LMFDB - Embedded newform 210.2.x.a.23.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.16
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.69314 + 0.365065i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.680454 + 2.13002i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.73346 + 1.23621i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.69314 + 0.365065i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.680454 + 2.13002i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.73346 + 1.23621i) q^{9} +(-0.105978 + 2.23356i) q^{10} +(2.97095 - 1.71528i) q^{11} +(1.64884 - 0.530415i) q^{12} +(-3.87719 - 3.87719i) q^{13} +(-1.97690 + 1.75837i) q^{14} +(-1.92970 + 3.35801i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.993622 - 3.70825i) q^{17} +(2.96027 + 0.486620i) q^{18} +(-5.97063 - 3.44715i) q^{19} +(0.475719 + 2.18488i) q^{20} +(-4.43692 + 1.14618i) q^{21} +(2.42577 - 2.42577i) q^{22} +(0.298332 + 1.11339i) q^{23} +(1.45537 - 0.939092i) q^{24} +(-4.07396 - 2.89876i) q^{25} +(-4.74857 - 2.74159i) q^{26} +(4.17683 + 3.09097i) q^{27} +(-1.45443 + 2.21012i) q^{28} +2.35616 q^{29} +(-0.994829 + 3.74304i) q^{30} +(3.58502 + 6.20943i) q^{31} +(0.258819 - 0.965926i) q^{32} +(5.65642 - 1.81962i) q^{33} -3.83906i q^{34} +(-0.918883 - 5.84428i) q^{35} +(2.98535 - 0.296136i) q^{36} +(1.28036 + 4.77836i) q^{37} +(-6.65937 - 1.78437i) q^{38} +(-5.14920 - 7.98005i) q^{39} +(1.02500 + 1.98730i) q^{40} +7.73718i q^{41} +(-3.98909 + 2.25548i) q^{42} +(-0.576172 - 0.576172i) q^{43} +(1.71528 - 2.97095i) q^{44} +(-4.49315 + 4.98113i) q^{45} +(0.576333 + 0.998238i) q^{46} +(-8.51756 + 2.28227i) q^{47} +(1.16273 - 1.28377i) q^{48} +(4.18301 - 5.61270i) q^{49} +(-4.68540 - 1.74557i) q^{50} +(3.03609 - 5.91585i) q^{51} +(-5.29634 - 1.41915i) q^{52} +(0.921459 + 0.246904i) q^{53} +(4.83451 + 1.90461i) q^{54} +(1.63198 + 7.49534i) q^{55} +(-0.832855 + 2.51125i) q^{56} +(-8.85069 - 8.01617i) q^{57} +(2.27587 - 0.609819i) q^{58} +(2.74415 + 4.75301i) q^{59} +(0.00783764 + 3.87298i) q^{60} +(0.442564 - 0.766543i) q^{61} +(5.06998 + 5.06998i) q^{62} +(-7.93077 + 0.320873i) q^{63} -1.00000i q^{64} +(10.8967 - 5.62024i) q^{65} +(4.99273 - 3.22161i) q^{66} +(-4.32230 - 1.15816i) q^{67} +(-0.993622 - 3.70825i) q^{68} +(0.0986585 + 1.99404i) q^{69} +(-2.40019 - 5.40732i) q^{70} +1.76324i q^{71} +(2.80698 - 1.05871i) q^{72} +(1.83002 - 6.82973i) q^{73} +(2.47346 + 4.28416i) q^{74} +(-5.83956 - 6.39527i) q^{75} -6.89429 q^{76} +(-4.98952 + 7.58193i) q^{77} +(-7.03914 - 6.37543i) q^{78} +(-4.97633 - 2.87309i) q^{79} +(1.50442 + 1.65430i) q^{80} +(5.94355 + 6.75827i) q^{81} +(2.00253 + 7.47354i) q^{82} +(-7.09854 + 7.09854i) q^{83} +(-3.26940 + 3.21108i) q^{84} +(7.22252 + 4.63972i) q^{85} +(-0.705664 - 0.407415i) q^{86} +(3.98931 + 0.860151i) q^{87} +(0.887893 - 3.31366i) q^{88} +(0.641651 - 1.11137i) q^{89} +(-3.05084 + 5.97431i) q^{90} +(13.7696 + 4.56669i) q^{91} +(0.815058 + 0.815058i) q^{92} +(3.80309 + 11.8222i) q^{93} +(-7.63664 + 4.40902i) q^{94} +(11.4052 - 10.3719i) q^{95} +(0.790843 - 1.54096i) q^{96} +(2.15837 - 2.15837i) q^{97} +(2.58780 - 6.50410i) q^{98} +(10.2414 - 1.01591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.69314	+	0.365065i	0.977536	+	0.210770i
$3$	1.69314	+	0.365065i	0.977536	+	0.210770i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.680454	+	2.13002i	−0.304308	+	0.952574i
$5$	−0.680454	+	2.13002i	−0.304308	+	0.952574i
$6$	1.72993	−	0.0855915i	0.706243	−	0.0349426i
$7$	−2.36464	+	1.18680i	−0.893748	+	0.448569i
$7$	−2.36464	+	1.18680i	−0.893748	+	0.448569i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.73346	+	1.23621i	0.911152	+	0.412071i
$10$	−0.105978	+	2.23356i	−0.0335133	+	0.706312i
$11$	2.97095	−	1.71528i	0.895774	−	0.517175i	0.0199474	−	0.999801i	$-0.493650\pi$
$11$	2.97095	−	1.71528i	0.895774	−	0.517175i	0.875827	+	0.482626i	$0.160317\pi$
$12$	1.64884	−	0.530415i	0.475978	−	0.153118i
$13$	−3.87719	−	3.87719i	−1.07534	−	1.07534i	−0.996921	−	0.0784181i	$-0.975013\pi$
$13$	−3.87719	−	3.87719i	−1.07534	−	1.07534i	−0.0784181	−	0.996921i	$-0.524987\pi$
$14$	−1.97690	+	1.75837i	−0.528348	+	0.469945i
$15$	−1.92970	+	3.35801i	−0.498246	+	0.867035i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.993622	−	3.70825i	0.240989	−	0.899382i	−0.734369	−	0.678751i	$-0.762522\pi$
$17$	0.993622	−	3.70825i	0.240989	−	0.899382i	0.975357	−	0.220631i	$-0.0708117\pi$
$18$	2.96027	+	0.486620i	0.697742	+	0.114697i
$19$	−5.97063	−	3.44715i	−1.36976	−	0.790829i	−0.378860	−	0.925454i	$-0.623684\pi$
$19$	−5.97063	−	3.44715i	−1.36976	−	0.790829i	−0.990897	+	0.134625i	$0.957017\pi$
$20$	0.475719	+	2.18488i	0.106374	+	0.488554i
$21$	−4.43692	+	1.14618i	−0.968216	+	0.250116i
$22$	2.42577	−	2.42577i	0.517175	−	0.517175i
$23$	0.298332	+	1.11339i	0.0622065	+	0.232158i	0.990029	−	0.140864i	$-0.0449882\pi$
$23$	0.298332	+	1.11339i	0.0622065	+	0.232158i	−0.927822	+	0.373022i	$0.878322\pi$
$24$	1.45537	−	0.939092i	0.297076	−	0.191691i
$25$	−4.07396	−	2.89876i	−0.814793	−	0.579752i
$26$	−4.74857	−	2.74159i	−0.931271	−	0.537669i
$27$	4.17683	+	3.09097i	0.803831	+	0.594858i
$28$	−1.45443	+	2.21012i	−0.274862	+	0.417673i
$29$	2.35616			0.437528			0.218764	−	0.975778i	$-0.429798\pi$
$29$	2.35616			0.437528			0.218764	+	0.975778i	$0.429798\pi$
$30$	−0.994829	+	3.74304i	−0.181630	+	0.683382i
$31$	3.58502	+	6.20943i	0.643888	+	1.11525i	0.984557	+	0.175063i	$0.0560130\pi$
$31$	3.58502	+	6.20943i	0.643888	+	1.11525i	−0.340669	+	0.940183i	$0.610654\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	5.65642	−	1.81962i	0.984656	−	0.316755i
$34$		−	3.83906i		−	0.658393i
$35$	−0.918883	−	5.84428i	−0.155320	−	0.987864i
$36$	2.98535	−	0.296136i	0.497558	−	0.0493559i
$37$	1.28036	+	4.77836i	0.210489	+	0.785557i	0.987706	+	0.156324i	$0.0499643\pi$
$37$	1.28036	+	4.77836i	0.210489	+	0.785557i	−0.777217	+	0.629233i	$0.783369\pi$
$38$	−6.65937	−	1.78437i	−1.08029	−	0.289464i
$39$	−5.14920	−	7.98005i	−0.824532	−	1.27783i
$40$	1.02500	+	1.98730i	0.162066	+	0.314220i
$41$			7.73718i			1.20834i	0.796854	+	0.604172i	$0.206496\pi$
$41$			7.73718i			1.20834i	−0.796854	+	0.604172i	$0.793504\pi$
$42$	−3.98909	+	2.25548i	−0.615529	+	0.348028i
$43$	−0.576172	−	0.576172i	−0.0878654	−	0.0878654i	0.661808	−	0.749673i	$-0.269789\pi$
$43$	−0.576172	−	0.576172i	−0.0878654	−	0.0878654i	−0.749673	+	0.661808i	$0.769789\pi$
$44$	1.71528	−	2.97095i	0.258588	−	0.447887i
$45$	−4.49315	+	4.98113i	−0.669799	+	0.742542i
$46$	0.576333	+	0.998238i	0.0849757	+	0.147182i
$47$	−8.51756	+	2.28227i	−1.24241	+	0.332904i	−0.819402	−	0.573220i	$-0.805694\pi$
$47$	−8.51756	+	2.28227i	−1.24241	+	0.332904i	−0.423013	+	0.906124i	$0.639027\pi$
$48$	1.16273	−	1.28377i	0.167825	−	0.185296i
$49$	4.18301	−	5.61270i	0.597572	−	0.801815i
$50$	−4.68540	−	1.74557i	−0.662616	−	0.246861i
$51$	3.03609	−	5.91585i	0.425138	−	0.828384i
$52$	−5.29634	−	1.41915i	−0.734470	−	0.196801i
$53$	0.921459	+	0.246904i	0.126572	+	0.0339149i	0.321549	−	0.946893i	$-0.395797\pi$
$53$	0.921459	+	0.246904i	0.126572	+	0.0339149i	−0.194977	+	0.980808i	$0.562463\pi$
$54$	4.83451	+	1.90461i	0.657893	+	0.259184i
$55$	1.63198	+	7.49534i	0.220056	+	1.01067i
$56$	−0.832855	+	2.51125i	−0.111295	+	0.335579i
$57$	−8.85069	−	8.01617i	−1.17230	−	1.06177i
$58$	2.27587	−	0.609819i	0.298837	−	0.0800731i
$59$	2.74415	+	4.75301i	0.357258	+	0.618789i	0.987502	−	0.157609i	$-0.0503784\pi$
$59$	2.74415	+	4.75301i	0.357258	+	0.618789i	−0.630244	+	0.776397i	$0.717045\pi$
$60$	0.00783764	+	3.87298i	0.00101183	+	0.499999i
$61$	0.442564	−	0.766543i	0.0566645	−	0.0981458i	−0.836302	−	0.548270i	$-0.815287\pi$
$61$	0.442564	−	0.766543i	0.0566645	−	0.0981458i	0.892966	+	0.450124i	$0.148620\pi$
$62$	5.06998	+	5.06998i	0.643888	+	0.643888i
$63$	−7.93077	+	0.320873i	−0.999183	+	0.0404262i
$64$		−	1.00000i		−	0.125000i
$65$	10.8967	−	5.62024i	1.35157	−	0.697105i
$66$	4.99273	−	3.22161i	0.614563	−	0.396552i
$67$	−4.32230	−	1.15816i	−0.528053	−	0.141491i	−0.0150642	−	0.999887i	$-0.504795\pi$
$67$	−4.32230	−	1.15816i	−0.528053	−	0.141491i	−0.512989	+	0.858395i	$0.671462\pi$
$68$	−0.993622	−	3.70825i	−0.120494	−	0.449691i
$69$	0.0986585	+	1.99404i	0.0118771	+	0.240054i
$70$	−2.40019	−	5.40732i	−0.286877	−	0.646298i
$71$			1.76324i			0.209258i	0.994511	+	0.104629i	$0.0333655\pi$
$71$			1.76324i			0.209258i	−0.994511	+	0.104629i	$0.966635\pi$
$72$	2.80698	−	1.05871i	0.330806	−	0.124770i
$73$	1.83002	−	6.82973i	0.214188	−	0.799360i	−0.772263	−	0.635303i	$-0.780875\pi$
$73$	1.83002	−	6.82973i	0.214188	−	0.799360i	0.986451	−	0.164057i	$-0.0524581\pi$
$74$	2.47346	+	4.28416i	0.287534	+	0.498023i
$75$	−5.83956	−	6.39527i	−0.674295	−	0.738462i
$76$	−6.89429			−0.790829
$77$	−4.98952	+	7.58193i	−0.568608	+	0.864041i
$78$	−7.03914	−	6.37543i	−0.797025	−	0.721875i
$79$	−4.97633	−	2.87309i	−0.559881	−	0.323248i	0.193217	−	0.981156i	$-0.438108\pi$
$79$	−4.97633	−	2.87309i	−0.559881	−	0.323248i	−0.753098	+	0.657909i	$0.771441\pi$
$80$	1.50442	+	1.65430i	0.168200	+	0.184956i
$81$	5.94355	+	6.75827i	0.660395	+	0.750919i
$82$	2.00253	+	7.47354i	0.221142	+	0.825315i
