LMFDB - Embedded newform 240.2.bc.d.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	240.43
Dual form			240.2.bc.d.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671462 + 1.24464i) q^{2} +1.00000i q^{3} +(-1.09828 + 1.67146i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.24464 + 0.671462i) q^{6} +(0.146365 - 0.146365i) q^{7} +(-2.81783 - 0.244644i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.671462 + 1.24464i) q^{2} +1.00000i q^{3} +(-1.09828 + 1.67146i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.24464 + 0.671462i) q^{6} +(0.146365 - 0.146365i) q^{7} +(-2.81783 - 0.244644i) q^{8} -1.00000 q^{9} +(0.0982788 + 3.16075i) q^{10} +(0.146365 - 0.146365i) q^{11} +(-1.67146 - 1.09828i) q^{12} +(0.280452 + 0.0838942i) q^{14} +(-1.00000 + 2.00000i) q^{15} +(-1.58757 - 3.67146i) q^{16} +(3.68585 - 3.68585i) q^{17} +(-0.671462 - 1.24464i) q^{18} +(-2.83221 + 2.83221i) q^{19} +(-3.86802 + 2.24464i) q^{20} +(0.146365 + 0.146365i) q^{21} +(0.280452 + 0.0838942i) q^{22} +(-2.83221 - 2.83221i) q^{23} +(0.244644 - 2.81783i) q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(0.0838942 + 0.405394i) q^{28} +(1.00000 + 1.00000i) q^{29} +(-3.16075 + 0.0982788i) q^{30} +0.292731i q^{31} +(3.50367 - 4.44120i) q^{32} +(0.146365 + 0.146365i) q^{33} +(7.06247 + 2.11266i) q^{34} +(0.439096 - 0.146365i) q^{35} +(1.09828 - 1.67146i) q^{36} +9.37169 q^{37} +(-5.42682 - 1.62337i) q^{38} +(-5.39101 - 3.30712i) q^{40} -4.00000i q^{41} +(-0.0838942 + 0.280452i) q^{42} +9.66442 q^{43} +(0.0838942 + 0.405394i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(1.62337 - 5.42682i) q^{46} +(-7.12494 - 7.12494i) q^{47} +(3.67146 - 1.58757i) q^{48} +6.95715i q^{49} +(-2.96419 + 6.41978i) q^{50} +(3.68585 + 3.68585i) q^{51} -11.9572i q^{53} +(1.24464 - 0.671462i) q^{54} +(0.439096 - 0.146365i) q^{55} +(-0.448240 + 0.376625i) q^{56} +(-2.83221 - 2.83221i) q^{57} +(-0.573183 + 1.91611i) q^{58} +(9.51806 + 9.51806i) q^{59} +(-2.24464 - 3.86802i) q^{60} +(1.68585 - 1.68585i) q^{61} +(-0.364346 + 0.196558i) q^{62} +(-0.146365 + 0.146365i) q^{63} +(7.88030 + 1.37873i) q^{64} +(-0.0838942 + 0.280452i) q^{66} -13.0790 q^{67} +(2.11266 + 10.2088i) q^{68} +(2.83221 - 2.83221i) q^{69} +(0.477009 + 0.448240i) q^{70} -4.58546 q^{71} +(2.81783 + 0.244644i) q^{72} +(-6.37169 + 6.37169i) q^{73} +(6.29273 + 11.6644i) q^{74} +(-4.00000 + 3.00000i) q^{75} +(-1.62337 - 7.84449i) q^{76} -0.0428457i q^{77} -4.58546 q^{79} +(0.496327 - 8.93049i) q^{80} +1.00000 q^{81} +(4.97858 - 2.68585i) q^{82} -8.58546i q^{83} +(-0.405394 + 0.0838942i) q^{84} +(11.0575 - 3.68585i) q^{85} +(6.48929 + 12.0288i) q^{86} +(-1.00000 + 1.00000i) q^{87} +(-0.448240 + 0.376625i) q^{88} -3.37169 q^{89} +(-0.0982788 - 3.16075i) q^{90} +(7.84449 - 1.62337i) q^{92} -0.292731 q^{93} +(4.08389 - 13.6521i) q^{94} +(-8.49663 + 2.83221i) q^{95} +(4.44120 + 3.50367i) q^{96} +(-3.58546 + 3.58546i) q^{97} +(-8.65918 + 4.67146i) q^{98} +(-0.146365 + 0.146365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	$ 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.671462	+	1.24464i	0.474795	+	0.880096i
$2$	0.671462	+	1.24464i	0.474795	+	0.880096i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.09828	+	1.67146i	−0.549139	+	0.835731i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	−1.24464	+	0.671462i	−0.508124	+	0.274123i
$7$	0.146365	−	0.146365i	0.0553210	−	0.0553210i	−0.678905	−	0.734226i	$-0.737545\pi$
$7$	0.146365	−	0.146365i	0.0553210	−	0.0553210i	0.734226	+	0.678905i	$0.237545\pi$
$8$	−2.81783	−	0.244644i	−0.996252	−	0.0864948i
$9$	−1.00000			−0.333333
$10$	0.0982788	+	3.16075i	0.0310785	+	0.999517i
$11$	0.146365	−	0.146365i	0.0441309	−	0.0441309i	−0.684697	−	0.728828i	$-0.740065\pi$
$11$	0.146365	−	0.146365i	0.0441309	−	0.0441309i	0.728828	+	0.684697i	$0.240065\pi$
$12$	−1.67146	−	1.09828i	−0.482509	−	0.317046i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	0.280452	+	0.0838942i	0.0749539	+	0.0224217i
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	−1.58757	−	3.67146i	−0.396892	−	0.917865i
$17$	3.68585	−	3.68585i	0.893949	−	0.893949i	−0.100943	−	0.994892i	$-0.532186\pi$
$17$	3.68585	−	3.68585i	0.893949	−	0.893949i	0.994892	+	0.100943i	$0.0321860\pi$
$18$	−0.671462	−	1.24464i	−0.158265	−	0.293365i
$19$	−2.83221	+	2.83221i	−0.649754	+	0.649754i	−0.952933	−	0.303180i	$-0.901952\pi$
$19$	−2.83221	+	2.83221i	−0.649754	+	0.649754i	0.303180	+	0.952933i	$0.401952\pi$
$20$	−3.86802	+	2.24464i	−0.864915	+	0.501918i
$21$	0.146365	+	0.146365i	0.0319396	+	0.0319396i
$22$	0.280452	+	0.0838942i	0.0597925	+	0.0178863i
$23$	−2.83221	−	2.83221i	−0.590557	−	0.590557i	0.347225	−	0.937782i	$-0.387124\pi$
$23$	−2.83221	−	2.83221i	−0.590557	−	0.590557i	−0.937782	+	0.347225i	$0.887124\pi$
$24$	0.244644	−	2.81783i	0.0499378	−	0.575187i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$	0.0838942	+	0.405394i	0.0158545	+	0.0766123i
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	0.793832	−	0.608137i	$-0.208083\pi$
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	−0.608137	+	0.793832i	$0.708083\pi$
$30$	−3.16075	+	0.0982788i	−0.577071	+	0.0179432i
$31$			0.292731i			0.0525760i	0.999654	+	0.0262880i	$0.00836870\pi$
$31$			0.292731i			0.0525760i	−0.999654	+	0.0262880i	$0.991631\pi$
$32$	3.50367	−	4.44120i	0.619368	−	0.785101i
$33$	0.146365	+	0.146365i	0.0254790	+	0.0254790i
$34$	7.06247	+	2.11266i	1.21120	+	0.362319i
$35$	0.439096	−	0.146365i	0.0742208	−	0.0247403i
$36$	1.09828	−	1.67146i	0.183046	−	0.278577i
$37$	9.37169			1.54070			0.770348	−	0.637623i	$-0.220082\pi$
$37$	9.37169			1.54070			0.770348	+	0.637623i	$0.220082\pi$
$38$	−5.42682	−	1.62337i	−0.880346	−	0.263346i
$39$		0			0
$40$	−5.39101	−	3.30712i	−0.852393	−	0.522901i
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$	−0.0838942	+	0.280452i	−0.0129452	+	0.0432746i
$43$	9.66442			1.47381			0.736905	−	0.675996i	$-0.236286\pi$
$43$	9.66442			1.47381			0.736905	+	0.675996i	$0.236286\pi$
$44$	0.0838942	+	0.405394i	0.0126475	+	0.0611155i
$45$	−2.00000	−	1.00000i	−0.298142	−	0.149071i
$46$	1.62337	−	5.42682i	0.239354	−	0.800141i
$47$	−7.12494	−	7.12494i	−1.03928	−	1.03928i	−0.999196	−	0.0400834i	$-0.987238\pi$
$47$	−7.12494	−	7.12494i	−1.03928	−	1.03928i	−0.0400834	−	0.999196i	$-0.512762\pi$
$48$	3.67146	−	1.58757i	0.529930	−	0.229146i
$49$			6.95715i			0.993879i
$50$	−2.96419	+	6.41978i	−0.419200	+	0.907894i
$51$	3.68585	+	3.68585i	0.516122	+	0.516122i
$52$		0			0
$53$		−	11.9572i		−	1.64244i	−0.570611	−	0.821221i	$-0.693293\pi$
$53$		−	11.9572i		−	1.64244i	0.570611	−	0.821221i	$-0.306707\pi$
$54$	1.24464	−	0.671462i	0.169375	−	0.0913743i
$55$	0.439096	−	0.146365i	0.0592078	−	0.0197359i
$56$	−0.448240	+	0.376625i	−0.0598986	+	0.0503287i
$57$	−2.83221	−	2.83221i	−0.375136	−	0.375136i
$58$	−0.573183	+	1.91611i	−0.0752626	+	0.251597i
$59$	9.51806	+	9.51806i	1.23915	+	1.23915i	0.960351	+	0.278795i	$0.0899350\pi$
$59$	9.51806	+	9.51806i	1.23915	+	1.23915i	0.278795	+	0.960351i	$0.410065\pi$
$60$	−2.24464	−	3.86802i	−0.289782	−	0.499359i
$61$	1.68585	−	1.68585i	0.215850	−	0.215850i	−0.590897	−	0.806747i	$-0.701226\pi$
$61$	1.68585	−	1.68585i	0.215850	−	0.215850i	0.806747	+	0.590897i	$0.201226\pi$
$62$	−0.364346	+	0.196558i	−0.0462720	+	0.0249628i
$63$	−0.146365	+	0.146365i	−0.0184403	+	0.0184403i
$64$	7.88030	+	1.37873i	0.985037	+	0.172341i
$65$		0			0
$66$	−0.0838942	+	0.280452i	−0.0103267	+	0.0345212i
$67$	−13.0790			−1.59785			−0.798925	−	0.601431i	$-0.794597\pi$
$67$	−13.0790			−1.59785			−0.798925	+	0.601431i	$0.794597\pi$
$68$	2.11266	+	10.2088i	0.256198	+	1.23800i
$69$	2.83221	−	2.83221i	0.340958	−	0.340958i
$70$	0.477009	+	0.448240i	0.0570135	+	0.0535749i
$71$	−4.58546			−0.544194			−0.272097	−	0.962270i	$-0.587717\pi$
$71$	−4.58546			−0.544194			−0.272097	+	0.962270i	$0.587717\pi$
$72$	2.81783	+	0.244644i	0.332084	+	0.0288316i
$73$	−6.37169	+	6.37169i	−0.745750	+	0.745750i	−0.973678	−	0.227928i	$-0.926805\pi$
$73$	−6.37169	+	6.37169i	−0.745750	+	0.745750i	0.227928	+	0.973678i	$0.426805\pi$
$74$	6.29273	+	11.6644i	0.731515	+	1.35596i
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	−1.62337	−	7.84449i	−0.186214	−	0.899825i
$77$		−	0.0428457i		−	0.00488272i
$78$		0			0
$79$	−4.58546			−0.515905			−0.257952	−	0.966158i	$-0.583048\pi$
$79$	−4.58546			−0.515905			−0.257952	+	0.966158i	$0.583048\pi$
$80$	0.496327	−	8.93049i	0.0554910	−	0.998459i
$81$	1.00000			0.111111
$82$	4.97858	−	2.68585i	0.549792	−	0.296602i
$83$		−	8.58546i		−	0.942377i	−0.882033	−	0.471188i	$-0.843825\pi$
$83$		−	8.58546i		−	0.942377i	0.882033	−	0.471188i	$-0.156175\pi$
$84$	−0.405394	+	0.0838942i	−0.0442322	+	0.00915360i
