LMFDB - Embedded newform 247.2.z.a.141.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [247,2,Mod(141,247)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("247.141"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(247, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([7, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 247 = 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	247.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.97230492993$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			141.11
Character	$\chi$	$=$	247.141
Dual form			247.2.z.a.240.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0597405 + 0.0597405i) q^{2} -0.623849i q^{3} +1.99286i q^{4} +(0.894356 - 0.239642i) q^{5} +(0.0372691 + 0.0372691i) q^{6} +(-1.18379 - 4.41795i) q^{7} +(-0.238536 - 0.238536i) q^{8} +2.61081 q^{9} +(-0.0391129 + 0.0677456i) q^{10} +(4.68028 + 1.25408i) q^{11} +1.24325 q^{12} +(0.690822 + 3.53875i) q^{13} +(0.334651 + 0.193211i) q^{14} +(-0.149500 - 0.557943i) q^{15} -3.95722 q^{16} +(0.911551 - 0.526284i) q^{17} +(-0.155971 + 0.155971i) q^{18} +(4.01270 + 1.70243i) q^{19} +(0.477573 + 1.78233i) q^{20} +(-2.75614 + 0.738505i) q^{21} +(-0.354522 + 0.204683i) q^{22} +(-0.818430 - 0.472521i) q^{23} +(-0.148810 + 0.148810i) q^{24} +(-3.58768 + 2.07135i) q^{25} +(-0.252677 - 0.170137i) q^{26} -3.50030i q^{27} +(8.80437 - 2.35912i) q^{28} +(-7.63952 - 4.41068i) q^{29} +(0.0422630 + 0.0244006i) q^{30} +(3.38575 - 3.38575i) q^{31} +(0.713478 - 0.713478i) q^{32} +(0.782356 - 2.91979i) q^{33} +(-0.0230160 + 0.0858970i) q^{34} +(-2.11745 - 3.66754i) q^{35} +5.20299i q^{36} +(1.26821 - 4.73304i) q^{37} +(-0.341425 + 0.138016i) q^{38} +(2.20765 - 0.430969i) q^{39} +(-0.270499 - 0.156173i) q^{40} +(-7.61486 + 7.61486i) q^{41} +(0.120534 - 0.208772i) q^{42} +(2.21103 - 1.27654i) q^{43} +(-2.49921 + 9.32716i) q^{44} +(2.33499 - 0.625660i) q^{45} +(0.0771221 - 0.0206648i) q^{46} +(-8.44379 - 2.26251i) q^{47} +2.46871i q^{48} +(-12.0548 + 6.95983i) q^{49} +(0.0905866 - 0.338074i) q^{50} +(-0.328322 - 0.568670i) q^{51} +(-7.05224 + 1.37671i) q^{52} +(-5.74693 + 3.31799i) q^{53} +(0.209110 + 0.209110i) q^{54} +4.48637 q^{55} +(-0.771464 + 1.33622i) q^{56} +(1.06206 - 2.50332i) q^{57} +(0.719886 - 0.192893i) q^{58} +(-2.27174 + 8.47824i) q^{59} +(1.11190 - 0.297934i) q^{60} +7.75119 q^{61} +0.404533i q^{62} +(-3.09065 - 11.5344i) q^{63} -7.82920i q^{64} +(1.46587 + 2.99935i) q^{65} +(0.127692 + 0.221168i) q^{66} +(1.70785 + 6.37378i) q^{67} +(1.04881 + 1.81659i) q^{68} +(-0.294782 + 0.510577i) q^{69} +(0.345598 + 0.0926028i) q^{70} +(1.89737 + 0.508399i) q^{71} +(-0.622772 - 0.622772i) q^{72} +(-1.70575 - 6.36595i) q^{73} +(0.206991 + 0.358518i) q^{74} +(1.29221 + 2.23817i) q^{75} +(-3.39271 + 7.99675i) q^{76} -22.1618i q^{77} +(-0.106140 + 0.157632i) q^{78} +(-4.71409 - 2.72168i) q^{79} +(-3.53917 + 0.948317i) q^{80} +5.64878 q^{81} -0.909832i q^{82} +(3.83484 + 3.83484i) q^{83} +(-1.47174 - 5.49260i) q^{84} +(0.689131 - 0.689131i) q^{85} +(-0.0558270 + 0.208349i) q^{86} +(-2.75160 + 4.76591i) q^{87} +(-0.817273 - 1.41556i) q^{88} +(-13.3303 + 3.57184i) q^{89} +(-0.102117 + 0.176871i) q^{90} +(14.8163 - 7.24115i) q^{91} +(0.941669 - 1.63102i) q^{92} +(-2.11220 - 2.11220i) q^{93} +(0.639600 - 0.369273i) q^{94} +(3.99675 + 0.560969i) q^{95} +(-0.445103 - 0.445103i) q^{96} +(6.53782 + 1.75180i) q^{97} +(0.304375 - 1.13594i) q^{98} +(12.2193 + 3.27416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 2 q^{5} + 14 q^{6} - 12 q^{7} + 12 q^{8} - 84 q^{9} - 6 q^{10} - 4 q^{11} + 36 q^{12} - 6 q^{13} - 12 q^{14} + 30 q^{15} - 92 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 24 q^{20} - 18 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 2 * q^5 + 14 * q^6 - 12 * q^7 + 12 * q^8 - 84 * q^9 - 6 * q^10 - 4 * q^11 + 36 * q^12 - 6 * q^13 - 12 * q^14 + 30 * q^15 - 92 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 24 * q^20 - 18 * q^22 - 30 * q^23 + 48 * q^24 + 12 * q^25 + 32 * q^26 + 18 * q^28 + 18 * q^29 + 60 * q^30 - 30 * q^31 - 12 * q^32 - 6 * q^33 - 6 * q^34 - 6 * q^35 - 12 * q^37 - 36 * q^38 + 18 * q^39 - 12 * q^40 - 6 * q^41 + 6 * q^42 + 12 * q^43 + 64 * q^44 - 38 * q^45 + 24 * q^46 + 64 * q^47 - 42 * q^49 - 24 * q^51 + 18 * q^52 - 66 * q^53 - 96 * q^54 - 36 * q^55 + 60 * q^56 + 64 * q^57 - 24 * q^58 - 6 * q^59 + 54 * q^60 - 28 * q^61 - 6 * q^63 + 44 * q^66 - 36 * q^67 - 12 * q^68 - 36 * q^69 + 114 * q^70 - 30 * q^71 - 66 * q^72 + 22 * q^73 + 6 * q^74 - 12 * q^75 + 38 * q^76 + 12 * q^78 - 24 * q^79 + 14 * q^80 + 64 * q^81 - 6 * q^83 - 18 * q^84 - 18 * q^85 - 6 * q^86 + 32 * q^87 + 42 * q^88 + 66 * q^89 + 18 * q^90 - 18 * q^91 + 104 * q^92 - 2 * q^93 - 84 * q^94 - 42 * q^95 - 174 * q^96 + 30 * q^97 - 60 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/247\mathbb{Z}\right)^\times$.

$n$	$40$	$210$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.0597405	+	0.0597405i	−0.0422429	+	0.0422429i	−0.727913	−	0.685670i	$-0.759509\pi$
$2$	−0.0597405	+	0.0597405i	−0.0422429	+	0.0422429i	0.685670	+	0.727913i	$0.259509\pi$
$3$		−	0.623849i		−	0.360179i	−0.983650	−	0.180090i	$-0.942361\pi$
$3$		−	0.623849i		−	0.360179i	0.983650	−	0.180090i	$-0.0576388\pi$
$4$			1.99286i			0.996431i
$5$	0.894356	−	0.239642i	0.399968	−	0.107171i	−0.0532271	−	0.998582i	$-0.516951\pi$
$5$	0.894356	−	0.239642i	0.399968	−	0.107171i	0.453195	+	0.891411i	$0.350284\pi$
$6$	0.0372691	+	0.0372691i	0.0152150	+	0.0152150i
$7$	−1.18379	−	4.41795i	−0.447429	−	1.66983i	−0.709441	−	0.704765i	$-0.751053\pi$
$7$	−1.18379	−	4.41795i	−0.447429	−	1.66983i	0.262012	−	0.965065i	$-0.415614\pi$
$8$	−0.238536	−	0.238536i	−0.0843351	−	0.0843351i
$9$	2.61081			0.870271
$10$	−0.0391129	+	0.0677456i	−0.0123686	+	0.0214230i
$11$	4.68028	+	1.25408i	1.41116	+	0.378119i	0.882339	−	0.470615i	$-0.155968\pi$
$11$	4.68028	+	1.25408i	1.41116	+	0.378119i	0.528820	+	0.848734i	$0.322635\pi$
$12$	1.24325			0.358894
$13$	0.690822	+	3.53875i	0.191600	+	0.981473i
$13$	0.690822	+	3.53875i	0.191600	+	0.981473i
$14$	0.334651	+	0.193211i	0.0894392	+	0.0516378i
$15$	−0.149500	−	0.557943i	−0.0386008	−	0.144060i
$16$	−3.95722			−0.989306
$17$	0.911551	−	0.526284i	0.221084	−	0.127643i	−0.385368	−	0.922763i	$-0.625926\pi$
$17$	0.911551	−	0.526284i	0.221084	−	0.127643i	0.606452	+	0.795120i	$0.292592\pi$
$18$	−0.155971	+	0.155971i	−0.0367628	+	0.0367628i
$19$	4.01270	+	1.70243i	0.920576	+	0.390564i
$19$	4.01270	+	1.70243i	0.920576	+	0.390564i
$20$	0.477573	+	1.78233i	0.106789	+	0.398541i
$21$	−2.75614	+	0.738505i	−0.601438	+	0.161155i
$22$	−0.354522	+	0.204683i	−0.0755843	+	0.0436386i
$23$	−0.818430	−	0.472521i	−0.170654	−	0.0985274i	0.412240	−	0.911075i	$-0.364747\pi$
$23$	−0.818430	−	0.472521i	−0.170654	−	0.0985274i	−0.582894	+	0.812548i	$0.698080\pi$
$24$	−0.148810	+	0.148810i	−0.0303758	+	0.0303758i
$25$	−3.58768	+	2.07135i	−0.717537	+	0.414270i
$26$	−0.252677	−	0.170137i	−0.0495540	−	0.0333666i
$27$		−	3.50030i		−	0.673633i
$28$	8.80437	−	2.35912i	1.66387	−	0.445833i
$29$	−7.63952	−	4.41068i	−1.41862	−	0.819043i	−0.422446	−	0.906388i	$-0.638828\pi$
$29$	−7.63952	−	4.41068i	−1.41862	−	0.819043i	−0.996178	+	0.0873451i	$0.972162\pi$
$30$	0.0422630	+	0.0244006i	0.00771614	+	0.00445492i
$31$	3.38575	−	3.38575i	0.608098	−	0.608098i	−0.334351	−	0.942449i	$-0.608517\pi$
$31$	3.38575	−	3.38575i	0.608098	−	0.608098i	0.942449	+	0.334351i	$0.108517\pi$
$32$	0.713478	−	0.713478i	0.126126	−	0.126126i
$33$	0.782356	−	2.91979i	0.136191	−	0.508270i
$34$	−0.0230160	+	0.0858970i	−0.00394722	+	0.0147312i
$35$	−2.11745	−	3.66754i	−0.357915	−	0.619927i
$36$			5.20299i			0.867165i
$37$	1.26821	−	4.73304i	0.208493	−	0.778107i	−0.779863	−	0.625950i	$-0.784711\pi$
$37$	1.26821	−	4.73304i	0.208493	−	0.778107i	0.988356	−	0.152157i	$-0.0486220\pi$
$38$	−0.341425	+	0.138016i	−0.0553864	+	0.0223892i
$39$	2.20765	−	0.430969i	0.353506	−	0.0690102i
$40$	−0.270499	−	0.156173i	−0.0427696	−	0.0246931i
$41$	−7.61486	+	7.61486i	−1.18924	+	1.18924i	−0.211964	+	0.977277i	$0.567986\pi$
$41$	−7.61486	+	7.61486i	−1.18924	+	1.18924i	−0.977277	+	0.211964i	$0.932014\pi$
$42$	0.120534	−	0.208772i	0.0185989	−	0.0322142i
$43$	2.21103	−	1.27654i	0.337179	−	0.194670i	−0.321845	−	0.946792i	$-0.604303\pi$
$43$	2.21103	−	1.27654i	0.337179	−	0.194670i	0.659024	+	0.752122i	$0.270970\pi$
$44$	−2.49921	+	9.32716i	−0.376769	+	1.40612i
$45$	2.33499	−	0.625660i	0.348080	−	0.0932679i
$46$	0.0771221	−	0.0206648i	0.0113710	−	0.00304686i
$47$	−8.44379	−	2.26251i	−1.23165	−	0.330021i	−0.416430	−	0.909168i	$-0.636719\pi$
$47$	−8.44379	−	2.26251i	−1.23165	−	0.330021i	−0.815223	+	0.579147i	$0.803386\pi$
$48$			2.46871i			0.356328i
$49$	−12.0548	+	6.95983i	−1.72211	+	0.994262i
$50$	0.0905866	−	0.338074i	0.0128109	−	0.0478108i
$51$	−0.328322	−	0.568670i	−0.0459743	−	0.0796297i
$52$	−7.05224	+	1.37671i	−0.977970	+	0.190916i
$53$	−5.74693	+	3.31799i	−0.789402	+	0.455761i	−0.839752	−	0.542970i	$-0.817300\pi$
$53$	−5.74693	+	3.31799i	−0.789402	+	0.455761i	0.0503503	+	0.998732i	$0.483966\pi$
$54$	0.209110	+	0.209110i	0.0284562	+	0.0284562i
$55$	4.48637			0.604942
$56$	−0.771464	+	1.33622i	−0.103091	+	0.178559i
$57$	1.06206	−	2.50332i	0.140673	−	0.331572i
$58$	0.719886	−	0.192893i	0.0945256	−	0.0253281i
$59$	−2.27174	+	8.47824i	−0.295755	+	1.10377i	0.644861	+	0.764300i	$0.276915\pi$
$59$	−2.27174	+	8.47824i	−0.295755	+	1.10377i	−0.940616	+	0.339473i	$0.889751\pi$
