LMFDB - Embedded newform 1110.2.u.f.401.15

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			401.15
Character	$\chi$	$=$	1110.401
Dual form			1110.2.u.f.191.15

$q$-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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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	−0.623358	−	0.781937i	$-0.714232\pi$
$13$	0.571765	−	0.571765i	0.158579	−	0.158579i	0.781937	+	0.623358i	$0.214232\pi$
$14$	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	0.872261	−	0.489041i	$-0.162653\pi$
$17$	1.58006	+	1.58006i	0.383220	+	0.383220i	−0.489041	+	0.872261i	$0.662653\pi$
$18$	0.513330	−	2.95576i	0.120993	−	0.696678i
$19$	2.90693	−	2.90693i	0.666896	−	0.666896i	−0.290100	−	0.956996i	$-0.593689\pi$
$19$	2.90693	−	2.90693i	0.666896	−	0.666896i	0.956996	+	0.290100i	$0.0936885\pi$
$20$	−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	0.887867	−	0.460100i	$-0.152186\pi$
$23$	2.05150	+	2.05150i	0.427768	+	0.427768i	−0.460100	+	0.887867i	$0.652186\pi$
$24$	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	−0.516070	−	0.856546i	$-0.672606\pi$
$29$	1.83352	−	1.83352i	0.340476	−	0.340476i	0.856546	+	0.516070i	$0.172606\pi$
$30$	1.65121	−	0.522966i	0.301469	−	0.0954800i
$31$	−6.33851	−	6.33851i	−1.13843	−	1.13843i	−0.988732	−	0.149699i	$-0.952169\pi$
$31$	−6.33851	−	6.33851i	−1.13843	−	1.13843i	−0.149699	−	0.988732i	$-0.547831\pi$
$32$	−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	−0.422348	−	0.906434i	$-0.638794\pi$
$43$	3.17436	−	3.17436i	0.484086	−	0.484086i	0.906434	+	0.422348i	$0.138794\pi$
$44$			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	$-0.804483\pi$
$47$		−	7.90227i		−	1.15266i	0.817216	−	0.576332i	$-0.195517\pi$
$48$	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	$-0.673204\pi$
$53$		−	12.4574i		−	1.71115i	0.517680	−	0.855574i	$-0.326796\pi$
$54$	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	0.564300	−	0.825570i	$-0.309146\pi$
$59$	−2.00686	−	2.00686i	−0.261271	−	0.261271i	−0.825570	+	0.564300i	$0.809146\pi$
$60$	0.797792	−	1.53738i	0.102995	−	0.198475i
$61$	2.00335	+	2.00335i	0.256502	+	0.256502i	0.823630	−	0.567128i	$-0.191945\pi$
$61$	2.00335	+	2.00335i	0.256502	+	0.256502i	−0.567128	+	0.823630i	$0.691945\pi$
$62$	−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	$-0.803670\pi$
$67$		−	9.46914i		−	1.15684i	0.815739	−	0.578420i	$-0.196330\pi$
$68$	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	$0.248385\pi$
$71$			11.8558i			1.40702i	−0.710685	+	0.703511i	$0.751615\pi$
$72$	−2.95576	−	0.513330i	−0.348339	−	0.0604965i
$73$			4.40734i			0.515841i	0.966166	+	0.257920i	$0.0830372\pi$
$73$			4.40734i			0.515841i	−0.966166	+	0.257920i	$0.916963\pi$
$74$	−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	−0.997277	−	0.0737442i	$-0.976505\pi$
$79$	−8.20854	+	8.20854i	−0.923533	+	0.923533i	0.0737442	+	0.997277i	$0.476505\pi$
$80$	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	$-0.797181\pi$
$83$		−	10.8401i		−	1.18986i	0.803779	−	0.594928i	$-0.202819\pi$
$84$	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	0.0517620	−	0.998659i	$-0.483516\pi$
