LMFDB - Embedded newform 690.2.q.a.11.2

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			11.2
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.2

$q$-expansion

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(-1.61107 + 0.635963i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.40602 + 1.01149i) q^{6} +(-3.41511 + 2.95921i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.19110 - 2.04916i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.61107 + 0.635963i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.40602 + 1.01149i) q^{6} +(-3.41511 + 2.95921i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.19110 - 2.04916i) q^{9} +(0.755750 + 0.654861i) q^{10} +(4.40521 + 2.83106i) q^{11} +(0.0907705 - 1.72967i) q^{12} +(-1.32881 + 1.53353i) q^{13} +(4.33580 + 1.27311i) q^{14} +(1.36664 - 1.06409i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.47114 - 3.22135i) q^{17} +(-2.90847 - 0.735409i) q^{18} +(0.151525 + 0.0691990i) q^{19} +(0.142315 - 0.989821i) q^{20} +(3.62004 - 6.93939i) q^{21} -5.23649i q^{22} +(-3.10773 - 3.65267i) q^{23} +(-1.50417 + 0.858770i) q^{24} +(0.841254 - 0.540641i) q^{25} +(2.00849 + 0.288778i) q^{26} +(-2.22683 + 4.69481i) q^{27} +(-1.27311 - 4.33580i) q^{28} +(-8.75985 + 4.00049i) q^{29} +(-1.63403 - 0.574398i) q^{30} +(-0.144804 - 1.00714i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-8.89756 - 1.75948i) q^{33} +(-1.91461 + 2.97920i) q^{34} +(2.44307 - 3.80149i) q^{35} +(0.953770 + 2.84435i) q^{36} +(1.17035 - 3.98585i) q^{37} +(-0.0237065 - 0.164883i) q^{38} +(1.16554 - 3.31570i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(-2.99903 - 10.2138i) q^{41} +(-7.79493 + 0.706346i) q^{42} +(7.79071 + 1.12013i) q^{43} +(-4.40521 + 2.83106i) q^{44} +(-1.52503 + 2.58346i) q^{45} +(-1.39266 + 4.58917i) q^{46} -0.999033i q^{47} +(1.53566 + 0.801099i) q^{48} +(1.90986 - 13.2834i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(4.41878 + 4.25423i) q^{51} +(-0.842939 - 1.84578i) q^{52} +(-4.56360 - 5.26667i) q^{53} +(5.15344 - 0.664881i) q^{54} +(-5.02437 - 1.47529i) q^{55} +(-2.95921 + 3.41511i) q^{56} +(-0.288125 - 0.0151204i) q^{57} +(8.10136 + 5.20643i) q^{58} +(-8.29680 - 7.18922i) q^{59} +(0.400211 + 1.68518i) q^{60} +(1.99940 - 0.287471i) q^{61} +(-0.768971 + 0.666317i) q^{62} +(-1.41894 + 13.4821i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.842939 - 1.84578i) q^{65} +(3.33021 + 8.43635i) q^{66} +(-2.50373 - 3.89588i) q^{67} +3.54138 q^{68} +(7.32974 + 3.90832i) q^{69} -4.51884 q^{70} +(8.41815 + 13.0989i) q^{71} +(1.87717 - 2.34013i) q^{72} +(-3.41305 + 7.47353i) q^{73} +(-3.98585 + 1.17035i) q^{74} +(-1.01149 + 1.40602i) q^{75} +(-0.125891 + 0.109085i) q^{76} +(-23.4220 + 3.36758i) q^{77} +(-3.41948 + 0.812087i) q^{78} +(-12.8555 - 11.1393i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.601847 - 8.97985i) q^{81} +(-6.97097 + 8.04493i) q^{82} +(6.98998 + 2.05244i) q^{83} +(4.80847 + 6.17563i) q^{84} +(2.31911 + 2.67640i) q^{85} +(-3.26966 - 7.15955i) q^{86} +(11.5686 - 12.0160i) q^{87} +(4.76328 + 2.17531i) q^{88} +(-1.03075 + 7.16903i) q^{89} +(2.99784 - 0.113789i) q^{90} -9.16940i q^{91} +(4.61359 - 1.30951i) q^{92} +(0.873793 + 1.53048i) q^{93} +(-0.840440 + 0.540118i) q^{94} +(-0.164883 - 0.0237065i) q^{95} +(-0.156311 - 1.72498i) q^{96} +(-2.70799 - 9.22258i) q^{97} +(-12.2072 + 5.57485i) q^{98} +(15.4536 - 2.82387i) 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
$3$	−1.61107	+	0.635963i	−0.930152	+	0.367174i
$3$	−1.61107	+	0.635963i	−0.930152	+	0.367174i
$4$	−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
$6$	1.40602	+	1.01149i	0.574004	+	0.412940i
$7$	−3.41511	+	2.95921i	−1.29079	+	1.11848i	−0.304669	+	0.952458i	$0.598546\pi$
$7$	−3.41511	+	2.95921i	−1.29079	+	1.11848i	−0.986123	+	0.166019i	$0.946909\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	2.19110	−	2.04916i	0.730367	−	0.683055i
$10$	0.755750	+	0.654861i	0.238989	+	0.207085i
$11$	4.40521	+	2.83106i	1.32822	+	0.853596i	0.995978	−	0.0895975i	$-0.0285581\pi$
$11$	4.40521	+	2.83106i	1.32822	+	0.853596i	0.332243	+	0.943194i	$0.392194\pi$
$12$	0.0907705	−	1.72967i	0.0262032	−	0.499313i
$13$	−1.32881	+	1.53353i	−0.368545	+	0.425324i	−0.909485	−	0.415738i	$-0.863523\pi$
$13$	−1.32881	+	1.53353i	−0.368545	+	0.425324i	0.540939	+	0.841062i	$0.318069\pi$
$14$	4.33580	+	1.27311i	1.15879	+	0.340252i
$15$	1.36664	−	1.06409i	0.352865	−	0.274748i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.47114	−	3.22135i	−0.356804	−	0.781293i	−0.999880	−	0.0154900i	$-0.995069\pi$
$17$	−1.47114	−	3.22135i	−0.356804	−	0.781293i	0.643076	−	0.765803i	$-0.277658\pi$
$18$	−2.90847	−	0.735409i	−0.685532	−	0.173338i
$19$	0.151525	+	0.0691990i	0.0347622	+	0.0158753i	0.432720	−	0.901528i	$-0.357554\pi$
$19$	0.151525	+	0.0691990i	0.0347622	+	0.0158753i	−0.397958	+	0.917404i	$0.630281\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	3.62004	−	6.93939i	0.789958	−	1.51430i
$22$		−	5.23649i		−	1.11642i
$23$	−3.10773	−	3.65267i	−0.648006	−	0.761635i
$23$	−3.10773	−	3.65267i	−0.648006	−	0.761635i
$24$	−1.50417	+	0.858770i	−0.307037	+	0.175296i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	2.00849	+	0.288778i	0.393898	+	0.0566340i
$27$	−2.22683	+	4.69481i	−0.428553	+	0.903517i
$28$	−1.27311	−	4.33580i	−0.240594	−	0.819389i
$29$	−8.75985	+	4.00049i	−1.62666	+	0.742872i	−0.999355	−	0.0358985i	$-0.988571\pi$
$29$	−8.75985	+	4.00049i	−1.62666	+	0.742872i	−0.627308	+	0.778771i	$0.715843\pi$
$30$	−1.63403	−	0.574398i	−0.298332	−	0.104870i
$31$	−0.144804	−	1.00714i	−0.0260077	−	0.180887i	0.972677	−	0.232163i	$-0.0745803\pi$
$31$	−0.144804	−	1.00714i	−0.0260077	−	0.180887i	−0.998685	+	0.0512759i	$0.983671\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	−8.89756	−	1.75948i	−1.54887	−	0.306287i
$34$	−1.91461	+	2.97920i	−0.328354	+	0.510928i
$35$	2.44307	−	3.80149i	0.412954	−	0.642570i
$36$	0.953770	+	2.84435i	0.158962	+	0.474058i
$37$	1.17035	−	3.98585i	0.192404	−	0.655269i	−0.805619	−	0.592433i	$-0.798167\pi$
$37$	1.17035	−	3.98585i	0.192404	−	0.655269i	0.998024	−	0.0628360i	$-0.0200145\pi$
$38$	−0.0237065	−	0.164883i	−0.00384571	−	0.0267475i
$39$	1.16554	−	3.31570i	0.186636	−	0.530936i
$40$	−0.909632	+	0.415415i	−0.143825	+	0.0656829i
$41$	−2.99903	−	10.2138i	−0.468370	−	1.59512i	−0.767592	−	0.640939i	$-0.778545\pi$
$41$	−2.99903	−	10.2138i	−0.468370	−	1.59512i	0.299221	−	0.954184i	$-0.403273\pi$
$42$	−7.79493	+	0.706346i	−1.20278	+	0.108992i
$43$	7.79071	+	1.12013i	1.18807	+	0.170819i	0.707872	−	0.706340i	$-0.249655\pi$
$43$	7.79071	+	1.12013i	1.18807	+	0.170819i	0.480199	+	0.877159i	$0.340564\pi$
$44$	−4.40521	+	2.83106i	−0.664111	+	0.426798i
$45$	−1.52503	+	2.58346i	−0.227338	+	0.385120i
$46$	−1.39266	+	4.58917i	−0.205337	+	0.676636i
$47$		−	0.999033i		−	0.145724i	−0.997342	−	0.0728620i	$-0.976787\pi$
$47$		−	0.999033i		−	0.145724i	0.997342	−	0.0728620i	$-0.0232133\pi$
$48$	1.53566	+	0.801099i	0.221653	+	0.115629i
$49$	1.90986	−	13.2834i	0.272837	−	1.89762i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	4.41878	+	4.25423i	0.618753	+	0.595712i
$52$	−0.842939	−	1.84578i	−0.116895	−	0.255963i
$53$	−4.56360	−	5.26667i	−0.626858	−	0.723433i	0.350136	−	0.936699i	$-0.386135\pi$
$53$	−4.56360	−	5.26667i	−0.626858	−	0.723433i	−0.976994	+	0.213266i	$0.931590\pi$
$54$	5.15344	−	0.664881i	0.701294	−	0.0904788i
