LMFDB - Embedded newform 1110.2.u.f.191.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.15
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.f.401.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} -1.00000 q^{10} -3.04782 q^{11} +(0.522966 - 1.65121i) q^{12} +(0.571765 + 0.571765i) q^{13} +(2.43416 + 2.43416i) q^{14} +(1.53738 - 0.797792i) q^{15} -1.00000 q^{16} +(1.58006 - 1.58006i) q^{17} +(0.513330 + 2.95576i) q^{18} +(2.90693 + 2.90693i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-5.68418 - 1.80027i) q^{21} +(-2.15513 - 2.15513i) q^{22} +(2.05150 - 2.05150i) q^{23} +(1.53738 - 0.797792i) q^{24} -1.00000i q^{25} +0.808598i q^{26} +(-3.14726 - 4.13458i) q^{27} +3.44243i q^{28} +(1.83352 + 1.83352i) q^{29} +(1.65121 + 0.522966i) q^{30} +(-6.33851 + 6.33851i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.03260 + 1.59390i) q^{33} +2.23454 q^{34} +(-2.43416 + 2.43416i) q^{35} +(-1.72706 + 2.45301i) q^{36} +(-1.89635 + 5.77961i) q^{37} +4.11103i q^{38} +(-0.645093 - 1.24312i) q^{39} -1.00000i q^{40} +8.00829 q^{41} +(-2.74634 - 5.29231i) q^{42} +(3.17436 + 3.17436i) q^{43} -3.04782i q^{44} +(-2.95576 + 0.513330i) q^{45} +2.90126 q^{46} +7.90227i q^{47} +(1.65121 + 0.522966i) q^{48} +4.85029 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.43533 + 1.78270i) q^{51} +(-0.571765 + 0.571765i) q^{52} +12.4574i q^{53} +(0.698141 - 5.14904i) q^{54} +(2.15513 - 2.15513i) q^{55} +(-2.43416 + 2.43416i) q^{56} +(-3.27974 - 6.32020i) q^{57} +2.59299i q^{58} +(-2.00686 + 2.00686i) q^{59} +(0.797792 + 1.53738i) q^{60} +(2.00335 - 2.00335i) q^{61} -8.96401 q^{62} +(8.44432 + 5.94526i) q^{63} -1.00000i q^{64} -0.808598 q^{65} +(2.43153 + 4.68565i) q^{66} +9.46914i q^{67} +(1.58006 + 1.58006i) q^{68} +(-4.46033 + 2.31460i) q^{69} -3.44243 q^{70} -11.8558i q^{71} +(-2.95576 + 0.513330i) q^{72} -4.40734i q^{73} +(-5.42772 + 2.74588i) q^{74} +(-0.522966 + 1.65121i) q^{75} +(-2.90693 + 2.90693i) q^{76} -10.4919 q^{77} +(0.422869 - 1.33517i) q^{78} +(-8.20854 - 8.20854i) q^{79} +(0.707107 - 0.707107i) q^{80} +(3.03456 + 8.47298i) q^{81} +(5.66272 + 5.66272i) q^{82} +10.8401i q^{83} +(1.80027 - 5.68418i) q^{84} +2.23454i q^{85} +4.48922i q^{86} +(-2.06867 - 3.98641i) q^{87} +(2.15513 - 2.15513i) q^{88} +(9.90966 + 9.90966i) q^{89} +(-2.45301 - 1.72706i) q^{90} +(1.96826 + 1.96826i) q^{91} +(2.05150 + 2.05150i) q^{92} +(13.7811 - 7.15142i) q^{93} +(-5.58775 + 5.58775i) q^{94} -4.11103 q^{95} +(0.797792 + 1.53738i) q^{96} +(2.40351 + 2.40351i) q^{97} +(3.42968 + 3.42968i) q^{98} +(-7.47635 - 5.26376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q + 24 * q^7 - 8 * q^9	$ 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) $ 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.65121	−	0.522966i	−0.953329	−	0.301934i
$3$	−1.65121	−	0.522966i	−0.953329	−	0.301934i
$4$			1.00000i			0.500000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.797792	−	1.53738i	−0.325697	−	0.627632i
$7$	3.44243			1.30111			0.650557	−	0.759457i	$-0.274535\pi$
$7$	3.44243			1.30111			0.650557	+	0.759457i	$0.274535\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.45301	+	1.72706i	0.817671	+	0.575685i
$10$	−1.00000			−0.316228
$11$	−3.04782			−0.918952			−0.459476	−	0.888190i	$-0.651963\pi$
$11$	−3.04782			−0.918952			−0.459476	+	0.888190i	$0.651963\pi$
$12$	0.522966	−	1.65121i	0.150967	−	0.476664i
$13$	0.571765	+	0.571765i	0.158579	+	0.158579i	0.781937	−	0.623358i	$-0.214232\pi$
$13$	0.571765	+	0.571765i	0.158579	+	0.158579i	−0.623358	+	0.781937i	$0.714232\pi$
$14$	2.43416	+	2.43416i	0.650557	+	0.650557i
$15$	1.53738	−	0.797792i	0.396949	−	0.205989i
$16$	−1.00000			−0.250000
$17$	1.58006	−	1.58006i	0.383220	−	0.383220i	−0.489041	−	0.872261i	$-0.662653\pi$
$17$	1.58006	−	1.58006i	0.383220	−	0.383220i	0.872261	+	0.489041i	$0.162653\pi$
$18$	0.513330	+	2.95576i	0.120993	+	0.696678i
$19$	2.90693	+	2.90693i	0.666896	+	0.666896i	0.956996	−	0.290100i	$-0.0936885\pi$
$19$	2.90693	+	2.90693i	0.666896	+	0.666896i	−0.290100	+	0.956996i	$0.593689\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$	−5.68418	−	1.80027i	−1.24039	−	0.392851i
$22$	−2.15513	−	2.15513i	−0.459476	−	0.459476i
$23$	2.05150	−	2.05150i	0.427768	−	0.427768i	−0.460100	−	0.887867i	$-0.652186\pi$
$23$	2.05150	−	2.05150i	0.427768	−	0.427768i	0.887867	+	0.460100i	$0.152186\pi$
$24$	1.53738	−	0.797792i	0.313816	−	0.162849i
$25$		−	1.00000i		−	0.200000i
$26$			0.808598i			0.158579i
$27$	−3.14726	−	4.13458i	−0.605691	−	0.795700i
$28$			3.44243i			0.650557i
$29$	1.83352	+	1.83352i	0.340476	+	0.340476i	0.856546	−	0.516070i	$-0.172606\pi$
$29$	1.83352	+	1.83352i	0.340476	+	0.340476i	−0.516070	+	0.856546i	$0.672606\pi$
$30$	1.65121	+	0.522966i	0.301469	+	0.0954800i
$31$	−6.33851	+	6.33851i	−1.13843	+	1.13843i	−0.149699	+	0.988732i	$0.547831\pi$
$31$	−6.33851	+	6.33851i	−1.13843	+	1.13843i	−0.988732	+	0.149699i	$0.952169\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.03260	+	1.59390i	0.876064	+	0.277463i
$34$	2.23454			0.383220
$35$	−2.43416	+	2.43416i	−0.411449	+	0.411449i
$36$	−1.72706	+	2.45301i	−0.287843	+	0.408836i
$37$	−1.89635	+	5.77961i	−0.311757	+	0.950162i
$37$	−1.89635	+	5.77961i	−0.311757	+	0.950162i
$38$			4.11103i			0.666896i
$39$	−0.645093	−	1.24312i	−0.103298	−	0.199059i
$40$		−	1.00000i		−	0.158114i
$41$	8.00829			1.25069			0.625343	−	0.780350i	$-0.284959\pi$
$41$	8.00829			1.25069			0.625343	+	0.780350i	$0.284959\pi$
$42$	−2.74634	−	5.29231i	−0.423769	−	0.816621i
$43$	3.17436	+	3.17436i	0.484086	+	0.484086i	0.906434	−	0.422348i	$-0.138794\pi$
$43$	3.17436	+	3.17436i	0.484086	+	0.484086i	−0.422348	+	0.906434i	$0.638794\pi$
$44$		−	3.04782i		−	0.459476i
$45$	−2.95576	+	0.513330i	−0.440618	+	0.0765227i
$46$	2.90126			0.427768
$47$			7.90227i			1.15266i	0.817216	+	0.576332i	$0.195517\pi$
$47$			7.90227i			1.15266i	−0.817216	+	0.576332i	$0.804483\pi$
$48$	1.65121	+	0.522966i	0.238332	+	0.0754836i
$49$	4.85029			0.692899
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	−3.43533	+	1.78270i	−0.481042	+	0.249627i
$52$	−0.571765	+	0.571765i	−0.0792896	+	0.0792896i
$53$			12.4574i			1.71115i	0.517680	+	0.855574i	$0.326796\pi$
$53$			12.4574i			1.71115i	−0.517680	+	0.855574i	$0.673204\pi$
$54$	0.698141	−	5.14904i	0.0950049	−	0.700695i
$55$	2.15513	−	2.15513i	0.290598	−	0.290598i
$56$	−2.43416	+	2.43416i	−0.325279	+	0.325279i
$57$	−3.27974	−	6.32020i	−0.434413	−	0.837131i
$58$			2.59299i			0.340476i
$59$	−2.00686	+	2.00686i	−0.261271	+	0.261271i	−0.825570	−	0.564300i	$-0.809146\pi$
$59$	−2.00686	+	2.00686i	−0.261271	+	0.261271i	0.564300	+	0.825570i	$0.309146\pi$
$60$	0.797792	+	1.53738i	0.102995	+	0.198475i
$61$	2.00335	−	2.00335i	0.256502	−	0.256502i	−0.567128	−	0.823630i	$-0.691945\pi$
$61$	2.00335	−	2.00335i	0.256502	−	0.256502i	0.823630	+	0.567128i	$0.191945\pi$
$62$	−8.96401			−1.13843
$63$	8.44432	+	5.94526i	1.06388	+	0.749032i
$64$		−	1.00000i		−	0.125000i
$65$	−0.808598			−0.100294
$66$	2.43153	+	4.68565i	0.299300	+	0.576763i
$67$			9.46914i			1.15684i	0.815739	+	0.578420i	$0.196330\pi$
$67$			9.46914i			1.15684i	−0.815739	+	0.578420i	$0.803670\pi$
$68$	1.58006	+	1.58006i	0.191610	+	0.191610i
$69$	−4.46033	+	2.31460i	−0.536961	+	0.278645i
$70$	−3.44243			−0.411449
$71$		−	11.8558i		−	1.40702i	−0.710685	−	0.703511i	$-0.751615\pi$
$71$		−	11.8558i		−	1.40702i	0.710685	−	0.703511i	$-0.248385\pi$
$72$	−2.95576	+	0.513330i	−0.348339	+	0.0604965i
$73$		−	4.40734i		−	0.515841i	−0.966166	−	0.257920i	$-0.916963\pi$
$73$		−	4.40734i		−	0.515841i	0.966166	−	0.257920i	$-0.0830372\pi$
$74$	−5.42772	+	2.74588i	−0.630960	+	0.319202i
$75$	−0.522966	+	1.65121i	−0.0603869	+	0.190666i
$76$	−2.90693	+	2.90693i	−0.333448	+	0.333448i
$77$	−10.4919			−1.19566
$78$	0.422869	−	1.33517i	0.0478805	−	0.151178i
$79$	−8.20854	−	8.20854i	−0.923533	−	0.923533i	0.0737442	−	0.997277i	$-0.476505\pi$
$79$	−8.20854	−	8.20854i	−0.923533	−	0.923533i	−0.997277	+	0.0737442i	$0.976505\pi$
$80$	0.707107	−	0.707107i	0.0790569	−	0.0790569i
$81$	3.03456	+	8.47298i	0.337173	+	0.941443i
$82$	5.66272	+	5.66272i	0.625343	+	0.625343i
$83$			10.8401i			1.18986i	0.803779	+	0.594928i	$0.202819\pi$
$83$			10.8401i			1.18986i	−0.803779	+	0.594928i	$0.797181\pi$
$84$	1.80027	−	5.68418i	0.196426	−	0.620195i
$85$			2.23454i			0.242370i
$86$			4.48922i			0.484086i
