LMFDB - Embedded newform 690.2.q.a.11.12

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.12

$q$-expansion

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(-0.162462 + 1.72441i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.53850 + 0.795618i) q^{6} +(0.461235 - 0.399662i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.94721 - 0.560302i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(-0.162462 + 1.72441i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.53850 + 0.795618i) q^{6} +(0.461235 - 0.399662i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.94721 - 0.560302i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-5.37960 - 3.45726i) q^{11} +(-1.50109 - 0.864128i) q^{12} +(-1.40018 + 1.61589i) q^{13} +(0.585580 + 0.171942i) q^{14} +(-0.329943 - 1.70033i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.579107 - 1.26807i) q^{17} +(-1.12203 - 2.78228i) q^{18} +(-1.70660 - 0.779379i) q^{19} +(0.142315 - 0.989821i) q^{20} +(0.614251 + 0.860290i) q^{21} -6.39475i q^{22} +(0.323878 + 4.78488i) q^{23} +(-0.0846018 - 1.72998i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.11636 - 0.304287i) q^{26} +(1.44500 - 4.99119i) q^{27} +(0.171942 + 0.585580i) q^{28} +(-2.48534 + 1.13502i) q^{29} +(1.25203 - 1.19684i) q^{30} +(1.19880 + 8.33783i) q^{31} +(0.281733 - 0.959493i) q^{32} +(6.83573 - 8.71500i) q^{33} +(0.753677 - 1.17274i) q^{34} +(-0.329954 + 0.513418i) q^{35} +(1.73399 - 2.44812i) q^{36} +(-2.27843 + 7.75963i) q^{37} +(-0.267003 - 1.85705i) q^{38} +(-2.55899 - 2.67700i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-1.65607 - 5.64005i) q^{41} +(-0.391633 + 0.981848i) q^{42} +(3.10873 + 0.446968i) q^{43} +(5.37960 - 3.45726i) q^{44} +(2.98569 - 0.292720i) q^{45} +(-3.85020 + 2.85937i) q^{46} -4.99298i q^{47} +(1.40962 - 1.00647i) q^{48} +(-0.943196 + 6.56007i) q^{49} +(0.909632 + 0.415415i) q^{50} +(2.28076 - 0.792608i) q^{51} +(-0.888210 - 1.94491i) q^{52} +(-0.888367 - 1.02523i) q^{53} +(4.98008 - 1.48283i) q^{54} +(6.13572 + 1.80161i) q^{55} +(-0.399662 + 0.461235i) q^{56} +(1.62123 - 2.81627i) q^{57} +(-2.29852 - 1.47717i) q^{58} +(-9.84131 - 8.52754i) q^{59} +(1.68374 + 0.406218i) q^{60} +(3.36348 - 0.483595i) q^{61} +(-6.36611 + 5.51627i) q^{62} +(-1.58329 + 0.919459i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.888210 - 1.94491i) q^{65} +(11.0272 + 1.03890i) q^{66} +(-6.61576 - 10.2943i) q^{67} +1.39404 q^{68} +(-8.30374 - 0.218860i) q^{69} -0.610301 q^{70} +(4.73042 + 7.36068i) q^{71} +(2.99695 + 0.135167i) q^{72} +(-5.31978 + 11.6487i) q^{73} +(-7.75963 + 2.27843i) q^{74} +(0.795618 + 1.53850i) q^{75} +(1.41790 - 1.22861i) q^{76} +(-3.86300 + 0.555415i) q^{77} +(0.868545 - 3.60005i) q^{78} +(1.63339 + 1.41534i) q^{79} +(0.841254 + 0.540641i) q^{80} +(8.37212 + 3.30266i) q^{81} +(3.84937 - 4.44241i) q^{82} +(10.4392 + 3.06521i) q^{83} +(-1.03772 + 0.201365i) q^{84} +(0.912905 + 1.05355i) q^{85} +(1.30469 + 2.85688i) q^{86} +(-1.55347 - 4.47016i) q^{87} +(5.81687 + 2.65647i) q^{88} +(-1.23916 + 8.61853i) q^{89} +(1.86043 + 2.35346i) q^{90} +1.30490i q^{91} +(-4.48703 - 1.69310i) q^{92} +(-14.5726 + 0.712650i) q^{93} +(4.20036 - 2.69941i) q^{94} +(1.85705 + 0.267003i) q^{95} +(1.60879 + 0.641705i) q^{96} +(-1.06339 - 3.62156i) q^{97} +(-6.02862 + 2.75318i) q^{98} +(13.9177 + 13.2035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) $	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	−0.162462	+	1.72441i	−0.0937972	+	0.995591i
$3$	−0.162462	+	1.72441i	−0.0937972	+	0.995591i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−1.53850	+	0.795618i	−0.628091	+	0.324810i
$7$	0.461235	−	0.399662i	0.174330	−	0.151058i	−0.563325	−	0.826235i	$-0.690478\pi$
$7$	0.461235	−	0.399662i	0.174330	−	0.151058i	0.737656	+	0.675177i	$0.235933\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	−2.94721	−	0.560302i	−0.982404	−	0.186767i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	−5.37960	−	3.45726i	−1.62201	−	1.04240i	−0.954676	−	0.297646i	$-0.903798\pi$
$11$	−5.37960	−	3.45726i	−1.62201	−	1.04240i	−0.667335	−	0.744757i	$-0.732565\pi$
$12$	−1.50109	−	0.864128i	−0.433328	−	0.249452i
$13$	−1.40018	+	1.61589i	−0.388339	+	0.448167i	−0.915934	−	0.401329i	$-0.868548\pi$
$13$	−1.40018	+	1.61589i	−0.388339	+	0.448167i	0.527595	+	0.849496i	$0.323094\pi$
$14$	0.585580	+	0.171942i	0.156503	+	0.0459534i
$15$	−0.329943	−	1.70033i	−0.0851909	−	0.439024i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.579107	−	1.26807i	−0.140454	−	0.307551i	0.826313	−	0.563212i	$-0.190434\pi$
$17$	−0.579107	−	1.26807i	−0.140454	−	0.307551i	−0.966767	+	0.255660i	$0.917707\pi$
$18$	−1.12203	−	2.78228i	−0.264464	−	0.655789i
$19$	−1.70660	−	0.779379i	−0.391521	−	0.178802i	0.209920	−	0.977718i	$-0.432680\pi$
$19$	−1.70660	−	0.779379i	−0.391521	−	0.178802i	−0.601442	+	0.798917i	$0.705407\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	0.614251	+	0.860290i	0.134040	+	0.187731i
$22$		−	6.39475i		−	1.36336i
$23$	0.323878	+	4.78488i	0.0675332	+	0.997717i
$23$	0.323878	+	4.78488i	0.0675332	+	0.997717i
$24$	−0.0846018	−	1.72998i	−0.0172693	−	0.353131i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−2.11636	−	0.304287i	−0.415053	−	0.0596756i
$27$	1.44500	−	4.99119i	0.278091	−	0.960555i
$28$	0.171942	+	0.585580i	0.0324939	+	0.110664i
$29$	−2.48534	+	1.13502i	−0.461517	+	0.210768i	−0.632584	−	0.774492i	$-0.718006\pi$
$29$	−2.48534	+	1.13502i	−0.461517	+	0.210768i	0.171067	+	0.985259i	$0.445278\pi$
$30$	1.25203	−	1.19684i	0.228589	−	0.218511i
$31$	1.19880	+	8.33783i	0.215311	+	1.49752i	0.755039	+	0.655680i	$0.227618\pi$
$31$	1.19880	+	8.33783i	0.215311	+	1.49752i	−0.539728	+	0.841839i	$0.681473\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	6.83573	−	8.71500i	1.18995	−	1.51709i
$34$	0.753677	−	1.17274i	0.129255	−	0.201124i
$35$	−0.329954	+	0.513418i	−0.0557724	+	0.0867835i
$36$	1.73399	−	2.44812i	0.288998	−	0.408020i
$37$	−2.27843	+	7.75963i	−0.374572	+	1.27568i	0.529506	+	0.848306i	$0.322377\pi$
$37$	−2.27843	+	7.75963i	−0.374572	+	1.27568i	−0.904077	+	0.427369i	$0.859441\pi$
$38$	−0.267003	−	1.85705i	−0.0433137	−	0.301253i
$39$	−2.55899	−	2.67700i	−0.409766	−	0.428664i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	−1.65607	−	5.64005i	−0.258634	−	0.880828i	−0.981762	−	0.190113i	$-0.939114\pi$
$41$	−1.65607	−	5.64005i	−0.258634	−	0.880828i	0.723128	−	0.690714i	$-0.242704\pi$
$42$	−0.391633	+	0.981848i	−0.0604303	+	0.151502i
$43$	3.10873	+	0.446968i	0.474076	+	0.0681619i	0.375212	−	0.926939i	$-0.377570\pi$
$43$	3.10873	+	0.446968i	0.474076	+	0.0681619i	0.0988644	+	0.995101i	$0.468479\pi$
$44$	5.37960	−	3.45726i	0.811006	−	0.521202i
$45$	2.98569	−	0.292720i	0.445080	−	0.0436361i
$46$	−3.85020	+	2.85937i	−0.567681	+	0.421591i
$47$		−	4.99298i		−	0.728301i	−0.931340	−	0.364151i	$-0.881359\pi$
$47$		−	4.99298i		−	0.728301i	0.931340	−	0.364151i	$-0.118641\pi$
$48$	1.40962	−	1.00647i	0.203460	−	0.145272i
$49$	−0.943196	+	6.56007i	−0.134742	+	0.937153i
$50$	0.909632	+	0.415415i	0.128641	+	0.0587486i
$51$	2.28076	−	0.792608i	0.319370	−	0.110987i
$52$	−0.888210	−	1.94491i	−0.123173	−	0.269710i
$53$	−0.888367	−	1.02523i	−0.122027	−	0.140826i	0.691449	−	0.722425i	$-0.256973\pi$
$53$	−0.888367	−	1.02523i	−0.122027	−	0.140826i	−0.813476	+	0.581599i	$0.802427\pi$
$54$	4.98008	−	1.48283i	0.677703	−	0.201787i
$55$	6.13572	+	1.80161i	0.827340	+	0.242929i
