LMFDB - Embedded newform 1110.2.o.a.487.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			487.15
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 + 1.11117i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 + 1.11117i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} -2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} +1.29147 q^{13} +(-0.636201 - 0.636201i) q^{14} +(0.586380 + 2.15781i) q^{15} +1.00000 q^{16} -5.74699i q^{17} -1.00000i q^{18} +(4.10165 - 4.10165i) q^{19} +(1.94044 + 1.11117i) q^{20} +0.899724i q^{21} +2.26858i q^{22} +8.53431 q^{23} +(-0.707107 - 0.707107i) q^{24} +(2.53060 + 4.31232i) q^{25} -1.29147 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.636201 + 0.636201i) q^{28} +(1.70155 + 1.70155i) q^{29} +(-0.586380 - 2.15781i) q^{30} +(-5.81155 + 5.81155i) q^{31} -1.00000 q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(0.527580 + 1.94144i) q^{35} +1.00000i q^{36} +(3.16223 + 5.19618i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(0.913209 + 0.913209i) q^{39} +(-1.94044 - 1.11117i) q^{40} -9.02011i q^{41} -0.899724i q^{42} +0.853087 q^{43} -2.26858i q^{44} +(-1.11117 + 1.94044i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.19050i q^{49} +(-2.53060 - 4.31232i) q^{50} +(4.06374 - 4.06374i) q^{51} +1.29147 q^{52} +(-6.79864 + 6.79864i) q^{53} +(0.707107 - 0.707107i) q^{54} +(2.52078 - 4.40204i) q^{55} +(-0.636201 - 0.636201i) q^{56} +5.80061 q^{57} +(-1.70155 - 1.70155i) q^{58} +(-3.51171 + 3.51171i) q^{59} +(0.586380 + 2.15781i) q^{60} +(-2.06460 + 2.06460i) q^{61} +(5.81155 - 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} +1.00000 q^{64} +(2.50602 + 1.43505i) q^{65} +(-1.60413 + 1.60413i) q^{66} +(-3.98347 + 3.98347i) q^{67} -5.74699i q^{68} +(6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000i q^{72} +(11.8322 + 11.8322i) q^{73} +(-3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 - 4.10165i) q^{76} +(1.44327 - 1.44327i) q^{77} +(-0.913209 - 0.913209i) q^{78} +(-9.04382 + 9.04382i) q^{79} +(1.94044 + 1.11117i) q^{80} -1.00000 q^{81} +9.02011i q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(6.38589 - 11.1517i) q^{85} -0.853087 q^{86} +2.40635i q^{87} +2.26858i q^{88} +(6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 + 0.821636i) q^{91} +8.53431 q^{92} -8.21877 q^{93} +(0.326713 + 0.326713i) q^{94} +(12.5166 - 3.40136i) q^{95} +(-0.707107 - 0.707107i) q^{96} +9.28197i q^{97} +6.19050i q^{98} +2.26858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	1.94044	+	1.11117i	0.867790	+	0.496931i
$5$	1.94044	+	1.11117i	0.867790	+	0.496931i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	0.636201	+	0.636201i	0.240461	+	0.240461i	0.817041	−	0.576580i	$-0.195613\pi$
$7$	0.636201	+	0.636201i	0.240461	+	0.240461i	−0.576580	+	0.817041i	$0.695613\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	−1.94044	−	1.11117i	−0.613620	−	0.351383i
$11$		−	2.26858i		−	0.684003i	−0.939699	−	0.342002i	$-0.888895\pi$
$11$		−	2.26858i		−	0.684003i	0.939699	−	0.342002i	$-0.111105\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.29147			0.358190			0.179095	−	0.983832i	$-0.442683\pi$
$13$	1.29147			0.358190			0.179095	+	0.983832i	$0.442683\pi$
$14$	−0.636201	−	0.636201i	−0.170032	−	0.170032i
$15$	0.586380	+	2.15781i	0.151403	+	0.557145i
$16$	1.00000			0.250000
$17$		−	5.74699i		−	1.39385i	−0.717144	−	0.696925i	$-0.754551\pi$
$17$		−	5.74699i		−	1.39385i	0.717144	−	0.696925i	$-0.245449\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.10165	−	4.10165i	0.940982	−	0.940982i	−0.0573705	−	0.998353i	$-0.518272\pi$
$19$	4.10165	−	4.10165i	0.940982	−	0.940982i	0.998353	+	0.0573705i	$0.0182716\pi$
$20$	1.94044	+	1.11117i	0.433895	+	0.248465i
$21$			0.899724i			0.196336i
$22$			2.26858i			0.483663i
$23$	8.53431			1.77953			0.889763	−	0.456423i	$-0.150869\pi$
$23$	8.53431			1.77953			0.889763	+	0.456423i	$0.150869\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	2.53060	+	4.31232i	0.506119	+	0.862464i
$26$	−1.29147			−0.253278
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.636201	+	0.636201i	0.120231	+	0.120231i
$29$	1.70155	+	1.70155i	0.315969	+	0.315969i	0.847217	−	0.531247i	$-0.178277\pi$
$29$	1.70155	+	1.70155i	0.315969	+	0.315969i	−0.531247	+	0.847217i	$0.678277\pi$
$30$	−0.586380	−	2.15781i	−0.107058	−	0.393961i
$31$	−5.81155	+	5.81155i	−1.04379	+	1.04379i	−0.0447888	+	0.998996i	$0.514261\pi$
$31$	−5.81155	+	5.81155i	−1.04379	+	1.04379i	−0.998996	+	0.0447888i	$0.985739\pi$
$32$	−1.00000			−0.176777
$33$	1.60413	−	1.60413i	0.279243	−	0.279243i
$34$			5.74699i			0.985601i
$35$	0.527580	+	1.94144i	0.0891773	+	0.328163i
$36$			1.00000i			0.166667i
$37$	3.16223	+	5.19618i	0.519868	+	0.854247i
$37$	3.16223	+	5.19618i	0.519868	+	0.854247i
$38$	−4.10165	+	4.10165i	−0.665375	+	0.665375i
$39$	0.913209	+	0.913209i	0.146230	+	0.146230i
$40$	−1.94044	−	1.11117i	−0.306810	−	0.175692i
$41$		−	9.02011i		−	1.40870i	−0.709851	−	0.704352i	$-0.751238\pi$
$41$		−	9.02011i		−	1.40870i	0.709851	−	0.704352i	$-0.248762\pi$
$42$		−	0.899724i		−	0.138830i
$43$	0.853087			0.130094			0.0650472	−	0.997882i	$-0.479280\pi$
$43$	0.853087			0.130094			0.0650472	+	0.997882i	$0.479280\pi$
$44$		−	2.26858i		−	0.342002i
$45$	−1.11117	+	1.94044i	−0.165644	+	0.289263i
$46$	−8.53431			−1.25832
$47$	−0.326713	−	0.326713i	−0.0476560	−	0.0476560i	0.682877	−	0.730533i	$-0.260728\pi$
$47$	−0.326713	−	0.326713i	−0.0476560	−	0.0476560i	−0.730533	+	0.682877i	$0.760728\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	6.19050i		−	0.884357i
$50$	−2.53060	−	4.31232i	−0.357880	−	0.609854i
$51$	4.06374	−	4.06374i	0.569037	−	0.569037i
$52$	1.29147			0.179095
$53$	−6.79864	+	6.79864i	−0.933866	+	0.933866i	−0.997945	−	0.0640792i	$-0.979589\pi$
$53$	−6.79864	+	6.79864i	−0.933866	+	0.933866i	0.0640792	+	0.997945i	$0.479589\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	2.52078	−	4.40204i	0.339902	−	0.593571i
$56$	−0.636201	−	0.636201i	−0.0850159	−	0.0850159i
$57$	5.80061			0.768309
$58$	−1.70155	−	1.70155i	−0.223424	−	0.223424i
$59$	−3.51171	+	3.51171i	−0.457186	+	0.457186i	−0.897731	−	0.440545i	$-0.854785\pi$
$59$	−3.51171	+	3.51171i	−0.457186	+	0.457186i	0.440545	+	0.897731i	$0.354785\pi$
$60$	0.586380	+	2.15781i	0.0757013	+	0.278573i
$61$	−2.06460	+	2.06460i	−0.264345	+	0.264345i	−0.826817	−	0.562472i	$-0.809851\pi$
$61$	−2.06460	+	2.06460i	−0.264345	+	0.264345i	0.562472	+	0.826817i	$0.309851\pi$
$62$	5.81155	−	5.81155i	0.738068	−	0.738068i
$63$	−0.636201	+	0.636201i	−0.0801538	+	0.0801538i
$64$	1.00000			0.125000
$65$	2.50602	+	1.43505i	0.310834	+	0.177996i
$66$	−1.60413	+	1.60413i	−0.197455	+	0.197455i
$67$	−3.98347	+	3.98347i	−0.486659	+	0.486659i	−0.907250	−	0.420591i	$-0.861823\pi$
$67$	−3.98347	+	3.98347i	−0.486659	+	0.486659i	0.420591	+	0.907250i	$0.361823\pi$
$68$		−	5.74699i		−	0.696925i
$69$	6.03467	+	6.03467i	0.726489	+	0.726489i
$70$	−0.527580	−	1.94144i	−0.0630579	−	0.232046i
$71$	−15.2892			−1.81450			−0.907248	−	0.420596i	$-0.861821\pi$
$71$	−15.2892			−1.81450			−0.907248	+	0.420596i	$0.861821\pi$
$72$		−	1.00000i		−	0.117851i
$73$	11.8322	+	11.8322i	1.38486	+	1.38486i	0.835751	+	0.549108i	$0.185032\pi$
$73$	11.8322	+	11.8322i	1.38486	+	1.38486i	0.549108	+	0.835751i	$0.314968\pi$
$74$	−3.16223	−	5.19618i	−0.367602	−	0.604044i
$75$	−1.25987	+	4.83867i	−0.145477	+	0.558722i
$76$	4.10165	−	4.10165i	0.470491	−	0.470491i
$77$	1.44327	−	1.44327i	0.164476	−	0.164476i
$78$	−0.913209	−	0.913209i	−0.103401	−	0.103401i
$79$	−9.04382	+	9.04382i	−1.01751	+	1.01751i	−0.0176652	+	0.999844i	$0.505623\pi$
$79$	−9.04382	+	9.04382i	−1.01751	+	1.01751i	−0.999844	+	0.0176652i	$0.994377\pi$
$80$	1.94044	+	1.11117i	0.216948	+	0.124233i
$81$	−1.00000			−0.111111
$82$			9.02011i			0.996104i
$83$	9.12362	−	9.12362i	1.00145	−	1.00145i	0.00144791	−	0.999999i	$-0.499539\pi$
$83$	9.12362	−	9.12362i	1.00145	−	1.00145i	0.999999	−	0.00144791i	$-0.000460883\pi$
$84$			0.899724i			0.0981680i
$85$	6.38589	−	11.1517i	0.692647	−	1.20957i
