LMFDB - Embedded newform 1110.2.l.a.697.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.16
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.23501 - 0.0687789i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.23501 - 0.0687789i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-0.0687789 - 2.23501i) q^{10} -2.07347i q^{11} +(-0.707107 - 0.707107i) q^{12} -4.31443i q^{13} +(2.13605 - 2.13605i) q^{14} +(1.62902 + 1.53176i) q^{15} +1.00000 q^{16} +2.62056 q^{17} +1.00000 q^{18} +(-1.48007 - 1.48007i) q^{19} +(-2.23501 + 0.0687789i) q^{20} +3.02083i q^{21} -2.07347 q^{22} +3.49438i q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.99054 - 0.307443i) q^{25} -4.31443 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.13605 - 2.13605i) q^{28} +(-0.364989 + 0.364989i) q^{29} +(1.53176 - 1.62902i) q^{30} +(0.391381 + 0.391381i) q^{31} -1.00000i q^{32} +(1.46616 - 1.46616i) q^{33} -2.62056i q^{34} +(4.92101 + 4.62718i) q^{35} -1.00000i q^{36} +(5.47103 - 2.65855i) q^{37} +(-1.48007 + 1.48007i) q^{38} +(3.05076 - 3.05076i) q^{39} +(0.0687789 + 2.23501i) q^{40} +3.80013i q^{41} +3.02083 q^{42} +6.28607i q^{43} +2.07347i q^{44} +(0.0687789 + 2.23501i) q^{45} +3.49438 q^{46} +(3.37898 + 3.37898i) q^{47} +(0.707107 + 0.707107i) q^{48} +2.12544i q^{49} +(-0.307443 - 4.99054i) q^{50} +(1.85302 + 1.85302i) q^{51} +4.31443i q^{52} +(-1.87850 + 1.87850i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-0.142611 - 4.63422i) q^{55} +(-2.13605 + 2.13605i) q^{56} -2.09313i q^{57} +(0.364989 + 0.364989i) q^{58} +(0.917356 + 0.917356i) q^{59} +(-1.62902 - 1.53176i) q^{60} +(5.87589 + 5.87589i) q^{61} +(0.391381 - 0.391381i) q^{62} +(-2.13605 + 2.13605i) q^{63} -1.00000 q^{64} +(-0.296742 - 9.64280i) q^{65} +(-1.46616 - 1.46616i) q^{66} +(3.05783 - 3.05783i) q^{67} -2.62056 q^{68} +(-2.47090 + 2.47090i) q^{69} +(4.62718 - 4.92101i) q^{70} -9.16581 q^{71} -1.00000 q^{72} +(-8.50139 - 8.50139i) q^{73} +(-2.65855 - 5.47103i) q^{74} +(3.74624 + 3.31145i) q^{75} +(1.48007 + 1.48007i) q^{76} +(4.42903 - 4.42903i) q^{77} +(-3.05076 - 3.05076i) q^{78} +(-9.01137 - 9.01137i) q^{79} +(2.23501 - 0.0687789i) q^{80} -1.00000 q^{81} +3.80013 q^{82} +(-0.381394 + 0.381394i) q^{83} -3.02083i q^{84} +(5.85698 - 0.180239i) q^{85} +6.28607 q^{86} -0.516172 q^{87} +2.07347 q^{88} +(-3.68659 + 3.68659i) q^{89} +(2.23501 - 0.0687789i) q^{90} +(9.21585 - 9.21585i) q^{91} -3.49438i q^{92} +0.553497i q^{93} +(3.37898 - 3.37898i) q^{94} +(-3.40977 - 3.20617i) q^{95} +(0.707107 - 0.707107i) q^{96} +14.1415 q^{97} +2.12544 q^{98} +2.07347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 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} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 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 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	2.23501	−	0.0687789i	0.999527	−	0.0307589i
$5$	2.23501	−	0.0687789i	0.999527	−	0.0307589i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	2.13605	+	2.13605i	0.807352	+	0.807352i	0.984232	−	0.176880i	$-0.0566006\pi$
$7$	2.13605	+	2.13605i	0.807352	+	0.807352i	−0.176880	+	0.984232i	$0.556601\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−0.0687789	−	2.23501i	−0.0217498	−	0.706772i
$11$		−	2.07347i		−	0.625174i	−0.949889	−	0.312587i	$-0.898804\pi$
$11$		−	2.07347i		−	0.625174i	0.949889	−	0.312587i	$-0.101196\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$		−	4.31443i		−	1.19661i	−0.801269	−	0.598304i	$-0.795842\pi$
$13$		−	4.31443i		−	1.19661i	0.801269	−	0.598304i	$-0.204158\pi$
$14$	2.13605	−	2.13605i	0.570884	−	0.570884i
$15$	1.62902	+	1.53176i	0.420612	+	0.395498i
$16$	1.00000			0.250000
$17$	2.62056			0.635579			0.317790	−	0.948161i	$-0.397059\pi$
$17$	2.62056			0.635579			0.317790	+	0.948161i	$0.397059\pi$
$18$	1.00000			0.235702
$19$	−1.48007	−	1.48007i	−0.339551	−	0.339551i	0.516647	−	0.856198i	$-0.327180\pi$
$19$	−1.48007	−	1.48007i	−0.339551	−	0.339551i	−0.856198	+	0.516647i	$0.827180\pi$
$20$	−2.23501	+	0.0687789i	−0.499763	+	0.0153794i
$21$			3.02083i			0.659200i
$22$	−2.07347			−0.442065
$23$			3.49438i			0.728628i	0.931276	+	0.364314i	$0.118697\pi$
$23$			3.49438i			0.728628i	−0.931276	+	0.364314i	$0.881303\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	4.99054	−	0.307443i	0.998108	−	0.0614886i
$26$	−4.31443			−0.846129
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.13605	−	2.13605i	−0.403676	−	0.403676i
$29$	−0.364989	+	0.364989i	−0.0677767	+	0.0677767i	−0.740183	−	0.672406i	$-0.765261\pi$
$29$	−0.364989	+	0.364989i	−0.0677767	+	0.0677767i	0.672406	+	0.740183i	$0.265261\pi$
$30$	1.53176	−	1.62902i	0.279659	−	0.297418i
$31$	0.391381	+	0.391381i	0.0702942	+	0.0702942i	0.741380	−	0.671086i	$-0.234172\pi$
$31$	0.391381	+	0.391381i	0.0702942	+	0.0702942i	−0.671086	+	0.741380i	$0.734172\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.46616	−	1.46616i	0.255226	−	0.255226i
$34$		−	2.62056i		−	0.449422i
$35$	4.92101	+	4.62718i	0.831803	+	0.782137i
$36$		−	1.00000i		−	0.166667i
$37$	5.47103	−	2.65855i	0.899431	−	0.437062i
$37$	5.47103	−	2.65855i	0.899431	−	0.437062i
$38$	−1.48007	+	1.48007i	−0.240099	+	0.240099i
$39$	3.05076	−	3.05076i	0.488513	−	0.488513i
$40$	0.0687789	+	2.23501i	0.0108749	+	0.353386i
$41$			3.80013i			0.593481i	0.954958	+	0.296740i	$0.0958996\pi$
$41$			3.80013i			0.593481i	−0.954958	+	0.296740i	$0.904100\pi$
$42$	3.02083			0.466125
$43$			6.28607i			0.958617i	0.877647	+	0.479308i	$0.159112\pi$
$43$			6.28607i			0.958617i	−0.877647	+	0.479308i	$0.840888\pi$
$44$			2.07347i			0.312587i
$45$	0.0687789	+	2.23501i	0.0102530	+	0.333176i
$46$	3.49438			0.515218
$47$	3.37898	+	3.37898i	0.492876	+	0.492876i	0.909211	−	0.416336i	$-0.136686\pi$
$47$	3.37898	+	3.37898i	0.492876	+	0.492876i	−0.416336	+	0.909211i	$0.636686\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$			2.12544i			0.303634i
$50$	−0.307443	−	4.99054i	−0.0434790	−	0.705769i
$51$	1.85302	+	1.85302i	0.259474	+	0.259474i
$52$			4.31443i			0.598304i
$53$	−1.87850	+	1.87850i	−0.258031	+	0.258031i	−0.824253	−	0.566222i	$-0.808405\pi$
$53$	−1.87850	+	1.87850i	−0.258031	+	0.258031i	0.566222	+	0.824253i	$0.308405\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−0.142611	−	4.63422i	−0.0192296	−	0.624878i
$56$	−2.13605	+	2.13605i	−0.285442	+	0.285442i
$57$		−	2.09313i		−	0.277242i
$58$	0.364989	+	0.364989i	0.0479254	+	0.0479254i
$59$	0.917356	+	0.917356i	0.119430	+	0.119430i	0.764296	−	0.644866i	$-0.223087\pi$
$59$	0.917356	+	0.917356i	0.119430	+	0.119430i	−0.644866	+	0.764296i	$0.723087\pi$
$60$	−1.62902	−	1.53176i	−0.210306	−	0.197749i
$61$	5.87589	+	5.87589i	0.752331	+	0.752331i	0.974914	−	0.222583i	$-0.0714489\pi$
$61$	5.87589	+	5.87589i	0.752331	+	0.752331i	−0.222583	+	0.974914i	$0.571449\pi$
$62$	0.391381	−	0.391381i	0.0497055	−	0.0497055i
$63$	−2.13605	+	2.13605i	−0.269117	+	0.269117i
$64$	−1.00000			−0.125000
$65$	−0.296742	−	9.64280i	−0.0368063	−	1.19604i
$66$	−1.46616	−	1.46616i	−0.180472	−	0.180472i
$67$	3.05783	−	3.05783i	0.373573	−	0.373573i	−0.495204	−	0.868777i	$-0.664907\pi$
$67$	3.05783	−	3.05783i	0.373573	−	0.373573i	0.868777	+	0.495204i	$0.164907\pi$
$68$	−2.62056			−0.317790
$69$	−2.47090	+	2.47090i	−0.297461	+	0.297461i
$70$	4.62718	−	4.92101i	0.553054	−	0.588174i
$71$	−9.16581			−1.08778			−0.543891	−	0.839156i	$-0.683049\pi$
$71$	−9.16581			−1.08778			−0.543891	+	0.839156i	$0.683049\pi$
$72$	−1.00000			−0.117851
$73$	−8.50139	−	8.50139i	−0.995012	−	0.995012i	0.00497545	−	0.999988i	$-0.498416\pi$
$73$	−8.50139	−	8.50139i	−0.995012	−	0.995012i	−0.999988	+	0.00497545i	$0.998416\pi$
$74$	−2.65855	−	5.47103i	−0.309050	−	0.635994i
$75$	3.74624	+	3.31145i	0.432578	+	0.382373i
$76$	1.48007	+	1.48007i	0.169776	+	0.169776i
$77$	4.42903	−	4.42903i	0.504735	−	0.504735i
$78$	−3.05076	−	3.05076i	−0.345431	−	0.345431i
$79$	−9.01137	−	9.01137i	−1.01386	−	1.01386i	−0.999903	−	0.0139555i	$-0.995558\pi$
$79$	−9.01137	−	9.01137i	−1.01386	−	1.01386i	−0.0139555	−	0.999903i	$-0.504442\pi$
$80$	2.23501	−	0.0687789i	0.249882	−	0.00768972i
$81$	−1.00000			−0.111111
