LMFDB - Embedded newform 539.2.q.h.422.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			422.5
Character	$\chi$	$=$	539.422
Dual form			539.2.q.h.410.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04369 - 0.909911i) q^{2} +(1.30576 - 0.277549i) q^{3} +(2.01049 - 2.23287i) q^{4} +(-0.0905565 - 0.861587i) q^{5} +(2.41604 - 1.75535i) q^{6} +(0.694498 - 2.13745i) q^{8} +(-1.11265 + 0.495385i) q^{9} +O(q^{10})$	\(q+(2.04369 - 0.909911i) q^{2} +(1.30576 - 0.277549i) q^{3} +(2.01049 - 2.23287i) q^{4} +(-0.0905565 - 0.861587i) q^{5} +(2.41604 - 1.75535i) q^{6} +(0.694498 - 2.13745i) q^{8} +(-1.11265 + 0.495385i) q^{9} +(-0.969038 - 1.67842i) q^{10} +(1.89678 - 2.72071i) q^{11} +(2.00549 - 3.47361i) q^{12} +(-2.73539 - 1.98738i) q^{13} +(-0.357378 - 1.09990i) q^{15} +(0.102593 + 0.976110i) q^{16} +(2.00586 + 0.893065i) q^{17} +(-1.82316 + 2.02483i) q^{18} +(2.40122 + 2.66683i) q^{19} +(-2.10587 - 1.53001i) q^{20} +(1.40083 - 7.28619i) q^{22} +(-0.834837 + 1.44598i) q^{23} +(0.313605 - 2.98375i) q^{24} +(4.15661 - 0.883514i) q^{25} +(-7.39864 - 1.57263i) q^{26} +(-4.55532 + 3.30963i) q^{27} +(0.473517 + 1.45734i) q^{29} +(-1.73118 - 1.92267i) q^{30} +(-0.927888 + 8.82827i) q^{31} +(3.34529 + 5.79421i) q^{32} +(1.72161 - 4.07904i) q^{33} +4.91197 q^{34} +(-1.13084 + 3.48037i) q^{36} +(-3.01788 - 0.641471i) q^{37} +(7.33394 + 3.26528i) q^{38} +(-4.12337 - 1.83584i) q^{39} +(-1.90449 - 0.404811i) q^{40} +(-0.203209 + 0.625414i) q^{41} -9.76359 q^{43} +(-2.26154 - 9.70519i) q^{44} +(0.527575 + 0.913787i) q^{45} +(-0.390438 + 3.71477i) q^{46} +(-8.82952 - 9.80618i) q^{47} +(0.404881 + 1.24609i) q^{48} +(7.69091 - 5.58777i) q^{50} +(2.86704 + 0.609409i) q^{51} +(-9.93702 + 2.11218i) q^{52} +(-0.686100 + 6.52780i) q^{53} +(-6.29821 + 10.9088i) q^{54} +(-2.51589 - 1.38786i) q^{55} +(3.87560 + 2.81579i) q^{57} +(2.29377 + 2.54749i) q^{58} +(9.74869 - 10.8270i) q^{59} +(-3.17443 - 1.41335i) q^{60} +(0.605886 + 5.76462i) q^{61} +(6.13662 + 18.8866i) q^{62} +(10.5209 + 7.64386i) q^{64} +(-1.46459 + 2.53675i) q^{65} +(-0.193116 - 9.90283i) q^{66} +(-2.64188 - 4.57587i) q^{67} +(6.02684 - 2.68332i) q^{68} +(-0.688770 + 2.11982i) q^{69} +(-6.33800 + 4.60483i) q^{71} +(0.286123 + 2.72228i) q^{72} +(3.95947 - 4.39744i) q^{73} +(-6.75131 + 1.43504i) q^{74} +(5.18232 - 2.30732i) q^{75} +10.7823 q^{76} -10.0974 q^{78} +(10.7382 - 4.78095i) q^{79} +(0.831714 - 0.176786i) q^{80} +(-2.58468 + 2.87058i) q^{81} +(0.153773 + 1.46306i) q^{82} +(-0.455953 + 0.331269i) q^{83} +(0.587810 - 1.80909i) q^{85} +(-19.9538 + 8.88400i) q^{86} +(1.02278 + 1.77151i) q^{87} +(-4.49805 - 5.94378i) q^{88} +(1.76101 - 3.05016i) q^{89} +(1.90967 + 1.38745i) q^{90} +(1.55026 + 4.77120i) q^{92} +(1.23867 + 11.7852i) q^{93} +(-26.9676 - 12.0067i) q^{94} +(2.08026 - 2.31036i) q^{95} +(5.97632 + 6.63738i) q^{96} +(-11.2566 - 8.17838i) q^{97} +(-0.762658 + 3.96683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	2.04369	−	0.909911i	1.44511	−	0.643404i	0.473673	−	0.880701i	$-0.342928\pi$
$2$	2.04369	−	0.909911i	1.44511	−	0.643404i	0.971437	+	0.237297i	$0.0762614\pi$
$3$	1.30576	−	0.277549i	0.753883	−	0.160243i	0.185088	−	0.982722i	$-0.440743\pi$
$3$	1.30576	−	0.277549i	0.753883	−	0.160243i	0.568795	+	0.822479i	$0.307410\pi$
$4$	2.01049	−	2.23287i	1.00524	−	1.11643i
$5$	−0.0905565	−	0.861587i	−0.0404981	−	0.385314i	−0.995932	−	0.0901084i	$-0.971279\pi$
$5$	−0.0905565	−	0.861587i	−0.0404981	−	0.385314i	0.955434	−	0.295205i	$-0.0953880\pi$
$6$	2.41604	−	1.75535i	0.986342	−	0.716620i
$7$		0			0
$7$		0			0
$8$	0.694498	−	2.13745i	0.245542	−	0.755701i
$9$	−1.11265	+	0.495385i	−0.370884	+	0.165128i
$10$	−0.969038	−	1.67842i	−0.306437	−	0.530764i
$11$	1.89678	−	2.72071i	0.571900	−	0.820323i
$11$	1.89678	−	2.72071i	0.571900	−	0.820323i
$12$	2.00549	−	3.47361i	0.578934	−	1.00274i
$13$	−2.73539	−	1.98738i	−0.758661	−	0.551200i	0.139838	−	0.990174i	$-0.455342\pi$
$13$	−2.73539	−	1.98738i	−0.758661	−	0.551200i	−0.898499	+	0.438975i	$0.855342\pi$
$14$		0			0
$15$	−0.357378	−	1.09990i	−0.0922745	−	0.283992i
$16$	0.102593	+	0.976110i	0.0256483	+	0.244028i
$17$	2.00586	+	0.893065i	0.486492	+	0.216600i	0.635299	−	0.772266i	$-0.280877\pi$
$17$	2.00586	+	0.893065i	0.486492	+	0.216600i	−0.148808	+	0.988866i	$0.547543\pi$
$18$	−1.82316	+	2.02483i	−0.429724	+	0.477257i
$19$	2.40122	+	2.66683i	0.550878	+	0.611813i	0.952703	−	0.303904i	$-0.0982903\pi$
$19$	2.40122	+	2.66683i	0.550878	+	0.611813i	−0.401824	+	0.915717i	$0.631624\pi$
$20$	−2.10587	−	1.53001i	−0.470888	−	0.342120i
$21$		0			0
$22$	1.40083	−	7.28619i	0.298658	−	1.55342i
$23$	−0.834837	+	1.44598i	−0.174076	+	0.301508i	−0.939841	−	0.341612i	$-0.889027\pi$
$23$	−0.834837	+	1.44598i	−0.174076	+	0.301508i	0.765765	+	0.643120i	$0.222360\pi$
$24$	0.313605	−	2.98375i	0.0640144	−	0.609056i
$25$	4.15661	−	0.883514i	0.831321	−	0.176703i
$26$	−7.39864	−	1.57263i	−1.45099	−	0.308418i
$27$	−4.55532	+	3.30963i	−0.876672	+	0.636939i
$28$		0			0
$29$	0.473517	+	1.45734i	0.0879300	+	0.270621i	0.985347	−	0.170563i	$-0.0545587\pi$
$29$	0.473517	+	1.45734i	0.0879300	+	0.270621i	−0.897417	+	0.441184i	$0.854559\pi$
$30$	−1.73118	−	1.92267i	−0.316068	−	0.351029i
$31$	−0.927888	+	8.82827i	−0.166654	+	1.58560i	0.517122	+	0.855912i	$0.327003\pi$
$31$	−0.927888	+	8.82827i	−0.166654	+	1.58560i	−0.683776	+	0.729692i	$0.739663\pi$
$32$	3.34529	+	5.79421i	0.591369	+	1.02428i
$33$	1.72161	−	4.07904i	0.299695	−	0.710070i
$34$	4.91197			0.842395
$35$		0			0
$36$	−1.13084	+	3.48037i	−0.188474	+	0.580062i
$37$	−3.01788	−	0.641471i	−0.496137	−	0.105457i	−0.0469542	−	0.998897i	$-0.514951\pi$
$37$	−3.01788	−	0.641471i	−0.496137	−	0.105457i	−0.449183	+	0.893440i	$0.648285\pi$
$38$	7.33394	+	3.26528i	1.18972	+	0.529699i
$39$	−4.12337	−	1.83584i	−0.660267	−	0.293970i
$40$	−1.90449	−	0.404811i	−0.301126	−	0.0640063i
$41$	−0.203209	+	0.625414i	−0.0317360	+	0.0976732i	−0.965670	−	0.259773i	$-0.916352\pi$
$41$	−0.203209	+	0.625414i	−0.0317360	+	0.0976732i	0.933934	+	0.357446i	$0.116352\pi$
$42$		0			0
$43$	−9.76359			−1.48893			−0.744467	−	0.667660i	$-0.767296\pi$
$43$	−9.76359			−1.48893			−0.744467	+	0.667660i	$0.767296\pi$
$44$	−2.26154	−	9.70519i	−0.340940	−	1.46311i
$45$	0.527575	+	0.913787i	0.0786463	+	0.136219i
$46$	−0.390438	+	3.71477i	−0.0575669	+	0.547713i
$47$	−8.82952	−	9.80618i	−1.28792	−	1.43038i	−0.845872	−	0.533385i	$-0.820920\pi$
$47$	−8.82952	−	9.80618i	−1.28792	−	1.43038i	−0.442046	−	0.896992i	$-0.645747\pi$
$48$	0.404881	+	1.24609i	0.0584395	+	0.179858i
$49$		0			0
$50$	7.69091	−	5.58777i	1.08766	−	0.790231i
$51$	2.86704	+	0.609409i	0.401466	+	0.0853343i
$52$	−9.93702	+	2.11218i	−1.37802	+	0.292907i
$53$	−0.686100	+	6.52780i	−0.0942430	+	0.896663i	0.840613	+	0.541636i	$0.182195\pi$
$53$	−0.686100	+	6.52780i	−0.0942430	+	0.896663i	−0.934856	+	0.355027i	$0.884472\pi$
$54$	−6.29821	+	10.9088i	−0.857078	+	1.48450i
$55$	−2.51589	−	1.38786i	−0.339243	−	0.187139i
$56$		0			0
$57$	3.87560	+	2.81579i	0.513336	+	0.372961i
$58$	2.29377	+	2.54749i	0.301187	+	0.334502i
$59$	9.74869	−	10.8270i	1.26917	−	1.40956i	0.398893	−	0.916998i	$-0.369395\pi$
$59$	9.74869	−	10.8270i	1.26917	−	1.40956i	0.870278	−	0.492560i	$-0.163939\pi$
$60$	−3.17443	−	1.41335i	−0.409817	−	0.182462i
$61$	0.605886	+	5.76462i	0.0775758	+	0.738084i	0.962304	+	0.271977i	$0.0876774\pi$
$61$	0.605886	+	5.76462i	0.0775758	+	0.738084i	−0.884728	+	0.466108i	$0.845656\pi$
$62$	6.13662	+	18.8866i	0.779351	+	2.39860i
$63$		0			0
$64$	10.5209	+	7.64386i	1.31511	+	0.955483i
$65$	−1.46459	+	2.53675i	−0.181660	+	0.314645i
$66$	−0.193116	−	9.90283i	−0.0237709	−	1.21895i
$67$	−2.64188	−	4.57587i	−0.322757	−	0.559032i	0.658299	−	0.752757i	$-0.271276\pi$
$67$	−2.64188	−	4.57587i	−0.322757	−	0.559032i	−0.981056	+	0.193725i	$0.937943\pi$
$68$	6.02684	−	2.68332i	0.730862	−	0.325401i
$69$	−0.688770	+	2.11982i	−0.0829181	+	0.255196i
$70$		0			0
$71$	−6.33800	+	4.60483i	−0.752183	+	0.546493i	−0.896503	−	0.443038i	$-0.853901\pi$
$71$	−6.33800	+	4.60483i	−0.752183	+	0.546493i	0.144320	+	0.989531i	$0.453901\pi$
$72$	0.286123	+	2.72228i	0.0337199	+	0.320824i
$73$	3.95947	−	4.39744i	0.463421	−	0.514681i	−0.465455	−	0.885071i	$-0.654109\pi$
$73$	3.95947	−	4.39744i	0.463421	−	0.514681i	0.928876	+	0.370390i	$0.120776\pi$
$74$	−6.75131	+	1.43504i	−0.784824	+	0.166820i
$75$	5.18232	−	2.30732i	0.598403	−	0.266426i
$76$	10.7823			1.23682
$77$		0			0
$78$	−10.0974			−1.14330
$79$	10.7382	−	4.78095i	1.20814	−	0.537899i	0.298945	−	0.954270i	$-0.403365\pi$
$79$	10.7382	−	4.78095i	1.20814	−	0.537899i	0.909194	+	0.416372i	$0.136699\pi$
$80$	0.831714	−	0.176786i	0.0929884	−	0.0197653i
$81$	−2.58468	+	2.87058i	−0.287187	+	0.318954i
$82$	0.153773	+	1.46306i	0.0169814	+	0.161568i