$87$	−2.06867	−	3.98641i	−0.221784	−	0.427388i
$88$	2.15513	−	2.15513i	0.229738	−	0.229738i
$89$	9.90966	+	9.90966i	1.05042	+	1.05042i	0.998659	+	0.0517620i	$0.0164837\pi$
$89$	9.90966	+	9.90966i	1.05042	+	1.05042i	0.0517620	+	0.998659i	$0.483516\pi$
$90$	−2.45301	−	1.72706i	−0.258570	−	0.182048i
$91$	1.96826	+	1.96826i	0.206330	+	0.206330i
$92$	2.05150	+	2.05150i	0.213884	+	0.213884i
$93$	13.7811	−	7.15142i	1.42903	−	0.741568i
$94$	−5.58775	+	5.58775i	−0.576332	+	0.576332i
$95$	−4.11103			−0.421782
$96$	0.797792	+	1.53738i	0.0814243	+	0.156908i
$97$	2.40351	+	2.40351i	0.244040	+	0.244040i	0.818519	−	0.574479i	$-0.194795\pi$
$97$	2.40351	+	2.40351i	0.244040	+	0.244040i	−0.574479	+	0.818519i	$0.694795\pi$
$98$	3.42968	+	3.42968i	0.346450	+	0.346450i
$99$	−7.47635	−	5.26376i	−0.751401	−	0.529027i
$100$	1.00000			0.100000
$101$	2.17467			0.216387			0.108194	−	0.994130i	$-0.465493\pi$
$101$	2.17467			0.216387			0.108194	+	0.994130i	$0.465493\pi$
$102$	−3.68970	−	1.16859i	−0.365335	−	0.115707i
$103$	−0.494936	+	0.494936i	−0.0487675	+	0.0487675i	−0.731070	−	0.682302i	$-0.760979\pi$
$103$	−0.494936	+	0.494936i	−0.0487675	+	0.0487675i	0.682302	+	0.731070i	$0.260979\pi$
$104$	−0.808598			−0.0792896
$105$	5.29231	−	2.74634i	0.516476	−	0.268015i
$106$	−8.80868	+	8.80868i	−0.855574	+	0.855574i
$107$		−	0.470042i		−	0.0454406i	−0.999742	−	0.0227203i	$-0.992767\pi$
$107$		−	0.470042i		−	0.0454406i	0.999742	−	0.0227203i	$-0.00723272\pi$
$108$	4.13458	−	3.14726i	0.397850	−	0.302845i
$109$	−3.18770	−	3.18770i	−0.305327	−	0.305327i	0.537767	−	0.843094i	$-0.319268\pi$
$109$	−3.18770	−	3.18770i	−0.305327	−	0.305327i	−0.843094	+	0.537767i	$0.819268\pi$
$110$	3.04782			0.290598
$111$	6.15381	−	8.55165i	0.584094	−	0.811686i
$112$	−3.44243			−0.325279
$113$	2.24895	+	2.24895i	0.211563	+	0.211563i	0.804931	−	0.593368i	$-0.202202\pi$
$113$	2.24895	+	2.24895i	0.211563	+	0.211563i	−0.593368	+	0.804931i	$0.702202\pi$
$114$	2.14992	−	6.78818i	0.201359	−	0.635772i
$115$			2.90126i			0.270544i
$116$	−1.83352	+	1.83352i	−0.170238	+	0.170238i
$117$	0.415078	+	2.39002i	0.0383740	+	0.220957i
$118$	−2.83813			−0.261271
$119$	5.43923	−	5.43923i	0.498613	−	0.498613i
$120$	−0.522966	+	1.65121i	−0.0477400	+	0.150735i
$121$	−1.71079			−0.155526
$122$	2.83316			0.256502
$123$	−13.2234	−	4.18806i	−1.19231	−	0.377625i
$124$	−6.33851	−	6.33851i	−0.569215	−	0.569215i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.76710	+	10.1750i	0.157426	+	0.906458i
$127$	−3.84862			−0.341510			−0.170755	−	0.985314i	$-0.554621\pi$
$127$	−3.84862			−0.341510			−0.170755	+	0.985314i	$0.554621\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.58147	−	6.90163i	−0.315331	−	0.607655i
$130$	−0.571765	−	0.571765i	−0.0501471	−	0.0501471i
$131$	−9.42329	−	9.42329i	−0.823317	−	0.823317i	0.163265	−	0.986582i	$-0.447797\pi$
$131$	−9.42329	−	9.42329i	−0.823317	−	0.823317i	−0.986582	+	0.163265i	$0.947797\pi$
$132$	−1.59390	+	5.03260i	−0.138732	+	0.438032i
$133$	10.0069	+	10.0069i	0.867709	+	0.867709i
$134$	−6.69569	+	6.69569i	−0.578420	+	0.578420i
$135$	5.14904	+	0.698141i	0.443159	+	0.0600864i
$136$			2.23454i			0.191610i
$137$		−	14.5392i		−	1.24217i	−0.783745	−	0.621083i	$-0.786693\pi$
$137$		−	14.5392i		−	1.24217i	0.783745	−	0.621083i	$-0.213307\pi$
$138$	−4.79060	−	1.51726i	−0.407803	−	0.129158i
$139$		−	16.7132i		−	1.41760i	−0.705410	−	0.708799i	$-0.749237\pi$
$139$		−	16.7132i		−	1.41760i	0.705410	−	0.708799i	$-0.250763\pi$
$140$	−2.43416	−	2.43416i	−0.205724	−	0.205724i
$141$	4.13261	−	13.0483i	0.348029	−	1.09887i
$142$	8.38330	−	8.38330i	0.703511	−	0.703511i
$143$	−1.74264	−	1.74264i	−0.145727	−	0.145727i
$144$	−2.45301	−	1.72706i	−0.204418	−	0.143921i
$145$	−2.59299			−0.215336
$146$	3.11646	−	3.11646i	0.257920	−	0.257920i
$147$	−8.00887	−	2.53654i	−0.660561	−	0.209210i
$148$	−5.77961	−	1.89635i	−0.475081	−	0.155879i
$149$			11.2348i			0.920388i	0.887818	+	0.460194i	$0.152220\pi$
$149$			11.2348i			0.920388i	−0.887818	+	0.460194i	$0.847780\pi$
$150$	−1.53738	+	0.797792i	−0.125526	+	0.0651394i
$151$		−	18.1204i		−	1.47462i	−0.675557	−	0.737308i	$-0.736097\pi$
$151$		−	18.1204i		−	1.47462i	0.675557	−	0.737308i	$-0.263903\pi$
$152$	−4.11103			−0.333448
$153$	6.60475	−	1.14706i	0.533962	−	0.0927339i
$154$	−7.41889	−	7.41889i	−0.597831	−	0.597831i
$155$		−	8.96401i		−	0.720007i
$156$	1.24312	−	0.645093i	0.0995293	−	0.0516488i
$157$	15.7039			1.25331			0.626653	−	0.779298i	$-0.284424\pi$
$157$	15.7039			1.25331			0.626653	+	0.779298i	$0.284424\pi$
$158$		−	11.6086i		−	0.923533i
$159$	6.51476	−	20.5697i	0.516654	−	1.63129i
$160$	1.00000			0.0790569
$161$	7.06214	−	7.06214i	0.556575	−	0.556575i
$162$	−3.84555	+	8.13706i	−0.302135	+	0.639308i
$163$	4.76257	−	4.76257i	0.373033	−	0.373033i	−0.495548	−	0.868581i	$-0.665033\pi$
$163$	4.76257	−	4.76257i	0.373033	−	0.373033i	0.868581	+	0.495548i	$0.165033\pi$
$164$			8.00829i			0.625343i
$165$	−4.68565	+	2.43153i	−0.364777	+	0.189294i
$166$	−7.66511	+	7.66511i	−0.594928	+	0.594928i
$167$	7.41766	−	7.41766i	0.573996	−	0.573996i	−0.359247	−	0.933243i	$-0.616966\pi$
$167$	7.41766	−	7.41766i	0.573996	−	0.573996i	0.933243	+	0.359247i	$0.116966\pi$
$168$	5.29231	−	2.74634i	0.408310	−	0.211885i
$169$		−	12.3462i		−	0.949705i
$170$	−1.58006	+	1.58006i	−0.121185	+	0.121185i
$171$	2.11031	+	12.1512i	0.161380	+	0.929225i
$172$	−3.17436	+	3.17436i	−0.242043	+	0.242043i
$173$	22.1763			1.68603			0.843016	−	0.537889i	$-0.180778\pi$
$173$	22.1763			1.68603			0.843016	+	0.537889i	$0.180778\pi$
$174$	1.35605	−	4.28158i	0.102802	−	0.324586i
$175$		−	3.44243i		−	0.260223i
$176$	3.04782			0.229738
$177$	4.36327	−	2.26423i	0.327963	−	0.170190i
$178$			14.0144i			1.05042i
$179$	6.95933	+	6.95933i	0.520165	+	0.520165i	0.917621	−	0.397456i	$-0.130107\pi$
$179$	6.95933	+	6.95933i	0.520165	+	0.520165i	−0.397456	+	0.917621i	$0.630107\pi$
$180$	−0.513330	−	2.95576i	−0.0382614	−	0.220309i
$181$	−0.826713			−0.0614491			−0.0307246	−	0.999528i	$-0.509781\pi$
$181$	−0.826713			−0.0614491			−0.0307246	+	0.999528i	$0.509781\pi$
$182$			2.78354i			0.206330i
$183$	−4.35563	+	2.26027i	−0.321978	+	0.167084i
$184$			2.90126i			0.213884i
$185$	−2.74588	−	5.42772i	−0.201881	−	0.399054i
$186$	14.8015	+	4.68787i	1.08530	+	0.343731i
$187$	−4.81573	+	4.81573i	−0.352161	+	0.352161i
$188$	−7.90227			−0.576332
$189$	−10.8342	−	14.2330i	−0.788073	−	1.03530i
$190$	−2.90693	−	2.90693i	−0.210891	−	0.210891i
$191$	1.75243	−	1.75243i	0.126801	−	0.126801i	−0.640858	−	0.767659i	$-0.721421\pi$
$191$	1.75243	−	1.75243i	0.126801	−	0.126801i	0.767659	+	0.640858i	$0.221421\pi$
$192$	−0.522966	+	1.65121i	−0.0377418	+	0.119166i
$193$	5.62234	+	5.62234i	0.404705	+	0.404705i	0.879887	−	0.475183i	$-0.157618\pi$
$193$	5.62234	+	5.62234i	0.404705	+	0.404705i	−0.475183	+	0.879887i	$0.657618\pi$
$194$			3.39908i			0.244040i
$195$	1.33517	+	0.422869i	0.0956134	+	0.0302823i
$196$			4.85029i			0.346450i
$197$		−	17.8517i		−	1.27188i	−0.771738	−	0.635941i	$-0.780612\pi$
$197$		−	17.8517i		−	1.27188i	0.771738	−	0.635941i	$-0.219388\pi$
$198$	−1.56454	−	9.00861i	−0.111187	−	0.640214i
$199$	1.86996	−	1.86996i	0.132558	−	0.132558i	−0.637715	−	0.770273i	$-0.720120\pi$
$199$	1.86996	−	1.86996i	0.132558	−	0.132558i	0.770273	+	0.637715i	$0.220120\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	4.95203	−	15.6356i	0.349290	−	1.10285i
$202$	1.53772	+	1.53772i	0.108194	+	0.108194i
$203$	6.31176	+	6.31176i	0.442999	+	0.442999i
$204$	−1.78270	−	3.43533i	−0.124814	−	0.240521i
$205$	−5.66272	+	5.66272i	−0.395501	+	0.395501i
$206$	−0.699945			−0.0487675
$207$	8.57542	−	1.48930i	0.596033	−	0.103514i
$208$	−0.571765	−	0.571765i	−0.0396448	−	0.0396448i
$209$	−8.85981	−	8.85981i	−0.612846	−	0.612846i
$210$	5.68418	+	1.80027i	0.392246	+	0.124230i
$211$	−19.4431			−1.33852			−0.669258	−	0.743030i	$-0.733388\pi$
$211$	−19.4431			−1.33852			−0.669258	+	0.743030i	$0.733388\pi$
$212$	−12.4574			−0.855574
$213$	−6.20016	+	19.5764i	−0.424828	+	1.34135i
$214$	0.332370	−	0.332370i	0.0227203	−	0.0227203i
$215$	−4.48922			−0.306163
$216$	5.14904	+	0.698141i	0.350348	+	0.0475024i
$217$	−21.8199	+	21.8199i	−1.48123	+	1.48123i
$218$		−	4.50809i		−	0.305327i
$219$	−2.30489	+	7.27747i	−0.155750	+	0.491766i
$220$	2.15513	+	2.15513i	0.145299	+	0.145299i
$221$	1.80684			0.121541
$222$	10.3983	−	1.69553i	0.697890	−	0.113796i