$85$	11.0575	−	3.68585i	1.19936	−	0.399786i
$86$	6.48929	+	12.0288i	0.699758	+	1.29710i
$87$	−1.00000	+	1.00000i	−0.107211	+	0.107211i
$88$	−0.448240	+	0.376625i	−0.0477826	+	0.0401484i
$89$	−3.37169			−0.357399			−0.178699	−	0.983904i	$-0.557189\pi$
$89$	−3.37169			−0.357399			−0.178699	+	0.983904i	$0.557189\pi$
$90$	−0.0982788	−	3.16075i	−0.0103595	−	0.333172i
$91$		0			0
$92$	7.84449	−	1.62337i	0.817845	−	0.169249i
$93$	−0.292731			−0.0303548
$94$	4.08389	−	13.6521i	0.421222	−	1.40811i
$95$	−8.49663	+	2.83221i	−0.871736	+	0.290579i
$96$	4.44120	+	3.50367i	0.453278	+	0.357592i
$97$	−3.58546	+	3.58546i	−0.364049	+	0.364049i	−0.865301	−	0.501253i	$-0.832873\pi$
$97$	−3.58546	+	3.58546i	−0.364049	+	0.364049i	0.501253	+	0.865301i	$0.332873\pi$
$98$	−8.65918	+	4.67146i	−0.874710	+	0.471889i
$99$	−0.146365	+	0.146365i	−0.0147103	+	0.0147103i
$100$	−9.98068	+	0.621269i	−0.998068	+	0.0621269i
$101$	−10.3717	−	10.3717i	−1.03202	−	1.03202i	−0.999470	−	0.0325519i	$-0.989637\pi$
$101$	−10.3717	−	10.3717i	−1.03202	−	1.03202i	−0.0325519	−	0.999470i	$-0.510363\pi$
$102$	−2.11266	+	7.06247i	−0.209185	+	0.699289i
$103$	−5.51806	−	5.51806i	−0.543710	−	0.543710i	0.380904	−	0.924615i	$-0.375613\pi$
$103$	−5.51806	−	5.51806i	−0.543710	−	0.543710i	−0.924615	+	0.380904i	$0.875613\pi$
$104$		0			0
$105$	0.146365	+	0.439096i	0.0142838	+	0.0428514i
$106$	14.8824	−	8.02877i	1.44551	−	0.779823i
$107$			11.3288i			1.09520i	0.836740	+	0.547600i	$0.184459\pi$
$107$			11.3288i			1.09520i	−0.836740	+	0.547600i	$0.815541\pi$
$108$	1.67146	+	1.09828i	0.160836	+	0.105682i
$109$	−10.2713	−	10.2713i	−0.983813	−	0.983813i	0.0160582	−	0.999871i	$-0.494888\pi$
$109$	−10.2713	−	10.2713i	−0.983813	−	0.983813i	−0.999871	+	0.0160582i	$0.994888\pi$
$110$	0.477009	+	0.448240i	0.0454811	+	0.0427380i
$111$			9.37169i			0.889522i
$112$	−0.769740	−	0.305010i	−0.0727336	−	0.0288208i
$113$	−1.68585	−	1.68585i	−0.158591	−	0.158591i	0.623351	−	0.781942i	$-0.285771\pi$
$113$	−1.68585	−	1.68585i	−0.158591	−	0.158591i	−0.781942	+	0.623351i	$0.785771\pi$
$114$	1.62337	−	5.42682i	0.152043	−	0.508268i
$115$	−2.83221	−	8.49663i	−0.264105	−	0.792315i
$116$	−2.76974	+	0.573183i	−0.257164	+	0.0532187i
$117$		0			0
$118$	−5.45559	+	18.2376i	−0.502227	+	1.67891i
$119$		−	1.07896i		−	0.0989082i
$120$	3.30712	−	5.39101i	0.301897	−	0.492130i
$121$			10.9572i			0.996105i
$122$	3.23026	+	0.966298i	0.292454	+	0.0874845i
$123$	4.00000			0.360668
$124$	−0.489289	−	0.321500i	−0.0439394	−	0.0288716i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−0.280452	−	0.0838942i	−0.0249846	−	0.00747389i
$127$	−3.85363	−	3.85363i	−0.341955	−	0.341955i	0.515147	−	0.857102i	$-0.327737\pi$
$127$	−3.85363	−	3.85363i	−0.341955	−	0.341955i	−0.857102	+	0.515147i	$0.827737\pi$
$128$	3.57529	+	10.7339i	0.316014	+	0.948755i
$129$			9.66442i			0.850905i
$130$		0			0
$131$	13.2253	+	13.2253i	1.15550	+	1.15550i	0.985432	+	0.170070i	$0.0543995\pi$
$131$	13.2253	+	13.2253i	1.15550	+	1.15550i	0.170070	+	0.985432i	$0.445601\pi$
$132$	−0.405394	+	0.0838942i	−0.0352851	+	0.00730205i
$133$			0.829076i			0.0718900i
$134$	−8.78202	−	16.2787i	−0.758651	−	1.40626i
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	−11.2878	+	9.48436i	−0.967921	+	0.813277i
$137$	−12.2713	−	12.2713i	−1.04841	−	1.04841i	−0.998767	−	0.0496415i	$-0.984192\pi$
$137$	−12.2713	−	12.2713i	−1.04841	−	1.04841i	−0.0496415	−	0.998767i	$-0.515808\pi$
$138$	5.42682	+	1.62337i	0.461961	+	0.138191i
$139$	−6.53948	−	6.53948i	−0.554672	−	0.554672i	0.373114	−	0.927786i	$-0.378290\pi$
$139$	−6.53948	−	6.53948i	−0.554672	−	0.554672i	−0.927786	+	0.373114i	$0.878290\pi$
$140$	−0.237606	+	0.894683i	−0.0200814	+	0.0756145i
$141$	7.12494	−	7.12494i	0.600028	−	0.600028i
$142$	−3.07896	−	5.70727i	−0.258381	−	0.478943i
$143$		0			0
$144$	1.58757	+	3.67146i	0.132297	+	0.305955i
$145$	1.00000	+	3.00000i	0.0830455	+	0.249136i
$146$	−12.2088	−	3.65214i	−1.01041	−	0.302254i
$147$	−6.95715			−0.573816
$148$	−10.2927	+	15.6644i	−0.846057	+	1.28761i
$149$	−8.37169	+	8.37169i	−0.685836	+	0.685836i	−0.961309	−	0.275473i	$-0.911166\pi$
$149$	−8.37169	+	8.37169i	−0.685836	+	0.685836i	0.275473	+	0.961309i	$0.411166\pi$
$150$	−6.41978	−	2.96419i	−0.524173	−	0.242025i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	8.67357	−	7.28780i	0.703519	−	0.591118i
$153$	−3.68585	+	3.68585i	−0.297983	+	0.297983i
$154$	0.0533277	−	0.0287692i	0.00429727	−	0.00231829i
$155$	−0.292731	+	0.585462i	−0.0235127	+	0.0470254i
$156$		0			0
$157$			24.7434i			1.97474i	0.158440	+	0.987369i	$0.449353\pi$
$157$			24.7434i			1.97474i	−0.158440	+	0.987369i	$0.550647\pi$
$158$	−3.07896	−	5.70727i	−0.244949	−	0.454046i
$159$	11.9572			0.948264
$160$	11.4485	−	5.37873i	0.905087	−	0.425226i
$161$	−0.829076			−0.0653403
$162$	0.671462	+	1.24464i	0.0527550	+	0.0977885i
$163$		−	7.41454i		−	0.580751i	−0.956913	−	0.290376i	$-0.906220\pi$
$163$		−	7.41454i		−	0.580751i	0.956913	−	0.290376i	$-0.0937803\pi$
$164$	6.68585	+	4.39312i	0.522077	+	0.343045i
$165$	0.146365	+	0.439096i	0.0113945	+	0.0341836i
$166$	10.6858	−	5.76481i	0.829383	−	0.447436i
$167$	12.2039	−	12.2039i	0.944366	−	0.944366i	−0.0541655	−	0.998532i	$-0.517250\pi$
$167$	12.2039	−	12.2039i	0.944366	−	0.944366i	0.998532	+	0.0541655i	$0.0172499\pi$
$168$	−0.376625	−	0.448240i	−0.0290573	−	0.0345825i
$169$	−13.0000			−1.00000
$170$	12.0123	+	11.2878i	0.921300	+	0.865735i
$171$	2.83221	−	2.83221i	0.216585	−	0.216585i
$172$	−10.6142	+	16.1537i	−0.809328	+	1.23171i
$173$	14.7434			1.12092			0.560459	−	0.828182i	$-0.310625\pi$
$173$	14.7434			1.12092			0.560459	+	0.828182i	$0.310625\pi$
$174$	−1.91611	−	0.573183i	−0.145260	−	0.0434529i
$175$	1.02456	+	0.146365i	0.0774493	+	0.0110642i
$176$	−0.769740	−	0.305010i	−0.0580214	−	0.0229910i
$177$	−9.51806	+	9.51806i	−0.715421	+	0.715421i
$178$	−2.26396	−	4.19656i	−0.169691	−	0.314545i
$179$	9.22533	−	9.22533i	0.689533	−	0.689533i	−0.272595	−	0.962129i	$-0.587882\pi$
$179$	9.22533	−	9.22533i	0.689533	−	0.689533i	0.962129	+	0.272595i	$0.0878821\pi$
$180$	3.86802	−	2.24464i	0.288305	−	0.167306i
$181$	−3.68585	−	3.68585i	−0.273967	−	0.273967i	0.556728	−	0.830695i	$-0.312057\pi$
$181$	−3.68585	−	3.68585i	−0.273967	−	0.273967i	−0.830695	+	0.556728i	$0.812057\pi$
$182$		0			0
$183$	1.68585	+	1.68585i	0.124621	+	0.124621i
$184$	7.28780	+	8.67357i	0.537264	+	0.639424i
$185$	18.7434	+	9.37169i	1.37804	+	0.689021i
$186$	−0.196558	−	0.364346i	−0.0144123	−	0.0267151i
$187$		−	1.07896i		−	0.0789015i
$188$	19.7342	−	4.08389i	1.43927	−	0.297849i
$189$	−0.146365	−	0.146365i	−0.0106465	−	0.0106465i
$190$	−9.23026	−	8.67357i	−0.669633	−	0.629247i
$191$			6.33558i			0.458426i	0.973376	+	0.229213i	$0.0736153\pi$
$191$			6.33558i			0.458426i	−0.973376	+	0.229213i	$0.926385\pi$
$192$	−1.37873	+	7.88030i	−0.0995013	+	0.568712i
$193$	0.414538	+	0.414538i	0.0298391	+	0.0298391i	0.721869	−	0.692030i	$-0.243283\pi$
$193$	0.414538	+	0.414538i	0.0298391	+	0.0298391i	−0.692030	+	0.721869i	$0.743283\pi$
$194$	−6.87012	−	2.05512i	−0.493246	−	0.147549i
$195$		0			0
$196$	−11.6286	−	7.64090i	−0.830615	−	0.545778i
$197$	−8.78623			−0.625993			−0.312996	−	0.949754i	$-0.601333\pi$
$197$	−8.78623			−0.625993			−0.312996	+	0.949754i	$0.601333\pi$
$198$	−0.280452	−	0.0838942i	−0.0199308	−	0.00596210i
$199$		−	11.7073i		−	0.829906i	−0.909843	−	0.414953i	$-0.863798\pi$
$199$		−	11.7073i		−	0.829906i	0.909843	−	0.414953i	$-0.136202\pi$
$200$	−7.47490	−	12.0052i	−0.528556	−	0.848899i
$201$		−	13.0790i		−	0.922519i
$202$	5.94488	−	19.8733i	0.418280	−	1.39828i
$203$	0.292731			0.0205457
$204$	−10.2088	+	2.11266i	−0.714762	+	0.147916i
$205$	4.00000	−	8.00000i	0.279372	−	0.558744i
$206$	3.16286	−	10.5732i	0.220367	−	0.736669i
$207$	2.83221	+	2.83221i	0.196852	+	0.196852i
$208$		0			0
$209$			0.829076i			0.0573484i
$210$	−0.448240	+	0.477009i	−0.0309315	+	0.0329168i
$211$	12.4966	+	12.4966i	0.860304	+	0.860304i	0.991373	−	0.131069i	$-0.0418411\pi$
$211$	12.4966	+	12.4966i	0.860304	+	0.860304i	−0.131069	+	0.991373i	$0.541841\pi$
$212$	19.9859	+	13.1323i	1.37264	+	0.901929i
$213$		−	4.58546i		−	0.314191i
$214$	−14.1004	+	7.60688i	−0.963882	+	0.519996i
$215$	19.3288	+	9.66442i	1.31822	+	0.659108i
$216$	−0.244644	+	2.81783i	−0.0166459	+	0.191729i
$217$	0.0428457	+	0.0428457i	0.00290856	+	0.00290856i
$218$	5.88734	−	19.6809i	0.398741	−	1.33296i
$219$	−6.37169	−	6.37169i	−0.430559	−	0.430559i
$220$	−0.237606	+	0.894683i	−0.0160194	+	0.0603195i
$221$		0			0
$222$	−11.6644	+	6.29273i	−0.782865	+	0.422340i
$223$	17.2253	−	17.2253i	1.15349	−	1.15349i	0.167646	−	0.985847i	$-0.446383\pi$
$223$	17.2253	−	17.2253i	1.15349	−	1.15349i	0.985847	−	0.167646i	$-0.0536165\pi$