$55$	−5.02437	−	1.47529i	−0.677486	−	0.198928i
$56$	−2.95921	+	3.41511i	−0.395441	+	0.456364i
$57$	−0.288125	−	0.0151204i	−0.0381631	−	0.00200274i
$58$	8.10136	+	5.20643i	1.06376	+	0.683638i
$59$	−8.29680	−	7.18922i	−1.08015	−	0.935957i	−0.0819940	−	0.996633i	$-0.526129\pi$
$59$	−8.29680	−	7.18922i	−1.08015	−	0.935957i	−0.998158	+	0.0606762i	$0.980674\pi$
$60$	0.400211	+	1.68518i	0.0516670	+	0.217556i
$61$	1.99940	−	0.287471i	0.255997	−	0.0368069i	−0.0131213	−	0.999914i	$-0.504177\pi$
$61$	1.99940	−	0.287471i	0.255997	−	0.0368069i	0.269119	+	0.963107i	$0.413268\pi$
$62$	−0.768971	+	0.666317i	−0.0976594	+	0.0846223i
$63$	−1.41894	+	13.4821i	−0.178770	+	1.69858i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	0.842939	−	1.84578i	0.104554	−	0.228941i
$66$	3.33021	+	8.43635i	0.409921	+	1.03844i
$67$	−2.50373	−	3.89588i	−0.305879	−	0.475957i	0.653952	−	0.756536i	$-0.273110\pi$
$67$	−2.50373	−	3.89588i	−0.305879	−	0.475957i	−0.959831	+	0.280579i	$0.909474\pi$
$68$	3.54138			0.429455
$69$	7.32974	+	3.90832i	0.882397	+	0.470506i
$70$	−4.51884			−0.540105
$71$	8.41815	+	13.0989i	0.999050	+	1.55455i	0.821315	+	0.570474i	$0.193241\pi$
$71$	8.41815	+	13.0989i	0.999050	+	1.55455i	0.177735	+	0.984078i	$0.443123\pi$
$72$	1.87717	−	2.34013i	0.221227	−	0.275787i
$73$	−3.41305	+	7.47353i	−0.399467	+	0.874711i	0.597857	+	0.801603i	$0.296019\pi$
$73$	−3.41305	+	7.47353i	−0.399467	+	0.874711i	−0.997324	+	0.0731081i	$0.976708\pi$
$74$	−3.98585	+	1.17035i	−0.463346	+	0.136051i
$75$	−1.01149	+	1.40602i	−0.116797	+	0.162353i
$76$	−0.125891	+	0.109085i	−0.0144407	+	0.0125130i
$77$	−23.4220	+	3.36758i	−2.66919	+	0.383771i
$78$	−3.41948	+	0.812087i	−0.387180	+	0.0919508i
$79$	−12.8555	−	11.1393i	−1.44635	−	1.25327i	−0.913359	−	0.407154i	$-0.866521\pi$
$79$	−12.8555	−	11.1393i	−1.44635	−	1.25327i	−0.532995	−	0.846119i	$-0.678933\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	0.601847	−	8.97985i	0.0668719	−	0.997762i
$82$	−6.97097	+	8.04493i	−0.769815	+	0.888414i
$83$	6.98998	+	2.05244i	0.767250	+	0.225285i	0.641859	−	0.766822i	$-0.278163\pi$
$83$	6.98998	+	2.05244i	0.767250	+	0.225285i	0.125391	+	0.992107i	$0.459982\pi$
$84$	4.80847	+	6.17563i	0.524647	+	0.673817i
$85$	2.31911	+	2.67640i	0.251543	+	0.290296i
$86$	−3.26966	−	7.15955i	−0.352576	−	0.772034i
$87$	11.5686	−	12.0160i	1.24028	−	1.28825i
$88$	4.76328	+	2.17531i	0.507767	+	0.231889i
$89$	−1.03075	+	7.16903i	−0.109259	+	0.759916i	0.859361	+	0.511370i	$0.170862\pi$
$89$	−1.03075	+	7.16903i	−0.109259	+	0.759916i	−0.968620	+	0.248546i	$0.920047\pi$
$90$	2.99784	−	0.113789i	0.316000	−	0.0119945i
$91$		−	9.16940i		−	0.961214i
$92$	4.61359	−	1.30951i	0.481000	−	0.136526i
$93$	0.873793	+	1.53048i	0.0906081	+	0.158703i
$94$	−0.840440	+	0.540118i	−0.0866848	+	0.0557089i
$95$	−0.164883	−	0.0237065i	−0.0169166	−	0.00243224i
$96$	−0.156311	−	1.72498i	−0.0159534	−	0.176055i
$97$	−2.70799	−	9.22258i	−0.274955	−	0.936411i	−0.974980	−	0.222293i	$-0.928646\pi$
$97$	−2.70799	−	9.22258i	−0.274955	−	0.936411i	0.700025	−	0.714118i	$-0.253172\pi$
$98$	−12.2072	+	5.57485i	−1.23311	+	0.563145i
$99$	15.4536	−	2.82387i	1.55314	−	0.283810i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	1.18797	−	4.04586i	0.118207	−	0.402578i	−0.879038	−	0.476752i	$-0.841814\pi$
$101$	1.18797	−	4.04586i	0.118207	−	0.402578i	0.997245	+	0.0741744i	$0.0236321\pi$
$102$	1.18992	−	6.01732i	0.117820	−	0.595804i
$103$	−3.45302	+	5.37300i	−0.340236	+	0.529417i	−0.968640	−	0.248470i	$-0.920072\pi$
$103$	−3.45302	+	5.37300i	−0.340236	+	0.529417i	0.628404	+	0.777887i	$0.283709\pi$
$104$	−1.09704	+	1.70703i	−0.107574	+	0.167388i
$105$	−1.51835	+	7.67818i	−0.148176	+	0.749314i
$106$	−1.96334	+	6.68652i	−0.190696	+	0.649452i
$107$	−1.08238	−	7.52814i	−0.104638	−	0.727773i	−0.972826	−	0.231538i	$-0.925624\pi$
$107$	−1.08238	−	7.52814i	−0.104638	−	0.727773i	0.868188	−	0.496235i	$-0.165285\pi$
$108$	−3.34549	−	3.97589i	−0.321920	−	0.382580i
$109$	6.22437	−	2.84257i	0.596186	−	0.272269i	−0.0943823	−	0.995536i	$-0.530088\pi$
$109$	6.22437	−	2.84257i	0.596186	−	0.272269i	0.690569	+	0.723267i	$0.257360\pi$
$110$	1.47529	+	5.02437i	0.140663	+	0.479055i
$111$	0.649336	+	7.16579i	0.0616322	+	0.680146i
$112$	4.47285	+	0.643098i	0.422644	+	0.0607671i
$113$	6.57088	−	4.22285i	0.618136	−	0.397252i	−0.193764	−	0.981048i	$-0.562070\pi$
$113$	6.57088	−	4.22285i	0.618136	−	0.397252i	0.811900	+	0.583796i	$0.198433\pi$
$114$	0.143052	+	0.250561i	0.0133981	+	0.0234672i
$115$	4.01092	+	2.62917i	0.374020	+	0.245171i
$116$		−	9.63011i		−	0.894133i
$117$	0.230895	+	6.08306i	0.0213463	+	0.562379i
$118$	−1.56237	+	10.8665i	−0.143828	+	1.00034i
$119$	14.5568	+	6.64786i	1.33442	+	0.609408i
$120$	1.20129	−	1.24776i	0.109663	−	0.113904i
$121$	6.82144	+	14.9369i	0.620131	+	1.35790i
$122$	−1.32279	−	1.52659i	−0.119760	−	0.138211i
$123$	11.3272	+	14.5478i	1.02134	+	1.31173i
$124$	0.976278	+	0.286661i	0.0876724	+	0.0257429i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	12.1090	−	6.09526i	1.07875	−	0.543009i
$127$	10.3964	+	6.68134i	0.922528	+	0.592873i	0.913390	−	0.407086i	$-0.133455\pi$
$127$	10.3964	+	6.68134i	0.922528	+	0.592873i	0.00913780	+	0.999958i	$0.497091\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−13.2637	+	3.14999i	−1.16781	+	0.277341i
$130$	−2.00849	+	0.288778i	−0.176157	+	0.0253275i
$131$	2.53738	−	2.19865i	0.221692	−	0.192097i	−0.536933	−	0.843625i	$-0.680417\pi$
$131$	2.53738	−	2.19865i	0.221692	−	0.192097i	0.758625	+	0.651528i	$0.225872\pi$
$132$	5.29666	−	7.36259i	0.461015	−	0.640831i
$133$	−0.722249	+	0.212071i	−0.0626269	+	0.0183889i
$134$	−1.92380	+	4.21254i	−0.166191	+	0.363908i
$135$	0.813943	−	5.13201i	0.0700531	−	0.441693i
$136$	−1.91461	−	2.97920i	−0.164177	−	0.255464i
$137$	−11.5005			−0.982552			−0.491276	−	0.871004i	$-0.663469\pi$
$137$	−11.5005			−0.982552			−0.491276	+	0.871004i	$0.663469\pi$
$138$	−0.674870	−	8.27916i	−0.0574487	−	0.704769i
$139$	4.00978			0.340105			0.170052	−	0.985435i	$-0.445606\pi$
$139$	4.00978			0.340105			0.170052	+	0.985435i	$0.445606\pi$
$140$	2.44307	+	3.80149i	0.206477	+	0.321285i
$141$	0.635348	+	1.60951i	0.0535060	+	0.135545i
$142$	6.46830	−	14.1636i	0.542807	−	1.18858i
$143$	−10.1952	+	2.99358i	−0.852565	+	0.250336i
$144$	−2.98352	−	0.314006i	−0.248627	−	0.0261672i
$145$	7.27795	−	6.30638i	0.604401	−	0.523716i
$146$	8.13237	−	1.16926i	0.673040	−	0.0967685i
$147$	5.37081	+	22.6150i	0.442977	+	1.86526i
$148$	3.13947	+	2.72037i	0.258063	+	0.223613i
$149$	−13.3957	−	8.60889i	−1.09742	−	0.705268i	−0.138902	−	0.990306i	$-0.544357\pi$
$149$	−13.3957	−	8.60889i	−1.09742	−	0.705268i	−0.958516	+	0.285038i	$0.907994\pi$
$150$	1.72967	+	0.0907705i	0.141227	+	0.00741138i
$151$	2.99352	−	3.45471i	0.243609	−	0.281140i	−0.620757	−	0.784003i	$-0.713175\pi$
$151$	2.99352	−	3.45471i	0.243609	−	0.281140i	0.864366	+	0.502863i	$0.167720\pi$
$152$	0.159830	+	0.0469305i	0.0129640	+	0.00380656i
$153$	−9.82450	−	4.04369i	−0.794264	−	0.326913i
$154$	15.4959	+	17.8832i	1.24869	+	1.44107i
$155$	0.422682	+	0.925545i	0.0339507	+	0.0743416i
$156$	2.53188	+	2.43760i	0.202713	+	0.195164i
$157$	−11.1266	−	5.08133i	−0.887996	−	0.405534i	−0.0814309	−	0.996679i	$-0.525949\pi$
$157$	−11.1266	−	5.08133i	−0.887996	−	0.405534i	−0.806566	+	0.591145i	$0.798676\pi$
$158$	−2.42081	+	16.8371i	−0.192589	+	1.33949i
$159$	10.7017	+	5.58270i	0.848699	+	0.442737i
$160$		−	1.00000i		−	0.0790569i
