LMFDB - Embedded newform 630.2.j.l.211.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.4
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.l.421.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.66483 - 0.477841i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.24624 - 1.20287i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.54334 - 1.59105i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.66483 - 0.477841i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.24624 - 1.20287i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.54334 - 1.59105i) q^{9} -1.00000 q^{10} +(3.08343 + 5.34065i) q^{11} +(-0.418594 + 1.68071i) q^{12} +(0.933868 - 1.61751i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.418594 - 1.68071i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.52303 q^{17} +(-2.64956 - 1.40707i) q^{18} +5.08667 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.24624 + 1.20287i) q^{21} +(3.08343 - 5.34065i) q^{22} +(-3.58343 + 6.20668i) q^{23} +(1.66483 - 0.477841i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.86774 q^{26} +(3.47396 - 3.86414i) q^{27} -1.00000 q^{28} +(-5.23872 - 9.07372i) q^{29} +(-1.66483 + 0.477841i) q^{30} +(4.08667 - 7.07832i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(7.68537 + 7.41790i) q^{33} +(0.761513 + 1.31898i) q^{34} +1.00000 q^{35} +(0.106223 + 2.99812i) q^{36} -4.21894 q^{37} +(-2.54334 - 4.40519i) q^{38} +(0.781823 - 3.13912i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.433868 + 0.751481i) q^{41} +(0.418594 - 1.68071i) q^{42} +(4.01729 + 6.95816i) q^{43} -6.16685 q^{44} +(-0.106223 - 2.99812i) q^{45} +7.16685 q^{46} +(-3.43711 - 5.95325i) q^{47} +(-1.24624 - 1.20287i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.53558 + 0.727765i) q^{51} +(0.933868 + 1.61751i) q^{52} +0.0455927 q^{53} +(-5.08343 - 1.07646i) q^{54} +6.16685 q^{55} +(0.500000 + 0.866025i) q^{56} +(8.46846 - 2.43062i) q^{57} +(-5.23872 + 9.07372i) q^{58} +(-3.62352 + 6.27612i) q^{59} +(1.24624 + 1.20287i) q^{60} +(1.32191 + 2.28962i) q^{61} -8.17334 q^{62} +(2.64956 + 1.40707i) q^{63} +1.00000 q^{64} +(-0.933868 - 1.61751i) q^{65} +(2.58141 - 10.3647i) q^{66} +(-0.244219 + 0.422999i) q^{67} +(0.761513 - 1.31898i) q^{68} +(-3.00000 + 12.0454i) q^{69} +(-0.500000 - 0.866025i) q^{70} +3.34471 q^{71} +(2.54334 - 1.59105i) q^{72} -4.73547 q^{73} +(2.10947 + 3.65371i) q^{74} +(-1.24624 - 1.20287i) q^{75} +(-2.54334 + 4.40519i) q^{76} +(-3.08343 + 5.34065i) q^{77} +(-3.10947 + 0.892481i) q^{78} +(-6.51729 - 11.2883i) q^{79} -1.00000 q^{80} +(3.93711 - 8.09315i) q^{81} +0.867736 q^{82} +(-7.38503 - 12.7912i) q^{83} +(-1.66483 + 0.477841i) q^{84} +(-0.761513 + 1.31898i) q^{85} +(4.01729 - 6.95816i) q^{86} +(-13.0574 - 12.6030i) q^{87} +(3.08343 + 5.34065i) q^{88} +3.57511 q^{89} +(-2.54334 + 1.59105i) q^{90} +1.86774 q^{91} +(-3.58343 - 6.20668i) q^{92} +(3.42131 - 13.7370i) q^{93} +(-3.43711 + 5.95325i) q^{94} +(2.54334 - 4.40519i) q^{95} +(-0.418594 + 1.68071i) q^{96} +(-5.01156 - 8.68028i) q^{97} +1.00000 q^{98} +(16.3394 + 8.67718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.66483	−	0.477841i	0.961192	−	0.275882i
$3$	1.66483	−	0.477841i	0.961192	−	0.275882i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.24624	−	1.20287i	−0.508775	−	0.491068i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	2.54334	−	1.59105i	0.847779	−	0.530350i
$10$	−1.00000			−0.316228
$11$	3.08343	+	5.34065i	0.929688	+	1.61027i	0.783843	+	0.620960i	$0.213257\pi$
$11$	3.08343	+	5.34065i	0.929688	+	1.61027i	0.145845	+	0.989307i	$0.453410\pi$
$12$	−0.418594	+	1.68071i	−0.120838	+	0.485179i
$13$	0.933868	−	1.61751i	0.259008	−	0.448616i	−0.706968	−	0.707245i	$-0.749938\pi$
$13$	0.933868	−	1.61751i	0.259008	−	0.448616i	0.965977	+	0.258630i	$0.0832709\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	0.418594	−	1.68071i	0.108080	−	0.433957i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.52303			−0.369388			−0.184694	−	0.982796i	$-0.559129\pi$
$17$	−1.52303			−0.369388			−0.184694	+	0.982796i	$0.559129\pi$
$18$	−2.64956	−	1.40707i	−0.624507	−	0.331649i
$19$	5.08667			1.16696			0.583481	−	0.812127i	$-0.301690\pi$
$19$	5.08667			1.16696			0.583481	+	0.812127i	$0.301690\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.24624	+	1.20287i	0.271952	+	0.262487i
$22$	3.08343	−	5.34065i	0.657389	−	1.13863i
$23$	−3.58343	+	6.20668i	−0.747196	+	1.29418i	0.201966	+	0.979393i	$0.435267\pi$
$23$	−3.58343	+	6.20668i	−0.747196	+	1.29418i	−0.949162	+	0.314789i	$0.898066\pi$
$24$	1.66483	−	0.477841i	0.339833	−	0.0975389i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.86774			−0.366293
$27$	3.47396	−	3.86414i	0.668564	−	0.743655i
$28$	−1.00000			−0.188982
$29$	−5.23872	−	9.07372i	−0.972805	−	1.68495i	−0.686995	−	0.726662i	$-0.741071\pi$
$29$	−5.23872	−	9.07372i	−0.972805	−	1.68495i	−0.285810	−	0.958286i	$-0.592263\pi$
$30$	−1.66483	+	0.477841i	−0.303955	+	0.0872415i
$31$	4.08667	−	7.07832i	0.733988	−	1.27130i	−0.221178	−	0.975233i	$-0.570990\pi$
$31$	4.08667	−	7.07832i	0.733988	−	1.27130i	0.955166	−	0.296071i	$-0.0956764\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	7.68537	+	7.41790i	1.33785	+	1.29129i
$34$	0.761513	+	1.31898i	0.130598	+	0.226203i
$35$	1.00000			0.169031
$36$	0.106223	+	2.99812i	0.0177038	+	0.499686i
$37$	−4.21894			−0.693589			−0.346794	−	0.937941i	$-0.612730\pi$
$37$	−4.21894			−0.693589			−0.346794	+	0.937941i	$0.612730\pi$
$38$	−2.54334	−	4.40519i	−0.412584	−	0.714616i
$39$	0.781823	−	3.13912i	0.125192	−	0.502661i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−0.433868	+	0.751481i	−0.0677588	+	0.117362i	−0.897914	−	0.440170i	$-0.854918\pi$
$41$	−0.433868	+	0.751481i	−0.0677588	+	0.117362i	0.830156	+	0.557532i	$0.188251\pi$
$42$	0.418594	−	1.68071i	0.0645904	−	0.259339i
$43$	4.01729	+	6.95816i	0.612632	+	1.06111i	0.990795	+	0.135370i	$0.0432224\pi$
$43$	4.01729	+	6.95816i	0.612632	+	1.06111i	−0.378163	+	0.925739i	$0.623444\pi$
$44$	−6.16685			−0.929688
$45$	−0.106223	−	2.99812i	−0.0158348	−	0.446933i
$46$	7.16685			1.05669
$47$	−3.43711	−	5.95325i	−0.501354	−	0.868371i	−0.999999	−	0.00156468i	$-0.999502\pi$
$47$	−3.43711	−	5.95325i	−0.501354	−	0.868371i	0.498644	−	0.866807i	$-0.333831\pi$
$48$	−1.24624	−	1.20287i	−0.179879	−	0.173619i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.53558	+	0.727765i	−0.355053	+	0.101907i
$52$	0.933868	+	1.61751i	0.129504	+	0.224308i
$53$	0.0455927			0.00626264			0.00313132	−	0.999995i	$-0.499003\pi$
$53$	0.0455927			0.00626264			0.00313132	+	0.999995i	$0.499003\pi$
$54$	−5.08343	−	1.07646i	−0.691767	−	0.146488i
$55$	6.16685			0.831538
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	8.46846	−	2.43062i	1.12167	−	0.321944i
$58$	−5.23872	+	9.07372i	−0.687877	+	1.19144i
$59$	−3.62352	+	6.27612i	−0.471742	+	0.817081i	−0.999477	−	0.0323280i	$-0.989708\pi$
$59$	−3.62352	+	6.27612i	−0.471742	+	0.817081i	0.527736	+	0.849409i	$0.323041\pi$
$60$	1.24624	+	1.20287i	0.160889	+	0.155289i
$61$	1.32191	+	2.28962i	0.169254	+	0.293156i	0.938158	−	0.346208i	$-0.112531\pi$
$61$	1.32191	+	2.28962i	0.169254	+	0.293156i	−0.768904	+	0.639364i	$0.779198\pi$
$62$	−8.17334			−1.03802
$63$	2.64956	+	1.40707i	0.333813	+	0.177274i
$64$	1.00000			0.125000
$65$	−0.933868	−	1.61751i	−0.115832	−	0.200627i
$66$	2.58141	−	10.3647i	0.317749	−	1.27580i
$67$	−0.244219	+	0.422999i	−0.0298361	+	0.0516776i	−0.880558	−	0.473939i	$-0.842832\pi$
$67$	−0.244219	+	0.422999i	−0.0298361	+	0.0516776i	0.850722	+	0.525616i	$0.176165\pi$
$68$	0.761513	−	1.31898i	0.0923470	−	0.159950i
$69$	−3.00000	+	12.0454i	−0.361158	+	1.45009i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	3.34471			0.396944			0.198472	−	0.980107i	$-0.436402\pi$
$71$	3.34471			0.396944			0.198472	+	0.980107i	$0.436402\pi$
$72$	2.54334	−	1.59105i	0.299735	−	0.187507i
$73$	−4.73547			−0.554245			−0.277123	−	0.960835i	$-0.589381\pi$
$73$	−4.73547			−0.554245			−0.277123	+	0.960835i	$0.589381\pi$
$74$	2.10947	+	3.65371i	0.245221	+	0.424735i
$75$	−1.24624	−	1.20287i	−0.143903	−	0.138895i
$76$	−2.54334	+	4.40519i	−0.291741	+	0.505310i
$77$	−3.08343	+	5.34065i	−0.351389	+	0.608624i
$78$	−3.10947	+	0.892481i	−0.352078	+	0.101054i
$79$	−6.51729	−	11.2883i	−0.733253	−	1.27003i	−0.955486	−	0.295038i	$-0.904668\pi$
$79$	−6.51729	−	11.2883i	−0.733253	−	1.27003i	0.222233	−	0.974994i	$-0.428666\pi$
$80$	−1.00000			−0.111803
$81$	3.93711	−	8.09315i	0.437457	−	0.899239i
$82$	0.867736			0.0958254
$83$	−7.38503	−	12.7912i	−0.810612	−	1.40402i	−0.912436	−	0.409219i	$-0.865801\pi$
