LMFDB - Embedded newform 429.2.be.a.89.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(89,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("429.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.be (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.19
Character	$\chi$	$=$	429.89
Dual form			429.2.be.a.188.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.745893 - 0.199861i) q^{2} +(-0.815569 + 1.52802i) q^{3} +(-1.21564 - 0.701849i) q^{4} +(-0.458199 + 0.458199i) q^{5} +(0.913720 - 0.976739i) q^{6} +(-0.672164 - 2.50855i) q^{7} +(1.85853 + 1.85853i) q^{8} +(-1.66969 - 2.49241i) q^{9} +O(q^{10})$	\(q+(-0.745893 - 0.199861i) q^{2} +(-0.815569 + 1.52802i) q^{3} +(-1.21564 - 0.701849i) q^{4} +(-0.458199 + 0.458199i) q^{5} +(0.913720 - 0.976739i) q^{6} +(-0.672164 - 2.50855i) q^{7} +(1.85853 + 1.85853i) q^{8} +(-1.66969 - 2.49241i) q^{9} +(0.433344 - 0.250191i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(2.06388 - 1.28511i) q^{12} +(3.60061 - 0.188710i) q^{13} +2.00545i q^{14} +(-0.326445 - 1.07383i) q^{15} +(0.388884 + 0.673567i) q^{16} +(-0.0349370 + 0.0605127i) q^{17} +(0.747275 + 2.19278i) q^{18} +(1.37772 - 0.369159i) q^{19} +(0.878592 - 0.235418i) q^{20} +(4.38131 + 1.01882i) q^{21} +(0.386103 - 0.668749i) q^{22} +(1.86776 + 3.23505i) q^{23} +(-4.35563 + 1.32411i) q^{24} +4.58011i q^{25} +(-2.72339 - 0.578866i) q^{26} +(5.17021 - 0.518589i) q^{27} +(-0.943516 + 3.52125i) q^{28} +(4.65969 - 2.69028i) q^{29} +(0.0288753 + 0.866207i) q^{30} +(5.63534 + 5.63534i) q^{31} +(-1.51598 - 5.65772i) q^{32} +(-1.26487 - 1.18326i) q^{33} +(0.0381535 - 0.0381535i) q^{34} +(1.45740 + 0.841432i) q^{35} +(0.280445 + 4.20175i) q^{36} +(-7.05285 - 1.88981i) q^{37} -1.10141 q^{38} +(-2.64819 + 5.65571i) q^{39} -1.70315 q^{40} +(9.20846 + 2.46740i) q^{41} +(-3.06437 - 1.63558i) q^{42} +(6.60798 + 3.81512i) q^{43} +(0.992565 - 0.992565i) q^{44} +(1.90707 + 0.376970i) q^{45} +(-0.746585 - 2.78629i) q^{46} +(0.845190 + 0.845190i) q^{47} +(-1.34639 + 0.0448823i) q^{48} +(0.221152 - 0.127682i) q^{49} +(0.915387 - 3.41627i) q^{50} +(-0.0639711 - 0.102737i) q^{51} +(-4.50949 - 2.29768i) q^{52} -10.8272i q^{53} +(-3.96007 - 0.646513i) q^{54} +(-0.323996 - 0.561177i) q^{55} +(3.41298 - 5.91145i) q^{56} +(-0.559544 + 2.40626i) q^{57} +(-4.01332 + 1.07536i) q^{58} +(1.32319 - 0.354549i) q^{59} +(-0.356829 + 1.53451i) q^{60} +(-1.29147 + 2.23689i) q^{61} +(-3.07707 - 5.32965i) q^{62} +(-5.13004 + 5.86382i) q^{63} +2.96751i q^{64} +(-1.56333 + 1.73626i) q^{65} +(0.706969 + 1.13538i) q^{66} +(0.757062 - 2.82539i) q^{67} +(0.0849417 - 0.0490411i) q^{68} +(-6.46650 + 0.215563i) q^{69} +(-0.918896 - 0.918896i) q^{70} +(-1.52818 - 5.70324i) q^{71} +(1.52905 - 7.73539i) q^{72} +(7.18240 - 7.18240i) q^{73} +(4.88297 + 2.81919i) q^{74} +(-6.99850 - 3.73539i) q^{75} +(-1.93390 - 0.518188i) q^{76} +2.59704 q^{77} +(3.10563 - 3.68928i) q^{78} -6.80061 q^{79} +(-0.486815 - 0.130442i) q^{80} +(-3.42425 + 8.32313i) q^{81} +(-6.37539 - 3.68083i) q^{82} +(-5.80460 + 5.80460i) q^{83} +(-4.61104 - 4.31354i) q^{84} +(-0.0117188 - 0.0437350i) q^{85} +(-4.16635 - 4.16635i) q^{86} +(0.310492 + 9.31421i) q^{87} +(-2.27622 + 1.31418i) q^{88} +(3.30626 - 12.3391i) q^{89} +(-1.34713 - 0.662330i) q^{90} +(-2.89359 - 8.90547i) q^{91} -5.24353i q^{92} +(-13.2069 + 4.01491i) q^{93} +(-0.461500 - 0.799342i) q^{94} +(-0.462122 + 0.800419i) q^{95} +(9.88151 + 2.29781i) q^{96} +(9.17280 - 2.45784i) q^{97} +(-0.190475 + 0.0510375i) q^{98} +(2.83963 - 0.967716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) $ 184 * q - 12 * q^6 + 12 * q^7	$ 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) $ 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−0.745893	−	0.199861i	−0.527426	−	0.141323i	−0.0147266	−	0.999892i	$-0.504688\pi$
$2$	−0.745893	−	0.199861i	−0.527426	−	0.141323i	−0.512699	+	0.858568i	$0.671354\pi$
$3$	−0.815569	+	1.52802i	−0.470869	+	0.882203i
$3$	−0.815569	+	1.52802i	−0.470869	+	0.882203i
$4$	−1.21564	−	0.701849i	−0.607819	−	0.350925i
$5$	−0.458199	+	0.458199i	−0.204913	+	0.204913i	−0.802101	−	0.597188i	$-0.796285\pi$
$5$	−0.458199	+	0.458199i	−0.204913	+	0.204913i	0.597188	+	0.802101i	$0.296285\pi$
$6$	0.913720	−	0.976739i	0.373025	−	0.398752i
$7$	−0.672164	−	2.50855i	−0.254054	−	0.948143i	−0.968614	−	0.248569i	$-0.920040\pi$
$7$	−0.672164	−	2.50855i	−0.254054	−	0.948143i	0.714560	−	0.699574i	$-0.246627\pi$
$8$	1.85853	+	1.85853i	0.657089	+	0.657089i
$9$	−1.66969	−	2.49241i	−0.556564	−	0.830804i
$10$	0.433344	−	0.250191i	0.137035	−	0.0791175i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$11$	−0.258819	+	0.965926i	−0.0780369	+	0.291238i
$12$	2.06388	−	1.28511i	0.595790	−	0.370981i
$13$	3.60061	−	0.188710i	0.998629	−	0.0523386i
$13$	3.60061	−	0.188710i	0.998629	−	0.0523386i
$14$			2.00545i			0.535979i
$15$	−0.326445	−	1.07383i	−0.0842877	−	0.277262i
$16$	0.388884	+	0.673567i	0.0972211	+	0.168392i
$17$	−0.0349370	+	0.0605127i	−0.00847348	+	0.0146765i	−0.870231	−	0.492644i	$-0.836031\pi$
$17$	−0.0349370	+	0.0605127i	−0.00847348	+	0.0146765i	0.861758	+	0.507320i	$0.169364\pi$
$18$	0.747275	+	2.19278i	0.176134	+	0.516843i
$19$	1.37772	−	0.369159i	0.316070	−	0.0846908i	−0.0972962	−	0.995255i	$-0.531019\pi$
$19$	1.37772	−	0.369159i	0.316070	−	0.0846908i	0.413367	+	0.910565i	$0.364353\pi$
$20$	0.878592	−	0.235418i	0.196459	−	0.0526411i
$21$	4.38131	+	1.01882i	0.956081	+	0.222324i
$22$	0.386103	−	0.668749i	0.0823174	−	0.142578i
$23$	1.86776	+	3.23505i	0.389454	+	0.674554i	0.992376	−	0.123246i	$-0.0393304\pi$
$23$	1.86776	+	3.23505i	0.389454	+	0.674554i	−0.602922	+	0.797800i	$0.705997\pi$
$24$	−4.35563	+	1.32411i	−0.889088	+	0.270283i
$25$			4.58011i			0.916021i
$26$	−2.72339	−	0.578866i	−0.534100	−	0.113525i
$27$	5.17021	−	0.518589i	0.995007	−	0.0998025i
$28$	−0.943516	+	3.52125i	−0.178308	+	0.665454i
$29$	4.65969	−	2.69028i	0.865283	−	0.499572i	−0.000494659	−	1.00000i	$-0.500157\pi$
$29$	4.65969	−	2.69028i	0.865283	−	0.499572i	0.865778	+	0.500428i	$0.166824\pi$
$30$	0.0288753	+	0.866207i	0.00527189	+	0.158147i
$31$	5.63534	+	5.63534i	1.01214	+	1.01214i	0.999925	+	0.0122118i	$0.00388724\pi$
$31$	5.63534	+	5.63534i	1.01214	+	1.01214i	0.0122118	+	0.999925i	$0.496113\pi$
$32$	−1.51598	−	5.65772i	−0.267990	−	1.00015i
$33$	−1.26487	−	1.18326i	−0.220186	−	0.205979i
$34$	0.0381535	−	0.0381535i	0.00654326	−	0.00654326i
$35$	1.45740	+	0.841432i	0.246346	+	0.142228i
$36$	0.280445	+	4.20175i	0.0467408	+	0.700291i
$37$	−7.05285	−	1.88981i	−1.15948	−	0.310682i	−0.372723	−	0.927943i	$-0.621576\pi$
$37$	−7.05285	−	1.88981i	−1.15948	−	0.310682i	−0.786759	+	0.617261i	$0.788242\pi$
$38$	−1.10141			−0.178673
$39$	−2.64819	+	5.65571i	−0.424051	+	0.905639i
$40$	−1.70315			−0.269292
$41$	9.20846	+	2.46740i	1.43812	+	0.385343i	0.891875	−	0.452283i	$-0.149390\pi$
$41$	9.20846	+	2.46740i	1.43812	+	0.385343i	0.546245	+	0.837626i	$0.316057\pi$
$42$	−3.06437	−	1.63558i	−0.472843	−	0.252376i
$43$	6.60798	+	3.81512i	1.00771	+	0.581800i	0.910520	−	0.413466i	$-0.135682\pi$
$43$	6.60798	+	3.81512i	1.00771	+	0.581800i	0.0971877	+	0.995266i	$0.469015\pi$
$44$	0.992565	−	0.992565i	0.149635	−	0.149635i
$45$	1.90707	+	0.376970i	0.284290	+	0.0561954i
$46$	−0.746585	−	2.78629i	−0.110078	−	0.410816i
$47$	0.845190	+	0.845190i	0.123284	+	0.123284i	0.766057	−	0.642773i	$-0.222216\pi$
$47$	0.845190	+	0.845190i	0.123284	+	0.123284i	−0.642773	+	0.766057i	$0.722216\pi$
$48$	−1.34639	+	0.0448823i	−0.194334	+	0.00647820i
$49$	0.221152	−	0.127682i	0.0315932	−	0.0182403i
$50$	0.915387	−	3.41627i	0.129455	−	0.483133i
$51$	−0.0639711	−	0.102737i	−0.00895775	−	0.0143860i
$52$	−4.50949	−	2.29768i	−0.625353	−	0.318631i
$53$		−	10.8272i		−	1.48723i	−0.668606	−	0.743616i	$-0.733109\pi$
$53$		−	10.8272i		−	1.48723i	0.668606	−	0.743616i	$-0.266891\pi$
$54$	−3.96007	−	0.646513i	−0.538897	−	0.0879793i
$55$	−0.323996	−	0.561177i	−0.0436876	−	0.0756691i
$56$	3.41298	−	5.91145i	0.456078	−	0.789950i
$57$	−0.559544	+	2.40626i	−0.0741134	+	0.318717i
$58$	−4.01332	+	1.07536i	−0.526974	+	0.141202i
$59$	1.32319	−	0.354549i	0.172265	−	0.0461583i	−0.171655	−	0.985157i	$-0.554912\pi$
$59$	1.32319	−	0.354549i	0.172265	−	0.0461583i	0.343921	+	0.938999i	$0.388245\pi$
$60$	−0.356829	+	1.53451i	−0.0460665	+	0.198104i
$61$	−1.29147	+	2.23689i	−0.165356	+	0.286404i	−0.936782	−	0.349915i	$-0.886211\pi$
$61$	−1.29147	+	2.23689i	−0.165356	+	0.286404i	0.771426	+	0.636319i	$0.219544\pi$
$62$	−3.07707	−	5.32965i	−0.390789	−	0.676866i
$63$	−5.13004	+	5.86382i	−0.646324	+	0.738772i
$64$			2.96751i			0.370938i
$65$	−1.56333	+	1.73626i	−0.193907	+	0.215357i
$66$	0.706969	+	1.13538i	0.0870219	+	0.139756i
$67$	0.757062	−	2.82539i	0.0924899	−	0.345177i	−0.904137	−	0.427243i	$-0.859485\pi$
$67$	0.757062	−	2.82539i	0.0924899	−	0.345177i	0.996627	+	0.0820656i	$0.0261517\pi$
$68$	0.0849417	−	0.0490411i	0.0103007	−	0.00594711i
$69$	−6.46650	+	0.215563i	−0.778476	+	0.0259507i
$70$	−0.918896	−	0.918896i	−0.109829	−	0.109829i
$71$	−1.52818	−	5.70324i	−0.181361	−	0.676850i	−0.995380	−	0.0960116i	$-0.969391\pi$
$71$	−1.52818	−	5.70324i	−0.181361	−	0.676850i	0.814019	−	0.580839i	$-0.197275\pi$
$72$	1.52905	−	7.73539i	0.180200	−	0.911624i