$60$	1.11190	−	0.297934i	0.143546	−	0.0384631i
$61$	7.75119			0.992438			0.496219	−	0.868197i	$-0.334721\pi$
$61$	7.75119			0.992438			0.496219	+	0.868197i	$0.334721\pi$
$62$			0.404533i			0.0513757i
$63$	−3.09065	−	11.5344i	−0.389385	−	1.45320i
$64$		−	7.82920i		−	0.978650i
$65$	1.46587	+	2.99935i	0.181819	+	0.372024i
$66$	0.127692	+	0.221168i	0.0157177	+	0.0272239i
$67$	1.70785	+	6.37378i	0.208647	+	0.778681i	0.988307	+	0.152478i	$0.0487252\pi$
$67$	1.70785	+	6.37378i	0.208647	+	0.778681i	−0.779660	+	0.626203i	$0.784608\pi$
$68$	1.04881	+	1.81659i	0.127187	+	0.220294i
$69$	−0.294782	+	0.510577i	−0.0354876	+	0.0614662i
$70$	0.345598	+	0.0926028i	0.0413069	+	0.0110682i
$71$	1.89737	+	0.508399i	0.225177	+	0.0603359i	0.369643	−	0.929174i	$-0.379480\pi$
$71$	1.89737	+	0.508399i	0.225177	+	0.0603359i	−0.144467	+	0.989510i	$0.546147\pi$
$72$	−0.622772	−	0.622772i	−0.0733944	−	0.0733944i
$73$	−1.70575	−	6.36595i	−0.199643	−	0.745078i	−0.991016	−	0.133744i	$-0.957300\pi$
$73$	−1.70575	−	6.36595i	−0.199643	−	0.745078i	0.791373	−	0.611334i	$-0.209367\pi$
$74$	0.206991	+	0.358518i	0.0240622	+	0.0416769i
$75$	1.29221	+	2.23817i	0.149212	+	0.258442i
$76$	−3.39271	+	7.99675i	−0.389171	+	0.917290i
$77$		−	22.1618i		−	2.52558i
$78$	−0.106140	+	0.157632i	−0.0120180	+	0.0178483i
$79$	−4.71409	−	2.72168i	−0.530376	−	0.306213i	0.210793	−	0.977531i	$-0.432395\pi$
$79$	−4.71409	−	2.72168i	−0.530376	−	0.306213i	−0.741170	+	0.671318i	$0.765729\pi$
$80$	−3.53917	+	0.948317i	−0.395691	+	0.106025i
$81$	5.64878			0.627642
$82$		−	0.909832i		−	0.100474i
$83$	3.83484	+	3.83484i	0.420928	+	0.420928i	0.885523	−	0.464595i	$-0.153800\pi$
$83$	3.83484	+	3.83484i	0.420928	+	0.420928i	−0.464595	+	0.885523i	$0.653800\pi$
$84$	−1.47174	−	5.49260i	−0.160580	−	0.599292i
$85$	0.689131	−	0.689131i	0.0747467	−	0.0747467i
$86$	−0.0558270	+	0.208349i	−0.00601998	+	0.0224669i
$87$	−2.75160	+	4.76591i	−0.295002	+	0.510959i
$88$	−0.817273	−	1.41556i	−0.0871215	−	0.150899i
$89$	−13.3303	+	3.57184i	−1.41301	+	0.378615i	−0.882998	−	0.469376i	$-0.844479\pi$
$89$	−13.3303	+	3.57184i	−1.41301	+	0.378615i	−0.530011	+	0.847991i	$0.677812\pi$
$90$	−0.102117	+	0.176871i	−0.0107640	+	0.0186438i
$91$	14.8163	−	7.24115i	1.55317	−	0.759079i
$92$	0.941669	−	1.63102i	0.0981758	−	0.170045i
$93$	−2.11220	−	2.11220i	−0.219024	−	0.219024i
$94$	0.639600	−	0.369273i	0.0659697	−	0.0380876i
$95$	3.99675	+	0.560969i	0.410058	+	0.0575542i
$96$	−0.445103	−	0.445103i	−0.0454281	−	0.0454281i
$97$	6.53782	+	1.75180i	0.663815	+	0.177869i	0.574967	−	0.818176i	$-0.305015\pi$
$97$	6.53782	+	1.75180i	0.663815	+	0.177869i	0.0888481	+	0.996045i	$0.471681\pi$
$98$	0.304375	−	1.13594i	0.0307465	−	0.114748i
$99$	12.2193	+	3.27416i	1.22809	+	0.329066i
$100$	−4.12791	−	7.14976i	−0.412791	−	0.714976i
$101$	3.34159	+	1.92927i	0.332501	+	0.191969i	0.656951	−	0.753933i	$-0.271846\pi$
$101$	3.34159	+	1.92927i	0.332501	+	0.191969i	−0.324450	+	0.945903i	$0.605179\pi$
$102$	0.0535868	+	0.0143585i	0.00530588	+	0.00142171i
$103$	−5.62351			−0.554101			−0.277051	−	0.960855i	$-0.589357\pi$
$103$	−5.62351			−0.554101			−0.277051	+	0.960855i	$0.589357\pi$
$104$	0.679333	−	1.00890i	0.0666141	−	0.0989312i
$105$	−2.28799	+	1.32097i	−0.223285	+	0.128914i
$106$	0.145106	−	0.541543i	0.0140939	−	0.0525993i
$107$	−9.36725	+	5.40818i	−0.905566	+	0.522829i	−0.879002	−	0.476818i	$-0.841790\pi$
$107$	−9.36725	+	5.40818i	−0.905566	+	0.522829i	−0.0265642	+	0.999647i	$0.508457\pi$
$108$	6.97562			0.671229
$109$	2.56685	+	9.57961i	0.245859	+	0.917560i	0.972950	+	0.231018i	$0.0742056\pi$
$109$	2.56685	+	9.57961i	0.245859	+	0.917560i	−0.727090	+	0.686542i	$0.759128\pi$
$110$	−0.268018	+	0.268018i	−0.0255545	+	0.0255545i
$111$	−2.95270	−	0.791175i	−0.280258	−	0.0750950i
$112$	4.68451	+	17.4828i	0.442645	+	1.65197i
$113$	−6.18156	−	3.56893i	−0.581512	−	0.335736i	0.180222	−	0.983626i	$-0.442318\pi$
$113$	−6.18156	−	3.56893i	−0.581512	−	0.335736i	−0.761734	+	0.647890i	$0.775652\pi$
$114$	0.0861014	+	0.212998i	0.00806414	+	0.0199490i
$115$	−0.845203	−	0.226472i	−0.0788156	−	0.0211186i
$116$	8.78988	−	15.2245i	0.816120	−	1.41356i
$117$	1.80361	+	9.23902i	0.166744	+	0.854147i
$118$	−0.370780	−	0.642209i	−0.0341330	−	0.0591202i
$119$	−3.40418	−	3.40418i	−0.312061	−	0.312061i
$120$	−0.0974281	+	0.168750i	−0.00889393	+	0.0154047i
$121$	10.8061	+	6.23889i	0.982370	+	0.567172i
$122$	−0.463060	+	0.463060i	−0.0419235	+	0.0419235i
$123$	4.75053	+	4.75053i	0.428340	+	0.428340i
$124$	6.74733	+	6.74733i	0.605928	+	0.605928i
$125$	−5.98585	+	5.98585i	−0.535391	+	0.535391i
$126$	0.873711	+	0.504437i	0.0778363	+	0.0449388i
$127$	3.77805	−	6.54378i	0.335248	−	0.580666i	−0.648285	−	0.761398i	$-0.724513\pi$
$127$	3.77805	−	6.54378i	0.335248	−	0.580666i	0.983532	+	0.180732i	$0.0578466\pi$
$128$	1.89468	+	1.89468i	0.167467	+	0.167467i
$129$	−0.796368	−	1.37935i	−0.0701163	−	0.121445i
$130$	−0.266755	−	0.0916108i	−0.0233960	−	0.00803480i
$131$	0.0936006	−	0.162121i	0.00817792	−	0.0141646i	−0.861907	−	0.507066i	$-0.830730\pi$
$131$	0.0936006	−	0.162121i	0.00817792	−	0.0141646i	0.870085	+	0.492901i	$0.164064\pi$
$132$	5.81874	+	1.55913i	0.506457	+	0.135705i
$133$	2.77108	−	19.7432i	0.240283	−	1.71195i
$134$	−0.482801	−	0.278745i	−0.0417076	−	0.0240799i
$135$	−0.838819	−	3.13051i	−0.0721940	−	0.269432i
$136$	−0.342975	−	0.0918998i	−0.0294099	−	0.00788035i
$137$	11.9698	−	11.9698i	1.02265	−	1.02265i	0.0229157	−	0.999737i	$-0.492705\pi$
$137$	11.9698	−	11.9698i	1.02265	−	1.02265i	0.999737	−	0.0229157i	$-0.00729494\pi$
$138$	−0.0128917	−	0.0481126i	−0.00109742	−	0.00409561i
$139$	8.05460			0.683183			0.341591	−	0.939849i	$-0.389034\pi$
$139$	8.05460			0.683183			0.341591	+	0.939849i	$0.389034\pi$
$140$	7.30890	−	4.21979i	0.617714	−	0.356638i
$141$	−1.41146	+	5.26765i	−0.118867	+	0.443616i
$142$	−0.143722	+	0.0829780i	−0.0120609	+	0.00696336i
$143$	−1.20463	+	17.4287i	−0.100736	+	1.45746i
$144$	−10.3316			−0.860964
$145$	−7.88944	−	2.11397i	−0.655182	−	0.175555i
$146$	0.482208	+	0.278403i	0.0399078	+	0.0230408i
$147$	4.34189	+	7.52037i	0.358113	+	0.620269i
$148$	9.43230	+	2.52738i	0.775330	+	0.207749i
$149$	5.32422	−	19.8703i	0.436177	−	1.62784i	−0.302056	−	0.953290i	$-0.597673\pi$
$149$	5.32422	−	19.8703i	0.436177	−	1.62784i	0.738234	−	0.674545i	$-0.235660\pi$
$150$	−0.210907	−	0.0565123i	−0.0172205	−	0.00461421i
$151$	3.91429	+	3.91429i	0.318540	+	0.318540i	0.848206	−	0.529666i	$-0.177683\pi$
$151$	3.91429	+	3.91429i	0.318540	+	0.318540i	−0.529666	+	0.848206i	$0.677683\pi$
$152$	−0.551081	−	1.36326i	−0.0446985	−	0.110575i
$153$	2.37989	−	1.37403i	0.192403	−	0.111084i
$154$	1.32396	+	1.32396i	0.106688	+	0.106688i
$155$	2.21669	−	3.83943i	0.178049	−	0.308390i
$156$	0.858861	+	4.39954i	0.0687639	+	0.352245i
$157$	−12.1766	+	21.0904i	−0.971796	+	1.68320i	−0.281670	+	0.959511i	$0.590888\pi$
$157$	−12.1766	+	21.0904i	−0.971796	+	1.68320i	−0.690126	+	0.723689i	$0.742445\pi$
$158$	0.444217	−	0.119028i	0.0353400	−	0.00946932i
$159$	2.06993	+	3.58522i	0.164156	+	0.284326i
$160$	0.467124	−	0.809082i	0.0369294	−	0.0639636i
$161$	−1.11873	+	4.17515i	−0.0881681	+	0.329048i
$162$	−0.337461	+	0.337461i	−0.0265134	+	0.0265134i
$163$	−3.41465	−	12.7436i	−0.267456	−	0.998158i	−0.960730	−	0.277485i	$-0.910499\pi$
$163$	−3.41465	−	12.7436i	−0.267456	−	0.998158i	0.693274	−	0.720674i	$-0.256167\pi$
$164$	−15.1754	−	15.1754i	−1.18500	−	1.18500i
$165$		−	2.79882i		−	0.217888i
$166$	−0.458190			−0.0355625
$167$	4.38192	−	1.17413i	0.339083	−	0.0908570i	−0.0852595	−	0.996359i	$-0.527172\pi$
$167$	4.38192	−	1.17413i	0.339083	−	0.0908570i	0.424343	+	0.905502i	$0.360505\pi$
$168$	0.833597	+	0.481277i	0.0643134	+	0.0371313i
$169$	−12.0455	+	4.88930i	−0.926579	+	0.376100i
$170$			0.0823381i			0.00631504i
$171$	10.4764	+	4.44473i	0.801150	+	0.339897i
$172$	2.54397	+	4.40628i	0.193976	+	0.335976i
$173$	1.11780	+	1.93608i	0.0849845	+	0.147197i	0.905385	−	0.424592i	$-0.139583\pi$
$173$	1.11780	+	1.93608i	0.0849845	+	0.147197i	−0.820400	+	0.571790i	$0.806249\pi$
$174$	−0.120336	−	0.449100i	−0.00912265	−	0.0340462i
$175$	13.3982	+	13.3982i	1.01281	+	1.01281i
$176$	−18.5209	−	4.96267i	−1.39607	−	0.374075i
$177$	5.28914	+	1.41722i	0.397556	+	0.106525i
$178$	0.582975	−	1.00974i	0.0436959	−	0.0756834i
$179$	−11.7482	−	20.3484i	−0.878098	−	1.52091i	−0.853425	−	0.521215i	$-0.825479\pi$
$179$	−11.7482	−	20.3484i	−0.878098	−	1.52091i	−0.0246731	−	0.999696i	$-0.507854\pi$
$180$	1.24685	+	4.65332i	0.0929350	+	0.346838i
$181$	2.31160	+	4.00380i	0.171820	+	0.297600i	0.939056	−	0.343764i	$-0.111702\pi$
$181$	2.31160	+	4.00380i	0.171820	+	0.297600i	−0.767237	+	0.641364i	$0.778369\pi$
$182$	−0.452541	+	1.31772i	−0.0335446	+	0.0976760i
$183$		−	4.83557i		−	0.357456i
$184$	0.0825117	+	0.307938i	0.00608284	+	0.0227015i
$185$		−	4.53694i		−	0.333562i
$186$	0.252367			0.0185045
$187$	4.92632	−	1.32000i	0.360248	−	0.0965282i
$188$	4.50886	−	16.8273i	0.328843	−	1.22726i
$189$	−15.4642	+	4.14361i	−1.12485	+	0.301403i
$190$	−0.272281	+	0.205255i	−0.0197533	+	0.0148908i
$191$	−6.54649	+	11.3389i	−0.473687	+	0.820450i	−0.999546	−	0.0301213i	$-0.990411\pi$
$191$	−6.54649	+	11.3389i	−0.473687	+	0.820450i	0.525859	+	0.850572i	$0.323744\pi$
$192$	−4.88424			−0.352490
$193$	−2.19187	−	2.19187i	−0.157774	−	0.157774i	0.623806	−	0.781580i	$-0.285586\pi$
$193$	−2.19187	−	2.19187i	−0.157774	−	0.157774i	−0.781580	+	0.623806i	$0.785586\pi$
