LMFDB - Embedded newform 690.2.i.e.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	690.47
Dual form			690.2.i.e.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.42268 - 0.987925i) q^{3} -1.00000i q^{4} +(2.16582 + 0.556076i) q^{5} +(1.70455 - 0.307415i) q^{6} +(3.32202 + 3.32202i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.04801 + 2.81099i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.42268 - 0.987925i) q^{3} -1.00000i q^{4} +(2.16582 + 0.556076i) q^{5} +(1.70455 - 0.307415i) q^{6} +(3.32202 + 3.32202i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.04801 + 2.81099i) q^{9} +(-1.92467 + 1.13826i) q^{10} -1.84760i q^{11} +(-0.987925 + 1.42268i) q^{12} +(-1.71935 + 1.71935i) q^{13} -4.69805 q^{14} +(-2.53190 - 2.93078i) q^{15} -1.00000 q^{16} +(-0.948261 + 0.948261i) q^{17} +(-2.72873 - 1.24662i) q^{18} +1.25446i q^{19} +(0.556076 - 2.16582i) q^{20} +(-1.44425 - 8.00806i) q^{21} +(1.30645 + 1.30645i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.307415 - 1.70455i) q^{24} +(4.38156 + 2.40872i) q^{25} -2.43152i q^{26} +(1.28607 - 5.03448i) q^{27} +(3.32202 - 3.32202i) q^{28} -6.59528 q^{29} +(3.86270 + 0.282055i) q^{30} -4.74469 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.82529 + 2.62853i) q^{33} -1.34104i q^{34} +(5.34761 + 9.04220i) q^{35} +(2.81099 - 1.04801i) q^{36} +(6.93789 + 6.93789i) q^{37} +(-0.887039 - 0.887039i) q^{38} +(4.14466 - 0.747487i) q^{39} +(1.13826 + 1.92467i) q^{40} +0.505725i q^{41} +(6.68380 + 4.64132i) q^{42} +(6.74120 - 6.74120i) q^{43} -1.84760 q^{44} +(0.706675 + 6.67088i) q^{45} -1.00000 q^{46} +(-7.17165 + 7.17165i) q^{47} +(1.42268 + 0.987925i) q^{48} +15.0717i q^{49} +(-4.80145 + 1.39501i) q^{50} +(2.28588 - 0.412257i) q^{51} +(1.71935 + 1.71935i) q^{52} +(7.30308 + 7.30308i) q^{53} +(2.65053 + 4.46931i) q^{54} +(1.02740 - 4.00156i) q^{55} +4.69805i q^{56} +(1.23932 - 1.78469i) q^{57} +(4.66357 - 4.66357i) q^{58} +7.06183 q^{59} +(-2.93078 + 2.53190i) q^{60} +3.82384 q^{61} +(3.35500 - 3.35500i) q^{62} +(-5.85667 + 12.8197i) q^{63} +1.00000i q^{64} +(-4.67988 + 2.76771i) q^{65} +(-0.567979 - 3.14932i) q^{66} +(-2.57400 - 2.57400i) q^{67} +(0.948261 + 0.948261i) q^{68} +(-0.307415 - 1.70455i) q^{69} +(-10.1751 - 2.61247i) q^{70} -11.8194i q^{71} +(-1.24662 + 2.72873i) q^{72} +(-3.30214 + 3.30214i) q^{73} -9.81166 q^{74} +(-3.85390 - 7.75548i) q^{75} +1.25446 q^{76} +(6.13775 - 6.13775i) q^{77} +(-2.40216 + 3.45927i) q^{78} -7.20508i q^{79} +(-2.16582 - 0.556076i) q^{80} +(-6.80335 + 5.89189i) q^{81} +(-0.357602 - 0.357602i) q^{82} +(11.2118 + 11.2118i) q^{83} +(-8.00806 + 1.44425i) q^{84} +(-2.58107 + 1.52646i) q^{85} +9.53349i q^{86} +(9.38294 + 6.51564i) q^{87} +(1.30645 - 1.30645i) q^{88} -9.35985 q^{89} +(-5.21672 - 4.21733i) q^{90} -11.4234 q^{91} +(0.707107 - 0.707107i) q^{92} +(6.75015 + 4.68739i) q^{93} -10.1422i q^{94} +(-0.697577 + 2.71694i) q^{95} +(-1.70455 + 0.307415i) q^{96} +(-5.09832 - 5.09832i) q^{97} +(-10.6573 - 10.6573i) q^{98} +(5.19358 - 1.93630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.42268	−	0.987925i	−0.821382	−	0.570379i
$3$	−1.42268	−	0.987925i	−0.821382	−	0.570379i
$4$		−	1.00000i		−	0.500000i
$5$	2.16582	+	0.556076i	0.968584	+	0.248685i
$5$	2.16582	+	0.556076i	0.968584	+	0.248685i
$6$	1.70455	−	0.307415i	0.695880	−	0.125502i
$7$	3.32202	+	3.32202i	1.25561	+	1.25561i	0.953169	+	0.302437i	$0.0978001\pi$
$7$	3.32202	+	3.32202i	1.25561	+	1.25561i	0.302437	+	0.953169i	$0.402200\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.04801	+	2.81099i	0.349337	+	0.936997i
$10$	−1.92467	+	1.13826i	−0.608635	+	0.359950i
$11$		−	1.84760i		−	0.557071i	−0.960426	−	0.278536i	$-0.910151\pi$
$11$		−	1.84760i		−	0.557071i	0.960426	−	0.278536i	$-0.0898490\pi$
$12$	−0.987925	+	1.42268i	−0.285189	+	0.410691i
$13$	−1.71935	+	1.71935i	−0.476861	+	0.476861i	−0.904126	−	0.427265i	$-0.859477\pi$
$13$	−1.71935	+	1.71935i	−0.476861	+	0.476861i	0.427265	+	0.904126i	$0.359477\pi$
$14$	−4.69805			−1.25561
$15$	−2.53190	−	2.93078i	−0.653733	−	0.756725i
$16$	−1.00000			−0.250000
$17$	−0.948261	+	0.948261i	−0.229987	+	0.229987i	−0.812687	−	0.582700i	$-0.801996\pi$
$17$	−0.948261	+	0.948261i	−0.229987	+	0.229987i	0.582700	+	0.812687i	$0.301996\pi$
$18$	−2.72873	−	1.24662i	−0.643167	−	0.293830i
$19$			1.25446i			0.287794i	0.989593	+	0.143897i	$0.0459633\pi$
$19$			1.25446i			0.287794i	−0.989593	+	0.143897i	$0.954037\pi$
$20$	0.556076	−	2.16582i	0.124342	−	0.484292i
$21$	−1.44425	−	8.00806i	−0.315161	−	1.74750i
$22$	1.30645	+	1.30645i	0.278536	+	0.278536i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$	−0.307415	−	1.70455i	−0.0627508	−	0.347940i
$25$	4.38156	+	2.40872i	0.876312	+	0.481745i
$26$		−	2.43152i		−	0.476861i
$27$	1.28607	−	5.03448i	0.247504	−	0.968887i
$28$	3.32202	−	3.32202i	0.627803	−	0.627803i
$29$	−6.59528			−1.22471			−0.612356	−	0.790582i	$-0.709778\pi$
$29$	−6.59528			−1.22471			−0.612356	+	0.790582i	$0.709778\pi$
$30$	3.86270	+	0.282055i	0.705229	+	0.0514959i
$31$	−4.74469			−0.852171			−0.426086	−	0.904683i	$-0.640108\pi$
$31$	−4.74469			−0.852171			−0.426086	+	0.904683i	$0.640108\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.82529	+	2.62853i	−0.317741	+	0.457568i
$34$		−	1.34104i		−	0.229987i
$35$	5.34761	+	9.04220i	0.903910	+	1.52841i
$36$	2.81099	−	1.04801i	0.468499	−	0.174668i
$37$	6.93789	+	6.93789i	1.14058	+	1.14058i	0.988344	+	0.152239i	$0.0486483\pi$
$37$	6.93789	+	6.93789i	1.14058	+	1.14058i	0.152239	+	0.988344i	$0.451352\pi$
$38$	−0.887039	−	0.887039i	−0.143897	−	0.143897i
$39$	4.14466	−	0.747487i	0.663676	−	0.119694i
$40$	1.13826	+	1.92467i	0.179975	+	0.304317i
$41$			0.505725i			0.0789810i	0.999220	+	0.0394905i	$0.0125735\pi$
$41$			0.505725i			0.0789810i	−0.999220	+	0.0394905i	$0.987427\pi$
$42$	6.68380	+	4.64132i	1.03133	+	0.716171i
$43$	6.74120	−	6.74120i	1.02802	−	1.02802i	0.0284272	−	0.999596i	$-0.490950\pi$
$43$	6.74120	−	6.74120i	1.02802	−	1.02802i	0.999596	−	0.0284272i	$-0.00904988\pi$
$44$	−1.84760			−0.278536
$45$	0.706675	+	6.67088i	0.105345	+	0.994436i
$46$	−1.00000			−0.147442
$47$	−7.17165	+	7.17165i	−1.04609	+	1.04609i	−0.0472070	+	0.998885i	$0.515032\pi$
$47$	−7.17165	+	7.17165i	−1.04609	+	1.04609i	−0.998885	+	0.0472070i	$0.984968\pi$
$48$	1.42268	+	0.987925i	0.205345	+	0.142595i
$49$			15.0717i			2.15309i
$50$	−4.80145	+	1.39501i	−0.679028	+	0.197284i
$51$	2.28588	−	0.412257i	0.320087	−	0.0577275i
$52$	1.71935	+	1.71935i	0.238430	+	0.238430i
$53$	7.30308	+	7.30308i	1.00315	+	1.00315i	0.999995	+	0.00315967i	$0.00100576\pi$
$53$	7.30308	+	7.30308i	1.00315	+	1.00315i	0.00315967	+	0.999995i	$0.498994\pi$
$54$	2.65053	+	4.46931i	0.360691	+	0.608196i
$55$	1.02740	−	4.00156i	0.138535	−	0.539570i
$56$			4.69805i			0.627803i
$57$	1.23932	−	1.78469i	0.164151	−	0.236388i
$58$	4.66357	−	4.66357i	0.612356	−	0.612356i
$59$	7.06183			0.919371			0.459686	−	0.888082i	$-0.347962\pi$
$59$	7.06183			0.919371			0.459686	+	0.888082i	$0.347962\pi$
$60$	−2.93078	+	2.53190i	−0.378363	+	0.326867i
$61$	3.82384			0.489593			0.244796	−	0.969574i	$-0.421279\pi$
$61$	3.82384			0.489593			0.244796	+	0.969574i	$0.421279\pi$
$62$	3.35500	−	3.35500i	0.426086	−	0.426086i
$63$	−5.85667	+	12.8197i	−0.737870	+	1.61513i
$64$			1.00000i			0.125000i
$65$	−4.67988	+	2.76771i	−0.580468	+	0.343292i
$66$	−0.567979	−	3.14932i	−0.0699134	−	0.387655i
$67$	−2.57400	−	2.57400i	−0.314464	−	0.314464i	0.532172	−	0.846636i	$-0.321376\pi$
$67$	−2.57400	−	2.57400i	−0.314464	−	0.314464i	−0.846636	+	0.532172i	$0.821376\pi$
$68$	0.948261	+	0.948261i	0.114994	+	0.114994i
$69$	−0.307415	−	1.70455i	−0.0370084	−	0.205204i
$70$	−10.1751	−	2.61247i	−1.21616	−	0.312250i
$71$		−	11.8194i		−	1.40271i	−0.712812	−	0.701355i	$-0.752579\pi$
$71$		−	11.8194i		−	1.40271i	0.712812	−	0.701355i	$-0.247421\pi$
$72$	−1.24662	+	2.72873i	−0.146915	+	0.321583i
$73$	−3.30214	+	3.30214i	−0.386486	+	0.386486i	−0.873432	−	0.486946i	$-0.838111\pi$
$73$	−3.30214	+	3.30214i	−0.386486	+	0.386486i	0.486946	+	0.873432i	$0.338111\pi$
$74$	−9.81166			−1.14058
$75$	−3.85390	−	7.75548i	−0.445010	−	0.895526i
$76$	1.25446			0.143897
$77$	6.13775	−	6.13775i	0.699462	−	0.699462i
$78$	−2.40216	+	3.45927i	−0.271991	+	0.391685i
$79$		−	7.20508i		−	0.810635i	−0.914176	−	0.405318i	$-0.867161\pi$
$79$		−	7.20508i		−	0.810635i	0.914176	−	0.405318i	$-0.132839\pi$
$80$	−2.16582	−	0.556076i	−0.242146	−	0.0621712i
$81$	−6.80335	+	5.89189i	−0.755928	+	0.654655i
$82$	−0.357602	−	0.357602i	−0.0394905	−	0.0394905i
$83$	11.2118	+	11.2118i	1.23065	+	1.23065i	0.963713	+	0.266940i	$0.0860125\pi$
