LMFDB - Embedded newform 114.2.h.e.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.e.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) 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} +(-2.22474 + 1.02494i) 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} +(4.44949 - 6.29253i) q^{21} +(0.275255 + 0.158919i) q^{22} +(-6.12372 + 3.53553i) q^{23} +(1.00000 - 1.41421i) 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} +(-0.449490 - 0.317837i) q^{33} +(-5.44949 + 3.14626i) q^{34} +(-5.44949 - 3.14626i) q^{35} +(-1.94949 + 2.28024i) 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} +(3.22474 + 6.99964i) 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} +(0.724745 + 1.57313i) q^{48} +12.7980 q^{49} +3.00000 q^{50} +(9.89898 - 4.56048i) q^{51} +(3.00000 + 1.73205i) q^{52} +(0.550510 + 0.953512i) q^{53} +(3.72474 - 3.62302i) q^{54} +(-0.224745 + 0.389270i) q^{55} +4.44949 q^{56} +(-2.39898 + 7.15855i) q^{57} -2.44949 q^{58} +(-3.27526 + 5.67291i) q^{59} +(2.00000 + 1.41421i) q^{60} +(3.22474 + 5.58542i) q^{61} +(-3.67423 - 2.12132i) q^{62} +(-4.44949 - 12.5851i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(0.500000 - 0.230351i) 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} +(-1.00000 - 2.82843i) 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} +(-4.89898 - 3.46410i) q^{78} +(7.34847 + 4.24264i) q^{79} +(1.22474 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) 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} +(-3.22474 - 2.75699i) q^{90} +(-13.3485 + 7.70674i) q^{91} +(6.12372 + 3.53553i) q^{92} +(6.00000 + 4.24264i) 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} +(-0.898979 + 0.317837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} - 2 q^{12} - 12 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 12 q^{17} + 2 q^{18} - 2 q^{19} + 8 q^{21} + 6 q^{22} + 4 q^{24} - 6 q^{25} - 20 q^{27} - 4 q^{28} - 4 q^{30} - 2 q^{32} + 8 q^{33} - 12 q^{34} - 12 q^{35} + 2 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} - 2 q^{48} + 12 q^{49} + 12 q^{50} + 20 q^{51} + 12 q^{52} + 12 q^{53} + 10 q^{54} + 4 q^{55} + 8 q^{56} + 10 q^{57} - 18 q^{59} + 8 q^{60} + 8 q^{61} - 8 q^{63} + 4 q^{64} + 2 q^{66} - 6 q^{67} + 20 q^{69} + 12 q^{70} - 12 q^{71} - 4 q^{72} + 2 q^{73} - 12 q^{74} - 6 q^{75} - 2 q^{76} - 28 q^{81} + 6 q^{82} - 16 q^{84} - 8 q^{85} + 8 q^{86} + 12 q^{87} - 24 q^{89} - 8 q^{90} - 24 q^{91} + 24 q^{93} + 24 q^{95} - 2 q^{96} - 18 q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 - 2 * q^12 - 12 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 12 * q^17 + 2 * q^18 - 2 * q^19 + 8 * q^21 + 6 * q^22 + 4 * q^24 - 6 * q^25 - 20 * q^27 - 4 * q^28 - 4 * q^30 - 2 * q^32 + 8 * q^33 - 12 * q^34 - 12 * q^35 + 2 * 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 - 2 * q^48 + 12 * q^49 + 12 * q^50 + 20 * q^51 + 12 * q^52 + 12 * q^53 + 10 * q^54 + 4 * q^55 + 8 * q^56 + 10 * q^57 - 18 * q^59 + 8 * q^60 + 8 * q^61 - 8 * q^63 + 4 * q^64 + 2 * q^66 - 6 * q^67 + 20 * q^69 + 12 * q^70 - 12 * q^71 - 4 * q^72 + 2 * q^73 - 12 * q^74 - 6 * q^75 - 2 * q^76 - 28 * q^81 + 6 * q^82 - 16 * q^84 - 8 * q^85 + 8 * q^86 + 12 * q^87 - 24 * q^89 - 8 * q^90 - 24 * q^91 + 24 * q^93 + 24 * q^95 - 2 * q^96 - 18 * q^97 - 6 * q^98 + 16 * 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
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	0.200480	−	0.979698i	$-0.435750\pi$
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	−0.748203	+	0.663470i	$0.769083\pi$
$6$	0.724745	+	1.57313i	0.295876	+	0.642229i
$7$	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
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$	1.22474	−	0.707107i	0.387298	−	0.223607i
$11$		−	0.317837i		−	0.0958315i	−0.998851	−	0.0479158i	$-0.984742\pi$
$11$		−	0.317837i		−	0.0958315i	0.998851	−	0.0479158i	$-0.0152579\pi$
$12$	−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
$15$	−2.22474	+	1.02494i	−0.574427	+	0.264639i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.44949	+	3.14626i	1.32170	+	0.763081i	0.983999	−	0.178174i	$-0.0570190\pi$
$17$	5.44949	+	3.14626i	1.32170	+	0.763081i	0.337696	+	0.941255i	$0.390352\pi$
$18$	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
$21$	4.44949	−	6.29253i	0.970958	−	1.37314i
$22$	0.275255	+	0.158919i	0.0586846	+	0.0338816i
$23$	−6.12372	+	3.53553i	−1.27688	+	0.737210i	−0.976274	−	0.216537i	$-0.930524\pi$
$23$	−6.12372	+	3.53553i	−1.27688	+	0.737210i	−0.300610	+	0.953747i	$0.597190\pi$
$24$	1.00000	−	1.41421i	0.204124	−	0.288675i
