LMFDB - Embedded newform 114.2.h.f.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(65,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("114.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	114.65
Dual form			114.2.h.f.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +4.44949 q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +4.44949 q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(1.22474 - 0.707107i) q^{10} +0.317837i q^{11} +(1.72474 - 0.158919i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-2.00000 + 1.41421i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.44949 - 3.14626i) q^{17} +(-2.94949 + 0.548188i) q^{18} +(-4.17423 + 1.25529i) q^{19} -1.41421i q^{20} +(-3.22474 + 6.99964i) q^{21} +(0.275255 + 0.158919i) q^{22} +(6.12372 - 3.53553i) q^{23} +(0.724745 - 1.57313i) q^{24} +(-1.50000 - 2.59808i) q^{25} +3.46410i q^{26} +(5.00000 - 1.41421i) q^{27} +(-2.22474 - 3.85337i) q^{28} +(-1.22474 - 2.12132i) q^{29} +(0.224745 + 2.43916i) q^{30} +4.24264i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.230351i) q^{33} +(-5.44949 + 3.14626i) q^{34} +(5.44949 + 3.14626i) q^{35} +(-1.00000 + 2.82843i) q^{36} -0.778539i q^{37} +(-1.00000 + 4.24264i) q^{38} +(-0.550510 - 5.97469i) q^{39} +(-1.22474 - 0.707107i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(4.44949 + 6.29253i) q^{42} +(-0.449490 + 0.778539i) q^{43} +(0.275255 - 0.158919i) q^{44} +(-0.775255 - 4.17121i) q^{45} -7.07107i q^{46} +(-5.57321 + 3.21770i) q^{47} +(-1.00000 - 1.41421i) q^{48} +12.7980 q^{49} -3.00000 q^{50} +(8.89898 - 6.29253i) q^{51} +(3.00000 + 1.73205i) q^{52} +(-0.550510 - 0.953512i) q^{53} +(1.27526 - 5.03723i) q^{54} +(-0.224745 + 0.389270i) q^{55} -4.44949 q^{56} +(1.05051 - 7.47639i) q^{57} -2.44949 q^{58} +(3.27526 - 5.67291i) q^{59} +(2.22474 + 1.02494i) q^{60} +(3.22474 + 5.58542i) q^{61} +(3.67423 + 2.12132i) q^{62} +(-8.67423 - 10.1459i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-0.449490 + 0.317837i) q^{66} +(-5.17423 + 2.98735i) q^{67} +6.29253i q^{68} +(1.12372 + 12.1958i) q^{69} +(5.44949 - 3.14626i) q^{70} +(3.00000 - 5.19615i) q^{71} +(1.94949 + 2.28024i) q^{72} +(5.39898 - 9.35131i) q^{73} +(-0.674235 - 0.389270i) q^{74} +(5.17423 - 0.476756i) q^{75} +(3.17423 + 2.98735i) q^{76} +1.41421i q^{77} +(-5.44949 - 2.51059i) q^{78} +(7.34847 + 4.24264i) q^{79} +(-1.22474 + 0.707107i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(1.50000 + 2.59808i) q^{82} +14.1742i q^{83} +(7.67423 - 0.707107i) q^{84} +(-4.44949 - 7.70674i) q^{85} +(0.449490 + 0.778539i) q^{86} +(4.22474 - 0.389270i) q^{87} -0.317837i q^{88} +(8.44949 + 14.6349i) q^{89} +(-4.00000 - 1.41421i) q^{90} +(-13.3485 + 7.70674i) q^{91} +(-6.12372 - 3.53553i) q^{92} +(-6.67423 - 3.07483i) q^{93} +6.43539i q^{94} +(-6.00000 - 1.41421i) q^{95} +(-1.72474 + 0.158919i) q^{96} +(-11.8485 - 6.84072i) q^{97} +(6.39898 - 11.0834i) q^{98} +(0.724745 - 0.619620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{12} - 12 q^{13} + 4 q^{14} - 8 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 8 q^{21} + 6 q^{22} - 2 q^{24} - 6 q^{25} + 20 q^{27} - 4 q^{28} - 4 q^{30} + 2 q^{32} - 2 q^{33} - 12 q^{34} + 12 q^{35} - 4 q^{36} - 4 q^{38} - 12 q^{39} - 6 q^{41} + 8 q^{42} + 8 q^{43} + 6 q^{44} - 8 q^{45} + 12 q^{47} - 4 q^{48} + 12 q^{49} - 12 q^{50} + 16 q^{51} + 12 q^{52} - 12 q^{53} + 10 q^{54} + 4 q^{55} - 8 q^{56} + 14 q^{57} + 18 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{63} + 4 q^{64} + 8 q^{66} - 6 q^{67} - 20 q^{69} + 12 q^{70} + 12 q^{71} - 2 q^{72} + 2 q^{73} + 12 q^{74} + 6 q^{75} - 2 q^{76} - 12 q^{78} + 14 q^{81} + 6 q^{82} + 16 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{89} - 16 q^{90} - 24 q^{91} - 12 q^{93} - 24 q^{95} - 2 q^{96} - 18 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^12 - 12 * q^13 + 4 * q^14 - 8 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 8 * q^21 + 6 * q^22 - 2 * q^24 - 6 * q^25 + 20 * q^27 - 4 * q^28 - 4 * q^30 + 2 * q^32 - 2 * q^33 - 12 * q^34 + 12 * q^35 - 4 * q^36 - 4 * q^38 - 12 * q^39 - 6 * q^41 + 8 * q^42 + 8 * q^43 + 6 * q^44 - 8 * q^45 + 12 * q^47 - 4 * q^48 + 12 * q^49 - 12 * q^50 + 16 * q^51 + 12 * q^52 - 12 * q^53 + 10 * q^54 + 4 * q^55 - 8 * q^56 + 14 * q^57 + 18 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^63 + 4 * q^64 + 8 * q^66 - 6 * q^67 - 20 * q^69 + 12 * q^70 + 12 * q^71 - 2 * q^72 + 2 * q^73 + 12 * q^74 + 6 * q^75 - 2 * q^76 - 12 * q^78 + 14 * q^81 + 6 * q^82 + 16 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^89 - 16 * q^90 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 2 * q^96 - 18 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	0.748203	−	0.663470i	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$	4.44949			1.68175			0.840875	−	0.541230i	$-0.182041\pi$
$7$	4.44949			1.68175			0.840875	+	0.541230i	$0.182041\pi$
$8$	−1.00000			−0.353553
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$	1.22474	−	0.707107i	0.387298	−	0.223607i
$11$			0.317837i			0.0958315i	0.998851	+	0.0479158i	$0.0152579\pi$
$11$			0.317837i			0.0958315i	−0.998851	+	0.0479158i	$0.984742\pi$
$12$	1.72474	−	0.158919i	0.497891	−	0.0458759i
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	2.22474	−	3.85337i	0.594588	−	1.02986i
$15$	−2.00000	+	1.41421i	−0.516398	+	0.365148i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.44949	−	3.14626i	−1.32170	−	0.763081i	−0.337696	−	0.941255i	$-0.609648\pi$
$17$	−5.44949	−	3.14626i	−1.32170	−	0.763081i	−0.983999	+	0.178174i	$0.942981\pi$
$18$	−2.94949	+	0.548188i	−0.695201	+	0.129209i
$19$	−4.17423	+	1.25529i	−0.957635	+	0.287984i
$19$	−4.17423	+	1.25529i	−0.957635	+	0.287984i
$20$		−	1.41421i		−	0.316228i
$21$	−3.22474	+	6.99964i	−0.703697	+	1.52745i
$22$	0.275255	+	0.158919i	0.0586846	+	0.0338816i
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.300610	−	0.953747i	$-0.402810\pi$
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.976274	+	0.216537i	$0.0694763\pi$
$24$	0.724745	−	1.57313i	0.147938	−	0.321114i
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$			3.46410i			0.679366i
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	−2.22474	−	3.85337i	−0.420437	−	0.728219i
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$	0.224745	+	2.43916i	0.0410326	+	0.445327i
$31$			4.24264i			0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$			4.24264i			0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.500000	−	0.230351i	−0.0870388	−	0.0400989i
$34$	−5.44949	+	3.14626i	−0.934580	+	0.539580i
$35$	5.44949	+	3.14626i	0.921132	+	0.531816i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		−	0.778539i		−	0.127991i	−0.997950	−	0.0639955i	$-0.979616\pi$
$37$		−	0.778539i		−	0.127991i	0.997950	−	0.0639955i	$-0.0203843\pi$
$38$	−1.00000	+	4.24264i	−0.162221	+	0.688247i
$39$	−0.550510	−	5.97469i	−0.0881522	−	0.956716i
$40$	−1.22474	−	0.707107i	−0.193649	−	0.111803i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	4.44949	+	6.29253i	0.686571	+	0.970958i
$43$	−0.449490	+	0.778539i	−0.0685465	+	0.118726i	−0.898262	−	0.439461i	$-0.855169\pi$
$43$	−0.449490	+	0.778539i	−0.0685465	+	0.118726i	0.829715	+	0.558187i	$0.188503\pi$
$44$	0.275255	−	0.158919i	0.0414963	−	0.0239579i
$45$	−0.775255	−	4.17121i	−0.115568	−	0.621807i
$46$		−	7.07107i		−	1.04257i
$47$	−5.57321	+	3.21770i	−0.812937	+	0.469349i	−0.847975	−	0.530037i	$-0.822178\pi$
$47$	−5.57321	+	3.21770i	−0.812937	+	0.469349i	0.0350379	+	0.999386i	$0.488845\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$	12.7980			1.82828
$50$	−3.00000			−0.424264
$51$	8.89898	−	6.29253i	1.24611	−	0.881130i
$52$	3.00000	+	1.73205i	0.416025	+	0.240192i
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	0.825737	−	0.564056i	$-0.190760\pi$
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	−0.901355	+	0.433081i	$0.857426\pi$
$54$	1.27526	−	5.03723i	0.173540	−	0.685481i
$55$	−0.224745	+	0.389270i	−0.0303046	+	0.0524891i
$56$	−4.44949			−0.594588
$57$	1.05051	−	7.47639i	0.139143	−	0.990272i
$58$	−2.44949			−0.321634
$59$	3.27526	−	5.67291i	0.426402	−	0.738550i	−0.570148	−	0.821542i	$-0.693114\pi$
$59$	3.27526	−	5.67291i	0.426402	−	0.738550i	0.996550	+	0.0829920i	$0.0264476\pi$
$60$	2.22474	+	1.02494i	0.287213	+	0.132320i
$61$	3.22474	+	5.58542i	0.412886	+	0.715140i	0.995204	−	0.0978213i	$-0.0311874\pi$
$61$	3.22474	+	5.58542i	0.412886	+	0.715140i	−0.582318	+	0.812961i	$0.697854\pi$
$62$	3.67423	+	2.12132i	0.466628	+	0.269408i
$63$	−8.67423	−	10.1459i	−1.09285	−	1.27826i
$64$	1.00000			0.125000
$65$	−4.89898			−0.607644
$66$	−0.449490	+	0.317837i	−0.0553284	+	0.0391231i
$67$	−5.17423	+	2.98735i	−0.632133	+	0.364962i	−0.781578	−	0.623808i	$-0.785585\pi$
$67$	−5.17423	+	2.98735i	−0.632133	+	0.364962i	0.149444	+	0.988770i	$0.452251\pi$
