LMFDB - Embedded newform 690.2.i.f.323.3

Newspace parameters

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

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			323.3
Character	$\chi$	$=$	690.323
Dual form			690.2.i.f.47.3

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.16628 + 1.28054i) q^{3} +1.00000i q^{4} +(-1.31868 + 1.80585i) q^{5} +(1.73017 - 0.0807905i) q^{6} +(1.43599 - 1.43599i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.279562 - 2.98695i) q^{9} +O(q^{10})$	\(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})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) $	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.381583	−	0.924335i	$-0.624621\pi$
$7$	1.43599	−	1.43599i	0.542752	−	0.542752i	0.924335	+	0.381583i	$0.124621\pi$
$8$	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	$-0.151403\pi$
$12$	−1.28054	−	1.16628i	−0.369660	−	0.336677i
$13$	−1.30218	−	1.30218i	−0.361159	−	0.361159i	0.503081	−	0.864239i	$-0.332200\pi$
$13$	−1.30218	−	1.30218i	−0.361159	−	0.361159i	−0.864239	+	0.503081i	$0.832200\pi$
$14$	−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	0.710582	−	0.703614i	$-0.248432\pi$
$17$	0.0287275	+	0.0287275i	0.00696745	+	0.00696745i	−0.703614	+	0.710582i	$0.748432\pi$
$18$	−1.91441	+	2.30977i	−0.451231	+	0.544418i
$19$			2.41296i			0.553572i	0.960932	+	0.276786i	$0.0892693\pi$
$19$			2.41296i			0.553572i	−0.960932	+	0.276786i	$0.910731\pi$
$20$	−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	−0.739204	−	0.673481i	$-0.764798\pi$
$37$	−0.399778	+	0.399778i	−0.0657230	+	0.0657230i	0.673481	+	0.739204i	$0.264798\pi$
$38$	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	$-0.264449\pi$
$42$	2.36848	−	2.60051i	0.365465	−	0.401267i
$43$	−0.108956	−	0.108956i	−0.0166156	−	0.0166156i	0.698750	−	0.715366i	$-0.253740\pi$
$43$	−0.108956	−	0.108956i	−0.0166156	−	0.0166156i	−0.715366	+	0.698750i	$0.753740\pi$
$44$	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	0.731543	−	0.681795i	$-0.238801\pi$
$47$	0.341054	+	0.341054i	0.0497478	+	0.0497478i	−0.681795	+	0.731543i	$0.738801\pi$
$48$	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	−0.698779	−	0.715338i	$-0.746273\pi$
$53$	0.120552	−	0.120552i	0.0165590	−	0.0165590i	0.715338	+	0.698779i	$0.246273\pi$
$54$	−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	−0.985692	−	0.168555i	$-0.946090\pi$
$67$	−6.68856	+	6.68856i	−0.817137	+	0.817137i	0.168555	+	0.985692i	$0.446090\pi$
$68$	−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	$-0.109763\pi$
$72$	−2.30977	−	1.91441i	−0.272209	−	0.225615i
$73$	6.43032	+	6.43032i	0.752612	+	0.752612i	0.974966	−	0.222354i	$-0.0713742\pi$
$73$	6.43032	+	6.43032i	0.752612	+	0.752612i	−0.222354	+	0.974966i	$0.571374\pi$
$74$	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	$-0.906481\pi$
$79$		−	5.14788i		−	0.579182i	0.957150	−	0.289591i	$-0.0935193\pi$
$80$	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	$-0.826640\pi$
$83$	−3.07224	+	3.07224i	−0.337223	+	0.337223i	0.518098	+	0.855321i	$0.326640\pi$
$84$	−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	−0.224890	−	0.974384i	$-0.572202\pi$
$97$	7.38166	−	7.38166i	0.749494	−	0.749494i	0.974384	+	0.224890i	$0.0722023\pi$
$98$	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	$-0.286637\pi$
$102$	0.0520243	+	0.0473825i	0.00515117	+	0.00469157i
$103$	−9.94078	−	9.94078i	−0.979494	−	0.979494i	0.0202999	−	0.999794i	$-0.493538\pi$
$103$	−9.94078	−	9.94078i	−0.979494	−	0.979494i	−0.999794	+	0.0202999i	$0.993538\pi$
