LMFDB - Embedded newform 966.2.l.d.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.11
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.45188 + 0.944479i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.52157 + 2.63544i) q^{5} +(-0.785127 - 1.54388i) q^{6} +(-0.624219 + 2.57106i) q^{7} -1.00000i q^{8} +(1.21592 + 2.74254i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.45188 + 0.944479i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.52157 + 2.63544i) q^{5} +(-0.785127 - 1.54388i) q^{6} +(-0.624219 + 2.57106i) q^{7} -1.00000i q^{8} +(1.21592 + 2.74254i) q^{9} +(2.63544 - 1.52157i) q^{10} +(-3.05420 + 1.76334i) q^{11} +(-0.0920021 + 1.72961i) q^{12} -5.68597i q^{13} +(1.82612 - 1.91449i) q^{14} +(-4.69825 + 2.38925i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.33683 + 4.04750i) q^{17} +(0.318255 - 2.98307i) q^{18} +(0.846810 + 0.488906i) q^{19} -3.04314 q^{20} +(-3.33460 + 3.14331i) q^{21} +3.52669 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.944479 - 1.45188i) q^{24} +(-2.13035 - 3.68988i) q^{25} +(-2.84299 + 4.92420i) q^{26} +(-0.824904 + 5.13026i) q^{27} +(-2.53871 + 0.744941i) q^{28} -4.24454i q^{29} +(5.26343 + 0.279975i) q^{30} +(-1.00386 + 0.579580i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.09977 - 0.324463i) q^{33} -4.67365i q^{34} +(-5.82607 - 5.55714i) q^{35} +(-1.76715 + 2.42429i) q^{36} +(1.58532 - 2.74586i) q^{37} +(-0.488906 - 0.846810i) q^{38} +(5.37028 - 8.25536i) q^{39} +(2.63544 + 1.52157i) q^{40} -7.78720 q^{41} +(4.45951 - 1.05489i) q^{42} -2.49959 q^{43} +(-3.05420 - 1.76334i) q^{44} +(-9.07790 - 0.968494i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-5.27913 + 9.14372i) q^{47} +(-1.54388 + 0.785127i) q^{48} +(-6.22070 - 3.20981i) q^{49} +4.26070i q^{50} +(-0.429986 + 8.08357i) q^{51} +(4.92420 - 2.84299i) q^{52} +(3.96204 - 2.28749i) q^{53} +(3.27952 - 4.03048i) q^{54} -10.7322i q^{55} +(2.57106 + 0.624219i) q^{56} +(0.767706 + 1.50963i) q^{57} +(-2.12227 + 3.67588i) q^{58} +(1.94490 + 3.36867i) q^{59} +(-4.41828 - 2.87418i) q^{60} +(-1.90050 - 1.09725i) q^{61} +1.15916 q^{62} +(-7.81024 + 1.41425i) q^{63} -1.00000 q^{64} +(14.9850 + 8.65161i) q^{65} +(5.12033 + 3.33088i) q^{66} +(-0.227183 - 0.393493i) q^{67} +(-2.33683 + 4.04750i) q^{68} +(-0.785127 - 1.54388i) q^{69} +(2.26696 + 7.72566i) q^{70} -6.16353i q^{71} +(2.74254 - 1.21592i) q^{72} +(1.97992 - 1.14311i) q^{73} +(-2.74586 + 1.58532i) q^{74} +(0.391994 - 7.36933i) q^{75} +0.977812i q^{76} +(-2.62717 - 8.95324i) q^{77} +(-8.77848 + 4.46421i) q^{78} +(-0.618207 + 1.07077i) q^{79} +(-1.52157 - 2.63544i) q^{80} +(-6.04308 + 6.66942i) q^{81} +(6.74392 + 3.89360i) q^{82} -1.86911 q^{83} +(-4.38949 - 1.31620i) q^{84} -14.2226 q^{85} +(2.16471 + 1.24980i) q^{86} +(4.00888 - 6.16257i) q^{87} +(1.76334 + 3.05420i) q^{88} +(8.03294 - 13.9135i) q^{89} +(7.37745 + 5.37769i) q^{90} +(14.6190 + 3.54929i) q^{91} -1.00000i q^{92} +(-2.00489 - 0.106645i) q^{93} +(9.14372 - 5.27913i) q^{94} +(-2.57696 + 1.48781i) q^{95} +(1.72961 + 0.0920021i) q^{96} +16.5414i q^{97} +(3.78238 + 5.89013i) q^{98} +(-8.54970 - 6.23219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.45188	+	0.944479i	0.838244	+	0.545295i
$3$	1.45188	+	0.944479i	0.838244	+	0.545295i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.52157	+	2.63544i	−0.680467	+	1.17860i	0.294372	+	0.955691i	$0.404890\pi$
$5$	−1.52157	+	2.63544i	−0.680467	+	1.17860i	−0.974839	+	0.222912i	$0.928444\pi$
$6$	−0.785127	−	1.54388i	−0.320527	−	0.630288i
$7$	−0.624219	+	2.57106i	−0.235933	+	0.971769i
$7$	−0.624219	+	2.57106i	−0.235933	+	0.971769i
$8$		−	1.00000i		−	0.353553i
$9$	1.21592	+	2.74254i	0.405306	+	0.914181i
$10$	2.63544	−	1.52157i	0.833398	−	0.481163i
$11$	−3.05420	+	1.76334i	−0.920876	+	0.531668i	−0.883914	−	0.467649i	$-0.845101\pi$
$11$	−3.05420	+	1.76334i	−0.920876	+	0.531668i	−0.0369614	+	0.999317i	$0.511768\pi$
$12$	−0.0920021	+	1.72961i	−0.0265587	+	0.499294i
$13$		−	5.68597i		−	1.57701i	−0.615031	−	0.788503i	$-0.710857\pi$
$13$		−	5.68597i		−	1.57701i	0.615031	−	0.788503i	$-0.289143\pi$
$14$	1.82612	−	1.91449i	0.488051	−	0.511670i
$15$	−4.69825	+	2.38925i	−1.21308	+	0.616902i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.33683	+	4.04750i	0.566763	+	0.981663i	0.996883	+	0.0788912i	$0.0251380\pi$
$17$	2.33683	+	4.04750i	0.566763	+	0.981663i	−0.430120	+	0.902772i	$0.641529\pi$
$18$	0.318255	−	2.98307i	0.0750134	−	0.703117i
$19$	0.846810	+	0.488906i	0.194272	+	0.112163i	0.593981	−	0.804479i	$-0.297556\pi$
$19$	0.846810	+	0.488906i	0.194272	+	0.112163i	−0.399709	+	0.916642i	$0.630889\pi$
$20$	−3.04314			−0.680467
$21$	−3.33460	+	3.14331i	−0.727670	+	0.685927i
$22$	3.52669			0.751892
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	0.944479	−	1.45188i	0.192791	−	0.296364i
$25$	−2.13035	−	3.68988i	−0.426070	−	0.737975i
$26$	−2.84299	+	4.92420i	−0.557556	+	0.965715i
$27$	−0.824904	+	5.13026i	−0.158753	+	0.987318i
$28$	−2.53871	+	0.744941i	−0.479772	+	0.140781i
$29$		−	4.24454i		−	0.788191i	−0.919070	−	0.394095i	$-0.871058\pi$
$29$		−	4.24454i		−	0.788191i	0.919070	−	0.394095i	$-0.128942\pi$
$30$	5.26343	+	0.279975i	0.960967	+	0.0511163i
$31$	−1.00386	+	0.579580i	−0.180299	+	0.104096i	−0.587433	−	0.809273i	$-0.699862\pi$
$31$	−1.00386	+	0.579580i	−0.180299	+	0.104096i	0.407134	+	0.913368i	$0.366528\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−6.09977	−	0.324463i	−1.06183	−	0.0564817i
$34$		−	4.67365i		−	0.801525i
$35$	−5.82607	−	5.55714i	−0.984786	−	0.939328i
$36$	−1.76715	+	2.42429i	−0.294525	+	0.404048i
$37$	1.58532	−	2.74586i	0.260626	−	0.451417i	−0.705783	−	0.708428i	$-0.749405\pi$
$37$	1.58532	−	2.74586i	0.260626	−	0.451417i	0.966408	+	0.257012i	$0.0827379\pi$
$38$	−0.488906	−	0.846810i	−0.0793110	−	0.137371i
$39$	5.37028	−	8.25536i	0.859933	−	1.32192i
$40$	2.63544	+	1.52157i	0.416699	+	0.240581i
$41$	−7.78720			−1.21616			−0.608078	−	0.793877i	$-0.708059\pi$
$41$	−7.78720			−1.21616			−0.608078	+	0.793877i	$0.708059\pi$
$42$	4.45951	−	1.05489i	0.688117	−	0.162773i
$43$	−2.49959			−0.381184			−0.190592	−	0.981669i	$-0.561041\pi$
$43$	−2.49959			−0.381184			−0.190592	+	0.981669i	$0.561041\pi$
$44$	−3.05420	−	1.76334i	−0.460438	−	0.265834i
$45$	−9.07790	−	0.968494i	−1.35325	−	0.144375i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−5.27913	+	9.14372i	−0.770040	+	1.33375i	0.167500	+	0.985872i	$0.446431\pi$
$47$	−5.27913	+	9.14372i	−0.770040	+	1.33375i	−0.937540	+	0.347877i	$0.886903\pi$
$48$	−1.54388	+	0.785127i	−0.222840	+	0.113323i
$49$	−6.22070	−	3.20981i	−0.888672	−	0.458544i
$50$			4.26070i			0.602554i
$51$	−0.429986	+	8.08357i	−0.0602101	+	1.13193i
$52$	4.92420	−	2.84299i	0.682863	−	0.394251i
$53$	3.96204	−	2.28749i	0.544229	−	0.314210i	−0.202562	−	0.979269i	$-0.564927\pi$
$53$	3.96204	−	2.28749i	0.544229	−	0.314210i	0.746791	+	0.665059i	$0.231594\pi$
$54$	3.27952	−	4.03048i	0.446286	−	0.548479i
$55$		−	10.7322i		−	1.44713i
$56$	2.57106	+	0.624219i	0.343572	+	0.0834148i
$57$	0.767706	+	1.50963i	0.101685	+	0.199955i
$58$	−2.12227	+	3.67588i	−0.278668	+	0.482666i
$59$	1.94490	+	3.36867i	0.253205	+	0.438564i	0.964406	−	0.264424i	$-0.0851820\pi$
$59$	1.94490	+	3.36867i	0.253205	+	0.438564i	−0.711202	+	0.702988i	$0.751849\pi$
$60$	−4.41828	−	2.87418i	−0.570397	−	0.371055i
$61$	−1.90050	−	1.09725i	−0.243334	−	0.140489i	0.373374	−	0.927681i	$-0.378201\pi$
$61$	−1.90050	−	1.09725i	−0.243334	−	0.140489i	−0.616708	+	0.787192i	$0.711534\pi$
$62$	1.15916			0.147214
$63$	−7.81024	+	1.41425i	−0.983998	+	0.178179i
$64$	−1.00000			−0.125000
$65$	14.9850	+	8.65161i	1.85866	+	1.07310i
$66$	5.12033	+	3.33088i	0.630269	+	0.410003i
$67$	−0.227183	−	0.393493i	−0.0277549	−	0.0480728i	0.851814	−	0.523844i	$-0.175502\pi$
$67$	−0.227183	−	0.393493i	−0.0277549	−	0.0480728i	−0.879569	+	0.475771i	$0.842169\pi$
$68$	−2.33683	+	4.04750i	−0.283382	+	0.490832i
$69$	−0.785127	−	1.54388i	−0.0945181	−	0.185862i
$70$	2.26696	+	7.72566i	0.270953	+	0.923393i
$71$		−	6.16353i		−	0.731476i	−0.930718	−	0.365738i	$-0.880817\pi$
$71$		−	6.16353i		−	0.731476i	0.930718	−	0.365738i	$-0.119183\pi$
$72$	2.74254	−	1.21592i	0.323212	−	0.143297i
$73$	1.97992	−	1.14311i	0.231733	−	0.133791i	−0.379638	−	0.925135i	$-0.623952\pi$
$73$	1.97992	−	1.14311i	0.231733	−	0.133791i	0.611371	+	0.791344i	$0.290618\pi$
$74$	−2.74586	+	1.58532i	−0.319200	+	0.184290i
$75$	0.391994	−	7.36933i	0.0452635	−	0.850937i
$76$			0.977812i			0.112163i
$77$	−2.62717	−	8.95324i	−0.299394	−	1.02032i
$78$	−8.77848	+	4.46421i	−0.993967	+	0.505472i
$79$	−0.618207	+	1.07077i	−0.0695537	+	0.120471i	−0.898705	−	0.438554i	$-0.855491\pi$
$79$	−0.618207	+	1.07077i	−0.0695537	+	0.120471i	0.829151	+	0.559024i	$0.188824\pi$