$68$			6.29253i			0.763081i
$69$	1.12372	+	12.1958i	0.135281	+	1.46820i
$70$	5.44949	−	3.14626i	0.651339	−	0.376051i
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	1.94949	+	2.28024i	0.229750	+	0.268729i
$73$	5.39898	−	9.35131i	0.631903	−	1.09449i	−0.355260	−	0.934768i	$-0.615608\pi$
$73$	5.39898	−	9.35131i	0.631903	−	1.09449i	0.987162	−	0.159720i	$-0.0510591\pi$
$74$	−0.674235	−	0.389270i	−0.0783782	−	0.0452517i
$75$	5.17423	−	0.476756i	0.597469	−	0.0550510i
$76$	3.17423	+	2.98735i	0.364110	+	0.342672i
$77$			1.41421i			0.161165i
$78$	−5.44949	−	2.51059i	−0.617033	−	0.284268i
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	0.852745	−	0.522328i	$-0.174936\pi$
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	−0.0259772	+	0.999663i	$0.508270\pi$
$80$	−1.22474	+	0.707107i	−0.136931	+	0.0790569i
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$			14.1742i			1.55583i	0.628372	+	0.777913i	$0.283721\pi$
$83$			14.1742i			1.55583i	−0.628372	+	0.777913i	$0.716279\pi$
$84$	7.67423	−	0.707107i	0.837328	−	0.0771517i
$85$	−4.44949	−	7.70674i	−0.482615	−	0.835914i
$86$	0.449490	+	0.778539i	0.0484697	+	0.0839520i
$87$	4.22474	−	0.389270i	0.452940	−	0.0417341i
$88$		−	0.317837i		−	0.0338816i
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.833005	+	0.553265i	$0.186618\pi$
$89$	8.44949	+	14.6349i	0.895644	+	1.55130i	0.0626387	+	0.998036i	$0.480048\pi$
$90$	−4.00000	−	1.41421i	−0.421637	−	0.149071i
$91$	−13.3485	+	7.70674i	−1.39930	+	0.807886i
$92$	−6.12372	−	3.53553i	−0.638442	−	0.368605i
$93$	−6.67423	−	3.07483i	−0.692086	−	0.318845i
$94$			6.43539i			0.663760i
$95$	−6.00000	−	1.41421i	−0.615587	−	0.145095i
$96$	−1.72474	+	0.158919i	−0.176031	+	0.0162196i
$97$	−11.8485	−	6.84072i	−1.20303	−	0.694570i	−0.241802	−	0.970326i	$-0.577738\pi$
$97$	−11.8485	−	6.84072i	−1.20303	−	0.694570i	−0.961228	+	0.275756i	$0.911072\pi$
$98$	6.39898	−	11.0834i	0.646395	−	1.11959i
$99$	0.724745	−	0.619620i	0.0728396	−	0.0622742i
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	−0.861684	−	0.507445i	$-0.830590\pi$
$101$	−8.57321	+	4.94975i	−0.853067	+	0.492518i	0.00861771	+	0.999963i	$0.497257\pi$
$102$	−1.00000	−	10.8530i	−0.0990148	−	1.07461i
$103$		−	11.9494i		−	1.17741i	−0.808349	−	0.588704i	$-0.799638\pi$
$103$		−	11.9494i		−	1.17741i	0.808349	−	0.588704i	$-0.200362\pi$
$104$	3.00000	−	1.73205i	0.294174	−	0.169842i
$105$	−8.89898	+	6.29253i	−0.868451	+	0.614088i
$106$	−1.10102			−0.106941
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$	−3.72474	−	3.62302i	−0.358414	−	0.348625i
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$	0.224745	+	0.389270i	0.0214286	+	0.0371154i
$111$	1.22474	+	0.564242i	0.116248	+	0.0535555i
$112$	−2.22474	+	3.85337i	−0.210219	+	0.364109i
$113$	0.797959			0.0750657			0.0375328	−	0.999295i	$-0.488050\pi$
$113$	0.797959			0.0750657			0.0375328	+	0.999295i	$0.488050\pi$
$114$	−5.94949	−	4.64796i	−0.557221	−	0.435322i
$115$	10.0000			0.932505
$116$	−1.22474	+	2.12132i	−0.113715	+	0.196960i
$117$	9.79796	+	3.46410i	0.905822	+	0.320256i
$118$	−3.27526	−	5.67291i	−0.301512	−	0.522234i
$119$	−24.2474	−	13.9993i	−2.22276	−	1.28331i
$120$	2.00000	−	1.41421i	0.182574	−	0.129099i
$121$	10.8990			0.990816
$122$	6.44949			0.583909
$123$	−3.00000	−	4.24264i	−0.270501	−	0.382546i
$124$	3.67423	−	2.12132i	0.329956	−	0.190500i
$125$		−	11.3137i		−	1.01193i
$126$	−13.1237	+	2.43916i	−1.16915	+	0.217297i
$127$	−9.00000	+	5.19615i	−0.798621	+	0.461084i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−9.00000	+	5.19615i	−0.798621	+	0.461084i	0.0443678	+	0.999015i	$0.485873\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.898979	−	1.27135i	−0.0791507	−	0.111936i
$130$	−2.44949	+	4.24264i	−0.214834	+	0.372104i
$131$	19.0732	+	11.0119i	1.66643	+	0.962116i	0.969537	+	0.244946i	$0.0787702\pi$
$131$	19.0732	+	11.0119i	1.66643	+	0.962116i	0.696898	+	0.717171i	$0.254563\pi$
$132$	0.0505103	+	0.548188i	0.00439635	+	0.0477137i
$133$	−18.5732	+	5.58542i	−1.61050	+	0.484318i
$134$			5.97469i			0.516135i
$135$	7.12372	+	1.80348i	0.613113	+	0.155219i
$136$	5.44949	+	3.14626i	0.467290	+	0.269790i
$137$	−6.39898	+	3.69445i	−0.546702	+	0.315638i	−0.747791	−	0.663935i	$-0.768885\pi$
$137$	−6.39898	+	3.69445i	−0.546702	+	0.315638i	0.201089	+	0.979573i	$0.435552\pi$
$138$	11.1237	+	5.12472i	0.946914	+	0.436245i
$139$	−0.174235	−	0.301783i	−0.0147784	−	0.0255969i	0.858542	−	0.512744i	$-0.171371\pi$
$139$	−0.174235	−	0.301783i	−0.0147784	−	0.0255969i	−0.873320	+	0.487147i	$0.838038\pi$
$140$		−	6.29253i		−	0.531816i
$141$	−1.02270	−	11.0994i	−0.0861272	−	0.934739i
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−0.550510	−	0.953512i	−0.0460360	−	0.0797367i
$144$	2.94949	−	0.548188i	0.245791	−	0.0456823i
$145$		−	3.46410i		−	0.287678i
$146$	−5.39898	−	9.35131i	−0.446823	−	0.773920i
$147$	−9.27526	+	20.1329i	−0.765010	+	1.66053i
$148$	−0.674235	+	0.389270i	−0.0554217	+	0.0319978i
$149$	4.22474	+	2.43916i	0.346105	+	0.199824i	0.662968	−	0.748648i	$-0.269296\pi$
$149$	4.22474	+	2.43916i	0.346105	+	0.199824i	−0.316864	+	0.948471i	$0.602630\pi$
$150$	2.17423	−	4.71940i	0.177526	−	0.385337i
$151$			18.0990i			1.47288i	0.676503	+	0.736440i	$0.263495\pi$
$151$			18.0990i			1.47288i	−0.676503	+	0.736440i	$0.736505\pi$
$152$	4.17423	−	1.25529i	0.338575	−	0.101818i
$153$	3.44949	+	18.5597i	0.278875	+	1.50047i
$154$	1.22474	+	0.707107i	0.0986928	+	0.0569803i
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$	−4.89898	+	3.46410i	−0.392232	+	0.277350i
$157$	9.34847	−	16.1920i	0.746089	−	1.29226i	−0.203595	−	0.979055i	$-0.565263\pi$
$157$	9.34847	−	16.1920i	0.746089	−	1.29226i	0.949684	−	0.313209i	$-0.101404\pi$
$158$	7.34847	−	4.24264i	0.584613	−	0.337526i
$159$	1.89898	−	0.174973i	0.150599	−	0.0138762i
$160$			1.41421i			0.111803i
$161$	27.2474	−	15.7313i	2.14740	−	1.23980i
$162$	7.00000	+	5.65685i	0.549972	+	0.444444i
$163$	3.65153			0.286010			0.143005	−	0.989722i	$-0.454324\pi$
$163$	3.65153			0.286010			0.143005	+	0.989722i	$0.454324\pi$
$164$	3.00000			0.234261
$165$	−0.449490	−	0.635674i	−0.0349927	−	0.0494872i
$166$	12.2753	+	7.08712i	0.952745	+	0.550067i
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	0.945099	−	0.326783i	$-0.105965\pi$
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	−0.755552	+	0.655089i	$0.772631\pi$
$168$	3.22474	−	6.99964i	0.248794	−	0.540034i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−8.89898			−0.682521
$171$	11.0000	+	7.07107i	0.841191	+	0.540738i
$172$	0.898979			0.0685465
$173$	5.44949	−	9.43879i	0.414317	−	0.717618i	−0.581039	−	0.813875i	$-0.697354\pi$
$173$	5.44949	−	9.43879i	0.414317	−	0.717618i	0.995356	+	0.0962572i	$0.0306871\pi$
$174$	1.77526	−	3.85337i	0.134582	−	0.292123i
$175$	−6.67423	−	11.5601i	−0.504525	−	0.873862i
$176$	−0.275255	−	0.158919i	−0.0207481	−	0.0119789i
$177$	6.55051	+	9.26382i	0.492367	+	0.696311i
$178$	16.8990			1.26663
$179$	−22.3485			−1.67040			−0.835202	−	0.549944i	$-0.814649\pi$
$179$	−22.3485			−1.67040			−0.835202	+	0.549944i	$0.814649\pi$
$180$	−3.22474	+	2.75699i	−0.240358	+	0.205494i
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	−0.0160509	−	0.999871i	$-0.505109\pi$
$181$	11.3258	−	6.53893i	0.841838	−	0.486035i	0.857888	+	0.513836i	$0.171776\pi$
$182$			15.4135i			1.14252i
$183$	−11.1237	+	1.02494i	−0.822289	+	0.0757660i
$184$	−6.12372	+	3.53553i	−0.451447	+	0.260643i
$185$	0.550510	−	0.953512i	0.0404743	−	0.0701036i
$186$	−6.00000	+	4.24264i	−0.439941	+	0.311086i
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	5.57321	+	3.21770i	0.406468	+	0.234675i
$189$	22.2474	−	6.29253i	1.61826	−	0.457714i
$190$	−4.22474	+	4.48905i	−0.306495	+	0.325670i
$191$		−	19.5133i		−	1.41193i	−0.708247	−	0.705965i	$-0.750514\pi$
$191$		−	19.5133i		−	1.41193i	0.708247	−	0.705965i	$-0.249486\pi$
$192$	−0.724745	+	1.57313i	−0.0523040	+	0.113531i
$193$	−7.65153	−	4.41761i	−0.550769	−	0.317987i	0.198663	−	0.980068i	$-0.436340\pi$
$193$	−7.65153	−	4.41761i	−0.550769	−	0.317987i	−0.749432	+	0.662081i	$0.769673\pi$
$194$	−11.8485	+	6.84072i	−0.850671	+	0.491135i
$195$	3.55051	−	7.70674i	0.254257	−	0.551891i
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$			0.492810i			0.0351113i	0.999846	+	0.0175556i	$0.00558842\pi$
$197$			0.492810i			0.0351113i	−0.999846	+	0.0175556i	$0.994412\pi$
$198$	−0.174235	−	0.937458i	−0.0123823	−	0.0666222i
$199$	−3.44949	−	5.97469i	−0.244528	−	0.423535i	0.717471	−	0.696588i	$-0.245300\pi$
$199$	−3.44949	−	5.97469i	−0.244528	−	0.423535i	−0.961999	+	0.273054i	$0.911966\pi$
$200$	1.50000	+	2.59808i	0.106066	+	0.183712i
$201$	−0.949490	−	10.3048i	−0.0669718	−	0.726846i
$202$			9.89949i			0.696526i
$203$	−5.44949	−	9.43879i	−0.382479	−	0.662473i
$204$	−9.89898	−	4.56048i	−0.693067	−	0.319297i
$205$	−3.67423	+	2.12132i	−0.256620	+	0.148159i
