LMFDB - Embedded newform 690.2.n.a.89.10

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.10
Character	$\chi$	$=$	690.89
Dual form			690.2.n.a.659.10

$q$-expansion

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.479764 + 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.20932 - 0.344845i) q^{5} +(1.71562 + 0.238029i) q^{6} +(2.74772 - 1.76585i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.479764 + 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.20932 - 0.344845i) q^{5} +(1.71562 + 0.238029i) q^{6} +(2.74772 - 1.76585i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +(-0.655753 - 2.13775i) q^{10} +(0.103499 - 0.719848i) q^{11} +(-0.00855129 - 1.73203i) q^{12} +(0.797957 - 1.24165i) q^{13} +(-2.13892 - 2.46844i) q^{14} +(-0.486034 + 3.84237i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.487896 - 1.66162i) q^{17} +(-1.21924 + 2.74107i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(-2.02267 + 0.953313i) q^{20} +(1.62061 + 5.42016i) q^{21} -0.727250 q^{22} +(1.82495 + 4.43504i) q^{23} +(-1.71318 + 0.254958i) q^{24} +(4.76216 - 1.52374i) q^{25} +(-1.34257 - 0.613130i) q^{26} +(3.87616 - 3.46054i) q^{27} +(-2.13892 + 2.46844i) q^{28} +(-1.91557 + 6.52384i) q^{29} +(3.87243 - 0.0657391i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.14837 + 0.517608i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(5.46163 - 4.84886i) q^{35} +(2.88668 + 0.816734i) q^{36} +(7.28503 + 8.40738i) q^{37} +(-5.36407 + 2.44969i) q^{38} +(1.68361 + 1.92372i) q^{39} +(1.23147 + 1.86641i) q^{40} +(-0.240142 - 0.208084i) q^{41} +(5.13435 - 2.37549i) q^{42} +(3.85328 - 8.43752i) q^{43} +(0.103499 + 0.719848i) q^{44} +(-6.16159 - 2.65233i) q^{45} +(4.13018 - 2.43755i) q^{46} +0.296017 q^{47} +(0.496174 + 1.65946i) q^{48} +(1.52381 - 3.33668i) q^{49} +(-2.18596 - 4.49684i) q^{50} +(2.53133 + 1.60918i) q^{51} +(-0.415822 + 1.41616i) q^{52} +(-1.32976 - 2.06915i) q^{53} +(-3.97696 - 3.34422i) q^{54} +(-0.0195746 - 1.62606i) q^{55} +(2.74772 + 1.76585i) q^{56} +(10.2137 - 0.0504267i) q^{57} +(6.73005 + 0.967635i) q^{58} +(4.64023 - 7.22033i) q^{59} +(-0.616174 - 3.82365i) q^{60} +(4.22497 - 1.92948i) q^{61} +(-3.27893 + 2.10724i) q^{62} +(-9.79817 + 0.0967525i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.33477 - 3.01836i) q^{65} +(0.348909 - 1.21035i) q^{66} +(0.0578385 + 0.402276i) q^{67} +1.73177i q^{68} +(-8.25669 + 0.909463i) q^{69} +(-5.57677 - 4.71598i) q^{70} +(7.98308 - 1.14779i) q^{71} +(0.397603 - 2.97354i) q^{72} +(0.808166 + 2.75236i) q^{73} +(7.28503 - 8.40738i) q^{74} +(0.251217 + 8.65661i) q^{75} +(3.18814 + 