LMFDB - Embedded newform 690.2.i.f.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.16628 - 1.28054i) q^{3} -1.00000i q^{4} +(-1.31868 - 1.80585i) q^{5} +(1.73017 + 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.279562 + 2.98695i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.16628 - 1.28054i) q^{3} -1.00000i q^{4} +(-1.31868 - 1.80585i) q^{5} +(1.73017 + 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.279562 + 2.98695i) q^{9} +(2.20937 + 0.344476i) q^{10} +3.03746i q^{11} +(-1.28054 + 1.16628i) q^{12} +(-1.30218 + 1.30218i) q^{13} -2.03079 q^{14} +(-0.774498 + 3.79475i) q^{15} -1.00000 q^{16} +(0.0287275 - 0.0287275i) q^{17} +(-1.91441 - 2.30977i) q^{18} -2.41296i q^{19} +(-1.80585 + 1.31868i) q^{20} +(0.164069 - 3.51361i) q^{21} +(-2.14781 - 2.14781i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(0.0807905 - 1.73017i) q^{24} +(-1.52216 + 4.76267i) q^{25} -1.84156i q^{26} +(4.15095 - 3.12564i) q^{27} +(1.43599 - 1.43599i) q^{28} +8.32611 q^{29} +(-2.13564 - 3.23095i) q^{30} +10.8038 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.88958 - 3.54254i) q^{33} +0.0406269i q^{34} +(0.699560 - 4.48678i) q^{35} +(2.98695 + 0.279562i) q^{36} +(-0.399778 - 0.399778i) q^{37} +(1.70622 + 1.70622i) q^{38} +(3.18620 + 0.148780i) q^{39} +(0.344476 - 2.20937i) q^{40} +9.45696i q^{41} +(2.36848 + 2.60051i) q^{42} +(-0.108956 + 0.108956i) q^{43} +3.03746 q^{44} +(5.76262 - 3.43399i) q^{45} +1.00000 q^{46} +(0.341054 - 0.341054i) q^{47} +(1.16628 + 1.28054i) q^{48} -2.87588i q^{49} +(-2.29139 - 4.44404i) q^{50} +(-0.0702912 - 0.00328227i) q^{51} +(1.30218 + 1.30218i) q^{52} +(0.120552 + 0.120552i) q^{53} +(-0.725006 + 5.14532i) q^{54} +(5.48518 - 4.00544i) q^{55} +2.03079i q^{56} +(-3.08990 + 2.81420i) q^{57} +(-5.88745 + 5.88745i) q^{58} +2.10585 q^{59} +(3.79475 + 0.774498i) q^{60} +10.7626 q^{61} +(-7.63947 + 7.63947i) q^{62} +(-4.69066 + 3.88777i) q^{63} +1.00000i q^{64} +(4.06869 + 0.634373i) q^{65} +(-0.245398 + 5.25530i) q^{66} +(-6.68856 - 6.68856i) q^{67} +(-0.0287275 - 0.0287275i) q^{68} +(-0.0807905 + 1.73017i) q^{69} +(2.67797 + 3.66730i) q^{70} +5.69670i q^{71} +(-2.30977 + 1.91441i) q^{72} +(6.43032 - 6.43032i) q^{73} +0.565371 q^{74} +(7.87405 - 3.60545i) q^{75} -2.41296 q^{76} +(-4.36175 + 4.36175i) q^{77} +(-2.35818 + 2.14778i) q^{78} +5.14788i q^{79} +(1.31868 + 1.80585i) q^{80} +(-8.84369 - 1.67007i) q^{81} +(-6.68708 - 6.68708i) q^{82} +(-3.07224 - 3.07224i) q^{83} +(-3.51361 - 0.164069i) q^{84} +(-0.0897600 - 0.0139950i) q^{85} -0.154087i q^{86} +(-9.71061 - 10.6619i) q^{87} +(-2.14781 + 2.14781i) q^{88} +12.0540 q^{89} +(-1.64659 + 6.50298i) q^{90} -3.73982 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-12.6004 - 13.8347i) q^{93} +0.482323i q^{94} +(-4.35744 + 3.18193i) q^{95} +(-1.73017 - 0.0807905i) q^{96} +(7.38166 + 7.38166i) q^{97} +(2.03356 + 2.03356i) q^{98} +(-9.07272 - 0.849157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.16628	−	1.28054i	−0.673355	−	0.739320i
$3$	−1.16628	−	1.28054i	−0.673355	−	0.739320i
$4$		−	1.00000i		−	0.500000i
$5$	−1.31868	−	1.80585i	−0.589733	−	0.807599i
$5$	−1.31868	−	1.80585i	−0.589733	−	0.807599i
$6$	1.73017	+	0.0807905i	0.706337	+	0.0329826i
$7$	1.43599	+	1.43599i	0.542752	+	0.542752i	0.924335	−	0.381583i	$-0.124621\pi$
$7$	1.43599	+	1.43599i	0.542752	+	0.542752i	−0.381583	+	0.924335i	$0.624621\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.279562	+	2.98695i	−0.0931873	+	0.995649i
$10$	2.20937	+	0.344476i	0.698666	+	0.108933i
$11$			3.03746i			0.915827i	0.888997	+	0.457914i	$0.151403\pi$
$11$			3.03746i			0.915827i	−0.888997	+	0.457914i	$0.848597\pi$
$12$	−1.28054	+	1.16628i	−0.369660	+	0.336677i
$13$	−1.30218	+	1.30218i	−0.361159	+	0.361159i	−0.864239	−	0.503081i	$-0.832200\pi$
$13$	−1.30218	+	1.30218i	−0.361159	+	0.361159i	0.503081	+	0.864239i	$0.332200\pi$
$14$	−2.03079			−0.542752
$15$	−0.774498	+	3.79475i	−0.199974	+	0.979801i
$16$	−1.00000			−0.250000
$17$	0.0287275	−	0.0287275i	0.00696745	−	0.00696745i	−0.703614	−	0.710582i	$-0.748432\pi$
$17$	0.0287275	−	0.0287275i	0.00696745	−	0.00696745i	0.710582	+	0.703614i	$0.248432\pi$
$18$	−1.91441	−	2.30977i	−0.451231	−	0.544418i
$19$		−	2.41296i		−	0.553572i	−0.960932	−	0.276786i	$-0.910731\pi$
$19$		−	2.41296i		−	0.553572i	0.960932	−	0.276786i	$-0.0892693\pi$
$20$	−1.80585	+	1.31868i	−0.403799	+	0.294866i
$21$	0.164069	−	3.51361i	0.0358028	−	0.766732i
$22$	−2.14781	−	2.14781i	−0.457914	−	0.457914i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	0.0807905	−	1.73017i	0.0164913	−	0.353169i
$25$	−1.52216	+	4.76267i	−0.304431	+	0.952534i
$26$		−	1.84156i		−	0.361159i
$27$	4.15095	−	3.12564i	0.798851	−	0.601529i
$28$	1.43599	−	1.43599i	0.271376	−	0.271376i
$29$	8.32611			1.54612			0.773060	−	0.634333i	$-0.218725\pi$
$29$	8.32611			1.54612			0.773060	+	0.634333i	$0.218725\pi$
$30$	−2.13564	−	3.23095i	−0.389913	−	0.589888i
$31$	10.8038			1.94043			0.970214	−	0.242250i	$-0.0778854\pi$
$31$	10.8038			1.94043			0.970214	+	0.242250i	$0.0778854\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.88958	−	3.54254i	0.677089	−	0.616676i
$34$			0.0406269i			0.00696745i
$35$	0.699560	−	4.48678i	0.118247	−	0.758405i
$36$	2.98695	+	0.279562i	0.497824	+	0.0465937i
$37$	−0.399778	−	0.399778i	−0.0657230	−	0.0657230i	0.673481	−	0.739204i	$-0.264798\pi$
$37$	−0.399778	−	0.399778i	−0.0657230	−	0.0657230i	−0.739204	+	0.673481i	$0.764798\pi$
$38$	1.70622	+	1.70622i	0.276786	+	0.276786i
$39$	3.18620	+	0.148780i	0.510200	+	0.0238239i
$40$	0.344476	−	2.20937i	0.0544665	−	0.349333i
$41$			9.45696i			1.47693i	0.674293	+	0.738464i	$0.264449\pi$
$41$			9.45696i			1.47693i	−0.674293	+	0.738464i	$0.735551\pi$
$42$	2.36848	+	2.60051i	0.365465	+	0.401267i
$43$	−0.108956	+	0.108956i	−0.0166156	+	0.0166156i	−0.715366	−	0.698750i	$-0.753740\pi$
$43$	−0.108956	+	0.108956i	−0.0166156	+	0.0166156i	0.698750	+	0.715366i	$0.253740\pi$
$44$	3.03746			0.457914
$45$	5.76262	−	3.43399i	0.859040	−	0.511908i
$46$	1.00000			0.147442
$47$	0.341054	−	0.341054i	0.0497478	−	0.0497478i	−0.681795	−	0.731543i	$-0.738801\pi$
$47$	0.341054	−	0.341054i	0.0497478	−	0.0497478i	0.731543	+	0.681795i	$0.238801\pi$
$48$	1.16628	+	1.28054i	0.168339	+	0.184830i
$49$		−	2.87588i		−	0.410840i
$50$	−2.29139	−	4.44404i	−0.324052	−	0.628483i
$51$	−0.0702912	−	0.00328227i	−0.00984274	−	0.000459609i
$52$	1.30218	+	1.30218i	0.180579	+	0.180579i
$53$	0.120552	+	0.120552i	0.0165590	+	0.0165590i	0.715338	−	0.698779i	$-0.246273\pi$
$53$	0.120552	+	0.120552i	0.0165590	+	0.0165590i	−0.698779	+	0.715338i	$0.746273\pi$
$54$	−0.725006	+	5.14532i	−0.0986608	+	0.700190i
$55$	5.48518	−	4.00544i	0.739621	−	0.540093i
$56$			2.03079i			0.271376i
$57$	−3.08990	+	2.81420i	−0.409267	+	0.372750i
$58$	−5.88745	+	5.88745i	−0.773060	+	0.773060i
$59$	2.10585			0.274159			0.137079	−	0.990560i	$-0.456228\pi$
$59$	2.10585			0.274159			0.137079	+	0.990560i	$0.456228\pi$
$60$	3.79475	+	0.774498i	0.489901	+	0.0999872i
$61$	10.7626			1.37801			0.689003	−	0.724758i	$-0.258049\pi$
$61$	10.7626			1.37801			0.689003	+	0.724758i	$0.258049\pi$
$62$	−7.63947	+	7.63947i	−0.970214	+	0.970214i
$63$	−4.69066	+	3.88777i	−0.590968	+	0.489813i
$64$			1.00000i			0.125000i
$65$	4.06869	+	0.634373i	0.504659	+	0.0786843i
$66$	−0.245398	+	5.25530i	−0.0302064	+	0.646883i
$67$	−6.68856	−	6.68856i	−0.817137	−	0.817137i	0.168555	−	0.985692i	$-0.446090\pi$
$67$	−6.68856	−	6.68856i	−0.817137	−	0.817137i	−0.985692	+	0.168555i	$0.946090\pi$
$68$	−0.0287275	−	0.0287275i	−0.00348373	−	0.00348373i
$69$	−0.0807905	+	1.73017i	−0.00972604	+	0.208287i
$70$	2.67797	+	3.66730i	0.320079	+	0.438326i
$71$			5.69670i			0.676074i	0.941133	+	0.338037i	$0.109763\pi$
$71$			5.69670i			0.676074i	−0.941133	+	0.338037i	$0.890237\pi$
$72$	−2.30977	+	1.91441i	−0.272209	+	0.225615i
$73$	6.43032	−	6.43032i	0.752612	−	0.752612i	−0.222354	−	0.974966i	$-0.571374\pi$
$73$	6.43032	−	6.43032i	0.752612	−	0.752612i	0.974966	+	0.222354i	$0.0713742\pi$
$74$	0.565371			0.0657230
$75$	7.87405	−	3.60545i	0.909217	−	0.416321i
$76$	−2.41296			−0.276786
$77$	−4.36175	+	4.36175i	−0.497067	+	0.497067i
$78$	−2.35818	+	2.14778i	−0.267012	+	0.243188i
$79$			5.14788i			0.579182i	0.957150	+	0.289591i	$0.0935193\pi$
$79$			5.14788i			0.579182i	−0.957150	+	0.289591i	$0.906481\pi$
$80$	1.31868	+	1.80585i	0.147433	+	0.201900i
$81$	−8.84369	−	1.67007i	−0.982632	−	0.185564i
$82$	−6.68708	−	6.68708i	−0.738464	−	0.738464i
$83$	−3.07224	−	3.07224i	−0.337223	−	0.337223i	0.518098	−	0.855321i	$-0.326640\pi$