$223$	24.8953			1.66711			0.833555	−	0.552436i	$-0.186302\pi$
$223$	24.8953			1.66711			0.833555	+	0.552436i	$0.186302\pi$
$224$	−2.43416	−	2.43416i	−0.162639	−	0.162639i
$225$	1.72706	−	2.45301i	0.115137	−	0.163534i
$226$			3.18049i			0.211563i
$227$	6.99137	−	6.99137i	0.464033	−	0.464033i	−0.435942	−	0.899975i	$-0.643585\pi$
$227$	6.99137	−	6.99137i	0.464033	−	0.464033i	0.899975	+	0.435942i	$0.143585\pi$
$228$	6.32020	−	3.27974i	0.418565	−	0.217206i
$229$	−19.5563			−1.29232			−0.646158	−	0.763204i	$-0.723625\pi$
$229$	−19.5563			−1.29232			−0.646158	+	0.763204i	$0.723625\pi$
$230$	−2.05150	+	2.05150i	−0.135272	+	0.135272i
$231$	17.3244	+	5.48690i	1.13986	+	0.361011i
$232$	−2.59299			−0.170238
$233$	−17.7356			−1.16190			−0.580949	−	0.813940i	$-0.697318\pi$
$233$	−17.7356			−1.16190			−0.580949	+	0.813940i	$0.697318\pi$
$234$	−1.39649	+	1.98350i	−0.0912917	+	0.129666i
$235$	−5.58775	−	5.58775i	−0.364504	−	0.364504i
$236$	−2.00686	−	2.00686i	−0.130635	−	0.130635i
$237$	9.26127	+	17.8468i	0.601584	+	1.15928i
$238$	7.69223			0.498613
$239$	4.92552	−	4.92552i	0.318606	−	0.318606i	−0.529626	−	0.848231i	$-0.677668\pi$
$239$	4.92552	−	4.92552i	0.318606	−	0.318606i	0.848231	+	0.529626i	$0.177668\pi$
$240$	−1.53738	+	0.797792i	−0.0992373	+	0.0514973i
$241$	18.5971	+	18.5971i	1.19794	+	1.19794i	0.974781	+	0.223163i	$0.0716383\pi$
$241$	18.5971	+	18.5971i	1.19794	+	1.19794i	0.223163	+	0.974781i	$0.428362\pi$
$242$	−1.20971	−	1.20971i	−0.0777632	−	0.0777632i
$243$	−0.579624	−	15.5777i	−0.0371829	−	0.999308i
$244$	2.00335	+	2.00335i	0.128251	+	0.128251i
$245$	−3.42968	+	3.42968i	−0.219114	+	0.219114i
$246$	−6.38895	−	12.3118i	−0.407345	−	0.784969i
$247$			3.32417i			0.211512i
$248$		−	8.96401i		−	0.569215i
$249$	5.66900	−	17.8993i	0.359258	−	1.13432i
$250$			1.00000i			0.0632456i
$251$	−15.0856	−	15.0856i	−0.952195	−	0.952195i	0.0467134	−	0.998908i	$-0.485125\pi$
$251$	−15.0856	−	15.0856i	−0.952195	−	0.952195i	−0.998908	+	0.0467134i	$0.985125\pi$
$252$	−5.94526	+	8.44432i	−0.374516	+	0.531942i
$253$	−6.25261	+	6.25261i	−0.393098	+	0.393098i
$254$	−2.72139	−	2.72139i	−0.170755	−	0.170755i
$255$	1.16859	−	3.68970i	0.0731797	−	0.231058i
$256$	1.00000			0.0625000
$257$	−2.20693	+	2.20693i	−0.137665	+	0.137665i	−0.772581	−	0.634916i	$-0.781035\pi$
$257$	−2.20693	+	2.20693i	−0.137665	+	0.137665i	0.634916	+	0.772581i	$0.281035\pi$
$258$	2.34771	−	7.41267i	0.146162	−	0.461493i
$259$	−6.52803	+	19.8959i	−0.405632	+	1.23627i
$260$		−	0.808598i		−	0.0501471i
$261$	1.33106	+	7.66425i	0.0823906	+	0.474405i
$262$		−	13.3265i		−	0.823317i
$263$	−4.11676			−0.253850			−0.126925	−	0.991912i	$-0.540511\pi$
$263$	−4.11676			−0.253850			−0.126925	+	0.991912i	$0.540511\pi$
$264$	−4.68565	+	2.43153i	−0.288382	+	0.149650i
$265$	−8.80868	−	8.80868i	−0.541113	−	0.541113i
$266$			14.1519i			0.867709i
$267$	−11.1806	−	21.5454i	−0.684239	−	1.31856i
$268$	−9.46914			−0.578420
$269$		−	5.19624i		−	0.316820i	−0.987373	−	0.158410i	$-0.949363\pi$
$269$		−	5.19624i		−	0.316820i	0.987373	−	0.158410i	$-0.0506368\pi$
$270$	3.14726	+	4.13458i	0.191536	+	0.251623i
$271$	−4.74810			−0.288426			−0.144213	−	0.989547i	$-0.546065\pi$
$271$	−4.74810			−0.288426			−0.144213	+	0.989547i	$0.546065\pi$
$272$	−1.58006	+	1.58006i	−0.0958050	+	0.0958050i
$273$	−2.22069	−	4.27935i	−0.134402	−	0.258998i
$274$	10.2807	−	10.2807i	0.621083	−	0.621083i
$275$			3.04782i			0.183790i
$276$	−2.31460	−	4.46033i	−0.139323	−	0.268480i
$277$	−2.25502	+	2.25502i	−0.135491	+	0.135491i	−0.771599	−	0.636109i	$-0.780543\pi$
$277$	−2.25502	+	2.25502i	−0.135491	+	0.135491i	0.636109	+	0.771599i	$0.280543\pi$
$278$	11.8180	−	11.8180i	0.708799	−	0.708799i
$279$	−26.4954	+	4.60150i	−1.58624	+	0.275484i
$280$		−	3.44243i		−	0.205724i
$281$	11.4729	−	11.4729i	0.684416	−	0.684416i	−0.276576	−	0.960992i	$-0.589200\pi$
$281$	11.4729	−	11.4729i	0.684416	−	0.684416i	0.960992	+	0.276576i	$0.0891999\pi$
$282$	12.1488	−	6.30437i	0.723448	−	0.375420i
$283$	−20.8649	+	20.8649i	−1.24029	+	1.24029i	−0.280407	+	0.959881i	$0.590469\pi$
$283$	−20.8649	+	20.8649i	−1.24029	+	1.24029i	−0.959881	+	0.280407i	$0.909531\pi$
$284$	11.8558			0.703511
$285$	6.78818	+	2.14992i	0.402097	+	0.127351i
$286$		−	2.46446i		−	0.145727i
$287$	27.5680			1.62728
$288$	−0.513330	−	2.95576i	−0.0302483	−	0.174170i
$289$			12.0068i			0.706285i
$290$	−1.83352	−	1.83352i	−0.107668	−	0.107668i
$291$	−2.71176	−	5.22567i	−0.158966	−	0.306334i
$292$	4.40734			0.257920
$293$		−	8.29342i		−	0.484507i	−0.970213	−	0.242253i	$-0.922113\pi$
$293$		−	8.29342i		−	0.484507i	0.970213	−	0.242253i	$-0.0778865\pi$
$294$	−3.86953	−	7.45673i	−0.225675	−	0.434885i
$295$		−	2.83813i		−	0.165242i
$296$	−2.74588	−	5.42772i	−0.159601	−	0.315480i
$297$	9.59228	+	12.6015i	0.556601	+	0.731211i
$298$	−7.94418	+	7.94418i	−0.460194	+	0.460194i
$299$	2.34596			0.135670
$300$	−1.65121	−	0.522966i	−0.0953329	−	0.0301934i
$301$	10.9275	+	10.9275i	0.629851	+	0.629851i
$302$	12.8130	−	12.8130i	0.737308	−	0.737308i
$303$	−3.59084	−	1.13727i	−0.206288	−	0.0653347i
$304$	−2.90693	−	2.90693i	−0.166724	−	0.166724i
$305$			2.83316i			0.162226i
$306$	5.48135	+	3.85917i	0.313348	+	0.220614i
$307$		−	7.03890i		−	0.401731i	−0.979619	−	0.200866i	$-0.935625\pi$
$307$		−	7.03890i		−	0.401731i	0.979619	−	0.200866i	$-0.0643755\pi$
$308$		−	10.4919i		−	0.597831i
$309$	1.07608	−	0.558411i	0.0612160	−	0.0317669i
$310$	6.33851	−	6.33851i	0.360003	−	0.360003i
$311$	−5.36146	−	5.36146i	−0.304020	−	0.304020i	0.538564	−	0.842585i	$-0.318967\pi$
$311$	−5.36146	−	5.36146i	−0.304020	−	0.304020i	−0.842585	+	0.538564i	$0.818967\pi$
$312$	1.33517	+	0.422869i	0.0755891	+	0.0239402i
$313$	16.4404	+	16.4404i	0.929266	+	0.929266i	0.997659	−	0.0683922i	$-0.0217869\pi$
$313$	16.4404	+	16.4404i	0.929266	+	0.929266i	−0.0683922	+	0.997659i	$0.521787\pi$
$314$	11.1043	+	11.1043i	0.626653	+	0.626653i
$315$	−10.1750	+	1.76710i	−0.573295	+	0.0995648i
$316$	8.20854	−	8.20854i	0.461766	−	0.461766i
$317$	−19.4530			−1.09259			−0.546296	−	0.837592i	$-0.683963\pi$
$317$	−19.4530			−1.09259			−0.546296	+	0.837592i	$0.683963\pi$
$318$	19.1516	−	9.93838i	1.07397	−	0.557316i
$319$	−5.58825	−	5.58825i	−0.312882	−	0.312882i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$	−0.245816	+	0.776139i	−0.0137201	+	0.0433199i
$322$	9.98738			0.556575
$323$	9.18624			0.511136
$324$	−8.47298	+	3.03456i	−0.470721	+	0.168586i
$325$	0.571765	−	0.571765i	0.0317158	−	0.0317158i
$326$	6.73529			0.373033
$327$	3.59652	+	6.93064i	0.198888	+	0.383265i
$328$	−5.66272	+	5.66272i	−0.312671	+	0.312671i
$329$			27.2030i			1.49975i
$330$	−5.03260	−	1.59390i	−0.277036	−	0.0877416i
$331$	−16.9551	−	16.9551i	−0.931938	−	0.931938i	0.0658890	−	0.997827i	$-0.479012\pi$
$331$	−16.9551	−	16.9551i	−0.931938	−	0.931938i	−0.997827	+	0.0658890i	$0.979012\pi$
$332$	−10.8401			−0.594928
$333$	−14.6335	+	10.9024i	−0.801909	+	0.597446i
$334$	10.4902			0.573996
$335$	−6.69569	−	6.69569i	−0.365825	−	0.365825i
$336$	5.68418	+	1.80027i	0.310097	+	0.0982128i
$337$			7.08308i			0.385840i	0.981214	+	0.192920i	$0.0617958\pi$
$337$			7.08308i			0.385840i	−0.981214	+	0.192920i	$0.938204\pi$
$338$	8.73006	−	8.73006i	0.474853	−	0.474853i
$339$	−2.53737	−	4.88961i	−0.137811	−	0.265567i
$340$	−2.23454			−0.121185
$341$	19.3187	−	19.3187i	1.04616	−	1.04616i
$342$	−7.09997	+	10.0844i	−0.383922	+	0.545302i
$343$	−7.40020			−0.399573
$344$	−4.48922			−0.242043
$345$	1.51726	−	4.79060i	0.0816865	−	0.257917i
$346$	15.6810	+	15.6810i	0.843016	+	0.843016i
$347$	−8.15272	−	8.15272i	−0.437661	−	0.437661i	0.453563	−	0.891224i	$-0.350153\pi$
$347$	−8.15272	−	8.15272i	−0.437661	−	0.437661i	−0.891224	+	0.453563i	$0.850153\pi$
$348$	3.98641	−	2.06867i	0.213694	−	0.110892i
$349$	−9.72270			−0.520444			−0.260222	−	0.965549i	$-0.583796\pi$
$349$	−9.72270			−0.520444			−0.260222	+	0.965549i	$0.583796\pi$
$350$	2.43416	−	2.43416i	0.130111	−	0.130111i
$351$	0.564515	−	4.16350i	0.0301316	−	0.222231i
$352$	2.15513	+	2.15513i	0.114869	+	0.114869i
$353$	0.400840	+	0.400840i	0.0213345	+	0.0213345i	0.717694	−	0.696359i	$-0.245198\pi$
$353$	0.400840	+	0.400840i	0.0213345	+	0.0213345i	−0.696359	+	0.717694i	$0.745198\pi$
$354$	4.68635	+	1.48424i	0.249077	+	0.0788866i
$355$	8.38330	+	8.38330i	0.444939	+	0.444939i
$356$	−9.90966	+	9.90966i	−0.525211	+	0.525211i
$357$	−11.8259	+	6.13680i	−0.625891	+	0.324794i