$206$	−10.3485	−	5.97469i	−0.721012	−	0.416276i
$207$	−20.0000	−	7.07107i	−1.39010	−	0.491473i
$208$		−	3.46410i		−	0.240192i
$209$	−0.398979	−	1.32673i	−0.0275980	−	0.0917716i
$210$	1.00000	+	10.8530i	0.0690066	+	0.748929i
$211$	13.3485	+	7.70674i	0.918947	+	0.530554i	0.883299	−	0.468810i	$-0.155317\pi$
$211$	13.3485	+	7.70674i	0.918947	+	0.530554i	0.0356477	+	0.999364i	$0.488651\pi$
$212$	−0.550510	+	0.953512i	−0.0378092	+	0.0654875i
$213$	6.00000	+	8.48528i	0.411113	+	0.581402i
$214$	2.44949	−	4.24264i	0.167444	−	0.290021i
$215$	−1.10102	+	0.635674i	−0.0750890	+	0.0433526i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$			18.8776i			1.28149i
$218$		0			0
$219$	10.7980	+	15.2706i	0.729658	+	1.03189i
$220$	0.449490			0.0303046
$221$	21.7980			1.46629
$222$	1.10102	−	0.778539i	0.0738957	−	0.0522521i
$223$	−8.32577	−	4.80688i	−0.557534	−	0.321893i	0.194621	−	0.980879i	$-0.437652\pi$
$223$	−8.32577	−	4.80688i	−0.557534	−	0.321893i	−0.752155	+	0.658986i	$0.770986\pi$
$224$	2.22474	+	3.85337i	0.148647	+	0.257464i
$225$	−3.00000	+	8.48528i	−0.200000	+	0.565685i
$226$	0.398979	−	0.691053i	0.0265397	−	0.0459681i
$227$	5.44949			0.361695			0.180848	−	0.983511i	$-0.442116\pi$
$227$	5.44949			0.361695			0.180848	+	0.983511i	$0.442116\pi$
$228$	−7.00000	+	2.82843i	−0.463586	+	0.187317i
$229$	−8.89898			−0.588061			−0.294031	−	0.955796i	$-0.594997\pi$
$229$	−8.89898			−0.588061			−0.294031	+	0.955796i	$0.594997\pi$
$230$	5.00000	−	8.66025i	0.329690	−	0.571040i
$231$	−2.22474	−	1.02494i	−0.146377	−	0.0674364i
$232$	1.22474	+	2.12132i	0.0804084	+	0.139272i
$233$	−5.60102	−	3.23375i	−0.366935	−	0.211850i	0.305184	−	0.952294i	$-0.401282\pi$
$233$	−5.60102	−	3.23375i	−0.366935	−	0.211850i	−0.672119	+	0.740443i	$0.734616\pi$
$234$	7.89898	−	6.75323i	0.516372	−	0.441472i
$235$	−9.10102			−0.593685
$236$	−6.55051			−0.426402
$237$	−12.0000	+	8.48528i	−0.779484	+	0.551178i
$238$	−24.2474	+	13.9993i	−1.57173	+	0.907438i
$239$		−	7.21393i		−	0.466630i	−0.972401	−	0.233315i	$-0.925043\pi$
$239$		−	7.21393i		−	0.466630i	0.972401	−	0.233315i	$-0.0749574\pi$
$240$	−0.224745	−	2.43916i	−0.0145072	−	0.157447i
$241$	8.84847	−	5.10867i	0.569980	−	0.329078i	−0.187161	−	0.982329i	$-0.559929\pi$
$241$	8.84847	−	5.10867i	0.569980	−	0.329078i	0.757141	+	0.653251i	$0.226595\pi$
$242$	5.44949	−	9.43879i	0.350306	−	0.606749i
$243$	−12.9722	−	8.64420i	−0.832167	−	0.554526i
$244$	3.22474	−	5.58542i	0.206443	−	0.357570i
$245$	15.6742	+	9.04952i	1.00139	+	0.578153i
$246$	−5.17423	+	0.476756i	−0.329897	+	0.0303968i
$247$	10.3485	−	10.9959i	0.658457	−	0.699651i
$248$		−	4.24264i		−	0.269408i
$249$	−22.2980	−	10.2727i	−1.41308	−	0.651007i
$250$	−9.79796	−	5.65685i	−0.619677	−	0.357771i
$251$	−5.72474	+	3.30518i	−0.361343	+	0.208621i	−0.669670	−	0.742659i	$-0.733564\pi$
$251$	−5.72474	+	3.30518i	−0.361343	+	0.208621i	0.308327	+	0.951280i	$0.400231\pi$
$252$	−4.44949	+	12.5851i	−0.280292	+	0.792784i
$253$	1.12372	+	1.94635i	0.0706479	+	0.122366i
$254$			10.3923i			0.652071i
$255$	15.3485	−	1.41421i	0.961158	−	0.0885615i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	−1.55051	+	0.142865i	−0.0965306	+	0.00889436i
$259$		−	3.46410i		−	0.215249i
$260$	2.44949	+	4.24264i	0.151911	+	0.263117i
$261$	−2.44949	+	6.92820i	−0.151620	+	0.428845i
$262$	19.0732	−	11.0119i	1.17835	−	0.680319i
$263$	10.2247	+	5.90326i	0.630485	+	0.364011i	0.780940	−	0.624606i	$-0.214741\pi$
$263$	10.2247	+	5.90326i	0.630485	+	0.364011i	−0.150455	+	0.988617i	$0.548074\pi$
$264$	0.500000	+	0.230351i	0.0307729	+	0.0141771i
$265$		−	1.55708i		−	0.0956506i
$266$	−4.44949	+	18.8776i	−0.272816	+	1.15746i
$267$	−29.1464	+	2.68556i	−1.78373	+	0.164354i
$268$	5.17423	+	2.98735i	0.316067	+	0.182481i
$269$	−12.2474	+	21.2132i	−0.746740	+	1.29339i	0.202637	+	0.979254i	$0.435049\pi$
$269$	−12.2474	+	21.2132i	−0.746740	+	1.29339i	−0.949377	+	0.314138i	$0.898285\pi$
$270$	5.12372	−	5.26758i	0.311820	−	0.320575i
$271$	−12.0227	+	20.8239i	−0.730327	+	1.26496i	0.226416	+	0.974031i	$0.427299\pi$
$271$	−12.0227	+	20.8239i	−0.730327	+	1.26496i	−0.956743	+	0.290933i	$0.906034\pi$
$272$	5.44949	−	3.14626i	0.330424	−	0.190770i
$273$	−2.44949	−	26.5843i	−0.148250	−	1.60896i
$274$			7.38891i			0.446380i
$275$	0.825765	−	0.476756i	0.0497955	−	0.0287495i
$276$	10.0000	−	7.07107i	0.601929	−	0.425628i
$277$	−4.24745			−0.255204			−0.127602	−	0.991825i	$-0.540728\pi$
$277$	−4.24745			−0.255204			−0.127602	+	0.991825i	$0.540728\pi$
$278$	−0.348469			−0.0208998
$279$	9.67423	−	8.27098i	0.579181	−	0.495171i
$280$	−5.44949	−	3.14626i	−0.325669	−	0.188025i
$281$	−8.29796	−	14.3725i	−0.495015	−	0.857391i	0.504969	−	0.863138i	$-0.331504\pi$
$281$	−8.29796	−	14.3725i	−0.495015	−	0.857391i	−0.999983	+	0.00574696i	$0.998171\pi$
$282$	−10.1237	−	4.66402i	−0.602859	−	0.277738i
$283$	2.27526	−	3.94086i	0.135250	−	0.234260i	−0.790443	−	0.612536i	$-0.790150\pi$
$283$	2.27526	−	3.94086i	0.135250	−	0.234260i	0.925693	+	0.378276i	$0.123483\pi$
$284$	−6.00000			−0.356034
$285$	6.57321	−	8.41385i	0.389364	−	0.498393i
$286$	−1.10102			−0.0651047
$287$	−6.67423	+	11.5601i	−0.393968	+	0.682372i
$288$	1.00000	−	2.82843i	0.0589256	−	0.166667i
$289$	11.2980	+	19.5686i	0.664586	+	1.15110i
$290$	−3.00000	−	1.73205i	−0.176166	−	0.101710i
$291$	19.3485	−	13.6814i	1.13423	−	0.802020i
$292$	−10.7980			−0.631903
$293$	−4.65153			−0.271745			−0.135873	−	0.990726i	$-0.543384\pi$
$293$	−4.65153			−0.271745			−0.135873	+	0.990726i	$0.543384\pi$
$294$	12.7980	+	18.0990i	0.746392	+	1.05556i
$295$	8.02270	−	4.63191i	0.467100	−	0.269680i
$296$			0.778539i			0.0452517i
$297$	0.449490	+	1.58919i	0.0260820	+	0.0922139i
$298$	4.22474	−	2.43916i	0.244733	−	0.141297i
$299$	−12.2474	+	21.2132i	−0.708288	+	1.22679i
$300$	−3.00000	−	4.24264i	−0.173205	−	0.244949i
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	15.6742	+	9.04952i	0.901951	+	0.520742i
$303$	−1.57321	−	17.0741i	−0.0903788	−	0.980882i
$304$	1.00000	−	4.24264i	0.0573539	−	0.243332i
$305$			9.12096i			0.522264i
$306$	17.7980	+	6.29253i	1.01744	+	0.359720i
$307$	−3.52270	−	2.03383i	−0.201051	−	0.116077i	0.396094	−	0.918210i	$-0.370365\pi$
$307$	−3.52270	−	2.03383i	−0.201051	−	0.116077i	−0.597146	+	0.802133i	$0.703699\pi$
$308$	1.22474	−	0.707107i	0.0697863	−	0.0402911i
$309$	18.7980	+	8.66025i	1.06938	+	0.492665i
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$			15.5563i			0.882120i	0.897478	+	0.441060i	$0.145397\pi$
$311$			15.5563i			0.882120i	−0.897478	+	0.441060i	$0.854603\pi$
$312$	0.550510	+	5.97469i	0.0311665	+	0.338250i
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$	−9.34847	−	16.1920i	−0.527565	−	0.913769i
$315$	−3.44949	−	18.5597i	−0.194357	−	1.04572i
$316$		−	8.48528i		−	0.477334i
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$	0.797959	−	1.73205i	0.0447473	−	0.0971286i
$319$	0.674235	−	0.389270i	0.0377499	−	0.0217949i
$320$	1.22474	+	0.707107i	0.0684653	+	0.0395285i
$321$	−3.55051	+	7.70674i	−0.198170	+	0.430148i
$322$		−	31.4626i		−	1.75334i
$323$	26.6969	+	6.29253i	1.48546	+	0.350126i
$324$	8.39898	−	3.23375i	0.466610	−	0.179653i
$325$	9.00000	+	5.19615i	0.499230	+	0.288231i
$326$	1.82577	−	3.16232i	0.101120	−	0.175145i
$327$		0			0
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$	−24.7980	+	14.3171i	−1.36716	+	0.789328i
$330$	−0.775255	+	0.0714323i	−0.0426764	+	0.00393222i
$331$		−	14.8099i		−	0.814027i	−0.913422	−	0.407013i	$-0.866570\pi$
$331$		−	14.8099i		−	0.814027i	0.913422	−	0.407013i	$-0.133430\pi$
$332$	12.2753	−	7.08712i	0.673692	−	0.388956i
$333$	−1.77526	+	1.51775i	−0.0972834	+	0.0831724i
$334$	4.89898			0.268060
$335$	−8.44949			−0.461645
$336$	−4.44949	−	6.29253i	−0.242740	−	0.343286i
$337$	−3.15153	−	1.81954i	−0.171675	−	0.0991165i	0.411701	−	0.911319i	$-0.364935\pi$
$337$	−3.15153	−	1.81954i	−0.171675	−	0.0991165i	−0.583375	+	0.812203i	$0.698268\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	−0.578317	+	1.25529i	−0.0314099	+	0.0681783i
$340$	−4.44949	+	7.70674i	−0.241307	+	0.417957i
$341$	−1.34847			−0.0730237
$342$	11.6237	−	5.99075i	0.628539	−	0.323942i
$343$	25.7980			1.39296
$344$	0.449490	−	0.778539i	0.0242349	−	0.0419760i
$345$	−7.24745	+	15.7313i	−0.390190	+	0.846946i
$346$	−5.44949	−	9.43879i	−0.292966	−	0.507433i
$347$	5.72474	+	3.30518i	0.307320	+	0.177432i	0.645727	−	0.763569i	$-0.276555\pi$
$347$	5.72474	+	3.30518i	0.307320	+	0.177432i	−0.338406	+	0.941000i	$0.609888\pi$
$348$	−2.44949	−	3.46410i	−0.131306	−	0.185695i
$349$	−16.4949			−0.882952			−0.441476	−	0.897273i	$-0.645545\pi$
$349$	−16.4949			−0.882952			−0.441476	+	0.897273i	$0.645545\pi$
$350$	−13.3485			−0.713506
$351$	−12.5505	+	12.9029i	−0.669897	+	0.688706i
$352$	−0.275255	+	0.158919i	−0.0146711	+	0.00847039i
$353$			14.6028i			0.777231i	0.921400	+	0.388615i	$0.127046\pi$