$86$	−0.853087			−0.0919907
$87$			2.40635i			0.257988i
$88$			2.26858i			0.241832i
$89$	6.32382	+	6.32382i	0.670323	+	0.670323i	0.957791	−	0.287467i	$-0.0928132\pi$
$89$	6.32382	+	6.32382i	0.670323	+	0.670323i	−0.287467	+	0.957791i	$0.592813\pi$
$90$	1.11117	−	1.94044i	0.117128	−	0.204540i
$91$	0.821636	+	0.821636i	0.0861308	+	0.0861308i
$92$	8.53431			0.889763
$93$	−8.21877			−0.852247
$94$	0.326713	+	0.326713i	0.0336979	+	0.0336979i
$95$	12.5166	−	3.40136i	1.28418	−	0.348972i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$			9.28197i			0.942441i	0.882015	+	0.471220i	$0.156186\pi$
$97$			9.28197i			0.942441i	−0.882015	+	0.471220i	$0.843814\pi$
$98$			6.19050i			0.625335i
$99$	2.26858			0.228001
$100$	2.53060	+	4.31232i	0.253060	+	0.431232i
$101$		−	1.47408i		−	0.146677i	−0.997307	−	0.0733383i	$-0.976635\pi$
$101$		−	1.47408i		−	0.146677i	0.997307	−	0.0733383i	$-0.0233653\pi$
$102$	−4.06374	+	4.06374i	−0.402370	+	0.402370i
$103$		−	1.02968i		−	0.101458i	−0.998712	−	0.0507289i	$-0.983846\pi$
$103$		−	1.02968i		−	0.101458i	0.998712	−	0.0507289i	$-0.0161544\pi$
$104$	−1.29147			−0.126639
$105$	−0.999748	+	1.74586i	−0.0975654	+	0.170378i
$106$	6.79864	−	6.79864i	0.660343	−	0.660343i
$107$	−13.8598	−	13.8598i	−1.33988	−	1.33988i	−0.896171	−	0.443708i	$-0.853663\pi$
$107$	−13.8598	−	13.8598i	−1.33988	−	1.33988i	−0.443708	−	0.896171i	$-0.646337\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−5.32683	+	5.32683i	−0.510218	+	0.510218i	−0.914593	−	0.404375i	$-0.867489\pi$
$109$	−5.32683	+	5.32683i	−0.510218	+	0.510218i	0.404375	+	0.914593i	$0.367489\pi$
$110$	−2.52078	+	4.40204i	−0.240347	+	0.419718i
$111$	−1.43822	+	5.91029i	−0.136510	+	0.560980i
$112$	0.636201	+	0.636201i	0.0601153	+	0.0601153i
$113$		−	17.2755i		−	1.62515i	−0.582859	−	0.812573i	$-0.698066\pi$
$113$		−	17.2755i		−	1.62515i	0.582859	−	0.812573i	$-0.301934\pi$
$114$	−5.80061			−0.543276
$115$	16.5603	+	9.48308i	1.54426	+	0.884302i
$116$	1.70155	+	1.70155i	0.157985	+	0.157985i
$117$			1.29147i			0.119397i
$118$	3.51171	−	3.51171i	0.323279	−	0.323279i
$119$	3.65624	−	3.65624i	0.335167	−	0.335167i
$120$	−0.586380	−	2.15781i	−0.0535289	−	0.196981i
$121$	5.85354			0.532140
$122$	2.06460	−	2.06460i	0.186920	−	0.186920i
$123$	6.37818	−	6.37818i	0.575101	−	0.575101i
$124$	−5.81155	+	5.81155i	−0.521893	+	0.521893i
$125$	0.118740	+	11.1797i	0.0106204	+	0.999944i
$126$	0.636201	−	0.636201i	0.0566773	−	0.0566773i
$127$	0.916380	+	0.916380i	0.0813156	+	0.0813156i	0.746595	−	0.665279i	$-0.231687\pi$
$127$	0.916380	+	0.916380i	0.0813156	+	0.0813156i	−0.665279	+	0.746595i	$0.731687\pi$
$128$	−1.00000			−0.0883883
$129$	0.603223	+	0.603223i	0.0531109	+	0.0531109i
$130$	−2.50602	−	1.43505i	−0.219793	−	0.125862i
$131$	−6.28943	+	6.28943i	−0.549510	+	0.549510i	−0.926299	−	0.376789i	$-0.877028\pi$
$131$	−6.28943	+	6.28943i	−0.549510	+	0.549510i	0.376789	+	0.926299i	$0.377028\pi$
$132$	1.60413	−	1.60413i	0.139622	−	0.139622i
$133$	5.21895			0.452540
$134$	3.98347	−	3.98347i	0.344120	−	0.344120i
$135$	−2.15781	+	0.586380i	−0.185715	+	0.0504675i
$136$			5.74699i			0.492800i
$137$	10.4523	+	10.4523i	0.893004	+	0.893004i	0.994805	−	0.101801i	$-0.0324605\pi$
$137$	10.4523	+	10.4523i	0.893004	+	0.893004i	−0.101801	+	0.994805i	$0.532461\pi$
$138$	−6.03467	−	6.03467i	−0.513705	−	0.513705i
$139$	14.4443			1.22515			0.612574	−	0.790414i	$-0.290134\pi$
$139$	14.4443			1.22515			0.612574	+	0.790414i	$0.290134\pi$
$140$	0.527580	+	1.94144i	0.0445887	+	0.164081i
$141$		−	0.462042i		−	0.0389110i
$142$	15.2892			1.28304
$143$		−	2.92981i		−	0.245003i
$144$			1.00000i			0.0833333i
$145$	1.41104	+	5.19246i	0.117180	+	0.431210i
$146$	−11.8322	−	11.8322i	−0.979243	−	0.979243i
$147$	4.37734	−	4.37734i	0.361037	−	0.361037i
$148$	3.16223	+	5.19618i	0.259934	+	0.427123i
$149$		−	19.0997i		−	1.56471i	−0.622831	−	0.782356i	$-0.714018\pi$
$149$		−	19.0997i		−	1.56471i	0.622831	−	0.782356i	$-0.285982\pi$
$150$	1.25987	−	4.83867i	0.102868	−	0.395076i
$151$			3.42513i			0.278733i	0.990241	+	0.139367i	$0.0445067\pi$
$151$			3.42513i			0.278733i	−0.990241	+	0.139367i	$0.955493\pi$
$152$	−4.10165	+	4.10165i	−0.332688	+	0.332688i
$153$	5.74699			0.464617
$154$	−1.44327	+	1.44327i	−0.116302	+	0.116302i
$155$	−17.7346	+	4.81932i	−1.42448	+	0.387097i
$156$	0.913209	+	0.913209i	0.0731152	+	0.0731152i
$157$	12.1068	+	12.1068i	0.966232	+	0.966232i	0.999448	−	0.0332164i	$-0.0105751\pi$
$157$	12.1068	+	12.1068i	0.966232	+	0.966232i	−0.0332164	+	0.999448i	$0.510575\pi$
$158$	9.04382	−	9.04382i	0.719488	−	0.719488i
$159$	−9.61473			−0.762498
$160$	−1.94044	−	1.11117i	−0.153405	−	0.0878458i
$161$	5.42954	+	5.42954i	0.427907	+	0.427907i
$162$	1.00000			0.0785674
$163$		−	24.2268i		−	1.89759i	−0.315894	−	0.948795i	$-0.602304\pi$
$163$		−	24.2268i		−	1.89759i	0.315894	−	0.948795i	$-0.397696\pi$
$164$		−	9.02011i		−	0.704352i
$165$	4.89518	−	1.33025i	0.381089	−	0.103560i
$166$	−9.12362	+	9.12362i	−0.708130	+	0.708130i
$167$			9.66372i			0.747801i	0.927469	+	0.373900i	$0.121980\pi$
$167$			9.66372i			0.747801i	−0.927469	+	0.373900i	$0.878020\pi$
$168$		−	0.899724i		−	0.0694152i
$169$	−11.3321			−0.871700
$170$	−6.38589	+	11.1517i	−0.489776	+	0.855295i
$171$	4.10165	+	4.10165i	0.313661	+	0.313661i
$172$	0.853087			0.0650472
$173$	6.77556	+	6.77556i	0.515136	+	0.515136i	0.916096	−	0.400959i	$-0.131323\pi$
$173$	6.77556	+	6.77556i	0.515136	+	0.515136i	−0.400959	+	0.916096i	$0.631323\pi$
$174$		−	2.40635i		−	0.182425i
$175$	−1.13353	+	4.35347i	−0.0856870	+	0.329091i
$176$		−	2.26858i		−	0.171001i
$177$	−4.96631			−0.373290
$178$	−6.32382	−	6.32382i	−0.473990	−	0.473990i
$179$	−7.36463	−	7.36463i	−0.550458	−	0.550458i	0.376115	−	0.926573i	$-0.377260\pi$
$179$	−7.36463	−	7.36463i	−0.550458	−	0.550458i	−0.926573	+	0.376115i	$0.877260\pi$
$180$	−1.11117	+	1.94044i	−0.0828218	+	0.144632i
$181$	−13.9651			−1.03802			−0.519008	−	0.854769i	$-0.673699\pi$
$181$	−13.9651			−1.03802			−0.519008	+	0.854769i	$0.673699\pi$
$182$	−0.821636	−	0.821636i	−0.0609037	−	0.0609037i
$183$	−2.91979			−0.215837
$184$	−8.53431			−0.629158
$185$	0.362266	+	13.5966i	0.0266343	+	0.999645i
$186$	8.21877			0.602630
$187$	−13.0375			−0.953398
$188$	−0.326713	−	0.326713i	−0.0238280	−	0.0238280i
$189$	−0.899724			−0.0654453
$190$	−12.5166	+	3.40136i	−0.908051	+	0.246760i
$191$	−11.6459	−	11.6459i	−0.842665	−	0.842665i	0.146540	−	0.989205i	$-0.453186\pi$
$191$	−11.6459	−	11.6459i	−0.842665	−	0.842665i	−0.989205	+	0.146540i	$0.953186\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−2.80664			−0.202026			−0.101013	−	0.994885i	$-0.532208\pi$
$193$	−2.80664			−0.202026			−0.101013	+	0.994885i	$0.532208\pi$
$194$		−	9.28197i		−	0.666406i
$195$	0.757293	+	2.78676i	0.0542309	+	0.199564i
$196$		−	6.19050i		−	0.442178i
$197$	11.5183	+	11.5183i	0.820643	+	0.820643i	0.986200	−	0.165557i	$-0.0529422\pi$
$197$	11.5183	+	11.5183i	0.820643	+	0.820643i	−0.165557	+	0.986200i	$0.552942\pi$
$198$	−2.26858			−0.161221
$199$	−10.3470	−	10.3470i	−0.733481	−	0.733481i	0.237827	−	0.971308i	$-0.423565\pi$
$199$	−10.3470	−	10.3470i	−0.733481	−	0.733481i	−0.971308	+	0.237827i	$0.923565\pi$
$200$	−2.53060	−	4.31232i	−0.178940	−	0.304927i
$201$	−5.63348			−0.397355
$202$			1.47408i			0.103716i
$203$			2.16505i			0.151957i
$204$	4.06374	−	4.06374i	0.284518	−	0.284518i
$205$	10.0229	−	17.5030i	0.700029	−	1.22246i
$206$			1.02968i			0.0717414i
$207$			8.53431i			0.593175i
$208$	1.29147			0.0895475
$209$	−9.30492	−	9.30492i	−0.643635	−	0.643635i
$210$	0.999748	−	1.74586i	0.0689892	−	0.120476i
$211$	−3.80993			−0.262286			−0.131143	−	0.991363i	$-0.541865\pi$
$211$	−3.80993			−0.262286			−0.131143	+	0.991363i	$0.541865\pi$
$212$	−6.79864	+	6.79864i	−0.466933	+	0.466933i
$213$	−10.8111	−	10.8111i	−0.740765	−	0.740765i
$214$	13.8598	+	13.8598i	0.947438	+	0.947438i
$215$	1.65536	+	0.947925i	0.112895	+	0.0646480i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−7.39463			−0.501980
$218$	5.32683	−	5.32683i	0.360779	−	0.360779i
$219$			16.7333i			1.13073i
