LMFDB - Embedded newform 770.2.o.b.549.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.14
Character	$\chi$	$=$	770.549
Dual form			770.2.o.b.439.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.340512 - 0.589784i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.839811 - 2.07237i) q^{5} +0.681024 q^{6} +(-2.52726 - 0.782908i) q^{7} -1.00000 q^{8} +(1.26810 + 2.19642i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.340512 - 0.589784i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.839811 - 2.07237i) q^{5} +0.681024 q^{6} +(-2.52726 - 0.782908i) q^{7} -1.00000 q^{8} +(1.26810 + 2.19642i) q^{9} +(1.37482 - 1.76348i) q^{10} +(-3.24014 + 0.708161i) q^{11} +(0.340512 + 0.589784i) q^{12} -2.05099i q^{13} +(-0.585613 - 2.58013i) q^{14} +(-1.50822 - 0.210360i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.89411 - 1.67092i) q^{17} +(-1.26810 + 2.19642i) q^{18} +(-2.31422 - 4.00835i) q^{19} +(2.21463 + 0.308888i) q^{20} +(-1.32231 + 1.22395i) q^{21} +(-2.23336 - 2.45196i) q^{22} +(2.24798 - 1.29787i) q^{23} +(-0.340512 + 0.589784i) q^{24} +(-3.58944 + 3.48080i) q^{25} +(1.77621 - 1.02549i) q^{26} +3.77029 q^{27} +(1.94165 - 1.79722i) q^{28} -0.208603i q^{29} +(-0.571931 - 1.41133i) q^{30} +(-7.69058 - 4.44016i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.685645 + 2.15212i) q^{33} -3.34183i q^{34} +(0.499946 + 5.89492i) q^{35} -2.53621 q^{36} +(-3.14069 + 1.81328i) q^{37} +(2.31422 - 4.00835i) q^{38} +(-1.20964 - 0.698386i) q^{39} +(0.839811 + 2.07237i) q^{40} -6.23454 q^{41} +(-1.72113 - 0.533179i) q^{42} -6.55137 q^{43} +(1.00678 - 3.16012i) q^{44} +(3.48683 - 4.47256i) q^{45} +(2.24798 + 1.29787i) q^{46} +(-6.57571 - 11.3895i) q^{47} -0.681024 q^{48} +(5.77411 + 3.95723i) q^{49} +(-4.80918 - 1.36814i) q^{50} +(-1.97096 + 1.13793i) q^{51} +(1.77621 + 1.02549i) q^{52} +(3.20093 + 1.84806i) q^{53} +(1.88514 + 3.26517i) q^{54} +(4.18868 + 6.12005i) q^{55} +(2.52726 + 0.782908i) q^{56} -3.15208 q^{57} +(0.180656 - 0.104302i) q^{58} +(4.99271 + 2.88254i) q^{59} +(0.936285 - 1.20097i) q^{60} +(5.38616 + 9.32910i) q^{61} -8.88032i q^{62} +(-1.48523 - 6.54374i) q^{63} +1.00000 q^{64} +(-4.25041 + 1.72244i) q^{65} +(-2.20661 + 0.482275i) q^{66} +(1.44891 + 0.836530i) q^{67} +(2.89411 - 1.67092i) q^{68} -1.76777i q^{69} +(-4.85518 + 3.38042i) q^{70} +5.74537 q^{71} +(-1.26810 - 2.19642i) q^{72} +(6.62663 + 3.82589i) q^{73} +(-3.14069 - 1.81328i) q^{74} +(0.830673 + 3.30225i) q^{75} +4.62844 q^{76} +(8.74311 + 0.747023i) q^{77} -1.39677i q^{78} +(13.3578 - 7.71215i) q^{79} +(-1.37482 + 1.76348i) q^{80} +(-2.52048 + 4.36560i) q^{81} +(-3.11727 - 5.39927i) q^{82} -1.84746i q^{83} +(-0.398816 - 1.75713i) q^{84} +(-1.03225 + 7.40093i) q^{85} +(-3.27568 - 5.67365i) q^{86} +(-0.123031 - 0.0710319i) q^{87} +(3.24014 - 0.708161i) q^{88} +(15.0268 - 8.67572i) q^{89} +(5.61676 + 0.783403i) q^{90} +(-1.60574 + 5.18339i) q^{91} +2.59575i q^{92} +(-5.23747 + 3.02386i) q^{93} +(6.57571 - 11.3895i) q^{94} +(-6.36328 + 8.16218i) q^{95} +(-0.340512 - 0.589784i) q^{96} -5.95329 q^{97} +(-0.540006 + 6.97914i) q^{98} +(-5.66425 - 6.21868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.340512	−	0.589784i	0.196595	−	0.340512i	−0.750827	−	0.660498i	$-0.770345\pi$
$3$	0.340512	−	0.589784i	0.196595	−	0.340512i	0.947422	+	0.319986i	$0.103678\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.839811	−	2.07237i	−0.375575	−	0.926792i
$5$	−0.839811	−	2.07237i	−0.375575	−	0.926792i
$6$	0.681024			0.278027
$7$	−2.52726	−	0.782908i	−0.955215	−	0.295911i
$7$	−2.52726	−	0.782908i	−0.955215	−	0.295911i
$8$	−1.00000			−0.353553
$9$	1.26810	+	2.19642i	0.422701	+	0.732140i
$10$	1.37482	−	1.76348i	0.434756	−	0.557662i
$11$	−3.24014	+	0.708161i	−0.976939	+	0.213519i
$11$	−3.24014	+	0.708161i	−0.976939	+	0.213519i
$12$	0.340512	+	0.589784i	0.0982973	+	0.170256i
$13$		−	2.05099i		−	0.568842i	−0.958699	−	0.284421i	$-0.908199\pi$
$13$		−	2.05099i		−	0.568842i	0.958699	−	0.284421i	$-0.0918013\pi$
$14$	−0.585613	−	2.58013i	−0.156512	−	0.689568i
$15$	−1.50822	−	0.210360i	−0.389420	−	0.0543147i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.89411	−	1.67092i	−0.701925	−	0.405257i	0.106139	−	0.994351i	$-0.466151\pi$
$17$	−2.89411	−	1.67092i	−0.701925	−	0.405257i	−0.808064	+	0.589095i	$0.799485\pi$
$18$	−1.26810	+	2.19642i	−0.298895	+	0.517701i
$19$	−2.31422	−	4.00835i	−0.530919	−	0.919578i	−0.999349	−	0.0360778i	$-0.988514\pi$
$19$	−2.31422	−	4.00835i	−0.530919	−	0.919578i	0.468430	−	0.883501i	$-0.344820\pi$
$20$	2.21463	+	0.308888i	0.495206	+	0.0690694i
$21$	−1.32231	+	1.22395i	−0.288552	+	0.267088i
$22$	−2.23336	−	2.45196i	−0.476153	−	0.522760i
$23$	2.24798	−	1.29787i	0.468737	−	0.270625i	−0.246974	−	0.969022i	$-0.579436\pi$
$23$	2.24798	−	1.29787i	0.468737	−	0.270625i	0.715711	+	0.698397i	$0.246103\pi$
$24$	−0.340512	+	0.589784i	−0.0695067	+	0.120389i
$25$	−3.58944	+	3.48080i	−0.717887	+	0.696159i
$26$	1.77621	−	1.02549i	0.348343	−	0.201116i
$27$	3.77029			0.725593
$28$	1.94165	−	1.79722i	0.366937	−	0.339643i
$29$		−	0.208603i		−	0.0387366i	−0.999812	−	0.0193683i	$-0.993834\pi$
$29$		−	0.208603i		−	0.0387366i	0.999812	−	0.0193683i	$-0.00616551\pi$
$30$	−0.571931	−	1.41133i	−0.104420	−	0.257673i
$31$	−7.69058	−	4.44016i	−1.38127	−	0.797476i	−0.388960	−	0.921255i	$-0.627165\pi$
$31$	−7.69058	−	4.44016i	−1.38127	−	0.797476i	−0.992310	+	0.123778i	$0.960499\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.685645	+	2.15212i	−0.119355	+	0.374636i
$34$		−	3.34183i		−	0.573120i
$35$	0.499946	+	5.89492i	0.0845063	+	0.996423i
$36$	−2.53621			−0.422701
$37$	−3.14069	+	1.81328i	−0.516326	+	0.298101i	−0.735430	−	0.677600i	$-0.763020\pi$
$37$	−3.14069	+	1.81328i	−0.516326	+	0.298101i	0.219104	+	0.975702i	$0.429687\pi$
$38$	2.31422	−	4.00835i	0.375416	−	0.650240i
$39$	−1.20964	−	0.698386i	−0.193697	−	0.111831i
$40$	0.839811	+	2.07237i	0.132786	+	0.327670i
$41$	−6.23454			−0.973671			−0.486836	−	0.873494i	$-0.661849\pi$
$41$	−6.23454			−0.973671			−0.486836	+	0.873494i	$0.661849\pi$
$42$	−1.72113	−	0.533179i	−0.265576	−	0.0822713i
$43$	−6.55137			−0.999074			−0.499537	−	0.866292i	$-0.666497\pi$
$43$	−6.55137			−0.999074			−0.499537	+	0.866292i	$0.666497\pi$
$44$	1.00678	−	3.16012i	0.151778	−	0.476407i
$45$	3.48683	−	4.47256i	0.519785	−	0.666729i
$46$	2.24798	+	1.29787i	0.331447	+	0.191361i
$47$	−6.57571	−	11.3895i	−0.959166	−	1.66132i	−0.724533	−	0.689240i	$-0.757944\pi$
$47$	−6.57571	−	11.3895i	−0.959166	−	1.66132i	−0.234633	−	0.972084i	$-0.575389\pi$
$48$	−0.681024			−0.0982973
$49$	5.77411	+	3.95723i	0.824873	+	0.565318i
$50$	−4.80918	−	1.36814i	−0.680120	−	0.193485i
$51$	−1.97096	+	1.13793i	−0.275990	+	0.159343i
$52$	1.77621	+	1.02549i	0.246316	+	0.142210i
$53$	3.20093	+	1.84806i	0.439682	+	0.253850i	0.703463	−	0.710732i	$-0.251636\pi$
$53$	3.20093	+	1.84806i	0.439682	+	0.253850i	−0.263781	+	0.964583i	$0.584970\pi$
$54$	1.88514	+	3.26517i	0.256536	+	0.444333i
$55$	4.18868	+	6.12005i	0.564801	+	0.825227i
$56$	2.52726	+	0.782908i	0.337720	+	0.104620i
$57$	−3.15208			−0.417503
$58$	0.180656	−	0.104302i	0.0237213	−	0.0136955i
$59$	4.99271	+	2.88254i	0.649995	+	0.375275i	0.788454	−	0.615093i	$-0.210882\pi$
$59$	4.99271	+	2.88254i	0.649995	+	0.375275i	−0.138459	+	0.990368i	$0.544215\pi$
$60$	0.936285	−	1.20097i	0.120874	−	0.155045i
$61$	5.38616	+	9.32910i	0.689627	+	1.19447i	0.971959	+	0.235152i	$0.0755589\pi$
$61$	5.38616	+	9.32910i	0.689627	+	1.19447i	−0.282331	+	0.959317i	$0.591108\pi$
$62$		−	8.88032i		−	1.12780i
$63$	−1.48523	−	6.54374i	−0.187122	−	0.824433i
$64$	1.00000			0.125000
$65$	−4.25041	+	1.72244i	−0.527198	+	0.213643i
$66$	−2.20661	+	0.482275i	−0.271615	+	0.0593639i
$67$	1.44891	+	0.836530i	0.177013	+	0.102198i	0.585888	−	0.810392i	$-0.300746\pi$
$67$	1.44891	+	0.836530i	0.177013	+	0.102198i	−0.408876	+	0.912590i	$0.634079\pi$
$68$	2.89411	−	1.67092i	0.350963	−	0.202628i
$69$		−	1.76777i		−	0.212814i
$70$	−4.85518	+	3.38042i	−0.580304	+	0.404038i
$71$	5.74537			0.681850			0.340925	−	0.940091i	$-0.389260\pi$
$71$	5.74537			0.681850			0.340925	+	0.940091i	$0.389260\pi$
$72$	−1.26810	−	2.19642i	−0.149447	−	0.258850i
$73$	6.62663	+	3.82589i	0.775589	+	0.447786i	0.834865	−	0.550455i	$-0.185546\pi$
$73$	6.62663	+	3.82589i	0.775589	+	0.447786i	−0.0592759	+	0.998242i	$0.518879\pi$
$74$	−3.14069	−	1.81328i	−0.365098	−	0.210789i
$75$	0.830673	+	3.30225i	0.0959178	+	0.381310i
$76$	4.62844			0.530919
$77$	8.74311	+	0.747023i	0.996370	+	0.0851312i
$78$		−	1.39677i		−	0.158153i
$79$	13.3578	−	7.71215i	1.50287	−	0.867685i	0.502880	−	0.864356i	$-0.332274\pi$
$79$	13.3578	−	7.71215i	1.50287	−	0.867685i	0.999994	−	0.00332822i	$-0.00105941\pi$
$80$	−1.37482	+	1.76348i	−0.153710	+	0.197163i
