LMFDB - Embedded newform 429.2.i.d.100.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.5
Root			$2.31940 - 0.319028i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.d.133.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24071 - 2.14896i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.07870 - 3.60041i) q^{4} -1.71458 q^{5} +(-1.24071 - 2.14896i) q^{6} +(-1.04859 - 1.81621i) q^{7} -5.35339 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.24071 - 2.14896i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.07870 - 3.60041i) q^{4} -1.71458 q^{5} +(-1.24071 - 2.14896i) q^{6} +(-1.04859 - 1.81621i) q^{7} -5.35339 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.12729 + 3.68457i) q^{10} +(-0.500000 + 0.866025i) q^{11} -4.15740 q^{12} +(3.60198 + 0.160483i) q^{13} -5.20396 q^{14} +(-0.857289 + 1.48487i) q^{15} +(-2.48458 + 4.30341i) q^{16} +(4.06409 + 7.03921i) q^{17} -2.48141 q^{18} +(-2.28929 - 3.96517i) q^{19} +(3.56409 + 6.17319i) q^{20} -2.09718 q^{21} +(1.24071 + 2.14896i) q^{22} +(3.30398 - 5.72266i) q^{23} +(-2.67669 + 4.63617i) q^{24} -2.06022 q^{25} +(4.81386 - 7.54141i) q^{26} -1.00000 q^{27} +(-4.35940 + 7.55070i) q^{28} +(3.63799 - 6.30118i) q^{29} +(2.12729 + 3.68457i) q^{30} -9.14162 q^{31} +(0.811867 + 1.40619i) q^{32} +(0.500000 + 0.866025i) q^{33} +20.1694 q^{34} +(1.79789 + 3.11403i) q^{35} +(-2.07870 + 3.60041i) q^{36} +(-1.64669 + 2.85216i) q^{37} -11.3614 q^{38} +(1.93997 - 3.03916i) q^{39} +9.17880 q^{40} +(1.93599 - 3.35323i) q^{41} +(-2.60198 + 4.50676i) q^{42} +(0.653413 + 1.13174i) q^{43} +4.15740 q^{44} +(0.857289 + 1.48487i) q^{45} +(-8.19853 - 14.2003i) q^{46} +6.30683 q^{47} +(2.48458 + 4.30341i) q^{48} +(1.30092 - 2.25327i) q^{49} +(-2.55612 + 4.42734i) q^{50} +8.12818 q^{51} +(-6.90962 - 13.3022i) q^{52} +13.5637 q^{53} +(-1.24071 + 2.14896i) q^{54} +(0.857289 - 1.48487i) q^{55} +(5.61350 + 9.72286i) q^{56} -4.57859 q^{57} +(-9.02734 - 15.6358i) q^{58} +(2.61154 + 4.52333i) q^{59} +7.12818 q^{60} +(2.56788 + 4.44771i) q^{61} +(-11.3421 + 19.6450i) q^{62} +(-1.04859 + 1.81621i) q^{63} -5.90915 q^{64} +(-6.17588 - 0.275160i) q^{65} +2.48141 q^{66} +(-1.35811 + 2.35231i) q^{67} +(16.8960 - 29.2648i) q^{68} +(-3.30398 - 5.72266i) q^{69} +8.92259 q^{70} +(3.29644 + 5.70961i) q^{71} +(2.67669 + 4.63617i) q^{72} +8.00164 q^{73} +(4.08612 + 7.07737i) q^{74} +(-1.03011 + 1.78420i) q^{75} +(-9.51750 + 16.4848i) q^{76} +2.09718 q^{77} +(-4.12412 - 7.93963i) q^{78} +2.75886 q^{79} +(4.26000 - 7.37854i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.80398 - 8.32074i) q^{82} +1.20254 q^{83} +(4.35940 + 7.55070i) q^{84} +(-6.96821 - 12.0693i) q^{85} +3.24277 q^{86} +(-3.63799 - 6.30118i) q^{87} +(2.67669 - 4.63617i) q^{88} +(0.0810464 - 0.140377i) q^{89} +4.25457 q^{90} +(-3.48552 - 6.71022i) q^{91} -27.4719 q^{92} +(-4.57081 + 7.91688i) q^{93} +(7.82491 - 13.5531i) q^{94} +(3.92517 + 6.79860i) q^{95} +1.62373 q^{96} +(6.00406 + 10.3993i) q^{97} +(-3.22813 - 5.59128i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.24071	−	2.14896i	0.877311	−	1.51955i	0.0230306	−	0.999735i	$-0.492668\pi$
$2$	1.24071	−	2.14896i	0.877311	−	1.51955i	0.854280	−	0.519812i	$-0.173998\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.07870	−	3.60041i	−1.03935	−	1.80021i
$5$	−1.71458			−0.766783			−0.383391	−	0.923586i	$-0.625244\pi$
$5$	−1.71458			−0.766783			−0.383391	+	0.923586i	$0.625244\pi$
$6$	−1.24071	−	2.14896i	−0.506516	−	0.877311i
$7$	−1.04859	−	1.81621i	−0.396329	−	0.686462i	0.596941	−	0.802285i	$-0.296383\pi$
$7$	−1.04859	−	1.81621i	−0.396329	−	0.686462i	−0.993270	+	0.115823i	$0.963049\pi$
$8$	−5.35339			−1.89271
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.12729	+	3.68457i	−0.672707	+	1.16516i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−4.15740			−1.20014
$13$	3.60198	+	0.160483i	0.999009	+	0.0445099i
$13$	3.60198	+	0.160483i	0.999009	+	0.0445099i
$14$	−5.20396			−1.39082
$15$	−0.857289	+	1.48487i	−0.221351	+	0.383391i
$16$	−2.48458	+	4.30341i	−0.621144	+	1.07585i
$17$	4.06409	+	7.03921i	0.985687	+	1.70726i	0.638843	+	0.769337i	$0.279413\pi$
$17$	4.06409	+	7.03921i	0.985687	+	1.70726i	0.346844	+	0.937923i	$0.387253\pi$
$18$	−2.48141			−0.584874
$19$	−2.28929	−	3.96517i	−0.525200	−	0.909673i	−0.999569	−	0.0293471i	$-0.990657\pi$
$19$	−2.28929	−	3.96517i	−0.525200	−	0.909673i	0.474369	−	0.880326i	$-0.342676\pi$
$20$	3.56409	+	6.17319i	0.796955	+	1.38037i
$21$	−2.09718			−0.457642
$22$	1.24071	+	2.14896i	0.264519	+	0.458161i
$23$	3.30398	−	5.72266i	0.688927	−	1.19326i	−0.283258	−	0.959044i	$-0.591415\pi$
$23$	3.30398	−	5.72266i	0.688927	−	1.19326i	0.972185	−	0.234213i	$-0.0752514\pi$
$24$	−2.67669	+	4.63617i	−0.546378	+	0.946354i
$25$	−2.06022			−0.412044
$26$	4.81386	−	7.54141i	0.944076	−	1.47899i
$27$	−1.00000			−0.192450
$28$	−4.35940	+	7.55070i	−0.823849	+	1.42695i
$29$	3.63799	−	6.30118i	0.675558	−	1.17010i	−0.300748	−	0.953704i	$-0.597236\pi$
$29$	3.63799	−	6.30118i	0.675558	−	1.17010i	0.976306	−	0.216396i	$-0.0694304\pi$
$30$	2.12729	+	3.68457i	0.388388	+	0.672707i
$31$	−9.14162			−1.64188			−0.820942	−	0.571012i	$-0.806551\pi$
$31$	−9.14162			−1.64188			−0.820942	+	0.571012i	$0.806551\pi$
$32$	0.811867	+	1.40619i	0.143519	+	0.248582i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	20.1694			3.45902
$35$	1.79789	+	3.11403i	0.303898	+	0.526368i
$36$	−2.07870	+	3.60041i	−0.346450	+	0.600068i
$37$	−1.64669	+	2.85216i	−0.270715	+	0.468892i	−0.969045	−	0.246884i	$-0.920593\pi$
$37$	−1.64669	+	2.85216i	−0.270715	+	0.468892i	0.698330	+	0.715776i	$0.253927\pi$
$38$	−11.3614			−1.84305
$39$	1.93997	−	3.03916i	0.310644	−	0.486656i
$40$	9.17880			1.45130
$41$	1.93599	−	3.35323i	0.302350	−	0.523686i	−0.674317	−	0.738442i	$-0.735562\pi$
$41$	1.93599	−	3.35323i	0.302350	−	0.523686i	0.976668	+	0.214755i	$0.0688954\pi$
$42$	−2.60198	+	4.50676i	−0.401494	+	0.695408i
$43$	0.653413	+	1.13174i	0.0996445	+	0.172589i	0.911538	−	0.411217i	$-0.134896\pi$
$43$	0.653413	+	1.13174i	0.0996445	+	0.172589i	−0.811893	+	0.583806i	$0.801563\pi$
$44$	4.15740			0.626751
$45$	0.857289	+	1.48487i	0.127797	+	0.221351i
$46$	−8.19853	−	14.2003i	−1.20881	−	2.09372i
$47$	6.30683			0.919945			0.459973	−	0.887933i	$-0.347859\pi$
$47$	6.30683			0.919945			0.459973	+	0.887933i	$0.347859\pi$
$48$	2.48458	+	4.30341i	0.358618	+	0.621144i
$49$	1.30092	−	2.25327i	0.185846	−	0.321895i
$50$	−2.55612	+	4.42734i	−0.361491	+	0.626120i
$51$	8.12818			1.13817
$52$	−6.90962	−	13.3022i	−0.958192	−	1.84468i
$53$	13.5637			1.86311			0.931557	−	0.363596i	$-0.118451\pi$
$53$	13.5637			1.86311			0.931557	+	0.363596i	$0.118451\pi$
$54$	−1.24071	+	2.14896i	−0.168839	+	0.292437i
$55$	0.857289	−	1.48487i	0.115597	−	0.200220i
$56$	5.61350	+	9.72286i	0.750135	+	1.29927i
$57$	−4.57859			−0.606449
$58$	−9.02734	−	15.6358i	−1.18535	−	2.05308i
$59$	2.61154	+	4.52333i	0.339994	+	0.588887i	0.984431	−	0.175770i	$-0.0562416\pi$
$59$	2.61154	+	4.52333i	0.339994	+	0.588887i	−0.644437	+	0.764657i	$0.722908\pi$
$60$	7.12818			0.920245
$61$	2.56788	+	4.44771i	0.328784	+	0.569470i	0.982271	−	0.187467i	$-0.0600279\pi$
$61$	2.56788	+	4.44771i	0.328784	+	0.569470i	−0.653487	+	0.756938i	$0.726695\pi$
$62$	−11.3421	+	19.6450i	−1.44044	+	2.49492i
$63$	−1.04859	+	1.81621i	−0.132110	+	0.228821i
$64$	−5.90915			−0.738644
$65$	−6.17588	−	0.275160i	−0.766023	−	0.0341294i
$66$	2.48141			0.305440
$67$	−1.35811	+	2.35231i	−0.165919	+	0.287380i	−0.936981	−	0.349379i	$-0.886392\pi$
$67$	−1.35811	+	2.35231i	−0.165919	+	0.287380i	0.771062	+	0.636760i	$0.219726\pi$
$68$	16.8960	−	29.2648i	2.04895	−	3.54888i
$69$	−3.30398	−	5.72266i	−0.397752	−	0.688927i
$70$	8.92259			1.06645
$71$	3.29644	+	5.70961i	0.391216	+	0.677606i	0.992610	−	0.121347i	$-0.0387213\pi$
$71$	3.29644	+	5.70961i	0.391216	+	0.677606i	−0.601394	+	0.798952i	$0.705388\pi$
$72$	2.67669	+	4.63617i	0.315451	+	0.546378i
$73$	8.00164			0.936521			0.468260	−	0.883591i	$-0.344881\pi$
$73$	8.00164			0.936521			0.468260	+	0.883591i	$0.344881\pi$
$74$	4.08612	+	7.07737i	0.475002	+	0.822728i
$75$	−1.03011	+	1.78420i	−0.118947	+	0.206022i
$76$	−9.51750	+	16.4848i	−1.09173	+	1.89094i
$77$	2.09718			0.238995
$78$	−4.12412	−	7.93963i	−0.466965	−	0.898986i
$79$	2.75886			0.310396			0.155198	−	0.987883i	$-0.450398\pi$
