+	12.5928i	−0.427673	+	0.740752i
$290$	2.06972	+	3.58487i	0.121538	+	0.210511i
$291$	−13.9438	+	11.8957i	−0.817399	+	0.697338i
$292$	−0.736023	−	0.424943i	−0.0430725	−	0.0248679i
$293$	20.3935			1.19140			0.595700	−	0.803207i	$-0.296875\pi$
$293$	20.3935			1.19140			0.595700	+	0.803207i	$0.296875\pi$
$294$	−9.06051	−	10.4386i	−0.528420	−	0.608791i
$295$	6.43029			0.374386
$296$	−26.6011	−	15.3581i	−1.54615	−	0.892673i
$297$	8.27766	−	15.1850i	0.480319	−	0.881122i
$298$	1.19985	+	2.07820i	0.0695054	+	0.120387i
$299$	−3.70660	+	6.42002i	−0.214358	+	0.371279i
$300$	4.36455	−	0.806407i	0.251987	−	0.0465579i
$301$	−31.0585	+	8.46440i	−1.79018	+	0.487880i
$302$		−	10.3181i		−	0.593743i
$303$	−3.44199	+	9.70269i	−0.197737	+	0.557405i
$304$	−1.26669	+	0.731322i	−0.0726495	+	0.0419442i
$305$	10.8716	−	6.27671i	0.622505	−	0.359403i
$306$	18.9681	+	3.02592i	1.08433	+	0.172980i
$307$			15.3648i			0.876913i	0.898752	+	0.438456i	$0.144475\pi$
$307$			15.3648i			0.876913i	−0.898752	+	0.438456i	$0.855525\pi$
$308$	−5.96340	−	1.57063i	−0.339796	−	0.0894948i
$309$	0.159950	+	0.865702i	0.00909922	+	0.0492481i
$310$	4.03717	−	6.99258i	0.229296	−	0.397152i
$311$	−16.1032	−	27.8916i	−0.913130	−	1.58159i	−0.809616	−	0.586960i	$-0.800325\pi$
$311$	−16.1032	−	27.8916i	−0.913130	−	1.58159i	−0.103514	−	0.994628i	$-0.533009\pi$
$312$	3.46063	+	4.05645i	0.195920	+	0.229651i
$313$	−1.42273	−	0.821415i	−0.0804176	−	0.0464291i	0.459252	−	0.888306i	$-0.348117\pi$
$313$	−1.42273	−	0.821415i	−0.0804176	−	0.0464291i	−0.539670	+	0.841877i	$0.681451\pi$
$314$	12.4516			0.702686
$315$	8.40791	+	3.71169i	0.473732	+	0.209130i
$316$	−7.59953			−0.427507
$317$	16.6075	+	9.58836i	0.932772	+	0.538536i	0.887687	−	0.460447i	$-0.152311\pi$
$317$	16.6075	+	9.58836i	0.932772	+	0.538536i	0.0450849	+	0.998983i	$0.485644\pi$
$318$	−14.5223	−	17.0226i	−0.814368	−	0.954579i
$319$	−5.21842	−	9.03856i	−0.292175	−	0.506062i
$320$	4.91892	−	8.51981i	0.274976	−	0.476272i
$321$	0.587044	+	3.17728i	0.0327656	+	0.177339i
$322$	−15.8785	−	15.7434i	−0.884873	−	0.877348i
$323$		−	3.89492i		−	0.216719i
$324$	1.29665	+	6.16782i	0.0720362	+	0.342657i
$325$	3.16897	−	1.82961i	0.175783	−	0.101488i
$326$	−2.63221	+	1.51971i	−0.145785	+	0.0841689i
$327$	−7.35251	+	20.7261i	−0.406595	+	1.14616i
$328$		−	18.2523i		−	1.00782i
$329$	1.81727	−	6.89988i	0.100190	−	0.380403i
$330$	−7.48346	+	1.38267i	−0.411951	+	0.0761133i
$331$	−1.32548	+	2.29580i	−0.0728551	+	0.126189i	−0.900152	−	0.435577i	$-0.856544\pi$
$331$	−1.32548	+	2.29580i	−0.0728551	+	0.126189i	0.827296	+	0.561766i	$0.189878\pi$
$332$	−4.08358	−	7.07297i	−0.224116	−	0.388180i
$333$	−23.2416	−	18.8636i	−1.27363	−	1.03372i
$334$	−4.29020	−	2.47695i	−0.234749	−	0.135533i
$335$	0.794250			0.0433945
$336$	−8.70767	+	4.19311i	−0.475042	+	0.228753i
$337$	29.9011			1.62882			0.814409	−	0.580291i	$-0.197061\pi$
$337$	29.9011			1.62882			0.814409	+	0.580291i	$0.197061\pi$
$338$	0.987309	+	0.570023i	0.0537026	+	0.0310052i
$339$	−14.6656	+	12.5115i	−0.796526	+	0.679531i
$340$	2.27702	+	3.94392i	0.123489	+	0.213889i
$341$	−10.1789	+	17.6305i	−0.551221	+	0.954742i
$342$	−2.21535	+	0.847563i	−0.119792	+	0.0458310i
$343$	−12.9270	+	13.2625i	−0.697991	+	0.716107i
$344$			37.4560i			2.01949i
$345$	14.0122	+	4.97077i	0.754392	+	0.267617i
$346$	0.0932117	−	0.0538158i	0.00501109	−	0.00289315i
$347$	2.69427	−	1.55554i	0.144636	−	0.0835057i	−0.425936	−	0.904754i	$-0.640055\pi$
$347$	2.69427	−	1.55554i	0.144636	−	0.0835057i	0.570572	+	0.821248i	$0.306722\pi$
$348$	3.58461	+	1.27162i	0.192155	+	0.0681662i
$349$		−	6.36171i		−	0.340535i	−0.985398	−	0.170267i	$-0.945537\pi$
$349$		−	6.36171i		−	0.340535i	0.985398	−	0.170267i	$-0.0544631\pi$
$350$	2.90214	+	10.6488i	0.155126	+	0.569204i
$351$	2.70757	+	4.43498i	0.144520	+	0.236722i
$352$	−6.24491	+	10.8165i	−0.332855	+	0.576522i
$353$	−8.99031	−	15.5717i	−0.478506	−	0.828797i	0.521190	−	0.853441i	$-0.325488\pi$
$353$	−8.99031	−	15.5717i	−0.478506	−	0.828797i	−0.999696	+	0.0246437i	$0.992155\pi$
$354$	−8.34230	+	7.11696i	−0.443388	+	0.378262i
$355$	−0.971626	−	0.560969i	−0.0515686	−	0.0297731i
$356$	1.53136			0.0811617
$357$	1.92397	−	25.6643i	0.101827	−	1.35830i
$358$	21.5044			1.13654
$359$	−9.45306	−	5.45773i	−0.498913	−	0.288048i	0.229351	−	0.973344i	$-0.426340\pi$
$359$	−9.45306	−	5.45773i	−0.498913	−	0.288048i	−0.728265	+	0.685296i	$0.759673\pi$
$360$	6.73912	−	8.30319i	0.355183	−	0.437617i
$361$	−9.25951	−	16.0379i	−0.487343	−	0.844102i
$362$	2.31237	−	4.00515i	0.121536	−	0.210506i
$363$	0.132676	−	0.0245136i	0.00696369	−	0.00128663i
$364$	1.30452	−	1.31571i	0.0683756	−	0.0689620i
$365$			1.40527i			0.0735553i
$366$	−7.15720	+	20.1756i	−0.374113	+	1.05459i
$367$	2.04478	−	1.18056i	0.106737	−	0.0616246i	−0.445681	−	0.895192i	$-0.647039\pi$
$367$	2.04478	−	1.18056i	0.106737	−	0.0616246i	0.552418	+	0.833567i	$0.313705\pi$
$368$	−13.5398	+	7.81722i	−0.705812	+	0.407501i
$369$	2.80209	−	17.5650i	0.145871	−	0.914398i
$370$			13.1716i			0.684757i
$371$	−21.1087	+	21.2898i	−1.09591	+	1.10531i
$372$	−1.34794	−	7.29551i	−0.0698874	−	0.378255i
$373$	11.4679	−	19.8630i	0.593785	−	1.02847i	−0.399932	−	0.916545i	$-0.630966\pi$
$373$	11.4679	−	19.8630i	0.593785	−	1.02847i	0.993717	−	0.111922i	$-0.0357005\pi$
$374$	10.6551	+	18.4552i	0.550963	+	0.954296i
$375$	−11.2715	−	13.2121i	−0.582055	−	0.682268i
$376$	−7.18986	−	4.15107i	−0.370789	−	0.214075i
$377$	3.13574			0.161499
$378$	−15.0160	+	4.49043i	−0.772340	+	0.230963i
$379$	10.5578			0.542318			0.271159	−	0.962535i	$-0.412593\pi$
$379$	10.5578			0.542318			0.271159	+	0.962535i	$0.412593\pi$
$380$	−0.487026	−	0.281185i	−0.0249839	−	0.0144245i
$381$	10.0929	+	11.8306i	0.517074	+	0.606099i
$382$	−9.15358	−	15.8545i	−0.468338	−	0.811185i
$383$	9.88272	−	17.1174i	0.504983	−	0.874657i	−0.495000	−	0.868893i	$-0.664832\pi$
$383$	9.88272	−	17.1174i	0.504983	−	0.874657i	0.999983	−	0.00576391i	$-0.00183472\pi$