$353$			14.6028i			0.777231i	−0.921400	+	0.388615i	$0.872954\pi$
$354$	11.2980	−	1.04100i	0.600480	−	0.0553284i
$355$	7.34847	−	4.24264i	0.390016	−	0.225176i
$356$	8.44949	−	14.6349i	0.447822	−	0.775651i
$357$	39.5959	−	27.9985i	2.09564	−	1.48184i
$358$	−11.1742	+	19.3543i	−0.590577	+	1.02291i
$359$	−20.8207	−	12.0208i	−1.09887	−	0.634434i	−0.162948	−	0.986635i	$-0.552100\pi$
$359$	−20.8207	−	12.0208i	−1.09887	−	0.634434i	−0.935925	+	0.352200i	$0.885434\pi$
$360$	0.775255	+	4.17121i	0.0408595	+	0.219842i
$361$	15.8485	−	10.4798i	0.834130	−	0.551568i
$362$		−	13.0779i		−	0.687357i
$363$	−7.89898	+	17.1455i	−0.414589	+	0.899907i
$364$	13.3485	+	7.70674i	0.699650	+	0.403943i
$365$	13.2247	−	7.63531i	0.692215	−	0.399650i
$366$	−4.67423	+	10.1459i	−0.244326	+	0.530335i
$367$	11.6742	+	20.2204i	0.609390	+	1.05549i	0.991341	+	0.131312i	$0.0419190\pi$
$367$	11.6742	+	20.2204i	0.609390	+	1.05549i	−0.381951	+	0.924183i	$0.624748\pi$
$368$			7.07107i			0.368605i
$369$	8.84847	−	1.64456i	0.460633	−	0.0856126i
$370$	−0.550510	−	0.953512i	−0.0286197	−	0.0495707i
$371$	−2.44949	−	4.24264i	−0.127171	−	0.220267i
$372$	0.674235	+	7.31747i	0.0349574	+	0.379393i
$373$		−	25.4558i		−	1.31805i	−0.752119	−	0.659027i	$-0.770968\pi$
$373$		−	25.4558i		−	1.31805i	0.752119	−	0.659027i	$-0.229032\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$	17.7980	+	8.19955i	0.919083	+	0.423423i
$376$	5.57321	−	3.21770i	0.287417	−	0.165940i
$377$	7.34847	+	4.24264i	0.378465	+	0.218507i
$378$	5.67423	−	22.4131i	0.291851	−	1.15281i
$379$			15.4135i			0.791738i	0.918307	+	0.395869i	$0.129556\pi$
$379$			15.4135i			0.791738i	−0.918307	+	0.395869i	$0.870444\pi$
$380$	1.77526	+	5.90326i	0.0910687	+	0.302831i
$381$	−1.65153	−	17.9241i	−0.0846105	−	0.918278i
$382$	−16.8990	−	9.75663i	−0.864627	−	0.499193i
$383$	7.77526	−	13.4671i	0.397297	−	0.688139i	−0.596094	−	0.802914i	$-0.703282\pi$
$383$	7.77526	−	13.4671i	0.397297	−	0.688139i	0.993391	+	0.114776i	$0.0366150\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$	−7.65153	+	4.41761i	−0.389453	+	0.224851i
$387$	2.65153	−	0.492810i	0.134785	−	0.0250509i
$388$			13.6814i			0.694570i
$389$	−22.8990	+	13.2207i	−1.16102	+	0.670318i	−0.951549	−	0.307496i	$-0.900509\pi$
$389$	−22.8990	+	13.2207i	−1.16102	+	0.670318i	−0.209475	+	0.977814i	$0.567176\pi$
$390$	−4.89898	−	6.92820i	−0.248069	−	0.350823i
$391$	−44.4949			−2.25020
$392$	−12.7980			−0.646395
$393$	−31.1464	+	22.0239i	−1.57113	+	1.11096i
$394$	0.426786	+	0.246405i	0.0215012	+	0.0124137i
$395$	6.00000	+	10.3923i	0.301893	+	0.522894i
$396$	−0.898979	−	0.317837i	−0.0451754	−	0.0159719i
$397$	−4.67423	+	8.09601i	−0.234593	+	0.406327i	−0.959154	−	0.282883i	$-0.908709\pi$
$397$	−4.67423	+	8.09601i	−0.234593	+	0.406327i	0.724561	+	0.689210i	$0.242042\pi$
$398$	−6.89898			−0.345815
$399$	4.67423	−	33.2661i	0.234004	−	1.66539i
$400$	3.00000			0.150000
$401$	6.39898	−	11.0834i	0.319550	−	0.553476i	−0.660844	−	0.750523i	$-0.729802\pi$
$401$	6.39898	−	11.0834i	0.319550	−	0.553476i	0.980394	+	0.197047i	$0.0631350\pi$
$402$	−9.39898	−	4.33013i	−0.468778	−	0.215967i
$403$	−7.34847	−	12.7279i	−0.366053	−	0.634023i
$404$	8.57321	+	4.94975i	0.426533	+	0.246259i
$405$	−8.00000	+	9.89949i	−0.397523	+	0.491910i
$406$	−10.8990			−0.540907
$407$	0.247449			0.0122656
$408$	−8.89898	+	6.29253i	−0.440565	+	0.311527i
$409$	17.8485	−	10.3048i	0.882550	−	0.509540i	0.0110517	−	0.999939i	$-0.496482\pi$
$409$	17.8485	−	10.3048i	0.882550	−	0.509540i	0.871498	+	0.490398i	$0.163149\pi$
$410$			4.24264i			0.209529i
$411$	−1.17423	−	12.7440i	−0.0579207	−	0.628614i
$412$	−10.3485	+	5.97469i	−0.509832	+	0.294352i
$413$	14.5732	−	25.2415i	0.717101	−	1.24206i
$414$	−16.1237	+	13.7850i	−0.792438	+	0.677495i
$415$	−10.0227	+	17.3598i	−0.491995	+	0.852161i
$416$	−3.00000	−	1.73205i	−0.147087	−	0.0849208i
$417$	0.601021	−	0.0553782i	0.0294321	−	0.00271188i
$418$	−1.34847	−	0.317837i	−0.0659558	−	0.0155459i
$419$		−	3.74983i		−	0.183191i	−0.995796	−	0.0915956i	$-0.970803\pi$
$419$		−	3.74983i		−	0.183191i	0.995796	−	0.0915956i	$-0.0291967\pi$
$420$	9.89898	+	4.56048i	0.483021	+	0.222529i
$421$	−26.0227	−	15.0242i	−1.26827	−	0.732235i	−0.293609	−	0.955926i	$-0.594856\pi$
$421$	−26.0227	−	15.0242i	−1.26827	−	0.732235i	−0.974660	+	0.223690i	$0.928190\pi$
$422$	13.3485	−	7.70674i	0.649793	−	0.375158i
$423$	18.2020	+	6.43539i	0.885014	+	0.312900i
$424$	0.550510	+	0.953512i	0.0267351	+	0.0463066i
$425$			18.8776i			0.915697i
$426$	10.3485	−	0.953512i	0.501385	−	0.0461978i
$427$	14.3485	+	24.8523i	0.694371	+	1.20269i
$428$	−2.44949	−	4.24264i	−0.118401	−	0.205076i
$429$	1.89898	−	0.174973i	0.0916836	−	0.00844776i
$430$			1.27135i			0.0613099i
$431$	16.3485	+	28.3164i	0.787478	+	1.36395i	0.927507	+	0.373805i	$0.121947\pi$
$431$	16.3485	+	28.3164i	0.787478	+	1.36395i	−0.140029	+	0.990147i	$0.544720\pi$
$432$	−1.27526	+	5.03723i	−0.0613557	+	0.242354i
$433$	11.6969	−	6.75323i	0.562119	−	0.324540i	−0.191877	−	0.981419i	$-0.561457\pi$
$433$	11.6969	−	6.75323i	0.562119	−	0.324540i	0.753996	+	0.656880i	$0.228124\pi$
$434$	16.3485	+	9.43879i	0.784752	+	0.453077i
$435$	5.44949	+	2.51059i	0.261283	+	0.120374i
$436$		0			0
$437$	−21.1237	+	22.4452i	−1.01048	+	1.07370i
$438$	18.6237	−	1.71600i	0.889876	−	0.0819935i
$439$	−2.32577	−	1.34278i	−0.111003	−	0.0640875i	0.443471	−	0.896289i	$-0.353747\pi$
$439$	−2.32577	−	1.34278i	−0.111003	−	0.0640875i	−0.554474	+	0.832201i	$0.687080\pi$
$440$	0.224745	−	0.389270i	0.0107143	−	0.0185577i
$441$	−24.9495	−	29.1824i	−1.18807	−	1.38964i
$442$	10.8990	−	18.8776i	0.518412	−	0.897915i
$443$	25.3207	−	14.6189i	1.20302	−	0.694564i	0.241795	−	0.970327i	$-0.422264\pi$
$443$	25.3207	−	14.6189i	1.20302	−	0.694564i	0.961226	+	0.275763i	$0.0889304\pi$
$444$	−0.123724	−	1.34278i	−0.00587170	−	0.0637256i
$445$			23.8988i			1.13291i
$446$	−8.32577	+	4.80688i	−0.394236	+	0.227613i
$447$	−6.89898	+	4.87832i	−0.326311	+	0.230736i
$448$	4.44949			0.210219
$449$	11.2020			0.528657			0.264329	−	0.964433i	$-0.414850\pi$
$449$	11.2020			0.528657			0.264329	+	0.964433i	$0.414850\pi$
$450$	5.84847	+	6.84072i	0.275699	+	0.322474i
$451$	−0.825765	−	0.476756i	−0.0388838	−	0.0224496i
$452$	−0.398979	−	0.691053i	−0.0187664	−	0.0325044i
$453$	−28.4722	−	13.1172i	−1.33774	−	0.616299i
$454$	2.72474	−	4.71940i	0.127879	−	0.221492i
$455$	−21.7980			−1.02190
$456$	−1.05051	+	7.47639i	−0.0491947	+	0.350114i
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	−4.44949	+	7.70674i	−0.207911	+	0.360112i
$459$	−31.6969	−	8.02458i	−1.47949	−	0.374555i
$460$	−5.00000	−	8.66025i	−0.233126	−	0.403786i
$461$	−8.75255	−	5.05329i	−0.407647	−	0.235355i	0.282131	−	0.959376i	$-0.408959\pi$
$461$	−8.75255	−	5.05329i	−0.407647	−	0.235355i	−0.689778	+	0.724021i	$0.742292\pi$
$462$	−2.00000	+	1.41421i	−0.0930484	+	0.0657952i
$463$	−0.202041			−0.00938964			−0.00469482	−	0.999989i	$-0.501494\pi$
$463$	−0.202041			−0.00938964			−0.00469482	+	0.999989i	$0.501494\pi$
$464$	2.44949			0.113715
$465$	−6.00000	−	8.48528i	−0.278243	−	0.393496i
$466$	−5.60102	+	3.23375i	−0.259462	+	0.149801i
$467$		−	32.4162i		−	1.50004i	−0.661415	−	0.750020i	$-0.730044\pi$
$467$		−	32.4162i		−	1.50004i	0.661415	−	0.750020i	$-0.269956\pi$
$468$	−1.89898	−	10.2173i	−0.0877804	−	0.472296i
$469$	−23.0227	+	13.2922i	−1.06309	+	0.613775i
$470$	−4.55051	+	7.88171i	−0.209899	+	0.363556i
$471$	18.6969	+	26.4415i	0.861509	+	1.21836i
$472$	−3.27526	+	5.67291i	−0.150756	+	0.261117i
$473$	−0.247449	−	0.142865i	−0.0113777	−	0.00656892i
$474$	1.34847	+	14.6349i	0.0619372	+	0.672205i
$475$	9.52270	+	8.96204i	0.436932	+	0.411206i
$476$			27.9985i			1.28331i
$477$	−1.10102	+	3.11416i	−0.0504123	+	0.142587i
$478$	−6.24745	−	3.60697i	−0.285752	−	0.164979i
$479$	35.1464	−	20.2918i	1.60588	−	0.927156i	0.615603	−	0.788057i	$-0.288913\pi$
$479$	35.1464	−	20.2918i	1.60588	−	0.927156i	0.990278	−	0.139099i	$-0.0444208\pi$
$480$	−2.22474	−	1.02494i	−0.101545	−	0.0467821i
$481$	1.34847	+	2.33562i	0.0614849	+	0.106495i
$482$		−	10.2173i		−	0.465387i
$483$	5.00000	+	54.2650i	0.227508	+	2.46914i
$484$	−5.44949	−	9.43879i	−0.247704	−	0.429036i
$485$	−9.67423	−	16.7563i	−0.439284	−	0.760863i
$486$	−13.9722	+	6.91215i	−0.633792	+	0.313541i
$487$		−	16.5420i		−	0.749588i	−0.927108	−	0.374794i	$-0.877713\pi$
$487$		−	16.5420i		−	0.749588i	0.927108	−	0.374794i	$-0.122287\pi$
$488$	−3.22474	−	5.58542i	−0.145977	−	0.252840i
$489$	−2.64643	+	5.74434i	−0.119676	+	0.259768i
$490$	15.6742	−	9.04952i	0.708090	−	0.408816i
$491$	−4.10102	−	2.36773i	−0.185076	−	0.106854i	0.404599	−	0.914494i	$-0.367411\pi$
$491$	−4.10102	−	2.36773i	−0.185076	−	0.106854i	−0.589676	+	0.807640i	$0.700744\pi$
$492$	−2.17423	+	4.71940i	−0.0980221	+	0.212767i
$493$			15.4135i			0.694188i
$494$	−4.34847	−	14.4600i	−0.195647	−	0.650585i
