LMFDB - Embedded newform 770.2.l.c.573.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.15
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.602672 + 0.602672i) q^{3} -1.00000i q^{4} +(-0.490670 - 2.18157i) q^{5} +0.852308i q^{6} +(-2.60076 + 0.485856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.27357i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.602672 + 0.602672i) q^{3} -1.00000i q^{4} +(-0.490670 - 2.18157i) q^{5} +0.852308i q^{6} +(-2.60076 + 0.485856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.27357i q^{9} +(-1.88956 - 1.19565i) q^{10} -1.00000 q^{11} +(0.602672 + 0.602672i) q^{12} +(-1.45991 + 1.45991i) q^{13} +(-1.49546 + 2.18257i) q^{14} +(1.61048 + 1.01906i) q^{15} -1.00000 q^{16} +(-0.392779 - 0.392779i) q^{17} +(1.60766 + 1.60766i) q^{18} -5.59795 q^{19} +(-2.18157 + 0.490670i) q^{20} +(1.27459 - 1.86022i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(2.20767 + 2.20767i) q^{23} +0.852308 q^{24} +(-4.51849 + 2.14086i) q^{25} +2.06463i q^{26} +(-3.17824 - 3.17824i) q^{27} +(0.485856 + 2.60076i) q^{28} +8.31663i q^{29} +(1.85937 - 0.418202i) q^{30} -0.356422i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.602672 - 0.602672i) q^{33} -0.555473 q^{34} +(2.33604 + 5.43534i) q^{35} +2.27357 q^{36} +(3.62131 - 3.62131i) q^{37} +(-3.95835 + 3.95835i) q^{38} -1.75970i q^{39} +(-1.19565 + 1.88956i) q^{40} +9.90307i q^{41} +(-0.414099 - 2.21665i) q^{42} +(-3.77817 - 3.77817i) q^{43} +1.00000i q^{44} +(4.95995 - 1.11557i) q^{45} +3.12211 q^{46} +(-4.76346 - 4.76346i) q^{47} +(0.602672 - 0.602672i) q^{48} +(6.52789 - 2.52719i) q^{49} +(-1.68124 + 4.70887i) q^{50} +0.473434 q^{51} +(1.45991 + 1.45991i) q^{52} +(-8.17933 - 8.17933i) q^{53} -4.49471 q^{54} +(0.490670 + 2.18157i) q^{55} +(2.18257 + 1.49546i) q^{56} +(3.37373 - 3.37373i) q^{57} +(5.88075 + 5.88075i) q^{58} -8.42834 q^{59} +(1.01906 - 1.61048i) q^{60} +2.21373i q^{61} +(-0.252028 - 0.252028i) q^{62} +(-1.10463 - 5.91301i) q^{63} +1.00000i q^{64} +(3.90124 + 2.46857i) q^{65} -0.852308i q^{66} +(-0.880000 + 0.880000i) q^{67} +(-0.392779 + 0.392779i) q^{68} -2.66100 q^{69} +(5.49520 + 2.19153i) q^{70} -5.71174 q^{71} +(1.60766 - 1.60766i) q^{72} +(-1.48454 + 1.48454i) q^{73} -5.12131i q^{74} +(1.43293 - 4.01340i) q^{75} +5.59795i q^{76} +(2.60076 - 0.485856i) q^{77} +(-1.24430 - 1.24430i) q^{78} -7.65896i q^{79} +(0.490670 + 2.18157i) q^{80} -2.98984 q^{81} +(7.00253 + 7.00253i) q^{82} +(-5.51022 + 5.51022i) q^{83} +(-1.86022 - 1.27459i) q^{84} +(-0.664150 + 1.04960i) q^{85} -5.34314 q^{86} +(-5.01221 - 5.01221i) q^{87} +(0.707107 + 0.707107i) q^{88} +12.1104 q^{89} +(2.71839 - 4.29605i) q^{90} +(3.08758 - 4.50619i) q^{91} +(2.20767 - 2.20767i) q^{92} +(0.214806 + 0.214806i) q^{93} -6.73655 q^{94} +(2.74675 + 12.2123i) q^{95} -0.852308i q^{96} +(2.77643 + 2.77643i) q^{97} +(2.82892 - 6.40291i) q^{98} -2.27357i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.602672	+	0.602672i	−0.347953	+	0.347953i	−0.859347	−	0.511394i	$-0.829129\pi$
$3$	−0.602672	+	0.602672i	−0.347953	+	0.347953i	0.511394	+	0.859347i	$0.329129\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.490670	−	2.18157i	−0.219434	−	0.975627i
$5$	−0.490670	−	2.18157i	−0.219434	−	0.975627i
$6$			0.852308i			0.347953i
$7$	−2.60076	+	0.485856i	−0.982994	+	0.183636i
$7$	−2.60076	+	0.485856i	−0.982994	+	0.183636i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			2.27357i			0.757857i
$10$	−1.88956	−	1.19565i	−0.597531	−	0.378097i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.602672	+	0.602672i	0.173977	+	0.173977i
$13$	−1.45991	+	1.45991i	−0.404908	+	0.404908i	−0.879958	−	0.475051i	$-0.842430\pi$
$13$	−1.45991	+	1.45991i	−0.404908	+	0.404908i	0.475051	+	0.879958i	$0.342430\pi$
$14$	−1.49546	+	2.18257i	−0.399679	+	0.583315i
$15$	1.61048	+	1.01906i	0.415825	+	0.263120i
$16$	−1.00000			−0.250000
$17$	−0.392779	−	0.392779i	−0.0952629	−	0.0952629i	0.657869	−	0.753132i	$-0.271458\pi$
$17$	−0.392779	−	0.392779i	−0.0952629	−	0.0952629i	−0.753132	+	0.657869i	$0.771458\pi$
$18$	1.60766	+	1.60766i	0.378929	+	0.378929i
$19$	−5.59795			−1.28426			−0.642129	−	0.766596i	$-0.721949\pi$
$19$	−5.59795			−1.28426			−0.642129	+	0.766596i	$0.721949\pi$
$20$	−2.18157	+	0.490670i	−0.487814	+	0.109717i
$21$	1.27459	−	1.86022i	0.278139	−	0.405933i
$22$	−0.707107	+	0.707107i	−0.150756	+	0.150756i
$23$	2.20767	+	2.20767i	0.460330	+	0.460330i	0.898764	−	0.438433i	$-0.144466\pi$
$23$	2.20767	+	2.20767i	0.460330	+	0.460330i	−0.438433	+	0.898764i	$0.644466\pi$
$24$	0.852308			0.173977
$25$	−4.51849	+	2.14086i	−0.903697	+	0.428172i
$26$			2.06463i			0.404908i
$27$	−3.17824	−	3.17824i	−0.611652	−	0.611652i
$28$	0.485856	+	2.60076i	0.0918182	+	0.491497i
$29$			8.31663i			1.54436i	0.635404	+	0.772180i	$0.280834\pi$
$29$			8.31663i			1.54436i	−0.635404	+	0.772180i	$0.719166\pi$
$30$	1.85937	−	0.418202i	0.339473	−	0.0763528i
$31$		−	0.356422i		−	0.0640153i	−0.999488	−	0.0320076i	$-0.989810\pi$
$31$		−	0.356422i		−	0.0640153i	0.999488	−	0.0320076i	$-0.0101901\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.602672	−	0.602672i	0.104912	−	0.104912i
$34$	−0.555473			−0.0952629
$35$	2.33604	+	5.43534i	0.394863	+	0.918740i
$36$	2.27357			0.378929
$37$	3.62131	−	3.62131i	0.595340	−	0.595340i	−0.343729	−	0.939069i	$-0.611690\pi$
$37$	3.62131	−	3.62131i	0.595340	−	0.595340i	0.939069	+	0.343729i	$0.111690\pi$
$38$	−3.95835	+	3.95835i	−0.642129	+	0.642129i
$39$		−	1.75970i		−	0.281778i
$40$	−1.19565	+	1.88956i	−0.189048	+	0.298765i
$41$			9.90307i			1.54660i	0.634041	+	0.773300i	$0.281395\pi$
$41$			9.90307i			1.54660i	−0.634041	+	0.773300i	$0.718605\pi$
$42$	−0.414099	−	2.21665i	−0.0638969	−	0.342036i
$43$	−3.77817	−	3.77817i	−0.576166	−	0.576166i	0.357679	−	0.933845i	$-0.383568\pi$
$43$	−3.77817	−	3.77817i	−0.576166	−	0.576166i	−0.933845	+	0.357679i	$0.883568\pi$
$44$			1.00000i			0.150756i
$45$	4.95995	−	1.11557i	0.739386	−	0.166300i
$46$	3.12211			0.460330
$47$	−4.76346	−	4.76346i	−0.694822	−	0.694822i	0.268467	−	0.963289i	$-0.413483\pi$
$47$	−4.76346	−	4.76346i	−0.694822	−	0.694822i	−0.963289	+	0.268467i	$0.913483\pi$
$48$	0.602672	−	0.602672i	0.0869883	−	0.0869883i
$49$	6.52789	−	2.52719i	0.932555	−	0.361027i
$50$	−1.68124	+	4.70887i	−0.237763	+	0.665935i
$51$	0.473434			0.0662941
$52$	1.45991	+	1.45991i	0.202454	+	0.202454i
$53$	−8.17933	−	8.17933i	−1.12352	−	1.12352i	−0.991209	−	0.132308i	$-0.957761\pi$
$53$	−8.17933	−	8.17933i	−1.12352	−	1.12352i	−0.132308	−	0.991209i	$-0.542239\pi$
$54$	−4.49471			−0.611652
$55$	0.490670	+	2.18157i	0.0661619	+	0.294163i
$56$	2.18257	+	1.49546i	0.291658	+	0.199839i
$57$	3.37373	−	3.37373i	0.446862	−	0.446862i
$58$	5.88075	+	5.88075i	0.772180	+	0.772180i
$59$	−8.42834			−1.09728			−0.548638	−	0.836060i	$-0.684854\pi$
$59$	−8.42834			−1.09728			−0.548638	+	0.836060i	$0.684854\pi$
$60$	1.01906	−	1.61048i	0.131560	−	0.207913i
$61$			2.21373i			0.283440i	0.989907	+	0.141720i	$0.0452632\pi$
$61$			2.21373i			0.283440i	−0.989907	+	0.141720i	$0.954737\pi$
$62$	−0.252028	−	0.252028i	−0.0320076	−	0.0320076i
$63$	−1.10463	−	5.91301i	−0.139170	−	0.744969i
$64$			1.00000i			0.125000i
$65$	3.90124	+	2.46857i	0.483889	+	0.306188i
$66$		−	0.852308i		−	0.104912i
$67$	−0.880000	+	0.880000i	−0.107509	+	0.107509i	−0.758815	−	0.651306i	$-0.774221\pi$
$67$	−0.880000	+	0.880000i	−0.107509	+	0.107509i	0.651306	+	0.758815i	$0.274221\pi$
$68$	−0.392779	+	0.392779i	−0.0476315	+	0.0476315i
$69$	−2.66100			−0.320347
$70$	5.49520	+	2.19153i	0.656802	+	0.261938i
$71$	−5.71174			−0.677859			−0.338929	−	0.940812i	$-0.610065\pi$
$71$	−5.71174			−0.677859			−0.338929	+	0.940812i	$0.610065\pi$
$72$	1.60766	−	1.60766i	0.189464	−	0.189464i
$73$	−1.48454	+	1.48454i	−0.173752	+	0.173752i	−0.788626	−	0.614874i	$-0.789207\pi$
$73$	−1.48454	+	1.48454i	−0.173752	+	0.173752i	0.614874	+	0.788626i	$0.289207\pi$
$74$		−	5.12131i		−	0.595340i
$75$	1.43293	−	4.01340i	0.165461	−	0.463428i
$76$			5.59795i			0.642129i
$77$	2.60076	−	0.485856i	0.296384	−	0.0553685i
$78$	−1.24430	−	1.24430i	−0.140889	−	0.140889i
$79$		−	7.65896i		−	0.861700i	−0.902424	−	0.430850i	$-0.858214\pi$
$79$		−	7.65896i		−	0.861700i	0.902424	−	0.430850i	$-0.141786\pi$
$80$	0.490670	+	2.18157i	0.0548585	+	0.243907i