$83$	−7.38503	−	12.7912i	−0.810612	−	1.40402i	0.101824	−	0.994802i	$-0.467532\pi$
$84$	−1.66483	+	0.477841i	−0.181648	+	0.0521367i
$85$	−0.761513	+	1.31898i	−0.0825977	+	0.143063i
$86$	4.01729	−	6.95816i	0.433196	−	0.750317i
$87$	−13.0574	−	12.6030i	−1.39990	−	1.35118i
$88$	3.08343	+	5.34065i	0.328694	+	0.569315i
$89$	3.57511			0.378961			0.189480	−	0.981885i	$-0.439320\pi$
$89$	3.57511			0.378961			0.189480	+	0.981885i	$0.439320\pi$
$90$	−2.54334	+	1.59105i	−0.268091	+	0.167712i
$91$	1.86774			0.195792
$92$	−3.58343	−	6.20668i	−0.373598	−	0.647091i
$93$	3.42131	−	13.7370i	0.354773	−	1.42446i
$94$	−3.43711	+	5.95325i	−0.354511	+	0.614031i
$95$	2.54334	−	4.40519i	0.260941	−	0.451963i
$96$	−0.418594	+	1.68071i	−0.0427225	+	0.171537i
$97$	−5.01156	−	8.68028i	−0.508847	−	0.881349i	−0.999948	−	0.0102460i	$-0.996739\pi$
$97$	−5.01156	−	8.68028i	−0.508847	−	0.881349i	0.491100	−	0.871103i	$-0.336595\pi$
$98$	1.00000			0.101015
$99$	16.3394	+	8.67718i	1.64218	+	0.872089i
$100$	1.00000			0.100000
$101$	8.12126	+	14.0664i	0.808096	+	1.39966i	0.914181	+	0.405306i	$0.132835\pi$
$101$	8.12126	+	14.0664i	0.808096	+	1.39966i	−0.106086	+	0.994357i	$0.533832\pi$
$102$	1.89805	+	1.83200i	0.187935	+	0.181395i
$103$	−5.14406	+	8.90977i	−0.506859	+	0.877905i	0.493110	+	0.869967i	$0.335860\pi$
$103$	−5.14406	+	8.90977i	−0.506859	+	0.877905i	−0.999968	+	0.00793823i	$0.997473\pi$
$104$	0.933868	−	1.61751i	0.0915733	−	0.158610i
$105$	1.66483	−	0.477841i	0.162471	−	0.0466325i
$106$	−0.0227964	−	0.0394845i	−0.00221418	−	0.00383507i
$107$	−10.7310			−1.03740			−0.518700	−	0.854956i	$-0.673584\pi$
$107$	−10.7310			−1.03740			−0.518700	+	0.854956i	$0.673584\pi$
$108$	1.60947	+	4.94061i	0.154871	+	0.475410i
$109$	15.7766			1.51112			0.755560	−	0.655080i	$-0.227365\pi$
$109$	15.7766			1.51112			0.755560	+	0.655080i	$0.227365\pi$
$110$	−3.08343	−	5.34065i	−0.293993	−	0.509211i
$111$	−7.02382	+	2.01598i	−0.666672	+	0.191348i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−7.90534	+	13.6925i	−0.743672	+	1.28808i	0.207141	+	0.978311i	$0.433584\pi$
$113$	−7.90534	+	13.6925i	−0.743672	+	1.28808i	−0.950813	+	0.309766i	$0.899749\pi$
$114$	−6.33921	−	6.11859i	−0.593721	−	0.573058i
$115$	3.58343	+	6.20668i	0.334156	+	0.578776i
$116$	10.4774			0.972805
$117$	−0.198396	−	5.59969i	−0.0183417	−	0.517692i
$118$	7.24703			0.667144
$119$	−0.761513	−	1.31898i	−0.0698078	−	0.120911i
$120$	0.418594	−	1.68071i	0.0382122	−	0.153427i
$121$	−13.5150	+	23.4087i	−1.22864	+	2.12807i
$122$	1.32191	−	2.28962i	0.119680	−	0.207293i
$123$	−0.363229	+	1.45841i	−0.0327512	+	0.131500i
$124$	4.08667	+	7.07832i	0.366994	+	0.635652i
$125$	−1.00000			−0.0894427
$126$	−0.106223	−	2.99812i	−0.00946308	−	0.267094i
$127$	5.16685			0.458484			0.229242	−	0.973369i	$-0.426375\pi$
$127$	5.16685			0.458484			0.229242	+	0.973369i	$0.426375\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	10.0130	+	9.66454i	0.881597	+	0.850915i
$130$	−0.933868	+	1.61751i	−0.0819056	+	0.141865i
$131$	−5.39378	+	9.34230i	−0.471257	+	0.816240i	−0.999459	−	0.0328780i	$-0.989533\pi$
$131$	−5.39378	+	9.34230i	−0.471257	+	0.816240i	0.528203	+	0.849118i	$0.322866\pi$
$132$	−10.2668	+	2.94678i	−0.893608	+	0.256484i
$133$	2.54334	+	4.40519i	0.220535	+	0.381978i
$134$	0.488437			0.0421946
$135$	−1.60947	−	4.94061i	−0.138521	−	0.425220i
$136$	−1.52303			−0.130598
$137$	−6.82765	−	11.8258i	−0.583325	−	1.01035i	−0.995082	−	0.0990550i	$-0.968418\pi$
$137$	−6.82765	−	11.8258i	−0.583325	−	1.01035i	0.411757	−	0.911294i	$-0.364915\pi$
$138$	11.9316	−	3.42462i	1.01569	−	0.291523i
$139$	−0.327415	+	0.567100i	−0.0277710	+	0.0481008i	−0.879577	−	0.475757i	$-0.842174\pi$
$139$	−0.327415	+	0.567100i	−0.0277710	+	0.0481008i	0.851806	+	0.523858i	$0.175508\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−8.56693	−	8.26878i	−0.721465	−	0.696357i
$142$	−1.67235	−	2.89660i	−0.140341	−	0.243078i
$143$	11.5181			0.963188
$144$	−2.64956	−	1.40707i	−0.220797	−	0.117256i
$145$	−10.4774			−0.870103
$146$	2.36774	+	4.10104i	0.195955	+	0.339404i
$147$	−0.418594	+	1.68071i	−0.0345250	+	0.138622i
$148$	2.10947	−	3.65371i	0.173397	−	0.300333i
$149$	−9.39152	+	16.2666i	−0.769383	+	1.33261i	0.168514	+	0.985699i	$0.446103\pi$
$149$	−9.39152	+	16.2666i	−0.769383	+	1.33261i	−0.937898	+	0.346912i	$0.887230\pi$
$150$	−0.418594	+	1.68071i	−0.0341780	+	0.137229i
$151$	2.17258	+	3.76303i	0.176802	+	0.306231i	0.940784	−	0.339008i	$-0.110091\pi$
$151$	2.17258	+	3.76303i	0.176802	+	0.306231i	−0.763981	+	0.645239i	$0.776758\pi$
$152$	5.08667			0.412584
$153$	−3.87357	+	2.42321i	−0.313159	+	0.195905i
$154$	6.16685			0.496939
$155$	−4.08667	−	7.07832i	−0.328249	−	0.568545i
$156$	2.32765	+	2.24664i	0.186361	+	0.179875i
$157$	6.58916	−	11.4128i	0.525872	−	0.910837i	−0.473674	−	0.880700i	$-0.657072\pi$
$157$	6.58916	−	11.4128i	0.525872	−	0.910837i	0.999546	−	0.0301367i	$-0.00959427\pi$
$158$	−6.51729	+	11.2883i	−0.518488	+	0.898048i
$159$	0.0759043	−	0.0217861i	0.00601960	−	0.00172775i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−7.16685			−0.564827
$162$	−8.97743	+	0.636937i	−0.705334	+	0.0500425i
$163$	1.47697			0.115686			0.0578428	−	0.998326i	$-0.481578\pi$
$163$	1.47697			0.115686			0.0578428	+	0.998326i	$0.481578\pi$
$164$	−0.433868	−	0.751481i	−0.0338794	−	0.0586808i
$165$	10.2668	−	2.94678i	0.799268	−	0.229406i
$166$	−7.38503	+	12.7912i	−0.573190	+	0.992793i
$167$	−11.5812	+	20.0592i	−0.896178	+	1.55223i	−0.0638377	+	0.997960i	$0.520334\pi$
$167$	−11.5812	+	20.0592i	−0.896178	+	1.55223i	−0.832340	+	0.554265i	$0.812999\pi$
$168$	1.24624	+	1.20287i	0.0961494	+	0.0928032i
$169$	4.75578	+	8.23725i	0.365829	+	0.633635i
$170$	1.52303			0.116811
$171$	12.9371	−	8.09315i	0.989326	−	0.618899i
$172$	−8.03459			−0.612632
$173$	4.08667	+	7.07832i	0.310704	+	0.538155i	0.978515	−	0.206176i	$-0.0661019\pi$
$173$	4.08667	+	7.07832i	0.310704	+	0.538155i	−0.667811	+	0.744331i	$0.732769\pi$
$174$	−4.38579	+	17.6095i	−0.332486	+	1.33497i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	3.08343	−	5.34065i	0.232422	−	0.402567i
$177$	−3.03356	+	12.1801i	−0.228017	+	0.915516i
$178$	−1.78755	−	3.09613i	−0.133983	−	0.232065i
$179$	−9.13272			−0.682612			−0.341306	−	0.939952i	$-0.610869\pi$
$179$	−9.13272			−0.682612			−0.341306	+	0.939952i	$0.610869\pi$
$180$	2.64956	+	1.40707i	0.197486	+	0.104877i
$181$	−10.7586			−0.799680			−0.399840	−	0.916585i	$-0.630934\pi$
$181$	−10.7586			−0.799680			−0.399840	+	0.916585i	$0.630934\pi$
$182$	−0.933868	−	1.61751i	−0.0692229	−	0.119898i
$183$	3.29484	+	3.18017i	0.243562	+	0.235085i
$184$	−3.58343	+	6.20668i	−0.264174	+	0.457562i
$185$	−2.10947	+	3.65371i	−0.155091	+	0.268626i
$186$	−13.6072	+	3.90556i	−0.997732	+	0.286370i
$187$	−4.69614	−	8.13395i	−0.343416	−	0.594813i
$188$	6.87423			0.501354
$189$	5.08343	+	1.07646i	0.369765	+	0.0783013i
$190$	−5.08667			−0.369026
$191$	−7.77609	−	13.4686i	−0.562658	−	0.974553i	−0.997263	−	0.0739315i	$-0.976445\pi$
$191$	−7.77609	−	13.4686i	−0.562658	−	0.974553i	0.434605	−	0.900621i	$-0.356888\pi$
$192$	1.66483	−	0.477841i	0.120149	−	0.0344852i
$193$	1.69538	−	2.93649i	0.122036	−	0.211373i	−0.798534	−	0.601949i	$-0.794391\pi$
$193$	1.69538	−	2.93649i	0.122036	−	0.211373i	0.920571	+	0.390576i	$0.127724\pi$
$194$	−5.01156	+	8.68028i	−0.359809	+	0.623208i
$195$	−2.32765	−	2.24664i	−0.166686	−	0.160885i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−6.55264			−0.466856			−0.233428	−	0.972374i	$-0.574994\pi$
$197$	−6.55264			−0.466856			−0.233428	+	0.972374i	$0.574994\pi$
$198$	−0.655060	−	18.4890i	−0.0465531	−	1.31395i
$199$	−1.85627			−0.131588			−0.0657938	−	0.997833i	$-0.520958\pi$
$199$	−1.85627			−0.131588			−0.0657938	+	0.997833i	$0.520958\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−0.204457	+	0.820921i	−0.0144213	+	0.0579033i
$202$	8.12126	−	14.0664i	0.571410	−	0.989711i
$203$	5.23872	−	9.07372i	0.367686	−	0.636851i
$204$	0.637529	−	2.55976i	0.0446360	−	0.179219i
$205$	0.433868	+	0.751481i	0.0303027	+	0.0524857i
$206$	10.2881			0.716807
$207$	0.761283	+	21.4871i	0.0529128	+	1.49346i
$208$	−1.86774			−0.129504
$209$	15.6844	+	27.1661i	1.08491	+	1.87912i
$210$	−1.24624	−	1.20287i	−0.0859987	−	0.0830057i
$211$	0.643069	−	1.11383i	0.0442707	−	0.0766791i	−0.843041	−	0.537849i	$-0.819237\pi$
$211$	0.643069	−	1.11383i	0.0442707	−	0.0766791i	0.887312	+	0.461170i	$0.152570\pi$
$212$	−0.0227964	+	0.0394845i	−0.00156566	+	0.00271180i
$213$	5.56838	−	1.59824i	0.381539	−	0.109510i
$214$	5.36548	+	9.29328i	0.366777	+	0.635276i
$215$	8.03459			0.547954