$83$	−3.07224	−	3.07224i	−0.337223	−	0.337223i	−0.855321	+	0.518098i	$0.826640\pi$
$84$	−3.51361	−	0.164069i	−0.383366	−	0.0179014i
$85$	−0.0897600	−	0.0139950i	−0.00973584	−	0.00151797i
$86$		−	0.154087i		−	0.0166156i
$87$	−9.71061	−	10.6619i	−1.04109	−	1.14308i
$88$	−2.14781	+	2.14781i	−0.228957	+	0.228957i
$89$	12.0540			1.27773			0.638863	−	0.769320i	$-0.279405\pi$
$89$	12.0540			1.27773			0.638863	+	0.769320i	$0.279405\pi$
$90$	−1.64659	+	6.50298i	−0.173566	+	0.685474i
$91$	−3.73982			−0.392040
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	−12.6004	−	13.8347i	−1.30660	−	1.43460i
$94$			0.482323i			0.0497478i
$95$	−4.35744	+	3.18193i	−0.447064	+	0.326459i
$96$	−1.73017	−	0.0807905i	−0.176584	−	0.00824565i
$97$	7.38166	+	7.38166i	0.749494	+	0.749494i	0.974384	−	0.224890i	$-0.0722023\pi$
$97$	7.38166	+	7.38166i	0.749494	+	0.749494i	−0.224890	+	0.974384i	$0.572202\pi$
$98$	2.03356	+	2.03356i	0.205420	+	0.205420i
$99$	−9.07272	−	0.849157i	−0.911842	−	0.0853435i
$100$	4.76267	+	1.52216i	0.476267	+	0.152216i
$101$			15.7509i			1.56727i	0.621222	+	0.783635i	$0.286637\pi$
$101$			15.7509i			1.56727i	−0.621222	+	0.783635i	$0.713363\pi$
$102$	0.0520243	−	0.0473825i	0.00515117	−	0.00469157i
$103$	−9.94078	+	9.94078i	−0.979494	+	0.979494i	−0.999794	−	0.0202999i	$-0.993538\pi$
$103$	−9.94078	+	9.94078i	−0.979494	+	0.979494i	0.0202999	+	0.999794i	$0.493538\pi$
$104$	−1.84156			−0.180579
$105$	−6.56139	+	4.33705i	−0.640326	+	0.423253i
$106$	−0.170486			−0.0165590
$107$	8.28163	−	8.28163i	0.800616	−	0.800616i	−0.182576	−	0.983192i	$-0.558444\pi$
$107$	8.28163	−	8.28163i	0.800616	−	0.800616i	0.983192	+	0.182576i	$0.0584436\pi$
$108$	−3.12564	−	4.15095i	−0.300765	−	0.399425i
$109$		−	5.16166i		−	0.494398i	−0.968965	−	0.247199i	$-0.920490\pi$
$109$		−	5.16166i		−	0.494398i	0.968965	−	0.247199i	$-0.0795101\pi$
$110$	−1.04633	+	6.71088i	−0.0997638	+	0.639857i
$111$	−0.0456766	+	0.978185i	−0.00433543	+	0.0928452i
$112$	−1.43599	−	1.43599i	−0.135688	−	0.135688i
$113$	10.2943	+	10.2943i	0.968407	+	0.968407i	0.999516	−	0.0311086i	$-0.00990378\pi$
$113$	10.2943	+	10.2943i	0.968407	+	0.968407i	−0.0311086	+	0.999516i	$0.509904\pi$
$114$	0.194945	−	4.17483i	0.0182582	−	0.391008i
$115$	−0.344476	+	2.20937i	−0.0321226	+	0.206025i
$116$		−	8.32611i		−	0.773060i
$117$	−3.52549	−	4.25357i	−0.325932	−	0.393243i
$118$	−1.48906	+	1.48906i	−0.137079	+	0.137079i
$119$	0.0825048			0.00756320
$120$	−3.23095	+	2.13564i	−0.294944	+	0.194957i
$121$	1.77386			0.161260
$122$	−7.61029	+	7.61029i	−0.689003	+	0.689003i
$123$	12.1100	−	11.0295i	1.09192	−	0.994496i
$124$		−	10.8038i		−	0.970214i
$125$	10.6079	−	3.53167i	0.948798	−	0.315882i
$126$	0.567733	−	6.06587i	0.0505776	−	0.540390i
$127$	−6.32534	−	6.32534i	−0.561283	−	0.561283i	0.368389	−	0.929672i	$-0.379910\pi$
$127$	−6.32534	−	6.32534i	−0.561283	−	0.561283i	−0.929672	+	0.368389i	$0.879910\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.266596	+	0.0124488i	0.0234725	+	0.00109605i
$130$	−3.32557	+	2.42843i	−0.291671	+	0.212987i
$131$		−	8.57676i		−	0.749355i	−0.927155	−	0.374677i	$-0.877753\pi$
$131$		−	8.57676i		−	0.749355i	0.927155	−	0.374677i	$-0.122247\pi$
$132$	−3.54254	−	3.88958i	−0.308338	−	0.338545i
$133$	3.46499	−	3.46499i	0.300452	−	0.300452i
$134$	9.45905			0.817137
$135$	−11.1182	−	3.37425i	−0.956902	−	0.290409i
$136$	0.0406269			0.00348373
$137$	−11.6408	+	11.6408i	−0.994543	+	0.994543i	−0.999985	−	0.00544239i	$-0.998268\pi$
$137$	−11.6408	+	11.6408i	−0.994543	+	0.994543i	0.00544239	+	0.999985i	$0.498268\pi$
$138$	−1.16628	−	1.28054i	−0.0992807	−	0.109007i
$139$		−	0.224301i		−	0.0190250i	−0.999955	−	0.00951249i	$-0.996972\pi$
$139$		−	0.224301i		−	0.0190250i	0.999955	−	0.00951249i	$-0.00302797\pi$
$140$	−4.48678	−	0.699560i	−0.379202	−	0.0591236i
$141$	−0.834498	−	0.0389671i	−0.0702774	−	0.00328162i
$142$	−4.02818	−	4.02818i	−0.338037	−	0.338037i
$143$	−3.95530	−	3.95530i	−0.330759	−	0.330759i
$144$	0.279562	−	2.98695i	0.0232968	−	0.248912i
$145$	−10.9795	−	15.0357i	−0.911797	−	1.24864i
$146$			9.09384i			0.752612i
$147$	−3.68268	+	3.35409i	−0.303742	+	0.276641i
$148$	−0.399778	+	0.399778i	−0.0328615	+	0.0328615i
$149$	5.49620			0.450266			0.225133	−	0.974328i	$-0.427718\pi$
$149$	5.49620			0.450266			0.225133	+	0.974328i	$0.427718\pi$
$150$	−3.01836	+	8.11724i	−0.246448	+	0.662769i
$151$	−9.44824			−0.768887			−0.384443	−	0.923149i	$-0.625607\pi$
$151$	−9.44824			−0.768887			−0.384443	+	0.923149i	$0.625607\pi$
$152$	1.70622	−	1.70622i	0.138393	−	0.138393i
$153$	0.0777765	+	0.0938387i	0.00628785	+	0.00758641i
$154$		−	6.16844i		−	0.497067i
$155$	−14.2468	−	19.5101i	−1.14433	−	1.56709i
$156$	0.148780	−	3.18620i	0.0119120	−	0.255100i
$157$	15.6517	+	15.6517i	1.24914	+	1.24914i	0.956100	+	0.293039i	$0.0946667\pi$
$157$	15.6517	+	15.6517i	1.24914	+	1.24914i	0.293039	+	0.956100i	$0.405333\pi$
$158$	−3.64010	−	3.64010i	−0.289591	−	0.289591i
$159$	0.0137736	−	0.294969i	0.00109232	−	0.0233925i
$160$	−2.20937	−	0.344476i	−0.174666	−	0.0272333i
$161$		−	2.03079i		−	0.160049i
$162$	7.43435	−	5.07251i	0.584098	−	0.398534i
$163$	2.69934	−	2.69934i	0.211429	−	0.211429i	−0.593446	−	0.804874i	$-0.702233\pi$
$163$	2.69934	−	2.69934i	0.211429	−	0.211429i	0.804874	+	0.593446i	$0.202233\pi$
$164$	9.45696			0.738464
$165$	−11.5264	−	2.35250i	−0.897329	−	0.183142i
$166$	4.34481			0.337223
$167$	−4.99243	+	4.99243i	−0.386326	+	0.386326i	−0.873375	−	0.487049i	$-0.838073\pi$
$167$	−4.99243	+	4.99243i	−0.386326	+	0.386326i	0.487049	+	0.873375i	$0.338073\pi$
$168$	2.60051	−	2.36848i	0.200634	−	0.182732i
$169$			9.60867i			0.739129i
$170$	0.0733659	−	0.0535739i	0.00562690	−	0.00410893i
$171$	7.20739	+	0.674573i	0.551163	+	0.0515859i
$172$	0.108956	+	0.108956i	0.00830781	+	0.00830781i
$173$	5.07836	+	5.07836i	0.386101	+	0.386101i	0.873294	−	0.487193i	$-0.161979\pi$
$173$	5.07836	+	5.07836i	0.386101	+	0.386101i	−0.487193	+	0.873294i	$0.661979\pi$
$174$	14.4055	+	0.672671i	1.09208	+	0.0509950i
$175$	−9.02493	+	4.65334i	−0.682221	+	0.351760i
$176$		−	3.03746i		−	0.228957i
$177$	−2.45602	−	2.69663i	−0.184606	−	0.202691i
$178$	−8.52350	+	8.52350i	−0.638863	+	0.638863i
$179$	9.09915			0.680103			0.340051	−	0.940407i	$-0.389556\pi$
$179$	9.09915			0.680103			0.340051	+	0.940407i	$0.389556\pi$
$180$	−3.43399	−	5.76262i	−0.255954	−	0.429520i
$181$	−25.4910			−1.89473			−0.947367	−	0.320150i	$-0.896267\pi$
$181$	−25.4910			−1.89473			−0.947367	+	0.320150i	$0.896267\pi$
$182$	2.64445	−	2.64445i	0.196020	−	0.196020i
$183$	−12.5522	−	13.7819i	−0.927887	−	1.01879i
$184$		−	1.00000i		−	0.0737210i
$185$	−0.194757	+	1.24912i	−0.0143188	+	0.0918368i
$186$	18.6924	+	0.872848i	1.37060	+	0.0640004i
$187$	0.0872586	+	0.0872586i	0.00638098	+	0.00638098i
$188$	−0.341054	−	0.341054i	−0.0248739	−	0.0248739i
$189$	10.4491	+	1.47234i	0.760059	+	0.107097i
$190$	0.831209	−	5.33114i	0.0603023	−	0.386762i
$191$		−	16.0457i		−	1.16103i	−0.814250	−	0.580514i	$-0.802851\pi$
$191$		−	16.0457i		−	1.16103i	0.814250	−	0.580514i	$-0.197149\pi$
$192$	1.28054	−	1.16628i	0.0924150	−	0.0841693i
$193$	−5.17234	+	5.17234i	−0.372313	+	0.372313i	−0.868319	−	0.496006i	$-0.834799\pi$
$193$	−5.17234	+	5.17234i	−0.372313	+	0.372313i	0.496006	+	0.868319i	$0.334799\pi$
$194$	−10.4392			−0.749494
$195$	−3.93291	−	5.94997i	−0.281641	−	0.426086i
$196$	−2.87588			−0.205420
$197$	−14.5337	+	14.5337i	−1.03548	+	1.03548i	−0.0361361	+	0.999347i	$0.511505\pi$
$197$	−14.5337	+	14.5337i	−1.03548	+	1.03548i	−0.999347	+	0.0361361i	$0.988495\pi$
$198$	7.01582	−	5.81493i	0.498593	−	0.413249i
$199$			12.8549i			0.911262i	0.890169	+	0.455631i	$0.150586\pi$
$199$			12.8549i			0.911262i	−0.890169	+	0.455631i	$0.849414\pi$
$200$	−4.44404	+	2.29139i	−0.314241	+	0.162026i
$201$	−0.764202	+	16.3657i	−0.0539026	+	1.15435i
$202$	−11.1375	−	11.1375i	−0.783635	−	0.783635i
$203$	11.9562	+	11.9562i	0.839160	+	0.839160i
$204$	−0.00328227	+	0.0702912i	−0.000229805	+	0.00492137i
$205$	17.0778	−	12.4707i	1.19277	−	0.870993i
$206$		−	14.0584i		−	0.979494i
$207$	2.30977	−	1.91441i	0.160540	−	0.133061i
$208$	1.30218	−	1.30218i	0.0902897	−	0.0902897i
$209$	7.32927			0.506976
$210$	1.57284	−	7.70636i	0.108537	−	0.531789i
$211$	−24.8100			−1.70799			−0.853996	−	0.520280i	$-0.825828\pi$
$211$	−24.8100			−1.70799			−0.853996	+	0.520280i	$0.825828\pi$
$212$	0.120552	−	0.120552i	0.00827952	−	0.00827952i
$213$	7.29485	−	6.64397i	0.499835	−	0.455238i
$214$			11.7120i			0.800616i
