LMFDB - Embedded newform 210.2.x.a.23.1

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			23.1
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-1.64884 - 0.530415i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.680454 - 2.13002i) q^{5} +(1.72993 + 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.43732 + 1.74913i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.64884 - 0.530415i) 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} +(2.43732 + 1.74913i) q^{9} +(-0.105978 + 2.23356i) q^{10} +(-2.97095 + 1.71528i) q^{11} +(-1.69314 + 0.365065i) q^{12} +(-3.87719 - 3.87719i) q^{13} +(1.97690 - 1.75837i) q^{14} +(-2.25175 + 3.15113i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.993622 + 3.70825i) q^{17} +(-2.80698 - 1.05871i) q^{18} +(-5.97063 - 3.44715i) q^{19} +(-0.475719 - 2.18488i) q^{20} +(4.52839 - 0.702601i) q^{21} +(2.42577 - 2.42577i) q^{22} +(-0.298332 - 1.11339i) q^{23} +(1.54096 - 0.790843i) q^{24} +(-4.07396 - 2.89876i) q^{25} +(4.74857 + 2.74159i) q^{26} +(-3.09097 - 4.17683i) q^{27} +(-1.45443 + 2.21012i) q^{28} -2.35616 q^{29} +(1.35945 - 3.62655i) q^{30} +(3.58502 + 6.20943i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(5.80841 - 1.25238i) 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} +(4.33633 + 8.44937i) q^{39} +(1.02500 + 1.98730i) q^{40} -7.73718i q^{41} +(-4.19225 + 1.85070i) q^{42} +(-0.576172 - 0.576172i) q^{43} +(-1.71528 + 2.97095i) q^{44} +(5.38418 - 4.00133i) q^{45} +(0.576333 + 0.998238i) q^{46} +(8.51756 - 2.28227i) q^{47} +(-1.28377 + 1.16273i) q^{48} +(4.18301 - 5.61270i) q^{49} +(4.68540 + 1.74557i) q^{50} +(3.60523 - 5.58726i) q^{51} +(-5.29634 - 1.41915i) q^{52} +(-0.921459 - 0.246904i) q^{53} +(4.06669 + 3.23450i) q^{54} +(1.63198 + 7.49534i) q^{55} +(0.832855 - 2.51125i) q^{56} +(8.01617 + 8.85069i) q^{57} +(2.27587 - 0.609819i) q^{58} +(-2.74415 - 4.75301i) q^{59} +(-0.374509 + 3.85483i) q^{60} +(0.442564 - 0.766543i) q^{61} +(-5.06998 - 5.06998i) q^{62} +(-7.83925 - 1.24345i) q^{63} -1.00000i q^{64} +(-10.8967 + 5.62024i) q^{65} +(-5.28636 + 2.71303i) 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} +(-2.96027 + 0.486620i) q^{72} +(1.83002 - 6.82973i) q^{73} +(-2.47346 - 4.28416i) q^{74} +(5.17975 + 6.94047i) q^{75} -6.89429 q^{76} +(4.98952 - 7.58193i) q^{77} +(-6.37543 - 7.03914i) q^{78} +(-4.97633 - 2.87309i) q^{79} +(-1.50442 - 1.65430i) q^{80} +(2.88105 + 8.52640i) q^{81} +(2.00253 + 7.47354i) q^{82} +(7.09854 - 7.09854i) q^{83} +(3.57040 - 2.87267i) q^{84} +(7.22252 + 4.63972i) q^{85} +(0.705664 + 0.407415i) q^{86} +(3.88492 + 1.24974i) q^{87} +(0.887893 - 3.31366i) q^{88} +(-0.641651 + 1.11137i) q^{89} +(-4.16509 + 5.25852i) q^{90} +(13.7696 + 4.56669i) q^{91} +(-0.815058 - 0.815058i) q^{92} +(-2.61753 - 12.1399i) q^{93} +(-7.63664 + 4.40902i) q^{94} +(-11.4052 + 10.3719i) q^{95} +(0.939092 - 1.45537i) 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
$3$	−1.64884	−	0.530415i	−0.951956	−	0.306235i
$3$	−1.64884	−	0.530415i	−0.951956	−	0.306235i
$4$	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
$9$	2.43732	+	1.74913i	0.812440	+	0.583045i
$10$	−0.105978	+	2.23356i	−0.0335133	+	0.706312i
$11$	−2.97095	+	1.71528i	−0.895774	+	0.517175i	−0.875827	−	0.482626i	$-0.839683\pi$
$11$	−2.97095	+	1.71528i	−0.895774	+	0.517175i	−0.0199474	+	0.999801i	$0.506350\pi$
$12$	−1.69314	+	0.365065i	−0.488768	+	0.105385i
$13$	−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
$15$	−2.25175	+	3.15113i	−0.581400	+	0.813618i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.993622	+	3.70825i	−0.240989	+	0.899382i	0.734369	+	0.678751i	$0.237478\pi$
$17$	−0.993622	+	3.70825i	−0.240989	+	0.899382i	−0.975357	+	0.220631i	$0.929188\pi$
$18$	−2.80698	−	1.05871i	−0.661611	−	0.249540i
$19$	−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
$21$	4.52839	−	0.702601i	0.988177	−	0.153320i
$22$	2.42577	−	2.42577i	0.517175	−	0.517175i
$23$	−0.298332	−	1.11339i	−0.0622065	−	0.232158i	0.927822	−	0.373022i	$-0.121678\pi$
$23$	−0.298332	−	1.11339i	−0.0622065	−	0.232158i	−0.990029	+	0.140864i	$0.955012\pi$
$24$	1.54096	−	0.790843i	0.314548	−	0.161430i
$25$	−4.07396	−	2.89876i	−0.814793	−	0.579752i
$26$	4.74857	+	2.74159i	0.931271	+	0.537669i
$27$	−3.09097	−	4.17683i	−0.594858	−	0.803831i
$28$	−1.45443	+	2.21012i	−0.274862	+	0.417673i
$29$	−2.35616			−0.437528			−0.218764	−	0.975778i	$-0.570202\pi$
$29$	−2.35616			−0.437528			−0.218764	+	0.975778i	$0.570202\pi$
$30$	1.35945	−	3.62655i	0.248201	−	0.662115i
$31$	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
$33$	5.80841	−	1.25238i	1.01111	−	0.218011i
$34$		−	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
$39$	4.33633	+	8.44937i	0.694368	+	1.35298i
$40$	1.02500	+	1.98730i	0.162066	+	0.314220i
$41$		−	7.73718i		−	1.20834i	−0.796854	−	0.604172i	$-0.793504\pi$
$41$		−	7.73718i		−	1.20834i	0.796854	−	0.604172i	$-0.206496\pi$
$42$	−4.19225	+	1.85070i	−0.646878	+	0.285568i
$43$	−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
$45$	5.38418	−	4.00133i	0.802625	−	0.596483i
$46$	0.576333	+	0.998238i	0.0849757	+	0.147182i
$47$	8.51756	−	2.28227i	1.24241	−	0.332904i	0.423013	−	0.906124i	$-0.360973\pi$
$47$	8.51756	−	2.28227i	1.24241	−	0.332904i	0.819402	+	0.573220i	$0.194306\pi$
$48$	−1.28377	+	1.16273i	−0.185296	+	0.167825i
$49$	4.18301	−	5.61270i	0.597572	−	0.801815i
$50$	4.68540	+	1.74557i	0.662616	+	0.246861i
$51$	3.60523	−	5.58726i	0.504833	−	0.782372i
$52$	−5.29634	−	1.41915i	−0.734470	−	0.196801i
$53$	−0.921459	−	0.246904i	−0.126572	−	0.0339149i	0.194977	−	0.980808i	$-0.437537\pi$
$53$	−0.921459	−	0.246904i	−0.126572	−	0.0339149i	−0.321549	+	0.946893i	$0.604203\pi$
$54$	4.06669	+	3.23450i	0.553407	+	0.440160i
$55$	1.63198	+	7.49534i	0.220056	+	1.01067i
$56$	0.832855	−	2.51125i	0.111295	−	0.335579i
$57$	8.01617	+	8.85069i	1.06177	+	1.17230i
$58$	2.27587	−	0.609819i	0.298837	−	0.0800731i
$59$	−2.74415	−	4.75301i	−0.357258	−	0.618789i	0.630244	−	0.776397i	$-0.282955\pi$
$59$	−2.74415	−	4.75301i	−0.357258	−	0.618789i	−0.987502	+	0.157609i	$0.949622\pi$
$60$	−0.374509	+	3.85483i	−0.0483489	+	0.497657i
$61$	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
$63$	−7.83925	−	1.24345i	−0.987653	−	0.156661i
$64$		−	1.00000i		−	0.125000i
$65$	−10.8967	+	5.62024i	−1.35157	+	0.697105i
$66$	−5.28636	+	2.71303i	−0.650706	+	0.333951i
$67$	−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	$-0.966635\pi$
$71$		−	1.76324i		−	0.209258i	0.994511	−	0.104629i	$-0.0333655\pi$
$72$	−2.96027	+	0.486620i	−0.348871	+	0.0573487i
$73$	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
$75$	5.17975	+	6.94047i	0.598106	+	0.801417i
$76$	−6.89429			−0.790829
$77$	4.98952	−	7.58193i	0.568608	−	0.864041i
$78$	−6.37543	−	7.03914i	−0.721875	−	0.797025i
