LMFDB - Embedded newform 115.2.e.a.22.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.e (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 $ x^20 - 6x^18 + 3x^16 + 80x^14 - 600x^12 + 3500x^10 - 15000x^8 + 50000x^6 + 46875x^4 - 2343750*x^2 + 9765625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.6
Root			$2.11159 + 0.735651i$ of defining polynomial
Character	$\chi$	$=$	115.22
Dual form			115.2.e.a.68.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459187 - 0.459187i) q^{2} +(-1.79404 + 1.79404i) q^{3} -1.57829i q^{4} +(0.735651 + 2.11159i) q^{5} +1.64760 q^{6} +(-2.52854 + 2.52854i) q^{7} +(-1.64311 + 1.64311i) q^{8} -3.43715i q^{9} +O(q^{10})$	\(q+(-0.459187 - 0.459187i) q^{2} +(-1.79404 + 1.79404i) q^{3} -1.57829i q^{4} +(0.735651 + 2.11159i) q^{5} +1.64760 q^{6} +(-2.52854 + 2.52854i) q^{7} +(-1.64311 + 1.64311i) q^{8} -3.43715i q^{9} +(0.631815 - 1.30742i) q^{10} +4.72931i q^{11} +(2.83152 + 2.83152i) q^{12} +(0.0648135 - 0.0648135i) q^{13} +2.32215 q^{14} +(-5.10806 - 2.46849i) q^{15} -1.64760 q^{16} +(4.37241 - 4.37241i) q^{17} +(-1.57829 + 1.57829i) q^{18} -1.60835 q^{19} +(3.33271 - 1.16107i) q^{20} -9.07259i q^{21} +(2.17164 - 2.17164i) q^{22} +(3.01543 - 3.72923i) q^{23} -5.89559i q^{24} +(-3.91764 + 3.10679i) q^{25} -0.0595231 q^{26} +(0.784256 + 0.784256i) q^{27} +(3.99078 + 3.99078i) q^{28} +3.20459i q^{29} +(1.21206 + 3.47906i) q^{30} +7.58141 q^{31} +(4.04277 + 4.04277i) q^{32} +(-8.48456 - 8.48456i) q^{33} -4.01551 q^{34} +(-7.19936 - 3.47912i) q^{35} -5.42483 q^{36} +(-4.93570 + 4.93570i) q^{37} +(0.738533 + 0.738533i) q^{38} +0.232556i q^{39} +(-4.67832 - 2.26082i) q^{40} +2.15659 q^{41} +(-4.16602 + 4.16602i) q^{42} +(-0.563291 - 0.563291i) q^{43} +7.46424 q^{44} +(7.25785 - 2.52854i) q^{45} +(-3.09706 + 0.327767i) q^{46} +(2.59257 + 2.59257i) q^{47} +(2.95586 - 2.95586i) q^{48} -5.78701i q^{49} +(3.22553 + 0.372332i) q^{50} +15.6885i q^{51} +(-0.102295 - 0.102295i) q^{52} +(6.28379 + 6.28379i) q^{53} -0.720241i q^{54} +(-9.98637 + 3.47912i) q^{55} -8.30932i q^{56} +(2.88544 - 2.88544i) q^{57} +(1.47151 - 1.47151i) q^{58} +5.31810i q^{59} +(-3.89600 + 8.06202i) q^{60} -5.90216i q^{61} +(-3.48129 - 3.48129i) q^{62} +(8.69095 + 8.69095i) q^{63} -0.417581i q^{64} +(0.184540 + 0.0891796i) q^{65} +7.79201i q^{66} +(0.206392 - 0.206392i) q^{67} +(-6.90095 - 6.90095i) q^{68} +(1.28058 + 12.1002i) q^{69} +(1.70829 + 4.90342i) q^{70} +3.84194 q^{71} +(5.64760 + 5.64760i) q^{72} +(2.10156 - 2.10156i) q^{73} +4.53282 q^{74} +(1.45470 - 12.6021i) q^{75} +2.53845i q^{76} +(-11.9582 - 11.9582i) q^{77} +(0.106787 - 0.106787i) q^{78} -9.58990 q^{79} +(-1.21206 - 3.47906i) q^{80} +7.49747 q^{81} +(-0.990278 - 0.990278i) q^{82} +(4.70018 + 4.70018i) q^{83} -14.3192 q^{84} +(12.4493 + 6.01618i) q^{85} +0.517313i q^{86} +(-5.74916 - 5.74916i) q^{87} +(-7.77076 - 7.77076i) q^{88} -8.50580 q^{89} +(-4.49378 - 2.17164i) q^{90} +0.327767i q^{91} +(-5.88582 - 4.75924i) q^{92} +(-13.6013 + 13.6013i) q^{93} -2.38095i q^{94} +(-1.18318 - 3.39617i) q^{95} -14.5058 q^{96} +(2.58241 - 2.58241i) q^{97} +(-2.65732 + 2.65732i) q^{98} +16.2553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.459187	−	0.459187i	−0.324695	−	0.324695i	0.525870	−	0.850565i	$-0.323740\pi$
$2$	−0.459187	−	0.459187i	−0.324695	−	0.324695i	−0.850565	+	0.525870i	$0.823740\pi$
$3$	−1.79404	+	1.79404i	−1.03579	+	1.03579i	−0.0364530	+	0.999335i	$0.511606\pi$
$3$	−1.79404	+	1.79404i	−1.03579	+	1.03579i	−0.999335	+	0.0364530i	$0.988394\pi$
$4$		−	1.57829i		−	0.789147i
$5$	0.735651	+	2.11159i	0.328993	+	0.944332i
$5$	0.735651	+	2.11159i	0.328993	+	0.944332i
$6$	1.64760			0.672630
$7$	−2.52854	+	2.52854i	−0.955698	+	0.955698i	−0.999059	−	0.0433619i	$-0.986193\pi$
$7$	−2.52854	+	2.52854i	−0.955698	+	0.955698i	0.0433619	+	0.999059i	$0.486193\pi$
$8$	−1.64311	+	1.64311i	−0.580926	+	0.580926i
$9$		−	3.43715i		−	1.14572i
$10$	0.631815	−	1.30742i	0.199797	−	0.413442i
$11$			4.72931i			1.42594i	0.701194	+	0.712970i	$0.252651\pi$
$11$			4.72931i			1.42594i	−0.701194	+	0.712970i	$0.747349\pi$
$12$	2.83152	+	2.83152i	0.817389	+	0.817389i
$13$	0.0648135	−	0.0648135i	0.0179760	−	0.0179760i	−0.698062	−	0.716038i	$-0.745954\pi$
$13$	0.0648135	−	0.0648135i	0.0179760	−	0.0179760i	0.716038	+	0.698062i	$0.245954\pi$
$14$	2.32215			0.620619
$15$	−5.10806	−	2.46849i	−1.31890	−	0.637361i
$16$	−1.64760			−0.411900
$17$	4.37241	−	4.37241i	1.06047	−	1.06047i	0.0624149	−	0.998050i	$-0.480120\pi$
$17$	4.37241	−	4.37241i	1.06047	−	1.06047i	0.998050	−	0.0624149i	$-0.0198802\pi$
$18$	−1.57829	+	1.57829i	−0.372007	+	0.372007i
$19$	−1.60835			−0.368980			−0.184490	−	0.982834i	$-0.559063\pi$
$19$	−1.60835			−0.368980			−0.184490	+	0.982834i	$0.559063\pi$
$20$	3.33271	−	1.16107i	0.745217	−	0.259624i
$21$		−	9.07259i		−	1.97980i
$22$	2.17164	−	2.17164i	0.462995	−	0.462995i
$23$	3.01543	−	3.72923i	0.628761	−	0.777598i
$23$	3.01543	−	3.72923i	0.628761	−	0.777598i
$24$		−	5.89559i		−	1.20343i
$25$	−3.91764	+	3.10679i	−0.783527	+	0.621357i
$26$	−0.0595231			−0.0116734
$27$	0.784256	+	0.784256i	0.150930	+	0.150930i
$28$	3.99078	+	3.99078i	0.754186	+	0.754186i
$29$			3.20459i			0.595077i	0.954710	+	0.297539i	$0.0961657\pi$
$29$			3.20459i			0.595077i	−0.954710	+	0.297539i	$0.903834\pi$
$30$	1.21206	+	3.47906i	0.221290	+	0.635186i
$31$	7.58141			1.36166			0.680831	−	0.732441i	$-0.261619\pi$
$31$	7.58141			1.36166			0.680831	+	0.732441i	$0.261619\pi$
$32$	4.04277	+	4.04277i	0.714668	+	0.714668i
$33$	−8.48456	−	8.48456i	−1.47697	−	1.47697i
$34$	−4.01551			−0.688654
$35$	−7.19936	−	3.47912i	−1.21691	−	0.588078i
$36$	−5.42483			−0.904138
$37$	−4.93570	+	4.93570i	−0.811424	+	0.811424i	−0.984847	−	0.173423i	$-0.944517\pi$
$37$	−4.93570	+	4.93570i	−0.811424	+	0.811424i	0.173423	+	0.984847i	$0.444517\pi$
$38$	0.738533	+	0.738533i	0.119806	+	0.119806i
$39$			0.232556i			0.0372387i
$40$	−4.67832	−	2.26082i	−0.739708	−	0.357467i
$41$	2.15659			0.336802			0.168401	−	0.985719i	$-0.446140\pi$
$41$	2.15659			0.336802			0.168401	+	0.985719i	$0.446140\pi$
$42$	−4.16602	+	4.16602i	−0.642830	+	0.642830i
$43$	−0.563291	−	0.563291i	−0.0859011	−	0.0859011i	0.662851	−	0.748752i	$-0.269346\pi$
$43$	−0.563291	−	0.563291i	−0.0859011	−	0.0859011i	−0.748752	+	0.662851i	$0.769346\pi$
$44$	7.46424			1.12528
$45$	7.25785	−	2.52854i	1.08194	−	0.376932i
$46$	−3.09706	+	0.327767i	−0.456637	+	0.0483266i
$47$	2.59257	+	2.59257i	0.378165	+	0.378165i	0.870440	−	0.492275i	$-0.163835\pi$
$47$	2.59257	+	2.59257i	0.378165	+	0.378165i	−0.492275	+	0.870440i	$0.663835\pi$
$48$	2.95586	−	2.95586i	0.426641	−	0.426641i
$49$		−	5.78701i		−	0.826716i
$50$	3.22553	+	0.372332i	0.456158	+	0.0526557i
$51$			15.6885i			2.19684i
$52$	−0.102295	−	0.102295i	−0.0141857	−	0.0141857i
$53$	6.28379	+	6.28379i	0.863145	+	0.863145i	0.991702	−	0.128557i	$-0.0410346\pi$
$53$	6.28379	+	6.28379i	0.863145	+	0.863145i	−0.128557	+	0.991702i	$0.541035\pi$
$54$		−	0.720241i		−	0.0980123i
$55$	−9.98637	+	3.47912i	−1.34656	+	0.469124i
$56$		−	8.30932i		−	1.11038i
$57$	2.88544	−	2.88544i	0.382185	−	0.382185i
$58$	1.47151	−	1.47151i	0.193218	−	0.193218i
$59$			5.31810i			0.692358i	0.938169	+	0.346179i	$0.112521\pi$
$59$			5.31810i			0.692358i	−0.938169	+	0.346179i	$0.887479\pi$
$60$	−3.89600	+	8.06202i	−0.502972	+	1.04080i
$61$		−	5.90216i		−	0.755694i	−0.925868	−	0.377847i	$-0.876665\pi$
$61$		−	5.90216i		−	0.755694i	0.925868	−	0.377847i	$-0.123335\pi$
$62$	−3.48129	−	3.48129i	−0.442124	−	0.442124i
$63$	8.69095	+	8.69095i	1.09496	+	1.09496i
$64$		−	0.417581i		−	0.0521976i
$65$	0.184540	+	0.0891796i	0.0228893	+	0.0110614i
$66$			7.79201i			0.959130i
$67$	0.206392	−	0.206392i	0.0252149	−	0.0252149i	−0.694387	−	0.719602i	$-0.744324\pi$
$67$	0.206392	−	0.206392i	0.0252149	−	0.0252149i	0.719602	+	0.694387i	$0.244324\pi$
$68$	−6.90095	−	6.90095i	−0.836863	−	0.836863i
$69$	1.28058	+	12.1002i	0.154164	+	1.45669i
$70$	1.70829	+	4.90342i	0.204179	+	0.586071i
$71$	3.84194			0.455954			0.227977	−	0.973667i	$-0.426789\pi$
$71$	3.84194			0.455954			0.227977	+	0.973667i	$0.426789\pi$
$72$	5.64760	+	5.64760i	0.665576	+	0.665576i
$73$	2.10156	−	2.10156i	0.245969	−	0.245969i	−0.573345	−	0.819314i	$-0.694355\pi$