$224$	−0.137222	−	1.16286i	−0.00916852	−	0.0776966i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	0.966298	−	3.23026i	0.0642772	−	0.214874i
$227$	8.29273			0.550408			0.275204	−	0.961386i	$-0.411255\pi$
$227$	8.29273			0.550408			0.275204	+	0.961386i	$0.411255\pi$
$228$	7.84449	−	1.62337i	0.519514	−	0.107511i
$229$	−10.2713	+	10.2713i	−0.678747	+	0.678747i	−0.959717	−	0.280970i	$-0.909344\pi$
$229$	−10.2713	+	10.2713i	−0.678747	+	0.678747i	0.280970	+	0.959717i	$0.409344\pi$
$230$	8.67357	−	9.23026i	0.571918	−	0.608625i
$231$	0.0428457			0.00281904
$232$	−2.57318	−	3.06247i	−0.168938	−	0.201061i
$233$	−8.27131	+	8.27131i	−0.541871	+	0.541871i	−0.924077	−	0.382206i	$-0.875165\pi$
$233$	−8.27131	+	8.27131i	−0.541871	+	0.541871i	0.382206	+	0.924077i	$0.375165\pi$
$234$		0			0
$235$	−7.12494	−	21.3748i	−0.464780	−	1.39434i
$236$	−26.3625	+	5.45559i	−1.71606	+	0.355128i
$237$		−	4.58546i		−	0.297858i
$238$	1.34292	−	0.724481i	0.0870488	−	0.0469611i
$239$	3.41454			0.220868			0.110434	−	0.993883i	$-0.464776\pi$
$239$	3.41454			0.220868			0.110434	+	0.993883i	$0.464776\pi$
$240$	8.93049	+	0.496327i	0.576461	+	0.0320378i
$241$	3.17092			0.204257			0.102129	−	0.994771i	$-0.467435\pi$
$241$	3.17092			0.204257			0.102129	+	0.994771i	$0.467435\pi$
$242$	−13.6378	+	7.35731i	−0.876668	+	0.472946i
$243$			1.00000i			0.0641500i
$244$	0.966298	+	4.66936i	0.0618609	+	0.298925i
$245$	−6.95715	+	13.9143i	−0.444476	+	0.888953i
$246$	2.68585	+	4.97858i	0.171243	+	0.317422i
$247$		0			0
$248$	0.0716150	−	0.824865i	0.00454755	−	0.0523790i
$249$	8.58546			0.544082
$250$	−12.3482	+	9.87537i	−0.780966	+	0.624573i
$251$	−3.85363	+	3.85363i	−0.243239	+	0.243239i	−0.818189	−	0.574950i	$-0.805022\pi$
$251$	−3.85363	+	3.85363i	−0.243239	+	0.243239i	0.574950	+	0.818189i	$0.305022\pi$
$252$	−0.0838942	−	0.405394i	−0.00528484	−	0.0255374i
$253$	−0.829076			−0.0521236
$254$	2.20884	−	7.38397i	0.138595	−	0.463312i
$255$	3.68585	+	11.0575i	0.230817	+	0.692450i
$256$	−10.9593	+	11.6574i	−0.684954	+	0.728587i
$257$	21.6430	−	21.6430i	1.35005	−	1.35005i	0.464458	−	0.885595i	$-0.346249\pi$
$257$	21.6430	−	21.6430i	1.35005	−	1.35005i	0.885595	−	0.464458i	$-0.153751\pi$
$258$	−12.0288	+	6.48929i	−0.748878	+	0.404005i
$259$	1.37169	−	1.37169i	0.0852328	−	0.0852328i
$260$		0			0
$261$	−1.00000	−	1.00000i	−0.0618984	−	0.0618984i
$262$	−7.58053	+	25.3411i	−0.468327	+	1.56558i
$263$	−14.2467	−	14.2467i	−0.878492	−	0.878492i	0.114886	−	0.993379i	$-0.463350\pi$
$263$	−14.2467	−	14.2467i	−0.878492	−	0.878492i	−0.993379	+	0.114886i	$0.963350\pi$
$264$	−0.376625	−	0.448240i	−0.0231797	−	0.0275873i
$265$	11.9572	−	23.9143i	0.734522	−	1.46904i
$266$	−1.03190	+	0.556693i	−0.0632701	+	0.0341330i
$267$		−	3.37169i		−	0.206344i
$268$	14.3643	−	21.8610i	0.877442	−	1.33537i
$269$	−11.7862	−	11.7862i	−0.718619	−	0.718619i	0.249703	−	0.968322i	$-0.419667\pi$
$269$	−11.7862	−	11.7862i	−0.718619	−	0.718619i	−0.968322	+	0.249703i	$0.919667\pi$
$270$	3.16075	−	0.0982788i	0.192357	−	0.00598106i
$271$			11.7073i			0.711166i	0.934645	+	0.355583i	$0.115718\pi$
$271$			11.7073i			0.711166i	−0.934645	+	0.355583i	$0.884282\pi$
$272$	−19.3840	−	7.68091i	−1.17533	−	0.465724i
$273$		0			0
$274$	7.03370	−	23.5131i	0.424921	−	1.42048i
$275$	1.02456	+	0.146365i	0.0617832	+	0.00882617i
$276$	1.62337	+	7.84449i	0.0977157	+	0.472183i
$277$	18.5426			1.11412			0.557059	−	0.830473i	$-0.311930\pi$
$277$	18.5426			1.11412			0.557059	+	0.830473i	$0.311930\pi$
$278$	3.74832	−	12.5303i	0.224809	−	0.751520i
$279$		−	0.292731i		−	0.0175253i
$280$	−1.27311	+	0.305010i	−0.0760826	+	0.0182278i
$281$			2.62831i			0.156792i	0.996922	+	0.0783958i	$0.0249798\pi$
$281$			2.62831i			0.156792i	−0.996922	+	0.0783958i	$0.975020\pi$
$282$	13.6521	+	4.08389i	0.812973	+	0.243192i
$283$	22.2499			1.32262			0.661309	−	0.750113i	$-0.270001\pi$
$283$	22.2499			1.32262			0.661309	+	0.750113i	$0.270001\pi$
$284$	5.03612	−	7.66442i	0.298838	−	0.454800i
$285$	−2.83221	−	8.49663i	−0.167766	−	0.503297i
$286$		0			0
$287$	−0.585462	−	0.585462i	−0.0345587	−	0.0345587i
$288$	−3.50367	+	4.44120i	−0.206456	+	0.261700i
$289$		−	10.1709i		−	0.598290i
$290$	−3.06247	+	3.25903i	−0.179835	+	0.191377i
$291$	−3.58546	−	3.58546i	−0.210184	−	0.210184i
$292$	−3.65214	−	17.6479i	−0.213726	−	1.03277i
$293$			21.9143i			1.28025i	0.768272	+	0.640124i	$0.221117\pi$
$293$			21.9143i			1.28025i	−0.768272	+	0.640124i	$0.778883\pi$
$294$	−4.67146	−	8.65918i	−0.272445	−	0.505014i
$295$	9.51806	+	28.5542i	0.554163	+	1.66249i
$296$	−26.4078	−	2.29273i	−1.53492	−	0.133262i
$297$	−0.146365	−	0.146365i	−0.00849299	−	0.00849299i
$298$	−16.0410	−	4.79851i	−0.929233	−	0.277970i
$299$		0			0
$300$	−0.621269	−	9.98068i	−0.0358690	−	0.576235i
$301$	1.41454	−	1.41454i	0.0815326	−	0.0815326i
$302$		0			0
$303$	10.3717	−	10.3717i	0.595838	−	0.595838i
$304$	14.8947	+	5.90203i	0.854269	+	0.338505i
$305$	5.05754	−	1.68585i	0.289594	−	0.0965313i
$306$	−7.06247	−	2.11266i	−0.403735	−	0.120773i
$307$	6.33558			0.361590			0.180795	−	0.983521i	$-0.442133\pi$
$307$	6.33558			0.361590			0.180795	+	0.983521i	$0.442133\pi$
$308$	0.0716150	+	0.0470565i	0.00408064	+	0.00268130i
$309$	5.51806	−	5.51806i	0.313911	−	0.313911i
$310$	−0.925249	+	0.0287692i	−0.0525506	+	0.00163398i
$311$	−7.32885			−0.415581			−0.207790	−	0.978173i	$-0.566627\pi$
$311$	−7.32885			−0.415581			−0.207790	+	0.978173i	$0.566627\pi$
$312$		0			0
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	−0.617220	−	0.786790i	$-0.711741\pi$
$313$	3.00000	−	3.00000i	0.169570	−	0.169570i	0.786790	+	0.617220i	$0.211741\pi$
$314$	−30.7967	+	16.6142i	−1.73796	+	0.937595i
$315$	−0.439096	+	0.146365i	−0.0247403	+	0.00824676i
$316$	5.03612	−	7.66442i	0.283304	−	0.431157i
$317$			19.9572i			1.12091i	0.828186	+	0.560453i	$0.189373\pi$
$317$			19.9572i			1.12091i	−0.828186	+	0.560453i	$0.810627\pi$
$318$	8.02877	+	14.8824i	0.450231	+	0.834564i
$319$	0.292731			0.0163898
$320$	14.3819	+	10.6378i	0.803971	+	0.594669i
$321$	−11.3288			−0.632315
$322$	−0.556693	−	1.03190i	−0.0310233	−	0.0575058i
$323$			20.8782i			1.16169i
$324$	−1.09828	+	1.67146i	−0.0610155	+	0.0928590i
$325$		0			0
$326$	9.22846	−	4.97858i	0.511117	−	0.275738i
$327$	10.2713	−	10.2713i	0.568005	−	0.568005i
$328$	−0.978577	+	11.2713i	−0.0540329	+	0.622354i
$329$	−2.08569			−0.114988
$330$	−0.448240	+	0.477009i	−0.0246748	+	0.0262585i
$331$	−12.4966	+	12.4966i	−0.686877	+	0.686877i	−0.961540	−	0.274663i	$-0.911434\pi$
$331$	−12.4966	+	12.4966i	−0.686877	+	0.686877i	0.274663	+	0.961540i	$0.411434\pi$
$332$	14.3503	+	9.42923i	0.787573	+	0.517496i
$333$	−9.37169			−0.513566
$334$	23.3840	+	6.99507i	1.27951	+	0.382753i
$335$	−26.1579	−	13.0790i	−1.42916	−	0.714580i
$336$	0.305010	−	0.769740i	0.0166397	−	0.0419928i
$337$	−15.5855	+	15.5855i	−0.848994	+	0.848994i	−0.990008	−	0.141013i	$-0.954964\pi$
$337$	−15.5855	+	15.5855i	−0.848994	+	0.848994i	0.141013	+	0.990008i	$0.454964\pi$
$338$	−8.72900	−	16.1804i	−0.474795	−	0.880096i
$339$	1.68585	−	1.68585i	0.0915626	−	0.0915626i
$340$	−5.98351	+	22.5303i	−0.324501	+	1.22188i
$341$	0.0428457	+	0.0428457i	0.00232023	+	0.00232023i
$342$	5.42682	+	1.62337i	0.293449	+	0.0877821i
$343$	2.04285	+	2.04285i	0.110303	+	0.110303i
$344$	−27.2327	−	2.36435i	−1.46829	−	0.127477i
$345$	8.49663	−	2.83221i	0.457443	−	0.152481i
$346$	9.89962	+	18.3503i	0.532207	+	0.986517i
$347$			14.7434i			0.791466i	0.918366	+	0.395733i	$0.129509\pi$
$347$			14.7434i			0.791466i	−0.918366	+	0.395733i	$0.870491\pi$
$348$	−0.573183	−	2.76974i	−0.0307258	−	0.148474i
$349$	−3.64300	−	3.64300i	−0.195005	−	0.195005i	0.602850	−	0.797855i	$-0.294032\pi$
$349$	−3.64300	−	3.64300i	−0.195005	−	0.195005i	−0.797855	+	0.602850i	$0.794032\pi$
$350$	0.505779	+	1.37349i	0.0270350	+	0.0734161i
$351$		0			0
$352$	−0.137222	−	1.16286i	−0.00731395	−	0.0619804i
$353$	3.68585	+	3.68585i	0.196178	+	0.196178i	0.798359	−	0.602181i	$-0.205702\pi$
$353$	3.68585	+	3.68585i	0.196178	+	0.196178i	−0.602181	+	0.798359i	$0.705702\pi$
$354$	−18.2376	−	5.45559i	−0.969318	−	0.289961i
$355$	−9.17092	−	4.58546i	−0.486742	−	0.243371i
$356$	3.70306	−	5.63565i	0.196262	−	0.298689i
$357$	1.07896			0.0571047
$358$	17.6767	+	5.28780i	0.934243	+	0.279469i
$359$			32.9933i			1.74132i	0.491887	+	0.870659i	$0.336307\pi$
$359$			32.9933i			1.74132i	−0.491887	+	0.870659i	$0.663693\pi$
$360$	5.39101	+	3.30712i	0.284131	+	0.174300i
$361$			2.95715i			0.155640i
$362$	2.11266	−	7.06247i	0.111039	−	0.371195i
$363$	−10.9572			−0.575101
$364$		0			0
$365$	−19.1151	+	6.37169i	−1.00053	+	0.333510i
$366$	−0.966298	+	3.23026i	−0.0505092	+	0.168848i
$367$	18.1035	+	18.1035i	0.944996	+	0.944996i	0.998564	−	0.0535682i	$-0.0170594\pi$
