LMFDB - Embedded newform 273.2.cd.e.44.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, 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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.11
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25001 + 0.334940i) q^{2} +(-1.60871 - 0.641920i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(-3.70264 + 0.992121i) q^{5} +(2.22591 + 0.263589i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(2.12780 - 2.12780i) q^{8} +(2.17588 + 2.06532i) q^{9} +O(q^{10})$	\(q+(-1.25001 + 0.334940i) q^{2} +(-1.60871 - 0.641920i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(-3.70264 + 0.992121i) q^{5} +(2.22591 + 0.263589i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(2.12780 - 2.12780i) q^{8} +(2.17588 + 2.06532i) q^{9} +(4.29606 - 2.48033i) q^{10} +(-1.43154 - 0.383581i) q^{11} +(0.557574 - 0.0808103i) q^{12} +(2.76474 + 2.31435i) q^{13} +(3.00038 + 1.64947i) q^{14} +(6.59333 + 0.780772i) q^{15} +(-1.62182 + 2.80907i) q^{16} +(0.890309 + 1.54206i) q^{17} +(-3.41164 - 1.85290i) q^{18} +(0.252802 + 0.943471i) q^{19} +(0.881676 - 0.881676i) q^{20} +(1.89648 + 4.17173i) q^{21} +1.91793 q^{22} +(2.91637 - 5.05131i) q^{23} +(-4.78889 + 2.05713i) q^{24} +(8.39515 - 4.84694i) q^{25} +(-4.23114 - 1.96694i) q^{26} +(-2.17457 - 4.71924i) q^{27} +(0.835765 + 0.205282i) q^{28} +2.31669i q^{29} +(-8.50327 + 1.23240i) q^{30} +(-3.04057 - 0.814718i) q^{31} +(-0.471235 + 1.75867i) q^{32} +(2.05670 + 1.53600i) q^{33} +(-1.62940 - 1.62940i) q^{34} +(8.88738 + 4.88586i) q^{35} +(-0.948846 - 0.227918i) q^{36} +(8.74289 - 2.34265i) q^{37} +(-0.632013 - 1.09468i) q^{38} +(-2.96203 - 5.49785i) q^{39} +(-5.76746 + 9.98953i) q^{40} +(-4.21804 - 4.21804i) q^{41} +(-3.76791 - 4.57952i) q^{42} +6.76194i q^{43} +(0.465650 - 0.124771i) q^{44} +(-10.1055 - 5.48843i) q^{45} +(-1.95362 + 7.29102i) q^{46} +(-0.850526 - 3.17421i) q^{47} +(4.41223 - 3.47790i) q^{48} +(0.293149 + 6.99386i) q^{49} +(-8.87062 + 8.87062i) q^{50} +(-0.442366 - 3.05223i) q^{51} +(-1.15523 - 0.202295i) q^{52} +(7.67909 - 4.43352i) q^{53} +(4.29891 + 5.17077i) q^{54} +5.68105 q^{55} +(-7.95976 + 0.166744i) q^{56} +(0.198949 - 1.68005i) q^{57} +(-0.775954 - 2.89590i) q^{58} +(7.36954 + 1.97466i) q^{59} +(-1.98432 + 0.852392i) q^{60} +(-5.58459 + 9.67280i) q^{61} +4.07364 q^{62} +(-0.372960 - 7.92849i) q^{63} -8.84347i q^{64} +(-12.5330 - 5.82625i) q^{65} +(-3.08538 - 1.23116i) q^{66} +(-7.79328 - 2.08820i) q^{67} +(-0.501599 - 0.289599i) q^{68} +(-7.93413 + 6.25399i) q^{69} +(-12.7458 - 3.13066i) q^{70} +(3.24997 + 3.24997i) q^{71} +(9.02444 - 0.235235i) q^{72} +(1.49640 - 5.58464i) q^{73} +(-10.1441 + 5.85669i) q^{74} +(-16.6167 + 2.40829i) q^{75} +(-0.224660 - 0.224660i) q^{76} +(2.03125 + 3.35398i) q^{77} +(5.54404 + 5.88029i) q^{78} +(7.93757 - 13.7483i) q^{79} +(3.21808 - 12.0100i) q^{80} +(0.468877 + 8.98778i) q^{81} +(6.68540 + 3.85982i) q^{82} +(2.04147 + 2.04147i) q^{83} +(-1.21273 - 0.866733i) q^{84} +(-4.82641 - 4.82641i) q^{85} +(-2.26485 - 8.45252i) q^{86} +(1.48713 - 3.72688i) q^{87} +(-3.86222 + 2.22986i) q^{88} +(0.172387 + 0.643357i) q^{89} +(14.4704 + 3.47586i) q^{90} +(-1.04144 - 9.48237i) q^{91} +1.89727i q^{92} +(4.36840 + 3.26245i) q^{93} +(2.12634 + 3.68293i) q^{94} +(-1.87207 - 3.24253i) q^{95} +(1.88701 - 2.52669i) q^{96} +(3.72661 - 3.72661i) q^{97} +(-2.70897 - 8.64424i) q^{98} +(-2.32264 - 3.79122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.25001	+	0.334940i	−0.883894	+	0.236839i	−0.672086	−	0.740473i	$-0.734602\pi$
$2$	−1.25001	+	0.334940i	−0.883894	+	0.236839i	−0.211807	+	0.977311i	$0.567935\pi$
$3$	−1.60871	−	0.641920i	−0.928787	−	0.370613i
$3$	−1.60871	−	0.641920i	−0.928787	−	0.370613i
$4$	−0.281700	+	0.162639i	−0.140850	+	0.0813197i
$5$	−3.70264	+	0.992121i	−1.65587	+	0.443690i	−0.961249	−	0.275683i	$-0.911096\pi$
$5$	−3.70264	+	0.992121i	−1.65587	+	0.443690i	−0.694624	+	0.719373i	$0.744429\pi$
$6$	2.22591	+	0.263589i	0.908725	+	0.107610i
$7$	−1.90960	−	1.83124i	−0.721761	−	0.692142i
$7$	−1.90960	−	1.83124i	−0.721761	−	0.692142i
$8$	2.12780	−	2.12780i	0.752292	−	0.752292i
$9$	2.17588	+	2.06532i	0.725292	+	0.688441i
$10$	4.29606	−	2.48033i	1.35853	−	0.784349i
$11$	−1.43154	−	0.383581i	−0.431626	−	0.115654i	0.0364632	−	0.999335i	$-0.488391\pi$
$11$	−1.43154	−	0.383581i	−0.431626	−	0.115654i	−0.468089	+	0.883681i	$0.655057\pi$
$12$	0.557574	−	0.0808103i	0.160958	−	0.0233279i
$13$	2.76474	+	2.31435i	0.766802	+	0.641884i
$13$	2.76474	+	2.31435i	0.766802	+	0.641884i
$14$	3.00038	+	1.64947i	0.801886	+	0.440839i
$15$	6.59333	+	0.780772i	1.70239	+	0.201594i
$16$	−1.62182	+	2.80907i	−0.405455	+	0.702268i
$17$	0.890309	+	1.54206i	0.215932	+	0.374005i	0.953560	−	0.301202i	$-0.0973878\pi$
$17$	0.890309	+	1.54206i	0.215932	+	0.374005i	−0.737629	+	0.675207i	$0.764054\pi$
$18$	−3.41164	−	1.85290i	−0.804131	−	0.436732i
$19$	0.252802	+	0.943471i	0.0579968	+	0.216447i	0.988842	−	0.148966i	$-0.0475944\pi$
$19$	0.252802	+	0.943471i	0.0579968	+	0.216447i	−0.930846	+	0.365413i	$0.880928\pi$
$20$	0.881676	−	0.881676i	0.197149	−	0.197149i
$21$	1.89648	+	4.17173i	0.413846	+	0.910347i
$22$	1.91793			0.408903
$23$	2.91637	−	5.05131i	0.608106	−	1.05327i	−0.383447	−	0.923563i	$-0.625263\pi$
$23$	2.91637	−	5.05131i	0.608106	−	1.05327i	0.991552	−	0.129707i	$-0.0414037\pi$
$24$	−4.78889	+	2.05713i	−0.977528	+	0.419910i
$25$	8.39515	−	4.84694i	1.67903	−	0.969388i
$26$	−4.23114	−	1.96694i	−0.829794	−	0.385749i
$27$	−2.17457	−	4.71924i	−0.418497	−	0.908218i
$28$	0.835765	+	0.205282i	0.157945	+	0.0387947i
$29$			2.31669i			0.430199i	0.976592	+	0.215099i	$0.0690076\pi$
$29$			2.31669i			0.430199i	−0.976592	+	0.215099i	$0.930992\pi$
$30$	−8.50327	+	1.23240i	−1.55248	+	0.225004i
$31$	−3.04057	−	0.814718i	−0.546102	−	0.146328i	−0.0247884	−	0.999693i	$-0.507891\pi$
$31$	−3.04057	−	0.814718i	−0.546102	−	0.146328i	−0.521314	+	0.853365i	$0.674558\pi$
$32$	−0.471235	+	1.75867i	−0.0833033	+	0.310892i
$33$	2.05670	+	1.53600i	0.358026	+	0.267384i
$34$	−1.62940	−	1.62940i	−0.279439	−	0.279439i
$35$	8.88738	+	4.88586i	1.50224	+	0.825861i
$36$	−0.948846	−	0.227918i	−0.158141	−	0.0379863i
$37$	8.74289	−	2.34265i	1.43732	−	0.385129i	0.545727	−	0.837963i	$-0.316253\pi$
$37$	8.74289	−	2.34265i	1.43732	−	0.385129i	0.891595	+	0.452833i	$0.149587\pi$
$38$	−0.632013	−	1.09468i	−0.102526	−	0.177580i
$39$	−2.96203	−	5.49785i	−0.474305	−	0.880361i
$40$	−5.76746	+	9.98953i	−0.911915	+	1.57948i
$41$	−4.21804	−	4.21804i	−0.658747	−	0.658747i	0.296337	−	0.955083i	$-0.404235\pi$
$41$	−4.21804	−	4.21804i	−0.658747	−	0.658747i	−0.955083	+	0.296337i	$0.904235\pi$
$42$	−3.76791	−	4.57952i	−0.581401	−	0.706635i
$43$			6.76194i			1.03119i	0.856834	+	0.515593i	$0.172428\pi$
$43$			6.76194i			1.03119i	−0.856834	+	0.515593i	$0.827572\pi$
$44$	0.465650	−	0.124771i	0.0701994	−	0.0188099i
$45$	−10.1055	−	5.48843i	−1.50645	−	0.818166i
$46$	−1.95362	+	7.29102i	−0.288046	+	1.07500i
$47$	−0.850526	−	3.17421i	−0.124062	−	0.463005i	0.875743	−	0.482778i	$-0.160372\pi$
$47$	−0.850526	−	3.17421i	−0.124062	−	0.463005i	−0.999804	+	0.0197729i	$0.993706\pi$
$48$	4.41223	−	3.47790i	0.636851	−	0.501991i
$49$	0.293149	+	6.99386i	0.0418785	+	0.999123i
$50$	−8.87062	+	8.87062i	−1.25450	+	1.25450i
$51$	−0.442366	−	3.05223i	−0.0619437	−	0.427398i
$52$	−1.15523	−	0.202295i	−0.160202	−	0.0280532i
$53$	7.67909	−	4.43352i	1.05480	−	0.608991i	0.130813	−	0.991407i	$-0.458241\pi$
$53$	7.67909	−	4.43352i	1.05480	−	0.608991i	0.923990	+	0.382416i	$0.124908\pi$
$54$	4.29891	+	5.17077i	0.585008	+	0.703652i
$55$	5.68105			0.766033
$56$	−7.95976	+	0.166744i	−1.06367	+	0.0222822i
$57$	0.198949	−	1.68005i	0.0263514	−	0.222528i
$58$	−0.775954	−	2.89590i	−0.101888	−	0.380250i
$59$	7.36954	+	1.97466i	0.959433	+	0.257079i	0.704360	−	0.709843i	$-0.251234\pi$
$59$	7.36954	+	1.97466i	0.959433	+	0.257079i	0.255073	+	0.966922i	$0.417901\pi$
$60$	−1.98432	+	0.852392i	−0.256175	+	0.110043i
$61$	−5.58459	+	9.67280i	−0.715034	+	1.23848i	0.247912	+	0.968782i	$0.420255\pi$
$61$	−5.58459	+	9.67280i	−0.715034	+	1.23848i	−0.962946	+	0.269693i	$0.913078\pi$
$62$	4.07364			0.517352
$63$	−0.372960	−	7.92849i	−0.0469886	−	0.998895i
$64$		−	8.84347i		−	1.10543i
$65$	−12.5330	−	5.82625i	−1.55452	−	0.722657i
$66$	−3.08538	−	1.23116i	−0.379784	−	0.151545i
$67$	−7.79328	−	2.08820i	−0.952100	−	0.255115i	−0.250847	−	0.968027i	$-0.580709\pi$
$67$	−7.79328	−	2.08820i	−0.952100	−	0.255115i	−0.701253	+	0.712912i	$0.747376\pi$
$68$	−0.501599	−	0.289599i	−0.0608279	−	0.0351190i
$69$	−7.93413	+	6.25399i	−0.955156	+	0.752892i
$70$	−12.7458	−	3.13066i	−1.52342	−	0.374185i
$71$	3.24997	+	3.24997i	0.385701	+	0.385701i	0.873151	−	0.487450i	$-0.162073\pi$
$71$	3.24997	+	3.24997i	0.385701	+	0.385701i	−0.487450	+	0.873151i	$0.662073\pi$
$72$	9.02444	−	0.235235i	1.06354	−	0.0277227i
$73$	1.49640	−	5.58464i	0.175140	−	0.653633i	−0.821387	−	0.570371i	$-0.806799\pi$
$73$	1.49640	−	5.58464i	0.175140	−	0.653633i	0.996528	−	0.0832621i	$-0.0265339\pi$
$74$	−10.1441	+	5.85669i	−1.17923	+	0.680827i
$75$	−16.6167	+	2.40829i	−1.91873	+	0.278086i
$76$	−0.224660	−	0.224660i	−0.0257703	−	0.0257703i