$80$	−1.52157	−	2.63544i	−0.170117	−	0.294651i
$81$	−6.04308	+	6.66942i	−0.671454	+	0.741047i
$82$	6.74392	+	3.89360i	0.744741	+	0.429976i
$83$	−1.86911			−0.205161			−0.102581	−	0.994725i	$-0.532710\pi$
$83$	−1.86911			−0.205161			−0.102581	+	0.994725i	$0.532710\pi$
$84$	−4.38949	−	1.31620i	−0.478933	−	0.143609i
$85$	−14.2226			−1.54265
$86$	2.16471	+	1.24980i	0.233427	+	0.134769i
$87$	4.00888	−	6.16257i	0.429797	−	0.660696i
$88$	1.76334	+	3.05420i	0.187973	+	0.325579i
$89$	8.03294	−	13.9135i	0.851489	−	1.47482i	−0.0283745	−	0.999597i	$-0.509033\pi$
$89$	8.03294	−	13.9135i	0.851489	−	1.47482i	0.879864	−	0.475226i	$-0.157634\pi$
$90$	7.37745	+	5.37769i	0.777651	+	0.566859i
$91$	14.6190	+	3.54929i	1.53249	+	0.372067i
$92$		−	1.00000i		−	0.104257i
$93$	−2.00489	−	0.106645i	−0.207898	−	0.0110586i
$94$	9.14372	−	5.27913i	0.943103	−	0.544501i
$95$	−2.57696	+	1.48781i	−0.264391	+	0.152646i
$96$	1.72961	+	0.0920021i	0.176527	+	0.00938993i
$97$			16.5414i			1.67952i	0.542957	+	0.839760i	$0.317305\pi$
$97$			16.5414i			1.67952i	−0.542957	+	0.839760i	$0.682695\pi$
$98$	3.78238	+	5.89013i	0.382078	+	0.594993i
$99$	−8.54970	−	6.23219i	−0.859277	−	0.626359i
$100$	2.13035	−	3.68988i	0.213035	−	0.368988i
$101$	4.86693	+	8.42978i	0.484278	+	0.838794i	0.999837	−	0.0180600i	$-0.00574900\pi$
$101$	4.86693	+	8.42978i	0.484278	+	0.838794i	−0.515559	+	0.856854i	$0.672416\pi$
$102$	4.41417	−	6.78559i	0.437067	−	0.671873i
$103$	10.4696	+	6.04463i	1.03160	+	0.595595i	0.917443	−	0.397867i	$-0.130250\pi$
$103$	10.4696	+	6.04463i	1.03160	+	0.595595i	0.114158	+	0.993463i	$0.463583\pi$
$104$	−5.68597			−0.557556
$105$	−3.21017	−	13.5709i	−0.313280	−	1.32439i
$106$	−4.57497			−0.444361
$107$	−12.8003	−	7.39027i	−1.23745	−	0.714445i	−0.268881	−	0.963173i	$-0.586654\pi$
$107$	−12.8003	−	7.39027i	−1.23745	−	0.714445i	−0.968573	+	0.248729i	$0.919987\pi$
$108$	−4.85538	+	1.85074i	−0.467210	+	0.178088i
$109$	8.40077	+	14.5506i	0.804647	+	1.39369i	0.916529	+	0.399969i	$0.130979\pi$
$109$	8.40077	+	14.5506i	0.804647	+	1.39369i	−0.111881	+	0.993722i	$0.535688\pi$
$110$	−5.36610	+	9.29436i	−0.511637	+	0.886182i
$111$	4.89511	−	2.48936i	0.464623	−	0.236280i
$112$	−1.91449	−	1.82612i	−0.180903	−	0.172552i
$113$			17.2044i			1.61845i	0.587495	+	0.809227i	$0.300114\pi$
$113$			17.2044i			1.61845i	−0.587495	+	0.809227i	$0.699886\pi$
$114$	0.0899608	−	1.69123i	0.00842560	−	0.158398i
$115$	2.63544	−	1.52157i	0.245756	−	0.141887i
$116$	3.67588	−	2.12227i	0.341297	−	0.197048i
$117$	15.5940	−	6.91368i	1.44167	−	0.639170i
$118$		−	3.88981i		−	0.358086i
$119$	−11.8651	+	3.48159i	−1.08767	+	0.319157i
$120$	2.38925	+	4.69825i	0.218108	+	0.428890i
$121$	0.718755	−	1.24492i	0.0653413	−	0.113175i
$122$	1.09725	+	1.90050i	0.0993406	+	0.172063i
$123$	−11.3061	−	7.35485i	−1.01944	−	0.663164i
$124$	−1.00386	−	0.579580i	−0.0901495	−	0.0520479i
$125$	−2.24979			−0.201227
$126$	7.47100	+	2.68034i	0.665569	+	0.238784i
$127$	9.55693			0.848040			0.424020	−	0.905653i	$-0.360619\pi$
$127$	9.55693			0.848040			0.424020	+	0.905653i	$0.360619\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.62911	−	2.36081i	−0.319526	−	0.207858i
$130$	−8.65161	−	14.9850i	−0.758796	−	1.31427i
$131$	4.93615	−	8.54967i	0.431274	−	0.746988i	−0.565709	−	0.824605i	$-0.691398\pi$
$131$	4.93615	−	8.54967i	0.431274	−	0.746988i	0.996983	+	0.0776164i	$0.0247310\pi$
$132$	−2.76889	−	5.44479i	−0.241001	−	0.473908i
$133$	−1.78560	+	1.87202i	−0.154831	+	0.162324i
$134$			0.454367i			0.0392513i
$135$	−12.2653	−	9.98003i	−1.05563	−	0.858944i
$136$	4.04750	−	2.33683i	0.347070	−	0.200381i
$137$	−16.4275	+	9.48443i	−1.40350	+	0.810310i	−0.994750	−	0.102338i	$-0.967368\pi$
$137$	−16.4275	+	9.48443i	−1.40350	+	0.810310i	−0.408748	+	0.912647i	$0.634034\pi$
$138$	−0.0920021	+	1.72961i	−0.00783174	+	0.147234i
$139$			16.5933i			1.40742i	0.710486	+	0.703711i	$0.248475\pi$
$139$			16.5933i			1.40742i	−0.710486	+	0.703711i	$0.751525\pi$
$140$	1.89959	−	7.82410i	0.160544	−	0.661257i
$141$	−16.3007	+	8.28957i	−1.37277	+	0.698108i
$142$	−3.08176	+	5.33777i	−0.258616	+	0.447936i
$143$	10.0263	+	17.3661i	0.838443	+	1.45223i
$144$	−2.98307	−	0.318255i	−0.248589	−	0.0265212i
$145$	11.1862	+	6.45836i	0.928964	+	0.536338i
$146$	−2.28622			−0.189209
$147$	−6.00012	−	10.5356i	−0.494882	−	0.868960i
$148$	3.17065			0.260626
$149$	12.7824	+	7.37990i	1.04717	+	0.604585i	0.921856	−	0.387532i	$-0.126672\pi$
$149$	12.7824	+	7.37990i	1.04717	+	0.604585i	0.125316	+	0.992117i	$0.460006\pi$
$150$	−4.02414	+	6.18603i	−0.328570	+	0.505088i
$151$	4.00264	+	6.93278i	0.325730	+	0.564181i	0.981660	−	0.190641i	$-0.0610565\pi$
$151$	4.00264	+	6.93278i	0.325730	+	0.564181i	−0.655930	+	0.754822i	$0.727723\pi$
$152$	0.488906	−	0.846810i	0.0396555	−	0.0686854i
$153$	−8.25905	+	11.3303i	−0.667705	+	0.915999i
$154$	−2.20142	+	9.06732i	−0.177396	+	0.730665i
$155$		−	3.52749i		−	0.283335i
$156$	9.83449	+	0.523122i	0.787390	+	0.0418832i
$157$	3.25253	−	1.87785i	0.259580	−	0.149868i	−0.364563	−	0.931179i	$-0.618782\pi$
$157$	3.25253	−	1.87785i	0.259580	−	0.149868i	0.624143	+	0.781310i	$0.285448\pi$
$158$	1.07077	−	0.618207i	0.0851855	−	0.0491819i
$159$	7.91290	+	0.420907i	0.627534	+	0.0333801i
$160$			3.04314i			0.240581i
$161$	1.82612	−	1.91449i	0.143918	−	0.150883i
$162$	8.56817	−	2.75435i	0.673179	−	0.216402i
$163$	−9.10902	+	15.7773i	−0.713473	+	1.23577i	0.250072	+	0.968227i	$0.419546\pi$
$163$	−9.10902	+	15.7773i	−0.713473	+	1.23577i	−0.963545	+	0.267545i	$0.913788\pi$
$164$	−3.89360	−	6.74392i	−0.304039	−	0.526611i
$165$	10.1363	−	15.5819i	0.789113	−	1.21305i
$166$	1.61869	+	0.934553i	0.125635	+	0.0725354i
$167$	0.0210684			0.00163032			0.000815161	−	1.00000i	$-0.499741\pi$
$167$	0.0210684			0.00163032			0.000815161		1.00000i	$0.499741\pi$
$168$	3.14331	+	3.33460i	0.242512	+	0.257270i
$169$	−19.3303			−1.48695
$170$	12.3171	+	7.11129i	0.944679	+	0.545411i
$171$	−0.311193	+	2.91688i	−0.0237976	+	0.223060i
$172$	−1.24980	−	2.16471i	−0.0952961	−	0.165058i
$173$	12.4404	−	21.5474i	0.945827	−	1.63822i	0.191740	−	0.981446i	$-0.438587\pi$
$173$	12.4404	−	21.5474i	0.945827	−	1.63822i	0.754087	−	0.656775i	$-0.228080\pi$
$174$	−6.55307	+	3.33250i	−0.496787	+	0.252636i
$175$	10.8167	−	3.17397i	0.817666	−	0.239930i
$176$		−	3.52669i		−	0.265834i
$177$	−0.357870	+	6.72783i	−0.0268992	+	0.505695i
$178$	−13.9135	+	8.03294i	−1.04286	+	0.602094i
$179$	−6.35355	+	3.66823i	−0.474887	+	0.274176i	−0.718283	−	0.695751i	$-0.755072\pi$
$179$	−6.35355	+	3.66823i	−0.474887	+	0.274176i	0.243396	+	0.969927i	$0.421738\pi$
$180$	−3.70021	−	8.34594i	−0.275797	−	0.622070i
$181$			21.2103i			1.57655i	0.615321	+	0.788276i	$0.289026\pi$
$181$			21.2103i			1.57655i	−0.615321	+	0.788276i	$0.710974\pi$
$182$	−10.8858	−	10.3833i	−0.806906	−	0.769659i
$183$	−1.72296	−	3.38806i	−0.127365	−	0.250453i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	4.82436	+	8.35604i	0.354694	+	0.614348i
$186$	1.68296	+	1.09480i	0.123401	+	0.0802749i
$187$	−14.2743	−	8.24125i	−1.04384	−	0.602660i
$188$	−10.5583			−0.770040
$189$	−12.6753	−	5.32328i	−0.921991	−	0.387212i
$190$	2.97562			0.215874
$191$	−4.57819	−	2.64322i	−0.331266	−	0.191257i	0.325137	−	0.945667i	$-0.394590\pi$
$191$	−4.57819	−	2.64322i	−0.331266	−	0.191257i	−0.656403	+	0.754410i	$0.727923\pi$
$192$	−1.45188	−	0.944479i	−0.104781	−	0.0681619i
$193$	−1.16570	−	2.01905i	−0.0839089	−	0.145334i	0.821017	−	0.570904i	$-0.193407\pi$
$193$	−1.16570	−	2.01905i	−0.0839089	−	0.145334i	−0.904926	+	0.425570i	$0.860074\pi$
$194$	8.27068	−	14.3252i	0.593800	−	1.02849i
$195$	13.5852	+	26.7141i	0.972857	+	1.91304i
$196$	−0.330574	−	6.99219i	−0.0236124	−	0.499442i
$197$		−	25.8937i		−	1.84485i	−0.386176	−	0.922425i	$-0.626204\pi$
$197$		−	25.8937i		−	1.84485i	0.386176	−	0.922425i	$-0.373796\pi$
$198$	4.28816	+	9.67209i	0.304747	+	0.687365i
$199$	23.8465	−	13.7678i	1.69043	−	0.975971i	0.736266	−	0.676692i	$-0.236587\pi$
$199$	23.8465	−	13.7678i	1.69043	−	0.975971i	0.954165	−	0.299279i	$-0.0967463\pi$
$200$	−3.68988	+	2.13035i	−0.260914	+	0.150639i
$201$	0.0418027	−	0.785875i	0.00294854	−	0.0554314i
$202$		−	9.73387i		−	0.684873i
$203$	10.9130	+	2.64952i	0.765940	+	0.185960i
$204$	−7.21557	+	3.66941i	−0.505191	+	0.256910i
$205$	11.8488	−	20.5227i	0.827554	−	1.43337i
$206$	−6.04463	−	10.4696i	−0.421150	−	0.729452i
$207$	0.318255	−	2.98307i	0.0221202	−	0.207338i
$208$	4.92420	+	2.84299i	0.341432	+	0.197126i
$209$	−3.44844			−0.238533
$210$	−4.00537	+	13.3578i	−0.276397	+	0.921778i
$211$	17.5665			1.20932			0.604662	−	0.796482i	$-0.293308\pi$
$211$	17.5665			1.20932			0.604662	+	0.796482i	$0.293308\pi$
$212$	3.96204	+	2.28749i	0.272114	+	0.157105i
$213$	5.82132	−	8.94871i	0.398870	−	0.613155i