$73$	2.10156	−	2.10156i	0.245969	−	0.245969i	0.819314	+	0.573345i	$0.194355\pi$
$74$	4.53282			0.526930
$75$	1.45470	−	12.6021i	0.167974	−	1.45516i
$76$			2.53845i			0.291180i
$77$	−11.9582	−	11.9582i	−1.36277	−	1.36277i
$78$	0.106787	−	0.106787i	0.0120912	−	0.0120912i
$79$	−9.58990			−1.07895			−0.539474	−	0.842002i	$-0.681377\pi$
$79$	−9.58990			−1.07895			−0.539474	+	0.842002i	$0.681377\pi$
$80$	−1.21206	−	3.47906i	−0.135512	−	0.388970i
$81$	7.49747			0.833052
$82$	−0.990278	−	0.990278i	−0.109358	−	0.109358i
$83$	4.70018	+	4.70018i	0.515911	+	0.515911i	0.916332	−	0.400420i	$-0.131136\pi$
$83$	4.70018	+	4.70018i	0.515911	+	0.515911i	−0.400420	+	0.916332i	$0.631136\pi$
$84$	−14.3192			−1.56235
$85$	12.4493	+	6.01618i	1.35032	+	0.652546i
$86$			0.517313i			0.0557833i
$87$	−5.74916	−	5.74916i	−0.616374	−	0.616374i
$88$	−7.77076	−	7.77076i	−0.828366	−	0.828366i
$89$	−8.50580			−0.901613			−0.450807	−	0.892622i	$-0.648864\pi$
$89$	−8.50580			−0.901613			−0.450807	+	0.892622i	$0.648864\pi$
$90$	−4.49378	−	2.17164i	−0.473686	−	0.228911i
$91$			0.327767i			0.0343593i
$92$	−5.88582	−	4.75924i	−0.613639	−	0.496185i
$93$	−13.6013	+	13.6013i	−1.41039	+	1.41039i
$94$		−	2.38095i		−	0.245576i
$95$	−1.18318	−	3.39617i	−0.121392	−	0.348440i
$96$	−14.5058			−1.48049
$97$	2.58241	−	2.58241i	0.262204	−	0.262204i	−0.563745	−	0.825949i	$-0.690640\pi$
$97$	2.58241	−	2.58241i	0.262204	−	0.262204i	0.825949	+	0.563745i	$0.190640\pi$
$98$	−2.65732	+	2.65732i	−0.268430	+	0.268430i
$99$	16.2553			1.63372
$100$	4.90342	+	6.18318i	0.490342	+	0.618318i
$101$	7.53167			0.749429			0.374715	−	0.927140i	$-0.377741\pi$
$101$	7.53167			0.749429			0.374715	+	0.927140i	$0.377741\pi$
$102$	7.20398	−	7.20398i	0.713300	−	0.713300i
$103$	−5.92689	−	5.92689i	−0.583994	−	0.583994i	0.352004	−	0.935998i	$-0.385500\pi$
$103$	−5.92689	−	5.92689i	−0.583994	−	0.583994i	−0.935998	+	0.352004i	$0.885500\pi$
$104$			0.212991i			0.0208855i
$105$	19.1576	−	6.67425i	1.86959	−	0.651340i
$106$		−	5.77087i		−	0.560517i
$107$	2.50380	−	2.50380i	0.242052	−	0.242052i	−0.575647	−	0.817699i	$-0.695250\pi$
$107$	2.50380	−	2.50380i	0.242052	−	0.242052i	0.817699	+	0.575647i	$0.195250\pi$
$108$	1.23779	−	1.23779i	0.119106	−	0.119106i
$109$	18.9903			1.81894			0.909468	−	0.415773i	$-0.136489\pi$
$109$	18.9903			1.81894			0.909468	+	0.415773i	$0.136489\pi$
$110$	6.18318	+	2.98805i	0.589543	+	0.284899i
$111$		−	17.7097i		−	1.68093i
$112$	4.16602	−	4.16602i	0.393652	−	0.393652i
$113$	0.920190	+	0.920190i	0.0865642	+	0.0865642i	0.749063	−	0.662499i	$-0.230504\pi$
$113$	0.920190	+	0.920190i	0.0865642	+	0.0865642i	−0.662499	+	0.749063i	$0.730504\pi$
$114$	−2.64991			−0.248187
$115$	10.0929	+	3.62395i	0.941169	+	0.337935i
$116$	5.05778			0.469603
$117$	−0.222774	−	0.222774i	−0.0205954	−	0.0205954i
$118$	2.44200	−	2.44200i	0.224805	−	0.224805i
$119$			22.1116i			2.02697i
$120$	12.4491	−	4.33710i	1.13644	−	0.395921i
$121$	−11.3664			−1.03331
$122$	−2.71020	+	2.71020i	−0.245370	+	0.245370i
$123$	−3.86900	+	3.86900i	−0.348856	+	0.348856i
$124$		−	11.9657i		−	1.07455i
$125$	−9.44228	−	5.98694i	−0.844543	−	0.535488i
$126$		−	7.98155i		−	0.711053i
$127$	−1.98007	−	1.98007i	−0.175703	−	0.175703i	0.613777	−	0.789480i	$-0.289649\pi$
$127$	−1.98007	−	1.98007i	−0.175703	−	0.175703i	−0.789480	+	0.613777i	$0.789649\pi$
$128$	7.89380	−	7.89380i	0.697720	−	0.697720i
$129$	2.02113			0.177951
$130$	−0.0437882	−	0.125689i	−0.00384048	−	0.0110236i
$131$	−7.58866			−0.663024			−0.331512	−	0.943451i	$-0.607559\pi$
$131$	−7.58866			−0.663024			−0.331512	+	0.943451i	$0.607559\pi$
$132$	−13.3911	+	13.3911i	−1.16555	+	1.16555i
$133$	4.06677	−	4.06677i	0.352634	−	0.352634i
$134$	−0.189546			−0.0163742
$135$	−1.07909	+	2.23297i	−0.0928732	+	0.192183i
$136$			14.3687i			1.23210i
$137$	−10.6809	+	10.6809i	−0.912534	+	0.912534i	−0.996471	−	0.0839372i	$-0.973250\pi$
$137$	−10.6809	+	10.6809i	−0.912534	+	0.912534i	0.0839372	+	0.996471i	$0.473250\pi$
$138$	4.96823	−	6.14428i	0.422923	−	0.523036i
$139$		−	15.5905i		−	1.32237i	−0.750223	−	0.661185i	$-0.770054\pi$
$139$		−	15.5905i		−	1.32237i	0.750223	−	0.661185i	$-0.229946\pi$
$140$	−5.49107	+	11.3627i	−0.464080	+	0.960324i
$141$	−9.30233			−0.783398
$142$	−1.76417	−	1.76417i	−0.148046	−	0.148046i
$143$	0.306523	+	0.306523i	0.0256328	+	0.0256328i
$144$			5.66304i			0.471920i
$145$	−6.76678	+	2.35746i	−0.561951	+	0.195776i
$146$	−1.93002			−0.159729
$147$	10.3821	+	10.3821i	0.856302	+	0.856302i
$148$	7.78999	+	7.78999i	0.640333	+	0.640333i
$149$	−8.93810			−0.732238			−0.366119	−	0.930568i	$-0.619314\pi$
$149$	−8.93810			−0.732238			−0.366119	+	0.930568i	$0.619314\pi$
$150$	−6.45470	+	5.11874i	−0.527024	+	0.417943i
$151$	−15.9033			−1.29419			−0.647097	−	0.762408i	$-0.724017\pi$
$151$	−15.9033			−1.29419			−0.647097	+	0.762408i	$0.724017\pi$
$152$	2.64269	−	2.64269i	0.214350	−	0.214350i
$153$	−15.0286	−	15.0286i	−1.21499	−	1.21499i
$154$			10.9821i			0.884966i
$155$	5.57727	+	16.0088i	0.447977	+	1.28586i
$156$	0.367042			0.0293868
$157$	13.8985	−	13.8985i	1.10922	−	1.10922i	0.115971	−	0.993253i	$-0.463002\pi$
$157$	13.8985	−	13.8985i	1.10922	−	1.10922i	0.993253	−	0.115971i	$-0.0369981\pi$
$158$	4.40356	+	4.40356i	0.350329	+	0.350329i
$159$	−22.5467			−1.78807
$160$	−5.56261	+	11.5107i	−0.439763	+	0.910005i
$161$	1.80487	+	17.0541i	0.142243	+	1.34405i
$162$	−3.44274	−	3.44274i	−0.270487	−	0.270487i
$163$	8.90642	−	8.90642i	0.697605	−	0.697605i	−0.266289	−	0.963893i	$-0.585797\pi$
$163$	8.90642	−	8.90642i	0.697605	−	0.697605i	0.963893	+	0.266289i	$0.0857974\pi$
$164$		−	3.40373i		−	0.265787i
$165$	11.6743	−	24.1576i	0.908839	−	1.88067i
$166$		−	4.31652i		−	0.335027i
$167$	10.5555	+	10.5555i	0.816810	+	0.816810i	0.985644	−	0.168834i	$-0.0540003\pi$
$167$	10.5555	+	10.5555i	0.816810	+	0.816810i	−0.168834	+	0.985644i	$0.554000\pi$
$168$	14.9072	+	14.9072i	1.15012	+	1.15012i
$169$			12.9916i			0.999354i
$170$	−2.95401	−	8.47912i	−0.226562	−	0.650319i
$171$			5.52812i			0.422746i
$172$	−0.889039	+	0.889039i	−0.0677886	+	0.0677886i
$173$	4.14681	−	4.14681i	0.315276	−	0.315276i	−0.531674	−	0.846949i	$-0.678437\pi$
$173$	4.14681	−	4.14681i	0.315276	−	0.315276i	0.846949	+	0.531674i	$0.178437\pi$
$174$			5.27988i			0.400267i
$175$	2.05026	−	17.7615i	0.154985	−	1.34264i
$176$		−	7.79201i		−	0.587345i
$177$	−9.54087	−	9.54087i	−0.717136	−	0.717136i
$178$	3.90576	+	3.90576i	0.292749	+	0.292749i
$179$			3.95924i			0.295928i	0.988993	+	0.147964i	$0.0472719\pi$
$179$			3.95924i			0.295928i	−0.988993	+	0.147964i	$0.952728\pi$
$180$	−3.99078	−	11.4550i	−0.297455	−	0.853806i
$181$			11.1132i			0.826040i	0.910722	+	0.413020i	$0.135526\pi$
$181$			11.1132i			0.826040i	−0.910722	+	0.413020i	$0.864474\pi$
$182$	0.150506	−	0.150506i	0.0111563	−	0.0111563i
$183$	10.5887	+	10.5887i	0.782739	+	0.782739i
$184$	1.17285	+	11.0822i	0.0864634	+	0.816991i
$185$	−14.0531	−	6.79123i	−1.03321	−	0.499301i
$186$	12.4911			0.915894
$187$	20.6785	+	20.6785i	1.51216	+	1.51216i
$188$	4.09183	−	4.09183i	0.298428	−	0.298428i
$189$	−3.96604			−0.288487
$190$	−1.01618	+	2.10278i	−0.0737213	+	0.152552i
$191$		−	5.38111i		−	0.389363i	−0.980866	−	0.194682i	$-0.937633\pi$
$191$		−	5.38111i		−	0.389363i	0.980866	−	0.194682i	$-0.0623674\pi$
$192$	0.749156	+	0.749156i	0.0540657	+	0.0540657i
$193$	−13.7523	+	13.7523i	−0.989910	+	0.989910i	−0.999950	−	0.0100391i	$-0.996804\pi$
$193$	−13.7523	+	13.7523i	−0.989910	+	0.989910i	0.0100391	+	0.999950i	$0.496804\pi$
$194$	−2.37162			−0.170272
$195$	−0.491063	+	0.171080i	−0.0351658	+	0.0122513i
$196$	−9.13360			−0.652400
$197$	−4.77126	−	4.77126i	−0.339938	−	0.339938i	0.516406	−	0.856344i	$-0.327270\pi$
$197$	−4.77126	−	4.77126i	−0.339938	−	0.339938i	−0.856344	+	0.516406i	$0.827270\pi$
$198$	−7.46424	−	7.46424i	−0.530460	−	0.530460i
$199$	23.5388			1.66862			0.834311	−	0.551294i	$-0.185866\pi$
$199$	23.5388			1.66862			0.834311	+	0.551294i	$0.185866\pi$
$200$	1.33231	−	11.5419i	0.0942088	−	0.816134i
$201$			0.740552i			0.0522345i
$202$	−3.45845	−	3.45845i	−0.243336	−	0.243336i
$203$	−8.10293	−	8.10293i	−0.568714	−	0.568714i
$204$	24.7611			1.73363
$205$	1.58649	+	4.55383i	0.110806	+	0.318053i
$206$			5.44311i			0.379239i
