LMFDB - Embedded newform 1110.2.l.b.43.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.15
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.b.697.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 - 1.19936i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 - 1.19936i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.19936 - 1.88721i) q^{10} -0.249077i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.83382i q^{13} +(1.50593 + 1.50593i) q^{14} +(0.486383 - 2.18253i) q^{15} +1.00000 q^{16} -7.29402 q^{17} -1.00000 q^{18} +(1.89479 - 1.89479i) q^{19} +(-1.88721 + 1.19936i) q^{20} +2.12971i q^{21} -0.249077 q^{22} -8.28835i q^{23} +(0.707107 + 0.707107i) q^{24} +(2.12309 - 4.52686i) q^{25} -2.83382 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.50593 - 1.50593i) q^{28} +(-2.37266 - 2.37266i) q^{29} +(-2.18253 - 0.486383i) q^{30} +(1.83366 - 1.83366i) q^{31} -1.00000i q^{32} +(-0.176124 - 0.176124i) q^{33} +7.29402i q^{34} +(-1.03586 + 4.64816i) q^{35} +1.00000i q^{36} +(3.06084 + 5.25654i) q^{37} +(-1.89479 - 1.89479i) q^{38} +(-2.00381 - 2.00381i) q^{39} +(1.19936 + 1.88721i) q^{40} -10.3232i q^{41} +2.12971 q^{42} -7.61240i q^{43} +0.249077i q^{44} +(-1.19936 - 1.88721i) q^{45} -8.28835 q^{46} +(-2.82753 + 2.82753i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.46433i q^{49} +(-4.52686 - 2.12309i) q^{50} +(-5.15765 + 5.15765i) q^{51} +2.83382i q^{52} +(4.20587 + 4.20587i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.298732 - 0.470059i) q^{55} +(-1.50593 - 1.50593i) q^{56} -2.67964i q^{57} +(-2.37266 + 2.37266i) q^{58} +(6.26117 - 6.26117i) q^{59} +(-0.486383 + 2.18253i) q^{60} +(-3.22008 + 3.22008i) q^{61} +(-1.83366 - 1.83366i) q^{62} +(1.50593 + 1.50593i) q^{63} -1.00000 q^{64} +(-3.39876 - 5.34800i) q^{65} +(-0.176124 + 0.176124i) q^{66} +(5.68165 + 5.68165i) q^{67} +7.29402 q^{68} +(-5.86075 - 5.86075i) q^{69} +(4.64816 + 1.03586i) q^{70} +3.37315 q^{71} +1.00000 q^{72} +(-7.48228 + 7.48228i) q^{73} +(5.25654 - 3.06084i) q^{74} +(-1.69973 - 4.70223i) q^{75} +(-1.89479 + 1.89479i) q^{76} +(0.375093 + 0.375093i) q^{77} +(-2.00381 + 2.00381i) q^{78} +(5.99818 - 5.99818i) q^{79} +(1.88721 - 1.19936i) q^{80} -1.00000 q^{81} -10.3232 q^{82} +(5.98449 + 5.98449i) q^{83} -2.12971i q^{84} +(-13.7653 + 8.74813i) q^{85} -7.61240 q^{86} -3.35545 q^{87} +0.249077 q^{88} +(5.37576 + 5.37576i) q^{89} +(-1.88721 + 1.19936i) q^{90} +(4.26754 + 4.26754i) q^{91} +8.28835i q^{92} -2.59319i q^{93} +(2.82753 + 2.82753i) q^{94} +(1.30333 - 5.84838i) q^{95} +(-0.707107 - 0.707107i) q^{96} -5.94731 q^{97} +2.46433 q^{98} -0.249077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	1.88721	−	1.19936i	0.843984	−	0.536368i
$5$	1.88721	−	1.19936i	0.843984	−	0.536368i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−1.50593	+	1.50593i	−0.569189	+	0.569189i	−0.931901	−	0.362712i	$-0.881851\pi$
$7$	−1.50593	+	1.50593i	−0.569189	+	0.569189i	0.362712	+	0.931901i	$0.381851\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.19936	−	1.88721i	−0.379270	−	0.596787i
$11$		−	0.249077i		−	0.0750994i	−0.999295	−	0.0375497i	$-0.988045\pi$
$11$		−	0.249077i		−	0.0750994i	0.999295	−	0.0375497i	$-0.0119553\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$		−	2.83382i		−	0.785959i	−0.919547	−	0.392980i	$-0.871444\pi$
$13$		−	2.83382i		−	0.785959i	0.919547	−	0.392980i	$-0.128556\pi$
$14$	1.50593	+	1.50593i	0.402478	+	0.402478i
$15$	0.486383	−	2.18253i	0.125583	−	0.563527i
$16$	1.00000			0.250000
$17$	−7.29402			−1.76906			−0.884530	−	0.466484i	$-0.845520\pi$
$17$	−7.29402			−1.76906			−0.884530	+	0.466484i	$0.845520\pi$
$18$	−1.00000			−0.235702
$19$	1.89479	−	1.89479i	0.434694	−	0.434694i	−0.455527	−	0.890222i	$-0.650549\pi$
$19$	1.89479	−	1.89479i	0.434694	−	0.434694i	0.890222	+	0.455527i	$0.150549\pi$
$20$	−1.88721	+	1.19936i	−0.421992	+	0.268184i
$21$			2.12971i			0.464741i
$22$	−0.249077			−0.0531033
$23$		−	8.28835i		−	1.72824i	−0.503286	−	0.864120i	$-0.667876\pi$
$23$		−	8.28835i		−	1.72824i	0.503286	−	0.864120i	$-0.332124\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	2.12309	−	4.52686i	0.424618	−	0.905373i
$26$	−2.83382			−0.555757
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.50593	−	1.50593i	0.284595	−	0.284595i
$29$	−2.37266	−	2.37266i	−0.440592	−	0.440592i	0.451619	−	0.892211i	$-0.350847\pi$
$29$	−2.37266	−	2.37266i	−0.440592	−	0.440592i	−0.892211	+	0.451619i	$0.850847\pi$
$30$	−2.18253	−	0.486383i	−0.398473	−	0.0888009i
$31$	1.83366	−	1.83366i	0.329335	−	0.329335i	−0.522999	−	0.852334i	$-0.675187\pi$
$31$	1.83366	−	1.83366i	0.329335	−	0.329335i	0.852334	+	0.522999i	$0.175187\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.176124	−	0.176124i	−0.0306592	−	0.0306592i
$34$			7.29402i			1.25091i
$35$	−1.03586	+	4.64816i	−0.175091	+	0.785682i
$36$			1.00000i			0.166667i
$37$	3.06084	+	5.25654i	0.503200	+	0.864170i
$37$	3.06084	+	5.25654i	0.503200	+	0.864170i
$38$	−1.89479	−	1.89479i	−0.307375	−	0.307375i
$39$	−2.00381	−	2.00381i	−0.320867	−	0.320867i
$40$	1.19936	+	1.88721i	0.189635	+	0.298393i
$41$		−	10.3232i		−	1.61221i	−0.591771	−	0.806106i	$-0.701571\pi$
$41$		−	10.3232i		−	1.61221i	0.591771	−	0.806106i	$-0.298429\pi$
$42$	2.12971			0.328622
$43$		−	7.61240i		−	1.16088i	−0.814303	−	0.580440i	$-0.802880\pi$
$43$		−	7.61240i		−	1.16088i	0.814303	−	0.580440i	$-0.197120\pi$
$44$			0.249077i			0.0375497i
$45$	−1.19936	−	1.88721i	−0.178789	−	0.281328i
$46$	−8.28835			−1.22205
$47$	−2.82753	+	2.82753i	−0.412437	+	0.412437i	−0.882587	−	0.470150i	$-0.844200\pi$
$47$	−2.82753	+	2.82753i	−0.412437	+	0.412437i	0.470150	+	0.882587i	$0.344200\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			2.46433i			0.352047i
$50$	−4.52686	−	2.12309i	−0.640195	−	0.300250i
$51$	−5.15765	+	5.15765i	−0.722215	+	0.722215i
$52$			2.83382i			0.392980i
$53$	4.20587	+	4.20587i	0.577721	+	0.577721i	0.934275	−	0.356554i	$-0.116048\pi$
$53$	4.20587	+	4.20587i	0.577721	+	0.577721i	−0.356554	+	0.934275i	$0.616048\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−0.298732	−	0.470059i	−0.0402810	−	0.0633827i
$56$	−1.50593	−	1.50593i	−0.201239	−	0.201239i
$57$		−	2.67964i		−	0.354926i
$58$	−2.37266	+	2.37266i	−0.311546	+	0.311546i
$59$	6.26117	−	6.26117i	0.815135	−	0.815135i	−0.170264	−	0.985398i	$-0.554462\pi$
$59$	6.26117	−	6.26117i	0.815135	−	0.815135i	0.985398	+	0.170264i	$0.0544620\pi$
$60$	−0.486383	+	2.18253i	−0.0627917	+	0.281763i
$61$	−3.22008	+	3.22008i	−0.412290	+	0.412290i	−0.882535	−	0.470246i	$-0.844165\pi$
$61$	−3.22008	+	3.22008i	−0.412290	+	0.412290i	0.470246	+	0.882535i	$0.344165\pi$
$62$	−1.83366	−	1.83366i	−0.232875	−	0.232875i
$63$	1.50593	+	1.50593i	0.189730	+	0.189730i
$64$	−1.00000			−0.125000
$65$	−3.39876	−	5.34800i	−0.421564	−	0.663337i
$66$	−0.176124	+	0.176124i	−0.0216793	+	0.0216793i
$67$	5.68165	+	5.68165i	0.694124	+	0.694124i	0.963137	−	0.269013i	$-0.0866974\pi$
$67$	5.68165	+	5.68165i	0.694124	+	0.694124i	−0.269013	+	0.963137i	$0.586697\pi$
$68$	7.29402			0.884530
$69$	−5.86075	−	5.86075i	−0.705551	−	0.705551i
$70$	4.64816	+	1.03586i	0.555561	+	0.123808i
$71$	3.37315			0.400320			0.200160	−	0.979763i	$-0.435854\pi$
$71$	3.37315			0.400320			0.200160	+	0.979763i	$0.435854\pi$
$72$	1.00000			0.117851
$73$	−7.48228	+	7.48228i	−0.875735	+	0.875735i	−0.993090	−	0.117355i	$-0.962558\pi$
$73$	−7.48228	+	7.48228i	−0.875735	+	0.875735i	0.117355	+	0.993090i	$0.462558\pi$
$74$	5.25654	−	3.06084i	0.611061	−	0.355816i
$75$	−1.69973	−	4.70223i	−0.196267	−	0.542966i
$76$	−1.89479	+	1.89479i	−0.217347	+	0.217347i
$77$	0.375093	+	0.375093i	0.0427458	+	0.0427458i
$78$	−2.00381	+	2.00381i	−0.226887	+	0.226887i
$79$	5.99818	−	5.99818i	0.674848	−	0.674848i	−0.283982	−	0.958830i	$-0.591655\pi$
$79$	5.99818	−	5.99818i	0.674848	−	0.674848i	0.958830	+	0.283982i	$0.0916554\pi$
$80$	1.88721	−	1.19936i	0.210996	−	0.134092i
$81$	−1.00000			−0.111111
$82$	−10.3232			−1.14001
$83$	5.98449	+	5.98449i	0.656883	+	0.656883i	0.954641	−	0.297759i	$-0.0962390\pi$
