LMFDB - Embedded newform 210.2.x.a.107.13

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			107.13
Character	$\chi$	$=$	210.107
Dual form			210.2.x.a.53.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.365065 - 1.69314i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50442 - 1.65430i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.73346 - 1.23621i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.365065 - 1.69314i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50442 - 1.65430i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.73346 - 1.23621i) q^{9} +(1.98730 + 1.02500i) q^{10} +(2.97095 - 1.71528i) q^{11} +(0.530415 + 1.64884i) 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} +(3.70825 + 0.993622i) q^{17} +(0.486620 - 2.96027i) 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} +(1.11339 - 0.298332i) q^{23} +(-1.45537 + 0.939092i) q^{24} +(-0.473417 - 4.97754i) q^{25} +(-4.74857 - 2.74159i) q^{26} +(-3.09097 + 4.17683i) q^{27} +(2.21012 + 1.45443i) q^{28} -2.35616 q^{29} +(2.46096 - 2.99060i) q^{30} +(3.58502 + 6.20943i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.81962 - 5.65642i) q^{33} +3.83906i q^{34} +(-5.69727 - 1.59409i) q^{35} +(2.98535 - 0.296136i) q^{36} +(-4.77836 + 1.28036i) q^{37} +(-1.78437 + 6.65937i) q^{38} +(5.14920 + 7.98005i) q^{39} +(-2.23356 + 0.105978i) q^{40} +7.73718i q^{41} +(-2.25548 - 3.98909i) q^{42} +(-0.576172 + 0.576172i) q^{43} +(-1.71528 + 2.97095i) q^{44} +(-6.15734 + 2.66217i) q^{45} +(0.576333 + 0.998238i) q^{46} +(-2.28227 - 8.51756i) q^{47} +(-1.28377 - 1.16273i) q^{48} +(-4.18301 + 5.61270i) q^{49} +(4.68540 - 1.74557i) q^{50} +(3.03609 - 5.91585i) q^{51} +(1.41915 - 5.29634i) q^{52} +(0.246904 - 0.921459i) q^{53} +(-4.83451 - 1.90461i) q^{54} +(1.63198 - 7.49534i) q^{55} +(-0.832855 + 2.51125i) q^{56} +(8.01617 - 8.85069i) q^{57} +(-0.609819 - 2.27587i) q^{58} +(-2.74415 - 4.75301i) q^{59} +(3.52564 + 1.60308i) q^{60} +(0.442564 - 0.766543i) q^{61} +(-5.06998 + 5.06998i) q^{62} +(0.320873 + 7.93077i) q^{63} +1.00000i q^{64} +(0.581098 + 12.2470i) q^{65} +(4.99273 - 3.22161i) q^{66} +(1.15816 - 4.32230i) q^{67} +(-3.70825 + 0.993622i) q^{68} +(-0.0986585 - 1.99404i) q^{69} +(0.0652109 - 5.91572i) q^{70} +1.76324i q^{71} +(1.05871 + 2.80698i) q^{72} +(-6.82973 - 1.83002i) q^{73} +(-2.47346 - 4.28416i) q^{74} +(-8.60050 - 1.01556i) q^{75} -6.89429 q^{76} +(-7.58193 - 4.98952i) q^{77} +(-6.37543 + 7.03914i) q^{78} +(4.97633 + 2.87309i) q^{79} +(-0.680454 - 2.13002i) q^{80} +(5.94355 + 6.75827i) q^{81} +(-7.47354 + 2.00253i) 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} +(-0.860151 + 3.98931i) q^{87} +(-3.31366 - 0.887893i) 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} +(11.8222 - 3.80309i) q^{93} +(7.63664 - 4.40902i) q^{94} +(14.6850 - 4.69125i) q^{95} +(0.790843 - 1.54096i) q^{96} +(2.15837 + 2.15837i) q^{97} +(-6.50410 - 2.58780i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.365065	−	1.69314i	0.210770	−	0.977536i
$3$	0.365065	−	1.69314i	0.210770	−	0.977536i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.50442	−	1.65430i	0.672799	−	0.739825i
$5$	1.50442	−	1.65430i	0.672799	−	0.739825i
$6$	1.72993	−	0.0855915i	0.706243	−	0.0349426i
$7$	−1.18680	−	2.36464i	−0.448569	−	0.893748i
$7$	−1.18680	−	2.36464i	−0.448569	−	0.893748i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.73346	−	1.23621i	−0.911152	−	0.412071i
$10$	1.98730	+	1.02500i	0.628441	+	0.324133i
$11$	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	$0.160317\pi$
$12$	0.530415	+	1.64884i	0.153118	+	0.475978i
$13$	−3.87719	+	3.87719i	−1.07534	+	1.07534i	−0.0784181	+	0.996921i	$0.524987\pi$
$13$	−3.87719	+	3.87719i	−1.07534	+	1.07534i	−0.996921	+	0.0784181i	$0.975013\pi$
$14$	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
$17$	3.70825	+	0.993622i	0.899382	+	0.240989i	0.678751	−	0.734369i	$-0.262522\pi$
$17$	3.70825	+	0.993622i	0.899382	+	0.240989i	0.220631	+	0.975357i	$0.429188\pi$
$18$	0.486620	−	2.96027i	0.114697	−	0.697742i
$19$	5.97063	+	3.44715i	1.36976	+	0.790829i	0.990897	−	0.134625i	$-0.0429829\pi$
$19$	5.97063	+	3.44715i	1.36976	+	0.790829i	0.378860	+	0.925454i	$0.376316\pi$
$20$	−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
$23$	1.11339	−	0.298332i	0.232158	−	0.0622065i	−0.140864	−	0.990029i	$-0.544988\pi$
$23$	1.11339	−	0.298332i	0.232158	−	0.0622065i	0.373022	+	0.927822i	$0.378322\pi$
$24$	−1.45537	+	0.939092i	−0.297076	+	0.191691i
$25$	−0.473417	−	4.97754i	−0.0946835	−	0.995507i
$26$	−4.74857	−	2.74159i	−0.931271	−	0.537669i
$27$	−3.09097	+	4.17683i	−0.594858	+	0.803831i
$28$	2.21012	+	1.45443i	0.417673	+	0.274862i
$29$	−2.35616			−0.437528			−0.218764	−	0.975778i	$-0.570202\pi$
$29$	−2.35616			−0.437528			−0.218764	+	0.975778i	$0.570202\pi$
$30$	2.46096	−	2.99060i	0.449308	−	0.546006i
$31$	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	$0.610654\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.81962	−	5.65642i	−0.316755	−	0.984656i
$34$			3.83906i			0.658393i
$35$	−5.69727	−	1.59409i	−0.963014	−	0.269450i
$36$	2.98535	−	0.296136i	0.497558	−	0.0493559i
$37$	−4.77836	+	1.28036i	−0.785557	+	0.210489i	−0.629233	−	0.777217i	$-0.716631\pi$
$37$	−4.77836	+	1.28036i	−0.785557	+	0.210489i	−0.156324	+	0.987706i	$0.549964\pi$
$38$	−1.78437	+	6.65937i	−0.289464	+	1.08029i
$39$	5.14920	+	7.98005i	0.824532	+	1.27783i
$40$	−2.23356	+	0.105978i	−0.353156	+	0.0167567i
$41$			7.73718i			1.20834i	0.796854	+	0.604172i	$0.206496\pi$
$41$			7.73718i			1.20834i	−0.796854	+	0.604172i	$0.793504\pi$
$42$	−2.25548	−	3.98909i	−0.348028	−	0.615529i
$43$	−0.576172	+	0.576172i	−0.0878654	+	0.0878654i	−0.749673	−	0.661808i	$-0.769789\pi$
$43$	−0.576172	+	0.576172i	−0.0878654	+	0.0878654i	0.661808	+	0.749673i	$0.269789\pi$
$44$	−1.71528	+	2.97095i	−0.258588	+	0.447887i
$45$	−6.15734	+	2.66217i	−0.917882	+	0.396852i
$46$	0.576333	+	0.998238i	0.0849757	+	0.147182i
$47$	−2.28227	−	8.51756i	−0.332904	−	1.24241i	−0.906124	−	0.423013i	$-0.860973\pi$
$47$	−2.28227	−	8.51756i	−0.332904	−	1.24241i	0.573220	−	0.819402i	$-0.305694\pi$
$48$	−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
$51$	3.03609	−	5.91585i	0.425138	−	0.828384i
$52$	1.41915	−	5.29634i	0.196801	−	0.734470i
$53$	0.246904	−	0.921459i	0.0339149	−	0.126572i	−0.946893	−	0.321549i	$-0.895797\pi$
$53$	0.246904	−	0.921459i	0.0339149	−	0.126572i	0.980808	+	0.194977i	$0.0624632\pi$
$54$	−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
$57$	8.01617	−	8.85069i	1.06177	−	1.17230i
$58$	−0.609819	−	2.27587i	−0.0800731	−	0.298837i
$59$	−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	$0.949622\pi$
$60$	3.52564	+	1.60308i	0.455158	+	0.206957i
$61$	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
$63$	0.320873	+	7.93077i	0.0404262	+	0.999183i
$64$			1.00000i			0.125000i
$65$	0.581098	+	12.2470i	0.0720763	+	1.51905i
$66$	4.99273	−	3.22161i	0.614563	−	0.396552i
$67$	1.15816	−	4.32230i	0.141491	−	0.528053i	−0.858395	−	0.512989i	$-0.828538\pi$
$67$	1.15816	−	4.32230i	0.141491	−	0.528053i	0.999887	−	0.0150642i	$-0.00479526\pi$
$68$	−3.70825	+	0.993622i	−0.449691	+	0.120494i
$69$	−0.0986585	−	1.99404i	−0.0118771	−	0.240054i
$70$	0.0652109	−	5.91572i	0.00779420	−	0.707064i
$71$			1.76324i			0.209258i	0.994511	+	0.104629i	$0.0333655\pi$
$71$			1.76324i			0.209258i	−0.994511	+	0.104629i	$0.966635\pi$
$72$	1.05871	+	2.80698i	0.124770	+	0.330806i
$73$	−6.82973	−	1.83002i	−0.799360	−	0.214188i	−0.164057	−	0.986451i	$-0.552458\pi$
$73$	−6.82973	−	1.83002i	−0.799360	−	0.214188i	−0.635303	+	0.772263i	$0.719125\pi$
$74$	−2.47346	−	4.28416i	−0.287534	−	0.498023i
$75$	−8.60050	−	1.01556i	−0.993100	−	0.117267i
$76$	−6.89429			−0.790829
$77$	−7.58193	−	4.98952i	−0.864041	−	0.568608i
$78$	−6.37543	+	7.03914i	−0.721875	+	0.797025i