$81$	−2.52048	+	4.36560i	−0.280053	+	0.485067i
$82$	−3.11727	−	5.39927i	−0.344245	−	0.596250i
$83$		−	1.84746i		−	0.202785i	−0.994846	−	0.101393i	$-0.967670\pi$
$83$		−	1.84746i		−	0.202785i	0.994846	−	0.101393i	$-0.0323298\pi$
$84$	−0.398816	−	1.75713i	−0.0435144	−	0.191718i
$85$	−1.03225	+	7.40093i	−0.111963	+	0.802743i
$86$	−3.27568	−	5.67365i	−0.353226	−	0.611806i
$87$	−0.123031	−	0.0710319i	−0.0131903	−	0.00761542i
$88$	3.24014	−	0.708161i	0.345400	−	0.0754902i
$89$	15.0268	−	8.67572i	1.59284	−	0.919624i	0.600018	−	0.799986i	$-0.295160\pi$
$89$	15.0268	−	8.67572i	1.59284	−	0.919624i	0.992818	−	0.119638i	$-0.0381733\pi$
$90$	5.61676	+	0.783403i	0.592058	+	0.0825779i
$91$	−1.60574	+	5.18339i	−0.168327	+	0.543367i
$92$			2.59575i			0.270625i
$93$	−5.23747	+	3.02386i	−0.543101	+	0.313559i
$94$	6.57571	−	11.3895i	0.678233	−	1.17473i
$95$	−6.36328	+	8.16218i	−0.652858	+	0.837422i
$96$	−0.340512	−	0.589784i	−0.0347534	−	0.0601946i
$97$	−5.95329			−0.604465			−0.302233	−	0.953234i	$-0.597732\pi$
$97$	−5.95329			−0.604465			−0.302233	+	0.953234i	$0.597732\pi$
$98$	−0.540006	+	6.97914i	−0.0545488	+	0.705000i
$99$	−5.66425	−	6.21868i	−0.569279	−	0.625001i
$100$	−1.21974	−	4.84894i	−0.121974	−	0.484894i
$101$	−2.30017	+	3.98401i	−0.228876	+	0.396424i	−0.957475	−	0.288516i	$-0.906838\pi$
$101$	−2.30017	+	3.98401i	−0.228876	+	0.396424i	0.728600	+	0.684940i	$0.240172\pi$
$102$	−1.97096	−	1.13793i	−0.195154	−	0.112672i
$103$	2.02004	+	3.49881i	0.199040	+	0.344748i	0.948217	−	0.317622i	$-0.102884\pi$
$103$	2.02004	+	3.49881i	0.199040	+	0.344748i	−0.749177	+	0.662369i	$0.769551\pi$
$104$			2.05099i			0.201116i
$105$	3.64697	+	1.71243i	0.355907	+	0.167116i
$106$			3.69612i			0.358999i
$107$	4.80623	+	8.32464i	0.464636	+	0.804773i	0.999185	−	0.0403642i	$-0.0128518\pi$
$107$	4.80623	+	8.32464i	0.464636	+	0.804773i	−0.534549	+	0.845138i	$0.679518\pi$
$108$	−1.88514	+	3.26517i	−0.181398	+	0.314191i
$109$	−15.1014	−	8.71882i	−1.44646	−	0.835112i	−0.448188	−	0.893939i	$-0.647930\pi$
$109$	−15.1014	−	8.71882i	−1.44646	−	0.835112i	−0.998268	+	0.0588278i	$0.981264\pi$
$110$	−3.20578	+	6.68752i	−0.305659	+	0.637630i
$111$			2.46977i			0.234420i
$112$	0.585613	+	2.58013i	0.0553352	+	0.243799i
$113$		−	10.5976i		−	0.996934i	−0.866909	−	0.498467i	$-0.833896\pi$
$113$		−	10.5976i		−	0.996934i	0.866909	−	0.498467i	$-0.166104\pi$
$114$	−1.57604	−	2.72978i	−0.147610	−	0.255668i
$115$	−4.57756	−	3.56869i	−0.426859	−	0.332782i
$116$	0.180656	+	0.104302i	0.0167735	+	0.00968416i
$117$	4.50483	−	2.60087i	0.416472	−	0.240450i
$118$			5.76508i			0.530719i
$119$	6.00601	+	6.48867i	0.550570	+	0.594815i
$120$	1.50822	+	0.210360i	0.137681	+	0.0192032i
$121$	9.99702	−	4.58908i	0.908820	−	0.417189i
$122$	−5.38616	+	9.32910i	−0.487640	+	0.844617i
$123$	−2.12294	+	3.67703i	−0.191419	+	0.331547i
$124$	7.69058	−	4.44016i	0.690635	−	0.398738i
$125$	10.2279	+	4.51543i	0.914815	+	0.403872i
$126$	4.92442	−	4.55812i	0.438703	−	0.406070i
$127$	12.3526			1.09612			0.548059	−	0.836440i	$-0.315367\pi$
$127$	12.3526			1.09612			0.548059	+	0.836440i	$0.315367\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.23082	+	3.86389i	−0.196413	+	0.340197i
$130$	−3.61688	−	2.81974i	−0.317222	−	0.247308i
$131$	3.55442	+	6.15643i	0.310551	+	0.537890i	0.978482	−	0.206333i	$-0.0661532\pi$
$131$	3.55442	+	6.15643i	0.310551	+	0.537890i	−0.667931	+	0.744223i	$0.732820\pi$
$132$	−1.52097	−	1.66985i	−0.132383	−	0.145341i
$133$	2.71048	+	11.9420i	0.235028	+	1.03550i
$134$			1.67306i			0.144530i
$135$	−3.16633	−	7.81344i	−0.272514	−	0.672473i
$136$	2.89411	+	1.67092i	0.248168	+	0.143280i
$137$	−16.1860	−	9.34499i	−1.38286	−	0.798397i	−0.390366	−	0.920660i	$-0.627651\pi$
$137$	−16.1860	−	9.34499i	−1.38286	−	0.798397i	−0.992498	+	0.122263i	$0.960985\pi$
$138$	1.53093	−	0.883883i	0.130322	−	0.0752412i
$139$	−19.6113			−1.66341			−0.831706	−	0.555216i	$-0.812636\pi$
$139$	−19.6113			−1.66341			−0.831706	+	0.555216i	$0.812636\pi$
$140$	−5.35512	−	2.51449i	−0.452590	−	0.212513i
$141$	−8.95643			−0.754268
$142$	2.87268	+	4.97564i	0.241070	+	0.417546i
$143$	1.45243	+	6.64549i	0.121458	+	0.555724i
$144$	1.26810	−	2.19642i	0.105675	−	0.183035i
$145$	−0.432303	+	0.175187i	−0.0359008	+	0.0145485i
$146$			7.65178i			0.633266i
$147$	4.30006	−	2.05799i	0.354663	−	0.169741i
$148$		−	3.62656i		−	0.298101i
$149$	4.37001	−	2.52303i	0.358005	−	0.206694i	−0.310200	−	0.950671i	$-0.600396\pi$
$149$	4.37001	−	2.52303i	0.358005	−	0.206694i	0.668205	+	0.743977i	$0.267063\pi$
$150$	−2.44449	+	2.37051i	−0.199592	+	0.193551i
$151$	2.05768	+	1.18800i	0.167452	+	0.0966784i	0.581384	−	0.813629i	$-0.302512\pi$
$151$	2.05768	+	1.18800i	0.167452	+	0.0966784i	−0.413932	+	0.910308i	$0.635845\pi$
$152$	2.31422	+	4.00835i	0.187708	+	0.325120i
$153$		−	8.47558i		−	0.685210i
$154$	3.72461	+	7.94527i	0.300138	+	0.640248i
$155$	−2.74302	+	19.6666i	−0.220325	+	1.57966i
$156$	1.20964	−	0.698386i	0.0968487	−	0.0559157i
$157$	0.279611	−	0.484300i	0.0223154	−	0.0386513i	−0.854652	−	0.519201i	$-0.826230\pi$
$157$	0.279611	−	0.484300i	0.0223154	−	0.0386513i	0.876967	+	0.480550i	$0.159563\pi$
$158$	13.3578	+	7.71215i	1.06269	+	0.613546i
$159$	2.17991	−	1.25857i	0.172878	−	0.0998113i
$160$	−2.21463	−	0.308888i	−0.175082	−	0.0244197i
$161$	−6.69736	+	1.52010i	−0.527826	+	0.119801i
$162$	−5.04096			−0.396055
$163$	−19.0284	+	10.9861i	−1.49042	+	0.860495i	−0.999940	−	0.0109567i	$-0.996512\pi$
$163$	−19.0284	+	10.9861i	−1.49042	+	0.860495i	−0.490481	+	0.871452i	$0.663179\pi$
$164$	3.11727	−	5.39927i	0.243418	−	0.421612i
$165$	5.03580	−	0.386464i	0.392037	−	0.0300862i
$166$	1.59995	−	0.923730i	0.124180	−	0.0716954i
$167$		−	10.5810i		−	0.818786i	−0.912358	−	0.409393i	$-0.865741\pi$
$167$		−	10.5810i		−	0.818786i	0.912358	−	0.409393i	$-0.134259\pi$
$168$	1.32231	−	1.22395i	0.102018	−	0.0944298i
$169$	8.79345			0.676419
$170$	−6.92551	+	2.80651i	−0.531163	+	0.215249i
$171$	5.86934	−	10.1660i	0.448840	−	0.777413i
$172$	3.27568	−	5.67365i	0.249769	−	0.432612i
$173$	3.43353	−	1.98235i	0.261046	−	0.150715i	−0.363766	−	0.931491i	$-0.618509\pi$
$173$	3.43353	−	1.98235i	0.261046	−	0.150715i	0.624812	+	0.780775i	$0.285176\pi$
$174$		−	0.142064i		−	0.0107698i
$175$	11.7966	−	5.98669i	0.891738	−	0.452551i
$176$	2.23336	+	2.45196i	0.168346	+	0.184824i
$177$	3.40015	−	1.96308i	0.255571	−	0.147554i
$178$	15.0268	+	8.67572i	1.12630	+	0.650272i
$179$	−0.740004	+	1.28173i	−0.0553105	+	0.0958006i	−0.892355	−	0.451334i	$-0.850948\pi$
$179$	−0.740004	+	1.28173i	−0.0553105	+	0.0958006i	0.837044	+	0.547135i	$0.184282\pi$
$180$	2.12993	+	5.25596i	0.158756	+	0.391756i
$181$			10.8158i			0.803935i	0.915654	+	0.401967i	$0.131674\pi$
$181$			10.8158i			0.803935i	−0.915654	+	0.401967i	$0.868326\pi$
$182$	−5.29181	+	1.20109i	−0.392255	+	0.0890304i
$183$	7.33621			0.542308
$184$	−2.24798	+	1.29787i	−0.165724	+	0.0956806i
$185$	6.39537	+	4.98586i	0.470197	+	0.366568i
$186$	−5.23747	−	3.02386i	−0.384030	−	0.221720i
$187$	10.5606	+	3.36451i	0.772268	+	0.246037i
$188$	13.1514			0.959166
$189$	−9.52851	−	2.95179i	−0.693097	−	0.214711i
$190$	−10.2503	−	1.42967i	−0.743634	−	0.103719i
$191$	−8.82641	−	15.2878i	−0.638657	−	1.10619i	−0.985728	−	0.168347i	$-0.946157\pi$
$191$	−8.82641	−	15.2878i	−0.638657	−	1.10619i	0.347071	−	0.937839i	$-0.387176\pi$
$192$	0.340512	−	0.589784i	0.0245743	−	0.0425640i
$193$	−10.8787	+	18.8425i	−0.783066	+	1.35631i	0.147081	+	0.989124i	$0.453012\pi$
$193$	−10.8787	+	18.8425i	−0.783066	+	1.35631i	−0.930147	+	0.367186i	$0.880321\pi$
$194$	−2.97665	−	5.15570i	−0.213711	−	0.370158i
$195$	−0.431446	+	3.09334i	−0.0308965	+	0.221518i
$196$	−6.31412	+	3.02191i	−0.451008	+	0.215851i
$197$	3.55637			0.253381			0.126690	−	0.991942i	$-0.459565\pi$
$197$	3.55637			0.253381			0.126690	+	0.991942i	$0.459565\pi$
$198$	2.55341	−	8.01473i	0.181463	−	0.569582i
$199$	−9.05521	−	5.22803i	−0.641907	−	0.370605i	0.143442	−	0.989659i	$-0.454183\pi$
$199$	−9.05521	−	5.22803i	−0.641907	−	0.370605i	−0.785349	+	0.619054i	$0.787516\pi$
$200$	3.58944	−	3.48080i	0.253811	−	0.246130i
$201$	0.986744	−	0.569697i	0.0695996	−	0.0401833i
$202$	−4.60034			−0.323679
$203$	−0.163317	+	0.527195i	−0.0114626	+	0.0370018i
$204$		−	2.27587i		−	0.159343i
$205$	5.23583	+	12.9203i	0.365686	+	0.902391i
$206$	−2.02004	+	3.49881i	−0.140743	+	0.243773i
$207$	5.70135	+	3.29168i	0.396271	+	0.228787i
$208$	−1.77621	+	1.02549i	−0.123158	+	0.0711052i
$209$	10.3370	+	11.3488i	0.715022	+	0.785011i
$210$	0.340475	+	4.01458i	0.0234950	+	0.277032i
$211$		−	24.6765i		−	1.69880i	−0.527747	−	0.849402i	$-0.676963\pi$
$211$		−	24.6765i		−	1.69880i	0.527747	−	0.849402i	$-0.323037\pi$
$212$	−3.20093	+	1.84806i	−0.219841	+	0.126925i