$83$	−0.455953	+	0.331269i	−0.0500473	+	0.0363615i	−0.612528	−	0.790449i	$-0.709847\pi$
$83$	−0.455953	+	0.331269i	−0.0500473	+	0.0363615i	0.562480	+	0.826811i	$0.309847\pi$
$84$		0			0
$85$	0.587810	−	1.80909i	0.0637569	−	0.196224i
$86$	−19.9538	+	8.88400i	−2.15167	+	0.957986i
$87$	1.02278	+	1.77151i	0.109654	+	0.189926i
$88$	−4.49805	−	5.94378i	−0.479494	−	0.633609i
$89$	1.76101	−	3.05016i	0.186667	−	0.323317i	−0.757470	−	0.652870i	$-0.773565\pi$
$89$	1.76101	−	3.05016i	0.186667	−	0.323317i	0.944137	+	0.329553i	$0.106898\pi$
$90$	1.90967	+	1.38745i	0.201297	+	0.146251i
$91$		0			0
$92$	1.55026	+	4.77120i	0.161626	+	0.497432i
$93$	1.23867	+	11.7852i	0.128444	+	1.22206i
$94$	−26.9676	−	12.0067i	−2.78149	−	1.23840i
$95$	2.08026	−	2.31036i	0.213430	−	0.237038i
$96$	5.97632	+	6.63738i	0.609956	+	0.677425i
$97$	−11.2566	−	8.17838i	−1.14293	−	0.830388i	−0.155406	−	0.987851i	$-0.549669\pi$
$97$	−11.2566	−	8.17838i	−1.14293	−	0.830388i	−0.987525	+	0.157462i	$0.949669\pi$
$98$		0			0
$99$	−0.762658	+	3.96683i	−0.0766500	+	0.398682i
$100$	6.38402	−	11.0575i	0.638402	−	1.10575i
$101$	−1.26876	+	12.0714i	−0.126246	+	1.20115i	0.729583	+	0.683892i	$0.239714\pi$
$101$	−1.26876	+	12.0714i	−0.126246	+	1.20115i	−0.855829	+	0.517259i	$0.826953\pi$
$102$	6.41386	−	1.36331i	0.635067	−	0.134988i
$103$	2.81798	+	0.598981i	0.277664	+	0.0590193i	0.344639	−	0.938735i	$-0.388001\pi$
$103$	2.81798	+	0.598981i	0.277664	+	0.0590193i	−0.0669748	+	0.997755i	$0.521335\pi$
$104$	−6.14764	+	4.46652i	−0.602825	+	0.437978i
$105$		0			0
$106$	4.53754	+	13.9651i	0.440725	+	1.35641i
$107$	−0.624629	−	0.693721i	−0.0603852	−	0.0670645i	0.712195	−	0.701981i	$-0.247701\pi$
$107$	−0.624629	−	0.693721i	−0.0603852	−	0.0670645i	−0.772580	+	0.634917i	$0.781034\pi$
$108$	−1.76842	+	16.8254i	−0.170166	+	1.61903i
$109$	−6.08365	−	10.5372i	−0.582708	−	1.00928i	−0.995157	−	0.0982988i	$-0.968660\pi$
$109$	−6.08365	−	10.5372i	−0.582708	−	1.00928i	0.412449	−	0.910981i	$-0.364673\pi$
$110$	−6.40454	−	0.547128i	−0.610649	−	0.0521666i
$111$	−4.11868			−0.390928
$112$		0			0
$113$	3.95376	−	12.1684i	0.371939	−	1.14471i	−0.573582	−	0.819148i	$-0.694447\pi$
$113$	3.95376	−	12.1684i	0.371939	−	1.14471i	0.945521	−	0.325562i	$-0.105553\pi$
$114$	10.4827	+	2.22816i	0.981792	+	0.208686i
$115$	1.32144	+	0.588342i	0.123225	+	0.0548632i
$116$	4.20604	+	1.87265i	0.390521	+	0.173871i
$117$	4.02806	+	0.856190i	0.372394	+	0.0791548i
$118$	10.0717	−	30.9975i	0.927176	−	2.85356i
$119$		0			0
$120$	−2.59916			−0.237270
$121$	−3.80447	−	10.3211i	−0.345861	−	0.938286i
$122$	6.48354	+	11.2298i	0.586992	+	1.01670i
$123$	−0.0917605	+	0.873043i	−0.00827376	+	0.0787196i
$124$	17.8469	+	19.8210i	1.60270	+	1.77997i
$125$	−2.47619	−	7.62093i	−0.221477	−	0.681637i
$126$		0			0
$127$	−1.79504	+	1.30417i	−0.159284	+	0.115727i	−0.664572	−	0.747224i	$-0.731386\pi$
$127$	−1.79504	+	1.30417i	−0.159284	+	0.115727i	0.505288	+	0.862951i	$0.331386\pi$
$128$	15.3679	+	3.26656i	1.35835	+	0.288726i
$129$	−12.7489	+	2.70987i	−1.12248	+	0.238591i
$130$	−0.684963	+	6.51699i	−0.0600752	+	0.571578i
$131$	0.633382	−	1.09705i	0.0553388	−	0.0958497i	−0.837029	−	0.547159i	$-0.815709\pi$
$131$	0.633382	−	1.09705i	0.0553388	−	0.0958497i	0.892368	+	0.451309i	$0.149043\pi$
$132$	−5.64670	−	12.0450i	−0.491482	−	1.04838i
$133$		0			0
$134$	−9.56284	−	6.94781i	−0.826103	−	0.600199i
$135$	3.26405	+	3.62510i	0.280925	+	0.311999i
$136$	3.30194	−	3.66718i	0.283139	−	0.314458i
$137$	5.95895	+	2.65309i	0.509107	+	0.226669i	0.645181	−	0.764030i	$-0.276782\pi$
$137$	5.95895	+	2.65309i	0.509107	+	0.226669i	−0.136074	+	0.990699i	$0.543449\pi$
$138$	0.521209	+	4.95897i	0.0443683	+	0.422136i
$139$	4.39304	+	13.5204i	0.372613	+	1.14678i	0.945075	+	0.326853i	$0.105988\pi$
$139$	4.39304	+	13.5204i	0.372613	+	1.14678i	−0.572463	+	0.819931i	$0.694012\pi$
$140$		0			0
$141$	−14.2510	−	10.3539i	−1.20015	−	0.871958i
$142$	−8.76295	+	15.1779i	−0.735371	+	1.27370i
$143$	−10.5955	+	3.67258i	−0.886040	+	0.307117i
$144$	−0.597701	−	1.03525i	−0.0498084	−	0.0862707i
$145$	1.21274	−	0.539948i	0.100713	−	0.0448402i
$146$	4.09067	−	12.5898i	0.338546	−	1.04194i
$147$		0			0
$148$	−7.49973	+	5.44888i	−0.616474	+	0.447895i
$149$	−0.384261	−	3.65599i	−0.0314798	−	0.299511i	−0.998922	−	0.0464188i	$-0.985219\pi$
$149$	−0.384261	−	3.65599i	−0.0314798	−	0.299511i	0.967442	−	0.253092i	$-0.0814475\pi$
$150$	8.49163	−	9.43091i	0.693339	−	0.770031i
$151$	8.65413	−	1.83949i	0.704263	−	0.149696i	0.158160	−	0.987414i	$-0.449444\pi$
$151$	8.65413	−	1.83949i	0.704263	−	0.149696i	0.546103	+	0.837718i	$0.316111\pi$
$152$	7.36785	−	3.28038i	0.597611	−	0.266074i
$153$	−2.67423			−0.216199
$154$		0			0
$155$	7.69035			0.617704
$156$	−12.3892	+	5.51601i	−0.991927	+	0.441634i
$157$	2.25627	−	0.479585i	0.180070	−	0.0382750i	−0.116994	−	0.993133i	$-0.537326\pi$
$157$	2.25627	−	0.479585i	0.180070	−	0.0382750i	0.297064	+	0.954858i	$0.403993\pi$
$158$	17.5953	−	19.5416i	1.39981	−	1.55464i
$159$	0.915898	+	8.71419i	0.0726354	+	0.691080i
$160$	4.68928	−	3.40696i	0.370720	−	0.269344i
$161$		0			0
$162$	−2.67033	+	8.21842i	−0.209801	+	0.645700i
$163$	−5.23657	+	2.33147i	−0.410160	+	0.182615i	−0.601435	−	0.798921i	$-0.705404\pi$
$163$	−5.23657	+	2.33147i	−0.410160	+	0.182615i	0.191275	+	0.981536i	$0.438738\pi$
$164$	0.987918	+	1.71112i	0.0771435	+	0.133616i
$165$	−3.67036	−	1.11394i	−0.285737	−	0.0867199i
$166$	−0.630402	+	1.09189i	−0.0489287	+	0.0847470i
$167$	2.60856	+	1.89523i	0.201857	+	0.146657i	0.684122	−	0.729368i	$-0.260186\pi$
$167$	2.60856	+	1.89523i	0.201857	+	0.146657i	−0.482265	+	0.876025i	$0.660186\pi$
$168$		0			0
$169$	−0.484526	−	1.49122i	−0.0372713	−	0.114709i
$170$	−0.444810	−	4.23209i	−0.0341154	−	0.324586i
$171$	−3.99283	−	1.77772i	−0.305340	−	0.135946i
$172$	−19.6295	+	21.8008i	−1.49674	+	1.66230i
$173$	5.62096	+	6.24271i	0.427354	+	0.474624i	0.917912	−	0.396784i	$-0.129874\pi$
$173$	5.62096	+	6.24271i	0.427354	+	0.474624i	−0.490558	+	0.871408i	$0.663207\pi$
$174$	3.70217	+	2.68979i	0.280661	+	0.203912i
$175$		0			0
$176$	2.85030	+	1.57234i	0.214850	+	0.118519i
$177$	9.72446	−	16.8433i	0.730935	−	1.26602i
$178$	0.823593	−	7.83597i	0.0617309	−	0.587331i
$179$	2.51173	−	0.533884i	0.187735	−	0.0399044i	−0.113084	−	0.993585i	$-0.536073\pi$
$179$	2.51173	−	0.533884i	0.187735	−	0.0399044i	0.300820	+	0.953681i	$0.402740\pi$
$180$	3.10105	+	0.659148i	0.231139	+	0.0491300i
$181$	1.43468	−	1.04235i	0.106639	−	0.0774775i	−0.533188	−	0.845997i	$-0.679006\pi$
$181$	1.43468	−	1.04235i	0.106639	−	0.0774775i	0.639827	+	0.768519i	$0.279006\pi$
$182$		0			0
$183$	2.39111	+	7.35907i	0.176756	+	0.543998i
$184$	2.51091	+	2.78865i	0.185107	+	0.205582i
$185$	−0.279394	+	2.65826i	−0.0205415	+	0.195439i
$186$	13.2549	+	22.9582i	0.971897	+	1.68338i
$187$	6.23443	−	3.76340i	0.455907	−	0.275207i
$188$	−39.6475			−2.89159
$189$		0			0
$190$	2.14919	−	6.61452i	0.155919	−	0.479868i
$191$	8.09990	+	1.72169i	0.586088	+	0.124577i	0.491406	−	0.870931i	$-0.336483\pi$
$191$	8.09990	+	1.72169i	0.586088	+	0.124577i	0.0946822	+	0.995508i	$0.469816\pi$
$192$	15.8593	+	7.06102i	1.14455	+	0.509585i
$193$	−17.3810	−	7.73850i	−1.25111	−	0.557029i	−0.329135	−	0.944283i	$-0.606757\pi$
$193$	−17.3810	−	7.73850i	−1.25111	−	0.557029i	−0.921973	+	0.387253i	$0.873424\pi$
$194$	−30.4466	−	6.47162i	−2.18594	−	0.464635i
$195$	−1.20834	+	3.71889i	−0.0865310	+	0.266315i
$196$		0			0
$197$	15.1831			1.08175			0.540877	−	0.841102i	$-0.318093\pi$
$197$	15.1831			1.08175			0.540877	+	0.841102i	$0.318093\pi$
$198$	2.05083	+	8.80094i	0.145746	+	0.625456i
$199$	−12.3023	−	21.3082i	−0.872086	−	1.51050i	−0.859835	−	0.510573i	$-0.829433\pi$
$199$	−12.3023	−	21.3082i	−0.872086	−	1.51050i	−0.0122517	−	0.999925i	$-0.503900\pi$
$200$	0.998292	−	9.49812i	0.0705899	−	0.671618i
$201$	−4.71970	−	5.24176i	−0.332902	−	0.369725i
$202$	8.39097	+	25.8247i	0.590386	+	1.81702i
$203$		0			0
$204$	7.12487	−	5.17652i	0.498841	−	0.362429i
$205$	0.557250	+	0.118447i	0.0389201	+	0.00827271i
$206$	6.30411	−	1.33998i	0.439228	−	0.0933609i
$207$	0.212567	−	2.02244i	0.0147744	−	0.140569i
$208$	1.65927	−	2.87394i	0.115049	−	0.199272i
$209$	11.8102	−	1.47464i	0.816931	−	0.102003i
$210$		0			0
$211$	14.0745	+	10.2257i	0.968930	+	0.703969i	0.955208	−	0.295937i	$-0.0956318\pi$
$211$	14.0745	+	10.2257i	0.968930	+	0.703969i	0.0137227	+	0.999906i	$0.495632\pi$
$212$	13.1963	+	14.6560i	0.906328	+	1.00658i
$213$	−6.99787	+	7.77192i	−0.479486	+	0.532523i
$214$	−1.90777	−	0.849396i	−0.130413	−	0.0580635i
$215$	0.884156	+	8.41218i	0.0602989	+	0.573706i
$216$	3.91050	+	12.0353i	0.266076	+	0.818898i
$217$		0			0
$218$	−22.0210	−	15.9992i	−1.49145	−	1.08360i
$219$	3.94963	−	6.84096i	0.266891	−	0.462269i