$56$	−0.399662	+	0.461235i	−0.0534071	+	0.0616351i
$57$	1.62123	−	2.81627i	0.214737	−	0.373024i
$58$	−2.29852	−	1.47717i	−0.301810	−	0.193962i
$59$	−9.84131	−	8.52754i	−1.28123	−	1.11019i	−0.988050	−	0.154134i	$-0.950741\pi$
$59$	−9.84131	−	8.52754i	−1.28123	−	1.11019i	−0.293179	−	0.956057i	$-0.594713\pi$
$60$	1.68374	+	0.406218i	0.217370	+	0.0524425i
$61$	3.36348	−	0.483595i	0.430649	−	0.0619180i	0.0764180	−	0.997076i	$-0.475652\pi$
$61$	3.36348	−	0.483595i	0.430649	−	0.0619180i	0.354231	+	0.935158i	$0.384743\pi$
$62$	−6.36611	+	5.51627i	−0.808497	+	0.700567i
$63$	−1.58329	+	0.919459i	−0.199476	+	0.115841i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	0.888210	−	1.94491i	0.110169	−	0.241236i
$66$	11.0272	+	1.03890i	1.35735	+	0.127880i
$67$	−6.61576	−	10.2943i	−0.808244	−	1.25765i	−0.962947	−	0.269691i	$-0.913078\pi$
$67$	−6.61576	−	10.2943i	−0.808244	−	1.25765i	0.154703	−	0.987961i	$-0.450558\pi$
$68$	1.39404			0.169053
$69$	−8.30374	−	0.218860i	−0.999653	−	0.0263477i
$70$	−0.610301			−0.0729449
$71$	4.73042	+	7.36068i	0.561398	+	0.873552i	0.999680	−	0.0252852i	$-0.00804938\pi$
$71$	4.73042	+	7.36068i	0.561398	+	0.873552i	−0.438282	+	0.898837i	$0.644413\pi$
$72$	2.99695	+	0.135167i	0.353194	+	0.0159296i
$73$	−5.31978	+	11.6487i	−0.622633	+	1.36338i	0.290956	+	0.956736i	$0.406027\pi$
$73$	−5.31978	+	11.6487i	−0.622633	+	1.36338i	−0.913589	+	0.406639i	$0.866701\pi$
$74$	−7.75963	+	2.27843i	−0.902038	+	0.264862i
$75$	0.795618	+	1.53850i	0.0918700	+	0.177651i
$76$	1.41790	−	1.22861i	0.162644	−	0.140932i
$77$	−3.86300	+	0.555415i	−0.440229	+	0.0632954i
$78$	0.868545	−	3.60005i	0.0983434	−	0.407626i
$79$	1.63339	+	1.41534i	0.183771	+	0.159239i	0.741888	−	0.670524i	$-0.233930\pi$
$79$	1.63339	+	1.41534i	0.183771	+	0.159239i	−0.558117	+	0.829762i	$0.688476\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	8.37212	+	3.30266i	0.930236	+	0.366962i
$82$	3.84937	−	4.44241i	0.425092	−	0.490582i
$83$	10.4392	+	3.06521i	1.14585	+	0.336451i	0.798918	−	0.601440i	$-0.205406\pi$
$83$	10.4392	+	3.06521i	1.14585	+	0.336451i	0.346929	+	0.937891i	$0.387224\pi$
$84$	−1.03772	+	0.201365i	−0.113224	+	0.0219707i
$85$	0.912905	+	1.05355i	0.0990184	+	0.114273i
$86$	1.30469	+	2.85688i	0.140689	+	0.308065i
$87$	−1.55347	−	4.47016i	−0.166549	−	0.479251i
$88$	5.81687	+	2.65647i	0.620080	+	0.283181i
$89$	−1.23916	+	8.61853i	−0.131350	+	0.913562i	0.812446	+	0.583036i	$0.198135\pi$
$89$	−1.23916	+	8.61853i	−0.131350	+	0.913562i	−0.943797	+	0.330526i	$0.892774\pi$
$90$	1.86043	+	2.35346i	0.196107	+	0.248077i
$91$			1.30490i			0.136791i
$92$	−4.48703	−	1.69310i	−0.467805	−	0.176518i
$93$	−14.5726	+	0.712650i	−1.51111	+	0.0738984i
$94$	4.20036	−	2.69941i	0.433235	−	0.278423i
$95$	1.85705	+	0.267003i	0.190529	+	0.0273940i
$96$	1.60879	+	0.641705i	0.164197	+	0.0654937i
$97$	−1.06339	−	3.62156i	−0.107970	−	0.367713i	0.887728	−	0.460369i	$-0.152283\pi$
$97$	−1.06339	−	3.62156i	−0.107970	−	0.367713i	−0.995698	+	0.0926552i	$0.970465\pi$
$98$	−6.02862	+	2.75318i	−0.608982	+	0.278113i
$99$	13.9177	+	13.2035i	1.39878	+	1.32700i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−3.76620	+	12.8265i	−0.374751	+	1.27629i	0.529144	+	0.848532i	$0.322513\pi$
$101$	−3.76620	+	12.8265i	−0.374751	+	1.27629i	−0.903895	+	0.427753i	$0.859305\pi$
$102$	1.89985	+	1.49018i	0.188114	+	0.147550i
$103$	7.01365	−	10.9135i	0.691075	−	1.07533i	−0.301472	−	0.953475i	$-0.597478\pi$
$103$	7.01365	−	10.9135i	0.691075	−	1.07533i	0.992547	−	0.121859i	$-0.0388857\pi$
$104$	1.15596	−	1.79871i	0.113351	−	0.176378i
$105$	−0.831741	−	0.652388i	−0.0811696	−	0.0636665i
$106$	0.382191	−	1.30162i	0.0371217	−	0.126425i
$107$	0.493401	+	3.43168i	0.0476989	+	0.331753i	0.999673	+	0.0255743i	$0.00814144\pi$
$107$	0.493401	+	3.43168i	0.0476989	+	0.331753i	−0.951974	+	0.306179i	$0.900949\pi$
$108$	3.93987	+	3.38784i	0.379114	+	0.325995i
$109$	2.94630	−	1.34553i	0.282205	−	0.128879i	−0.269284	−	0.963061i	$-0.586787\pi$
$109$	2.94630	−	1.34553i	0.282205	−	0.128879i	0.551489	+	0.834182i	$0.314060\pi$
$110$	1.80161	+	6.13572i	0.171777	+	0.585018i
$111$	−13.0107	−	5.18960i	−1.23492	−	0.492575i
$112$	−0.604089	−	0.0868549i	−0.0570811	−	0.00820702i
$113$	−10.3236	+	6.63455i	−0.971160	+	0.624126i	−0.927065	−	0.374901i	$-0.877677\pi$
$113$	−10.3236	+	6.63455i	−0.971160	+	0.624126i	−0.0440947	+	0.999027i	$0.514040\pi$
$114$	3.24570	−	0.158725i	0.303988	−	0.0148660i
$115$	−1.65882	−	4.49981i	−0.154685	−	0.419610i
$116$		−	2.73225i		−	0.253683i
$117$	5.03200	−	3.97785i	0.465209	−	0.367752i
$118$	1.85321	−	12.8894i	0.170602	−	1.18656i
$119$	−0.773903	−	0.353430i	−0.0709436	−	0.0323988i
$120$	0.568568	+	1.63607i	0.0519029	+	0.149352i
$121$	12.4179	+	27.1914i	1.12890	+	2.47195i
$122$	2.22526	+	2.56809i	0.201466	+	0.232504i
$123$	9.99483	−	1.93946i	0.901203	−	0.174875i
$124$	−8.08236	−	2.37319i	−0.725817	−	0.213119i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−1.62949	−	0.834850i	−0.145166	−	0.0743744i
$127$	−14.4106	−	9.26116i	−1.27874	−	0.821795i	−0.288007	−	0.957628i	$-0.592992\pi$
$127$	−14.4106	−	9.26116i	−1.27874	−	0.821795i	−0.990732	+	0.135833i	$0.956629\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−1.27581	+	5.28812i	−0.112328	+	0.465593i
$130$	2.11636	−	0.304287i	0.185617	−	0.0266878i
$131$	−12.6117	+	10.9281i	−1.10189	+	0.954790i	−0.999203	−	0.0399239i	$-0.987288\pi$
$131$	−12.6117	+	10.9281i	−1.10189	+	0.954790i	−0.102684	+	0.994714i	$0.532743\pi$
$132$	5.08777	+	9.83834i	0.442834	+	0.856318i
$133$	−1.09863	+	0.322588i	−0.0952635	+	0.0279719i
$134$	5.08339	−	11.1311i	0.439138	−	0.961578i
$135$	0.0197109	+	5.19612i	0.00169644	+	0.447210i
$136$	0.753677	+	1.17274i	0.0646273	+	0.100562i
$137$	2.26583			0.193583			0.0967916	−	0.995305i	$-0.469142\pi$
$137$	2.26583			0.193583			0.0967916	+	0.995305i	$0.469142\pi$
$138$	−4.30522	−	7.10388i	−0.366485	−	0.604722i
$139$	−16.2548			−1.37872			−0.689358	−	0.724421i	$-0.742107\pi$
$139$	−16.2548			−1.37872			−0.689358	+	0.724421i	$0.742107\pi$
$140$	−0.329954	−	0.513418i	−0.0278862	−	0.0433917i
$141$	8.60997	+	0.811168i	0.725091	+	0.0683127i
$142$	−3.63474	+	7.95897i	−0.305021	+	0.667902i
$143$	13.1189	−	3.85207i	1.09706	−	0.322126i
$144$	1.50657	+	2.59427i	0.125547	+	0.216190i
$145$	2.06490	−	1.78924i	0.171480	−	0.148589i
$146$	−12.6756	+	1.82247i	−1.04904	+	0.150829i
$147$	−11.1591	−	2.69222i	−0.920383	−	0.222051i
$148$	−6.11191	−	5.29600i	−0.502396	−	0.435329i
$149$	−5.90128	−	3.79252i	−0.483452	−	0.310696i	0.276115	−	0.961125i	$-0.410953\pi$
$149$	−5.90128	−	3.79252i	−0.483452	−	0.310696i	−0.759567	+	0.650429i	$0.774589\pi$
$150$	−0.864128	+	1.50109i	−0.0705558	+	0.122564i
$151$	1.96309	−	2.26552i	0.159754	−	0.184366i	−0.670230	−	0.742154i	$-0.733804\pi$
$151$	1.96309	−	2.26552i	0.159754	−	0.184366i	0.829983	+	0.557788i	$0.188350\pi$
$152$	1.80015	+	0.528571i	0.146011	+	0.0428728i
$153$	0.996250	+	4.06174i	0.0805420	+	0.328372i
$154$	−2.55574	−	2.94948i	−0.205947	−	0.237676i
$155$	−3.49928	−	7.66235i	−0.281069	−	0.615455i
$156$	3.49813	−	1.21567i	0.280075	−	0.0973315i
$157$	−12.0907	−	5.52164i	−0.964944	−	0.440675i	−0.130306	−	0.991474i	$-0.541596\pi$
$157$	−12.0907	−	5.52164i	−0.964944	−	0.440675i	−0.834638	+	0.550799i	$0.814323\pi$
$158$	−0.307584	+	2.13929i	−0.0244700	+	0.170193i
$159$	1.91225	−	1.36535i	0.151651	−	0.108280i
$160$			1.00000i			0.0790569i