$213$	1.95637	−	3.38853i	0.134048	−	0.232178i
$214$	−4.80623	+	8.32464i	−0.328547	+	0.569061i
$215$	5.50191	+	13.5769i	0.375227	+	0.925934i
$216$	−3.77029			−0.256536
$217$	15.9599	+	17.2425i	1.08343	+	1.17050i
$218$		−	17.4376i		−	1.18103i
$219$	4.51290	−	2.60552i	0.304953	−	0.176065i
$220$	−7.39446	+	0.567475i	−0.498534	+	0.0382592i
$221$	−3.42703	+	5.93579i	−0.230527	+	0.399285i
$222$	−2.13889	+	1.23489i	−0.143553	+	0.0828801i
$223$	−25.7283			−1.72290			−0.861448	−	0.507846i	$-0.830442\pi$
$223$	−25.7283			−1.72290			−0.861448	+	0.507846i	$0.830442\pi$
$224$	−1.94165	+	1.79722i	−0.129732	+	0.120082i
$225$	−12.1971	−	3.46990i	−0.813138	−	0.231326i
$226$	9.17775	−	5.29878i	0.610495	−	0.352470i
$227$	−9.94984	−	5.74454i	−0.660394	−	0.381279i	0.132033	−	0.991245i	$-0.457850\pi$
$227$	−9.94984	−	5.74454i	−0.660394	−	0.381279i	−0.792427	+	0.609967i	$0.791183\pi$
$228$	1.57604	−	2.72978i	0.104376	−	0.180784i
$229$	16.3220	−	9.42353i	1.07859	−	0.622725i	0.148075	−	0.988976i	$-0.452692\pi$
$229$	16.3220	−	9.42353i	1.07859	−	0.622725i	0.930516	+	0.366252i	$0.119359\pi$
$230$	0.801795	−	5.74862i	0.0528688	−	0.379053i
$231$	3.41772	−	4.90218i	0.224869	−	0.322540i
$232$			0.208603i			0.0136955i
$233$	−4.53084	−	7.84765i	−0.296825	−	0.514116i	0.678583	−	0.734524i	$-0.262595\pi$
$233$	−4.53084	−	7.84765i	−0.296825	−	0.514116i	−0.975408	+	0.220408i	$0.929261\pi$
$234$	4.50483	+	2.60087i	0.294490	+	0.170024i
$235$	−18.0808	+	23.1923i	−1.17946	+	1.51290i
$236$	−4.99271	+	2.88254i	−0.324998	+	0.187637i
$237$		−	10.5043i		−	0.682329i
$238$	−2.61635	+	8.44569i	−0.169593	+	0.547453i
$239$		−	19.0580i		−	1.23276i	−0.787450	−	0.616379i	$-0.788599\pi$
$239$		−	19.0580i		−	1.23276i	0.787450	−	0.616379i	$-0.211401\pi$
$240$	0.571931	+	1.41133i	0.0369180	+	0.0911012i
$241$	−3.67875	+	6.37178i	−0.236969	+	0.410442i	−0.959843	−	0.280537i	$-0.909487\pi$
$241$	−3.67875	+	6.37178i	−0.236969	+	0.410442i	0.722874	+	0.690980i	$0.242821\pi$
$242$	8.97277	+	6.36313i	0.576791	+	0.409037i
$243$	7.37194	+	12.7686i	0.472910	+	0.819105i
$244$	−10.7723			−0.689627
$245$	3.35168	−	15.2894i	0.214131	−	0.976805i
$246$	−4.24587			−0.270707
$247$	−8.22108	+	4.74644i	−0.523095	+	0.302009i
$248$	7.69058	+	4.44016i	0.488353	+	0.281950i
$249$	−1.08960	−	0.629082i	−0.0690508	−	0.0398665i
$250$	1.20350	+	11.1154i	0.0761158	+	0.702998i
$251$		−	9.88938i		−	0.624212i	−0.950047	−	0.312106i	$-0.898966\pi$
$251$		−	9.88938i		−	0.624212i	0.950047	−	0.312106i	$-0.101034\pi$
$252$	6.40966	+	1.98562i	0.403771	+	0.125082i
$253$	−6.36468	+	5.79723i	−0.400144	+	0.364469i
$254$	6.17631	+	10.6977i	0.387536	+	0.671233i
$255$	4.01345	+	3.12891i	0.251332	+	0.195940i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.66287	+	15.0045i	0.540375	+	0.935957i	0.998882	+	0.0472660i	$0.0150509\pi$
$257$	8.66287	+	15.0045i	0.540375	+	0.935957i	−0.458508	+	0.888690i	$0.651616\pi$
$258$	−4.46164			−0.277770
$259$	9.35698	−	2.12376i	0.581414	−	0.131964i
$260$	0.633525	−	4.54218i	0.0392896	−	0.281694i
$261$	0.458180	−	0.264530i	0.0283606	−	0.0163740i
$262$	−3.55442	+	6.15643i	−0.219593	+	0.380346i
$263$	5.94935	−	10.3046i	0.366853	−	0.635407i	−0.622219	−	0.782843i	$-0.713769\pi$
$263$	5.94935	−	10.3046i	0.366853	−	0.635407i	0.989072	+	0.147436i	$0.0471020\pi$
$264$	0.685645	−	2.15212i	0.0421985	−	0.132454i
$265$	1.14169	−	8.18553i	0.0701332	−	0.502833i
$266$	−8.98681	+	8.31833i	−0.551017	+	0.510029i
$267$		−	11.8167i		−	0.723173i
$268$	−1.44891	+	0.836530i	−0.0885064	+	0.0510992i
$269$	0.208607	+	0.120439i	0.0127190	+	0.00734332i	0.506346	−	0.862330i	$-0.330996\pi$
$269$	0.208607	+	0.120439i	0.0127190	+	0.00734332i	−0.493627	+	0.869674i	$0.664329\pi$
$270$	5.18347	−	6.64884i	0.315456	−	0.404635i
$271$	4.79043	+	8.29727i	0.290998	+	0.504024i	0.974046	−	0.226350i	$-0.0726793\pi$
$271$	4.79043	+	8.29727i	0.290998	+	0.504024i	−0.683048	+	0.730374i	$0.739346\pi$
$272$			3.34183i			0.202628i
$273$	2.51031	+	2.71204i	0.151931	+	0.164140i
$274$		−	18.6900i		−	1.12910i
$275$	9.16531	−	13.8202i	0.552689	−	0.833388i
$276$	1.53093	+	0.883883i	0.0921512	+	0.0532035i
$277$	−12.4107	+	21.4960i	−0.745687	+	1.29157i	0.204186	+	0.978932i	$0.434545\pi$
$277$	−12.4107	+	21.4960i	−0.745687	+	1.29157i	−0.949873	+	0.312635i	$0.898788\pi$
$278$	−9.80567	−	16.9839i	−0.588105	−	1.01863i
$279$		−	22.5223i		−	1.34838i
$280$	−0.499946	−	5.89492i	−0.0298775	−	0.352289i
$281$			23.1359i			1.38017i	0.723726	+	0.690087i	$0.242428\pi$
$281$			23.1359i			1.38017i	−0.723726	+	0.690087i	$0.757572\pi$
$282$	−4.47822	−	7.75650i	−0.266674	−	0.461893i
$283$	−26.4747	−	15.2852i	−1.57376	−	0.908610i	−0.995702	−	0.0926142i	$-0.970478\pi$
$283$	−26.4747	−	15.2852i	−1.57376	−	0.908610i	−0.578057	−	0.815996i	$-0.696189\pi$
$284$	−2.87268	+	4.97564i	−0.170462	+	0.295250i
$285$	2.64715	+	6.53228i	0.156804	+	0.386939i
$286$	−5.02895	+	4.58059i	−0.297368	+	0.270856i
$287$	15.7563	+	4.88107i	0.930066	+	0.288121i
$288$	2.53621			0.149447
$289$	−2.91608	−	5.05079i	−0.171534	−	0.297105i
$290$	−0.367868	−	0.286792i	−0.0216020	−	0.0168410i
$291$	−2.02717	+	3.51116i	−0.118835	+	0.205828i
$292$	−6.62663	+	3.82589i	−0.387794	+	0.223893i
$293$		−	4.51666i		−	0.263866i	−0.991259	−	0.131933i	$-0.957882\pi$
$293$		−	4.51666i		−	0.263866i	0.991259	−	0.131933i	$-0.0421184\pi$
$294$	3.93231	+	2.69497i	0.229337	+	0.157174i
$295$	1.78076	−	12.7675i	0.103680	−	0.743354i
$296$	3.14069	−	1.81328i	0.182549	−	0.105395i
$297$	−12.2163	+	2.66997i	−0.708860	+	0.154927i
$298$	4.37001	+	2.52303i	0.253148	+	0.146155i
$299$	−2.66193	−	4.61059i	−0.153943	−	0.266637i
$300$	−3.27516	−	0.931739i	−0.189092	−	0.0537940i
$301$	16.5570	+	5.12912i	0.954331	+	0.295638i
$302$			2.37601i			0.136724i
$303$	1.56647	+	2.71321i	0.0899915	+	0.155870i
$304$	−2.31422	+	4.00835i	−0.132730	+	0.229895i
$305$	14.8100	−	18.9968i	0.848018	−	1.08775i
$306$	7.34007	−	4.23779i	0.419604	−	0.242258i
$307$			30.0596i			1.71559i	0.513992	+	0.857795i	$0.328166\pi$
$307$			30.0596i			1.71559i	−0.513992	+	0.857795i	$0.671834\pi$
$308$	−5.01850	+	7.19824i	−0.285955	+	0.410158i
$309$	2.75139			0.156521
$310$	−18.4033	+	7.45779i	−1.04524	+	0.423574i
$311$	−0.971429	−	0.560855i	−0.0550847	−	0.0318032i	0.472205	−	0.881489i	$-0.343458\pi$
$311$	−0.971429	−	0.560855i	−0.0550847	−	0.0318032i	−0.527289	+	0.849686i	$0.676792\pi$
$312$	1.20964	+	0.698386i	0.0684824	+	0.0395383i
$313$	−10.3195	−	17.8740i	−0.583294	−	1.01030i	−0.995086	−	0.0990174i	$-0.968430\pi$
$313$	−10.3195	−	17.8740i	−0.583294	−	1.01030i	0.411791	−	0.911278i	$-0.364903\pi$
$314$	0.559221			0.0315587
$315$	−12.3137	+	8.57346i	−0.693800	+	0.483059i
$316$			15.4243i			0.867685i
$317$	18.3880	−	10.6163i	1.03277	−	0.596272i	0.114995	−	0.993366i	$-0.463315\pi$
$317$	18.3880	−	10.6163i	1.03277	−	0.596272i	0.917778	+	0.397095i	$0.129981\pi$
$318$	2.17991	+	1.25857i	0.122243	+	0.0705772i
$319$	0.147725	+	0.675904i	0.00827099	+	0.0378433i
$320$	−0.839811	−	2.07237i	−0.0469468	−	0.115849i
$321$	6.54632			0.365380
$322$	−4.66513	−	5.04003i	−0.259977	−	0.280870i
$323$			15.4675i			0.860634i
$324$	−2.52048	−	4.36560i	−0.140027	−	0.242533i
$325$	7.13908	+	7.36189i	0.396005	+	0.408364i
$326$	−19.0284	−	10.9861i	−1.05389	−	0.608462i
$327$	−10.2844	+	5.93773i	−0.568731	+	0.328357i
$328$	6.23454			0.344245
$329$	7.70164	+	33.9323i	0.424605	+	1.87075i
$330$	2.85259	+	4.16790i	0.157030	+	0.229435i
$331$	−8.87838	−	15.3778i	−0.488000	−	0.845241i	0.511905	−	0.859042i	$-0.328940\pi$
$331$	−8.87838	−	15.3778i	−0.488000	−	0.845241i	−0.999905	+	0.0138013i	$0.995607\pi$
$332$	1.59995	+	0.923730i	0.0878085	+	0.0506963i
$333$	−7.96544	−	4.59885i	−0.436503	−	0.252015i
$334$	9.16345	−	5.29052i	0.501402	−	0.289484i
$335$	0.516788	−	3.70521i	0.0282351	−	0.202437i
$336$	1.72113	+	0.533179i	0.0938951	+	0.0290873i
$337$	−11.5799			−0.630798			−0.315399	−	0.948959i	$-0.602138\pi$
$337$	−11.5799			−0.630798			−0.315399	+	0.948959i	$0.602138\pi$
$338$	4.39672	+	7.61535i	0.239150	+	0.414220i
$339$	−6.25027	−	3.60860i	−0.339468	−	0.195992i
$340$	−5.89326	−	4.59442i	−0.319607	−	0.249167i
$341$	28.0629	+	8.94057i	1.51969	+	0.484159i
$342$	11.7387			0.634755
$343$	−11.4945	−	14.5216i	−0.620647	−	0.784090i
$344$	6.55137			0.353226
$345$	−3.66347	+	1.48459i	−0.197234	+	0.0799276i
$346$	3.43353	+	1.98235i	0.184588	+	0.106572i
$347$	4.34117	−	7.51913i	0.233046	−	0.403648i	−0.725657	−	0.688057i	$-0.758464\pi$
$347$	4.34117	−	7.51913i	0.233046	−	0.403648i	0.958703	+	0.284409i	$0.0917973\pi$
$348$	0.123031	−	0.0710319i	0.00659515	−	0.00380771i
$349$	10.3147			0.552134			0.276067	−	0.961138i	$-0.410969\pi$
$349$	10.3147			0.552134			0.276067	+	0.961138i	$0.410969\pi$
$350$	11.0829	+	7.22280i	0.592407	+	0.386075i
$351$		−	7.73282i		−	0.412747i
