LMFDB - Embedded newform 1110.2.u.e.191.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (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			191.11
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.72167 - 0.189341i) q^{6} -3.77650 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.651967 - 2.92830i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.72167 - 0.189341i) q^{6} -3.77650 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.651967 - 2.92830i) q^{9} +1.00000 q^{10} -1.81549 q^{11} +(1.35129 + 1.08352i) q^{12} +(-3.90798 - 3.90798i) q^{13} +(-2.67039 - 2.67039i) q^{14} +(-0.189341 - 1.72167i) q^{15} -1.00000 q^{16} +(1.04463 - 1.04463i) q^{17} +(1.60961 - 2.53163i) q^{18} +(-1.01091 - 1.01091i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-4.09191 + 5.10314i) q^{21} +(-1.28375 - 1.28375i) q^{22} +(5.79126 - 5.79126i) q^{23} +(0.189341 + 1.72167i) q^{24} -1.00000i q^{25} -5.52672i q^{26} +(-4.66340 - 2.29188i) q^{27} -3.77650i q^{28} +(-3.80924 - 3.80924i) q^{29} +(1.08352 - 1.35129i) q^{30} +(4.46840 - 4.46840i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.96712 + 2.45325i) q^{33} +1.47733 q^{34} +(-2.67039 + 2.67039i) q^{35} +(2.92830 - 0.651967i) q^{36} +(5.83886 + 1.70519i) q^{37} -1.42964i q^{38} +(-9.51519 + 1.04644i) q^{39} +1.00000i q^{40} -9.74155 q^{41} +(-6.50188 + 0.715047i) q^{42} +(6.17939 + 6.17939i) q^{43} -1.81549i q^{44} +(-2.53163 - 1.60961i) q^{45} +8.19007 q^{46} +7.59431i q^{47} +(-1.08352 + 1.35129i) q^{48} +7.26192 q^{49} +(0.707107 - 0.707107i) q^{50} +(-0.279720 - 2.54347i) q^{51} +(3.90798 - 3.90798i) q^{52} -1.46832i q^{53} +(-1.67692 - 4.91812i) q^{54} +(-1.28375 + 1.28375i) q^{55} +(2.67039 - 2.67039i) q^{56} +(-2.46137 + 0.270690i) q^{57} -5.38709i q^{58} +(3.27282 - 3.27282i) q^{59} +(1.72167 - 0.189341i) q^{60} +(-0.251587 + 0.251587i) q^{61} +6.31927 q^{62} +(2.46215 + 11.0587i) q^{63} -1.00000i q^{64} -5.52672 q^{65} +(-3.12568 + 0.343748i) q^{66} +1.79916i q^{67} +(1.04463 + 1.04463i) q^{68} +(-1.55072 - 14.1006i) q^{69} -3.77650 q^{70} +14.5030i q^{71} +(2.53163 + 1.60961i) q^{72} +7.13983i q^{73} +(2.92295 + 5.33445i) q^{74} +(-1.35129 - 1.08352i) q^{75} +(1.01091 - 1.01091i) q^{76} +6.85620 q^{77} +(-7.46820 - 5.98831i) q^{78} +(-8.05198 - 8.05198i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-8.14988 + 3.81831i) q^{81} +(-6.88832 - 6.88832i) q^{82} +7.15345i q^{83} +(-5.10314 - 4.09191i) q^{84} -1.47733i q^{85} +8.73898i q^{86} +(-9.27479 + 1.02000i) q^{87} +(1.28375 - 1.28375i) q^{88} +(-7.47158 - 7.47158i) q^{89} +(-0.651967 - 2.92830i) q^{90} +(14.7585 + 14.7585i) q^{91} +(5.79126 + 5.79126i) q^{92} +(-1.19650 - 10.8797i) q^{93} +(-5.36999 + 5.36999i) q^{94} -1.42964 q^{95} +(-1.72167 + 0.189341i) q^{96} +(3.22614 + 3.22614i) q^{97} +(5.13495 + 5.13495i) q^{98} +(1.18364 + 5.31630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.08352	−	1.35129i	0.625571	−	0.780167i
$3$	1.08352	−	1.35129i	0.625571	−	0.780167i
$4$			1.00000i			0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	1.72167	−	0.189341i	0.702869	−	0.0772983i
$7$	−3.77650			−1.42738			−0.713691	−	0.700461i	$-0.752978\pi$
$7$	−3.77650			−1.42738			−0.713691	+	0.700461i	$0.752978\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.651967	−	2.92830i	−0.217322	−	0.976100i
$10$	1.00000			0.316228
$11$	−1.81549			−0.547391			−0.273696	−	0.961816i	$-0.588246\pi$
$11$	−1.81549			−0.547391			−0.273696	+	0.961816i	$0.588246\pi$
$12$	1.35129	+	1.08352i	0.390084	+	0.312785i
$13$	−3.90798	−	3.90798i	−1.08388	−	1.08388i	−0.996144	−	0.0877350i	$-0.972037\pi$
$13$	−3.90798	−	3.90798i	−1.08388	−	1.08388i	−0.0877350	−	0.996144i	$-0.527963\pi$
$14$	−2.67039	−	2.67039i	−0.713691	−	0.713691i
$15$	−0.189341	−	1.72167i	−0.0488878	−	0.444533i
$16$	−1.00000			−0.250000
$17$	1.04463	−	1.04463i	0.253360	−	0.253360i	−0.568987	−	0.822347i	$-0.692664\pi$
$17$	1.04463	−	1.04463i	0.253360	−	0.253360i	0.822347	+	0.568987i	$0.192664\pi$
$18$	1.60961	−	2.53163i	0.379389	−	0.596711i
$19$	−1.01091	−	1.01091i	−0.231918	−	0.231918i	0.581575	−	0.813493i	$-0.302437\pi$
$19$	−1.01091	−	1.01091i	−0.231918	−	0.231918i	−0.813493	+	0.581575i	$0.802437\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	−4.09191	+	5.10314i	−0.892928	+	1.11360i
$22$	−1.28375	−	1.28375i	−0.273696	−	0.273696i
$23$	5.79126	−	5.79126i	1.20756	−	1.20756i	0.235746	−	0.971815i	$-0.424247\pi$
$23$	5.79126	−	5.79126i	1.20756	−	1.20756i	0.971815	−	0.235746i	$-0.0757532\pi$
$24$	0.189341	+	1.72167i	0.0386492	+	0.351435i
$25$		−	1.00000i		−	0.200000i
$26$		−	5.52672i		−	1.08388i
$27$	−4.66340	−	2.29188i	−0.897472	−	0.441072i
$28$		−	3.77650i		−	0.713691i
$29$	−3.80924	−	3.80924i	−0.707359	−	0.707359i	0.258620	−	0.965979i	$-0.416732\pi$
$29$	−3.80924	−	3.80924i	−0.707359	−	0.707359i	−0.965979	+	0.258620i	$0.916732\pi$
$30$	1.08352	−	1.35129i	0.197823	−	0.246711i
$31$	4.46840	−	4.46840i	0.802548	−	0.802548i	−0.180945	−	0.983493i	$-0.557916\pi$
$31$	4.46840	−	4.46840i	0.802548	−	0.802548i	0.983493	+	0.180945i	$0.0579156\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.96712	+	2.45325i	−0.342432	+	0.427057i
$34$	1.47733			0.253360
$35$	−2.67039	+	2.67039i	−0.451378	+	0.451378i
$36$	2.92830	−	0.651967i	0.488050	−	0.108661i
$37$	5.83886	+	1.70519i	0.959903	+	0.280332i
$37$	5.83886	+	1.70519i	0.959903	+	0.280332i
$38$		−	1.42964i		−	0.231918i
$39$	−9.51519	+	1.04644i	−1.52365	+	0.167564i
$40$			1.00000i			0.158114i
$41$	−9.74155			−1.52138			−0.760688	−	0.649118i	$-0.775138\pi$
$41$	−9.74155			−1.52138			−0.760688	+	0.649118i	$0.775138\pi$
$42$	−6.50188	+	0.715047i	−1.00326	+	0.110334i
$43$	6.17939	+	6.17939i	0.942348	+	0.942348i	0.998426	−	0.0560783i	$-0.0178596\pi$
$43$	6.17939	+	6.17939i	0.942348	+	0.942348i	−0.0560783	+	0.998426i	$0.517860\pi$
$44$		−	1.81549i		−	0.273696i
$45$	−2.53163	−	1.60961i	−0.377393	−	0.239946i
$46$	8.19007			1.20756
$47$			7.59431i			1.10774i	0.832602	+	0.553872i	$0.186850\pi$
$47$			7.59431i			1.10774i	−0.832602	+	0.553872i	$0.813150\pi$
$48$	−1.08352	+	1.35129i	−0.156393	+	0.195042i
$49$	7.26192			1.03742
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−0.279720	−	2.54347i	−0.0391686	−	0.356157i
$52$	3.90798	−	3.90798i	0.541939	−	0.541939i
$53$		−	1.46832i		−	0.201689i	−0.994902	−	0.100844i	$-0.967846\pi$
$53$		−	1.46832i		−	0.201689i	0.994902	−	0.100844i	$-0.0321544\pi$
$54$	−1.67692	−	4.91812i	−0.228200	−	0.669272i
$55$	−1.28375	+	1.28375i	−0.173100	+	0.173100i
$56$	2.67039	−	2.67039i	0.356845	−	0.356845i
$57$	−2.46137	+	0.270690i	−0.326016	+	0.0358537i
$58$		−	5.38709i		−	0.707359i
$59$	3.27282	−	3.27282i	0.426084	−	0.426084i	−0.461208	−	0.887292i	$-0.652584\pi$
$59$	3.27282	−	3.27282i	0.426084	−	0.426084i	0.887292	+	0.461208i	$0.152584\pi$
$60$	1.72167	−	0.189341i	0.222267	−	0.0244439i
$61$	−0.251587	+	0.251587i	−0.0322125	+	0.0322125i	−0.723030	−	0.690817i	$-0.757251\pi$
$61$	−0.251587	+	0.251587i	−0.0322125	+	0.0322125i	0.690817	+	0.723030i	$0.257251\pi$
$62$	6.31927			0.802548
$63$	2.46215	+	11.0587i	0.310202	+	1.39327i
$64$		−	1.00000i		−	0.125000i
$65$	−5.52672			−0.685505
$66$	−3.12568	+	0.343748i	−0.384744	+	0.0423124i
$67$			1.79916i			0.219802i	0.993943	+	0.109901i	$0.0350534\pi$
$67$			1.79916i			0.219802i	−0.993943	+	0.109901i	$0.964947\pi$
$68$	1.04463	+	1.04463i	0.126680	+	0.126680i
$69$	−1.55072	−	14.1006i	−0.186685	−	1.69751i
$70$	−3.77650			−0.451378
$71$			14.5030i			1.72119i	0.509292	+	0.860594i	$0.329907\pi$
$71$			14.5030i			1.72119i	−0.509292	+	0.860594i	$0.670093\pi$
$72$	2.53163	+	1.60961i	0.298356	+	0.189694i
$73$			7.13983i			0.835653i	0.908527	+	0.417827i	$0.137208\pi$
$73$			7.13983i			0.835653i	−0.908527	+	0.417827i	$0.862792\pi$
$74$	2.92295	+	5.33445i	0.339786	+	0.620118i
$75$	−1.35129	−	1.08352i	−0.156033	−	0.125114i
$76$	1.01091	−	1.01091i	0.115959	−	0.115959i
$77$	6.85620			0.781336
$78$	−7.46820	−	5.98831i	−0.845607	−	0.678043i
$79$	−8.05198	−	8.05198i	−0.905918	−	0.905918i	0.0900218	−	0.995940i	$-0.471306\pi$
$79$	−8.05198	−	8.05198i	−0.905918	−	0.905918i	−0.995940	+	0.0900218i	$0.971306\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	−8.14988	+	3.81831i	−0.905542	+	0.424257i
$82$	−6.88832	−	6.88832i	−0.760688	−	0.760688i