$216$	3.47396	−	3.86414i	0.236373	−	0.262922i
$217$	8.17334			0.554843
$218$	−7.88828	−	13.6629i	−0.534261	−	0.925368i
$219$	−7.88377	+	2.26280i	−0.532736	+	0.152906i
$220$	−3.08343	+	5.34065i	−0.207885	+	0.360067i
$221$	−1.42231	+	2.46351i	−0.0956746	+	0.165713i
$222$	5.25780	+	5.07482i	0.352881	+	0.340599i
$223$	−0.620272	−	1.07434i	−0.0415365	−	0.0719433i	0.844510	−	0.535540i	$-0.179892\pi$
$223$	−0.620272	−	1.07434i	−0.0415365	−	0.0719433i	−0.886046	+	0.463597i	$0.846559\pi$
$224$	−1.00000			−0.0668153
$225$	−2.64956	−	1.40707i	−0.176637	−	0.0938045i
$226$	15.8107			1.05171
$227$	9.85650	+	17.0720i	0.654199	+	1.13311i	0.982094	+	0.188392i	$0.0603275\pi$
$227$	9.85650	+	17.0720i	0.654199	+	1.13311i	−0.327895	+	0.944714i	$0.606339\pi$
$228$	−2.12925	+	8.54921i	−0.141013	+	0.566185i
$229$	−3.05739	+	5.29555i	−0.202038	+	0.349940i	−0.949185	−	0.314719i	$-0.898090\pi$
$229$	−3.05739	+	5.29555i	−0.202038	+	0.349940i	0.747147	+	0.664659i	$0.231423\pi$
$230$	3.58343	−	6.20668i	0.236284	−	0.409256i
$231$	−2.58141	+	10.3647i	−0.169844	+	0.681946i
$232$	−5.23872	−	9.07372i	−0.343939	−	0.595719i
$233$	−5.30561			−0.347582			−0.173791	−	0.984783i	$-0.555602\pi$
$233$	−5.30561			−0.347582			−0.173791	+	0.984783i	$0.555602\pi$
$234$	−4.75028	+	2.97166i	−0.310535	+	0.194264i
$235$	−6.87423			−0.448425
$236$	−3.62352	−	6.27612i	−0.235871	−	0.408540i
$237$	−16.2442	−	15.6789i	−1.05517	−	1.01845i
$238$	−0.761513	+	1.31898i	−0.0493616	+	0.0854967i
$239$	11.9088	−	20.6267i	0.770317	−	1.33423i	−0.167072	−	0.985945i	$-0.553431\pi$
$239$	11.9088	−	20.6267i	0.770317	−	1.33423i	0.937389	−	0.348284i	$-0.113235\pi$
$240$	−1.66483	+	0.477841i	−0.107464	+	0.0308445i
$241$	4.73600	+	8.20299i	0.305073	+	0.528401i	0.977277	−	0.211964i	$-0.0679859\pi$
$241$	4.73600	+	8.20299i	0.305073	+	0.528401i	−0.672205	+	0.740365i	$0.734653\pi$
$242$	27.0301			1.73756
$243$	2.68739	−	15.3551i	0.172396	−	0.985028i
$244$	−2.64383			−0.169254
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	1.44464	−	0.414640i	0.0921066	−	0.0264365i
$247$	4.75028	−	8.22773i	0.302253	−	0.523518i
$248$	4.08667	−	7.07832i	0.259504	−	0.449474i
$249$	−18.4070	−	17.7664i	−1.16650	−	1.12590i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	22.2771			1.40612			0.703059	−	0.711131i	$-0.251817\pi$
$251$	22.2771			1.40612			0.703059	+	0.711131i	$0.251817\pi$
$252$	−2.54334	+	1.59105i	−0.160215	+	0.100227i
$253$	−44.1969			−2.77864
$254$	−2.58343	−	4.47463i	−0.162099	−	0.280763i
$255$	−0.637529	+	2.55976i	−0.0399236	+	0.160299i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.0982	−	19.2227i	0.692289	−	1.19908i	−0.278797	−	0.960350i	$-0.589936\pi$
$257$	11.0982	−	19.2227i	0.692289	−	1.19908i	0.971086	−	0.238729i	$-0.0767309\pi$
$258$	3.36323	−	13.5038i	0.209385	−	0.840710i
$259$	−2.10947	−	3.65371i	−0.131076	−	0.227030i
$260$	1.86774			0.115832
$261$	−27.7606	−	14.7425i	−1.71834	−	0.912535i
$262$	10.7876			0.666457
$263$	−5.71569	−	9.89987i	−0.352445	−	0.610452i	0.634233	−	0.773142i	$-0.281316\pi$
$263$	−5.71569	−	9.89987i	−0.352445	−	0.610452i	−0.986677	+	0.162690i	$0.947983\pi$
$264$	7.68537	+	7.41790i	0.473002	+	0.456540i
$265$	0.0227964	−	0.0394845i	0.00140037	−	0.00242551i
$266$	2.54334	−	4.40519i	0.155942	−	0.270099i
$267$	5.95196	−	1.70833i	0.364254	−	0.104548i
$268$	−0.244219	−	0.422999i	−0.0149180	−	0.0258388i
$269$	4.37930			0.267011			0.133505	−	0.991048i	$-0.457377\pi$
$269$	4.37930			0.267011			0.133505	+	0.991048i	$0.457377\pi$
$270$	−3.47396	+	3.86414i	−0.211418	+	0.235164i
$271$	−17.9614			−1.09107			−0.545537	−	0.838087i	$-0.683674\pi$
$271$	−17.9614			−1.09107			−0.545537	+	0.838087i	$0.683674\pi$
$272$	0.761513	+	1.31898i	0.0461735	+	0.0799749i
$273$	3.10947	−	0.892481i	0.188194	−	0.0540154i
$274$	−6.82765	+	11.8258i	−0.412473	+	0.714424i
$275$	3.08343	−	5.34065i	0.185938	−	0.322053i
$276$	−8.93161	−	8.62077i	−0.537620	−	0.518909i
$277$	−8.12126	−	14.0664i	−0.487959	−	0.845170i	0.511945	−	0.859018i	$-0.328925\pi$
$277$	−8.12126	−	14.0664i	−0.487959	−	0.845170i	−0.999904	+	0.0138481i	$0.995592\pi$
$278$	0.654831			0.0392741
$279$	−0.868195	−	24.5047i	−0.0519775	−	1.46706i
$280$	1.00000			0.0597614
$281$	−0.381556	−	0.660874i	−0.0227617	−	0.0394244i	0.854420	−	0.519583i	$-0.173913\pi$
$281$	−0.381556	−	0.660874i	−0.0227617	−	0.0394244i	−0.877182	+	0.480158i	$0.840579\pi$
$282$	−2.87751	+	11.5536i	−0.171353	+	0.688005i
$283$	4.43711	−	7.68530i	0.263759	−	0.456844i	−0.703479	−	0.710716i	$-0.748371\pi$
$283$	4.43711	−	7.68530i	0.263759	−	0.456844i	0.967238	+	0.253872i	$0.0817043\pi$
$284$	−1.67235	+	2.89660i	−0.0992360	+	0.171882i
$285$	2.12925	−	8.54921i	0.126126	−	0.506411i
$286$	−5.75903	−	9.97493i	−0.340538	−	0.589830i
$287$	−0.867736			−0.0512208
$288$	0.106223	+	2.99812i	0.00625924	+	0.176666i
$289$	−14.6804			−0.863552
$290$	5.23872	+	9.07372i	0.307628	+	0.532827i
$291$	−12.4912	−	12.0565i	−0.732248	−	0.706764i
$292$	2.36774	−	4.10104i	0.138561	−	0.239995i
$293$	−5.68156	+	9.84075i	−0.331920	+	0.574903i	−0.982888	−	0.184202i	$-0.941030\pi$
$293$	−5.68156	+	9.84075i	−0.331920	+	0.574903i	0.650968	+	0.759105i	$0.274363\pi$
$294$	1.66483	−	0.477841i	0.0970950	−	0.0278683i
$295$	3.62352	+	6.27612i	0.210969	+	0.365410i
$296$	−4.21894			−0.245221
$297$	31.3487	+	6.63840i	1.81904	+	0.385199i
$298$	18.7830			1.08807
$299$	6.69289	+	11.5924i	0.387060	+	0.670408i
$300$	1.66483	−	0.477841i	0.0961192	−	0.0275882i
$301$	−4.01729	+	6.95816i	−0.231553	+	0.401062i
$302$	2.17258	−	3.76303i	0.125018	−	0.216538i
$303$	20.2421	+	19.5376i	1.16288	+	1.12241i
$304$	−2.54334	−	4.40519i	−0.145870	−	0.252655i
$305$	2.64383			0.151385
$306$	4.03535	+	2.14300i	0.230685	+	0.122507i
$307$	30.1678			1.72177			0.860883	−	0.508803i	$-0.169912\pi$
$307$	30.1678			1.72177			0.860883	+	0.508803i	$0.169912\pi$
$308$	−3.08343	−	5.34065i	−0.175695	−	0.304312i
$309$	−4.30654	+	17.2913i	−0.244991	+	0.983668i
$310$	−4.08667	+	7.07832i	−0.232107	+	0.402022i
$311$	3.85627	−	6.67926i	0.218669	−	0.378746i	−0.735732	−	0.677273i	$-0.763162\pi$
$311$	3.85627	−	6.67926i	0.218669	−	0.378746i	0.954401	+	0.298526i	$0.0964951\pi$
$312$	0.781823	−	3.13912i	0.0442620	−	0.177718i
$313$	1.23276	+	2.13519i	0.0696794	+	0.120688i	0.898760	−	0.438441i	$-0.144469\pi$
$313$	1.23276	+	2.13519i	0.0696794	+	0.120688i	−0.829081	+	0.559129i	$0.811136\pi$
$314$	−13.1783			−0.743695
$315$	2.54334	−	1.59105i	0.143301	−	0.0896456i
$316$	13.0346			0.733253
$317$	−9.79935	−	16.9730i	−0.550386	−	0.953297i	−0.998247	−	0.0591933i	$-0.981147\pi$
$317$	−9.79935	−	16.9730i	−0.550386	−	0.953297i	0.447860	−	0.894104i	$-0.352186\pi$
$318$	−0.0568194	−	0.0548420i	−0.00318628	−	0.00307539i
$319$	32.3064	−	55.9563i	1.80881	−	3.13295i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−17.8652	+	5.12769i	−0.997141	+	0.286200i
$322$	3.58343	+	6.20668i	0.199697	+	0.345885i
$323$	−7.74713			−0.431062
$324$	5.04032	+	7.45622i	0.280018	+	0.414234i
$325$	−1.86774			−0.103603
$326$	−0.738487	−	1.27910i	−0.0409010	−	0.0708426i
$327$	26.2653	−	7.53868i	1.45248	−	0.416890i
$328$	−0.433868	+	0.751481i	−0.0239563	+	0.0414936i
$329$	3.43711	−	5.95325i	0.189494	−	0.328214i
$330$	−7.68537	−	7.41790i	−0.423066	−	0.408342i
$331$	−12.5238	−	21.6918i	−0.688369	−	1.19229i	−0.972365	−	0.233465i	$-0.924993\pi$
$331$	−12.5238	−	21.6918i	−0.688369	−	1.19229i	0.283996	−	0.958826i	$-0.408340\pi$
$332$	14.7701			0.810612
$333$	−10.7302	+	6.71254i	−0.588010	+	0.367845i
$334$	23.1623			1.26739
$335$	0.244219	+	0.422999i	0.0133431	+	0.0231109i
$336$	0.418594	−	1.68071i	0.0228362	−	0.0916901i
$337$	1.09217	−	1.89170i	0.0594945	−	0.103047i	−0.834744	−	0.550638i	$-0.814384\pi$
$337$	1.09217	−	1.89170i	0.0594945	−	0.103047i	0.894239	+	0.447591i	$0.147718\pi$
$338$	4.75578	−	8.23725i	0.258680	−	0.448048i
$339$	−6.61825	+	26.5731i	−0.359454	+	1.44325i
$340$	−0.761513	−	1.31898i	−0.0412988	−	0.0715317i
$341$	50.4038			2.72952
$342$	−13.4774	−	7.15729i	−0.728776	−	0.387022i
$343$	−1.00000			−0.0539949
$344$	4.01729	+	6.95816i	0.216598	+	0.375159i
$345$	8.93161	+	8.62077i	0.480862	+	0.464127i
$346$	4.08667	−	7.07832i	0.219701	−	0.380533i
$347$	−1.96823	+	3.40907i	−0.105660	+	0.183008i	−0.914008	−	0.405697i	$-0.867029\pi$
$347$	−1.96823	+	3.40907i	−0.105660	+	0.183008i	0.808348	+	0.588705i	$0.200362\pi$
$348$	17.4432	−	5.00655i	0.935052	−	0.268379i
$349$	−17.9206	−	31.0394i	−0.959268	−	1.66150i	−0.724284	−	0.689502i	$-0.757829\pi$
$349$	−17.9206	−	31.0394i	−0.959268	−	1.66150i	−0.234984	−	0.971999i	$-0.575504\pi$
$350$	−1.00000			−0.0534522