$367$	18.1035	+	18.1035i	0.944996	+	0.944996i	−0.0535682	+	0.998564i	$0.517059\pi$
$368$	−5.90203	+	14.8947i	−0.307665	+	0.776439i
$369$			4.00000i			0.208232i
$370$	0.921039	+	29.6216i	0.0478825	+	1.53995i
$371$	−1.75011	−	1.75011i	−0.0908614	−	0.0908614i
$372$	0.321500	−	0.489289i	0.0166690	−	0.0253684i
$373$			13.9143i			0.720456i	0.932864	+	0.360228i	$0.117301\pi$
$373$			13.9143i			0.720456i	−0.932864	+	0.360228i	$0.882699\pi$
$374$	1.34292	−	0.724481i	0.0694409	−	0.0374620i
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$	18.3338	+	21.8199i	0.945492	+	1.12528i
$377$		0			0
$378$	0.0838942	−	0.280452i	0.00431505	−	0.0144249i
$379$	−7.71040	−	7.71040i	−0.396057	−	0.396057i	0.480783	−	0.876840i	$-0.340353\pi$
$379$	−7.71040	−	7.71040i	−0.396057	−	0.396057i	−0.876840	+	0.480783i	$0.840353\pi$
$380$	4.59774	−	17.3124i	0.235859	−	0.888105i
$381$	3.85363	−	3.85363i	0.197428	−	0.197428i
$382$	−7.88554	+	4.25410i	−0.403459	+	0.217658i
$383$	−14.8322	+	14.8322i	−0.757891	+	0.757891i	−0.975938	−	0.218048i	$-0.930031\pi$
$383$	−14.8322	+	14.8322i	−0.757891	+	0.757891i	0.218048	+	0.975938i	$0.430031\pi$
$384$	−10.7339	+	3.57529i	−0.547764	+	0.182451i
$385$	0.0428457	−	0.0856914i	0.00218362	−	0.00436724i
$386$	−0.237606	+	0.794299i	−0.0120938	+	0.0404287i
$387$	−9.66442			−0.491270
$388$	−2.05512	−	9.93080i	−0.104333	−	0.504160i
$389$	−16.3717	+	16.3717i	−0.830078	+	0.830078i	−0.987527	−	0.157449i	$-0.949673\pi$
$389$	−16.3717	+	16.3717i	−0.830078	+	0.830078i	0.157449	+	0.987527i	$0.449673\pi$
$390$		0			0
$391$	−20.8782			−1.05586
$392$	1.70203	−	19.6041i	0.0859654	−	0.990154i
$393$	−13.2253	+	13.2253i	−0.667129	+	0.667129i
$394$	−5.89962	−	10.9357i	−0.297218	−	0.550934i
$395$	−9.17092	−	4.58546i	−0.461439	−	0.230720i
$396$	−0.0838942	−	0.405394i	−0.00421584	−	0.0203718i
$397$		−	0.628308i		−	0.0315339i	−0.999876	−	0.0157669i	$-0.994981\pi$
$397$		−	0.628308i		−	0.0315339i	0.999876	−	0.0157669i	$-0.00501898\pi$
$398$	14.5714	−	7.86098i	0.730398	−	0.394035i
$399$	−0.829076			−0.0415057
$400$	9.92314	−	17.3647i	0.496157	−	0.868233i
$401$	−8.54262			−0.426598			−0.213299	−	0.976987i	$-0.568421\pi$
$401$	−8.54262			−0.426598			−0.213299	+	0.976987i	$0.568421\pi$
$402$	16.2787	−	8.78202i	0.811905	−	0.438007i
$403$		0			0
$404$	28.7269	−	5.94488i	1.42922	−	0.295769i
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	0.196558	+	0.364346i	0.00975499	+	0.0180822i
$407$	1.37169	−	1.37169i	0.0679923	−	0.0679923i
$408$	−9.48436	−	11.2878i	−0.469546	−	0.558829i
$409$	38.7005			1.91362			0.956809	−	0.290716i	$-0.0938936\pi$
$409$	38.7005			1.91362			0.956809	+	0.290716i	$0.0938936\pi$
$410$	12.6430	−	0.393115i	0.624393	−	0.0194146i
$411$	12.2713	−	12.2713i	0.605299	−	0.605299i
$412$	15.2836	−	3.16286i	0.752968	−	0.155823i
$413$	2.78623			0.137101
$414$	−1.62337	+	5.42682i	−0.0797845	+	0.266714i
$415$	8.58546	−	17.1709i	0.421444	−	0.842888i
$416$		0			0
$417$	6.53948	−	6.53948i	0.320240	−	0.320240i
$418$	−1.03190	+	0.556693i	−0.0504721	+	0.0272287i
$419$	9.81079	−	9.81079i	0.479288	−	0.479288i	−0.425616	−	0.904904i	$-0.639942\pi$
$419$	9.81079	−	9.81079i	0.479288	−	0.479288i	0.904904	+	0.425616i	$0.139942\pi$
$420$	−0.894683	−	0.237606i	−0.0436561	−	0.0115940i
$421$	−20.2713	−	20.2713i	−0.987963	−	0.987963i	0.0119653	−	0.999928i	$-0.496191\pi$
$421$	−20.2713	−	20.2713i	−0.987963	−	0.987963i	−0.999928	+	0.0119653i	$0.996191\pi$
$422$	−7.16286	+	23.9449i	−0.348682	+	1.16562i
$423$	7.12494	+	7.12494i	0.346427	+	0.346427i
$424$	−2.92525	+	33.6932i	−0.142063	+	1.63629i
$425$	25.8009	+	3.68585i	1.25153	+	0.178790i
$426$	5.70727	−	3.07896i	0.276518	−	0.149176i
$427$		−	0.493499i		−	0.0238821i
$428$	−18.9357	−	12.4422i	−0.915293	−	0.601418i
$429$		0			0
$430$	0.949808	+	30.5468i	0.0458038	+	1.47310i
$431$		−	29.0790i		−	1.40068i	−0.713807	−	0.700342i	$-0.753031\pi$
$431$		−	29.0790i		−	1.40068i	0.713807	−	0.700342i	$-0.246969\pi$
$432$	−3.67146	+	1.58757i	−0.176643	+	0.0763819i
$433$	−8.95715	−	8.95715i	−0.430453	−	0.430453i	0.458329	−	0.888783i	$-0.348448\pi$
$433$	−8.95715	−	8.95715i	−0.430453	−	0.430453i	−0.888783	+	0.458329i	$0.848448\pi$
$434$	−0.0245584	+	0.0820969i	−0.00117884	+	0.00394078i
$435$	−3.00000	+	1.00000i	−0.143839	+	0.0479463i
$436$	28.4489	−	5.88734i	1.36245	−	0.281952i
$437$	16.0428			0.767433
$438$	3.65214	−	12.2088i	0.174506	−	0.583361i
$439$			7.03612i			0.335815i	0.985803	+	0.167908i	$0.0537011\pi$
$439$			7.03612i			0.335815i	−0.985803	+	0.167908i	$0.946299\pi$
$440$	−1.27311	+	0.305010i	−0.0606929	+	0.0145408i
$441$		−	6.95715i		−	0.331293i
$442$		0			0
$443$	−33.8652			−1.60898			−0.804492	−	0.593964i	$-0.797562\pi$
$443$	−33.8652			−1.60898			−0.804492	+	0.593964i	$0.797562\pi$
$444$	−15.6644	−	10.2927i	−0.743401	−	0.488471i
$445$	−6.74338	−	3.37169i	−0.319667	−	0.159834i
$446$	33.0055	+	9.87326i	1.56286	+	0.467512i
$447$	−8.37169	−	8.37169i	−0.395967	−	0.395967i
$448$	1.35520	−	0.951605i	0.0640273	−	0.0449591i
$449$		−	32.1151i		−	1.51560i	−0.652484	−	0.757802i	$-0.726273\pi$
$449$		−	32.1151i		−	1.51560i	0.652484	−	0.757802i	$-0.273727\pi$
$450$	2.96419	−	6.41978i	0.139733	−	0.302631i
$451$	−0.585462	−	0.585462i	−0.0275683	−	0.0275683i
$452$	4.66936	−	0.966298i	0.219628	−	0.0454508i
$453$		0			0
$454$	5.56825	+	10.3215i	0.261331	+	0.484412i
$455$		0			0
$456$	7.28780	+	8.67357i	0.341282	+	0.406177i
$457$	−4.41454	−	4.41454i	−0.206503	−	0.206503i	0.596276	−	0.802779i	$-0.296646\pi$
$457$	−4.41454	−	4.41454i	−0.206503	−	0.206503i	−0.802779	+	0.596276i	$0.796646\pi$
$458$	−19.6809	−	5.88734i	−0.919629	−	0.275097i
$459$	−3.68585	−	3.68585i	−0.172041	−	0.172041i
$460$	17.3124	+	4.59774i	0.807193	+	0.214371i
$461$	4.95715	−	4.95715i	0.230878	−	0.230878i	−0.582181	−	0.813059i	$-0.697801\pi$
$461$	4.95715	−	4.95715i	0.230878	−	0.230878i	0.813059	+	0.582181i	$0.197801\pi$
$462$	0.0287692	+	0.0533277i	0.00133847	+	0.00248103i
$463$	−2.77467	+	2.77467i	−0.128950	+	0.128950i	−0.768636	−	0.639686i	$-0.779064\pi$
$463$	−2.77467	+	2.77467i	−0.128950	+	0.128950i	0.639686	+	0.768636i	$0.279064\pi$
$464$	2.08389	−	5.25903i	0.0967424	−	0.244144i
$465$	−0.585462	−	0.292731i	−0.0271501	−	0.0135751i
$466$	−15.8487	−	4.74097i	−0.734177	−	0.219621i
$467$	−23.0361			−1.06598			−0.532992	−	0.846120i	$-0.678932\pi$
$467$	−23.0361			−1.06598			−0.532992	+	0.846120i	$0.678932\pi$
$468$		0			0
$469$	−1.91431	+	1.91431i	−0.0883946	+	0.0883946i
$470$	21.8199	−	23.2204i	1.00648	−	1.07108i
$471$	−24.7434			−1.14011
$472$	−24.4917	−	29.1488i	−1.12732	−	1.34168i
$473$	1.41454	−	1.41454i	0.0650405	−	0.0650405i
$474$	5.70727	−	3.07896i	0.262144	−	0.141421i
$475$	−19.8255	−	2.83221i	−0.909655	−	0.129951i
$476$	1.80344	+	1.18500i	0.0826606	+	0.0543144i
$477$			11.9572i			0.547480i
$478$	2.29273	+	4.24989i	0.104867	+	0.194385i
$479$	20.5855			0.940574			0.470287	−	0.882514i	$-0.344150\pi$
$479$	20.5855			0.940574			0.470287	+	0.882514i	$0.344150\pi$
$480$	5.37873	+	11.4485i	0.245504	+	0.522552i
$481$		0			0
$482$	2.12915	+	3.94667i	0.0969803	+	0.179766i
$483$		−	0.829076i		−	0.0377243i
$484$	−18.3145	−	12.0340i	−0.832476	−	0.547000i
$485$	−10.7564	+	3.58546i	−0.488422	+	0.162807i
$486$	−1.24464	+	0.671462i	−0.0564582	+	0.0304581i
$487$	5.31729	−	5.31729i	0.240949	−	0.240949i	−0.576293	−	0.817243i	$-0.695501\pi$
$487$	5.31729	−	5.31729i	0.240949	−	0.240949i	0.817243	+	0.576293i	$0.195501\pi$
$488$	−5.16286	+	4.33799i	−0.233711	+	0.196372i
$489$	7.41454			0.335297
$490$	−21.9898	+	0.683741i	−0.993399	+	0.0308883i
$491$	21.5181	−	21.5181i	0.971096	−	0.971096i	−0.0284975	−	0.999594i	$-0.509072\pi$
$491$	21.5181	−	21.5181i	0.971096	−	0.971096i	0.999594	+	0.0284975i	$0.00907227\pi$
$492$	−4.39312	+	6.68585i	−0.198057	+	0.301421i
$493$	7.37169			0.332004
$494$		0			0
$495$	−0.439096	+	0.146365i	−0.0197359	+	0.00657864i
$496$	1.07475	−	0.464730i	0.0482577	−	0.0208670i
$497$	−0.671153	+	0.671153i	−0.0301053	+	0.0301053i
$498$	5.76481	+	10.6858i	0.258327	+	0.478844i
$499$	−2.83221	+	2.83221i	−0.126787	+	0.126787i	−0.767653	−	0.640866i	$-0.778576\pi$
$499$	−2.83221	+	2.83221i	−0.126787	+	0.126787i	0.640866	+	0.767653i	$0.278576\pi$
$500$	−20.5826	−	8.73814i	−0.920483	−	0.390782i
$501$	12.2039	+	12.2039i	0.545230	+	0.545230i
$502$	−7.38397	−	2.20884i	−0.329563	−	0.0985852i
$503$	7.32571	+	7.32571i	0.326637	+	0.326637i	0.851306	−	0.524669i	$-0.175811\pi$
$503$	7.32571	+	7.32571i	0.326637	+	0.326637i	−0.524669	+	0.851306i	$0.675811\pi$
$504$	0.448240	−	0.376625i	0.0199662	−	0.0167762i
$505$	−10.3717	−	31.1151i	−0.461534	−	1.38460i
$506$	−0.556693	−	1.03190i	−0.0247480	−	0.0458738i
$507$		−	13.0000i		−	0.577350i
$508$	10.6736	−	2.20884i	0.473563	−	0.0980013i
$509$	10.1709	+	10.1709i	0.450818	+	0.450818i	0.895626	−	0.444808i	$-0.146728\pi$