$83$	−7.09854	+	7.09854i	−0.779166	+	0.779166i	−0.979689	−	0.200523i	$-0.935736\pi$
$83$	−7.09854	+	7.09854i	−0.779166	+	0.779166i	0.200523	+	0.979689i	$0.435736\pi$
$84$	−3.26940	+	3.21108i	−0.356721	+	0.350357i
$85$	7.22252	+	4.63972i	0.783392	+	0.503249i
$86$	−0.705664	−	0.407415i	−0.0760937	−	0.0439327i
$87$	3.98931	+	0.860151i	0.427699	+	0.0922179i
$88$	0.887893	−	3.31366i	0.0946497	−	0.353237i
$89$	0.641651	−	1.11137i	0.0680149	−	0.117805i	−0.830013	−	0.557745i	$-0.811667\pi$
$89$	0.641651	−	1.11137i	0.0680149	−	0.117805i	0.898027	+	0.439940i	$0.145000\pi$
$90$	−3.05084	+	5.97431i	−0.321587	+	0.629748i
$91$	13.7696	+	4.56669i	1.44345	+	0.478719i
$92$	0.815058	+	0.815058i	0.0849757	+	0.0849757i
$93$	3.80309	+	11.8222i	0.394362	+	1.22591i
$94$	−7.63664	+	4.40902i	−0.787659	+	0.454755i
$95$	11.4052	−	10.3719i	1.17015	−	1.06414i
$96$	0.790843	−	1.54096i	0.0807151	−	0.157274i
$97$	2.15837	−	2.15837i	0.219150	−	0.219150i	−0.588990	−	0.808140i	$-0.700474\pi$
$97$	2.15837	−	2.15837i	0.219150	−	0.219150i	0.808140	+	0.588990i	$0.200474\pi$
$98$	2.58780	−	6.50410i	0.261407	−	0.657013i
$99$	10.2414	−	1.01591i	1.02930	−	0.102103i
$100$	−4.97754	−	0.473417i	−0.497754	−	0.0473417i
$101$	16.2068	−	9.35702i	1.61264	−	0.931059i	0.623885	−	0.781516i	$-0.285553\pi$
$101$	16.2068	−	9.35702i	1.61264	−	0.931059i	0.988755	−	0.149543i	$-0.0477801\pi$
$102$	1.40151	−	6.50007i	0.138770	−	0.643603i
$103$	−8.57874	+	2.29867i	−0.845288	+	0.226494i	−0.655372	−	0.755306i	$-0.727488\pi$
$103$	−8.57874	+	2.29867i	−0.845288	+	0.226494i	−0.189916	+	0.981800i	$0.560822\pi$
$104$	−5.48317			−0.537669
$105$	0.577744	−	10.2307i	0.0563821	−	0.998409i
$106$	0.953965			0.0926572
$107$	−6.54257	+	1.75308i	−0.632494	+	0.169476i	−0.560801	−	0.827950i	$-0.689507\pi$
$107$	−6.54257	+	1.75308i	−0.632494	+	0.169476i	−0.0716931	+	0.997427i	$0.522840\pi$
$108$	5.16273	+	0.588447i	0.496783	+	0.0566233i
$109$	12.2546	−	7.07519i	1.17378	−	0.677680i	0.219209	−	0.975678i	$-0.429652\pi$
$109$	12.2546	−	7.07519i	1.17378	−	0.677680i	0.954566	+	0.297998i	$0.0963189\pi$
$110$	3.51631	+	6.81756i	0.335267	+	0.650028i
$111$	0.423414	+	8.55785i	0.0401887	+	0.812275i
$112$	−0.154518	+	2.64124i	−0.0146006	+	0.249573i
$113$	3.82501	−	3.82501i	0.359827	−	0.359827i	−0.503922	−	0.863749i	$-0.668110\pi$
$113$	3.82501	−	3.82501i	0.359827	−	0.359827i	0.863749	+	0.503922i	$0.168110\pi$
$114$	−10.6238	−	5.45230i	−0.995014	−	0.510655i
$115$	−2.57454	−	0.122158i	−0.240077	−	0.0113913i
$116$	2.04049	−	1.17808i	0.189455	−	0.109382i
$117$	−5.80509	−	15.3912i	−0.536681	−	1.42291i
$118$	3.88081	+	3.88081i	0.357258	+	0.357258i
$119$	2.05140	+	9.94788i	0.188051	+	0.911921i
$120$	1.00997	+	3.73898i	0.0921973	+	0.341320i
$121$	0.384350	−	0.665714i	0.0349409	−	0.0605195i
$122$	0.229088	−	0.854968i	0.0207407	−	0.0774052i
$123$	−2.82457	+	13.1001i	−0.254683	+	1.18120i
$124$	6.20943	+	3.58502i	0.557623	+	0.321944i
$125$	8.94656	−	6.70515i	0.800205	−	0.599727i
$126$	−7.57748	+	2.36257i	−0.675056	+	0.210475i
$127$	−4.52922	+	4.52922i	−0.401903	+	0.401903i	−0.878903	−	0.477000i	$-0.841724\pi$
$127$	−4.52922	+	4.52922i	−0.401903	+	0.401903i	0.477000	+	0.878903i	$0.341724\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−0.765201	−	1.18588i	−0.0673722	−	0.104411i
$130$	9.07081	−	8.24902i	0.795563	−	0.723487i
$131$	10.5767	+	6.10644i	0.924088	+	0.533522i	0.884937	−	0.465711i	$-0.154201\pi$
$131$	10.5767	+	6.10644i	0.924088	+	0.533522i	0.0391509	+	0.999233i	$0.487535\pi$
$132$	3.98880	−	4.40405i	0.347180	−	0.383323i
$133$	18.2094	+	1.06529i	1.57896	+	0.0923726i
$134$	−4.47478			−0.386562
$135$	−9.42597	+	6.79346i	−0.811258	+	0.584688i
$136$	−1.91953	−	3.32472i	−0.164598	−	0.285093i
$137$	−0.910941	+	3.39968i	−0.0778270	+	0.290454i	−0.993859	−	0.110650i	$-0.964707\pi$
$137$	−0.910941	+	3.39968i	−0.0778270	+	0.290454i	0.916032	+	0.401104i	$0.131373\pi$
$138$	0.611391	+	1.90056i	0.0520451	+	0.161786i
$139$			9.33303i			0.791618i	0.918333	+	0.395809i	$0.129536\pi$
$139$			9.33303i			0.791618i	−0.918333	+	0.395809i	$0.870464\pi$
$140$	−3.71792	−	4.60186i	−0.314221	−	0.388928i
$141$	−15.2546	+	0.754749i	−1.28467	+	0.0635613i
$142$	0.456359	+	1.70316i	0.0382968	+	0.142926i
$143$	−18.1694	−	4.86847i	−1.51940	−	0.407122i
$144$	2.43732	−	1.74913i	0.203110	−	0.145761i
$145$	−1.60326	+	5.01866i	−0.133143	+	0.416777i
$146$		−	7.07066i		−	0.585172i
$147$	9.13142	−	7.97603i	0.753147	−	0.657852i
$148$	3.49800	+	3.49800i	0.287534	+	0.287534i
$149$	1.00095	−	1.73369i	0.0820008	−	0.142029i	−0.822108	−	0.569331i	$-0.807202\pi$
$149$	1.00095	−	1.73369i	0.0820008	−	0.142029i	0.904109	+	0.427301i	$0.140536\pi$
$150$	−7.29580	−	4.66597i	−0.595700	−	0.380975i
$151$	−7.46876	−	12.9363i	−0.607799	−	1.05274i	−0.991602	−	0.129324i	$-0.958719\pi$
$151$	−7.46876	−	12.9363i	−0.607799	−	1.05274i	0.383803	−	0.923415i	$-0.374614\pi$
$152$	−6.65937	+	1.78437i	−0.540146	+	0.144732i
$153$	7.30020	−	8.90800i	0.590186	−	0.720169i
$154$	−2.85715	+	8.61496i	−0.230236	+	0.694213i
$155$	−15.6656	+	3.41092i	−1.25829	+	0.273972i
$156$	−8.44937	−	4.33633i	−0.676491	−	0.347184i
$157$	13.6086	+	3.64642i	1.08609	+	0.291016i	0.757088	−	0.653313i	$-0.226622\pi$
$157$	13.6086	+	3.64642i	1.08609	+	0.291016i	0.329000	+	0.944330i	$0.393288\pi$
$158$	−5.55038	−	1.48722i	−0.441564	−	0.118317i
$159$	1.47002	+	0.754436i	0.116581	+	0.0598307i
$160$	1.88133	+	1.20856i	0.148732	+	0.0955449i
$161$	−2.02682	−	2.27870i	−0.159736	−	0.179587i
$162$	7.49020	+	4.98968i	0.588486	+	0.392026i
$163$	5.82648	−	1.56120i	0.456365	−	0.122283i	−0.0233112	−	0.999728i	$-0.507421\pi$
$163$	5.82648	−	1.56120i	0.456365	−	0.122283i	0.479676	+	0.877446i	$0.340754\pi$
$164$	3.86859	+	6.70060i	0.302086	+	0.523229i
$165$	0.0268874	+	13.2865i	0.00209318	+	1.03435i
$166$	−5.01942	+	8.69390i	−0.389583	+	0.674777i
$167$	5.93525	+	5.93525i	0.459284	+	0.459284i	0.898420	−	0.439137i	$-0.144716\pi$
$167$	5.93525	+	5.93525i	0.459284	+	0.459284i	−0.439137	+	0.898420i	$0.644716\pi$
$168$	−2.32691	+	3.94785i	−0.179525	+	0.304583i
$169$			17.0652i			1.31271i
$170$	8.17727	+	2.61230i	0.627168	+	0.200354i
$171$	−12.0590	−	16.8036i	−0.922178	−	1.28500i
$172$	−0.787066	−	0.210894i	−0.0600132	−	0.0160805i
$173$	−3.16440	−	11.8097i	−0.240585	−	0.897875i	−0.975551	−	0.219772i	$-0.929469\pi$
$173$	−3.16440	−	11.8097i	−0.240585	−	0.897875i	0.734966	−	0.678104i	$-0.237198\pi$
$174$	4.07600	−	0.201667i	0.309001	−	0.0152884i
$175$	13.0737	+	2.01953i	0.988278	+	0.152662i
$176$		−	3.43055i		−	0.258588i
$177$	2.91108	+	9.04930i	0.218810	+	0.680187i
$178$	0.332143	−	1.23958i	0.0248952	−	0.0929101i
$179$	0.740048	+	1.28180i	0.0553138	+	0.0958063i	0.892356	−	0.451331i	$-0.149051\pi$
$179$	0.740048	+	1.28180i	0.0553138	+	0.0958063i	−0.837043	+	0.547138i	$0.815717\pi$
$180$	−1.40062	+	6.56036i	−0.104396	+	0.488980i
$181$	−15.6223			−1.16120			−0.580599	−	0.814189i	$-0.697182\pi$
$181$	−15.6223			−1.16120			−0.580599	+	0.814189i	$0.697182\pi$
$182$	14.4823	+	0.847250i	1.07350	+	0.0628023i
$183$	1.02916	−	1.13630i	0.0760778	−	0.0839978i
$184$	0.998238	+	0.576333i	0.0735911	+	0.0424878i
$185$	−11.0492	−	0.524267i	−0.812354	−	0.0385449i
$186$	6.73332	+	10.4351i	0.493711	+	0.765136i
$187$	−3.40867	−	12.7213i	−0.249267	−	0.930276i
$188$	−6.23529	+	6.23529i	−0.454755	+	0.454755i
$189$	−13.5450	−	2.35196i	−0.985257	−	0.171080i
$190$	8.33215	−	12.9704i	0.604477	−	0.940972i
$191$	−13.1103	−	7.56922i	−0.948627	−	0.547690i	−0.0559725	−	0.998432i	$-0.517826\pi$
$191$	−13.1103	−	7.56922i	−0.948627	−	0.547690i	−0.892654	+	0.450743i	$0.851159\pi$
$192$	0.365065	−	1.69314i	0.0263463	−	0.122192i
$193$	−4.35769	+	16.2631i	−0.313673	+	1.17065i	0.611545	+	0.791210i	$0.290548\pi$
$193$	−4.35769	+	16.2631i	−0.313673	+	1.17065i	−0.925218	+	0.379436i	$0.876118\pi$
$194$	1.52620	−	2.64346i	0.109575	−	0.189789i
$195$	20.5015	−	5.53784i	1.46814	−	0.396573i
$196$	0.816238	−	6.95225i	0.0583027	−	0.496589i
$197$	−3.26809	−	3.26809i	−0.232842	−	0.232842i	0.581036	−	0.813878i	$-0.302648\pi$
$197$	−3.26809	−	3.26809i	−0.232842	−	0.232842i	−0.813878	+	0.581036i	$0.802648\pi$
$198$	9.62949	−	3.63196i	0.684338	−	0.258112i
$199$	4.35724	−	2.51565i	0.308876	−	0.178330i	−0.337547	−	0.941309i	$-0.609597\pi$
$199$	4.35724	−	2.51565i	0.308876	−	0.178330i	0.646424	+	0.762979i	$0.276264\pi$
$200$	−4.93046	+	0.830995i	−0.348636	+	0.0587602i
$201$	−6.89547	−	3.53885i	−0.486369	−	0.249611i
$202$	13.2328	−	13.2328i	0.931059	−	0.931059i
$203$	−5.57146	+	2.79629i	−0.391040	+	0.196261i
$204$	−0.328591	−	6.64132i	−0.0230060	−	0.464985i
$205$	−16.4803	−	5.26480i	−1.15104	−	0.367709i
$206$	−7.69148	+	4.44068i	−0.535891	+	0.309397i
$207$	−0.560910	+	3.41220i	−0.0389860	+	0.237165i
$208$	−5.29634	+	1.41915i	−0.367235	+	0.0984003i
$209$	−23.6512			−1.63599
$210$	−2.08983	−	10.0316i	−0.144212	−	0.692245i
$211$	2.58896			0.178231			0.0891156	−	0.996021i	$-0.471596\pi$
$211$	2.58896			0.178231			0.0891156	+	0.996021i	$0.471596\pi$
$212$	0.921459	−	0.246904i	0.0632861	−	0.0169575i
$213$	−0.643696	+	2.98541i	−0.0441053	+	0.204557i
$214$	−5.86591	+	3.38669i	−0.400985	+	0.231509i