$161$	21.4223	+	3.27787i	1.68831	+	0.258332i
$162$	−7.87972	+	4.34857i	−0.619089	+	0.341656i
$163$	20.6122	−	13.2467i	1.61447	−	1.03756i	0.655052	−	0.755584i	$-0.272647\pi$
$163$	20.6122	−	13.2467i	1.61447	−	1.03756i	0.959422	−	0.281975i	$-0.0909895\pi$
$164$	10.5366	+	1.51494i	0.822772	+	0.118297i
$165$	9.03285	−	0.818522i	0.703206	−	0.0637218i
$166$	−2.05244	−	6.98998i	−0.159301	−	0.542528i
$167$	−16.5650	+	7.56496i	−1.28184	+	0.585394i	−0.935702	−	0.352791i	$-0.885233\pi$
$167$	−16.5650	+	7.56496i	−1.28184	+	0.585394i	−0.346133	+	0.938185i	$0.612505\pi$
$168$	2.59562	−	7.38394i	0.200256	−	0.569684i
$169$	1.26412	+	8.79215i	0.0972400	+	0.676319i
$170$	0.997722	−	3.39793i	0.0765218	−	0.260609i
$171$	0.473806	−	0.158877i	0.0362329	−	0.0121496i
$172$	−4.25529	+	6.62136i	−0.324463	+	0.504874i
$173$	−1.91245	+	2.97584i	−0.145401	+	0.226249i	−0.906313	−	0.422606i	$-0.861115\pi$
$173$	−1.91245	+	2.97584i	−0.145401	+	0.226249i	0.760912	+	0.648855i	$0.224752\pi$
$174$	−16.3630	−	3.23576i	−1.24047	−	0.245302i
$175$	−1.27311	+	4.33580i	−0.0962377	+	0.327756i
$176$	−0.745230	−	5.18319i	−0.0561738	−	0.390697i
$177$	17.9388	+	6.30588i	1.34836	+	0.473979i
$178$	6.58824	−	3.00875i	0.493809	−	0.225515i
$179$	−1.05340	−	3.58756i	−0.0787350	−	0.268147i	0.910712	−	0.413042i	$-0.135534\pi$
$179$	−1.05340	−	3.58756i	−0.0787350	−	0.268147i	−0.989447	+	0.144895i	$0.953716\pi$
$180$	−1.71648	−	2.46043i	−0.127939	−	0.183389i
$181$	−5.97449	−	0.859001i	−0.444080	−	0.0638491i	−0.0833521	−	0.996520i	$-0.526563\pi$
$181$	−5.97449	−	0.859001i	−0.444080	−	0.0638491i	−0.360728	+	0.932671i	$0.617472\pi$
$182$	−7.71379	+	4.95735i	−0.571784	+	0.367463i
$183$	−3.03836	+	1.73468i	−0.224602	+	0.128231i
$184$	−3.59593	−	3.17322i	−0.265095	−	0.233933i
$185$			4.15412i			0.305417i
$186$	0.815113	−	1.56252i	0.0597670	−	0.114570i
$187$	2.63914	−	18.3556i	0.192993	−	1.34230i
$188$	0.908752	+	0.415013i	0.0662776	+	0.0302680i
$189$	−6.28808	−	22.6230i	−0.457391	−	1.64558i
$190$	0.0691990	+	0.151525i	0.00502023	+	0.0109928i
$191$	1.09829	+	1.26749i	0.0794692	+	0.0917123i	0.794092	−	0.607798i	$-0.207947\pi$
$191$	1.09829	+	1.26749i	0.0794692	+	0.0917123i	−0.714623	+	0.699510i	$0.753402\pi$
$192$	−1.36664	+	1.06409i	−0.0986287	+	0.0767943i
$193$	10.3101	+	3.02731i	0.742135	+	0.217910i	0.630879	−	0.775881i	$-0.282694\pi$
$193$	10.3101	+	3.02731i	0.742135	+	0.217910i	0.111256	+	0.993792i	$0.464513\pi$
$194$	−6.29448	+	7.26421i	−0.451917	+	0.521540i
$195$	−0.184187	+	3.50976i	−0.0131899	+	0.251339i
$196$	11.2896	+	7.25537i	0.806398	+	0.518241i
$197$	16.1051	+	13.9552i	1.14744	+	0.994263i	0.999987	+	0.00519446i	$0.00165345\pi$
$197$	16.1051	+	13.9552i	1.14744	+	0.994263i	0.147455	+	0.989069i	$0.452892\pi$
$198$	−10.7304	−	11.4737i	−0.762578	−	0.815398i
$199$	−17.9901	+	2.58658i	−1.27528	+	0.183358i	−0.746492	−	0.665395i	$-0.768263\pi$
$199$	−17.9901	+	2.58658i	−1.27528	+	0.183358i	−0.528790	+	0.848753i	$0.677354\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	6.51132	+	4.68426i	0.459273	+	0.330402i
$202$	−4.04586	+	1.18797i	−0.284665	+	0.0835853i
$203$	18.0776	−	39.5844i	1.26880	−	2.77828i
$204$	−5.70541	+	2.25219i	−0.399459	+	0.157685i
$205$	5.75510	+	8.95512i	0.401954	+	0.625452i
$206$	6.38690			0.444996
$207$	−14.2943	−	1.63513i	−0.993521	−	0.113650i
$208$	2.02915			0.140696
$209$	0.471592	+	0.733812i	0.0326207	+	0.0507588i
$210$	7.28018	−	2.87382i	0.502380	−	0.198312i
$211$	−8.84927	+	19.3772i	−0.609209	+	1.33398i	0.313905	+	0.949454i	$0.398363\pi$
$211$	−8.84927	+	19.3772i	−0.609209	+	1.33398i	−0.923114	+	0.384527i	$0.874365\pi$
$212$	6.68652	−	1.96334i	0.459232	−	0.134843i
$213$	−21.8927	−	15.7496i	−1.50006	−	1.07915i
$214$	−5.74790	+	4.98058i	−0.392918	+	0.340465i
$215$	−7.79071	+	1.12013i	−0.531322	+	0.0763925i
$216$	−1.53602	+	4.96393i	−0.104513	+	0.337753i
$217$	3.47486	+	3.01098i	0.235889	+	0.204399i
$218$	−5.75647	−	3.69946i	−0.389878	−	0.250559i
$219$	0.745770	−	14.2110i	0.0503945	−	0.960288i
$220$	3.42917	−	3.95747i	0.231195	−	0.266813i
$221$	6.89490	+	2.02453i	0.463801	+	0.136184i
$222$	5.67719	−	4.42037i	0.381028	−	0.296676i
$223$	−13.8689	−	16.0056i	−0.928732	−	1.07181i	−0.997246	−	0.0741633i	$-0.976371\pi$
$223$	−13.8689	−	16.0056i	−0.928732	−	1.07181i	0.0685145	−	0.997650i	$-0.478174\pi$
$224$	−1.87720	−	4.11048i	−0.125425	−	0.274643i
$225$	0.735409	−	2.90847i	0.0490273	−	0.193898i
$226$	−7.10497	−	3.24473i	−0.472616	−	0.215836i
$227$	−1.43316	+	9.96784i	−0.0951221	+	0.661589i	0.885349	+	0.464927i	$0.153919\pi$
$227$	−1.43316	+	9.96784i	−0.0951221	+	0.661589i	−0.980471	+	0.196662i	$0.936990\pi$
$228$	0.133446	−	0.255807i	0.00883765	−	0.0169412i
$229$		−	6.90084i		−	0.456020i	−0.973659	−	0.228010i	$-0.926778\pi$
$229$		−	6.90084i		−	0.456020i	0.973659	−	0.228010i	$-0.0732220\pi$
$230$	0.0433291	−	4.79564i	0.00285703	−	0.316215i
$231$	35.5929	−	20.3209i	2.34184	−	1.33702i
$232$	−8.10136	+	5.20643i	−0.531880	+	0.341819i
$233$	−13.6671	−	1.96504i	−0.895363	−	0.128734i	−0.320755	−	0.947162i	$-0.603936\pi$
$233$	−13.6671	−	1.96504i	−0.895363	−	0.128734i	−0.574608	+	0.818429i	$0.694846\pi$
$234$	4.99257	−	3.48299i	0.326374	−	0.227690i
$235$	0.281460	+	0.958565i	0.0183604	+	0.0625299i
$236$	9.98616	−	4.56053i	0.650044	−	0.296865i
$237$	27.7953	+	9.77065i	1.80550	+	0.634672i
$238$	−2.27746	−	15.8401i	−0.147626	−	1.02676i
$239$	0.128907	−	0.439018i	0.00833831	−	0.0283977i	−0.955219	−	0.295901i	$-0.904380\pi$
$239$	0.128907	−	0.439018i	0.00833831	−	0.0283977i	0.963557	+	0.267503i	$0.0861985\pi$
$240$	−1.69915	−	0.336004i	−0.109679	−	0.0216890i
$241$	−3.01399	+	4.68986i	−0.194148	+	0.302100i	−0.924656	−	0.380804i	$-0.875647\pi$
$241$	−3.01399	+	4.68986i	−0.194148	+	0.302100i	0.730508	+	0.682905i	$0.239284\pi$
$242$	8.87775	−	13.8140i	0.570683	−	0.888000i
$243$	4.74124	+	14.8499i	0.304151	+	0.952624i
$244$	−0.569089	+	1.93814i	−0.0364322	+	0.124077i
$245$	1.90986	+	13.2834i	0.122016	+	0.848642i
$246$	6.11445	−	17.3942i	0.389843	−	1.10902i
$247$	−0.307466	+	0.140415i	−0.0195636	+	0.00893440i
$248$	−0.286661	−	0.976278i	−0.0182030	−	0.0619937i
$249$	−12.5666	+	1.13874i	−0.796378	+	0.0721647i
$250$	0.989821	+	0.142315i	0.0626018	+	0.00900078i
$251$	−14.2389	+	9.15081i	−0.898754	+	0.577594i	−0.906420	−	0.422377i	$-0.861196\pi$
$251$	−14.2389	+	9.15081i	−0.898754	+	0.577594i	0.00766679	+	0.999971i	$0.497560\pi$
$252$	−11.6743	−	6.89137i	−0.735410	−	0.434116i
$253$	−3.34927	−	24.8890i	−0.210567	−	1.56476i
$254$		−	12.3582i		−	0.775421i
$255$	−5.43834	−	2.83700i	−0.340562	−	0.177660i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−19.2858	−	8.80751i	−1.20301	−	0.549398i	−0.289881	−	0.957063i	$-0.593616\pi$
$257$	−19.2858	−	8.80751i	−1.20301	−	0.549398i	−0.913132	+	0.407665i	$0.866343\pi$
$258$	9.82086	+	9.45516i	0.611420	+	0.588653i
$259$	7.79809	+	17.0754i	0.484550	+	1.06102i
$260$	1.32881	+	1.53353i	0.0824093	+	0.0951054i
$261$	−10.9961	+	26.7159i	−0.680639	+	1.65367i
$262$	−3.22144	−	0.945899i	−0.199021	−	0.0584378i
$263$	−11.9092	+	13.7439i	−0.734353	+	0.847488i	−0.992955	−	0.118496i	$-0.962193\pi$
$263$	−11.9092	+	13.7439i	−0.734353	+	0.847488i	0.258602	+	0.965984i	$0.416738\pi$
$264$	−9.05740	−	0.475318i	−0.557444	−	0.0292538i
$265$	5.86253	+	3.76762i	0.360132	+	0.231443i
$266$	0.568883	+	0.492940i	0.0348805	+	0.0302241i
$267$	−2.89863	−	12.2053i	−0.177393	−	0.746954i