$79$	2.75886			0.310396			0.155198	+	0.987883i	$0.450398\pi$
$80$	4.26000	−	7.37854i	0.476283	−	0.824946i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.80398	−	8.32074i	−0.530511	−	0.918872i
$83$	1.20254			0.131996			0.0659981	−	0.997820i	$-0.478977\pi$
$83$	1.20254			0.131996			0.0659981	+	0.997820i	$0.478977\pi$
$84$	4.35940	+	7.55070i	0.475649	+	0.823849i
$85$	−6.96821	−	12.0693i	−0.755808	−	1.30910i
$86$	3.24277			0.349677
$87$	−3.63799	−	6.30118i	−0.390033	−	0.675558i
$88$	2.67669	−	4.63617i	0.285336	−	0.494217i
$89$	0.0810464	−	0.140377i	0.00859090	−	0.0148799i	−0.861698	−	0.507421i	$-0.830599\pi$
$89$	0.0810464	−	0.140377i	0.00859090	−	0.0148799i	0.870289	+	0.492542i	$0.163932\pi$
$90$	4.25457			0.448471
$91$	−3.48552	−	6.71022i	−0.365382	−	0.703423i
$92$	−27.4719			−2.86414
$93$	−4.57081	+	7.91688i	−0.473971	+	0.820942i
$94$	7.82491	−	13.5531i	0.807078	−	1.39790i
$95$	3.92517	+	6.79860i	0.402714	+	0.697522i
$96$	1.62373			0.165722
$97$	6.00406	+	10.3993i	0.609620	+	1.05589i	0.991303	+	0.131600i	$0.0420114\pi$
$97$	6.00406	+	10.3993i	0.609620	+	1.05589i	−0.381683	+	0.924293i	$0.624655\pi$
$98$	−3.22813	−	5.59128i	−0.326090	−	0.564805i
$99$	1.00000			0.100504
$100$	4.28257	+	7.41764i	0.428257	+	0.741764i
$101$	−6.48352	+	11.2298i	−0.645134	+	1.11741i	0.339136	+	0.940737i	$0.389865\pi$
$101$	−6.48352	+	11.2298i	−0.645134	+	1.11741i	−0.984271	+	0.176668i	$0.943468\pi$
$102$	10.0847	−	17.4672i	0.998532	−	1.72951i
$103$	−4.89993			−0.482805			−0.241402	−	0.970425i	$-0.577607\pi$
$103$	−4.89993			−0.482805			−0.241402	+	0.970425i	$0.577607\pi$
$104$	−19.2828	−	0.859126i	−1.89083	−	0.0842442i
$105$	3.59577			0.350912
$106$	16.8285	−	29.1478i	1.63453	−	2.83109i
$107$	−8.50535	+	14.7317i	−0.822244	+	1.42417i	0.0817642	+	0.996652i	$0.473945\pi$
$107$	−8.50535	+	14.7317i	−0.822244	+	1.42417i	−0.904008	+	0.427516i	$0.859389\pi$
$108$	2.07870	+	3.60041i	0.200023	+	0.346450i
$109$	−5.95485			−0.570372			−0.285186	−	0.958472i	$-0.592055\pi$
$109$	−5.95485			−0.570372			−0.285186	+	0.958472i	$0.592055\pi$
$110$	−2.12729	−	3.68457i	−0.202829	−	0.351310i
$111$	1.64669	+	2.85216i	0.156297	+	0.270715i
$112$	10.4212			0.984710
$113$	−6.14053	−	10.6357i	−0.577652	−	1.00052i	−0.995748	−	0.0921201i	$-0.970636\pi$
$113$	−6.14053	−	10.6357i	−0.577652	−	1.00052i	0.418096	−	0.908403i	$-0.362698\pi$
$114$	−5.68068	+	9.83922i	−0.532044	+	0.921527i
$115$	−5.66493	+	9.81195i	−0.528258	+	0.914969i
$116$	−30.2491			−2.80856
$117$	−1.66201	−	3.19965i	−0.153653	−	0.295807i
$118$	12.9606			1.19312
$119$	8.52312	−	14.7625i	0.781313	−	1.35327i
$120$	4.58940	−	7.94907i	0.418953	−	0.725648i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	12.7440			1.15378
$123$	−1.93599	−	3.35323i	−0.174562	−	0.302350i
$124$	19.0027	+	32.9136i	1.70649	+	2.95573i
$125$	12.1053			1.08273
$126$	2.60198	+	4.50676i	0.231803	+	0.401494i
$127$	2.74000	−	4.74582i	0.243136	−	0.421123i	−0.718470	−	0.695558i	$-0.755157\pi$
$127$	2.74000	−	4.74582i	0.243136	−	0.421123i	0.961606	+	0.274435i	$0.0884907\pi$
$128$	−8.95525	+	15.5110i	−0.791540	+	1.37099i
$129$	1.30683			0.115060
$130$	−8.25375	+	12.9303i	−0.723902	+	1.13407i
$131$	−11.7454			−1.02620			−0.513099	−	0.858330i	$-0.671502\pi$
$131$	−11.7454			−1.02620			−0.513099	+	0.858330i	$0.671502\pi$
$132$	2.07870	−	3.60041i	0.180927	−	0.313376i
$133$	−4.80105	+	8.31567i	−0.416304	+	0.721060i
$134$	3.37002	+	5.83705i	0.291125	+	0.504244i
$135$	1.71458			0.147567
$136$	−21.7566	−	37.6836i	−1.86562	−	3.23134i
$137$	2.24996	+	3.89705i	0.192227	+	0.332947i	0.945988	−	0.324201i	$-0.105096\pi$
$137$	2.24996	+	3.89705i	0.192227	+	0.332947i	−0.753761	+	0.657149i	$0.771762\pi$
$138$	−16.3971			−1.39581
$139$	1.09096	+	1.88959i	0.0925337	+	0.160273i	0.908577	−	0.417718i	$-0.137170\pi$
$139$	1.09096	+	1.88959i	0.0925337	+	0.160273i	−0.816043	+	0.577991i	$0.803837\pi$
$140$	7.47453	−	12.9463i	0.631713	−	1.09416i
$141$	3.15341	−	5.46187i	0.265565	−	0.459973i
$142$	16.3597			1.37287
$143$	−1.93997	+	3.03916i	−0.162229	+	0.254148i
$144$	4.96915			0.414096
$145$	−6.23762	+	10.8039i	−0.518006	+	0.897213i
$146$	9.92767	−	17.1952i	0.821620	−	1.42309i
$147$	−1.30092	−	2.25327i	−0.107298	−	0.185846i
$148$	13.6919			1.12547
$149$	0.340728	+	0.590159i	0.0279136	+	0.0483477i	0.879645	−	0.475631i	$-0.157780\pi$
$149$	0.340728	+	0.590159i	0.0279136	+	0.0483477i	−0.851731	+	0.523979i	$0.824447\pi$
$150$	2.55612	+	4.42734i	0.208707	+	0.361491i
$151$	−6.17333			−0.502379			−0.251189	−	0.967938i	$-0.580822\pi$
$151$	−6.17333			−0.502379			−0.251189	+	0.967938i	$0.580822\pi$
$152$	12.2555	+	21.2271i	0.994050	+	1.72174i
$153$	4.06409	−	7.03921i	0.328562	−	0.569087i
$154$	2.60198	−	4.50676i	0.209673	−	0.363165i
$155$	15.6740			1.25897
$156$	−14.9749	−	0.667190i	−1.19895	−	0.0534180i
$157$	17.5114			1.39756			0.698782	−	0.715335i	$-0.253726\pi$
$157$	17.5114			1.39756			0.698782	+	0.715335i	$0.253726\pi$
$158$	3.42294	−	5.92870i	0.272314	−	0.471662i
$159$	6.78184	−	11.7465i	0.537835	−	0.931557i
$160$	−1.39201	−	2.41103i	−0.110048	−	0.190609i
$161$	−13.8581			−1.09217
$162$	1.24071	+	2.14896i	0.0974790	+	0.168839i
$163$	−8.17751	−	14.1639i	−0.640512	−	1.10940i	−0.985319	−	0.170726i	$-0.945389\pi$
$163$	−8.17751	−	14.1639i	−0.640512	−	1.10940i	0.344807	−	0.938674i	$-0.387945\pi$
$164$	−16.0973			−1.25699
$165$	−0.857289	−	1.48487i	−0.0667399	−	0.115597i
$166$	1.49200	−	2.58422i	0.115802	−	0.200575i
$167$	5.86526	−	10.1589i	0.453867	−	0.786121i	−0.544755	−	0.838595i	$-0.683377\pi$
$167$	5.86526	−	10.1589i	0.453867	−	0.786121i	0.998622	+	0.0524742i	$0.0167107\pi$
$168$	11.2270			0.866182
$169$	12.9485	+	1.15611i	0.996038	+	0.0889316i
$170$	−34.5820			−2.65231
$171$	−2.28929	+	3.96517i	−0.175067	+	0.303224i
$172$	2.71650	−	4.70511i	0.207131	−	0.358761i
$173$	1.70528	+	2.95363i	0.129650	+	0.224560i	0.923541	−	0.383500i	$-0.125281\pi$
$173$	1.70528	+	2.95363i	0.129650	+	0.224560i	−0.793891	+	0.608060i	$0.791948\pi$
$174$	−18.0547			−1.36872
$175$	2.16032	+	3.74179i	0.163305	+	0.282853i
$176$	−2.48458	−	4.30341i	−0.187282	−	0.324382i
$177$	5.22309			0.392591
$178$	−0.201109	−	0.348332i	−0.0150738	−	0.0261086i
$179$	0.323515	−	0.560345i	0.0241807	−	0.0418822i	−0.853682	−	0.520795i	$-0.825636\pi$
$179$	0.323515	−	0.560345i	0.0241807	−	0.0418822i	0.877863	+	0.478913i	$0.158969\pi$
$180$	3.56409	−	6.17319i	0.265652	−	0.460122i
$181$	5.81214			0.432013			0.216006	−	0.976392i	$-0.430697\pi$
$181$	5.81214			0.432013			0.216006	+	0.976392i	$0.430697\pi$
$182$	−18.7445	−	0.835145i	−1.38944	−	0.0619051i
$183$	5.13577			0.379647
$184$	−17.6875	+	30.6356i	−1.30394	+	2.25849i
$185$	2.82339	−	4.89025i	0.207580	−	0.359538i
$186$	11.3421	+	19.6450i	0.831640	+	1.44044i
$187$	−8.12818			−0.594392
$188$	−13.1100	−	22.7072i	−0.956144	−	1.65609i
$189$	1.04859	+	1.81621i	0.0762736	+	0.132110i
$190$	19.4799			1.41322
$191$	10.0890	+	17.4747i	0.730018	+	1.26443i	0.956875	+	0.290500i	$0.0938217\pi$
$191$	10.0890	+	17.4747i	0.730018	+	1.26443i	−0.226857	+	0.973928i	$0.572845\pi$
$192$	−2.95458	+	5.11748i	−0.213228	+	0.369322i
$193$	−3.04504	+	5.27416i	−0.219186	+	0.379642i	−0.954559	−	0.298020i	$-0.903674\pi$
$193$	−3.04504	+	5.27416i	−0.219186	+	0.379642i	0.735373	+	0.677663i	$0.237007\pi$
$194$	29.7971			2.13931
$195$	−3.32623	+	5.21088i	−0.238197	+	0.373159i
$196$	−10.8169			−0.772637
$197$	−10.0297	+	17.3719i	−0.714586	+	1.23770i	0.248533	+	0.968623i	$0.420052\pi$
$197$	−10.0297	+	17.3719i	−0.714586	+	1.23770i	−0.963119	+	0.269076i	$0.913282\pi$
$198$	1.24071	−	2.14896i	0.0881731	−	0.152720i
$199$	0.180565	+	0.312748i	0.0127999	+	0.0221701i	0.872354	−	0.488874i	$-0.162592\pi$
$199$	0.180565	+	0.312748i	0.0127999	+	0.0221701i	−0.859555	+	0.511044i	$0.829259\pi$
$200$	11.0291			0.779879
$201$	1.35811	+	2.35231i	0.0957935	+	0.165919i
$202$	16.0883	+	27.8657i	1.13197	+	1.96062i
$203$	−15.2590			−1.07097
$204$	−16.8960	−	29.2648i	−1.18296	−	2.04895i
$205$	−3.31940	+	5.74938i	−0.231837	+	0.401554i
$206$	−6.07937	+	10.5298i	−0.423570	+	0.733645i
$207$	−6.60796			−0.459285
$208$	−9.64001	+	15.1021i	−0.668415	+	1.04714i
$209$	4.57859			0.316707
$210$	4.46130	−	7.72719i	0.307859	−	0.533227i
$211$	3.51968	−	6.09627i	0.242305	−	0.419685i	−0.719065	−	0.694942i	$-0.755430\pi$