$384$	0.686290	+	3.71444i	0.0350221	+	0.189552i
$385$	2.68112	+	9.83785i	0.136643	+	0.501383i
$386$		−	16.7423i		−	0.852163i
$387$	−5.75024	+	36.0456i	−0.292301	+	1.83230i
$388$	6.41769	−	3.70526i	0.325809	−	0.188106i
$389$	−15.2961	+	8.83122i	−0.775544	+	0.447761i	−0.834849	−	0.550479i	$-0.814445\pi$
$389$	−15.2961	+	8.83122i	−0.775544	+	0.447761i	0.0593046	+	0.998240i	$0.481112\pi$
$390$	0.764436	−	2.15488i	0.0387087	−	0.109117i
$391$		−	41.6334i		−	2.10549i
$392$	10.9336	+	18.5695i	0.552230	+	0.937900i
$393$	−10.8295	+	2.00089i	−0.546276	+	0.100932i
$394$	−4.41201	+	7.64182i	−0.222274	+	0.384989i
$395$	6.28284	+	10.8822i	0.316124	+	0.547543i
$396$	−4.40655	+	5.42926i	−0.221437	+	0.272830i
$397$	−31.0871	−	17.9481i	−1.56022	−	0.900791i	−0.997234	−	0.0743205i	$-0.976321\pi$
$397$	−31.0871	−	17.9481i	−1.56022	−	0.900791i	−0.562981	−	0.826470i	$-0.690345\pi$
$398$	24.4498			1.22556
$399$	1.37886	+	2.86343i	0.0690294	+	0.143351i
$400$	7.71729			0.385864
$401$	21.4826	+	12.4030i	1.07279	+	0.619376i	0.928943	−	0.370224i	$-0.120719\pi$
$401$	21.4826	+	12.4030i	1.07279	+	0.619376i	0.143848	+	0.989600i	$0.454052\pi$
$402$	−1.03042	+	0.879066i	−0.0513925	+	0.0438438i
$403$	−3.05826	−	5.29706i	−0.152343	−	0.263865i
$404$	2.08123	−	3.60480i	0.103545	−	0.179346i
$405$	7.76006	−	6.95594i	0.385601	−	0.345644i
$406$	−2.40895	+	9.14636i	−0.119554	+	0.453926i
$407$		−	33.2096i		−	1.64614i
$408$	−28.2223	−	10.0117i	−1.39721	−	0.495654i
$409$	14.4326	−	8.33269i	0.713648	−	0.412025i	−0.0987624	−	0.995111i	$-0.531488\pi$
$409$	14.4326	−	8.33269i	0.713648	−	0.412025i	0.812410	+	0.583086i	$0.198155\pi$
$410$	−6.77825	+	3.91342i	−0.334754	+	0.193270i
$411$	3.30193	+	1.17135i	0.162872	+	0.0577782i
$412$		−	0.355940i		−	0.0175359i
$413$	10.4335	+	10.3448i	0.513400	+	0.509034i
$414$	−23.6803	+	9.05974i	−1.16382	+	0.445262i
$415$	−6.75213	+	11.6950i	−0.331449	+	0.574087i
$416$	−1.87628	−	3.24981i	−0.0919922	−	0.159335i
$417$	−10.7522	+	9.17286i	−0.526536	+	0.449197i
$418$	−2.27900	−	1.31578i	−0.111469	−	0.0643568i
$419$	3.86092			0.188618			0.0943092	−	0.995543i	$-0.469936\pi$
$419$	3.86092			0.188618			0.0943092	+	0.995543i	$0.469936\pi$
$420$	−3.07020	−	2.09335i	−0.149811	−	0.102145i
$421$	6.23300			0.303778			0.151889	−	0.988398i	$-0.451464\pi$
$421$	6.23300			0.303778			0.151889	+	0.988398i	$0.451464\pi$
$422$	18.0650	+	10.4298i	0.879391	+	0.507717i
$423$	−6.28185	−	5.09854i	−0.305434	−	0.247900i
$424$	17.4419	+	30.2103i	0.847053	+	1.46714i
$425$	−10.2753	+	17.7973i	−0.498425	+	0.863298i
$426$	1.88141	−	0.347614i	0.0911545	−	0.0168420i
$427$	27.7375	+	7.30544i	1.34231	+	0.353535i
$428$		−	1.30637i		−	0.0631455i
$429$	−1.92738	+	5.43313i	−0.0930547	+	0.262314i
$430$	13.9098	−	8.03084i	0.670791	−	0.387281i
$431$	1.84655	−	1.06611i	0.0889452	−	0.0513525i	−0.454868	−	0.890559i	$-0.650313\pi$
$431$	1.84655	−	1.06611i	0.0889452	−	0.0513525i	0.543813	+	0.839207i	$0.316980\pi$
$432$	0.268556	+	10.9554i	0.0129209	+	0.527092i
$433$			15.9100i			0.764585i	0.924041	+	0.382293i	$0.124865\pi$
$433$			15.9100i			0.764585i	−0.924041	+	0.382293i	$0.875135\pi$
$434$	17.7999	−	4.85104i	0.854424	−	0.232857i
$435$	−1.14263	−	6.18431i	−0.0547850	−	0.296515i
$436$	4.44577	−	7.70030i	0.212914	−	0.368778i
$437$	2.57061	+	4.45243i	0.122969	+	0.212989i
$438$	−1.55534	−	1.82312i	−0.0743169	−	0.0871121i
$439$	−5.90758	−	3.41074i	−0.281953	−	0.162786i	0.352354	−	0.935867i	$-0.385381\pi$
$439$	−5.90758	−	3.41074i	−0.281953	−	0.162786i	−0.634307	+	0.773081i	$0.718715\pi$
$440$	11.8643			0.565608
$441$	7.67111	+	19.5488i	0.365291	+	0.930893i
$442$	−6.40265			−0.304543
$443$	0.693051	+	0.400133i	0.0329279	+	0.0190109i	0.516374	−	0.856363i	$-0.327282\pi$
$443$	0.693051	+	0.400133i	0.0329279	+	0.0190109i	−0.483446	+	0.875374i	$0.660615\pi$
$444$	7.85482	+	9.20719i	0.372773	+	0.436954i
$445$	−1.26604	−	2.19284i	−0.0600159	−	0.103951i
$446$	−6.29921	+	10.9105i	−0.298276	+	0.516629i
$447$	−0.662400	−	3.58514i	−0.0313305	−	0.169571i
$448$	21.6876	−	5.91054i	1.02464	−	0.279247i
$449$		−	4.17909i		−	0.197223i	−0.995126	−	0.0986117i	$-0.968560\pi$
$449$		−	4.17909i		−	0.197223i	0.995126	−	0.0986117i	$-0.0314402\pi$
$450$	12.3588	+	1.97155i	0.582597	+	0.0929398i
$451$	17.0901	−	9.86695i	0.804740	−	0.464617i
$452$	6.74991	−	3.89706i	0.317489	−	0.183302i
$453$	−5.24104	+	14.7741i	−0.246246	+	0.694147i
$454$			24.1814i			1.13489i
$455$	−2.96255	−	0.780269i	−0.138886	−	0.0365796i
$456$	3.63636	−	0.671864i	0.170288	−	0.0314629i
$457$	19.3764	−	33.5609i	0.906388	−	1.56991i	0.0873453	−	0.996178i	$-0.472162\pi$
$457$	19.3764	−	33.5609i	0.906388	−	1.56991i	0.819043	−	0.573732i	$-0.194505\pi$
$458$	−0.256512	−	0.444291i	−0.0119860	−	0.0207604i
$459$	−25.6226	−	13.9674i	−1.19596	−	0.651943i
$460$	−5.20590	−	3.00563i	−0.242726	−	0.140138i
$461$	−32.8166			−1.52842			−0.764211	−	0.644966i	$-0.776872\pi$
$461$	−32.8166			−1.52842			−0.764211	+	0.644966i	$0.776872\pi$
$462$	−14.3668	−	9.79565i	−0.668402	−	0.455735i
$463$	−6.83806			−0.317792			−0.158896	−	0.987295i	$-0.550793\pi$
$463$	−6.83806			−0.317792			−0.158896	+	0.987295i	$0.550793\pi$
$464$	5.72727	+	3.30664i	0.265882	+	0.153507i
$465$	−9.33247	+	7.96170i	−0.432783	+	0.369215i
$466$	−7.39529	−	12.8090i	−0.342580	−	0.593366i
$467$	−16.9174	+	29.3017i	−0.782842	+	1.35592i	0.147438	+	0.989071i	$0.452897\pi$
$467$	−16.9174	+	29.3017i	−0.782842	+	1.35592i	−0.930280	+	0.366851i	$0.880436\pi$
$468$	−0.750702	−	1.96218i	−0.0347012	−	0.0907017i
$469$	1.28872	+	1.27776i	0.0595075	+	0.0590014i
$470$			3.56007i			0.164214i
$471$	−17.8289	−	6.32473i	−0.821512	−	0.291428i
$472$	14.8052	−	8.54779i	0.681465	−	0.393444i
$473$	−35.0710	+	20.2482i	−1.61256	+	0.931014i
$474$	−20.1953	−	7.16420i	−0.927601	−	0.329062i
$475$		−	2.53775i		−	0.116440i
$476$	−2.65022	+	10.0624i	−0.121473	+	0.461210i
$477$	12.1472	+	31.7504i	0.556184	+	1.45375i