$207$	−12.8179	−	10.3645i	−0.890906	−	0.720381i
$208$	−0.106787	+	0.106787i	−0.00740433	+	0.00740433i
$209$		−	7.60637i		−	0.526144i
$210$	−11.8617	−	5.73219i	−0.818532	−	0.395559i
$211$	−4.83469			−0.332834			−0.166417	−	0.986055i	$-0.553220\pi$
$211$	−4.83469			−0.332834			−0.166417	+	0.986055i	$0.553220\pi$
$212$	9.91767	−	9.91767i	0.681148	−	0.681148i
$213$	−6.89258	+	6.89258i	−0.472272	+	0.472272i
$214$	−2.29943			−0.157186
$215$	0.775056	−	1.60383i	0.0528584	−	0.109380i
$216$	−2.57723			−0.175358
$217$	−19.1699	+	19.1699i	−1.30134	+	1.30134i
$218$	−8.72009	−	8.72009i	−0.590599	−	0.590599i
$219$			7.54055i			0.509543i
$220$	5.49107	+	15.7614i	0.370208	+	1.06263i
$221$		−	0.566783i		−	0.0381259i
$222$	−8.13206	+	8.13206i	−0.545788	+	0.545788i
$223$	13.4411	−	13.4411i	0.900080	−	0.900080i	−0.0953624	−	0.995443i	$-0.530401\pi$
$223$	13.4411	−	13.4411i	0.900080	−	0.900080i	0.995443	+	0.0953624i	$0.0304010\pi$
$224$	−20.4446			−1.36601
$225$	10.6785	+	13.4655i	0.711899	+	0.897699i
$226$		−	0.845080i		−	0.0562139i
$227$	−8.15679	+	8.15679i	−0.541385	+	0.541385i	−0.923935	−	0.382550i	$-0.875046\pi$
$227$	−8.15679	+	8.15679i	−0.541385	+	0.541385i	0.382550	+	0.923935i	$0.375046\pi$
$228$	−4.55407	−	4.55407i	−0.301600	−	0.301600i
$229$	−1.36560			−0.0902413			−0.0451206	−	0.998982i	$-0.514367\pi$
$229$	−1.36560			−0.0902413			−0.0451206	+	0.998982i	$0.514367\pi$
$230$	−2.97047	−	6.29861i	−0.195867	−	0.415318i
$231$	42.9071			2.82308
$232$	−5.26549	−	5.26549i	−0.345696	−	0.345696i
$233$	−1.62307	+	1.62307i	−0.106331	+	0.106331i	−0.758271	−	0.651940i	$-0.773955\pi$
$233$	−1.62307	+	1.62307i	−0.106331	+	0.106331i	0.651940	+	0.758271i	$0.273955\pi$
$234$			0.204590i			0.0133744i
$235$	−3.56722	+	7.38167i	−0.232700	+	0.481527i
$236$	8.39352			0.546372
$237$	17.2046	−	17.2046i	1.11756	−	1.11756i
$238$	10.1534	−	10.1534i	0.658145	−	0.658145i
$239$		−	26.9697i		−	1.74452i	−0.489040	−	0.872261i	$-0.662653\pi$
$239$		−	26.9697i		−	1.74452i	0.489040	−	0.872261i	$-0.337347\pi$
$240$	8.41604	+	4.06708i	0.543253	+	0.262529i
$241$		−	25.9104i		−	1.66904i	−0.550980	−	0.834519i	$-0.685746\pi$
$241$		−	25.9104i		−	1.66904i	0.550980	−	0.834519i	$-0.314254\pi$
$242$	5.21929	+	5.21929i	0.335509	+	0.335509i
$243$	−15.8035	+	15.8035i	−1.01380	+	1.01380i
$244$	−9.31534			−0.596353
$245$	12.2198	−	4.25722i	0.780694	−	0.271984i
$246$	3.55319			0.226543
$247$	−0.104243	+	0.104243i	−0.00663280	+	0.00663280i
$248$	−12.4571	+	12.4571i	−0.791025	+	0.791025i
$249$	−16.8646			−1.06875
$250$	1.58665	+	7.08490i	0.100348	+	0.448088i
$251$		−	3.73401i		−	0.235688i	−0.993032	−	0.117844i	$-0.962402\pi$
$251$		−	3.73401i		−	0.235688i	0.993032	−	0.117844i	$-0.0375984\pi$
$252$	13.7169	−	13.7169i	0.864082	−	0.864082i
$253$	17.6367	+	14.2609i	1.10881	+	0.896576i
$254$			1.81845i			0.114099i
$255$	−33.1278	+	11.5413i	−2.07454	+	0.722743i
$256$	−8.08462			−0.505289
$257$	−1.27851	−	1.27851i	−0.0797511	−	0.0797511i	0.666106	−	0.745857i	$-0.267960\pi$
$257$	−1.27851	−	1.27851i	−0.0797511	−	0.0797511i	−0.745857	+	0.666106i	$0.767960\pi$
$258$	−0.928079	−	0.928079i	−0.0577796	−	0.0577796i
$259$		−	24.9602i		−	1.55095i
$260$	0.140752	−	0.291258i	0.00872904	−	0.0180631i
$261$	11.0146			0.681789
$262$	3.48462	+	3.48462i	0.215280	+	0.215280i
$263$	−7.28258	−	7.28258i	−0.449063	−	0.449063i	0.445980	−	0.895043i	$-0.352855\pi$
$263$	−7.28258	−	7.28258i	−0.449063	−	0.449063i	−0.895043	+	0.445980i	$0.852855\pi$
$264$	27.8821			1.71602
$265$	−8.64612	+	17.8915i	−0.531127	+	1.09906i
$266$	−3.73482			−0.228996
$267$	15.2597	−	15.2597i	0.933881	−	0.933881i
$268$	−0.325748	−	0.325748i	−0.0198982	−	0.0198982i
$269$			19.1149i			1.16546i	0.812666	+	0.582729i	$0.198015\pi$
$269$			19.1149i			1.16546i	−0.812666	+	0.582729i	$0.801985\pi$
$270$	1.52085	−	0.529845i	0.0925562	−	0.0322454i
$271$	−21.9588			−1.33390			−0.666952	−	0.745101i	$-0.732401\pi$
$271$	−21.9588			−1.33390			−0.666952	+	0.745101i	$0.732401\pi$
$272$	−7.20398	+	7.20398i	−0.436805	+	0.436805i
$273$	−0.588026	−	0.588026i	−0.0355890	−	0.0355890i
$274$	9.80910			0.592589
$275$	−14.6930	−	18.5277i	−0.886018	−	1.11726i
$276$	19.0976	−	2.02113i	1.14954	−	0.121658i
$277$	6.88936	+	6.88936i	0.413942	+	0.413942i	0.883109	−	0.469167i	$-0.155446\pi$
$277$	6.88936	+	6.88936i	0.413942	+	0.413942i	−0.469167	+	0.883109i	$0.655446\pi$
$278$	−7.15897	+	7.15897i	−0.429366	+	0.429366i
$279$		−	26.0584i		−	1.56008i
$280$	17.5459	−	6.11276i	1.04857	−	0.365307i
$281$		−	10.1497i		−	0.605480i	−0.953073	−	0.302740i	$-0.902099\pi$
$281$		−	10.1497i		−	0.605480i	0.953073	−	0.302740i	$-0.0979014\pi$
$282$	4.27151	+	4.27151i	0.254365	+	0.254365i
$283$	−20.4965	−	20.4965i	−1.21839	−	1.21839i	−0.968196	−	0.250191i	$-0.919507\pi$
$283$	−20.4965	−	20.4965i	−1.21839	−	1.21839i	−0.250191	−	0.968196i	$-0.580493\pi$
$284$		−	6.06370i		−	0.359815i
$285$	8.21554	+	3.97019i	0.486646	+	0.235174i
$286$		−	0.281503i		−	0.0166456i
$287$	−5.45301	+	5.45301i	−0.321881	+	0.321881i
$288$	13.8956	−	13.8956i	0.818806	−	0.818806i
$289$		−	21.2359i		−	1.24917i
$290$	4.18974	+	2.02471i	0.246030	+	0.118895i
$291$			9.26587i			0.543175i
$292$	−3.31687	−	3.31687i	−0.194105	−	0.194105i
$293$	−6.66982	−	6.66982i	−0.389655	−	0.389655i	0.484909	−	0.874564i	$-0.338853\pi$
$293$	−6.66982	−	6.66982i	−0.389655	−	0.389655i	−0.874564	+	0.484909i	$0.838853\pi$
$294$		−	9.53467i		−	0.556073i
$295$	−11.2297	+	3.91226i	−0.653816	+	0.227781i
$296$		−	16.2198i		−	0.942755i
$297$	−3.70899	+	3.70899i	−0.215217	+	0.215217i
$298$	4.10426	+	4.10426i	0.237754	+	0.237754i
$299$	−0.0462638	−	0.437146i	−0.00267550	−	0.0252808i
$300$	−19.8898	−	2.29594i	−1.14834	−	0.132556i
$301$	2.84861			0.164191
$302$	7.30260	+	7.30260i	0.420217	+	0.420217i
$303$	−13.5121	+	13.5121i	−0.776250	+	0.776250i
$304$	2.64991			0.151983
$305$	12.4629	−	4.34192i	0.713626	−	0.248618i
$306$			13.8019i			0.789002i
$307$	−2.18915	−	2.18915i	−0.124941	−	0.124941i	0.641871	−	0.766813i	$-0.278158\pi$
$307$	−2.18915	−	2.18915i	−0.124941	−	0.124941i	−0.766813	+	0.641871i	$0.778158\pi$
$308$	−18.8736	+	18.8736i	−1.07542	+	1.07542i
$309$	21.2661			1.20979
$310$	4.79005	−	9.91207i	0.272056	−	0.562968i
$311$	32.7348			1.85622			0.928110	−	0.372307i	$-0.121433\pi$
$311$	32.7348			1.85622			0.928110	+	0.372307i	$0.121433\pi$
$312$	−0.382114	−	0.382114i	−0.0216330	−	0.0216330i
$313$	12.1979	+	12.1979i	0.689469	+	0.689469i	0.962114	−	0.272646i	$-0.0878987\pi$
$313$	12.1979	+	12.1979i	0.689469	+	0.689469i	−0.272646	+	0.962114i	$0.587899\pi$
$314$	−12.7641			−0.720318
$315$	−11.9582	+	24.7452i	−0.673770	+	1.39424i
$316$			15.1357i			0.851449i
$317$	0.370368	+	0.370368i	0.0208020	+	0.0208020i	0.717431	−	0.696629i	$-0.245318\pi$
$317$	0.370368	+	0.370368i	0.0208020	+	0.0208020i	−0.696629	+	0.717431i	$0.745318\pi$
$318$	10.3532	+	10.3532i	0.580577	+	0.580577i
$319$	−15.1555			−0.848545
$320$	0.881760	−	0.307194i	0.0492919	−	0.0171726i
$321$			8.98384i			0.501429i
$322$	7.00227	−	8.65982i	0.390221	−	0.482593i
$323$	−7.03236	+	7.03236i	−0.391291	+	0.391291i
$324$		−	11.8332i		−	0.657400i
$325$	−0.0525540	+	0.455278i	−0.00291517	+	0.0252543i
$326$	−8.17943			−0.453017
$327$	−34.0692	+	34.0692i	−1.88403	+	1.88403i
$328$	−3.54351	+	3.54351i	−0.195657	+	0.195657i
$329$	−13.1108			−0.722823
$330$	−16.4535	+	5.73219i	−0.905737	+	0.315547i
$331$	14.6888			0.807372			0.403686	−	0.914898i	$-0.367729\pi$
$331$	14.6888			0.807372			0.403686	+	0.914898i	$0.367729\pi$
$332$	7.41826	−	7.41826i	0.407130	−	0.407130i
$333$	16.9647	+	16.9647i	0.929661	+	0.929661i
$334$		−	9.69392i		−	0.530428i
$335$	0.587649	+	0.283984i	0.0321067	+	0.0155157i
$336$			14.9480i			0.815480i
$337$	9.43939	−	9.43939i	0.514197	−	0.514197i	−0.401613	−	0.915809i	$-0.631550\pi$
$337$	9.43939	−	9.43939i	0.514197	−	0.514197i	0.915809	+	0.401613i	$0.131550\pi$
$338$	5.96558	−	5.96558i	0.324485	−	0.324485i
$339$	−3.30171			−0.179324
$340$	9.49530	−	19.6487i	0.514955	−	1.06560i
$341$			35.8548i			1.94165i
$342$	2.53845	−	2.53845i	0.137263	−	0.137263i
$343$	−3.06709	−	3.06709i	−0.165608	−	0.165608i
$344$	1.85110			0.0998044
$345$	−24.6086	+	11.6056i	−1.32488	+	0.624823i
$346$	−3.80832			−0.204737
$347$	18.6129	+	18.6129i	0.999191	+	0.999191i	1.00000		0.000808207i	$-0.000257260\pi$