$83$	11.2118	+	11.2118i	1.23065	+	1.23065i	0.266940	+	0.963713i	$0.413988\pi$
$84$	−8.00806	+	1.44425i	−0.873752	+	0.157581i
$85$	−2.58107	+	1.52646i	−0.279956	+	0.165568i
$86$			9.53349i			1.02802i
$87$	9.38294	+	6.51564i	1.00596	+	0.698550i
$88$	1.30645	−	1.30645i	0.139268	−	0.139268i
$89$	−9.35985			−0.992142			−0.496071	−	0.868282i	$-0.665224\pi$
$89$	−9.35985			−0.992142			−0.496071	+	0.868282i	$0.665224\pi$
$90$	−5.21672	−	4.21733i	−0.549890	−	0.444545i
$91$	−11.4234			−1.19750
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	6.75015	+	4.68739i	0.699958	+	0.486060i
$94$		−	10.1422i		−	1.04609i
$95$	−0.697577	+	2.71694i	−0.0715699	+	0.278752i
$96$	−1.70455	+	0.307415i	−0.173970	+	0.0313754i
$97$	−5.09832	−	5.09832i	−0.517656	−	0.517656i	0.399206	−	0.916861i	$-0.369286\pi$
$97$	−5.09832	−	5.09832i	−0.517656	−	0.517656i	−0.916861	+	0.399206i	$0.869286\pi$
$98$	−10.6573	−	10.6573i	−1.07655	−	1.07655i
$99$	5.19358	−	1.93630i	0.521974	−	0.194605i
$100$	2.40872	−	4.38156i	0.240872	−	0.438156i
$101$			12.0814i			1.20214i	0.799196	+	0.601071i	$0.205259\pi$
$101$			12.0814i			1.20214i	−0.799196	+	0.601071i	$0.794741\pi$
$102$	−1.32485	+	1.90787i	−0.131180	+	0.188907i
$103$	9.21304	−	9.21304i	0.907788	−	0.907788i	−0.0883058	−	0.996093i	$-0.528145\pi$
$103$	9.21304	−	9.21304i	0.907788	−	0.907788i	0.996093	+	0.0883058i	$0.0281453\pi$
$104$	−2.43152			−0.238430
$105$	1.32511	−	18.1471i	0.129317	−	1.77098i
$106$	−10.3281			−1.00315
$107$	8.07473	−	8.07473i	0.780614	−	0.780614i	−0.199321	−	0.979934i	$-0.563874\pi$
$107$	8.07473	−	8.07473i	0.780614	−	0.780614i	0.979934	+	0.199321i	$0.0638735\pi$
$108$	−5.03448	−	1.28607i	−0.484443	−	0.123752i
$109$		−	13.1231i		−	1.25697i	−0.777823	−	0.628484i	$-0.783676\pi$
$109$		−	13.1231i		−	1.25697i	0.777823	−	0.628484i	$-0.216324\pi$
$110$	2.10305	+	3.55602i	0.200518	+	0.339053i
$111$	−3.01625	−	16.7245i	−0.286290	−	1.58742i
$112$	−3.32202	−	3.32202i	−0.313902	−	0.313902i
$113$	−2.14024	−	2.14024i	−0.201337	−	0.201337i	0.599236	−	0.800573i	$-0.295471\pi$
$113$	−2.14024	−	2.14024i	−0.201337	−	0.201337i	−0.800573	+	0.599236i	$0.795471\pi$
$114$	0.385641	+	2.13830i	0.0361186	+	0.200270i
$115$	1.13826	+	1.92467i	0.106143	+	0.179477i
$116$			6.59528i			0.612356i
$117$	−6.63496	−	3.03118i	−0.613402	−	0.280232i
$118$	−4.99347	+	4.99347i	−0.459686	+	0.459686i
$119$	−6.30029			−0.577546
$120$	0.282055	−	3.86270i	0.0257480	−	0.352615i
$121$	7.58639			0.689672
$122$	−2.70387	+	2.70387i	−0.244796	+	0.244796i
$123$	0.499619	−	0.719483i	0.0450491	−	0.0648736i
$124$			4.74469i			0.426086i
$125$	8.15024	+	7.65334i	0.728979	+	0.684536i
$126$	−4.92360	−	13.2062i	−0.438629	−	1.17650i
$127$	1.46864	+	1.46864i	0.130321	+	0.130321i	0.769258	−	0.638938i	$-0.220626\pi$
$127$	1.46864	+	1.46864i	0.130321	+	0.130321i	−0.638938	+	0.769258i	$0.720626\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−16.2503	+	2.93074i	−1.43076	+	0.258037i
$130$	1.35211	−	5.26624i	0.118588	−	0.461880i
$131$		−	3.62572i		−	0.316781i	−0.987377	−	0.158390i	$-0.949370\pi$
$131$		−	3.62572i		−	0.316781i	0.987377	−	0.158390i	$-0.0506304\pi$
$132$	2.62853	+	1.82529i	0.228784	+	0.158871i
$133$	−4.16735	+	4.16735i	−0.361355	+	0.361355i
$134$	3.64019			0.314464
$135$	5.58496	−	10.1886i	0.480676	−	0.876898i
$136$	−1.34104			−0.114994
$137$	−4.25154	+	4.25154i	−0.363233	+	0.363233i	−0.865002	−	0.501769i	$-0.832683\pi$
$137$	−4.25154	+	4.25154i	−0.363233	+	0.363233i	0.501769	+	0.865002i	$0.332683\pi$
$138$	1.42268	+	0.987925i	0.121106	+	0.0840977i
$139$		−	9.87234i		−	0.837361i	−0.908134	−	0.418680i	$-0.862493\pi$
$139$		−	9.87234i		−	0.837361i	0.908134	−	0.418680i	$-0.137507\pi$
$140$	9.04220	−	5.34761i	0.764205	−	0.451955i
$141$	17.2880	−	3.11788i	1.45591	−	0.262573i
$142$	8.35761	+	8.35761i	0.701355	+	0.701355i
$143$	3.17666	+	3.17666i	0.265645	+	0.265645i
$144$	−1.04801	−	2.81099i	−0.0873341	−	0.234249i
$145$	−14.2842	−	3.66748i	−1.18624	−	0.304567i
$146$		−	4.66993i		−	0.386486i
$147$	14.8897	−	21.4421i	1.22808	−	1.76851i
$148$	6.93789	−	6.93789i	0.570291	−	0.570291i
$149$	−2.39241			−0.195994			−0.0979968	−	0.995187i	$-0.531244\pi$
$149$	−2.39241			−0.195994			−0.0979968	+	0.995187i	$0.531244\pi$
$150$	8.20907	+	2.75884i	0.670268	+	0.225258i
$151$	10.6559			0.867165			0.433582	−	0.901114i	$-0.357249\pi$
$151$	10.6559			0.867165			0.433582	+	0.901114i	$0.357249\pi$
$152$	−0.887039	+	0.887039i	−0.0719484	+	0.0719484i
$153$	−3.65934	−	1.67177i	−0.295840	−	0.135154i
$154$			8.68009i			0.699462i
$155$	−10.2761	−	2.63841i	−0.825400	−	0.211922i
$156$	−0.747487	−	4.14466i	−0.0598468	−	0.331838i
$157$	0.651151	+	0.651151i	0.0519675	+	0.0519675i	0.732613	−	0.680645i	$-0.238301\pi$
$157$	0.651151	+	0.651151i	0.0519675	+	0.0519675i	−0.680645	+	0.732613i	$0.738301\pi$
$158$	5.09476	+	5.09476i	0.405318	+	0.405318i
$159$	−3.17502	−	17.6048i	−0.251795	−	1.39615i
$160$	1.92467	−	1.13826i	0.152159	−	0.0899874i
$161$			4.69805i			0.370258i
$162$	0.644498	−	8.97689i	0.0506366	−	0.705291i
$163$	−4.88731	+	4.88731i	−0.382804	+	0.382804i	−0.872111	−	0.489307i	$-0.837250\pi$
$163$	−4.88731	+	4.88731i	−0.382804	+	0.382804i	0.489307	+	0.872111i	$0.337250\pi$
$164$	0.505725			0.0394905
$165$	−5.41490	+	4.67792i	−0.421550	+	0.364176i
$166$	−15.8559			−1.23065
$167$	−3.50266	+	3.50266i	−0.271044	+	0.271044i	−0.829520	−	0.558477i	$-0.811386\pi$
$167$	−3.50266	+	3.50266i	−0.271044	+	0.271044i	0.558477	+	0.829520i	$0.311386\pi$
$168$	4.64132	−	6.68380i	0.358085	−	0.515666i
$169$			7.08770i			0.545208i
$170$	0.745722	−	2.90446i	0.0571943	−	0.222762i
$171$	−3.52629	+	1.31469i	−0.269662	+	0.100537i
$172$	−6.74120	−	6.74120i	−0.514012	−	0.514012i
$173$	−1.69609	−	1.69609i	−0.128952	−	0.128952i	0.639685	−	0.768637i	$-0.279065\pi$
$173$	−1.69609	−	1.69609i	−0.128952	−	0.128952i	−0.768637	+	0.639685i	$0.779065\pi$
$174$	−11.2420	+	2.02749i	−0.852253	+	0.153703i
$175$	6.55380	+	22.5575i	0.495421	+	1.70518i
$176$			1.84760i			0.139268i
$177$	−10.0467	−	6.97655i	−0.755155	−	0.524390i
$178$	6.61841	−	6.61841i	0.496071	−	0.496071i
$179$	−15.4433			−1.15429			−0.577145	−	0.816642i	$-0.695833\pi$
$179$	−15.4433			−1.15429			−0.577145	+	0.816642i	$0.695833\pi$
$180$	6.67088	−	0.706675i	0.497218	−	0.0526725i
$181$	15.1508			1.12615			0.563076	−	0.826405i	$-0.309618\pi$
$181$	15.1508			1.12615			0.563076	+	0.826405i	$0.309618\pi$
$182$	8.07757	−	8.07757i	0.598749	−	0.598749i
$183$	−5.44009	−	3.77767i	−0.402143	−	0.279253i
$184$			1.00000i			0.0737210i
$185$	11.1682	+	18.8842i	0.821105	+	1.38840i
$186$	−8.08756	+	1.45859i	−0.593009	+	0.106949i
$187$	1.75200	+	1.75200i	0.128119	+	0.128119i
$188$	7.17165	+	7.17165i	0.523046	+	0.523046i
$189$	20.9970	−	12.4523i	1.52731	−	0.905772i
$190$	−1.42791	−	2.41443i	−0.103591	−	0.175161i
$191$			5.46374i			0.395342i	0.980268	+	0.197671i	$0.0633378\pi$
$191$			5.46374i			0.395342i	−0.980268	+	0.197671i	$0.936662\pi$
$192$	0.987925	−	1.42268i	0.0712973	−	0.102673i
$193$	−15.8524	+	15.8524i	−1.14108	+	1.14108i	−0.152829	+	0.988253i	$0.548838\pi$
$193$	−15.8524	+	15.8524i	−1.14108	+	1.14108i	−0.988253	+	0.152829i	$0.951162\pi$
$194$	7.21011			0.517656
$195$	9.39224	+	0.685822i	0.672592	+	0.0491128i
$196$	15.0717			1.07655
$197$	15.9133	−	15.9133i	1.13378	−	1.13378i	0.144232	−	0.989544i	$-0.453929\pi$
$197$	15.9133	−	15.9133i	1.13378	−	1.13378i	0.989544	−	0.144232i	$-0.0460712\pi$
$198$	−2.30324	+	5.04158i	−0.163684	+	0.358290i
$199$		−	18.2044i		−	1.29048i	−0.763981	−	0.645238i	$-0.776758\pi$
$199$		−	18.2044i		−	1.29048i	0.763981	−	0.645238i	$-0.223242\pi$
$200$	1.39501	+	4.80145i	0.0986418	+	0.339514i
$201$	1.11905	+	6.20489i	0.0789316	+	0.437659i
$202$	−8.54283	−	8.54283i	−0.601071	−	0.601071i
$203$	−21.9097	−	21.9097i	−1.53776	−	1.53776i
$204$	−0.412257	−	2.28588i	−0.0288638	−	0.160043i
$205$	−0.281222	+	1.09531i	−0.0196414	+	0.0764998i
$206$			13.0292i			0.907788i
$207$	−1.24662	+	2.72873i	−0.0866459	+	0.189660i
$208$	1.71935	−	1.71935i	0.119215	−	0.119215i
$209$	2.31774			0.160321
$210$	11.8950	+	13.7690i	0.820831	+	0.950149i
$211$	−24.0819			−1.65787			−0.828935	−	0.559346i	$-0.811052\pi$
$211$	−24.0819			−1.65787			−0.828935	+	0.559346i	$0.811052\pi$
$212$	7.30308	−	7.30308i	0.501577	−	0.501577i
$213$	−11.6767	+	16.8152i	−0.800076	+	1.15216i
$214$			11.4194i			0.780614i
$215$	18.3488	−	10.8516i	1.25138	−	0.740073i
$216$	4.46931	−	2.65053i	0.304098	−	0.180346i
$217$	−15.7620	−	15.7620i	−1.06999	−	1.06999i
$218$	9.27945	+	9.27945i	0.628484	+	0.628484i
$219$	7.96014	−	1.43561i	0.537896	−	0.0970093i