$82$	3.80013			0.419654
$83$	−0.381394	+	0.381394i	−0.0418634	+	0.0418634i	−0.727729	−	0.685865i	$-0.759424\pi$
$83$	−0.381394	+	0.381394i	−0.0418634	+	0.0418634i	0.685865	+	0.727729i	$0.259424\pi$
$84$		−	3.02083i		−	0.329600i
$85$	5.85698	−	0.180239i	0.635278	−	0.0195497i
$86$	6.28607			0.677844
$87$	−0.516172			−0.0553395
$88$	2.07347			0.221032
$89$	−3.68659	+	3.68659i	−0.390778	+	0.390778i	−0.874965	−	0.484187i	$-0.839116\pi$
$89$	−3.68659	+	3.68659i	−0.390778	+	0.390778i	0.484187	+	0.874965i	$0.339116\pi$
$90$	2.23501	−	0.0687789i	0.235591	−	0.00724994i
$91$	9.21585	−	9.21585i	0.966084	−	0.966084i
$92$		−	3.49438i		−	0.364314i
$93$			0.553497i			0.0573950i
$94$	3.37898	−	3.37898i	0.348516	−	0.348516i
$95$	−3.40977	−	3.20617i	−0.349835	−	0.328946i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	14.1415			1.43586			0.717928	−	0.696117i	$-0.245091\pi$
$97$	14.1415			1.43586			0.717928	+	0.696117i	$0.245091\pi$
$98$	2.12544			0.214702
$99$	2.07347			0.208391
$100$	−4.99054	+	0.307443i	−0.499054	+	0.0307443i
$101$		−	7.64384i		−	0.760591i	−0.924865	−	0.380295i	$-0.875822\pi$
$101$		−	7.64384i		−	0.760591i	0.924865	−	0.380295i	$-0.124178\pi$
$102$	1.85302	−	1.85302i	0.183476	−	0.183476i
$103$	−9.85885			−0.971422			−0.485711	−	0.874120i	$-0.661439\pi$
$103$	−9.85885			−0.971422			−0.485711	+	0.874120i	$0.661439\pi$
$104$	4.31443			0.423065
$105$	0.207770	+	6.75159i	0.0202763	+	0.658888i
$106$	1.87850	+	1.87850i	0.182456	+	0.182456i
$107$	4.17096	+	4.17096i	0.403222	+	0.403222i	0.879367	−	0.476145i	$-0.157966\pi$
$107$	4.17096	+	4.17096i	0.403222	+	0.403222i	−0.476145	+	0.879367i	$0.657966\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	0.461041	+	0.461041i	0.0441597	+	0.0441597i	0.728842	−	0.684682i	$-0.240059\pi$
$109$	0.461041	+	0.461041i	0.0441597	+	0.0441597i	−0.684682	+	0.728842i	$0.740059\pi$
$110$	−4.63422	+	0.142611i	−0.441856	+	0.0135974i
$111$	5.74848	+	1.98872i	0.545621	+	0.188761i
$112$	2.13605	+	2.13605i	0.201838	+	0.201838i
$113$	−17.3203			−1.62936			−0.814678	−	0.579913i	$-0.803086\pi$
$113$	−17.3203			−1.62936			−0.814678	+	0.579913i	$0.803086\pi$
$114$	−2.09313			−0.196040
$115$	0.240340	+	7.80997i	0.0224118	+	0.728284i
$116$	0.364989	−	0.364989i	0.0338884	−	0.0338884i
$117$	4.31443			0.398869
$118$	0.917356	−	0.917356i	0.0844495	−	0.0844495i
$119$	5.59765	+	5.59765i	0.513136	+	0.513136i
$120$	−1.53176	+	1.62902i	−0.139830	+	0.148709i
$121$	6.70073			0.609158
$122$	5.87589	−	5.87589i	0.531978	−	0.531978i
$123$	−2.68710	+	2.68710i	−0.242287	+	0.242287i
$124$	−0.391381	−	0.391381i	−0.0351471	−	0.0351471i
$125$	11.1328	−	1.03038i	0.995744	−	0.0921602i
$126$	2.13605	+	2.13605i	0.190295	+	0.190295i
$127$	−6.18161	−	6.18161i	−0.548529	−	0.548529i	0.377486	−	0.926015i	$-0.376789\pi$
$127$	−6.18161	−	6.18161i	−0.548529	−	0.548529i	−0.926015	+	0.377486i	$0.876789\pi$
$128$			1.00000i			0.0883883i
$129$	−4.44492	+	4.44492i	−0.391354	+	0.391354i
$130$	−9.64280	+	0.296742i	−0.845729	+	0.0260260i
$131$	1.03836	+	1.03836i	0.0907217	+	0.0907217i	0.751011	−	0.660289i	$-0.229566\pi$
$131$	1.03836	+	1.03836i	0.0907217	+	0.0907217i	−0.660289	+	0.751011i	$0.729566\pi$
$132$	−1.46616	+	1.46616i	−0.127613	+	0.127613i
$133$		−	6.32301i		−	0.548275i
$134$	−3.05783	−	3.05783i	−0.264156	−	0.264156i
$135$	−1.53176	+	1.62902i	−0.131833	+	0.140204i
$136$			2.62056i			0.224711i
$137$	−13.3475	−	13.3475i	−1.14035	−	1.14035i	−0.988386	−	0.151966i	$-0.951440\pi$
$137$	−13.3475	−	13.3475i	−1.14035	−	1.14035i	−0.151966	−	0.988386i	$-0.548560\pi$
$138$	2.47090	+	2.47090i	0.210337	+	0.210337i
$139$	12.1026			1.02653			0.513267	−	0.858229i	$-0.328435\pi$
$139$	12.1026			1.02653			0.513267	+	0.858229i	$0.328435\pi$
$140$	−4.92101	−	4.62718i	−0.415902	−	0.391068i
$141$			4.77861i			0.402431i
$142$			9.16581i			0.769177i
$143$	−8.94583			−0.748088
$144$			1.00000i			0.0833333i
$145$	−0.790650	+	0.840857i	−0.0656599	+	0.0698294i
$146$	−8.50139	+	8.50139i	−0.703580	+	0.703580i
$147$	−1.50291	+	1.50291i	−0.123958	+	0.123958i
$148$	−5.47103	+	2.65855i	−0.449716	+	0.218531i
$149$			1.78006i			0.145828i	0.997338	+	0.0729141i	$0.0232299\pi$
$149$			1.78006i			0.145828i	−0.997338	+	0.0729141i	$0.976770\pi$
$150$	3.31145	−	3.74624i	0.270379	−	0.305879i
$151$			14.7620i			1.20132i	0.799506	+	0.600658i	$0.205095\pi$
$151$			14.7620i			1.20132i	−0.799506	+	0.600658i	$0.794905\pi$
$152$	1.48007	−	1.48007i	0.120049	−	0.120049i
$153$			2.62056i			0.211860i
$154$	−4.42903	−	4.42903i	−0.356902	−	0.356902i
$155$	0.901660	+	0.847823i	0.0724231	+	0.0680988i
$156$	−3.05076	+	3.05076i	−0.244257	+	0.244257i
$157$	3.02964	+	3.02964i	0.241792	+	0.241792i	0.817591	−	0.575799i	$-0.195309\pi$
$157$	3.02964	+	3.02964i	0.241792	+	0.241792i	−0.575799	+	0.817591i	$0.695309\pi$
$158$	−9.01137	+	9.01137i	−0.716906	+	0.716906i
$159$	−2.65660			−0.210682
$160$	−0.0687789	−	2.23501i	−0.00543745	−	0.176693i
$161$	−7.46418	+	7.46418i	−0.588260	+	0.588260i
$162$			1.00000i			0.0785674i
$163$	6.39530			0.500918			0.250459	−	0.968127i	$-0.419418\pi$
$163$	6.39530			0.500918			0.250459	+	0.968127i	$0.419418\pi$
$164$		−	3.80013i		−	0.296740i
$165$	3.17605	−	3.37773i	0.247255	−	0.262956i
$166$	0.381394	+	0.381394i	0.0296019	+	0.0296019i
$167$	−7.40255			−0.572826			−0.286413	−	0.958106i	$-0.592463\pi$
$167$	−7.40255			−0.572826			−0.286413	+	0.958106i	$0.592463\pi$
$168$	−3.02083			−0.233062
$169$	−5.61431			−0.431870
$170$	−0.180239	−	5.85698i	−0.0138237	−	0.449210i
$171$	1.48007	−	1.48007i	0.113184	−	0.113184i
$172$		−	6.28607i		−	0.479308i
$173$	−16.3983	−	16.3983i	−1.24674	−	1.24674i	−0.957152	−	0.289586i	$-0.906483\pi$
$173$	−16.3983	−	16.3983i	−1.24674	−	1.24674i	−0.289586	−	0.957152i	$-0.593517\pi$
$174$			0.516172i			0.0391309i
$175$	11.3168	+	10.0033i	0.855467	+	0.756181i
$176$		−	2.07347i		−	0.156293i
$177$			1.29734i			0.0975139i
$178$	3.68659	+	3.68659i	0.276322	+	0.276322i
$179$	−16.2448	+	16.2448i	−1.21419	+	1.21419i	−0.244559	+	0.969634i	$0.578643\pi$
$179$	−16.2448	+	16.2448i	−1.21419	+	1.21419i	−0.969634	+	0.244559i	$0.921357\pi$
$180$	−0.0687789	−	2.23501i	−0.00512648	−	0.166588i
$181$	−5.45708			−0.405621			−0.202811	−	0.979218i	$-0.565008\pi$
$181$	−5.45708			−0.405621			−0.202811	+	0.979218i	$0.565008\pi$
$182$	−9.21585	−	9.21585i	−0.683124	−	0.683124i
$183$			8.30976i			0.614275i
$184$	−3.49438			−0.257609
$185$	12.0449	−	6.31817i	0.885562	−	0.464521i
$186$	0.553497			0.0405844
$187$		−	5.43364i		−	0.397347i
$188$	−3.37898	−	3.37898i	−0.246438	−	0.246438i
$189$	−3.02083			−0.219733
$190$	−3.20617	+	3.40977i	−0.232600	+	0.247370i
$191$	−8.47691	+	8.47691i	−0.613367	+	0.613367i	−0.943822	−	0.330455i	$-0.892798\pi$
$191$	−8.47691	+	8.47691i	−0.613367	+	0.613367i	0.330455	+	0.943822i	$0.392798\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$			0.815237i			0.0586820i	0.999569	+	0.0293410i	$0.00934088\pi$
$193$			0.815237i			0.0586820i	−0.999569	+	0.0293410i	$0.990659\pi$
$194$		−	14.1415i		−	1.01530i
$195$	6.60866	−	7.02831i	0.473256	−	0.503308i
$196$		−	2.12544i		−	0.151817i
$197$	−12.1517	−	12.1517i	−0.865772	−	0.865772i	0.126229	−	0.992001i	$-0.459713\pi$
$197$	−12.1517	−	12.1517i	−0.865772	−	0.865772i	−0.992001	+	0.126229i	$0.959713\pi$
$198$		−	2.07347i		−	0.147355i
$199$	6.43148	−	6.43148i	0.455915	−	0.455915i	−0.441397	−	0.897312i	$-0.645517\pi$
$199$	6.43148	−	6.43148i	0.455915	−	0.455915i	0.897312	+	0.441397i	$0.145517\pi$
$200$	0.307443	+	4.99054i	0.0217395	+	0.352884i
$201$	4.32442			0.305021
$202$	−7.64384			−0.537819
$203$	−1.55927			−0.109439
$204$	−1.85302	−	1.85302i	−0.129737	−	0.129737i
$205$	0.261369	+	8.49333i	0.0182548	+	0.593200i
$206$			9.85885i			0.686899i
$207$	−3.49438			−0.242876
$208$		−	4.31443i		−	0.299152i
$209$	−3.06887	+	3.06887i	−0.212279	+	0.212279i
$210$	6.75159	−	0.207770i	0.465904	−	0.0143375i
$211$	−1.84896			−0.127287			−0.0636437	−	0.997973i	$-0.520272\pi$
$211$	−1.84896			−0.127287			−0.0636437	+	0.997973i	$0.520272\pi$
$212$	1.87850	−	1.87850i	0.129016	−	0.129016i
$213$	−6.48120	−	6.48120i	−0.444085	−	0.444085i
$214$	4.17096	−	4.17096i	0.285121	−	0.285121i