$104$	−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	0.983192	−	0.182576i	$-0.0584436\pi$
$107$	8.28163	+	8.28163i	0.800616	+	0.800616i	−0.182576	+	0.983192i	$0.558444\pi$
$108$	−3.12564	+	4.15095i	−0.300765	+	0.399425i
$109$			5.16166i			0.494398i	0.968965	+	0.247199i	$0.0795101\pi$
$109$			5.16166i			0.494398i	−0.968965	+	0.247199i	$0.920490\pi$
$110$	−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	$-0.509904\pi$
$113$	10.2943	−	10.2943i	0.968407	−	0.968407i	0.999516	+	0.0311086i	$0.00990378\pi$
$114$	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	−0.929672	−	0.368389i	$-0.879910\pi$
$127$	−6.32534	+	6.32534i	−0.561283	+	0.561283i	0.368389	+	0.929672i	$0.379910\pi$
$128$	−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	$0.877753\pi$
$132$	−3.54254	+	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	0.00544239	−	0.999985i	$-0.498268\pi$
$137$	−11.6408	−	11.6408i	−0.994543	−	0.994543i	−0.999985	+	0.00544239i	$0.998268\pi$
$138$	−1.16628	+	1.28054i	−0.0992807	+	0.109007i
$139$			0.224301i			0.0190250i	0.999955	+	0.00951249i	$0.00302797\pi$
$139$			0.224301i			0.0190250i	−0.999955	+	0.00951249i	$0.996972\pi$
$140$	−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	0.293039	−	0.956100i	$-0.405333\pi$
$157$	15.6517	−	15.6517i	1.24914	−	1.24914i	0.956100	−	0.293039i	$-0.0946667\pi$
$158$	−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	0.804874	−	0.593446i	$-0.202233\pi$
$163$	2.69934	+	2.69934i	0.211429	+	0.211429i	−0.593446	+	0.804874i	$0.702233\pi$
$164$	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	0.487049	−	0.873375i	$-0.338073\pi$
$167$	−4.99243	−	4.99243i	−0.386326	−	0.386326i	−0.873375	+	0.487049i	$0.838073\pi$
$168$	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	−0.487193	−	0.873294i	$-0.661979\pi$
$173$	5.07836	−	5.07836i	0.386101	−	0.386101i	0.873294	+	0.487193i	$0.161979\pi$
$174$	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	$0.197149\pi$
$191$			16.0457i			1.16103i	−0.814250	+	0.580514i	$0.802851\pi$
$192$	1.28054	+	1.16628i	0.0924150	+	0.0841693i
$193$	−5.17234	−	5.17234i	−0.372313	−	0.372313i	0.496006	−	0.868319i	$-0.334799\pi$
$193$	−5.17234	−	5.17234i	−0.372313	−	0.372313i	−0.868319	+	0.496006i	$0.834799\pi$
$194$	−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	−0.999347	−	0.0361361i	$-0.988495\pi$
$197$	−14.5337	−	14.5337i	−1.03548	−	1.03548i	−0.0361361	−	0.999347i	$-0.511505\pi$
$198$	7.01582	+	5.81493i	0.498593	+	0.413249i
$199$		−	12.8549i		−	0.911262i	−0.890169	−	0.455631i	$-0.849414\pi$
$199$		−	12.8549i		−	0.911262i	0.890169	−	0.455631i	$-0.150586\pi$
$200$	−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	0.893441	−	0.449181i	$-0.148284\pi$
$223$	6.63422	+	6.63422i	0.444260	+	0.444260i	−0.449181	+	0.893441i	$0.648284\pi$
$224$	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	0.852172	−	0.523261i	$-0.175285\pi$
$227$	4.95555	+	4.95555i	0.328911	+	0.328911i	−0.523261	+	0.852172i	$0.675285\pi$
$228$	2.81420	−	3.08990i	0.186375	−	0.204633i
$229$			11.2747i			0.745053i	0.928021	+	0.372527i	$0.121509\pi$
$229$			11.2747i			0.745053i	−0.928021	+	0.372527i	$0.878491\pi$
$230$	−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	$-0.947490\pi$
$233$	−12.5504	+	12.5504i	−0.822206	+	0.822206i	0.164218	+	0.986424i	$0.447490\pi$
$234$	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	$0.114275\pi$
$251$			11.1326i			0.702686i	−0.936247	+	0.351343i	$0.885725\pi$