4.96084i) q^{76} +(-0.986759 - 2.16070i) q^{77} +(1.66454 - 1.94025i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(1.67216 - 1.48455i) q^{80} +(3.89967 + 8.11126i) q^{81} +(-0.171790 + 0.267311i) q^{82} +(-11.9849 + 10.3850i) q^{83} +(-3.08200 - 4.74403i) q^{84} +(0.504916 - 3.83929i) q^{85} +(-8.90001 - 2.61328i) q^{86} +(-9.93847 - 6.31795i) q^{87} +(0.697792 - 0.204890i) q^{88} +(3.56233 - 7.80041i) q^{89} +(-1.74844 + 6.47634i) q^{90} -4.82076i q^{91} +(-3.00053 - 3.74124i) q^{92} +(6.67742 - 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(-5.62165 - 11.9276i) q^{95} +(1.57196 - 0.727290i) q^{96} +(-8.74637 + 10.0938i) q^{97} +(-3.51958 - 1.03344i) q^{98} +(-1.41239 + 1.66288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} + O(q^{10}) $	$ 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} - 9q^{12} + 11q^{15} - 24q^{16} - 6q^{18} - 4q^{23} + 2q^{24} - 12q^{25} + 2q^{27} + 22q^{30} + 28q^{31} - 24q^{32} - 36q^{35} - 6q^{36} - 4q^{46} + 104q^{47} - 9q^{48} + 70q^{49} + 54q^{50} - 9q^{54} - 26q^{55} - 44q^{57} - 11q^{60} + 44q^{61} + 28q^{62} - 121q^{63} - 24q^{64} + 44q^{65} + 44q^{66} - 102q^{69} - 36q^{70} + 16q^{72} - 82q^{75} + 8q^{77} - 44q^{79} + 74q^{81} - 11q^{84} + 22q^{85} - 93q^{87} - 4q^{92} + 172q^{93} + 16q^{94} + 26q^{95} + 2q^{96} + 4q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.479764	+	1.66428i	−0.276992	+	0.960872i
$3$	−0.479764	+	1.66428i	−0.276992	+	0.960872i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.20932	−	0.344845i	0.988037	−	0.154219i
$5$	2.20932	−	0.344845i	0.988037	−	0.154219i
$6$	1.71562	+	0.238029i	0.700398	+	0.0971750i
$7$	2.74772	−	1.76585i	1.03854	−	0.667429i	0.0939141	−	0.995580i	$-0.470062\pi$
$7$	2.74772	−	1.76585i	1.03854	−	0.667429i	0.944625	+	0.328152i	$0.106426\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−2.53965	−	1.59692i	−0.846551	−	0.532308i
$10$	−0.655753	−	2.13775i	−0.207367	−	0.676017i
$11$	0.103499	−	0.719848i	0.0312060	−	0.217042i	−0.968251	−	0.249978i	$-0.919577\pi$
$11$	0.103499	−	0.719848i	0.0312060	−	0.217042i	0.999457	+	0.0329357i	$0.0104857\pi$
$12$	−0.00855129	−	1.73203i	−0.00246855	−	0.499994i
$13$	0.797957	−	1.24165i	0.221313	−	0.344370i	−0.712787	−	0.701380i	$-0.752567\pi$
$13$	0.797957	−	1.24165i	0.221313	−	0.344370i	0.934101	+	0.357010i	$0.116204\pi$
$14$	−2.13892	−	2.46844i	−0.571650	−	0.659719i
$15$	−0.486034	+	3.84237i	−0.125493	+	0.992094i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.487896	−	1.66162i	0.118332	−	0.403002i	−0.878930	−	0.476951i	$-0.841742\pi$
$17$	0.487896	−	1.66162i	0.118332	−	0.403002i	0.997262	+	0.0739488i	$0.0235601\pi$