$89$	9.90966	−	9.90966i	1.05042	−	1.05042i	0.998659	−	0.0517620i	$-0.0164837\pi$
$90$	−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	−0.574479	−	0.818519i	$-0.694795\pi$
$97$	2.40351	−	2.40351i	0.244040	−	0.244040i	0.818519	+	0.574479i	$0.194795\pi$
$98$	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	0.682302	−	0.731070i	$-0.260979\pi$
$103$	−0.494936	−	0.494936i	−0.0487675	−	0.0487675i	−0.731070	+	0.682302i	$0.760979\pi$
$104$	−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	$0.00723272\pi$
$107$			0.470042i			0.0454406i	−0.999742	+	0.0227203i	$0.992767\pi$
$108$	4.13458	+	3.14726i	0.397850	+	0.302845i
$109$	−3.18770	+	3.18770i	−0.305327	+	0.305327i	−0.843094	−	0.537767i	$-0.819268\pi$
$109$	−3.18770	+	3.18770i	−0.305327	+	0.305327i	0.537767	+	0.843094i	$0.319268\pi$
$110$	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	−0.593368	−	0.804931i	$-0.702202\pi$
$113$	2.24895	−	2.24895i	0.211563	−	0.211563i	0.804931	+	0.593368i	$0.202202\pi$
$114$	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	−0.986582	−	0.163265i	$-0.947797\pi$
$131$	−9.42329	+	9.42329i	−0.823317	+	0.823317i	0.163265	+	0.986582i	$0.447797\pi$
$132$	−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	$0.213307\pi$
$137$			14.5392i			1.24217i	−0.783745	+	0.621083i	$0.786693\pi$
$138$	−4.79060	+	1.51726i	−0.407803	+	0.129158i
$139$			16.7132i			1.41760i	0.705410	+	0.708799i	$0.250763\pi$
$139$			16.7132i			1.41760i	−0.705410	+	0.708799i	$0.749237\pi$
$140$	−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	$-0.847780\pi$
$149$		−	11.2348i		−	0.920388i	0.887818	−	0.460194i	$-0.152220\pi$
$150$	−1.53738	−	0.797792i	−0.125526	−	0.0651394i
$151$			18.1204i			1.47462i	0.675557	+	0.737308i	$0.263903\pi$
$151$			18.1204i			1.47462i	−0.675557	+	0.737308i	$0.736097\pi$
$152$	−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	0.868581	−	0.495548i	$-0.165033\pi$
$163$	4.76257	+	4.76257i	0.373033	+	0.373033i	−0.495548	+	0.868581i	$0.665033\pi$
$164$		−	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	0.933243	−	0.359247i	$-0.116966\pi$
$167$	7.41766	+	7.41766i	0.573996	+	0.573996i	−0.359247	+	0.933243i	$0.616966\pi$
$168$	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	−0.397456	−	0.917621i	$-0.630107\pi$
$179$	6.95933	−	6.95933i	0.520165	−	0.520165i	0.917621	+	0.397456i	$0.130107\pi$
$180$	−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	0.767659	−	0.640858i	$-0.221421\pi$
$191$	1.75243	+	1.75243i	0.126801	+	0.126801i	−0.640858	+	0.767659i	$0.721421\pi$
$192$	−0.522966	−	1.65121i	−0.0377418	−	0.119166i
$193$	5.62234	−	5.62234i	0.404705	−	0.404705i	−0.475183	−	0.879887i	$-0.657618\pi$
$193$	5.62234	−	5.62234i	0.404705	−	0.404705i	0.879887	+	0.475183i	$0.157618\pi$
$194$		−	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	$0.219388\pi$
$197$			17.8517i			1.27188i	−0.771738	+	0.635941i	$0.780612\pi$
$198$	−1.56454	+	9.00861i	−0.111187	+	0.640214i
$199$	1.86996	+	1.86996i	0.132558	+	0.132558i	0.770273	−	0.637715i	$-0.220120\pi$
$199$	1.86996	+	1.86996i	0.132558	+	0.132558i	−0.637715	+	0.770273i	$0.720120\pi$
$200$	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	0.899975	−	0.435942i	$-0.143585\pi$