$77$	2.03125	+	3.35398i	0.231482	+	0.382221i
$78$	5.54404	+	5.88029i	0.627739	+	0.665811i
$79$	7.93757	−	13.7483i	0.893047	−	1.54680i	0.0568434	−	0.998383i	$-0.481896\pi$
$79$	7.93757	−	13.7483i	0.893047	−	1.54680i	0.836203	−	0.548419i	$-0.184770\pi$
$80$	3.21808	−	12.0100i	0.359792	−	1.34276i
$81$	0.468877	+	8.98778i	0.0520974	+	0.998642i
$82$	6.68540	+	3.85982i	0.738279	+	0.426245i
$83$	2.04147	+	2.04147i	0.224081	+	0.224081i	0.810214	−	0.586134i	$-0.199351\pi$
$83$	2.04147	+	2.04147i	0.224081	+	0.224081i	−0.586134	+	0.810214i	$0.699351\pi$
$84$	−1.21273	−	0.866733i	−0.132319	−	0.0945684i
$85$	−4.82641	−	4.82641i	−0.523498	−	0.523498i
$86$	−2.26485	−	8.45252i	−0.244225	−	0.911459i
$87$	1.48713	−	3.72688i	0.159437	−	0.399563i
$88$	−3.86222	+	2.22986i	−0.411714	+	0.237703i
$89$	0.172387	+	0.643357i	0.0182730	+	0.0681957i	0.974460	−	0.224560i	$-0.0720944\pi$
$89$	0.172387	+	0.643357i	0.0182730	+	0.0681957i	−0.956187	+	0.292756i	$0.905428\pi$
$90$	14.4704	+	3.47586i	1.52531	+	0.366388i
$91$	−1.04144	−	9.48237i	−0.109172	−	0.994023i
$92$			1.89727i			0.197804i
$93$	4.36840	+	3.26245i	0.452982	+	0.338300i
$94$	2.12634	+	3.68293i	0.219315	+	0.379865i
$95$	−1.87207	−	3.24253i	−0.192071	−	0.332676i
$96$	1.88701	−	2.52669i	0.192592	−	0.257879i
$97$	3.72661	−	3.72661i	0.378380	−	0.378380i	−0.492138	−	0.870517i	$-0.663784\pi$
$97$	3.72661	−	3.72661i	0.378380	−	0.378380i	0.870517	+	0.492138i	$0.163784\pi$
$98$	−2.70897	−	8.64424i	−0.273647	−	0.873200i
$99$	−2.32264	−	3.79122i	−0.233434	−	0.381032i
$100$	−1.57661	+	2.73076i	−0.157661	+	0.273076i
$101$	4.91090	+	8.50593i	0.488653	+	0.846371i	0.999915	−	0.0130535i	$-0.00415518\pi$
$101$	4.91090	+	8.50593i	0.488653	+	0.846371i	−0.511262	+	0.859425i	$0.670822\pi$
$102$	1.57528	+	3.66717i	0.155976	+	0.363104i
$103$	9.68840	+	5.59360i	0.954627	+	0.551154i	0.894515	−	0.447038i	$-0.147521\pi$
$103$	9.68840	+	5.59360i	0.954627	+	0.551154i	0.0601115	+	0.998192i	$0.480854\pi$
$104$	10.8073	−	0.958352i	1.05974	−	0.0939742i
$105$	−11.1609	−	13.5649i	−1.08919	−	1.32380i
$106$	−8.11400	+	8.11400i	−0.788102	+	0.788102i
$107$	14.9833	+	8.65062i	1.44849	+	0.836287i	0.998392	−	0.0566907i	$-0.0180549\pi$
$107$	14.9833	+	8.65062i	1.44849	+	0.836287i	0.450100	+	0.892978i	$0.351388\pi$
$108$	1.38011	+	0.975737i	0.132801	+	0.0938903i
$109$	8.01976	+	2.14889i	0.768154	+	0.205826i	0.621556	−	0.783370i	$-0.286501\pi$
$109$	8.01976	+	2.14889i	0.768154	+	0.205826i	0.146598	+	0.989196i	$0.453168\pi$
$110$	−7.10140	+	1.90281i	−0.677092	+	0.181426i
$111$	−15.5685	−	1.84360i	−1.47770	−	0.174987i
$112$	8.24110	−	2.39427i	0.778711	−	0.226238i
$113$			8.40669i			0.790835i	0.918501	+	0.395418i	$0.129400\pi$
$113$			8.40669i			0.790835i	−0.918501	+	0.395418i	$0.870600\pi$
$114$	0.314027	+	2.16672i	0.0294114	+	0.202932i
$115$	−5.78679	+	21.5966i	−0.539621	+	2.01389i
$116$	−0.376785	−	0.652611i	−0.0349836	−	0.0605934i
$117$	1.23586	+	10.7458i	0.114256	+	0.993451i
$118$	−9.87343			−0.908923
$119$	1.12374	−	4.57509i	0.103013	−	0.419398i
$120$	15.6906	−	12.3680i	1.43235	−	1.12904i
$121$	−7.62410	−	4.40178i	−0.693100	−	0.400161i
$122$	3.74101	−	13.9616i	0.338695	−	1.26403i
$123$	4.07794	+	9.49323i	0.367696	+	0.855976i
$124$	0.989032	−	0.265010i	0.0888177	−	0.0237986i
$125$	−12.7229	+	12.7229i	−1.13797	+	1.13797i
$126$	3.12178	+	9.78580i	0.278110	+	0.871789i
$127$		−	12.9225i		−	1.14669i	−0.819314	−	0.573345i	$-0.805645\pi$
$127$		−	12.9225i		−	1.14669i	0.819314	−	0.573345i	$-0.194355\pi$
$128$	2.01957	+	7.53713i	0.178506	+	0.666194i
$129$	4.34063	−	10.8780i	0.382171	−	0.957752i
$130$	17.6178	+	3.08509i	1.54519	+	0.270581i
$131$	−3.75893	−	2.17022i	−0.328419	−	0.189613i	0.326720	−	0.945121i	$-0.394057\pi$
$131$	−3.75893	−	2.17022i	−0.328419	−	0.189613i	−0.655139	+	0.755508i	$0.727390\pi$
$132$	−0.829187	−	0.0981910i	−0.0721715	−	0.00854643i
$133$	1.24497	−	2.26459i	0.107952	−	0.196365i
$134$	10.4411			0.901977
$135$	12.7337	+	15.3162i	1.09595	+	1.31821i
$136$	5.17560	+	1.38680i	0.443804	+	0.118917i
$137$	18.7248	+	5.01729i	1.59977	+	0.428656i	0.944972	−	0.327152i	$-0.106089\pi$
$137$	18.7248	+	5.01729i	1.59977	+	0.428656i	0.654794	+	0.755808i	$0.272755\pi$
$138$	7.82306	−	10.4750i	0.665943	−	0.891695i
$139$	18.2780			1.55032			0.775160	−	0.631765i	$-0.217669\pi$
$139$	18.2780			1.55032			0.775160	+	0.631765i	$0.217669\pi$
$140$	−3.29820	+	0.0690922i	−0.278749	+	0.00583935i
$141$	−0.669340	+	5.65234i	−0.0563686	+	0.476013i
$142$	−5.15106	−	2.97397i	−0.432267	−	0.249570i
$143$	−3.07011	−	4.37359i	−0.256735	−	0.365738i
$144$	−9.33052	+	2.76261i	−0.777543	+	0.230218i
$145$	−2.29844	−	8.57789i	−0.190875	−	0.712355i
$146$			7.48209i			0.619222i
$147$	4.01791	−	11.4392i	0.331392	−	0.943493i
$148$	−2.08186	+	2.08186i	−0.171128	+	0.171128i
$149$	−6.63217	+	1.77708i	−0.543328	+	0.145584i	−0.520036	−	0.854144i	$-0.674081\pi$
$149$	−6.63217	+	1.77708i	−0.543328	+	0.145584i	−0.0232922	+	0.999729i	$0.507415\pi$
$150$	19.9645	−	8.57600i	1.63009	−	0.700227i
$151$	0.928800	−	3.46633i	0.0755847	−	0.282086i	−0.917781	−	0.397088i	$-0.870021\pi$
$151$	0.928800	−	3.46633i	0.0755847	−	0.282086i	0.993365	+	0.115002i	$0.0366875\pi$
$152$	2.54543	+	1.46961i	0.206462	+	0.119201i
$153$	−1.24765	+	5.19411i	−0.100867	+	0.419919i
$154$	−3.66247	−	3.51217i	−0.295130	−	0.283019i
$155$	12.0664			0.969200
$156$	1.72857	+	1.06700i	0.138396	+	0.0854283i
$157$	−7.33140	−	12.6984i	−0.585110	−	1.01344i	−0.994862	−	0.101243i	$-0.967718\pi$
$157$	−7.33140	−	12.6984i	−0.585110	−	1.01344i	0.409752	−	0.912197i	$-0.365615\pi$
$158$	−5.31723	+	19.8442i	−0.423016	+	1.57872i
$159$	−15.1994	+	2.20288i	−1.20539	+	0.174700i
$160$		−	6.97926i		−	0.551759i
$161$	−14.8192	+	4.30541i	−1.16792	+	0.339314i
$162$	−3.59647	−	11.0778i	−0.282566	−	0.870355i
$163$	−17.5190	+	4.69421i	−1.37219	+	0.367679i	−0.868280	−	0.496075i	$-0.834774\pi$
$163$	−17.5190	+	4.69421i	−1.37219	+	0.367679i	−0.503915	+	0.863753i	$0.668108\pi$
$164$	1.87424	+	0.502200i	0.146353	+	0.0392153i
$165$	−9.13915	−	3.64678i	−0.711482	−	0.283902i
$166$	−3.23564	−	1.86810i	−0.251134	−	0.144993i
$167$	7.84652	−	7.84652i	0.607182	−	0.607182i	−0.335027	−	0.942209i	$-0.608745\pi$
$167$	7.84652	−	7.84652i	0.607182	−	0.607182i	0.942209	+	0.335027i	$0.108745\pi$
$168$	12.9120	+	4.84129i	0.996179	+	0.373514i
$169$	2.28760	+	12.7971i	0.175969	+	0.984396i
$170$	7.64964	+	4.41652i	0.586701	+	0.338732i
$171$	−1.39851	+	2.57500i	−0.106946	+	0.196915i
$172$	−1.09976	−	1.90483i	−0.0838557	−	0.145242i
$173$	9.63489	−	16.6881i	0.732527	−	1.26877i	−0.223272	−	0.974756i	$-0.571674\pi$
$173$	9.63489	−	16.6881i	0.732527	−	1.26877i	0.955800	−	0.294019i	$-0.0949927\pi$
$174$	−0.610654	+	5.15675i	−0.0462936	+	0.390932i
$175$	−24.9073	−	6.11778i	−1.88281	−	0.462460i
$176$	3.39921	−	3.39921i	0.256225	−	0.256225i
$177$	−10.5879	−	7.90731i	−0.795832	−	0.594350i
$178$	−0.430972	−	0.746466i	−0.0323027	−	0.0559500i
$179$	2.58824	+	4.48296i	0.193454	+	0.335072i	0.946393	−	0.323019i	$-0.104698\pi$
$179$	2.58824	+	4.48296i	0.193454	+	0.335072i	−0.752939	+	0.658091i	$0.771364\pi$
$180$	3.73936	−	0.0974718i	0.278716	−	0.00726512i
$181$		−	2.66916i		−	0.198397i	−0.995068	−	0.0991987i	$-0.968372\pi$
$181$		−	2.66916i		−	0.198397i	0.995068	−	0.0991987i	$-0.0316279\pi$
$182$	4.47784	+	11.5043i	0.331920	+	0.852754i
$183$	15.1931	−	11.9758i	1.12311	−	0.885279i
$184$	−4.54272	−	16.9536i	−0.334893	−	1.24984i
$185$	−30.0476	+	17.3480i	−2.20915	+	1.27545i
$186$	−6.55329	−	2.61495i	−0.480510	−	0.191737i
$187$	−0.683011	−	2.54903i	−0.0499467	−	0.186404i
$188$	0.755843	+	0.755843i	0.0551255	+	0.0551255i
$189$	−4.48947	+	12.9940i	−0.326561	+	0.945176i
$190$	3.42617	+	3.42617i	0.248561	+	0.248561i
$191$	3.97121	+	2.29278i	0.287347	+	0.165900i	0.636745	−	0.771075i	$-0.280281\pi$
$191$	3.97121	+	2.29278i	0.287347	+	0.165900i	−0.349398	+	0.936974i	$0.613614\pi$
$192$	−5.67681	+	14.2266i	−0.409688	+	1.02671i
$193$	−1.84201	+	6.87446i	−0.132590	+	0.494834i	−0.999996	−	0.00276724i	$-0.999119\pi$
$193$	−1.84201	+	6.87446i	−0.132590	+	0.494834i	0.867406	+	0.497602i	$0.165786\pi$
$194$	−3.41012	+	5.90651i	−0.244833	+	0.424063i
$195$	16.4219	+	17.4179i	1.17600	+	1.24732i
$196$	−1.22006	−	1.92249i	−0.0871469	−	0.137321i
$197$	−11.0026	−	11.0026i	−0.783905	−	0.783905i	0.196582	−	0.980487i	$-0.437016\pi$
$197$	−11.0026	−	11.0026i	−0.783905	−	0.783905i	−0.980487	+	0.196582i	$0.937016\pi$
$198$	4.17317	+	3.96114i	0.296574	+	0.281506i
$199$	7.74931	−	4.47407i	0.549334	−	0.317158i	−0.199519	−	0.979894i	$-0.563938\pi$
$199$	7.74931	−	4.47407i	0.549334	−	0.317158i	0.748853	+	0.662736i	$0.230605\pi$
$200$	7.54988	−	28.1765i	0.533857	−	1.99238i
$201$	11.1966	+	8.36197i	0.789750	+	0.589808i
$202$	−8.98767	−	8.98767i	−0.632370	−	0.632370i
$203$	4.24241	−	4.42396i	0.297759	−	0.310501i
$204$	0.621027	+	0.787866i	0.0434806	+	0.0551617i
$205$	19.8027	+	11.4331i	1.38308	+	0.798522i
$206$	−13.9842	−	3.74705i	−0.974323	−	0.261069i
$207$	16.7782	−	4.96776i	1.16617	−	0.345283i
$208$	−10.9851	+	4.01291i	−0.761678	+	0.278245i
$209$		−	1.44759i		−	0.100132i
$210$	18.4947	+	13.2181i	1.27625	+	0.912137i
$211$	7.52078			0.517752			0.258876	−	0.965911i	$-0.416648\pi$