$220$	−8.15708	+	2.82738i	−0.549950	+	0.190622i
$221$	−3.71194	−	6.42928i	−0.249692	−	0.432480i
$222$	−8.41732	+	3.74763i	−0.564934	+	0.251525i
$223$	−0.832077	+	2.56087i	−0.0557200	+	0.171488i	−0.975043	−	0.222014i	$-0.928737\pi$
$223$	−0.832077	+	2.56087i	−0.0557200	+	0.171488i	0.919323	+	0.393503i	$0.128737\pi$
$224$		0			0
$225$	−4.18718	+	3.04216i	−0.279145	+	0.202811i
$226$	−2.99191	−	28.4661i	−0.199019	−	1.89354i
$227$	15.3932	−	17.0959i	1.02168	−	1.13469i	0.0308607	−	0.999524i	$-0.490175\pi$
$227$	15.3932	−	17.0959i	1.02168	−	1.13469i	0.990822	−	0.135170i	$-0.0431582\pi$
$228$	14.0791	−	2.99261i	0.932414	−	0.198191i
$229$	−16.3594	+	7.28370i	−1.08106	+	0.481320i	−0.868430	−	0.495812i	$-0.834870\pi$
$229$	−16.3594	+	7.28370i	−1.08106	+	0.481320i	−0.212633	+	0.977132i	$0.568204\pi$
$230$	3.23595			0.213372
$231$		0			0
$232$	3.44384			0.226099
$233$	−18.6946	+	8.32336i	−1.22472	+	0.545281i	−0.914192	−	0.405282i	$-0.867173\pi$
$233$	−18.6946	+	8.32336i	−1.22472	+	0.545281i	−0.310530	+	0.950563i	$0.600507\pi$
$234$	9.01117	−	1.91538i	0.589079	−	0.125213i
$235$	−7.64931	+	8.49542i	−0.498986	+	0.554180i
$236$	−4.57572	−	43.5351i	−0.297854	−	2.83389i
$237$	12.6946	−	9.22315i	0.824601	−	0.599108i
$238$		0			0
$239$	2.16824	−	6.67315i	0.140252	−	0.431650i	−0.856118	−	0.516780i	$-0.827130\pi$
$239$	2.16824	−	6.67315i	0.140252	−	0.431650i	0.996370	+	0.0851298i	$0.0271305\pi$
$240$	1.03695	−	0.461682i	0.0669351	−	0.0298014i
$241$	5.56584	+	9.64031i	0.358527	+	0.620987i	0.987715	−	0.156266i	$-0.0499458\pi$
$241$	5.56584	+	9.64031i	0.358527	+	0.620987i	−0.629188	+	0.777253i	$0.716612\pi$
$242$	−17.1665	−	17.6315i	−1.10350	−	1.13340i
$243$	5.86777	−	10.1633i	0.376418	−	0.651975i
$244$	14.0898	+	10.2368i	0.902006	+	0.655346i
$245$		0			0
$246$	0.606861	+	1.86773i	0.0386920	+	0.119082i
$247$	−1.26829	−	12.0670i	−0.0806993	−	0.767802i
$248$	18.2255	+	8.11453i	1.15732	+	0.515273i
$249$	−0.503423	+	0.559108i	−0.0319031	+	0.0354320i
$250$	−11.9949	−	13.3217i	−0.758627	−	0.842540i
$251$	8.56766	+	6.22477i	0.540786	+	0.392904i	0.824377	−	0.566041i	$-0.191526\pi$
$251$	8.56766	+	6.22477i	0.540786	+	0.392904i	−0.283591	+	0.958945i	$0.591526\pi$
$252$		0			0
$253$	2.35059	+	5.01405i	0.147780	+	0.315230i
$254$	−2.48183	+	4.29866i	−0.155724	+	0.269722i
$255$	0.265429	−	2.52539i	0.0166218	−	0.158146i
$256$	8.93898	−	1.90004i	0.558687	−	0.118752i
$257$	0.588165	+	0.125018i	0.0366887	+	0.00779843i	0.226219	−	0.974076i	$-0.427363\pi$
$257$	0.588165	+	0.125018i	0.0366887	+	0.00779843i	−0.189531	+	0.981875i	$0.560697\pi$
$258$	−23.5892	+	17.1385i	−1.46860	+	1.06700i
$259$		0			0
$260$	2.71969	+	8.37034i	0.168668	+	0.519106i
$261$	−1.24880	−	1.38694i	−0.0772989	−	0.0858492i
$262$	0.296221	−	2.81835i	0.0183006	−	0.174119i
$263$	8.60688	+	14.9076i	0.530723	+	0.919240i	0.999357	+	0.0358472i	$0.0114130\pi$
$263$	8.60688	+	14.9076i	0.530723	+	0.919240i	−0.468634	+	0.883392i	$0.655254\pi$
$264$	−7.52308	−	6.51275i	−0.463013	−	0.400832i
$265$	5.68640			0.349313
$266$		0			0
$267$	1.45290	−	4.47156i	0.0889159	−	0.273655i
$268$	−15.5288	−	3.30075i	−0.948572	−	0.201625i
$269$	−19.0273	−	8.47152i	−1.16012	−	0.516517i	−0.265834	−	0.964019i	$-0.585647\pi$
$269$	−19.0273	−	8.47152i	−1.16012	−	0.516517i	−0.894283	+	0.447501i	$0.852314\pi$
$270$	9.96924	+	4.43859i	0.606709	+	0.270124i
$271$	−22.7170	−	4.82865i	−1.37996	−	0.293320i	−0.542610	−	0.839985i	$-0.682564\pi$
$271$	−22.7170	−	4.82865i	−1.37996	−	0.293320i	−0.837351	+	0.546665i	$0.815897\pi$
$272$	−0.665942	+	2.04956i	−0.0403787	+	0.124273i
$273$		0			0
$274$	14.5923			0.881556
$275$	5.48037	−	12.9847i	0.330479	−	0.783009i
$276$	3.34851	+	5.79979i	0.201557	+	0.349106i
$277$	−0.828505	+	7.88270i	−0.0497800	+	0.473625i	0.941026	+	0.338335i	$0.109864\pi$
$277$	−0.828505	+	7.88270i	−0.0497800	+	0.473625i	−0.990806	+	0.135291i	$0.956803\pi$
$278$	21.2804	+	23.6342i	1.27631	+	1.41749i
$279$	−3.34097	−	10.2825i	−0.200019	−	0.615594i
$280$		0			0
$281$	−7.85059	+	5.70379i	−0.468327	+	0.340260i	−0.796789	−	0.604258i	$-0.793470\pi$
$281$	−7.85059	+	5.70379i	−0.468327	+	0.340260i	0.328462	+	0.944517i	$0.393470\pi$
$282$	−38.5457	−	8.19315i	−2.29537	−	0.487895i
$283$	12.2682	−	2.60768i	0.729266	−	0.155010i	0.171708	−	0.985148i	$-0.445072\pi$
$283$	12.2682	−	2.60768i	0.729266	−	0.155010i	0.557558	+	0.830138i	$0.311738\pi$
$284$	−2.46048	+	23.4099i	−0.146002	+	1.38912i
$285$	2.07509	−	3.59416i	0.122918	−	0.212900i
$286$	−18.3122	+	17.1466i	−1.08283	+	1.01390i
$287$		0			0
$288$	−6.59250	−	4.78973i	−0.388467	−	0.282238i
$289$	−8.14933	−	9.05074i	−0.479372	−	0.532397i
$290$	1.98717	−	2.20698i	0.116691	−	0.129598i
$291$	−16.9683	−	7.55478i	−0.994700	−	0.442869i
$292$	−1.85845	−	17.6820i	−0.108758	−	1.03476i
$293$	2.05861	+	6.33575i	0.120265	+	0.370138i	0.993009	−	0.118041i	$-0.0376613\pi$
$293$	2.05861	+	6.33575i	0.120265	+	0.370138i	−0.872744	+	0.488179i	$0.837661\pi$
$294$		0			0
$295$	−10.2112	−	7.41889i	−0.594521	−	0.431945i
$296$	−3.46702	+	6.00506i	−0.201517	+	0.349037i
$297$	0.364110	+	18.6713i	0.0211278	+	1.08342i
$298$	−4.11194	−	7.12209i	−0.238198	−	0.412572i
$299$	5.15732	−	2.29619i	0.298255	−	0.132792i
$300$	5.26704	−	16.2103i	0.304093	−	0.935901i
$301$		0			0
$302$	16.0126	−	11.6338i	0.921422	−	0.669453i
$303$	1.69371	+	16.1146i	0.0973010	+	0.925757i
$304$	−2.35677	+	2.61746i	−0.135170	+	0.150121i
$305$	4.91186	−	1.04405i	0.281252	−	0.0597820i
$306$	−5.46531	+	2.43331i	−0.312431	+	0.139103i
$307$	2.06252			0.117714			0.0588572	−	0.998266i	$-0.481254\pi$
$307$	2.06252			0.117714			0.0588572	+	0.998266i	$0.481254\pi$
$308$		0			0
$309$	3.84586			0.218784
$310$	15.7167	−	6.99753i	0.892650	−	0.397433i
$311$	3.46666	−	0.736862i	0.196576	−	0.0417836i	−0.108571	−	0.994089i	$-0.534628\pi$
$311$	3.46666	−	0.736862i	0.196576	−	0.0417836i	0.305148	+	0.952305i	$0.401294\pi$
$312$	−6.78768	+	7.53848i	−0.384277	+	0.426783i
$313$	−1.62599	−	15.4702i	−0.0919063	−	0.874430i	−0.939215	−	0.343329i	$-0.888445\pi$
$313$	−1.62599	−	15.4702i	−0.0919063	−	0.874430i	0.847309	−	0.531101i	$-0.178221\pi$
$314$	4.17474	−	3.03313i	0.235594	−	0.171169i
$315$		0			0
$316$	10.9137	−	33.5890i	0.613945	−	1.88953i
$317$	−15.1841	+	6.76041i	−0.852826	+	0.379702i	−0.786123	−	0.618071i	$-0.787915\pi$
$317$	−15.1841	+	6.76041i	−0.852826	+	0.379702i	−0.0667028	+	0.997773i	$0.521248\pi$
$318$	9.80095	+	16.9757i	0.549610	+	0.951953i
$319$	4.86314	+	1.47594i	0.272284	+	0.0826369i
$320$	5.63312	−	9.75685i	0.314901	−	0.545425i
$321$	−1.00816	−	0.732470i	−0.0562699	−	0.0408825i
$322$		0			0
$323$	2.43486	+	7.49372i	0.135479	+	0.416962i
$324$	1.21317	+	11.5425i	0.0673982	+	0.641251i
$325$	−13.1258	−	5.84399i	−0.728090	−	0.324166i
$326$	−8.58052	+	9.52963i	−0.475231	+	0.527797i
$327$	−10.8684	−	12.0706i	−0.601023	−	0.667504i
$328$	1.19566	+	0.868697i	0.0660192	+	0.0479658i
$329$		0			0
$330$	−8.51467	+	1.06315i	−0.468717	+	0.0585246i
$331$	−10.5203	+	18.2217i	−0.578249	+	1.00156i	0.417431	+	0.908709i	$0.362930\pi$
$331$	−10.5203	+	18.2217i	−0.578249	+	1.00156i	−0.995680	+	0.0928482i	$0.970403\pi$
$332$	−0.177005	+	1.68409i	−0.00971444	+	0.0924267i
$333$	3.67563	−	0.781280i	0.201423	−	0.0428139i
$334$	7.05559	+	1.49971i	0.386065	+	0.0820606i
$335$	−3.70328	+	2.69059i	−0.202332	+	0.147002i
$336$		0			0
$337$	−9.35330	−	28.7865i	−0.509507	−	1.56810i	−0.793060	−	0.609144i	$-0.791513\pi$
$337$	−9.35330	−	28.7865i	−0.509507	−	1.56810i	0.283553	−	0.958957i	$-0.408487\pi$
$338$	−2.34710	−	2.60672i	−0.127665	−	0.141787i
$339$	1.78535	−	16.9865i	0.0969668	−	0.922577i
$340$	−2.85769	−	4.94966i	−0.154980	−	0.268433i
$341$	22.2591	+	19.2698i	1.20540	+	1.04352i
$342$	−9.77770			−0.528717
$343$		0			0
$344$	−6.78079	+	20.8691i	−0.365596	+	1.12519i
$345$	1.88878	+	0.401472i	0.101688	+	0.0216145i
$346$	17.1678	+	7.64361i	0.922949	+	0.410923i
$347$	23.9532	+	10.6647i	1.28588	+	0.572509i	0.931890	−	0.362741i	$-0.118159\pi$
$347$	23.9532	+	10.6647i	1.28588	+	0.572509i	0.353987	+	0.935251i	$0.384826\pi$
$348$	6.01185	+	1.27786i	0.322269	+	0.0685004i
$349$	3.29993	−	10.1562i	0.176641	−	0.543646i	−0.823063	−	0.567950i	$-0.807737\pi$
$349$	3.29993	−	10.1562i	0.176641	−	0.543646i	0.999705	+	0.0243034i	$0.00773676\pi$
$350$		0			0
$351$	19.0381			1.01618
$352$	22.1096	+	1.88878i	1.17845	+	0.100672i
$353$	1.94930	+	3.37628i	0.103751	+	0.179701i	0.913227	−	0.407451i	$-0.133582\pi$
$353$	1.94930	+	3.37628i	0.103751	+	0.179701i	−0.809476	+	0.587152i	$0.800249\pi$
$354$	4.54795	−	43.2708i	0.241721	−	2.29982i
$355$	4.54141	+	5.04375i	0.241033	+	0.267694i
$356$	−3.27013	−	10.0644i	−0.173317	−	0.533413i
$357$		0			0
$358$	4.64742	−	3.37655i	0.245624	−	0.178456i
$359$	20.8679	+	4.43560i	1.10136	+	0.234102i	0.722514	−	0.691356i	$-0.242986\pi$