$347$	18.6129	+	18.6129i	0.999191	+	0.999191i	−0.000808207		1.00000i	$0.500257\pi$
$348$	−9.07386	+	9.07386i	−0.486410	+	0.486410i
$349$			12.3226i			0.659614i	0.944048	+	0.329807i	$0.106984\pi$
$349$			12.3226i			0.659614i	−0.944048	+	0.329807i	$0.893016\pi$
$350$	−9.09732	+	7.21441i	−0.486272	+	0.385626i
$351$	0.101661			0.00542625
$352$	−19.1195	+	19.1195i	−1.01907	+	1.01907i
$353$	10.6464	−	10.6464i	0.566653	−	0.566653i	−0.364536	−	0.931189i	$-0.618772\pi$
$353$	10.6464	−	10.6464i	0.566653	−	0.566653i	0.931189	+	0.364536i	$0.118772\pi$
$354$			8.76210i			0.465700i
$355$	2.82632	+	8.11260i	0.150006	+	0.430572i
$356$			13.4247i			0.711506i
$357$	−39.6691	−	39.6691i	−2.09951	−	2.09951i
$358$	1.81803	−	1.81803i	0.0960861	−	0.0960861i
$359$	16.0163			0.845308			0.422654	−	0.906291i	$-0.361098\pi$
$359$	16.0163			0.845308			0.422654	+	0.906291i	$0.361098\pi$
$360$	−7.77076	+	16.0801i	−0.409555	+	0.847495i
$361$	−16.4132			−0.863854
$362$	5.10305	−	5.10305i	0.268211	−	0.268211i
$363$	20.3917	−	20.3917i	1.07029	−	1.07029i
$364$	0.517313			0.0271145
$365$	5.98364	+	2.89162i	0.313198	+	0.151354i
$366$		−	9.72439i		−	0.508302i
$367$	14.0118	−	14.0118i	0.731409	−	0.731409i	−0.239490	−	0.970899i	$-0.576980\pi$
$367$	14.0118	−	14.0118i	0.731409	−	0.731409i	0.970899	+	0.239490i	$0.0769802\pi$
$368$	−4.96823	+	6.14428i	−0.258987	+	0.320293i
$369$		−	7.41251i		−	0.385880i
$370$	3.33457	+	9.57147i	0.173356	+	0.497597i
$371$	−31.7776			−1.64981
$372$	21.4669	+	21.4669i	1.11301	+	1.11301i
$373$	−7.09974	−	7.09974i	−0.367610	−	0.367610i	0.498995	−	0.866605i	$-0.333703\pi$
$373$	−7.09974	−	7.09974i	−0.367610	−	0.367610i	−0.866605	+	0.498995i	$0.833703\pi$
$374$		−	18.9906i		−	0.981980i
$375$	27.6806	−	6.19901i	1.42942	−	0.320115i
$376$	−8.51974			−0.439372
$377$	0.207701	+	0.207701i	0.0106971	+	0.0106971i
$378$	1.82116	+	1.82116i	0.0936702	+	0.0936702i
$379$	−22.2457			−1.14269			−0.571343	−	0.820712i	$-0.693577\pi$
$379$	−22.2457			−1.14269			−0.571343	+	0.820712i	$0.693577\pi$
$380$	−5.36016	+	1.86741i	−0.274970	+	0.0957960i
$381$	7.10464			0.363982
$382$	−2.47094	+	2.47094i	−0.126424	+	0.126424i
$383$	24.7690	+	24.7690i	1.26564	+	1.26564i	0.948319	+	0.317319i	$0.102782\pi$
$383$	24.7690	+	24.7690i	1.26564	+	1.26564i	0.317319	+	0.948319i	$0.397218\pi$
$384$			28.3235i			1.44538i
$385$	16.4538	−	34.0480i	0.838565	−	1.73525i
$386$	12.6297			0.642837
$387$	−1.93611	+	1.93611i	−0.0984182	+	0.0984182i
$388$	−4.07579	−	4.07579i	−0.206917	−	0.206917i
$389$	19.8848			1.00820			0.504100	−	0.863645i	$-0.331824\pi$
$389$	19.8848			1.00820			0.504100	+	0.863645i	$0.331824\pi$
$390$	0.304048	+	0.146932i	0.0153961	+	0.00744020i
$391$	−3.12102	−	29.4904i	−0.157837	−	1.49140i
$392$	9.50868	+	9.50868i	0.480261	+	0.480261i
$393$	13.6143	−	13.6143i	0.686753	−	0.686753i
$394$			4.38180i			0.220752i
$395$	−7.05481	−	20.2499i	−0.354966	−	1.01889i
$396$		−	25.6557i		−	1.28925i
$397$	12.1483	+	12.1483i	0.609706	+	0.609706i	0.942869	−	0.333163i	$-0.108116\pi$
$397$	12.1483	+	12.1483i	0.609706	+	0.609706i	−0.333163	+	0.942869i	$0.608116\pi$
$398$	−10.8087	−	10.8087i	−0.541792	−	0.541792i
$399$			14.5919i			0.730507i
$400$	6.45470	−	5.11874i	0.322735	−	0.255937i
$401$		−	6.80871i		−	0.340011i	−0.985443	−	0.170005i	$-0.945622\pi$
$401$		−	6.80871i		−	0.340011i	0.985443	−	0.170005i	$-0.0543785\pi$
$402$	0.340052	−	0.340052i	0.0169603	−	0.0169603i
$403$	0.491378	−	0.491378i	0.0244773	−	0.0244773i
$404$		−	11.8872i		−	0.591410i
$405$	5.51552	+	15.8316i	0.274068	+	0.786678i
$406$			7.44152i			0.369317i
$407$	−23.3425	−	23.3425i	−1.15704	−	1.15704i
$408$	−25.7780	−	25.7780i	−1.27620	−	1.27620i
$409$			15.9374i			0.788054i	0.919099	+	0.394027i	$0.128918\pi$
$409$			15.9374i			0.788054i	−0.919099	+	0.394027i	$0.871082\pi$
$410$	1.36256	−	2.81956i	0.0672922	−	0.139248i
$411$		−	38.3240i		−	1.89038i
$412$	−9.35438	+	9.35438i	−0.460857	+	0.460857i
$413$	−13.4470	−	13.4470i	−0.661684	−	0.661684i
$414$	1.12658	+	10.6451i	0.0553685	+	0.523176i
$415$	−6.46717	+	13.3825i	−0.317461	+	0.656923i
$416$	0.524053			0.0256938
$417$	27.9700	+	27.9700i	1.36970	+	1.36970i
$418$	−3.49275	+	3.49275i	−0.170836	+	0.170836i
$419$	13.2084			0.645271			0.322635	−	0.946523i	$-0.395431\pi$
$419$	13.2084			0.645271			0.322635	+	0.946523i	$0.395431\pi$
$420$	−10.5339	−	30.2363i	−0.514003	−	1.47538i
$421$			19.7655i			0.963313i	0.876360	+	0.481656i	$0.159965\pi$
$421$			19.7655i			0.963313i	−0.876360	+	0.481656i	$0.840035\pi$
$422$	2.22003	+	2.22003i	0.108069	+	0.108069i
$423$	8.91103	−	8.91103i	0.433269	−	0.433269i
$424$	−20.6499			−1.00285
$425$	−3.54537	+	30.7137i	−0.171976	+	1.48983i
$426$	6.32997			0.306688
$427$	14.9238	+	14.9238i	0.722214	+	0.722214i
$428$	−3.95174	−	3.95174i	−0.191014	−	0.191014i
$429$	−1.09983			−0.0531002
$430$	−1.09235	+	0.380561i	−0.0526779	+	0.0183523i
$431$		−	14.1759i		−	0.682830i	−0.939913	−	0.341415i	$-0.889094\pi$
$431$		−	14.1759i		−	0.682830i	0.939913	−	0.341415i	$-0.110906\pi$
$432$	−1.29214	−	1.29214i	−0.0621681	−	0.0621681i
$433$	13.7696	+	13.7696i	0.661723	+	0.661723i	0.955786	−	0.294063i	$-0.0950076\pi$
$433$	13.7696	+	13.7696i	0.661723	+	0.661723i	−0.294063	+	0.955786i	$0.595008\pi$
$434$	17.6051			0.845074
$435$	7.91050	−	16.3692i	0.379279	−	0.784845i
$436$		−	29.9722i		−	1.43541i
$437$	−4.84986	+	5.99790i	−0.232000	+	0.286918i
$438$	3.46252	−	3.46252i	0.165446	−	0.165446i
$439$			2.77558i			0.132471i	0.997804	+	0.0662357i	$0.0210989\pi$
$439$			2.77558i			0.132471i	−0.997804	+	0.0662357i	$0.978901\pi$
$440$	10.6921	−	22.1252i	0.509726	−	1.05478i
$441$	−19.8908			−0.947181
$442$	−0.260259	+	0.260259i	−0.0123793	+	0.0123793i
$443$	−21.1388	+	21.1388i	−1.00433	+	1.00433i	−0.00434272	+	0.999991i	$0.501382\pi$
$443$	−21.1388	+	21.1388i	−1.00433	+	1.00433i	−0.999991	+	0.00434272i	$0.998618\pi$
$444$	−27.9511			−1.32650
$445$	−6.25730	−	17.9608i	−0.296624	−	0.851423i
$446$	−12.3439			−0.584502
$447$	16.0353	−	16.0353i	0.758443	−	0.758443i
$448$	1.05587	+	1.05587i	0.0498851	+	0.0498851i
$449$			26.8682i			1.26799i	0.773337	+	0.633995i	$0.218586\pi$
$449$			26.8682i			1.26799i	−0.773337	+	0.633995i	$0.781414\pi$
$450$	1.27976	−	11.0866i	0.0603284	−	0.522628i
$451$			10.1992i			0.480260i
$452$	1.45233	−	1.45233i	0.0683119	−	0.0683119i
$453$	28.5311	−	28.5311i	1.34051	−	1.34051i
$454$	7.49099			0.351570
$455$	−0.692110	+	0.241122i	−0.0324466	+	0.0113040i
$456$			9.48217i			0.444043i
$457$	−1.71050	+	1.71050i	−0.0800137	+	0.0800137i	−0.745981	−	0.665967i	$-0.768019\pi$
$457$	−1.71050	+	1.71050i	−0.0800137	+	0.0800137i	0.665967	+	0.745981i	$0.268019\pi$
$458$	0.627066	+	0.627066i	0.0293009	+	0.0293009i
$459$	6.85818			0.320112
$460$	5.71966	−	15.9296i	0.266681	−	0.742721i
$461$	−13.0297			−0.606852			−0.303426	−	0.952855i	$-0.598131\pi$
$461$	−13.0297			−0.606852			−0.303426	+	0.952855i	$0.598131\pi$
$462$	−19.7024	−	19.7024i	−0.916638	−	0.916638i
$463$	4.19572	−	4.19572i	0.194992	−	0.194992i	−0.602857	−	0.797849i	$-0.705971\pi$
$463$	4.19572	−	4.19572i	0.194992	−	0.194992i	0.797849	+	0.602857i	$0.205971\pi$
$464$		−	5.27988i		−	0.245112i
$465$	−38.7263	−	18.7146i	−1.79589	−	0.867871i
$466$	1.49059			0.0690502
$467$	9.47777	−	9.47777i	0.438579	−	0.438579i	−0.452955	−	0.891534i	$-0.649630\pi$
$467$	9.47777	−	9.47777i	0.438579	−	0.438579i	0.891534	+	0.452955i	$0.149630\pi$
$468$	−0.351602	+	0.351602i	−0.0162528	+	0.0162528i
$469$			1.04374i			0.0481955i
$470$	5.02759	−	1.75155i	0.231906	−	0.0807928i
$471$			49.8690i			2.29784i
$472$	−8.73821	−	8.73821i	−0.402209	−	0.402209i
$473$	2.66398	−	2.66398i	0.122490	−	0.122490i
$474$	−15.8003			−0.725732
$475$	6.30092	−	4.99679i	0.289106	−	0.229269i
$476$	34.8986			1.59958
$477$	21.5983	−	21.5983i	0.988918	−	0.988918i
$478$	−12.3841	+	12.3841i	−0.566437	+	0.566437i
$479$	28.8261			1.31710			0.658549	−	0.752538i	$-0.271170\pi$
$479$	28.8261			1.31710			0.658549	+	0.752538i	$0.271170\pi$
$480$	−10.6712	−	30.6303i	−0.487070	−	1.39807i
$481$			0.639801i			0.0291724i
$482$	−11.8977	+	11.8977i	−0.541927	+	0.541927i
$483$	−33.8338	−	27.3578i	−1.53949	−	1.24482i
$484$			17.9395i			0.815430i
$485$	7.35273	+	3.55324i	0.333870	+	0.161344i