$215$	0.340436	+	0.0530793i	0.0232175	+	0.00361998i
$216$	5.14532	+	0.725006i	0.350095	+	0.0493304i
$217$	15.5142	+	15.5142i	1.05317	+	1.05317i
$218$	3.64985	+	3.64985i	0.247199	+	0.247199i
$219$	−15.7338	−	0.734696i	−1.06320	−	0.0496462i
$220$	−4.00544	−	5.48518i	−0.270047	−	0.369810i
$221$			0.0748167i			0.00503271i
$222$	−0.659383	−	0.723980i	−0.0442549	−	0.0485903i
$223$	6.63422	−	6.63422i	0.444260	−	0.444260i	−0.449181	−	0.893441i	$-0.648284\pi$
$223$	6.63422	−	6.63422i	0.444260	−	0.444260i	0.893441	+	0.449181i	$0.148284\pi$
$224$	2.03079			0.135688
$225$	−13.8003	−	5.87806i	−0.920020	−	0.391870i
$226$	−14.5584			−0.968407
$227$	4.95555	−	4.95555i	0.328911	−	0.328911i	−0.523261	−	0.852172i	$-0.675285\pi$
$227$	4.95555	−	4.95555i	0.328911	−	0.328911i	0.852172	+	0.523261i	$0.175285\pi$
$228$	2.81420	+	3.08990i	0.186375	+	0.204633i
$229$		−	11.2747i		−	0.745053i	−0.928021	−	0.372527i	$-0.878491\pi$
$229$		−	11.2747i		−	0.745053i	0.928021	−	0.372527i	$-0.121509\pi$
$230$	−1.31868	−	1.80585i	−0.0869513	−	0.119074i
$231$	10.6724	+	0.498352i	0.702194	+	0.0327891i
$232$	5.88745	+	5.88745i	0.386530	+	0.386530i
$233$	−12.5504	−	12.5504i	−0.822206	−	0.822206i	0.164218	−	0.986424i	$-0.447490\pi$
$233$	−12.5504	−	12.5504i	−0.822206	−	0.822206i	−0.986424	+	0.164218i	$0.947490\pi$
$234$	5.50063	+	0.514829i	0.359587	+	0.0336554i
$235$	−1.06563	−	0.166149i	−0.0695141	−	0.0108384i
$236$		−	2.10585i		−	0.137079i
$237$	6.59207	−	6.00390i	0.428201	−	0.389995i
$238$	−0.0583397	+	0.0583397i	−0.00378160	+	0.00378160i
$239$	−1.23240			−0.0797173			−0.0398586	−	0.999205i	$-0.512691\pi$
$239$	−1.23240			−0.0797173			−0.0398586	+	0.999205i	$0.512691\pi$
$240$	0.774498	−	3.79475i	0.0499936	−	0.244950i
$241$	−10.0383			−0.646625			−0.323312	−	0.946292i	$-0.604796\pi$
$241$	−10.0383			−0.646625			−0.323312	+	0.946292i	$0.604796\pi$
$242$	−1.25431	+	1.25431i	−0.0806301	+	0.0806301i
$243$	8.17566	+	13.2725i	0.524469	+	0.851430i
$244$		−	10.7626i		−	0.689003i
$245$	−5.19340	+	3.79237i	−0.331794	+	0.242286i
$246$	−0.764033	+	16.3621i	−0.0487129	+	1.04321i
$247$	3.14211	+	3.14211i	0.199927	+	0.199927i
$248$	7.63947	+	7.63947i	0.485107	+	0.485107i
$249$	−0.351019	+	7.51724i	−0.0222450	+	0.476386i
$250$	−5.00364	+	9.99818i	−0.316458	+	0.632340i
$251$		−	11.1326i		−	0.702686i	−0.936247	−	0.351343i	$-0.885725\pi$
$251$		−	11.1326i		−	0.702686i	0.936247	−	0.351343i	$-0.114275\pi$
$252$	3.88777	+	4.69066i	0.244906	+	0.295484i
$253$	2.14781	−	2.14781i	0.135031	−	0.135031i
$254$	8.94538			0.561283
$255$	0.0867645	+	0.131263i	0.00543340	+	0.00822003i
$256$	1.00000			0.0625000
$257$	−0.426761	+	0.426761i	−0.0266206	+	0.0266206i	−0.720292	−	0.693671i	$-0.755992\pi$
$257$	−0.426761	+	0.426761i	−0.0266206	+	0.0266206i	0.693671	+	0.720292i	$0.255992\pi$
$258$	−0.197314	+	0.179709i	−0.0122843	+	0.0111882i
$259$		−	1.14815i		−	0.0713426i
$260$	0.634373	−	4.06869i	0.0393421	−	0.252329i
$261$	−2.32766	+	24.8696i	−0.144079	+	1.53939i
$262$	6.06468	+	6.06468i	0.374677	+	0.374677i
$263$	−13.9902	−	13.9902i	−0.862670	−	0.862670i	0.128977	−	0.991648i	$-0.458831\pi$
$263$	−13.9902	−	13.9902i	−0.862670	−	0.862670i	−0.991648	+	0.128977i	$0.958831\pi$
$264$	5.25530	+	0.245398i	0.323441	+	0.0151032i
$265$	0.0587283	−	0.376667i	0.00360765	−	0.0231385i
$266$			4.90023i			0.300452i
$267$	−14.0584	−	15.4357i	−0.860363	−	0.944649i
$268$	−6.68856	+	6.68856i	−0.408569	+	0.408569i
$269$	15.5476			0.947954			0.473977	−	0.880537i	$-0.342818\pi$
$269$	15.5476			0.947954			0.473977	+	0.880537i	$0.342818\pi$
$270$	10.2477	−	5.47580i	0.623656	−	0.333247i
$271$	3.09413			0.187955			0.0939775	−	0.995574i	$-0.470042\pi$
$271$	3.09413			0.187955			0.0939775	+	0.995574i	$0.470042\pi$
$272$	−0.0287275	+	0.0287275i	−0.00174186	+	0.00174186i
$273$	4.36169	+	4.78898i	0.263982	+	0.289843i
$274$		−	16.4626i		−	0.994543i
$275$	−14.4664	−	4.62348i	−0.872357	−	0.278806i
$276$	1.73017	+	0.0807905i	0.104144	+	0.00486302i
$277$	4.78402	+	4.78402i	0.287444	+	0.287444i	0.836069	−	0.548625i	$-0.184849\pi$
$277$	4.78402	+	4.78402i	0.287444	+	0.287444i	−0.548625	+	0.836069i	$0.684849\pi$
$278$	0.158605	+	0.158605i	0.00951249	+	0.00951249i
$279$	−3.02034	+	32.2705i	−0.180823	+	1.93198i
$280$	3.66730	−	2.67797i	0.219163	−	0.160039i
$281$			6.07800i			0.362583i	0.983429	+	0.181292i	$0.0580278\pi$
$281$			6.07800i			0.362583i	−0.983429	+	0.181292i	$0.941972\pi$
$282$	0.617633	−	0.562525i	0.0367795	−	0.0334979i
$283$	1.63214	−	1.63214i	0.0970206	−	0.0970206i	−0.656931	−	0.753951i	$-0.728146\pi$
$283$	1.63214	−	1.63214i	0.0970206	−	0.0970206i	0.753951	+	0.656931i	$0.228146\pi$
$284$	5.69670			0.338037
$285$	9.15660	+	1.86884i	0.542390	+	0.110700i
$286$	5.59364			0.330759
$287$	−13.5801	+	13.5801i	−0.801606	+	0.801606i
$288$	1.91441	+	2.30977i	0.112808	+	0.136104i
$289$			16.9983i			0.999903i
$290$	18.3955	+	2.86815i	1.08022	+	0.168423i
$291$	0.843392	−	18.0616i	0.0494405	−	1.05879i
$292$	−6.43032	−	6.43032i	−0.376306	−	0.376306i
$293$	−9.90593	−	9.90593i	−0.578711	−	0.578711i	0.355837	−	0.934548i	$-0.384196\pi$
$293$	−9.90593	−	9.90593i	−0.578711	−	0.578711i	−0.934548	+	0.355837i	$0.884196\pi$
$294$	0.232344	−	4.97575i	0.0135506	−	0.290192i
$295$	−2.77695	−	3.80284i	−0.161680	−	0.221410i
$296$		−	0.565371i		−	0.0328615i
$297$	9.49399	+	12.6083i	0.550897	+	0.731609i
$298$	−3.88640	+	3.88640i	−0.225133	+	0.225133i
$299$	1.84156			0.106500
$300$	−3.60545	−	7.87405i	−0.208161	−	0.454609i
$301$	−0.312919			−0.0180363
$302$	6.68091	−	6.68091i	0.384443	−	0.384443i
$303$	20.1696	−	18.3700i	1.15871	−	1.05533i
$304$			2.41296i			0.138393i
$305$	−14.1924	−	19.4355i	−0.812655	−	1.11288i
$306$	−0.121350	−	0.0113577i	−0.00693713	−	0.000649278i
$307$	22.4079	+	22.4079i	1.27889	+	1.27889i	0.941292	+	0.337594i	$0.109613\pi$
$307$	22.4079	+	22.4079i	1.27889	+	1.27889i	0.337594	+	0.941292i	$0.390387\pi$
$308$	4.36175	+	4.36175i	0.248534	+	0.248534i
$309$	24.3233	+	1.13578i	1.38371	+	0.0646125i
$310$	23.8697	+	3.72167i	1.35571	+	0.211377i
$311$			22.1020i			1.25329i	0.779304	+	0.626646i	$0.215573\pi$
$311$			22.1020i			1.25329i	−0.779304	+	0.626646i	$0.784427\pi$
$312$	2.14778	+	2.35818i	0.121594	+	0.133506i
$313$	3.23645	−	3.23645i	0.182935	−	0.182935i	−0.609698	−	0.792633i	$-0.708709\pi$
$313$	3.23645	−	3.23645i	0.182935	−	0.182935i	0.792633	+	0.609698i	$0.208709\pi$
$314$	−22.1348			−1.24914
$315$	13.2062	+	3.34388i	0.744085	+	0.188406i
$316$	5.14788			0.289591
$317$	11.0713	−	11.0713i	0.621826	−	0.621826i	−0.324172	−	0.945998i	$-0.605086\pi$
$317$	11.0713	−	11.0713i	0.621826	−	0.621826i	0.945998	+	0.324172i	$0.105086\pi$
$318$	0.198835	+	0.218314i	0.0111501	+	0.0122424i
$319$			25.2902i			1.41598i
$320$	1.80585	−	1.31868i	0.100950	−	0.0737166i
$321$	−20.2637	−	0.946218i	−1.13101	−	0.0528128i
$322$	1.43599	+	1.43599i	0.0800244	+	0.0800244i
$323$	−0.0693185	−	0.0693185i	−0.00385699	−	0.00385699i
$324$	−1.67007	+	8.84369i	−0.0927818	+	0.491316i
$325$	−4.21973	−	8.18396i	−0.234068	−	0.453964i
$326$			3.81744i			0.211429i
$327$	−6.60971	+	6.01997i	−0.365518	+	0.332905i
$328$	−6.68708	+	6.68708i	−0.369232	+	0.369232i
$329$	0.979497			0.0540014
$330$	9.81386	−	6.48692i	0.540235	−	0.357093i
$331$	27.5838			1.51614			0.758070	−	0.652173i	$-0.226142\pi$
$331$	27.5838			1.51614			0.758070	+	0.652173i	$0.226142\pi$
$332$	−3.07224	+	3.07224i	−0.168611	+	0.168611i
$333$	1.30588	−	1.08235i	0.0715616	−	0.0593125i
$334$		−	7.06036i		−	0.386326i
$335$	−3.25842	+	20.8986i	−0.178026	+	1.14181i
$336$	−0.164069	+	3.51361i	−0.00895069	+	0.191683i
$337$	16.5924	+	16.5924i	0.903845	+	0.903845i	0.995766	−	0.0919212i	$-0.0293008\pi$
$337$	16.5924	+	16.5924i	0.903845	+	0.903845i	−0.0919212	+	0.995766i	$0.529301\pi$
$338$	−6.79436	−	6.79436i	−0.369564	−	0.369564i
$339$	1.17618	−	25.1884i	0.0638812	−	1.36804i
$340$	−0.0139950	+	0.0897600i	−0.000758986	+	0.00486792i
$341$			32.8162i			1.77710i
$342$	−5.57339	+	4.61940i	−0.301375	+	0.249789i
$343$	14.1816	−	14.1816i	0.765737	−	0.765737i
$344$	−0.154087			−0.00830781
$345$	3.23095	−	2.13564i	0.173948	−	0.114979i
$346$	−7.18189			−0.386101
$347$	−9.47770	+	9.47770i	−0.508789	+	0.508789i	−0.914155	−	0.405365i	$-0.867144\pi$
$347$	−9.47770	+	9.47770i	−0.508789	+	0.508789i	0.405365	+	0.914155i	$0.367144\pi$
$348$	−10.6619	+	9.71061i	−0.571538	+	0.520543i
$349$		−	17.3941i		−	0.931085i	−0.885025	−	0.465543i	$-0.845859\pi$
$349$		−	17.3941i		−	0.931085i	0.885025	−	0.465543i	$-0.154141\pi$
$350$	3.09118	−	9.67200i	0.165231	−	0.516990i
$351$	−1.33514	+	9.47540i	−0.0712644	+	0.505760i