$83$	5.98449	+	5.98449i	0.656883	+	0.656883i	−0.297759	+	0.954641i	$0.596239\pi$
$84$		−	2.12971i		−	0.232371i
$85$	−13.7653	+	8.74813i	−1.49306	+	0.948867i
$86$	−7.61240			−0.820867
$87$	−3.35545			−0.359742
$88$	0.249077			0.0265517
$89$	5.37576	+	5.37576i	0.569829	+	0.569829i	0.932081	−	0.362251i	$-0.117992\pi$
$89$	5.37576	+	5.37576i	0.569829	+	0.569829i	−0.362251	+	0.932081i	$0.617992\pi$
$90$	−1.88721	+	1.19936i	−0.198929	+	0.126423i
$91$	4.26754	+	4.26754i	0.447360	+	0.447360i
$92$			8.28835i			0.864120i
$93$		−	2.59319i		−	0.268901i
$94$	2.82753	+	2.82753i	0.291637	+	0.291637i
$95$	1.30333	−	5.84838i	0.133719	−	0.600031i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−5.94731			−0.603858			−0.301929	−	0.953330i	$-0.597631\pi$
$97$	−5.94731			−0.603858			−0.301929	+	0.953330i	$0.597631\pi$
$98$	2.46433			0.248935
$99$	−0.249077			−0.0250331
$100$	−2.12309	+	4.52686i	−0.212309	+	0.452686i
$101$			10.2985i			1.02474i	0.858766	+	0.512368i	$0.171232\pi$
$101$			10.2985i			1.02474i	−0.858766	+	0.512368i	$0.828768\pi$
$102$	5.15765	+	5.15765i	0.510683	+	0.510683i
$103$	−8.34427			−0.822186			−0.411093	−	0.911594i	$-0.634853\pi$
$103$	−8.34427			−0.822186			−0.411093	+	0.911594i	$0.634853\pi$
$104$	2.83382			0.277879
$105$	2.55428	+	4.01920i	0.249273	+	0.392234i
$106$	4.20587	−	4.20587i	0.408511	−	0.408511i
$107$	−2.10671	+	2.10671i	−0.203663	+	0.203663i	−0.801568	−	0.597904i	$-0.796000\pi$
$107$	−2.10671	+	2.10671i	−0.203663	+	0.203663i	0.597904	+	0.801568i	$0.296000\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	−10.6743	+	10.6743i	−1.02242	+	1.02242i	−0.0226738	+	0.999743i	$0.507218\pi$
$109$	−10.6743	+	10.6743i	−1.02242	+	1.02242i	−0.999743	+	0.0226738i	$0.992782\pi$
$110$	−0.470059	+	0.298732i	−0.0448183	+	0.0284829i
$111$	5.88128	+	1.55259i	0.558226	+	0.147366i
$112$	−1.50593	+	1.50593i	−0.142297	+	0.142297i
$113$	4.25290			0.400080			0.200040	−	0.979788i	$-0.435893\pi$
$113$	4.25290			0.400080			0.200040	+	0.979788i	$0.435893\pi$
$114$	−2.67964			−0.250971
$115$	−9.94068	−	15.6418i	−0.926973	−	1.45861i
$116$	2.37266	+	2.37266i	0.220296	+	0.220296i
$117$	−2.83382			−0.261986
$118$	−6.26117	−	6.26117i	−0.576387	−	0.576387i
$119$	10.9843	−	10.9843i	1.00693	−	1.00693i
$120$	2.18253	+	0.486383i	0.199237	+	0.0444005i
$121$	10.9380			0.994360
$122$	3.22008	+	3.22008i	0.291533	+	0.291533i
$123$	−7.29960	−	7.29960i	−0.658183	−	0.658183i
$124$	−1.83366	+	1.83366i	−0.164668	+	0.164668i
$125$	−1.42262	−	11.0895i	−0.127243	−	0.991872i
$126$	1.50593	−	1.50593i	0.134159	−	0.134159i
$127$	12.5469	−	12.5469i	1.11336	−	1.11336i	0.120665	−	0.992693i	$-0.461497\pi$
$127$	12.5469	−	12.5469i	1.11336	−	1.11336i	0.992693	−	0.120665i	$-0.0385026\pi$
$128$			1.00000i			0.0883883i
$129$	−5.38278	−	5.38278i	−0.473928	−	0.473928i
$130$	−5.34800	+	3.39876i	−0.469050	+	0.298091i
$131$	3.81040	−	3.81040i	0.332916	−	0.332916i	−0.520777	−	0.853693i	$-0.674358\pi$
$131$	3.81040	−	3.81040i	0.332916	−	0.332916i	0.853693	+	0.520777i	$0.174358\pi$
$132$	0.176124	+	0.176124i	0.0153296	+	0.0153296i
$133$			5.70685i			0.494847i
$134$	5.68165	−	5.68165i	0.490820	−	0.490820i
$135$	−2.18253	−	0.486383i	−0.187842	−	0.0418612i
$136$		−	7.29402i		−	0.625457i
$137$	−2.72768	+	2.72768i	−0.233041	+	0.233041i	−0.813961	−	0.580920i	$-0.802693\pi$
$137$	−2.72768	+	2.72768i	−0.233041	+	0.233041i	0.580920	+	0.813961i	$0.302693\pi$
$138$	−5.86075	+	5.86075i	−0.498900	+	0.498900i
$139$	2.31516			0.196369			0.0981847	−	0.995168i	$-0.468696\pi$
$139$	2.31516			0.196369			0.0981847	+	0.995168i	$0.468696\pi$
$140$	1.03586	−	4.64816i	0.0875457	−	0.392841i
$141$			3.99873i			0.336753i
$142$		−	3.37315i		−	0.283069i
$143$	−0.705838			−0.0590251
$144$		−	1.00000i		−	0.0833333i
$145$	−7.32336	−	1.63203i	−0.608172	−	0.135533i
$146$	7.48228	+	7.48228i	0.619238	+	0.619238i
$147$	1.74254	+	1.74254i	0.143722	+	0.143722i
$148$	−3.06084	−	5.25654i	−0.251600	−	0.432085i
$149$		−	8.45695i		−	0.692821i	−0.938083	−	0.346410i	$-0.887400\pi$
$149$		−	8.45695i		−	0.692821i	0.938083	−	0.346410i	$-0.112600\pi$
$150$	−4.70223	+	1.69973i	−0.383935	+	0.138782i
$151$			12.3871i			1.00805i	0.863690	+	0.504024i	$0.168148\pi$
$151$			12.3871i			1.00805i	−0.863690	+	0.504024i	$0.831852\pi$
$152$	1.89479	+	1.89479i	0.153688	+	0.153688i
$153$			7.29402i			0.589686i
$154$	0.375093	−	0.375093i	0.0302259	−	0.0302259i
$155$	1.26128	−	5.65970i	0.101309	−	0.454598i
$156$	2.00381	+	2.00381i	0.160433	+	0.160433i
$157$	−10.3496	+	10.3496i	−0.825986	+	0.825986i	−0.986959	−	0.160973i	$-0.948537\pi$
$157$	−10.3496	+	10.3496i	−0.825986	+	0.825986i	0.160973	+	0.986959i	$0.448537\pi$
$158$	−5.99818	−	5.99818i	−0.477190	−	0.477190i
$159$	5.94800			0.471707
$160$	−1.19936	−	1.88721i	−0.0948174	−	0.149197i
$161$	12.4817	+	12.4817i	0.983696	+	0.983696i
$162$			1.00000i			0.0785674i
$163$	−8.69039			−0.680684			−0.340342	−	0.940302i	$-0.610543\pi$
$163$	−8.69039			−0.680684			−0.340342	+	0.940302i	$0.610543\pi$
$164$			10.3232i			0.806106i
$165$	−0.543617	−	0.121147i	−0.0423205	−	0.00943125i
$166$	5.98449	−	5.98449i	0.464486	−	0.464486i
$167$	−18.5233			−1.43337			−0.716687	−	0.697395i	$-0.754342\pi$
$167$	−18.5233			−1.43337			−0.716687	+	0.697395i	$0.754342\pi$
$168$	−2.12971			−0.164311
$169$	4.96948			0.382268
$170$	8.74813	+	13.7653i	0.670951	+	1.05575i
$171$	−1.89479	−	1.89479i	−0.144898	−	0.144898i
$172$			7.61240i			0.580440i
$173$	6.60085	−	6.60085i	0.501854	−	0.501854i	−0.410160	−	0.912014i	$-0.634527\pi$
$173$	6.60085	−	6.60085i	0.501854	−	0.501854i	0.912014	+	0.410160i	$0.134527\pi$
$174$			3.35545i			0.254376i
$175$	3.61993	+	10.0144i	0.273641	+	0.757017i
$176$		−	0.249077i		−	0.0187749i
$177$		−	8.85463i		−	0.665555i
$178$	5.37576	−	5.37576i	0.402930	−	0.402930i
$179$	11.1031	+	11.1031i	0.829883	+	0.829883i	0.987500	−	0.157617i	$-0.0503812\pi$
$179$	11.1031	+	11.1031i	0.829883	+	0.829883i	−0.157617	+	0.987500i	$0.550381\pi$
$180$	1.19936	+	1.88721i	0.0893947	+	0.140664i
$181$	19.1102			1.42045			0.710223	−	0.703977i	$-0.248594\pi$
$181$	19.1102			1.42045			0.710223	+	0.703977i	$0.248594\pi$
$182$	4.26754	−	4.26754i	0.316331	−	0.316331i
$183$			4.55389i			0.336633i
$184$	8.28835			0.611025
$185$	12.0809	+	6.24913i	0.888206	+	0.459445i
$186$	−2.59319			−0.190142
$187$			1.81677i			0.132855i
$188$	2.82753	−	2.82753i	0.206219	−	0.206219i
$189$	2.12971			0.154914
$190$	−5.84838	−	1.30333i	−0.424286	−	0.0945534i
$191$	−4.13848	−	4.13848i	−0.299450	−	0.299450i	0.541349	−	0.840798i	$-0.317914\pi$
$191$	−4.13848	−	4.13848i	−0.299450	−	0.299450i	−0.840798	+	0.541349i	$0.817914\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$		−	1.65600i		−	0.119201i	−0.998222	−	0.0596007i	$-0.981017\pi$
$193$		−	1.65600i		−	0.119201i	0.998222	−	0.0596007i	$-0.0189827\pi$
$194$			5.94731i			0.426992i
$195$	−6.18489	−	1.37832i	−0.442909	−	0.0987035i
$196$		−	2.46433i		−	0.176023i
$197$	14.1878	−	14.1878i	1.01084	−	1.01084i	0.0108958	−	0.999941i	$-0.496532\pi$
$197$	14.1878	−	14.1878i	1.01084	−	1.01084i	0.999941	−	0.0108958i	$-0.00346830\pi$
$198$			0.249077i			0.0177011i
$199$	−3.69181	−	3.69181i	−0.261705	−	0.261705i	0.564041	−	0.825747i	$-0.309246\pi$
$199$	−3.69181	−	3.69181i	−0.261705	−	0.261705i	−0.825747	+	0.564041i	$0.809246\pi$
$200$	4.52686	+	2.12309i	0.320098	+	0.150125i
$201$	8.03506			0.566750
$202$	10.2985			0.724598
$203$	7.14614			0.501561
$204$	5.15765	−	5.15765i	0.361108	−	0.361108i
$205$	−12.3812	−	19.4820i	−0.864740	−	1.36068i
$206$			8.34427i			0.581373i
$207$	−8.28835			−0.576080
$208$		−	2.83382i		−	0.196490i
$209$	−0.471948	−	0.471948i	−0.0326453	−	0.0326453i
$210$	4.01920	−	2.55428i	0.277351	−	0.176262i
$211$	−8.15505			−0.561417			−0.280708	−	0.959793i	$-0.590569\pi$
$211$	−8.15505			−0.561417			−0.280708	+	0.959793i	$0.590569\pi$
$212$	−4.20587	−	4.20587i	−0.288861	−	0.288861i
$213$	2.38518	−	2.38518i	0.163430	−	0.163430i
$214$	2.10671	+	2.10671i	0.144012	+	0.144012i
$215$	−9.12998	−	14.3662i	−0.622660	−	0.979765i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$			5.52274i			0.374908i