$486$	14.5135			0.658348
$487$	2.01855	+	2.01855i	0.0914693	+	0.0914693i	0.751361	−	0.659892i	$-0.229398\pi$
$487$	2.01855	+	2.01855i	0.0914693	+	0.0914693i	−0.659892	+	0.751361i	$0.729398\pi$
$488$	9.69788	+	9.69788i	0.439002	+	0.439002i
$489$			31.9569i			1.44514i
$490$	−7.56604	−	3.65632i	−0.341799	−	0.165176i
$491$	6.85643			0.309427			0.154713	−	0.987959i	$-0.450555\pi$
$491$	6.85643			0.309427			0.154713	+	0.987959i	$0.450555\pi$
$492$	6.10642	+	6.10642i	0.275299	+	0.275299i
$493$	14.0118	+	14.0118i	0.631059	+	0.631059i
$494$	0.0957339			0.00430727
$495$	11.9582	+	34.3246i	0.537483	+	1.54278i
$496$	−12.4911			−0.560868
$497$	−9.71448	+	9.71448i	−0.435754	+	0.435754i
$498$	7.74401	+	7.74401i	0.347017	+	0.347017i
$499$		−	27.6178i		−	1.23634i	−0.786043	−	0.618171i	$-0.787874\pi$
$499$		−	27.6178i		−	1.23634i	0.786043	−	0.618171i	$-0.212126\pi$
$500$	−9.44915	+	14.9027i	−0.422579	+	0.666468i
$501$	−37.8740			−1.69209
$502$	−1.71461	+	1.71461i	−0.0765268	+	0.0765268i
$503$	12.7717	+	12.7717i	0.569461	+	0.569461i	0.931977	−	0.362517i	$-0.118082\pi$
$503$	12.7717	+	12.7717i	0.569461	+	0.569461i	−0.362517	+	0.931977i	$0.618082\pi$
$504$	−28.5603			−1.27218
$505$	5.54068	+	15.9038i	0.246557	+	0.707711i
$506$	−1.55011	−	14.6470i	−0.0689109	−	0.651137i
$507$	−23.3074	−	23.3074i	−1.03512	−	1.03512i
$508$	−3.12513	+	3.12513i	−0.138655	+	0.138655i
$509$		−	12.2985i		−	0.545123i	−0.962138	−	0.272561i	$-0.912129\pi$
$509$		−	12.2985i		−	0.545123i	0.962138	−	0.272561i	$-0.0878708\pi$
$510$	20.5115	+	9.91225i	0.908263	+	0.438922i
$511$			10.6277i			0.470143i
$512$	−12.0752	−	12.0752i	−0.533655	−	0.533655i
$513$	−1.26136	−	1.26136i	−0.0556902	−	0.0556902i
$514$			1.17415i			0.0517895i
$515$	8.15505	−	16.8753i	0.359354	−	0.743614i
$516$		−	3.18994i		−	0.140429i
$517$	−12.2611	+	12.2611i	−0.539241	+	0.539241i
$518$	−11.4614	+	11.4614i	−0.503586	+	0.503586i
$519$			14.8791i			0.653118i
$520$	−0.449750	+	0.156687i	−0.0197229	+	0.00687118i
$521$		−	6.95572i		−	0.304736i	−0.988324	−	0.152368i	$-0.951310\pi$
$521$		−	6.95572i		−	0.304736i	0.988324	−	0.152368i	$-0.0486898\pi$
$522$	−5.05778	−	5.05778i	−0.221373	−	0.221373i
$523$	−9.61813	−	9.61813i	−0.420571	−	0.420571i	0.464829	−	0.885400i	$-0.346116\pi$
$523$	−9.61813	−	9.61813i	−0.420571	−	0.420571i	−0.885400	+	0.464829i	$0.846116\pi$
$524$			11.9771i			0.523223i
$525$	28.1866	+	35.5431i	1.23016	+	1.55123i
$526$			6.68814i			0.291617i
$527$	33.1490	−	33.1490i	1.44400	−	1.44400i
$528$	13.9792	+	13.9792i	0.608365	+	0.608365i
$529$	−4.81433	−	22.4905i	−0.209319	−	0.977848i
$530$	12.1857	−	4.24535i	0.529314	−	0.184406i
$531$	18.2791			0.793245
$532$	−6.41856	−	6.41856i	−0.278280	−	0.278280i
$533$	0.139776	−	0.139776i	0.00605437	−	0.00605437i
$534$	−14.0142			−0.606452
$535$	7.12893	+	3.44508i	0.308211	+	0.148944i
$536$			0.678250i			0.0292959i
$537$	−7.10303	−	7.10303i	−0.306519	−	0.306519i
$538$	8.77734	−	8.77734i	0.378418	−	0.378418i
$539$	27.3686			1.17885
$540$	3.52428	+	1.70312i	0.151661	+	0.0732906i
$541$	32.2358			1.38593			0.692964	−	0.720973i	$-0.256305\pi$
$541$	32.2358			1.38593			0.692964	+	0.720973i	$0.256305\pi$
$542$	10.0832	+	10.0832i	0.433111	+	0.433111i
$543$	−19.9376	−	19.9376i	−0.855602	−	0.855602i
$544$	35.3533			1.51576
$545$	13.9702	+	40.0997i	0.598417	+	1.71768i
$546$			0.540029i			0.0231111i
$547$	19.1302	+	19.1302i	0.817947	+	0.817947i	0.985810	−	0.167864i	$-0.0536868\pi$
$547$	19.1302	+	19.1302i	0.817947	+	0.817947i	−0.167864	+	0.985810i	$0.553687\pi$
$548$	16.8577	+	16.8577i	0.720123	+	0.720123i
$549$	−20.2866			−0.865810
$550$	−1.76087	+	15.2545i	−0.0750839	+	0.650455i
$551$		−	5.15409i		−	0.219572i
$552$	−21.9860	−	17.7778i	−0.935788	−	0.756672i
$553$	24.2484	−	24.2484i	1.03115	−	1.03115i
$554$		−	6.32702i		−	0.268809i
$555$	37.3956	−	13.0281i	1.58735	−	0.553013i
$556$	−24.6064			−1.04354
$557$	16.8655	−	16.8655i	0.714614	−	0.714614i	−0.252883	−	0.967497i	$-0.581379\pi$
$557$	16.8655	−	16.8655i	0.714614	−	0.714614i	0.967497	+	0.252883i	$0.0813787\pi$
$558$	−11.9657	+	11.9657i	−0.506548	+	0.506548i
$559$	−0.0730178			−0.00308832
$560$	11.8617	+	5.73219i	0.501247	+	0.242229i
$561$	−74.1960			−3.13256
$562$	−4.66061	+	4.66061i	−0.196596	+	0.196596i
$563$	16.8690	+	16.8690i	0.710943	+	0.710943i	0.966733	−	0.255789i	$-0.0823354\pi$
$563$	16.8690	+	16.8690i	0.710943	+	0.710943i	−0.255789	+	0.966733i	$0.582335\pi$
$564$			14.6818i			0.618216i
$565$	−1.26613	+	2.62000i	−0.0532664	+	0.110224i
$566$			18.8234i			0.791208i
$567$	−18.9576	+	18.9576i	−0.796146	+	0.796146i
$568$	−6.31271	+	6.31271i	−0.264876	+	0.264876i
$569$	−39.9056			−1.67293			−0.836465	−	0.548020i	$-0.815382\pi$
$569$	−39.9056			−1.67293			−0.836465	+	0.548020i	$0.815382\pi$
$570$	−1.94941	−	5.59553i	−0.0816518	−	0.234371i
$571$		−	26.3727i		−	1.10366i	−0.833956	−	0.551831i	$-0.813929\pi$
$571$		−	26.3727i		−	1.10366i	0.833956	−	0.551831i	$-0.186071\pi$
$572$	0.483784	−	0.483784i	0.0202280	−	0.0202280i
$573$	9.65392	+	9.65392i	0.403298	+	0.403298i
$574$	5.00791			0.209026
$575$	−0.227445	+	23.9781i	−0.00948513	+	0.999955i
$576$	−1.43529			−0.0598036
$577$	−24.6951	−	24.6951i	−1.02807	−	1.02807i	−0.999594	−	0.0284752i	$-0.990935\pi$
$577$	−24.6951	−	24.6951i	−1.02807	−	1.02807i	−0.0284752	−	0.999594i	$-0.509065\pi$
$578$	−9.75128	+	9.75128i	−0.405600	+	0.405600i
$579$		−	49.3442i		−	2.05068i
$580$	3.72076	+	10.6800i	0.154496	+	0.443462i
$581$	−23.7692			−0.986111
$582$	4.25477	−	4.25477i	0.176366	−	0.176366i
$583$	−29.7180	+	29.7180i	−1.23079	+	1.23079i
$584$			6.90617i			0.285779i
$585$	0.306523	−	0.634290i	0.0126732	−	0.0262247i
$586$			6.12539i			0.253038i
$587$	−28.0118	−	28.0118i	−1.15617	−	1.15617i	−0.985292	−	0.170878i	$-0.945340\pi$
$587$	−28.0118	−	28.0118i	−1.15617	−	1.15617i	−0.170878	−	0.985292i	$-0.554660\pi$
$588$	16.3860	−	16.3860i	0.675748	−	0.675748i
$589$	−12.1935			−0.502426
$590$	6.95298	+	3.36005i	0.286250	+	0.138331i
$591$	17.1196			0.704208
$592$	8.13206	−	8.13206i	0.334226	−	0.334226i
$593$	10.9159	−	10.9159i	0.448262	−	0.448262i	−0.446514	−	0.894776i	$-0.647335\pi$
$593$	10.9159	−	10.9159i	0.448262	−	0.448262i	0.894776	+	0.446514i	$0.147335\pi$
$594$	3.40624			0.139760
$595$	−46.6907	+	16.2664i	−1.91413	+	0.666858i
$596$			14.1069i			0.577843i
$597$	−42.2295	+	42.2295i	−1.72834	+	1.72834i
$598$	−0.179488	+	0.221975i	−0.00733981	+	0.00907725i
$599$			10.4715i			0.427853i	0.976850	+	0.213926i	$0.0686253\pi$
$599$			10.4715i			0.427853i	−0.976850	+	0.213926i	$0.931375\pi$
$600$	18.3164	+	23.0968i	0.747762	+	0.942923i
$601$	−21.7432			−0.886923			−0.443462	−	0.896293i	$-0.646250\pi$
$601$	−21.7432			−0.886923			−0.443462	+	0.896293i	$0.646250\pi$
$602$	−1.30804	−	1.30804i	−0.0533119	−	0.0533119i
$603$	−0.709401	−	0.709401i	−0.0288890	−	0.0288890i
$604$			25.1001i			1.02131i
$605$	−8.36167	−	24.0011i	−0.339950	−	0.975784i
$606$	12.4092			0.504088
$607$	19.4351	+	19.4351i	0.788846	+	0.788846i	0.981305	−	0.192459i	$-0.0616464\pi$
$607$	19.4351	+	19.4351i	0.788846	+	0.788846i	−0.192459	+	0.981305i	$0.561646\pi$
$608$	−6.50218	−	6.50218i	−0.263698	−	0.263698i
$609$	29.0739			1.17813
$610$	−7.71658	−	3.72907i	−0.312435	−	0.150986i
$611$	0.336067			0.0135958
$612$	−23.7196	+	23.7196i	−0.958806	+	0.958806i
$613$	−8.06455	−	8.06455i	−0.325724	−	0.325724i	0.525234	−	0.850958i	$-0.323978\pi$
$613$	−8.06455	−	8.06455i	−0.325724	−	0.325724i	−0.850958	+	0.525234i	$0.823978\pi$
$614$			2.01046i			0.0811356i
$615$	−11.0160	−	5.32352i	−0.444207	−	0.214665i
$616$	39.2973			1.58333
$617$	−25.7148	+	25.7148i	−1.03524	+	1.03524i	−0.0358848	+	0.999356i	$0.511425\pi$
$617$	−25.7148	+	25.7148i	−1.03524	+	1.03524i	−0.999356	+	0.0358848i	$0.988575\pi$
$618$	−9.76514	−	9.76514i	−0.392812	−	0.392812i
$619$	9.68692			0.389350			0.194675	−	0.980868i	$-0.437635\pi$
$619$	9.68692			0.389350			0.194675	+	0.980868i	$0.437635\pi$
$620$	25.2667	−	8.80257i	1.01473	−	0.353520i
$621$	5.28954	−	0.559800i	0.212262	−	0.0224640i
$622$	−15.0314	−	15.0314i	−0.602704	−	0.602704i
$623$	21.5072	−	21.5072i	0.861670	−	0.861670i
$624$		−	0.383159i		−	0.0153386i
$625$	5.69575	−	24.3425i	0.227830	−	0.973701i
$626$		−	11.2023i		−	0.447733i
$627$	13.6461	+	13.6461i	0.544974	+	0.544974i