$227$	6.99137	+	6.99137i	0.464033	+	0.464033i	−0.435942	+	0.899975i	$0.643585\pi$
$228$	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	0.848231	−	0.529626i	$-0.177668\pi$
$239$	4.92552	+	4.92552i	0.318606	+	0.318606i	−0.529626	+	0.848231i	$0.677668\pi$
$240$	−1.53738	−	0.797792i	−0.0992373	−	0.0514973i
$241$	18.5971	−	18.5971i	1.19794	−	1.19794i	0.223163	−	0.974781i	$-0.428362\pi$
$241$	18.5971	−	18.5971i	1.19794	−	1.19794i	0.974781	−	0.223163i	$-0.0716383\pi$
$242$	−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	−0.998908	−	0.0467134i	$-0.985125\pi$
$251$	−15.0856	+	15.0856i	−0.952195	+	0.952195i	0.0467134	+	0.998908i	$0.485125\pi$
$252$	−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	0.634916	−	0.772581i	$-0.281035\pi$
$257$	−2.20693	−	2.20693i	−0.137665	−	0.137665i	−0.772581	+	0.634916i	$0.781035\pi$
$258$	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	$0.0506368\pi$
$269$			5.19624i			0.316820i	−0.987373	+	0.158410i	$0.949363\pi$
$270$	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	0.636109	−	0.771599i	$-0.280543\pi$
$277$	−2.25502	−	2.25502i	−0.135491	−	0.135491i	−0.771599	+	0.636109i	$0.780543\pi$
$278$	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	0.960992	−	0.276576i	$-0.0891999\pi$
$281$	11.4729	+	11.4729i	0.684416	+	0.684416i	−0.276576	+	0.960992i	$0.589200\pi$
$282$	12.1488	+	6.30437i	0.723448	+	0.375420i
$283$	−20.8649	−	20.8649i	−1.24029	−	1.24029i	−0.959881	−	0.280407i	$-0.909531\pi$
$283$	−20.8649	−	20.8649i	−1.24029	−	1.24029i	−0.280407	−	0.959881i	$-0.590469\pi$
$284$	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	$0.0778865\pi$
$293$			8.29342i			0.484507i	−0.970213	+	0.242253i	$0.922113\pi$
$294$	−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	$0.0643755\pi$
$307$			7.03890i			0.401731i	−0.979619	+	0.200866i	$0.935625\pi$
$308$			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	−0.842585	−	0.538564i	$-0.818967\pi$
$311$	−5.36146	+	5.36146i	−0.304020	+	0.304020i	0.538564	+	0.842585i	$0.318967\pi$
$312$	1.33517	−	0.422869i	0.0755891	−	0.0239402i
$313$	16.4404	−	16.4404i	0.929266	−	0.929266i	−0.0683922	−	0.997659i	$-0.521787\pi$
$313$	16.4404	−	16.4404i	0.929266	−	0.929266i	0.997659	+	0.0683922i	$0.0217869\pi$
$314$	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	−0.997827	−	0.0658890i	$-0.979012\pi$
$331$	−16.9551	+	16.9551i	−0.931938	+	0.931938i	0.0658890	+	0.997827i	$0.479012\pi$
$332$	−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	$-0.938204\pi$
$337$		−	7.08308i		−	0.385840i	0.981214	−	0.192920i	$-0.0617958\pi$
$338$	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	−0.891224	−	0.453563i	$-0.850153\pi$
$347$	−8.15272	+	8.15272i	−0.437661	+	0.437661i	0.453563	+	0.891224i	$0.350153\pi$
$348$	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	−0.696359	−	0.717694i	$-0.745198\pi$
$353$	0.400840	−	0.400840i	0.0213345	−	0.0213345i	0.717694	+	0.696359i	$0.245198\pi$
$354$	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	$0.382590\pi$
$359$			35.3458i			1.86548i	−0.360548	+	0.932741i	$0.617410\pi$
$360$	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	$-0.676460\pi$