$214$	7.39027	+	12.8003i	0.505189	+	0.875013i
$215$	3.80331	−	6.58752i	0.259383	−	0.449265i
$216$	5.13026	+	0.824904i	0.349070	+	0.0561276i
$217$	−0.863506	−	2.94278i	−0.0586186	−	0.199769i
$218$		−	16.8015i		−	1.13794i
$219$	3.95426	+	0.210337i	0.267204	+	0.0142133i
$220$	9.29436	−	5.36610i	0.626625	−	0.361782i
$221$	23.0140	−	13.2871i	1.54809	−	0.893789i
$222$	−5.48397	−	0.291706i	−0.368060	−	0.0195780i
$223$		−	5.99709i		−	0.401595i	−0.979633	−	0.200798i	$-0.935647\pi$
$223$		−	5.99709i		−	0.401595i	0.979633	−	0.200798i	$-0.0643533\pi$
$224$	0.744941	+	2.53871i	0.0497734	+	0.169625i
$225$	7.52931	−	10.3292i	0.501954	−	0.688611i
$226$	8.60221	−	14.8995i	0.572210	−	0.991097i
$227$	12.5340	+	21.7096i	0.831912	+	1.44091i	0.896520	+	0.443004i	$0.146087\pi$
$227$	12.5340	+	21.7096i	0.831912	+	1.44091i	−0.0646074	+	0.997911i	$0.520580\pi$
$228$	−0.923523	+	1.41967i	−0.0611618	+	0.0940198i
$229$	−18.0080	−	10.3969i	−1.19000	−	0.687047i	−0.231694	−	0.972789i	$-0.574427\pi$
$229$	−18.0080	−	10.3969i	−1.19000	−	0.687047i	−0.958307	+	0.285742i	$0.907760\pi$
$230$	−3.04314			−0.200659
$231$	4.64181	−	15.4804i	0.305409	−	1.01853i
$232$	−4.24454			−0.278668
$233$	4.28541	+	2.47418i	0.280747	+	0.162089i	0.633761	−	0.773529i	$-0.281510\pi$
$233$	4.28541	+	2.47418i	0.280747	+	0.162089i	−0.353015	+	0.935618i	$0.614843\pi$
$234$	−16.9617	−	1.80959i	−1.10882	−	0.118296i
$235$	−16.0651	−	27.8256i	−1.04797	−	1.81514i
$236$	−1.94490	+	3.36867i	−0.126602	+	0.219282i
$237$	−1.90888	+	0.970741i	−0.123995	+	0.0630564i
$238$	12.0162	+	2.91738i	0.778897	+	0.189106i
$239$			15.3365i			0.992034i	0.868313	+	0.496017i	$0.165205\pi$
$239$			15.3365i			0.992034i	−0.868313	+	0.496017i	$0.834795\pi$
$240$	0.279975	−	5.26343i	0.0180723	−	0.339753i
$241$	6.78601	−	3.91790i	0.437125	−	0.252374i	−0.265252	−	0.964179i	$-0.585455\pi$
$241$	6.78601	−	3.91790i	0.437125	−	0.252374i	0.702377	+	0.711805i	$0.252122\pi$
$242$	−1.24492	+	0.718755i	−0.0800265	+	0.0462033i
$243$	−15.0730	+	3.97564i	−0.966931	+	0.255038i
$244$		−	2.19450i		−	0.140489i
$245$	17.9245	−	11.5103i	1.14515	−	0.735367i
$246$	6.11394	+	12.0225i	0.389811	+	0.766529i
$247$	2.77991	−	4.81494i	0.176881	−	0.306367i
$248$	0.579580	+	1.00386i	0.0368034	+	0.0637454i
$249$	−2.71372	−	1.76533i	−0.171975	−	0.111873i
$250$	1.94837	+	1.12489i	0.123226	+	0.0711445i
$251$	−0.640271			−0.0404136			−0.0202068	−	0.999796i	$-0.506432\pi$
$251$	−0.640271			−0.0404136			−0.0202068	+	0.999796i	$0.506432\pi$
$252$	−5.12990	−	6.05674i	−0.323153	−	0.381539i
$253$	3.52669			0.221721
$254$	−8.27654	−	4.77846i	−0.519316	−	0.299827i
$255$	−20.6495	−	13.4329i	−1.29312	−	0.841202i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.68269	−	13.3068i	0.479233	−	0.830056i	−0.520483	−	0.853872i	$-0.674248\pi$
$257$	7.68269	−	13.3068i	0.479233	−	0.830056i	0.999716	+	0.0238158i	$0.00758151\pi$
$258$	1.96250	+	3.85908i	0.122180	+	0.240256i
$259$	6.07018	+	5.78998i	0.377183	+	0.359772i
$260$			17.3032i			1.07310i
$261$	11.6408	−	5.16101i	0.720549	−	0.319459i
$262$	−8.54967	+	4.93615i	−0.528200	+	0.304957i
$263$	−8.73105	+	5.04087i	−0.538379	+	0.310834i	−0.744422	−	0.667710i	$-0.767275\pi$
$263$	−8.73105	+	5.04087i	−0.538379	+	0.310834i	0.206042	+	0.978543i	$0.433942\pi$
$264$	−0.324463	+	6.09977i	−0.0199693	+	0.375415i
$265$			13.9223i			0.855239i
$266$	2.48238	−	0.728412i	0.152205	−	0.0446618i
$267$	24.8038	−	12.6137i	1.51797	−	0.771949i
$268$	0.227183	−	0.393493i	0.0138774	−	0.0240364i
$269$	2.04027	+	3.53385i	0.124398	+	0.215463i	0.921497	−	0.388385i	$-0.126967\pi$
$269$	2.04027	+	3.53385i	0.124398	+	0.215463i	−0.797100	+	0.603848i	$0.793634\pi$
$270$	5.63206	+	14.7756i	0.342756	+	0.899215i
$271$	13.1812	+	7.61019i	0.800703	+	0.462286i	0.843717	−	0.536788i	$-0.180363\pi$
$271$	13.1812	+	7.61019i	0.800703	+	0.462286i	−0.0430140	+	0.999074i	$0.513696\pi$
$272$	−4.67365			−0.283382
$273$	17.8728	+	18.9605i	1.08171	+	1.14754i
$274$	18.9689			1.14595
$275$	13.0130	+	7.51308i	0.784715	+	0.453056i
$276$	0.944479	−	1.45188i	0.0568510	−	0.0873930i
$277$	−2.80266	−	4.85435i	−0.168396	−	0.291670i	0.769460	−	0.638695i	$-0.220525\pi$
$277$	−2.80266	−	4.85435i	−0.168396	−	0.291670i	−0.937856	+	0.347025i	$0.887192\pi$
$278$	8.29663	−	14.3702i	0.497599	−	0.861867i
$279$	−2.81014	−	2.04841i	−0.168239	−	0.122635i
$280$	−5.55714	+	5.82607i	−0.332103	+	0.348174i
$281$			0.569158i			0.0339531i	0.999856	+	0.0169766i	$0.00540407\pi$
$281$			0.569158i			0.0339531i	−0.999856	+	0.0169766i	$0.994596\pi$
$282$	18.2616	+	0.971382i	1.08746	+	0.0578450i
$283$	19.6549	−	11.3477i	1.16836	−	0.674553i	0.215067	−	0.976599i	$-0.431003\pi$
$283$	19.6549	−	11.3477i	1.16836	−	0.674553i	0.953293	+	0.302046i	$0.0976697\pi$
$284$	5.33777	−	3.08176i	0.316738	−	0.182869i
$285$	−5.14665	−	0.273763i	−0.304861	−	0.0162163i
$286$		−	20.0526i		−	1.18574i
$287$	4.86092	−	20.0214i	0.286931	−	1.18182i
$288$	2.42429	+	1.76715i	0.142853	+	0.104130i
$289$	−2.42151	+	4.19417i	−0.142442	+	0.246716i
$290$	−6.45836	−	11.1862i	−0.379248	−	0.656877i
$291$	−15.6230	+	24.0161i	−0.915834	+	1.40785i
$292$	1.97992	+	1.14311i	0.115866	+	0.0668954i
$293$	7.07105			0.413095			0.206548	−	0.978437i	$-0.433777\pi$
$293$	7.07105			0.413095			0.206548	+	0.978437i	$0.433777\pi$
$294$	−0.0715338	+	12.1241i	−0.00417193	+	0.707094i
$295$	−11.8372			−0.689190
$296$	−2.74586	−	1.58532i	−0.159600	−	0.0921450i
$297$	−6.52698	−	17.1234i	−0.378734	−	0.993601i
$298$	−7.37990	−	12.7824i	−0.427506	−	0.740462i
$299$	−2.84299	+	4.92420i	−0.164414	+	0.284774i
$300$	6.57803	−	3.34519i	0.379783	−	0.193135i
$301$	1.56029	−	6.42660i	0.0899338	−	0.370423i
$302$		−	8.00528i		−	0.460652i
$303$	−0.895536	+	16.8358i	−0.0514472	+	0.967189i
$304$	−0.846810	+	0.488906i	−0.0485679	+	0.0280407i
$305$	5.78348	−	3.33909i	0.331161	−	0.191196i
$306$	12.8177	−	5.68278i	0.732738	−	0.324863i
$307$			5.74460i			0.327862i	0.986472	+	0.163931i	$0.0524174\pi$
$307$			5.74460i			0.327862i	−0.986472	+	0.163931i	$0.947583\pi$
$308$	6.44015	−	6.75182i	0.366962	−	0.384721i
$309$	9.49160	+	18.6644i	0.539959	+	1.06178i
$310$	−1.76374	+	3.05490i	−0.100174	+	0.173506i
$311$	14.5349	+	25.1752i	0.824199	+	1.42755i	0.902530	+	0.430627i	$0.141707\pi$
$311$	14.5349	+	25.1752i	0.824199	+	1.42755i	−0.0783316	+	0.996927i	$0.524959\pi$
$312$	−8.25536	−	5.37028i	−0.467368	−	0.304032i
$313$	−3.05084	−	1.76140i	−0.172444	−	0.0995604i	0.411294	−	0.911503i	$-0.365077\pi$
$313$	−3.05084	−	1.76140i	−0.172444	−	0.0995604i	−0.583738	+	0.811942i	$0.698410\pi$
$314$	−3.75569			−0.211946
$315$	8.15666	−	22.7353i	0.459576	−	1.28099i
$316$	−1.23641			−0.0695537
$317$	−6.58767	−	3.80339i	−0.370000	−	0.213620i	0.303458	−	0.952845i	$-0.401859\pi$
$317$	−6.58767	−	3.80339i	−0.370000	−	0.213620i	−0.673459	+	0.739225i	$0.735192\pi$
$318$	−6.64232	−	4.32097i	−0.372483	−	0.242308i
$319$	7.48457	+	12.9637i	0.419056	+	0.725826i
$320$	1.52157	−	2.63544i	0.0850584	−	0.147325i
$321$	−11.6046	−	22.8194i	−0.647706	−	1.27366i
$322$	−2.53871	+	0.744941i	−0.141477	+	0.0415139i
$323$			4.56995i			0.254279i
$324$	−8.79743	−	1.89875i	−0.488746	−	0.105486i
$325$	−20.9805	+	12.1131i	−1.16379	+	0.671915i
$326$	15.7773	−	9.10902i	0.873823	−	0.504502i
$327$	−1.54578	+	29.0600i	−0.0854816	+	1.60702i
$328$			7.78720i			0.429976i
$329$	−20.2137	−	19.2807i	−1.11442	−	1.06298i
$330$	−16.5693	+	8.42613i	−0.912108	+	0.463843i
$331$	−17.2879	+	29.9436i	−0.950230	+	1.64585i	−0.205305	+	0.978698i	$0.565819\pi$
$331$	−17.2879	+	29.9436i	−0.950230	+	1.64585i	−0.744925	+	0.667149i	$0.767515\pi$
$332$	−0.934553	−	1.61869i	−0.0512903	−	0.0888373i
$333$	9.45826	+	1.00907i	0.518310	+	0.0552969i
$334$	−0.0182458	−	0.0105342i	−0.000998364	−	0.000576406i
$335$	1.38270			0.0755451
$336$	−1.05489	−	4.45951i	−0.0575488	−	0.243286i
$337$	−20.3499			−1.10853			−0.554266	−	0.832340i	$-0.687001\pi$
$337$	−20.3499			−1.10853			−0.554266	+	0.832340i	$0.687001\pi$
$338$	16.7405	+	9.66515i	0.910565	+	0.525715i
$339$	−16.2492	+	24.9788i	−0.882536	+	1.35666i
$340$	−7.11129	−	12.3171i	−0.385664	−	0.667989i
$341$	2.04400	−	3.54031i	0.110689	−	0.191718i
$342$	1.72794	−	2.37050i	0.0934365	−	0.128182i
$343$	12.1357	−	13.9902i	0.655266	−	0.755398i
$344$			2.49959i			0.134769i
$345$	5.26343	+	0.279975i	0.283374	+	0.0150734i
$346$	−21.5474	+	12.4404i	−1.15840	+	0.668801i
$347$	−6.65135	+	3.84016i	−0.357063	+	0.206151i	−0.667792	−	0.744348i	$-0.732760\pi$
$347$	−6.65135	+	3.84016i	−0.357063	+	0.206151i	0.310728	+	0.950499i	$0.399427\pi$
$348$	7.34138	+	0.390506i	0.393539	+	0.0209333i
$349$		−	15.7671i		−	0.843991i	−0.906598	−	0.421996i	$-0.861330\pi$
$349$		−	15.7671i		−	0.843991i	0.906598	−	0.421996i	$-0.138670\pi$
