LMFDB - Embedded newform 690.2.i.f.47.13

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			47.13
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.28054 + 1.16628i) q^{3} -1.00000i q^{4} +(1.31868 + 1.80585i) q^{5} +(1.73017 - 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.279562 + 2.98695i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.28054 + 1.16628i) 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} +(1.16628 - 1.28054i) q^{12} +(-1.30218 + 1.30218i) q^{13} +2.03079 q^{14} +(-0.417505 + 3.85041i) q^{15} -1.00000 q^{16} +(-0.0287275 + 0.0287275i) q^{17} +(2.30977 + 1.91441i) 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} +(-3.12564 + 4.15095i) q^{27} +(1.43599 - 1.43599i) q^{28} -8.32611 q^{29} +(2.42743 + 3.01787i) q^{30} +10.8038 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.54254 - 3.88958i) 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} +(2.60051 + 2.36848i) q^{42} +(-0.108956 + 0.108956i) q^{43} -3.03746 q^{44} +(-5.02531 + 4.44368i) q^{45} +1.00000 q^{46} +(-0.341054 + 0.341054i) q^{47} +(-1.28054 - 1.16628i) 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} +(2.81420 - 3.08990i) q^{57} +(-5.88745 + 5.88745i) q^{58} -2.10585 q^{59} +(3.85041 + 0.417505i) q^{60} +10.7626 q^{61} +(7.63947 - 7.63947i) q^{62} +(-3.88777 + 4.69066i) 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} +(1.91441 - 2.30977i) q^{72} +(6.43032 - 6.43032i) q^{73} -0.565371 q^{74} +(-7.50381 + 4.32352i) q^{75} -2.41296 q^{76} +(4.36175 - 4.36175i) q^{77} +(-2.14778 + 2.35818i) 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} +(-10.6619 - 9.71061i) q^{87} +(-2.14781 + 2.14781i) q^{88} -12.0540 q^{89} +(-0.411275 + 6.69558i) q^{90} -3.73982 q^{91} +(0.707107 - 0.707107i) q^{92} +(13.8347 + 12.6004i) 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
$3$	1.28054	+	1.16628i	0.739320	+	0.673355i
$3$	1.28054	+	1.16628i	0.739320	+	0.673355i
$4$		−	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	$-0.848597\pi$
$11$		−	3.03746i		−	0.915827i	0.888997	−	0.457914i	$-0.151403\pi$
$12$	1.16628	−	1.28054i	0.336677	−	0.369660i
$13$	−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
$15$	−0.417505	+	3.85041i	−0.107799	+	0.994173i
$16$	−1.00000			−0.250000
$17$	−0.0287275	+	0.0287275i	−0.00696745	+	0.00696745i	−0.710582	−	0.703614i	$-0.751568\pi$
$17$	−0.0287275	+	0.0287275i	−0.00696745	+	0.00696745i	0.703614	+	0.710582i	$0.251568\pi$
$18$	2.30977	+	1.91441i	0.544418	+	0.451231i
$19$		−	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
$27$	−3.12564	+	4.15095i	−0.601529	+	0.798851i
$28$	1.43599	−	1.43599i	0.271376	−	0.271376i
$29$	−8.32611			−1.54612			−0.773060	−	0.634333i	$-0.781275\pi$
$29$	−8.32611			−1.54612			−0.773060	+	0.634333i	$0.781275\pi$
$30$	2.42743	+	3.01787i	0.443187	+	0.550986i
$31$	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
$33$	3.54254	−	3.88958i	0.616676	−	0.677089i
$34$			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	$-0.735551\pi$
$41$		−	9.45696i		−	1.47693i	0.674293	−	0.738464i	$-0.264449\pi$
$42$	2.60051	+	2.36848i	0.401267	+	0.365465i
$43$	−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
$45$	−5.02531	+	4.44368i	−0.749129	+	0.662424i
$46$	1.00000			0.147442
$47$	−0.341054	+	0.341054i	−0.0497478	+	0.0497478i	−0.731543	−	0.681795i	$-0.761199\pi$
$47$	−0.341054	+	0.341054i	−0.0497478	+	0.0497478i	0.681795	+	0.731543i	$0.261199\pi$
$48$	−1.28054	−	1.16628i	−0.184830	−	0.168339i
$49$		−	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	0.698779	−	0.715338i	$-0.253727\pi$
$53$	−0.120552	−	0.120552i	−0.0165590	−	0.0165590i	−0.715338	+	0.698779i	$0.753727\pi$
$54$	0.725006	+	5.14532i	0.0986608	+	0.700190i
$55$	5.48518	−	4.00544i	0.739621	−	0.540093i
$56$		−	2.03079i		−	0.271376i
$57$	2.81420	−	3.08990i	0.372750	−	0.409267i
$58$	−5.88745	+	5.88745i	−0.773060	+	0.773060i
$59$	−2.10585			−0.274159			−0.137079	−	0.990560i	$-0.543772\pi$
$59$	−2.10585			−0.274159			−0.137079	+	0.990560i	$0.543772\pi$
$60$	3.85041	+	0.417505i	0.497086	+	0.0538996i
$61$	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
$63$	−3.88777	+	4.69066i	−0.489813	+	0.590968i
$64$			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	$-0.890237\pi$
$71$		−	5.69670i		−	0.676074i	0.941133	−	0.338037i	$-0.109763\pi$
$72$	1.91441	−	2.30977i	0.225615	−	0.272209i
$73$	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
$75$	−7.50381	+	4.32352i	−0.866465	+	0.499237i
$76$	−2.41296			−0.276786
$77$	4.36175	−	4.36175i	0.497067	−	0.497067i
$78$	−2.14778	+	2.35818i	−0.243188	+	0.267012i
$79$			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	0.855321	−	0.518098i	$-0.173360\pi$
$83$	3.07224	+	3.07224i	0.337223	+	0.337223i	−0.518098	+	0.855321i	$0.673360\pi$
$84$	3.51361	−	0.164069i	0.383366	−	0.0179014i