$509$	10.1709	+	10.1709i	0.450818	+	0.450818i	−0.444808	+	0.895626i	$0.646728\pi$
$510$	−11.2878	+	12.0123i	−0.499832	+	0.531913i
$511$			1.86519i			0.0825112i
$512$	−21.8680	−	5.81289i	−0.966439	−	0.256896i
$513$	2.83221	+	2.83221i	0.125045	+	0.125045i
$514$	41.4703	+	12.4054i	1.82918	+	0.547178i
$515$	−5.51806	−	16.5542i	−0.243155	−	0.729464i
$516$	−16.1537	−	10.6142i	−0.711128	−	0.467265i
$517$	−2.08569			−0.0917286
$518$	2.62831	+	0.786230i	0.115481	+	0.0345450i
$519$			14.7434i			0.647163i
$520$		0			0
$521$			8.11508i			0.355528i	0.984073	+	0.177764i	$0.0568864\pi$
$521$			8.11508i			0.355528i	−0.984073	+	0.177764i	$0.943114\pi$
$522$	0.573183	−	1.91611i	0.0250875	−	0.0838657i
$523$	5.07896			0.222087			0.111044	−	0.993816i	$-0.464581\pi$
$523$	5.07896			0.222087			0.111044	+	0.993816i	$0.464581\pi$
$524$	−36.6307	+	7.58053i	−1.60022	+	0.331157i
$525$	−0.146365	+	1.02456i	−0.00638791	+	0.0447154i
$526$	8.16599	−	27.2983i	0.356054	−	1.19026i
$527$	1.07896	+	1.07896i	0.0470003	+	0.0470003i
$528$	0.305010	−	0.769740i	0.0132739	−	0.0334986i
$529$		−	6.95715i		−	0.302485i
$530$	37.7936	−	1.17513i	1.64165	−	0.0510446i
$531$	−9.51806	−	9.51806i	−0.413049	−	0.413049i
$532$	−1.38577	−	0.910557i	−0.0600807	−	0.0394776i
$533$		0			0
$534$	4.19656	−	2.26396i	0.181603	−	0.0979712i
$535$	−11.3288	+	22.6577i	−0.489789	+	0.979578i
$536$	36.8543	+	3.19969i	1.59186	+	0.138206i
$537$	9.22533	+	9.22533i	0.398102	+	0.398102i
$538$	6.75566	−	22.5837i	0.291257	−	0.973651i
$539$	1.01829	+	1.01829i	0.0438607	+	0.0438607i
$540$	2.24464	+	3.86802i	0.0965941	+	0.166453i
$541$	26.3864	−	26.3864i	1.13444	−	1.13444i	0.145009	−	0.989430i	$-0.453679\pi$
$541$	26.3864	−	26.3864i	1.13444	−	1.13444i	0.989430	−	0.145009i	$-0.0463211\pi$
$542$	−14.5714	+	7.86098i	−0.625895	+	0.337658i
$543$	3.68585	−	3.68585i	0.158175	−	0.158175i
$544$	−3.45559	−	29.2836i	−0.148157	−	1.25552i
$545$	−10.2713	−	30.8139i	−0.439974	−	1.31992i
$546$		0			0
$547$	−33.6644			−1.43939			−0.719693	−	0.694292i	$-0.755718\pi$
$547$	−33.6644			−1.43939			−0.719693	+	0.694292i	$0.755718\pi$
$548$	33.9883	−	7.03370i	1.45191	−	0.300465i
$549$	−1.68585	+	1.68585i	−0.0719502	+	0.0719502i
$550$	0.505779	+	1.37349i	0.0215665	+	0.0585658i
$551$	−5.66442			−0.241313
$552$	−8.67357	+	7.28780i	−0.369172	+	0.310189i
$553$	−0.671153	+	0.671153i	−0.0285403	+	0.0285403i
$554$	12.4507	+	23.0790i	0.528978	+	0.980531i
$555$	−9.37169	+	18.7434i	−0.397806	+	0.795612i
$556$	18.1127	−	3.74832i	0.768148	−	0.158964i
$557$		−	8.82908i		−	0.374100i	−0.982350	−	0.187050i	$-0.940107\pi$
$557$		−	8.82908i		−	0.374100i	0.982350	−	0.187050i	$-0.0598926\pi$
$558$	0.364346	−	0.196558i	0.0154240	−	0.00832095i
$559$		0			0
$560$	−1.23447	−	1.37976i	−0.0521659	−	0.0583055i
$561$	1.07896			0.0455538
$562$	−3.27131	+	1.76481i	−0.137992	+	0.0744439i
$563$			6.74338i			0.284200i	0.989852	+	0.142100i	$0.0453854\pi$
$563$			6.74338i			0.284200i	−0.989852	+	0.142100i	$0.954615\pi$
$564$	4.08389	+	19.7342i	0.171963	+	0.830961i
$565$	−1.68585	−	5.05754i	−0.0709241	−	0.212772i
$566$	14.9399	+	27.6932i	0.627973	+	1.16403i
$567$	0.146365	−	0.146365i	0.00614677	−	0.00614677i
$568$	12.9210	+	1.12181i	0.542155	+	0.0470700i
$569$	23.3717			0.979792			0.489896	−	0.871781i	$-0.337035\pi$
$569$	23.3717			0.979792			0.489896	+	0.871781i	$0.337035\pi$
$570$	8.67357	−	9.23026i	0.363296	−	0.386613i
$571$	−22.5395	+	22.5395i	−0.943248	+	0.943248i	−0.998474	−	0.0552260i	$-0.982412\pi$
$571$	−22.5395	+	22.5395i	−0.943248	+	0.943248i	0.0552260	+	0.998474i	$0.482412\pi$
$572$		0			0
$573$	−6.33558			−0.264673
$574$	0.335577	−	1.12181i	0.0140067	−	0.0468233i
$575$	2.83221	−	19.8255i	0.118111	−	0.826780i
$576$	−7.88030	−	1.37873i	−0.328346	−	0.0574471i
$577$	21.5855	−	21.5855i	0.898615	−	0.898615i	−0.0966991	−	0.995314i	$-0.530828\pi$
$577$	21.5855	−	21.5855i	0.898615	−	0.898615i	0.995314	+	0.0966991i	$0.0308285\pi$
$578$	12.6592	−	6.82938i	0.526553	−	0.284065i
$579$	−0.414538	+	0.414538i	−0.0172276	+	0.0172276i
$580$	−6.11266	−	1.62337i	−0.253815	−	0.0674070i
$581$	−1.25662	−	1.25662i	−0.0521332	−	0.0521332i
$582$	2.05512	−	6.87012i	0.0851877	−	0.284776i
$583$	−1.75011	−	1.75011i	−0.0724823	−	0.0724823i
$584$	19.5131	−	16.3955i	0.807459	−	0.678452i
$585$		0			0
$586$	−27.2755	+	14.7146i	−1.12674	+	0.607855i
$587$			16.5855i			0.684555i	0.939599	+	0.342278i	$0.111198\pi$
$587$			16.5855i			0.684555i	−0.939599	+	0.342278i	$0.888802\pi$
$588$	7.64090	−	11.6286i	0.315105	−	0.479556i
$589$	−0.829076	−	0.829076i	−0.0341615	−	0.0341615i
$590$	−29.1488	+	31.0196i	−1.20004	+	1.27706i
$591$		−	8.78623i		−	0.361417i
$592$	−14.8782	−	34.4078i	−0.611490	−	1.41415i
$593$	8.85677	+	8.85677i	0.363704	+	0.363704i	0.865175	−	0.501471i	$-0.167207\pi$
$593$	8.85677	+	8.85677i	0.363704	+	0.363704i	−0.501471	+	0.865175i	$0.667207\pi$
$594$	0.0838942	−	0.280452i	0.00344222	−	0.0115071i
$595$	1.07896	−	2.15792i	0.0442331	−	0.0884662i
$596$	−4.79851	−	23.1874i	−0.196555	−	0.949793i
$597$	11.7073			0.479147
$598$		0			0
$599$			24.9933i			1.02120i	0.859819	+	0.510599i	$0.170576\pi$
$599$			24.9933i			1.02120i	−0.859819	+	0.510599i	$0.829424\pi$
$600$	12.0052	−	7.47490i	0.490112	−	0.305162i
$601$			39.8286i			1.62464i	0.583210	+	0.812322i	$0.301797\pi$
$601$			39.8286i			1.62464i	−0.583210	+	0.812322i	$0.698203\pi$
$602$	2.71040	+	0.810789i	0.110468	+	0.0330453i
$603$	13.0790			0.532616
$604$		0			0
$605$	−10.9572	+	21.9143i	−0.445472	+	0.890943i
$606$	19.8733	+	5.94488i	0.807296	+	0.241494i
$607$	16.8469	+	16.8469i	0.683795	+	0.683795i	0.960853	−	0.277058i	$-0.0893595\pi$
$607$	16.8469	+	16.8469i	0.683795	+	0.683795i	−0.277058	+	0.960853i	$0.589360\pi$
$608$	2.65528	+	22.5016i	0.107686	+	0.912559i
$609$			0.292731i			0.0118621i
$610$	5.49422	+	5.16286i	0.222455	+	0.209038i
$611$		0			0
$612$	−2.11266	−	10.2088i	−0.0853994	−	0.412668i
$613$			8.62831i			0.348494i	0.984702	+	0.174247i	$0.0557491\pi$
$613$			8.62831i			0.348494i	−0.984702	+	0.174247i	$0.944251\pi$
$614$	4.25410	+	7.88554i	0.171681	+	0.318234i
$615$	8.00000	+	4.00000i	0.322591	+	0.161296i
$616$	−0.0104820	+	0.120732i	−0.000422330	+	0.00486442i
$617$	−11.0147	−	11.0147i	−0.443435	−	0.443435i	0.449730	−	0.893165i	$-0.351520\pi$
$617$	−11.0147	−	11.0147i	−0.443435	−	0.443435i	−0.893165	+	0.449730i	$0.851520\pi$
$618$	10.5732	+	3.16286i	0.425316	+	0.127229i
$619$	−6.53948	−	6.53948i	−0.262844	−	0.262844i	0.563365	−	0.826208i	$-0.309507\pi$
$619$	−6.53948	−	6.53948i	−0.262844	−	0.262844i	−0.826208	+	0.563365i	$0.809507\pi$
$620$	−0.657077	−	1.13229i	−0.0263888	−	0.0454738i
$621$	−2.83221	+	2.83221i	−0.113653	+	0.113653i
$622$	−4.92104	−	9.12181i	−0.197316	−	0.365751i
$623$	−0.493499	+	0.493499i	−0.0197716	+	0.0197716i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	5.74832	+	1.71955i	0.229749	+	0.0687270i
$627$	−0.829076			−0.0331101
$628$	−41.3576	−	27.1751i	−1.65035	−	1.08441i
$629$	34.5426	−	34.5426i	1.37730	−	1.37730i
$630$	−0.477009	−	0.448240i	−0.0190045	−	0.0178583i
$631$	42.0722			1.67487			0.837435	−	0.546538i	$-0.184054\pi$
$631$	42.0722			1.67487			0.837435	+	0.546538i	$0.184054\pi$
$632$	12.9210	+	1.12181i	0.513971	+	0.0446231i
$633$	−12.4966	+	12.4966i	−0.496697	+	0.496697i
$634$	−24.8396	+	13.4005i	−0.986505	+	0.532200i
$635$	−3.85363	−	11.5609i	−0.152927	−	0.458780i
$636$	−13.1323	+	19.9859i	−0.520729	+	0.792493i
$637$		0			0
$638$	0.196558	+	0.364346i	0.00778179	+	0.0144246i
$639$	4.58546			0.181398
$640$	−3.58336	+	25.0432i	−0.141645	+	0.989918i
$641$	16.8291			0.664709			0.332354	−	0.943155i	$-0.392157\pi$
$641$	16.8291			0.664709			0.332354	+	0.943155i	$0.392157\pi$
$642$	−7.60688	−	14.1004i	−0.300220	−	0.556498i
$643$			38.0722i			1.50142i	0.660631	+	0.750711i	$0.270289\pi$
$643$			38.0722i			1.50142i	−0.660631	+	0.750711i	$0.729711\pi$
$644$	0.910557	−	1.38577i	0.0358810	−	0.0546069i
$645$	−9.66442	+	19.3288i	−0.380536	+	0.761073i
$646$	−25.9859	+	14.0189i	−1.02240	+	0.551566i
$647$	−1.36856	+	1.36856i	−0.0538035	+	0.0538035i	−0.733497	−	0.679693i	$-0.762113\pi$
$647$	−1.36856	+	1.36856i	−0.0538035	+	0.0538035i	0.679693	+	0.733497i	$0.262113\pi$
$648$	−2.81783	−	0.244644i	−0.110695	−	0.00961054i
$649$	2.78623			0.109369
$650$		0			0
$651$	−0.0428457	+	0.0428457i	−0.00167926	+	0.00167926i
$652$	12.3931	+	8.14323i	0.485352	+	0.318913i
$653$	17.9572			0.702718			0.351359	−	0.936241i	$-0.385720\pi$
$653$	17.9572			0.702718			0.351359	+	0.936241i	$0.385720\pi$
$654$	19.6809	+	5.88734i	0.769585	+	0.230213i
$655$	13.2253	+	39.6760i	0.516756	+	1.55027i
$656$	−14.6858	+	6.35027i	−0.573386	+	0.247936i
$657$	6.37169	−	6.37169i	0.248583	−	0.248583i
$658$	−1.40046	−	2.59594i	−0.0545957	−	0.101200i