$73$	7.18240	−	7.18240i	0.840636	−	0.840636i	−0.148305	−	0.988942i	$-0.547382\pi$
$73$	7.18240	−	7.18240i	0.840636	−	0.840636i	0.988942	+	0.148305i	$0.0473818\pi$
$74$	4.88297	+	2.81919i	0.567634	+	0.327724i
$75$	−6.99850	−	3.73539i	−0.808117	−	0.431326i
$76$	−1.93390	−	0.518188i	−0.221834	−	0.0594402i
$77$	2.59704			0.295961
$78$	3.10563	−	3.68928i	0.351643	−	0.417729i
$79$	−6.80061			−0.765128			−0.382564	−	0.923929i	$-0.624959\pi$
$79$	−6.80061			−0.765128			−0.382564	+	0.923929i	$0.624959\pi$
$80$	−0.486815	−	0.130442i	−0.0544276	−	0.0145838i
$81$	−3.42425	+	8.32313i	−0.380472	+	0.924792i
$82$	−6.37539	−	3.68083i	−0.704044	−	0.406480i
$83$	−5.80460	+	5.80460i	−0.637138	+	0.637138i	−0.949848	−	0.312711i	$-0.898763\pi$
$83$	−5.80460	+	5.80460i	−0.637138	+	0.637138i	0.312711	+	0.949848i	$0.398763\pi$
$84$	−4.61104	−	4.31354i	−0.503106	−	0.470645i
$85$	−0.0117188	−	0.0437350i	−0.00127108	−	0.00474373i
$86$	−4.16635	−	4.16635i	−0.449269	−	0.449269i
$87$	0.310492	+	9.31421i	0.0332883	+	0.998588i
$88$	−2.27622	+	1.31418i	−0.242646	+	0.140092i
$89$	3.30626	−	12.3391i	0.350463	−	1.30794i	−0.535637	−	0.844449i	$-0.679928\pi$
$89$	3.30626	−	12.3391i	0.350463	−	1.30794i	0.886099	−	0.463496i	$-0.153405\pi$
$90$	−1.34713	−	0.662330i	−0.142000	−	0.0698157i
$91$	−2.89359	−	8.90547i	−0.303331	−	0.933547i
$92$		−	5.24353i		−	0.546676i
$93$	−13.2069	+	4.01491i	−1.36949	+	0.416326i
$94$	−0.461500	−	0.799342i	−0.0476001	−	0.0824458i
$95$	−0.462122	+	0.800419i	−0.0474127	+	0.0821212i
$96$	9.88151	+	2.29781i	1.00853	+	0.234520i
$97$	9.17280	−	2.45784i	0.931357	−	0.249556i	0.238924	−	0.971038i	$-0.423205\pi$
$97$	9.17280	−	2.45784i	0.931357	−	0.249556i	0.692433	+	0.721482i	$0.256539\pi$
$98$	−0.190475	+	0.0510375i	−0.0192408	+	0.00515557i
$99$	2.83963	−	0.967716i	0.285394	−	0.0972591i
$100$	3.21455	−	5.56776i	0.321455	−	0.556776i
$101$	8.98770	+	15.5672i	0.894310	+	1.54899i	0.834657	+	0.550771i	$0.185666\pi$
$101$	8.98770	+	15.5672i	0.894310	+	1.54899i	0.0596529	+	0.998219i	$0.481001\pi$
$102$	0.0271825	+	0.0894161i	0.00269147	+	0.00885351i
$103$			14.5831i			1.43691i	0.695573	+	0.718456i	$0.255151\pi$
$103$			14.5831i			1.43691i	−0.695573	+	0.718456i	$0.744849\pi$
$104$	7.04255	+	6.34111i	0.690579	+	0.621797i
$105$	−2.47434	+	1.54069i	−0.241471	+	0.150356i
$106$	−2.16394	+	8.07595i	−0.210181	+	0.784405i
$107$	−6.82405	+	3.93987i	−0.659706	+	0.380882i	−0.792165	−	0.610307i	$-0.791046\pi$
$107$	−6.82405	+	3.93987i	−0.659706	+	0.380882i	0.132459	+	0.991189i	$0.457713\pi$
$108$	−6.64908	−	2.99829i	−0.639808	−	0.288511i
$109$	−1.84321	−	1.84321i	−0.176548	−	0.176548i	0.613301	−	0.789849i	$-0.289841\pi$
$109$	−1.84321	−	1.84321i	−0.176548	−	0.176548i	−0.789849	+	0.613301i	$0.789841\pi$
$110$	0.129509	+	0.483333i	0.0123482	+	0.0460840i
$111$	8.63975	−	9.23563i	0.820049	−	0.876608i
$112$	1.42828	−	1.42828i	0.134960	−	0.134960i
$113$	0.451325	+	0.260573i	0.0424571	+	0.0245126i	0.521078	−	0.853509i	$-0.325530\pi$
$113$	0.451325	+	0.260573i	0.0424571	+	0.0245126i	−0.478621	+	0.878021i	$0.658863\pi$
$114$	0.898278	−	1.68298i	0.0841314	−	0.157626i
$115$	−2.33810	−	0.626493i	−0.218029	−	0.0584207i
$116$	−7.55267			−0.701248
$117$	−6.48226	−	8.65912i	−0.599285	−	0.800536i
$118$	−1.05782			−0.0973803
$119$	0.175283	+	0.0469669i	0.0160681	+	0.00430545i
$120$	1.38904	−	2.60245i	0.126801	−	0.237570i
$121$	−0.866025	−	0.500000i	−0.0787296	−	0.0454545i
$122$	1.41037	−	1.41037i	0.127689	−	0.127689i
$123$	−11.2804	+	12.0584i	−1.01712	+	1.08727i
$124$	−2.89538	−	10.8057i	−0.260013	−	0.970381i
$125$	−4.38960	−	4.38960i	−0.392618	−	0.392618i
$126$	4.99841	−	3.34849i	0.445294	−	0.298307i
$127$	−10.9330	+	6.31214i	−0.970143	+	0.560112i	−0.899280	−	0.437374i	$-0.855909\pi$
$127$	−10.9330	+	6.31214i	−0.970143	+	0.560112i	−0.0708630	+	0.997486i	$0.522575\pi$
$128$	−2.43887	+	9.10200i	−0.215568	+	0.804511i
$129$	−11.2188	+	6.98563i	−0.987764	+	0.615051i
$130$	1.51309	−	0.982618i	0.132707	−	0.0861813i
$131$		−	16.8444i		−	1.47170i	−0.677145	−	0.735849i	$-0.736783\pi$
$131$		−	16.8444i		−	1.47170i	0.677145	−	0.735849i	$-0.263217\pi$
$132$	0.707154	+	2.32617i	0.0615499	+	0.202467i
$133$	−1.85211	−	3.20794i	−0.160598	−	0.278164i
$134$	−1.12937	+	1.95613i	−0.0975631	+	0.168984i
$135$	−2.13137	+	2.60660i	−0.183439	+	0.224341i
$136$	−0.177396	+	0.0475331i	−0.0152116	+	0.00407593i
$137$	11.3630	−	3.04471i	0.970808	−	0.260127i	0.261639	−	0.965166i	$-0.415737\pi$
$137$	11.3630	−	3.04471i	0.970808	−	0.260127i	0.709169	+	0.705038i	$0.249070\pi$
$138$	4.86640	+	1.13162i	0.414256	+	0.0963297i
$139$	−0.569147	+	0.985791i	−0.0482744	+	0.0836137i	−0.889153	−	0.457610i	$-0.848706\pi$
$139$	−0.569147	+	0.985791i	−0.0482744	+	0.0836137i	0.840879	+	0.541224i	$0.182039\pi$
$140$	−1.18112	−	2.04575i	−0.0998226	−	0.172898i
$141$	−1.98078	+	0.602156i	−0.166812	+	0.0507107i
$142$			4.55943i			0.382619i
$143$	−0.749627	+	3.52676i	−0.0626869	+	0.294923i
$144$	1.02949	−	2.09391i	0.0857909	−	0.174493i
$145$	−0.902386	+	3.36775i	−0.0749391	+	0.279677i
$146$	−6.79279	+	3.92182i	−0.562175	+	0.324572i
$147$	0.0147362	+	0.442059i	0.00121542	+	0.0364604i
$148$	7.24736	+	7.24736i	0.595729	+	0.595729i
$149$	−1.47373	−	5.50003i	−0.120733	−	0.450580i	0.878919	−	0.476971i	$-0.158265\pi$
$149$	−1.47373	−	5.50003i	−0.120733	−	0.450580i	−0.999652	+	0.0263908i	$0.991599\pi$
$150$	4.47357	+	4.18493i	0.365265	+	0.341698i
$151$	6.44402	−	6.44402i	0.524407	−	0.524407i	−0.394492	−	0.918899i	$-0.629080\pi$
$151$	6.44402	−	6.44402i	0.524407	−	0.524407i	0.918899	+	0.394492i	$0.129080\pi$
$152$	3.24662	+	1.87444i	0.263336	+	0.152037i
$153$	0.209157	−	0.0139601i	0.0169093	−	0.00112861i
$154$	−1.93712	−	0.519049i	−0.156097	−	0.0418262i
$155$	−5.16422			−0.414800
$156$	7.18871	−	5.01667i	0.575557	−	0.401655i
$157$	−22.7918			−1.81899			−0.909493	−	0.415719i	$-0.863530\pi$
$157$	−22.7918			−1.81899			−0.909493	+	0.415719i	$0.863530\pi$
$158$	5.07252	+	1.35918i	0.403548	+	0.108130i
$159$	16.5442	+	8.83035i	1.31204	+	0.700292i
$160$	3.28699	+	1.89774i	0.259859	+	0.150030i
$161$	6.85985	−	6.85985i	0.540632	−	0.540632i
$162$	4.21760	−	5.52379i	0.331366	−	0.433990i
$163$	3.97508	+	14.8352i	0.311352	+	1.16198i	0.927338	+	0.374225i	$0.122091\pi$
$163$	3.97508	+	14.8352i	0.311352	+	1.16198i	−0.615985	+	0.787758i	$0.711242\pi$
$164$	−9.46242	−	9.46242i	−0.738891	−	0.738891i
$165$	1.12173	−	0.0373933i	0.0873267	−	0.00291106i
$166$	5.48973	−	3.16950i	0.426086	−	0.246001i
$167$	−4.56919	+	17.0524i	−0.353575	+	1.31956i	0.528694	+	0.848812i	$0.322682\pi$
$167$	−4.56919	+	17.0524i	−0.353575	+	1.31956i	−0.882269	+	0.470746i	$0.843985\pi$
$168$	6.24929	+	10.0363i	0.482143	+	0.774317i
$169$	12.9288	−	1.35894i	0.994521	−	0.104534i
$170$			0.0349638i			0.00268160i
$171$	−3.22046	−	2.81746i	−0.246275	−	0.215457i
$172$	−5.35528	−	9.27561i	−0.408336	−	0.707259i
$173$	−3.79546	+	6.57393i	−0.288564	+	0.499807i	−0.973467	−	0.228827i	$-0.926511\pi$
$173$	−3.79546	+	6.57393i	−0.288564	+	0.499807i	0.684903	+	0.728634i	$0.259844\pi$
$174$	1.62996	−	7.00946i	0.123567	−	0.531386i
$175$	11.4894	−	3.07858i	0.868519	−	0.232719i
$176$	−0.751267	+	0.201301i	−0.0566289	+	0.0151737i
$177$	−0.537398	+	2.31103i	−0.0403933	+	0.173707i
$178$	−4.93223	+	8.54287i	−0.369686	+	0.640315i
$179$	0.932994	+	1.61599i	0.0697353	+	0.120785i	0.898785	−	0.438390i	$-0.144451\pi$
$179$	0.932994	+	1.61599i	0.0697353	+	0.120785i	−0.829049	+	0.559175i	$0.811118\pi$
$180$	−2.05374	−	1.79674i	−0.153077	−	0.133921i
$181$		−	11.1954i		−	0.832144i	−0.909332	−	0.416072i	$-0.863406\pi$
$181$		−	11.1954i		−	0.832144i	0.909332	−	0.416072i	$-0.136594\pi$
$182$	0.378448	+	7.22085i	0.0280524	+	0.535245i
$183$	−2.36473	−	3.79773i	−0.174806	−	0.280736i
$184$	−2.54115	+	9.48370i	−0.187336	+	0.699148i
$185$	4.09752	−	2.36570i	0.301256	−	0.173930i
$186$	10.6534	−	0.355134i	0.781144	−	0.0260397i
$187$	−0.0494084	−	0.0494084i	−0.00361310	−	0.00361310i
$188$	−0.434250	−	1.62064i	−0.0316709	−	0.118197i
$189$	−4.77614	−	12.6212i	−0.347413	−	0.918054i
$190$	0.504666	−	0.504666i	0.0366123	−	0.0366123i
$191$	15.3381	+	8.85544i	1.10982	+	0.640757i	0.938784	−	0.344507i	$-0.111954\pi$
$191$	15.3381	+	8.85544i	1.10982	+	0.640757i	0.171040	+	0.985264i	$0.445287\pi$
$192$	−4.53441	−	2.42021i	−0.327243	−	0.174663i
$193$	16.1364	+	4.32374i	1.16152	+	0.311229i	0.787574	−	0.616219i	$-0.211337\pi$
$193$	16.1364	+	4.32374i	1.16152	+	0.311229i	0.373950	+	0.927449i	$0.378003\pi$
$194$	−7.33316			−0.526490
$195$	−1.37804	−	3.80484i	−0.0986836	−	0.272471i
$196$	−0.358455			−0.0256039
$197$	8.53238	+	2.28624i	0.607907	+	0.162888i	0.549624	−	0.835412i	$-0.314771\pi$
$197$	8.53238	+	2.28624i	0.607907	+	0.162888i	0.0582824	+	0.998300i	$0.481438\pi$
$198$	−2.31147	+	0.154279i	−0.164269	+	0.0109641i
$199$	13.1851	+	7.61240i	0.934665	+	0.539629i	0.888284	−	0.459295i	$-0.151898\pi$
$199$	13.1851	+	7.61240i	0.934665	+	0.539629i	0.0463809	+	0.998924i	$0.485231\pi$
$200$	−8.51225	+	8.51225i	−0.601907	+	0.601907i
$201$	3.69982	+	3.46111i	0.260965	+	0.244128i
$202$	−3.59259	−	13.4077i	−0.252774	−	0.943364i
$203$	−9.88077	−	9.88077i	−0.693494	−	0.693494i
$204$	0.00565997	+	0.169789i	0.000396277	+	0.0118876i
$205$	−5.34987	+	3.08875i	−0.373651	+	0.215728i