$628$	−21.9360	−	21.9360i	−0.875341	−	0.875341i
$629$			43.1618i			1.72097i
$630$	16.8538	−	5.87163i	0.671471	−	0.233931i
$631$			47.1576i			1.87732i	0.344850	+	0.938658i	$0.387930\pi$
$631$			47.1576i			1.87732i	−0.344850	+	0.938658i	$0.612070\pi$
$632$	15.7572	−	15.7572i	0.626789	−	0.626789i
$633$	8.67362	−	8.67362i	0.344745	−	0.344745i
$634$		−	0.340137i		−	0.0135086i
$635$	2.72446	−	5.63773i	0.108117	−	0.223727i
$636$			35.5853i			1.41105i
$637$	−0.375077	−	0.375077i	−0.0148611	−	0.0148611i
$638$	6.95921	+	6.95921i	0.275518	+	0.275518i
$639$		−	13.2053i		−	0.522393i
$640$	22.4755	+	10.8614i	0.888424	+	0.429334i
$641$			21.0501i			0.831431i	0.909495	+	0.415715i	$0.136469\pi$
$641$			21.0501i			0.831431i	−0.909495	+	0.415715i	$0.863531\pi$
$642$	4.12526	−	4.12526i	0.162811	−	0.162811i
$643$	−10.9648	−	10.9648i	−0.432410	−	0.432410i	0.457037	−	0.889447i	$-0.348911\pi$
$643$	−10.9648	−	10.9648i	−0.432410	−	0.432410i	−0.889447	+	0.457037i	$0.848911\pi$
$644$	26.9164	−	2.84861i	1.06066	−	0.112251i
$645$	1.48685	+	4.26781i	0.0585446	+	0.168045i
$646$	6.45834			0.254100
$647$	−4.51232	−	4.51232i	−0.177398	−	0.177398i	0.612823	−	0.790220i	$-0.290034\pi$
$647$	−4.51232	−	4.51232i	−0.177398	−	0.177398i	−0.790220	+	0.612823i	$0.790034\pi$
$648$	−12.3191	+	12.3191i	−0.483942	+	0.483942i
$649$	−25.1509			−0.987261
$650$	0.233190	−	0.184926i	0.00914646	−	0.00725338i
$651$		−	68.7830i		−	2.69582i
$652$	−14.0570	−	14.0570i	−0.550513	−	0.550513i
$653$	4.43758	−	4.43758i	0.173656	−	0.173656i	−0.614928	−	0.788584i	$-0.710815\pi$
$653$	4.43758	−	4.43758i	0.173656	−	0.173656i	0.788584	+	0.614928i	$0.210815\pi$
$654$	31.2883			1.22347
$655$	−5.58260	−	16.0241i	−0.218130	−	0.626115i
$656$	−3.55319			−0.138729
$657$	−7.22336	−	7.22336i	−0.281810	−	0.281810i
$658$	6.02032	+	6.02032i	0.234697	+	0.234697i
$659$	−38.7983			−1.51137			−0.755683	−	0.654938i	$-0.772695\pi$
$659$	−38.7983			−1.51137			−0.755683	+	0.654938i	$0.772695\pi$
$660$	−38.1278	−	18.4254i	−1.48412	−	0.717208i
$661$		−	29.4127i		−	1.14402i	−0.820246	−	0.572011i	$-0.806164\pi$
$661$		−	29.4127i		−	1.14402i	0.820246	−	0.572011i	$-0.193836\pi$
$662$	−6.74493	−	6.74493i	−0.262149	−	0.262149i
$663$	1.01683	+	1.01683i	0.0394904	+	0.0394904i
$664$	−15.4458			−0.599413
$665$	11.5791	+	5.59563i	0.449017	+	0.216989i
$666$		−	15.5800i		−	0.603712i
$667$	11.9507	+	9.66323i	0.462731	+	0.374162i
$668$	16.6597	−	16.6597i	0.644583	−	0.644583i
$669$			48.2276i			1.86459i
$670$	−0.139439	−	0.400243i	−0.00538701	−	0.0154627i
$671$	27.9131			1.07757
$672$	36.6784	−	36.6784i	1.41490	−	1.41490i
$673$	20.9657	−	20.9657i	0.808169	−	0.808169i	−0.176188	−	0.984357i	$-0.556377\pi$
$673$	20.9657	−	20.9657i	0.808169	−	0.808169i	0.984357	+	0.176188i	$0.0563766\pi$
$674$	−8.66890			−0.333914
$675$	−5.50894	−	0.635914i	−0.212039	−	0.0244763i
$676$	20.5046			0.788637
$677$	12.8997	−	12.8997i	0.495777	−	0.495777i	−0.414343	−	0.910121i	$-0.635989\pi$
$677$	12.8997	−	12.8997i	0.495777	−	0.495777i	0.910121	+	0.414343i	$0.135989\pi$
$678$	1.51611	+	1.51611i	0.0582257	+	0.0582257i
$679$			13.0594i			0.501174i
$680$	−30.3408	+	10.5703i	−1.16352	+	0.405354i
$681$		−	29.2672i		−	1.12152i
$682$	16.4641	−	16.4641i	0.630443	−	0.630443i
$683$	−22.6437	+	22.6437i	−0.866437	+	0.866437i	−0.992076	−	0.125639i	$-0.959902\pi$
$683$	−22.6437	+	22.6437i	−0.866437	+	0.866437i	0.125639	+	0.992076i	$0.459902\pi$
$684$	8.72501			0.333609
$685$	−30.4112	−	14.6963i	−1.16195	−	0.561518i
$686$			2.81674i			0.107544i
$687$	2.44994	−	2.44994i	0.0934709	−	0.0934709i
$688$	0.928079	+	0.928079i	0.0353827	+	0.0353827i
$689$	0.814549			0.0310319
$690$	16.6291	+	5.97082i	0.633058	+	0.227305i
$691$	−21.9932			−0.836659			−0.418330	−	0.908295i	$-0.637384\pi$
$691$	−21.9932			−0.836659			−0.418330	+	0.908295i	$0.637384\pi$
$692$	−6.54488	−	6.54488i	−0.248799	−	0.248799i
$693$	−41.1022	+	41.1022i	−1.56134	+	1.56134i
$694$		−	17.0936i		−	0.648864i
$695$	32.9208	−	11.4692i	1.24876	−	0.435051i
$696$	18.8930			0.716136
$697$	9.42949	−	9.42949i	0.357167	−	0.357167i
$698$	5.65838	−	5.65838i	0.214173	−	0.214173i
$699$		−	5.82371i		−	0.220273i
$700$	−28.0329	−	3.23592i	−1.05954	−	0.122306i
$701$		−	31.3567i		−	1.18433i	−0.805818	−	0.592164i	$-0.798274\pi$
$701$		−	31.3567i		−	1.18433i	0.805818	−	0.592164i	$-0.201726\pi$
$702$	−0.0466813	−	0.0466813i	−0.00176187	−	0.00176187i
$703$	7.93832	−	7.93832i	0.299400	−	0.299400i
$704$	1.97487			0.0744307
$705$	−6.84327	−	19.6427i	−0.257732	−	0.739788i
$706$	−9.77742			−0.367978
$707$	−19.0441	+	19.0441i	−0.716228	+	0.716228i
$708$	−15.0583	+	15.0583i	−0.565926	+	0.565926i
$709$	34.3936			1.29168			0.645839	−	0.763474i	$-0.276508\pi$
$709$	34.3936			1.29168			0.645839	+	0.763474i	$0.276508\pi$
$710$	2.42739	−	5.02301i	0.0910984	−	0.188510i
$711$			32.9619i			1.23617i
$712$	13.9760	−	13.9760i	0.523771	−	0.523771i
$713$	22.8612	−	28.2728i	0.856160	−	1.05883i
$714$			36.4311i			1.36340i
$715$	−0.421758	+	0.872746i	−0.0157728	+	0.0326388i
$716$	6.24885			0.233530
$717$	48.3846	+	48.3846i	1.80696	+	1.80696i
$718$	−7.35449	−	7.35449i	−0.274467	−	0.274467i
$719$		−	38.4456i		−	1.43378i	−0.697186	−	0.716890i	$-0.745565\pi$
$719$		−	38.4456i		−	1.43378i	0.697186	−	0.716890i	$-0.254435\pi$
$720$	−11.9580	+	4.16602i	−0.445649	+	0.155258i
$721$	29.9727			1.11624
$722$	7.53674	+	7.53674i	0.280489	+	0.280489i
$723$	46.4843	+	46.4843i	1.72877	+	1.72877i
$724$	17.5399			0.651867
$725$	−9.95598	−	12.5544i	−0.369756	−	0.466259i
$726$	−18.7272			−0.695032
$727$	10.5986	−	10.5986i	0.393080	−	0.393080i	−0.482704	−	0.875784i	$-0.660345\pi$
$727$	10.5986	−	10.5986i	0.393080	−	0.393080i	0.875784	+	0.482704i	$0.160345\pi$
$728$	−0.538556	−	0.538556i	−0.0199602	−	0.0199602i
$729$		−	34.2118i		−	1.26710i
$730$	−1.41982	−	4.07541i	−0.0525498	−	0.150838i
$731$	−4.92588			−0.182190
$732$	16.7121	−	16.7121i	0.617696	−	0.617696i
$733$	−10.2320	−	10.2320i	−0.377929	−	0.377929i	0.492426	−	0.870355i	$-0.336110\pi$
$733$	−10.2320	−	10.2320i	−0.377929	−	0.377929i	−0.870355	+	0.492426i	$0.836110\pi$
$734$	−12.8681			−0.474969
$735$	−14.2852	+	29.5604i	−0.526917	+	1.09035i
$736$	27.2671	−	2.88572i	1.00508	−	0.106369i
$737$	0.976094	+	0.976094i	0.0359549	+	0.0359549i
$738$	−3.40373	+	3.40373i	−0.125293	+	0.125293i
$739$		−	4.63797i		−	0.170610i	−0.996355	−	0.0853052i	$-0.972813\pi$
$739$		−	4.63797i		−	0.170610i	0.996355	−	0.0853052i	$-0.0271865\pi$
$740$	−10.7186	+	22.1800i	−0.394022	+	0.815352i
$741$		−	0.374031i		−	0.0137404i
$742$	14.5919	+	14.5919i	0.535685	+	0.535685i
$743$	−1.49859	−	1.49859i	−0.0549781	−	0.0549781i	0.679083	−	0.734061i	$-0.262378\pi$
$743$	−1.49859	−	1.49859i	−0.0549781	−	0.0549781i	−0.734061	+	0.679083i	$0.762378\pi$
$744$		−	44.6969i		−	1.63867i
$745$	−6.57532	−	18.8736i	−0.240901	−	0.691476i
$746$			6.52022i			0.238722i
$747$	16.1552	−	16.1552i	0.591088	−	0.591088i
$748$	32.6367	−	32.6367i	1.19332	−	1.19332i
$749$			12.6619i			0.462657i
$750$	−15.5571	−	9.86408i	−0.568065	−	0.360185i
$751$			34.7333i			1.26744i	0.773564	+	0.633718i	$0.218472\pi$
$751$			34.7333i			1.26744i	−0.773564	+	0.633718i	$0.781528\pi$
$752$	−4.27151	−	4.27151i	−0.155766	−	0.155766i
$753$	6.69895	+	6.69895i	0.244123	+	0.244123i
$754$		−	0.190747i		−	0.00694660i
$755$	−11.6993	−	33.5813i	−0.425780	−	1.22215i
$756$			6.25958i			0.227659i
$757$	−26.5759	+	26.5759i	−0.965916	+	0.965916i	−0.999438	−	0.0335216i	$-0.989328\pi$
$757$	−26.5759	+	26.5759i	−0.965916	+	0.965916i	0.0335216	+	0.999438i	$0.489328\pi$
$758$	10.2149	+	10.2149i	0.371024	+	0.371024i
$759$	−57.2255	+	6.05626i	−2.07715	+	0.219828i
$760$	7.52437	+	3.63618i	0.272938	+	0.131898i
$761$	−44.0823			−1.59798			−0.798991	−	0.601343i	$-0.794632\pi$
$761$	−44.0823			−1.59798			−0.798991	+	0.601343i	$0.794632\pi$
$762$	−3.26236	−	3.26236i	−0.118183	−	0.118183i
$763$	−48.0176	+	48.0176i	−1.73835	+	1.73835i
$764$	−8.49297			−0.307265
$765$	20.6785	−	42.7901i	0.747632	−	1.54708i
$766$		−	22.7472i		−	0.821891i
$767$	0.344685	+	0.344685i	0.0124458	+	0.0124458i
$768$	14.5041	−	14.5041i	0.523373	−	0.523373i
$769$	−35.5733			−1.28281			−0.641404	−	0.767203i	$-0.721648\pi$
$769$	−35.5733			−1.28281			−0.641404	+	0.767203i	$0.721648\pi$