$478$	−10.0603	+	17.4249i	−0.460145	+	0.796995i
$479$	−16.0537	−	27.8059i	−0.733514	−	1.27048i	−0.955372	−	0.295405i	$-0.904545\pi$
$479$	−16.0537	−	27.8059i	−0.733514	−	1.27048i	0.221858	−	0.975079i	$-0.428788\pi$
$480$	−5.72559	+	4.88460i	−0.261336	+	0.222951i
$481$	8.64102	+	4.98890i	0.393997	+	0.227474i
$482$	−21.8603			−0.995708
$483$	14.7389	+	30.6077i	0.670642	+	1.39270i
$484$	−0.0545508			−0.00247958
$485$	−10.6115	−	6.12658i	−0.481845	−	0.278194i
$486$	−2.36872	+	17.6130i	−0.107448	+	0.798942i
$487$	4.88254	+	8.45680i	0.221249	+	0.383214i	0.955187	−	0.296001i	$-0.0956533\pi$
$487$	4.88254	+	8.45680i	0.221249	+	0.383214i	−0.733939	+	0.679216i	$0.762320\pi$
$488$	16.6873	−	28.9032i	0.755398	−	1.30839i
$489$	4.54087	−	0.838985i	0.205345	−	0.0379402i
$490$	4.55179	−	8.04177i	0.205629	−	0.363290i
$491$			10.3757i			0.468250i	0.972207	+	0.234125i	$0.0752225\pi$
$491$			10.3757i			0.468250i	−0.972207	+	0.234125i	$0.924778\pi$
$492$	−2.40438	+	6.77776i	−0.108398	+	0.305565i
$493$	−15.2513	+	8.80536i	−0.686885	+	0.396573i
$494$	0.684723	−	0.395325i	0.0308071	−	0.0177865i
$495$	11.4175	+	1.82140i	0.513181	+	0.0818660i
$496$		−	12.8997i		−	0.579216i
$497$	−0.674057	−	2.47332i	−0.0302356	−	0.110944i
$498$	−4.18408	−	22.6457i	−0.187493	−	1.01478i
$499$	−7.31298	+	12.6665i	−0.327374	+	0.567028i	−0.981990	−	0.188933i	$-0.939497\pi$
$499$	−7.31298	+	12.6665i	−0.327374	+	0.567028i	0.654616	+	0.755962i	$0.272830\pi$
$500$	3.51082	+	6.08092i	0.157009	+	0.271947i
$501$	4.88479	+	5.72581i	0.218236	+	0.255810i
$502$	5.82283	+	3.36181i	0.259886	+	0.150045i
$503$	33.1403			1.47765			0.738825	−	0.673897i	$-0.235381\pi$
$503$	33.1403			1.47765			0.738825	+	0.673897i	$0.235381\pi$
$504$	24.2925	−	2.63078i	1.08207	−	0.117184i
$505$	−6.88257			−0.306270
$506$	−24.3606	−	14.0646i	−1.08296	−	0.625247i
$507$	−1.12414	−	1.31769i	−0.0499249	−	0.0585206i
$508$	−3.14372	−	5.44508i	−0.139480	−	0.241586i
$509$	21.1317	−	36.6011i	0.936645	−	1.62232i	0.164971	−	0.986298i	$-0.447247\pi$
$509$	21.1317	−	36.6011i	0.936645	−	1.62232i	0.771674	−	0.636018i	$-0.219420\pi$
$510$	2.33306	+	12.6273i	0.103310	+	0.559147i
$511$	−2.26075	+	2.28014i	−0.100010	+	0.100867i
$512$		−	20.8991i		−	0.923619i
$513$	3.60257	−	0.0883120i	0.159058	−	0.00389907i
$514$	−11.1796	+	6.45452i	−0.493109	+	0.284697i
$515$	−0.509692	+	0.294271i	−0.0224597	+	0.0129671i
$516$	4.93409	−	13.9088i	0.217211	−	0.612301i
$517$		−	8.97604i		−	0.394766i
$518$	−21.1899	+	21.3716i	−0.931030	+	0.939016i
$519$	−0.160801	+	0.0297100i	−0.00705838	+	0.00130413i
$520$	−1.78231	+	3.08705i	−0.0781595	+	0.135376i
$521$	−20.9354	−	36.2612i	−0.917196	−	1.58863i	−0.803654	−	0.595097i	$-0.797114\pi$
$521$	−20.9354	−	36.2612i	−0.917196	−	1.58863i	−0.113542	−	0.993533i	$-0.536220\pi$
$522$	8.32711	+	6.75854i	0.364468	+	0.295813i
$523$	8.15800	+	4.71002i	0.356724	+	0.205955i	0.667643	−	0.744482i	$-0.267303\pi$
$523$	8.15800	+	4.71002i	0.356724	+	0.205955i	−0.310919	+	0.950437i	$0.600637\pi$
$524$	4.45264			0.194514
$525$	1.25357	−	16.7217i	0.0547103	−	0.729795i
$526$	−2.78563			−0.121459
$527$	29.7490	+	17.1756i	1.29588	+	0.748179i
$528$	−9.24950	+	7.89091i	−0.402533	+	0.343408i
$529$	15.9777	+	27.6742i	0.694684	+	1.20323i
$530$	7.47933	−	12.9546i	0.324881	−	0.562711i
$531$	15.5600	−	5.95303i	0.675245	−	0.258340i
$532$	−0.337870	−	1.23975i	−0.0146485	−	0.0537499i
$533$			5.92904i			0.256815i
$534$	4.06949	+	1.44363i	0.176104	+	0.0624722i
$535$	−1.87066	+	1.08003i	−0.0808757	+	0.0466936i
$536$	1.82870	−	1.05580i	0.0789876	−	0.0456035i
$537$	−30.7912	−	10.9230i	−1.32874	−	0.471364i
$538$			3.79829i			0.163756i
$539$	−11.4765	+	20.2758i	−0.494327	+	0.873340i
$540$	−3.59626	+	2.19553i	−0.154759	+	0.0944808i
$541$	4.14442	−	7.17834i	0.178182	−	0.308621i	−0.763076	−	0.646309i	$-0.776312\pi$
$541$	4.14442	−	7.17834i	0.178182	−	0.308621i	0.941258	+	0.337688i	$0.109645\pi$
$542$	−17.2269	−	29.8379i	−0.739959	−	1.28165i
$543$	−5.34537	+	4.56023i	−0.229392	+	0.195698i
$544$	18.2514	+	10.5374i	0.782521	+	0.451789i
$545$	−14.7020			−0.629765
$546$	4.70704	−	2.26663i	0.201443	−	0.0970030i
$547$	4.39634			0.187974			0.0939870	−	0.995573i	$-0.470039\pi$
$547$	4.39634			0.187974			0.0939870	+	0.995573i	$0.470039\pi$
$548$	−1.22675	−	0.708266i	−0.0524043	−	0.0302556i
$549$	20.4961	−	25.2530i	0.874754	−	1.07777i
$550$	6.94239	+	12.0246i	0.296025	+	0.512730i
$551$	1.08736	−	1.88336i	0.0463229	−	0.0802336i
$552$	38.8696	−	7.18167i	1.65440	−	0.305672i
$553$	−7.31258	+	27.7646i	−0.310963	+	1.18067i
$554$		−	14.4749i		−	0.614980i
$555$	6.69041	−	18.8597i	0.283992	−	0.800552i
$556$	4.94873	−	2.85715i	0.209873	−	0.121170i
$557$	25.4288	−	14.6813i	1.07745	−	0.622069i	0.147246	−	0.989100i	$-0.452959\pi$
$557$	25.4288	−	14.6813i	1.07745	−	0.622069i	0.930209	+	0.367031i	$0.119626\pi$
$558$	3.29552	−	20.6581i	0.139511	−	0.874528i
$559$		−	12.1671i		−	0.514615i
$560$	−4.58815	−	4.54913i	−0.193885	−	0.192236i
$561$	−5.88236	−	31.8374i	−0.248354	−	1.34417i
$562$	10.7601	−	18.6370i	0.453888	−	0.786156i
$563$	19.3315	+	33.4831i	0.814724	+	1.41114i	0.909526	+	0.415647i	$0.136445\pi$
$563$	19.3315	+	33.4831i	0.814724	+	1.41114i	−0.0948018	+	0.995496i	$0.530222\pi$
$564$	2.12304	+	2.48856i	0.0893960	+	0.104787i
$565$	−11.1609	−	6.44373i	−0.469541	−	0.271090i
$566$	10.7799			0.453115
$567$	23.7816	+	1.19766i	0.998734	+	0.0502968i
$568$	−2.98279			−0.125155
$569$	23.8868	+	13.7910i	1.00139	+	0.578150i	0.908658	−	0.417541i	$-0.137108\pi$
$569$	23.8868	+	13.7910i	1.00139	+	0.578150i	0.0927276	+	0.995692i	$0.470441\pi$
$570$	−1.02917	−	1.20636i	−0.0431070	−	0.0505288i
$571$	−21.8712	−	37.8821i	−0.915282	−	1.58532i	−0.806488	−	0.591251i	$-0.798634\pi$
$571$	−21.8712	−	37.8821i	−0.915282	−	1.58532i	−0.108794	−	0.994064i	$-0.534699\pi$
$572$	1.16541	−	2.01855i	0.0487282	−	0.0843998i
$573$	5.05341	+	27.3508i	0.211109	+	1.14260i
$574$	−17.2939	−	4.55482i	−0.721833	−	0.190115i