$206$	2.91459	−	10.8774i	0.203069	−	0.757865i
$207$	4.94450	−	10.0568i	0.343666	−	0.698993i
$208$	1.52733	+	2.35187i	0.105901	+	0.163073i
$209$			1.42632i			0.0986606i
$210$	2.15352	−	0.654669i	0.148607	−	0.0451764i
$211$	4.35682	+	7.54624i	0.299936	+	0.519505i	0.976121	−	0.217227i	$-0.0697013\pi$
$211$	4.35682	+	7.54624i	0.299936	+	0.519505i	−0.676185	+	0.736732i	$0.736368\pi$
$212$	−7.59908	+	13.1620i	−0.521907	+	0.903969i
$213$	9.96100	+	2.31630i	0.682517	+	0.158710i
$214$	5.87744	−	1.57486i	0.401774	−	0.107655i
$215$	−4.77586	+	1.27969i	−0.325711	+	0.0872739i
$216$	10.5728	+	8.64516i	0.719387	+	0.588229i
$217$	10.3487	−	17.9244i	0.702513	−	1.21679i
$218$	1.00645	+	1.74323i	0.0681655	+	0.118066i
$219$	5.11711	+	16.8326i	0.345782	+	1.13744i
$220$			0.909586i			0.0613242i
$221$	−0.114375	+	0.224476i	−0.00769372	+	0.0150999i
$222$	−8.29018	+	5.16204i	−0.556400	+	0.346454i
$223$	5.31778	−	19.8462i	0.356105	−	1.32900i	−0.522984	−	0.852342i	$-0.675181\pi$
$223$	5.31778	−	19.8462i	0.356105	−	1.32900i	0.879089	−	0.476658i	$-0.158152\pi$
$224$	−13.1737	+	7.60584i	−0.880205	+	0.508187i
$225$	11.4155	−	7.64737i	0.761035	−	0.509825i
$226$	−0.284562	−	0.284562i	−0.0189288	−	0.0189288i
$227$	5.81765	+	21.7117i	0.386131	+	1.44106i	0.836377	+	0.548155i	$0.184670\pi$
$227$	5.81765	+	21.7117i	0.386131	+	1.44106i	−0.450246	+	0.892904i	$0.648664\pi$
$228$	2.36903	−	2.53243i	0.156893	−	0.167714i
$229$	15.1422	−	15.1422i	1.00063	−	1.00063i	0.000627550	−	1.00000i	$-0.499800\pi$
$229$	15.1422	−	15.1422i	1.00063	−	1.00063i	1.00000		0.000627550i	$-0.000199755\pi$
$230$	1.61876	+	0.934593i	0.106738	+	0.0616252i
$231$	−2.11807	+	3.96834i	−0.139359	+	0.261097i
$232$	13.6601	+	3.66022i	0.896831	+	0.240305i
$233$	−11.5533			−0.756882			−0.378441	−	0.925625i	$-0.623540\pi$
$233$	−11.5533			−0.756882			−0.378441	+	0.925625i	$0.623540\pi$
$234$	3.10444	+	7.75433i	0.202944	+	0.506916i
$235$	−0.774531			−0.0505248
$236$	−1.85736	−	0.497679i	−0.120904	−	0.0323962i
$237$	5.54637	−	10.3915i	0.360275	−	0.674998i
$238$	−0.121355	−	0.0700645i	−0.00786630	−	0.00454161i
$239$	−3.92746	+	3.92746i	−0.254046	+	0.254046i	−0.822627	−	0.568581i	$-0.807493\pi$
$239$	−3.92746	+	3.92746i	−0.254046	+	0.254046i	0.568581	+	0.822627i	$0.307493\pi$
$240$	0.596349	−	0.637479i	0.0384941	−	0.0411491i
$241$	−5.57104	−	20.7914i	−0.358862	−	1.33929i	−0.875554	−	0.483120i	$-0.839503\pi$
$241$	−5.57104	−	20.7914i	−0.358862	−	1.33929i	0.516692	−	0.856171i	$-0.327163\pi$
$242$	0.546032	+	0.546032i	0.0351002	+	0.0351002i
$243$	−9.92520	−	12.0204i	−0.636702	−	0.771110i
$244$	3.13992	−	1.81283i	0.201013	−	0.116055i
$245$	−0.0428279	+	0.159836i	−0.00273617	+	0.0102115i
$246$	10.8240	−	6.73975i	0.690110	−	0.429711i
$247$	4.89097	−	1.58919i	0.311205	−	0.101117i
$248$			20.9469i			1.33013i
$249$	−4.13550	−	13.6036i	−0.262076	−	0.862094i
$250$	2.39686	+	4.15148i	0.151591	+	0.262563i
$251$	5.16218	−	8.94116i	0.325834	−	0.564361i	−0.655847	−	0.754894i	$-0.727688\pi$
$251$	5.16218	−	8.94116i	0.325834	−	0.564361i	0.981681	+	0.190533i	$0.0610216\pi$
$252$	10.3518	−	3.52778i	0.652102	−	0.222229i
$253$	−3.60823	+	0.966822i	−0.226847	+	0.0607836i
$254$	9.41637	−	2.52311i	0.590836	−	0.158314i
$255$	0.0763855	+	0.0177624i	0.00478345	+	0.00111233i
$256$	6.60578	−	11.4416i	0.412862	−	0.715097i
$257$	2.63997	+	4.57256i	0.164677	+	0.285229i	0.936540	−	0.350560i	$-0.114009\pi$
$257$	2.63997	+	4.57256i	0.164677	+	0.285229i	−0.771864	+	0.635788i	$0.780675\pi$
$258$	9.76422	−	2.96832i	0.607894	−	0.184800i
$259$			18.9627i			1.17828i
$260$	3.11904	−	1.01345i	0.193435	−	0.0628513i
$261$	−14.4855	−	7.12195i	−0.896632	−	0.440838i
$262$	−3.36654	+	12.5641i	−0.207985	+	0.776212i
$263$	−2.79868	+	1.61582i	−0.172574	+	0.0996357i	−0.583799	−	0.811898i	$-0.698434\pi$
$263$	−2.79868	+	1.61582i	−0.172574	+	0.0996357i	0.411225	+	0.911534i	$0.365101\pi$
$264$	−0.151673	−	4.54992i	−0.00933483	−	0.280028i
$265$	4.96103	+	4.96103i	0.304753	+	0.304753i
$266$	0.740330	+	2.76295i	0.0453925	+	0.169407i
$267$	16.1579	+	15.1154i	0.988850	+	0.925050i
$268$	−2.90332	+	2.90332i	−0.177348	+	0.177348i
$269$	−16.4088	−	9.47364i	−1.00046	−	0.577618i	−0.0920784	−	0.995752i	$-0.529351\pi$
$269$	−16.4088	−	9.47364i	−1.00046	−	0.577618i	−0.908386	+	0.418134i	$0.862684\pi$
$270$	2.11073	−	1.51827i	0.128455	−	0.0923989i
$271$	3.15459	+	0.845270i	0.191628	+	0.0513465i	0.353356	−	0.935489i	$-0.385040\pi$
$271$	3.15459	+	0.845270i	0.191628	+	0.0513465i	−0.161729	+	0.986835i	$0.551707\pi$
$272$	−0.0543459			−0.00329520
$273$	15.9677	+	2.84157i	0.966407	+	0.171979i
$274$	−9.08412			−0.548792
$275$	−4.42404	−	1.18542i	−0.266780	−	0.0714834i
$276$	8.01223	+	4.27647i	0.482279	+	0.257413i
$277$	−13.0550	−	7.53729i	−0.784397	−	0.452872i	0.0535893	−	0.998563i	$-0.482934\pi$
$277$	−13.0550	−	7.53729i	−0.784397	−	0.452872i	−0.837986	+	0.545691i	$0.816267\pi$
$278$	0.621544	−	0.621544i	0.0372777	−	0.0372777i
$279$	4.63631	−	23.4549i	0.277569	−	1.40421i
$280$	1.14480	+	4.27245i	0.0684148	+	0.255327i
$281$	16.0436	+	16.0436i	0.957084	+	0.957084i	0.999116	−	0.0420326i	$-0.0133833\pi$
$281$	16.0436	+	16.0436i	0.957084	+	0.957084i	−0.0420326	+	0.999116i	$0.513383\pi$
$282$	1.59780	−	0.0532631i	0.0951474	−	0.00317177i
$283$	−22.0284	+	12.7181i	−1.30945	+	0.756013i	−0.982005	−	0.188856i	$-0.939522\pi$
$283$	−22.0284	+	12.7181i	−1.30945	+	0.756013i	−0.327449	+	0.944869i	$0.606189\pi$
$284$	−2.14510	+	8.00563i	−0.127288	+	0.475047i
$285$	−0.846164	−	1.35893i	−0.0501224	−	0.0804960i
$286$	1.26401	−	2.48077i	0.0747422	−	0.146691i
$287$		−	24.7584i		−	1.46144i
$288$	−11.5702	+	13.2251i	−0.681778	+	0.779297i
$289$	8.49756	+	14.7182i	0.499856	+	0.865777i
$290$	1.34617	−	2.33163i	0.0790497	−	0.136918i
$291$	−3.72542	+	16.0208i	−0.218388	+	0.939154i
$292$	−13.7722	+	3.69024i	−0.805955	+	0.215955i
$293$	14.2206	−	3.81039i	0.830775	−	0.222605i	0.181723	−	0.983350i	$-0.441833\pi$
$293$	14.2206	−	3.81039i	0.830775	−	0.222605i	0.649052	+	0.760744i	$0.275166\pi$
$294$	0.0773589	−	0.332674i	0.00451166	−	0.0194019i
$295$	−0.443832	+	0.768740i	−0.0258409	+	0.0447578i
$296$	−9.59566	−	16.6202i	−0.557736	−	0.966028i
$297$	−0.837230	+	5.12826i	−0.0485810	+	0.297572i
$298$			4.39697i			0.254710i
$299$	7.33554	+	11.2957i	0.424225	+	0.653246i
$300$	5.88596	+	9.45278i	0.339826	+	0.545757i
$301$	5.12877	−	19.1408i	0.295618	−	1.10326i
$302$	−6.09446	+	3.51864i	−0.350697	+	0.202475i
$303$	−31.1170	+	1.03730i	−1.78763	+	0.0595911i
$304$	0.784427	+	0.784427i	0.0449900	+	0.0449900i
$305$	−0.433191	−	1.61669i	−0.0248045	−	0.0925715i
$306$	−0.158799	−	0.0313896i	−0.00907792	−	0.00179443i
$307$	−1.96885	+	1.96885i	−0.112368	+	0.112368i	−0.761055	−	0.648687i	$-0.775318\pi$
$307$	−1.96885	+	1.96885i	−0.112368	+	0.112368i	0.648687	+	0.761055i	$0.275318\pi$
$308$	−3.15707	−	1.82273i	−0.179891	−	0.103860i
$309$	−22.2832	−	11.8935i	−1.26765	−	0.676597i
$310$	3.85196	+	1.03213i	0.218776	+	0.0586210i
$311$	−28.4912			−1.61559			−0.807794	−	0.589465i	$-0.799339\pi$
$311$	−28.4912			−1.61559			−0.807794	+	0.589465i	$0.799339\pi$
$312$	−15.4330	+	5.58955i	−0.873724	+	0.316446i
$313$	−27.8252			−1.57277			−0.786387	−	0.617734i	$-0.788051\pi$
$313$	−27.8252			−1.57277			−0.786387	+	0.617734i	$0.788051\pi$
$314$	17.0003	+	4.55521i	0.959381	+	0.257065i
$315$	−0.336219	−	5.03738i	−0.0189438	−	0.283824i
$316$	8.26708	+	4.77300i	0.465060	+	0.268502i
$317$	−8.35583	+	8.35583i	−0.469310	+	0.469310i	−0.901691	−	0.432381i	$-0.857674\pi$
$317$	−8.35583	+	8.35583i	−0.469310	+	0.469310i	0.432381	+	0.901691i	$0.357674\pi$
$318$	−10.5754	−	9.89305i	−0.593037	−	0.554774i
$319$	1.39259	+	5.19721i	0.0779700	+	0.290988i
$320$	−1.35971	−	1.35971i	−0.0760101	−	0.0760101i
$321$	−0.454712	−	13.6405i	−0.0253795	−	0.761340i
$322$	−6.48773	+	3.74569i	−0.361547	+	0.208739i
$323$	−0.0257946	+	0.0962669i	−0.00143525	+	0.00535643i
$324$	10.0042	−	7.71461i	0.555791	−	0.428590i
$325$	0.864310	+	16.4912i	0.0479433	+	0.914766i
$326$		−	11.8599i		−	0.656861i
$327$	4.31973	−	1.31320i	0.238882	−	0.0726200i
$328$	12.5284	+	21.6999i	0.691768	+	1.19818i
$329$	1.55210	−	2.68831i	0.0855698	−	0.148211i
$330$	−0.844165	−	0.196300i	−0.0464698	−	0.0108059i
$331$	−16.5367	+	4.43100i	−0.908939	+	0.243550i	−0.682851	−	0.730557i	$-0.739260\pi$
$331$	−16.5367	+	4.43100i	−0.908939	+	0.243550i	−0.226088	+	0.974107i	$0.572594\pi$
$332$	11.1303	−	2.98234i	0.610852	−	0.163677i
$333$	7.06592	+	20.7340i	0.387210	+	1.13622i
$334$	6.81625	−	11.8061i	0.372969	−	0.646001i
$335$	0.947709	+	1.64148i	0.0517789	+	0.0896836i
$336$	1.01758	+	3.34731i	0.0555137	+	0.182611i
$337$			15.0167i			0.818011i	0.912532	+	0.409006i	$0.134124\pi$
$337$			15.0167i			0.818011i	−0.912532	+	0.409006i	$0.865876\pi$
$338$	−9.91508	−	1.57034i	−0.539310	−	0.0854153i
$339$	−0.766247	+	0.477119i	−0.0416168	+	0.0259135i
$340$	−0.0164496	+	0.0613908i	−0.000892106	+	0.00332939i
$341$	−6.90186	+	3.98479i	−0.373756	+	0.215788i
$342$	1.83902	+	2.74517i	0.0994428	+	0.148442i
$343$	−13.3237	−	13.3237i	−0.719410	−	0.719410i
$344$	5.19061	+	19.3716i	0.279859	+	1.04445i
$345$	2.86418	−	3.06172i	0.154202	−	0.164837i
$346$	4.14489	−	4.14489i	0.222830	−	0.222830i