$220$	2.52078	−	4.40204i	0.169951	−	0.296786i
$221$		−	7.42208i		−	0.499263i
$222$	1.43822	−	5.91029i	0.0965269	−	0.396673i
$223$	16.8923	−	16.8923i	1.13119	−	1.13119i	0.141210	−	0.989980i	$-0.454901\pi$
$223$	16.8923	−	16.8923i	1.13119	−	1.13119i	0.989980	−	0.141210i	$-0.0450992\pi$
$224$	−0.636201	−	0.636201i	−0.0425080	−	0.0425080i
$225$	−4.31232	+	2.53060i	−0.287488	+	0.168706i
$226$			17.2755i			1.14915i
$227$		−	25.0030i		−	1.65950i	−0.558132	−	0.829752i	$-0.688482\pi$
$227$		−	25.0030i		−	1.65950i	0.558132	−	0.829752i	$-0.311518\pi$
$228$	5.80061			0.384154
$229$		−	11.3572i		−	0.750503i	−0.926923	−	0.375252i	$-0.877556\pi$
$229$		−	11.3572i		−	0.750503i	0.926923	−	0.375252i	$-0.122444\pi$
$230$	−16.5603	−	9.48308i	−1.09195	−	0.625296i
$231$	2.04110			0.134294
$232$	−1.70155	−	1.70155i	−0.111712	−	0.111712i
$233$	−4.77274	−	4.77274i	−0.312673	−	0.312673i	0.533271	−	0.845944i	$-0.320962\pi$
$233$	−4.77274	−	4.77274i	−0.312673	−	0.312673i	−0.845944	+	0.533271i	$0.820962\pi$
$234$		−	1.29147i		−	0.0844262i
$235$	−0.270932	−	0.997001i	−0.0176737	−	0.0650371i
$236$	−3.51171	+	3.51171i	−0.228593	+	0.228593i
$237$	−12.7899			−0.830793
$238$	−3.65624	+	3.65624i	−0.236999	+	0.236999i
$239$	2.96858	−	2.96858i	0.192022	−	0.192022i	−0.604547	−	0.796569i	$-0.706646\pi$
$239$	2.96858	−	2.96858i	0.192022	−	0.192022i	0.796569	+	0.604547i	$0.206646\pi$
$240$	0.586380	+	2.15781i	0.0378507	+	0.139286i
$241$	−5.75647	−	5.75647i	−0.370807	−	0.370807i	0.496964	−	0.867771i	$-0.334448\pi$
$241$	−5.75647	−	5.75647i	−0.370807	−	0.370807i	−0.867771	+	0.496964i	$0.834448\pi$
$242$	−5.85354			−0.376279
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−2.06460	+	2.06460i	−0.132172	+	0.132172i
$245$	6.87870	−	12.0123i	0.439464	−	0.767436i
$246$	−6.37818	+	6.37818i	−0.406658	+	0.406658i
$247$	5.29716	−	5.29716i	0.337050	−	0.337050i
$248$	5.81155	−	5.81155i	0.369034	−	0.369034i
$249$	12.9027			0.817678
$250$	−0.118740	−	11.1797i	−0.00750979	−	0.707067i
$251$	−14.7749	+	14.7749i	−0.932584	+	0.932584i	−0.997867	−	0.0652824i	$-0.979205\pi$
$251$	−14.7749	+	14.7749i	−0.932584	+	0.932584i	0.0652824	+	0.997867i	$0.479205\pi$
$252$	−0.636201	+	0.636201i	−0.0400769	+	0.0400769i
$253$		−	19.3608i		−	1.21720i
$254$	−0.916380	−	0.916380i	−0.0574988	−	0.0574988i
$255$	12.4009	−	3.36992i	0.776577	−	0.211033i
$256$	1.00000			0.0625000
$257$			1.80027i			0.112298i	0.998422	+	0.0561488i	$0.0178821\pi$
$257$			1.80027i			0.112298i	−0.998422	+	0.0561488i	$0.982118\pi$
$258$	−0.603223	−	0.603223i	−0.0375550	−	0.0375550i
$259$	−1.29400	+	5.31763i	−0.0804053	+	0.330421i
$260$	2.50602	+	1.43505i	0.155417	+	0.0889978i
$261$	−1.70155	+	1.70155i	−0.105323	+	0.105323i
$262$	6.28943	−	6.28943i	0.388563	−	0.388563i
$263$	9.25899	+	9.25899i	0.570934	+	0.570934i	0.932389	−	0.361456i	$-0.117720\pi$
$263$	9.25899	+	9.25899i	0.570934	+	0.570934i	−0.361456	+	0.932389i	$0.617720\pi$
$264$	−1.60413	+	1.60413i	−0.0987274	+	0.0987274i
$265$	−20.7468	+	5.63789i	−1.27447	+	0.346333i
$266$	−5.21895			−0.319994
$267$			8.94323i			0.547317i
$268$	−3.98347	+	3.98347i	−0.243329	+	0.243329i
$269$			0.689017i			0.0420101i	0.999779	+	0.0210051i	$0.00668661\pi$
$269$			0.689017i			0.0420101i	−0.999779	+	0.0210051i	$0.993313\pi$
$270$	2.15781	−	0.586380i	0.131320	−	0.0356859i
$271$	−14.7629			−0.896783			−0.448392	−	0.893837i	$-0.648003\pi$
$271$	−14.7629			−0.896783			−0.448392	+	0.893837i	$0.648003\pi$
$272$		−	5.74699i		−	0.348462i
$273$			1.16197i			0.0703255i
$274$	−10.4523	−	10.4523i	−0.631449	−	0.631449i
$275$	9.78285	−	5.74087i	0.589928	−	0.346187i
$276$	6.03467	+	6.03467i	0.363244	+	0.363244i
$277$	−32.3771			−1.94535			−0.972675	−	0.232172i	$-0.925417\pi$
$277$	−32.3771			−1.94535			−0.972675	+	0.232172i	$0.925417\pi$
$278$	−14.4443			−0.866310
$279$	−5.81155	−	5.81155i	−0.347928	−	0.347928i
$280$	−0.527580	−	1.94144i	−0.0315289	−	0.116023i
$281$	5.74725	+	5.74725i	0.342852	+	0.342852i	0.857439	−	0.514586i	$-0.172054\pi$
$281$	5.74725	+	5.74725i	0.342852	+	0.342852i	−0.514586	+	0.857439i	$0.672054\pi$
$282$			0.462042i			0.0275142i
$283$		−	6.56809i		−	0.390433i	−0.980760	−	0.195216i	$-0.937459\pi$
$283$		−	6.56809i		−	0.390433i	0.980760	−	0.195216i	$-0.0625409\pi$
$284$	−15.2892			−0.907248
$285$	11.2557	+	6.44547i	0.666731	+	0.381797i
$286$			2.92981i			0.173243i
$287$	5.73860	−	5.73860i	0.338739	−	0.338739i
$288$		−	1.00000i		−	0.0589256i
$289$	−16.0279			−0.942818
$290$	−1.41104	−	5.19246i	−0.0828589	−	0.304912i
$291$	−6.56334	+	6.56334i	−0.384750	+	0.384750i
$292$	11.8322	+	11.8322i	0.692430	+	0.692430i
$293$	−22.0187	+	22.0187i	−1.28634	+	1.28634i	−0.349353	+	0.936991i	$0.613599\pi$
$293$	−22.0187	+	22.0187i	−1.28634	+	1.28634i	−0.936991	+	0.349353i	$0.886401\pi$
$294$	−4.37734	+	4.37734i	−0.255292	+	0.255292i
$295$	−10.7164	+	2.91214i	−0.623931	+	0.169551i
$296$	−3.16223	−	5.19618i	−0.183801	−	0.302022i
$297$	1.60413	+	1.60413i	0.0930811	+	0.0930811i
$298$			19.0997i			1.10642i
$299$	11.0218			0.637408
$300$	−1.25987	+	4.83867i	−0.0727385	+	0.279361i
$301$	0.542735	+	0.542735i	0.0312827	+	0.0312827i
$302$		−	3.42513i		−	0.197094i
$303$	1.04233	−	1.04233i	0.0598805	−	0.0598805i
$304$	4.10165	−	4.10165i	0.235246	−	0.235246i
$305$	−6.30035	+	1.71210i	−0.360757	+	0.0980347i
$306$	−5.74699			−0.328534
$307$	−5.03677	+	5.03677i	−0.287464	+	0.287464i	−0.836077	−	0.548613i	$-0.815156\pi$
$307$	−5.03677	+	5.03677i	−0.287464	+	0.287464i	0.548613	+	0.836077i	$0.315156\pi$
$308$	1.44327	−	1.44327i	0.0822382	−	0.0822382i
$309$	0.728096	−	0.728096i	0.0414199	−	0.0414199i
$310$	17.7346	−	4.81932i	1.00726	−	0.273719i
$311$	3.85553	−	3.85553i	0.218627	−	0.218627i	−0.589293	−	0.807920i	$-0.700594\pi$
$311$	3.85553	−	3.85553i	0.218627	−	0.218627i	0.807920	+	0.589293i	$0.200594\pi$
$312$	−0.913209	−	0.913209i	−0.0517003	−	0.0517003i
$313$	19.5460			1.10481			0.552404	−	0.833577i	$-0.313711\pi$
$313$	19.5460			1.10481			0.552404	+	0.833577i	$0.313711\pi$
$314$	−12.1068	−	12.1068i	−0.683229	−	0.683229i
$315$	−1.94144	+	0.527580i	−0.109388	+	0.0297258i
$316$	−9.04382	+	9.04382i	−0.508755	+	0.508755i
$317$	−5.03252	+	5.03252i	−0.282655	+	0.282655i	−0.834167	−	0.551512i	$-0.814051\pi$
$317$	−5.03252	+	5.03252i	−0.282655	+	0.282655i	0.551512	+	0.834167i	$0.314051\pi$
$318$	9.61473			0.539168
$319$	3.86010	−	3.86010i	0.216124	−	0.216124i
$320$	1.94044	+	1.11117i	0.108474	+	0.0621164i
$321$		−	19.6007i		−	1.09401i
$322$	−5.42954	−	5.42954i	−0.302576	−	0.302576i
$323$	−23.5721	−	23.5721i	−1.31159	−	1.31159i
$324$	−1.00000			−0.0555556
$325$	3.26819	+	5.56924i	0.181287	+	0.308926i
$326$			24.2268i			1.34180i
$327$	−7.53328			−0.416591
$328$			9.02011i			0.498052i
$329$		−	0.415710i		−	0.0229189i
$330$	−4.89518	+	1.33025i	−0.269471	+	0.0732279i
$331$	−3.25748	−	3.25748i	−0.179048	−	0.179048i	0.611893	−	0.790941i	$-0.290408\pi$
$331$	−3.25748	−	3.25748i	−0.179048	−	0.179048i	−0.790941	+	0.611893i	$0.790408\pi$
$332$	9.12362	−	9.12362i	0.500723	−	0.500723i
$333$	−5.19618	+	3.16223i	−0.284749	+	0.173289i
$334$		−	9.66372i		−	0.528775i
$335$	−12.1560	+	3.30336i	−0.664154	+	0.180482i
$336$			0.899724i			0.0490840i
$337$	−15.5648	+	15.5648i	−0.847866	+	0.847866i	−0.989867	−	0.142000i	$-0.954647\pi$
$337$	−15.5648	+	15.5648i	−0.847866	+	0.847866i	0.142000	+	0.989867i	$0.454647\pi$
$338$	11.3321			0.616385
$339$	12.2157	−	12.2157i	0.663463	−	0.663463i
$340$	6.38589	−	11.1517i	0.346324	−	0.604785i
$341$	13.1840	+	13.1840i	0.713953	+	0.713953i
$342$	−4.10165	−	4.10165i	−0.221792	−	0.221792i
$343$	8.39181	−	8.39181i	0.453115	−	0.453115i
$344$	−0.853087			−0.0459953
$345$	5.00435	+	18.4154i	0.269425	+	0.991454i
$346$	−6.77556	−	6.77556i	−0.364256	−	0.364256i
$347$	−19.7799			−1.06184			−0.530920	−	0.847422i	$-0.678154\pi$
$347$	−19.7799			−1.06184			−0.530920	+	0.847422i	$0.678154\pi$
$348$			2.40635i			0.128994i
$349$			5.47518i			0.293080i	0.989205	+	0.146540i	$0.0468137\pi$
$349$			5.47518i			0.293080i	−0.989205	+	0.146540i	$0.953186\pi$