$495$	1.32577	−	0.246405i	0.0595887	−	0.0110751i
$496$	−3.67423	−	2.12132i	−0.164978	−	0.0952501i
$497$	13.3485	−	23.1202i	0.598761	−	1.03708i
$498$	−20.0454	+	14.1742i	−0.898256	+	0.635163i
$499$	−1.27526	+	2.20881i	−0.0570883	+	0.0988798i	−0.893157	−	0.449745i	$-0.851515\pi$
$499$	−1.27526	+	2.20881i	−0.0570883	+	0.0988798i	0.836069	+	0.548624i	$0.184848\pi$
$500$	−9.79796	+	5.65685i	−0.438178	+	0.252982i
$501$	−8.44949	+	0.778539i	−0.377495	+	0.0347826i
$502$			6.61037i			0.295035i
$503$	13.4722	−	7.77817i	0.600695	−	0.346812i	−0.168620	−	0.985681i	$-0.553931\pi$
$503$	13.4722	−	7.77817i	0.600695	−	0.346812i	0.769315	+	0.638870i	$0.220598\pi$
$504$	8.67423	+	10.1459i	0.386381	+	0.451934i
$505$	−14.0000			−0.622992
$506$	2.24745			0.0999113
$507$	−1.00000	−	1.41421i	−0.0444116	−	0.0628074i
$508$	9.00000	+	5.19615i	0.399310	+	0.230542i
$509$	−20.6969	−	35.8481i	−0.917376	−	1.58894i	−0.803385	−	0.595459i	$-0.796970\pi$
$509$	−20.6969	−	35.8481i	−0.917376	−	1.58894i	−0.113990	−	0.993482i	$-0.536363\pi$
$510$	6.44949	−	13.9993i	0.285588	−	0.619898i
$511$	24.0227	−	41.6085i	1.06270	−	1.84065i
$512$	−1.00000			−0.0441942
$513$	−19.0959	+	12.1797i	−0.843105	+	0.537748i
$514$	−15.0000			−0.661622
$515$	8.44949	−	14.6349i	0.372329	−	0.644893i
$516$	−0.651531	+	1.41421i	−0.0286820	+	0.0622573i
$517$	−1.02270	−	1.77138i	−0.0449785	−	0.0779050i
$518$	−3.00000	−	1.73205i	−0.131812	−	0.0761019i
$519$	10.8990	+	15.4135i	0.478412	+	0.676577i
$520$	4.89898			0.214834
$521$	−16.1010			−0.705399			−0.352699	−	0.935737i	$-0.614736\pi$
$521$	−16.1010			−0.705399			−0.352699	+	0.935737i	$0.614736\pi$
$522$	4.77526	+	5.58542i	0.209007	+	0.244467i
$523$	23.6969	−	13.6814i	1.03619	−	0.598247i	0.117442	−	0.993080i	$-0.462531\pi$
$523$	23.6969	−	13.6814i	1.03619	−	0.598247i	0.918753	+	0.394832i	$0.129197\pi$
$524$		−	22.0239i		−	0.962116i
$525$	23.0227	−	2.12132i	1.00479	−	0.0925820i
$526$	10.2247	−	5.90326i	0.445820	−	0.257394i
$527$	13.3485	−	23.1202i	0.581468	−	1.00713i
$528$	0.449490	−	0.317837i	0.0195615	−	0.0138321i
$529$	13.5000	−	23.3827i	0.586957	−	1.01664i
$530$	−1.34847	−	0.778539i	−0.0585738	−	0.0338176i
$531$	−19.3207	+	3.59091i	−0.838445	+	0.155832i
$532$	14.1237	+	13.2922i	0.612341	+	0.576288i
$533$		−	10.3923i		−	0.450141i
$534$	−12.2474	+	26.5843i	−0.529999	+	1.15042i
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	5.17423	−	2.98735i	0.223493	−	0.129034i
$537$	16.1969	−	35.1571i	0.698949	−	1.51714i
$538$	12.2474	+	21.2132i	0.528025	+	0.914566i
$539$			4.06767i			0.175207i
$540$	−2.00000	−	7.07107i	−0.0860663	−	0.304290i
$541$	9.34847	+	16.1920i	0.401922	+	0.696149i	0.993958	−	0.109762i	$-0.0350089\pi$
$541$	9.34847	+	16.1920i	0.401922	+	0.696149i	−0.592036	+	0.805912i	$0.701676\pi$
$542$	12.0227	+	20.8239i	0.516419	+	0.894465i
$543$	2.07832	+	22.5560i	0.0891891	+	0.967970i
$544$		−	6.29253i		−	0.269790i
$545$		0			0
$546$	−24.2474	−	11.1708i	−1.03770	−	0.478068i
$547$	26.3939	−	15.2385i	1.12852	−	0.651552i	0.184958	−	0.982746i	$-0.440785\pi$
$547$	26.3939	−	15.2385i	1.12852	−	0.651552i	0.943562	+	0.331195i	$0.107452\pi$
$548$	6.39898	+	3.69445i	0.273351	+	0.157819i
$549$	6.44949	−	18.2419i	0.275258	−	0.778546i
$550$		−	0.953512i		−	0.0406579i
$551$	7.77526	+	7.31747i	0.331237	+	0.311735i
$552$	−1.12372	−	12.1958i	−0.0478289	−	0.519087i
$553$	32.6969	+	18.8776i	1.39042	+	0.802757i
$554$	−2.12372	+	3.67840i	−0.0902284	+	0.156280i
$555$	1.10102	+	1.55708i	0.0467357	+	0.0660943i
$556$	−0.174235	+	0.301783i	−0.00738919	+	0.0127985i
$557$	−24.2474	+	13.9993i	−1.02740	+	0.593168i	−0.916238	−	0.400634i	$-0.868790\pi$
$557$	−24.2474	+	13.9993i	−1.02740	+	0.593168i	−0.111159	+	0.993803i	$0.535456\pi$
$558$	−2.32577	−	12.5136i	−0.0984575	−	0.529744i
$559$		−	3.11416i		−	0.131715i
$560$	−5.44949	+	3.14626i	−0.230283	+	0.132954i
$561$	2.00000	+	2.82843i	0.0844401	+	0.119416i
$562$	−16.5959			−0.700057
$563$	−22.8434			−0.962733			−0.481367	−	0.876519i	$-0.659859\pi$
$563$	−22.8434			−0.962733			−0.481367	+	0.876519i	$0.659859\pi$
$564$	−9.10102	+	6.43539i	−0.383222	+	0.270979i
$565$	0.977296	+	0.564242i	0.0411152	+	0.0237378i
$566$	−2.27526	−	3.94086i	−0.0956361	−	0.165647i
$567$	−6.22474	+	39.5587i	−0.261415	+	1.66131i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	34.2929			1.43763			0.718816	−	0.695201i	$-0.244685\pi$
$569$	34.2929			1.43763			0.718816	+	0.695201i	$0.244685\pi$
$570$	−4.00000	−	9.89949i	−0.167542	−	0.414644i
$571$	−11.0454			−0.462236			−0.231118	−	0.972926i	$-0.574238\pi$
$571$	−11.0454			−0.462236			−0.231118	+	0.972926i	$0.574238\pi$
$572$	−0.550510	+	0.953512i	−0.0230180	+	0.0398683i
$573$	30.6969	+	14.1421i	1.28238	+	0.590796i
$574$	6.67423	+	11.5601i	0.278577	+	0.482510i
$575$	−18.3712	−	10.6066i	−0.766131	−	0.442326i
$576$	−1.94949	−	2.28024i	−0.0812287	−	0.0950100i
$577$	−20.5959			−0.857419			−0.428710	−	0.903442i	$-0.641032\pi$
$577$	−20.5959			−0.857419			−0.428710	+	0.903442i	$0.641032\pi$
$578$	22.5959			0.939866
$579$	12.4949	−	8.83523i	0.519270	−	0.367179i
$580$	−3.00000	+	1.73205i	−0.124568	+	0.0719195i
$581$			63.0682i			2.61651i
$582$	−2.17423	−	23.5970i	−0.0901249	−	0.978126i
$583$	0.303062	−	0.174973i	0.0125515	−	0.00724663i
$584$	−5.39898	+	9.35131i	−0.223411	+	0.386960i
$585$	9.55051	+	11.1708i	0.394865	+	0.461858i
$586$	−2.32577	+	4.02834i	−0.0960765	+	0.166409i
$587$	−4.10102	−	2.36773i	−0.169267	−	0.0977265i	0.412973	−	0.910743i	$-0.364490\pi$
$587$	−4.10102	−	2.36773i	−0.169267	−	0.0977265i	−0.582240	+	0.813017i	$0.697824\pi$
$588$	22.0732	−	2.03383i	0.910284	−	0.0838739i
$589$	−5.32577	−	17.7098i	−0.219444	−	0.729719i
$590$		−	9.26382i		−	0.381385i
$591$	−0.775255	−	0.357161i	−0.0318897	−	0.0146917i
$592$	0.674235	+	0.389270i	0.0277109	+	0.0159989i
$593$	−24.0959	+	13.9118i	−0.989501	+	0.571289i	−0.905125	−	0.425145i	$-0.860223\pi$
$593$	−24.0959	+	13.9118i	−0.989501	+	0.571289i	−0.0843757	+	0.996434i	$0.526890\pi$
$594$	1.60102	+	0.405324i	0.0656907	+	0.0166306i
$595$	−19.7980	−	34.2911i	−0.811637	−	1.40580i
$596$		−	4.87832i		−	0.199824i
$597$	11.8990	−	1.09638i	0.486993	−	0.0448717i
$598$	12.2474	+	21.2132i	0.500835	+	0.867472i
$599$	14.5732	+	25.2415i	0.595445	+	1.03134i	0.993484	+	0.113973i	$0.0363577\pi$
$599$	14.5732	+	25.2415i	0.595445	+	1.03134i	−0.398038	+	0.917369i	$0.630309\pi$
$600$	−5.17423	+	0.476756i	−0.211237	+	0.0194635i
$601$			31.0019i			1.26460i	0.774725	+	0.632298i	$0.217888\pi$
$601$			31.0019i			1.26460i	−0.774725	+	0.632298i	$0.782112\pi$
$602$	2.00000	+	3.46410i	0.0815139	+	0.141186i
$603$	16.8990	+	5.97469i	0.688180	+	0.243308i
$604$	15.6742	−	9.04952i	0.637776	−	0.368220i
$605$	13.3485	+	7.70674i	0.542692	+	0.313324i
$606$	−15.5732	−	7.17461i	−0.632619	−	0.291449i
$607$		−	36.9766i		−	1.50084i	−0.660964	−	0.750418i	$-0.729852\pi$
$607$		−	36.9766i		−	1.50084i	0.660964	−	0.750418i	$-0.270148\pi$
$608$	−3.17423	−	2.98735i	−0.128732	−	0.121153i
$609$	18.7980	−	1.73205i	0.761732	−	0.0701862i
$610$	7.89898	+	4.56048i	0.319820	+	0.184648i
$611$	11.1464	−	19.3062i	0.450936	−	0.781044i
$612$	14.3485	−	12.2672i	0.580002	−	0.495873i
$613$	−14.1010	+	24.4237i	−0.569535	+	0.986463i	0.427077	+	0.904215i	$0.359543\pi$
$613$	−14.1010	+	24.4237i	−0.569535	+	0.986463i	−0.996612	+	0.0822481i	$0.973790\pi$
$614$	−3.52270	+	2.03383i	−0.142165	+	0.0820789i
$615$	−0.674235	−	7.31747i	−0.0271878	−	0.295069i
$616$		−	1.41421i		−	0.0569803i
$617$	12.9495	−	7.47639i	0.521327	−	0.300988i	−0.216151	−	0.976360i	$-0.569350\pi$
$617$	12.9495	−	7.47639i	0.521327	−	0.300988i	0.737477	+	0.675372i	$0.236017\pi$
$618$	16.8990	−	11.9494i	0.679777	−	0.480675i
$619$	−1.30306			−0.0523745			−0.0261872	−	0.999657i	$-0.508337\pi$
$619$	−1.30306			−0.0523745			−0.0261872	+	0.999657i	$0.508337\pi$
$620$	6.00000			0.240966
$621$	25.6186	−	26.3379i	1.02804	−	1.05690i
$622$	13.4722	+	7.77817i	0.540186	+	0.311876i
$623$	37.5959	+	65.1180i	1.50625	+	2.60890i
$624$	5.44949	+	2.51059i	0.218154	+	0.100504i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	19.0000			0.759393
$627$	2.37628	+	0.333891i	0.0948993	+	0.0133343i
$628$	−18.6969			−0.746089
$629$	−2.44949	+	4.24264i	−0.0976676	+	0.169165i
$630$	−17.7980	−	6.29253i	−0.709088	−	0.250700i
$631$	4.87628	+	8.44596i	0.194121	+	0.336228i	0.946612	−	0.322375i	$-0.104481\pi$
$631$	4.87628	+	8.44596i	0.194121	+	0.336228i	−0.752491	+	0.658603i	$0.771148\pi$
$632$	−7.34847	−	4.24264i	−0.292306	−	0.168763i
$633$	−21.7980	+	15.4135i	−0.866391	+	0.612631i
$634$	−6.00000			−0.238290
$635$	−14.6969			−0.583230
$636$	−1.10102	−	1.55708i	−0.0436583	−	0.0617422i
$637$	−38.3939	+	22.1667i	−1.52122	+	0.878277i
$638$		−	0.778539i		−	0.0308227i
$639$	−17.6969	+	3.28913i	−0.700080	+	0.130116i
$640$	1.22474	−	0.707107i	0.0484123	−	0.0279508i
$641$	16.1969	−	28.0539i	0.639741	−	1.10806i	−0.345749	−	0.938327i	$-0.612375\pi$