$347$	−4.64326	−	2.68079i	−0.249263	−	0.143912i	0.370164	−	0.928967i	$-0.379302\pi$
$347$	−4.64326	−	2.68079i	−0.249263	−	0.143912i	−0.619427	+	0.785054i	$0.712635\pi$
$348$	6.15973	−	11.5406i	0.330196	−	0.618643i
$349$	−20.8996	−	5.60002i	−1.11873	−	0.299762i	−0.348359	−	0.937361i	$-0.613261\pi$
$349$	−20.8996	−	5.60002i	−1.11873	−	0.299762i	−0.770369	+	0.637599i	$0.779928\pi$
$350$	−9.18518			−0.490968
$351$	18.5180	−	2.84291i	0.988420	−	0.151743i
$352$	5.85731			0.312195
$353$	−12.4722	−	3.34192i	−0.663830	−	0.177873i	−0.0888561	−	0.996044i	$-0.528321\pi$
$353$	−12.4722	−	3.34192i	−0.663830	−	0.177873i	−0.574974	+	0.818172i	$0.694988\pi$
$354$	0.862727	−	1.61637i	0.0458534	−	0.0859092i
$355$	3.31343	+	1.91301i	0.175859	+	0.101532i
$356$	−12.6794	+	12.6794i	−0.672008	+	0.672008i
$357$	−0.214722	+	0.229531i	−0.0113643	+	0.0121481i
$358$	−0.372939	−	1.39183i	−0.0197104	−	0.0735604i
$359$	7.46317	+	7.46317i	0.393891	+	0.393891i	0.876072	−	0.482181i	$-0.160155\pi$
$359$	7.46317	+	7.46317i	0.393891	+	0.393891i	−0.482181	+	0.876072i	$0.660155\pi$
$360$	2.84374	+	4.24496i	0.149878	+	0.223729i
$361$	−14.6927	+	8.48281i	−0.773297	+	0.446463i
$362$	−2.23752	+	8.35054i	−0.117601	+	0.438894i
$363$	1.47031	−	0.915520i	0.0771715	−	0.0480523i
$364$	−2.73274	+	12.8567i	−0.143235	+	0.673874i
$365$			6.58194i			0.344515i
$366$	1.00482	+	3.30532i	0.0525226	+	0.172772i
$367$	−3.39152	−	5.87428i	−0.177036	−	0.306635i	0.763828	−	0.645420i	$-0.223318\pi$
$367$	−3.39152	−	5.87428i	−0.177036	−	0.306635i	−0.940864	+	0.338785i	$0.889984\pi$
$368$	−1.45268	+	2.51612i	−0.0757263	+	0.131162i
$369$	−9.22552	−	27.0711i	−0.480261	−	1.40926i
$370$	−3.52913	+	0.945626i	−0.183470	+	0.0491608i
$371$	−27.1606	+	7.27767i	−1.41011	+	0.377838i
$372$	18.8727	+	4.38860i	0.978505	+	0.227538i
$373$	−5.78968	+	10.0280i	−0.299778	+	0.519231i	−0.976085	−	0.217389i	$-0.930246\pi$
$373$	−5.78968	+	10.0280i	−0.299778	+	0.519231i	0.676307	+	0.736620i	$0.263579\pi$
$374$	0.0269786	+	0.0467283i	0.00139503	+	0.00241626i
$375$	10.2874	−	3.12737i	0.531240	−	0.161497i
$376$			3.14162i			0.162017i
$377$	16.2701	−	10.5660i	0.837950	−	0.544175i
$378$	1.04001	+	10.3686i	0.0534921	+	0.533303i
$379$	5.15003	−	19.2202i	0.264539	−	0.987273i	−0.697993	−	0.716105i	$-0.745923\pi$
$379$	5.15003	−	19.2202i	0.264539	−	0.987273i	0.962532	−	0.271169i	$-0.0874101\pi$
$380$	1.12355	−	0.648680i	0.0576367	−	0.0332766i
$381$	−0.728503	−	21.8538i	−0.0373223	−	1.11960i
$382$	−9.67070	−	9.67070i	−0.494796	−	0.494796i
$383$	−3.79326	−	14.1566i	−0.193827	−	0.723370i	−0.992567	−	0.121695i	$-0.961167\pi$
$383$	−3.79326	−	14.1566i	−0.193827	−	0.723370i	0.798741	−	0.601675i	$-0.205500\pi$
$384$	−11.9190	−	11.1500i	−0.608238	−	0.568994i
$385$	−1.18996	+	1.18996i	−0.0606462	+	0.0606462i
$386$	−11.1719	−	6.45009i	−0.568634	−	0.328301i
$387$	−1.52444	−	22.8399i	−0.0774919	−	1.16102i
$388$	−12.8758	−	3.45007i	−0.653672	−	0.175151i
$389$	33.1573			1.68114			0.840571	−	0.541701i	$-0.182219\pi$
$389$	33.1573			1.68114			0.840571	+	0.541701i	$0.182219\pi$
$390$	0.267430	+	3.11342i	0.0135419	+	0.157654i
$391$	−0.261015			−0.0132001
$392$	0.648318	+	0.173716i	0.0327450	+	0.00877400i
$393$	25.7385	+	13.7377i	1.29834	+	0.692978i
$394$	−5.90731	−	3.41059i	−0.297606	−	0.171823i
$395$	3.11603	−	3.11603i	0.156785	−	0.156785i
$396$	−4.13116	−	0.816603i	−0.207599	−	0.0410359i
$397$	−1.55222	−	5.79296i	−0.0779037	−	0.290740i	0.915972	−	0.401241i	$-0.131421\pi$
$397$	−1.55222	−	5.79296i	−0.0779037	−	0.290740i	−0.993876	+	0.110501i	$0.964754\pi$
$398$	−8.31322	−	8.31322i	−0.416704	−	0.416704i
$399$	6.41233	−	0.213757i	0.321018	−	0.0107012i
$400$	−3.08501	+	1.78113i	−0.154251	+	0.0890566i
$401$	8.88760	−	33.1690i	0.443825	−	1.65638i	−0.275194	−	0.961389i	$-0.588742\pi$
$401$	8.88760	−	33.1690i	0.443825	−	1.65638i	0.719019	−	0.694990i	$-0.244591\pi$
$402$	−2.06793	−	3.32107i	−0.103139	−	0.165640i
$403$	21.3541	+	19.2272i	1.06372	+	0.957776i
$404$		−	25.2321i		−	1.25534i
$405$	−2.24466	−	5.38264i	−0.111538	−	0.267466i
$406$	5.39521	+	9.34479i	0.267760	+	0.463774i
$407$	3.65082	−	6.32341i	0.180965	−	0.313440i
$408$	0.0720472	−	0.309831i	0.00356687	−	0.0153389i
$409$	−26.0872	+	6.99005i	−1.28993	+	0.345636i	−0.837634	−	0.546232i	$-0.816062\pi$
$409$	−26.0872	+	6.99005i	−1.28993	+	0.345636i	−0.452297	+	0.891868i	$0.649395\pi$
$410$	4.60775	−	1.23464i	0.227561	−	0.0609747i
$411$	−4.61495	+	19.8461i	−0.227639	+	0.978936i
$412$	10.2351	−	17.7277i	0.504248	−	0.873383i
$413$	−1.77881	−	3.08098i	−0.0875293	−	0.151605i
$414$	−5.69802	+	6.51305i	−0.280043	+	0.320099i
$415$		−	5.31933i		−	0.261116i
$416$	−6.52613	−	20.0852i	−0.319970	−	0.984757i
$417$	−1.04213	−	1.67365i	−0.0510333	−	0.0819589i
$418$	0.285066	−	1.06388i	0.0139431	−	0.0520362i
$419$	−22.1952	+	12.8144i	−1.08431	+	0.626025i	−0.932055	−	0.362317i	$-0.881986\pi$
$419$	−22.1952	+	12.8144i	−1.08431	+	0.626025i	−0.152252	+	0.988342i	$0.548653\pi$
$420$	4.08924	−	0.136316i	0.199534	−	0.00665154i
$421$	−14.8255	−	14.8255i	−0.722549	−	0.722549i	0.246575	−	0.969124i	$-0.420695\pi$
$421$	−14.8255	−	14.8255i	−0.722549	−	0.722549i	−0.969124	+	0.246575i	$0.920695\pi$
$422$	−1.74152	−	6.49945i	−0.0847760	−	0.316388i
$423$	0.695355	−	3.51777i	0.0338093	−	0.171040i
$424$	20.1227	−	20.1227i	0.977244	−	0.977244i
$425$	−0.277155	−	0.160015i	−0.0134440	−	0.00776189i
$426$	−6.96690	−	3.71853i	−0.337548	−	0.180164i
$427$	6.47943	+	1.73616i	0.313562	+	0.0840186i
$428$	11.0608			0.534643
$429$	−4.77759	−	4.02177i	−0.230664	−	0.194173i
$430$	3.81804			0.184122
$431$	6.45975	+	1.73089i	0.311155	+	0.0833738i	0.411017	−	0.911627i	$-0.365174\pi$
$431$	6.45975	+	1.73089i	0.311155	+	0.0833738i	−0.0998621	+	0.995001i	$0.531840\pi$
$432$	2.35992	+	3.28081i	0.113542	+	0.157848i
$433$	−12.9603	−	7.48260i	−0.622830	−	0.359591i	0.155140	−	0.987892i	$-0.450417\pi$
$433$	−12.9603	−	7.48260i	−0.622830	−	0.359591i	−0.777970	+	0.628301i	$0.783750\pi$
$434$	−11.3014	+	11.3014i	−0.542485	+	0.542485i
$435$	−4.41003	−	4.12550i	−0.211445	−	0.197803i
$436$	0.947022	+	3.53434i	0.0453541	+	0.169264i
$437$	3.76749	+	3.76749i	0.180223	+	0.180223i
$438$	−0.452628	−	13.5780i	−0.0216274	−	0.648783i
$439$	13.8723	−	8.00920i	0.662091	−	0.382258i	−0.130982	−	0.991385i	$-0.541813\pi$
$439$	13.8723	−	8.00920i	0.662091	−	0.382258i	0.793073	+	0.609126i	$0.208480\pi$
$440$	0.440808	−	1.64512i	0.0210147	−	0.0784280i
$441$	−0.687493	−	0.338013i	−0.0327378	−	0.0160958i
$442$	0.130176	−	0.144576i	0.00619183	−	0.00687676i
$443$		−	16.8320i		−	0.799711i	−0.916578	−	0.399856i	$-0.869060\pi$
$443$		−	16.8320i		−	0.799711i	0.916578	−	0.399856i	$-0.130940\pi$
$444$	−16.9848	+	5.16339i	−0.806065	+	0.245044i
$445$	4.13885	+	7.16870i	0.196200	+	0.339829i
$446$	−7.93298	+	13.7403i	−0.375638	+	0.650624i
$447$	9.60608	+	2.23377i	0.454352	+	0.105654i
$448$	7.44414	−	1.99465i	0.351703	−	0.0942384i
$449$	16.2062	−	4.34244i	0.764818	−	0.204932i	0.144737	−	0.989470i	$-0.453766\pi$
$449$	16.2062	−	4.34244i	0.764818	−	0.204932i	0.620081	+	0.784538i	$0.287100\pi$
$450$	−10.0432	+	3.42260i	−0.473440	+	0.161343i
$451$	−4.76665	+	8.25608i	−0.224453	+	0.388764i
$452$	−0.365765	−	0.633524i	−0.0172042	−	0.0297985i
$453$	4.59105	+	15.1021i	0.215706	+	0.709560i
$454$		−	17.3574i		−	0.814621i
$455$	5.40632	+	2.75464i	0.253452	+	0.129140i
$456$	−5.51202	+	3.43217i	−0.258124	+	0.160726i
$457$	1.24718	−	4.65452i	0.0583404	−	0.217729i	−0.930601	−	0.366035i	$-0.880715\pi$
$457$	1.24718	−	4.65452i	0.0583404	−	0.217729i	0.988942	+	0.148305i	$0.0473818\pi$
$458$	−14.3208	+	8.26814i	−0.669169	+	0.386345i
$459$	−0.149251	+	0.330981i	−0.00696642	+	0.0154489i
$460$	2.40258	+	2.40258i	0.112021	+	0.112021i
$461$	2.41037	+	8.99561i	0.112262	+	0.418968i	0.999068	−	0.0431753i	$-0.0137474\pi$
$461$	2.41037	+	8.99561i	0.112262	+	0.418968i	−0.886806	+	0.462143i	$0.847081\pi$
$462$	2.37297	−	2.53663i	0.110401	−	0.118015i
$463$	−8.60688	+	8.60688i	−0.399995	+	0.399995i	−0.878231	−	0.478236i	$-0.841276\pi$
$463$	−8.60688	+	8.60688i	−0.399995	+	0.399995i	0.478236	+	0.878231i	$0.341276\pi$
$464$	3.62416	+	2.09241i	0.168248	+	0.0971378i
$465$	4.21178	−	7.89104i	0.195317	−	0.365938i
$466$	8.61753	+	2.30906i	0.399199	+	0.106965i
$467$	1.68701			0.0780655			0.0390327	−	0.999238i	$-0.487572\pi$
$467$	1.68701			0.0780655			0.0390327	+	0.999238i	$0.487572\pi$
$468$	1.80268	+	15.0759i	0.0833290	+	0.696885i
$469$	−7.59652			−0.350775
$470$	0.577717	+	0.154799i	0.0266481	+	0.00714034i
$471$	18.5883	−	34.8264i	0.856505	−	1.60472i
$472$	3.11813	+	1.80025i	0.143524	+	0.0828633i
$473$	−5.39539	+	5.39539i	−0.248080	+	0.248080i
$474$	−6.21385	+	6.64242i	−0.285412	+	0.305096i
$475$	1.69079	+	6.31010i	0.0775786	+	0.289527i
$476$	−0.180117	−	0.180117i	−0.00825564	−	0.00825564i
$477$	−26.9859	+	18.0781i	−1.23560	+	0.827741i
$478$	3.71441	−	2.14452i	0.169893	−	0.0980879i
$479$	10.1492	−	37.8774i	0.463729	−	1.73066i	−0.197339	−	0.980335i	$-0.563230\pi$
$479$	10.1492	−	37.8774i	0.463729	−	1.73066i	0.661068	−	0.750326i	$-0.270104\pi$
$480$	−5.58056	+	3.47484i	−0.254716	+	0.158604i
$481$	−25.7512	−	5.47351i	−1.17415	−	0.249571i
$482$			16.6216i			0.757093i
$483$	4.88730	+	16.0767i	0.222380	+	0.731514i
$484$	0.701849	+	1.21564i	0.0319022	+	0.0552563i