$352$	−1.00678	+	3.16012i	−0.0536618	+	0.168435i
$353$	5.58273	−	9.66958i	0.297139	−	0.514660i	−0.678341	−	0.734747i	$-0.737301\pi$
$353$	5.58273	−	9.66958i	0.297139	−	0.514660i	0.975480	+	0.220087i	$0.0706342\pi$
$354$	3.40015	+	1.96308i	0.180716	+	0.104336i
$355$	−4.82502	−	11.9065i	−0.256086	−	0.631933i
$356$			17.3514i			0.919624i
$357$	5.87203	−	1.33278i	0.310781	−	0.0705381i
$358$	−1.48001			−0.0782209
$359$	16.5110	−	9.53265i	0.871419	−	0.503114i	0.00359971	−	0.999994i	$-0.498854\pi$
$359$	16.5110	−	9.53265i	0.871419	−	0.503114i	0.867820	+	0.496879i	$0.165521\pi$
$360$	−3.48683	+	4.47256i	−0.183772	+	0.235724i
$361$	−1.21124	+	2.09793i	−0.0637496	+	0.110418i
$362$	−9.36679	+	5.40792i	−0.492308	+	0.284234i
$363$	0.697537	−	7.45872i	0.0366112	−	0.391481i
$364$	−3.68608	−	3.98230i	−0.193203	−	0.208729i
$365$	2.36354	−	16.9459i	0.123713	−	0.886987i
$366$	3.66810	+	6.35334i	0.191735	+	0.332095i
$367$	3.01556	−	5.22310i	0.157411	−	0.272644i	−0.776523	−	0.630088i	$-0.783019\pi$
$367$	3.01556	−	5.22310i	0.157411	−	0.272644i	0.933934	+	0.357445i	$0.116352\pi$
$368$	−2.24798	−	1.29787i	−0.117184	−	0.0676564i
$369$	−7.90604	−	13.6937i	−0.411572	−	0.712863i
$370$	−1.12020	+	8.03148i	−0.0582364	+	0.417537i
$371$	−6.64273	−	7.17656i	−0.344873	−	0.372589i
$372$		−	6.04771i		−	0.313559i
$373$	−0.803802	−	1.39223i	−0.0416193	−	0.0720867i	0.844465	−	0.535610i	$-0.179918\pi$
$373$	−0.803802	−	1.39223i	−0.0416193	−	0.0720867i	−0.886085	+	0.463523i	$0.846585\pi$
$374$	2.36656	+	10.8280i	0.122372	+	0.559903i
$375$	6.14587	−	4.49472i	0.317371	−	0.232106i
$376$	6.57571	+	11.3895i	0.339116	+	0.587367i
$377$	−0.427843			−0.0220350
$378$	−2.20793	−	9.72783i	−0.113564	−	0.500345i
$379$	−21.0081			−1.07912			−0.539558	−	0.841949i	$-0.681409\pi$
$379$	−21.0081			−1.07912			−0.539558	+	0.841949i	$0.681409\pi$
$380$	−3.88702	−	9.59185i	−0.199400	−	0.492051i
$381$	4.20622	−	7.28538i	0.215491	−	0.373241i
$382$	8.82641	−	15.2878i	0.451598	−	0.782191i
$383$	−15.2258	−	26.3718i	−0.778000	−	1.34754i	−0.933093	−	0.359636i	$-0.882901\pi$
$383$	−15.2258	−	26.3718i	−0.778000	−	1.34754i	0.155092	−	0.987900i	$-0.450433\pi$
$384$	0.681024			0.0347534
$385$	−5.79445	−	18.7463i	−0.295312	−	0.955401i
$386$	−21.7574			−1.10742
$387$	−8.30781	−	14.3896i	−0.422310	−	0.731462i
$388$	2.97665	−	5.15570i	0.151116	−	0.261741i
$389$	14.4555	−	25.0377i	0.732924	−	1.26946i	−0.222705	−	0.974886i	$-0.571489\pi$
$389$	14.4555	−	25.0377i	0.732924	−	1.26946i	0.955628	−	0.294575i	$-0.0951781\pi$
$390$	−2.89463	+	1.17302i	−0.146575	+	0.0593984i
$391$	−8.67456			−0.438691
$392$	−5.77411	−	3.95723i	−0.291637	−	0.199870i
$393$	4.84129			0.244211
$394$	1.77819	+	3.07991i	0.0895837	+	0.155164i
$395$	−27.2005	−	21.2056i	−1.36860	−	1.06697i
$396$	8.21766	−	1.79604i	0.412953	−	0.0902545i
$397$	11.2369	+	19.4629i	0.563963	+	0.976813i	0.997145	+	0.0755063i	$0.0240573\pi$
$397$	11.2369	+	19.4629i	0.563963	+	0.976813i	−0.433182	+	0.901306i	$0.642609\pi$
$398$		−	10.4561i		−	0.524115i
$399$	7.96613	+	2.46779i	0.398806	+	0.123544i
$400$	4.80918	+	1.36814i	0.240459	+	0.0684072i
$401$	−10.8958	−	18.8721i	−0.544111	−	0.942429i	−0.998662	−	0.0517079i	$-0.983534\pi$
$401$	−10.8958	−	18.8721i	−0.544111	−	0.942429i	0.454551	−	0.890721i	$-0.349800\pi$
$402$	0.986744	+	0.569697i	0.0492143	+	0.0284139i
$403$	−9.10672	+	15.7733i	−0.453638	+	0.785724i
$404$	−2.30017	−	3.98401i	−0.114438	−	0.198212i
$405$	11.1639	+	1.55709i	0.554737	+	0.0773725i
$406$	−0.538223	+	0.122161i	−0.0267116	+	0.00606273i
$407$	8.89218	−	8.09939i	0.440769	−	0.401472i
$408$	1.97096	−	1.13793i	0.0975771	−	0.0563361i
$409$	6.88836	−	11.9310i	0.340608	−	0.589950i	−0.643938	−	0.765078i	$-0.722701\pi$
$409$	6.88836	−	11.9310i	0.340608	−	0.589950i	0.984546	+	0.175128i	$0.0560339\pi$
$410$	−8.57137	+	10.9945i	−0.423310	+	0.542980i
$411$	−11.0231	+	6.36416i	−0.543727	+	0.313921i
$412$	−4.04007			−0.199040
$413$	−10.3611	−	11.1938i	−0.509837	−	0.550809i
$414$			6.58335i			0.323554i
$415$	−3.82862	+	1.55152i	−0.187940	+	0.0761610i
$416$	−1.77621	−	1.02549i	−0.0870858	−	0.0502790i
$417$	−6.67790	+	11.5665i	−0.327018	+	0.566412i
$418$	−4.65985	+	14.6265i	−0.227920	+	0.715403i
$419$			3.32031i			0.162208i	0.996706	+	0.0811039i	$0.0258446\pi$
$419$			3.32031i			0.162208i	−0.996706	+	0.0811039i	$0.974155\pi$
$420$	−3.30649	+	2.30215i	−0.161340	+	0.112333i
$421$	−1.32850			−0.0647471			−0.0323735	−	0.999476i	$-0.510307\pi$
$421$	−1.32850			−0.0647471			−0.0323735	+	0.999476i	$0.510307\pi$
$422$	21.3705	−	12.3383i	1.04030	−	0.600618i
$423$	16.6774	−	28.8860i	0.810881	−	1.40449i
$424$	−3.20093	−	1.84806i	−0.155451	−	0.0897497i
$425$	16.2044	−	4.07617i	0.786027	−	0.197723i
$426$	3.91273			0.189573
$427$	−6.30841	−	27.7940i	−0.305285	−	1.34504i
$428$	−9.61247			−0.464636
$429$	4.41397	+	1.40625i	0.213109	+	0.0678943i
$430$	−9.00695	+	11.5532i	−0.434354	+	0.557146i
$431$	18.2668	+	10.5464i	0.879882	+	0.508000i	0.870619	−	0.491957i	$-0.163718\pi$
$431$	18.2668	+	10.5464i	0.879882	+	0.508000i	0.00926235	+	0.999957i	$0.497052\pi$
$432$	−1.88514	−	3.26517i	−0.0906991	−	0.157095i
$433$	−5.00434			−0.240493			−0.120247	−	0.992744i	$-0.538369\pi$
$433$	−5.00434			−0.240493			−0.120247	+	0.992744i	$0.538369\pi$
$434$	−6.95248	+	22.4429i	−0.333730	+	1.07729i
$435$	−0.0438818	+	0.314619i	−0.00210397	+	0.0150848i
$436$	15.1014	−	8.71882i	0.723228	−	0.417556i
$437$	−10.4047	−	6.00714i	−0.497723	−	0.287360i
$438$	4.51290	+	2.60552i	0.215635	+	0.124497i
$439$	4.57091	+	7.91705i	0.218158	+	0.377860i	0.954245	−	0.299027i	$-0.0966620\pi$
$439$	4.57091	+	7.91705i	0.218158	+	0.377860i	−0.736087	+	0.676887i	$0.763329\pi$
$440$	−4.18868	−	6.12005i	−0.199687	−	0.291762i
$441$	−1.36957	+	17.7005i	−0.0652174	+	0.842883i
$442$	−6.85406			−0.326014
$443$	4.23828	−	2.44697i	0.201367	−	0.116259i	−0.395926	−	0.918282i	$-0.629576\pi$
$443$	4.23828	−	2.44697i	0.201367	−	0.116259i	0.597293	+	0.802023i	$0.296243\pi$
$444$	−2.13889	−	1.23489i	−0.101507	−	0.0586051i
$445$	−30.5989	−	23.8551i	−1.45053	−	1.13084i
$446$	−12.8642	−	22.2814i	−0.609136	−	1.05505i
$447$		−	3.43648i		−	0.162540i
$448$	−2.52726	−	0.782908i	−0.119402	−	0.0369889i
$449$	3.19516			0.150789			0.0753945	−	0.997154i	$-0.475978\pi$
$449$	3.19516			0.150789			0.0753945	+	0.997154i	$0.475978\pi$
$450$	−3.09351	−	12.2979i	−0.145830	−	0.579729i
$451$	20.2008	−	4.41506i	0.951218	−	0.207897i
$452$	9.17775	+	5.29878i	0.431685	+	0.249234i
$453$	1.40133	−	0.809059i	0.0658403	−	0.0380129i
$454$		−	11.4891i		−	0.539210i
$455$	12.0904	−	1.02538i	0.566807	−	0.0480708i
$456$	3.15208			0.147610
$457$	−7.73790	−	13.4024i	−0.361964	−	0.626939i	0.626320	−	0.779566i	$-0.284560\pi$
$457$	−7.73790	−	13.4024i	−0.361964	−	0.626939i	−0.988284	+	0.152626i	$0.951227\pi$
$458$	16.3220	+	9.42353i	0.762679	+	0.440333i
$459$	−10.9116	−	6.29984i	−0.509312	−	0.294051i
$460$	5.37935	−	2.17994i	0.250814	−	0.101640i
$461$	2.55725			0.119103			0.0595515	−	0.998225i	$-0.481033\pi$
$461$	2.55725			0.119103			0.0595515	+	0.998225i	$0.481033\pi$
$462$	5.95427	+	0.508741i	0.277018	+	0.0236688i
$463$			32.5823i			1.51423i	0.653283	+	0.757113i	$0.273391\pi$
$463$			32.5823i			1.51423i	−0.653283	+	0.757113i	$0.726609\pi$
$464$	−0.180656	+	0.104302i	−0.00838673	+	0.00484208i
$465$	10.6650	+	8.31451i	0.494579	+	0.385576i
$466$	4.53084	−	7.84765i	0.209887	−	0.363535i
$467$	0.161793	+	0.280233i	0.00748687	+	0.0129676i	0.869745	−	0.493502i	$-0.164283\pi$
$467$	0.161793	+	0.280233i	0.00748687	+	0.0129676i	−0.862258	+	0.506470i	$0.830950\pi$
$468$			5.20173i			0.240450i
$469$	−3.00686	−	3.24850i	−0.138844	−	0.150002i
$470$	−29.1255	−	4.06231i	−1.34346	−	0.187381i
$471$	−0.190422	−	0.329820i	−0.00877416	−	0.0151973i
$472$	−4.99271	−	2.88254i	−0.229808	−	0.132680i
$473$	21.2274	−	4.63942i	0.976035	−	0.213321i
$474$	9.09701	−	5.25216i	0.417839	−	0.241240i
$475$	22.2590	+	6.33238i	1.02131	+	0.290549i
$476$	−8.62235	+	1.95702i	−0.395205	+	0.0896999i
$477$			9.37411i			0.429211i
$478$	16.5047	−	9.52898i	0.754906	−	0.435845i
$479$	−12.2943	+	21.2944i	−0.561743	+	0.972968i	0.435601	+	0.900140i	$0.356536\pi$
$479$	−12.2943	+	21.2944i	−0.561743	+	0.972968i	−0.997345	+	0.0728280i	$0.976798\pi$
$480$	−0.936285	+	1.20097i	−0.0427354	+	0.0548167i
$481$	3.71901	+	6.44152i	0.169572	+	0.293708i
$482$	−7.35750			−0.335125
$483$	−1.38400	+	4.46761i	−0.0629741	+	0.203283i
$484$	−1.02425	+	10.9522i	−0.0465567	+	0.497828i
$485$	4.99964	+	12.3374i	0.227022	+	0.560214i
$486$	−7.37194	+	12.7686i	−0.334398	+	0.579194i
$487$	−26.5133	−	15.3075i	−1.20143	−	0.693648i	−0.240560	−	0.970634i	$-0.577331\pi$
$487$	−26.5133	−	15.3075i	−1.20143	−	0.693648i	−0.960874	+	0.276986i	$0.910665\pi$