$83$			7.15345i			0.785193i	0.919711	+	0.392597i	$0.128423\pi$
$83$			7.15345i			0.785193i	−0.919711	+	0.392597i	$0.871577\pi$
$84$	−5.10314	−	4.09191i	−0.556798	−	0.446464i
$85$		−	1.47733i		−	0.160239i
$86$			8.73898i			0.942348i
$87$	−9.27479	+	1.02000i	−0.994361	+	0.109355i
$88$	1.28375	−	1.28375i	0.136848	−	0.136848i
$89$	−7.47158	−	7.47158i	−0.791985	−	0.791985i	0.189831	−	0.981817i	$-0.439206\pi$
$89$	−7.47158	−	7.47158i	−0.791985	−	0.791985i	−0.981817	+	0.189831i	$0.939206\pi$
$90$	−0.651967	−	2.92830i	−0.0687234	−	0.308670i
$91$	14.7585	+	14.7585i	1.54711	+	1.54711i
$92$	5.79126	+	5.79126i	0.603780	+	0.603780i
$93$	−1.19650	−	10.8797i	−0.124071	−	1.12817i
$94$	−5.36999	+	5.36999i	−0.553872	+	0.553872i
$95$	−1.42964			−0.146678
$96$	−1.72167	+	0.189341i	−0.175717	+	0.0193246i
$97$	3.22614	+	3.22614i	0.327565	+	0.327565i	0.851660	−	0.524095i	$-0.175596\pi$
$97$	3.22614	+	3.22614i	0.327565	+	0.327565i	−0.524095	+	0.851660i	$0.675596\pi$
$98$	5.13495	+	5.13495i	0.518709	+	0.518709i
$99$	1.18364	+	5.31630i	0.118960	+	0.534309i
$100$	1.00000			0.100000
$101$	1.91970			0.191017			0.0955085	−	0.995429i	$-0.469552\pi$
$101$	1.91970			0.191017			0.0955085	+	0.995429i	$0.469552\pi$
$102$	1.60072	−	1.99630i	0.158494	−	0.197663i
$103$	11.1661	−	11.1661i	1.10022	−	1.10022i	0.105842	−	0.994383i	$-0.466246\pi$
$103$	11.1661	−	11.1661i	1.10022	−	1.10022i	0.994383	−	0.105842i	$-0.0337537\pi$
$104$	5.52672			0.541939
$105$	0.715047	+	6.50188i	0.0697815	+	0.634519i
$106$	1.03826	−	1.03826i	0.100844	−	0.100844i
$107$		−	16.4971i		−	1.59484i	−0.603428	−	0.797418i	$-0.706199\pi$
$107$		−	16.4971i		−	1.59484i	0.603428	−	0.797418i	$-0.293801\pi$
$108$	2.29188	−	4.66340i	0.220536	−	0.448736i
$109$	5.92062	+	5.92062i	0.567093	+	0.567093i	0.931313	−	0.364220i	$-0.118664\pi$
$109$	5.92062	+	5.92062i	0.567093	+	0.567093i	−0.364220	+	0.931313i	$0.618664\pi$
$110$	−1.81549			−0.173100
$111$	8.63074	−	6.04238i	0.819193	−	0.573518i
$112$	3.77650			0.356845
$113$	−7.61785	−	7.61785i	−0.716627	−	0.716627i	0.251286	−	0.967913i	$-0.419147\pi$
$113$	−7.61785	−	7.61785i	−0.716627	−	0.716627i	−0.967913	+	0.251286i	$0.919147\pi$
$114$	−1.93185	−	1.54904i	−0.180935	−	0.145081i
$115$		−	8.19007i		−	0.763728i
$116$	3.80924	−	3.80924i	0.353679	−	0.353679i
$117$	−8.89586	+	13.9916i	−0.822423	+	1.29353i
$118$	4.62846			0.426084
$119$	−3.94504	+	3.94504i	−0.361641	+	0.361641i
$120$	1.35129	+	1.08352i	0.123355	+	0.0989114i
$121$	−7.70399			−0.700363
$122$	−0.355798			−0.0322125
$123$	−10.5552	+	13.1637i	−0.951728	+	1.18693i
$124$	4.46840	+	4.46840i	0.401274	+	0.401274i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−6.07869	+	9.56069i	−0.541532	+	0.851734i
$127$	17.1125			1.51849			0.759245	−	0.650805i	$-0.225568\pi$
$127$	17.1125			1.51849			0.759245	+	0.650805i	$0.225568\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	15.0456	−	1.65465i	1.32469	−	0.145684i
$130$	−3.90798	−	3.90798i	−0.342753	−	0.342753i
$131$	3.38184	+	3.38184i	0.295473	+	0.295473i	0.839238	−	0.543765i	$-0.183002\pi$
$131$	3.38184	+	3.38184i	0.295473	+	0.295473i	−0.543765	+	0.839238i	$0.683002\pi$
$132$	−2.45325	−	1.96712i	−0.213528	−	0.171216i
$133$	3.81768	+	3.81768i	0.331035	+	0.331035i
$134$	−1.27220	+	1.27220i	−0.109901	+	0.109901i
$135$	−4.91812	+	1.67692i	−0.423285	+	0.144326i
$136$			1.47733i			0.126680i
$137$		−	4.14104i		−	0.353793i	−0.984229	−	0.176896i	$-0.943394\pi$
$137$		−	4.14104i		−	0.353793i	0.984229	−	0.176896i	$-0.0566057\pi$
$138$	8.87411	−	11.0672i	0.755414	−	0.942099i
$139$			1.38210i			0.117229i	0.998281	+	0.0586143i	$0.0186682\pi$
$139$			1.38210i			0.117229i	−0.998281	+	0.0586143i	$0.981332\pi$
$140$	−2.67039	−	2.67039i	−0.225689	−	0.225689i
$141$	10.2621	+	8.22859i	0.864226	+	0.692972i
$142$	−10.2552	+	10.2552i	−0.860594	+	0.860594i
$143$	7.09491	+	7.09491i	0.593306	+	0.593306i
$144$	0.651967	+	2.92830i	0.0543306	+	0.244025i
$145$	−5.38709			−0.447373
$146$	−5.04862	+	5.04862i	−0.417827	+	0.417827i
$147$	7.86844	−	9.81296i	0.648978	−	0.809359i
$148$	−1.70519	+	5.83886i	−0.140166	+	0.479952i
$149$		−	10.6466i		−	0.872206i	−0.899897	−	0.436103i	$-0.856358\pi$
$149$		−	10.6466i		−	0.872206i	0.899897	−	0.436103i	$-0.143642\pi$
$150$	−0.189341	−	1.72167i	−0.0154597	−	0.140574i
$151$		−	5.50361i		−	0.447877i	−0.974603	−	0.223939i	$-0.928108\pi$
$151$		−	5.50361i		−	0.447877i	0.974603	−	0.223939i	$-0.0718915\pi$
$152$	1.42964			0.115959
$153$	−3.74005	−	2.37792i	−0.302365	−	0.192244i
$154$	4.84806	+	4.84806i	0.390668	+	0.390668i
$155$		−	6.31927i		−	0.507576i
$156$	−1.04644	−	9.51519i	−0.0837820	−	0.761825i
$157$	−12.5462			−1.00130			−0.500649	−	0.865650i	$-0.666905\pi$
$157$	−12.5462			−1.00130			−0.500649	+	0.865650i	$0.666905\pi$
$158$		−	11.3872i		−	0.905918i
$159$	−1.98412	−	1.59095i	−0.157351	−	0.126171i
$160$	−1.00000			−0.0790569
$161$	−21.8707	+	21.8707i	−1.72365	+	1.72365i
$162$	−8.46279	−	3.06288i	−0.664899	−	0.240643i
$163$	15.7971	−	15.7971i	1.23732	−	1.23732i	0.276233	−	0.961091i	$-0.410914\pi$
$163$	15.7971	−	15.7971i	1.23732	−	1.23732i	0.961091	−	0.276233i	$-0.0890863\pi$
$164$		−	9.74155i		−	0.760688i
$165$	0.343748	+	3.12568i	0.0267607	+	0.243334i
$166$	−5.05825	+	5.05825i	−0.392597	+	0.392597i
$167$	−1.29474	+	1.29474i	−0.100190	+	0.100190i	−0.755425	−	0.655235i	$-0.772570\pi$
$167$	−1.29474	+	1.29474i	−0.100190	+	0.100190i	0.655235	+	0.755425i	$0.272570\pi$
$168$	−0.715047	−	6.50188i	−0.0551671	−	0.501631i
$169$			17.5446i			1.34959i
$170$	1.04463	−	1.04463i	0.0801194	−	0.0801194i
$171$	−2.30116	+	3.61932i	−0.175974	+	0.276776i
$172$	−6.17939	+	6.17939i	−0.471174	+	0.471174i
$173$	−2.17732			−0.165538			−0.0827691	−	0.996569i	$-0.526376\pi$
$173$	−2.17732			−0.165538			−0.0827691	+	0.996569i	$0.526376\pi$
$174$	−7.27951	−	5.83702i	−0.551858	−	0.442503i
$175$			3.77650i			0.285476i
$176$	1.81549			0.136848
$177$	−0.876360	−	7.96869i	−0.0658712	−	0.598963i
$178$		−	10.5664i		−	0.791985i
$179$	−1.96418	−	1.96418i	−0.146810	−	0.146810i	0.629881	−	0.776691i	$-0.283103\pi$
$179$	−1.96418	−	1.96418i	−0.146810	−	0.146810i	−0.776691	+	0.629881i	$0.783103\pi$
$180$	1.60961	−	2.53163i	0.119973	−	0.188697i
$181$	21.1962			1.57550			0.787749	−	0.615997i	$-0.211247\pi$
$181$	21.1962			1.57550			0.787749	+	0.615997i	$0.211247\pi$
$182$			20.8716i			1.54711i
$183$	0.0673674	+	0.612567i	0.00497994	+	0.0452823i
$184$			8.19007i			0.603780i
$185$	5.33445	−	2.92295i	0.392197	−	0.214899i
$186$	6.84706	−	8.53917i	0.502051	−	0.626122i
$187$	−1.89651	+	1.89651i	−0.138687	+	0.138687i
$188$	−7.59431			−0.553872
$189$	17.6113	+	8.65526i	1.28103	+	0.629577i
$190$	−1.01091	−	1.01091i	−0.0733389	−	0.0733389i
$191$	17.7208	−	17.7208i	1.28223	−	1.28223i	0.342832	−	0.939397i	$-0.388614\pi$
$191$	17.7208	−	17.7208i	1.28223	−	1.28223i	0.939397	−	0.342832i	$-0.111386\pi$
$192$	−1.35129	−	1.08352i	−0.0975209	−	0.0781963i
$193$	13.8252	+	13.8252i	0.995162	+	0.995162i	0.999988	−	0.00482599i	$-0.00153616\pi$
$193$	13.8252	+	13.8252i	0.995162	+	0.995162i	−0.00482599	+	0.999988i	$0.501536\pi$
$194$			4.56246i			0.327565i
$195$	−5.98831	+	7.46820i	−0.428832	+	0.534809i
$196$			7.26192i			0.518709i
$197$		−	14.5766i		−	1.03854i	−0.854610	−	0.519271i	$-0.826204\pi$
$197$		−	14.5766i		−	1.03854i	0.854610	−	0.519271i	$-0.173796\pi$
$198$	−2.92223	+	4.59615i	−0.207674	+	0.326635i
$199$	−5.37468	+	5.37468i	−0.381001	+	0.381001i	−0.871463	−	0.490462i	$-0.836828\pi$
$199$	−5.37468	+	5.37468i	−0.381001	+	0.381001i	0.490462	+	0.871463i	$0.336828\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	2.43118	+	1.94942i	0.171482	+	0.137502i
$202$	1.35743	+	1.35743i	0.0955085	+	0.0955085i
$203$	14.3856	+	14.3856i	1.00967	+	1.00967i
$204$	2.54347	−	0.279720i	0.178079	−	0.0195843i
$205$	−6.88832	+	6.88832i	−0.481101	+	0.481101i
$206$	15.7912			1.10022
$207$	−20.7342	−	13.1828i	−1.44113	−	0.916270i
$208$	3.90798	+	3.90798i	0.270970	+	0.270970i
$209$	1.83529	+	1.83529i	0.126950	+	0.126950i
$210$	−4.09191	+	5.10314i	−0.282369	+	0.352150i
$211$	−9.97747			−0.686877			−0.343439	−	0.939175i	$-0.611592\pi$
$211$	−9.97747			−0.686877			−0.343439	+	0.939175i	$0.611592\pi$
$212$	1.46832			0.100844
$213$	19.5977	+	15.7143i	1.34281	+	1.07672i
$214$	11.6652	−	11.6652i	0.797418	−	0.797418i
$215$	8.73898			0.595993