$485$	−3.07679	+	5.32915i	−0.139710	+	0.241984i
$486$	5.00072	+	10.9496i	0.226837	+	0.496684i
$487$	−13.4741	+	3.61037i	−0.610568	+	0.163601i	−0.550837	−	0.834613i	$-0.685691\pi$
$487$	−13.4741	+	3.61037i	−0.610568	+	0.163601i	−0.0597318	+	0.998214i	$0.519025\pi$
$488$	−6.55755	+	1.75709i	−0.296846	+	0.0795398i
$489$	−25.9105	−	6.02513i	−1.17171	−	0.272466i
$490$	0.0638900	−	0.110661i	0.00288626	−	0.00499914i
$491$	11.8340	+	20.4971i	0.534063	+	0.925023i	0.999208	+	0.0397892i	$0.0126686\pi$
$491$	11.8340	+	20.4971i	0.534063	+	0.925023i	−0.465146	+	0.885234i	$0.653998\pi$
$492$	22.1760	−	6.74151i	0.999773	−	0.303931i
$493$			0.375961i			0.0169324i
$494$	−3.96575	+	0.207847i	−0.178428	+	0.00935148i
$495$	−0.857712	+	1.74453i	−0.0385513	+	0.0784106i
$496$	−1.60429	+	5.98728i	−0.0720346	+	0.268837i
$497$	−13.2797	+	7.66703i	−0.595675	+	0.343913i
$498$	0.365801	+	10.9734i	0.0163919	+	0.491728i
$499$	18.5162	+	18.5162i	0.828901	+	0.828901i	0.987365	−	0.158464i	$-0.0506542\pi$
$499$	18.5162	+	18.5162i	0.828901	+	0.828901i	−0.158464	+	0.987365i	$0.550654\pi$
$500$	2.25533	+	8.41701i	0.100861	+	0.376420i
$501$	−22.3300	−	20.8893i	−0.997631	−	0.933264i
$502$	−5.63743	+	5.63743i	−0.251611	+	0.251611i
$503$	18.0550	+	10.4241i	0.805034	+	0.464787i	0.845228	−	0.534405i	$-0.179464\pi$
$503$	18.0550	+	10.4241i	0.805034	+	0.464787i	−0.0401943	+	0.999192i	$0.512798\pi$
$504$	−20.4324	+	1.36376i	−0.910131	+	0.0607465i
$505$	−11.2510	−	3.01470i	−0.500664	−	0.134152i
$506$	2.88458			0.128235
$507$	−8.46783	+	20.8637i	−0.376069	+	0.926591i
$508$	17.7207			0.786229
$509$	16.7253	+	4.48152i	0.741334	+	0.198640i	0.609671	−	0.792655i	$-0.291302\pi$
$509$	16.7253	+	4.48152i	0.741334	+	0.198640i	0.131663	+	0.991295i	$0.457968\pi$
$510$	−0.0534254	−	0.0285154i	−0.00236572	−	0.00126268i
$511$	−22.8452	−	13.1897i	−1.01061	−	0.583476i
$512$	6.11232	−	6.11232i	0.270129	−	0.270129i
$513$	6.93166	−	2.62310i	0.306040	−	0.115813i
$514$	−1.05526	−	3.93827i	−0.0465454	−	0.173710i
$515$	−6.68195	−	6.68195i	−0.294442	−	0.294442i
$516$	18.5409	−	0.618068i	0.816219	−	0.0272089i
$517$	−1.03514	+	0.597639i	−0.0455255	+	0.0262842i
$518$	3.78991	−	14.1441i	0.166519	−	0.621458i
$519$	−6.94964	−	11.1610i	−0.305055	−	0.489915i
$520$	−6.13239	+	0.321401i	−0.268923	+	0.0140944i
$521$		−	3.49638i		−	0.153179i	−0.997063	−	0.0765896i	$-0.975597\pi$
$521$		−	3.49638i		−	0.153179i	0.997063	−	0.0765896i	$-0.0244031\pi$
$522$	9.38126	+	8.20731i	0.410606	+	0.359224i
$523$	5.01613	+	8.68820i	0.219340	+	0.379908i	0.954606	−	0.297870i	$-0.0962762\pi$
$523$	5.01613	+	8.68820i	0.219340	+	0.379908i	−0.735266	+	0.677778i	$0.762943\pi$
$524$	−11.8222	+	20.4767i	−0.516455	+	0.894527i
$525$	−4.66629	+	20.0669i	−0.203654	+	0.875791i
$526$	2.41046	−	0.645880i	0.105101	−	0.0281617i
$527$	−0.537892	+	0.144128i	−0.0234309	+	0.00627830i
$528$	0.305118	−	1.31213i	0.0132785	−	0.0571030i
$529$	4.52298	−	7.83402i	0.196651	−	0.340610i
$530$	−2.70888	−	4.69191i	−0.117666	−	0.203804i
$531$	−3.09301	−	2.70596i	−0.134225	−	0.117429i
$532$			5.19960i			0.225431i
$533$	33.6217	+	7.14642i	1.45632	+	0.309546i
$534$	−9.03111	−	14.5039i	−0.390814	−	0.627643i
$535$	1.32153	−	4.93202i	0.0571348	−	0.213230i
$536$	6.65809	−	3.84405i	0.287586	−	0.166038i
$537$	−3.23019	+	0.107680i	−0.139393	+	0.00464671i
$538$	10.3458	+	10.3458i	0.446040	+	0.446040i
$539$	0.0660932	+	0.246663i	0.00284684	+	0.0106245i
$540$	4.42042	−	1.67279i	0.190225	−	0.0719854i
$541$	−3.75577	+	3.75577i	−0.161473	+	0.161473i	−0.783219	−	0.621746i	$-0.786424\pi$
$541$	−3.75577	+	3.75577i	−0.161473	+	0.161473i	0.621746	+	0.783219i	$0.286424\pi$
$542$	−2.18405	−	1.26096i	−0.0938130	−	0.0541629i
$543$	17.1067	+	9.13059i	0.734120	+	0.391831i
$544$	0.395328	+	0.105928i	0.0169496	+	0.00454162i
$545$	1.68912			0.0723538
$546$	−11.3422	−	5.31082i	−0.485403	−	0.227282i
$547$	30.6562			1.31076			0.655382	−	0.755297i	$-0.272507\pi$
$547$	30.6562			1.31076			0.655382	+	0.755297i	$0.272507\pi$
$548$	−15.9503	−	4.27386i	−0.681361	−	0.182570i
$549$	7.73161	−	0.516045i	0.329977	−	0.0220243i
$550$	3.06294	+	1.76839i	0.130604	+	0.0754045i
$551$	5.42661	−	5.42661i	0.231181	−	0.231181i
$552$	−12.4188	−	11.6175i	−0.528579	−	0.494476i
$553$	4.57112	+	17.0597i	0.194384	+	0.725451i
$554$	8.23120	+	8.23120i	0.349710	+	0.349710i
$555$	0.273033	+	8.19049i	0.0115896	+	0.347667i
$556$	1.38375	−	0.798911i	0.0586842	−	0.0338814i
$557$	6.45714	−	24.0984i	0.273598	−	1.02108i	−0.683177	−	0.730253i	$-0.739402\pi$
$557$	6.45714	−	24.0984i	0.273598	−	1.02108i	0.956775	−	0.290829i	$-0.0939310\pi$
$558$	−8.14592	+	16.5682i	−0.344844	+	0.701389i
$559$	24.5127	+	12.4898i	1.03678	+	0.528261i
$560$			1.30888i			0.0553102i
$561$	0.115793	−	0.0352011i	0.00488879	−	0.00148619i
$562$	−8.76034	−	15.1733i	−0.369533	−	0.640049i
$563$	17.6355	−	30.5456i	0.743249	−	1.28735i	−0.207759	−	0.978180i	$-0.566617\pi$
$563$	17.6355	−	30.5456i	0.743249	−	1.28735i	0.951008	−	0.309165i	$-0.100050\pi$
$564$	2.83053	+	0.658203i	0.119187	+	0.0277154i
$565$	−0.326191	+	0.0874026i	−0.0137230	+	0.00367706i
$566$	18.9727	−	5.08372i	0.797482	−	0.213685i
$567$	23.1807	+	2.99539i	0.973496	+	0.125795i
$568$	7.75947	−	13.4398i	0.325580	−	0.563921i
$569$	13.8890	+	24.0565i	0.582257	+	1.00850i	0.995211	+	0.0977475i	$0.0311638\pi$
$569$	13.8890	+	24.0565i	0.582257	+	1.00850i	−0.412954	+	0.910752i	$0.635503\pi$
$570$	0.359550	+	1.18273i	0.0150599	+	0.0495391i
$571$		−	28.4429i		−	1.19030i	−0.803615	−	0.595150i	$-0.797093\pi$
$571$		−	28.4429i		−	1.19030i	0.803615	−	0.595150i	$-0.202907\pi$
$572$	3.38653	−	3.76115i	0.141598	−	0.157261i
$573$	−26.0406	+	16.2147i	−1.08786	+	0.677377i
$574$	−4.94825	+	18.4671i	−0.206536	+	0.770802i
$575$	−14.8169	+	8.55452i	−0.617906	+	0.356748i
$576$	7.39625	−	4.95482i	0.308177	−	0.206451i
$577$	−0.968514	−	0.968514i	−0.0403198	−	0.0403198i	0.686659	−	0.726979i	$-0.259076\pi$
$577$	−0.968514	−	0.968514i	−0.0403198	−	0.0403198i	−0.726979	+	0.686659i	$0.759076\pi$
$578$	−3.39667	−	12.6765i	−0.141283	−	0.527275i
$579$	−19.7671	+	21.1305i	−0.821494	+	0.878152i
$580$	3.46063	−	3.46063i	0.143695	−	0.143695i
$581$	18.4628	+	10.6595i	0.765966	+	0.442230i
$582$	5.98070	−	11.2052i	0.247908	−	0.464471i
$583$	10.4583	+	2.80229i	0.433138	+	0.116059i
$584$	26.6974			1.10475
$585$	6.93777	+	0.997438i	0.286841	+	0.0412390i
$586$	−11.3686			−0.469632
$587$	−15.3190	−	4.10470i	−0.632281	−	0.169419i	−0.0715765	−	0.997435i	$-0.522803\pi$
$587$	−15.3190	−	4.10470i	−0.632281	−	0.169419i	−0.560705	+	0.828016i	$0.689470\pi$
$588$	0.292345	−	0.547727i	0.0120561	−	0.0225879i
$589$	9.84426	+	5.68358i	0.405625	+	0.234188i
$590$	0.484693	−	0.484693i	0.0199545	−	0.0199545i
$591$	−10.4522	+	11.1731i	−0.429945	+	0.459598i
$592$	−1.46983	−	5.48549i	−0.0604097	−	0.225452i
$593$	−22.8541	−	22.8541i	−0.938506	−	0.938506i	0.0597098	−	0.998216i	$-0.480982\pi$
$593$	−22.8541	−	22.8541i	−0.938506	−	0.938506i	−0.998216	+	0.0597098i	$0.980982\pi$
$594$	1.64943	−	3.65780i	0.0676767	−	0.150081i
$595$	−0.101835	+	0.0587943i	−0.00417481	+	0.00241033i
$596$	−2.06867	+	7.72039i	−0.0847361	+	0.316239i
$597$	−22.3852	+	13.9386i	−0.916167	+	0.570469i
$598$	−3.21396	−	9.89146i	−0.131429	−	0.404492i
$599$			38.1977i			1.56072i	0.625333	+	0.780358i	$0.284963\pi$
$599$			38.1977i			1.56072i	−0.625333	+	0.780358i	$0.715037\pi$
$600$	−6.06456	−	19.9492i	−0.247585	−	0.814424i
$601$	10.2032	+	17.6725i	0.416197	+	0.720875i	0.995553	−	0.0941995i	$-0.0300292\pi$
$601$	10.2032	+	17.6725i	0.416197	+	0.720875i	−0.579356	+	0.815075i	$0.696696\pi$
$602$	−7.65103	+	13.2520i	−0.311833	+	0.540110i
$603$	−8.30611	+	2.83063i	−0.338251	+	0.115272i
$604$	−12.3563	+	3.31087i	−0.502772	+	0.134717i
$605$	0.625912	−	0.167713i	0.0254469	−	0.00681849i
$606$	23.4173	+	5.44538i	0.951262	+	0.221203i
$607$	−2.88367	+	4.99467i	−0.117045	+	0.202727i	−0.918595	−	0.395200i	$-0.870675\pi$
$607$	−2.88367	+	4.99467i	−0.117045	+	0.202727i	0.801551	+	0.597927i	$0.204009\pi$
$608$	−4.17720	−	7.23512i	−0.169408	−	0.293423i
$609$	23.1565	−	7.03957i	0.938348	−	0.285258i
$610$			1.29246i			0.0523301i
$611$	3.20269	+	2.88370i	0.129567	+	0.116662i
$612$	−0.264057	−	0.129826i	−0.0106739	−	0.00524791i
$613$	3.76559	−	14.0534i	0.152091	−	0.567611i	−0.847246	−	0.531200i	$-0.821741\pi$
$613$	3.76559	−	14.0534i	0.152091	−	0.567611i	0.999337	−	0.0364100i	$-0.0115922\pi$
$614$	1.86205	−	1.07506i	0.0751463	−	0.0433858i
$615$	−0.356481	−	10.6938i	−0.0143747	−	0.431216i
$616$	4.82668	+	4.82668i	0.194472	+	0.194472i
$617$	12.6951	+	47.3789i	0.511087	+	1.90740i	0.408727	+	0.912657i	$0.365973\pi$
$617$	12.6951	+	47.3789i	0.511087	+	1.90740i	0.102361	+	0.994747i	$0.467360\pi$
$618$	14.2438	+	13.3248i	0.572971	+	0.536003i
$619$	11.0854	−	11.0854i	0.445560	−	0.445560i	−0.448315	−	0.893875i	$-0.647976\pi$
$619$	11.0854	−	11.0854i	0.445560	−	0.445560i	0.893875	+	0.448315i	$0.147976\pi$
$620$	6.27783	+	3.62451i	0.252124	+	0.145564i
$621$	11.3344	+	15.7573i	0.454832	+	0.632318i
$622$	21.2514	+	5.69429i	0.852103	+	0.228320i
$623$	−33.1757			−1.32916
$624$	−4.83934	+	0.415680i	−0.193729	+	0.0166405i
$625$	−18.8779			−0.755116
$626$	20.7546	+	5.56119i	0.829522	+	0.222270i
$627$	−2.17945	−	1.16326i	−0.0870387	−	0.0464562i
