LMFDB - Embedded newform 308.2.l.a.243.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(199,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("308.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.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:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			243.4
Character	$\chi$	$=$	308.243
Dual form			308.2.l.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36546 - 0.368132i) q^{2} +(0.591585 + 1.02466i) q^{3} +(1.72896 + 1.00534i) q^{4} +(-3.61040 - 2.08447i) q^{5} +(-0.430577 - 1.61691i) q^{6} +(2.05863 + 1.66194i) q^{7} +(-1.99072 - 2.00923i) q^{8} +(0.800054 - 1.38573i) q^{9} +O(q^{10})$	\(q+(-1.36546 - 0.368132i) q^{2} +(0.591585 + 1.02466i) q^{3} +(1.72896 + 1.00534i) q^{4} +(-3.61040 - 2.08447i) q^{5} +(-0.430577 - 1.61691i) q^{6} +(2.05863 + 1.66194i) q^{7} +(-1.99072 - 2.00923i) q^{8} +(0.800054 - 1.38573i) q^{9} +(4.16249 + 4.17536i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-0.00730050 + 2.36633i) q^{12} -3.06252i q^{13} +(-2.19916 - 3.02716i) q^{14} -4.93256i q^{15} +(1.97859 + 3.47638i) q^{16} +(3.05949 - 1.76639i) q^{17} +(-1.60257 + 1.59764i) q^{18} +(1.82875 - 3.16749i) q^{19} +(-4.14663 - 7.23363i) q^{20} +(-0.485065 + 3.09257i) q^{21} +(-1.36659 + 0.363918i) q^{22} +(4.09107 + 2.36198i) q^{23} +(0.881091 - 3.22844i) q^{24} +(6.18999 + 10.7214i) q^{25} +(-1.12741 + 4.18174i) q^{26} +5.44271 q^{27} +(1.88846 + 4.94305i) q^{28} -2.48827 q^{29} +(-1.81583 + 6.73520i) q^{30} +(-2.78801 - 4.82897i) q^{31} +(-1.42191 - 5.47523i) q^{32} +(1.02466 + 0.591585i) q^{33} +(-4.82787 + 1.28565i) q^{34} +(-3.96821 - 10.2914i) q^{35} +(2.77639 - 1.59155i) q^{36} +(4.17805 - 7.23659i) q^{37} +(-3.66314 + 3.65186i) q^{38} +(3.13803 - 1.81174i) q^{39} +(2.99913 + 11.4037i) q^{40} -6.95486i q^{41} +(1.80081 - 4.04420i) q^{42} -2.12355i q^{43} +(1.99999 + 0.00617028i) q^{44} +(-5.77703 + 3.33537i) q^{45} +(-4.71667 - 4.73125i) q^{46} +(-2.26428 + 3.92184i) q^{47} +(-2.39159 + 4.08394i) q^{48} +(1.47589 + 6.84264i) q^{49} +(-4.50529 - 16.9183i) q^{50} +(3.61989 + 2.08995i) q^{51} +(3.07887 - 5.29496i) q^{52} +(2.58566 + 4.47849i) q^{53} +(-7.43180 - 2.00364i) q^{54} -4.16893 q^{55} +(-0.758926 - 7.44473i) q^{56} +4.32745 q^{57} +(3.39763 + 0.916012i) q^{58} +(1.43322 + 2.48241i) q^{59} +(4.95889 - 8.52818i) q^{60} +(-11.0628 - 6.38708i) q^{61} +(2.02921 + 7.62012i) q^{62} +(3.95002 - 1.52307i) q^{63} +(-0.0740424 + 7.99966i) q^{64} +(-6.38371 + 11.0569i) q^{65} +(-1.18134 - 1.18499i) q^{66} +(-12.9230 + 7.46108i) q^{67} +(7.06555 + 0.0217983i) q^{68} +5.58926i q^{69} +(1.62982 + 15.5133i) q^{70} +9.35052i q^{71} +(-4.37695 + 1.15112i) q^{72} +(5.79374 - 3.34501i) q^{73} +(-8.36898 + 8.34320i) q^{74} +(-7.32381 + 12.6852i) q^{75} +(6.34623 - 3.63794i) q^{76} +(2.61379 + 0.409971i) q^{77} +(-4.95181 + 1.31865i) q^{78} +(-5.60206 - 3.23435i) q^{79} +(0.102893 - 16.6754i) q^{80} +(0.819667 + 1.41971i) q^{81} +(-2.56031 + 9.49658i) q^{82} +6.95184 q^{83} +(-3.94773 + 4.85926i) q^{84} -14.7280 q^{85} +(-0.781746 + 2.89962i) q^{86} +(-1.47202 - 2.54962i) q^{87} +(-2.72863 - 0.744686i) q^{88} +(0.589097 + 0.340115i) q^{89} +(9.11615 - 2.42760i) q^{90} +(5.08973 - 6.30459i) q^{91} +(4.69870 + 8.19668i) q^{92} +(3.29869 - 5.71350i) q^{93} +(4.53554 - 4.52157i) q^{94} +(-13.2050 + 7.62394i) q^{95} +(4.76904 - 4.69604i) q^{96} +11.5160i q^{97} +(0.503723 - 9.88667i) q^{98} -1.60011i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) $ 80 * q + 12 * q^8 - 40 * q^9	$ 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) $ 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.36546	−	0.368132i	−0.965525	−	0.260309i
$2$	−1.36546	−	0.368132i	−0.965525	−	0.260309i
$3$	0.591585	+	1.02466i	0.341552	+	0.591585i	0.984721	−	0.174139i	$-0.0557141\pi$
$3$	0.591585	+	1.02466i	0.341552	+	0.591585i	−0.643169	+	0.765724i	$0.722381\pi$
$4$	1.72896	+	1.00534i	0.864479	+	0.502669i
$5$	−3.61040	−	2.08447i	−1.61462	−	0.932201i	−0.988280	−	0.152651i	$-0.951219\pi$
$5$	−3.61040	−	2.08447i	−1.61462	−	0.932201i	−0.626340	−	0.779550i	$-0.715448\pi$
$6$	−0.430577	−	1.61691i	−0.175782	−	0.660100i
$7$	2.05863	+	1.66194i	0.778088	+	0.628155i
$7$	2.05863	+	1.66194i	0.778088	+	0.628155i
$8$	−1.99072	−	2.00923i	−0.703827	−	0.710371i
$9$	0.800054	−	1.38573i	0.266685	−	0.461911i
$10$	4.16249	+	4.17536i	1.31630	+	1.32036i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−0.00730050	+	2.36633i	−0.00210747	+	0.683101i
$13$		−	3.06252i		−	0.849390i	−0.905337	−	0.424695i	$-0.860381\pi$
$13$		−	3.06252i		−	0.849390i	0.905337	−	0.424695i	$-0.139619\pi$
$14$	−2.19916	−	3.02716i	−0.587749	−	0.809043i
$15$		−	4.93256i		−	1.27358i
$16$	1.97859	+	3.47638i	0.494647	+	0.869094i
$17$	3.05949	−	1.76639i	0.742034	−	0.428414i	−0.0807742	−	0.996732i	$-0.525739\pi$
$17$	3.05949	−	1.76639i	0.742034	−	0.428414i	0.822809	+	0.568319i	$0.192406\pi$
$18$	−1.60257	+	1.59764i	−0.377730	+	0.376567i
$19$	1.82875	−	3.16749i	0.419544	−	0.726672i	−0.576349	−	0.817204i	$-0.695523\pi$
$19$	1.82875	−	3.16749i	0.419544	−	0.726672i	0.995894	+	0.0905313i	$0.0288565\pi$
$20$	−4.14663	−	7.23363i	−0.927215	−	1.61749i
$21$	−0.485065	+	3.09257i	−0.105850	+	0.674853i
$22$	−1.36659	+	0.363918i	−0.291358	+	0.0775875i
$23$	4.09107	+	2.36198i	0.853048	+	0.492507i	0.861678	−	0.507455i	$-0.169414\pi$
$23$	4.09107	+	2.36198i	0.853048	+	0.492507i	−0.00863010	+	0.999963i	$0.502747\pi$
$24$	0.881091	−	3.22844i	0.179852	−	0.659002i
$25$	6.18999	+	10.7214i	1.23800	+	2.14428i
$26$	−1.12741	+	4.18174i	−0.221104	+	0.820108i
$27$	5.44271			1.04745
$28$	1.88846	+	4.94305i	0.356886	+	0.934148i
$29$	−2.48827			−0.462060			−0.231030	−	0.972947i	$-0.574210\pi$
$29$	−2.48827			−0.462060			−0.231030	+	0.972947i	$0.574210\pi$
$30$	−1.81583	+	6.73520i	−0.331524	+	1.22967i
$31$	−2.78801	−	4.82897i	−0.500741	−	0.867309i	−1.00000		0.000856180i	$-0.999727\pi$
$31$	−2.78801	−	4.82897i	−0.500741	−	0.867309i	0.499258	−	0.866453i	$-0.333606\pi$
$32$	−1.42191	−	5.47523i	−0.251361	−	0.967893i
$33$	1.02466	+	0.591585i	0.178370	+	0.102982i
$34$	−4.82787	+	1.28565i	−0.827973	+	0.220486i
$35$	−3.96821	−	10.2914i	−0.670749	−	1.73957i
$36$	2.77639	−	1.59155i	0.462732	−	0.265258i
$37$	4.17805	−	7.23659i	0.686867	−	1.18969i	−0.285979	−	0.958236i	$-0.592319\pi$
$37$	4.17805	−	7.23659i	0.686867	−	1.18969i	0.972846	−	0.231452i	$-0.0743478\pi$
$38$	−3.66314	+	3.65186i	−0.594240	+	0.592409i
$39$	3.13803	−	1.81174i	0.502487	−	0.290111i
$40$	2.99913	+	11.4037i	0.474204	+	1.80309i
$41$		−	6.95486i		−	1.08617i	−0.839679	−	0.543083i	$-0.817257\pi$
$41$		−	6.95486i		−	1.08617i	0.839679	−	0.543083i	$-0.182743\pi$
$42$	1.80081	−	4.04420i	0.277871	−	0.624034i
$43$		−	2.12355i		−	0.323838i	−0.986804	−	0.161919i	$-0.948232\pi$
$43$		−	2.12355i		−	0.323838i	0.986804	−	0.161919i	$-0.0517683\pi$
$44$	1.99999	+	0.00617028i	0.301510	+	0.000930205i
$45$	−5.77703	+	3.33537i	−0.861188	+	0.497207i
$46$	−4.71667	−	4.73125i	−0.695436	−	0.697584i
$47$	−2.26428	+	3.92184i	−0.330279	+	0.572060i	−0.982566	−	0.185912i	$-0.940476\pi$
$47$	−2.26428	+	3.92184i	−0.330279	+	0.572060i	0.652288	+	0.757972i	$0.273809\pi$
$48$	−2.39159	+	4.08394i	−0.345196	+	0.589467i
$49$	1.47589	+	6.84264i	0.210842	+	0.977520i
$50$	−4.50529	−	16.9183i	−0.637145	−	2.39261i
$51$	3.61989	+	2.08995i	0.506887	+	0.292651i
$52$	3.07887	−	5.29496i	0.426962	−	0.734279i
$53$	2.58566	+	4.47849i	0.355168	+	0.615168i	0.987147	−	0.159817i	$-0.0510904\pi$
$53$	2.58566	+	4.47849i	0.355168	+	0.615168i	−0.631979	+	0.774986i	$0.717757\pi$
$54$	−7.43180	−	2.00364i	−1.01134	−	0.272660i
$55$	−4.16893			−0.562138
$56$	−0.758926	−	7.44473i	−0.101416	−	0.994844i
$57$	4.32745			0.573185
$58$	3.39763	+	0.916012i	0.446131	+	0.120278i
$59$	1.43322	+	2.48241i	0.186589	+	0.323182i	0.944111	−	0.329628i	$-0.106923\pi$
$59$	1.43322	+	2.48241i	0.186589	+	0.323182i	−0.757522	+	0.652810i	$0.773590\pi$
$60$	4.95889	−	8.52818i	0.640190	−	1.10098i
$61$	−11.0628	−	6.38708i	−1.41644	−	0.817782i	−0.420456	−	0.907313i	$-0.638130\pi$
$61$	−11.0628	−	6.38708i	−1.41644	−	0.817782i	−0.995984	+	0.0895308i	$0.971463\pi$
$62$	2.02921	+	7.62012i	0.257710	+	0.967757i
$63$	3.95002	−	1.52307i	0.497656	−	0.191888i
$64$	−0.0740424	+	7.99966i	−0.00925531	+	0.999957i
$65$	−6.38371	+	11.0569i	−0.791802	+	1.37144i
$66$	−1.18134	−	1.18499i	−0.145413	−	0.145863i
$67$	−12.9230	+	7.46108i	−1.57879	+	0.911516i	−0.583764	+	0.811923i	$0.698421\pi$
$67$	−12.9230	+	7.46108i	−1.57879	+	0.911516i	−0.995028	+	0.0995929i	$0.968246\pi$
$68$	7.06555	+	0.0217983i	0.856823	+	0.00264343i
$69$			5.58926i			0.672868i
$70$	1.62982	+	15.5133i	0.194801	+	1.85420i
$71$			9.35052i			1.10970i	0.831949	+	0.554851i	$0.187225\pi$
$71$			9.35052i			1.10970i	−0.831949	+	0.554851i	$0.812775\pi$
$72$	−4.37695	+	1.15112i	−0.515828	+	0.135660i
$73$	5.79374	−	3.34501i	0.678105	−	0.391504i	−0.121035	−	0.992648i	$-0.538621\pi$