$218$	10.6743	+	10.6743i	0.722958	+	0.722958i
$219$			10.5815i			0.715034i
$220$	0.298732	+	0.470059i	0.0201405	+	0.0316914i
$221$			20.6699i			1.39041i
$222$	1.55259	−	5.88128i	0.104203	−	0.394726i
$223$	18.0980	+	18.0980i	1.21193	+	1.21193i	0.970390	+	0.241543i	$0.0776536\pi$
$223$	18.0980	+	18.0980i	1.21193	+	1.21193i	0.241543	+	0.970390i	$0.422346\pi$
$224$	1.50593	+	1.50593i	0.100619	+	0.100619i
$225$	−4.52686	−	2.12309i	−0.301791	−	0.141539i
$226$		−	4.25290i		−	0.282899i
$227$	−15.2040			−1.00913			−0.504563	−	0.863375i	$-0.668346\pi$
$227$	−15.2040			−1.00913			−0.504563	+	0.863375i	$0.668346\pi$
$228$			2.67964i			0.177463i
$229$			22.1160i			1.46147i	0.682662	+	0.730735i	$0.260822\pi$
$229$			22.1160i			1.46147i	−0.682662	+	0.730735i	$0.739178\pi$
$230$	−15.6418	+	9.94068i	−1.03139	+	0.655469i
$231$	0.530462			0.0349018
$232$	2.37266	−	2.37266i	0.155773	−	0.155773i
$233$	−4.77285	+	4.77285i	−0.312680	+	0.312680i	−0.845947	−	0.533267i	$-0.820964\pi$
$233$	−4.77285	+	4.77285i	−0.312680	+	0.312680i	0.533267	+	0.845947i	$0.320964\pi$
$234$			2.83382i			0.185252i
$235$	−1.94491	+	8.72733i	−0.126872	+	0.569308i
$236$	−6.26117	+	6.26117i	−0.407567	+	0.407567i
$237$		−	8.48271i		−	0.551011i
$238$	−10.9843	−	10.9843i	−0.712007	−	0.712007i
$239$	19.8498	−	19.8498i	1.28398	−	1.28398i	0.345593	−	0.938385i	$-0.387678\pi$
$239$	19.8498	−	19.8498i	1.28398	−	1.28398i	0.938385	−	0.345593i	$-0.112322\pi$
$240$	0.486383	−	2.18253i	0.0313959	−	0.140882i
$241$	21.3229	+	21.3229i	1.37353	+	1.37353i	0.855150	+	0.518380i	$0.173465\pi$
$241$	21.3229	+	21.3229i	1.37353	+	1.37353i	0.518380	+	0.855150i	$0.326535\pi$
$242$		−	10.9380i		−	0.703119i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.22008	−	3.22008i	0.206145	−	0.206145i
$245$	2.95561	+	4.65069i	0.188827	+	0.297122i
$246$	−7.29960	+	7.29960i	−0.465405	+	0.465405i
$247$	−5.36948	−	5.36948i	−0.341652	−	0.341652i
$248$	1.83366	+	1.83366i	0.116438	+	0.116438i
$249$	8.46334			0.536342
$250$	−11.0895	+	1.42262i	−0.701359	+	0.0899742i
$251$	14.6439	−	14.6439i	0.924315	−	0.924315i	−0.0730156	−	0.997331i	$-0.523262\pi$
$251$	14.6439	−	14.6439i	0.924315	−	0.924315i	0.997331	+	0.0730156i	$0.0232623\pi$
$252$	−1.50593	−	1.50593i	−0.0948649	−	0.0948649i
$253$	−2.06443			−0.129790
$254$	−12.5469	−	12.5469i	−0.787263	−	0.787263i
$255$	−3.54768	+	15.9194i	−0.222165	+	0.996912i
$256$	1.00000			0.0625000
$257$	17.8930			1.11614			0.558069	−	0.829795i	$-0.311543\pi$
$257$	17.8930			1.11614			0.558069	+	0.829795i	$0.311543\pi$
$258$	−5.38278	+	5.38278i	−0.335117	+	0.335117i
$259$	−12.5254	−	3.30658i	−0.778293	−	0.205461i
$260$	3.39876	+	5.34800i	0.210782	+	0.331669i
$261$	−2.37266	+	2.37266i	−0.146864	+	0.146864i
$262$	−3.81040	−	3.81040i	−0.235407	−	0.235407i
$263$	21.7610	−	21.7610i	1.34184	−	1.34184i	0.447617	−	0.894225i	$-0.352273\pi$
$263$	21.7610	−	21.7610i	1.34184	−	1.34184i	0.894225	−	0.447617i	$-0.147727\pi$
$264$	0.176124	−	0.176124i	0.0108397	−	0.0108397i
$265$	12.9817	+	2.89301i	0.797459	+	0.177716i
$266$	5.70685			0.349910
$267$	7.60247			0.465264
$268$	−5.68165	−	5.68165i	−0.347062	−	0.347062i
$269$		−	17.8478i		−	1.08820i	−0.839020	−	0.544101i	$-0.816871\pi$
$269$		−	17.8478i		−	1.08820i	0.839020	−	0.544101i	$-0.183129\pi$
$270$	−0.486383	+	2.18253i	−0.0296003	+	0.132824i
$271$	2.29360			0.139327			0.0696633	−	0.997571i	$-0.477808\pi$
$271$	2.29360			0.139327			0.0696633	+	0.997571i	$0.477808\pi$
$272$	−7.29402			−0.442265
$273$	6.03521			0.365268
$274$	2.72768	+	2.72768i	0.164785	+	0.164785i
$275$	−1.12754	−	0.528812i	−0.0679930	−	0.0318886i
$276$	5.86075	+	5.86075i	0.352776	+	0.352776i
$277$		−	1.48608i		−	0.0892897i	−0.999003	−	0.0446448i	$-0.985784\pi$
$277$		−	1.48608i		−	0.0892897i	0.999003	−	0.0446448i	$-0.0142156\pi$
$278$		−	2.31516i		−	0.138854i
$279$	−1.83366	−	1.83366i	−0.109778	−	0.109778i
$280$	−4.64816	−	1.03586i	−0.277781	−	0.0619042i
$281$	−18.5876	−	18.5876i	−1.10884	−	1.10884i	−0.993303	−	0.115541i	$-0.963140\pi$
$281$	−18.5876	−	18.5876i	−1.10884	−	1.10884i	−0.115541	−	0.993303i	$-0.536860\pi$
$282$	3.99873			0.238121
$283$	−16.6153			−0.987676			−0.493838	−	0.869554i	$-0.664406\pi$
$283$	−16.6153			−0.987676			−0.493838	+	0.869554i	$0.664406\pi$
$284$	−3.37315			−0.200160
$285$	−3.21384	−	5.05702i	−0.190371	−	0.299552i
$286$			0.705838i			0.0417371i
$287$	15.5460	+	15.5460i	0.917654	+	0.917654i
$288$	−1.00000			−0.0589256
$289$	36.2027			2.12957
$290$	−1.63203	+	7.32336i	−0.0958362	+	0.430043i
$291$	−4.20538	+	4.20538i	−0.246524	+	0.246524i
$292$	7.48228	−	7.48228i	0.437867	−	0.437867i
$293$	9.37884	+	9.37884i	0.547918	+	0.547918i	0.925838	−	0.377920i	$-0.123361\pi$
$293$	9.37884	+	9.37884i	0.547918	+	0.547918i	−0.377920	+	0.925838i	$0.623361\pi$
$294$	1.74254	−	1.74254i	0.101627	−	0.101627i
$295$	4.30674	−	19.3255i	0.250748	−	1.12517i
$296$	−5.25654	+	3.06084i	−0.305530	+	0.177908i
$297$	−0.176124	+	0.176124i	−0.0102197	+	0.0102197i
$298$	−8.45695			−0.489898
$299$	−23.4877			−1.35833
$300$	1.69973	+	4.70223i	0.0981337	+	0.271483i
$301$	11.4638	+	11.4638i	0.660761	+	0.660761i
$302$	12.3871			0.712797
$303$	7.28212	+	7.28212i	0.418347	+	0.418347i
$304$	1.89479	−	1.89479i	0.108674	−	0.108674i
$305$	−2.21493	+	9.93899i	−0.126827	+	0.569105i
$306$	7.29402			0.416971
$307$	3.36862	+	3.36862i	0.192258	+	0.192258i	0.796671	−	0.604413i	$-0.206592\pi$
$307$	3.36862	+	3.36862i	0.192258	+	0.192258i	−0.604413	+	0.796671i	$0.706592\pi$
$308$	−0.375093	−	0.375093i	−0.0213729	−	0.0213729i
$309$	−5.90029	+	5.90029i	−0.335656	+	0.335656i
$310$	−5.65970	−	1.26128i	−0.321450	−	0.0716360i
$311$	22.4334	−	22.4334i	1.27208	−	1.27208i	0.327087	−	0.944994i	$-0.393933\pi$
$311$	22.4334	−	22.4334i	1.27208	−	1.27208i	0.944994	−	0.327087i	$-0.106067\pi$
$312$	2.00381	−	2.00381i	0.113443	−	0.113443i
$313$		−	19.2752i		−	1.08950i	−0.838599	−	0.544750i	$-0.816625\pi$
$313$		−	19.2752i		−	1.08950i	0.838599	−	0.544750i	$-0.183375\pi$
$314$	10.3496	+	10.3496i	0.584060	+	0.584060i
$315$	4.64816	+	1.03586i	0.261894	+	0.0583638i
$316$	−5.99818	+	5.99818i	−0.337424	+	0.337424i
$317$	−3.94817	−	3.94817i	−0.221751	−	0.221751i	0.587484	−	0.809236i	$-0.300118\pi$
$317$	−3.94817	−	3.94817i	−0.221751	−	0.221751i	−0.809236	+	0.587484i	$0.800118\pi$
$318$		−	5.94800i		−	0.333548i
$319$	−0.590974	+	0.590974i	−0.0330882	+	0.0330882i
$320$	−1.88721	+	1.19936i	−0.105498	+	0.0670461i
$321$			2.97934i			0.166291i
$322$	12.4817	−	12.4817i	0.695578	−	0.695578i
$323$	−13.8206	+	13.8206i	−0.769000	+	0.769000i
$324$	1.00000			0.0555556
$325$	−12.8283	−	6.01645i	−0.711586	−	0.333732i
$326$			8.69039i			0.481316i
$327$			15.0958i			0.834800i
$328$	10.3232			0.570003
$329$		−	8.51613i		−	0.469510i
$330$	−0.121147	+	0.543617i	−0.00666890	+	0.0299251i
$331$	−2.89997	−	2.89997i	−0.159397	−	0.159397i	0.622902	−	0.782299i	$-0.285953\pi$
$331$	−2.89997	−	2.89997i	−0.159397	−	0.159397i	−0.782299	+	0.622902i	$0.785953\pi$
$332$	−5.98449	−	5.98449i	−0.328441	−	0.328441i
$333$	5.25654	−	3.06084i	0.288057	−	0.167733i
$334$			18.5233i			1.01355i
$335$	17.5368	+	3.90812i	0.958135	+	0.213523i
$336$			2.12971i			0.116185i
$337$	−1.55976	−	1.55976i	−0.0849654	−	0.0849654i	0.663347	−	0.748312i	$-0.269135\pi$
$337$	−1.55976	−	1.55976i	−0.0849654	−	0.0849654i	−0.748312	+	0.663347i	$0.769135\pi$
$338$		−	4.96948i		−	0.270304i
$339$	3.00726	−	3.00726i	0.163332	−	0.163332i
$340$	13.7653	−	8.74813i	0.746529	−	0.474434i
$341$	−0.456722	−	0.456722i	−0.0247329	−	0.0247329i
$342$	−1.89479	+	1.89479i	−0.102458	+	0.102458i
$343$	−14.2526	−	14.2526i	−0.769571	−	0.769571i
$344$	7.61240			0.410433
$345$	−18.0896	−	4.03131i	−0.973909	−	0.217038i
$346$	−6.60085	−	6.60085i	−0.354864	−	0.354864i
$347$			9.43617i			0.506560i	0.967393	+	0.253280i	$0.0815094\pi$
$347$			9.43617i			0.506560i	−0.967393	+	0.253280i	$0.918491\pi$
$348$	3.35545			0.179871
$349$		−	7.25908i		−	0.388569i	−0.980945	−	0.194285i	$-0.937761\pi$
$349$		−	7.25908i		−	0.388569i	0.980945	−	0.194285i	$-0.0622386\pi$