$351$	−3.00606	−	9.22775i	−0.160452	−	0.492541i
$352$	−6.16685			−0.328694
$353$	3.75277	+	6.49998i	0.199740	+	0.345959i	0.948444	−	0.316945i	$-0.102657\pi$
$353$	3.75277	+	6.49998i	0.199740	+	0.345959i	−0.748704	+	0.662904i	$0.769324\pi$
$354$	12.0651	−	3.46293i	0.641253	−	0.184053i
$355$	1.67235	−	2.89660i	0.0887594	−	0.153736i
$356$	−1.78755	+	3.09613i	−0.0947402	+	0.164095i
$357$	−1.89805	−	1.83200i	−0.100456	−	0.0969596i
$358$	4.56636	+	7.90917i	0.241340	+	0.418013i
$359$	28.6218			1.51060			0.755301	−	0.655378i	$-0.227491\pi$
$359$	28.6218			1.51060			0.755301	+	0.655378i	$0.227491\pi$
$360$	−0.106223	−	2.99812i	−0.00559843	−	0.158015i
$361$	6.87423			0.361801
$362$	5.37930	+	9.31722i	0.282730	+	0.489702i
$363$	−11.3146	+	45.4297i	−0.593864	+	2.38444i
$364$	−0.933868	+	1.61751i	−0.0489480	+	0.0847804i
$365$	−2.36774	+	4.10104i	−0.123933	+	0.214658i
$366$	1.10669	−	4.44350i	0.0578476	−	0.232266i
$367$	−3.93085	−	6.80844i	−0.205189	−	0.355398i	0.745004	−	0.667060i	$-0.232448\pi$
$367$	−3.93085	−	6.80844i	−0.205189	−	0.355398i	−0.950193	+	0.311662i	$0.899114\pi$
$368$	7.16685			0.373598
$369$	0.0921733	+	2.60158i	0.00479835	+	0.135433i
$370$	4.21894			0.219332
$371$	0.0227964	+	0.0394845i	0.00118353	+	0.00204993i
$372$	10.1859	+	9.83144i	0.528116	+	0.509737i
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	−0.581122	−	0.813816i	$-0.697386\pi$
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	0.995347	+	0.0963587i	$0.0307196\pi$
$374$	−4.69614	+	8.13395i	−0.242832	+	0.420597i
$375$	−1.66483	+	0.477841i	−0.0859716	+	0.0246756i
$376$	−3.43711	−	5.95325i	−0.177256	−	0.307016i
$377$	−19.5691			−1.00786
$378$	−1.60947	−	4.94061i	−0.0827821	−	0.254117i
$379$	−4.25201			−0.218411			−0.109205	−	0.994019i	$-0.534831\pi$
$379$	−4.25201			−0.218411			−0.109205	+	0.994019i	$0.534831\pi$
$380$	2.54334	+	4.40519i	0.130470	+	0.225981i
$381$	8.60195	−	2.46893i	0.440691	−	0.126487i
$382$	−7.77609	+	13.4686i	−0.397859	+	0.689113i
$383$	7.12699	−	12.3443i	0.364172	−	0.630765i	−0.624471	−	0.781048i	$-0.714685\pi$
$383$	7.12699	−	12.3443i	0.364172	−	0.630765i	0.988643	+	0.150283i	$0.0480186\pi$
$384$	−1.24624	−	1.20287i	−0.0635969	−	0.0613835i
$385$	3.08343	+	5.34065i	0.157146	+	0.272185i
$386$	−3.39076			−0.172585
$387$	21.2881	+	11.3052i	1.08214	+	0.574676i
$388$	10.0231			0.508847
$389$	−6.65605	−	11.5286i	−0.337475	−	0.584524i	0.646482	−	0.762929i	$-0.276240\pi$
$389$	−6.65605	−	11.5286i	−0.337475	−	0.584524i	−0.983957	+	0.178405i	$0.942906\pi$
$390$	−0.781823	+	3.13912i	−0.0395891	+	0.158955i
$391$	5.45765	−	9.45293i	0.276005	−	0.478055i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−4.51560	+	18.1307i	−0.227782	+	0.914574i
$394$	3.27632	+	5.67475i	0.165059	+	0.285890i
$395$	−13.0346			−0.655841
$396$	−15.6844	+	9.81178i	−0.788170	+	0.493060i
$397$	−21.7880			−1.09351			−0.546755	−	0.837293i	$-0.684137\pi$
$397$	−21.7880			−1.09351			−0.546755	+	0.837293i	$0.684137\pi$
$398$	0.928136	+	1.60758i	0.0465233	+	0.0805807i
$399$	6.33921	+	6.11859i	0.317357	+	0.306313i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	0.839438	−	1.45395i	0.0419195	−	0.0726067i	−0.844304	−	0.535864i	$-0.819986\pi$
$401$	0.839438	−	1.45395i	0.0419195	−	0.0726067i	0.886224	+	0.463257i	$0.153319\pi$
$402$	0.813166	−	0.233395i	0.0405571	−	0.0116407i
$403$	−7.63282	−	13.2204i	−0.380218	−	0.658557i
$404$	−16.2425			−0.808096
$405$	−5.04032	−	7.45622i	−0.250456	−	0.370502i
$406$	−10.4774			−0.519986
$407$	−13.0088	−	22.5319i	−0.644821	−	1.11686i
$408$	−2.53558	+	0.727765i	−0.125530	+	0.0360297i
$409$	−9.29663	+	16.1022i	−0.459689	+	0.796204i	−0.998944	−	0.0459379i	$-0.985372\pi$
$409$	−9.29663	+	16.1022i	−0.459689	+	0.796204i	0.539256	+	0.842142i	$0.318706\pi$
$410$	0.433868	−	0.751481i	0.0214272	−	0.0371130i
$411$	−17.0178	−	16.4255i	−0.839424	−	0.810210i
$412$	−5.14406	−	8.90977i	−0.253429	−	0.438953i
$413$	−7.24703			−0.356603
$414$	18.2277	−	11.4028i	0.895843	−	0.560418i
$415$	−14.7701			−0.725034
$416$	0.933868	+	1.61751i	0.0457866	+	0.0793048i
$417$	−0.274108	+	1.10058i	−0.0134231	+	0.0538956i
$418$	15.6844	−	27.1661i	0.767148	−	1.32874i
$419$	17.9920	−	31.1631i	0.878967	−	1.52242i	0.0264916	−	0.999649i	$-0.491566\pi$
$419$	17.9920	−	31.1631i	0.878967	−	1.52242i	0.852476	−	0.522767i	$-0.175100\pi$
$420$	−0.418594	+	1.68071i	−0.0204253	+	0.0820102i
$421$	2.54357	+	4.40558i	0.123966	+	0.214715i	0.921328	−	0.388786i	$-0.127105\pi$
$421$	2.54357	+	4.40558i	0.123966	+	0.214715i	−0.797362	+	0.603501i	$0.793772\pi$
$422$	−1.28614			−0.0626082
$423$	−18.2137	−	9.67250i	−0.885579	−	0.470293i
$424$	0.0455927			0.00221418
$425$	0.761513	+	1.31898i	0.0369388	+	0.0639799i
$426$	−4.16831	−	4.02324i	−0.201955	−	0.194927i
$427$	−1.32191	+	2.28962i	−0.0639719	+	0.110803i
$428$	5.36548	−	9.29328i	0.259350	−	0.449208i
$429$	19.1756	−	5.50380i	0.925808	−	0.265726i
$430$	−4.01729	−	6.95816i	−0.193731	−	0.335552i
$431$	24.3452			1.17267			0.586333	−	0.810070i	$-0.300571\pi$
$431$	24.3452			1.17267			0.586333	+	0.810070i	$0.300571\pi$
$432$	−5.08343	−	1.07646i	−0.244576	−	0.0517914i
$433$	−4.20701			−0.202176			−0.101088	−	0.994877i	$-0.532232\pi$
$433$	−4.20701			−0.202176			−0.101088	+	0.994877i	$0.532232\pi$
$434$	−4.08667	−	7.07832i	−0.196167	−	0.339770i
$435$	−17.4432	+	5.00655i	−0.836336	+	0.240046i
$436$	−7.88828	+	13.6629i	−0.377780	+	0.654334i
$437$	−18.2277	+	31.5713i	−0.871950	+	1.51026i
$438$	5.90153	+	5.69614i	0.281986	+	0.272172i
$439$	12.4577	+	21.5773i	0.594571	+	1.02983i	0.993607	+	0.112892i	$0.0360115\pi$
$439$	12.4577	+	21.5773i	0.594571	+	1.02983i	−0.399036	+	0.916935i	$0.630655\pi$
$440$	6.16685			0.293993
$441$	0.106223	+	2.99812i	0.00505823	+	0.142768i
$442$	2.84461			0.135304
$443$	−14.1500	−	24.5086i	−0.672288	−	1.16444i	−0.977254	−	0.212073i	$-0.931978\pi$
$443$	−14.1500	−	24.5086i	−0.672288	−	1.16444i	0.304966	−	0.952363i	$-0.401355\pi$
$444$	1.76602	−	7.09080i	0.0838116	−	0.336514i
$445$	1.78755	−	3.09613i	0.0847382	−	0.146771i
$446$	−0.620272	+	1.07434i	−0.0293707	+	0.0508716i
$447$	−7.86246	+	31.5688i	−0.371882	+	1.49315i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−3.60275			−0.170024			−0.0850121	−	0.996380i	$-0.527093\pi$
$449$	−3.60275			−0.170024			−0.0850121	+	0.996380i	$0.527093\pi$
$450$	0.106223	+	2.99812i	0.00500739	+	0.141333i
$451$	−5.35120			−0.251978
$452$	−7.90534	−	13.6925i	−0.371836	−	0.644039i
$453$	5.41512	+	5.22666i	0.254424	+	0.245570i
$454$	9.85650	−	17.0720i	0.462589	−	0.801227i
$455$	0.933868	−	1.61751i	0.0437804	−	0.0758299i
$456$	8.46846	−	2.43062i	0.396572	−	0.113824i
$457$	14.1302	+	24.4743i	0.660985	+	1.14486i	0.980357	+	0.197230i	$0.0631945\pi$
$457$	14.1302	+	24.4743i	0.660985	+	1.14486i	−0.319373	+	0.947629i	$0.603472\pi$
$458$	6.11477			0.285724
$459$	−5.29093	+	5.88519i	−0.246959	+	0.274697i
$460$	−7.16685			−0.334156
$461$	16.2768	+	28.1922i	0.758085	+	1.31304i	0.943826	+	0.330443i	$0.107198\pi$
$461$	16.2768	+	28.1922i	0.758085	+	1.31304i	−0.185741	+	0.982599i	$0.559468\pi$
$462$	10.2668	−	2.94678i	0.477654	−	0.137096i
$463$	−17.4204	+	30.1730i	−0.809594	+	1.40226i	0.103552	+	0.994624i	$0.466979\pi$
$463$	−17.4204	+	30.1730i	−0.809594	+	1.40226i	−0.913146	+	0.407633i	$0.866354\pi$
$464$	−5.23872	+	9.07372i	−0.243201	+	0.421237i
$465$	−10.1859	−	9.83144i	−0.472362	−	0.455922i
$466$	2.65280	+	4.59479i	0.122889	+	0.212850i
$467$	−42.1518			−1.95055			−0.975276	−	0.220989i	$-0.929071\pi$
$467$	−42.1518			−1.95055			−0.975276	+	0.220989i	$0.929071\pi$
$468$	4.94868	+	2.62803i	0.228753	+	0.121481i
$469$	−0.488437			−0.0225539
$470$	3.43711	+	5.95325i	0.158542	+	0.274603i
$471$	5.51636	−	22.1489i	0.254181	−	1.02057i
$472$	−3.62352	+	6.27612i	−0.166786	+	0.288882i
$473$	−24.7741	+	42.9099i	−1.13911	+	1.97300i
$474$	−5.45620	+	21.9073i	−0.250611	+	1.00624i
$475$	−2.54334	−	4.40519i	−0.116696	−	0.202124i
$476$	1.52303			0.0698078
$477$	0.115958	−	0.0725404i	0.00530933	−	0.00332139i
$478$	−23.8176			−1.08939
$479$	−7.74379	−	13.4126i	−0.353823	−	0.612839i	0.633093	−	0.774076i	$-0.281785\pi$
$479$	−7.74379	−	13.4126i	−0.353823	−	0.612839i	−0.986916	+	0.161237i	$0.948452\pi$
$480$	1.24624	+	1.20287i	0.0568828	+	0.0549031i
$481$	−3.93993	+	6.82416i	−0.179645	+	0.311155i
$482$	4.73600	−	8.20299i	0.215719	−	0.373636i
$483$	−11.9316	+	3.42462i	−0.542907	+	0.155825i
$484$	−13.5150	−	23.4087i	−0.614320	−	1.06403i
$485$	−10.0231			−0.455127
$486$	−14.6416	+	5.35018i	−0.664155	+	0.242689i
$487$	12.0009			0.543814			0.271907	−	0.962324i	$-0.412346\pi$
$487$	12.0009			0.543814			0.271907	+	0.962324i	$0.412346\pi$