$211$	3.51968	−	6.09627i	0.242305	−	0.419685i	0.961370	+	0.275258i	$0.0887632\pi$
$212$	−28.1948	−	48.8348i	−1.93643	−	3.35399i
$213$	6.59289			0.451737
$214$	21.1053	+	36.5554i	1.44273	+	2.49888i
$215$	−1.12033	−	1.94046i	−0.0764057	−	0.132339i
$216$	5.35339			0.364252
$217$	9.58580	+	16.6031i	0.650726	+	1.12709i
$218$	−7.38822	+	12.7968i	−0.500393	+	0.866706i
$219$	4.00082	−	6.92962i	0.270350	−	0.468260i
$220$	−7.12818			−0.480582
$221$	13.5091	+	26.0073i	0.908720	+	1.74944i
$222$	8.17225			0.548485
$223$	−11.7295	+	20.3162i	−0.785468	+	1.36047i	0.143251	+	0.989686i	$0.454244\pi$
$223$	−11.7295	+	20.3162i	−0.785468	+	1.36047i	−0.928719	+	0.370784i	$0.879089\pi$
$224$	1.70263	−	2.94904i	0.113762	−	0.197041i
$225$	1.03011	+	1.78420i	0.0686740	+	0.118947i
$226$	−30.4743			−2.02712
$227$	−8.87185	−	15.3665i	−0.588845	−	1.01991i	−0.994384	−	0.105832i	$-0.966249\pi$
$227$	−8.87185	−	15.3665i	−0.588845	−	1.01991i	0.405539	−	0.914078i	$-0.367084\pi$
$228$	9.51750	+	16.4848i	0.630312	+	1.09173i
$229$	−10.7707			−0.711751			−0.355875	−	0.934533i	$-0.615817\pi$
$229$	−10.7707			−0.711751			−0.355875	+	0.934533i	$0.615817\pi$
$230$	14.0570	+	24.3475i	0.926893	+	1.60543i
$231$	1.04859	−	1.81621i	0.0689921	−	0.119498i
$232$	−19.4756	+	33.7327i	−1.27863	+	2.21466i
$233$	−20.3286			−1.33177			−0.665887	−	0.746053i	$-0.731947\pi$
$233$	−20.3286			−1.33177			−0.665887	+	0.746053i	$0.731947\pi$
$234$	−8.93798	−	0.398223i	−0.584294	−	0.0260327i
$235$	−10.8135			−0.705398
$236$	10.8572	−	18.8053i	0.706745	−	1.22412i
$237$	1.37943	−	2.38925i	0.0896037	−	0.155198i
$238$	−21.1494	−	36.6318i	−1.37091	−	2.37448i
$239$	11.6449			0.753247			0.376623	−	0.926366i	$-0.377085\pi$
$239$	11.6449			0.753247			0.376623	+	0.926366i	$0.377085\pi$
$240$	−4.26000	−	7.37854i	−0.274982	−	0.476283i
$241$	−1.78307	−	3.08837i	−0.114858	−	0.198940i	0.802865	−	0.596161i	$-0.203308\pi$
$241$	−1.78307	−	3.08837i	−0.114858	−	0.198940i	−0.917723	+	0.397221i	$0.869975\pi$
$242$	−2.48141			−0.159511
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	10.6757	−	18.4909i	0.683443	−	1.18376i
$245$	−2.23054	+	3.86340i	−0.142504	+	0.246824i
$246$	−9.60796			−0.612581
$247$	−7.60964	−	14.6499i	−0.484190	−	0.932148i
$248$	48.9386			3.10761
$249$	0.601272	−	1.04143i	0.0381040	−	0.0659981i
$250$	15.0191	−	26.0139i	0.949892	−	1.64526i
$251$	5.59092	+	9.68377i	0.352896	+	0.611234i	0.986756	−	0.162214i	$-0.0518636\pi$
$251$	5.59092	+	9.68377i	0.352896	+	0.611234i	−0.633860	+	0.773448i	$0.718530\pi$
$252$	8.71880			0.549232
$253$	3.30398	+	5.72266i	0.207719	+	0.359781i
$254$	−6.79906	−	11.7763i	−0.426611	−	0.738912i
$255$	−13.9364			−0.872732
$256$	16.3125	+	28.2541i	1.01953	+	1.76588i
$257$	−4.97813	+	8.62238i	−0.310527	+	0.537849i	−0.978477	−	0.206358i	$-0.933839\pi$
$257$	−4.97813	+	8.62238i	−0.310527	+	0.537849i	0.667949	+	0.744207i	$0.267172\pi$
$258$	1.62139	−	2.80832i	0.100943	−	0.174838i
$259$	6.90682			0.429169
$260$	11.8471	+	22.8077i	0.734725	+	1.41447i
$261$	−7.27598			−0.450372
$262$	−14.5725	+	25.2404i	−0.900294	+	1.55935i
$263$	7.07105	−	12.2474i	0.436020	−	0.755208i	−0.561359	−	0.827573i	$-0.689721\pi$
$263$	7.07105	−	12.2474i	0.436020	−	0.755208i	0.997378	+	0.0723645i	$0.0230545\pi$
$264$	−2.67669	−	4.63617i	−0.164739	−	0.285336i
$265$	−23.2560			−1.42860
$266$	11.9134	+	20.6346i	0.730456	+	1.26519i
$267$	−0.0810464	−	0.140377i	−0.00495996	−	0.00859090i
$268$	11.2924			0.689792
$269$	13.5008	+	23.3840i	0.823157	+	1.42575i	0.903319	+	0.428969i	$0.141123\pi$
$269$	13.5008	+	23.3840i	0.823157	+	1.42575i	−0.0801619	+	0.996782i	$0.525544\pi$
$270$	2.12729	−	3.68457i	0.129463	−	0.224236i
$271$	4.87001	−	8.43511i	0.295832	−	0.512397i	−0.679346	−	0.733818i	$-0.737736\pi$
$271$	4.87001	−	8.43511i	0.295832	−	0.512397i	0.975178	+	0.221422i	$0.0710697\pi$
$272$	−40.3902			−2.44901
$273$	−7.55398	−	0.336561i	−0.457188	−	0.0203696i
$274$	11.1662			0.674572
$275$	1.03011	−	1.78420i	0.0621180	−	0.107591i
$276$	−13.7360	+	23.7914i	−0.826807	+	1.43207i
$277$	−16.4154	−	28.4323i	−0.986306	−	1.70833i	−0.635981	−	0.771705i	$-0.719404\pi$
$277$	−16.4154	−	28.4323i	−0.986306	−	1.70833i	−0.350326	−	0.936628i	$-0.613929\pi$
$278$	5.41422			0.324723
$279$	4.57081	+	7.91688i	0.273647	+	0.473971i
$280$	−9.62478	−	16.6706i	−0.575191	−	0.996260i
$281$	−13.6637			−0.815108			−0.407554	−	0.913181i	$-0.633618\pi$
$281$	−13.6637			−0.815108			−0.407554	+	0.913181i	$0.633618\pi$
$282$	−7.82491	−	13.5531i	−0.465967	−	0.807078i
$283$	10.7388	−	18.6002i	0.638357	−	1.10567i	−0.347436	−	0.937704i	$-0.612948\pi$
$283$	10.7388	−	18.6002i	0.638357	−	1.10567i	0.985793	−	0.167963i	$-0.0537190\pi$
$284$	13.7046	−	23.7371i	0.813220	−	1.40854i
$285$	7.85035			0.465014
$286$	4.12412	+	7.93963i	0.243864	+	0.469480i
$287$	−8.12022			−0.479321
$288$	0.811867	−	1.40619i	0.0478397	−	0.0828608i
$289$	−24.5337	+	42.4936i	−1.44316	+	2.49962i
$290$	15.4781	+	26.8088i	0.908905	+	1.57427i
$291$	12.0081			0.703929
$292$	−16.6330	−	28.8092i	−0.973372	−	1.68593i
$293$	−10.2165	−	17.6954i	−0.596852	−	1.03378i	−0.993283	−	0.115714i	$-0.963085\pi$
$293$	−10.2165	−	17.6954i	−0.596852	−	1.03378i	0.396430	−	0.918065i	$-0.370249\pi$
$294$	−6.45626			−0.376536
$295$	−4.47770	−	7.75560i	−0.260702	−	0.451548i
$296$	8.81539	−	15.2687i	0.512384	−	0.887475i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	1.69097			0.0979555
$299$	12.8192	−	20.0827i	0.741356	−	1.16141i
$300$	8.56515			0.494509
$301$	1.37032	−	2.37347i	0.0789841	−	0.136804i
$302$	−7.65928	+	13.2663i	−0.440742	+	0.763388i
$303$	6.48352	+	11.2298i	0.372468	+	0.645134i
$304$	22.7517			1.30490
$305$	−4.40284	−	7.62594i	−0.252106	−	0.436660i
$306$	−10.0847	−	17.4672i	−0.576503	−	0.998532i
$307$	−9.82605			−0.560803			−0.280401	−	0.959883i	$-0.590468\pi$
$307$	−9.82605			−0.560803			−0.280401	+	0.959883i	$0.590468\pi$
$308$	−4.35940	−	7.55070i	−0.248400	−	0.430241i
$309$	−2.44997	+	4.24347i	−0.139374	+	0.241402i
$310$	19.4468	−	33.6829i	1.10451	−	1.91306i
$311$	29.7164			1.68506			0.842530	−	0.538649i	$-0.181065\pi$
$311$	29.7164			1.68506			0.842530	+	0.538649i	$0.181065\pi$
$312$	−10.3854	+	16.2698i	−0.587958	+	0.921097i
$313$	20.6042			1.16462			0.582309	−	0.812967i	$-0.302149\pi$
$313$	20.6042			1.16462			0.582309	+	0.812967i	$0.302149\pi$
$314$	21.7265	−	37.6314i	1.22610	−	2.12366i
$315$	1.79789	−	3.11403i	0.101299	−	0.175456i
$316$	−5.73485	−	9.93305i	−0.322610	−	0.558777i
$317$	−20.2447			−1.13705			−0.568527	−	0.822664i	$-0.692487\pi$
$317$	−20.2447			−1.13705			−0.568527	+	0.822664i	$0.692487\pi$
$318$	−16.8285	−	29.1478i	−0.943696	−	1.63453i
$319$	3.63799	+	6.30118i	0.203688	+	0.352798i
$320$	10.1317			0.566380
$321$	8.50535	+	14.7317i	0.474723	+	0.822244i
$322$	−17.1938	+	29.7805i	−0.958171	+	1.65960i
$323$	18.6078	−	32.2297i	1.03537	−	1.79331i
$324$	4.15740			0.230966
$325$	−7.42087	−	0.330630i	−0.411636	−	0.0183400i
$326$	−40.5835			−2.24771
$327$	−2.97743	+	5.15705i	−0.164652	+	0.285186i
$328$	−10.3641	+	17.9511i	−0.572261	+	0.991185i
$329$	−6.61326	−	11.4545i	−0.364601	−	0.631508i
$330$	−4.25457			−0.234207
$331$	−13.9870	−	24.2262i	−0.768797	−	1.33159i	−0.938216	−	0.346051i	$-0.887522\pi$
$331$	−13.9870	−	24.2262i	−0.768797	−	1.33159i	0.169419	−	0.985544i	$-0.445811\pi$
$332$	−2.49972	−	4.32965i	−0.137190	−	0.237620i
$333$	3.29339			0.180477
$334$	−14.5541	−	25.2085i	−0.796365	−	1.37935i
$335$	2.32858	−	4.03322i	0.127224	−	0.220358i
$336$	5.21060	−	9.02502i	0.284261	−	0.492355i
$337$	−17.6006			−0.958764			−0.479382	−	0.877606i	$-0.659139\pi$
$337$	−17.6006			−0.958764			−0.479382	+	0.877606i	$0.659139\pi$
$338$	18.5497	−	26.3915i	1.00897	−	1.43551i
$339$	−12.2811			−0.667015
$340$	−28.9696	+	50.1768i	−1.57110	+	2.72122i
$341$	4.57081	−	7.91688i	0.247523	−	0.428723i
$342$	5.68068	+	9.83922i	0.307176	+	0.532044i
$343$	−20.1368			−1.08728
$344$	−3.49797	−	6.05866i	−0.188598	−	0.326661i
$345$	5.66493	+	9.81195i	0.304990	+	0.528258i
$346$	8.46299			0.454973
$347$	9.31460	+	16.1334i	0.500034	+	0.866084i	1.00000		3.93101e-5i	$1.25128e-5\pi$
$347$	9.31460	+	16.1334i	0.500034	+	0.866084i	−0.499966	+	0.866045i	$0.666654\pi$
$348$	−15.1246	+	26.1965i	−0.810762	+	1.40428i
$349$	0.309174	−	0.535505i	0.0165497	−	0.0286649i	−0.857632	−	0.514264i	$-0.828065\pi$