$215$	1.61932	−	0.835199i	0.110436	−	0.0569601i
$216$	5.13911	−	0.767816i	0.349672	−	0.0522432i
$217$	−15.8466	−	10.4283i	−1.07574	−	0.707922i
$218$	10.0058	−	10.0058i	0.677680	−	0.677680i
$219$	5.59178	−	10.8956i	0.377858	−	0.736258i
$220$	5.16101	+	5.67517i	0.347955	+	0.382620i
$221$	−18.2300	+	10.5251i	−1.22628	+	0.707996i
$222$	2.62392	+	8.15666i	0.176106	+	0.547439i
$223$	−7.72857	−	7.72857i	−0.517543	−	0.517543i	0.399284	−	0.916827i	$-0.369259\pi$
$223$	−7.72857	−	7.72857i	−0.517543	−	0.517543i	−0.916827	+	0.399284i	$0.869259\pi$
$224$	0.534349	+	2.59123i	0.0357027	+	0.173134i
$225$	−7.55251	−	12.9599i	−0.503501	−	0.863995i
$226$	2.70469	−	4.68466i	0.179913	−	0.311619i
$227$	−1.96153	+	7.32054i	−0.130191	+	0.485881i	−0.999971	−	0.00755864i	$-0.997594\pi$
$227$	−1.96153	+	7.32054i	−0.130191	+	0.485881i	0.869780	+	0.493440i	$0.164261\pi$
$228$	−11.6730	−	2.51686i	−0.773064	−	0.166683i
$229$	−4.05881	−	2.34336i	−0.268214	−	0.154853i	0.359862	−	0.933006i	$-0.382824\pi$
$229$	−4.05881	−	2.34336i	−0.268214	−	0.154853i	−0.628076	+	0.778152i	$0.716157\pi$
$230$	−2.51843	+	0.548345i	−0.166061	+	0.0361568i
$231$	−11.2159	+	11.0158i	−0.737949	+	0.724785i
$232$	1.66606	−	1.66606i	0.109382	−	0.109382i
$233$	−0.486355	−	1.81510i	−0.0318622	−	0.118911i	0.948163	−	0.317784i	$-0.102939\pi$
$233$	−0.486355	−	1.81510i	−0.0318622	−	0.118911i	−0.980025	+	0.198873i	$0.936272\pi$
$234$	−9.59081	−	13.3642i	−0.626971	−	0.873648i
$235$	0.934521	−	19.6956i	0.0609614	−	1.28480i
$236$	4.75301	+	2.74415i	0.309394	+	0.178629i
$237$	−7.37677	−	6.68123i	−0.479173	−	0.433992i
$238$	4.55620	+	9.07798i	0.295334	+	0.588438i
$239$	18.5117			1.19742			0.598712	−	0.800964i	$-0.295679\pi$
$239$	18.5117			1.19742			0.598712	+	0.800964i	$0.295679\pi$
$240$	1.94328	+	3.35018i	0.125438	+	0.216253i
$241$	−4.18303	−	7.24521i	−0.269452	−	0.466705i	0.699268	−	0.714859i	$-0.253509\pi$
$241$	−4.18303	−	7.24521i	−0.269452	−	0.466705i	−0.968721	+	0.248154i	$0.920176\pi$
$242$	0.198954	−	0.742508i	0.0127893	−	0.0477302i
$243$	7.59607	+	13.6125i	0.487288	+	0.873241i
$244$		−	0.885128i		−	0.0566645i
$245$	9.10883	+	12.7291i	0.581942	+	0.813231i
$246$	0.662237	+	13.3848i	0.0422227	+	0.853385i
$247$	9.78403	+	36.5145i	0.622543	+	2.32336i
$248$	6.92572	+	1.85574i	0.439784	+	0.117840i
$249$	−14.6103	+	9.42740i	−0.925887	+	0.597437i
$250$	6.90629	−	8.79222i	0.436792	−	0.556069i
$251$		−	29.1045i		−	1.83706i	−0.395355	−	0.918528i	$-0.629378\pi$
$251$		−	29.1045i		−	1.83706i	0.395355	−	0.918528i	$-0.370622\pi$
$252$	−6.70781	+	4.24327i	−0.422552	+	0.267301i
$253$	2.79610	+	2.79610i	0.175789	+	0.175789i
$254$	−3.20264	+	5.54713i	−0.200951	+	0.348058i
$255$	10.5349	+	10.4924i	0.659724	+	0.657059i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	18.5540	−	4.97152i	1.15737	−	0.310115i	0.371452	−	0.928452i	$-0.378860\pi$
$257$	18.5540	−	4.97152i	1.15737	−	0.310115i	0.785913	+	0.618337i	$0.212193\pi$
$258$	−1.04606	−	0.947425i	−0.0651246	−	0.0589841i
$259$	−8.69853	−	9.77954i	−0.540501	−	0.607671i
$260$	6.62673	−	10.3156i	0.410972	−	0.639749i
$261$	6.44045	+	2.91271i	0.398654	+	0.180293i
$262$	11.7967	+	3.16093i	0.728805	+	0.195283i
$263$	7.96472	+	2.13414i	0.491126	+	0.131597i	0.495878	−	0.868392i	$-0.334846\pi$
$263$	7.96472	+	2.13414i	0.491126	+	0.131597i	−0.00475276	+	0.999989i	$0.501513\pi$
$264$	2.71303	−	5.28636i	0.166975	−	0.325353i
$265$	−1.15292	+	1.79472i	−0.0708234	+	0.110249i
$266$	17.8647	−	3.68396i	1.09535	−	0.225878i
$267$	1.49213	−	1.64747i	0.0913169	−	0.100823i
$268$	−4.32230	+	1.15816i	−0.264027	+	0.0707457i
$269$	2.64417	+	4.57984i	0.161218	+	0.279238i	0.935306	−	0.353841i	$-0.115124\pi$
$269$	2.64417	+	4.57984i	0.161218	+	0.279238i	−0.774088	+	0.633078i	$0.781791\pi$
$270$	−7.34651	+	9.00160i	−0.447094	+	0.547820i
$271$	−11.2806	+	19.5386i	−0.685247	+	1.18688i	0.288112	+	0.957597i	$0.406973\pi$
$271$	−11.2806	+	19.5386i	−0.685247	+	1.18688i	−0.973359	+	0.229286i	$0.926361\pi$
$272$	−2.71462	−	2.71462i	−0.164598	−	0.164598i
$273$	21.6467	+	12.7588i	1.31012	+	0.772200i
$274$			3.51961i			0.212627i
$275$	−17.0757	−	1.62408i	−1.02970	−	0.0979359i
$276$	1.08246	+	1.67756i	0.0651564	+	0.100977i
$277$	−24.3091	−	6.51359i	−1.46059	−	0.391364i	−0.560896	−	0.827886i	$-0.689543\pi$
$277$	−24.3091	−	6.51359i	−1.46059	−	0.391364i	−0.899693	+	0.436522i	$0.856210\pi$
$278$	2.41557	+	9.01502i	0.144876	+	0.540685i
$279$	2.12330	+	21.4050i	0.127119	+	1.28149i
$280$	−4.78228	−	3.48278i	−0.285796	−	0.208136i
$281$			29.4678i			1.75790i	0.476910	+	0.878952i	$0.341757\pi$
$281$			29.4678i			1.75790i	−0.476910	+	0.878952i	$0.658243\pi$
$282$	−14.5395	+	4.67722i	−0.865814	+	0.278524i
$283$	0.269428	−	1.00552i	0.0160158	−	0.0597719i	−0.957455	−	0.288581i	$-0.906817\pi$
$283$	0.269428	−	1.00552i	0.0160158	−	0.0597719i	0.973471	+	0.228809i	$0.0734832\pi$
$284$	0.881618	+	1.52701i	0.0523144	+	0.0906112i
$285$	23.0971	−	13.3975i	1.36815	−	0.793600i
$286$	−18.8103			−1.11228
$287$	−9.18249	−	18.2956i	−0.542025	−	1.07996i
$288$	1.90156	−	2.32036i	0.112051	−	0.136728i
$289$	1.95863	+	1.13081i	0.115213	+	0.0665185i
$290$	−0.249702	+	5.26261i	−0.0146630	+	0.309031i
$291$	4.44238	−	2.86649i	0.260417	−	0.168036i
$292$	−1.83002	−	6.82973i	−0.107094	−	0.399680i
$293$	12.5118	−	12.5118i	0.730947	−	0.730947i	−0.239860	−	0.970807i	$-0.577102\pi$
$293$	12.5118	−	12.5118i	0.730947	−	0.730947i	0.970807	+	0.239860i	$0.0771017\pi$
$294$	6.75593	−	10.0676i	0.394014	−	0.587157i
$295$	−11.9913	+	2.61089i	−0.698158	+	0.152012i
$296$	4.28416	+	2.47346i	0.249012	+	0.143767i
$297$	17.7110	+	2.01870i	1.02770	+	0.117137i
$298$	0.518128	−	1.93368i	0.0300144	−	0.112015i
$299$	3.16013	−	5.47351i	0.182755	−	0.316541i
$300$	−8.25485	−	2.61869i	−0.476594	−	0.151190i
$301$	2.04624	+	0.678636i	0.117943	+	0.0391159i
$302$	−10.5624	−	10.5624i	−0.607799	−	0.607799i
$303$	30.8564	−	9.92621i	1.77265	−	0.570246i
$304$	−5.97063	+	3.44715i	−0.342439	+	0.197707i
$305$	1.33161	+	1.46427i	0.0762476	+	0.0838437i
$306$	4.74590	−	10.4939i	0.271305	−	0.599896i
$307$	21.9524	−	21.9524i	1.25289	−	1.25289i	0.298469	−	0.954419i	$-0.403524\pi$
$307$	21.9524	−	21.9524i	1.25289	−	1.25289i	0.954419	−	0.298469i	$-0.0964760\pi$
$308$	−0.530083	+	9.06090i	−0.0302043	+	0.516293i
$309$	−15.3642	+	0.760169i	−0.874037	+	0.0432445i
$310$	−14.2490	+	7.34926i	−0.809291	+	0.417410i
$311$	9.54424	−	5.51037i	0.541204	−	0.312465i	−0.204362	−	0.978895i	$-0.565512\pi$
$311$	9.54424	−	5.51037i	0.541204	−	0.312465i	0.745567	+	0.666431i	$0.232179\pi$
$312$	−9.28379	−	2.00171i	−0.525591	−	0.113325i
$313$	−8.87281	+	2.37746i	−0.501521	+	0.134382i	−0.500706	−	0.865618i	$-0.666926\pi$
$313$	−8.87281	+	2.37746i	−0.501521	+	0.134382i	−0.000815167		1.00000i	$0.500259\pi$
$314$	14.0887			0.795071
$315$	4.71305	−	17.1110i	0.265551	−	0.964097i
$316$	−5.74617			−0.323248
$317$	4.91615	−	1.31728i	0.276118	−	0.0739857i	−0.118103	−	0.993001i	$-0.537681\pi$
$317$	4.91615	−	1.31728i	0.276118	−	0.0739857i	0.394221	+	0.919016i	$0.371014\pi$
$318$	1.61520	+	0.348259i	0.0905758	+	0.0195294i
$319$	7.00002	−	4.04147i	0.391926	−	0.226279i
$320$	2.13002	+	0.680454i	0.119072	+	0.0380385i
$321$	−11.7175	+	0.579743i	−0.654006	+	0.0323581i
$322$	−2.54753	−	1.67648i	−0.141968	−	0.0934264i
$323$	−18.7154	+	18.7154i	−1.04135	+	1.04135i
$324$	8.52640	+	2.88105i	0.473689	+	0.160059i
$325$	4.55649	+	27.0346i	0.252749	+	1.49961i
$326$	5.22388	−	3.01601i	0.289324	−	0.167041i
$327$	23.3316	−	7.50557i	1.29024	−	0.415059i
$328$	5.47101	+	5.47101i	0.302086	+	0.302086i
$329$	17.4323	−	15.5054i	0.961076	−	0.854840i
$330$	3.46476	+	12.8268i	0.190729	+	0.706090i
$331$	17.0080	−	29.4586i	0.934842	−	1.61919i	0.159925	−	0.987129i	$-0.448875\pi$
$331$	17.0080	−	29.4586i	0.934842	−	1.61919i	0.774916	−	0.632064i	$-0.217792\pi$
$332$	−2.59824	+	9.69678i	−0.142597	+	0.532180i
$333$	−2.40727	+	14.6442i	−0.131918	+	0.802498i
$334$	7.26917	+	4.19686i	0.397751	+	0.229642i
$335$	5.40803	−	8.41852i	0.295472	−	0.459953i
$336$	−1.22584	+	4.41558i	−0.0668753	+	0.240889i
$337$	19.0320	−	19.0320i	1.03674	−	1.03674i	0.0374412	−	0.999299i	$-0.488079\pi$
$337$	19.0320	−	19.0320i	1.03674	−	1.03674i	0.999299	−	0.0374412i	$-0.0119207\pi$
$338$	4.41679	+	16.4837i	0.240242	+	0.896595i
$339$	7.87266	−	5.07990i	0.427584	−	0.275903i
$340$	8.57475	+	0.406857i	0.465031	+	0.0220649i
$341$	21.3018	+	12.2986i	1.15356	+	0.666006i
$342$	−15.9972	−	13.1099i	−0.865031	−	0.708903i
$343$	−3.23013	+	18.2364i	−0.174410	+	0.984673i
$344$	−0.814830			−0.0439327
$345$	−4.31447	−	1.14671i	−0.232283	−	0.0617366i
$346$	−6.11315	−	10.5883i	−0.328645	−	0.569230i
$347$	−7.08212	+	26.4308i	−0.380188	+	1.41888i	0.465425	+	0.885087i	$0.345901\pi$
$347$	−7.08212	+	26.4308i	−0.380188	+	1.41888i	−0.845614	+	0.533795i	$0.820765\pi$
$348$	3.88492	−	1.24974i	0.208254	−	0.0669932i
$349$		−	7.53522i		−	0.403351i	−0.979452	−	0.201675i	$-0.935361\pi$
$349$		−	7.53522i		−	0.403351i	0.979452	−	0.201675i	$-0.0646386\pi$
$350$	13.1509	−	1.43301i	0.702946	−	0.0765975i
$351$	−4.21007	−	28.1786i	−0.224717	−	1.50406i
$352$	−0.887893	−	3.31366i	−0.0473248	−	0.176619i