$79$	4.97633	+	2.87309i	0.559881	+	0.323248i	0.753098	−	0.657909i	$-0.228559\pi$
$79$	4.97633	+	2.87309i	0.559881	+	0.323248i	−0.193217	+	0.981156i	$0.561892\pi$
$80$	−0.680454	−	2.13002i	−0.0760771	−	0.238143i
$81$	5.94355	+	6.75827i	0.660395	+	0.750919i
$82$	−7.47354	+	2.00253i	−0.825315	+	0.221142i
$83$	7.09854	+	7.09854i	0.779166	+	0.779166i	0.979689	−	0.200523i	$-0.0642642\pi$
$83$	7.09854	+	7.09854i	0.779166	+	0.779166i	−0.200523	+	0.979689i	$0.564264\pi$
$84$	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
$87$	−0.860151	+	3.98931i	−0.0922179	+	0.427699i
$88$	−3.31366	−	0.887893i	−0.353237	−	0.0946497i
$89$	−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
$93$	11.8222	−	3.80309i	1.22591	−	0.394362i
$94$	7.63664	−	4.40902i	0.787659	−	0.454755i
$95$	14.6850	−	4.69125i	1.50665	−	0.481312i
$96$	0.790843	−	1.54096i	0.0807151	−	0.157274i
$97$	2.15837	+	2.15837i	0.219150	+	0.219150i	0.808140	−	0.588990i	$-0.200474\pi$
$97$	2.15837	+	2.15837i	0.219150	+	0.219150i	−0.588990	+	0.808140i	$0.700474\pi$
$98$	−6.50410	−	2.58780i	−0.657013	−	0.261407i
$99$	−10.2414	+	1.01591i	−1.02930	+	0.102103i
$100$	2.89876	+	4.07396i	0.289876	+	0.407396i
$101$	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	$-0.0477801\pi$
$102$	6.50007	+	1.40151i	0.643603	+	0.138770i
$103$	2.29867	+	8.57874i	0.226494	+	0.845288i	0.981800	+	0.189916i	$0.0608215\pi$
$103$	2.29867	+	8.57874i	0.226494	+	0.845288i	−0.755306	+	0.655372i	$0.772512\pi$
$104$	5.48317			0.537669
$105$	−4.77889	+	9.06434i	−0.466372	+	0.884589i
$106$	0.953965			0.0926572
$107$	−1.75308	−	6.54257i	−0.169476	−	0.632494i	−0.997427	−	0.0716931i	$-0.977160\pi$
$107$	−1.75308	−	6.54257i	−0.169476	−	0.632494i	0.827950	−	0.560801i	$-0.189507\pi$
$108$	0.588447	−	5.16273i	0.0566233	−	0.496783i
$109$	−12.2546	+	7.07519i	−1.17378	+	0.677680i	−0.954566	−	0.297998i	$-0.903681\pi$
$109$	−12.2546	+	7.07519i	−1.17378	+	0.677680i	−0.219209	+	0.975678i	$0.570348\pi$
$110$	7.66233	−	0.363565i	0.730575	−	0.0346645i
$111$	0.423414	+	8.55785i	0.0401887	+	0.812275i
$112$	−2.64124	−	0.154518i	−0.249573	−	0.0146006i
$113$	−3.82501	−	3.82501i	−0.359827	−	0.359827i	0.503922	−	0.863749i	$-0.331890\pi$
$113$	−3.82501	−	3.82501i	−0.359827	−	0.359827i	−0.863749	+	0.503922i	$0.831890\pi$
$114$	10.6238	+	5.45230i	0.995014	+	0.510655i
$115$	1.18148	−	2.29070i	0.110174	−	0.213609i
$116$	2.04049	−	1.17808i	0.189455	−	0.109382i
$117$	15.3912	−	5.80509i	1.42291	−	0.536681i
$118$	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
$122$	0.854968	+	0.229088i	0.0774052	+	0.0207407i
$123$	13.1001	+	2.82457i	1.18120	+	0.254683i
$124$	−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	0.477000	−	0.878903i	$-0.341724\pi$
$127$	−4.52922	−	4.52922i	−0.401903	−	0.401903i	−0.878903	+	0.477000i	$0.841724\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	0.765201	+	1.18588i	0.0673722	+	0.104411i
$130$	−11.6793	+	3.73105i	−1.02434	+	0.327234i
$131$	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	$0.487535\pi$
$132$	4.40405	+	3.98880i	0.383323	+	0.347180i
$133$	1.06529	−	18.2094i	0.0923726	−	1.57896i
$134$	4.47478			0.386562
$135$	2.25959	+	11.3971i	0.194475	+	0.980908i
$136$	−1.91953	−	3.32472i	−0.164598	−	0.285093i
$137$	−3.39968	−	0.910941i	−0.290454	−	0.0778270i	0.110650	−	0.993859i	$-0.464707\pi$
$137$	−3.39968	−	0.910941i	−0.290454	−	0.0778270i	−0.401104	+	0.916032i	$0.631373\pi$
$138$	1.90056	−	0.611391i	0.161786	−	0.0520451i
$139$		−	9.33303i		−	0.791618i	−0.918333	−	0.395809i	$-0.870464\pi$
$139$		−	9.33303i		−	0.791618i	0.918333	−	0.395809i	$-0.129536\pi$
$140$	5.73102	−	1.46811i	0.484360	−	0.124078i
$141$	−15.2546	+	0.754749i	−1.28467	+	0.0635613i
$142$	−1.70316	+	0.456359i	−0.142926	+	0.0382968i
$143$	−4.86847	+	18.1694i	−0.407122	+	1.51940i
$144$	−2.43732	+	1.74913i	−0.203110	+	0.145761i
$145$	−3.54466	+	3.89779i	−0.294368	+	0.323694i
$146$		−	7.07066i		−	0.585172i
$147$	7.97603	+	9.13142i	0.657852	+	0.753147i
$148$	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	$0.192798\pi$
$150$	−1.24502	−	8.57029i	−0.101655	−	0.699762i
$151$	−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	$-0.374614\pi$
$152$	−1.78437	−	6.65937i	−0.144732	−	0.540146i
$153$	−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
$156$	−8.44937	−	4.33633i	−0.676491	−	0.347184i
$157$	−3.64642	+	13.6086i	−0.291016	+	1.08609i	0.653313	+	0.757088i	$0.273378\pi$
$157$	−3.64642	+	13.6086i	−0.291016	+	1.08609i	−0.944330	+	0.329000i	$0.893288\pi$
$158$	−1.48722	+	5.55038i	−0.118317	+	0.441564i
$159$	−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
$162$	−4.98968	+	7.49020i	−0.392026	+	0.588486i
$163$	−1.56120	−	5.82648i	−0.122283	−	0.456365i	0.877446	−	0.479676i	$-0.159246\pi$
$163$	−1.56120	−	5.82648i	−0.122283	−	0.456365i	−0.999728	+	0.0233112i	$0.992579\pi$
$164$	−3.86859	−	6.70060i	−0.302086	−	0.523229i
$165$	−12.0949	−	5.49946i	−0.941586	−	0.428132i
$166$	−5.01942	+	8.69390i	−0.389583	+	0.674777i
$167$	−5.93525	+	5.93525i	−0.459284	+	0.459284i	−0.898420	−	0.439137i	$-0.855284\pi$
$167$	−5.93525	+	5.93525i	−0.459284	+	0.459284i	0.439137	+	0.898420i	$0.355284\pi$
$168$	3.94785	+	2.32691i	0.304583	+	0.179525i
$169$		−	17.0652i		−	1.31271i
$170$	6.35095	+	5.77557i	0.487096	+	0.442966i
$171$	−12.0590	−	16.8036i	−0.922178	−	1.28500i
$172$	0.210894	−	0.787066i	0.0160805	−	0.0600132i
$173$	−11.8097	+	3.16440i	−0.897875	+	0.240585i	−0.678104	−	0.734966i	$-0.737198\pi$
$173$	−11.8097	+	3.16440i	−0.897875	+	0.240585i	−0.219772	+	0.975551i	$0.570531\pi$
$174$	−4.07600	+	0.201667i	−0.309001	+	0.0152884i
$175$	−11.2082	+	7.02681i	−0.847261	+	0.531177i
$176$		−	3.43055i		−	0.258588i
$177$	−9.04930	+	2.91108i	−0.680187	+	0.218810i
$178$	−1.23958	−	0.332143i	−0.0929101	−	0.0248952i
$179$	−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	$0.850949\pi$
$180$	4.00133	−	5.38418i	0.298242	−	0.401313i
$181$	−15.6223			−1.16120			−0.580599	−	0.814189i	$-0.697182\pi$
$181$	−15.6223			−1.16120			−0.580599	+	0.814189i	$0.697182\pi$
$182$	−0.847250	+	14.4823i	−0.0628023	+	1.07350i
$183$	−1.13630	−	1.02916i	−0.0839978	−	0.0760778i
$184$	−0.998238	−	0.576333i	−0.0735911	−	0.0424878i
$185$	−5.07058	+	9.83103i	−0.372796	+	0.722792i
$186$	6.73332	+	10.4351i	0.493711	+	0.765136i
$187$	12.7213	−	3.40867i	0.930276	−	0.249267i
$188$	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	$0.851159\pi$
$192$	1.69314	+	0.365065i	0.122192	+	0.0263463i
$193$	16.2631	+	4.35769i	1.17065	+	0.313673i	0.791210	−	0.611545i	$-0.209452\pi$
$193$	16.2631	+	4.35769i	1.17065	+	0.313673i	0.379436	+	0.925218i	$0.376118\pi$
$194$	−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	−0.581036	−	0.813878i	$-0.697352\pi$
$197$	3.26809	−	3.26809i	0.232842	−	0.232842i	0.813878	+	0.581036i	$0.197352\pi$
$198$	−3.63196	−	9.62949i	−0.258112	−	0.684338i
$199$	−4.35724	+	2.51565i	−0.308876	+	0.178330i	−0.646424	−	0.762979i	$-0.723736\pi$
$199$	−4.35724	+	2.51565i	−0.308876	+	0.178330i	0.337547	+	0.941309i	$0.390403\pi$
$200$	−3.18489	+	3.85441i	−0.225206	+	0.272548i
$201$	−6.89547	−	3.53885i	−0.486369	−	0.249611i
$202$	13.2328	+	13.2328i	0.931059	+	0.931059i
$203$	2.79629	+	5.57146i	0.196261	+	0.391040i
$204$	0.328591	+	6.64132i	0.0230060	+	0.464985i
$205$	12.7996	+	11.6400i	0.893964	+	0.812973i
$206$	−7.69148	+	4.44068i	−0.535891	+	0.309397i
$207$	−3.41220	−	0.560910i	−0.237165	−	0.0389860i
$208$	1.41915	+	5.29634i	0.0984003	+	0.367235i
$209$	23.6512			1.63599
$210$	−9.99234	−	2.27003i	−0.689537	−	0.156647i
$211$	2.58896			0.178231			0.0891156	−	0.996021i	$-0.471596\pi$
$211$	2.58896			0.178231			0.0891156	+	0.996021i	$0.471596\pi$
$212$	0.246904	+	0.921459i	0.0169575	+	0.0632861i
$213$	2.98541	+	0.643696i	0.204557	+	0.0441053i
$214$	5.86591	−	3.38669i	0.400985	−	0.231509i