$349$	0.309174	−	0.535505i	0.0165497	−	0.0286649i	0.874182	+	0.485599i	$0.161398\pi$
$350$	10.7213			0.573077
$351$	−3.60198	−	0.160483i	−0.192259	−	0.00856593i
$352$	−1.62373			−0.0865453
$353$	−2.94783	+	5.10579i	−0.156897	+	0.271754i	−0.933748	−	0.357931i	$-0.883482\pi$
$353$	−2.94783	+	5.10579i	−0.156897	+	0.271754i	0.776851	+	0.629684i	$0.216816\pi$
$354$	6.48031	−	11.2242i	0.344425	−	0.596561i
$355$	−5.65201	−	9.78957i	−0.299978	−	0.519576i
$356$	−0.673884			−0.0357158
$357$	−8.52312	−	14.7625i	−0.451091	−	0.781313i
$358$	−0.802775	−	1.39045i	−0.0424280	−	0.0734874i
$359$	27.1425			1.43253			0.716263	−	0.697831i	$-0.245851\pi$
$359$	27.1425			1.43253			0.716263	+	0.697831i	$0.245851\pi$
$360$	−4.58940	−	7.94907i	−0.241883	−	0.418953i
$361$	−0.981730	+	1.70041i	−0.0516700	+	0.0894950i
$362$	7.21115	−	12.4901i	0.379010	−	0.656464i
$363$	−1.00000			−0.0524864
$364$	−16.9142	+	26.4978i	−0.886546	+	1.38886i
$365$	−13.7194			−0.718108
$366$	6.37198	−	11.0366i	0.333068	−	0.576892i
$367$	11.1734	−	19.3529i	0.583248	−	1.01022i	−0.411843	−	0.911255i	$-0.635115\pi$
$367$	11.1734	−	19.3529i	0.583248	−	1.01022i	0.995091	−	0.0989607i	$-0.0315518\pi$
$368$	16.4180	+	28.4368i	0.855846	+	1.48237i
$369$	−3.87198			−0.201567
$370$	−7.00598	−	12.1347i	−0.364224	−	0.630854i
$371$	−14.2227	−	24.6345i	−0.738406	−	1.27896i
$372$	38.0053			1.97049
$373$	5.92927	+	10.2698i	0.307006	+	0.531750i	0.977706	−	0.209979i	$-0.0673395\pi$
$373$	5.92927	+	10.2698i	0.307006	+	0.531750i	−0.670700	+	0.741729i	$0.734006\pi$
$374$	−10.0847	+	17.4672i	−0.521466	+	0.903206i
$375$	6.05265	−	10.4835i	0.312558	−	0.541366i
$376$	−33.7629			−1.74119
$377$	14.1152	−	22.1129i	0.726969	−	1.13887i
$378$	5.20396			0.267663
$379$	−9.78233	+	16.9435i	−0.502485	+	0.870329i	0.497511	+	0.867458i	$0.334247\pi$
$379$	−9.78233	+	16.9435i	−0.502485	+	0.870329i	−0.999996	+	0.00287157i	$0.999086\pi$
$380$	16.3185	−	28.2645i	0.837122	−	1.44994i
$381$	−2.74000	−	4.74582i	−0.140374	−	0.243136i
$382$	50.0701			2.56181
$383$	−1.89502	−	3.28227i	−0.0968311	−	0.167716i	0.813540	−	0.581509i	$-0.197537\pi$
$383$	−1.89502	−	3.28227i	−0.0968311	−	0.167716i	−0.910371	+	0.413792i	$0.864204\pi$
$384$	8.95525	+	15.5110i	0.456996	+	0.791540i
$385$	−3.59577			−0.183258
$386$	7.55598	+	13.0873i	0.384589	+	0.666128i
$387$	0.653413	−	1.13174i	0.0332148	−	0.0575298i
$388$	24.9613	−	43.2342i	1.26722	−	2.19488i
$389$	7.37888			0.374124			0.187062	−	0.982348i	$-0.440103\pi$
$389$	7.37888			0.374124			0.187062	+	0.982348i	$0.440103\pi$
$390$	7.07113	+	13.6131i	0.358061	+	0.689327i
$391$	53.7107			2.71627
$392$	−6.96435	+	12.0626i	−0.351753	+	0.609254i
$393$	−5.87268	+	10.1718i	−0.296238	+	0.513099i
$394$	24.8878	+	43.1069i	1.25383	+	2.17169i
$395$	−4.73029			−0.238007
$396$	−2.07870	−	3.60041i	−0.104459	−	0.180927i
$397$	5.07307	+	8.78682i	0.254610	+	0.440998i	0.964790	−	0.263023i	$-0.0847195\pi$
$397$	5.07307	+	8.78682i	0.254610	+	0.440998i	−0.710179	+	0.704021i	$0.751386\pi$
$398$	0.896112			0.0449180
$399$	4.80105	+	8.31567i	0.240353	+	0.416304i
$400$	5.11877	−	8.86597i	0.255939	−	0.443299i
$401$	−4.87609	+	8.44563i	−0.243500	+	0.421755i	−0.961709	−	0.274073i	$-0.911629\pi$
$401$	−4.87609	+	8.44563i	−0.243500	+	0.421755i	0.718209	+	0.695828i	$0.244962\pi$
$402$	6.74004			0.336163
$403$	−32.9279	−	1.46707i	−1.64026	−	0.0730801i
$404$	53.9091			2.68208
$405$	0.857289	−	1.48487i	0.0425991	−	0.0737837i
$406$	−18.9319	+	32.7911i	−0.939576	+	1.62739i
$407$	−1.64669	−	2.85216i	−0.0816236	−	0.141376i
$408$	−43.5133			−2.15423
$409$	−10.2520	−	17.7569i	−0.506927	−	0.878023i	−0.999968	−	0.00801692i	$-0.997448\pi$
$409$	−10.2520	−	17.7569i	−0.506927	−	0.878023i	0.493041	−	0.870006i	$-0.335885\pi$
$410$	8.23680	+	14.2666i	0.406787	+	0.704575i
$411$	4.49993			0.221965
$412$	10.1855	+	17.6418i	0.501803	+	0.869148i
$413$	5.47687	−	9.48621i	0.269499	−	0.466786i
$414$	−8.19853	+	14.2003i	−0.402936	+	0.697905i
$415$	−2.06185			−0.101212
$416$	2.69866	+	5.19537i	0.132313	+	0.254724i
$417$	2.18191			0.106849
$418$	5.68068	−	9.83922i	0.277851	−	0.481252i
$419$	−15.9266	+	27.5858i	−0.778068	+	1.34765i	0.154986	+	0.987917i	$0.450467\pi$
$419$	−15.9266	+	27.5858i	−0.778068	+	1.34765i	−0.933054	+	0.359736i	$0.882867\pi$
$420$	−7.47453	−	12.9463i	−0.364720	−	0.631713i
$421$	19.0756			0.929690			0.464845	−	0.885392i	$-0.346110\pi$
$421$	19.0756			0.929690			0.464845	+	0.885392i	$0.346110\pi$
$422$	−8.73378	−	15.1273i	−0.425154	−	0.736388i
$423$	−3.15341	−	5.46187i	−0.153324	−	0.265565i
$424$	−72.6116			−3.52633
$425$	−8.37292	−	14.5023i	−0.406146	−	0.703466i
$426$	8.17983	−	14.1679i	0.396314	−	0.686436i
$427$	5.38531	−	9.32763i	0.260613	−	0.451396i
$428$	70.7203			3.41839
$429$	1.66201	+	3.19965i	0.0802424	+	0.154480i
$430$	−5.55999			−0.268126
$431$	−1.10991	+	1.92242i	−0.0534624	+	0.0925996i	−0.891518	−	0.452985i	$-0.850359\pi$
$431$	−1.10991	+	1.92242i	−0.0534624	+	0.0925996i	0.838056	+	0.545585i	$0.183692\pi$
$432$	2.48458	−	4.30341i	0.119539	−	0.207048i
$433$	7.98037	+	13.8224i	0.383512	+	0.664262i	0.991562	−	0.129637i	$-0.0413811\pi$
$433$	7.98037	+	13.8224i	0.383512	+	0.664262i	−0.608049	+	0.793899i	$0.708048\pi$
$434$	47.5726			2.28356
$435$	6.23762	+	10.8039i	0.299071	+	0.518006i
$436$	12.3783	+	21.4399i	0.592815	+	1.02679i
$437$	−30.2551			−1.44730
$438$	−9.92767	−	17.1952i	−0.474362	−	0.821620i
$439$	8.02140	−	13.8935i	0.382841	−	0.663100i	−0.608626	−	0.793457i	$-0.708279\pi$
$439$	8.02140	−	13.8935i	0.382841	−	0.663100i	0.991467	+	0.130357i	$0.0416125\pi$
$440$	−4.58940	+	7.94907i	−0.218791	+	0.378957i
$441$	−2.60185			−0.123898
$442$	72.6496	+	3.23683i	3.45559	+	0.153960i
$443$	−30.1760			−1.43371			−0.716853	−	0.697225i	$-0.754418\pi$
$443$	−30.1760			−1.43371			−0.716853	+	0.697225i	$0.754418\pi$
$444$	6.84596	−	11.8576i	0.324895	−	0.562734i
$445$	−0.138960	+	0.240687i	−0.00658736	+	0.0114096i
$446$	29.1058	+	50.4127i	1.37820	+	2.38711i
$447$	0.681457			0.0322318
$448$	6.19627	+	10.7323i	0.292746	+	0.507051i
$449$	−4.95554	−	8.58325i	−0.233866	−	0.405069i	0.725076	−	0.688669i	$-0.241805\pi$
$449$	−4.95554	−	8.58325i	−0.233866	−	0.405069i	−0.958943	+	0.283600i	$0.908471\pi$
$450$	5.11225			0.240994
$451$	1.93599	+	3.35323i	0.0911621	+	0.157897i
$452$	−25.5286	+	44.2168i	−1.20076	+	2.07979i
$453$	−3.08667	+	5.34626i	−0.145024	+	0.251189i
$454$	−44.0294			−2.06640
$455$	5.97620	+	11.5052i	0.280169	+	0.539372i
$456$	24.5109			1.14783
$457$	7.22749	−	12.5184i	0.338088	−	0.585585i	−0.645985	−	0.763350i	$-0.723553\pi$
$457$	7.22749	−	12.5184i	0.338088	−	0.585585i	0.984073	+	0.177765i	$0.0568867\pi$
$458$	−13.3633	+	23.1459i	−0.624427	+	1.08154i
$459$	−4.06409	−	7.03921i	−0.189696	−	0.328562i
$460$	47.1027			2.19618
$461$	14.0918	+	24.4077i	0.656321	+	1.13678i	0.981561	+	0.191150i	$0.0612216\pi$
$461$	14.0918	+	24.4077i	0.656321	+	1.13678i	−0.325240	+	0.945632i	$0.605445\pi$
$462$	−2.60198	−	4.50676i	−0.121055	−	0.209673i
$463$	20.2581			0.941472			0.470736	−	0.882274i	$-0.343988\pi$
$463$	20.2581			0.941472			0.470736	+	0.882274i	$0.343988\pi$
$464$	18.0777	+	31.3115i	0.839237	+	1.45360i
$465$	7.83702	−	13.5741i	0.363433	−	0.629484i
$466$	−25.2219	+	43.6855i	−1.16838	+	2.02369i
$467$	−8.66625			−0.401026			−0.200513	−	0.979691i	$-0.564261\pi$
$467$	−8.66625			−0.401026			−0.200513	+	0.979691i	$0.564261\pi$
$468$	−8.06523	+	12.6350i	−0.372815	+	0.584053i
$469$	5.69638			0.263034
$470$	−13.4164	+	23.2379i	−0.618854	+	1.07189i
$471$	8.75571	−	15.1653i	0.403442	−	0.698782i
$472$	−13.9806	−	24.2151i	−0.643509	−	1.11459i
$473$	−1.30683			−0.0600879
$474$	−3.42294	−	5.92870i	−0.157221	−	0.272314i
$475$	4.71645	+	8.16913i	0.216405	+	0.374825i
$476$	−70.8680			−3.24823
$477$	−6.78184	−	11.7465i	−0.310519	−	0.537835i
$478$	14.4479	−	25.0245i	0.660832	−	1.14459i
$479$	2.00818	−	3.47826i	0.0917559	−	0.158926i	−0.816494	−	0.577354i	$-0.804085\pi$
$479$	2.00818	−	3.47826i	0.0917559	−	0.158926i	0.908250	+	0.418428i	$0.137419\pi$
$480$	−2.78402			−0.127073
$481$	−6.38908	+	10.0091i	−0.291317	+	0.456378i
$482$	−8.84907			−0.403064
$483$	−6.92903	+	12.0014i	−0.315282	+	0.546084i
$484$	−2.07870	+	3.60041i	−0.0944863	+	0.163655i
$485$	−10.2944	−	17.8305i	−0.467446	−	0.809641i
$486$	2.48141			0.112559