$81$	−2.98984			−0.332205
$82$	7.00253	+	7.00253i	0.773300	+	0.773300i
$83$	−5.51022	+	5.51022i	−0.604825	+	0.604825i	−0.941589	−	0.336764i	$-0.890667\pi$
$83$	−5.51022	+	5.51022i	−0.604825	+	0.604825i	0.336764	+	0.941589i	$0.390667\pi$
$84$	−1.86022	−	1.27459i	−0.202966	−	0.139070i
$85$	−0.664150	+	1.04960i	−0.0720372	+	0.113845i
$86$	−5.34314			−0.576166
$87$	−5.01221	−	5.01221i	−0.537365	−	0.537365i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	12.1104			1.28370			0.641850	−	0.766830i	$-0.278167\pi$
$89$	12.1104			1.28370			0.641850	+	0.766830i	$0.278167\pi$
$90$	2.71839	−	4.29605i	0.286543	−	0.452843i
$91$	3.08758	−	4.50619i	0.323666	−	0.472378i
$92$	2.20767	−	2.20767i	0.230165	−	0.230165i
$93$	0.214806	+	0.214806i	0.0222743	+	0.0222743i
$94$	−6.73655			−0.694822
$95$	2.74675	+	12.2123i	0.281810	+	1.25296i
$96$		−	0.852308i		−	0.0869883i
$97$	2.77643	+	2.77643i	0.281904	+	0.281904i	0.833868	−	0.551964i	$-0.186121\pi$
$97$	2.77643	+	2.77643i	0.281904	+	0.281904i	−0.551964	+	0.833868i	$0.686121\pi$
$98$	2.82892	−	6.40291i	0.285764	−	0.646791i
$99$		−	2.27357i		−	0.228503i
$100$	2.14086	+	4.51849i	0.214086	+	0.451849i
$101$		−	13.9318i		−	1.38627i	−0.720808	−	0.693134i	$-0.756229\pi$
$101$		−	13.9318i		−	1.38627i	0.720808	−	0.693134i	$-0.243771\pi$
$102$	0.334769	−	0.334769i	0.0331470	−	0.0331470i
$103$	2.39874	−	2.39874i	0.236355	−	0.236355i	−0.578984	−	0.815339i	$-0.696551\pi$
$103$	2.39874	−	2.39874i	0.236355	−	0.236355i	0.815339	+	0.578984i	$0.196551\pi$
$104$	2.06463			0.202454
$105$	−4.68360	−	1.86786i	−0.457072	−	0.182285i
$106$	−11.5673			−1.12352
$107$	3.31488	−	3.31488i	0.320461	−	0.320461i	−0.528483	−	0.848944i	$-0.677239\pi$
$107$	3.31488	−	3.31488i	0.320461	−	0.320461i	0.848944	+	0.528483i	$0.177239\pi$
$108$	−3.17824	+	3.17824i	−0.305826	+	0.305826i
$109$			2.63426i			0.252316i	0.992010	+	0.126158i	$0.0402647\pi$
$109$			2.63426i			0.252316i	−0.992010	+	0.126158i	$0.959735\pi$
$110$	1.88956	+	1.19565i	0.180162	+	0.114000i
$111$			4.36493i			0.414301i
$112$	2.60076	−	0.485856i	0.245749	−	0.0459091i
$113$	−5.68215	−	5.68215i	−0.534531	−	0.534531i	0.387386	−	0.921918i	$-0.373378\pi$
$113$	−5.68215	−	5.68215i	−0.534531	−	0.534531i	−0.921918	+	0.387386i	$0.873378\pi$
$114$		−	4.77118i		−	0.446862i
$115$	3.73294	−	5.89941i	0.348099	−	0.550123i
$116$	8.31663			0.772180
$117$	−3.31922	−	3.31922i	−0.306862	−	0.306862i
$118$	−5.95974	+	5.95974i	−0.548638	+	0.548638i
$119$	1.21236	+	0.830689i	0.111137	+	0.0761492i
$120$	−0.418202	−	1.85937i	−0.0381764	−	0.169736i
$121$	1.00000			0.0909091
$122$	1.56535	+	1.56535i	0.141720	+	0.141720i
$123$	−5.96831	−	5.96831i	−0.538144	−	0.538144i
$124$	−0.356422			−0.0320076
$125$	6.88752	+	8.80693i	0.616038	+	0.787716i
$126$	−4.96222	−	3.40004i	−0.442070	−	0.302900i
$127$	9.39175	−	9.39175i	0.833383	−	0.833383i	−0.154595	−	0.987978i	$-0.549407\pi$
$127$	9.39175	−	9.39175i	0.833383	−	0.833383i	0.987978	+	0.154595i	$0.0494073\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	4.55400			0.400957
$130$	4.50414	−	1.01305i	0.395039	−	0.0888506i
$131$		−	5.09686i		−	0.445315i	−0.974897	−	0.222658i	$-0.928527\pi$
$131$		−	5.09686i		−	0.445315i	0.974897	−	0.222658i	$-0.0714732\pi$
$132$	−0.602672	−	0.602672i	−0.0524559	−	0.0524559i
$133$	14.5589	−	2.71980i	1.26242	−	0.235837i
$134$			1.24451i			0.107509i
$135$	−5.37408	+	8.49301i	−0.462527	+	0.730962i
$136$			0.555473i			0.0476315i
$137$	7.15243	−	7.15243i	0.611074	−	0.611074i	−0.332152	−	0.943226i	$-0.607775\pi$
$137$	7.15243	−	7.15243i	0.611074	−	0.611074i	0.943226	+	0.332152i	$0.107775\pi$
$138$	−1.88161	+	1.88161i	−0.160173	+	0.160173i
$139$	−3.63290			−0.308139			−0.154069	−	0.988060i	$-0.549238\pi$
$139$	−3.63290			−0.308139			−0.154069	+	0.988060i	$0.549238\pi$
$140$	5.43534	−	2.33604i	0.459370	−	0.197432i
$141$	5.74161			0.483531
$142$	−4.03881	+	4.03881i	−0.338929	+	0.338929i
$143$	1.45991	−	1.45991i	0.122084	−	0.122084i
$144$		−	2.27357i		−	0.189464i
$145$	18.1433	−	4.08072i	1.50672	−	0.338885i
$146$			2.09946i			0.173752i
$147$	−2.41111	+	5.45725i	−0.198865	+	0.450106i
$148$	−3.62131	−	3.62131i	−0.297670	−	0.297670i
$149$			5.64736i			0.462650i	0.972877	+	0.231325i	$0.0743060\pi$
$149$			5.64736i			0.462650i	−0.972877	+	0.231325i	$0.925694\pi$
$150$	−1.82467	−	3.85114i	−0.148984	−	0.314444i
$151$	11.9658			0.973763			0.486882	−	0.873468i	$-0.338134\pi$
$151$	11.9658			0.973763			0.486882	+	0.873468i	$0.338134\pi$
$152$	3.95835	+	3.95835i	0.321065	+	0.321065i
$153$	0.893011	−	0.893011i	0.0721957	−	0.0721957i
$154$	1.49546	−	2.18257i	0.120508	−	0.175876i
$155$	−0.777559	+	0.174885i	−0.0624551	+	0.0140471i
$156$	−1.75970			−0.140889
$157$	3.49278	+	3.49278i	0.278754	+	0.278754i	0.832611	−	0.553858i	$-0.186845\pi$
$157$	3.49278	+	3.49278i	0.278754	+	0.278754i	−0.553858	+	0.832611i	$0.686845\pi$
$158$	−5.41570	−	5.41570i	−0.430850	−	0.430850i
$159$	9.85891			0.781862
$160$	1.88956	+	1.19565i	0.149383	+	0.0945241i
$161$	−6.81422	−	4.66900i	−0.537036	−	0.367969i
$162$	−2.11414	+	2.11414i	−0.166102	+	0.166102i
$163$	−7.73170	−	7.73170i	−0.605594	−	0.605594i	0.336198	−	0.941791i	$-0.390859\pi$
$163$	−7.73170	−	7.73170i	−0.605594	−	0.605594i	−0.941791	+	0.336198i	$0.890859\pi$
$164$	9.90307			0.773300
$165$	−1.61048	−	1.01906i	−0.125376	−	0.0793336i
$166$			7.79262i			0.604825i
$167$	3.83084	+	3.83084i	0.296440	+	0.296440i	0.839618	−	0.543178i	$-0.182779\pi$
$167$	3.83084	+	3.83084i	0.296440	+	0.296440i	−0.543178	+	0.839618i	$0.682779\pi$
$168$	−2.21665	+	0.414099i	−0.171018	+	0.0319484i
$169$			8.73730i			0.672100i
$170$	0.272554	+	1.21180i	0.0209039	+	0.0929411i
$171$		−	12.7274i		−	0.973285i
$172$	−3.77817	+	3.77817i	−0.288083	+	0.288083i
$173$	−14.3691	+	14.3691i	−1.09246	+	1.09246i	−0.0971993	+	0.995265i	$0.530988\pi$
$173$	−14.3691	+	14.3691i	−1.09246	+	1.09246i	−0.995265	+	0.0971993i	$0.969012\pi$
$174$	−7.08833			−0.537365
$175$	10.7113	−	7.76319i	0.809701	−	0.586842i
$176$	1.00000			0.0753778
$177$	5.07953	−	5.07953i	0.381801	−	0.381801i
$178$	8.56334	−	8.56334i	0.641850	−	0.641850i
$179$			8.48638i			0.634302i	0.948375	+	0.317151i	$0.102726\pi$
$179$			8.48638i			0.634302i	−0.948375	+	0.317151i	$0.897274\pi$
$180$	−1.11557	−	4.95995i	−0.0831499	−	0.369693i
$181$		−	0.273128i		−	0.0203014i	−0.999948	−	0.0101507i	$-0.996769\pi$
$181$		−	0.273128i		−	0.0203014i	0.999948	−	0.0101507i	$-0.00323113\pi$
$182$	−1.00311	−	5.36961i	−0.0743558	−	0.398022i
$183$	−1.33416	−	1.33416i	−0.0986237	−	0.0986237i
$184$		−	3.12211i		−	0.230165i
$185$	−9.67701	−	6.12327i	−0.711468	−	0.450192i
$186$	0.303781			0.0222743
$187$	0.392779	+	0.392779i	0.0287229	+	0.0287229i
$188$	−4.76346	+	4.76346i	−0.347411	+	0.347411i
$189$	9.80999	+	6.72166i	0.713572	+	0.488929i
$190$	10.5777	+	6.69317i	0.767384	+	0.485574i
$191$	−4.91555			−0.355676			−0.177838	−	0.984060i	$-0.556910\pi$
$191$	−4.91555			−0.355676			−0.177838	+	0.984060i	$0.556910\pi$
$192$	−0.602672	−	0.602672i	−0.0434941	−	0.0434941i
$193$	−1.52160	−	1.52160i	−0.109527	−	0.109527i	0.650219	−	0.759747i	$-0.274677\pi$
$193$	−1.52160	−	1.52160i	−0.109527	−	0.109527i	−0.759747	+	0.650219i	$0.774677\pi$
$194$	3.92647			0.281904
$195$	−3.83891	+	0.863432i	−0.274910	+	0.0618316i
$196$	−2.52719	−	6.52789i	−0.180514	−	0.466278i
$197$	7.78477	−	7.78477i	0.554642	−	0.554642i	−0.373135	−	0.927777i	$-0.621717\pi$
$197$	7.78477	−	7.78477i	0.554642	−	0.554642i	0.927777	+	0.373135i	$0.121717\pi$
$198$	−1.60766	−	1.60766i	−0.114251	−	0.114251i
$199$	1.41376			0.100219			0.0501093	−	0.998744i	$-0.484043\pi$
$199$	1.41376			0.100219			0.0501093	+	0.998744i	$0.484043\pi$
$200$	4.70887	+	1.68124i	0.332967	+	0.118881i
$201$		−	1.06070i		−	0.0748163i
$202$	−9.85129	−	9.85129i	−0.693134	−	0.693134i
$203$	−4.04069	−	21.6296i	−0.283601	−	1.51810i
$204$		−	0.473434i		−	0.0331470i
$205$	21.6042	−	4.85914i	1.50890	−	0.339377i
$206$		−	3.39233i		−	0.236355i
$207$	−5.01929	+	5.01929i	−0.348865	+	0.348865i
$208$	1.45991	−	1.45991i	0.101227	−	0.101227i
$209$	5.59795			0.387219
$210$	−4.63258	+	1.99103i	−0.319678	+	0.137394i
$211$	−8.35392			−0.575107			−0.287554	−	0.957765i	$-0.592842\pi$
$211$	−8.35392			−0.575107			−0.287554	+	0.957765i	$0.592842\pi$
$212$	−8.17933	+	8.17933i	−0.561758	+	0.561758i