$353$	14.4208	+	3.86404i	0.767542	+	0.205662i	0.621285	−	0.783584i	$-0.286611\pi$
$353$	14.4208	+	3.86404i	0.767542	+	0.205662i	0.146257	+	0.989247i	$0.453277\pi$
$354$	5.15402	+	7.98751i	0.273933	+	0.424532i
$355$	−3.75573	−	1.19980i	−0.199333	−	0.0636788i
$356$		−	1.28330i		−	0.0680149i
$357$	−0.158319	+	17.5921i	−0.00837913	+	0.931071i
$358$	1.04659	+	1.04659i	0.0553138	+	0.0553138i
$359$	−15.4927	+	26.8342i	−0.817675	+	1.41625i	0.0897169	+	0.995967i	$0.471404\pi$
$359$	−15.4927	+	26.8342i	−0.817675	+	1.41625i	−0.907391	+	0.420287i	$0.861930\pi$
$360$	0.345053	+	6.69932i	0.0181859	+	0.353085i
$361$	14.2656	+	24.7088i	0.750822	+	1.30046i
$362$	−15.0900	+	4.04336i	−0.793113	+	0.212514i
$363$	0.893789	−	0.986836i	0.0469117	−	0.0517954i
$364$	14.2082	−	2.92993i	0.744710	−	0.153570i
$365$	13.3022	+	8.54530i	0.696270	+	0.447282i
$366$	0.699997	−	1.36395i	0.0365894	−	0.0712948i
$367$	−9.66937	−	2.59090i	−0.504737	−	0.135244i	−0.00253931	−	0.999997i	$-0.500808\pi$
$367$	−9.66937	−	2.59090i	−0.504737	−	0.135244i	−0.502197	+	0.864753i	$0.667475\pi$
$368$	1.11339	+	0.298332i	0.0580395	+	0.0155516i
$369$	−9.56481	+	21.1492i	−0.497924	+	1.10099i
$370$	−10.8084	+	2.35334i	−0.561903	+	0.122345i
$371$	−2.47194	+	0.509750i	−0.128337	+	0.0264649i
$372$	9.20468	+	8.33678i	0.477240	+	0.432242i
$373$	−13.8184	+	3.70262i	−0.715489	+	0.191715i	−0.598158	−	0.801378i	$-0.704100\pi$
$373$	−13.8184	+	3.70262i	−0.715489	+	0.191715i	−0.117331	+	0.993093i	$0.537434\pi$
$374$	−6.58505	−	11.4056i	−0.340505	−	0.589772i
$375$	17.5956	−	8.08669i	0.908633	−	0.417595i
$376$	−4.40902	+	7.63664i	−0.227378	+	0.393830i
$377$	−9.13527	−	9.13527i	−0.470490	−	0.470490i
$378$	−13.6922	+	1.23390i	−0.704253	+	0.0634647i
$379$		−	2.99621i		−	0.153905i	−0.997035	−	0.0769524i	$-0.975481\pi$
$379$		−	2.99621i		−	0.153905i	0.997035	−	0.0769524i	$-0.0245189\pi$
$380$	4.69125	−	14.6850i	0.240656	−	0.753323i
$381$	−9.32206	+	6.01514i	−0.477584	+	0.308165i
$382$	−14.6226	−	3.91812i	−0.748158	−	0.200468i
$383$	−2.17034	−	8.09984i	−0.110899	−	0.413882i	0.888048	−	0.459751i	$-0.152061\pi$
$383$	−2.17034	−	8.09984i	−0.110899	−	0.413882i	−0.998947	+	0.0458683i	$0.985395\pi$
$384$	−0.0855915	−	1.72993i	−0.00436782	−	0.0882804i
$385$	−12.7545	−	15.7869i	−0.650030	−	0.804576i
$386$			16.8368i			0.856972i
$387$	−0.862669	−	2.28721i	−0.0438519	−	0.116266i
$388$	0.790020	−	2.94839i	0.0401072	−	0.149682i
$389$	−13.0941	−	22.6796i	−0.663895	−	1.14990i	−0.979584	−	0.201037i	$-0.935569\pi$
$389$	−13.0941	−	22.6796i	−0.663895	−	1.14990i	0.315688	−	0.948863i	$-0.397765\pi$
$390$	18.3696	−	10.6553i	0.930181	−	0.539553i
$391$	4.42515			0.223790
$392$	−1.01095	−	6.92661i	−0.0510606	−	0.349847i
$393$	15.6785	+	14.2002i	0.790878	+	0.716307i
$394$	−4.00258	−	2.31089i	−0.201647	−	0.116421i
$395$	9.50590	−	8.64468i	0.478294	−	0.434961i
$396$	8.36136	−	6.00050i	0.420174	−	0.301537i
$397$	1.80333	+	6.73010i	0.0905063	+	0.337774i	0.996300	−	0.0859451i	$-0.0273910\pi$
$397$	1.80333	+	6.73010i	0.0905063	+	0.337774i	−0.905794	+	0.423719i	$0.860724\pi$
$398$	3.55767	−	3.55767i	0.178330	−	0.178330i
$399$	30.4423	+	8.45132i	1.52402	+	0.423095i
$400$	−4.54738	+	2.07878i	−0.227369	+	0.103939i
$401$	−16.7034	−	9.64369i	−0.834126	−	0.481583i	0.0211370	−	0.999777i	$-0.493271\pi$
$401$	−16.7034	−	9.64369i	−0.834126	−	0.481583i	−0.855263	+	0.518193i	$0.826605\pi$
$402$	−7.57643	−	1.63358i	−0.377878	−	0.0814758i
$403$	10.1753	−	37.9749i	0.506870	−	1.89167i
$404$	9.35702	−	16.2068i	0.465529	−	0.806320i
$405$	−18.4396	+	8.06120i	−0.916269	+	0.400564i
$406$	−4.65788	+	4.14301i	−0.231167	+	0.205614i
$407$	12.0001	+	12.0001i	0.594822	+	0.594822i
$408$	−2.03629	−	6.32998i	−0.100812	−	0.313381i
$409$	−30.3259	+	17.5087i	−1.49952	+	0.865747i	−1.00000		0.000555857i	$-0.999823\pi$
$409$	−30.3259	+	17.5087i	−1.49952	+	0.865747i	−0.499519	+	0.866303i	$0.666490\pi$
$410$	−17.2814	−	0.819974i	−0.853469	−	0.0404956i
$411$	−2.78346	+	5.42359i	−0.137298	+	0.267526i
$412$	−6.28007	+	6.28007i	−0.309397	+	0.309397i
$413$	−12.1298	−	7.98237i	−0.596868	−	0.392787i
$414$	0.341345	+	3.44111i	0.0167762	+	0.169121i
$415$	−10.2898	−	19.9502i	−0.505106	−	0.979319i
$416$	−4.74857	+	2.74159i	−0.232818	+	0.134417i
$417$	−3.40716	+	15.8021i	−0.166850	+	0.773834i
$418$	−22.8453	+	6.12139i	−1.11740	+	0.299407i
$419$	−8.91090			−0.435326			−0.217663	−	0.976024i	$-0.569843\pi$
$419$	−8.91090			−0.435326			−0.217663	+	0.976024i	$0.569843\pi$
$420$	−4.61498	−	9.14888i	−0.225188	−	0.446419i
$421$	18.8014			0.916324			0.458162	−	0.888869i	$-0.348508\pi$
$421$	18.8014			0.916324			0.458162	+	0.888869i	$0.348508\pi$
$422$	2.50074	−	0.670072i	0.121734	−	0.0326186i
$423$	−26.1038	−	4.29103i	−1.26921	−	0.208637i
$424$	0.826158	−	0.476982i	0.0401218	−	0.0231643i
$425$	−14.7973	+	12.2270i	−0.717774	+	0.593096i
$426$	0.150918	+	3.05028i	0.00731201	+	0.147787i
$427$	−0.136768	+	2.33783i	−0.00661869	+	0.113136i
$428$	−4.78950	+	4.78950i	−0.231509	+	0.231509i
$429$	−28.9860	−	14.8760i	−1.39946	−	0.718220i
$430$	1.34797	−	1.22585i	0.0650051	−	0.0591158i
$431$	−28.5894	+	16.5061i	−1.37710	+	0.795069i	−0.991810	−	0.127726i	$-0.959232\pi$
$431$	−28.5894	+	16.5061i	−1.37710	+	0.795069i	−0.385291	+	0.922795i	$0.625899\pi$
$432$	4.76527	−	2.07175i	0.229269	−	0.0996772i
$433$	−27.9007	−	27.9007i	−1.34082	−	1.34082i	−0.895242	−	0.445581i	$-0.852997\pi$
$433$	−27.9007	−	27.9007i	−1.34082	−	1.34082i	−0.445581	−	0.895242i	$-0.647003\pi$
$434$	−18.0057	−	5.97160i	−0.864302	−	0.286646i
$435$	−4.54668	+	7.91201i	−0.217997	+	0.379352i
$436$	7.07519	−	12.2546i	0.338840	−	0.586888i
$437$	2.05679	−	7.67603i	0.0983895	−	0.367194i
$438$	2.58125	−	11.9716i	0.123337	−	0.572027i
$439$	13.8443	+	7.99298i	0.660750	+	0.381484i	0.792563	−	0.609790i	$-0.208746\pi$
$439$	13.8443	+	7.99298i	0.660750	+	0.381484i	−0.131813	+	0.991275i	$0.542080\pi$
$440$	6.45399	+	4.14602i	0.307682	+	0.197654i
$441$	18.3726	−	10.1710i	0.874884	−	0.484333i
$442$	−14.8848	+	14.8848i	−0.707996	+	0.707996i
$443$	−4.88974	−	18.2487i	−0.232318	−	0.867024i	−0.979339	−	0.202224i	$-0.935183\pi$
$443$	−4.88974	−	18.2487i	−0.232318	−	0.867024i	0.747021	−	0.664801i	$-0.231483\pi$
$444$	4.64561	+	7.19960i	0.220471	+	0.341678i
$445$	1.93063	+	2.12297i	0.0915207	+	0.100638i
$446$	−9.46552	−	5.46492i	−0.448205	−	0.258772i
$447$	2.32765	−	2.56997i	0.110094	−	0.121556i
$448$	1.18680	+	2.36464i	0.0560711	+	0.111719i
$449$	6.78726			0.320311			0.160155	−	0.987092i	$-0.448801\pi$
$449$	6.78726			0.320311			0.160155	+	0.987092i	$0.448801\pi$
$450$	−10.6494	−	10.5636i	−0.502020	−	0.497972i
$451$	13.2714	+	22.9868i	0.624926	+	1.08240i
$452$	1.40005	−	5.22506i	0.0658528	−	0.245766i
$453$	−7.92309	−	24.6295i	−0.372259	−	1.15720i
$454$			7.57878i			0.355690i
$455$	−19.0967	+	26.2221i	−0.895267	+	1.22931i
$456$	−11.9267	+	0.590093i	−0.558518	+	0.0276336i
$457$	1.37469	+	5.13040i	0.0643051	+	0.239990i	0.990596	−	0.136819i	$-0.0436880\pi$
$457$	1.37469	+	5.13040i	0.0643051	+	0.239990i	−0.926291	+	0.376809i	$0.877021\pi$
$458$	−4.52702	−	1.21301i	−0.211534	−	0.0566803i
$459$	15.6123	−	12.4174i	0.728718	−	0.579597i
$460$	−2.29070	+	1.18148i	−0.106804	+	0.0550868i
$461$		−	28.0988i		−	1.30869i	−0.756195	−	0.654347i	$-0.772944\pi$
$461$		−	28.0988i		−	1.30869i	0.756195	−	0.654347i	$-0.227056\pi$
$462$	−7.98259	+	13.5433i	−0.371384	+	0.630091i
$463$	−7.61828	−	7.61828i	−0.354051	−	0.354051i	0.507563	−	0.861615i	$-0.330546\pi$
$463$	−7.61828	−	7.61828i	−0.354051	−	0.354051i	−0.861615	+	0.507563i	$0.830546\pi$
$464$	1.17808	−	2.04049i	0.0546910	−	0.0947275i
$465$	−27.7694	+	0.0561961i	−1.28777	+	0.00260603i
$466$	−0.939566	−	1.62738i	−0.0435246	−	0.0753867i
$467$	8.84631	−	2.37036i	0.409358	−	0.109687i	−0.0482625	−	0.998835i	$-0.515368\pi$
$467$	8.84631	−	2.37036i	0.409358	−	0.109687i	0.457621	+	0.889147i	$0.348702\pi$
$468$	−12.7229	−	10.4266i	−0.588118	−	0.481969i
$469$	11.5952	−	2.39109i	0.535416	−	0.110410i
$470$	−4.19491	−	19.2663i	−0.193497	−	0.888689i
$471$	21.7102	+	11.1420i	1.00035	+	0.513394i
$472$	5.30129	+	1.42048i	0.244012	+	0.0653827i
$473$	−2.70007	−	0.723482i	−0.124149	−	0.0332657i
$474$	−8.85464	−	4.54432i	−0.406707	−	0.208728i
$475$	14.3317	+	31.3510i	0.657583	+	1.43848i
$476$	6.75050	+	7.58942i	0.309409	+	0.347861i
$477$	2.21354	+	1.81402i	0.101351	+	0.0830583i
$478$	17.8810	−	4.79119i	0.817856	−	0.219144i
$479$	−7.76447	−	13.4485i	−0.354768	−	0.614476i	0.632310	−	0.774715i	$-0.282107\pi$
$479$	−7.76447	−	13.4485i	−0.354768	−	0.614476i	−0.987078	+	0.160239i	$0.948773\pi$
$480$	2.74415	+	2.73307i	0.125253	+	0.124747i
$481$	13.5624	−	23.4908i	0.618392	−	1.07109i
$482$	−5.91569	−	5.91569i	−0.269452	−	0.269452i
$483$	−2.59982	−	4.59808i	−0.118296	−	0.209220i
$484$		−	0.768701i		−	0.0349409i
$485$	3.12870	+	6.06605i	0.142067	+	0.275445i
$486$	10.8604	+	11.1826i	0.492638	+	0.507255i
$487$	3.17410	+	0.850498i	0.143832	+	0.0385397i	0.330017	−	0.943975i	$-0.392946\pi$
$487$	3.17410	+	0.850498i	0.143832	+	0.0385397i	−0.186185	+	0.982515i	$0.559612\pi$
$488$	−0.229088	−	0.854968i	−0.0103703	−	0.0387026i
$489$	10.4350	−	0.516289i	0.471886	−	0.0233474i