$268$	4.58390	−	0.659066i	0.280006	−	0.0402588i
$269$	−8.31349	+	7.20368i	−0.506882	+	0.439216i	−0.870381	−	0.492379i	$-0.836128\pi$
$269$	−8.31349	+	7.20368i	−0.506882	+	0.439216i	0.363499	+	0.931595i	$0.381582\pi$
$270$	−4.75737	+	2.08984i	−0.289524	+	0.127184i
$271$	−23.2588	+	6.82941i	−1.41287	+	0.414857i	−0.897085	−	0.441858i	$-0.854319\pi$
$271$	−23.2588	+	6.82941i	−1.41287	+	0.414857i	−0.515789	+	0.856715i	$0.672501\pi$
$272$	−1.47114	+	3.22135i	−0.0892011	+	0.195323i
$273$	5.83140	+	14.7726i	0.352933	+	0.894076i
$274$	6.21763	+	9.67481i	0.375620	+	0.584477i
$275$	5.23649			0.315772
$276$	−6.60001	+	5.04379i	−0.397274	+	0.303601i
$277$	14.9499			0.898252			0.449126	−	0.893468i	$-0.351735\pi$
$277$	14.9499			0.898252			0.449126	+	0.893468i	$0.351735\pi$
$278$	−2.16785	−	3.37324i	−0.130019	−	0.202313i
$279$	−2.38107	−	1.91001i	−0.142551	−	0.114349i
$280$	1.87720	−	4.11048i	0.112184	−	0.245648i
$281$	−4.15636	+	1.22042i	−0.247947	+	0.0728039i	−0.403345	−	0.915048i	$-0.632152\pi$
$281$	−4.15636	+	1.22042i	−0.247947	+	0.0728039i	0.155397	+	0.987852i	$0.450334\pi$
$282$	1.01051	−	1.40466i	0.0601752	−	0.0836461i
$283$	−13.2618	+	11.4914i	−0.788332	+	0.683094i	−0.952904	−	0.303271i	$-0.901921\pi$
$283$	−13.2618	+	11.4914i	−0.788332	+	0.683094i	0.164572	+	0.986365i	$0.447376\pi$
$284$	−15.4122	+	2.21594i	−0.914546	+	0.131492i
$285$	0.280714	−	0.0666664i	0.0166281	−	0.00394897i
$286$	8.03030	+	6.95829i	0.474841	+	0.411452i
$287$	40.4668	+	26.0064i	2.38868	+	1.53511i
$288$	1.34885	+	2.67966i	0.0794820	+	0.157901i
$289$	2.91978	−	3.36961i	0.171752	−	0.198212i
$290$	−9.24002	−	2.71311i	−0.542593	−	0.159320i
$291$	10.2280	+	13.1360i	0.599576	+	0.770049i
$292$	−5.38033	−	6.20924i	−0.314860	−	0.363368i
$293$	−1.36656	−	2.99235i	−0.0798354	−	0.174815i	0.865505	−	0.500900i	$-0.166998\pi$
$293$	−1.36656	−	2.99235i	−0.0798354	−	0.174815i	−0.945340	+	0.326085i	$0.894270\pi$
$294$	16.1213	−	16.7448i	0.940213	−	0.976578i
$295$	9.98616	+	4.56053i	0.581417	+	0.265524i
$296$	0.591193	−	4.11184i	0.0343624	−	0.238996i
$297$	−23.1009	+	14.3774i	−1.34045	+	0.834259i
$298$			15.9235i			0.922424i
$299$	9.73105	+	0.0879211i	0.562761	+	0.00508461i
$300$	−0.858770	−	1.50417i	−0.0495811	−	0.0868431i
$301$	−29.9209	+	19.2290i	−1.72461	+	1.10834i
$302$	−4.52470	−	0.650554i	−0.260367	−	0.0374352i
$303$	0.659111	+	7.27367i	0.0378650	+	0.417861i
$304$	−0.0469305	−	0.159830i	−0.00269165	−	0.00916691i
$305$	−1.83742	+	0.839123i	−0.105211	+	0.0480480i
$306$	1.90975	+	10.4511i	0.109173	+	0.597449i
$307$	2.27369	+	15.8139i	0.129766	+	0.902545i	0.945848	+	0.324609i	$0.105233\pi$
$307$	2.27369	+	15.8139i	0.129766	+	0.902545i	−0.816082	+	0.577936i	$0.803858\pi$
$308$	6.66660	−	22.7043i	0.379865	−	1.29370i
$309$	2.14602	−	10.8523i	0.122083	−	0.617364i
$310$	0.550099	−	0.855970i	0.0312435	−	0.0486159i
$311$	9.58486	−	14.9143i	0.543508	−	0.845715i	−0.455501	−	0.890235i	$-0.650540\pi$
$311$	9.58486	−	14.9143i	0.543508	−	0.845715i	0.999008	+	0.0445208i	$0.0141761\pi$
$312$	0.681803	−	3.44782i	0.0385995	−	0.195194i
$313$	4.73574	−	16.1285i	0.267680	−	0.911634i	−0.710469	−	0.703729i	$-0.751517\pi$
$313$	4.73574	−	16.1285i	0.267680	−	0.911634i	0.978149	−	0.207906i	$-0.0666647\pi$
$314$	1.74079	+	12.1074i	0.0982383	+	0.683262i
$315$	−2.43687	−	13.3357i	−0.137302	−	0.751382i
$316$	15.4731	−	7.06631i	0.870427	−	0.397511i
$317$	1.94950	+	6.63938i	0.109495	+	0.372905i	0.995950	−	0.0899096i	$-0.0286578\pi$
$317$	1.94950	+	6.63938i	0.109495	+	0.372905i	−0.886455	+	0.462814i	$0.846840\pi$
$318$	−1.08930	−	12.0211i	−0.0610850	−	0.674108i
$319$	−49.9146	−	7.17664i	−2.79468	−	0.401815i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	6.53142	+	11.4400i	0.364548	+	0.638520i
$322$	−8.82424	−	19.7937i	−0.491756	−	1.10306i
$323$		−	0.589916i		−	0.0328238i
$324$	7.91835	+	4.27783i	0.439908	+	0.237657i
$325$	−0.288778	+	2.00849i	−0.0160185	+	0.111411i
$326$	−22.2876	−	10.1784i	−1.23440	−	0.563730i
$327$	−8.22013	+	8.53806i	−0.454574	+	0.472156i
$328$	−4.42208	−	9.68300i	−0.244168	−	0.534654i
$329$	2.95635	+	3.41181i	0.162989	+	0.188099i
$330$	−5.57211	−	7.15639i	−0.306735	−	0.393946i
$331$	−16.2350	−	4.76702i	−0.892355	−	0.262019i	−0.196759	−	0.980452i	$-0.563042\pi$
$331$	−16.2350	−	4.76702i	−0.892355	−	0.262019i	−0.695596	+	0.718433i	$0.744860\pi$
$332$	−4.77071	+	5.50569i	−0.261827	+	0.302164i
$333$	−5.60330	−	11.1316i	−0.307059	−	0.610010i
$334$	15.3197	+	9.84540i	0.838259	+	0.538716i
$335$	3.49991	+	3.03269i	0.191220	+	0.165693i
$336$	−7.61506	+	1.80849i	−0.415436	+	0.0986612i
$337$	−23.6628	+	3.40219i	−1.28899	+	0.185329i	−0.752509	−	0.658581i	$-0.771157\pi$
$337$	−23.6628	+	3.40219i	−1.28899	+	0.185329i	−0.536484	+	0.843911i	$0.680248\pi$
$338$	6.71299	−	5.81684i	0.365139	−	0.316394i
$339$	−7.90058	+	10.9821i	−0.429100	+	0.596468i
$340$	−3.39793	+	0.997722i	−0.184279	+	0.0541091i
$341$	2.21337	−	4.84660i	0.119861	−	0.262458i
$342$	−0.389815	−	0.312696i	−0.0210788	−	0.0169086i
$343$	15.6844	+	24.4054i	0.846877	+	1.31777i
$344$	7.87082			0.424366
$345$	−8.13393	−	1.68498i	−0.437916	−	0.0907161i
$346$	3.53738			0.190171
$347$	2.66157	+	4.14148i	0.142880	+	0.222326i	0.905317	−	0.424737i	$-0.139633\pi$
$347$	2.66157	+	4.14148i	0.142880	+	0.222326i	−0.762436	+	0.647063i	$0.775997\pi$
$348$	6.12440	+	15.5148i	0.328302	+	0.831680i
$349$	7.41376	−	16.2339i	0.396849	−	0.868979i	−0.600731	−	0.799451i	$-0.705124\pi$
$349$	7.41376	−	16.2339i	0.396849	−	0.868979i	0.997580	−	0.0695273i	$-0.0221491\pi$
$350$	4.33580	−	1.27311i	0.231758	−	0.0680503i
$351$	−4.24059	−	9.65341i	−0.226346	−	0.515261i
$352$	−3.95747	+	3.42917i	−0.210934	+	0.182775i
$353$	−8.56577	+	1.23157i	−0.455910	+	0.0655499i	−0.366444	−	0.930440i	$-0.619425\pi$
$353$	−8.56577	+	1.23157i	−0.455910	+	0.0655499i	−0.0894655	+	0.995990i	$0.528516\pi$
$354$	−4.39361	−	18.5003i	−0.233518	−	0.983280i
$355$	−11.7675	−	10.1966i	−0.624556	−	0.541181i
$356$	−6.09299	−	3.91573i	−0.322928	−	0.207533i
$357$	−27.6798	−	1.45259i	−1.46497	−	0.0768795i
$358$	−2.44853	+	2.82576i	−0.129409	+	0.149346i
$359$	−9.31231	−	2.73434i	−0.491485	−	0.144313i	0.0265931	−	0.999646i	$-0.491534\pi$
$359$	−9.31231	−	2.73434i	−0.491485	−	0.144313i	−0.518078	+	0.855333i	$0.673352\pi$
$360$	−1.14184	+	2.77420i	−0.0601803	+	0.146213i
$361$	−12.4242	−	14.3383i	−0.653904	−	0.754646i
$362$	2.50741	+	5.49047i	0.131787	+	0.288573i
$363$	−20.4891	−	19.7262i	−1.07540	−	1.03536i
$364$	8.34078	+	3.80911i	0.437176	+	0.199651i
$365$	1.16926	−	8.13237i	0.0612018	−	0.425668i
$366$	3.10197	+	1.61819i	0.162143	+	0.0845842i
$367$			36.4849i			1.90450i	0.305325	+	0.952248i	$0.401235\pi$
$367$			36.4849i			1.90450i	−0.305325	+	0.952248i	$0.598765\pi$
$368$	−0.725378	+	4.74066i	−0.0378130	+	0.247124i
$369$	−27.5009	−	16.2339i	−1.43164	−	0.845103i
$370$	3.49467	−	2.24589i	0.181679	−	0.116758i
$371$	31.1704	+	4.48163i	1.61829	+	0.232674i
$372$	−1.75516	+	0.159046i	−0.0910008	+	0.00824614i
$373$	−6.35699	−	21.6499i	−0.329152	−	1.12099i	−0.943339	−	0.331829i	$-0.892334\pi$
$373$	−6.35699	−	21.6499i	−0.329152	−	1.12099i	0.614187	−	0.789160i	$-0.289484\pi$
$374$	−16.8686	+	7.70362i	−0.872253	+	0.398344i
$375$	0.574398	−	1.63403i	0.0296618	−	0.0843811i
$376$	−0.142177	−	0.988864i	−0.00733223	−	0.0509968i
$377$	5.50531	−	18.7494i	0.283538	−	0.965641i
$378$	−15.6321	+	17.5208i	−0.804026	+	0.901171i