$215$	0.432349	+	14.0494i	0.0294860	+	0.958163i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$			1.67202i			0.113504i
$218$	0.461041	−	0.461041i	0.0312256	−	0.0312256i
$219$		−	12.0228i		−	0.812424i
$220$	0.142611	+	4.63422i	0.00961482	+	0.312439i
$221$		−	11.3062i		−	0.760539i
$222$	1.98872	−	5.74848i	0.133474	−	0.385812i
$223$	4.85478	−	4.85478i	0.325100	−	0.325100i	−0.525620	−	0.850720i	$-0.676166\pi$
$223$	4.85478	−	4.85478i	0.325100	−	0.325100i	0.850720	+	0.525620i	$0.176166\pi$
$224$	2.13605	−	2.13605i	0.142721	−	0.142721i
$225$	0.307443	+	4.99054i	0.0204962	+	0.332703i
$226$			17.3203i			1.15213i
$227$	−19.5601			−1.29825			−0.649123	−	0.760683i	$-0.724864\pi$
$227$	−19.5601			−1.29825			−0.649123	+	0.760683i	$0.724864\pi$
$228$			2.09313i			0.138621i
$229$			5.52626i			0.365186i	0.983189	+	0.182593i	$0.0584490\pi$
$229$			5.52626i			0.365186i	−0.983189	+	0.182593i	$0.941551\pi$
$230$	7.80997	−	0.240340i	0.514974	−	0.0158475i
$231$	6.26360			0.412115
$232$	−0.364989	−	0.364989i	−0.0239627	−	0.0239627i
$233$	−8.07622	−	8.07622i	−0.529091	−	0.529091i	0.391210	−	0.920301i	$-0.372056\pi$
$233$	−8.07622	−	8.07622i	−0.529091	−	0.529091i	−0.920301	+	0.391210i	$0.872056\pi$
$234$		−	4.31443i		−	0.282043i
$235$	7.78447	+	7.31966i	0.507803	+	0.477482i
$236$	−0.917356	−	0.917356i	−0.0597148	−	0.0597148i
$237$		−	12.7440i		−	0.827812i
$238$	5.59765	−	5.59765i	0.362842	−	0.362842i
$239$	1.04218	+	1.04218i	0.0674129	+	0.0674129i	0.740009	−	0.672597i	$-0.234821\pi$
$239$	1.04218	+	1.04218i	0.0674129	+	0.0674129i	−0.672597	+	0.740009i	$0.734821\pi$
$240$	1.62902	+	1.53176i	0.105153	+	0.0988745i
$241$	2.39676	−	2.39676i	0.154389	−	0.154389i	−0.625686	−	0.780075i	$-0.715181\pi$
$241$	2.39676	−	2.39676i	0.154389	−	0.154389i	0.780075	+	0.625686i	$0.215181\pi$
$242$		−	6.70073i		−	0.430739i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−5.87589	−	5.87589i	−0.376165	−	0.376165i
$245$	0.146186	+	4.75038i	0.00933945	+	0.303491i
$246$	2.68710	+	2.68710i	0.171323	+	0.171323i
$247$	−6.38566	+	6.38566i	−0.406310	+	0.406310i
$248$	−0.391381	+	0.391381i	−0.0248527	+	0.0248527i
$249$	−0.539372			−0.0341813
$250$	−1.03038	−	11.1328i	−0.0651671	−	0.704097i
$251$	14.2994	+	14.2994i	0.902571	+	0.902571i	0.995658	−	0.0930871i	$-0.0296735\pi$
$251$	14.2994	+	14.2994i	0.902571	+	0.902571i	−0.0930871	+	0.995658i	$0.529674\pi$
$252$	2.13605	−	2.13605i	0.134559	−	0.134559i
$253$	7.24548			0.455519
$254$	−6.18161	+	6.18161i	−0.387869	+	0.387869i
$255$	4.26896	+	4.01406i	0.267332	+	0.251370i
$256$	1.00000			0.0625000
$257$	−22.9481			−1.43146			−0.715731	−	0.698376i	$-0.753906\pi$
$257$	−22.9481			−1.43146			−0.715731	+	0.698376i	$0.753906\pi$
$258$	4.44492	+	4.44492i	0.276729	+	0.276729i
$259$	17.3652	+	6.00760i	1.07902	+	0.373294i
$260$	0.296742	+	9.64280i	0.0184032	+	0.598021i
$261$	−0.364989	−	0.364989i	−0.0225922	−	0.0225922i
$262$	1.03836	−	1.03836i	0.0641499	−	0.0641499i
$263$	−0.797307	−	0.797307i	−0.0491641	−	0.0491641i	0.682097	−	0.731261i	$-0.261068\pi$
$263$	−0.797307	−	0.797307i	−0.0491641	−	0.0491641i	−0.731261	+	0.682097i	$0.761068\pi$
$264$	1.46616	+	1.46616i	0.0902361	+	0.0902361i
$265$	−4.06926	+	4.32766i	−0.249973	+	0.265846i
$266$	−6.32301			−0.387689
$267$	−5.21363			−0.319069
$268$	−3.05783	+	3.05783i	−0.186787	+	0.186787i
$269$			17.8697i			1.08954i	0.838587	+	0.544768i	$0.183382\pi$
$269$			17.8697i			1.08954i	−0.838587	+	0.544768i	$0.816618\pi$
$270$	1.62902	+	1.53176i	0.0991393	+	0.0932197i
$271$	−20.7623			−1.26122			−0.630610	−	0.776100i	$-0.717195\pi$
$271$	−20.7623			−1.26122			−0.630610	+	0.776100i	$0.717195\pi$
$272$	2.62056			0.158895
$273$	13.0332			0.788804
$274$	−13.3475	+	13.3475i	−0.806350	+	0.806350i
$275$	−0.637473	−	10.3477i	−0.0384411	−	0.623991i
$276$	2.47090	−	2.47090i	0.148731	−	0.148731i
$277$			17.8467i			1.07230i	0.844122	+	0.536152i	$0.180122\pi$
$277$			17.8467i			1.07230i	−0.844122	+	0.536152i	$0.819878\pi$
$278$		−	12.1026i		−	0.725869i
$279$	−0.391381	+	0.391381i	−0.0234314	+	0.0234314i
$280$	−4.62718	+	4.92101i	−0.276527	+	0.294087i
$281$	−10.2645	+	10.2645i	−0.612330	+	0.612330i	−0.943553	−	0.331223i	$-0.892539\pi$
$281$	−10.2645	+	10.2645i	−0.612330	+	0.612330i	0.331223	+	0.943553i	$0.392539\pi$
$282$	4.77861			0.284562
$283$	−9.49377			−0.564346			−0.282173	−	0.959364i	$-0.591055\pi$
$283$	−9.49377			−0.564346			−0.282173	+	0.959364i	$0.591055\pi$
$284$	9.16581			0.543891
$285$	−0.143963	−	4.67818i	−0.00852766	−	0.277111i
$286$			8.94583i			0.528978i
$287$	−8.11728	+	8.11728i	−0.479148	+	0.479148i
$288$	1.00000			0.0589256
$289$	−10.1327			−0.596039
$290$	0.840857	+	0.790650i	0.0493768	+	0.0464286i
$291$	9.99958	+	9.99958i	0.586186	+	0.586186i
$292$	8.50139	+	8.50139i	0.497506	+	0.497506i
$293$	−1.37161	+	1.37161i	−0.0801303	+	0.0801303i	−0.746036	−	0.665906i	$-0.768045\pi$
$293$	−1.37161	+	1.37161i	−0.0801303	+	0.0801303i	0.665906	+	0.746036i	$0.268045\pi$
$294$	1.50291	+	1.50291i	0.0876517	+	0.0876517i
$295$	2.11340	+	1.98721i	0.123047	+	0.115700i
$296$	2.65855	+	5.47103i	0.154525	+	0.317997i
$297$	1.46616	+	1.46616i	0.0850754	+	0.0850754i
$298$	1.78006			0.103116
$299$	15.0763			0.871882
$300$	−3.74624	−	3.31145i	−0.216289	−	0.191187i
$301$	−13.4274	+	13.4274i	−0.773941	+	0.773941i
$302$	14.7620			0.849459
$303$	5.40501	−	5.40501i	0.310510	−	0.310510i
$304$	−1.48007	−	1.48007i	−0.0848878	−	0.0848878i
$305$	13.5368	+	12.7285i	0.775115	+	0.728834i
$306$	2.62056			0.149807
$307$	−12.9742	+	12.9742i	−0.740476	+	0.740476i	−0.972670	−	0.232194i	$-0.925410\pi$
$307$	−12.9742	+	12.9742i	−0.740476	+	0.740476i	0.232194	+	0.972670i	$0.425410\pi$
$308$	−4.42903	+	4.42903i	−0.252368	+	0.252368i
$309$	−6.97126	−	6.97126i	−0.396581	−	0.396581i
$310$	0.847823	−	0.901660i	0.0481531	−	0.0512109i
$311$	21.1073	+	21.1073i	1.19689	+	1.19689i	0.975094	+	0.221794i	$0.0711911\pi$
$311$	21.1073	+	21.1073i	1.19689	+	1.19689i	0.221794	+	0.975094i	$0.428809\pi$
$312$	3.05076	+	3.05076i	0.172715	+	0.172715i
$313$		−	27.9746i		−	1.58122i	−0.612323	−	0.790608i	$-0.709765\pi$
$313$		−	27.9746i		−	1.58122i	0.612323	−	0.790608i	$-0.290235\pi$
$314$	3.02964	−	3.02964i	0.170973	−	0.170973i
$315$	−4.62718	+	4.92101i	−0.260712	+	0.277268i
$316$	9.01137	+	9.01137i	0.506929	+	0.506929i
$317$	−4.72175	+	4.72175i	−0.265200	+	0.265200i	−0.827163	−	0.561963i	$-0.810046\pi$
$317$	−4.72175	+	4.72175i	−0.265200	+	0.265200i	0.561963	+	0.827163i	$0.310046\pi$
$318$			2.65660i			0.148975i
$319$	0.756793	+	0.756793i	0.0423722	+	0.0423722i
$320$	−2.23501	+	0.0687789i	−0.124941	+	0.00384486i
$321$			5.89863i			0.329229i
$322$	7.46418	+	7.46418i	0.415962	+	0.415962i
$323$	−3.87861	−	3.87861i	−0.215812	−	0.215812i
$324$	1.00000			0.0555556
$325$	−1.32644	−	21.5313i	−0.0735778	−	1.19434i
$326$		−	6.39530i		−	0.354203i
$327$			0.652011i			0.0360563i
$328$	−3.80013			−0.209827
$329$			14.4354i			0.795848i
$330$	−3.37773	−	3.17605i	−0.185938	−	0.174836i
$331$	5.59691	−	5.59691i	0.307634	−	0.307634i	−0.536357	−	0.843991i	$-0.680200\pi$
$331$	5.59691	−	5.59691i	0.307634	−	0.307634i	0.843991	+	0.536357i	$0.180200\pi$
$332$	0.381394	−	0.381394i	0.0209317	−	0.0209317i
$333$	2.65855	+	5.47103i	0.145687	+	0.299810i
$334$			7.40255i			0.405049i
$335$	6.62397	−	7.04459i	0.361906	−	0.384887i
$336$			3.02083i			0.164800i
$337$	15.5752	−	15.5752i	0.848433	−	0.848433i	−0.141505	−	0.989938i	$-0.545194\pi$
$337$	15.5752	−	15.5752i	0.848433	−	0.848433i	0.989938	+	0.141505i	$0.0451941\pi$
$338$			5.61431i			0.305378i
$339$	−12.2473	−	12.2473i	−0.665182	−	0.665182i
$340$	−5.85698	+	0.180239i	−0.317639	+	0.00977485i
$341$	0.811517	−	0.811517i	0.0439461	−	0.0439461i
$342$	−1.48007	−	1.48007i	−0.0800330	−	0.0800330i
$343$	10.4123	−	10.4123i	0.562212	−	0.562212i
$344$	−6.28607			−0.338922
$345$	−5.35254	+	5.69243i	−0.288171	+	0.306470i
$346$	−16.3983	+	16.3983i	−0.881577	+	0.881577i
$347$			7.34661i			0.394386i	0.980365	+	0.197193i	$0.0631826\pi$
$347$			7.34661i			0.394386i	−0.980365	+	0.197193i	$0.936817\pi$
$348$	0.516172			0.0276697
$349$		−	5.62756i		−	0.301236i	−0.988592	−	0.150618i	$-0.951874\pi$