$352$	2.14781	+	2.14781i	0.114478	+	0.114478i
$353$	21.9958	+	21.9958i	1.17072	+	1.17072i	0.982038	+	0.188681i	$0.0604212\pi$
$353$	21.9958	+	21.9958i	1.17072	+	1.17072i	0.188681	+	0.982038i	$0.439579\pi$
$354$	3.64347	+	0.170133i	0.193648	+	0.00904247i
$355$	10.2874	−	7.51214i	0.545997	−	0.398703i
$356$		−	12.0540i		−	0.638863i
$357$	−0.0962240	−	0.105651i	−0.00509271	−	0.00559162i
$358$	−6.43407	+	6.43407i	−0.340051	+	0.340051i
$359$	−23.7395			−1.25292			−0.626461	−	0.779453i	$-0.715497\pi$
$359$	−23.7395			−1.25292			−0.626461	+	0.779453i	$0.715497\pi$
$360$	6.50298	+	1.64659i	0.342737	+	0.0867829i
$361$	13.1776			0.693558
$362$	18.0249	−	18.0249i	0.947367	−	0.947367i
$363$	−2.06883	−	2.27150i	−0.108585	−	0.119223i
$364$			3.73982i			0.196020i
$365$	−20.0917	−	3.13261i	−1.05165	−	0.163969i
$366$	18.6210	+	0.869514i	0.973337	+	0.0454502i
$367$	20.2624	+	20.2624i	1.05769	+	1.05769i	0.998231	+	0.0594601i	$0.0189379\pi$
$367$	20.2624	+	20.2624i	1.05769	+	1.05769i	0.0594601	+	0.998231i	$0.481062\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	−28.2474	−	2.64381i	−1.47050	−	0.137631i
$370$	−0.745544	−	1.02097i	−0.0387590	−	0.0530778i
$371$			0.346221i			0.0179749i
$372$	−13.8347	+	12.6004i	−0.717298	+	0.653298i
$373$	17.2579	−	17.2579i	0.893581	−	0.893581i	−0.101277	−	0.994858i	$-0.532293\pi$
$373$	17.2579	−	17.2579i	0.893581	−	0.893581i	0.994858	+	0.101277i	$0.0322930\pi$
$374$	−0.123402			−0.00638098
$375$	−16.8943	−	9.46488i	−0.872416	−	0.488764i
$376$	0.482323			0.0248739
$377$	−10.8421	+	10.8421i	−0.558395	+	0.558395i
$378$	−8.42972	+	6.34752i	−0.433578	+	0.326481i
$379$			15.5004i			0.796200i	0.917342	+	0.398100i	$0.130330\pi$
$379$			15.5004i			0.796200i	−0.917342	+	0.398100i	$0.869670\pi$
$380$	3.18193	+	4.35744i	0.163230	+	0.223532i
$381$	−0.722702	+	15.4770i	−0.0370252	+	0.792911i
$382$	11.3461	+	11.3461i	0.580514	+	0.580514i
$383$	−24.7143	−	24.7143i	−1.26284	−	1.26284i	−0.949710	−	0.313131i	$-0.898622\pi$
$383$	−24.7143	−	24.7143i	−1.26284	−	1.26284i	−0.313131	−	0.949710i	$-0.601378\pi$
$384$	−0.0807905	+	1.73017i	−0.00412283	+	0.0882921i
$385$	13.6284	+	2.12488i	0.694568	+	0.108294i
$386$		−	7.31479i		−	0.372313i
$387$	−0.294986	−	0.355906i	−0.0149950	−	0.0180917i
$388$	7.38166	−	7.38166i	0.374747	−	0.374747i
$389$	−12.7778			−0.647858			−0.323929	−	0.946081i	$-0.605004\pi$
$389$	−12.7778			−0.647858			−0.323929	+	0.946081i	$0.605004\pi$
$390$	6.98825	+	1.42628i	0.353864	+	0.0722226i
$391$	−0.0406269			−0.00205459
$392$	2.03356	−	2.03356i	0.102710	−	0.102710i
$393$	−10.9829	+	10.0029i	−0.554013	+	0.504582i
$394$		−	20.5538i		−	1.03548i
$395$	9.29628	−	6.78842i	0.467747	−	0.341563i
$396$	−0.849157	+	9.07272i	−0.0426718	+	0.455921i
$397$	−20.0396	−	20.0396i	−1.00576	−	1.00576i	−0.999983	−	0.00577503i	$-0.998162\pi$
$397$	−20.0396	−	20.0396i	−1.00576	−	1.00576i	−0.00577503	−	0.999983i	$-0.501838\pi$
$398$	−9.08981	−	9.08981i	−0.455631	−	0.455631i
$399$	−8.47821	−	0.395892i	−0.424441	−	0.0198194i
$400$	1.52216	−	4.76267i	0.0761078	−	0.238134i
$401$		−	3.91057i		−	0.195284i	−0.995222	−	0.0976422i	$-0.968870\pi$
$401$		−	3.91057i		−	0.195284i	0.995222	−	0.0976422i	$-0.0311301\pi$
$402$	−11.0319	−	12.1127i	−0.550223	−	0.604126i
$403$	−14.0685	+	14.0685i	−0.700803	+	0.700803i
$404$	15.7509			0.783635
$405$	8.64612	+	18.1726i	0.429629	+	0.903005i
$406$	−16.9086			−0.839160
$407$	1.21431	−	1.21431i	0.0601909	−	0.0601909i
$408$	−0.0473825	−	0.0520243i	−0.00234578	−	0.00257559i
$409$		−	8.76129i		−	0.433218i	−0.976258	−	0.216609i	$-0.930500\pi$
$409$		−	8.76129i		−	0.433218i	0.976258	−	0.216609i	$-0.0694996\pi$
$410$	−3.25770	+	20.8940i	−0.160886	+	1.03188i
$411$	28.4830	+	1.33002i	1.40497	+	0.0656052i
$412$	9.94078	+	9.94078i	0.489747	+	0.489747i
$413$	3.02398	+	3.02398i	0.148800	+	0.148800i
$414$	−0.279562	+	2.98695i	−0.0137397	+	0.146800i
$415$	−1.49668	+	9.59931i	−0.0734693	+	0.471212i
$416$			1.84156i			0.0902897i
$417$	−0.287227	+	0.261599i	−0.0140655	+	0.0128106i
$418$	−5.18258	+	5.18258i	−0.253488	+	0.253488i
$419$	14.3441			0.700754			0.350377	−	0.936609i	$-0.386054\pi$
$419$	14.3441			0.700754			0.350377	+	0.936609i	$0.386054\pi$
$420$	4.33705	+	6.56139i	0.211626	+	0.320163i
$421$	−8.54877			−0.416641			−0.208321	−	0.978061i	$-0.566800\pi$
$421$	−8.54877			−0.416641			−0.208321	+	0.978061i	$0.566800\pi$
$422$	17.5433	−	17.5433i	0.853996	−	0.853996i
$423$	0.923363	+	1.11405i	0.0448955	+	0.0541672i
$424$			0.170486i			0.00827952i
$425$	0.0930921	+	0.180548i	0.00451563	+	0.00875785i
$426$	−0.460240	+	9.85624i	−0.0222987	+	0.477536i
$427$	15.4549	+	15.4549i	0.747916	+	0.747916i
$428$	−8.28163	−	8.28163i	−0.400308	−	0.400308i
$429$	−0.451914	+	9.67793i	−0.0218186	+	0.467255i
$430$	−0.278257	+	0.203192i	−0.0134188	+	0.00979878i
$431$		−	34.3396i		−	1.65408i	−0.562141	−	0.827041i	$-0.690022\pi$
$431$		−	34.3396i		−	1.65408i	0.562141	−	0.827041i	$-0.309978\pi$
$432$	−4.15095	+	3.12564i	−0.199713	+	0.150382i
$433$	−12.5838	+	12.5838i	−0.604740	+	0.604740i	−0.941567	−	0.336827i	$-0.890646\pi$
$433$	−12.5838	+	12.5838i	−0.604740	+	0.604740i	0.336827	+	0.941567i	$0.390646\pi$
$434$	−21.9404			−1.05317
$435$	−6.44855	+	31.5955i	−0.309184	+	1.51489i
$436$	−5.16166			−0.247199
$437$	−1.70622	+	1.70622i	−0.0816197	+	0.0816197i
$438$	11.6450	−	10.6060i	0.556421	−	0.506774i
$439$		−	15.6542i		−	0.747133i	−0.927603	−	0.373567i	$-0.878135\pi$
$439$		−	15.6542i		−	0.747133i	0.927603	−	0.373567i	$-0.121865\pi$
$440$	6.71088	+	1.04633i	0.319929	+	0.0498819i
$441$	8.59010	+	0.803987i	0.409052	+	0.0382851i
$442$	−0.0529034	−	0.0529034i	−0.00251636	−	0.00251636i
$443$	−21.4453	−	21.4453i	−1.01890	−	1.01890i	−0.999818	−	0.0190784i	$-0.993927\pi$
$443$	−21.4453	−	21.4453i	−1.01890	−	1.01890i	−0.0190784	−	0.999818i	$-0.506073\pi$
$444$	0.978185	+	0.0456766i	0.0464226	+	0.00216772i
$445$	−15.8955	−	21.7677i	−0.753517	−	1.03189i
$446$			9.38220i			0.444260i
$447$	−6.41013	−	7.03810i	−0.303189	−	0.332891i
$448$	−1.43599	+	1.43599i	−0.0678440	+	0.0678440i
$449$	19.2237			0.907224			0.453612	−	0.891199i	$-0.350135\pi$
$449$	19.2237			0.907224			0.453612	+	0.891199i	$0.350135\pi$
$450$	13.9147	−	5.60188i	0.655945	−	0.264075i
$451$	−28.7251			−1.35261
$452$	10.2943	−	10.2943i	0.484204	−	0.484204i
$453$	11.0193	+	12.0988i	0.517733	+	0.568453i
$454$			7.00820i			0.328911i
$455$	4.93163	+	6.75353i	0.231198	+	0.316611i
$456$	−4.17483	−	0.194945i	−0.195504	−	0.00912912i
$457$	−11.6854	−	11.6854i	−0.546620	−	0.546620i	0.378842	−	0.925461i	$-0.376322\pi$
$457$	−11.6854	−	11.6854i	−0.546620	−	0.546620i	−0.925461	+	0.378842i	$0.876322\pi$
$458$	7.97242	+	7.97242i	0.372527	+	0.372527i
$459$	0.0294547	−	0.209038i	0.00137483	−	0.00975708i
$460$	2.20937	+	0.344476i	0.103013	+	0.0160613i
$461$		−	30.4595i		−	1.41864i	−0.704886	−	0.709320i	$-0.749002\pi$
$461$		−	30.4595i		−	1.41864i	0.704886	−	0.709320i	$-0.250998\pi$
$462$	−7.89893	+	7.19416i	−0.367492	+	0.334703i
$463$	9.14602	−	9.14602i	0.425052	−	0.425052i	−0.461887	−	0.886939i	$-0.652827\pi$
$463$	9.14602	−	9.14602i	0.425052	−	0.425052i	0.886939	+	0.461887i	$0.152827\pi$
$464$	−8.32611			−0.386530
$465$	−8.36755	+	40.9979i	−0.388036	+	1.90123i
$466$	17.7490			0.822206
$467$	27.1900	−	27.1900i	1.25820	−	1.25820i	0.306251	−	0.951951i	$-0.400925\pi$
$467$	27.1900	−	27.1900i	1.25820	−	1.25820i	0.951951	−	0.306251i	$-0.0990745\pi$
$468$	−4.25357	+	3.52549i	−0.196621	+	0.162966i
$469$		−	19.2094i		−	0.887006i
$470$	0.871000	−	0.636030i	0.0401762	−	0.0293379i
$471$	1.78828	−	38.2969i	0.0823998	−	1.76463i
$472$	1.48906	+	1.48906i	0.0685397	+	0.0685397i
$473$	−0.330949	−	0.330949i	−0.0152170	−	0.0152170i
$474$	−0.415900	+	8.90669i	−0.0191029	+	0.409098i
$475$	11.4922	+	3.67291i	0.527296	+	0.168524i
$476$		−	0.0825048i		−	0.00378160i
$477$	−0.393783	+	0.326380i	−0.0180301	+	0.0149439i
$478$	0.871438	−	0.871438i	0.0398586	−	0.0398586i
$479$	7.60429			0.347449			0.173724	−	0.984794i	$-0.444420\pi$
$479$	7.60429			0.347449			0.173724	+	0.984794i	$0.444420\pi$
$480$	2.13564	+	3.23095i	0.0974783	+	0.147472i
$481$	1.04116			0.0474729
$482$	7.09816	−	7.09816i	0.323312	−	0.323312i
$483$	−2.60051	+	2.36848i	−0.118327	+	0.107770i
$484$		−	1.77386i		−	0.0806301i
$485$	3.59607	−	23.0642i	0.163289	−	1.04729i
$486$	−15.1661	−	3.60399i	−0.687949	−	0.163480i
$487$	18.0300	+	18.0300i	0.817017	+	0.817017i	0.985675	−	0.168658i	$-0.0539433\pi$
$487$	18.0300	+	18.0300i	0.817017	+	0.817017i	−0.168658	+	0.985675i	$0.553943\pi$