$18$	−1.21924	+	2.74107i	−0.287377	+	0.646076i
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	−0.897247	−	0.441530i	$-0.854436\pi$
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	0.516103	−	0.856527i	$-0.327382\pi$
$20$	−2.02267	+	0.953313i	−0.452283	+	0.213167i
$21$	1.62061	+	5.42016i	0.353647	+	1.18278i
$22$	−0.727250			−0.155050
$23$	1.82495	+	4.43504i	0.380529	+	0.924769i
$23$	1.82495	+	4.43504i	0.380529	+	0.924769i
$24$	−1.71318	+	0.254958i	−0.349702	+	0.0520430i
$25$	4.76216	−	1.52374i	0.952433	−	0.304748i
$26$	−1.34257	−	0.613130i	−0.263299	−	0.120245i
$27$	3.87616	−	3.46054i	0.745968	−	0.665982i
$28$	−2.13892	+	2.46844i	−0.404217	+	0.466492i
$29$	−1.91557	+	6.52384i	−0.355713	+	1.21145i	0.566271	+	0.824219i	$0.308385\pi$
$29$	−1.91557	+	6.52384i	−0.355713	+	1.21145i	−0.921984	+	0.387228i	$0.873433\pi$
$30$	3.87243	−	0.0657391i	0.707005	−	0.0120023i
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	0.706687	−	0.707527i	$-0.250189\pi$
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	−0.997494	+	0.0707465i	$0.977462\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.14837	+	0.517608i	0.199906	+	0.0901040i
$34$	−1.71414	−	0.246456i	−0.293973	−	0.0422669i
$35$	5.46163	−	4.84886i	0.923184	−	0.819607i
$36$	2.88668	+	0.816734i	0.481114	+	0.136122i
$37$	7.28503	+	8.40738i	1.19765	+	1.38216i	0.904707	+	0.426035i	$0.140090\pi$
$37$	7.28503	+	8.40738i	1.19765	+	1.38216i	0.292945	+	0.956129i	$0.405365\pi$
$38$	−5.36407	+	2.44969i	−0.870167	+	0.397392i
$39$	1.68361	+	1.92372i	0.269594	+	0.308042i
$40$	1.23147	+	1.86641i	0.194712	+	0.295106i
$41$	−0.240142	−	0.208084i	−0.0375038	−	0.0324973i	0.635907	−	0.771766i	$-0.280626\pi$
$41$	−0.240142	−	0.208084i	−0.0375038	−	0.0324973i	−0.673411	+	0.739268i	$0.735172\pi$
$42$	5.13435	−	2.37549i	0.792248	−	0.366545i
$43$	3.85328	−	8.43752i	0.587620	−	1.28671i	−0.349249	−	0.937030i	$-0.613563\pi$
$43$	3.85328	−	8.43752i	0.587620	−	1.28671i	0.936870	−	0.349679i	$-0.113709\pi$
$44$	0.103499	+	0.719848i	0.0156030	+	0.108521i
$45$	−6.16159	−	2.65233i	−0.918515	−	0.395385i
$46$	4.13018	−	2.43755i	0.608961	−	0.359397i
$47$	0.296017			0.0431785			0.0215892	−	0.999767i	$-0.493127\pi$
$47$	0.296017			0.0431785			0.0215892	+	0.999767i	$0.493127\pi$
$48$	0.496174	+	1.65946i	0.0716166	+	0.239523i
$49$	1.52381	−	3.33668i	0.217688	−	0.476669i
$50$	−2.18596	−	4.49684i	−0.309141	−	0.635949i
$51$	2.53133	+	1.60918i	0.354456	+	0.225330i
$52$	−0.415822	+	1.41616i	−0.0576642	+	0.196386i
$53$	−1.32976	−	2.06915i	−0.182656	−	0.284219i	0.737835	−	0.674981i	$-0.235848\pi$