$349$		−	5.62756i		−	0.301236i	0.988592	−	0.150618i	$-0.0481264\pi$
$350$	10.0033	−	11.3168i	0.534701	−	0.604907i
$351$	3.05076	+	3.05076i	0.162838	+	0.162838i
$352$	−2.07347			−0.110516
$353$	25.6724			1.36640			0.683201	−	0.730231i	$-0.260587\pi$
$353$	25.6724			1.36640			0.683201	+	0.730231i	$0.260587\pi$
$354$	1.29734			0.0689527
$355$	−20.4857	+	0.630414i	−1.08727	+	0.0334589i
$356$	3.68659	−	3.68659i	0.195389	−	0.195389i
$357$			7.91628i			0.418974i
$358$	16.2448	+	16.2448i	0.858564	+	0.858564i
$359$		−	29.6458i		−	1.56465i	−0.622872	−	0.782324i	$-0.714034\pi$
$359$		−	29.6458i		−	1.56465i	0.622872	−	0.782324i	$-0.285966\pi$
$360$	−2.23501	+	0.0687789i	−0.117795	+	0.00362497i
$361$		−	14.6188i		−	0.769410i
$362$			5.45708i			0.286818i
$363$	4.73813	+	4.73813i	0.248688	+	0.248688i
$364$	−9.21585	+	9.21585i	−0.483042	+	0.483042i
$365$	−19.5854	−	18.4160i	−1.02515	−	0.963936i
$366$	8.30976			0.434358
$367$	−22.3758	−	22.3758i	−1.16801	−	1.16801i	−0.982677	−	0.185329i	$-0.940665\pi$
$367$	−22.3758	−	22.3758i	−1.16801	−	1.16801i	−0.185329	−	0.982677i	$-0.559335\pi$
$368$			3.49438i			0.182157i
$369$	−3.80013			−0.197827
$370$	−6.31817	−	12.0449i	−0.328466	−	0.626187i
$371$	−8.02514			−0.416644
$372$		−	0.553497i		−	0.0286975i
$373$	−2.58745	−	2.58745i	−0.133973	−	0.133973i	0.636940	−	0.770913i	$-0.280200\pi$
$373$	−2.58745	−	2.58745i	−0.133973	−	0.133973i	−0.770913	+	0.636940i	$0.780200\pi$
$374$	−5.43364			−0.280967
$375$	8.60064	+	7.14346i	0.444135	+	0.368887i
$376$	−3.37898	+	3.37898i	−0.174258	+	0.174258i
$377$	1.57472	+	1.57472i	0.0811022	+	0.0811022i
$378$			3.02083i			0.155375i
$379$			30.1390i			1.54814i	0.633102	+	0.774069i	$0.281781\pi$
$379$			30.1390i			1.54814i	−0.633102	+	0.774069i	$0.718219\pi$
$380$	3.40977	+	3.20617i	0.174917	+	0.164473i
$381$		−	8.74212i		−	0.447872i
$382$	8.47691	+	8.47691i	0.433716	+	0.433716i
$383$			27.3379i			1.39690i	0.715658	+	0.698451i	$0.246127\pi$
$383$			27.3379i			1.39690i	−0.715658	+	0.698451i	$0.753873\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	9.59431	−	10.2036i	0.488971	−	0.520022i
$386$	0.815237			0.0414945
$387$	−6.28607			−0.319539
$388$	−14.1415			−0.717928
$389$	7.29908	+	7.29908i	0.370078	+	0.370078i	0.867506	−	0.497428i	$-0.165722\pi$
$389$	7.29908	+	7.29908i	0.370078	+	0.370078i	−0.497428	+	0.867506i	$0.665722\pi$
$390$	−7.02831	−	6.60866i	−0.355893	−	0.334642i
$391$			9.15723i			0.463101i
$392$	−2.12544			−0.107351
$393$			1.46846i			0.0740739i
$394$	−12.1517	+	12.1517i	−0.612194	+	0.612194i
$395$	−20.7603	−	19.5207i	−1.04456	−	0.982193i
$396$	−2.07347			−0.104196
$397$	23.8828	−	23.8828i	1.19864	−	1.19864i	0.224069	−	0.974573i	$-0.428066\pi$
$397$	23.8828	−	23.8828i	1.19864	−	1.19864i	0.974573	−	0.224069i	$-0.0719342\pi$
$398$	−6.43148	−	6.43148i	−0.322381	−	0.322381i
$399$	4.47104	−	4.47104i	0.223832	−	0.223832i
$400$	4.99054	−	0.307443i	0.249527	−	0.0153722i
$401$	9.30160	+	9.30160i	0.464500	+	0.464500i	0.900127	−	0.435627i	$-0.143473\pi$
$401$	9.30160	+	9.30160i	0.464500	+	0.464500i	−0.435627	+	0.900127i	$0.643473\pi$
$402$		−	4.32442i		−	0.215683i
$403$	1.68859	−	1.68859i	0.0841146	−	0.0841146i
$404$			7.64384i			0.380295i
$405$	−2.23501	+	0.0687789i	−0.111059	+	0.00341765i
$406$			1.55927i			0.0773853i
$407$	−5.51241	−	11.3440i	−0.273240	−	0.562301i
$408$	−1.85302	+	1.85302i	−0.0917379	+	0.0917379i
$409$	−24.5847	+	24.5847i	−1.21563	+	1.21563i	−0.246487	+	0.969146i	$0.579276\pi$
$409$	−24.5847	+	24.5847i	−1.21563	+	1.21563i	−0.969146	+	0.246487i	$0.920724\pi$
$410$	8.49333	−	0.261369i	0.419456	−	0.0129081i
$411$		−	18.8762i		−	0.931093i
$412$	9.85885			0.485711
$413$			3.91904i			0.192844i
$414$			3.49438i			0.171739i
$415$	−0.826187	+	0.878651i	−0.0405559	+	0.0431313i
$416$	−4.31443			−0.211532
$417$	8.55786	+	8.55786i	0.419080	+	0.419080i
$418$	3.06887	+	3.06887i	0.150104	+	0.150104i
$419$		−	23.6748i		−	1.15659i	−0.815829	−	0.578294i	$-0.803719\pi$
$419$		−	23.6748i		−	1.15659i	0.815829	−	0.578294i	$-0.196281\pi$
$420$	−0.207770	−	6.75159i	−0.0101381	−	0.329444i
$421$	−26.6921	−	26.6921i	−1.30089	−	1.30089i	−0.927790	−	0.373102i	$-0.878294\pi$
$421$	−26.6921	−	26.6921i	−1.30089	−	1.30089i	−0.373102	−	0.927790i	$-0.621706\pi$
$422$			1.84896i			0.0900058i
$423$	−3.37898	+	3.37898i	−0.164292	+	0.164292i
$424$	−1.87850	−	1.87850i	−0.0912279	−	0.0912279i
$425$	13.0780	−	0.805673i	0.634376	−	0.0390809i
$426$	−6.48120	+	6.48120i	−0.314015	+	0.314015i
$427$			25.1024i			1.21479i
$428$	−4.17096	−	4.17096i	−0.201611	−	0.201611i
$429$	−6.32566	−	6.32566i	−0.305406	−	0.305406i
$430$	14.0494	−	0.432349i	0.677524	−	0.0208497i
$431$	25.8053	+	25.8053i	1.24300	+	1.24300i	0.958752	+	0.284245i	$0.0917428\pi$
$431$	25.8053	+	25.8053i	1.24300	+	1.24300i	0.284245	+	0.958752i	$0.408257\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−2.62555	+	2.62555i	−0.126176	+	0.126176i	−0.767375	−	0.641199i	$-0.778437\pi$
$433$	−2.62555	+	2.62555i	−0.126176	+	0.126176i	0.641199	+	0.767375i	$0.278437\pi$
$434$	1.67202			0.0802597
$435$	−1.15365	+	0.0355018i	−0.0553133	+	0.00170218i
$436$	−0.461041	−	0.461041i	−0.0220799	−	0.0220799i
$437$	5.17192	−	5.17192i	0.247407	−	0.247407i
$438$	−12.0228			−0.574471
$439$	4.04448	−	4.04448i	0.193033	−	0.193033i	−0.603973	−	0.797005i	$-0.706416\pi$
$439$	4.04448	−	4.04448i	0.193033	−	0.193033i	0.797005	+	0.603973i	$0.206416\pi$
$440$	4.63422	−	0.142611i	0.220928	−	0.00679871i
$441$	−2.12544			−0.101211
$442$	−11.3062			−0.537782
$443$	0.534873	+	0.534873i	0.0254126	+	0.0254126i	0.719699	−	0.694286i	$-0.244280\pi$
$443$	0.534873	+	0.534873i	0.0254126	+	0.0254126i	−0.694286	+	0.719699i	$0.744280\pi$
$444$	−5.74848	−	1.98872i	−0.272811	−	0.0943806i
$445$	−7.98601	+	8.49313i	−0.378573	+	0.402613i
$446$	−4.85478	−	4.85478i	−0.229881	−	0.229881i
$447$	−1.25869	+	1.25869i	−0.0595341	+	0.0595341i
$448$	−2.13605	−	2.13605i	−0.100919	−	0.100919i
$449$	−15.2168	−	15.2168i	−0.718124	−	0.718124i	0.250097	−	0.968221i	$-0.419538\pi$
$449$	−15.2168	−	15.2168i	−0.718124	−	0.718124i	−0.968221	+	0.250097i	$0.919538\pi$
$450$	4.99054	−	0.307443i	0.235256	−	0.0144930i
$451$	7.87944			0.371029
$452$	17.3203			0.814678
$453$	−10.4383	+	10.4383i	−0.490435	+	0.490435i
$454$			19.5601i			0.917999i
$455$	19.9637	−	21.2314i	0.935911	−	0.995342i
$456$	2.09313			0.0980200
$457$	−26.8366			−1.25536			−0.627682	−	0.778470i	$-0.715996\pi$
$457$	−26.8366			−1.25536			−0.627682	+	0.778470i	$0.715996\pi$
$458$	5.52626			0.258225
$459$	−1.85302	+	1.85302i	−0.0864914	+	0.0864914i
$460$	−0.240340	−	7.80997i	−0.0112059	−	0.364142i
$461$	9.31792	−	9.31792i	0.433979	−	0.433979i	−0.456001	−	0.889980i	$-0.650718\pi$
$461$	9.31792	−	9.31792i	0.433979	−	0.433979i	0.889980	+	0.456001i	$0.150718\pi$
$462$		−	6.26360i		−	0.291409i
$463$		−	31.8446i		−	1.47995i	−0.672637	−	0.739973i	$-0.734838\pi$
$463$		−	31.8446i		−	1.47995i	0.672637	−	0.739973i	$-0.265162\pi$
$464$	−0.364989	+	0.364989i	−0.0169442	+	0.0169442i
$465$	0.0380689	+	1.23707i	0.00176540	+	0.0573678i
$466$	−8.07622	+	8.07622i	−0.374124	+	0.374124i
$467$	24.6295			1.13972			0.569859	−	0.821743i	$-0.306998\pi$
$467$	24.6295			1.13972			0.569859	+	0.821743i	$0.306998\pi$
$468$	−4.31443			−0.199435
$469$	13.0634			0.603210
$470$	7.31966	−	7.78447i	0.337631	−	0.359071i
$471$			4.28456i			0.197422i
$472$	−0.917356	+	0.917356i	−0.0422248	+	0.0422248i
$473$	13.0340			0.599302
$474$	−12.7440			−0.585351
$475$	−7.84138	−	6.93131i	−0.359787	−	0.318030i
$476$	−5.59765	−	5.59765i	−0.256568	−	0.256568i
$477$	−1.87850	−	1.87850i	−0.0860105	−	0.0860105i
$478$	1.04218	−	1.04218i	0.0476681	−	0.0476681i
$479$	−3.98964	−	3.98964i	−0.182291	−	0.182291i	0.610062	−	0.792353i	$-0.291144\pi$
$479$	−3.98964	−	3.98964i	−0.182291	−	0.182291i	−0.792353	+	0.610062i	$0.791144\pi$
$480$	1.53176	−	1.62902i	0.0699148	−	0.0743545i
$481$	−11.4701	−	23.6044i	−0.522992	−	1.07627i
$482$	−2.39676	−	2.39676i	−0.109169	−	0.109169i
$483$	−10.5559			−0.480312
$484$	−6.70073			−0.304579