$488$	7.61029	+	7.61029i	0.344502	+	0.344502i
$489$	−6.60481	−	0.308413i	−0.298680	−	0.0139469i
$490$	0.990673	−	6.35390i	0.0447541	−	0.287040i
$491$			4.29319i			0.193749i	0.995297	+	0.0968745i	$0.0308845\pi$
$491$			4.29319i			0.193749i	−0.995297	+	0.0968745i	$0.969115\pi$
$492$	−11.0295	−	12.1100i	−0.497248	−	0.545961i
$493$	0.239189	−	0.239189i	0.0107725	−	0.0107725i
$494$	−4.44361			−0.199927
$495$	10.4306	+	17.5037i	0.468820	+	0.786732i
$496$	−10.8038			−0.485107
$497$	−8.18039	+	8.18039i	−0.366941	+	0.366941i
$498$	−5.06728	−	5.56370i	−0.227070	−	0.249315i
$499$		−	11.6589i		−	0.521925i	−0.965349	−	0.260963i	$-0.915960\pi$
$499$		−	11.6589i		−	0.521925i	0.965349	−	0.260963i	$-0.0840399\pi$
$500$	−3.53167	−	10.6079i	−0.157941	−	0.474399i
$501$	12.2156	+	0.570410i	0.545753	+	0.0254841i
$502$	7.87197	+	7.87197i	0.351343	+	0.351343i
$503$	21.7405	+	21.7405i	0.969360	+	0.969360i	0.999544	−	0.0301846i	$-0.00960952\pi$
$503$	21.7405	+	21.7405i	0.969360	+	0.969360i	−0.0301846	+	0.999544i	$0.509610\pi$
$504$	−6.06587	−	0.567733i	−0.270195	−	0.0252888i
$505$	28.4436	−	20.7704i	1.26572	−	0.924270i
$506$			3.03746i			0.135031i
$507$	12.3043	−	11.2064i	0.546452	−	0.497696i
$508$	−6.32534	+	6.32534i	−0.280642	+	0.280642i
$509$	−36.4307			−1.61476			−0.807381	−	0.590031i	$-0.799116\pi$
$509$	−36.4307			−1.61476			−0.807381	+	0.590031i	$0.799116\pi$
$510$	−0.154169	−	0.0314654i	−0.00682672	−	0.00139331i
$511$	18.4677			0.816963
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.54205	−	10.0161i	−0.332990	−	0.442221i
$514$		−	0.603532i		−	0.0266206i
$515$	31.0602	+	4.84278i	1.36868	+	0.213398i
$516$	0.0124488	−	0.266596i	0.000548027	−	0.0117362i
$517$	1.03594	+	1.03594i	0.0455604	+	0.0455604i
$518$	0.811865	+	0.811865i	0.0356713	+	0.0356713i
$519$	0.580229	−	12.4259i	0.0254692	−	0.545435i
$520$	2.42843	+	3.32557i	0.106494	+	0.145836i
$521$		−	40.9950i		−	1.79602i	−0.439972	−	0.898012i	$-0.645011\pi$
$521$		−	40.9950i		−	1.79602i	0.439972	−	0.898012i	$-0.354989\pi$
$522$	−15.9396	−	19.2314i	−0.697657	−	0.841735i
$523$	−11.8550	+	11.8550i	−0.518381	+	0.518381i	−0.917081	−	0.398700i	$-0.869461\pi$
$523$	−11.8550	+	11.8550i	−0.518381	+	0.518381i	0.398700	+	0.917081i	$0.369461\pi$
$524$	−8.57676			−0.374677
$525$	16.4844	+	6.12966i	0.719439	+	0.267520i
$526$	19.7851			0.862670
$527$	0.310368	−	0.310368i	0.0135198	−	0.0135198i
$528$	−3.88958	+	3.54254i	−0.169272	+	0.154169i
$529$			1.00000i			0.0434783i
$530$	0.224817	+	0.307871i	0.00976541	+	0.0133731i
$531$	−0.588717	+	6.29007i	−0.0255481	+	0.272966i
$532$	−3.46499	−	3.46499i	−0.150226	−	0.150226i
$533$	−12.3146	−	12.3146i	−0.533406	−	0.533406i
$534$	20.8555	+	0.973853i	0.902506	+	0.0421427i
$535$	−25.8762	−	4.03451i	−1.11872	−	0.174427i
$536$		−	9.45905i		−	0.408569i
$537$	−10.6122	−	11.6518i	−0.457950	−	0.502813i
$538$	−10.9938	+	10.9938i	−0.473977	+	0.473977i
$539$	8.73536			0.376259
$540$	−3.37425	+	11.1182i	−0.145205	+	0.478451i
$541$	−18.7415			−0.805758			−0.402879	−	0.915253i	$-0.631991\pi$
$541$	−18.7415			−0.805758			−0.402879	+	0.915253i	$0.631991\pi$
$542$	−2.18788	+	2.18788i	−0.0939775	+	0.0939775i
$543$	29.7298	+	32.6423i	1.27583	+	1.40081i
$544$		−	0.0406269i		−	0.00174186i
$545$	−9.32117	+	6.80659i	−0.399275	+	0.291562i
$546$	−6.47051	−	0.302142i	−0.276912	−	0.0129305i
$547$	3.00042	+	3.00042i	0.128288	+	0.128288i	0.768336	−	0.640047i	$-0.221085\pi$
$547$	3.00042	+	3.00042i	0.128288	+	0.128288i	−0.640047	+	0.768336i	$0.721085\pi$
$548$	11.6408	+	11.6408i	0.497271	+	0.497271i
$549$	−3.00881	+	32.1472i	−0.128413	+	1.37201i
$550$	13.4986	−	6.96000i	0.575582	−	0.296775i
$551$		−	20.0906i		−	0.855888i
$552$	−1.28054	+	1.16628i	−0.0545034	+	0.0496404i
$553$	−7.39230	+	7.39230i	−0.314352	+	0.314352i
$554$	−6.76562			−0.287444
$555$	1.82668	−	1.20743i	0.0775384	−	0.0512526i
$556$	−0.224301			−0.00951249
$557$	−21.5167	+	21.5167i	−0.911692	+	0.911692i	−0.996405	−	0.0847134i	$-0.973003\pi$
$557$	−21.5167	+	21.5167i	−0.911692	+	0.911692i	0.0847134	+	0.996405i	$0.473003\pi$
$558$	−20.6830	−	24.9544i	−0.875580	−	1.05640i
$559$		−	0.283760i		−	0.0120018i
$560$	−0.699560	+	4.48678i	−0.0295618	+	0.189601i
$561$	0.00996974	−	0.213506i	0.000420923	−	0.00901425i
$562$	−4.29779	−	4.29779i	−0.181292	−	0.181292i
$563$	−5.98181	−	5.98181i	−0.252103	−	0.252103i	0.569729	−	0.821832i	$-0.307048\pi$
$563$	−5.98181	−	5.98181i	−0.252103	−	0.252103i	−0.821832	+	0.569729i	$0.807048\pi$
$564$	−0.0389671	+	0.834498i	−0.00164081	+	0.0351387i
$565$	5.01501	−	32.1649i	0.210983	−	1.35319i
$566$			2.30819i			0.0970206i
$567$	−10.3012	−	15.0976i	−0.432611	−	0.634041i
$568$	−4.02818	+	4.02818i	−0.169019	+	0.169019i
$569$	20.4479			0.857222			0.428611	−	0.903489i	$-0.359003\pi$
$569$	20.4479			0.857222			0.428611	+	0.903489i	$0.359003\pi$
$570$	−7.79616	+	5.15323i	−0.326545	+	0.215845i
$571$	−24.0739			−1.00746			−0.503730	−	0.863861i	$-0.668039\pi$
$571$	−24.0739			−1.00746			−0.503730	+	0.863861i	$0.668039\pi$
$572$	−3.95530	+	3.95530i	−0.165380	+	0.165380i
$573$	−20.5472	+	18.7139i	−0.858372	+	0.781784i
$574$		−	19.2051i		−	0.801606i
$575$	4.44404	−	2.29139i	0.185329	−	0.0955576i
$576$	−2.98695	−	0.279562i	−0.124456	−	0.0116484i
$577$	−8.20948	−	8.20948i	−0.341765	−	0.341765i	0.515266	−	0.857031i	$-0.327693\pi$
$577$	−8.20948	−	8.20948i	−0.341765	−	0.341765i	−0.857031	+	0.515266i	$0.827693\pi$
$578$	−12.0196	−	12.0196i	−0.499951	−	0.499951i
$579$	12.6558	+	0.590966i	0.525957	+	0.0245597i
$580$	−15.0357	+	10.9795i	−0.624322	+	0.455899i
$581$		−	8.82341i		−	0.366057i
$582$	12.1751	+	13.3679i	0.504675	+	0.554116i
$583$	−0.366170	+	0.366170i	−0.0151652	+	0.0151652i
$584$	9.09384			0.376306
$585$	−3.03229	+	11.9756i	−0.125370	+	0.495130i
$586$	14.0091			0.578711
$587$	29.6663	−	29.6663i	1.22446	−	1.22446i	0.258426	−	0.966031i	$-0.416796\pi$
$587$	29.6663	−	29.6663i	1.22446	−	1.22446i	0.966031	−	0.258426i	$-0.0832039\pi$
$588$	3.35409	+	3.68268i	0.138321	+	0.151871i
$589$		−	26.0693i		−	1.07417i
$590$	4.65262	+	0.725417i	0.191545	+	0.0298649i
$591$	35.5614	+	1.66055i	1.46280	+	0.0683058i
$592$	0.399778	+	0.399778i	0.0164308	+	0.0164308i
$593$	28.7282	+	28.7282i	1.17972	+	1.17972i	0.979814	+	0.199911i	$0.0640652\pi$
$593$	28.7282	+	28.7282i	1.17972	+	1.17972i	0.199911	+	0.979814i	$0.435935\pi$
$594$	−15.6287	−	2.20217i	−0.641253	−	0.0903562i
$595$	−0.108798	−	0.148991i	−0.00446026	−	0.00610803i
$596$		−	5.49620i		−	0.225133i
$597$	16.4613	−	14.9925i	0.673714	−	0.613603i
$598$	−1.30218	+	1.30218i	−0.0532500	+	0.0532500i
$599$	−46.9570			−1.91861			−0.959305	−	0.282371i	$-0.908879\pi$
$599$	−46.9570			−1.91861			−0.959305	+	0.282371i	$0.908879\pi$
$600$	8.11724	+	3.01836i	0.331385	+	0.123224i
$601$	−18.4761			−0.753656			−0.376828	−	0.926283i	$-0.622985\pi$
$601$	−18.4761			−0.753656			−0.376828	+	0.926283i	$0.622985\pi$
$602$	0.221267	−	0.221267i	0.00901817	−	0.00901817i
$603$	21.8482	−	18.1085i	0.889728	−	0.737435i
$604$			9.44824i			0.384443i
$605$	−2.33916	−	3.20332i	−0.0951004	−	0.130234i
$606$	−1.27252	+	27.2516i	−0.0516926	+	1.10702i
$607$	−29.6024	−	29.6024i	−1.20152	−	1.20152i	−0.973703	−	0.227821i	$-0.926840\pi$
$607$	−29.6024	−	29.6024i	−1.20152	−	1.20152i	−0.227821	−	0.973703i	$-0.573160\pi$
$608$	−1.70622	−	1.70622i	−0.0691965	−	0.0691965i
$609$	1.36606	−	29.2547i	0.0553553	−	1.18546i
$610$	23.7786	+	3.70745i	0.962766	+	0.150110i
$611$			0.888224i			0.0359337i
$612$	0.0938387	−	0.0777765i	0.00379321	−	0.00314393i
$613$	−26.0428	+	26.0428i	−1.05186	+	1.05186i	−0.0532791	+	0.998580i	$0.516967\pi$
$613$	−26.0428	+	26.0428i	−1.05186	+	1.05186i	−0.998580	+	0.0532791i	$0.983033\pi$
$614$	−31.6895			−1.27889
$615$	−35.8868	−	7.32439i	−1.44710	−	0.295348i
$616$	−6.16844			−0.248534
$617$	9.82533	−	9.82533i	0.395553	−	0.395553i	−0.481108	−	0.876661i	$-0.659766\pi$
$617$	9.82533	−	9.82533i	0.395553	−	0.395553i	0.876661	+	0.481108i	$0.159766\pi$
$618$	−18.0023	+	16.3961i	−0.724159	+	0.659547i
$619$		−	11.5924i		−	0.465937i	−0.972484	−	0.232968i	$-0.925156\pi$
$619$		−	11.5924i		−	0.465937i	0.972484	−	0.232968i	$-0.0748438\pi$
$620$	−19.5101	+	14.2468i	−0.783543	+	0.572167i
$621$	−5.14532	−	0.725006i	−0.206475	−	0.0290935i
$622$	−15.6285	−	15.6285i	−0.626646	−	0.626646i
$623$	17.3095	+	17.3095i	0.693489	+	0.693489i
$624$	−3.18620	−	0.148780i	−0.127550	−	0.00595598i
$625$	−20.3661	−	14.4991i	−0.814644	−	0.579962i
$626$			4.57703i			0.182935i
$627$	−8.54801	−	9.38542i	−0.341375	−	0.374818i
$628$	15.6517	−	15.6517i	0.624570	−	0.624570i