$487$	0.929562	+	1.61005i	0.0421225	+	0.0729583i	0.886318	−	0.463077i	$-0.153255\pi$
$487$	0.929562	+	1.61005i	0.0421225	+	0.0729583i	−0.844196	+	0.536035i	$0.819921\pi$
$488$	−13.7469	−	23.8103i	−0.622292	−	1.07784i
$489$	−16.3550			−0.739600
$490$	5.53488	+	9.58669i	0.250040	+	0.433083i
$491$	−13.1498	+	22.7761i	−0.593441	+	1.02787i	0.400323	+	0.916374i	$0.368898\pi$
$491$	−13.1498	+	22.7761i	−0.593441	+	1.02787i	−0.993765	+	0.111497i	$0.964436\pi$
$492$	−8.04867	+	13.9407i	−0.362862	+	0.628495i
$493$	59.1405			2.66355
$494$	−40.9233	−	1.82330i	−1.84123	−	0.0820342i
$495$	−1.71458			−0.0770646
$496$	22.7131	−	39.3402i	1.01985	−	1.76643i
$497$	6.91322	−	11.9741i	0.310100	−	0.537110i
$498$	−1.49200	−	2.58422i	−0.0668582	−	0.115802i
$499$	18.2384			0.816464			0.408232	−	0.912878i	$-0.366146\pi$
$499$	18.2384			0.816464			0.408232	+	0.912878i	$0.366146\pi$
$500$	−25.1633	−	43.5841i	−1.12534	−	1.94914i
$501$	−5.86526	−	10.1589i	−0.262040	−	0.453867i
$502$	27.7468			1.23840
$503$	−7.60604	−	13.1740i	−0.339137	−	0.587402i	0.645134	−	0.764069i	$-0.276802\pi$
$503$	−7.60604	−	13.1740i	−0.339137	−	0.587402i	−0.984271	+	0.176668i	$0.943468\pi$
$504$	5.61350	−	9.72286i	0.250045	−	0.433091i
$505$	11.1165	−	19.2543i	0.494678	−	0.856807i
$506$	16.3971			0.728938
$507$	7.47547	−	10.6357i	0.331997	−	0.472347i
$508$	−22.7825			−1.01081
$509$	16.2467	−	28.1401i	0.720122	−	1.24729i	−0.240829	−	0.970568i	$-0.577419\pi$
$509$	16.2467	−	28.1401i	0.720122	−	1.24729i	0.960951	−	0.276720i	$-0.0892474\pi$
$510$	−17.2910	+	29.9488i	−0.765657	+	1.32616i
$511$	−8.39042	−	14.5326i	−0.371170	−	0.642886i
$512$	45.1350			1.99470
$513$	2.28929	+	3.96517i	0.101075	+	0.175067i
$514$	12.3528	+	21.3957i	0.544858	+	0.943722i
$515$	8.40132			0.370207
$516$	−2.71650	−	4.70511i	−0.119587	−	0.207131i
$517$	−3.15341	+	5.46187i	−0.138687	+	0.240213i
$518$	8.56932	−	14.8425i	0.376514	−	0.652142i
$519$	3.41056			0.149707
$520$	33.0618	+	1.47304i	1.44986	+	0.0645970i
$521$	23.8625			1.04544			0.522718	−	0.852506i	$-0.324918\pi$
$521$	23.8625			1.04544			0.522718	+	0.852506i	$0.324918\pi$
$522$	−9.02734	+	15.6358i	−0.395116	+	0.684361i
$523$	1.73372	−	3.00289i	0.0758103	−	0.131307i	−0.825628	−	0.564215i	$-0.809179\pi$
$523$	1.73372	−	3.00289i	0.0758103	−	0.131307i	0.901438	+	0.432907i	$0.142512\pi$
$524$	24.4151	+	42.2881i	1.06658	+	1.84737i
$525$	4.32064			0.188568
$526$	−17.5462	−	30.3909i	−0.765050	−	1.32510i
$527$	−37.1524	−	64.3498i	−1.61838	−	2.80312i
$528$	−4.96915			−0.216255
$529$	−10.3326	−	17.8965i	−0.449242	−	0.778109i
$530$	−28.8538	+	49.9763i	−1.25333	+	2.17083i
$531$	2.61154	−	4.52333i	0.113331	−	0.196296i
$532$	39.9198			1.73074
$533$	7.51152	−	11.7676i	0.325360	−	0.509710i
$534$	−0.402219			−0.0174057
$535$	14.5831	−	25.2587i	0.630482	−	1.09203i
$536$	7.27047	−	12.5928i	0.314036	−	0.543927i
$537$	−0.323515	−	0.560345i	−0.0139607	−	0.0241807i
$538$	67.0020			2.88866
$539$	1.30092	+	2.25327i	0.0560348	+	0.0970551i
$540$	−3.56409	−	6.17319i	−0.153374	−	0.265652i
$541$	−32.6221			−1.40253			−0.701267	−	0.712899i	$-0.747382\pi$
$541$	−32.6221			−1.40253			−0.701267	+	0.712899i	$0.747382\pi$
$542$	−12.0845	−	20.9310i	−0.519074	−	0.899062i
$543$	2.90607	−	5.03346i	0.124711	−	0.216006i
$544$	−6.59900	+	11.4298i	−0.282930	+	0.490049i
$545$	10.2101			0.437351
$546$	−10.0955	+	15.8157i	−0.432049	+	0.676848i
$547$	−18.2734			−0.781315			−0.390658	−	0.920536i	$-0.627752\pi$
$547$	−18.2734			−0.781315			−0.390658	+	0.920536i	$0.627752\pi$
$548$	9.35399	−	16.2016i	0.399583	−	0.692097i
$549$	2.56788	−	4.44771i	0.109595	−	0.189823i
$550$	−2.55612	−	4.42734i	−0.108994	−	0.188782i
$551$	−33.3137			−1.41921
$552$	17.6875	+	30.6356i	0.752829	+	1.30394i
$553$	−2.89291	−	5.01067i	−0.123019	−	0.213075i
$554$	−81.4667			−3.46119
$555$	−2.82339	−	4.89025i	−0.119846	−	0.207580i
$556$	4.53554	−	7.85578i	0.192350	−	0.333159i
$557$	0.100670	−	0.174365i	0.00426551	−	0.00738809i	−0.863885	−	0.503689i	$-0.831976\pi$
$557$	0.100670	−	0.174365i	0.00426551	−	0.00738809i	0.868150	+	0.496301i	$0.165309\pi$
$558$	22.6841			0.960295
$559$	2.17195	+	4.18138i	0.0918638	+	0.176854i
$560$	−17.8680			−0.755059
$561$	−4.06409	+	7.03921i	−0.171586	+	0.297196i
$562$	−16.9526	+	29.3628i	−0.715103	+	1.23860i
$563$	−11.7075	−	20.2779i	−0.493411	−	0.854613i	0.506560	−	0.862205i	$-0.330917\pi$
$563$	−11.7075	−	20.2779i	−0.493411	−	0.854613i	−0.999971	+	0.00759187i	$0.997583\pi$
$564$	−26.2200			−1.10406
$565$	10.5284	+	18.2358i	0.442934	+	0.767184i
$566$	−26.6474	−	46.1547i	−1.12008	−	1.94003i
$567$	2.09718			0.0880731
$568$	−17.6471	−	30.5657i	−0.740457	−	1.28251i
$569$	−10.5557	+	18.2830i	−0.442517	+	0.766462i	−0.997876	−	0.0651492i	$-0.979248\pi$
$569$	−10.5557	+	18.2830i	−0.442517	+	0.766462i	0.555359	+	0.831611i	$0.312581\pi$
$570$	9.73997	−	16.8701i	0.407962	−	0.706611i
$571$	−35.2696			−1.47599			−0.737993	−	0.674809i	$-0.764226\pi$
$571$	−35.2696			−1.47599			−0.737993	+	0.674809i	$0.764226\pi$
$572$	14.9749	+	0.667190i	0.626130	+	0.0278966i
$573$	20.1781			0.842952
$574$	−10.0748	+	17.4501i	−0.420514	+	0.728351i
$575$	−6.80692	+	11.7899i	−0.283868	+	0.491674i
$576$	2.95458	+	5.11748i	0.123107	+	0.213228i
$577$	21.3658			0.889470			0.444735	−	0.895662i	$-0.353298\pi$
$577$	21.3658			0.889470			0.444735	+	0.895662i	$0.353298\pi$
$578$	60.8781	+	105.444i	2.53220	+	4.38589i
$579$	3.04504	+	5.27416i	0.126547	+	0.219186i
$580$	51.8645			2.15356
$581$	−1.26097	−	2.18407i	−0.0523140	−	0.0906104i
$582$	14.8985	−	25.8050i	0.617564	−	1.06965i
$583$	−6.78184	+	11.7465i	−0.280875	+	0.486490i
$584$	−42.8358			−1.77256
$585$	2.84964	+	5.48604i	0.117818	+	0.226820i
$586$	−50.7025			−2.09450
$587$	−3.74191	+	6.48118i	−0.154445	+	0.267507i	−0.932857	−	0.360247i	$-0.882692\pi$
$587$	−3.74191	+	6.48118i	−0.154445	+	0.267507i	0.778412	+	0.627754i	$0.216026\pi$
$588$	−5.40846	+	9.36773i	−0.223041	+	0.386319i
$589$	20.9279	+	36.2481i	0.862317	+	1.49358i
$590$	−22.2220			−0.914865
$591$	10.0297	+	17.3719i	0.412566	+	0.714586i
$592$	−8.18267	−	14.1728i	−0.336306	−	0.582499i
$593$	25.2441			1.03665			0.518326	−	0.855183i	$-0.326555\pi$
$593$	25.2441			1.03665			0.518326	+	0.855183i	$0.326555\pi$
$594$	−1.24071	−	2.14896i	−0.0509067	−	0.0881731i
$595$	−14.6136	+	25.3114i	−0.599098	+	1.03767i
$596$	1.41654	−	2.45352i	0.0580239	−	0.100500i
$597$	0.361130			0.0147801
$598$	−27.2520	−	52.4648i	−1.11442	−	2.14544i
$599$	20.1313			0.822543			0.411272	−	0.911513i	$-0.365085\pi$
$599$	20.1313			0.822543			0.411272	+	0.911513i	$0.365085\pi$
$600$	5.51457	−	9.55152i	0.225132	−	0.389939i
$601$	−23.9824	+	41.5387i	−0.978262	+	1.69440i	−0.309543	+	0.950886i	$0.600176\pi$
$601$	−23.9824	+	41.5387i	−0.978262	+	1.69440i	−0.668720	+	0.743515i	$0.733157\pi$
$602$	−3.40033	−	5.88955i	−0.138587	−	0.240040i
$603$	2.71621			0.110613
$604$	12.8325	+	22.2265i	0.522147	+	0.904385i
$605$	0.857289	+	1.48487i	0.0348538	+	0.0603685i
$606$	32.1765			1.30708
$607$	−4.15349	−	7.19406i	−0.168585	−	0.291998i	0.769338	−	0.638842i	$-0.220586\pi$
$607$	−4.15349	−	7.19406i	−0.168585	−	0.291998i	−0.937923	+	0.346845i	$0.887253\pi$
$608$	3.71720	−	6.43838i	0.150752	−	0.261111i
$609$	−7.62951	+	13.2147i	−0.309163	+	0.535486i
$610$	−21.8505			−0.884701
$611$	22.7170	+	1.01214i	0.919033	+	0.0409467i
$612$	−33.7921			−1.36596
$613$	−21.3176	+	36.9232i	−0.861011	+	1.49131i	0.00994416	+	0.999951i	$0.496835\pi$
$613$	−21.3176	+	36.9232i	−0.861011	+	1.49131i	−0.870955	+	0.491363i	$0.836499\pi$
$614$	−12.1912	+	21.1158i	−0.491998	+	0.852166i
$615$	3.31940	+	5.74938i	0.133851	+	0.231837i
$616$	−11.2270			−0.452349
$617$	−9.49261	−	16.4417i	−0.382158	−	0.661917i	0.609212	−	0.793007i	$-0.291486\pi$
$617$	−9.49261	−	16.4417i	−0.382158	−	0.661917i	−0.991370	+	0.131090i	$0.958152\pi$
$618$	6.07937	+	10.5298i	0.244548	+	0.423570i
$619$	−6.49630			−0.261108			−0.130554	−	0.991441i	$-0.541676\pi$
$619$	−6.49630			−0.261108			−0.130554	+	0.991441i	$0.541676\pi$
$620$	−32.5816	−	56.4329i	−1.30851	−	2.26640i
$621$	−3.30398	+	5.72266i	−0.132584	+	0.229642i
$622$	36.8693	−	63.8594i	1.47832	−	2.56053i
$623$	−0.339937			−0.0136193
$624$	8.25876	+	15.8995i	0.330615	+	0.636490i
$625$	−10.4544			−0.418176
$626$	25.5637	−	44.2777i	1.02173	−	1.76969i
$627$	2.28929	−	3.96517i	0.0914256	−	0.158354i