$25$	−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	0.957046	−	0.289938i	$-0.0936346\pi$
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	−0.729616	+	0.683857i	$0.760301\pi$
$30$	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
$33$	−0.449490	−	0.317837i	−0.0782461	−	0.0553284i
$34$	−5.44949	+	3.14626i	−0.934580	+	0.539580i
$35$	−5.44949	−	3.14626i	−0.921132	−	0.531816i
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$		−	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	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	3.22474	+	6.99964i	0.497589	+	1.08007i
$43$	−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	−0.0350379	−	0.999386i	$-0.511155\pi$
$47$	5.57321	−	3.21770i	0.812937	−	0.469349i	0.847975	+	0.530037i	$0.177822\pi$
$48$	0.724745	+	1.57313i	0.104608	+	0.227062i
$49$	12.7980			1.82828
$50$	3.00000			0.424264
$51$	9.89898	−	4.56048i	1.38613	−	0.638595i
$52$	3.00000	+	1.73205i	0.416025	+	0.240192i
$53$	0.550510	+	0.953512i	0.0756184	+	0.130975i	0.901355	−	0.433081i	$-0.142574\pi$
$53$	0.550510	+	0.953512i	0.0756184	+	0.130975i	−0.825737	+	0.564056i	$0.809240\pi$
$54$	3.72474	−	3.62302i	0.506874	−	0.493031i
$55$	−0.224745	+	0.389270i	−0.0303046	+	0.0524891i
$56$	4.44949			0.594588
$57$	−2.39898	+	7.15855i	−0.317753	+	0.948174i
$58$	−2.44949			−0.321634
$59$	−3.27526	+	5.67291i	−0.426402	+	0.738550i	−0.996550	−	0.0829920i	$-0.973552\pi$
$59$	−3.27526	+	5.67291i	−0.426402	+	0.738550i	0.570148	+	0.821542i	$0.306886\pi$
$60$	2.00000	+	1.41421i	0.258199	+	0.182574i
$61$	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
$63$	−4.44949	−	12.5851i	−0.560583	−	1.58557i
$64$	1.00000			0.125000
$65$	4.89898			0.607644
$66$	0.500000	−	0.230351i	0.0615457	−	0.0283542i
$67$	−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	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−1.00000	−	2.82843i	−0.117851	−	0.333333i
$73$	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
$78$	−4.89898	−	3.46410i	−0.554700	−	0.392232i
$79$	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
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$		−	14.1742i		−	1.55583i	−0.628372	−	0.777913i	$-0.716279\pi$
$83$		−	14.1742i		−	1.55583i	0.628372	−	0.777913i	$-0.283721\pi$
$84$	−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	$-0.813382\pi$
$89$	−8.44949	−	14.6349i	−0.895644	−	1.55130i	−0.0626387	−	0.998036i	$-0.519952\pi$
$90$	−3.22474	−	2.75699i	−0.339918	−	0.290613i
$91$	−13.3485	+	7.70674i	−1.39930	+	0.807886i
$92$	6.12372	+	3.53553i	0.638442	+	0.368605i
$93$	6.00000	+	4.24264i	0.622171	+	0.439941i
$94$			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
$99$	−0.898979	+	0.317837i	−0.0903508	+	0.0319438i
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	8.57321	−	4.94975i	0.853067	−	0.492518i	−0.00861771	−	0.999963i	$-0.502743\pi$
$101$	8.57321	−	4.94975i	0.853067	−	0.492518i	0.861684	+	0.507445i	$0.169410\pi$
$102$	−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
$105$	−9.89898	+	4.56048i	−0.966041	+	0.445057i
$106$	−1.10102			−0.106941
$107$	−4.89898			−0.473602			−0.236801	−	0.971558i	$-0.576099\pi$
$107$	−4.89898			−0.473602			−0.236801	+	0.971558i	$0.576099\pi$
$108$	1.27526	+	5.03723i	0.122711	+	0.484708i
$109$		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
$111$	−1.10102	−	0.778539i	−0.104504	−	0.0738957i
$112$	−2.22474	+	3.85337i	−0.210219	+	0.364109i
$113$	−0.797959			−0.0750657			−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	−0.797959			−0.0750657			−0.0375328	+	0.999295i	$0.511950\pi$
$114$	−5.00000	−	5.65685i	−0.468293	−	0.529813i
$115$	10.0000			0.932505
$116$	1.22474	−	2.12132i	0.113715	−	0.196960i
$117$	7.89898	+	6.75323i	0.730261	+	0.624336i
$118$	−3.27526	−	5.67291i	−0.301512	−	0.522234i
$119$	24.2474	+	13.9993i	2.22276	+	1.28331i
$120$	−2.22474	+	1.02494i	−0.203090	+	0.0935642i
$121$	10.8990			0.990816
$122$	−6.44949			−0.583909
$123$	−2.17423	−	4.71940i	−0.196044	−	0.425534i
$124$	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
$129$	0.651531	+	1.41421i	0.0573641	+	0.124515i
$130$	−2.44949	+	4.24264i	−0.214834	+	0.372104i
$131$	−19.0732	−	11.0119i	−1.66643	−	0.962116i	−0.969537	−	0.244946i	$-0.921230\pi$
$131$	−19.0732	−	11.0119i	−1.66643	−	0.962116i	−0.696898	−	0.717171i	$-0.745437\pi$
$132$	−0.0505103	+	0.548188i	−0.00439635	+	0.0477137i
$133$	−18.5732	+	5.58542i	−1.61050	+	0.484318i
$134$		−	5.97469i		−	0.516135i
$135$	5.12372	+	5.26758i	0.440980	+	0.453362i
$136$	5.44949	+	3.14626i	0.467290	+	0.269790i
$137$	6.39898	−	3.69445i	0.546702	−	0.315638i	−0.201089	−	0.979573i	$-0.564448\pi$