$216$	4.91812	−	1.67692i	0.334636	−	0.114100i
$217$	−16.8749	+	16.8749i	−1.14554	+	1.14554i
$218$			8.37303i			0.567093i
$219$	9.64797	+	7.73615i	0.651950	+	0.522760i
$220$	−1.28375	−	1.28375i	−0.0865502	−	0.0865502i
$221$	−8.16478			−0.549222
$222$	10.3755	+	1.83024i	0.696355	+	0.122838i
$223$	15.2765			1.02299			0.511493	−	0.859287i	$-0.329092\pi$
$223$	15.2765			1.02299			0.511493	+	0.859287i	$0.329092\pi$
$224$	2.67039	+	2.67039i	0.178423	+	0.178423i
$225$	−2.92830	+	0.651967i	−0.195220	+	0.0434645i
$226$		−	10.7733i		−	0.716627i
$227$	−0.894036	+	0.894036i	−0.0593392	+	0.0593392i	−0.736154	−	0.676814i	$-0.763360\pi$
$227$	−0.894036	+	0.894036i	−0.0593392	+	0.0593392i	0.676814	+	0.736154i	$0.263360\pi$
$228$	−0.270690	−	2.46137i	−0.0179269	−	0.163008i
$229$	−22.6190			−1.49471			−0.747354	−	0.664426i	$-0.768676\pi$
$229$	−22.6190			−1.49471			−0.747354	+	0.664426i	$0.768676\pi$
$230$	5.79126	−	5.79126i	0.381864	−	0.381864i
$231$	7.42883	−	9.26471i	0.488781	−	0.609573i
$232$	5.38709			0.353679
$233$	2.55770			0.167561			0.0837804	−	0.996484i	$-0.473301\pi$
$233$	2.55770			0.167561			0.0837804	+	0.996484i	$0.473301\pi$
$234$	−16.1839	+	3.60324i	−1.05797	+	0.235551i
$235$	5.36999	+	5.36999i	0.350299	+	0.350299i
$236$	3.27282	+	3.27282i	0.213042	+	0.213042i
$237$	−19.6050	+	2.15607i	−1.27348	+	0.140052i
$238$	−5.57912			−0.361641
$239$	20.5707	−	20.5707i	1.33061	−	1.33061i	0.425785	−	0.904825i	$-0.359998\pi$
$239$	20.5707	−	20.5707i	1.33061	−	1.33061i	0.904825	−	0.425785i	$-0.140002\pi$
$240$	0.189341	+	1.72167i	0.0122219	+	0.111133i
$241$	4.22260	+	4.22260i	0.272001	+	0.272001i	0.829905	−	0.557904i	$-0.188394\pi$
$241$	4.22260	+	4.22260i	0.272001	+	0.272001i	−0.557904	+	0.829905i	$0.688394\pi$
$242$	−5.44754	−	5.44754i	−0.350181	−	0.350181i
$243$	−3.67091	+	15.1501i	−0.235489	+	0.971877i
$244$	−0.251587	−	0.251587i	−0.0161062	−	0.0161062i
$245$	5.13495	−	5.13495i	0.328060	−	0.328060i
$246$	−16.7717	+	1.84448i	−1.06933	+	0.117600i
$247$			7.90121i			0.502742i
$248$			6.31927i			0.401274i
$249$	9.66638	+	7.75091i	0.612582	+	0.491194i
$250$		−	1.00000i		−	0.0632456i
$251$	−16.0961	−	16.0961i	−1.01597	−	1.01597i	−0.999870	−	0.0161034i	$-0.994874\pi$
$251$	−16.0961	−	16.0961i	−1.01597	−	1.01597i	−0.0161034	−	0.999870i	$-0.505126\pi$
$252$	−11.0587	+	2.46215i	−0.696633	+	0.155101i
$253$	−10.5140	+	10.5140i	−0.661008	+	0.661008i
$254$	12.1004	+	12.1004i	0.759245	+	0.759245i
$255$	−1.99630	−	1.60072i	−0.125013	−	0.100241i
$256$	1.00000			0.0625000
$257$	−1.47800	+	1.47800i	−0.0921953	+	0.0921953i	−0.751700	−	0.659505i	$-0.770766\pi$
$257$	−1.47800	+	1.47800i	−0.0921953	+	0.0921953i	0.659505	+	0.751700i	$0.270766\pi$
$258$	11.8089	+	9.46886i	0.735189	+	0.589505i
$259$	−22.0504	−	6.43965i	−1.37015	−	0.400140i
$260$		−	5.52672i		−	0.342753i
$261$	−8.67111	+	13.6381i	−0.536728	+	0.844178i
$262$			4.78265i			0.295473i
$263$	−10.6468			−0.656507			−0.328253	−	0.944590i	$-0.606460\pi$
$263$	−10.6468			−0.656507			−0.328253	+	0.944590i	$0.606460\pi$
$264$	−0.343748	−	3.12568i	−0.0211562	−	0.192372i
$265$	−1.03826	−	1.03826i	−0.0637796	−	0.0637796i
$266$			5.39902i			0.331035i
$267$	−18.1919	+	2.00066i	−1.11332	+	0.122438i
$268$	−1.79916			−0.109901
$269$		−	5.61239i		−	0.342194i	−0.985254	−	0.171097i	$-0.945269\pi$
$269$		−	5.61239i		−	0.342194i	0.985254	−	0.171097i	$-0.0547311\pi$
$270$	−4.66340	−	2.29188i	−0.283806	−	0.139479i
$271$	21.9439			1.33300			0.666499	−	0.745506i	$-0.267792\pi$
$271$	21.9439			1.33300			0.666499	+	0.745506i	$0.267792\pi$
$272$	−1.04463	+	1.04463i	−0.0633399	+	0.0633399i
$273$	35.9341	−	3.95187i	2.17483	−	0.239178i
$274$	2.92815	−	2.92815i	0.176896	−	0.176896i
$275$			1.81549i			0.109478i
$276$	14.1006	−	1.55072i	0.848757	−	0.0933424i
$277$	9.61698	−	9.61698i	0.577829	−	0.577829i	−0.356476	−	0.934305i	$-0.616022\pi$
$277$	9.61698	−	9.61698i	0.577829	−	0.577829i	0.934305	+	0.356476i	$0.116022\pi$
$278$	−0.977295	+	0.977295i	−0.0586143	+	0.0586143i
$279$	−15.9981	−	10.1716i	−0.957779	−	0.608956i
$280$		−	3.77650i		−	0.225689i
$281$	0.242604	−	0.242604i	0.0144726	−	0.0144726i	−0.699833	−	0.714306i	$-0.746742\pi$
$281$	0.242604	−	0.242604i	0.0144726	−	0.0144726i	0.714306	+	0.699833i	$0.246742\pi$
$282$	1.43792	+	13.0749i	0.0856268	+	0.778599i
$283$	−16.6943	+	16.6943i	−0.992374	+	0.992374i	−0.999971	−	0.00759709i	$-0.997582\pi$
$283$	−16.6943	+	16.6943i	−0.992374	+	0.992374i	0.00759709	+	0.999971i	$0.497582\pi$
$284$	−14.5030			−0.860594
$285$	−1.54904	+	1.93185i	−0.0917573	+	0.114433i
$286$			10.0337i			0.593306i
$287$	36.7889			2.17158
$288$	−1.60961	+	2.53163i	−0.0948472	+	0.149178i
$289$			14.8175i			0.871618i
$290$	−3.80924	−	3.80924i	−0.223687	−	0.223687i
$291$	7.85505	−	0.863862i	0.460471	−	0.0506405i
$292$	−7.13983			−0.417827
$293$			26.8829i			1.57051i	0.619170	+	0.785257i	$0.287469\pi$
$293$			26.8829i			1.57051i	−0.619170	+	0.785257i	$0.712531\pi$
$294$	12.5026	−	1.37498i	0.729169	−	0.0801906i
$295$		−	4.62846i		−	0.269479i
$296$	−5.33445	+	2.92295i	−0.310059	+	0.169893i
$297$	8.46636	+	4.16088i	0.491268	+	0.241439i
$298$	7.52830	−	7.52830i	0.436103	−	0.436103i
$299$	−45.2642			−2.61770
$300$	1.08352	−	1.35129i	0.0625571	−	0.0780167i
$301$	−23.3364	−	23.3364i	−1.34509	−	1.34509i
$302$	3.89164	−	3.89164i	0.223939	−	0.223939i
$303$	2.08003	−	2.59407i	0.119495	−	0.149025i
$304$	1.01091	+	1.01091i	0.0579795	+	0.0579795i
$305$			0.355798i			0.0203729i
$306$	−0.963170	−	4.32606i	−0.0550608	−	0.247304i
$307$			26.7254i			1.52530i	0.646812	+	0.762649i	$0.276102\pi$
$307$			26.7254i			1.52530i	−0.646812	+	0.762649i	$0.723898\pi$
$308$			6.85620i			0.390668i
$309$	−2.98993	−	27.1872i	−0.170091	−	1.54663i
$310$	4.46840	−	4.46840i	0.253788	−	0.253788i
$311$	3.11089	+	3.11089i	0.176403	+	0.176403i	0.789786	−	0.613383i	$-0.210192\pi$
$311$	3.11089	+	3.11089i	0.176403	+	0.176403i	−0.613383	+	0.789786i	$0.710192\pi$
$312$	5.98831	−	7.46820i	0.339021	−	0.422803i
$313$	1.42025	+	1.42025i	0.0802770	+	0.0802770i	0.746105	−	0.665828i	$-0.231922\pi$
$313$	1.42025	+	1.42025i	0.0802770	+	0.0802770i	−0.665828	+	0.746105i	$0.731922\pi$
$314$	−8.87153	−	8.87153i	−0.500649	−	0.500649i
$315$	9.56069	+	6.07869i	0.538684	+	0.342495i
$316$	8.05198	−	8.05198i	0.452959	−	0.452959i
$317$	1.15291			0.0647537			0.0323768	−	0.999476i	$-0.489692\pi$
$317$	1.15291			0.0647537			0.0323768	+	0.999476i	$0.489692\pi$
$318$	−0.278013	−	2.52796i	−0.0155902	−	0.141761i
$319$	6.91565	+	6.91565i	0.387202	+	0.387202i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	−22.2924	−	17.8749i	−1.24424	−	0.997682i
$322$	−30.9298			−1.72365
$323$	−2.11204			−0.117517
$324$	−3.81831	−	8.14988i	−0.212128	−	0.452771i
$325$	−3.90798	+	3.90798i	−0.216776	+	0.216776i
$326$	22.3405			1.23732
$327$	14.4156	−	1.58536i	0.797184	−	0.0876707i
$328$	6.88832	−	6.88832i	0.380344	−	0.380344i
$329$		−	28.6799i		−	1.58117i
$330$	−1.96712	+	2.45325i	−0.108287	+	0.135047i
$331$	−20.7988	−	20.7988i	−1.14321	−	1.14321i	−0.987860	−	0.155348i	$-0.950350\pi$
$331$	−20.7988	−	20.7988i	−1.14321	−	1.14321i	−0.155348	−	0.987860i	$-0.549650\pi$
$332$	−7.15345			−0.392597
$333$	1.18657	−	18.2097i	0.0650234	−	0.997884i
$334$	−1.83104			−0.100190
$335$	1.27220	+	1.27220i	0.0695075	+	0.0695075i
$336$	4.09191	−	5.10314i	0.223232	−	0.278399i
$337$		−	30.6964i		−	1.67214i	−0.548625	−	0.836069i	$-0.684848\pi$
$337$		−	30.6964i		−	1.67214i	0.548625	−	0.836069i	$-0.315152\pi$
$338$	−12.4059	+	12.4059i	−0.674793	+	0.674793i
$339$	−18.5480	+	2.03983i	−1.00739	+	0.110788i
$340$	1.47733			0.0801194
$341$	−8.11234	+	8.11234i	−0.439308	+	0.439308i
$342$	−4.18641	+	0.932077i	−0.226375	+	0.0504010i
$343$	−0.989146			−0.0534088
$344$	−8.73898			−0.471174
$345$	−11.0672	−	8.87411i	−0.595836	−	0.477766i
$346$	−1.53960	−	1.53960i	−0.0827691	−	0.0827691i
$347$	9.91190	+	9.91190i	0.532099	+	0.532099i	0.921196	−	0.389098i	$-0.127213\pi$
$347$	9.91190	+	9.91190i	0.532099	+	0.532099i	−0.389098	+	0.921196i	$0.627213\pi$
$348$	−1.02000	−	9.27479i	−0.0546777	−	0.497181i
$349$	−2.62293			−0.140402			−0.0702011	−	0.997533i	$-0.522364\pi$
$349$	−2.62293			−0.140402			−0.0702011	+	0.997533i	$0.522364\pi$
$350$	−2.67039	+	2.67039i	−0.142738	+	0.142738i
$351$	9.26788	+	27.1811i	0.494683	+	1.45082i