$252$	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	0.693671	−	0.720292i	$-0.255992\pi$
$257$	−0.426761	−	0.426761i	−0.0266206	−	0.0266206i	−0.720292	+	0.693671i	$0.755992\pi$
$258$	−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	−0.991648	−	0.128977i	$-0.958831\pi$
$263$	−13.9902	+	13.9902i	−0.862670	+	0.862670i	0.128977	+	0.991648i	$0.458831\pi$
$264$	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	−0.548625	−	0.836069i	$-0.684849\pi$
$277$	4.78402	−	4.78402i	0.287444	−	0.287444i	0.836069	+	0.548625i	$0.184849\pi$
$278$	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	$-0.0580278\pi$
$282$	0.617633	+	0.562525i	0.0367795	+	0.0334979i
$283$	1.63214	+	1.63214i	0.0970206	+	0.0970206i	0.753951	−	0.656931i	$-0.228146\pi$
$283$	1.63214	+	1.63214i	0.0970206	+	0.0970206i	−0.656931	+	0.753951i	$0.728146\pi$
$284$	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	−0.934548	−	0.355837i	$-0.884196\pi$
$293$	−9.90593	+	9.90593i	−0.578711	+	0.578711i	0.355837	+	0.934548i	$0.384196\pi$
$294$	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	0.337594	−	0.941292i	$-0.390387\pi$
$307$	22.4079	−	22.4079i	1.27889	−	1.27889i	0.941292	−	0.337594i	$-0.109613\pi$
$308$	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	$-0.215573\pi$
$312$	2.14778	−	2.35818i	0.121594	−	0.133506i
$313$	3.23645	+	3.23645i	0.182935	+	0.182935i	0.792633	−	0.609698i	$-0.208709\pi$
$313$	3.23645	+	3.23645i	0.182935	+	0.182935i	−0.609698	+	0.792633i	$0.708709\pi$
$314$	−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	0.945998	−	0.324172i	$-0.105086\pi$
$317$	11.0713	+	11.0713i	0.621826	+	0.621826i	−0.324172	+	0.945998i	$0.605086\pi$
$318$	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	−0.0919212	−	0.995766i	$-0.529301\pi$
$337$	16.5924	−	16.5924i	0.903845	−	0.903845i	0.995766	+	0.0919212i	$0.0293008\pi$
$338$	−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	0.405365	−	0.914155i	$-0.367144\pi$
$347$	−9.47770	−	9.47770i	−0.508789	−	0.508789i	−0.914155	+	0.405365i	$0.867144\pi$
$348$	−10.6619	−	9.71061i	−0.571538	−	0.520543i
$349$			17.3941i			0.931085i	0.885025	+	0.465543i	$0.154141\pi$
$349$			17.3941i			0.931085i	−0.885025	+	0.465543i	$0.845859\pi$
$350$	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	0.188681	−	0.982038i	$-0.439579\pi$
$353$	21.9958	−	21.9958i	1.17072	−	1.17072i	0.982038	−	0.188681i	$-0.0604212\pi$
$354$	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	0.0594601	−	0.998231i	$-0.481062\pi$
$367$	20.2624	−	20.2624i	1.05769	−	1.05769i	0.998231	−	0.0594601i	$-0.0189379\pi$
$368$	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	0.994858	−	0.101277i	$-0.0322930\pi$
$373$	17.2579	+	17.2579i	0.893581	+	0.893581i	−0.101277	+	0.994858i	$0.532293\pi$
$374$	−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	$-0.869670\pi$
$379$		−	15.5004i		−	0.796200i	0.917342	−	0.398100i	$-0.130330\pi$
$380$	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	−0.313131	+	0.949710i	$0.601378\pi$
$383$	−24.7143	+	24.7143i	−1.26284	+	1.26284i	−0.949710	+	0.313131i	$0.898622\pi$
$384$	−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	−0.00577503	+	0.999983i	$0.501838\pi$
$397$	−20.0396	+	20.0396i	−1.00576	+	1.00576i	−0.999983	+	0.00577503i	$0.998162\pi$
$398$	−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	$0.968870\pi$
$402$	−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	$0.0694996\pi$
$409$			8.76129i			0.433218i	−0.976258	+	0.216609i	$0.930500\pi$
$410$	−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	$0.309978\pi$