$379$	1.86759	−	2.90602i	0.0959314	−	0.149272i	−0.789970	−	0.613145i	$-0.789904\pi$
$379$	1.86759	−	2.90602i	0.0959314	−	0.149272i	0.885902	+	0.463873i	$0.153541\pi$
$380$	0.0900589	−	0.140134i	0.00461992	−	0.00718874i
$381$	−20.9984	−	4.15240i	−1.07578	−	0.212734i
$382$	0.472502	−	1.60919i	0.0241753	−	0.0823335i
$383$	1.74854	+	12.1614i	0.0893462	+	0.621417i	0.984464	+	0.175587i	$0.0561823\pi$
$383$	1.74854	+	12.1614i	0.0893462	+	0.621417i	−0.895118	+	0.445830i	$0.852909\pi$
$384$	1.63403	+	0.574398i	0.0833864	+	0.0293121i
$385$	21.5245	−	9.82991i	1.09699	−	0.500978i
$386$	−3.02731	−	10.3101i	−0.154086	−	0.524769i
$387$	19.3656	−	13.5101i	0.984407	−	0.686758i
$388$	9.51409	+	1.36792i	0.483005	+	0.0694456i
$389$	16.5965	−	10.6659i	0.841475	−	0.540783i	−0.0474303	−	0.998875i	$-0.515103\pi$
$389$	16.5965	−	10.6659i	0.841475	−	0.540783i	0.888905	+	0.458092i	$0.151467\pi$
$390$	3.05217	−	1.74257i	0.154553	−	0.0882385i
$391$	−7.19464	+	15.3847i	−0.363849	+	0.778037i
$392$		−	13.4199i		−	0.677810i
$393$	−2.68964	+	5.15587i	−0.135674	+	0.260079i
$394$	3.03274	−	21.0932i	0.152787	−	1.06266i
$395$	15.4731	+	7.06631i	0.778534	+	0.355544i
$396$	−3.85096	+	15.2301i	−0.193518	+	0.765343i
$397$	−3.47173	−	7.60202i	−0.174241	−	0.381534i	0.802283	−	0.596944i	$-0.203619\pi$
$397$	−3.47173	−	7.60202i	−0.174241	−	0.381534i	−0.976524	+	0.215410i	$0.930891\pi$
$398$	11.9021	+	13.7358i	0.596600	+	0.688513i
$399$	1.02872	−	0.800986i	0.0515007	−	0.0400995i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	4.98798	−	5.75643i	0.249088	−	0.287462i	−0.617412	−	0.786640i	$-0.711819\pi$
$401$	4.98798	−	5.75643i	0.249088	−	0.287462i	0.866500	+	0.499177i	$0.166364\pi$
$402$	0.420362	−	8.01017i	0.0209657	−	0.399511i
$403$	1.73689	+	1.11623i	0.0865207	+	0.0556035i
$404$	3.18674	+	2.76133i	0.158546	+	0.137381i
$405$	1.95245	+	8.78567i	0.0970180	+	0.436563i
$406$	−43.0740	+	6.19311i	−2.13773	+	0.307359i
$407$	16.4398	−	14.2452i	0.814891	−	0.706107i
$408$	4.97924	+	3.58208i	0.246509	+	0.177339i
$409$	−14.1597	+	4.15767i	−0.700153	+	0.205583i	−0.612387	−	0.790558i	$-0.709791\pi$
$409$	−14.1597	+	4.15767i	−0.700153	+	0.205583i	−0.0877653	+	0.996141i	$0.527973\pi$
$410$	4.42208	−	9.68300i	0.218391	−	0.478209i
$411$	18.5281	−	7.31388i	0.913923	−	0.360767i
$412$	−3.45302	−	5.37300i	−0.170118	−	0.264709i
$413$	49.6090			2.44110
$414$	6.35251	+	12.9091i	0.312209	+	0.634449i
$415$	−7.28508			−0.357610
$416$	−1.09704	−	1.70703i	−0.0537868	−	0.0836939i
$417$	−6.46003	+	2.55007i	−0.316349	+	0.124878i
$418$	0.362360	−	0.793457i	0.0177236	−	0.0388093i
$419$	−21.3666	+	6.27380i	−1.04383	+	0.306495i	−0.758321	−	0.651881i	$-0.773980\pi$
$419$	−21.3666	+	6.27380i	−1.04383	+	0.306495i	−0.285506	+	0.958377i	$0.592162\pi$
$420$	−6.35357	−	4.57077i	−0.310023	−	0.223031i
$421$	9.09573	−	7.88149i	0.443299	−	0.384120i	−0.404414	−	0.914576i	$-0.632525\pi$
$421$	9.09573	−	7.88149i	0.443299	−	0.384120i	0.847713	+	0.530456i	$0.177979\pi$
$422$	21.0854	−	3.03162i	1.02642	−	0.147577i
$423$	−2.04718	−	2.18898i	−0.0995374	−	0.106432i
$424$	−5.26667	−	4.56360i	−0.255772	−	0.221628i
$425$	−2.97920	−	1.91461i	−0.144512	−	0.0928724i
$426$	−1.41336	+	26.9322i	−0.0684775	+	1.30487i
$427$	−5.97750	+	6.89840i	−0.289272	+	0.333837i
$428$	7.29748	+	2.14273i	0.352737	+	0.103573i
$429$	14.5214	−	11.3066i	0.701099	−	0.545890i
$430$	5.15429	+	5.94837i	0.248562	+	0.286856i
$431$	1.35364	+	2.96406i	0.0652027	+	0.142774i	0.939428	−	0.342747i	$-0.111357\pi$
$431$	1.35364	+	2.96406i	0.0652027	+	0.142774i	−0.874225	+	0.485521i	$0.838630\pi$
$432$	5.00636	−	1.39152i	0.240869	−	0.0669497i
$433$	−9.47491	−	4.32705i	−0.455335	−	0.207945i	0.174526	−	0.984653i	$-0.444161\pi$
$433$	−9.47491	−	4.32705i	−0.455335	−	0.207945i	−0.629861	+	0.776708i	$0.716888\pi$
$434$	0.654349	−	4.55110i	0.0314097	−	0.218460i
$435$	−7.71467	+	14.7885i	−0.369890	+	0.709056i
$436$			6.84273i			0.327707i
$437$	−0.218136	−	0.768522i	−0.0104349	−	0.0367634i
$438$	−12.3582	+	7.05565i	−0.590499	+	0.337132i
$439$	20.3781	−	13.0962i	0.972594	−	0.625048i	0.0451383	−	0.998981i	$-0.485627\pi$
$439$	20.3781	−	13.0962i	0.972594	−	0.625048i	0.927456	+	0.373932i	$0.121991\pi$
$440$	−5.18319	−	0.745230i	−0.247099	−	0.0355274i
$441$	−23.0351	−	33.0188i	−1.09691	−	1.57232i
$442$	−2.02453	−	6.89490i	−0.0962968	−	0.327957i
$443$	24.7096	−	11.2845i	1.17399	−	0.536142i	0.269649	−	0.962959i	$-0.413092\pi$
$443$	24.7096	−	11.2845i	1.17399	−	0.536142i	0.904338	+	0.426817i	$0.140365\pi$
$444$	−6.78797	−	2.38612i	−0.322143	−	0.113240i
$445$	−1.03075	−	7.16903i	−0.0488623	−	0.339845i
$446$	−5.96665	+	20.3206i	−0.282529	+	0.962206i
$447$	27.0564	+	5.35037i	1.27972	+	0.253064i
$448$	−2.44307	+	3.80149i	−0.115424	+	0.179604i
$449$	−14.0622	+	21.8813i	−0.663638	+	1.03264i	0.332350	+	0.943156i	$0.392159\pi$
$449$	−14.0622	+	21.8813i	−0.663638	+	1.03264i	−0.995988	+	0.0894854i	$0.971478\pi$
$450$	−2.84435	+	0.953770i	−0.134084	+	0.0449611i
$451$	15.7044	−	53.4843i	0.739491	−	2.51848i
$452$	1.11160	+	7.73132i	0.0522851	+	0.363651i
$453$	−2.62571	+	7.46955i	−0.123366	+	0.350950i
$454$	9.16031	−	4.18337i	0.429915	−	0.196335i
$455$	2.58332	+	8.79798i	0.121108	+	0.412456i
$456$	−0.287344	+	0.0260380i	−0.0134561	+	0.00121934i
$457$	5.50225	+	0.791104i	0.257384	+	0.0370063i	0.269799	−	0.962917i	$-0.413043\pi$
$457$	5.50225	+	0.791104i	0.257384	+	0.0370063i	−0.0124146	+	0.999923i	$0.503952\pi$
$458$	−5.80536	+	3.73088i	−0.271267	+	0.174332i
$459$	18.3996	+	0.266657i	0.858820	+	0.0124465i
$460$	−4.05777	+	2.55627i	−0.189195	+	0.119187i
$461$		−	8.01026i		−	0.373075i	−0.982448	−	0.186538i	$-0.940273\pi$
$461$		−	8.01026i		−	0.373075i	0.982448	−	0.186538i	$-0.0597266\pi$
$462$	−36.3380	−	18.9563i	−1.69060	−	0.881927i
$463$	3.33236	−	23.1771i	0.154868	−	1.07713i	−0.753044	−	0.657970i	$-0.771415\pi$
$463$	3.33236	−	23.1771i	0.154868	−	1.07713i	0.907912	−	0.419161i	$-0.137676\pi$
$464$	8.75985	+	4.00049i	0.406666	+	0.185718i
$465$	−1.26958	−	1.22231i	−0.0588756	−	0.0566832i
$466$	5.73591	+	12.5599i	0.265711	+	0.581826i
$467$	−12.6247	−	14.5697i	−0.584204	−	0.674207i	0.384299	−	0.923209i	$-0.374443\pi$
$467$	−12.6247	−	14.5697i	−0.584204	−	0.674207i	−0.968503	+	0.249001i	$0.919898\pi$
$468$	−5.62927	−	2.31697i	−0.260213	−	0.107102i
$469$	20.0793	+	5.89580i	0.927174	+	0.272243i
$470$	0.654227	−	0.755019i	0.0301773	−	0.0348264i
$471$	21.1572	+	1.11030i	0.974874	+	0.0511599i
$472$	−9.23548	−	5.93529i	−0.425098	−	0.273194i
$473$	31.1486	+	26.9904i	1.43221	+	1.24102i
$474$	−6.80768	−	28.6653i	−0.312687	−	1.31664i
$475$	0.164883	−	0.0237065i	0.00756533	−	0.00108773i
$476$	−12.0942	+	10.4797i	−0.554337	+	0.480336i
$477$	−20.7916	−	2.18825i	−0.951981	−	0.100193i
$478$	−0.439018	+	0.128907i	−0.0200802	+	0.00589608i
$479$	2.02304	−	4.42984i	0.0924351	−	0.202405i	−0.857767	−	0.514038i	$-0.828149\pi$
$479$	2.02304	−	4.42984i	0.0924351	−	0.202405i	0.950202	+	0.311634i	$0.100876\pi$
$480$	0.635963	+	1.61107i	0.0290276	+	0.0735350i
$481$	4.55724	+	7.09120i	0.207792	+	0.323331i
$482$	5.57484			0.253927
$483$	−36.5974	+	8.34291i	−1.66524	+	0.379615i
$484$	−16.4208			−0.746399
$485$	5.19660	+	8.08607i	0.235966	+	0.367170i
$486$	9.92925	−	12.0171i	0.450400	−	0.545105i
$487$	−11.6295	+	25.4651i	−0.526985	+	1.15394i	0.439742	+	0.898124i	$0.355070\pi$
$487$	−11.6295	+	25.4651i	−0.526985	+	1.15394i	−0.966727	+	0.255812i	$0.917657\pi$
$488$	1.93814	−	0.569089i	0.0877355	−	0.0257615i