$79$	−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
$81$	2.88105	+	8.52640i	0.320117	+	0.947378i
$82$	2.00253	+	7.47354i	0.221142	+	0.825315i
$83$	7.09854	−	7.09854i	0.779166	−	0.779166i	−0.200523	−	0.979689i	$-0.564264\pi$
$83$	7.09854	−	7.09854i	0.779166	−	0.779166i	0.979689	+	0.200523i	$0.0642642\pi$
$84$	3.57040	−	2.87267i	0.389563	−	0.313434i
$85$	7.22252	+	4.63972i	0.783392	+	0.503249i
$86$	0.705664	+	0.407415i	0.0760937	+	0.0439327i
$87$	3.88492	+	1.24974i	0.416507	+	0.133986i
$88$	0.887893	−	3.31366i	0.0946497	−	0.353237i
$89$	−0.641651	+	1.11137i	−0.0680149	+	0.117805i	−0.898027	−	0.439940i	$-0.855000\pi$
$89$	−0.641651	+	1.11137i	−0.0680149	+	0.117805i	0.830013	+	0.557745i	$0.188333\pi$
$90$	−4.16509	+	5.25852i	−0.439039	+	0.554296i
$91$	13.7696	+	4.56669i	1.44345	+	0.478719i
$92$	−0.815058	−	0.815058i	−0.0849757	−	0.0849757i
$93$	−2.61753	−	12.1399i	−0.271425	−	1.25885i
$94$	−7.63664	+	4.40902i	−0.787659	+	0.454755i
$95$	−11.4052	+	10.3719i	−1.17015	+	1.06414i
$96$	0.939092	−	1.45537i	0.0958457	−	0.148538i
$97$	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	$0.714447\pi$
$101$	−16.2068	+	9.35702i	−1.61264	+	0.931059i	−0.988755	+	0.149543i	$0.952220\pi$
$102$	−2.03629	+	6.32998i	−0.201623	+	0.626761i
$103$	−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
$105$	1.58481	−	10.1237i	0.154662	−	0.987968i
$106$	0.953965			0.0926572
$107$	6.54257	−	1.75308i	0.632494	−	0.169476i	0.0716931	−	0.997427i	$-0.477160\pi$
$107$	6.54257	−	1.75308i	0.632494	−	0.169476i	0.560801	+	0.827950i	$0.310493\pi$
$108$	−4.76527	−	2.07175i	−0.458539	−	0.199354i
$109$	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	−0.863749	−	0.503922i	$-0.831890\pi$
$113$	−3.82501	+	3.82501i	−0.359827	+	0.359827i	0.503922	+	0.863749i	$0.331890\pi$
$114$	−10.0338	−	6.47437i	−0.939747	−	0.606380i
$115$	−2.57454	−	0.122158i	−0.240077	−	0.0113913i
$116$	−2.04049	+	1.17808i	−0.189455	+	0.109382i
$117$	−2.66822	−	16.2317i	−0.246677	−	1.50062i
$118$	3.88081	+	3.88081i	0.357258	+	0.357258i
$119$	−2.05140	−	9.94788i	−0.188051	−	0.911921i
$120$	−0.635956	−	3.82041i	−0.0580546	−	0.348754i
$121$	0.384350	−	0.665714i	0.0349409	−	0.0605195i
$122$	−0.229088	+	0.854968i	−0.0207407	+	0.0774052i
$123$	−4.10392	+	12.7573i	−0.370038	+	1.15029i
$124$	6.20943	+	3.58502i	0.557623	+	0.321944i
$125$	−8.94656	+	6.70515i	−0.800205	+	0.599727i
$126$	7.89396	−	0.827862i	0.703250	−	0.0737518i
$127$	−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
$129$	0.644403	+	1.25562i	0.0567365	+	0.110552i
$130$	9.07081	−	8.24902i	0.795563	−	0.723487i
$131$	−10.5767	−	6.10644i	−0.924088	−	0.533522i	−0.0391509	−	0.999233i	$-0.512465\pi$
$131$	−10.5767	−	6.10644i	−0.924088	−	0.533522i	−0.884937	+	0.465711i	$0.845799\pi$
$132$	4.40405	−	3.98880i	0.383323	−	0.347180i
$133$	18.2094	+	1.06529i	1.57896	+	0.0923726i
$134$	4.47478			0.386562
$135$	−11.0000	+	3.74169i	−0.946728	+	0.322034i
$136$	−1.91953	−	3.32472i	−0.164598	−	0.285093i
$137$	0.910941	−	3.39968i	0.0778270	−	0.290454i	−0.916032	−	0.401104i	$-0.868627\pi$
$137$	0.910941	−	3.39968i	0.0778270	−	0.290454i	0.993859	+	0.110650i	$0.0352932\pi$
$138$	−0.420798	−	1.95163i	−0.0358207	−	0.166133i
$139$			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
$144$	2.73346	−	1.23621i	0.227788	−	0.103018i
$145$	−1.60326	+	5.01866i	−0.133143	+	0.416777i
$146$			7.07066i			0.585172i
$147$	−9.87416	+	7.03570i	−0.814407	+	0.580295i
$148$	3.49800	+	3.49800i	0.287534	+	0.287534i
$149$	−1.00095	+	1.73369i	−0.0820008	+	0.142029i	−0.904109	−	0.427301i	$-0.859464\pi$
$149$	−1.00095	+	1.73369i	−0.0820008	+	0.142029i	0.822108	+	0.569331i	$0.192798\pi$
$150$	−6.79958	−	5.36336i	−0.555184	−	0.437917i
$151$	−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
$153$	−8.90800	+	7.30020i	−0.720169	+	0.590186i
$154$	−2.85715	+	8.61496i	−0.230236	+	0.694213i
$155$	15.6656	−	3.41092i	1.25829	−	0.273972i
$156$	7.98005	+	5.14920i	0.638916	+	0.412266i
$157$	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
$159$	1.38837	+	0.895860i	0.110105	+	0.0710464i
$160$	1.88133	+	1.20856i	0.148732	+	0.0955449i
$161$	2.02682	+	2.27870i	0.159736	+	0.179587i
$162$	−4.98968	−	7.49020i	−0.392026	−	0.588486i
$163$	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
$165$	1.28477	−	13.2242i	0.100020	−	1.02950i
$166$	−5.01942	+	8.69390i	−0.389583	+	0.674777i
$167$	−5.93525	−	5.93525i	−0.459284	−	0.459284i	0.439137	−	0.898420i	$-0.355284\pi$
$167$	−5.93525	−	5.93525i	−0.459284	−	0.459284i	−0.898420	+	0.439137i	$0.855284\pi$
$168$	−2.70524	+	3.69887i	−0.208714	+	0.285374i
$169$			17.0652i			1.31271i
$170$	−8.17727	−	2.61230i	−0.627168	−	0.200354i
$171$	−8.52281	−	18.8452i	−0.651756	−	1.44113i
$172$	−0.787066	−	0.210894i	−0.0600132	−	0.0160805i
$173$	3.16440	+	11.8097i	0.240585	+	0.897875i	0.975551	+	0.219772i	$0.0705313\pi$
$173$	3.16440	+	11.8097i	0.240585	+	0.897875i	−0.734966	+	0.678104i	$0.762802\pi$
$174$	−4.07600	−	0.201667i	−0.309001	−	0.0152884i
$175$	13.0737	+	2.01953i	0.988278	+	0.152662i
$176$			3.43055i			0.258588i
$177$	2.00359	+	9.29246i	0.150599	+	0.698464i
$178$	0.332143	−	1.23958i	0.0248952	−	0.0929101i
$179$	−0.740048	−	1.28180i	−0.0553138	−	0.0958063i	0.837043	−	0.547138i	$-0.184283\pi$
$179$	−0.740048	−	1.28180i	−0.0553138	−	0.0958063i	−0.892356	+	0.451331i	$0.850949\pi$
$180$	2.66217	−	6.15734i	0.198426	−	0.458941i
$181$	−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
$183$	−1.13630	+	1.02916i	−0.0839978	+	0.0760778i
$184$	0.998238	+	0.576333i	0.0735911	+	0.0424878i
$185$	11.0492	+	0.524267i	0.812354	+	0.0385449i
$186$	5.67037	+	11.0488i	0.415772	+	0.810134i
$187$	−3.40867	−	12.7213i	−0.249267	−	0.930276i
$188$	6.23529	−	6.23529i	0.454755	−	0.454755i
$189$	12.2661	+	6.20831i	0.892227	+	0.451588i
$190$	8.33215	−	12.9704i	0.604477	−	0.940972i
$191$	13.1103	+	7.56922i	0.948627	+	0.547690i	0.892654	−	0.450743i	$-0.148841\pi$
$191$	13.1103	+	7.56922i	0.948627	+	0.547690i	0.0559725	+	0.998432i	$0.482174\pi$
$192$	−0.530415	+	1.64884i	−0.0382794	+	0.118994i
$193$	−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
$195$	20.9480	−	3.48706i	1.50012	−	0.249713i
$196$	0.816238	−	6.95225i	0.0583027	−	0.496589i
$197$	3.26809	+	3.26809i	0.232842	+	0.232842i	0.813878	−	0.581036i	$-0.197352\pi$
$197$	3.26809	+	3.26809i	0.232842	+	0.232842i	−0.581036	+	0.813878i	$0.697352\pi$
$198$	10.1554	−	1.66938i	0.721711	−	0.118637i
$199$	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
$201$	6.51246	+	4.20223i	0.459354	+	0.296402i
$202$	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
$207$	1.22034	−	3.23551i	0.0848194	−	0.224883i
$208$	−5.29634	+	1.41915i	−0.367235	+	0.0984003i
$209$	23.6512			1.63599
$210$	1.08939	+	10.1889i	0.0751748	+	0.703099i
$211$	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