$359$	20.8679	+	4.43560i	1.10136	+	0.234102i	0.378850	+	0.925458i	$0.376320\pi$
$360$	2.31957	−	0.493040i	0.122252	−	0.0259855i
$361$	0.639939	−	6.08861i	0.0336810	−	0.320453i
$362$	1.98359	−	3.43568i	0.104255	−	0.180575i
$363$	−7.83236	−	12.4210i	−0.411092	−	0.651936i
$364$		0			0
$365$	−4.14733	−	3.01321i	−0.217081	−	0.157719i
$366$	11.5828	+	12.8640i	0.605442	+	0.672412i
$367$	−0.393460	+	0.436981i	−0.0205384	+	0.0228102i	−0.753327	−	0.657647i	$-0.771552\pi$
$367$	−0.393460	+	0.436981i	−0.0205384	+	0.0228102i	0.732788	+	0.680457i	$0.238219\pi$
$368$	−1.49708	−	0.666545i	−0.0780409	−	0.0347461i
$369$	−0.0837192	−	0.796535i	−0.00435825	−	0.0414659i
$370$	1.84778	+	5.68689i	0.0960617	+	0.295648i
$371$		0			0
$372$	28.8051	+	20.9281i	1.49347	+	1.08507i
$373$	6.65785	−	11.5317i	0.344730	−	0.597090i	−0.640575	−	0.767896i	$-0.721304\pi$
$373$	6.65785	−	11.5317i	0.344730	−	0.597090i	0.985305	+	0.170806i	$0.0546371\pi$
$374$	9.31690	−	13.3640i	0.481766	−	0.691036i
$375$	−5.34850	−	9.26387i	−0.276195	−	0.478384i
$376$	−27.0923	+	12.0623i	−1.39718	+	0.622063i
$377$	1.60102	−	4.92744i	0.0824569	−	0.253776i
$378$		0			0
$379$	−7.03443	+	5.11081i	−0.361334	+	0.262525i	−0.753608	−	0.657324i	$-0.771689\pi$
$379$	−7.03443	+	5.11081i	−0.361334	+	0.262525i	0.392274	+	0.919848i	$0.371689\pi$
$380$	−0.976408	−	9.28990i	−0.0500887	−	0.476562i
$381$	−1.98193	+	2.20115i	−0.101537	+	0.112768i
$382$	18.1203	−	3.85159i	0.927115	−	0.197064i
$383$	−28.1944	+	12.5529i	−1.44067	+	0.641426i	−0.970489	−	0.241147i	$-0.922477\pi$
$383$	−28.1944	+	12.5529i	−1.44067	+	0.641426i	−0.470177	+	0.882572i	$0.655810\pi$
$384$	20.9735			1.07030
$385$		0			0
$386$	−42.5627			−2.16638
$387$	10.8635	−	4.83673i	0.552222	−	0.245865i
$388$	−40.8924	+	8.69195i	−2.07600	+	0.441267i
$389$	3.43117	−	3.81070i	0.173967	−	0.193210i	−0.649856	−	0.760058i	$-0.725171\pi$
$389$	3.43117	−	3.81070i	0.173967	−	0.193210i	0.823822	+	0.566848i	$0.191837\pi$
$390$	0.914381	+	8.69975i	0.0463015	+	0.440529i
$391$	−2.96592	+	2.15486i	−0.149993	+	0.108976i
$392$		0			0
$393$	0.522562	−	1.60828i	0.0263598	−	0.0811270i
$394$	31.0297	−	13.8153i	1.56325	−	0.696005i
$395$	−5.09161	−	8.81894i	−0.256187	−	0.443729i
$396$	7.32411	+	9.67818i	0.368050	+	0.486347i
$397$	−14.6266	+	25.3340i	−0.734088	+	1.27148i	0.221034	+	0.975266i	$0.429057\pi$
$397$	−14.6266	+	25.3340i	−0.734088	+	1.27148i	−0.955122	+	0.296212i	$0.904277\pi$
$398$	−44.5307	−	32.3534i	−2.23212	−	1.62173i
$399$		0			0
$400$	1.28885	+	3.96666i	0.0644423	+	0.198333i
$401$	−1.51804	−	14.4432i	−0.0758075	−	0.721260i	−0.964737	−	0.263216i	$-0.915217\pi$
$401$	−1.51804	−	14.4432i	−0.0758075	−	0.721260i	0.888929	−	0.458044i	$-0.151450\pi$
$402$	−14.4152	−	6.41804i	−0.718962	−	0.320103i
$403$	20.0832	−	22.3047i	1.00042	−	1.11108i
$404$	24.4031	+	27.1024i	1.21410	+	1.34839i
$405$	2.70732	+	1.96698i	0.134528	+	0.0977401i
$406$		0			0
$407$	−7.46951	+	6.99405i	−0.370250	+	0.346682i
$408$	3.29373	−	5.70491i	0.163064	−	0.282435i
$409$	1.24752	−	11.8694i	0.0616860	−	0.586903i	−0.919399	−	0.393326i	$-0.871324\pi$
$409$	1.24752	−	11.8694i	0.0616860	−	0.586903i	0.981085	−	0.193577i	$-0.0620090\pi$
$410$	1.24663	−	0.264978i	0.0615665	−	0.0130864i
$411$	8.51734	+	1.81042i	0.420129	+	0.0893012i
$412$	7.00296	−	5.08795i	0.345011	−	0.250665i
$413$		0			0
$414$	−1.40582	−	4.32666i	−0.0690922	−	0.212644i
$415$	0.326707	+	0.362844i	0.0160374	+	0.0178113i
$416$	2.36461	−	22.4978i	0.115935	−	1.10304i
$417$	9.48883	+	16.4351i	0.464670	+	0.804832i
$418$	22.7947	−	13.7600i	1.11493	−	0.673023i
$419$	15.3521			0.749999			0.374999	−	0.927025i	$-0.377643\pi$
$419$	15.3521			0.749999			0.374999	+	0.927025i	$0.377643\pi$
$420$		0			0
$421$	−2.34650	+	7.22177i	−0.114361	+	0.351968i	−0.991813	−	0.127697i	$-0.959242\pi$
$421$	−2.34650	+	7.22177i	−0.114361	+	0.351968i	0.877452	+	0.479664i	$0.159242\pi$
$422$	38.0685	+	8.09172i	1.85315	+	0.393899i
$423$	14.6820	+	6.53686i	0.713864	+	0.317833i
$424$	13.4763	+	6.00005i	0.654468	+	0.291388i
$425$	9.12659	+	1.93992i	0.442705	+	0.0940998i
$426$	−7.22974	+	22.2509i	−0.350282	+	1.07806i
$427$		0			0
$428$	−2.80480			−0.135575
$429$	−12.8159	+	7.73628i	−0.618757	+	0.373511i
$430$	9.46128	+	16.3874i	0.456264	+	0.790272i
$431$	−2.75406	+	26.2031i	−0.132658	+	1.26216i	0.702314	+	0.711867i	$0.252150\pi$
$431$	−2.75406	+	26.2031i	−0.132658	+	1.26216i	−0.834972	+	0.550292i	$0.814516\pi$
$432$	−3.69791	−	4.10695i	−0.177916	−	0.197596i
$433$	−2.29633	−	7.06737i	−0.110354	−	0.339636i	0.880595	−	0.473869i	$-0.157143\pi$
$433$	−2.29633	−	7.06737i	−0.110354	−	0.339636i	−0.990950	+	0.134233i	$0.957143\pi$
$434$		0			0
$435$	1.43369	−	1.04164i	0.0687403	−	0.0499428i
$436$	−35.7593	−	7.60086i	−1.71256	−	0.364015i
$437$	−5.86081	+	1.24575i	−0.280361	+	0.0595925i
$438$	1.84717	−	17.5746i	0.0882611	−	0.839748i
$439$	9.49372	−	16.4436i	0.453111	−	0.784811i	−0.545467	−	0.838133i	$-0.683648\pi$
$439$	9.49372	−	16.4436i	0.453111	−	0.784811i	0.998577	+	0.0533218i	$0.0169809\pi$
$440$	−4.71376	+	4.41371i	−0.224720	+	0.210415i
$441$		0			0
$442$	−13.4361	−	9.76193i	−0.639092	−	0.464328i
$443$	−3.49964	−	3.88675i	−0.166273	−	0.184665i	0.654250	−	0.756278i	$-0.272984\pi$
$443$	−3.49964	−	3.88675i	−0.166273	−	0.184665i	−0.820523	+	0.571613i	$0.806318\pi$
$444$	−8.28055	+	9.19648i	−0.392977	+	0.436446i
$445$	−2.78745	−	1.24105i	−0.132138	−	0.0588316i
$446$	0.629653	+	5.99075i	0.0298149	+	0.283670i
$447$	−1.51647	−	4.66721i	−0.0717265	−	0.220752i
$448$		0			0
$449$	11.4942	+	8.35101i	0.542444	+	0.394109i	0.824992	−	0.565145i	$-0.191180\pi$
$449$	11.4942	+	8.35101i	0.542444	+	0.394109i	−0.282548	+	0.959253i	$0.591180\pi$
$450$	−5.78921	+	10.0272i	−0.272906	+	0.472687i
$451$	1.31612	+	1.73914i	0.0619738	+	0.0818930i
$452$	−19.2215	−	33.2927i	−0.904106	−	1.56596i
$453$	10.7897	−	4.80388i	0.506944	−	0.225706i
$454$	15.9033	−	48.9452i	0.746377	−	2.29711i
$455$		0			0
$456$	8.71020	−	6.32833i	0.407892	−	0.296351i
$457$	3.26591	+	31.0730i	0.152773	+	1.45353i	0.755270	+	0.655414i	$0.227506\pi$
$457$	3.26591	+	31.0730i	0.152773	+	1.45353i	−0.602497	+	0.798121i	$0.705828\pi$
$458$	−26.8062	+	29.7713i	−1.25257	+	1.39112i
$459$	−12.0930	+	2.57045i	−0.564455	+	0.119979i
$460$	3.97042	−	1.76775i	0.185122	−	0.0824216i
$461$	24.4883			1.14053			0.570266	−	0.821460i	$-0.306840\pi$
$461$	24.4883			1.14053			0.570266	+	0.821460i	$0.306840\pi$
$462$		0			0
$463$	−4.68038			−0.217516			−0.108758	−	0.994068i	$-0.534687\pi$
$463$	−4.68038			−0.217516			−0.108758	+	0.994068i	$0.534687\pi$
$464$	−1.37394	+	0.611718i	−0.0637836	+	0.0283983i
$465$	10.0418	−	2.13444i	0.465676	−	0.0989825i
$466$	−30.6325	+	34.0208i	−1.41902	+	1.57598i
$467$	3.65829	+	34.8063i	0.169286	+	1.61065i	0.668192	+	0.743989i	$0.267069\pi$
$467$	3.65829	+	34.8063i	0.169286	+	1.61065i	−0.498906	+	0.866656i	$0.666265\pi$
$468$	10.0101	−	7.27277i	0.462717	−	0.336184i
$469$		0			0
$470$	−7.90277	+	24.3222i	−0.364528	+	1.12190i
$471$	2.81304	−	1.25245i	0.129618	−	0.0577097i
$472$	−16.3717	−	28.3566i	−0.753569	−	1.30522i
$473$	−18.5193	+	26.5638i	−0.851521	+	1.22141i
$474$	17.5516	−	30.4002i	0.806171	−	1.39633i
$475$	12.3371	+	8.96344i	0.566066	+	0.411271i
$476$		0			0
$477$	−2.47038	−	7.60306i	−0.113111	−	0.348120i
$478$	−1.64076	−	15.6108i	−0.0750466	−	0.714021i
$479$	38.8676	+	17.3050i	1.77591	+	0.790684i	0.983552	+	0.180623i	$0.0578113\pi$
$479$	38.8676	+	17.3050i	1.77591	+	0.790684i	0.792354	+	0.610062i	$0.208855\pi$
$480$	5.17749	−	5.75018i	0.236319	−	0.262459i
$481$	6.98025	+	7.75235i	0.318272	+	0.353477i
$482$	20.1467	+	14.6374i	0.917657	+	0.666717i
$483$		0			0
$484$	−30.6946	−	12.2556i	−1.39521	−	0.557073i
$485$	−6.02703	+	10.4391i	−0.273673	+	0.474016i
$486$	2.74425	−	26.1098i	0.124482	−	1.18436i
$487$	20.4533	−	4.34749i	0.926828	−	0.197003i	0.280317	−	0.959908i	$-0.409561\pi$
$487$	20.4533	−	4.34749i	0.926828	−	0.197003i	0.646512	+	0.762904i	$0.276227\pi$
$488$	12.7424	+	2.70847i	0.576819	+	0.122607i
$489$	−6.19062	+	4.49775i	−0.279950	+	0.203395i
$490$		0			0
$491$	3.71603	+	11.4368i	0.167702	+	0.516134i	0.999225	−	0.0393561i	$-0.0125307\pi$
$491$	3.71603	+	11.4368i	0.167702	+	0.516134i	−0.831523	+	0.555490i	$0.812531\pi$
$492$	1.76491	+	1.96013i	0.0795682	+	0.0883694i
$493$	−0.351688	+	3.34609i	−0.0158392	+	0.150700i
$494$	−13.5719	−	23.5071i	−0.610627	−	1.05764i
$495$	3.48684	+	0.297874i	0.156722	+	0.0133884i
$496$	−8.71256			−0.391205
$497$		0			0
$498$	−0.520104	+	1.60072i	−0.0233064	+	0.0717298i
$499$	−19.7300	−	4.19373i	−0.883234	−	0.187737i	−0.256102	−	0.966650i	$-0.582438\pi$
$499$	−19.7300	−	4.19373i	−0.883234	−	0.187737i	−0.627132	+	0.778913i	$0.715772\pi$
$500$	−21.9949	−	9.79276i	−0.983641	−	0.437945i
$501$	3.93218	+	1.75072i	0.175677	+	0.0782164i