$350$	−10.9545	−	2.65961i	−0.585544	−	0.142162i
$351$	29.1705	+	4.69038i	1.55701	+	0.250354i
$352$	−1.76334	+	3.05420i	−0.0939865	+	0.162789i
$353$	−10.9738	−	19.0072i	−0.584077	−	1.01165i	−0.994990	−	0.0999762i	$-0.968123\pi$
$353$	−10.9738	−	19.0072i	−0.584077	−	1.01165i	0.410913	−	0.911675i	$-0.365210\pi$
$354$	3.67384	−	5.64754i	0.195262	−	0.300163i
$355$	16.2436	+	9.37824i	0.862120	+	0.497745i
$356$	16.0659			0.851489
$357$	−20.5149	−	6.15144i	−1.08577	−	0.325569i
$358$	7.33645			0.387744
$359$	5.62294	+	3.24641i	0.296767	+	0.171339i	0.640990	−	0.767549i	$-0.278524\pi$
$359$	5.62294	+	3.24641i	0.296767	+	0.171339i	−0.344222	+	0.938888i	$0.611857\pi$
$360$	−0.968494	+	9.07790i	−0.0510441	+	0.478448i
$361$	−9.02194	−	15.6265i	−0.474839	−	0.822445i
$362$	10.6052	−	18.3687i	0.557395	−	0.965437i
$363$	2.21935	−	1.12863i	0.116486	−	0.0592376i
$364$	4.23571	+	14.4351i	0.222012	+	0.756602i
$365$			6.95729i			0.364161i
$366$	−0.201899	+	3.79563i	−0.0105534	+	0.198401i
$367$	−30.9762	+	17.8841i	−1.61694	+	0.933543i	−0.629239	+	0.777212i	$0.716633\pi$
$367$	−30.9762	+	17.8841i	−1.61694	+	0.933543i	−0.987705	+	0.156331i	$0.950033\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−9.46861	−	21.3567i	−0.492916	−	1.11179i
$370$		−	9.64872i		−	0.501613i
$371$	3.40808	+	11.6145i	0.176939	+	0.602997i
$372$	−0.910088	−	1.78961i	−0.0471859	−	0.0927869i
$373$	17.4543	−	30.2317i	0.903749	−	1.56534i	0.0811610	−	0.996701i	$-0.474137\pi$
$373$	17.4543	−	30.2317i	0.903749	−	1.56534i	0.822588	−	0.568638i	$-0.192529\pi$
$374$	8.24125	+	14.2743i	0.426145	+	0.738104i
$375$	−3.26642	−	2.12488i	−0.168677	−	0.109728i
$376$	9.14372	+	5.27913i	0.471552	+	0.272250i
$377$	−24.1343			−1.24298
$378$	8.31547	+	10.9477i	0.427702	+	0.563091i
$379$	−18.3104			−0.940540			−0.470270	−	0.882523i	$-0.655843\pi$
$379$	−18.3104			−0.940540			−0.470270	+	0.882523i	$0.655843\pi$
$380$	−2.57696	−	1.48781i	−0.132195	−	0.0763230i
$381$	13.8755	+	9.02632i	0.710865	+	0.462432i
$382$	2.64322	+	4.57819i	0.135239	+	0.234240i
$383$	1.43642	−	2.48795i	0.0733976	−	0.127128i	−0.826991	−	0.562216i	$-0.809949\pi$
$383$	1.43642	−	2.48795i	0.0733976	−	0.127128i	0.900388	+	0.435087i	$0.143282\pi$
$384$	0.785127	+	1.54388i	0.0400658	+	0.0787860i
$385$	27.5931	+	6.69924i	1.40628	+	0.341425i
$386$			2.33140i			0.118665i
$387$	−3.03930	−	6.85524i	−0.154496	−	0.348471i
$388$	−14.3252	+	8.27068i	−0.727254	+	0.419880i
$389$	−14.1331	+	8.15973i	−0.716575	+	0.413715i	−0.813491	−	0.581578i	$-0.802436\pi$
$389$	−14.1331	+	8.15973i	−0.716575	+	0.413715i	0.0969155	+	0.995293i	$0.469102\pi$
$390$	1.59193	−	29.9277i	0.0806106	−	1.51545i
$391$		−	4.67365i		−	0.236357i
$392$	−3.20981	+	6.22070i	−0.162120	+	0.314193i
$393$	15.2417	−	7.75101i	0.768842	−	0.390987i
$394$	−12.9469	+	22.4246i	−0.652253	+	1.12974i
$395$	−1.88129	−	3.25849i	−0.0946580	−	0.163952i
$396$	1.12238	−	10.5204i	0.0564019	−	0.528668i
$397$	21.3496	+	12.3262i	1.07150	+	0.618633i	0.928592	−	0.371103i	$-0.121020\pi$
$397$	21.3496	+	12.3262i	1.07150	+	0.618633i	0.142912	+	0.989735i	$0.454354\pi$
$398$	−27.5355			−1.38023
$399$	−4.36056	+	1.03148i	−0.218301	+	0.0516386i
$400$	4.26070			0.213035
$401$	10.7698	+	6.21795i	0.537818	+	0.310509i	0.744194	−	0.667963i	$-0.232834\pi$
$401$	10.7698	+	6.21795i	0.537818	+	0.310509i	−0.206376	+	0.978473i	$0.566167\pi$
$402$	−0.429140	+	0.659687i	−0.0214035	+	0.0329022i
$403$	3.29548	+	5.70794i	0.164160	+	0.284333i
$404$	−4.86693	+	8.42978i	−0.242139	+	0.419397i
$405$	−8.38186	−	26.0742i	−0.416498	−	1.29563i
$406$	−8.12614	−	7.75103i	−0.403294	−	0.384677i
$407$			11.1819i			0.554265i
$408$	8.08357	+	0.429986i	0.400196	+	0.0212875i
$409$	−17.1469	+	9.89977i	−0.847860	+	0.489512i	−0.859928	−	0.510415i	$-0.829492\pi$
$409$	−17.1469	+	9.89977i	−0.847860	+	0.489512i	0.0120681	+	0.999927i	$0.496159\pi$
$410$	−20.5227	+	11.8488i	−1.01354	+	0.585169i
$411$	−32.8087	−	1.74518i	−1.61833	−	0.0860832i
$412$			12.0893i			0.595595i
$413$	−9.87510	+	2.89767i	−0.485922	+	0.142585i
$414$	−1.76715	+	2.42429i	−0.0868508	+	0.119147i
$415$	2.84398	−	4.92591i	0.139605	−	0.241803i
$416$	−2.84299	−	4.92420i	−0.139389	−	0.241429i
$417$	−15.6720	+	24.0915i	−0.767461	+	1.17976i
$418$	2.98643	+	1.72422i	0.146071	+	0.0843343i
$419$	27.5888			1.34780			0.673902	−	0.738821i	$-0.264617\pi$
$419$	27.5888			1.34780			0.673902	+	0.738821i	$0.264617\pi$
$420$	10.1477	−	9.56554i	0.495156	−	0.466751i
$421$	−4.84341			−0.236054			−0.118027	−	0.993010i	$-0.537657\pi$
$421$	−4.84341			−0.236054			−0.118027	+	0.993010i	$0.537657\pi$
$422$	−15.2130	−	8.78323i	−0.740557	−	0.427561i
$423$	−31.4960	−	3.36022i	−1.53139	−	0.163379i
$424$	−2.28749	−	3.96204i	−0.111090	−	0.192414i
$425$	9.95652	−	17.2452i	0.482962	−	0.836515i
$426$	−9.51576	+	4.83915i	−0.461040	+	0.234457i
$427$	4.00743	−	4.20137i	0.193933	−	0.203318i
$428$		−	14.7805i		−	0.714445i
$429$	−1.84489	+	34.6832i	−0.0890719	+	1.67452i
$430$	−6.58752	+	3.80331i	−0.317678	+	0.183412i
$431$	−26.5405	+	15.3232i	−1.27841	+	0.738090i	−0.976556	−	0.215264i	$-0.930939\pi$
$431$	−26.5405	+	15.3232i	−1.27841	+	0.738090i	−0.301854	+	0.953354i	$0.597606\pi$
$432$	−4.03048	−	3.27952i	−0.193917	−	0.157786i
$433$		−	33.9937i		−	1.63363i	−0.576899	−	0.816815i	$-0.695737\pi$
$433$		−	33.9937i		−	1.63363i	0.576899	−	0.816815i	$-0.304263\pi$
$434$	−0.723570	+	2.98027i	−0.0347325	+	0.143058i
$435$	10.1413	+	19.9419i	0.486236	+	0.956142i
$436$	−8.40077	+	14.5506i	−0.402324	+	0.696845i
$437$	−0.488906	−	0.846810i	−0.0233875	−	0.0405084i
$438$	−3.31932	−	2.15929i	−0.158603	−	0.103175i
$439$	9.44907	+	5.45542i	0.450979	+	0.260373i	0.708244	−	0.705968i	$-0.249488\pi$
$439$	9.44907	+	5.45542i	0.450979	+	0.260373i	−0.257264	+	0.966341i	$0.582821\pi$
$440$	−10.7322			−0.511637
$441$	1.23917	−	20.9634i	0.0590082	−	0.998257i
$442$	−26.5743			−1.26401
$443$	14.8072	+	8.54892i	0.703510	+	0.406172i	0.808653	−	0.588285i	$-0.200197\pi$
$443$	14.8072	+	8.54892i	0.703510	+	0.406172i	−0.105143	+	0.994457i	$0.533530\pi$
$444$	4.60340	+	2.99461i	0.218468	+	0.142118i
$445$	24.4453	+	42.3406i	1.15882	+	2.00714i
$446$	−2.99855	+	5.19364i	−0.141985	+	0.245926i
$447$	11.5883	+	22.7874i	0.548108	+	1.07781i
$448$	0.624219	−	2.57106i	0.0294916	−	0.121471i
$449$		−	15.1529i		−	0.715109i	−0.933892	−	0.357555i	$-0.883611\pi$
$449$		−	15.1529i		−	0.715109i	0.933892	−	0.357555i	$-0.116389\pi$
$450$	−11.6852	+	5.18067i	−0.550844	+	0.244219i
$451$	23.7837	−	13.7315i	1.11993	−	0.646591i
$452$	−14.8995	+	8.60221i	−0.700812	+	0.404614i
$453$	−0.736503	+	13.8460i	−0.0346039	+	0.650541i
$454$		−	25.0680i		−	1.17650i
$455$	−31.5977	+	33.1269i	−1.48132	+	1.55301i
$456$	1.50963	−	0.767706i	0.0706948	−	0.0359511i
$457$	−7.07697	+	12.2577i	−0.331047	+	0.573389i	−0.982717	−	0.185112i	$-0.940735\pi$
$457$	−7.07697	+	12.2577i	−0.331047	+	0.573389i	0.651671	+	0.758502i	$0.274068\pi$
$458$	10.3969	+	18.0080i	0.485816	+	0.841457i
$459$	−22.6924	+	8.64971i	−1.05919	+	0.403734i
$460$	2.63544	+	1.52157i	0.122878	+	0.0709436i
$461$	40.8123			1.90082			0.950410	−	0.310999i	$-0.100664\pi$
$461$	40.8123			1.90082			0.950410	+	0.310999i	$0.100664\pi$
$462$	−11.7601	+	11.0855i	−0.547129	+	0.515743i
$463$	−33.3378			−1.54934			−0.774669	−	0.632367i	$-0.782083\pi$
$463$	−33.3378			−1.54934			−0.774669	+	0.632367i	$0.782083\pi$
$464$	3.67588	+	2.12227i	0.170648	+	0.0985239i
$465$	3.33164	−	5.12150i	0.154501	−	0.237504i
$466$	−2.47418	−	4.28541i	−0.114614	−	0.198518i
$467$	5.45274	−	9.44443i	0.252323	−	0.437036i	−0.711842	−	0.702340i	$-0.752139\pi$
$467$	5.45274	−	9.44443i	0.252323	−	0.437036i	0.964165	+	0.265303i	$0.0854721\pi$
$468$	13.7844	+	10.0480i	0.637186	+	0.464468i
$469$	1.15351	−	0.338476i	0.0532640	−	0.0156294i
$470$			32.1303i			1.48206i
$471$	6.49587	+	0.345532i	0.299314	+	0.0159213i
$472$	3.36867	−	1.94490i	0.155056	−	0.0895214i
$473$	7.63425	−	4.40764i	0.351023	−	0.202663i
$474$	2.13851	+	0.113753i	0.0982249	+	0.00522483i
$475$		−	4.16617i		−	0.191157i
$476$	−8.94768	−	8.53465i	−0.410116	−	0.391185i
$477$	11.0911	+	8.08468i	0.507824	+	0.370172i
$478$	7.66824	−	13.2818i	0.350737	−	0.607494i
$479$	11.0475	+	19.1349i	0.504774	+	0.874294i	0.999985	+	0.00552108i	$0.00175742\pi$
$479$	11.0475	+	19.1349i	0.504774	+	0.874294i	−0.495211	+	0.868773i	$0.664909\pi$
$480$	−2.87418	+	4.41828i	−0.131188	+	0.201666i
$481$	−15.6129	−	9.01411i	−0.711887	−	0.411008i
$482$	−7.83581			−0.356911
$483$	4.45951	−	1.05489i	0.202915	−	0.0479990i
$484$	1.43751			0.0653413
$485$	−43.5937	−	25.1688i	−1.97949	−	1.14286i
$486$	15.0414	+	4.09348i	0.682291	+	0.185684i
$487$	−19.1558	−	33.1788i	−0.868032	−	1.50347i	−0.864005	−	0.503483i	$-0.832052\pi$
$487$	−19.1558	−	33.1788i	−0.868032	−	1.50347i	−0.00402648	−	0.999992i	$-0.501282\pi$