$488$	1.32191	+	2.28962i	0.0598402	+	0.103646i
$489$	2.45891	−	0.705759i	0.111196	−	0.0319155i
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	−11.9953	+	20.7764i	−0.541338	+	0.937625i	0.457489	+	0.889215i	$0.348749\pi$
$491$	−11.9953	+	20.7764i	−0.541338	+	0.937625i	−0.998828	+	0.0484103i	$0.984584\pi$
$492$	−1.08141	−	1.04377i	−0.0487536	−	0.0470568i
$493$	7.97870	+	13.8195i	0.359343	+	0.622400i
$494$	−9.50056			−0.427450
$495$	15.6844	−	9.81178i	0.704960	−	0.441007i
$496$	−8.17334			−0.366994
$497$	1.67235	+	2.89660i	0.0750154	+	0.129930i
$498$	−6.18266	+	24.8242i	−0.277051	+	1.11240i
$499$	−11.7273	+	20.3122i	−0.524984	+	0.909299i	0.474593	+	0.880206i	$0.342595\pi$
$499$	−11.7273	+	20.3122i	−0.524984	+	0.909299i	−0.999577	+	0.0290934i	$0.990738\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−9.69561	+	38.9291i	−0.433168	+	1.73923i
$502$	−11.1386	−	19.2925i	−0.497138	−	0.861068i
$503$	23.8968			1.06550			0.532752	−	0.846272i	$-0.321158\pi$
$503$	23.8968			1.06550			0.532752	+	0.846272i	$0.321158\pi$
$504$	2.64956	+	1.40707i	0.118021	+	0.0626758i
$505$	16.2425			0.722783
$506$	22.0985	+	38.2757i	0.982397	+	1.70156i
$507$	11.8537	+	11.4411i	0.526440	+	0.508119i
$508$	−2.58343	+	4.47463i	−0.114621	+	0.198529i
$509$	1.32191	−	2.28962i	0.0585928	−	0.101486i	−0.835241	−	0.549884i	$-0.814672\pi$
$509$	1.32191	−	2.28962i	0.0585928	−	0.101486i	0.893834	+	0.448398i	$0.148005\pi$
$510$	2.53558	−	0.727765i	0.112278	−	0.0322260i
$511$	−2.36774	−	4.10104i	−0.104742	−	0.181419i
$512$	1.00000			0.0441942
$513$	17.6709	−	19.6556i	0.780189	−	0.867817i
$514$	−22.1965			−0.979044
$515$	5.14406	+	8.90977i	0.226674	+	0.392611i
$516$	−13.3762	+	3.83926i	−0.588856	+	0.169014i
$517$	21.1962	−	36.7128i	0.932206	−	1.61463i
$518$	−2.10947	+	3.65371i	−0.0926847	+	0.160535i
$519$	10.1859	+	9.83144i	0.447113	+	0.431552i
$520$	−0.933868	−	1.61751i	−0.0409528	−	0.0709324i
$521$	38.3227			1.67895			0.839474	−	0.543400i	$-0.182863\pi$
$521$	38.3227			1.67895			0.839474	+	0.543400i	$0.182863\pi$
$522$	1.11294	+	31.4126i	0.0487122	+	1.37489i
$523$	27.9043			1.22017			0.610085	−	0.792336i	$-0.291135\pi$
$523$	27.9043			1.22017			0.610085	+	0.792336i	$0.291135\pi$
$524$	−5.39378	−	9.34230i	−0.235628	−	0.408120i
$525$	0.418594	−	1.68071i	0.0182689	−	0.0733521i
$526$	−5.71569	+	9.89987i	−0.249216	+	0.431655i
$527$	−6.22411	+	10.7805i	−0.271126	+	0.469605i
$528$	2.58141	−	10.3647i	0.112341	−	0.451065i
$529$	−14.1819	−	24.5638i	−0.616604	−	1.06799i
$530$	−0.0455927			−0.00198042
$531$	0.769800	+	21.7275i	0.0334065	+	0.942892i
$532$	−5.08667			−0.220535
$533$	0.810351	+	1.40357i	0.0351002	+	0.0607953i
$534$	−4.45544	−	4.30038i	−0.192806	−	0.186096i
$535$	−5.36548	+	9.29328i	−0.231970	+	0.401784i
$536$	−0.244219	+	0.422999i	−0.0105486	+	0.0182708i
$537$	−15.2045	+	4.36399i	−0.656121	+	0.188320i
$538$	−2.18965	−	3.79258i	−0.0944025	−	0.163510i
$539$	−6.16685			−0.265625
$540$	5.08343	+	1.07646i	0.218756	+	0.0463237i
$541$	−19.0355			−0.818400			−0.409200	−	0.912445i	$-0.634192\pi$
$541$	−19.0355			−0.818400			−0.409200	+	0.912445i	$0.634192\pi$
$542$	8.98068	+	15.5550i	0.385753	+	0.668144i
$543$	−17.9113	+	5.14090i	−0.768646	+	0.220617i
$544$	0.761513	−	1.31898i	0.0326496	−	0.0565508i
$545$	7.88828	−	13.6629i	0.337897	−	0.585254i
$546$	−2.32765	−	2.24664i	−0.0996140	−	0.0961472i
$547$	11.8113	+	20.4578i	0.505016	+	0.874714i	0.999983	+	0.00580213i	$0.00184688\pi$
$547$	11.8113	+	20.4578i	0.505016	+	0.874714i	−0.494967	+	0.868912i	$0.664820\pi$
$548$	13.6553			0.583325
$549$	7.00497	+	3.72004i	0.298965	+	0.158768i
$550$	−6.16685			−0.262955
$551$	−26.6476	−	46.1550i	−1.13523	−	1.96627i
$552$	−3.00000	+	12.0454i	−0.127688	+	0.512686i
$553$	6.51729	−	11.2883i	0.277144	−	0.480027i
$554$	−8.12126	+	14.0664i	−0.345039	+	0.597626i
$555$	−1.76602	+	7.09080i	−0.0749634	+	0.300988i
$556$	−0.327415	−	0.567100i	−0.0138855	−	0.0240504i
$557$	16.8628			0.714498			0.357249	−	0.934009i	$-0.383715\pi$
$557$	16.8628			0.714498			0.357249	+	0.934009i	$0.383715\pi$
$558$	−20.7876	+	13.0042i	−0.880007	+	0.550512i
$559$	15.0065			0.634707
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	−11.7050	−	11.2977i	−0.494186	−	0.476988i
$562$	−0.381556	+	0.660874i	−0.0160950	+	0.0278773i
$563$	8.99224	−	15.5750i	0.378978	−	0.656409i	−0.611936	−	0.790907i	$-0.709609\pi$
$563$	8.99224	−	15.5750i	0.378978	−	0.656409i	0.990914	+	0.134499i	$0.0429423\pi$
$564$	11.4444	−	3.28479i	0.481898	−	0.138315i
$565$	7.90534	+	13.6925i	0.332580	+	0.576046i
$566$	−8.87423			−0.373012
$567$	8.97743	−	0.636937i	0.377017	−	0.0267489i
$568$	3.34471			0.140341
$569$	−3.75005	−	6.49528i	−0.157210	−	0.272296i	0.776651	−	0.629931i	$-0.216917\pi$
$569$	−3.75005	−	6.49528i	−0.157210	−	0.272296i	−0.933862	+	0.357635i	$0.883583\pi$
$570$	−8.46846	+	2.43062i	−0.354705	+	0.101808i
$571$	−0.0177236	+	0.0306981i	−0.000741709	+	0.00128468i	−0.866396	−	0.499358i	$-0.833569\pi$
$571$	−0.0177236	+	0.0306981i	−0.000741709	+	0.00128468i	0.865654	+	0.500642i	$0.166903\pi$
$572$	−5.75903	+	9.97493i	−0.240797	+	0.417073i
$573$	−19.3817	−	18.7072i	−0.809684	−	0.781505i
$574$	0.433868	+	0.751481i	0.0181093	+	0.0313662i
$575$	7.16685			0.298878
$576$	2.54334	−	1.59105i	0.105972	−	0.0662938i
$577$	−29.0402			−1.20896			−0.604480	−	0.796620i	$-0.706619\pi$
$577$	−29.0402			−1.20896			−0.604480	+	0.796620i	$0.706619\pi$
$578$	7.34020	+	12.7136i	0.305312	+	0.528816i
$579$	1.41935	−	5.69888i	0.0589863	−	0.236837i
$580$	5.23872	−	9.07372i	0.217526	−	0.376766i
$581$	7.38503	−	12.7912i	0.306383	−	0.530670i
$582$	−4.19562	+	16.8459i	−0.173914	+	0.698287i
$583$	0.140582	+	0.243495i	0.00582230	+	0.0100845i
$584$	−4.73547			−0.195955
$585$	−4.94868	−	2.62803i	−0.204603	−	0.108656i
$586$	11.3631			0.469406
$587$	18.2445	+	31.6005i	0.753033	+	1.30429i	0.946346	+	0.323154i	$0.104743\pi$
$587$	18.2445	+	31.6005i	0.753033	+	1.30429i	−0.193313	+	0.981137i	$0.561923\pi$
$588$	−1.24624	−	1.20287i	−0.0513940	−	0.0496054i
$589$	20.7876	−	36.0051i	0.856536	−	1.48356i
$590$	3.62352	−	6.27612i	0.149178	−	0.258384i
$591$	−10.9091	+	3.13112i	−0.448738	+	0.128797i
$592$	2.10947	+	3.65371i	0.0866986	+	0.150166i
$593$	2.60426			0.106944			0.0534722	−	0.998569i	$-0.482971\pi$
$593$	2.60426			0.106944			0.0534722	+	0.998569i	$0.482971\pi$
$594$	−9.92535	−	30.4680i	−0.407242	−	1.25012i
$595$	−1.52303			−0.0624380
$596$	−9.39152	−	16.2666i	−0.384692	−	0.666305i
$597$	−3.09038	+	0.887003i	−0.126481	+	0.0363026i
$598$	6.69289	−	11.5924i	0.273693	−	0.474050i
$599$	−1.79329	+	3.10606i	−0.0732717	+	0.126910i	−0.900333	−	0.435201i	$-0.856677\pi$
$599$	−1.79329	+	3.10606i	−0.0732717	+	0.126910i	0.827062	+	0.562111i	$0.190011\pi$
$600$	−1.24624	−	1.20287i	−0.0508775	−	0.0491068i
$601$	8.55467	+	14.8171i	0.348952	+	0.604403i	0.986064	−	0.166369i	$-0.0532042\pi$
$601$	8.55467	+	14.8171i	0.348952	+	0.604403i	−0.637111	+	0.770772i	$0.719871\pi$
$602$	8.03459			0.327465
$603$	0.0518832	+	1.46439i	0.00211285	+	0.0596347i
$604$	−4.34517			−0.176802
$605$	13.5150	+	23.4087i	0.549464	+	0.951700i
$606$	6.79902	−	27.2989i	0.276191	−	1.10894i
$607$	0.689419	−	1.19411i	0.0279827	−	0.0484674i	−0.851695	−	0.524038i	$-0.824425\pi$
$607$	0.689419	−	1.19411i	0.0279827	−	0.0484674i	0.879678	+	0.475570i	$0.157758\pi$
$608$	−2.54334	+	4.40519i	−0.103146	+	0.178654i
$609$	4.38579	−	17.6095i	0.177721	−	0.713573i
$610$	−1.32191	−	2.28962i	−0.0535227	−	0.0927040i
$611$	−12.8392			−0.519420
$612$	−0.161780	−	4.56621i	−0.00653957	−	0.184578i
$613$	−35.8859			−1.44942			−0.724709	−	0.689055i	$-0.758026\pi$
$613$	−35.8859			−1.44942			−0.724709	+	0.689055i	$0.758026\pi$
$614$	−15.0839	−	26.1261i	−0.608736	−	1.05436i
$615$	1.08141	+	1.04377i	0.0436065	+	0.0420889i
$616$	−3.08343	+	5.34065i	−0.124235	+	0.215181i
$617$	5.21841	−	9.03855i	0.210085	−	0.363878i	−0.741656	−	0.670781i	$-0.765959\pi$
$617$	5.21841	−	9.03855i	0.210085	−	0.363878i	0.951741	+	0.306902i	$0.0992925\pi$
$618$	17.1280	−	4.91608i	0.688989	−	0.197754i
$619$	−13.9082	−	24.0896i	−0.559016	−	0.968244i	−0.997579	−	0.0695436i	$-0.977846\pi$
$619$	−13.9082	−	24.0896i	−0.559016	−	0.968244i	0.438563	−	0.898700i	$-0.355488\pi$
$620$	8.17334			0.328249
$621$	11.5348	+	35.4086i	0.462876	+	1.42090i
$622$	−7.71254			−0.309245
$623$	1.78755	+	3.09613i	0.0716169	+	0.124044i
$624$	−3.10947	+	0.892481i	−0.124478	+	0.0357278i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.23276	−	2.13519i	0.0492708	−	0.0853395i
$627$	39.0930	+	37.7324i	1.56122	+	1.50689i
$628$	6.58916	+	11.4128i	0.262936	+	0.455419i