$161$	2.06172	+	2.07751i	0.162486	+	0.163731i
$162$	1.74794	+	8.82863i	0.137331	+	0.693643i
$163$	10.4484	−	6.71476i	0.818379	−	0.525940i	−0.0631866	−	0.998002i	$-0.520126\pi$
$163$	10.4484	−	6.71476i	0.818379	−	0.525940i	0.881566	+	0.472061i	$0.156490\pi$
$164$	5.81832	+	0.836549i	0.454335	+	0.0653235i
$165$	−4.10354	+	10.2878i	−0.319460	+	0.800906i
$166$	3.06521	+	10.4392i	0.237907	+	0.810236i
$167$	−4.47364	+	2.04304i	−0.346181	+	0.158095i	−0.580915	−	0.813964i	$-0.697305\pi$
$167$	−4.47364	+	2.04304i	−0.346181	+	0.158095i	0.234735	+	0.972060i	$0.424578\pi$
$168$	−0.730430	−	0.764116i	−0.0563539	−	0.0589529i
$169$	1.19949	+	8.34262i	0.0922683	+	0.641740i
$170$	−0.392748	+	1.33758i	−0.0301224	+	0.102587i
$171$	4.59303	+	3.25321i	0.351238	+	0.248779i
$172$	−1.69799	+	2.64212i	−0.129470	+	0.201460i
$173$	1.32607	−	2.06341i	0.100819	−	0.156878i	−0.787179	−	0.616725i	$-0.788459\pi$
$173$	1.32607	−	2.06341i	0.100819	−	0.156878i	0.887998	+	0.459847i	$0.152096\pi$
$174$	2.92067	−	3.72361i	0.221415	−	0.282286i
$175$	0.171942	−	0.585580i	0.0129976	−	0.0442657i
$176$	0.910067	+	6.32966i	0.0685989	+	0.477116i
$177$	16.3039	−	15.5851i	1.22547	−	1.17145i
$178$	−7.92031	+	3.61708i	−0.593652	+	0.271112i
$179$	2.52495	+	8.59919i	0.188724	+	0.642734i	0.998436	+	0.0559066i	$0.0178049\pi$
$179$	2.52495	+	8.59919i	0.188724	+	0.642734i	−0.809712	+	0.586827i	$0.800377\pi$
$180$	−0.974031	+	2.83747i	−0.0726000	+	0.211493i
$181$	11.5517	+	1.66088i	0.858630	+	0.123452i	0.557547	−	0.830146i	$-0.311743\pi$
$181$	11.5517	+	1.66088i	0.858630	+	0.123452i	0.301083	+	0.953598i	$0.402652\pi$
$182$	−1.09775	+	0.705483i	−0.0813709	+	0.0522939i
$183$	0.287483	+	5.87860i	0.0212513	+	0.434558i
$184$	−1.00154	−	4.69009i	−0.0738346	−	0.345758i
$185$		−	8.08722i		−	0.594584i
$186$	−8.47808	−	11.8740i	−0.621643	−	0.870644i
$187$	−1.26867	+	8.82382i	−0.0927747	+	0.645262i
$188$	4.54178	+	2.07416i	0.331243	+	0.151274i
$189$	−1.32830	−	2.87962i	−0.0966199	−	0.209462i
$190$	0.779379	+	1.70660i	0.0565421	+	0.123810i
$191$	−0.400564	−	0.462276i	−0.0289838	−	0.0334491i	0.741073	−	0.671425i	$-0.234317\pi$
$191$	−0.400564	−	0.462276i	−0.0289838	−	0.0334491i	−0.770056	+	0.637976i	$0.779772\pi$
$192$	0.329943	+	1.70033i	0.0238116	+	0.122711i
$193$	14.2434	+	4.18223i	1.02526	+	0.301044i	0.750783	−	0.660549i	$-0.229677\pi$
$193$	14.2434	+	4.18223i	1.02526	+	0.301044i	0.274479	+	0.961593i	$0.411495\pi$
$194$	2.47174	−	2.85254i	0.177460	−	0.204800i
$195$	3.20953	+	1.84762i	0.229839	+	0.132311i
$196$	−5.57544	−	3.58311i	−0.398245	−	0.255937i
$197$	15.7249	+	13.6257i	1.12035	+	0.970789i	0.999760	−	0.0219134i	$-0.00697580\pi$
$197$	15.7249	+	13.6257i	1.12035	+	0.970789i	0.120590	+	0.992702i	$0.461521\pi$
$198$	−3.58299	+	18.8467i	−0.254632	+	1.33938i
$199$	5.51496	−	0.792932i	0.390945	−	0.0562094i	0.0559605	−	0.998433i	$-0.482178\pi$
$199$	5.51496	−	0.792932i	0.390945	−	0.0562094i	0.334985	+	0.942224i	$0.391269\pi$
$200$	−0.755750	+	0.654861i	−0.0534396	+	0.0463056i
$201$	18.8265	−	9.73589i	1.32792	−	0.686716i
$202$	−12.8265	+	3.76620i	−0.902470	+	0.264989i
$203$	−0.692703	+	1.51681i	−0.0486182	+	0.106459i
$204$	−0.226479	+	2.40391i	−0.0158567	+	0.168307i
$205$	3.17797	+	4.94502i	0.221959	+	0.345375i
$206$	12.9728			0.903861
$207$	1.72644	−	14.2835i	0.119996	−	0.992774i
$208$	2.13813			0.148252
$209$	6.48633	+	10.0929i	0.448669	+	0.698142i
$210$	0.0991505	−	1.05241i	0.00684203	−	0.0726233i
$211$	5.49638	−	12.0354i	0.378387	−	0.828551i	−0.620625	−	0.784107i	$-0.713121\pi$
$211$	5.49638	−	12.0354i	0.378387	−	0.828551i	0.999012	−	0.0444439i	$-0.0141516\pi$
$212$	1.30162	−	0.382191i	0.0893959	−	0.0262490i
$213$	−13.4614	+	6.96138i	−0.922359	+	0.476986i
$214$	−2.62016	+	2.27038i	−0.179110	+	0.155200i
$215$	−3.10873	+	0.446968i	−0.212013	+	0.0304829i
$216$	−0.719974	+	5.14603i	−0.0489880	+	0.350143i
$217$	3.88525	+	3.36658i	0.263748	+	0.228539i
$218$	2.72483	+	1.75114i	0.184549	+	0.118602i
$219$	−19.2229	−	11.0660i	−1.29896	−	0.747768i
$220$	−4.18767	+	4.83283i	−0.282333	+	0.325829i
$221$	2.85991	+	0.839745i	0.192378	+	0.0564873i
$222$	−2.66832	−	13.7510i	−0.179086	−	0.922905i
$223$	−11.7998	−	13.6177i	−0.790173	−	0.911909i	0.207626	−	0.978208i	$-0.433426\pi$
$223$	−11.7998	−	13.6177i	−0.790173	−	0.911909i	−0.997800	+	0.0662996i	$0.978881\pi$
$224$	−0.253528	−	0.555149i	−0.0169396	−	0.0370925i
$225$	−2.78228	+	1.12203i	−0.185485	+	0.0748018i
$226$	−11.1627	−	5.09783i	−0.742531	−	0.339102i
$227$	3.53477	−	24.5848i	0.234611	−	1.63175i	−0.443133	−	0.896456i	$-0.646133\pi$
$227$	3.53477	−	24.5848i	0.234611	−	1.63175i	0.677744	−	0.735298i	$-0.262958\pi$
$228$	1.88829	+	2.64464i	0.125055	+	0.175146i
$229$		−	25.3898i		−	1.67781i	−0.544281	−	0.838903i	$-0.683197\pi$
$229$		−	25.3898i		−	1.67781i	0.544281	−	0.838903i	$-0.316803\pi$
$230$	2.88866	−	3.82827i	0.190473	−	0.252429i
$231$	−0.330177	−	6.75164i	−0.0217241	−	0.444226i
$232$	2.29852	−	1.47717i	0.150905	−	0.0969808i
$233$	9.03362	+	1.29884i	0.591812	+	0.0850897i	0.431713	−	0.902011i	$-0.357909\pi$
$233$	9.03362	+	1.29884i	0.591812	+	0.0850897i	0.160099	+	0.987101i	$0.448819\pi$
$234$	6.06688	+	2.08260i	0.396605	+	0.136144i
$235$	1.40669	+	4.79073i	0.0917621	+	0.312513i
$236$	11.8452	−	5.40950i	0.771054	−	0.352128i
$237$	−2.70600	+	2.58671i	−0.175774	+	0.168025i
$238$	−0.121080	−	0.842127i	−0.00784842	−	0.0545870i
$239$	−2.60994	+	8.88865i	−0.168823	+	0.574959i	0.831002	+	0.556269i	$0.187768\pi$
$239$	−2.60994	+	8.88865i	−0.168823	+	0.574959i	−0.999825	+	0.0186897i	$0.994051\pi$
$240$	−1.06896	+	1.36284i	−0.0690011	+	0.0879707i
$241$	−12.2763	+	19.1023i	−0.790788	+	1.23049i	0.178349	+	0.983967i	$0.442924\pi$
$241$	−12.2763	+	19.1023i	−0.790788	+	1.23049i	−0.969137	+	0.246523i	$0.920712\pi$
$242$	−16.1613	+	25.1474i	−1.03889	+	1.61654i
$243$	−7.05530	+	13.9005i	−0.452598	+	0.891715i
$244$	−0.957346	+	3.26042i	−0.0612878	+	0.208727i
$245$	−0.943196	−	6.56007i	−0.0602586	−	0.419108i
$246$	7.03519	+	7.35964i	0.448547	+	0.469233i
$247$	3.64893	−	1.66641i	0.232176	−	0.106031i
$248$	−2.37319	−	8.08236i	−0.150698	−	0.513230i
$249$	−6.98166	+	17.5035i	−0.442445	+	1.10924i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	−10.6357	+	6.83512i	−0.671317	+	0.431429i	−0.831400	−	0.555674i	$-0.812460\pi$
$251$	−10.6357	+	6.83512i	−0.671317	+	0.431429i	0.160083	+	0.987104i	$0.448824\pi$
$252$	−0.178647	−	1.82217i	−0.0112537	−	0.114786i
$253$	14.8003	−	26.8605i	0.930484	−	1.68871i
$254$		−	17.1300i		−	1.07483i
$255$	−1.96507	+	1.40307i	−0.123057	+	0.0878634i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	3.37681	+	1.54214i	0.210640	+	0.0961960i	0.517941	−	0.855416i	$-0.326699\pi$
$257$	3.37681	+	1.54214i	0.210640	+	0.0961960i	−0.307301	+	0.951612i	$0.599426\pi$
$258$	−5.13840	+	1.78570i	−0.319903	+	0.111173i
$259$	2.05034	+	4.48961i	0.127402	+	0.278971i
$260$	1.40018	+	1.61589i	0.0868352	+	0.100213i
$261$	7.96079	−	1.95260i	0.492760	−	0.120863i
$262$	−16.0117	−	4.70145i	−0.989204	−	0.290456i
$263$	−6.93839	+	8.00733i	−0.427840	+	0.493753i	−0.928209	−	0.372059i	$-0.878652\pi$
$263$	−6.93839	+	8.00733i	−0.427840	+	0.493753i	0.500370	+	0.865812i	$0.333197\pi$
$264$	−5.52588	+	9.59912i	−0.340094	+	0.590785i
$265$	1.14122	+	0.733420i	0.0701048	+	0.0450536i
$266$	−0.865344	−	0.749825i	−0.0530576	−	0.0459747i
$267$	−14.6606	−	3.53700i	−0.897214	−	0.216461i
$268$	12.1123	−	1.74149i	0.739879	−	0.106379i