$358$			9.84198i			0.520165i
$359$		−	35.3458i		−	1.86548i	−0.360548	−	0.932741i	$-0.617410\pi$
$359$		−	35.3458i		−	1.86548i	0.360548	−	0.932741i	$-0.382590\pi$
$360$	1.72706	−	2.45301i	0.0910238	−	0.129285i
$361$		−	2.09946i		−	0.110498i
$362$	−0.584575	−	0.584575i	−0.0307246	−	0.0307246i
$363$	2.82488	+	0.894685i	0.148268	+	0.0469588i
$364$	−1.96826	+	1.96826i	−0.103165	+	0.103165i
$365$	3.11646	+	3.11646i	0.163123	+	0.163123i
$366$	−4.67815	−	1.48164i	−0.244531	−	0.0774468i
$367$	4.27483			0.223144			0.111572	−	0.993756i	$-0.464411\pi$
$367$	4.27483			0.223144			0.111572	+	0.993756i	$0.464411\pi$
$368$	−2.05150	+	2.05150i	−0.106942	+	0.106942i
$369$	19.6445	+	13.8308i	1.02265	+	0.720001i
$370$	1.89635	−	5.77961i	0.0985863	−	0.300468i
$371$			42.8835i			2.22640i
$372$	7.15142	+	13.7811i	0.370784	+	0.714515i
$373$			32.8415i			1.70047i	0.526405	+	0.850234i	$0.323540\pi$
$373$			32.8415i			1.70047i	−0.526405	+	0.850234i	$0.676460\pi$
$374$	−6.81047			−0.352161
$375$	−0.797792	−	1.53738i	−0.0411978	−	0.0793898i
$376$	−5.58775	−	5.58775i	−0.288166	−	0.288166i
$377$			2.09669i			0.107985i
$378$	2.40330	−	17.7252i	0.123612	−	0.911685i
$379$	7.66460			0.393704			0.196852	−	0.980433i	$-0.436928\pi$
$379$	7.66460			0.393704			0.196852	+	0.980433i	$0.436928\pi$
$380$		−	4.11103i		−	0.210891i
$381$	6.35490	+	2.01270i	0.325571	+	0.103114i
$382$	2.47831			0.126801
$383$	−3.54407	+	3.54407i	−0.181094	+	0.181094i	−0.791832	−	0.610739i	$-0.790873\pi$
$383$	−3.54407	+	3.54407i	−0.181094	+	0.181094i	0.610739	+	0.791832i	$0.290873\pi$
$384$	−1.53738	+	0.797792i	−0.0784539	+	0.0407122i
$385$	7.41889	−	7.41889i	0.378102	−	0.378102i
$386$			7.95118i			0.404705i
$387$	2.30445	+	13.2691i	0.117142	+	0.674504i
$388$	−2.40351	+	2.40351i	−0.122020	+	0.122020i
$389$	18.3139	−	18.3139i	0.928551	−	0.928551i	−0.0690616	−	0.997612i	$-0.522000\pi$
$389$	18.3139	−	18.3139i	0.928551	−	0.928551i	0.997612	+	0.0690616i	$0.0220005\pi$
$390$	0.645093	+	1.24312i	0.0326656	+	0.0629479i
$391$		−	6.48298i		−	0.327858i
$392$	−3.42968	+	3.42968i	−0.173225	+	0.173225i
$393$	10.6318	+	20.4879i	0.536304	+	1.03348i
$394$	12.6231	−	12.6231i	0.635941	−	0.635941i
$395$	11.6086			0.584094
$396$	5.26376	−	7.47635i	0.264514	−	0.375701i
$397$		−	0.886715i		−	0.0445029i	−0.999752	−	0.0222515i	$-0.992917\pi$
$397$		−	0.886715i		−	0.0445029i	0.999752	−	0.0222515i	$-0.00708345\pi$
$398$	2.64453			0.132558
$399$	−11.2903	−	21.7568i	−0.565221	−	1.08920i
$400$			1.00000i			0.0500000i
$401$	21.7682	+	21.7682i	1.08705	+	1.08705i	0.995831	+	0.0912209i	$0.0290769\pi$
$401$	21.7682	+	21.7682i	1.08705	+	1.08705i	0.0912209	+	0.995831i	$0.470923\pi$
$402$	14.5576	−	7.55440i	0.726069	−	0.376779i
$403$	−7.24829			−0.361063
$404$			2.17467i			0.108194i
$405$	−8.13706	−	3.84555i	−0.404334	−	0.191087i
$406$			8.92618i			0.442999i
$407$	5.77972	−	17.6152i	0.286490	−	0.873153i
$408$	1.16859	−	3.68970i	0.0578536	−	0.182667i
$409$	9.72183	−	9.72183i	0.480713	−	0.480713i	−0.424646	−	0.905359i	$-0.639601\pi$
$409$	9.72183	−	9.72183i	0.480713	−	0.480713i	0.905359	+	0.424646i	$0.139601\pi$
$410$	−8.00829			−0.395501
$411$	−7.60348	+	24.0073i	−0.375052	+	1.18419i
$412$	−0.494936	−	0.494936i	−0.0243837	−	0.0243837i
$413$	−6.90846	+	6.90846i	−0.339943	+	0.339943i
$414$	7.11684	+	5.01064i	0.349773	+	0.246260i
$415$	−7.66511	−	7.66511i	−0.376266	−	0.376266i
$416$		−	0.808598i		−	0.0396448i
$417$	−8.74045	+	27.5971i	−0.428021	+	1.35144i
$418$		−	12.5297i		−	0.612846i
$419$			36.1112i			1.76415i	0.471109	+	0.882075i	$0.343854\pi$
$419$			36.1112i			1.76415i	−0.471109	+	0.882075i	$0.656146\pi$
$420$	2.74634	+	5.29231i	0.134008	+	0.258238i
$421$	16.4019	−	16.4019i	0.799382	−	0.799382i	−0.183616	−	0.982998i	$-0.558780\pi$
$421$	16.4019	−	16.4019i	0.799382	−	0.799382i	0.982998	+	0.183616i	$0.0587803\pi$
$422$	−13.7483	−	13.7483i	−0.669258	−	0.669258i
$423$	−13.6477	+	19.3844i	−0.663572	+	0.942501i
$424$	−8.80868	−	8.80868i	−0.427787	−	0.427787i
$425$	−1.58006	−	1.58006i	−0.0766440	−	0.0766440i
$426$	−18.2268	+	9.45844i	−0.883091	+	0.458263i
$427$	6.89637	−	6.89637i	0.333739	−	0.333739i
$428$	0.470042			0.0227203
$429$	1.96613	+	3.78881i	0.0949256	+	0.182925i
$430$	−3.17436	−	3.17436i	−0.153081	−	0.153081i
$431$	18.1679	+	18.1679i	0.875118	+	0.875118i	0.993025	−	0.117906i	$-0.0376183\pi$
$431$	18.1679	+	18.1679i	0.875118	+	0.875118i	−0.117906	+	0.993025i	$0.537618\pi$
$432$	3.14726	+	4.13458i	0.151423	+	0.198925i
$433$	31.3276			1.50551			0.752755	−	0.658301i	$-0.228725\pi$
$433$	31.3276			1.50551			0.752755	+	0.658301i	$0.228725\pi$
$434$	−30.8579			−1.48123
$435$	4.28158	+	1.35605i	0.205286	+	0.0650174i
$436$	3.18770	−	3.18770i	0.152663	−	0.152663i
$437$	11.9272			0.570553
$438$	−6.77575	+	3.51614i	−0.323758	+	0.168008i
$439$	21.7605	−	21.7605i	1.03857	−	1.03857i	0.0393487	−	0.999226i	$-0.487472\pi$
$439$	21.7605	−	21.7605i	1.03857	−	1.03857i	0.999226	−	0.0393487i	$-0.0125283\pi$
$440$			3.04782i			0.145299i
$441$	11.8978	+	8.37673i	0.566564	+	0.398892i
$442$	1.27763	+	1.27763i	0.0607707	+	0.0607707i
$443$	−7.20883			−0.342502			−0.171251	−	0.985227i	$-0.554781\pi$
$443$	−7.20883			−0.342502			−0.171251	+	0.985227i	$0.554781\pi$
$444$	8.55165	+	6.15381i	0.405843	+	0.292047i
$445$	−14.0144			−0.664345
$446$	17.6036	+	17.6036i	0.833555	+	0.833555i
$447$	5.87540	−	18.5510i	0.277897	−	0.877432i
$448$		−	3.44243i		−	0.162639i
$449$	−2.23081	+	2.23081i	−0.105278	+	0.105278i	−0.757784	−	0.652506i	$-0.773718\pi$
$449$	−2.23081	+	2.23081i	−0.105278	+	0.105278i	0.652506	+	0.757784i	$0.273718\pi$
$450$	2.95576	−	0.513330i	0.139336	−	0.0241986i
$451$	−24.4078			−1.14932
$452$	−2.24895	+	2.24895i	−0.105782	+	0.105782i
$453$	−9.47633	+	29.9206i	−0.445237	+	1.40579i
$454$	9.88729			0.464033
$455$	−2.78354			−0.130494
$456$	6.78818	+	2.14992i	0.317886	+	0.100679i
$457$	1.56539	+	1.56539i	0.0732256	+	0.0732256i	0.742771	−	0.669545i	$-0.233511\pi$
$457$	1.56539	+	1.56539i	0.0732256	+	0.0732256i	−0.669545	+	0.742771i	$0.733511\pi$
$458$	−13.8284	−	13.8284i	−0.646158	−	0.646158i
$459$	−11.5057	−	1.56002i	−0.537041	−	0.0728155i
$460$	−2.90126			−0.135272
$461$	5.71858	−	5.71858i	0.266341	−	0.266341i	−0.561283	−	0.827624i	$-0.689692\pi$
$461$	5.71858	−	5.71858i	0.266341	−	0.266341i	0.827624	+	0.561283i	$0.189692\pi$
$462$	8.37035	+	16.1300i	0.389424	+	0.750435i
$463$	−24.0600	−	24.0600i	−1.11816	−	1.11816i	−0.992011	−	0.126154i	$-0.959737\pi$
$463$	−24.0600	−	24.0600i	−1.11816	−	1.11816i	−0.126154	−	0.992011i	$-0.540263\pi$
$464$	−1.83352	−	1.83352i	−0.0851191	−	0.0851191i
$465$	−4.68787	+	14.8015i	−0.217395	+	0.686403i
$466$	−12.5410	−	12.5410i	−0.580949	−	0.580949i
$467$	2.39895	−	2.39895i	0.111010	−	0.111010i	−0.649420	−	0.760430i	$-0.724988\pi$
$467$	2.39895	−	2.39895i	0.111010	−	0.111010i	0.760430	+	0.649420i	$0.224988\pi$
$468$	−2.39002	+	0.415078i	−0.110479	+	0.0191870i
$469$			32.5968i			1.50518i
$470$		−	7.90227i		−	0.364504i
$471$	−25.9305	−	8.21259i	−1.19481	−	0.378416i
$472$		−	2.83813i		−	0.130635i
$473$	−9.67488	−	9.67488i	−0.444852	−	0.444852i
$474$	−6.07091	+	19.1683i	−0.278846	+	0.880431i
$475$	2.90693	−	2.90693i	0.133379	−	0.133379i
$476$	5.43923	+	5.43923i	0.249307	+	0.249307i
$477$	−21.5145	+	30.5581i	−0.985083	+	1.39916i
$478$	6.96574			0.318606
$479$	−11.9467	+	11.9467i	−0.545859	+	0.545859i	−0.925240	−	0.379381i	$-0.876137\pi$
$479$	−11.9467	+	11.9467i	−0.545859	+	0.545859i	0.379381	+	0.925240i	$0.376137\pi$
$480$	−1.65121	−	0.522966i	−0.0753673	−	0.0238700i
$481$	−4.38885	+	2.22032i	−0.200114	+	0.101238i
$482$			26.3003i			1.19794i
$483$	−15.3544	+	7.96785i	−0.698648	+	0.362550i
$484$		−	1.71079i		−	0.0777632i
$485$	−3.39908			−0.154344
$486$	10.6052	−	11.4249i	0.481063	−	0.518246i
$487$	−13.5166	−	13.5166i	−0.612496	−	0.612496i	0.331100	−	0.943596i	$-0.392580\pi$
$487$	−13.5166	−	13.5166i	−0.612496	−	0.612496i	−0.943596	+	0.331100i	$0.892580\pi$
$488$			2.83316i			0.128251i
$489$	−10.3547	+	5.37336i	−0.468255	+	0.242992i
$490$	−4.85029			−0.219114
$491$		−	22.2070i		−	1.00219i	−0.865392	−	0.501095i	$-0.832931\pi$
$491$		−	22.2070i		−	1.00219i	0.865392	−	0.501095i	$-0.167069\pi$
$492$	4.18806	−	13.2234i	0.188812	−	0.596157i
$493$	5.79414			0.260955
$494$	−2.35054	+	2.35054i	−0.105756	+	0.105756i
$495$	9.00861	−	1.56454i	0.404907	−	0.0703208i