$575$		−	27.1265i		−	1.13125i
$576$	4.01529	−	25.1700i	0.167304	−	1.04875i
$577$	−11.5339	+	6.65907i	−0.480161	+	0.277221i	−0.720483	−	0.693472i	$-0.756080\pi$
$577$	−11.5339	+	6.65907i	−0.480161	+	0.277221i	0.240323	+	0.970693i	$0.422747\pi$
$578$	14.3564	−	8.28865i	0.597146	−	0.344762i
$579$	−8.50417	+	23.9726i	−0.353421	+	0.996267i
$580$			2.54273i			0.105581i
$581$	−29.7703	+	8.11333i	−1.23508	+	0.336598i
$582$	20.5477	−	3.79644i	0.851728	−	0.157368i
$583$	−18.8577	+	32.6625i	−0.781006	+	1.35274i
$584$	1.86803	+	3.23552i	0.0772997	+	0.133887i
$585$	−2.18912	+	2.69719i	−0.0905090	+	0.111515i
$586$	−20.1347	−	11.6248i	−0.831756	−	0.480214i
$587$	−19.6830			−0.812406			−0.406203	−	0.913783i	$-0.633147\pi$
$587$	−19.6830			−0.812406			−0.406203	+	0.913783i	$0.633147\pi$
$588$	−1.61389	−	8.33581i	−0.0665556	−	0.343763i
$589$	−4.24195			−0.174787
$590$	−6.34868	−	3.66541i	−0.261371	−	0.150903i
$591$	10.1990	−	8.70092i	0.419529	−	0.357908i
$592$	10.5216	+	18.2239i	0.432435	+	0.748999i
$593$	0.992042	−	1.71827i	0.0407383	−	0.0705608i	−0.844937	−	0.534865i	$-0.820362\pi$
$593$	0.992042	−	1.71827i	0.0407383	−	0.0705608i	0.885676	+	0.464305i	$0.153696\pi$
$594$	−16.8284	+	10.2738i	−0.690478	+	0.421540i
$595$	16.6000	−	4.52402i	0.680534	−	0.185467i
$596$			1.47406i			0.0603797i
$597$	−35.0086	−	12.4191i	−1.43281	−	0.508281i
$598$	7.31912	−	4.22569i	0.299301	−	0.172801i
$599$	−24.3041	+	14.0320i	−0.993037	+	0.573330i	−0.906181	−	0.422891i	$-0.861015\pi$
$599$	−24.3041	+	14.0320i	−0.993037	+	0.573330i	−0.0868565	+	0.996221i	$0.527682\pi$
$600$	−18.3884	−	6.52319i	−0.750701	−	0.266308i
$601$		−	29.9548i		−	1.22188i	−0.791676	−	0.610941i	$-0.790791\pi$
$601$		−	29.9548i		−	1.22188i	0.791676	−	0.610941i	$-0.209209\pi$
$602$	35.4892	+	9.34707i	1.44643	+	0.380958i
$603$	1.92192	−	0.735301i	0.0782667	−	0.0299438i
$604$	3.16905	−	5.48896i	0.128947	−	0.223343i
$605$	0.0450994	+	0.0781145i	0.00183355	+	0.00317581i
$606$	8.92906	−	7.61754i	0.362718	−	0.309441i
$607$	−37.7283	−	21.7824i	−1.53134	−	0.884122i	−0.999300	−	0.0374048i	$-0.988091\pi$
$607$	−37.7283	−	21.7824i	−1.53134	−	0.884122i	−0.532044	−	0.846717i	$-0.678576\pi$
$608$	−2.60249			−0.105545
$609$	8.09510	−	11.8726i	0.328030	−	0.481104i
$610$	−14.3115			−0.579455
$611$	2.33554	+	1.34842i	0.0944857	+	0.0545514i
$612$	9.16112	+	7.43545i	0.370316	+	0.300560i
$613$	7.60454	+	13.1714i	0.307144	+	0.531990i	0.977736	−	0.209837i	$-0.0672932\pi$
$613$	7.60454	+	13.1714i	0.307144	+	0.531990i	−0.670592	+	0.741826i	$0.733960\pi$
$614$	8.75827	−	15.1698i	0.353455	−	0.612202i
$615$	11.6933	−	2.16048i	0.471518	−	0.0871190i
$616$	19.2505	+	19.0868i	0.775626	+	0.769030i
$617$			13.7286i			0.552692i	0.961058	+	0.276346i	$0.0891236\pi$
$617$			13.7286i			0.552692i	−0.961058	+	0.276346i	$0.910876\pi$
$618$	0.335551	−	0.945891i	0.0134978	−	0.0380493i
$619$	31.9696	−	18.4576i	1.28497	−	0.741875i	0.307213	−	0.951641i	$-0.400603\pi$
$619$	31.9696	−	18.4576i	1.28497	−	0.741875i	0.977752	+	0.209766i	$0.0672701\pi$
$620$	4.29531	−	2.47990i	0.172504	−	0.0995952i
$621$	38.5085	−	0.943982i	1.54529	−	0.0378807i
$622$			36.7169i			1.47221i
$623$	1.47354	−	5.59476i	0.0590360	−	0.224149i
$624$	−0.663687	−	3.59210i	−0.0265687	−	0.143799i
$625$	−3.34295	+	5.79017i	−0.133718	+	0.231607i
$626$	0.936452	+	1.62198i	0.0374281	+	0.0648274i
$627$	2.59485	+	3.04161i	0.103628	+	0.121470i
$628$	6.62390	+	3.82431i	0.264322	+	0.152607i
$629$	−56.0366			−2.23432
$630$	−6.18546	−	8.45729i	−0.246434	−	0.336947i
$631$	9.47126			0.377045			0.188523	−	0.982069i	$-0.439630\pi$
$631$	9.47126			0.377045			0.188523	+	0.982069i	$0.439630\pi$
$632$	28.9315	+	16.7036i	1.15083	+	0.664433i
$633$	−20.5687	−	24.1100i	−0.817532	−	0.958288i
$634$	−10.9312	−	18.9334i	−0.434133	−	0.751940i
$635$	−5.19808	+	9.00334i	−0.206280	+	0.357287i
$636$	−2.49722	−	13.5158i	−0.0990211	−	0.535936i
$637$	−3.55164	−	6.03207i	−0.140721	−	0.238999i
$638$			11.8985i			0.471065i
$639$	−2.87047	−	0.457917i	−0.113554	−	0.0181149i
$640$	−2.18691	+	1.26262i	−0.0864454	+	0.0499093i
$641$	−15.5481	+	8.97668i	−0.614112	+	0.354557i	−0.774573	−	0.632485i	$-0.782035\pi$
$641$	−15.5481	+	8.97668i	−0.614112	+	0.354557i	0.160461	+	0.987042i	$0.448702\pi$
$642$	1.23153	−	3.47159i	0.0486047	−	0.137013i
$643$			16.1616i			0.637350i	0.947864	+	0.318675i	$0.103238\pi$
$643$			16.1616i			0.637350i	−0.947864	+	0.318675i	$0.896762\pi$
$644$	−3.61155	−	13.2519i	−0.142315	−	0.522197i
$645$	−23.9960	+	4.43358i	−0.944843	+	0.174572i
$646$	−2.22020	+	3.84549i	−0.0873524	+	0.151299i
$647$	11.7745	+	20.3941i	0.462904	+	0.801773i	0.999104	−	0.0423177i	$-0.0134742\pi$
$647$	11.7745	+	20.3941i	0.462904	+	0.801773i	−0.536200	+	0.844091i	$0.680141\pi$
$648$	8.62037	−	26.3310i	0.338640	−	1.03438i
$649$	16.0070	+	9.24164i	0.628329	+	0.362766i
$650$	−4.17167			−0.163627
$651$	−27.9510	−	2.09539i	−1.09548	−	0.0821249i
$652$	−1.86702			−0.0731180
$653$	1.05254	+	0.607686i	0.0411892	+	0.0237806i	0.520453	−	0.853890i	$-0.325763\pi$
$653$	1.05254	+	0.607686i	0.0411892	+	0.0237806i	−0.479264	+	0.877671i	$0.659096\pi$
$654$	19.0736	−	16.2720i	0.745836	−	0.636286i
$655$	−3.68118	−	6.37599i	−0.143836	−	0.249131i
$656$	−6.25218	+	10.8291i	−0.244107	+	0.422805i
$657$	1.30097	+	3.40047i	0.0507558	+	0.132665i
$658$	−5.72731	+	5.77643i	−0.223274	+	0.225189i
$659$			24.3604i			0.948948i	0.880270	+	0.474474i	$0.157362\pi$
$659$			24.3604i			0.948948i	−0.880270	+	0.474474i	$0.842638\pi$
$660$	−4.40565	−	1.56289i	−0.171490	−	0.0608352i
$661$	−39.1761	+	22.6183i	−1.52377	+	0.879751i	−0.524169	+	0.851614i	$0.675624\pi$
$661$	−39.1761	+	22.6183i	−1.52377	+	0.879751i	−0.999604	+	0.0281362i	$0.991043\pi$
$662$	2.61732	−	1.51111i	0.101725	−	0.0587310i
$663$	9.16766	+	3.25219i	0.356042	+	0.126304i
$664$			35.9025i			1.39329i
$665$	−1.49594	+	1.50877i	−0.0580099	+	0.0585074i
$666$	12.1940	+	31.8725i	0.472507	+	1.23503i