$659$	11.1825	−	11.1825i	0.435608	−	0.435608i	−0.454923	−	0.890531i	$-0.650333\pi$
$659$	11.1825	−	11.1825i	0.435608	−	0.435608i	0.890531	+	0.454923i	$0.150333\pi$
$660$	−0.894683	−	0.237606i	−0.0348255	−	0.00924880i
$661$	−3.01469	−	3.01469i	−0.117258	−	0.117258i	0.646043	−	0.763301i	$-0.276423\pi$
$661$	−3.01469	−	3.01469i	−0.117258	−	0.117258i	−0.763301	+	0.646043i	$0.776423\pi$
$662$	−23.9449	−	7.16286i	−0.930644	−	0.278392i
$663$		0			0
$664$	−2.10038	+	24.1923i	−0.0815107	+	0.938845i
$665$	−0.829076	+	1.65815i	−0.0321502	+	0.0643004i
$666$	−6.29273	−	11.6644i	−0.243838	−	0.451987i
$667$		−	5.66442i		−	0.219327i
$668$	6.99507	+	33.8016i	0.270647	+	1.30782i
$669$	17.2253	+	17.2253i	0.665970	+	0.665970i
$670$	−1.28538	−	41.3393i	−0.0496587	−	1.59708i
$671$		−	0.493499i		−	0.0190513i
$672$	1.16286	−	0.137222i	0.0448581	−	0.00529345i
$673$	−12.5725	−	12.5725i	−0.484633	−	0.484633i	0.421975	−	0.906608i	$-0.361337\pi$
$673$	−12.5725	−	12.5725i	−0.484633	−	0.484633i	−0.906608	+	0.421975i	$0.861337\pi$
$674$	−29.8634	−	8.93332i	−1.15029	−	0.344099i
$675$	4.00000	−	3.00000i	0.153960	−	0.115470i
$676$	14.2776	−	21.7290i	0.549139	−	0.835731i
$677$	−16.7862			−0.645147			−0.322574	−	0.946544i	$-0.604548\pi$
$677$	−16.7862			−0.645147			−0.322574	+	0.946544i	$0.604548\pi$
$678$	3.23026	+	0.966298i	0.124057	+	0.0371104i
$679$			1.04958i			0.0402790i
$680$	−32.0600	+	7.68091i	−1.22944	+	0.294550i
$681$			8.29273i			0.317778i
$682$	−0.0245584	+	0.0820969i	−0.000940391	+	0.00314365i
$683$	0.378422			0.0144799			0.00723997	−	0.999974i	$-0.497695\pi$
$683$	0.378422			0.0144799			0.00723997	+	0.999974i	$0.497695\pi$
$684$	1.62337	+	7.84449i	0.0620713	+	0.299942i
$685$	−12.2713	−	36.8139i	−0.468863	−	1.40659i
$686$	−1.17092	+	3.91431i	−0.0447061	+	0.149449i
$687$	−10.2713	−	10.2713i	−0.391875	−	0.391875i
$688$	−15.3429	−	35.4826i	−0.584943	−	1.35276i
$689$		0			0
$690$	9.23026	+	8.67357i	0.351390	+	0.330197i
$691$	7.79610	+	7.79610i	0.296577	+	0.296577i	0.839672	−	0.543094i	$-0.182747\pi$
$691$	7.79610	+	7.79610i	0.296577	+	0.296577i	−0.543094	+	0.839672i	$0.682747\pi$
$692$	−16.1923	+	24.6430i	−0.615541	+	0.936786i
$693$			0.0428457i			0.00162757i
$694$	−18.3503	+	9.89962i	−0.696567	+	0.375784i
$695$	−6.53948	−	19.6184i	−0.248057	−	0.744170i
$696$	3.06247	−	2.57318i	0.116083	−	0.0975362i
$697$	−14.7434	−	14.7434i	−0.558446	−	0.558446i
$698$	2.08810	−	6.98037i	0.0790359	−	0.264211i
$699$	−8.27131	−	8.27131i	−0.312850	−	0.312850i
$700$	−1.36990	+	1.55176i	−0.0517772	+	0.0586510i
$701$	−1.78623	+	1.78623i	−0.0674650	+	0.0674650i	−0.740034	−	0.672569i	$-0.765191\pi$
$701$	−1.78623	+	1.78623i	−0.0674650	+	0.0674650i	0.672569	+	0.740034i	$0.265191\pi$
$702$		0			0
$703$	−26.5426	+	26.5426i	−1.00107	+	1.00107i
$704$	1.35520	−	0.951605i	0.0510761	−	0.0358650i
$705$	21.3748	−	7.12494i	0.805023	−	0.268341i
$706$	−2.11266	+	7.06247i	−0.0795111	+	0.265800i
$707$	−3.03612			−0.114185
$708$	−5.45559	−	26.3625i	−0.205033	−	0.990765i
$709$	−21.6858	+	21.6858i	−0.814429	+	0.814429i	−0.985294	−	0.170865i	$-0.945344\pi$
$709$	−21.6858	+	21.6858i	−0.814429	+	0.814429i	0.170865	+	0.985294i	$0.445344\pi$
$710$	−0.450654	−	14.4935i	−0.0169127	−	0.543931i
$711$	4.58546			0.171968
$712$	9.50085	+	0.824865i	0.356059	+	0.0309131i
$713$	0.829076	−	0.829076i	0.0310491	−	0.0310491i
$714$	0.724481	+	1.34292i	0.0271130	+	0.0502576i
$715$		0			0
$716$	5.28780	+	25.5518i	0.197614	+	0.954914i
$717$			3.41454i			0.127518i
$718$	−41.0649	+	22.1537i	−1.53253	+	0.826769i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$	−0.496327	+	8.93049i	−0.0184970	+	0.332820i
$721$	−1.61531			−0.0601572
$722$	−3.68061	+	1.98562i	−0.136978	+	0.0738970i
$723$			3.17092i			0.117928i
$724$	10.2088	−	2.11266i	0.379408	−	0.0785165i
$725$	−1.00000	+	7.00000i	−0.0371391	+	0.259973i
$726$	−7.35731	−	13.6378i	−0.273055	−	0.506145i
$727$	33.6331	−	33.6331i	1.24738	−	1.24738i	0.290513	−	0.956871i	$-0.406174\pi$
$727$	33.6331	−	33.6331i	1.24738	−	1.24738i	0.956871	−	0.290513i	$-0.0938259\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−20.7655	−	19.5131i	−0.768567	−	0.722213i
$731$	35.6216	−	35.6216i	1.31751	−	1.31751i
$732$	−4.66936	+	0.966298i	−0.172584	+	0.0357154i
$733$	−20.1151			−0.742967			−0.371484	−	0.928439i	$-0.621151\pi$
$733$	−20.1151			−0.742967			−0.371484	+	0.928439i	$0.621151\pi$
$734$	−10.3766	+	34.6883i	−0.383008	+	1.28037i
$735$	−13.9143	−	6.95715i	−0.513237	−	0.256619i
$736$	−22.5016	+	2.65528i	−0.829419	+	0.0978749i
$737$	−1.91431	+	1.91431i	−0.0705145	+	0.0705145i
$738$	−4.97858	+	2.68585i	−0.183264	+	0.0988674i
$739$	17.7533	−	17.7533i	0.653064	−	0.653064i	−0.300666	−	0.953730i	$-0.597209\pi$
$739$	17.7533	−	17.7533i	0.653064	−	0.653064i	0.953730	+	0.300666i	$0.0972088\pi$
$740$	−36.2499	+	21.0361i	−1.33257	+	0.773303i
$741$		0			0
$742$	1.00314	−	3.35341i	0.0368263	−	0.123107i
$743$	−0.203904	−	0.203904i	−0.00748051	−	0.00748051i	0.703357	−	0.710837i	$-0.251684\pi$
$743$	−0.203904	−	0.203904i	−0.00748051	−	0.00748051i	−0.710837	+	0.703357i	$0.751684\pi$
$744$	0.824865	+	0.0716150i	0.0302410	+	0.00262553i
$745$	−25.1151	+	8.37169i	−0.920145	+	0.306715i
$746$	−17.3184	+	9.34292i	−0.634070	+	0.342069i
$747$			8.58546i			0.314126i
$748$	1.80344	+	1.18500i	0.0659404	+	0.0433279i
$749$	1.65815	+	1.65815i	0.0605876	+	0.0605876i
$750$	−9.87537	−	12.3482i	−0.360597	−	0.450891i
$751$		−	2.45065i		−	0.0894256i	−0.999000	−	0.0447128i	$-0.985763\pi$
$751$		−	2.45065i		−	0.0894256i	0.999000	−	0.0447128i	$-0.0142373\pi$
$752$	−14.8476	+	37.4703i	−0.541437	+	1.36640i
$753$	−3.85363	−	3.85363i	−0.140434	−	0.140434i
$754$		0			0
$755$		0			0
$756$	0.405394	−	0.0838942i	0.0147441	−	0.00305120i
$757$	37.2860			1.35518			0.677591	−	0.735439i	$-0.263024\pi$
$757$	37.2860			1.35518			0.677591	+	0.735439i	$0.263024\pi$
$758$	4.41947	−	14.7740i	0.160522	−	0.536614i
$759$		−	0.829076i		−	0.0300936i
$760$	24.6349	−	5.90203i	0.893603	−	0.214089i
$761$			12.2008i			0.442278i	0.975242	+	0.221139i	$0.0709774\pi$
$761$			12.2008i			0.442278i	−0.975242	+	0.221139i	$0.929023\pi$
$762$	7.38397	+	2.20884i	0.267493	+	0.0800177i
$763$	−3.00673			−0.108851
$764$	−10.5897	−	6.95823i	−0.383121	−	0.251740i
$765$	−11.0575	+	3.68585i	−0.399786	+	0.133262i
$766$	−28.4201	−	8.50157i	−1.02686	−	0.307174i
$767$		0			0
$768$	−11.6574	−	10.9593i	−0.420650	−	0.395458i
$769$		−	3.21377i		−	0.115891i	−0.998320	−	0.0579457i	$-0.981545\pi$
$769$		−	3.21377i		−	0.115891i	0.998320	−	0.0579457i	$-0.0184550\pi$
$770$	0.135425	−	0.00421083i	0.00488036	−	0.000151748i
$771$	21.6430	+	21.6430i	0.779454	+	0.779454i
$772$	−1.14816	+	0.237606i	−0.0413233	+	0.00855163i
$773$		−	42.6148i		−	1.53275i	−0.642394	−	0.766375i	$-0.722059\pi$
$773$		−	42.6148i		−	1.53275i	0.642394	−	0.766375i	$-0.277941\pi$
$774$	−6.48929	−	12.0288i	−0.233253	−	0.432365i
$775$	−1.17092	+	0.878193i	−0.0420608	+	0.0315456i
$776$	10.9804	−	9.22605i	0.394172	−	0.331196i
$777$	1.37169	+	1.37169i	0.0492092	+	0.0492092i
$778$	−31.3699	−	9.38397i	−1.12467	−	0.336432i
$779$	11.3288	+	11.3288i	0.405898	+	0.405898i
$780$		0			0
$781$	−0.671153	+	0.671153i	−0.0240158	+	0.0240158i
$782$	−14.0189	−	25.9859i	−0.501315	−	0.929255i
$783$	1.00000	−	1.00000i	0.0357371	−	0.0357371i
$784$	25.5429	−	11.0450i	0.912247	−	0.394463i
$785$	−24.7434	+	49.4868i	−0.883129	+	1.76626i
$786$	−25.3411	−	7.58053i	−0.903888	−	0.270389i
$787$	47.2369			1.68381			0.841907	−	0.539623i	$-0.181433\pi$
$787$	47.2369			1.68381			0.841907	+	0.539623i	$0.181433\pi$
$788$	9.64973	−	14.6858i	0.343757	−	0.523162i
$789$	14.2467	−	14.2467i	0.507198	−	0.507198i
$790$	−0.450654	−	14.4935i	−0.0160335	−	0.515656i
$791$	−0.493499			−0.0175468
$792$	0.448240	−	0.376625i	0.0159275	−	0.0133828i
$793$		0			0
$794$	0.782020	−	0.421884i	0.0277528	−	0.0149721i
$795$	23.9143	+	11.9572i	0.848153	+	0.424077i
$796$	19.5682	+	12.8578i	0.693578	+	0.455734i
$797$		−	19.8715i		−	0.703883i	−0.936022	−	0.351942i	$-0.885522\pi$
$797$		−	19.8715i		−	0.703883i	0.936022	−	0.351942i	$-0.114478\pi$
$798$	−0.556693	−	1.03190i	−0.0197067	−	0.0365290i
$799$	−52.5229			−1.85813
$800$	28.2758	+	0.691087i	0.999701	+	0.0244336i
$801$	3.37169			0.119133
$802$	−5.73604	−	10.6325i	−0.202547	−	0.375447i
$803$			1.86519i			0.0658212i
$804$	21.8610	+	14.3643i	0.770977	+	0.506591i
$805$	−1.65815	−	0.829076i	−0.0584422	−	0.0292211i
$806$		0			0
$807$	11.7862	−	11.7862i	0.414895	−	0.414895i
$808$	26.6883	+	31.7630i	0.938890	+	1.11742i
$809$	−38.3158			−1.34711			−0.673557	−	0.739136i	$-0.735234\pi$
$809$	−38.3158			−1.34711			−0.673557	+	0.739136i	$0.735234\pi$
$810$	0.0982788	+	3.16075i	0.00345316	+	0.111057i