$220$	−4.00156	−	1.02740i	−0.269785	−	0.0692676i
$221$		−	3.26078i		−	0.219344i
$222$	13.9588	+	9.69318i	0.936854	+	0.650564i
$223$	−2.75191	+	2.75191i	−0.184282	+	0.184282i	−0.793219	−	0.608937i	$-0.791596\pi$
$223$	−2.75191	+	2.75191i	−0.184282	+	0.184282i	0.608937	+	0.793219i	$0.291596\pi$
$224$	4.69805			0.313902
$225$	−2.17899	+	14.8409i	−0.145266	+	0.989393i
$226$	3.02676			0.201337
$227$	5.47594	−	5.47594i	0.363451	−	0.363451i	−0.501631	−	0.865082i	$-0.667266\pi$
$227$	5.47594	−	5.47594i	0.363451	−	0.363451i	0.865082	+	0.501631i	$0.167266\pi$
$228$	−1.78469	−	1.23932i	−0.118194	−	0.0820756i
$229$		−	27.5633i		−	1.82144i	−0.413030	−	0.910718i	$-0.635529\pi$
$229$		−	27.5633i		−	1.82144i	0.413030	−	0.910718i	$-0.364471\pi$
$230$	−2.16582	−	0.556076i	−0.142810	−	0.0366666i
$231$	−14.7957	+	2.66839i	−0.973483	+	0.175567i
$232$	−4.66357	−	4.66357i	−0.306178	−	0.306178i
$233$	−4.58254	−	4.58254i	−0.300212	−	0.300212i	0.540885	−	0.841097i	$-0.318090\pi$
$233$	−4.58254	−	4.58254i	−0.300212	−	0.300212i	−0.841097	+	0.540885i	$0.818090\pi$
$234$	6.83499	−	2.54826i	0.446817	−	0.166585i
$235$	−19.5205	+	11.5445i	−1.27338	+	0.753081i
$236$		−	7.06183i		−	0.459686i
$237$	−7.11808	+	10.2505i	−0.462369	+	0.665841i
$238$	4.45497	−	4.45497i	0.288773	−	0.288773i
$239$	−5.95432			−0.385153			−0.192576	−	0.981282i	$-0.561684\pi$
$239$	−5.95432			−0.385153			−0.192576	+	0.981282i	$0.561684\pi$
$240$	2.53190	+	2.93078i	0.163433	+	0.189181i
$241$	16.3480			1.05307			0.526534	−	0.850154i	$-0.323491\pi$
$241$	16.3480			1.05307			0.526534	+	0.850154i	$0.323491\pi$
$242$	−5.36439	+	5.36439i	−0.344836	+	0.344836i
$243$	15.4997	−	1.66105i	0.994307	−	0.106557i
$244$		−	3.82384i		−	0.244796i
$245$	−8.38099	+	32.6425i	−0.535442	+	2.08545i
$246$	0.155468	+	0.862035i	0.00991225	+	0.0549613i
$247$	−2.15686	−	2.15686i	−0.137237	−	0.137237i
$248$	−3.35500	−	3.35500i	−0.213043	−	0.213043i
$249$	−4.87433	−	27.0271i	−0.308898	−	1.71277i
$250$	−11.1748	+	0.351357i	−0.706758	+	0.0222217i
$251$		−	22.8963i		−	1.44520i	−0.691266	−	0.722601i	$-0.742947\pi$
$251$		−	22.8963i		−	1.44520i	0.691266	−	0.722601i	$-0.257053\pi$
$252$	12.8197	+	5.85667i	0.807564	+	0.368935i
$253$	1.30645	−	1.30645i	0.0821357	−	0.0821357i
$254$	−2.07697			−0.130321
$255$	5.18005	+	0.378248i	0.324387	+	0.0236868i
$256$	1.00000			0.0625000
$257$	−13.1981	+	13.1981i	−0.823275	+	0.823275i	−0.986576	−	0.163301i	$-0.947786\pi$
$257$	−13.1981	+	13.1981i	−0.823275	+	0.823275i	0.163301	+	0.986576i	$0.447786\pi$
$258$	9.41837	−	13.5631i	0.586362	−	0.844400i
$259$			46.0957i			2.86424i
$260$	2.76771	+	4.67988i	0.171646	+	0.290234i
$261$	−6.91192	−	18.5393i	−0.427837	−	1.14755i
$262$	2.56377	+	2.56377i	0.158390	+	0.158390i
$263$	−16.5451	−	16.5451i	−1.02021	−	1.02021i	−0.999791	−	0.0204218i	$-0.993499\pi$
$263$	−16.5451	−	16.5451i	−1.02021	−	1.02021i	−0.0204218	−	0.999791i	$-0.506501\pi$
$264$	−3.14932	+	0.567979i	−0.193827	+	0.0349567i
$265$	11.7561	+	19.8782i	0.722171	+	1.22111i
$266$		−	5.89353i		−	0.361355i
$267$	13.3160	+	9.24683i	0.814928	+	0.565897i
$268$	−2.57400	+	2.57400i	−0.157232	+	0.157232i
$269$	9.22484			0.562449			0.281224	−	0.959642i	$-0.409260\pi$
$269$	9.22484			0.562449			0.281224	+	0.959642i	$0.409260\pi$
$270$	3.25529	+	11.1536i	0.198111	+	0.678787i
$271$	12.2145			0.741979			0.370990	−	0.928637i	$-0.379019\pi$
$271$	12.2145			0.741979			0.370990	+	0.928637i	$0.379019\pi$
$272$	0.948261	−	0.948261i	0.0574968	−	0.0574968i
$273$	16.2518	+	11.2855i	0.983604	+	0.683028i
$274$		−	6.01258i		−	0.363233i
$275$	4.45035	−	8.09535i	0.268366	−	0.488168i
$276$	−1.70455	+	0.307415i	−0.102602	+	0.0185042i
$277$	−7.60344	−	7.60344i	−0.456846	−	0.456846i	0.440773	−	0.897619i	$-0.354705\pi$
$277$	−7.60344	−	7.60344i	−0.456846	−	0.456846i	−0.897619	+	0.440773i	$0.854705\pi$
$278$	6.98080	+	6.98080i	0.418680	+	0.418680i
$279$	−4.97248	−	13.3373i	−0.297695	−	0.798482i
$280$	−2.61247	+	10.1751i	−0.156125	+	0.608080i
$281$		−	7.76150i		−	0.463012i	−0.972833	−	0.231506i	$-0.925635\pi$
$281$		−	7.76150i		−	0.463012i	0.972833	−	0.231506i	$-0.0743653\pi$
$282$	−10.0198	+	14.4291i	−0.596669	+	0.859241i
$283$	−21.0879	+	21.0879i	−1.25355	+	1.25355i	−0.299430	+	0.954118i	$0.596796\pi$
$283$	−21.0879	+	21.0879i	−1.25355	+	1.25355i	−0.954118	+	0.299430i	$0.903204\pi$
$284$	−11.8194			−0.701355
$285$	3.67656	−	3.17617i	0.217781	−	0.188140i
$286$	−4.49247			−0.265645
$287$	−1.68003	+	1.68003i	−0.0991691	+	0.0991691i
$288$	2.72873	+	1.24662i	0.160792	+	0.0734576i
$289$			15.2016i			0.894212i
$290$	12.6937	−	7.50715i	0.745402	−	0.440835i
$291$	2.21650	+	12.2900i	0.129933	+	0.720453i
$292$	3.30214	+	3.30214i	0.193243	+	0.193243i
$293$	−14.1881	−	14.1881i	−0.828875	−	0.828875i	0.158486	−	0.987361i	$-0.449339\pi$
$293$	−14.1881	−	14.1881i	−0.828875	−	0.828875i	−0.987361	+	0.158486i	$0.949339\pi$
$294$	4.63325	+	25.6904i	0.270217	+	1.49830i
$295$	15.2946	+	3.92691i	0.890489	+	0.228634i
$296$			9.81166i			0.570291i
$297$	−9.30169	−	2.37614i	−0.539739	−	0.137878i
$298$	1.69169	−	1.69169i	0.0979968	−	0.0979968i
$299$	−2.43152			−0.140619
$300$	−7.75548	+	3.85390i	−0.447763	+	0.222505i
$301$	44.7888			2.58158
$302$	−7.53486	+	7.53486i	−0.433582	+	0.433582i
$303$	11.9355	−	17.1879i	0.685676	−	0.987418i
$304$		−	1.25446i		−	0.0719484i
$305$	8.28176	+	2.12635i	0.474212	+	0.121754i
$306$	3.76966	−	1.40543i	0.215497	−	0.0803429i
$307$	−12.0813	−	12.0813i	−0.689518	−	0.689518i	0.272607	−	0.962125i	$-0.412114\pi$
$307$	−12.0813	−	12.0813i	−0.689518	−	0.689518i	−0.962125	+	0.272607i	$0.912114\pi$
$308$	−6.13775	−	6.13775i	−0.349731	−	0.349731i
$309$	−22.2090	+	4.00537i	−1.26342	+	0.227858i
$310$	9.13197	−	5.40069i	0.518661	−	0.306739i
$311$		−	24.1187i		−	1.36765i	−0.729647	−	0.683824i	$-0.760315\pi$
$311$		−	24.1187i		−	1.36765i	0.729647	−	0.683824i	$-0.239685\pi$
$312$	3.45927	+	2.40216i	0.195842	+	0.135996i
$313$	5.08762	−	5.08762i	0.287569	−	0.287569i	−0.548549	−	0.836118i	$-0.684820\pi$
$313$	5.08762	−	5.08762i	0.287569	−	0.287569i	0.836118	+	0.548549i	$0.184820\pi$
$314$	−0.920866			−0.0519675
$315$	−19.8132	+	24.5084i	−1.11635	+	1.38089i
$316$	−7.20508			−0.405318
$317$	10.9530	−	10.9530i	0.615184	−	0.615184i	−0.329108	−	0.944292i	$-0.606748\pi$
$317$	10.9530	−	10.9530i	0.615184	−	0.615184i	0.944292	+	0.329108i	$0.106748\pi$
$318$	14.6935	+	10.2034i	0.823973	+	0.572178i
$319$			12.1854i			0.682252i
$320$	−0.556076	+	2.16582i	−0.0310856	+	0.121073i
$321$	−19.4649	+	3.51049i	−1.08643	+	0.195937i
$322$	−3.32202	−	3.32202i	−0.185129	−	0.185129i
$323$	−1.18956	−	1.18956i	−0.0661888	−	0.0661888i
$324$	5.89189	+	6.80335i	0.327327	+	0.377964i
$325$	−11.6748	+	3.39199i	−0.647604	+	0.188154i
$326$		−	6.91170i		−	0.382804i
$327$	−12.9647	+	18.6699i	−0.716947	+	1.03245i
$328$	−0.357602	+	0.357602i	−0.0197453	+	0.0197453i
$329$	−47.6487			−2.62696
$330$	0.521123	−	7.13671i	0.0286869	−	0.392863i
$331$	24.6028			1.35229			0.676146	−	0.736767i	$-0.263649\pi$
$331$	24.6028			1.35229			0.676146	+	0.736767i	$0.263649\pi$
$332$	11.2118	−	11.2118i	0.615327	−	0.615327i
$333$	−12.2314	+	26.7733i	−0.670276	+	1.46717i
$334$		−	4.95351i		−	0.271044i
$335$	−4.14349	−	7.00617i	−0.226383	−	0.382788i
$336$	1.44425	+	8.00806i	0.0787903	+	0.436876i
$337$	−13.0595	−	13.0595i	−0.711398	−	0.711398i	0.255430	−	0.966828i	$-0.417783\pi$
$337$	−13.0595	−	13.0595i	−0.711398	−	0.711398i	−0.966828	+	0.255430i	$0.917783\pi$
$338$	−5.01176	−	5.01176i	−0.272604	−	0.272604i
$339$	0.930471	+	5.15926i	0.0505362	+	0.280213i
$340$	1.52646	+	2.58107i	0.0827838	+	0.139978i
$341$			8.76627i			0.474720i
$342$	1.56383	−	3.42309i	0.0845625	−	0.185099i
$343$	−26.8142	+	26.8142i	−1.44783	+	1.44783i
$344$	9.53349			0.514012
$345$	0.282055	−	3.86270i	0.0151853	−	0.207961i
$346$	2.39864			0.128952
$347$	−7.05463	+	7.05463i	−0.378712	+	0.378712i	−0.870637	−	0.491925i	$-0.836293\pi$
$347$	−7.05463	+	7.05463i	−0.378712	+	0.378712i	0.491925	+	0.870637i	$0.336293\pi$
$348$	6.51564	−	9.38294i	0.349275	−	0.502978i
$349$			28.6619i			1.53424i	0.641505	+	0.767119i	$0.278311\pi$
$349$			28.6619i			1.53424i	−0.641505	+	0.767119i	$0.721689\pi$
$350$	−20.5848	−	11.3163i	−1.10030	−	0.604881i
$351$	6.44482	+	10.8672i	0.343999	+	0.580049i
$352$	−1.30645	−	1.30645i	−0.0696339	−	0.0696339i
$353$	−4.92849	−	4.92849i	−0.262317	−	0.262317i	0.563678	−	0.825995i	$-0.309386\pi$
$353$	−4.92849	−	4.92849i	−0.262317	−	0.262317i	−0.825995	+	0.563678i	$0.809386\pi$
$354$	12.0372	−	2.17091i	0.639772	−	0.115383i
$355$	6.57252	−	25.5988i	0.348833	−	1.35864i
$356$			9.35985i			0.496071i
$357$	8.96326	+	6.22421i	0.474386	+	0.329420i