$85$	−0.0897600	−	0.0139950i	−0.00973584	−	0.00151797i
$86$			0.154087i			0.0166156i
$87$	−10.6619	−	9.71061i	−1.14308	−	1.04109i
$88$	−2.14781	+	2.14781i	−0.228957	+	0.228957i
$89$	−12.0540			−1.27773			−0.638863	−	0.769320i	$-0.720595\pi$
$89$	−12.0540			−1.27773			−0.638863	+	0.769320i	$0.720595\pi$
$90$	−0.411275	+	6.69558i	−0.0433522	+	0.705777i
$91$	−3.73982			−0.392040
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	13.8347	+	12.6004i	1.43460	+	1.30660i
$94$			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	$-0.713363\pi$
$101$		−	15.7509i		−	1.56727i	0.621222	−	0.783635i	$-0.286637\pi$
$102$	−0.0473825	+	0.0520243i	−0.00469157	+	0.00515117i
$103$	−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
$105$	−6.12868	+	4.92961i	−0.598098	+	0.481081i
$106$	−0.170486			−0.0165590
$107$	−8.28163	+	8.28163i	−0.800616	+	0.800616i	−0.983192	−	0.182576i	$-0.941556\pi$
$107$	−8.28163	+	8.28163i	−0.800616	+	0.800616i	0.182576	+	0.983192i	$0.441556\pi$
$108$	4.15095	+	3.12564i	0.399425	+	0.300765i
$109$		−	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	0.0311086	−	0.999516i	$-0.490096\pi$
$113$	−10.2943	−	10.2943i	−0.968407	−	0.968407i	−0.999516	+	0.0311086i	$0.990096\pi$
$114$	−0.194945	−	4.17483i	−0.0182582	−	0.391008i
$115$	−0.344476	+	2.20937i	−0.0321226	+	0.206025i
$116$			8.32611i			0.773060i
$117$	−4.25357	−	3.52549i	−0.393243	−	0.325932i
$118$	−1.48906	+	1.48906i	−0.137079	+	0.137079i
$119$	−0.0825048			−0.00756320
$120$	3.01787	−	2.42743i	0.275493	−	0.221593i
$121$	1.77386			0.161260
$122$	7.61029	−	7.61029i	0.689003	−	0.689003i
$123$	11.0295	−	12.1100i	0.994496	−	1.09192i
$124$		−	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	$0.122247\pi$
$131$			8.57676i			0.749355i	−0.927155	+	0.374677i	$0.877753\pi$
$132$	−3.88958	−	3.54254i	−0.338545	−	0.308338i
$133$	3.46499	−	3.46499i	0.300452	−	0.300452i
$134$	−9.45905			−0.817137
$135$	−11.6177	−	0.170634i	−0.999892	−	0.0146859i
$136$	0.0406269			0.00348373
$137$	11.6408	−	11.6408i	0.994543	−	0.994543i	−0.00544239	−	0.999985i	$-0.501732\pi$
$137$	11.6408	−	11.6408i	0.994543	−	0.994543i	0.999985	+	0.00544239i	$0.00173237\pi$
$138$	1.28054	+	1.16628i	0.109007	+	0.0992807i
$139$		−	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
$147$	3.35409	−	3.68268i	0.276641	−	0.303742i
$148$	−0.399778	+	0.399778i	−0.0328615	+	0.0328615i
$149$	−5.49620			−0.450266			−0.225133	−	0.974328i	$-0.572282\pi$
$149$	−5.49620			−0.450266			−0.225133	+	0.974328i	$0.572282\pi$
$150$	−2.24880	+	8.36319i	−0.183614	+	0.682851i
$151$	−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
$153$	−0.0938387	−	0.0777765i	−0.00758641	−	0.00628785i
$154$		−	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
$162$	−5.07251	+	7.43435i	−0.398534	+	0.584098i
$163$	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
$165$	11.6955	+	1.26815i	0.910491	+	0.0987255i
$166$	4.34481			0.337223
$167$	4.99243	−	4.99243i	0.386326	−	0.386326i	−0.487049	−	0.873375i	$-0.661927\pi$
$167$	4.99243	−	4.99243i	0.386326	−	0.386326i	0.873375	+	0.487049i	$0.161927\pi$
$168$	2.36848	−	2.60051i	0.182732	−	0.200634i
$169$			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	0.487193	−	0.873294i	$-0.338021\pi$
$173$	−5.07836	−	5.07836i	−0.386101	−	0.386101i	−0.873294	+	0.487193i	$0.838021\pi$
$174$	−14.4055	+	0.672671i	−1.09208	+	0.0509950i
$175$	−9.02493	+	4.65334i	−0.682221	+	0.351760i
$176$			3.03746i			0.228957i
$177$	−2.69663	−	2.45602i	−0.202691	−	0.184606i
$178$	−8.52350	+	8.52350i	−0.638863	+	0.638863i
$179$	−9.09915			−0.680103			−0.340051	−	0.940407i	$-0.610444\pi$
$179$	−9.09915			−0.680103			−0.340051	+	0.940407i	$0.610444\pi$
$180$	4.44368	+	5.02531i	0.331212	+	0.374564i
$181$	−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
$183$	13.7819	+	12.5522i	1.01879	+	0.927887i
$184$		−	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	$0.197149\pi$
$191$			16.0457i			1.16103i	−0.814250	+	0.580514i	$0.802851\pi$
$192$	−1.16628	+	1.28054i	−0.0841693	+	0.0924150i
$193$	−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
$195$	−4.47026	−	5.55758i	−0.320122	−	0.397987i
$196$	−2.87588			−0.205420
$197$	14.5337	−	14.5337i	1.03548	−	1.03548i	0.0361361	−	0.999347i	$-0.488495\pi$
$197$	14.5337	−	14.5337i	1.03548	−	1.03548i	0.999347	−	0.0361361i	$-0.0115050\pi$
$198$	5.81493	−	7.01582i	0.413249	−	0.498593i
$199$			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
$207$	−1.91441	+	2.30977i	−0.133061	+	0.160540i
$208$	1.30218	−	1.30218i	0.0902897	−	0.0902897i
$209$	−7.32927			−0.506976
$210$	−0.847866	+	7.81939i	−0.0585083	+	0.539589i
$211$	−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
$213$	6.64397	−	7.29485i	0.455238	−	0.499835i
$214$			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
$222$	−0.723980	−	0.659383i	−0.0485903	−	0.0442549i