$137$	6.39898	−	3.69445i	0.546702	−	0.315638i	0.747791	+	0.663935i	$0.231115\pi$
$138$	−10.0000	−	7.07107i	−0.851257	−	0.601929i
$139$	−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
$147$	12.7980	−	18.0990i	1.05556	−	1.49278i
$148$	−0.674235	+	0.389270i	−0.0554217	+	0.0319978i
$149$	−4.22474	−	2.43916i	−0.346105	−	0.199824i	0.316864	−	0.948471i	$-0.397370\pi$
$149$	−4.22474	−	2.43916i	−0.346105	−	0.199824i	−0.662968	+	0.748648i	$0.730704\pi$
$150$	3.00000	−	4.24264i	0.244949	−	0.346410i
$151$			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
$156$	5.44949	−	2.51059i	0.436308	−	0.201008i
$157$	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
$162$	−1.39898	−	8.89060i	−0.109914	−	0.698512i
$163$	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
$165$	0.325765	+	0.707107i	0.0253608	+	0.0550482i
$166$	12.2753	+	7.08712i	0.952745	+	0.550067i
$167$	−2.44949	−	4.24264i	−0.189547	−	0.328305i	0.755552	−	0.655089i	$-0.227369\pi$
$167$	−2.44949	−	4.24264i	−0.189547	−	0.328305i	−0.945099	+	0.326783i	$0.894035\pi$
$168$	4.44949	−	6.29253i	0.343286	−	0.485479i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	8.89898			0.682521
$171$	7.72474	+	10.5512i	0.590726	+	0.806872i
$172$	0.898979			0.0685465
$173$	−5.44949	+	9.43879i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$173$	−5.44949	+	9.43879i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$174$	−2.44949	+	3.46410i	−0.185695	+	0.262613i
$175$	−6.67423	−	11.5601i	−0.504525	−	0.873862i
$176$	0.275255	+	0.158919i	0.0207481	+	0.0119789i
$177$	4.74745	+	10.3048i	0.356840	+	0.774558i
$178$	16.8990			1.26663
$179$	22.3485			1.67040			0.835202	−	0.549944i	$-0.185351\pi$
$179$	22.3485			1.67040			0.835202	+	0.549944i	$0.185351\pi$
$180$	4.00000	−	1.41421i	0.298142	−	0.105409i
$181$	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
$186$	−6.67423	+	3.07483i	−0.489379	+	0.225458i
$187$	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	$0.249486\pi$
$191$			19.5133i			1.41193i	−0.708247	+	0.705965i	$0.750514\pi$
$192$	1.00000	−	1.41421i	0.0721688	−	0.102062i
$193$	−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
$195$	4.89898	−	6.92820i	0.350823	−	0.496139i
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$		−	0.492810i		−	0.0351113i	−0.999846	−	0.0175556i	$-0.994412\pi$
$197$		−	0.492810i		−	0.0351113i	0.999846	−	0.0175556i	$-0.00558842\pi$
$198$	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
$204$	−8.89898	−	6.29253i	−0.623053	−	0.440565i
$205$	−3.67423	+	2.12132i	−0.256620	+	0.148159i
$206$	10.3485	+	5.97469i	0.721012	+	0.416276i
$207$	16.1237	+	13.7850i	1.12068	+	0.958122i
$208$		−	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
$213$	4.34847	+	9.43879i	0.297952	+	0.646735i
$214$	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
$219$	−7.82577	−	16.9866i	−0.528816	−	1.14785i
$220$	0.449490			0.0303046
$221$	−21.7980			−1.46629
$222$	1.22474	−	0.564242i	0.0821995	−	0.0378695i
$223$	−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
$225$	−5.84847	+	6.84072i	−0.389898	+	0.456048i
$226$	0.398979	−	0.691053i	0.0265397	−	0.0459681i
$227$	−5.44949			−0.361695			−0.180848	−	0.983511i	$-0.557884\pi$
$227$	−5.44949			−0.361695			−0.180848	+	0.983511i	$0.557884\pi$
$228$	7.39898	−	1.50170i	0.490009	−	0.0994525i
$229$	−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
$231$	−2.00000	−	1.41421i	−0.131590	−	0.0930484i
$232$	1.22474	+	2.12132i	0.0804084	+	0.139272i
$233$	5.60102	+	3.23375i	0.366935	+	0.211850i	0.672119	−	0.740443i	$-0.265384\pi$
$233$	5.60102	+	3.23375i	0.366935	+	0.211850i	−0.305184	+	0.952294i	$0.598718\pi$
$234$	−9.79796	+	3.46410i	−0.640513	+	0.226455i
$235$	−9.10102			−0.593685
$236$	6.55051			0.426402
$237$	13.3485	−	6.14966i	0.867076	−	0.399464i
$238$	−24.2474	+	13.9993i	−1.57173	+	0.907438i
$239$			7.21393i			0.466630i	0.972401	+	0.233315i	$0.0749574\pi$
$239$			7.21393i			0.466630i	−0.972401	+	0.233315i	$0.925043\pi$
$240$	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
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$	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
$249$	−20.0454	−	14.1742i	−1.27033	−	0.898256i
$250$	−9.79796	−	5.65685i	−0.619677	−	0.357771i
$251$	5.72474	−	3.30518i	0.361343	−	0.208621i	−0.308327	−	0.951280i	$-0.599769\pi$
$251$	5.72474	−	3.30518i	0.361343	−	0.208621i	0.669670	+	0.742659i	$0.266436\pi$
$252$	−8.67423	+	10.1459i	−0.546425	+	0.639132i
$253$	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	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	−1.55051	−	0.142865i	−0.0965306	−	0.00889436i