$628$	27.7066	+	15.9964i	1.10562	+	0.638327i
$629$	0.360763	−	0.360763i	0.0143846	−	0.0143846i
$630$	−0.755995	+	3.82455i	−0.0301196	+	0.152374i
$631$	−5.82837	−	21.7518i	−0.232024	−	0.865925i	−0.979468	−	0.201600i	$-0.935386\pi$
$631$	−5.82837	−	21.7518i	−0.232024	−	0.865925i	0.747444	−	0.664325i	$-0.231281\pi$
$632$	−12.6391	−	12.6391i	−0.502757	−	0.502757i
$633$	−15.0841	+	0.502834i	−0.599539	+	0.0199858i
$634$	7.90257	−	4.56255i	0.313851	−	0.181202i
$635$	2.11725	−	7.90169i	0.0840206	−	0.313569i
$636$	−13.9142	−	22.3461i	−0.551734	−	0.886079i
$637$	0.772188	−	0.501468i	0.0305952	−	0.0198689i
$638$		−	4.15489i		−	0.164494i
$639$	−11.6632	+	13.3315i	−0.461391	+	0.527387i
$640$	−3.05304	−	5.28802i	−0.120682	−	0.209028i
$641$	−6.53340	+	11.3162i	−0.258054	+	0.446962i	−0.965721	−	0.259584i	$-0.916415\pi$
$641$	−6.53340	+	11.3162i	−0.258054	+	0.446962i	0.707667	+	0.706546i	$0.249748\pi$
$642$	−2.38705	+	10.2653i	−0.0942093	+	0.405137i
$643$	20.3685	−	5.45772i	0.803254	−	0.215231i	0.166242	−	0.986085i	$-0.446837\pi$
$643$	20.3685	−	5.45772i	0.803254	−	0.215231i	0.637012	+	0.770854i	$0.280170\pi$
$644$	−13.1537	+	3.52452i	−0.518327	+	0.138885i
$645$	1.93965	−	8.34128i	0.0763738	−	0.328438i
$646$	0.0384801	−	0.0666494i	0.00151398	−	0.00262229i
$647$	−14.6886	−	25.4414i	−0.577468	−	1.00020i	−0.995769	−	0.0918957i	$-0.970707\pi$
$647$	−14.6886	−	25.4414i	−0.577468	−	1.00020i	0.418300	−	0.908309i	$-0.362626\pi$
$648$	−21.8328	+	9.10471i	−0.857674	+	0.357667i
$649$			1.36987i			0.0537721i
$650$	2.65127	−	12.4734i	0.103991	−	0.489247i
$651$	18.9488	+	30.4316i	0.742663	+	1.19271i
$652$	5.57982	−	20.8242i	0.218523	−	0.815537i
$653$	−37.0748	+	21.4051i	−1.45085	+	0.837648i	−0.998530	−	0.0542087i	$-0.982736\pi$
$653$	−37.0748	+	21.4051i	−1.45085	+	0.837648i	−0.452319	+	0.891856i	$0.649403\pi$
$654$	−3.48451	+	0.116157i	−0.136255	+	0.00454212i
$655$	7.71808	+	7.71808i	0.301570	+	0.301570i
$656$	1.91907	+	7.16205i	0.0749269	+	0.279631i
$657$	−29.8939	−	5.90911i	−1.16627	−	0.230536i
$658$	−1.69499	+	1.69499i	−0.0660775	+	0.0660775i
$659$	24.5538	+	14.1761i	0.956480	+	0.552224i	0.895088	−	0.445890i	$-0.147113\pi$
$659$	24.5538	+	14.1761i	0.956480	+	0.552224i	0.0613923	+	0.998114i	$0.480446\pi$
$660$	−1.38987	−	0.741830i	−0.0541004	−	0.0288757i
$661$	−3.36325	−	0.901180i	−0.130815	−	0.0350518i	0.192817	−	0.981235i	$-0.438238\pi$
$661$	−3.36325	−	0.901180i	−0.130815	−	0.0350518i	−0.323633	+	0.946183i	$0.604904\pi$
$662$	13.2202			0.513818
$663$	−0.249722	−	0.357843i	−0.00969842	−	0.0138975i
$664$	−21.5760			−0.837312
$665$	2.31851	+	0.621244i	0.0899081	+	0.0240908i
$666$	−1.12649	−	16.8776i	−0.0436506	−	0.653992i
$667$	17.4063	+	10.0496i	0.673976	+	0.389120i
$668$	17.5227	−	17.5227i	0.677975	−	0.677975i
$669$	25.9884	+	24.3116i	1.00477	+	0.939942i
$670$	−0.378821	−	1.41378i	−0.0146351	−	0.0546190i
$671$	−1.82641	−	1.82641i	−0.0705079	−	0.0705079i
$672$	−0.877812	−	26.3328i	−0.0338623	−	1.01581i
$673$	33.3610	−	19.2610i	1.28597	−	0.742457i	0.308040	−	0.951373i	$-0.400327\pi$
$673$	33.3610	−	19.2610i	1.28597	−	0.742457i	0.977934	+	0.208916i	$0.0669936\pi$
$674$	3.00126	−	11.2008i	0.115604	−	0.431441i
$675$	2.37519	+	23.6801i	0.0914213	+	0.911448i
$676$	−16.6705	−	7.42208i	−0.641173	−	0.285464i
$677$		−	38.5210i		−	1.48048i	−0.672342	−	0.740241i	$-0.734712\pi$
$677$		−	38.5210i		−	1.48048i	0.672342	−	0.740241i	$-0.265288\pi$
$678$	0.666896	−	0.202736i	0.0256120	−	0.00778604i
$679$	−12.3313	−	21.3584i	−0.473230	−	0.819659i
$680$	0.0595031	−	0.103062i	0.00228184	−	0.00395226i
$681$	−37.9207	−	8.81796i	−1.45312	−	0.337905i
$682$	5.94445	−	1.59281i	0.227625	−	0.0609919i
$683$	−27.4866	+	7.36502i	−1.05175	+	0.281815i	−0.742974	−	0.669321i	$-0.766585\pi$
$683$	−27.4866	+	7.36502i	−1.05175	+	0.281815i	−0.308774	+	0.951136i	$0.599919\pi$
$684$	1.93749	+	5.68530i	0.0740817	+	0.217383i
$685$	−3.81144	+	6.60162i	−0.145628	+	0.252235i
$686$	7.27514	+	12.6009i	0.277766	+	0.481105i
$687$	10.7881	+	35.4872i	0.411592	+	1.35392i
$688$			5.93456i			0.226253i
$689$	−2.04320	−	38.9846i	−0.0778397	−	1.48519i
$690$	−2.74829	+	1.71128i	−0.104626	+	0.0651472i
$691$	−3.45831	+	12.9066i	−0.131560	+	0.490990i	−0.999988	−	0.00482539i	$-0.998464\pi$
$691$	−3.45831	+	12.9066i	−0.131560	+	0.490990i	0.868428	+	0.495815i	$0.165131\pi$
$692$	9.22782	−	5.32769i	0.350789	−	0.202528i
$693$	−4.33627	−	6.47291i	−0.164721	−	0.245885i
$694$	2.92759	+	2.92759i	0.111130	+	0.111130i
$695$	−0.190906	−	0.712472i	−0.00724148	−	0.0270256i
$696$	−16.7337	+	17.8878i	−0.634288	+	0.678034i
$697$	−0.471025	+	0.471025i	−0.0178414	+	0.0178414i
$698$	14.4696	+	8.35404i	0.547683	+	0.316205i
$699$	9.42252	−	17.6537i	0.356392	−	0.667724i
$700$	−16.1277	−	4.32141i	−0.609570	−	0.163334i
$701$	−17.9712			−0.678762			−0.339381	−	0.940649i	$-0.610218\pi$
$701$	−17.9712			−0.678762			−0.339381	+	0.940649i	$0.610218\pi$
$702$	−14.3807	−	1.58054i	−0.542763	−	0.0596536i
$703$	−10.4145			−0.392790
$704$	−2.86639	−	0.768047i	−0.108031	−	0.0289469i
$705$	0.631684	−	1.18350i	0.0237906	−	0.0445732i
$706$	8.63503	+	4.98544i	0.324984	+	0.187629i
$707$	33.0098	−	33.0098i	1.24146	−	1.24146i
$708$	2.27527	−	2.43220i	0.0855100	−	0.0914077i
$709$	−5.11287	−	19.0815i	−0.192018	−	0.716620i	−0.993019	−	0.117957i	$-0.962366\pi$
$709$	−5.11287	−	19.0815i	−0.192018	−	0.716620i	0.801001	−	0.598663i	$-0.204301\pi$
$710$	−2.08913	−	2.08913i	−0.0784036	−	0.0784036i
$711$	11.3549	+	16.9499i	0.425843	+	0.635672i
$712$	29.0774	−	16.7878i	1.08972	−	0.629150i
$713$	−7.70516	+	28.7560i	−0.288560	+	1.07692i
$714$	0.206034	−	0.128291i	0.00771062	−	0.00480117i
$715$	−1.27248	−	1.95944i	−0.0475881	−	0.0732789i
$716$		−	2.61929i		−	0.0978873i
$717$	−2.79812	−	9.20435i	−0.104498	−	0.343743i
$718$	−4.07512	−	7.05832i	−0.152082	−	0.263414i
$719$	19.7471	−	34.2030i	0.736443	−	1.27556i	−0.217644	−	0.976028i	$-0.569837\pi$
$719$	19.7471	−	34.2030i	0.736443	−	1.27556i	0.954087	−	0.299529i	$-0.0968296\pi$
$720$	0.487717	+	1.43114i	0.0181761	+	0.0533355i
$721$	36.5824	−	9.80221i	1.36240	−	0.365054i
$722$	12.6545	−	3.39077i	0.470953	−	0.126191i
$723$	36.3133	+	8.44417i	1.35050	+	0.314042i
$724$	−7.85745	+	13.6095i	−0.292020	+	0.505793i
$725$	12.3217	+	21.3419i	0.457618	+	0.792618i
$726$	−1.27967	+	0.389021i	−0.0474932	+	0.0144379i
$727$		−	20.6590i		−	0.766199i	−0.923707	−	0.383099i	$-0.874857\pi$
$727$		−	20.6590i		−	0.766199i	0.923707	−	0.383099i	$-0.125143\pi$
$728$	11.1732	−	21.9289i	0.414108	−	0.812738i
$729$	26.4621	−	5.36243i	0.980079	−	0.198609i
$730$	1.31548	−	4.90943i	0.0486880	−	0.181706i
$731$	−0.461726	+	0.266578i	−0.0170776	+	0.00985974i
$732$	0.209224	+	6.27635i	0.00773315	+	0.231981i
$733$	10.8077	+	10.8077i	0.399191	+	0.399191i	0.877948	−	0.478756i	$-0.158912\pi$
$733$	10.8077	+	10.8077i	0.399191	+	0.399191i	−0.478756	+	0.877948i	$0.658912\pi$
$734$	1.35567	+	5.05942i	0.0500386	+	0.186747i
$735$	−0.209303	−	0.195799i	−0.00772027	−	0.00722216i
$736$	15.4715	−	15.4715i	0.570288	−	0.570288i
$737$	2.53318	+	1.46253i	0.0933109	+	0.0538731i
$738$	1.47079	+	22.0360i	0.0541404	+	0.811155i
$739$	−9.76658	−	2.61695i	−0.359270	−	0.0962660i	0.0746692	−	0.997208i	$-0.476210\pi$
$739$	−9.76658	−	2.61695i	−0.359270	−	0.0962660i	−0.433939	+	0.900942i	$0.642877\pi$
$740$	−6.64147			−0.244145
$741$	−1.56061	+	8.76959i	−0.0573306	+	0.322159i
$742$	21.7135			0.797126
$743$	−25.5275	−	6.84007i	−0.936513	−	0.250938i	−0.241883	−	0.970305i	$-0.577765\pi$
$743$	−25.5275	−	6.84007i	−0.936513	−	0.250938i	−0.694630	+	0.719367i	$0.744432\pi$
$744$	−32.0072	−	17.0836i	−1.17344	−	0.626316i
$745$	3.19537	+	1.84485i	0.117069	+	0.0675900i
$746$	6.32270	−	6.32270i	0.231490	−	0.231490i
$747$	24.1594	+	4.77556i	0.883945	+	0.174729i
$748$	0.0253855	+	0.0947401i	0.000928187	+	0.00346404i
$749$	14.4703	+	14.4703i	0.528731	+	0.528731i
$750$	−8.29836	+	0.276628i	−0.303013	+	0.0101010i
$751$	28.8022	−	16.6290i	1.05101	−	0.606800i	0.128077	−	0.991764i	$-0.459120\pi$
$751$	28.8022	−	16.6290i	1.05101	−	0.606800i	0.922931	+	0.384964i	$0.125786\pi$
$752$	−0.240611	+	0.897973i	−0.00877419	+	0.0327457i
$753$	9.45216	+	15.1801i	0.344456	+	0.553192i
$754$	−14.2474	+	4.62932i	−0.518861	+	0.168590i
$755$			5.90529i			0.214916i
$756$	−3.05209	+	18.6949i	−0.111004	+	0.679927i
$757$	−10.8406	−	18.7764i	−0.394007	−	0.682441i	0.598967	−	0.800774i	$-0.295578\pi$
$757$	−10.8406	−	18.7764i	−0.394007	−	0.682441i	−0.992974	+	0.118333i	$0.962245\pi$
$758$	−7.68274	+	13.3069i	−0.279050	+	0.483328i
$759$	1.46544	−	6.30196i	0.0531920	−	0.228746i
$760$	−2.34647	+	0.628734i	−0.0851153	+	0.0228066i
$761$	23.2086	−	6.21871i	0.841309	−	0.225428i	0.187668	−	0.982233i	$-0.439907\pi$
$761$	23.2086	−	6.21871i	0.841309	−	0.225428i	0.653641	+	0.756804i	$0.273240\pi$
$762$	−3.82434	+	16.4462i	−0.138541	+	0.595782i
$763$	−3.38485	+	5.86273i	−0.122540	+	0.212245i
$764$	−12.4304	−	21.5300i	−0.449715	−	0.778929i
$765$	−0.0894390	+	0.102232i	−0.00323368	+	0.00369621i
$766$			11.3175i			0.408917i
$767$	4.69740	−	1.52629i	0.169613	−	0.0551111i
$768$	12.0955	+	19.4252i	0.436457	+	0.700945i
$769$	−1.24834	+	4.65885i	−0.0450161	+	0.168003i	−0.984774	−	0.173837i	$-0.944383\pi$
$769$	−1.24834	+	4.65885i	−0.0450161	+	0.168003i	0.939758	+	0.341840i	$0.111050\pi$