$211$	7.52078			0.517752			0.258876	+	0.965911i	$0.416648\pi$
$212$	−1.44213	+	2.49784i	−0.0990459	+	0.171553i
$213$	−3.14203	−	7.31448i	−0.215288	−	0.501180i
$214$	−21.6268	−	5.79489i	−1.47838	−	0.396130i
$215$	−6.70866	−	25.0371i	−0.457527	−	1.70751i
$216$	−14.6687	−	5.41455i	−0.998077	−	0.368413i
$217$	4.31433	+	7.12378i	0.292876	+	0.483594i
$218$	−10.7446			−0.727714
$219$	−5.99217	+	8.02349i	−0.404913	+	0.542177i
$220$	−1.60035	+	0.923962i	−0.107896	+	0.0622935i
$221$	−1.10739	+	6.32389i	−0.0744910	+	0.425391i
$222$	20.0784	−	2.91001i	1.34757	−	0.195307i
$223$	−1.48166	+	1.48166i	−0.0992194	+	0.0992194i	−0.754974	−	0.655755i	$-0.772351\pi$
$223$	−1.48166	+	1.48166i	−0.0992194	+	0.0992194i	0.655755	+	0.754974i	$0.272351\pi$
$224$	4.12041	−	2.49542i	0.275307	−	0.166732i
$225$	28.2773	+	6.79235i	1.88515	+	0.452823i
$226$	−2.81574	−	10.5085i	−0.187300	−	0.699014i
$227$	1.64074	−	6.12331i	0.108899	−	0.406418i	−0.889859	−	0.456236i	$-0.849197\pi$
$227$	1.64074	−	6.12331i	0.108899	−	0.406418i	0.998758	+	0.0498176i	$0.0158640\pi$
$228$	0.217198	+	0.505626i	0.0143843	+	0.0334859i
$229$	0.221569	−	0.0593693i	0.0146417	−	0.00392324i	−0.251491	−	0.967860i	$-0.580921\pi$
$229$	0.221569	−	0.0593693i	0.0146417	−	0.00392324i	0.266132	+	0.963936i	$0.414254\pi$
$230$		−	28.9343i		−	1.90787i
$231$	−1.11470	−	6.69947i	−0.0733416	−	0.440793i
$232$	4.92946	+	4.92946i	0.323635	+	0.323635i
$233$	−3.45351	+	5.98165i	−0.226247	+	0.391871i	−0.956693	−	0.291100i	$-0.905979\pi$
$233$	−3.45351	+	5.98165i	−0.226247	+	0.391871i	0.730446	+	0.682970i	$0.239312\pi$
$234$	−5.14406	−	13.0185i	−0.336277	−	0.851045i
$235$	6.29839	+	10.9091i	0.410862	+	0.711633i
$236$	−2.39715	+	0.642316i	−0.156041	+	0.0418112i
$237$	−21.5945	+	17.0217i	−1.40272	+	1.10568i
$238$	0.127687	+	6.09531i	0.00827673	+	0.395100i
$239$	−11.9412	−	11.9412i	−0.772411	−	0.772411i	0.206116	−	0.978527i	$-0.433917\pi$
$239$	−11.9412	−	11.9412i	−0.772411	−	0.772411i	−0.978527	+	0.206116i	$0.933917\pi$
$240$	−12.8864	+	17.2549i	−0.831816	+	1.11380i
$241$	−4.68923	+	17.5004i	−0.302060	+	1.12730i	0.633387	+	0.773835i	$0.281664\pi$
$241$	−4.68923	+	17.5004i	−0.302060	+	1.12730i	−0.935447	+	0.353467i	$0.885003\pi$
$242$	11.0046	+	2.94867i	0.707400	+	0.189547i
$243$	5.01515	−	14.7597i	0.321722	−	0.946834i
$244$		−	3.63310i		−	0.232585i
$245$	−8.02418	−	25.6049i	−0.512646	−	1.63584i
$246$	−8.27715	−	10.5008i	−0.527732	−	0.669507i
$247$	−1.48459	+	3.19353i	−0.0944620	+	0.203199i
$248$	−8.20329	+	4.73617i	−0.520909	+	0.300747i
$249$	−1.97367	−	4.59459i	−0.125076	−	0.291170i
$250$	11.6424	−	20.1652i	0.736329	−	1.27536i
$251$	−27.0736			−1.70887			−0.854435	−	0.519558i	$-0.826096\pi$
$251$	−27.0736			−1.70887			−0.854435	+	0.519558i	$0.826096\pi$
$252$	1.39455	+	2.17279i	0.0878482	+	0.136873i
$253$	−6.11249	+	6.11249i	−0.384289	+	0.384289i
$254$	4.32828	+	16.1534i	0.271581	+	1.01355i
$255$	4.66611	+	10.8624i	0.292203	+	0.680233i
$256$	3.79450	+	6.57226i	0.237156	+	0.410766i
$257$	−3.59554	+	6.22766i	−0.224284	+	0.388471i	−0.956104	−	0.293027i	$-0.905338\pi$
$257$	−3.59554	+	6.22766i	−0.224284	+	0.388471i	0.731821	+	0.681497i	$0.238671\pi$
$258$	−1.78237	+	15.0515i	−0.110966	+	0.937064i
$259$	−20.9854	−	11.5368i	−1.30397	−	0.716860i
$260$	4.47811	−	0.397103i	0.277721	−	0.0246273i
$261$	−4.78472	+	5.04084i	−0.296167	+	0.312020i
$262$	5.42561	+	1.45379i	0.335195	+	0.0898153i
$263$	9.20203	−	5.31279i	0.567421	−	0.327601i	−0.188698	−	0.982035i	$-0.560427\pi$
$263$	9.20203	−	5.31279i	0.567421	−	0.327601i	0.756119	+	0.654434i	$0.227093\pi$
$264$	7.64457	−	1.10794i	0.470491	−	0.0681893i
$265$	−24.0343	+	24.0343i	−1.47642	+	1.47642i
$266$	−0.797723	+	3.24777i	−0.0489115	+	0.199133i
$267$	0.135664	−	1.14563i	0.00830249	−	0.0701115i
$268$	2.53499	−	0.679248i	0.154849	−	0.0414917i
$269$	2.77348	−	1.60127i	0.169102	−	0.0976313i	−0.413060	−	0.910704i	$-0.635540\pi$
$269$	2.77348	−	1.60127i	0.169102	−	0.0976313i	0.582162	+	0.813072i	$0.302207\pi$
$270$	−21.0474	−	14.8805i	−1.28090	−	0.905596i
$271$	6.41316	−	1.71840i	0.389572	−	0.104385i	−0.0587161	−	0.998275i	$-0.518701\pi$
$271$	6.41316	−	1.71840i	0.389572	−	0.104385i	0.448288	+	0.893889i	$0.352034\pi$
$272$	−5.77568			−0.350202
$273$	−4.41156	+	15.9229i	−0.267000	+	0.963697i
$274$	−25.0867			−1.51555
$275$	−13.8772	+	3.71838i	−0.836827	+	0.224227i
$276$	1.21789	−	3.05215i	0.0733086	−	0.183718i
$277$	−20.1422	+	11.6291i	−1.21023	+	0.698724i	−0.962808	−	0.270185i	$-0.912915\pi$
$277$	−20.1422	+	11.6291i	−1.21023	+	0.698724i	−0.247417	+	0.968909i	$0.579582\pi$
$278$	−22.8478	+	6.12204i	−1.37032	+	0.367176i
$279$	−4.93325	−	8.05248i	−0.295346	−	0.482090i
$280$	29.3067	−	8.51444i	1.75141	−	0.508835i
$281$	−8.31033	+	8.31033i	−0.495753	+	0.495753i	−0.910113	−	0.414360i	$-0.864005\pi$
$281$	−8.31033	+	8.31033i	−0.495753	+	0.495753i	0.414360	+	0.910113i	$0.364005\pi$
$282$	−1.05651	−	7.28969i	−0.0629143	−	0.434095i
$283$	16.9426	−	9.78183i	1.00713	−	0.581469i	0.0967832	−	0.995305i	$-0.469145\pi$
$283$	16.9426	−	9.78183i	1.00713	−	0.581469i	0.910351	+	0.413836i	$0.135811\pi$
$284$	−1.44409	−	0.386943i	−0.0856909	−	0.0229608i
$285$	0.930175	+	6.41800i	0.0550988	+	0.380170i
$286$	5.30257	+	4.43874i	0.313547	+	0.262468i
$287$	0.330545	+	15.7790i	0.0195114	+	0.931404i
$288$	−4.65757	+	2.85340i	−0.274450	+	0.168138i
$289$	6.91470	−	11.9766i	0.406747	−	0.704506i
$290$	5.74616	+	9.95264i	0.337426	+	0.584439i
$291$	−8.38721	+	3.60284i	−0.491667	+	0.211202i
$292$	0.486747	+	1.81657i	0.0284847	+	0.106306i
$293$	−3.10734	+	3.10734i	−0.181533	+	0.181533i	−0.792024	−	0.610491i	$-0.790972\pi$
$293$	−3.10734	+	3.10734i	−0.181533	+	0.181533i	0.610491	+	0.792024i	$0.290972\pi$
$294$	−1.19098	+	15.6450i	−0.0694593	+	0.912434i
$295$	−29.2459			−1.70276
$296$	13.6184	−	23.5878i	0.791556	−	1.37102i
$297$	1.30279	+	7.58992i	0.0755953	+	0.440412i
$298$	7.69509	−	4.44276i	0.445764	−	0.257362i
$299$	19.7535	−	7.21606i	1.14237	−	0.417316i
$300$	4.28923	−	3.38094i	0.247639	−	0.195199i
$301$	12.3827	−	12.9126i	0.713727	−	0.744270i
$302$			4.64405i			0.267235i
$303$	−2.44007	−	16.8359i	−0.140178	−	0.967200i
$304$	−3.06028	−	0.819999i	−0.175519	−	0.0470302i
$305$	11.0812	−	41.3555i	0.634507	−	2.36801i
$306$	−0.180135	−	6.91060i	−0.0102976	−	0.395053i
$307$	12.7457	+	12.7457i	0.727435	+	0.727435i	0.970108	−	0.242673i	$-0.0780242\pi$
$307$	12.7457	+	12.7457i	0.727435	+	0.727435i	−0.242673	+	0.970108i	$0.578024\pi$
$308$	−1.11769	−	0.614453i	−0.0636863	−	0.0350117i
$309$	−11.9952	−	15.2176i	−0.682380	−	0.865702i
$310$	−15.0832	+	4.04154i	−0.856670	+	0.229544i
$311$	2.79666	+	4.84396i	0.158584	+	0.274676i	0.934358	−	0.356335i	$-0.115974\pi$
$311$	2.79666	+	4.84396i	0.158584	+	0.274676i	−0.775774	+	0.631011i	$0.782640\pi$
$312$	−18.0010	−	5.39572i	−1.01910	−	0.305472i
$313$	−7.93436	+	13.7427i	−0.448477	+	0.776785i	−0.998287	−	0.0585049i	$-0.981367\pi$
$313$	−7.93436	+	13.7427i	−0.448477	+	0.776785i	0.549810	+	0.835290i	$0.314700\pi$
$314$	13.4176	+	13.4176i	0.757196	+	0.757196i
$315$	9.24695	+	28.9863i	0.521007	+	1.63320i
$316$			5.16385i			0.290489i
$317$	12.4356	−	3.33212i	0.698455	−	0.187151i	0.107917	−	0.994160i	$-0.465582\pi$
$317$	12.4356	−	3.33212i	0.698455	−	0.187151i	0.590539	+	0.807009i	$0.298915\pi$
$318$	18.2616	−	7.84451i	1.02406	−	0.439898i
$319$	0.888638	−	3.31644i	0.0497542	−	0.185685i
$320$	8.77379	+	32.7442i	0.490470	+	1.83046i
$321$	−18.5508	−	23.5344i	−1.03540	−	1.31356i
$322$	17.0822	−	10.3454i	0.951954	−	0.576526i
$323$	−1.22982	+	1.22982i	−0.0684289	+	0.0684289i
$324$	−1.59385	−	2.45560i	−0.0885471	−	0.136422i
$325$	34.4279	+	6.02874i	1.90972	+	0.334414i
$326$	20.3267	−	11.7356i	1.12579	−	0.649978i
$327$	−11.5220	−	8.60498i	−0.637170	−	0.475856i
$328$	−17.9503			−0.991139
$329$	−4.18856	+	7.61898i	−0.230923	+	0.420048i
$330$	12.6455	+	1.49746i	0.696113	+	0.0824325i
$331$	6.27644	+	23.4240i	0.344985	+	1.28750i	0.892630	+	0.450790i	$0.148858\pi$
$331$	6.27644	+	23.4240i	0.344985	+	1.28750i	−0.547646	+	0.836710i	$0.684476\pi$
$332$	−0.907105	−	0.243058i	−0.0497839	−	0.0133395i
$333$	23.8618	+	12.9596i	1.30762	+	0.710181i
$334$	−7.18015	+	12.4364i	−0.392880	+	0.680488i
$335$	30.9275			1.68975
$336$	−14.7944	−	1.43845i	−0.807103	−	0.0784736i
$337$			2.85524i			0.155535i	0.996972	+	0.0777674i	$0.0247792\pi$
$337$			2.85524i			0.155535i	−0.996972	+	0.0777674i	$0.975221\pi$
$338$	−7.14581	−	15.2304i	−0.388681	−	0.828425i
$339$	5.39643	−	13.5239i	0.293094	−	0.734518i
$340$	2.14456	+	0.574634i	0.116305	+	0.0311639i
$341$	4.04019	+	2.33261i	0.218789	+	0.126318i
$342$	0.885684	−	3.68720i	0.0478923	−	0.199381i
$343$	12.2476	−	13.8923i	0.661309	−	0.750114i
$344$	14.3881	+	14.3881i	0.775753	+	0.775753i
$345$	23.1725	−	31.0279i	1.24757	−	1.67049i
$346$	−6.45423	+	24.0875i	−0.346982	+	1.29495i
$347$	−24.9745	+	14.4190i	−1.34070	+	0.774053i	−0.986910	−	0.161272i	$-0.948441\pi$
$347$	−24.9745	+	14.4190i	−1.34070	+	0.774053i	−0.353790	+	0.935325i	$0.615107\pi$
$348$	0.187213	+	1.29173i	0.0100357	+	0.0692438i
$349$	3.66496	+	3.66496i	0.196181	+	0.196181i	0.798361	−	0.602180i	$-0.205701\pi$