$215$	0.0863545	+	1.81997i	0.00588933	+	0.124121i
$216$	5.13911	−	0.767816i	0.349672	−	0.0522432i
$217$	10.4283	−	15.8466i	0.707922	−	1.07574i
$218$	−10.0058	−	10.0058i	−0.677680	−	0.677680i
$219$	−5.59178	+	10.8956i	−0.377858	+	0.736258i
$220$	2.33433	+	7.30715i	0.157381	+	0.492648i
$221$	−18.2300	+	10.5251i	−1.22628	+	0.707996i
$222$	−8.15666	+	2.62392i	−0.547439	+	0.176106i
$223$	−7.72857	+	7.72857i	−0.517543	+	0.517543i	−0.916827	−	0.399284i	$-0.869259\pi$
$223$	−7.72857	+	7.72857i	−0.517543	+	0.517543i	0.399284	+	0.916827i	$0.369259\pi$
$224$	−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
$227$	−7.32054	−	1.96153i	−0.485881	−	0.130191i	0.00755864	−	0.999971i	$-0.497594\pi$
$227$	−7.32054	−	1.96153i	−0.485881	−	0.130191i	−0.493440	+	0.869780i	$0.664261\pi$
$228$	−2.51686	+	11.6730i	−0.166683	+	0.773064i
$229$	4.05881	+	2.34336i	0.268214	+	0.154853i	0.628076	−	0.778152i	$-0.283843\pi$
$229$	4.05881	+	2.34336i	0.268214	+	0.154853i	−0.359862	+	0.933006i	$0.617176\pi$
$230$	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
$233$	−1.81510	+	0.486355i	−0.118911	+	0.0318622i	−0.317784	−	0.948163i	$-0.602939\pi$
$233$	−1.81510	+	0.486355i	−0.118911	+	0.0318622i	0.198873	+	0.980025i	$0.436272\pi$
$234$	9.59081	+	13.3642i	0.626971	+	0.873648i
$235$	−17.5241	−	9.03846i	−1.14315	−	0.589604i
$236$	4.75301	+	2.74415i	0.309394	+	0.178629i
$237$	6.68123	−	7.37677i	0.433992	−	0.479173i
$238$	9.07798	−	4.55620i	0.588438	−	0.295334i
$239$	−18.5117			−1.19742			−0.598712	−	0.800964i	$-0.704321\pi$
$239$	−18.5117			−1.19742			−0.598712	+	0.800964i	$0.704321\pi$
$240$	−3.85483	+	0.374509i	−0.248828	+	0.0241745i
$241$	−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	$0.920176\pi$
$242$	0.742508	+	0.198954i	0.0477302	+	0.0127893i
$243$	13.6125	−	7.59607i	0.873241	−	0.487288i
$244$			0.885128i			0.0566645i
$245$	2.99208	+	15.3638i	0.191157	+	0.981559i
$246$	0.662237	+	13.3848i	0.0422227	+	0.853385i
$247$	−36.5145	+	9.78403i	−2.32336	+	0.622543i
$248$	1.85574	−	6.92572i	0.117840	−	0.439784i
$249$	14.6103	−	9.42740i	0.925887	−	0.597437i
$250$	4.16114	−	10.3771i	0.263174	−	0.656308i
$251$		−	29.1045i		−	1.83706i	−0.395355	−	0.918528i	$-0.629378\pi$
$251$		−	29.1045i		−	1.83706i	0.395355	−	0.918528i	$-0.370622\pi$
$252$	−4.24327	−	6.70781i	−0.267301	−	0.422552i
$253$	2.79610	−	2.79610i	0.175789	−	0.175789i
$254$	3.20264	−	5.54713i	0.200951	−	0.348058i
$255$	−5.21902	−	13.9226i	−0.326828	−	0.871864i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.97152	+	18.5540i	0.310115	+	1.15737i	0.928452	+	0.371452i	$0.121140\pi$
$257$	4.97152	+	18.5540i	0.310115	+	1.15737i	−0.618337	+	0.785913i	$0.712193\pi$
$258$	−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
$261$	6.44045	+	2.91271i	0.398654	+	0.180293i
$262$	−3.16093	+	11.7967i	−0.195283	+	0.728805i
$263$	2.13414	−	7.96472i	0.131597	−	0.491126i	−0.868392	−	0.495878i	$-0.834846\pi$
$263$	2.13414	−	7.96472i	0.131597	−	0.491126i	0.999989	+	0.00475276i	$0.00151285\pi$
$264$	−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
$267$	1.64747	+	1.49213i	0.100823	+	0.0913169i
$268$	1.15816	+	4.32230i	0.0707457	+	0.264027i
$269$	−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	$0.884876\pi$
$270$	−10.4239	+	5.13239i	−0.634381	+	0.312347i
$271$	−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
$273$	12.7588	−	21.6467i	0.772200	−	1.31012i
$274$		−	3.51961i		−	0.212627i
$275$	−9.94435	−	13.9760i	−0.599667	−	0.842782i
$276$	1.08246	+	1.67756i	0.0651564	+	0.100977i
$277$	6.51359	−	24.3091i	0.391364	−	1.46059i	−0.436522	−	0.899693i	$-0.643790\pi$
$277$	6.51359	−	24.3091i	0.391364	−	1.46059i	0.827886	−	0.560896i	$-0.189543\pi$
$278$	9.01502	−	2.41557i	0.540685	−	0.144876i
$279$	−2.12330	−	21.4050i	−0.127119	−	1.28149i
$280$	2.90139	+	5.15577i	0.173391	+	0.308116i
$281$			29.4678i			1.75790i	0.476910	+	0.878952i	$0.341757\pi$
$281$			29.4678i			1.75790i	−0.476910	+	0.878952i	$0.658243\pi$
$282$	−4.67722	−	14.5395i	−0.278524	−	0.865814i
$283$	−1.00552	−	0.269428i	−0.0597719	−	0.0160158i	0.228809	−	0.973471i	$-0.426517\pi$
$283$	−1.00552	−	0.269428i	−0.0597719	−	0.0160158i	−0.288581	+	0.957455i	$0.593183\pi$
$284$	−0.881618	−	1.52701i	−0.0523144	−	0.0906112i
$285$	−2.58198	−	26.5763i	−0.152943	−	1.57425i
$286$	−18.8103			−1.11228
$287$	18.2956	−	9.18249i	1.07996	−	0.542025i
$288$	−2.32036	−	1.90156i	−0.136728	−	0.112051i
$289$	−1.95863	−	1.13081i	−0.115213	−	0.0665185i
$290$	−4.68241	−	2.41506i	−0.274960	−	0.141817i
$291$	4.44238	−	2.86649i	0.260417	−	0.168036i
$292$	6.82973	−	1.83002i	0.399680	−	0.107094i
$293$	−12.5118	−	12.5118i	−0.730947	−	0.730947i	0.239860	−	0.970807i	$-0.422898\pi$
$293$	−12.5118	−	12.5118i	−0.730947	−	0.730947i	−0.970807	+	0.239860i	$0.922898\pi$
$294$	−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
$297$	−2.01870	+	17.7110i	−0.117137	+	1.02770i
$298$	−1.93368	−	0.518128i	−0.112015	−	0.0300144i
$299$	−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
$303$	−9.92621	−	30.8564i	−0.570246	−	1.77265i
$304$	5.97063	−	3.44715i	0.342439	−	0.197707i
$305$	−0.602289	−	1.88534i	−0.0344870	−	0.107954i
$306$	4.74590	−	10.4939i	0.271305	−	0.599896i
$307$	21.9524	+	21.9524i	1.25289	+	1.25289i	0.954419	+	0.298469i	$0.0964760\pi$
$307$	21.9524	+	21.9524i	1.25289	+	1.25289i	0.298469	+	0.954419i	$0.403524\pi$
$308$	9.06090	+	0.530083i	0.516293	+	0.0302043i
$309$	15.3642	−	0.760169i	0.874037	−	0.0432445i
$310$	0.759869	+	16.0147i	0.0431576	+	0.909572i
$311$	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	$0.232179\pi$
$312$	2.00171	−	9.28379i	0.113325	−	0.525591i
$313$	2.37746	+	8.87281i	0.134382	+	0.501521i	1.00000		0.000815167i	$0.000259476\pi$
$313$	2.37746	+	8.87281i	0.134382	+	0.501521i	−0.865618	+	0.500706i	$0.833074\pi$
$314$	−14.0887			−0.795071
$315$	13.6026	+	11.4004i	0.766419	+	0.642341i
$316$	−5.74617			−0.323248
$317$	1.31728	+	4.91615i	0.0739857	+	0.276118i	0.993001	−	0.118103i	$-0.0376812\pi$
$317$	1.31728	+	4.91615i	0.0739857	+	0.276118i	−0.919016	+	0.394221i	$0.871014\pi$
$318$	0.348259	−	1.61520i	0.0195294	−	0.0905758i
$319$	−7.00002	+	4.04147i	−0.391926	+	0.226279i
$320$	1.65430	+	1.50442i	0.0924782	+	0.0840999i
$321$	−11.7175	+	0.579743i	−0.654006	+	0.0323581i
$322$	1.67648	−	2.54753i	0.0934264	−	0.141968i
$323$	18.7154	+	18.7154i	1.04135	+	1.04135i
$324$	−8.52640	−	2.88105i	−0.473689	−	0.160059i
$325$	21.1344	+	17.4633i	1.17232	+	0.968691i
$326$	5.22388	−	3.01601i	0.289324	−	0.167041i
$327$	7.50557	+	23.3316i	0.415059	+	1.29024i
$328$	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	$-0.217792\pi$
$332$	−9.69678	−	2.59824i	−0.532180	−	0.142597i
$333$	14.6442	+	2.40727i	0.802498	+	0.131918i
$334$	−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	0.999299	+	0.0374412i	$0.0119207\pi$
$337$	19.0320	+	19.0320i	1.03674	+	1.03674i	0.0374412	+	0.999299i	$0.488079\pi$
$338$	16.4837	−	4.41679i	0.896595	−	0.240242i
$339$	−7.87266	+	5.07990i	−0.427584	+	0.275903i
$340$	−3.93503	+	7.62938i	−0.213407	+	0.413761i
$341$	21.3018	+	12.2986i	1.15356	+	0.666006i
$342$	13.1099	−	15.9972i	0.708903	−	0.865031i
$343$	18.2364	+	3.23013i	0.984673	+	0.174410i
$344$	0.814830			0.0439327
$345$	−3.44716	−	2.83667i	−0.185589	−	0.152721i
$346$	−6.11315	−	10.5883i	−0.328645	−	0.569230i
$347$	−26.4308	−	7.08212i	−1.41888	−	0.380188i	−0.533795	−	0.845614i	$-0.679235\pi$
$347$	−26.4308	−	7.08212i	−1.41888	−	0.380188i	−0.885087	+	0.465425i	$0.845901\pi$
$348$	−1.24974	−	3.88492i	−0.0669932	−	0.208254i
$349$			7.53522i			0.403351i	0.979452	+	0.201675i	$0.0646386\pi$
$349$			7.53522i			0.403351i	−0.979452	+	0.201675i	$0.935361\pi$
$350$	−9.68827	−	9.00763i	−0.517860	−	0.481478i
$351$	−4.21007	−	28.1786i	−0.224717	−	1.50406i
$352$	3.31366	−	0.887893i	0.176619	−	0.0473248i