$259$		−	3.46410i		−	0.215249i
$260$	−2.44949	−	4.24264i	−0.151911	−	0.263117i
$261$	4.77526	−	5.58542i	0.295581	−	0.345729i
$262$	19.0732	−	11.0119i	1.17835	−	0.680319i
$263$	−10.2247	−	5.90326i	−0.630485	−	0.364011i	0.150455	−	0.988617i	$-0.451926\pi$
$263$	−10.2247	−	5.90326i	−0.630485	−	0.364011i	−0.780940	+	0.624606i	$0.785259\pi$
$264$	−0.449490	−	0.317837i	−0.0276642	−	0.0195615i
$265$		−	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	$-0.564951\pi$
$269$	12.2474	−	21.2132i	0.746740	−	1.29339i	0.949377	−	0.314138i	$-0.101715\pi$
$270$	−7.12372	+	1.80348i	−0.433536	+	0.109756i
$271$	−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
$276$	11.1237	−	5.12472i	0.669570	−	0.308472i
$277$	−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
$279$	12.0000	−	4.24264i	0.718421	−	0.254000i
$280$	−5.44949	−	3.14626i	−0.325669	−	0.188025i
$281$	8.29796	+	14.3725i	0.495015	+	0.857391i	0.999983	−	0.00574696i	$-0.00182932\pi$
$281$	8.29796	+	14.3725i	0.495015	+	0.857391i	−0.504969	+	0.863138i	$0.668496\pi$
$282$	9.10102	+	6.43539i	0.541958	+	0.383222i
$283$	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
$285$	8.00000	−	7.07107i	0.473879	−	0.418854i
$286$	−1.10102			−0.0651047
$287$	6.67423	−	11.5601i	0.393968	−	0.682372i
$288$	−1.94949	+	2.28024i	−0.114875	+	0.134364i
$289$	11.2980	+	19.5686i	0.664586	+	1.15110i
$290$	3.00000	+	1.73205i	0.176166	+	0.101710i
$291$	−21.5227	+	9.91555i	−1.26168	+	0.581260i
$292$	−10.7980			−0.631903
$293$	4.65153			0.271745			0.135873	−	0.990726i	$-0.456616\pi$
$293$	4.65153			0.271745			0.135873	+	0.990726i	$0.456616\pi$
$294$	9.27526	+	20.1329i	0.540944	+	1.17417i
$295$	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
$300$	2.17423	+	4.71940i	0.125529	+	0.272474i
$301$	−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
$306$	14.3485	+	12.2672i	0.820247	+	0.701270i
$307$	−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
$309$	−16.8990	−	11.9494i	−0.961349	−	0.679777i
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$		−	15.5563i		−	0.882120i	−0.897478	−	0.441060i	$-0.854603\pi$
$311$		−	15.5563i		−	0.882120i	0.897478	−	0.441060i	$-0.145397\pi$
$312$	−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	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	−1.10102	+	1.55708i	−0.0617422	+	0.0873166i
$319$	0.674235	−	0.389270i	0.0377499	−	0.0217949i
$320$	−1.22474	−	0.707107i	−0.0684653	−	0.0395285i
$321$	−4.89898	+	6.92820i	−0.273434	+	0.386695i
$322$		−	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
$333$	−2.20204	+	0.778539i	−0.120671	+	0.0426637i
$334$	4.89898			0.268060
$335$	8.44949			0.461645
$336$	3.22474	+	6.99964i	0.175924	+	0.381861i
$337$	−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
$339$	−0.797959	+	1.12848i	−0.0433392	+	0.0612909i
$340$	−4.44949	+	7.70674i	−0.241307	+	0.417957i
$341$	1.34847			0.0730237
$342$	−13.0000	+	1.41421i	−0.702959	+	0.0764719i
$343$	25.7980			1.39296
$344$	−0.449490	+	0.778539i	−0.0242349	+	0.0419760i
$345$	10.0000	−	14.1421i	0.538382	−	0.761387i
$346$	−5.44949	−	9.43879i	−0.292966	−	0.507433i
$347$	−5.72474	−	3.30518i	−0.307320	−	0.177432i	0.338406	−	0.941000i	$-0.390112\pi$
$347$	−5.72474	−	3.30518i	−0.307320	−	0.177432i	−0.645727	+	0.763569i	$0.723445\pi$
$348$	−1.77526	−	3.85337i	−0.0951637	−	0.206562i
$349$	−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
$351$	17.4495	−	4.41761i	0.931385	−	0.235795i
$352$	−0.275255	+	0.158919i	−0.0146711	+	0.00847039i
$353$		−	14.6028i		−	0.777231i	−0.921400	−	0.388615i	$-0.872954\pi$
$353$		−	14.6028i		−	0.777231i	0.921400	−	0.388615i	$-0.127046\pi$
$354$	−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
$357$	44.0454	−	20.2918i	2.33113	−	1.07396i
$358$	−11.1742	+	19.3543i	−0.590577	+	1.02291i
$359$	20.8207	+	12.0208i	1.09887	+	0.634434i	0.935925	−	0.352200i	$-0.114566\pi$
$359$	20.8207	+	12.0208i	1.09887	+	0.634434i	0.162948	+	0.986635i	$0.447900\pi$
$360$	−0.775255	+	4.17121i	−0.0408595	+	0.219842i
$361$	15.8485	−	10.4798i	0.834130	−	0.551568i
$362$			13.0779i			0.687357i
$363$	10.8990	−	15.4135i	0.572048	−	0.808998i
$364$	13.3485	+	7.70674i	0.699650	+	0.403943i
$365$	−13.2247	+	7.63531i	−0.692215	+	0.399650i
$366$	−6.44949	+	9.12096i	−0.337120	+	0.476760i
$367$	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
$375$	16.0000	+	11.3137i	0.826236	+	0.584237i
$376$	5.57321	−	3.21770i	0.287417	−	0.165940i
$377$	−7.34847	−	4.24264i	−0.378465	−	0.218507i
$378$	16.5732	−	16.1206i	0.852434	−	0.829154i