$194$	−0.495227	+	0.285919i	−0.0355552	+	0.0205278i
$195$	1.87114	−	0.914484i	0.133995	−	0.0654876i
$196$	−13.8700	−	24.0235i	−0.990713	−	1.71597i
$197$	2.23256	−	8.33203i	0.159063	−	0.593632i	−0.839660	−	0.543113i	$-0.817246\pi$
$197$	2.23256	−	8.33203i	0.159063	−	0.593632i	0.998723	−	0.0505196i	$-0.0160877\pi$
$198$	−0.925590	+	0.534390i	−0.0657788	+	0.0379774i
$199$		−	1.98400i		−	0.140642i	−0.997524	−	0.0703210i	$-0.977598\pi$
$199$		−	1.98400i		−	0.140642i	0.997524	−	0.0703210i	$-0.0224023\pi$
$200$	1.34988	+	0.361700i	0.0954510	+	0.0255760i
$201$	3.97628	−	1.06544i	0.280465	−	0.0751503i
$202$	−0.314884	+	0.0843729i	−0.0221552	+	0.00593646i
$203$	−10.4426	+	38.9724i	−0.732928	+	2.73532i
$204$	1.13328	−	0.654300i	0.0793455	−	0.0458102i
$205$	−4.98556	+	8.63524i	−0.348206	+	0.603111i
$206$	0.335952	−	0.335952i	0.0234069	−	0.0234069i
$207$	−2.13677	−	1.23366i	−0.148516	−	0.0857455i
$208$	−2.73374	−	14.0036i	−0.189551	−	0.970977i
$209$	16.6456	+	13.0001i	1.15140	+	0.899236i
$210$	0.0577702	−	0.215601i	0.00398652	−	0.0148779i
$211$		−	19.7068i		−	1.35667i	−0.734753	−	0.678335i	$-0.762702\pi$
$211$		−	19.7068i		−	1.35667i	0.734753	−	0.678335i	$-0.237298\pi$
$212$	−6.61230	−	11.4528i	−0.454135	−	0.786584i
$213$	0.317165	−	1.18367i	0.0217318	−	0.0811040i
$214$	0.236517	−	0.882692i	0.0161679	−	0.0603396i
$215$	1.67154	−	1.67154i	0.113998	−	0.113998i
$216$	−0.834947	+	0.834947i	−0.0568109	+	0.0568109i
$217$	−18.9661	−	10.9501i	−1.28750	−	0.743339i
$218$	−0.725636	−	0.418946i	−0.0491462	−	0.0283746i
$219$	−3.97139	+	1.06413i	−0.268362	+	0.0719074i
$220$			8.94072i			0.602783i
$221$	2.49211	+	2.86218i	0.167637	+	0.192531i
$222$	0.223661	−	0.129131i	0.0150112	−	0.00866670i
$223$	9.84599	−	9.84599i	0.659337	−	0.659337i	−0.295887	−	0.955223i	$-0.595615\pi$
$223$	9.84599	−	9.84599i	0.659337	−	0.659337i	0.955223	+	0.295887i	$0.0956150\pi$
$224$	−3.99672	−	2.30751i	−0.267042	−	0.154177i
$225$	−9.36677	+	5.40791i	−0.624451	+	0.360527i
$226$	0.582499	−	0.156080i	0.0387473	−	0.0103823i
$227$	2.03363	+	7.58961i	0.134977	+	0.503740i	0.999998	+	0.00200494i	$0.000638194\pi$
$227$	2.03363	+	7.58961i	0.134977	+	0.503740i	−0.865021	+	0.501735i	$0.832695\pi$
$228$	4.98877	+	2.11654i	0.330389	+	0.140171i
$229$	−3.30880	+	3.30880i	−0.218651	+	0.218651i	−0.807930	−	0.589278i	$-0.799412\pi$
$229$	−3.30880	+	3.30880i	−0.218651	+	0.218651i	0.589278	+	0.807930i	$0.299412\pi$
$230$	0.0640224	−	0.0369634i	0.00422151	−	0.00243729i
$231$	−13.8256			−0.909661
$232$	0.770194	+	2.87440i	0.0505657	+	0.188714i
$233$	17.7313	+	10.2372i	1.16162	+	0.670659i	0.951691	−	0.307058i	$-0.0993447\pi$
$233$	17.7313	+	10.2372i	1.16162	+	0.670659i	0.209925	+	0.977717i	$0.432678\pi$
$234$	−0.659692	−	0.444195i	−0.0431254	−	0.0290380i
$235$	−8.09394			−0.527991
$236$	−16.8960	−	4.52726i	−1.09983	−	0.294699i
$237$	−1.69792	+	2.94088i	−0.110292	+	0.191031i
$238$	0.406735			0.0263647
$239$	14.8966	+	14.8966i	0.963579	+	0.963579i	0.999360	−	0.0357805i	$-0.0113917\pi$
$239$	14.8966	+	14.8966i	0.963579	+	0.963579i	−0.0357805	+	0.999360i	$0.511392\pi$
$240$	0.591606	+	2.20791i	0.0381880	+	0.142520i
$241$	11.3089	+	11.3089i	0.728469	+	0.728469i	0.970315	−	0.241846i	$-0.0777529\pi$
$241$	11.3089	+	11.3089i	0.728469	+	0.728469i	−0.241846	+	0.970315i	$0.577753\pi$
$242$	−1.01828	+	0.272846i	−0.0654572	+	0.0175392i
$243$		−	14.0249i		−	0.899697i
$244$			15.4471i			0.988896i
$245$	−9.11340	+	9.11340i	−0.582234	+	0.582234i
$246$	−0.567598			−0.0361887
$247$	−3.25242	+	15.3760i	−0.206947	+	0.978352i
$248$	−1.61524			−0.102568
$249$	2.39236	−	2.39236i	0.151610	−	0.151610i
$250$		−	0.715196i		−	0.0452330i
$251$		−	6.62864i		−	0.418396i	−0.977873	−	0.209198i	$-0.932915\pi$
$251$		−	6.62864i		−	0.418396i	0.977873	−	0.209198i	$-0.0670853\pi$
$252$	22.9866	−	6.15923i	1.44802	−	0.387995i
$253$	−3.23791	−	3.23791i	−0.203566	−	0.203566i
$254$	0.165226	+	0.616631i	0.0103672	+	0.0386909i
$255$	−0.429914	−	0.429914i	−0.0269222	−	0.0269222i
$256$	15.4320			0.964501
$257$	−14.8948	+	25.7986i	−0.929113	+	1.60927i	−0.144304	+	0.989533i	$0.546094\pi$
$257$	−14.8948	+	25.7986i	−0.929113	+	1.60927i	−0.784809	+	0.619738i	$0.787239\pi$
$258$	0.129979	+	0.0348276i	0.00809211	+	0.00216827i
$259$	−22.4117			−1.39259
$260$	−5.97730	+	2.92128i	−0.370696	+	0.181170i
$261$	−19.9454	−	11.5155i	−1.23459	−	0.712789i
$262$	0.00409345	+	0.0152769i	0.000252894	+	0.000943813i
$263$	5.81552			0.358600			0.179300	−	0.983794i	$-0.442617\pi$
$263$	5.81552			0.358600			0.179300	+	0.983794i	$0.442617\pi$
$264$	−0.883094	+	0.509855i	−0.0543507	+	0.0313794i
$265$	−4.34467	+	4.34467i	−0.266891	+	0.266891i
$266$	1.01392	+	1.34502i	0.0621677	+	0.0824682i
$267$	2.22829	+	8.31610i	0.136369	+	0.508937i
$268$	−12.7021	+	3.40351i	−0.775902	+	0.207902i
$269$	−14.1064	+	8.14431i	−0.860079	+	0.496567i	−0.864039	−	0.503425i	$-0.832073\pi$
$269$	−14.1064	+	8.14431i	−0.860079	+	0.496567i	0.00395947	+	0.999992i	$0.498740\pi$
$270$	0.237130	+	0.136907i	0.0144313	+	0.00833190i
$271$	9.98561	−	9.98561i	0.606583	−	0.606583i	−0.335469	−	0.942051i	$-0.608895\pi$
$271$	9.98561	−	9.98561i	0.606583	−	0.606583i	0.942051	+	0.335469i	$0.108895\pi$
$272$	−3.60721	+	2.08262i	−0.218719	+	0.126278i
$273$	−4.51738	−	9.24311i	−0.273405	−	0.559418i
$274$			1.43017i			0.0863997i
$275$	−19.3890	+	5.19527i	−1.16920	+	0.313287i
$276$	−1.01751	−	0.587459i	−0.0612469	−	0.0353609i
$277$	−9.78082	−	5.64696i	−0.587673	−	0.339293i	0.176504	−	0.984300i	$-0.443521\pi$
$277$	−9.78082	−	5.64696i	−0.587673	−	0.339293i	−0.764177	+	0.645007i	$0.776854\pi$
$278$	−0.481186	+	0.481186i	−0.0288596	+	0.0288596i
$279$	8.83955	−	8.83955i	0.529210	−	0.529210i
$280$	−0.369750	+	1.37993i	−0.0220968	+	0.0824664i
$281$	4.21873	−	15.7445i	0.251668	−	0.939239i	−0.718245	−	0.695790i	$-0.755054\pi$
$281$	4.21873	−	15.7445i	0.251668	−	0.939239i	0.969914	−	0.243449i	$-0.0782790\pi$
$282$	−0.230371	−	0.399014i	−0.0137184	−	0.0237609i
$283$		−	19.6419i		−	1.16759i	−0.811902	−	0.583794i	$-0.801568\pi$
$283$		−	19.6419i		−	1.16759i	0.811902	−	0.583794i	$-0.198432\pi$
$284$	−1.01317	+	3.78120i	−0.0601206	+	0.224373i
$285$	0.349960	−	2.49337i	0.0207298	−	0.147694i
$286$	−0.969235	−	1.11317i	−0.0573121	−	0.0658229i
$287$	42.6565	+	24.6277i	2.51793	+	1.45373i
$288$	1.86276	−	1.86276i	0.109764	−	0.109764i
$289$	−7.94605	+	13.7630i	−0.467415	+	0.809586i
$290$	0.597609	−	0.345030i	0.0350928	−	0.0202608i
$291$	1.09286	−	4.07862i	0.0640647	−	0.239093i
$292$	12.6865	−	3.39933i	0.742419	−	0.198931i
$293$	23.5226	−	6.30287i	1.37421	−	0.368217i	0.505193	−	0.863007i	$-0.331421\pi$
$293$	23.5226	−	6.30287i	1.37421	−	0.368217i	0.869013	+	0.494789i	$0.164755\pi$
$294$	−0.708657	−	0.189884i	−0.0413297	−	0.0110743i
$295$			8.12696i			0.473170i
$296$	−1.43151	+	0.826485i	−0.0832050	+	0.0480385i
$297$	4.38965	−	16.3824i	0.254713	−	0.950603i
$298$	0.868988	+	1.50513i	0.0503391	+	0.0871899i
$299$	1.10674	−	3.22265i	0.0640047	−	0.186371i
$300$	−4.46037	+	2.57520i	−0.257520	+	0.148679i
$301$	−8.25708	−	8.25708i	−0.475930	−	0.475930i
$302$	−0.467683			−0.0269121
$303$	1.20357	−	2.08465i	0.0691435	−	0.119760i
$304$	−15.8791	−	6.73690i	−0.910731	−	0.386388i
$305$	6.93232	−	1.85751i	0.396943	−	0.106361i
$306$	−0.0600905	+	0.224261i	−0.00343515	+	0.0128201i
$307$	15.5331	−	4.16207i	0.886518	−	0.237542i	0.213301	−	0.976987i	$-0.431579\pi$
$307$	15.5331	−	4.16207i	0.886518	−	0.237542i	0.673217	+	0.739445i	$0.264912\pi$
$308$	44.1655			2.51656
$309$			3.50822i			0.199576i
$310$	0.0969429	+	0.361796i	0.00550599	+	0.0205486i
$311$		−	15.7171i		−	0.891235i	−0.895224	−	0.445617i	$-0.852984\pi$
$311$		−	15.7171i		−	0.891235i	0.895224	−	0.445617i	$-0.147016\pi$
$312$	−0.629404	−	0.423801i	−0.0356330	−	0.0239930i
$313$	−2.36766	−	4.10090i	−0.133828	−	0.231797i	0.791321	−	0.611401i	$-0.209394\pi$
$313$	−2.36766	−	4.10090i	−0.133828	−	0.231797i	−0.925149	+	0.379604i	$0.876060\pi$
$314$	−0.532519	−	1.98739i	−0.0300518	−	0.112155i
$315$	−5.52827	−	9.57525i	−0.311483	−	0.539504i
$316$	5.42393	−	9.39453i	0.305120	−	0.528483i
$317$	−29.1398	−	7.80799i	−1.63665	−	0.438540i	−0.680821	−	0.732450i	$-0.738377\pi$
$317$	−29.1398	−	7.80799i	−1.63665	−	0.438540i	−0.955833	+	0.293909i	$0.905044\pi$
$318$	−0.337841	−	0.0905243i	−0.0189452	−	0.00507635i
$319$	−30.2238	−	30.2238i	−1.69221	−	1.69221i
$320$	−1.87620	−	7.00209i	−0.104883	−	0.391429i
$321$	3.37389	+	5.84375i	0.188312	+	0.326166i
$322$	−0.182592	−	0.316259i	−0.0101755	−	0.0176244i
$323$	4.55374	−	0.559966i	0.253377	−	0.0311573i
$324$			11.2572i			0.625402i
$325$	−9.80844	−	11.2650i	−0.544075	−	0.624869i
$326$	0.965304	+	0.557319i	0.0534633	+	0.0308670i
$327$	5.97623	−	1.60133i	0.330486	−	0.0885535i
$328$	3.63283			0.200590
$329$			39.9826i			2.20431i
$330$	0.167203	+	0.167203i	0.00920421	+	0.00920421i
$331$	−2.03593	−	7.59818i	−0.111905	−	0.417634i	0.887132	−	0.461516i	$-0.152694\pi$
$331$	−2.03593	−	7.59818i	−0.111905	−	0.417634i	−0.999037	+	0.0438819i	$0.986027\pi$
$332$	−7.64230	+	7.64230i	−0.419426	+	0.419426i
$333$	3.31107	−	12.3571i	0.181446	−	0.677164i
$334$	−0.191635	+	0.331921i	−0.0104858	+	0.0181619i
$335$	3.05485	+	5.29115i	0.166904	+	0.289087i
$336$	10.9066	−	2.92243i	0.595006	−	0.159432i
$337$	6.57223	−	11.3834i	0.358012	−	0.620096i	−0.629616	−	0.776906i	$-0.716788\pi$
$337$	6.57223	−	11.3834i	0.358012	−	0.620096i	0.987629	+	0.156811i	$0.0501212\pi$
$338$	0.427517	−	1.01170i	0.0232539	−	0.0550290i