$223$	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
$225$	−14.6514	−	3.21513i	−0.976759	−	0.214342i
$226$	−14.5584			−0.968407
$227$	−4.95555	+	4.95555i	−0.328911	+	0.328911i	−0.852172	−	0.523261i	$-0.824715\pi$
$227$	−4.95555	+	4.95555i	−0.328911	+	0.328911i	0.523261	+	0.852172i	$0.324715\pi$
$228$	−3.08990	−	2.81420i	−0.204633	−	0.186375i
$229$		−	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	0.986424	−	0.164218i	$-0.0525099\pi$
$233$	12.5504	+	12.5504i	0.822206	+	0.822206i	−0.164218	+	0.986424i	$0.552510\pi$
$234$	−5.50063	+	0.514829i	−0.359587	+	0.0336554i
$235$	−1.06563	−	0.166149i	−0.0695141	−	0.0108384i
$236$			2.10585i			0.137079i
$237$	−6.00390	+	6.59207i	−0.389995	+	0.428201i
$238$	−0.0583397	+	0.0583397i	−0.00378160	+	0.00378160i
$239$	1.23240			0.0797173			0.0398586	−	0.999205i	$-0.487309\pi$
$239$	1.23240			0.0797173			0.0398586	+	0.999205i	$0.487309\pi$
$240$	0.417505	−	3.85041i	0.0269498	−	0.248543i
$241$	−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
$243$	−13.2725	−	8.17566i	−0.851430	−	0.524469i
$244$		−	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	$0.114275\pi$
$251$			11.1326i			0.702686i	−0.936247	+	0.351343i	$0.885725\pi$
$252$	4.69066	+	3.88777i	0.295484	+	0.244906i
$253$	2.14781	−	2.14781i	0.135031	−	0.135031i
$254$	−8.94538			−0.561283
$255$	−0.0986190	−	0.122607i	−0.00617576	−	0.00767794i
$256$	1.00000			0.0625000
$257$	0.426761	−	0.426761i	0.0266206	−	0.0266206i	−0.693671	−	0.720292i	$-0.744008\pi$
$257$	0.426761	−	0.426761i	0.0266206	−	0.0266206i	0.720292	+	0.693671i	$0.244008\pi$
$258$	−0.179709	+	0.197314i	−0.0111882	+	0.0122843i
$259$		−	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	0.991648	−	0.128977i	$-0.0411694\pi$
$263$	13.9902	+	13.9902i	0.862670	+	0.862670i	−0.128977	+	0.991648i	$0.541169\pi$
$264$	−5.25530	+	0.245398i	−0.323441	+	0.0151032i
$265$	0.0587283	−	0.376667i	0.00360765	−	0.0231385i
$266$		−	4.90023i		−	0.300452i
$267$	−15.4357	−	14.0584i	−0.944649	−	0.860363i
$268$	−6.68856	+	6.68856i	−0.408569	+	0.408569i
$269$	−15.5476			−0.947954			−0.473977	−	0.880537i	$-0.657182\pi$
$269$	−15.5476			−0.947954			−0.473977	+	0.880537i	$0.657182\pi$
$270$	−8.33561	+	8.09430i	−0.507289	+	0.492603i
$271$	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
$273$	−4.78898	−	4.36169i	−0.289843	−	0.263982i
$274$		−	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	$-0.941972\pi$
$281$		−	6.07800i		−	0.362583i	0.983429	−	0.181292i	$-0.0580278\pi$
$282$	−0.562525	+	0.617633i	−0.0334979	+	0.0367795i
$283$	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
$285$	9.29091	+	1.00742i	0.550346	+	0.0596746i
$286$	5.59364			0.330759
$287$	13.5801	−	13.5801i	0.801606	−	0.801606i
$288$	−2.30977	−	1.91441i	−0.136104	−	0.112808i
$289$			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	0.934548	−	0.355837i	$-0.115804\pi$
$293$	9.90593	+	9.90593i	0.578711	+	0.578711i	−0.355837	+	0.934548i	$0.615804\pi$
$294$	−0.232344	−	4.97575i	−0.0135506	−	0.290192i
$295$	−2.77695	−	3.80284i	−0.161680	−	0.221410i
$296$			0.565371i			0.0328615i
$297$	12.6083	+	9.49399i	0.731609	+	0.550897i
$298$	−3.88640	+	3.88640i	−0.225133	+	0.225133i
$299$	−1.84156			−0.106500
$300$	4.32352	+	7.50381i	0.249619	+	0.433233i
$301$	−0.312919			−0.0180363
$302$	−6.68091	+	6.68091i	−0.384443	+	0.384443i
$303$	18.3700	−	20.1696i	1.05533	−	1.15871i
$304$			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	$-0.784427\pi$
$311$		−	22.1020i		−	1.25329i	0.779304	−	0.626646i	$-0.215573\pi$
$312$	2.35818	+	2.14778i	0.133506	+	0.121594i
$313$	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
$315$	−13.5973	−	0.835215i	−0.766124	−	0.0470590i
$316$	5.14788			0.289591
$317$	−11.0713	+	11.0713i	−0.621826	+	0.621826i	−0.945998	−	0.324172i	$-0.894914\pi$
$317$	−11.0713	+	11.0713i	−0.621826	+	0.621826i	0.324172	+	0.945998i	$0.394914\pi$
$318$	−0.218314	−	0.198835i	−0.0122424	−	0.0111501i
$319$			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
$327$	6.01997	−	6.60971i	0.332905	−	0.365518i
$328$	−6.68708	+	6.68708i	−0.369232	+	0.369232i
$329$	−0.979497			−0.0540014
$330$	9.16666	−	7.37322i	0.504608	−	0.405883i
$331$	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
$333$	1.08235	−	1.30588i	0.0593125	−	0.0715616i
$334$		−	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
$342$	4.61940	−	5.57339i	0.249789	−	0.301375i
$343$	14.1816	−	14.1816i	0.765737	−	0.765737i
$344$	0.154087			0.00830781
$345$	−3.01787	+	2.42743i	−0.162477	+	0.130689i
$346$	−7.18189			−0.386101
$347$	9.47770	−	9.47770i	0.508789	−	0.508789i	−0.405365	−	0.914155i	$-0.632856\pi$
$347$	9.47770	−	9.47770i	0.508789	−	0.508789i	0.914155	+	0.405365i	$0.132856\pi$
$348$	−9.71061	+	10.6619i	−0.520543	+	0.571538i
$349$		−	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	$-0.939579\pi$