$379$			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	−0.993391	−	0.114776i	$-0.963385\pi$
$383$	−7.77526	+	13.4671i	−0.397297	+	0.688139i	0.596094	+	0.802914i	$0.296718\pi$
$384$	0.724745	+	1.57313i	0.0369845	+	0.0802786i
$385$	−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	0.209475	−	0.977814i	$-0.432824\pi$
$389$	22.8990	−	13.2207i	1.16102	−	0.670318i	0.951549	+	0.307496i	$0.0994912\pi$
$390$	3.55051	+	7.70674i	0.179787	+	0.390246i
$391$	−44.4949			−2.25020
$392$	12.7980			0.646395
$393$	−34.6464	+	15.9617i	−1.74768	+	0.805160i
$394$	0.426786	+	0.246405i	0.0215012	+	0.0124137i
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$	0.724745	+	0.619620i	0.0364198	+	0.0311371i
$397$	−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
$399$	−10.6742	+	31.8519i	−0.534380	+	1.59459i
$400$	3.00000			0.150000
$401$	−6.39898	+	11.0834i	−0.319550	+	0.553476i	−0.980394	−	0.197047i	$-0.936865\pi$
$401$	−6.39898	+	11.0834i	−0.319550	+	0.553476i	0.660844	+	0.750523i	$0.270198\pi$
$402$	−8.44949	−	5.97469i	−0.421422	−	0.297991i
$403$	−7.34847	−	12.7279i	−0.366053	−	0.634023i
$404$	−8.57321	−	4.94975i	−0.426533	−	0.246259i
$405$	12.5732	−	1.97846i	0.624768	−	0.0983103i
$406$	−10.8990			−0.540907
$407$	−0.247449			−0.0122656
$408$	9.89898	−	4.56048i	0.490073	−	0.225777i
$409$	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
$414$	−20.0000	+	7.07107i	−0.982946	+	0.347524i
$415$	−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	$0.0291967\pi$
$419$			3.74983i			0.183191i	−0.995796	+	0.0915956i	$0.970803\pi$
$420$	8.89898	+	6.29253i	0.434226	+	0.307044i
$421$	−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
$423$	−14.6742	−	12.5457i	−0.713486	−	0.609994i
$424$	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	$-0.878053\pi$
$431$	−16.3485	−	28.3164i	−0.787478	−	1.36395i	0.140029	−	0.990147i	$-0.455280\pi$
$432$	3.72474	−	3.62302i	0.179207	−	0.174313i
$433$	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
$435$	−4.89898	−	3.46410i	−0.234888	−	0.166091i
$436$		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
$441$	−12.7980	−	36.1981i	−0.609427	−	1.72372i
$442$	10.8990	−	18.8776i	0.518412	−	0.897915i
$443$	−25.3207	+	14.6189i	−1.20302	+	0.694564i	−0.961226	−	0.275763i	$-0.911070\pi$
$443$	−25.3207	+	14.6189i	−1.20302	+	0.694564i	−0.241795	+	0.970327i	$0.577736\pi$
$444$	−0.123724	+	1.34278i	−0.00587170	+	0.0637256i
$445$			23.8988i			1.13291i
$446$	8.32577	−	4.80688i	0.394236	−	0.227613i
$447$	−7.67423	+	3.53553i	−0.362979	+	0.167225i
$448$	4.44949			0.210219
$449$	−11.2020			−0.528657			−0.264329	−	0.964433i	$-0.585150\pi$
$449$	−11.2020			−0.528657			−0.264329	+	0.964433i	$0.585150\pi$
$450$	−3.00000	−	8.48528i	−0.141421	−	0.400000i
$451$	−0.825765	−	0.476756i	−0.0388838	−	0.0224496i
$452$	0.398979	+	0.691053i	0.0187664	+	0.0325044i
$453$	25.5959	+	18.0990i	1.20260	+	0.850367i
$454$	2.72474	−	4.71940i	0.127879	−	0.221492i
$455$	21.7980			1.02190
$456$	−2.39898	+	7.15855i	−0.112343	+	0.335230i
$457$	−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
$459$	−22.7980	−	23.4381i	−1.06412	−	1.09400i
$460$	−5.00000	−	8.66025i	−0.233126	−	0.403786i
$461$	8.75255	+	5.05329i	0.407647	+	0.235355i	0.689778	−	0.724021i	$-0.257708\pi$
$461$	8.75255	+	5.05329i	0.407647	+	0.235355i	−0.282131	+	0.959376i	$0.591041\pi$
$462$	2.22474	−	1.02494i	0.103504	−	0.0476847i
$463$	−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
$465$	−4.34847	−	9.43879i	−0.201655	−	0.437714i
$466$	−5.60102	+	3.23375i	−0.259462	+	0.149801i
$467$			32.4162i			1.50004i	0.661415	+	0.750020i	$0.269956\pi$
$467$			32.4162i			1.50004i	−0.661415	+	0.750020i	$0.730044\pi$
$468$	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
$471$	−13.5505	−	29.4128i	−0.624375	−	1.35527i
$472$	−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
$477$	2.14643	−	2.51059i	0.0982782	−	0.114952i
$478$	−6.24745	−	3.60697i	−0.285752	−	0.164979i
$479$	−35.1464	+	20.2918i	−1.60588	+	0.927156i	−0.615603	+	0.788057i	$0.711087\pi$
$479$	−35.1464	+	20.2918i	−1.60588	+	0.927156i	−0.990278	+	0.139099i	$0.955579\pi$
$480$	2.00000	+	1.41421i	0.0912871	+	0.0645497i
$481$	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
$489$	3.65153	−	5.16404i	0.165128	−	0.233526i
$490$	15.6742	−	9.04952i	0.708090	−	0.408816i
$491$	4.10102	+	2.36773i	0.185076	+	0.106854i	0.589676	−	0.807640i	$-0.299256\pi$
$491$	4.10102	+	2.36773i	0.185076	+	0.106854i	−0.404599	+	0.914494i	$0.632589\pi$
$492$	−3.00000	+	4.24264i	−0.135250	+	0.191273i
$493$			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
$498$	22.2980	−	10.2727i	0.999195	−	0.460331i