$667$	11.6229	−	20.1315i	0.450042	−	0.779495i
$668$	−1.52151	−	2.63533i	−0.0588690	−	0.101964i
$669$	14.5615	−	12.4227i	0.562980	−	0.480288i
$670$	−0.784170	−	0.452741i	−0.0302951	−	0.0174909i
$671$	36.0837			1.39299
$672$	−17.1483	−	1.28555i	−0.661509	−	0.0495912i
$673$	−15.6186			−0.602051			−0.301025	−	0.953616i	$-0.597329\pi$
$673$	−15.6186			−0.602051			−0.301025	+	0.953616i	$0.597329\pi$
$674$	−29.5217	−	17.0443i	−1.13713	−	0.656524i
$675$	−16.6945	−	9.10053i	−0.642571	−	0.350280i
$676$	0.350147	+	0.606472i	0.0134672	+	0.0233258i
$677$	17.3645	−	30.0762i	0.667373	−	1.15592i	−0.311263	−	0.950324i	$-0.600752\pi$
$677$	17.3645	−	30.0762i	0.667373	−	1.15592i	0.978636	−	0.205600i	$-0.0659145\pi$
$678$	21.6113	−	3.99297i	0.829978	−	0.153349i
$679$	−7.36166	−	27.0122i	−0.282515	−	1.03663i
$680$		−	20.0194i		−	0.767708i
$681$	12.2828	−	34.6242i	0.470677	−	1.32680i
$682$	20.0995	−	11.6045i	0.769651	−	0.444358i
$683$	35.7178	−	20.6217i	1.36671	−	0.789068i	0.376200	−	0.926539i	$-0.377231\pi$
$683$	35.7178	−	20.6217i	1.36671	−	0.789068i	0.990506	+	0.137471i	$0.0438973\pi$
$684$	−1.43882	−	0.229530i	−0.0550146	−	0.00877630i
$685$			2.34221i			0.0894913i
$686$	20.3228	−	5.72550i	0.775930	−	0.218601i
$687$	0.141612	+	0.766454i	0.00540284	+	0.0292420i
$688$	12.8303	−	22.2227i	0.489149	−	0.847231i
$689$	−5.66579	−	9.81343i	−0.215849	−	0.373862i
$690$	−11.0009	−	12.8950i	−0.418798	−	0.490903i
$691$	−1.68394	−	0.972223i	−0.0640601	−	0.0369851i	0.467628	−	0.883925i	$-0.345109\pi$
$691$	−1.68394	−	0.972223i	−0.0640601	−	0.0369851i	−0.531688	+	0.846940i	$0.678442\pi$
$692$	0.0661146			0.00251330
$693$	15.5954	+	21.3234i	0.592422	+	0.810011i
$694$	−3.54678			−0.134634
$695$	−8.18264	−	4.72425i	−0.310385	−	0.179201i
$696$	−10.8516	−	12.7200i	−0.411330	−	0.482150i
$697$	−16.6491	−	28.8371i	−0.630631	−	1.09228i
$698$	−3.62632	+	6.28098i	−0.137258	+	0.237739i
$699$	4.08271	+	22.0970i	0.154422	+	0.835787i
$700$	−1.72676	+	6.55622i	−0.0652654	+	0.247802i
$701$		−	8.15085i		−	0.307853i	−0.988082	−	0.153927i	$-0.950808\pi$
$701$		−	8.15085i		−	0.307853i	0.988082	−	0.153927i	$-0.0491920\pi$
$702$	−0.145171	−	5.92208i	−0.00547914	−	0.223514i
$703$	5.99276	−	3.45992i	0.226021	−	0.130493i
$704$	24.4894	−	14.1390i	0.922980	−	0.532883i
$705$	1.80832	−	5.09750i	0.0681051	−	0.191983i
$706$			20.4988i			0.771481i
$707$	−11.1674	−	11.0724i	−0.419992	−	0.416421i
$708$	−6.62372	+	1.22382i	−0.248935	+	0.0459939i
$709$	−10.3034	+	17.8461i	−0.386953	+	0.670223i	−0.992038	−	0.125938i	$-0.959806\pi$
$709$	−10.3034	+	17.8461i	−0.386953	+	0.670223i	0.605085	+	0.796161i	$0.293139\pi$
$710$	0.639530	+	1.10770i	0.0240011	+	0.0415712i
$711$	25.2777	+	20.5162i	0.947989	+	0.769416i
$712$	−5.82989	−	3.36589i	−0.218484	−	0.126142i
$713$	−45.3429			−1.69811
$714$	−16.5288	+	24.2419i	−0.618575	+	0.907231i
$715$	−3.85397			−0.144130
$716$	11.4397	+	6.60473i	0.427523	+	0.246830i
$717$	23.2557	−	19.8398i	0.868499	−	0.740932i
$718$	6.22206	+	10.7769i	0.232205	+	0.402191i
$719$	6.89752	−	11.9469i	0.257234	−	0.445543i	−0.708266	−	0.705946i	$-0.750522\pi$
$719$	6.89752	−	11.9469i	0.257234	−	0.445543i	0.965500	+	0.260403i	$0.0838555\pi$
$720$	−6.84251	+	2.61785i	−0.255005	+	0.0975615i
$721$	−1.30042	−	0.342501i	−0.0484300	−	0.0127554i
$722$			21.1126i			0.785728i
$723$	31.3007	+	11.1038i	1.16409	+	0.412955i
$724$	2.46023	−	1.42042i	0.0914338	−	0.0527893i
$725$	−9.93707	+	5.73717i	−0.369054	+	0.213073i
$726$	−0.144966	−	0.0514259i	−0.00538018	−	0.00190860i
$727$		−	12.0151i		−	0.445614i	−0.974863	−	0.222807i	$-0.928478\pi$
$727$		−	12.0151i		−	0.445614i	0.974863	−	0.222807i	$-0.0715220\pi$
$728$	−7.85824	+	2.14162i	−0.291246	+	0.0793735i
$729$	12.3381	−	24.0161i	0.456966	−	0.889484i
$730$	0.801038	−	1.38744i	0.0296477	−	0.0513514i
$731$	34.1661	+	59.1774i	1.26368	+	2.18876i
$732$	−10.0040	+	8.53461i	−0.369760	+	0.315448i
$733$	20.2559	+	11.6948i	0.748169	+	0.431956i	0.825032	−	0.565086i	$-0.191157\pi$
$733$	20.2559	+	11.6948i	0.748169	+	0.431956i	−0.0768629	+	0.997042i	$0.524490\pi$
$734$	−2.69178			−0.0993554
$735$	−10.6023	+	9.20258i	−0.391071	+	0.339442i
$736$	−27.8185			−1.02540
$737$	1.97714	+	1.14150i	0.0728288	+	0.0420477i
$738$	−12.7790	+	15.7449i	−0.470402	+	0.579576i
$739$	1.41970	+	2.45899i	0.0522244	+	0.0904553i	0.890956	−	0.454090i	$-0.150036\pi$
$739$	1.41970	+	2.45899i	0.0522244	+	0.0904553i	−0.838731	+	0.544545i	$0.816702\pi$
$740$	−4.04543	+	7.00689i	−0.148713	+	0.257578i
$741$	−1.18123	+	0.218247i	−0.0433934	+	0.00801749i
$742$	32.9765	−	8.98712i	1.21060	−	0.329928i
$743$			31.2604i			1.14683i	0.819265	+	0.573416i	$0.194382\pi$
$743$			31.2604i			1.14683i	−0.819265	+	0.573416i	$0.805618\pi$
$744$	−10.9038	+	30.7368i	−0.399751	+	1.12687i
$745$	2.11079	−	1.21866i	0.0773333	−	0.0446484i
$746$	−22.6447	+	13.0739i	−0.829083	+	0.478671i
$747$	−5.51174	+	34.5506i	−0.201664	+	1.26414i
$748$			13.0902i			0.478625i
$749$	−4.77276	−	1.25704i	−0.174393	−	0.0459312i
$750$	3.59722	+	19.4694i	0.131352	+	0.710922i
$751$	−2.60689	+	4.51527i	−0.0951268	+	0.164764i	−0.909662	−	0.415350i	$-0.863659\pi$
$751$	−2.60689	+	4.51527i	−0.0951268	+	0.164764i	0.814535	+	0.580115i	$0.196992\pi$
$752$	2.84383	+	4.92565i	0.103704	+	0.179620i
$753$	−6.62983	−	7.77130i	−0.241604	−	0.283202i
$754$	−3.09595	−	1.78745i	−0.112748	−	0.0650949i
$755$	−10.4799			−0.381404
$756$	−9.36725	−	2.22315i	−0.340683	−	0.0808550i
$757$	−36.3568			−1.32141			−0.660705	−	0.750646i	$-0.729742\pi$
$757$	−36.3568			−1.32141			−0.660705	+	0.750646i	$0.729742\pi$
$758$	−10.4238	−	6.01820i	−0.378610	−	0.218591i
$759$	27.7368	+	32.5122i	1.00678	+	1.18012i
$760$	1.23608	+	2.14095i	0.0448372	+	0.0776603i
$761$	−4.11661	+	7.13018i	−0.149227	+	0.258469i	−0.930942	−	0.365167i	$-0.881012\pi$
$761$	−4.11661	+	7.13018i	−0.149227	+	0.258469i	0.781715	+	0.623636i	$0.214345\pi$
$762$	−3.22109	−	17.4336i	−0.116688	−	0.631553i
$763$	−23.8549	−	23.6520i	−0.863606	−	0.856262i