$339$	−2.22647	+	3.85636i	−0.120925	+	0.209449i
$340$	1.37334	+	1.37334i	0.0744800	+	0.0744800i
$341$	20.0923	−	11.6003i	1.08806	−	0.628190i
$342$	−0.891396	+	0.360335i	−0.0482012	+	0.0194847i
$343$	22.3794	+	22.3794i	1.20837	+	1.20837i
$344$	−0.831910	−	0.222910i	−0.0448536	−	0.0120185i
$345$	−0.141284	+	0.527279i	−0.00760648	+	0.0283878i
$346$	−0.182440	−	0.0488847i	−0.00980804	−	0.00262806i
$347$	0.319455	+	0.553312i	0.0171492	+	0.0297033i	0.874473	−	0.485075i	$-0.161208\pi$
$347$	0.319455	+	0.553312i	0.0171492	+	0.0297033i	−0.857323	+	0.514778i	$0.827874\pi$
$348$	−9.49780	−	5.48356i	−0.509136	−	0.293950i
$349$	−5.34309	−	1.43168i	−0.286009	−	0.0766358i	0.112962	−	0.993599i	$-0.463966\pi$
$349$	−5.34309	−	1.43168i	−0.286009	−	0.0766358i	−0.398971	+	0.916963i	$0.630633\pi$
$350$	−1.60083			−0.0855679
$351$	12.3867	−	2.41808i	0.661153	−	0.129068i
$352$	4.23404	−	2.44452i	0.225675	−	0.130294i
$353$	−7.29422	+	27.2224i	−0.388232	+	1.44890i	0.444776	+	0.895642i	$0.353283\pi$
$353$	−7.29422	+	27.2224i	−0.388232	+	1.44890i	−0.833008	+	0.553261i	$0.813383\pi$
$354$	−0.400642	+	0.231311i	−0.0212939	+	0.0122940i
$355$	1.81876			0.0965297
$356$	−7.11819	−	26.5655i	−0.377263	−	1.40797i
$357$	−2.12369	+	2.12369i	−0.112398	+	0.112398i
$358$	1.91747	+	0.513783i	0.101341	+	0.0271543i
$359$	2.53423	+	9.45787i	0.133751	+	0.499167i	1.00000		0.000446166i	$-0.000142019\pi$
$359$	2.53423	+	9.45787i	0.133751	+	0.499167i	−0.866248	+	0.499614i	$0.833475\pi$
$360$	−0.706222	−	0.407737i	−0.0372212	−	0.0214896i
$361$	13.2035	+	13.6627i	0.694919	+	0.719088i
$362$	−0.377285	−	0.101093i	−0.0198297	−	0.00531334i
$363$	3.89213	−	6.74136i	0.204284	−	0.353830i
$364$	14.4306	+	29.5268i	0.756370	+	1.54762i
$365$	−3.05110	−	5.28466i	−0.159702	−	0.276611i
$366$	0.288880	+	0.288880i	0.0151000	+	0.0151000i
$367$	−16.8585	+	29.1998i	−0.880006	+	1.52422i	−0.0286732	+	0.999589i	$0.509128\pi$
$367$	−16.8585	+	29.1998i	−0.880006	+	1.52422i	−0.851333	+	0.524626i	$0.824205\pi$
$368$	3.23871	+	1.86987i	0.168830	+	0.0974738i
$369$	−19.8810	+	19.8810i	−1.03496	+	1.03496i
$370$	0.271039	+	0.271039i	0.0140907	+	0.0140907i
$371$	21.4619	+	21.4619i	1.11425	+	1.11425i
$372$	4.20931	−	4.20931i	0.218243	−	0.218243i
$373$	9.60206	+	5.54375i	0.497176	+	0.287045i	0.727547	−	0.686058i	$-0.240661\pi$
$373$	9.60206	+	5.54375i	0.497176	+	0.287045i	−0.230371	+	0.973103i	$0.573994\pi$
$374$	−0.215443	+	0.373159i	−0.0111403	+	0.0192956i
$375$	3.73427	+	3.73427i	0.192837	+	0.192837i
$376$	1.47446	+	2.55383i	0.0760393	+	0.131704i
$377$	10.3308	−	30.0814i	0.532061	−	1.54927i
$378$	0.676296	−	1.17138i	0.0347849	−	0.0602492i
$379$	28.2391	+	7.56665i	1.45055	+	0.388673i	0.896214	−	0.443623i	$-0.146307\pi$
$379$	28.2391	+	7.56665i	1.45055	+	0.388673i	0.554332	+	0.832296i	$0.312974\pi$
$380$	−1.11793	+	7.96497i	−0.0573488	+	0.408595i
$381$	−4.08233	−	2.35693i	−0.209144	−	0.120749i
$382$	−0.286298	−	1.06848i	−0.0146483	−	0.0546682i
$383$	−6.83903	−	1.83251i	−0.349458	−	0.0936370i	0.0798202	−	0.996809i	$-0.474565\pi$
$383$	−6.83903	−	1.83251i	−0.349458	−	0.0936370i	−0.429278	+	0.903172i	$0.641232\pi$
$384$	1.18199	−	1.18199i	0.0603183	−	0.0603183i
$385$	−5.31091	−	19.8206i	−0.270669	−	1.01015i
$386$	0.261887			0.0133297
$387$	5.77259	−	3.33280i	0.293437	−	0.169416i
$388$	−3.49110	+	13.0290i	−0.177234	+	0.661446i
$389$	5.96279	−	3.44262i	0.302325	−	0.174548i	−0.341162	−	0.940005i	$-0.610820\pi$
$389$	5.96279	−	3.44262i	0.302325	−	0.174548i	0.643487	+	0.765457i	$0.277487\pi$
$390$	−0.0571513	+	0.166415i	−0.00289397	+	0.00842674i
$391$	−0.994721			−0.0503052
$392$	4.53567	+	1.21533i	0.229086	+	0.0613833i
$393$	−0.101139	−	0.0583927i	−0.00510179	−	0.00294552i
$394$	0.364385	+	0.631134i	0.0183575	+	0.0317961i
$395$	−4.86830	−	1.30446i	−0.244951	−	0.0656344i
$396$	−6.52496	+	24.3515i	−0.327891	+	1.22371i
$397$	26.3381	+	7.05727i	1.32187	+	0.354194i	0.849679	−	0.527301i	$-0.176796\pi$
$397$	26.3381	+	7.05727i	1.32187	+	0.354194i	0.472193	+	0.881495i	$0.343463\pi$
$398$	0.118525	+	0.118525i	0.00594113	+	0.00594113i
$399$	−12.3168	−	1.72874i	−0.616611	−	0.0865452i
$400$	14.1973	−	8.19679i	0.709863	−	0.409840i
$401$	0.843841	+	0.843841i	0.0421394	+	0.0421394i	0.727863	−	0.685723i	$-0.240514\pi$
$401$	0.843841	+	0.843841i	0.0421394	+	0.0421394i	−0.685723	+	0.727863i	$0.740514\pi$
$402$	−0.173895	+	0.301195i	−0.00867309	+	0.0150222i
$403$	14.3203	+	9.64237i	0.713343	+	0.480321i
$404$	−3.84477	+	6.65933i	−0.191284	+	0.331314i
$405$	5.05202	−	1.35368i	0.251037	−	0.0672651i
$406$	−1.70438	−	2.95208i	−0.0845871	−	0.146509i
$407$	11.8712	−	20.5615i	0.588434	−	1.01920i
$408$	−0.0573316	+	0.213965i	−0.00283834	+	0.0105928i
$409$	−10.6218	+	10.6218i	−0.525216	+	0.525216i	−0.919142	−	0.393926i	$-0.871117\pi$
$409$	−10.6218	+	10.6218i	−0.525216	+	0.525216i	0.393926	+	0.919142i	$0.371117\pi$
$410$	−0.218034	−	0.813713i	−0.0107679	−	0.0401864i
$411$	−7.46738	−	7.46738i	−0.368339	−	0.368339i
$412$		−	11.2069i		−	0.552124i
$413$	40.1457			1.97544
$414$	0.201351	−	0.0539519i	0.00989588	−	0.00265159i
$415$	4.34870	+	2.51072i	0.213469	+	0.123246i
$416$	3.01771	+	2.03194i	0.147955	+	0.0996238i
$417$		−	5.02486i		−	0.246068i
$418$	−1.77105	+	0.217783i	−0.0866248	+	0.0106521i
$419$	−10.9803	−	19.0184i	−0.536421	−	0.929108i	−0.999093	−	0.0425790i	$-0.986443\pi$
$419$	−10.9803	−	19.0184i	−0.536421	−	0.929108i	0.462672	−	0.886529i	$-0.346891\pi$
$420$	−2.63251	−	4.55965i	−0.128454	−	0.222488i
$421$	−4.77594	−	17.8241i	−0.232765	−	0.868691i	−0.979144	−	0.203169i	$-0.934876\pi$
$421$	−4.77594	−	17.8241i	−0.232765	−	0.868691i	0.746379	−	0.665522i	$-0.231791\pi$
$422$	1.17729	+	1.17729i	0.0573097	+	0.0573097i
$423$	−22.0452	−	5.90698i	−1.07187	−	0.287207i
$424$	2.16231	+	0.579389i	0.105011	+	0.0281376i
$425$	−2.18024	+	3.77628i	−0.105757	+	0.183177i
$426$	0.0517657	+	0.0896609i	0.00250806	+	0.00434408i
$427$	−9.17576	−	34.2444i	−0.444046	−	1.65720i
$428$	−10.7778	−	18.6676i	−0.520963	−	0.902334i
$429$	10.8729	+	0.751506i	0.524948	+	0.0362831i
$430$			0.199717i			0.00963120i
$431$	−0.613331	−	2.28898i	−0.0295431	−	0.110256i	0.949580	−	0.313525i	$-0.101510\pi$
$431$	−0.613331	−	2.28898i	−0.0295431	−	0.110256i	−0.979123	+	0.203269i	$0.934843\pi$
$432$			13.8515i			0.666429i
$433$	−5.81735			−0.279564			−0.139782	−	0.990182i	$-0.544640\pi$
$433$	−5.81735			−0.279564			−0.139782	+	0.990182i	$0.544640\pi$
$434$	1.78721	−	0.478880i	0.0857886	−	0.0229870i
$435$	−1.31880	+	4.92182i	−0.0632315	+	0.235983i
$436$	−19.0908	+	5.11537i	−0.914285	+	0.244982i
$437$	−2.47968	−	3.28940i	−0.118619	−	0.157354i
$438$	0.173681	−	0.300825i	0.00829882	−	0.0143740i
$439$	25.1818			1.20186			0.600932	−	0.799300i	$-0.294796\pi$
$439$	25.1818			1.20186			0.600932	+	0.799300i	$0.294796\pi$
$440$	−1.07016	−	1.07016i	−0.0510178	−	0.0510178i
$441$	−31.4728	+	18.1708i	−1.49870	+	0.865277i
$442$	−0.319868	−	0.0221085i	−0.0152146	−	0.00105159i
$443$	−7.86764	−	13.6272i	−0.373803	−	0.647446i	0.616344	−	0.787477i	$-0.288613\pi$
$443$	−7.86764	−	13.6272i	−0.373803	−	0.647446i	−0.990147	+	0.140031i	$0.955280\pi$
$444$	1.57670	−	5.88433i	0.0748270	−	0.279258i
$445$	−11.0661	+	6.38900i	−0.524582	+	0.302868i
$446$			1.17641i			0.0557046i
$447$	−12.3960	−	3.32151i	−0.586313	−	0.157102i
$448$	−34.5890	+	9.26811i	−1.63418	+	0.437877i
$449$	23.3239	−	6.24961i	1.10072	−	0.294937i	0.337663	−	0.941267i	$-0.390364\pi$
$449$	23.3239	−	6.24961i	1.10072	−	0.294937i	0.763058	+	0.646330i	$0.223697\pi$
$450$	0.236504	−	0.882647i	0.0111489	−	0.0416084i
$451$	−45.1894	+	26.0901i	−2.12788	+	1.22853i
$452$	7.11238	−	12.3190i	0.334538	−	0.579437i
$453$	2.44192	−	2.44192i	0.114732	−	0.114732i
$454$	−0.574898	−	0.331917i	−0.0269813	−	0.0155777i
$455$	11.5157	−	10.0268i	0.539865	−	0.470062i
$456$	−0.850470	+	0.343791i	−0.0398269	+	0.0160995i
$457$	−0.103630	+	0.386751i	−0.00484759	+	0.0180915i	−0.968307	−	0.249762i	$-0.919648\pi$
$457$	−0.103630	+	0.386751i	−0.00484759	+	0.0180915i	0.963460	+	0.267853i	$0.0863143\pi$
$458$		−	0.395339i		−	0.0184730i
$459$	−1.84215	−	3.19070i	−0.0859843	−	0.148929i
$460$	0.451327	−	1.68437i	0.0210432	−	0.0785343i
$461$	−3.49322	+	13.0369i	−0.162695	+	0.607187i	0.835628	+	0.549296i	$0.185104\pi$
$461$	−3.49322	+	13.0369i	−0.162695	+	0.607187i	−0.998323	+	0.0578907i	$0.981563\pi$
$462$	0.825951	−	0.825951i	0.0384267	−	0.0384267i
$463$	14.2243	−	14.2243i	0.661059	−	0.661059i	−0.294570	−	0.955630i	$-0.595177\pi$
$463$	14.2243	−	14.2243i	0.661059	−	0.661059i	0.955630	+	0.294570i	$0.0951766\pi$
$464$	30.2313	+	17.4541i	1.40345	+	0.810284i
$465$	−2.39522	−	1.38288i	−0.111076	−	0.0641297i
$466$	−1.67085	+	0.447703i	−0.0774007	+	0.0207394i
$467$			8.07336i			0.373591i	0.982399	+	0.186795i	$0.0598101\pi$
$467$			8.07336i			0.373591i	−0.982399	+	0.186795i	$0.940190\pi$
$468$	−18.4121	+	3.59434i	−0.851099	+	0.166148i
$469$	26.1373	−	15.0904i	1.20691	−	0.696809i
$470$	0.483537	−	0.483537i	0.0223039	−	0.0223039i
$471$	13.1573	+	7.59634i	0.606254	+	0.350021i
$472$	2.56425	−	1.48047i	0.118029	−	0.0681443i
$473$	11.9491	−	3.20176i	0.549422	−	0.147217i
$474$	−0.0742552	−	0.277124i	−0.00341065	−	0.0127287i
$475$	−17.9226	+	2.20391i	−0.822346	+	0.101123i
$476$	6.78406	−	6.78406i	0.310947	−	0.310947i
$477$	−15.0042	+	8.66265i	−0.686993	+	0.396636i
$478$	−1.77986			−0.0814088
$479$	−3.79601	−	14.1669i	−0.173444	−	0.647303i	−0.996811	−	0.0797936i	$-0.974574\pi$