$488$	−1.09725	+	1.90050i	−0.0496703	+	0.0860315i
$489$	−28.1265	+	14.3035i	−1.27193	+	0.646825i
$490$	−21.2782	+	1.00598i	−0.961252	+	0.0454457i
$491$		−	24.7789i		−	1.11826i	−0.829081	−	0.559129i	$-0.811136\pi$
$491$		−	24.7789i		−	1.11826i	0.829081	−	0.559129i	$-0.188864\pi$
$492$	0.716439	−	13.4688i	0.0322996	−	0.607220i
$493$	17.1798	−	9.91874i	0.773738	−	0.446718i
$494$	−4.81494	+	2.77991i	−0.216634	+	0.125074i
$495$	29.4335	−	13.0495i	1.32294	−	0.586531i
$496$		−	1.15916i		−	0.0520479i
$497$	15.8468	+	3.84739i	0.710826	+	0.172579i
$498$	1.46748	+	2.88568i	0.0657596	+	0.129310i
$499$	−11.2185	+	19.4311i	−0.502211	+	0.869855i	0.497786	+	0.867300i	$0.334147\pi$
$499$	−11.2185	+	19.4311i	−0.502211	+	0.869855i	−0.999997	+	0.00255484i	$0.999187\pi$
$500$	−1.12489	−	1.94837i	−0.0503068	−	0.0871339i
$501$	0.0305888	+	0.0198987i	0.00136661	+	0.000889007i
$502$	0.554491	+	0.320136i	0.0247482	+	0.0142884i
$503$	−14.3124			−0.638157			−0.319079	−	0.947728i	$-0.603373\pi$
$503$	−14.3124			−0.638157			−0.319079	+	0.947728i	$0.603373\pi$
$504$	1.41425	+	7.81024i	0.0629958	+	0.347896i
$505$	−29.6215			−1.31814
$506$	−3.05420	−	1.76334i	−0.135776	−	0.0783901i
$507$	−28.0653	−	18.2571i	−1.24642	−	0.810824i
$508$	4.77846	+	8.27654i	0.212010	+	0.367212i
$509$	−4.59903	+	7.96576i	−0.203849	+	0.353076i	−0.949765	−	0.312963i	$-0.898678\pi$
$509$	−4.59903	+	7.96576i	−0.203849	+	0.353076i	0.745917	+	0.666039i	$0.232012\pi$
$510$	11.1665	+	21.9580i	0.494462	+	0.972316i
$511$	1.70310	+	5.80406i	0.0753406	+	0.256756i
$512$			1.00000i			0.0441942i
$513$	−3.20675	+	3.94105i	−0.141582	+	0.174002i
$514$	−13.3068	+	7.68269i	−0.586938	+	0.338869i
$515$	−31.8605	+	18.3947i	−1.40394	+	0.810566i
$516$	0.229968	−	4.32331i	0.0101238	−	0.190323i
$517$		−	37.2357i		−	1.63762i
$518$	−2.36194	−	8.04936i	−0.103778	−	0.353669i
$519$	38.4131	−	19.5346i	1.68615	−	0.857474i
$520$	8.65161	−	14.9850i	0.379398	−	0.657137i
$521$	13.1054	+	22.6993i	0.574160	+	0.994474i	0.996132	+	0.0878652i	$0.0280045\pi$
$521$	13.1054	+	22.6993i	0.574160	+	0.994474i	−0.421973	+	0.906609i	$0.638662\pi$
$522$	−12.6618	−	1.35084i	−0.554190	−	0.0591249i
$523$	26.9092	+	15.5360i	1.17666	+	0.679343i	0.955239	−	0.295836i	$-0.0955981\pi$
$523$	26.9092	+	15.5360i	1.17666	+	0.679343i	0.221418	+	0.975179i	$0.428931\pi$
$524$	9.87231			0.431274
$525$	18.7023	+	5.60792i	0.816236	+	0.244750i
$526$	10.0817			0.439585
$527$	−4.69170	−	2.70876i	−0.204374	−	0.117995i
$528$	3.33088	−	5.12033i	0.144958	−	0.222834i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	6.96114	−	12.0571i	0.302373	−	0.523725i
$531$	−6.87388	+	9.43001i	−0.298301	+	0.409228i
$532$	−2.51401	−	0.610369i	−0.108996	−	0.0264629i
$533$			44.2778i			1.91789i
$534$	−27.7876	−	1.47809i	−1.20249	−	0.0639634i
$535$	38.9532	−	22.4896i	1.68409	−	0.972312i
$536$	−0.393493	+	0.227183i	−0.0169963	+	0.00981283i
$537$	−12.6892	−	0.674969i	−0.547578	−	0.0291271i
$538$		−	4.08054i		−	0.175925i
$539$	24.6593	−	1.16583i	1.06215	−	0.0502159i
$540$	2.51030	−	15.6121i	0.108026	−	0.671837i
$541$	−17.4839	+	30.2831i	−0.751693	+	1.30197i	0.195309	+	0.980742i	$0.437429\pi$
$541$	−17.4839	+	30.2831i	−0.751693	+	1.30197i	−0.947002	+	0.321228i	$0.895904\pi$
$542$	−7.61019	−	13.1812i	−0.326886	−	0.566182i
$543$	−20.0327	+	30.7949i	−0.859687	+	1.32154i
$544$	4.04750	+	2.33683i	0.173535	+	0.100191i
$545$	−51.1294			−2.19014
$546$	−5.99806	−	25.3566i	−0.256693	−	1.08516i
$547$	7.12654			0.304709			0.152354	−	0.988326i	$-0.451314\pi$
$547$	7.12654			0.304709			0.152354	+	0.988326i	$0.451314\pi$
$548$	−16.4275	−	9.48443i	−0.701749	−	0.405155i
$549$	0.698412	−	6.54636i	0.0298075	−	0.279392i
$550$	−7.51308	−	13.0130i	−0.320359	−	0.554878i
$551$	2.07518	−	3.59432i	0.0884057	−	0.153123i
$552$	−1.54388	+	0.785127i	−0.0657120	+	0.0334172i
$553$	−2.36711	−	2.25784i	−0.100660	−	0.0960131i
$554$			5.60532i			0.238147i
$555$	−0.887703	+	16.6885i	−0.0376809	+	0.708387i
$556$	−14.3702	+	8.29663i	−0.609432	+	0.351856i
$557$	−5.99987	+	3.46403i	−0.254223	+	0.146776i	−0.621696	−	0.783258i	$-0.713556\pi$
$557$	−5.99987	+	3.46403i	−0.254223	+	0.146776i	0.367474	+	0.930034i	$0.380223\pi$
$558$	1.40945	+	3.17905i	0.0596666	+	0.134580i
$559$			14.2126i			0.601130i
$560$	7.72566	−	2.26696i	0.326469	−	0.0957965i
$561$	−12.9408	−	25.4471i	−0.546363	−	1.07438i
$562$	0.284579	−	0.492905i	0.0120042	−	0.0207920i
$563$	−9.32151	−	16.1453i	−0.392855	−	0.680445i	0.599970	−	0.800023i	$-0.295179\pi$
$563$	−9.32151	−	16.1453i	−0.392855	−	0.680445i	−0.992825	+	0.119578i	$0.961846\pi$
$564$	−15.3293	−	9.97206i	−0.645482	−	0.419899i
$565$	−45.3411	−	26.1777i	−1.90752	−	1.10130i
$566$	−22.6955			−0.953962
$567$	−13.3753	−	19.7003i	−0.561709	−	0.827335i
$568$	−6.16353			−0.258616
$569$	−7.01975	−	4.05285i	−0.294283	−	0.169904i	0.345589	−	0.938386i	$-0.387679\pi$
$569$	−7.01975	−	4.05285i	−0.294283	−	0.169904i	−0.639872	+	0.768482i	$0.721013\pi$
$570$	4.32025	+	2.81041i	0.180955	+	0.117715i
$571$	18.6326	+	32.2726i	0.779751	+	1.35057i	0.932085	+	0.362239i	$0.117988\pi$
$571$	18.6326	+	32.2726i	0.779751	+	1.35057i	−0.152335	+	0.988329i	$0.548679\pi$
$572$	−10.0263	+	17.3661i	−0.419222	+	0.726113i
$573$	−4.15052	−	8.16164i	−0.173391	−	0.340957i
$574$	−14.2204	+	14.9086i	−0.593547	+	0.622271i
$575$			4.26070i			0.177684i
$576$	−1.21592	−	2.74254i	−0.0506633	−	0.114273i
$577$	−28.5191	+	16.4655i	−1.18727	+	0.685469i	−0.957684	−	0.287821i	$-0.907069\pi$
$577$	−28.5191	+	16.4655i	−1.18727	+	0.685469i	−0.229582	+	0.973289i	$0.573736\pi$
$578$	4.19417	−	2.42151i	0.174455	−	0.100721i
$579$	0.214494	−	4.03240i	0.00891405	−	0.167581i
$580$			12.9167i			0.536338i
$581$	1.16673	−	4.80558i	0.0484042	−	0.199369i
$582$	25.5379	−	12.9871i	1.05858	−	0.538331i
$583$	−8.06725	+	13.9729i	−0.334111	+	0.578698i
$584$	−1.14311	−	1.97992i	−0.0473022	−	0.0819299i
$585$	−5.50683	+	51.6167i	−0.227679	+	2.13409i
$586$	−6.12371	−	3.53552i	−0.252968	−	0.146051i
$587$	22.2473			0.918243			0.459121	−	0.888374i	$-0.348164\pi$
$587$	22.2473			0.918243			0.459121	+	0.888374i	$0.348164\pi$
$588$	6.12402	−	10.4641i	0.252550	−	0.431530i
$589$	−1.13344			−0.0467027
$590$	10.2513	+	5.91861i	0.422041	+	0.243665i
$591$	24.4561	−	37.5946i	1.00599	−	1.54643i
$592$	1.58532	+	2.74586i	0.0651564	+	0.112854i
$593$	−17.5830	+	30.4547i	−0.722047	+	1.25062i	0.238131	+	0.971233i	$0.423465\pi$
$593$	−17.5830	+	30.4547i	−0.722047	+	1.25062i	−0.960178	+	0.279389i	$0.909868\pi$
$594$	−2.90918	+	18.0928i	−0.119365	+	0.742357i
$595$	8.87800	−	36.5671i	0.363963	−	1.49910i
$596$			14.7598i			0.604585i
$597$	47.6256	+	2.53333i	1.94919	+	0.103682i
$598$	4.92420	−	2.84299i	0.201365	−	0.116258i
$599$	17.7942	−	10.2735i	0.727051	−	0.419763i	−0.0902913	−	0.995915i	$-0.528780\pi$
$599$	17.7942	−	10.2735i	0.727051	−	0.419763i	0.817342	+	0.576152i	$0.195446\pi$
$600$	−7.36933	−	0.391994i	−0.300852	−	0.0160031i
$601$		−	24.7569i		−	1.00986i	−0.863161	−	0.504928i	$-0.831519\pi$
$601$		−	24.7569i		−	1.00986i	0.863161	−	0.504928i	$-0.168481\pi$
$602$	−4.56456	+	4.78546i	−0.186037	+	0.195041i
$603$	0.802935	−	1.10152i	0.0326980	−	0.0448572i
$604$	−4.00264	+	6.93278i	−0.162865	+	0.282091i
$605$	2.18727	+	3.78847i	0.0889252	+	0.154023i
$606$	9.19343	−	14.1324i	0.373458	−	0.574090i
$607$	−8.18046	−	4.72299i	−0.332035	−	0.191700i	0.324709	−	0.945814i	$-0.394733\pi$
$607$	−8.18046	−	4.72299i	−0.332035	−	0.191700i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	0.977812			0.0396555
$609$	13.3419	+	14.1539i	0.540641	+	0.573543i
$610$	−6.67819			−0.270392
$611$	51.9910	+	30.0170i	2.10333	+	1.21436i
$612$	−13.9418	−	1.48741i	−0.563565	−	0.0601251i
$613$	−6.92878	−	12.0010i	−0.279851	−	0.484716i	0.691497	−	0.722380i	$-0.256952\pi$
$613$	−6.92878	−	12.0010i	−0.279851	−	0.484716i	−0.971347	+	0.237664i	$0.923618\pi$
$614$	2.87230	−	4.97497i	0.115917	−	0.200773i
$615$	36.5863	−	18.6056i	1.47530	−	0.750249i
$616$	−8.95324	+	2.62717i	−0.360736	+	0.105852i
$617$			44.3914i			1.78713i	0.448933	+	0.893565i	$0.351804\pi$
$617$			44.3914i			1.78713i	−0.448933	+	0.893565i	$0.648196\pi$
$618$	1.11224	−	20.9097i	0.0447408	−	0.841110i
$619$	22.8194	−	13.1748i	0.917191	−	0.529541i	0.0344533	−	0.999406i	$-0.489031\pi$
$619$	22.8194	−	13.1748i	0.917191	−	0.529541i	0.882738	+	0.469866i	$0.155698\pi$
$620$	3.05490	−	1.76374i	0.122688	−	0.0708337i
$621$	3.27952	−	4.03048i	0.131602	−	0.161738i
$622$		−	29.0698i		−	1.16559i
$623$	30.7580	+	29.3382i	1.23229	+	1.17541i
$624$	4.46421	+	8.77848i	0.178711	+	0.351420i
$625$	14.0750	−	24.3786i	0.562999	−	0.975142i
$626$	1.76140	+	3.05084i	0.0703998	+	0.121936i
$627$	−5.00672	−	3.25698i	−0.199949	−	0.130071i
$628$	3.25253	+	1.87785i	0.129790	+	0.0749342i