$53$	−1.32976	−	2.06915i	−0.182656	−	0.284219i	−0.920492	+	0.390762i	$0.872212\pi$
$54$	−3.97696	−	3.34422i	−0.541195	−	0.455091i
$55$	−0.0195746	−	1.62606i	−0.00263944	−	0.219258i
$56$	2.74772	+	1.76585i	0.367179	+	0.235972i
$57$	10.2137	−	0.0504267i	1.35284	−	0.00667918i
$58$	6.73005	+	0.967635i	0.883699	+	0.127057i
$59$	4.64023	−	7.22033i	0.604106	−	0.940008i	−0.395660	−	0.918397i	$-0.629484\pi$
$59$	4.64023	−	7.22033i	0.604106	−	0.940008i	0.999766	−	0.0216106i	$-0.00687940\pi$
$60$	−0.616174	−	3.82365i	−0.0795477	−	0.493632i
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	−0.126149	−	0.992011i	$-0.540262\pi$
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	0.667102	+	0.744966i	$0.267535\pi$
$62$	−3.27893	+	2.10724i	−0.416424	+	0.267619i
$63$	−9.79817	+	0.0967525i	−1.23445	+	0.0121897i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	1.33477	−	3.01836i	0.165557	−	0.374381i
$66$	0.348909	−	1.21035i	0.0429477	−	0.148984i
$67$	0.0578385	+	0.402276i	0.00706610	+	0.0491458i	0.993049	−	0.117698i	$-0.0375515\pi$
$67$	0.0578385	+	0.402276i	0.00706610	+	0.0491458i	−0.985983	+	0.166844i	$0.946642\pi$
$68$			1.73177i			0.210008i
$69$	−8.25669	+	0.909463i	−0.993988	+	0.109486i
$70$	−5.57677	−	4.71598i	−0.666552	−	0.563667i
$71$	7.98308	−	1.14779i	0.947417	−	0.136218i	0.348750	−	0.937216i	$-0.386606\pi$
$71$	7.98308	−	1.14779i	0.947417	−	0.136218i	0.598667	+	0.800998i	$0.295697\pi$
$72$	0.397603	−	2.97354i	0.0468580	−	0.350434i
$73$	0.808166	+	2.75236i	0.0945887	+	0.322140i	0.993171	−	0.116665i	$-0.0372203\pi$
$73$	0.808166	+	2.75236i	0.0945887	+	0.322140i	−0.898583	+	0.438804i	$0.855402\pi$
$74$	7.28503	−	8.40738i	0.846868	−	0.977337i
$75$	0.251217	+	8.65661i	0.0290080	+	0.999579i
$76$	3.18814	+	4.96084i	0.365705	+	0.569048i
$77$	−0.986759	−	2.16070i	−0.112452	−	0.246235i
$78$	1.66454	−	1.94025i	0.188472	−	0.219690i
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	−0.927098	−	0.374819i	$-0.877705\pi$
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	0.726078	+	0.687612i	$0.241341\pi$
$80$	1.67216	−	1.48455i	0.186953	−	0.165978i
$81$	3.89967	+	8.11126i	0.433297	+	0.901251i
$82$	−0.171790	+	0.267311i	−0.0189711	+	0.0295196i
$83$	−11.9849	+	10.3850i	−1.31552	+	1.13990i	−0.335272	+	0.942122i	$0.608828\pi$
$83$	−11.9849	+	10.3850i	−1.31552	+	1.13990i	−0.980246	+	0.197781i	$0.936626\pi$
$84$	−3.08200	−	4.74403i	−0.336274	−	0.517616i
$85$	0.504916	−	3.83929i	0.0547658	−	0.416430i
$86$	−8.90001	−	2.61328i	−0.959713	−	0.281797i
$87$	−9.93847	−	6.31795i	−1.06552	−	0.677356i
$88$	0.697792	−	0.204890i	0.0743848	−	0.0218414i
$89$	3.56233	−	7.80041i	0.377606	−	0.826841i	−0.621452	−	0.783452i	$-0.713457\pi$