$479$	−3.79601	−	14.1669i	−0.173444	−	0.647303i	0.823367	−	0.567509i	$-0.192093\pi$
$480$	−0.504745	−	0.291415i	−0.0230384	−	0.0133012i
$481$	17.6252	+	1.21821i	0.803639	+	0.0555455i
$482$	−1.35120			−0.0615453
$483$	2.60466	+	0.697918i	0.118516	+	0.0317564i
$484$	−12.4332	+	21.5350i	−0.565148	+	0.978864i
$485$	6.26694			0.284567
$486$	0.837854	+	0.837854i	0.0380058	+	0.0380058i
$487$	−0.480622	−	1.79370i	−0.0217790	−	0.0812805i	0.954181	−	0.299230i	$-0.0967298\pi$
$487$	−0.480622	−	1.79370i	−0.0217790	−	0.0812805i	−0.975960	+	0.217950i	$0.930063\pi$
$488$	−1.84894	−	1.84894i	−0.0836974	−	0.0836974i
$489$	−7.95011	+	2.13022i	−0.359516	+	0.0963321i
$490$		−	1.08888i		−	0.0491905i
$491$			6.78935i			0.306399i	0.988195	+	0.153200i	$0.0489577\pi$
$491$			6.78935i			0.306399i	−0.988195	+	0.153200i	$0.951042\pi$
$492$	−9.46714	+	9.46714i	−0.426812	+	0.426812i
$493$	−9.28508			−0.418179
$494$	−0.724270	−	1.11287i	−0.0325864	−	0.0500705i
$495$	11.7131			0.526463
$496$	−13.3982	+	13.3982i	−0.601595	+	0.601595i
$497$		−	8.98434i		−	0.403003i
$498$			0.285842i			0.0128089i
$499$	1.17238	−	0.314137i	0.0524828	−	0.0140627i	−0.232482	−	0.972601i	$-0.574685\pi$
$499$	1.17238	−	0.314137i	0.0524828	−	0.0140627i	0.284965	+	0.958538i	$0.408018\pi$
$500$	−11.9290	−	11.9290i	−0.533480	−	0.533480i
$501$	−0.732481	−	2.73366i	−0.0327248	−	0.122131i
$502$	0.395999	+	0.395999i	0.0176743	+	0.0176743i
$503$	10.8341			0.483069			0.241535	−	0.970392i	$-0.422349\pi$
$503$	10.8341			0.483069			0.241535	+	0.970392i	$0.422349\pi$
$504$	−2.01415	+	3.48861i	−0.0897173	+	0.155395i
$505$	3.45091	+	0.924667i	0.153563	+	0.0411472i
$506$	0.386869			0.0171984
$507$	3.05018	+	7.51459i	0.135463	+	0.333735i
$508$	13.0408	+	7.52913i	0.578594	+	0.334051i
$509$	3.58277	+	13.3711i	0.158804	+	0.592663i	0.998750	+	0.0499932i	$0.0159200\pi$
$509$	3.58277	+	13.3711i	0.158804	+	0.592663i	−0.839946	+	0.542670i	$0.817413\pi$
$510$	0.0513665			0.00227455
$511$	−26.1052	+	15.0719i	−1.15483	+	0.666740i
$512$	−4.71127	+	4.71127i	−0.208211	+	0.208211i
$513$	5.95902	−	14.0456i	0.263097	−	0.620130i
$514$	−0.651397	−	2.43105i	−0.0287319	−	0.107229i
$515$	−5.02942	+	1.34763i	−0.221623	+	0.0593836i
$516$	2.74885	−	1.58705i	0.121012	−	0.0698660i
$517$	−36.6820	−	21.1784i	−1.61327	−	0.931423i
$518$	1.33888	−	1.33888i	0.0588272	−	0.0588272i
$519$	1.20782	−	0.697336i	0.0530175	−	0.0306097i
$520$	0.365789	−	1.06512i	0.0160409	−	0.0467084i
$521$		−	33.2721i		−	1.45768i	−0.684686	−	0.728838i	$-0.740061\pi$
$521$		−	33.2721i		−	1.45768i	0.684686	−	0.728838i	$-0.259939\pi$
$522$	1.87949	−	0.503607i	0.0822629	−	0.0220423i
$523$	10.3868	+	5.99682i	0.454183	+	0.262223i	0.709595	−	0.704610i	$-0.248878\pi$
$523$	10.3868	+	5.99682i	0.454183	+	0.262223i	−0.255412	+	0.966832i	$0.582211\pi$
$524$	0.323085	+	0.186533i	0.0141140	+	0.00814874i
$525$	8.35844	−	8.35844i	0.364792	−	0.364792i
$526$	−0.347422	+	0.347422i	−0.0151483	+	0.0151483i
$527$	1.30442	−	4.86814i	0.0568212	−	0.212060i
$528$	−3.09596	+	11.5543i	−0.134734	+	0.502835i
$529$	−11.0534	−	19.1451i	−0.480585	−	0.832397i
$530$		−	0.519106i		−	0.0225485i
$531$	−5.93108	+	22.1351i	−0.257387	+	0.960581i
$532$	39.3455	+	5.52239i	1.70584	+	0.239426i
$533$	−32.2076	−	21.6866i	−1.39507	−	0.939351i
$534$	−0.629927	−	0.363689i	−0.0272596	−	0.0157384i
$535$	−7.08162	+	7.08162i	−0.306165	+	0.306165i
$536$	1.11299	−	1.92776i	0.0480739	−	0.0832664i
$537$	−12.6943	+	7.32908i	−0.547801	+	0.316273i
$538$	0.356176	−	1.32927i	0.0153558	−	0.0573087i
$539$	−65.1480	+	17.4564i	−2.80612	+	0.751898i
$540$	6.23868	−	1.67165i	0.268470	−	0.0719364i
$541$	9.28234	+	2.48719i	0.399079	+	0.106933i	0.452776	−	0.891624i	$-0.350434\pi$
$541$	9.28234	+	2.48719i	0.399079	+	0.106933i	−0.0536969	+	0.998557i	$0.517100\pi$
$542$			1.19309i			0.0512477i
$543$	2.49777	−	1.44209i	0.107189	−	0.0618859i
$544$	0.274879	−	1.02586i	0.0117854	−	0.0439835i
$545$	4.59135	+	7.95245i	0.196672	+	0.340646i
$546$	0.822059	+	0.282317i	0.0351809	+	0.0120821i
$547$	−10.7234	+	6.19116i	−0.458500	+	0.264715i	−0.711413	−	0.702774i	$-0.751945\pi$
$547$	−10.7234	+	6.19116i	−0.458500	+	0.264715i	0.252913	+	0.967489i	$0.418611\pi$
$548$	23.8543	+	23.8543i	1.01900	+	1.01900i
$549$	20.2369			0.863690
$550$	0.847942	−	1.46868i	0.0361564	−	0.0626246i
$551$	−23.1462	−	30.7045i	−0.986062	−	1.30806i
$552$	0.192107	−	0.0514749i	0.00817661	−	0.00219092i
$553$	−6.44378	+	24.0485i	−0.274017	+	1.02265i
$554$	0.921664	−	0.246959i	0.0391577	−	0.0104923i
$555$	−2.83037			−0.120142
$556$			16.0517i			0.680744i
$557$	−0.867073	−	3.23596i	−0.0367391	−	0.137112i	0.945120	−	0.326722i	$-0.105944\pi$
$557$	−0.867073	−	3.23596i	−0.0367391	−	0.137112i	−0.981859	+	0.189610i	$0.939278\pi$
$558$			1.05616i			0.0447108i
$559$	6.04479	+	6.94243i	0.255667	+	0.293633i
$560$	8.37924	+	14.5133i	0.354087	+	0.613297i
$561$	−0.823483	−	3.07328i	−0.0347675	−	0.129754i
$562$	0.688557	+	1.19262i	0.0290450	+	0.0503074i
$563$	−9.60982	+	16.6447i	−0.405006	+	0.701491i	−0.994322	−	0.106412i	$-0.966064\pi$
$563$	−9.60982	+	16.6447i	−0.405006	+	0.701491i	0.589316	+	0.807902i	$0.299397\pi$
$564$	−10.4977	−	2.81285i	−0.442033	−	0.118442i
$565$	−6.38378	−	1.71053i	−0.268568	−	0.0719625i
$566$	1.17342	+	1.17342i	0.0493224	+	0.0493224i
$567$	−6.68695	−	24.9560i	−0.280826	−	1.04806i
$568$	−0.331320	−	0.573862i	−0.0139019	−	0.0240787i
$569$	−16.3871	−	28.3833i	−0.686984	−	1.18989i	−0.972809	−	0.231609i	$-0.925601\pi$
$569$	−16.3871	−	28.3833i	−0.686984	−	1.18989i	0.285825	−	0.958282i	$-0.407732\pi$
$570$	0.128048	+	0.169862i	0.00536336	+	0.00711474i
$571$			9.77426i			0.409040i	0.978862	+	0.204520i	$0.0655634\pi$
$571$			9.77426i			0.409040i	−0.978862	+	0.204520i	$0.934437\pi$
$572$	−34.7330	−	2.40066i	−1.45226	−	0.100377i
$573$	7.07373	+	4.08402i	0.295509	+	0.170612i
$574$	−4.01959	+	1.07705i	−0.167775	+	0.0449551i
$575$	3.91502			0.163268
$576$		−	20.4406i		−	0.851691i
$577$	10.5692	+	10.5692i	0.440003	+	0.440003i	0.892013	−	0.452010i	$-0.149293\pi$
$577$	10.5692	+	10.5692i	0.440003	+	0.440003i	−0.452010	+	0.892013i	$0.649293\pi$
$578$	−0.347505	−	1.29691i	−0.0144543	−	0.0539443i
$579$	−1.36739	+	1.36739i	−0.0568270	+	0.0568270i
$580$	4.21285	−	15.7226i	0.174929	−	0.652844i
$581$	12.4025	−	21.4818i	0.514542	−	0.891214i
$582$	0.178370	+	0.308947i	0.00739369	+	0.0128063i
$583$	−31.0583	+	8.32204i	−1.28630	+	0.344664i
$584$	−1.11162	+	1.92539i	−0.0459993	+	0.0796732i
$585$	3.82712	+	7.83075i	0.158232	+	0.323762i
$586$	−1.02872	+	1.78179i	−0.0424959	+	0.0736051i
$587$	−12.2950	−	12.2950i	−0.507471	−	0.507471i	0.406279	−	0.913749i	$-0.366826\pi$
$587$	−12.2950	−	12.2950i	−0.507471	−	0.507471i	−0.913749	+	0.406279i	$0.866826\pi$
$588$	−14.9871	+	8.65278i	−0.618056	+	0.356835i
$589$	19.3500	−	7.82197i	0.797302	−	0.322299i
$590$	−0.485509	−	0.485509i	−0.0199881	−	0.0199881i
$591$	−5.19793	−	1.39278i	−0.213814	−	0.0572913i
$592$	−5.01861	+	18.7297i	−0.206264	+	0.769786i
$593$	12.2823	+	3.29104i	0.504375	+	0.135147i	0.502030	−	0.864850i	$-0.332587\pi$
$593$	12.2823	+	3.29104i	0.504375	+	0.135147i	0.00234510	+	0.999997i	$0.499254\pi$
$594$	0.716453	+	1.24093i	0.0293964	+	0.0509161i
$595$	−3.86033	−	2.22876i	−0.158258	−	0.0913704i
$596$	39.5987	+	10.6104i	1.62203	+	0.434620i
$597$	−1.23772			−0.0506563
$598$	0.126405	+	0.258640i	0.00516910	+	0.0105766i
$599$	1.70761	−	0.985888i	0.0697710	−	0.0402823i	−0.464709	−	0.885464i	$-0.653841\pi$
$599$	1.70761	−	0.985888i	0.0697710	−	0.0402823i	0.534480	+	0.845181i	$0.320508\pi$
$600$	0.225646	−	0.842122i	0.00921196	−	0.0343795i
$601$	8.22559	−	4.74905i	0.335529	−	0.193718i	−0.322764	−	0.946479i	$-0.604612\pi$
$601$	8.22559	−	4.74905i	0.335529	−	0.193718i	0.658293	+	0.752762i	$0.271279\pi$
$602$	0.986565			0.0402094
$603$	4.45887	+	16.6407i	0.181579	+	0.677663i
$604$	−7.80063	+	7.80063i	−0.317403	+	0.317403i
$605$	11.1596	+	2.99020i	0.453701	+	0.121569i
$606$	0.0526360	+	0.196440i	0.00213819	+	0.00797984i
$607$	−20.8098	−	12.0145i	−0.844644	−	0.487655i	0.0141960	−	0.999899i	$-0.495481\pi$
$607$	−20.8098	−	12.0145i	−0.844644	−	0.487655i	−0.858840	+	0.512244i	$0.828814\pi$
$608$	4.07762	−	1.64832i	0.165369	−	0.0668483i
$609$	24.3129	+	6.51462i	0.985208	+	0.263986i
$610$	−0.303172	+	0.525109i	−0.0122751	+	0.0212610i
$611$	2.17329	−	31.4435i	0.0879220	−	1.27207i
$612$	2.73825	+	4.74279i	0.110687	+	0.191716i
$613$	−17.4637	−	17.4637i	−0.705354	−	0.705354i	0.260201	−	0.965555i	$-0.416211\pi$
$613$	−17.4637	−	17.4637i	−0.705354	−	0.705354i	−0.965555	+	0.260201i	$0.916211\pi$
$614$	−0.679309	+	1.17660i	−0.0274147	+	0.0474836i
$615$	5.38708	+	3.11023i	0.217228	+	0.125417i
$616$	−5.28639	+	5.28639i	−0.212995	+	0.212995i
$617$	16.6906	+	16.6906i	0.671940	+	0.671940i	0.958163	−	0.286223i	$-0.0923998\pi$
$617$	16.6906	+	16.6906i	0.671940	+	0.671940i	−0.286223	+	0.958163i	$0.592400\pi$
$618$	−0.209583	−	0.209583i	−0.00843067	−	0.00843067i
$619$	8.06468	−	8.06468i	0.324147	−	0.324147i	−0.526209	−	0.850355i	$-0.676387\pi$
$619$	8.06468	−	8.06468i	0.324147	−	0.324147i	0.850355	+	0.526209i	$0.176387\pi$
$620$	7.65145	+	4.41757i	0.307290	+	0.177414i
$621$	−1.65397	+	2.86475i	−0.0663713	+	0.114959i
$622$	0.938948	+	0.938948i	0.0376484	+	0.0376484i
$623$	31.5605	+	54.6644i	1.26444	+	2.19008i
$624$	−8.73615	+	1.70544i	−0.349726	+	0.0682722i
$625$	6.43773	−	11.1505i	0.257509	−	0.446019i
$626$	0.386435	+	0.103545i	0.0154451	+	0.00413849i
$627$	8.11010	−	10.3843i	0.323886	−	0.414710i