$73$	5.79374	−	3.34501i	0.678105	−	0.391504i	0.799141	+	0.601144i	$0.205288\pi$
$74$	−8.36898	+	8.34320i	−0.972874	+	0.969877i
$75$	−7.32381	+	12.6852i	−0.845681	+	1.46476i
$76$	6.34623	−	3.63794i	0.727963	−	0.417300i
$77$	2.61379	+	0.409971i	0.297870	+	0.0467205i
$78$	−4.95181	+	1.31865i	−0.560682	+	0.149308i
$79$	−5.60206	−	3.23435i	−0.630281	−	0.363893i	0.150580	−	0.988598i	$-0.451886\pi$
$79$	−5.60206	−	3.23435i	−0.630281	−	0.363893i	−0.780861	+	0.624705i	$0.785219\pi$
$80$	0.102893	−	16.6754i	0.0115038	−	1.86437i
$81$	0.819667	+	1.41971i	0.0910742	+	0.157745i
$82$	−2.56031	+	9.49658i	−0.282739	+	1.04872i
$83$	6.95184			0.763063			0.381532	−	0.924356i	$-0.375397\pi$
$83$	6.95184			0.763063			0.381532	+	0.924356i	$0.375397\pi$
$84$	−3.94773	+	4.85926i	−0.430733	+	0.530189i
$85$	−14.7280			−1.59747
$86$	−0.781746	+	2.89962i	−0.0842978	+	0.312674i
$87$	−1.47202	−	2.54962i	−0.157817	−	0.273348i
$88$	−2.72863	−	0.744686i	−0.290873	−	0.0793838i
$89$	0.589097	+	0.340115i	0.0624441	+	0.0360521i	0.530897	−	0.847436i	$-0.321855\pi$
$89$	0.589097	+	0.340115i	0.0624441	+	0.0360521i	−0.468453	+	0.883488i	$0.655188\pi$
$90$	9.11615	−	2.42760i	0.960927	−	0.255891i
$91$	5.08973	−	6.30459i	0.533549	−	0.660900i
$92$	4.69870	+	8.19668i	0.489873	+	0.854563i
$93$	3.29869	−	5.71350i	0.342058	−	0.592462i
$94$	4.53554	−	4.52157i	0.467805	−	0.466364i
$95$	−13.2050	+	7.62394i	−1.35481	+	0.782200i
$96$	4.76904	−	4.69604i	0.486739	−	0.479288i
$97$			11.5160i			1.16928i	0.811294	+	0.584639i	$0.198764\pi$
$97$			11.5160i			1.16928i	−0.811294	+	0.584639i	$0.801236\pi$
$98$	0.503723	−	9.88667i	0.0508837	−	0.998705i
$99$		−	1.60011i		−	0.160817i
$100$	−0.0763880	+	24.7598i	−0.00763880	+	2.47598i
$101$	−10.9984	+	6.34991i	−1.09438	+	0.631840i	−0.934739	−	0.355335i	$-0.884367\pi$
$101$	−10.9984	+	6.34991i	−1.09438	+	0.631840i	−0.159640	+	0.987175i	$0.551033\pi$
$102$	−4.17344	−	4.18634i	−0.413232	−	0.414509i
$103$	−1.29799	+	2.24819i	−0.127895	+	0.221520i	−0.922861	−	0.385134i	$-0.874155\pi$
$103$	−1.29799	+	2.24819i	−0.127895	+	0.221520i	0.794966	+	0.606654i	$0.207489\pi$
$104$	−6.15332	+	6.09663i	−0.603382	+	0.597823i
$105$	8.19762	−	10.1543i	0.800006	−	0.990958i
$106$	−1.88194	−	7.06707i	−0.182790	−	0.686414i
$107$	11.4759	+	6.62561i	1.10942	+	0.640522i	0.938678	−	0.344795i	$-0.112052\pi$
$107$	11.4759	+	6.62561i	1.10942	+	0.640522i	0.170738	+	0.985316i	$0.445385\pi$
$108$	9.41022	+	5.47177i	0.905499	+	0.526521i
$109$	1.67494	+	2.90108i	0.160430	+	0.277873i	0.935023	−	0.354587i	$-0.115379\pi$
$109$	1.67494	+	2.90108i	0.160430	+	0.277873i	−0.774593	+	0.632460i	$0.782045\pi$
$110$	5.69250	+	1.53472i	0.542759	+	0.146330i
$111$	9.88669			0.938403
$112$	−1.70436	+	10.4449i	−0.161047	+	0.986947i
$113$	1.78352			0.167779			0.0838897	−	0.996475i	$-0.473266\pi$
$113$	1.78352			0.167779			0.0838897	+	0.996475i	$0.473266\pi$
$114$	−5.90896	−	1.59307i	−0.553424	−	0.149205i
$115$	−9.84694	−	17.0554i	−0.918232	−	1.59042i
$116$	−4.30211	−	2.50155i	−0.399441	−	0.232263i
$117$	−4.24384	−	2.45018i	−0.392343	−	0.226519i
$118$	−1.04315	−	3.91724i	−0.0960296	−	0.360611i
$119$	9.23399	+	1.44834i	0.846478	+	0.132769i
$120$	−9.91066	+	9.81935i	−0.904715	+	0.896380i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	12.7544	+	12.7939i	1.15473	+	1.15830i
$123$	7.12634	−	4.11439i	0.642560	−	0.370982i
$124$	0.0344056	−	11.1520i	0.00308972	−	1.00148i
$125$		−	30.7666i		−	2.75185i
$126$	−5.95428	+	0.625554i	−0.530450	+	0.0557288i
$127$		−	2.71947i		−	0.241314i	−0.992694	−	0.120657i	$-0.961500\pi$
$127$		−	2.71947i		−	0.241314i	0.992694	−	0.120657i	$-0.0385001\pi$
$128$	3.04603	−	10.8959i	0.269234	−	0.963075i
$129$	2.17590	−	1.25626i	0.191578	−	0.110607i
$130$	12.7871	−	12.7477i	1.12150	−	1.11805i
$131$	0.510260	−	0.883796i	0.0445816	−	0.0772176i	−0.842874	−	0.538112i	$-0.819138\pi$
$131$	0.510260	−	0.883796i	0.0445816	−	0.0772176i	0.887455	+	0.460894i	$0.152471\pi$
$132$	1.17684	+	2.05295i	0.102431	+	0.178687i
$133$	9.02891	−	3.48140i	0.782905	−	0.301876i
$134$	20.3925	−	5.43044i	1.76164	−	0.469119i
$135$	−19.6504	−	11.3451i	−1.69123	−	0.976434i
$136$	−9.63969	−	2.63082i	−0.826597	−	0.225591i
$137$	−9.63779	−	16.6931i	−0.823412	−	1.42619i	−0.903127	−	0.429374i	$-0.858734\pi$
$137$	−9.63779	−	16.6931i	−0.823412	−	1.42619i	0.0797150	−	0.996818i	$-0.474599\pi$
$138$	2.05759	−	7.63190i	0.175153	−	0.649671i
$139$	0.687255			0.0582922			0.0291461	−	0.999575i	$-0.490721\pi$
$139$	0.687255			0.0582922			0.0291461	+	0.999575i	$0.490721\pi$
$140$	3.48550	−	21.7828i	0.294578	−	1.84098i
$141$	−5.35805			−0.451230
$142$	3.44223	−	12.7678i	0.288865	−	1.07145i
$143$	−1.53126	−	2.65222i	−0.128050	−	0.221790i
$144$	6.40031	+	0.0394923i	0.533359	+	0.00329102i
$145$	8.98364	+	5.18671i	0.746051	+	0.430733i
$146$	−9.14252	+	2.43462i	−0.756640	+	0.201491i
$147$	−6.13823	+	5.56029i	−0.506273	+	0.458605i
$148$	14.4989	−	8.31140i	1.19180	−	0.683193i
$149$	4.45240	−	7.71178i	0.364755	−	0.631773i	−0.623982	−	0.781439i	$-0.714486\pi$
$149$	4.45240	−	7.71178i	0.364755	−	0.631773i	0.988737	+	0.149665i	$0.0478196\pi$
$150$	14.6702	−	14.6250i	1.19782	−	1.19413i
$151$	−5.48540	+	3.16700i	−0.446395	+	0.257726i	−0.706307	−	0.707906i	$-0.749640\pi$
$151$	−5.48540	+	3.16700i	−0.446395	+	0.257726i	0.259911	+	0.965632i	$0.416307\pi$
$152$	−10.0048	+	2.63121i	−0.811494	+	0.213419i
$153$		−	5.65284i		−	0.457005i
$154$	−3.41811	−	1.52202i	−0.275439	−	0.122648i
$155$			23.2460i			1.86717i
$156$	7.24693	+	0.0223579i	0.580219	+	0.00179007i
$157$	8.35547	−	4.82404i	0.666839	−	0.385000i	−0.128039	−	0.991769i	$-0.540868\pi$
$157$	8.35547	−	4.82404i	0.666839	−	0.385000i	0.794878	+	0.606769i	$0.207535\pi$
$158$	6.45872	+	6.47867i	0.513828	+	0.515416i
$159$	−3.05928	+	5.29882i	−0.242616	+	0.420224i
$160$	−6.27925	+	22.7317i	−0.496418	+	1.79710i
$161$	4.49652	+	11.6616i	0.354375	+	0.919061i
$162$	−0.596583	−	2.24030i	−0.0468720	−	0.176014i
$163$	13.4234	+	7.75002i	1.05140	+	0.607028i	0.923042	−	0.384699i	$-0.125695\pi$
$163$	13.4234	+	7.75002i	1.05140	+	0.607028i	0.128362	+	0.991727i	$0.459028\pi$
$164$	6.99199	−	12.0247i	0.545983	−	0.938968i
$165$	−2.46628	−	4.27172i	−0.191999	−	0.332553i
$166$	−9.49245	−	2.55919i	−0.736757	−	0.198632i
$167$	−15.7612			−1.21964			−0.609820	−	0.792540i	$-0.708758\pi$
$167$	−15.7612			−1.21964			−0.609820	+	0.792540i	$0.708758\pi$
$168$	7.17932	−	5.18183i	0.553896	−	0.399787i
$169$	3.62098			0.278537
$170$	20.1104	+	5.42183i	1.54240	+	0.415836i
$171$	−2.92620	−	5.06832i	−0.223772	−	0.387584i
$172$	2.13488	−	3.67152i	0.162783	−	0.279951i
$173$	11.5656	+	6.67742i	0.879319	+	0.507675i	0.870434	−	0.492286i	$-0.163838\pi$
$173$	11.5656	+	6.67742i	0.879319	+	0.507675i	0.00888492	+	0.999961i	$0.497172\pi$
$174$	1.07139	+	4.02330i	0.0812219	+	0.305006i
$175$	−5.07543	+	32.3587i	−0.383666	+	2.44609i
$176$	3.45170	+	2.02134i	0.260181	+	0.152364i
$177$	−1.69574	+	2.93711i	−0.127460	+	0.220767i
$178$	−0.679180	−	0.681279i	−0.0509067	−	0.0510640i
$179$	−1.35014	+	0.779501i	−0.100914	+	0.0582627i	−0.549608	−	0.835423i	$-0.685223\pi$
$179$	−1.35014	+	0.779501i	−0.100914	+	0.0582627i	0.448694	+	0.893686i	$0.351889\pi$
$180$	−13.3414	−	0.0411603i	−0.994410	−	0.00306791i
$181$		−	0.688440i		−	0.0511713i	−0.999673	−	0.0255857i	$-0.991855\pi$
$181$		−	0.688440i		−	0.0511713i	0.999673	−	0.0255857i	$-0.00814506\pi$
$182$	−9.27074	+	6.73496i	−0.687193	+	0.499228i
$183$		−	15.1140i		−	1.11726i
$184$	−3.39842	−	12.9220i	−0.250535	−	0.952621i
$185$	−30.1688	+	17.4180i	−2.21806	+	1.28060i
$186$	−6.60755	+	6.58720i	−0.484489	+	0.482997i
$187$	1.76639	−	3.05949i	0.129172	−	0.223732i
$188$	−7.85762	+	4.50434i	−0.573076	+	0.328512i
$189$	11.2045	+	9.04547i	0.815009	+	0.657961i
$190$	20.8376	−	5.54897i	1.51172	−	0.402565i
$191$	10.3550	+	5.97848i	0.749264	+	0.432588i	0.825428	−	0.564508i	$-0.190934\pi$
$191$	10.3550	+	5.97848i	0.749264	+	0.432588i	−0.0761639	+	0.997095i	$0.524267\pi$
$192$	−8.24070	+	4.65661i	−0.594721	+	0.336062i
$193$	4.89973	+	8.48658i	0.352690	+	0.610877i	0.986720	−	0.162431i	$-0.0519336\pi$
$193$	4.89973	+	8.48658i	0.352690	+	0.610877i	−0.634030	+	0.773309i	$0.718600\pi$
$194$	4.23943	−	15.7247i	0.304373	−	1.12897i
$195$	−15.1060			−1.08177
$196$	−4.32742	+	13.3144i	−0.309101	+	0.951029i
$197$	7.56647			0.539089			0.269544	−	0.962988i	$-0.413127\pi$
$197$	7.56647			0.539089			0.269544	+	0.962988i	$0.413127\pi$
$198$	−0.589051	+	2.18488i	−0.0418620	+	0.155273i
$199$	5.62178	+	9.73721i	0.398518	+	0.690253i	0.993543	−	0.113454i	$-0.0361914\pi$
$199$	5.62178	+	9.73721i	0.398518	+	0.690253i	−0.595026	+	0.803707i	$0.702858\pi$
$200$	9.21920	−	33.7804i	0.651896	−	2.38864i
$201$	−15.2901	−	8.82773i	−1.07848	−	0.622660i
$202$	17.3554	−	4.62169i	1.22112	−	0.325181i
$203$	−5.12242	−	4.13536i	−0.359523	−	0.290245i
$204$	4.15754	+	7.25265i	0.291086	+	0.507787i
$205$	−14.4972	+	25.1098i	−1.01253	+	1.75375i
$206$	2.59998	−	2.59197i	0.181149	−	0.180591i