$770$	1.12541	−	0.649758i	0.0405571	−	0.0234157i
$771$	−9.14004	+	0.304686i	−0.329171	+	0.0109730i
$772$	−16.5814	−	16.5814i	−0.596779	−	0.596779i
$773$	−6.38401	−	23.8255i	−0.229617	−	0.856942i	−0.980502	−	0.196509i	$-0.937039\pi$
$773$	−6.38401	−	23.8255i	−0.229617	−	0.856942i	0.750885	−	0.660433i	$-0.229627\pi$
$774$	−3.42774	+	17.3408i	−0.123208	+	0.623302i
$775$	−25.8105	+	25.8105i	−0.927139	+	0.927139i
$776$	21.6159	+	12.4799i	0.775964	+	0.448003i
$777$	−28.9754	−	15.4654i	−1.03949	−	0.554818i
$778$	−24.7318	−	6.62687i	−0.886678	−	0.237585i
$779$	13.5975			0.487182
$780$	−0.995227	+	5.59250i	−0.0356348	+	0.200243i
$781$	5.90443			0.211277
$782$	0.194690	+	0.0521669i	0.00696209	+	0.00186549i
$783$	22.6964	−	16.3258i	0.811105	−	0.583435i
$784$	0.172005	+	0.0993073i	0.00614305	+	0.00354669i
$785$	10.4432	−	10.4432i	0.372734	−	0.372734i
$786$	−16.4525	−	15.3910i	−0.586843	−	0.548980i
$787$	10.8910	+	40.6459i	0.388224	+	1.44887i	0.833022	+	0.553240i	$0.186609\pi$
$787$	10.8910	+	40.6459i	0.388224	+	1.44887i	−0.444798	+	0.895631i	$0.646725\pi$
$788$	−8.76769	−	8.76769i	−0.312336	−	0.312336i
$789$	−0.186486	−	5.59426i	−0.00663909	−	0.199161i
$790$	−2.94700	+	1.70145i	−0.104850	+	0.0605350i
$791$	0.350295	−	1.30732i	0.0124551	−	0.0464829i
$792$	7.07606	+	3.47901i	0.251437	+	0.123621i
$793$	−4.22795	+	8.29788i	−0.150139	+	0.294666i
$794$			4.63116i			0.164354i
$795$	−11.6266	+	3.53449i	−0.412353	+	0.125355i
$796$	−10.6855	−	18.5079i	−0.378738	−	0.655994i
$797$	4.14739	−	7.18349i	0.146908	−	0.254452i	−0.783175	−	0.621801i	$-0.786401\pi$
$797$	4.14739	−	7.18349i	0.146908	−	0.254452i	0.930083	+	0.367349i	$0.119735\pi$
$798$	−4.82563	−	1.12214i	−0.170826	−	0.0397232i
$799$	−0.0806732	+	0.0216163i	−0.00285401	+	0.000764730i
$800$	25.9130	−	6.94336i	0.916162	−	0.245485i
$801$	−36.2746	+	12.3620i	−1.28170	+	0.436789i
$802$	−13.2584	+	22.9642i	−0.468170	+	0.810895i
$803$	5.07872	+	8.79661i	0.179224	+	0.310426i
$804$	−2.06847	−	6.80418i	−0.0729493	−	0.239965i
$805$			6.28635i			0.221565i
$806$	−12.0851	−	18.6093i	−0.425680	−	0.655485i
$807$	27.8585	−	17.3466i	0.980664	−	0.610630i
$808$	−12.2281	+	45.6359i	−0.430183	+	1.60546i
$809$	9.11187	−	5.26074i	0.320356	−	0.184958i	−0.331195	−	0.943562i	$-0.607452\pi$
$809$	9.11187	−	5.26074i	0.320356	−	0.184958i	0.651551	+	0.758605i	$0.274119\pi$
$810$	0.598497	+	4.46350i	0.0210290	+	0.156831i
$811$	−22.0458	−	22.0458i	−0.774132	−	0.774132i	0.204694	−	0.978826i	$-0.434380\pi$
$811$	−22.0458	−	22.0458i	−0.774132	−	0.774132i	−0.978826	+	0.204694i	$0.934380\pi$
$812$	5.07664	+	18.9463i	0.178155	+	0.664884i
$813$	−3.86438	+	4.13090i	−0.135530	+	0.144877i
$814$	−3.98693	+	3.98693i	−0.139742	+	0.139742i
$815$	−8.61886	−	4.97610i	−0.301906	−	0.174305i
$816$	0.0443228	−	0.0830416i	0.00155161	−	0.00290704i
$817$	10.5123	+	2.81677i	0.367780	+	0.0985463i
$818$	20.8553			0.729190
$819$	−17.3647	+	22.0814i	−0.606772	+	0.771587i
$820$	8.67135			0.302817
$821$	−3.53120	−	0.946181i	−0.123240	−	0.0330220i	0.196672	−	0.980469i	$-0.436987\pi$
$821$	−3.53120	−	0.946181i	−0.123240	−	0.0330220i	−0.319912	+	0.947447i	$0.603653\pi$
$822$	7.40873	−	13.8807i	0.258409	−	0.484146i
$823$	−4.80786	−	2.77582i	−0.167591	−	0.0967590i	0.413858	−	0.910341i	$-0.364181\pi$
$823$	−4.80786	−	2.77582i	−0.167591	−	0.0967590i	−0.581450	+	0.813582i	$0.697514\pi$
$824$	−27.1030	+	27.1030i	−0.944178	+	0.944178i
$825$	5.41946	−	5.79324i	0.188681	−	0.201695i
$826$	0.711030	+	2.65360i	0.0247399	+	0.0923305i
$827$	−31.8549	−	31.8549i	−1.10770	−	1.10770i	−0.993452	−	0.114253i	$-0.963553\pi$
$827$	−31.8549	−	31.8549i	−1.10770	−	1.10770i	−0.114253	−	0.993452i	$-0.536447\pi$
$828$	−13.0691	+	8.75509i	−0.454181	+	0.304261i
$829$	−11.7477	+	6.78255i	−0.408015	+	0.235568i	−0.689937	−	0.723870i	$-0.742362\pi$
$829$	−11.7477	+	6.78255i	−0.408015	+	0.235568i	0.281921	+	0.959438i	$0.409028\pi$
$830$	−1.06313	+	3.96765i	−0.0369018	+	0.137719i
$831$	22.1644	−	13.8011i	0.768873	−	0.478754i
$832$	0.559997	+	10.6848i	0.0194144	+	0.370430i
$833$			0.0178434i			0.000618236i
$834$	0.442820	+	1.45664i	0.0153336	+	0.0504395i
$835$	−5.71982	−	9.90702i	−0.197943	−	0.342847i
$836$	1.00106	−	1.73389i	0.0346225	−	0.0599678i
$837$	32.0583	+	26.2135i	1.10810	+	0.906070i
$838$	19.1164	−	5.12221i	0.660364	−	0.176944i
$839$	−8.45438	+	2.26534i	−0.291878	+	0.0782084i	−0.401787	−	0.915733i	$-0.631611\pi$
$839$	−8.45438	+	2.26534i	−0.291878	+	0.0782084i	0.109909	+	0.993942i	$0.464944\pi$
$840$	−7.46205	−	1.73520i	−0.257465	−	0.0598701i
$841$	−0.0248393	+	0.0430230i	−0.000856529	+	0.00148355i
$842$	8.09517	+	14.0212i	0.278978	+	0.483204i
$843$	−37.5997	+	11.4303i	−1.29500	+	0.393681i
$844$		−	12.2313i		−	0.421020i
$845$	−5.30129	+	6.54662i	−0.182370	+	0.225211i
$846$	−1.22173	+	2.48491i	−0.0420038	+	0.0854328i
$847$	−0.672164	+	2.50855i	−0.0230958	+	0.0861948i
$848$	7.29286	−	4.21054i	0.250438	−	0.144590i
$849$	−1.46783	−	44.0324i	−0.0503759	−	1.51119i
$850$	0.174747	+	0.174747i	0.00599377	+	0.00599377i
$851$	−7.05939	−	26.3460i	−0.241993	−	0.903130i
$852$	−10.4833	−	9.80691i	−0.359152	−	0.335979i
$853$	−16.5410	+	16.5410i	−0.566352	+	0.566352i	−0.931104	−	0.364753i	$-0.881154\pi$
$853$	−16.5410	+	16.5410i	−0.566352	+	0.566352i	0.364753	+	0.931104i	$0.381154\pi$
$854$	−4.48597	−	2.58998i	−0.153507	−	0.0886272i
$855$	2.76658	−	0.184655i	0.0946149	−	0.00631506i
$856$	−20.0050	−	5.36034i	−0.683758	−	0.183213i
$857$	−44.6928			−1.52668			−0.763339	−	0.645998i	$-0.776441\pi$
$857$	−44.6928			−1.52668			−0.763339	+	0.645998i	$0.776441\pi$
$858$	2.75978	+	3.95466i	0.0942173	+	0.135010i
$859$	−17.0382			−0.581335			−0.290668	−	0.956824i	$-0.593877\pi$
$859$	−17.0382			−0.581335			−0.290668	+	0.956824i	$0.593877\pi$
$860$	6.70387	+	1.79630i	0.228600	+	0.0612532i
$861$	37.8313	+	20.1922i	1.28929	+	0.688148i
$862$	−4.47235	−	2.58211i	−0.152329	−	0.0879471i
$863$	−33.6703	+	33.6703i	−1.14615	+	1.14615i	−0.158848	+	0.987303i	$0.550778\pi$
$863$	−33.6703	+	33.6703i	−1.14615	+	1.14615i	−0.987303	+	0.158848i	$0.949222\pi$
$864$	−10.7720	−	28.4654i	−0.366470	−	0.968414i
$865$	−1.27309	−	4.75125i	−0.0432865	−	0.161547i
$866$	8.17148	+	8.17148i	0.277678	+	0.277678i
$867$	−29.4201	+	0.980728i	−0.999158	+	0.0333073i
$868$	−25.1605	+	14.5264i	−0.854003	+	0.493059i
$869$	1.76013	−	6.56888i	0.0597082	−	0.222834i
$870$	2.46489	+	3.95858i	0.0835675	+	0.134208i
$871$	2.19271	−	10.3160i	0.0742970	−	0.349545i
$872$		−	6.85132i		−	0.232015i
$873$	−21.4417	−	18.7586i	−0.725692	−	0.634881i
$874$	−2.05717	−	3.56312i	−0.0695848	−	0.120524i
$875$	−8.06100	+	13.9621i	−0.272512	+	0.472004i
$876$	5.59339	−	24.0538i	0.188983	−	0.812703i
$877$	−6.65637	+	1.78357i	−0.224770	+	0.0602268i	−0.369446	−	0.929252i	$-0.620453\pi$
$877$	−6.65637	+	1.78357i	−0.224770	+	0.0602268i	0.144676	+	0.989479i	$0.453786\pi$
$878$	−11.9480	+	3.20146i	−0.403226	+	0.108044i
$879$	−5.77551	+	24.8370i	−0.194803	+	0.837730i
$880$	0.251994	−	0.436466i	0.00849471	−	0.0147133i
$881$	17.3541	+	30.0581i	0.584673	+	1.01268i	0.994916	+	0.100707i	$0.0321105\pi$
$881$	17.3541	+	30.0581i	0.584673	+	1.01268i	−0.410243	+	0.911976i	$0.634556\pi$
$882$	0.445241	+	0.389525i	0.0149920	+	0.0131160i
$883$			43.5934i			1.46704i	0.679670	+	0.733518i	$0.262123\pi$
$883$			43.5934i			1.46704i	−0.679670	+	0.733518i	$0.737877\pi$
$884$	0.296587	−	0.192607i	0.00997531	−	0.00647808i
$885$	−0.812675	−	1.30515i	−0.0273178	−	0.0438720i
$886$	−3.36406	+	12.5549i	−0.113018	+	0.421789i
$887$	28.2343	−	16.3011i	0.948014	−	0.547336i	0.0555506	−	0.998456i	$-0.482309\pi$
$887$	28.2343	−	16.3011i	0.948014	−	0.547336i	0.892463	+	0.451120i	$0.148975\pi$
$888$	33.2219	−	1.10746i	1.11485	−	0.0371640i
$889$	23.1831	+	23.1831i	0.777536	+	0.777536i
$890$	−1.65439	−	6.17428i	−0.0554554	−	0.206962i
$891$	−7.15327	−	5.46176i	−0.239643	−	0.182976i
$892$	−20.3935	+	20.3935i	−0.682827	+	0.682827i
$893$	1.47644	+	0.852425i	0.0494073	+	0.0285253i
$894$	−6.71867	−	3.58604i	−0.224706	−	0.119935i
$895$	−1.16794	−	0.312950i	−0.0390401	−	0.0104608i
$896$	24.4722			0.817558
$897$	−23.2427	+	1.99645i	−0.776050	+	0.0666595i
$898$	−12.9560			−0.432346
$899$	41.4196	+	11.0983i	1.38142	+	0.370150i
$900$	−19.2445	+	1.28447i	−0.641482	+	0.0428156i
$901$	0.655185	+	0.378271i	0.0218274	+	0.0126020i
$902$	5.20548	−	5.20548i	0.173324	−	0.173324i
$903$	25.0647	+	23.4476i	0.834102	+	0.780286i
$904$	0.354518	+	1.32308i	0.0117911	+	0.0440050i
$905$	5.12970	+	5.12970i	0.170517	+	0.170517i
$906$	−0.406096	−	12.1822i	−0.0134916	−	0.404725i
$907$	−5.86707	+	3.38735i	−0.194813	+	0.112475i	−0.594234	−	0.804292i	$-0.702545\pi$
$907$	−5.86707	+	3.38735i	−0.194813	+	0.112475i	0.399421	+	0.916768i	$0.369211\pi$
$908$	8.16622	−	30.4768i	0.271006	−	1.01141i
$909$	23.7931	−	48.3934i	0.789167	−	1.60511i
$910$	−3.48199	−	3.13518i	−0.115427	−	0.103930i
$911$		−	4.55059i		−	0.150768i	−0.997155	−	0.0753839i	$-0.975982\pi$
$911$		−	4.55059i		−	0.150768i	0.997155	−	0.0753839i	$-0.0240182\pi$
$912$	−1.83837	+	0.558866i	−0.0608747	+	0.0185059i
$913$	−4.10447	−	7.10916i	−0.135838	−	0.235279i
$914$	−1.86052	+	3.22251i	−0.0615405	+	0.106591i
$915$	2.82364	+	0.656599i	0.0933465	+	0.0217065i