$496$	6.33851	−	6.33851i	0.284608	−	0.284608i
$497$		−	40.8126i		−	1.83070i
$498$	16.6653	−	8.64815i	0.746791	−	0.387533i
$499$	14.5069	−	14.5069i	0.649417	−	0.649417i	−0.303435	−	0.952852i	$-0.598134\pi$
$499$	14.5069	−	14.5069i	0.649417	−	0.649417i	0.952852	+	0.303435i	$0.0981336\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$	−16.1273	+	8.36896i	−0.720516	+	0.373898i
$502$		−	21.3343i		−	0.952195i
$503$	−29.5224	+	29.5224i	−1.31634	+	1.31634i	−0.399686	+	0.916652i	$0.630881\pi$
$503$	−29.5224	+	29.5224i	−1.31634	+	1.31634i	−0.916652	+	0.399686i	$0.869119\pi$
$504$	−10.1750	+	1.76710i	−0.453229	+	0.0787129i
$505$	−1.53772	+	1.53772i	−0.0684277	+	0.0684277i
$506$	−8.84252			−0.393098
$507$	−6.45662	+	20.3862i	−0.286749	+	0.905381i
$508$		−	3.84862i		−	0.170755i
$509$	10.8887			0.482631			0.241316	−	0.970447i	$-0.422421\pi$
$509$	10.8887			0.482631			0.241316	+	0.970447i	$0.422421\pi$
$510$	3.43533	−	1.78270i	0.152119	−	0.0789391i
$511$		−	15.1720i		−	0.671168i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.87007	−	21.1678i	0.126717	−	0.934583i
$514$	−3.12108			−0.137665
$515$		−	0.699945i		−	0.0308433i
$516$	6.90163	−	3.58147i	0.303827	−	0.157665i
$517$		−	24.0847i		−	1.05924i
$518$	−18.6845	+	9.45249i	−0.820951	+	0.415319i
$519$	−36.6178	−	11.5974i	−1.60734	−	0.509071i
$520$	0.571765	−	0.571765i	0.0250736	−	0.0250736i
$521$	−3.34544			−0.146566			−0.0732831	−	0.997311i	$-0.523348\pi$
$521$	−3.34544			−0.146566			−0.0732831	+	0.997311i	$0.523348\pi$
$522$	−4.47824	+	6.36064i	−0.196007	+	0.278398i
$523$	13.0218	+	13.0218i	0.569405	+	0.569405i	0.931962	−	0.362557i	$-0.118096\pi$
$523$	13.0218	+	13.0218i	0.569405	+	0.569405i	−0.362557	+	0.931962i	$0.618096\pi$
$524$	9.42329	−	9.42329i	0.411658	−	0.411658i
$525$	−1.80027	+	5.68418i	−0.0785702	+	0.248078i
$526$	−2.91099	−	2.91099i	−0.126925	−	0.126925i
$527$			20.0304i			0.872539i
$528$	−5.03260	−	1.59390i	−0.219016	−	0.0693658i
$529$			14.5827i			0.634030i
$530$		−	12.4574i		−	0.541113i
$531$	−8.38881	+	1.45690i	−0.364043	+	0.0632239i
$532$	−10.0069	+	10.0069i	−0.433854	+	0.433854i
$533$	4.57887	+	4.57887i	0.198333	+	0.198333i
$534$	7.32903	−	23.1407i	0.317158	−	1.00140i
$535$	0.332370	+	0.332370i	0.0143696	+	0.0143696i
$536$	−6.69569	−	6.69569i	−0.289210	−	0.289210i
$537$	−7.85185	−	15.1308i	−0.338833	−	0.652944i
$538$	3.67429	−	3.67429i	0.158410	−	0.158410i
$539$	−14.7828			−0.636741
$540$	−0.698141	+	5.14904i	−0.0300432	+	0.221579i
$541$	2.84989	+	2.84989i	0.122526	+	0.122526i	0.765711	−	0.643185i	$-0.222387\pi$
$541$	2.84989	+	2.84989i	0.122526	+	0.122526i	−0.643185	+	0.765711i	$0.722387\pi$
$542$	−3.35741	−	3.35741i	−0.144213	−	0.144213i
$543$	1.36508	+	0.432343i	0.0585812	+	0.0185536i
$544$	−2.23454			−0.0958050
$545$	4.50809			0.193105
$546$	1.45570	−	4.59622i	0.0622980	−	0.196700i
$547$	31.6848	−	31.6848i	1.35474	−	1.35474i	0.474475	−	0.880269i	$-0.342638\pi$
$547$	31.6848	−	31.6848i	1.35474	−	1.35474i	0.880269	−	0.474475i	$-0.157362\pi$
$548$	14.5392			0.621083
$549$	8.37412	−	1.45435i	0.357399	−	0.0620700i
$550$	−2.15513	+	2.15513i	−0.0918952	+	0.0918952i
$551$			10.6599i			0.454125i
$552$	1.51726	−	4.79060i	0.0645789	−	0.203902i
$553$	−28.2573	−	28.2573i	−1.20162	−	1.20162i
$554$	−3.18907			−0.135491
$555$	1.69553	+	10.3983i	0.0719711	+	0.441384i
$556$	16.7132			0.708799
$557$	−30.2213	−	30.2213i	−1.28052	−	1.28052i	−0.940374	−	0.340143i	$-0.889525\pi$
$557$	−30.2213	−	30.2213i	−1.28052	−	1.28052i	−0.340143	−	0.940374i	$-0.610475\pi$
$558$	−21.9889	−	15.4814i	−0.930862	−	0.655378i
$559$			3.62998i			0.153532i
$560$	2.43416	−	2.43416i	0.102862	−	0.102862i
$561$	10.4703	−	5.43334i	0.442055	−	0.229396i
$562$	16.2251			0.684416
$563$	−10.7209	+	10.7209i	−0.451833	+	0.451833i	−0.895963	−	0.444129i	$-0.853513\pi$
$563$	−10.7209	+	10.7209i	−0.451833	+	0.451833i	0.444129	+	0.895963i	$0.353513\pi$
$564$	13.0483	+	4.13261i	0.549434	+	0.174014i
$565$	−3.18049			−0.133804
$566$	−29.5074			−1.24029
$567$	10.4462	+	29.1676i	0.438701	+	1.22492i
$568$	8.38330	+	8.38330i	0.351755	+	0.351755i
$569$	−30.3297	−	30.3297i	−1.27149	−	1.27149i	−0.945308	−	0.326179i	$-0.894239\pi$
$569$	−30.3297	−	30.3297i	−1.27149	−	1.27149i	−0.326179	−	0.945308i	$-0.605761\pi$
$570$	3.27974	+	6.32020i	0.137373	+	0.264724i
$571$	26.1370			1.09380			0.546900	−	0.837198i	$-0.315808\pi$
$571$	26.1370			1.09380			0.546900	+	0.837198i	$0.315808\pi$
$572$	1.74264	−	1.74264i	0.0728634	−	0.0728634i
$573$	−3.81010	+	1.97718i	−0.159169	+	0.0825978i
$574$	19.4935	+	19.4935i	0.813642	+	0.813642i
$575$	−2.05150	−	2.05150i	−0.0855535	−	0.0855535i
$576$	1.72706	−	2.45301i	0.0719607	−	0.102209i
$577$	18.6883	+	18.6883i	0.778004	+	0.778004i	0.979491	−	0.201487i	$-0.0645775\pi$
$577$	18.6883	+	18.6883i	0.778004	+	0.778004i	−0.201487	+	0.979491i	$0.564578\pi$
$578$	−8.49012	+	8.49012i	−0.353142	+	0.353142i
$579$	−6.34339	−	12.2240i	−0.263622	−	0.508011i
$580$		−	2.59299i		−	0.107668i
$581$			37.3163i			1.54814i
$582$	1.77760	−	5.61261i	0.0736840	−	0.232650i
$583$		−	37.9678i		−	1.57246i
$584$	3.11646	+	3.11646i	0.128960	+	0.128960i
$585$	−1.98350	−	1.39649i	−0.0820078	−	0.0577379i
$586$	5.86433	−	5.86433i	0.242253	−	0.242253i
$587$	6.84341	+	6.84341i	0.282458	+	0.282458i	0.834088	−	0.551631i	$-0.185994\pi$
$587$	6.84341	+	6.84341i	0.282458	+	0.282458i	−0.551631	+	0.834088i	$0.685994\pi$
$588$	2.53654	−	8.00887i	0.104605	−	0.330280i
$589$	−36.8513			−1.51843
$590$	2.00686	−	2.00686i	0.0826210	−	0.0826210i
$591$	−9.33583	+	29.4770i	−0.384025	+	1.21252i
$592$	1.89635	−	5.77961i	0.0779393	−	0.237540i
$593$		−	25.8530i		−	1.06166i	−0.847480	−	0.530828i	$-0.821881\pi$
$593$		−	25.8530i		−	1.06166i	0.847480	−	0.530828i	$-0.178119\pi$
$594$	−2.12781	+	15.6933i	−0.0873050	+	0.643906i
$595$			7.69223i			0.315351i
$596$	−11.2348			−0.460194
$597$	−4.06564	+	2.10978i	−0.166395	+	0.0863477i
$598$	1.65884	+	1.65884i	0.0678351	+	0.0678351i
$599$			28.9337i			1.18220i	0.806598	+	0.591100i	$0.201306\pi$
$599$			28.9337i			1.18220i	−0.806598	+	0.591100i	$0.798694\pi$
$600$	−0.797792	−	1.53738i	−0.0325697	−	0.0627632i
$601$	−6.17236			−0.251776			−0.125888	−	0.992044i	$-0.540178\pi$
$601$	−6.17236			−0.251776			−0.125888	+	0.992044i	$0.540178\pi$
$602$			15.4538i			0.629851i
$603$	−16.3537	+	23.2279i	−0.665976	+	0.945915i
$604$	18.1204			0.737308
$605$	1.20971	−	1.20971i	0.0491818	−	0.0491818i
$606$	−1.73493	−	3.34328i	−0.0704767	−	0.135811i
$607$	−9.27354	+	9.27354i	−0.376401	+	0.376401i	−0.869802	−	0.493401i	$-0.835754\pi$
$607$	−9.27354	+	9.27354i	−0.376401	+	0.376401i	0.493401	+	0.869802i	$0.335754\pi$
$608$		−	4.11103i		−	0.166724i
$609$	−7.12124	−	13.7229i	−0.288567	−	0.556080i
$610$	−2.00335	+	2.00335i	−0.0811131	+	0.0811131i
$611$	−4.51824	+	4.51824i	−0.182789	+	0.182789i
$612$	1.14706	+	6.60475i	0.0463670	+	0.266981i
$613$		−	3.85367i		−	0.155648i	−0.996967	−	0.0778241i	$-0.975203\pi$
$613$		−	3.85367i		−	0.155648i	0.996967	−	0.0778241i	$-0.0247973\pi$
$614$	4.97725	−	4.97725i	0.200866	−	0.200866i
$615$	12.3118	−	6.38895i	0.496458	−	0.257627i
$616$	7.41889	−	7.41889i	0.298916	−	0.298916i
$617$	−25.4539			−1.02474			−0.512369	−	0.858766i	$-0.671232\pi$
$617$	−25.4539			−1.02474			−0.512369	+	0.858766i	$0.671232\pi$
$618$	1.15576	+	0.366047i	0.0464914	+	0.0147246i
$619$		−	13.3502i		−	0.536588i	−0.963337	−	0.268294i	$-0.913540\pi$
$619$		−	13.3502i		−	0.536588i	0.963337	−	0.268294i	$-0.0864599\pi$
$620$	8.96401			0.360003
$621$	−14.9387	−	2.02549i	−0.599470	−	0.0812800i
$622$		−	7.58225i		−	0.304020i
$623$	34.1133	+	34.1133i	1.36672	+	1.36672i
$624$	0.645093	+	1.24312i	0.0258244	+	0.0497647i
$625$	−1.00000			−0.0400000
$626$			23.2502i			0.929266i
$627$	9.99607	+	19.2628i	0.399205	+	0.769283i
$628$			15.7039i			0.626653i
$629$	6.13577	+	12.1284i	0.244649	+	0.483593i
$630$	−8.44432	−	5.94526i	−0.336430	−	0.236865i
$631$	−34.7483	+	34.7483i	−1.38331	+	1.38331i	−0.544631	+	0.838676i	$0.683330\pi$
$631$	−34.7483	+	34.7483i	−1.38331	+	1.38331i	−0.838676	+	0.544631i	$0.816670\pi$
$632$	11.6086			0.461766
$633$	32.1047	+	10.1681i	1.27605	+	0.404144i
$634$	−13.7554	−	13.7554i	−0.546296	−	0.546296i
$635$	2.72139	−	2.72139i	0.107995	−	0.107995i
$636$	20.5697	+	6.51476i	0.815644	+	0.258327i
$637$	2.77323	+	2.77323i	0.109879	+	0.109879i
$638$		−	7.90297i		−	0.312882i
$639$	20.4756	−	29.0824i	0.810001	−	1.15048i