$207$	6.54616	−	3.77943i	0.454989	−	0.262688i
$208$	10.6465	−	6.05946i	0.738200	−	0.420148i
$209$		−	3.65750i		−	0.252995i
$210$	−14.9316	+	10.8475i	−1.03038	+	0.748546i
$211$		−	3.31004i		−	0.227873i	−0.993488	−	0.113936i	$-0.963654\pi$
$211$		−	3.31004i		−	0.227873i	0.993488	−	0.113936i	$-0.0363460\pi$
$212$	−0.0319085	+	10.3426i	−0.00219148	+	0.710332i
$213$	−9.58107	+	5.53163i	−0.656484	+	0.379021i
$214$	−13.2308	−	13.2716i	−0.904436	−	0.907231i
$215$	−4.42646	+	7.66685i	−0.301882	+	0.522875i
$216$	−10.8349	−	10.9357i	−0.737224	−	0.744079i
$217$	2.28600	−	14.5746i	0.155184	−	0.989386i
$218$	−1.21908	−	4.57790i	−0.0825665	−	0.310055i
$219$	6.85498	+	3.95772i	0.463216	+	0.267438i
$220$	−7.20790	−	4.19119i	−0.485957	−	0.282570i
$221$	−5.40962	−	9.36973i	−0.363890	−	0.630276i
$222$	−13.4999	−	3.63961i	−0.906052	−	0.244274i
$223$	15.9542			1.06837			0.534187	−	0.845366i	$-0.320618\pi$
$223$	15.9542			1.06837			0.534187	+	0.845366i	$0.320618\pi$
$224$	6.17233	−	13.6346i	0.412406	−	0.911000i
$225$	19.8093			1.32062
$226$	−2.43532	−	0.656571i	−0.161995	−	0.0436745i
$227$	4.62582	+	8.01215i	0.307026	+	0.531785i	0.977710	−	0.209958i	$-0.0673328\pi$
$227$	4.62582	+	8.01215i	0.307026	+	0.531785i	−0.670684	+	0.741743i	$0.733999\pi$
$228$	7.48198	+	4.35055i	0.495506	+	0.288122i
$229$	−2.42152	−	1.39807i	−0.160019	−	0.0923867i	0.417852	−	0.908515i	$-0.362783\pi$
$229$	−2.42152	−	1.39807i	−0.160019	−	0.0923867i	−0.577871	+	0.816128i	$0.696116\pi$
$230$	7.16695	+	26.9134i	0.472575	+	1.77462i
$231$	1.12620	+	2.92077i	0.0740988	+	0.192173i
$232$	4.95345	+	4.99951i	0.325210	+	0.328234i
$233$	−4.28115	+	7.41518i	−0.280468	+	0.485784i	−0.971500	−	0.237040i	$-0.923823\pi$
$233$	−4.28115	+	7.41518i	−0.280468	+	0.485784i	0.691032	+	0.722824i	$0.257156\pi$
$234$	4.89279	+	4.90791i	0.319852	+	0.320840i
$235$	16.3499	−	9.43962i	1.06655	−	0.615773i
$236$	−0.0176867	+	5.73285i	−0.00115131	+	0.373177i
$237$		−	7.65358i		−	0.497153i
$238$	−12.0755	−	5.37698i	−0.782735	−	0.348538i
$239$		−	7.57661i		−	0.490090i	−0.969512	−	0.245045i	$-0.921197\pi$
$239$		−	7.57661i		−	0.490090i	0.969512	−	0.245045i	$-0.0788027\pi$
$240$	17.1474	−	9.75949i	1.10686	−	0.629973i
$241$	−10.3544	+	5.97809i	−0.666983	+	0.385083i	−0.794932	−	0.606698i	$-0.792494\pi$
$241$	−10.3544	+	5.97809i	−0.666983	+	0.385083i	0.127950	+	0.991781i	$0.459160\pi$
$242$	−1.00154	+	0.998456i	−0.0643815	+	0.0641832i
$243$	7.19426	−	12.4608i	0.461512	−	0.799362i
$244$	−12.7058	−	22.1648i	−0.813408	−	1.41896i
$245$	8.93468	−	27.7811i	0.570816	−	1.77487i
$246$	−11.2454	+	2.99460i	−0.716978	+	0.190929i
$247$	−9.70050	−	5.60059i	−0.617228	−	0.356357i
$248$	−4.15238	+	15.2149i	−0.263677	+	0.966148i
$249$	4.11260	+	7.12324i	0.260626	+	0.451417i
$250$	−11.3262	+	42.0106i	−0.716331	+	2.65698i
$251$	−25.0539			−1.58139			−0.790695	−	0.612211i	$-0.790280\pi$
$251$	−25.0539			−1.58139			−0.790695	+	0.612211i	$0.790280\pi$
$252$	8.36062	+	1.33779i	0.526669	+	0.0842731i
$253$	4.72397			0.296993
$254$	−1.00113	+	3.71333i	−0.0628162	+	0.232995i
$255$	−8.71284	−	15.0911i	−0.545619	−	0.945040i
$256$	−8.17038	+	13.7566i	−0.510649	+	0.859789i
$257$	4.73958	+	2.73640i	0.295647	+	0.170692i	0.640486	−	0.767970i	$-0.278733\pi$
$257$	4.73958	+	2.73640i	0.295647	+	0.170692i	−0.344839	+	0.938662i	$0.612066\pi$
$258$	−3.43358	+	0.914350i	−0.213765	+	0.0569250i
$259$	20.6278	−	7.95377i	1.28175	−	0.494223i
$260$	−22.1531	+	12.6991i	−1.37388	+	0.787567i
$261$	−1.99075	+	3.44808i	−0.123224	+	0.213431i
$262$	−1.02209	+	1.01894i	−0.0631451	+	0.0629506i
$263$	22.3104	−	12.8809i	1.37572	−	0.794271i	0.384077	−	0.923301i	$-0.374520\pi$
$263$	22.3104	−	12.8809i	1.37572	−	0.794271i	0.991641	+	0.129030i	$0.0411862\pi$
$264$	−0.851173	−	3.23646i	−0.0523861	−	0.199190i
$265$		−	21.5589i		−	1.32435i
$266$	−13.6102	+	1.42988i	−0.834496	+	0.0876718i
$267$			0.804829i			0.0492547i
$268$	−29.8442	−	0.0920740i	−1.82302	−	0.00562431i
$269$	−25.3595	+	14.6413i	−1.54620	+	0.892698i	−0.547771	+	0.836628i	$0.684524\pi$
$269$	−25.3595	+	14.6413i	−1.54620	+	0.892698i	−0.998427	+	0.0560700i	$0.982143\pi$
$270$	22.6553	+	22.7253i	1.37876	+	1.38302i
$271$	5.15292	−	8.92512i	0.313018	−	0.542163i	−0.665996	−	0.745955i	$-0.731993\pi$
$271$	5.15292	−	8.92512i	0.313018	−	0.542163i	0.979014	+	0.203792i	$0.0653267\pi$
$272$	12.1941	+	7.14096i	0.739377	+	0.432984i
$273$	9.47104	+	1.48552i	0.573213	+	0.0899079i
$274$	7.01473	+	26.3418i	0.423775	+	1.59137i
$275$	10.7214	+	6.18999i	0.646523	+	0.373270i
$276$	−5.61910	+	9.66359i	−0.338230	+	0.581680i
$277$	14.2289	+	24.6452i	0.854934	+	1.48079i	0.876706	+	0.481026i	$0.159736\pi$
$277$	14.2289	+	24.6452i	0.854934	+	1.48079i	−0.0217725	+	0.999763i	$0.506931\pi$
$278$	−0.938418	−	0.253000i	−0.0562826	−	0.0151740i
$279$	−8.92223			−0.534160
$280$	−12.7783	+	28.4604i	−0.763647	+	1.70083i
$281$	−3.85446			−0.229938			−0.114969	−	0.993369i	$-0.536677\pi$
$281$	−3.85446			−0.229938			−0.114969	+	0.993369i	$0.536677\pi$
$282$	7.31620	+	1.97247i	0.435674	+	0.117459i
$283$	5.12041	+	8.86882i	0.304377	+	0.527196i	0.977122	−	0.212678i	$-0.0682184\pi$
$283$	5.12041	+	8.86882i	0.304377	+	0.527196i	−0.672745	+	0.739874i	$0.734885\pi$
$284$	−9.40044	+	16.1667i	−0.557814	+	0.959315i
$285$	−15.6238	−	9.02042i	−0.925475	−	0.534324i
$286$	1.11451	+	4.18520i	0.0659021	+	0.247476i
$287$	11.5586	−	14.3175i	0.682281	−	0.845133i
$288$	−8.72482	−	2.41008i	−0.514115	−	0.142016i
$289$	−2.25970	+	3.91391i	−0.132923	+	0.230230i
$290$	−10.3574	−	10.3894i	−0.608208	−	0.610087i
$291$	−11.8000	+	6.81272i	−0.691727	+	0.399369i
$292$	13.3800	+	0.0412794i	0.783005	+	0.00241569i
$293$			13.5023i			0.788810i	0.918937	+	0.394405i	$0.129049\pi$
$293$			13.5023i			0.788810i	−0.918937	+	0.394405i	$0.870951\pi$
$294$	10.4284	−	5.33267i	0.608198	−	0.311007i
$295$		−	11.9500i		−	0.695755i
$296$	−22.8573	+	6.01137i	−1.32856	+	0.349404i
$297$	4.71353	−	2.72136i	0.273507	−	0.157909i
$298$	−8.91852	+	8.89105i	−0.516636	+	0.515045i
$299$	7.23362	−	12.5290i	0.418331	−	0.724570i
$300$	−25.4155	+	14.5693i	−1.46736	+	0.841158i
$301$	3.52921	−	4.37159i	0.203420	−	0.251974i
$302$	8.65596	−	2.30505i	0.498095	−	0.132641i
$303$	−13.0130	−	7.51303i	−0.747575	−	0.431612i
$304$	14.6297	+	0.0902709i	0.839073	+	0.00517739i
$305$	26.6273	+	46.1198i	1.52467	+	2.64081i
$306$	−2.08099	+	7.71873i	−0.118962	+	0.441250i
$307$	−33.6047			−1.91792			−0.958961	−	0.283539i	$-0.908491\pi$
$307$	−33.6047			−1.91792			−0.958961	+	0.283539i	$0.908491\pi$
$308$	4.10698	+	3.33657i	0.234017	+	0.190119i
$309$	−3.07149			−0.174731
$310$	8.55761	−	31.7415i	0.486040	−	1.80280i
$311$	−4.07661	−	7.06089i	−0.231163	−	0.400386i	0.726988	−	0.686651i	$-0.240920\pi$
$311$	−4.07661	−	7.06089i	−0.231163	−	0.400386i	−0.958151	+	0.286264i	$0.907586\pi$
$312$	−9.88716	−	2.69836i	−0.559750	−	0.152764i
$313$	10.8335	+	6.25472i	0.612346	+	0.353538i	0.773883	−	0.633329i	$-0.218312\pi$
$313$	10.8335	+	6.25472i	0.612346	+	0.353538i	−0.161537	+	0.986867i	$0.551645\pi$
$314$	−13.1849	+	3.51110i	−0.744069	+	0.198143i
$315$	−17.4359	−	2.73481i	−0.982404	−	0.154089i
$316$	−6.43411	−	11.2240i	−0.361947	−	0.631401i
$317$	10.3556	−	17.9364i	0.581628	−	1.00741i	−0.413659	−	0.910432i	$-0.635749\pi$
$317$	10.3556	−	17.9364i	0.581628	−	1.00741i	0.995287	−	0.0969768i	$-0.0309173\pi$
$318$	6.12798	−	6.10911i	0.343640	−	0.342582i
$319$	−2.15490	+	1.24413i	−0.120651	+	0.0696582i
$320$	16.9423	−	28.7276i	0.947105	−	1.60592i
$321$			15.6784i			0.875086i
$322$	−1.84681	−	17.5787i	−0.102919	−	0.979624i
$323$		−	12.9212i		−	0.718954i
$324$	−0.0101152	+	3.27865i	−0.000561953	+	0.182147i
$325$	32.8344	−	18.9570i	1.82133	−	1.05154i
$326$	−15.4761	−	15.5239i	−0.857143	−	0.859791i
$327$	−1.98174	+	3.43247i	−0.109590	+	0.189816i
$328$	−13.9739	+	13.8452i	−0.771582	+	0.764473i
$329$	−11.1792	+	4.31052i	−0.616328	+	0.237647i
$330$	1.79504	+	6.74077i	0.0988140	+	0.371067i
$331$	−21.2582	−	12.2734i	−1.16845	−	0.674608i	−0.215139	−	0.976583i	$-0.569020\pi$
$331$	−21.2582	−	12.2734i	−1.16845	−	0.674608i	−0.953316	+	0.301976i	$0.902354\pi$
$332$	12.0194	+	6.98895i	0.659652	+	0.383569i
$333$	−6.68532	−	11.5793i	−0.366354	−	0.634543i
$334$	21.5213	+	5.80221i	1.17759	+	0.317483i
$335$	62.2095			3.39887
$336$	−11.7107	+	4.43264i	−0.638869	+	0.241820i
$337$	−20.5653			−1.12026			−0.560131	−	0.828404i	$-0.689249\pi$
$337$	−20.5653			−1.12026			−0.560131	+	0.828404i	$0.689249\pi$
$338$	−4.94430	−	1.33300i	−0.268934	−	0.0725056i
$339$	1.05510	+	1.82749i	0.0573054	+	0.0992559i
$340$	−25.4640	−	14.8066i	−1.38098	−	0.803000i
$341$	−4.82897	−	2.78801i	−0.261504	−	0.150979i
$342$	2.12979	+	7.99782i	0.115166	+	0.432472i
$343$	−8.33376	+	16.5393i	−0.449981	+	0.893038i
$344$	−4.26670	+	4.22739i	−0.230045	+	0.227926i
$345$	11.6506	−	20.1795i	0.627248	−	1.08643i
$346$	−13.3342	−	13.3754i	−0.716852	−	0.719067i
$347$	−18.5623	+	10.7170i	−0.996477	+	0.575316i	−0.907204	−	0.420691i	$-0.861788\pi$