$358$	10.9201	−	10.9201i	0.577145	−	0.577145i
$359$	−9.91548			−0.523319			−0.261660	−	0.965160i	$-0.584270\pi$
$359$	−9.91548			−0.523319			−0.261660	+	0.965160i	$0.584270\pi$
$360$	−4.21733	+	5.21672i	−0.222273	+	0.274945i
$361$	17.4263			0.917175
$362$	−10.7133	+	10.7133i	−0.563076	+	0.563076i
$363$	−10.7930	−	7.49478i	−0.566484	−	0.393374i
$364$			11.4234i			0.598749i
$365$	−8.98808	+	5.31560i	−0.470458	+	0.278231i
$366$	6.51794	−	1.17551i	0.340698	−	0.0614447i
$367$	9.89573	+	9.89573i	0.516553	+	0.516553i	0.916527	−	0.399974i	$-0.130981\pi$
$367$	9.89573	+	9.89573i	0.516553	+	0.516553i	−0.399974	+	0.916527i	$0.630981\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−1.42159	+	0.530005i	−0.0740050	+	0.0275910i
$370$	−21.2503	−	5.45603i	−1.10475	−	0.283646i
$371$			48.5220i			2.51913i
$372$	4.68739	−	6.75015i	0.243030	−	0.349979i
$373$	23.6341	−	23.6341i	1.22373	−	1.22373i	0.257430	−	0.966297i	$-0.417124\pi$
$373$	23.6341	−	23.6341i	1.22373	−	1.22373i	0.966297	−	0.257430i	$-0.0828756\pi$
$374$	−2.47771			−0.128119
$375$	−4.03421	−	18.9400i	−0.208326	−	0.978059i
$376$	−10.1422			−0.523046
$377$	11.3396	−	11.3396i	0.584017	−	0.584017i
$378$	−6.04202	+	23.6522i	−0.310768	+	1.21654i
$379$		−	24.1573i		−	1.24088i	−0.784255	−	0.620439i	$-0.786954\pi$
$379$		−	24.1573i		−	1.24088i	0.784255	−	0.620439i	$-0.213046\pi$
$380$	2.71694	+	0.697577i	0.139376	+	0.0357850i
$381$	−0.638491	−	3.54030i	−0.0327109	−	0.181375i
$382$	−3.86345	−	3.86345i	−0.197671	−	0.197671i
$383$	16.8899	+	16.8899i	0.863033	+	0.863033i	0.991689	−	0.128656i	$-0.0410663\pi$
$383$	16.8899	+	16.8899i	0.863033	+	0.863033i	−0.128656	+	0.991689i	$0.541066\pi$
$384$	0.307415	+	1.70455i	0.0156877	+	0.0869850i
$385$	16.7063	−	9.88021i	0.851433	−	0.503542i
$386$		−	22.4187i		−	1.14108i
$387$	26.0143	+	11.8846i	1.32238	+	0.604129i
$388$	−5.09832	+	5.09832i	−0.258828	+	0.258828i
$389$	0.696017			0.0352895			0.0176447	−	0.999844i	$-0.494383\pi$
$389$	0.696017			0.0352895			0.0176447	+	0.999844i	$0.494383\pi$
$390$	−7.12627	+	6.15637i	−0.360853	+	0.311740i
$391$	−1.34104			−0.0678195
$392$	−10.6573	+	10.6573i	−0.538273	+	0.538273i
$393$	−3.58194	+	5.15822i	−0.180685	+	0.260198i
$394$			22.5048i			1.13378i
$395$	4.00658	−	15.6049i	0.201593	−	0.785169i
$396$	−1.93630	−	5.19358i	−0.0973026	−	0.260987i
$397$	−22.8095	−	22.8095i	−1.14478	−	1.14478i	−0.987565	−	0.157213i	$-0.949749\pi$
$397$	−22.8095	−	22.8095i	−1.14478	−	1.14478i	−0.157213	−	0.987565i	$-0.550251\pi$
$398$	12.8725	+	12.8725i	0.645238	+	0.645238i
$399$	10.0458	−	1.81176i	0.502920	−	0.0907014i
$400$	−4.38156	−	2.40872i	−0.219078	−	0.120436i
$401$		−	25.2746i		−	1.26216i	−0.775720	−	0.631078i	$-0.782613\pi$
$401$		−	25.2746i		−	1.26216i	0.775720	−	0.631078i	$-0.217387\pi$
$402$	−5.17881	−	3.59623i	−0.258295	−	0.179364i
$403$	8.15776	−	8.15776i	0.406367	−	0.406367i
$404$	12.0814			0.601071
$405$	−18.0112	+	8.97760i	−0.894983	+	0.446101i
$406$	30.9849			1.53776
$407$	12.8184	−	12.8184i	0.635386	−	0.635386i
$408$	1.90787	+	1.32485i	0.0944536	+	0.0655898i
$409$			1.78568i			0.0882962i	0.999025	+	0.0441481i	$0.0140574\pi$
$409$			1.78568i			0.0882962i	−0.999025	+	0.0441481i	$0.985943\pi$
$410$	−0.575648	−	0.973355i	−0.0284292	−	0.0480706i
$411$	10.2488	−	1.84836i	0.505534	−	0.0911728i
$412$	−9.21304	−	9.21304i	−0.453894	−	0.453894i
$413$	23.4595	+	23.4595i	1.15437	+	1.15437i
$414$	−1.04801	−	2.81099i	−0.0515069	−	0.138153i
$415$	18.0481	+	30.5173i	0.885947	+	1.49804i
$416$			2.43152i			0.119215i
$417$	−9.75313	+	14.0451i	−0.477613	+	0.687793i
$418$	−1.63889	+	1.63889i	−0.0801607	+	0.0801607i
$419$	35.8107			1.74946			0.874732	−	0.484606i	$-0.161037\pi$
$419$	35.8107			1.74946			0.874732	+	0.484606i	$0.161037\pi$
$420$	−18.1471	−	1.32511i	−0.885490	−	0.0646586i
$421$	20.9681			1.02192			0.510962	−	0.859603i	$-0.329289\pi$
$421$	20.9681			1.02192			0.510962	+	0.859603i	$0.329289\pi$
$422$	17.0285	−	17.0285i	0.828935	−	0.828935i
$423$	−27.6754	−	12.6435i	−1.34562	−	0.614747i
$424$			10.3281i			0.501577i
$425$	−6.43896	+	1.87076i	−0.312335	+	0.0907453i
$426$	−3.63348	−	20.1469i	−0.176043	−	0.976119i
$427$	12.7029	+	12.7029i	0.614736	+	0.614736i
$428$	−8.07473	−	8.07473i	−0.390307	−	0.390307i
$429$	−1.38105	−	7.65765i	−0.0666779	−	0.369715i
$430$	−5.30135	+	20.6478i	−0.255654	+	0.995727i
$431$			20.7370i			0.998867i	0.866352	+	0.499434i	$0.166459\pi$
$431$			20.7370i			0.998867i	−0.866352	+	0.499434i	$0.833541\pi$
$432$	−1.28607	+	5.03448i	−0.0618761	+	0.242222i
$433$	18.7131	−	18.7131i	0.899293	−	0.899293i	−0.0960806	−	0.995374i	$-0.530631\pi$
$433$	18.7131	−	18.7131i	0.899293	−	0.899293i	0.995374	+	0.0960806i	$0.0306307\pi$
$434$	22.2908			1.06999
$435$	16.6986	+	19.3293i	0.800635	+	0.926771i
$436$	−13.1231			−0.628484
$437$	−0.887039	+	0.887039i	−0.0424328	+	0.0424328i
$438$	−4.61354	+	6.64379i	−0.220443	+	0.317453i
$439$			17.8021i			0.849646i	0.905276	+	0.424823i	$0.139664\pi$
$439$			17.8021i			0.849646i	−0.905276	+	0.424823i	$0.860336\pi$
$440$	3.55602	−	2.10305i	0.169526	−	0.100259i
$441$	−42.3663	+	15.7952i	−2.01744	+	0.752154i
$442$	2.30572	+	2.30572i	0.109672	+	0.109672i
$443$	29.1309	+	29.1309i	1.38405	+	1.38405i	0.837290	+	0.546759i	$0.184139\pi$
$443$	29.1309	+	29.1309i	1.38405	+	1.38405i	0.546759	+	0.837290i	$0.315861\pi$
$444$	−16.7245	+	3.01625i	−0.793709	+	0.143145i
$445$	−20.2718	−	5.20479i	−0.960974	−	0.246731i
$446$		−	3.89179i		−	0.184282i
$447$	3.40362	+	2.36352i	0.160986	+	0.111791i
$448$	−3.32202	+	3.32202i	−0.156951	+	0.156951i
$449$	−5.24969			−0.247748			−0.123874	−	0.992298i	$-0.539532\pi$
$449$	−5.24969			−0.247748			−0.123874	+	0.992298i	$0.539532\pi$
$450$	−8.95332	−	12.0349i	−0.422063	−	0.567329i
$451$	0.934376			0.0439981
$452$	−2.14024	+	2.14024i	−0.100668	+	0.100668i
$453$	−15.1599	−	10.5272i	−0.712274	−	0.494612i
$454$			7.74414i			0.363451i
$455$	−24.7411	−	6.35229i	−1.15988	−	0.297800i
$456$	2.13830	−	0.385641i	0.100135	−	0.0180593i
$457$	−8.60192	−	8.60192i	−0.402381	−	0.402381i	0.476691	−	0.879071i	$-0.341836\pi$
$457$	−8.60192	−	8.60192i	−0.402381	−	0.402381i	−0.879071	+	0.476691i	$0.841836\pi$
$458$	19.4902	+	19.4902i	0.910718	+	0.910718i
$459$	3.55447	+	5.99353i	0.165909	+	0.279754i
$460$	1.92467	−	1.13826i	0.0897383	−	0.0530717i
$461$		−	1.17403i		−	0.0546799i	−0.999626	−	0.0273400i	$-0.991296\pi$
$461$		−	1.17403i		−	0.0546799i	0.999626	−	0.0273400i	$-0.00870366\pi$
$462$	8.57528	−	12.3490i	0.398958	−	0.574525i
$463$	7.56540	−	7.56540i	0.351594	−	0.351594i	−0.509108	−	0.860702i	$-0.670025\pi$
$463$	7.56540	−	7.56540i	0.351594	−	0.351594i	0.860702	+	0.509108i	$0.170025\pi$
$464$	6.59528			0.306178
$465$	12.0131	+	13.9057i	0.557093	+	0.644859i
$466$	6.48069			0.300212
$467$	−21.1971	+	21.1971i	−0.980883	+	0.980883i	−0.999821	−	0.0189378i	$-0.993972\pi$
$467$	−21.1971	+	21.1971i	−0.980883	+	0.980883i	0.0189378	+	0.999821i	$0.493972\pi$
$468$	−3.03118	+	6.63496i	−0.140116	+	0.306701i
$469$		−	17.1018i		−	0.789687i
$470$	5.63986	−	21.9663i	0.260147	−	1.01323i
$471$	−0.283088	−	1.56966i	−0.0130440	−	0.0723263i
$472$	4.99347	+	4.99347i	0.229843	+	0.229843i
$473$	−12.4550	−	12.4550i	−0.572682	−	0.572682i
$474$	−2.21495	−	12.2814i	−0.101736	−	0.564105i
$475$	−3.02165	+	5.49650i	−0.138643	+	0.252197i
$476$			6.30029i			0.288773i
$477$	−12.8752	+	28.1826i	−0.589515	+	1.29039i
$478$	4.21034	−	4.21034i	0.192576	−	0.192576i
$479$	8.11220			0.370656			0.185328	−	0.982677i	$-0.440665\pi$
$479$	8.11220			0.370656			0.185328	+	0.982677i	$0.440665\pi$
$480$	−3.86270	−	0.282055i	−0.176307	−	0.0128740i
$481$	−23.8573			−1.08780
$482$	−11.5598	+	11.5598i	−0.526534	+	0.526534i
$483$	4.64132	−	6.68380i	0.211187	−	0.304123i
$484$		−	7.58639i		−	0.344836i
$485$	−8.20699	−	13.8771i	−0.372660	−	0.630126i
$486$	−9.78541	+	12.1345i	−0.443875	+	0.550432i
$487$	8.77478	+	8.77478i	0.397623	+	0.397623i	0.877394	−	0.479771i	$-0.159280\pi$
$487$	8.77478	+	8.77478i	0.397623	+	0.397623i	−0.479771	+	0.877394i	$0.659280\pi$
$488$	2.70387	+	2.70387i	0.122398	+	0.122398i
$489$	11.7814	−	2.12476i	0.532771	−	0.0960851i
$490$	−17.1555	−	29.0080i	−0.775006	−	1.31045i
$491$		−	34.5844i		−	1.56077i	−0.625299	−	0.780385i	$-0.715023\pi$
$491$		−	34.5844i		−	1.56077i	0.625299	−	0.780385i	$-0.284977\pi$
$492$	−0.719483	−	0.499619i	−0.0324368	−	0.0225245i
$493$	6.25404	−	6.25404i	0.281668	−	0.281668i
$494$	3.05026			0.137237
$495$	12.3251	−	1.30565i	0.553971	−	0.0586846i
$496$	4.74469			0.213043
$497$	39.2645	−	39.2645i	1.76125	−	1.76125i
$498$	22.5577	+	15.6644i	1.01084	+	0.701938i