$629$	14.8185			0.590852
$630$	−18.4315	+	15.6110i	−0.734329	+	0.621957i
$631$	0.674815			0.0268640			0.0134320	−	0.999910i	$-0.495724\pi$
$631$	0.674815			0.0268640			0.0134320	+	0.999910i	$0.495724\pi$
$632$	1.07077	+	0.618207i	0.0425928	+	0.0245909i
$633$	25.5044	+	16.5911i	1.01371	+	0.659439i
$634$	3.80339	+	6.58767i	0.151052	+	0.261630i
$635$	−14.5415	+	25.1867i	−0.577063	+	0.999503i
$636$	3.59193	+	7.06323i	0.142429	+	0.280075i
$637$	−18.2509	+	35.3707i	−0.723127	+	1.40144i
$638$		−	14.9691i		−	0.592634i
$639$	16.9037	−	7.49435i	0.668701	−	0.296472i
$640$	−2.63544	+	1.52157i	−0.104175	+	0.0601453i
$641$	10.5081	−	6.06688i	0.415047	−	0.239627i	−0.277909	−	0.960607i	$-0.589641\pi$
$641$	10.5081	−	6.06688i	0.415047	−	0.239627i	0.692956	+	0.720980i	$0.256308\pi$
$642$	−1.35984	+	25.5645i	−0.0536687	+	1.00895i
$643$			14.1206i			0.556863i	0.960456	+	0.278431i	$0.0898145\pi$
$643$			14.1206i			0.556863i	−0.960456	+	0.278431i	$0.910186\pi$
$644$	2.57106	+	0.624219i	0.101314	+	0.0245977i
$645$	11.7437	−	5.97215i	0.462409	−	0.235153i
$646$	2.28498	−	3.95770i	0.0899012	−	0.155713i
$647$	−5.02349	−	8.70094i	−0.197494	−	0.342069i	0.750221	−	0.661187i	$-0.229947\pi$
$647$	−5.02349	−	8.70094i	−0.197494	−	0.342069i	−0.947715	+	0.319117i	$0.896614\pi$
$648$	6.66942	+	6.04308i	0.262000	+	0.237395i
$649$	−11.8802	−	6.85906i	−0.466340	−	0.269242i
$650$	24.2262			0.950231
$651$	1.52568	−	5.08813i	0.0597962	−	0.199419i
$652$	−18.2180			−0.713473
$653$	1.96845	+	1.13648i	0.0770313	+	0.0444741i	0.538021	−	0.842931i	$-0.319172\pi$
$653$	1.96845	+	1.13648i	0.0770313	+	0.0444741i	−0.460990	+	0.887406i	$0.652505\pi$
$654$	15.8687	−	24.3938i	0.620515	−	0.953874i
$655$	15.0214	+	26.0178i	0.586935	+	1.01660i
$656$	3.89360	−	6.74392i	0.152020	−	0.263306i
$657$	5.54246	+	4.04010i	0.216232	+	0.157619i
$658$	7.86528	+	26.8044i	0.306620	+	1.04494i
$659$			11.8370i			0.461102i	0.973060	+	0.230551i	$0.0740529\pi$
$659$			11.8370i			0.461102i	−0.973060	+	0.230551i	$0.925947\pi$
$660$	18.5625	+	0.987385i	0.722543	+	0.0384339i
$661$	35.8305	−	20.6867i	1.39364	−	0.804621i	0.399928	−	0.916547i	$-0.369035\pi$
$661$	35.8305	−	20.6867i	1.39364	−	0.804621i	0.993717	+	0.111926i	$0.0357018\pi$
$662$	29.9436	−	17.2879i	1.16379	−	0.671914i
$663$	45.9630	+	2.44489i	1.78505	+	0.0949516i
$664$			1.86911i			0.0725354i
$665$	−2.21666	−	7.55424i	−0.0859584	−	0.292941i
$666$	−7.68656	−	5.60302i	−0.297848	−	0.217112i
$667$	−2.12227	+	3.67588i	−0.0821746	+	0.142331i
$668$	0.0105342	+	0.0182458i	0.000407581	+	0.000705950i
$669$	5.66413	−	8.70707i	0.218988	−	0.336635i
$670$	−1.19745	−	0.691351i	−0.0462617	−	0.0267092i
$671$	7.73933			0.298773
$672$	−1.31620	+	4.38949i	−0.0507734	+	0.169328i
$673$	−9.57325			−0.369022			−0.184511	−	0.982830i	$-0.559070\pi$
$673$	−9.57325			−0.369022			−0.184511	+	0.982830i	$0.559070\pi$
$674$	17.6236	+	10.1750i	0.678834	+	0.391925i
$675$	20.6873	−	7.88545i	0.796256	−	0.303511i
$676$	−9.66515	−	16.7405i	−0.371736	−	0.643866i
$677$	−21.6457	+	37.4915i	−0.831912	+	1.44091i	0.0646072	+	0.997911i	$0.479421\pi$
$677$	−21.6457	+	37.4915i	−0.831912	+	1.44091i	−0.896520	+	0.443004i	$0.853913\pi$
$678$	26.5616	−	13.5076i	1.02009	−	0.518758i
$679$	−42.5288	−	10.3254i	−1.63211	−	0.396254i
$680$			14.2226i			0.545411i
$681$	−2.30631	+	43.3578i	−0.0883781	+	1.66148i
$682$	−3.54031	+	2.04400i	−0.135565	+	0.0782687i
$683$	20.2102	−	11.6684i	0.773324	−	0.446479i	−0.0607353	−	0.998154i	$-0.519345\pi$
$683$	20.2102	−	11.6684i	0.773324	−	0.446479i	0.834059	+	0.551675i	$0.186011\pi$
$684$	−2.68169	+	1.18894i	−0.102537	+	0.0454603i
$685$		−	57.7249i		−	2.20556i
$686$	−17.5049	+	6.04800i	−0.668340	+	0.230914i
$687$	−16.3258	−	32.1032i	−0.622867	−	1.22481i
$688$	1.24980	−	2.16471i	0.0476480	−	0.0825288i
$689$	−13.0066	−	22.5281i	−0.495512	−	0.858251i
$690$	−4.41828	−	2.87418i	−0.168201	−	0.109418i
$691$	13.4781	+	7.78158i	0.512731	+	0.296025i	0.733955	−	0.679198i	$-0.237672\pi$
$691$	13.4781	+	7.78158i	0.512731	+	0.296025i	−0.221225	+	0.975223i	$0.571005\pi$
$692$	24.8808			0.945827
$693$	21.3602	−	18.0915i	0.811408	−	0.687241i
$694$	7.68032			0.291541
$695$	−43.7305	−	25.2478i	−1.65879	−	0.957704i
$696$	−6.16257	−	4.00888i	−0.233591	−	0.151956i
$697$	−18.1973	−	31.5187i	−0.689273	−	1.19386i
$698$	−7.88353	+	13.6547i	−0.298396	+	0.516837i
$699$	3.88510	+	7.63970i	0.146948	+	0.288960i
$700$	8.15709	+	7.78055i	0.308309	+	0.294077i
$701$		−	24.7791i		−	0.935894i	−0.883757	−	0.467947i	$-0.844994\pi$
$701$		−	24.7791i		−	0.935894i	0.883757	−	0.467947i	$-0.155006\pi$
$702$	−22.9172	−	18.6472i	−0.864954	−	0.703795i
$703$	2.68494	−	1.55015i	0.101264	−	0.0584650i
$704$	3.05420	−	1.76334i	0.115109	−	0.0664585i
$705$	2.95605	−	55.5727i	0.111331	−	2.09299i
$706$			21.9476i			0.826009i
$707$	−24.7115	+	7.25115i	−0.929371	+	0.272708i
$708$	−6.00541	+	3.05399i	−0.225697	+	0.114776i
$709$	12.3205	−	21.3398i	0.462708	−	0.801433i	−0.536387	−	0.843972i	$-0.680211\pi$
$709$	12.3205	−	21.3398i	0.462708	−	0.801433i	0.999095	+	0.0425387i	$0.0135446\pi$
$710$	−9.37824	−	16.2436i	−0.351959	−	0.609611i
$711$	−3.68831	−	0.393494i	−0.138322	−	0.0147572i
$712$	−13.9135	−	8.03294i	−0.521429	−	0.301047i
$713$	1.15916			0.0434109
$714$	14.6907	+	15.5848i	0.549787	+	0.583246i
$715$	−61.0230			−2.28213
$716$	−6.35355	−	3.66823i	−0.237443	−	0.137088i
$717$	−14.4850	+	22.2667i	−0.540952	+	0.831567i
$718$	−3.24641	−	5.62294i	−0.121155	−	0.209846i
$719$	7.09273	−	12.2850i	0.264514	−	0.458152i	−0.702922	−	0.711267i	$-0.748122\pi$
$719$	7.09273	−	12.2850i	0.264514	−	0.458152i	0.967436	+	0.253115i	$0.0814551\pi$
$720$	5.37769	−	7.37745i	0.200415	−	0.274941i
$721$	−22.0764	+	23.1448i	−0.822170	+	0.861958i
$722$			18.0439i			0.671524i
$723$	13.5529	+	0.720911i	0.504036	+	0.0268110i
$724$	−18.3687	+	10.6052i	−0.682667	+	0.394138i
$725$	−15.6618	+	9.04236i	−0.581665	+	0.335825i
$726$	−2.48632	−	0.132254i	−0.0922762	−	0.00490840i
$727$		−	37.6549i		−	1.39654i	−0.715833	−	0.698271i	$-0.753953\pi$
$727$		−	37.6549i		−	1.39654i	0.715833	−	0.698271i	$-0.246047\pi$
$728$	3.54929	−	14.6190i	0.131546	−	0.541815i
$729$	−25.6391	−	8.46394i	−0.949595	−	0.313479i
$730$	3.47864	−	6.02519i	0.128750	−	0.223002i
$731$	−5.84111	−	10.1171i	−0.216041	−	0.374195i
$732$	2.07266	−	3.18616i	0.0766079	−	0.117764i
$733$	4.65799	+	2.68929i	0.172047	+	0.0993313i	0.583551	−	0.812077i	$-0.301663\pi$
$733$	4.65799	+	2.68929i	0.172047	+	0.0993313i	−0.411504	+	0.911408i	$0.634996\pi$
$734$	35.7682			1.32023
$735$	36.8955	+	0.217687i	1.36091	+	0.00802952i
$736$	−1.00000			−0.0368605
$737$	1.38773	+	0.801204i	0.0511176	+	0.0295127i
$738$	−2.47831	+	23.2298i	−0.0912280	+	0.855100i
$739$	5.74650	+	9.95323i	0.211388	+	0.366135i	0.952149	−	0.305633i	$-0.0988682\pi$
$739$	5.74650	+	9.95323i	0.211388	+	0.366135i	−0.740761	+	0.671769i	$0.765535\pi$
$740$	−4.82436	+	8.35604i	−0.177347	+	0.307174i
$741$	8.58371	−	4.36516i	0.315330	−	0.160358i
$742$	2.85579	−	11.7625i	0.104839	−	0.431816i
$743$		−	48.1050i		−	1.76480i	−0.470499	−	0.882400i	$-0.655926\pi$
$743$		−	48.1050i		−	1.76480i	0.470499	−	0.882400i	$-0.344074\pi$
$744$	−0.106645	+	2.00489i	−0.00390980	+	0.0735029i
$745$	−38.8985	+	22.4581i	−1.42513	+	0.822800i
$746$	−30.2317	+	17.4543i	−1.10686	+	0.639047i
$747$	−2.27268	−	5.12610i	−0.0831530	−	0.187554i
$748$		−	16.4825i		−	0.602660i
$749$	26.9910	−	28.2973i	0.986231	−	1.03396i
$750$	1.76637	+	3.47341i	0.0644986	+	0.126831i
$751$	−9.05517	+	15.6840i	−0.330428	+	0.572318i	−0.982596	−	0.185757i	$-0.940526\pi$
$751$	−9.05517	+	15.6840i	−0.330428	+	0.572318i	0.652168	+	0.758075i	$0.273860\pi$
$752$	−5.27913	−	9.14372i	−0.192510	−	0.333437i
$753$	−0.929598	−	0.604723i	−0.0338764	−	0.0220373i
$754$	20.9009	+	12.0672i	0.761167	+	0.439460i
$755$	−24.3612			−0.886594
$756$	−1.72754	−	13.6388i	−0.0628301	−	0.496037i
$757$	8.15678			0.296463			0.148232	−	0.988953i	$-0.452642\pi$
$757$	8.15678			0.296463			0.148232	+	0.988953i	$0.452642\pi$
$758$	15.8572	+	9.15518i	0.575961	+	0.332531i
$759$	5.12033	+	3.33088i	0.185856	+	0.120903i
$760$	1.48781	+	2.57696i	0.0539685	+	0.0934762i
$761$	−0.321462	+	0.556789i	−0.0116530	+	0.0201836i	−0.871793	−	0.489874i	$-0.837043\pi$
$761$	−0.321462	+	0.556789i	−0.0116530	+	0.0201836i	0.860140	+	0.510058i	$0.170376\pi$
$762$	−7.50340	−	14.7548i	−0.271819	−	0.534509i
$763$	−42.6543	+	12.5161i	−1.54419	+	0.453115i
$764$		−	5.28644i		−	0.191257i
$765$	−17.2935	−	39.0060i	−0.625248	−	1.41027i
$766$	−2.48795	+	1.43642i	−0.0898934	+	0.0519000i
$767$	19.1542	−	11.0587i	0.691617	−	0.399305i
$768$	0.0920021	−	1.72961i	0.00331984	−	0.0624118i
$769$		−	54.5680i		−	1.96777i	−0.178794	−	0.983887i	$-0.557220\pi$
$769$		−	54.5680i		−	1.96777i	0.178794	−	0.983887i	$-0.442780\pi$