$350$	1.13353	−	4.35347i	0.0605899	−	0.232703i
$351$	−0.913209	+	0.913209i	−0.0487435	+	0.0487435i
$352$			2.26858i			0.120916i
$353$		−	28.1816i		−	1.49995i	−0.661465	−	0.749976i	$-0.730065\pi$
$353$		−	28.1816i		−	1.49995i	0.661465	−	0.749976i	$-0.269935\pi$
$354$	4.96631			0.263956
$355$	−29.6678	−	16.9889i	−1.57460	−	0.901679i
$356$	6.32382	+	6.32382i	0.335162	+	0.335162i
$357$	5.17071			0.273663
$358$	7.36463	+	7.36463i	0.389233	+	0.389233i
$359$			2.05043i			0.108218i	0.998535	+	0.0541089i	$0.0172318\pi$
$359$			2.05043i			0.108218i	−0.998535	+	0.0541089i	$0.982768\pi$
$360$	1.11117	−	1.94044i	0.0585639	−	0.102270i
$361$		−	14.6470i		−	0.770896i
$362$	13.9651			0.733988
$363$	4.13907	+	4.13907i	0.217245	+	0.217245i
$364$	0.821636	+	0.821636i	0.0430654	+	0.0430654i
$365$	9.81208	+	36.1074i	0.513588	+	1.88995i
$366$	2.91979			0.152620
$367$	−8.13886	−	8.13886i	−0.424845	−	0.424845i	0.462023	−	0.886868i	$-0.347124\pi$
$367$	−8.13886	−	8.13886i	−0.424845	−	0.424845i	−0.886868	+	0.462023i	$0.847124\pi$
$368$	8.53431			0.444882
$369$	9.02011			0.469568
$370$	−0.362266	−	13.5966i	−0.0188333	−	0.706856i
$371$	−8.65061			−0.449117
$372$	−8.21877			−0.426124
$373$	9.78820	+	9.78820i	0.506814	+	0.506814i	0.913547	−	0.406733i	$-0.133332\pi$
$373$	9.78820	+	9.78820i	0.506814	+	0.506814i	−0.406733	+	0.913547i	$0.633332\pi$
$374$	13.0375			0.674154
$375$	−7.82129	+	7.98921i	−0.403889	+	0.412561i
$376$	0.326713	+	0.326713i	0.0168489	+	0.0168489i
$377$	2.19750	+	2.19750i	0.113177	+	0.113177i
$378$	0.899724			0.0462768
$379$		−	22.6146i		−	1.16164i	−0.814034	−	0.580818i	$-0.802733\pi$
$379$		−	22.6146i		−	1.16164i	0.814034	−	0.580818i	$-0.197267\pi$
$380$	12.5166	−	3.40136i	0.642089	−	0.174486i
$381$			1.29596i			0.0663939i
$382$	11.6459	+	11.6459i	0.595854	+	0.595854i
$383$	−9.52538			−0.486724			−0.243362	−	0.969936i	$-0.578250\pi$
$383$	−9.52538			−0.486724			−0.243362	+	0.969936i	$0.578250\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	4.40431	−	1.19686i	0.224464	−	0.0609976i
$386$	2.80664			0.142854
$387$			0.853087i			0.0433648i
$388$			9.28197i			0.471220i
$389$	−7.75553	+	7.75553i	−0.393221	+	0.393221i	−0.875834	−	0.482613i	$-0.839688\pi$
$389$	−7.75553	+	7.75553i	−0.393221	+	0.393221i	0.482613	+	0.875834i	$0.339688\pi$
$390$	−0.757293	−	2.78676i	−0.0383470	−	0.141113i
$391$		−	49.0466i		−	2.48039i
$392$			6.19050i			0.312667i
$393$	−8.89460			−0.448673
$394$	−11.5183	−	11.5183i	−0.580282	−	0.580282i
$395$	−27.5982	+	7.49973i	−1.38862	+	0.377353i
$396$	2.26858			0.114001
$397$	18.6690	−	18.6690i	0.936970	−	0.936970i	−0.0611581	−	0.998128i	$-0.519479\pi$
$397$	18.6690	−	18.6690i	0.936970	−	0.936970i	0.998128	+	0.0611581i	$0.0194794\pi$
$398$	10.3470	+	10.3470i	0.518649	+	0.518649i
$399$	3.69035	+	3.69035i	0.184749	+	0.184749i
$400$	2.53060	+	4.31232i	0.126530	+	0.215616i
$401$	13.9114	−	13.9114i	0.694702	−	0.694702i	−0.268561	−	0.963263i	$-0.586548\pi$
$401$	13.9114	−	13.9114i	0.694702	−	0.694702i	0.963263	+	0.268561i	$0.0865481\pi$
$402$	5.63348			0.280973
$403$	−7.50545	+	7.50545i	−0.373873	+	0.373873i
$404$		−	1.47408i		−	0.0733383i
$405$	−1.94044	−	1.11117i	−0.0964211	−	0.0552146i
$406$		−	2.16505i		−	0.107450i
$407$	11.7880	−	7.17378i	0.584308	−	0.355591i
$408$	−4.06374	+	4.06374i	−0.201185	+	0.201185i
$409$	7.16339	+	7.16339i	0.354207	+	0.354207i	0.861672	−	0.507465i	$-0.169418\pi$
$409$	7.16339	+	7.16339i	0.354207	+	0.354207i	−0.507465	+	0.861672i	$0.669418\pi$
$410$	−10.0229	+	17.5030i	−0.494995	+	0.864409i
$411$			14.7818i			0.729134i
$412$		−	1.02968i		−	0.0507289i
$413$	−4.46831			−0.219871
$414$		−	8.53431i		−	0.419438i
$415$	27.8417	−	7.56591i	1.36670	−	0.371396i
$416$	−1.29147			−0.0633196
$417$	10.2136	+	10.2136i	0.500164	+	0.500164i
$418$	9.30492	+	9.30492i	0.455119	+	0.455119i
$419$			23.8546i			1.16537i	0.812698	+	0.582686i	$0.197998\pi$
$419$			23.8546i			1.16537i	−0.812698	+	0.582686i	$0.802002\pi$
$420$	−0.999748	+	1.74586i	−0.0487827	+	0.0851892i
$421$	−12.3787	+	12.3787i	−0.603301	+	0.603301i	−0.941187	−	0.337886i	$-0.890288\pi$
$421$	−12.3787	+	12.3787i	−0.603301	+	0.603301i	0.337886	+	0.941187i	$0.390288\pi$
$422$	3.80993			0.185464
$423$	0.326713	−	0.326713i	0.0158853	−	0.0158853i
$424$	6.79864	−	6.79864i	0.330171	−	0.330171i
$425$	24.7828	−	14.5433i	1.20214	−	0.705454i
$426$	10.8111	+	10.8111i	0.523800	+	0.523800i
$427$	−2.62700			−0.127130
$428$	−13.8598	−	13.8598i	−0.669940	−	0.669940i
$429$	2.07169	−	2.07169i	0.100022	−	0.100022i
$430$	−1.65536	−	0.947925i	−0.0798286	−	0.0457130i
$431$	5.50143	−	5.50143i	0.264995	−	0.264995i	−0.562085	−	0.827080i	$-0.690001\pi$
$431$	5.50143	−	5.50143i	0.264995	−	0.264995i	0.827080	+	0.562085i	$0.190001\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	4.53175	−	4.53175i	0.217782	−	0.217782i	−0.589781	−	0.807563i	$-0.700786\pi$
$433$	4.53175	−	4.53175i	0.217782	−	0.217782i	0.807563	+	0.589781i	$0.200786\pi$
$434$	7.39463			0.354954
$435$	−2.67387	+	4.66938i	−0.128202	+	0.223879i
$436$	−5.32683	+	5.32683i	−0.255109	+	0.255109i
$437$	35.0047	−	35.0047i	1.67450	−	1.67450i
$438$		−	16.7333i		−	0.799549i
$439$	−22.7618	−	22.7618i	−1.08636	−	1.08636i	−0.995900	−	0.0904591i	$-0.971167\pi$
$439$	−22.7618	−	22.7618i	−1.08636	−	1.08636i	−0.0904591	−	0.995900i	$-0.528833\pi$
$440$	−2.52078	+	4.40204i	−0.120174	+	0.209859i
$441$	6.19050			0.294786
$442$			7.42208i			0.353032i
$443$	18.5368	+	18.5368i	0.880708	+	0.880708i	0.993606	−	0.112899i	$-0.0360136\pi$
$443$	18.5368	+	18.5368i	0.880708	+	0.880708i	−0.112899	+	0.993606i	$0.536014\pi$
$444$	−1.43822	+	5.91029i	−0.0682549	+	0.280490i
$445$	5.24413	+	19.2978i	0.248596	+	0.914804i
$446$	−16.8923	+	16.8923i	−0.799872	+	0.799872i
$447$	13.5056	−	13.5056i	0.638791	−	0.638791i
$448$	0.636201	+	0.636201i	0.0300577	+	0.0300577i
$449$	−9.96142	+	9.96142i	−0.470109	+	0.470109i	−0.901950	−	0.431841i	$-0.857864\pi$
$449$	−9.96142	+	9.96142i	−0.470109	+	0.470109i	0.431841	+	0.901950i	$0.357864\pi$
$450$	4.31232	−	2.53060i	0.203285	−	0.119293i
$451$	−20.4629			−0.963558
$452$		−	17.2755i		−	0.812573i
$453$	−2.42193	+	2.42193i	−0.113792	+	0.113792i
$454$			25.0030i			1.17345i
$455$	0.681355	+	2.50731i	0.0319424	+	0.117545i
$456$	−5.80061			−0.271638
$457$		−	6.81678i		−	0.318876i	−0.987208	−	0.159438i	$-0.949032\pi$
$457$		−	6.81678i		−	0.318876i	0.987208	−	0.159438i	$-0.0509681\pi$
$458$			11.3572i			0.530686i
$459$	4.06374	+	4.06374i	0.189679	+	0.189679i
$460$	16.5603	+	9.48308i	0.772128	+	0.442151i
$461$	24.7125	+	24.7125i	1.15097	+	1.15097i	0.986358	+	0.164617i	$0.0526389\pi$
$461$	24.7125	+	24.7125i	1.15097	+	1.15097i	0.164617	+	0.986358i	$0.447361\pi$
$462$	−2.04110			−0.0949605
$463$	−32.0736			−1.49059			−0.745293	−	0.666737i	$-0.767690\pi$
$463$	−32.0736			−1.49059			−0.745293	+	0.666737i	$0.767690\pi$
$464$	1.70155	+	1.70155i	0.0789924	+	0.0789924i
$465$	−15.9480	−	9.13247i	−0.739572	−	0.423508i
$466$	4.77274	+	4.77274i	0.221093	+	0.221093i
$467$			13.7531i			0.636416i	0.948021	+	0.318208i	$0.103081\pi$
$467$			13.7531i			0.636416i	−0.948021	+	0.318208i	$0.896919\pi$
$468$			1.29147i			0.0596983i
$469$	−5.06858			−0.234045
$470$	0.270932	+	0.997001i	0.0124972	+	0.0459882i
$471$			17.1217i			0.788925i
$472$	3.51171	−	3.51171i	0.161640	−	0.161640i
$473$		−	1.93530i		−	0.0889851i
$474$	12.7899			0.587459
$475$	28.0672	+	7.30799i	1.28781	+	0.335314i
$476$	3.65624	−	3.65624i	0.167584	−	0.167584i
$477$	−6.79864	−	6.79864i	−0.311289	−	0.311289i
$478$	−2.96858	+	2.96858i	−0.135780	+	0.135780i
$479$	−15.9554	+	15.9554i	−0.729021	+	0.729021i	−0.970425	−	0.241404i	$-0.922392\pi$
$479$	−15.9554	+	15.9554i	−0.729021	+	0.729021i	0.241404	+	0.970425i	$0.422392\pi$
$480$	−0.586380	−	2.15781i	−0.0267645	−	0.0984903i
$481$	4.08393	+	6.71072i	0.186211	+	0.305983i
$482$	5.75647	+	5.75647i	0.262200	+	0.262200i
$483$			7.67852i			0.349385i
$484$	5.85354			0.266070
$485$	−10.3139	+	18.0111i	−0.468328	+	0.817841i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$			22.5078i			1.01992i	0.860197	+	0.509962i	$0.170341\pi$