$629$	6.42555			0.256203
$630$	−2.64956	−	1.40707i	−0.105561	−	0.0560589i
$631$	18.5412			0.738113			0.369056	−	0.929407i	$-0.379681\pi$
$631$	18.5412			0.738113			0.369056	+	0.929407i	$0.379681\pi$
$632$	−6.51729	−	11.2883i	−0.259244	−	0.449024i
$633$	0.538369	−	2.16162i	0.0213982	−	0.0859167i
$634$	−9.79935	+	16.9730i	−0.389182	+	0.674083i
$635$	2.58343	−	4.47463i	0.102520	−	0.177570i
$636$	−0.0190848	+	0.0766281i	−0.000756763	+	0.00303850i
$637$	0.933868	+	1.61751i	0.0370012	+	0.0640880i
$638$	−64.6128			−2.55804
$639$	8.50672	−	5.32160i	0.336521	−	0.210519i
$640$	−1.00000			−0.0395285
$641$	−8.40458	−	14.5572i	−0.331961	−	0.574973i	0.650935	−	0.759133i	$-0.274377\pi$
$641$	−8.40458	−	14.5572i	−0.331961	−	0.574973i	−0.982896	+	0.184160i	$0.941044\pi$
$642$	13.3733	+	12.9079i	0.527804	+	0.509435i
$643$	8.85650	−	15.3399i	0.349266	−	0.604947i	−0.636853	−	0.770985i	$-0.719764\pi$
$643$	8.85650	−	15.3399i	0.349266	−	0.604947i	0.986119	+	0.166038i	$0.0530975\pi$
$644$	3.58343	−	6.20668i	0.141207	−	0.244577i
$645$	13.3762	−	3.83926i	0.526689	−	0.151171i
$646$	3.87357	+	6.70921i	0.152403	+	0.263971i
$647$	−7.15990			−0.281485			−0.140742	−	0.990046i	$-0.544949\pi$
$647$	−7.15990			−0.281485			−0.140742	+	0.990046i	$0.544949\pi$
$648$	3.93711	−	8.09315i	0.154664	−	0.317929i
$649$	−44.6914			−1.75429
$650$	0.933868	+	1.61751i	0.0366293	+	0.0634438i
$651$	13.6072	−	3.90556i	0.533310	−	0.153071i
$652$	−0.738487	+	1.27910i	−0.0289214	+	0.0500933i
$653$	17.1619	−	29.7252i	0.671596	−	1.16324i	−0.305855	−	0.952078i	$-0.598942\pi$
$653$	17.1619	−	29.7252i	0.671596	−	1.16324i	0.977451	−	0.211161i	$-0.0677243\pi$
$654$	−19.6614	−	18.9771i	−0.768820	−	0.742063i
$655$	5.39378	+	9.34230i	0.210752	+	0.365034i
$656$	0.867736			0.0338794
$657$	−12.0439	+	7.53438i	−0.469877	+	0.293944i
$658$	−6.87423			−0.267985
$659$	9.43062	+	16.3343i	0.367365	+	0.636295i	0.989153	−	0.146891i	$-0.0469267\pi$
$659$	9.43062	+	16.3343i	0.367365	+	0.636295i	−0.621788	+	0.783186i	$0.713593\pi$
$660$	−2.58141	+	10.3647i	−0.100481	+	0.403445i
$661$	1.69439	−	2.93477i	0.0659043	−	0.114150i	−0.831190	−	0.555988i	$-0.812340\pi$
$661$	1.69439	−	2.93477i	0.0659043	−	0.114150i	0.897095	+	0.441838i	$0.145673\pi$
$662$	−12.5238	+	21.6918i	−0.486751	+	0.843077i
$663$	−1.19074	+	4.78096i	−0.0462444	+	0.185677i
$664$	−7.38503	−	12.7912i	−0.286595	−	0.496397i
$665$	5.08667			0.197253
$666$	11.1783	+	5.93633i	0.433151	+	0.230028i
$667$	75.0902			2.90751
$668$	−11.5812	−	20.0592i	−0.448089	−	0.776113i
$669$	−1.54601	−	1.49221i	−0.0597724	−	0.0576922i
$670$	0.244219	−	0.422999i	0.00943499	−	0.0163419i
$671$	−8.15205	+	14.1198i	−0.314706	+	0.545087i
$672$	−1.66483	+	0.477841i	−0.0642223	+	0.0184331i
$673$	16.2535	+	28.1519i	0.626527	+	1.08518i	0.988243	+	0.152889i	$0.0488576\pi$
$673$	16.2535	+	28.1519i	0.626527	+	1.08518i	−0.361716	+	0.932288i	$0.617809\pi$
$674$	−2.18435			−0.0841379
$675$	−5.08343	−	1.07646i	−0.195661	−	0.0414331i
$676$	−9.51156			−0.365829
$677$	3.26757	+	5.65960i	0.125583	+	0.217516i	0.921961	−	0.387283i	$-0.126587\pi$
$677$	3.26757	+	5.65960i	0.125583	+	0.217516i	−0.796378	+	0.604800i	$0.793253\pi$
$678$	26.3221	−	7.55499i	1.01090	−	0.290148i
$679$	5.01156	−	8.68028i	0.192326	−	0.333119i
$680$	−0.761513	+	1.31898i	−0.0292027	+	0.0505805i
$681$	24.5671	+	23.7121i	0.941414	+	0.908650i
$682$	−25.2019	−	43.6510i	−0.965031	−	1.67148i
$683$	−15.6629			−0.599324			−0.299662	−	0.954045i	$-0.596874\pi$
$683$	−15.6629			−0.599324			−0.299662	+	0.954045i	$0.596874\pi$
$684$	0.540321	+	15.2504i	0.0206597	+	0.583115i
$685$	−13.6553			−0.521742
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−2.55960	+	10.2771i	−0.0976550	+	0.392097i
$688$	4.01729	−	6.95816i	0.153158	−	0.265277i
$689$	0.0425776	−	0.0737465i	0.00162208	−	0.00280952i
$690$	3.00000	−	12.0454i	0.114208	−	0.458560i
$691$	12.6789	+	21.9605i	0.482327	+	0.835415i	0.999794	−	0.0202880i	$-0.00645832\pi$
$691$	12.6789	+	21.9605i	0.482327	+	0.835415i	−0.517467	+	0.855703i	$0.673125\pi$
$692$	−8.17334			−0.310704
$693$	0.655060	+	18.4890i	0.0248837	+	0.702337i
$694$	3.93645			0.149426
$695$	0.327415	+	0.567100i	0.0124196	+	0.0215113i
$696$	−13.0574	−	12.6030i	−0.494939	−	0.477714i
$697$	0.660792	−	1.14453i	0.0250293	−	0.0433520i
$698$	−17.9206	+	31.0394i	−0.678305	+	1.17486i
$699$	−8.83295	+	2.53524i	−0.334093	+	0.0958915i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	16.1103			0.608476			0.304238	−	0.952596i	$-0.401598\pi$
$701$	16.1103			0.608476			0.304238	+	0.952596i	$0.401598\pi$
$702$	−6.48844	+	7.21720i	−0.244890	+	0.272396i
$703$	−21.4603			−0.809392
$704$	3.08343	+	5.34065i	0.116211	+	0.201283i
$705$	−11.4444	+	3.28479i	−0.431022	+	0.123712i
$706$	3.75277	−	6.49998i	0.141237	−	0.244630i
$707$	−8.12126	+	14.0664i	−0.305431	+	0.529023i
$708$	−9.03154	−	8.71722i	−0.339426	−	0.327613i
$709$	−12.8484	−	22.2541i	−0.482532	−	0.835771i	0.517267	−	0.855824i	$-0.326950\pi$
$709$	−12.8484	−	22.2541i	−0.482532	−	0.835771i	−0.999799	+	0.0200538i	$0.993616\pi$
$710$	−3.34471			−0.125525
$711$	−34.5359	−	18.3405i	−1.29520	−	0.687824i
$712$	3.57511			0.133983
$713$	29.2886	+	50.7293i	1.09687	+	1.89983i
$714$	−0.637529	+	2.55976i	−0.0238589	+	0.0957967i
$715$	5.75903	−	9.97493i	0.215375	−	0.373041i
$716$	4.56636	−	7.90917i	0.170653	−	0.295580i
$717$	9.96991	−	40.0305i	0.372333	−	1.49497i
$718$	−14.3109	−	24.7872i	−0.534078	−	0.925051i
$719$	−32.4545			−1.21035			−0.605174	−	0.796093i	$-0.706897\pi$
$719$	−32.4545			−1.21035			−0.605174	+	0.796093i	$0.706897\pi$
$720$	−2.54334	+	1.59105i	−0.0947845	+	0.0592950i
$721$	−10.2881			−0.383149
$722$	−3.43711	−	5.95325i	−0.127916	−	0.221557i
$723$	11.8044	+	11.3936i	0.439009	+	0.423731i
$724$	5.37930	−	9.31722i	0.199920	−	0.346272i
$725$	−5.23872	+	9.07372i	−0.194561	+	0.336990i
$726$	45.0006	−	12.9161i	1.67013	−	0.479361i
$727$	25.6162	+	44.3686i	0.950053	+	1.64554i	0.745303	+	0.666726i	$0.232305\pi$
$727$	25.6162	+	44.3686i	0.950053	+	1.64554i	0.204750	+	0.978814i	$0.434362\pi$
$728$	1.86774			0.0692229
$729$	−2.86322	−	26.8478i	−0.106045	−	0.994361i
$730$	4.73547			0.175268
$731$	−6.11844	−	10.5975i	−0.226299	−	0.391961i
$732$	−4.40153	+	1.26333i	−0.162685	+	0.0466940i
$733$	17.6586	−	30.5857i	0.652237	−	1.12971i	−0.330342	−	0.943861i	$-0.607164\pi$
$733$	17.6586	−	30.5857i	0.652237	−	1.12971i	0.982579	−	0.185846i	$-0.0595024\pi$
$734$	−3.93085	+	6.80844i	−0.145090	+	0.251304i
$735$	1.24624	+	1.20287i	0.0459682	+	0.0443684i
$736$	−3.58343	−	6.20668i	−0.132087	−	0.228781i
$737$	−3.01212			−0.110953
$738$	2.20694	−	1.38061i	0.0812387	−	0.0508210i
$739$	9.54509			0.351122			0.175561	−	0.984469i	$-0.443826\pi$
$739$	9.54509			0.351122			0.175561	+	0.984469i	$0.443826\pi$
$740$	−2.10947	−	3.65371i	−0.0775456	−	0.134313i
$741$	3.97687	−	15.9677i	0.146094	−	0.586587i
$742$	0.0227964	−	0.0394845i	0.000836881	−	0.00144952i
$743$	6.03459	−	10.4522i	0.221388	−	0.383455i	−0.733842	−	0.679320i	$-0.762275\pi$
$743$	6.03459	−	10.4522i	0.221388	−	0.383455i	0.955230	+	0.295866i	$0.0956081\pi$
$744$	3.42131	−	13.7370i	0.125431	−	0.503623i
$745$	9.39152	+	16.2666i	0.344079	+	0.595962i
$746$	−16.0000			−0.585802
$747$	−39.1341	−	20.7825i	−1.43184	−	0.760391i
$748$	9.39228			0.343416
$749$	−5.36548	−	9.29328i	−0.196050	−	0.339569i
$750$	1.24624	+	1.20287i	0.0455062	+	0.0439225i
$751$	−15.5283	+	26.8959i	−0.566637	+	0.981444i	0.430259	+	0.902706i	$0.358422\pi$
$751$	−15.5283	+	26.8959i	−0.566637	+	0.981444i	−0.996895	+	0.0787380i	$0.974911\pi$
$752$	−3.43711	+	5.95325i	−0.125339	+	0.217093i
$753$	37.0877	−	10.6449i	1.35155	−	0.387922i
$754$	9.78454	+	16.9473i	0.356332	+	0.617185i
$755$	4.34517			0.158137
$756$	−3.47396	+	3.86414i	−0.126347	+	0.140538i
$757$	−16.2548			−0.590792			−0.295396	−	0.955375i	$-0.595452\pi$
$757$	−16.2548			−0.590792			−0.295396	+	0.955375i	$0.595452\pi$
$758$	2.12600	+	3.68235i	0.0772199	+	0.133749i
$759$	−73.5805	+	21.1191i	−2.67080	+	0.766575i
$760$	2.54334	−	4.40519i	0.0922565	−	0.159793i
$761$	5.43184	−	9.40822i	0.196904	−	0.341048i	−0.750619	−	0.660735i	$-0.770245\pi$
$761$	5.43184	−	9.40822i	0.196904	−	0.341048i	0.947523	+	0.319687i	$0.103578\pi$
$762$	−6.43913	−	6.21504i	−0.233265	−	0.225147i
$763$	7.88828	+	13.6629i	0.285575	+	0.494630i
$764$	15.5522			0.562658
$765$	0.161780	+	4.56621i	0.00584917	+	0.165092i
$766$	−14.2540			−0.515017
$767$	6.76777	+	11.7221i	0.244370	+	0.423261i
$768$	−0.418594	+	1.68071i	−0.0151047	+	0.0606473i
$769$	−2.25502	+	3.90581i	−0.0813182	+	0.140847i	−0.903816	−	0.427920i	$-0.859246\pi$