$770$	−20.5467	−	19.5983i	−0.740453	−	0.706273i
$771$	23.7224	−	12.0638i	0.854340	−	0.434466i
$772$	1.16570	−	2.01905i	0.0419544	−	0.0726672i
$773$	−9.53441	−	16.5141i	−0.342929	−	0.593970i	0.642046	−	0.766666i	$-0.278086\pi$
$773$	−9.53441	−	16.5141i	−0.342929	−	0.593970i	−0.984975	+	0.172696i	$0.944752\pi$
$774$	−0.795507	+	7.45646i	−0.0285939	+	0.268017i
$775$	4.27716	+	2.46942i	0.153640	+	0.0887042i
$776$	16.5414			0.593800
$777$	3.34467	+	14.1395i	0.119989	+	0.507253i
$778$	16.3195			0.585081
$779$	−6.59428	−	3.80721i	−0.236265	−	0.136407i
$780$	−16.3425	+	25.1222i	−0.585156	+	0.899520i
$781$	10.8684	+	18.8246i	0.388902	+	0.673598i
$782$	−2.33683	+	4.04750i	−0.0835647	+	0.144738i
$783$	21.7756	+	3.50134i	0.778195	+	0.125128i
$784$	5.89013	−	3.78238i	0.210362	−	0.135085i
$785$			11.4291i			0.407922i
$786$	−17.0752	−	0.908273i	−0.609052	−	0.0323970i
$787$	12.1476	−	7.01344i	0.433016	−	0.250002i	−0.267614	−	0.963526i	$-0.586235\pi$
$787$	12.1476	−	7.01344i	0.433016	−	0.250002i	0.700631	+	0.713524i	$0.252902\pi$
$788$	22.4246	−	12.9469i	0.798844	−	0.461213i
$789$	−17.4374	−	0.927542i	−0.620789	−	0.0330214i
$790$			3.76258i			0.133867i
$791$	−44.2336	−	10.7393i	−1.57276	−	0.381846i
$792$	−6.23219	+	8.54970i	−0.221451	+	0.303800i
$793$	−6.23895	+	10.8062i	−0.221552	+	0.383739i
$794$	−12.3262	−	21.3496i	−0.437439	−	0.757667i
$795$	−13.1493	+	20.2135i	−0.466358	+	0.716899i
$796$	23.8465	+	13.7678i	0.845216	+	0.487986i
$797$	−8.93003			−0.316318			−0.158159	−	0.987414i	$-0.550556\pi$
$797$	−8.93003			−0.316318			−0.158159	+	0.987414i	$0.550556\pi$
$798$	4.29210	+	1.28699i	0.151939	+	0.0455590i
$799$	−49.3456			−1.74572
$800$	−3.68988	−	2.13035i	−0.130457	−	0.0753193i
$801$	47.9256	+	5.11304i	1.69337	+	0.180660i
$802$	−6.21795	−	10.7698i	−0.219563	−	0.380295i
$803$	−4.03139	+	6.98257i	−0.142265	+	0.246410i
$804$	0.701489	−	0.356735i	0.0247396	−	0.0125811i
$805$	2.26696	+	7.72566i	0.0798998	+	0.272294i
$806$		−	6.59096i		−	0.232157i
$807$	−0.375419	+	7.05773i	−0.0132154	+	0.248444i
$808$	8.42978	−	4.86693i	0.296559	−	0.171218i
$809$	37.2478	−	21.5050i	1.30956	−	0.756076i	0.327539	−	0.944838i	$-0.393781\pi$
$809$	37.2478	−	21.5050i	1.30956	−	0.756076i	0.982023	+	0.188762i	$0.0604474\pi$
$810$	−5.77817	+	26.7718i	−0.203024	+	0.940665i
$811$			25.8254i			0.906854i	0.891293	+	0.453427i	$0.149799\pi$
$811$			25.8254i			0.906854i	−0.891293	+	0.453427i	$0.850201\pi$
$812$	3.16193	+	10.7757i	0.110962	+	0.378152i
$813$	11.9499	+	23.4985i	0.419102	+	0.824128i
$814$	5.59094	−	9.68379i	0.195962	−	0.339417i
$815$	−27.7200	−	48.0125i	−0.970990	−	1.68180i
$816$	−6.78559	−	4.41417i	−0.237543	−	0.154527i
$817$	−2.11668	−	1.22207i	−0.0740533	−	0.0427547i
$818$	19.7995			0.692275
$819$	8.04141	+	44.4088i	0.280989	+	1.55177i
$820$	23.6975			0.827554
$821$	−1.57039	−	0.906664i	−0.0548069	−	0.0316428i	0.472346	−	0.881413i	$-0.343407\pi$
$821$	−1.57039	−	0.906664i	−0.0548069	−	0.0316428i	−0.527153	+	0.849770i	$0.676741\pi$
$822$	27.5405	+	17.9157i	0.960587	+	0.624882i
$823$	−2.10323	−	3.64289i	−0.0733138	−	0.126983i	0.827038	−	0.562146i	$-0.190024\pi$
$823$	−2.10323	−	3.64289i	−0.0733138	−	0.126983i	−0.900352	+	0.435163i	$0.856691\pi$
$824$	6.04463	−	10.4696i	0.210575	−	0.364726i
$825$	11.7974	+	23.1986i	0.410734	+	0.807673i
$826$	10.0009	+	2.42809i	0.347977	+	0.0844841i
$827$		−	8.25878i		−	0.287186i	−0.989637	−	0.143593i	$-0.954134\pi$
$827$		−	8.25878i		−	0.287186i	0.989637	−	0.143593i	$-0.0458656\pi$
$828$	2.74254	−	1.21592i	0.0953100	−	0.0422561i
$829$	24.4639	−	14.1243i	0.849667	−	0.490556i	−0.0108712	−	0.999941i	$-0.503460\pi$
$829$	24.4639	−	14.1243i	0.849667	−	0.490556i	0.860539	+	0.509385i	$0.170127\pi$
$830$	−4.92591	+	2.84398i	−0.170981	+	0.0987158i
$831$	0.515701	−	9.69500i	0.0178895	−	0.336316i
$832$			5.68597i			0.197126i
$833$	−1.54499	−	32.6791i	−0.0535306	−	1.13226i
$834$	25.6181	−	13.0278i	0.887081	−	0.451116i
$835$	−0.0320571	+	0.0555244i	−0.00110938	+	0.00192150i
$836$	−1.72422	−	2.98643i	−0.0596333	−	0.103288i
$837$	−2.14531	−	5.62817i	−0.0741526	−	0.194538i
$838$	−23.8926	−	13.7944i	−0.825358	−	0.476520i
$839$	−35.9817			−1.24223			−0.621114	−	0.783720i	$-0.713319\pi$
$839$	−35.9817			−1.24223			−0.621114	+	0.783720i	$0.713319\pi$
$840$	−13.5709	+	3.21017i	−0.468241	+	0.110761i
$841$	10.9839			0.378755
$842$	4.19452	+	2.42171i	0.144553	+	0.0834575i
$843$	−0.537558	+	0.826350i	−0.0185145	+	0.0284610i
$844$	8.78323	+	15.2130i	0.302331	+	0.523653i
$845$	29.4124	−	50.9438i	1.01182	−	1.75252i
$846$	25.5963	+	18.6581i	0.880018	+	0.641477i
$847$	2.75210	+	2.62506i	0.0945634	+	0.0901983i
$848$			4.57497i			0.157105i
$849$	39.2542	+	2.08803i	1.34720	+	0.0716611i
$850$	−17.2452	+	9.95652i	−0.591505	+	0.341506i
$851$	−2.74586	+	1.58532i	−0.0941269	+	0.0543442i
$852$	10.6605	+	0.567057i	0.365222	+	0.0194271i
$853$			19.0791i			0.653256i	0.945153	+	0.326628i	$0.105912\pi$
$853$			19.0791i			0.653256i	−0.945153	+	0.326628i	$0.894088\pi$
$854$	−5.57122	+	1.63478i	−0.190643	+	0.0559409i
$855$	−7.21376	−	5.25837i	−0.246705	−	0.179833i
$856$	−7.39027	+	12.8003i	−0.252594	+	0.437506i
$857$	−4.52673	−	7.84052i	−0.154630	−	0.267827i	0.778294	−	0.627900i	$-0.216085\pi$
$857$	−4.52673	−	7.84052i	−0.154630	−	0.267827i	−0.932924	+	0.360073i	$0.882752\pi$
$858$	18.9393	−	29.1141i	0.646577	−	0.993937i
$859$	14.2201	+	8.20997i	0.485183	+	0.280120i	0.722574	−	0.691294i	$-0.242959\pi$
$859$	14.2201	+	8.20997i	0.485183	+	0.280120i	−0.237391	+	0.971414i	$0.576292\pi$
$860$	7.60661			0.259383
$861$	25.9672	−	24.4776i	0.884961	−	0.834195i
$862$	30.6463			1.04382
$863$	39.3064	+	22.6936i	1.33801	+	0.772498i	0.986512	−	0.163692i	$-0.0523403\pi$
$863$	39.3064	+	22.6936i	1.33801	+	0.772498i	0.351494	+	0.936190i	$0.385674\pi$
$864$	1.85074	+	4.85538i	0.0629635	+	0.165184i
$865$	37.8579	+	65.5718i	1.28721	+	2.22951i
$866$	−16.9968	+	29.4394i	−0.577576	+	1.00039i
$867$	−7.47705	+	3.80238i	−0.253934	+	0.129136i
$868$	2.11677	−	2.21921i	0.0718477	−	0.0753248i
$869$		−	4.36044i		−	0.147918i
$870$	1.18837	−	22.3408i	0.0402894	−	0.757425i
$871$	−2.23739	+	1.29176i	−0.0758111	+	0.0437696i
$872$	14.5506	−	8.40077i	0.492744	−	0.284486i
$873$	−45.3654	+	20.1130i	−1.53539	+	0.680720i
$874$			0.977812i			0.0330750i
$875$	1.40436	−	5.78434i	0.0474760	−	0.195546i
$876$	1.79497	+	3.52966i	0.0606465	+	0.119256i
$877$	21.6964	−	37.5793i	0.732637	−	1.26896i	−0.223116	−	0.974792i	$-0.571623\pi$
$877$	21.6964	−	37.5793i	0.732637	−	1.26896i	0.955752	−	0.294172i	$-0.0950439\pi$
$878$	−5.45542	−	9.44907i	−0.184112	−	0.318891i
$879$	10.2663	+	6.67846i	0.346274	+	0.225259i
$880$	9.29436	+	5.36610i	0.313313	+	0.180891i
$881$	26.7940			0.902712			0.451356	−	0.892344i	$-0.350941\pi$
$881$	26.7940			0.902712			0.451356	+	0.892344i	$0.350941\pi$
$882$	−11.5549	+	17.5353i	−0.389072	+	0.590443i
$883$	11.9573			0.402396			0.201198	−	0.979551i	$-0.435517\pi$
$883$	11.9573			0.402396			0.201198	+	0.979551i	$0.435517\pi$
$884$	23.0140	+	13.2871i	0.774044	+	0.446894i
$885$	−17.1863	−	11.1800i	−0.577709	−	0.375812i
$886$	−8.54892	−	14.8072i	−0.287207	−	0.497457i
$887$	−25.1650	+	43.5870i	−0.844957	+	1.46351i	0.0407022	+	0.999171i	$0.487041\pi$
$887$	−25.1650	+	43.5870i	−0.844957	+	1.46351i	−0.885659	+	0.464337i	$0.846293\pi$
$888$	−2.48936	−	4.89511i	−0.0835374	−	0.164269i
$889$	−5.96562	+	24.5714i	−0.200080	+	0.824099i
$890$		−	48.8907i		−	1.63882i
$891$	6.69631	−	31.0258i	0.224335	−	1.03940i
$892$	5.19364	−	2.99855i	0.173896	−	0.100399i
$893$	−8.94084	+	5.16200i	−0.299194	+	0.172740i
$894$	1.35793	−	25.5286i	0.0454161	−	0.853805i
$895$		−	22.3259i		−	0.746271i
$896$	−1.82612	+	1.91449i	−0.0610064	+	0.0639588i
$897$	−8.77848	+	4.46421i	−0.293105	+	0.149056i
$898$	−7.57645	+	13.1228i	−0.252829	+	0.437913i
$899$	2.46005	+	4.26093i	0.0820473	+	0.142110i
$900$	12.7100	+	1.35599i	0.423666	+	0.0451996i
$901$	18.5172	+	10.6909i	0.616898	+	0.356166i
$902$	−27.4630			−0.914418
$903$	8.33515	−	7.85700i	0.277377	−	0.261465i
$904$	17.2044			0.572210
$905$	−55.8985	−	32.2730i	−1.85813	−	1.07279i
$906$	7.56082	−	11.6227i	0.251191	−	0.386139i
$907$	0.351720	+	0.609197i	0.0116787	+	0.0202280i	0.871806	−	0.489852i	$-0.162949\pi$
$907$	0.351720	+	0.609197i	0.0116787	+	0.0202280i	−0.860127	+	0.510080i	$0.829616\pi$
$908$	−12.5340	+	21.7096i	−0.415956	+	0.720457i
$909$	−17.2012	+	23.5977i	−0.570529	+	0.782686i
$910$	43.9279	−	12.8899i	1.45620	−	0.427295i
$911$		−	5.61577i		−	0.186059i	−0.995663	−	0.0930294i	$-0.970345\pi$
$911$		−	5.61577i		−	0.186059i	0.995663	−	0.0930294i	$-0.0296551\pi$
$912$	−1.69123	−	0.0899608i	−0.0560022	−	0.00297890i
$913$	5.70862	−	3.29587i	0.188928	−	0.109078i