$502$	23.1737	+	4.92571i	1.03429	+	0.219845i
$503$	−1.03536	+	3.18651i	−0.0461644	+	0.142079i	−0.971482	−	0.237114i	$-0.923798\pi$
$503$	−1.03536	+	3.18651i	−0.0461644	+	0.142079i	0.925317	+	0.379193i	$0.123798\pi$
$504$		0			0
$505$	10.5155			0.467932
$506$	9.36622	+	8.10835i	0.416379	+	0.360460i
$507$	−1.04656	−	1.81270i	−0.0464795	−	0.0805048i
$508$	−0.696853	+	6.63012i	−0.0309179	+	0.294164i
$509$	−19.5478	−	21.7100i	−0.866440	−	0.962279i	0.133144	−	0.991097i	$-0.457493\pi$
$509$	−19.5478	−	21.7100i	−0.866440	−	0.962279i	−0.999585	+	0.0288172i	$0.990826\pi$
$510$	−1.75543	−	5.40265i	−0.0777316	−	0.239233i
$511$		0			0
$512$	−8.88170	+	6.45293i	−0.392519	+	0.285182i
$513$	−19.7646	−	4.20109i	−0.872627	−	0.185483i
$514$	1.31578	−	0.279679i	0.0580368	−	0.0123361i
$515$	0.260888	−	2.48218i	0.0114961	−	0.109378i
$516$	−19.5808	+	33.9149i	−0.861995	+	1.49302i
$517$	−43.4274	+	5.42239i	−1.90993	+	0.238476i
$518$		0			0
$519$	9.07230	+	6.59141i	0.398230	+	0.289331i
$520$	4.40501	+	4.89225i	0.193172	+	0.214540i
$521$	−25.4302	+	28.2431i	−1.11412	+	1.23735i	−0.145351	+	0.989380i	$0.546431\pi$
$521$	−25.4302	+	28.2431i	−1.11412	+	1.23735i	−0.968767	+	0.247973i	$0.920235\pi$
$522$	−3.81416	−	1.69817i	−0.166941	−	0.0743270i
$523$	0.0630228	+	0.599622i	0.00275579	+	0.0262196i	0.995813	−	0.0914096i	$-0.0291372\pi$
$523$	0.0630228	+	0.599622i	0.00275579	+	0.0262196i	−0.993058	+	0.117629i	$0.962471\pi$
$524$	−1.17616	−	3.61986i	−0.0513810	−	0.158134i
$525$		0			0
$526$	31.1544	+	22.6350i	1.35840	+	0.986932i
$527$	−9.74542	+	16.8796i	−0.424517	+	0.735286i
$528$	4.15822	+	1.26200i	0.180963	+	0.0549216i
$529$	10.1061	+	17.5043i	0.439395	+	0.761055i
$530$	11.6213	−	5.17412i	0.504795	−	0.224749i
$531$	−5.48336	+	16.8761i	−0.237958	+	0.732359i
$532$		0			0
$533$	1.79879	−	1.30690i	0.0779143	−	0.0566080i
$534$	−1.09944	−	10.4605i	−0.0475776	−	0.452670i
$535$	−0.541137	+	0.600993i	−0.0233954	+	0.0259832i
$536$	−11.6155	+	2.46894i	−0.501712	+	0.106642i
$537$	3.13154	−	1.39425i	0.135136	−	0.0601665i
$538$	−46.5944			−2.00883
$539$		0			0
$540$	14.6567			0.630724
$541$	−5.74408	+	2.55743i	−0.246957	+	0.109952i	−0.526483	−	0.850186i	$-0.676489\pi$
$541$	−5.74408	+	2.55743i	−0.246957	+	0.109952i	0.279526	+	0.960138i	$0.409823\pi$
$542$	−50.8203	+	10.8022i	−2.18292	+	0.463994i
$543$	1.58404	−	1.75926i	0.0679778	−	0.0754970i
$544$	1.53556	+	14.6099i	0.0658367	+	0.626394i
$545$	−8.52779	+	6.19580i	−0.365291	+	0.265399i
$546$		0			0
$547$	0.941825	−	2.89864i	0.0402695	−	0.123937i	−0.928901	−	0.370329i	$-0.879245\pi$
$547$	0.941825	−	2.89864i	0.0402695	−	0.123937i	0.969170	+	0.246392i	$0.0792450\pi$
$548$	17.9044	−	7.97155i	0.764838	−	0.340528i
$549$	−3.52985	−	6.11388i	−0.150650	−	0.260934i
$550$	−0.614740	−	31.5235i	−0.0262126	−	1.34416i
$551$	−2.74945	+	4.76218i	−0.117130	+	0.202876i
$552$	4.05264	+	2.94442i	0.172492	+	0.125323i
$553$		0			0
$554$	5.47934	+	16.8637i	0.232795	+	0.716469i
$555$	0.372973	+	3.54860i	0.0158318	+	0.150630i
$556$	39.0214	+	17.3734i	1.65488	+	0.736798i
$557$	−22.7399	+	25.2552i	−0.963521	+	1.07010i	0.0339782	+	0.999423i	$0.489182\pi$
$557$	−22.7399	+	25.2552i	−0.963521	+	1.07010i	−0.997499	+	0.0706761i	$0.977484\pi$
$558$	−16.1840	−	17.9742i	−0.685125	−	0.760909i
$559$	26.7072	+	19.4039i	1.12960	+	0.820699i
$560$		0			0
$561$	7.09616	−	6.64446i	0.299600	−	0.280529i
$562$	−10.8543	+	18.8001i	−0.457860	+	0.793036i
$563$	−4.40357	+	41.8972i	−0.185588	+	1.76575i	0.365029	+	0.930996i	$0.381059\pi$
$563$	−4.40357	+	41.8972i	−0.185588	+	1.76575i	−0.550617	+	0.834758i	$0.685607\pi$
$564$	−51.7703	+	11.0041i	−2.17992	+	0.463357i
$565$	−10.8422	−	2.30458i	−0.456135	−	0.0969545i
$566$	22.6996	−	16.4922i	0.954135	−	0.693220i
$567$		0			0
$568$	5.44084	+	16.7452i	0.228293	+	0.702612i
$569$	14.9611	+	16.6160i	0.627201	+	0.696578i	0.970075	−	0.242804i	$-0.0780671\pi$
$569$	14.9611	+	16.6160i	0.627201	+	0.696578i	−0.342874	+	0.939381i	$0.611400\pi$
$570$	0.970481	−	9.23351i	0.0406490	−	0.386749i
$571$	−9.49191	−	16.4405i	−0.397224	−	0.688012i	0.596158	−	0.802867i	$-0.296693\pi$
$571$	−9.49191	−	16.4405i	−0.397224	−	0.688012i	−0.993382	+	0.114855i	$0.963360\pi$
$572$	−13.1017	+	31.0420i	−0.547810	+	1.29793i
$573$	11.0544			0.461804
$574$		0			0
$575$	−2.19255	+	6.74796i	−0.0914355	+	0.281409i
$576$	−15.4927	−	3.29308i	−0.645530	−	0.137212i
$577$	−25.2676	−	11.2499i	−1.05190	−	0.468338i	−0.193387	−	0.981122i	$-0.561947\pi$
$577$	−25.2676	−	11.2499i	−1.05190	−	0.468338i	−0.858518	+	0.512784i	$0.828614\pi$
$578$	−24.8901	−	11.0818i	−1.03529	−	0.460942i
$579$	−24.8432	−	5.28059i	−1.03245	−	0.219454i
$580$	1.23257	−	3.79345i	0.0511796	−	0.157515i
$581$		0			0
$582$	−41.5522			−1.72239
$583$	16.4588	+	14.2485i	0.681656	+	0.590111i
$584$	−6.64944	−	11.5172i	−0.275156	−	0.476584i
$585$	0.372916	−	3.54806i	0.0154182	−	0.146694i
$586$	9.97213	+	11.0752i	0.411945	+	0.457511i
$587$	6.84645	+	21.0712i	0.282583	+	0.869701i	0.987113	+	0.160027i	$0.0511581\pi$
$587$	6.84645	+	21.0712i	0.282583	+	0.869701i	−0.704530	+	0.709675i	$0.748842\pi$
$588$		0			0
$589$	−25.7715	+	18.7241i	−1.06190	+	0.771514i
$590$	−27.6192	−	5.87063i	−1.13706	−	0.241690i
$591$	19.8256	−	4.21406i	0.815515	−	0.173343i
$592$	0.316532	−	3.01160i	0.0130094	−	0.123776i
$593$	−6.11706	+	10.5951i	−0.251198	+	0.435087i	−0.963856	−	0.266424i	$-0.914158\pi$
$593$	−6.11706	+	10.5951i	−0.251198	+	0.435087i	0.712658	+	0.701511i	$0.247491\pi$
$594$	17.7334	+	37.8272i	0.727609	+	1.55207i
$595$		0			0
$596$	−8.93591	−	6.49232i	−0.366029	−	0.265936i
$597$	−21.9779	−	24.4090i	−0.899497	−	0.998993i
$598$	8.45065	−	9.38540i	0.345573	−	0.383798i
$599$	−6.98887	−	3.11165i	−0.285558	−	0.127138i	0.258959	−	0.965888i	$-0.416620\pi$
$599$	−6.98887	−	3.11165i	−0.285558	−	0.127138i	−0.544517	+	0.838750i	$0.683287\pi$
$600$	−1.33266	−	12.6794i	−0.0544054	−	0.517633i
$601$	0.852504	+	2.62374i	0.0347744	+	0.107025i	0.966937	−	0.255015i	$-0.0820805\pi$
$601$	0.852504	+	2.62374i	0.0347744	+	0.107025i	−0.932163	+	0.362040i	$0.882080\pi$
$602$		0			0
$603$	5.20631	+	3.78261i	0.212017	+	0.154040i
$604$	13.2917	−	23.0218i	0.540830	−	0.936744i
$605$	−8.54805	+	4.21253i	−0.347527	+	0.171264i
$606$	18.1242	+	31.3921i	0.736247	+	1.27522i
$607$	−2.71592	+	1.20921i	−0.110236	+	0.0490802i	−0.461114	−	0.887341i	$-0.652550\pi$
$607$	−2.71592	+	1.20921i	−0.110236	+	0.0490802i	0.350878	+	0.936421i	$0.385883\pi$
$608$	−7.41938	+	22.8345i	−0.300895	+	0.926061i
$609$		0			0
$610$	9.08835	−	6.60307i	0.367976	−	0.267351i
$611$	4.66362	+	44.3713i	0.188670	+	1.79507i
$612$	−5.37650	+	5.97121i	−0.217332	+	0.241372i
$613$	14.2952	−	3.03853i	0.577376	−	0.122725i	0.0900377	−	0.995938i	$-0.471301\pi$
$613$	14.2952	−	3.03853i	0.577376	−	0.122725i	0.487338	+	0.873213i	$0.337968\pi$
$614$	4.21517	−	1.87671i	0.170110	−	0.0757380i
$615$	0.760512			0.0306668
$616$		0			0
$617$	−8.43040			−0.339395			−0.169697	−	0.985496i	$-0.554279\pi$
$617$	−8.43040			−0.339395			−0.169697	+	0.985496i	$0.554279\pi$
$618$	7.85977	−	3.49940i	0.316166	−	0.140766i
$619$	43.4276	−	9.23083i	1.74550	−	0.371018i	0.778871	−	0.627184i	$-0.215793\pi$
$619$	43.4276	−	9.23083i	1.74550	−	0.371018i	0.966633	+	0.256166i	$0.0824593\pi$
$620$	15.4613	−	17.1715i	0.620942	−	0.689626i
$621$	−0.982715	−	9.34991i	−0.0394350	−	0.375199i
$622$	6.41432	−	4.66028i	0.257191	−	0.186860i
$623$		0			0
$624$	1.36895	−	4.21321i	0.0548020	−	0.168663i
$625$	13.0685	−	5.81849i	0.522742	−	0.232740i
$626$	−17.3996	−	30.1369i	−0.695427	−	1.20451i
$627$	15.0121	−	5.20345i	0.599525	−	0.207806i
$628$	3.46534	−	6.00215i	0.138282	−	0.239512i
$629$	−5.48057	−	3.98186i	−0.218524	−	0.158767i
$630$		0			0
$631$	−12.0351	−	37.0403i	−0.479110	−	1.47455i	−0.840333	−	0.542070i	$-0.817641\pi$
$631$	−12.0351	−	37.0403i	−0.479110	−	1.47455i	0.361223	−	0.932479i	$-0.382359\pi$
$632$	−2.76137	−	26.2726i	−0.109841	−	1.04507i
$633$	21.2161	+	9.44603i	0.843266	+	0.375446i
$634$	−24.8803	+	27.6324i	−0.988124	+	1.09742i
$635$	1.28621	+	1.42848i	0.0510418	+	0.0566876i
$636$	21.2990	+	15.4747i	0.844562	+	0.613610i
$637$		0			0
$638$	11.2817	−	1.40865i	0.446649	−	0.0557691i
$639$	4.77083	−	8.26332i	0.188731	−	0.326892i
$640$	1.42276	−	13.5366i	0.0562394	−	0.535083i
$641$	11.1353	−	2.36687i	0.439816	−	0.0934859i	0.0173191	−	0.999850i	$-0.494487\pi$
$641$	11.1353	−	2.36687i	0.439816	−	0.0934859i	0.422497	+	0.906364i	$0.361154\pi$
$642$	−2.72685	−	0.579610i	−0.107620	−	0.0228754i
$643$	15.4231	−	11.2055i	0.608227	−	0.441903i	−0.240563	−	0.970634i	$-0.577332\pi$
$643$	15.4231	−	11.2055i	0.608227	−	0.441903i	0.848789	+	0.528731i	$0.177332\pi$
$644$		0			0
$645$	3.48929	+	10.7389i	0.137391	+	0.422845i
$646$	11.7947	+	13.0994i	0.464057	+	0.515388i