$347$	−18.5623	+	10.7170i	−0.996477	+	0.575316i	−0.0892728	+	0.996007i	$0.528454\pi$
$348$	0.0181656	−	5.88807i	0.000973778	−	0.315633i
$349$			0.779511i			0.0417263i	0.999782	+	0.0208631i	$0.00664143\pi$
$349$			0.779511i			0.0417263i	−0.999782	+	0.0208631i	$0.993359\pi$
$350$	18.8426	−	42.3161i	1.00718	−	2.26189i
$351$		−	16.6684i		−	0.889694i
$352$	−3.96903	−	4.03073i	−0.211550	−	0.214839i
$353$	−8.48827	+	4.90070i	−0.451785	+	0.260838i	−0.708584	−	0.705627i	$-0.750666\pi$
$353$	−8.48827	+	4.90070i	−0.451785	+	0.260838i	0.256799	+	0.966465i	$0.417332\pi$
$354$	3.39671	−	3.38625i	0.180533	−	0.179977i
$355$	19.4908	−	33.7591i	1.03447	−	1.79175i
$356$	0.676592	+	1.18029i	0.0358593	+	0.0625551i
$357$	3.97864	+	10.3185i	0.210572	+	0.546112i
$358$	2.13052	−	0.567349i	0.112601	−	0.0299853i
$359$	24.3654	+	14.0674i	1.28596	+	0.742448i	0.977931	−	0.208930i	$-0.0669981\pi$
$359$	24.3654	+	14.0674i	1.28596	+	0.742448i	0.308027	+	0.951378i	$0.400331\pi$
$360$	18.2020	+	4.96760i	0.959329	+	0.261816i
$361$	2.81134	+	4.86938i	0.147965	+	0.256283i
$362$	−0.253437	+	0.940037i	−0.0133203	+	0.0494072i
$363$	1.18317			0.0621004
$364$	15.1382	−	5.78346i	0.793456	−	0.303135i
$365$	−27.8903			−1.45984
$366$	−5.56396	+	20.6376i	−0.290833	+	1.07874i
$367$	9.13179	+	15.8167i	0.476675	+	0.825626i	0.999643	−	0.0267267i	$-0.00850839\pi$
$367$	9.13179	+	15.8167i	0.476675	+	0.825626i	−0.522967	+	0.852353i	$0.675175\pi$
$368$	−0.116592	+	18.8955i	−0.00607779	+	0.984996i
$369$	−9.63758	−	5.56426i	−0.501713	−	0.289664i
$370$	47.6064	−	12.6774i	2.47494	−	0.659068i
$371$	−2.12009	+	13.5168i	−0.110070	+	0.701756i
$372$	11.4473	−	6.56210i	0.593515	−	0.340229i
$373$	2.10032	−	3.63787i	0.108751	−	0.188362i	−0.806514	−	0.591215i	$-0.798648\pi$
$373$	2.10032	−	3.63787i	0.108751	−	0.188362i	0.915264	+	0.402854i	$0.131982\pi$
$374$	−3.53824	+	3.52734i	−0.182958	+	0.182394i
$375$	31.5252	−	18.2011i	1.62795	−	0.939900i
$376$	12.3875	−	3.25784i	0.638834	−	0.168010i
$377$			7.62037i			0.392469i
$378$	−11.9694	−	16.4760i	−0.615638	−	0.847432i
$379$			37.6272i			1.93278i	0.257080	+	0.966390i	$0.417240\pi$
$379$			37.6272i			1.93278i	−0.257080	+	0.966390i	$0.582760\pi$
$380$	−30.4956	−	0.0940837i	−1.56439	−	0.00482639i
$381$	2.78652	−	1.60880i	0.142758	−	0.0824213i
$382$	−11.9385	−	11.9754i	−0.610827	−	0.612714i
$383$	−8.56069	+	14.8276i	−0.437431	+	0.757652i	−0.997491	−	0.0707998i	$-0.977445\pi$
$383$	−8.56069	+	14.8276i	−0.437431	+	0.757652i	0.560060	+	0.828452i	$0.310778\pi$
$384$	12.9666	−	3.32475i	0.661698	−	0.169665i
$385$	−8.58227	−	6.92852i	−0.437393	−	0.353110i
$386$	−3.56620	−	13.3918i	−0.181515	−	0.681626i
$387$	−2.94267	−	1.69895i	−0.149584	−	0.0863626i
$388$	−11.5775	+	19.9108i	−0.587760	+	1.01082i
$389$	−1.81384	−	3.14166i	−0.0919652	−	0.159288i	0.816373	−	0.577525i	$-0.195982\pi$
$389$	−1.81384	−	3.14166i	−0.0919652	−	0.159288i	−0.908338	+	0.418237i	$0.862648\pi$
$390$	20.6267	+	5.56102i	1.04447	+	0.281593i
$391$	16.6888			0.843988
$392$	10.8104	−	16.5872i	0.546006	−	0.837781i
$393$	1.20745			0.0609077
$394$	−10.3317	−	2.78546i	−0.520504	−	0.140330i
$395$	13.4838	+	23.3546i	0.678443	+	1.17510i
$396$	1.60865	−	2.76652i	0.0808377	−	0.139023i
$397$	−14.7185	−	8.49773i	−0.738700	−	0.426489i	0.0828965	−	0.996558i	$-0.473583\pi$
$397$	−14.7185	−	8.49773i	−0.738700	−	0.426489i	−0.821596	+	0.570070i	$0.806916\pi$
$398$	−4.09173	−	15.3653i	−0.205100	−	0.770194i
$399$	8.90861	+	7.19197i	0.445988	+	0.360049i
$400$	−25.0241	+	42.7319i	−1.25121	+	2.13660i
$401$	3.88261	−	6.72487i	0.193888	−	0.335824i	−0.752647	−	0.658424i	$-0.771223\pi$
$401$	3.88261	−	6.72487i	0.193888	−	0.335824i	0.946535	+	0.322600i	$0.104557\pi$
$402$	17.6282	+	17.6827i	0.879215	+	0.881932i
$403$	−14.7888	+	8.53833i	−0.736684	+	0.425325i
$404$	−25.3995	−	0.0783615i	−1.26367	−	0.00389863i
$405$		−	6.83427i		−	0.339598i
$406$	5.47209	+	7.53239i	0.271575	+	0.373826i
$407$		−	8.35610i		−	0.414196i
$408$	−3.00701	−	11.4337i	−0.148869	−	0.566053i
$409$	6.02147	−	3.47650i	0.297742	−	0.171902i	−0.343686	−	0.939085i	$-0.611676\pi$
$409$	6.02147	−	3.47650i	0.297742	−	0.171902i	0.641428	+	0.767183i	$0.278342\pi$
$410$	29.0390	−	28.9496i	1.43413	−	1.42972i
$411$	11.4031	−	19.7508i	0.562476	−	0.974237i
$412$	−4.50436	+	2.58210i	−0.221914	+	0.127211i
$413$	−1.17516	+	7.49228i	−0.0578256	+	0.368671i
$414$	−10.3298	+	2.75080i	−0.507684	+	0.135194i
$415$	−25.0989	−	14.4909i	−1.23206	−	0.711328i
$416$	−16.7680	+	4.35464i	−0.822119	+	0.213504i
$417$	0.406570	+	0.704199i	0.0199098	+	0.0344848i
$418$	−1.34644	+	4.99417i	−0.0658568	+	0.244273i
$419$	−17.0449			−0.832696			−0.416348	−	0.909205i	$-0.636690\pi$
$419$	−17.0449			−0.832696			−0.416348	+	0.909205i	$0.636690\pi$
$420$	24.3819	−	9.31495i	1.18971	−	0.454523i
$421$	−3.61863			−0.176361			−0.0881805	−	0.996105i	$-0.528105\pi$
$421$	−3.61863			−0.176361			−0.0881805	+	0.996105i	$0.528105\pi$
$422$	−1.21853	+	4.51972i	−0.0593172	+	0.220017i
$423$	3.62309	+	6.27537i	0.176161	+	0.305119i
$424$	3.85101	−	14.1106i	0.187022	−	0.685273i
$425$	37.8764	+	21.8679i	1.83727	+	1.06075i
$426$	15.1189	−	4.02612i	0.732514	−	0.195066i
$427$	−12.1591	−	31.5343i	−0.588421	−	1.52605i
$428$	13.1803	+	22.9925i	0.637096	+	1.11139i
$429$	1.81174	−	3.13803i	0.0874717	−	0.151505i
$430$	8.86657	−	8.83925i	0.427584	−	0.426267i
$431$	−22.6257	+	13.0630i	−1.08984	+	0.629221i	−0.933534	−	0.358488i	$-0.883292\pi$
$431$	−22.6257	+	13.0630i	−1.08984	+	0.629221i	−0.156308	+	0.987708i	$0.549959\pi$
$432$	10.7689	+	18.9209i	0.518118	+	0.910333i
$433$		−	11.4983i		−	0.552573i	−0.961075	−	0.276286i	$-0.910896\pi$
$433$		−	11.4983i		−	0.552573i	0.961075	−	0.276286i	$-0.0891039\pi$
$434$	−8.48681	+	19.0594i	−0.407380	+	0.914882i
$435$			12.2735i			0.588470i
$436$	−0.0206697	+	6.69972i	−0.000989898	+	0.320858i
$437$	14.9631	−	8.63896i	0.715783	−	0.413257i
$438$	−7.90323	−	7.92765i	−0.377631	−	0.378798i
$439$	15.4107	−	26.6921i	0.735514	−	1.27395i	−0.218984	−	0.975728i	$-0.570274\pi$
$439$	15.4107	−	26.6921i	0.735514	−	1.27395i	0.954498	−	0.298218i	$-0.0963924\pi$
$440$	8.29919	+	8.37636i	0.395648	+	0.399327i
$441$	10.6629	+	3.42928i	0.507756	+	0.163299i
$442$	3.93731	+	14.7854i	0.187279	+	0.703272i
$443$	−4.25187	−	2.45482i	−0.202013	−	0.116632i	0.395581	−	0.918431i	$-0.370543\pi$
$443$	−4.25187	−	2.45482i	−0.202013	−	0.116632i	−0.597594	+	0.801799i	$0.703876\pi$
$444$	17.0937	+	9.93947i	0.811229	+	0.471706i
$445$	−1.41792	−	2.45590i	−0.0672157	−	0.116421i
$446$	−21.7848	−	5.87326i	−1.03154	−	0.278107i
$447$	10.5359			0.498331
$448$	−13.4474	+	16.3453i	−0.635330	+	0.772241i
$449$	18.8248			0.888397			0.444199	−	0.895928i	$-0.353488\pi$
$449$	18.8248			0.888397			0.444199	+	0.895928i	$0.353488\pi$
$450$	−27.0488	−	7.29244i	−1.27509	−	0.343769i
$451$	−3.47743	−	6.02309i	−0.163746	−	0.283616i
$452$	3.08363	+	1.79304i	0.145042	+	0.0843376i
$453$	−6.49016	−	3.74710i	−0.304934	−	0.176054i
$454$	−3.36683	−	12.6432i	−0.158013	−	0.593373i
$455$	−31.5176	+	12.1527i	−1.47757	+	0.569728i
$456$	−8.61476	−	8.69486i	−0.403423	−	0.407174i
$457$	5.89880	−	10.2170i	0.275934	−	0.477932i	−0.694436	−	0.719554i	$-0.744346\pi$
$457$	5.89880	−	10.2170i	0.275934	−	0.477932i	0.970370	+	0.241622i	$0.0776794\pi$
$458$	2.79181	+	2.80044i	0.130453	+	0.130856i
$459$	16.6519	−	9.61398i	0.777244	−	0.448742i
$460$	0.121517	−	39.3876i	0.00566575	−	1.83646i
$461$			31.3107i			1.45828i	0.684362	+	0.729142i	$0.260081\pi$
$461$			31.3107i			1.45828i	−0.684362	+	0.729142i	$0.739919\pi$
$462$	−0.462555	−	4.40279i	−0.0215200	−	0.204836i
$463$			13.2237i			0.614555i	0.951620	+	0.307278i	$0.0994180\pi$
$463$			13.2237i			0.614555i	−0.951620	+	0.307278i	$0.900582\pi$
$464$	−4.92326	−	8.65016i	−0.228557	−	0.401574i
$465$	−23.8192	+	13.7520i	−1.10459	+	0.637734i
$466$	8.57551	−	8.54909i	0.397253	−	0.396029i
$467$	−7.02421	+	12.1663i	−0.325042	+	0.562989i	−0.981521	−	0.191355i	$-0.938712\pi$
$467$	−7.02421	+	12.1663i	−0.325042	+	0.562989i	0.656479	+	0.754344i	$0.272045\pi$
$468$	−4.87415	−	8.50275i	−0.225308	−	0.393040i
$469$	−39.0035	−	6.11765i	−1.80101	−	0.282487i
$470$	−25.8001	+	6.87049i	−1.19007	+	0.316912i
$471$	9.88595	+	5.70766i	0.455521	+	0.262995i
$472$	2.13460	−	7.82146i	0.0982528	−	0.360012i
$473$	−1.06177	−	1.83905i	−0.0488204	−	0.0845594i
$474$	−2.81753	+	10.4507i	−0.129413	+	0.480014i
$475$	45.2798			2.07758
$476$	14.5091	+	11.7874i	0.665024	+	0.540275i
$477$	8.27467			0.378871
$478$	−2.78919	+	10.3455i	−0.127575	+	0.473194i
$479$	−4.19567	−	7.26712i	−0.191705	−	0.332043i	0.754110	−	0.656748i	$-0.228068\pi$
$479$	−4.19567	−	7.26712i	−0.191705	−	0.332043i	−0.945815	+	0.324705i	$0.894735\pi$
$480$	−27.0069	+	7.01367i	−1.23269	+	0.320129i
$481$	−22.1622	−	12.7953i	−1.01051	−	0.583418i
$482$	16.3392	−	4.35107i	0.744229	−	0.198186i
$483$	−9.28903	+	11.5062i	−0.422665	+	0.523550i
$484$	1.73513	−	0.994652i	0.0788694	−	0.0452114i