$487$			22.5078i			1.01992i	−0.860197	+	0.509962i	$0.829659\pi$
$488$	2.06460	−	2.06460i	0.0934600	−	0.0934600i
$489$	17.1309	−	17.1309i	0.774688	−	0.774688i
$490$	−6.87870	+	12.0123i	−0.310748	+	0.542659i
$491$	31.0223			1.40002			0.700008	−	0.714135i	$-0.253180\pi$
$491$	31.0223			1.40002			0.700008	+	0.714135i	$0.253180\pi$
$492$	6.37818	−	6.37818i	0.287550	−	0.287550i
$493$	9.77878	−	9.77878i	0.440414	−	0.440414i
$494$	−5.29716	+	5.29716i	−0.238331	+	0.238331i
$495$	4.40204	+	2.52078i	0.197857	+	0.113301i
$496$	−5.81155	+	5.81155i	−0.260946	+	0.260946i
$497$	−9.72702	−	9.72702i	−0.436316	−	0.436316i
$498$	−12.9027			−0.578186
$499$	−5.68409	−	5.68409i	−0.254455	−	0.254455i	0.568339	−	0.822794i	$-0.307586\pi$
$499$	−5.68409	−	5.68409i	−0.254455	−	0.254455i	−0.822794	+	0.568339i	$0.807586\pi$
$500$	0.118740	+	11.1797i	0.00531022	+	0.499972i
$501$	−6.83328	+	6.83328i	−0.305288	+	0.305288i
$502$	14.7749	−	14.7749i	0.659437	−	0.659437i
$503$	3.69027			0.164541			0.0822705	−	0.996610i	$-0.473783\pi$
$503$	3.69027			0.164541			0.0822705	+	0.996610i	$0.473783\pi$
$504$	0.636201	−	0.636201i	0.0283386	−	0.0283386i
$505$	1.63796	−	2.86036i	0.0728882	−	0.127285i
$506$			19.3608i			0.860692i
$507$	−8.01300	−	8.01300i	−0.355870	−	0.355870i
$508$	0.916380	+	0.916380i	0.0406578	+	0.0406578i
$509$	−5.91876			−0.262345			−0.131172	−	0.991360i	$-0.541874\pi$
$509$	−5.91876			−0.262345			−0.131172	+	0.991360i	$0.541874\pi$
$510$	−12.4009	+	3.36992i	−0.549123	+	0.149223i
$511$			15.0554i			0.666010i
$512$	−1.00000			−0.0441942
$513$			5.80061i			0.256103i
$514$		−	1.80027i		−	0.0794064i
$515$	1.14415	−	1.99804i	0.0504175	−	0.0880440i
$516$	0.603223	+	0.603223i	0.0265554	+	0.0265554i
$517$	−0.741175	+	0.741175i	−0.0325969	+	0.0325969i
$518$	1.29400	−	5.31763i	0.0568551	−	0.233643i
$519$			9.58209i			0.420607i
$520$	−2.50602	−	1.43505i	−0.109896	−	0.0629310i
$521$		−	21.8007i		−	0.955107i	−0.878603	−	0.477554i	$-0.841524\pi$
$521$		−	21.8007i		−	0.955107i	0.878603	−	0.477554i	$-0.158476\pi$
$522$	1.70155	−	1.70155i	0.0744747	−	0.0744747i
$523$	−17.1466			−0.749767			−0.374883	−	0.927072i	$-0.622317\pi$
$523$	−17.1466			−0.749767			−0.374883	+	0.927072i	$0.622317\pi$
$524$	−6.28943	+	6.28943i	−0.274755	+	0.274755i
$525$	−3.87990	+	2.27684i	−0.169333	+	0.0993694i
$526$	−9.25899	−	9.25899i	−0.403711	−	0.403711i
$527$	33.3989	+	33.3989i	1.45488	+	1.45488i
$528$	1.60413	−	1.60413i	0.0698108	−	0.0698108i
$529$	49.8344			2.16671
$530$	20.7468	−	5.63789i	0.901184	−	0.244894i
$531$	−3.51171	−	3.51171i	−0.152395	−	0.152395i
$532$	5.21895			0.226270
$533$		−	11.6492i		−	0.504583i
$534$		−	8.94323i		−	0.387011i
$535$	−11.4935	−	42.2948i	−0.496907	−	1.82856i
$536$	3.98347	−	3.98347i	0.172060	−	0.172060i
$537$		−	10.4152i		−	0.449447i
$538$		−	0.689017i		−	0.0297056i
$539$	−14.0436			−0.604903
$540$	−2.15781	+	0.586380i	−0.0928575	+	0.0252338i
$541$	−11.6362	−	11.6362i	−0.500279	−	0.500279i	0.411245	−	0.911525i	$-0.365094\pi$
$541$	−11.6362	−	11.6362i	−0.500279	−	0.500279i	−0.911525	+	0.411245i	$0.865094\pi$
$542$	14.7629			0.634122
$543$	−9.87480	−	9.87480i	−0.423768	−	0.423768i
$544$			5.74699i			0.246400i
$545$	−16.2554	+	4.41736i	−0.696305	+	0.189219i
$546$		−	1.16197i		−	0.0497277i
$547$	37.0105			1.58245			0.791226	−	0.611523i	$-0.209443\pi$
$547$	37.0105			1.58245			0.791226	+	0.611523i	$0.209443\pi$
$548$	10.4523	+	10.4523i	0.446502	+	0.446502i
$549$	−2.06460	−	2.06460i	−0.0881150	−	0.0881150i
$550$	−9.78285	+	5.74087i	−0.417142	+	0.244791i
$551$	13.9583			0.594643
$552$	−6.03467	−	6.03467i	−0.256853	−	0.256853i
$553$	−11.5074			−0.489343
$554$	32.3771			1.37557
$555$	−9.35812	+	9.87044i	−0.397230	+	0.418977i
$556$	14.4443			0.612574
$557$	−5.02764			−0.213028			−0.106514	−	0.994311i	$-0.533969\pi$
$557$	−5.02764			−0.213028			−0.106514	+	0.994311i	$0.533969\pi$
$558$	5.81155	+	5.81155i	0.246023	+	0.246023i
$559$	1.10174			0.0465985
$560$	0.527580	+	1.94144i	0.0222943	+	0.0820407i
$561$	−9.21892	−	9.21892i	−0.389223	−	0.389223i
$562$	−5.74725	−	5.74725i	−0.242433	−	0.242433i
$563$	−14.7235			−0.620522			−0.310261	−	0.950651i	$-0.600416\pi$
$563$	−14.7235			−0.620522			−0.310261	+	0.950651i	$0.600416\pi$
$564$		−	0.462042i		−	0.0194555i
$565$	19.1961	−	33.5221i	0.807586	−	1.41029i
$566$			6.56809i			0.276078i
$567$	−0.636201	−	0.636201i	−0.0267179	−	0.0267179i
$568$	15.2892			0.641521
$569$	15.1302	+	15.1302i	0.634291	+	0.634291i	0.949141	−	0.314850i	$-0.101954\pi$
$569$	15.1302	+	15.1302i	0.634291	+	0.634291i	−0.314850	+	0.949141i	$0.601954\pi$
$570$	−11.2557	−	6.44547i	−0.471450	−	0.269971i
$571$	−0.732604			−0.0306585			−0.0153293	−	0.999882i	$-0.504880\pi$
$571$	−0.732604			−0.0306585			−0.0153293	+	0.999882i	$0.504880\pi$
$572$		−	2.92981i		−	0.122502i
$573$		−	16.4697i		−	0.688033i
$574$	−5.73860	+	5.73860i	−0.239525	+	0.239525i
$575$	21.5969	+	36.8026i	0.900653	+	1.53478i
$576$			1.00000i			0.0416667i
$577$			13.0938i			0.545102i	0.962141	+	0.272551i	$0.0878673\pi$
$577$			13.0938i			0.545102i	−0.962141	+	0.272551i	$0.912133\pi$
$578$	16.0279			0.666673
$579$	−1.98459	−	1.98459i	−0.0824768	−	0.0824768i
$580$	1.41104	+	5.19246i	0.0585901	+	0.215605i
$581$	11.6089			0.481619
$582$	6.56334	−	6.56334i	0.272059	−	0.272059i
$583$	15.4233	+	15.4233i	0.638767	+	0.638767i
$584$	−11.8322	−	11.8322i	−0.489622	−	0.489622i
$585$	−1.43505	+	2.50602i	−0.0593319	+	0.103611i
$586$	22.0187	−	22.0187i	0.909583	−	0.909583i
$587$	−25.6946			−1.06053			−0.530265	−	0.847832i	$-0.677908\pi$
$587$	−25.6946			−1.06053			−0.530265	+	0.847832i	$0.677908\pi$
$588$	4.37734	−	4.37734i	0.180519	−	0.180519i
$589$			47.6739i			1.96437i
$590$	10.7164	−	2.91214i	0.441186	−	0.119891i
$591$			16.2893i			0.670052i
$592$	3.16223	+	5.19618i	0.129967	+	0.213562i
$593$	−32.7884	+	32.7884i	−1.34646	+	1.34646i	−0.456986	+	0.889474i	$0.651071\pi$
$593$	−32.7884	+	32.7884i	−1.34646	+	1.34646i	−0.889474	+	0.456986i	$0.848929\pi$
$594$	−1.60413	−	1.60413i	−0.0658182	−	0.0658182i
$595$	11.1574	−	3.03200i	0.457410	−	0.124300i
$596$		−	19.0997i		−	0.782356i
$597$		−	14.6329i		−	0.598885i
$598$	−11.0218			−0.450716
$599$		−	32.7946i		−	1.33995i	−0.742383	−	0.669975i	$-0.766305\pi$
$599$		−	32.7946i		−	1.33995i	0.742383	−	0.669975i	$-0.233695\pi$
$600$	1.25987	−	4.83867i	0.0514339	−	0.197538i
$601$	27.3053			1.11381			0.556904	−	0.830577i	$-0.311989\pi$
$601$	27.3053			1.11381			0.556904	+	0.830577i	$0.311989\pi$
$602$	−0.542735	−	0.542735i	−0.0221202	−	0.0221202i
$603$	−3.98347	−	3.98347i	−0.162220	−	0.162220i
$604$			3.42513i			0.139367i
$605$	11.3584	+	6.50428i	0.461785	+	0.264437i
$606$	−1.04233	+	1.04233i	−0.0423419	+	0.0423419i
$607$	−26.7432			−1.08547			−0.542737	−	0.839903i	$-0.682612\pi$
$607$	−26.7432			−1.08547			−0.542737	+	0.839903i	$0.682612\pi$
$608$	−4.10165	+	4.10165i	−0.166344	+	0.166344i
$609$	−1.53092	+	1.53092i	−0.0620362	+	0.0620362i
$610$	6.30035	−	1.71210i	0.255094	−	0.0693210i
$611$	−0.421941	−	0.421941i	−0.0170699	−	0.0170699i
$612$	5.74699			0.232308
$613$	23.6704	+	23.6704i	0.956040	+	0.956040i	0.999074	−	0.0430339i	$-0.0137024\pi$
$613$	23.6704	+	23.6704i	0.956040	+	0.956040i	−0.0430339	+	0.999074i	$0.513702\pi$
$614$	5.03677	−	5.03677i	0.203268	−	0.203268i
$615$	19.4637	−	5.28921i	0.784852	−	0.213281i
$616$	−1.44327	+	1.44327i	−0.0581512	+	0.0581512i
$617$	−3.77510	+	3.77510i	−0.151980	+	0.151980i	−0.779002	−	0.627022i	$-0.784274\pi$
$617$	−3.77510	+	3.77510i	−0.151980	+	0.151980i	0.627022	+	0.779002i	$0.284274\pi$
$618$	−0.728096	+	0.728096i	−0.0292883	+	0.0292883i
$619$	−9.65130			−0.387918			−0.193959	−	0.981010i	$-0.562133\pi$
$619$	−9.65130			−0.387918			−0.193959	+	0.981010i	$0.562133\pi$
$620$	−17.7346	+	4.81932i	−0.712238	+	0.193549i
$621$	−6.03467	+	6.03467i	−0.242163	+	0.242163i
$622$	−3.85553	+	3.85553i	−0.154593	+	0.154593i
$623$			8.04644i			0.322374i
$624$	0.913209	+	0.913209i	0.0365576	+	0.0365576i
$625$	−12.1922	+	21.8255i	−0.487687	+	0.873019i
$626$	−19.5460			−0.781217