$499$		−	14.6311i		−	0.654977i	−0.944855	−	0.327489i	$-0.893798\pi$
$499$		−	14.6311i		−	0.654977i	0.944855	−	0.327489i	$-0.106202\pi$
$500$	7.65334	−	8.15024i	0.342268	−	0.364490i
$501$	8.44351	−	1.52278i	0.377228	−	0.0680329i
$502$	16.1901	+	16.1901i	0.722601	+	0.722601i
$503$	−10.2330	−	10.2330i	−0.456268	−	0.456268i	0.441160	−	0.897428i	$-0.354567\pi$
$503$	−10.2330	−	10.2330i	−0.456268	−	0.456268i	−0.897428	+	0.441160i	$0.854567\pi$
$504$	−13.2062	+	4.92360i	−0.588250	+	0.219315i
$505$	−6.71817	+	26.1661i	−0.298955	+	1.16438i
$506$			1.84760i			0.0821357i
$507$	7.00211	−	10.0835i	0.310975	−	0.447824i
$508$	1.46864	−	1.46864i	0.0651603	−	0.0651603i
$509$	−6.98622			−0.309659			−0.154829	−	0.987941i	$-0.549483\pi$
$509$	−6.98622			−0.309659			−0.154829	+	0.987941i	$0.549483\pi$
$510$	−3.93031	+	3.39538i	−0.174037	+	0.150350i
$511$	−21.9396			−0.970549
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.31557	+	1.61333i	0.278839	+	0.0712302i
$514$		−	18.6649i		−	0.823275i
$515$	25.0769	−	14.8306i	1.10502	−	0.653516i
$516$	2.93074	+	16.2503i	0.129019	+	0.715381i
$517$	13.2503	+	13.2503i	0.582748	+	0.582748i
$518$	−32.5946	−	32.5946i	−1.43212	−	1.43212i
$519$	0.737378	+	4.08861i	0.0323673	+	0.179470i
$520$	−5.26624	−	1.35211i	−0.230940	−	0.0592940i
$521$			28.2975i			1.23973i	0.784707	+	0.619867i	$0.212813\pi$
$521$			28.2975i			1.23973i	−0.784707	+	0.619867i	$0.787187\pi$
$522$	17.9967	+	8.22178i	0.787695	+	0.359858i
$523$	−9.90039	+	9.90039i	−0.432914	+	0.432914i	−0.889618	−	0.456705i	$-0.849030\pi$
$523$	−9.90039	+	9.90039i	−0.432914	+	0.432914i	0.456705	+	0.889618i	$0.349030\pi$
$524$	−3.62572			−0.158390
$525$	12.9611	−	38.5666i	0.565671	−	1.68318i
$526$	23.3983			1.02021
$527$	4.49920	−	4.49920i	0.195988	−	0.195988i
$528$	1.82529	−	2.62853i	0.0794354	−	0.114392i
$529$			1.00000i			0.0434783i
$530$	−22.3688	−	5.74322i	−0.971640	−	0.249469i
$531$	7.40086	+	19.8507i	0.321170	+	0.861449i
$532$	4.16735	+	4.16735i	0.180678	+	0.180678i
$533$	−0.869517	−	0.869517i	−0.0376630	−	0.0376630i
$534$	−15.9544	+	2.87736i	−0.690412	+	0.124516i
$535$	21.9786	−	12.9983i	0.950217	−	0.561964i
$536$		−	3.64019i		−	0.157232i
$537$	21.9709	+	15.2569i	0.948113	+	0.658382i
$538$	−6.52295	+	6.52295i	−0.281224	+	0.281224i
$539$	27.8463			1.19943
$540$	−10.1886	−	5.58496i	−0.438449	−	0.240338i
$541$	3.24241			0.139402			0.0697011	−	0.997568i	$-0.477795\pi$
$541$	3.24241			0.139402			0.0697011	+	0.997568i	$0.477795\pi$
$542$	−8.63697	+	8.63697i	−0.370990	+	0.370990i
$543$	−21.5547	−	14.9679i	−0.925001	−	0.642333i
$544$			1.34104i			0.0574968i
$545$	7.29746	−	28.4223i	0.312589	−	1.21748i
$546$	−19.4718	+	3.51173i	−0.833316	+	0.150288i
$547$	−28.5515	−	28.5515i	−1.22077	−	1.22077i	−0.967357	−	0.253416i	$-0.918446\pi$
$547$	−28.5515	−	28.5515i	−1.22077	−	1.22077i	−0.253416	−	0.967357i	$-0.581554\pi$
$548$	4.25154	+	4.25154i	0.181617	+	0.181617i
$549$	4.00742	+	10.7488i	0.171033	+	0.458747i
$550$	2.57741	+	8.87115i	0.109901	+	0.378267i
$551$		−	8.27353i		−	0.352464i
$552$	0.987925	−	1.42268i	0.0420489	−	0.0605531i
$553$	23.9354	−	23.9354i	1.01784	−	1.01784i
$554$	10.7529			0.456846
$555$	2.76743	−	37.8995i	0.117471	−	1.60874i
$556$	−9.87234			−0.418680
$557$	6.90279	−	6.90279i	0.292481	−	0.292481i	−0.545579	−	0.838059i	$-0.683690\pi$
$557$	6.90279	−	6.90279i	0.292481	−	0.292481i	0.838059	+	0.545579i	$0.183690\pi$
$558$	12.9470	+	5.91481i	0.548088	+	0.250394i
$559$			23.1809i			0.980448i
$560$	−5.34761	−	9.04220i	−0.225978	−	0.382103i
$561$	−0.761684	−	4.22338i	−0.0321583	−	0.178311i
$562$	5.48821	+	5.48821i	0.231506	+	0.231506i
$563$	6.94658	+	6.94658i	0.292764	+	0.292764i	0.838171	−	0.545407i	$-0.183625\pi$
$563$	6.94658	+	6.94658i	0.292764	+	0.292764i	−0.545407	+	0.838171i	$0.683625\pi$
$564$	−3.11788	−	17.2880i	−0.131286	−	0.727955i
$565$	−3.44524	−	5.82552i	−0.144942	−	0.245081i
$566$		−	29.8229i		−	1.25355i
$567$	−42.1739	−	3.02788i	−1.77114	−	0.127159i
$568$	8.35761	−	8.35761i	0.350678	−	0.350678i
$569$	28.0632			1.17647			0.588236	−	0.808689i	$-0.299823\pi$
$569$	28.0632			1.17647			0.588236	+	0.808689i	$0.299823\pi$
$570$	−0.353827	+	4.84561i	−0.0148202	+	0.202960i
$571$	−23.3485			−0.977103			−0.488552	−	0.872535i	$-0.662475\pi$
$571$	−23.3485			−0.977103			−0.488552	+	0.872535i	$0.662475\pi$
$572$	3.17666	−	3.17666i	0.132823	−	0.132823i
$573$	5.39776	−	7.77313i	0.225495	−	0.324727i
$574$		−	2.37592i		−	0.0991691i
$575$	1.39501	+	4.80145i	0.0581757	+	0.200234i
$576$	−2.81099	+	1.04801i	−0.117125	+	0.0436671i
$577$	−10.4763	−	10.4763i	−0.436134	−	0.436134i	0.454575	−	0.890709i	$-0.349791\pi$
$577$	−10.4763	−	10.4763i	−0.436134	−	0.436134i	−0.890709	+	0.454575i	$0.849791\pi$
$578$	−10.7492	−	10.7492i	−0.447106	−	0.447106i
$579$	38.2138	−	6.89185i	1.58811	−	0.286415i
$580$	−3.66748	+	14.2842i	−0.152284	+	0.593119i
$581$			74.4916i			3.09043i
$582$	−10.2576	−	7.12304i	−0.425193	−	0.295260i
$583$	13.4931	−	13.4931i	0.558828	−	0.558828i
$584$	−4.66993			−0.193243
$585$	−12.6846	−	10.2545i	−0.524442	−	0.423973i
$586$	20.0649			0.828875
$587$	20.7853	−	20.7853i	0.857899	−	0.857899i	−0.133191	−	0.991090i	$-0.542522\pi$
$587$	20.7853	−	20.7853i	0.857899	−	0.857899i	0.991090	+	0.133191i	$0.0425224\pi$
$588$	−21.4421	−	14.8897i	−0.884256	−	0.614039i
$589$		−	5.95204i		−	0.245249i
$590$	−13.5917	+	8.03820i	−0.559561	+	0.330928i
$591$	−38.3606	+	6.91832i	−1.57794	+	0.284582i
$592$	−6.93789	−	6.93789i	−0.285146	−	0.285146i
$593$	10.7822	+	10.7822i	0.442772	+	0.442772i	0.892942	−	0.450171i	$-0.148637\pi$
$593$	10.7822	+	10.7822i	0.442772	+	0.442772i	−0.450171	+	0.892942i	$0.648637\pi$
$594$	8.25747	−	4.89710i	0.338808	−	0.200931i
$595$	−13.6453	−	3.50344i	−0.559402	−	0.143627i
$596$			2.39241i			0.0979968i
$597$	−17.9846	+	25.8990i	−0.736060	+	1.05997i
$598$	1.71935	−	1.71935i	0.0703093	−	0.0703093i
$599$	−39.1541			−1.59979			−0.799896	−	0.600139i	$-0.795112\pi$
$599$	−39.1541			−1.59979			−0.799896	+	0.600139i	$0.795112\pi$
$600$	2.75884	−	8.20907i	0.112629	−	0.335134i
$601$	−46.8771			−1.91216			−0.956078	−	0.293113i	$-0.905309\pi$
$601$	−46.8771			−1.91216			−0.956078	+	0.293113i	$0.905309\pi$
$602$	−31.6705	+	31.6705i	−1.29079	+	1.29079i
$603$	4.53792	−	9.93308i	0.184798	−	0.404506i
$604$		−	10.6559i		−	0.433582i
$605$	16.4308	+	4.21861i	0.668005	+	0.171511i
$606$	3.71400	+	20.5933i	0.150871	+	0.836547i
$607$	−28.6698	−	28.6698i	−1.16367	−	1.16367i	−0.983666	−	0.180005i	$-0.942389\pi$
$607$	−28.6698	−	28.6698i	−1.16367	−	1.16367i	−0.180005	−	0.983666i	$-0.557611\pi$
$608$	0.887039	+	0.887039i	0.0359742	+	0.0359742i
$609$	9.52524	+	52.8154i	0.385982	+	2.14019i
$610$	−7.35964	+	4.35253i	−0.297983	+	0.176229i
$611$		−	24.6611i		−	0.997681i
$612$	−1.67177	+	3.65934i	−0.0675772	+	0.147920i
$613$	13.3096	−	13.3096i	0.537571	−	0.537571i	−0.385244	−	0.922815i	$-0.625883\pi$
$613$	13.3096	−	13.3096i	0.537571	−	0.537571i	0.922815	+	0.385244i	$0.125883\pi$
$614$	17.0856			0.689518
$615$	1.48217	−	1.28045i	0.0597669	−	0.0516325i
$616$	8.68009			0.349731
$617$	20.0482	−	20.0482i	0.807111	−	0.807111i	−0.177084	−	0.984196i	$-0.556667\pi$
$617$	20.0482	−	20.0482i	0.807111	−	0.807111i	0.984196	+	0.177084i	$0.0566666\pi$
$618$	12.8719	−	18.5363i	0.517783	−	0.745640i
$619$			41.4746i			1.66700i	0.552517	+	0.833502i	$0.313668\pi$
$619$			41.4746i			1.66700i	−0.552517	+	0.833502i	$0.686332\pi$
$620$	−2.63841	+	10.2761i	−0.105961	+	0.412700i
$621$	4.46931	−	2.65053i	0.179347	−	0.106362i
$622$	17.0545	+	17.0545i	0.683824	+	0.683824i
$623$	−31.0936	−	31.0936i	−1.24574	−	1.24574i
$624$	−4.14466	+	0.747487i	−0.165919	+	0.0299234i
$625$	13.3961	+	21.1079i	0.535844	+	0.844317i
$626$			7.19498i			0.287569i
$627$	−3.29739	−	2.28975i	−0.131685	−	0.0914439i
$628$	0.651151	−	0.651151i	0.0259837	−	0.0259837i
$629$	−13.1579			−0.524638
$630$	−3.31999	−	31.3401i	−0.132272	−	1.24862i
$631$	−0.161420			−0.00642604			−0.00321302	−	0.999995i	$-0.501023\pi$
$631$	−0.161420			−0.00642604			−0.00321302	+	0.999995i	$0.501023\pi$
$632$	5.09476	−	5.09476i	0.202659	−	0.202659i
$633$	34.2608	+	23.7911i	1.36174	+	0.945613i
$634$			15.4899i			0.615184i
$635$	2.36413	+	3.99748i	0.0938177	+	0.158635i
$636$	−17.6048	+	3.17502i	−0.698076	+	0.125898i
$637$	−25.9134	−	25.9134i	−1.02673	−	1.02673i
$638$	−8.61639	−	8.61639i	−0.341126	−	0.341126i
$639$	33.2244	−	12.3869i	1.31434	−	0.490018i
$640$	−1.13826	−	1.92467i	−0.0449937	−	0.0760793i
$641$		−	31.1595i		−	1.23073i	−0.788244	−	0.615363i	$-0.789009\pi$
$641$		−	31.1595i		−	1.23073i	0.788244	−	0.615363i	$-0.210991\pi$