$769$	−2.25502	+	3.90581i	−0.0813182	+	0.140847i	0.822498	+	0.568768i	$0.192580\pi$
$770$	3.08343	−	5.34065i	0.111119	−	0.192464i
$771$	9.29130	−	37.3058i	0.334618	−	1.34353i
$772$	1.69538	+	2.93649i	0.0610181	+	0.105686i
$773$	−4.25936			−0.153198			−0.0765992	−	0.997062i	$-0.524406\pi$
$773$	−4.25936			−0.153198			−0.0765992	+	0.997062i	$0.524406\pi$
$774$	−0.853457	−	24.0887i	−0.0306769	−	0.865849i
$775$	−8.17334			−0.293595
$776$	−5.01156	−	8.68028i	−0.179905	−	0.311604i
$777$	−5.25780	−	5.07482i	−0.188623	−	0.182058i
$778$	−6.65605	+	11.5286i	−0.238631	+	0.413321i
$779$	−2.20694	+	3.82254i	−0.0790720	+	0.136957i
$780$	3.10947	−	0.892481i	0.111337	−	0.0319559i
$781$	10.3132	+	17.8629i	0.369034	+	0.639186i
$782$	−10.9153			−0.390330
$783$	−53.2613	−	11.2786i	−1.90340	−	0.403064i
$784$	1.00000			0.0357143
$785$	−6.58916	−	11.4128i	−0.235177	−	0.407339i
$786$	17.9595	−	5.15474i	0.640593	−	0.183863i
$787$	−9.29836	+	16.1052i	−0.331451	+	0.574089i	−0.982797	−	0.184692i	$-0.940871\pi$
$787$	−9.29836	+	16.1052i	−0.331451	+	0.574089i	0.651346	+	0.758781i	$0.274205\pi$
$788$	3.27632	−	5.67475i	0.116714	−	0.202155i
$789$	−14.2462	−	13.7504i	−0.507179	−	0.489528i
$790$	6.51729	+	11.2883i	0.231875	+	0.401619i
$791$	−15.8107			−0.562163
$792$	16.3394	+	8.67718i	0.580597	+	0.308330i
$793$	4.93797			0.175352
$794$	10.8940	+	18.8690i	0.386614	+	0.669635i
$795$	0.0190848	−	0.0766281i	0.000676869	−	0.00271772i
$796$	0.928136	−	1.60758i	0.0328969	−	0.0569791i
$797$	8.18359	−	14.1744i	0.289878	−	0.502083i	−0.683903	−	0.729573i	$-0.739719\pi$
$797$	8.18359	−	14.1744i	0.289878	−	0.502083i	0.973780	+	0.227491i	$0.0730521\pi$
$798$	2.12925	−	8.54921i	0.0753746	−	0.302639i
$799$	5.23481	+	9.06696i	0.185194	+	0.320766i
$800$	1.00000			0.0353553
$801$	9.09270	−	5.68818i	0.321275	−	0.200982i
$802$	−1.67888			−0.0592831
$803$	−14.6015	−	25.2905i	−0.515275	−	0.892482i
$804$	−0.608710	−	0.587525i	−0.0214675	−	0.0207204i
$805$	−3.58343	+	6.20668i	−0.126299	+	0.218757i
$806$	−7.63282	+	13.2204i	−0.268855	+	0.465670i
$807$	7.29080	−	2.09261i	0.256648	−	0.0736633i
$808$	8.12126	+	14.0664i	0.285705	+	0.494855i
$809$	56.6845			1.99292			0.996461	−	0.0840616i	$-0.0267892\pi$
$809$	56.6845			1.99292			0.996461	+	0.0840616i	$0.0267892\pi$
$810$	−3.93711	+	8.09315i	−0.138336	+	0.284364i
$811$	21.4204			0.752171			0.376086	−	0.926585i	$-0.377270\pi$
$811$	21.4204			0.752171			0.376086	+	0.926585i	$0.377270\pi$
$812$	5.23872	+	9.07372i	0.183843	+	0.318425i
$813$	−29.9027	+	8.58268i	−1.04873	+	0.301008i
$814$	−13.0088	+	22.5319i	−0.455957	+	0.789741i
$815$	0.738487	−	1.27910i	0.0258681	−	0.0448048i
$816$	1.89805	+	1.83200i	0.0664452	+	0.0641327i
$817$	20.4347	+	35.3939i	0.714918	+	1.23827i
$818$	18.5933			0.650098
$819$	4.75028	−	2.97166i	0.165988	−	0.103838i
$820$	−0.867736			−0.0303027
$821$	−15.7971	−	27.3614i	−0.551322	−	0.954918i	−0.998180	−	0.0603129i	$-0.980790\pi$
$821$	−15.7971	−	27.3614i	−0.551322	−	0.954918i	0.446857	−	0.894605i	$-0.352543\pi$
$822$	−5.71602	+	22.9506i	−0.199369	+	0.800493i
$823$	14.1000	−	24.4219i	0.491494	−	0.851292i	−0.508458	−	0.861087i	$-0.669784\pi$
$823$	14.1000	−	24.4219i	0.491494	−	0.851292i	0.999952	+	0.00979442i	$0.00311771\pi$
$824$	−5.14406	+	8.90977i	−0.179202	+	0.310386i
$825$	2.58141	−	10.3647i	0.0898730	−	0.360852i
$826$	3.62352	+	6.27612i	0.126078	+	0.218374i
$827$	−16.0402			−0.557773			−0.278887	−	0.960324i	$-0.589965\pi$
$827$	−16.0402			−0.557773			−0.278887	+	0.960324i	$0.589965\pi$
$828$	−18.9890	−	10.0842i	−0.659913	−	0.350452i
$829$	18.6804			0.648797			0.324398	−	0.945921i	$-0.394838\pi$
$829$	18.6804			0.648797			0.324398	+	0.945921i	$0.394838\pi$
$830$	7.38503	+	12.7912i	0.256338	+	0.443991i
$831$	−20.2421	−	19.5376i	−0.702189	−	0.677751i
$832$	0.933868	−	1.61751i	0.0323760	−	0.0560770i
$833$	0.761513	−	1.31898i	0.0263849	−	0.0456999i
$834$	1.09018	−	0.312905i	0.0377500	−	0.0108350i
$835$	11.5812	+	20.0592i	0.400783	+	0.694176i
$836$	−31.3688			−1.08491
$837$	−13.1547	−	40.3813i	−0.454694	−	1.39578i
$838$	−35.9840			−1.24305
$839$	18.5378	+	32.1085i	0.639997	+	1.10851i	0.985433	+	0.170065i	$0.0543978\pi$
$839$	18.5378	+	32.1085i	0.639997	+	1.10851i	−0.345436	+	0.938442i	$0.612269\pi$
$840$	1.66483	−	0.477841i	0.0574422	−	0.0164871i
$841$	−40.3883	+	69.9546i	−1.39270	+	2.41223i
$842$	2.54357	−	4.40558i	0.0876571	−	0.151826i
$843$	−0.951019	−	0.917921i	−0.0327548	−	0.0316149i
$844$	0.643069	+	1.11383i	0.0221353	+	0.0383395i
$845$	9.51156			0.327208
$846$	0.730200	+	20.6097i	0.0251048	+	0.708578i
$847$	−27.0301			−0.928764
$848$	−0.0227964	−	0.0394845i	−0.000782830	−	0.00135590i
$849$	3.71470	−	14.9150i	0.127488	−	0.511881i
$850$	0.761513	−	1.31898i	0.0261197	−	0.0452406i
$851$	15.1182	−	26.1856i	0.518247	−	0.897630i
$852$	−1.40007	+	5.62148i	−0.0479658	+	0.192589i
$853$	3.44284	+	5.96318i	0.117881	+	0.204175i	0.918928	−	0.394426i	$-0.129057\pi$
$853$	3.44284	+	5.96318i	0.117881	+	0.204175i	−0.801047	+	0.598602i	$0.795723\pi$
$854$	2.64383			0.0904699
$855$	−0.540321	−	15.2504i	−0.0184786	−	0.521554i
$856$	−10.7310			−0.366777
$857$	−8.72672	−	15.1151i	−0.298099	−	0.516323i	0.677602	−	0.735429i	$-0.263019\pi$
$857$	−8.72672	−	15.1151i	−0.298099	−	0.516323i	−0.975701	+	0.219106i	$0.929686\pi$
$858$	−14.3542	−	13.8547i	−0.490046	−	0.472991i
$859$	8.26085	−	14.3082i	0.281857	−	0.488190i	−0.689985	−	0.723823i	$-0.742383\pi$
$859$	8.26085	−	14.3082i	0.281857	−	0.488190i	0.971842	+	0.235633i	$0.0757164\pi$
$860$	−4.01729	+	6.95816i	−0.136989	+	0.237271i
$861$	−1.44464	+	0.414640i	−0.0492330	+	0.0141309i
$862$	−12.1726	−	21.0835i	−0.414600	−	0.718108i
$863$	29.8077			1.01467			0.507333	−	0.861750i	$-0.330632\pi$
$863$	29.8077			1.01467			0.507333	+	0.861750i	$0.330632\pi$
$864$	1.60947	+	4.94061i	0.0547552	+	0.168083i
$865$	8.17334			0.277902
$866$	2.10351	+	3.64338i	0.0714801	+	0.123807i
$867$	−24.4404	+	7.01489i	−0.830039	+	0.238238i
$868$	−4.08667	+	7.07832i	−0.138711	+	0.240254i
$869$	40.1912	−	69.6132i	1.36339	−	2.36147i
$870$	13.0574	+	12.6030i	0.442687	+	0.427280i
$871$	0.456136	+	0.790051i	0.0154556	+	0.0267698i
$872$	15.7766			0.534261
$873$	−26.5569	−	14.1032i	−0.898813	−	0.477322i
$874$	36.4554			1.23312
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	1.98224	−	7.95895i	0.0669736	−	0.268908i
$877$	−12.9952	+	22.5083i	−0.438815	+	0.760050i	−0.997598	−	0.0692635i	$-0.977935\pi$
$877$	−12.9952	+	22.5083i	−0.438815	+	0.760050i	0.558783	+	0.829314i	$0.311268\pi$
$878$	12.4577	−	21.5773i	0.420425	−	0.728198i
$879$	−4.75653	+	19.0981i	−0.160434	+	0.644163i
$880$	−3.08343	−	5.34065i	−0.103942	−	0.180033i
$881$	6.08819			0.205116			0.102558	−	0.994727i	$-0.467297\pi$
$881$	6.08819			0.205116			0.102558	+	0.994727i	$0.467297\pi$
$882$	2.54334	−	1.59105i	0.0856386	−	0.0535735i
$883$	17.1558			0.577340			0.288670	−	0.957429i	$-0.406787\pi$
$883$	17.1558			0.577340			0.288670	+	0.957429i	$0.406787\pi$
$884$	−1.42231	−	2.46351i	−0.0478373	−	0.0828566i
$885$	9.03154	+	8.71722i	0.303592	+	0.293026i
$886$	−14.1500	+	24.5086i	−0.475379	+	0.823381i
$887$	−16.1327	+	27.9427i	−0.541684	+	0.938224i	0.457124	+	0.889403i	$0.348880\pi$
$887$	−16.1327	+	27.9427i	−0.541684	+	0.938224i	−0.998808	+	0.0488208i	$0.984454\pi$
$888$	−7.02382	+	2.01598i	−0.235704	+	0.0676519i
$889$	2.58343	+	4.47463i	0.0866453	+	0.150074i
$890$	−3.57511			−0.119838
$891$	55.3625	−	3.92790i	1.85471	−	0.131590i
$892$	1.24054			0.0415365
$893$	−17.4835	−	30.2822i	−0.585062	−	1.01336i
$894$	31.2706	−	8.97531i	1.04585	−	0.300179i
$895$	−4.56636	+	7.90917i	−0.152637	+	0.264374i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	16.6819	+	16.1013i	0.556992	+	0.537607i
$898$	1.80137	+	3.12007i	0.0601126	+	0.104118i
$899$	−85.6357			−2.85611
$900$	2.54334	−	1.59105i	0.0847779	−	0.0530350i
$901$	−0.0694389			−0.00231335
$902$	2.67560	+	4.63427i	0.0890877	+	0.154304i
$903$	−3.36323	+	13.5038i	−0.111921	+	0.449378i
$904$	−7.90534	+	13.6925i	−0.262928	+	0.455404i
$905$	−5.37930	+	9.31722i	−0.178814	+	0.309715i
$906$	1.81886	−	7.30296i	0.0604276	−	0.242625i
$907$	2.71668	+	4.70543i	0.0902058	+	0.156241i	0.907598	−	0.419841i	$-0.137914\pi$
$907$	2.71668	+	4.70543i	0.0902058	+	0.156241i	−0.817392	+	0.576082i	$0.804581\pi$
$908$	−19.7130			−0.654199
$909$	43.0355	+	22.8543i	1.42740	+	0.758030i
$910$	−1.86774			−0.0619148
$911$	18.0406	+	31.2473i	0.597713	+	1.03527i	0.993158	+	0.116780i	$0.0372573\pi$
$911$	18.0406	+	31.2473i	0.597713	+	1.03527i	−0.395444	+	0.918490i	$0.629409\pi$
$912$	−6.33921	−	6.11859i	−0.209912	−	0.202607i