$627$		−	13.1592i		−	0.525526i
$628$	12.1068	+	12.1068i	0.483116	+	0.483116i
$629$	29.8624	−	18.1733i	1.19069	−	0.724618i
$630$	1.94144	−	0.527580i	0.0773487	−	0.0210193i
$631$	9.32454	−	9.32454i	0.371204	−	0.371204i	−0.496712	−	0.867916i	$-0.665459\pi$
$631$	9.32454	−	9.32454i	0.371204	−	0.371204i	0.867916	+	0.496712i	$0.165459\pi$
$632$	9.04382	−	9.04382i	0.359744	−	0.359744i
$633$	−2.69402	−	2.69402i	−0.107078	−	0.107078i
$634$	5.03252	−	5.03252i	0.199867	−	0.199867i
$635$	0.759923	+	2.79643i	0.0301566	+	0.110973i
$636$	−9.61473			−0.381249
$637$		−	7.99485i		−	0.316768i
$638$	−3.86010	+	3.86010i	−0.152823	+	0.152823i
$639$		−	15.2892i		−	0.604832i
$640$	−1.94044	−	1.11117i	−0.0767025	−	0.0439229i
$641$	−7.81012			−0.308481			−0.154241	−	0.988033i	$-0.549293\pi$
$641$	−7.81012			−0.308481			−0.154241	+	0.988033i	$0.549293\pi$
$642$			19.6007i			0.773580i
$643$			39.3070i			1.55012i	0.631890	+	0.775058i	$0.282279\pi$
$643$			39.3070i			1.55012i	−0.631890	+	0.775058i	$0.717721\pi$
$644$	5.42954	+	5.42954i	0.213954	+	0.213954i
$645$	0.500233	+	1.84080i	0.0196966	+	0.0724815i
$646$	23.5721	+	23.5721i	0.927433	+	0.927433i
$647$	−31.8619			−1.25262			−0.626311	−	0.779573i	$-0.715436\pi$
$647$	−31.8619			−1.25262			−0.626311	+	0.779573i	$0.715436\pi$
$648$	1.00000			0.0392837
$649$	7.96660	+	7.96660i	0.312716	+	0.312716i
$650$	−3.26819	−	5.56924i	−0.128189	−	0.218443i
$651$	−5.22879	−	5.22879i	−0.204933	−	0.204933i
$652$		−	24.2268i		−	0.948795i
$653$		−	40.2027i		−	1.57325i	−0.617430	−	0.786626i	$-0.711826\pi$
$653$		−	40.2027i		−	1.57325i	0.617430	−	0.786626i	$-0.288174\pi$
$654$	7.53328			0.294575
$655$	−19.1929	+	5.21562i	−0.749929	+	0.203791i
$656$		−	9.02011i		−	0.352176i
$657$	−11.8322	+	11.8322i	−0.461620	+	0.461620i
$658$			0.415710i			0.0162061i
$659$	22.6033			0.880499			0.440250	−	0.897875i	$-0.354890\pi$
$659$	22.6033			0.880499			0.440250	+	0.897875i	$0.354890\pi$
$660$	4.89518	−	1.33025i	0.190545	−	0.0517799i
$661$	20.1421	−	20.1421i	0.783436	−	0.783436i	−0.196973	−	0.980409i	$-0.563111\pi$
$661$	20.1421	−	20.1421i	0.783436	−	0.783436i	0.980409	+	0.196973i	$0.0631111\pi$
$662$	3.25748	+	3.25748i	0.126606	+	0.126606i
$663$	5.24820	−	5.24820i	0.203823	−	0.203823i
$664$	−9.12362	+	9.12362i	−0.354065	+	0.354065i
$665$	10.1270	+	5.79914i	0.392710	+	0.224881i
$666$	5.19618	−	3.16223i	0.201348	−	0.122534i
$667$	14.5215	+	14.5215i	0.562276	+	0.562276i
$668$			9.66372i			0.373900i
$669$	23.8893			0.923612
$670$	12.1560	−	3.30336i	0.469628	−	0.127620i
$671$	4.68371	+	4.68371i	0.180813	+	0.180813i
$672$		−	0.899724i		−	0.0347076i
$673$	23.9631	−	23.9631i	0.923709	−	0.923709i	−0.0735806	−	0.997289i	$-0.523443\pi$
$673$	23.9631	−	23.9631i	0.923709	−	0.923709i	0.997289	+	0.0735806i	$0.0234426\pi$
$674$	15.5648	−	15.5648i	0.599532	−	0.599532i
$675$	−4.83867	−	1.25987i	−0.186241	−	0.0484923i
$676$	−11.3321			−0.435850
$677$	18.3439	−	18.3439i	0.705012	−	0.705012i	−0.260470	−	0.965482i	$-0.583878\pi$
$677$	18.3439	−	18.3439i	0.705012	−	0.705012i	0.965482	+	0.260470i	$0.0838776\pi$
$678$	−12.2157	+	12.2157i	−0.469139	+	0.469139i
$679$	−5.90520	+	5.90520i	−0.226621	+	0.226621i
$680$	−6.38589	+	11.1517i	−0.244888	+	0.427647i
$681$	17.6798	−	17.6798i	0.677490	−	0.677490i
$682$	−13.1840	−	13.1840i	−0.504841	−	0.504841i
$683$	2.79715			0.107030			0.0535149	−	0.998567i	$-0.482958\pi$
$683$	2.79715			0.107030			0.0535149	+	0.998567i	$0.482958\pi$
$684$	4.10165	+	4.10165i	0.156830	+	0.156830i
$685$	8.66777	+	31.8965i	0.331179	+	1.21870i
$686$	−8.39181	+	8.39181i	−0.320401	+	0.320401i
$687$	8.03073	−	8.03073i	0.306392	−	0.306392i
$688$	0.853087			0.0325236
$689$	−8.78026	+	8.78026i	−0.334501	+	0.334501i
$690$	−5.00435	−	18.4154i	−0.190512	−	0.701064i
$691$		−	7.07761i		−	0.269245i	−0.990897	−	0.134623i	$-0.957018\pi$
$691$		−	7.07761i		−	0.269245i	0.990897	−	0.134623i	$-0.0429822\pi$
$692$	6.77556	+	6.77556i	0.257568	+	0.257568i
$693$	1.44327	+	1.44327i	0.0548255	+	0.0548255i
$694$	19.7799			0.750835
$695$	28.0282	+	16.0501i	1.06317	+	0.608813i
$696$		−	2.40635i		−	0.0912125i
$697$	−51.8385			−1.96352
$698$		−	5.47518i		−	0.207239i
$699$		−	6.74968i		−	0.255296i
$700$	−1.13353	+	4.35347i	−0.0428435	+	0.164546i
$701$	−25.0871	−	25.0871i	−0.947527	−	0.947527i	0.0511635	−	0.998690i	$-0.483707\pi$
$701$	−25.0871	−	25.0871i	−0.947527	−	0.947527i	−0.998690	+	0.0511635i	$0.983707\pi$
$702$	0.913209	−	0.913209i	0.0344668	−	0.0344668i
$703$	34.2833	+	8.34254i	1.29302	+	0.314645i
$704$		−	2.26858i		−	0.0855004i
$705$	0.513408	−	0.896564i	0.0193361	−	0.0337665i
$706$			28.1816i			1.06063i
$707$	0.937812	−	0.937812i	0.0352701	−	0.0352701i
$708$	−4.96631			−0.186645
$709$	6.08101	−	6.08101i	0.228377	−	0.228377i	−0.583637	−	0.812014i	$-0.698371\pi$
$709$	6.08101	−	6.08101i	0.228377	−	0.228377i	0.812014	+	0.583637i	$0.198371\pi$
$710$	29.6678	+	16.9889i	1.11341	+	0.637584i
$711$	−9.04382	−	9.04382i	−0.339170	−	0.339170i
$712$	−6.32382	−	6.32382i	−0.236995	−	0.236995i
$713$	−49.5976	+	49.5976i	−1.85744	+	1.85744i
$714$	−5.17071			−0.193509
$715$	3.25552	−	5.68511i	0.121750	−	0.212611i
$716$	−7.36463	−	7.36463i	−0.275229	−	0.275229i
$717$	4.19821			0.156785
$718$		−	2.05043i		−	0.0765215i
$719$			37.1763i			1.38644i	0.720724	+	0.693222i	$0.243809\pi$
$719$			37.1763i			1.38644i	−0.720724	+	0.693222i	$0.756191\pi$
$720$	−1.11117	+	1.94044i	−0.0414109	+	0.0723158i
$721$	0.655086	−	0.655086i	0.0243967	−	0.0243967i
$722$			14.6470i			0.545106i
$723$		−	8.14088i		−	0.302762i
$724$	−13.9651			−0.519008
$725$	−3.03168	+	11.6435i	−0.112594	+	0.432430i
$726$	−4.13907	−	4.13907i	−0.153615	−	0.153615i
$727$	−10.8041			−0.400701			−0.200350	−	0.979724i	$-0.564208\pi$
$727$	−10.8041			−0.400701			−0.200350	+	0.979724i	$0.564208\pi$
$728$	−0.821636	−	0.821636i	−0.0304519	−	0.0304519i
$729$		−	1.00000i		−	0.0370370i
$730$	−9.81208	−	36.1074i	−0.363161	−	1.33639i
$731$		−	4.90268i		−	0.181332i
$732$	−2.91979			−0.107918
$733$	2.31409	+	2.31409i	0.0854728	+	0.0854728i	0.748551	−	0.663078i	$-0.230750\pi$
$733$	2.31409	+	2.31409i	0.0854728	+	0.0854728i	−0.663078	+	0.748551i	$0.730750\pi$
$734$	8.13886	+	8.13886i	0.300411	+	0.300411i
$735$	13.3579	−	3.62998i	0.492715	−	0.133894i
$736$	−8.53431			−0.314579
$737$	9.03684	+	9.03684i	0.332876	+	0.332876i
$738$	−9.02011			−0.332035
$739$	3.59606			0.132283			0.0661416	−	0.997810i	$-0.478931\pi$
$739$	3.59606			0.132283			0.0661416	+	0.997810i	$0.478931\pi$
$740$	0.362266	+	13.5966i	0.0133172	+	0.499823i
$741$	7.49132			0.275201
$742$	8.65061			0.317574
$743$	−7.78930	−	7.78930i	−0.285762	−	0.285762i	0.549640	−	0.835402i	$-0.314765\pi$
$743$	−7.78930	−	7.78930i	−0.285762	−	0.285762i	−0.835402	+	0.549640i	$0.814765\pi$
$744$	8.21877			0.301315
$745$	21.2231	−	37.0619i	0.777554	−	1.35784i
$746$	−9.78820	−	9.78820i	−0.358371	−	0.358371i
$747$	9.12362	+	9.12362i	0.333816	+	0.333816i
$748$	−13.0375			−0.476699
$749$		−	17.6353i		−	0.644379i
$750$	7.82129	−	7.98921i	0.285593	−	0.291725i
$751$		−	31.8319i		−	1.16156i	−0.814059	−	0.580782i	$-0.802747\pi$
$751$		−	31.8319i		−	1.16156i	0.814059	−	0.580782i	$-0.197253\pi$
$752$	−0.326713	−	0.326713i	−0.0119140	−	0.0119140i
$753$	−20.8949			−0.761452
$754$	−2.19750	−	2.19750i	−0.0800283	−	0.0800283i
$755$	−3.80591	+	6.64625i	−0.138511	+	0.241882i
$756$	−0.899724			−0.0327227
$757$			2.85691i			0.103836i	0.998651	+	0.0519182i	$0.0165335\pi$
$757$			2.85691i			0.103836i	−0.998651	+	0.0519182i	$0.983467\pi$
$758$			22.6146i			0.821400i
$759$	13.6901	−	13.6901i	0.496921	−	0.496921i
$760$	−12.5166	+	3.40136i	−0.454026	+	0.123380i
$761$			3.11943i			0.113079i	0.998400	+	0.0565396i	$0.0180067\pi$
$761$			3.11943i			0.113079i	−0.998400	+	0.0565396i	$0.981993\pi$
$762$		−	1.29596i		−	0.0469476i
$763$	−6.77787			−0.245376
$764$	−11.6459	−	11.6459i	−0.421332	−	0.421332i
$765$	11.1517	+	6.38589i	0.403190	+	0.230882i
$766$	9.52538			0.344166
$767$	−4.53527	+	4.53527i	−0.163759	+	0.163759i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−22.4056	−	22.4056i	−0.807966	−	0.807966i	0.176360	−	0.984326i	$-0.443568\pi$