$647$	2.88324	−	27.4322i	0.113352	−	1.07847i	−0.778967	−	0.627064i	$-0.784256\pi$
$647$	2.88324	−	27.4322i	0.113352	−	1.07847i	0.892319	−	0.451405i	$-0.149077\pi$
$648$	4.34066	+	7.51824i	0.170517	+	0.295344i
$649$	−10.9660	−	47.0597i	−0.430454	−	1.84726i
$650$	−32.1427			−1.26074
$651$		0			0
$652$	−5.32218	+	16.3800i	−0.208432	+	0.641489i
$653$	3.35565	+	0.713266i	0.131317	+	0.0279123i	0.273101	−	0.961985i	$-0.411951\pi$
$653$	3.35565	+	0.713266i	0.131317	+	0.0279123i	−0.141784	+	0.989898i	$0.545284\pi$
$654$	−33.1948	−	14.7793i	−1.29802	−	0.577915i
$655$	−1.00256	−	0.446369i	−0.0391733	−	0.0174411i
$656$	−0.631321	−	0.134191i	−0.0246489	−	0.00523929i
$657$	−2.22709	+	6.85428i	−0.0868871	+	0.267411i
$658$		0			0
$659$	12.7090			0.495073			0.247536	−	0.968879i	$-0.420379\pi$
$659$	12.7090			0.495073			0.247536	+	0.968879i	$0.420379\pi$
$660$	−9.86647	+	5.95587i	−0.384052	+	0.231832i
$661$	−1.25158	−	2.16780i	−0.0486808	−	0.0843177i	0.840658	−	0.541566i	$-0.182168\pi$
$661$	−1.25158	−	2.16780i	−0.0486808	−	0.0843177i	−0.889339	+	0.457248i	$0.848835\pi$
$662$	−4.92016	+	46.8122i	−0.191227	+	1.81941i
$663$	−6.63136	−	7.36487i	−0.257541	−	0.286028i
$664$	0.391411	+	1.20464i	0.0151897	+	0.0467491i
$665$		0			0
$666$	6.80097	−	4.94119i	0.263532	−	0.191467i
$667$	−2.50259	−	0.531942i	−0.0969007	−	0.0205969i
$668$	9.47628	−	2.01425i	0.366648	−	0.0779335i
$669$	−0.375730	+	3.57483i	−0.0145266	+	0.138211i
$670$	−5.12017	+	8.86839i	−0.197809	+	0.342616i
$671$	16.8331	+	9.28577i	0.649834	+	0.358473i
$672$		0			0
$673$	22.9659	+	16.6857i	0.885269	+	0.643185i	0.934640	−	0.355595i	$-0.115722\pi$
$673$	22.9659	+	16.6857i	0.885269	+	0.643185i	−0.0493715	+	0.998780i	$0.515722\pi$
$674$	−45.3084	−	50.3201i	−1.74522	−	1.93826i
$675$	−16.0106	+	17.7815i	−0.616247	+	0.684412i
$676$	−4.30383	−	1.91619i	−0.165532	−	0.0736996i
$677$	2.78843	+	26.5302i	0.107168	+	1.01964i	0.907492	+	0.420069i	$0.137994\pi$
$677$	2.78843	+	26.5302i	0.107168	+	1.01964i	−0.800324	+	0.599568i	$0.795339\pi$
$678$	−11.8075	−	36.3396i	−0.453463	−	1.39561i
$679$		0			0
$680$	−3.45861	−	2.51282i	−0.132631	−	0.0963624i
$681$	15.3549	−	26.5955i	0.588403	−	1.01914i
$682$	63.0246	+	19.1277i	2.41334	+	0.732437i
$683$	−2.30840	−	3.99827i	−0.0883286	−	0.152990i	0.818476	−	0.574541i	$-0.194819\pi$
$683$	−2.30840	−	3.99827i	−0.0883286	−	0.152990i	−0.906805	+	0.421551i	$0.861486\pi$
$684$	−11.9970	+	5.34139i	−0.458715	+	0.204233i
$685$	1.74625	−	5.37441i	0.0667208	−	0.205346i
$686$		0			0
$687$	−19.3400	+	14.0513i	−0.737866	+	0.536091i
$688$	−1.00168	−	9.53034i	−0.0381886	−	0.363341i
$689$	14.8500	−	16.4926i	0.565739	−	0.628316i
$690$	4.22539	−	0.898134i	0.160858	−	0.0341914i
$691$	18.6121	−	8.28665i	0.708039	−	0.315239i	−0.0209349	−	0.999781i	$-0.506664\pi$
$691$	18.6121	−	8.28665i	0.708039	−	0.315239i	0.728974	+	0.684542i	$0.239998\pi$
$692$	25.2400			0.959482
$693$		0			0
$694$	58.6570			2.22659
$695$	11.2512	−	5.00934i	0.426781	−	0.190015i
$696$	4.49683	−	0.955831i	0.170452	−	0.0362307i
$697$	−0.966143	+	1.07301i	−0.0365953	+	0.0406432i
$698$	−2.49714	−	23.7587i	−0.0945182	−	0.899281i
$699$	−22.1005	+	16.0570i	−0.835919	+	0.607331i
$700$		0			0
$701$	−13.3158	+	40.9820i	−0.502932	+	1.54787i	0.301286	+	0.953534i	$0.402584\pi$
$701$	−13.3158	+	40.9820i	−0.502932	+	1.54787i	−0.804219	+	0.594333i	$0.797416\pi$
$702$	38.9080	−	17.3230i	1.46849	−	0.653813i
$703$	−5.53592	−	9.58850i	−0.208791	−	0.361637i
$704$	40.7525	−	14.1255i	1.53592	−	0.532375i
$705$	−7.63029	+	13.2161i	−0.287373	+	0.497745i
$706$	7.05588	+	5.12640i	0.265552	+	0.192935i
$707$		0			0
$708$	−18.0579	−	55.5766i	−0.678658	−	2.08869i
$709$	2.05380	+	19.5406i	0.0771320	+	0.733862i	0.962923	+	0.269777i	$0.0869501\pi$
$709$	2.05380	+	19.5406i	0.0771320	+	0.733862i	−0.885791	+	0.464085i	$0.846383\pi$
$710$	13.8706	+	6.17559i	0.520555	+	0.231766i
$711$	−9.57946	+	10.6391i	−0.359258	+	0.398996i
$712$	−5.29654	−	5.88240i	−0.198496	−	0.220452i
$713$	−11.9909	−	8.71187i	−0.449061	−	0.326262i
$714$		0			0
$715$	4.12374	+	8.79637i	0.154219	+	0.328966i
$716$	3.85770	−	6.68173i	0.144169	−	0.249708i
$717$	0.979082	−	9.31534i	0.0365645	−	0.347888i
$718$	46.6835	−	9.92289i	1.74221	−	0.370319i
$719$	16.5812	+	3.52443i	0.618373	+	0.131439i	0.506438	−	0.862276i	$-0.330962\pi$
$719$	16.5812	+	3.52443i	0.618373	+	0.131439i	0.111935	+	0.993716i	$0.464295\pi$
$720$	−0.837831	+	0.608720i	−0.0312241	+	0.0226857i
$721$		0			0
$722$	−4.23226	−	13.0255i	−0.157508	−	0.484761i
$723$	9.94332	+	11.0432i	0.369796	+	0.410700i
$724$	0.556956	−	5.29908i	0.0206991	−	0.196939i
$725$	3.25580	+	5.63921i	0.120917	+	0.209435i
$726$	−27.3090	−	18.2581i	−1.01353	−	0.677620i
$727$	4.90596			0.181952			0.0909760	−	0.995853i	$-0.471001\pi$
$727$	4.90596			0.181952			0.0909760	+	0.995853i	$0.471001\pi$
$728$		0			0
$729$	8.42208	−	25.9205i	0.311929	−	0.960019i
$730$	−11.2176	−	2.38438i	−0.415183	−	0.0882499i
$731$	−19.5844	−	8.71951i	−0.724353	−	0.322503i
$732$	21.2391	+	9.45627i	0.785021	+	0.349514i
$733$	15.1811	+	3.22684i	0.560726	+	0.119186i	0.479551	−	0.877514i	$-0.340799\pi$
$733$	15.1811	+	3.22684i	0.560726	+	0.119186i	0.0811750	+	0.996700i	$0.474133\pi$
$734$	−0.406497	+	1.25107i	−0.0150041	+	0.0461778i
$735$		0			0
$736$	−11.1711			−0.411771
$737$	−17.4607	−	1.49163i	−0.643172	−	0.0549449i
$738$	−0.895872	−	1.55170i	−0.0329775	−	0.0571187i
$739$	1.54631	−	14.7122i	0.0568820	−	0.541196i	−0.928560	−	0.371183i	$-0.878952\pi$
$739$	1.54631	−	14.7122i	0.0568820	−	0.541196i	0.985442	−	0.170013i	$-0.0543810\pi$
$740$	5.37383	+	5.96824i	0.197546	+	0.219397i
$741$	−5.00525	−	15.4046i	−0.183873	−	0.565901i
$742$		0			0
$743$	1.22647	−	0.891080i	0.0449947	−	0.0326906i	−0.565061	−	0.825049i	$-0.691147\pi$
$743$	1.22647	−	0.891080i	0.0449947	−	0.0326906i	0.610055	+	0.792359i	$0.291147\pi$
$744$	26.0504	+	5.53718i	0.955054	+	0.203003i
$745$	−3.11516	+	0.662148i	−0.114131	+	0.0242592i
$746$	3.11375	−	29.6254i	0.114003	−	1.08466i
$747$	0.343211	−	0.594459i	0.0125574	−	0.0217501i
$748$	4.13105	−	21.4869i	0.151046	−	0.785640i
$749$		0			0
$750$	−19.3600	−	14.0659i	−0.706927	−	0.513612i
$751$	28.1583	+	31.2729i	1.02751	+	1.14117i	0.989885	+	0.141874i	$0.0453128\pi$
$751$	28.1583	+	31.2729i	1.02751	+	1.14117i	0.0376258	+	0.999292i	$0.488021\pi$
$752$	8.66606	−	9.62463i	0.316019	−	0.350974i
$753$	12.9150	+	5.75013i	0.470649	+	0.209546i
$754$	−1.21153	−	11.5270i	−0.0441215	−	0.419788i
$755$	−2.36857	−	7.28971i	−0.0862011	−	0.265300i
$756$		0			0
$757$	−34.7238	−	25.2283i	−1.26206	−	0.916940i	−0.263202	−	0.964741i	$-0.584779\pi$
$757$	−34.7238	−	25.2283i	−1.26206	−	0.916940i	−0.998857	+	0.0478008i	$0.984779\pi$
$758$	−9.72584	+	16.8456i	−0.353258	+	0.611861i
$759$	4.46095	+	5.89476i	0.161922	+	0.213966i
$760$	−3.49354	−	6.05098i	−0.126724	−	0.219492i
$761$	37.9083	−	16.8779i	1.37418	−	0.611823i	0.419034	−	0.907970i	$-0.362369\pi$
$761$	37.9083	−	16.8779i	1.37418	−	0.611823i	0.955142	+	0.296148i	$0.0957021\pi$
$762$	−2.04760	+	6.30186i	−0.0741767	+	0.228292i
$763$		0			0
$764$	20.1290	−	14.6246i	0.728243	−	0.529099i
$765$	0.242169	+	2.30408i	0.00875564	+	0.0833043i
$766$	−46.1986	+	51.3088i	−1.66922	+	1.85386i
$767$	−48.1839	+	10.2418i	−1.73982	+	0.369810i
$768$	11.1448	−	4.96200i	0.402155	−	0.179051i
$769$	−36.1695			−1.30430			−0.652152	−	0.758088i	$-0.726134\pi$
$769$	−36.1695			−1.30430			−0.652152	+	0.758088i	$0.726134\pi$
$770$		0			0
$771$	0.802702			0.0289086
$772$	−52.2232	+	23.2513i	−1.87955	+	0.836832i
$773$	1.31846	−	0.280248i	0.0474218	−	0.0100798i	−0.184140	−	0.982900i	$-0.558950\pi$
$773$	1.31846	−	0.280248i	0.0474218	−	0.0100798i	0.231562	+	0.972820i	$0.425617\pi$
$774$	17.8006	−	19.7696i	0.639830	−	0.710604i
$775$	3.94303	+	37.5154i	0.141638	+	1.34759i
$776$	−25.2985	+	18.3804i	−0.908163	+	0.659819i
$777$		0			0
$778$	3.54486	−	10.9100i	0.127089	−	0.391141i
$779$	−2.15582	+	0.959834i	−0.0772403	+	0.0343896i
$780$	5.87444	+	10.1748i	0.210339	+	0.364318i
$781$	0.506601	+	25.9782i	0.0181276	+	0.929572i
$782$	−4.10069	+	7.10260i	−0.146640	+	0.253989i
$783$	−6.98028	−	5.07147i	−0.249455	−	0.181239i
$784$		0			0
$785$	−0.617524	−	1.90054i	−0.0220404	−	0.0678333i
$786$	−0.395436	−	3.76232i	−0.0141047	−	0.134197i
$787$	18.6386	+	8.29845i	0.664395	+	0.295808i	0.711090	−	0.703101i	$-0.248202\pi$
$787$	18.6386	+	8.29845i	0.664395	+	0.295808i	−0.0466945	+	0.998909i	$0.514869\pi$
$788$	30.5255	−	33.9020i	1.08742	−	1.20771i
$789$	15.3761	+	17.0769i	0.547404	+	0.607954i
$790$	−18.4301	−	13.3903i	−0.655715	−	0.476405i
$791$		0			0
$792$	7.94923	+	4.38510i	0.282463	+	0.155818i
$793$	9.79915	−	16.9726i	0.347978	−	0.602716i
$794$	−6.84059	+	65.0839i	−0.242764	+	2.30974i
$795$	7.42509	−	1.57825i	0.263341	−	0.0559748i
$796$	−72.3120	−	15.3704i	−2.56303	−	0.544789i