$628$	−36.4010	−	63.0483i	−1.45256	−	2.51590i
$629$	−26.7693			−1.06736
$630$	−4.46130	−	7.72719i	−0.177742	−	0.307859i
$631$	−17.2231	−	29.8313i	−0.685640	−	1.18756i	−0.973235	−	0.229812i	$-0.926189\pi$
$631$	−17.2231	−	29.8313i	−0.685640	−	1.18756i	0.287595	−	0.957752i	$-0.407144\pi$
$632$	−14.7693			−0.587490
$633$	−3.51968	−	6.09627i	−0.139895	−	0.242305i
$634$	−25.1177	+	43.5051i	−0.997551	+	1.72781i
$635$	−4.69794	+	8.13708i	−0.186432	+	0.322910i
$636$	−56.3896			−2.23599
$637$	5.04751	−	7.90744i	0.199990	−	0.313304i
$638$	18.0547			0.714792
$639$	3.29644	−	5.70961i	0.130405	−	0.225869i
$640$	15.3545	−	26.5947i	0.606939	−	1.05125i
$641$	−23.2619	−	40.2908i	−0.918789	−	1.59139i	−0.801257	−	0.598320i	$-0.795835\pi$
$641$	−23.2619	−	40.2908i	−0.918789	−	1.59139i	−0.117532	−	0.993069i	$-0.537498\pi$
$642$	42.2105			1.66592
$643$	23.6809	+	41.0165i	0.933883	+	1.61753i	0.776614	+	0.629976i	$0.216935\pi$
$643$	23.6809	+	41.0165i	0.933883	+	1.61753i	0.157268	+	0.987556i	$0.449731\pi$
$644$	28.8067	+	49.8947i	1.13514	+	1.96613i
$645$	−2.24066			−0.0882257
$646$	−46.1736	−	79.9750i	−1.81668	−	3.14657i
$647$	−3.56405	+	6.17311i	−0.140117	+	0.242690i	−0.927541	−	0.373722i	$-0.878081\pi$
$647$	−3.56405	+	6.17311i	−0.140117	+	0.242690i	0.787423	+	0.616413i	$0.211415\pi$
$648$	2.67669	−	4.63617i	0.105150	−	0.182126i
$649$	−5.22309			−0.205024
$650$	−9.91762	+	15.5370i	−0.389001	+	0.609410i
$651$	19.1716			0.751394
$652$	−33.9972	+	58.8848i	−1.33143	+	2.30611i
$653$	−16.0545	+	27.8071i	−0.628259	+	1.08818i	0.359641	+	0.933091i	$0.382899\pi$
$653$	−16.0545	+	27.8071i	−0.628259	+	1.08818i	−0.987901	+	0.155087i	$0.950434\pi$
$654$	7.38822	+	12.7968i	0.288902	+	0.500393i
$655$	20.1384			0.786870
$656$	9.62022	+	16.6627i	0.375606	+	0.650569i
$657$	−4.00082	−	6.92962i	−0.156087	−	0.270350i
$658$	−32.8204			−1.27947
$659$	2.50135	+	4.33246i	0.0974386	+	0.168769i	0.910624	−	0.413236i	$-0.135602\pi$
$659$	2.50135	+	4.33246i	0.0974386	+	0.168769i	−0.813185	+	0.582005i	$0.802268\pi$
$660$	−3.56409	+	6.17319i	−0.138732	+	0.240291i
$661$	−24.6534	+	42.7010i	−0.958907	+	1.66088i	−0.233745	+	0.972298i	$0.575098\pi$
$661$	−24.6534	+	42.7010i	−0.958907	+	1.66088i	−0.725162	+	0.688578i	$0.758235\pi$
$662$	−69.4151			−2.69789
$663$	29.2775	+	1.30443i	1.13705	+	0.0506600i
$664$	−6.43768			−0.249830
$665$	8.23178	−	14.2579i	0.319215	−	0.552896i
$666$	4.08612	−	7.07737i	0.158334	−	0.274243i
$667$	−24.0397	−	41.6379i	−0.930820	−	1.61223i
$668$	−48.7684			−1.88691
$669$	11.7295	+	20.3162i	0.453490	+	0.785468i
$670$	−5.77817	−	10.0081i	−0.223230	−	0.386646i
$671$	−5.13577			−0.198264
$672$	−1.70263	−	2.94904i	−0.0656803	−	0.113762i
$673$	7.14128	−	12.3691i	0.275276	−	0.476792i	−0.694929	−	0.719079i	$-0.744564\pi$
$673$	7.14128	−	12.3691i	0.275276	−	0.476792i	0.970205	+	0.242286i	$0.0778973\pi$
$674$	−21.8371	+	37.8230i	−0.841134	+	1.45689i
$675$	2.06022			0.0792979
$676$	−22.7535	−	49.0231i	−0.875136	−	1.88550i
$677$	−18.5948			−0.714656			−0.357328	−	0.933979i	$-0.616312\pi$
$677$	−18.5948			−0.714656			−0.357328	+	0.933979i	$0.616312\pi$
$678$	−15.2372	+	26.3915i	−0.585180	+	1.01356i
$679$	12.5916	−	21.8093i	0.483221	−	0.836963i
$680$	37.3035	+	64.6115i	1.43052	+	2.47774i
$681$	−17.7437			−0.679940
$682$	−11.3421	−	19.6450i	−0.434310	−	0.752247i
$683$	−6.85983	−	11.8816i	−0.262484	−	0.454636i	0.704417	−	0.709786i	$-0.251208\pi$
$683$	−6.85983	−	11.8816i	−0.262484	−	0.454636i	−0.966901	+	0.255150i	$0.917875\pi$
$684$	19.0350			0.727821
$685$	−3.85774	−	6.68180i	−0.147397	−	0.255298i
$686$	−24.9838	+	43.2732i	−0.953886	+	1.65218i
$687$	−5.38537	+	9.32773i	−0.205465	+	0.355875i
$688$	−6.49382			−0.247574
$689$	48.8561	+	2.17674i	1.86127	+	0.0829270i
$690$	28.1140			1.07028
$691$	4.40601	−	7.63143i	0.167612	−	0.290313i	−0.769968	−	0.638083i	$-0.779728\pi$
$691$	4.40601	−	7.63143i	0.167612	−	0.290313i	0.937580	+	0.347770i	$0.113061\pi$
$692$	7.08952	−	12.2794i	0.269503	−	0.466793i
$693$	−1.04859	−	1.81621i	−0.0398326	−	0.0689921i
$694$	46.2267			1.75474
$695$	−1.87053	−	3.23985i	−0.0709533	−	0.122895i
$696$	19.4756	+	33.7327i	0.738219	+	1.27863i
$697$	31.4721			1.19209
$698$	−0.767188	−	1.32881i	−0.0290385	−	0.0502961i
$699$	−10.1643	+	17.6051i	−0.384450	+	0.665887i
$700$	8.98132	−	15.5561i	0.339462	−	0.587965i
$701$	8.42103			0.318058			0.159029	−	0.987274i	$-0.449164\pi$
$701$	8.42103			0.318058			0.159029	+	0.987274i	$0.449164\pi$
$702$	−4.81386	+	7.54141i	−0.181688	+	0.284632i
$703$	15.0791			0.568718
$704$	2.95458	−	5.11748i	0.111355	−	0.192872i
$705$	−5.40677	+	9.36481i	−0.203631	+	0.352699i
$706$	7.31477	+	12.6695i	0.275295	+	0.476825i
$707$	27.1942			1.02274
$708$	−10.8572	−	18.8053i	−0.408039	−	0.706745i
$709$	−14.6153	−	25.3144i	−0.548889	−	0.950704i	−0.998351	−	0.0574045i	$-0.981718\pi$
$709$	−14.6153	−	25.3144i	−0.548889	−	0.950704i	0.449462	−	0.893300i	$-0.351616\pi$
$710$	−28.0499			−1.05269
$711$	−1.37943	−	2.38925i	−0.0517327	−	0.0896037i
$712$	−0.433873	+	0.751490i	−0.0162601	+	0.0281633i
$713$	−30.2037	+	52.3144i	−1.13114	+	1.95919i
$714$	−42.2987			−1.58299
$715$	3.32623	−	5.21088i	0.124394	−	0.194876i
$716$	−2.68996			−0.100529
$717$	5.82246	−	10.0848i	0.217444	−	0.376623i
$718$	33.6758	−	58.3282i	1.25677	−	2.17679i
$719$	−21.1239	−	36.5877i	−0.787789	−	1.36449i	−0.927319	−	0.374272i	$-0.877893\pi$
$719$	−21.1239	−	36.5877i	−0.787789	−	1.36449i	0.139530	−	0.990218i	$-0.455441\pi$
$720$	−8.52000			−0.317522
$721$	5.13801	+	8.89930i	0.191350	+	0.331427i
$722$	2.43607	+	4.21940i	0.0906613	+	0.157030i
$723$	−3.56615			−0.132626
$724$	−12.0817	−	20.9261i	−0.449012	−	0.777712i
$725$	−7.49506	+	12.9818i	−0.278359	+	0.482133i
$726$	−1.24071	+	2.14896i	−0.0460469	+	0.0797555i
$727$	28.7391			1.06587			0.532937	−	0.846155i	$-0.321088\pi$
$727$	28.7391			1.06587			0.532937	+	0.846155i	$0.321088\pi$
$728$	18.6593	+	35.9224i	0.691561	+	1.33137i
$729$	1.00000			0.0370370
$730$	−17.0218	+	29.4826i	−0.630004	+	1.09120i
$731$	−5.31106	+	9.19903i	−0.196437	+	0.340238i
$732$	−10.6757	−	18.4909i	−0.394586	−	0.683443i
$733$	−15.8737			−0.586308			−0.293154	−	0.956065i	$-0.594705\pi$
$733$	−15.8737			−0.586308			−0.293154	+	0.956065i	$0.594705\pi$
$734$	−27.7259	−	48.0226i	−1.02338	−	1.77255i
$735$	2.23054	+	3.86340i	0.0822746	+	0.142504i
$736$	10.7296			0.395497
$737$	−1.35811	−	2.35231i	−0.0500265	−	0.0866485i
$738$	−4.80398	+	8.32074i	−0.176837	+	0.306291i
$739$	−4.50657	+	7.80561i	−0.165777	+	0.287134i	−0.936931	−	0.349515i	$-0.886347\pi$
$739$	−4.50657	+	7.80561i	−0.165777	+	0.287134i	0.771154	+	0.636649i	$0.219680\pi$
$740$	−23.4759			−0.862990
$741$	−16.4920	−	0.734784i	−0.605848	−	0.0269930i
$742$	−70.5848			−2.59125
$743$	−24.5250	+	42.4786i	−0.899736	+	1.55839i	−0.0719054	+	0.997411i	$0.522908\pi$
$743$	−24.5250	+	42.4786i	−0.899736	+	1.55839i	−0.827831	+	0.560978i	$0.810425\pi$
$744$	24.4693	−	42.3821i	0.897088	−	1.55380i
$745$	−0.584206	−	1.01187i	−0.0214036	−	0.0370722i
$746$	29.4259			1.07736
$747$	−0.601272	−	1.04143i	−0.0219994	−	0.0381040i
$748$	16.8960	+	29.2648i	0.617780	+	1.07003i
$749$	35.6745			1.30352
$750$	−15.0191	−	26.0139i	−0.548420	−	0.949892i
$751$	−4.25862	+	7.37615i	−0.155399	+	0.269160i	−0.933204	−	0.359346i	$-0.883000\pi$
$751$	−4.25862	+	7.37615i	−0.155399	+	0.269160i	0.777805	+	0.628506i	$0.216333\pi$
$752$	−15.6698	+	27.1409i	−0.571418	+	0.989726i
$753$	11.1818			0.407489
$754$	−30.0070	−	57.7686i	−1.09279	−	2.10381i
$755$	10.5847			0.385215
$756$	4.35940	−	7.55070i	0.158550	−	0.274616i
$757$	2.84225	−	4.92293i	0.103303	−	0.178927i	−0.809740	−	0.586788i	$-0.800392\pi$
$757$	2.84225	−	4.92293i	0.103303	−	0.178927i	0.913044	+	0.407862i	$0.133725\pi$
$758$	24.2740	+	42.0438i	0.881671	+	1.52710i
$759$	6.60796			0.239854
$760$	−21.0130	−	36.3955i	−0.762221	−	1.32020i
$761$	17.3126	+	29.9863i	0.627582	+	1.08700i	0.988035	+	0.154227i	$0.0492886\pi$
$761$	17.3126	+	29.9863i	0.627582	+	1.08700i	−0.360453	+	0.932777i	$0.617378\pi$
$762$	−13.5981			−0.492608
$763$	6.24419	+	10.8153i	0.226055	+	0.391539i
$764$	41.9442	−	72.6494i	1.51749	−	2.62836i
$765$	−6.96821	+	12.0693i	−0.251936	+	0.436366i
$766$	−9.40465			−0.339804
$767$	8.68081	+	16.7120i	0.313446	+	0.603436i
$768$	32.6250			1.17725