$488$	−5.38616	−	9.32910i	−0.243820	−	0.422309i
$489$			14.9635i			0.676675i
$490$	14.9169	−	4.74206i	0.673875	−	0.214225i
$491$			12.1960i			0.550399i	0.961387	+	0.275200i	$0.0887439\pi$
$491$			12.1960i			0.550399i	−0.961387	+	0.275200i	$0.911256\pi$
$492$	−2.12294	−	3.67703i	−0.0957093	−	0.165773i
$493$	−0.348559	+	0.603721i	−0.0156983	+	0.0271902i
$494$	−8.22108	−	4.74644i	−0.369884	−	0.213553i
$495$	−8.13052	+	16.9609i	−0.365440	+	0.762338i
$496$			8.88032i			0.398738i
$497$	−14.5201	−	4.49810i	−0.651314	−	0.201767i
$498$		−	1.25816i		−	0.0563797i
$499$	−3.86443	−	6.69338i	−0.172995	−	0.299637i	0.766470	−	0.642280i	$-0.222011\pi$
$499$	−3.86443	−	6.69338i	−0.172995	−	0.299637i	−0.939466	+	0.342643i	$0.888678\pi$
$500$	−9.02445	+	6.59995i	−0.403586	+	0.295159i
$501$	−6.24053	−	3.60297i	−0.278806	−	0.160969i
$502$	8.56446	−	4.94469i	0.382250	−	0.220692i
$503$		−	3.46254i		−	0.154387i	−0.997016	−	0.0771936i	$-0.975404\pi$
$503$		−	3.46254i		−	0.154387i	0.997016	−	0.0771936i	$-0.0245960\pi$
$504$	1.48523	+	6.54374i	0.0661576	+	0.291481i
$505$	10.1881	+	1.42099i	0.453363	+	0.0632332i
$506$	−8.20289	−	2.61336i	−0.364663	−	0.116178i
$507$	2.99427	−	5.18623i	0.132980	−	0.230329i
$508$	−6.17631	+	10.6977i	−0.274030	+	0.474633i
$509$	2.67778	−	1.54601i	0.118690	−	0.0685259i	−0.439480	−	0.898253i	$-0.644837\pi$
$509$	2.67778	−	1.54601i	0.118690	−	0.0685259i	0.558170	+	0.829727i	$0.311504\pi$
$510$	−0.702988	+	5.04021i	−0.0311288	+	0.223184i
$511$	−13.7519	−	14.8571i	−0.608349	−	0.657238i
$512$	−1.00000			−0.0441942
$513$	−8.72528	−	15.1126i	−0.385231	−	0.667239i
$514$	−8.66287	+	15.0045i	−0.382103	+	0.661821i
$515$	5.55437	−	7.12460i	0.244755	−	0.313947i
$516$	−2.23082	−	3.86389i	−0.0982064	−	0.170098i
$517$	29.3718	+	32.2468i	1.29177	+	1.41821i
$518$	6.51772	+	7.04150i	0.286372	+	0.309386i
$519$		−	2.70005i		−	0.118519i
$520$	4.25041	−	1.72244i	0.186393	−	0.0755341i
$521$	−11.0075	−	6.35516i	−0.482245	−	0.278424i	0.239106	−	0.970993i	$-0.423146\pi$
$521$	−11.0075	−	6.35516i	−0.482245	−	0.278424i	−0.721352	+	0.692569i	$0.756479\pi$
$522$	0.458180	+	0.264530i	0.0200540	+	0.0115782i
$523$	5.73591	−	3.31163i	0.250814	−	0.144808i	−0.369323	−	0.929301i	$-0.620410\pi$
$523$	5.73591	−	3.31163i	0.250814	−	0.144808i	0.620137	+	0.784494i	$0.287077\pi$
$524$	−7.10883			−0.310551
$525$	0.486027	−	8.99598i	0.0212120	−	0.392617i
$526$	11.8987			0.518808
$527$	14.8383	+	25.7006i	0.646365	+	1.11954i
$528$	2.20661	−	0.482275i	0.0960305	−	0.0209883i
$529$	−8.13105	+	14.0834i	−0.353524	+	0.612321i
$530$	7.65972	−	3.10404i	0.332717	−	0.134831i
$531$			14.6214i			0.634516i
$532$	−11.6973	−	3.62365i	−0.507142	−	0.157105i
$533$			12.7870i			0.553865i
$534$	10.2336	−	5.90837i	0.442851	−	0.255680i
$535$	13.2154	−	16.9514i	0.571352	−	0.732874i
$536$	−1.44891	−	0.836530i	−0.0625835	−	0.0361326i
$537$	0.503961	+	0.872886i	0.0217475	+	0.0376678i
$538$			0.240879i			0.0103850i
$539$	−21.5113	−	8.73298i	−0.926556	−	0.376156i
$540$	8.34980	+	1.16460i	0.359318	+	0.0501162i
$541$	−9.24839	+	5.33956i	−0.397619	+	0.229566i	−0.685456	−	0.728114i	$-0.740397\pi$
$541$	−9.24839	+	5.33956i	−0.397619	+	0.229566i	0.287837	+	0.957679i	$0.407064\pi$
$542$	−4.79043	+	8.29727i	−0.205767	+	0.356398i
$543$	6.37901	+	3.68292i	0.273749	+	0.158049i
$544$	−2.89411	+	1.67092i	−0.124084	+	0.0716400i
$545$	−5.38627	+	38.6179i	−0.230723	+	1.65421i
$546$	−1.09354	+	3.53001i	−0.0467994	+	0.151071i
$547$	29.6241			1.26663			0.633317	−	0.773893i	$-0.281693\pi$
$547$	29.6241			1.26663			0.633317	+	0.773893i	$0.281693\pi$
$548$	16.1860	−	9.34499i	0.691432	−	0.399198i
$549$	−13.6604	+	23.6605i	−0.583012	+	1.00981i
$550$	16.5513	+	1.02731i	0.705749	+	0.0438046i
$551$	−0.836155	+	0.482754i	−0.0356214	+	0.0205660i
$552$			1.76777i			0.0752412i
$553$	−39.7967	+	9.03267i	−1.69233	+	0.384108i
$554$	−24.8214			−1.05456
$555$	5.11828	−	2.07414i	0.217259	−	0.0880424i
$556$	9.80567	−	16.9839i	0.415853	−	0.720279i
$557$	1.83613	−	3.18026i	0.0777991	−	0.134752i	−0.824501	−	0.565861i	$-0.808544\pi$
$557$	1.83613	−	3.18026i	0.0777991	−	0.134752i	0.902300	+	0.431109i	$0.141877\pi$
$558$	19.5049	−	11.2612i	0.825709	−	0.476723i
$559$			13.4368i			0.568315i
$560$	4.85518	−	3.38042i	0.205169	−	0.142849i
$561$	5.58035	−	5.08282i	0.235602	−	0.214597i
$562$	−20.0363	+	11.5680i	−0.845181	+	0.487965i
$563$	24.2556	+	14.0040i	1.02225	+	0.590198i	0.914756	−	0.404007i	$-0.132383\pi$
$563$	24.2556	+	14.0040i	1.02225	+	0.590198i	0.107498	+	0.994205i	$0.465716\pi$
$564$	4.47822	−	7.75650i	0.188567	−	0.326608i
$565$	−21.9621	+	8.89994i	−0.923951	+	0.374423i
$566$		−	30.5704i		−	1.28497i
$567$	9.78778	−	9.05971i	0.411048	−	0.380472i
$568$	−5.74537			−0.241070
$569$	7.59248	−	4.38352i	0.318293	−	0.183767i	−0.332338	−	0.943160i	$-0.607838\pi$
$569$	7.59248	−	4.38352i	0.318293	−	0.183767i	0.650632	+	0.759394i	$0.274504\pi$
$570$	−4.33354	+	5.55864i	−0.181512	+	0.232826i
$571$	−21.6883	−	12.5217i	−0.907626	−	0.524018i	−0.0279594	−	0.999609i	$-0.508901\pi$
$571$	−21.6883	−	12.5217i	−0.907626	−	0.524018i	−0.879667	+	0.475591i	$0.842234\pi$
$572$	−6.48138	−	2.06490i	−0.271000	−	0.0863380i
$573$	−12.0220			−0.502226
$574$	3.65103	+	16.0859i	0.152391	+	0.671413i
$575$	−3.55136	+	12.4834i	−0.148102	+	0.520594i
$576$	1.26810	+	2.19642i	0.0528376	+	0.0915175i
$577$	12.2420	−	21.2037i	0.509640	−	0.882722i	−0.490298	−	0.871555i	$-0.663112\pi$
$577$	12.2420	−	21.2037i	0.509640	−	0.882722i	0.999938	−	0.0111668i	$-0.00355458\pi$
$578$	2.91608	−	5.05079i	0.121293	−	0.210085i
$579$	7.40866	+	12.8322i	0.307893	+	0.533287i
$580$	0.0644350	−	0.461979i	0.00267552	−	0.0191826i
$581$	−1.44639	+	4.66902i	−0.0600064	+	0.193703i
$582$	−4.05434			−0.168058
$583$	−11.6802	−	3.72119i	−0.483744	−	0.154116i
$584$	−6.62663	−	3.82589i	−0.274212	−	0.158316i
$585$	−9.17316	−	7.15144i	−0.379263	−	0.295676i
$586$	3.91154	−	2.25833i	0.161584	−	0.0932907i
$587$	−3.07712			−0.127006			−0.0635031	−	0.997982i	$-0.520227\pi$
$587$	−3.07712			−0.127006			−0.0635031	+	0.997982i	$0.520227\pi$
$588$	−0.367757	+	4.75296i	−0.0151660	+	0.196009i
$589$			41.1021i			1.69358i
$590$	11.9474	−	4.84158i	0.491866	−	0.199325i
$591$	1.21099	−	2.09749i	0.0498134	−	0.0862793i
$592$	3.14069	+	1.81328i	0.129082	+	0.0745253i
$593$	24.6596	−	14.2372i	1.01265	−	0.584652i	0.100682	−	0.994919i	$-0.467898\pi$
$593$	24.6596	−	14.2372i	1.01265	−	0.584652i	0.911966	+	0.410266i	$0.134564\pi$
$594$	−8.42040	−	9.24461i	−0.345493	−	0.379311i
$595$	8.40301	−	17.8959i	0.344490	−	0.733661i
$596$			5.04605i			0.206694i
$597$	−6.16681	+	3.56041i	−0.252391	+	0.145718i
$598$	2.66193	−	4.61059i	0.108854	−	0.188541i
$599$	−13.1686	+	22.8086i	−0.538053	+	0.931934i	0.460956	+	0.887423i	$0.347506\pi$
$599$	−13.1686	+	22.8086i	−0.538053	+	0.931934i	−0.999009	+	0.0445115i	$0.985827\pi$
$600$	−0.830673	−	3.30225i	−0.0339121	−	0.134814i
$601$	−28.6070			−1.16690			−0.583452	−	0.812148i	$-0.698298\pi$
$601$	−28.6070			−1.16690			−0.583452	+	0.812148i	$0.698298\pi$
$602$	3.83657	+	16.9034i	0.156367	+	0.688930i
$603$			4.24322i			0.172797i
$604$	−2.05768	+	1.18800i	−0.0837259	+	0.0483392i
$605$	−17.9059	−	16.8636i	−0.727977	−	0.685601i
$606$	−1.56647	+	2.71321i	−0.0636336	+	0.110217i
$607$	6.93601	−	4.00451i	0.281524	−	0.162538i	−0.352589	−	0.935778i	$-0.614699\pi$
$607$	6.93601	−	4.00451i	0.281524	−	0.162538i	0.634113	+	0.773240i	$0.281365\pi$
$608$	−4.62844			−0.187708
$609$	0.255320	+	0.275838i	0.0103461	+	0.0111775i
$610$	23.8567	+	3.32744i	0.965930	+	0.134724i
$611$	−23.3597	+	13.4867i	−0.945031	+	0.545614i
$612$	7.34007	+	4.23779i	0.296705	+	0.171302i
$613$	−12.8523	+	22.2608i	−0.519099	+	0.899105i	0.480655	+	0.876910i	$0.340399\pi$
$613$	−12.8523	+	22.2608i	−0.519099	+	0.899105i	−0.999754	+	0.0221956i	$0.992934\pi$
$614$	−26.0324	+	15.0298i	−1.05058	+	0.606553i
$615$	9.40303	+	1.31150i	0.379167	+	0.0528847i
$616$	−8.74311	−	0.747023i	−0.352270	−	0.0300984i
$617$			32.5391i			1.30998i	0.755640	+	0.654988i	$0.227326\pi$
$617$			32.5391i			1.30998i	−0.755640	+	0.654988i	$0.772674\pi$
$618$	1.37569	+	2.38277i	0.0553385	+	0.0958491i
$619$	−33.3383	−	19.2479i	−1.33998	−	0.773637i	−0.353175	−	0.935557i	$-0.614898\pi$
$619$	−33.3383	−	19.2479i	−1.33998	−	0.773637i	−0.986804	+	0.161920i	$0.948231\pi$
$620$	−15.6603	−	12.2088i	−0.628932	−	0.490319i
$621$	8.47555	−	4.89336i	0.340112	−	0.196364i
$622$		−	1.12171i		−	0.0449765i
$623$	−44.7689	+	10.1612i	−1.79363	+	0.407101i
$624$			1.39677i			0.0559157i
$625$	0.768105	−	24.9882i	0.0307242	−	0.999528i
$626$	10.3195	−	17.8740i	0.412451	−	0.714387i
$627$	10.2132	−	2.23218i	0.407875	−	0.0891447i
$628$	0.279611	+	0.484300i	0.0111577	+	0.0193257i
$629$	12.1193			0.483230
$630$	−13.5817	−	6.37727i	−0.541108	−	0.254077i