$353$	3.86404	−	14.4208i	0.205662	−	0.767542i	−0.783584	−	0.621285i	$-0.786611\pi$
$353$	3.86404	−	14.4208i	0.205662	−	0.767542i	0.989247	−	0.146257i	$-0.0467225\pi$
$354$	−5.15402	−	7.98751i	−0.273933	−	0.424532i
$355$	2.91692	+	2.65266i	0.154814	+	0.140788i
$356$		−	1.28330i		−	0.0680149i
$357$	−17.5921	−	0.158319i	−0.931071	−	0.00837913i
$358$	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	$-0.138070\pi$
$360$	6.23633	+	2.47146i	0.328684	+	0.130258i
$361$	14.2656	+	24.7088i	0.750822	+	1.30046i
$362$	−4.04336	−	15.0900i	−0.212514	−	0.793113i
$363$	−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
$366$	0.699997	−	1.36395i	0.0365894	−	0.0712948i
$367$	2.59090	−	9.66937i	0.135244	−	0.504737i	−0.864753	−	0.502197i	$-0.832525\pi$
$367$	2.59090	−	9.66937i	0.135244	−	0.504737i	0.999997	−	0.00253931i	$-0.000808289\pi$
$368$	0.298332	−	1.11339i	0.0155516	−	0.0580395i
$369$	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
$372$	−8.33678	+	9.20468i	−0.432242	+	0.477240i
$373$	3.70262	+	13.8184i	0.191715	+	0.715489i	0.993093	+	0.117331i	$0.0374338\pi$
$373$	3.70262	+	13.8184i	0.191715	+	0.715489i	−0.801378	+	0.598158i	$0.795900\pi$
$374$	6.58505	+	11.4056i	0.340505	+	0.589772i
$375$	−14.6188	+	12.7000i	−0.754914	+	0.655824i
$376$	−4.40902	+	7.63664i	−0.227378	+	0.393830i
$377$	9.13527	−	9.13527i	0.470490	−	0.470490i
$378$	1.23390	+	13.6922i	0.0634647	+	0.704253i
$379$			2.99621i			0.153905i	0.997035	+	0.0769524i	$0.0245189\pi$
$379$			2.99621i			0.153905i	−0.997035	+	0.0769524i	$0.975481\pi$
$380$	−10.3719	+	11.4052i	−0.532069	+	0.585076i
$381$	−9.32206	+	6.01514i	−0.477584	+	0.308165i
$382$	3.91812	−	14.6226i	0.200468	−	0.748158i
$383$	−8.09984	+	2.17034i	−0.413882	+	0.110899i	−0.459751	−	0.888048i	$-0.652061\pi$
$383$	−8.09984	+	2.17034i	−0.413882	+	0.110899i	0.0458683	+	0.998947i	$0.485395\pi$
$384$	0.0855915	+	1.72993i	0.00436782	+	0.0882804i
$385$	−19.6606	+	5.03644i	−1.00200	+	0.256681i
$386$			16.8368i			0.856972i
$387$	2.28721	−	0.862669i	0.116266	−	0.0438519i
$388$	−2.94839	−	0.790020i	−0.149682	−	0.0401072i
$389$	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	$0.602235\pi$
$390$	2.05350	+	21.1367i	0.103983	+	1.07030i
$391$	4.42515			0.223790
$392$	6.92661	−	1.01095i	0.349847	−	0.0510606i
$393$	14.2002	−	15.6785i	0.716307	−	0.790878i
$394$	4.00258	+	2.31089i	0.201647	+	0.116421i
$395$	12.2395	−	3.91001i	0.615834	−	0.196734i
$396$	8.36136	−	6.00050i	0.420174	−	0.301537i
$397$	−6.73010	+	1.80333i	−0.337774	+	0.0905063i	−0.423719	−	0.905794i	$-0.639276\pi$
$397$	−6.73010	+	1.80333i	−0.337774	+	0.0905063i	0.0859451	+	0.996300i	$0.472609\pi$
$398$	−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	$0.826605\pi$
$402$	1.63358	−	7.57643i	0.0814758	−	0.377878i
$403$	−37.9749	−	10.1753i	−1.89167	−	0.506870i
$404$	−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
$408$	−6.32998	+	2.03629i	−0.313381	+	0.100812i
$409$	30.3259	−	17.5087i	1.49952	−	0.865747i	0.499519	−	0.866303i	$-0.333510\pi$
$409$	30.3259	−	17.5087i	1.49952	−	0.865747i	1.00000		0.000555857i	$0.000176935\pi$
$410$	−7.93059	+	15.3761i	−0.391664	+	0.759373i
$411$	−2.78346	+	5.42359i	−0.137298	+	0.267526i
$412$	−6.28007	−	6.28007i	−0.309397	−	0.309397i
$413$	−7.98237	+	12.1298i	−0.392787	+	0.596868i
$414$	−0.341345	−	3.44111i	−0.0167762	−	0.169121i
$415$	22.4223	−	1.06390i	1.10067	−	0.0522249i
$416$	−4.74857	+	2.74159i	−0.232818	+	0.134417i
$417$	−15.8021	−	3.40716i	−0.773834	−	0.166850i
$418$	6.12139	+	22.8453i	0.299407	+	1.11740i
$419$	8.91090			0.435326			0.217663	−	0.976024i	$-0.430157\pi$
$419$	8.91090			0.435326			0.217663	+	0.976024i	$0.430157\pi$
$420$	−0.393525	−	10.2394i	−0.0192020	−	0.499631i
$421$	18.8014			0.916324			0.458162	−	0.888869i	$-0.348508\pi$
$421$	18.8014			0.916324			0.458162	+	0.888869i	$0.348508\pi$
$422$	0.670072	+	2.50074i	0.0326186	+	0.121734i
$423$	−4.29103	+	26.1038i	−0.208637	+	1.26921i
$424$	−0.826158	+	0.476982i	−0.0401218	+	0.0231643i
$425$	3.19024	−	18.9283i	0.154749	−	0.918159i
$426$	0.150918	+	3.05028i	0.00731201	+	0.147787i
$427$	−2.33783	−	0.136768i	−0.113136	−	0.00661869i
$428$	4.78950	+	4.78950i	0.231509	+	0.231509i
$429$	28.9860	+	14.8760i	1.39946	+	0.718220i
$430$	−1.73560	+	0.554455i	−0.0836983	+	0.0267382i
$431$	−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	$0.625899\pi$
$432$	2.07175	+	4.76527i	0.0996772	+	0.229269i
$433$	−27.9007	+	27.9007i	−1.34082	+	1.34082i	−0.445581	+	0.895242i	$0.647003\pi$
$433$	−27.9007	+	27.9007i	−1.34082	+	1.34082i	−0.895242	+	0.445581i	$0.852997\pi$
$434$	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
$437$	7.67603	+	2.05679i	0.367194	+	0.0983895i
$438$	−11.9716	−	2.58125i	−0.572027	−	0.123337i
$439$	−13.8443	−	7.99298i	−0.660750	−	0.381484i	0.131813	−	0.991275i	$-0.457920\pi$
$439$	−13.8443	−	7.99298i	−0.660750	−	0.381484i	−0.792563	+	0.609790i	$0.791254\pi$
$440$	−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
$443$	−18.2487	+	4.88974i	−0.867024	+	0.232318i	−0.664801	−	0.747021i	$-0.731483\pi$
$443$	−18.2487	+	4.88974i	−0.867024	+	0.232318i	−0.202224	+	0.979339i	$0.564817\pi$
$444$	−4.64561	−	7.19960i	−0.220471	−	0.341678i
$445$	0.873228	+	2.73346i	0.0413950	+	0.129578i
$446$	−9.46552	−	5.46492i	−0.448205	−	0.258772i
$447$	2.56997	+	2.32765i	0.121556	+	0.110094i
$448$	2.36464	−	1.18680i	0.111719	−	0.0560711i
$449$	−6.78726			−0.320311			−0.160155	−	0.987092i	$-0.551199\pi$
$449$	−6.78726			−0.320311			−0.160155	+	0.987092i	$0.551199\pi$
$450$	−14.9652	−	1.02073i	−0.705468	−	0.0481175i
$451$	13.2714	+	22.9868i	0.624926	+	1.08240i
$452$	5.22506	+	1.40005i	0.245766	+	0.0658528i
$453$	−24.6295	+	7.92309i	−1.15720	+	0.372259i
$454$		−	7.57878i		−	0.355690i
$455$	28.2700	−	15.9088i	1.32532	−	0.745816i
$456$	−11.9267	+	0.590093i	−0.558518	+	0.0276336i
$457$	−5.13040	+	1.37469i	−0.239990	+	0.0643051i	−0.376809	−	0.926291i	$-0.622979\pi$
$457$	−5.13040	+	1.37469i	−0.239990	+	0.0643051i	0.136819	+	0.990596i	$0.456312\pi$
$458$	−1.21301	+	4.52702i	−0.0566803	+	0.211534i
$459$	−15.6123	+	12.4174i	−0.728718	+	0.579597i
$460$	0.122158	+	2.57454i	0.00569563	+	0.120039i
$461$		−	28.0988i		−	1.30869i	−0.756195	−	0.654347i	$-0.772944\pi$
$461$		−	28.0988i		−	1.30869i	0.756195	−	0.654347i	$-0.227056\pi$
$462$	−13.5433	−	7.98259i	−0.630091	−	0.371384i
$463$	−7.61828	+	7.61828i	−0.354051	+	0.354051i	−0.861615	−	0.507563i	$-0.830546\pi$
$463$	−7.61828	+	7.61828i	−0.354051	+	0.354051i	0.507563	+	0.861615i	$0.330546\pi$
$464$	−1.17808	+	2.04049i	−0.0546910	+	0.0947275i
$465$	11.4942	−	25.2789i	0.533029	−	1.17228i
$466$	−0.939566	−	1.62738i	−0.0435246	−	0.0753867i
$467$	2.37036	+	8.84631i	0.109687	+	0.409358i	0.998835	−	0.0482625i	$-0.0153684\pi$
$467$	2.37036	+	8.84631i	0.109687	+	0.409358i	−0.889147	+	0.457621i	$0.848702\pi$
$468$	−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
$471$	21.7102	+	11.1420i	1.00035	+	0.513394i
$472$	−1.42048	+	5.30129i	−0.0653827	+	0.244012i
$473$	−0.723482	+	2.70007i	−0.0332657	+	0.124149i
$474$	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
$477$	−1.81402	+	2.21354i	−0.0830583	+	0.101351i
$478$	−4.79119	−	17.8810i	−0.219144	−	0.817856i
$479$	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	$0.717893\pi$
$480$	−1.35945	−	3.62655i	−0.0620502	−	0.165529i
$481$	13.5624	−	23.4908i	0.618392	−	1.07109i
$482$	5.91569	−	5.91569i	0.269452	−	0.269452i
$483$	−4.59808	+	2.59982i	−0.209220	+	0.118296i
$484$			0.768701i			0.0349409i
$485$	6.81771	−	0.323489i	0.309576	−	0.0146889i
$486$	10.8604	+	11.1826i	0.492638	+	0.507255i
$487$	−0.850498	+	3.17410i	−0.0385397	+	0.143832i	−0.982515	−	0.186185i	$-0.940388\pi$
$487$	−0.850498	+	3.17410i	−0.0385397	+	0.143832i	0.943975	+	0.330017i	$0.107054\pi$
$488$	−0.854968	+	0.229088i	−0.0387026	+	0.0103703i
$489$	−10.4350	+	0.516289i	−0.471886	+	0.0233474i