$499$	−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	−0.769315	−	0.638870i	$-0.779402\pi$
$503$	−13.4722	+	7.77817i	−0.600695	+	0.346812i	0.168620	+	0.985681i	$0.446069\pi$
$504$	−4.44949	−	12.5851i	−0.198196	−	0.560583i
$505$	−14.0000			−0.622992
$506$	−2.24745			−0.0999113
$507$	0.724745	+	1.57313i	0.0321870	+	0.0698653i
$508$	9.00000	+	5.19615i	0.399310	+	0.230542i
$509$	20.6969	+	35.8481i	0.917376	+	1.58894i	0.803385	+	0.595459i	$0.203030\pi$
$509$	20.6969	+	35.8481i	0.917376	+	1.58894i	0.113990	+	0.993482i	$0.463637\pi$
$510$	8.89898	−	12.5851i	0.394053	−	0.557276i
$511$	24.0227	−	41.6085i	1.06270	−	1.84065i
$512$	1.00000			0.0441942
$513$	22.6464	−	0.373215i	0.999864	−	0.0164779i
$514$	−15.0000			−0.661622
$515$	−8.44949	+	14.6349i	−0.372329	+	0.644893i
$516$	0.898979	−	1.27135i	0.0395754	−	0.0559680i
$517$	−1.02270	−	1.77138i	−0.0449785	−	0.0779050i
$518$	3.00000	+	1.73205i	0.131812	+	0.0761019i
$519$	7.89898	+	17.1455i	0.346727	+	0.752605i
$520$	4.89898			0.214834
$521$	16.1010			0.705399			0.352699	−	0.935737i	$-0.385264\pi$
$521$	16.1010			0.705399			0.352699	+	0.935737i	$0.385264\pi$
$522$	2.44949	+	6.92820i	0.107211	+	0.303239i
$523$	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
$528$	0.500000	−	0.230351i	0.0217597	−	0.0100247i
$529$	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
$534$	16.8990	−	23.8988i	0.731290	−	1.03420i
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	−5.17423	+	2.98735i	−0.223493	+	0.129034i
$537$	22.3485	−	31.6055i	0.964408	−	1.36388i
$538$	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
$546$	−21.7980	−	15.4135i	−0.932867	−	0.659636i
$547$	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
$549$	12.5732	−	14.7064i	0.536612	−	0.627653i
$550$		−	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
$555$	0.797959	+	1.73205i	0.0338715	+	0.0735215i
$556$	−0.174235	+	0.301783i	−0.00738919	+	0.0127985i
$557$	24.2474	−	13.9993i	1.02740	−	0.593168i	0.111159	−	0.993803i	$-0.464544\pi$
$557$	24.2474	−	13.9993i	1.02740	−	0.593168i	0.916238	+	0.400634i	$0.131210\pi$
$558$	−2.32577	+	12.5136i	−0.0984575	+	0.529744i
$559$		−	3.11416i		−	0.131715i
$560$	5.44949	−	3.14626i	0.230283	−	0.132954i
$561$	−1.44949	−	3.14626i	−0.0611975	−	0.132835i
$562$	−16.5959			−0.700057
$563$	22.8434			0.962733			0.481367	−	0.876519i	$-0.340141\pi$
$563$	22.8434			0.962733			0.481367	+	0.876519i	$0.340141\pi$
$564$	−10.1237	+	4.66402i	−0.426286	+	0.196391i
$565$	0.977296	+	0.564242i	0.0411152	+	0.0237378i
$566$	2.27526	+	3.94086i	0.0956361	+	0.165647i
$567$	−31.1464	+	25.1701i	−1.30803	+	1.05705i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−34.2929			−1.43763			−0.718816	−	0.695201i	$-0.755315\pi$
$569$	−34.2929			−1.43763			−0.718816	+	0.695201i	$0.755315\pi$
$570$	2.12372	+	10.4637i	0.0889530	+	0.438278i
$571$	−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
$573$	27.5959	+	19.5133i	1.15284	+	0.815178i
$574$	6.67423	+	11.5601i	0.278577	+	0.482510i
$575$	18.3712	+	10.6066i	0.766131	+	0.442326i
$576$	−1.00000	−	2.82843i	−0.0416667	−	0.117851i
$577$	−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
$579$	−13.8990	+	6.40329i	−0.577622	+	0.266111i
$580$	−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
$585$	−4.89898	−	13.8564i	−0.202548	−	0.572892i
$586$	−2.32577	+	4.02834i	−0.0960765	+	0.166409i
$587$	4.10102	+	2.36773i	0.169267	+	0.0977265i	0.582240	−	0.813017i	$-0.302176\pi$
$587$	4.10102	+	2.36773i	0.169267	+	0.0977265i	−0.412973	+	0.910743i	$0.635510\pi$
$588$	−22.0732	−	2.03383i	−0.910284	−	0.0838739i
$589$	−5.32577	−	17.7098i	−0.219444	−	0.729719i
$590$			9.26382i			0.381385i
$591$	−0.696938	−	0.492810i	−0.0286682	−	0.0202715i
$592$	0.674235	+	0.389270i	0.0277109	+	0.0159989i
$593$	24.0959	−	13.9118i	0.989501	−	0.571289i	0.0843757	−	0.996434i	$-0.473110\pi$
$593$	24.0959	−	13.9118i	0.989501	−	0.571289i	0.905125	+	0.425145i	$0.139777\pi$
$594$	−1.15153	−	1.18386i	−0.0472479	−	0.0485745i
$595$	−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	$-0.963642\pi$
$599$	−14.5732	−	25.2415i	−0.595445	−	1.03134i	0.398038	−	0.917369i	$-0.369691\pi$
$600$	−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
$603$	13.6237	+	11.6476i	0.554801	+	0.474327i
$604$	15.6742	−	9.04952i	0.637776	−	0.368220i
$605$	−13.3485	−	7.70674i	−0.542692	−	0.313324i
$606$	14.0000	+	9.89949i	0.568711	+	0.402139i
$607$		−	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
$612$	−17.7980	+	6.29253i	−0.719440	+	0.254360i
$613$	−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	−0.737477	−	0.675372i	$-0.763983\pi$