$640$			1.00000i			0.0395285i
$641$		−	5.61943i		−	0.221954i	−0.993823	−	0.110977i	$-0.964602\pi$
$641$		−	5.61943i		−	0.221954i	0.993823	−	0.110977i	$-0.0353980\pi$
$642$	−0.722631	+	0.374995i	−0.0285200	+	0.0147999i
$643$	20.4006	−	20.4006i	0.804522	−	0.804522i	−0.179277	−	0.983799i	$-0.557376\pi$
$643$	20.4006	−	20.4006i	0.804522	−	0.804522i	0.983799	+	0.179277i	$0.0573757\pi$
$644$	7.06214	+	7.06214i	0.278287	+	0.278287i
$645$	7.41267	+	2.34771i	0.291874	+	0.0924410i
$646$	6.49565	+	6.49565i	0.255568	+	0.255568i
$647$	26.1415	+	26.1415i	1.02773	+	1.02773i	0.999604	+	0.0281258i	$0.00895389\pi$
$647$	26.1415	+	26.1415i	1.02773	+	1.02773i	0.0281258	+	0.999604i	$0.491046\pi$
$648$	−8.13706	−	3.84555i	−0.319654	−	0.151067i
$649$	6.11654	−	6.11654i	0.240095	−	0.240095i
$650$	0.808598			0.0317158
$651$	47.4403	−	24.6182i	1.85933	−	0.964864i
$652$	4.76257	+	4.76257i	0.186517	+	0.186517i
$653$	21.1720	+	21.1720i	0.828525	+	0.828525i	0.987313	−	0.158788i	$-0.0507585\pi$
$653$	21.1720	+	21.1720i	0.828525	+	0.828525i	−0.158788	+	0.987313i	$0.550758\pi$
$654$	−2.35758	+	7.44383i	−0.0921886	+	0.291077i
$655$	13.3265			0.520711
$656$	−8.00829			−0.312671
$657$	7.61173	−	10.8113i	0.296962	−	0.421788i
$658$	−19.2354	+	19.2354i	−0.749874	+	0.749874i
$659$	−28.6785			−1.11716			−0.558578	−	0.829452i	$-0.688653\pi$
$659$	−28.6785			−1.11716			−0.558578	+	0.829452i	$0.688653\pi$
$660$	−2.43153	−	4.68565i	−0.0946471	−	0.182389i
$661$	−9.63627	+	9.63627i	−0.374807	+	0.374807i	−0.869225	−	0.494417i	$-0.835382\pi$
$661$	−9.63627	+	9.63627i	−0.374807	+	0.374807i	0.494417	+	0.869225i	$0.335382\pi$
$662$		−	23.9782i		−	0.931938i
$663$	−2.98348	−	0.944917i	−0.115869	−	0.0366975i
$664$	−7.66511	−	7.66511i	−0.297464	−	0.297464i
$665$	−14.1519			−0.548787
$666$	−18.0566	−	2.63829i	−0.699678	−	0.102232i
$667$	7.52295			0.291290
$668$	7.41766	+	7.41766i	0.286998	+	0.286998i
$669$	−41.1074	−	13.0194i	−1.58930	−	0.503358i
$670$		−	9.46914i		−	0.365825i
$671$	−6.10584	+	6.10584i	−0.235713	+	0.235713i
$672$	2.74634	+	5.29231i	0.105942	+	0.204155i
$673$	−32.2049			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$673$	−32.2049			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$674$	−5.00850	+	5.00850i	−0.192920	+	0.192920i
$675$	−4.13458	+	3.14726i	−0.159140	+	0.121138i
$676$	12.3462			0.474853
$677$	4.54053			0.174507			0.0872533	−	0.996186i	$-0.472191\pi$
$677$	4.54053			0.174507			0.0872533	+	0.996186i	$0.472191\pi$
$678$	1.66329	−	5.25167i	0.0638782	−	0.201689i
$679$	8.27392	+	8.27392i	0.317524	+	0.317524i
$680$	−1.58006	−	1.58006i	−0.0605924	−	0.0605924i
$681$	−15.2005	+	7.88800i	−0.582484	+	0.302269i
$682$	27.3207			1.04616
$683$	17.4943	−	17.4943i	0.669399	−	0.669399i	−0.288178	−	0.957577i	$-0.593049\pi$
$683$	17.4943	−	17.4943i	0.669399	−	0.669399i	0.957577	+	0.288178i	$0.0930493\pi$
$684$	−12.1512	+	2.11031i	−0.464612	+	0.0806899i
$685$	10.2807	+	10.2807i	0.392807	+	0.392807i
$686$	−5.23273	−	5.23273i	−0.199787	−	0.199787i
$687$	32.2916	+	10.2273i	1.23200	+	0.390194i
$688$	−3.17436	−	3.17436i	−0.121021	−	0.121021i
$689$	−7.12268	+	7.12268i	−0.271353	+	0.271353i
$690$	4.46033	−	2.31460i	0.169802	−	0.0881154i
$691$		−	5.34751i		−	0.203429i	−0.994814	−	0.101714i	$-0.967567\pi$
$691$		−	5.34751i		−	0.203429i	0.994814	−	0.101714i	$-0.0324328\pi$
$692$			22.1763i			0.843016i
$693$	−25.7368	−	18.1201i	−0.977659	−	0.688325i
$694$		−	11.5297i		−	0.437661i
$695$	11.8180	+	11.8180i	0.448284	+	0.448284i
$696$	4.28158	+	1.35605i	0.162293	+	0.0514008i
$697$	12.6536	−	12.6536i	0.479288	−	0.479288i
$698$	−6.87499	−	6.87499i	−0.260222	−	0.260222i
$699$	29.2853	+	9.27511i	1.10767	+	0.350817i
$700$	3.44243			0.130111
$701$	14.9583	−	14.9583i	0.564967	−	0.564967i	−0.365747	−	0.930714i	$-0.619186\pi$
$701$	14.9583	−	14.9583i	0.564967	−	0.564967i	0.930714	+	0.365747i	$0.119186\pi$
$702$	3.34322	−	2.54487i	0.126182	−	0.0960499i
$703$	−22.3135	+	11.2884i	−0.841569	+	0.425750i
$704$			3.04782i			0.114869i
$705$	6.30437	+	12.1488i	0.237436	+	0.457549i
$706$			0.566873i			0.0213345i
$707$	7.48612			0.281545
$708$	2.26423	+	4.36327i	0.0850951	+	0.163982i
$709$	−30.3690	−	30.3690i	−1.14053	−	1.14053i	−0.988353	−	0.152178i	$-0.951371\pi$
$709$	−30.3690	−	30.3690i	−1.14053	−	1.14053i	−0.152178	−	0.988353i	$-0.548629\pi$
$710$			11.8558i			0.444939i
$711$	−5.95906	−	34.3123i	−0.223482	−	1.28681i
$712$	−14.0144			−0.525211
$713$			26.0069i			0.973968i
$714$	−12.7015	−	4.02277i	−0.475342	−	0.150548i
$715$	2.46446			0.0921657
$716$	−6.95933	+	6.95933i	−0.260082	+	0.260082i
$717$	−10.7090	+	5.55721i	−0.399934	+	0.207538i
$718$	24.9933	−	24.9933i	0.932741	−	0.932741i
$719$			12.6121i			0.470351i	0.971953	+	0.235175i	$0.0755665\pi$
$719$			12.6121i			0.470351i	−0.971953	+	0.235175i	$0.924434\pi$
$720$	2.95576	−	0.513330i	0.110155	−	0.0191307i
$721$	−1.70378	+	1.70378i	−0.0634521	+	0.0634521i
$722$	1.48455	−	1.48455i	0.0552491	−	0.0552491i
$723$	−20.9821	−	40.4334i	−0.780334	−	1.50374i
$724$		−	0.826713i		−	0.0307246i
$725$	1.83352	−	1.83352i	0.0680953	−	0.0680953i
$726$	1.36486	+	2.63013i	0.0506545	+	0.0976133i
$727$	−0.256819	+	0.256819i	−0.00952488	+	0.00952488i	−0.711853	−	0.702328i	$-0.752144\pi$
$727$	−0.256819	+	0.256819i	−0.00952488	+	0.00952488i	0.702328	+	0.711853i	$0.252144\pi$
$728$	−2.78354			−0.103165
$729$	−7.18951	+	26.0252i	−0.266278	+	0.963896i
$730$			4.40734i			0.163123i
$731$	10.0313			0.371022
$732$	−2.26027	−	4.35563i	−0.0835420	−	0.160989i
$733$		−	12.0159i		−	0.443816i	−0.975068	−	0.221908i	$-0.928771\pi$
$733$		−	12.0159i		−	0.443816i	0.975068	−	0.221908i	$-0.0712285\pi$
$734$	3.02276	+	3.02276i	0.111572	+	0.111572i
$735$	7.45673	−	3.86953i	0.275046	−	0.142730i
$736$	−2.90126			−0.106942
$737$		−	28.8602i		−	1.06308i
$738$	4.11090	+	23.6706i	0.151324	+	0.871325i
$739$			44.3596i			1.63179i	0.578198	+	0.815896i	$0.303756\pi$
$739$			44.3596i			1.63179i	−0.578198	+	0.815896i	$0.696244\pi$
$740$	5.42772	−	2.74588i	0.199527	−	0.100941i
$741$	1.73843	−	5.48891i	0.0638627	−	0.201640i
$742$	−30.3232	+	30.3232i	−1.11320	+	1.11320i
$743$	−40.0701			−1.47003			−0.735014	−	0.678052i	$-0.762824\pi$
$743$	−40.0701			−1.47003			−0.735014	+	0.678052i	$0.762824\pi$
$744$	−4.68787	+	14.8015i	−0.171866	+	0.542649i
$745$	−7.94418	−	7.94418i	−0.291052	−	0.291052i
$746$	−23.2224	+	23.2224i	−0.850234	+	0.850234i
$747$	−18.7215	+	26.5909i	−0.684983	+	0.972911i
$748$	−4.81573	−	4.81573i	−0.176080	−	0.176080i
$749$		−	1.61808i		−	0.0591235i
$750$	0.522966	−	1.65121i	0.0190960	−	0.0602938i
$751$		−	44.0250i		−	1.60650i	−0.595645	−	0.803248i	$-0.703103\pi$
$751$		−	44.0250i		−	1.60650i	0.595645	−	0.803248i	$-0.296897\pi$
$752$		−	7.90227i		−	0.288166i
$753$	17.0203	+	32.7988i	0.620255	+	1.19526i
$754$	−1.48258	+	1.48258i	−0.0539925	+	0.0539925i
$755$	12.8130	+	12.8130i	0.466314	+	0.466314i
$756$	14.2330	−	10.8342i	0.517649	−	0.394036i
$757$	4.69837	+	4.69837i	0.170765	+	0.170765i	0.787315	−	0.616550i	$-0.211470\pi$
$757$	4.69837	+	4.69837i	0.170765	+	0.170765i	−0.616550	+	0.787315i	$0.711470\pi$
$758$	5.41969	+	5.41969i	0.196852	+	0.196852i
$759$	13.5943	−	7.05449i	0.493442	−	0.256062i
$760$	2.90693	−	2.90693i	0.105446	−	0.105446i
$761$	−10.9188			−0.395805			−0.197902	−	0.980222i	$-0.563413\pi$
$761$	−10.9188			−0.395805			−0.197902	+	0.980222i	$0.563413\pi$
$762$	3.07040	+	5.91678i	0.111229	+	0.214342i
$763$	−10.9734	−	10.9734i	−0.397265	−	0.397265i
$764$	1.75243	+	1.75243i	0.0634007	+	0.0634007i
$765$	−3.85917	+	5.48135i	−0.139529	+	0.198179i
$766$	−5.01207			−0.181094
$767$	−2.29490			−0.0828642
$768$	−1.65121	−	0.522966i	−0.0595830	−	0.0188709i
$769$	32.6754	−	32.6754i	1.17830	−	1.17830i	0.198128	−	0.980176i	$-0.436514\pi$
$769$	32.6754	−	32.6754i	1.17830	−	1.17830i	0.980176	−	0.198128i	$-0.0634863\pi$
$770$	10.4919			0.378102
$771$	4.79827	−	2.48997i	0.172806	−	0.0896741i
$772$	−5.62234	+	5.62234i	−0.202352	+	0.202352i
$773$		−	46.7775i		−	1.68247i	−0.540669	−	0.841235i	$-0.681829\pi$
$773$		−	46.7775i		−	1.68247i	0.540669	−	0.841235i	$-0.318171\pi$
$774$	−7.75314	+	11.0121i	−0.278681	+	0.395823i
$775$	6.33851	+	6.33851i	0.227686	+	0.227686i
$776$	−3.39908			−0.122020
$777$	21.1840	−	29.4384i	0.759973	−	1.05610i
$778$	25.8997			0.928551
$779$	23.2796	+	23.2796i	0.834078	+	0.834078i
$780$	−0.422869	+	1.33517i	−0.0151411	+	0.0478067i