$485$	24.0048	−	41.5775i	1.09000	−	1.88794i
$486$	−14.4107	+	14.3663i	−0.653683	+	0.651669i
$487$	−30.7318	+	17.7430i	−1.39259	+	0.804012i	−0.993601	−	0.112944i	$-0.963972\pi$
$487$	−30.7318	+	17.7430i	−1.39259	+	0.804012i	−0.398989	+	0.916956i	$0.630639\pi$
$488$	9.18973	+	34.9426i	0.416000	+	1.58178i
$489$			18.3392i			0.829327i
$490$	−22.4271	+	34.6448i	−1.01315	+	1.56509i
$491$		−	13.7457i		−	0.620333i	−0.950682	−	0.310167i	$-0.899615\pi$
$491$		−	13.7457i		−	0.620333i	0.950682	−	0.310167i	$-0.100385\pi$
$492$	16.4575	+	0.0507739i	0.741961	+	0.00228907i
$493$	−7.61282	+	4.39527i	−0.342864	+	0.197953i
$494$	11.1839	+	11.2184i	0.503187	+	0.504741i
$495$	−3.33537	+	5.77703i	−0.149914	+	0.259658i
$496$	11.2710	−	19.2467i	0.506083	−	0.864203i
$497$	−15.5400	+	19.2492i	−0.697066	+	0.863447i
$498$	−2.99330	−	11.2405i	−0.134133	−	0.503698i
$499$	24.9249	+	14.3904i	1.11579	+	0.644204i	0.940324	−	0.340281i	$-0.110522\pi$
$499$	24.9249	+	14.3904i	1.11579	+	0.644204i	0.175470	+	0.984485i	$0.443855\pi$
$500$	30.9309	−	53.1942i	1.38327	−	2.37892i
$501$	−9.32411	−	16.1498i	−0.416570	−	0.721521i
$502$	34.2101	+	9.22315i	1.52687	+	0.411649i
$503$	0.0843866			0.00376261			0.00188131	−	0.999998i	$-0.499401\pi$
$503$	0.0843866			0.00376261			0.00188131	+	0.999998i	$0.499401\pi$
$504$	−10.9236	−	4.90452i	−0.486576	−	0.218464i
$505$	52.9447			2.35601
$506$	−6.45038	−	1.73904i	−0.286754	−	0.0773099i
$507$	2.14212	+	3.71026i	0.0951348	+	0.164778i
$508$	2.73399	−	4.70185i	0.121301	−	0.208611i
$509$	11.1239	+	6.42241i	0.493060	+	0.284668i	0.725843	−	0.687860i	$-0.241450\pi$
$509$	11.1239	+	6.42241i	0.493060	+	0.284668i	−0.232783	+	0.972529i	$0.574783\pi$
$510$	6.34152	+	23.8137i	0.280807	+	1.05449i
$511$	17.4864	+	2.74272i	0.773551	+	0.121331i
$512$	16.2206	−	15.7763i	0.716855	−	0.697222i
$513$	9.95337	−	17.2397i	0.439452	−	0.761153i
$514$	−5.46435	−	5.48123i	−0.241022	−	0.241767i
$515$	9.37253	−	5.41123i	0.413003	−	0.238447i
$516$	5.02501	+	0.0155029i	0.221214	+	0.000682479i
$517$			4.52856i			0.199166i
$518$	−31.0945	+	3.26678i	−1.36621	+	0.143534i
$519$			15.8011i			0.693589i
$520$	34.9241	−	9.18489i	1.53152	−	0.402784i
$521$	15.2053	−	8.77881i	0.666158	−	0.384607i	−0.128461	−	0.991715i	$-0.541004\pi$
$521$	15.2053	−	8.77881i	0.666158	−	0.384607i	0.794619	+	0.607108i	$0.207670\pi$
$522$	3.98763	−	3.97535i	0.174534	−	0.173996i
$523$	−9.61935	+	16.6612i	−0.420625	+	0.728544i	−0.996001	−	0.0893453i	$-0.971523\pi$
$523$	−9.61935	+	16.6612i	−0.420625	+	0.728544i	0.575376	+	0.817889i	$0.304856\pi$
$524$	1.77073	−	1.01506i	0.0773548	−	0.0443432i
$525$	−36.1591	+	13.9424i	−1.57811	+	0.608495i
$526$	−35.2058	+	9.37519i	−1.53505	+	0.408778i
$527$	−17.0598	−	9.84945i	−0.743134	−	0.429049i
$528$	−0.0292018	+	4.73259i	−0.00127085	+	0.205960i
$529$	−0.342073	−	0.592488i	−0.0148727	−	0.0257603i
$530$	−7.93651	+	29.4378i	−0.344740	+	1.27869i
$531$	4.58661			0.199042
$532$	19.1106	+	3.05791i	0.828549	+	0.132577i
$533$	−21.2994			−0.922579
$534$	0.296283	−	1.09896i	0.0128214	−	0.0475567i
$535$	−27.6217	−	47.8422i	−1.19419	−	2.06840i
$536$	40.7171	+	11.1123i	1.75871	+	0.479979i
$537$	−1.59744	−	0.922283i	−0.0689347	−	0.0397995i
$538$	40.0174	−	10.6565i	1.72527	−	0.459434i
$539$	4.69948	+	5.18795i	0.202421	+	0.223461i
$540$	−22.5689	−	39.3705i	−0.971212	−	1.69424i
$541$	−6.60691	+	11.4435i	−0.284053	+	0.491994i	−0.972379	−	0.233407i	$-0.925013\pi$
$541$	−6.60691	+	11.4435i	−0.284053	+	0.491994i	0.688326	+	0.725401i	$0.258346\pi$
$542$	−10.3217	+	10.2899i	−0.443356	+	0.441990i
$543$	0.705414	−	0.407271i	0.0302722	−	0.0174777i
$544$	−14.0217	−	14.2397i	−0.601178	−	0.610523i
$545$		−	13.9654i		−	0.598212i
$546$	−12.3854	−	5.51501i	−0.530048	−	0.236021i
$547$		−	45.3174i		−	1.93763i	−0.247782	−	0.968816i	$-0.579702\pi$
$547$		−	45.3174i		−	1.93763i	0.247782	−	0.968816i	$-0.420298\pi$
$548$	0.118936	−	38.5510i	0.00508068	−	1.64682i
$549$	−17.7016	+	10.2200i	−0.755485	+	0.436180i
$550$	−12.3609	−	12.3991i	−0.527069	−	0.528698i
$551$	−4.55043	+	7.88157i	−0.193855	+	0.335766i
$552$	11.2301	−	11.1267i	0.477986	−	0.473582i
$553$	−6.15725	−	15.9686i	−0.261833	−	0.679055i
$554$	−10.3563	−	38.8902i	−0.439998	−	1.65229i
$555$	−35.6949	−	20.6085i	−1.51516	−	0.874780i
$556$	1.18823	+	0.690924i	0.0503923	+	0.0293017i
$557$	−2.78471	−	4.82327i	−0.117992	−	0.204368i	0.800980	−	0.598691i	$-0.204312\pi$
$557$	−2.78471	−	4.82327i	−0.117992	−	0.204368i	−0.918972	+	0.394323i	$0.870979\pi$
$558$	12.1829	+	3.28456i	0.515745	+	0.139046i
$559$	−6.50340			−0.275065
$560$	27.9254	−	34.1574i	1.18006	−	1.44342i
$561$	4.17989			0.176475
$562$	5.26311	+	1.41895i	0.222011	+	0.0598548i
$563$	19.6889	+	34.1021i	0.829786	+	1.43723i	0.898206	+	0.439576i	$0.144871\pi$
$563$	19.6889	+	34.1021i	0.829786	+	1.43723i	−0.0684192	+	0.997657i	$0.521796\pi$
$564$	−9.26385	−	5.38666i	−0.390078	−	0.226819i
$565$	−6.43922	−	3.71769i	−0.270900	−	0.156404i
$566$	−3.72682	−	13.9950i	−0.156650	−	0.588254i
$567$	−0.672079	+	4.28489i	−0.0282247	+	0.179948i
$568$	18.7874	−	18.6143i	0.788301	−	0.781039i
$569$	15.5373	−	26.9115i	0.651359	−	1.12819i	−0.331434	−	0.943478i	$-0.607532\pi$
$569$	15.5373	−	26.9115i	0.651359	−	1.12819i	0.982793	−	0.184709i	$-0.0591342\pi$
$570$	18.0130	+	18.0686i	0.754481	+	0.756812i
$571$	−7.89363	+	4.55739i	−0.330338	+	0.190721i	−0.655991	−	0.754768i	$-0.727749\pi$
$571$	−7.89363	+	4.55739i	−0.330338	+	0.190721i	0.325653	+	0.945489i	$0.394416\pi$
$572$	0.0188966	−	6.12501i	0.000790107	−	0.256099i
$573$			14.1471i			0.591005i
$574$	−21.0535	+	15.2948i	−0.878756	+	0.638394i
$575$			58.4826i			2.43889i
$576$	11.0262	+	6.50276i	0.459423	+	0.270948i
$577$	35.6612	−	20.5890i	1.48460	−	0.857132i	0.484750	−	0.874653i	$-0.338911\pi$
$577$	35.6612	−	20.5890i	1.48460	−	0.857132i	0.999846	+	0.0175209i	$0.00557736\pi$
$578$	4.52636	−	4.51242i	0.188272	−	0.187692i
$579$	−5.79722	+	10.0411i	−0.240924	+	0.417293i
$580$	10.3179	+	17.9992i	0.428429	+	0.747376i
$581$	14.3112	+	11.5536i	0.593730	+	0.479322i
$582$	18.6204	−	4.95854i	0.771840	−	0.205538i
$583$	4.47849	+	2.58566i	0.185480	+	0.107087i
$584$	−18.2546	−	4.98197i	−0.755382	−	0.206155i
$585$	10.2146	+	17.6923i	0.422323	+	0.731485i
$586$	4.97061	−	18.4368i	0.205334	−	0.761616i
$587$	−18.0455			−0.744816			−0.372408	−	0.928069i	$-0.621468\pi$
$587$	−18.0455			−0.744816			−0.372408	+	0.928069i	$0.621468\pi$
$588$	−16.2027	+	3.44250i	−0.668189	+	0.141966i
$589$	−20.3943			−0.840333
$590$	−4.39917	+	16.3172i	−0.181111	+	0.671769i
$591$	4.47621	+	7.75303i	0.184127	+	0.318917i
$592$	33.4237	+	0.206237i	1.37371	+	0.00847628i
$593$	4.75289	+	2.74408i	0.195178	+	0.112686i	0.594404	−	0.804166i	$-0.297388\pi$
$593$	4.75289	+	2.74408i	0.195178	+	0.112686i	−0.399226	+	0.916852i	$0.630721\pi$
$594$	−7.43795	+	1.98070i	−0.305183	+	0.0812691i
$595$	−30.3194	−	24.4770i	−1.24297	−	1.00346i
$596$	15.4510	−	8.85717i	0.632896	−	0.362804i
$597$	−6.65153	+	11.5208i	−0.272229	+	0.471514i
$598$	−14.4895	+	14.4449i	−0.592521	+	0.590696i
$599$	3.90440	−	2.25421i	0.159529	−	0.0921044i	−0.418110	−	0.908396i	$-0.637307\pi$
$599$	3.90440	−	2.25421i	0.159529	−	0.0921044i	0.577639	+	0.816292i	$0.303974\pi$
$600$	40.0673	−	10.5375i	1.63574	−	0.430192i
$601$		−	42.8909i		−	1.74955i	−0.484525	−	0.874777i	$-0.661008\pi$
$601$		−	42.8909i		−	1.74955i	0.484525	−	0.874777i	$-0.338992\pi$
$602$	−6.42832	+	4.67001i	−0.261999	+	0.190336i
$603$			23.8771i			0.972349i
$604$	−12.6679	−	0.0390825i	−0.515450	−	0.00159025i
$605$	−3.61040	+	2.08447i	−0.146784	+	0.0847456i
$606$	15.0029	+	15.0492i	0.609450	+	0.611333i
$607$	−15.8197	+	27.4005i	−0.642102	+	1.11215i	0.342861	+	0.939386i	$0.388604\pi$
$607$	−15.8197	+	27.4005i	−0.642102	+	1.11215i	−0.984963	+	0.172767i	$0.944729\pi$
$608$	−19.9431	−	5.50894i	−0.808798	−	0.223417i
$609$	1.20697	−	7.69513i	0.0489090	−	0.311823i
$610$	−19.3803	−	72.7771i	−0.784685	−	2.94666i
$611$	12.0107	+	6.93439i	0.485902	+	0.280536i
$612$	5.68302	−	9.77352i	0.229723	−	0.395071i
$613$	−21.4615	−	37.1724i	−0.866822	−	1.50138i	−0.865227	−	0.501380i	$-0.832826\pi$
$613$	−21.4615	−	37.1724i	−0.866822	−	1.50138i	−0.00159445	−	0.999999i	$-0.500508\pi$
$614$	45.8858	+	12.3710i	1.85180	+	0.499252i
$615$	−34.3052			−1.38332
$616$	−4.37962	−	6.06786i	−0.176460	−	0.244481i
$617$	−15.2477			−0.613851			−0.306925	−	0.951734i	$-0.599300\pi$
$617$	−15.2477			−0.613851			−0.306925	+	0.951734i	$0.599300\pi$
$618$	4.19399	+	1.13071i	0.168707	+	0.0454840i
$619$	15.4927	+	26.8342i	0.622705	+	1.07856i	0.988980	+	0.148050i	$0.0472998\pi$
$619$	15.4927	+	26.8342i	0.622705	+	1.07856i	−0.366274	+	0.930507i	$0.619367\pi$
$620$	−23.3701	+	40.1914i	−0.938567	+	1.61413i
$621$	22.2665	+	12.8556i	0.893525	+	0.515877i
$622$	2.96710	+	11.1421i	0.118970	+	0.446757i
$623$	0.647479	+	1.67922i	0.0259407	+	0.0672764i
$624$	12.5072	+	7.32428i	0.500687	+	0.293206i
$625$	−33.1820	+	57.4729i	−1.32728	+	2.29892i