$490$	12.0930	+	9.93780i	0.546305	+	0.448944i
$491$		−	11.6805i		−	0.527133i	−0.964641	−	0.263567i	$-0.915101\pi$
$491$		−	11.6805i		−	0.527133i	0.964641	−	0.263567i	$-0.0848989\pi$
$492$	4.10392	+	12.7573i	0.185019	+	0.575145i
$493$	2.34113	−	8.73722i	0.105439	−	0.393504i
$494$	18.9013	+	32.7380i	0.850409	+	1.47295i
$495$	−4.80489	+	22.5057i	−0.215964	+	1.01155i
$496$	7.17003			0.321944
$497$	−2.09261	−	4.16941i	−0.0938664	−	0.187024i
$498$	−11.6724	+	12.8876i	−0.523054	+	0.577506i
$499$	2.51013	+	1.44922i	0.112369	+	0.0648762i	0.555131	−	0.831763i	$-0.312668\pi$
$499$	2.51013	+	1.44922i	0.112369	+	0.0648762i	−0.442762	+	0.896639i	$0.646001\pi$
$500$	4.39537	−	10.2801i	0.196567	−	0.459741i
$501$	7.88247	+	12.2160i	0.352163	+	0.545769i
$502$	−7.53279	−	28.1127i	−0.336205	−	1.25473i
$503$	−14.8328	+	14.8328i	−0.661362	+	0.661362i	−0.955701	−	0.294339i	$-0.904901\pi$
$503$	−14.8328	+	14.8328i	−0.661362	+	0.661362i	0.294339	+	0.955701i	$0.404901\pi$
$504$	−5.38101	+	5.83479i	−0.239689	+	0.259902i
$505$	8.90263	+	40.8879i	0.396162	+	1.81949i
$506$	3.42451	+	1.97714i	0.152238	+	0.0878947i
$507$	−6.22990	+	28.8938i	−0.276680	+	1.28322i
$508$	−1.65781	+	6.18702i	−0.0735533	+	0.274505i
$509$	−9.66165	+	16.7345i	−0.428245	+	0.741742i	−0.996717	−	0.0809602i	$-0.974201\pi$
$509$	−9.66165	+	16.7345i	−0.428245	+	0.741742i	0.568472	+	0.822702i	$0.307535\pi$
$510$	12.8916	+	7.40823i	0.570850	+	0.328042i
$511$	3.77820	+	18.3217i	0.167138	+	0.810505i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−14.2833	−	32.8532i	−0.630622	−	1.45050i
$514$	16.6350	−	9.60425i	0.733740	−	0.423625i
$515$	0.941233	−	19.8370i	0.0414757	−	0.874123i
$516$	−1.25562	−	0.644403i	−0.0552758	−	0.0283683i
$517$	−21.3905	+	21.3905i	−0.940753	+	0.940753i
$518$	−10.9333	−	7.19497i	−0.480380	−	0.316129i
$519$	−1.04647	−	21.1507i	−0.0459349	−	0.928413i
$520$	3.73105	−	11.6793i	0.163617	−	0.512170i
$521$	−27.4522	+	15.8496i	−1.20270	+	0.694382i	−0.961156	−	0.276007i	$-0.910989\pi$
$521$	−27.4522	+	15.8496i	−1.20270	+	0.694382i	−0.241549	+	0.970389i	$0.577655\pi$
$522$	6.97487	+	1.14655i	0.305282	+	0.0501833i
$523$	15.5807	−	4.17483i	0.681295	−	0.182552i	0.0984575	−	0.995141i	$-0.468609\pi$
$523$	15.5807	−	4.17483i	0.681295	−	0.182552i	0.582837	+	0.812589i	$0.301942\pi$
$524$	12.2129			0.533522
$525$	21.3984	+	8.19209i	0.933901	+	0.357532i
$526$	8.24568			0.359529
$527$	26.5882	−	7.12430i	1.15820	−	0.310339i
$528$	1.25238	−	5.80841i	0.0545026	−	0.252779i
$529$	18.7679	−	10.8357i	0.815998	−	0.471117i
$530$	−0.649129	+	2.03196i	−0.0281964	+	0.0882628i
$531$	1.62528	+	16.3845i	0.0705311	+	0.711026i
$532$	16.3025	−	8.18215i	0.706802	−	0.354741i
$533$	29.9985	−	29.9985i	1.29938	−	1.29938i
$534$	1.01489	−	1.97752i	0.0439186	−	0.0855758i
$535$	0.717831	−	15.1287i	0.0310346	−	0.654071i
$536$	−3.87527	+	2.23739i	−0.167386	+	0.0966405i
$537$	0.785066	+	2.44044i	0.0338781	+	0.105313i
$538$	3.73942	+	3.73942i	0.161218	+	0.161218i
$539$	2.80015	−	23.8501i	0.120611	−	1.02729i
$540$	−4.76640	+	10.5963i	−0.205113	+	0.455992i
$541$	3.17726	−	5.50318i	0.136601	−	0.236600i	−0.789607	−	0.613613i	$-0.789715\pi$
$541$	3.17726	−	5.50318i	0.136601	−	0.236600i	0.926208	+	0.377013i	$0.123049\pi$
$542$	−5.83926	+	21.7924i	−0.250818	+	0.936065i
$543$	−26.4508	−	5.70317i	−1.13511	−	0.244746i
$544$	−3.32472	−	1.91953i	−0.142546	−	0.0822991i
$545$	6.73160	+	30.9168i	0.288350	+	1.32433i
$546$	24.2114	+	6.72151i	1.03615	+	0.287654i
$547$	−1.75965	+	1.75965i	−0.0752374	+	0.0752374i	−0.743724	−	0.668487i	$-0.766942\pi$
$547$	−1.75965	+	1.75965i	−0.0752374	+	0.0752374i	0.668487	+	0.743724i	$0.266942\pi$
$548$	0.910941	+	3.39968i	0.0389135	+	0.145227i
$549$	2.15734	−	1.54821i	0.0920730	−	0.0660759i
$550$	−16.9142	+	2.85077i	−0.721224	+	0.121557i
$551$	−14.0678	−	8.12202i	−0.599307	−	0.346010i
$552$	1.47976	+	1.34024i	0.0629827	+	0.0570442i
$553$	15.1770	+	0.887888i	0.645392	+	0.0377569i
$554$	−25.1666			−1.06923
$555$	−18.5165	−	4.92134i	−0.785981	−	0.208899i
$556$	4.66652	+	8.08264i	0.197904	+	0.342780i
$557$	12.0540	−	44.9860i	0.510742	−	1.90612i	0.0982317	−	0.995164i	$-0.468681\pi$
$557$	12.0540	−	44.9860i	0.510742	−	1.90612i	0.412511	−	0.910953i	$-0.364652\pi$
$558$	7.59098	+	20.1261i	0.321352	+	0.852007i
$559$			4.46786i			0.188970i
$560$	−5.52074	−	2.12637i	−0.233294	−	0.0898554i
$561$	−1.12725	−	22.7834i	−0.0475925	−	0.961916i
$562$	7.62684	+	28.4638i	0.321719	+	1.20067i
$563$	39.9714	+	10.7103i	1.68459	+	0.451386i	0.968986	−	0.247115i	$-0.0794827\pi$
$563$	39.9714	+	10.7103i	1.68459	+	0.451386i	0.715609	+	0.698501i	$0.246149\pi$
$564$	−12.8335	+	8.28094i	−0.540388	+	0.348690i
$565$	5.54460	+	10.7501i	0.233263	+	0.452260i
$566$		−	1.04099i		−	0.0437561i
$567$	−22.0751	−	8.92702i	−0.927065	−	0.374900i
$568$	1.24680	+	1.24680i	0.0523144	+	0.0523144i
$569$	−16.0682	+	27.8309i	−0.673614	+	1.16673i	0.303258	+	0.952908i	$0.401926\pi$
$569$	−16.0682	+	27.8309i	−0.673614	+	1.16673i	−0.976872	+	0.213825i	$0.931408\pi$
$570$	18.8425	−	18.9190i	0.789227	−	0.792428i
$571$	0.490240	+	0.849121i	0.0205159	+	0.0355346i	0.876101	−	0.482127i	$-0.160136\pi$
$571$	0.490240	+	0.849121i	0.0205159	+	0.0355346i	−0.855585	+	0.517662i	$0.826802\pi$
$572$	−18.1694	+	4.86847i	−0.759700	+	0.203561i
$573$	−19.4343	−	17.6019i	−0.811879	−	0.735329i
$574$	−13.6049	−	15.2956i	−0.567856	−	0.638426i
$575$	2.01206	−	5.40070i	0.0839085	−	0.225225i
$576$	1.23621	−	2.73346i	0.0515089	−	0.113894i
$577$	−24.0992	−	6.45735i	−1.00326	−	0.268823i	−0.280450	−	0.959869i	$-0.590484\pi$
$577$	−24.0992	−	6.45735i	−1.00326	−	0.268823i	−0.722811	+	0.691046i	$0.757150\pi$
$578$	2.18457	+	0.585353i	0.0908659	+	0.0243475i
$579$	−13.3153	+	25.9449i	−0.553364	+	1.07823i
$580$	1.12087	+	5.14792i	0.0465416	+	0.213756i
$581$	8.36091	−	25.2100i	0.346869	−	1.04589i
$582$	3.54911	−	3.91858i	0.147115	−	0.162431i
$583$	3.16112	−	0.847018i	0.130920	−	0.0350799i
$584$	−3.53533	−	6.12337i	−0.146293	−	0.253387i
$585$	36.7335	−	1.89198i	1.51875	−	0.0782238i
$586$	8.84718	−	15.3238i	0.365473	−	0.633019i
$587$	26.5508	+	26.5508i	1.09587	+	1.09587i	0.994888	+	0.100982i	$0.0321986\pi$
$587$	26.5508	+	26.5508i	1.09587	+	1.09587i	0.100982	+	0.994888i	$0.467801\pi$
$588$	3.92003	−	11.4732i	0.161659	−	0.473145i
$589$		−	49.4323i		−	2.03682i
$590$	−10.9069	+	5.62549i	−0.449031	+	0.231598i
$591$	−4.34028	−	6.72641i	−0.178535	−	0.276688i
$592$	4.77836	+	1.28036i	0.196389	+	0.0526223i
$593$	5.39739	+	20.1433i	0.221644	+	0.827188i	0.983721	+	0.179701i	$0.0575131\pi$
$593$	5.39739	+	20.1433i	0.221644	+	0.827188i	−0.762077	+	0.647487i	$0.775820\pi$
$594$	17.6300	−	2.63403i	0.723368	−	0.108076i
$595$	−22.5851	−	2.39956i	−0.925897	−	0.0983724i
$596$		−	2.00189i		−	0.0820008i
$597$	8.29579	−	2.66868i	0.339524	−	0.109222i
$598$	1.63581	−	6.10491i	0.0668931	−	0.249648i
$599$	14.8838	+	25.7795i	0.608134	+	1.05332i	0.991548	+	0.129743i	$0.0414152\pi$
$599$	14.8838	+	25.7795i	0.608134	+	1.05332i	−0.383413	+	0.923577i	$0.625251\pi$
$600$	−8.65133	−	0.392946i	−0.353189	−	0.0160420i
$601$	13.1980			0.538359			0.269180	−	0.963090i	$-0.413247\pi$
$601$	13.1980			0.538359			0.269180	+	0.963090i	$0.413247\pi$
$602$	2.15216	+	0.125906i	0.0877155	+	0.00513155i
$603$	−10.3831	−	8.50906i	−0.422832	−	0.346516i
$604$	−12.9363	−	7.46876i	−0.526369	−	0.303900i
$605$	1.15645	+	1.27166i	0.0470165	+	0.0517004i
$606$	27.2359	−	17.5742i	1.10638	−	0.713903i
$607$	8.34043	+	31.1269i	0.338528	+	1.26340i	0.899994	+	0.435903i	$0.143571\pi$
$607$	8.34043	+	31.1269i	0.338528	+	1.26340i	−0.561466	+	0.827500i	$0.689763\pi$
$608$	−4.87500	+	4.87500i	−0.197707	+	0.197707i
$609$	−10.4541	+	2.70057i	−0.423621	+	0.109433i
$610$	1.66521	+	1.06973i	0.0674226	+	0.0433120i
$611$	41.8730	+	24.1754i	1.69400	+	0.978032i
$612$	1.86816	−	11.3647i	0.0755160	−	0.459389i
$613$	−10.2788	+	38.3608i	−0.415155	+	1.54938i	0.369370	+	0.929282i	$0.379573\pi$
$613$	−10.2788	+	38.3608i	−0.415155	+	1.54938i	−0.784525	+	0.620097i	$0.787093\pi$
$614$	15.5227	−	26.8861i	0.626444	−	1.08503i
$615$	−25.9816	−	14.9304i	−1.04768	−	0.602053i
$616$	1.83311	+	8.88935i	0.0738582	+	0.358162i
$617$	7.74923	+	7.74923i	0.311972	+	0.311972i	0.845673	−	0.533701i	$-0.179199\pi$
$617$	7.74923	+	7.74923i	0.311972	+	0.311972i	−0.533701	+	0.845673i	$0.679199\pi$
$618$	−14.6439	+	4.71081i	−0.589064	+	0.189497i
$619$	1.24931	−	0.721289i	0.0502140	−	0.0289911i	−0.474683	−	0.880157i	$-0.657437\pi$
$619$	1.24931	−	0.721289i	0.0502140	−	0.0289911i	0.524897	+	0.851166i	$0.324104\pi$
$620$	−11.8614	+	10.7868i	−0.476365	+	0.433207i
$621$	−2.19538	+	5.57257i	−0.0880974	+	0.223620i
$622$	7.79284	−	7.79284i	0.312465	−	0.312465i
$623$	−0.198294	+	3.38950i	−0.00794447	+	0.135798i
$624$	−9.48553	+	0.469313i	−0.379725	+	0.0187876i
$625$	8.19438	+	23.6189i	0.327775	+	0.944756i
$626$	−7.95515	+	4.59291i	−0.317952	+	0.183569i
$627$	−40.0449	−	8.63424i	−1.59924	−	0.344818i
$628$	13.6086	−	3.64642i	0.543044	−	0.145508i
$629$	18.9915			0.757241
$630$	0.123803	−	17.7478i	0.00493241	−	0.707090i
$631$	−17.0499			−0.678748			−0.339374	−	0.940652i	$-0.610215\pi$
$631$	−17.0499			−0.678748			−0.339374	+	0.940652i	$0.610215\pi$