$769$	23.0396	−	39.9058i	0.830830	−	1.43904i	−0.0665508	−	0.997783i	$-0.521199\pi$
$769$	23.0396	−	39.9058i	0.830830	−	1.43904i	0.897381	−	0.441257i	$-0.145467\pi$
$770$	−4.46130	+	7.72719i	−0.160774	+	0.278469i
$771$	4.97813	+	8.62238i	0.179283	+	0.310527i
$772$	25.3188			0.911245
$773$	7.20523	+	12.4798i	0.259154	+	0.448868i	0.966016	−	0.258484i	$-0.0832229\pi$
$773$	7.20523	+	12.4798i	0.259154	+	0.448868i	−0.706861	+	0.707352i	$0.749890\pi$
$774$	−1.62139	−	2.80832i	−0.0582795	−	0.100943i
$775$	18.8337			0.676528
$776$	−32.1421	−	55.6717i	−1.15383	−	1.99850i
$777$	3.45341	−	5.98148i	0.123890	−	0.214584i
$778$	9.15502	−	15.8570i	0.328223	−	0.568499i
$779$	−17.7282			−0.635178
$780$	25.6756	+	1.14395i	0.919333	+	0.0409600i
$781$	−6.59289			−0.235912
$782$	66.6391	−	115.422i	2.38301	−	4.12750i
$783$	−3.63799	+	6.30118i	−0.130011	+	0.225186i
$784$	6.46449	+	11.1968i	0.230875	+	0.399887i
$785$	−30.0247			−1.07163
$786$	14.5725	+	25.2404i	0.519785	+	0.900294i
$787$	4.04004	+	6.99755i	0.144012	+	0.249436i	0.929004	−	0.370070i	$-0.120666\pi$
$787$	4.04004	+	6.99755i	0.144012	+	0.249436i	−0.784992	+	0.619506i	$0.787333\pi$
$788$	83.3948			2.97082
$789$	−7.07105	−	12.2474i	−0.251736	−	0.436020i
$790$	−5.86890	+	10.1652i	−0.208806	+	0.361662i
$791$	−12.8778	+	22.3050i	−0.457881	+	0.793073i
$792$	−5.35339			−0.190224
$793$	8.53568	+	16.4326i	0.303111	+	0.583540i
$794$	25.1768			0.893490
$795$	−11.6280	+	20.1403i	−0.412402	+	0.714302i
$796$	0.750680	−	1.30022i	0.0266072	−	0.0460849i
$797$	−0.856928	−	1.48424i	−0.0303539	−	0.0525745i	0.850449	−	0.526057i	$-0.176330\pi$
$797$	−0.856928	−	1.48424i	−0.0303539	−	0.0525745i	−0.880803	+	0.473482i	$0.842997\pi$
$798$	23.8268			0.843458
$799$	25.6315	+	44.3951i	0.906778	+	1.57059i
$800$	−1.67262	−	2.89707i	−0.0591362	−	0.102427i
$801$	−0.162093			−0.00572727
$802$	12.0996	+	20.9571i	0.427251	+	0.740020i
$803$	−4.00082	+	6.92962i	−0.141186	+	0.244541i
$804$	5.64619	−	9.77949i	0.199126	−	0.344896i
$805$	23.7607			0.837456
$806$	−44.0065	+	68.9407i	−1.55006	+	2.42833i
$807$	27.0016			0.950500
$808$	34.7088	−	60.1174i	1.22105	−	2.11492i
$809$	13.7887	−	23.8828i	0.484786	−	0.839675i	−0.515061	−	0.857154i	$-0.672231\pi$
$809$	13.7887	−	23.8828i	0.484786	−	0.839675i	0.999847	+	0.0174788i	$0.00556397\pi$
$810$	−2.12729	−	3.68457i	−0.0747452	−	0.129463i
$811$	40.1330			1.40926			0.704630	−	0.709575i	$-0.251113\pi$
$811$	40.1330			1.40926			0.704630	+	0.709575i	$0.251113\pi$
$812$	31.7189	+	54.9387i	1.11311	+	1.92797i
$813$	−4.87001	−	8.43511i	−0.170799	−	0.295832i
$814$	−8.17225			−0.286437
$815$	14.0210	+	24.2851i	0.491134	+	0.850669i
$816$	−20.1951	+	34.9789i	−0.706970	+	1.22451i
$817$	2.99171	−	5.18179i	0.104667	−	0.181288i
$818$	−50.8786			−1.77893
$819$	−4.06846	+	6.37366i	−0.142164	+	0.222714i
$820$	27.6002			0.963839
$821$	4.85647	−	8.41166i	0.169492	−	0.293569i	−0.768749	−	0.639550i	$-0.779121\pi$
$821$	4.85647	−	8.41166i	0.169492	−	0.293569i	0.938241	+	0.345981i	$0.112454\pi$
$822$	5.58308	−	9.67018i	0.194732	−	0.337286i
$823$	−8.44416	−	14.6257i	−0.294345	−	0.509821i	0.680487	−	0.732760i	$-0.261768\pi$
$823$	−8.44416	−	14.6257i	−0.294345	−	0.509821i	−0.974832	+	0.222939i	$0.928435\pi$
$824$	26.2312			0.913808
$825$	−1.03011	−	1.78420i	−0.0358638	−	0.0621180i
$826$	−13.5904	−	23.5392i	−0.472869	−	0.819033i
$827$	32.3586			1.12522			0.562610	−	0.826723i	$-0.309797\pi$
$827$	32.3586			1.12522			0.562610	+	0.826723i	$0.309797\pi$
$828$	13.7360	+	23.7914i	0.477357	+	0.826807i
$829$	−3.80030	+	6.58232i	−0.131990	+	0.228613i	−0.924444	−	0.381319i	$-0.875470\pi$
$829$	−3.80030	+	6.58232i	−0.131990	+	0.228613i	0.792454	+	0.609932i	$0.208803\pi$
$830$	−2.55815	+	4.43085i	−0.0887948	+	0.153797i
$831$	−32.8308			−1.13889
$832$	−21.2846	−	0.948317i	−0.737912	−	0.0328770i
$833$	21.1483			0.732745
$834$	2.70711	−	4.68885i	0.0937396	−	0.162362i
$835$	−10.0564	+	17.4183i	−0.348018	+	0.602784i
$836$	−9.51750	−	16.4848i	−0.329170	−	0.570139i
$837$	9.14162			0.315981
$838$	39.5205	+	68.4516i	1.36521	+	2.36462i
$839$	9.94147	+	17.2191i	0.343218	+	0.594470i	0.985028	−	0.172393i	$-0.0551498\pi$
$839$	9.94147	+	17.2191i	0.343218	+	0.594470i	−0.641811	+	0.766863i	$0.721816\pi$
$840$	−19.2496			−0.664173
$841$	−11.9699	−	20.7325i	−0.412756	−	0.714915i
$842$	23.6673	−	40.9929i	0.815627	−	1.41271i
$843$	−6.83185	+	11.8331i	−0.235301	+	0.407554i
$844$	−29.2654			−1.00736
$845$	−22.2012	−	1.98224i	−0.763745	−	0.0681912i
$846$	−15.6498			−0.538052
$847$	−1.04859	+	1.81621i	−0.0360299	+	0.0624057i
$848$	−33.7000	+	58.3701i	−1.15726	+	2.00444i
$849$	−10.7388	−	18.6002i	−0.368556	−	0.638357i
$850$	−41.5533			−1.42527
$851$	10.8813	+	18.8469i	0.373006	+	0.646065i
$852$	−13.7046	−	23.7371i	−0.469513	−	0.813220i
$853$	−3.32953			−0.114001			−0.0570006	−	0.998374i	$-0.518154\pi$
$853$	−3.32953			−0.114001			−0.0570006	+	0.998374i	$0.518154\pi$
$854$	−13.3632	−	23.1457i	−0.457278	−	0.792029i
$855$	3.92517	−	6.79860i	0.134238	−	0.232507i
$856$	45.5324	−	78.8645i	1.55627	−	2.69553i
$857$	−15.5857			−0.532397			−0.266198	−	0.963918i	$-0.585768\pi$
$857$	−15.5857			−0.532397			−0.266198	+	0.963918i	$0.585768\pi$
$858$	8.93798	+	0.398223i	0.305138	+	0.0135951i
$859$	−53.7857			−1.83515			−0.917573	−	0.397568i	$-0.869854\pi$
$859$	−53.7857			−1.83515			−0.917573	+	0.397568i	$0.869854\pi$
$860$	−4.65765	+	8.06728i	−0.158824	+	0.275092i
$861$	−4.06011	+	7.03231i	−0.138368	+	0.239661i
$862$	2.75414	+	4.77031i	0.0938063	+	0.162477i
$863$	50.6790			1.72513			0.862567	−	0.505944i	$-0.168856\pi$
$863$	50.6790			1.72513			0.862567	+	0.505944i	$0.168856\pi$
$864$	−0.811867	−	1.40619i	−0.0276203	−	0.0478397i
$865$	−2.92383	−	5.06423i	−0.0994133	−	0.172189i
$866$	39.6051			1.34584
$867$	24.5337	+	42.4936i	0.833208	+	1.44316i
$868$	39.8520	−	69.0256i	1.35266	−	2.34288i
$869$	−1.37943	+	2.38925i	−0.0467940	+	0.0810496i
$870$	30.9562			1.04951
$871$	−5.26938	+	8.25502i	−0.178546	+	0.279711i
$872$	31.8786			1.07955
$873$	6.00406	−	10.3993i	0.203207	−	0.351964i
$874$	−37.5377	+	65.0172i	−1.26973	+	2.19924i
$875$	−12.6935	−	21.9858i	−0.429118	−	0.743254i
$876$	−33.2660			−1.12395
$877$	9.89948	+	17.1464i	0.334282	+	0.578993i	0.983347	−	0.181740i	$-0.0581730\pi$
$877$	9.89948	+	17.1464i	0.334282	+	0.578993i	−0.649065	+	0.760733i	$0.724840\pi$
$878$	−19.9044	−	34.4754i	−0.671741	−	1.16349i
$879$	−20.4329			−0.689186
$880$	4.26000	+	7.37854i	0.143605	+	0.248730i
$881$	−6.75148	+	11.6939i	−0.227463	+	0.393977i	−0.957056	−	0.289905i	$-0.906376\pi$
$881$	−6.75148	+	11.6939i	−0.227463	+	0.393977i	0.729593	+	0.683882i	$0.239710\pi$
$882$	−3.22813	+	5.59128i	−0.108697	+	0.188268i
$883$	−29.4402			−0.990743			−0.495372	−	0.868681i	$-0.664968\pi$
$883$	−29.4402			−0.990743			−0.495372	+	0.868681i	$0.664968\pi$
$884$	65.5557	−	102.700i	2.20488	−	3.45416i
$885$	−8.95539			−0.301032
$886$	−37.4395	+	64.8472i	−1.25781	+	2.17858i
$887$	6.43031	−	11.1376i	0.215909	−	0.373965i	−0.737645	−	0.675189i	$-0.764062\pi$
$887$	6.43031	−	11.1376i	0.215909	−	0.373965i	0.953553	+	0.301225i	$0.0973954\pi$
$888$	−8.81539	−	15.2687i	−0.295825	−	0.512384i
$889$	−11.4925			−0.385447
$890$	0.344818	+	0.597242i	0.0115583	+	0.0200196i
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	97.5287			3.26550
$893$	−14.4382	−	25.0077i	−0.483155	−	0.836849i
$894$	0.845487	−	1.46443i	0.0282773	−	0.0489777i
$895$	−0.554693	+	0.960756i	−0.0185413	+	0.0321145i
$896$	37.5615			1.25484
$897$	−10.9825	−	21.1431i	−0.366694	−	0.705948i
$898$	−24.5935			−0.820695
$899$	−33.2571	+	57.6030i	−1.10919	+	1.92117i
$900$	4.28257	−	7.41764i	0.142752	−	0.247255i
$901$	55.1240	+	95.4776i	1.83645	+	3.18082i
$902$	9.60796			0.319910
$903$	−1.37032	−	2.37347i	−0.0456015	−	0.0789841i
$904$	32.8726	+	56.9370i	1.09333	+	1.89370i
$905$	−9.96537			−0.331260
$906$	7.65928	+	13.2663i	0.254463	+	0.440742i
$907$	−1.56723	+	2.71453i	−0.0520391	+	0.0901344i	−0.890872	−	0.454255i	$-0.849905\pi$
$907$	−1.56723	+	2.71453i	−0.0520391	+	0.0901344i	0.838832	+	0.544390i	$0.183239\pi$
$908$	−36.8838	+	63.8846i	−1.22403	+	2.12008i
$909$	12.9670			0.430089
$910$	32.1390	+	1.43192i	1.06540	+	0.0474677i
$911$	13.6385			0.451864			0.225932	−	0.974143i	$-0.427457\pi$
$911$	13.6385			0.451864			0.225932	+	0.974143i	$0.427457\pi$
$912$	11.3758	−	19.7035i	0.376692	−	0.652450i