$373$		−	32.8415i		−	1.70047i	0.526405	−	0.850234i	$-0.323540\pi$
$374$	−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	0.610739	−	0.791832i	$-0.290873\pi$
$383$	−3.54407	−	3.54407i	−0.181094	−	0.181094i	−0.791832	+	0.610739i	$0.790873\pi$
$384$	−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	0.997612	−	0.0690616i	$-0.0220005\pi$
$389$	18.3139	+	18.3139i	0.928551	+	0.928551i	−0.0690616	+	0.997612i	$0.522000\pi$
$390$	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	$0.00708345\pi$
$397$			0.886715i			0.0445029i	−0.999752	+	0.0222515i	$0.992917\pi$
$398$	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	0.0912209	−	0.995831i	$-0.470923\pi$
$401$	21.7682	−	21.7682i	1.08705	−	1.08705i	0.995831	−	0.0912209i	$-0.0290769\pi$
$402$	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	0.905359	−	0.424646i	$-0.139601\pi$
$409$	9.72183	+	9.72183i	0.480713	+	0.480713i	−0.424646	+	0.905359i	$0.639601\pi$
$410$	−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	$-0.656146\pi$
$419$		−	36.1112i		−	1.76415i	0.471109	−	0.882075i	$-0.343854\pi$
$420$	2.74634	−	5.29231i	0.134008	−	0.258238i
$421$	16.4019	+	16.4019i	0.799382	+	0.799382i	0.982998	−	0.183616i	$-0.0587803\pi$
$421$	16.4019	+	16.4019i	0.799382	+	0.799382i	−0.183616	+	0.982998i	$0.558780\pi$
$422$	−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	−0.117906	−	0.993025i	$-0.537618\pi$
$431$	18.1679	−	18.1679i	0.875118	−	0.875118i	0.993025	+	0.117906i	$0.0376183\pi$
$432$	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	0.999226	+	0.0393487i	$0.0125283\pi$
$439$	21.7605	+	21.7605i	1.03857	+	1.03857i	0.0393487	+	0.999226i	$0.487472\pi$
$440$		−	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	0.652506	−	0.757784i	$-0.273718\pi$
$449$	−2.23081	−	2.23081i	−0.105278	−	0.105278i	−0.757784	+	0.652506i	$0.773718\pi$
$450$	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	−0.669545	−	0.742771i	$-0.733511\pi$
$457$	1.56539	−	1.56539i	0.0732256	−	0.0732256i	0.742771	+	0.669545i	$0.233511\pi$
$458$	−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	0.827624	−	0.561283i	$-0.189692\pi$
$461$	5.71858	+	5.71858i	0.266341	+	0.266341i	−0.561283	+	0.827624i	$0.689692\pi$
$462$	8.37035	−	16.1300i	0.389424	−	0.750435i
$463$	−24.0600	+	24.0600i	−1.11816	+	1.11816i	−0.126154	+	0.992011i	$0.540263\pi$
$463$	−24.0600	+	24.0600i	−1.11816	+	1.11816i	−0.992011	+	0.126154i	$0.959737\pi$
$464$	−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	0.760430	−	0.649420i	$-0.224988\pi$
$467$	2.39895	+	2.39895i	0.111010	+	0.111010i	−0.649420	+	0.760430i	$0.724988\pi$
$468$	−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	0.379381	−	0.925240i	$-0.376137\pi$
$479$	−11.9467	−	11.9467i	−0.545859	−	0.545859i	−0.925240	+	0.379381i	$0.876137\pi$
$480$	−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	−0.943596	−	0.331100i	$-0.892580\pi$
$487$	−13.5166	+	13.5166i	−0.612496	+	0.612496i	0.331100	+	0.943596i	$0.392580\pi$
$488$		−	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	$0.167069\pi$
$491$			22.2070i			1.00219i	−0.865392	+	0.501095i	$0.832931\pi$
$492$	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	0.952852	−	0.303435i	$-0.0981336\pi$