$632$	−5.55038	+	1.48722i	−0.220782	+	0.0591584i
$633$	4.38347	+	0.945138i	0.174227	+	0.0375659i
$634$	4.40770	−	2.54478i	0.175052	−	0.101066i
$635$	−6.56539	−	12.7292i	−0.260540	−	0.505144i
$636$	1.65030	−	0.0816513i	0.0654385	−	0.00323768i
$637$	−37.9798	+	5.54321i	−1.50482	+	0.219630i
$638$	5.71550	−	5.71550i	0.226279	−	0.226279i
$639$	−2.17974	+	4.81973i	−0.0862290	+	0.190666i
$640$	2.23356	+	0.105978i	0.0882890	+	0.00418917i
$641$	14.6651	−	8.46692i	0.579238	−	0.334423i	−0.181592	−	0.983374i	$-0.558125\pi$
$641$	14.6651	−	8.46692i	0.579238	−	0.334423i	0.760831	+	0.648951i	$0.224792\pi$
$642$	−11.1682	+	3.59270i	−0.440773	+	0.141792i
$643$	22.8061	+	22.8061i	0.899385	+	0.899385i	0.995382	−	0.0959964i	$-0.0306037\pi$
$643$	22.8061	+	22.8061i	0.899385	+	0.899385i	−0.0959964	+	0.995382i	$0.530604\pi$
$644$	−2.89463	−	0.960004i	−0.114064	−	0.0378295i
$645$	3.04663	−	0.822955i	0.119961	−	0.0324038i
$646$	−13.2338	+	22.9216i	−0.520677	+	0.901838i
$647$	10.2045	−	38.0837i	0.401181	−	1.49723i	−0.409812	−	0.912170i	$-0.634406\pi$
$647$	10.2045	−	38.0837i	0.401181	−	1.49723i	0.810993	−	0.585056i	$-0.198928\pi$
$648$	8.98154	+	0.576089i	0.352828	+	0.0226309i
$649$	16.3054	+	9.41395i	0.640045	+	0.369530i
$650$	11.3983	+	24.9341i	0.447078	+	0.977995i
$651$	−23.0235	−	23.4417i	−0.902364	−	0.918753i
$652$	4.26528	−	4.26528i	0.167041	−	0.167041i
$653$	8.48981	+	31.6844i	0.332232	+	1.23991i	0.906839	+	0.421477i	$0.138488\pi$
$653$	8.48981	+	31.6844i	0.332232	+	1.23991i	−0.574607	+	0.818429i	$0.694845\pi$
$654$	20.5940	−	13.2885i	0.805291	−	0.519621i
$655$	−20.2038	+	18.3734i	−0.789427	+	0.717906i
$656$	6.70060	+	3.86859i	0.261614	+	0.151043i
$657$	13.4453	−	16.4065i	0.524551	−	0.640078i
$658$	12.8252	−	19.4889i	0.499980	−	0.759756i
$659$	−9.95001			−0.387597			−0.193799	−	0.981041i	$-0.562081\pi$
$659$	−9.95001			−0.387597			−0.193799	+	0.981041i	$0.562081\pi$
$660$	6.66651	+	11.4930i	0.259494	+	0.447363i
$661$	−17.3986	−	30.1353i	−0.676727	−	1.17213i	−0.975961	−	0.217946i	$-0.930064\pi$
$661$	−17.3986	−	30.1353i	−0.676727	−	1.17213i	0.299233	−	0.954180i	$-0.403269\pi$
$662$	8.80396	−	32.8568i	0.342176	−	1.27702i
$663$	−34.7084	+	11.1654i	−1.34796	+	0.433626i
$664$			10.0388i			0.389583i
$665$	−14.6598	+	38.0616i	−0.568482	+	1.47596i
$666$	1.46496	+	14.7683i	0.0567660	+	0.572259i
$667$	0.702917	+	2.62332i	0.0272171	+	0.101575i
$668$	8.10770	+	2.17245i	0.313697	+	0.0840547i
$669$	−10.2641	−	15.9070i	−0.396834	−	0.614999i
$670$	3.04488	−	9.53136i	0.117634	−	0.368229i
$671$		−	3.03648i		−	0.117222i
$672$	−0.0412390	+	4.58239i	−0.00159083	+	0.176770i
$673$	−27.9121	−	27.9121i	−1.07593	−	1.07593i	−0.996870	−	0.0790609i	$-0.974808\pi$
$673$	−27.9121	−	27.9121i	−1.07593	−	1.07593i	−0.0790609	−	0.996870i	$-0.525192\pi$
$674$	13.4577	−	23.3094i	0.518370	−	0.897843i
$675$	−8.05626	−	24.7001i	−0.310086	−	0.950709i
$676$	8.53259	+	14.7789i	0.328177	+	0.568419i
$677$	−11.3933	+	3.05281i	−0.437878	+	0.117329i	−0.471022	−	0.882121i	$-0.656115\pi$
$677$	−11.3933	+	3.05281i	−0.437878	+	0.117329i	0.0331437	+	0.999451i	$0.489448\pi$
$678$	6.28963	−	6.94440i	0.241552	−	0.266698i
$679$	−2.54221	+	7.66533i	−0.0975610	+	0.294168i
$680$	8.38787	−	1.82631i	0.321660	−	0.0700360i
$681$	−5.99362	+	11.6786i	−0.229676	+	0.447526i
$682$	23.7591	+	6.36622i	0.909781	+	0.243775i
$683$	35.6240	+	9.54542i	1.36311	+	0.365245i	0.864959	−	0.501843i	$-0.167344\pi$
$683$	35.6240	+	9.54542i	1.36311	+	0.365245i	0.498155	+	0.867088i	$0.334011\pi$
$684$	−18.8452	−	8.52281i	−0.720565	−	0.325878i
$685$	−6.62153	−	4.25365i	−0.252996	−	0.162524i
$686$	1.59987	+	18.4510i	0.0610832	+	0.704464i
$687$	−6.01667	−	5.44937i	−0.229550	−	0.207906i
$688$	−0.787066	+	0.210894i	−0.0300066	+	0.00804024i
$689$	−2.61538	−	4.52997i	−0.0996379	−	0.172578i
$690$	−4.46425	+	0.00903418i	−0.169951	+	0.000343925i
$691$	−7.51839	+	13.0222i	−0.286013	+	0.495389i	−0.972854	−	0.231418i	$-0.925663\pi$
$691$	−7.51839	+	13.0222i	−0.286013	+	0.495389i	0.686841	+	0.726807i	$0.258997\pi$
$692$	−8.64531	−	8.64531i	−0.328645	−	0.328645i
$693$	−23.0115	+	14.5568i	−0.874134	+	0.552965i
$694$			27.3632i			1.03869i
$695$	−19.8795	−	6.35070i	−0.754074	−	0.240896i
$696$	3.42909	−	2.21265i	0.129979	−	0.0838703i
$697$	28.6914	+	7.68783i	1.08676	+	0.291197i
$698$	−1.95026	−	7.27846i	−0.0738183	−	0.275494i
$699$	−0.160838	−	3.25078i	−0.00608344	−	0.122956i
$700$	12.3319	−	4.78789i	0.466103	−	0.180965i
$701$		−	7.15756i		−	0.270337i	−0.990823	−	0.135169i	$-0.956842\pi$
$701$		−	7.15756i		−	0.270337i	0.990823	−	0.135169i	$-0.0431576\pi$
$702$	−11.3598	−	26.1288i	−0.428747	−	0.986169i
$703$	8.82715	−	32.9434i	0.332922	−	1.24248i
$704$	−1.71528	−	2.97095i	−0.0646469	−	0.111972i
$705$	8.77243	−	33.0062i	0.330389	−	1.24309i
$706$	14.9295			0.561880
$707$	−27.2183	+	41.3602i	−1.02365	+	1.55551i
$708$	7.04572	+	6.38139i	0.264794	+	0.239827i
$709$	13.4922	+	7.78971i	0.506709	+	0.292549i	0.731480	−	0.681863i	$-0.238830\pi$
$709$	13.4922	+	7.78971i	0.506709	+	0.292549i	−0.224771	+	0.974412i	$0.572163\pi$
$710$	−3.93829	−	0.186865i	−0.147801	−	0.00701292i
$711$	−10.0508	−	14.0053i	−0.376936	−	0.525238i
$712$	−0.332143	−	1.23958i	−0.0124476	−	0.0464550i
$713$	−5.84399	+	5.84399i	−0.218859	+	0.218859i
$714$	4.40024	+	17.0336i	0.164675	+	0.637467i
$715$	22.7334	−	35.3883i	0.850179	−	1.32345i
$716$	1.28180	+	0.740048i	0.0479032	+	0.0276569i
$717$	31.3430	+	6.75798i	1.17052	+	0.252382i
$718$	−8.01962	+	29.9296i	−0.299290	+	1.11696i
$719$	2.68898	−	4.65745i	0.100282	−	0.173694i	−0.811519	−	0.584326i	$-0.801359\pi$
$719$	2.68898	−	4.65745i	0.100282	−	0.173694i	0.911801	+	0.410633i	$0.134692\pi$
$720$	2.06721	+	6.38174i	0.0770403	+	0.237834i
$721$	17.5575	−	15.6168i	0.653877	−	0.581599i
$722$	20.1746	+	20.1746i	0.750822	+	0.750822i
$723$	−4.43748	−	13.7942i	−0.165032	−	0.513014i
$724$	−13.5293	+	7.81117i	−0.502814	+	0.290300i
$725$	−9.59891	−	6.82994i	−0.356495	−	0.253658i
$726$	0.607922	−	1.18454i	0.0225621	−	0.0439624i
$727$	26.8316	−	26.8316i	0.995128	−	0.995128i	−0.00486049	−	0.999988i	$-0.501547\pi$
$727$	26.8316	−	26.8316i	0.995128	−	0.995128i	0.999988	+	0.00486049i	$0.00154715\pi$
$728$	12.9657	−	6.50743i	0.480541	−	0.241182i
$729$	7.89178	+	25.8209i	0.292288	+	0.956330i
$730$	15.0606	+	4.81126i	0.557420	+	0.178073i
$731$	−2.70909	+	1.56409i	−0.100199	+	0.0578500i
$732$	0.323129	−	1.49865i	0.0119432	−	0.0553916i
$733$	26.5233	−	7.10691i	0.979662	−	0.262500i	0.266760	−	0.963763i	$-0.414047\pi$
$733$	26.5233	−	7.10691i	0.979662	−	0.262500i	0.712902	+	0.701263i	$0.247380\pi$
$734$	−10.0105			−0.369493
$735$	10.7756	+	24.8774i	0.397464	+	0.917618i
$736$	1.15267			0.0424878
$737$	−14.8279	+	3.97312i	−0.546193	+	0.146352i
$738$	−3.76507	+	22.9041i	−0.138594	+	0.843113i
$739$	−31.1498	+	17.9843i	−1.14586	+	0.661565i	−0.947876	−	0.318640i	$-0.896774\pi$
$739$	−31.1498	+	17.9843i	−1.14586	+	0.661565i	−0.197988	+	0.980205i	$0.563441\pi$
$740$	−9.83103	+	5.07058i	−0.361396	+	0.186398i
$741$	3.23558	+	65.3960i	0.118862	+	2.40238i
$742$	−2.25578	+	1.13217i	−0.0828123	+	0.0415631i
$743$	−11.3545	+	11.3545i	−0.416555	+	0.416555i	−0.884015	−	0.467459i	$-0.845169\pi$
$743$	−11.3545	+	11.3545i	−0.416555	+	0.416555i	0.467459	+	0.884015i	$0.345169\pi$
$744$	11.0488	+	5.67037i	0.405067	+	0.207886i
$745$	3.01170	+	3.31173i	0.110340	+	0.121333i
$746$	−12.3892	+	7.15292i	−0.453602	+	0.261887i
$747$	−28.1788	+	10.6282i	−1.03101	+	0.388866i
$748$	−9.31267	−	9.31267i	−0.340505	−	0.340505i
$749$	13.3903	−	11.9101i	0.489269	−	0.435186i
$750$	14.9031	−	12.3652i	0.544183	−	0.451514i
$751$	−1.62249	+	2.81024i	−0.0592056	+	0.102547i	−0.894109	−	0.447849i	$-0.852190\pi$
$751$	−1.62249	+	2.81024i	−0.0592056	+	0.102547i	0.834903	+	0.550396i	$0.185523\pi$
$752$	−2.28227	+	8.51756i	−0.0832260	+	0.310604i
$753$	10.6250	−	49.2779i	0.387197	−	1.79579i
$754$	−11.1884	−	6.45961i	−0.407457	−	0.235245i
$755$	32.6367	−	7.10607i	1.18777	−	0.258616i
$756$	−12.9063	+	4.73566i	−0.469399	+	0.172234i
$757$	−3.87448	+	3.87448i	−0.140820	+	0.140820i	−0.774003	−	0.633182i	$-0.781748\pi$
$757$	−3.87448	+	3.87448i	−0.140820	+	0.140820i	0.633182	+	0.774003i	$0.281748\pi$
$758$	−0.775475	−	2.89411i	−0.0281665	−	0.105119i
$759$	3.71343	+	5.75495i	0.134789	+	0.208892i
$760$	0.730646	−	15.3988i	0.0265033	−	0.558572i
$761$	9.71823	+	5.61082i	0.352286	+	0.203392i	0.665691	−	0.746227i	$-0.268137\pi$
$761$	9.71823	+	5.61082i	0.352286	+	0.203392i	−0.313406	+	0.949619i	$0.601470\pi$
$762$	−7.44759	+	8.22291i	−0.269798	+	0.297885i
$763$	−20.5808	+	31.2740i	−0.745074	+	1.13219i
$764$	−15.1384			−0.547690
$765$	14.0068	+	21.6111i	0.506415	+	0.781349i
$766$	−4.19278	−	7.26211i	−0.151491	−	0.262391i
$767$	7.78872	−	29.0679i	0.281234	−	1.04958i
$768$	−0.530415	−	1.64884i	−0.0191397	−	0.0594972i
$769$		−	23.3486i		−	0.841972i	−0.907067	−	0.420986i	$-0.861684\pi$
$769$		−	23.3486i		−	0.841972i	0.907067	−	0.420986i	$-0.138316\pi$
$770$	−16.4059	−	11.9479i	−0.591227	−	0.430572i
$771$	33.2294	−	1.64408i	1.19673	−	0.0592103i
$772$	4.35769	+	16.2631i	0.156837	+	0.585323i