$642$	11.2815	−	16.2461i	0.445245	−	0.641182i
$643$	−26.5729	+	26.5729i	−1.04793	+	1.04793i	−0.0491393	+	0.998792i	$0.515648\pi$
$643$	−26.5729	+	26.5729i	−1.04793	+	1.04793i	−0.998792	+	0.0491393i	$0.984352\pi$
$644$	4.69805			0.185129
$645$	−36.8250	−	2.68897i	−1.44998	−	0.105878i
$646$	1.68229			0.0661888
$647$	16.8647	−	16.8647i	0.663020	−	0.663020i	−0.293071	−	0.956091i	$-0.594677\pi$
$647$	16.8647	−	16.8647i	0.663020	−	0.663020i	0.956091	+	0.293071i	$0.0946771\pi$
$648$	−8.97689	−	0.644498i	−0.352646	−	0.0253183i
$649$		−	13.0474i		−	0.512155i
$650$	5.85686	−	10.6539i	0.229725	−	0.417879i
$651$	6.85252	+	37.9958i	0.268571	+	1.48917i
$652$	4.88731	+	4.88731i	0.191402	+	0.191402i
$653$	−21.5295	−	21.5295i	−0.842515	−	0.842515i	0.146670	−	0.989185i	$-0.453144\pi$
$653$	−21.5295	−	21.5295i	−0.842515	−	0.842515i	−0.989185	+	0.146670i	$0.953144\pi$
$654$	−4.03425	−	22.3690i	−0.157752	−	0.874699i
$655$	2.01618	−	7.85266i	0.0787785	−	0.306829i
$656$		−	0.505725i		−	0.0197453i
$657$	−12.7430	−	5.82161i	−0.497150	−	0.227123i
$658$	33.6927	−	33.6927i	1.31348	−	1.31348i
$659$	3.43028			0.133625			0.0668124	−	0.997766i	$-0.478717\pi$
$659$	3.43028			0.133625			0.0668124	+	0.997766i	$0.478717\pi$
$660$	4.67792	+	5.41490i	0.182088	+	0.210775i
$661$	−9.37004			−0.364452			−0.182226	−	0.983257i	$-0.558330\pi$
$661$	−9.37004			−0.364452			−0.182226	+	0.983257i	$0.558330\pi$
$662$	−17.3968	+	17.3968i	−0.676146	+	0.676146i
$663$	−3.22140	+	4.63903i	−0.125109	+	0.180165i
$664$			15.8559i			0.615327i
$665$	−11.3431	+	6.70837i	−0.439867	+	0.260140i
$666$	−10.2827	−	27.5805i	−0.398447	−	1.06872i
$667$	−4.66357	−	4.66357i	−0.180574	−	0.180574i
$668$	3.50266	+	3.50266i	0.135522	+	0.135522i
$669$	6.63376	−	1.19640i	0.256476	−	0.0462553i
$670$	7.88400	+	2.02422i	0.304585	+	0.0782025i
$671$		−	7.06492i		−	0.272738i
$672$	−6.68380	−	4.64132i	−0.257833	−	0.179043i
$673$	2.35869	−	2.35869i	0.0909206	−	0.0909206i	−0.660184	−	0.751104i	$-0.729522\pi$
$673$	2.35869	−	2.35869i	0.0909206	−	0.0909206i	0.751104	+	0.660184i	$0.229522\pi$
$674$	18.4690			0.711398
$675$	17.7617	−	18.9611i	0.683647	−	0.729813i
$676$	7.08770			0.272604
$677$	−19.9993	+	19.9993i	−0.768634	+	0.768634i	−0.977866	−	0.209232i	$-0.932904\pi$
$677$	−19.9993	+	19.9993i	−0.768634	+	0.768634i	0.209232	+	0.977866i	$0.432904\pi$
$678$	−4.30609	−	2.99021i	−0.165375	−	0.114838i
$679$		−	33.8734i		−	1.29994i
$680$	−2.90446	−	0.745722i	−0.111381	−	0.0285971i
$681$	−13.2003	+	2.38067i	−0.505836	+	0.0912273i
$682$	−6.19869	−	6.19869i	−0.237360	−	0.237360i
$683$	11.5301	+	11.5301i	0.441189	+	0.441189i	0.892411	−	0.451223i	$-0.149012\pi$
$683$	11.5301	+	11.5301i	0.441189	+	0.441189i	−0.451223	+	0.892411i	$0.649012\pi$
$684$	1.31469	+	3.52629i	0.0502684	+	0.134831i
$685$	−11.5722	+	6.84389i	−0.442153	+	0.261492i
$686$		−	37.9210i		−	1.44783i
$687$	−27.2305	+	39.2136i	−1.03891	+	1.49609i
$688$	−6.74120	+	6.74120i	−0.257006	+	0.257006i
$689$	−25.1130			−0.956730
$690$	2.53190	+	2.93078i	0.0963877	+	0.111573i
$691$	−26.9565			−1.02548			−0.512738	−	0.858545i	$-0.671369\pi$
$691$	−26.9565			−1.02548			−0.512738	+	0.858545i	$0.671369\pi$
$692$	−1.69609	+	1.69609i	−0.0644758	+	0.0644758i
$693$	23.6856	+	10.8207i	0.899742	+	0.411046i
$694$		−	9.97675i		−	0.378712i
$695$	5.48977	−	21.3817i	0.208239	−	0.811055i
$696$	2.02749	+	11.2420i	0.0768517	+	0.426127i
$697$	−0.479560	−	0.479560i	−0.0181646	−	0.0181646i
$698$	−20.2671	−	20.2671i	−0.767119	−	0.767119i
$699$	1.99226	+	11.0467i	0.0753543	+	0.417824i
$700$	22.5575	−	6.55380i	0.852592	−	0.247710i
$701$			14.1410i			0.534099i	0.963683	+	0.267050i	$0.0860488\pi$
$701$			14.1410i			0.534099i	−0.963683	+	0.267050i	$0.913951\pi$
$702$	−12.2415	−	3.12711i	−0.462024	−	0.118025i
$703$	−8.70333	+	8.70333i	−0.328252	+	0.328252i
$704$	1.84760			0.0696339
$705$	39.1764	+	2.86067i	1.47547	+	0.107739i
$706$	6.96994			0.262317
$707$	−40.1346	+	40.1346i	−1.50942	+	1.50942i
$708$	−6.97655	+	10.0467i	−0.262195	+	0.377578i
$709$		−	46.4972i		−	1.74624i	−0.487506	−	0.873120i	$-0.662093\pi$
$709$		−	46.4972i		−	1.74624i	0.487506	−	0.873120i	$-0.337907\pi$
$710$	13.4536	+	22.7486i	0.504905	+	0.853738i
$711$	20.2534	−	7.55100i	0.759563	−	0.283185i
$712$	−6.61841	−	6.61841i	−0.248036	−	0.248036i
$713$	−3.35500	−	3.35500i	−0.125646	−	0.125646i
$714$	−10.7392	+	1.93680i	−0.401903	+	0.0724830i
$715$	5.11361	+	8.64653i	0.191238	+	0.323362i
$716$			15.4433i			0.577145i
$717$	8.47106	+	5.88242i	0.316357	+	0.219683i
$718$	7.01130	−	7.01130i	0.261660	−	0.261660i
$719$	5.67119			0.211500			0.105750	−	0.994393i	$-0.466276\pi$
$719$	5.67119			0.211500			0.105750	+	0.994393i	$0.466276\pi$
$720$	−0.706675	−	6.67088i	−0.0263362	−	0.248609i
$721$	61.2118			2.27965
$722$	−12.3223	+	12.3223i	−0.458587	+	0.458587i
$723$	−23.2579	−	16.1506i	−0.864972	−	0.600648i
$724$		−	15.1508i		−	0.563076i
$725$	−28.8976	−	15.8862i	−1.07323	−	0.589999i
$726$	12.9314	−	2.33217i	0.479929	−	0.0865550i
$727$	4.22102	+	4.22102i	0.156549	+	0.156549i	0.781036	−	0.624487i	$-0.214692\pi$
$727$	4.22102	+	4.22102i	0.156549	+	0.156549i	−0.624487	+	0.781036i	$0.714692\pi$
$728$	−8.07757	−	8.07757i	−0.299375	−	0.299375i
$729$	−23.6920	−	12.9494i	−0.877483	−	0.479608i
$730$	2.59684	−	10.1142i	0.0961132	−	0.374344i
$731$			12.7848i			0.472864i
$732$	−3.77767	+	5.44009i	−0.139627	+	0.201071i
$733$	−0.654319	+	0.654319i	−0.0241678	+	0.0241678i	−0.719087	−	0.694920i	$-0.755440\pi$
$733$	−0.654319	+	0.654319i	−0.0241678	+	0.0241678i	0.694920	+	0.719087i	$0.255440\pi$
$734$	−13.9947			−0.516553
$735$	44.1718	−	38.1599i	1.62930	−	1.40755i
$736$	1.00000			0.0368605
$737$	−4.75572	+	4.75572i	−0.175179	+	0.175179i
$738$	0.630446	−	1.37999i	0.0232070	−	0.0507980i
$739$		−	28.6232i		−	1.05292i	−0.850199	−	0.526461i	$-0.823519\pi$
$739$		−	28.6232i		−	1.05292i	0.850199	−	0.526461i	$-0.176481\pi$
$740$	18.8842	−	11.1682i	0.694198	−	0.410552i
$741$	0.937694	+	5.19932i	0.0344471	+	0.191002i
$742$	−34.3102	−	34.3102i	−1.25957	−	1.25957i
$743$	3.48132	+	3.48132i	0.127717	+	0.127717i	0.768076	−	0.640359i	$-0.221214\pi$
$743$	3.48132	+	3.48132i	0.127717	+	0.127717i	−0.640359	+	0.768076i	$0.721214\pi$
$744$	1.45859	+	8.08756i	0.0534744	+	0.296505i
$745$	−5.18153	−	1.33036i	−0.189836	−	0.0487407i
$746$			33.4237i			1.22373i
$747$	−19.7662	+	43.2663i	−0.723206	+	1.58303i
$748$	1.75200	−	1.75200i	0.0640596	−	0.0640596i
$749$	53.6489			1.96029
$750$	16.2453	+	10.5400i	0.593193	+	0.384867i
$751$	1.84306			0.0672543			0.0336271	−	0.999434i	$-0.489294\pi$
$751$	1.84306			0.0672543			0.0336271	+	0.999434i	$0.489294\pi$
$752$	7.17165	−	7.17165i	0.261523	−	0.261523i
$753$	−22.6198	+	32.5740i	−0.824312	+	1.18706i
$754$			16.0366i			0.584017i
$755$	23.0788	+	5.92549i	0.839922	+	0.215651i
$756$	−12.4523	−	20.9970i	−0.452886	−	0.763654i
$757$	35.9978	+	35.9978i	1.30836	+	1.30836i	0.922596	+	0.385768i	$0.126063\pi$
$757$	35.9978	+	35.9978i	1.30836	+	1.30836i	0.385768	+	0.922596i	$0.373937\pi$
$758$	17.0818	+	17.0818i	0.620439	+	0.620439i
$759$	−3.14932	+	0.567979i	−0.114313	+	0.0206163i
$760$	−2.41443	+	1.42791i	−0.0875806	+	0.0517956i
$761$			15.0705i			0.546305i	0.961971	+	0.273152i	$0.0880663\pi$
$761$			15.0705i			0.546305i	−0.961971	+	0.273152i	$0.911934\pi$
$762$	2.95485	+	2.05189i	0.107043	+	0.0743320i
$763$	43.5953	−	43.5953i	1.57826	−	1.57826i
$764$	5.46374			0.197671
$765$	−6.99584	−	5.65562i	−0.252935	−	0.204479i
$766$	−23.8859			−0.863033
$767$	−12.1417	+	12.1417i	−0.438412	+	0.438412i
$768$	−1.42268	−	0.987925i	−0.0513364	−	0.0356487i
$769$			20.8224i			0.750876i	0.926847	+	0.375438i	$0.122508\pi$
$769$			20.8224i			0.750876i	−0.926847	+	0.375438i	$0.877492\pi$
$770$	−4.82679	+	18.7995i	−0.173946	+	0.677488i
$771$	31.8153	−	5.73788i	1.14580	−	0.206645i
$772$	15.8524	+	15.8524i	0.570541	+	0.570541i
$773$	18.5904	+	18.5904i	0.668650	+	0.668650i	0.957404	−	0.288753i	$-0.0932408\pi$
$773$	18.5904	+	18.5904i	0.668650	+	0.668650i	−0.288753	+	0.957404i	$0.593241\pi$
$774$	−26.7986	+	9.99119i	−0.963255	+	0.359126i
$775$	−20.7891	−	11.4286i	−0.746767	−	0.410529i
$776$		−	7.21011i		−	0.258828i
$777$	45.5390	−	65.5792i	1.63370	−	2.35264i
$778$	−0.492158	+	0.492158i	−0.0176447	+	0.0176447i
$779$	−0.634414			−0.0227302
$780$	0.685822	−	9.39224i	0.0245564	−	0.336296i
$781$	−21.8376			−0.781409
$782$	0.948261	−	0.948261i	0.0339097	−	0.0339097i
$783$	−8.48200	+	33.2038i	−0.303122	+	1.18661i
$784$		−	15.0717i		−	0.538273i
$785$	1.04819	+	1.77237i	0.0374114	+	0.0632584i
$786$	−1.11460	−	6.18023i	−0.0397565	−	0.220441i
$787$	−12.5673	−	12.5673i	−0.447976	−	0.447976i	0.446705	−	0.894681i	$-0.352597\pi$