$269$	10.1911	−	8.83064i	0.621362	−	0.538413i	−0.286287	−	0.958144i	$-0.592421\pi$
$269$	10.1911	−	8.83064i	0.621362	−	0.538413i	0.907649	+	0.419731i	$0.137875\pi$
$270$	−4.36059	+	2.82581i	−0.265377	+	0.171974i
$271$	13.9986	−	4.11035i	0.850352	−	0.249686i	0.172614	−	0.984990i	$-0.444779\pi$
$271$	13.9986	−	4.11035i	0.850352	−	0.249686i	0.677738	+	0.735304i	$0.262960\pi$
$272$	−0.579107	+	1.26807i	−0.0351135	+	0.0768879i
$273$	−2.25019	−	0.211996i	−0.136188	−	0.0128306i
$274$	1.22500	+	1.90614i	0.0740050	+	0.115154i
$275$	−6.39475			−0.385618
$276$	3.64858	−	7.46243i	0.219619	−	0.449185i
$277$	−10.8732			−0.653310			−0.326655	−	0.945144i	$-0.605921\pi$
$277$	−10.8732			−0.653310			−0.326655	+	0.945144i	$0.605921\pi$
$278$	−8.78802	−	13.6744i	−0.527070	−	0.820137i
$279$	1.13859	−	25.2451i	0.0681656	−	1.51138i
$280$	0.253528	−	0.555149i	0.0151512	−	0.0331765i
$281$	17.8325	−	5.23609i	1.06380	−	0.312359i	0.297418	−	0.954747i	$-0.403875\pi$
$281$	17.8325	−	5.23609i	1.06380	−	0.312359i	0.766379	+	0.642388i	$0.222056\pi$
$282$	3.97251	+	7.68172i	0.236559	+	0.457440i
$283$	20.5399	−	17.7979i	1.22097	−	1.05798i	0.224460	−	0.974483i	$-0.427938\pi$
$283$	20.5399	−	17.7979i	1.22097	−	1.05798i	0.996508	−	0.0834921i	$-0.0266073\pi$
$284$	−8.66060	+	1.24521i	−0.513912	+	0.0738894i
$285$	−0.762124	+	3.15894i	−0.0451443	+	0.187120i
$286$	10.3332	+	8.95377i	0.611015	+	0.529448i
$287$	−3.01795	−	1.93952i	−0.178144	−	0.114486i
$288$	−1.36793	+	2.66997i	−0.0806062	+	0.157330i
$289$	9.86000	−	11.3790i	0.580000	−	0.669356i
$290$	2.62158	+	0.769764i	0.153944	+	0.0452021i
$291$	6.41783	−	1.24535i	0.376220	−	0.0730039i
$292$	−8.38610	−	9.67808i	−0.490759	−	0.566367i
$293$	0.588198	+	1.28797i	0.0343629	+	0.0752443i	0.926035	−	0.377437i	$-0.123195\pi$
$293$	0.588198	+	1.28797i	0.0343629	+	0.0752443i	−0.891672	+	0.452682i	$0.850467\pi$
$294$	−3.76820	−	10.8431i	−0.219766	−	0.632384i
$295$	11.8452	+	5.40950i	0.689652	+	0.314953i
$296$	1.15093	−	8.00490i	0.0668965	−	0.465275i
$297$	−25.0294	+	21.8549i	−1.45235	+	1.26815i
$298$		−	7.01487i		−	0.406360i
$299$	−8.18532	−	6.17633i	−0.473370	−	0.357186i
$300$	−1.72998	+	0.0846018i	−0.0998806	+	0.00488449i
$301$	1.61249	−	1.03628i	0.0929423	−	0.0597304i
$302$	2.96720	+	0.426619i	0.170743	+	0.0245492i
$303$	−21.5064	−	8.57831i	−1.23551	−	0.492811i
$304$	0.528571	+	1.80015i	0.0303156	+	0.103246i
$305$	−3.09099	+	1.41161i	−0.176989	+	0.0808284i
$306$	−2.87834	+	3.03404i	−0.164544	+	0.173445i
$307$	2.35821	+	16.4017i	0.134590	+	0.936097i	0.939463	+	0.342650i	$0.111324\pi$
$307$	2.35821	+	16.4017i	0.134590	+	0.936097i	−0.804873	+	0.593447i	$0.797767\pi$
$308$	1.09952	−	3.74463i	0.0626512	−	0.213370i
$309$	17.6799	+	13.8675i	1.00577	+	0.788892i
$310$	4.55413	−	7.08636i	0.258657	−	0.402478i
$311$	−3.97654	+	6.18762i	−0.225489	+	0.350868i	−0.935502	−	0.353320i	$-0.885053\pi$
$311$	−3.97654	+	6.18762i	−0.225489	+	0.350868i	0.710013	+	0.704188i	$0.248689\pi$
$312$	2.91392	+	2.28557i	0.164968	+	0.129395i
$313$	−4.54039	+	15.4631i	−0.256638	+	0.874028i	0.725874	+	0.687828i	$0.241436\pi$
$313$	−4.54039	+	15.4631i	−0.256638	+	0.874028i	−0.982512	+	0.186201i	$0.940383\pi$
$314$	−1.89163	−	13.1566i	−0.106751	−	0.742469i
$315$	1.26011	−	1.32828i	0.0709993	−	0.0748400i
$316$	−1.96598	+	0.897833i	−0.110595	+	0.0505070i
$317$	−1.17266	−	3.99372i	−0.0658633	−	0.224310i	0.919984	−	0.391956i	$-0.128202\pi$
$317$	−1.17266	−	3.99372i	−0.0658633	−	0.224310i	−0.985847	+	0.167646i	$0.946383\pi$
$318$	2.18245	+	0.870520i	0.122386	+	0.0488163i
$319$	17.2942	+	2.48653i	0.968290	+	0.139219i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−5.99780	+	0.293312i	−0.334765	+	0.0163711i
$322$	−0.633065	+	2.85762i	−0.0352793	+	0.159249i
$323$			2.61543i			0.145526i
$324$	−6.48211	+	6.24358i	−0.360117	+	0.346865i
$325$	−0.304287	+	2.11636i	−0.0168788	+	0.117395i
$326$	11.2976	+	5.15945i	0.625718	+	0.285756i
$327$	1.84159	+	5.29925i	0.101840	+	0.293049i
$328$	2.44187	+	5.34696i	0.134830	+	0.295236i
$329$	−1.99551	−	2.30294i	−0.110016	−	0.126965i
$330$	−10.8732	+	2.10990i	−0.598551	+	0.116146i
$331$	−24.5930	−	7.22117i	−1.35176	−	0.396911i	−0.475906	−	0.879496i	$-0.657880\pi$
$331$	−24.5930	−	7.22117i	−1.35176	−	0.396911i	−0.875849	+	0.482585i	$0.839698\pi$
$332$	−7.12480	+	8.22246i	−0.391024	+	0.451266i
$333$	11.0628	−	21.5927i	0.606236	−	1.18327i
$334$	−4.13735	−	2.65891i	−0.226386	−	0.145489i
$335$	9.24803	+	8.01346i	0.505274	+	0.437822i
$336$	0.247915	−	1.02759i	0.0135249	−	0.0560596i
$337$	10.0082	−	1.43896i	0.545181	−	0.0783852i	0.135779	−	0.990739i	$-0.456646\pi$
$337$	10.0082	−	1.43896i	0.545181	−	0.0783852i	0.409402	+	0.912354i	$0.365737\pi$
$338$	−6.36977	+	5.51944i	−0.346470	+	0.300218i
$339$	−9.76354	−	18.8800i	−0.530283	−	1.02542i
$340$	−1.33758	+	0.392748i	−0.0725402	+	0.0212997i
$341$	22.3770	−	48.9988i	1.21178	−	2.65343i
$342$	−0.253593	+	5.62272i	−0.0137128	+	0.304042i
$343$	4.49645	+	6.99662i	0.242786	+	0.377782i
$344$	−3.14070			−0.169335
$345$	8.02904	−	2.12944i	0.432269	−	0.114645i
$346$	2.45278			0.131862
$347$	−12.4789	−	19.4176i	−0.669903	−	1.04239i	−0.995303	−	0.0968131i	$-0.969135\pi$
$347$	−12.4789	−	19.4176i	−0.669903	−	1.04239i	0.325399	−	0.945577i	$-0.394501\pi$
$348$	4.71154	+	0.443886i	0.252565	+	0.0237948i
$349$	4.53964	−	9.94042i	0.243001	−	0.532099i	−0.748355	−	0.663299i	$-0.769156\pi$
$349$	4.53964	−	9.94042i	0.243001	−	0.532099i	0.991356	+	0.131200i	$0.0418831\pi$
$350$	0.585580	−	0.171942i	0.0313005	−	0.00919067i
$351$	6.04195	+	9.32350i	0.322495	+	0.497652i
$352$	−4.83283	+	4.18767i	−0.257591	+	0.223204i
$353$	−35.4192	+	5.09251i	−1.88517	+	0.271047i	−0.986025	−	0.166599i	$-0.946722\pi$
$353$	−35.4192	+	5.09251i	−1.88517	+	0.271047i	−0.899148	+	0.437645i	$0.855813\pi$
$354$	21.9256	+	5.28973i	1.16533	+	0.281146i
$355$	−6.61255	−	5.72981i	−0.350958	−	0.304107i
$356$	−7.32493	−	4.70744i	−0.388220	−	0.249494i
$357$	0.735189	−	1.27711i	0.0389103	−	0.0675919i
$358$	−5.86901	+	6.77319i	−0.310187	+	0.357974i
$359$	25.7374	+	7.55718i	1.35837	+	0.398853i	0.878187	−	0.478317i	$-0.158753\pi$
$359$	25.7374	+	7.55718i	1.35837	+	0.398853i	0.480180	+	0.877170i	$0.340571\pi$
$360$	−2.91364	+	0.714647i	−0.153562	+	0.0376652i
$361$	−10.1373	−	11.6991i	−0.533542	−	0.615740i
$362$	4.84809	+	10.6158i	0.254810	+	0.557956i
$363$	−48.9068	+	16.9961i	−2.56694	+	0.892062i
$364$	−1.18698	−	0.542076i	−0.0622147	−	0.0284125i
$365$	1.82247	−	12.6756i	0.0953926	−	0.663470i
$366$	−4.78996	+	3.42005i	−0.250375	+	0.178769i
$367$		−	6.99368i		−	0.365067i	−0.983200	−	0.182533i	$-0.941570\pi$
$367$		−	6.99368i		−	0.365067i	0.983200	−	0.182533i	$-0.0584298\pi$
$368$	3.40408	−	3.37820i	0.177450	−	0.176101i
$369$	1.72065	+	17.5503i	0.0895735	+	0.913633i
$370$	6.80340	−	4.37228i	0.353692	−	0.227304i
$371$	−0.819492	−	0.117825i	−0.0425459	−	0.00611718i
$372$	5.40545	−	13.5518i	0.280259	−	0.702627i
$373$	−0.182486	−	0.621489i	−0.00944875	−	0.0321795i	0.954634	−	0.297783i	$-0.0962471\pi$
$373$	−0.182486	−	0.621489i	−0.00944875	−	0.0321795i	−0.964082	+	0.265603i	$0.914429\pi$
$374$	−8.10897	+	3.70324i	−0.419305	+	0.191490i
$375$	−1.19684	−	1.25203i	−0.0618043	−	0.0646546i
$376$	0.710576	+	4.94216i	0.0366451	+	0.254873i
$377$	1.64585	−	5.60526i	0.0847658	−	0.288686i
$378$	1.70436	−	2.67428i	0.0876627	−	0.137550i
$379$	5.85621	−	9.11244i	0.300813	−	0.468075i	−0.657637	−	0.753335i	$-0.728444\pi$