$213$	3.44231	−	3.44231i	0.235863	−	0.235863i
$214$		−	4.68794i		−	0.320461i
$215$	−6.38850	+	10.0962i	−0.435692	+	0.688553i
$216$			4.49471i			0.305826i
$217$	0.173170	+	0.926967i	0.0117555	+	0.0629266i
$218$	1.86270	+	1.86270i	0.126158	+	0.126158i
$219$		−	1.78938i		−	0.120915i
$220$	2.18157	−	0.490670i	0.147081	−	0.0330809i
$221$	1.14685			0.0771453
$222$	3.08647	+	3.08647i	0.207150	+	0.207150i
$223$	−20.7571	+	20.7571i	−1.39000	+	1.39000i	−0.564704	+	0.825294i	$0.691009\pi$
$223$	−20.7571	+	20.7571i	−1.39000	+	1.39000i	−0.825294	+	0.564704i	$0.808991\pi$
$224$	1.49546	−	2.18257i	0.0999197	−	0.145829i
$225$	−4.86740	−	10.2731i	−0.324493	−	0.684874i
$226$	−8.03577			−0.534531
$227$	−20.4313	−	20.4313i	−1.35607	−	1.35607i	−0.878705	−	0.477365i	$-0.841592\pi$
$227$	−20.4313	−	20.4313i	−1.35607	−	1.35607i	−0.477365	−	0.878705i	$-0.658408\pi$
$228$	−3.37373	−	3.37373i	−0.223431	−	0.223431i
$229$	−2.20499			−0.145710			−0.0728550	−	0.997343i	$-0.523211\pi$
$229$	−2.20499			−0.145710			−0.0728550	+	0.997343i	$0.523211\pi$
$230$	−1.53193	−	6.81111i	−0.101012	−	0.449111i
$231$	−1.27459	+	1.86022i	−0.0838621	+	0.122393i
$232$	5.88075	−	5.88075i	0.386090	−	0.386090i
$233$	−19.2656	−	19.2656i	−1.26213	−	1.26213i	−0.950057	−	0.312076i	$-0.898976\pi$
$233$	−19.2656	−	19.2656i	−1.26213	−	1.26213i	−0.312076	−	0.950057i	$-0.601024\pi$
$234$	−4.69409			−0.306862
$235$	−8.05453	+	12.7291i	−0.525420	+	0.830355i
$236$			8.42834i			0.548638i
$237$	4.61584	+	4.61584i	0.299831	+	0.299831i
$238$	1.44465	−	0.269880i	0.0936429	−	0.0174937i
$239$			28.8687i			1.86736i	0.358109	+	0.933680i	$0.383421\pi$
$239$			28.8687i			1.86736i	−0.358109	+	0.933680i	$0.616579\pi$
$240$	−1.61048	−	1.01906i	−0.103956	−	0.0657799i
$241$			26.1600i			1.68512i	0.538606	+	0.842558i	$0.318951\pi$
$241$			26.1600i			1.68512i	−0.538606	+	0.842558i	$0.681049\pi$
$242$	0.707107	−	0.707107i	0.0454545	−	0.0454545i
$243$	11.3366	−	11.3366i	0.727244	−	0.727244i
$244$	2.21373			0.141720
$245$	−8.71628	−	13.0010i	−0.556862	−	0.830605i
$246$	−8.44046			−0.538144
$247$	8.17254	−	8.17254i	0.520006	−	0.520006i
$248$	−0.252028	+	0.252028i	−0.0160038	+	0.0160038i
$249$		−	6.64171i		−	0.420901i
$250$	11.0977	+	1.35723i	0.701877	+	0.0858389i
$251$			9.18664i			0.579856i	0.957049	+	0.289928i	$0.0936313\pi$
$251$			9.18664i			0.579856i	−0.957049	+	0.289928i	$0.906369\pi$
$252$	−5.91301	+	1.10463i	−0.372485	+	0.0695851i
$253$	−2.20767	−	2.20767i	−0.138795	−	0.138795i
$254$		−	13.2819i		−	0.833383i
$255$	−0.232300	−	1.03283i	−0.0145472	−	0.0646783i
$256$	1.00000			0.0625000
$257$	−16.3952	−	16.3952i	−1.02271	−	1.02271i	−0.999736	−	0.0229691i	$-0.992688\pi$
$257$	−16.3952	−	16.3952i	−1.02271	−	1.02271i	−0.0229691	−	0.999736i	$-0.507312\pi$
$258$	3.22016	−	3.22016i	0.200479	−	0.200479i
$259$	−7.65872	+	11.1776i	−0.475890	+	0.694542i
$260$	2.46857	−	3.90124i	0.153094	−	0.241945i
$261$	−18.9085			−1.17040
$262$	−3.60403	−	3.60403i	−0.222658	−	0.222658i
$263$	21.7690	+	21.7690i	1.34233	+	1.34233i	0.893731	+	0.448603i	$0.148078\pi$
$263$	21.7690	+	21.7690i	1.34233	+	1.34233i	0.448603	+	0.893731i	$0.351922\pi$
$264$	−0.852308			−0.0524559
$265$	−13.8304	+	21.8571i	−0.849596	+	1.34267i
$266$	8.37153	−	12.2179i	0.513291	−	0.749128i
$267$	−7.29860	+	7.29860i	−0.446667	+	0.446667i
$268$	0.880000	+	0.880000i	0.0537546	+	0.0537546i
$269$	30.2070			1.84175			0.920876	−	0.389856i	$-0.127475\pi$
$269$	30.2070			1.84175			0.920876	+	0.389856i	$0.127475\pi$
$270$	2.20542	+	9.80551i	0.134217	+	0.596744i
$271$			8.12621i			0.493632i	0.969062	+	0.246816i	$0.0793844\pi$
$271$			8.12621i			0.493632i	−0.969062	+	0.246816i	$0.920616\pi$
$272$	0.392779	+	0.392779i	0.0238157	+	0.0238157i
$273$	0.854962	+	4.57656i	0.0517446	+	0.276986i
$274$		−	10.1151i		−	0.611074i
$275$	4.51849	−	2.14086i	0.272475	−	0.129099i
$276$			2.66100i			0.160173i
$277$	0.626744	−	0.626744i	0.0376574	−	0.0376574i	−0.688027	−	0.725685i	$-0.741523\pi$
$277$	0.626744	−	0.626744i	0.0376574	−	0.0376574i	0.725685	+	0.688027i	$0.241523\pi$
$278$	−2.56885	+	2.56885i	−0.154069	+	0.154069i
$279$	0.810351			0.0485144
$280$	2.19153	−	5.49520i	0.130969	−	0.328401i
$281$	−7.40067			−0.441487			−0.220743	−	0.975332i	$-0.570848\pi$
$281$	−7.40067			−0.441487			−0.220743	+	0.975332i	$0.570848\pi$
$282$	4.05993	−	4.05993i	0.241765	−	0.241765i
$283$	−7.77492	+	7.77492i	−0.462171	+	0.462171i	−0.899366	−	0.437196i	$-0.855972\pi$
$283$	−7.77492	+	7.77492i	−0.462171	+	0.462171i	0.437196	+	0.899366i	$0.355972\pi$
$284$			5.71174i			0.338929i
$285$	−9.01542	−	5.70464i	−0.534027	−	0.337914i
$286$		−	2.06463i		−	0.122084i
$287$	−4.81147	−	25.7555i	−0.284012	−	1.52030i
$288$	−1.60766	−	1.60766i	−0.0947322	−	0.0947322i
$289$		−	16.6914i		−	0.981850i
$290$	9.94375	−	15.7148i	0.583917	−	0.922803i
$291$	−3.34656			−0.196179
$292$	1.48454	+	1.48454i	0.0868761	+	0.0868761i
$293$	−15.7614	+	15.7614i	−0.920788	+	0.920788i	−0.997085	−	0.0762970i	$-0.975690\pi$
$293$	−15.7614	+	15.7614i	−0.920788	+	0.920788i	0.0762970	+	0.997085i	$0.475690\pi$
$294$	2.15394	+	5.56377i	0.125621	+	0.324486i
$295$	4.13553	+	18.3870i	0.240780	+	1.07053i
$296$	−5.12131			−0.297670
$297$	3.17824	+	3.17824i	0.184420	+	0.184420i
$298$	3.99328	+	3.99328i	0.231325	+	0.231325i
$299$	−6.44601			−0.372783
$300$	−4.01340	−	1.43293i	−0.231714	−	0.0827303i
$301$	11.6618	+	7.99046i	0.672172	+	0.460562i
$302$	8.46110	−	8.46110i	0.486882	−	0.486882i
$303$	8.39633	+	8.39633i	0.482357	+	0.482357i
$304$	5.59795			0.321065
$305$	4.82942	−	1.08621i	0.276532	−	0.0621964i
$306$		−	1.26291i		−	0.0721957i
$307$	14.8376	+	14.8376i	0.846828	+	0.846828i	0.989736	−	0.142908i	$-0.0456453\pi$
$307$	14.8376	+	14.8376i	0.846828	+	0.846828i	−0.142908	+	0.989736i	$0.545645\pi$
$308$	−0.485856	−	2.60076i	−0.0276842	−	0.148192i
$309$			2.89131i			0.164481i
$310$	−0.426155	+	0.673480i	−0.0242040	+	0.0382511i
$311$		−	17.9513i		−	1.01793i	−0.860788	−	0.508964i	$-0.830029\pi$
$311$		−	17.9513i		−	1.01793i	0.860788	−	0.508964i	$-0.169971\pi$
$312$	−1.24430	+	1.24430i	−0.0704444	+	0.0704444i
$313$	18.3300	−	18.3300i	1.03607	−	1.03607i	0.0367489	−	0.999325i	$-0.488300\pi$
$313$	18.3300	−	18.3300i	1.03607	−	1.03607i	0.999325	−	0.0367489i	$-0.0117002\pi$
$314$	4.93953			0.278754
$315$	−12.3576	+	5.31116i	−0.696274	+	0.299250i
$316$	−7.65896			−0.430850
$317$	−13.4787	+	13.4787i	−0.757041	+	0.757041i	−0.975783	−	0.218742i	$-0.929805\pi$
$317$	−13.4787	+	13.4787i	−0.757041	+	0.757041i	0.218742	+	0.975783i	$0.429805\pi$
$318$	6.97130	−	6.97130i	0.390931	−	0.390931i
$319$		−	8.31663i		−	0.465642i
$320$	2.18157	−	0.490670i	0.121953	−	0.0274293i
$321$			3.99557i			0.223011i
$322$	−8.11986	+	1.51690i	−0.452502	+	0.0845335i
$323$	2.19876	+	2.19876i	0.122342	+	0.122342i
$324$			2.98984i			0.166102i
$325$	3.47113	−	9.72208i	0.192544	−	0.539284i
$326$	−10.9343			−0.605594
$327$	−1.58760	−	1.58760i	−0.0877943	−	0.0877943i
$328$	7.00253	−	7.00253i	0.386650	−	0.386650i
$329$	14.7030	+	10.0743i	0.810601	+	0.555411i
$330$	−1.85937	+	0.418202i	−0.102355	+	0.0230212i
$331$	−26.2694			−1.44390			−0.721948	−	0.691947i	$-0.756753\pi$
$331$	−26.2694			−1.44390			−0.721948	+	0.691947i	$0.756753\pi$
$332$	5.51022	+	5.51022i	0.302412	+	0.302412i
$333$	8.23331	+	8.23331i	0.451183	+	0.451183i
$334$	5.41763			0.296440
$335$	2.35157	+	1.48799i	0.128480	+	0.0812977i
$336$	−1.27459	+	1.86022i	−0.0695348	+	0.101483i
$337$	23.9070	−	23.9070i	1.30230	−	1.30230i	0.375460	−	0.926839i	$-0.377485\pi$
$337$	23.9070	−	23.9070i	1.30230	−	1.30230i	0.926839	−	0.375460i	$-0.122515\pi$
$338$	6.17820	+	6.17820i	0.336050	+	0.336050i
$339$	6.84895			0.371984
$340$	1.04960	+	0.664150i	0.0569225	+	0.0360186i
$341$			0.356422i			0.0193013i
$342$	−8.99960	−	8.99960i	−0.486642	−	0.486642i
$343$	−15.7496	+	9.74423i	−0.850399	+	0.526139i
$344$			5.34314i			0.288083i
$345$	1.30567	+	5.80516i	0.0702950	+	0.312539i
$346$			20.3210i			1.09246i
$347$	−5.36355	+	5.36355i	−0.287930	+	0.287930i	−0.836261	−	0.548331i	$-0.815263\pi$
$347$	−5.36355	+	5.36355i	−0.287930	+	0.287930i	0.548331	+	0.836261i	$0.315263\pi$
$348$	−5.01221	+	5.01221i	−0.268682	+	0.268682i
$349$	−0.780667			−0.0417881			−0.0208941	−	0.999782i	$-0.506651\pi$
$349$	−0.780667			−0.0417881			−0.0208941	+	0.999782i	$0.506651\pi$