$213$	−0.935247	+	2.90729i	−0.0640821	+	0.199204i
$214$	−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
$219$	−6.64000	+	10.2904i	−0.448690	+	0.695364i
$220$	5.16101	+	5.67517i	0.347955	+	0.382620i
$221$	18.2300	−	10.5251i	1.22628	−	0.707996i
$222$	1.80595	+	8.37583i	0.121207	+	0.562149i
$223$	−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
$225$	−4.85923	−	14.1911i	−0.323949	−	0.946075i
$226$	2.70469	−	4.68466i	0.179913	−	0.311619i
$227$	1.96153	−	7.32054i	0.130191	−	0.485881i	−0.869780	−	0.493440i	$-0.835739\pi$
$227$	1.96153	−	7.32054i	0.130191	−	0.485881i	0.999971	+	0.00755864i	$0.00240601\pi$
$228$	11.3676	+	3.65684i	0.752835	+	0.242180i
$229$	−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
$231$	−12.2485	+	9.85484i	−0.805890	+	0.648401i
$232$	1.66606	−	1.66606i	0.109382	−	0.109382i
$233$	0.486355	+	1.81510i	0.0318622	+	0.118911i	0.980025	−	0.198873i	$-0.0637280\pi$
$233$	0.486355	+	1.81510i	0.0318622	+	0.118911i	−0.948163	+	0.317784i	$0.897061\pi$
$234$	6.77837	+	14.9880i	0.443116	+	0.979797i
$235$	0.934521	−	19.6956i	0.0609614	−	1.28480i
$236$	−4.75301	−	2.74415i	−0.309394	−	0.178629i
$237$	6.68123	+	7.37677i	0.433992	+	0.479173i
$238$	4.55620	+	9.07798i	0.295334	+	0.588438i
$239$	−18.5117			−1.19742			−0.598712	−	0.800964i	$-0.704321\pi$
$239$	−18.5117			−1.19742			−0.598712	+	0.800964i	$0.704321\pi$
$240$	1.60308	+	3.52564i	0.103479	+	0.227579i
$241$	−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
$243$	−0.227852	−	15.5868i	−0.0146167	−	0.999893i
$244$		−	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
$249$	−15.4695	+	7.93915i	−0.980339	+	0.503123i
$250$	6.90629	−	8.79222i	0.436792	−	0.556069i
$251$			29.1045i			1.83706i	0.395355	+	0.918528i	$0.370622\pi$
$251$			29.1045i			1.83706i	−0.395355	+	0.918528i	$0.629378\pi$
$252$	−7.41072	+	2.84276i	−0.466831	+	0.179077i
$253$	2.79610	+	2.79610i	0.175789	+	0.175789i
$254$	3.20264	−	5.54713i	0.200951	−	0.348058i
$255$	−9.44777	−	11.4811i	−0.591643	−	0.718973i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−18.5540	+	4.97152i	−1.15737	+	0.310115i	−0.785913	−	0.618337i	$-0.787807\pi$
$257$	−18.5540	+	4.97152i	−1.15737	+	0.310115i	−0.371452	+	0.928452i	$0.621140\pi$
$258$	−0.947425	−	1.04606i	−0.0589841	−	0.0651246i
$259$	−8.69853	−	9.77954i	−0.540501	−	0.607671i
$260$	−6.62673	+	10.3156i	−0.410972	+	0.639749i
$261$	−5.74271	−	4.12124i	−0.355465	−	0.255098i
$262$	11.7967	+	3.16093i	0.728805	+	0.195283i
$263$	−7.96472	−	2.13414i	−0.491126	−	0.131597i	0.00475276	−	0.999989i	$-0.498487\pi$
$263$	−7.96472	−	2.13414i	−0.491126	−	0.131597i	−0.495878	+	0.868392i	$0.665154\pi$
$264$	−3.22161	+	4.99273i	−0.198276	+	0.307281i
$265$	−1.15292	+	1.79472i	−0.0708234	+	0.110249i
$266$	−17.8647	+	3.68396i	−1.09535	+	0.225878i
$267$	1.64747	−	1.49213i	0.100823	−	0.0913169i
$268$	−4.32230	+	1.15816i	−0.264027	+	0.0707457i
$269$	−2.64417	−	4.57984i	−0.161218	−	0.279238i	0.774088	−	0.633078i	$-0.218209\pi$
$269$	−2.64417	−	4.57984i	−0.161218	−	0.279238i	−0.935306	+	0.353841i	$0.884876\pi$
$270$	9.65675	−	6.46120i	0.587691	−	0.393216i
$271$	−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
$273$	−20.2816	−	14.8333i	−1.22750	−	0.897753i
$274$			3.51961i			0.212627i
$275$	17.0757	+	1.62408i	1.02970	+	0.0979359i
$276$	0.911578	+	1.77622i	0.0548705	+	0.106916i
$277$	−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	$-0.658243\pi$
$281$		−	29.4678i		−	1.75790i	0.476910	−	0.878952i	$-0.341757\pi$
$282$	14.9302	−	3.21915i	0.889079	−	0.191698i
$283$	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
$285$	24.3068	−	11.0521i	1.43981	−	0.654671i
$286$	−18.8103			−1.11228
$287$	9.18249	+	18.2956i	0.542025	+	1.07996i
$288$	−2.32036	+	1.90156i	−0.136728	+	0.112051i
$289$	1.95863	+	1.13081i	0.115213	+	0.0665185i
$290$	0.249702	−	5.26261i	0.0146630	−	0.309031i
$291$	−4.70364	+	2.41397i	−0.275732	+	0.141509i
$292$	−1.83002	−	6.82973i	−0.107094	−	0.399680i
$293$	−12.5118	+	12.5118i	−0.730947	+	0.730947i	−0.970807	−	0.239860i	$-0.922898\pi$
$293$	−12.5118	+	12.5118i	−0.730947	+	0.730947i	0.239860	+	0.970807i	$0.422898\pi$
$294$	7.71673	−	9.35158i	0.450049	−	0.545395i
$295$	−11.9913	+	2.61089i	−0.698158	+	0.152012i
$296$	−4.28416	−	2.47346i	−0.249012	−	0.143767i
$297$	16.3475	+	7.10726i	0.948580	+	0.412405i
$298$	0.518128	−	1.93368i	0.0300144	−	0.112015i
$299$	−3.16013	+	5.47351i	−0.182755	+	0.316541i
$300$	7.95603	+	3.42075i	0.459342	+	0.197497i
$301$	2.04624	+	0.678636i	0.117943	+	0.0391159i
$302$	10.5624	+	10.5624i	0.607799	+	0.607799i
$303$	31.6855	−	6.83184i	1.82029	−	0.392479i
$304$	−5.97063	+	3.44715i	−0.342439	+	0.197707i
$305$	−1.33161	−	1.46427i	−0.0762476	−	0.0838437i
$306$	6.71503	−	9.35701i	0.383873	−	0.534905i
$307$	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	−0.745567	−	0.666431i	$-0.767821\pi$
$311$	−9.54424	+	5.51037i	−0.541204	+	0.312465i	0.204362	+	0.978895i	$0.434488\pi$
$312$	−9.04085	−	2.90836i	−0.511837	−	0.164653i
$313$	−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
$315$	−7.98283	+	15.8516i	−0.449781	+	0.893139i
$316$	−5.74617			−0.323248
$317$	−4.91615	+	1.31728i	−0.276118	+	0.0739857i	−0.394221	−	0.919016i	$-0.628986\pi$
$317$	−4.91615	+	1.31728i	−0.276118	+	0.0739857i	0.118103	+	0.993001i	$0.462319\pi$
$318$	−1.57293	−	0.505997i	−0.0882056	−	0.0283749i
$319$	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
$324$	6.75827	+	5.94355i	0.375459	+	0.330197i
$325$	4.55649	+	27.0346i	0.252749	+	1.49961i
$326$	−5.22388	+	3.01601i	−0.289324	+	0.167041i
$327$	−23.9586	+	5.16580i	−1.32491	+	0.285670i
$328$	5.47101	+	5.47101i	0.302086	+	0.302086i
$329$	−17.4323	+	15.5054i	−0.961076	+	0.854840i
$330$	2.18168	+	13.1061i	0.120098	+	0.721469i
$331$	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
$333$	−5.23735	+	13.8859i	−0.287005	+	0.760942i
$334$	7.26917	+	4.19686i	0.397751	+	0.229642i
$335$	−5.40803	+	8.41852i	−0.295472	+	0.459953i
$336$	1.65573	−	4.27300i	0.0903273	−	0.233112i
$337$	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
$339$	8.33566	−	4.27797i	0.452731	−	0.232347i
$340$	8.57475	+	0.406857i	0.465031	+	0.0220649i
$341$	−21.3018	−	12.2986i	−1.15356	−	0.666006i
$342$	13.1099	+	15.9972i	0.708903	+	0.865031i
$343$	−3.23013	+	18.2364i	−0.174410	+	0.984673i
$344$	0.814830			0.0439327
$345$	4.18020	+	1.56699i	0.225055	+	0.0843642i
$346$	−6.11315	−	10.5883i	−0.328645	−	0.569230i
$347$	7.08212	−	26.4308i	0.380188	−	1.41888i	−0.465425	−	0.885087i	$-0.654099\pi$
$347$	7.08212	−	26.4308i	0.380188	−	1.41888i	0.845614	−	0.533795i	$-0.179235\pi$
$348$	3.98931	−	0.860151i	0.213849	−	0.0461089i
$349$		−	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	−0.146257	−	0.989247i	$-0.546723\pi$