$350$	10.0144	−	3.61993i	0.535292	−	0.193493i
$351$	−2.00381	+	2.00381i	−0.106956	+	0.106956i
$352$	−0.249077			−0.0132758
$353$	−6.63465			−0.353127			−0.176563	−	0.984289i	$-0.556498\pi$
$353$	−6.63465			−0.353127			−0.176563	+	0.984289i	$0.556498\pi$
$354$	−8.85463			−0.470618
$355$	6.36583	−	4.04561i	0.337863	−	0.214719i
$356$	−5.37576	−	5.37576i	−0.284915	−	0.284915i
$357$		−	15.5342i		−	0.822155i
$358$	11.1031	−	11.1031i	0.586816	−	0.586816i
$359$			3.64712i			0.192488i	0.995358	+	0.0962438i	$0.0306828\pi$
$359$			3.64712i			0.192488i	−0.995358	+	0.0962438i	$0.969317\pi$
$360$	1.88721	−	1.19936i	0.0994645	−	0.0632116i
$361$			11.8196i			0.622082i
$362$		−	19.1102i		−	1.00441i
$363$	7.73431	−	7.73431i	0.405946	−	0.405946i
$364$	−4.26754	−	4.26754i	−0.223680	−	0.223680i
$365$	−5.14668	+	23.0945i	−0.269390	+	1.20882i
$366$	4.55389			0.238036
$367$	−2.67398	+	2.67398i	−0.139580	+	0.139580i	−0.773444	−	0.633864i	$-0.781468\pi$
$367$	−2.67398	+	2.67398i	−0.139580	+	0.139580i	0.633864	+	0.773444i	$0.281468\pi$
$368$		−	8.28835i		−	0.432060i
$369$	−10.3232			−0.537404
$370$	6.24913	−	12.0809i	0.324877	−	0.628057i
$371$	−12.6675			−0.657666
$372$			2.59319i			0.134450i
$373$	8.22916	−	8.22916i	0.426090	−	0.426090i	−0.461204	−	0.887294i	$-0.652582\pi$
$373$	8.22916	−	8.22916i	0.426090	−	0.426090i	0.887294	+	0.461204i	$0.152582\pi$
$374$	1.81677			0.0939429
$375$	−8.84738	−	6.83549i	−0.456877	−	0.352983i
$376$	−2.82753	−	2.82753i	−0.145819	−	0.145819i
$377$	−6.72369	+	6.72369i	−0.346287	+	0.346287i
$378$		−	2.12971i		−	0.109541i
$379$		−	23.2988i		−	1.19678i	−0.801206	−	0.598389i	$-0.795808\pi$
$379$		−	23.2988i		−	1.19678i	0.801206	−	0.598389i	$-0.204192\pi$
$380$	−1.30333	+	5.84838i	−0.0668593	+	0.300016i
$381$		−	17.7440i		−	0.909053i
$382$	−4.13848	+	4.13848i	−0.211743	+	0.211743i
$383$			1.82589i			0.0932984i	0.998911	+	0.0466492i	$0.0148543\pi$
$383$			1.82589i			0.0932984i	−0.998911	+	0.0466492i	$0.985146\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	1.15775	+	0.258007i	0.0590043	+	0.0131493i
$386$	−1.65600			−0.0842881
$387$	−7.61240			−0.386960
$388$	5.94731			0.301929
$389$	1.87840	−	1.87840i	0.0952388	−	0.0952388i	−0.657882	−	0.753121i	$-0.728547\pi$
$389$	1.87840	−	1.87840i	0.0952388	−	0.0952388i	0.753121	+	0.657882i	$0.228547\pi$
$390$	−1.37832	+	6.18489i	−0.0697939	+	0.313184i
$391$			60.4554i			3.05736i
$392$	−2.46433			−0.124467
$393$		−	5.38872i		−	0.271825i
$394$	−14.1878	−	14.1878i	−0.714769	−	0.714769i
$395$	4.12584	−	18.5138i	0.207594	−	0.931528i
$396$	0.249077			0.0125166
$397$	12.0046	+	12.0046i	0.602492	+	0.602492i	0.940973	−	0.338481i	$-0.109913\pi$
$397$	12.0046	+	12.0046i	0.602492	+	0.602492i	−0.338481	+	0.940973i	$0.609913\pi$
$398$	−3.69181	+	3.69181i	−0.185054	+	0.185054i
$399$	4.03535	+	4.03535i	0.202020	+	0.202020i
$400$	2.12309	−	4.52686i	0.106154	−	0.226343i
$401$	−23.2046	+	23.2046i	−1.15878	+	1.15878i	−0.174043	+	0.984738i	$0.555683\pi$
$401$	−23.2046	+	23.2046i	−1.15878	+	1.15878i	−0.984738	+	0.174043i	$0.944317\pi$
$402$		−	8.03506i		−	0.400753i
$403$	−5.19626	−	5.19626i	−0.258844	−	0.258844i
$404$		−	10.2985i		−	0.512368i
$405$	−1.88721	+	1.19936i	−0.0937760	+	0.0595965i
$406$		−	7.14614i		−	0.354657i
$407$	1.30928	−	0.762385i	0.0648987	−	0.0377900i
$408$	−5.15765	−	5.15765i	−0.255342	−	0.255342i
$409$	12.7469	+	12.7469i	0.630292	+	0.630292i	0.948141	−	0.317850i	$-0.102961\pi$
$409$	12.7469	+	12.7469i	0.630292	+	0.630292i	−0.317850	+	0.948141i	$0.602961\pi$
$410$	−19.4820	+	12.3812i	−0.962147	+	0.611463i
$411$			3.85752i			0.190278i
$412$	8.34427			0.411093
$413$			18.8578i			0.927932i
$414$			8.28835i			0.407350i
$415$	18.4715	+	4.11642i	0.906729	+	0.202067i
$416$	−2.83382			−0.138939
$417$	1.63707	−	1.63707i	0.0801675	−	0.0801675i
$418$	−0.471948	+	0.471948i	−0.0230837	+	0.0230837i
$419$			22.1539i			1.08229i	0.840929	+	0.541145i	$0.182009\pi$
$419$			22.1539i			1.08229i	−0.840929	+	0.541145i	$0.817991\pi$
$420$	−2.55428	−	4.01920i	−0.124636	−	0.196117i
$421$	−18.3106	+	18.3106i	−0.892404	+	0.892404i	−0.994749	−	0.102345i	$-0.967365\pi$
$421$	−18.3106	+	18.3106i	−0.892404	+	0.892404i	0.102345	+	0.994749i	$0.467365\pi$
$422$			8.15505i			0.396981i
$423$	2.82753	+	2.82753i	0.137479	+	0.137479i
$424$	−4.20587	+	4.20587i	−0.204255	+	0.204255i
$425$	−15.4858	+	33.0190i	−0.751174	+	1.60166i
$426$	−2.38518	−	2.38518i	−0.115562	−	0.115562i
$427$		−	9.69847i		−	0.469342i
$428$	2.10671	−	2.10671i	0.101832	−	0.101832i
$429$	−0.499103	+	0.499103i	−0.0240969	+	0.0240969i
$430$	−14.3662	+	9.12998i	−0.692798	+	0.440287i
$431$	−8.32782	+	8.32782i	−0.401137	+	0.401137i	−0.878634	−	0.477497i	$-0.841544\pi$
$431$	−8.32782	+	8.32782i	−0.401137	+	0.401137i	0.477497	+	0.878634i	$0.341544\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−6.11268	−	6.11268i	−0.293757	−	0.293757i	0.544806	−	0.838562i	$-0.316603\pi$
$433$	−6.11268	−	6.11268i	−0.293757	−	0.293757i	−0.838562	+	0.544806i	$0.816603\pi$
$434$	5.52274			0.265100
$435$	−6.33242	+	4.02438i	−0.303616	+	0.192954i
$436$	10.6743	−	10.6743i	0.511208	−	0.511208i
$437$	−15.7047	−	15.7047i	−0.751256	−	0.751256i
$438$	10.5815			0.505606
$439$	16.2052	+	16.2052i	0.773431	+	0.773431i	0.978705	−	0.205273i	$-0.0658084\pi$
$439$	16.2052	+	16.2052i	0.773431	+	0.773431i	−0.205273	+	0.978705i	$0.565808\pi$
$440$	0.470059	−	0.298732i	0.0224092	−	0.0142415i
$441$	2.46433			0.117349
$442$	20.6699			0.983167
$443$	−6.30399	+	6.30399i	−0.299512	+	0.299512i	−0.840823	−	0.541311i	$-0.817928\pi$
$443$	−6.30399	+	6.30399i	−0.299512	+	0.299512i	0.541311	+	0.840823i	$0.317928\pi$
$444$	−5.88128	−	1.55259i	−0.279113	−	0.0736828i
$445$	16.5926	+	3.69771i	0.786565	+	0.175288i
$446$	18.0980	−	18.0980i	0.856966	−	0.856966i
$447$	−5.97997	−	5.97997i	−0.282843	−	0.282843i
$448$	1.50593	−	1.50593i	0.0711487	−	0.0711487i
$449$	−19.8634	+	19.8634i	−0.937412	+	0.937412i	−0.998154	−	0.0607412i	$-0.980654\pi$
$449$	−19.8634	+	19.8634i	−0.937412	+	0.937412i	0.0607412	+	0.998154i	$0.480654\pi$
$450$	−2.12309	+	4.52686i	−0.100083	+	0.213398i
$451$	−2.57127			−0.121076
$452$	−4.25290			−0.200040
$453$	8.75900	+	8.75900i	0.411534	+	0.411534i
$454$			15.2040i			0.713560i
$455$	13.1720	+	2.93542i	0.617514	+	0.137615i
$456$	2.67964			0.125485
$457$	−40.2606			−1.88331			−0.941657	−	0.336575i	$-0.890731\pi$
$457$	−40.2606			−1.88331			−0.941657	+	0.336575i	$0.890731\pi$
$458$	22.1160			1.03341
$459$	5.15765	+	5.15765i	0.240738	+	0.240738i
$460$	9.94068	+	15.6418i	0.463487	+	0.729303i
$461$	−15.0948	−	15.0948i	−0.703036	−	0.703036i	0.262025	−	0.965061i	$-0.415610\pi$
$461$	−15.0948	−	15.0948i	−0.703036	−	0.703036i	−0.965061	+	0.262025i	$0.915610\pi$
$462$		−	0.530462i		−	0.0246793i
$463$		−	25.5478i		−	1.18730i	−0.804722	−	0.593652i	$-0.797685\pi$
$463$		−	25.5478i		−	1.18730i	0.804722	−	0.593652i	$-0.202315\pi$
$464$	−2.37266	−	2.37266i	−0.110148	−	0.110148i
$465$	−3.11015	−	4.89388i	−0.144230	−	0.226948i
$466$	4.77285	+	4.77285i	0.221098	+	0.221098i
$467$	−30.7343			−1.42221			−0.711106	−	0.703085i	$-0.751805\pi$
$467$	−30.7343			−1.42221			−0.711106	+	0.703085i	$0.751805\pi$
$468$	2.83382			0.130993
$469$	−17.1124			−0.790176
$470$	8.72733	+	1.94491i	0.402562	+	0.0897121i
$471$			14.6365i			0.674415i
$472$	6.26117	+	6.26117i	0.288194	+	0.288194i
$473$	−1.89607			−0.0871815
$474$	−8.48271			−0.389624
$475$	−4.55464	−	12.6003i	−0.208981	−	0.578139i
$476$	−10.9843	+	10.9843i	−0.503465	+	0.503465i
$477$	4.20587	−	4.20587i	0.192574	−	0.192574i
$478$	−19.8498	−	19.8498i	−0.907909	−	0.907909i
$479$	−0.00977229	+	0.00977229i	−0.000446507	+	0.000446507i	−0.707330	−	0.706883i	$-0.750100\pi$
$479$	−0.00977229	+	0.00977229i	−0.000446507	+	0.000446507i	0.706883	+	0.707330i	$0.250100\pi$
$480$	−2.18253	−	0.486383i	−0.0996184	−	0.0222002i
$481$	14.8961	−	8.67387i	0.679203	−	0.395495i
$482$	21.3229	−	21.3229i	0.971233	−	0.971233i
$483$	17.6518			0.803184
$484$	−10.9380			−0.497180
$485$	−11.2238	+	7.13294i	−0.509646	+	0.323890i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−0.0126739			−0.000574311			−0.000287155	−	1.00000i	$-0.500091\pi$