$641$	16.1969	−	28.0539i	0.639741	−	1.10806i	0.985490	−	0.169736i	$-0.0542916\pi$
$642$	4.89898	+	6.92820i	0.193347	+	0.273434i
$643$	12.0732	−	20.9114i	0.476121	−	0.824666i	−0.523505	−	0.852023i	$-0.675376\pi$
$643$	12.0732	−	20.9114i	0.476121	−	0.824666i	0.999626	+	0.0273569i	$0.00870906\pi$
$644$	−27.2474	−	15.7313i	−1.07370	−	0.619901i
$645$	−0.202041	−	2.19275i	−0.00795536	−	0.0863396i
$646$	18.7980	−	19.9740i	0.739596	−	0.785865i
$647$			7.84961i			0.308600i	0.988024	+	0.154300i	$0.0493122\pi$
$647$			7.84961i			0.308600i	−0.988024	+	0.154300i	$0.950688\pi$
$648$	1.39898	−	8.89060i	0.0549571	−	0.349256i
$649$	1.80306	+	1.04100i	0.0707764	+	0.0408627i
$650$	9.00000	−	5.19615i	0.353009	−	0.203810i
$651$	−29.6969	−	13.6814i	−1.16391	−	0.536218i
$652$	−1.82577	−	3.16232i	−0.0715025	−	0.123846i
$653$		−	19.5133i		−	0.763613i	−0.924242	−	0.381806i	$-0.875302\pi$
$653$		−	19.5133i		−	0.763613i	0.924242	−	0.381806i	$-0.124698\pi$
$654$		0			0
$655$	15.5732	+	26.9736i	0.608496	+	1.05395i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$	−31.8485	+	5.91931i	−1.24253	+	0.230934i
$658$			28.6342i			1.11628i
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$	−0.325765	+	0.707107i	−0.0126804	+	0.0275241i
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.908360	−	0.418189i	$-0.862665\pi$
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.0920180	+	0.995757i	$0.529332\pi$
$662$	−12.8258	−	7.40496i	−0.498488	−	0.287802i
$663$	−15.7980	+	34.2911i	−0.613542	+	1.33175i
$664$		−	14.1742i		−	0.550067i
$665$	−26.6969	−	6.29253i	−1.03526	−	0.244014i
$666$	0.426786	+	2.29629i	0.0165376	+	0.0889795i
$667$	−15.0000	−	8.66025i	−0.580802	−	0.335326i
$668$	2.44949	−	4.24264i	0.0947736	−	0.164153i
$669$	13.5959	−	9.61377i	0.525649	−	0.371690i
$670$	−4.22474	+	7.31747i	−0.163216	+	0.282699i
$671$	−1.77526	+	1.02494i	−0.0685330	+	0.0395675i
$672$	−7.67423	+	0.707107i	−0.296040	+	0.0272772i
$673$		−	3.46410i		−	0.133531i	−0.997769	−	0.0667657i	$-0.978732\pi$
$673$		−	3.46410i		−	0.133531i	0.997769	−	0.0667657i	$-0.0212680\pi$
$674$	−3.15153	+	1.81954i	−0.121392	+	0.0700860i
$675$	−11.1742	−	10.8691i	−0.430096	−	0.418350i
$676$	1.00000			0.0384615
$677$	−3.30306			−0.126947			−0.0634735	−	0.997984i	$-0.520218\pi$
$677$	−3.30306			−0.126947			−0.0634735	+	0.997984i	$0.520218\pi$
$678$	0.797959	+	1.12848i	0.0306454	+	0.0433392i
$679$	−52.7196	−	30.4377i	−2.02319	−	1.16809i
$680$	4.44949	+	7.70674i	0.170630	+	0.295540i
$681$	−3.94949	+	8.57277i	−0.151345	+	0.328509i
$682$	−0.674235	+	1.16781i	−0.0258178	+	0.0447177i
$683$	−41.3939			−1.58389			−0.791946	−	0.610591i	$-0.790932\pi$
$683$	−41.3939			−1.58389			−0.791946	+	0.610591i	$0.790932\pi$
$684$	0.623724	−	13.0618i	0.0238487	−	0.499431i
$685$	−10.4495			−0.399254
$686$	12.8990	−	22.3417i	0.492485	−	0.853010i
$687$	6.44949	−	13.9993i	0.246063	−	0.534106i
$688$	−0.449490	−	0.778539i	−0.0171366	−	0.0296815i
$689$	3.30306	+	1.90702i	0.125837	+	0.0726518i
$690$	10.0000	+	14.1421i	0.380693	+	0.538382i
$691$	−40.0000			−1.52167			−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000			−1.52167			−0.760836	+	0.648944i	$0.775211\pi$
$692$	−10.8990			−0.414317
$693$	3.22474	−	2.75699i	0.122498	−	0.104730i
$694$	5.72474	−	3.30518i	0.217308	−	0.125463i
$695$		−	0.492810i		−	0.0186933i
$696$	−4.22474	+	0.389270i	−0.160139	+	0.0147552i
$697$	16.3485	−	9.43879i	0.619242	−	0.357520i
$698$	−8.24745	+	14.2850i	−0.312171	+	0.540695i
$699$	9.14643	−	6.46750i	0.345950	−	0.244623i
$700$	−6.67423	+	11.5601i	−0.252262	+	0.436931i
$701$	8.57321	+	4.94975i	0.323806	+	0.186949i	0.653088	−	0.757282i	$-0.273473\pi$
$701$	8.57321	+	4.94975i	0.323806	+	0.186949i	−0.329282	+	0.944232i	$0.606807\pi$
$702$	4.89898	+	17.3205i	0.184900	+	0.653720i
$703$	0.977296	+	3.24980i	0.0368594	+	0.122569i
$704$			0.317837i			0.0119789i
$705$	6.59592	−	14.3171i	0.248417	−	0.539213i
$706$	12.6464	+	7.30142i	0.475955	+	0.274793i
$707$	−38.1464	+	22.0239i	−1.43464	+	0.828292i
$708$	4.74745	−	10.3048i	0.178420	−	0.387279i
$709$	1.32577	+	2.29629i	0.0497902	+	0.0862391i	0.889846	−	0.456260i	$-0.150811\pi$
$709$	1.32577	+	2.29629i	0.0497902	+	0.0862391i	−0.840056	+	0.542499i	$0.817478\pi$
$710$		−	8.48528i		−	0.318447i
$711$	−4.65153	−	25.0273i	−0.174446	−	0.938595i
$712$	−8.44949	−	14.6349i	−0.316658	−	0.548468i
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$	−4.44949	−	48.2903i	−0.166518	−	1.80722i
$715$		−	1.55708i		−	0.0582314i
$716$	11.1742	+	19.3543i	0.417601	+	0.723306i
$717$	11.3485	+	5.22826i	0.423816	+	0.195253i
$718$	−20.8207	+	12.0208i	−0.777020	+	0.448613i
$719$	−8.14643	−	4.70334i	−0.303811	−	0.175405i	0.340343	−	0.940301i	$-0.389457\pi$
$719$	−8.14643	−	4.70334i	−0.303811	−	0.175405i	−0.644153	+	0.764896i	$0.722790\pi$
$720$	4.00000	+	1.41421i	0.149071	+	0.0527046i
$721$		−	53.1687i		−	1.98010i
$722$	−1.15153	−	18.9651i	−0.0428555	−	0.705807i
$723$	1.62372	+	17.6223i	0.0603870	+	0.655380i
$724$	−11.3258	−	6.53893i	−0.420919	−	0.243018i
$725$	−3.67423	+	6.36396i	−0.136458	+	0.236352i
$726$	10.8990	+	15.4135i	0.404499	+	0.572048i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	13.3485	−	7.70674i	0.494727	−	0.285631i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		−	15.2706i		−	0.565191i
$731$	4.89898	−	2.82843i	0.181195	−	0.104613i
$732$	6.44949	+	9.12096i	0.238380	+	0.337120i
$733$	24.0454			0.888137			0.444069	−	0.895993i	$-0.353535\pi$
$733$	24.0454			0.888137			0.444069	+	0.895993i	$0.353535\pi$
$734$	23.3485			0.861808
$735$	−25.5959	+	18.0990i	−0.944120	+	0.667593i
$736$	6.12372	+	3.53553i	0.225723	+	0.130322i
$737$	−0.949490	−	1.64456i	−0.0349749	−	0.0605783i
$738$	3.00000	−	8.48528i	0.110432	−	0.312348i
$739$	−4.82577	+	8.35847i	−0.177519	+	0.307471i	−0.941030	−	0.338323i	$-0.890140\pi$
$739$	−4.82577	+	8.35847i	−0.177519	+	0.307471i	0.763511	+	0.645794i	$0.223474\pi$
$740$	−1.10102			−0.0404743
$741$	9.79796	+	24.2487i	0.359937	+	0.890799i
$742$	−4.89898			−0.179847
$743$	−9.67423	+	16.7563i	−0.354913	+	0.614728i	−0.987103	−	0.160086i	$-0.948823\pi$
$743$	−9.67423	+	16.7563i	−0.354913	+	0.614728i	0.632190	+	0.774814i	$0.282156\pi$
$744$	6.67423	+	3.07483i	0.244689	+	0.112729i
$745$	3.44949	+	5.97469i	0.126380	+	0.218896i
$746$	−22.0454	−	12.7279i	−0.807140	−	0.466002i
$747$	32.3207	−	27.6325i	1.18255	−	1.01102i
$748$	−2.00000			−0.0731272
$749$	21.7980			0.796480
$750$	16.0000	−	11.3137i	0.584237	−	0.413118i
$751$	−11.6969	+	6.75323i	−0.426827	+	0.246429i	−0.697994	−	0.716103i	$-0.745924\pi$
$751$	−11.6969	+	6.75323i	−0.426827	+	0.246429i	0.271167	+	0.962532i	$0.412591\pi$
$752$		−	6.43539i		−	0.234675i
$753$	−1.05051	−	11.4012i	−0.0382827	−	0.415483i
$754$	7.34847	−	4.24264i	0.267615	−	0.154508i
$755$	−12.7980	+	22.1667i	−0.465765	+	0.806729i
$756$	−16.5732	−	16.1206i	−0.602762	−	0.586300i
$757$	−9.69694	+	16.7956i	−0.352441	+	0.610446i	−0.986677	−	0.162694i	$-0.947982\pi$
$757$	−9.69694	+	16.7956i	−0.352441	+	0.610446i	0.634235	+	0.773140i	$0.281315\pi$
$758$	13.3485	+	7.70674i	0.484838	+	0.279921i
$759$	−3.87628	+	0.357161i	−0.140700	+	0.0129641i
$760$	6.00000	+	1.41421i	0.217643	+	0.0512989i
$761$			41.9657i			1.52126i	0.649188	+	0.760628i	$0.275109\pi$
$761$			41.9657i			1.52126i	−0.649188	+	0.760628i	$0.724891\pi$
$762$	−16.3485	−	7.53177i	−0.592243	−	0.272847i
$763$		0			0
$764$	−16.8990	+	9.75663i	−0.611384	+	0.352982i
$765$	−8.89898	+	25.1701i	−0.321743	+	0.910027i
$766$	−7.77526	−	13.4671i	−0.280931	−	0.486587i
$767$			22.6916i			0.819347i
$768$	1.72474	−	0.158919i	0.0622364	−	0.00573448i
$769$	17.7980	+	30.8270i	0.641811	+	1.11165i	0.985028	+	0.172393i	$0.0551499\pi$
$769$	17.7980	+	30.8270i	0.641811	+	1.11165i	−0.343217	+	0.939256i	$0.611517\pi$
$770$	1.00000	+	1.73205i	0.0360375	+	0.0624188i
$771$	25.8712	−	2.38378i	0.931728	−	0.0858497i
$772$			8.83523i			0.317987i
$773$	1.22474	+	2.12132i	0.0440510	+	0.0762986i	0.887210	−	0.461365i	$-0.152640\pi$
$773$	1.22474	+	2.12132i	0.0440510	+	0.0762986i	−0.843159	+	0.537664i	$0.819307\pi$
$774$	0.898979	−	2.54270i	0.0323132	−	0.0913954i
$775$	11.0227	−	6.36396i	0.395947	−	0.228600i
$776$	11.8485	+	6.84072i	0.425335	+	0.245567i
$777$	5.44949	+	2.51059i	0.195499	+	0.0900669i
$778$			26.4415i			0.947972i
$779$	3.00000	−	12.7279i	0.107486	−	0.456025i
$780$	−8.44949	+	0.778539i	−0.302540	+	0.0278762i
$781$	1.65153	+	0.953512i	0.0590964	+	0.0341193i
$782$	−22.2474	+	38.5337i	−0.795567	+	1.37796i
$783$	−9.12372	−	8.87455i	−0.326055	−	0.317151i
$784$	−6.39898	+	11.0834i	−0.228535	+	0.395834i
$785$	22.8990	−	13.2207i	0.817300	−	0.471868i
$786$	3.50000	+	37.9855i	0.124841	+	1.35490i
$787$			17.9241i			0.638924i	0.947599	+	0.319462i	$0.103502\pi$
$787$			17.9241i			0.638924i	−0.947599	+	0.319462i	$0.896498\pi$
$788$	0.426786	−	0.246405i	0.0152036	−	0.00877781i