$349$	3.66496	+	3.66496i	0.196181	+	0.196181i	−0.602180	+	0.798361i	$0.705701\pi$
$350$	33.1835	−	0.695143i	1.77373	−	0.0371569i
$351$	4.90982	−	18.0802i	0.262067	−	0.965050i
$352$	1.34918	−	2.33686i	0.0719118	−	0.124555i
$353$	6.76121	−	25.2332i	0.359863	−	1.34303i	−0.514390	−	0.857557i	$-0.671981\pi$
$353$	6.76121	−	25.2332i	0.359863	−	1.34303i	0.874253	−	0.485471i	$-0.161352\pi$
$354$	15.8835	+	6.33796i	0.844196	+	0.336859i
$355$	−15.2579	−	8.80913i	−0.809803	−	0.467540i
$356$	−0.153196	−	0.153196i	−0.00811939	−	0.00811939i
$357$	−4.74461	+	6.63862i	−0.251112	+	0.351353i
$358$	−4.73686	−	4.73686i	−0.250351	−	0.250351i
$359$	5.98702	+	22.3439i	0.315983	+	1.17926i	0.923071	+	0.384630i	$0.125671\pi$
$359$	5.98702	+	22.3439i	0.315983	+	1.17926i	−0.607088	+	0.794635i	$0.707662\pi$
$360$	−33.1809	+	9.82432i	−1.74879	+	0.517787i
$361$	15.6283	−	9.02298i	0.822540	−	0.474893i
$362$	0.894011	+	3.33649i	0.0469882	+	0.175362i
$363$	9.43935	+	11.9752i	0.495438	+	0.628537i
$364$	1.83558	+	2.50180i	0.0962105	+	0.131130i
$365$			22.1626i			1.16004i
$366$	−14.9805	+	20.0588i	−0.783041	+	1.04849i
$367$	−7.46154	−	12.9238i	−0.389489	−	0.674616i	0.602891	−	0.797823i	$-0.294015\pi$
$367$	−7.46154	−	12.9238i	−0.389489	−	0.674616i	−0.992381	+	0.123208i	$0.960682\pi$
$368$	9.45965	+	16.3846i	0.493119	+	0.854106i
$369$	−0.466316	−	17.8895i	−0.0242755	−	0.931292i
$370$	31.7494	−	31.7494i	1.65057	−	1.65057i
$371$	−22.7828	−	5.59596i	−1.18282	−	0.290528i
$372$	−1.76118	−	0.208556i	−0.0913128	−	0.0108131i
$373$	15.1061	−	26.1645i	0.782164	−	1.35475i	−0.148515	−	0.988910i	$-0.547449\pi$
$373$	15.1061	−	26.1645i	0.782164	−	1.35475i	0.930679	−	0.365837i	$-0.119217\pi$
$374$	1.70755	+	2.95756i	0.0882951	+	0.152932i
$375$	28.6345	−	12.3003i	1.47868	−	0.635185i
$376$	−8.56383	−	4.94433i	−0.441646	−	0.254984i
$377$	−5.36163	+	6.40506i	−0.276138	+	0.329877i
$378$	1.25968	−	17.7464i	0.0647912	−	0.912778i
$379$	−15.3869	+	15.3869i	−0.790374	+	0.790374i	−0.981555	−	0.191181i	$-0.938768\pi$
$379$	−15.3869	+	15.3869i	−0.790374	+	0.790374i	0.191181	+	0.981555i	$0.438768\pi$
$380$	1.05473	+	0.608946i	0.0541063	+	0.0312383i
$381$	−8.29525	+	20.7886i	−0.424978	+	1.06503i
$382$	−5.73202	−	1.53589i	−0.293276	−	0.0785829i
$383$	17.6074	−	4.71790i	0.899698	−	0.241073i	0.220811	−	0.975317i	$-0.429130\pi$
$383$	17.6074	−	4.71790i	0.899698	−	0.241073i	0.678886	+	0.734243i	$0.262463\pi$
$384$	1.58934	−	13.4214i	0.0811059	−	0.684910i
$385$	−10.8485	−	10.4033i	−0.552893	−	0.530204i
$386$		−	9.21013i		−	0.468784i
$387$	−13.9656	+	14.7131i	−0.709911	+	0.747911i
$388$	−0.443691	+	1.65588i	−0.0225250	+	0.0840644i
$389$	4.78065	+	8.28033i	0.242389	+	0.419829i	0.961394	−	0.275175i	$-0.0887358\pi$
$389$	4.78065	+	8.28033i	0.242389	+	0.419829i	−0.719006	+	0.695004i	$0.755402\pi$
$390$	−26.3616	−	16.2723i	−1.33487	−	0.823978i
$391$	10.3859			0.525237
$392$	15.5053	+	14.2578i	0.783137	+	0.720127i
$393$	4.65391	+	5.90418i	0.234759	+	0.297826i
$394$	17.4387	+	10.0682i	0.878548	+	0.507230i
$395$	−15.7501	+	58.7800i	−0.792472	+	2.95754i
$396$	1.27089	+	0.690233i	0.0638646	+	0.0346855i
$397$	4.95510	−	1.32771i	0.248689	−	0.0666360i	−0.132321	−	0.991207i	$-0.542243\pi$
$397$	4.95510	−	1.32771i	0.248689	−	0.0666360i	0.381010	+	0.924571i	$0.375576\pi$
$398$	−8.18821	+	8.18821i	−0.410438	+	0.410438i
$399$	−3.45648	+	2.84390i	−0.173040	+	0.142373i
$400$			31.4434i			1.57217i
$401$	−6.47542	−	24.1666i	−0.323367	−	1.20682i	−0.915943	−	0.401308i	$-0.868556\pi$
$401$	−6.47542	−	24.1666i	−0.323367	−	1.20682i	0.592576	−	0.805515i	$-0.298111\pi$
$402$	−16.7967	−	6.70238i	−0.837744	−	0.334284i
$403$	−6.52085	−	9.28941i	−0.324827	−	0.462739i
$404$	−2.76680	−	1.59741i	−0.137653	−	0.0794741i
$405$	−10.6530	−	32.8134i	−0.529354	−	1.63051i
$406$	−3.82131	+	6.95096i	−0.189649	+	0.344971i
$407$	−13.4144			−0.664928
$408$	−7.43581	−	5.55328i	−0.368128	−	0.274928i
$409$	38.4401	+	10.3000i	1.90074	+	0.509301i	0.996633	+	0.0819915i	$0.0261280\pi$
$409$	38.4401	+	10.3000i	1.90074	+	0.509301i	0.904105	+	0.427310i	$0.140539\pi$
$410$	−28.5831	−	7.65881i	−1.41162	−	0.378242i
$411$	−26.9020	−	20.0912i	−1.32698	−	0.991024i
$412$	−3.63896			−0.179279
$413$	−10.4568	−	17.2662i	−0.514546	−	0.849614i
$414$	−19.3091	+	11.8295i	−0.948993	+	0.581388i
$415$	−9.58423	−	5.53346i	−0.470471	−	0.271627i
$416$	−5.37302	+	3.77167i	−0.263434	+	0.184921i
$417$	−29.4040	−	11.7330i	−1.43992	−	0.574569i
$418$	0.484856	+	1.80951i	0.0237151	+	0.0885059i
$419$		−	35.0848i		−	1.71401i	−0.515312	−	0.857003i	$-0.672324\pi$
$419$		−	35.0848i		−	1.71401i	0.515312	−	0.857003i	$-0.327676\pi$
$420$	5.35020	+	2.00604i	0.261063	+	0.0978845i
$421$	7.19039	−	7.19039i	0.350438	−	0.350438i	−0.509834	−	0.860273i	$-0.670293\pi$
$421$	7.19039	−	7.19039i	0.350438	−	0.350438i	0.860273	+	0.509834i	$0.170293\pi$
$422$	−9.40108	+	2.51901i	−0.457637	+	0.122624i
$423$	4.70512	−	8.66329i	0.228771	−	0.421224i
$424$	6.90592	−	25.7732i	0.335381	−	1.25166i
$425$	14.9486	+	8.63055i	0.725111	+	0.418643i
$426$	6.37750	+	8.09081i	0.308991	+	0.392001i
$427$	28.3775	−	8.24448i	1.37328	−	0.398978i
$428$	−5.62773			−0.272026
$429$	2.13141	+	9.00658i	0.102905	+	0.434842i
$430$	16.7718	+	29.0497i	0.808810	+	1.40090i
$431$	−6.53304	+	24.3816i	−0.314685	+	1.17442i	0.609597	+	0.792712i	$0.291331\pi$
$431$	−6.53304	+	24.3816i	−0.314685	+	1.17442i	−0.924282	+	0.381710i	$0.875335\pi$
$432$	16.7834	+	1.54521i	0.807494	+	0.0743441i
$433$		−	15.7187i		−	0.755394i	−0.925929	−	0.377697i	$-0.876716\pi$
$433$		−	15.7187i		−	0.755394i	0.925929	−	0.377697i	$-0.123284\pi$
$434$	−7.77902	−	7.45979i	−0.373405	−	0.358081i
$435$	−1.80881	+	15.2747i	−0.0867257	+	0.732367i
$436$	−2.60866	+	0.698987i	−0.124932	+	0.0334754i
$437$	5.50303	+	1.47453i	0.263246	+	0.0705364i
$438$	4.80291	−	12.0365i	0.229492	−	0.575126i
$439$	9.47409	+	5.46987i	0.452174	+	0.261063i	0.708748	−	0.705462i	$-0.249260\pi$
$439$	9.47409	+	5.46987i	0.452174	+	0.261063i	−0.256574	+	0.966525i	$0.582594\pi$
$440$	12.0882	−	12.0882i	0.576280	−	0.576280i
$441$	−13.8067	+	15.8232i	−0.657463	+	0.753487i
$442$	−0.733873	−	8.27586i	−0.0349068	−	0.393642i
$443$	−11.9352	−	6.89078i	−0.567058	−	0.327391i	0.188916	−	0.981993i	$-0.439503\pi$
$443$	−11.9352	−	6.89078i	−0.567058	−	0.327391i	−0.755973	+	0.654602i	$0.772836\pi$
$444$	4.68549	−	2.01272i	0.222364	−	0.0955193i
$445$	−1.27658	−	2.21109i	−0.0605155	−	0.104816i
$446$	1.35583	−	2.34837i	0.0642004	−	0.111198i
$447$	11.8100	+	1.39852i	0.558592	+	0.0661475i
$448$	−16.1945	+	16.8875i	−0.765118	+	0.797859i
$449$	17.2469	−	17.2469i	0.813931	−	0.813931i	−0.171289	−	0.985221i	$-0.554793\pi$
$449$	17.2469	−	17.2469i	0.813931	−	0.813931i	0.985221	+	0.171289i	$0.0547933\pi$
$450$	−37.6221	+	0.980673i	−1.77352	+	0.0462294i
$451$	4.42034	+	7.65626i	0.208146	+	0.360519i
$452$	−1.36726	−	2.36816i	−0.0643104	−	0.111389i
$453$	−3.71927	+	4.98009i	−0.174747	+	0.233985i
$454$			8.20377i			0.385022i
$455$	13.2637	+	34.0766i	0.621813	+	1.59754i
$456$	−3.15149	−	3.99813i	−0.147582	−	0.187230i
$457$	−1.05340	−	3.93136i	−0.0492761	−	0.183901i	0.936901	−	0.349594i	$-0.113681\pi$
$457$	−1.05340	−	3.93136i	−0.0492761	−	0.183901i	−0.986177	+	0.165693i	$0.947014\pi$
$458$	−0.257080	+	0.148425i	−0.0120125	+	0.00693545i
$459$	5.34131	−	7.55491i	0.249311	−	0.352633i
$460$	−1.88232	−	7.02491i	−0.0877635	−	0.327538i
$461$	6.28561	+	6.28561i	0.292750	+	0.292750i	0.838166	−	0.545416i	$-0.183628\pi$
$461$	6.28561	+	6.28561i	0.292750	+	0.292750i	−0.545416	+	0.838166i	$0.683628\pi$
$462$	3.63731	+	8.00107i	0.169223	+	0.372244i
$463$	−20.3623	−	20.3623i	−0.946318	−	0.946318i	0.0523129	−	0.998631i	$-0.483341\pi$
$463$	−20.3623	−	20.3623i	−0.946318	−	0.946318i	−0.998631	+	0.0523129i	$0.983341\pi$
$464$	−6.50775	−	3.75725i	−0.302115	−	0.174426i
$465$	−19.4114	−	7.74570i	−0.900181	−	0.359198i
$466$	2.31344	−	8.63387i	0.107168	−	0.399956i
$467$	−7.33823	+	12.7102i	−0.339573	+	0.588158i	−0.984352	−	0.176211i	$-0.943616\pi$
$467$	−7.33823	+	12.7102i	−0.339573	+	0.588158i	0.644779	+	0.764369i	$0.276949\pi$
$468$	−2.09583	−	2.82609i	−0.0968800	−	0.130636i
$469$	11.0581	+	18.2590i	0.510614	+	0.843121i
$470$	−11.5270	−	11.5270i	−0.531700	−	0.531700i
$471$	3.64274	+	25.1341i	0.167849	+	1.15812i
$472$	19.8826	−	11.4792i	0.915172	−	0.528375i
$473$	2.59375	−	9.68000i	0.119261	−	0.445087i
$474$	21.2922	−	28.5102i	0.977985	−	1.30952i
$475$	6.69526	+	6.69526i	0.307200	+	0.307200i
$476$	0.427531	+	1.47156i	0.0195959	+	0.0674491i
$477$	25.8654	+	6.21300i	1.18430	+	0.284474i
$478$	18.9262	+	10.9271i	0.865666	+	0.499793i
$479$	20.6864	+	5.54291i	0.945187	+	0.253262i	0.698319	−	0.715787i	$-0.253932\pi$
$479$	20.6864	+	5.54291i	0.945187	+	0.253262i	0.246868	+	0.969049i	$0.420598\pi$
$480$	−4.48013	+	11.2276i	−0.204489	+	0.512467i
$481$	29.5935	+	13.7573i	1.34935	+	0.627277i
$482$		−	23.4464i		−	1.06796i
$483$	26.6035	+	2.58663i	1.21050	+	0.117696i
$484$	2.86361			0.130164
$485$	−10.1011	+	17.4956i	−0.458666	+	0.794432i
$486$	−1.32540	+	20.1296i	−0.0601213	+	0.913097i
$487$	−2.67104	−	0.715703i	−0.121036	−	0.0324316i	0.197792	−	0.980244i	$-0.436623\pi$
$487$	−2.67104	−	0.715703i	−0.121036	−	0.0324316i	−0.318829	+	0.947812i	$0.603289\pi$