$617$	−12.9495	+	7.47639i	−0.521327	+	0.300988i	0.216151	+	0.976360i	$0.430650\pi$
$618$	18.7980	−	8.66025i	0.756165	−	0.348367i
$619$	−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
$621$	35.6186	−	9.01742i	1.42933	−	0.361856i
$622$	13.4722	+	7.77817i	0.540186	+	0.311876i
$623$	−37.5959	−	65.1180i	−1.50625	−	2.60890i
$624$	−4.89898	−	3.46410i	−0.196116	−	0.138675i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−19.0000			−0.759393
$627$	2.27526	+	0.762485i	0.0908649	+	0.0304507i
$628$	−18.6969			−0.746089
$629$	2.44949	−	4.24264i	0.0976676	−	0.169165i
$630$	−14.3485	−	12.2672i	−0.571657	−	0.488738i
$631$	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
$633$	24.2474	−	11.1708i	0.963750	−	0.444001i
$634$	−6.00000			−0.238290
$635$	14.6969			0.583230
$636$	−0.797959	−	1.73205i	−0.0316411	−	0.0686803i
$637$	−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	$0.387625\pi$
$641$	−16.1969	+	28.0539i	−0.639741	+	1.10806i	−0.985490	+	0.169736i	$0.945708\pi$
$642$	−3.55051	−	7.70674i	−0.140127	−	0.304161i
$643$	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	$-0.950688\pi$
$647$		−	7.84961i		−	0.308600i	0.988024	−	0.154300i	$-0.0493122\pi$
$648$	−7.00000	+	5.65685i	−0.274986	+	0.222222i
$649$	1.80306	+	1.04100i	0.0707764	+	0.0408627i
$650$	−9.00000	+	5.19615i	−0.353009	+	0.203810i
$651$	26.6969	+	18.8776i	1.04634	+	0.739871i
$652$	−1.82577	−	3.16232i	−0.0715025	−	0.123846i
$653$			19.5133i			0.763613i	0.924242	+	0.381806i	$0.124698\pi$
$653$			19.5133i			0.763613i	−0.924242	+	0.381806i	$0.875302\pi$
$654$		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	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$	0.449490	−	0.635674i	0.0174964	−	0.0247436i
$661$	−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
$663$	−21.7980	+	30.8270i	−0.846563	+	1.19722i
$664$		−	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
$669$	−15.1237	+	6.96753i	−0.584717	+	0.269380i
$670$	−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
$675$	3.82577	+	15.1117i	0.147254	+	0.581650i
$676$	1.00000			0.0384615
$677$	3.30306			0.126947			0.0634735	−	0.997984i	$-0.479782\pi$
$677$	3.30306			0.126947			0.0634735	+	0.997984i	$0.479782\pi$
$678$	−0.578317	−	1.25529i	−0.0222101	−	0.0482093i
$679$	−52.7196	−	30.4377i	−2.02319	−	1.16809i
$680$	−4.44949	−	7.70674i	−0.170630	−	0.295540i
$681$	−5.44949	+	7.70674i	−0.208825	+	0.295323i
$682$	−0.674235	+	1.16781i	−0.0258178	+	0.0447177i
$683$	41.3939			1.58389			0.791946	−	0.610591i	$-0.209068\pi$
$683$	41.3939			1.58389			0.791946	+	0.610591i	$0.209068\pi$
$684$	5.27526	−	11.9654i	0.201704	−	0.457510i
$685$	−10.4495			−0.399254
$686$	−12.8990	+	22.3417i	−0.492485	+	0.853010i
$687$	−8.89898	+	12.5851i	−0.339517	+	0.480150i
$688$	−0.449490	−	0.778539i	−0.0171366	−	0.0296815i
$689$	−3.30306	−	1.90702i	−0.125837	−	0.0726518i
$690$	7.24745	+	15.7313i	0.275906	+	0.598881i
$691$	−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
$693$	−4.00000	+	1.41421i	−0.151947	+	0.0537215i
$694$	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
$699$	10.1742	−	4.68729i	0.384825	−	0.177290i
$700$	−6.67423	+	11.5601i	−0.252262	+	0.436931i
$701$	−8.57321	−	4.94975i	−0.323806	−	0.186949i	0.329282	−	0.944232i	$-0.393193\pi$
$701$	−8.57321	−	4.94975i	−0.323806	−	0.186949i	−0.653088	+	0.757282i	$0.726527\pi$
$702$	−4.89898	+	17.3205i	−0.184900	+	0.653720i
$703$	0.977296	+	3.24980i	0.0368594	+	0.122569i
$704$		−	0.317837i		−	0.0119789i
$705$	−9.10102	+	12.8708i	−0.342764	+	0.484742i
$706$	12.6464	+	7.30142i	0.475955	+	0.274793i
$707$	38.1464	−	22.0239i	1.43464	−	0.828292i
$708$	6.55051	−	9.26382i	0.246183	−	0.348156i
$709$	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
$717$	10.2020	+	7.21393i	0.381002	+	0.269409i
$718$	−20.8207	+	12.0208i	−0.777020	+	0.448613i
$719$	8.14643	+	4.70334i	0.303811	+	0.175405i	0.644153	−	0.764896i	$-0.277210\pi$
$719$	8.14643	+	4.70334i	0.303811	+	0.175405i	−0.340343	+	0.940301i	$0.610543\pi$
$720$	−3.22474	−	2.75699i	−0.120179	−	0.102747i
$721$		−	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
$726$	7.89898	+	17.1455i	0.293159	+	0.636331i
$727$	−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
$732$	−4.67423	−	10.1459i	−0.172765	−	0.375003i
$733$	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
$735$	−28.4722	+	13.1172i	−1.05021	+	0.483835i
$736$	6.12372	+	3.53553i	0.225723	+	0.130322i
$737$	0.949490	+	1.64456i	0.0349749	+	0.0605783i
$738$	5.84847	−	6.84072i	0.215285	−	0.251810i
$739$	−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