$379$	5.85621	−	9.11244i	0.300813	−	0.468075i	0.958450	+	0.285260i	$0.0920801\pi$
$380$	−1.01432	+	1.57831i	−0.0520336	+	0.0809658i
$381$	18.3113	−	23.3454i	0.938114	−	1.19602i
$382$	0.172330	−	0.586901i	0.00881716	−	0.0300285i
$383$	2.21272	+	15.3898i	0.113065	+	0.786382i	0.964909	+	0.262586i	$0.0845754\pi$
$383$	2.21272	+	15.3898i	0.113065	+	0.786382i	−0.851844	+	0.523796i	$0.824516\pi$
$384$	−1.25203	+	1.19684i	−0.0638925	+	0.0610758i
$385$	3.55004	−	1.62125i	0.180927	−	0.0826265i
$386$	4.18223	+	14.2434i	0.212870	+	0.724969i
$387$	−8.91164	−	3.05914i	−0.453004	−	0.155505i
$388$	3.73603	+	0.537160i	0.189668	+	0.0272702i
$389$	−10.5958	+	6.80951i	−0.537229	+	0.345256i	−0.780954	−	0.624588i	$-0.785267\pi$
$389$	−10.5958	+	6.80951i	−0.537229	+	0.345256i	0.243725	+	0.969844i	$0.421630\pi$
$390$	0.180890	+	3.69892i	0.00915970	+	0.187302i
$391$	5.87999	−	3.18166i	0.297364	−	0.160903i
$392$		−	6.62753i		−	0.334741i
$393$	−16.7956	−	23.5231i	−0.847227	−	1.18659i
$394$	−2.96114	+	20.5952i	−0.149180	+	1.03757i
$395$	−1.96598	−	0.897833i	−0.0989192	−	0.0451749i
$396$	−17.7919	+	7.17508i	−0.894079	+	0.360561i
$397$	9.63176	+	21.0906i	0.483404	+	1.05851i	0.981513	+	0.191393i	$0.0613006\pi$
$397$	9.63176	+	21.0906i	0.483404	+	1.05851i	−0.498109	+	0.867114i	$0.665972\pi$
$398$	3.64867	+	4.21079i	0.182891	+	0.211068i
$399$	−0.377789	−	1.94691i	−0.0189131	−	0.0974672i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−9.48039	+	10.9409i	−0.473428	+	0.546365i	−0.941362	−	0.337398i	$-0.890453\pi$
$401$	−9.48039	+	10.9409i	−0.473428	+	0.546365i	0.467934	+	0.883763i	$0.344998\pi$
$402$	18.3687	+	10.5742i	0.916149	+	0.527395i
$403$	−15.1515	−	9.73731i	−0.754752	−	0.485050i
$404$	−10.1029	−	8.75418i	−0.502636	−	0.435537i
$405$	−8.96346	−	0.810179i	−0.445398	−	0.0402581i
$406$	−1.65052	+	0.237309i	−0.0819141	+	0.0117775i
$407$	39.0841	−	33.8666i	1.93733	−	1.67870i
$408$	−2.14474	+	1.10913i	−0.106181	+	0.0549099i
$409$	−22.4708	+	6.59801i	−1.11111	+	0.326251i	−0.785257	−	0.619170i	$-0.787469\pi$
$409$	−22.4708	+	6.59801i	−1.11111	+	0.326251i	−0.325851	+	0.945421i	$0.605651\pi$
$410$	−2.44187	+	5.34696i	−0.120596	+	0.264067i
$411$	−0.368111	+	3.90723i	−0.0181576	+	0.192730i
$412$	7.01365	+	10.9135i	0.345538	+	0.537667i
$413$	−7.94729			−0.391061
$414$	12.9495	−	6.26989i	0.636431	−	0.308148i
$415$	−10.8799			−0.534072
$416$	1.15596	+	1.79871i	0.0566755	+	0.0881889i
$417$	2.64078	−	28.0300i	0.129320	−	1.37264i
$418$	−4.98393	+	10.9133i	−0.243772	+	0.533786i
$419$	−4.97915	+	1.46201i	−0.243247	+	0.0714239i	−0.401084	−	0.916041i	$-0.631366\pi$
$419$	−4.97915	+	1.46201i	−0.243247	+	0.0714239i	0.157836	+	0.987465i	$0.449548\pi$
$420$	0.938950	−	0.485566i	0.0458161	−	0.0236932i
$421$	−29.2000	+	25.3020i	−1.42312	+	1.23314i	−0.490920	+	0.871205i	$0.663339\pi$
$421$	−29.2000	+	25.3020i	−1.42312	+	1.23314i	−0.932202	+	0.361938i	$0.882115\pi$
$422$	13.0964	−	1.88298i	0.637522	−	0.0916619i
$423$	−2.79758	+	14.7154i	−0.136023	+	0.715486i
$424$	1.02523	+	0.888367i	0.0497896	+	0.0431429i
$425$	−1.17274	−	0.753677i	−0.0568865	−	0.0365587i
$426$	−13.1341	−	7.56083i	−0.636347	−	0.366323i
$427$	1.35808	−	1.56731i	0.0657220	−	0.0758473i
$428$	−3.32653	−	0.976758i	−0.160794	−	0.0472134i
$429$	4.51124	+	23.2483i	0.217805	+	1.12244i
$430$	−2.05672	−	2.37358i	−0.0991837	−	0.114464i
$431$	−13.1707	−	28.8398i	−0.634411	−	1.38917i	−0.904560	−	0.426347i	$-0.859800\pi$
$431$	−13.1707	−	28.8398i	−0.634411	−	1.38917i	0.270149	−	0.962818i	$-0.412927\pi$
$432$	−4.71836	+	2.17647i	−0.227012	+	0.104716i
$433$	21.3050	+	9.72964i	1.02385	+	0.467577i	0.855309	−	0.518118i	$-0.173367\pi$
$433$	21.3050	+	9.72964i	1.02385	+	0.467577i	0.168541	+	0.985695i	$0.446094\pi$
$434$	−0.731629	+	5.08859i	−0.0351193	+	0.244260i
$435$	2.74993	+	3.85142i	0.131849	+	0.184662i
$436$			3.23901i			0.155120i
$437$	3.17651	−	8.41831i	0.151953	−	0.402703i
$438$	−1.08341	−	22.1540i	−0.0517671	−	1.05856i
$439$	−14.7021	+	9.44844i	−0.701691	+	0.450950i	−0.842225	−	0.539126i	$-0.818755\pi$
$439$	−14.7021	+	9.44844i	−0.701691	+	0.450950i	0.140534	+	0.990076i	$0.455118\pi$
$440$	−6.32966	−	0.910067i	−0.301755	−	0.0433858i
$441$	6.45542	−	18.8055i	0.307401	−	0.895498i
$442$	0.839745	+	2.85991i	0.0399426	+	0.136032i
$443$	16.1533	−	7.37695i	0.767464	−	0.350489i	0.00709055	−	0.999975i	$-0.497743\pi$
$443$	16.1533	−	7.37695i	0.767464	−	0.350489i	0.760374	+	0.649486i	$0.225016\pi$
$444$	10.1255	−	9.67907i	0.480533	−	0.459348i
$445$	−1.23916	−	8.61853i	−0.0587417	−	0.408557i
$446$	5.07648	−	17.2889i	0.240378	−	0.818654i
$447$	7.49862	−	9.56012i	0.354672	−	0.452178i
$448$	0.329954	−	0.513418i	0.0155888	−	0.0242567i
$449$	15.1589	−	23.5877i	0.715394	−	1.11317i	−0.273111	−	0.961983i	$-0.588052\pi$
$449$	15.1589	−	23.5877i	0.715394	−	1.11317i	0.988504	−	0.151192i	$-0.0483111\pi$
$450$	−2.44812	−	1.73399i	−0.115406	−	0.0817408i
$451$	−10.5901	+	36.0667i	−0.498670	+	1.69831i
$452$	−1.74644	−	12.1467i	−0.0821455	−	0.571335i
$453$	3.58777	+	3.75323i	0.168568	+	0.176342i
$454$	22.5931	−	10.3179i	1.06035	−	0.484245i
$455$	−0.367633	−	1.25204i	−0.0172349	−	0.0586967i
$456$	−1.20393	+	3.01833i	−0.0563792	+	0.141346i
$457$	24.8101	+	3.56715i	1.16057	+	0.166864i	0.695577	−	0.718451i	$-0.255149\pi$
$457$	24.8101	+	3.56715i	1.16057	+	0.166864i	0.464990	+	0.885316i	$0.346058\pi$
$458$	21.3593	−	13.7268i	0.998053	−	0.641410i
$459$	−7.16597	+	1.05807i	−0.334479	+	0.0493866i
$460$	4.78227	+	0.360379i	0.222975	+	0.0168027i
$461$			18.6764i			0.869847i	0.900467	+	0.434924i	$0.143225\pi$
$461$			18.6764i			0.869847i	−0.900467	+	0.434924i	$0.856775\pi$
$462$	5.50134	−	3.92798i	0.255945	−	0.182746i
$463$	3.17877	−	22.1089i	0.147730	−	1.02749i	−0.772193	−	0.635388i	$-0.780840\pi$
$463$	3.17877	−	22.1089i	0.147730	−	1.02749i	0.919923	−	0.392098i	$-0.128251\pi$
$464$	2.48534	+	1.13502i	0.115379	+	0.0526919i
$465$	13.7816	−	4.78937i	0.639105	−	0.222102i
$466$	3.79129	+	8.30177i	0.175628	+	0.384572i
$467$	14.8219	+	17.1054i	0.685878	+	0.791545i	0.986772	−	0.162112i	$-0.0518306\pi$
$467$	14.8219	+	17.1054i	0.685878	+	0.791545i	−0.300894	+	0.953657i	$0.597285\pi$
$468$	1.52801	+	6.22973i	0.0706322	+	0.287969i
$469$	−7.16567	−	2.10403i	−0.330880	−	0.0971552i
$470$	−3.26971	+	3.77344i	−0.150820	+	0.174056i
$471$	11.4859	−	19.9524i	0.529242	−	0.919356i
$472$	10.9547	+	7.04018i	0.504233	+	0.324051i
$473$	−15.1784	−	13.1522i	−0.697905	−	0.604738i
$474$	−3.63906	−	0.877955i	−0.167147	−	0.0403258i
$475$	−1.85705	+	0.267003i	−0.0852073	+	0.0122510i
$476$	0.642982	−	0.557147i	0.0294710	−	0.0255368i
$477$	2.04377	+	3.51933i	0.0935777	+	0.161139i
$478$	−8.88865	+	2.60994i	−0.406557	+	0.119376i
$479$	7.69724	−	16.8546i	0.351696	−	0.770107i	−0.648266	−	0.761414i	$-0.724506\pi$
$479$	7.69724	−	16.8546i	0.351696	−	0.770107i	0.999962	−	0.00869317i	$-0.00276716\pi$
$480$	−1.72441	−	0.162462i	−0.0787084	−	0.00741532i
$481$	−9.34849	−	14.5465i	−0.426255	−	0.663265i
$482$	−22.7070			−1.03428
$483$	−3.91744	+	3.21775i	−0.178250	+	0.146412i
$484$	−29.8928			−1.35876
$485$	2.04062	+	3.17527i	0.0926598	+	0.144182i
$486$	−15.5082	+	1.57986i	−0.703466	+	0.0716637i
$487$	13.6490	−	29.8872i	0.618497	−	1.35432i	−0.298111	−	0.954531i	$-0.596356\pi$
$487$	13.6490	−	29.8872i	0.618497	−	1.35432i	0.916608	−	0.399788i	$-0.130916\pi$
$488$	−3.26042	+	0.957346i	−0.147592	+	0.0433370i
$489$	9.88157	+	19.1082i	0.446860	+	0.864103i