$488$	8.69890	+	32.4647i	0.393780	+	1.46961i
$489$	31.1963	+	3.69421i	1.41074	+	0.167058i
$490$	18.6065	+	29.3189i	0.840555	+	1.32449i
$491$	−3.45508			−0.155925			−0.0779627	−	0.996956i	$-0.524842\pi$
$491$	−3.45508			−0.155925			−0.0779627	+	0.996956i	$0.524842\pi$
$492$	−2.69273	−	2.01100i	−0.121397	−	0.0906631i
$493$	−3.57248	+	2.06257i	−0.160896	+	0.0928936i
$494$	0.786113	−	4.48920i	0.0353689	−	0.201979i
$495$	12.3613	+	11.7332i	0.555598	+	0.527368i
$496$	7.21985	−	7.21985i	0.324181	−	0.324181i
$497$	−0.254683	−	12.1576i	−0.0114241	−	0.545344i
$498$	4.00603	+	5.08225i	0.179514	+	0.227741i
$499$	5.87182	+	21.9139i	0.262859	+	0.981003i	0.963548	+	0.267536i	$0.0862094\pi$
$499$	5.87182	+	21.9139i	0.262859	+	0.981003i	−0.700689	+	0.713467i	$0.747124\pi$
$500$	1.51479	−	5.65327i	0.0677434	−	0.252822i
$501$	−17.6596	+	7.58591i	−0.788972	+	0.338913i
$502$	33.8424	−	9.06804i	1.51046	−	0.404726i
$503$			21.8711i			0.975184i	0.873072	+	0.487592i	$0.162125\pi$
$503$			21.8711i			0.975184i	−0.873072	+	0.487592i	$0.837875\pi$
$504$	−17.6638	−	16.0767i	−0.786810	−	0.716112i
$505$	−26.6222	−	26.6222i	−1.18467	−	1.18467i
$506$	5.59339	−	9.68803i	0.248656	−	0.430685i
$507$	4.53467	−	22.0553i	0.201392	−	0.979511i
$508$	2.10171	+	3.64028i	0.0932485	+	0.161511i
$509$	34.7228	−	9.30395i	1.53906	−	0.412390i	0.613099	−	0.790006i	$-0.289922\pi$
$509$	34.7228	−	9.30395i	1.53906	−	0.412390i	0.925963	+	0.377615i	$0.123256\pi$
$510$	−9.47098	−	12.0154i	−0.419382	−	0.532049i
$511$	−13.0843	+	7.92418i	−0.578817	+	0.350545i
$512$	−17.9796	−	17.9796i	−0.794594	−	0.794594i
$513$	3.90273	−	3.24468i	0.172310	−	0.143256i
$514$	2.40858	−	8.98895i	0.106238	−	0.396486i
$515$	−41.4222	−	11.0991i	−1.82528	−	0.489083i
$516$	0.546434	+	3.77028i	0.0240554	+	0.165977i
$517$			4.87025i			0.214194i
$518$	30.0962	+	7.39228i	1.32235	+	0.324798i
$519$	−26.2122	+	20.6615i	−1.15059	+	0.906938i
$520$	−39.0648	+	14.2706i	−1.71310	+	0.625806i
$521$	15.3735	−	8.87590i	0.673525	−	0.388860i	−0.123886	−	0.992296i	$-0.539536\pi$
$521$	15.3735	−	8.87590i	0.673525	−	0.388860i	0.797411	+	0.603436i	$0.206202\pi$
$522$	4.29259	−	7.90371i	0.187882	−	0.345936i
$523$	−1.56142	+	2.70445i	−0.0682759	+	0.118257i	−0.898142	−	0.439705i	$-0.855083\pi$
$523$	−1.56142	+	2.70445i	−0.0682759	+	0.118257i	0.829867	+	0.557962i	$0.188416\pi$
$524$	1.41185			0.0616770
$525$	36.1414	+	25.8302i	1.57734	+	1.12732i
$526$	−9.72320	+	9.72320i	−0.423952	+	0.423952i
$527$	−1.45070	−	5.41409i	−0.0631936	−	0.235842i
$528$	−7.65035	+	3.28631i	−0.332939	+	0.143018i
$529$	−5.51046	−	9.54440i	−0.239585	−	0.414974i
$530$	21.9932	−	38.0933i	0.955324	−	1.65467i
$531$	11.9569	+	19.5171i	0.518885	+	0.846971i
$532$	0.0176054	+	0.840416i	0.000763290	+	0.0364366i
$533$	−1.89978	−	21.4238i	−0.0822888	−	0.927967i
$534$	0.214136	+	1.47749i	0.00926659	+	0.0639375i
$535$	−64.0604	−	17.1649i	−2.76957	−	0.742104i
$536$	−21.0258	+	12.1393i	−0.908178	+	0.524337i
$537$	−1.28601	−	8.87321i	−0.0554956	−	0.382907i
$538$	−2.93056	+	2.93056i	−0.126346	+	0.126346i
$539$	2.26305	−	10.1245i	0.0974766	−	0.436091i
$540$	−6.07811	−	2.24357i	−0.261560	−	0.0965479i
$541$	−5.65703	+	1.51580i	−0.243215	+	0.0651691i	−0.378367	−	0.925656i	$-0.623514\pi$
$541$	−5.65703	+	1.51580i	−0.243215	+	0.0651691i	0.135152	+	0.990825i	$0.456848\pi$
$542$	−7.44098	+	4.29605i	−0.319617	+	0.184531i
$543$	−1.71339	+	4.29390i	−0.0735286	+	0.184269i
$544$	−3.13152	+	0.839089i	−0.134263	+	0.0359756i
$545$	−31.8263			−1.36329
$546$	0.181298	−	21.3814i	0.00775883	−	0.915041i
$547$	1.31098			0.0560535			0.0280268	−	0.999607i	$-0.491078\pi$
$547$	1.31098			0.0560535			0.0280268	+	0.999607i	$0.491078\pi$
$548$	−6.09077	+	1.63202i	−0.260185	+	0.0697163i
$549$	−32.1288	+	9.51283i	−1.37123	+	0.405997i
$550$	16.1013	−	9.29607i	0.686560	−	0.396386i
$551$	−2.18573	+	0.585665i	−0.0931153	+	0.0249502i
$552$	−3.57499	+	30.1895i	−0.152162	+	1.28495i
$553$	−40.3339	+	11.7182i	−1.71517	+	0.498307i
$554$	21.2829	−	21.2829i	0.904226	−	0.904226i
$555$	59.4739	−	8.61968i	2.52453	−	0.365885i
$556$	−5.14891	+	2.97272i	−0.218362	+	0.126072i
$557$	−4.16840	−	1.11692i	−0.176621	−	0.0473254i	0.169425	−	0.985543i	$-0.445809\pi$
$557$	−4.16840	−	1.11692i	−0.176621	−	0.0473254i	−0.346045	+	0.938218i	$0.612476\pi$
$558$	8.86373	+	8.41338i	0.375232	+	0.356167i
$559$	−15.6495	+	18.6950i	−0.661902	+	0.790715i
$560$	−28.1385	+	17.0413i	−1.18907	+	0.720127i
$561$	−0.537511	+	4.53908i	−0.0226937	+	0.191640i
$562$	7.60457	−	13.1715i	0.320779	−	0.555606i
$563$	−17.4211	−	30.1742i	−0.734211	−	1.27169i	−0.955069	−	0.296384i	$-0.904219\pi$
$563$	−17.4211	−	30.1742i	−0.734211	−	1.27169i	0.220858	−	0.975306i	$-0.429114\pi$
$564$	−0.730739	−	1.70112i	−0.0307697	−	0.0716302i
$565$	−8.34045	−	31.1270i	−0.350886	−	1.30952i
$566$	−17.9022	+	17.9022i	−0.752486	+	0.752486i
$567$	15.5634	−	18.0217i	0.653600	−	0.756840i
$568$	13.8306			0.580319
$569$	−23.0336	+	39.8954i	−0.965620	+	1.67250i	−0.257678	+	0.966231i	$0.582957\pi$
$569$	−23.0336	+	39.8954i	−0.965620	+	1.67250i	−0.707941	+	0.706271i	$0.750376\pi$
$570$	−3.31238	−	7.71104i	−0.138740	−	0.322980i
$571$	−12.9813	+	7.49477i	−0.543252	+	0.313647i	−0.746396	−	0.665502i	$-0.768217\pi$
$571$	−12.9813	+	7.49477i	−0.543252	+	0.313647i	0.203144	+	0.979149i	$0.434884\pi$
$572$	1.57616	+	0.732717i	0.0659028	+	0.0306365i
$573$	−4.91673	−	6.23761i	−0.205400	−	0.260580i
$574$	−5.69821	−	19.6132i	−0.237839	−	0.818641i
$575$		−	56.5419i		−	2.35796i
$576$	18.2646	−	19.2423i	0.761026	−	0.801763i
$577$	18.6297	+	4.99180i	0.775563	+	0.207812i	0.624828	−	0.780763i	$-0.285169\pi$
$577$	18.6297	+	4.99180i	0.775563	+	0.207812i	0.150735	+	0.988574i	$0.451836\pi$
$578$	−4.63202	+	17.2869i	−0.192667	+	0.719042i
$579$	7.37610	−	9.87657i	0.306540	−	0.410456i
$580$	2.04257	+	2.04257i	0.0848131	+	0.0848131i
$581$	−0.159979	−	7.63681i	−0.00663705	−	0.316828i
$582$	9.27740	−	7.31281i	0.384560	−	0.303126i
$583$	−12.6936	+	3.40123i	−0.525713	+	0.140864i
$584$	−8.69897	−	15.0671i	−0.359966	−	0.623480i
$585$	−15.2371	−	38.5618i	−0.629977	−	1.59434i
$586$	2.84345	−	4.92500i	0.117462	−	0.203450i
$587$	27.9851	+	27.9851i	1.15507	+	1.15507i	0.985522	+	0.169548i	$0.0542306\pi$
$587$	27.9851	+	27.9851i	1.15507	+	1.15507i	0.169548	+	0.985522i	$0.445769\pi$
$588$	0.728628	+	3.87590i	0.0300481	+	0.159839i
$589$		−	3.07465i		−	0.126689i
$590$	36.5578	−	9.79563i	1.50506	−	0.403280i
$591$	10.6372	+	24.7628i	0.437556	+	1.01861i
$592$	−7.59871	+	28.3588i	−0.312305	+	1.16554i
$593$	1.21118	+	4.52020i	0.0497374	+	0.185622i	0.986325	−	0.164810i	$-0.0527012\pi$
$593$	1.21118	+	4.52020i	0.0497374	+	0.185622i	−0.936588	+	0.350433i	$0.886035\pi$
$594$	−4.17067	−	9.05115i	−0.171125	−	0.371373i
$595$	0.378220	+	18.0548i	0.0155055	+	0.740175i
$596$	1.57925	−	1.57925i	0.0646888	−	0.0646888i
$597$	−15.3384	+	2.22302i	−0.627758	+	0.0909823i
$598$	−22.2752	+	15.6364i	−0.910901	+	0.639421i
$599$	−1.70959	+	0.987035i	−0.0698521	+	0.0403291i	−0.534519	−	0.845156i	$-0.679507\pi$
$599$	−1.70959	+	0.987035i	−0.0698521	+	0.0403291i	0.464667	+	0.885485i	$0.346174\pi$
$600$	−30.2326	+	40.4814i	−1.23424	+	1.65265i
$601$	22.1442			0.903281			0.451641	−	0.892200i	$-0.350839\pi$
$601$	22.1442			0.903281			0.451641	+	0.892200i	$0.350839\pi$
$602$	−11.1536	+	20.2884i	−0.454587	+	0.826894i
$603$	−12.6444	−	20.6393i	−0.514920	−	0.840498i
$604$	0.302119	+	1.12752i	0.0122930	+	0.0458783i
$605$	32.5964	+	8.73419i	1.32523	+	0.355095i
$606$	8.68916	+	20.2279i	0.352973	+	0.821702i
$607$	3.46982	−	6.00991i	0.140836	−	0.243935i	−0.786976	−	0.616984i	$-0.788354\pi$
$607$	3.46982	−	6.00991i	0.140836	−	0.243935i	0.927812	+	0.373049i	$0.121688\pi$
$608$	−1.77839			−0.0721230
$609$	−9.66462	+	4.39356i	−0.391630	+	0.178036i
$610$			55.4066i			2.24335i
$611$	4.99473	−	10.7443i	0.202065	−	0.434667i
$612$	−0.493304	−	1.66610i	−0.0199406	−	0.0673479i
$613$	14.1349	+	3.78743i	0.570903	+	0.152973i	0.532711	−	0.846298i	$-0.321173\pi$
$613$	14.1349	+	3.78743i	0.570903	+	0.152973i	0.0381921	+	0.999270i	$0.487840\pi$
$614$	−20.2013	−	11.6633i	−0.815260	−	0.470691i
$615$	−24.5176	−	31.1042i	−0.988645	−	1.25424i
$616$	11.4587	+	2.81451i	0.461684	+	0.113400i
$617$	24.6732	+	24.6732i	0.993306	+	0.993306i	0.999978	−	0.00667207i	$-0.00212380\pi$
$617$	24.6732	+	24.6732i	0.993306	+	0.993306i	−0.00667207	+	0.999978i	$0.502124\pi$
$618$	20.0911	+	15.0046i	0.808183	+	0.603574i
$619$	3.26864	−	12.1987i	0.131378	−	0.490309i	−0.868609	−	0.495499i	$-0.834985\pi$
$619$	3.26864	−	12.1987i	0.131378	−	0.490309i	0.999987	+	0.00519004i	$0.00165205\pi$
$620$	−3.39911	+	1.96248i	−0.136512	+	0.0788150i
$621$	−30.1802	−	2.77862i	−1.21109	−	0.111502i
$622$	−5.11831	−	5.11831i	−0.205225	−	0.205225i
$623$	0.848948	−	1.54424i	0.0340124	−	0.0618685i
$624$	20.2477	+	0.595949i	0.810558	+	0.0238570i
$625$	10.2510	−	17.7552i	0.410039	−	0.710208i
$626$	5.31508	−	19.8361i	0.212433	−	0.792812i
$627$	−0.929237	+	2.32875i	−0.0371102	+	0.0930012i
$628$	4.13051	+	2.38475i	0.164825	+	0.0951618i
$629$	11.3964	+	11.3964i	0.454404	+	0.454404i
$630$	−21.2675	−	33.1362i	−0.847319	−	1.32018i
$631$	4.81881	+	4.81881i	0.191834	+	0.191834i	0.796488	−	0.604654i	$-0.206689\pi$