$770$	−23.1898	+	8.07902i	−0.835702	+	0.291148i
$771$	4.58738			0.165211
$772$	21.7051	+	21.7051i	0.781185	+	0.781185i
$773$	−33.7415	−	33.7415i	−1.21360	−	1.21360i	−0.969835	−	0.243761i	$-0.921619\pi$
$773$	−33.7415	−	33.7415i	−1.21360	−	1.21360i	−0.243761	−	0.969835i	$-0.578381\pi$
$774$	1.77808			0.0639117
$775$	−29.7012	+	23.5538i	−1.06690	+	0.846079i
$776$			8.48634i			0.304642i
$777$	44.7796	+	44.7796i	1.60646	+	1.60646i
$778$	−9.13085	−	9.13085i	−0.327357	−	0.327357i
$779$	−3.46854			−0.124273
$780$	0.270014	+	0.775042i	0.00966806	+	0.0277510i
$781$			18.1697i			0.650163i
$782$	−12.1085	+	14.9748i	−0.432999	+	0.535497i
$783$	−2.51322	+	2.51322i	−0.0898151	+	0.0898151i
$784$			9.53467i			0.340524i
$785$	39.5725	+	19.1236i	1.41240	+	0.682549i
$786$	−12.5031			−0.445970
$787$	−19.2374	+	19.2374i	−0.685739	+	0.685739i	−0.961287	−	0.275548i	$-0.911141\pi$
$787$	−19.2374	+	19.2374i	−0.685739	+	0.685739i	0.275548	+	0.961287i	$0.411141\pi$
$788$	−7.53045	+	7.53045i	−0.268261	+	0.268261i
$789$	26.1305			0.930269
$790$	−6.05904	+	12.5380i	−0.215571	+	0.446082i
$791$	−4.65347			−0.165458
$792$	−26.7092	+	26.7092i	−0.949072	+	0.949072i
$793$	−0.382540	−	0.382540i	−0.0135844	−	0.0135844i
$794$		−	11.1567i		−	0.395936i
$795$	−16.5865	−	47.6095i	−0.588263	−	1.68853i
$796$		−	37.1512i		−	1.31679i
$797$	9.21870	−	9.21870i	0.326543	−	0.326543i	−0.524727	−	0.851270i	$-0.675833\pi$
$797$	9.21870	−	9.21870i	0.326543	−	0.326543i	0.851270	+	0.524727i	$0.175833\pi$
$798$	6.70040	−	6.70040i	0.237192	−	0.237192i
$799$	22.6715			0.802062
$800$	−28.3981	−	3.27808i	−1.00403	−	0.115898i
$801$			29.2357i			1.03299i
$802$	−3.12647	+	3.12647i	−0.110400	+	0.110400i
$803$	9.93891	+	9.93891i	0.350737	+	0.350737i
$804$	1.16881			0.0412207
$805$	−34.6836	+	16.3570i	−1.22244	+	0.576509i
$806$	−0.451269			−0.0158953
$807$	−34.2929	−	34.2929i	−1.20717	−	1.20717i
$808$	−12.3753	+	12.3753i	−0.435363	+	0.435363i
$809$		−	26.2047i		−	0.921310i	−0.887579	−	0.460655i	$-0.847615\pi$
$809$		−	26.2047i		−	0.921310i	0.887579	−	0.460655i	$-0.152385\pi$
$810$	4.73701	−	9.80232i	0.166442	−	0.344418i
$811$	−25.3145			−0.888914			−0.444457	−	0.895800i	$-0.646603\pi$
$811$	−25.3145			−0.888914			−0.444457	+	0.895800i	$0.646603\pi$
$812$	−12.7888	+	12.7888i	−0.448799	+	0.448799i
$813$	39.3950	−	39.3950i	1.38164	−	1.38164i
$814$			21.4371i			0.751371i
$815$	25.3587	+	12.2547i	0.888278	+	0.429264i
$816$		−	25.8484i		−	0.904876i
$817$	0.905968	+	0.905968i	0.0316958	+	0.0316958i
$818$	7.31826	−	7.31826i	0.255877	−	0.255877i
$819$	1.12658			0.0393660
$820$	7.18729	−	2.50396i	0.250991	−	0.0874419i
$821$	44.5923			1.55628			0.778141	−	0.628089i	$-0.216163\pi$
$821$	44.5923			1.55628			0.778141	+	0.628089i	$0.216163\pi$
$822$	−17.5979	+	17.5979i	−0.613797	+	0.613797i
$823$	17.7237	−	17.7237i	0.617810	−	0.617810i	−0.327159	−	0.944969i	$-0.606091\pi$
$823$	17.7237	−	17.7237i	0.617810	−	0.617810i	0.944969	+	0.327159i	$0.106091\pi$
$824$	19.4770			0.678515
$825$	59.5991	+	6.87970i	2.07498	+	0.239521i
$826$			12.3494i			0.429691i
$827$	0.817135	−	0.817135i	0.0284146	−	0.0284146i	−0.692757	−	0.721171i	$-0.743604\pi$
$827$	0.817135	−	0.817135i	0.0284146	−	0.0284146i	0.721171	+	0.692757i	$0.243604\pi$
$828$	−16.3582	+	20.2304i	−0.568487	+	0.703056i
$829$			22.9852i			0.798308i	0.916884	+	0.399154i	$0.130696\pi$
$829$			22.9852i			0.798308i	−0.916884	+	0.399154i	$0.869304\pi$
$830$	9.11474	−	3.17545i	0.316377	−	0.110222i
$831$	−24.7196			−0.857512
$832$	−0.0270649	−	0.0270649i	−0.000938306	−	0.000938306i
$833$	−25.3032	−	25.3032i	−0.876703	−	0.876703i
$834$		−	25.6869i		−	0.889466i
$835$	−14.5238	+	30.0541i	−0.502616	+	1.04007i
$836$	−12.0051			−0.415205
$837$	5.94577	+	5.94577i	0.205516	+	0.205516i
$838$	−6.06511	−	6.06511i	−0.209516	−	0.209516i
$839$	−34.9215			−1.20563			−0.602813	−	0.797883i	$-0.705953\pi$
$839$	−34.9215			−1.20563			−0.602813	+	0.797883i	$0.705953\pi$
$840$	−20.5115	+	42.4445i	−0.707713	+	1.46447i
$841$	18.7306			0.645883
$842$	9.07608	−	9.07608i	0.312782	−	0.312782i
$843$	18.2089	+	18.2089i	0.627149	+	0.627149i
$844$			7.63056i			0.262655i
$845$	−27.4329	+	9.55728i	−0.943722	+	0.328780i
$846$	−8.18367			−0.281360
$847$	28.7403	−	28.7403i	0.987528	−	0.987528i
$848$	−10.3532	−	10.3532i	−0.355529	−	0.355529i
$849$	73.5428			2.52398
$850$	15.7313	−	12.4753i	0.539580	−	0.427901i
$851$	3.52309	+	33.2896i	0.120770	+	1.14115i
$852$	10.8785	+	10.8785i	0.372692	+	0.372692i
$853$	−12.9244	+	12.9244i	−0.442523	+	0.442523i	−0.892859	−	0.450336i	$-0.851304\pi$
$853$	−12.9244	+	12.9244i	−0.442523	+	0.442523i	0.450336	+	0.892859i	$0.351304\pi$
$854$		−	13.7057i		−	0.468998i
$855$	−11.6731	+	4.06677i	−0.399213	+	0.139081i
$856$			8.22803i			0.281228i
$857$	0.653568	+	0.653568i	0.0223254	+	0.0223254i	0.718181	−	0.695856i	$-0.244975\pi$
$857$	0.653568	+	0.653568i	0.0223254	+	0.0223254i	−0.695856	+	0.718181i	$0.744975\pi$
$858$	0.505028	+	0.505028i	0.0172414	+	0.0172414i
$859$		−	35.1106i		−	1.19796i	−0.800765	−	0.598979i	$-0.795573\pi$
$859$		−	35.1106i		−	1.19796i	0.800765	−	0.598979i	$-0.204427\pi$
$860$	−2.53131	−	1.22327i	−0.0863170	−	0.0417130i
$861$		−	19.5658i		−	0.666802i
$862$	−6.50941	+	6.50941i	−0.221711	+	0.221711i
$863$	−11.1928	+	11.1928i	−0.381006	+	0.381006i	−0.871464	−	0.490459i	$-0.836829\pi$
$863$	−11.1928	+	11.1928i	−0.381006	+	0.381006i	0.490459	+	0.871464i	$0.336829\pi$
$864$			6.34113i			0.215730i
$865$	11.8070	+	5.70576i	0.401449	+	0.194002i
$866$		−	12.6456i		−	0.429715i
$867$	38.0981	+	38.0981i	1.29388	+	1.29388i
$868$	30.2557	+	30.2557i	1.02695	+	1.02695i
$869$		−	45.3536i		−	1.53852i
$870$	−11.1489	+	3.88415i	−0.377985	+	0.131685i
$871$		−	0.0267541i		−	0.000906527i
$872$	−31.2030	+	31.2030i	−1.05667	+	1.05667i
$873$	−8.87610	−	8.87610i	−0.300411	−	0.300411i
$874$	4.98116	−	0.527163i	0.168490	−	0.0178316i
$875$	39.0134	−	8.73695i	1.31889	−	0.295363i
$876$	11.9012			0.402104
$877$	−27.9872	−	27.9872i	−0.945060	−	0.945060i	0.0535078	−	0.998567i	$-0.482960\pi$
$877$	−27.9872	−	27.9872i	−0.945060	−	0.945060i	−0.998567	+	0.0535078i	$0.982960\pi$
$878$	1.27451	−	1.27451i	0.0430127	−	0.0430127i
$879$	23.9318			0.807200
$880$	16.4535	−	5.73219i	0.554649	−	0.193232i
$881$		−	7.23594i		−	0.243785i	−0.992543	−	0.121893i	$-0.961104\pi$
$881$		−	7.23594i		−	0.243785i	0.992543	−	0.121893i	$-0.0388963\pi$
$882$	9.13360	+	9.13360i	0.307544	+	0.307544i
$883$	−22.2102	+	22.2102i	−0.747431	+	0.747431i	−0.973996	−	0.226565i	$-0.927250\pi$
$883$	−22.2102	+	22.2102i	−0.747431	+	0.747431i	0.226565	+	0.973996i	$0.427250\pi$
$884$	−0.894550			−0.0300870
$885$	13.1277	−	27.1652i	0.441282	−	0.913147i
$886$	19.4133			0.652203
$887$	11.9959	+	11.9959i	0.402782	+	0.402782i	0.879212	−	0.476430i	$-0.158069\pi$
$887$	11.9959	+	11.9959i	0.402782	+	0.402782i	−0.476430	+	0.879212i	$0.658069\pi$
$888$	29.0989	+	29.0989i	0.976495	+	0.976495i
$889$	10.0134			0.335837
$890$	−5.37409	+	11.1206i	−0.180140	+	0.372765i
$891$			35.4578i			1.18788i
$892$	−21.2139	−	21.2139i	−0.710296	−	0.710296i
$893$	−4.16975	−	4.16975i	−0.139535	−	0.139535i
$894$	−14.7264			−0.492525
$895$	−8.36030	+	2.91262i	−0.279454	+	0.0973581i
$896$			39.9195i			1.33362i
$897$	0.867255	+	0.701257i	0.0289568	+	0.0234143i
$898$	12.3375	−	12.3375i	0.411709	−	0.411709i
$899$			24.2953i			0.810294i
$900$	21.2525	−	16.8538i	0.708417	−	0.561793i
$901$	54.9506			1.83067
$902$	4.68333	−	4.68333i	0.155938	−	0.155938i
$903$	−5.11051	+	5.11051i	−0.170067	+	0.170067i
$904$	−3.02394			−0.100575
$905$	−23.4666	+	8.17545i	−0.780056	+	0.271761i
$906$	−26.2023			−0.870513
$907$	−39.2532	+	39.2532i	−1.30338	+	1.30338i	−0.377283	+	0.926098i	$0.623142\pi$
$907$	−39.2532	+	39.2532i	−1.30338	+	1.30338i	−0.926098	+	0.377283i	$0.876858\pi$
$908$	12.8738	+	12.8738i	0.427233	+	0.427233i
$909$		−	25.8875i		−	0.858633i
$910$	0.428528	+	0.207088i	0.0142056	+	0.00686490i
$911$		−	34.8753i		−	1.15547i	−0.816225	−	0.577735i	$-0.803937\pi$
$911$		−	34.8753i		−	1.15547i	0.816225	−	0.577735i	$-0.196063\pi$
$912$	−4.75404	+	4.75404i	−0.157422	+	0.157422i
$913$	−22.2286	+	22.2286i	−0.735659	+	0.735659i
$914$	1.57088			0.0519600
$915$	−14.5694	+	30.1486i	−0.481650	+	0.996681i
$916$			2.15532i			0.0712136i