$499$	14.5069	+	14.5069i	0.649417	+	0.649417i	−0.303435	+	0.952852i	$0.598134\pi$
$500$	−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	−0.916652	−	0.399686i	$-0.869119\pi$
$503$	−29.5224	−	29.5224i	−1.31634	−	1.31634i	−0.399686	−	0.916652i	$-0.630881\pi$
$504$	−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	−0.362557	−	0.931962i	$-0.618096\pi$
$523$	13.0218	−	13.0218i	0.569405	−	0.569405i	0.931962	+	0.362557i	$0.118096\pi$
$524$	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	−0.643185	−	0.765711i	$-0.722387\pi$
$541$	2.84989	−	2.84989i	0.122526	−	0.122526i	0.765711	+	0.643185i	$0.222387\pi$
$542$	−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	0.880269	+	0.474475i	$0.157362\pi$
$547$	31.6848	+	31.6848i	1.35474	+	1.35474i	0.474475	+	0.880269i	$0.342638\pi$
$548$	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	−0.340143	+	0.940374i	$0.610475\pi$
$557$	−30.2213	+	30.2213i	−1.28052	+	1.28052i	−0.940374	+	0.340143i	$0.889525\pi$
$558$	−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	0.444129	−	0.895963i	$-0.353513\pi$
$563$	−10.7209	−	10.7209i	−0.451833	−	0.451833i	−0.895963	+	0.444129i	$0.853513\pi$
$564$	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	−0.326179	+	0.945308i	$0.605761\pi$
$569$	−30.3297	+	30.3297i	−1.27149	+	1.27149i	−0.945308	+	0.326179i	$0.894239\pi$
$570$	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	−0.201487	−	0.979491i	$-0.564578\pi$
$577$	18.6883	−	18.6883i	0.778004	−	0.778004i	0.979491	+	0.201487i	$0.0645775\pi$
$578$	−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	−0.551631	−	0.834088i	$-0.685994\pi$
$587$	6.84341	−	6.84341i	0.282458	−	0.282458i	0.834088	+	0.551631i	$0.185994\pi$
$588$	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	$0.178119\pi$
$593$			25.8530i			1.06166i	−0.847480	+	0.530828i	$0.821881\pi$
$594$	−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	$-0.798694\pi$
$599$		−	28.9337i		−	1.18220i	0.806598	−	0.591100i	$-0.201306\pi$
$600$	−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	0.493401	−	0.869802i	$-0.335754\pi$
$607$	−9.27354	−	9.27354i	−0.376401	−	0.376401i	−0.869802	+	0.493401i	$0.835754\pi$
$608$			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	$0.0247973\pi$
$613$			3.85367i			0.155648i	−0.996967	+	0.0778241i	$0.975203\pi$
$614$	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	$0.0864599\pi$
$619$			13.3502i			0.536588i	−0.963337	+	0.268294i	$0.913540\pi$
$620$	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	−0.838676	−	0.544631i	$-0.816670\pi$
$631$	−34.7483	−	34.7483i	−1.38331	−	1.38331i	−0.544631	−	0.838676i	$-0.683330\pi$
$632$	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	$0.0353980\pi$
$641$			5.61943i			0.221954i	−0.993823	+	0.110977i	$0.964602\pi$
$642$	−0.722631	−	0.374995i	−0.0285200	−	0.0147999i
$643$	20.4006	+	20.4006i	0.804522	+	0.804522i	0.983799	−	0.179277i	$-0.0573757\pi$
$643$	20.4006	+	20.4006i	0.804522	+	0.804522i	−0.179277	+	0.983799i	$0.557376\pi$
$644$	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	0.0281258	−	0.999604i	$-0.491046\pi$
$647$	26.1415	−	26.1415i	1.02773	−	1.02773i	0.999604	−	0.0281258i	$-0.00895389\pi$