$431$			34.3396i			1.65408i	−0.562141	+	0.827041i	$0.690022\pi$
$432$	−4.15095	−	3.12564i	−0.199713	−	0.150382i
$433$	−12.5838	−	12.5838i	−0.604740	−	0.604740i	0.336827	−	0.941567i	$-0.390646\pi$
$433$	−12.5838	−	12.5838i	−0.604740	−	0.604740i	−0.941567	+	0.336827i	$0.890646\pi$
$434$	−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	$0.121865\pi$
$439$			15.6542i			0.747133i	−0.927603	+	0.373567i	$0.878135\pi$
$440$	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	−0.0190784	+	0.999818i	$0.506073\pi$
$443$	−21.4453	+	21.4453i	−1.01890	+	1.01890i	−0.999818	+	0.0190784i	$0.993927\pi$
$444$	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	−0.925461	−	0.378842i	$-0.876322\pi$
$457$	−11.6854	+	11.6854i	−0.546620	+	0.546620i	0.378842	+	0.925461i	$0.376322\pi$
$458$	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	$0.749002\pi$
$462$	−7.89893	−	7.19416i	−0.367492	−	0.334703i
$463$	9.14602	+	9.14602i	0.425052	+	0.425052i	0.886939	−	0.461887i	$-0.152827\pi$
$463$	9.14602	+	9.14602i	0.425052	+	0.425052i	−0.461887	+	0.886939i	$0.652827\pi$
$464$	−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	0.951951	+	0.306251i	$0.0990745\pi$
$467$	27.1900	+	27.1900i	1.25820	+	1.25820i	0.306251	+	0.951951i	$0.400925\pi$
$468$	−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	−0.168658	−	0.985675i	$-0.553943\pi$
$487$	18.0300	−	18.0300i	0.817017	−	0.817017i	0.985675	+	0.168658i	$0.0539433\pi$
$488$	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	$-0.0308845\pi$
$492$	−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	$0.0840399\pi$
$499$			11.6589i			0.521925i	−0.965349	+	0.260963i	$0.915960\pi$
$500$	−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	$-0.509610\pi$
$503$	21.7405	−	21.7405i	0.969360	−	0.969360i	0.999544	+	0.0301846i	$0.00960952\pi$
$504$	−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	$0.354989\pi$
$521$			40.9950i			1.79602i	−0.439972	+	0.898012i	$0.645011\pi$
$522$	−15.9396	+	19.2314i	−0.697657	+	0.841735i
$523$	−11.8550	−	11.8550i	−0.518381	−	0.518381i	0.398700	−	0.917081i	$-0.369461\pi$
$523$	−11.8550	−	11.8550i	−0.518381	−	0.518381i	−0.917081	+	0.398700i	$0.869461\pi$
$524$	−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	−0.640047	−	0.768336i	$-0.721085\pi$
$547$	3.00042	−	3.00042i	0.128288	−	0.128288i	0.768336	+	0.640047i	$0.221085\pi$
$548$	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	0.0847134	−	0.996405i	$-0.473003\pi$
$557$	−21.5167	−	21.5167i	−0.911692	−	0.911692i	−0.996405	+	0.0847134i	$0.973003\pi$
$558$	−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	−0.821832	−	0.569729i	$-0.807048\pi$
$563$	−5.98181	+	5.98181i	−0.252103	+	0.252103i	0.569729	+	0.821832i	$0.307048\pi$
$564$	−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	−0.857031	−	0.515266i	$-0.827693\pi$
$577$	−8.20948	+	8.20948i	−0.341765	+	0.341765i	0.515266	+	0.857031i	$0.327693\pi$
$578$	−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	0.966031	+	0.258426i	$0.0832039\pi$
$587$	29.6663	+	29.6663i	1.22446	+	1.22446i	0.258426	+	0.966031i	$0.416796\pi$
$588$	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	0.199911	−	0.979814i	$-0.435935\pi$
$593$	28.7282	−	28.7282i	1.17972	−	1.17972i	0.979814	−	0.199911i	$-0.0640652\pi$
$594$	−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	−0.227821	+	0.973703i	$0.573160\pi$
$607$	−29.6024	+	29.6024i	−1.20152	+	1.20152i	−0.973703	+	0.227821i	$0.926840\pi$