$487$	−0.0126739			−0.000574311			−0.000287155		1.00000i	$0.500091\pi$
$488$	−3.22008	−	3.22008i	−0.145766	−	0.145766i
$489$	−6.14503	+	6.14503i	−0.277888	+	0.277888i
$490$	4.65069	−	2.95561i	0.210097	−	0.133521i
$491$	24.8512			1.12152			0.560760	−	0.827979i	$-0.310509\pi$
$491$	24.8512			1.12152			0.560760	+	0.827979i	$0.310509\pi$
$492$	7.29960	+	7.29960i	0.329091	+	0.329091i
$493$	17.3062	+	17.3062i	0.779433	+	0.779433i
$494$	−5.36948	+	5.36948i	−0.241584	+	0.241584i
$495$	−0.470059	+	0.298732i	−0.0211276	+	0.0134270i
$496$	1.83366	−	1.83366i	0.0823338	−	0.0823338i
$497$	−5.07975	+	5.07975i	−0.227858	+	0.227858i
$498$		−	8.46334i		−	0.379251i
$499$	30.1549	+	30.1549i	1.34992	+	1.34992i	0.885744	+	0.464175i	$0.153649\pi$
$499$	30.1549	+	30.1549i	1.34992	+	1.34992i	0.464175	+	0.885744i	$0.346351\pi$
$500$	1.42262	+	11.0895i	0.0636214	+	0.495936i
$501$	−13.0979	+	13.0979i	−0.585172	+	0.585172i
$502$	−14.6439	−	14.6439i	−0.653590	−	0.653590i
$503$		−	33.2862i		−	1.48416i	−0.670312	−	0.742080i	$-0.733840\pi$
$503$		−	33.2862i		−	1.48416i	0.670312	−	0.742080i	$-0.266160\pi$
$504$	−1.50593	+	1.50593i	−0.0670796	+	0.0670796i
$505$	12.3515	+	19.4353i	0.549636	+	0.864861i
$506$			2.06443i			0.0917753i
$507$	3.51395	−	3.51395i	0.156060	−	0.156060i
$508$	−12.5469	+	12.5469i	−0.556679	+	0.556679i
$509$	35.6979			1.58228			0.791140	−	0.611635i	$-0.209488\pi$
$509$	35.6979			1.58228			0.791140	+	0.611635i	$0.209488\pi$
$510$	15.9194	+	3.54768i	0.704923	+	0.157094i
$511$		−	22.5356i		−	0.996918i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.67964			−0.118309
$514$		−	17.8930i		−	0.789228i
$515$	−15.7474	+	10.0078i	−0.693911	+	0.440994i
$516$	5.38278	+	5.38278i	0.236964	+	0.236964i
$517$	0.704271	+	0.704271i	0.0309738	+	0.0309738i
$518$	−3.30658	+	12.5254i	−0.145283	+	0.550336i
$519$		−	9.33502i		−	0.409762i
$520$	5.34800	−	3.39876i	0.234525	−	0.149045i
$521$		−	0.701242i		−	0.0307220i	−0.999882	−	0.0153610i	$-0.995110\pi$
$521$		−	0.701242i		−	0.0307220i	0.999882	−	0.0153610i	$-0.00488975\pi$
$522$	2.37266	+	2.37266i	0.103849	+	0.103849i
$523$		−	35.1652i		−	1.53767i	−0.639449	−	0.768833i	$-0.720838\pi$
$523$		−	35.1652i		−	1.53767i	0.639449	−	0.768833i	$-0.279162\pi$
$524$	−3.81040	+	3.81040i	−0.166458	+	0.166458i
$525$	9.64092	+	4.52157i	0.420764	+	0.197337i
$526$	−21.7610	−	21.7610i	−0.948826	−	0.948826i
$527$	−13.3747	+	13.3747i	−0.582613	+	0.582613i
$528$	−0.176124	−	0.176124i	−0.00766480	−	0.00766480i
$529$	−45.6967			−1.98681
$530$	2.89301	−	12.9817i	0.125664	−	0.563889i
$531$	−6.26117	−	6.26117i	−0.271712	−	0.271712i
$532$		−	5.70685i		−	0.247423i
$533$	−29.2540			−1.26713
$534$		−	7.60247i		−	0.328991i
$535$	−1.44910	+	6.50250i	−0.0626500	+	0.281127i
$536$	−5.68165	+	5.68165i	−0.245410	+	0.245410i
$537$	15.7021			0.677597
$538$	−17.8478			−0.769475
$539$	0.613806			0.0264385
$540$	2.18253	+	0.486383i	0.0939211	+	0.0209306i
$541$	−5.47295	−	5.47295i	−0.235300	−	0.235300i	0.579600	−	0.814901i	$-0.303209\pi$
$541$	−5.47295	−	5.47295i	−0.235300	−	0.235300i	−0.814901	+	0.579600i	$0.803209\pi$
$542$		−	2.29360i		−	0.0985188i
$543$	13.5129	−	13.5129i	0.579895	−	0.579895i
$544$			7.29402i			0.312728i
$545$	−7.34234	+	32.9470i	−0.314511	+	1.41130i
$546$		−	6.03521i		−	0.258283i
$547$		−	14.4568i		−	0.618127i	−0.951041	−	0.309064i	$-0.899984\pi$
$547$		−	14.4568i		−	0.618127i	0.951041	−	0.309064i	$-0.100016\pi$
$548$	2.72768	−	2.72768i	0.116521	−	0.116521i
$549$	3.22008	+	3.22008i	0.137430	+	0.137430i
$550$	−0.528812	+	1.12754i	−0.0225486	+	0.0480783i
$551$	−8.99138			−0.383046
$552$	5.86075	−	5.86075i	0.249450	−	0.249450i
$553$			18.0657i			0.768233i
$554$	−1.48608			−0.0631373
$555$	12.9613	−	4.12369i	0.550176	−	0.175041i
$556$	−2.31516			−0.0981847
$557$		−	16.2684i		−	0.689316i	−0.938728	−	0.344658i	$-0.887995\pi$
$557$		−	16.2684i		−	0.689316i	0.938728	−	0.344658i	$-0.112005\pi$
$558$	−1.83366	+	1.83366i	−0.0776250	+	0.0776250i
$559$	−21.5722			−0.912405
$560$	−1.03586	+	4.64816i	−0.0437729	+	0.196421i
$561$	1.28465	+	1.28465i	0.0542380	+	0.0542380i
$562$	−18.5876	+	18.5876i	−0.784071	+	0.784071i
$563$			6.03926i			0.254525i	0.991869	+	0.127262i	$0.0406190\pi$
$563$			6.03926i			0.254525i	−0.991869	+	0.127262i	$0.959381\pi$
$564$		−	3.99873i		−	0.168377i
$565$	8.02610	−	5.10075i	0.337661	−	0.214590i
$566$			16.6153i			0.698392i
$567$	1.50593	−	1.50593i	0.0632433	−	0.0632433i
$568$			3.37315i			0.141534i
$569$	−13.8974	−	13.8974i	−0.582609	−	0.582609i	0.353010	−	0.935620i	$-0.385158\pi$
$569$	−13.8974	−	13.8974i	−0.582609	−	0.582609i	−0.935620	+	0.353010i	$0.885158\pi$
$570$	−5.05702	+	3.21384i	−0.211815	+	0.134613i
$571$	−28.3787			−1.18761			−0.593805	−	0.804609i	$-0.702375\pi$
$571$	−28.3787			−1.18761			−0.593805	+	0.804609i	$0.702375\pi$
$572$	0.705838			0.0295126
$573$	−5.85269			−0.244500
$574$	15.5460	−	15.5460i	0.648879	−	0.648879i
$575$	−37.5202	−	17.5969i	−1.56470	−	0.733841i
$576$			1.00000i			0.0416667i
$577$	−35.3160			−1.47023			−0.735113	−	0.677945i	$-0.762871\pi$
$577$	−35.3160			−1.47023			−0.735113	+	0.677945i	$0.762871\pi$
$578$		−	36.2027i		−	1.50583i
$579$	−1.17097	−	1.17097i	−0.0486638	−	0.0486638i
$580$	7.32336	+	1.63203i	0.304086	+	0.0677665i
$581$	−18.0245			−0.747781
$582$	4.20538	+	4.20538i	0.174319	+	0.174319i
$583$	1.04759	−	1.04759i	0.0433865	−	0.0433865i
$584$	−7.48228	−	7.48228i	−0.309619	−	0.309619i
$585$	−5.34800	+	3.39876i	−0.221112	+	0.140521i
$586$	9.37884	−	9.37884i	0.387436	−	0.387436i
$587$			33.3247i			1.37546i	0.725968	+	0.687729i	$0.241392\pi$
$587$			33.3247i			1.37546i	−0.725968	+	0.687729i	$0.758608\pi$
$588$	−1.74254	−	1.74254i	−0.0718612	−	0.0718612i
$589$		−	6.94879i		−	0.286320i
$590$	−19.3255	−	4.30674i	−0.795617	−	0.177306i
$591$		−	20.0645i		−	0.825344i
$592$	3.06084	+	5.25654i	0.125800	+	0.216043i
$593$	29.5804	+	29.5804i	1.21472	+	1.21472i	0.969456	+	0.245266i	$0.0788753\pi$
$593$	29.5804	+	29.5804i	1.21472	+	1.21472i	0.245266	+	0.969456i	$0.421125\pi$
$594$	0.176124	+	0.176124i	0.00722645	+	0.00722645i
$595$	7.55555	−	33.9037i	0.309747	−	1.38992i
$596$			8.45695i			0.346410i
$597$	−5.22101			−0.213682
$598$			23.4877i			0.960482i
$599$		−	16.4095i		−	0.670473i	−0.942134	−	0.335236i	$-0.891184\pi$
$599$		−	16.4095i		−	0.670473i	0.942134	−	0.335236i	$-0.108816\pi$
$600$	4.70223	−	1.69973i	0.191968	−	0.0693910i
$601$	−24.3063			−0.991473			−0.495736	−	0.868473i	$-0.665102\pi$
$601$	−24.3063			−0.991473			−0.495736	+	0.868473i	$0.665102\pi$
$602$	11.4638	−	11.4638i	0.467229	−	0.467229i
$603$	5.68165	−	5.68165i	0.231375	−	0.231375i
$604$		−	12.3871i		−	0.504024i
$605$	20.6422	−	13.1185i	0.839224	−	0.533343i
$606$	7.28212	−	7.28212i	0.295816	−	0.295816i
$607$			2.93171i			0.118994i	0.998228	+	0.0594972i	$0.0189497\pi$
$607$			2.93171i			0.118994i	−0.998228	+	0.0594972i	$0.981050\pi$
$608$	−1.89479	−	1.89479i	−0.0768438	−	0.0768438i
$609$	5.05308	−	5.05308i	0.204761	−	0.204761i
$610$	9.93899	+	2.21493i	0.402418	+	0.0896800i
$611$	8.01269	+	8.01269i	0.324159	+	0.324159i
$612$		−	7.29402i		−	0.294843i
$613$	−15.0778	+	15.0778i	−0.608986	+	0.608986i	−0.942681	−	0.333695i	$-0.891704\pi$
$613$	−15.0778	+	15.0778i	−0.608986	+	0.608986i	0.333695	+	0.942681i	$0.391704\pi$
$614$	3.36862	−	3.36862i	0.135947	−	0.135947i
$615$	−22.5307	−	5.02102i	−0.908524	−	0.202467i
$616$	−0.375093	+	0.375093i	−0.0151129	+	0.0151129i
$617$	−31.1997	−	31.1997i	−1.25605	−	1.25605i	−0.952962	−	0.303091i	$-0.901981\pi$
$617$	−31.1997	−	31.1997i	−1.25605	−	1.25605i	−0.303091	−	0.952962i	$-0.598019\pi$
$618$	5.90029	+	5.90029i	0.237345	+	0.237345i
$619$	−11.1366			−0.447619			−0.223809	−	0.974633i	$-0.571849\pi$
$619$	−11.1366			−0.447619			−0.223809	+	0.974633i	$0.571849\pi$
$620$	−1.26128	+	5.65970i	−0.0506543	+	0.227299i
$621$	−5.86075	+	5.86075i	−0.235184	+	0.235184i
$622$	−22.4334	−	22.4334i	−0.899497	−	0.899497i
$623$	−16.1911			−0.648682
$624$	−2.00381	−	2.00381i	−0.0802166	−	0.0802166i