$485$	31.6065	−	0.972640i	1.43518	−	0.0441653i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	33.5571			1.52062			0.760309	−	0.649561i	$-0.225047\pi$
$487$	33.5571			1.52062			0.760309	+	0.649561i	$0.225047\pi$
$488$	−5.87589	+	5.87589i	−0.265989	+	0.265989i
$489$	4.52216	+	4.52216i	0.204499	+	0.204499i
$490$	4.75038	−	0.146186i	0.214600	−	0.00660399i
$491$	31.9342			1.44117			0.720585	−	0.693366i	$-0.243873\pi$
$491$	31.9342			1.44117			0.720585	+	0.693366i	$0.243873\pi$
$492$	2.68710	−	2.68710i	0.121144	−	0.121144i
$493$	−0.956475	+	0.956475i	−0.0430775	+	0.0430775i
$494$	6.38566	+	6.38566i	0.287304	+	0.287304i
$495$	4.63422	−	0.142611i	0.208293	−	0.00640988i
$496$	0.391381	+	0.391381i	0.0175735	+	0.0175735i
$497$	−19.5786	−	19.5786i	−0.878222	−	0.878222i
$498$			0.539372i			0.0241698i
$499$	−25.1910	+	25.1910i	−1.12770	+	1.12770i	−0.137154	+	0.990550i	$0.543796\pi$
$499$	−25.1910	+	25.1910i	−1.12770	+	1.12770i	−0.990550	+	0.137154i	$0.956204\pi$
$500$	−11.1328	+	1.03038i	−0.497872	+	0.0460801i
$501$	−5.23439	−	5.23439i	−0.233855	−	0.233855i
$502$	14.2994	−	14.2994i	0.638214	−	0.638214i
$503$		−	6.19986i		−	0.276438i	−0.990402	−	0.138219i	$-0.955862\pi$
$503$		−	6.19986i		−	0.276438i	0.990402	−	0.138219i	$-0.0441378\pi$
$504$	−2.13605	−	2.13605i	−0.0951473	−	0.0951473i
$505$	−0.525735	−	17.0841i	−0.0233949	−	0.760231i
$506$		−	7.24548i		−	0.322101i
$507$	−3.96992	−	3.96992i	−0.176310	−	0.176310i
$508$	6.18161	+	6.18161i	0.274265	+	0.274265i
$509$	−2.76652			−0.122624			−0.0613120	−	0.998119i	$-0.519528\pi$
$509$	−2.76652			−0.122624			−0.0613120	+	0.998119i	$0.519528\pi$
$510$	4.01406	−	4.26896i	0.177746	−	0.189033i
$511$		−	36.3188i		−	1.60665i
$512$		−	1.00000i		−	0.0441942i
$513$	2.09313			0.0924141
$514$			22.9481i			1.01220i
$515$	−22.0346	+	0.678081i	−0.970962	+	0.0298798i
$516$	4.44492	−	4.44492i	0.195677	−	0.195677i
$517$	7.00621	−	7.00621i	0.308133	−	0.308133i
$518$	6.00760	−	17.3652i	0.263959	−	0.762983i
$519$		−	23.1907i		−	1.01796i
$520$	9.64280	−	0.296742i	0.422865	−	0.0130130i
$521$		−	9.79854i		−	0.429282i	−0.976693	−	0.214641i	$-0.931142\pi$
$521$		−	9.79854i		−	0.429282i	0.976693	−	0.214641i	$-0.0688581\pi$
$522$	−0.364989	+	0.364989i	−0.0159751	+	0.0159751i
$523$			10.5951i			0.463289i	0.972800	+	0.231645i	$0.0744107\pi$
$523$			10.5951i			0.463289i	−0.972800	+	0.231645i	$0.925589\pi$
$524$	−1.03836	−	1.03836i	−0.0453608	−	0.0453608i
$525$	0.928735	+	15.0756i	0.0405333	+	0.657953i
$526$	−0.797307	+	0.797307i	−0.0347642	+	0.0347642i
$527$	1.02564	+	1.02564i	0.0446775	+	0.0446775i
$528$	1.46616	−	1.46616i	0.0638065	−	0.0638065i
$529$	10.7893			0.469101
$530$	4.32766	+	4.06926i	0.187982	+	0.176757i
$531$	−0.917356	+	0.917356i	−0.0398099	+	0.0398099i
$532$			6.32301i			0.274137i
$533$	16.3954			0.710163
$534$			5.21363i			0.225616i
$535$	9.60901	+	9.03526i	0.415434	+	0.390629i
$536$	3.05783	+	3.05783i	0.132078	+	0.132078i
$537$	−22.9736			−0.991385
$538$	17.8697			0.770418
$539$	4.40703			0.189824
$540$	1.53176	−	1.62902i	0.0659163	−	0.0701021i
$541$	23.3766	−	23.3766i	1.00504	−	1.00504i	0.00505037	−	0.999987i	$-0.498392\pi$
$541$	23.3766	−	23.3766i	1.00504	−	1.00504i	0.999987	−	0.00505037i	$-0.00160759\pi$
$542$			20.7623i			0.891818i
$543$	−3.85874	−	3.85874i	−0.165594	−	0.165594i
$544$		−	2.62056i		−	0.112356i
$545$	1.06214	+	0.998722i	0.0454971	+	0.0427805i
$546$		−	13.0332i		−	0.557769i
$547$		−	17.2554i		−	0.737787i	−0.929472	−	0.368894i	$-0.879737\pi$
$547$		−	17.2554i		−	0.737787i	0.929472	−	0.368894i	$-0.120263\pi$
$548$	13.3475	+	13.3475i	0.570176	+	0.570176i
$549$	−5.87589	+	5.87589i	−0.250777	+	0.250777i
$550$	−10.3477	+	0.637473i	−0.441228	+	0.0271820i
$551$	1.08042			0.0460273
$552$	−2.47090	−	2.47090i	−0.105168	−	0.105168i
$553$		−	38.4975i		−	1.63708i
$554$	17.8467			0.758233
$555$	12.9847	+	4.04944i	0.551169	+	0.171889i
$556$	−12.1026			−0.513267
$557$			17.6010i			0.745779i	0.927876	+	0.372889i	$0.121633\pi$
$557$			17.6010i			0.745779i	−0.927876	+	0.372889i	$0.878367\pi$
$558$	0.391381	+	0.391381i	0.0165685	+	0.0165685i
$559$	27.1208			1.14709
$560$	4.92101	+	4.62718i	0.207951	+	0.195534i
$561$	3.84217	−	3.84217i	0.162216	−	0.162216i
$562$	10.2645	+	10.2645i	0.432983	+	0.432983i
$563$		−	24.3413i		−	1.02586i	−0.858429	−	0.512932i	$-0.828559\pi$
$563$		−	24.3413i		−	1.02586i	0.858429	−	0.512932i	$-0.171441\pi$
$564$		−	4.77861i		−	0.201216i
$565$	−38.7110	+	1.19127i	−1.62859	+	0.0501172i
$566$			9.49377i			0.399053i
$567$	−2.13605	−	2.13605i	−0.0897058	−	0.0897058i
$568$		−	9.16581i		−	0.384589i
$569$	−3.96188	+	3.96188i	−0.166090	+	0.166090i	−0.785259	−	0.619168i	$-0.787470\pi$
$569$	−3.96188	+	3.96188i	−0.166090	+	0.166090i	0.619168	+	0.785259i	$0.287470\pi$
$570$	−4.67818	+	0.143963i	−0.195947	+	0.00602997i
$571$	−12.7277			−0.532638			−0.266319	−	0.963885i	$-0.585807\pi$
$571$	−12.7277			−0.532638			−0.266319	+	0.963885i	$0.585807\pi$
$572$	8.94583			0.374044
$573$	−11.9882			−0.500812
$574$	8.11728	+	8.11728i	0.338809	+	0.338809i
$575$	1.07432	+	17.4388i	0.0448024	+	0.727250i
$576$		−	1.00000i		−	0.0416667i
$577$	−30.3340			−1.26282			−0.631410	−	0.775449i	$-0.717524\pi$
$577$	−30.3340			−1.26282			−0.631410	+	0.775449i	$0.717524\pi$
$578$			10.1327i			0.421463i
$579$	−0.576459	+	0.576459i	−0.0239568	+	0.0239568i
$580$	0.790650	−	0.840857i	0.0328300	−	0.0349147i
$581$	−1.62935			−0.0675970
$582$	9.99958	−	9.99958i	0.414496	−	0.414496i
$583$	3.89500	+	3.89500i	0.161315	+	0.161315i
$584$	8.50139	−	8.50139i	0.351790	−	0.351790i
$585$	9.64280	−	0.296742i	0.398681	−	0.0122688i
$586$	1.37161	+	1.37161i	0.0566606	+	0.0566606i
$587$		−	25.0340i		−	1.03327i	−0.856207	−	0.516633i	$-0.827185\pi$
$587$		−	25.0340i		−	1.03327i	0.856207	−	0.516633i	$-0.172815\pi$
$588$	1.50291	−	1.50291i	0.0619791	−	0.0619791i
$589$		−	1.15854i		−	0.0477369i
$590$	1.98721	−	2.11340i	0.0818120	−	0.0870071i
$591$		−	17.1851i		−	0.706900i
$592$	5.47103	−	2.65855i	0.224858	−	0.109266i
$593$	16.2930	−	16.2930i	0.669073	−	0.669073i	−0.288428	−	0.957502i	$-0.593133\pi$
$593$	16.2930	−	16.2930i	0.669073	−	0.669073i	0.957502	+	0.288428i	$0.0931327\pi$
$594$	1.46616	−	1.46616i	0.0601574	−	0.0601574i
$595$	12.8958	+	12.1258i	0.528677	+	0.497110i
$596$		−	1.78006i		−	0.0729141i
$597$	9.09548			0.372253
$598$		−	15.0763i		−	0.616514i
$599$			18.7185i			0.764818i	0.923993	+	0.382409i	$0.124905\pi$
$599$			18.7185i			0.764818i	−0.923993	+	0.382409i	$0.875095\pi$
$600$	−3.31145	+	3.74624i	−0.135189	+	0.152940i
$601$	−34.1418			−1.39267			−0.696337	−	0.717715i	$-0.745188\pi$
$601$	−34.1418			−1.39267			−0.696337	+	0.717715i	$0.745188\pi$
$602$	13.4274	+	13.4274i	0.547259	+	0.547259i
$603$	3.05783	+	3.05783i	0.124524	+	0.124524i
$604$		−	14.7620i		−	0.600658i
$605$	14.9762	−	0.460869i	0.608869	−	0.0187370i
$606$	−5.40501	−	5.40501i	−0.219564	−	0.219564i
$607$			15.4550i			0.627298i	0.949539	+	0.313649i	$0.101551\pi$
$607$			15.4550i			0.627298i	−0.949539	+	0.313649i	$0.898449\pi$
$608$	−1.48007	+	1.48007i	−0.0600247	+	0.0600247i
$609$	−1.10257	−	1.10257i	−0.0446784	−	0.0446784i
$610$	12.7285	−	13.5368i	0.515363	−	0.548089i
$611$	14.5784	−	14.5784i	0.589779	−	0.589779i
$612$		−	2.62056i		−	0.105930i
$613$	25.2055	+	25.2055i	1.01804	+	1.01804i	0.999834	+	0.0182063i	$0.00579555\pi$
$613$	25.2055	+	25.2055i	1.01804	+	1.01804i	0.0182063	+	0.999834i	$0.494204\pi$
$614$	12.9742	+	12.9742i	0.523596	+	0.523596i
$615$	−5.82087	+	6.19050i	−0.234720	+	0.249625i
$616$	4.42903	+	4.42903i	0.178451	+	0.178451i
$617$	−14.0812	+	14.0812i	−0.566887	+	0.566887i	−0.931255	−	0.364368i	$-0.881285\pi$
$617$	−14.0812	+	14.0812i	−0.566887	+	0.566887i	0.364368	+	0.931255i	$0.381285\pi$
$618$	−6.97126	+	6.97126i	−0.280425	+	0.280425i
$619$	11.5159			0.462861			0.231431	−	0.972851i	$-0.425659\pi$
$619$	11.5159			0.462861			0.231431	+	0.972851i	$0.425659\pi$
$620$	−0.901660	−	0.847823i	−0.0362115	−	0.0340494i
$621$	−2.47090	−	2.47090i	−0.0991538	−	0.0991538i
$622$	21.1073	−	21.1073i	0.846327	−	0.846327i
$623$	−15.7495			−0.630991
$624$	3.05076	−	3.05076i	0.122128	−	0.122128i
$625$	24.8110	−	3.06861i	0.992438	−	0.122745i
$626$	−27.9746			−1.11809