$608$	−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	−0.998580	−	0.0532791i	$-0.983033\pi$
$613$	−26.0428	−	26.0428i	−1.05186	−	1.05186i	−0.0532791	−	0.998580i	$-0.516967\pi$
$614$	−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	0.876661	−	0.481108i	$-0.159766\pi$
$617$	9.82533	+	9.82533i	0.395553	+	0.395553i	−0.481108	+	0.876661i	$0.659766\pi$
$618$	−18.0023	−	16.3961i	−0.724159	−	0.659547i
$619$			11.5924i			0.465937i	0.972484	+	0.232968i	$0.0748438\pi$
$619$			11.5924i			0.465937i	−0.972484	+	0.232968i	$0.925156\pi$
$620$	−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	$0.331055\pi$
$641$			43.6697i			1.72485i	−0.506186	+	0.862424i	$0.668945\pi$
$642$	14.9977	+	13.6595i	0.591911	+	0.539098i
$643$	4.13381	+	4.13381i	0.163021	+	0.163021i	0.783904	−	0.620882i	$-0.213226\pi$
$643$	4.13381	+	4.13381i	0.163021	+	0.163021i	−0.620882	+	0.783904i	$0.713226\pi$
$644$	−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	0.999204	−	0.0398886i	$-0.0127003\pi$
$647$	24.4013	+	24.4013i	0.959316	+	0.959316i	−0.0398886	+	0.999204i	$0.512700\pi$
$648$	−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	−0.629188	−	0.777253i	$-0.716612\pi$
$653$	3.78364	−	3.78364i	0.148065	−	0.148065i	0.777253	+	0.629188i	$0.216612\pi$
$654$	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	0.292264	−	0.956338i	$-0.405592\pi$
$673$	−17.2276	−	17.2276i	−0.664074	−	0.664074i	−0.956338	+	0.292264i	$0.905592\pi$
$674$	−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	0.533750	−	0.845642i	$-0.320782\pi$
$677$	−8.11519	−	8.11519i	−0.311892	−	0.311892i	−0.845642	+	0.533750i	$0.820782\pi$
$678$	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	−0.378589	−	0.925565i	$-0.623591\pi$
$683$	14.2948	−	14.2948i	0.546975	−	0.546975i	0.925565	+	0.378589i	$0.123591\pi$
$684$	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	$-0.747604\pi$
$701$		−	37.7240i		−	1.42482i	0.701765	−	0.712408i	$-0.252396\pi$
$702$	−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	$0.107328\pi$
$709$			17.6180i			0.661657i	−0.943691	+	0.330828i	$0.892672\pi$
$710$	−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	−0.731032	−	0.682343i	$-0.760961\pi$
$727$	−1.31281	+	1.31281i	−0.0486893	+	0.0486893i	0.682343	+	0.731032i	$0.260961\pi$
$728$	−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	0.966056	+	0.258332i	$0.0831728\pi$
$733$	33.1490	+	33.1490i	1.22439	+	1.22439i	0.258332	+	0.966056i	$0.416827\pi$
$734$	−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	$-0.876654\pi$
$739$		−	20.5449i		−	0.755758i	0.925855	−	0.377879i	$-0.123346\pi$
$740$	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	$-0.958473\pi$
$743$	−23.4804	+	23.4804i	−0.861411	+	0.861411i	0.130091	+	0.991502i	$0.458473\pi$
$744$	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	−0.833177	−	0.553007i	$-0.813480\pi$
$757$	−7.70849	+	7.70849i	−0.280170	+	0.280170i	0.553007	+	0.833177i	$0.313480\pi$
$758$	−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	$-0.0335586\pi$
$762$	−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	$0.0566235\pi$
$769$			9.81402i			0.353903i	−0.984220	+	0.176951i	$0.943376\pi$
$770$	−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	$-0.788356\pi$
$773$	−4.72645	+	4.72645i	−0.169999	+	0.169999i	0.616980	+	0.786979i	$0.288356\pi$
$774$	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	−

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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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