$626$	−12.4901	−	12.5287i	−0.499206	−	0.500749i
$627$	3.74768	−	2.16373i	0.149668	−	0.0864109i
$628$	19.2960	+	0.0595313i	0.769996	+	0.00237556i
$629$		−	29.5203i		−	1.17705i
$630$	22.8013	+	10.1530i	0.908425	+	0.404505i
$631$		−	34.4297i		−	1.37063i	−0.728248	−	0.685313i	$-0.759665\pi$
$631$		−	34.4297i		−	1.37063i	0.728248	−	0.685313i	$-0.240335\pi$
$632$	4.65358	+	17.6946i	0.185110	+	0.703851i
$633$	3.39165	−	1.95817i	0.134806	−	0.0778303i
$634$	−20.7431	+	20.6792i	−0.823814	+	0.821276i
$635$	−5.66865	+	9.81838i	−0.224953	+	0.389631i
$636$	−10.6165	+	6.08583i	−0.420970	+	0.241319i
$637$	20.9557	−	4.51995i	0.830296	−	0.179087i
$638$	3.40044	−	0.905525i	0.134625	−	0.0358501i
$639$	12.9573	+	7.48092i	0.512584	+	0.295941i
$640$	−33.7096	+	32.9894i	−1.33249	+	1.30402i
$641$	9.10990	+	15.7788i	0.359819	+	0.623226i	0.987930	−	0.154898i	$-0.0495049\pi$
$641$	9.10990	+	15.7788i	0.359819	+	0.623226i	−0.628111	+	0.778124i	$0.716172\pi$
$642$	5.77174	−	21.4083i	0.227792	−	0.844917i
$643$	−23.3548			−0.921022			−0.460511	−	0.887654i	$-0.652334\pi$
$643$	−23.3548			−0.921022			−0.460511	+	0.887654i	$0.652334\pi$
$644$	−3.94954	+	24.6829i	−0.155634	+	0.972642i
$645$	−10.4745			−0.412434
$646$	−4.75671	+	17.6434i	−0.187150	+	0.694169i
$647$	−2.02355	−	3.50489i	−0.0795540	−	0.137792i	0.823504	−	0.567311i	$-0.192016\pi$
$647$	−2.02355	−	3.50489i	−0.0795540	−	0.137792i	−0.903058	+	0.429519i	$0.858683\pi$
$648$	1.22079	−	4.47314i	0.0479572	−	0.175722i
$649$	2.48241	+	1.43322i	0.0974431	+	0.0562588i
$650$	−51.8127	+	13.7975i	−2.03226	+	0.541184i
$651$	16.2863	−	6.27973i	0.638310	−	0.246122i
$652$	15.4171	+	26.8946i	0.603782	+	1.05327i
$653$	−13.6948	+	23.7202i	−0.535921	+	0.928242i	0.463197	+	0.886255i	$0.346702\pi$
$653$	−13.6948	+	23.7202i	−0.535921	+	0.928242i	−0.999118	+	0.0419870i	$0.986631\pi$
$654$	3.96959	−	3.95736i	0.155223	−	0.154745i
$655$	−3.68448	+	2.12724i	−0.143965	+	0.0831180i
$656$	24.1777	−	13.7608i	0.943981	−	0.537269i
$657$		−	10.7048i		−	0.417633i
$658$	16.8516	−	1.77042i	0.656942	−	0.0690181i
$659$		−	30.2824i		−	1.17963i	−0.807537	−	0.589817i	$-0.799200\pi$
$659$		−	30.2824i		−	1.17963i	0.807537	−	0.589817i	$-0.200800\pi$
$660$	0.0304353	−	9.86506i	0.00118469	−	0.383997i
$661$	1.37280	−	0.792585i	0.0533956	−	0.0308280i	−0.473065	−	0.881028i	$-0.656852\pi$
$661$	1.37280	−	0.792585i	0.0533956	−	0.0308280i	0.526460	+	0.850200i	$0.323519\pi$
$662$	24.5089	+	24.5847i	0.952566	+	0.955510i
$663$	6.40050	−	11.0860i	0.248575	−	0.430544i
$664$	−13.8392	−	13.9679i	−0.537064	−	0.542058i
$665$	−39.8548	−	6.25118i	−1.54550	−	0.242410i
$666$	4.86582	+	18.2722i	0.188547	+	0.708032i
$667$	−10.1797	−	5.87725i	−0.394159	−	0.227568i
$668$	−27.2505	−	15.8454i	−1.05435	−	0.613076i
$669$	9.43829	+	16.3476i	0.364905	+	0.632034i
$670$	−84.9445	−	22.9013i	−3.28169	−	0.884755i
$671$	−12.7742			−0.493141
$672$	17.6222	−	1.74152i	0.679792	−	0.0671806i
$673$	−42.3394			−1.63206			−0.816032	−	0.578007i	$-0.803831\pi$
$673$	−42.3394			−1.63206			−0.816032	+	0.578007i	$0.803831\pi$
$674$	28.0810	+	7.57074i	1.08164	+	0.291614i
$675$	33.6903	+	58.3534i	1.29674	+	2.24602i
$676$	6.26052	+	3.64031i	0.240789	+	0.140012i
$677$	23.2296	+	13.4116i	0.892787	+	0.515451i	0.874853	−	0.484388i	$-0.160958\pi$
$677$	23.2296	+	13.4116i	0.892787	+	0.515451i	0.0179340	+	0.999839i	$0.494291\pi$
$678$	−0.767943	−	2.88379i	−0.0294927	−	0.110751i
$679$	−19.1390	+	23.7073i	−0.734488	+	0.909801i
$680$	29.3193	+	29.5919i	1.12434	+	1.13480i
$681$	−5.47313	+	9.47974i	−0.209731	+	0.363264i
$682$	5.56741	+	5.58461i	0.213187	+	0.213846i
$683$	0.0128288	−	0.00740673i	0.000490882	−	0.000283411i	−0.499755	−	0.866167i	$-0.666576\pi$
$683$	0.0128288	−	0.00740673i	0.000490882	−	0.000283411i	0.500245	+	0.865884i	$0.333243\pi$
$684$	0.0361109	−	11.7047i	0.00138074	−	0.447542i
$685$			80.3585i			3.07034i
$686$	17.4681	−	19.5158i	0.666934	−	0.745117i
$687$		−	3.30830i		−	0.126219i
$688$	7.38225	−	4.20162i	0.281446	−	0.160185i
$689$	13.7155	−	7.91863i	0.522518	−	0.301676i
$690$	−23.3371	+	23.2653i	−0.888430	+	0.885693i
$691$	−6.96674	+	12.0668i	−0.265027	+	0.459041i	−0.967571	−	0.252600i	$-0.918714\pi$
$691$	−6.96674	+	12.0668i	−0.265027	+	0.459041i	0.702543	+	0.711641i	$0.252048\pi$
$692$	13.2834	+	23.1724i	0.504960	+	0.880881i
$693$	2.65929	−	3.29402i	0.101018	−	0.125130i
$694$	29.2913	−	7.80018i	1.11188	−	0.296091i
$695$	−2.48126	−	1.43256i	−0.0941197	−	0.0543400i
$696$	−2.19239	+	8.03323i	−0.0831024	+	0.304499i
$697$	−12.2850	−	21.2783i	−0.465329	−	0.805973i
$698$	0.286963	−	1.06439i	0.0108617	−	0.0402878i
$699$	−10.1307			−0.383177
$700$	−41.3067	+	50.8443i	−1.56125	+	1.92174i
$701$	16.1182			0.608776			0.304388	−	0.952548i	$-0.401548\pi$
$701$	16.1182			0.608776			0.304388	+	0.952548i	$0.401548\pi$
$702$	−6.13618	+	22.7600i	−0.231595	+	0.859022i
$703$	−15.2812	−	26.4679i	−0.576342	−	0.998254i
$704$	3.93571	+	6.96493i	0.148333	+	0.262501i
$705$	19.3447	+	11.1687i	0.728564	+	0.420637i
$706$	13.3945	−	3.56691i	0.504108	−	0.134242i
$707$	−33.1947	−	5.20656i	−1.24842	−	0.195813i
$708$	−5.88466	+	3.37335i	−0.221159	+	0.126778i
$709$	15.1903	−	26.3103i	0.570483	−	0.988106i	−0.426033	−	0.904708i	$-0.640089\pi$
$709$	15.1903	−	26.3103i	0.570483	−	0.988106i	0.996516	−	0.0833983i	$-0.0265774\pi$
$710$	−39.0418	+	38.9215i	−1.46521	+	1.46070i
$711$	−8.96390	+	5.17531i	−0.336172	+	0.194089i
$712$	−0.489358	−	1.86071i	−0.0183395	−	0.0697330i
$713$		−	26.3409i		−	0.986475i
$714$	−1.63411	−	15.5541i	−0.0611550	−	0.582098i
$715$			12.7674i			0.477475i
$716$	−3.11799	−	0.00961949i	−0.116525	−	0.000359497i
$717$	7.76341	−	4.48221i	0.289930	−	0.167391i
$718$	−28.0913	−	28.1781i	−1.04836	−	1.05160i
$719$	−0.00270659	+	0.00468794i	−0.000100939	+	0.000174831i	−0.866076	−	0.499913i	$-0.833365\pi$
$719$	−0.00270659	+	0.00468794i	−0.000100939	+	0.000174831i	0.865975	+	0.500087i	$0.166699\pi$
$720$	−23.0253	−	13.4838i	−0.858104	−	0.502512i
$721$	−6.40843	+	2.47099i	−0.238663	+	0.0920245i
$722$	−2.04619	−	7.68388i	−0.0761513	−	0.285964i
$723$	−12.2510	−	7.07310i	−0.455618	−	0.263051i
$724$	0.692116	−	1.19028i	0.0257223	−	0.0442365i
$725$	−15.4024	−	26.6777i	−0.572029	−	0.990784i
$726$	−1.61557	−	0.435563i	−0.0599595	−	0.0161653i
$727$	44.9946			1.66876			0.834378	−	0.551192i	$-0.185827\pi$
$727$	44.9946			1.66876			0.834378	+	0.551192i	$0.185827\pi$
$728$	−22.7996	+	2.32422i	−0.845011	+	0.0861415i
$729$	21.9421			0.812670
$730$	38.0830	+	10.2673i	1.40952	+	0.380010i
$731$	−3.75102	−	6.49696i	−0.138737	−	0.240299i
$732$	15.1947	−	26.1315i	0.561613	−	0.965848i
$733$	25.2111	+	14.5556i	0.931193	+	0.537625i	0.887189	−	0.461407i	$-0.152655\pi$
$733$	25.2111	+	14.5556i	0.931193	+	0.537625i	0.0440043	+	0.999031i	$0.485988\pi$
$734$	−6.64644	−	24.9588i	−0.245325	−	0.921246i
$735$	33.7517	−	7.27993i	1.24495	−	0.268524i
$736$	7.11524	−	25.7581i	0.262271	−	0.949457i
$737$	−7.46108	+	12.9230i	−0.274832	+	0.476024i
$738$	11.1113	+	11.1457i	0.409014	+	0.410278i
$739$	25.7005	−	14.8382i	0.945409	−	0.545832i	0.0537575	−	0.998554i	$-0.482880\pi$
$739$	25.7005	−	14.8382i	0.945409	−	0.545832i	0.891652	+	0.452722i	$0.149547\pi$
$740$	−69.6716	−	0.214948i	−2.56118	−	0.00790164i
$741$		−	13.2529i		−	0.486857i
$742$	7.87085	−	17.6761i	0.288948	−	0.648911i
$743$		−	2.53287i		−	0.0929219i	−0.998920	−	0.0464610i	$-0.985206\pi$
$743$		−	2.53287i		−	0.0929219i	0.998920	−	0.0464610i	$-0.0147943\pi$
$744$	−18.0465	+	4.74616i	−0.661618	+	0.174003i
$745$	−32.1499	+	18.5617i	−1.17788	+	0.680049i
$746$	−4.20712	+	4.19416i	−0.154034	+	0.153559i
$747$	5.56184	−	9.63339i	0.203497	−	0.352467i
$748$	6.12984	−	3.51390i	0.224129	−	0.128481i
$749$	12.6132	+	32.7119i	0.460876	+	1.19527i
$750$	−49.7468	+	13.2474i	−1.81650	+	0.483726i
$751$	−20.5467	−	11.8626i	−0.749759	−	0.432874i	0.0758476	−	0.997119i	$-0.475834\pi$
$751$	−20.5467	−	11.8626i	−0.749759	−	0.432874i	−0.825607	+	0.564246i	$0.809167\pi$
$752$	−18.1139	−	0.111769i	−0.660545	−	0.00407581i
$753$	−14.8215	−	25.6716i	−0.540126	−	0.935527i
$754$	2.80530	−	10.4053i	0.102163	−	0.378939i
$755$	26.4060			0.961012
$756$	10.2784	+	26.9036i	0.373820	+	0.978474i
$757$	22.2250			0.807780			0.403890	−	0.914808i	$-0.367658\pi$
$757$	22.2250			0.807780			0.403890	+	0.914808i	$0.367658\pi$
$758$	13.8518	−	51.3784i	0.503120	−	1.86615i
$759$	2.79463	+	4.84044i	0.101439	+	0.175697i
$760$	41.6059	+	11.3549i	1.50920	+	0.411885i
$761$	−29.6904	−	17.1418i	−1.07628	−	0.621389i	−0.146388	−	0.989227i	$-0.546765\pi$
$761$	−29.6904	−	17.1418i	−1.07628	−	0.621389i	−0.929890	+	0.367838i	$0.880098\pi$
$762$	−4.39713	+	1.17094i	−0.159291	+	0.0424187i
$763$	−1.37335	+	8.75589i	−0.0497187	+	0.316985i
$764$	11.8930	+	20.7469i	0.430274	+	0.750595i
$765$	−11.7832	+	20.4090i	−0.426021	+	0.737890i
$766$	17.1478	−	17.0950i	0.619574	−	0.617666i
$767$	7.60242	−	4.38926i	0.274508	−	0.158487i
$768$	−18.9293	−	0.233610i	−0.683052	−	0.00842969i