$914$	12.2577	−	7.07697i	0.405448	−	0.234085i
$915$	11.5506	+	0.614407i	0.381852	+	0.0203117i
$916$		−	20.7938i		−	0.687047i
$917$	18.9005	+	18.0280i	0.624149	+	0.595338i
$918$	23.9770	+	3.85531i	0.791360	+	0.127244i
$919$	−14.9481	+	25.8909i	−0.493092	+	0.854061i	−0.999968	−	0.00795807i	$-0.997467\pi$
$919$	−14.9481	+	25.8909i	−0.493092	+	0.854061i	0.506876	+	0.862019i	$0.330800\pi$
$920$	−1.52157	−	2.63544i	−0.0501647	−	0.0868878i
$921$	−5.42565	+	8.34048i	−0.178781	+	0.274828i
$922$	−35.3445	−	20.4062i	−1.16401	−	0.672041i
$923$	−35.0456			−1.15354
$924$	15.7273	−	3.72025i	0.517390	−	0.122387i
$925$	−13.5092			−0.444179
$926$	28.8714	+	16.6689i	0.948772	+	0.547774i
$927$	−3.84747	+	36.0631i	−0.126367	+	1.18447i
$928$	−2.12227	−	3.67588i	−0.0696669	−	0.120667i
$929$	28.3091	−	49.0328i	0.928792	−	1.60872i	0.143446	−	0.989658i	$-0.454182\pi$
$929$	28.3091	−	49.0328i	0.928792	−	1.60872i	0.785346	−	0.619057i	$-0.212485\pi$
$930$	−5.44603	+	2.76953i	−0.178582	+	0.0908163i
$931$	−3.69846	−	5.75944i	−0.121212	−	0.188758i
$932$			4.94837i			0.162089i
$933$	−2.67448	+	50.2793i	−0.0875587	+	1.64607i
$934$	−9.44443	+	5.45274i	−0.309031	+	0.178419i
$935$	43.4386	−	25.0793i	1.42059	−	0.820180i
$936$	−6.91368	−	15.5940i	−0.225981	−	0.509707i
$937$			10.0984i			0.329901i	0.986302	+	0.164950i	$0.0527464\pi$
$937$			10.0984i			0.329901i	−0.986302	+	0.164950i	$0.947254\pi$
$938$	−1.16820	−	0.283624i	−0.0381432	−	0.00926066i
$939$	−2.76585	−	5.43880i	−0.0902601	−	0.177489i
$940$	16.0651	−	27.8256i	0.523987	−	0.907572i
$941$	19.5579	+	33.8752i	0.637569	+	1.10430i	0.985965	+	0.166954i	$0.0533931\pi$
$941$	19.5579	+	33.8752i	0.637569	+	1.10430i	−0.348396	+	0.937347i	$0.613274\pi$
$942$	−5.45282	−	3.54717i	−0.177662	−	0.115573i
$943$	6.74392	+	3.89360i	0.219612	+	0.126793i
$944$	−3.88981			−0.126602
$945$	33.3155	−	25.3051i	1.08375	−	0.823176i
$946$	−8.81528			−0.286609
$947$	−23.5396	−	13.5906i	−0.764935	−	0.441636i	0.0661297	−	0.997811i	$-0.478935\pi$
$947$	−23.5396	−	13.5906i	−0.764935	−	0.441636i	−0.831065	+	0.556175i	$0.812268\pi$
$948$	−1.79513	−	1.16777i	−0.0583030	−	0.0379273i
$949$	−6.49969	−	11.2578i	−0.210989	−	0.365444i
$950$	−2.08308	+	3.60801i	−0.0675841	+	0.117059i
$951$	−5.97229	−	11.7440i	−0.193665	−	0.380825i
$952$	3.48159	+	11.8651i	0.112839	+	0.384549i
$953$		−	18.6849i		−	0.605263i	−0.953108	−	0.302631i	$-0.902135\pi$
$953$		−	18.6849i		−	0.605263i	0.953108	−	0.302631i	$-0.0978651\pi$
$954$	−5.56280	−	12.5471i	−0.180102	−	0.406226i
$955$	13.9321	−	8.04368i	0.450831	−	0.260287i
$956$	−13.2818	+	7.66824i	−0.429563	+	0.248009i
$957$	−1.37719	+	25.8907i	−0.0445183	+	0.836928i
$958$		−	22.0950i		−	0.713858i
$959$	−14.1307	−	48.1565i	−0.456303	−	1.55505i
$960$	4.69825	−	2.38925i	0.151635	−	0.0771127i
$961$	−14.8282	+	25.6831i	−0.478328	+	0.828489i
$962$	9.01411	+	15.6129i	0.290626	+	0.503380i
$963$	4.70398	−	44.0914i	0.151584	−	1.42083i
$964$	6.78601	+	3.91790i	0.218563	+	0.126187i
$965$	7.09477			0.228389
$966$	−4.38949	−	1.31620i	−0.141230	−	0.0423479i
$967$	31.5483			1.01452			0.507262	−	0.861792i	$-0.330657\pi$
$967$	31.5483			1.01452			0.507262	+	0.861792i	$0.330657\pi$
$968$	−1.24492	−	0.718755i	−0.0400132	−	0.0231017i
$969$	−4.31622	+	6.63503i	−0.138657	+	0.213148i
$970$	25.1688	+	43.5937i	0.808123	+	1.39971i
$971$	12.0558	−	20.8812i	0.386888	−	0.670109i	−0.605142	−	0.796118i	$-0.706883\pi$
$971$	12.0558	−	20.8812i	0.386888	−	0.670109i	0.992029	+	0.126009i	$0.0402168\pi$
$972$	−10.9795	−	11.0658i	−0.352167	−	0.354934i
$973$	−42.6623	−	10.3578i	−1.36769	−	0.332057i
$974$			38.3116i			1.22758i
$975$	−41.9018	−	2.22887i	−1.34193	−	0.0713808i
$976$	1.90050	−	1.09725i	0.0608334	−	0.0351222i
$977$	−24.5854	+	14.1944i	−0.786556	+	0.454118i	−0.838749	−	0.544519i	$-0.816712\pi$
$977$	−24.5854	+	14.1944i	−0.786556	+	0.454118i	0.0521929	+	0.998637i	$0.483379\pi$
$978$	31.5100	+	1.67610i	1.00758	+	0.0535957i
$979$			56.6593i			1.81084i
$980$	18.9305	+	9.76790i	0.604712	+	0.312024i
$981$	−29.6909	+	40.7318i	−0.947956	+	1.30046i
$982$	−12.3895	+	21.4592i	−0.395364	+	0.684790i
$983$	−1.76916	−	3.06427i	−0.0564273	−	0.0977350i	0.836432	−	0.548071i	$-0.184638\pi$
$983$	−1.76916	−	3.06427i	−0.0564273	−	0.0977350i	−0.892859	+	0.450336i	$0.851304\pi$
$984$	−7.35485	+	11.3061i	−0.234464	+	0.360425i
$985$	68.2412	+	39.3991i	2.17435	+	1.25536i
$986$	−19.8375			−0.631754
$987$	−11.1378	−	47.0847i	−0.354519	−	1.49872i
$988$	5.55981			0.176881
$989$	2.16471	+	1.24980i	0.0688338	+	0.0397412i
$990$	−32.0149	−	3.41557i	−1.01750	−	0.108554i
$991$	2.95871	+	5.12463i	0.0939864	+	0.162789i	0.909185	−	0.416392i	$-0.136706\pi$
$991$	2.95871	+	5.12463i	0.0939864	+	0.162789i	−0.815199	+	0.579181i	$0.803372\pi$
$992$	−0.579580	+	1.00386i	−0.0184017	+	0.0318727i
$993$	−53.3811	+	27.1464i	−1.69400	+	0.861465i
$994$	−11.8000	−	11.2553i	−0.374274	−	0.356998i
$995$			83.7945i			2.65646i
$996$	0.171962	−	3.23282i	0.00544881	−	0.102436i
$997$	−16.4777	+	9.51342i	−0.521855	+	0.301293i	−0.737693	−	0.675136i	$-0.764085\pi$
$997$	−16.4777	+	9.51342i	−0.521855	+	0.301293i	0.215838	+	0.976429i	$0.430752\pi$
$998$	19.4311	−	11.2185i	0.615080	−	0.355117i
$999$	12.7792	+	10.3982i	0.404317	+	0.328984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.11	✓	56
3.2	odd	2	inner	966.2.l.d.47.22	yes	56
7.3	odd	6	inner	966.2.l.d.185.22	yes	56
21.17	even	6	inner	966.2.l.d.185.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.11	✓	56	1.1	even	1	trivial
966.2.l.d.47.22	yes	56	3.2	odd	2	inner
966.2.l.d.185.11	yes	56	21.17	even	6	inner
966.2.l.d.185.22	yes	56	7.3	odd	6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.45188 + 0.944479i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.52157 + 2.63544i) q^{5} +(-0.785127 - 1.54388i) q^{6} +(-0.624219 + 2.57106i) q^{7} -1.00000i q^{8} +(1.21592 + 2.74254i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.45188 + 0.944479i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.52157 + 2.63544i) q^{5} +(-0.785127 - 1.54388i) q^{6} +(-0.624219 + 2.57106i) q^{7} -1.00000i q^{8} +(1.21592 + 2.74254i) q^{9} +(2.63544 - 1.52157i) q^{10} +(-3.05420 + 1.76334i) q^{11} +(-0.0920021 + 1.72961i) q^{12} -5.68597i q^{13} +(1.82612 - 1.91449i) q^{14} +(-4.69825 + 2.38925i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.33683 + 4.04750i) q^{17} +(0.318255 - 2.98307i) q^{18} +(0.846810 + 0.488906i) q^{19} -3.04314 q^{20} +(-3.33460 + 3.14331i) q^{21} +3.52669 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.944479 - 1.45188i) q^{24} +(-2.13035 - 3.68988i) q^{25} +(-2.84299 + 4.92420i) q^{26} +(-0.824904 + 5.13026i) q^{27} +(-2.53871 + 0.744941i) q^{28} -4.24454i q^{29} +(5.26343 + 0.279975i) q^{30} +(-1.00386 + 0.579580i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.09977 - 0.324463i) q^{33} -4.67365i q^{34} +(-5.82607 - 5.55714i) q^{35} +(-1.76715 + 2.42429i) q^{36} +(1.58532 - 2.74586i) q^{37} +(-0.488906 - 0.846810i) q^{38} +(5.37028 - 8.25536i) q^{39} +(2.63544 + 1.52157i) q^{40} -7.78720 q^{41} +(4.45951 - 1.05489i) q^{42} -2.49959 q^{43} +(-3.05420 - 1.76334i) q^{44} +(-9.07790 - 0.968494i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-5.27913 + 9.14372i) q^{47} +(-1.54388 + 0.785127i) q^{48} +(-6.22070 - 3.20981i) q^{49} +4.26070i q^{50} +(-0.429986 + 8.08357i) q^{51} +(4.92420 - 2.84299i) q^{52} +(3.96204 - 2.28749i) q^{53} +(3.27952 - 4.03048i) q^{54} -10.7322i q^{55} +(2.57106 + 0.624219i) q^{56} +(0.767706 + 1.50963i) q^{57} +(-2.12227 + 3.67588i) q^{58} +(1.94490 + 3.36867i) q^{59} +(-4.41828 - 2.87418i) q^{60} +(-1.90050 - 1.09725i) q^{61} +1.15916 q^{62} +(-7.81024 + 1.41425i) q^{63} -1.00000 q^{64} +(14.9850 + 8.65161i) q^{65} +(5.12033 + 3.33088i) q^{66} +(-0.227183 - 0.393493i) q^{67} +(-2.33683 + 4.04750i) q^{68} +(-0.785127 - 1.54388i) q^{69} +(2.26696 + 7.72566i) q^{70} -6.16353i q^{71} +(2.74254 - 1.21592i) q^{72} +(1.97992 - 1.14311i) q^{73} +(-2.74586 + 1.58532i) q^{74} +(0.391994 - 7.36933i) q^{75} +0.977812i q^{76} +(-2.62717 - 8.95324i) q^{77} +(-8.77848 + 4.46421i) q^{78} +(-0.618207 + 1.07077i) q^{79} +(-1.52157 - 2.63544i) q^{80} +(-6.04308 + 6.66942i) q^{81} +(6.74392 + 3.89360i) q^{82} -1.86911 q^{83} +(-4.38949 - 1.31620i) q^{84} -14.2226 q^{85} +(2.16471 + 1.24980i) q^{86} +(4.00888 - 6.16257i) q^{87} +(1.76334 + 3.05420i) q^{88} +(8.03294 - 13.9135i) q^{89} +(7.37745 + 5.37769i) q^{90} +(14.6190 + 3.54929i) q^{91} -1.00000i q^{92} +(-2.00489 - 0.106645i) q^{93} +(9.14372 - 5.27913i) q^{94} +(-2.57696 + 1.48781i) q^{95} +(1.72961 + 0.0920021i) q^{96} +16.5414i q^{97} +(3.78238 + 5.89013i) q^{98} +(-8.54970 - 6.23219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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