$648$	−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	−0.158788	−	0.987313i	$-0.550758\pi$
$653$	21.1720	−	21.1720i	0.828525	−	0.828525i	0.987313	+	0.158788i	$0.0507585\pi$
$654$	−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	0.494417	−	0.869225i	$-0.335382\pi$
$661$	−9.63627	−	9.63627i	−0.374807	−	0.374807i	−0.869225	+	0.494417i	$0.835382\pi$
$662$			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	0.957577	−	0.288178i	$-0.0930493\pi$
$683$	17.4943	+	17.4943i	0.669399	+	0.669399i	−0.288178	+	0.957577i	$0.593049\pi$
$684$	−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	$0.0324328\pi$
$691$			5.34751i			0.203429i	−0.994814	+	0.101714i	$0.967567\pi$
$692$		−	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	0.930714	−	0.365747i	$-0.119186\pi$
$701$	14.9583	+	14.9583i	0.564967	+	0.564967i	−0.365747	+	0.930714i	$0.619186\pi$
$702$	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	−0.152178	+	0.988353i	$0.548629\pi$
$709$	−30.3690	+	30.3690i	−1.14053	+	1.14053i	−0.988353	+	0.152178i	$0.951371\pi$
$710$		−	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	$-0.924434\pi$
$719$		−	12.6121i		−	0.470351i	0.971953	−	0.235175i	$-0.0755665\pi$
$720$	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	0.702328	−	0.711853i	$-0.252144\pi$
$727$	−0.256819	−	0.256819i	−0.00952488	−	0.00952488i	−0.711853	+	0.702328i	$0.752144\pi$
$728$	−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	$0.0712285\pi$
$733$			12.0159i			0.443816i	−0.975068	+	0.221908i	$0.928771\pi$
$734$	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	$-0.696244\pi$
$739$		−	44.3596i		−	1.63179i	0.578198	−	0.815896i	$-0.303756\pi$
$740$	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	$0.296897\pi$
$751$			44.0250i			1.60650i	−0.595645	+	0.803248i	$0.703103\pi$
$752$			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	−0.616550	−	0.787315i	$-0.711470\pi$
$757$	4.69837	−	4.69837i	0.170765	−	0.170765i	0.787315	+	0.616550i	$0.211470\pi$
$758$	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	0.980176	+	0.198128i	$0.0634863\pi$
$769$	32.6754	+	32.6754i	1.17830	+	1.17830i	0.198128	+	0.980176i	$0.436514\pi$
$770$	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	$0.318171\pi$
$773$			46.7775i			1.68247i	−0.540669	+	0.841235i	$0.681829\pi$
$774$	−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	−0.694211	−	0.719771i	$-0.744247\pi$
$797$	0.721582	−	0.721582i	0.0255597	−	0.0255597i	0.719771	+	0.694211i	$0.244247\pi$
$798$	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	−0.103994	−	0.994578i	$-0.533162\pi$
$809$	25.3308	−	25.3308i	0.890584	−	0.890584i	0.994578	+	0.103994i	$0.0331621\pi$
$810$	−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	$0.257272\pi$
$821$			41.4366i			1.44615i	−0.690770	+	0.723074i	$0.742728\pi$
$822$	−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	0.771775	−	0.635895i	$-0.219369\pi$
$827$	3.90758	+	3.90758i	0.135880	+	0.135880i	−0.635895	+	0.771775i	$0.719369\pi$
$828$	1.48930	−	8.57542i	0.0517569	−	0.298016i
$829$	−23.7888	−	23.7888i	−0.826221	−	0.826221i	0.160771	−	0.986992i	$-0.448602\pi$
$829$	−23.7888	−	23.7888i	−0.826221	−	0.826221i	−0.986992	+	0.160771i	$0.948602\pi$