$352$	1.28375	+	1.28375i	0.0684239	+	0.0684239i
$353$	−22.8322	−	22.8322i	−1.21523	−	1.21523i	−0.969282	−	0.245950i	$-0.920900\pi$
$353$	−22.8322	−	22.8322i	−1.21523	−	1.21523i	−0.245950	−	0.969282i	$-0.579100\pi$
$354$	5.01503	−	6.25439i	0.266546	−	0.332417i
$355$	10.2552	+	10.2552i	0.544287	+	0.544287i
$356$	7.47158	−	7.47158i	0.395993	−	0.395993i
$357$	1.05636	+	9.60541i	0.0559085	+	0.508372i
$358$		−	2.77777i		−	0.146810i
$359$			6.29555i			0.332266i	0.986103	+	0.166133i	$0.0531282\pi$
$359$			6.29555i			0.332266i	−0.986103	+	0.166133i	$0.946872\pi$
$360$	2.92830	−	0.651967i	0.154335	−	0.0343617i
$361$		−	16.9561i		−	0.892428i
$362$	14.9879	+	14.9879i	0.787749	+	0.787749i
$363$	−8.34743	+	10.4103i	−0.438126	+	0.546400i
$364$	−14.7585	+	14.7585i	−0.773554	+	0.773554i
$365$	5.04862	+	5.04862i	0.264257	+	0.264257i
$366$	−0.385515	+	0.480787i	−0.0201512	+	0.0251311i
$367$	31.6625			1.65277			0.826386	−	0.563105i	$-0.190393\pi$
$367$	31.6625			1.65277			0.826386	+	0.563105i	$0.190393\pi$
$368$	−5.79126	+	5.79126i	−0.301890	+	0.301890i
$369$	6.35118	+	28.5262i	0.330629	+	1.48501i
$370$	5.83886	+	1.70519i	0.303548	+	0.0886487i
$371$			5.54509i			0.287887i
$372$	10.8797	−	1.19650i	0.564086	−	0.0620357i
$373$			9.39721i			0.486569i	0.969955	+	0.243284i	$0.0782248\pi$
$373$			9.39721i			0.486569i	−0.969955	+	0.243284i	$0.921775\pi$
$374$	−2.68208			−0.138687
$375$	−1.72167	+	0.189341i	−0.0889067	+	0.00977755i
$376$	−5.36999	−	5.36999i	−0.276936	−	0.276936i
$377$			29.7729i			1.53338i
$378$	6.33289	+	18.5733i	0.325729	+	0.955306i
$379$	−10.9284			−0.561354			−0.280677	−	0.959802i	$-0.590559\pi$
$379$	−10.9284			−0.561354			−0.280677	+	0.959802i	$0.590559\pi$
$380$		−	1.42964i		−	0.0733389i
$381$	18.5418	−	23.1240i	0.949923	−	1.18468i
$382$	25.0609			1.28223
$383$	−4.41045	+	4.41045i	−0.225363	+	0.225363i	−0.810752	−	0.585389i	$-0.800942\pi$
$383$	−4.41045	+	4.41045i	−0.225363	+	0.225363i	0.585389	+	0.810752i	$0.300942\pi$
$384$	−0.189341	−	1.72167i	−0.00966229	−	0.0878586i
$385$	4.84806	−	4.84806i	0.247080	−	0.247080i
$386$			19.5518i			0.995162i
$387$	14.0663	−	22.1239i	0.715032	−	1.12462i
$388$	−3.22614	+	3.22614i	−0.163783	+	0.163783i
$389$	−6.54945	+	6.54945i	−0.332071	+	0.332071i	−0.853372	−	0.521302i	$-0.825447\pi$
$389$	−6.54945	+	6.54945i	−0.332071	+	0.332071i	0.521302	+	0.853372i	$0.325447\pi$
$390$	−9.51519	+	1.04644i	−0.481820	+	0.0529884i
$391$		−	12.0994i		−	0.611894i
$392$	−5.13495	+	5.13495i	−0.259354	+	0.259354i
$393$	8.23415	−	0.905554i	0.415358	−	0.0456792i
$394$	10.3072	−	10.3072i	0.519271	−	0.519271i
$395$	−11.3872			−0.572953
$396$	−5.31630	+	1.18364i	−0.267154	+	0.0594802i
$397$		−	17.8138i		−	0.894049i	−0.894522	−	0.447024i	$-0.852484\pi$
$397$		−	17.8138i		−	0.894049i	0.894522	−	0.447024i	$-0.147516\pi$
$398$	−7.60095			−0.381001
$399$	9.29534	−	1.02226i	0.465349	−	0.0511769i
$400$			1.00000i			0.0500000i
$401$	15.1233	+	15.1233i	0.755220	+	0.755220i	0.975448	−	0.220229i	$-0.0706803\pi$
$401$	15.1233	+	15.1233i	0.755220	+	0.755220i	−0.220229	+	0.975448i	$0.570680\pi$
$402$	0.340655	+	3.09756i	0.0169903	+	0.154492i
$403$	−34.9248			−1.73973
$404$			1.91970i			0.0955085i
$405$	−3.06288	+	8.46279i	−0.152196	+	0.420519i
$406$			20.3443i			1.00967i
$407$	−10.6004	−	3.09576i	−0.525443	−	0.153451i
$408$	1.99630	+	1.60072i	0.0988315	+	0.0792472i
$409$	−17.1329	+	17.1329i	−0.847169	+	0.847169i	−0.989779	−	0.142610i	$-0.954451\pi$
$409$	−17.1329	+	17.1329i	−0.847169	+	0.847169i	0.142610	+	0.989779i	$0.454451\pi$
$410$	−9.74155			−0.481101
$411$	−5.59574	−	4.48690i	−0.276017	−	0.221322i
$412$	11.1661	+	11.1661i	0.550112	+	0.550112i
$413$	−12.3598	+	12.3598i	−0.608185	+	0.608185i
$414$	−5.33966	−	23.9830i	−0.262430	−	1.17870i
$415$	5.05825	+	5.05825i	0.248300	+	0.248300i
$416$			5.52672i			0.270970i
$417$	1.86762	+	1.49754i	0.0914579	+	0.0733347i
$418$			2.59550i			0.126950i
$419$		−	2.98599i		−	0.145875i	−0.997337	−	0.0729375i	$-0.976763\pi$
$419$		−	2.98599i		−	0.145875i	0.997337	−	0.0729375i	$-0.0232374\pi$
$420$	−6.50188	+	0.715047i	−0.317259	+	0.0348907i
$421$	22.4754	−	22.4754i	1.09538	−	1.09538i	0.100440	−	0.994943i	$-0.467975\pi$
$421$	22.4754	−	22.4754i	1.09538	−	1.09538i	0.994943	−	0.100440i	$-0.0320251\pi$
$422$	−7.05514	−	7.05514i	−0.343439	−	0.343439i
$423$	22.2384	−	4.95124i	1.08127	−	0.240738i
$424$	1.03826	+	1.03826i	0.0504222	+	0.0504222i
$425$	−1.04463	−	1.04463i	−0.0506719	−	0.0506719i
$426$	2.74602	+	24.9694i	0.133045	+	1.20977i
$427$	0.950119	−	0.950119i	0.0459795	−	0.0459795i
$428$	16.4971			0.797418
$429$	17.2747	−	1.89980i	0.834033	−	0.0917231i
$430$	6.17939	+	6.17939i	0.297997	+	0.297997i
$431$	−3.42819	−	3.42819i	−0.165130	−	0.165130i	0.619705	−	0.784835i	$-0.287252\pi$
$431$	−3.42819	−	3.42819i	−0.165130	−	0.165130i	−0.784835	+	0.619705i	$0.787252\pi$
$432$	4.66340	+	2.29188i	0.224368	+	0.110268i
$433$	−5.54788			−0.266614			−0.133307	−	0.991075i	$-0.542560\pi$
$433$	−5.54788			−0.266614			−0.133307	+	0.991075i	$0.542560\pi$
$434$	−23.8647			−1.14554
$435$	−5.83702	+	7.27951i	−0.279864	+	0.349026i
$436$	−5.92062	+	5.92062i	−0.283546	+	0.283546i
$437$	−11.7088			−0.560110
$438$	1.35187	+	12.2924i	0.0645946	+	0.587355i
$439$	−19.5185	+	19.5185i	−0.931565	+	0.931565i	−0.997804	−	0.0662388i	$-0.978900\pi$
$439$	−19.5185	+	19.5185i	−0.931565	+	0.931565i	0.0662388	+	0.997804i	$0.478900\pi$
$440$		−	1.81549i		−	0.0865502i
$441$	−4.73454	−	21.2651i	−0.225454	−	1.01262i
$442$	−5.77337	−	5.77337i	−0.274611	−	0.274611i
$443$	34.0155			1.61612			0.808062	−	0.589098i	$-0.200517\pi$
$443$	34.0155			1.61612			0.808062	+	0.589098i	$0.200517\pi$
$444$	6.04238	+	8.63074i	0.286759	+	0.409597i
$445$	−10.5664			−0.500896
$446$	10.8021	+	10.8021i	0.511493	+	0.511493i
$447$	−14.3867	−	11.5358i	−0.680467	−	0.545626i
$448$			3.77650i			0.178423i
$449$	−13.9432	+	13.9432i	−0.658020	+	0.658020i	−0.954911	−	0.296891i	$-0.904050\pi$
$449$	−13.9432	+	13.9432i	−0.658020	+	0.658020i	0.296891	+	0.954911i	$0.404050\pi$
$450$	−2.53163	−	1.60961i	−0.119342	−	0.0758777i
$451$	17.6857			0.832788
$452$	7.61785	−	7.61785i	0.358314	−	0.358314i
$453$	−7.43697	−	5.96327i	−0.349419	−	0.280179i
$454$	−1.26436			−0.0593392
$455$	20.8716			0.978477
$456$	1.54904	−	1.93185i	0.0725405	−	0.0904674i
$457$	22.7546	+	22.7546i	1.06442	+	1.06442i	0.997777	+	0.0666382i	$0.0212273\pi$
$457$	22.7546	+	22.7546i	1.06442	+	1.06442i	0.0666382	+	0.997777i	$0.478773\pi$
$458$	−15.9941	−	15.9941i	−0.747354	−	0.747354i
$459$	−7.26568	+	2.47736i	−0.339133	+	0.115633i
$460$	8.19007			0.381864
$461$	19.4728	−	19.4728i	0.906938	−	0.906938i	−0.0890855	−	0.996024i	$-0.528394\pi$
$461$	19.4728	−	19.4728i	0.906938	−	0.906938i	0.996024	+	0.0890855i	$0.0283944\pi$
$462$	11.8041	−	1.29816i	0.549177	−	0.0603960i
$463$	−5.56886	−	5.56886i	−0.258807	−	0.258807i	0.565762	−	0.824569i	$-0.308582\pi$
$463$	−5.56886	−	5.56886i	−0.258807	−	0.258807i	−0.824569	+	0.565762i	$0.808582\pi$
$464$	3.80924	+	3.80924i	0.176840	+	0.176840i
$465$	−8.53917	−	6.84706i	−0.395994	−	0.317525i
$466$	1.80857	+	1.80857i	0.0837804	+	0.0837804i
$467$	2.99722	−	2.99722i	0.138695	−	0.138695i	−0.634351	−	0.773045i	$-0.718732\pi$
$467$	2.99722	−	2.99722i	0.138695	−	0.138695i	0.773045	+	0.634351i	$0.218732\pi$
$468$	−13.9916	−	8.89586i	−0.646763	−	0.411211i
$469$		−	6.79451i		−	0.313741i
$470$			7.59431i			0.350299i
$471$	−13.5941	+	16.9536i	−0.626383	+	0.781181i
$472$			4.62846i			0.213042i
$473$	−11.2186	−	11.2186i	−0.515833	−	0.515833i
$474$	−15.3874	−	12.3383i	−0.706768	−	0.566716i
$475$	−1.01091	+	1.01091i	−0.0463836	+	0.0463836i
$476$	−3.94504	−	3.94504i	−0.180820	−	0.180820i
$477$	−4.29967	+	0.957294i	−0.196868	+	0.0438315i
$478$	29.0914			1.33061
$479$	−4.22623	+	4.22623i	−0.193101	+	0.193101i	−0.797035	−	0.603933i	$-0.793599\pi$
$479$	−4.22623	+	4.22623i	−0.193101	+	0.193101i	0.603933	+	0.797035i	$0.293599\pi$
$480$	−1.08352	+	1.35129i	−0.0494557	+	0.0616777i
$481$	−16.1543	−	29.4820i	−0.736573	−	1.34426i
$482$			5.97165i			0.272001i
$483$	5.85629	+	53.2509i	0.266470	+	2.42300i
$484$		−	7.70399i		−	0.350181i
$485$	4.56246			0.207170
$486$	−13.3084	+	8.11699i	−0.603683	+	0.368194i
$487$	3.09555	+	3.09555i	0.140273	+	0.140273i	0.773756	−	0.633483i	$-0.218376\pi$