$353$	−21.9958	−	21.9958i	−1.17072	−	1.17072i	−0.188681	−	0.982038i	$-0.560421\pi$
$354$	−3.64347	+	0.170133i	−0.193648	+	0.00904247i
$355$	10.2874	−	7.51214i	0.545997	−	0.398703i
$356$			12.0540i			0.638863i
$357$	−0.105651	−	0.0962240i	−0.00559162	−	0.00509271i
$358$	−6.43407	+	6.43407i	−0.340051	+	0.340051i
$359$	23.7395			1.25292			0.626461	−	0.779453i	$-0.284503\pi$
$359$	23.7395			1.25292			0.626461	+	0.779453i	$0.284503\pi$
$360$	6.69558	+	0.411275i	0.352888	+	0.0216761i
$361$	13.1776			0.693558
$362$	−18.0249	+	18.0249i	−0.947367	+	0.947367i
$363$	2.27150	+	2.06883i	0.119223	+	0.108585i
$364$			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
$372$	12.6004	−	13.8347i	0.653298	−	0.717298i
$373$	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
$375$	−17.7028	−	7.84937i	−0.914166	−	0.405340i
$376$	0.482323			0.0248739
$377$	10.8421	−	10.8421i	0.558395	−	0.558395i
$378$	−6.34752	+	8.42972i	−0.326481	+	0.433578i
$379$			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	$0.101378\pi$
$383$	24.7143	+	24.7143i	1.26284	+	1.26284i	0.313131	+	0.949710i	$0.398622\pi$
$384$	0.0807905	+	1.73017i	0.00412283	+	0.0882921i
$385$	13.6284	+	2.12488i	0.694568	+	0.108294i
$386$			7.31479i			0.372313i
$387$	−0.355906	−	0.294986i	−0.0180917	−	0.0149950i
$388$	7.38166	−	7.38166i	0.374747	−	0.374747i
$389$	12.7778			0.647858			0.323929	−	0.946081i	$-0.394996\pi$
$389$	12.7778			0.647858			0.323929	+	0.946081i	$0.394996\pi$
$390$	−7.09075	−	0.768858i	−0.359054	−	0.0389327i
$391$	−0.0406269			−0.00205459
$392$	−2.03356	+	2.03356i	−0.102710	+	0.102710i
$393$	−10.0029	+	10.9829i	−0.504582	+	0.554013i
$394$		−	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	$0.0311301\pi$
$401$			3.91057i			0.195284i	−0.995222	+	0.0976422i	$0.968870\pi$
$402$	−12.1127	−	11.0319i	−0.604126	−	0.550223i
$403$	−14.0685	+	14.0685i	−0.700803	+	0.700803i
$404$	−15.7509			−0.783635
$405$	−14.6779	−	13.7680i	−0.729351	−	0.684139i
$406$	−16.9086			−0.839160
$407$	−1.21431	+	1.21431i	−0.0601909	+	0.0601909i
$408$	0.0520243	+	0.0473825i	0.00257559	+	0.00234578i
$409$		−	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
$417$	0.261599	−	0.287227i	0.0128106	−	0.0140655i
$418$	−5.18258	+	5.18258i	−0.253488	+	0.253488i
$419$	−14.3441			−0.700754			−0.350377	−	0.936609i	$-0.613946\pi$
$419$	−14.3441			−0.700754			−0.350377	+	0.936609i	$0.613946\pi$
$420$	4.92961	+	6.12868i	0.240541	+	0.299049i
$421$	−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
$423$	−1.11405	−	0.923363i	−0.0541672	−	0.0448955i
$424$			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	$0.309978\pi$
$431$			34.3396i			1.65408i	−0.562141	+	0.827041i	$0.690022\pi$
$432$	3.12564	−	4.15095i	0.150382	−	0.199713i
$433$	−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
$435$	3.47619	−	32.0590i	0.166671	−	1.53711i
$436$	−5.16166			−0.247199
$437$	1.70622	−	1.70622i	0.0816197	−	0.0816197i
$438$	10.6060	−	11.6450i	0.506774	−	0.556421i
$439$		−	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	$0.00607322\pi$
$443$	21.4453	+	21.4453i	1.01890	+	1.01890i	0.0190784	+	0.999818i	$0.493927\pi$
$444$	−0.978185	+	0.0456766i	−0.0464226	+	0.00216772i
$445$	−15.8955	−	21.7677i	−0.753517	−	1.03189i
$446$		−	9.38220i		−	0.444260i
$447$	−7.03810	−	6.41013i	−0.332891	−	0.303189i
$448$	−1.43599	+	1.43599i	−0.0678440	+	0.0678440i
$449$	−19.2237			−0.907224			−0.453612	−	0.891199i	$-0.649865\pi$
$449$	−19.2237			−0.907224			−0.453612	+	0.891199i	$0.649865\pi$
$450$	−12.6335	+	8.08665i	−0.595550	+	0.381208i
$451$	−28.7251			−1.35261
$452$	−10.2943	+	10.2943i	−0.484204	+	0.484204i
$453$	−12.0988	−	11.0193i	−0.568453	−	0.517733i
$454$			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	$0.250998\pi$
$461$			30.4595i			1.41864i	−0.704886	+	0.709320i	$0.749002\pi$
$462$	7.19416	−	7.89893i	0.334703	−	0.367492i
$463$	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
$465$	−4.51066	+	41.5993i	−0.209177	+	1.92912i
$466$	17.7490			0.822206
$467$	−27.1900	+	27.1900i	−1.25820	+	1.25820i	−0.306251	+	0.951951i	$0.599075\pi$
$467$	−27.1900	+	27.1900i	−1.25820	+	1.25820i	−0.951951	+	0.306251i	$0.900925\pi$
$468$	−3.52549	+	4.25357i	−0.162966	+	0.196621i
$469$		−	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
$477$	0.326380	−	0.393783i	0.0149439	−	0.0180301i
$478$	0.871438	−	0.871438i	0.0398586	−	0.0398586i
$479$	−7.60429			−0.347449			−0.173724	−	0.984794i	$-0.555580\pi$
$479$	−7.60429			−0.347449			−0.173724	+	0.984794i	$0.555580\pi$
$480$	−2.42743	−	3.01787i	−0.110797	−	0.137746i
$481$	1.04116			0.0474729
$482$	−7.09816	+	7.09816i	−0.323312	+	0.323312i
$483$	−2.36848	+	2.60051i	−0.107770	+	0.118327i
$484$		−	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	$-0.969115\pi$
$491$		−	4.29319i		−	0.193749i	0.995297	−	0.0968745i	$-0.0308845\pi$