$350$	2.08465	−	13.0635i	0.111429	−	0.698272i
$351$	9.27991			0.495325
$352$	0.707107	−	0.707107i	0.0376889	−	0.0376889i
$353$	−11.4507	+	11.4507i	−0.609459	+	0.609459i	−0.942805	−	0.333346i	$-0.891822\pi$
$353$	−11.4507	+	11.4507i	−0.609459	+	0.609459i	0.333346	+	0.942805i	$0.391822\pi$
$354$		−	7.18354i		−	0.381801i
$355$	2.80258	+	12.4606i	0.148745	+	0.661338i
$356$		−	12.1104i		−	0.641850i
$357$	−1.23129	+	0.230021i	−0.0651667	+	0.0121740i
$358$	6.00078	+	6.00078i	0.317151	+	0.317151i
$359$			33.3997i			1.76277i	0.472400	+	0.881384i	$0.343388\pi$
$359$			33.3997i			1.76277i	−0.472400	+	0.881384i	$0.656612\pi$
$360$	−4.29605	−	2.71839i	−0.226422	−	0.143272i
$361$	12.3371			0.649321
$362$	−0.193131	−	0.193131i	−0.0101507	−	0.0101507i
$363$	−0.602672	+	0.602672i	−0.0316321	+	0.0316321i
$364$	−4.50619	−	3.08758i	−0.236189	−	0.161833i
$365$	3.96704	+	2.51021i	0.207644	+	0.131390i
$366$	−1.88678			−0.0986237
$367$	15.0446	+	15.0446i	0.785323	+	0.785323i	0.980723	−	0.195401i	$-0.0626008\pi$
$367$	15.0446	+	15.0446i	0.785323	+	0.785323i	−0.195401	+	0.980723i	$0.562601\pi$
$368$	−2.20767	−	2.20767i	−0.115083	−	0.115083i
$369$	−22.5153			−1.17210
$370$	−11.1725	+	2.51287i	−0.580830	+	0.130638i
$371$	25.2464	+	17.2985i	1.31073	+	0.898092i
$372$	0.214806	−	0.214806i	0.0111372	−	0.0111372i
$373$	13.0079	+	13.0079i	0.673523	+	0.673523i	0.958527	−	0.285003i	$-0.0919947\pi$
$373$	13.0079	+	13.0079i	0.673523	+	0.673523i	−0.285003	+	0.958527i	$0.591995\pi$
$374$	0.555473			0.0287229
$375$	−9.45861	−	1.15678i	−0.488441	−	0.0597358i
$376$			6.73655i			0.347411i
$377$	−12.1416	−	12.1416i	−0.625323	−	0.625323i
$378$	11.6896	−	2.18378i	0.601250	−	0.112322i
$379$			2.30622i			0.118462i	0.998244	+	0.0592312i	$0.0188649\pi$
$379$			2.30622i			0.118462i	−0.998244	+	0.0592312i	$0.981135\pi$
$380$	12.2123	−	2.74675i	0.626479	−	0.140905i
$381$			11.3203i			0.579956i
$382$	−3.47582	+	3.47582i	−0.177838	+	0.177838i
$383$	−5.99363	+	5.99363i	−0.306260	+	0.306260i	−0.843457	−	0.537197i	$-0.819483\pi$
$383$	−5.99363	+	5.99363i	−0.306260	+	0.306260i	0.537197	+	0.843457i	$0.319483\pi$
$384$	−0.852308			−0.0434941
$385$	−2.33604	−	5.43534i	−0.119056	−	0.277011i
$386$	−2.15187			−0.109527
$387$	8.58994	−	8.58994i	0.436651	−	0.436651i
$388$	2.77643	−	2.77643i	0.140952	−	0.140952i
$389$		−	16.9416i		−	0.858971i	−0.903074	−	0.429486i	$-0.858695\pi$
$389$		−	16.9416i		−	0.858971i	0.903074	−	0.429486i	$-0.141305\pi$
$390$	−2.10398	+	3.32506i	−0.106539	+	0.168371i
$391$		−	1.73425i		−	0.0877049i
$392$	−6.40291	−	2.82892i	−0.323396	−	0.142882i
$393$	3.07174	+	3.07174i	0.154949	+	0.154949i
$394$		−	11.0093i		−	0.554642i
$395$	−16.7085	+	3.75802i	−0.840698	+	0.189086i
$396$	−2.27357			−0.114251
$397$	6.25698	+	6.25698i	0.314029	+	0.314029i	0.846468	−	0.532439i	$-0.178725\pi$
$397$	6.25698	+	6.25698i	0.314029	+	0.314029i	−0.532439	+	0.846468i	$0.678725\pi$
$398$	0.999678	−	0.999678i	0.0501093	−	0.0501093i
$399$	−7.13511	+	10.4134i	−0.357202	+	0.521323i
$400$	4.51849	−	2.14086i	0.225924	−	0.107043i
$401$	−5.72675			−0.285980			−0.142990	−	0.989724i	$-0.545672\pi$
$401$	−5.72675			−0.285980			−0.142990	+	0.989724i	$0.545672\pi$
$402$	−0.750031	−	0.750031i	−0.0374081	−	0.0374081i
$403$	0.520346	+	0.520346i	0.0259203	+	0.0259203i
$404$	−13.9318			−0.693134
$405$	1.46703	+	6.52255i	0.0728971	+	0.324108i
$406$	−18.1516	−	12.4372i	−0.900849	−	0.617248i
$407$	−3.62131	+	3.62131i	−0.179502	+	0.179502i
$408$	−0.334769	−	0.334769i	−0.0165735	−	0.0165735i
$409$	37.7563			1.86693			0.933466	−	0.358667i	$-0.116769\pi$
$409$	37.7563			1.86693			0.933466	+	0.358667i	$0.116769\pi$
$410$	11.8406	−	18.7124i	0.584764	−	0.924141i
$411$			8.62115i			0.425250i
$412$	−2.39874	−	2.39874i	−0.118178	−	0.118178i
$413$	21.9201	−	4.09496i	1.07862	−	0.201500i
$414$			7.09835i			0.348865i
$415$	14.7246	+	9.31722i	0.722803	+	0.457364i
$416$		−	2.06463i		−	0.101227i
$417$	2.18945	−	2.18945i	0.107218	−	0.107218i
$418$	3.95835	−	3.95835i	0.193609	−	0.193609i
$419$	−8.75815			−0.427864			−0.213932	−	0.976849i	$-0.568627\pi$
$419$	−8.75815			−0.427864			−0.213932	+	0.976849i	$0.568627\pi$
$420$	−1.86786	+	4.68360i	−0.0911423	+	0.228536i
$421$	36.4605			1.77698			0.888488	−	0.458900i	$-0.151756\pi$
$421$	36.4605			1.77698			0.888488	+	0.458900i	$0.151756\pi$
$422$	−5.90711	+	5.90711i	−0.287554	+	0.287554i
$423$	10.8301	−	10.8301i	0.526576	−	0.526576i
$424$			11.5673i			0.561758i
$425$	2.61565	+	0.933882i	0.126878	+	0.0452999i
$426$		−	4.86816i		−	0.235863i
$427$	−1.07556	−	5.75739i	−0.0520499	−	0.278620i
$428$	−3.31488	−	3.31488i	−0.160231	−	0.160231i
$429$			1.75970i			0.0849592i
$430$	2.62172	+	11.6564i	0.126430	+	0.562123i
$431$	23.8020			1.14650			0.573252	−	0.819379i	$-0.305682\pi$
$431$	23.8020			1.14650			0.573252	+	0.819379i	$0.305682\pi$
$432$	3.17824	+	3.17824i	0.152913	+	0.152913i
$433$	−20.7311	+	20.7311i	−0.996274	+	0.996274i	−0.999993	−	0.00371909i	$-0.998816\pi$
$433$	−20.7311	+	20.7311i	−0.996274	+	0.996274i	0.00371909	+	0.999993i	$0.498816\pi$
$434$	0.777915	+	0.533015i	0.0373411	+	0.0255856i
$435$	−8.47514	+	13.3938i	−0.406352	+	0.642184i
$436$	2.63426			0.126158
$437$	−12.3584	−	12.3584i	−0.591183	−	0.591183i
$438$	−1.26528	−	1.26528i	−0.0604576	−	0.0604576i
$439$	−24.3629			−1.16278			−0.581390	−	0.813625i	$-0.697491\pi$
$439$	−24.3629			−1.16278			−0.581390	+	0.813625i	$0.697491\pi$
$440$	1.19565	−	1.88956i	0.0570002	−	0.0900811i
$441$	5.74575	+	14.8416i	0.273607	+	0.706744i
$442$	0.810944	−	0.810944i	0.0385727	−	0.0385727i
$443$	8.38458	+	8.38458i	0.398363	+	0.398363i	0.877655	−	0.479292i	$-0.159107\pi$
$443$	8.38458	+	8.38458i	0.398363	+	0.398363i	−0.479292	+	0.877655i	$0.659107\pi$
$444$	4.36493			0.207150
$445$	−5.94220	−	26.4197i	−0.281688	−	1.25241i
$446$			29.3550i			1.39000i
$447$	−3.40351	−	3.40351i	−0.160980	−	0.160980i
$448$	−0.485856	−	2.60076i	−0.0229546	−	0.122874i
$449$			13.5424i			0.639106i	0.947568	+	0.319553i	$0.103533\pi$
$449$			13.5424i			0.639106i	−0.947568	+	0.319553i	$0.896467\pi$
$450$	−10.7060	−	3.82241i	−0.504683	−	0.180190i
$451$		−	9.90307i		−	0.466317i
$452$	−5.68215	+	5.68215i	−0.267266	+	0.267266i
$453$	−7.21146	+	7.21146i	−0.338824	+	0.338824i
$454$	−28.8942			−1.35607
$455$	−11.3456	−	4.52471i	−0.531888	−	0.212122i
$456$	−4.77118			−0.223431
$457$	−14.1168	+	14.1168i	−0.660357	+	0.660357i	−0.955464	−	0.295107i	$-0.904645\pi$
$457$	−14.1168	+	14.1168i	−0.660357	+	0.660357i	0.295107	+	0.955464i	$0.404645\pi$
$458$	−1.55917	+	1.55917i	−0.0728550	+	0.0728550i
$459$			2.49669i			0.116535i
$460$	−5.89941	−	3.73294i	−0.275062	−	0.174049i
$461$			17.4866i			0.814432i	0.913332	+	0.407216i	$0.133500\pi$
$461$			17.4866i			0.814432i	−0.913332	+	0.407216i	$0.866500\pi$
$462$	0.414099	+	2.21665i	0.0192656	+	0.103128i
$463$	−15.5767	−	15.5767i	−0.723912	−	0.723912i	0.245487	−	0.969400i	$-0.421052\pi$
$463$	−15.5767	−	15.5767i	−0.723912	−	0.723912i	−0.969400	+	0.245487i	$0.921052\pi$
$464$		−	8.31663i		−	0.386090i
$465$	0.363215	−	0.574012i	0.0168437	−	0.0266192i
$466$	−27.2457			−1.26213
$467$	−12.9917	−	12.9917i	−0.601186	−	0.601186i	0.339441	−	0.940627i	$-0.389762\pi$
$467$	−12.9917	−	12.9917i	−0.601186	−	0.601186i	−0.940627	+	0.339441i	$0.889762\pi$
$468$	−3.31922	+	3.31922i	−0.153431	+	0.153431i
$469$	1.86111	−	2.71622i	0.0859383	−	0.125423i
$470$	3.30542	+	14.6962i	0.152468	+	0.677887i
$471$	−4.21000			−0.193986
$472$	5.95974	+	5.95974i	0.274319	+	0.274319i
$473$	3.77817	+	3.77817i	0.173720	+	0.173720i
$474$	6.52779			0.299831
$475$	25.2943	−	11.9844i	1.16058	−	0.549884i
$476$	0.830689	−	1.21236i	0.0380746	−	0.0555683i
$477$	18.5963	−	18.5963i	0.851465	−	0.851465i
$478$	20.4132	+	20.4132i	0.933680	+	0.933680i
$479$	−38.4730			−1.75788			−0.878939	−	0.476935i	$-0.841748\pi$
$479$	−38.4730			−1.75788			−0.878939	+	0.476935i	$0.841748\pi$
$480$	−1.85937	+	0.418202i	−0.0848681	+	0.0190882i
$481$			10.5736i			0.482115i
$482$	18.4979	+	18.4979i	0.842558	+	0.842558i
$483$	6.92062	−	1.29286i	0.314899	−	0.0588274i
$484$		−	1.00000i		−	0.0454545i
$485$	4.69466	−	7.41929i	0.213174	−	0.336892i
$486$		−	16.0324i		−	0.727244i
$487$	−16.7323	+	16.7323i	−0.758213	+	0.758213i	−0.975997	−	0.217784i	$-0.930117\pi$