$789$	−16.6969	+	11.8065i	−0.594427	+	0.420323i
$790$	12.0000			0.426941
$791$	3.55051			0.126242
$792$	−0.724745	+	0.619620i	−0.0257527	+	0.0220173i
$793$	−19.3485	−	11.1708i	−0.687084	−	0.396688i
$794$	4.67423	+	8.09601i	0.165882	+	0.287317i
$795$	2.44949	+	1.12848i	0.0868744	+	0.0400232i
$796$	−3.44949	+	5.97469i	−0.122264	+	0.211767i
$797$	22.6515			0.802358			0.401179	−	0.916000i	$-0.368600\pi$
$797$	22.6515			0.802358			0.401179	+	0.916000i	$0.368600\pi$
$798$	−26.4722	−	20.6811i	−0.937105	−	0.732102i
$799$	40.4949			1.43261
$800$	1.50000	−	2.59808i	0.0530330	−	0.0918559i
$801$	16.8990	−	47.7975i	0.597096	−	1.68884i
$802$	−6.39898	−	11.0834i	−0.225956	−	0.391367i
$803$	2.97219	+	1.71600i	0.104886	+	0.0605562i
$804$	−8.44949	+	5.97469i	−0.297991	+	0.210711i
$805$	44.4949			1.56824
$806$	−14.6969			−0.517678
$807$	−24.4949	−	34.6410i	−0.862261	−	1.21942i
$808$	8.57321	−	4.94975i	0.301605	−	0.174132i
$809$		−	2.36773i		−	0.0832448i	−0.999133	−	0.0416224i	$-0.986747\pi$
$809$		−	2.36773i		−	0.0832448i	0.999133	−	0.0416224i	$-0.0132526\pi$
$810$	4.57321	+	11.8780i	0.160686	+	0.417349i
$811$	3.00000	−	1.73205i	0.105344	−	0.0608205i	−0.446402	−	0.894832i	$-0.647295\pi$
$811$	3.00000	−	1.73205i	0.105344	−	0.0608205i	0.551746	+	0.834012i	$0.313962\pi$
$812$	−5.44949	+	9.43879i	−0.191240	+	0.331237i
$813$	−24.0454	−	34.0053i	−0.843309	−	1.19262i
$814$	0.123724	−	0.214297i	0.00433654	−	0.00751110i
$815$	4.47219	+	2.58202i	0.156654	+	0.0904443i
$816$	1.00000	+	10.8530i	0.0350070	+	0.379931i
$817$	0.898979	−	3.81405i	0.0314513	−	0.133437i
$818$		−	20.6096i		−	0.720599i
$819$	43.5959	+	15.4135i	1.52336	+	0.538591i
$820$	3.67423	+	2.12132i	0.128310	+	0.0740797i
$821$	−0.550510	+	0.317837i	−0.0192129	+	0.0110926i	−0.509576	−	0.860426i	$-0.670198\pi$
$821$	−0.550510	+	0.317837i	−0.0192129	+	0.0110926i	0.490363	+	0.871518i	$0.336864\pi$
$822$	−11.6237	−	5.35507i	−0.405424	−	0.186780i
$823$	9.65153	+	16.7169i	0.336431	+	0.582716i	0.983759	−	0.179496i	$-0.0574467\pi$
$823$	9.65153	+	16.7169i	0.336431	+	0.582716i	−0.647327	+	0.762212i	$0.724113\pi$
$824$			11.9494i			0.416276i
$825$	0.151531	+	1.64456i	0.00527562	+	0.0572564i
$826$	−14.5732	−	25.2415i	−0.507067	−	0.878266i
$827$	1.62372	+	2.81237i	0.0564624	+	0.0977958i	0.892875	−	0.450304i	$-0.148685\pi$
$827$	1.62372	+	2.81237i	0.0564624	+	0.0977958i	−0.836413	+	0.548100i	$0.815351\pi$
$828$	3.87628	+	20.8560i	0.134710	+	0.724798i
$829$		−	36.1981i		−	1.25721i	−0.777724	−	0.628606i	$-0.783626\pi$
$829$		−	36.1981i		−	1.25721i	0.777724	−	0.628606i	$-0.216374\pi$
$830$	10.0227	+	17.3598i	0.347893	+	0.602569i
$831$	3.07832	−	6.68180i	0.106786	−	0.231789i
$832$	−3.00000	+	1.73205i	−0.104006	+	0.0600481i
$833$	−69.7423	−	40.2658i	−2.41643	−	1.39513i
$834$	0.252551	−	0.548188i	0.00874514	−	0.0189822i
$835$			6.92820i			0.239760i
$836$	−0.949490	+	1.00889i	−0.0328388	+	0.0348932i
$837$	6.00000	+	21.2132i	0.207390	+	0.733236i
$838$	−3.24745	−	1.87492i	−0.112181	−	0.0647679i
$839$	−0.674235	+	1.16781i	−0.0232772	+	0.0403172i	−0.877429	−	0.479706i	$-0.840743\pi$
$839$	−0.674235	+	1.16781i	−0.0232772	+	0.0403172i	0.854152	+	0.520023i	$0.174077\pi$
$840$	8.89898	−	6.29253i	0.307044	−	0.217113i
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	−26.0227	+	15.0242i	−0.896802	+	0.517769i
$843$	28.6237	−	2.63740i	0.985853	−	0.0908369i
$844$		−	15.4135i		−	0.530554i
$845$	−1.22474	+	0.707107i	−0.0421325	+	0.0243252i
$846$	14.6742	−	12.5457i	0.504511	−	0.431331i
$847$	48.4949			1.66630
$848$	1.10102			0.0378092
$849$	4.55051	+	6.43539i	0.156173	+	0.220862i
$850$	16.3485	+	9.43879i	0.560748	+	0.323748i
$851$	−2.75255	−	4.76756i	−0.0943562	−	0.163430i
$852$	4.34847	−	9.43879i	0.148976	−	0.323368i
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	28.6969			0.981989
$855$	8.47219	+	16.4384i	0.289743	+	0.562182i
$856$	−4.89898			−0.167444
$857$	−11.2980	+	19.5686i	−0.385931	+	0.668452i	−0.991898	−	0.127038i	$-0.959453\pi$
$857$	−11.2980	+	19.5686i	−0.385931	+	0.668452i	0.605967	+	0.795490i	$0.292786\pi$
$858$	0.797959	−	1.73205i	0.0272419	−	0.0591312i
$859$	22.4217	+	38.8355i	0.765018	+	1.32505i	0.940237	+	0.340521i	$0.110603\pi$
$859$	22.4217	+	38.8355i	0.765018	+	1.32505i	−0.175219	+	0.984529i	$0.556063\pi$
$860$	1.10102	+	0.635674i	0.0375445	+	0.0216763i
$861$	−13.3485	−	18.8776i	−0.454915	−	0.643346i
$862$	32.6969			1.11366
$863$	31.3485			1.06711			0.533557	−	0.845764i	$-0.320855\pi$
$863$	31.3485			1.06711			0.533557	+	0.845764i	$0.320855\pi$
$864$	3.72474	+	3.62302i	0.126718	+	0.123258i
$865$	13.3485	−	7.70674i	0.453862	−	0.262037i
$866$		−	13.5065i		−	0.458968i
$867$	−38.9722	+	3.59091i	−1.32357	+	0.121954i
$868$	16.3485	−	9.43879i	0.554903	−	0.320374i
$869$	−1.34847	+	2.33562i	−0.0457437	+	0.0792304i
$870$	4.89898	−	3.46410i	0.166091	−	0.117444i
$871$	10.3485	−	17.9241i	0.350645	−	0.607334i
$872$		0			0
$873$	7.50000	+	40.3532i	0.253837	+	1.36575i
$874$	8.87628	+	29.5163i	0.300245	+	0.998404i
$875$		−	50.3402i		−	1.70181i
$876$	7.82577	−	16.9866i	0.264408	−	0.573925i
$877$	0.371173	+	0.214297i	0.0125336	+	0.00723629i	0.506254	−	0.862385i	$-0.331030\pi$
$877$	0.371173	+	0.214297i	0.0125336	+	0.00723629i	−0.493720	+	0.869621i	$0.664363\pi$
$878$	−2.32577	+	1.34278i	−0.0784908	+	0.0453167i
$879$	3.37117	−	7.31747i	0.113707	−	0.246812i
$880$	−0.224745	−	0.389270i	−0.00757615	−	0.0131223i
$881$		−	55.5364i		−	1.87107i	−0.353236	−	0.935534i	$-0.614919\pi$
$881$		−	55.5364i		−	1.87107i	0.353236	−	0.935534i	$-0.385081\pi$
$882$	−37.7474	+	7.01569i	−1.27102	+	0.236231i
$883$	−21.4217	−	37.1034i	−0.720897	−	1.24863i	−0.960641	−	0.277794i	$-0.910397\pi$
$883$	−21.4217	−	37.1034i	−0.720897	−	1.24863i	0.239744	−	0.970836i	$-0.422937\pi$
$884$	−10.8990	−	18.8776i	−0.366572	−	0.634922i
$885$	1.47219	+	15.9777i	0.0494872	+	0.537085i
$886$		−	29.2378i		−	0.982263i
$887$	−16.0454	−	27.7915i	−0.538752	−	0.933146i	−0.998972	−	0.0453408i	$-0.985563\pi$
$887$	−16.0454	−	27.7915i	−0.538752	−	0.933146i	0.460220	−	0.887805i	$-0.347771\pi$
$888$	−1.22474	−	0.564242i	−0.0410997	−	0.0189347i
$889$	−40.0454	+	23.1202i	−1.34308	+	0.775428i
$890$	20.6969	+	11.9494i	0.693763	+	0.400544i
$891$	−2.82577	−	0.444648i	−0.0946667	−	0.0148963i
$892$			9.61377i			0.321893i
$893$	19.2247	−	20.4274i	0.643332	−	0.683578i
$894$	0.775255	+	8.41385i	0.0259284	+	0.281401i
$895$	−27.3712	−	15.8028i	−0.914917	−	0.528228i
$896$	2.22474	−	3.85337i	0.0743235	−	0.128732i
$897$	−24.4949	−	34.6410i	−0.817861	−	1.15663i
$898$	5.60102	−	9.70125i	0.186908	−	0.323735i
$899$	9.00000	−	5.19615i	0.300167	−	0.173301i
$900$	8.84847	−	1.64456i	0.294949	−	0.0548188i
$901$			6.92820i			0.230812i
$902$	−0.825765	+	0.476756i	−0.0274950	+	0.0158742i
$903$	−4.00000	−	5.65685i	−0.133112	−	0.188248i
$904$	−0.797959			−0.0265397
$905$	18.4949			0.614791
$906$	−25.5959	+	18.0990i	−0.850367	+	0.601301i
$907$	47.9166	+	27.6647i	1.59104	+	0.918590i	0.993128	+	0.117031i	$0.0373376\pi$
$907$	47.9166	+	27.6647i	1.59104	+	0.918590i	0.597916	+	0.801559i	$0.295996\pi$
$908$	−2.72474	−	4.71940i	−0.0904238	−	0.156619i
$909$	28.0000	+	9.89949i	0.928701	+	0.328346i
$910$	−10.8990	+	18.8776i	−0.361298	+	0.625786i
$911$	−43.3485			−1.43620			−0.718099	−	0.695941i	$-0.754988\pi$
$911$	−43.3485			−1.43620			−0.718099	+	0.695941i	$0.754988\pi$
$912$	5.94949	+	4.64796i	0.197007	+	0.153909i
$913$	−4.50510			−0.149097
$914$	−6.50000	+	11.2583i	−0.215001	+	0.372392i
$915$	−14.3485	−	6.61037i	−0.474346	−	0.218532i
$916$	4.44949	+	7.70674i	0.147015	+	0.254638i
$917$	84.8661	+	48.9974i	2.80252	+	1.61804i
$918$	−22.7980	+	23.4381i	−0.752445	+	0.773571i
$919$	−7.30306			−0.240906			−0.120453	−	0.992719i	$-0.538435\pi$
$919$	−7.30306			−0.240906			−0.120453	+	0.992719i	$0.538435\pi$
$920$	−10.0000			−0.329690
$921$	5.75255	−	4.06767i	0.189553	−	0.134034i
$922$	−8.75255	+	5.05329i	−0.288250	+	0.166421i
$923$			20.7846i			0.684134i
$924$	0.224745	+	2.43916i	0.00739356	+	0.0802424i
$925$	−2.02270	+	1.16781i	−0.0665061	+	0.0383973i
$926$	−0.101021	+	0.174973i	−0.00331974	+	0.00574996i
$927$	−27.2474	+	23.2952i	−0.894924	+	0.765115i
$928$	1.22474	−	2.12132i	0.0402042	−	0.0696358i
$929$	15.0959	+	8.71563i	0.495281	+	0.285951i	0.726763	−	0.686889i	$-0.241024\pi$
$929$	15.0959	+	8.71563i	0.495281	+	0.285951i	−0.231482	+	0.972839i	$0.574357\pi$
$930$	−10.3485	+	0.953512i	−0.339340	+	0.0312669i
$931$	−53.4217	+	16.0652i	−1.75082	+	0.526516i
$932$			6.46750i			0.211850i
$933$	−24.4722	−	11.2744i	−0.801184	−	0.369107i
$934$	−28.0732	−	16.2081i	−0.918584	−	0.530345i
$935$	2.44949	−	1.41421i	0.0801069	−	0.0462497i
$936$	−9.79796	−	3.46410i	−0.320256	−	0.113228i
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$			26.5843i			0.868009i
$939$	−32.7702	+	3.01945i	−1.06941	+	0.0985362i