$489$	−24.7834	+	34.4499i	−1.12074	+	1.55788i
$490$	10.1421	−	8.78820i	0.458174	−	0.397010i
$491$	−37.0449	+	5.32625i	−1.67181	+	0.240370i	−0.912124	−	0.409915i	$-0.865558\pi$
$491$	−37.0449	+	5.32625i	−1.67181	+	0.240370i	−0.759690	+	0.650286i	$0.774649\pi$
$492$	−17.9387	+	4.26023i	−0.808738	+	0.192066i
$493$	25.7740	+	22.3333i	1.16080	+	1.00584i
$494$	0.284353	+	0.182743i	0.0127937	+	0.00822199i
$495$	−14.0320	+	7.06326i	−0.630692	+	0.317470i
$496$	−0.666317	+	0.768971i	−0.0299185	+	0.0345278i
$497$	−67.5114	−	19.8231i	−3.02830	−	0.889189i
$498$	7.75200	+	9.95608i	0.347376	+	0.446143i
$499$	19.0763	+	22.0152i	0.853972	+	0.985536i	0.999993	−	0.00374564i	$-0.00119228\pi$
$499$	19.0763	+	22.0152i	0.853972	+	0.985536i	−0.146021	+	0.989281i	$0.546647\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	21.8763	−	22.7224i	0.977361	−	1.01516i
$502$	15.3963	+	7.03125i	0.687170	+	0.313820i
$503$	−2.98705	+	20.7754i	−0.133186	+	0.926330i	0.808178	+	0.588938i	$0.200454\pi$
$503$	−2.98705	+	20.7754i	−0.133186	+	0.926330i	−0.941364	+	0.337392i	$0.890455\pi$
$504$	0.514196	+	13.5468i	0.0229041	+	0.603421i
$505$			4.21666i			0.187639i
$506$	−19.1272	+	16.2736i	−0.850307	+	0.723449i
$507$	−7.62807	−	13.3608i	−0.338775	−	0.593376i
$508$	−10.3964	+	6.68134i	−0.461264	+	0.296436i
$509$	39.6442	+	5.69997i	1.75720	+	0.252647i	0.944142	−	0.329539i	$-0.106893\pi$
$509$	39.6442	+	5.69997i	1.75720	+	0.252647i	0.813056	+	0.582186i	$0.197802\pi$
$510$	0.553557	+	6.10882i	0.0245119	+	0.270503i
$511$	−10.4598	−	35.6229i	−0.462716	−	1.57586i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−0.662296	+	0.557286i	−0.0292411	+	0.0246048i
$514$	3.01732	+	20.9859i	0.133088	+	0.925649i
$515$	1.79940	−	6.12818i	0.0792909	−	0.270040i
$516$	2.64463	−	13.3737i	0.116423	−	0.588743i
$517$	2.82832	−	4.40095i	0.124389	−	0.193554i
$518$	10.1488	−	15.7919i	0.445913	−	0.693854i
$519$	1.18858	−	6.01053i	0.0521727	−	0.263833i
$520$	0.571677	−	1.94695i	0.0250697	−	0.0853795i
$521$	1.82902	+	12.7211i	0.0801309	+	0.557322i	0.989852	+	0.142102i	$0.0453863\pi$
$521$	1.82902	+	12.7211i	0.0801309	+	0.557322i	−0.909721	+	0.415220i	$0.863705\pi$
$522$	28.4197	−	5.19321i	1.24390	−	0.227301i
$523$	−9.42136	+	4.30259i	−0.411967	+	0.188139i	−0.610608	−	0.791933i	$-0.709075\pi$
$523$	−9.42136	+	4.30259i	−0.411967	+	0.188139i	0.198640	+	0.980072i	$0.436347\pi$
$524$	0.945899	+	3.22144i	0.0413218	+	0.140729i
$525$	−0.706346	−	7.79493i	−0.0308275	−	0.340199i
$526$	18.0007	+	2.58812i	0.784870	+	0.112847i
$527$	−3.03132	+	1.94811i	−0.132046	+	0.0848609i
$528$	4.49693	+	7.87654i	0.195704	+	0.342783i
$529$	−3.68406	+	22.7030i	−0.160176	+	0.987088i
$530$		−	6.96880i		−	0.302705i
$531$	−32.9110	+	1.24921i	−1.42822	+	0.0542110i
$532$	0.107126	−	0.745078i	0.00464451	−	0.0323032i
$533$	19.6482	+	8.97305i	0.851060	+	0.388666i
$534$	−8.70067	+	9.03718i	−0.376515	+	0.391077i
$535$	3.15946	+	6.91826i	0.136595	+	0.299102i
$536$	−3.03269	−	3.49991i	−0.130992	−	0.151173i
$537$	3.97866	+	5.10989i	0.171692	+	0.220508i
$538$	10.5547	+	3.09915i	0.455047	+	0.133614i
$539$	46.0193	−	53.1091i	1.98219	−	2.28757i
$540$	4.33011	+	2.87230i	0.186338	+	0.123604i
$541$	−30.9418	−	19.8851i	−1.33029	−	0.854926i	−0.334134	−	0.942525i	$-0.608444\pi$
$541$	−30.9418	−	19.8851i	−1.33029	−	0.854926i	−0.996156	+	0.0876000i	$0.972080\pi$
$542$	18.3200	+	15.8743i	0.786909	+	0.681861i
$543$	10.1716	−	2.41564i	0.436506	−	0.103665i
$544$	3.50533	−	0.503991i	0.150290	−	0.0216084i
$545$	−5.17139	+	4.48104i	−0.221518	+	0.191947i
$546$	9.27477	−	12.8923i	0.396924	−	0.551741i
$547$	4.50388	−	1.32246i	0.192572	−	0.0565442i	−0.184024	−	0.982922i	$-0.558913\pi$
$547$	4.50388	−	1.32246i	0.192572	−	0.0565442i	0.376596	+	0.926377i	$0.377094\pi$
$548$	4.77747	−	10.4612i	0.204083	−	0.446880i
$549$	3.79182	−	4.72698i	0.161831	−	0.201743i
$550$	−2.83106	−	4.40521i	−0.120717	−	0.187839i
$551$	−1.60416			−0.0683397
$552$	7.81134	+	2.82541i	0.332473	+	0.120257i
$553$	76.8666			3.26870
$554$	−8.08252	−	12.5766i	−0.343393	−	0.534331i
$555$	−2.64187	−	6.69258i	−0.112141	−	0.284084i
$556$	−1.66572	+	3.64742i	−0.0706423	+	0.154685i
$557$	5.20496	−	1.52831i	0.220541	−	0.0647567i	−0.169595	−	0.985514i	$-0.554246\pi$
$557$	5.20496	−	1.52831i	0.220541	−	0.0647567i	0.390136	+	0.920757i	$0.372428\pi$
$558$	−0.319499	+	3.03572i	−0.0135255	+	0.128512i
$559$	−12.0701	+	10.4588i	−0.510512	+	0.442361i
$560$	−4.47285	+	0.643098i	−0.189012	+	0.0271759i
$561$	7.42166	+	31.2506i	0.313343	+	1.31940i
$562$	3.27377	+	2.83674i	0.138096	+	0.119661i
$563$	−32.1219	−	20.6435i	−1.35378	−	0.870019i	−0.355860	−	0.934539i	$-0.615812\pi$
$563$	−32.1219	−	20.6435i	−1.35378	−	0.870019i	−0.997916	+	0.0645202i	$0.979448\pi$
$564$	−1.72800	−	0.0906827i	−0.0727618	−	0.00381843i
$565$	−5.11500	+	5.90302i	−0.215190	+	0.248342i
$566$	16.8371	+	4.94381i	0.707715	+	0.207804i
$567$	24.5179	+	32.4482i	1.02966	+	1.36270i
$568$	10.1966	+	11.7675i	0.427841	+	0.493755i
$569$	−5.28456	−	11.5716i	−0.221540	−	0.485105i	0.765927	−	0.642927i	$-0.222280\pi$
$569$	−5.28456	−	11.5716i	−0.221540	−	0.485105i	−0.987468	+	0.157822i	$0.949553\pi$
$570$	−0.207849	−	0.200109i	−0.00870583	−	0.00838165i
$571$	27.5484	+	12.5809i	1.15287	+	0.526496i	0.897790	−	0.440425i	$-0.145172\pi$
$571$	27.5484	+	12.5809i	1.15287	+	0.526496i	0.255077	+	0.966921i	$0.417899\pi$
$572$	1.51218	−	10.5175i	0.0632275	−	0.439757i
$573$	−2.57549	−	1.34355i	−0.107593	−	0.0561274i
$574$		−	48.1029i		−	2.00778i
$575$	−4.58917	−	1.39266i	−0.191382	−	0.0580780i
$576$	1.52503	−	2.58346i	0.0635429	−	0.107644i
$577$	20.9014	−	13.4325i	0.870136	−	0.559203i	−0.0276583	−	0.999617i	$-0.508805\pi$
$577$	20.9014	−	13.4325i	0.870136	−	0.559203i	0.897794	+	0.440415i	$0.145169\pi$
$578$	−4.41325	−	0.634529i	−0.183567	−	0.0263929i
$579$	−18.5355	+	1.67962i	−0.770310	+	0.0698024i
$580$	2.71311	+	9.24002i	0.112656	+	0.383671i
$581$	−29.9452	+	13.6755i	−1.24234	+	0.567356i
$582$	5.52107	−	15.7062i	0.228856	−	0.651044i
$583$	−5.19336	−	36.1206i	−0.215087	−	1.49596i
$584$	−2.31471	+	7.88319i	−0.0957835	+	0.326209i
$585$	−1.93534	−	5.77161i	−0.0800164	−	0.238627i
$586$	−1.77851	+	2.76741i	−0.0734695	+	0.114321i
$587$	20.3555	−	31.6738i	0.840161	−	1.30732i	−0.109485	−	0.993989i	$-0.534920\pi$
$587$	20.3555	−	31.6738i	0.840161	−	1.30732i	0.949645	−	0.313327i	$-0.101444\pi$
$588$	−22.8025	−	4.50916i	−0.940358	−	0.185955i
$589$	0.0477515	−	0.162627i	0.00196756	−	0.00670091i
$590$	−1.56237	−	10.8665i	−0.0643216	−	0.447367i
$591$	−34.8214	−	12.2405i	−1.43236	−	0.503506i
$592$	−3.77872	+	1.72568i	−0.155304	+	0.0709252i
$593$	−3.43438	−	11.6964i	−0.141033	−	0.480314i	0.858435	−	0.512922i	$-0.171437\pi$
$593$	−3.43438	−	11.6964i	−0.141033	−	0.480314i	−0.999468	+	0.0326076i	$0.989619\pi$
$594$	24.5843	+	11.6607i	1.00871	+	0.478446i
$595$	−15.8401	−	2.27746i	−0.649379	−	0.0933666i
$596$	13.3957	−	8.60889i	0.548709	−	0.352634i
$597$	27.3383	−	15.6082i	1.11888	−	0.638801i
$598$	−5.18704	−	8.23382i	−0.212114	−	0.336706i
$599$			10.8054i			0.441498i	0.975331	+	0.220749i	$0.0708501\pi$
$599$			10.8054i			0.441498i	−0.975331	+	0.220749i	$0.929150\pi$
$600$	−0.801099	+	1.53566i	−0.0327047	+	0.0626929i
$601$	−1.82368	+	12.6840i	−0.0743894	+	0.517389i	0.918223	+	0.396063i	$0.129624\pi$
$601$	−1.82368	+	12.6840i	−0.0743894	+	0.517389i	−0.992613	+	0.121326i	$0.961285\pi$