$353$	−14.4208	−	3.86404i	−0.767542	−	0.205662i	−0.621285	+	0.783584i	$0.713389\pi$
$354$	−4.34038	−	8.45726i	−0.230689	−	0.449499i
$355$	−3.75573	−	1.19980i	−0.199333	−	0.0636788i
$356$			1.28330i			0.0680149i
$357$	−1.89409	+	17.4905i	−0.100246	+	0.925696i
$358$	1.04659	+	1.04659i	0.0553138	+	0.0553138i
$359$	15.4927	−	26.8342i	0.817675	−	1.41625i	−0.0897169	−	0.995967i	$-0.528596\pi$
$359$	15.4927	−	26.8342i	0.817675	−	1.41625i	0.907391	−	0.420287i	$-0.138070\pi$
$360$	−0.977818	+	6.63656i	−0.0515355	+	0.349777i
$361$	14.2656	+	24.7088i	0.750822	+	1.30046i
$362$	15.0900	−	4.04336i	0.793113	−	0.212514i
$363$	−0.986836	+	0.893789i	−0.0517954	+	0.0469117i
$364$	14.2082	−	2.92993i	0.744710	−	0.153570i
$365$	−13.3022	−	8.54530i	−0.696270	−	0.447282i
$366$	0.831216	−	1.28819i	0.0434484	−	0.0673348i
$367$	−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
$369$	13.5334	−	18.8580i	0.704519	−	0.981707i
$370$	−10.8084	+	2.35334i	−0.561903	+	0.122345i
$371$	2.47194	−	0.509750i	0.128337	−	0.0264649i
$372$	−8.33678	−	9.20468i	−0.432242	−	0.477240i
$373$	−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
$375$	18.3079	−	6.31030i	0.945417	−	0.325863i
$376$	−4.40902	+	7.63664i	−0.227378	+	0.393830i
$377$	9.13527	+	9.13527i	0.470490	+	0.470490i
$378$	−13.4550	−	2.82207i	−0.692048	−	0.145152i
$379$		−	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
$381$	9.87030	−	5.06557i	0.505671	−	0.259517i
$382$	−14.6226	−	3.91812i	−0.748158	−	0.200468i
$383$	2.17034	+	8.09984i	0.110899	+	0.413882i	0.998947	−	0.0458683i	$-0.0146055\pi$
$383$	2.17034	+	8.09984i	0.110899	+	0.413882i	−0.888048	+	0.459751i	$0.847939\pi$
$384$	0.0855915	−	1.72993i	0.00436782	−	0.0882804i
$385$	−12.7545	−	15.7869i	−0.650030	−	0.804576i
$386$		−	16.8368i		−	0.856972i
$387$	−0.396513	−	2.41212i	−0.0201559	−	0.122615i
$388$	0.790020	−	2.94839i	0.0401072	−	0.149682i
$389$	13.0941	+	22.6796i	0.663895	+	1.14990i	0.979584	+	0.201037i	$0.0644312\pi$
$389$	13.0941	+	22.6796i	0.663895	+	1.14990i	−0.315688	+	0.948863i	$0.602235\pi$
$390$	−19.3317	+	8.78998i	−0.978898	+	0.445098i
$391$	4.42515			0.223790
$392$	1.01095	+	6.92661i	0.0510606	+	0.349847i
$393$	14.2002	+	15.6785i	0.716307	+	0.790878i
$394$	−4.00258	−	2.31089i	−0.201647	−	0.116421i
$395$	−9.50590	+	8.64468i	−0.478294	+	0.434961i
$396$	−9.37727	+	4.24090i	−0.471225	+	0.213113i
$397$	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
$399$	−29.4593	−	11.4151i	−1.47481	−	0.571468i
$400$	−4.54738	+	2.07878i	−0.227369	+	0.103939i
$401$	16.7034	+	9.64369i	0.834126	+	0.481583i	0.855263	−	0.518193i	$-0.173395\pi$
$401$	16.7034	+	9.64369i	0.834126	+	0.481583i	−0.0211370	+	0.999777i	$0.506729\pi$
$402$	−7.37817	−	2.37349i	−0.367990	−	0.118379i
$403$	10.1753	−	37.9749i	0.506870	−	1.89167i
$404$	−9.35702	+	16.2068i	−0.465529	+	0.806320i
$405$	20.1218	−	0.334876i	0.999862	−	0.0166401i
$406$	−4.65788	+	4.14301i	−0.231167	+	0.205614i
$407$	−12.0001	−	12.0001i	−0.594822	−	0.594822i
$408$	1.40151	+	6.50007i	0.0693849	+	0.321801i
$409$	−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
$411$	−3.30523	+	5.12234i	−0.163035	+	0.252666i
$412$	−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
$417$	4.95038	−	15.3886i	0.242421	−	0.753585i
$418$	−22.8453	+	6.12139i	−1.11740	+	0.299407i
$419$	8.91090			0.435326			0.217663	−	0.976024i	$-0.430157\pi$
$419$	8.91090			0.435326			0.217663	+	0.976024i	$0.430157\pi$
$420$	−3.68934	−	9.55975i	−0.180021	−	0.466468i
$421$	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
$423$	24.7520	+	9.33574i	1.20348	+	0.453919i
$424$	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
$429$	−27.3760	−	17.6646i	−1.32173	−	0.852856i
$430$	1.34797	−	1.22585i	0.0650051	−	0.0591158i
$431$	28.5894	−	16.5061i	1.37710	−	0.795069i	0.385291	−	0.922795i	$-0.374101\pi$
$431$	28.5894	−	16.5061i	1.37710	−	0.795069i	0.991810	+	0.127726i	$0.0407677\pi$
$432$	−5.16273	+	0.588447i	−0.248392	+	0.0283117i
$433$	−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
$435$	5.30548	−	7.42456i	0.254378	−	0.355980i
$436$	7.07519	−	12.2546i	0.338840	−	0.586888i
$437$	−2.05679	+	7.67603i	−0.0983895	+	0.367194i
$438$	3.75039	−	11.6584i	0.179200	−	0.557058i
$439$	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
$441$	20.0127	−	6.36331i	0.952986	−	0.303015i
$442$	−14.8848	+	14.8848i	−0.707996	+	0.707996i
$443$	4.88974	+	18.2487i	0.232318	+	0.867024i	0.979339	+	0.202224i	$0.0648168\pi$
$443$	4.88974	+	18.2487i	0.232318	+	0.867024i	−0.747021	+	0.664801i	$0.768517\pi$
$444$	−3.91224	−	7.62302i	−0.185666	−	0.361772i
$445$	1.93063	+	2.12297i	0.0915207	+	0.100638i
$446$	9.46552	+	5.46492i	0.448205	+	0.258772i
$447$	2.56997	−	2.32765i	0.121556	−	0.110094i
$448$	1.18680	+	2.36464i	0.0560711	+	0.111719i
$449$	−6.78726			−0.320311			−0.160155	−	0.987092i	$-0.551199\pi$
$449$	−6.78726			−0.320311			−0.160155	+	0.987092i	$0.551199\pi$
$450$	8.36659	+	12.4499i	0.394405	+	0.586894i
$451$	13.2714	+	22.9868i	0.624926	+	1.08240i
$452$	−1.40005	+	5.22506i	−0.0658528	+	0.245766i
$453$	5.45317	+	25.2913i	0.256212	+	1.18829i
$454$			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
$459$	18.5600	−	7.31190i	0.866305	−	0.341290i
$460$	−2.29070	+	1.18148i	−0.106804	+	0.0550868i
$461$			28.0988i			1.30869i	0.756195	+	0.654347i	$0.227056\pi$
$461$			28.0988i			1.30869i	−0.756195	+	0.654347i	$0.772944\pi$
$462$	9.28049	−	12.6892i	0.431767	−	0.590354i
$463$	−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
$465$	−27.6393	−	2.68524i	−1.28174	−	0.124525i
$466$	−0.939566	−	1.62738i	−0.0435246	−	0.0753867i
$467$	−8.84631	+	2.37036i	−0.409358	+	0.109687i	−0.457621	−	0.889147i	$-0.651298\pi$
$467$	−8.84631	+	2.37036i	−0.409358	+	0.109687i	0.0482625	+	0.998835i	$0.484632\pi$
$468$	−10.4266	−	12.7229i	−0.481969	−	0.588118i
$469$	11.5952	−	2.39109i	0.535416	−	0.110410i
$470$	4.19491	+	19.2663i	0.193497	+	0.888689i
$471$	−20.5043	−	13.2306i	−0.944788	−	0.609633i
$472$	5.30129	+	1.42048i	0.244012	+	0.0653827i
$473$	2.70007	+	0.723482i	0.124149	+	0.0332657i
$474$	−8.36282	−	5.39618i	−0.384117	−	0.247855i
$475$	14.3317	+	31.3510i	0.657583	+	1.43848i
$476$	−6.75050	−	7.58942i	−0.309409	−	0.347861i
$477$	−1.81402	−	2.21354i	−0.0830583	−	0.101351i
$478$	17.8810	−	4.79119i	0.817856	−	0.219144i
$479$	7.76447	+	13.4485i	0.354768	+	0.614476i	0.987078	−	0.160239i	$-0.0512266\pi$
$479$	7.76447	+	13.4485i	0.354768	+	0.614476i	−0.632310	+	0.774715i	$0.717893\pi$
$480$	−2.46096	−	2.99060i	−0.112327	−	0.136501i
$481$	13.5624	−	23.4908i	0.618392	−	1.07109i
$482$	5.91569	+	5.91569i	0.269452	+	0.269452i
$483$	−2.13323	−	4.83226i	−0.0970655	−	0.219875i
$484$		−	0.768701i		−	0.0349409i
$485$	−3.12870	−	6.06605i	−0.142067	−	0.275445i
$486$	4.25425	+	14.9967i	0.192977	+	0.680265i
$487$	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	$0.0848989\pi$