$487$	−16.7323	+	16.7323i	−0.758213	+	0.758213i	0.217784	+	0.975997i	$0.430117\pi$
$488$	1.56535	−	1.56535i	0.0708599	−	0.0708599i
$489$	9.31937			0.421437
$490$	−15.3564	−	3.02977i	−0.693734	−	0.136871i
$491$	−30.4024			−1.37204			−0.686020	−	0.727583i	$-0.740644\pi$
$491$	−30.4024			−1.37204			−0.686020	+	0.727583i	$0.740644\pi$
$492$	−5.96831	+	5.96831i	−0.269072	+	0.269072i
$493$	3.26660	−	3.26660i	0.147120	−	0.147120i
$494$		−	11.5577i		−	0.520006i
$495$	−4.95995	+	1.11557i	−0.222933	+	0.0501413i
$496$			0.356422i			0.0160038i
$497$	14.8549	−	2.77509i	0.666331	−	0.124480i
$498$	−4.69640	−	4.69640i	−0.210451	−	0.210451i
$499$		−	20.0174i		−	0.896101i	−0.894008	−	0.448050i	$-0.852119\pi$
$499$		−	20.0174i		−	0.896101i	0.894008	−	0.448050i	$-0.147881\pi$
$500$	8.80693	−	6.88752i	0.393858	−	0.308019i
$501$	−4.61749			−0.206294
$502$	6.49593	+	6.49593i	0.289928	+	0.289928i
$503$	−12.1188	+	12.1188i	−0.540352	+	0.540352i	−0.923632	−	0.383280i	$-0.874794\pi$
$503$	−12.1188	+	12.1188i	−0.540352	+	0.540352i	0.383280	+	0.923632i	$0.374794\pi$
$504$	−3.40004	+	4.96222i	−0.151450	+	0.221035i
$505$	−30.3932	+	6.83593i	−1.35248	+	0.304195i
$506$	−3.12211			−0.138795
$507$	−5.26573	−	5.26573i	−0.233859	−	0.233859i
$508$	−9.39175	−	9.39175i	−0.416691	−	0.416691i
$509$	−18.9108			−0.838204			−0.419102	−	0.907939i	$-0.637655\pi$
$509$	−18.9108			−0.838204			−0.419102	+	0.907939i	$0.637655\pi$
$510$	−0.894582	−	0.566060i	−0.0396127	−	0.0250656i
$511$	3.13965	−	4.58220i	0.138890	−	0.202705i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	17.7916	+	17.7916i	0.785519	+	0.785519i
$514$	−23.1863			−1.02271
$515$	−6.41001	−	4.05603i	−0.282459	−	0.178730i
$516$		−	4.55400i		−	0.200479i
$517$	4.76346	+	4.76346i	0.209497	+	0.209497i
$518$	2.48822	+	13.3193i	0.109326	+	0.585216i
$519$		−	17.3197i		−	0.760253i
$520$	−1.01305	−	4.50414i	−0.0444253	−	0.197519i
$521$		−	42.9916i		−	1.88349i	−0.336322	−	0.941747i	$-0.609183\pi$
$521$		−	42.9916i		−	1.88349i	0.336322	−	0.941747i	$-0.390817\pi$
$522$	−13.3703	+	13.3703i	−0.585202	+	0.585202i
$523$	2.18542	−	2.18542i	0.0955616	−	0.0955616i	−0.657710	−	0.753271i	$-0.728475\pi$
$523$	2.18542	−	2.18542i	0.0955616	−	0.0955616i	0.753271	+	0.657710i	$0.228475\pi$
$524$	−5.09686			−0.222658
$525$	−1.77677	+	11.1341i	−0.0775445	+	0.485932i
$526$	30.7860			1.34233
$527$	−0.139995	+	0.139995i	−0.00609828	+	0.00609828i
$528$	−0.602672	+	0.602672i	−0.0262280	+	0.0262280i
$529$		−	13.2524i		−	0.576192i
$530$	5.67573	+	25.2349i	0.246538	+	1.09613i
$531$		−	19.1624i		−	0.831579i
$532$	−2.71980	−	14.5589i	−0.117918	−	0.631210i
$533$	−14.4576	−	14.4576i	−0.626230	−	0.626230i
$534$			10.3218i			0.446667i
$535$	−8.85814	−	5.60512i	−0.382971	−	0.242330i
$536$	1.24451			0.0537546
$537$	−5.11451	−	5.11451i	−0.220707	−	0.220707i
$538$	21.3596	−	21.3596i	0.920876	−	0.920876i
$539$	−6.52789	+	2.52719i	−0.281176	+	0.108854i
$540$	8.49301	+	5.37408i	0.365481	+	0.231263i
$541$	−36.1401			−1.55378			−0.776891	−	0.629635i	$-0.783205\pi$
$541$	−36.1401			−1.55378			−0.776891	+	0.629635i	$0.783205\pi$
$542$	5.74610	+	5.74610i	0.246816	+	0.246816i
$543$	0.164607	+	0.164607i	0.00706395	+	0.00706395i
$544$	0.555473			0.0238157
$545$	5.74682	−	1.29255i	0.246167	−	0.0553669i
$546$	3.84066	+	2.63156i	0.164365	+	0.112621i
$547$	21.5240	−	21.5240i	0.920301	−	0.920301i	−0.0767496	−	0.997050i	$-0.524454\pi$
$547$	21.5240	−	21.5240i	0.920301	−	0.920301i	0.997050	+	0.0767496i	$0.0244542\pi$
$548$	−7.15243	−	7.15243i	−0.305537	−	0.305537i
$549$	−5.03309			−0.214807
$550$	1.68124	−	4.70887i	0.0716881	−	0.200787i
$551$		−	46.5561i		−	1.98336i
$552$	1.88161	+	1.88161i	0.0800867	+	0.0800867i
$553$	3.72115	+	19.9191i	0.158240	+	0.847046i
$554$		−	0.886350i		−	0.0376574i
$555$	9.52239	−	2.14174i	0.404203	−	0.0909117i
$556$			3.63290i			0.154069i
$557$	9.89775	−	9.89775i	0.419381	−	0.419381i	−0.465609	−	0.884990i	$-0.654165\pi$
$557$	9.89775	−	9.89775i	0.419381	−	0.419381i	0.884990	+	0.465609i	$0.154165\pi$
$558$	0.573005	−	0.573005i	0.0242572	−	0.0242572i
$559$	11.0316			0.466588
$560$	−2.33604	−	5.43534i	−0.0987158	−	0.229685i
$561$	−0.473434			−0.0199884
$562$	−5.23306	+	5.23306i	−0.220743	+	0.220743i
$563$	18.4342	−	18.4342i	0.776910	−	0.776910i	−0.202394	−	0.979304i	$-0.564872\pi$
$563$	18.4342	−	18.4342i	0.776910	−	0.776910i	0.979304	+	0.202394i	$0.0648721\pi$
$564$		−	5.74161i		−	0.241765i
$565$	−9.60794	+	15.1840i	−0.404209	+	0.638798i
$566$			10.9954i			0.462171i
$567$	7.77586	−	1.45263i	0.326556	−	0.0610049i
$568$	4.03881	+	4.03881i	0.169465	+	0.169465i
$569$			33.7151i			1.41341i	0.707507	+	0.706706i	$0.249820\pi$
$569$			33.7151i			1.41341i	−0.707507	+	0.706706i	$0.750180\pi$
$570$	−10.4087	+	2.34107i	−0.435971	+	0.0980568i
$571$	−17.0245			−0.712454			−0.356227	−	0.934399i	$-0.615937\pi$
$571$	−17.0245			−0.712454			−0.356227	+	0.934399i	$0.615937\pi$
$572$	−1.45991	−	1.45991i	−0.0610421	−	0.0610421i
$573$	2.96246	−	2.96246i	0.123759	−	0.123759i
$574$	−21.6141	−	14.8097i	−0.902155	−	0.618143i
$575$	−14.7016	−	5.24901i	−0.613100	−	0.218899i
$576$	−2.27357			−0.0947322
$577$	7.46843	+	7.46843i	0.310915	+	0.310915i	0.845264	−	0.534349i	$-0.179443\pi$
$577$	7.46843	+	7.46843i	0.310915	+	0.310915i	−0.534349	+	0.845264i	$0.679443\pi$
$578$	−11.8026	−	11.8026i	−0.490925	−	0.490925i
$579$	1.83405			0.0762206
$580$	−4.08072	−	18.1433i	−0.169443	−	0.753360i
$581$	11.6536	−	17.0079i	0.483471	−	0.705607i
$582$	−2.36637	+	2.36637i	−0.0980893	+	0.0980893i
$583$	8.17933	+	8.17933i	0.338753	+	0.338753i
$584$	2.09946			0.0868761
$585$	−5.61247	+	8.86975i	−0.232047	+	0.366719i
$586$			22.2899i			0.920788i
$587$	13.3244	+	13.3244i	0.549959	+	0.549959i	0.926429	−	0.376470i	$-0.122862\pi$
$587$	13.3244	+	13.3244i	0.549959	+	0.549959i	−0.376470	+	0.926429i	$0.622862\pi$
$588$	5.45725	+	2.41111i	0.225053	+	0.0994325i
$589$			1.99523i			0.0822122i
$590$	15.9258	+	10.0773i	0.655657	+	0.414877i
$591$			9.38334i			0.385979i
$592$	−3.62131	+	3.62131i	−0.148835	+	0.148835i
$593$	0.165153	−	0.165153i	0.00678202	−	0.00678202i	−0.703708	−	0.710490i	$-0.748474\pi$
$593$	0.165153	−	0.165153i	0.00678202	−	0.00678202i	0.710490	+	0.703708i	$0.248474\pi$
$594$	4.49471			0.184420
$595$	1.21734	−	3.05244i	0.0499060	−	0.125138i
$596$	5.64736			0.231325
$597$	−0.852033	+	0.852033i	−0.0348714	+	0.0348714i
$598$	−4.55802	+	4.55802i	−0.186391	+	0.186391i
$599$			19.5296i			0.797960i	0.916960	+	0.398980i	$0.130636\pi$
$599$			19.5296i			0.797960i	−0.916960	+	0.398980i	$0.869364\pi$
$600$	−3.85114	+	1.82467i	−0.157222	+	0.0744919i
$601$			31.5171i			1.28561i	0.766030	+	0.642805i	$0.222229\pi$
$601$			31.5171i			1.28561i	−0.766030	+	0.642805i	$0.777771\pi$
$602$	13.8962	−	2.59600i	0.566367	−	0.105805i
$603$	−2.00074	−	2.00074i	−0.0814766	−	0.0814766i
$604$		−	11.9658i		−	0.486882i
$605$	−0.490670	−	2.18157i	−0.0199486	−	0.0886934i
$606$	11.8742			0.482357
$607$	7.21146	+	7.21146i	0.292704	+	0.292704i	0.838148	−	0.545443i	$-0.183639\pi$
$607$	7.21146	+	7.21146i	0.292704	+	0.292704i	−0.545443	+	0.838148i	$0.683639\pi$
$608$	3.95835	−	3.95835i	0.160532	−	0.160532i
$609$	15.4708	+	10.6003i	0.626906	+	0.429547i
$610$	2.64684	−	4.18298i	0.107168	−	0.169364i
$611$	13.9085			0.562677
$612$	−0.893011	−	0.893011i	−0.0360978	−	0.0360978i
$613$	21.7136	+	21.7136i	0.877004	+	0.877004i	0.993224	−	0.116220i	$-0.0370777\pi$
$613$	21.7136	+	21.7136i	0.877004	+	0.877004i	−0.116220	+	0.993224i	$0.537078\pi$
$614$	20.9836			0.846828
$615$	−10.0918	+	15.9487i	−0.406941	+	0.643115i
$616$	−2.18257	−	1.49546i	−0.0879381	−	0.0602539i
$617$	−31.8200	+	31.8200i	−1.28102	+	1.28102i	−0.340938	+	0.940086i	$0.610745\pi$
$617$	−31.8200	+	31.8200i	−1.28102	+	1.28102i	−0.940086	+	0.340938i	$0.889255\pi$
$618$	2.04447	+	2.04447i	0.0822405	+	0.0822405i
$619$	18.1326			0.728811			0.364405	−	0.931240i	$-0.381272\pi$
$619$	18.1326			0.728811			0.364405	+	0.931240i	$0.381272\pi$
$620$	0.174885	+	0.777559i	0.00702357	+	0.0312275i
$621$		−	14.0330i		−	0.563124i
$622$	−12.6935	−	12.6935i	−0.508964	−	0.508964i
$623$	−31.4962	+	5.88391i	−1.26187	+	0.235734i
$624$			1.75970i			0.0704444i
$625$	15.8334	−	19.3469i	0.633338	−	0.773876i
$626$		−	25.9225i		−	1.03607i
$627$	−3.37373	+	3.37373i	−0.134734	+	0.134734i