$89$	3.56233	−	7.80041i	0.377606	−	0.826841i	0.999058	−	0.0433895i	$-0.0138156\pi$
$90$	−1.74844	+	6.47634i	−0.184302	+	0.682666i
$91$		−	4.82076i		−	0.505353i
$92$	−3.00053	−	3.74124i	−0.312826	−	0.390051i
$93$	6.67742	−	0.993741i	0.692416	−	0.103046i
$94$	−0.0421276	−	0.293004i	−0.00434513	−	0.0302210i
$95$	−5.62165	−	11.9276i	−0.576769	−	1.22375i
$96$	1.57196	−	0.727290i	0.160437	−	0.0742287i
$97$	−8.74637	+	10.0938i	−0.888059	+	1.02487i	0.111457	+	0.993769i	$0.464448\pi$
$97$	−8.74637	+	10.0938i	−0.888059	+	1.02487i	−0.999516	+	0.0311057i	$0.990097\pi$
$98$	−3.51958	−	1.03344i	−0.355532	−	0.104394i
$99$	−1.41239	+	1.66288i	−0.141951	+	0.167126i
$100$	−4.13998	+	2.80368i	−0.413998	+	0.280368i
$101$	−4.21978	+	3.65646i	−0.419884	+	0.363831i	−0.839028	−	0.544088i	$-0.816876\pi$
$101$	−4.21978	+	3.65646i	−0.419884	+	0.363831i	0.419144	+	0.907920i	$0.362330\pi$
$102$	1.23256	−	2.73457i	0.122041	−	0.270763i
$103$	−2.60682	+	18.1308i	−0.256857	+	1.78648i	0.298030	+	0.954557i	$0.403671\pi$
$103$	−2.60682	+	18.1308i	−0.256857	+	1.78648i	−0.554887	+	0.831926i	$0.687239\pi$
$104$	1.46092	+	0.210049i	0.143255	+	0.0205970i
$105$	5.44956	+	11.4160i	0.531822	+	1.11409i
$106$	−1.85884	+	1.61069i	−0.180547	+	0.156444i
$107$	−9.34180	+	4.26626i	−0.903106	+	0.412435i	−0.812169	−	0.583422i	$-0.801713\pi$
$107$	−9.34180	+	4.26626i	−0.903106	+	0.412435i	−0.0909369	+	0.995857i	$0.528986\pi$
$108$	−2.74420	+	4.41241i	−0.264061	+	0.424584i
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	0.612922	+	0.790143i	$0.289994\pi$
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	−0.942807	+	0.333340i	$0.891824\pi$
$110$	−1.60673	+	0.250788i	−0.153195	+	0.0239117i
$111$	−17.4873	+	8.09077i	−1.65982	+	0.767942i
$112$	1.35684	−	2.97106i	0.128209	−	0.280738i
$113$	−9.35371	+	1.34486i	−0.879923	+	0.126514i	−0.567445	−	0.823411i	$-0.692068\pi$
$113$	−9.35371	+	1.34486i	−0.879923	+	0.126514i	−0.312478	+	0.949925i	$0.601159\pi$
$114$	−1.50348	−	10.1026i	−0.140814	−	0.946194i
$115$	5.56130	+	9.16907i	0.518594	+	0.855021i
$116$		−	6.79926i		−	0.631295i
$117$	−4.00935	+	1.87907i	−0.370664	+	0.173720i
$118$	−7.80722	−	3.56544i	−0.718712	−	0.328225i
$119$	−1.59357	−	5.42721i	−0.146083	−	0.497512i
$120$	−3.69704	+	1.15406i	−0.337492	+	0.105351i
$121$	10.0470	+	2.95005i	0.913359	+	0.268187i
$122$	−2.51112	−	3.90738i	−0.227346	−	0.353757i
$123$	0.461521	−	0.299832i	0.0416140	−	0.0270349i
$124$	2.55243	+	2.94566i	0.229215	+	0.264528i
$125$	9.99568	−	5.00864i	0.894041	−	0.447986i
$126$	1.49019	+	9.68467i	0.132757	+	0.862779i
$127$	−11.0052	−	1.58231i	−0.976553	−	0.140407i	−0.364482	−	0.931210i	$-0.618754\pi$