$490$	−14.0659	+	6.86658i	−0.635433	+	0.310201i
$491$		−	11.6805i		−	0.527133i	−0.964641	−	0.263567i	$-0.915101\pi$
$491$		−	11.6805i		−	0.527133i	0.964641	−	0.263567i	$-0.0848989\pi$
$492$	−12.7573	+	4.10392i	−0.575145	+	0.185019i
$493$	−8.73722	−	2.34113i	−0.393504	−	0.105439i
$494$	−18.9013	−	32.7380i	−0.850409	−	1.47295i
$495$	−13.7268	+	18.4707i	−0.616973	+	0.830196i
$496$	7.17003			0.321944
$497$	4.16941	−	2.09261i	0.187024	−	0.0938664i
$498$	12.8876	+	11.6724i	0.577506	+	0.523054i
$499$	−2.51013	−	1.44922i	−0.112369	−	0.0648762i	0.442762	−	0.896639i	$-0.353999\pi$
$499$	−2.51013	−	1.44922i	−0.112369	−	0.0648762i	−0.555131	+	0.831763i	$0.687332\pi$
$500$	11.1005	+	1.33355i	0.496431	+	0.0596382i
$501$	7.88247	+	12.2160i	0.352163	+	0.545769i
$502$	28.1127	−	7.53279i	1.25473	−	0.336205i
$503$	14.8328	+	14.8328i	0.661362	+	0.661362i	0.955701	−	0.294339i	$-0.0950994\pi$
$503$	14.8328	+	14.8328i	0.661362	+	0.661362i	−0.294339	+	0.955701i	$0.595099\pi$
$504$	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
$507$	−28.8938	−	6.22990i	−1.28322	−	0.276680i
$508$	6.18702	+	1.65781i	0.274505	+	0.0735533i
$509$	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
$513$	−32.8532	+	14.2833i	−1.45050	+	0.630622i
$514$	−16.6350	+	9.60425i	−0.733740	+	0.423625i
$515$	17.6500	+	9.10337i	0.777751	+	0.401143i
$516$	−1.25562	−	0.644403i	−0.0552758	−	0.0283683i
$517$	−21.3905	−	21.3905i	−0.940753	−	0.940753i
$518$	−7.19497	+	10.9333i	−0.316129	+	0.480380i
$519$	1.04647	+	21.1507i	0.0459349	+	0.928413i
$520$	8.24902	−	9.07081i	0.361743	−	0.397781i
$521$	−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	$0.577655\pi$
$522$	−1.14655	+	6.97487i	−0.0501833	+	0.305282i
$523$	−4.17483	−	15.5807i	−0.182552	−	0.681295i	−0.995141	−	0.0984575i	$-0.968609\pi$
$523$	−4.17483	−	15.5807i	−0.182552	−	0.681295i	0.812589	−	0.582837i	$-0.198058\pi$
$524$	−12.2129			−0.533522
$525$	7.80565	+	21.5423i	0.340666	+	0.940184i
$526$	8.24568			0.359529
$527$	7.12430	+	26.5882i	0.310339	+	1.15820i
$528$	−5.80841	−	1.25238i	−0.252779	−	0.0545026i
$529$	−18.7679	+	10.8357i	−0.815998	+	0.471117i
$530$	1.43517	−	1.57814i	0.0623397	−	0.0685502i
$531$	1.62528	+	16.3845i	0.0705311	+	0.711026i
$532$	8.18215	+	16.3025i	0.354741	+	0.706802i
$533$	−29.9985	−	29.9985i	−1.29938	−	1.29938i
$534$	−1.01489	+	1.97752i	−0.0439186	+	0.0855758i
$535$	−13.4608	−	6.94269i	−0.581959	−	0.300159i
$536$	−3.87527	+	2.23739i	−0.167386	+	0.0966405i
$537$	−2.44044	+	0.785066i	−0.105313	+	0.0338781i
$538$	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	$0.123049\pi$
$542$	−21.7924	−	5.83926i	−0.936065	−	0.250818i
$543$	−5.70317	+	26.4508i	−0.244746	+	1.13511i
$544$	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	0.668487	−	0.743724i	$-0.266942\pi$
$547$	−1.75965	−	1.75965i	−0.0752374	−	0.0752374i	−0.743724	+	0.668487i	$0.766942\pi$
$548$	3.39968	−	0.910941i	0.145227	−	0.0389135i
$549$	−2.15734	+	1.54821i	−0.0920730	+	0.0660759i
$550$	10.9259	−	13.2228i	0.465884	−	0.563820i
$551$	−14.0678	−	8.12202i	−0.599307	−	0.346010i
$552$	−1.34024	+	1.47976i	−0.0570442	+	0.0629827i
$553$	0.887888	−	15.1770i	0.0377569	−	0.645392i
$554$	25.1666			1.06923
$555$	14.7942	+	12.1742i	0.627980	+	0.516765i
$556$	4.66652	+	8.08264i	0.197904	+	0.342780i
$557$	44.9860	+	12.0540i	1.90612	+	0.510742i	0.995164	+	0.0982317i	$0.0313186\pi$
$557$	44.9860	+	12.0540i	1.90612	+	0.510742i	0.910953	+	0.412511i	$0.135348\pi$
$558$	20.1261	−	7.59098i	0.852007	−	0.321352i
$559$		−	4.46786i		−	0.188970i
$560$	−4.22916	+	4.13693i	−0.178715	+	0.174817i
$561$	−1.12725	−	22.7834i	−0.0475925	−	0.961916i
$562$	−28.4638	+	7.62684i	−1.20067	+	0.321719i
$563$	10.7103	−	39.9714i	0.451386	−	1.68459i	−0.247115	−	0.968986i	$-0.579483\pi$
$563$	10.7103	−	39.9714i	0.451386	−	1.68459i	0.698501	−	0.715609i	$-0.253851\pi$
$564$	12.8335	−	8.28094i	0.540388	−	0.348690i
$565$	−12.0821	+	0.573278i	−0.508300	+	0.0241180i
$566$		−	1.04099i		−	0.0437561i
$567$	8.92702	−	22.0751i	0.374900	−	0.927065i
$568$	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	$-0.0685922\pi$
$570$	25.0025	−	9.37246i	1.04724	−	0.392569i
$571$	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	$0.826802\pi$
$572$	−4.86847	−	18.1694i	−0.203561	−	0.759700i
$573$	−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
$576$	1.23621	−	2.73346i	0.0515089	−	0.113894i
$577$	6.45735	−	24.0992i	0.268823	−	1.00326i	−0.691046	−	0.722811i	$-0.742850\pi$
$577$	6.45735	−	24.0992i	0.268823	−	1.00326i	0.959869	−	0.280450i	$-0.0904837\pi$
$578$	0.585353	−	2.18457i	0.0243475	−	0.0908659i
$579$	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
$582$	3.91858	+	3.54911i	0.162431	+	0.147115i
$583$	−0.847018	−	3.16112i	−0.0350799	−	0.130920i
$584$	3.53533	+	6.12337i	0.146293	+	0.253387i
$585$	13.5515	−	34.1949i	0.560284	−	1.41379i
$586$	8.84718	−	15.3238i	0.365473	−	0.633019i
$587$	−26.5508	+	26.5508i	−1.09587	+	1.09587i	−0.100982	+	0.994888i	$0.532199\pi$
$587$	−26.5508	+	26.5508i	−1.09587	+	1.09587i	−0.994888	+	0.100982i	$0.967801\pi$
$588$	−11.4732	−	3.92003i	−0.473145	−	0.161659i
$589$			49.4323i			2.03682i
$590$	−0.581641	−	12.2584i	−0.0239458	−	0.504671i
$591$	−4.34028	−	6.72641i	−0.178535	−	0.276688i
$592$	−1.28036	+	4.77836i	−0.0526223	+	0.196389i
$593$	20.1433	−	5.39739i	0.827188	−	0.221644i	0.179701	−	0.983721i	$-0.442487\pi$
$593$	20.1433	−	5.39739i	0.827188	−	0.221644i	0.647487	+	0.762077i	$0.275820\pi$
$594$	−17.6300	+	2.63403i	−0.723368	+	0.108076i
$595$	−19.5430	−	11.5722i	−0.801183	−	0.474414i
$596$		−	2.00189i		−	0.0820008i
$597$	2.66868	+	8.29579i	0.109222	+	0.339524i
$598$	−6.10491	−	1.63581i	−0.249648	−	0.0668931i
$599$	−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	$-0.374749\pi$
$600$	5.36336	+	6.79958i	0.218958	+	0.277592i
$601$	13.1980			0.538359			0.269180	−	0.963090i	$-0.413247\pi$
$601$	13.1980			0.538359			0.269180	+	0.963090i	$0.413247\pi$
$602$	−0.125906	+	2.15216i	−0.00513155	+	0.0877155i
$603$	−8.50906	+	10.3831i	−0.346516	+	0.422832i
$604$	12.9363	+	7.46876i	0.526369	+	0.303900i
$605$	−0.523065	−	1.63735i	−0.0212656	−	0.0665676i
$606$	27.2359	−	17.5742i	1.10638	−	0.713903i
$607$	−31.1269	+	8.34043i	−1.26340	+	0.338528i	−0.827500	−	0.561466i	$-0.810237\pi$
$607$	−31.1269	+	8.34043i	−1.26340	+	0.338528i	−0.435903	+	0.899994i	$0.643571\pi$
$608$	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
$612$	11.3647	+	1.86816i	0.459389	+	0.0755160i
$613$	38.3608	+	10.2788i	1.54938	+	0.415155i	0.929282	−	0.369370i	$-0.120427\pi$
$613$	38.3608	+	10.2788i	1.54938	+	0.415155i	0.620097	+	0.784525i	$0.287093\pi$
$614$	−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	−0.845673	−	0.533701i	$-0.820801\pi$
$617$	−7.74923	+	7.74923i	−0.311972	+	0.311972i	0.533701	+	0.845673i	$0.320801\pi$
$618$	4.71081	+	14.6439i	0.189497	+	0.589064i
$619$	−1.24931	+	0.721289i	−0.0502140	+	0.0289911i	−0.524897	−	0.851166i	$-0.675896\pi$
$619$	−1.24931	+	0.721289i	−0.0502140	+	0.0289911i	0.474683	+	0.880157i	$0.342563\pi$
$620$	−15.2723	+	4.87888i	−0.613351	+	0.195940i
$621$	−2.19538	+	5.57257i	−0.0880974	+	0.223620i
$622$	7.79284	+	7.79284i	0.312465	+	0.312465i
$623$	3.38950	+	0.198294i	0.135798	+	0.00794447i
$624$	9.48553	−	0.469313i	0.379725	−	0.0187876i
$625$	−24.5518	+	4.71290i	−0.982070	+	0.188516i
$626$	−7.95515	+	4.59291i	−0.317952	+	0.183569i
$627$	8.63424	−	40.0449i	0.344818	−	1.59924i
$628$	−3.64642	−	13.6086i	−0.145508	−	0.543044i
$629$	−18.9915			−0.757241
$630$	−7.49134	+	16.0897i	−0.298462	+	0.641031i
$631$	−17.0499			−0.678748			−0.339374	−	0.940652i	$-0.610215\pi$
$631$	−17.0499			−0.678748			−0.339374	+	0.940652i	$0.610215\pi$
$632$	−1.48722	−	5.55038i	−0.0591584	−	0.220782i
$633$	0.945138	−	4.38347i	0.0375659	−	0.174227i
$634$	−4.40770	+	2.54478i	−0.175052	+	0.101066i