$628$	3.49278	−	3.49278i	0.139377	−	0.139377i
$629$	−2.84475			−0.113428
$630$	−4.98261	+	12.4937i	−0.198512	+	0.497762i
$631$	27.6725			1.10162			0.550812	−	0.834630i	$-0.314318\pi$
$631$	27.6725			1.10162			0.550812	+	0.834630i	$0.314318\pi$
$632$	−5.41570	+	5.41570i	−0.215425	+	0.215425i
$633$	5.03468	−	5.03468i	0.200110	−	0.200110i
$634$			19.0618i			0.757041i
$635$	−25.0970	−	15.8805i	−0.995944	−	0.630198i
$636$		−	9.85891i		−	0.390931i
$637$	−5.84068	+	13.2196i	−0.231416	+	0.523781i
$638$	−5.88075	−	5.88075i	−0.232821	−	0.232821i
$639$		−	12.9861i		−	0.513720i
$640$	1.19565	−	1.88956i	0.0472621	−	0.0746913i
$641$	−42.4456			−1.67650			−0.838250	−	0.545285i	$-0.816421\pi$
$641$	−42.4456			−1.67650			−0.838250	+	0.545285i	$0.816421\pi$
$642$	2.82529	+	2.82529i	0.111505	+	0.111505i
$643$	29.2552	−	29.2552i	1.15371	−	1.15371i	0.167908	−	0.985803i	$-0.446299\pi$
$643$	29.2552	−	29.2552i	1.15371	−	1.15371i	0.985803	−	0.167908i	$-0.0537012\pi$
$644$	−4.66900	+	6.81422i	−0.183984	+	0.268518i
$645$	−2.23451	−	9.93486i	−0.0879837	−	0.391185i
$646$	3.10952			0.122342
$647$	23.3040	+	23.3040i	0.916175	+	0.916175i	0.996749	−	0.0805732i	$-0.0256751\pi$
$647$	23.3040	+	23.3040i	0.916175	+	0.916175i	−0.0805732	+	0.996749i	$0.525675\pi$
$648$	2.11414	+	2.11414i	0.0830512	+	0.0830512i
$649$	8.42834			0.330841
$650$	−4.42009	−	9.32901i	−0.173370	−	0.365914i
$651$	−0.663022	−	0.454293i	−0.0259859	−	0.0178051i
$652$	−7.73170	+	7.73170i	−0.302797	+	0.302797i
$653$	−29.9842	−	29.9842i	−1.17337	−	1.17337i	−0.981400	−	0.191973i	$-0.938512\pi$
$653$	−29.9842	−	29.9842i	−1.17337	−	1.17337i	−0.191973	−	0.981400i	$-0.561488\pi$
$654$	−2.24520			−0.0877943
$655$	−11.1192	+	2.50088i	−0.434461	+	0.0977173i
$656$		−	9.90307i		−	0.386650i
$657$	−3.37521	−	3.37521i	−0.131679	−	0.131679i
$658$	17.5201	−	3.27300i	0.683006	−	0.127595i
$659$			13.1845i			0.513595i	0.966465	+	0.256797i	$0.0826673\pi$
$659$			13.1845i			0.513595i	−0.966465	+	0.256797i	$0.917333\pi$
$660$	−1.01906	+	1.61048i	−0.0396668	+	0.0626880i
$661$		−	4.36456i		−	0.169762i	−0.996391	−	0.0848808i	$-0.972949\pi$
$661$		−	4.36456i		−	0.169762i	0.996391	−	0.0848808i	$-0.0270509\pi$
$662$	−18.5753	+	18.5753i	−0.721948	+	0.721948i
$663$	−0.691174	+	0.691174i	−0.0268430	+	0.0268430i
$664$	7.79262			0.302412
$665$	−13.0771	−	30.4268i	−0.507107	−	1.17990i
$666$	11.6437			0.451183
$667$	−18.3604	+	18.3604i	−0.710916	+	0.710916i
$668$	3.83084	−	3.83084i	0.148220	−	0.148220i
$669$		−	25.0194i		−	0.967308i
$670$	2.71498	−	0.610643i	0.104889	−	0.0235912i
$671$		−	2.21373i		−	0.0854603i
$672$	0.414099	+	2.21665i	0.0159742	+	0.0855090i
$673$	7.23186	+	7.23186i	0.278768	+	0.278768i	0.832617	−	0.553849i	$-0.186842\pi$
$673$	7.23186	+	7.23186i	0.278768	+	0.278768i	−0.553849	+	0.832617i	$0.686842\pi$
$674$		−	33.8096i		−	1.30230i
$675$	21.1650	+	7.55666i	0.814640	+	0.290856i
$676$	8.73730			0.336050
$677$	−0.644048	−	0.644048i	−0.0247528	−	0.0247528i	0.694622	−	0.719375i	$-0.255572\pi$
$677$	−0.644048	−	0.644048i	−0.0247528	−	0.0247528i	−0.719375	+	0.694622i	$0.755572\pi$
$678$	4.84294	−	4.84294i	0.185992	−	0.185992i
$679$	−8.56977	−	5.87188i	−0.328878	−	0.225342i
$680$	1.21180	−	0.272554i	0.0464706	−	0.0104520i
$681$	24.6267			0.943698
$682$	0.252028	+	0.252028i	0.00965067	+	0.00965067i
$683$	−1.63779	−	1.63779i	−0.0626682	−	0.0626682i	0.675078	−	0.737746i	$-0.264110\pi$
$683$	−1.63779	−	1.63779i	−0.0626682	−	0.0626682i	−0.737746	+	0.675078i	$0.764110\pi$
$684$	−12.7274			−0.486642
$685$	−19.1130	−	12.0940i	−0.730271	−	0.462090i
$686$	−4.24645	+	18.0269i	−0.162130	+	0.688269i
$687$	1.32889	−	1.32889i	0.0507003	−	0.0507003i
$688$	3.77817	+	3.77817i	0.144041	+	0.144041i
$689$	23.8822			0.909841
$690$	5.02812	+	3.18162i	0.191417	+	0.121122i
$691$		−	36.2278i		−	1.37817i	−0.724680	−	0.689086i	$-0.758012\pi$
$691$		−	36.2278i		−	1.37817i	0.724680	−	0.689086i	$-0.241988\pi$
$692$	14.3691	+	14.3691i	0.546232	+	0.546232i
$693$	1.10463	+	5.91301i	0.0419614	+	0.224617i
$694$			7.58520i			0.287930i
$695$	1.78256	+	7.92543i	0.0676162	+	0.300629i
$696$			7.08833i			0.268682i
$697$	3.88972	−	3.88972i	0.147334	−	0.147334i
$698$	−0.552015	+	0.552015i	−0.0208941	+	0.0208941i
$699$	23.2217			0.878326
$700$	−7.76319	−	10.7113i	−0.293421	−	0.404851i
$701$	−12.0121			−0.453690			−0.226845	−	0.973931i	$-0.572841\pi$
$701$	−12.0121			−0.453690			−0.226845	+	0.973931i	$0.572841\pi$
$702$	6.56189	−	6.56189i	0.247662	−	0.247662i
$703$	−20.2719	+	20.2719i	−0.764570	+	0.764570i
$704$		−	1.00000i		−	0.0376889i
$705$	−2.81724	−	12.5257i	−0.106103	−	0.471746i
$706$			16.1937i			0.609459i
$707$	6.76887	+	36.2333i	0.254569	+	1.36269i
$708$	−5.07953	−	5.07953i	−0.190900	−	0.190900i
$709$			2.52540i			0.0948435i	0.998875	+	0.0474217i	$0.0151005\pi$
$709$			2.52540i			0.0948435i	−0.998875	+	0.0474217i	$0.984900\pi$
$710$	10.7927	+	6.82922i	0.405042	+	0.256296i
$711$	17.4132			0.653046
$712$	−8.56334	−	8.56334i	−0.320925	−	0.320925i
$713$	0.786861	−	0.786861i	0.0294682	−	0.0294682i
$714$	−0.708003	+	1.03330i	−0.0264963	+	0.0386703i
$715$	−3.90124	−	2.46857i	−0.145898	−	0.0923192i
$716$	8.48638			0.317151
$717$	−17.3984	−	17.3984i	−0.649753	−	0.649753i
$718$	23.6171	+	23.6171i	0.881384	+	0.881384i
$719$	26.3654			0.983263			0.491631	−	0.870803i	$-0.336401\pi$
$719$	26.3654			0.983263			0.491631	+	0.870803i	$0.336401\pi$
$720$	−4.95995	+	1.11557i	−0.184847	+	0.0415749i
$721$	−5.07310	+	7.40399i	−0.188932	+	0.275739i
$722$	8.72364	−	8.72364i	0.324660	−	0.324660i
$723$	−15.7659	−	15.7659i	−0.586341	−	0.586341i
$724$	−0.273128			−0.0101507
$725$	−17.8047	−	37.5786i	−0.661252	−	1.39563i
$726$			0.852308i			0.0316321i
$727$	8.34531	+	8.34531i	0.309510	+	0.309510i	0.844720	−	0.535209i	$-0.179767\pi$
$727$	8.34531	+	8.34531i	0.309510	+	0.309510i	−0.535209	+	0.844720i	$0.679767\pi$
$728$	−5.36961	+	1.00311i	−0.199011	+	0.0371779i
$729$			4.69499i			0.173888i
$730$	4.58011	−	1.03014i	0.169517	−	0.0381272i
$731$			2.96797i			0.109774i
$732$	−1.33416	+	1.33416i	−0.0493119	+	0.0493119i
$733$	28.2803	−	28.2803i	1.04456	−	1.04456i	0.0455952	−	0.998960i	$-0.485482\pi$
$733$	28.2803	−	28.2803i	1.04456	−	1.04456i	0.998960	−	0.0455952i	$-0.0145184\pi$
$734$	21.2763			0.785323
$735$	13.0884	+	2.58230i	0.482773	+	0.0952495i
$736$	−3.12211			−0.115083
$737$	0.880000	−	0.880000i	0.0324152	−	0.0324152i
$738$	−15.9207	+	15.9207i	−0.586051	+	0.586051i
$739$		−	31.3041i		−	1.15154i	−0.817612	−	0.575770i	$-0.804702\pi$
$739$		−	31.3041i		−	1.15154i	0.817612	−	0.575770i	$-0.195298\pi$
$740$	−6.12327	+	9.67701i	−0.225096	+	0.355734i
$741$			9.85073i			0.361875i
$742$	30.0838	−	5.62005i	1.10441	−	0.206319i
$743$	−23.4067	−	23.4067i	−0.858709	−	0.858709i	0.132477	−	0.991186i	$-0.457707\pi$
$743$	−23.4067	−	23.4067i	−0.858709	−	0.858709i	−0.991186	+	0.132477i	$0.957707\pi$
$744$		−	0.303781i		−	0.0111372i
$745$	12.3201	−	2.77099i	0.451373	−	0.101521i
$746$	18.3959			0.673523
$747$	−12.5279	−	12.5279i	−0.458371	−	0.458371i
$748$	0.392779	−	0.392779i	0.0143614	−	0.0143614i
$749$	−7.01064	+	10.2317i	−0.256163	+	0.373860i
$750$	−7.50622	+	5.87028i	−0.274088	+	0.214352i
$751$	51.4924			1.87898			0.939492	−	0.342572i	$-0.111298\pi$
$751$	51.4924			1.87898			0.939492	+	0.342572i	$0.111298\pi$
$752$	4.76346	+	4.76346i	0.173706	+	0.173706i
$753$	−5.53653	−	5.53653i	−0.201763	−	0.201763i
$754$	−17.1708			−0.625323
$755$	−5.87126	−	26.1042i	−0.213677	−	0.950030i
$756$	6.72166	−	9.80999i	0.244464	−	0.356786i
$757$	6.80621	−	6.80621i	0.247376	−	0.247376i	−0.572517	−	0.819893i	$-0.694033\pi$
$757$	6.80621	−	6.80621i	0.247376	−	0.247376i	0.819893	+	0.572517i	$0.194033\pi$
$758$	1.63074	+	1.63074i	0.0592312	+	0.0592312i
$759$	2.66100			0.0965882
$760$	6.69317	−	10.5777i	0.242787	−	0.383692i
$761$			3.62385i			0.131364i	0.997841	+	0.0656822i	$0.0209223\pi$
$761$			3.62385i			0.131364i	−0.997841	+	0.0656822i	$0.979078\pi$
$762$	8.00466	+	8.00466i	0.289978	+	0.289978i
$763$	−1.27987	−	6.85108i	−0.0463345	−	0.248026i
$764$			4.91555i			0.177838i
$765$	−2.38634	−	1.50999i	−0.0862783	−	0.0545939i
$766$			8.47627i			0.306260i
$767$	12.3047	−	12.3047i	0.444296	−	0.444296i
$768$	−0.602672	+	0.602672i	−0.0217471	+	0.0217471i
$769$	−27.6088			−0.995600			−0.497800	−	0.867292i	$-0.665859\pi$