$769$	−22.4056	−	22.4056i	−0.807966	−	0.807966i	−0.984326	+	0.176360i	$0.943568\pi$
$770$	−4.40431	+	1.19686i	−0.158720	+	0.0431318i
$771$	−1.27298	+	1.27298i	−0.0458453	+	0.0458453i
$772$	−2.80664			−0.101013
$773$	−1.90608	+	1.90608i	−0.0685571	+	0.0685571i	−0.740554	−	0.671997i	$-0.765437\pi$
$773$	−1.90608	+	1.90608i	−0.0685571	+	0.0685571i	0.671997	+	0.740554i	$0.265437\pi$
$774$		−	0.853087i		−	0.0306636i
$775$	−39.7679	−	10.3546i	−1.42851	−	0.371947i
$776$		−	9.28197i		−	0.333203i
$777$	−4.67513	+	2.84514i	−0.167719	+	0.102069i
$778$	7.75553	−	7.75553i	0.278049	−	0.278049i
$779$	−36.9973	−	36.9973i	−1.32557	−	1.32557i
$780$	0.757293	+	2.78676i	0.0271154	+	0.0997819i
$781$			34.6848i			1.24112i
$782$			49.0466i			1.75390i
$783$	−2.40635			−0.0859960
$784$		−	6.19050i		−	0.221089i
$785$	10.0398	+	36.9454i	0.358336	+	1.31864i
$786$	8.89460			0.317260
$787$	−24.9409	−	24.9409i	−0.889045	−	0.889045i	0.105386	−	0.994431i	$-0.466392\pi$
$787$	−24.9409	−	24.9409i	−0.889045	−	0.889045i	−0.994431	+	0.105386i	$0.966392\pi$
$788$	11.5183	+	11.5183i	0.410322	+	0.410322i
$789$			13.0942i			0.466165i
$790$	27.5982	−	7.49973i	0.981900	−	0.266829i
$791$	10.9907	−	10.9907i	0.390785	−	0.390785i
$792$	−2.26858			−0.0806106
$793$	−2.66637	+	2.66637i	−0.0946857	+	0.0946857i
$794$	−18.6690	+	18.6690i	−0.662538	+	0.662538i
$795$	−18.6568	−	10.6836i	−0.661688	−	0.378909i
$796$	−10.3470	−	10.3470i	−0.366740	−	0.366740i
$797$	−33.5854			−1.18966			−0.594828	−	0.803853i	$-0.702780\pi$
$797$	−33.5854			−1.18966			−0.594828	+	0.803853i	$0.702780\pi$
$798$	−3.69035	−	3.69035i	−0.130637	−	0.130637i
$799$	−1.87762	+	1.87762i	−0.0664253	+	0.0664253i
$800$	−2.53060	−	4.31232i	−0.0894701	−	0.152463i
$801$	−6.32382	+	6.32382i	−0.223441	+	0.223441i
$802$	−13.9114	+	13.9114i	−0.491228	+	0.491228i
$803$	26.8424	−	26.8424i	0.947248	−	0.947248i
$804$	−5.63348			−0.198678
$805$	4.50253	+	16.5688i	0.158693	+	0.583974i
$806$	7.50545	−	7.50545i	0.264368	−	0.264368i
$807$	−0.487209	+	0.487209i	−0.0171506	+	0.0171506i
$808$			1.47408i			0.0518580i
$809$	4.59489	+	4.59489i	0.161548	+	0.161548i	0.783252	−	0.621704i	$-0.213559\pi$
$809$	4.59489	+	4.59489i	0.161548	+	0.161548i	−0.621704	+	0.783252i	$0.713559\pi$
$810$	1.94044	+	1.11117i	0.0681800	+	0.0390426i
$811$	−26.4363			−0.928304			−0.464152	−	0.885756i	$-0.653641\pi$
$811$	−26.4363			−0.928304			−0.464152	+	0.885756i	$0.653641\pi$
$812$			2.16505i			0.0759785i
$813$	−10.4390	−	10.4390i	−0.366110	−	0.366110i
$814$	−11.7880	+	7.17378i	−0.413168	+	0.251441i
$815$	26.9201	−	47.0106i	0.942971	−	1.64671i
$816$	4.06374	−	4.06374i	0.142259	−	0.142259i
$817$	3.49906	−	3.49906i	0.122417	−	0.122417i
$818$	−7.16339	−	7.16339i	−0.250462	−	0.250462i
$819$	−0.821636	+	0.821636i	−0.0287103	+	0.0287103i
$820$	10.0229	−	17.5030i	0.350014	−	0.611230i
$821$	38.5813			1.34650			0.673248	−	0.739417i	$-0.264899\pi$
$821$	38.5813			1.34650			0.673248	+	0.739417i	$0.264899\pi$
$822$		−	14.7818i		−	0.515576i
$823$	9.95130	−	9.95130i	0.346881	−	0.346881i	−0.512066	−	0.858946i	$-0.671120\pi$
$823$	9.95130	−	9.95130i	0.346881	−	0.346881i	0.858946	+	0.512066i	$0.171120\pi$
$824$			1.02968i			0.0358707i
$825$	10.9769	+	2.85811i	0.382167	+	0.0995067i
$826$	4.46831			0.155472
$827$			3.10451i			0.107954i	0.998542	+	0.0539772i	$0.0171898\pi$
$827$			3.10451i			0.107954i	−0.998542	+	0.0539772i	$0.982810\pi$
$828$			8.53431i			0.296588i
$829$	8.47013	+	8.47013i	0.294180	+	0.294180i	0.838729	−	0.544549i	$-0.183299\pi$
$829$	8.47013	+	8.47013i	0.294180	+	0.294180i	−0.544549	+	0.838729i	$0.683299\pi$
$830$	−27.8417	+	7.56591i	−0.966400	+	0.262616i
$831$	−22.8940	−	22.8940i	−0.794186	−	0.794186i
$832$	1.29147			0.0447737
$833$	−35.5767			−1.23266
$834$	−10.2136	−	10.2136i	−0.353669	−	0.353669i
$835$	−10.7380	+	18.7518i	−0.371605	+	0.648934i
$836$	−9.30492	−	9.30492i	−0.321818	−	0.321818i
$837$		−	8.21877i		−	0.284082i
$838$		−	23.8546i		−	0.824042i
$839$	−6.41357			−0.221421			−0.110711	−	0.993853i	$-0.535313\pi$
$839$	−6.41357			−0.221421			−0.110711	+	0.993853i	$0.535313\pi$
$840$	0.999748	−	1.74586i	0.0344946	−	0.0602378i
$841$		−	23.2095i		−	0.800327i
$842$	12.3787	−	12.3787i	0.426598	−	0.426598i
$843$			8.12784i			0.279938i
$844$	−3.80993			−0.131143
$845$	−21.9892	−	12.5919i	−0.756453	−	0.433175i
$846$	−0.326713	+	0.326713i	−0.0112326	+	0.0112326i
$847$	3.72403	+	3.72403i	0.127959	+	0.127959i
$848$	−6.79864	+	6.79864i	−0.233466	+	0.233466i
$849$	4.64434	−	4.64434i	0.159393	−	0.159393i
$850$	−24.7828	+	14.5433i	−0.850045	+	0.498832i
$851$	26.9875	+	44.3458i	0.925118	+	1.52015i
$852$	−10.8111	−	10.8111i	−0.370382	−	0.370382i
$853$			46.7208i			1.59969i	0.600207	+	0.799845i	$0.295085\pi$
$853$			46.7208i			1.59969i	−0.600207	+	0.799845i	$0.704915\pi$
$854$	2.62700			0.0898941
$855$	3.40136	+	12.5166i	0.116324	+	0.428060i
$856$	13.8598	+	13.8598i	0.473719	+	0.473719i
$857$		−	36.8302i		−	1.25810i	−0.777367	−	0.629048i	$-0.783445\pi$
$857$		−	36.8302i		−	1.25810i	0.777367	−	0.629048i	$-0.216555\pi$
$858$	−2.07169	+	2.07169i	−0.0707263	+	0.0707263i
$859$	−33.3859	+	33.3859i	−1.13911	+	1.13911i	−0.150502	+	0.988610i	$0.548089\pi$
$859$	−33.3859	+	33.3859i	−1.13911	+	1.13911i	−0.988610	+	0.150502i	$0.951911\pi$
$860$	1.65536	+	0.947925i	0.0564474	+	0.0323240i
$861$	8.11561			0.276579
$862$	−5.50143	+	5.50143i	−0.187379	+	0.187379i
$863$	−1.49779	+	1.49779i	−0.0509855	+	0.0509855i	−0.732140	−	0.681154i	$-0.761478\pi$
$863$	−1.49779	+	1.49779i	−0.0509855	+	0.0509855i	0.681154	+	0.732140i	$0.261478\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	5.61875	+	20.6764i	0.191043	+	0.703018i
$866$	−4.53175	+	4.53175i	−0.153995	+	0.153995i
$867$	−11.3334	−	11.3334i	−0.384904	−	0.384904i
$868$	−7.39463			−0.250990
$869$	20.5166	+	20.5166i	0.695980	+	0.695980i
$870$	2.67387	−	4.66938i	0.0906527	−	0.158307i
$871$	−5.14455	+	5.14455i	−0.174316	+	0.174316i
$872$	5.32683	−	5.32683i	0.180389	−	0.180389i
$873$	−9.28197			−0.314147
$874$	−35.0047	+	35.0047i	−1.18405	+	1.18405i
$875$	−7.03700	+	7.18809i	−0.237894	+	0.243002i
$876$			16.7333i			0.565366i
$877$	8.78482	+	8.78482i	0.296642	+	0.296642i	0.839697	−	0.543055i	$-0.182732\pi$
$877$	8.78482	+	8.78482i	0.296642	+	0.296642i	−0.543055	+	0.839697i	$0.682732\pi$
$878$	22.7618	+	22.7618i	0.768172	+	0.768172i
$879$	−31.1391			−1.05030
$880$	2.52078	−	4.40204i	0.0849756	−	0.148393i
$881$			19.0001i			0.640128i	0.947396	+	0.320064i	$0.103704\pi$
$881$			19.0001i			0.640128i	−0.947396	+	0.320064i	$0.896296\pi$
$882$	−6.19050			−0.208445
$883$			10.1981i			0.343193i	0.985167	+	0.171596i	$0.0548925\pi$
$883$			10.1981i			0.343193i	−0.985167	+	0.171596i	$0.945108\pi$
$884$		−	7.42208i		−	0.249631i
$885$	−9.63681	−	5.51842i	−0.323938	−	0.185500i
$886$	−18.5368	−	18.5368i	−0.622754	−	0.622754i
$887$	−12.1095	+	12.1095i	−0.406597	+	0.406597i	−0.880550	−	0.473953i	$-0.842827\pi$
$887$	−12.1095	+	12.1095i	−0.406597	+	0.406597i	0.473953	+	0.880550i	$0.342827\pi$
$888$	1.43822	−	5.91029i	0.0482635	−	0.198336i
$889$			1.16600i			0.0391065i
$890$	−5.24413	−	19.2978i	−0.175784	−	0.646864i
$891$			2.26858i			0.0760004i
$892$	16.8923	−	16.8923i	0.565595	−	0.565595i
$893$	−2.68012			−0.0896869
$894$	−13.5056	+	13.5056i	−0.451694	+	0.451694i
$895$	−6.10724	−	22.4740i	−0.204143	−	0.751222i
$896$	−0.636201	−	0.636201i	−0.0212540	−	0.0212540i
$897$	7.79360	+	7.79360i	0.260221	+	0.260221i
$898$	9.96142	−	9.96142i	0.332417	−	0.332417i
$899$	−19.7773			−0.659609
$900$	−4.31232	+	2.53060i	−0.143744	+	0.0843532i
$901$	39.0717	+	39.0717i	1.30167	+	1.30167i
$902$	20.4629			0.681338
$903$			0.767543i			0.0255422i
$904$			17.2755i			0.574576i
$905$	−27.0984	−	15.5176i	−0.900780	−	0.515822i
$906$	2.42193	−	2.42193i	0.0804634	−	0.0804634i
$907$			0.471868i			0.0156681i	0.999969	+	0.00783407i	$0.00249369\pi$
$907$			0.471868i			0.0156681i	−0.999969	+	0.00783407i	$0.997506\pi$
$908$		−	25.0030i		−	0.829752i
$909$	1.47408			0.0488922