$764$		−	11.2455i		−	0.406848i
$765$	3.07337	−	19.2655i	0.111118	−	0.696547i
$766$	−19.5146	+	11.2668i	−0.705091	+	0.407085i
$767$	−4.80929	+	2.77665i	−0.173653	+	0.100259i
$768$	−8.40010	+	23.6792i	−0.303113	+	0.854451i
$769$			2.60147i			0.0938112i	0.998899	+	0.0469056i	$0.0149360\pi$
$769$			2.60147i			0.0938112i	−0.998899	+	0.0469056i	$0.985064\pi$
$770$	2.96071	−	11.2413i	0.106697	−	0.405108i
$771$	19.2860	−	3.56335i	0.694570	−	0.128331i
$772$	5.14214	−	8.90645i	0.185070	−	0.320550i
$773$	−18.3748	−	31.8261i	−0.660896	−	1.14471i	−0.980381	−	0.197114i	$-0.936843\pi$
$773$	−18.3748	−	31.8261i	−0.660896	−	1.14471i	0.319485	−	0.947591i	$-0.396490\pi$
$774$	26.2241	−	32.3104i	0.942606	−	1.16137i
$775$	19.3831	+	11.1908i	0.696260	+	0.401986i
$776$	−32.5763			−1.16942
$777$	41.1964	−	19.8378i	1.47791	−	0.711677i
$778$	20.1360			0.721911
$779$	3.56104	+	2.05597i	0.127587	+	0.0736626i
$780$	1.06850	−	0.911552i	0.0382583	−	0.0326388i
$781$	−1.61245	−	2.79285i	−0.0576981	−	0.0999361i
$782$	−23.7320	+	41.1051i	−0.848656	+	1.46992i
$783$	−8.49025	−	13.9069i	−0.303417	−	0.496994i
$784$	−0.126079	−	14.7625i	−0.00450283	−	0.527231i
$785$		−	12.6469i		−	0.451386i
$786$	11.8326	+	4.19757i	0.422056	+	0.149722i
$787$	−36.9061	+	21.3077i	−1.31556	+	0.759539i	−0.983011	−	0.183547i	$-0.941242\pi$
$787$	−36.9061	+	21.3077i	−1.31556	+	0.759539i	−0.332549	+	0.943086i	$0.607909\pi$
$788$	−4.69412	+	2.71015i	−0.167221	+	0.0965452i
$789$	3.98862	+	1.41495i	0.141999	+	0.0503734i
$790$		−	14.3255i		−	0.509677i
$791$	−7.74275	−	28.4105i	−0.275301	−	1.01016i
$792$	28.7092	−	10.9837i	1.02014	−	0.390290i
$793$	−5.42066	+	9.38886i	−0.192493	+	0.333408i
$794$	20.4617	+	35.4407i	0.726159	+	1.25774i
$795$	−17.2895	+	14.7500i	−0.613196	+	0.523128i
$796$	13.0066	+	7.50936i	0.461007	+	0.266162i
$797$	−7.89346			−0.279601			−0.139800	−	0.990180i	$-0.544646\pi$
$797$	−7.89346			−0.279601			−0.139800	+	0.990180i	$0.544646\pi$
$798$	0.270860	−	3.61307i	0.00958835	−	0.127901i
$799$	−15.1458			−0.535821
$800$	11.8918	+	6.86571i	0.420437	+	0.242740i
$801$	−5.09363	−	4.13415i	−0.179975	−	0.146073i
$802$	−14.1400	−	24.4912i	−0.499300	−	0.864814i
$803$	−2.01966	+	3.49816i	−0.0712724	+	0.123447i
$804$	−0.818142	+	0.151162i	−0.0288537	+	0.00533109i
$805$	−15.9903	+	16.1275i	−0.563584	+	0.568418i
$806$			6.97311i			0.245617i
$807$	1.92932	−	5.43859i	0.0679152	−	0.191448i
$808$	−15.8466	+	9.14901i	−0.557480	+	0.321861i
$809$	12.1069	−	6.98992i	0.425656	−	0.245752i	−0.271839	−	0.962343i	$-0.587632\pi$
$809$	12.1069	−	6.98992i	0.425656	−	0.245752i	0.697494	+	0.716591i	$0.254298\pi$
$810$	−11.6266	+	2.44425i	−0.408518	+	0.0858822i
$811$		−	42.9291i		−	1.50745i	−0.657192	−	0.753723i	$-0.728256\pi$
$811$		−	42.9291i		−	1.50745i	0.657192	−	0.753723i	$-0.271744\pi$
$812$	−4.09065	+	4.12573i	−0.143554	+	0.144785i
$813$	9.51045	+	51.4738i	0.333546	+	1.80526i
$814$	−18.9302	+	32.7881i	−0.663504	+	1.14922i
$815$	1.54354	+	2.67349i	0.0540678	+	0.0936482i
$816$	13.3148	+	15.6073i	0.466112	+	0.546363i
$817$	−7.30770	−	4.21910i	−0.255664	−	0.147608i
$818$	−18.9993			−0.664295
$819$	−7.89112	+	0.854577i	−0.275738	+	0.0298614i
$820$	−4.80778			−0.167895
$821$	28.8892	+	16.6792i	1.00824	+	0.582108i	0.910676	−	0.413121i	$-0.135561\pi$
$821$	28.8892	+	16.6792i	1.00824	+	0.582108i	0.0975648	+	0.995229i	$0.468895\pi$
$822$	−2.59233	−	3.03866i	−0.0904180	−	0.105985i
$823$	7.74800	+	13.4199i	0.270078	+	0.467789i	0.968882	−	0.247525i	$-0.0796171\pi$
$823$	7.74800	+	13.4199i	0.270078	+	0.467789i	−0.698803	+	0.715314i	$0.746284\pi$
$824$	−0.782349	+	1.35507i	−0.0272544	+	0.0472061i
$825$	−3.83268	−	20.7438i	−0.133437	−	0.722206i
$826$	−4.40434	−	16.1609i	−0.153247	−	0.562309i
$827$		−	2.96186i		−	0.102994i	−0.998673	−	0.0514970i	$-0.983601\pi$
$827$		−	2.96186i		−	0.102994i	0.998673	−	0.0514970i	$-0.0163993\pi$
$828$	−15.3798	−	2.45348i	−0.534484	−	0.0852645i
$829$	−6.06376	+	3.50091i	−0.210603	+	0.121592i	−0.601592	−	0.798804i	$-0.705467\pi$
$829$	−6.06376	+	3.50091i	−0.210603	+	0.121592i	0.390989	+	0.920396i	$0.372133\pi$
$830$	13.3329	−	7.69775i	0.462791	−	0.267193i
$831$	−7.35244	+	20.7260i	−0.255053	+	0.718976i
$832$			8.49610i			0.294549i
$833$	34.2126	+	19.3650i	1.18540	+	0.670956i
$834$	15.8445	−	2.92747i	0.548649	−	0.101370i
$835$	−2.51579	+	4.35748i	−0.0870625	+	0.150797i
$836$	−0.808240	−	1.39991i	−0.0279536	−	0.0484170i
$837$	−15.2119	+	27.9055i	−0.525800	+	0.964555i
$838$	−3.81192	−	2.20082i	−0.131681	−	0.0760259i
$839$	14.5751			0.503188			0.251594	−	0.967833i	$-0.419045\pi$
$839$	14.5751			0.503188			0.251594	+	0.967833i	$0.419045\pi$
$840$	7.08716	+	14.7177i	0.244530	+	0.507807i
$841$	19.1671			0.660936
$842$	−6.15390	−	3.55295i	−0.212077	−	0.122443i
$843$	−24.8735	+	21.2200i	−0.856688	+	0.730856i
$844$	6.40671	+	11.0968i	0.220528	+	0.381966i
$845$	0.578962	−	1.00279i	0.0199169	−	0.0344971i
$846$	3.29584	+	8.61464i	0.113313	+	0.296178i
$847$	−0.0524911	+	0.199300i	−0.00180361	+	0.00684802i
$848$		−	23.8983i		−	0.820671i
$849$	−15.4353	−	5.47561i	−0.529738	−	0.187922i
$850$	20.2898	−	11.7143i	0.695935	−	0.401798i
$851$	64.0576	−	36.9837i	2.19587	−	1.26778i
$852$	1.10762	+	0.392923i	0.0379464	+	0.0134613i
$853$			8.44787i			0.289250i	0.989487	+	0.144625i	$0.0461975\pi$
$853$			8.44787i			0.289250i	−0.989487	+	0.144625i	$0.953802\pi$
$854$	−23.2212	−	23.0238i	−0.794614	−	0.787857i
$855$	0.860853	+	2.25009i	0.0294406	+	0.0769514i
$856$	−2.87136	+	4.97335i	−0.0981412	+	0.169986i
$857$	−9.45837	−	16.3824i	−0.323092	−	0.559612i	0.658032	−	0.752990i	$-0.271389\pi$
$857$	−9.45837	−	16.3824i	−0.323092	−	0.559612i	−0.981124	+	0.193378i	$0.938056\pi$
$858$	4.99993	−	4.26553i	0.170695	−	0.145623i
$859$	−6.72524	−	3.88282i	−0.229462	−	0.132480i	0.380862	−	0.924632i	$-0.375627\pi$
$859$	−6.72524	−	3.88282i	−0.229462	−	0.132480i	−0.610324	+	0.792152i	$0.708961\pi$
$860$	9.86616			0.336433