$811$	7.50337	−	7.50337i	0.263479	−	0.263479i	−0.562987	−	0.826466i	$-0.690348\pi$
$811$	7.50337	−	7.50337i	0.263479	−	0.263479i	0.826466	+	0.562987i	$0.190348\pi$
$812$	−0.321500	+	0.489289i	−0.0112824	+	0.0171707i
$813$	−11.7073			−0.410592
$814$	2.62831	+	0.786230i	0.0921221	+	0.0275574i
$815$	7.41454	−	14.8291i	0.259720	−	0.519440i
$816$	7.68091	−	19.3840i	0.268886	−	0.678575i
$817$	−27.3717	+	27.3717i	−0.957614	+	0.957614i
$818$	25.9859	+	48.1684i	0.908577	+	1.68417i
$819$		0			0
$820$	8.97858	+	15.4721i	0.313546	+	0.540308i
$821$	35.1151	+	35.1151i	1.22552	+	1.22552i	0.965640	+	0.259885i	$0.0836847\pi$
$821$	35.1151	+	35.1151i	1.22552	+	1.22552i	0.259885	+	0.965640i	$0.416315\pi$
$822$	23.5131	+	7.03370i	0.820114	+	0.245329i
$823$	−30.8041	−	30.8041i	−1.07376	−	1.07376i	−0.997054	−	0.0767084i	$-0.975559\pi$
$823$	−30.8041	−	30.8041i	−1.07376	−	1.07376i	−0.0767084	−	0.997054i	$-0.524441\pi$
$824$	14.1990	+	16.8989i	0.494645	+	0.588701i
$825$	−0.146365	+	1.02456i	−0.00509579	+	0.0356705i
$826$	1.87085	+	3.46787i	0.0650951	+	0.120662i
$827$			23.9143i			0.831582i	0.909460	+	0.415791i	$0.136495\pi$
$827$			23.9143i			0.831582i	−0.909460	+	0.415791i	$0.863505\pi$
$828$	−7.84449	+	1.62337i	−0.272615	+	0.0564162i
$829$	8.47208	+	8.47208i	0.294247	+	0.294247i	0.838756	−	0.544508i	$-0.183284\pi$
$829$	8.47208	+	8.47208i	0.294247	+	0.294247i	−0.544508	+	0.838756i	$0.683284\pi$
$830$	27.1365	−	0.843769i	0.941922	−	0.0292876i
$831$			18.5426i			0.643236i
$832$		0			0
$833$	25.6430	+	25.6430i	0.888477	+	0.888477i
$834$	12.5303	+	3.74832i	0.433890	+	0.129794i
$835$	36.6117	−	12.2039i	1.26700	−	0.422334i
$836$	−1.38577	−	0.910557i	−0.0479278	−	0.0314923i
$837$	0.292731			0.0101183
$838$	18.7985	+	5.62337i	0.649384	+	0.194256i
$839$		−	49.5787i		−	1.71165i	−0.517267	−	0.855824i	$-0.673051\pi$
$839$		−	49.5787i		−	1.71165i	0.517267	−	0.855824i	$-0.326949\pi$
$840$	−0.305010	−	1.27311i	−0.0105239	−	0.0439263i
$841$		−	27.0000i		−	0.931034i
$842$	11.6192	−	38.8420i	0.400423	−	1.33858i
$843$	−2.62831			−0.0905237
$844$	−34.6124	+	7.16286i	−1.19141	+	0.246556i
$845$	−26.0000	−	13.0000i	−0.894427	−	0.447214i
$846$	−4.08389	+	13.6521i	−0.140407	+	0.469370i
$847$	1.60375	+	1.60375i	0.0551055	+	0.0551055i
$848$	−43.9002	+	18.9828i	−1.50754	+	0.651872i
$849$			22.2499i			0.763614i
$850$	12.7368	+	34.5879i	0.436867	+	1.18635i
$851$	−26.5426	−	26.5426i	−0.909869	−	0.909869i
$852$	7.66442	+	5.03612i	0.262579	+	0.172534i
$853$		−	28.6283i		−	0.980215i	−0.871662	−	0.490107i	$-0.836958\pi$
$853$		−	28.6283i		−	0.980215i	0.871662	−	0.490107i	$-0.163042\pi$
$854$	0.614231	−	0.331366i	0.0210186	−	0.0113391i
$855$	8.49663	−	2.83221i	0.290579	−	0.0968596i
$856$	2.77154	−	31.9227i	0.0947292	−	1.09110i
$857$	0.899616	+	0.899616i	0.0307303	+	0.0307303i	0.722305	−	0.691575i	$-0.243083\pi$
$857$	0.899616	+	0.899616i	0.0307303	+	0.0307303i	−0.691575	+	0.722305i	$0.743083\pi$
$858$		0			0
$859$	38.0754	+	38.0754i	1.29911	+	1.29911i	0.928977	+	0.370138i	$0.120690\pi$
$859$	38.0754	+	38.0754i	1.29911	+	1.29911i	0.370138	+	0.928977i	$0.379310\pi$
$860$	−37.3822	+	21.6932i	−1.27472	+	0.739732i
$861$	0.585462	−	0.585462i	0.0199525	−	0.0199525i
$862$	36.1930	−	19.5254i	1.23274	−	0.665038i
$863$	3.12494	−	3.12494i	0.106374	−	0.106374i	−0.651916	−	0.758291i	$-0.726035\pi$
$863$	3.12494	−	3.12494i	0.106374	−	0.106374i	0.758291	+	0.651916i	$0.226035\pi$
$864$	−4.44120	−	3.50367i	−0.151093	−	0.119197i
$865$	29.4868	+	14.7434i	1.00258	+	0.501290i
$866$	5.13409	−	17.1629i	0.174463	−	0.583218i
$867$	10.1709			0.345423
$868$	−0.118671	+	0.0245584i	−0.00402797	+	0.000833567i
$869$	−0.671153	+	0.671153i	−0.0227673	+	0.0227673i
$870$	−3.25903	−	3.06247i	−0.110491	−	0.103828i
$871$		0			0
$872$	26.4300	+	31.4556i	0.895031	+	1.06522i
$873$	3.58546	−	3.58546i	0.121350	−	0.121350i
$874$	10.7722	+	19.9676i	0.364374	+	0.675415i
$875$	1.90275	+	1.31729i	0.0643247	+	0.0445325i
$876$	17.6479	−	3.65214i	0.596268	−	0.123395i
$877$			0.743385i			0.0251023i	0.999921	+	0.0125512i	$0.00399526\pi$
$877$			0.743385i			0.0251023i	−0.999921	+	0.0125512i	$0.996005\pi$
$878$	−8.75746	+	4.72448i	−0.295550	+	0.159444i
$879$	−21.9143			−0.739151
$880$	−1.23447	−	1.37976i	−0.0416140	−	0.0465117i
$881$	−35.2860			−1.18882			−0.594408	−	0.804164i	$-0.702613\pi$
$881$	−35.2860			−1.18882			−0.594408	+	0.804164i	$0.702613\pi$
$882$	8.65918	−	4.67146i	0.291570	−	0.157296i
$883$			32.9870i			1.11010i	0.831817	+	0.555050i	$0.187301\pi$
$883$			32.9870i			1.11010i	−0.831817	+	0.555050i	$0.812699\pi$
$884$		0			0
$885$	−28.5542	+	9.51806i	−0.959838	+	0.319946i
$886$	−22.7392	−	42.1501i	−0.763937	−	1.41606i
$887$	−5.16779	+	5.16779i	−0.173517	+	0.173517i	−0.788523	−	0.615005i	$-0.789154\pi$
$887$	−5.16779	+	5.16779i	−0.173517	+	0.173517i	0.615005	+	0.788523i	$0.289154\pi$
$888$	2.29273	−	26.4078i	0.0769390	−	0.886188i
$889$	−1.12808			−0.0378345
$890$	−0.331366	−	10.6571i	−0.0111074	−	0.357226i
$891$	0.146365	−	0.146365i	0.00490343	−	0.00490343i
$892$	9.87326	+	47.7097i	0.330581	+	1.59744i
$893$	40.3587			1.35055
$894$	4.79851	−	16.0410i	0.160486	−	0.536493i
$895$	27.6760	−	9.22533i	0.925106	−	0.308369i
$896$	2.09438	+	1.04778i	0.0699682	+	0.0350038i
$897$		0			0
$898$	39.9718	−	21.5640i	1.33388	−	0.719601i
$899$	−0.292731	+	0.292731i	−0.00976312	+	0.00976312i
$900$	9.98068	−	0.621269i	0.332689	−	0.0207090i
$901$	−44.0722	−	44.0722i	−1.46826	−	1.46826i
$902$	0.335577	−	1.12181i	0.0111735	−	0.0373521i
$903$	1.41454	+	1.41454i	0.0470729	+	0.0470729i
$904$	4.33799	+	5.16286i	0.144279	+	0.171714i
$905$	−3.68585	−	11.0575i	−0.122522	−	0.367565i
$906$		0			0
$907$			6.74338i			0.223910i	0.993713	+	0.111955i	$0.0357113\pi$
$907$			6.74338i			0.223910i	−0.993713	+	0.111955i	$0.964289\pi$
$908$	−9.10773	+	13.8610i	−0.302251	+	0.459993i
$909$	10.3717	+	10.3717i	0.344007	+	0.344007i
$910$		0			0
$911$		−	1.16465i		−	0.0385867i	−0.999814	−	0.0192933i	$-0.993858\pi$
$911$		−	1.16465i		−	0.0385867i	0.999814	−	0.0192933i	$-0.00614164\pi$
$912$	−5.90203	+	14.8947i	−0.195436	+	0.493212i
$913$	−1.25662	−	1.25662i	−0.0415879	−	0.0415879i
$914$	2.53034	−	8.45872i	0.0836961	−	0.279790i
$915$	1.68585	+	5.05754i	0.0557324	+	0.167197i
$916$	−5.88734	−	28.4489i	−0.194523	−	0.939977i
$917$	3.87146			0.127847
$918$	2.11266	−	7.06247i	0.0697283	−	0.233096i
$919$		−	25.8652i		−	0.853214i	−0.904437	−	0.426607i	$-0.859709\pi$
$919$		−	25.8652i		−	0.853214i	0.904437	−	0.426607i	$-0.140291\pi$
$920$	5.90203	+	24.6349i	0.194584	+	0.812190i
$921$			6.33558i			0.208764i
$922$	9.49843	+	2.84136i	0.312814	+	0.0935751i
$923$		0			0
$924$	−0.0470565	+	0.0716150i	−0.00154805	+	0.00235596i
$925$	28.1151	+	37.4868i	0.924418	+	1.23256i
$926$	−5.31657	−	1.59039i	−0.174713	−	0.0522636i
$927$	5.51806	+	5.51806i	0.181237	+	0.181237i
$928$	7.94488	−	0.937529i	0.260803	−	0.0307759i
$929$			37.2003i			1.22050i	0.792208	+	0.610251i	$0.208932\pi$
$929$			37.2003i			1.22050i	−0.792208	+	0.610251i	$0.791068\pi$
$930$	−0.0287692	−	0.925249i	−0.000943381	−	0.0303401i
$931$	−19.7041	−	19.7041i	−0.645777	−	0.645777i
$932$	−4.74097	−	22.9094i	−0.155296	−	0.750422i
$933$		−	7.32885i		−	0.239936i
$934$	−15.4679	−	28.6718i	−0.506124	−	0.938169i
$935$	1.07896	−	2.15792i	0.0352858	−	0.0705716i
$936$		0			0
$937$	−20.9143	−	20.9143i	−0.683241	−	0.683241i	0.277488	−	0.960729i	$-0.410498\pi$
$937$	−20.9143	−	20.9143i	−0.683241	−	0.683241i	−0.960729	+	0.277488i	$0.910498\pi$
$938$	−3.66802	−	1.09725i	−0.119765	−	0.0358264i
$939$	3.00000	+	3.00000i	0.0979013	+	0.0979013i
$940$	43.5524	+	11.5665i	1.42052	+	0.377256i
$941$	−5.58546	+	5.58546i	−0.182081	+	0.182081i	−0.792262	−	0.610181i	$-0.791097\pi$
$941$	−5.58546	+	5.58546i	−0.182081	+	0.182081i	0.610181	+	0.792262i	$0.291097\pi$
$942$	−16.6142	−	30.7967i	−0.541321	−	1.00341i
$943$	−11.3288	+	11.3288i	−0.368918	+	0.368918i
$944$	19.8346	−	50.0557i	0.645562	−	1.62918i
$945$	−0.146365	−	0.439096i	−0.00476127	−	0.0142838i
$946$	2.71040	+	0.810789i	0.0881229	+	0.0263610i
$947$	−20.7925			−0.675666			−0.337833	−	0.941206i	$-0.609694\pi$
$947$	−20.7925			−0.675666			−0.337833	+	0.941206i	$0.609694\pi$
$948$	7.66442	+	5.03612i	0.248929	+	0.163565i
$949$		0			0
$950$	−9.78695	−	26.5774i	−0.317531	−	0.862285i
$951$	−19.9572			−0.647155
$952$	−0.263962	+	3.04033i	−0.00855505	+	0.0985375i
$953$	16.3142	−	16.3142i	0.528467	−	0.528467i	−0.391648	−	0.920115i	$-0.628095\pi$
$953$	16.3142	−	16.3142i	0.528467	−	0.528467i	0.920115	+	0.391648i	$0.128095\pi$
$954$	−14.8824	+	8.02877i	−0.481836	+	0.259941i
$955$	−6.33558	+	12.6712i	−0.205014	+	0.410029i
$956$	−3.75011	+	5.70727i	−0.121287	+	0.184586i
$957$			0.292731i			0.00946265i
$958$	13.8223	+	25.6216i	0.446580	+	0.827796i