$787$	−12.5673	−	12.5673i	−0.447976	−	0.447976i	−0.894681	+	0.446705i	$0.852597\pi$
$788$	−15.9133	−	15.9133i	−0.566888	−	0.566888i
$789$	7.19298	+	39.8836i	0.256077	+	1.41989i
$790$	8.20127	+	13.8674i	0.291788	+	0.493381i
$791$		−	14.2199i		−	0.505600i
$792$	5.04158	+	2.30324i	0.179145	+	0.0818422i
$793$	−6.57451	+	6.57451i	−0.233468	+	0.233468i
$794$	32.2575			1.14478
$795$	2.91309	−	39.8944i	0.103317	−	1.41491i
$796$	−18.2044			−0.645238
$797$	−29.2967	+	29.2967i	−1.03774	+	1.03774i	−0.0384846	+	0.999259i	$0.512253\pi$
$797$	−29.2967	+	29.2967i	−1.03774	+	1.03774i	−0.999259	+	0.0384846i	$0.987747\pi$
$798$	−5.82236	+	8.38458i	−0.206109	+	0.296811i
$799$		−	13.6012i		−	0.481175i
$800$	4.80145	−	1.39501i	0.169757	−	0.0493209i
$801$	−9.80922	−	26.3105i	−0.346592	−	0.929635i
$802$	17.8719	+	17.8719i	0.631078	+	0.631078i
$803$	6.10102	+	6.10102i	0.215300	+	0.215300i
$804$	6.20489	−	1.11905i	0.218830	−	0.0394658i
$805$	−2.61247	+	10.1751i	−0.0920776	+	0.358626i
$806$			11.5368i			0.406367i
$807$	−13.1240	−	9.11345i	−0.461985	−	0.320809i
$808$	−8.54283	+	8.54283i	−0.300536	+	0.300536i
$809$	−7.19305			−0.252894			−0.126447	−	0.991973i	$-0.540357\pi$
$809$	−7.19305			−0.252894			−0.126447	+	0.991973i	$0.540357\pi$
$810$	6.38771	−	19.0840i	0.224441	−	0.670542i
$811$	9.26127			0.325207			0.162604	−	0.986691i	$-0.448011\pi$
$811$	9.26127			0.325207			0.162604	+	0.986691i	$0.448011\pi$
$812$	−21.9097	+	21.9097i	−0.768878	+	0.768878i
$813$	−17.3773	−	12.0670i	−0.609448	−	0.423209i
$814$			18.1280i			0.635386i
$815$	−13.3028	+	7.86732i	−0.465975	+	0.275580i
$816$	−2.28588	+	0.412257i	−0.0800217	+	0.0144319i
$817$	8.45658	+	8.45658i	0.295858	+	0.295858i
$818$	−1.26267	−	1.26267i	−0.0441481	−	0.0441481i
$819$	−11.9718	−	32.1111i	−0.418330	−	1.12205i
$820$	1.09531	+	0.281222i	0.0382499	+	0.00982070i
$821$		−	24.0845i		−	0.840555i	−0.907396	−	0.420277i	$-0.861933\pi$
$821$		−	24.0845i		−	0.840555i	0.907396	−	0.420277i	$-0.138067\pi$
$822$	−5.93998	+	8.55395i	−0.207181	+	0.298353i
$823$	−14.2232	+	14.2232i	−0.495791	+	0.495791i	−0.910125	−	0.414334i	$-0.864015\pi$
$823$	−14.2232	+	14.2232i	−0.495791	+	0.495791i	0.414334	+	0.910125i	$0.364015\pi$
$824$	13.0292			0.453894
$825$	−14.3290	+	7.12045i	−0.498871	+	0.247902i
$826$	−33.1768			−1.15437
$827$	−0.719388	+	0.719388i	−0.0250156	+	0.0250156i	−0.719504	−	0.694488i	$-0.755631\pi$
$827$	−0.719388	+	0.719388i	−0.0250156	+	0.0250156i	0.694488	+	0.719504i	$0.255631\pi$
$828$	2.72873	+	1.24662i	0.0948298	+	0.0433229i
$829$		−	7.68796i		−	0.267014i	−0.991048	−	0.133507i	$-0.957376\pi$
$829$		−	7.68796i		−	0.267014i	0.991048	−	0.133507i	$-0.0426238\pi$
$830$	−34.3409	−	8.81706i	−1.19199	−	0.306045i
$831$	3.30560	+	18.3288i	0.114670	+	0.635821i
$832$	−1.71935	−	1.71935i	−0.0596076	−	0.0596076i
$833$	−14.2919	−	14.2919i	−0.495184	−	0.495184i
$834$	−3.03491	−	16.8279i	−0.105090	−	0.582703i
$835$	−9.53387	+	5.63838i	−0.329933	+	0.195124i
$836$		−	2.31774i		−	0.0801607i
$837$	−6.10200	+	23.8871i	−0.210916	+	0.825657i
$838$	−25.3220	+	25.3220i	−0.874732	+	0.874732i
$839$	38.2353			1.32003			0.660014	−	0.751253i	$-0.270550\pi$
$839$	38.2353			1.32003			0.660014	+	0.751253i	$0.270550\pi$
$840$	13.7690	−	11.8950i	0.475074	−	0.410416i
$841$	14.4977			0.499921
$842$	−14.8267	+	14.8267i	−0.510962	+	0.510962i
$843$	−7.66777	+	11.0421i	−0.264092	+	0.380310i
$844$			24.0819i			0.828935i
$845$	−3.94130	+	15.3507i	−0.135585	+	0.528080i
$846$	28.5098	−	10.6292i	0.980186	−	0.365438i
$847$	25.2022	+	25.2022i	0.865956	+	0.865956i
$848$	−7.30308	−	7.30308i	−0.250789	−	0.250789i
$849$	50.8346	−	9.16800i	1.74464	−	0.314645i
$850$	3.23020	−	5.87586i	0.110795	−	0.201540i
$851$			9.81166i			0.336339i
$852$	16.8152	+	11.6767i	0.576081	+	0.400038i
$853$	−0.699678	+	0.699678i	−0.0239565	+	0.0239565i	−0.718984	−	0.695027i	$-0.755392\pi$
$853$	−0.699678	+	0.699678i	−0.0239565	+	0.0239565i	0.695027	+	0.718984i	$0.255392\pi$
$854$	−17.9646			−0.614736
$855$	−8.36837	+	0.886498i	−0.286192	+	0.0303176i
$856$	11.4194			0.390307
$857$	−14.0885	+	14.0885i	−0.481253	+	0.481253i	−0.905532	−	0.424278i	$-0.860528\pi$
$857$	−14.0885	+	14.0885i	−0.481253	+	0.481253i	0.424278	+	0.905532i	$0.360528\pi$
$858$	6.39133	+	4.43822i	0.218196	+	0.151518i
$859$			14.8178i			0.505577i	0.967522	+	0.252789i	$0.0813477\pi$
$859$			14.8178i			0.505577i	−0.967522	+	0.252789i	$0.918652\pi$
$860$	−10.8516	−	18.3488i	−0.370037	−	0.625690i
$861$	4.04988	−	0.730394i	0.138020	−	0.0248918i
$862$	−14.6633	−	14.6633i	−0.499434	−	0.499434i
$863$	−8.29672	−	8.29672i	−0.282424	−	0.282424i	0.551651	−	0.834075i	$-0.313998\pi$
$863$	−8.29672	−	8.29672i	−0.282424	−	0.282424i	−0.834075	+	0.551651i	$0.813998\pi$
$864$	−2.65053	−	4.46931i	−0.0901728	−	0.152049i
$865$	−2.73028	−	4.61659i	−0.0928323	−	0.156969i
$866$			26.4643i			0.899293i
$867$	15.0180	−	21.6269i	0.510039	−	0.734490i
$868$	−15.7620	+	15.7620i	−0.534996	+	0.534996i
$869$	−13.3121			−0.451582
$870$	−25.4756	−	1.86023i	−0.863703	−	0.0630677i
$871$	8.85120			0.299912
$872$	9.27945	−	9.27945i	0.314242	−	0.314242i
$873$	8.98824	−	19.6744i	0.304206	−	0.665878i
$874$		−	1.25446i		−	0.0424328i
$875$	1.65069	+	52.4998i	0.0558035	+	1.77482i
$876$	−1.43561	−	7.96014i	−0.0485047	−	0.268948i
$877$	−5.35773	−	5.35773i	−0.180918	−	0.180918i	0.610838	−	0.791756i	$-0.290833\pi$
$877$	−5.35773	−	5.35773i	−0.180918	−	0.180918i	−0.791756	+	0.610838i	$0.790833\pi$
$878$	−12.5880	−	12.5880i	−0.424823	−	0.424823i
$879$	6.16827	+	34.2017i	0.208050	+	1.15360i
$880$	−1.02740	+	4.00156i	−0.0346338	+	0.134893i
$881$			13.0986i			0.441305i	0.975353	+	0.220652i	$0.0708186\pi$
$881$			13.0986i			0.441305i	−0.975353	+	0.220652i	$0.929181\pi$
$882$	18.7886	−	41.1264i	0.632644	−	1.38480i
$883$	−26.7110	+	26.7110i	−0.898897	+	0.898897i	−0.995339	−	0.0964414i	$-0.969254\pi$
$883$	−26.7110	+	26.7110i	−0.898897	+	0.898897i	0.0964414	+	0.995339i	$0.469254\pi$
$884$	−3.26078			−0.109672
$885$	−17.8798	−	20.6967i	−0.601024	−	0.695711i
$886$	−41.1973			−1.38405
$887$	1.13171	−	1.13171i	0.0379992	−	0.0379992i	−0.687852	−	0.725851i	$-0.741446\pi$
$887$	1.13171	−	1.13171i	0.0379992	−	0.0379992i	0.725851	+	0.687852i	$0.241446\pi$
$888$	9.69318	−	13.9588i	0.325282	−	0.468427i
$889$			9.75769i			0.327263i
$890$	18.0146	−	10.6540i	0.603852	−	0.357121i
$891$	10.8858	+	12.5698i	0.364689	+	0.421106i
$892$	2.75191	+	2.75191i	0.0921408	+	0.0921408i
$893$	−8.99657	−	8.99657i	−0.301059	−	0.301059i
$894$	−4.07798	+	0.735462i	−0.136388	+	0.0245975i
$895$	−33.4475	−	8.58768i	−1.11803	−	0.287054i
$896$		−	4.69805i		−	0.156951i
$897$	3.45927	+	2.40216i	0.115502	+	0.0802058i
$898$	3.71209	−	3.71209i	0.123874	−	0.123874i
$899$	31.2925			1.04366
$900$	14.8409	+	2.17899i	0.494696	+	0.0726328i
$901$	−13.8504			−0.461425
$902$	−0.660704	+	0.660704i	−0.0219990	+	0.0219990i
$903$	−63.7199	−	44.2480i	−2.12047	−	1.47248i
$904$		−	3.02676i		−	0.100668i
$905$	32.8140	+	8.42501i	1.09077	+	0.280057i
$906$	18.1635	−	3.27578i	0.603443	−	0.108831i
$907$	18.6482	+	18.6482i	0.619203	+	0.619203i	0.945327	−	0.326124i	$-0.105743\pi$
$907$	18.6482	+	18.6482i	0.619203	+	0.619203i	−0.326124	+	0.945327i	$0.605743\pi$
$908$	−5.47594	−	5.47594i	−0.181725	−	0.181725i
$909$	−33.9607	+	12.6614i	−1.12640	+	0.419952i
$910$	21.9863	−	13.0028i	0.728839	−	0.431039i
$911$			6.38602i			0.211578i	0.994389	+	0.105789i	$0.0337369\pi$
$911$			6.38602i			0.211578i	−0.994389	+	0.105789i	$0.966263\pi$
$912$	−1.23932	+	1.78469i	−0.0410378	+	0.0590971i
$913$	20.7148	−	20.7148i	0.685561	−	0.685561i
$914$	12.1649			0.402381
$915$	−9.68158	−	11.2069i	−0.320063	−	0.370487i
$916$	−27.5633			−0.910718
$917$	12.0447	−	12.0447i	0.397752	−	0.397752i
$918$	−6.75146	−	1.72468i	−0.222831	−	0.0569228i
$919$		−	8.47456i		−	0.279550i	−0.990183	−	0.139775i	$-0.955362\pi$
$919$		−	8.47456i		−	0.279550i	0.990183	−	0.139775i	$-0.0446379\pi$
$920$	−0.556076	+	2.16582i	−0.0183333	+	0.0714050i
$921$	5.25237	+	29.1233i	0.173071	+	0.959644i
$922$	0.830163	+	0.830163i	0.0273400	+	0.0273400i
$923$	20.3217	+	20.3217i	0.668898	+	0.668898i
$924$	2.66839	+	14.7957i	0.0877836	+	0.486742i
$925$	13.6873	+	47.1102i	0.450036	+	1.54898i
$926$			10.6991i			0.351594i
$927$	35.5531	+	16.2424i	1.16772	+	0.533471i
$928$	−4.66357	+	4.66357i	−0.153089	+	0.153089i
$929$	24.0411			0.788764			0.394382	−	0.918947i	$-0.370959\pi$
$929$	24.0411			0.788764			0.394382	+	0.918947i	$0.370959\pi$
$930$	−18.3273	−	1.33826i	−0.600976	−	0.0438833i
$931$	−18.9068			−0.619646
$932$	−4.58254	+	4.58254i	−0.150106	+	0.150106i