$492$	−12.1100	−	11.0295i	−0.545961	−	0.497248i
$493$	0.239189	−	0.239189i	0.0107725	−	0.0107725i
$494$	4.44361			0.199927
$495$	13.4975	+	15.2642i	0.606666	+	0.686073i
$496$	−10.8038			−0.485107
$497$	8.18039	−	8.18039i	0.366941	−	0.366941i
$498$	5.56370	+	5.06728i	0.249315	+	0.227070i
$499$		−	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	0.0301846	−	0.999544i	$-0.490390\pi$
$503$	−21.7405	−	21.7405i	−0.969360	−	0.969360i	−0.999544	+	0.0301846i	$0.990390\pi$
$504$	6.06587	−	0.567733i	0.270195	−	0.0252888i
$505$	28.4436	−	20.7704i	1.26572	−	0.924270i
$506$		−	3.03746i		−	0.135031i
$507$	−11.2064	+	12.3043i	−0.497696	+	0.546452i
$508$	−6.32534	+	6.32534i	−0.280642	+	0.280642i
$509$	36.4307			1.61476			0.807381	−	0.590031i	$-0.200884\pi$
$509$	36.4307			1.61476			0.807381	+	0.590031i	$0.200884\pi$
$510$	−0.156430	−	0.0169619i	−0.00692685	−	0.000751086i
$511$	18.4677			0.816963
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	10.0161	+	7.54205i	0.442221	+	0.332990i
$514$		−	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	$0.354989\pi$
$521$			40.9950i			1.79602i	−0.439972	+	0.898012i	$0.645011\pi$
$522$	−19.2314	−	15.9396i	−0.841735	−	0.697657i
$523$	−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
$525$	−16.9839	−	4.56685i	−0.741238	−	0.199314i
$526$	19.7851			0.862670
$527$	−0.310368	+	0.310368i	−0.0135198	+	0.0135198i
$528$	−3.54254	+	3.88958i	−0.154169	+	0.169272i
$529$			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
$537$	−11.6518	−	10.6122i	−0.502813	−	0.457950i
$538$	−10.9938	+	10.9938i	−0.473977	+	0.473977i
$539$	−8.73536			−0.376259
$540$	−0.170634	+	11.6177i	−0.00734294	+	0.499946i
$541$	−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
$543$	−32.6423	−	29.7298i	−1.40081	−	1.27583i
$544$		−	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
$552$	1.16628	−	1.28054i	0.0496404	−	0.0545034i
$553$	−7.39230	+	7.39230i	−0.314352	+	0.314352i
$554$	6.76562			0.287444
$555$	1.70622	−	1.37240i	0.0724249	−	0.0582551i
$556$	−0.224301			−0.00951249
$557$	21.5167	−	21.5167i	0.911692	−	0.911692i	−0.0847134	−	0.996405i	$-0.526997\pi$
$557$	21.5167	−	21.5167i	0.911692	−	0.911692i	0.996405	+	0.0847134i	$0.0269975\pi$
$558$	24.9544	+	20.6830i	1.05640	+	0.875580i
$559$		−	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	0.821832	−	0.569729i	$-0.192952\pi$
$563$	5.98181	+	5.98181i	0.252103	+	0.252103i	−0.569729	+	0.821832i	$0.692952\pi$
$564$	0.0389671	+	0.834498i	0.00164081	+	0.0351387i
$565$	5.01501	−	32.1649i	0.210983	−	1.35319i
$566$		−	2.30819i		−	0.0970206i
$567$	−15.0976	−	10.3012i	−0.634041	−	0.432611i
$568$	−4.02818	+	4.02818i	−0.169019	+	0.169019i
$569$	−20.4479			−0.857222			−0.428611	−	0.903489i	$-0.640997\pi$
$569$	−20.4479			−0.857222			−0.428611	+	0.903489i	$0.640997\pi$
$570$	7.28202	−	5.85731i	0.305010	−	0.245336i
$571$	−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
$573$	−18.7139	+	20.5472i	−0.781784	+	0.858372i
$574$		−	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
$582$	13.3679	+	12.1751i	0.554116	+	0.504675i
$583$	−0.366170	+	0.366170i	−0.0151652	+	0.0151652i
$584$	−9.09384			−0.376306
$585$	0.757387	−	12.3303i	0.0313141	−	0.509795i
$586$	14.0091			0.578711
$587$	−29.6663	+	29.6663i	−1.22446	+	1.22446i	−0.258426	+	0.966031i	$0.583204\pi$
$587$	−29.6663	+	29.6663i	−1.22446	+	1.22446i	−0.966031	+	0.258426i	$0.916796\pi$
$588$	−3.68268	−	3.35409i	−0.151871	−	0.138321i
$589$		−	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	$-0.935935\pi$
$593$	−28.7282	−	28.7282i	−1.17972	−	1.17972i	−0.199911	−	0.979814i	$-0.564065\pi$
$594$	15.6287	−	2.20217i	0.641253	−	0.0903562i
$595$	−0.108798	−	0.148991i	−0.00446026	−	0.00610803i
$596$			5.49620i			0.225133i
$597$	−14.9925	+	16.4613i	−0.613603	+	0.673714i
$598$	−1.30218	+	1.30218i	−0.0532500	+	0.0532500i
$599$	46.9570			1.91861			0.959305	−	0.282371i	$-0.0911211\pi$
$599$	46.9570			1.91861			0.959305	+	0.282371i	$0.0911211\pi$
$600$	8.36319	+	2.24880i	0.341426	+	0.0918069i
$601$	−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
$603$	18.1085	−	21.8482i	0.737435	−	0.889728i
$604$			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
$612$	−0.0777765	+	0.0938387i	−0.00314393	+	0.00379321i
$613$	−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
$615$	36.4132	+	3.94832i	1.46832	+	0.159212i
$616$	−6.16844			−0.248534
$617$	−9.82533	+	9.82533i	−0.395553	+	0.395553i	−0.876661	−	0.481108i	$-0.840234\pi$
$617$	−9.82533	+	9.82533i	−0.395553	+	0.395553i	0.481108	+	0.876661i	$0.340234\pi$
$618$	−16.3961	+	18.0023i	−0.659547	+	0.724159i
$619$		−	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
$627$	−9.38542	−	8.54801i	−0.374818	−	0.341375i
$628$	15.6517	−	15.6517i	0.624570	−	0.624570i
$629$	0.0229693			0.000915844
$630$	−10.2054	+	9.02419i	−0.406591	+	0.359532i