$769$			34.9659i			1.26090i	0.776228	+	0.630452i	$0.217130\pi$
$769$			34.9659i			1.26090i	−0.776228	+	0.630452i	$0.782870\pi$
$770$	9.16813	+	12.6200i	0.330397	+	0.454794i
$771$			6.47525i			0.233201i
$772$	−0.0604654	+	19.5988i	−0.00217620	+	0.705377i
$773$	23.8836	−	13.7892i	0.859032	−	0.495962i	−0.00465617	−	0.999989i	$-0.501482\pi$
$773$	23.8836	−	13.7892i	0.859032	−	0.495962i	0.863688	+	0.504027i	$0.168149\pi$
$774$	3.39266	+	3.40314i	0.121947	+	0.122323i
$775$	34.5155	−	59.7826i	1.23983	−	2.14745i
$776$	23.1384	−	22.9253i	0.830621	−	0.822969i
$777$	20.3530	+	16.4311i	0.730160	+	0.589463i
$778$	1.32017	+	4.95754i	0.0473306	+	0.177736i
$779$	−22.0295	−	12.7187i	−0.789287	−	0.455695i
$780$	−26.1177	−	15.1867i	−0.935164	−	0.543771i
$781$	4.67526	+	8.09779i	0.167294	+	0.289762i
$782$	−22.7878	−	6.14368i	−0.814892	−	0.219697i
$783$	−13.5429			−0.483985
$784$	−20.8674	+	18.6695i	−0.745265	+	0.666769i
$785$	−40.2221			−1.43559
$786$	−1.64872	−	0.444501i	−0.0588080	−	0.0158548i
$787$	−10.7961	−	18.6994i	−0.384839	−	0.666560i	0.606908	−	0.794772i	$-0.292410\pi$
$787$	−10.7961	−	18.6994i	−0.384839	−	0.666560i	−0.991747	+	0.128212i	$0.959076\pi$
$788$	13.0821	+	7.60687i	0.466031	+	0.270983i
$789$	26.3970	+	15.2403i	0.939758	+	0.542570i
$790$	−9.81398	−	36.8536i	−0.349166	−	1.31119i
$791$	3.67160	+	2.96411i	0.130547	+	0.105392i
$792$	−3.21499	+	3.18537i	−0.114240	+	0.113187i
$793$	−19.5606	+	33.8799i	−0.694616	+	1.20311i
$794$	16.9692	+	17.0216i	0.602215	+	0.604076i
$795$	22.0904	−	12.7539i	0.783467	−	0.452335i
$796$	−0.0693760	+	22.4870i	−0.00245897	+	0.797032i
$797$		−	6.96364i		−	0.246665i	−0.992365	−	0.123332i	$-0.960642\pi$
$797$		−	6.96364i		−	0.246665i	0.992365	−	0.123332i	$-0.0393581\pi$
$798$	−9.51674	−	13.0999i	−0.336889	−	0.463731i
$799$			15.9984i			0.565984i
$800$	49.9004	−	49.1365i	1.76424	−	1.73724i
$801$	0.942618	−	0.544221i	0.0333058	−	0.0192291i
$802$	−7.77718	+	7.75322i	−0.274622	+	0.273776i
$803$	3.34501	−	5.79374i	0.118043	−	0.204457i
$804$	−17.5610	−	30.6345i	−0.619330	−	1.08040i
$805$	8.07392	−	51.4758i	0.284568	−	1.81428i
$806$	23.3368	−	6.21450i	0.822003	−	0.218896i
$807$	−30.0047	−	17.3232i	−1.05621	−	0.609805i
$808$	34.6532	+	9.45739i	1.21909	+	0.332710i
$809$	−5.32841	−	9.22908i	−0.187337	−	0.324477i	0.757025	−	0.653386i	$-0.226652\pi$
$809$	−5.32841	−	9.22908i	−0.187337	−	0.324477i	−0.944361	+	0.328909i	$0.893319\pi$
$810$	−2.51592	+	9.33192i	−0.0884003	+	0.327890i
$811$	37.4796			1.31609			0.658044	−	0.752980i	$-0.271384\pi$
$811$	37.4796			1.31609			0.658044	+	0.752980i	$0.271384\pi$
$812$	−4.69901	−	12.2996i	−0.164903	−	0.431632i
$813$	12.1936			0.427647
$814$	−3.07615	+	11.4099i	−0.107819	+	0.399917i
$815$	−32.3093	−	55.9613i	−1.13175	−	1.96024i
$816$	−0.103164	+	16.7193i	−0.00361146	+	0.585291i
$817$	−6.72632	−	3.88344i	−0.235324	−	0.135864i
$818$	−9.50188	+	2.53032i	−0.332225	+	0.0884705i
$819$	−4.66442	−	12.0970i	−0.162988	−	0.422704i
$820$	−50.3089	+	28.8393i	−1.75686	+	1.00711i
$821$	−0.732793	+	1.26923i	−0.0255746	+	0.0442966i	−0.878529	−	0.477688i	$-0.841475\pi$
$821$	−0.732793	+	1.26923i	−0.0255746	+	0.0442966i	0.852955	+	0.521985i	$0.174808\pi$
$822$	−22.8415	+	22.7711i	−0.796687	+	0.794233i
$823$	−3.46624	+	2.00123i	−0.120825	+	0.0697586i	−0.559195	−	0.829036i	$-0.688890\pi$
$823$	−3.46624	+	2.00123i	−0.120825	+	0.0697586i	0.438369	+	0.898795i	$0.355556\pi$
$824$	7.10107	−	1.86755i	0.247378	−	0.0650591i
$825$			14.6476i			0.509965i
$826$	4.36278	−	9.79779i	0.151800	−	0.340909i
$827$		−	13.0913i		−	0.455228i	−0.973751	−	0.227614i	$-0.926908\pi$
$827$		−	13.0913i		−	0.455228i	0.973751	−	0.227614i	$-0.0730925\pi$
$828$	15.1176	+	0.0466403i	0.525374	+	0.00162086i
$829$	24.7671	−	14.2993i	0.860197	−	0.496635i	−0.00388103	−	0.999992i	$-0.501235\pi$
$829$	24.7671	−	14.2993i	0.860197	−	0.496635i	0.864078	+	0.503357i	$0.167902\pi$
$830$	28.9370	+	29.0264i	1.00442	+	1.00752i
$831$	−16.8353	+	29.1595i	−0.584009	+	1.01153i
$832$	24.4991	+	0.226756i	0.849354	+	0.00786136i
$833$	16.6023	+	18.3280i	0.575235	+	0.635026i
$834$	−0.295916	−	1.11123i	−0.0102467	−	0.0384786i
$835$	56.9043	+	32.8537i	1.96925	+	1.13695i
$836$	3.67703	−	6.32367i	0.127173	−	0.218709i
$837$	−15.1743	−	26.2827i	−0.524502	−	0.908464i
$838$	23.2741	+	6.27476i	0.803989	+	0.216758i
$839$	−17.2061			−0.594019			−0.297010	−	0.954874i	$-0.595989\pi$
$839$	−17.2061			−0.594019			−0.297010	+	0.954874i	$0.595989\pi$
$840$	−36.7216	+	3.74344i	−1.26701	+	0.129161i
$841$	−22.8085			−0.786501
$842$	4.94108	+	1.33213i	0.170281	+	0.0459083i
$843$	−2.28024	−	3.94949i	−0.0785357	−	0.136028i
$844$	3.32771	−	5.72292i	0.114545	−	0.196991i
$845$	−13.0732	−	7.54780i	−0.449731	−	0.259652i
$846$	−2.63701	−	9.90254i	−0.0906623	−	0.340456i
$847$	2.46860	−	0.951852i	0.0848220	−	0.0327060i
$848$	−10.4530	+	17.8498i	−0.358957	+	0.612965i
$849$	−6.05832	+	10.4933i	−0.207921	+	0.360130i
$850$	−43.6683	−	43.8033i	−1.49781	−	1.50244i
$851$	34.1854	−	19.7370i	1.17186	−	0.676574i
$852$	−22.1264	−	0.0682635i	−0.758039	−	0.00233867i
$853$			41.2358i			1.41189i	0.708269	+	0.705943i	$0.249476\pi$
$853$			41.2358i			1.41189i	−0.708269	+	0.705943i	$0.750524\pi$
$854$	4.99400	+	47.5349i	0.170891	+	1.62661i
$855$			24.3982i			0.834402i
$856$	−9.53292	−	36.2475i	−0.325829	−	1.23891i
$857$	−9.47282	+	5.46914i	−0.323585	+	0.186822i	−0.652990	−	0.757367i	$-0.726485\pi$
$857$	−9.47282	+	5.46914i	−0.323585	+	0.186822i	0.329404	+	0.944189i	$0.393152\pi$
$858$	−3.62907	+	3.61789i	−0.123894	+	0.123513i
$859$	−3.76924	+	6.52852i	−0.128605	+	0.222750i	−0.923136	−	0.384473i	$-0.874383\pi$
$859$	−3.76924	+	6.52852i	−0.128605	+	0.222750i	0.794531	+	0.607223i	$0.207717\pi$
$860$	−15.3609	+	8.80557i	−0.523804	+	0.300267i
$861$	21.5084	+	3.37356i	0.733003	+	0.114971i
$862$	35.7034	−	9.50769i	1.21606	−	0.323833i
$863$	−6.25503	−	3.61134i	−0.212924	−	0.122932i	0.389746	−	0.920922i	$-0.372563\pi$
$863$	−6.25503	−	3.61134i	−0.212924	−	0.122932i	−0.602669	+	0.797991i	$0.705896\pi$
$864$	−7.73907	−	29.8001i	−0.263289	−	1.01382i
$865$	−27.8377	−	48.2163i	−0.946510	−	1.63940i
$866$	−4.23289	+	15.7005i	−0.143840	+	0.533523i
$867$	−5.34722			−0.181601
$868$	18.6048	−	22.9006i	0.631488	−	0.777297i
$869$	−6.46870			−0.219436
$870$	4.51828	−	16.7590i	0.153184	−	0.568183i
$871$	22.8497	+	39.5768i	0.774233	+	1.34101i
$872$	2.49461	−	9.14059i	0.0844780	−	0.309539i
$873$	15.9582	+	9.21346i	0.540102	+	0.311828i
$874$	−23.6118	+	6.28774i	−0.798681	+	0.212686i
$875$	51.1324	−	63.3370i	1.72859	−	2.14118i
$876$	7.87311	+	13.7343i	0.266008	+	0.464039i
$877$	1.44213	−	2.49784i	0.0486971	−	0.0843459i	−0.840649	−	0.541580i	$-0.817826\pi$
$877$	1.44213	−	2.49784i	0.0486971	−	0.0843459i	0.889347	+	0.457234i	$0.151160\pi$
$878$	−30.8689	+	30.7739i	−1.04178	+	1.03857i
$879$	−13.8352	+	7.98773i	−0.466648	+	0.269420i
$880$	−8.24859	−	14.4928i	−0.278060	−	0.488551i
$881$		−	1.70833i		−	0.0575552i	−0.999586	−	0.0287776i	$-0.990839\pi$
$881$		−	1.70833i		−	0.0575552i	0.999586	−	0.0287776i	$-0.00916146\pi$
$882$	−13.2973	−	8.60789i	−0.447743	−	0.289843i
$883$			50.6403i			1.70418i	0.523395	+	0.852090i	$0.324665\pi$
$883$			50.6403i			1.70418i	−0.523395	+	0.852090i	$0.675335\pi$
$884$	0.0667577	−	21.6384i	0.00224531	−	0.727777i
$885$	12.2446	−	7.06943i	0.411598	−	0.237636i
$886$	4.90206	+	4.91721i	0.164688	+	0.165197i
$887$	−20.9676	+	36.3170i	−0.704025	+	1.21941i	0.263018	+	0.964791i	$0.415282\pi$
$887$	−20.9676	+	36.3170i	−0.704025	+	1.21941i	−0.967042	+	0.254615i	$0.918051\pi$
$888$	−19.6817	−	19.8647i	−0.660473	−	0.666615i
$889$	4.51961	−	5.59838i	0.151583	−	0.187764i
$890$	1.03201	+	3.87542i	0.0345931	+	0.129904i
$891$	1.41971	+	0.819667i	0.0475619	+	0.0274599i
$892$	27.5842	+	16.0394i	0.923587	+	0.537039i
$893$	8.28160	+	14.3442i	0.277133	+	0.480009i
$894$	−14.3863	−	3.87860i	−0.481151	−	0.129720i
$895$	6.49937			0.217250
$896$	24.3791	−	17.3684i	0.814448	−	0.580236i
$897$	17.1172			0.571527
$898$	−25.7045	−	6.93002i	−0.857770	−	0.231258i
$899$	6.93732	+	12.0158i	0.231372	+	0.400749i
$900$	34.2494	+	19.9151i	1.14165	+	0.663835i
$901$	15.8216	+	9.13459i	0.527093	+	0.304317i
$902$	2.53100	+	9.50443i	0.0842730	+	0.316463i
$903$	6.56721	+	1.03006i	0.218543	+	0.0342782i
$904$	−3.55050	−	3.58351i	−0.118088	−	0.119186i
$905$	−1.43503	+	2.48554i	−0.0477020	+	0.0826223i
$906$	7.48262	+	7.50574i	0.248594	+	0.249362i
$907$	−11.0621	+	6.38672i	−0.367312	+	0.212068i	−0.672283	−	0.740294i	$-0.734686\pi$
$907$	−11.0621	+	6.38672i	−0.367312	+	0.212068i	0.304972	+	0.952361i	$0.401353\pi$
$908$	−0.0570852	+	18.5032i	−0.00189444	+	0.614049i
$909$			20.3211i			0.674008i
$910$	47.5099	−	4.99136i	1.57494	−	0.165462i
$911$		−	14.8466i		−	0.491891i	−0.969284	−	0.245945i	$-0.920902\pi$
$911$		−	14.8466i		−	0.491891i	0.969284	−	0.245945i	$-0.0790984\pi$
$912$	8.56224	+	15.0438i	0.283524	+	0.498151i
$913$	6.02047	−	3.47592i	0.199248	−	0.115036i
$914$	−11.8158	+	11.7794i	−0.390832	+	0.389628i