$627$	−4.34004			−0.173325
$628$	−3.02964	−	3.02964i	−0.120896	−	0.120896i
$629$	14.3372	−	6.96688i	0.571660	−	0.277788i
$630$	4.92101	+	4.62718i	0.196058	+	0.184351i
$631$	24.9435	+	24.9435i	0.992985	+	0.992985i	0.999976	−	0.00699059i	$-0.00222519\pi$
$631$	24.9435	+	24.9435i	0.992985	+	0.992985i	−0.00699059	+	0.999976i	$0.502225\pi$
$632$	9.01137	−	9.01137i	0.358453	−	0.358453i
$633$	−1.30741	−	1.30741i	−0.0519649	−	0.0519649i
$634$	4.72175	+	4.72175i	0.187525	+	0.187525i
$635$	−14.2411	−	13.3908i	−0.565142	−	0.531398i
$636$	2.65660			0.105341
$637$	9.17007			0.363331
$638$	0.756793	−	0.756793i	0.0299617	−	0.0299617i
$639$		−	9.16581i		−	0.362594i
$640$	0.0687789	+	2.23501i	0.00271873	+	0.0883465i
$641$	41.0494			1.62136			0.810678	−	0.585492i	$-0.199099\pi$
$641$	41.0494			1.62136			0.810678	+	0.585492i	$0.199099\pi$
$642$	5.89863			0.232800
$643$	16.4624			0.649212			0.324606	−	0.945849i	$-0.394768\pi$
$643$	16.4624			0.649212			0.324606	+	0.945849i	$0.394768\pi$
$644$	7.46418	−	7.46418i	0.294130	−	0.294130i
$645$	−9.62873	+	10.2402i	−0.379131	+	0.403206i
$646$	−3.87861	+	3.87861i	−0.152602	+	0.152602i
$647$			40.3405i			1.58595i	0.609256	+	0.792974i	$0.291468\pi$
$647$			40.3405i			1.58595i	−0.609256	+	0.792974i	$0.708532\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	1.90211	−	1.90211i	0.0746643	−	0.0746643i
$650$	−21.5313	+	1.32644i	−0.844528	+	0.0520273i
$651$	−1.18230	+	1.18230i	−0.0463379	+	0.0463379i
$652$	−6.39530			−0.250459
$653$	−34.2938			−1.34202			−0.671009	−	0.741449i	$-0.734139\pi$
$653$	−34.2938			−1.34202			−0.671009	+	0.741449i	$0.734139\pi$
$654$	0.652011			0.0254956
$655$	2.39216	+	2.24932i	0.0934692	+	0.0878883i
$656$			3.80013i			0.148370i
$657$	8.50139	−	8.50139i	0.331671	−	0.331671i
$658$	14.4354			0.562750
$659$	−35.9415			−1.40008			−0.700040	−	0.714104i	$-0.746835\pi$
$659$	−35.9415			−1.40008			−0.700040	+	0.714104i	$0.746835\pi$
$660$	−3.17605	+	3.37773i	−0.123627	+	0.131478i
$661$	15.5165	+	15.5165i	0.603520	+	0.603520i	0.941245	−	0.337725i	$-0.109657\pi$
$661$	15.5165	+	15.5165i	0.603520	+	0.603520i	−0.337725	+	0.941245i	$0.609657\pi$
$662$	−5.59691	−	5.59691i	−0.217530	−	0.217530i
$663$	7.99471	−	7.99471i	0.310489	−	0.310489i
$664$	−0.381394	−	0.381394i	−0.0148009	−	0.0148009i
$665$	−0.434890	−	14.1320i	−0.0168643	−	0.548015i
$666$	5.47103	−	2.65855i	0.211998	−	0.103017i
$667$	−1.27541	−	1.27541i	−0.0493841	−	0.0493841i
$668$	7.40255			0.286413
$669$	6.86570			0.265443
$670$	−7.04459	−	6.62397i	−0.272156	−	0.255906i
$671$	12.1835	−	12.1835i	0.470337	−	0.470337i
$672$	3.02083			0.116531
$673$	32.7754	−	32.7754i	1.26340	−	1.26340i	0.313966	−	0.949434i	$-0.398342\pi$
$673$	32.7754	−	32.7754i	1.26340	−	1.26340i	0.949434	−	0.313966i	$-0.101658\pi$
$674$	−15.5752	−	15.5752i	−0.599933	−	0.599933i
$675$	−3.31145	+	3.74624i	−0.127458	+	0.144193i
$676$	5.61431			0.215935
$677$	5.04971	−	5.04971i	0.194076	−	0.194076i	−0.603379	−	0.797455i	$-0.706179\pi$
$677$	5.04971	−	5.04971i	0.194076	−	0.194076i	0.797455	+	0.603379i	$0.206179\pi$
$678$	−12.2473	+	12.2473i	−0.470355	+	0.470355i
$679$	30.2071	+	30.2071i	1.15924	+	1.15924i
$680$	0.180239	+	5.85698i	0.00691186	+	0.224605i
$681$	−13.8310	−	13.8310i	−0.530007	−	0.530007i
$682$	−0.811517	−	0.811517i	−0.0310746	−	0.0310746i
$683$		−	35.9730i		−	1.37647i	−0.725488	−	0.688235i	$-0.758386\pi$
$683$		−	35.9730i		−	1.37647i	0.725488	−	0.688235i	$-0.241614\pi$
$684$	−1.48007	+	1.48007i	−0.0565919	+	0.0565919i
$685$	−30.7498	−	28.9137i	−1.17489	−	1.10474i
$686$	−10.4123	−	10.4123i	−0.397544	−	0.397544i
$687$	−3.90766	+	3.90766i	−0.149086	+	0.149086i
$688$			6.28607i			0.239654i
$689$	8.10465	+	8.10465i	0.308762	+	0.308762i
$690$	5.69243	+	5.35254i	0.216707	+	0.203768i
$691$			18.4832i			0.703135i	0.936163	+	0.351567i	$0.114351\pi$
$691$			18.4832i			0.703135i	−0.936163	+	0.351567i	$0.885649\pi$
$692$	16.3983	+	16.3983i	0.623369	+	0.623369i
$693$	4.42903	+	4.42903i	0.168245	+	0.168245i
$694$	7.34661			0.278873
$695$	27.0495	−	0.832407i	1.02605	−	0.0315750i
$696$		−	0.516172i		−	0.0195655i
$697$			9.95847i			0.377204i
$698$	−5.62756			−0.213006
$699$		−	11.4215i		−	0.432001i
$700$	−11.3168	−	10.0033i	−0.427734	−	0.378091i
$701$	−14.1983	+	14.1983i	−0.536264	+	0.536264i	−0.922429	−	0.386166i	$-0.873799\pi$
$701$	−14.1983	+	14.1983i	−0.536264	+	0.536264i	0.386166	+	0.922429i	$0.373799\pi$
$702$	3.05076	−	3.05076i	0.115144	−	0.115144i
$703$	−12.0323	−	4.16266i	−0.453808	−	0.156998i
$704$			2.07347i			0.0781467i
$705$	0.328667	+	10.6802i	0.0123783	+	0.402241i
$706$		−	25.6724i		−	0.966192i
$707$	16.3276	−	16.3276i	0.614064	−	0.614064i
$708$		−	1.29734i		−	0.0487569i
$709$	−19.8820	−	19.8820i	−0.746684	−	0.746684i	0.227171	−	0.973855i	$-0.427053\pi$
$709$	−19.8820	−	19.8820i	−0.746684	−	0.746684i	−0.973855	+	0.227171i	$0.927053\pi$
$710$	0.630414	+	20.4857i	0.0236590	+	0.768814i
$711$	9.01137	−	9.01137i	0.337953	−	0.337953i
$712$	−3.68659	−	3.68659i	−0.138161	−	0.138161i
$713$	−1.36764	+	1.36764i	−0.0512183	+	0.0512183i
$714$	7.91628			0.296259
$715$	−19.9940	+	0.615285i	−0.747734	+	0.0230103i
$716$	16.2448	−	16.2448i	0.607097	−	0.607097i
$717$			1.47386i			0.0550424i
$718$	−29.6458			−1.10637
$719$		−	5.03356i		−	0.187720i	−0.995585	−	0.0938601i	$-0.970079\pi$
$719$		−	5.03356i		−	0.187720i	0.995585	−	0.0938601i	$-0.0299206\pi$
$720$	0.0687789	+	2.23501i	0.00256324	+	0.0832939i
$721$	−21.0590	−	21.0590i	−0.784279	−	0.784279i
$722$	−14.6188			−0.544055
$723$	3.38953			0.126058
$724$	5.45708			0.202811
$725$	−1.70928	+	1.93370i	−0.0634810	+	0.0718160i
$726$	4.73813	−	4.73813i	0.175849	−	0.175849i
$727$		−	6.59381i		−	0.244551i	−0.992496	−	0.122275i	$-0.960981\pi$
$727$		−	6.59381i		−	0.244551i	0.992496	−	0.122275i	$-0.0390191\pi$
$728$	9.21585	+	9.21585i	0.341562	+	0.341562i
$729$		−	1.00000i		−	0.0370370i
$730$	−18.4160	+	19.5854i	−0.681606	+	0.724888i
$731$			16.4730i			0.609277i
$732$		−	8.30976i		−	0.307138i
$733$	−32.6674	−	32.6674i	−1.20660	−	1.20660i	−0.972122	−	0.234474i	$-0.924663\pi$
$733$	−32.6674	−	32.6674i	−1.20660	−	1.20660i	−0.234474	−	0.972122i	$-0.575337\pi$
$734$	−22.3758	+	22.3758i	−0.825904	+	0.825904i
$735$	−3.25566	+	3.46240i	−0.120087	+	0.127712i
$736$	3.49438			0.128805
$737$	−6.34031	−	6.34031i	−0.233548	−	0.233548i
$738$			3.80013i			0.139885i
$739$	2.57619			0.0947665			0.0473833	−	0.998877i	$-0.484912\pi$
$739$	2.57619			0.0947665			0.0473833	+	0.998877i	$0.484912\pi$
$740$	−12.0449	+	6.31817i	−0.442781	+	0.232261i
$741$	−9.03068			−0.331750
$742$			8.02514i			0.294612i
$743$	16.2323	+	16.2323i	0.595504	+	0.595504i	0.939113	−	0.343609i	$-0.111649\pi$
$743$	16.2323	+	16.2323i	0.595504	+	0.595504i	−0.343609	+	0.939113i	$0.611649\pi$
$744$	−0.553497			−0.0202922
$745$	0.122431	+	3.97845i	0.00448551	+	0.145759i
$746$	−2.58745	+	2.58745i	−0.0947334	+	0.0947334i
$747$	−0.381394	−	0.381394i	−0.0139545	−	0.0139545i
$748$			5.43364i			0.198674i
$749$			17.8188i			0.651084i
$750$	7.14346	−	8.60064i	0.260842	−	0.314051i
$751$			9.18070i			0.335009i	0.985871	+	0.167504i	$0.0535708\pi$
$751$			9.18070i			0.335009i	−0.985871	+	0.167504i	$0.946429\pi$
$752$	3.37898	+	3.37898i	0.123219	+	0.123219i
$753$			20.2224i			0.736946i
$754$	1.57472	−	1.57472i	0.0573479	−	0.0573479i
$755$	1.01532	+	32.9933i	0.0369511	+	1.20075i
$756$	3.02083			0.109867
$757$	7.11882			0.258738			0.129369	−	0.991597i	$-0.458705\pi$
$757$	7.11882			0.258738			0.129369	+	0.991597i	$0.458705\pi$
$758$	30.1390			1.09470
$759$	5.12333	+	5.12333i	0.185965	+	0.185965i
$760$	3.20617	−	3.40977i	0.116300	−	0.123685i
$761$		−	7.70500i		−	0.279306i	−0.990200	−	0.139653i	$-0.955401\pi$
$761$		−	7.70500i		−	0.279306i	0.990200	−	0.139653i	$-0.0445987\pi$
$762$	−8.74212			−0.316694
$763$			1.96962i			0.0713049i
$764$	8.47691	−	8.47691i	0.306684	−	0.306684i
$765$	0.180239	+	5.85698i	0.00651656	+	0.211759i
$766$	27.3379			0.987759
$767$	3.95787	−	3.95787i	0.142910	−	0.142910i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	30.6954	−	30.6954i	1.10690	−	1.10690i	0.113349	−	0.993555i	$-0.463842\pi$