$491$			11.6805i			0.527133i	−0.964641	+	0.263567i	$0.915101\pi$
$492$	2.82457	+	13.1001i	0.127342	+	0.590600i
$493$	2.34113	−	8.73722i	0.105439	−	0.393504i
$494$	−18.9013	−	32.7380i	−0.850409	−	1.47295i
$495$	−9.13271	+	21.1231i	−0.410485	+	0.949413i
$496$	7.17003			0.321944
$497$	2.09261	+	4.16941i	0.0938664	+	0.187024i
$498$	12.8876	−	11.6724i	0.577506	−	0.523054i
$499$	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
$501$	6.63811	+	12.9344i	0.296569	+	0.577867i
$502$	−7.53279	−	28.1127i	−0.336205	−	1.25473i
$503$	14.8328	−	14.8328i	0.661362	−	0.661362i	−0.294339	−	0.955701i	$-0.595099\pi$
$503$	14.8328	−	14.8328i	0.661362	−	0.661362i	0.955701	+	0.294339i	$0.0950994\pi$
$504$	6.42244	−	4.66393i	0.286078	−	0.207748i
$505$	8.90263	+	40.8879i	0.396162	+	1.81949i
$506$	−3.42451	−	1.97714i	−0.152238	−	0.0878947i
$507$	9.05163	−	28.1377i	0.401997	−	1.24964i
$508$	−1.65781	+	6.18702i	−0.0735533	+	0.274505i
$509$	9.66165	−	16.7345i	0.428245	−	0.741742i	−0.568472	−	0.822702i	$-0.692465\pi$
$509$	9.66165	−	16.7345i	0.428245	−	0.741742i	0.996717	+	0.0809602i	$0.0257987\pi$
$510$	12.0974	+	8.64461i	0.535681	+	0.382790i
$511$	3.77820	+	18.3217i	0.167138	+	0.810505i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.05692	+	35.5933i	0.179118	+	1.57148i
$514$	16.6350	−	9.60425i	0.733740	−	0.423625i
$515$	−0.941233	+	19.8370i	−0.0414757	+	0.874123i
$516$	1.18588	+	0.765201i	0.0522055	+	0.0336861i
$517$	−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	0.241549	−	0.970389i	$-0.422345\pi$
$521$	27.4522	−	15.8496i	1.20270	−	0.694382i	0.961156	+	0.276007i	$0.0890112\pi$
$522$	6.61369	+	2.49449i	0.289473	+	0.109181i
$523$	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
$525$	−20.4852	−	10.2644i	−0.894047	−	0.447973i
$526$	8.24568			0.359529
$527$	−26.5882	+	7.12430i	−1.15820	+	0.310339i
$528$	1.81962	−	5.65642i	0.0791887	−	0.246164i
$529$	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
$534$	−1.20514	+	1.86768i	−0.0521515	+	0.0808225i
$535$	0.717831	−	15.1287i	0.0310346	−	0.654071i
$536$	3.87527	−	2.23739i	0.167386	−	0.0966405i
$537$	0.540331	+	2.50601i	0.0233170	+	0.108142i
$538$	3.73942	+	3.73942i	0.161218	+	0.161218i
$539$	−2.80015	+	23.8501i	−0.120611	+	1.02729i
$540$	−7.65542	+	8.74039i	−0.329437	+	0.376127i
$541$	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
$543$	25.7587	+	8.28632i	1.10541	+	0.355600i
$544$	−3.32472	−	1.91953i	−0.142546	−	0.0822991i
$545$	−6.73160	−	30.9168i	−0.288350	−	1.32433i
$546$	23.4296	+	9.07863i	1.00270	+	0.388530i
$547$	−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
$549$	2.41946	−	1.09421i	0.103260	−	0.0466996i
$550$	−16.9142	+	2.85077i	−0.721224	+	0.121557i
$551$	14.0678	+	8.12202i	0.599307	+	0.346010i
$552$	−1.34024	−	1.47976i	−0.0570442	−	0.0629827i
$553$	15.1770	+	0.887888i	0.645392	+	0.0377569i
$554$	25.1666			1.06923
$555$	−17.9403	−	6.72510i	−0.761522	−	0.285465i
$556$	4.66652	+	8.08264i	0.197904	+	0.342780i
$557$	−12.0540	+	44.9860i	−0.510742	+	1.90612i	−0.0982317	+	0.995164i	$0.531319\pi$
$557$	−12.0540	+	44.9860i	−0.510742	+	1.90612i	−0.412511	+	0.910953i	$0.635348\pi$
$558$	−3.48908	−	21.2252i	−0.147705	−	0.898536i
$559$			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	−0.715609	−	0.698501i	$-0.753851\pi$
$563$	−39.9714	−	10.7103i	−1.68459	−	0.451386i	−0.968986	+	0.247115i	$0.920517\pi$
$564$	−13.5883	+	6.97368i	−0.572169	+	0.293645i
$565$	5.54460	+	10.7501i	0.233263	+	0.452260i
$566$			1.04099i			0.0437561i
$567$	−16.9318	−	16.7426i	−0.711068	−	0.703123i
$568$	1.24680	+	1.24680i	0.0523144	+	0.0523144i
$569$	16.0682	−	27.8309i	0.673614	−	1.16673i	−0.303258	−	0.952908i	$-0.598074\pi$
$569$	16.0682	−	27.8309i	0.673614	−	1.16673i	0.976872	−	0.213825i	$-0.0685922\pi$
$570$	−20.6180	+	16.9666i	−0.863595	+	0.710652i
$571$	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
$573$	−17.6019	−	19.4343i	−0.735329	−	0.811879i
$574$	−13.6049	−	15.2956i	−0.567856	−	0.638426i
$575$	−2.01206	+	5.40070i	−0.0839085	+	0.225225i
$576$	1.74913	−	2.43732i	0.0728806	−	0.101555i
$577$	−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
$579$	15.8113	−	24.5038i	0.657096	−	1.01834i
$580$	1.12087	+	5.14792i	0.0465416	+	0.213756i
$581$	−8.36091	+	25.2100i	−0.346869	+	1.04589i
$582$	3.91858	−	3.54911i	0.162431	−	0.147115i
$583$	3.16112	−	0.847018i	0.130920	−	0.0350799i
$584$	3.53533	+	6.12337i	0.146293	+	0.253387i
$585$	−36.3894	−	5.36154i	−1.50452	−	0.221673i
$586$	8.84718	−	15.3238i	0.365473	−	0.633019i
$587$	−26.5508	−	26.5508i	−1.09587	−	1.09587i	−0.994888	−	0.100982i	$-0.967801\pi$
$587$	−26.5508	−	26.5508i	−1.09587	−	1.09587i	−0.100982	−	0.994888i	$-0.532199\pi$
$588$	−5.03342	+	11.0302i	−0.207575	+	0.454877i
$589$		−	49.4323i		−	2.03682i
$590$	10.9069	−	5.62549i	0.449031	−	0.231598i
$591$	−3.65511	−	7.12200i	−0.150351	−	0.292960i
$592$	4.77836	+	1.28036i	0.196389	+	0.0526223i
$593$	−5.39739	−	20.1433i	−0.221644	−	0.827188i	−0.983721	−	0.179701i	$-0.942487\pi$
$593$	−5.39739	−	20.1433i	−0.221644	−	0.827188i	0.762077	−	0.647487i	$-0.224180\pi$
$594$	−17.6300	−	2.63403i	−0.723368	−	0.108076i
$595$	−22.5851	−	2.39956i	−0.925897	−	0.0983724i
$596$			2.00189i			0.0820008i
$597$	−8.51871	+	1.83675i	−0.348648	+	0.0751733i
$598$	1.63581	−	6.10491i	0.0668931	−	0.249648i
$599$	−14.8838	−	25.7795i	−0.608134	−	1.05332i	−0.991548	−	0.129743i	$-0.958585\pi$
$599$	−14.8838	−	25.7795i	−0.608134	−	1.05332i	0.383413	−	0.923577i	$-0.374749\pi$
$600$	−8.57029	−	1.24502i	−0.349881	−	0.0508276i
$601$	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
$603$	−8.50906	−	10.3831i	−0.346516	−	0.422832i
$604$	−12.9363	−	7.46876i	−0.526369	−	0.303900i
$605$	−1.15645	−	1.27166i	−0.0470165	−	0.0517004i
$606$	−28.8377	+	14.7999i	−1.17145	+	0.601204i
$607$	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
$609$	−10.6696	+	1.65544i	−0.432355	+	0.0670818i
$610$	1.66521	+	1.06973i	0.0674226	+	0.0433120i
$611$	−41.8730	−	24.1754i	−1.69400	−	0.978032i
$612$	−4.06445	+	10.7762i	−0.164296	+	0.435600i
$613$	−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
$615$	24.3809	+	17.4222i	0.983131	+	0.702531i
$616$	1.83311	+	8.88935i	0.0738582	+	0.358162i
$617$	−7.74923	−	7.74923i	−0.311972	−	0.311972i	0.533701	−	0.845673i	$-0.320801\pi$
$617$	−7.74923	−	7.74923i	−0.311972	−	0.311972i	−0.845673	+	0.533701i	$0.820801\pi$
$618$	−15.0374	+	3.24227i	−0.604893	+	0.130423i
$619$	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
$621$	−3.72830	+	4.68754i	−0.149612	+	0.188104i
$622$	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
$627$	−38.9970	−	12.5450i	−1.55739	−	0.500998i
$628$	13.6086	−	3.64642i	0.543044	−	0.145508i
$629$	−18.9915			−0.757241
$630$	3.60812	−	17.3776i	0.143751	−	0.692341i