$487$	3.09555	+	3.09555i	0.140273	+	0.140273i	−0.633483	+	0.773756i	$0.718376\pi$
$488$		−	0.355798i		−	0.0161062i
$489$	−4.22998	−	38.4629i	−0.191286	−	1.73935i
$490$	7.26192			0.328060
$491$		−	14.1328i		−	0.637804i	−0.947788	−	0.318902i	$-0.896686\pi$
$491$		−	14.1328i		−	0.637804i	0.947788	−	0.318902i	$-0.103314\pi$
$492$	−13.1637	−	10.5552i	−0.593464	−	0.475864i
$493$	−7.95849			−0.358433
$494$	−5.58700	+	5.58700i	−0.251371	+	0.251371i
$495$	4.59615	+	2.92223i	0.206582	+	0.131345i
$496$	−4.46840	+	4.46840i	−0.200637	+	0.200637i
$497$		−	54.7704i		−	2.45679i
$498$	1.35445	+	12.3159i	0.0606941	+	0.551888i
$499$	9.16440	−	9.16440i	0.410255	−	0.410255i	−0.471572	−	0.881827i	$-0.656313\pi$
$499$	9.16440	−	9.16440i	0.410255	−	0.410255i	0.881827	+	0.471572i	$0.156313\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	0.346692	+	3.15245i	0.0154890	+	0.140841i
$502$		−	22.7633i		−	1.01597i
$503$	6.66777	−	6.66777i	0.297301	−	0.297301i	−0.542655	−	0.839956i	$-0.682581\pi$
$503$	6.66777	−	6.66777i	0.297301	−	0.297301i	0.839956	+	0.542655i	$0.182581\pi$
$504$	−9.56069	−	6.07869i	−0.425867	−	0.270766i
$505$	1.35743	−	1.35743i	0.0604049	−	0.0604049i
$506$	−14.8690			−0.661008
$507$	23.7079	+	19.0100i	1.05290	+	0.844262i
$508$			17.1125i			0.759245i
$509$	−7.17963			−0.318232			−0.159116	−	0.987260i	$-0.550864\pi$
$509$	−7.17963			−0.318232			−0.159116	+	0.987260i	$0.550864\pi$
$510$	−0.279720	−	2.54347i	−0.0123862	−	0.112627i
$511$		−	26.9635i		−	1.19280i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.39739	+	7.03113i	0.105847	+	0.310432i
$514$	−2.09021			−0.0921953
$515$		−	15.7912i		−	0.695843i
$516$	1.65465	+	15.0456i	0.0728419	+	0.662347i
$517$		−	13.7874i		−	0.606370i
$518$	−11.0385	−	20.1455i	−0.485004	−	0.885144i
$519$	−2.35917	+	2.94218i	−0.103556	+	0.129148i
$520$	3.90798	−	3.90798i	0.171376	−	0.171376i
$521$	−2.92647			−0.128211			−0.0641056	−	0.997943i	$-0.520419\pi$
$521$	−2.92647			−0.128211			−0.0641056	+	0.997943i	$0.520419\pi$
$522$	−15.7750	+	3.51220i	−0.690453	+	0.153725i
$523$	24.4456	+	24.4456i	1.06893	+	1.06893i	0.997441	+	0.0714897i	$0.0227753\pi$
$523$	24.4456	+	24.4456i	1.06893	+	1.06893i	0.0714897	+	0.997441i	$0.477225\pi$
$524$	−3.38184	+	3.38184i	−0.147737	+	0.147737i
$525$	5.10314	+	4.09191i	0.222719	+	0.178586i
$526$	−7.52839	−	7.52839i	−0.328253	−	0.328253i
$527$		−	9.33564i		−	0.406667i
$528$	1.96712	−	2.45325i	0.0856080	−	0.106764i
$529$		−	44.0773i		−	1.91640i
$530$		−	1.46832i		−	0.0637796i
$531$	−11.7176	−	7.45002i	−0.508499	−	0.323303i
$532$	−3.81768	+	3.81768i	−0.165518	+	0.165518i
$533$	38.0698	+	38.0698i	1.64899	+	1.64899i
$534$	−14.2783	−	11.4489i	−0.617881	−	0.495443i
$535$	−11.6652	−	11.6652i	−0.504331	−	0.504331i
$536$	−1.27220	−	1.27220i	−0.0549505	−	0.0549505i
$537$	−4.78241	+	0.525948i	−0.206376	+	0.0226963i
$538$	3.96856	−	3.96856i	0.171097	−	0.171097i
$539$	−13.1840			−0.567873
$540$	−1.67692	−	4.91812i	−0.0721632	−	0.211642i
$541$	4.39040	+	4.39040i	0.188758	+	0.188758i	0.795159	−	0.606401i	$-0.207387\pi$
$541$	4.39040	+	4.39040i	0.188758	+	0.188758i	−0.606401	+	0.795159i	$0.707387\pi$
$542$	15.5167	+	15.5167i	0.666499	+	0.666499i
$543$	22.9665	−	28.6421i	0.985585	−	1.22915i
$544$	−1.47733			−0.0633399
$545$	8.37303			0.358661
$546$	28.2036	+	22.6148i	1.20700	+	0.967826i
$547$	19.6365	−	19.6365i	0.839596	−	0.839596i	−0.149210	−	0.988806i	$-0.547673\pi$
$547$	19.6365	−	19.6365i	0.839596	−	0.839596i	0.988806	+	0.149210i	$0.0476730\pi$
$548$	4.14104			0.176896
$549$	0.900750	+	0.572696i	0.0384431	+	0.0244421i
$550$	−1.28375	+	1.28375i	−0.0547391	+	0.0547391i
$551$			7.70158i			0.328098i
$552$	11.0672	+	8.87411i	0.471050	+	0.377707i
$553$	30.4083	+	30.4083i	1.29309	+	1.29309i
$554$	13.6005			0.577829
$555$	1.83024	−	10.3755i	0.0776894	−	0.440414i
$556$	−1.38210			−0.0586143
$557$	−18.2860	−	18.2860i	−0.774802	−	0.774802i	0.204139	−	0.978942i	$-0.434560\pi$
$557$	−18.2860	−	18.2860i	−0.774802	−	0.774802i	−0.978942	+	0.204139i	$0.934560\pi$
$558$	−4.11996	−	18.5047i	−0.174412	−	0.783367i
$559$		−	48.2979i		−	2.04278i
$560$	2.67039	−	2.67039i	0.112844	−	0.112844i
$561$	0.507829	+	4.61765i	0.0214405	+	0.194957i
$562$	0.343094			0.0144726
$563$	−18.2223	+	18.2223i	−0.767978	+	0.767978i	−0.977750	−	0.209772i	$-0.932728\pi$
$563$	−18.2223	+	18.2223i	−0.767978	+	0.767978i	0.209772	+	0.977750i	$0.432728\pi$
$564$	−8.22859	+	10.2621i	−0.346486	+	0.432113i
$565$	−10.7733			−0.453235
$566$	−23.6093			−0.992374
$567$	30.7780	−	14.4198i	1.29255	−	0.605576i
$568$	−10.2552	−	10.2552i	−0.430297	−	0.430297i
$569$	−20.9822	−	20.9822i	−0.879619	−	0.879619i	0.113876	−	0.993495i	$-0.463673\pi$
$569$	−20.9822	−	20.9822i	−0.879619	−	0.879619i	−0.993495	+	0.113876i	$0.963673\pi$
$570$	−2.46137	+	0.270690i	−0.103095	+	0.0113379i
$571$	18.1815			0.760873			0.380437	−	0.924807i	$-0.375774\pi$
$571$	18.1815			0.760873			0.380437	+	0.924807i	$0.375774\pi$
$572$	−7.09491	+	7.09491i	−0.296653	+	0.296653i
$573$	−4.74507	−	43.1467i	−0.198228	−	1.80248i
$574$	26.0137	+	26.0137i	1.08579	+	1.08579i
$575$	−5.79126	−	5.79126i	−0.241512	−	0.241512i
$576$	−2.92830	+	0.651967i	−0.122012	+	0.0271653i
$577$	−1.13510	−	1.13510i	−0.0472550	−	0.0472550i	0.683084	−	0.730339i	$-0.260638\pi$
$577$	−1.13510	−	1.13510i	−0.0472550	−	0.0472550i	−0.730339	+	0.683084i	$0.760638\pi$
$578$	−10.4776	+	10.4776i	−0.435809	+	0.435809i
$579$	33.6618	−	3.70197i	1.39894	−	0.153849i
$580$		−	5.38709i		−	0.223687i
$581$		−	27.0150i		−	1.12077i
$582$	6.16520	+	4.94351i	0.255556	+	0.204915i
$583$			2.66571i			0.110403i
$584$	−5.04862	−	5.04862i	−0.208913	−	0.208913i
$585$	3.60324	+	16.1839i	0.148976	+	0.669122i
$586$	−19.0091	+	19.0091i	−0.785257	+	0.785257i
$587$	14.5649	+	14.5649i	0.601156	+	0.601156i	0.940619	−	0.339463i	$-0.110245\pi$
$587$	14.5649	+	14.5649i	0.601156	+	0.601156i	−0.339463	+	0.940619i	$0.610245\pi$
$588$	9.81296	+	7.86844i	0.404680	+	0.324489i
$589$	−9.03427			−0.372251
$590$	3.27282	−	3.27282i	0.134740	−	0.134740i
$591$	−19.6972	−	15.7941i	−0.810236	−	0.649681i
$592$	−5.83886	−	1.70519i	−0.239976	−	0.0700830i
$593$		−	5.14451i		−	0.211260i	−0.994406	−	0.105630i	$-0.966314\pi$
$593$		−	5.14451i		−	0.211260i	0.994406	−	0.105630i	$-0.0336859\pi$
$594$	3.04444	+	8.92881i	0.124915	+	0.366354i
$595$			5.57912i			0.228722i
$596$	10.6466			0.436103
$597$	1.43917	+	13.0863i	0.0589015	+	0.535588i
$598$	−32.0066	−	32.0066i	−1.30885	−	1.30885i
$599$			21.5927i			0.882252i	0.897445	+	0.441126i	$0.145421\pi$
$599$			21.5927i			0.882252i	−0.897445	+	0.441126i	$0.854579\pi$
$600$	1.72167	−	0.189341i	0.0702869	−	0.00772983i
$601$	26.1906			1.06834			0.534168	−	0.845379i	$-0.320625\pi$
$601$	26.1906			1.06834			0.534168	+	0.845379i	$0.320625\pi$
$602$		−	33.0027i		−	1.34509i
$603$	5.26847	−	1.17299i	0.214549	−	0.0477679i
$604$	5.50361			0.223939
$605$	−5.44754	+	5.44754i	−0.221474	+	0.221474i
$606$	3.30509	−	0.363478i	0.134260	−	0.0147653i
$607$	−5.21725	+	5.21725i	−0.211761	+	0.211761i	−0.805015	−	0.593254i	$-0.797843\pi$
$607$	−5.21725	+	5.21725i	−0.211761	+	0.211761i	0.593254	+	0.805015i	$0.297843\pi$
$608$			1.42964i			0.0579795i
$609$	35.0262	−	3.85202i	1.41933	−	0.156092i
$610$	−0.251587	+	0.251587i	−0.0101865	+	0.0101865i
$611$	29.6784	−	29.6784i	1.20066	−	1.20066i
$612$	2.37792	−	3.74005i	0.0961218	−	0.151183i
$613$		−	23.3868i		−	0.944582i	−0.881443	−	0.472291i	$-0.843427\pi$
$613$		−	23.3868i		−	0.944582i	0.881443	−	0.472291i	$-0.156573\pi$
$614$	−18.8977	+	18.8977i	−0.762649	+	0.762649i
$615$	1.84448	+	16.7717i	0.0743766	+	0.676302i
$616$	−4.84806	+	4.84806i	−0.195334	+	0.195334i
$617$	17.0385			0.685946			0.342973	−	0.939345i	$-0.388566\pi$
$617$	17.0385			0.685946			0.342973	+	0.939345i	$0.388566\pi$
$618$	17.1101	−	21.3385i	0.688268	−	0.858360i
$619$		−	37.2757i		−	1.49824i	−0.662435	−	0.749119i	$-0.730477\pi$
$619$		−	37.2757i		−	1.49824i	0.662435	−	0.749119i	$-0.269523\pi$
$620$	6.31927			0.253788
$621$	−40.2798	+	13.7341i	−1.61637	+	0.551131i
$622$			4.39947i			0.176403i
$623$	28.2164	+	28.2164i	1.13047	+	1.13047i
$624$	9.51519	−	1.04644i	0.380912	−	0.0418910i
$625$	−1.00000			−0.0400000
$626$			2.00853i			0.0802770i
$627$	4.46859	−	0.491435i	0.178458	−	0.0196260i
$628$		−	12.5462i		−	0.500649i
$629$	7.88074	−	4.31815i	0.314226	−	0.172176i