$127$	−11.0052	−	1.58231i	−0.976553	−	0.140407i	−0.612070	+	0.790803i	$0.709663\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	12.1937	+	10.4610i	1.07360	+	0.921036i
$130$	−3.17759	−	0.891622i	−0.278693	−	0.0782004i
$131$	−7.01612	−	10.9173i	−0.613001	−	0.953848i	−0.999502	−	0.0315591i	$-0.989953\pi$
$131$	−7.01612	−	10.9173i	−0.613001	−	0.953848i	0.386501	−	0.922289i	$-0.373684\pi$
$132$	−1.24768	−	0.173107i	−0.108597	−	0.0150670i
$133$	−14.5563	−	12.6131i	−1.26219	−	1.09370i
$134$	0.389950	−	0.114500i	0.0336866	−	0.00989126i
$135$	7.37032	−	8.98211i	0.634336	−	0.773057i
$136$	1.71414	−	0.246456i	0.146986	−	0.0211335i
$137$			2.34987i			0.200763i	0.994949	+	0.100382i	$0.0320064\pi$
$137$			2.34987i			0.200763i	−0.994949	+	0.100382i	$0.967994\pi$
$138$	2.07526	+	8.04322i	0.176657	+	0.684684i
$139$	0.917075			0.0777853			0.0388926	−	0.999243i	$-0.487617\pi$
$139$	0.917075			0.0777853			0.0388926	+	0.999243i	$0.487617\pi$
$140$	−3.87432	+	6.19116i	−0.327440	+	0.523249i
$141$	−0.142018	+	0.492655i	−0.0119601	+	0.0414890i
$142$	−2.27222	−	7.73848i	−0.190681	−	0.649398i
$143$	−0.811209	−	0.702916i	−0.0678367	−	0.0587808i
$144$	−2.99985	+	0.0296222i	−0.249988	+	0.00246852i
$145$	−1.98240	+	15.0738i	−0.164629	+	1.25181i
$146$	2.60933	−	1.19164i	0.215950	−	0.0986210i
$147$	4.82211	+	4.13687i	0.397721	+	0.341204i
$148$	−9.35857	−	6.01439i	−0.769270	−	0.494380i
$149$	−1.45041	+	10.0879i	−0.118823	+	0.826429i	0.840033	+	0.542535i	$0.182535\pi$
$149$	−1.45041	+	10.0879i	−0.118823	+	0.826429i	−0.958856	+	0.283894i	$0.908374\pi$
$150$	8.53275	−	1.48062i	0.696696	−	0.120892i
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.999417	−	0.0341294i	$-0.989134\pi$
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.446218	−	0.894924i	$-0.647229\pi$
$152$	4.45663	−	3.86169i	0.361480	−	0.313225i
$153$	−3.89257	+	3.44081i	−0.314695	+	0.278173i
$154$	−1.99828	+	1.28422i	−0.161026	+	0.103485i
$155$	−4.79984	−	7.27465i	−0.385533	−	0.584314i
$156$	−2.15739	−	1.37147i	−0.172729	−	0.109805i
$157$	15.3988	−	4.52150i	1.22896	−	0.360855i	0.398103	−	0.917341i	$-0.369669\pi$
$157$	15.3988	−	4.52150i	1.22896	−	0.360855i	0.830857	+	0.556485i	$0.187851\pi$
$158$	3.00614	+	1.37286i	0.239156	+	0.109219i
$159$	4.08161	−	1.22039i	0.323692	−	0.0967831i
$160$	−1.70741	−	1.44387i	−0.134983	−	0.114148i
$161$	12.8461	+	8.96362i	1.01241	+	0.706432i
$162$	7.47372	−	5.01433i	0.587191	−	0.393963i
$163$	14.5365	−	2.09003i	1.13859	−	0.163704i	0.452872	−	0.891575i	$-0.350399\pi$
$163$	14.5365	−	2.09003i	1.13859	−	0.163704i	0.685714	+	0.727871i	$0.259490\pi$