$913$	45.5424	−	78.8817i	1.50723	−	2.61060i
$914$	14.1302	−	24.4743i	0.467387	−	0.809538i
$915$	4.40153	−	1.26333i	0.145510	−	0.0417644i
$916$	−3.05739	−	5.29555i	−0.101019	−	0.174970i
$917$	−10.7876			−0.356236
$918$	7.74219	+	1.63948i	0.255530	+	0.0541110i
$919$	−15.4945			−0.511117			−0.255559	−	0.966794i	$-0.582259\pi$
$919$	−15.4945			−0.511117			−0.255559	+	0.966794i	$0.582259\pi$
$920$	3.58343	+	6.20668i	0.118142	+	0.204628i
$921$	50.2243	−	14.4154i	1.65495	−	0.475004i
$922$	16.2768	−	28.1922i	0.536047	−	0.928461i
$923$	3.12352	−	5.41009i	0.102812	−	0.178075i
$924$	−7.68537	−	7.41790i	−0.252830	−	0.244031i
$925$	2.10947	+	3.65371i	0.0693589	+	0.120133i
$926$	34.8408			1.14494
$927$	1.09283	+	30.8450i	0.0358933	+	1.01308i
$928$	10.4774			0.343939
$929$	16.9544	+	29.3659i	0.556256	+	0.963464i	0.997805	+	0.0662264i	$0.0210960\pi$
$929$	16.9544	+	29.3659i	0.556256	+	0.963464i	−0.441549	+	0.897237i	$0.645571\pi$
$930$	−3.42131	+	13.7370i	−0.112189	+	0.450454i
$931$	−2.54334	+	4.40519i	−0.0833545	+	0.144374i
$932$	2.65280	−	4.59479i	0.0868955	−	0.150507i
$933$	3.22842	−	12.9625i	0.105694	−	0.424374i
$934$	21.0759	+	36.5045i	0.689624	+	1.19446i
$935$	−9.39228			−0.307160
$936$	−0.198396	−	5.59969i	−0.00648478	−	0.183032i
$937$	39.9726			1.30585			0.652923	−	0.757424i	$-0.273542\pi$
$937$	39.9726			1.30585			0.652923	+	0.757424i	$0.273542\pi$
$938$	0.244219	+	0.422999i	0.00797402	+	0.0138114i
$939$	3.07261	+	2.96568i	0.100271	+	0.0967813i
$940$	3.43711	−	5.95325i	0.112106	−	0.194174i
$941$	−7.94143	+	13.7550i	−0.258883	+	0.448399i	−0.965943	−	0.258755i	$-0.916688\pi$
$941$	−7.94143	+	13.7550i	−0.258883	+	0.448399i	0.707060	+	0.707154i	$0.250021\pi$
$942$	−21.9397	+	6.29714i	−0.714834	+	0.205172i
$943$	−3.10947	−	5.38576i	−0.101258	−	0.175384i
$944$	7.24703			0.235871
$945$	3.47396	−	3.86414i	0.113008	−	0.125701i
$946$	49.5481			1.61095
$947$	−20.2307	−	35.0405i	−0.657408	−	1.13866i	−0.981284	−	0.192565i	$-0.938319\pi$
$947$	−20.2307	−	35.0405i	−0.657408	−	1.13866i	0.323876	−	0.946099i	$-0.395014\pi$
$948$	21.7004	−	6.22846i	0.704797	−	0.202291i
$949$	−4.42231	+	7.65966i	−0.143554	+	0.248643i
$950$	−2.54334	+	4.40519i	−0.0825167	+	0.142923i
$951$	−24.4247	−	23.5746i	−0.792024	−	0.764459i
$952$	−0.761513	−	1.31898i	−0.0246808	−	0.0427484i
$953$	53.5261			1.73388			0.866941	−	0.498412i	$-0.166083\pi$
$953$	53.5261			1.73388			0.866941	+	0.498412i	$0.166083\pi$
$954$	−0.120801	−	0.0641521i	−0.00391106	−	0.00207700i
$955$	−15.5522			−0.503257
$956$	11.9088	+	20.6267i	0.385159	+	0.667114i
$957$	27.0465	−	108.595i	0.874290	−	3.51039i
$958$	−7.74379	+	13.4126i	−0.250190	+	0.433343i
$959$	6.82765	−	11.8258i	0.220476	−	0.381876i
$960$	0.418594	−	1.68071i	0.0135101	−	0.0542446i
$961$	−17.9018	−	31.0068i	−0.577476	−	1.00022i
$962$	7.87986			0.254057
$963$	−27.2924	+	17.0735i	−0.879486	+	0.550186i
$964$	−9.47200			−0.305073
$965$	−1.69538	−	2.93649i	−0.0545762	−	0.0945288i
$966$	8.93161	+	8.62077i	0.287370	+	0.277369i
$967$	−24.0647	+	41.6812i	−0.773867	+	1.34038i	0.161561	+	0.986863i	$0.448347\pi$
$967$	−24.0647	+	41.6812i	−0.773867	+	1.34038i	−0.935429	+	0.353515i	$0.884986\pi$
$968$	−13.5150	+	23.4087i	−0.434390	+	0.752385i
$969$	−12.8977	+	3.70190i	−0.414333	+	0.118922i
$970$	5.01156	+	8.68028i	0.160912	+	0.278707i
$971$	34.5982			1.11031			0.555155	−	0.831747i	$-0.312659\pi$
$971$	34.5982			1.11031			0.555155	+	0.831747i	$0.312659\pi$
$972$	11.9542	+	10.0049i	0.383430	+	0.320907i
$973$	−0.654831			−0.0209929
$974$	−6.00046	−	10.3931i	−0.192267	−	0.333016i
$975$	−3.10947	+	0.892481i	−0.0995827	+	0.0285823i
$976$	1.32191	−	2.28962i	0.0423134	−	0.0732890i
$977$	−20.7646	+	35.9653i	−0.664317	+	1.15063i	0.315153	+	0.949041i	$0.397944\pi$
$977$	−20.7646	+	35.9653i	−0.664317	+	1.15063i	−0.979470	+	0.201590i	$0.935389\pi$
$978$	−1.84066	−	1.77660i	−0.0588579	−	0.0568095i
$979$	11.0236	+	19.0934i	0.352315	+	0.610228i
$980$	−1.00000			−0.0319438
$981$	40.1251	−	25.1013i	1.28109	−	0.801423i
$982$	23.9905			0.765568
$983$	−3.93767	−	6.82025i	−0.125592	−	0.217532i	0.796372	−	0.604807i	$-0.206750\pi$
$983$	−3.93767	−	6.82025i	−0.125592	−	0.217532i	−0.921964	+	0.387275i	$0.873416\pi$
$984$	−0.363229	+	1.45841i	−0.0115793	+	0.0464924i
$985$	−3.27632	+	5.67475i	−0.104392	+	0.180813i
$986$	7.97870	−	13.8195i	0.254094	−	0.440103i
$987$	2.87751	−	11.5536i	0.0915921	−	0.367754i
$988$	4.75028	+	8.22773i	0.151127	+	0.261759i
$989$	−57.5827			−1.83102
$990$	−16.3394	−	8.67718i	−0.519301	−	0.275779i
$991$	34.7251			1.10308			0.551540	−	0.834148i	$-0.314040\pi$
$991$	34.7251			1.10308			0.551540	+	0.834148i	$0.314040\pi$
$992$	4.08667	+	7.07832i	0.129752	+	0.224737i
$993$	−31.2153	−	30.1289i	−0.990586	−	0.956111i
$994$	1.67235	−	2.89660i	0.0530439	−	0.0918747i
$995$	−0.928136	+	1.60758i	−0.0294239	+	0.0509637i
$996$	24.5897	−	7.05774i	0.779154	−	0.223633i
$997$	12.4074	+	21.4902i	0.392946	+	0.680603i	0.992837	−	0.119479i	$-0.0381225\pi$
$997$	12.4074	+	21.4902i	0.392946	+	0.680603i	−0.599890	+	0.800082i	$0.704789\pi$
$998$	23.4545			0.742439
$999$	−14.6564	+	16.3026i	−0.463708	+	0.515791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.l.211.4	✓	8
3.2	odd	2		1890.2.j.l.631.1		8
9.2	odd	6		1890.2.j.l.1261.1		8
9.4	even	3		5670.2.a.bw.1.1		4
9.5	odd	6		5670.2.a.bv.1.4		4
9.7	even	3	inner	630.2.j.l.421.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.l.211.4	✓	8	1.1	even	1	trivial
630.2.j.l.421.4	yes	8	9.7	even	3	inner
1890.2.j.l.631.1		8	3.2	odd	2
1890.2.j.l.1261.1		8	9.2	odd	6
5670.2.a.bv.1.4		4	9.5	odd	6
5670.2.a.bw.1.1		4	9.4	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.66483 - 0.477841i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.24624 - 1.20287i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.54334 - 1.59105i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.66483 - 0.477841i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.24624 - 1.20287i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.54334 - 1.59105i) q^{9} -1.00000 q^{10} +(3.08343 + 5.34065i) q^{11} +(-0.418594 + 1.68071i) q^{12} +(0.933868 - 1.61751i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.418594 - 1.68071i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.52303 q^{17} +(-2.64956 - 1.40707i) q^{18} +5.08667 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.24624 + 1.20287i) q^{21} +(3.08343 - 5.34065i) q^{22} +(-3.58343 + 6.20668i) q^{23} +(1.66483 - 0.477841i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.86774 q^{26} +(3.47396 - 3.86414i) q^{27} -1.00000 q^{28} +(-5.23872 - 9.07372i) q^{29} +(-1.66483 + 0.477841i) q^{30} +(4.08667 - 7.07832i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(7.68537 + 7.41790i) q^{33} +(0.761513 + 1.31898i) q^{34} +1.00000 q^{35} +(0.106223 + 2.99812i) q^{36} -4.21894 q^{37} +(-2.54334 - 4.40519i) q^{38} +(0.781823 - 3.13912i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.433868 + 0.751481i) q^{41} +(0.418594 - 1.68071i) q^{42} +(4.01729 + 6.95816i) q^{43} -6.16685 q^{44} +(-0.106223 - 2.99812i) q^{45} +7.16685 q^{46} +(-3.43711 - 5.95325i) q^{47} +(-1.24624 - 1.20287i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.53558 + 0.727765i) q^{51} +(0.933868 + 1.61751i) q^{52} +0.0455927 q^{53} +(-5.08343 - 1.07646i) q^{54} +6.16685 q^{55} +(0.500000 + 0.866025i) q^{56} +(8.46846 - 2.43062i) q^{57} +(-5.23872 + 9.07372i) q^{58} +(-3.62352 + 6.27612i) q^{59} +(1.24624 + 1.20287i) q^{60} +(1.32191 + 2.28962i) q^{61} -8.17334 q^{62} +(2.64956 + 1.40707i) q^{63} +1.00000 q^{64} +(-0.933868 - 1.61751i) q^{65} +(2.58141 - 10.3647i) q^{66} +(-0.244219 + 0.422999i) q^{67} +(0.761513 - 1.31898i) q^{68} +(-3.00000 + 12.0454i) q^{69} +(-0.500000 - 0.866025i) q^{70} +3.34471 q^{71} +(2.54334 - 1.59105i) q^{72} -4.73547 q^{73} +(2.10947 + 3.65371i) q^{74} +(-1.24624 - 1.20287i) q^{75} +(-2.54334 + 4.40519i) q^{76} +(-3.08343 + 5.34065i) q^{77} +(-3.10947 + 0.892481i) q^{78} +(-6.51729 - 11.2883i) q^{79} -1.00000 q^{80} +(3.93711 - 8.09315i) q^{81} +0.867736 q^{82} +(-7.38503 - 12.7912i) q^{83} +(-1.66483 + 0.477841i) q^{84} +(-0.761513 + 1.31898i) q^{85} +(4.01729 - 6.95816i) q^{86} +(-13.0574 - 12.6030i) q^{87} +(3.08343 + 5.34065i) q^{88} +3.57511 q^{89} +(-2.54334 + 1.59105i) q^{90} +1.86774 q^{91} +(-3.58343 - 6.20668i) q^{92} +(3.42131 - 13.7370i) q^{93} +(-3.43711 + 5.95325i) q^{94} +(2.54334 - 4.40519i) q^{95} +(-0.418594 + 1.68071i) q^{96} +(-5.01156 - 8.68028i) q^{97} +1.00000 q^{98} +(16.3394 + 8.67718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more