$630$	2.46215	+	11.0587i	0.0980945	+	0.440590i
$631$	16.9809	−	16.9809i	0.676000	−	0.676000i	−0.283093	−	0.959093i	$-0.591360\pi$
$631$	16.9809	−	16.9809i	0.676000	−	0.676000i	0.959093	+	0.283093i	$0.0913604\pi$
$632$	11.3872			0.452959
$633$	−10.8108	+	13.4825i	−0.429690	+	0.535879i
$634$	0.815228	+	0.815228i	0.0323768	+	0.0323768i
$635$	12.1004	−	12.1004i	0.480189	−	0.480189i
$636$	1.59095	−	1.98412i	0.0630853	−	0.0786755i
$637$	−28.3794	−	28.3794i	−1.12443	−	1.12443i
$638$			9.78021i			0.387202i
$639$	42.4691	−	9.45547i	1.68005	−	0.374053i
$640$		−	1.00000i		−	0.0395285i
$641$		−	15.5373i		−	0.613687i	−0.951760	−	0.306844i	$-0.900727\pi$
$641$		−	15.5373i		−	0.613687i	0.951760	−	0.306844i	$-0.0992729\pi$
$642$	−3.12359	−	28.4026i	−0.123278	−	1.12096i
$643$	17.0643	−	17.0643i	0.672950	−	0.672950i	−0.285445	−	0.958395i	$-0.592141\pi$
$643$	17.0643	−	17.0643i	0.672950	−	0.672950i	0.958395	+	0.285445i	$0.0921414\pi$
$644$	−21.8707	−	21.8707i	−0.861825	−	0.861825i
$645$	9.46886	−	11.8089i	0.372836	−	0.464975i
$646$	−1.49344	−	1.49344i	−0.0587586	−	0.0587586i
$647$	−3.54892	−	3.54892i	−0.139522	−	0.139522i	0.633896	−	0.773418i	$-0.281455\pi$
$647$	−3.54892	−	3.54892i	−0.139522	−	0.139522i	−0.773418	+	0.633896i	$0.781455\pi$
$648$	3.06288	−	8.46279i	0.120321	−	0.332450i
$649$	−5.94177	+	5.94177i	−0.233235	+	0.233235i
$650$	−5.52672			−0.216776
$651$	4.51858	+	41.0872i	0.177097	+	1.61033i
$652$	15.7971	+	15.7971i	0.618662	+	0.618662i
$653$	−23.7536	−	23.7536i	−0.929549	−	0.929549i	0.0681273	−	0.997677i	$-0.478298\pi$
$653$	−23.7536	−	23.7536i	−0.929549	−	0.929549i	−0.997677	+	0.0681273i	$0.978298\pi$
$654$	11.3144	+	9.07234i	0.442427	+	0.354757i
$655$	4.78265			0.186874
$656$	9.74155			0.380344
$657$	20.9075	−	4.65493i	0.815681	−	0.181606i
$658$	20.2797	−	20.2797i	0.790587	−	0.790587i
$659$	−35.4935			−1.38263			−0.691315	−	0.722553i	$-0.742968\pi$
$659$	−35.4935			−1.38263			−0.691315	+	0.722553i	$0.742968\pi$
$660$	−3.12568	+	0.343748i	−0.121667	+	0.0133804i
$661$	0.325551	−	0.325551i	0.0126625	−	0.0126625i	−0.700747	−	0.713410i	$-0.747150\pi$
$661$	0.325551	−	0.325551i	0.0126625	−	0.0126625i	0.713410	+	0.700747i	$0.247150\pi$
$662$		−	29.4140i		−	1.14321i
$663$	−8.84670	+	11.0330i	−0.343578	+	0.428486i
$664$	−5.05825	−	5.05825i	−0.196298	−	0.196298i
$665$	5.39902			0.209365
$666$	13.7152	−	12.0372i	0.531454	−	0.466430i
$667$	−44.1206			−1.70836
$668$	−1.29474	−	1.29474i	−0.0500950	−	0.0500950i
$669$	16.5523	−	20.6429i	0.639951	−	0.798101i
$670$			1.79916i			0.0695075i
$671$	0.456755	−	0.456755i	0.0176328	−	0.0176328i
$672$	6.50188	−	0.715047i	0.250816	−	0.0275836i
$673$	−38.7813			−1.49491			−0.747455	−	0.664312i	$-0.768725\pi$
$673$	−38.7813			−1.49491			−0.747455	+	0.664312i	$0.768725\pi$
$674$	21.7056	−	21.7056i	0.836069	−	0.836069i
$675$	−2.29188	+	4.66340i	−0.0882143	+	0.179494i
$676$	−17.5446			−0.674793
$677$	12.6745			0.487122			0.243561	−	0.969886i	$-0.421684\pi$
$677$	12.6745			0.487122			0.243561	+	0.969886i	$0.421684\pi$
$678$	−14.5578	−	11.6731i	−0.559089	−	0.448301i
$679$	−12.1835	−	12.1835i	−0.467560	−	0.467560i
$680$	1.04463	+	1.04463i	0.0400597	+	0.0400597i
$681$	0.239395	+	2.17681i	0.00917365	+	0.0834154i
$682$	−11.4726			−0.439308
$683$	−14.3090	+	14.3090i	−0.547518	+	0.547518i	−0.925722	−	0.378204i	$-0.876542\pi$
$683$	−14.3090	+	14.3090i	−0.547518	+	0.547518i	0.378204	+	0.925722i	$0.376542\pi$
$684$	−3.61932	−	2.30116i	−0.138388	−	0.0879870i
$685$	−2.92815	−	2.92815i	−0.111879	−	0.111879i
$686$	−0.699432	−	0.699432i	−0.0267044	−	0.0267044i
$687$	−24.5082	+	30.5649i	−0.935045	+	1.16612i
$688$	−6.17939	−	6.17939i	−0.235587	−	0.235587i
$689$	−5.73815	+	5.73815i	−0.218606	+	0.218606i
$690$	−1.55072	−	14.1006i	−0.0590349	−	0.536801i
$691$			40.9622i			1.55827i	0.626854	+	0.779137i	$0.284342\pi$
$691$			40.9622i			1.55827i	−0.626854	+	0.779137i	$0.715658\pi$
$692$		−	2.17732i		−	0.0827691i
$693$	−4.47002	−	20.0770i	−0.169802	−	0.762662i
$694$			14.0175i			0.532099i
$695$	0.977295	+	0.977295i	0.0370709	+	0.0370709i
$696$	5.83702	−	7.27951i	0.221252	−	0.275929i
$697$	−10.1763	+	10.1763i	−0.385455	+	0.385455i
$698$	−1.85469	−	1.85469i	−0.0702011	−	0.0702011i
$699$	2.77132	−	3.45620i	0.104821	−	0.130725i
$700$	−3.77650			−0.142738
$701$	−28.6764	+	28.6764i	−1.08309	+	1.08309i	−0.0868723	+	0.996219i	$0.527687\pi$
$701$	−28.6764	+	28.6764i	−1.08309	+	1.08309i	−0.996219	+	0.0868723i	$0.972313\pi$
$702$	−12.6666	+	25.7733i	−0.478068	+	0.972751i
$703$	−4.17875	−	7.62633i	−0.157605	−	0.287633i
$704$			1.81549i			0.0684239i
$705$	13.0749	−	1.43792i	0.492429	−	0.0541551i
$706$		−	32.2895i		−	1.21523i
$707$	−7.24973			−0.272654
$708$	7.96869	−	0.876360i	0.299482	−	0.0329356i
$709$	18.4451	+	18.4451i	0.692722	+	0.692722i	0.962830	−	0.270108i	$-0.0870594\pi$
$709$	18.4451	+	18.4451i	0.692722	+	0.692722i	−0.270108	+	0.962830i	$0.587059\pi$
$710$			14.5030i			0.544287i
$711$	−18.3290	+	28.8282i	−0.687390	+	1.08114i
$712$	10.5664			0.395993
$713$		−	51.7553i		−	1.93825i
$714$	−6.04509	+	7.53901i	−0.226232	+	0.282140i
$715$	10.0337			0.375240
$716$	1.96418	−	1.96418i	0.0734050	−	0.0734050i
$717$	−5.50821	−	50.0858i	−0.205708	−	1.87049i
$718$	−4.45163	+	4.45163i	−0.166133	+	0.166133i
$719$			48.9218i			1.82448i	0.409660	+	0.912238i	$0.365647\pi$
$719$			48.9218i			1.82448i	−0.409660	+	0.912238i	$0.634353\pi$
$720$	2.53163	+	1.60961i	0.0943483	+	0.0599866i
$721$	−42.1686	+	42.1686i	−1.57044	+	1.57044i
$722$	11.9898	−	11.9898i	0.446214	−	0.446214i
$723$	10.2812	−	1.13068i	0.382363	−	0.0420505i
$724$			21.1962i			0.787749i
$725$	−3.80924	+	3.80924i	−0.141472	+	0.141472i
$726$	−13.2637	+	1.45869i	−0.492263	+	0.0541369i
$727$	−8.85958	+	8.85958i	−0.328584	+	0.328584i	−0.852048	−	0.523464i	$-0.824639\pi$
$727$	−8.85958	+	8.85958i	−0.328584	+	0.328584i	0.523464	+	0.852048i	$0.324639\pi$
$728$	−20.8716			−0.773554
$729$	16.4946	+	21.3759i	0.610912	+	0.791699i
$730$			7.13983i			0.264257i
$731$	12.9103			0.477506
$732$	−0.612567	+	0.0673674i	−0.0226411	+	0.00248997i
$733$			8.30705i			0.306828i	0.988162	+	0.153414i	$0.0490268\pi$
$733$			8.30705i			0.306828i	−0.988162	+	0.153414i	$0.950973\pi$
$734$	22.3888	+	22.3888i	0.826386	+	0.826386i
$735$	−1.37498	−	12.5026i	−0.0507170	−	0.461167i
$736$	−8.19007			−0.301890
$737$		−	3.26636i		−	0.120318i
$738$	−15.6801	+	24.6620i	−0.577193	+	0.907822i
$739$		−	17.1146i		−	0.629569i	−0.949163	−	0.314785i	$-0.898068\pi$
$739$		−	17.1146i		−	0.629569i	0.949163	−	0.314785i	$-0.101932\pi$
$740$	2.92295	+	5.33445i	0.107450	+	0.196098i
$741$	10.6768	+	8.56112i	0.392223	+	0.314501i
$742$	−3.92097	+	3.92097i	−0.143943	+	0.143943i
$743$	12.6952			0.465743			0.232871	−	0.972508i	$-0.425188\pi$
$743$	12.6952			0.465743			0.232871	+	0.972508i	$0.425188\pi$
$744$	8.53917	+	6.84706i	0.313061	+	0.251025i
$745$	−7.52830	−	7.52830i	−0.275816	−	0.275816i
$746$	−6.64483	+	6.64483i	−0.243284	+	0.243284i
$747$	20.9474	−	4.66382i	0.766427	−	0.170640i
$748$	−1.89651	−	1.89651i	−0.0693435	−	0.0693435i
$749$			62.3012i			2.27644i
$750$	−1.35129	−	1.08352i	−0.0493421	−	0.0395646i
$751$			28.7797i			1.05018i	0.851045	+	0.525092i	$0.175969\pi$
$751$			28.7797i			1.05018i	−0.851045	+	0.525092i	$0.824031\pi$
$752$		−	7.59431i		−	0.276936i
$753$	−39.1908	+	4.31003i	−1.42819	+	0.157066i
$754$	−21.0526	+	21.0526i	−0.766691	+	0.766691i
$755$	−3.89164	−	3.89164i	−0.141631	−	0.141631i
$756$	−8.65526	+	17.6113i	−0.314789	+	0.640517i
$757$	−10.1110	−	10.1110i	−0.367489	−	0.367489i	0.499072	−	0.866561i	$-0.333674\pi$
$757$	−10.1110	−	10.1110i	−0.367489	−	0.367489i	−0.866561	+	0.499072i	$0.833674\pi$
$758$	−7.72755	−	7.72755i	−0.280677	−	0.280677i
$759$	2.81532	+	25.5995i	0.102190	+	0.929204i
$760$	1.01091	−	1.01091i	0.0366694	−	0.0366694i
$761$	−47.0638			−1.70606			−0.853031	−	0.521860i	$-0.825238\pi$
$761$	−47.0638			−1.70606			−0.853031	+	0.521860i	$0.825238\pi$
$762$	29.4621	−	3.24011i	1.06730	−	0.117377i
$763$	−22.3592	−	22.3592i	−0.809458	−	0.809458i
$764$	17.7208	+	17.7208i	0.641114	+	0.641114i
$765$	−4.32606	+	0.963170i	−0.156409	+	0.0348235i
$766$	−6.23731			−0.225363
$767$	−25.5802			−0.923648
$768$	1.08352	−	1.35129i	0.0390982	−	0.0487605i
$769$	−5.52401	+	5.52401i	−0.199201	+	0.199201i	−0.799657	−	0.600457i	$-0.794986\pi$