$625$	−15.9850	−	19.2219i	−0.639399	−	0.768875i
$626$	−19.2752			−0.770393
$627$	−0.667435			−0.0266548
$628$	10.3496	−	10.3496i	0.412993	−	0.412993i
$629$	−22.3259	−	38.3413i	−0.890190	−	1.52877i
$630$	1.03586	−	4.64816i	0.0412695	−	0.185187i
$631$	19.2236	−	19.2236i	0.765279	−	0.765279i	−0.211992	−	0.977271i	$-0.567995\pi$
$631$	19.2236	−	19.2236i	0.765279	−	0.765279i	0.977271	+	0.211992i	$0.0679951\pi$
$632$	5.99818	+	5.99818i	0.238595	+	0.238595i
$633$	−5.76649	+	5.76649i	−0.229197	+	0.229197i
$634$	−3.94817	+	3.94817i	−0.156802	+	0.156802i
$635$	8.63038	−	38.7268i	0.342486	−	1.53683i
$636$	−5.94800			−0.235854
$637$	6.98345			0.276694
$638$	0.590974	+	0.590974i	0.0233969	+	0.0233969i
$639$		−	3.37315i		−	0.133440i
$640$	1.19936	+	1.88721i	0.0474087	+	0.0745983i
$641$	8.52699			0.336796			0.168398	−	0.985719i	$-0.446141\pi$
$641$	8.52699			0.336796			0.168398	+	0.985719i	$0.446141\pi$
$642$	2.97934			0.117585
$643$	−11.8650			−0.467910			−0.233955	−	0.972247i	$-0.575167\pi$
$643$	−11.8650			−0.467910			−0.233955	+	0.972247i	$0.575167\pi$
$644$	−12.4817	−	12.4817i	−0.491848	−	0.491848i
$645$	−16.6143	−	3.70254i	−0.654187	−	0.145787i
$646$	13.8206	+	13.8206i	0.543765	+	0.543765i
$647$			1.01194i			0.0397836i	0.999802	+	0.0198918i	$0.00633217\pi$
$647$			1.01194i			0.0397836i	−0.999802	+	0.0198918i	$0.993668\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−1.55951	−	1.55951i	−0.0612161	−	0.0612161i
$650$	−6.01645	+	12.8283i	−0.235984	+	0.503167i
$651$	3.90517	+	3.90517i	0.153056	+	0.153056i
$652$	8.69039			0.340342
$653$	14.7798			0.578377			0.289189	−	0.957272i	$-0.406614\pi$
$653$	14.7798			0.578377			0.289189	+	0.957272i	$0.406614\pi$
$654$	15.0958			0.590293
$655$	2.62098	−	11.7610i	0.102410	−	0.459541i
$656$		−	10.3232i		−	0.403053i
$657$	7.48228	+	7.48228i	0.291912	+	0.291912i
$658$	−8.51613			−0.331993
$659$	−1.79646			−0.0699802			−0.0349901	−	0.999388i	$-0.511140\pi$
$659$	−1.79646			−0.0699802			−0.0349901	+	0.999388i	$0.511140\pi$
$660$	0.543617	+	0.121147i	0.0211603	+	0.00471562i
$661$	11.0318	−	11.0318i	0.429086	−	0.429086i	−0.459231	−	0.888317i	$-0.651875\pi$
$661$	11.0318	−	11.0318i	0.429086	−	0.429086i	0.888317	+	0.459231i	$0.151875\pi$
$662$	−2.89997	+	2.89997i	−0.112711	+	0.112711i
$663$	14.6158	+	14.6158i	0.567632	+	0.567632i
$664$	−5.98449	+	5.98449i	−0.232243	+	0.232243i
$665$	6.84455	+	10.7700i	0.265420	+	0.417643i
$666$	−3.06084	−	5.25654i	−0.118605	−	0.203687i
$667$	−19.6654	+	19.6654i	−0.761449	+	0.761449i
$668$	18.5233			0.716687
$669$	25.5945			0.989539
$670$	3.90812	−	17.5368i	0.150984	−	0.677504i
$671$	0.802048	+	0.802048i	0.0309627	+	0.0309627i
$672$	2.12971			0.0821554
$673$	12.5759	+	12.5759i	0.484766	+	0.484766i	0.906650	−	0.421884i	$-0.138631\pi$
$673$	12.5759	+	12.5759i	0.484766	+	0.484766i	−0.421884	+	0.906650i	$0.638631\pi$
$674$	−1.55976	+	1.55976i	−0.0600796	+	0.0600796i
$675$	−4.70223	+	1.69973i	−0.180989	+	0.0654225i
$676$	−4.96948			−0.191134
$677$	−18.9213	−	18.9213i	−0.727203	−	0.727203i	0.242859	−	0.970062i	$-0.421915\pi$
$677$	−18.9213	−	18.9213i	−0.727203	−	0.727203i	−0.970062	+	0.242859i	$0.921915\pi$
$678$	−3.00726	−	3.00726i	−0.115493	−	0.115493i
$679$	8.95625	−	8.95625i	0.343710	−	0.343710i
$680$	−8.74813	−	13.7653i	−0.335475	−	0.527876i
$681$	−10.7509	+	10.7509i	−0.411974	+	0.411974i
$682$	−0.456722	+	0.456722i	−0.0174888	+	0.0174888i
$683$			36.6018i			1.40053i	0.713883	+	0.700265i	$0.246935\pi$
$683$			36.6018i			1.40053i	−0.713883	+	0.700265i	$0.753065\pi$
$684$	1.89479	+	1.89479i	0.0724490	+	0.0724490i
$685$	−1.87623	+	8.41915i	−0.0716871	+	0.321679i
$686$	−14.2526	+	14.2526i	−0.544169	+	0.544169i
$687$	15.6384	+	15.6384i	0.596642	+	0.596642i
$688$		−	7.61240i		−	0.290220i
$689$	11.9187	−	11.9187i	0.454066	−	0.454066i
$690$	−4.03131	+	18.0896i	−0.153469	+	0.688658i
$691$		−	23.7209i		−	0.902385i	−0.892427	−	0.451193i	$-0.850999\pi$
$691$		−	23.7209i		−	0.902385i	0.892427	−	0.451193i	$-0.149001\pi$
$692$	−6.60085	+	6.60085i	−0.250927	+	0.250927i
$693$	0.375093	−	0.375093i	0.0142486	−	0.0142486i
$694$	9.43617			0.358192
$695$	4.36918	−	2.77670i	0.165733	−	0.105326i
$696$		−	3.35545i		−	0.127188i
$697$			75.2975i			2.85210i
$698$	−7.25908			−0.274760
$699$			6.74984i			0.255302i
$700$	−3.61993	−	10.0144i	−0.136820	−	0.378508i
$701$	−12.5087	−	12.5087i	−0.472447	−	0.472447i	0.430259	−	0.902706i	$-0.358422\pi$
$701$	−12.5087	−	12.5087i	−0.472447	−	0.472447i	−0.902706	+	0.430259i	$0.858422\pi$
$702$	2.00381	+	2.00381i	0.0756290	+	0.0756290i
$703$	15.7597	+	4.16038i	0.594388	+	0.156912i
$704$			0.249077i			0.00938743i
$705$	4.79590	+	7.54642i	0.180624	+	0.284214i
$706$			6.63465i			0.249698i
$707$	−15.5088	−	15.5088i	−0.583269	−	0.583269i
$708$			8.85463i			0.332777i
$709$	−16.9567	+	16.9567i	−0.636822	+	0.636822i	−0.949770	−	0.312948i	$-0.898683\pi$
$709$	−16.9567	+	16.9567i	−0.636822	+	0.636822i	0.312948	+	0.949770i	$0.398683\pi$
$710$	−4.04561	−	6.36583i	−0.151829	−	0.238906i
$711$	−5.99818	−	5.99818i	−0.224949	−	0.224949i
$712$	−5.37576	+	5.37576i	−0.201465	+	0.201465i
$713$	−15.1980	−	15.1980i	−0.569170	−	0.569170i
$714$	−15.5342			−0.581351
$715$	−1.33206	+	0.846551i	−0.0498162	+	0.0316592i
$716$	−11.1031	−	11.1031i	−0.414942	−	0.414942i
$717$		−	28.0719i		−	1.04836i
$718$	3.64712			0.136109
$719$		−	6.40855i		−	0.238998i	−0.992834	−	0.119499i	$-0.961871\pi$
$719$		−	6.40855i		−	0.238998i	0.992834	−	0.119499i	$-0.0381289\pi$
$720$	−1.19936	−	1.88721i	−0.0446974	−	0.0703320i
$721$	12.5659	−	12.5659i	0.467979	−	0.467979i
$722$	11.8196			0.439878
$723$	30.1552			1.12148
$724$	−19.1102			−0.710223
$725$	−15.7781	+	5.70334i	−0.585983	+	0.211817i
$726$	−7.73431	−	7.73431i	−0.287047	−	0.287047i
$727$			6.09536i			0.226064i	0.993591	+	0.113032i	$0.0360563\pi$
$727$			6.09536i			0.226064i	−0.993591	+	0.113032i	$0.963944\pi$
$728$	−4.26754	+	4.26754i	−0.158166	+	0.158166i
$729$			1.00000i			0.0370370i
$730$	23.0945	+	5.14668i	0.854767	+	0.190487i
$731$			55.5250i			2.05367i
$732$		−	4.55389i		−	0.168317i
$733$	5.99617	−	5.99617i	0.221474	−	0.221474i	−0.587645	−	0.809119i	$-0.699945\pi$
$733$	5.99617	−	5.99617i	0.221474	−	0.221474i	0.809119	+	0.587645i	$0.199945\pi$
$734$	2.67398	+	2.67398i	0.0986982	+	0.0986982i
$735$	5.37846	+	1.19861i	0.198388	+	0.0442113i
$736$	−8.28835			−0.305513
$737$	1.41517	−	1.41517i	0.0521283	−	0.0521283i
$738$			10.3232i			0.380002i
$739$	31.2325			1.14891			0.574453	−	0.818538i	$-0.305215\pi$
$739$	31.2325			1.14891			0.574453	+	0.818538i	$0.305215\pi$
$740$	−12.0809	−	6.24913i	−0.444103	−	0.229723i
$741$	−7.59360			−0.278958
$742$			12.6675i			0.465040i
$743$	−28.7095	+	28.7095i	−1.05325	+	1.05325i	−0.0547482	+	0.998500i	$0.517436\pi$
$743$	−28.7095	+	28.7095i	−1.05325	+	1.05325i	−0.998500	+	0.0547482i	$0.982564\pi$
$744$	2.59319			0.0950708
$745$	−10.1429	−	15.9600i	−0.371607	−	0.584730i
$746$	−8.22916	−	8.22916i	−0.301291	−	0.301291i
$747$	5.98449	−	5.98449i	0.218961	−	0.218961i
$748$		−	1.81677i		−	0.0664277i
$749$		−	6.34514i		−	0.231846i
$750$	−6.83549	+	8.84738i	−0.249597	+	0.323060i
$751$			4.99355i			0.182217i	0.995841	+	0.0911086i	$0.0290410\pi$
$751$			4.99355i			0.182217i	−0.995841	+	0.0911086i	$0.970959\pi$
$752$	−2.82753	+	2.82753i	−0.103109	+	0.103109i
$753$		−	20.7096i		−	0.754700i
$754$	6.72369	+	6.72369i	0.244862	+	0.244862i
$755$	14.8565	+	23.3770i	0.540685	+	0.850776i
$756$	−2.12971			−0.0774569
$757$	20.7849			0.755438			0.377719	−	0.925920i	$-0.376708\pi$
$757$	20.7849			0.755438			0.377719	+	0.925920i	$0.376708\pi$
$758$	−23.2988			−0.846250
$759$	−1.45978	+	1.45978i	−0.0529865	+	0.0529865i
$760$	5.84838	+	1.30333i	0.212143	+	0.0472767i
$761$		−	10.4423i		−	0.378532i	−0.981926	−	0.189266i	$-0.939389\pi$
$761$		−	10.4423i		−	0.378532i	0.981926	−	0.189266i	$-0.0606109\pi$
$762$	−17.7440			−0.642798
$763$		−	32.1497i		−	1.16390i
$764$	4.13848	+	4.13848i	0.149725	+	0.149725i
$765$	8.74813	+	13.7653i	0.316289	+	0.497686i
$766$	1.82589			0.0659719