$861$	22.4487	+	15.3062i	0.765050	+	0.521633i
$862$	−2.43082			−0.0827941
$863$	−33.5286	−	19.3577i	−1.14133	−	0.658945i	−0.194568	−	0.980889i	$-0.562330\pi$
$863$	−33.5286	−	19.3577i	−1.14133	−	0.658945i	−0.946759	+	0.321944i	$0.895664\pi$
$864$	−9.33269	+	17.1204i	−0.317504	+	0.582447i
$865$	−0.0546597	−	0.0946733i	−0.00185848	−	0.00321899i
$866$	9.06907	−	15.7081i	0.308179	−	0.533782i
$867$	−24.7664	+	4.57591i	−0.841110	+	0.155406i
$868$	10.9590	+	2.88635i	0.371972	+	0.0979690i
$869$			36.1189i			1.22525i
$870$	−2.39707	+	6.75716i	−0.0812684	+	0.229089i
$871$	−0.594029	+	0.342963i	−0.0201279	+	0.0116209i
$872$	−33.8502	+	19.5434i	−1.14631	+	0.661824i
$873$	−31.3496	−	5.00111i	−1.06102	−	0.169262i
$874$		−	5.86124i		−	0.198259i
$875$	25.5947	−	6.97535i	0.865259	−	0.235810i
$876$	−0.267453	−	1.44754i	−0.00903639	−	0.0489080i
$877$	−29.4725	+	51.0479i	−0.995217	+	1.72377i	−0.413008	+	0.910727i	$0.635522\pi$
$877$	−29.4725	+	51.0479i	−0.995217	+	1.72377i	−0.582209	+	0.813039i	$0.697811\pi$
$878$	3.88841	+	6.73492i	0.131227	+	0.227292i
$879$	22.9252	+	26.8723i	0.773248	+	0.906379i
$880$	−7.03908	−	4.06402i	−0.237287	−	0.136998i
$881$	53.4226			1.79985			0.899927	−	0.436040i	$-0.143619\pi$
$881$	53.4226			1.79985			0.899927	+	0.436040i	$0.143619\pi$
$882$	3.56949	−	23.6734i	0.120191	−	0.797124i
$883$	−22.3497			−0.752126			−0.376063	−	0.926594i	$-0.622722\pi$
$883$	−22.3497			−0.752126			−0.376063	+	0.926594i	$0.622722\pi$
$884$	−3.40602	−	1.96647i	−0.114557	−	0.0661395i
$885$	7.22856	+	8.47311i	0.242985	+	0.284821i
$886$	−0.456171	−	0.790111i	−0.0153254	−	0.0265443i
$887$	−19.6148	+	33.9738i	−0.658601	+	1.14073i	0.322377	+	0.946611i	$0.395518\pi$
$887$	−19.6148	+	33.9738i	−0.658601	+	1.14073i	−0.980978	+	0.194119i	$0.937815\pi$
$888$	−9.66617	−	52.3166i	−0.324375	−	1.75563i
$889$	−22.9184	+	6.24599i	−0.768660	+	0.209484i
$890$			2.88668i			0.0967617i
$891$	29.3143	−	6.16271i	0.982067	−	0.206459i
$892$	−6.70199	+	3.86940i	−0.224399	+	0.129557i
$893$	1.61975	−	0.935164i	0.0542029	−	0.0312941i
$894$	−1.38962	+	3.91722i	−0.0464758	+	0.131012i
$895$		−	21.8416i		−	0.730084i
$896$	−5.57965	−	1.46955i	−0.186403	−	0.0490944i
$897$	−12.6263	+	2.33288i	−0.421581	+	0.0778925i
$898$	−2.38218	+	4.12605i	−0.0794943	+	0.137688i
$899$	9.58990	+	16.6102i	0.319841	+	0.553981i
$900$	5.96897	+	4.84460i	0.198966	+	0.161487i
$901$	55.1135	+	31.8198i	1.83610	+	1.06007i
$902$	−22.4976			−0.749087
$903$	−46.0676	−	31.4102i	−1.53303	−	1.04527i
$904$	−34.2627			−1.13956
$905$	−4.06795	−	2.34863i	−0.135223	−	0.0780712i
$906$	13.5961	−	11.5991i	0.451700	−	0.385354i
$907$	2.73986	+	4.74558i	0.0909757	+	0.157575i	0.907922	−	0.419139i	$-0.137668\pi$
$907$	2.73986	+	4.74558i	0.0909757	+	0.157575i	−0.816946	+	0.576714i	$0.804335\pi$
$908$	−7.42692	+	12.8638i	−0.246471	+	0.426900i
$909$	−16.6544	+	6.37174i	−0.552392	+	0.211337i
$910$	2.48018	+	2.45909i	0.0822172	+	0.0815180i
$911$		−	30.6455i		−	1.01533i	−0.861554	−	0.507665i	$-0.830509\pi$
$911$		−	30.6455i		−	1.01533i	0.861554	−	0.507665i	$-0.169491\pi$
$912$	−2.38759	−	0.846988i	−0.0790610	−	0.0280466i
$913$	−33.6163	+	19.4084i	−1.11254	+	0.642324i
$914$	−38.2609	+	22.0900i	−1.26556	+	0.730671i
$915$	20.4920	+	7.26943i	0.677443	+	0.240320i
$916$		−	0.315134i		−	0.0104123i
$917$	4.28451	−	16.2676i	0.141487	−	0.537202i
$918$	17.3356	+	28.3956i	0.572161	+	0.937195i
$919$	6.25122	−	10.8274i	0.206209	−	0.357164i	−0.744308	−	0.667836i	$-0.767221\pi$
$919$	6.25122	−	10.8274i	0.206209	−	0.357164i	0.950517	+	0.310672i	$0.100554\pi$
$920$	13.2126	+	22.8849i	0.435607	+	0.754494i
$921$	−20.2460	+	17.2722i	−0.667127	+	0.569138i
$922$	32.4002	+	18.7062i	1.06704	+	0.616057i
$923$	0.968922			0.0318924
$924$	−4.63412	−	9.62352i	−0.152451	−	0.316590i
$925$	−36.5109			−1.20047
$926$	6.75128	+	3.89786i	0.221861	+	0.128091i
$927$	−0.960919	+	1.18394i	−0.0315607	+	0.0388856i
$928$	5.88353	+	10.1906i	0.193136	+	0.334522i
$929$	11.4307	−	19.7985i	0.375028	−	0.649567i	−0.615303	−	0.788290i	$-0.710966\pi$
$929$	11.4307	−	19.7985i	0.375028	−	0.649567i	0.990331	+	0.138723i	$0.0442998\pi$
$930$	13.7524	−	2.54093i	0.450959	−	0.0833204i
$931$	−4.85449	+	0.0414599i	−0.159100	+	0.00135879i
$932$		−	9.08537i		−	0.297601i
$933$	18.6501	−	52.5732i	0.610577	−	1.72117i
$934$	33.4053	−	19.2866i	1.09306	−	0.631076i
$935$	18.7446	−	10.8222i	0.613014	−	0.353924i
$936$	−1.45489	+	9.12006i	−0.0475547	+	0.298099i
$937$		−	50.6242i		−	1.65382i	−0.562335	−	0.826910i	$-0.690097\pi$
$937$		−	50.6242i		−	1.65382i	0.562335	−	0.826910i	$-0.309903\pi$
$938$	−0.544011	−	1.99614i	−0.0177626	−	0.0651764i
$939$	−0.516986	−	2.79811i	−0.0168712	−	0.0913127i
$940$	−1.09342	+	1.89386i	−0.0356634	+	0.0617707i
$941$	20.8202	+	36.0616i	0.678718	+	1.17557i	0.975367	+	0.220587i	$0.0707973\pi$
$941$	20.8202	+	36.0616i	0.678718	+	1.17557i	−0.296650	+	0.954986i	$0.595869\pi$
$942$	13.9974	+	16.4074i	0.456060	+	0.534580i
$943$	38.0645	+	21.9766i	1.23955	+	0.715655i
$944$	−11.7119			−0.381190
$945$	4.56084	+	15.2515i	0.148364	+	0.496130i
$946$	46.1678			1.50105
$947$	37.4658	+	21.6309i	1.21747	+	0.702909i	0.964377	−	0.264531i	$-0.0852173\pi$
$947$	37.4658	+	21.6309i	1.21747	+	0.702909i	0.253098	+	0.967441i	$0.418551\pi$
$948$	−8.54295	−	10.0138i	−0.277462	−	0.325233i
$949$	−0.606807	−	1.05102i	−0.0196978	−	0.0341176i
$950$	−1.44658	+	2.50555i	−0.0469332	+	0.0812907i
$951$	6.03477	+	32.6622i	0.195691	+	1.05915i
$952$	32.2064	−	32.4826i	1.04382	−	1.05277i
$953$			14.1029i			0.456838i	0.973563	+	0.228419i	$0.0733556\pi$
$953$			14.1029i			0.456838i	−0.973563	+	0.228419i	$0.926644\pi$
$954$	6.10535	−	38.2716i	0.197668	−	1.23909i
$955$	−16.1031	+	9.29712i	−0.521083	+	0.300848i
$956$	−10.7035	+	6.17969i	−0.346177	+	0.199865i
$957$	6.04376	−	17.0369i	0.195367	−	0.550724i
$958$			36.6040i			1.18262i
$959$	−3.76806	+	3.80038i	−0.121677	+	0.122721i
$960$	16.7560	−	3.09589i	0.540798	−	0.0999194i