$628$	−42.0303	−	24.2662i	−1.67719	−	0.968328i
$629$	−1.33488	−	4.98185i	−0.0532252	−	0.198639i
$630$	0.902292	+	0.241769i	0.0359482	+	0.00963229i
$631$	−1.70206	+	1.70206i	−0.0677578	+	0.0677578i	−0.740174	−	0.672416i	$-0.765257\pi$
$631$	−1.70206	+	1.70206i	−0.0677578	+	0.0677578i	0.672416	+	0.740174i	$0.265257\pi$
$632$	0.475260	+	1.77370i	0.0189048	+	0.0705538i
$633$	−12.2940			−0.488645
$634$	2.20728	−	1.27437i	0.0876623	−	0.0506119i
$635$	1.81076	−	6.75784i	0.0718577	−	0.268177i
$636$	−7.14484	+	4.12508i	−0.283311	+	0.163570i
$637$	−32.9568	−	37.8509i	−1.30580	−	1.49971i
$638$	3.61117			0.142968
$639$	4.95368	+	1.32734i	0.195965	+	0.0525086i
$640$	2.14856	+	1.24047i	0.0849292	+	0.0490339i
$641$	14.5202	+	25.1498i	0.573515	+	0.993357i	0.996201	+	0.0870809i	$0.0277539\pi$
$641$	14.5202	+	25.1498i	0.573515	+	0.993357i	−0.422686	+	0.906276i	$0.638913\pi$
$642$	−0.550667	−	0.147551i	−0.0217331	−	0.00582336i
$643$	4.07708	−	15.2159i	0.160784	−	0.600055i	−0.837756	−	0.546045i	$-0.816133\pi$
$643$	4.07708	−	15.2159i	0.160784	−	0.600055i	0.998540	−	0.0540106i	$-0.0172005\pi$
$644$	−8.32050	−	2.22947i	−0.327874	−	0.0878535i
$645$	−1.04279	−	1.04279i	−0.0410597	−	0.0410597i
$646$	−0.238590	+	0.305495i	−0.00938720	+	0.0120196i
$647$	−25.1161	+	14.5008i	−0.987415	+	0.570084i	−0.904500	−	0.426473i	$-0.859756\pi$
$647$	−25.1161	+	14.5008i	−0.987415	+	0.570084i	−0.0829141	+	0.996557i	$0.526423\pi$
$648$	−1.34744	−	1.34744i	−0.0529322	−	0.0529322i
$649$	−21.2648	+	36.8316i	−0.834715	+	1.44577i
$650$	1.25894	+	0.0870146i	0.0493796	+	0.00341299i
$651$	−6.83119	+	11.8320i	−0.267735	+	0.463731i
$652$	25.3963	−	6.80492i	0.994596	−	0.266501i
$653$	9.76060	+	16.9059i	0.381962	+	0.661577i	0.991343	−	0.131300i	$-0.0419152\pi$
$653$	9.76060	+	16.9059i	0.381962	+	0.661577i	−0.609381	+	0.792878i	$0.708582\pi$
$654$	−0.261359	+	0.452687i	−0.0102199	+	0.0177015i
$655$	0.0448613	−	0.167424i	0.00175287	−	0.00654182i
$656$	30.1337	−	30.1337i	1.17652	−	1.17652i
$657$	−4.45340	−	16.6203i	−0.173744	−	0.648420i
$658$	−2.38858	−	2.38858i	−0.0931166	−	0.0931166i
$659$		−	15.0127i		−	0.584810i	−0.956295	−	0.292405i	$-0.905544\pi$
$659$		−	15.0127i		−	0.584810i	0.956295	−	0.292405i	$-0.0944556\pi$
$660$	5.57766			0.217110
$661$	33.3857	−	8.94568i	1.29855	−	0.347947i	0.457651	−	0.889132i	$-0.348691\pi$
$661$	33.3857	−	8.94568i	1.29855	−	0.347947i	0.840903	+	0.541185i	$0.182024\pi$
$662$	0.575546	+	0.332292i	0.0223692	+	0.0129149i
$663$	1.78557	−	1.55470i	0.0693458	−	0.0603795i
$664$		−	1.82949i		−	0.0709980i
$665$	−2.25297	−	18.3215i	−0.0873664	−	0.710478i
$666$	0.540414	+	0.936024i	0.0209406	+	0.0362702i
$667$	4.16828	+	7.21967i	0.161396	+	0.279547i
$668$	2.33988	+	8.73256i	0.0905328	+	0.337873i
$669$	−6.14242	−	6.14242i	−0.237479	−	0.237479i
$670$	−0.498594	−	0.133598i	−0.0192624	−	0.00516134i
$671$	36.2778	+	9.72060i	1.40049	+	0.375260i
$672$	−1.43954	+	2.49335i	−0.0555313	+	0.0961831i
$673$	18.5439	+	32.1189i	0.714814	+	1.23809i	0.963031	+	0.269390i	$0.0868220\pi$
$673$	18.5439	+	32.1189i	0.714814	+	1.23809i	−0.248217	+	0.968704i	$0.579845\pi$
$674$	0.287424	+	1.07268i	0.0110712	+	0.0413181i
$675$	7.25035	+	12.5580i	0.279066	+	0.483356i
$676$	−9.74369	−	24.0051i	−0.374757	−	0.923272i
$677$			48.3169i			1.85697i	0.371372	+	0.928484i	$0.378887\pi$
$677$			48.3169i			1.85697i	−0.371372	+	0.928484i	$0.621113\pi$
$678$	−0.0973705	−	0.363392i	−0.00373949	−	0.0139560i
$679$		−	30.9576i		−	1.18804i
$680$	−0.328765			−0.0126075
$681$	4.73477	−	1.26868i	0.181437	−	0.0486159i
$682$	−0.507316	+	1.89333i	−0.0194261	+	0.0724993i
$683$	−1.15253	+	0.308820i	−0.0441004	+	0.0118167i	−0.280802	−	0.959766i	$-0.590600\pi$
$683$	−1.15253	+	0.308820i	−0.0441004	+	0.0118167i	0.236701	+	0.971582i	$0.423934\pi$
$684$	−8.85773	+	20.8780i	−0.338684	+	0.798291i
$685$	7.83682	−	13.5738i	0.299430	−	0.518627i
$686$	−2.67391			−0.102090
$687$	2.06419	+	2.06419i	0.0787538	+	0.0787538i
$688$	−8.74954	+	5.05155i	−0.333573	+	0.192589i
$689$	−15.7117	−	18.0448i	−0.598566	−	0.687453i
$690$	−0.0230596	−	0.0399403i	−0.000877863	−	0.00152050i
$691$	−2.78030	+	10.3762i	−0.105768	+	0.394730i	−0.998431	−	0.0559935i	$-0.982167\pi$
$691$	−2.78030	+	10.3762i	−0.105768	+	0.394730i	0.892663	+	0.450724i	$0.148834\pi$
$692$	−3.85834	+	2.22761i	−0.146672	+	0.0846812i
$693$		−	57.8604i		−	2.19794i
$694$	−0.0521395	−	0.0139707i	−0.00197919	−	0.000530322i
$695$	7.20368	−	1.93022i	0.273251	−	0.0732174i
$696$	1.79319	−	0.480485i	0.0679709	−	0.0182127i
$697$	−2.93375	+	10.9489i	−0.111124	+	0.414720i
$698$	0.404728	−	0.233670i	0.0153192	−	0.00884453i
$699$	6.38645	−	11.0617i	0.241558	−	0.418390i
$700$	−26.7007	+	26.7007i	−1.00919	+	1.00919i
$701$	0.962485	+	0.555691i	0.0363526	+	0.0209882i	0.518066	−	0.855341i	$-0.326652\pi$
$701$	0.962485	+	0.555691i	0.0363526	+	0.0209882i	−0.481714	+	0.876329i	$0.659985\pi$
$702$	−0.595530	+	0.884445i	−0.0224768	+	0.0333812i
$703$	13.1466	−	16.8332i	0.495835	−	0.634876i
$704$	9.81843	−	36.6429i	0.370046	−	1.38103i
$705$			5.04940i			0.190171i
$706$	−1.19052	−	2.06204i	−0.0448058	−	0.0776060i
$707$	4.56769	−	17.0468i	0.171786	−	0.641113i
$708$	−2.82433	+	10.5405i	−0.106145	+	0.396137i
$709$	21.6787	−	21.6787i	0.814161	−	0.814161i	−0.171094	−	0.985255i	$-0.554730\pi$
$709$	21.6787	−	21.6787i	0.814161	−	0.814161i	0.985255	+	0.171094i	$0.0547301\pi$
$710$	−0.108654	+	0.108654i	−0.00407770	+	0.00407770i
$711$	−12.3076	−	7.10580i	−0.461571	−	0.266488i
$712$	4.03177	+	2.32774i	0.151097	+	0.0872358i
$713$	−4.37083	+	1.17116i	−0.163689	+	0.0438603i
$714$		−	0.253741i		−	0.00949603i
$715$	3.09928	+	15.8761i	0.115907	+	0.593734i
$716$	40.5516	−	23.4125i	1.51548	−	0.874964i
$717$	9.29321	−	9.29321i	0.347061	−	0.347061i
$718$	−0.716414	−	0.413622i	−0.0267363	−	0.0154362i
$719$	−32.5176	+	18.7740i	−1.21270	+	0.700153i	−0.963347	−	0.268260i	$-0.913551\pi$
$719$	−32.5176	+	18.7740i	−1.21270	+	0.700153i	−0.249354	+	0.968413i	$0.580218\pi$
$720$	−9.24010	+	2.47588i	−0.344358	+	0.0922705i
$721$	6.65704	+	24.8444i	0.247921	+	0.925254i
$722$	−1.60500	−	0.0274340i	−0.0597318	−	0.00102099i
$723$	7.05503	−	7.05503i	0.262379	−	0.262379i
$724$	−7.97902	+	4.60669i	−0.296538	+	0.171206i
$725$	36.5443			1.35722
$726$	0.170215	+	0.635250i	0.00631726	+	0.0235763i
$727$	9.24589	+	5.33812i	0.342911	+	0.197980i	0.661559	−	0.749894i	$-0.269895\pi$
$727$	9.24589	+	5.33812i	0.342911	+	0.197980i	−0.318648	+	0.947873i	$0.603229\pi$
$728$	−5.26148	−	1.80693i	−0.195003	−	0.0669694i
$729$	8.19692			0.303590
$730$	0.497982	+	0.133434i	0.0184311	+	0.00493861i
$731$	1.34364	−	2.32726i	0.0496965	−	0.0860768i
$732$	9.63663			0.356180
$733$	−10.8356	−	10.8356i	−0.400223	−	0.400223i	0.478089	−	0.878312i	$-0.341330\pi$
$733$	−10.8356	−	10.8356i	−0.400223	−	0.400223i	−0.878312	+	0.478089i	$0.841330\pi$
$734$	−0.737274	−	2.75154i	−0.0272133	−	0.101561i
$735$	5.68539	+	5.68539i	0.209709	+	0.209709i
$736$	−0.921065	+	0.246799i	−0.0339509	+	0.00909712i
$737$			31.9729i			1.17774i
$738$		−	2.37540i		−	0.0874397i
$739$	19.3963	−	19.3963i	0.713504	−	0.713504i	−0.253762	−	0.967267i	$-0.581668\pi$
$739$	19.3963	−	19.3963i	0.713504	−	0.713504i	0.967267	+	0.253762i	$0.0816681\pi$
$740$	9.04150			0.332372
$741$	9.59231	+	2.02902i	0.352382	+	0.0745379i
$742$	−2.56429			−0.0941380
$743$	0.269175	−	0.269175i	0.00987509	−	0.00987509i	−0.702152	−	0.712027i	$-0.747777\pi$
$743$	0.269175	−	0.269175i	0.00987509	−	0.00987509i	0.712027	+	0.702152i	$0.247777\pi$
$744$			1.00767i			0.0369429i
$745$		−	19.0470i		−	0.697828i
$746$	−0.904819	+	0.242446i	−0.0331278	+	0.00887656i
$747$	10.0120	+	10.0120i	0.366321	+	0.366321i
$748$	2.63058	+	9.81747i	0.0961837	+	0.358962i
$749$	34.9819	+	34.9819i	1.27821	+	1.27821i
$750$	−0.446174			−0.0162920
$751$	11.0751	−	19.1826i	0.404136	−	0.699983i	−0.590085	−	0.807341i	$-0.700906\pi$
$751$	11.0751	−	19.1826i	0.404136	−	0.699983i	0.994220	+	0.107358i	$0.0342391\pi$
$752$	33.4140	+	8.95325i	1.21848	+	0.326491i
$753$	−4.13527			−0.150698
$754$	1.17991	+	2.41424i	0.0429699	+	0.0879215i
$755$	4.43879	+	2.56274i	0.161544	+	0.0932676i
$756$	−8.25764	−	30.8179i	−0.300328	−	1.12084i
$757$	32.6878			1.18806			0.594029	−	0.804444i	$-0.297536\pi$
$757$	32.6878			1.18806			0.594029	+	0.804444i	$0.297536\pi$
$758$	−2.13905	+	1.23498i	−0.0776940	+	0.0448566i
$759$	−2.01997	+	2.01997i	−0.0733201	+	0.0733201i
$760$	−0.819557	−	1.08718i	−0.0297284	−	0.0394361i
$761$	3.09299	+	11.5432i	0.112121	+	0.418441i	0.999055	−	0.0434542i	$-0.0138362\pi$
$761$	3.09299	+	11.5432i	0.112121	+	0.418441i	−0.886934	+	0.461895i	$0.847170\pi$
$762$	0.384685	−	0.103076i	0.0139357	−	0.00373405i
$763$	39.2837	−	22.6804i	1.42216	−	0.821087i
$764$	−22.5968	−	13.0462i	−0.817522	−	0.471997i
$765$	1.79919	−	1.79919i	0.0650499	−	0.0650499i
$766$	0.518043	−	0.299092i	0.0187176	−	0.0108066i
$767$	−31.5717	−	2.18216i	−1.13999	−	0.0787932i
$768$		−	9.62725i		−	0.347394i
$769$	−4.78582	+	1.28236i	−0.172581	+	0.0462430i	−0.344075	−	0.938942i	$-0.611807\pi$
$769$	−4.78582	+	1.28236i	−0.172581	+	0.0462430i	0.171494	+	0.985185i	$0.445141\pi$
$770$	1.50137	+	0.866815i	0.0541055	+	0.0312378i
$771$	16.0944	+	9.29212i	0.579626	+	0.334648i
$772$	4.36809	−	4.36809i	0.157211	−	0.157211i
$773$	−13.9465	+	13.9465i	−0.501619	+	0.501619i	−0.911941	−	0.410322i	$-0.865416\pi$
$773$	−13.9465	+	13.9465i	−0.501619	+	0.501619i	0.410322	+	0.911941i	$0.365416\pi$