$631$	4.81881	+	4.81881i	0.191834	+	0.191834i	−0.604654	+	0.796488i	$0.706689\pi$
$632$	−12.3640	−	46.1432i	−0.491815	−	1.83548i
$633$	−12.0987	−	4.82774i	−0.480881	−	0.191885i
$634$	−14.4287	+	8.33040i	−0.573036	+	0.330842i
$635$	12.8207	+	47.8476i	0.508775	+	1.89877i
$636$	3.92338	−	3.09256i	0.155572	−	0.122628i
$637$	−15.3757	+	20.0147i	−0.609209	+	0.793010i
$638$			4.44324i			0.175910i
$639$	0.359294	+	13.7838i	0.0142134	+	0.545278i
$640$	−14.9555	−	25.9037i	−0.591167	−	1.02393i
$641$	−4.86631	−	8.42869i	−0.192208	−	0.332913i	0.753774	−	0.657134i	$-0.228231\pi$
$641$	−4.86631	−	8.42869i	−0.192208	−	0.332913i	−0.945982	+	0.324220i	$0.894898\pi$
$642$	31.0713	+	23.2050i	1.22629	+	0.915827i
$643$	9.13194	−	9.13194i	0.360129	−	0.360129i	−0.503732	−	0.863860i	$-0.668040\pi$
$643$	9.13194	−	9.13194i	0.360129	−	0.360129i	0.863860	+	0.503732i	$0.168040\pi$
$644$	3.47434	−	3.62302i	0.136908	−	0.142767i
$645$	−5.27953	+	44.5837i	−0.207881	+	1.75548i
$646$	1.12537	−	1.94921i	0.0442773	−	0.0766905i
$647$	−12.3473	−	21.3862i	−0.485423	−	0.840777i	0.514437	−	0.857528i	$-0.328001\pi$
$647$	−12.3473	−	21.3862i	−0.485423	−	0.840777i	−0.999860	+	0.0167510i	$0.994668\pi$
$648$	20.1219	+	18.1265i	0.790463	+	0.712078i
$649$	−9.79237	−	5.65363i	−0.384384	−	0.221924i
$650$	−45.0547	+	3.99529i	−1.76719	+	0.156708i
$651$	−2.36759	−	14.2295i	−0.0927932	−	0.557700i
$652$	4.17164	−	4.17164i	0.163374	−	0.163374i
$653$	21.5537	+	12.4440i	0.843460	+	0.486972i	0.858439	−	0.512916i	$-0.171435\pi$
$653$	21.5537	+	12.4440i	0.843460	+	0.486972i	−0.0149789	+	0.999888i	$0.504768\pi$
$654$	17.2849	+	6.89715i	0.675891	+	0.269700i
$655$	16.0711	+	4.30624i	0.627950	+	0.168259i
$656$	18.6897	−	5.00788i	0.729709	−	0.195525i
$657$	14.7901	−	9.06094i	0.577016	−	0.353501i
$658$	2.68385	−	10.9268i	0.104627	−	0.425969i
$659$		−	24.4285i		−	0.951600i	−0.879554	−	0.475800i	$-0.842159\pi$
$659$		−	24.4285i		−	0.951600i	0.879554	−	0.475800i	$-0.157841\pi$
$660$	3.16760	−	0.459088i	0.123299	−	0.0178700i
$661$	3.26929	−	12.2012i	0.127161	−	0.474570i	−0.872747	−	0.488173i	$-0.837663\pi$
$661$	3.26929	−	12.2012i	0.127161	−	0.474570i	0.999907	+	0.0136029i	$0.00433007\pi$
$662$	−15.6913	−	27.1781i	−0.609859	−	1.05631i
$663$	5.84089	−	9.46242i	0.226842	−	0.367490i
$664$	8.68770			0.337148
$665$	−2.36292	+	9.62015i	−0.0916301	+	0.373053i
$666$	−34.1683	−	8.20739i	−1.32399	−	0.318030i
$667$	11.7023	+	6.75634i	0.453116	+	0.261606i
$668$	−0.934209	+	3.48651i	−0.0361456	+	0.134897i
$669$	3.33467	−	1.43245i	0.128926	−	0.0553817i
$670$	−38.6598	+	10.3589i	−1.49356	+	0.400198i
$671$	11.7049	−	11.7049i	0.451862	−	0.451862i
$672$	−8.23040	+	1.36942i	−0.317494	+	0.0528265i
$673$		−	32.5521i		−	1.25479i	−0.778700	−	0.627396i	$-0.784121\pi$
$673$		−	32.5521i		−	1.25479i	0.778700	−	0.627396i	$-0.215879\pi$
$674$	−0.956335	−	3.56909i	−0.0368367	−	0.137476i
$675$	−41.1298	−	29.0787i	−1.58308	−	1.11924i
$676$	−2.72573	−	3.23290i	−0.104836	−	0.124342i
$677$	−27.7679	−	16.0318i	−1.06721	−	0.616152i	−0.139789	−	0.990181i	$-0.544642\pi$
$677$	−27.7679	−	16.0318i	−1.06721	−	0.616152i	−0.927417	+	0.374030i	$0.877976\pi$
$678$	−2.21591	+	18.7126i	−0.0851015	+	0.718652i
$679$	−13.9406	+	0.292034i	−0.534993	+	0.0112072i
$680$	−20.5393			−0.787646
$681$	−6.57014	+	8.79739i	−0.251768	+	0.337117i
$682$	−5.83158	−	1.56257i	−0.223303	−	0.0598338i
$683$	−25.3970	−	6.80511i	−0.971790	−	0.260390i	−0.262207	−	0.965012i	$-0.584450\pi$
$683$	−25.3970	−	6.80511i	−0.971790	−	0.260390i	−0.709583	+	0.704621i	$0.751117\pi$
$684$	−0.0248368	−	0.952827i	−0.000949659	−	0.0364323i
$685$	−74.3089			−2.83920
$686$	−10.6566	+	21.4678i	−0.406871	+	0.819644i
$687$	−0.394551	−	0.0467220i	−0.0150530	−	0.00178256i
$688$	−18.9948	−	10.9666i	−0.724169	−	0.418099i
$689$	31.4914	+	5.51452i	1.19973	+	0.210087i
$690$	−18.5735	+	46.5468i	−0.707081	+	1.77201i
$691$	1.39650	+	5.21180i	0.0531252	+	0.198266i	0.987388	−	0.158319i	$-0.0506075\pi$
$691$	1.39650	+	5.21180i	0.0531252	+	0.198266i	−0.934263	+	0.356585i	$0.883941\pi$
$692$			6.26805i			0.238276i
$693$	−2.50731	+	11.4930i	−0.0952447	+	0.436584i
$694$	26.3889	−	26.3889i	1.00171	−	1.00171i
$695$	−67.6770	+	18.1340i	−2.56713	+	0.687862i
$696$	−4.76574	−	11.0944i	−0.180645	−	0.420532i
$697$	2.74911	−	10.2598i	0.104130	−	0.388619i
$698$	−5.80880	−	3.35371i	−0.219866	−	0.126940i
$699$	9.39542	−	7.40584i	0.355367	−	0.280115i
$700$	8.01136	−	2.32753i	0.302801	−	0.0879723i
$701$	34.6806			1.30987			0.654935	−	0.755685i	$-0.272696\pi$
$701$	34.6806			1.30987			0.654935	+	0.755685i	$0.272696\pi$
$702$	−0.0815567	+	24.2450i	−0.00307816	+	0.915069i
$703$	4.42045	+	7.65644i	0.166720	+	0.288768i
$704$	−3.39218	+	12.6598i	−0.127848	+	0.477134i
$705$	−3.12947	−	21.5927i	−0.117863	−	0.813227i
$706$			33.8065i			1.27232i
$707$	6.19850	−	25.2359i	0.233119	−	0.949095i
$708$	4.26864	+	0.505485i	0.160425	+	0.0189973i
$709$	14.4578	−	3.87395i	0.542974	−	0.145489i	0.0231010	−	0.999733i	$-0.492646\pi$
$709$	14.4578	−	3.87395i	0.542974	−	0.145489i	0.519873	+	0.854244i	$0.325979\pi$
$710$	22.0231	+	5.90107i	0.826512	+	0.221463i
$711$	45.6658	−	13.5209i	1.71260	−	0.507073i
$712$	1.73574	+	1.00213i	0.0650497	+	0.0375564i
$713$	−12.9828	+	12.9828i	−0.486210	+	0.486210i
$714$	3.70729	−	9.88754i	0.138742	−	0.370032i
$715$	15.7066	+	13.1479i	0.587395	+	0.491704i
$716$	−1.45821	−	0.841899i	−0.0544959	−	0.0314632i
$717$	11.5446	+	26.8752i	0.431140	+	1.00367i
$718$	−14.9677	−	25.9249i	−0.558591	−	0.967507i
$719$	−13.5897	+	23.5381i	−0.506812	+	0.877824i	0.493157	+	0.869940i	$0.335843\pi$
$719$	−13.5897	+	23.5381i	−0.506812	+	0.877824i	−0.999969	+	0.00788373i	$0.997491\pi$
$720$	31.8067	−	19.4860i	1.18537	−	0.726199i
$721$	−8.25777	−	28.4233i	−0.307536	−	1.05854i
$722$	−16.5134	+	16.5134i	−0.614565	+	0.614565i
$723$	18.7775	−	25.1430i	0.698342	−	0.935077i
$724$	0.434111	+	0.751902i	0.0161336	+	0.0279442i
$725$	11.2289	+	19.4490i	0.417030	+	0.722317i
$726$	−15.8103	−	11.8076i	−0.586776	−	0.438221i
$727$			19.6171i			0.727559i	0.931485	+	0.363780i	$0.118514\pi$
$727$			19.6171i			0.727559i	−0.931485	+	0.363780i	$0.881486\pi$
$728$	−22.3926	−	17.9606i	−0.829925	−	0.665666i
$729$	−17.5425	+	20.5247i	−0.649720	+	0.760173i
$730$	−7.42314	−	27.7035i	−0.274743	−	1.02535i
$731$	−10.4273	+	6.02022i	−0.385668	+	0.222666i
$732$	−2.33216	+	5.84459i	−0.0861991	+	0.216022i
$733$	−9.35544	−	34.9150i	−0.345551	−	1.28961i	−0.891967	−	0.452100i	$-0.850675\pi$
$733$	−9.35544	−	34.9150i	−0.345551	−	1.28961i	0.546416	−	0.837514i	$-0.315992\pi$
$734$	13.6557	+	13.6557i	0.504042	+	0.504042i
$735$	−3.52778	+	46.3417i	−0.130124	+	1.70934i
$736$	7.50929	+	7.50929i	0.276796	+	0.276796i
$737$	10.3554	+	5.97870i	0.381447	+	0.220228i
$738$	6.57483	+	22.2060i	0.242023	+	0.817414i
$739$	−1.84955	+	6.90263i	−0.0680369	+	0.253917i	−0.991564	−	0.129615i	$-0.958626\pi$
$739$	−1.84955	+	6.90263i	−0.0680369	+	0.253917i	0.923527	+	0.383532i	$0.125293\pi$
$740$	5.64294	−	9.77385i	0.207438	−	0.359294i
$741$	4.43825	−	4.18446i	0.163043	−	0.153720i
$742$	30.3532	−	0.635851i	1.11430	−	0.0233428i
$743$	−4.27421	−	4.27421i	−0.156806	−	0.156806i	0.624344	−	0.781150i	$-0.285366\pi$
$743$	−4.27421	−	4.27421i	−0.156806	−	0.156806i	−0.781150	+	0.624344i	$0.785366\pi$
$744$	16.2369	−	2.35325i	0.595275	−	0.0862744i
$745$	22.7935	−	13.1598i	0.835088	−	0.482138i
$746$	−10.1193	+	37.7657i	−0.370493	+	1.38270i
$747$	0.225691	+	8.65829i	0.00825759	+	0.316790i
$748$	0.606976	+	0.606976i	0.0221933	+	0.0221933i
$749$	−12.7708	−	43.9572i	−0.466636	−	1.60616i
$750$	−31.6736	+	24.9664i	−1.15656	+	0.911644i
$751$	16.4809	+	9.51527i	0.601398	+	0.347217i	0.769591	−	0.638537i	$-0.220460\pi$
$751$	16.4809	+	9.51527i	0.601398	+	0.347217i	−0.168193	+	0.985754i	$0.553793\pi$
$752$	10.2960	+	2.75880i	0.375455	+	0.100603i
$753$	43.5535	+	17.3791i	1.58718	+	0.633329i
$754$	4.55680	−	9.80224i	0.165949	−	0.356977i
$755$			13.7561i			0.500635i
$756$	−0.848656	−	4.39058i	−0.0308653	−	0.159684i
$757$	−0.926509			−0.0336745			−0.0168373	−	0.999858i	$-0.505360\pi$
$757$	−0.926509			−0.0336745			−0.0168373	+	0.999858i	$0.505360\pi$
$758$	14.0802	−	24.3876i	0.511416	−	0.885798i
$759$	13.7569	−	5.90948i	0.499346	−	0.214500i
$760$	−10.8829	−	2.91606i	−0.394763	−	0.105776i
$761$	−0.157093	−	0.586277i	−0.00569460	−	0.0212525i	0.963020	−	0.269430i	$-0.0868352\pi$
$761$	−0.157093	−	0.586277i	−0.00569460	−	0.0212525i	−0.968715	+	0.248177i	$0.920169\pi$
$762$	3.40624	−	28.7645i	0.123395	−	1.04203i
$763$	−11.3794	−	18.7896i	−0.411962	−	0.680229i
$764$	−1.49158			−0.0539636
$765$	−0.533574	−	20.4698i	−0.0192914	−	0.740086i
$766$	−20.4293	+	11.7949i	−0.738142	+	0.426166i
$767$	15.8048	+	22.5151i	0.570679	+	0.812974i
$768$	−1.88537	−	13.0086i	−0.0680323	−	0.469408i
$769$	−10.9430	+	10.9430i	−0.394614	+	0.394614i	−0.876328	−	0.481714i	$-0.840014\pi$
$769$	−10.9430	+	10.9430i	−0.394614	+	0.394614i	0.481714	+	0.876328i	$0.340014\pi$
$770$	17.0453	+	9.37072i	0.614271	+	0.337697i
$771$	9.78183	−	7.71043i	0.352284	−	0.277684i
$772$	−0.599165	−	2.23611i	−0.0215644	−	0.0804795i
$773$	−6.73753	+	25.1448i	−0.242332	+	0.904395i	0.732374	+	0.680903i	$0.238412\pi$