$959$	−3.59219			−0.115998
$960$	−10.6378	+	14.3819i	−0.343332	+	0.464173i
$961$	30.9143			0.997236
$962$		0			0
$963$		−	11.3288i		−	0.365067i
$964$	−3.48256	+	5.30008i	−0.112166	+	0.170704i
$965$	0.414538	+	1.24361i	0.0133445	+	0.0400334i
$966$	1.03190	−	0.556693i	0.0332010	−	0.0179113i
$967$	−19.5672	+	19.5672i	−0.629238	+	0.629238i	−0.947876	−	0.318638i	$-0.896774\pi$
$967$	−19.5672	+	19.5672i	−0.629238	+	0.629238i	0.318638	+	0.947876i	$0.396774\pi$
$968$	2.68061	−	30.8754i	0.0861579	−	0.992372i
$969$	−20.8782			−0.670704
$970$	−11.6851	−	10.9804i	−0.375187	−	0.352559i
$971$	12.8469	−	12.8469i	0.412277	−	0.412277i	−0.470254	−	0.882531i	$-0.655838\pi$
$971$	12.8469	−	12.8469i	0.412277	−	0.412277i	0.882531	+	0.470254i	$0.155838\pi$
$972$	−1.67146	−	1.09828i	−0.0536122	−	0.0352273i
$973$	−1.91431			−0.0613699
$974$	10.1885	+	3.04778i	0.326460	+	0.0976571i
$975$		0			0
$976$	−8.86591	−	3.51313i	−0.283791	−	0.112452i
$977$	−27.6430	+	27.6430i	−0.884378	+	0.884378i	−0.993976	−	0.109598i	$-0.965044\pi$
$977$	−27.6430	+	27.6430i	−0.884378	+	0.884378i	0.109598	+	0.993976i	$0.465044\pi$
$978$	4.97858	+	9.22846i	0.159197	+	0.295094i
$979$	−0.493499	+	0.493499i	−0.0157723	+	0.0157723i
$980$	−15.6163	−	26.9104i	−0.498846	−	0.859621i
$981$	10.2713	+	10.2713i	0.327938	+	0.327938i
$982$	41.2309	+	12.3338i	1.31573	+	0.393587i
$983$	−22.1611	−	22.1611i	−0.706828	−	0.706828i	0.259039	−	0.965867i	$-0.416594\pi$
$983$	−22.1611	−	22.1611i	−0.706828	−	0.706828i	−0.965867	+	0.259039i	$0.916594\pi$
$984$	−11.2713	−	0.978577i	−0.359316	−	0.0311959i
$985$	−17.5725	−	8.78623i	−0.559905	−	0.279953i
$986$	4.94981	+	9.17513i	0.157634	+	0.292196i
$987$		−	2.08569i		−	0.0663883i
$988$		0			0
$989$	−27.3717	−	27.3717i	−0.870369	−	0.870369i
$990$	−0.477009	−	0.448240i	−0.0151604	−	0.0142460i
$991$		−	50.9504i		−	1.61849i	−0.587469	−	0.809247i	$-0.699876\pi$
$991$		−	50.9504i		−	1.61849i	0.587469	−	0.809247i	$-0.300124\pi$
$992$	1.30008	+	1.02563i	0.0412775	+	0.0325639i
$993$	−12.4966	−	12.4966i	−0.396569	−	0.396569i
$994$	−1.28600	−	0.384694i	−0.0407895	−	0.0122017i
$995$	11.7073	−	23.4145i	0.371145	−	0.742291i
$996$	−9.42923	+	14.3503i	−0.298777	+	0.454706i
$997$	−19.9143			−0.630692			−0.315346	−	0.948977i	$-0.602121\pi$
$997$	−19.9143			−0.630692			−0.315346	+	0.948977i	$0.602121\pi$
$998$	−5.42682	−	1.62337i	−0.171783	−	0.0513870i
$999$		−	9.37169i		−	0.296507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bc.d.43.3	yes	6
3.2	odd	2		720.2.bd.e.523.1		6
4.3	odd	2		960.2.bc.d.463.2		6
5.2	odd	4		240.2.y.d.187.1	yes	6
8.3	odd	2		1920.2.bc.h.1183.2		6
8.5	even	2		1920.2.bc.g.1183.2		6
15.2	even	4		720.2.z.e.667.3		6
16.3	odd	4		240.2.y.d.163.1	✓	6
16.5	even	4		1920.2.y.h.223.2		6
16.11	odd	4		1920.2.y.g.223.2		6
16.13	even	4		960.2.y.d.943.2		6
20.7	even	4		960.2.y.d.847.2		6
40.27	even	4		1920.2.y.h.1567.2		6
40.37	odd	4		1920.2.y.g.1567.2		6
48.35	even	4		720.2.z.e.163.3		6
80.27	even	4		1920.2.bc.g.607.2		6
80.37	odd	4		1920.2.bc.h.607.2		6
80.67	even	4	inner	240.2.bc.d.67.3	yes	6
80.77	odd	4		960.2.bc.d.367.2		6
240.227	odd	4		720.2.bd.e.307.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.1	✓	6	16.3	odd	4
240.2.y.d.187.1	yes	6	5.2	odd	4
240.2.bc.d.43.3	yes	6	1.1	even	1	trivial
240.2.bc.d.67.3	yes	6	80.67	even	4	inner
720.2.z.e.163.3		6	48.35	even	4
720.2.z.e.667.3		6	15.2	even	4
720.2.bd.e.307.1		6	240.227	odd	4
720.2.bd.e.523.1		6	3.2	odd	2
960.2.y.d.847.2		6	20.7	even	4
960.2.y.d.943.2		6	16.13	even	4
960.2.bc.d.367.2		6	80.77	odd	4
960.2.bc.d.463.2		6	4.3	odd	2
1920.2.y.g.223.2		6	16.11	odd	4
1920.2.y.g.1567.2		6	40.37	odd	4
1920.2.y.h.223.2		6	16.5	even	4
1920.2.y.h.1567.2		6	40.27	even	4
1920.2.bc.g.607.2		6	80.27	even	4
1920.2.bc.g.1183.2		6	8.5	even	2
1920.2.bc.h.607.2		6	80.37	odd	4
1920.2.bc.h.1183.2		6	8.3	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.671462 + 1.24464i) q^{2} +1.00000i q^{3} +(-1.09828 + 1.67146i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.24464 + 0.671462i) q^{6} +(0.146365 - 0.146365i) q^{7} +(-2.81783 - 0.244644i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.671462 + 1.24464i) q^{2} +1.00000i q^{3} +(-1.09828 + 1.67146i) q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.24464 + 0.671462i) q^{6} +(0.146365 - 0.146365i) q^{7} +(-2.81783 - 0.244644i) q^{8} -1.00000 q^{9} +(0.0982788 + 3.16075i) q^{10} +(0.146365 - 0.146365i) q^{11} +(-1.67146 - 1.09828i) q^{12} +(0.280452 + 0.0838942i) q^{14} +(-1.00000 + 2.00000i) q^{15} +(-1.58757 - 3.67146i) q^{16} +(3.68585 - 3.68585i) q^{17} +(-0.671462 - 1.24464i) q^{18} +(-2.83221 + 2.83221i) q^{19} +(-3.86802 + 2.24464i) q^{20} +(0.146365 + 0.146365i) q^{21} +(0.280452 + 0.0838942i) q^{22} +(-2.83221 - 2.83221i) q^{23} +(0.244644 - 2.81783i) q^{24} +(3.00000 + 4.00000i) q^{25} -1.00000i q^{27} +(0.0838942 + 0.405394i) q^{28} +(1.00000 + 1.00000i) q^{29} +(-3.16075 + 0.0982788i) q^{30} +0.292731i q^{31} +(3.50367 - 4.44120i) q^{32} +(0.146365 + 0.146365i) q^{33} +(7.06247 + 2.11266i) q^{34} +(0.439096 - 0.146365i) q^{35} +(1.09828 - 1.67146i) q^{36} +9.37169 q^{37} +(-5.42682 - 1.62337i) q^{38} +(-5.39101 - 3.30712i) q^{40} -4.00000i q^{41} +(-0.0838942 + 0.280452i) q^{42} +9.66442 q^{43} +(0.0838942 + 0.405394i) q^{44} +(-2.00000 - 1.00000i) q^{45} +(1.62337 - 5.42682i) q^{46} +(-7.12494 - 7.12494i) q^{47} +(3.67146 - 1.58757i) q^{48} +6.95715i q^{49} +(-2.96419 + 6.41978i) q^{50} +(3.68585 + 3.68585i) q^{51} -11.9572i q^{53} +(1.24464 - 0.671462i) q^{54} +(0.439096 - 0.146365i) q^{55} +(-0.448240 + 0.376625i) q^{56} +(-2.83221 - 2.83221i) q^{57} +(-0.573183 + 1.91611i) q^{58} +(9.51806 + 9.51806i) q^{59} +(-2.24464 - 3.86802i) q^{60} +(1.68585 - 1.68585i) q^{61} +(-0.364346 + 0.196558i) q^{62} +(-0.146365 + 0.146365i) q^{63} +(7.88030 + 1.37873i) q^{64} +(-0.0838942 + 0.280452i) q^{66} -13.0790 q^{67} +(2.11266 + 10.2088i) q^{68} +(2.83221 - 2.83221i) q^{69} +(0.477009 + 0.448240i) q^{70} -4.58546 q^{71} +(2.81783 + 0.244644i) q^{72} +(-6.37169 + 6.37169i) q^{73} +(6.29273 + 11.6644i) q^{74} +(-4.00000 + 3.00000i) q^{75} +(-1.62337 - 7.84449i) q^{76} -0.0428457i q^{77} -4.58546 q^{79} +(0.496327 - 8.93049i) q^{80} +1.00000 q^{81} +(4.97858 - 2.68585i) q^{82} -8.58546i q^{83} +(-0.405394 + 0.0838942i) q^{84} +(11.0575 - 3.68585i) q^{85} +(6.48929 + 12.0288i) q^{86} +(-1.00000 + 1.00000i) q^{87} +(-0.448240 + 0.376625i) q^{88} -3.37169 q^{89} +(-0.0982788 - 3.16075i) q^{90} +(7.84449 - 1.62337i) q^{92} -0.292731 q^{93} +(4.08389 - 13.6521i) q^{94} +(-8.49663 + 2.83221i) q^{95} +(4.44120 + 3.50367i) q^{96} +(-3.58546 + 3.58546i) q^{97} +(-8.65918 + 4.67146i) q^{98} +(-0.146365 + 0.146365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9	\( 6 q - 2 q^{2} - 2 q^{4} + 12 q^{5} - 2 q^{7} - 8 q^{8} - 6 q^{9} - 4 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{14} - 6 q^{15} + 10 q^{16} - 2 q^{17} + 2 q^{18} + 10 q^{19} - 8 q^{20} - 2 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 18 q^{25} + 14 q^{28} + 6 q^{29} + 2 q^{30} - 12 q^{32} - 2 q^{33} + 26 q^{34} - 6 q^{35} + 2 q^{36} + 8 q^{37} - 34 q^{38} - 22 q^{40} - 14 q^{42} + 4 q^{43} + 14 q^{44} - 12 q^{45} + 2 q^{46} - 10 q^{47} + 16 q^{48} - 6 q^{50} - 2 q^{51} - 6 q^{55} - 34 q^{56} + 10 q^{57} - 2 q^{58} + 6 q^{59} - 6 q^{60} - 14 q^{61} - 20 q^{62} + 2 q^{63} + 22 q^{64} - 14 q^{66} - 36 q^{67} - 10 q^{68} - 10 q^{69} - 2 q^{70} - 16 q^{71} + 8 q^{72} + 10 q^{73} + 32 q^{74} - 24 q^{75} - 2 q^{76} - 16 q^{79} + 36 q^{80} + 6 q^{81} + 26 q^{84} - 6 q^{85} + 24 q^{86} - 6 q^{87} - 34 q^{88} + 28 q^{89} + 4 q^{90} + 10 q^{92} + 4 q^{93} + 38 q^{94} + 30 q^{95} + 10 q^{96} - 10 q^{97} - 56 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 + 12 * q^5 - 2 * q^7 - 8 * q^8 - 6 * q^9 - 4 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^14 - 6 * q^15 + 10 * q^16 - 2 * q^17 + 2 * q^18 + 10 * q^19 - 8 * q^20 - 2 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 18 * q^25 + 14 * q^28 + 6 * q^29 + 2 * q^30 - 12 * q^32 - 2 * q^33 + 26 * q^34 - 6 * q^35 + 2 * q^36 + 8 * q^37 - 34 * q^38 - 22 * q^40 - 14 * q^42 + 4 * q^43 + 14 * q^44 - 12 * q^45 + 2 * q^46 - 10 * q^47 + 16 * q^48 - 6 * q^50 - 2 * q^51 - 6 * q^55 - 34 * q^56 + 10 * q^57 - 2 * q^58 + 6 * q^59 - 6 * q^60 - 14 * q^61 - 20 * q^62 + 2 * q^63 + 22 * q^64 - 14 * q^66 - 36 * q^67 - 10 * q^68 - 10 * q^69 - 2 * q^70 - 16 * q^71 + 8 * q^72 + 10 * q^73 + 32 * q^74 - 24 * q^75 - 2 * q^76 - 16 * q^79 + 36 * q^80 + 6 * q^81 + 26 * q^84 - 6 * q^85 + 24 * q^86 - 6 * q^87 - 34 * q^88 + 28 * q^89 + 4 * q^90 + 10 * q^92 + 4 * q^93 + 38 * q^94 + 30 * q^95 + 10 * q^96 - 10 * q^97 - 56 * q^98 + 2 * q^99

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