$774$	−0.145754	+	0.543961i	−0.00523901	+	0.0195523i
$775$	−5.13392	+	19.1601i	−0.184416	+	0.688249i
$776$	−1.14164	−	1.97737i	−0.0409824	−	0.0709835i
$777$			13.9815i			0.501583i
$778$	−0.150556	+	0.561884i	−0.00539771	+	0.0201445i
$779$	−43.5199	+	17.5924i	−1.55926	+	0.630311i
$780$	1.82244	+	3.72893i	0.0652538	+	0.133517i
$781$	8.24267	+	4.75891i	0.294946	+	0.170287i
$782$	0.0594251	−	0.0594251i	0.00212504	−	0.00212504i
$783$	−15.4387	+	26.7406i	−0.551735	+	0.955632i
$784$	47.7035	−	27.5416i	1.70370	−	0.983629i
$785$	−5.83603	+	21.7804i	−0.208297	+	0.777375i
$786$	0.00953051	−	0.00255369i	0.000339942	−	9.10872e-5i
$787$	−32.3964	+	8.68060i	−1.15481	+	0.309430i	−0.784890	−	0.619635i	$-0.787281\pi$
$787$	−32.3964	+	8.68060i	−1.15481	+	0.309430i	−0.369918	+	0.929065i	$0.620614\pi$
$788$	16.6046	+	4.44918i	0.591514	+	0.158496i
$789$		−	3.62801i		−	0.129160i
$790$	0.368764	−	0.212906i	0.0131200	−	0.00757485i
$791$	−8.44970	+	31.5347i	−0.300437	+	1.12124i
$792$	−2.13375	−	3.69575i	−0.0758193	−	0.131323i
$793$	5.35469	+	27.4295i	0.190151	+	0.974051i
$794$	−1.99506	+	1.15185i	−0.0708019	+	0.0408775i
$795$	2.71042	+	2.71042i	0.0961286	+	0.0961286i
$796$	3.95384			0.140140
$797$	−6.40263	+	11.0897i	−0.226793	+	0.392816i	−0.956856	−	0.290563i	$-0.906157\pi$
$797$	−6.40263	+	11.0897i	−0.226793	+	0.392816i	0.730063	+	0.683380i	$0.239491\pi$
$798$	0.839087	−	0.632536i	0.0297034	−	0.0223915i
$799$	−8.88767	+	2.38144i	−0.314423	+	0.0842494i
$800$	−1.08187	+	4.03760i	−0.0382499	+	0.142751i
$801$	−34.8029	+	9.32541i	−1.22970	+	0.329497i
$802$	−0.100823			−0.00356018
$803$		−	31.9336i		−	1.12691i
$804$	2.12327	+	7.92417i	0.0748821	+	0.279464i
$805$			4.00216i			0.141058i
$806$	−1.43154	+	0.279460i	−0.0504239	+	0.00984356i
$807$	5.08082	+	8.80023i	0.178853	+	0.309783i
$808$	−0.336889	−	1.25729i	−0.0118517	−	0.0442313i
$809$	18.9615	+	32.8422i	0.666650	+	1.15467i	0.978835	+	0.204650i	$0.0656056\pi$
$809$	18.9615	+	32.8422i	0.666650	+	1.15467i	−0.312186	+	0.950021i	$0.601061\pi$
$810$	−0.220940	+	0.382680i	−0.00776305	+	0.0134460i
$811$	−35.5338	−	9.52124i	−1.24776	−	0.334336i	−0.426289	−	0.904587i	$-0.640179\pi$
$811$	−35.5338	−	9.52124i	−1.24776	−	0.334336i	−0.821470	+	0.570251i	$0.806846\pi$
$812$	−77.6666	−	20.8107i	−2.72556	−	0.730312i
$813$	−6.22951	−	6.22951i	−0.218479	−	0.218479i
$814$	0.519165	+	1.93755i	0.0181967	+	0.0679111i
$815$	−6.10782	−	10.5790i	−0.213947	−	0.370568i
$816$	1.29924	+	2.25035i	0.0454826	+	0.0787782i
$817$	11.0454	−	1.35824i	0.386430	−	0.0475187i
$818$		−	1.26911i		−	0.0443733i
$819$	38.6825	−	18.9053i	1.35167	−	0.660604i
$820$	−17.2088	−	9.93553i	−0.600959	−	0.346964i
$821$	−50.2561	+	13.4661i	−1.75395	+	0.469970i	−0.985462	−	0.169894i	$-0.945657\pi$
$821$	−50.2561	+	13.4661i	−1.75395	+	0.469970i	−0.768488	+	0.639864i	$0.778991\pi$
$822$	0.892210			0.0311194
$823$		−	35.6220i		−	1.24170i	−0.783928	−	0.620852i	$-0.786787\pi$
$823$		−	35.6220i		−	1.24170i	0.783928	−	0.620852i	$-0.213213\pi$
$824$	1.34141	+	1.34141i	0.0467302	+	0.0467302i
$825$	3.24107	+	12.0958i	0.112839	+	0.421122i
$826$	−2.39833	+	2.39833i	−0.0834484	+	0.0834484i
$827$	7.47275	−	27.8887i	0.259853	−	0.969785i	−0.705473	−	0.708737i	$-0.749265\pi$
$827$	7.47275	−	27.8887i	0.259853	−	0.969785i	0.965326	−	0.261048i	$-0.0840680\pi$
$828$	2.45852	−	4.25828i	0.0854395	−	0.147986i
$829$	7.63432	+	13.2230i	0.265151	+	0.459255i	0.967603	−	0.252476i	$-0.0812448\pi$
$829$	7.63432	+	13.2230i	0.265151	+	0.459255i	−0.702452	+	0.711731i	$0.747912\pi$
$830$	−0.409785	+	0.109802i	−0.0142238	+	0.00381127i
$831$	−3.52285	+	6.10176i	−0.122206	+	0.211668i
$832$	27.7056	−	5.40859i	0.960519	−	0.187509i
$833$	−7.32570	+	12.6885i	−0.253820	+	0.439630i
$834$	0.300188	+	0.300188i	0.0103946	+	0.0103946i
$835$	3.63762	−	2.10018i	0.125885	−	0.0726798i
$836$	−25.9074	+	33.1723i	−0.896026	+	1.14729i
$837$	−11.8511	−	11.8511i	−0.409635	−	0.409635i
$838$	1.79213	+	0.480201i	0.0619083	+	0.0165883i
$839$	12.6889	−	47.3558i	0.438071	−	1.63490i	−0.295537	−	0.955331i	$-0.595499\pi$
$839$	12.6889	−	47.3558i	0.438071	−	1.63490i	0.733608	−	0.679572i	$-0.237835\pi$
$840$	0.860866	+	0.230668i	0.0297027	+	0.00795881i
$841$	24.4082	+	42.2763i	0.841663	+	1.45780i
$842$	1.35014	+	0.779501i	0.0465287	+	0.0268634i
$843$	−9.82221	−	2.63185i	−0.338295	−	0.0906458i
$844$	39.2729			1.35183
$845$	−9.60131	+	7.25938i	−0.330295	+	0.249730i
$846$	1.66988	−	0.964103i	0.0574115	−	0.0331465i
$847$	14.7710	−	55.1263i	0.507539	−	1.89416i
$848$	22.7419	−	13.1300i	0.780960	−	0.450887i
$849$	−12.2536			−0.420541
$850$	−0.0953485	−	0.355845i	−0.00327043	−	0.0122054i
$851$	−3.27441	+	3.27441i	−0.112245	+	0.112245i
$852$	2.35890	+	0.632065i	0.0808146	+	0.0216542i
$853$	−8.82798	−	32.9465i	−0.302264	−	1.12807i	−0.935275	−	0.353923i	$-0.884848\pi$
$853$	−8.82798	−	32.9465i	−0.302264	−	1.12807i	0.633010	−	0.774143i	$-0.281819\pi$
$854$	2.59394	+	1.49761i	0.0887629	+	0.0512473i
$855$	10.4348	+	1.46458i	0.356861	+	0.0500877i
$856$	3.52447	+	0.944378i	0.120464	+	0.0322782i
$857$	−1.94333	+	3.36595i	−0.0663829	+	0.114979i	−0.897307	−	0.441408i	$-0.854479\pi$
$857$	−1.94333	+	3.36595i	−0.0663829	+	0.114979i	0.830924	+	0.556386i	$0.187813\pi$
$858$	−0.694447	+	0.604657i	−0.0237080	+	0.0206426i
$859$	4.35252	+	7.53879i	0.148506	+	0.257220i	0.930676	−	0.365846i	$-0.119220\pi$
$859$	4.35252	+	7.53879i	0.148506	+	0.257220i	−0.782169	+	0.623066i	$0.785887\pi$
$860$	3.33114	+	3.33114i	0.113591	+	0.113591i
$861$	15.3640	−	26.6112i	0.523603	−	0.906908i
$862$	0.173386	+	0.100104i	0.00590555	+	0.00340957i
$863$	20.5880	−	20.5880i	0.700823	−	0.700823i	−0.263764	−	0.964587i	$-0.584964\pi$
$863$	20.5880	−	20.5880i	0.700823	−	0.700823i	0.964587	+	0.263764i	$0.0849640\pi$
$864$	−2.49739	−	2.49739i	−0.0849628	−	0.0849628i
$865$	1.46367	+	1.46367i	0.0497664	+	0.0497664i
$866$	0.347532	−	0.347532i	0.0118096	−	0.0118096i
$867$	8.58601	+	4.95714i	0.291596	+	0.168353i
$868$	21.8220	−	37.7968i	0.740686	−	1.28291i
$869$	−18.6501	−	18.6501i	−0.632660	−	0.632660i
$870$	−0.215246	−	0.372818i	−0.00729754	−	0.0126397i
$871$	−21.3754	+	10.4468i	−0.724278	+	0.353976i
$872$	1.67279	−	2.89736i	0.0566479	−	0.0981171i
$873$	17.0690	+	4.57363i	0.577699	+	0.154794i
$874$	0.344648	+	0.0483735i	0.0116579	+	0.00163626i
$875$	33.5312	+	19.3592i	1.13356	+	0.654462i
$876$	−2.12067	−	7.91444i	−0.0716507	−	0.267404i
$877$	−11.0131	−	2.95096i	−0.371888	−	0.0996470i	0.0680344	−	0.997683i	$-0.478327\pi$
$877$	−11.0131	−	2.95096i	−0.371888	−	0.0996470i	−0.439922	+	0.898036i	$0.644994\pi$
$878$	−1.50438	+	1.50438i	−0.0507702	+	0.0507702i
$879$	−3.93204	−	14.6746i	−0.132624	−	0.494961i
$880$	−17.7536			−0.598473
$881$	−2.03834	+	1.17684i	−0.0686735	+	0.0396487i	−0.533944	−	0.845520i	$-0.679291\pi$
$881$	−2.03834	+	1.17684i	−0.0686735	+	0.0396487i	0.465270	+	0.885169i	$0.345957\pi$
$882$	0.794666	−	2.96573i	0.0267578	−	0.0998615i
$883$	−23.5416	+	13.5918i	−0.792239	+	0.457399i	−0.840750	−	0.541423i	$-0.817886\pi$
$883$	−23.5416	+	13.5918i	−0.792239	+	0.457399i	0.0485111	+	0.998823i	$0.484552\pi$
$884$	−5.70394	+	4.96643i	−0.191844	+	0.167039i
$885$	5.07000			0.170426
$886$	1.28411	+	0.344076i	0.0431405	+	0.0115595i
$887$	2.78658	+	1.60883i	0.0935641	+	0.0540192i	0.546052	−	0.837751i	$-0.316130\pi$
$887$	2.78658	+	1.60883i	0.0935641	+	0.0540192i	−0.452488	+	0.891771i	$0.649463\pi$
$888$	0.515602	+	0.893049i	0.0173025	+	0.0299687i
$889$	−33.3825	−	8.94481i	−1.11961	−	0.299999i
$890$	0.279411	−	1.04277i	0.00936587	−	0.0349539i
$891$	26.4379	+	7.08401i	0.885703	+	0.237323i
$892$	19.6217	+	19.6217i	0.656983	+	0.656983i
$893$	−30.0306	−	23.4537i	−1.00494	−	0.784849i
$894$	0.938975	−	0.542118i	0.0314040	−	0.0181311i
$895$	−15.3834	−	15.3834i	−0.514209	−	0.514209i
$896$	6.12770	−	10.6135i	0.204712	−	0.354572i
$897$	−2.01045	−	0.690442i	−0.0671269	−	0.0230532i
$898$	−1.02003	+	1.76674i	−0.0340387	+	0.0589567i
$899$	−40.7989	+	10.9320i	−1.36072	+	0.364604i
$900$	−10.7772	−	18.6667i	−0.359240	−	0.622223i
$901$	−3.49241	+	6.04903i	−0.116349	+	0.201523i
$902$	1.14100	−	4.25827i	0.0379912	−	0.141785i
$903$	−5.15117	+	5.15117i	−0.171420	+	0.171420i
$904$	0.623207	+	2.32584i	0.0207275	+	0.0773562i
$905$	3.02687	+	3.02687i	0.100616	+	0.100616i
$906$			0.291764i			0.00969320i
$907$	50.5219			1.67755			0.838777	−	0.544475i	$-0.183271\pi$
$907$	50.5219			1.67755			0.838777	+	0.544475i	$0.183271\pi$
$908$	−15.1251	+	4.05275i	−0.501942	+	0.134495i
$909$	8.72427	+	5.03696i	0.289366	+	0.167065i
$910$	−0.0889513	+	1.28696i	−0.00294871	+	0.0426623i
$911$		−	6.76361i		−	0.224088i	−0.993703	−	0.112044i	$-0.964260\pi$
$911$		−	6.76361i		−	0.224088i	0.993703	−	0.112044i	$-0.0357398\pi$
$912$	−4.20281	+	9.90619i	−0.139169	+	0.328027i
$913$	13.1389	+	22.7573i	0.434835	+	0.753157i
$914$	−0.0169138	−	0.0292956i	−0.000559460	−	0.000969012i
$915$	−1.15881	−	4.32472i	−0.0383089	−	0.142971i
$916$	−6.59398	−	6.59398i	−0.217871	−	0.217871i
$917$	−0.827046	−	0.221606i	−0.0273115	−	0.00731809i
$918$	0.300665	+	0.0805630i	0.00992343	+	0.00265898i
$919$	−25.1457	+	43.5537i	−0.829481	+	1.43670i	0.0689656	+	0.997619i	$0.478030\pi$
$919$	−25.1457	+	43.5537i	−0.829481	+	1.43670i	−0.898446	+	0.439084i	$0.855303\pi$
$920$	0.147590	+	0.255633i	0.00486589	+	0.00842796i
$921$	−2.59650	−	9.69028i	−0.0855577	−	0.319306i
$922$	−0.570142	−	0.987515i	−0.0187766	−	0.0325221i
$923$	−0.488352	+	7.06554i	−0.0160743	+	0.232565i