$631$	−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
$633$	−31.7702	−	28.9355i	−1.26275	−	1.15008i
$634$			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	$0.331055\pi$
$641$			43.6697i			1.72485i	−0.506186	+	0.862424i	$0.668945\pi$
$642$	−13.6595	+	14.9977i	−0.539098	+	0.591911i
$643$	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
$645$	−0.374036	−	0.465015i	−0.0147277	−	0.0183100i
$646$	0.0980312			0.00385699
$647$	−24.4013	+	24.4013i	−0.959316	+	0.959316i	−0.999204	−	0.0398886i	$-0.987300\pi$
$647$	−24.4013	+	24.4013i	−0.959316	+	0.959316i	0.0398886	+	0.999204i	$0.487300\pi$
$648$	7.43435	+	5.07251i	0.292049	+	0.199267i
$649$			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	0.629188	−	0.777253i	$-0.283388\pi$
$653$	−3.78364	−	3.78364i	−0.148065	−	0.148065i	−0.777253	+	0.629188i	$0.783388\pi$
$654$	−0.417014	−	8.93053i	−0.0163065	−	0.349211i
$655$	−15.4883	+	11.3100i	−0.605178	+	0.441919i
$656$			9.45696i			0.369232i
$657$	21.0047	+	17.4093i	0.819471	+	0.679203i
$658$	−0.692609	+	0.692609i	−0.0270007	+	0.0270007i
$659$	21.1564			0.824137			0.412069	−	0.911153i	$-0.364806\pi$
$659$	21.1564			0.824137			0.412069	+	0.911153i	$0.364806\pi$
$660$	1.26815	−	11.6955i	0.0493628	−	0.455245i
$661$	−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
$663$	0.0872575	−	0.0958057i	0.00338880	−	0.00372078i
$664$		−	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
$672$	−2.60051	−	2.36848i	−0.100317	−	0.0913662i
$673$	−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
$675$	−15.0119	−	21.2048i	−0.577809	−	0.816172i
$676$	9.60867			0.369564
$677$	8.11519	−	8.11519i	0.311892	−	0.311892i	−0.533750	−	0.845642i	$-0.679218\pi$
$677$	8.11519	−	8.11519i	0.311892	−	0.311892i	0.845642	+	0.533750i	$0.179218\pi$
$678$	−18.6425	−	16.9792i	−0.715963	−	0.652082i
$679$			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	0.378589	−	0.925565i	$-0.376409\pi$
$683$	−14.2948	−	14.2948i	−0.546975	−	0.546975i	−0.925565	+	0.378589i	$0.876409\pi$
$684$	−0.674573	−	7.20739i	−0.0257929	−	0.275582i
$685$	36.3721	+	5.67098i	1.38971	+	0.216677i
$686$		−	20.0559i		−	0.765737i
$687$	13.1495	−	14.4377i	0.501685	−	0.550833i
$688$	0.108956	−	0.108956i	0.00415391	−	0.00415391i
$689$	0.313959			0.0119609
$690$	−0.417505	+	3.85041i	−0.0158941	+	0.146583i
$691$	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
$693$	14.2477	+	11.8089i	0.541225	+	0.448584i
$694$		−	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	$-0.747604\pi$
$701$		−	37.7240i		−	1.42482i	0.701765	−	0.712408i	$-0.252396\pi$
$702$	−7.64421	−	5.75604i	−0.288512	−	0.217248i
$703$	−0.964649	+	0.964649i	−0.0363824	+	0.0363824i
$704$	3.03746			0.114478
$705$	−1.17081	−	1.45559i	−0.0440951	−	0.0548207i
$706$	−31.1068			−1.17072
$707$	22.6180	−	22.6180i	0.850639	−	0.850639i
$708$	−2.45602	+	2.69663i	−0.0923030	+	0.101345i
$709$		−	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
$717$	1.57814	+	1.43733i	0.0589366	+	0.0536780i
$718$	16.7863	−	16.7863i	0.626461	−	0.626461i
$719$	23.4101			0.873050			0.436525	−	0.899692i	$-0.356209\pi$
$719$	23.4101			0.873050			0.436525	+	0.899692i	$0.356209\pi$
$720$	5.02531	−	4.44368i	0.187282	−	0.165606i
$721$	−28.5497			−1.06325
$722$	9.31797	−	9.31797i	0.346779	−	0.346779i
$723$	−12.8545	−	11.7075i	−0.478062	−	0.435408i
$724$			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
$732$	12.5522	−	13.7819i	0.463944	−	0.509394i
$733$	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
$735$	11.0733	+	1.20069i	0.408446	+	0.0442883i
$736$	−1.00000			−0.0368605
$737$	−20.3162	+	20.3162i	−0.748357	+	0.748357i
$738$	18.1045	−	21.8434i	0.666435	−	0.804066i
$739$			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	0.991502	−	0.130091i	$-0.0415269\pi$
$743$	23.4804	+	23.4804i	0.861411	+	0.861411i	−0.130091	+	0.991502i	$0.541527\pi$
$744$	−0.872848	−	18.6924i	−0.0320002	−	0.685298i
$745$	−7.24774	−	9.92529i	−0.265537	−	0.363635i
$746$		−	24.4064i		−	0.893581i
$747$	−8.31774	+	10.0355i	−0.304330	+	0.367180i
$748$	0.0872586	−	0.0872586i	0.00319049	−	0.00319049i
$749$	−23.7846			−0.869072
$750$	−18.0681	+	6.96740i	−0.659753	+	0.254413i
$751$	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
$753$	−12.9838	+	14.2558i	−0.473157	+	0.519510i
$754$		−	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	$-0.966441\pi$
$761$		−	5.80591i		−	0.210464i	0.994448	−	0.105232i	$-0.0335586\pi$
$762$	−11.4549	−	10.4329i	−0.414968	−	0.377943i
$763$	7.41208	−	7.41208i	0.268335	−	0.268335i
$764$	16.0457			0.580514
$765$	0.0167088	−	0.272021i	0.000604109	−	0.00983493i
$766$	34.9513			1.26284
$767$	2.74219	−	2.74219i	0.0990148	−	0.0990148i
$768$	1.28054	+	1.16628i	0.0462075	+	0.0420847i
$769$		−	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	0.786979	−	0.616980i	$-0.211644\pi$