$767$	−17.7430	−	17.7430i	−0.640663	−	0.640663i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	36.5206	+	36.5206i	1.31697	+	1.31697i	0.916165	+	0.400801i	$0.131268\pi$
$769$	36.5206	+	36.5206i	1.31697	+	1.31697i	0.400801	+	0.916165i	$0.368732\pi$
$770$	0.258007	−	1.15775i	0.00929794	−	0.0417223i
$771$	12.6523	−	12.6523i	0.455661	−	0.455661i
$772$			1.65600i			0.0596007i
$773$	36.9436	+	36.9436i	1.32877	+	1.32877i	0.906445	+	0.422323i	$0.138785\pi$
$773$	36.9436	+	36.9436i	1.32877	+	1.32877i	0.422323	+	0.906445i	$0.361215\pi$
$774$			7.61240i			0.273622i
$775$	−4.40771	−	12.1938i	−0.158329	−	0.438012i
$776$		−	5.94731i		−	0.213496i
$777$	−11.1949	+	6.51872i	−0.401616	+	0.233858i
$778$	−1.87840	−	1.87840i	−0.0673440	−	0.0673440i
$779$	−19.5603	−	19.5603i	−0.700819	−	0.700819i
$780$	6.18489	+	1.37832i	0.221454	+	0.0493518i
$781$		−	0.840174i		−	0.0300638i
$782$	60.4554			2.16188
$783$			3.35545i			0.119914i
$784$			2.46433i			0.0880117i
$785$	−7.11895	+	31.9446i	−0.254086	+	1.14015i
$786$	−5.38872			−0.192209
$787$	−5.06401	+	5.06401i	−0.180512	+	0.180512i	−0.791579	−	0.611067i	$-0.790741\pi$
$787$	−5.06401	+	5.06401i	−0.180512	+	0.180512i	0.611067	+	0.791579i	$0.290741\pi$
$788$	−14.1878	+	14.1878i	−0.505418	+	0.505418i
$789$		−	30.7747i		−	1.09561i
$790$	−18.5138	−	4.12584i	−0.658690	−	0.146791i
$791$	−6.40459	+	6.40459i	−0.227721	+	0.227721i
$792$		−	0.249077i		−	0.00885055i
$793$	9.12513	+	9.12513i	0.324043	+	0.324043i
$794$	12.0046	−	12.0046i	0.426026	−	0.426026i
$795$	11.2251	−	7.13378i	0.398114	−	0.253009i
$796$	3.69181	+	3.69181i	0.130853	+	0.130853i
$797$			21.7157i			0.769210i	0.923081	+	0.384605i	$0.125662\pi$
$797$			21.7157i			0.769210i	−0.923081	+	0.384605i	$0.874338\pi$
$798$	4.03535	−	4.03535i	0.142850	−	0.142850i
$799$	20.6240	−	20.6240i	0.729625	−	0.729625i
$800$	−4.52686	−	2.12309i	−0.160049	−	0.0750625i
$801$	5.37576	−	5.37576i	0.189943	−	0.189943i
$802$	23.2046	+	23.2046i	0.819382	+	0.819382i
$803$	1.86366	+	1.86366i	0.0657672	+	0.0657672i
$804$	−8.03506			−0.283375
$805$	38.5255	+	8.58553i	1.35785	+	0.302600i
$806$	−5.19626	+	5.19626i	−0.183030	+	0.183030i
$807$	−12.6203	−	12.6203i	−0.444257	−	0.444257i
$808$	−10.2985			−0.362299
$809$	−23.1152	−	23.1152i	−0.812687	−	0.812687i	0.172349	−	0.985036i	$-0.444864\pi$
$809$	−23.1152	−	23.1152i	−0.812687	−	0.812687i	−0.985036	+	0.172349i	$0.944864\pi$
$810$	1.19936	+	1.88721i	0.0421411	+	0.0663096i
$811$	45.9301			1.61282			0.806412	−	0.591354i	$-0.201407\pi$
$811$	45.9301			1.61282			0.806412	+	0.591354i	$0.201407\pi$
$812$	−7.14614			−0.250780
$813$	1.62182	−	1.62182i	0.0568798	−	0.0568798i
$814$	−0.762385	−	1.30928i	−0.0267216	−	0.0458903i
$815$	−16.4006	+	10.4229i	−0.574486	+	0.365097i
$816$	−5.15765	+	5.15765i	−0.180554	+	0.180554i
$817$	−14.4239	−	14.4239i	−0.504628	−	0.504628i
$818$	12.7469	−	12.7469i	0.445683	−	0.445683i
$819$	4.26754	−	4.26754i	0.149120	−	0.149120i
$820$	12.3812	+	19.4820i	0.432370	+	0.680340i
$821$	−31.8102			−1.11018			−0.555092	−	0.831789i	$-0.687317\pi$
$821$	−31.8102			−1.11018			−0.555092	+	0.831789i	$0.687317\pi$
$822$	3.85752			0.134547
$823$	0.924037	+	0.924037i	0.0322099	+	0.0322099i	0.723028	−	0.690818i	$-0.242750\pi$
$823$	0.924037	+	0.924037i	0.0322099	+	0.0322099i	−0.690818	+	0.723028i	$0.742750\pi$
$824$		−	8.34427i		−	0.290686i
$825$	−1.17121	+	0.423362i	−0.0407765	+	0.0147396i
$826$	18.8578			0.656147
$827$	5.29174			0.184012			0.0920059	−	0.995758i	$-0.470672\pi$
$827$	5.29174			0.184012			0.0920059	+	0.995758i	$0.470672\pi$
$828$	8.28835			0.288040
$829$	−14.0039	−	14.0039i	−0.486376	−	0.486376i	0.420784	−	0.907161i	$-0.361755\pi$
$829$	−14.0039	−	14.0039i	−0.486376	−	0.486376i	−0.907161	+	0.420784i	$0.861755\pi$
$830$	4.11642	−	18.4715i	0.142883	−	0.641155i
$831$	−1.05081	−	1.05081i	−0.0364523	−	0.0364523i
$832$			2.83382i			0.0982449i
$833$		−	17.9748i		−	0.622791i
$834$	−1.63707	−	1.63707i	−0.0566870	−	0.0566870i
$835$	−34.9572	+	22.2160i	−1.20974	+	0.768816i
$836$	0.471948	+	0.471948i	0.0163226	+	0.0163226i
$837$	−2.59319			−0.0896336
$838$	22.1539			0.765295
$839$	5.45096			0.188188			0.0940941	−	0.995563i	$-0.470005\pi$
$839$	5.45096			0.188188			0.0940941	+	0.995563i	$0.470005\pi$
$840$	−4.01920	+	2.55428i	−0.138676	+	0.0881312i
$841$		−	17.7410i		−	0.611757i
$842$	18.3106	+	18.3106i	0.631025	+	0.631025i
$843$	−26.2868			−0.905367
$844$	8.15505			0.280708
$845$	9.37843	−	5.96018i	0.322628	−	0.205036i
$846$	2.82753	−	2.82753i	0.0972123	−	0.0972123i
$847$	−16.4718	+	16.4718i	−0.565979	+	0.565979i
$848$	4.20587	+	4.20587i	0.144430	+	0.144430i
$849$	−11.7488	+	11.7488i	−0.403217	+	0.403217i
$850$	33.0190	+	15.4858i	1.13254	+	0.531160i
$851$	43.5680	−	25.3693i	1.49349	−	0.869650i
$852$	−2.38518	+	2.38518i	−0.0817149	+	0.0817149i
$853$	1.69992			0.0582041			0.0291021	−	0.999576i	$-0.490735\pi$
$853$	1.69992			0.0582041			0.0291021	+	0.999576i	$0.490735\pi$
$854$	−9.69847			−0.331875
$855$	−5.84838	−	1.30333i	−0.200010	−	0.0445729i
$856$	−2.10671	−	2.10671i	−0.0720059	−	0.0720059i
$857$	48.8147			1.66748			0.833738	−	0.552160i	$-0.186196\pi$
$857$	48.8147			1.66748			0.833738	+	0.552160i	$0.186196\pi$
$858$	0.499103	+	0.499103i	0.0170391	+	0.0170391i
$859$	−2.09107	+	2.09107i	−0.0713463	+	0.0713463i	−0.741879	−	0.670533i	$-0.766065\pi$
$859$	−2.09107	+	2.09107i	−0.0713463	+	0.0713463i	0.670533	+	0.741879i	$0.266065\pi$
$860$	9.12998	+	14.3662i	0.311330	+	0.489882i
$861$	21.9854			0.749261
$862$	8.32782	+	8.32782i	0.283647	+	0.283647i
$863$	−5.37396	−	5.37396i	−0.182932	−	0.182932i	0.609700	−	0.792632i	$-0.291290\pi$
$863$	−5.37396	−	5.37396i	−0.182932	−	0.182932i	−0.792632	+	0.609700i	$0.791290\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	4.54039	−	20.3739i	0.154378	−	0.692735i
$866$	−6.11268	+	6.11268i	−0.207717	+	0.207717i
$867$	25.5992	−	25.5992i	0.869393	−	0.869393i
$868$		−	5.52274i		−	0.187454i
$869$	−1.49401	−	1.49401i	−0.0506807	−	0.0506807i
$870$	4.02438	+	6.33242i	0.136439	+	0.214689i
$871$	16.1008	−	16.1008i	0.545553	−	0.545553i
$872$	−10.6743	−	10.6743i	−0.361479	−	0.361479i
$873$			5.94731i			0.201286i
$874$	−15.7047	+	15.7047i	−0.531218	+	0.531218i
$875$	18.8424	+	14.5576i	0.636988	+	0.492138i
$876$		−	10.5815i		−	0.357517i
$877$	−6.91171	+	6.91171i	−0.233392	+	0.233392i	−0.814107	−	0.580715i	$-0.802773\pi$
$877$	−6.91171	+	6.91171i	−0.233392	+	0.233392i	0.580715	+	0.814107i	$0.302773\pi$
$878$	16.2052	−	16.2052i	0.546899	−	0.546899i
$879$	13.2637			0.447373
$880$	−0.298732	−	0.470059i	−0.0100702	−	0.0158457i
$881$			8.64906i			0.291394i	0.989329	+	0.145697i	$0.0465425\pi$
$881$			8.64906i			0.291394i	−0.989329	+	0.145697i	$0.953457\pi$
$882$		−	2.46433i		−	0.0829782i
$883$	18.4508			0.620919			0.310460	−	0.950587i	$-0.399517\pi$
$883$	18.4508			0.620919			0.310460	+	0.950587i	$0.399517\pi$
$884$		−	20.6699i		−	0.695204i
$885$	−10.6199	−	16.7105i	−0.356982	−	0.561717i
$886$	6.30399	+	6.30399i	0.211787	+	0.211787i
$887$	27.1337	+	27.1337i	0.911062	+	0.911062i	0.996356	−	0.0852937i	$-0.0271829\pi$
$887$	27.1337	+	27.1337i	0.911062	+	0.911062i	−0.0852937	+	0.996356i	$0.527183\pi$
$888$	−1.55259	+	5.88128i	−0.0521016	+	0.197363i
$889$			37.7896i			1.26742i
$890$	3.69771	−	16.5926i	0.123948	−	0.556186i
$891$			0.249077i			0.00834438i
$892$	−18.0980	−	18.0980i	−0.605967	−	0.605967i
$893$			10.7151i			0.358568i
$894$	−5.97997	+	5.97997i	−0.200000	+	0.200000i
$895$	34.2703	+	7.63724i	1.14553	+	0.255285i
$896$	−1.50593	−	1.50593i	−0.0503097	−	0.0503097i
$897$	−16.6083	+	16.6083i	−0.554534	+	0.554534i
$898$	19.8634	+	19.8634i	0.662851	+	0.662851i
$899$	−8.70130			−0.290205
$900$	4.52686	+	2.12309i	0.150895	+	0.0707696i
$901$	−30.6777	−	30.6777i	−1.02202	−	1.02202i
$902$			2.57127i			0.0856138i
$903$	16.2122			0.539509
$904$			4.25290i			0.141449i
$905$	36.0648	−	22.9199i	1.19883	−	0.761883i
$906$	8.75900	−	8.75900i	0.290998	−	0.290998i
$907$	20.4243			0.678179			0.339090	−	0.940754i	$-0.389881\pi$
$907$	20.4243			0.678179			0.339090	+	0.940754i	$0.389881\pi$
$908$	15.2040			0.504563
$909$	10.2985			0.341579