$797$	44.3283	−	32.2064i	1.57019	−	1.14081i	0.643210	−	0.765690i	$-0.277602\pi$
$797$	44.3283	−	32.2064i	1.57019	−	1.14081i	0.926977	−	0.375118i	$-0.122398\pi$
$798$		0			0
$799$	−8.95320	−	27.5551i	−0.316741	−	0.974830i
$800$	19.0243	+	21.1286i	0.672610	+	0.747010i
$801$	−0.448391	+	4.26615i	−0.0158431	+	0.150737i
$802$	−16.2445	−	28.1363i	−0.573612	−	0.993526i
$803$	−4.45390	−	19.1135i	−0.157175	−	0.674501i
$804$	−21.1930			−0.747421
$805$		0			0
$806$	20.7487	−	63.8580i	0.730842	−	2.24930i
$807$	−27.1965	−	5.78078i	−0.957360	−	0.203493i
$808$	24.9208	+	11.0955i	0.876712	+	0.390338i
$809$	21.7007	+	9.66179i	0.762958	+	0.339691i	0.751056	−	0.660239i	$-0.229545\pi$
$809$	21.7007	+	9.66179i	0.762958	+	0.339691i	0.0119016	+	0.999929i	$0.496212\pi$
$810$	7.32271	+	1.55649i	0.257294	+	0.0546895i
$811$	9.02569	−	27.7782i	0.316935	−	0.975426i	−0.658016	−	0.753004i	$-0.728604\pi$
$811$	9.02569	−	27.7782i	0.316935	−	0.975426i	0.974951	−	0.222421i	$-0.0713961\pi$
$812$		0			0
$813$	−31.0032			−1.08733
$814$	−8.90143	+	21.0903i	−0.311995	+	0.739214i
$815$	2.48297	+	4.30063i	0.0869747	+	0.150645i
$816$	−0.300711	+	2.86107i	−0.0105270	+	0.100157i
$817$	−23.4446	−	26.0378i	−0.820221	−	0.910948i
$818$	−8.25053	−	25.3925i	−0.288473	−	0.887829i
$819$		0			0
$820$	1.38482	−	1.00613i	0.0483600	−	0.0351356i
$821$	11.1890	+	2.37829i	0.390498	+	0.0830029i	0.398977	−	0.916961i	$-0.369365\pi$
$821$	11.1890	+	2.37829i	0.390498	+	0.0830029i	−0.00847849	+	0.999964i	$0.502699\pi$
$822$	19.0541	−	4.05008i	0.664590	−	0.141263i
$823$	1.21088	−	11.5208i	0.0422087	−	0.401589i	−0.952936	−	0.303170i	$-0.901955\pi$
$823$	1.21088	−	11.5208i	0.0422087	−	0.401589i	0.995145	−	0.0984187i	$-0.0313784\pi$
$824$	3.23737	−	5.60730i	0.112779	−	0.195339i
$825$	3.55218	−	18.4760i	0.123671	−	0.643253i
$826$		0			0
$827$	22.5394	+	16.3758i	0.783770	+	0.569442i	0.906108	−	0.423046i	$-0.139039\pi$
$827$	22.5394	+	16.3758i	0.783770	+	0.569442i	−0.122338	+	0.992489i	$0.539039\pi$
$828$	−4.08848	−	4.54072i	−0.142085	−	0.157801i
$829$	−8.52154	+	9.46413i	−0.295965	+	0.328703i	−0.872726	−	0.488210i	$-0.837650\pi$
$829$	−8.52154	+	9.46413i	−0.295965	+	0.328703i	0.576761	+	0.816913i	$0.304317\pi$
$830$	0.997845	+	0.444269i	0.0346357	+	0.0154208i
$831$	1.10600	+	10.5229i	0.0383667	+	0.365035i
$832$	−13.5875	−	41.8179i	−0.471061	−	1.44978i
$833$		0			0
$834$	34.3468	+	24.9544i	1.18933	+	0.864100i
$835$	1.39668	−	2.41913i	0.0483343	−	0.0837174i
$836$	20.4516	−	29.3355i	0.707335	−	1.01459i
$837$	−24.9915	−	43.2866i	−0.863833	−	1.49620i
$838$	31.3750	−	13.9690i	1.08383	−	0.482552i
$839$	−1.11854	+	3.44252i	−0.0386164	+	0.118849i	−0.968506	−	0.248989i	$-0.919902\pi$
$839$	−1.11854	+	3.44252i	−0.0386164	+	0.118849i	0.929890	+	0.367838i	$0.119902\pi$
$840$		0			0
$841$	21.5619	−	15.6656i	0.743513	−	0.540194i
$842$	1.77565	+	16.8942i	0.0611930	+	0.582212i
$843$	−8.66794	+	9.62672i	−0.298540	+	0.331562i
$844$	51.1294	−	10.8679i	1.75995	−	0.374088i
$845$	−1.24094	+	0.552501i	−0.0426896	+	0.0190066i
$846$	35.9535			1.23611
$847$		0			0
$848$	−6.44224			−0.221228
$849$	15.2955	−	6.81002i	0.524942	−	0.233719i
$850$	20.4171	−	4.33979i	0.700301	−	0.148854i
$851$	3.44700	−	3.82828i	0.118162	−	0.131232i
$852$	3.28458	+	31.2507i	0.112528	+	1.07063i
$853$	−39.8352	+	28.9420i	−1.36393	+	0.990955i	−0.365749	+	0.930714i	$0.619187\pi$
$853$	−39.8352	+	28.9420i	−1.36393	+	0.990955i	−0.998184	+	0.0602414i	$0.980813\pi$
$854$		0			0
$855$	−1.17009	+	3.60116i	−0.0400161	+	0.123157i
$856$	−1.91659	+	0.853323i	−0.0655078	+	0.0291660i
$857$	−12.0693	−	20.9046i	−0.412278	−	0.714087i	0.582860	−	0.812572i	$-0.301933\pi$
$857$	−12.0693	−	20.9046i	−0.412278	−	0.714087i	−0.995138	+	0.0984857i	$0.968600\pi$
$858$	−19.1524	+	27.4719i	−0.653853	+	0.937876i
$859$	−0.0926485	+	0.160472i	−0.00316113	+	0.00547523i	−0.867602	−	0.497260i	$-0.834340\pi$
$859$	−0.0926485	+	0.160472i	−0.00316113	+	0.00547523i	0.864441	+	0.502735i	$0.167673\pi$
$860$	20.5609	+	14.9384i	0.701121	+	0.509394i
$861$		0			0
$862$	18.2141	+	56.0571i	0.620373	+	1.90931i
$863$	−4.00638	−	38.1182i	−0.136379	−	1.29756i	−0.821953	−	0.569555i	$-0.807115\pi$
$863$	−4.00638	−	38.1182i	−0.136379	−	1.29756i	0.685574	−	0.728003i	$-0.259551\pi$
$864$	−34.4156	−	15.3228i	−1.17084	−	0.521292i
$865$	4.86963	−	5.40827i	0.165572	−	0.183887i
$866$	−11.1237	−	12.3541i	−0.377997	−	0.419809i
$867$	−13.1531	−	9.55629i	−0.446703	−	0.324549i
$868$		0			0
$869$	7.36039	−	38.2838i	0.249684	−	1.29869i
$870$	1.98223	−	3.43332i	0.0672039	−	0.116401i
$871$	−1.86741	+	17.7672i	−0.0632748	+	0.602019i
$872$	−26.7477	+	5.68541i	−0.905793	+	0.192532i
$873$	16.5761	+	3.52336i	0.561016	+	0.119248i
$874$	−10.8442	+	7.87876i	−0.366810	+	0.266503i
$875$		0			0
$876$	−7.33430	−	22.5726i	−0.247803	−	0.762659i
$877$	−17.7953	−	19.7637i	−0.600906	−	0.667373i	0.363563	−	0.931569i	$-0.381560\pi$
$877$	−17.7953	−	19.7637i	−0.600906	−	0.667373i	−0.964469	+	0.264196i	$0.914893\pi$
$878$	4.44004	−	42.2442i	0.149844	−	1.42567i
$879$	4.44653	+	7.70162i	0.149978	+	0.259769i
$880$	1.09659	−	2.59817i	0.0369661	−	0.0875844i
$881$	−1.78266			−0.0600595			−0.0300297	−	0.999549i	$-0.509560\pi$
$881$	−1.78266			−0.0600595			−0.0300297	+	0.999549i	$0.509560\pi$
$882$		0			0
$883$	13.9329	−	42.8811i	0.468880	−	1.44306i	−0.385157	−	0.922851i	$-0.625853\pi$
$883$	13.9329	−	42.8811i	0.468880	−	1.44306i	0.854037	−	0.520213i	$-0.174147\pi$
$884$	−21.8185	−	4.63768i	−0.733837	−	0.155982i
$885$	−15.3925	−	6.85320i	−0.517415	−	0.230368i
$886$	−10.6888	−	4.75896i	−0.359097	−	0.159880i
$887$	−18.1028	−	3.84787i	−0.607832	−	0.129199i	−0.106295	−	0.994335i	$-0.533899\pi$
$887$	−18.1028	−	3.84787i	−0.607832	−	0.129199i	−0.501537	+	0.865136i	$0.667232\pi$
$888$	−2.86042	+	8.80346i	−0.0959893	+	0.295425i
$889$		0			0
$890$	−6.82595			−0.228806
$891$	2.90744	+	12.4770i	0.0974029	+	0.417996i
$892$	4.04521	+	7.00651i	0.135444	+	0.234595i
$893$	4.94974	−	47.0936i	0.165637	−	1.57593i
$894$	−7.34595	−	8.15850i	−0.245685	−	0.272861i
$895$	−0.687441	−	2.11573i	−0.0229786	−	0.0707210i
$896$		0			0
$897$	6.09693	−	4.42968i	0.203571	−	0.147903i
$898$	31.0893	+	6.60823i	1.03746	+	0.220519i
$899$	−13.3051	+	2.82809i	−0.443751	+	0.0943222i
$900$	−1.62551	+	15.4656i	−0.0541835	+	0.515522i
$901$	−7.20597	+	12.4811i	−0.240066	+	0.415806i
$902$	4.27222	+	2.35672i	0.142249	+	0.0784702i
$903$		0			0
$904$	−23.2635	−	16.9019i	−0.773732	−	0.562149i
$905$	−1.02800	−	1.14171i	−0.0341718	−	0.0379516i
$906$	17.6797	−	19.6353i	0.587370	−	0.652340i
$907$	13.8652	+	6.17318i	0.460386	+	0.204977i	0.623806	−	0.781580i	$-0.285586\pi$
$907$	13.8652	+	6.17318i	0.460386	+	0.204977i	−0.163419	+	0.986557i	$0.552252\pi$
$908$	−7.22508	−	68.7421i	−0.239773	−	2.28129i
$909$	−4.56831	−	14.0598i	−0.151521	−	0.466335i
$910$		0			0
$911$	25.7264	+	18.6913i	0.852353	+	0.619271i	0.925794	−	0.378029i	$-0.123398\pi$
$911$	25.7264	+	18.6913i	0.852353	+	0.619271i	−0.0734407	+	0.997300i	$0.523398\pi$
$912$	−2.35091	+	4.07190i	−0.0778464	+	0.134834i
$913$	0.0364446	+	1.86886i	0.00120614	+	0.0618501i
$914$	34.9482	+	60.5321i	1.15598	+	2.00222i
$915$	6.12395	−	2.72656i	0.202452	−	0.0901373i
$916$	−16.6269	+	51.1723i	−0.549368	+	1.69078i
$917$		0			0
$918$	−22.3756	+	16.2568i	−0.738504	+	0.536555i
$919$	−2.28580	−	21.7480i	−0.0754017	−	0.717399i	−0.965283	−	0.261207i	$-0.915880\pi$
$919$	−2.28580	−	21.7480i	−0.0754017	−	0.717399i	0.889881	−	0.456192i	$-0.150787\pi$
$920$	2.17529	−	2.41590i	0.0717171	−	0.0796499i
$921$	2.69317	−	0.572450i	0.0887429	−	0.0188629i
$922$	50.0465	−	22.2821i	1.64819	−	0.733823i
$923$	26.4885			0.871878
$924$		0			0
$925$	−13.1109			−0.431084
$926$	−9.56527	+	4.25873i	−0.314334	+	0.139951i
$927$	−3.43216	+	0.729529i	−0.112727	+	0.0239609i
$928$	−6.86006	+	7.61887i	−0.225192	+	0.250102i
$929$	−3.21144	−	30.5548i	−0.105364	−	1.00247i	−0.911657	−	0.410953i	$-0.865196\pi$
$929$	−3.21144	−	30.5548i	−0.105364	−	1.00247i	0.806293	−	0.591517i	$-0.201471\pi$
$930$	18.5802	−	13.4993i	0.609267	−	0.442659i
$931$		0			0
$932$	−19.0002	+	58.4765i	−0.622372	+	1.91546i
$933$	4.32213	−	1.92433i	0.141500	−	0.0629999i
$934$	39.1471	+	67.8048i	1.28093	+	2.21864i
$935$	−3.80706	−	5.03070i	−0.124504	−	0.164522i
$936$	4.62754	−	8.01513i	0.151256	−	0.261983i
$937$	35.8545	+	26.0498i	1.17132	+	0.851010i	0.991166	−	0.132629i	$-0.0423419\pi$
$937$	35.8545	+	26.0498i	1.17132	+	0.851010i	0.180149	+	0.983639i	$0.442342\pi$
$938$		0			0
$939$	−6.41690	−	19.7492i	−0.209408	−	0.644490i
$940$	3.59034	+	34.1598i	0.117104	+	1.11417i
$941$	−22.3006	−	9.92889i	−0.726980	−	0.323673i	0.00966354	−	0.999953i	$-0.496924\pi$
$941$	−22.3006	−	9.92889i	−0.726980	−	0.323673i	−0.736644	+	0.676281i	$0.763591\pi$