$940$	4.55051	+	7.88171i	0.148421	+	0.257073i
$941$	−27.4949	−	47.6226i	−0.896308	−	1.55245i	−0.832177	−	0.554510i	$-0.812906\pi$
$941$	−27.4949	−	47.6226i	−0.896308	−	1.55245i	−0.0641307	−	0.997942i	$-0.520427\pi$
$942$	32.2474	−	2.97129i	1.05068	−	0.0968099i
$943$			21.2132i			0.690797i
$944$	3.27526	+	5.67291i	0.106600	+	0.184637i
$945$	31.6969	+	8.02458i	1.03110	+	0.261040i
$946$	−0.247449	+	0.142865i	−0.00804525	+	0.00464493i
$947$	−11.4495	−	6.61037i	−0.372058	−	0.214808i	0.302299	−	0.953213i	$-0.402246\pi$
$947$	−11.4495	−	6.61037i	−0.372058	−	0.214808i	−0.674357	+	0.738405i	$0.735579\pi$
$948$	13.3485	+	6.14966i	0.433538	+	0.199732i
$949$			37.4052i			1.21423i
$950$	12.5227	−	3.76588i	0.406290	−	0.122181i
$951$	10.3485	−	0.953512i	0.335572	−	0.0309197i
$952$	24.2474	+	13.9993i	0.785864	+	0.453719i
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	−0.905074	−	0.425255i	$-0.860184\pi$
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	0.820818	+	0.571189i	$0.193518\pi$
$954$	2.14643	+	2.51059i	0.0694932	+	0.0812833i
$955$	13.7980	−	23.8988i	0.446491	−	0.773346i
$956$	−6.24745	+	3.60697i	−0.202057	+	0.116658i
$957$	0.123724	+	1.34278i	0.00399944	+	0.0434060i
$958$		−	40.5836i		−	1.31120i
$959$	−28.4722	+	16.4384i	−0.919415	+	0.530825i
$960$	−2.00000	+	1.41421i	−0.0645497	+	0.0456435i
$961$	13.0000			0.419355
$962$	2.69694			0.0869528
$963$	−9.55051	−	11.1708i	−0.307761	−	0.359975i
$964$	−8.84847	−	5.10867i	−0.284990	−	0.164539i
$965$	−6.24745	−	10.8209i	−0.201112	−	0.348337i
$966$	49.4949	+	22.8024i	1.59247	+	0.733655i
$967$	−3.69694	+	6.40329i	−0.118886	+	0.205916i	−0.919326	−	0.393496i	$-0.871265\pi$
$967$	−3.69694	+	6.40329i	−0.118886	+	0.205916i	0.800441	+	0.599412i	$0.204599\pi$
$968$	−10.8990			−0.350306
$969$	−29.2474	+	37.4373i	−0.939563	+	1.20266i
$970$	−19.3485			−0.621242
$971$	13.0732	−	22.6435i	0.419539	−	0.726664i	−0.576354	−	0.817200i	$-0.695525\pi$
$971$	13.0732	−	22.6435i	0.419539	−	0.726664i	0.995893	+	0.0905368i	$0.0288583\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	−0.775255	−	1.34278i	−0.0248535	−	0.0430476i
$974$	−14.3258	−	8.27098i	−0.459027	−	0.265019i
$975$	−14.6969	+	10.3923i	−0.470679	+	0.332820i
$976$	−6.44949			−0.206443
$977$	49.8990			1.59641			0.798205	−	0.602386i	$-0.205783\pi$
$977$	49.8990			1.59641			0.798205	+	0.602386i	$0.205783\pi$
$978$	3.65153	+	5.16404i	0.116763	+	0.165128i
$979$	−4.65153	+	2.68556i	−0.148664	+	0.0858310i
$980$		−	18.0990i		−	0.578153i
$981$		0			0
$982$	−4.10102	+	2.36773i	−0.130869	+	0.0755572i
$983$	−19.1010	+	33.0839i	−0.609228	+	1.05521i	0.382140	+	0.924104i	$0.375187\pi$
$983$	−19.1010	+	33.0839i	−0.609228	+	1.05521i	−0.991368	+	0.131109i	$0.958146\pi$
$984$	3.00000	+	4.24264i	0.0956365	+	0.135250i
$985$	−0.348469	+	0.603566i	−0.0111032	+	0.0192312i
$986$	13.3485	+	7.70674i	0.425102	+	0.245433i
$987$	−4.55051	−	49.3867i	−0.144844	−	1.57200i
$988$	−14.6969	−	3.46410i	−0.467572	−	0.110208i
$989$			6.35674i			0.202133i
$990$	0.449490	−	1.27135i	0.0142857	−	0.0404061i
$991$	44.6969	+	25.8058i	1.41985	+	0.819748i	0.996285	−	0.0861200i	$-0.0274468\pi$
$991$	44.6969	+	25.8058i	1.41985	+	0.819748i	0.423560	+	0.905868i	$0.360780\pi$
$992$	−3.67423	+	2.12132i	−0.116657	+	0.0673520i
$993$	23.2980	+	10.7334i	0.739338	+	0.340615i
$994$	−13.3485	−	23.1202i	−0.423388	−	0.733329i
$995$		−	9.75663i		−	0.309306i
$996$	2.25255	+	24.4470i	0.0713748	+	0.774631i
$997$	−29.7196	−	51.4759i	−0.941231	−	1.63026i	−0.763128	−	0.646247i	$-0.776338\pi$
$997$	−29.7196	−	51.4759i	−0.941231	−	1.63026i	−0.178102	−	0.984012i	$-0.556996\pi$
$998$	1.27526	+	2.20881i	0.0403675	+	0.0699186i
$999$	−1.10102	−	3.89270i	−0.0348347	−	0.123159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.h.f.65.1	yes	4
3.2	odd	2		114.2.h.e.65.1	✓	4
4.3	odd	2		912.2.bn.h.65.2		4
12.11	even	2		912.2.bn.g.65.2		4
19.12	odd	6		114.2.h.e.107.2	yes	4
57.50	even	6	inner	114.2.h.f.107.1	yes	4
76.31	even	6		912.2.bn.g.449.1		4
228.107	odd	6		912.2.bn.h.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.e.65.1	✓	4	3.2	odd	2
114.2.h.e.107.2	yes	4	19.12	odd	6
114.2.h.f.65.1	yes	4	1.1	even	1	trivial
114.2.h.f.107.1	yes	4	57.50	even	6	inner
912.2.bn.g.65.2		4	12.11	even	2
912.2.bn.g.449.1		4	76.31	even	6
912.2.bn.h.65.2		4	4.3	odd	2
912.2.bn.h.449.2		4	228.107	odd	6

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +4.44949 q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22474 + 0.707107i) q^{5} +(1.00000 + 1.41421i) q^{6} +4.44949 q^{7} -1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(1.22474 - 0.707107i) q^{10} +0.317837i q^{11} +(1.72474 - 0.158919i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-2.00000 + 1.41421i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.44949 - 3.14626i) q^{17} +(-2.94949 + 0.548188i) q^{18} +(-4.17423 + 1.25529i) q^{19} -1.41421i q^{20} +(-3.22474 + 6.99964i) q^{21} +(0.275255 + 0.158919i) q^{22} +(6.12372 - 3.53553i) q^{23} +(0.724745 - 1.57313i) q^{24} +(-1.50000 - 2.59808i) q^{25} +3.46410i q^{26} +(5.00000 - 1.41421i) q^{27} +(-2.22474 - 3.85337i) q^{28} +(-1.22474 - 2.12132i) q^{29} +(0.224745 + 2.43916i) q^{30} +4.24264i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.230351i) q^{33} +(-5.44949 + 3.14626i) q^{34} +(5.44949 + 3.14626i) q^{35} +(-1.00000 + 2.82843i) q^{36} -0.778539i q^{37} +(-1.00000 + 4.24264i) q^{38} +(-0.550510 - 5.97469i) q^{39} +(-1.22474 - 0.707107i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(4.44949 + 6.29253i) q^{42} +(-0.449490 + 0.778539i) q^{43} +(0.275255 - 0.158919i) q^{44} +(-0.775255 - 4.17121i) q^{45} -7.07107i q^{46} +(-5.57321 + 3.21770i) q^{47} +(-1.00000 - 1.41421i) q^{48} +12.7980 q^{49} -3.00000 q^{50} +(8.89898 - 6.29253i) q^{51} +(3.00000 + 1.73205i) q^{52} +(-0.550510 - 0.953512i) q^{53} +(1.27526 - 5.03723i) q^{54} +(-0.224745 + 0.389270i) q^{55} -4.44949 q^{56} +(1.05051 - 7.47639i) q^{57} -2.44949 q^{58} +(3.27526 - 5.67291i) q^{59} +(2.22474 + 1.02494i) q^{60} +(3.22474 + 5.58542i) q^{61} +(3.67423 + 2.12132i) q^{62} +(-8.67423 - 10.1459i) q^{63} +1.00000 q^{64} -4.89898 q^{65} +(-0.449490 + 0.317837i) q^{66} +(-5.17423 + 2.98735i) q^{67} +6.29253i q^{68} +(1.12372 + 12.1958i) q^{69} +(5.44949 - 3.14626i) q^{70} +(3.00000 - 5.19615i) q^{71} +(1.94949 + 2.28024i) q^{72} +(5.39898 - 9.35131i) q^{73} +(-0.674235 - 0.389270i) q^{74} +(5.17423 - 0.476756i) q^{75} +(3.17423 + 2.98735i) q^{76} +1.41421i q^{77} +(-5.44949 - 2.51059i) q^{78} +(7.34847 + 4.24264i) q^{79} +(-1.22474 + 0.707107i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(1.50000 + 2.59808i) q^{82} +14.1742i q^{83} +(7.67423 - 0.707107i) q^{84} +(-4.44949 - 7.70674i) q^{85} +(0.449490 + 0.778539i) q^{86} +(4.22474 - 0.389270i) q^{87} -0.317837i q^{88} +(8.44949 + 14.6349i) q^{89} +(-4.00000 - 1.41421i) q^{90} +(-13.3485 + 7.70674i) q^{91} +(-6.12372 - 3.53553i) q^{92} +(-6.67423 - 3.07483i) q^{93} +6.43539i q^{94} +(-6.00000 - 1.41421i) q^{95} +(-1.72474 + 0.158919i) q^{96} +(-11.8485 - 6.84072i) q^{97} +(6.39898 - 11.0834i) q^{98} +(0.724745 - 0.619620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{12} - 12 q^{13} + 4 q^{14} - 8 q^{15} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 8 q^{21} + 6 q^{22} - 2 q^{24} - 6 q^{25} + 20 q^{27} - 4 q^{28} - 4 q^{30} + 2 q^{32} - 2 q^{33} - 12 q^{34} + 12 q^{35} - 4 q^{36} - 4 q^{38} - 12 q^{39} - 6 q^{41} + 8 q^{42} + 8 q^{43} + 6 q^{44} - 8 q^{45} + 12 q^{47} - 4 q^{48} + 12 q^{49} - 12 q^{50} + 16 q^{51} + 12 q^{52} - 12 q^{53} + 10 q^{54} + 4 q^{55} - 8 q^{56} + 14 q^{57} + 18 q^{59} + 4 q^{60} + 8 q^{61} - 20 q^{63} + 4 q^{64} + 8 q^{66} - 6 q^{67} - 20 q^{69} + 12 q^{70} + 12 q^{71} - 2 q^{72} + 2 q^{73} + 12 q^{74} + 6 q^{75} - 2 q^{76} - 12 q^{78} + 14 q^{81} + 6 q^{82} + 16 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{89} - 16 q^{90} - 24 q^{91} - 12 q^{93} - 24 q^{95} - 2 q^{96} - 18 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^12 - 12 * q^13 + 4 * q^14 - 8 * q^15 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 8 * q^21 + 6 * q^22 - 2 * q^24 - 6 * q^25 + 20 * q^27 - 4 * q^28 - 4 * q^30 + 2 * q^32 - 2 * q^33 - 12 * q^34 + 12 * q^35 - 4 * q^36 - 4 * q^38 - 12 * q^39 - 6 * q^41 + 8 * q^42 + 8 * q^43 + 6 * q^44 - 8 * q^45 + 12 * q^47 - 4 * q^48 + 12 * q^49 - 12 * q^50 + 16 * q^51 + 12 * q^52 - 12 * q^53 + 10 * q^54 + 4 * q^55 - 8 * q^56 + 14 * q^57 + 18 * q^59 + 4 * q^60 + 8 * q^61 - 20 * q^63 + 4 * q^64 + 8 * q^66 - 6 * q^67 - 20 * q^69 + 12 * q^70 + 12 * q^71 - 2 * q^72 + 2 * q^73 + 12 * q^74 + 6 * q^75 - 2 * q^76 - 12 * q^78 + 14 * q^81 + 6 * q^82 + 16 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^89 - 16 * q^90 - 24 * q^91 - 12 * q^93 - 24 * q^95 - 2 * q^96 - 18 * q^97 + 6 * q^98 - 2 * q^99

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