$910$	−0.681355	−	2.50731i	−0.0225867	−	0.0831166i
$911$	18.6659	+	18.6659i	0.618430	+	0.618430i	0.945129	−	0.326698i	$-0.105936\pi$
$911$	18.6659	+	18.6659i	0.618430	+	0.618430i	−0.326698	+	0.945129i	$0.605936\pi$
$912$	5.80061			0.192077
$913$	−20.6977	−	20.6977i	−0.684993	−	0.684993i
$914$			6.81678i			0.225479i
$915$	−5.66566	−	3.24438i	−0.187301	−	0.107256i
$916$		−	11.3572i		−	0.375252i
$917$	−8.00269			−0.264272
$918$	−4.06374	−	4.06374i	−0.134123	−	0.134123i
$919$	−24.0718	−	24.0718i	−0.794054	−	0.794054i	0.188096	−	0.982151i	$-0.439768\pi$
$919$	−24.0718	−	24.0718i	−0.794054	−	0.794054i	−0.982151	+	0.188096i	$0.939768\pi$
$920$	−16.5603	−	9.48308i	−0.545977	−	0.312648i
$921$	−7.12307			−0.234713
$922$	−24.7125	−	24.7125i	−0.813862	−	0.813862i
$923$	−19.7456			−0.649934
$924$	2.04110			0.0671472
$925$	−14.4052	+	26.7860i	−0.473642	+	0.880718i
$926$	32.0736			1.05400
$927$	1.02968			0.0338192
$928$	−1.70155	−	1.70155i	−0.0558560	−	0.0558560i
$929$	8.12677			0.266631			0.133315	−	0.991074i	$-0.457438\pi$
$929$	8.12677			0.266631			0.133315	+	0.991074i	$0.457438\pi$
$930$	15.9480	+	9.13247i	0.522956	+	0.299465i
$931$	−25.3912	−	25.3912i	−0.832164	−	0.832164i
$932$	−4.77274	−	4.77274i	−0.156336	−	0.156336i
$933$	5.45254			0.178508
$934$		−	13.7531i		−	0.450014i
$935$	−25.2985	−	14.4869i	−0.827349	−	0.473773i
$936$		−	1.29147i		−	0.0422131i
$937$	−21.4124	−	21.4124i	−0.699513	−	0.699513i	0.264793	−	0.964305i	$-0.414696\pi$
$937$	−21.4124	−	21.4124i	−0.699513	−	0.699513i	−0.964305	+	0.264793i	$0.914696\pi$
$938$	5.06858			0.165495
$939$	13.8211	+	13.8211i	0.451036	+	0.451036i
$940$	−0.270932	−	0.997001i	−0.00883683	−	0.0325186i
$941$	−6.32110			−0.206062			−0.103031	−	0.994678i	$-0.532854\pi$
$941$	−6.32110			−0.206062			−0.103031	+	0.994678i	$0.532854\pi$
$942$		−	17.1217i		−	0.557854i
$943$		−	76.9804i		−	2.50683i
$944$	−3.51171	+	3.51171i	−0.114296	+	0.114296i
$945$	−1.74586	−	0.999748i	−0.0567928	−	0.0325218i
$946$			1.93530i			0.0629219i
$947$			29.6137i			0.962316i	0.876634	+	0.481158i	$0.159784\pi$
$947$			29.6137i			0.962316i	−0.876634	+	0.481158i	$0.840216\pi$
$948$	−12.7899			−0.415396
$949$	15.2810	+	15.2810i	0.496043	+	0.496043i
$950$	−28.0672	−	7.30799i	−0.910621	−	0.237103i
$951$	−7.11706			−0.230787
$952$	−3.65624	+	3.65624i	−0.118499	+	0.118499i
$953$	−25.1832	−	25.1832i	−0.815765	−	0.815765i	0.169727	−	0.985491i	$-0.445712\pi$
$953$	−25.1832	−	25.1832i	−0.815765	−	0.815765i	−0.985491	+	0.169727i	$0.945712\pi$
$954$	6.79864	+	6.79864i	0.220114	+	0.220114i
$955$	−9.65751	−	35.5386i	−0.312510	−	1.15000i
$956$	2.96858	−	2.96858i	0.0960109	−	0.0960109i
$957$	5.45901			0.176465
$958$	15.9554	−	15.9554i	0.515496	−	0.515496i
$959$			13.2996i			0.429466i
$960$	0.586380	+	2.15781i	0.0189253	+	0.0696431i
$961$		−	36.5482i		−	1.17898i
$962$	−4.08393	−	6.71072i	−0.131671	−	0.216362i
$963$	13.8598	−	13.8598i	0.446627	−	0.446627i
$964$	−5.75647	−	5.75647i	−0.185403	−	0.185403i
$965$	−5.44611	−	3.11866i	−0.175316	−	0.100393i
$966$		−	7.67852i		−	0.247052i
$967$			12.3262i			0.396385i	0.980163	+	0.198192i	$0.0635071\pi$
$967$			12.3262i			0.396385i	−0.980163	+	0.198192i	$0.936493\pi$
$968$	−5.85354			−0.188140
$969$		−	33.3360i		−	1.07091i
$970$	10.3139	−	18.0111i	0.331158	−	0.578301i
$971$	4.53299			0.145471			0.0727353	−	0.997351i	$-0.476827\pi$
$971$	4.53299			0.145471			0.0727353	+	0.997351i	$0.476827\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	9.18946	+	9.18946i	0.294601	+	0.294601i
$974$		−	22.5078i		−	0.721195i
$975$	−1.62708	+	6.24901i	−0.0521084	+	0.200128i
$976$	−2.06460	+	2.06460i	−0.0660862	+	0.0660862i
$977$	42.8715			1.37158			0.685790	−	0.727799i	$-0.259457\pi$
$977$	42.8715			1.37158			0.685790	+	0.727799i	$0.259457\pi$
$978$	−17.1309	+	17.1309i	−0.547787	+	0.547787i
$979$	14.3461	−	14.3461i	0.458503	−	0.458503i
$980$	6.87870	−	12.0123i	0.219732	−	0.383718i
$981$	−5.32683	−	5.32683i	−0.170073	−	0.170073i
$982$	−31.0223			−0.989961
$983$	−23.7970	−	23.7970i	−0.759006	−	0.759006i	0.217136	−	0.976141i	$-0.430329\pi$
$983$	−23.7970	−	23.7970i	−0.759006	−	0.759006i	−0.976141	+	0.217136i	$0.930329\pi$
$984$	−6.37818	+	6.37818i	−0.203329	+	0.203329i
$985$	9.55172	+	35.1493i	0.304343	+	1.11995i
$986$	−9.77878	+	9.77878i	−0.311420	+	0.311420i
$987$	0.293952	−	0.293952i	0.00935658	−	0.00935658i
$988$	5.29716	−	5.29716i	0.168525	−	0.168525i
$989$	7.28050			0.231507
$990$	−4.40204	−	2.52078i	−0.139906	−	0.0801158i
$991$	−3.21857	+	3.21857i	−0.102241	+	0.102241i	−0.756377	−	0.654136i	$-0.773032\pi$
$991$	−3.21857	+	3.21857i	−0.102241	+	0.102241i	0.654136	+	0.756377i	$0.273032\pi$
$992$	5.81155	−	5.81155i	0.184517	−	0.184517i
$993$		−	4.60678i		−	0.146192i
$994$	9.72702	+	9.72702i	0.308522	+	0.308522i
$995$	−8.58044	−	31.5751i	−0.272018	−	1.00100i
$996$	12.9027			0.408839
$997$			27.5415i			0.872248i	0.899887	+	0.436124i	$0.143649\pi$
$997$			27.5415i			0.872248i	−0.899887	+	0.436124i	$0.856351\pi$
$998$	5.68409	+	5.68409i	0.179927	+	0.179927i
$999$	−5.91029	−	1.43822i	−0.186993	−	0.0455032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.487.15	yes	36
5.3	odd	4		1110.2.l.a.43.4	✓	36
37.31	odd	4		1110.2.l.a.697.4	yes	36
185.68	even	4	inner	1110.2.o.a.253.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.4	✓	36	5.3	odd	4
1110.2.l.a.697.4	yes	36	37.31	odd	4
1110.2.o.a.253.15	yes	36	185.68	even	4	inner
1110.2.o.a.487.15	yes	36	1.1	even	1	trivial

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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 + 1.11117i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(1.94044 + 1.11117i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} -1.00000 q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} -2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} +1.29147 q^{13} +(-0.636201 - 0.636201i) q^{14} +(0.586380 + 2.15781i) q^{15} +1.00000 q^{16} -5.74699i q^{17} -1.00000i q^{18} +(4.10165 - 4.10165i) q^{19} +(1.94044 + 1.11117i) q^{20} +0.899724i q^{21} +2.26858i q^{22} +8.53431 q^{23} +(-0.707107 - 0.707107i) q^{24} +(2.53060 + 4.31232i) q^{25} -1.29147 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.636201 + 0.636201i) q^{28} +(1.70155 + 1.70155i) q^{29} +(-0.586380 - 2.15781i) q^{30} +(-5.81155 + 5.81155i) q^{31} -1.00000 q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(0.527580 + 1.94144i) q^{35} +1.00000i q^{36} +(3.16223 + 5.19618i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(0.913209 + 0.913209i) q^{39} +(-1.94044 - 1.11117i) q^{40} -9.02011i q^{41} -0.899724i q^{42} +0.853087 q^{43} -2.26858i q^{44} +(-1.11117 + 1.94044i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.19050i q^{49} +(-2.53060 - 4.31232i) q^{50} +(4.06374 - 4.06374i) q^{51} +1.29147 q^{52} +(-6.79864 + 6.79864i) q^{53} +(0.707107 - 0.707107i) q^{54} +(2.52078 - 4.40204i) q^{55} +(-0.636201 - 0.636201i) q^{56} +5.80061 q^{57} +(-1.70155 - 1.70155i) q^{58} +(-3.51171 + 3.51171i) q^{59} +(0.586380 + 2.15781i) q^{60} +(-2.06460 + 2.06460i) q^{61} +(5.81155 - 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} +1.00000 q^{64} +(2.50602 + 1.43505i) q^{65} +(-1.60413 + 1.60413i) q^{66} +(-3.98347 + 3.98347i) q^{67} -5.74699i q^{68} +(6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000i q^{72} +(11.8322 + 11.8322i) q^{73} +(-3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 - 4.10165i) q^{76} +(1.44327 - 1.44327i) q^{77} +(-0.913209 - 0.913209i) q^{78} +(-9.04382 + 9.04382i) q^{79} +(1.94044 + 1.11117i) q^{80} -1.00000 q^{81} +9.02011i q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(6.38589 - 11.1517i) q^{85} -0.853087 q^{86} +2.40635i q^{87} +2.26858i q^{88} +(6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 + 0.821636i) q^{91} +8.53431 q^{92} -8.21877 q^{93} +(0.326713 + 0.326713i) q^{94} +(12.5166 - 3.40136i) q^{95} +(-0.707107 - 0.707107i) q^{96} +9.28197i q^{97} +6.19050i q^{98} +2.26858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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