$490$	5.00875	−	4.34011i	0.226272	−	0.196066i
$491$	−16.2126	+	2.33102i	−0.731663	+	0.105197i	−0.498070	−	0.867137i	$-0.665958\pi$
$491$	−16.2126	+	2.33102i	−0.731663	+	0.105197i	−0.233593	+	0.972334i	$0.575048\pi$
$492$	−2.38781	+	9.89730i	−0.107651	+	0.446205i
$493$	2.87856	+	2.49429i	0.129644	+	0.112337i
$494$	3.37464	+	2.16875i	0.151832	+	0.0975765i
$495$	−17.0738	−	8.74758i	−0.767411	−	0.393174i
$496$	5.51627	−	6.36611i	0.247688	−	0.285847i
$497$	5.12362	+	1.50443i	0.229826	+	0.0674830i
$498$	−18.4994	+	3.58974i	−0.828979	+	0.160860i
$499$	2.66886	+	3.08003i	0.119475	+	0.137881i	0.812336	−	0.583190i	$-0.198196\pi$
$499$	2.66886	+	3.08003i	0.119475	+	0.137881i	−0.692861	+	0.721071i	$0.743650\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−2.79626	−	8.04633i	−0.124928	−	0.359483i
$502$	−11.5001	−	5.25194i	−0.513276	−	0.234405i
$503$	−6.17677	+	42.9604i	−0.275408	+	1.91551i	0.112204	+	0.993685i	$0.464209\pi$
$503$	−6.17677	+	42.9604i	−0.275408	+	1.91551i	−0.387613	+	0.921822i	$0.626700\pi$
$504$	1.43632	−	1.13543i	0.0639788	−	0.0505759i
$505$		−	13.3680i		−	0.594868i
$506$	30.5981	−	2.07112i	1.36025	−	0.0920724i
$507$	−14.5810	+	0.713059i	−0.647565	+	0.0316681i
$508$	14.4106	−	9.26116i	0.639369	−	0.410898i
$509$	0.656434	+	0.0943810i	0.0290959	+	0.00418336i	0.156847	−	0.987623i	$-0.449867\pi$
$509$	0.656434	+	0.0943810i	0.0290959	+	0.00418336i	−0.127751	+	0.991806i	$0.540776\pi$
$510$	−2.24273	−	0.894565i	−0.0993097	−	0.0396120i
$511$	2.20187	+	7.49889i	0.0974051	+	0.331731i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	−6.35607	+	7.39177i	−0.280627	+	0.326355i
$514$	0.528313	+	3.67450i	0.0233029	+	0.162075i
$515$	−3.65487	+	12.4474i	−0.161053	+	0.548496i
$516$	−4.28025	−	3.35728i	−0.188428	−	0.147796i
$517$	−17.2620	+	26.8603i	−0.759184	+	1.18131i
$518$	−2.66841	+	4.15212i	−0.117243	+	0.182434i
$519$	3.34274	+	2.62192i	0.146730	+	0.115090i
$520$	−0.602380	+	2.05152i	−0.0264161	+	0.0899650i
$521$	−1.50362	−	10.4579i	−0.0658749	−	0.458170i	−0.995884	−	0.0906342i	$-0.971111\pi$
$521$	−1.50362	−	10.4579i	−0.0658749	−	0.458170i	0.930009	−	0.367536i	$-0.119799\pi$
$522$	5.94656	+	5.64139i	0.260274	+	0.246917i
$523$	−20.0183	+	9.14206i	−0.875340	+	0.399754i	−0.801839	−	0.597541i	$-0.796145\pi$
$523$	−20.0183	+	9.14206i	−0.875340	+	0.399754i	−0.0735015	+	0.997295i	$0.523417\pi$
$524$	−4.70145	−	16.0117i	−0.205384	−	0.699473i
$525$	0.981848	+	0.391633i	0.0428514	+	0.0170923i
$526$	−10.4874	−	1.50786i	−0.457271	−	0.0657457i
$527$	9.87870	−	6.34866i	0.430323	−	0.276552i
$528$	−11.0628	+	0.541007i	−0.481447	+	0.0235443i
$529$	−22.7902	+	3.09943i	−0.990879	+	0.134758i
$530$			1.35657i			0.0589258i
$531$	24.2264	+	30.6466i	1.05134	+	1.32995i
$532$	0.162952	−	1.13336i	0.00706488	−	0.0491374i
$533$	11.4325	+	5.22104i	0.495196	+	0.226148i
$534$	−4.95061	−	14.2455i	−0.214234	−	0.616464i
$535$	−1.44023	−	3.15367i	−0.0622666	−	0.136345i
$536$	8.01346	+	9.24803i	0.346129	+	0.399454i
$537$	−15.2388	+	2.95702i	−0.657602	+	0.127605i
$538$	12.9385	+	3.79909i	0.557820	+	0.163791i
$539$	27.7539	−	32.0297i	1.19545	−	1.37962i
$540$	−4.73474	−	2.14061i	−0.203751	−	0.0921174i
$541$	−10.5483	−	6.77896i	−0.453506	−	0.291450i	0.293878	−	0.955843i	$-0.405054\pi$
$541$	−10.5483	−	6.77896i	−0.453506	−	0.291450i	−0.747384	+	0.664393i	$0.768690\pi$
$542$	11.0260	+	9.55412i	0.473609	+	0.410384i
$543$	−4.74075	+	19.6501i	−0.203445	+	0.843265i
$544$	−1.37985	+	0.198393i	−0.0591608	+	0.00850604i
$545$	−2.44788	+	2.12110i	−0.104856	+	0.0908579i
$546$	−1.03820	−	2.00760i	−0.0444310	−	0.0859172i
$547$	−1.34608	+	0.395243i	−0.0575540	+	0.0168994i	−0.310383	−	0.950612i	$-0.600457\pi$
$547$	−1.34608	+	0.395243i	−0.0575540	+	0.0168994i	0.252829	+	0.967511i	$0.418639\pi$
$548$	−0.941261	+	2.06107i	−0.0402087	+	0.0880447i
$549$	−10.1838	−	0.459307i	−0.434636	−	0.0196027i
$550$	−3.45726	−	5.37960i	−0.147418	−	0.229387i
$551$	5.12610			0.218379
$552$	8.25037	−	0.965113i	0.351159	−	0.0410779i
$553$	1.31904			0.0560912
$554$	−5.87852	−	9.14715i	−0.249754	−	0.388625i
$555$	13.9457	+	1.31386i	0.591963	+	0.0557703i
$556$	6.75249	−	14.7859i	0.286370	−	0.627062i
$557$	−2.45513	+	0.720890i	−0.104027	+	0.0305451i	−0.333332	−	0.942810i	$-0.608173\pi$
$557$	−2.45513	+	0.720890i	−0.104027	+	0.0305451i	0.229305	+	0.973355i	$0.426355\pi$
$558$	21.8531	−	12.6907i	0.925114	−	0.537239i
$559$	−5.07501	+	4.39752i	−0.214650	+	0.185995i
$560$	0.604089	−	0.0868549i	0.0255274	−	0.00367029i
$561$	−15.0098	−	3.62125i	−0.633715	−	0.152889i
$562$	14.0459	+	12.1708i	0.592489	+	0.513394i
$563$	−5.39076	−	3.46443i	−0.227193	−	0.146008i	0.422092	−	0.906553i	$-0.361296\pi$
$563$	−5.39076	−	3.46443i	−0.227193	−	0.146008i	−0.649286	+	0.760544i	$0.724932\pi$
$564$	−4.31458	+	7.49494i	−0.181676	+	0.315594i
$565$	8.03622	−	9.27429i	0.338086	−	0.390172i
$566$	26.0772	+	7.65697i	1.09611	+	0.321846i
$567$	5.18146	−	1.82272i	0.217601	−	0.0765470i
$568$	−5.72981	−	6.61255i	−0.240417	−	0.277456i
$569$	16.7269	+	36.6267i	0.701227	+	1.53547i	0.838478	+	0.544936i	$0.183446\pi$
$569$	16.7269	+	36.6267i	0.701227	+	1.53547i	−0.137251	+	0.990536i	$0.543827\pi$
$570$	−3.06951	+	1.06672i	−0.128568	+	0.0446798i
$571$	−37.6231	−	17.1819i	−1.57448	−	0.719039i	−0.579114	−	0.815246i	$-0.696602\pi$
$571$	−37.6231	−	17.1819i	−1.57448	−	0.719039i	−0.995361	+	0.0962073i	$0.969329\pi$
$572$	−1.94584	+	13.5336i	−0.0813597	+	0.565869i
$573$	0.862231	−	0.615637i	0.0360202	−	0.0257186i
$574$		−	3.58744i		−	0.149737i
$575$	2.85937	+	3.85020i	0.119244	+	0.160564i
$576$	−2.98569	+	0.292720i	−0.124404	+	0.0121966i
$577$	−2.86423	+	1.84073i	−0.119239	+	0.0766306i	−0.598901	−	0.800823i	$-0.704396\pi$
$577$	−2.86423	+	1.84073i	−0.119239	+	0.0766306i	0.479662	+	0.877454i	$0.340759\pi$
$578$	14.9034	+	2.14278i	0.619899	+	0.0891280i
$579$	−9.52591	+	23.8820i	−0.395883	+	0.992504i
$580$	0.769764	+	2.62158i	0.0319627	+	0.108855i
$581$	6.03996	−	2.75836i	0.250580	−	0.114436i
$582$	4.51740	+	4.72573i	0.187252	+	0.195888i
$583$	1.23457	+	8.58665i	0.0511309	+	0.355623i
$584$	3.60785	−	12.2872i	0.149294	−	0.508448i
$585$	−3.70748	+	5.23439i	−0.153285	+	0.216416i
$586$	−0.765509	+	1.19116i	−0.0316229	+	0.0492062i
$587$	−3.86156	+	6.00871i	−0.159384	+	0.248006i	−0.911756	−	0.410732i	$-0.865273\pi$
$587$	−3.86156	+	6.00871i	−0.159384	+	0.248006i	0.752372	+	0.658738i	$0.228909\pi$
$588$	7.08457	−	9.03224i	0.292163	−	0.372483i
$589$	4.45246	−	15.1637i	0.183460	−	0.624809i
$590$	1.85321	+	12.8894i	0.0762955	+	0.530647i
$591$	−26.0510	+	24.9025i	−1.07159	+	1.02435i
$592$	7.35639	−	3.35955i	0.302346	−	0.138077i
$593$	−2.49832	−	8.50851i	−0.102594	−	0.349403i	0.892157	−	0.451725i	$-0.149191\pi$
$593$	−2.49832	−	8.50851i	−0.102594	−	0.349403i	−0.994751	+	0.102322i	$0.967373\pi$
$594$	−31.9174	−	9.24043i	−1.30959	−	0.379139i
$595$	0.842127	+	0.121080i	0.0345238	+	0.00496378i
$596$	5.90128	−	3.79252i	0.241726	−	0.155348i
$597$	0.471374	+	9.63890i	0.0192920	+	0.394494i
$598$	0.770535	−	10.2251i	0.0315095	−	0.418136i
$599$			33.1679i			1.35520i	0.735429	+	0.677602i	$0.236981\pi$
$599$			33.1679i			1.35520i	−0.735429	+	0.677602i	$0.763019\pi$
$600$	−1.00647	−	1.40962i	−0.0410890	−	0.0575473i
$601$	−2.53474	+	17.6295i	−0.103394	+	0.719123i	0.870508	+	0.492155i	$0.163791\pi$
$601$	−2.53474	+	17.6295i	−0.103394	+	0.719123i	−0.973902	+	0.226968i	$0.927119\pi$