$635$	−14.3065	+	0.678821i	−0.567738	+	0.0269382i
$636$	1.65030	−	0.0816513i	0.0654385	−	0.00323768i
$637$	−5.54321	−	37.9798i	−0.219630	−	1.50482i
$638$	−5.71550	−	5.71550i	−0.226279	−	0.226279i
$639$	2.17974	−	4.81973i	0.0862290	−	0.190666i
$640$	−1.02500	+	1.98730i	−0.0405166	+	0.0785551i
$641$	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	$0.224792\pi$
$642$	−3.59270	−	11.1682i	−0.141792	−	0.440773i
$643$	22.8061	−	22.8061i	0.899385	−	0.899385i	−0.0959964	−	0.995382i	$-0.530604\pi$
$643$	22.8061	−	22.8061i	0.899385	−	0.899385i	0.995382	+	0.0959964i	$0.0306037\pi$
$644$	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
$647$	38.0837	+	10.2045i	1.49723	+	0.401181i	0.912170	−	0.409812i	$-0.134406\pi$
$647$	38.0837	+	10.2045i	1.49723	+	0.401181i	0.585056	+	0.810993i	$0.301072\pi$
$648$	0.576089	−	8.98154i	0.0226309	−	0.352828i
$649$	−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
$653$	31.6844	−	8.48981i	1.23991	−	0.332232i	0.421477	−	0.906839i	$-0.361512\pi$
$653$	31.6844	−	8.48981i	1.23991	−	0.332232i	0.818429	+	0.574607i	$0.194845\pi$
$654$	−20.5940	+	13.2885i	−0.805291	+	0.519621i
$655$	26.0137	−	8.31030i	1.01644	−	0.324710i
$656$	6.70060	+	3.86859i	0.261614	+	0.151043i
$657$	16.4065	+	13.4453i	0.640078	+	0.524551i
$658$	−19.4889	−	12.8252i	−0.759756	−	0.499980i
$659$	9.95001			0.387597			0.193799	−	0.981041i	$-0.437919\pi$
$659$	9.95001			0.387597			0.193799	+	0.981041i	$0.437919\pi$
$660$	13.2242	−	1.28477i	0.514752	−	0.0500098i
$661$	−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	$-0.403269\pi$
$662$	32.8568	+	8.80396i	1.27702	+	0.342176i
$663$	11.1654	+	34.7084i	0.433626	+	1.34796i
$664$		−	10.0388i		−	0.389583i
$665$	−28.5212	−	29.1570i	−1.10601	−	1.13066i
$666$	1.46496	+	14.7683i	0.0567660	+	0.572259i
$667$	−2.62332	+	0.702917i	−0.101575	+	0.0272171i
$668$	2.17245	−	8.10770i	0.0840547	−	0.313697i
$669$	10.2641	+	15.9070i	0.396834	+	0.614999i
$670$	6.73196	−	7.40263i	0.260078	−	0.285988i
$671$		−	3.03648i		−	0.117222i
$672$	−4.58239	−	0.0412390i	−0.176770	−	0.00159083i
$673$	−27.9121	+	27.9121i	−1.07593	+	1.07593i	−0.0790609	+	0.996870i	$0.525192\pi$
$673$	−27.9121	+	27.9121i	−1.07593	+	1.07593i	−0.996870	+	0.0790609i	$0.974808\pi$
$674$	−13.4577	+	23.3094i	−0.518370	+	0.897843i
$675$	22.2536	+	13.4080i	0.856543	+	0.516076i
$676$	8.53259	+	14.7789i	0.328177	+	0.568419i
$677$	−3.05281	−	11.3933i	−0.117329	−	0.437878i	0.882121	−	0.471022i	$-0.156115\pi$
$677$	−3.05281	−	11.3933i	−0.117329	−	0.437878i	−0.999451	+	0.0331437i	$0.989448\pi$
$678$	−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
$681$	−5.99362	+	11.6786i	−0.229676	+	0.447526i
$682$	−6.36622	+	23.7591i	−0.243775	+	0.909781i
$683$	9.54542	−	35.6240i	0.365245	−	1.36311i	−0.501843	−	0.864959i	$-0.667344\pi$
$683$	9.54542	−	35.6240i	0.365245	−	1.36311i	0.867088	−	0.498155i	$-0.165989\pi$
$684$	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
$687$	5.44937	−	6.01667i	0.207906	−	0.229550i
$688$	0.210894	+	0.787066i	0.00804024	+	0.0300066i
$689$	2.61538	+	4.52997i	0.0996379	+	0.172578i
$690$	1.84782	−	4.06388i	0.0703453	−	0.154709i
$691$	−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
$693$	14.5568	+	23.0115i	0.552965	+	0.874134i
$694$		−	27.3632i		−	1.03869i
$695$	−15.4396	−	14.0408i	−0.585659	−	0.532599i
$696$	3.42909	−	2.21265i	0.129979	−	0.0838703i
$697$	−7.68783	+	28.6914i	−0.291197	+	1.08676i
$698$	−7.27846	+	1.95026i	−0.275494	+	0.0738183i
$699$	0.160838	+	3.25078i	0.00608344	+	0.122956i
$700$	6.19319	−	11.6895i	0.234081	−	0.441821i
$701$		−	7.15756i		−	0.270337i	−0.990823	−	0.135169i	$-0.956842\pi$
$701$		−	7.15756i		−	0.270337i	0.990823	−	0.135169i	$-0.0431576\pi$
$702$	26.1288	−	11.3598i	0.986169	−	0.428747i
$703$	−32.9434	−	8.82715i	−1.24248	−	0.332922i
$704$	1.71528	+	2.97095i	0.0646469	+	0.111972i
$705$	−21.7008	+	26.3712i	−0.817301	+	0.993196i
$706$	14.9295			0.561880
$707$	−41.3602	−	27.2183i	−1.55551	−	1.02365i
$708$	6.38139	−	7.04572i	0.239827	−	0.264794i
$709$	−13.4922	−	7.78971i	−0.506709	−	0.292549i	0.224771	−	0.974412i	$-0.427837\pi$
$709$	−13.4922	−	7.78971i	−0.506709	−	0.292549i	−0.731480	+	0.681863i	$0.761170\pi$
$710$	−1.80731	+	3.50409i	−0.0678273	+	0.131506i
$711$	−10.0508	−	14.0053i	−0.376936	−	0.525238i
$712$	1.23958	−	0.332143i	0.0464550	−	0.0124476i
$713$	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
$717$	−6.75798	+	31.3430i	−0.252382	+	1.17052i
$718$	29.9296	+	8.01962i	1.11696	+	0.299290i
$719$	−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
$723$	−13.7942	+	4.43748i	−0.513014	+	0.165032i
$724$	13.5293	−	7.81117i	0.502814	−	0.290300i
$725$	1.11545	+	11.7279i	0.0414266	+	0.435562i
$726$	0.607922	−	1.18454i	0.0225621	−	0.0439624i
$727$	26.8316	+	26.8316i	0.995128	+	0.995128i	0.999988	−	0.00486049i	$-0.00154715\pi$
$727$	26.8316	+	26.8316i	0.995128	+	0.995128i	−0.00486049	+	0.999988i	$0.501547\pi$
$728$	−6.50743	−	12.9657i	−0.241182	−	0.480541i
$729$	−7.89178	−	25.8209i	−0.292288	−	0.956330i
$730$	−11.6970	−	10.6373i	−0.432925	−	0.393703i
$731$	−2.70909	+	1.56409i	−0.100199	+	0.0578500i
$732$	1.49865	+	0.323129i	0.0553916	+	0.0119432i
$733$	−7.10691	−	26.5233i	−0.262500	−	0.979662i	−0.963763	−	0.266760i	$-0.914047\pi$
$733$	−7.10691	−	26.5233i	−0.262500	−	0.979662i	0.701263	−	0.712902i	$-0.252620\pi$
$734$	10.0105			0.369493
$735$	27.1054	+	0.542781i	0.999800	+	0.0200208i
$736$	1.15267			0.0424878
$737$	−3.97312	−	14.8279i	−0.146352	−	0.546193i
$738$	22.9041	+	3.76507i	0.843113	+	0.138594i
$739$	31.1498	−	17.9843i	1.14586	−	0.661565i	0.197988	−	0.980205i	$-0.436559\pi$
$739$	31.1498	−	17.9843i	1.14586	−	0.661565i	0.947876	+	0.318640i	$0.103226\pi$
$740$	−0.524267	−	11.0492i	−0.0192724	−	0.406177i
$741$	3.23558	+	65.3960i	0.118862	+	2.40238i
$742$	−1.13217	−	2.25578i	−0.0415631	−	0.0828123i
$743$	11.3545	+	11.3545i	0.416555	+	0.416555i	0.884015	−	0.467459i	$-0.154831\pi$
$743$	11.3545	+	11.3545i	0.416555	+	0.416555i	−0.467459	+	0.884015i	$0.654831\pi$
$744$	−11.0488	−	5.67037i	−0.405067	−	0.207886i
$745$	1.36220	+	4.26407i	0.0499070	+	0.156224i
$746$	−12.3892	+	7.15292i	−0.453602	+	0.261887i
$747$	−10.6282	−	28.1788i	−0.388866	−	1.03101i
$748$	−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	$0.185523\pi$
$752$	−8.51756	−	2.28227i	−0.310604	−	0.0832260i
$753$	−49.2779	−	10.6250i	−1.79579	−	0.387197i
$754$	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	0.633182	−	0.774003i	$-0.281748\pi$
$757$	−3.87448	−	3.87448i	−0.140820	−	0.140820i	−0.774003	+	0.633182i	$0.781748\pi$
$758$	−2.89411	+	0.775475i	−0.105119	+	0.0281665i
$759$	−3.71343	−	5.75495i	−0.134789	−	0.208892i
$760$	−13.7011	−	7.06663i	−0.496990	−	0.256334i
$761$	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	$0.601470\pi$
$762$	−8.22291	−	7.44759i	−0.297885	−	0.269798i
$763$	31.2740	+	20.5808i	1.13219	+	0.745074i
$764$	15.1384			0.547690
$765$	−25.4781	+	3.75390i	−0.921164	+	0.135723i
$766$	−4.19278	−	7.26211i	−0.151491	−	0.262391i
$767$	29.0679	+	7.78872i	1.04958	+	0.281234i
$768$	−1.64884	+	0.530415i	−0.0594972	+	0.0191397i
$769$			23.3486i			0.841972i	0.907067	+	0.420986i	$0.138316\pi$
$769$			23.3486i			0.841972i	−0.907067	+	0.420986i	$0.861684\pi$
$770$	−9.95336	−	17.6871i	−0.358694	−	0.637400i
$771$	33.2294	−	1.64408i	1.19673	−	0.0592103i
$772$	−16.2631	+	4.35769i	−0.585323	+	0.156837i
$773$	5.68254	−	21.2075i	0.204387	−	0.762782i	−0.785249	−	0.619181i	$-0.787465\pi$
$773$	5.68254	−	21.2075i	0.204387	−	0.762782i	0.989636	−	0.143602i	$-0.0458684\pi$
$774$	1.42525	+	1.98600i	0.0512295	+	0.0713854i
$775$	29.2105	−	20.7842i	1.04927	−	0.746591i
$776$		−	3.05240i		−	0.109575i
$777$	19.7337	−	11.1577i	0.707942	−	0.400280i
$778$	−18.5178	+	18.5178i	−0.663895	+	0.663895i
$779$	−26.6712	+	46.1958i	−0.955594	+	1.65514i