$961$	3.20588	−	5.55275i	0.103416	−	0.179121i
$962$	−5.68758	−	9.85117i	−0.183375	−	0.317614i
$963$	−3.52675	+	4.34526i	−0.113648	+	0.140024i
$964$	−11.6290	−	6.71403i	−0.374546	−	0.216244i
$965$	−17.0049			−0.547406
$966$	2.89527	−	38.6208i	0.0931538	−	1.24260i
$967$	49.0258			1.57656			0.788282	−	0.615314i	$-0.210971\pi$
$967$	49.0258			1.57656			0.788282	+	0.615314i	$0.210971\pi$
$968$	0.207676	+	0.119902i	0.00667494	+	0.00385378i
$969$	5.13229	−	4.37845i	0.164873	−	0.140656i
$970$	6.98459	+	12.0977i	0.224262	+	0.388432i
$971$	−15.5426	+	26.9206i	−0.498786	+	0.863923i	−0.999999	−	0.00140100i	$-0.999554\pi$
$971$	−15.5426	+	26.9206i	−0.498786	+	0.863923i	0.501213	+	0.865324i	$0.332887\pi$
$972$	−6.66964	+	8.64209i	−0.213929	+	0.277195i
$973$	−5.67663	−	20.8293i	−0.181985	−	0.667757i
$974$		−	11.1326i		−	0.356713i
$975$	5.97323	+	2.11898i	0.191296	+	0.0678616i
$976$	−19.8011	+	11.4322i	−0.633818	+	0.365935i
$977$	33.1698	−	19.1506i	1.06119	−	0.612681i	0.135432	−	0.990787i	$-0.456758\pi$
$977$	33.1698	−	19.1506i	1.06119	−	0.612681i	0.925763	+	0.378105i	$0.123424\pi$
$978$	−4.96149	−	1.76007i	−0.158651	−	0.0562807i
$979$		−	7.27821i		−	0.232613i
$980$	4.89132	−	2.87998i	0.156247	−	0.0919976i
$981$	−35.5759	+	13.6108i	−1.13585	+	0.434561i
$982$	5.91440	−	10.2440i	0.188736	−	0.326901i
$983$	5.05807	+	8.76083i	0.161327	+	0.279427i	0.935345	−	0.353737i	$-0.115089\pi$
$983$	5.05807	+	8.76083i	0.161327	+	0.279427i	−0.774018	+	0.633164i	$0.781756\pi$
$984$	24.0509	−	20.5182i	0.766714	−	0.654097i
$985$	7.76165	+	4.48119i	0.247307	+	0.142783i
$986$	20.0770			0.639383
$987$	11.1348	−	5.36185i	0.354424	−	0.170670i
$988$	0.485670			0.0154512
$989$	−78.1132	−	45.0987i	−2.48385	−	1.43405i
$990$	−10.2344	−	8.30656i	−0.325271	−	0.264000i
$991$	−8.27729	−	14.3367i	−0.262937	−	0.455420i	0.704084	−	0.710117i	$-0.251358\pi$
$991$	−8.27729	−	14.3367i	−0.262937	−	0.455420i	−0.967021	+	0.254697i	$0.918024\pi$
$992$	11.4763	−	19.8775i	0.364373	−	0.631112i
$993$	−4.51518	+	0.834238i	−0.143285	+	0.0264737i
$994$	−0.744347	+	2.82616i	−0.0236093	+	0.0896404i
$995$		−	24.8332i		−	0.787266i
$996$	4.72944	−	13.3319i	0.149858	−	0.422438i
$997$	−25.3308	+	14.6248i	−0.802236	+	0.463171i	−0.844252	−	0.535946i	$-0.819955\pi$
$997$	−25.3308	+	14.6248i	−0.802236	+	0.463171i	0.0420167	+	0.999117i	$0.486622\pi$
$998$	14.4403	−	8.33714i	0.457101	−	0.263908i
$999$	−1.27055	−	51.8306i	−0.0401985	−	1.63985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.12	✓	64
3.2	odd	2	inner	273.2.bh.a.131.21	yes	64
7.3	odd	6	inner	273.2.bh.a.248.21	yes	64
21.17	even	6	inner	273.2.bh.a.248.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.12	✓	64	1.1	even	1	trivial
273.2.bh.a.131.21	yes	64	3.2	odd	2	inner
273.2.bh.a.248.12	yes	64	21.17	even	6	inner
273.2.bh.a.248.21	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987309 - 0.570023i) q^{2} +(1.12414 + 1.31769i) q^{3} +(-0.350147 - 0.606472i) q^{4} +(-0.578962 + 1.00279i) q^{5} +(-0.358764 - 1.94175i) q^{6} +(-2.55265 + 0.695677i) q^{7} +3.07846i q^{8} +(-0.472604 + 2.96254i) q^{9} +O(q^{10})\)	\(q+(-0.987309 - 0.570023i) q^{2} +(1.12414 + 1.31769i) q^{3} +(-0.350147 - 0.606472i) q^{4} +(-0.578962 + 1.00279i) q^{5} +(-0.358764 - 1.94175i) q^{6} +(-2.55265 + 0.695677i) q^{7} +3.07846i q^{8} +(-0.472604 + 2.96254i) q^{9} +(1.14323 - 0.660043i) q^{10} +(-2.88243 + 1.66417i) q^{11} +(0.405526 - 1.14315i) q^{12} -1.00000i q^{13} +(2.91681 + 0.768223i) q^{14} +(-1.97220 + 0.364390i) q^{15} +(1.05450 - 1.82645i) q^{16} +(2.80806 + 4.86371i) q^{17} +(2.15532 - 2.65555i) q^{18} +(-0.600609 - 0.346762i) q^{19} +0.810886 q^{20} +(-3.78623 - 2.58156i) q^{21} +3.79447 q^{22} +(-6.42002 - 3.70660i) q^{23} +(-4.05645 + 3.46063i) q^{24} +(1.82961 + 3.16897i) q^{25} +(-0.570023 + 0.987309i) q^{26} +(-4.43498 + 2.70757i) q^{27} +(1.31571 + 1.30452i) q^{28} +3.13574i q^{29} +(2.15488 + 0.764436i) q^{30} +(5.29706 - 3.05826i) q^{31} +(3.24981 - 1.87628i) q^{32} +(-5.43313 - 1.92738i) q^{33} -6.40265i q^{34} +(0.780269 - 2.96255i) q^{35} +(1.96218 - 0.750702i) q^{36} +(-4.98890 + 8.64102i) q^{37} +(0.395325 + 0.684723i) q^{38} +(1.31769 - 1.12414i) q^{39} +(-3.08705 - 1.78231i) q^{40} -5.92904 q^{41} +(2.26663 + 4.70704i) q^{42} +12.1671 q^{43} +(2.01855 + 1.16541i) q^{44} +(-2.69719 - 2.18912i) q^{45} +(4.22569 + 7.31912i) q^{46} +(-1.34842 + 2.33554i) q^{47} +(3.59210 - 0.663687i) q^{48} +(6.03207 - 3.55164i) q^{49} -4.17167i q^{50} +(-3.25219 + 9.16766i) q^{51} +(-0.606472 + 0.350147i) q^{52} +(9.81343 - 5.66579i) q^{53} +(5.92208 - 0.145171i) q^{54} -3.85397i q^{55} +(-2.14162 - 7.85824i) q^{56} +(-0.218247 - 1.18123i) q^{57} +(1.78745 - 3.09595i) q^{58} +(-2.77665 - 4.80929i) q^{59} +(0.911552 + 1.06850i) q^{60} +(-9.38886 - 5.42066i) q^{61} -6.97311 q^{62} +(-0.854577 - 7.89112i) q^{63} -8.49610 q^{64} +(1.00279 + 0.578962i) q^{65} +(4.26553 + 4.99993i) q^{66} +(-0.342963 - 0.594029i) q^{67} +(1.96647 - 3.40602i) q^{68} +(-2.33288 - 12.6263i) q^{69} +(-2.45909 + 2.48018i) q^{70} +0.968922i q^{71} +(-9.12006 - 1.45489i) q^{72} +(1.05102 - 0.606807i) q^{73} +(9.85117 - 5.68758i) q^{74} +(-2.11898 + 5.97323i) q^{75} +0.485670i q^{76} +(6.20012 - 6.25330i) q^{77} +(-1.94175 + 0.358764i) q^{78} +(5.42596 - 9.39803i) q^{79} +(1.22103 + 2.11489i) q^{80} +(-8.55329 - 2.80022i) q^{81} +(5.85380 + 3.37969i) q^{82} +11.6625 q^{83} +(-0.239906 + 3.20017i) q^{84} -6.50305 q^{85} +(-12.0127 - 6.93555i) q^{86} +(-4.13193 + 3.52502i) q^{87} +(-5.12309 - 8.87346i) q^{88} +(-1.09337 + 1.89377i) q^{89} +(1.41511 + 3.69880i) q^{90} +(0.695677 + 2.55265i) q^{91} +5.19141i q^{92} +(9.98448 + 3.54195i) q^{93} +(2.66262 - 1.53727i) q^{94} +(0.695460 - 0.401524i) q^{95} +(6.12561 + 2.17303i) q^{96} +10.5820i q^{97} +(-7.98004 + 0.0681537i) q^{98} +(-3.56793 - 9.32582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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