$773$	21.2075	+	5.68254i	0.762782	+	0.204387i	0.619181	−	0.785249i	$-0.287465\pi$
$773$	21.2075	+	5.68254i	0.762782	+	0.204387i	0.143602	+	0.989636i	$0.454132\pi$
$774$	−1.42525	−	1.98600i	−0.0512295	−	0.0713854i
$775$	3.39442	−	35.6891i	0.121931	−	1.28199i
$776$		−	3.05240i		−	0.109575i
$777$	−11.1577	−	19.7337i	−0.400280	−	0.707942i
$778$	−18.5178	−	18.5178i	−0.663895	−	0.663895i
$779$	26.6712	−	46.1958i	0.955594	−	1.65514i
$780$	14.9859	−	15.0466i	0.536580	−	0.538756i
$781$	3.02444	+	5.23848i	0.108223	+	0.187448i
$782$	4.27437	−	1.14531i	0.152851	−	0.0409563i
$783$	9.84127	+	7.28282i	0.351698	+	0.260267i
$784$	−2.76924	−	6.42894i	−0.0989015	−	0.229605i
$785$	−17.0270	+	26.5054i	−0.607720	+	0.946020i
$786$	18.8196	+	9.65847i	0.671273	+	0.344506i
$787$	−41.0323	−	10.9946i	−1.46264	−	0.391914i	−0.562241	−	0.826973i	$-0.690061\pi$
$787$	−41.0323	−	10.9946i	−1.46264	−	0.391914i	−0.900402	+	0.435060i	$0.856727\pi$
$788$	−4.46430	−	1.19621i	−0.159034	−	0.0426131i
$789$	12.7063	+	6.52104i	0.452356	+	0.232155i
$790$	6.94458	−	10.8104i	0.247077	−	0.384618i
$791$	−4.50523	+	13.5843i	−0.160188	+	0.483001i
$792$	6.52341	−	7.96012i	0.231799	−	0.282850i
$793$	−4.68794	+	1.25613i	−0.166474	+	0.0446064i
$794$	3.48376	+	6.03404i	0.123634	+	0.214140i
$795$	−2.60725	+	2.61782i	−0.0924695	+	0.0928446i
$796$	2.51565	−	4.35724i	0.0891649	−	0.154438i
$797$	7.12389	+	7.12389i	0.252341	+	0.252341i	0.821930	−	0.569589i	$-0.192897\pi$
$797$	7.12389	+	7.12389i	0.252341	+	0.252341i	−0.569589	+	0.821930i	$0.692897\pi$
$798$	31.5923	+	0.284314i	1.11836	+	0.0100646i
$799$			33.8529i			1.19763i
$800$	−3.85441	+	3.18489i	−0.136274	+	0.112603i
$801$	3.12782	−	2.24467i	0.110516	−	0.0793115i
$802$	−18.6302	−	4.99194i	−0.657855	−	0.176272i
$803$	−6.27799	−	23.4298i	−0.221545	−	0.826819i
$804$	−7.74107	+	0.383003i	−0.273007	+	0.0135075i
$805$	6.23283	−	2.76661i	0.219679	−	0.0975103i
$806$		−	39.3145i		−	1.38479i
$807$	2.80501	+	8.71960i	0.0987412	+	0.306945i
$808$	4.84355	−	18.0764i	0.170396	−	0.635925i
$809$	−23.4131	−	40.5526i	−0.823159	−	1.42575i	−0.903318	−	0.428971i	$-0.858876\pi$
$809$	−23.4131	−	40.5526i	−0.823159	−	1.42575i	0.0801590	−	0.996782i	$-0.474457\pi$
$810$	−15.7248	+	12.5590i	−0.552515	+	0.441279i
$811$	−18.0213			−0.632815			−0.316408	−	0.948623i	$-0.602477\pi$
$811$	−18.0213			−0.632815			−0.316408	+	0.948623i	$0.602477\pi$
$812$	−3.42688	+	5.20739i	−0.120260	+	0.182744i
$813$	−26.2325	+	28.9634i	−0.920013	+	1.01579i
$814$	14.6970	+	8.48533i	0.515131	+	0.297411i
$815$	−0.639263	+	13.4728i	−0.0223924	+	0.471933i
$816$	−3.60523	−	5.58726i	−0.126208	−	0.195593i
$817$	1.45396	+	5.42626i	0.0508677	+	0.189841i
$818$	−24.7610	+	24.7610i	−0.865747	+	0.865747i
$819$	31.9932	+	29.5050i	1.11793	+	1.03099i
$820$	−16.9048	+	3.68073i	−0.590341	+	0.128537i
$821$	−27.1356	−	15.6667i	−0.947039	−	0.546773i	−0.0548791	−	0.998493i	$-0.517477\pi$
$821$	−27.1356	−	15.6667i	−0.947039	−	0.546773i	−0.892160	+	0.451720i	$0.850811\pi$
$822$	−1.28489	+	5.95919i	−0.0448155	+	0.207851i
$823$	−0.0837114	+	0.312415i	−0.00291799	+	0.0108901i	−0.967369	−	0.253370i	$-0.918461\pi$
$823$	−0.0837114	+	0.312415i	−0.00291799	+	0.0108901i	0.964451	+	0.264260i	$0.0851277\pi$
$824$	−4.44068	+	7.69148i	−0.154698	+	0.267946i
$825$	−28.3187	−	8.98355i	−0.985930	−	0.312767i
$826$	−13.7825	−	4.57096i	−0.479553	−	0.159044i
$827$	−31.9770	−	31.9770i	−1.11195	−	1.11195i	−0.992887	−	0.119062i	$-0.962011\pi$
$827$	−31.9770	−	31.9770i	−1.11195	−	1.11195i	−0.119062	−	0.992887i	$-0.537989\pi$
$828$	1.22034	+	3.23551i	0.0424097	+	0.112442i
$829$	35.8756	−	20.7128i	1.24601	−	0.719385i	0.275700	−	0.961244i	$-0.411090\pi$
$829$	35.8756	−	20.7128i	1.24601	−	0.719385i	0.970311	+	0.241859i	$0.0777572\pi$
$830$	−15.1027	−	16.6073i	−0.524222	−	0.576447i
$831$	−38.7808	−	19.9028i	−1.34529	−	0.690421i
$832$	−3.87719	+	3.87719i	−0.134417	+	0.134417i
$833$	−16.6570	−	21.0885i	−0.577130	−	0.730674i
$834$	0.798829	+	16.1455i	0.0276612	+	0.559074i
$835$	−16.6809	+	8.60354i	−0.577265	+	0.297738i
$836$	−20.4826	+	11.8256i	−0.708405	+	0.408998i
$837$	−4.21918	+	37.0169i	−0.145836	+	1.27949i
$838$	−8.60727	+	2.30631i	−0.297333	+	0.0796702i
$839$	−17.8925			−0.617717			−0.308858	−	0.951108i	$-0.599947\pi$
$839$	−17.8925			−0.617717			−0.308858	+	0.951108i	$0.599947\pi$
$840$	−6.82564	−	7.64269i	−0.235507	−	0.263698i
$841$	−23.4485			−0.808569
$842$	18.1608	−	4.86616i	0.625861	−	0.167699i
$843$	−10.7577	+	49.8932i	−0.370514	+	1.71841i
$844$	2.24210	−	1.29448i	0.0771764	−	0.0445578i
$845$	−36.3492	−	11.6121i	−1.25045	−	0.399467i
$846$	−26.3249	+	2.61133i	−0.905068	+	0.0897794i
$847$	−0.118778	+	2.03032i	−0.00408127	+	0.0697626i
$848$	0.674555	−	0.674555i	0.0231643	−	0.0231643i
$849$	0.823259	−	1.60413i	0.0282542	−	0.0550535i
$850$	−11.1285	+	15.6402i	−0.381705	+	0.536454i
$851$	−4.93820	+	2.85107i	−0.169279	+	0.0977335i
$852$	0.935247	+	2.90729i	0.0320410	+	0.0996020i
$853$	38.0442	+	38.0442i	1.30261	+	1.30261i	0.926627	+	0.375983i	$0.122695\pi$
$853$	38.0442	+	38.0442i	1.30261	+	1.30261i	0.375983	+	0.926627i	$0.377305\pi$
$854$	0.472967	+	2.29357i	0.0161846	+	0.0784844i
$855$	43.9976	−	14.2519i	1.50469	−	0.487406i
$856$	−3.38669	+	5.86591i	−0.115755	+	0.200493i
$857$	1.09133	−	4.07290i	0.0372791	−	0.139127i	−0.944778	−	0.327711i	$-0.893723\pi$
$857$	1.09133	−	4.07290i	0.0372791	−	0.139127i	0.982057	+	0.188583i	$0.0603895\pi$
$858$	−31.8485	−	6.86699i	−1.08729	−	0.234435i
$859$	−34.2434	−	19.7704i	−1.16837	−	0.674558i	−0.215073	−	0.976598i	$-0.568999\pi$
$859$	−34.2434	−	19.7704i	−1.16837	−	0.674558i	−0.953295	+	0.302040i	$0.902332\pi$
$860$	0.984770	−	1.53296i	0.0335804	−	0.0522736i
$861$	−8.86817	−	34.3293i	−0.302226	−	1.16994i
$862$	−23.3431	+	23.3431i	−0.795069	+	0.795069i
$863$	4.83143	+	18.0311i	0.164464	+	0.613787i	0.998108	+	0.0614855i	$0.0195838\pi$
$863$	4.83143	+	18.0311i	0.164464	+	0.613787i	−0.833644	+	0.552302i	$0.813750\pi$
$864$	4.06669	−	3.23450i	0.138352	−	0.110040i
$865$	27.3081	+	1.29573i	0.928504	+	0.0440560i
$866$	−34.1713	−	19.7288i	−1.16119	−	0.670411i
$867$	2.90341	+	2.62965i	0.0986051	+	0.0893078i
$868$	−18.9377	−	1.10790i	−0.642789	−	0.0376046i
$869$	−19.7126			−0.668703
$870$	−2.34398	+	8.81919i	−0.0794682	+	0.298998i
$871$	12.2680	+	21.2488i	0.415685	+	0.719988i
$872$	3.66239	−	13.6682i	0.124024	−	0.462864i
$873$	8.56803	−	3.23161i	0.289984	−	0.109373i
$874$		−	7.94681i		−	0.268805i
$875$	−13.1977	+	26.4730i	−0.446163	+	0.894952i
$876$	−0.605189	−	12.2318i	−0.0204474	−	0.413274i
$877$	−12.7584	−	47.6148i	−0.430819	−	1.60784i	−0.750878	−	0.660440i	$-0.770370\pi$
$877$	−12.7584	−	47.6148i	−0.430819	−	1.60784i	0.320060	−	0.947397i	$-0.396297\pi$
$878$	15.4413	+	4.13747i	0.521117	+	0.139633i
$879$	25.7519	−	16.6166i	0.868589	−	0.560465i
$880$	7.30715	+	2.33433i	0.246324	+	0.0786904i
$881$			58.4991i			1.97089i	0.170007	+	0.985443i	$0.445621\pi$
$881$			58.4991i			1.97089i	−0.170007	+	0.985443i	$0.554379\pi$
$882$	15.1141	−	14.5796i	0.508918	−	0.490920i
$883$	−4.87858	−	4.87858i	−0.164177	−	0.164177i	0.620237	−	0.784414i	$-0.287036\pi$
$883$	−4.87858	−	4.87858i	−0.164177	−	0.164177i	−0.784414	+	0.620237i	$0.787036\pi$
$884$	−10.5251	+	18.2300i	−0.353998	+	0.613142i
$885$	−21.2560	+	0.0430153i	−0.714514	+	0.00144594i
$886$	−9.44625	−	16.3614i	−0.317353	−	0.549671i
$887$	43.3986	−	11.6286i	1.45718	−	0.390451i	0.558666	−	0.829393i	$-0.311313\pi$
$887$	43.3986	−	11.6286i	1.45718	−	0.390451i	0.898515	+	0.438942i	$0.144647\pi$
$888$	6.35071	+	5.75191i	0.213116	+	0.193022i
$889$	5.33467	−	16.0852i	0.178919	−	0.539481i
$890$	2.41431	+	1.55095i	0.0809279	+	0.0519878i
$891$	29.2503	+	9.88361i	0.979921	+	0.331113i
$892$	−10.5574	−	2.82885i	−0.353488	−	0.0947169i
$893$	58.7226	+	15.7347i	1.96508	+	0.526540i
$894$	1.58318	−	3.08484i	0.0529496	−	0.103173i
$895$	−3.23383	+	0.704110i	−0.108095	+	0.0235358i
$896$	1.75837	+	1.97690i	0.0587432	+	0.0660435i
$897$	7.34874	−	8.11378i	0.245367	−	0.270911i
$898$	6.55599	−	1.75667i	0.218776	−	0.0586209i
$899$	8.44687	+	14.6304i	0.281719	+	0.487951i
$900$	−13.0206	−	7.44736i	−0.434021	−	0.248245i
$901$	1.83116	−	3.17167i	0.0610049	−	0.105664i
$902$	18.7686	+	18.7686i	0.624926	+	0.624926i
$903$	3.21683	+	1.89604i	0.107049	+	0.0630961i
$904$		−	5.40938i		−	0.179913i
$905$	10.6303	−	33.2759i	0.353362	−	1.10613i
$906$	−14.0277	−	21.7396i	−0.466039	−	0.722251i
$907$	52.6001	+	14.0941i	1.74656	+	0.467988i	0.983886	−	0.178798i	$-0.0572210\pi$
$907$	52.6001	+	14.0941i	1.74656	+	0.467988i	0.762671	+	0.646787i	$0.223888\pi$
$908$	1.96153	+	7.32054i	0.0650957	+	0.242941i
$909$	55.8679	−	5.54189i	1.85302	−	0.183813i
$910$	−11.6592	+	30.2712i	−0.386500	+	1.00348i
$911$		−	7.37432i		−	0.244322i	−0.992510	−	0.122161i	$-0.961018\pi$
$911$		−	7.37432i		−	0.244322i	0.992510	−	0.122161i	$-0.0389824\pi$
$912$	−11.3676	+	3.65684i	−0.376417	+	0.121090i
$913$	−8.91342	+	33.2653i	−0.294991	+	1.10092i
$914$	2.65569	+	4.59979i	0.0878424	+	0.152147i
$915$	1.72005	+	2.96533i	0.0568630	+	0.0980309i
$916$	−4.68671			−0.154853
$917$	−32.2571	−	1.88711i	−1.06522	−	0.0623180i
$918$	11.8664	−	16.0351i	0.391650	−	0.529237i