$769$	−5.52401	+	5.52401i	−0.199201	+	0.199201i	0.600457	+	0.799657i	$0.294986\pi$
$770$	6.85620			0.247080
$771$	0.395764	+	3.59866i	0.0142531	+	0.129602i
$772$	−13.8252	+	13.8252i	−0.497581	+	0.497581i
$773$		−	1.33377i		−	0.0479722i	−0.999712	−	0.0239861i	$-0.992364\pi$
$773$		−	1.33377i		−	0.0479722i	0.999712	−	0.0239861i	$-0.00763575\pi$
$774$	25.5903	−	5.69753i	0.919826	−	0.204793i
$775$	−4.46840	−	4.46840i	−0.160510	−	0.160510i
$776$	−4.56246			−0.163783
$777$	−32.5939	+	22.8190i	−1.16930	+	0.818629i
$778$	−9.26233			−0.332071
$779$	9.84780	+	9.84780i	0.352834	+	0.352834i
$780$	−7.46820	−	5.98831i	−0.267404	−	0.214416i
$781$		−	26.3300i		−	0.942163i
$782$	8.55559	−	8.55559i	0.305947	−	0.305947i
$783$	9.03372	+	26.4943i	0.322839	+	0.946831i
$784$	−7.26192			−0.259354
$785$	−8.87153	+	8.87153i	−0.316638	+	0.316638i
$786$	6.46275	+	5.18210i	0.230519	+	0.184839i
$787$	−46.5716			−1.66010			−0.830049	−	0.557690i	$-0.811688\pi$
$787$	−46.5716			−1.66010			−0.830049	+	0.557690i	$0.811688\pi$
$788$	14.5766			0.519271
$789$	−11.5360	+	14.3868i	−0.410691	+	0.512185i
$790$	−8.05198	−	8.05198i	−0.286476	−	0.286476i
$791$	28.7688	+	28.7688i	1.02290	+	1.02290i
$792$	−4.59615	−	2.92223i	−0.163317	−	0.103837i
$793$	1.96640			0.0698288
$794$	12.5963	−	12.5963i	0.447024	−	0.447024i
$795$	−2.52796	+	0.278013i	−0.0896574	+	0.00986011i
$796$	−5.37468	−	5.37468i	−0.190500	−	0.190500i
$797$	−0.503100	−	0.503100i	−0.0178207	−	0.0178207i	0.698140	−	0.715961i	$-0.254011\pi$
$797$	−0.503100	−	0.503100i	−0.0178207	−	0.0178207i	−0.715961	+	0.698140i	$0.754011\pi$
$798$	7.29564	+	5.84995i	0.258263	+	0.207086i
$799$	7.93324	+	7.93324i	0.280658	+	0.280658i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	−17.0078	+	26.7502i	−0.600941	+	0.945173i
$802$			21.3875i			0.755220i
$803$		−	12.9623i		−	0.457429i
$804$	−1.94942	+	2.43118i	−0.0687509	+	0.0857412i
$805$			30.9298i			1.09013i
$806$	−24.6956	−	24.6956i	−0.869865	−	0.869865i
$807$	−7.58397	−	6.08114i	−0.266968	−	0.214066i
$808$	−1.35743	+	1.35743i	−0.0477543	+	0.0477543i
$809$	6.46702	+	6.46702i	0.227368	+	0.227368i	0.811592	−	0.584224i	$-0.198601\pi$
$809$	6.46702	+	6.46702i	0.227368	+	0.227368i	−0.584224	+	0.811592i	$0.698601\pi$
$810$	−8.14988	+	3.81831i	−0.286357	+	0.134162i
$811$	−10.3858			−0.364696			−0.182348	−	0.983234i	$-0.558370\pi$
$811$	−10.3858			−0.364696			−0.182348	+	0.983234i	$0.558370\pi$
$812$	−14.3856	+	14.3856i	−0.504835	+	0.504835i
$813$	23.7767	−	29.6526i	0.833884	−	1.03996i
$814$	−5.30658	−	9.68465i	−0.185996	−	0.339447i
$815$		−	22.3405i		−	0.782552i
$816$	0.279720	+	2.54347i	0.00979214	+	0.0890394i
$817$		−	12.4936i		−	0.437095i
$818$	−24.2296			−0.847169
$819$	33.5952	−	52.8393i	1.17391	−	1.84635i
$820$	−6.88832	−	6.88832i	−0.240551	−	0.240551i
$821$		−	48.2408i		−	1.68361i	−0.539778	−	0.841807i	$-0.681492\pi$
$821$		−	48.2408i		−	1.68361i	0.539778	−	0.841807i	$-0.318508\pi$
$822$	−0.784070	−	7.12950i	−0.0273476	−	0.248670i
$823$	23.2971			0.812086			0.406043	−	0.913854i	$-0.366908\pi$
$823$	23.2971			0.812086			0.406043	+	0.913854i	$0.366908\pi$
$824$			15.7912i			0.550112i
$825$	2.45325	+	1.96712i	0.0854114	+	0.0684864i
$826$	−17.4794			−0.608185
$827$	12.0735	−	12.0735i	0.419837	−	0.419837i	−0.465311	−	0.885147i	$-0.654057\pi$
$827$	12.0735	−	12.0735i	0.419837	−	0.419837i	0.885147	+	0.465311i	$0.154057\pi$
$828$	13.1828	−	20.7342i	0.458135	−	0.720565i
$829$	21.5000	−	21.5000i	0.746726	−	0.746726i	−0.227137	−	0.973863i	$-0.572937\pi$
$829$	21.5000	−	21.5000i	0.746726	−	0.746726i	0.973863	+	0.227137i	$0.0729365\pi$
$830$			7.15345i			0.248300i
$831$	−2.57513	−	23.4155i	−0.0893304	−	0.812276i
$832$	−3.90798	+	3.90798i	−0.135485	+	0.135485i
$833$	7.58601	−	7.58601i	0.262840	−	0.262840i
$834$	0.261690	+	2.37953i	0.00906157	+	0.0823963i
$835$			1.83104i			0.0633657i
$836$	−1.83529	+	1.83529i	−0.0634749	+	0.0634749i
$837$	−31.0790	+	10.5969i	−1.07425	+	0.366283i
$838$	2.11141	−	2.11141i	0.0729375	−	0.0729375i
$839$	−16.3634			−0.564928			−0.282464	−	0.959278i	$-0.591152\pi$
$839$	−16.3634			−0.564928			−0.282464	+	0.959278i	$0.591152\pi$
$840$	−5.10314	−	4.09191i	−0.176075	−	0.141184i
$841$			0.0206861i			0.000713315i
$842$	31.7850			1.09538
$843$	−0.0649620	−	0.590696i	−0.00223741	−	0.0203446i
$844$		−	9.97747i		−	0.343439i
$845$	12.4059	+	12.4059i	0.426777	+	0.426777i
$846$	19.2260	+	12.2239i	0.661003	+	0.420266i
$847$	29.0941			0.999685
$848$			1.46832i			0.0504222i
$849$	4.47023	+	40.6475i	0.153418	+	1.39502i
$850$		−	1.47733i		−	0.0506719i
$851$	43.6896	−	23.9391i	1.49766	−	0.820623i
$852$	−15.7143	+	19.5977i	−0.538362	+	0.671407i
$853$	−16.6880	+	16.6880i	−0.571385	+	0.571385i	−0.932515	−	0.361130i	$-0.882391\pi$
$853$	−16.6880	+	16.6880i	−0.571385	+	0.571385i	0.361130	+	0.932515i	$0.382391\pi$
$854$	1.34367			0.0459795
$855$	0.932077	+	4.18641i	0.0318764	+	0.143172i
$856$	11.6652	+	11.6652i	0.398709	+	0.398709i
$857$	6.77996	−	6.77996i	0.231599	−	0.231599i	−0.581761	−	0.813360i	$-0.697636\pi$
$857$	6.77996	−	6.77996i	0.231599	−	0.231599i	0.813360	+	0.581761i	$0.197636\pi$
$858$	13.5585	+	10.8717i	0.462878	+	0.371155i
$859$	1.71469	+	1.71469i	0.0585046	+	0.0585046i	0.735754	−	0.677249i	$-0.236828\pi$
$859$	1.71469	+	1.71469i	0.0585046	+	0.0585046i	−0.677249	+	0.735754i	$0.736828\pi$
$860$			8.73898i			0.297997i
$861$	39.8616	−	49.7125i	1.35848	−	1.69420i
$862$		−	4.84819i		−	0.165130i
$863$			24.8856i			0.847115i	0.905869	+	0.423558i	$0.139219\pi$
$863$			24.8856i			0.847115i	−0.905869	+	0.423558i	$0.860781\pi$
$864$	1.67692	+	4.91812i	0.0570500	+	0.167318i
$865$	−1.53960	+	1.53960i	−0.0523478	+	0.0523478i
$866$	−3.92294	−	3.92294i	−0.133307	−	0.133307i
$867$	20.0227	+	16.0551i	0.680008	+	0.545259i
$868$	−16.8749	−	16.8749i	−0.572771	−	0.572771i
$869$	14.6183	+	14.6183i	0.495892	+	0.495892i
$870$	−9.27479	+	1.02000i	−0.314445	+	0.0345812i
$871$	7.03107	−	7.03107i	0.238239	−	0.238239i
$872$	−8.37303			−0.283546
$873$	7.34377	−	11.5505i	0.248549	−	0.390924i
$874$	−8.27940	−	8.27940i	−0.280055	−	0.280055i
$875$	2.67039	+	2.67039i	0.0902755	+	0.0902755i
$876$	−7.73615	+	9.64797i	−0.261380	+	0.325975i
$877$	−8.12342			−0.274309			−0.137154	−	0.990550i	$-0.543796\pi$
$877$	−8.12342			−0.274309			−0.137154	+	0.990550i	$0.543796\pi$
$878$	−27.6033			−0.931565
$879$	36.3265	+	29.1281i	1.22526	+	0.982468i
$880$	1.28375	−	1.28375i	0.0432751	−	0.0432751i
$881$	−16.6693			−0.561605			−0.280802	−	0.959766i	$-0.590601\pi$
$881$	−16.6693			−0.561605			−0.280802	+	0.959766i	$0.590601\pi$
$882$	11.6889	−	18.3845i	0.393584	−	0.619039i
$883$	−30.6559	+	30.6559i	−1.03165	+	1.03165i	−0.0321725	+	0.999482i	$0.510243\pi$
$883$	−30.6559	+	30.6559i	−1.03165	+	1.03165i	−0.999482	+	0.0321725i	$0.989757\pi$
$884$		−	8.16478i		−	0.274611i
$885$	−6.25439	−	5.01503i	−0.210239	−	0.168578i
$886$	24.0526	+	24.0526i	0.808062	+	0.808062i
$887$	57.7333			1.93850			0.969248	−	0.246087i	$-0.0791447\pi$
$887$	57.7333			1.93850			0.969248	+	0.246087i	$0.0791447\pi$
$888$	−1.83024	+	10.3755i	−0.0614188	+	0.348178i
$889$	−64.6253			−2.16746
$890$	−7.47158	−	7.47158i	−0.250448	−	0.250448i
$891$	14.7960	−	6.93211i	0.495686	−	0.232235i
$892$			15.2765i			0.511493i
$893$	7.67714	−	7.67714i	0.256906	−	0.256906i
$894$	−2.01585	−	18.3300i	−0.0674201	−	0.613047i
$895$	−2.77777			−0.0928508
$896$	−2.67039	+	2.67039i	−0.0892113	+	0.0892113i
$897$	−49.0447	+	61.1651i	−1.63756	+	2.04224i
$898$	−19.7187			−0.658020
$899$	−34.0425			−1.13538
$900$	−0.651967	−	2.92830i	−0.0217322	−	0.0976100i
$901$	−1.53385	−	1.53385i	−0.0510998	−	0.0510998i
$902$	12.5057	+	12.5057i	0.416394	+	0.416394i
$903$	−56.8198	+	6.24878i	−1.89084	+	0.207946i
$904$	10.7733			0.358314
$905$	14.9879	−	14.9879i	0.498216	−	0.498216i
$906$	−1.04206	−	9.47540i	−0.0346202	−	0.314799i
$907$	15.3616	+	15.3616i	0.510073	+	0.510073i	0.914549	−	0.404476i	$-0.132546\pi$
$907$	15.3616	+	15.3616i	0.510073	+	0.510073i	−0.404476	+	0.914549i	$0.632546\pi$
$908$	−0.894036	−	0.894036i	−0.0296696	−	0.0296696i
$909$	−1.25158	−	5.62145i	−0.0415123	−	0.186452i
$910$	14.7585	+	14.7585i	0.489239	+	0.489239i
$911$	−38.7894	+	38.7894i	−1.28515	+	1.28515i	−0.347452	+	0.937698i	$0.612953\pi$
$911$	−38.7894	+	38.7894i	−1.28515	+	1.28515i	−0.937698	+	0.347452i	$0.887047\pi$