$942$	4.60938	−	5.11924i	0.150182	−	0.166794i
$943$	−0.734689	−	0.815955i	−0.0239248	−	0.0265712i
$944$	11.5685	+	8.40502i	0.376523	+	0.273560i
$945$		0			0
$946$	−13.6771	+	71.1393i	−0.444682	+	2.31294i
$947$	26.4671	−	45.8424i	0.860066	−	1.48968i	−0.0117992	−	0.999930i	$-0.503756\pi$
$947$	26.4671	−	45.8424i	0.860066	−	1.48968i	0.871865	−	0.489747i	$-0.162911\pi$
$948$	4.92816	−	46.8883i	0.160059	−	1.52286i
$949$	−19.5701	+	4.15975i	−0.635272	+	0.135031i
$950$	33.3692	+	7.09285i	1.08264	+	0.230122i
$951$	−17.9505	+	13.0418i	−0.582086	+	0.422910i
$952$		0			0
$953$	−1.48389	−	4.56695i	−0.0480680	−	0.147938i	0.924142	−	0.382050i	$-0.124782\pi$
$953$	−1.48389	−	4.56695i	−0.0480680	−	0.147938i	−0.972210	+	0.234112i	$0.924782\pi$
$954$	−11.9668	−	13.2905i	−0.387440	−	0.430296i
$955$	0.749885	−	7.13468i	0.0242657	−	0.230873i
$956$	−10.5411	−	18.2577i	−0.340922	−	0.590495i
$957$	6.75975	+	0.577473i	0.218512	+	0.0186671i
$958$	95.1795			3.07511
$959$		0			0
$960$	4.64752	−	14.3036i	0.149998	−	0.461647i
$961$	−46.7547	−	9.93803i	−1.50822	−	0.320582i
$962$	21.3194	+	9.49203i	0.687366	+	0.306035i
$963$	1.03865	+	0.462438i	0.0334701	+	0.0149019i
$964$	32.7156	+	6.95391i	1.05370	+	0.223970i
$965$	−5.09344	+	15.6760i	−0.163963	+	0.504628i
$966$		0			0
$967$	10.0231			0.322320			0.161160	−	0.986928i	$-0.448477\pi$
$967$	10.0231			0.322320			0.161160	+	0.986928i	$0.448477\pi$
$968$	−24.7031	+	0.963838i	−0.793987	+	0.0309789i
$969$	5.25922	+	9.10924i	0.168950	+	0.292631i
$970$	−2.81873	+	26.8184i	−0.0905040	+	0.861088i
$971$	−1.01235	−	1.12433i	−0.0324879	−	0.0360814i	0.726682	−	0.686974i	$-0.241061\pi$
$971$	−1.01235	−	1.12433i	−0.0324879	−	0.0360814i	−0.759170	+	0.650893i	$0.774395\pi$
$972$	−10.8962	−	33.5351i	−0.349496	−	1.07564i
$973$		0			0
$974$	37.8445	−	27.4956i	1.21262	−	0.881017i
$975$	−18.7612	−	3.98782i	−0.600839	−	0.127712i
$976$	−5.56475	+	1.18282i	−0.178123	+	0.0378613i
$977$	1.91632	−	18.2326i	0.0613085	−	0.583312i	−0.920140	−	0.391588i	$-0.871926\pi$
$977$	1.91632	−	18.2326i	0.0613085	−	0.583312i	0.981449	−	0.191723i	$-0.0614076\pi$
$978$	−8.55919	+	14.8249i	−0.273693	+	0.474050i
$979$	−4.95835	−	10.5767i	−0.158469	−	0.338032i
$980$		0			0
$981$	11.9889	+	8.71048i	0.382778	+	0.278104i
$982$	18.0009	+	19.9920i	0.574431	+	0.637970i
$983$	19.5483	−	21.7106i	0.623494	−	0.692460i	−0.345816	−	0.938302i	$-0.612398\pi$
$983$	19.5483	−	21.7106i	0.623494	−	0.692460i	0.969310	+	0.245843i	$0.0790646\pi$
$984$	1.80235	+	0.802460i	0.0574569	+	0.0255815i
$985$	−1.37493	−	13.0816i	−0.0438090	−	0.416814i
$986$	2.32590	+	7.15839i	0.0740718	+	0.227969i
$987$		0			0
$988$	−29.4938	−	21.4285i	−0.938324	−	0.681732i
$989$	8.15100	−	14.1180i	0.259187	−	0.448925i
$990$	7.39707	−	2.56395i	0.235094	−	0.0814876i
$991$	22.6187	+	39.1768i	0.718508	+	1.24449i	0.961591	+	0.274487i	$0.0885079\pi$
$991$	22.6187	+	39.1768i	0.718508	+	1.24449i	−0.243083	+	0.970005i	$0.578159\pi$
$992$	−54.2568	+	24.1567i	−1.72266	+	0.766976i
$993$	−8.67963	+	26.7132i	−0.275440	+	0.847716i
$994$		0			0
$995$	−17.2448	+	12.5291i	−0.546697	+	0.397199i
$996$	0.236291	+	2.24816i	0.00748716	+	0.0712355i
$997$	9.42214	−	10.4643i	0.298402	−	0.331409i	−0.575234	−	0.817989i	$-0.695089\pi$
$997$	9.42214	−	10.4643i	0.298402	−	0.331409i	0.873636	+	0.486580i	$0.161756\pi$
$998$	−44.1379	+	9.38180i	−1.39716	+	0.296976i
$999$	15.8705	−	7.06599i	0.502119	−	0.223558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.h.422.5		40
7.2	even	3		539.2.f.g.246.1		20
7.3	odd	6		77.2.m.b.4.1	✓	40
7.4	even	3	inner	539.2.q.h.312.1		40
7.5	odd	6		539.2.f.h.246.1		20
7.6	odd	2		77.2.m.b.37.5	yes	40
11.3	even	5	inner	539.2.q.h.520.1		40
21.17	even	6		693.2.by.b.235.5		40
21.20	even	2		693.2.by.b.37.1		40
77.3	odd	30		77.2.m.b.25.5	yes	40
77.5	odd	30		5929.2.a.bw.1.9		10
77.6	even	10		847.2.e.h.485.9		20
77.10	even	6		847.2.n.j.81.5		40
77.13	even	10		847.2.n.h.632.5		40
77.16	even	15		5929.2.a.bx.1.9		10
77.17	even	30		847.2.e.h.606.9		20
77.20	odd	10		847.2.n.i.632.1		40
77.24	even	30		847.2.n.h.753.1		40
77.25	even	15	inner	539.2.q.h.410.5		40
77.27	odd	10		847.2.e.i.485.2		20
77.31	odd	30		847.2.n.i.753.5		40
77.38	odd	30		847.2.e.i.606.2		20
77.41	even	10		847.2.n.j.366.5		40
77.47	odd	30		539.2.f.h.344.1		20
77.48	odd	10		847.2.n.i.9.5		40
77.52	even	30		847.2.n.j.487.1		40
77.58	even	15		539.2.f.g.344.1		20
77.59	odd	30		847.2.n.i.130.1		40
77.61	even	30		5929.2.a.by.1.2		10
77.62	even	10		847.2.n.h.9.1		40
77.69	odd	10		77.2.m.b.58.1	yes	40
77.72	odd	30		5929.2.a.bz.1.2		10
77.73	even	30		847.2.n.h.130.5		40
77.76	even	2		847.2.n.j.807.1		40
231.80	even	30		693.2.by.b.487.1		40
231.146	even	10		693.2.by.b.289.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.1	✓	40	7.3	odd	6
77.2.m.b.25.5	yes	40	77.3	odd	30
77.2.m.b.37.5	yes	40	7.6	odd	2
77.2.m.b.58.1	yes	40	77.69	odd	10
539.2.f.g.246.1		20	7.2	even	3
539.2.f.g.344.1		20	77.58	even	15
539.2.f.h.246.1		20	7.5	odd	6
539.2.f.h.344.1		20	77.47	odd	30
539.2.q.h.312.1		40	7.4	even	3	inner
539.2.q.h.410.5		40	77.25	even	15	inner
539.2.q.h.422.5		40	1.1	even	1	trivial
539.2.q.h.520.1		40	11.3	even	5	inner
693.2.by.b.37.1		40	21.20	even	2
693.2.by.b.235.5		40	21.17	even	6
693.2.by.b.289.5		40	231.146	even	10
693.2.by.b.487.1		40	231.80	even	30
847.2.e.h.485.9		20	77.6	even	10
847.2.e.h.606.9		20	77.17	even	30
847.2.e.i.485.2		20	77.27	odd	10
847.2.e.i.606.2		20	77.38	odd	30
847.2.n.h.9.1		40	77.62	even	10
847.2.n.h.130.5		40	77.73	even	30
847.2.n.h.632.5		40	77.13	even	10
847.2.n.h.753.1		40	77.24	even	30
847.2.n.i.9.5		40	77.48	odd	10
847.2.n.i.130.1		40	77.59	odd	30
847.2.n.i.632.1		40	77.20	odd	10
847.2.n.i.753.5		40	77.31	odd	30
847.2.n.j.81.5		40	77.10	even	6
847.2.n.j.366.5		40	77.41	even	10
847.2.n.j.487.1		40	77.52	even	30
847.2.n.j.807.1		40	77.76	even	2
5929.2.a.bw.1.9		10	77.5	odd	30
5929.2.a.bx.1.9		10	77.16	even	15
5929.2.a.by.1.2		10	77.61	even	30
5929.2.a.bz.1.2		10	77.72	odd	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.04369 - 0.909911i) q^{2} +(1.30576 - 0.277549i) q^{3} +(2.01049 - 2.23287i) q^{4} +(-0.0905565 - 0.861587i) q^{5} +(2.41604 - 1.75535i) q^{6} +(0.694498 - 2.13745i) q^{8} +(-1.11265 + 0.495385i) q^{9} +O(q^{10})\)	\(q+(2.04369 - 0.909911i) q^{2} +(1.30576 - 0.277549i) q^{3} +(2.01049 - 2.23287i) q^{4} +(-0.0905565 - 0.861587i) q^{5} +(2.41604 - 1.75535i) q^{6} +(0.694498 - 2.13745i) q^{8} +(-1.11265 + 0.495385i) q^{9} +(-0.969038 - 1.67842i) q^{10} +(1.89678 - 2.72071i) q^{11} +(2.00549 - 3.47361i) q^{12} +(-2.73539 - 1.98738i) q^{13} +(-0.357378 - 1.09990i) q^{15} +(0.102593 + 0.976110i) q^{16} +(2.00586 + 0.893065i) q^{17} +(-1.82316 + 2.02483i) q^{18} +(2.40122 + 2.66683i) q^{19} +(-2.10587 - 1.53001i) q^{20} +(1.40083 - 7.28619i) q^{22} +(-0.834837 + 1.44598i) q^{23} +(0.313605 - 2.98375i) q^{24} +(4.15661 - 0.883514i) q^{25} +(-7.39864 - 1.57263i) q^{26} +(-4.55532 + 3.30963i) q^{27} +(0.473517 + 1.45734i) q^{29} +(-1.73118 - 1.92267i) q^{30} +(-0.927888 + 8.82827i) q^{31} +(3.34529 + 5.79421i) q^{32} +(1.72161 - 4.07904i) q^{33} +4.91197 q^{34} +(-1.13084 + 3.48037i) q^{36} +(-3.01788 - 0.641471i) q^{37} +(7.33394 + 3.26528i) q^{38} +(-4.12337 - 1.83584i) q^{39} +(-1.90449 - 0.404811i) q^{40} +(-0.203209 + 0.625414i) q^{41} -9.76359 q^{43} +(-2.26154 - 9.70519i) q^{44} +(0.527575 + 0.913787i) q^{45} +(-0.390438 + 3.71477i) q^{46} +(-8.82952 - 9.80618i) q^{47} +(0.404881 + 1.24609i) q^{48} +(7.69091 - 5.58777i) q^{50} +(2.86704 + 0.609409i) q^{51} +(-9.93702 + 2.11218i) q^{52} +(-0.686100 + 6.52780i) q^{53} +(-6.29821 + 10.9088i) q^{54} +(-2.51589 - 1.38786i) q^{55} +(3.87560 + 2.81579i) q^{57} +(2.29377 + 2.54749i) q^{58} +(9.74869 - 10.8270i) q^{59} +(-3.17443 - 1.41335i) q^{60} +(0.605886 + 5.76462i) q^{61} +(6.13662 + 18.8866i) q^{62} +(10.5209 + 7.64386i) q^{64} +(-1.46459 + 2.53675i) q^{65} +(-0.193116 - 9.90283i) q^{66} +(-2.64188 - 4.57587i) q^{67} +(6.02684 - 2.68332i) q^{68} +(-0.688770 + 2.11982i) q^{69} +(-6.33800 + 4.60483i) q^{71} +(0.286123 + 2.72228i) q^{72} +(3.95947 - 4.39744i) q^{73} +(-6.75131 + 1.43504i) q^{74} +(5.18232 - 2.30732i) q^{75} +10.7823 q^{76} -10.0974 q^{78} +(10.7382 - 4.78095i) q^{79} +(0.831714 - 0.176786i) q^{80} +(-2.58468 + 2.87058i) q^{81} +(0.153773 + 1.46306i) q^{82} +(-0.455953 + 0.331269i) q^{83} +(0.587810 - 1.80909i) q^{85} +(-19.9538 + 8.88400i) q^{86} +(1.02278 + 1.77151i) q^{87} +(-4.49805 - 5.94378i) q^{88} +(1.76101 - 3.05016i) q^{89} +(1.90967 + 1.38745i) q^{90} +(1.55026 + 4.77120i) q^{92} +(1.23867 + 11.7852i) q^{93} +(-26.9676 - 12.0067i) q^{94} +(2.08026 - 2.31036i) q^{95} +(5.97632 + 6.63738i) q^{96} +(-11.2566 - 8.17838i) q^{97} +(-0.762658 + 3.96683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more