$631$	41.5135			1.65262			0.826312	−	0.563212i	$-0.190435\pi$
$631$	41.5135			1.65262			0.826312	+	0.563212i	$0.190435\pi$
$632$	−13.3578	+	7.71215i	−0.531346	+	0.306773i
$633$	−14.5538	−	8.40266i	−0.578463	−	0.333976i
$634$	18.3880	+	10.6163i	0.730281	+	0.421628i
$635$	−10.3739	−	25.5992i	−0.411674	−	1.01587i
$636$			2.51714i			0.0998113i
$637$	8.11623	−	11.8426i	0.321577	−	0.469222i
$638$	−0.511487	+	0.465885i	−0.0202500	+	0.0184446i
$639$	7.28572	+	12.6192i	0.288219	+	0.499209i
$640$	1.37482	−	1.76348i	0.0543445	−	0.0697078i
$641$	6.91276	−	11.9732i	0.273038	−	0.472915i	−0.696601	−	0.717459i	$-0.745305\pi$
$641$	6.91276	−	11.9732i	0.273038	−	0.472915i	0.969638	+	0.244544i	$0.0786383\pi$
$642$	3.27316	+	5.66928i	0.129181	+	0.223749i
$643$	1.24361			0.0490430			0.0245215	−	0.999699i	$-0.492194\pi$
$643$	1.24361			0.0490430			0.0245215	+	0.999699i	$0.492194\pi$
$644$	2.03223	−	6.56014i	0.0800812	−	0.258506i
$645$	9.88088	+	1.37815i	0.389059	+	0.0542644i
$646$	−13.3952	+	7.73374i	−0.527028	+	0.304280i
$647$	−5.28986	+	9.16230i	−0.207966	+	0.360207i	−0.951074	−	0.308964i	$-0.900018\pi$
$647$	−5.28986	+	9.16230i	−0.207966	+	0.360207i	0.743108	+	0.669172i	$0.233351\pi$
$648$	2.52048	−	4.36560i	0.0990138	−	0.171497i
$649$	−18.2184	−	5.80420i	−0.715134	−	0.227835i
$650$	−2.80605	+	9.86357i	−0.110062	+	0.386881i
$651$	15.6039	−	3.54162i	0.611564	−	0.138807i
$652$		−	21.9721i		−	0.860495i
$653$	−15.2726	+	8.81765i	−0.597663	+	0.345061i	−0.768122	−	0.640304i	$-0.778808\pi$
$653$	−15.2726	+	8.81765i	−0.597663	+	0.345061i	0.170458	+	0.985365i	$0.445475\pi$
$654$	−10.2844	−	5.93773i	−0.402154	−	0.232183i
$655$	9.77337	−	12.5363i	0.381877	−	0.489834i
$656$	3.11727	+	5.39927i	0.121709	+	0.210806i
$657$			19.4065i			0.757119i
$658$	−25.5355	+	23.6360i	−0.995476	+	0.921427i
$659$		−	14.3408i		−	0.558639i	−0.960198	−	0.279319i	$-0.909891\pi$
$659$		−	14.3408i		−	0.558639i	0.960198	−	0.279319i	$-0.0901088\pi$
$660$	−2.18321	+	4.55436i	−0.0849814	+	0.177278i
$661$	−19.0348	−	10.9898i	−0.740369	−	0.427452i	0.0818346	−	0.996646i	$-0.473922\pi$
$661$	−19.0348	−	10.9898i	−0.740369	−	0.427452i	−0.822203	+	0.569194i	$0.807255\pi$
$662$	8.87838	−	15.3778i	0.345068	−	0.597676i
$663$	2.33389	+	4.04242i	0.0906408	+	0.156994i
$664$			1.84746i			0.0716954i
$665$	22.4719	−	15.6461i	0.871423	−	0.606730i
$666$		−	9.19770i		−	0.356403i
$667$	−0.270741	−	0.468937i	−0.0104831	−	0.0181573i
$668$	9.16345	+	5.29052i	0.354545	+	0.204696i
$669$	−8.76080	+	15.1742i	−0.338712	+	0.586667i
$670$	3.46720	−	1.40505i	0.133950	−	0.0542820i
$671$	−24.0584	−	26.4133i	−0.928765	−	1.01968i
$672$	0.398816	+	1.75713i	0.0153847	+	0.0677827i
$673$	17.7793			0.685341			0.342670	−	0.939456i	$-0.388669\pi$
$673$	17.7793			0.685341			0.342670	+	0.939456i	$0.388669\pi$
$674$	−5.78996	−	10.0285i	−0.223021	−	0.386284i
$675$	−13.5332	+	13.1236i	−0.520894	+	0.505128i
$676$	−4.39672	+	7.61535i	−0.169105	+	0.292898i
$677$	−21.8386	+	12.6085i	−0.839325	+	0.484585i	−0.857035	−	0.515259i	$-0.827696\pi$
$677$	−21.8386	+	12.6085i	−0.839325	+	0.484585i	0.0177096	+	0.999843i	$0.494363\pi$
$678$		−	7.21719i		−	0.277175i
$679$	15.0455	+	4.66088i	0.577395	+	0.178868i
$680$	1.03225	−	7.40093i	0.0395850	−	0.283813i
$681$	−6.77608	+	3.91217i	−0.259660	+	0.149915i
$682$	6.28870	+	28.7735i	0.240807	+	1.10179i
$683$	18.6523	+	10.7689i	0.713712	+	0.412062i	0.812434	−	0.583053i	$-0.198142\pi$
$683$	18.6523	+	10.7689i	0.713712	+	0.412062i	−0.0987218	+	0.995115i	$0.531475\pi$
$684$	5.86934	+	10.1660i	0.224420	+	0.388707i
$685$	−5.77311	+	41.3914i	−0.220579	+	1.58148i
$686$	6.82876	−	17.2153i	0.260723	−	0.657285i
$687$		−	12.8353i		−	0.489697i
$688$	3.27568	+	5.67365i	0.124884	+	0.216306i
$689$	3.79035	−	6.56507i	0.144401	−	0.250109i
$690$	−3.11743	−	2.43036i	−0.118678	−	0.0925223i
$691$	−25.7641	+	14.8749i	−0.980114	+	0.565869i	−0.902305	−	0.431099i	$-0.858126\pi$
$691$	−25.7641	+	14.8749i	−0.980114	+	0.565869i	−0.0778094	+	0.996968i	$0.524793\pi$
$692$			3.96470i			0.150715i
$693$	9.44639	+	20.1508i	0.358839	+	0.765467i
$694$	8.68234			0.329577
$695$	16.4698	+	40.6420i	0.624736	+	1.54164i
$696$	0.123031	+	0.0710319i	0.00466347	+	0.00269246i
$697$	18.0435	+	10.4174i	0.683445	+	0.394587i
$698$	5.15736	+	8.93281i	0.195209	+	0.338112i
$699$	−6.17122			−0.233417
$700$	−0.713672	+	13.2095i	−0.0269742	+	0.499272i
$701$		−	27.1878i		−	1.02687i	−0.858128	−	0.513435i	$-0.828373\pi$
$701$		−	27.1878i		−	1.02687i	0.858128	−	0.513435i	$-0.171627\pi$
$702$	6.69682	−	3.86641i	0.252755	−	0.145928i
$703$	14.5365	+	8.39266i	0.548255	+	0.316535i
$704$	−3.24014	+	0.708161i	−0.122117	+	0.0266898i
$705$	7.52171	+	18.5610i	0.283284	+	0.699049i
$706$	11.1655			0.420218
$707$	8.93225	−	8.26782i	0.335932	−	0.310944i
$708$			3.92616i			0.147554i
$709$	18.0630	+	31.2859i	0.678368	+	1.17497i	0.975472	+	0.220123i	$0.0706460\pi$
$709$	18.0630	+	31.2859i	0.678368	+	1.17497i	−0.297104	+	0.954845i	$0.596021\pi$
$710$	7.89885	−	10.1319i	0.296439	−	0.380242i
$711$	33.8782	+	19.5596i	1.27053	+	0.733542i
$712$	−15.0268	+	8.67572i	−0.563152	+	0.325136i
$713$	−23.0511			−0.863270
$714$	4.09023	+	4.41894i	0.153073	+	0.165375i
$715$	12.5522	−	8.59093i	0.469424	−	0.321282i
$716$	−0.740004	−	1.28173i	−0.0276553	−	0.0479003i
$717$	−11.2401	−	6.48946i	−0.419769	−	0.242353i
$718$	16.5110	+	9.53265i	0.616187	+	0.355755i
$719$	24.3745	−	14.0726i	0.909016	−	0.524821i	0.0289015	−	0.999582i	$-0.490799\pi$
$719$	24.3745	−	14.0726i	0.909016	−	0.524821i	0.880114	+	0.474762i	$0.157466\pi$
$720$	−5.61676	−	0.783403i	−0.209324	−	0.0291957i
$721$	−2.36592	−	10.4239i	−0.0881114	−	0.388206i
$722$	−2.42248			−0.0901555
$723$	2.50532	+	4.33933i	0.0931737	+	0.161382i
$724$	−9.36679	−	5.40792i	−0.348114	−	0.200984i
$725$	0.726105	+	0.748768i	0.0269669	+	0.0278085i
$726$	6.80821	−	3.12527i	0.252676	−	0.115990i
$727$	6.28055			0.232933			0.116466	−	0.993195i	$-0.462843\pi$
$727$	6.28055			0.232933			0.116466	+	0.993195i	$0.462843\pi$
$728$	1.60574	−	5.18339i	0.0595125	−	0.192109i
$729$	−5.08195			−0.188220
$730$	15.8573	−	6.42604i	0.586906	−	0.237839i
$731$	18.9604	+	10.9468i	0.701276	+	0.404882i
$732$	−3.66810	+	6.35334i	−0.135577	+	0.234826i
$733$	32.5279	−	18.7800i	1.20144	−	0.693655i	0.240569	−	0.970632i	$-0.422666\pi$
$733$	32.5279	−	18.7800i	1.20144	−	0.693655i	0.960876	+	0.276978i	$0.0893328\pi$
$734$	6.03112			0.222613
$735$	−7.87617	−	7.18300i	−0.290517	−	0.264949i
$736$		−	2.59575i		−	0.0956806i
$737$	−5.28708	−	1.68441i	−0.194752	−	0.0620461i
$738$	7.90604	−	13.6937i	0.291025	−	0.504071i
$739$	−9.42805	−	5.44329i	−0.346817	−	0.200235i	0.316466	−	0.948604i	$-0.397504\pi$
$739$	−9.42805	−	5.44329i	−0.346817	−	0.200235i	−0.663282	+	0.748369i	$0.730837\pi$
$740$	−7.51557	+	3.04562i	−0.276278	+	0.111959i
$741$			6.46488i			0.237493i
$742$	2.89372	−	9.34106i	0.106232	−	0.342921i
$743$	18.1135			0.664520			0.332260	−	0.943188i	$-0.392189\pi$
$743$	18.1135			0.664520			0.332260	+	0.943188i	$0.392189\pi$
$744$	5.23747	−	3.02386i	0.192015	−	0.110860i
$745$	−8.89863	−	6.93741i	−0.326020	−	0.254167i
$746$	0.803802	−	1.39223i	0.0294293	−	0.0509730i
$747$	4.05780	−	2.34277i	0.148467	−	0.0857175i
$748$	−8.19405	+	7.46350i	−0.299604	+	0.272893i
$749$	−5.62918	−	24.8014i	−0.205686	−	0.906223i
$750$	6.96548	+	3.07512i	0.254343	+	0.112287i
$751$	15.8194	+	27.4001i	0.577260	+	0.999843i	0.995792	+	0.0916410i	$0.0292112\pi$
$751$	15.8194	+	27.4001i	0.577260	+	0.999843i	−0.418533	+	0.908202i	$0.637455\pi$
$752$	−6.57571	+	11.3895i	−0.239792	+	0.415331i
$753$	−5.83260	−	3.36745i	−0.212552	−	0.122717i
$754$	−0.213921	−	0.370523i	−0.00779056	−	0.0134936i
$755$	0.733920	−	5.26198i	0.0267101	−	0.191503i
$756$	7.32058	−	6.77604i	0.266247	−	0.246442i
$757$			28.5956i			1.03932i	0.854372	+	0.519662i	$0.173942\pi$
$757$			28.5956i			1.03932i	−0.854372	+	0.519662i	$0.826058\pi$
$758$	−10.5041	−	18.1936i	−0.381525	−	0.660821i
$759$	1.25186	+	5.72781i	0.0454398	+	0.207906i
$760$	6.36328	−	8.16218i	0.230820	−	0.296073i
$761$	−18.0463	−	31.2572i	−0.654179	−	1.13307i	−0.982099	−	0.188366i	$-0.939681\pi$
$761$	−18.0463	−	31.2572i	−0.654179	−	1.13307i	0.327920	−	0.944706i	$-0.393652\pi$
$762$	8.41243			0.304750
$763$	31.3393	+	33.8578i	1.13456	+	1.22573i
$764$	17.6528			0.638657
$765$	−17.5645	+	7.11788i	−0.635047	+	0.257347i
$766$	15.2258	−	26.3718i	0.550129	−	0.952852i
$767$	5.91206	−	10.2400i	0.213472	−	0.369744i
$768$	0.340512	+	0.589784i	0.0122872	+	0.0212820i
$769$	28.3685			1.02299			0.511497	−	0.859285i	$-0.329091\pi$
$769$	28.3685			1.02299			0.511497	+	0.859285i	$0.329091\pi$
$770$	13.3376	−	14.3913i	0.480652	−	0.518626i
$771$	11.7992			0.424939
$772$	−10.8787	−	18.8425i	−0.391533	−	0.678155i