$602$	1.74356	+	0.796255i	0.0710620	+	0.0324529i
$603$	13.7301	+	34.0464i	0.559134	+	1.38648i
$604$	1.24530	+	2.72682i	0.0506704	+	0.110953i
$605$	−19.5756	−	22.5915i	−0.795862	−	0.918474i
$606$	−4.41068	−	22.7301i	−0.179172	−	0.923346i
$607$	42.9858	+	12.6218i	1.74474	+	0.512302i	0.989673	−	0.143344i	$-0.0457854\pi$
$607$	42.9858	+	12.6218i	1.74474	+	0.512302i	0.755068	+	0.655646i	$0.227604\pi$
$608$	−1.22861	+	1.41790i	−0.0498269	+	0.0575033i
$609$	−2.50307	−	1.44093i	−0.101429	−	0.0583894i
$610$	−2.85863	−	1.83713i	−0.115743	−	0.0743833i
$611$	8.06811	+	6.99105i	0.326401	+	0.282828i
$612$	−4.10854	−	0.781086i	−0.166078	−	0.0315735i
$613$	23.6523	−	3.40069i	0.955308	−	0.137353i	0.353006	−	0.935621i	$-0.385159\pi$
$613$	23.6523	−	3.40069i	0.955308	−	0.137353i	0.602302	+	0.798268i	$0.294250\pi$
$614$	−12.5231	+	10.8513i	−0.505390	+	0.437923i
$615$	−9.04356	+	4.67676i	−0.364672	+	0.188585i
$616$	3.74463	−	1.09952i	0.150876	−	0.0443011i
$617$	−0.192588	+	0.421710i	−0.00775332	+	0.0169774i	−0.913469	−	0.406908i	$-0.866607\pi$
$617$	−0.192588	+	0.421710i	−0.00775332	+	0.0169774i	0.905716	+	0.423886i	$0.139334\pi$
$618$	−2.10759	+	22.3706i	−0.0847797	+	0.899876i
$619$	12.2638	+	19.0828i	0.492923	+	0.767003i	0.995216	−	0.0976940i	$-0.0311467\pi$
$619$	12.2638	+	19.0828i	0.492923	+	0.767003i	−0.502294	+	0.864697i	$0.667510\pi$
$620$	8.42357			0.338299
$621$	24.3503	+	5.29763i	0.977142	+	0.212587i
$622$	−7.35524			−0.294918
$623$	2.87296	+	4.47041i	0.115103	+	0.179103i
$624$	−0.347364	+	3.68702i	−0.0139057	+	0.147599i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−15.4631	+	4.54039i	−0.618031	+	0.181470i
$627$	−18.4582	+	9.54540i	−0.737148	+	0.381207i
$628$	10.0453	−	8.70433i	0.400852	−	0.347340i
$629$	11.1592	−	1.60445i	0.444946	−	0.0639736i
$630$	1.79869	+	0.341953i	0.0716614	+	0.0136237i
$631$	−3.37017	−	2.92027i	−0.134164	−	0.116254i	0.585194	−	0.810894i	$-0.301018\pi$
$631$	−3.37017	−	2.92027i	−0.134164	−	0.116254i	−0.719358	+	0.694639i	$0.755564\pi$
$632$	−1.81819	−	1.16848i	−0.0723239	−	0.0464797i
$633$	19.8611	+	11.4333i	0.789407	+	0.454434i
$634$	2.72574	−	3.14568i	0.108253	−	0.124931i
$635$	16.4361	+	4.82607i	0.652246	+	0.191517i
$636$	0.447592	+	2.30663i	0.0177482	+	0.0914639i
$637$	−9.27971	−	10.7094i	−0.367675	−	0.424320i
$638$	7.25816	+	15.8931i	0.287353	+	0.629216i
$639$	−9.81735	−	24.3440i	−0.388369	−	0.963032i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	−0.377453	+	2.62524i	−0.0149085	+	0.103691i	−0.995917	−	0.0902741i	$-0.971226\pi$
$641$	−0.377453	+	2.62524i	−0.0149085	+	0.103691i	0.981008	+	0.193965i	$0.0621348\pi$
$642$	−3.48940	−	4.88709i	−0.137716	−	0.192878i
$643$			6.06592i			0.239217i	0.992821	+	0.119608i	$0.0381639\pi$
$643$			6.06592i			0.239217i	−0.992821	+	0.119608i	$0.961836\pi$
$644$	−2.74624	+	1.01238i	−0.108217	+	0.0398932i
$645$	−0.265709	−	5.43335i	−0.0104623	−	0.213938i
$646$	−2.20024	+	1.41401i	−0.0865673	+	0.0556334i
$647$	−34.6297	−	4.97900i	−1.36143	−	0.195745i	−0.577399	−	0.816462i	$-0.695932\pi$
$647$	−34.6297	−	4.97900i	−1.36143	−	0.195745i	−0.784034	+	0.620717i	$0.786841\pi$
$648$	−8.75692	−	2.07757i	−0.344004	−	0.0816145i
$649$	23.4604	+	79.8988i	0.920901	+	3.13630i
$650$	−1.94491	+	0.888210i	−0.0762856	+	0.0348385i
$651$	−6.43659	+	6.15283i	−0.252270	+	0.241149i
$652$	1.76755	+	12.2936i	0.0692226	+	0.481454i
$653$	−6.13248	+	20.8853i	−0.239982	+	0.817305i	0.748127	+	0.663555i	$0.230953\pi$
$653$	−6.13248	+	20.8853i	−0.239982	+	0.817305i	−0.988110	+	0.153750i	$0.950865\pi$
$654$	−3.46237	+	4.41424i	−0.135389	+	0.172610i
$655$	9.02201	−	14.0385i	0.352519	−	0.548531i
$656$	−3.17797	+	4.94502i	−0.124079	+	0.193071i
$657$	22.2053	−	31.3505i	0.866311	−	1.22310i
$658$	0.858502	−	2.92379i	0.0334679	−	0.113981i
$659$	2.89667	+	20.1468i	0.112838	+	0.784809i	0.965136	+	0.261751i	$0.0842998\pi$
$659$	2.89667	+	20.1468i	0.112838	+	0.784809i	−0.852297	+	0.523058i	$0.824791\pi$
$660$	−7.65346	−	8.00643i	−0.297911	−	0.311650i
$661$	−32.7797	+	14.9700i	−1.27498	+	0.582264i	−0.933821	−	0.357741i	$-0.883547\pi$
$661$	−32.7797	+	14.9700i	−1.27498	+	0.582264i	−0.341160	+	0.940005i	$0.610820\pi$
$662$	−7.22117	−	24.5930i	−0.280659	−	0.955836i
$663$	−1.91269	+	4.79524i	−0.0742828	+	0.186232i
$664$	−10.7691	−	1.54837i	−0.417923	−	0.0600883i
$665$	0.963247	−	0.619041i	0.0373531	−	0.0240054i
$666$	24.1459	−	2.36729i	0.935634	−	0.0917305i
$667$	−6.23588	−	11.5245i	−0.241454	−	0.446229i
$668$		−	4.91808i		−	0.190286i
$669$	25.3996	−	18.1354i	0.982004	−	0.701155i
$670$	−1.74149	+	12.1123i	−0.0672797	+	0.467940i
$671$	−19.7661	−	9.02687i	−0.763062	−	0.348479i
$672$	0.998497	−	0.346997i	0.0385178	−	0.0133857i
$673$	4.81553	+	10.5446i	0.185625	+	0.406463i	0.979451	−	0.201683i	$-0.0646410\pi$
$673$	4.81553	+	10.5446i	0.185625	+	0.406463i	−0.793826	+	0.608145i	$0.791914\pi$
$674$	6.62137	+	7.64147i	0.255046	+	0.294338i
$675$	−1.48283	−	4.98008i	−0.0570740	−	0.191683i
$676$	−8.08700	−	2.37456i	−0.311039	−	0.0913291i
$677$	10.5812	−	12.2113i	0.406668	−	0.469320i	−0.515062	−	0.857153i	$-0.672231\pi$
$677$	10.5812	−	12.2113i	0.406668	−	0.469320i	0.921729	+	0.387834i	$0.126776\pi$
$678$	10.6043	−	18.4209i	0.407255	−	0.707450i
$679$	−1.93787	−	1.24539i	−0.0743686	−	0.0477938i
$680$	−1.05355	−	0.912905i	−0.0404017	−	0.0350083i
$681$	41.8202	+	10.0895i	1.60255	+	0.386630i
$682$	53.3183	−	7.66602i	2.04166	−	0.293547i
$683$	29.7614	−	25.7884i	1.13879	−	0.986765i	0.138793	−	0.990321i	$-0.455678\pi$
$683$	29.7614	−	25.7884i	1.13879	−	0.986765i	0.999994	+	0.00355685i	$0.00113218\pi$
$684$	−4.86724	+	2.82654i	−0.186103	+	0.108075i
$685$	−2.17405	+	0.638359i	−0.0830662	+	0.0243904i
$686$	−3.45496	+	7.56532i	−0.131911	+	0.288845i
$687$	43.7826	+	4.12487i	1.67041	+	0.157374i
$688$	−1.69799	−	2.64212i	−0.0647352	−	0.100730i
$689$	2.90053			0.110501
$690$	6.13223	+	5.60320i	0.233450	+	0.213310i
$691$	−8.83854			−0.336234			−0.168117	−	0.985767i	$-0.553769\pi$
$691$	−8.83854			−0.336234			−0.168117	+	0.985767i	$0.553769\pi$
$692$	1.32607	+	2.06341i	0.0504097	+	0.0784390i
$693$	11.6963	+	0.527520i	0.444305	+	0.0200388i
$694$	9.58849	−	20.9959i	0.363974	−	0.796992i
$695$	15.5964	−	4.57951i	0.591604	−	0.173711i
$696$	2.17383	+	4.20358i	0.0823987	+	0.159336i
$697$	−6.19292	+	5.36620i	−0.234574	+	0.203259i
$698$	10.8167	−	1.55521i	0.409419	−	0.0588656i
$699$	−3.70735	+	15.3667i	−0.140225	+	0.581222i
$700$	0.461235	+	0.399662i	0.0174330	+	0.0151058i
$701$	11.4334	+	7.34782i	0.431835	+	0.277523i	0.738447	−	0.674311i	$-0.235559\pi$
$701$	11.4334	+	7.34782i	0.431835	+	0.277523i	−0.306613	+	0.951834i	$0.599196\pi$
$702$	−4.57691	+	10.1235i	−0.172744	+	0.382086i
$703$	9.93607	−	11.4668i	0.374746	−	0.432480i
$704$	−6.13572	−	1.80161i	−0.231248	−	0.0679007i
$705$	−8.48974	+	1.64740i	−0.319742	+	0.0620447i
$706$	−23.4331	−	27.0433i	−0.881918	−	1.01779i
$707$	3.38917	+	7.42124i	0.127463	+	0.279104i
$708$	7.40384	+	21.3048i	0.278253	+	0.800683i
$709$	18.0091	+	8.22448i	0.676346	+	0.308877i	0.723813	−	0.689996i	$-0.242388\pi$
$709$	18.0091	+	8.22448i	0.676346	+	0.308877i	−0.0474672	+	0.998873i	$0.515115\pi$
$710$	1.24521	−	8.66060i	0.0467318	−	0.325027i
$711$	−4.02094	−	5.08652i	−0.150797	−	0.190759i
$712$		−	8.70716i		−	0.326314i
$713$	−39.5073	+	8.43655i	−1.47956	+	0.315951i
$714$	1.47185	−	0.0719781i	0.0550825	−	0.00269371i
$715$	−11.5023	+	7.39207i	−0.430161	+	0.276448i