$924$		−	27.5526i		−	0.906414i
$925$	5.25383	+	19.6076i	0.172745	+	0.644693i
$926$			1.69953i			0.0558502i
$927$	−14.6819			−0.482218
$928$	−8.59756	+	2.30371i	−0.282229	+	0.0756229i
$929$	4.01313	−	14.9772i	0.131666	−	0.491386i	−0.868323	−	0.495999i	$-0.834802\pi$
$929$	4.01313	−	14.9772i	0.131666	−	0.491386i	0.999989	+	0.00461341i	$0.00146850\pi$
$930$	0.225706	−	0.0604778i	0.00740120	−	0.00198314i
$931$	−60.2208	+	7.40526i	−1.97366	+	0.242697i
$932$	−20.4013	+	35.3360i	−0.668266	+	1.15747i
$933$	−9.80510			−0.321004
$934$	−0.482307	−	0.482307i	−0.0157816	−	0.0157816i
$935$	4.08955	−	2.36110i	0.133743	−	0.0772164i
$936$	1.77361	−	2.63406i	0.0579723	−	0.0860969i
$937$	16.7136	+	28.9488i	0.546009	+	0.945715i	0.998543	+	0.0539679i	$0.0171869\pi$
$937$	16.7136	+	28.9488i	0.546009	+	0.945715i	−0.452534	+	0.891747i	$0.649480\pi$
$938$	−0.659950	+	2.46297i	−0.0215481	+	0.0804187i
$939$	−2.55834	+	1.47706i	−0.0834884	+	0.0482021i
$940$		−	16.1301i		−	0.526106i
$941$	44.9046	+	12.0321i	1.46385	+	0.392237i	0.900817	−	0.434200i	$-0.142969\pi$
$941$	44.9046	+	12.0321i	1.46385	+	0.392237i	0.563030	+	0.826436i	$0.309635\pi$
$942$	−1.23983	+	0.332212i	−0.0403959	+	0.0108240i
$943$	9.83042	−	2.63405i	0.320122	−	0.0857765i
$944$	8.98977	−	33.5503i	0.292592	−	1.09197i
$945$	−12.8375	+	7.41172i	−0.417603	+	0.241103i
$946$	−0.522573	+	0.905123i	−0.0169903	+	0.0294281i
$947$	−39.4371	+	39.4371i	−1.28153	+	1.28153i	−0.341741	+	0.939794i	$0.611016\pi$
$947$	−39.4371	+	39.4371i	−1.28153	+	1.28153i	−0.939794	+	0.341741i	$0.888984\pi$
$948$	−5.86077	−	3.38372i	−0.190349	−	0.109898i
$949$	21.3492	−	10.4340i	0.693023	−	0.338701i
$950$	0.939043	−	1.20237i	0.0304666	−	0.0390100i
$951$	−4.87101	+	18.1788i	−0.157953	+	0.589489i
$952$			1.62404i			0.0526353i
$953$	12.0680	+	20.9025i	0.390922	+	0.677097i	0.992571	−	0.121663i	$-0.0388228\pi$
$953$	12.0680	+	20.9025i	0.390922	+	0.677097i	−0.601649	+	0.798761i	$0.705489\pi$
$954$	0.378845	−	1.41387i	0.0122655	−	0.0457757i
$955$	−3.13763	+	11.7098i	−0.101531	+	0.378920i
$956$	−29.6868	+	29.6868i	−0.960140	+	0.960140i
$957$	−18.8551	+	18.8551i	−0.609499	+	0.609499i
$958$	1.07311	+	0.619563i	0.0346708	+	0.0200172i
$959$	−67.0520	−	38.7125i	−2.16522	−	1.25009i
$960$	−4.36825	+	1.17047i	−0.140985	+	0.0377767i
$961$			8.07344i			0.260434i
$962$	−1.12571	+	0.980161i	−0.0362945	+	0.0316016i
$963$	−24.4561	+	14.1198i	−0.788088	+	0.455003i
$964$	−22.5370	+	22.5370i	−0.725869	+	0.725869i
$965$	−2.48557	−	1.43505i	−0.0800134	−	0.0461958i
$966$	−0.197298	+	0.113910i	−0.00634796	+	0.00366500i
$967$	−11.9238	+	3.19497i	−0.383443	+	0.102743i	−0.445391	−	0.895336i	$-0.646935\pi$
$967$	−11.9238	+	3.19497i	−0.383443	+	0.102743i	0.0619481	+	0.998079i	$0.480269\pi$
$968$	−1.08944	−	4.06583i	−0.0350158	−	0.130681i
$969$	−0.349334	−	2.84085i	−0.0112222	−	0.0912611i
$970$	−0.374391	+	0.374391i	−0.0120210	+	0.0120210i
$971$	25.3043	−	14.6094i	0.812052	−	0.468838i	−0.0356159	−	0.999366i	$-0.511339\pi$
$971$	25.3043	−	14.6094i	0.812052	−	0.468838i	0.847668	+	0.530527i	$0.178006\pi$
$972$	27.9497			0.896486
$973$	−9.53494	−	35.5849i	−0.305676	−	1.14080i
$974$	0.135869	+	0.0784442i	0.00435354	+	0.00251352i
$975$	−7.02765	+	6.11899i	−0.225065	+	0.195964i
$976$	−30.6732			−0.981825
$977$	19.0399	+	5.10173i	0.609141	+	0.163219i	0.550187	−	0.835042i	$-0.314557\pi$
$977$	19.0399	+	5.10173i	0.609141	+	0.163219i	0.0589546	+	0.998261i	$0.481223\pi$
$978$	0.347683	−	0.602204i	0.0111177	−	0.0192564i
$979$	−66.8690			−2.13714
$980$	−18.1617	−	18.1617i	−0.580156	−	0.580156i
$981$	6.70156	+	25.0106i	0.213964	+	0.798526i
$982$	−0.405599	−	0.405599i	−0.0129432	−	0.0129432i
$983$	30.9789	−	8.30077i	0.988074	−	0.264754i	0.271633	−	0.962401i	$-0.412436\pi$
$983$	30.9789	−	8.30077i	0.988074	−	0.264754i	0.716441	+	0.697647i	$0.245770\pi$
$984$		−	2.26634i		−	0.0722483i
$985$		−	7.98681i		−	0.254481i
$986$	0.554696	−	0.554696i	0.0176651	−	0.0176651i
$987$	24.9431			0.793948
$988$	−30.6423	−	6.48163i	−0.974861	−	0.206208i
$989$	−2.41277			−0.0767215
$990$	−0.699745	+	0.699745i	−0.0222394	+	0.0222394i
$991$			51.6750i			1.64151i	0.571280	+	0.820755i	$0.306447\pi$
$991$			51.6750i			1.64151i	−0.571280	+	0.820755i	$0.693553\pi$
$992$		−	4.83131i		−	0.153394i
$993$	−4.74012	+	1.27011i	−0.150423	+	0.0403057i
$994$	0.536729	+	0.536729i	0.0170240	+	0.0170240i
$995$	−0.475449	−	1.77440i	−0.0150728	−	0.0562523i
$996$	4.76764	+	4.76764i	0.151069	+	0.151069i
$997$	0.734195			0.0232522			0.0116261	−	0.999932i	$-0.496299\pi$
$997$	0.734195			0.0232522			0.0116261	+	0.999932i	$0.496299\pi$
$998$	−0.0512717	+	0.0888051i	−0.00162298	+	0.00281108i
$999$	−16.5671	−	4.43913i	−0.524159	−	0.140448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	247.2.z.a.141.11	✓	88
13.6	odd	12		247.2.bf.a.84.12	yes	88
19.12	odd	6		247.2.bf.a.50.12	yes	88
247.240	even	12	inner	247.2.z.a.240.11	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
247.2.z.a.141.11	✓	88	1.1	even	1	trivial
247.2.z.a.240.11	yes	88	247.240	even	12	inner
247.2.bf.a.50.12	yes	88	19.12	odd	6
247.2.bf.a.84.12	yes	88	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 247 = 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	247.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0597405 + 0.0597405i) q^{2} -0.623849i q^{3} +1.99286i q^{4} +(0.894356 - 0.239642i) q^{5} +(0.0372691 + 0.0372691i) q^{6} +(-1.18379 - 4.41795i) q^{7} +(-0.238536 - 0.238536i) q^{8} +2.61081 q^{9} +(-0.0391129 + 0.0677456i) q^{10} +(4.68028 + 1.25408i) q^{11} +1.24325 q^{12} +(0.690822 + 3.53875i) q^{13} +(0.334651 + 0.193211i) q^{14} +(-0.149500 - 0.557943i) q^{15} -3.95722 q^{16} +(0.911551 - 0.526284i) q^{17} +(-0.155971 + 0.155971i) q^{18} +(4.01270 + 1.70243i) q^{19} +(0.477573 + 1.78233i) q^{20} +(-2.75614 + 0.738505i) q^{21} +(-0.354522 + 0.204683i) q^{22} +(-0.818430 - 0.472521i) q^{23} +(-0.148810 + 0.148810i) q^{24} +(-3.58768 + 2.07135i) q^{25} +(-0.252677 - 0.170137i) q^{26} -3.50030i q^{27} +(8.80437 - 2.35912i) q^{28} +(-7.63952 - 4.41068i) q^{29} +(0.0422630 + 0.0244006i) q^{30} +(3.38575 - 3.38575i) q^{31} +(0.713478 - 0.713478i) q^{32} +(0.782356 - 2.91979i) q^{33} +(-0.0230160 + 0.0858970i) q^{34} +(-2.11745 - 3.66754i) q^{35} +5.20299i q^{36} +(1.26821 - 4.73304i) q^{37} +(-0.341425 + 0.138016i) q^{38} +(2.20765 - 0.430969i) q^{39} +(-0.270499 - 0.156173i) q^{40} +(-7.61486 + 7.61486i) q^{41} +(0.120534 - 0.208772i) q^{42} +(2.21103 - 1.27654i) q^{43} +(-2.49921 + 9.32716i) q^{44} +(2.33499 - 0.625660i) q^{45} +(0.0771221 - 0.0206648i) q^{46} +(-8.44379 - 2.26251i) q^{47} +2.46871i q^{48} +(-12.0548 + 6.95983i) q^{49} +(0.0905866 - 0.338074i) q^{50} +(-0.328322 - 0.568670i) q^{51} +(-7.05224 + 1.37671i) q^{52} +(-5.74693 + 3.31799i) q^{53} +(0.209110 + 0.209110i) q^{54} +4.48637 q^{55} +(-0.771464 + 1.33622i) q^{56} +(1.06206 - 2.50332i) q^{57} +(0.719886 - 0.192893i) q^{58} +(-2.27174 + 8.47824i) q^{59} +(1.11190 - 0.297934i) q^{60} +7.75119 q^{61} +0.404533i q^{62} +(-3.09065 - 11.5344i) q^{63} -7.82920i q^{64} +(1.46587 + 2.99935i) q^{65} +(0.127692 + 0.221168i) q^{66} +(1.70785 + 6.37378i) q^{67} +(1.04881 + 1.81659i) q^{68} +(-0.294782 + 0.510577i) q^{69} +(0.345598 + 0.0926028i) q^{70} +(1.89737 + 0.508399i) q^{71} +(-0.622772 - 0.622772i) q^{72} +(-1.70575 - 6.36595i) q^{73} +(0.206991 + 0.358518i) q^{74} +(1.29221 + 2.23817i) q^{75} +(-3.39271 + 7.99675i) q^{76} -22.1618i q^{77} +(-0.106140 + 0.157632i) q^{78} +(-4.71409 - 2.72168i) q^{79} +(-3.53917 + 0.948317i) q^{80} +5.64878 q^{81} -0.909832i q^{82} +(3.83484 + 3.83484i) q^{83} +(-1.47174 - 5.49260i) q^{84} +(0.689131 - 0.689131i) q^{85} +(-0.0558270 + 0.208349i) q^{86} +(-2.75160 + 4.76591i) q^{87} +(-0.817273 - 1.41556i) q^{88} +(-13.3303 + 3.57184i) q^{89} +(-0.102117 + 0.176871i) q^{90} +(14.8163 - 7.24115i) q^{91} +(0.941669 - 1.63102i) q^{92} +(-2.11220 - 2.11220i) q^{93} +(0.639600 - 0.369273i) q^{94} +(3.99675 + 0.560969i) q^{95} +(-0.445103 - 0.445103i) q^{96} +(6.53782 + 1.75180i) q^{97} +(0.304375 - 1.13594i) q^{98} +(12.2193 + 3.27416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 2 q^{5} + 14 q^{6} - 12 q^{7} + 12 q^{8} - 84 q^{9} - 6 q^{10} - 4 q^{11} + 36 q^{12} - 6 q^{13} - 12 q^{14} + 30 q^{15} - 92 q^{16} - 6 q^{17} + 6 q^{18} - 14 q^{19} - 24 q^{20} - 18 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 2 * q^5 + 14 * q^6 - 12 * q^7 + 12 * q^8 - 84 * q^9 - 6 * q^10 - 4 * q^11 + 36 * q^12 - 6 * q^13 - 12 * q^14 + 30 * q^15 - 92 * q^16 - 6 * q^17 + 6 * q^18 - 14 * q^19 - 24 * q^20 - 18 * q^22 - 30 * q^23 + 48 * q^24 + 12 * q^25 + 32 * q^26 + 18 * q^28 + 18 * q^29 + 60 * q^30 - 30 * q^31 - 12 * q^32 - 6 * q^33 - 6 * q^34 - 6 * q^35 - 12 * q^37 - 36 * q^38 + 18 * q^39 - 12 * q^40 - 6 * q^41 + 6 * q^42 + 12 * q^43 + 64 * q^44 - 38 * q^45 + 24 * q^46 + 64 * q^47 - 42 * q^49 - 24 * q^51 + 18 * q^52 - 66 * q^53 - 96 * q^54 - 36 * q^55 + 60 * q^56 + 64 * q^57 - 24 * q^58 - 6 * q^59 + 54 * q^60 - 28 * q^61 - 6 * q^63 + 44 * q^66 - 36 * q^67 - 12 * q^68 - 36 * q^69 + 114 * q^70 - 30 * q^71 - 66 * q^72 + 22 * q^73 + 6 * q^74 - 12 * q^75 + 38 * q^76 + 12 * q^78 - 24 * q^79 + 14 * q^80 + 64 * q^81 - 6 * q^83 - 18 * q^84 - 18 * q^85 - 6 * q^86 + 32 * q^87 + 42 * q^88 + 66 * q^89 + 18 * q^90 - 18 * q^91 + 104 * q^92 - 2 * q^93 - 84 * q^94 - 42 * q^95 - 174 * q^96 + 30 * q^97 - 60 * q^98 + 28 * q^99

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