$769$	−27.6088			−0.995600			−0.497800	+	0.867292i	$0.665859\pi$
$770$	−5.49520	−	2.19153i	−0.198033	−	0.0789774i
$771$	19.7619			0.711707
$772$	−1.52160	+	1.52160i	−0.0547636	+	0.0547636i
$773$	38.4363	−	38.4363i	1.38246	−	1.38246i	0.542227	−	0.840232i	$-0.317581\pi$
$773$	38.4363	−	38.4363i	1.38246	−	1.38246i	0.840232	−	0.542227i	$-0.182419\pi$
$774$		−	12.1480i		−	0.436651i
$775$	0.763049	+	1.61049i	0.0274095	+	0.0578504i
$776$		−	3.92647i		−	0.140952i
$777$	−2.12073	−	11.3521i	−0.0760807	−	0.407255i
$778$	−11.9795	−	11.9795i	−0.429486	−	0.429486i
$779$		−	55.4369i		−	1.98623i
$780$	0.863432	+	3.83891i	0.0309158	+	0.137455i
$781$	5.71174			0.204382
$782$	−1.22630	−	1.22630i	−0.0438524	−	0.0438524i
$783$	26.4322	−	26.4322i	0.944611	−	0.944611i
$784$	−6.52789	+	2.52719i	−0.233139	+	0.0902568i
$785$	5.90593	−	9.33353i	0.210792	−	0.333128i
$786$	4.34409			0.154949
$787$	−4.21746	−	4.21746i	−0.150336	−	0.150336i	0.627932	−	0.778268i	$-0.283902\pi$
$787$	−4.21746	−	4.21746i	−0.150336	−	0.150336i	−0.778268	+	0.627932i	$0.783902\pi$
$788$	−7.78477	−	7.78477i	−0.277321	−	0.277321i
$789$	−26.2392			−0.934139
$790$	−9.15741	+	14.4720i	−0.325806	+	0.514892i
$791$	17.5386	+	12.0172i	0.623601	+	0.427282i
$792$	−1.60766	+	1.60766i	−0.0571256	+	0.0571256i
$793$	−3.23186	−	3.23186i	−0.114767	−	0.114767i
$794$	8.84871			0.314029
$795$	−4.83747	−	21.5079i	−0.171567	−	0.762806i
$796$		−	1.41376i		−	0.0501093i
$797$	14.8340	+	14.8340i	0.525446	+	0.525446i	0.919211	−	0.393765i	$-0.128828\pi$
$797$	14.8340	+	14.8340i	0.525446	+	0.525446i	−0.393765	+	0.919211i	$0.628828\pi$
$798$	2.31811	+	12.4087i	0.0820601	+	0.439263i
$799$			3.74197i			0.132382i
$800$	1.68124	−	4.70887i	0.0594407	−	0.166484i
$801$			27.5339i			0.972861i
$802$	−4.04942	+	4.04942i	−0.142990	+	0.142990i
$803$	1.48454	−	1.48454i	0.0523882	−	0.0523882i
$804$	−1.06070			−0.0374081
$805$	−6.84222	+	17.1566i	−0.241156	+	0.604692i
$806$	0.735880			0.0259203
$807$	−18.2049	+	18.2049i	−0.640843	+	0.640843i
$808$	−9.85129	+	9.85129i	−0.346567	+	0.346567i
$809$		−	14.9815i		−	0.526722i	−0.964697	−	0.263361i	$-0.915169\pi$
$809$		−	14.9815i		−	0.526722i	0.964697	−	0.263361i	$-0.0848310\pi$
$810$	5.64949	+	3.57480i	0.198503	+	0.125606i
$811$		−	44.7312i		−	1.57072i	−0.619036	−	0.785362i	$-0.712477\pi$
$811$		−	44.7312i		−	1.57072i	0.619036	−	0.785362i	$-0.287523\pi$
$812$	−21.6296	+	4.04069i	−0.759049	+	0.141800i
$813$	−4.89744	−	4.89744i	−0.171761	−	0.171761i
$814$			5.12131i			0.179502i
$815$	−13.0735	+	20.6610i	−0.457946	+	0.723722i
$816$	−0.473434			−0.0165735
$817$	21.1500	+	21.1500i	0.739946	+	0.739946i
$818$	26.6978	−	26.6978i	0.933466	−	0.933466i
$819$	10.2452	+	7.01983i	0.357995	+	0.245293i
$820$	−4.85914	−	21.6042i	−0.169688	−	0.754452i
$821$	−34.1255			−1.19099			−0.595495	−	0.803359i	$-0.703044\pi$
$821$	−34.1255			−1.19099			−0.595495	+	0.803359i	$0.703044\pi$
$822$	6.09607	+	6.09607i	0.212625	+	0.212625i
$823$	−4.10553	−	4.10553i	−0.143110	−	0.143110i	0.631922	−	0.775032i	$-0.282266\pi$
$823$	−4.10553	−	4.10553i	−0.143110	−	0.143110i	−0.775032	+	0.631922i	$0.782266\pi$
$824$	−3.39233			−0.118178
$825$	−1.43293	+	4.01340i	−0.0498882	+	0.139729i
$826$	12.6043	−	18.3954i	0.438558	−	0.640058i
$827$	16.2849	−	16.2849i	0.566281	−	0.566281i	−0.364804	−	0.931084i	$-0.618864\pi$
$827$	16.2849	−	16.2849i	0.566281	−	0.566281i	0.931084	+	0.364804i	$0.118864\pi$
$828$	5.01929	+	5.01929i	0.174432	+	0.174432i
$829$	−7.17163			−0.249081			−0.124540	−	0.992215i	$-0.539746\pi$
$829$	−7.17163			−0.249081			−0.124540	+	0.992215i	$0.539746\pi$
$830$	17.0001	−	3.82360i	0.590083	−	0.132719i
$831$			0.755443i			0.0262060i
$832$	−1.45991	−	1.45991i	−0.0506134	−	0.0506134i
$833$	−3.55664	−	1.57139i	−0.123230	−	0.0544454i
$834$		−	3.09635i		−	0.107218i
$835$	6.47757	−	10.2369i	0.224166	−	0.354264i
$836$		−	5.59795i		−	0.193609i
$837$	−1.13279	+	1.13279i	−0.0391551	+	0.0391551i
$838$	−6.19295	+	6.19295i	−0.213932	+	0.213932i
$839$	39.7456			1.37217			0.686086	−	0.727520i	$-0.259327\pi$
$839$	39.7456			1.37217			0.686086	+	0.727520i	$0.259327\pi$
$840$	1.99103	+	4.63258i	0.0686969	+	0.159839i
$841$	−40.1664			−1.38505
$842$	25.7815	−	25.7815i	0.888488	−	0.888488i
$843$	4.46018	−	4.46018i	0.153617	−	0.153617i
$844$			8.35392i			0.287554i
$845$	19.0610	−	4.28713i	0.655719	−	0.147482i
$846$		−	15.3160i		−	0.526576i
$847$	−2.60076	+	0.485856i	−0.0893631	+	0.0166942i
$848$	8.17933	+	8.17933i	0.280879	+	0.280879i
$849$		−	9.37146i		−	0.321628i
$850$	2.50990	−	1.18919i	0.0860888	−	0.0407889i
$851$	15.9893			0.548106
$852$	−3.44231	−	3.44231i	−0.117932	−	0.117932i
$853$	23.5964	−	23.5964i	0.807924	−	0.807924i	−0.176396	−	0.984319i	$-0.556444\pi$
$853$	23.5964	−	23.5964i	0.807924	−	0.807924i	0.984319	+	0.176396i	$0.0564438\pi$
$854$	−4.83162	−	3.31056i	−0.165335	−	0.113285i
$855$	−27.7656	+	6.24493i	−0.949563	+	0.213572i
$856$	−4.68794			−0.160231
$857$	22.0897	+	22.0897i	0.754570	+	0.754570i	0.975329	−	0.220758i	$-0.0708532\pi$
$857$	22.0897	+	22.0897i	0.754570	+	0.754570i	−0.220758	+	0.975329i	$0.570853\pi$
$858$	1.24430	+	1.24430i	0.0424796	+	0.0424796i
$859$	45.4932			1.55221			0.776103	−	0.630606i	$-0.217194\pi$
$859$	45.4932			1.55221			0.776103	+	0.630606i	$0.217194\pi$
$860$	10.0962	+	6.38850i	0.344277	+	0.217846i
$861$	18.4219	+	12.6224i	0.627815	+	0.430170i
$862$	16.8306	−	16.8306i	0.573252	−	0.573252i
$863$	−9.79219	−	9.79219i	−0.333330	−	0.333330i	0.520520	−	0.853850i	$-0.325738\pi$
$863$	−9.79219	−	9.79219i	−0.333330	−	0.333330i	−0.853850	+	0.520520i	$0.825738\pi$
$864$	4.49471			0.152913
$865$	38.3977	+	24.2967i	1.30556	+	0.826114i
$866$			29.3182i			0.996274i
$867$	10.0595	+	10.0595i	0.341638	+	0.341638i
$868$	0.926967	−	0.173170i	0.0314633	−	0.00587777i
$869$			7.65896i			0.259812i
$870$	3.47803	+	15.4637i	0.117916	+	0.524268i
$871$		−	2.56945i		−	0.0870625i
$872$	1.86270	−	1.86270i	0.0630791	−	0.0630791i
$873$	−6.31241	+	6.31241i	−0.213643	+	0.213643i
$874$	−17.4774			−0.591183
$875$	−22.1917	−	19.5584i	−0.750216	−	0.661193i
$876$	−1.78938			−0.0604576
$877$	−28.3343	+	28.3343i	−0.956783	+	0.956783i	−0.999104	−	0.0423213i	$-0.986525\pi$
$877$	−28.3343	+	28.3343i	−0.956783	+	0.956783i	0.0423213	+	0.999104i	$0.486525\pi$
$878$	−17.2272	+	17.2272i	−0.581390	+	0.581390i
$879$		−	18.9979i		−	0.640782i
$880$	−0.490670	−	2.18157i	−0.0165405	−	0.0735407i
$881$		−	15.7718i		−	0.531366i	−0.964060	−	0.265683i	$-0.914403\pi$
$881$		−	15.7718i		−	0.531366i	0.964060	−	0.265683i	$-0.0855974\pi$
$882$	14.5575	+	6.43175i	0.490175	+	0.216568i
$883$	14.4446	+	14.4446i	0.486098	+	0.486098i	0.907072	−	0.420974i	$-0.138312\pi$
$883$	14.4446	+	14.4446i	0.486098	+	0.486098i	−0.420974	+	0.907072i	$0.638312\pi$
$884$		−	1.14685i		−	0.0385727i
$885$	−13.5737	−	8.58897i	−0.456276	−	0.288715i
$886$	11.8576			0.398363
$887$	−14.0219	−	14.0219i	−0.470808	−	0.470808i	0.431368	−	0.902176i	$-0.358031\pi$
$887$	−14.0219	−	14.0219i	−0.470808	−	0.470808i	−0.902176	+	0.431368i	$0.858031\pi$
$888$	3.08647	−	3.08647i	0.103575	−	0.103575i
$889$	−19.8626	+	28.9887i	−0.666171	+	0.972250i
$890$	−22.8833	−	14.4797i	−0.767050	−	0.485362i
$891$	2.98984			0.100164
$892$	20.7571	+	20.7571i	0.694999	+	0.694999i
$893$	26.6656	+	26.6656i	0.892331	+	0.892331i
$894$	−4.81328			−0.160980
$895$	18.5136	−	4.16401i	0.618842	−	0.139188i
$896$	−2.18257	−	1.49546i	−0.0729144	−	0.0499599i
$897$	3.88483	−	3.88483i	0.129711	−	0.129711i
$898$	9.57593	+	9.57593i	0.319553	+	0.319553i
$899$	2.96423			0.0988627
$900$	−10.2731	+	4.86740i	−0.342437	+	0.162247i
$901$			6.42534i			0.214059i
$902$	−7.00253	−	7.00253i	−0.233159	−	0.233159i
$903$	−11.8438	+	2.21259i	−0.394139	+	0.0736303i
$904$			8.03577i			0.267266i
$905$	−0.595847	+	0.134016i	−0.0198066	+	0.00445483i
$906$			10.1985i			0.338824i
$907$	−5.86020	+	5.86020i	−0.194585	+	0.194585i	−0.797674	−	0.603089i	$-0.793936\pi$
$907$	−5.86020	+	5.86020i	−0.194585	+	0.194585i	0.603089	+	0.797674i	$0.293936\pi$
$908$	−20.4313	+	20.4313i	−0.678035	+	0.678035i
$909$	31.6750			1.05059
$910$	−11.2220	+	4.82307i	−0.372005	+	0.159883i
$911$	37.2733			1.23492			0.617460	−	0.786602i	$-0.288162\pi$
$911$	37.2733			1.23492			0.617460	+	0.786602i	$0.288162\pi$
$912$	−3.37373	+	3.37373i	−0.111715	+	0.111715i