$910$	2.93542	−	13.1720i	0.0973084	−	0.436648i
$911$	26.7806	+	26.7806i	0.887279	+	0.887279i	0.994261	−	0.106982i	$-0.0341186\pi$
$911$	26.7806	+	26.7806i	0.887279	+	0.887279i	−0.106982	+	0.994261i	$0.534119\pi$
$912$		−	2.67964i		−	0.0887316i
$913$	1.49060	−	1.49060i	0.0493315	−	0.0493315i
$914$			40.2606i			1.33170i
$915$	5.46173	+	8.59412i	0.180559	+	0.284113i
$916$		−	22.1160i		−	0.730735i
$917$			11.4764i			0.378985i
$918$	5.15765	−	5.15765i	0.170228	−	0.170228i
$919$	31.0865	+	31.0865i	1.02545	+	1.02545i	0.999668	+	0.0257801i	$0.00820698\pi$
$919$	31.0865	+	31.0865i	1.02545	+	1.02545i	0.0257801	+	0.999668i	$0.491793\pi$
$920$	15.6418	−	9.94068i	0.515695	−	0.327735i
$921$	4.76395			0.156978
$922$	−15.0948	+	15.0948i	−0.497121	+	0.497121i
$923$		−	9.55890i		−	0.314635i
$924$	−0.530462			−0.0174509
$925$	30.2941	−	2.69592i	0.996064	−	0.0886413i
$926$	−25.5478			−0.839551
$927$			8.34427i			0.274062i
$928$	−2.37266	+	2.37266i	−0.0778864	+	0.0778864i
$929$	−47.3305			−1.55286			−0.776431	−	0.630202i	$-0.782972\pi$
$929$	−47.3305			−1.55286			−0.776431	+	0.630202i	$0.782972\pi$
$930$	−4.89388	+	3.11015i	−0.160477	+	0.101986i
$931$	4.66938	+	4.66938i	0.153033	+	0.153033i
$932$	4.77285	−	4.77285i	0.156340	−	0.156340i
$933$		−	31.7256i		−	1.03865i
$934$			30.7343i			1.00566i
$935$	2.17895	+	3.42862i	0.0712594	+	0.112128i
$936$		−	2.83382i		−	0.0926262i
$937$	−17.0130	+	17.0130i	−0.555791	+	0.555791i	−0.928106	−	0.372315i	$-0.878564\pi$
$937$	−17.0130	+	17.0130i	−0.555791	+	0.555791i	0.372315	+	0.928106i	$0.378564\pi$
$938$			17.1124i			0.558739i
$939$	−13.6296	−	13.6296i	−0.444787	−	0.444787i
$940$	1.94491	−	8.72733i	0.0634360	−	0.284654i
$941$	19.9394			0.650005			0.325002	−	0.945713i	$-0.394635\pi$
$941$	19.9394			0.650005			0.325002	+	0.945713i	$0.394635\pi$
$942$	14.6365			0.476883
$943$	−85.5622			−2.78629
$944$	6.26117	−	6.26117i	0.203784	−	0.203784i
$945$	4.01920	−	2.55428i	0.130745	−	0.0830908i
$946$			1.89607i			0.0616466i
$947$	51.9641			1.68861			0.844304	−	0.535865i	$-0.180014\pi$
$947$	51.9641			1.68861			0.844304	+	0.535865i	$0.180014\pi$
$948$			8.48271i			0.275506i
$949$	21.2034	+	21.2034i	0.688292	+	0.688292i
$950$	−12.6003	+	4.55464i	−0.408806	+	0.147772i
$951$	−5.58356			−0.181059
$952$	10.9843	+	10.9843i	0.356003	+	0.356003i
$953$	1.57228	−	1.57228i	0.0509312	−	0.0509312i	−0.681182	−	0.732114i	$-0.738534\pi$
$953$	1.57228	−	1.57228i	0.0509312	−	0.0509312i	0.732114	+	0.681182i	$0.238534\pi$
$954$	−4.20587	−	4.20587i	−0.136170	−	0.136170i
$955$	−12.7737	−	2.84665i	−0.413346	−	0.0921154i
$956$	−19.8498	+	19.8498i	−0.641989	+	0.641989i
$957$			0.835764i			0.0270164i
$958$	0.00977229	+	0.00977229i	0.000315728	+	0.000315728i
$959$		−	8.21541i		−	0.265289i
$960$	−0.486383	+	2.18253i	−0.0156979	+	0.0704408i
$961$			24.2754i			0.783077i
$962$	−8.67387	−	14.8961i	−0.279657	−	0.480269i
$963$	2.10671	+	2.10671i	0.0678878	+	0.0678878i
$964$	−21.3229	−	21.3229i	−0.686765	−	0.686765i
$965$	−1.98613	−	3.12521i	−0.0639358	−	0.100604i
$966$		−	17.6518i		−	0.567937i
$967$	31.3573			1.00838			0.504192	−	0.863592i	$-0.331790\pi$
$967$	31.3573			1.00838			0.504192	+	0.863592i	$0.331790\pi$
$968$			10.9380i			0.351559i
$969$			19.5453i			0.627886i
$970$	7.13294	+	11.2238i	0.229025	+	0.360374i
$971$	−32.7570			−1.05122			−0.525611	−	0.850725i	$-0.676163\pi$
$971$	−32.7570			−1.05122			−0.525611	+	0.850725i	$0.676163\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−3.48648	+	3.48648i	−0.111771	+	0.111771i
$974$			0.0126739i			0.000406099i
$975$	−13.3252	+	4.81671i	−0.426750	+	0.154258i
$976$	−3.22008	+	3.22008i	−0.103072	+	0.103072i
$977$			10.8286i			0.346436i	0.984883	+	0.173218i	$0.0554166\pi$
$977$			10.8286i			0.346436i	−0.984883	+	0.173218i	$0.944583\pi$
$978$	6.14503	+	6.14503i	0.196497	+	0.196497i
$979$	1.33898	−	1.33898i	0.0427939	−	0.0427939i
$980$	−2.95561	−	4.65069i	−0.0944134	−	0.148561i
$981$	10.6743	+	10.6743i	0.340806	+	0.340806i
$982$		−	24.8512i		−	0.793034i
$983$	32.0672	−	32.0672i	1.02279	−	1.02279i	0.0230521	−	0.999734i	$-0.492662\pi$
$983$	32.0672	−	32.0672i	1.02279	−	1.02279i	0.999734	−	0.0230521i	$-0.00733836\pi$
$984$	7.29960	−	7.29960i	0.232703	−	0.232703i
$985$	9.75904	−	43.7914i	0.310949	−	1.39531i
$986$	17.3062	−	17.3062i	0.551142	−	0.551142i
$987$	−6.02182	−	6.02182i	−0.191677	−	0.191677i
$988$	5.36948	+	5.36948i	0.170826	+	0.170826i
$989$	−63.0943			−2.00628
$990$	0.298732	+	0.470059i	0.00949431	+	0.0149394i
$991$	10.7854	−	10.7854i	0.342609	−	0.342609i	−0.514738	−	0.857347i	$-0.672111\pi$
$991$	10.7854	−	10.7854i	0.342609	−	0.342609i	0.857347	+	0.514738i	$0.172111\pi$
$992$	−1.83366	−	1.83366i	−0.0582188	−	0.0582188i
$993$	−4.10118			−0.130147
$994$	5.07975	+	5.07975i	0.161120	+	0.161120i
$995$	−11.3950	−	2.53941i	−0.361246	−	0.0805046i
$996$	−8.46334			−0.268171
$997$	27.7799			0.879799			0.439900	−	0.898047i	$-0.355014\pi$
$997$	27.7799			0.879799			0.439900	+	0.898047i	$0.355014\pi$
$998$	30.1549	−	30.1549i	0.954536	−	0.954536i
$999$	1.55259	−	5.88128i	0.0491219	−	0.186075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.43.15	✓	40
5.2	odd	4		1110.2.o.b.487.6	yes	40
37.31	odd	4		1110.2.o.b.253.6	yes	40
185.142	even	4	inner	1110.2.l.b.697.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.15	✓	40	1.1	even	1	trivial
1110.2.l.b.697.15	yes	40	185.142	even	4	inner
1110.2.o.b.253.6	yes	40	37.31	odd	4
1110.2.o.b.487.6	yes	40	5.2	odd	4

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 - 1.19936i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.88721 - 1.19936i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.19936 - 1.88721i) q^{10} -0.249077i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.83382i q^{13} +(1.50593 + 1.50593i) q^{14} +(0.486383 - 2.18253i) q^{15} +1.00000 q^{16} -7.29402 q^{17} -1.00000 q^{18} +(1.89479 - 1.89479i) q^{19} +(-1.88721 + 1.19936i) q^{20} +2.12971i q^{21} -0.249077 q^{22} -8.28835i q^{23} +(0.707107 + 0.707107i) q^{24} +(2.12309 - 4.52686i) q^{25} -2.83382 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.50593 - 1.50593i) q^{28} +(-2.37266 - 2.37266i) q^{29} +(-2.18253 - 0.486383i) q^{30} +(1.83366 - 1.83366i) q^{31} -1.00000i q^{32} +(-0.176124 - 0.176124i) q^{33} +7.29402i q^{34} +(-1.03586 + 4.64816i) q^{35} +1.00000i q^{36} +(3.06084 + 5.25654i) q^{37} +(-1.89479 - 1.89479i) q^{38} +(-2.00381 - 2.00381i) q^{39} +(1.19936 + 1.88721i) q^{40} -10.3232i q^{41} +2.12971 q^{42} -7.61240i q^{43} +0.249077i q^{44} +(-1.19936 - 1.88721i) q^{45} -8.28835 q^{46} +(-2.82753 + 2.82753i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.46433i q^{49} +(-4.52686 - 2.12309i) q^{50} +(-5.15765 + 5.15765i) q^{51} +2.83382i q^{52} +(4.20587 + 4.20587i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.298732 - 0.470059i) q^{55} +(-1.50593 - 1.50593i) q^{56} -2.67964i q^{57} +(-2.37266 + 2.37266i) q^{58} +(6.26117 - 6.26117i) q^{59} +(-0.486383 + 2.18253i) q^{60} +(-3.22008 + 3.22008i) q^{61} +(-1.83366 - 1.83366i) q^{62} +(1.50593 + 1.50593i) q^{63} -1.00000 q^{64} +(-3.39876 - 5.34800i) q^{65} +(-0.176124 + 0.176124i) q^{66} +(5.68165 + 5.68165i) q^{67} +7.29402 q^{68} +(-5.86075 - 5.86075i) q^{69} +(4.64816 + 1.03586i) q^{70} +3.37315 q^{71} +1.00000 q^{72} +(-7.48228 + 7.48228i) q^{73} +(5.25654 - 3.06084i) q^{74} +(-1.69973 - 4.70223i) q^{75} +(-1.89479 + 1.89479i) q^{76} +(0.375093 + 0.375093i) q^{77} +(-2.00381 + 2.00381i) q^{78} +(5.99818 - 5.99818i) q^{79} +(1.88721 - 1.19936i) q^{80} -1.00000 q^{81} -10.3232 q^{82} +(5.98449 + 5.98449i) q^{83} -2.12971i q^{84} +(-13.7653 + 8.74813i) q^{85} -7.61240 q^{86} -3.35545 q^{87} +0.249077 q^{88} +(5.37576 + 5.37576i) q^{89} +(-1.88721 + 1.19936i) q^{90} +(4.26754 + 4.26754i) q^{91} +8.28835i q^{92} -2.59319i q^{93} +(2.82753 + 2.82753i) q^{94} +(1.30333 - 5.84838i) q^{95} +(-0.707107 - 0.707107i) q^{96} -5.94731 q^{97} +2.46433 q^{98} -0.249077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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