$631$	−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
$633$	−4.26877	−	1.37322i	−0.169668	−	0.0545807i
$634$	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
$639$	3.08414	−	4.29757i	0.122007	−	0.170009i
$640$	2.23356	+	0.105978i	0.0882890	+	0.00418917i
$641$	−14.6651	+	8.46692i	−0.579238	+	0.334423i	−0.760831	−	0.648951i	$-0.775208\pi$
$641$	−14.6651	+	8.46692i	−0.579238	+	0.334423i	0.181592	+	0.983374i	$0.441875\pi$
$642$	11.4683	−	2.47272i	0.452617	−	0.0975905i
$643$	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
$645$	3.11299	−	0.518197i	0.122574	−	0.0204040i
$646$	−13.2338	+	22.9216i	−0.520677	+	0.901838i
$647$	−10.2045	+	38.0837i	−0.401181	+	1.49723i	0.409812	+	0.912170i	$0.365594\pi$
$647$	−10.2045	+	38.0837i	−0.401181	+	1.49723i	−0.810993	+	0.585056i	$0.801072\pi$
$648$	−8.06629	−	3.99186i	−0.316874	−	0.156815i
$649$	16.3054	+	9.41395i	0.640045	+	0.369530i
$650$	−11.3983	−	24.9341i	−0.447078	−	0.977995i
$651$	20.5971	+	25.5999i	0.807265	+	1.00334i
$652$	4.26528	−	4.26528i	0.167041	−	0.167041i
$653$	−8.48981	−	31.6844i	−0.332232	−	1.23991i	−0.906839	−	0.421477i	$-0.861512\pi$
$653$	−8.48981	−	31.6844i	−0.332232	−	1.23991i	0.574607	−	0.818429i	$-0.305155\pi$
$654$	21.8052	−	11.1907i	0.852651	−	0.437592i
$655$	−20.2038	+	18.3734i	−0.789427	+	0.717906i
$656$	−6.70060	−	3.86859i	−0.261614	−	0.151043i
$657$	16.4065	−	13.4453i	0.640078	−	0.524551i
$658$	12.8252	−	19.4889i	0.499980	−	0.759756i
$659$	9.95001			0.387597			0.193799	−	0.981041i	$-0.437919\pi$
$659$	9.95001			0.387597			0.193799	+	0.981041i	$0.437919\pi$
$660$	−5.49946	−	12.0949i	−0.214066	−	0.470793i
$661$	−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
$663$	−35.6410	+	7.68470i	−1.38418	+	0.298449i
$664$			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
$669$	8.64379	+	16.8425i	0.334188	+	0.651168i
$670$	3.04488	−	9.53136i	0.117634	−	0.368229i
$671$			3.03648i			0.117222i
$672$	−0.493374	+	4.55594i	−0.0190323	+	0.175749i
$673$	−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
$675$	0.484892	+	25.9762i	0.0186635	+	0.999826i
$676$	8.53259	+	14.7789i	0.328177	+	0.568419i
$677$	11.3933	−	3.05281i	0.437878	−	0.117329i	−0.0331437	−	0.999451i	$-0.510552\pi$
$677$	11.3933	−	3.05281i	0.437878	−	0.117329i	0.471022	+	0.882121i	$0.343885\pi$
$678$	−6.94440	+	6.28963i	−0.266698	+	0.241552i
$679$	−2.54221	+	7.66533i	−0.0975610	+	0.294168i
$680$	−8.38787	+	1.82631i	−0.321660	+	0.0700360i
$681$	−7.11717	+	11.0299i	−0.272730	+	0.422668i
$682$	23.7591	+	6.36622i	0.909781	+	0.243775i
$683$	−35.6240	−	9.54542i	−1.36311	−	0.365245i	−0.498155	−	0.867088i	$-0.665989\pi$
$683$	−35.6240	−	9.54542i	−1.36311	−	0.365245i	−0.864959	+	0.501843i	$0.832656\pi$
$684$	−16.8036	−	12.0590i	−0.642501	−	0.461089i
$685$	−6.62153	−	4.25365i	−0.252996	−	0.162524i
$686$	−1.59987	−	18.4510i	−0.0610832	−	0.704464i
$687$	5.44937	+	6.01667i	0.207906	+	0.229550i
$688$	−0.787066	+	0.210894i	−0.0300066	+	0.00804024i
$689$	2.61538	+	4.52997i	0.0996379	+	0.172578i
$690$	−4.44334	−	0.431684i	−0.169155	−	0.0164339i
$691$	−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
$693$	25.4229	−	9.75225i	0.965735	−	0.370457i
$694$			27.3632i			1.03869i
$695$	19.8795	+	6.35070i	0.754074	+	0.240896i
$696$	−3.63075	+	1.86335i	−0.137623	+	0.0706302i
$697$	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	$0.0431576\pi$
$701$			7.15756i			0.270337i	−0.990823	+	0.135169i	$0.956842\pi$
$702$	−3.22656	−	28.3081i	−0.121778	−	1.06842i
$703$	8.82715	−	32.9434i	0.332922	−	1.24248i
$704$	1.71528	+	2.97095i	0.0646469	+	0.111972i
$705$	−11.9877	+	31.9791i	−0.451483	+	1.20440i
$706$	14.9295			0.561880
$707$	27.2183	−	41.3602i	1.02365	−	1.55551i
$708$	6.38139	+	7.04572i	0.239827	+	0.264794i
$709$	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
$711$	−7.10350	−	15.7069i	−0.266402	−	0.589055i
$712$	−0.332143	−	1.23958i	−0.0124476	−	0.0464550i
$713$	5.84399	−	5.84399i	0.218859	−	0.218859i
$714$	−2.69733	−	17.3848i	−0.100945	−	0.650609i
$715$	22.7334	−	35.3883i	0.850179	−	1.32345i
$716$	−1.28180	−	0.740048i	−0.0479032	−	0.0276569i
$717$	30.5228	+	9.81890i	1.13990	+	0.366694i
$718$	−8.01962	+	29.9296i	−0.299290	+	1.11696i
$719$	−2.68898	+	4.65745i	−0.100282	+	0.173694i	−0.911801	−	0.410633i	$-0.865308\pi$
$719$	−2.68898	+	4.65745i	−0.100282	+	0.173694i	0.811519	+	0.584326i	$0.198641\pi$
$720$	−0.773168	−	6.66350i	−0.0288143	−	0.248334i
$721$	17.5575	−	15.6168i	0.653877	−	0.581599i
$722$	−20.1746	−	20.1746i	−0.750822	−	0.750822i
$723$	3.05415	+	14.1649i	0.113585	+	0.526799i
$724$	−13.5293	+	7.81117i	−0.502814	+	0.290300i
$725$	9.59891	+	6.82994i	0.356495	+	0.253658i
$726$	0.721881	−	1.11875i	0.0267915	−	0.0415205i
$727$	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
$732$	−0.469485	+	1.45943i	−0.0173527	+	0.0539421i
$733$	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
$735$	8.26727	+	25.8196i	0.304943	+	0.952371i
$736$	1.15267			0.0424878
$737$	14.8279	−	3.97312i	0.546193	−	0.146352i
$738$	−8.19143	+	21.7181i	−0.301531	+	0.799455i
$739$	−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	−0.467459	−	0.884015i	$-0.654831\pi$
$743$	11.3545	−	11.3545i	0.416555	−	0.416555i	0.884015	+	0.467459i	$0.154831\pi$
$744$	10.4351	+	6.73332i	0.382568	+	0.246855i
$745$	3.01170	+	3.31173i	0.110340	+	0.121333i
$746$	12.3892	−	7.15292i	0.453602	−	0.261887i
$747$	29.7177	−	4.88510i	1.08731	−	0.178737i
$748$	−9.31267	−	9.31267i	−0.340505	−	0.340505i
$749$	−13.3903	+	11.9101i	−0.489269	+	0.435186i
$750$	−16.0509	+	10.8337i	−0.586095	+	0.395592i
$751$	−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
$753$	15.4374	−	47.9885i	0.562572	−	1.74880i
$754$	−11.1884	−	6.45961i	−0.407457	−	0.235245i
$755$	−32.6367	+	7.10607i	−1.18777	+	0.258616i
$756$	13.7269	−	0.756491i	0.499242	−	0.0275133i
$757$	−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
$759$	−3.12722	−	6.09340i	−0.113511	−	0.221177i
$760$	0.730646	−	15.3988i	0.0265033	−	0.558572i
$761$	−9.71823	−	5.61082i	−0.352286	−	0.203392i	0.313406	−	0.949619i	$-0.398530\pi$
$761$	−9.71823	−	5.61082i	−0.352286	−	0.203392i	−0.665691	+	0.746227i	$0.731863\pi$
$762$	−8.22291	+	7.44759i	−0.297885	+	0.269798i
$763$	−20.5808	+	31.2740i	−0.745074	+	1.13219i
$764$	15.1384			0.547690
$765$	9.48809	+	23.9417i	0.343043	+	0.865612i
$766$	−4.19278	−	7.26211i	−0.151491	−	0.262391i
$767$	−7.78872	+	29.0679i	−0.281234	+	1.04958i
$768$	0.365065	+	1.69314i	0.0131731	+	0.0610960i
$769$		−	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	−0.143602	−	0.989636i	$-0.545868\pi$
$773$	−21.2075	−	5.68254i	−0.762782	−	0.204387i	−0.619181	+	0.785249i	$0.712535\pi$
$774$	1.00730	+	2.22730i	0.0362068	+	0.0800587i
$775$	3.39442	−	35.6891i	0.121931	−	1.28199i
$776$			3.05240i			0.109575i
$777$	9.15524	+	20.7387i	0.328442	+	0.743997i