$773$	4.72645	+	4.72645i	0.169999	+	0.169999i	−0.616980	+	0.786979i	$0.711644\pi$
$774$	−0.460250	+	0.0430769i	−0.0165433	+	0.00154837i
$775$	−16.4451	+	51.4552i	−0.590726	+	1.84832i
$776$		−	10.4392i		−	0.374747i
$777$	1.33907	−	1.47025i	0.0480389	−	0.0527450i
$778$	9.03524	−	9.03524i	0.323929	−	0.323929i
$779$	−22.8193			−0.817586
$780$	−5.55758	+	4.47026i	−0.198993	+	0.160061i
$781$	−17.3035			−0.619167
$782$	−0.0287275	+	0.0287275i	−0.00102729	+	0.00102729i
$783$	26.0244	−	34.5613i	0.930036	−	1.23512i
$784$			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
$792$	−7.01582	−	5.81493i	−0.249296	−	0.206625i
$793$	−14.0148	+	14.0148i	−0.497679	+	0.497679i
$794$	−28.3403			−1.00576
$795$	0.514505	−	0.413843i	0.0182476	−	0.0146775i
$796$	12.8549			0.455631
$797$	−16.3453	+	16.3453i	−0.578980	+	0.578980i	−0.934622	−	0.355642i	$-0.884262\pi$
$797$	−16.3453	+	16.3453i	−0.578980	+	0.578980i	0.355642	+	0.934622i	$0.384262\pi$
$798$	5.71506	−	6.27494i	0.202311	−	0.222130i
$799$		−	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
$807$	−19.9093	−	18.1329i	−0.700841	−	0.638309i
$808$	−11.1375	+	11.1375i	−0.391817	+	0.391817i
$809$	−45.2033			−1.58926			−0.794632	−	0.607091i	$-0.792336\pi$
$809$	−45.2033			−1.58926			−0.794632	+	0.607091i	$0.792336\pi$
$810$	−20.1143	+	0.643374i	−0.706745	+	0.0226059i
$811$	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
$813$	3.96215	+	3.60863i	0.138959	+	0.126560i
$814$			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	$0.0347356\pi$
$821$			6.24113i			0.217817i	−0.994052	+	0.108909i	$0.965264\pi$
$822$	19.2001	−	21.0810i	0.669680	−	0.735285i
$823$	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
$825$	13.1325	+	22.7925i	0.457215	+	0.793533i
$826$	−4.27655			−0.148800
$827$	−3.32709	+	3.32709i	−0.115694	+	0.115694i	−0.762584	−	0.646890i	$-0.776069\pi$
$827$	−3.32709	+	3.32709i	−0.115694	+	0.115694i	0.646890	+	0.762584i	$0.276069\pi$
$828$	2.30977	+	1.91441i	0.0802700	+	0.0665303i
$829$			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
$837$	−33.7689	+	44.8462i	−1.16722	+	1.55011i
$838$	−10.1428	+	10.1428i	−0.350377	+	0.350377i
$839$	6.74222			0.232767			0.116384	−	0.993204i	$-0.462870\pi$
$839$	6.74222			0.232767			0.116384	+	0.993204i	$0.462870\pi$
$840$	7.81939	+	0.847866i	0.269795	+	0.0292541i
$841$	40.3241			1.39049
$842$	−6.04489	+	6.04489i	−0.208321	+	0.208321i
$843$	7.08868	−	7.78312i	0.244147	−	0.268065i
$844$			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
$852$	−7.29485	−	6.64397i	−0.249918	−	0.227619i
$853$	−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
$855$	10.7224	+	12.1259i	0.366700	+	0.414697i
$856$	11.7120			0.400308
$857$	−3.66827	+	3.66827i	−0.125306	+	0.125306i	−0.766979	−	0.641673i	$-0.778241\pi$
$857$	−3.66827	+	3.66827i	−0.125306	+	0.125306i	0.641673	+	0.766979i	$0.278241\pi$
$858$	7.16288	+	6.52378i	0.244537	+	0.222718i
$859$		−	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	0.758933	−	0.651169i	$-0.225721\pi$
$863$	3.16578	+	3.16578i	0.107764	+	0.107764i	−0.651169	+	0.758933i	$0.725721\pi$
$864$	−0.725006	−	5.14532i	−0.0246652	−	0.175048i
$865$	2.47399	−	15.8675i	0.0841183	−	0.539511i
$866$			17.7962i			0.604740i
$867$	−19.8249	+	21.7671i	−0.673289	+	0.739248i
$868$	15.5142	−	15.5142i	0.526586	−	0.526586i
$869$	15.6365			0.530431
$870$	−20.2111	−	25.1272i	−0.685220	−	0.851890i
$871$	17.4194			0.590233
$872$	−3.64985	+	3.64985i	−0.123599	+	0.123599i
$873$	−19.9850	+	24.1122i	−0.676389	+	0.816076i
$874$		−	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	$0.0701294\pi$
$881$			12.9732i			0.437080i	−0.975828	+	0.218540i	$0.929871\pi$
$882$	5.50561	−	6.64262i	0.185384	−	0.223669i
$883$	−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
$885$	0.879204	−	8.10841i	0.0295541	−	0.272561i
$886$	30.3282			1.01890
$887$	31.5863	−	31.5863i	1.06056	−	1.06056i	0.0625206	−	0.998044i	$-0.480086\pi$
$887$	31.5863	−	31.5863i	1.06056	−	1.06056i	0.998044	−	0.0625206i	$-0.0199139\pi$
$888$	−0.659383	+	0.723980i	−0.0221275	+	0.0242952i
$889$		−	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
$897$	−2.35818	−	2.14778i	−0.0787375	−	0.0717122i
$898$	−13.5932	+	13.5932i	−0.453612	+	0.453612i
$899$	−89.9540			−3.00013
$900$	−3.21513	+	14.6514i	−0.107171	+	0.488379i
$901$	0.00692630			0.000230749
$902$	−20.3117	+	20.3117i	−0.676306	+	0.676306i
$903$	−0.400705	−	0.364952i	−0.0133346	−	0.0121449i
$904$			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	$-0.911139\pi$
$911$		−	16.6340i		−	0.551109i	0.961285	−	0.275554i	$-0.0888614\pi$
$912$	−2.81420	+	3.08990i	−0.0931875	+	0.102317i
$913$	9.33180	−	9.33180i	0.308838	−	0.308838i
$914$	−16.5256			−0.546620
$915$	−4.49343	+	41.4404i	−0.148548	+	1.36998i
$916$	−11.2747			−0.372527
$917$	−12.3161	+	12.3161i	−0.406714	+	0.406714i
$918$	−0.168640	−	0.126985i	−0.00556595	−	0.00419113i