$602$	32.3529	+	14.7751i	1.31861	+	0.602187i
$603$	−13.4692	−	3.40571i	−0.548509	−	0.138691i
$604$	1.89896	+	4.15814i	0.0772675	+	0.169192i
$605$	−10.7533	−	12.4100i	−0.437185	−	0.504538i
$606$	5.76266	−	4.48692i	0.234092	−	0.182269i
$607$	15.1685	+	4.45388i	0.615671	+	0.180777i	0.574675	−	0.818382i	$-0.305129\pi$
$607$	15.1685	+	4.45388i	0.615671	+	0.180777i	0.0409963	+	0.999159i	$0.486947\pi$
$608$	−0.109085	+	0.125891i	−0.00442400	+	0.00510557i
$609$	−3.95005	+	75.2700i	−0.160064	+	3.05009i
$610$	1.69930	+	1.09207i	0.0688027	+	0.0442168i
$611$	1.53204	+	1.32752i	0.0619799	+	0.0537059i
$612$	7.75952	−	7.25687i	0.313660	−	0.293342i
$613$	14.2001	−	2.04167i	0.573538	−	0.0824623i	0.150558	−	0.988601i	$-0.451893\pi$
$613$	14.2001	−	2.04167i	0.573538	−	0.0824623i	0.422980	+	0.906139i	$0.360984\pi$
$614$	12.0742	−	10.4624i	0.487276	−	0.422227i
$615$	−14.9670	−	10.7673i	−0.603528	−	0.434179i
$616$	−22.7043	+	6.66660i	−0.914784	+	0.268605i
$617$	−2.53588	+	5.55281i	−0.102091	+	0.223548i	−0.953784	−	0.300493i	$-0.902849\pi$
$617$	−2.53588	+	5.55281i	−0.102091	+	0.223548i	0.851693	+	0.524041i	$0.175576\pi$
$618$	−10.2897	+	4.06183i	−0.413914	+	0.163391i
$619$	−11.4982	−	17.8915i	−0.462151	−	0.719121i	0.529466	−	0.848331i	$-0.322392\pi$
$619$	−11.4982	−	17.8915i	−0.462151	−	0.719121i	−0.991617	+	0.129210i	$0.958756\pi$
$620$	−1.01749			−0.0408635
$621$	24.0690	−	6.45632i	0.965855	−	0.259083i
$622$	−17.7287			−0.710856
$623$	−17.6946	−	27.5333i	−0.708917	−	1.10310i
$624$	−3.26910	+	1.29046i	−0.130869	+	0.0516599i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−16.1285	+	4.73574i	−0.644623	+	0.189278i
$627$	−1.22645	−	0.882308i	−0.0489795	−	0.0352360i
$628$	9.24428	−	8.01022i	0.368887	−	0.319642i
$629$	−14.5616	+	2.09364i	−0.580608	+	0.0834788i
$630$	−9.90124	+	9.25985i	−0.394475	+	0.368921i
$631$	−5.56668	−	4.82356i	−0.221606	−	0.192023i	0.536981	−	0.843594i	$-0.319565\pi$
$631$	−5.56668	−	4.82356i	−0.221606	−	0.192023i	−0.758587	+	0.651571i	$0.774110\pi$
$632$	−14.3099	−	9.19643i	−0.569218	−	0.365814i
$633$	1.93361	−	36.8458i	0.0768543	−	1.46449i
$634$	4.53143	−	5.22954i	0.179966	−	0.207692i
$635$	−11.8576	−	3.48170i	−0.470554	−	0.138167i
$636$	−9.52384	+	7.41546i	−0.377645	+	0.294042i
$637$	17.8325	+	20.5799i	0.706551	+	0.815404i
$638$	20.9485	+	45.8708i	0.829360	+	1.81604i
$639$	45.2868	+	11.4508i	1.79152	+	0.452988i
$640$	0.909632	+	0.415415i	0.0359564	+	0.0164207i
$641$	−5.65358	+	39.3215i	−0.223303	+	1.55311i	0.502117	+	0.864800i	$0.332555\pi$
$641$	−5.65358	+	39.3215i	−0.223303	+	1.55311i	−0.725420	+	0.688306i	$0.758355\pi$
$642$	6.09280	−	11.6795i	0.240464	−	0.460954i
$643$			1.75134i			0.0690661i	0.999404	+	0.0345330i	$0.0109944\pi$
$643$			1.75134i			0.0690661i	−0.999404	+	0.0345330i	$0.989006\pi$
$644$	−11.8808	+	18.1247i	−0.468169	+	0.714214i
$645$	11.8390	−	6.75922i	0.466161	−	0.266144i
$646$	−0.496269	+	0.318933i	−0.0195254	+	0.0125482i
$647$	−0.484442	−	0.0696523i	−0.0190454	−	0.00273831i	0.132786	−	0.991145i	$-0.457608\pi$
$647$	−0.484442	−	0.0696523i	−0.0190454	−	0.00273831i	−0.151831	+	0.988406i	$0.548517\pi$
$648$	−0.682245	−	8.97410i	−0.0268011	−	0.352536i
$649$	−16.1961	−	55.1588i	−0.635752	−	2.16517i
$650$	1.84578	−	0.842939i	0.0723974	−	0.0330628i
$651$	−7.51312	−	2.64102i	−0.294462	−	0.103510i
$652$	3.48697	+	24.2524i	0.136560	+	0.949797i
$653$	−6.38104	+	21.7318i	−0.249709	+	0.850432i	0.735272	+	0.677772i	$0.237054\pi$
$653$	−6.38104	+	21.7318i	−0.249709	+	0.850432i	−0.984982	+	0.172660i	$0.944764\pi$
$654$	11.6268	+	2.29919i	0.454644	+	0.0899054i
$655$	−1.81517	+	2.82446i	−0.0709244	+	0.110361i
$656$	−5.75510	+	8.95512i	−0.224699	+	0.349639i
$657$	7.83617	+	23.3692i	0.305718	+	0.911718i
$658$	1.27187	−	4.33161i	0.0495828	−	0.168864i
$659$	3.91705	+	27.2437i	0.152587	+	1.06126i	0.911863	+	0.410495i	$0.134644\pi$
$659$	3.91705	+	27.2437i	0.152587	+	1.06126i	−0.759276	+	0.650768i	$0.774447\pi$
$660$	−3.00783	+	8.55660i	−0.117080	+	0.333065i
$661$	−13.3489	+	6.09622i	−0.519211	+	0.237116i	−0.657743	−	0.753242i	$-0.728489\pi$
$661$	−13.3489	+	6.09622i	−0.519211	+	0.237116i	0.138532	+	0.990358i	$0.455762\pi$
$662$	4.76702	+	16.2350i	0.185276	+	0.630991i
$663$	−12.3957	+	1.12325i	−0.481409	+	0.0436234i
$664$	7.21093	+	1.03677i	0.279838	+	0.0402347i
$665$	0.633245	−	0.406962i	0.0245562	−	0.0157813i
$666$	−6.33516	+	10.7320i	−0.245482	+	0.415857i
$667$	41.8357	+	19.5645i	1.61989	+	0.757539i
$668$		−	18.2106i		−	0.704590i
$669$	32.5228	+	16.9660i	1.25740	+	0.655944i
$670$	0.659066	−	4.58390i	0.0254619	−	0.177092i
$671$	9.62164	+	4.39406i	0.371439	+	0.169631i
$672$	5.63841	+	5.42846i	0.217507	+	0.209407i
$673$	0.204072	+	0.446856i	0.00786640	+	0.0172250i	0.913524	−	0.406784i	$-0.133350\pi$
$673$	0.204072	+	0.446856i	0.00786640	+	0.0172250i	−0.905658	+	0.424009i	$0.860623\pi$
$674$	15.6552	+	18.0670i	0.603014	+	0.695916i
$675$	0.664881	+	5.15344i	0.0255913	+	0.198356i
$676$	−8.52275	−	2.50251i	−0.327798	−	0.0962502i
$677$	3.61044	−	4.16667i	0.138760	−	0.160138i	−0.682116	−	0.731244i	$-0.738940\pi$
$677$	3.61044	−	4.16667i	0.138760	−	0.160138i	0.820876	+	0.571106i	$0.193486\pi$
$678$	13.5101	+	0.708992i	0.518854	+	0.0272287i
$679$	36.5397	+	23.4826i	1.40226	+	0.901181i
$680$	2.67640	+	2.31911i	0.102635	+	0.0889338i
$681$	−4.03026	−	16.9703i	−0.154440	−	0.650305i
$682$	−5.27386	+	0.758267i	−0.201947	+	0.0290355i
$683$	2.52124	−	2.18467i	0.0964725	−	0.0835939i	−0.605289	−	0.796006i	$-0.706943\pi$
$683$	2.52124	−	2.18467i	0.0964725	−	0.0835939i	0.701762	+	0.712412i	$0.252397\pi$
$684$	−0.0523065	+	0.496989i	−0.00199999	+	0.0190029i
$685$	11.0346	−	3.24006i	0.421611	−	0.123796i
$686$	12.0515	−	26.3891i	0.460128	−	1.00754i
$687$	4.38868	+	11.1177i	0.167439	+	0.424169i
$688$	−4.25529	−	6.62136i	−0.162231	−	0.252437i
$689$	14.1407			0.538719
$690$	2.98004	+	7.75367i	0.113448	+	0.295177i
$691$	16.5110			0.628109			0.314055	−	0.949405i	$-0.398313\pi$
$691$	16.5110			0.628109			0.314055	+	0.949405i	$0.398313\pi$
$692$	−1.91245	−	2.97584i	−0.0727006	−	0.113124i
$693$	−44.4193	+	55.3743i	−1.68735	+	2.10349i
$694$	2.04508	−	4.47810i	0.0776302	−	0.169986i
$695$	−3.84735	+	1.12968i	−0.145938	+	0.0428514i
$696$	9.74077	−	13.5401i	0.369223	−	0.513236i
$697$	−28.4901	+	24.6869i	−1.07914	+	0.935081i
$698$	−17.6650	+	2.53984i	−0.668629	+	0.0961343i
$699$	23.2684	−	5.52598i	0.880092	−	0.209012i
$700$	−3.41511	−	2.95921i	−0.129079	−	0.111848i
$701$	4.22145	+	2.71296i	0.159442	+	0.102467i	0.617929	−	0.786234i	$-0.287972\pi$
$701$	4.22145	+	2.71296i	0.159442	+	0.102467i	−0.458487	+	0.888701i	$0.651608\pi$
$702$	−5.82832	+	8.78644i	−0.219976	+	0.331623i
$703$	0.453154	−	0.522968i	0.0170910	−	0.0197241i
$704$	5.02437	+	1.47529i	0.189363	+	0.0556020i
$705$	−1.06306	−	1.36532i	−0.0400373	−	0.0514209i
$706$	5.66707	+	6.54015i	0.213283	+	0.246142i
$707$	7.91549	+	17.3325i	0.297693	+	0.651856i
$708$	−13.1881	+	13.6982i	−0.495639	+	0.514809i
$709$	14.7866	+	6.75281i	0.555322	+	0.253607i	0.673250	−	0.739415i	$-0.264898\pi$
$709$	14.7866	+	6.75281i	0.555322	+	0.253607i	−0.117928	+	0.993022i	$0.537625\pi$
$710$	−2.21594	+	15.4122i	−0.0831627	+	0.578410i
$711$	−50.9940	+	1.93558i	−1.91242	+	0.0725901i
$712$			7.24275i			0.271434i
$713$	−3.22873	+	3.65883i	−0.120917	+	0.137024i
$714$	13.7428	+	24.0711i	0.514313	+	0.900837i
$715$	8.93883	−	5.74464i	0.334293	−	0.214837i
$716$	3.70096	+	0.532117i	0.138311	+	0.0198862i