$778$	−18.5178	−	18.5178i	−0.663895	−	0.663895i
$779$	−26.6712	+	46.1958i	−0.955594	+	1.65514i
$780$	16.3980	−	13.4939i	0.587141	−	0.483158i
$781$	3.02444	+	5.23848i	0.108223	+	0.187448i
$782$	−4.27437	+	1.14531i	−0.152851	+	0.0409563i
$783$	7.28282	+	9.84127i	0.260267	+	0.351698i
$784$	−2.76924	−	6.42894i	−0.0989015	−	0.229605i
$785$	17.0270	−	26.5054i	0.607720	−	0.946020i
$786$	−17.7743	−	11.4690i	−0.633988	−	0.409086i
$787$	−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
$789$	12.0005	+	7.74345i	0.427230	+	0.275674i
$790$	6.94458	−	10.8104i	0.247077	−	0.384618i
$791$	4.50523	−	13.5843i	0.160188	−	0.483001i
$792$	7.96012	−	6.52341i	0.282850	−	0.231799i
$793$	−4.68794	+	1.25613i	−0.166474	+	0.0446064i
$794$	−3.48376	−	6.03404i	−0.123634	−	0.214140i
$795$	2.85292	−	2.34767i	0.101183	−	0.0832633i
$796$	2.51565	−	4.35724i	0.0891649	−	0.154438i
$797$	−7.12389	−	7.12389i	−0.252341	−	0.252341i	0.569589	−	0.821930i	$-0.307103\pi$
$797$	−7.12389	−	7.12389i	−0.252341	−	0.252341i	−0.821930	+	0.569589i	$0.807103\pi$
$798$	31.4100	+	3.40146i	1.11190	+	0.120410i
$799$			33.8529i			1.19763i
$800$	3.85441	−	3.18489i	0.136274	−	0.112603i
$801$	−3.50785	+	1.58644i	−0.123944	+	0.0560539i
$802$	−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
$807$	1.93059	+	8.95390i	0.0679599	+	0.315192i
$808$	4.84355	−	18.0764i	0.170396	−	0.635925i
$809$	23.4131	+	40.5526i	0.823159	+	1.42575i	0.903318	+	0.428971i	$0.141124\pi$
$809$	23.4131	+	40.5526i	0.823159	+	1.42575i	−0.0801590	+	0.996782i	$0.525543\pi$
$810$	−19.3495	+	5.53138i	−0.679873	+	0.194353i
$811$	−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
$813$	28.9634	−	26.2325i	1.01579	−	0.920013i
$814$	14.6970	+	8.48533i	0.515131	+	0.297411i
$815$	0.639263	−	13.4728i	0.0223924	−	0.471933i
$816$	−3.03609	−	5.91585i	−0.106284	−	0.207096i
$817$	1.45396	+	5.42626i	0.0508677	+	0.189841i
$818$	24.7610	−	24.7610i	0.865747	−	0.865747i
$819$	25.5731	+	35.2154i	0.893598	+	1.23052i
$820$	−16.9048	+	3.68073i	−0.590341	+	0.128537i
$821$	27.1356	+	15.6667i	0.947039	+	0.546773i	0.892160	−	0.451720i	$-0.149189\pi$
$821$	27.1356	+	15.6667i	0.947039	+	0.546773i	0.0548791	+	0.998493i	$0.482523\pi$
$822$	1.86685	−	5.80326i	0.0651140	−	0.202412i
$823$	−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
$825$	−27.2936	−	11.7351i	−0.950241	−	0.408562i
$826$	−13.7825	−	4.57096i	−0.479553	−	0.159044i
$827$	31.9770	+	31.9770i	1.11195	+	1.11195i	0.992887	+	0.119062i	$0.0379887\pi$
$827$	31.9770	+	31.9770i	1.11195	+	1.11195i	0.119062	+	0.992887i	$0.462011\pi$
$828$	−0.560910	−	3.41220i	−0.0194930	−	0.118582i
$829$	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
$831$	36.6267	+	23.6337i	1.27057	+	0.819845i
$832$	−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
$837$	14.8545	−	34.1672i	0.513448	−	1.18099i
$838$	−8.60727	+	2.30631i	−0.297333	+	0.0796702i
$839$	17.8925			0.617717			0.308858	−	0.951108i	$-0.400053\pi$
$839$	17.8925			0.617717			0.308858	+	0.951108i	$0.400053\pi$
$840$	6.03788	+	8.27913i	0.208327	+	0.285657i
$841$	−23.4485			−0.808569
$842$	−18.1608	+	4.86616i	−0.625861	+	0.167699i
$843$	−15.6302	+	48.5876i	−0.538332	+	1.67345i
$844$	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
$849$	−0.977585	+	1.51503i	−0.0335506	+	0.0519956i
$850$	−11.1285	+	15.6402i	−0.381705	+	0.536454i
$851$	4.93820	−	2.85107i	0.169279	−	0.0977335i
$852$	0.643696	+	2.98541i	0.0220527	+	0.102278i
$853$	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
$855$	−45.9401	+	5.33044i	−1.57112	+	0.182297i
$856$	−3.38669	+	5.86591i	−0.115755	+	0.200493i
$857$	−1.09133	+	4.07290i	−0.0372791	+	0.139127i	−0.982057	−	0.188583i	$-0.939610\pi$
$857$	−1.09133	+	4.07290i	−0.0372791	+	0.139127i	0.944778	+	0.327711i	$0.106277\pi$
$858$	31.0151	+	9.97728i	1.05884	+	0.340619i
$859$	−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
$861$	−5.43615	−	35.0370i	−0.185264	−	1.19406i
$862$	−23.3431	+	23.3431i	−0.795069	+	0.795069i
$863$	−4.83143	−	18.0311i	−0.164464	−	0.613787i	−0.998108	−	0.0614855i	$-0.980416\pi$
$863$	−4.83143	−	18.0311i	−0.164464	−	0.613787i	0.833644	−	0.552302i	$-0.186250\pi$
$864$	4.83451	−	1.90461i	0.164473	−	0.0647961i
$865$	27.3081	+	1.29573i	0.928504	+	0.0440560i
$866$	34.1713	+	19.7288i	1.16119	+	0.670411i
$867$	−2.62965	−	2.90341i	−0.0893078	−	0.0986051i
$868$	−18.9377	−	1.10790i	−0.642789	−	0.0376046i
$869$	19.7126			0.668703
$870$	−3.20309	+	8.54474i	−0.108595	+	0.289694i
$871$	12.2680	+	21.2488i	0.415685	+	0.719988i
$872$	−3.66239	+	13.6682i	−0.124024	+	0.462864i
$873$	9.03593	−	1.48536i	0.305820	−	0.0502718i
$874$		−	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
$879$	27.2663	−	13.9935i	0.919671	−	0.471987i
$880$	7.30715	+	2.33433i	0.246324	+	0.0786904i
$881$		−	58.4991i		−	1.97089i	−0.170007	−	0.985443i	$-0.554379\pi$
$881$		−	58.4991i		−	1.97089i	0.170007	−	0.985443i	$-0.445621\pi$
$882$	−17.6838	+	11.3262i	−0.595446	+	0.381371i
$883$	−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
$885$	21.1565	+	2.05542i	0.711167	+	0.0690921i
$886$	−9.44625	−	16.3614i	−0.317353	−	0.549671i
$887$	−43.3986	+	11.6286i	−1.45718	+	0.390451i	−0.898515	−	0.438942i	$-0.855353\pi$
$887$	−43.3986	+	11.6286i	−1.45718	+	0.390451i	−0.558666	+	0.829393i	$0.688687\pi$
$888$	5.75191	+	6.35071i	0.193022	+	0.213116i
$889$	5.33467	−	16.0852i	0.178919	−	0.539481i
$890$	−2.41431	−	1.55095i	−0.0809279	−	0.0519878i
$891$	−23.1846	−	20.3897i	−0.776713	−	0.683080i
$892$	−10.5574	−	2.82885i	−0.353488	−	0.0947169i
$893$	−58.7226	−	15.7347i	−1.96508	−	0.526540i
$894$	−1.87996	+	2.91350i	−0.0628753	+	0.0974420i
$895$	−3.23383	+	0.704110i	−0.108095	+	0.0235358i
$896$	−1.75837	−	1.97690i	−0.0587432	−	0.0660435i
$897$	8.11378	−	7.34874i	0.270911	−	0.245367i
$898$	6.55599	−	1.75667i	0.218776	−	0.0586209i
$899$	−8.44687	−	14.6304i	−0.281719	−	0.487951i
$900$	−11.3038	−	9.86025i	−0.376793	−	0.328675i
$901$	1.83116	−	3.17167i	0.0610049	−	0.105664i
$902$	−18.7686	−	18.7686i	−0.624926	−	0.624926i
$903$	−3.01395	−	2.20432i	−0.100298	−	0.0733550i
$904$		−	5.40938i		−	0.179913i
$905$	−10.6303	+	33.2759i	−0.353362	+	1.10613i
$906$	−11.8132	−	23.0182i	−0.392468	−	0.764727i
$907$	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	$0.0389824\pi$
$911$			7.37432i			0.244322i	−0.992510	+	0.122161i	$0.961018\pi$
$912$	11.6730	−	2.51686i	0.386532	−	0.0833417i
$913$	−8.91342	+	33.2653i	−0.294991	+	1.10092i
$914$	−2.65569	−	4.59979i	−0.0878424	−	0.152147i
$915$	1.41893	+	3.12064i	0.0469085	+	0.103165i
$916$	−4.68671			−0.154853
$917$	32.2571	+	1.88711i	1.06522	+	0.0623180i
$918$	−16.0351	+	11.8664i	−0.529237	+	0.391650i
$919$	−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
$921$	−47.8397	+	24.5520i	−1.57637	+	0.809016i
$922$	−7.27251	−	27.1414i	−0.239507	−	0.893854i