$769$	30.6954	−	30.6954i	1.10690	−	1.10690i	0.993555	−	0.113349i	$-0.0361579\pi$
$770$	−10.2036	−	9.59431i	−0.367711	−	0.345755i
$771$	−16.2267	−	16.2267i	−0.584392	−	0.584392i
$772$		−	0.815237i		−	0.0293410i
$773$	−26.9674	+	26.9674i	−0.969949	+	0.969949i	−0.999561	−	0.0296121i	$-0.990573\pi$
$773$	−26.9674	+	26.9674i	−0.969949	+	0.969949i	0.0296121	+	0.999561i	$0.490573\pi$
$774$			6.28607i			0.225948i
$775$	2.07353	+	1.83288i	0.0744835	+	0.0658389i
$776$			14.1415i			0.507652i
$777$	8.03103	+	16.5271i	0.288112	+	0.592905i
$778$	7.29908	−	7.29908i	0.261685	−	0.261685i
$779$	5.62445	−	5.62445i	0.201517	−	0.201517i
$780$	−6.60866	+	7.02831i	−0.236628	+	0.251654i
$781$			19.0050i			0.680052i
$782$	9.15723			0.327462
$783$		−	0.516172i		−	0.0184465i
$784$			2.12544i			0.0759086i
$785$	6.97966	+	6.56290i	0.249115	+	0.234240i
$786$	1.46846			0.0523782
$787$	5.73093	+	5.73093i	0.204286	+	0.204286i	0.801833	−	0.597548i	$-0.203858\pi$
$787$	5.73093	+	5.73093i	0.204286	+	0.204286i	−0.597548	+	0.801833i	$0.703858\pi$
$788$	12.1517	+	12.1517i	0.432886	+	0.432886i
$789$		−	1.12756i		−	0.0401423i
$790$	−19.5207	+	20.7603i	−0.694515	+	0.738618i
$791$	−36.9971	−	36.9971i	−1.31546	−	1.31546i
$792$			2.07347i			0.0736774i
$793$	25.3511	−	25.3511i	0.900245	−	0.900245i
$794$	−23.8828	−	23.8828i	−0.847568	−	0.847568i
$795$	−5.93752	+	0.182718i	−0.210582	+	0.00648033i
$796$	−6.43148	+	6.43148i	−0.227958	+	0.227958i
$797$			53.4909i			1.89474i	0.320135	+	0.947372i	$0.396272\pi$
$797$			53.4909i			1.89474i	−0.320135	+	0.947372i	$0.603728\pi$
$798$	−4.47104	−	4.47104i	−0.158273	−	0.158273i
$799$	8.85483	+	8.85483i	0.313261	+	0.313261i
$800$	−0.307443	−	4.99054i	−0.0108698	−	0.176442i
$801$	−3.68659	−	3.68659i	−0.130259	−	0.130259i
$802$	9.30160	−	9.30160i	0.328451	−	0.328451i
$803$	−17.6273	+	17.6273i	−0.622056	+	0.622056i
$804$	−4.32442			−0.152511
$805$	−16.1691	+	17.1959i	−0.569887	+	0.606075i
$806$	−1.68859	−	1.68859i	−0.0594780	−	0.0594780i
$807$	−12.6358	+	12.6358i	−0.444801	+	0.444801i
$808$	7.64384			0.268909
$809$	18.8689	−	18.8689i	0.663396	−	0.663396i	−0.292783	−	0.956179i	$-0.594581\pi$
$809$	18.8689	−	18.8689i	0.663396	−	0.663396i	0.956179	+	0.292783i	$0.0945815\pi$
$810$	0.0687789	+	2.23501i	0.00241665	+	0.0785302i
$811$	−7.19705			−0.252723			−0.126361	−	0.991984i	$-0.540330\pi$
$811$	−7.19705			−0.252723			−0.126361	+	0.991984i	$0.540330\pi$
$812$	1.55927			0.0547197
$813$	−14.6812	−	14.6812i	−0.514891	−	0.514891i
$814$	−11.3440	+	5.51241i	−0.397607	+	0.193210i
$815$	14.2936	−	0.439862i	0.500681	−	0.0154077i
$816$	1.85302	+	1.85302i	0.0648685	+	0.0648685i
$817$	9.30382	−	9.30382i	0.325499	−	0.325499i
$818$	24.5847	+	24.5847i	0.859583	+	0.859583i
$819$	9.21585	+	9.21585i	0.322028	+	0.322028i
$820$	−0.261369	−	8.49333i	−0.00912739	−	0.296600i
$821$	18.4340			0.643352			0.321676	−	0.946850i	$-0.395754\pi$
$821$	18.4340			0.643352			0.321676	+	0.946850i	$0.395754\pi$
$822$	−18.8762			−0.658382
$823$	−34.1801	+	34.1801i	−1.19144	+	1.19144i	−0.214782	+	0.976662i	$0.568904\pi$
$823$	−34.1801	+	34.1801i	−1.19144	+	1.19144i	−0.976662	+	0.214782i	$0.931096\pi$
$824$		−	9.85885i		−	0.343449i
$825$	6.86618	−	7.76770i	0.239050	−	0.270437i
$826$	3.91904			0.136361
$827$	22.3642			0.777681			0.388840	−	0.921305i	$-0.372876\pi$
$827$	22.3642			0.777681			0.388840	+	0.921305i	$0.372876\pi$
$828$	3.49438			0.121438
$829$	−13.4981	+	13.4981i	−0.468809	+	0.468809i	−0.901529	−	0.432719i	$-0.857554\pi$
$829$	−13.4981	+	13.4981i	−0.468809	+	0.468809i	0.432719	+	0.901529i	$0.357554\pi$
$830$	0.878651	+	0.826187i	0.0304984	+	0.0286774i
$831$	−12.6195	+	12.6195i	−0.437766	+	0.437766i
$832$			4.31443i			0.149576i
$833$			5.56984i			0.192984i
$834$	8.55786	−	8.55786i	0.296335	−	0.296335i
$835$	−16.5448	+	0.509139i	−0.572555	+	0.0176195i
$836$	3.06887	−	3.06887i	0.106139	−	0.106139i
$837$	−0.553497			−0.0191317
$838$	−23.6748			−0.817831
$839$	17.9355			0.619202			0.309601	−	0.950867i	$-0.399805\pi$
$839$	17.9355			0.619202			0.309601	+	0.950867i	$0.399805\pi$
$840$	−6.75159	+	0.207770i	−0.232952	+	0.00716874i
$841$			28.7336i			0.990813i
$842$	−26.6921	+	26.6921i	−0.919870	+	0.919870i
$843$	−14.5162			−0.499965
$844$	1.84896			0.0636437
$845$	−12.5480	+	0.386146i	−0.431666	+	0.0132838i
$846$	3.37898	+	3.37898i	0.116172	+	0.116172i
$847$	14.3131	+	14.3131i	0.491805	+	0.491805i
$848$	−1.87850	+	1.87850i	−0.0645079	+	0.0645079i
$849$	−6.71311	−	6.71311i	−0.230393	−	0.230393i
$850$	−0.805673	−	13.0780i	−0.0276344	−	0.448572i
$851$	9.28997	+	19.1178i	0.318456	+	0.655351i
$852$	6.48120	+	6.48120i	0.222042	+	0.222042i
$853$	48.5949			1.66386			0.831929	−	0.554883i	$-0.187237\pi$
$853$	48.5949			1.66386			0.831929	+	0.554883i	$0.187237\pi$
$854$	25.1024			0.858987
$855$	3.20617	−	3.40977i	0.109649	−	0.116612i
$856$	−4.17096	+	4.17096i	−0.142560	+	0.142560i
$857$	−27.6764			−0.945409			−0.472704	−	0.881221i	$-0.656722\pi$
$857$	−27.6764			−0.945409			−0.472704	+	0.881221i	$0.656722\pi$
$858$	−6.32566	+	6.32566i	−0.215954	+	0.215954i
$859$	1.92645	+	1.92645i	0.0657295	+	0.0657295i	0.739207	−	0.673478i	$-0.235200\pi$
$859$	1.92645	+	1.92645i	0.0657295	+	0.0657295i	−0.673478	+	0.739207i	$0.735200\pi$
$860$	−0.432349	−	14.0494i	−0.0147430	−	0.479081i
$861$	−11.4796			−0.391222
$862$	25.8053	−	25.8053i	0.878931	−	0.878931i
$863$	4.85716	−	4.85716i	0.165340	−	0.165340i	−0.619588	−	0.784927i	$-0.712700\pi$
$863$	4.85716	−	4.85716i	0.165340	−	0.165340i	0.784927	+	0.619588i	$0.212700\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−37.7782	−	35.5224i	−1.28450	−	1.20780i
$866$	2.62555	+	2.62555i	0.0892197	+	0.0892197i
$867$	−7.16488	−	7.16488i	−0.243332	−	0.243332i
$868$		−	1.67202i		−	0.0567522i
$869$	−18.6848	+	18.6848i	−0.633838	+	0.633838i
$870$	0.0355018	+	1.15365i	0.00120362	+	0.0391124i
$871$	−13.1928	−	13.1928i	−0.447021	−	0.447021i
$872$	−0.461041	+	0.461041i	−0.0156128	+	0.0156128i
$873$			14.1415i			0.478619i
$874$	−5.17192	−	5.17192i	−0.174943	−	0.174943i
$875$	25.9811	+	21.5792i	0.878322	+	0.729510i
$876$			12.0228i			0.406212i
$877$	41.2031	+	41.2031i	1.39133	+	1.39133i	0.822353	+	0.568978i	$0.192661\pi$
$877$	41.2031	+	41.2031i	1.39133	+	1.39133i	0.568978	+	0.822353i	$0.307339\pi$
$878$	−4.04448	−	4.04448i	−0.136495	−	0.136495i
$879$	−1.93975			−0.0654261
$880$	−0.142611	−	4.63422i	−0.00480741	−	0.156220i
$881$		−	4.54000i		−	0.152957i	−0.997071	−	0.0764783i	$-0.975632\pi$
$881$		−	4.54000i		−	0.152957i	0.997071	−	0.0764783i	$-0.0243676\pi$
$882$			2.12544i			0.0715673i
$883$	−0.358056			−0.0120495			−0.00602477	−	0.999982i	$-0.501918\pi$
$883$	−0.358056			−0.0120495			−0.00602477	+	0.999982i	$0.501918\pi$
$884$			11.3062i			0.380269i
$885$	0.0892295	+	2.89956i	0.00299942	+	0.0974678i
$886$	0.534873	−	0.534873i	0.0179694	−	0.0179694i
$887$	−15.5018	+	15.5018i	−0.520498	+	0.520498i	−0.917722	−	0.397223i	$-0.869974\pi$
$887$	−15.5018	+	15.5018i	−0.520498	+	0.520498i	0.397223	+	0.917722i	$0.369974\pi$
$888$	−1.98872	+	5.74848i	−0.0667372	+	0.192906i
$889$		−	26.4085i		−	0.885712i
$890$	8.49313	+	7.98601i	0.284690	+	0.267692i
$891$			2.07347i			0.0694638i
$892$	−4.85478	+	4.85478i	−0.162550	+	0.162550i
$893$		−	10.0023i		−	0.334713i
$894$	1.25869	+	1.25869i	0.0420970	+	0.0420970i
$895$	−35.1900	+	37.4246i	−1.17627	+	1.25097i
$896$	−2.13605	+	2.13605i	−0.0713605	+	0.0713605i
$897$	10.6605	+	10.6605i	0.355945	+	0.355945i
$898$	−15.2168	+	15.2168i	−0.507790	+	0.507790i
$899$	−0.285700			−0.00952862
$900$	−0.307443	−	4.99054i	−0.0102481	−	0.166351i
$901$	−4.92271	+	4.92271i	−0.163999	+	0.163999i
$902$		−	7.87944i		−	0.262357i
$903$	−18.9892			−0.631920
$904$		−	17.3203i		−	0.576064i
$905$	−12.1966	+	0.375332i	−0.405429	+	0.0124765i
$906$	10.4383	+	10.4383i	0.346790	+	0.346790i
$907$	−28.0078			−0.929984			−0.464992	−	0.885315i	$-0.653943\pi$
$907$	−28.0078			−0.929984			−0.464992	+	0.885315i	$0.653943\pi$
$908$	19.5601			0.649123
$909$	7.64384			0.253530
$910$	−21.2314	−	19.9637i	−0.703813	−	0.661789i
$911$	−28.1566	+	28.1566i	−0.932870	+	0.932870i	−0.997884	−	0.0650140i	$-0.979291\pi$