$773$	−6.73753	+	25.1448i	−0.242332	+	0.904395i	−0.974706	+	0.223492i	$0.928254\pi$
$774$	12.5292	−	23.0693i	0.450351	−	0.829208i
$775$	−29.4749	+	7.89778i	−1.05877	+	0.283697i
$776$		−	15.8590i		−	0.569304i
$777$	26.3536	+	32.0302i	0.945431	+	1.14908i
$778$	−8.74930	−	8.74930i	−0.313678	−	0.313678i
$779$	2.91327	−	5.04593i	0.104379	−	0.180789i
$780$	−7.45887	−	2.23577i	−0.267070	−	0.0800533i
$781$	−3.40585	−	5.89910i	−0.121871	−	0.211086i
$782$	−12.9825	+	3.47866i	−0.464254	+	0.124396i
$783$	10.9330	−	5.03782i	0.390714	−	0.180037i
$784$	−20.1217	−	10.5193i	−0.718632	−	0.375689i
$785$	39.7439	+	39.7439i	1.41852	+	1.41852i
$786$	−7.79500	−	5.82153i	−0.278038	−	0.207647i
$787$	−4.04618	+	15.1006i	−0.144231	+	0.538277i	0.855558	+	0.517708i	$0.173215\pi$
$787$	−4.04618	+	15.1006i	−0.144231	+	0.538277i	−0.999788	+	0.0205692i	$0.993452\pi$
$788$	4.88890	+	1.30998i	0.174160	+	0.0466660i
$789$	−18.2138	+	2.63976i	−0.648427	+	0.0939779i
$790$		−	78.7512i		−	2.80184i
$791$	15.3946	−	16.0534i	0.547370	−	0.570794i
$792$	−13.0091	−	3.12485i	−0.462258	−	0.111037i
$793$	−37.8262	+	13.8181i	−1.34325	+	0.490696i
$794$	−5.74924	+	3.31932i	−0.204033	+	0.117798i
$795$	54.0923	−	23.2361i	1.91846	−	0.824099i
$796$	−1.45532	+	2.52069i	−0.0515824	+	0.0893433i
$797$	34.0241			1.20519			0.602597	−	0.798045i	$-0.294133\pi$
$797$	34.0241			1.20519			0.602597	+	0.798045i	$0.294133\pi$
$798$	3.36811	−	4.71263i	0.119230	−	0.166825i
$799$	4.13759	−	4.13759i	0.146377	−	0.146377i
$800$	4.56809	+	17.0484i	0.161506	+	0.602750i
$801$	−0.953647	+	1.75590i	−0.0336955	+	0.0620417i
$802$	16.1887	+	28.0397i	0.571645	+	0.990117i
$803$	−4.28432	+	7.42066i	−0.151190	+	0.261870i
$804$	−4.51407	−	0.534549i	−0.159199	−	0.0188521i
$805$	50.5989	−	30.6439i	1.78338	−	1.08005i
$806$	11.2626	+	9.42781i	0.396707	+	0.332080i
$807$	−5.48961	+	0.795621i	−0.193243	+	0.0280072i
$808$	28.5484	+	7.64951i	1.00433	+	0.269109i
$809$	6.04265	−	3.48873i	0.212448	−	0.122657i	−0.390000	−	0.920815i	$-0.627525\pi$
$809$	6.04265	−	3.48873i	0.212448	−	0.122657i	0.602449	+	0.798158i	$0.294192\pi$
$810$	24.3070	+	37.4491i	0.854060	+	1.31583i
$811$	13.5578	−	13.5578i	0.476080	−	0.476080i	−0.427796	−	0.903875i	$-0.640710\pi$
$811$	13.5578	−	13.5578i	0.476080	−	0.476080i	0.903875	+	0.427796i	$0.140710\pi$
$812$	−0.475576	+	1.93621i	−0.0166894	+	0.0679476i
$813$	−11.4200	−	1.35233i	−0.400516	−	0.0474284i
$814$	16.7682	−	4.49303i	0.587726	−	0.157481i
$815$	60.2095	−	34.7619i	2.10905	−	1.21766i
$816$	9.29138	+	3.70753i	0.325263	+	0.129789i
$817$	−6.37969	+	1.70943i	−0.223197	+	0.0598055i
$818$	−51.5005			−1.80067
$819$	17.3181	−	22.7834i	0.605144	−	0.796116i
$820$	−7.43788			−0.259742
$821$	30.6778	−	8.22009i	1.07066	−	0.286883i	0.319897	−	0.947452i	$-0.396352\pi$
$821$	30.6778	−	8.22009i	1.07066	−	0.286883i	0.750765	+	0.660569i	$0.229685\pi$
$822$	40.3572	+	16.1037i	1.40762	+	0.561681i
$823$	12.0020	−	6.92934i	0.418362	−	0.241541i	−0.276014	−	0.961154i	$-0.589014\pi$
$823$	12.0020	−	6.92934i	0.418362	−	0.241541i	0.694376	+	0.719612i	$0.255680\pi$
$824$	32.5171	−	8.71293i	1.13279	−	0.303529i
$825$	24.7113	+	2.92627i	0.860336	+	0.101880i
$826$	18.8543	+	18.0806i	0.656025	+	0.629104i
$827$	−8.15226	+	8.15226i	−0.283482	+	0.283482i	−0.834496	−	0.551014i	$-0.814241\pi$
$827$	−8.15226	+	8.15226i	−0.283482	+	0.283482i	0.551014	+	0.834496i	$0.314241\pi$
$828$	−3.91847	+	4.12822i	−0.136176	+	0.143466i
$829$	−17.9082	+	10.3393i	−0.621978	+	0.359099i	−0.777639	−	0.628711i	$-0.783583\pi$
$829$	−17.9082	+	10.3393i	−0.621978	+	0.359099i	0.155661	+	0.987811i	$0.450249\pi$
$830$	13.8338	+	3.70676i	0.480178	+	0.128663i
$831$	39.8678	−	5.77812i	1.38300	−	0.200441i
$832$	20.4669	−	24.4499i	0.709561	−	0.847649i
$833$	−10.5240	+	6.67875i	−0.364634	+	0.231405i
$834$	40.6852	+	4.81788i	1.40881	+	0.166830i
$835$	−21.2682	+	36.8376i	−0.736016	+	1.27482i
$836$	0.235435	+	0.407785i	0.00814269	+	0.0141035i
$837$	2.76709	+	16.1208i	0.0956447	+	0.557218i
$838$	11.7513	+	43.8565i	0.405943	+	1.51500i
$839$	23.7018	−	23.7018i	0.818279	−	0.818279i	−0.167580	−	0.985859i	$-0.553595\pi$
$839$	23.7018	−	23.7018i	0.818279	−	0.818279i	0.985859	+	0.167580i	$0.0535952\pi$
$840$	−52.6115	−	5.11535i	−1.81527	−	0.176496i
$841$	23.6329			0.814929
$842$	−6.57974	+	11.3964i	−0.226753	+	0.392747i
$843$	18.7035	−	8.03432i	0.644181	−	0.276717i
$844$	−2.11860	+	1.22317i	−0.0729252	+	0.0421034i
$845$	−21.1665	−	45.1137i	−0.728149	−	1.55196i
$846$	−2.97979	+	12.4052i	−0.102447	+	0.426499i
$847$	6.49830	+	22.3672i	0.223284	+	0.768545i
$848$			28.7615i			0.987673i
$849$	−33.5349	+	4.86028i	−1.15091	+	0.166804i
$850$	−21.5766	−	5.78144i	−0.740072	−	0.198302i
$851$	13.6641	−	50.9951i	0.468399	−	1.74809i
$852$	2.07473	+	1.54947i	0.0710791	+	0.0530839i
$853$	32.3425	+	32.3425i	1.10739	+	1.10739i	0.993493	+	0.113892i	$0.0363319\pi$
$853$	32.3425	+	32.3425i	1.10739	+	1.10739i	0.113892	+	0.993493i	$0.463668\pi$
$854$	−32.7109	+	19.8105i	−1.11934	+	0.677901i
$855$	2.62347	−	10.9218i	0.0897207	−	0.373517i
$856$	50.2884	−	13.4747i	1.71882	−	0.460557i
$857$	−23.1753	−	40.1408i	−0.791654	−	1.37118i	−0.924942	−	0.380107i	$-0.875887\pi$
$857$	−23.1753	−	40.1408i	−0.791654	−	1.37118i	0.133289	−	0.991077i	$-0.457446\pi$
$858$	−5.68096	−	10.5445i	−0.193945	−	0.359982i
$859$	−5.68192	+	9.84137i	−0.193865	+	0.335783i	−0.946528	−	0.322623i	$-0.895436\pi$
$859$	−5.68192	+	9.84137i	−0.193865	+	0.335783i	0.752663	+	0.658406i	$0.228769\pi$
$860$	5.96183	+	5.96183i	0.203297	+	0.203297i
$861$	9.59710	−	25.5960i	0.327068	−	0.872308i
$862$		−	32.6656i		−	1.11259i
$863$	−3.23552	+	0.866956i	−0.110139	+	0.0295115i	−0.313467	−	0.949599i	$-0.601491\pi$
$863$	−3.23552	+	0.866956i	−0.110139	+	0.0295115i	0.203329	+	0.979111i	$0.434824\pi$
$864$	9.32433	−	1.60049i	0.317220	−	0.0544499i
$865$	−19.1180	+	71.3492i	−0.650030	+	2.42594i
$866$	5.26484	+	19.6487i	0.178907	+	0.667688i
$867$	−18.8118	+	14.8282i	−0.638881	+	0.503591i
$868$	−2.37395	−	1.30509i	−0.0805772	−	0.0442975i
$869$	−16.6365	+	16.6365i	−0.564356	+	0.564356i
$870$	−2.85509	−	19.6995i	−0.0967965	−	0.667875i
$871$	−16.7136	−	23.8097i	−0.566318	−	0.806760i
$872$	21.6369	−	12.4921i	0.732717	−	0.423034i
$873$	15.8053	−	0.411987i	0.534928	−	0.0139437i
$874$	−7.37275			−0.249387
$875$	47.5942	−	0.997023i	1.60898	−	0.0337055i
$876$	0.383057	−	3.23477i	0.0129423	−	0.109293i
$877$	−7.76004	−	28.9609i	−0.262038	−	0.977939i	−0.964038	−	0.265763i	$-0.914376\pi$
$877$	−7.76004	−	28.9609i	−0.262038	−	0.977939i	0.702000	−	0.712177i	$-0.252290\pi$
$878$	−13.6748	−	3.66416i	−0.461503	−	0.123659i
$879$	6.99347	−	3.00414i	0.235884	−	0.101327i
$880$	−9.21363	+	15.9585i	−0.310591	+	0.537960i
$881$	−10.4997			−0.353745			−0.176872	−	0.984234i	$-0.556598\pi$
$881$	−10.4997			−0.353745			−0.176872	+	0.984234i	$0.556598\pi$
$882$	11.9588	−	24.4037i	0.402673	−	0.821715i
$883$			5.98699i			0.201478i	0.994913	+	0.100739i	$0.0321208\pi$
$883$			5.98699i			0.201478i	−0.994913	+	0.100739i	$0.967879\pi$
$884$	−0.716562	−	1.96154i	−0.0241006	−	0.0659737i
$885$	47.0481	+	18.7735i	1.58150	+	0.631066i
$886$	17.2272	+	4.61600i	0.578758	+	0.155078i
$887$	11.3970	+	6.58006i	0.382674	+	0.220937i	0.678981	−	0.734156i	$-0.262422\pi$
$887$	11.3970	+	6.58006i	0.382674	+	0.220937i	−0.296307	+	0.955093i	$0.595755\pi$
$888$	−37.0496	+	29.2040i	−1.24330	+	0.980021i
$889$	−23.6642	+	24.6769i	−0.793673	+	0.827637i
$890$	2.33632	+	2.33632i	0.0783137	+	0.0783137i
$891$	2.77632	−	13.0462i	0.0930102	−	0.437065i
$892$	0.176407	−	0.658360i	0.00590654	−	0.0220435i
$893$	2.77976	−	1.60489i	0.0930210	−	0.0537057i
$894$	−15.2310	+	2.20747i	−0.509402	+	0.0738287i
$895$	−14.0310	−	14.0310i	−0.469003	−	0.469003i
$896$	9.94569	−	18.0912i	0.332262	−	0.604385i
$897$	−36.4097	−	1.07164i	−1.21569	−	0.0357811i
$898$	−15.7822	+	27.3356i	−0.526658	+	0.912199i
$899$	1.88745	−	7.04406i	0.0629500	−	0.234933i
$900$	−9.07041	+	2.68560i	−0.302347	+	0.0895200i
$901$	13.6735	+	7.89441i	0.455531	+	0.263001i
$902$	−8.08988	−	8.08988i	−0.269364	−	0.269364i
$903$	−28.2090	+	12.8239i	−0.938737	+	0.426752i
$904$	17.8878	+	17.8878i	0.594939	+	0.594939i
$905$	2.64813	+	9.88296i	0.0880269	+	0.328521i
$906$	2.98111	−	7.47092i	0.0990409	−	0.248205i
$907$	−50.0583	+	28.9012i	−1.66216	+	0.959648i	−0.690478	+	0.723354i	$0.742600\pi$
$907$	−50.0583	+	28.9012i	−1.66216	+	0.959648i	−0.971682	+	0.236294i	$0.924067\pi$
$908$	0.533696	+	1.99178i	0.0177113	+	0.0660996i
$909$	−6.88198	+	28.6504i	−0.228261	+	0.950275i
$910$	−27.9935	−	38.1537i	−0.927975	−	1.26478i
$911$			21.8759i			0.724780i	0.932027	+	0.362390i	$0.118039\pi$
$911$			21.8759i			0.724780i	−0.932027	+	0.362390i	$0.881961\pi$
$912$	4.39672	+	3.28359i	0.145590	+	0.108731i
$913$	−2.13938	−	3.70552i	−0.0708033	−	0.122635i
$914$	2.63354	+	4.56143i	0.0871098	+	0.150879i
$915$	−44.3733	+	59.4157i	−1.46694	+	1.96422i
$916$	−0.0527602	+	0.0527602i	−0.00174325	+	0.00174325i
$917$	3.20387	+	11.0277i	0.105801	+	0.364168i
$918$	−4.14627	+	11.2328i	−0.136847	+	0.370737i
$919$	10.3917	−	17.9989i	0.342789	−	0.593728i	−0.642161	−	0.766570i	$-0.721962\pi$