$915$	−31.5046	+	54.5676i	−1.04151	+	1.80395i
$916$	−2.78118	−	4.85164i	−0.0918926	−	0.160303i
$917$	2.51925	−	0.971384i	0.0831931	−	0.0320779i
$918$	−26.2767	+	6.99740i	−0.867260	+	0.230948i
$919$	43.4063	+	25.0606i	1.43184	+	0.826673i	0.997261	−	0.0739604i	$-0.0235638\pi$
$919$	43.4063	+	25.0606i	1.43184	+	0.826673i	0.434579	+	0.900634i	$0.356897\pi$
$920$	−14.6658	+	53.7374i	−0.483516	+	1.77167i
$921$	−19.8800	−	34.4332i	−0.655070	−	1.13461i
$922$	11.5265	−	42.7535i	0.379604	−	1.40801i
$923$	28.6362			0.942570
$924$	−0.989208	+	6.18211i	−0.0325426	+	0.203376i
$925$	103.448			3.40136
$926$	4.86805	−	18.0564i	0.159974	−	0.593369i
$927$	2.07692	+	3.59734i	0.0682151	+	0.118152i
$928$	3.53811	+	13.6238i	0.116144	+	0.447225i
$929$	8.68459	+	5.01405i	0.284932	+	0.164506i	0.635654	−	0.771974i	$-0.280730\pi$
$929$	8.68459	+	5.01405i	0.284932	+	0.164506i	−0.350722	+	0.936480i	$0.614064\pi$
$930$	37.5867	−	10.0092i	1.23252	−	0.328215i
$931$	24.3730	+	7.83861i	0.798794	+	0.256900i
$932$	−14.8567	+	8.51651i	−0.486647	+	0.278968i
$933$	4.82332	−	8.35424i	0.157908	−	0.273505i
$934$	14.0701	−	14.0267i	0.460387	−	0.458969i
$935$	−12.7548	+	7.36398i	−0.417126	+	0.240828i
$936$	3.52532	+	13.4045i	0.115229	+	0.438139i
$937$			8.28324i			0.270602i	0.990805	+	0.135301i	$0.0432001\pi$
$937$			8.28324i			0.270602i	−0.990805	+	0.135301i	$0.956800\pi$
$938$	51.0055	+	22.7118i	1.66539	+	0.741568i
$939$			14.8008i			0.483006i
$940$	37.7583	+	0.116490i	1.23154	+	0.00379949i
$941$	−26.5737	+	15.3424i	−0.866279	+	0.500146i	−0.866110	−	0.499854i	$-0.833387\pi$
$941$	−26.5737	+	15.3424i	−0.866279	+	0.500146i	−0.000169114		1.00000i	$0.500054\pi$
$942$	−11.3977	−	11.4329i	−0.371357	−	0.372504i
$943$	16.4273	−	28.4529i	0.534945	−	0.926552i
$944$	−5.79404	+	9.89407i	−0.188580	+	0.322025i
$945$	−21.5978	−	56.0132i	−0.702577	−	1.82211i
$946$	0.772797	+	2.90201i	0.0251258	+	0.0943526i
$947$	−48.3963	−	27.9416i	−1.57267	−	0.907981i	−0.995840	−	0.0911165i	$-0.970956\pi$
$947$	−48.3963	−	27.9416i	−1.57267	−	0.907981i	−0.576829	−	0.816865i	$-0.695710\pi$
$948$	7.69444	−	13.2327i	0.249904	−	0.429779i
$949$	−10.2442	−	17.7434i	−0.332540	−	0.575976i
$950$	−61.8277	−	16.6690i	−2.00596	−	0.540812i
$951$	24.5049			0.794624
$952$	−15.4723	−	21.4365i	−0.501459	−	0.694761i
$953$	−0.818847			−0.0265251			−0.0132625	−	0.999912i	$-0.504222\pi$
$953$	−0.818847			−0.0265251			−0.0132625	+	0.999912i	$0.504222\pi$
$954$	−11.2987	−	3.04617i	−0.365810	−	0.0986234i
$955$	−24.9239	−	43.1694i	−0.806518	−	1.39693i
$956$	7.61706	−	13.0996i	0.246353	−	0.423672i
$957$	−2.54962	−	1.47202i	−0.0824175	−	0.0475838i
$958$	3.05376	+	11.4675i	0.0986625	+	0.370499i
$959$	7.90242	−	50.3824i	0.255183	−	1.62693i
$960$	39.4588	+	0.365219i	1.27353	+	0.0117874i
$961$	−0.0459941	+	0.0796640i	−0.00148368	+	0.00256981i
$962$	25.5512	+	25.6301i	0.823804	+	0.826349i
$963$	18.3627	−	10.6017i	0.591728	−	0.341634i
$964$	−23.9122	−	0.0737730i	−0.770161	−	0.00237607i
$965$		−	40.8533i		−	1.31511i
$966$	16.9196	−	12.2917i	0.544379	−	0.395478i
$967$			10.5942i			0.340686i	0.985385	+	0.170343i	$0.0544875\pi$
$967$			10.5942i			0.340686i	−0.985385	+	0.170343i	$0.945512\pi$
$968$	−2.73541	+	0.719400i	−0.0879194	+	0.0231224i
$969$	13.2398	−	7.64399i	0.425323	−	0.245560i
$970$	−48.0836	+	47.9355i	−1.54387	+	1.53912i
$971$	24.0679	−	41.6868i	0.772374	−	1.33779i	−0.163884	−	0.986480i	$-0.552402\pi$
$971$	24.0679	−	41.6868i	0.772374	−	1.33779i	0.936258	−	0.351312i	$-0.114264\pi$
$972$	24.9659	−	14.3116i	0.800782	−	0.459044i
$973$	1.41480	+	1.14218i	0.0453564	+	0.0366165i
$974$	48.4948	−	12.9140i	1.55387	−	0.413791i
$975$	38.8487	+	22.4293i	1.24415	+	0.718313i
$976$	0.315279	−	51.0957i	0.0100918	−	1.63553i
$977$	−28.7299	−	49.7616i	−0.919151	−	1.59202i	−0.800708	−	0.599055i	$-0.795543\pi$
$977$	−28.7299	−	49.7616i	−0.919151	−	1.59202i	−0.118443	−	0.992961i	$-0.537790\pi$
$978$	6.75125	−	25.0414i	0.215881	−	0.800736i
$979$	0.680230			0.0217403
$980$	43.3771	−	39.0500i	1.38563	−	1.24741i
$981$	5.36016			0.171137
$982$	−5.06022	+	18.7691i	−0.161478	+	0.598947i
$983$	−13.1767	−	22.8226i	−0.420270	−	0.727929i	0.575696	−	0.817664i	$-0.304731\pi$
$983$	−13.1767	−	22.8226i	−0.420270	−	0.727929i	−0.995966	+	0.0897349i	$0.971398\pi$
$984$	−22.4533	−	6.12786i	−0.715787	−	0.195349i
$985$	−27.3180	−	15.7720i	−0.870423	−	0.502539i
$986$	12.0130	−	3.19903i	0.382573	−	0.101878i
$987$	−11.0302	−	8.90478i	−0.351096	−	0.283442i
$988$	−11.1413	−	19.4355i	−0.354451	−	0.618324i
$989$	5.01578	−	8.68759i	0.159493	−	0.276249i
$990$	6.68102	−	6.66044i	0.212337	−	0.211683i
$991$	−38.6264	+	22.3010i	−1.22701	+	0.708414i	−0.966403	−	0.257031i	$-0.917256\pi$
$991$	−38.6264	+	22.3010i	−1.22701	+	0.708414i	−0.260606	+	0.965445i	$0.583922\pi$
$992$	−22.4754	+	22.1314i	−0.713596	+	0.702672i
$993$		−	29.0431i		−	0.921654i
$994$	28.3055	−	20.5633i	0.897797	−	0.652227i
$995$		−	46.8736i		−	1.48599i
$996$	−0.0507519	+	16.4503i	−0.00160813	+	0.521249i
$997$	13.4640	−	7.77344i	0.426409	−	0.246187i	−0.271407	−	0.962465i	$-0.587489\pi$
$997$	13.4640	−	7.77344i	0.426409	−	0.246187i	0.697816	+	0.716277i	$0.254155\pi$
$998$	−28.7364	−	28.8252i	−0.909636	−	0.912446i
$999$	22.7399	−	39.3867i	0.719459	−	1.24614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.l.a.243.4	yes	80
4.3	odd	2	inner	308.2.l.a.243.31	yes	80
7.3	odd	6	inner	308.2.l.a.199.31	yes	80
28.3	even	6	inner	308.2.l.a.199.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.l.a.199.4	✓	80	28.3	even	6	inner
308.2.l.a.199.31	yes	80	7.3	odd	6	inner
308.2.l.a.243.4	yes	80	1.1	even	1	trivial
308.2.l.a.243.31	yes	80	4.3	odd	2	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36546 - 0.368132i) q^{2} +(0.591585 + 1.02466i) q^{3} +(1.72896 + 1.00534i) q^{4} +(-3.61040 - 2.08447i) q^{5} +(-0.430577 - 1.61691i) q^{6} +(2.05863 + 1.66194i) q^{7} +(-1.99072 - 2.00923i) q^{8} +(0.800054 - 1.38573i) q^{9} +O(q^{10})\)	\(q+(-1.36546 - 0.368132i) q^{2} +(0.591585 + 1.02466i) q^{3} +(1.72896 + 1.00534i) q^{4} +(-3.61040 - 2.08447i) q^{5} +(-0.430577 - 1.61691i) q^{6} +(2.05863 + 1.66194i) q^{7} +(-1.99072 - 2.00923i) q^{8} +(0.800054 - 1.38573i) q^{9} +(4.16249 + 4.17536i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-0.00730050 + 2.36633i) q^{12} -3.06252i q^{13} +(-2.19916 - 3.02716i) q^{14} -4.93256i q^{15} +(1.97859 + 3.47638i) q^{16} +(3.05949 - 1.76639i) q^{17} +(-1.60257 + 1.59764i) q^{18} +(1.82875 - 3.16749i) q^{19} +(-4.14663 - 7.23363i) q^{20} +(-0.485065 + 3.09257i) q^{21} +(-1.36659 + 0.363918i) q^{22} +(4.09107 + 2.36198i) q^{23} +(0.881091 - 3.22844i) q^{24} +(6.18999 + 10.7214i) q^{25} +(-1.12741 + 4.18174i) q^{26} +5.44271 q^{27} +(1.88846 + 4.94305i) q^{28} -2.48827 q^{29} +(-1.81583 + 6.73520i) q^{30} +(-2.78801 - 4.82897i) q^{31} +(-1.42191 - 5.47523i) q^{32} +(1.02466 + 0.591585i) q^{33} +(-4.82787 + 1.28565i) q^{34} +(-3.96821 - 10.2914i) q^{35} +(2.77639 - 1.59155i) q^{36} +(4.17805 - 7.23659i) q^{37} +(-3.66314 + 3.65186i) q^{38} +(3.13803 - 1.81174i) q^{39} +(2.99913 + 11.4037i) q^{40} -6.95486i q^{41} +(1.80081 - 4.04420i) q^{42} -2.12355i q^{43} +(1.99999 + 0.00617028i) q^{44} +(-5.77703 + 3.33537i) q^{45} +(-4.71667 - 4.73125i) q^{46} +(-2.26428 + 3.92184i) q^{47} +(-2.39159 + 4.08394i) q^{48} +(1.47589 + 6.84264i) q^{49} +(-4.50529 - 16.9183i) q^{50} +(3.61989 + 2.08995i) q^{51} +(3.07887 - 5.29496i) q^{52} +(2.58566 + 4.47849i) q^{53} +(-7.43180 - 2.00364i) q^{54} -4.16893 q^{55} +(-0.758926 - 7.44473i) q^{56} +4.32745 q^{57} +(3.39763 + 0.916012i) q^{58} +(1.43322 + 2.48241i) q^{59} +(4.95889 - 8.52818i) q^{60} +(-11.0628 - 6.38708i) q^{61} +(2.02921 + 7.62012i) q^{62} +(3.95002 - 1.52307i) q^{63} +(-0.0740424 + 7.99966i) q^{64} +(-6.38371 + 11.0569i) q^{65} +(-1.18134 - 1.18499i) q^{66} +(-12.9230 + 7.46108i) q^{67} +(7.06555 + 0.0217983i) q^{68} +5.58926i q^{69} +(1.62982 + 15.5133i) q^{70} +9.35052i q^{71} +(-4.37695 + 1.15112i) q^{72} +(5.79374 - 3.34501i) q^{73} +(-8.36898 + 8.34320i) q^{74} +(-7.32381 + 12.6852i) q^{75} +(6.34623 - 3.63794i) q^{76} +(2.61379 + 0.409971i) q^{77} +(-4.95181 + 1.31865i) q^{78} +(-5.60206 - 3.23435i) q^{79} +(0.102893 - 16.6754i) q^{80} +(0.819667 + 1.41971i) q^{81} +(-2.56031 + 9.49658i) q^{82} +6.95184 q^{83} +(-3.94773 + 4.85926i) q^{84} -14.7280 q^{85} +(-0.781746 + 2.89962i) q^{86} +(-1.47202 - 2.54962i) q^{87} +(-2.72863 - 0.744686i) q^{88} +(0.589097 + 0.340115i) q^{89} +(9.11615 - 2.42760i) q^{90} +(5.08973 - 6.30459i) q^{91} +(4.69870 + 8.19668i) q^{92} +(3.29869 - 5.71350i) q^{93} +(4.53554 - 4.52157i) q^{94} +(-13.2050 + 7.62394i) q^{95} +(4.76904 - 4.69604i) q^{96} +11.5160i q^{97} +(0.503723 - 9.88667i) q^{98} -1.60011i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) \) 80 * q + 12 * q^8 - 40 * q^9	\( 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) \) 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more