$911$	−28.1566	+	28.1566i	−0.932870	+	0.932870i	0.0650140	+	0.997884i	$0.479291\pi$
$912$		−	2.09313i		−	0.0693106i
$913$	0.790807	+	0.790807i	0.0261719	+	0.0261719i
$914$			26.8366i			0.887676i
$915$	0.571537	+	18.5724i	0.0188944	+	0.613985i
$916$		−	5.52626i		−	0.182593i
$917$			4.43597i			0.146489i
$918$	1.85302	+	1.85302i	0.0611586	+	0.0611586i
$919$	−23.6708	+	23.6708i	−0.780828	+	0.780828i	−0.979970	−	0.199143i	$-0.936184\pi$
$919$	−23.6708	+	23.6708i	−0.780828	+	0.780828i	0.199143	+	0.979970i	$0.436184\pi$
$920$	−7.80997	+	0.240340i	−0.257487	+	0.00792376i
$921$	−18.3483			−0.604596
$922$	−9.31792	−	9.31792i	−0.306869	−	0.306869i
$923$			39.5452i			1.30165i
$924$	−6.26360			−0.206057
$925$	26.4860	−	14.9496i	0.870855	−	0.491540i
$926$	−31.8446			−1.04648
$927$		−	9.85885i		−	0.323807i
$928$	0.364989	+	0.364989i	0.0119813	+	0.0119813i
$929$	23.2278			0.762081			0.381040	−	0.924558i	$-0.375566\pi$
$929$	23.2278			0.762081			0.381040	+	0.924558i	$0.375566\pi$
$930$	1.23707	−	0.0380689i	0.0405652	−	0.00124833i
$931$	3.14580	−	3.14580i	0.103099	−	0.103099i
$932$	8.07622	+	8.07622i	0.264545	+	0.264545i
$933$			29.8503i			0.977254i
$934$		−	24.6295i		−	0.805902i
$935$	−0.373720	−	12.1442i	−0.0122220	−	0.397159i
$936$			4.31443i			0.141022i
$937$	12.8916	+	12.8916i	0.421152	+	0.421152i	0.885600	−	0.464449i	$-0.153747\pi$
$937$	12.8916	+	12.8916i	0.421152	+	0.421152i	−0.464449	+	0.885600i	$0.653747\pi$
$938$		−	13.0634i		−	0.426534i
$939$	19.7810	−	19.7810i	0.645529	−	0.645529i
$940$	−7.78447	−	7.31966i	−0.253901	−	0.238741i
$941$	13.8545			0.451643			0.225821	−	0.974169i	$-0.427493\pi$
$941$	13.8545			0.451643			0.225821	+	0.974169i	$0.427493\pi$
$942$	4.28456			0.139599
$943$	−13.2791			−0.432427
$944$	0.917356	+	0.917356i	0.0298574	+	0.0298574i
$945$	−6.75159	+	0.207770i	−0.219629	+	0.00675875i
$946$		−	13.0340i		−	0.423771i
$947$	−45.6796			−1.48439			−0.742194	−	0.670185i	$-0.766215\pi$
$947$	−45.6796			−1.48439			−0.742194	+	0.670185i	$0.766215\pi$
$948$			12.7440i			0.413906i
$949$	−36.6786	+	36.6786i	−1.19064	+	1.19064i
$950$	−6.93131	+	7.84138i	−0.224881	+	0.254408i
$951$	−6.67756			−0.216535
$952$	−5.59765	+	5.59765i	−0.181421	+	0.181421i
$953$	−9.42694	−	9.42694i	−0.305368	−	0.305368i	0.537741	−	0.843110i	$-0.319278\pi$
$953$	−9.42694	−	9.42694i	−0.305368	−	0.305368i	−0.843110	+	0.537741i	$0.819278\pi$
$954$	−1.87850	+	1.87850i	−0.0608186	+	0.0608186i
$955$	−18.3629	+	19.5290i	−0.594211	+	0.631944i
$956$	−1.04218	−	1.04218i	−0.0337065	−	0.0337065i
$957$			1.07027i			0.0345968i
$958$	−3.98964	+	3.98964i	−0.128899	+	0.128899i
$959$		−	57.0218i		−	1.84133i
$960$	−1.62902	−	1.53176i	−0.0525765	−	0.0494372i
$961$		−	30.6936i		−	0.990117i
$962$	−23.6044	+	11.4701i	−0.761035	+	0.369811i
$963$	−4.17096	+	4.17096i	−0.134407	+	0.134407i
$964$	−2.39676	+	2.39676i	−0.0771944	+	0.0771944i
$965$	0.0560711	+	1.82206i	0.00180499	+	0.0586543i
$966$			10.5559i			0.339632i
$967$	44.8271			1.44154			0.720772	−	0.693173i	$-0.243788\pi$
$967$	44.8271			1.44154			0.720772	+	0.693173i	$0.243788\pi$
$968$			6.70073i			0.215370i
$969$		−	5.48518i		−	0.176209i
$970$	−0.972640	−	31.6065i	−0.0312296	−	1.01482i
$971$	14.5531			0.467030			0.233515	−	0.972353i	$-0.424977\pi$
$971$	14.5531			0.467030			0.233515	+	0.972353i	$0.424977\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	25.8519	+	25.8519i	0.828774	+	0.828774i
$974$		−	33.5571i		−	1.07524i
$975$	14.2870	−	16.1629i	0.457551	−	0.517627i
$976$	5.87589	+	5.87589i	0.188083	+	0.188083i
$977$			3.38584i			0.108323i	0.998532	+	0.0541613i	$0.0172485\pi$
$977$			3.38584i			0.108323i	−0.998532	+	0.0541613i	$0.982751\pi$
$978$	4.52216	−	4.52216i	0.144603	−	0.144603i
$979$	7.64403	+	7.64403i	0.244304	+	0.244304i
$980$	−0.146186	−	4.75038i	−0.00466973	−	0.151745i
$981$	−0.461041	+	0.461041i	−0.0147199	+	0.0147199i
$982$		−	31.9342i		−	1.01906i
$983$	22.1865	+	22.1865i	0.707640	+	0.707640i	0.966038	−	0.258398i	$-0.0831947\pi$
$983$	22.1865	+	22.1865i	0.707640	+	0.707640i	−0.258398	+	0.966038i	$0.583195\pi$
$984$	−2.68710	−	2.68710i	−0.0856615	−	0.0856615i
$985$	−27.9949	−	26.3234i	−0.891993	−	0.838733i
$986$	0.956475	+	0.956475i	0.0304604	+	0.0304604i
$987$	−10.2074	+	10.2074i	−0.324904	+	0.324904i
$988$	6.38566	−	6.38566i	0.203155	−	0.203155i
$989$	−21.9659			−0.698475
$990$	−0.142611	−	4.63422i	−0.00453247	−	0.147285i
$991$	−0.255920	−	0.255920i	−0.00812958	−	0.00812958i	0.703030	−	0.711160i	$-0.251830\pi$
$991$	−0.255920	−	0.255920i	−0.00812958	−	0.00812958i	−0.711160	+	0.703030i	$0.751830\pi$
$992$	0.391381	−	0.391381i	0.0124264	−	0.0124264i
$993$	7.91522			0.251182
$994$	−19.5786	+	19.5786i	−0.620997	+	0.620997i
$995$	13.9321	−	14.8168i	0.441676	−	0.469723i
$996$	0.539372			0.0170907
$997$	−35.1093			−1.11192			−0.555962	−	0.831208i	$-0.687650\pi$
$997$	−35.1093			−1.11192			−0.555962	+	0.831208i	$0.687650\pi$
$998$	25.1910	+	25.1910i	0.797407	+	0.797407i
$999$	−1.98872	+	5.74848i	−0.0629204	+	0.181874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.697.16	yes	36
5.3	odd	4		1110.2.o.a.253.3	yes	36
37.6	odd	4		1110.2.o.a.487.3	yes	36
185.43	even	4	inner	1110.2.l.a.43.16	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.16	✓	36	185.43	even	4	inner
1110.2.l.a.697.16	yes	36	1.1	even	1	trivial
1110.2.o.a.253.3	yes	36	5.3	odd	4
1110.2.o.a.487.3	yes	36	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.23501 - 0.0687789i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(2.23501 - 0.0687789i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.13605 + 2.13605i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-0.0687789 - 2.23501i) q^{10} -2.07347i q^{11} +(-0.707107 - 0.707107i) q^{12} -4.31443i q^{13} +(2.13605 - 2.13605i) q^{14} +(1.62902 + 1.53176i) q^{15} +1.00000 q^{16} +2.62056 q^{17} +1.00000 q^{18} +(-1.48007 - 1.48007i) q^{19} +(-2.23501 + 0.0687789i) q^{20} +3.02083i q^{21} -2.07347 q^{22} +3.49438i q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.99054 - 0.307443i) q^{25} -4.31443 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.13605 - 2.13605i) q^{28} +(-0.364989 + 0.364989i) q^{29} +(1.53176 - 1.62902i) q^{30} +(0.391381 + 0.391381i) q^{31} -1.00000i q^{32} +(1.46616 - 1.46616i) q^{33} -2.62056i q^{34} +(4.92101 + 4.62718i) q^{35} -1.00000i q^{36} +(5.47103 - 2.65855i) q^{37} +(-1.48007 + 1.48007i) q^{38} +(3.05076 - 3.05076i) q^{39} +(0.0687789 + 2.23501i) q^{40} +3.80013i q^{41} +3.02083 q^{42} +6.28607i q^{43} +2.07347i q^{44} +(0.0687789 + 2.23501i) q^{45} +3.49438 q^{46} +(3.37898 + 3.37898i) q^{47} +(0.707107 + 0.707107i) q^{48} +2.12544i q^{49} +(-0.307443 - 4.99054i) q^{50} +(1.85302 + 1.85302i) q^{51} +4.31443i q^{52} +(-1.87850 + 1.87850i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-0.142611 - 4.63422i) q^{55} +(-2.13605 + 2.13605i) q^{56} -2.09313i q^{57} +(0.364989 + 0.364989i) q^{58} +(0.917356 + 0.917356i) q^{59} +(-1.62902 - 1.53176i) q^{60} +(5.87589 + 5.87589i) q^{61} +(0.391381 - 0.391381i) q^{62} +(-2.13605 + 2.13605i) q^{63} -1.00000 q^{64} +(-0.296742 - 9.64280i) q^{65} +(-1.46616 - 1.46616i) q^{66} +(3.05783 - 3.05783i) q^{67} -2.62056 q^{68} +(-2.47090 + 2.47090i) q^{69} +(4.62718 - 4.92101i) q^{70} -9.16581 q^{71} -1.00000 q^{72} +(-8.50139 - 8.50139i) q^{73} +(-2.65855 - 5.47103i) q^{74} +(3.74624 + 3.31145i) q^{75} +(1.48007 + 1.48007i) q^{76} +(4.42903 - 4.42903i) q^{77} +(-3.05076 - 3.05076i) q^{78} +(-9.01137 - 9.01137i) q^{79} +(2.23501 - 0.0687789i) q^{80} -1.00000 q^{81} +3.80013 q^{82} +(-0.381394 + 0.381394i) q^{83} -3.02083i q^{84} +(5.85698 - 0.180239i) q^{85} +6.28607 q^{86} -0.516172 q^{87} +2.07347 q^{88} +(-3.68659 + 3.68659i) q^{89} +(2.23501 - 0.0687789i) q^{90} +(9.21585 - 9.21585i) q^{91} -3.49438i q^{92} +0.553497i q^{93} +(3.37898 - 3.37898i) q^{94} +(-3.40977 - 3.20617i) q^{95} +(0.707107 - 0.707107i) q^{96} +14.1415 q^{97} +2.12544 q^{98} +2.07347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 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 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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