$716$	−8.87100	−	1.27546i	−0.331525	−	0.0476661i
$717$	−14.9037	−	5.94469i	−0.556589	−	0.222008i
$718$	7.55718	+	25.7374i	0.282031	+	0.960511i
$719$	−47.1700	+	21.5418i	−1.75914	+	0.803374i	−0.773660	+	0.633601i	$0.781576\pi$
$719$	−47.1700	+	21.5418i	−1.75914	+	0.803374i	−0.985483	+	0.169773i	$0.945696\pi$
$720$	−2.17643	−	2.06474i	−0.0811108	−	0.0769483i
$721$	−1.12676	−	7.83675i	−0.0419626	−	0.291856i
$722$	4.36124	−	14.8530i	0.162309	−	0.552772i
$723$	−30.9459	−	24.2729i	−1.15089	−	0.902718i
$724$	−6.30953	+	9.81783i	−0.234492	+	0.364877i
$725$	−1.47717	+	2.29852i	−0.0548606	+	0.0853648i
$726$	−40.7390	−	31.9542i	−1.51197	−	1.18593i
$727$	−1.64874	+	5.61508i	−0.0611483	+	0.208252i	−0.984400	−	0.175943i	$-0.943703\pi$
$727$	−1.64874	+	5.61508i	−0.0611483	+	0.208252i	0.923252	+	0.384195i	$0.125521\pi$
$728$	−0.185707	−	1.29162i	−0.00688275	−	0.0478706i
$729$	−22.8239	−	14.4246i	−0.845331	−	0.534243i
$730$	11.6487	−	5.31978i	0.431137	−	0.196894i
$731$	−1.23350	−	4.20092i	−0.0456227	−	0.155377i
$732$	−5.46678	−	2.18055i	−0.202058	−	0.0805956i
$733$	−28.7121	−	4.12818i	−1.06051	−	0.152478i	−0.410082	−	0.912049i	$-0.634500\pi$
$733$	−28.7121	−	4.12818i	−1.06051	−	0.152478i	−0.650425	+	0.759571i	$0.725409\pi$
$734$	5.88345	−	3.78107i	0.217162	−	0.139562i
$735$	11.4655	−	0.560702i	0.422912	−	0.0206818i
$736$	4.68231	+	1.03730i	0.172592	+	0.0382353i
$737$			78.2518i			2.88244i
$738$	−13.8340	+	10.9359i	−0.509237	+	0.402557i
$739$	−1.63391	+	11.3641i	−0.0601045	+	0.418036i	0.937449	+	0.348124i	$0.113181\pi$
$739$	−1.63391	+	11.3641i	−0.0601045	+	0.418036i	−0.997553	+	0.0699125i	$0.977728\pi$
$740$	7.35639	+	3.35955i	0.270426	+	0.123500i
$741$	2.28077	+	6.56300i	0.0837863	+	0.241098i
$742$	−0.343930	−	0.753102i	−0.0126261	−	0.0276472i
$743$	−7.16578	−	8.26975i	−0.262887	−	0.303388i	0.608926	−	0.793227i	$-0.291601\pi$
$743$	−7.16578	−	8.26975i	−0.262887	−	0.303388i	−0.871813	+	0.489840i	$0.837055\pi$
$744$	14.3229	−	2.77930i	0.525103	−	0.101894i
$745$	6.73072	+	1.97632i	0.246594	+	0.0724067i
$746$	0.424171	−	0.489519i	0.0155300	−	0.0179226i
$747$	−29.0490	−	14.8829i	−1.06285	−	0.544538i
$748$	−7.49941	−	4.81958i	−0.274205	−	0.176221i
$749$	1.59909	+	1.38562i	0.0584294	+	0.0506293i
$750$	0.406218	−	1.68374i	0.0148330	−	0.0614816i
$751$	31.6399	−	4.54913i	1.15456	−	0.166000i	0.461673	−	0.887050i	$-0.347249\pi$
$751$	31.6399	−	4.54913i	1.15456	−	0.166000i	0.692883	+	0.721050i	$0.256340\pi$
$752$	−3.77344	+	3.26971i	−0.137603	+	0.119234i
$753$	−10.0587	−	19.4507i	−0.366559	−	0.708824i
$754$	5.60526	−	1.64585i	0.204132	−	0.0599385i
$755$	−1.24530	+	2.72682i	−0.0453210	+	0.0992391i
$756$	3.17120	−	0.0120296i	0.115335	−	0.000437511i
$757$	−4.50845	−	7.01529i	−0.163862	−	0.254975i	0.749606	−	0.661884i	$-0.230243\pi$
$757$	−4.50845	−	7.01529i	−0.163862	−	0.254975i	−0.913469	+	0.406909i	$0.866607\pi$
$758$	10.8320			0.393435
$759$	43.9142	+	29.8856i	1.59398	+	1.08478i
$760$	−1.87615			−0.0680549
$761$	17.4064	+	27.0850i	0.630983	+	0.981829i	0.998654	+	0.0518727i	$0.0165190\pi$
$761$	17.4064	+	27.0850i	0.630983	+	0.981829i	−0.367671	+	0.929956i	$0.619845\pi$
$762$	29.5392	+	2.78296i	1.07009	+	0.100816i
$763$	0.821180	−	1.79813i	0.0297287	−	0.0650968i
$764$	0.586901	−	0.172330i	0.0212333	−	0.00623467i
$765$	−2.10022	−	3.61653i	−0.0759336	−	0.130756i
$766$	−11.7504	+	10.1818i	−0.424560	+	0.367884i
$767$	27.5591	−	3.96240i	0.995102	−	0.143074i
$768$	−1.68374	−	0.406218i	−0.0607568	−	0.0146581i
$769$	−10.2783	−	8.90616i	−0.370643	−	0.321164i	0.449545	−	0.893258i	$-0.351586\pi$
$769$	−10.2783	−	8.90616i	−0.370643	−	0.321164i	−0.820189	+	0.572093i	$0.806132\pi$
$770$	3.28318	+	2.10997i	0.118318	+	0.0760381i
$771$	−3.20789	+	5.57249i	−0.115529	+	0.200688i
$772$	−9.72121	+	11.2189i	−0.349874	+	0.403776i
$773$	16.1289	+	4.73588i	0.580117	+	0.170338i	0.558609	−	0.829431i	$-0.311335\pi$
$773$	16.1289	+	4.73588i	0.580117	+	0.170338i	0.0215077	+	0.999769i	$0.493153\pi$

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.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.162462 + 1.72441i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.53850 + 0.795618i) q^{6} +(0.461235 - 0.399662i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.94721 - 0.560302i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.162462 + 1.72441i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.53850 + 0.795618i) q^{6} +(0.461235 - 0.399662i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.94721 - 0.560302i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-5.37960 - 3.45726i) q^{11} +(-1.50109 - 0.864128i) q^{12} +(-1.40018 + 1.61589i) q^{13} +(0.585580 + 0.171942i) q^{14} +(-0.329943 - 1.70033i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.579107 - 1.26807i) q^{17} +(-1.12203 - 2.78228i) q^{18} +(-1.70660 - 0.779379i) q^{19} +(0.142315 - 0.989821i) q^{20} +(0.614251 + 0.860290i) q^{21} -6.39475i q^{22} +(0.323878 + 4.78488i) q^{23} +(-0.0846018 - 1.72998i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-2.11636 - 0.304287i) q^{26} +(1.44500 - 4.99119i) q^{27} +(0.171942 + 0.585580i) q^{28} +(-2.48534 + 1.13502i) q^{29} +(1.25203 - 1.19684i) q^{30} +(1.19880 + 8.33783i) q^{31} +(0.281733 - 0.959493i) q^{32} +(6.83573 - 8.71500i) q^{33} +(0.753677 - 1.17274i) q^{34} +(-0.329954 + 0.513418i) q^{35} +(1.73399 - 2.44812i) q^{36} +(-2.27843 + 7.75963i) q^{37} +(-0.267003 - 1.85705i) q^{38} +(-2.55899 - 2.67700i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-1.65607 - 5.64005i) q^{41} +(-0.391633 + 0.981848i) q^{42} +(3.10873 + 0.446968i) q^{43} +(5.37960 - 3.45726i) q^{44} +(2.98569 - 0.292720i) q^{45} +(-3.85020 + 2.85937i) q^{46} -4.99298i q^{47} +(1.40962 - 1.00647i) q^{48} +(-0.943196 + 6.56007i) q^{49} +(0.909632 + 0.415415i) q^{50} +(2.28076 - 0.792608i) q^{51} +(-0.888210 - 1.94491i) q^{52} +(-0.888367 - 1.02523i) q^{53} +(4.98008 - 1.48283i) q^{54} +(6.13572 + 1.80161i) q^{55} +(-0.399662 + 0.461235i) q^{56} +(1.62123 - 2.81627i) q^{57} +(-2.29852 - 1.47717i) q^{58} +(-9.84131 - 8.52754i) q^{59} +(1.68374 + 0.406218i) q^{60} +(3.36348 - 0.483595i) q^{61} +(-6.36611 + 5.51627i) q^{62} +(-1.58329 + 0.919459i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.888210 - 1.94491i) q^{65} +(11.0272 + 1.03890i) q^{66} +(-6.61576 - 10.2943i) q^{67} +1.39404 q^{68} +(-8.30374 - 0.218860i) q^{69} -0.610301 q^{70} +(4.73042 + 7.36068i) q^{71} +(2.99695 + 0.135167i) q^{72} +(-5.31978 + 11.6487i) q^{73} +(-7.75963 + 2.27843i) q^{74} +(0.795618 + 1.53850i) q^{75} +(1.41790 - 1.22861i) q^{76} +(-3.86300 + 0.555415i) q^{77} +(0.868545 - 3.60005i) q^{78} +(1.63339 + 1.41534i) q^{79} +(0.841254 + 0.540641i) q^{80} +(8.37212 + 3.30266i) q^{81} +(3.84937 - 4.44241i) q^{82} +(10.4392 + 3.06521i) q^{83} +(-1.03772 + 0.201365i) q^{84} +(0.912905 + 1.05355i) q^{85} +(1.30469 + 2.85688i) q^{86} +(-1.55347 - 4.47016i) q^{87} +(5.81687 + 2.65647i) q^{88} +(-1.23916 + 8.61853i) q^{89} +(1.86043 + 2.35346i) q^{90} +1.30490i q^{91} +(-4.48703 - 1.69310i) q^{92} +(-14.5726 + 0.712650i) q^{93} +(4.20036 - 2.69941i) q^{94} +(1.85705 + 0.267003i) q^{95} +(1.60879 + 0.641705i) q^{96} +(-1.06339 - 3.62156i) q^{97} +(-6.02862 + 2.75318i) q^{98} +(13.9177 + 13.2035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) \)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Properties

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