$741$	−5.20204	−	25.6308i	−0.191102	−	0.941572i
$742$	−4.89898			−0.179847
$743$	9.67423	−	16.7563i	0.354913	−	0.614728i	−0.632190	−	0.774814i	$-0.717844\pi$
$743$	9.67423	−	16.7563i	0.354913	−	0.614728i	0.987103	+	0.160086i	$0.0511771\pi$
$744$	6.00000	+	4.24264i	0.219971	+	0.155543i
$745$	3.44949	+	5.97469i	0.126380	+	0.218896i
$746$	22.0454	+	12.7279i	0.807140	+	0.466002i
$747$	−40.0908	+	14.1742i	−1.46685	+	0.518608i
$748$	−2.00000			−0.0731272
$749$	−21.7980			−0.796480
$750$	−17.7980	+	8.19955i	−0.649890	+	0.299405i
$751$	−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
$756$	5.67423	+	22.4131i	0.206370	+	0.815157i
$757$	−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	$-0.724891\pi$
$761$		−	41.9657i		−	1.52126i	0.649188	−	0.760628i	$-0.275109\pi$
$762$	−14.6969	−	10.3923i	−0.532414	−	0.376473i
$763$		0			0
$764$	16.8990	−	9.75663i	0.611384	−	0.352982i
$765$	−17.3485	+	20.2918i	−0.627235	+	0.733652i
$766$	−7.77526	−	13.4671i	−0.280931	−	0.486587i
$767$		−	22.6916i		−	0.819347i
$768$	−1.72474	−	0.158919i	−0.0622364	−	0.00573448i
$769$

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(0.724745 + 1.57313i) q^{6} +4.44949 q^{7} +1.00000 q^{8} +(-1.00000 - 2.82843i) 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} +(-2.22474 + 1.02494i) 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} +(4.44949 - 6.29253i) q^{21} +(0.275255 + 0.158919i) q^{22} +(-6.12372 + 3.53553i) q^{23} +(1.00000 - 1.41421i) 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} +(-0.449490 - 0.317837i) q^{33} +(-5.44949 + 3.14626i) q^{34} +(-5.44949 - 3.14626i) q^{35} +(-1.94949 + 2.28024i) 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} +(3.22474 + 6.99964i) 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} +(0.724745 + 1.57313i) q^{48} +12.7980 q^{49} +3.00000 q^{50} +(9.89898 - 4.56048i) q^{51} +(3.00000 + 1.73205i) q^{52} +(0.550510 + 0.953512i) q^{53} +(3.72474 - 3.62302i) q^{54} +(-0.224745 + 0.389270i) q^{55} +4.44949 q^{56} +(-2.39898 + 7.15855i) q^{57} -2.44949 q^{58} +(-3.27526 + 5.67291i) q^{59} +(2.00000 + 1.41421i) q^{60} +(3.22474 + 5.58542i) q^{61} +(-3.67423 - 2.12132i) q^{62} +(-4.44949 - 12.5851i) q^{63} +1.00000 q^{64} +4.89898 q^{65} +(0.500000 - 0.230351i) 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} +(-1.00000 - 2.82843i) 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} +(-4.89898 - 3.46410i) q^{78} +(7.34847 + 4.24264i) q^{79} +(1.22474 - 0.707107i) q^{80} +(-7.00000 + 5.65685i) 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} +(-3.22474 - 2.75699i) q^{90} +(-13.3485 + 7.70674i) q^{91} +(6.12372 + 3.53553i) q^{92} +(6.00000 + 4.24264i) 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} +(-0.898979 + 0.317837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 2 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} - 2 q^{12} - 12 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 12 q^{17} + 2 q^{18} - 2 q^{19} + 8 q^{21} + 6 q^{22} + 4 q^{24} - 6 q^{25} - 20 q^{27} - 4 q^{28} - 4 q^{30} - 2 q^{32} + 8 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} + 4 q^{38} - 12 q^{39} + 6 q^{41} + 8 q^{42} + 8 q^{43} - 6 q^{44} - 8 q^{45} - 12 q^{47} - 2 q^{48} + 12 q^{49} + 12 q^{50} + 20 q^{51} + 12 q^{52} + 12 q^{53} + 10 q^{54} + 4 q^{55} + 8 q^{56} + 10 q^{57} - 18 q^{59} + 8 q^{60} + 8 q^{61} - 8 q^{63} + 4 q^{64} + 2 q^{66} - 6 q^{67} + 20 q^{69} + 12 q^{70} - 12 q^{71} - 4 q^{72} + 2 q^{73} - 12 q^{74} - 6 q^{75} - 2 q^{76} - 28 q^{81} + 6 q^{82} - 16 q^{84} - 8 q^{85} + 8 q^{86} + 12 q^{87} - 24 q^{89} - 8 q^{90} - 24 q^{91} + 24 q^{93} + 24 q^{95} - 2 q^{96} - 18 q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 2 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 - 2 * q^12 - 12 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 + 12 * q^17 + 2 * q^18 - 2 * q^19 + 8 * q^21 + 6 * q^22 + 4 * q^24 - 6 * q^25 - 20 * q^27 - 4 * q^28 - 4 * q^30 - 2 * q^32 + 8 * q^33 - 12 * q^34 - 12 * q^35 + 2 * 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 - 2 * q^48 + 12 * q^49 + 12 * q^50 + 20 * q^51 + 12 * q^52 + 12 * q^53 + 10 * q^54 + 4 * q^55 + 8 * q^56 + 10 * q^57 - 18 * q^59 + 8 * q^60 + 8 * q^61 - 8 * q^63 + 4 * q^64 + 2 * q^66 - 6 * q^67 + 20 * q^69 + 12 * q^70 - 12 * q^71 - 4 * q^72 + 2 * q^73 - 12 * q^74 - 6 * q^75 - 2 * q^76 - 28 * q^81 + 6 * q^82 - 16 * q^84 - 8 * q^85 + 8 * q^86 + 12 * q^87 - 24 * q^89 - 8 * q^90 - 24 * q^91 + 24 * q^93 + 24 * q^95 - 2 * q^96 - 18 * q^97 - 6 * q^98 + 16 * q^99

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