$913$	−0.601272	+	1.04143i	−0.0198992	+	0.0344664i
$914$	−17.9344	−	31.0632i	−0.593216	−	1.02748i
$915$	−8.80568			−0.291107
$916$	22.3891	+	38.7791i	0.739757	+	1.28130i
$917$	12.3161	+	21.3320i	0.406712	+	0.704446i
$918$	−20.1694			−0.665688
$919$	25.0219	+	43.3392i	0.825397	+	1.42963i	0.901616	+	0.432538i	$0.142382\pi$
$919$	25.0219	+	43.3392i	0.825397	+	1.42963i	−0.0762186	+	0.997091i	$0.524285\pi$
$920$	30.3266	−	52.5272i	0.999837	−	1.73177i
$921$	−4.91303	+	8.50961i	−0.161890	+	0.280401i
$922$	69.9351			2.30319
$923$	10.9574	+	21.0949i	0.360668	+	0.694347i
$924$	−8.71880			−0.286827
$925$	3.39255	−	5.87607i	0.111546	−	0.193204i
$926$	25.1343	−	43.5339i	0.825964	−	1.43061i
$927$	2.44997	+	4.24347i	0.0804675	+	0.139374i
$928$	11.8143			0.387822
$929$	−25.0702	−	43.4229i	−0.822527	−	1.42466i	−0.903795	−	0.427966i	$-0.859230\pi$
$929$	−25.0702	−	43.4229i	−0.822527	−	1.42466i	0.0812675	−	0.996692i	$-0.474103\pi$
$930$	−19.4468	−	33.6829i	−0.637687	−	1.10451i
$931$	−11.9128			−0.390426
$932$	42.2571	+	73.1915i	1.38418	+	2.39747i
$933$	14.8582	−	25.7351i	0.486435	−	0.842530i
$934$	−10.7523	+	18.6235i	−0.351825	+	0.609378i
$935$	13.9364			0.455769
$936$	8.89736	+	17.1289i	0.290819	+	0.559877i
$937$	24.1277			0.788216			0.394108	−	0.919064i	$-0.371054\pi$
$937$	24.1277			0.788216			0.394108	+	0.919064i	$0.371054\pi$
$938$	7.06753	−	12.2413i	0.230763	−	0.399693i
$939$	10.3021	−	17.8438i	0.336196	−	0.582309i
$940$	22.4781	+	38.9332i	0.733155	+	1.26986i
$941$	−20.2804			−0.661123			−0.330562	−	0.943784i	$-0.607238\pi$
$941$	−20.2804			−0.661123			−0.330562	+	0.943784i	$0.607238\pi$
$942$	−21.7265	−	37.6314i	−0.707888	−	1.22610i
$943$	−12.7929	−	22.1580i	−0.416595	−	0.721564i
$944$	−25.9543			−0.844741
$945$	−1.79789	−	3.11403i	−0.0584853	−	0.101299i
$946$	−1.62139	+	2.80832i	−0.0527158	+	0.0913064i
$947$	−8.26345	+	14.3127i	−0.268526	+	0.465101i	−0.968481	−	0.249086i	$-0.919870\pi$
$947$	−8.26345	+	14.3127i	−0.268526	+	0.465101i	0.699955	+	0.714187i	$0.253203\pi$
$948$	−11.4697			−0.372518
$949$	28.8217	+	1.28412i	0.935592	+	0.0416844i
$950$	23.4069			0.759419
$951$	−10.1223	+	17.5324i	−0.328239	+	0.568527i
$952$	−45.6275	+	79.0292i	−1.47880	+	2.56135i
$953$	18.7128	+	32.4115i	0.606167	+	1.04991i	0.991866	+	0.127287i	$0.0406268\pi$
$953$	18.7128	+	32.4115i	0.606167	+	1.04991i	−0.385699	+	0.922624i	$0.626040\pi$
$954$	−33.6570			−1.08969
$955$	−17.2985	−	29.9618i	−0.559765	−	0.969542i
$956$	−24.2063	−	41.9265i	−0.782887	−	1.35600i
$957$	7.27598			0.235199
$958$	−4.98311	−	8.63099i	−0.160997	−	0.278855i
$959$	4.71857	−	8.17280i	0.152371	−	0.263914i
$960$	5.06586	−	8.77432i	0.163500	−	0.283190i
$961$	52.5692			1.69578
$962$	13.5823	+	26.1483i	0.437912	+	0.843055i
$963$	17.0107			0.548162
$964$	−7.41294	+	12.8396i	−0.238755	+	0.413535i
$965$	5.22095	−	9.04296i	0.168068	−	0.291103i
$966$	17.1938	+	29.7805i	0.553200	+	0.958171i
$967$	−24.9551			−0.802502			−0.401251	−	0.915968i	$-0.631425\pi$
$967$	−24.9551			−0.802502			−0.401251	+	0.915968i	$0.631425\pi$
$968$	2.67669	+	4.63617i	0.0860322	+	0.149012i
$969$	−18.6078	−	32.2297i	−0.597769	−	1.03537i
$970$	−51.0895			−1.64038
$971$	14.6611	+	25.3938i	0.470497	+	0.814925i	0.999431	−	0.0337380i	$-0.0107412\pi$
$971$	14.6611	+	25.3938i	0.470497	+	0.814925i	−0.528933	+	0.848663i	$0.677408\pi$
$972$	2.07870	−	3.60041i	0.0666743	−	0.115483i
$973$	2.28793	−	3.96281i	0.0733476	−	0.127042i
$974$	4.61325			0.147818
$975$	−3.99677	+	6.26134i	−0.127999	+	0.200523i
$976$	−25.5204			−0.816889
$977$	5.75567	−	9.96911i	0.184140	−	0.318940i	−0.759146	−	0.650920i	$-0.774383\pi$
$977$	5.75567	−	9.96911i	0.184140	−	0.318940i	0.943286	+	0.331980i	$0.107717\pi$
$978$	−20.2918	+	35.1464i	−0.648859	+	1.12386i
$979$	0.0810464	+	0.140377i	0.00259025	+	0.00448645i
$980$	18.5465			0.592445
$981$	2.97743	+	5.15705i	0.0950619	+	0.164652i
$982$	32.6300	+	56.5168i	1.04127	+	1.80352i
$983$	15.2590			0.486686			0.243343	−	0.969940i	$-0.421756\pi$
$983$	15.2590			0.486686			0.243343	+	0.969940i	$0.421756\pi$
$984$	10.3641	+	17.9511i	0.330395	+	0.572261i
$985$	17.1967	−	29.7856i	0.547932	−	0.949047i
$986$	73.3759	−	127.091i	2.33676	−	4.04740i
$987$	−13.2265			−0.421005
$988$	−36.9274	+	57.8505i	−1.17482	+	1.84047i
$989$	8.63545			0.274591
$990$	−2.12729	+	3.68457i	−0.0676096	+	0.117103i
$991$	−5.85635	+	10.1435i	−0.186033	+	0.322219i	−0.943924	−	0.330162i	$-0.892896\pi$
$991$	−5.85635	+	10.1435i	−0.186033	+	0.322219i	0.757891	+	0.652381i	$0.226230\pi$
$992$	−7.42178	−	12.8549i	−0.235642	−	0.408143i
$993$	−27.9741			−0.887730
$994$	−17.1545	−	29.7125i	−0.544109	−	0.942425i
$995$	−0.309593	−	0.536231i	−0.00981475	−	0.0169997i
$996$	−4.99945			−0.158414
$997$	−2.48689	−	4.30742i	−0.0787605	−	0.136417i	0.823955	−	0.566655i	$-0.191763\pi$
$997$	−2.48689	−	4.30742i	−0.0787605	−	0.136417i	−0.902715	+	0.430238i	$0.858430\pi$
$998$	22.6285	−	39.1937i	0.716293	−	1.24066i
$999$	1.64669	−	2.85216i	0.0520991	−	0.0902383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.d.100.5	✓	10
13.3	even	3	inner	429.2.i.d.133.5	yes	10
13.4	even	6		5577.2.a.s.1.5		5
13.9	even	3		5577.2.a.r.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.d.100.5	✓	10	1.1	even	1	trivial
429.2.i.d.133.5	yes	10	13.3	even	3	inner
5577.2.a.r.1.1		5	13.9	even	3
5577.2.a.s.1.5		5	13.4	even	6

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24071 - 2.14896i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.07870 - 3.60041i) q^{4} -1.71458 q^{5} +(-1.24071 - 2.14896i) q^{6} +(-1.04859 - 1.81621i) q^{7} -5.35339 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.24071 - 2.14896i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.07870 - 3.60041i) q^{4} -1.71458 q^{5} +(-1.24071 - 2.14896i) q^{6} +(-1.04859 - 1.81621i) q^{7} -5.35339 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.12729 + 3.68457i) q^{10} +(-0.500000 + 0.866025i) q^{11} -4.15740 q^{12} +(3.60198 + 0.160483i) q^{13} -5.20396 q^{14} +(-0.857289 + 1.48487i) q^{15} +(-2.48458 + 4.30341i) q^{16} +(4.06409 + 7.03921i) q^{17} -2.48141 q^{18} +(-2.28929 - 3.96517i) q^{19} +(3.56409 + 6.17319i) q^{20} -2.09718 q^{21} +(1.24071 + 2.14896i) q^{22} +(3.30398 - 5.72266i) q^{23} +(-2.67669 + 4.63617i) q^{24} -2.06022 q^{25} +(4.81386 - 7.54141i) q^{26} -1.00000 q^{27} +(-4.35940 + 7.55070i) q^{28} +(3.63799 - 6.30118i) q^{29} +(2.12729 + 3.68457i) q^{30} -9.14162 q^{31} +(0.811867 + 1.40619i) q^{32} +(0.500000 + 0.866025i) q^{33} +20.1694 q^{34} +(1.79789 + 3.11403i) q^{35} +(-2.07870 + 3.60041i) q^{36} +(-1.64669 + 2.85216i) q^{37} -11.3614 q^{38} +(1.93997 - 3.03916i) q^{39} +9.17880 q^{40} +(1.93599 - 3.35323i) q^{41} +(-2.60198 + 4.50676i) q^{42} +(0.653413 + 1.13174i) q^{43} +4.15740 q^{44} +(0.857289 + 1.48487i) q^{45} +(-8.19853 - 14.2003i) q^{46} +6.30683 q^{47} +(2.48458 + 4.30341i) q^{48} +(1.30092 - 2.25327i) q^{49} +(-2.55612 + 4.42734i) q^{50} +8.12818 q^{51} +(-6.90962 - 13.3022i) q^{52} +13.5637 q^{53} +(-1.24071 + 2.14896i) q^{54} +(0.857289 - 1.48487i) q^{55} +(5.61350 + 9.72286i) q^{56} -4.57859 q^{57} +(-9.02734 - 15.6358i) q^{58} +(2.61154 + 4.52333i) q^{59} +7.12818 q^{60} +(2.56788 + 4.44771i) q^{61} +(-11.3421 + 19.6450i) q^{62} +(-1.04859 + 1.81621i) q^{63} -5.90915 q^{64} +(-6.17588 - 0.275160i) q^{65} +2.48141 q^{66} +(-1.35811 + 2.35231i) q^{67} +(16.8960 - 29.2648i) q^{68} +(-3.30398 - 5.72266i) q^{69} +8.92259 q^{70} +(3.29644 + 5.70961i) q^{71} +(2.67669 + 4.63617i) q^{72} +8.00164 q^{73} +(4.08612 + 7.07737i) q^{74} +(-1.03011 + 1.78420i) q^{75} +(-9.51750 + 16.4848i) q^{76} +2.09718 q^{77} +(-4.12412 - 7.93963i) q^{78} +2.75886 q^{79} +(4.26000 - 7.37854i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.80398 - 8.32074i) q^{82} +1.20254 q^{83} +(4.35940 + 7.55070i) q^{84} +(-6.96821 - 12.0693i) q^{85} +3.24277 q^{86} +(-3.63799 - 6.30118i) q^{87} +(2.67669 - 4.63617i) q^{88} +(0.0810464 - 0.140377i) q^{89} +4.25457 q^{90} +(-3.48552 - 6.71022i) q^{91} -27.4719 q^{92} +(-4.57081 + 7.91688i) q^{93} +(7.82491 - 13.5531i) q^{94} +(3.92517 + 6.79860i) q^{95} +1.62373 q^{96} +(6.00406 + 10.3993i) q^{97} +(-3.22813 - 5.59128i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Introduction

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