$629$	−0.0229693			−0.000915844
$630$	−11.7027	+	6.97371i	−0.466246	+	0.277839i
$631$	−24.8506			−0.989288			−0.494644	−	0.869096i	$-0.664702\pi$
$631$	−24.8506			−0.989288			−0.494644	+	0.869096i	$0.664702\pi$
$632$	−3.64010	+	3.64010i	−0.144796	+	0.144796i
$633$	28.9355	+	31.7702i	1.15008	+	1.26275i
$634$			15.6572i			0.621826i
$635$	−3.08147	+	19.7637i	−0.122285	+	0.784299i
$636$	−0.294969	−	0.0137736i	−0.0116963	−	0.000546160i
$637$	3.74491	+	3.74491i	0.148379	+	0.148379i
$638$	−17.8829	−	17.8829i	−0.707989	−	0.707989i
$639$	−17.0157	−	1.59258i	−0.673132	−	0.0630016i
$640$	−0.344476	+	2.20937i	−0.0136166	+	0.0873332i
$641$		−	43.6697i		−	1.72485i	−0.506186	−	0.862424i	$-0.668945\pi$
$641$		−	43.6697i		−	1.72485i	0.506186	−	0.862424i	$-0.331055\pi$
$642$	14.9977	−	13.6595i	0.591911	−	0.539098i
$643$	4.13381	−	4.13381i	0.163021	−	0.163021i	−0.620882	−	0.783904i	$-0.713226\pi$
$643$	4.13381	−	4.13381i	0.163021	−	0.163021i	0.783904	+	0.620882i	$0.213226\pi$
$644$	−2.03079			−0.0800244
$645$	−0.329075	−	0.497847i	−0.0129573	−	0.0196027i
$646$	0.0980312			0.00385699
$647$	24.4013	−	24.4013i	0.959316	−	0.959316i	−0.0398886	−	0.999204i	$-0.512700\pi$
$647$	24.4013	−	24.4013i	0.959316	−	0.959316i	0.999204	+	0.0398886i	$0.0127003\pi$
$648$	−5.07251	−	7.43435i	−0.199267	−	0.292049i
$649$			6.39644i			0.251082i
$650$	8.77073	+	2.80313i	0.344016	+	0.109948i
$651$	1.77257	−	37.9605i	0.0694727	−	1.48779i
$652$	−2.69934	−	2.69934i	−0.105714	−	0.105714i
$653$	3.78364	+	3.78364i	0.148065	+	0.148065i	0.777253	−	0.629188i	$-0.216612\pi$
$653$	3.78364	+	3.78364i	0.148065	+	0.148065i	−0.629188	+	0.777253i	$0.716612\pi$
$654$	0.417014	−	8.93053i	0.0163065	−	0.349211i
$655$	−15.4883	+	11.3100i	−0.605178	+	0.441919i
$656$		−	9.45696i		−	0.369232i
$657$	17.4093	+	21.0047i	0.679203	+	0.819471i
$658$	−0.692609	+	0.692609i	−0.0270007	+	0.0270007i
$659$	−21.1564			−0.824137			−0.412069	−	0.911153i	$-0.635194\pi$
$659$	−21.1564			−0.824137			−0.412069	+	0.911153i	$0.635194\pi$
$660$	−2.35250	+	11.5264i	−0.0915711	+	0.448664i
$661$	−13.6642			−0.531475			−0.265737	−	0.964045i	$-0.585615\pi$
$661$	−13.6642			−0.531475			−0.265737	+	0.964045i	$0.585615\pi$
$662$	−19.5047	+	19.5047i	−0.758070	+	0.758070i
$663$	0.0958057	−	0.0872575i	0.00372078	−	0.00338880i
$664$		−	4.34481i		−	0.168611i
$665$	−10.8264	−	1.68801i	−0.419831	−	0.0654584i
$666$	−0.158056	+	1.68873i	−0.00612455	+	0.0654370i
$667$	−5.88745	−	5.88745i	−0.227963	−	0.227963i
$668$	4.99243	+	4.99243i	0.193163	+	0.193163i
$669$	−16.2328	−	0.757993i	−0.627595	−	0.0293057i
$670$	−12.4735	−	17.0816i	−0.481892	−	0.659919i
$671$			32.6908i			1.26202i
$672$	−2.36848	−	2.60051i	−0.0913662	−	0.100317i
$673$	−17.2276	+	17.2276i	−0.664074	+	0.664074i	−0.956338	−	0.292264i	$-0.905592\pi$
$673$	−17.2276	+	17.2276i	−0.664074	+	0.664074i	0.292264	+	0.956338i	$0.405592\pi$
$674$	−23.4652			−0.903845
$675$	8.56800	+	24.5273i	0.329782	+	0.944057i
$676$	9.60867			0.369564
$677$	−8.11519	+	8.11519i	−0.311892	+	0.311892i	−0.845642	−	0.533750i	$-0.820782\pi$
$677$	−8.11519	+	8.11519i	−0.311892	+	0.311892i	0.533750	+	0.845642i	$0.320782\pi$
$678$	16.9792	+	18.6425i	0.652082	+	0.715963i
$679$			21.1999i			0.813579i
$680$	−0.0535739	−	0.0733659i	−0.00205447	−	0.00281345i
$681$	−12.1253	−	0.566196i	−0.464644	−	0.0216967i
$682$	−23.2046	−	23.2046i	−0.888548	−	0.888548i
$683$	14.2948	+	14.2948i	0.546975	+	0.546975i	0.925565	−	0.378589i	$-0.123591\pi$
$683$	14.2948	+	14.2948i	0.546975	+	0.546975i	−0.378589	+	0.925565i	$0.623591\pi$
$684$	0.674573	−	7.20739i	0.0257929	−	0.275582i
$685$	36.3721	+	5.67098i	1.38971	+	0.216677i
$686$			20.0559i			0.765737i
$687$	−14.4377	+	13.1495i	−0.550833	+	0.501685i
$688$	0.108956	−	0.108956i	0.00415391	−	0.00415391i
$689$	−0.313959			−0.0119609
$690$	−0.774498	+	3.79475i	−0.0294846	+	0.144464i
$691$	5.32354			0.202517			0.101258	−	0.994860i	$-0.467713\pi$
$691$	5.32354			0.202517			0.101258	+	0.994860i	$0.467713\pi$
$692$	5.07836	−	5.07836i	0.193050	−	0.193050i
$693$	−11.8089	−	14.2477i	−0.448584	−	0.541225i
$694$		−	13.4035i		−	0.508789i
$695$	−0.405053	+	0.295782i	−0.0153646	+	0.0112197i
$696$	0.672671	−	14.4055i	0.0254975	−	0.546041i
$697$	0.271675	+	0.271675i	0.0102904	+	0.0102904i
$698$	12.2995	+	12.2995i	0.465543	+	0.465543i
$699$	−1.43395	+	30.7087i	−0.0542370	+	1.16151i
$700$	4.65334	+	9.02493i	0.175880	+	0.341110i
$701$			37.7240i			1.42482i	0.701765	+	0.712408i	$0.252396\pi$
$701$			37.7240i			1.42482i	−0.701765	+	0.712408i	$0.747604\pi$
$702$	−5.75604	−	7.64421i	−0.217248	−	0.288512i
$703$	−0.964649	+	0.964649i	−0.0363824	+	0.0363824i
$704$	−3.03746			−0.114478
$705$	1.03007	+	1.55836i	0.0387947	+	0.0586912i
$706$	−31.1068			−1.17072
$707$	−22.6180	+	22.6180i	−0.850639	+	0.850639i
$708$	−2.69663	+	2.45602i	−0.101345	+	0.0923030i
$709$		−	17.6180i		−	0.661657i	−0.943691	−	0.330828i	$-0.892672\pi$
$709$		−	17.6180i		−	0.661657i	0.943691	−	0.330828i	$-0.107328\pi$
$710$	−1.96238	+	12.5862i	−0.0736468	+	0.472350i
$711$	−15.3764	−	1.43915i	−0.576662	−	0.0539724i
$712$	8.52350	+	8.52350i	0.319432	+	0.319432i
$713$	−7.63947	−	7.63947i	−0.286100	−	0.286100i
$714$	0.142747	+	0.00666560i	0.00534217	+	0.000249454i
$715$	−1.92688	+	12.3585i	−0.0720612	+	0.462180i
$716$		−	9.09915i		−	0.340051i
$717$	1.43733	+	1.57814i	0.0536780	+	0.0589366i
$718$	16.7863	−	16.7863i	0.626461	−	0.626461i
$719$	−23.4101			−0.873050			−0.436525	−	0.899692i	$-0.643791\pi$
$719$	−23.4101			−0.873050			−0.436525	+	0.899692i	$0.643791\pi$
$720$	−5.76262	+	3.43399i	−0.214760	+	0.127977i
$721$	−28.5497			−1.06325
$722$	−9.31797	+	9.31797i	−0.346779	+	0.346779i
$723$	11.7075	+	12.8545i	0.435408	+	0.478062i
$724$			25.4910i			0.947367i
$725$	−12.6736	+	39.6545i	−0.470687	+	1.47273i
$726$	3.06908	+	0.143311i	0.113904	+	0.00531878i
$727$	−1.31281	−	1.31281i	−0.0486893	−	0.0486893i	0.682343	−	0.731032i	$-0.260961\pi$
$727$	−1.31281	−	1.31281i	−0.0486893	−	0.0486893i	−0.731032	+	0.682343i	$0.760961\pi$
$728$	−2.64445	−	2.64445i	−0.0980099	−	0.0980099i
$729$	7.46078	−	25.9487i	0.276325	−	0.961064i
$730$	16.4221	−	11.9919i	0.607808	−	0.443840i
$731$			0.00626007i			0.000231537i
$732$	−13.7819	+	12.5522i	−0.509394	+	0.463944i
$733$	33.1490	−	33.1490i	1.22439	−	1.22439i	0.258332	−	0.966056i	$-0.416827\pi$
$733$	33.1490	−	33.1490i	1.22439	−	1.22439i	0.966056	−	0.258332i	$-0.0831728\pi$
$734$	−28.6554			−1.05769
$735$	10.9133	+	2.22736i	0.402542	+	0.0821576i
$736$	−1.00000			−0.0368605
$737$	20.3162	−	20.3162i	0.748357	−	0.748357i
$738$	21.8434	−	18.1045i	0.804066	−	0.666435i
$739$			20.5449i			0.755758i	0.925855	+	0.377879i	$0.123346\pi$
$739$			20.5449i			0.755758i	−0.925855	+	0.377879i	$0.876654\pi$
$740$	1.24912	+	0.194757i	0.0459184	+	0.00715941i
$741$	0.359002	−	7.68818i	0.0131883	−	0.282432i
$742$	−0.244815	−	0.244815i	−0.00898746	−	0.00898746i
$743$	−23.4804	−	23.4804i	−0.861411	−	0.861411i	0.130091	−	0.991502i	$-0.458473\pi$
$743$	−23.4804	−	23.4804i	−0.861411	−	0.861411i	−0.991502	+	0.130091i	$0.958473\pi$
$744$	0.872848	−	18.6924i	0.0320002	−	0.685298i
$745$	−7.24774	−	9.92529i	−0.265537	−	0.363635i
$746$			24.4064i			0.893581i
$747$	10.0355	−	8.31774i	0.367180	−	0.304330i
$748$	0.0872586	−	0.0872586i	0.00319049	−	0.00319049i
$749$	23.7846			0.869072
$750$	18.6387	−	5.25336i	0.680590	−	0.191826i
$751$	9.33331			0.340577			0.170289	−	0.985394i	$-0.445530\pi$
$751$	9.33331			0.340577			0.170289	+	0.985394i	$0.445530\pi$
$752$	−0.341054	+	0.341054i	−0.0124369	+	0.0124369i
$753$	−14.2558	+	12.9838i	−0.519510	+	0.473157i
$754$		−	15.3330i		−	0.558395i
$755$	12.4592	+	17.0621i	0.453437	+	0.620952i
$756$	1.47234	−	10.4491i	0.0535483	−	0.380030i
$757$	−7.70849	−	7.70849i	−0.280170	−	0.280170i	0.553007	−	0.833177i	$-0.313480\pi$
$757$	−7.70849	−	7.70849i	−0.280170	−	0.280170i	−0.833177	+	0.553007i	$0.813480\pi$
$758$	−10.9604	−	10.9604i	−0.398100	−	0.398100i
$759$	−5.25530	−	0.245398i	−0.190755	−	0.00890737i
$760$	−5.33114	−	0.831209i	−0.193381	−	0.0301511i
$761$			5.80591i			0.210464i	0.994448	+	0.105232i	$0.0335586\pi$
$761$			5.80591i			0.210464i	−0.994448	+	0.105232i	$0.966441\pi$
$762$	−10.4329	−	11.4549i	−0.377943	−	0.414968i
$763$	7.41208	−	7.41208i	0.268335	−	0.268335i
$764$	−16.0457			−0.580514
$765$	0.0668958	−	0.264196i	0.00241862	−	0.00955202i
$766$	34.9513			1.26284
$767$	−2.74219	+	2.74219i	−0.0990148	+	0.0990148i
$768$	−1.16628	−	1.28054i	−0.0420847	−	0.0462075i
$769$		−	9.81402i		−	0.353903i	−0.984220	−	0.176951i	$-0.943376\pi$