$919$	−39.9069	−	23.0403i	−1.31641	−	0.760028i	−0.333258	−	0.942836i	$-0.608148\pi$
$919$	−39.9069	−	23.0403i	−1.31641	−	0.760028i	−0.983149	+	0.182808i	$0.941481\pi$
$920$	−1.90686	+	1.73410i	−0.0628672	+	0.0571715i
$921$	45.1825	−	29.1544i	1.48881	−	0.960671i
$922$	−7.27251	−	27.1414i	−0.239507	−	0.893854i
$923$	6.83640	−	6.83640i	0.225023	−	0.225023i
$924$	−4.20532	+	15.1479i	−0.138345	+	0.498328i
$925$	8.63518	−	23.1783i	0.283923	−	0.762098i
$926$	−9.33045	−	5.38694i	−0.306617	−	0.177026i
$927$	−26.2912	−	4.32185i	−0.863517	−	0.141948i
$928$	0.609819	−	2.27587i	0.0200183	−	0.0747093i
$929$	−1.40166	+	2.42774i	−0.0459869	+	0.0796516i	−0.888103	−	0.459645i	$-0.847977\pi$
$929$	−1.40166	+	2.42774i	−0.0459869	+	0.0796516i	0.842116	+	0.539297i	$0.181310\pi$
$930$	−26.8086	+	7.24152i	−0.879088	+	0.237459i
$931$	−44.3230	+	19.0920i	−1.45263	+	0.625714i
$932$	−1.32875	−	1.32875i	−0.0435246	−	0.0435246i
$933$	18.1714	−	5.84557i	0.594905	−	0.191375i
$934$	7.93138	−	4.57919i	0.259523	−	0.149836i
$935$	29.4161	+	1.39575i	0.962011	+	0.0456458i
$936$	−14.9880	−	6.77837i	−0.489898	−	0.221558i
$937$	9.16753	−	9.16753i	0.299490	−	0.299490i	−0.541324	−	0.840814i	$-0.682077\pi$
$937$	9.16753	−	9.16753i	0.299490	−	0.299490i	0.840814	+	0.541324i	$0.182077\pi$
$938$	10.5812	−	5.31067i	0.345489	−	0.173400i
$939$	−15.8909	+	0.786228i	−0.518578	+	0.0256576i
$940$	−9.03846	−	17.5241i	−0.294802	−	0.571574i
$941$	−16.1104	+	9.30133i	−0.525183	+	0.303215i	−0.739053	−	0.673648i	$-0.764727\pi$
$941$	−16.1104	+	9.30133i	−0.525183	+	0.303215i	0.213869	+	0.976862i	$0.431393\pi$
$942$	23.8542	+	5.14329i	0.777211	+	0.167578i
$943$	−8.61450	+	2.30825i	−0.280527	+	0.0751669i
$944$	5.48830			0.178629
$945$	14.2265	−	27.2508i	0.462788	−	0.886469i
$946$	−2.79532			−0.0908837
$947$	−4.48811	+	1.20259i	−0.145844	+	0.0390788i	−0.331002	−	0.943630i	$-0.607387\pi$
$947$	−4.48811	+	1.20259i	−0.145844	+	0.0390788i	0.185158	+	0.982709i	$0.440720\pi$
$948$	−9.72908	−	2.09773i	−0.315986	−	0.0681310i
$949$	−33.5755	+	19.3848i	−1.08991	+	0.629258i
$950$	21.9576	+	26.5734i	0.712398	+	0.862155i
$951$	8.80462	−	0.435624i	0.285509	−	0.0141261i
$952$	8.48477	+	5.58366i	0.274993	+	0.180967i
$953$	−12.6014	+	12.6014i	−0.408198	+	0.408198i	−0.881110	−	0.472912i	$-0.843203\pi$
$953$	−12.6014	+	12.6014i	−0.408198	+	0.408198i	0.472912	+	0.881110i	$0.343203\pi$
$954$	2.60762	+	1.17930i	0.0844248	+	0.0381814i
$955$	25.0435	−	22.7746i	0.810390	−	0.736970i
$956$	16.0316	−	9.25587i	0.518500	−	0.299356i
$957$	13.3274	−	4.28731i	0.430815	−	0.138589i
$958$	−10.9806	−	10.9806i	−0.354768	−	0.354768i
$959$	−1.88070	−	9.12011i	−0.0607309	−	0.294504i
$960$	3.35801	+	1.92970i	0.108379	+	0.0622808i
$961$	−10.2047	+	17.6750i	−0.329183	+	0.570162i
$962$	7.02042	−	26.2006i	0.226347	−	0.844740i
$963$	−20.0510	−	3.29606i	−0.646135	−	0.106214i
$964$	−7.24521	−	4.18303i	−0.233353	−	0.134726i
$965$	−31.6756	−	20.3483i	−1.01967	−	0.655034i
$966$	−3.70130	−	3.76853i	−0.119087	−	0.121250i
$967$	22.1599	−	22.1599i	0.712613	−	0.712613i	−0.254468	−	0.967081i	$-0.581900\pi$
$967$	22.1599	−	22.1599i	0.712613	−	0.712613i	0.967081	+	0.254468i	$0.0819003\pi$
$968$	−0.198954	−	0.742508i	−0.00639464	−	0.0238651i
$969$	−38.5202	+	24.8555i	−1.23745	+	0.798473i
$970$	4.59211	+	5.04959i	0.147444	+	0.162132i
$971$	13.6776	+	7.89677i	0.438935	+	0.253419i	0.703146	−	0.711046i	$-0.251778\pi$
$971$	13.6776	+	7.89677i	0.438935	+	0.253419i	−0.264211	+	0.964465i	$0.585111\pi$
$972$	13.3846	+	7.99072i	0.429312	+	0.256303i
$973$	−11.0765	−	22.0692i	−0.355095	−	0.707507i
$974$	3.28607			0.105292
$975$	−2.15459	+	47.4368i	−0.0690021	+	1.51919i
$976$	−0.442564	−	0.766543i	−0.0141661	−	0.0245365i
$977$	−12.1987	+	45.5260i	−0.390270	+	1.45651i	0.439420	+	0.898282i	$0.355184\pi$
$977$	−12.1987	+	45.5260i	−0.390270	+	1.45651i	−0.829690	+	0.558225i	$0.811483\pi$
$978$	9.94580	−	3.19947i	0.318032	−	0.102308i
$979$		−	4.40244i		−	0.140703i
$980$	14.2530	+	6.46929i	0.455296	+	0.206654i
$981$	42.2438	−	4.19043i	1.34874	−	0.133790i
$982$	−3.02313	−	11.2825i	−0.0964721	−	0.360039i
$983$	−40.9232	−	10.9653i	−1.30525	−	0.349740i	−0.461816	−	0.886976i	$-0.652802\pi$
$983$	−40.9232	−	10.9653i	−1.30525	−	0.349740i	−0.843432	+	0.537236i	$0.819469\pi$
$984$	7.26592	+	11.2605i	0.231629	+	0.358971i
$985$	9.18489	−	4.73732i	0.292655	−	0.150943i
$986$		−	9.04543i		−	0.288065i
$987$	35.1759	−	19.8889i	1.11966	−	0.633071i
$988$	26.7305	+	26.7305i	0.850409	+	0.850409i
$989$	0.469614	−	0.813395i	0.0149328	−	0.0258645i
$990$	1.18372	+	22.9824i	0.0376211	+	0.730428i
$991$	0.654060	+	1.13287i	0.0207769	+	0.0359867i	0.876227	−	0.481899i	$-0.160053\pi$
$991$	0.654060	+	1.13287i	0.0207769	+	0.0359867i	−0.855450	+	0.517885i	$0.826719\pi$
$992$	6.92572	−	1.85574i	0.219892	−	0.0589198i
$993$	39.5512	−	43.6686i	1.25512	−	1.38578i
$994$	−3.10043	−	3.48574i	−0.0983397	−	0.110561i
$995$	2.39349	+	10.9928i	0.0758787	+	0.348495i
$996$	−7.93915	+	15.4695i	−0.251562	+	0.490170i
$997$	49.1577	+	13.1718i	1.55684	+	0.417154i	0.931662	−	0.363327i	$-0.118359\pi$
$997$	49.1577	+	13.1718i	1.55684	+	0.417154i	0.625179	+	0.780482i	$0.285026\pi$
$998$	2.79969	+	0.750174i	0.0886225	+	0.0237463i
$999$	−9.42194	+	23.9159i	−0.298097	+	0.756666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.23.16	yes	64
3.2	odd	2	inner	210.2.x.a.23.1	✓	64
5.2	odd	4	inner	210.2.x.a.107.13	yes	64
7.4	even	3	inner	210.2.x.a.53.4	yes	64
15.2	even	4	inner	210.2.x.a.107.4	yes	64
21.11	odd	6	inner	210.2.x.a.53.13	yes	64
35.32	odd	12	inner	210.2.x.a.137.1	yes	64
105.32	even	12	inner	210.2.x.a.137.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.1	✓	64	3.2	odd	2	inner
210.2.x.a.23.16	yes	64	1.1	even	1	trivial
210.2.x.a.53.4	yes	64	7.4	even	3	inner
210.2.x.a.53.13	yes	64	21.11	odd	6	inner
210.2.x.a.107.4	yes	64	15.2	even	4	inner
210.2.x.a.107.13	yes	64	5.2	odd	4	inner
210.2.x.a.137.1	yes	64	35.32	odd	12	inner
210.2.x.a.137.16	yes	64	105.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.69314 + 0.365065i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.680454 + 2.13002i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.73346 + 1.23621i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.69314 + 0.365065i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.680454 + 2.13002i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.73346 + 1.23621i) q^{9} +(-0.105978 + 2.23356i) q^{10} +(2.97095 - 1.71528i) q^{11} +(1.64884 - 0.530415i) q^{12} +(-3.87719 - 3.87719i) q^{13} +(-1.97690 + 1.75837i) q^{14} +(-1.92970 + 3.35801i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.993622 - 3.70825i) q^{17} +(2.96027 + 0.486620i) q^{18} +(-5.97063 - 3.44715i) q^{19} +(0.475719 + 2.18488i) q^{20} +(-4.43692 + 1.14618i) q^{21} +(2.42577 - 2.42577i) q^{22} +(0.298332 + 1.11339i) q^{23} +(1.45537 - 0.939092i) q^{24} +(-4.07396 - 2.89876i) q^{25} +(-4.74857 - 2.74159i) q^{26} +(4.17683 + 3.09097i) q^{27} +(-1.45443 + 2.21012i) q^{28} +2.35616 q^{29} +(-0.994829 + 3.74304i) q^{30} +(3.58502 + 6.20943i) q^{31} +(0.258819 - 0.965926i) q^{32} +(5.65642 - 1.81962i) q^{33} -3.83906i q^{34} +(-0.918883 - 5.84428i) q^{35} +(2.98535 - 0.296136i) q^{36} +(1.28036 + 4.77836i) q^{37} +(-6.65937 - 1.78437i) q^{38} +(-5.14920 - 7.98005i) q^{39} +(1.02500 + 1.98730i) q^{40} +7.73718i q^{41} +(-3.98909 + 2.25548i) q^{42} +(-0.576172 - 0.576172i) q^{43} +(1.71528 - 2.97095i) q^{44} +(-4.49315 + 4.98113i) q^{45} +(0.576333 + 0.998238i) q^{46} +(-8.51756 + 2.28227i) q^{47} +(1.16273 - 1.28377i) q^{48} +(4.18301 - 5.61270i) q^{49} +(-4.68540 - 1.74557i) q^{50} +(3.03609 - 5.91585i) q^{51} +(-5.29634 - 1.41915i) q^{52} +(0.921459 + 0.246904i) q^{53} +(4.83451 + 1.90461i) q^{54} +(1.63198 + 7.49534i) q^{55} +(-0.832855 + 2.51125i) q^{56} +(-8.85069 - 8.01617i) q^{57} +(2.27587 - 0.609819i) q^{58} +(2.74415 + 4.75301i) q^{59} +(0.00783764 + 3.87298i) q^{60} +(0.442564 - 0.766543i) q^{61} +(5.06998 + 5.06998i) q^{62} +(-7.93077 + 0.320873i) q^{63} -1.00000i q^{64} +(10.8967 - 5.62024i) q^{65} +(4.99273 - 3.22161i) q^{66} +(-4.32230 - 1.15816i) q^{67} +(-0.993622 - 3.70825i) q^{68} +(0.0986585 + 1.99404i) q^{69} +(-2.40019 - 5.40732i) q^{70} +1.76324i q^{71} +(2.80698 - 1.05871i) q^{72} +(1.83002 - 6.82973i) q^{73} +(2.47346 + 4.28416i) q^{74} +(-5.83956 - 6.39527i) q^{75} -6.89429 q^{76} +(-4.98952 + 7.58193i) q^{77} +(-7.03914 - 6.37543i) q^{78} +(-4.97633 - 2.87309i) q^{79} +(1.50442 + 1.65430i) q^{80} +(5.94355 + 6.75827i) q^{81} +(2.00253 + 7.47354i) q^{82} +(-7.09854 + 7.09854i) q^{83} +(-3.26940 + 3.21108i) q^{84} +(7.22252 + 4.63972i) q^{85} +(-0.705664 - 0.407415i) q^{86} +(3.98931 + 0.860151i) q^{87} +(0.887893 - 3.31366i) q^{88} +(0.641651 - 1.11137i) q^{89} +(-3.05084 + 5.97431i) q^{90} +(13.7696 + 4.56669i) q^{91} +(0.815058 + 0.815058i) q^{92} +(3.80309 + 11.8222i) q^{93} +(-7.63664 + 4.40902i) q^{94} +(11.4052 - 10.3719i) q^{95} +(0.790843 - 1.54096i) q^{96} +(2.15837 - 2.15837i) q^{97} +(2.58780 - 6.50410i) q^{98} +(10.2414 - 1.01591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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