$717$	0.0715205	+	0.789269i	0.00267098	+	0.0294758i
$718$	2.73434	+	9.31231i	0.102045	+	0.347532i
$719$	−14.5982	+	6.66677i	−0.544420	+	0.248628i	−0.668588	−	0.743633i	$-0.733101\pi$
$719$	−14.5982	+	6.66677i	−0.544420	+	0.248628i	0.124168	+	0.992261i	$0.460374\pi$
$720$	2.95113	−	0.539268i	0.109982	−	0.0200973i
$721$	−4.10740	−	28.5676i	−0.152968	−	1.06391i
$722$	−5.34510	+	18.2037i	−0.198924	+	0.677473i
$723$	1.87317	−	9.47248i	0.0696640	−	0.352285i
$724$	3.26327	−	5.07774i	0.121278	−	0.188713i
$725$	−5.20643	+	8.10136i	−0.193362	+	0.300877i
$726$	−5.51746	+	27.9013i	−0.204772	+	1.03552i
$727$	8.79272	−	29.9452i	0.326104	−	1.11061i	−0.619421	−	0.785059i	$-0.712633\pi$
$727$	8.79272	−	29.9452i	0.326104	−	1.11061i	0.945525	−	0.325549i	$-0.105549\pi$
$728$	−1.30494	−	9.07607i	−0.0483644	−	0.336382i
$729$	−17.0825	−	20.9091i	−0.632685	−	0.774409i
$730$	−7.47353	+	3.41305i	−0.276608	+	0.126323i
$731$	−7.85289	−	26.7445i	−0.290450	−	0.989181i
$732$	−0.315743	−	3.48440i	−0.0116702	−	0.128787i
$733$	52.3202	+	7.52251i	1.93249	+	0.277850i	0.997121	−	0.0758232i	$-0.0241584\pi$
$733$	52.3202	+	7.52251i	1.93249	+	0.277850i	0.935369	+	0.353673i	$0.115068\pi$
$734$	30.6931	−	19.7252i	1.13290	−	0.728071i
$735$	−11.5246	−	20.1858i	−0.425093	−	0.744565i
$736$	4.38026	−	1.95277i	0.161459	−	0.0719799i
$737$		−	24.2504i		−	0.893274i
$738$	1.21128	+	31.9119i	0.0445880	+	1.17469i
$739$	−6.20118	+	43.1302i	−0.228114	+	1.58657i	0.477928	+	0.878399i	$0.341388\pi$
$739$	−6.20118	+	43.1302i	−0.228114	+	1.58657i	−0.706042	+	0.708170i	$0.749521\pi$
$740$	−3.77872	−	1.72568i	−0.138909	−	0.0634374i
$741$	0.406051	−	0.421756i	0.0149167	−	0.0154936i
$742$	−13.0818	−	28.6452i	−0.480248	−	1.05160i
$743$	−16.1840	−	18.6773i	−0.593734	−	0.685205i	0.376766	−	0.926309i	$-0.377036\pi$
$743$	−16.1840	−	18.6773i	−0.593734	−	0.685205i	−0.970499	+	0.241103i	$0.922491\pi$
$744$	1.08271	+	1.39055i	0.0396940	+	0.0509800i
$745$	15.2785	+	4.48617i	0.559760	+	0.164360i
$746$	−14.7762	+	17.0527i	−0.540996	+	0.624342i
$747$	19.5215	−	9.82651i	0.714256	−	0.359533i
$748$	15.6005	+	10.0259i	0.570412	+	0.366581i
$749$	25.9738	+	22.5065i	0.949064	+	0.822368i
$750$	−1.68518	+	0.400211i	−0.0615341	+	0.0146136i
$751$	11.9947	−	1.72457i	0.437692	−	0.0629305i	0.0800529	−	0.996791i	$-0.474491\pi$
$751$	11.9947	−	1.72457i	0.437692	−	0.0629305i	0.357639	+	0.933860i	$0.383582\pi$
$752$	−0.755019	+	0.654227i	−0.0275327	+	0.0238572i
$753$	17.1204	−	23.7980i	0.623901	−	0.867249i
$754$	−18.7494	+	5.50531i	−0.682812	+	0.200492i
$755$	−1.89896	+	4.15814i	−0.0691102	+	0.151330i
$756$	23.1907	+	3.67808i	0.843439	+	0.133770i
$757$	9.40225	+	14.6302i	0.341731	+	0.531743i	0.969000	−	0.247059i	$-0.0794641\pi$
$757$	9.40225	+	14.6302i	0.341731	+	0.531743i	−0.627270	+	0.778802i	$0.715828\pi$
$758$	−3.45439			−0.125469
$759$	21.2244	+	37.9679i	0.770396	+	1.37815i
$760$	−0.166578			−0.00604242
$761$	−6.15388	−	9.57562i	−0.223078	−	0.347116i	0.711617	−	0.702568i	$-0.247963\pi$
$761$	−6.15388	−	9.57562i	−0.223078	−	0.347116i	−0.934695	+	0.355452i	$0.884327\pi$
$762$	7.85935	+	19.9099i	0.284714	+	0.721260i
$763$	−12.8451	+	28.1269i	−0.465025	+	1.01826i
$764$	−1.60919	+	0.472502i	−0.0582186	+	0.0170945i
$765$	10.5658	+	1.11201i	0.382007	+	0.0402050i
$766$	9.28546	−	8.04589i	0.335497	−	0.290710i
$767$	22.0497	−	3.17027i	0.796170	−	0.114472i
$768$	−0.400211	−	1.68518i	−0.0144414	−	0.0608087i
$769$	−3.73526	−	3.23662i	−0.134697	−	0.116715i	0.584907	−	0.811100i	$-0.301131\pi$
$769$	−3.73526	−	3.23662i	−0.134697	−	0.116715i	−0.719604	+	0.694385i	$0.755677\pi$
$770$	−19.9065	−	12.7931i	−0.717379	−	0.461032i
$771$	36.6720	+	1.92449i	1.32071	+	0.0693088i
$772$	−7.03669	+	8.12078i	−0.253256	+	0.292273i
$773$	12.6512	+	3.71473i	0.455032	+	0.133610i	0.501214	−	0.865324i	$-0.332887\pi$
$773$	12.6512	+	3.71473i	0.455032	+	0.133610i	−0.0461814	+	0.998933i	$0.514705\pi$
$774$	−21.8352	−

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)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.61107 + 0.635963i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.40602 + 1.01149i) q^{6} +(-3.41511 + 2.95921i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.19110 - 2.04916i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(-1.61107 + 0.635963i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.40602 + 1.01149i) q^{6} +(-3.41511 + 2.95921i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.19110 - 2.04916i) q^{9} +(0.755750 + 0.654861i) q^{10} +(4.40521 + 2.83106i) q^{11} +(0.0907705 - 1.72967i) q^{12} +(-1.32881 + 1.53353i) q^{13} +(4.33580 + 1.27311i) q^{14} +(1.36664 - 1.06409i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.47114 - 3.22135i) q^{17} +(-2.90847 - 0.735409i) q^{18} +(0.151525 + 0.0691990i) q^{19} +(0.142315 - 0.989821i) q^{20} +(3.62004 - 6.93939i) q^{21} -5.23649i q^{22} +(-3.10773 - 3.65267i) q^{23} +(-1.50417 + 0.858770i) q^{24} +(0.841254 - 0.540641i) q^{25} +(2.00849 + 0.288778i) q^{26} +(-2.22683 + 4.69481i) q^{27} +(-1.27311 - 4.33580i) q^{28} +(-8.75985 + 4.00049i) q^{29} +(-1.63403 - 0.574398i) q^{30} +(-0.144804 - 1.00714i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(-8.89756 - 1.75948i) q^{33} +(-1.91461 + 2.97920i) q^{34} +(2.44307 - 3.80149i) q^{35} +(0.953770 + 2.84435i) q^{36} +(1.17035 - 3.98585i) q^{37} +(-0.0237065 - 0.164883i) q^{38} +(1.16554 - 3.31570i) q^{39} +(-0.909632 + 0.415415i) q^{40} +(-2.99903 - 10.2138i) q^{41} +(-7.79493 + 0.706346i) q^{42} +(7.79071 + 1.12013i) q^{43} +(-4.40521 + 2.83106i) q^{44} +(-1.52503 + 2.58346i) q^{45} +(-1.39266 + 4.58917i) q^{46} -0.999033i q^{47} +(1.53566 + 0.801099i) q^{48} +(1.90986 - 13.2834i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(4.41878 + 4.25423i) q^{51} +(-0.842939 - 1.84578i) q^{52} +(-4.56360 - 5.26667i) q^{53} +(5.15344 - 0.664881i) q^{54} +(-5.02437 - 1.47529i) q^{55} +(-2.95921 + 3.41511i) q^{56} +(-0.288125 - 0.0151204i) q^{57} +(8.10136 + 5.20643i) q^{58} +(-8.29680 - 7.18922i) q^{59} +(0.400211 + 1.68518i) q^{60} +(1.99940 - 0.287471i) q^{61} +(-0.768971 + 0.666317i) q^{62} +(-1.41894 + 13.4821i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.842939 - 1.84578i) q^{65} +(3.33021 + 8.43635i) q^{66} +(-2.50373 - 3.89588i) q^{67} +3.54138 q^{68} +(7.32974 + 3.90832i) q^{69} -4.51884 q^{70} +(8.41815 + 13.0989i) q^{71} +(1.87717 - 2.34013i) q^{72} +(-3.41305 + 7.47353i) q^{73} +(-3.98585 + 1.17035i) q^{74} +(-1.01149 + 1.40602i) q^{75} +(-0.125891 + 0.109085i) q^{76} +(-23.4220 + 3.36758i) q^{77} +(-3.41948 + 0.812087i) q^{78} +(-12.8555 - 11.1393i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.601847 - 8.97985i) q^{81} +(-6.97097 + 8.04493i) q^{82} +(6.98998 + 2.05244i) q^{83} +(4.80847 + 6.17563i) q^{84} +(2.31911 + 2.67640i) q^{85} +(-3.26966 - 7.15955i) q^{86} +(11.5686 - 12.0160i) q^{87} +(4.76328 + 2.17531i) q^{88} +(-1.03075 + 7.16903i) q^{89} +(2.99784 - 0.113789i) q^{90} -9.16940i q^{91} +(4.61359 - 1.30951i) q^{92} +(0.873793 + 1.53048i) q^{93} +(-0.840440 + 0.540118i) q^{94} +(-0.164883 - 0.0237065i) q^{95} +(-0.156311 - 1.72498i) q^{96} +(-2.70799 - 9.22258i) q^{97} +(-12.2072 + 5.57485i) q^{98} +(15.4536 - 2.82387i) 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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Groups

Properties

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