$769$		−	9.81402i		−	0.353903i	0.984220	−	0.176951i	$-0.0566235\pi$
$770$	−11.1393	+	8.13422i	−0.401431	+	0.293137i
$771$	1.04421	+	0.0487597i	0.0376063	+	0.00175604i
$772$	5.17234	+	5.17234i	0.186156	+	0.186156i
$773$	−4.72645	−	4.72645i	−0.169999	−	0.169999i	0.616980	−	0.786979i	$-0.288356\pi$
$773$	−4.72645	−	4.72645i	−0.169999	−	0.169999i	−0.786979	+	0.616980i	$0.788356\pi$
$774$	0.460250	+	0.0430769i	0.0165433	+	0.00154837i
$775$	−16.4451	+	51.4552i	−0.590726	+	1.84832i
$776$			10.4392i			0.374747i
$777$	−1.47025	+	1.33907i	−0.0527450	+	0.0480389i
$778$	9.03524	−	9.03524i	0.323929	−	0.323929i
$779$	22.8193			0.817586
$780$	−5.94997	+	3.93291i	−0.213043	+	0.140821i
$781$	−17.3035			−0.619167
$782$	0.0287275	−	0.0287275i	0.00102729	−	0.00102729i
$783$	34.5613	−	26.0244i	1.23512	−	0.930036i
$784$			2.87588i			0.102710i
$785$	7.62492	−	48.9041i	0.272145	−	1.74546i
$786$	0.692921	−	14.8392i	0.0247157	−	0.529297i
$787$	−36.7991	−	36.7991i	−1.31175	−	1.31175i	−0.920127	−	0.391619i	$-0.871915\pi$
$787$	−36.7991	−	36.7991i	−1.31175	−	1.31175i	−0.391619	−	0.920127i	$-0.628085\pi$
$788$	14.5337	+	14.5337i	0.517741	+	0.517741i
$789$	−1.59845	+	34.2315i	−0.0569062	+	1.21867i
$790$	−1.77332	+	11.3736i	−0.0630921	+	0.404655i
$791$			29.5650i			1.05121i
$792$	−5.81493	−	7.01582i	−0.206625	−	0.249296i
$793$	−14.0148	+	14.0148i	−0.497679	+	0.497679i
$794$	28.3403			1.00576
$795$	−0.550831	+	0.364097i	−0.0195360	+	0.0129132i
$796$	12.8549			0.455631
$797$	16.3453	−	16.3453i	0.578980	−	0.578980i	−0.355642	−	0.934622i	$-0.615738\pi$
$797$	16.3453	−	16.3453i	0.578980	−	0.578980i	0.934622	+	0.355642i	$0.115738\pi$
$798$	6.27494	−	5.71506i	0.222130	−	0.202311i
$799$		−	0.0195953i		−	0.000693231i
$800$	2.29139	+	4.44404i	0.0810129	+	0.157121i
$801$	−3.36985	+	36.0048i	−0.119068	+	1.27217i
$802$	2.76519	+	2.76519i	0.0976422	+	0.0976422i
$803$	19.5318	+	19.5318i	0.689262	+	0.689262i
$804$	16.3657	+	0.764202i	0.577174	+	0.0269513i
$805$	−3.66730	+	2.67797i	−0.129255	+	0.0943860i
$806$		−	19.8959i		−	0.700803i
$807$	−18.1329	−	19.9093i	−0.638309	−	0.700841i
$808$	−11.1375	+	11.1375i	−0.391817	+	0.391817i
$809$	45.2033			1.58926			0.794632	−	0.607091i	$-0.207664\pi$
$809$	45.2033			1.58926			0.794632	+	0.607091i	$0.207664\pi$
$810$	−18.9637	−	6.73626i	−0.666317	−	0.236688i
$811$	7.65829			0.268919			0.134460	−	0.990919i	$-0.457070\pi$
$811$	7.65829			0.268919			0.134460	+	0.990919i	$0.457070\pi$
$812$	11.9562	−	11.9562i	0.419580	−	0.419580i
$813$	−3.60863	−	3.96215i	−0.126560	−	0.138959i
$814$			1.71729i			0.0601909i
$815$	−8.43416	−	1.31502i	−0.295436	−	0.0460631i
$816$	0.0702912	+	0.00328227i	0.00246068	+	0.000114902i
$817$	0.262907	+	0.262907i	0.00919795	+	0.00919795i
$818$	6.19516	+	6.19516i	0.216609	+	0.216609i
$819$	1.04551	−	11.1706i	0.0365331	−	0.390334i
$820$	−12.4707	−	17.0778i	−0.435496	−	0.596383i
$821$		−	6.24113i		−	0.217817i	−0.994052	−	0.108909i	$-0.965264\pi$
$821$		−	6.24113i		−	0.217817i	0.994052	−	0.108909i	$-0.0347356\pi$
$822$	−21.0810	+	19.2001i	−0.735285	+	0.669680i
$823$	14.4815	−	14.4815i	0.504792	−	0.504792i	−0.408131	−	0.912923i	$-0.633819\pi$
$823$	14.4815	−	14.4815i	0.504792	−	0.504792i	0.912923	+	0.408131i	$0.133819\pi$
$824$	−14.0584			−0.489747
$825$	10.9514	+	23.9171i	0.381279	+	0.832686i
$826$	−4.27655			−0.148800
$827$	3.32709	−	3.32709i	0.115694	−	0.115694i	−0.646890	−	0.762584i	$-0.723931\pi$
$827$	3.32709	−	3.32709i	0.115694	−	0.115694i	0.762584	+	0.646890i	$0.223931\pi$
$828$	−1.91441	−	2.30977i	−0.0665303	−	0.0802700i
$829$			41.4160i			1.43844i	0.694784	+	0.719219i	$0.255500\pi$
$829$			41.4160i			1.43844i	−0.694784	+	0.719219i	$0.744500\pi$
$830$	−5.72942	−	7.84605i	−0.198871	−	0.272340i
$831$	0.546598	−	11.7056i	0.0189613	−	0.406064i
$832$	−1.30218	−	1.30218i	−0.0451449	−	0.0451449i
$833$	−0.0826170	−	0.0826170i	−0.00286251	−	0.00286251i
$834$	0.0181214	−	0.388078i	0.000627493	−	0.0134381i
$835$	15.5990	+	2.43213i	0.539825	+	0.0841673i
$836$		−	7.32927i		−	0.253488i
$837$	44.8462	−	33.7689i	1.55011	−	1.16722i
$838$	−10.1428	+	10.1428i	−0.350377	+	0.350377i
$839$	−6.74222			−0.232767			−0.116384	−	0.993204i	$-0.537130\pi$
$839$	−6.74222			−0.232767			−0.116384	+	0.993204i	$0.537130\pi$
$840$	−7.70636	−	1.57284i	−0.265895	−	0.0542683i
$841$	40.3241			1.39049
$842$	6.04489	−	6.04489i	0.208321	−	0.208321i
$843$	7.78312	−	7.08868i	0.268065	−	0.244147i
$844$			24.8100i			0.853996i
$845$	17.3518	−	12.6708i	0.596919	−	0.435888i
$846$	−1.44067	−	0.134839i	−0.0495313	−	0.00463586i
$847$	2.54724	+	2.54724i	0.0875244	+	0.0875244i
$848$	−0.120552	−	0.120552i	−0.00413976	−	0.00413976i
$849$	−3.99356	−	0.186480i	−0.137059	−	0.00639999i
$850$	−0.193492	−	0.0618404i	−0.00663674	−	0.00212111i
$851$			0.565371i			0.0193807i
$852$	−6.64397	−	7.29485i	−0.227619	−	0.249918i
$853$	−37.0320	+	37.0320i	−1.26795	+	1.26795i	−0.320805	+	0.947145i	$0.603953\pi$
$853$	−37.0320	+	37.0320i	−1.26795	+	1.26795i	−0.947145	+	0.320805i	$0.896047\pi$
$854$	−21.8566			−0.747916
$855$	−8.28609	−	13.9050i	−0.283378	−	0.475540i
$856$	11.7120			0.400308
$857$	3.66827	−	3.66827i	0.125306	−	0.125306i	−0.641673	−	0.766979i	$-0.721759\pi$
$857$	3.66827	−	3.66827i	0.125306	−	0.125306i	0.766979	+	0.641673i	$0.221759\pi$
$858$	−6.52378	−	7.16288i	−0.222718	−	0.244537i
$859$		−	7.96847i		−	0.271881i	−0.990717	−	0.135940i	$-0.956594\pi$
$859$		−	7.96847i		−	0.271881i	0.990717	−	0.135940i	$-0.0434056\pi$
$860$	0.0530793	−	0.340436i	0.00180999	−	0.0116088i
$861$	33.2280	+	1.55159i	1.13241	+	0.0528781i
$862$	24.2818	+	24.2818i	0.827041	+	0.827041i
$863$	−3.16578	−	3.16578i	−0.107764	−	0.107764i	0.651169	−	0.758933i	$-0.274279\pi$
$863$	−3.16578	−	3.16578i	−0.107764	−	0.107764i	−0.758933	+	0.651169i	$0.774279\pi$
$864$	0.725006	−	5.14532i	0.0246652	−	0.175048i
$865$	2.47399	−	15.8675i	0.0841183	−	0.539511i
$866$		−	17.7962i		−	0.604740i
$867$	21.7671	−	19.8249i	0.739248	−	0.673289i
$868$	15.5142	−	15.5142i	0.526586	−	0.526586i
$869$	−15.6365			−0.530431
$870$	−17.7816	−	26.9012i	−0.602853	−	0.912037i
$871$	17.4194			0.590233
$872$	3.64985	−	3.64985i	0.123599	−	0.123599i
$873$	−24.1122	+	19.9850i	−0.816076	+	0.676389i
$874$		−	2.41296i		−	0.0816197i
$875$	20.3042	+	10.1614i	0.686408	+	0.343516i
$876$	−0.734696	+	15.7338i	−0.0248231	+	0.531598i
$877$	31.0507	+	31.0507i	1.04851	+	1.04851i	0.998762	+	0.0497443i	$0.0158406\pi$
$877$	31.0507	+	31.0507i	1.04851	+	1.04851i	0.0497443	+	0.998762i	$0.484159\pi$
$878$	11.0692	+	11.0692i	0.373567	+	0.373567i
$879$	−1.13180	+	24.2381i	−0.0381748	+	0.817530i
$880$	−5.48518	+	4.00544i	−0.184905	+	0.135023i
$881$		−	12.9732i		−	0.437080i	−0.975828	−	0.218540i	$-0.929871\pi$
$881$		−	12.9732i		−	0.437080i	0.975828	−	0.218540i	$-0.0701294\pi$
$882$	−6.64262	+	5.50561i	−0.223669	+	0.185384i
$883$	−15.5946	+	15.5946i	−0.524800	+	0.524800i	−0.919017	−	0.394217i	$-0.871016\pi$
$883$	−15.5946	+	15.5946i	−0.524800	+	0.524800i	0.394217	+	0.919017i	$0.371016\pi$
$884$	0.0748167			0.00251636
$885$	−1.63098	+	7.99119i	−0.0548247	+	0.268621i
$886$	30.3282			1.01890
$887$	−31.5863	+	31.5863i	−1.06056	+	1.06056i	−0.0625206	+	0.998044i	$0.519914\pi$
$887$	−31.5863	+	31.5863i	−1.06056	+	1.06056i	−0.998044	+	0.0625206i	$0.980086\pi$
$888$	−0.723980	+	0.659383i	−0.0242952	+	0.0221275i
$889$		−	18.1662i		−	0.609276i
$890$	26.6319	+	4.15234i	0.892704	+	0.139187i
$891$	5.07277	−	26.8623i	0.169944	−	0.899921i
$892$	−6.63422	−	6.63422i	−0.222130	−	0.222130i
$893$	−0.822950	−	0.822950i	−0.0275390	−	0.0275390i
$894$	9.50934	+	0.444041i	0.318040	+	0.0148510i
$895$	−11.9989	−	16.4317i	−0.401079	−	0.549250i
$896$		−	2.03079i		−	0.0678440i
$897$	−2.14778	−	2.35818i	−0.0717122	−	0.0787375i
$898$	−13.5932	+	13.5932i	−0.453612	+	0.453612i
$899$	89.9540			3.00013
$900$	−5.87806	+	13.8003i	−0.195935	+	0.460010i
$901$	0.00692630			0.000230749
$902$	20.3117	−	20.3117i	0.676306	−	0.676306i
$903$	0.364952	+	0.400705i	0.0121449	+	0.0133346i
$904$			14.5584i			0.484204i
$905$	33.6146	+	46.0329i	1.11739	+	1.53018i
$906$	−16.3470	−	0.763328i	−0.543093	−	0.0253599i
$907$	−7.13670	−	7.13670i	−0.236970	−	0.236970i	0.578624	−	0.815594i	$-0.303590\pi$
$907$	−7.13670	−	7.13670i	−0.236970	−	0.236970i	−0.815594	+	0.578624i	$0.803590\pi$
$908$	−4.95555	−	4.95555i	−0.164456	−	0.164456i
$909$	−47.0470	−	4.40334i	−1.56045	−	0.146050i
$910$	−8.26266	−	1.28828i	−0.273905	−	0.0427060i
$911$			16.6340i			0.551109i	0.961285	+	0.275554i	$0.0888614\pi$
$911$			16.6340i			0.551109i	−0.961285	+	0.275554i	$0.911139\pi$