$780$	−19.8850	+	7.45411i	−0.711998	+	0.266900i
$781$	3.02444	+	5.23848i	0.108223	+	0.187448i
$782$	1.14531	+	4.27437i	0.0409563	+	0.152851i
$783$	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
$786$	18.8196	+	9.65847i	0.671273	+	0.344506i
$787$	10.9946	−	41.0323i	0.391914	−	1.46264i	−0.435060	−	0.900402i	$-0.643273\pi$
$787$	10.9946	−	41.0323i	0.391914	−	1.46264i	0.826973	−	0.562241i	$-0.190061\pi$
$788$	−1.19621	+	4.46430i	−0.0426131	+	0.159034i
$789$	−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
$792$	7.96012	+	6.52341i	0.282850	+	0.231799i
$793$	1.25613	+	4.68794i	0.0446064	+	0.166474i
$794$	−3.48376	−	6.03404i	−0.123634	−	0.214140i
$795$	−3.45960	+	1.29687i	−0.122700	+	0.0459952i
$796$	2.51565	−	4.35724i	0.0891649	−	0.154438i
$797$	−7.12389	+	7.12389i	−0.252341	+	0.252341i	−0.821930	−	0.569589i	$-0.807103\pi$
$797$	−7.12389	+	7.12389i	−0.252341	+	0.252341i	0.569589	+	0.821930i	$0.307103\pi$
$798$	0.284314	−	31.5923i	0.0100646	−	1.11836i
$799$		−	33.8529i		−	1.19763i
$800$	0.830995	−	4.93046i	0.0293801	−	0.174318i
$801$	3.12782	−	2.24467i	0.110516	−	0.0793115i
$802$	4.99194	−	18.6302i	0.176272	−	0.657855i
$803$	−23.4298	+	6.27799i	−0.826819	+	0.221545i
$804$	7.74107	−	0.383003i	0.273007	−	0.0135075i
$805$	−6.81885	−	0.0751664i	−0.240333	−	0.00264927i
$806$		−	39.3145i		−	1.38479i
$807$	−8.71960	+	2.80501i	−0.306945	+	0.0987412i
$808$	−18.0764	−	4.84355i	−0.635925	−	0.170396i
$809$	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	$0.525543\pi$
$810$	4.88445	+	19.5229i	0.171622	+	0.685963i
$811$	−18.0213			−0.632815			−0.316408	−	0.948623i	$-0.602477\pi$
$811$	−18.0213			−0.632815			−0.316408	+	0.948623i	$0.602477\pi$
$812$	−5.20739	−	3.42688i	−0.182744	−	0.120260i
$813$	28.9634	+	26.2325i	1.01579	+	0.920013i
$814$	−14.6970	−	8.48533i	−0.515131	−	0.297411i
$815$	−11.9874	−	6.18280i	−0.419902	−	0.216574i
$816$	−3.60523	−	5.58726i	−0.126208	−	0.195593i
$817$	−5.42626	+	1.45396i	−0.189841	+	0.0508677i
$818$	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	$0.850811\pi$
$822$	−5.95919	−	1.28489i	−0.207851	−	0.0448155i
$823$	0.312415	+	0.0837114i	0.0108901	+	0.00291799i	0.264260	−	0.964451i	$-0.414872\pi$
$823$	0.312415	+	0.0837114i	0.0108901	+	0.00291799i	−0.253370	+	0.967369i	$0.581539\pi$
$824$	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	0.119062	−	0.992887i	$-0.462011\pi$
$827$	31.9770	−	31.9770i	1.11195	−	1.11195i	0.992887	−	0.119062i	$-0.0379887\pi$
$828$	3.23551	−	1.22034i	0.112442	−	0.0424097i
$829$	−35.8756	+	20.7128i	−1.24601	+	0.719385i	−0.970311	−	0.241859i	$-0.922243\pi$
$829$	−35.8756	+	20.7128i	−1.24601	+	0.719385i	−0.275700	+	0.961244i	$0.588910\pi$
$830$	6.83097	+	21.3829i	0.237107	+	0.742213i
$831$	−38.7808	−	19.9028i	−1.34529	−	0.690421i
$832$	−3.87719	−	3.87719i	−0.134417	−	0.134417i
$833$	−21.0885	+	16.6570i	−0.730674	+	0.577130i
$834$	−0.798829	−	16.1455i	−0.0276612	−	0.559074i
$835$	0.889553	+	18.7478i	0.0307842	+	0.648795i
$836$	−20.4826	+	11.8256i	−0.708405	+	0.408998i
$837$	−37.0169	−	4.21918i	−1.27949	−	0.145836i
$838$	2.30631	+	8.60727i	0.0796702	+	0.297333i
$839$	17.8925			0.617717			0.308858	−	0.951108i	$-0.400053\pi$
$839$	17.8925			0.617717			0.308858	+	0.951108i	$0.400053\pi$
$840$	9.78864	−	3.03027i	0.337740	−	0.104554i
$841$	−23.4485			−0.808569
$842$	4.86616	+	18.1608i	0.167699	+	0.625861i
$843$	49.8932	+	10.7577i	1.71841	+	0.370514i
$844$	−2.24210	+	1.29448i	−0.0771764	+	0.0445578i
$845$	−28.2309	−	25.6733i	−0.971174	−	0.883187i
$846$	−26.3249	+	2.61133i	−0.905068	+	0.0897794i
$847$	−2.03032	−	0.118778i	−0.0697626	−	0.00408127i
$848$	−0.674555	−	0.674555i	−0.0231643	−	0.0231643i
$849$	−0.823259	+	1.60413i	−0.0282542	+	0.0550535i
$850$	19.1091	−	1.81748i	0.655435	−	0.0623389i
$851$	−4.93820	+	2.85107i	−0.169279	+	0.0977335i
$852$	−2.90729	+	0.935247i	−0.0996020	+	0.0320410i
$853$	38.0442	−	38.0442i	1.30261	−	1.30261i	0.375983	−	0.926627i	$-0.377305\pi$
$853$	38.0442	−	38.0442i	1.30261	−	1.30261i	0.926627	−	0.375983i	$-0.122695\pi$
$854$	−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
$857$	4.07290	+	1.09133i	0.139127	+	0.0372791i	0.327711	−	0.944778i	$-0.393723\pi$
$857$	4.07290	+	1.09133i	0.139127	+	0.0372791i	−0.188583	+	0.982057i	$0.560390\pi$
$858$	−6.86699	+	31.8485i	−0.234435	+	1.08729i
$859$	34.2434	+	19.7704i	1.16837	+	0.674558i	0.953295	−	0.302040i	$-0.0976677\pi$
$859$	34.2434	+	19.7704i	1.16837	+	0.674558i	0.215073	+	0.976598i	$0.431001\pi$
$860$	−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
$863$	18.0311	−	4.83143i	0.613787	−	0.164464i	0.0614855	−	0.998108i	$-0.480416\pi$
$863$	18.0311	−	4.83143i	0.613787	−	0.164464i	0.552302	+	0.833644i	$0.313750\pi$
$864$	−4.06669	+	3.23450i	−0.138352	+	0.110040i
$865$	−12.5319	+	24.2974i	−0.426099	+	0.826136i
$866$	−34.1713	−	19.7288i	−1.16119	−	0.670411i
$867$	−2.62965	+	2.90341i	−0.0893078	+	0.0986051i
$868$	−1.10790	+	18.9377i	−0.0376046	+	0.642789i
$869$	19.7126			0.668703
$870$	−5.79842	+	7.04632i	−0.196585	+	0.238893i
$871$	12.2680	+	21.2488i	0.415685	+	0.719988i
$872$	13.6682	+	3.66239i	0.462864	+	0.124024i
$873$	−3.23161	−	8.56803i	−0.109373	−	0.289984i
$874$			7.94681i			0.268805i
$875$	−5.23746	+	29.1130i	−0.177058	+	0.984200i
$876$	−0.605189	−	12.2318i	−0.0204474	−	0.413274i
$877$	47.6148	−	12.7584i	1.60784	−	0.430819i	0.660440	−	0.750878i	$-0.270370\pi$
$877$	47.6148	−	12.7584i	1.60784	−	0.430819i	0.947397	+	0.320060i	$0.103703\pi$
$878$	4.13747	−	15.4413i	0.139633	−	0.521117i
$879$	−25.7519	+	16.6166i	−0.868589	+	0.560465i
$880$	−5.67517	−	5.16101i	−0.191310	−	0.173978i
$881$			58.4991i			1.97089i	0.170007	+	0.985443i	$0.445621\pi$
$881$			58.4991i			1.97089i	−0.170007	+	0.985443i	$0.554379\pi$
$882$	14.5796	+	15.1141i	0.490920	+	0.508918i
$883$	−4.87858	+	4.87858i	−0.164177	+	0.164177i	−0.784414	−	0.620237i	$-0.787036\pi$
$883$	−4.87858	+	4.87858i	−0.164177	+	0.164177i	0.620237	+	0.784414i	$0.287036\pi$
$884$	10.5251	−	18.2300i	0.353998	−	0.613142i
$885$	−8.79819	+	19.3498i	−0.295748	+	0.650435i
$886$	−9.44625	−	16.3614i	−0.317353	−	0.549671i
$887$	11.6286	+	43.3986i	0.390451	+	1.45718i	0.829393	+	0.558666i	$0.188687\pi$
$887$	11.6286	+	43.3986i	0.390451	+	1.45718i	−0.438942	+	0.898515i	$0.644647\pi$
$888$	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
$891$	29.2503	+	9.88361i	0.979921	+	0.331113i
$892$	2.82885	−	10.5574i	0.0947169	−	0.353488i
$893$	15.7347	−	58.7226i	0.526540	−	1.96508i
$894$	−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
$897$	8.11378	+	7.34874i	0.270911	+	0.245367i
$898$	−1.75667	−	6.55599i	−0.0586209	−	0.218776i
$899$	−8.44687	−	14.6304i	−0.281719	−	0.487951i
$900$	−2.88734	−	14.7195i	−0.0962447	−	0.490650i
$901$	1.83116	−	3.17167i	0.0610049	−	0.105664i
$902$	−18.7686	+	18.7686i	−0.624926	+	0.624926i
$903$	1.89604	−	3.21683i	0.0630961	−	0.107049i
$904$			5.40938i			0.179913i
$905$	−23.5026	+	25.8440i	−0.781253	+	0.859084i
$906$	−14.0277	−	21.7396i	−0.466039	−	0.722251i
$907$	−14.0941	+	52.6001i	−0.467988	+	1.74656i	0.178798	+	0.983886i	$0.442779\pi$
$907$	−14.0941	+	52.6001i	−0.467988	+	1.74656i	−0.646787	+	0.762671i	$0.723888\pi$
$908$	7.32054	−	1.96153i	0.242941	−	0.0650957i
$909$	−55.8679	+	5.54189i	−1.85302	+	0.183813i
$910$	22.6835	+	23.1892i	0.751952	+	0.768714i
$911$		−	7.37432i		−	0.244322i	−0.992510	−	0.122161i	$-0.961018\pi$
$911$		−	7.37432i		−	0.244322i	0.992510	−	0.122161i	$-0.0389824\pi$
$912$	−3.65684	−	11.3676i	−0.121090	−	0.376417i
$913$	33.2653	+	8.91342i	1.10092	+	0.294991i
$914$	−2.65569	−	4.59979i	−0.0878424	−	0.152147i
$915$	−3.41202	+	0.331489i	−0.112798	+	0.0109587i
$916$	−4.68671			−0.154853
$917$	1.88711	−	32.2571i	0.0623180	−	1.06522i
$918$	−16.0351	−	11.8664i	−0.529237	−	0.391650i
$919$	39.9069	+	23.0403i	1.31641	+	0.760028i	0.983149	−	0.182808i	$-0.0585186\pi$