$933$	−23.8275	+	34.3131i	−0.780077	+	1.12336i
$934$		−	29.9772i		−	0.980883i
$935$	2.82028	+	4.76877i	0.0922329	+	0.155955i
$936$	−2.54826	−	6.83499i	−0.0832925	−	0.223409i
$937$	−11.1439	−	11.1439i	−0.364055	−	0.364055i	0.501249	−	0.865303i	$-0.332874\pi$
$937$	−11.1439	−	11.1439i	−0.364055	−	0.364055i	−0.865303	+	0.501249i	$0.832874\pi$
$938$	12.0928	+	12.0928i	0.394843	+	0.394843i
$939$	−12.2642	+	2.21184i	−0.400227	+	0.0721808i
$940$	11.5445	+	19.5205i	0.376541	+	0.636688i
$941$		−	49.5446i		−	1.61511i	−0.589794	−	0.807554i	$-0.700791\pi$
$941$		−	49.5446i		−	1.61511i	0.589794	−	0.807554i	$-0.299209\pi$
$942$	1.31009	+	0.909747i	0.0426852	+	0.0296411i
$943$	−0.357602	+	0.357602i	−0.0116451	+	0.0116451i
$944$	−7.06183			−0.229843
$945$	52.4002	−	15.2935i	1.70458	−	0.497498i
$946$	17.6140			0.572682
$947$	−13.1798	+	13.1798i	−0.428286	+	0.428286i	−0.888044	−	0.459758i	$-0.847936\pi$
$947$	−13.1798	+	13.1798i	−0.428286	+	0.428286i	0.459758	+	0.888044i	$0.347936\pi$
$948$	10.2505	+	7.11808i	0.332921	+	0.231185i
$949$		−	11.3550i		−	0.368600i
$950$	−1.74998	−	6.02325i	−0.0567769	−	0.195420i
$951$	−26.4034	+	4.76184i	−0.856188	+	0.154413i
$952$	−4.45497	−	4.45497i	−0.144387	−	0.144387i
$953$	38.2438	+	38.2438i	1.23884	+	1.23884i	0.960477	+	0.278361i	$0.0897912\pi$
$953$	38.2438	+	38.2438i	1.23884	+	1.23884i	0.278361	+	0.960477i	$0.410209\pi$
$954$	−10.8240	−	29.0322i	−0.350439	−	0.939953i
$955$	−3.03826	+	11.8335i	−0.0983156	+	0.382922i
$956$			5.95432i			0.192576i
$957$	12.0383	−	17.3359i	0.389142	−	0.560389i
$958$	−5.73619	+	5.73619i	−0.185328	+	0.185328i
$959$	−28.2474			−0.912156
$960$	2.93078	−	2.53190i	0.0945906	−	0.0817167i
$961$	−8.48794			−0.273804
$962$	16.8696	−	16.8696i	0.543899	−	0.543899i
$963$	31.1604	+	14.2356i	1.00413	+	0.458736i
$964$		−	16.3480i		−	0.526534i
$965$	−43.1486	+	25.5183i	−1.38900	+	0.821464i
$966$	1.44425	+	8.00806i	0.0464680	+	0.257655i
$967$	−8.40687	−	8.40687i	−0.270347	−	0.270347i	0.558893	−	0.829240i	$-0.311226\pi$
$967$	−8.40687	−	8.40687i	−0.270347	−	0.270347i	−0.829240	+	0.558893i	$0.811226\pi$
$968$	5.36439	+	5.36439i	0.172418	+	0.172418i
$969$	0.517161	+	2.86755i	0.0166136	+	0.0921189i
$970$	15.6158	+	4.00937i	0.501393	+	0.128733i
$971$			5.54281i			0.177877i	0.996037	+	0.0889386i	$0.0283475\pi$
$971$			5.54281i			0.177877i	−0.996037	+	0.0889386i	$0.971653\pi$
$972$	−1.66105	−	15.4997i	−0.0532783	−	0.497153i
$973$	32.7961	−	32.7961i	1.05140	−	1.05140i
$974$	−12.4094			−0.397623
$975$	19.9605	+	6.70817i	0.639249	+	0.214833i
$976$	−3.82384			−0.122398
$977$	31.9373	−	31.9373i	1.02177	−	1.02177i	0.0220078	−	0.999758i	$-0.492994\pi$
$977$	31.9373	−	31.9373i	1.02177	−	1.02177i	0.999758	−	0.0220078i	$-0.00700586\pi$
$978$	−6.82824	+	9.83311i	−0.218343	+	0.314428i
$979$			17.2932i			0.552694i
$980$	32.6425	+	8.38099i	1.04273	+	0.267721i
$981$	36.8890	−	13.7532i	1.17778	−	0.439105i
$982$	24.4548	+	24.4548i	0.780385	+	0.780385i
$983$	23.3509	+	23.3509i	0.744777	+	0.744777i	0.973493	−	0.228716i	$-0.0734529\pi$
$983$	23.3509	+	23.3509i	0.744777	+	0.744777i	−0.228716	+	0.973493i	$0.573453\pi$
$984$	0.862035	−	0.155468i	0.0274807	−	0.00495613i
$985$	43.3144	−	25.6164i	1.38011	−	0.816205i
$986$			8.84455i			0.281668i
$987$	67.7887	+	47.0734i	2.15774	+	1.49836i
$988$	−2.15686	+	2.15686i	−0.0686187	+	0.0686187i
$989$	9.53349			0.303147
$990$	−7.79192	+	9.63839i	−0.247643	+	0.306328i
$991$	−48.3027			−1.53439			−0.767193	−	0.641416i	$-0.778347\pi$
$991$	−48.3027			−1.53439			−0.767193	+	0.641416i	$0.778347\pi$
$992$	−3.35500	+	3.35500i	−0.106521	+	0.106521i
$993$	−35.0018	−	24.3057i	−1.11075	−	0.771319i
$994$			55.5283i			1.76125i
$995$	10.1230	−	39.4275i	0.320922	−	1.24994i
$996$	−27.0271	+	4.87433i	−0.856387	+	0.154449i
$997$	31.8848	+	31.8848i	1.00980	+	1.00980i	0.999951	+	0.00985083i	$0.00313567\pi$
$997$	31.8848	+	31.8848i	1.00980	+	1.00980i	0.00985083	+	0.999951i	$0.496864\pi$
$998$	10.3457	+	10.3457i	0.327489	+	0.327489i
$999$	43.8513	−	26.0061i	1.38739	−	0.822796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.e.47.1	✓	32
3.2	odd	2	inner	690.2.i.e.47.14	yes	32
5.3	odd	4	inner	690.2.i.e.323.14	yes	32
15.8	even	4	inner	690.2.i.e.323.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.e.47.1	✓	32	1.1	even	1	trivial
690.2.i.e.47.14	yes	32	3.2	odd	2	inner
690.2.i.e.323.1	yes	32	15.8	even	4	inner
690.2.i.e.323.14	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.42268 - 0.987925i) q^{3} -1.00000i q^{4} +(2.16582 + 0.556076i) q^{5} +(1.70455 - 0.307415i) q^{6} +(3.32202 + 3.32202i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.04801 + 2.81099i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.42268 - 0.987925i) q^{3} -1.00000i q^{4} +(2.16582 + 0.556076i) q^{5} +(1.70455 - 0.307415i) q^{6} +(3.32202 + 3.32202i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.04801 + 2.81099i) q^{9} +(-1.92467 + 1.13826i) q^{10} -1.84760i q^{11} +(-0.987925 + 1.42268i) q^{12} +(-1.71935 + 1.71935i) q^{13} -4.69805 q^{14} +(-2.53190 - 2.93078i) q^{15} -1.00000 q^{16} +(-0.948261 + 0.948261i) q^{17} +(-2.72873 - 1.24662i) q^{18} +1.25446i q^{19} +(0.556076 - 2.16582i) q^{20} +(-1.44425 - 8.00806i) q^{21} +(1.30645 + 1.30645i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-0.307415 - 1.70455i) q^{24} +(4.38156 + 2.40872i) q^{25} -2.43152i q^{26} +(1.28607 - 5.03448i) q^{27} +(3.32202 - 3.32202i) q^{28} -6.59528 q^{29} +(3.86270 + 0.282055i) q^{30} -4.74469 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.82529 + 2.62853i) q^{33} -1.34104i q^{34} +(5.34761 + 9.04220i) q^{35} +(2.81099 - 1.04801i) q^{36} +(6.93789 + 6.93789i) q^{37} +(-0.887039 - 0.887039i) q^{38} +(4.14466 - 0.747487i) q^{39} +(1.13826 + 1.92467i) q^{40} +0.505725i q^{41} +(6.68380 + 4.64132i) q^{42} +(6.74120 - 6.74120i) q^{43} -1.84760 q^{44} +(0.706675 + 6.67088i) q^{45} -1.00000 q^{46} +(-7.17165 + 7.17165i) q^{47} +(1.42268 + 0.987925i) q^{48} +15.0717i q^{49} +(-4.80145 + 1.39501i) q^{50} +(2.28588 - 0.412257i) q^{51} +(1.71935 + 1.71935i) q^{52} +(7.30308 + 7.30308i) q^{53} +(2.65053 + 4.46931i) q^{54} +(1.02740 - 4.00156i) q^{55} +4.69805i q^{56} +(1.23932 - 1.78469i) q^{57} +(4.66357 - 4.66357i) q^{58} +7.06183 q^{59} +(-2.93078 + 2.53190i) q^{60} +3.82384 q^{61} +(3.35500 - 3.35500i) q^{62} +(-5.85667 + 12.8197i) q^{63} +1.00000i q^{64} +(-4.67988 + 2.76771i) q^{65} +(-0.567979 - 3.14932i) q^{66} +(-2.57400 - 2.57400i) q^{67} +(0.948261 + 0.948261i) q^{68} +(-0.307415 - 1.70455i) q^{69} +(-10.1751 - 2.61247i) q^{70} -11.8194i q^{71} +(-1.24662 + 2.72873i) q^{72} +(-3.30214 + 3.30214i) q^{73} -9.81166 q^{74} +(-3.85390 - 7.75548i) q^{75} +1.25446 q^{76} +(6.13775 - 6.13775i) q^{77} +(-2.40216 + 3.45927i) q^{78} -7.20508i q^{79} +(-2.16582 - 0.556076i) q^{80} +(-6.80335 + 5.89189i) q^{81} +(-0.357602 - 0.357602i) q^{82} +(11.2118 + 11.2118i) q^{83} +(-8.00806 + 1.44425i) q^{84} +(-2.58107 + 1.52646i) q^{85} +9.53349i q^{86} +(9.38294 + 6.51564i) q^{87} +(1.30645 - 1.30645i) q^{88} -9.35985 q^{89} +(-5.21672 - 4.21733i) q^{90} -11.4234 q^{91} +(0.707107 - 0.707107i) q^{92} +(6.75015 + 4.68739i) q^{93} -10.1422i q^{94} +(-0.697577 + 2.71694i) q^{95} +(-1.70455 + 0.307415i) q^{96} +(-5.09832 - 5.09832i) q^{97} +(-10.6573 - 10.6573i) q^{98} +(5.19358 - 1.93630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 32 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 4 q^{15} - 32 q^{16} + 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{27} - 8 q^{28} + 20 q^{30} - 24 q^{31} + 20 q^{36} - 32 q^{37} - 16 q^{40} + 8 q^{42} + 144 q^{43} + 36 q^{45} - 32 q^{46} - 4 q^{48} + 12 q^{51} - 64 q^{55} + 52 q^{57} + 16 q^{58} + 4 q^{60} - 24 q^{61} - 116 q^{63} + 12 q^{66} - 16 q^{67} - 80 q^{70} - 8 q^{72} + 40 q^{73} + 44 q^{75} + 24 q^{76} - 36 q^{78} - 108 q^{81} - 32 q^{82} - 80 q^{85} + 68 q^{87} - 8 q^{88} + 16 q^{90} + 120 q^{91} + 12 q^{93} + 4 q^{96} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 4 * q^15 - 32 * q^16 + 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^27 - 8 * q^28 + 20 * q^30 - 24 * q^31 + 20 * q^36 - 32 * q^37 - 16 * q^40 + 8 * q^42 + 144 * q^43 + 36 * q^45 - 32 * q^46 - 4 * q^48 + 12 * q^51 - 64 * q^55 + 52 * q^57 + 16 * q^58 + 4 * q^60 - 24 * q^61 - 116 * q^63 + 12 * q^66 - 16 * q^67 - 80 * q^70 - 8 * q^72 + 40 * q^73 + 44 * q^75 + 24 * q^76 - 36 * q^78 - 108 * q^81 - 32 * q^82 - 80 * q^85 + 68 * q^87 - 8 * q^88 + 16 * q^90 + 120 * q^91 + 12 * q^93 + 4 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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