$916$	−29.0351	+	7.77992i	−0.959346	+	0.257056i
$917$	−42.2549	+	11.3222i	−1.39538	+	0.373891i
$918$	0.177475	−	0.217047i	0.00585756	−	0.00716363i
$919$	−7.52644	+	13.0362i	−0.248274	+	0.430024i	−0.963047	−	0.269333i	$-0.913197\pi$
$919$	−7.52644	+	13.0362i	−0.248274	+	0.430024i	0.714773	+	0.699357i	$0.246530\pi$
$920$	−3.18107	−	5.50978i	−0.104877	−	0.181652i
$921$	−1.40271	−	4.61419i	−0.0462209	−	0.152043i
$922$		−	7.19151i		−	0.236840i
$923$	−6.57863	−	20.2468i	−0.216538	−	0.666430i
$924$	5.35998	−	3.33750i	0.176330	−	0.109796i
$925$	8.65551	−	32.3028i	0.284592	−	1.06211i
$926$	8.13999	−	4.69963i	0.267497	−	0.154439i
$927$	36.3470	−	24.3492i	1.19379	−	0.799734i
$928$	−22.2848	−	22.2848i	−0.731536	−	0.731536i
$929$	1.97692	+	7.37796i	0.0648606	+	0.242063i	0.990743	−	0.135748i	$-0.0433437\pi$
$929$	1.97692	+	7.37796i	0.0648606	+	0.242063i	−0.925883	+	0.377811i	$0.876677\pi$
$930$	−4.71865	+	5.04410i	−0.154731	+	0.165402i
$931$	0.257551	−	0.257551i	0.00844088	−	0.00844088i
$932$	14.0446	+	8.10868i	0.460048	+	0.265609i
$933$	23.2366	−	43.5352i	0.760731	−	1.42528i
$934$	−1.25833	−	0.337168i	−0.0411738	−	0.0110325i
$935$	0.0452778			0.00148074
$936$	4.04576	−	28.1407i	0.132240	−	0.919806i
$937$	53.8540			1.75933			0.879667	−	0.475591i	$-0.157766\pi$
$937$	53.8540			1.75933			0.879667	+	0.475591i	$0.157766\pi$
$938$	5.66619	+	1.51825i	0.185008	+	0.0495727i
$939$	22.6934	−	42.5175i	0.740571	−	1.38751i
$940$	0.941550	+	0.543604i	0.0307100	+	0.0177304i
$941$	−3.79560	+	3.79560i	−0.123733	+	0.123733i	−0.766262	−	0.642529i	$-0.777885\pi$
$941$	−3.79560	+	3.79560i	−0.123733	+	0.123733i	0.642529	+	0.766262i	$0.277885\pi$
$942$	−20.8254	+	22.2617i	−0.678527	+	0.725324i
$943$	9.21700	+	34.3983i	0.300147	+	1.12016i
$944$	0.753381	+	0.753381i	0.0245205	+	0.0245205i
$945$	7.97143	+	3.59458i	0.259311	+	0.116932i
$946$	5.10272	−	2.94605i	0.165904	−	0.0957845i
$947$	−12.1826	+	45.4659i	−0.395880	+	1.47744i	0.424396	+	0.905477i	$0.360486\pi$
$947$	−12.1826	+	45.4659i	−0.395880	+	1.47744i	−0.820276	+	0.571968i	$0.806180\pi$
$948$	−14.0356	+	8.73956i	−0.455856	+	0.283848i
$949$	24.5056	−	27.2164i	0.795486	−	0.883482i
$950$		−	5.04458i		−	0.163668i
$951$	−5.95312	−	19.5826i	−0.193043	−	0.635011i
$952$	0.238479	+	0.413057i	0.00772913	+	0.0133873i
$953$	−6.89009	+	11.9340i	−0.223192	+	0.386580i	−0.955775	−	0.294097i	$-0.904981\pi$
$953$	−6.89009	+	11.9340i	−0.223192	+	0.386580i	0.732583	+	0.680677i	$0.238314\pi$
$954$	23.7417	−	8.09091i	0.768667	−	0.261953i
$955$	−11.0855	+	2.97034i	−0.358717	+	0.0961179i
$956$	7.53086	−	2.01789i	0.243565	−	0.0652631i
$957$	−9.07720	−	2.11078i	−0.293424	−	0.0682319i
$958$	−15.1405	+	26.2240i	−0.489166	+	0.847260i
$959$	−15.2756	−	26.4582i	−0.493276	−	0.854379i
$960$	3.18660	−	0.968726i	0.102847	−	0.0312655i
$961$			32.5142i			1.04884i
$962$	18.1137	+	9.22933i	0.584009	+	0.297565i
$963$	21.2139	+	10.4300i	0.683607	+	0.336102i
$964$	−7.82006	+	29.1849i	−0.251867	+	0.939981i
$965$	−9.37483	+	5.41256i	−0.301786	+	0.174236i
$966$	−0.432301	−	12.9683i	−0.0139091	−	0.417247i
$967$	−7.38117	−	7.38117i	−0.237363	−	0.237363i	0.578395	−	0.815757i	$-0.303679\pi$
$967$	−7.38117	−	7.38117i	−0.237363	−	0.237363i	−0.815757	+	0.578395i	$0.803679\pi$
$968$	−0.680268	−	2.53880i	−0.0218646	−	0.0816000i
$969$	−0.126060	−	0.117927i	−0.00404965	−	0.00378836i
$970$	3.36005	−	3.36005i	0.107885	−	0.107885i
$971$	−24.4363	−	14.1083i	−0.784199	−	0.452757i	0.0537176	−	0.998556i	$-0.482893\pi$
$971$	−24.4363	−	14.1083i	−0.784199	−	0.452757i	−0.837916	+	0.545799i	$0.816226\pi$
$972$	3.62894	+	21.5785i	0.116398	+	0.692130i
$973$	2.85547	+	0.765120i	0.0915421	+	0.0245286i
$974$	10.7718			0.345150
$975$	−25.9038	−	12.1290i	−0.829584	−	0.388439i
$976$	−2.00893			−0.0643042
$977$	46.9920	+	12.5915i	1.50341	+	0.402837i	0.914240	−	0.405174i	$-0.132789\pi$
$977$	46.9920	+	12.5915i	1.50341	+	0.402837i	0.589168	+	0.808011i	$0.299456\pi$
$978$	18.1222	+	9.67260i	0.579485	+	0.309296i
$979$	11.0630	+	6.38720i	0.353574	+	0.204136i
$980$	0.164244	−	0.164244i	0.00524658	−	0.00524658i
$981$	−1.51645	+	7.67164i	−0.0484164	+	0.244937i
$982$	−4.73033	−	17.6538i	−0.150951	−	0.563357i
$983$	−17.9672	−	17.9672i	−0.573065	−	0.573065i	0.359919	−	0.932984i	$-0.382804\pi$
$983$	−17.9672	−	17.9672i	−0.573065	−	0.573065i	−0.932984	+	0.359919i	$0.882804\pi$
$984$	−43.3757	+	1.44594i	−1.38277	+	0.0460950i
$985$	−4.95708	+	2.86197i	−0.157946	+	0.0911901i
$986$	0.0751401	−	0.280427i	0.00239295	−	0.00893061i
$987$	2.84195	+	4.56414i	0.0904602	+	0.145278i
$988$	−7.06102	−	1.50085i	−0.224641	−	0.0477483i
$989$			28.5028i			0.906337i
$990$	0.988425	−	1.12981i	0.0314142	−	0.0359076i
$991$	−28.2692	−	48.9637i	−0.898001	−	1.55538i	−0.830046	−	0.557694i	$-0.811686\pi$
$991$	−28.2692	−	48.9637i	−0.898001	−	1.55538i	−0.0679542	−	0.997688i	$-0.521647\pi$
$992$	23.3401	−	40.4263i	0.741050	−	1.28354i
$993$	6.71618	−	28.8822i	0.213131	−	0.916549i
$994$	11.4376	−	3.06469i	0.362778	−	0.0972060i
$995$	−9.52939	+	2.55339i	−0.302102	+	0.0809480i
$996$	−4.52042	+	19.4396i	−0.143235	+	0.615966i
$997$	−4.06627	+	7.04299i	−0.128780	+	0.223054i	−0.923204	−	0.384310i	$-0.874439\pi$
$997$	−4.06627	+	7.04299i	−0.128780	+	0.223054i	0.794424	+	0.607363i	$0.207773\pi$
$998$	−10.1105	−	17.5118i	−0.320041	−	0.554327i
$999$	−37.4448	−	6.11316i	−1.18470	−	0.193412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.be.a.89.19	✓	184
3.2	odd	2	inner	429.2.be.a.89.28	yes	184
13.6	odd	12	inner	429.2.be.a.188.28	yes	184
39.32	even	12	inner	429.2.be.a.188.19	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.be.a.89.19	✓	184	1.1	even	1	trivial
429.2.be.a.89.28	yes	184	3.2	odd	2	inner
429.2.be.a.188.19	yes	184	39.32	even	12	inner
429.2.be.a.188.28	yes	184	13.6	odd	12	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.745893 - 0.199861i) q^{2} +(-0.815569 + 1.52802i) q^{3} +(-1.21564 - 0.701849i) q^{4} +(-0.458199 + 0.458199i) q^{5} +(0.913720 - 0.976739i) q^{6} +(-0.672164 - 2.50855i) q^{7} +(1.85853 + 1.85853i) q^{8} +(-1.66969 - 2.49241i) q^{9} +O(q^{10})\)	\(q+(-0.745893 - 0.199861i) q^{2} +(-0.815569 + 1.52802i) q^{3} +(-1.21564 - 0.701849i) q^{4} +(-0.458199 + 0.458199i) q^{5} +(0.913720 - 0.976739i) q^{6} +(-0.672164 - 2.50855i) q^{7} +(1.85853 + 1.85853i) q^{8} +(-1.66969 - 2.49241i) q^{9} +(0.433344 - 0.250191i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(2.06388 - 1.28511i) q^{12} +(3.60061 - 0.188710i) q^{13} +2.00545i q^{14} +(-0.326445 - 1.07383i) q^{15} +(0.388884 + 0.673567i) q^{16} +(-0.0349370 + 0.0605127i) q^{17} +(0.747275 + 2.19278i) q^{18} +(1.37772 - 0.369159i) q^{19} +(0.878592 - 0.235418i) q^{20} +(4.38131 + 1.01882i) q^{21} +(0.386103 - 0.668749i) q^{22} +(1.86776 + 3.23505i) q^{23} +(-4.35563 + 1.32411i) q^{24} +4.58011i q^{25} +(-2.72339 - 0.578866i) q^{26} +(5.17021 - 0.518589i) q^{27} +(-0.943516 + 3.52125i) q^{28} +(4.65969 - 2.69028i) q^{29} +(0.0288753 + 0.866207i) q^{30} +(5.63534 + 5.63534i) q^{31} +(-1.51598 - 5.65772i) q^{32} +(-1.26487 - 1.18326i) q^{33} +(0.0381535 - 0.0381535i) q^{34} +(1.45740 + 0.841432i) q^{35} +(0.280445 + 4.20175i) q^{36} +(-7.05285 - 1.88981i) q^{37} -1.10141 q^{38} +(-2.64819 + 5.65571i) q^{39} -1.70315 q^{40} +(9.20846 + 2.46740i) q^{41} +(-3.06437 - 1.63558i) q^{42} +(6.60798 + 3.81512i) q^{43} +(0.992565 - 0.992565i) q^{44} +(1.90707 + 0.376970i) q^{45} +(-0.746585 - 2.78629i) q^{46} +(0.845190 + 0.845190i) q^{47} +(-1.34639 + 0.0448823i) q^{48} +(0.221152 - 0.127682i) q^{49} +(0.915387 - 3.41627i) q^{50} +(-0.0639711 - 0.102737i) q^{51} +(-4.50949 - 2.29768i) q^{52} -10.8272i q^{53} +(-3.96007 - 0.646513i) q^{54} +(-0.323996 - 0.561177i) q^{55} +(3.41298 - 5.91145i) q^{56} +(-0.559544 + 2.40626i) q^{57} +(-4.01332 + 1.07536i) q^{58} +(1.32319 - 0.354549i) q^{59} +(-0.356829 + 1.53451i) q^{60} +(-1.29147 + 2.23689i) q^{61} +(-3.07707 - 5.32965i) q^{62} +(-5.13004 + 5.86382i) q^{63} +2.96751i q^{64} +(-1.56333 + 1.73626i) q^{65} +(0.706969 + 1.13538i) q^{66} +(0.757062 - 2.82539i) q^{67} +(0.0849417 - 0.0490411i) q^{68} +(-6.46650 + 0.215563i) q^{69} +(-0.918896 - 0.918896i) q^{70} +(-1.52818 - 5.70324i) q^{71} +(1.52905 - 7.73539i) q^{72} +(7.18240 - 7.18240i) q^{73} +(4.88297 + 2.81919i) q^{74} +(-6.99850 - 3.73539i) q^{75} +(-1.93390 - 0.518188i) q^{76} +2.59704 q^{77} +(3.10563 - 3.68928i) q^{78} -6.80061 q^{79} +(-0.486815 - 0.130442i) q^{80} +(-3.42425 + 8.32313i) q^{81} +(-6.37539 - 3.68083i) q^{82} +(-5.80460 + 5.80460i) q^{83} +(-4.61104 - 4.31354i) q^{84} +(-0.0117188 - 0.0437350i) q^{85} +(-4.16635 - 4.16635i) q^{86} +(0.310492 + 9.31421i) q^{87} +(-2.27622 + 1.31418i) q^{88} +(3.30626 - 12.3391i) q^{89} +(-1.34713 - 0.662330i) q^{90} +(-2.89359 - 8.90547i) q^{91} -5.24353i q^{92} +(-13.2069 + 4.01491i) q^{93} +(-0.461500 - 0.799342i) q^{94} +(-0.462122 + 0.800419i) q^{95} +(9.88151 + 2.29781i) q^{96} +(9.17280 - 2.45784i) q^{97} +(-0.190475 + 0.0510375i) q^{98} +(2.83963 - 0.967716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \) 184 * q - 12 * q^6 + 12 * q^7	\( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) \) 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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