$919$	39.9069	+	23.0403i	1.31641	+	0.760028i	0.333258	+	0.942836i	$0.391852\pi$
$920$	−2.45520	+	0.784336i	−0.0809456	+	0.0258588i
$921$	45.1825	−	29.1544i	1.48881	−	0.960671i
$922$	27.1414	−	7.27251i	0.893854	−	0.239507i
$923$	−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
$927$	4.32185	−	26.2912i	0.141948	−	0.863517i
$928$	−2.27587	−	0.609819i	−0.0747093	−	0.0200183i
$929$	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
$933$	−5.84557	−	18.1714i	−0.191375	−	0.594905i
$934$	−7.93138	+	4.57919i	−0.259523	+	0.149836i
$935$	13.4993	−	26.1730i	0.441475	−	0.855949i
$936$	−14.9880	−	6.77837i	−0.489898	−	0.221558i
$937$	9.16753	+	9.16753i	0.299490	+	0.299490i	0.840814	−	0.541324i	$-0.182077\pi$
$937$	9.16753	+	9.16753i	0.299490	+	0.299490i	−0.541324	+	0.840814i	$0.682077\pi$
$938$	−5.31067	−	10.5812i	−0.173400	−	0.345489i
$939$	15.8909	−	0.786228i	0.518578	−	0.0256576i
$940$	19.6956	−	0.934521i	0.642398	−	0.0304807i
$941$	−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	$0.431393\pi$
$942$	−5.14329	+	23.8542i	−0.167578	+	0.777211i
$943$	2.30825	+	8.61450i	0.0751669	+	0.280527i
$944$	−5.48830			−0.178629
$945$	24.2683	−	18.8692i	0.789449	−	0.613816i
$946$	−2.79532			−0.0908837
$947$	−1.20259	−	4.48811i	−0.0390788	−	0.145844i	0.943630	−	0.331002i	$-0.107387\pi$
$947$	−1.20259	−	4.48811i	−0.0390788	−	0.145844i	−0.982709	+	0.185158i	$0.940720\pi$
$948$	−2.09773	+	9.72908i	−0.0681310	+	0.315986i
$949$	33.5755	−	19.3848i	1.08991	−	0.629258i
$950$	33.9920	+	5.72912i	1.10285	+	0.185877i
$951$	8.80462	−	0.435624i	0.285509	−	0.0141261i
$952$	−5.58366	+	8.48477i	−0.180967	+	0.274993i
$953$	12.6014	+	12.6014i	0.408198	+	0.408198i	0.881110	−	0.472912i	$-0.156797\pi$
$953$	12.6014	+	12.6014i	0.408198	+	0.408198i	−0.472912	+	0.881110i	$0.656797\pi$
$954$	−2.60762	−	1.17930i	−0.0844248	−	0.0381814i
$955$	−32.2452	+	10.3010i	−1.04343	+	0.333333i
$956$	16.0316	−	9.25587i	0.518500	−	0.299356i
$957$	4.28731	+	13.3274i	0.138589	+	0.430815i
$958$	−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
$962$	26.2006	+	7.02042i	0.844740	+	0.226347i
$963$	−3.29606	+	20.0510i	−0.106214	+	0.646135i
$964$	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	0.967081	−	0.254468i	$-0.0819003\pi$
$967$	22.1599	+	22.1599i	0.712613	+	0.712613i	−0.254468	+	0.967081i	$0.581900\pi$
$968$	−0.742508	+	0.198954i	−0.0238651	+	0.00639464i
$969$	38.5202	−	24.8555i	1.23745	−	0.798473i
$970$	2.07702	+	6.50167i	0.0666890	+	0.208756i
$971$	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	$0.585111\pi$
$972$	−7.99072	+	13.3846i	−0.256303	+	0.429312i
$973$	−22.0692	+	11.0765i	−0.707507	+	0.355095i
$974$	−3.28607			−0.105292
$975$	37.2833	−	29.4082i	1.19402	−	0.941818i
$976$	−0.442564	−	0.766543i	−0.0141661	−	0.0245365i
$977$	−45.5260	−	12.1987i	−1.45651	−	0.390270i	−0.558225	−	0.829690i	$-0.688517\pi$
$977$	−45.5260	−	12.1987i	−1.45651	−	0.390270i	−0.898282	+	0.439420i	$0.855184\pi$
$978$	−3.19947	−	9.94580i	−0.102308	−	0.318032i
$979$			4.40244i			0.140703i
$980$	−10.2731	−	11.8094i	−0.328163	−	0.377238i
$981$	42.2438	−	4.19043i	1.34874	−	0.133790i
$982$	11.2825	−	3.02313i	0.360039	−	0.0964721i
$983$	−10.9653	+	40.9232i	−0.349740	+	1.30525i	0.537236	+	0.843432i	$0.319469\pi$
$983$	−10.9653	+	40.9232i	−0.349740	+	1.30525i	−0.886976	+	0.461816i	$0.847198\pi$
$984$	−7.26592	−	11.2605i	−0.231629	−	0.358971i
$985$	−0.489809	−	10.3230i	−0.0156066	−	0.328918i
$986$		−	9.04543i		−	0.288065i
$987$	19.8889	+	35.1759i	0.633071	+	1.11966i
$988$	26.7305	−	26.7305i	0.850409	−	0.850409i
$989$	−0.469614	+	0.813395i	−0.0149328	+	0.0258645i
$990$	−21.3941	−	8.47849i	−0.679949	−	0.269464i
$991$	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	$0.826719\pi$
$992$	1.85574	+	6.92572i	0.0589198	+	0.219892i
$993$	−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
$996$	−7.93915	+	15.4695i	−0.251562	+	0.490170i
$997$	−13.1718	+	49.1577i	−0.417154	+	1.55684i	0.363327	+	0.931662i	$0.381641\pi$
$997$	−13.1718	+	49.1577i	−0.417154	+	1.55684i	−0.780482	+	0.625179i	$0.785026\pi$
$998$	0.750174	−	2.79969i	0.0237463	−	0.0886225i
$999$	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.107.13	yes	64
3.2	odd	2	inner	210.2.x.a.107.4	yes	64
5.3	odd	4	inner	210.2.x.a.23.16	yes	64
7.4	even	3	inner	210.2.x.a.137.1	yes	64
15.8	even	4	inner	210.2.x.a.23.1	✓	64
21.11	odd	6	inner	210.2.x.a.137.16	yes	64
35.18	odd	12	inner	210.2.x.a.53.4	yes	64
105.53	even	12	inner	210.2.x.a.53.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.1	✓	64	15.8	even	4	inner
210.2.x.a.23.16	yes	64	5.3	odd	4	inner
210.2.x.a.53.4	yes	64	35.18	odd	12	inner
210.2.x.a.53.13	yes	64	105.53	even	12	inner
210.2.x.a.107.4	yes	64	3.2	odd	2	inner
210.2.x.a.107.13	yes	64	1.1	even	1	trivial
210.2.x.a.137.1	yes	64	7.4	even	3	inner
210.2.x.a.137.16	yes	64	21.11	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.365065 - 1.69314i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50442 - 1.65430i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.73346 - 1.23621i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.365065 - 1.69314i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.50442 - 1.65430i) q^{5} +(1.72993 - 0.0855915i) q^{6} +(-1.18680 - 2.36464i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.73346 - 1.23621i) q^{9} +(1.98730 + 1.02500i) q^{10} +(2.97095 - 1.71528i) q^{11} +(0.530415 + 1.64884i) 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} +(3.70825 + 0.993622i) q^{17} +(0.486620 - 2.96027i) 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} +(1.11339 - 0.298332i) q^{23} +(-1.45537 + 0.939092i) q^{24} +(-0.473417 - 4.97754i) q^{25} +(-4.74857 - 2.74159i) q^{26} +(-3.09097 + 4.17683i) q^{27} +(2.21012 + 1.45443i) q^{28} -2.35616 q^{29} +(2.46096 - 2.99060i) q^{30} +(3.58502 + 6.20943i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.81962 - 5.65642i) q^{33} +3.83906i q^{34} +(-5.69727 - 1.59409i) q^{35} +(2.98535 - 0.296136i) q^{36} +(-4.77836 + 1.28036i) q^{37} +(-1.78437 + 6.65937i) q^{38} +(5.14920 + 7.98005i) q^{39} +(-2.23356 + 0.105978i) q^{40} +7.73718i q^{41} +(-2.25548 - 3.98909i) q^{42} +(-0.576172 + 0.576172i) q^{43} +(-1.71528 + 2.97095i) q^{44} +(-6.15734 + 2.66217i) q^{45} +(0.576333 + 0.998238i) q^{46} +(-2.28227 - 8.51756i) q^{47} +(-1.28377 - 1.16273i) q^{48} +(-4.18301 + 5.61270i) q^{49} +(4.68540 - 1.74557i) q^{50} +(3.03609 - 5.91585i) q^{51} +(1.41915 - 5.29634i) q^{52} +(0.246904 - 0.921459i) q^{53} +(-4.83451 - 1.90461i) q^{54} +(1.63198 - 7.49534i) q^{55} +(-0.832855 + 2.51125i) q^{56} +(8.01617 - 8.85069i) q^{57} +(-0.609819 - 2.27587i) q^{58} +(-2.74415 - 4.75301i) q^{59} +(3.52564 + 1.60308i) q^{60} +(0.442564 - 0.766543i) q^{61} +(-5.06998 + 5.06998i) q^{62} +(0.320873 + 7.93077i) q^{63} +1.00000i q^{64} +(0.581098 + 12.2470i) q^{65} +(4.99273 - 3.22161i) q^{66} +(1.15816 - 4.32230i) q^{67} +(-3.70825 + 0.993622i) q^{68} +(-0.0986585 - 1.99404i) q^{69} +(0.0652109 - 5.91572i) q^{70} +1.76324i q^{71} +(1.05871 + 2.80698i) q^{72} +(-6.82973 - 1.83002i) q^{73} +(-2.47346 - 4.28416i) q^{74} +(-8.60050 - 1.01556i) q^{75} -6.89429 q^{76} +(-7.58193 - 4.98952i) q^{77} +(-6.37543 + 7.03914i) q^{78} +(4.97633 + 2.87309i) q^{79} +(-0.680454 - 2.13002i) q^{80} +(5.94355 + 6.75827i) q^{81} +(-7.47354 + 2.00253i) 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} +(-0.860151 + 3.98931i) q^{87} +(-3.31366 - 0.887893i) 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} +(11.8222 - 3.80309i) q^{93} +(7.63664 - 4.40902i) q^{94} +(14.6850 - 4.69125i) q^{95} +(0.790843 - 1.54096i) q^{96} +(2.15837 + 2.15837i) q^{97} +(-6.50410 - 2.58780i) 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

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