$773$	14.6951	−	25.4526i	0.528545	−	0.915466i	−0.470901	−	0.882186i	$-0.656071\pi$
$773$	14.6951	−	25.4526i	0.528545	−	0.915466i	0.999446	−	0.0332805i	$-0.0105955\pi$
$774$	8.30781	−	14.3896i	0.298618	−	0.517222i
$775$	43.0602	−	10.8317i	1.54677	−	0.389086i
$776$	5.95329			0.213711
$777$	1.93360	−	6.24176i	0.0693677	−	0.223922i
$778$	28.9110			1.03651
$779$	14.4281	+	24.9902i	0.516940	+	0.895367i
$780$	−2.46318	−	1.92031i	−0.0881961	−	0.0687582i
$781$	−18.6158	+	4.06865i	−0.666126	+	0.145588i
$782$	−4.33728	−	7.51239i	−0.155101	−	0.268642i
$783$		−	0.786494i		−	0.0281070i
$784$	0.540006	−	6.97914i	0.0192859	−	0.249255i
$785$	−1.23847	−	0.172737i	−0.0442028	−	0.00616523i
$786$	2.42064	+	4.19268i	0.0863415	+	0.149548i
$787$	25.2858	+	14.5988i	0.901341	+	0.520390i	0.877635	−	0.479329i	$-0.159120\pi$
$787$	25.2858	+	14.5988i	0.901341	+	0.520390i	0.0237062	+	0.999719i	$0.492453\pi$
$788$	−1.77819	+	3.07991i	−0.0633452	+	0.109717i
$789$	−4.05165	−	7.01766i	−0.144243	−	0.249835i
$790$	4.76438	−	34.1591i	0.169509	−	1.21533i
$791$	−8.29691	+	26.7828i	−0.295004	+	0.952287i
$792$	5.66425	+	6.21868i	0.201270	+	0.220971i
$793$	19.1339	−	11.0470i	0.679464	−	0.392289i
$794$	−11.2369	+	19.4629i	−0.398782	+	0.690711i
$795$	−4.43894	−	3.46062i	−0.157433	−	0.122736i
$796$	9.05521	−	5.22803i	0.320953	−	0.185303i
$797$	−46.8193			−1.65843			−0.829213	−	0.558933i	$-0.811211\pi$
$797$	−46.8193			−1.65843			−0.829213	+	0.558933i	$0.811211\pi$
$798$	1.84590	+	8.13277i	0.0653441	+	0.287897i
$799$			43.9499i			1.55483i
$800$	1.21974	+	4.84894i	0.0431243	+	0.171436i
$801$	38.1110	+	22.0034i	1.34659	+	0.777452i
$802$	10.8958	−	18.8721i	0.384745	−	0.666398i
$803$	−24.1806	−	7.70369i	−0.853314	−	0.271857i
$804$			1.13939i			0.0401833i
$805$	8.77473	+	12.6028i	0.309269	+	0.444191i
$806$	−18.2134			−0.641541
$807$	0.142066	−	0.0820221i	0.00500097	−	0.00288731i
$808$	2.30017	−	3.98401i	0.0809197	−	0.140157i
$809$	21.5069	+	12.4170i	0.756141	+	0.436558i	0.827908	−	0.560863i	$-0.189531\pi$
$809$	21.5069	+	12.4170i	0.756141	+	0.436558i	−0.0717676	+	0.997421i	$0.522864\pi$
$810$	4.23345	+	10.4467i	0.148748	+	0.367061i
$811$	16.5834			0.582322			0.291161	−	0.956674i	$-0.405958\pi$
$811$	16.5834			0.582322			0.291161	+	0.956674i	$0.405958\pi$
$812$	−0.374906	−	0.405034i	−0.0131566	−	0.0142139i
$813$	6.52480			0.228835
$814$	11.4604	+	3.65116i	0.401686	+	0.127973i
$815$	38.7475	+	30.2077i	1.35726	+	1.05813i
$816$	1.97096	+	1.13793i	0.0689974	+	0.0398357i
$817$	15.1613	+	26.2602i	0.530427	+	0.918727i
$818$	13.7767			0.481692
$819$	−13.4211	+	3.04620i	−0.468972	+	0.106443i
$820$	−13.8072	−	1.92577i	−0.482168	−	0.0672509i
$821$	26.5267	−	15.3152i	0.925789	−	0.534504i	0.0403114	−	0.999187i	$-0.487165\pi$
$821$	26.5267	−	15.3152i	0.925789	−	0.534504i	0.885477	+	0.464683i	$0.153832\pi$
$822$	−11.0231	−	6.36416i	−0.384473	−	0.221976i
$823$	24.0405	+	13.8798i	0.837998	+	0.483819i	0.856583	−	0.516009i	$-0.172583\pi$
$823$	24.0405	+	13.8798i	0.837998	+	0.483819i	−0.0185849	+	0.999827i	$0.505916\pi$
$824$	−2.02004	−	3.49881i	−0.0703713	−	0.121887i
$825$	−5.03002	−	10.1115i	−0.175123	−	0.352037i
$826$	4.51353	−	14.5699i	0.157046	−	0.506951i
$827$	16.1744			0.562438			0.281219	−	0.959644i	$-0.409261\pi$
$827$	16.1744			0.562438			0.281219	+	0.959644i	$0.409261\pi$
$828$	−5.70135	+	3.29168i	−0.198136	+	0.114394i
$829$	−8.64849	−	4.99321i	−0.300375	−	0.173421i	0.342237	−	0.939614i	$-0.388816\pi$
$829$	−8.64849	−	4.99321i	−0.300375	−	0.173421i	−0.642611	+	0.766192i	$0.722149\pi$
$830$	−3.25796	−	2.53993i	−0.113086	−	0.0881621i
$831$	8.45199	+	14.6393i	0.293196	+	0.507831i
$832$		−	2.05099i		−	0.0711052i
$833$	−10.0987	−	21.1007i	−0.349900	−	0.731097i
$834$	−13.3558			−0.462473
$835$	−21.9278	+	8.88607i	−0.758844	+	0.307515i
$836$	−14.9968	+	3.27768i	−0.518675	+	0.113361i
$837$	−28.9957	−	16.7407i	−1.00224	−	0.578643i
$838$	−2.87547	+	1.66015i	−0.0993316	+	0.0573491i
$839$		−	36.2333i		−	1.25091i	−0.780259	−	0.625456i	$-0.784913\pi$
$839$		−	36.2333i		−	1.25091i	0.780259	−	0.625456i	$-0.215087\pi$
$840$	−3.64697	−	1.71243i	−0.125832	−	0.0590844i
$841$	28.9565			0.998499
$842$	−0.664249	−	1.15051i	−0.0228915	−	0.0396493i
$843$	13.6452	+	7.87806i	0.469966	+	0.271335i
$844$	21.3705	+	12.3383i	0.735603	+	0.424701i
$845$	−7.38483	−	18.2233i	−0.254046	−	0.626900i
$846$	33.3547			1.14676
$847$	−28.8579	+	3.77107i	−0.991570	+	0.129575i
$848$		−	3.69612i		−	0.126925i
$849$	−18.0299	+	10.4096i	−0.618785	+	0.357256i
$850$	11.6322	+	11.9953i	0.398983	+	0.411435i
$851$	−4.70681	+	8.15244i	−0.161348	+	0.279462i
$852$	1.95637	+	3.38853i	0.0670240	+	0.116089i
$853$		−	6.56955i		−	0.224937i	−0.993655	−	0.112468i	$-0.964124\pi$
$853$		−	6.56955i		−	0.224937i	0.993655	−	0.112468i	$-0.0358757\pi$
$854$	20.9161	−	19.3602i	0.715733	−	0.662493i
$855$	−25.9969	−	3.62594i	−0.889074	−	0.124004i
$856$	−4.80623	−	8.32464i	−0.164274	−	0.284530i
$857$	6.09840	+	3.52092i	0.208318	+	0.120272i	0.600529	−	0.799603i	$-0.294957\pi$
$857$	6.09840	+	3.52092i	0.208318	+	0.120272i	−0.392212	+	0.919875i	$0.628290\pi$
$858$	0.989140	+	4.52574i	0.0337687	+	0.154506i
$859$	−6.18365	+	3.57013i	−0.210983	+	0.121811i	−0.601768	−	0.798671i	$-0.705537\pi$
$859$	−6.18365	+	3.57013i	−0.210983	+	0.121811i	0.390785	+	0.920482i	$0.372204\pi$
$860$	−14.5089	−	2.02364i	−0.494748	−	0.0690055i
$861$	8.24399	−	7.63076i	0.280955	−	0.260056i
$862$			21.0927i			0.718420i
$863$	−40.0293	+	23.1109i	−1.36261	+	0.786706i	−0.989971	−	0.141269i	$-0.954882\pi$
$863$	−40.0293	+	23.1109i	−1.36261	+	0.786706i	−0.372643	+	0.927975i	$0.621548\pi$
$864$	1.88514	−	3.26517i	0.0641339	−	0.111083i
$865$	−6.99167	−	5.45074i	−0.237724	−	0.185331i
$866$	−2.50217	−	4.33389i	−0.0850272	−	0.147271i
$867$	−3.97184			−0.134891
$868$	−22.9124	+	5.20043i	−0.777696	+	0.176514i
$869$	−37.8198	+	34.4479i	−1.28295	+	1.16857i
$870$	−0.294409	+	0.119307i	−0.00998139	+	0.00404488i
$871$	1.71571	−	2.97170i	0.0581347	−	0.100692i
$872$	15.1014	+	8.71882i	0.511399	+	0.295257i
$873$	−7.54939	−	13.0759i	−0.255508	−	0.442553i
$874$		−	12.0143i		−	0.406389i
$875$	−22.3135	−	19.4192i	−0.754335	−	0.656489i
$876$			5.21104i			0.176065i
$877$	13.3820	+	23.1784i	0.451879	+	0.782678i	0.998503	−	0.0547006i	$-0.0174205\pi$
$877$	13.3820	+	23.1784i	0.451879	+	0.782678i	−0.546624	+	0.837378i	$0.684087\pi$
$878$	−4.57091	+	7.91705i	−0.154261	+	0.267187i
$879$	−2.66385	−	1.53798i	−0.0898495	−	0.0518746i
$880$	3.20578	−	6.68752i	0.108067	−	0.225436i
$881$			4.15297i			0.139917i	0.997550	+	0.0699586i	$0.0222867\pi$
$881$			4.15297i			0.139917i	−0.997550	+	0.0699586i	$0.977713\pi$
$882$	−16.0139	+	7.66419i	−0.539216	+	0.258067i
$883$		−	8.52040i		−	0.286734i	−0.989670	−	0.143367i	$-0.954207\pi$
$883$		−	8.52040i		−	0.286734i	0.989670	−	0.143367i	$-0.0457930\pi$
$884$	−3.42703	−	5.93579i	−0.115264	−	0.199642i
$885$	−6.92371	−	5.39776i	−0.232738	−	0.181444i
$886$	4.23828	+	2.44697i	0.142388	+	0.0822076i
$887$	1.73379	−	1.00101i	0.0582150	−	0.0336105i	−0.470610	−	0.882341i	$-0.655966\pi$
$887$	1.73379	−	1.00101i	0.0582150	−	0.0336105i	0.528825	+	0.848731i	$0.322633\pi$
$888$		−	2.46977i		−	0.0828801i
$889$	−31.2183	−	9.67097i	−1.04703	−	0.324354i
$890$	5.35965	−	38.4270i	0.179656	−	1.28808i
$891$	5.07516	−	15.9301i	0.170024	−	0.533677i
$892$	12.8642	−	22.2814i	0.430724	−	0.746036i
$893$	−30.4353	+	52.7155i	−1.01848	+	1.76406i
$894$	2.97608	−	1.71824i	0.0995351	−	0.0574666i
$895$	3.27767	+	0.457157i	0.109561	+	0.0152811i
$896$	−0.585613	−	2.58013i	−0.0195640	−	0.0861960i
$897$	−3.62567			−0.121058
$898$	1.59758	+	2.76709i	0.0533120	+	0.0923390i
$899$	−0.926232	+	1.60428i	−0.0308916	+	0.0535058i
$900$	9.10355	−	8.82802i	0.303452	−	0.294267i
$901$	−6.17590	−	10.6970i	−0.205749	−	0.356368i
$902$	13.9239	+	15.2869i	0.463617	+	0.508997i
$903$	8.66294	−	8.01855i	0.288285	−	0.266840i
$904$			10.5976i			0.352470i
$905$	22.4144	−	9.08326i	0.745081	−	0.301938i
$906$	1.40133	+	0.809059i	0.0465561	+	0.0268792i
$907$	−28.8503	−	16.6567i	−0.957958	−	0.553077i	−0.0624140	−	0.998050i	$-0.519880\pi$
$907$	−28.8503	−	16.6567i	−0.957958	−	0.553077i	−0.895544	+	0.444973i	$0.853213\pi$
$908$	9.94984	−	5.74454i	0.330197	−	0.190639i
$909$	−11.6674			−0.386984
$910$	6.93321	+	9.95791i	0.229834	+	0.330101i
$911$	7.49371			0.248278			0.124139	−	0.992265i	$-0.460383\pi$
$911$	7.49371			0.248278			0.124139	+	0.992265i	$0.460383\pi$
$912$	1.57604	+	2.72978i	0.0521879	+	0.0903921i
$913$	1.30830	+	5.98603i	0.0432984	+	0.198109i
$914$	7.73790	−	13.4024i	0.255947	−	0.443313i
$915$	−6.16103	−	15.2033i	−0.203677	−	0.502607i
$916$			18.8471i			0.622725i
$917$	−4.16302	−	18.3417i	−0.137475	−	0.605696i
$918$		−	12.5997i		−	0.415851i
$919$	−43.7672	+	25.2690i	−1.44375	+	0.833547i	−0.998097	−	0.0616610i	$-0.980360\pi$