$917$	19.1882	−	19.1882i	0.633651	−	0.633651i
$918$	−3.14919	−	3.14919i	−0.103939	−	0.103939i
$919$	2.37539			0.0783569			0.0391785	−	0.999232i	$-0.487526\pi$
$919$	2.37539			0.0783569			0.0391785	+	0.999232i	$0.487526\pi$
$920$	−22.5383	+	10.6292i	−0.743065	+	0.350435i
$921$	7.85484			0.258826
$922$	5.98306	+	5.98306i	0.197042	+	0.197042i
$923$	0.249009	−	0.249009i	0.00819625	−	0.00819625i
$924$		−	67.7200i		−	2.22782i
$925$	4.00211	−	34.6705i	0.131589	−	1.13996i
$926$	−3.85324			−0.126625
$927$	−20.3716	+	20.3716i	−0.669091	+	0.669091i
$928$	−12.9554	+	12.9554i	−0.425283	+	0.425283i
$929$			54.1771i			1.77749i	0.458398	+	0.888747i	$0.348423\pi$
$929$			54.1771i			1.77749i	−0.458398	+	0.888747i	$0.651577\pi$
$930$	9.18911	+	26.3762i	0.301323	+	0.864909i
$931$			9.30752i			0.305042i
$932$	2.56168	+	2.56168i	0.0839108	+	0.0839108i
$933$	−58.7275	+	58.7275i	−1.92265	+	1.92265i
$934$	−8.70414			−0.284808
$935$	−28.4524	+	58.8766i	−0.930492	+	1.92547i
$936$	0.732082			0.0239288
$937$	19.6245	−	19.6245i	0.641106	−	0.641106i	−0.309721	−	0.950827i	$-0.600236\pi$
$937$	19.6245	−	19.6245i	0.641106	−	0.641106i	0.950827	+	0.309721i	$0.100236\pi$
$938$	0.479273	−	0.479273i	0.0156488	−	0.0156488i
$939$	−43.7672			−1.42829
$940$	11.6504	+	5.63012i	0.379996	+	0.183634i
$941$		−	25.0801i		−	0.817588i	−0.912627	−	0.408794i	$-0.865949\pi$
$941$		−	25.0801i		−	0.817588i	0.912627	−	0.408794i	$-0.134051\pi$
$942$	22.8992	−	22.8992i	0.746097	−	0.746097i
$943$	6.50305	−	8.04241i	0.211768	−	0.261897i
$944$		−	8.76210i		−	0.285182i
$945$	−2.91762	−	8.37466i	−0.0949102	−	0.272428i
$946$	−2.44653			−0.0795436
$947$	21.4551	+	21.4551i	0.697196	+	0.697196i	0.963805	−	0.266609i	$-0.0859031\pi$
$947$	21.4551	+	21.4551i	0.697196	+	0.697196i	−0.266609	+	0.963805i	$0.585903\pi$
$948$	−27.1540	−	27.1540i	−0.881921	−	0.881921i
$949$		−	0.272419i		−	0.00884308i
$950$	−5.18777	−	0.598839i	−0.168313	−	0.0194289i
$951$	−1.32891			−0.0430929
$952$	−36.3318	−	36.3318i	−1.17752	−	1.17752i
$953$	−14.9127	−	14.9127i	−0.483071	−	0.483071i	0.423040	−	0.906111i	$-0.360963\pi$
$953$	−14.9127	−	14.9127i	−0.483071	−	0.483071i	−0.906111	+	0.423040i	$0.860963\pi$
$954$	−19.8353			−0.642193
$955$	11.3627	−	3.95862i	0.367688	−	0.128098i
$956$	−42.5661			−1.37668
$957$	27.1895	−	27.1895i	0.878913	−	0.878913i
$958$	−13.2366	−	13.2366i	−0.427655	−	0.427655i
$959$		−	54.0143i		−	1.74421i
$960$	−1.03079	+	2.13303i	−0.0332687	+	0.0688432i
$961$	26.4778			0.854124
$962$	0.293788	−	0.293788i	0.00947212	−	0.00947212i
$963$	−8.60594	−	8.60594i	−0.277322	−	0.277322i
$964$	−40.8943			−1.31712
$965$	−39.1561	−	18.9223i	−1.26048	−	0.609131i
$966$	2.97369	+	28.0984i	0.0956771	+	0.904051i
$967$	−21.5085	−	21.5085i	−0.691668	−	0.691668i	0.270931	−	0.962599i	$-0.412668\pi$
$967$	−21.5085	−	21.5085i	−0.691668	−	0.691668i	−0.962599	+	0.270931i	$0.912668\pi$
$968$	18.6762	−	18.6762i	0.600274	−	0.600274i
$969$		−	25.2326i		−	0.810589i
$970$	−1.74468	−	5.00788i	−0.0560183	−	0.160793i
$971$		−	1.70133i		−	0.0545982i	−0.999627	−	0.0272991i	$-0.991309\pi$
$971$		−	1.70133i		−	0.0545982i	0.999627	−	0.0272991i	$-0.00869065\pi$
$972$	24.9426	+	24.9426i	0.800034	+	0.800034i
$973$	39.4212	+	39.4212i	1.26379	+	1.26379i
$974$		−	1.85379i		−	0.0593991i
$975$	−0.722502	−	0.911070i	−0.0231386	−	0.0291776i
$976$			9.72439i			0.311270i
$977$	−8.21439	+	8.21439i	−0.262802	+	0.262802i	−0.826191	−	0.563390i	$-0.809497\pi$
$977$	−8.21439	+	8.21439i	−0.262802	+	0.262802i	0.563390	+	0.826191i	$0.309497\pi$
$978$	14.6742	−	14.6742i	0.469230	−	0.469230i
$979$		−	40.2266i		−	1.28565i
$980$	−6.71914	−	19.2864i	−0.214635	−	0.616082i
$981$		−	65.2723i		−	2.08398i
$982$	−3.14839	−	3.14839i	−0.100469	−	0.100469i
$983$	8.13489	+	8.13489i	0.259463	+	0.259463i	0.824835	−	0.565373i	$-0.191268\pi$
$983$	8.13489	+	8.13489i	0.259463	+	0.259463i	−0.565373	+	0.824835i	$0.691268\pi$
$984$		−	12.7144i		−	0.405319i
$985$	6.56497	−	13.5849i	0.209177	−	0.432852i
$986$		−	12.8681i		−	0.409803i
$987$	23.5213	−	23.5213i	0.748691	−	0.748691i
$988$	0.164526	+	0.164526i	0.00523426	+	0.00523426i
$989$	−3.79921	+	0.402076i	−0.120808	+	0.0127853i
$990$	10.2704	−	21.2525i	0.326413	−	0.675449i
$991$	39.2907			1.24811			0.624055	−	0.781380i	$-0.285484\pi$
$991$	39.2907			1.24811			0.624055	+	0.781380i	$0.285484\pi$
$992$	30.6499	+	30.6499i	0.973136	+	0.973136i
$993$	−26.3523	+	26.3523i	−0.836266	+	0.836266i
$994$	8.92153			0.282974
$995$	17.3163	+	49.7044i	0.548965	+	1.57573i
$996$			26.6173i			0.843401i
$997$	−7.56550	−	7.56550i	−0.239602	−	0.239602i	0.577083	−	0.816685i	$-0.304191\pi$
$997$	−7.56550	−	7.56550i	−0.239602	−	0.239602i	−0.816685	+	0.577083i	$0.804191\pi$
$998$	−12.6817	+	12.6817i	−0.401434	+	0.401434i
$999$	−7.74170			−0.244937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.e.a.22.6	yes	20
5.2	odd	4		575.2.e.d.68.5		20
5.3	odd	4	inner	115.2.e.a.68.5	yes	20
5.4	even	2		575.2.e.d.482.6		20
23.22	odd	2	inner	115.2.e.a.22.5	✓	20
115.22	even	4		575.2.e.d.68.6		20
115.68	even	4	inner	115.2.e.a.68.6	yes	20
115.114	odd	2		575.2.e.d.482.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.e.a.22.5	✓	20	23.22	odd	2	inner
115.2.e.a.22.6	yes	20	1.1	even	1	trivial
115.2.e.a.68.5	yes	20	5.3	odd	4	inner
115.2.e.a.68.6	yes	20	115.68	even	4	inner
575.2.e.d.68.5		20	5.2	odd	4
575.2.e.d.68.6		20	115.22	even	4
575.2.e.d.482.5		20	115.114	odd	2
575.2.e.d.482.6		20	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459187 - 0.459187i) q^{2} +(-1.79404 + 1.79404i) q^{3} -1.57829i q^{4} +(0.735651 + 2.11159i) q^{5} +1.64760 q^{6} +(-2.52854 + 2.52854i) q^{7} +(-1.64311 + 1.64311i) q^{8} -3.43715i q^{9} +O(q^{10})\)	\(q+(-0.459187 - 0.459187i) q^{2} +(-1.79404 + 1.79404i) q^{3} -1.57829i q^{4} +(0.735651 + 2.11159i) q^{5} +1.64760 q^{6} +(-2.52854 + 2.52854i) q^{7} +(-1.64311 + 1.64311i) q^{8} -3.43715i q^{9} +(0.631815 - 1.30742i) q^{10} +4.72931i q^{11} +(2.83152 + 2.83152i) q^{12} +(0.0648135 - 0.0648135i) q^{13} +2.32215 q^{14} +(-5.10806 - 2.46849i) q^{15} -1.64760 q^{16} +(4.37241 - 4.37241i) q^{17} +(-1.57829 + 1.57829i) q^{18} -1.60835 q^{19} +(3.33271 - 1.16107i) q^{20} -9.07259i q^{21} +(2.17164 - 2.17164i) q^{22} +(3.01543 - 3.72923i) q^{23} -5.89559i q^{24} +(-3.91764 + 3.10679i) q^{25} -0.0595231 q^{26} +(0.784256 + 0.784256i) q^{27} +(3.99078 + 3.99078i) q^{28} +3.20459i q^{29} +(1.21206 + 3.47906i) q^{30} +7.58141 q^{31} +(4.04277 + 4.04277i) q^{32} +(-8.48456 - 8.48456i) q^{33} -4.01551 q^{34} +(-7.19936 - 3.47912i) q^{35} -5.42483 q^{36} +(-4.93570 + 4.93570i) q^{37} +(0.738533 + 0.738533i) q^{38} +0.232556i q^{39} +(-4.67832 - 2.26082i) q^{40} +2.15659 q^{41} +(-4.16602 + 4.16602i) q^{42} +(-0.563291 - 0.563291i) q^{43} +7.46424 q^{44} +(7.25785 - 2.52854i) q^{45} +(-3.09706 + 0.327767i) q^{46} +(2.59257 + 2.59257i) q^{47} +(2.95586 - 2.95586i) q^{48} -5.78701i q^{49} +(3.22553 + 0.372332i) q^{50} +15.6885i q^{51} +(-0.102295 - 0.102295i) q^{52} +(6.28379 + 6.28379i) q^{53} -0.720241i q^{54} +(-9.98637 + 3.47912i) q^{55} -8.30932i q^{56} +(2.88544 - 2.88544i) q^{57} +(1.47151 - 1.47151i) q^{58} +5.31810i q^{59} +(-3.89600 + 8.06202i) q^{60} -5.90216i q^{61} +(-3.48129 - 3.48129i) q^{62} +(8.69095 + 8.69095i) q^{63} -0.417581i q^{64} +(0.184540 + 0.0891796i) q^{65} +7.79201i q^{66} +(0.206392 - 0.206392i) q^{67} +(-6.90095 - 6.90095i) q^{68} +(1.28058 + 12.1002i) q^{69} +(1.70829 + 4.90342i) q^{70} +3.84194 q^{71} +(5.64760 + 5.64760i) q^{72} +(2.10156 - 2.10156i) q^{73} +4.53282 q^{74} +(1.45470 - 12.6021i) q^{75} +2.53845i q^{76} +(-11.9582 - 11.9582i) q^{77} +(0.106787 - 0.106787i) q^{78} -9.58990 q^{79} +(-1.21206 - 3.47906i) q^{80} +7.49747 q^{81} +(-0.990278 - 0.990278i) q^{82} +(4.70018 + 4.70018i) q^{83} -14.3192 q^{84} +(12.4493 + 6.01618i) q^{85} +0.517313i q^{86} +(-5.74916 - 5.74916i) q^{87} +(-7.77076 - 7.77076i) q^{88} -8.50580 q^{89} +(-4.49378 - 2.17164i) q^{90} +0.327767i q^{91} +(-5.88582 - 4.75924i) q^{92} +(-13.6013 + 13.6013i) q^{93} -2.38095i q^{94} +(-1.18318 - 3.39617i) q^{95} -14.5058 q^{96} +(2.58241 - 2.58241i) q^{97} +(-2.65732 + 2.65732i) q^{98} +16.2553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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