$781$			36.1343i			1.29299i
$782$	4.58416	−	4.58416i	0.163929	−	0.163929i
$783$	1.81027	−	13.3514i	0.0646939	−	0.477141i
$784$	−4.85029			−0.173225
$785$	−11.1043	+	11.1043i	−0.396330	+	0.396330i
$786$	−6.96932	+	22.0050i	−0.248588	+	0.784892i
$787$	20.1224			0.717286			0.358643	−	0.933475i	$-0.383240\pi$
$787$	20.1224			0.717286			0.358643	+	0.933475i	$0.383240\pi$
$788$	17.8517			0.635941
$789$	6.79765	+	2.15292i	0.242003	+	0.0766461i
$790$	8.20854	+	8.20854i	0.292047	+	0.292047i
$791$	7.74183	+	7.74183i	0.275268	+	0.275268i
$792$	9.00861	−	1.56454i	0.320107	−	0.0555934i
$793$	2.29089			0.0813518
$794$	0.627002	−	0.627002i	0.0222515	−	0.0222515i
$795$	9.93838	+	19.1516i	0.352478	+	0.679239i
$796$	1.86996	+	1.86996i	0.0662791	+	0.0662791i
$797$	0.721582	+	0.721582i	0.0255597	+	0.0255597i	0.719771	−	0.694211i	$-0.244247\pi$
$797$	0.721582	+	0.721582i	0.0255597	+	0.0255597i	−0.694211	+	0.719771i	$0.744247\pi$
$798$	7.40096	−	23.3678i	0.261991	−	0.827212i
$799$	12.4860	+	12.4860i	0.441724	+	0.441724i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	7.19400	+	41.4231i	0.254187	+	1.46361i
$802$			30.7849i			1.08705i
$803$			13.4328i			0.474033i
$804$	15.6356	+	4.95203i	0.551424	+	0.174645i
$805$			9.98738i			0.352009i
$806$	−5.12531	−	5.12531i	−0.180531	−	0.180531i
$807$	−2.71745	+	8.58010i	−0.0956588	+	0.302034i
$808$	−1.53772	+	1.53772i	−0.0540968	+	0.0540968i
$809$	25.3308	+	25.3308i	0.890584	+	0.890584i	0.994578	−	0.103994i	$-0.0331621\pi$
$809$	25.3308	+	25.3308i	0.890584	+	0.890584i	−0.103994	+	0.994578i	$0.533162\pi$
$810$	−3.03456	−	8.47298i	−0.106623	−	0.297710i
$811$	−45.6593			−1.60331			−0.801657	−	0.597784i	$-0.796048\pi$
$811$	−45.6593			−1.60331			−0.801657	+	0.597784i	$0.796048\pi$
$812$	−6.31176	+	6.31176i	−0.221499	+	0.221499i
$813$	7.84013	+	2.48309i	0.274965	+	0.0870858i
$814$	16.5427	−	8.36895i	0.579822	−	0.293332i
$815$			6.73529i			0.235927i
$816$	3.43533	−	1.78270i	0.120260	−	0.0624068i
$817$			18.4553i			0.645670i
$818$	13.7487			0.480713
$819$	1.42887	+	8.22746i	0.0499289	+	0.287491i
$820$	−5.66272	−	5.66272i	−0.197751	−	0.197751i
$821$		−	41.4366i		−	1.44615i	−0.690770	−	0.723074i	$-0.742728\pi$
$821$		−	41.4366i		−	1.44615i	0.690770	−	0.723074i	$-0.257272\pi$
$822$	−22.3522	+	11.5992i	−0.779622	+	0.404570i
$823$	48.2079			1.68042			0.840210	−	0.542261i	$-0.182431\pi$
$823$	48.2079			1.68042			0.840210	+	0.542261i	$0.182431\pi$
$824$		−	0.699945i		−	0.0243837i
$825$	1.59390	−	5.03260i	0.0554926	−	0.175213i
$826$	−9.77004			−0.339943
$827$	3.90758	−	3.90758i	0.135880	−	0.135880i	−0.635895	−	0.771775i	$-0.719369\pi$
$827$	3.90758	−	3.90758i	0.135880	−	0.135880i	0.771775	+	0.635895i	$0.219369\pi$
$828$	1.48930	+	8.57542i	0.0517569	+	0.298016i
$829$	−23.7888	+	23.7888i	−0.826221	+	0.826221i	−0.986992	−	0.160771i	$-0.948602\pi$
$829$	−23.7888	+	23.7888i	−0.826221	+	0.826221i	0.160771	+	0.986992i	$0.448602\pi$
$830$		−	10.8401i		−	0.376266i
$831$	4.90281	−	2.54422i	0.170077	−	0.0882579i
$832$	0.571765	−	0.571765i	0.0198224	−	0.0198224i
$833$	7.66374	−	7.66374i	0.265533	−	0.265533i
$834$	−25.6945	+	13.3337i	−0.889729	+	0.461708i
$835$			10.4902i			0.363027i
$836$	8.85981	−	8.85981i	0.306423	−	0.306423i
$837$	46.1561	+	6.25814i	1.59539	+	0.216313i
$838$	−25.5345	+	25.5345i	−0.882075	+	0.882075i
$839$	34.3994			1.18760			0.593799	−	0.804613i	$-0.297627\pi$
$839$	34.3994			1.18760			0.593799	+	0.804613i	$0.297627\pi$
$840$	−1.80027	+	5.68418i	−0.0621152	+	0.196123i
$841$		−	22.2764i		−	0.768152i
$842$	23.1959			0.799382
$843$	−24.9441	+	12.9443i	−0.859122	+	0.445825i
$844$		−	19.4431i		−	0.669258i
$845$	8.73006	+	8.73006i	0.300323	+	0.300323i
$846$	−23.3572	+	4.05647i	−0.803036	+	0.139464i
$847$	−5.88927			−0.202358
$848$		−	12.4574i		−	0.427787i
$849$	45.3640	−	23.5408i	1.55689	−	0.807917i
$850$		−	2.23454i		−	0.0766440i
$851$	7.96652	+	15.7472i	0.273089	+	0.539808i
$852$	−19.5764	−	6.20016i	−0.670677	−	0.212414i
$853$	1.23013	−	1.23013i	0.0421189	−	0.0421189i	−0.685734	−	0.727853i	$-0.740519\pi$
$853$	1.23013	−	1.23013i	0.0421189	−	0.0421189i	0.727853	+	0.685734i	$0.240519\pi$
$854$	9.75294			0.333739
$855$	−10.0844	−	7.09997i	−0.344879	−	0.242814i
$856$	0.332370	+	0.332370i	0.0113602	+	0.0113602i
$857$	−3.69140	+	3.69140i	−0.126096	+	0.126096i	−0.767338	−	0.641242i	$-0.778419\pi$
$857$	−3.69140	+	3.69140i	−0.126096	+	0.126096i	0.641242	+	0.767338i	$0.278419\pi$
$858$	−1.28883	+	4.06936i	−0.0439999	+	0.138925i
$859$	22.5969	+	22.5969i	0.770995	+	0.770995i	0.978281	−	0.207285i	$-0.0664629\pi$
$859$	22.5969	+	22.5969i	0.770995	+	0.770995i	−0.207285	+	0.978281i	$0.566463\pi$
$860$		−	4.48922i		−	0.153081i
$861$	−45.5206	−	14.4171i	−1.55134	−	0.491333i
$862$			25.6933i			0.875118i
$863$			10.7938i			0.367427i	0.982980	+	0.183713i	$0.0588118\pi$
$863$			10.7938i			0.367427i	−0.982980	+	0.183713i	$0.941188\pi$
$864$	−0.698141	+	5.14904i	−0.0237512	+	0.175174i
$865$	−15.6810	+	15.6810i	−0.533170	+	0.533170i
$866$	22.1520	+	22.1520i	0.752755	+	0.752755i
$867$	6.27917	−	19.8259i	0.213252	−	0.673322i
$868$	−21.8199	−	21.8199i	−0.740614	−	0.740614i
$869$	25.0182	+	25.0182i	0.848683	+	0.848683i
$870$	2.06867	+	3.98641i	0.0701344	+	0.135152i
$871$	−5.41413	+	5.41413i	−0.183451	+	0.183451i
$872$	4.50809			0.152663
$873$	1.74485	+	10.0469i	0.0590543	+	0.340035i
$874$	8.43378	+	8.43378i	0.285277	+	0.285277i
$875$	2.43416	+	2.43416i	0.0822897	+	0.0822897i
$876$	−7.27747	−	2.30489i	−0.245883	−	0.0778750i
$877$	20.3881			0.688456			0.344228	−	0.938886i	$-0.388141\pi$
$877$	20.3881			0.688456			0.344228	+	0.938886i	$0.388141\pi$
$878$	30.7741			1.03857
$879$	−4.33717	+	13.6942i	−0.146289	+	0.461894i
$880$	−2.15513	+	2.15513i	−0.0726496	+	0.0726496i
$881$	−36.8813			−1.24256			−0.621281	−	0.783588i	$-0.713387\pi$
$881$	−36.8813			−1.24256			−0.621281	+	0.783588i	$0.713387\pi$
$882$	2.48980	+	14.3363i	0.0838360	+	0.482728i
$883$	10.5222	−	10.5222i	0.354100	−	0.354100i	−0.507533	−	0.861633i	$-0.669442\pi$
$883$	10.5222	−	10.5222i	0.354100	−	0.354100i	0.861633	+	0.507533i	$0.169442\pi$
$884$			1.80684i			0.0607707i
$885$	−1.48424	+	4.68635i	−0.0498922	+	0.157530i
$886$	−5.09741	−	5.09741i	−0.171251	−	0.171251i
$887$	4.34349			0.145840			0.0729201	−	0.997338i	$-0.476768\pi$
$887$	4.34349			0.145840			0.0729201	+	0.997338i	$0.476768\pi$
$888$	1.69553	+	10.3983i	0.0568982	+	0.348945i
$889$	−13.2486			−0.444344
$890$	−9.90966	−	9.90966i	−0.332172	−	0.332172i
$891$	−9.24878	−	25.8241i	−0.309846	−	0.865141i
$892$			24.8953i			0.833555i
$893$	−22.9714	+	22.9714i	−0.768708	+	0.768708i
$894$	17.2721	−	8.96301i	0.577665	−	0.299768i
$895$	−9.84198			−0.328981
$896$	2.43416	−	2.43416i	0.0813197	−	0.0813197i
$897$	−3.87367	−	1.22685i	−0.129338	−	0.0409635i
$898$	−3.15484			−0.105278
$899$	−23.2436			−0.775218
$900$	2.45301	+	1.72706i	0.0817671	+	0.0575685i
$901$	19.6833	+	19.6833i	0.655746	+	0.655746i
$902$	−17.2589	−	17.2589i	−0.574660	−	0.574660i
$903$	−12.3289	−	23.7584i	−0.410281	−	0.790628i
$904$	−3.18049			−0.105782
$905$	0.584575	−	0.584575i	0.0194319	−	0.0194319i
$906$	−27.8579	+	14.4563i	−0.925515	+	0.480278i
$907$	−9.06099	−	9.06099i	−0.300865	−	0.300865i	0.540487	−	0.841352i	$-0.318240\pi$
$907$	−9.06099	−	9.06099i	−0.300865	−	0.300865i	−0.841352	+	0.540487i	$0.818240\pi$
$908$	6.99137	+	6.99137i	0.232017	+	0.232017i
$909$	5.33448	+	3.75577i	0.176934	+	0.124571i
$910$	−1.96826	−	1.96826i	−0.0652472	−	0.0652472i
$911$	24.1539	−	24.1539i	0.800254	−	0.800254i	−0.182881	−	0.983135i	$-0.558542\pi$
$911$	24.1539	−	24.1539i	0.800254	−	0.800254i	0.983135	+	0.182881i	$0.0585423\pi$
$912$	3.27974	+	6.32020i	0.108603	+	0.209283i
$913$		−	33.0387i		−	1.09342i
$914$			2.21379i			0.0732256i
$915$	1.48164	−	4.67815i	0.0489816	−	0.154655i
$916$		−	19.5563i		−	0.646158i
$917$	−32.4390	−	32.4390i	−1.07123	−	1.07123i
$918$	−7.03267	−	9.23887i	−0.232113	−	0.304928i
$919$	−40.5578	+	40.5578i	−1.33788	+	1.33788i	−0.439768	+	0.898111i	$0.644939\pi$
$919$	−40.5578	+	40.5578i	−1.33788	+	1.33788i	−0.898111	+	0.439768i	$0.855061\pi$
$920$	−2.05150	−	2.05150i	−0.0676360	−	0.0676360i
$921$	−3.68110	+	11.6227i	−0.121296	+	0.382982i
$922$	8.08730			0.266341
$923$	6.77872	−	6.77872i	0.223124	−	0.223124i
$924$	−5.48690	+	17.3244i	−0.180506	+	0.569930i
$925$	5.77961	+	1.89635i	0.190032	+	0.0623515i
$926$		−	34.0260i		−	1.11816i