$913$	5.51022	−	5.51022i	0.182362	−	0.182362i
$914$			19.9642i			0.660357i
$915$	−2.25592	+	3.56519i	−0.0745786	+	0.117861i
$916$			2.20499i			0.0728550i
$917$	2.47634	+	13.2557i	0.0817761	+	0.437742i
$918$	1.76543	+	1.76543i	0.0582677	+	0.0582677i
$919$		−	53.1092i		−	1.75191i	−0.482391	−	0.875956i	$-0.660232\pi$
$919$		−	53.1092i		−	1.75191i	0.482391	−	0.875956i	$-0.339768\pi$
$920$	−6.81111	+	1.53193i	−0.224555	+	0.0505061i
$921$	−17.8845			−0.589313
$922$	12.3649	+	12.3649i	0.407216	+	0.407216i
$923$	8.33866	−	8.33866i	0.274470	−	0.274470i
$924$	1.86022	+	1.27459i	0.0611967	+	0.0419310i
$925$	−8.61013	+	24.1156i	−0.283099	+	0.792915i
$926$	−22.0288			−0.723912
$927$	5.45371	+	5.45371i	0.179123	+	0.179123i
$928$	−5.88075	−	5.88075i	−0.193045	−	0.193045i
$929$	−15.8188			−0.518997			−0.259499	−	0.965743i	$-0.583557\pi$
$929$	−15.8188			−0.518997			−0.259499	+	0.965743i	$0.583557\pi$
$930$	−0.149056	−	0.662720i	−0.00488775	−	0.0217314i
$931$	−36.5428	+	14.1471i	−1.19764	+	0.463652i
$932$	−19.2656	+	19.2656i	−0.631066	+	0.631066i
$933$	10.8188	+	10.8188i	0.354191	+	0.354191i
$934$	−18.3731			−0.601186
$935$	0.664150	−	1.04960i	0.0217200	−	0.0343256i
$936$			4.69409i			0.153431i
$937$	−38.8638	−	38.8638i	−1.26962	−	1.26962i	−0.946282	−	0.323343i	$-0.895193\pi$
$937$	−38.8638	−	38.8638i	−1.26962	−	1.26962i	−0.323343	−	0.946282i	$-0.604807\pi$
$938$	−0.604652	−	3.23667i	−0.0197426	−	0.105681i
$939$			22.0940i			0.721010i
$940$	12.7291	+	8.05453i	0.415178	+	0.262710i
$941$		−	16.4706i		−	0.536925i	−0.963290	−	0.268463i	$-0.913484\pi$
$941$		−	16.4706i		−	0.536925i	0.963290	−	0.268463i	$-0.0865156\pi$
$942$	−2.97692	+	2.97692i	−0.0969932	+	0.0969932i
$943$	−21.8627	+	21.8627i	−0.711947	+	0.711947i
$944$	8.42834			0.274319
$945$	9.85030	−	24.6993i	0.320430	−	0.803468i
$946$	5.34314			0.173720
$947$	−37.5789	+	37.5789i	−1.22115	+	1.22115i	−0.253926	+	0.967224i	$0.581722\pi$
$947$	−37.5789	+	37.5789i	−1.22115	+	1.22115i	−0.967224	+	0.253926i	$0.918278\pi$
$948$	4.61584	−	4.61584i	0.149916	−	0.149916i
$949$		−	4.33460i		−	0.140707i
$950$	9.41148	−	26.3600i	0.305349	−	0.855232i
$951$		−	16.2465i		−	0.526830i
$952$	−0.269880	−	1.44465i	−0.00874687	−	0.0468214i
$953$	4.56435	+	4.56435i	0.147854	+	0.147854i	0.777159	−	0.629305i	$-0.216660\pi$
$953$	4.56435	+	4.56435i	0.147854	+	0.147854i	−0.629305	+	0.777159i	$0.716660\pi$
$954$		−	26.2991i		−	0.851465i
$955$	2.41191	+	10.7236i	0.0780476	+	0.347008i
$956$	28.8687			0.933680
$957$	5.01221	+	5.01221i	0.162022	+	0.162022i
$958$	−27.2045	+	27.2045i	−0.878939	+	0.878939i
$959$	−15.1267	+	22.0768i	−0.488467	+	0.712897i
$960$	−1.01906	+	1.61048i	−0.0328900	+	0.0519782i
$961$	30.8730			0.995902
$962$	7.47667	+	7.47667i	0.241058	+	0.241058i
$963$	7.53661	+	7.53661i	0.242864	+	0.242864i
$964$	26.1600			0.842558
$965$	−2.57287	+	4.06608i	−0.0828237	+	0.130892i
$966$	3.97942	−	5.80781i	0.128036	−	0.186863i
$967$	−9.73514	+	9.73514i	−0.313061	+	0.313061i	−0.846094	−	0.533033i	$-0.821052\pi$
$967$	−9.73514	+	9.73514i	−0.313061	+	0.313061i	0.533033	+	0.846094i	$0.321052\pi$
$968$	−0.707107	−	0.707107i	−0.0227273	−	0.0227273i
$969$	−2.65026			−0.0851387
$970$	−1.92660	−	8.56586i	−0.0618593	−	0.275033i
$971$		−	53.7645i		−	1.72539i	−0.505728	−	0.862693i	$-0.668776\pi$
$971$		−	53.7645i		−	1.72539i	0.505728	−	0.862693i	$-0.331224\pi$
$972$	−11.3366	−	11.3366i	−0.363622	−	0.363622i
$973$	9.44830	−	1.76507i	0.302899	−	0.0565855i
$974$			23.6631i			0.758213i
$975$	3.76727	+	7.95118i	0.120649	+	0.254642i
$976$		−	2.21373i		−	0.0708599i
$977$	−31.1328	+	31.1328i	−0.996028	+	0.996028i	−0.999992	−	0.00396437i	$-0.998738\pi$
$977$	−31.1328	+	31.1328i	−0.996028	+	0.996028i	0.00396437	+	0.999992i	$0.498738\pi$
$978$	6.58979	−	6.58979i	0.210718	−	0.210718i
$979$	−12.1104			−0.387050
$980$	−13.0010	+	8.71628i	−0.415302	+	0.278431i
$981$	−5.98918			−0.191220
$982$	−21.4977	+	21.4977i	−0.686020	+	0.686020i
$983$	−32.4473	+	32.4473i	−1.03491	+	1.03491i	−0.0355389	+	0.999368i	$0.511315\pi$
$983$	−32.4473	+	32.4473i	−1.03491	+	1.03491i	−0.999368	+	0.0355389i	$0.988685\pi$
$984$			8.44046i			0.269072i
$985$	−20.8028	−	13.1633i	−0.662831	−	0.419417i
$986$		−	4.61967i		−	0.147120i
$987$	−14.9325	+	2.78960i	−0.475308	+	0.0887939i
$988$	−8.17254	−	8.17254i	−0.260003	−	0.260003i
$989$		−	16.6819i		−	0.530453i
$990$	−2.71839	+	4.29605i	−0.0863960	+	0.136537i
$991$	16.7305			0.531462			0.265731	−	0.964047i	$-0.414387\pi$
$991$	16.7305			0.531462			0.265731	+	0.964047i	$0.414387\pi$
$992$	0.252028	+	0.252028i	0.00800191	+	0.00800191i
$993$	15.8318	−	15.8318i	0.502408	−	0.502408i
$994$	8.54169	−	12.4663i	0.270926	−	0.395406i
$995$	−0.693688	−	3.08421i	−0.0219914	−	0.0977761i
$996$	−6.64171			−0.210451
$997$	20.3596	+	20.3596i	0.644796	+	0.644796i	0.951731	−	0.306935i	$-0.0993034\pi$
$997$	20.3596	+	20.3596i	0.644796	+	0.644796i	−0.306935	+	0.951731i	$0.599303\pi$
$998$	−14.1544	−	14.1544i	−0.448050	−	0.448050i
$999$	−23.0188			−0.728281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.15	✓	40
5.2	odd	4	inner	770.2.l.c.727.16	yes	40
7.6	odd	2	inner	770.2.l.c.573.16	yes	40
35.27	even	4	inner	770.2.l.c.727.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.15	✓	40	1.1	even	1	trivial
770.2.l.c.573.16	yes	40	7.6	odd	2	inner
770.2.l.c.727.15	yes	40	35.27	even	4	inner
770.2.l.c.727.16	yes	40	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.602672 + 0.602672i) q^{3} -1.00000i q^{4} +(-0.490670 - 2.18157i) q^{5} +0.852308i q^{6} +(-2.60076 + 0.485856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.27357i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.602672 + 0.602672i) q^{3} -1.00000i q^{4} +(-0.490670 - 2.18157i) q^{5} +0.852308i q^{6} +(-2.60076 + 0.485856i) q^{7} +(-0.707107 - 0.707107i) q^{8} +2.27357i q^{9} +(-1.88956 - 1.19565i) q^{10} -1.00000 q^{11} +(0.602672 + 0.602672i) q^{12} +(-1.45991 + 1.45991i) q^{13} +(-1.49546 + 2.18257i) q^{14} +(1.61048 + 1.01906i) q^{15} -1.00000 q^{16} +(-0.392779 - 0.392779i) q^{17} +(1.60766 + 1.60766i) q^{18} -5.59795 q^{19} +(-2.18157 + 0.490670i) q^{20} +(1.27459 - 1.86022i) q^{21} +(-0.707107 + 0.707107i) q^{22} +(2.20767 + 2.20767i) q^{23} +0.852308 q^{24} +(-4.51849 + 2.14086i) q^{25} +2.06463i q^{26} +(-3.17824 - 3.17824i) q^{27} +(0.485856 + 2.60076i) q^{28} +8.31663i q^{29} +(1.85937 - 0.418202i) q^{30} -0.356422i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.602672 - 0.602672i) q^{33} -0.555473 q^{34} +(2.33604 + 5.43534i) q^{35} +2.27357 q^{36} +(3.62131 - 3.62131i) q^{37} +(-3.95835 + 3.95835i) q^{38} -1.75970i q^{39} +(-1.19565 + 1.88956i) q^{40} +9.90307i q^{41} +(-0.414099 - 2.21665i) q^{42} +(-3.77817 - 3.77817i) q^{43} +1.00000i q^{44} +(4.95995 - 1.11557i) q^{45} +3.12211 q^{46} +(-4.76346 - 4.76346i) q^{47} +(0.602672 - 0.602672i) q^{48} +(6.52789 - 2.52719i) q^{49} +(-1.68124 + 4.70887i) q^{50} +0.473434 q^{51} +(1.45991 + 1.45991i) q^{52} +(-8.17933 - 8.17933i) q^{53} -4.49471 q^{54} +(0.490670 + 2.18157i) q^{55} +(2.18257 + 1.49546i) q^{56} +(3.37373 - 3.37373i) q^{57} +(5.88075 + 5.88075i) q^{58} -8.42834 q^{59} +(1.01906 - 1.61048i) q^{60} +2.21373i q^{61} +(-0.252028 - 0.252028i) q^{62} +(-1.10463 - 5.91301i) q^{63} +1.00000i q^{64} +(3.90124 + 2.46857i) q^{65} -0.852308i q^{66} +(-0.880000 + 0.880000i) q^{67} +(-0.392779 + 0.392779i) q^{68} -2.66100 q^{69} +(5.49520 + 2.19153i) q^{70} -5.71174 q^{71} +(1.60766 - 1.60766i) q^{72} +(-1.48454 + 1.48454i) q^{73} -5.12131i q^{74} +(1.43293 - 4.01340i) q^{75} +5.59795i q^{76} +(2.60076 - 0.485856i) q^{77} +(-1.24430 - 1.24430i) q^{78} -7.65896i q^{79} +(0.490670 + 2.18157i) q^{80} -2.98984 q^{81} +(7.00253 + 7.00253i) q^{82} +(-5.51022 + 5.51022i) q^{83} +(-1.86022 - 1.27459i) q^{84} +(-0.664150 + 1.04960i) q^{85} -5.34314 q^{86} +(-5.01221 - 5.01221i) q^{87} +(0.707107 + 0.707107i) q^{88} +12.1104 q^{89} +(2.71839 - 4.29605i) q^{90} +(3.08758 - 4.50619i) q^{91} +(2.20767 - 2.20767i) q^{92} +(0.214806 + 0.214806i) q^{93} -6.73655 q^{94} +(2.74675 + 12.2123i) q^{95} -0.852308i q^{96} +(2.77643 + 2.77643i) q^{97} +(2.82892 - 6.40291i) q^{98} -2.27357i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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