$919$		−	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
$927$	−32.4716	−	26.9135i	−1.06651	−	0.883955i
$928$	5.88745	−	5.88745i	0.193265	−	0.193265i
$929$	−0.182246			−0.00597931			−0.00298966	−	0.999996i	$-0.500952\pi$
$929$	−0.182246			−0.00597931			−0.00298966	+	0.999996i	$0.500952\pi$
$930$	26.2256	+	32.6046i	0.859972	+	1.06915i
$931$	−6.93940			−0.227430
$932$	12.5504	−	12.5504i	0.411103	−	0.411103i
$933$	25.7773	−	28.3025i	0.843910	−	0.926583i
$934$			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	$0.116546\pi$
$941$			21.9646i			0.716025i	−0.933717	+	0.358013i	$0.883454\pi$
$942$	28.3445	+	25.8155i	0.923514	+	0.841114i
$943$	6.68708	−	6.68708i	0.217761	−	0.217761i
$944$	2.10585			0.0685397
$945$	−16.4378	−	16.9279i	−0.534723	−	0.550664i
$946$	0.468032			0.0152170
$947$	2.78553	−	2.78553i	0.0905177	−	0.0905177i	−0.660398	−	0.750916i	$-0.729612\pi$
$947$	2.78553	−	2.78553i	0.0905177	−	0.0905177i	0.750916	+	0.660398i	$0.229612\pi$
$948$	6.59207	+	6.00390i	0.214100	+	0.194997i
$949$			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	0.619280	−	0.785170i	$-0.287425\pi$
$953$	−5.12116	−	5.12116i	−0.165891	−	0.165891i	−0.785170	+	0.619280i	$0.787425\pi$
$954$	−0.0476613	−	0.509232i	−0.00154309	−	0.0164870i
$955$	−28.9761	+	21.1592i	−0.937645	+	0.684697i
$956$		−	1.23240i		−	0.0398586i
$957$	−29.4955	+	32.3851i	−0.953456	+	1.04686i
$958$	−5.37704	+	5.37704i	−0.173724	+	0.173724i
$959$	33.4322			1.07958
$960$	−3.85041	−	0.417505i	−0.124272	−	0.0134749i
$961$	85.7231			2.76526
$962$	0.736213	−	0.736213i	0.0237365	−	0.0237365i
$963$	−27.0520	−	22.4216i	−0.871739	−	0.722524i
$964$			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	$-0.770785\pi$
$971$		−	41.0986i		−	1.31892i	0.751741	−	0.659459i	$-0.229215\pi$
$972$	−8.17566	+	13.2725i	−0.262234	+	0.425715i
$973$	0.322094	−	0.322094i	0.0103259	−	0.0103259i
$974$	25.4983			0.817017
$975$	4.14129	−	15.4013i	0.132628	−	0.493236i
$976$	−10.7626			−0.344502
$977$	−5.84940	+	5.84940i	−0.187139	+	0.187139i	−0.794458	−	0.607319i	$-0.792245\pi$
$977$	−5.84940	+	5.84940i	−0.187139	+	0.187139i	0.607319	+	0.794458i	$0.292245\pi$
$978$	4.45222	−	4.88838i	0.142366	−	0.156313i
$979$			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	0.900646	−	0.434554i	$-0.143094\pi$
$983$	14.6133	+	14.6133i	0.466092	+	0.466092i	−0.434554	+	0.900646i	$0.643094\pi$
$984$	−16.3621	+	0.764033i	−0.521605	+	0.0243565i
$985$	45.4109	+	7.08028i	1.44691	+	0.225597i
$986$		−	0.338264i		−	0.0107725i
$987$	−1.25429	−	1.14237i	−0.0399243	−	0.0363621i
$988$	3.14211	−	3.14211i	0.0999637	−	0.0999637i
$989$	−0.154087			−0.00489968
$990$	20.3375	+	1.24923i	0.646369	+	0.0397032i
$991$	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
$993$	35.3221	+	32.1705i	1.12091	+	1.02090i
$994$		−	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.47.13	yes	32
3.2	odd	2	inner	690.2.i.f.47.3	✓	32
5.3	odd	4	inner	690.2.i.f.323.3	yes	32
15.8	even	4	inner	690.2.i.f.323.13	yes	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.28054 + 1.16628i) q^{3} -1.00000i q^{4} +(1.31868 + 1.80585i) q^{5} +(1.73017 - 0.0807905i) q^{6} +(1.43599 + 1.43599i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.279562 + 2.98695i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.28054 + 1.16628i) 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} +(1.16628 - 1.28054i) q^{12} +(-1.30218 + 1.30218i) q^{13} +2.03079 q^{14} +(-0.417505 + 3.85041i) q^{15} -1.00000 q^{16} +(-0.0287275 + 0.0287275i) q^{17} +(2.30977 + 1.91441i) 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} +(-3.12564 + 4.15095i) q^{27} +(1.43599 - 1.43599i) q^{28} -8.32611 q^{29} +(2.42743 + 3.01787i) q^{30} +10.8038 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.54254 - 3.88958i) 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} +(2.60051 + 2.36848i) q^{42} +(-0.108956 + 0.108956i) q^{43} -3.03746 q^{44} +(-5.02531 + 4.44368i) q^{45} +1.00000 q^{46} +(-0.341054 + 0.341054i) q^{47} +(-1.28054 - 1.16628i) 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} +(2.81420 - 3.08990i) q^{57} +(-5.88745 + 5.88745i) q^{58} -2.10585 q^{59} +(3.85041 + 0.417505i) q^{60} +10.7626 q^{61} +(7.63947 - 7.63947i) q^{62} +(-3.88777 + 4.69066i) 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} +(1.91441 - 2.30977i) q^{72} +(6.43032 - 6.43032i) q^{73} -0.565371 q^{74} +(-7.50381 + 4.32352i) q^{75} -2.41296 q^{76} +(4.36175 - 4.36175i) q^{77} +(-2.14778 + 2.35818i) 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} +(-10.6619 - 9.71061i) q^{87} +(-2.14781 + 2.14781i) q^{88} -12.0540 q^{89} +(-0.411275 + 6.69558i) q^{90} -3.73982 q^{91} +(0.707107 - 0.707107i) q^{92} +(13.8347 + 12.6004i) 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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