$919$	10.3917	−	17.9989i	0.342789	−	0.593728i	0.984950	+	0.172842i	$0.0552951\pi$
$920$	33.6401	+	58.2664i	1.10908	+	1.92099i
$921$	−12.3224	−	28.6858i	−0.406036	−	0.945229i
$922$	−9.96241	−	5.75180i	−0.328094	−	0.189425i
$923$	1.46377	+	16.5069i	0.0481807	+	0.543331i
$924$	1.40361	+	1.70594i	0.0461752	+	0.0561214i
$925$	62.0432	−	62.0432i	2.03997	−	2.03997i
$926$	32.2734	+	18.6330i	1.06057	+	0.612320i
$927$	9.52817	+	32.1807i	0.312946	+	1.05695i
$928$	−4.07430	−	1.09171i	−0.133745	−	0.0358370i
$929$	−51.7619	+	13.8696i	−1.69825	+	0.455045i	−0.972499	−	0.232909i	$-0.925176\pi$
$929$	−51.7619	+	13.8696i	−1.69825	+	0.455045i	−0.725754	+	0.687954i	$0.758509\pi$
$930$	26.8588	+	3.18058i	0.880736	+	0.104295i
$931$	−6.52440	+	2.04464i	−0.213828	+	0.0670104i
$932$		−	2.24670i		−	0.0735932i
$933$	−1.38957	−	9.58775i	−0.0454926	−	0.313889i
$934$	4.91574	−	18.3458i	0.160848	−	0.600293i
$935$	5.05789	+	8.76053i	0.165411	+	0.286500i
$936$	25.4947	+	20.2353i	0.833319	+	0.661412i
$937$	19.4261			0.634624			0.317312	−	0.948321i	$-0.397220\pi$
$937$	19.4261			0.634624			0.317312	+	0.948321i	$0.397220\pi$
$938$	−19.9384	−	19.1202i	−0.651012	−	0.624296i
$939$	21.5858	−	17.0148i	0.704426	−	0.555257i
$940$	−3.54851	−	2.04873i	−0.115740	−	0.0668223i
$941$	−9.75204	+	36.3951i	−0.317907	+	1.18645i	0.603345	+	0.797480i	$0.293834\pi$
$941$	−9.75204	+	36.3951i	−0.317907	+	1.18645i	−0.921252	+	0.388966i	$0.872832\pi$
$942$	−12.9719	−	30.1979i	−0.422648	−	0.983901i
$943$	−33.6080	+	9.00523i	−1.09443	+	0.293251i
$944$	−17.4990	+	17.4990i	−0.569545	+	0.569545i
$945$	3.73129	−	52.5663i	0.121379	−	1.70998i
$946$			12.9689i			0.421655i
$947$	−2.99008	−	11.1591i	−0.0971644	−	0.362623i	0.900174	−	0.435530i	$-0.143439\pi$
$947$	−2.99008	−	11.1591i	−0.0971644	−	0.362623i	−0.997339	+	0.0729072i	$0.976772\pi$
$948$	3.31478	−	8.30712i	0.107659	−	0.269803i
$949$	17.0620	−	11.9769i	0.553855	−	0.388787i
$950$	−10.6117	−	6.12666i	−0.344289	−	0.198775i
$951$	−22.1443	−	2.62229i	−0.718077	−	0.0850335i
$952$	−7.34378	−	12.1260i	−0.238013	−	0.393005i
$953$	31.4054			1.01732			0.508660	−	0.860968i	$-0.330141\pi$
$953$	31.4054			1.01732			0.508660	+	0.860968i	$0.330141\pi$
$954$	−34.4131	+	0.897027i	−1.11417	+	0.0290423i
$955$	−16.9787	−	4.54943i	−0.549418	−	0.147216i
$956$	5.30593	+	1.42172i	0.171606	+	0.0459817i
$957$	−3.55845	+	4.76475i	−0.115028	+	0.154022i
$958$	−27.7149			−0.895427
$959$	−26.5690	−	43.8705i	−0.857958	−	1.41665i
$960$	6.90473	−	58.3080i	0.222849	−	1.88188i
$961$	−18.2655	−	10.5456i	−0.589210	−	0.340180i
$962$	−41.6002	−	7.28470i	−1.34125	−	0.234868i
$963$	14.7355	+	49.7681i	0.474845	+	1.60375i
$964$	−1.52531	−	5.69252i	−0.0491268	−	0.183344i
$965$		−	27.2812i		−	0.878212i
$966$	−34.1212	+	5.67728i	−1.09783	+	0.182663i
$967$	−13.4501	+	13.4501i	−0.432526	+	0.432526i	−0.889487	−	0.456961i	$-0.848938\pi$
$967$	−13.4501	+	13.4501i	−0.432526	+	0.432526i	0.456961	+	0.889487i	$0.348938\pi$
$968$	−25.5887	+	6.85647i	−0.822452	+	0.220375i
$969$	2.76786	−	1.18897i	0.0889165	−	0.0381953i
$970$	6.76651	−	25.2530i	0.217259	−	0.810823i
$971$	−34.3678	−	19.8423i	−1.10292	−	0.636769i	−0.165931	−	0.986137i	$-0.553063\pi$
$971$	−34.3678	−	19.8423i	−1.10292	−	0.636769i	−0.936985	+	0.349368i	$0.886396\pi$
$972$	0.987739	+	4.97346i	0.0316817	+	0.159524i
$973$	−34.9037	−	33.4714i	−1.11896	−	1.07304i
$974$	3.57856			0.114664
$975$	−51.5145	−	31.7985i	−1.64978	−	1.01837i
$976$	−18.1144	−	31.3750i	−0.579828	−	1.00429i
$977$	0.539931	−	2.01505i	0.0172739	−	0.0644672i	−0.956751	−	0.290908i	$-0.906042\pi$
$977$	0.539931	−	2.01505i	0.0172739	−	0.0644672i	0.974025	+	0.226441i	$0.0727091\pi$
$978$	−40.2331	+	5.83107i	−1.28651	+	0.186457i
$979$		−	0.987117i		−	0.0315484i
$980$	6.42478	+	5.90785i	0.205232	+	0.188719i
$981$	13.0119	+	21.2391i	0.415437	+	0.678113i
$982$	4.31889	−	1.15724i	0.137821	−	0.0369292i
$983$	−11.0216	−	2.95323i	−0.351534	−	0.0941933i	0.0787308	−	0.996896i	$-0.474913\pi$
$983$	−11.0216	−	2.95323i	−0.351534	−	0.0941933i	−0.430265	+	0.902703i	$0.641580\pi$
$984$	28.8768	+	11.5227i	0.920558	+	0.367329i
$985$	51.6548	+	29.8229i	1.64586	+	0.950237i
$986$	3.77481	−	3.77481i	0.120215	−	0.120215i
$987$	11.6289	−	9.56799i	0.370153	−	0.304552i
$988$	−0.101186	−	1.14107i	−0.00321915	−	0.0363022i
$989$	34.1566	+	19.7203i	1.08612	+	0.627070i
$990$	−19.3817	−	10.5264i	−0.615990	−	0.334551i
$991$	−20.4842	−	35.4796i	−0.650701	−	1.12705i	−0.982953	−	0.183856i	$-0.941142\pi$
$991$	−20.4842	−	35.4796i	−0.650701	−	1.12705i	0.332253	−	0.943190i	$-0.392191\pi$
$992$	2.86564	−	4.96344i	0.0909842	−	0.157589i
$993$	4.93939	−	41.7113i	0.156747	−	1.32367i
$994$	4.39043	+	15.1119i	0.139256	+	0.479320i
$995$	−24.2541	+	24.2541i	−0.768908	+	0.768908i
$996$	1.30324	+	0.973299i	0.0412948	+	0.0308402i
$997$	−7.33796	−	12.7097i	−0.232396	−	0.402521i	0.726117	−	0.687571i	$-0.241323\pi$
$997$	−7.33796	−	12.7097i	−0.232396	−	0.402521i	−0.958513	+	0.285050i	$0.907990\pi$
$998$	−14.6797	−	25.4260i	−0.464679	−	0.804847i
$999$	−30.0676	−	36.1655i	−0.951297	−	1.14423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.11	✓	112
3.2	odd	2	inner	273.2.cd.e.44.18	yes	112
7.4	even	3	inner	273.2.cd.e.200.18	yes	112
13.8	odd	4	inner	273.2.cd.e.86.11	yes	112
21.11	odd	6	inner	273.2.cd.e.200.11	yes	112
39.8	even	4	inner	273.2.cd.e.86.18	yes	112
91.60	odd	12	inner	273.2.cd.e.242.18	yes	112
273.242	even	12	inner	273.2.cd.e.242.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.11	✓	112	1.1	even	1	trivial
273.2.cd.e.44.18	yes	112	3.2	odd	2	inner
273.2.cd.e.86.11	yes	112	13.8	odd	4	inner
273.2.cd.e.86.18	yes	112	39.8	even	4	inner
273.2.cd.e.200.11	yes	112	21.11	odd	6	inner
273.2.cd.e.200.18	yes	112	7.4	even	3	inner
273.2.cd.e.242.11	yes	112	273.242	even	12	inner
273.2.cd.e.242.18	yes	112	91.60	odd	12	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.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25001 + 0.334940i) q^{2} +(-1.60871 - 0.641920i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(-3.70264 + 0.992121i) q^{5} +(2.22591 + 0.263589i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(2.12780 - 2.12780i) q^{8} +(2.17588 + 2.06532i) q^{9} +O(q^{10})\)	\(q+(-1.25001 + 0.334940i) q^{2} +(-1.60871 - 0.641920i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(-3.70264 + 0.992121i) q^{5} +(2.22591 + 0.263589i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(2.12780 - 2.12780i) q^{8} +(2.17588 + 2.06532i) q^{9} +(4.29606 - 2.48033i) q^{10} +(-1.43154 - 0.383581i) q^{11} +(0.557574 - 0.0808103i) q^{12} +(2.76474 + 2.31435i) q^{13} +(3.00038 + 1.64947i) q^{14} +(6.59333 + 0.780772i) q^{15} +(-1.62182 + 2.80907i) q^{16} +(0.890309 + 1.54206i) q^{17} +(-3.41164 - 1.85290i) q^{18} +(0.252802 + 0.943471i) q^{19} +(0.881676 - 0.881676i) q^{20} +(1.89648 + 4.17173i) q^{21} +1.91793 q^{22} +(2.91637 - 5.05131i) q^{23} +(-4.78889 + 2.05713i) q^{24} +(8.39515 - 4.84694i) q^{25} +(-4.23114 - 1.96694i) q^{26} +(-2.17457 - 4.71924i) q^{27} +(0.835765 + 0.205282i) q^{28} +2.31669i q^{29} +(-8.50327 + 1.23240i) q^{30} +(-3.04057 - 0.814718i) q^{31} +(-0.471235 + 1.75867i) q^{32} +(2.05670 + 1.53600i) q^{33} +(-1.62940 - 1.62940i) q^{34} +(8.88738 + 4.88586i) q^{35} +(-0.948846 - 0.227918i) q^{36} +(8.74289 - 2.34265i) q^{37} +(-0.632013 - 1.09468i) q^{38} +(-2.96203 - 5.49785i) q^{39} +(-5.76746 + 9.98953i) q^{40} +(-4.21804 - 4.21804i) q^{41} +(-3.76791 - 4.57952i) q^{42} +6.76194i q^{43} +(0.465650 - 0.124771i) q^{44} +(-10.1055 - 5.48843i) q^{45} +(-1.95362 + 7.29102i) q^{46} +(-0.850526 - 3.17421i) q^{47} +(4.41223 - 3.47790i) q^{48} +(0.293149 + 6.99386i) q^{49} +(-8.87062 + 8.87062i) q^{50} +(-0.442366 - 3.05223i) q^{51} +(-1.15523 - 0.202295i) q^{52} +(7.67909 - 4.43352i) q^{53} +(4.29891 + 5.17077i) q^{54} +5.68105 q^{55} +(-7.95976 + 0.166744i) q^{56} +(0.198949 - 1.68005i) q^{57} +(-0.775954 - 2.89590i) q^{58} +(7.36954 + 1.97466i) q^{59} +(-1.98432 + 0.852392i) q^{60} +(-5.58459 + 9.67280i) q^{61} +4.07364 q^{62} +(-0.372960 - 7.92849i) q^{63} -8.84347i q^{64} +(-12.5330 - 5.82625i) q^{65} +(-3.08538 - 1.23116i) q^{66} +(-7.79328 - 2.08820i) q^{67} +(-0.501599 - 0.289599i) q^{68} +(-7.93413 + 6.25399i) q^{69} +(-12.7458 - 3.13066i) q^{70} +(3.24997 + 3.24997i) q^{71} +(9.02444 - 0.235235i) q^{72} +(1.49640 - 5.58464i) q^{73} +(-10.1441 + 5.85669i) q^{74} +(-16.6167 + 2.40829i) q^{75} +(-0.224660 - 0.224660i) q^{76} +(2.03125 + 3.35398i) q^{77} +(5.54404 + 5.88029i) q^{78} +(7.93757 - 13.7483i) q^{79} +(3.21808 - 12.0100i) q^{80} +(0.468877 + 8.98778i) q^{81} +(6.68540 + 3.85982i) q^{82} +(2.04147 + 2.04147i) q^{83} +(-1.21273 - 0.866733i) q^{84} +(-4.82641 - 4.82641i) q^{85} +(-2.26485 - 8.45252i) q^{86} +(1.48713 - 3.72688i) q^{87} +(-3.86222 + 2.22986i) q^{88} +(0.172387 + 0.643357i) q^{89} +(14.4704 + 3.47586i) q^{90} +(-1.04144 - 9.48237i) q^{91} +1.89727i q^{92} +(4.36840 + 3.26245i) q^{93} +(2.12634 + 3.68293i) q^{94} +(-1.87207 - 3.24253i) q^{95} +(1.88701 - 2.52669i) q^{96} +(3.72661 - 3.72661i) q^{97} +(-2.70897 - 8.64424i) q^{98} +(-2.32264 - 3.79122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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