$912$	3.08990	−	2.81420i	0.102317	−	0.0931875i
$913$	9.33180	−	9.33180i	0.308838	−	0.308838i
$914$	16.5256			0.546620
$915$	−8.33559	+	40.8413i	−0.275566	+	1.35017i
$916$	−11.2747			−0.372527
$917$	12.3161	−	12.3161i	0.406714	−	0.406714i
$918$	0.126985	+	0.168640i	0.00419113	+	0.00556595i
$919$		−	41.3582i		−	1.36428i	−0.731221	−	0.682141i	$-0.761049\pi$
$919$		−	41.3582i		−	1.36428i	0.731221	−	0.682141i	$-0.238951\pi$
$920$	−1.80585	+	1.31868i	−0.0595370	+	0.0434757i
$921$	2.56022	−	54.8282i	0.0843620	−	1.80665i
$922$	21.5381	+	21.5381i	0.709320	+	0.709320i
$923$	−7.41811	−	7.41811i	−0.244170	−	0.244170i
$924$	0.498352	−	10.6724i	0.0163946	−	0.351097i
$925$	2.51253	−	1.29549i	0.0826116	−	0.0425953i
$926$			12.9344i			0.425052i
$927$	−26.9135	−	32.4716i	−0.883955	−	1.06651i
$928$	5.88745	−	5.88745i	0.193265	−	0.193265i
$929$	0.182246			0.00597931			0.00298966	−	0.999996i	$-0.499048\pi$
$929$	0.182246			0.00597931			0.00298966	+	0.999996i	$0.499048\pi$
$930$	−23.0732	−	34.9067i	−0.756599	−	1.14463i
$931$	−6.93940			−0.227430
$932$	−12.5504	+	12.5504i	−0.411103	+	0.411103i
$933$	28.3025	−	25.7773i	0.926583	−	0.843910i
$934$			38.4524i			1.25820i
$935$	0.0425092	−	0.272642i	0.00139020	−	0.00891635i
$936$	0.514829	−	5.50063i	0.0168277	−	0.179794i
$937$	39.5274	+	39.5274i	1.29130	+	1.29130i	0.933981	+	0.357322i	$0.116310\pi$
$937$	39.5274	+	39.5274i	1.29130	+	1.29130i	0.357322	+	0.933981i	$0.383690\pi$
$938$	13.5831	+	13.5831i	0.443503	+	0.443503i
$939$	−7.91902	−	0.369781i	−0.258428	−	0.0120673i
$940$	−0.166149	+	1.06563i	−0.00541918	+	0.0347571i
$941$		−	21.9646i		−	0.716025i	−0.933717	−	0.358013i	$-0.883454\pi$
$941$		−	21.9646i		−	0.716025i	0.933717	−	0.358013i	$-0.116546\pi$
$942$	25.8155	+	28.3445i	0.841114	+	0.923514i
$943$	6.68708	−	6.68708i	0.217761	−	0.217761i
$944$	−2.10585			−0.0685397
$945$	−11.1202	−	20.8110i	−0.361741	−	0.676981i
$946$	0.468032			0.0152170
$947$	−2.78553	+	2.78553i	−0.0905177	+	0.0905177i	−0.750916	−	0.660398i	$-0.770388\pi$
$947$	−2.78553	+	2.78553i	−0.0905177	+	0.0905177i	0.660398	+	0.750916i	$0.270388\pi$
$948$	−6.00390	−	6.59207i	−0.194997	−	0.214100i
$949$			16.7468i			0.543625i
$950$	−10.7233	+	5.52905i	−0.347910	+	0.179386i
$951$	−27.0895	−	1.26495i	−0.878438	−	0.0410189i
$952$	0.0583397	+	0.0583397i	0.00189080	+	0.00189080i
$953$	5.12116	+	5.12116i	0.165891	+	0.165891i	0.785170	−	0.619280i	$-0.212575\pi$
$953$	5.12116	+	5.12116i	0.165891	+	0.165891i	−0.619280	+	0.785170i	$0.712575\pi$
$954$	0.0476613	−	0.509232i	0.00154309	−	0.0164870i
$955$	−28.9761	+	21.1592i	−0.937645	+	0.684697i
$956$			1.23240i			0.0398586i
$957$	32.3851	−	29.4955i	1.04686	−	0.953456i
$958$	−5.37704	+	5.37704i	−0.173724	+	0.173724i
$959$	−33.4322			−1.07958
$960$	−3.79475	−	0.774498i	−0.122475	−	0.0249968i
$961$	85.7231			2.76526
$962$	−0.736213	+	0.736213i	−0.0237365	+	0.0237365i
$963$	22.4216	+	27.0520i	0.722524	+	0.871739i
$964$			10.0383i			0.323312i
$965$	16.1611	+	2.51977i	0.520244	+	0.0811143i
$966$	0.164069	−	3.51361i	0.00527883	−	0.113048i
$967$	−8.28190	−	8.28190i	−0.266328	−	0.266328i	0.561291	−	0.827619i	$-0.310305\pi$
$967$	−8.28190	−	8.28190i	−0.266328	−	0.266328i	−0.827619	+	0.561291i	$0.810305\pi$
$968$	1.25431	+	1.25431i	0.0403151	+	0.0403151i
$969$	−0.00791999	+	0.169610i	−0.000254427	+	0.00544866i
$970$	13.7660	+	18.8517i	0.442001	+	0.605290i
$971$			41.0986i			1.31892i	0.751741	+	0.659459i	$0.229215\pi$
$971$			41.0986i			1.31892i	−0.751741	+	0.659459i	$0.770785\pi$
$972$	13.2725	−	8.17566i	0.425715	−	0.262234i
$973$	0.322094	−	0.322094i	0.0103259	−	0.0103259i
$974$	−25.4983			−0.817017
$975$	−5.55848	+	14.9483i	−0.178014	+	0.478730i
$976$	−10.7626			−0.344502
$977$	5.84940	−	5.84940i	0.187139	−	0.187139i	−0.607319	−	0.794458i	$-0.707755\pi$
$977$	5.84940	−	5.84940i	0.187139	−	0.187139i	0.794458	+	0.607319i	$0.207755\pi$
$978$	4.88838	−	4.45222i	0.156313	−	0.142366i
$979$			36.6136i			1.17018i
$980$	3.79237	+	5.19340i	0.121143	+	0.165897i
$981$	15.4176	+	1.44301i	0.492246	+	0.0460716i
$982$	−3.03574	−	3.03574i	−0.0968745	−	0.0968745i
$983$	−14.6133	−	14.6133i	−0.466092	−	0.466092i	0.434554	−	0.900646i	$-0.356906\pi$
$983$	−14.6133	−	14.6133i	−0.466092	−	0.466092i	−0.900646	+	0.434554i	$0.856906\pi$
$984$	16.3621	+	0.764033i	0.521605	+	0.0243565i
$985$	45.4109	+	7.08028i	1.44691	+	0.225597i
$986$			0.338264i			0.0107725i
$987$	−1.14237	−	1.25429i	−0.0363621	−	0.0399243i
$988$	3.14211	−	3.14211i	0.0999637	−	0.0999637i
$989$	0.154087			0.00489968
$990$	−19.7525	−	5.00144i	−0.627776	−	0.158956i
$991$	9.65620			0.306739			0.153370	−	0.988169i	$-0.450988\pi$
$991$	9.65620			0.306739			0.153370	+	0.988169i	$0.450988\pi$
$992$	7.63947	−	7.63947i	0.242553	−	0.242553i
$993$	−32.1705	−	35.3221i	−1.02090	−	1.12091i
$994$		−	11.5688i		−	0.366941i
$995$	23.2140	−	16.9516i	0.735934	−	0.537401i
$996$	7.51724	+	0.351019i	0.238193	+	0.0111225i
$997$	−6.06407	−	6.06407i	−0.192051	−	0.192051i	0.604531	−	0.796582i	$-0.293361\pi$
$997$	−6.06407	−	6.06407i	−0.192051	−	0.192051i	−0.796582	+	0.604531i	$0.793361\pi$
$998$	8.24410	+	8.24410i	0.260963	+	0.260963i
$999$	−2.90902	−	0.409897i	−0.0920372	−	0.0129686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.3	✓	32
3.2	odd	2	inner	690.2.i.f.47.13	yes	32
5.3	odd	4	inner	690.2.i.f.323.13	yes	32
15.8	even	4	inner	690.2.i.f.323.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.3	✓	32	1.1	even	1	trivial
690.2.i.f.47.13	yes	32	3.2	odd	2	inner
690.2.i.f.323.3	yes	32	15.8	even	4	inner
690.2.i.f.323.13	yes	32	5.3	odd	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.16628 - 1.28054i) q^{3} -1.00000i q^{4} +(-1.31868 - 1.80585i) q^{5} +(1.73017 + 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.279562 + 2.98695i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.16628 - 1.28054i) q^{3} -1.00000i q^{4} +(-1.31868 - 1.80585i) q^{5} +(1.73017 + 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.279562 + 2.98695i) q^{9} +(2.20937 + 0.344476i) q^{10} +3.03746i q^{11} +(-1.28054 + 1.16628i) q^{12} +(-1.30218 + 1.30218i) q^{13} -2.03079 q^{14} +(-0.774498 + 3.79475i) q^{15} -1.00000 q^{16} +(0.0287275 - 0.0287275i) q^{17} +(-1.91441 - 2.30977i) q^{18} -2.41296i q^{19} +(-1.80585 + 1.31868i) q^{20} +(0.164069 - 3.51361i) q^{21} +(-2.14781 - 2.14781i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(0.0807905 - 1.73017i) q^{24} +(-1.52216 + 4.76267i) q^{25} -1.84156i q^{26} +(4.15095 - 3.12564i) q^{27} +(1.43599 - 1.43599i) q^{28} +8.32611 q^{29} +(-2.13564 - 3.23095i) q^{30} +10.8038 q^{31} +(0.707107 - 0.707107i) q^{32} +(3.88958 - 3.54254i) q^{33} +0.0406269i q^{34} +(0.699560 - 4.48678i) q^{35} +(2.98695 + 0.279562i) q^{36} +(-0.399778 - 0.399778i) q^{37} +(1.70622 + 1.70622i) q^{38} +(3.18620 + 0.148780i) q^{39} +(0.344476 - 2.20937i) q^{40} +9.45696i q^{41} +(2.36848 + 2.60051i) q^{42} +(-0.108956 + 0.108956i) q^{43} +3.03746 q^{44} +(5.76262 - 3.43399i) q^{45} +1.00000 q^{46} +(0.341054 - 0.341054i) q^{47} +(1.16628 + 1.28054i) q^{48} -2.87588i q^{49} +(-2.29139 - 4.44404i) q^{50} +(-0.0702912 - 0.00328227i) q^{51} +(1.30218 + 1.30218i) q^{52} +(0.120552 + 0.120552i) q^{53} +(-0.725006 + 5.14532i) q^{54} +(5.48518 - 4.00544i) q^{55} +2.03079i q^{56} +(-3.08990 + 2.81420i) q^{57} +(-5.88745 + 5.88745i) q^{58} +2.10585 q^{59} +(3.79475 + 0.774498i) q^{60} +10.7626 q^{61} +(-7.63947 + 7.63947i) q^{62} +(-4.69066 + 3.88777i) q^{63} +1.00000i q^{64} +(4.06869 + 0.634373i) q^{65} +(-0.245398 + 5.25530i) q^{66} +(-6.68856 - 6.68856i) q^{67} +(-0.0287275 - 0.0287275i) q^{68} +(-0.0807905 + 1.73017i) q^{69} +(2.67797 + 3.66730i) q^{70} +5.69670i q^{71} +(-2.30977 + 1.91441i) q^{72} +(6.43032 - 6.43032i) q^{73} +0.565371 q^{74} +(7.87405 - 3.60545i) q^{75} -2.41296 q^{76} +(-4.36175 + 4.36175i) q^{77} +(-2.35818 + 2.14778i) q^{78} +5.14788i q^{79} +(1.31868 + 1.80585i) q^{80} +(-8.84369 - 1.67007i) q^{81} +(-6.68708 - 6.68708i) q^{82} +(-3.07224 - 3.07224i) q^{83} +(-3.51361 - 0.164069i) q^{84} +(-0.0897600 - 0.0139950i) q^{85} -0.154087i q^{86} +(-9.71061 - 10.6619i) q^{87} +(-2.14781 + 2.14781i) q^{88} +12.0540 q^{89} +(-1.64659 + 6.50298i) q^{90} -3.73982 q^{91} +(-0.707107 + 0.707107i) q^{92} +(-12.6004 - 13.8347i) q^{93} +0.482323i q^{94} +(-4.35744 + 3.18193i) q^{95} +(-1.73017 - 0.0807905i) q^{96} +(7.38166 + 7.38166i) q^{97} +(2.03356 + 2.03356i) q^{98} +(-9.07272 - 0.849157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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