$830$			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	0.727853	−	0.685734i	$-0.240519\pi$
$853$	1.23013	+	1.23013i	0.0421189	+	0.0421189i	−0.685734	+	0.727853i	$0.740519\pi$
$854$	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	0.641242	−	0.767338i	$-0.278419\pi$
$857$	−3.69140	−	3.69140i	−0.126096	−	0.126096i	−0.767338	+	0.641242i	$0.778419\pi$
$858$	−1.28883	−	4.06936i	−0.0439999	−	0.138925i
$859$	22.5969	−	22.5969i	0.770995	−	0.770995i	−0.207285	−	0.978281i	$-0.566463\pi$
$859$	22.5969	−	22.5969i	0.770995	−	0.770995i	0.978281	+	0.207285i	$0.0664629\pi$
$860$			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	$-0.941188\pi$
$863$		−	10.7938i		−	0.367427i	0.982980	−	0.183713i	$-0.0588118\pi$
$864$	−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	0.861633	−	0.507533i	$-0.169442\pi$
$883$	10.5222	+	10.5222i	0.354100	+	0.354100i	−0.507533	+	0.861633i	$0.669442\pi$
$884$		−	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	−0.841352	−	0.540487i	$-0.818240\pi$
$907$	−9.06099	+	9.06099i	−0.300865	+	0.300865i	0.540487	+	0.841352i	$0.318240\pi$
$908$	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	0.983135	−	0.182881i	$-0.0585423\pi$
$911$	24.1539	+	24.1539i	0.800254	+	0.800254i	−0.182881	+	0.983135i	$0.558542\pi$
$912$	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	−0.898111	−	0.439768i	$-0.855061\pi$
$919$	−40.5578	−	40.5578i	−1.33788	−	1.33788i	−0.439768	−	0.898111i	$-0.644939\pi$
$920$	−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	$0.321848\pi$
$941$			51.9908i			1.69485i	−0.530915	+	0.847425i	$0.678152\pi$
$942$	−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	0.998908	+	0.0467229i	$0.0148778\pi$
$947$	32.1776	+	32.1776i	1.04563	+	1.04563i	0.0467229	+	0.998908i	$0.485122\pi$
$948$	−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	−0.202900	+	0.979199i	$0.565037\pi$
$967$	−36.7593	+	36.7593i	−1.18210	+	1.18210i	−0.979199	+	0.202900i	$0.934963\pi$
$968$	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	$-0.994171\pi$
$971$		−	1.14129i		−	0.0366258i	0.999832	−	0.0183129i	$-0.00582950\pi$
$972$	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	−0.983248	−	0.182271i	$-0.941655\pi$
$977$	−25.0361	+	25.0361i	−0.800977	+	0.800977i	0.182271	+	0.983248i	$0.441655\pi$
$978$	−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	0.849554	−	0.527501i	$-0.176871\pi$
$991$	10.1383	+	10.1383i	0.322053	+	0.322053i	−0.527501	+	0.849554i	$0.676871\pi$
$992$	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	−0.873497	−	0.486830i	$-0.838153\pi$
$997$	−12.2091	+	12.2091i	−0.386667	+	0.386667i	0.486830	+	0.873497i	$0.338153\pi$
$998$	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.401.15	yes	40
3.2	odd	2	inner	1110.2.u.f.401.9	yes	40
37.6	odd	4	inner	1110.2.u.f.191.9	✓	40
111.80	even	4	inner	1110.2.u.f.191.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.f.191.9	✓	40	37.6	odd	4	inner
1110.2.u.f.191.15	yes	40	111.80	even	4	inner
1110.2.u.f.401.9	yes	40	3.2	odd	2	inner
1110.2.u.f.401.15	yes	40	1.1	even	1	trivial

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

Related objects

Downloads

Learn more