$923$	−6.83640	+	6.83640i	−0.225023	+	0.225023i
$924$	−5.68006	+	14.6588i	−0.186860	+	0.482238i
$925$	8.63518	−	23.1783i	0.283923	−	0.762098i
$926$	9.33045	+	5.38694i	0.306617	+	0.177026i
$927$	−24.9298	−	9.40279i	−0.818802	−	0.308828i
$928$	0.609819	−	2.27587i	0.0200183	−	0.0747093i
$929$	1.40166	−	2.42774i	0.0459869	−	0.0796516i	−0.842116	−	0.539297i	$-0.818690\pi$
$929$	1.40166	−	2.42774i	0.0459869	−	0.0796516i	0.888103	+	0.459645i	$0.152023\pi$
$930$	27.3925	−	4.55983i	0.898235	−	0.149523i
$931$	−44.3230	+	19.0920i	−1.45263	+	0.625714i
$932$	1.32875	+	1.32875i	0.0435246	+	0.0435246i
$933$	18.6597	−	4.02329i	0.610890	−	0.131717i
$934$	7.93138	−	4.57919i	0.259523	−	0.149836i
$935$	−29.4161	−	1.39575i	−0.962011	−	0.0456458i
$936$	13.3642	+	9.59081i	0.436824	+	0.313485i
$937$	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	−0.213869	−	0.976862i	$-0.568607\pi$
$941$	16.1104	−	9.30133i	0.525183	−	0.303215i	0.739053	+	0.673648i	$0.235273\pi$
$942$	23.2300	+	7.47286i	0.756873	+	0.243479i
$943$	−8.61450	+	2.30825i	−0.280527	+	0.0751669i
$944$	−5.48830			−0.178629
$945$	21.5703	−	21.9025i	0.701683	−	0.712490i
$946$	−2.79532			−0.0908837
$947$	4.48811	−	1.20259i	0.145844	−	0.0390788i	−0.185158	−	0.982709i	$-0.559280\pi$
$947$	4.48811	−	1.20259i	0.145844	−	0.0390788i	0.331002	+	0.943630i	$0.392613\pi$
$948$	9.47450	+	3.04786i	0.307717	+	0.0989898i
$949$	−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	−0.472912	−	0.881110i	$-0.656797\pi$
$953$	12.6014	−	12.6014i	0.408198	−	0.408198i	0.881110	+	0.472912i	$0.156797\pi$
$954$	2.32512	+	1.66861i	0.0752784	+	0.0540233i
$955$	25.0435	−	22.7746i	0.810390	−	0.736970i
$956$	−16.0316	+	9.25587i	−0.518500	+	0.299356i
$957$	−13.6855	+	2.95079i	−0.442391	+	0.0953857i
$958$	−10.9806	−	10.9806i	−0.354768	−	0.354768i
$959$	1.88070	+	9.12011i	0.0607309	+	0.294504i
$960$	3.15113	+	2.25175i	0.101702	+	0.0726750i
$961$	−10.2047	+	17.6750i	−0.329183	+	0.570162i
$962$	−7.02042	+	26.2006i	−0.226347	+	0.844740i
$963$	19.0127	+	7.17103i	0.612676	+	0.231083i
$964$	−7.24521	−	4.18303i	−0.233353	−	0.134726i
$965$	31.6756	+	20.3483i	1.01967	+	0.655034i
$966$	3.31123	+	4.11548i	0.106537	+	0.132413i
$967$	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
$969$	−40.7856	+	20.9317i	−1.31022	+	0.672423i
$970$	4.59211	+	5.04959i	0.147444	+	0.162132i
$971$	−13.6776	−	7.89677i	−0.438935	−	0.253419i	0.264211	−	0.964465i	$-0.414889\pi$
$971$	−13.6776	−	7.89677i	−0.438935	−	0.253419i	−0.703146	+	0.711046i	$0.748222\pi$
$972$	−7.99072	−	13.3846i	−0.256303	−	0.429312i
$973$	−11.0765	−	22.0692i	−0.355095	−	0.707507i
$974$	−3.28607			−0.105292
$975$	6.82664	−	46.9924i	0.218627	−	1.50496i
$976$	−0.442564	−	0.766543i	−0.0141661	−	0.0245365i
$977$	12.1987	−	45.5260i	0.390270	−	1.45651i	−0.439420	−	0.898282i	$-0.644816\pi$
$977$	12.1987	−	45.5260i	0.390270	−	1.45651i	0.829690	−	0.558225i	$-0.188517\pi$
$978$	10.2130	−	2.20208i	0.326577	−	0.0704146i
$979$		−	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	0.843432	−	0.537236i	$-0.180531\pi$
$983$	40.9232	+	10.9653i	1.30525	+	0.349740i	0.461816	+	0.886976i	$0.347198\pi$
$984$	−6.11889	−	11.9227i	−0.195063	−	0.380082i
$985$	9.18489	−	4.73732i	0.292655	−	0.150943i
$986$			9.04543i			0.288065i
$987$	36.9674	−	16.3195i	1.17668	−	0.519455i
$988$	26.7305	+	26.7305i	0.850409	+	0.850409i
$989$	−0.469614	+	0.813395i	−0.0149328	+	0.0258645i
$990$	3.35446	−	22.7671i	0.106612	−	0.723585i
$991$	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
$993$	−43.6686	+	39.5512i	−1.38578	+	1.25512i
$994$	−3.10043	−	3.48574i	−0.0983397	−	0.110561i
$995$	−2.39349	−	10.9928i	−0.0758787	−	0.348495i
$996$	−9.42740	+	14.6103i	−0.298719	+	0.462944i
$997$	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
$999$	16.0008	−	20.1176i	0.506244	−	0.636493i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.64884 - 0.530415i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.680454 - 2.13002i) q^{5} +(1.72993 + 0.0855915i) q^{6} +(-2.36464 + 1.18680i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.43732 + 1.74913i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.64884 - 0.530415i) 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} +(2.43732 + 1.74913i) q^{9} +(-0.105978 + 2.23356i) q^{10} +(-2.97095 + 1.71528i) q^{11} +(-1.69314 + 0.365065i) q^{12} +(-3.87719 - 3.87719i) q^{13} +(1.97690 - 1.75837i) q^{14} +(-2.25175 + 3.15113i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.993622 + 3.70825i) q^{17} +(-2.80698 - 1.05871i) q^{18} +(-5.97063 - 3.44715i) q^{19} +(-0.475719 - 2.18488i) q^{20} +(4.52839 - 0.702601i) q^{21} +(2.42577 - 2.42577i) q^{22} +(-0.298332 - 1.11339i) q^{23} +(1.54096 - 0.790843i) q^{24} +(-4.07396 - 2.89876i) q^{25} +(4.74857 + 2.74159i) q^{26} +(-3.09097 - 4.17683i) q^{27} +(-1.45443 + 2.21012i) q^{28} -2.35616 q^{29} +(1.35945 - 3.62655i) q^{30} +(3.58502 + 6.20943i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(5.80841 - 1.25238i) 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} +(4.33633 + 8.44937i) q^{39} +(1.02500 + 1.98730i) q^{40} -7.73718i q^{41} +(-4.19225 + 1.85070i) q^{42} +(-0.576172 - 0.576172i) q^{43} +(-1.71528 + 2.97095i) q^{44} +(5.38418 - 4.00133i) q^{45} +(0.576333 + 0.998238i) q^{46} +(8.51756 - 2.28227i) q^{47} +(-1.28377 + 1.16273i) q^{48} +(4.18301 - 5.61270i) q^{49} +(4.68540 + 1.74557i) q^{50} +(3.60523 - 5.58726i) q^{51} +(-5.29634 - 1.41915i) q^{52} +(-0.921459 - 0.246904i) q^{53} +(4.06669 + 3.23450i) q^{54} +(1.63198 + 7.49534i) q^{55} +(0.832855 - 2.51125i) q^{56} +(8.01617 + 8.85069i) q^{57} +(2.27587 - 0.609819i) q^{58} +(-2.74415 - 4.75301i) q^{59} +(-0.374509 + 3.85483i) q^{60} +(0.442564 - 0.766543i) q^{61} +(-5.06998 - 5.06998i) q^{62} +(-7.83925 - 1.24345i) q^{63} -1.00000i q^{64} +(-10.8967 + 5.62024i) q^{65} +(-5.28636 + 2.71303i) 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} +(-2.96027 + 0.486620i) q^{72} +(1.83002 - 6.82973i) q^{73} +(-2.47346 - 4.28416i) q^{74} +(5.17975 + 6.94047i) q^{75} -6.89429 q^{76} +(4.98952 - 7.58193i) q^{77} +(-6.37543 - 7.03914i) q^{78} +(-4.97633 - 2.87309i) q^{79} +(-1.50442 - 1.65430i) q^{80} +(2.88105 + 8.52640i) q^{81} +(2.00253 + 7.47354i) q^{82} +(7.09854 - 7.09854i) q^{83} +(3.57040 - 2.87267i) q^{84} +(7.22252 + 4.63972i) q^{85} +(0.705664 + 0.407415i) q^{86} +(3.88492 + 1.24974i) q^{87} +(0.887893 - 3.31366i) q^{88} +(-0.641651 + 1.11137i) q^{89} +(-4.16509 + 5.25852i) q^{90} +(13.7696 + 4.56669i) q^{91} +(-0.815058 - 0.815058i) q^{92} +(-2.61753 - 12.1399i) q^{93} +(-7.63664 + 4.40902i) q^{94} +(-11.4052 + 10.3719i) q^{95} +(0.939092 - 1.45537i) 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

Groups

Database

Properties

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