$912$	2.46137	−	0.270690i	0.0815040	−	0.00896343i
$913$		−	12.9870i		−	0.429808i
$914$			32.1799i			1.06442i
$915$	0.480787	+	0.385515i	0.0158943	+	0.0127447i
$916$		−	22.6190i		−	0.747354i
$917$	−12.7715	−	12.7715i	−0.421753	−	0.421753i
$918$	−6.88937	−	3.38585i	−0.227383	−	0.111750i
$919$	−31.3044	+	31.3044i	−1.03264	+	1.03264i	−0.0331880	+	0.999449i	$0.510566\pi$
$919$	−31.3044	+	31.3044i	−1.03264	+	1.03264i	−0.999449	+	0.0331880i	$0.989434\pi$
$920$	5.79126	+	5.79126i	0.190932	+	0.190932i
$921$	36.1137	+	28.9575i	1.18999	+	0.954182i
$922$	27.5387			0.906938
$923$	56.6774	−	56.6774i	1.86556	−	1.86556i
$924$	9.26471	+	7.42883i	0.304786	+	0.244391i
$925$	1.70519	−	5.83886i	0.0560664	−	0.191981i
$926$		−	7.87556i		−	0.258807i
$927$	−39.9775	−	25.4177i	−1.31303	−	0.834826i
$928$			5.38709i			0.176840i
$929$	21.4506			0.703772			0.351886	−	0.936043i	$-0.385540\pi$
$929$	21.4506			0.703772			0.351886	+	0.936043i	$0.385540\pi$
$930$	−1.19650	−	10.8797i	−0.0392348	−	0.356760i
$931$	−7.34112	−	7.34112i	−0.240596	−	0.240596i
$932$			2.55770i			0.0837804i
$933$	7.57443	−	0.833002i	0.247976	−	0.0272713i
$934$	4.23871			0.138695
$935$			2.68208i			0.0877133i
$936$	−3.60324	−	16.1839i	−0.117776	−	0.528987i
$937$	32.1470			1.05020			0.525098	−	0.851042i	$-0.324029\pi$
$937$	32.1470			1.05020			0.525098	+	0.851042i	$0.324029\pi$
$938$	4.80444	−	4.80444i	0.156871	−	0.156871i
$939$	3.45803	−	0.380298i	0.112848	−	0.0124106i
$940$	−5.36999	+	5.36999i	−0.175150	+	0.175150i
$941$		−	5.16763i		−	0.168460i	−0.996446	−	0.0842300i	$-0.973157\pi$
$941$		−	5.16763i		−	0.168460i	0.996446	−	0.0842300i	$-0.0268430\pi$
$942$	−21.6005	+	2.37552i	−0.703782	+	0.0773987i
$943$	−56.4158	+	56.4158i	−1.83715	+	1.83715i
$944$	−3.27282	+	3.27282i	−0.106521	+	0.106521i
$945$	18.5733	−	6.33289i	0.604189	−	0.206009i
$946$		−	15.8655i		−	0.515833i
$947$	5.43912	−	5.43912i	0.176748	−	0.176748i	−0.613189	−	0.789936i	$-0.710114\pi$
$947$	5.43912	−	5.43912i	0.176748	−	0.176748i	0.789936	+	0.613189i	$0.210114\pi$
$948$	−2.15607	−	19.6050i	−0.0700260	−	0.636742i
$949$	27.9023	−	27.9023i	0.905747	−	0.905747i
$950$	−1.42964			−0.0463836
$951$	1.24920	−	1.55791i	0.0405080	−	0.0505187i
$952$		−	5.57912i		−	0.180820i
$953$	−42.6988			−1.38315			−0.691574	−	0.722305i	$-0.743083\pi$
$953$	−42.6988			−1.38315			−0.691574	+	0.722305i	$0.743083\pi$
$954$	−3.71723	−	2.36342i	−0.120350	−	0.0765184i
$955$		−	25.0609i		−	0.810952i
$956$	20.5707	+	20.5707i	0.665305	+	0.665305i
$957$	16.8383	−	1.85180i	0.544305	−	0.0598602i
$958$	−5.97679			−0.193101
$959$			15.6386i			0.504997i
$960$	−1.72167	+	0.189341i	−0.0555667	+	0.00611097i
$961$		−	8.93320i		−	0.288168i
$962$	9.42412	−	32.2698i	0.303846	−	1.04042i
$963$	−48.3085	+	10.7556i	−1.55672	+	0.346594i
$964$	−4.22260	+	4.22260i	−0.136001	+	0.136001i
$965$	19.5518			0.629396
$966$	−33.5130	+	41.7951i	−1.07826	+	1.34473i
$967$	41.8337	+	41.8337i	1.34528	+	1.34528i	0.890710	+	0.454573i	$0.150208\pi$
$967$	41.8337	+	41.8337i	1.34528	+	1.34528i	0.454573	+	0.890710i	$0.349792\pi$
$968$	5.44754	−	5.44754i	0.175091	−	0.175091i
$969$	−2.28844	+	2.85398i	−0.0735154	+	0.0916832i
$970$	3.22614	+	3.22614i	0.103585	+	0.103585i
$971$			24.5843i			0.788948i	0.918907	+	0.394474i	$0.129073\pi$
$971$			24.5843i			0.788948i	−0.918907	+	0.394474i	$0.870927\pi$
$972$	−15.1501	−	3.67091i	−0.485938	−	0.117745i
$973$		−	5.21951i		−	0.167330i
$974$			4.37777i			0.140273i
$975$	1.04644	+	9.51519i	0.0335128	+	0.304730i
$976$	0.251587	−	0.251587i	0.00805312	−	0.00805312i
$977$	30.6814	+	30.6814i	0.981584	+	0.981584i	0.999833	−	0.0182494i	$-0.00580928\pi$
$977$	30.6814	+	30.6814i	0.981584	+	0.981584i	−0.0182494	+	0.999833i	$0.505809\pi$
$978$	24.2063	−	30.1884i	0.774034	−	0.965320i
$979$	13.5646	+	13.5646i	0.433526	+	0.433526i
$980$	5.13495	+	5.13495i	0.164030	+	0.164030i
$981$	13.4773	−	21.1974i	0.430297	−	0.676781i
$982$	9.99339	−	9.99339i	0.318902	−	0.318902i
$983$	−46.4725			−1.48224			−0.741121	−	0.671372i	$-0.765705\pi$
$983$	−46.4725			−1.48224			−0.741121	+	0.671372i	$0.765705\pi$
$984$	−1.84448	−	16.7717i	−0.0587999	−	0.534664i
$985$	−10.3072	−	10.3072i	−0.328416	−	0.328416i
$986$	−5.62750	−	5.62750i	−0.179216	−	0.179216i
$987$	−38.7548	−	31.0752i	−1.23358	−	0.989136i
$988$	−7.90121			−0.251371
$989$	71.5729			2.27588
$990$	1.18364	+	5.31630i	0.0376186	+	0.168963i
$991$	30.0892	−	30.0892i	0.955814	−	0.955814i	−0.0432501	−	0.999064i	$-0.513771\pi$
$991$	30.0892	−	30.0892i	0.955814	−	0.955814i	0.999064	+	0.0432501i	$0.0137712\pi$
$992$	−6.31927			−0.200637
$993$	−50.6412	+	5.56929i	−1.60705	+	0.176736i
$994$	38.7286	−	38.7286i	1.22840	−	1.22840i
$995$			7.60095i			0.240966i
$996$	−7.75091	+	9.66638i	−0.245597	+	0.306291i
$997$	−43.2407	−	43.2407i	−1.36945	−	1.36945i	−0.861227	−	0.508221i	$-0.830303\pi$
$997$	−43.2407	−	43.2407i	−1.36945	−	1.36945i	−0.508221	−	0.861227i	$-0.669697\pi$
$998$	12.9604			0.410255
$999$	−23.3209	−	21.3339i	−0.737840	−	0.674976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.11	yes	40
3.2	odd	2	inner	1110.2.u.e.191.5	✓	40
37.31	odd	4	inner	1110.2.u.e.401.5	yes	40
111.68	even	4	inner	1110.2.u.e.401.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.5	✓	40	3.2	odd	2	inner
1110.2.u.e.191.11	yes	40	1.1	even	1	trivial
1110.2.u.e.401.5	yes	40	37.31	odd	4	inner
1110.2.u.e.401.11	yes	40	111.68	even	4	inner

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.72167 - 0.189341i) q^{6} -3.77650 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.651967 - 2.92830i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.08352 - 1.35129i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.72167 - 0.189341i) q^{6} -3.77650 q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.651967 - 2.92830i) q^{9} +1.00000 q^{10} -1.81549 q^{11} +(1.35129 + 1.08352i) q^{12} +(-3.90798 - 3.90798i) q^{13} +(-2.67039 - 2.67039i) q^{14} +(-0.189341 - 1.72167i) q^{15} -1.00000 q^{16} +(1.04463 - 1.04463i) q^{17} +(1.60961 - 2.53163i) q^{18} +(-1.01091 - 1.01091i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-4.09191 + 5.10314i) q^{21} +(-1.28375 - 1.28375i) q^{22} +(5.79126 - 5.79126i) q^{23} +(0.189341 + 1.72167i) q^{24} -1.00000i q^{25} -5.52672i q^{26} +(-4.66340 - 2.29188i) q^{27} -3.77650i q^{28} +(-3.80924 - 3.80924i) q^{29} +(1.08352 - 1.35129i) q^{30} +(4.46840 - 4.46840i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.96712 + 2.45325i) q^{33} +1.47733 q^{34} +(-2.67039 + 2.67039i) q^{35} +(2.92830 - 0.651967i) q^{36} +(5.83886 + 1.70519i) q^{37} -1.42964i q^{38} +(-9.51519 + 1.04644i) q^{39} +1.00000i q^{40} -9.74155 q^{41} +(-6.50188 + 0.715047i) q^{42} +(6.17939 + 6.17939i) q^{43} -1.81549i q^{44} +(-2.53163 - 1.60961i) q^{45} +8.19007 q^{46} +7.59431i q^{47} +(-1.08352 + 1.35129i) q^{48} +7.26192 q^{49} +(0.707107 - 0.707107i) q^{50} +(-0.279720 - 2.54347i) q^{51} +(3.90798 - 3.90798i) q^{52} -1.46832i q^{53} +(-1.67692 - 4.91812i) q^{54} +(-1.28375 + 1.28375i) q^{55} +(2.67039 - 2.67039i) q^{56} +(-2.46137 + 0.270690i) q^{57} -5.38709i q^{58} +(3.27282 - 3.27282i) q^{59} +(1.72167 - 0.189341i) q^{60} +(-0.251587 + 0.251587i) q^{61} +6.31927 q^{62} +(2.46215 + 11.0587i) q^{63} -1.00000i q^{64} -5.52672 q^{65} +(-3.12568 + 0.343748i) q^{66} +1.79916i q^{67} +(1.04463 + 1.04463i) q^{68} +(-1.55072 - 14.1006i) q^{69} -3.77650 q^{70} +14.5030i q^{71} +(2.53163 + 1.60961i) q^{72} +7.13983i q^{73} +(2.92295 + 5.33445i) q^{74} +(-1.35129 - 1.08352i) q^{75} +(1.01091 - 1.01091i) q^{76} +6.85620 q^{77} +(-7.46820 - 5.98831i) q^{78} +(-8.05198 - 8.05198i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-8.14988 + 3.81831i) q^{81} +(-6.88832 - 6.88832i) q^{82} +7.15345i q^{83} +(-5.10314 - 4.09191i) q^{84} -1.47733i q^{85} +8.73898i q^{86} +(-9.27479 + 1.02000i) q^{87} +(1.28375 - 1.28375i) q^{88} +(-7.47158 - 7.47158i) q^{89} +(-0.651967 - 2.92830i) q^{90} +(14.7585 + 14.7585i) q^{91} +(5.79126 + 5.79126i) q^{92} +(-1.19650 - 10.8797i) q^{93} +(-5.36999 + 5.36999i) q^{94} -1.42964 q^{95} +(-1.72167 + 0.189341i) q^{96} +(3.22614 + 3.22614i) q^{97} +(5.13495 + 5.13495i) q^{98} +(1.18364 + 5.31630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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