$927$	−2.06887	+	0.359303i	−0.0679505	+	0.0118011i
$928$		−	2.59299i		−	0.0851191i
$929$	−31.9349			−1.04775			−0.523874	−	0.851796i	$-0.675514\pi$
$929$	−31.9349			−1.04775			−0.523874	+	0.851796i	$0.675514\pi$
$930$	−13.7811	+	7.15142i	−0.451899	+	0.234504i
$931$	14.0995	+	14.0995i	0.462092	+	0.462092i
$932$		−	17.7356i		−	0.580949i
$933$	6.04906	+	11.6568i	0.198037	+	0.381626i
$934$	3.39263			0.111010
$935$		−	6.81047i		−	0.222726i
$936$	−1.98350	−	1.39649i	−0.0648328	−	0.0456459i
$937$	23.4147			0.764926			0.382463	−	0.923971i	$-0.375076\pi$
$937$	23.4147			0.764926			0.382463	+	0.923971i	$0.375076\pi$
$938$	−23.0494	+	23.0494i	−0.752590	+	0.752590i
$939$	−18.5489	−	35.7444i	−0.605319	−	1.16647i
$940$	5.58775	−	5.58775i	0.182252	−	0.182252i
$941$		−	51.9908i		−	1.69485i	−0.530915	−	0.847425i	$-0.678152\pi$
$941$		−	51.9908i		−	1.69485i	0.530915	−	0.847425i	$-0.321848\pi$
$942$	−12.5284	−	24.1428i	−0.408199	−	0.786615i
$943$	16.4290	−	16.4290i	0.535003	−	0.535003i
$944$	2.00686	−	2.00686i	0.0653177	−	0.0653177i
$945$	17.7252	+	2.40330i	0.576600	+	0.0781793i
$946$		−	13.6824i		−	0.444852i
$947$	32.1776	−	32.1776i	1.04563	−	1.04563i	0.0467229	−	0.998908i	$-0.485122\pi$
$947$	32.1776	−	32.1776i	1.04563	−	1.04563i	0.998908	−	0.0467229i	$-0.0148778\pi$
$948$	−17.8468	+	9.26127i	−0.579638	+	0.300792i
$949$	2.51997	−	2.51997i	0.0818016	−	0.0818016i
$950$	4.11103			0.133379
$951$	32.1211	+	10.1733i	1.04160	+	0.329891i
$952$			7.69223i			0.249307i
$953$	56.7619			1.83870			0.919349	−	0.393443i	$-0.128716\pi$
$953$	56.7619			1.83870			0.919349	+	0.393443i	$0.128716\pi$
$954$	−36.8209	+	6.39473i	−1.19212	+	0.207037i
$955$			2.47831i			0.0801963i
$956$	4.92552	+	4.92552i	0.159303	+	0.159303i
$957$	6.30493	+	12.1498i	0.203809	+	0.392749i
$958$	−16.8952			−0.545859
$959$		−	50.0500i		−	1.61620i
$960$	−0.797792	−	1.53738i	−0.0257486	−	0.0496186i
$961$		−	49.3535i		−	1.59205i
$962$	−4.67338	−	1.53338i	−0.150676	−	0.0494382i
$963$	0.811788	−	1.15302i	0.0261595	−	0.0371555i
$964$	−18.5971	+	18.5971i	−0.598972	+	0.598972i
$965$	−7.95118			−0.255958
$966$	−16.4913	−	5.22305i	−0.530599	−	0.168049i
$967$	−36.7593	−	36.7593i	−1.18210	−	1.18210i	−0.979199	−	0.202900i	$-0.934963\pi$
$967$	−36.7593	−	36.7593i	−1.18210	−	1.18210i	−0.202900	−	0.979199i	$-0.565037\pi$
$968$	1.20971	−	1.20971i	0.0388816	−	0.0388816i
$969$	−15.1684	−	4.80409i	−0.487281	−	0.154330i
$970$	−2.40351	−	2.40351i	−0.0771722	−	0.0771722i
$971$			1.14129i			0.0366258i	0.999832	+	0.0183129i	$0.00582950\pi$
$971$			1.14129i			0.0366258i	−0.999832	+	0.0183129i	$0.994171\pi$
$972$	15.5777	−	0.579624i	0.499654	−	0.0185914i
$973$		−	57.5341i		−	1.84446i
$974$		−	19.1154i		−	0.612496i
$975$	−1.24312	+	0.645093i	−0.0398117	+	0.0206595i
$976$	−2.00335	+	2.00335i	−0.0641255	+	0.0641255i
$977$	−25.0361	−	25.0361i	−0.800977	−	0.800977i	0.182271	−	0.983248i	$-0.441655\pi$
$977$	−25.0361	−	25.0361i	−0.800977	−	0.800977i	−0.983248	+	0.182271i	$0.941655\pi$
$978$	−11.1214	−	3.52233i	−0.355623	−	0.112632i
$979$	−30.2029	−	30.2029i	−0.965287	−	0.965287i
$980$	−3.42968	−	3.42968i	−0.109557	−	0.109557i
$981$	−2.31414	−	13.3248i	−0.0738848	−	0.425429i
$982$	15.7028	−	15.7028i	0.501095	−	0.501095i
$983$	21.8595			0.697210			0.348605	−	0.937270i	$-0.386656\pi$
$983$	21.8595			0.697210			0.348605	+	0.937270i	$0.386656\pi$
$984$	12.3118	−	6.38895i	0.392485	−	0.203672i
$985$	12.6231	+	12.6231i	0.402204	+	0.402204i
$986$	4.09707	+	4.09707i	0.130477	+	0.130477i
$987$	14.2262	−	44.9179i	0.452825	−	1.42975i
$988$	−3.32417			−0.105756
$989$	13.0244			0.414152
$990$	7.47635	+	5.26376i	0.237614	+	0.167293i
$991$	10.1383	−	10.1383i	0.322053	−	0.322053i	−0.527501	−	0.849554i	$-0.676871\pi$
$991$	10.1383	−	10.1383i	0.322053	−	0.322053i	0.849554	+	0.527501i	$0.176871\pi$
$992$	8.96401			0.284608
$993$	19.1296	+	36.8635i	0.607059	+	1.16983i
$994$	28.8589	−	28.8589i	0.915348	−	0.915348i
$995$			2.64453i			0.0838372i
$996$	17.8993	+	5.66900i	0.567162	+	0.179629i
$997$	−12.2091	−	12.2091i	−0.386667	−	0.386667i	0.486830	−	0.873497i	$-0.338153\pi$
$997$	−12.2091	−	12.2091i	−0.386667	−	0.386667i	−0.873497	+	0.486830i	$0.838153\pi$
$998$	20.5158			0.649417
$999$	29.8645	−	10.3493i	0.944872	−	0.327439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.f.191.15	yes	40
3.2	odd	2	inner	1110.2.u.f.191.9	✓	40
37.31	odd	4	inner	1110.2.u.f.401.9	yes	40
111.68	even	4	inner	1110.2.u.f.401.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.9	✓	40	3.2	odd	2	inner
1110.2.u.f.191.15	yes	40	1.1	even	1	trivial
1110.2.u.f.401.9	yes	40	37.31	odd	4	inner
1110.2.u.f.401.15	yes	40	111.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.65121 - 0.522966i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.797792 - 1.53738i) q^{6} +3.44243 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.45301 + 1.72706i) q^{9} -1.00000 q^{10} -3.04782 q^{11} +(0.522966 - 1.65121i) q^{12} +(0.571765 + 0.571765i) q^{13} +(2.43416 + 2.43416i) q^{14} +(1.53738 - 0.797792i) q^{15} -1.00000 q^{16} +(1.58006 - 1.58006i) q^{17} +(0.513330 + 2.95576i) q^{18} +(2.90693 + 2.90693i) q^{19} +(-0.707107 - 0.707107i) q^{20} +(-5.68418 - 1.80027i) q^{21} +(-2.15513 - 2.15513i) q^{22} +(2.05150 - 2.05150i) q^{23} +(1.53738 - 0.797792i) q^{24} -1.00000i q^{25} +0.808598i q^{26} +(-3.14726 - 4.13458i) q^{27} +3.44243i q^{28} +(1.83352 + 1.83352i) q^{29} +(1.65121 + 0.522966i) q^{30} +(-6.33851 + 6.33851i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.03260 + 1.59390i) q^{33} +2.23454 q^{34} +(-2.43416 + 2.43416i) q^{35} +(-1.72706 + 2.45301i) q^{36} +(-1.89635 + 5.77961i) q^{37} +4.11103i q^{38} +(-0.645093 - 1.24312i) q^{39} -1.00000i q^{40} +8.00829 q^{41} +(-2.74634 - 5.29231i) q^{42} +(3.17436 + 3.17436i) q^{43} -3.04782i q^{44} +(-2.95576 + 0.513330i) q^{45} +2.90126 q^{46} +7.90227i q^{47} +(1.65121 + 0.522966i) q^{48} +4.85029 q^{49} +(0.707107 - 0.707107i) q^{50} +(-3.43533 + 1.78270i) q^{51} +(-0.571765 + 0.571765i) q^{52} +12.4574i q^{53} +(0.698141 - 5.14904i) q^{54} +(2.15513 - 2.15513i) q^{55} +(-2.43416 + 2.43416i) q^{56} +(-3.27974 - 6.32020i) q^{57} +2.59299i q^{58} +(-2.00686 + 2.00686i) q^{59} +(0.797792 + 1.53738i) q^{60} +(2.00335 - 2.00335i) q^{61} -8.96401 q^{62} +(8.44432 + 5.94526i) q^{63} -1.00000i q^{64} -0.808598 q^{65} +(2.43153 + 4.68565i) q^{66} +9.46914i q^{67} +(1.58006 + 1.58006i) q^{68} +(-4.46033 + 2.31460i) q^{69} -3.44243 q^{70} -11.8558i q^{71} +(-2.95576 + 0.513330i) q^{72} -4.40734i q^{73} +(-5.42772 + 2.74588i) q^{74} +(-0.522966 + 1.65121i) q^{75} +(-2.90693 + 2.90693i) q^{76} -10.4919 q^{77} +(0.422869 - 1.33517i) q^{78} +(-8.20854 - 8.20854i) q^{79} +(0.707107 - 0.707107i) q^{80} +(3.03456 + 8.47298i) q^{81} +(5.66272 + 5.66272i) q^{82} +10.8401i q^{83} +(1.80027 - 5.68418i) q^{84} +2.23454i q^{85} +4.48922i q^{86} +(-2.06867 - 3.98641i) q^{87} +(2.15513 - 2.15513i) q^{88} +(9.90966 + 9.90966i) q^{89} +(-2.45301 - 1.72706i) q^{90} +(1.96826 + 1.96826i) q^{91} +(2.05150 + 2.05150i) q^{92} +(13.7811 - 7.15142i) q^{93} +(-5.58775 + 5.58775i) q^{94} -4.11103 q^{95} +(0.797792 + 1.53738i) q^{96} +(2.40351 + 2.40351i) q^{97} +(3.42968 + 3.42968i) q^{98} +(-7.47635 - 5.26376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q + 24 * q^7 - 8 * q^9	\( 40 q + 24 q^{7} - 8 q^{9} - 40 q^{10} + 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 16 q^{22} - 8 q^{31} + 24 q^{33} + 24 q^{34} + 32 q^{37} + 16 q^{39} + 12 q^{42} + 32 q^{43} + 8 q^{45} - 56 q^{46} - 32 q^{49} - 44 q^{51} - 16 q^{52} - 24 q^{54} + 16 q^{55} + 8 q^{57} - 72 q^{61} + 24 q^{63} - 28 q^{66} + 16 q^{69} - 24 q^{70} + 8 q^{72} - 16 q^{76} - 48 q^{79} + 120 q^{81} - 24 q^{82} - 24 q^{84} + 20 q^{87} + 16 q^{88} + 8 q^{90} - 92 q^{93} - 8 q^{94} - 40 q^{97}+O(q^{100}) \) 40 * q + 24 * q^7 - 8 * q^9 - 40 * q^10 + 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 16 * q^22 - 8 * q^31 + 24 * q^33 + 24 * q^34 + 32 * q^37 + 16 * q^39 + 12 * q^42 + 32 * q^43 + 8 * q^45 - 56 * q^46 - 32 * q^49 - 44 * q^51 - 16 * q^52 - 24 * q^54 + 16 * q^55 + 8 * q^57 - 72 * q^61 + 24 * q^63 - 28 * q^66 + 16 * q^69 - 24 * q^70 + 8 * q^72 - 16 * q^76 - 48 * q^79 + 120 * q^81 - 24 * q^82 - 24 * q^84 + 20 * q^87 + 16 * q^88 + 8 * q^90 - 92 * q^93 - 8 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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