$919$	−43.7672	+	25.2690i	−1.44375	+	0.833547i	−0.445649	+	0.895208i	$0.647027\pi$
$920$	4.57756	+	3.56869i	0.150918	+	0.117656i
$921$	17.7287	+	10.2356i	0.584179	+	0.337276i
$922$	1.27863	+	2.21464i	0.0421093	+	0.0729354i
$923$		−	11.7837i		−	0.387865i
$924$	2.53655	+	5.41092i	0.0834464	+	0.178006i
$925$	4.96165	−	17.4408i	0.163138	−	0.573448i
$926$	−28.2171	+	16.2911i	−0.927271	+	0.535360i
$927$	−5.12323	+	8.87369i	−0.168269	+	0.291450i
$928$	−0.180656	−	0.104302i	−0.00593031	−	0.00342387i
$929$	−43.2077	+	24.9460i	−1.41760	+	0.818450i	−0.996087	−	0.0883737i	$-0.971833\pi$
$929$	−43.2077	+	24.9460i	−1.41760	+	0.818450i	−0.421510	+	0.906824i	$0.638500\pi$
$930$	−1.86806	+	13.3934i	−0.0612562	+	0.439188i
$931$	2.49938	−	32.3026i	0.0819140	−	1.05867i
$932$	9.06168			0.296825
$933$	−0.661566	+	0.381956i	−0.0216587	+	0.0125047i
$934$	−0.161793	+	0.280233i	−0.00529402	+	0.00916951i
$935$	−1.89641	−	24.7110i	−0.0620192	−	0.808137i
$936$	−4.50483	+	2.60087i	−0.147245	+	0.0850119i
$937$		−	46.4297i		−	1.51679i	−0.651794	−	0.758396i	$-0.725983\pi$
$937$		−	46.4297i		−	1.51679i	0.651794	−	0.758396i	$-0.274017\pi$
$938$	1.30985	−	4.22826i	0.0427682	−	0.138058i
$939$	−14.0557			−0.458690
$940$	−11.0447	−	27.2546i	−0.360239	−	0.888948i
$941$	−18.9088	+	32.7510i	−0.616409	+	1.06765i	0.373727	+	0.927539i	$0.378080\pi$
$941$	−18.9088	+	32.7510i	−0.616409	+	1.06765i	−0.990136	+	0.140112i	$0.955254\pi$
$942$	0.190422	−	0.329820i	0.00620427	−	0.0107461i
$943$	−14.0151	+	8.09165i	−0.456396	+	0.263500i
$944$		−	5.76508i		−	0.187637i
$945$	1.88494	+	22.2255i	0.0613172	+	0.722997i
$946$	14.6315	+	16.0637i	0.475712	+	0.522276i
$947$	−10.1023	+	5.83256i	−0.328280	+	0.189533i	−0.655077	−	0.755562i	$-0.727364\pi$
$947$	−10.1023	+	5.83256i	−0.328280	+	0.189533i	0.326797	+	0.945095i	$0.394031\pi$
$948$	9.09701	+	5.25216i	0.295457	+	0.170582i
$949$	7.84685	−	13.5911i	0.254720	−	0.441187i
$950$	5.64550	+	22.4430i	0.183164	+	0.728149i
$951$		−	14.4599i		−	0.468895i
$952$	−6.00601	−	6.48867i	−0.194656	−	0.210299i
$953$	31.7232			1.02761			0.513807	−	0.857906i	$-0.328235\pi$
$953$	31.7232			1.02761			0.513807	+	0.857906i	$0.328235\pi$
$954$	−8.11822	+	4.68706i	−0.262837	+	0.151749i
$955$	−24.2694	+	31.1304i	−0.785341	+	1.00736i
$956$	16.5047	+	9.52898i	0.533799	+	0.308189i
$957$	0.448939	+	0.143028i	0.0145121	+	0.00462343i
$958$	−24.5887			−0.794425
$959$	33.5900	+	36.2894i	1.08468	+	1.17185i
$960$	−1.50822	−	0.210360i	−0.0486775	−	0.00678934i
$961$	23.9301	+	41.4481i	0.771937	+	1.33703i
$962$	−3.71901	+	6.44152i	−0.119906	+	0.207683i
$963$	−12.1896	+	21.1130i	−0.392804	+	0.680357i
$964$	−3.67875	−	6.37178i	−0.118485	−	0.205221i
$965$	48.1846	+	6.72060i	1.55112	+	0.216344i
$966$	−4.56106	+	1.03523i	−0.146750	+	0.0333079i
$967$	−23.7319			−0.763167			−0.381583	−	0.924334i	$-0.624621\pi$
$967$	−23.7319			−0.763167			−0.381583	+	0.924334i	$0.624621\pi$
$968$	−9.99702	+	4.58908i	−0.321316	+	0.147499i
$969$	9.12248	+	5.26686i	0.293056	+	0.169196i
$970$	−8.18471	+	10.4985i	−0.262795	+	0.337087i
$971$	−44.9933	+	25.9769i	−1.44390	+	0.833637i	−0.998107	−	0.0614977i	$-0.980412\pi$
$971$	−44.9933	+	25.9769i	−1.44390	+	0.833637i	−0.445795	+	0.895135i	$0.647079\pi$
$972$	−14.7439			−0.472910
$973$	49.5630	+	15.3539i	1.58892	+	0.492223i
$974$		−	30.6150i		−	0.980967i
$975$	6.77287	−	1.70370i	0.216905	−	0.0545621i
$976$	5.38616	−	9.32910i	0.172407	−	0.298617i
$977$	12.5562	+	7.24930i	0.401707	+	0.231926i	0.687220	−	0.726449i	$-0.258831\pi$
$977$	12.5562	+	7.24930i	0.401707	+	0.231926i	−0.285513	+	0.958375i	$0.592164\pi$
$978$	−12.9588	+	7.48177i	−0.414377	+	0.239241i
$979$	−42.5451	+	38.7519i	−1.35975	+	1.23852i
$980$	11.5652	+	10.5474i	0.369436	+	0.336923i
$981$		−	44.2255i		−	1.41201i
$982$	−10.5621	+	6.09802i	−0.337049	+	0.194595i
$983$	12.6199	−	21.8583i	0.402511	−	0.697170i	−0.591517	−	0.806293i	$-0.701471\pi$
$983$	12.6199	−	21.8583i	0.402511	−	0.697170i	0.994028	+	0.109122i	$0.0348040\pi$
$984$	2.12294	−	3.67703i	0.0676767	−	0.117219i
$985$	−2.98668	−	7.37012i	−0.0951635	−	0.234831i
$986$	−0.697117			−0.0222007
$987$	22.6353	+	7.01207i	0.720488	+	0.223196i
$988$		−	9.49288i		−	0.302009i
$989$	−14.7274	+	8.50285i	−0.468303	+	0.270375i
$990$	−18.7539	+	1.43923i	−0.596037	+	0.0457419i
$991$	3.63988	−	6.30446i	0.115625	−	0.200268i	−0.802405	−	0.596780i	$-0.796446\pi$
$991$	3.63988	−	6.30446i	0.115625	−	0.200268i	0.918029	+	0.396513i	$0.129780\pi$
$992$	−7.69058	+	4.44016i	−0.244176	+	0.140975i
$993$	−12.0928			−0.383753
$994$	−3.36456	−	14.8238i	−0.106717	−	0.470182i
$995$	−3.22975	+	23.1563i	−0.102390	+	0.734104i
$996$	1.08960	−	0.629082i	0.0345254	−	0.0199332i
$997$	−47.8438	−	27.6227i	−1.51523	−	0.874818i	−0.999840	−	0.0178623i	$-0.994314\pi$
$997$	−47.8438	−	27.6227i	−1.51523	−	0.874818i	−0.515389	−	0.856956i	$-0.672353\pi$
$998$	3.86443	−	6.69338i	0.122326	−	0.211875i
$999$	−11.8413	+	6.83658i	−0.374643	+	0.216300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.b.549.14	yes	48
5.4	even	2		770.2.o.a.549.11	yes	48
7.5	odd	6	inner	770.2.o.b.439.11	yes	48
11.10	odd	2		770.2.o.a.549.14	yes	48
35.19	odd	6		770.2.o.a.439.14	yes	48
55.54	odd	2	inner	770.2.o.b.549.11	yes	48
77.54	even	6		770.2.o.a.439.11	✓	48
385.54	even	6	inner	770.2.o.b.439.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.11	✓	48	77.54	even	6
770.2.o.a.439.14	yes	48	35.19	odd	6
770.2.o.a.549.11	yes	48	5.4	even	2
770.2.o.a.549.14	yes	48	11.10	odd	2
770.2.o.b.439.11	yes	48	7.5	odd	6	inner
770.2.o.b.439.14	yes	48	385.54	even	6	inner
770.2.o.b.549.11	yes	48	55.54	odd	2	inner
770.2.o.b.549.14	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.340512 - 0.589784i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.839811 - 2.07237i) q^{5} +0.681024 q^{6} +(-2.52726 - 0.782908i) q^{7} -1.00000 q^{8} +(1.26810 + 2.19642i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.340512 - 0.589784i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.839811 - 2.07237i) q^{5} +0.681024 q^{6} +(-2.52726 - 0.782908i) q^{7} -1.00000 q^{8} +(1.26810 + 2.19642i) q^{9} +(1.37482 - 1.76348i) q^{10} +(-3.24014 + 0.708161i) q^{11} +(0.340512 + 0.589784i) q^{12} -2.05099i q^{13} +(-0.585613 - 2.58013i) q^{14} +(-1.50822 - 0.210360i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.89411 - 1.67092i) q^{17} +(-1.26810 + 2.19642i) q^{18} +(-2.31422 - 4.00835i) q^{19} +(2.21463 + 0.308888i) q^{20} +(-1.32231 + 1.22395i) q^{21} +(-2.23336 - 2.45196i) q^{22} +(2.24798 - 1.29787i) q^{23} +(-0.340512 + 0.589784i) q^{24} +(-3.58944 + 3.48080i) q^{25} +(1.77621 - 1.02549i) q^{26} +3.77029 q^{27} +(1.94165 - 1.79722i) q^{28} -0.208603i q^{29} +(-0.571931 - 1.41133i) q^{30} +(-7.69058 - 4.44016i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.685645 + 2.15212i) q^{33} -3.34183i q^{34} +(0.499946 + 5.89492i) q^{35} -2.53621 q^{36} +(-3.14069 + 1.81328i) q^{37} +(2.31422 - 4.00835i) q^{38} +(-1.20964 - 0.698386i) q^{39} +(0.839811 + 2.07237i) q^{40} -6.23454 q^{41} +(-1.72113 - 0.533179i) q^{42} -6.55137 q^{43} +(1.00678 - 3.16012i) q^{44} +(3.48683 - 4.47256i) q^{45} +(2.24798 + 1.29787i) q^{46} +(-6.57571 - 11.3895i) q^{47} -0.681024 q^{48} +(5.77411 + 3.95723i) q^{49} +(-4.80918 - 1.36814i) q^{50} +(-1.97096 + 1.13793i) q^{51} +(1.77621 + 1.02549i) q^{52} +(3.20093 + 1.84806i) q^{53} +(1.88514 + 3.26517i) q^{54} +(4.18868 + 6.12005i) q^{55} +(2.52726 + 0.782908i) q^{56} -3.15208 q^{57} +(0.180656 - 0.104302i) q^{58} +(4.99271 + 2.88254i) q^{59} +(0.936285 - 1.20097i) q^{60} +(5.38616 + 9.32910i) q^{61} -8.88032i q^{62} +(-1.48523 - 6.54374i) q^{63} +1.00000 q^{64} +(-4.25041 + 1.72244i) q^{65} +(-2.20661 + 0.482275i) q^{66} +(1.44891 + 0.836530i) q^{67} +(2.89411 - 1.67092i) q^{68} -1.76777i q^{69} +(-4.85518 + 3.38042i) q^{70} +5.74537 q^{71} +(-1.26810 - 2.19642i) q^{72} +(6.62663 + 3.82589i) q^{73} +(-3.14069 - 1.81328i) q^{74} +(0.830673 + 3.30225i) q^{75} +4.62844 q^{76} +(8.74311 + 0.747023i) q^{77} -1.39677i q^{78} +(13.3578 - 7.71215i) q^{79} +(-1.37482 + 1.76348i) q^{80} +(-2.52048 + 4.36560i) q^{81} +(-3.11727 - 5.39927i) q^{82} -1.84746i q^{83} +(-0.398816 - 1.75713i) q^{84} +(-1.03225 + 7.40093i) q^{85} +(-3.27568 - 5.67365i) q^{86} +(-0.123031 - 0.0710319i) q^{87} +(3.24014 - 0.708161i) q^{88} +(15.0268 - 8.67572i) q^{89} +(5.61676 + 0.783403i) q^{90} +(-1.60574 + 5.18339i) q^{91} +2.59575i q^{92} +(-5.23747 + 3.02386i) q^{93} +(6.57571 - 11.3895i) q^{94} +(-6.36328 + 8.16218i) q^{95} +(-0.340512 - 0.589784i) q^{96} -5.95329 q^{97} +(-0.540006 + 6.97914i) q^{98} +(-5.66425 - 6.21868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

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