$164$	0.289038	+	0.131999i	0.0225701	+	0.0103074i
$165$	2.71562	+	0.747549i	0.211410	+	0.0581966i
$166$	11.9849	+	10.3850i	0.930212	+	0.806033i
$167$	4.12542	+	1.21133i	0.319234	+	0.0937357i	0.437424	−	0.899255i	$-0.355891\pi$
$167$	4.12542	+	1.21133i	0.319234	+	0.0937357i	−0.118190	+	0.992991i	$0.537709\pi$
$168$	−4.25712	+	3.72578i	−0.328444	+	0.287450i
$169$	4.49545	+	9.84366i	0.345804	+	0.757204i
$170$	−3.87207	+	0.0466122i	−0.296974	+	0.00357499i
$171$	−4.81625	+	17.0227i	−0.368308	+	1.30176i
$172$	−1.32008	+	9.18133i	−0.100655	+	0.700070i
$173$	2.27457	−	15.8200i	0.172932	−	1.20277i	−0.699716	−	0.714421i	$-0.746690\pi$
$173$	2.27457	−	15.8200i	0.172932	−	1.20277i	0.872648	−	0.488349i	$-0.162401\pi$
$174$	−4.83925	+	10.7364i	−0.366863	+	0.813928i
$175$	10.3944	−	12.5961i	0.785741	−	0.952174i
$176$	−0.302111	−	0.661530i	−0.0227725	−	0.0498647i
$177$	9.79044	+	11.1867i	0.735895	+	0.840843i
$178$	−8.22798	−	2.41595i	−0.616713	−	0.181083i
$179$	−13.3592	−	11.5758i	−0.998511	−	0.865215i	−0.00763206	−	0.999971i	$-0.502429\pi$
$179$	−13.3592	−	11.5758i	−0.998511	−	0.865215i	−0.990879	+	0.134756i	$0.956975\pi$
$180$	6.65925	+	0.808967i	0.496351	+	0.0602969i
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.412238	−	0.911076i	$-0.635253\pi$
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.958504	+	0.285080i	$0.907980\pi$
$182$	−4.77169	+	0.686066i	−0.353701	+	0.0508546i
$183$	1.18420	+	7.95724i	0.0875389	+	0.588216i
$184$	−3.27614	+	3.50242i	−0.241520	+	0.258202i
$185$	18.9942	+	16.0624i	1.39648	+	1.18093i
$186$	−1.93392	−	6.46803i	−0.141802	−	0.474259i
$187$	−1.14562	−	0.523186i	−0.0837758	−	0.0382591i
$188$	−0.284026	+	0.0833976i	−0.0207147	+	0.00608239i
$189$	4.53979	−	16.3533i	0.330221	−	1.18953i
$190$	−11.0062	+	7.26191i	−0.798471	+	0.526834i
$191$	−0.401041	+	0.257733i	−0.0290183	+	0.0186489i	−0.555070	−	0.831804i	$-0.687308\pi$
$191$	−0.401041	+	0.257733i	−0.0290183	+	0.0186489i	0.526051	+	0.850453i	$0.323672\pi$
$192$	−0.943600	−	1.45245i	−0.0680984	−	0.104822i
$193$	−2.50162	+	2.16767i	−0.180070	+	0.156032i	−0.740232	−	0.672351i	$-0.765284\pi$
$193$	−2.50162	+	2.16767i	−0.180070	+	0.156032i	0.560162	+	0.828383i	$0.310739\pi$
$194$	11.2358	+	7.22084i	0.806687	+	0.518426i
$195$	4.38302	+	3.66952i	0.313875	+	0.262780i
$196$	−0.522035	+	3.63083i	−0.0372882	+	0.259345i
$197$	2.16157	+	1.38916i	0.154006	+	0.0989735i	0.615374	−	0.788235i	$-0.289005\pi$
$197$	2.16157	+	1.38916i	0.154006	+	0.0989735i	−0.461368	+	0.887209i	$0.652641\pi$
$198$	1.84696	+	1.16136i	0.131258	+	0.0825345i
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	−0.103130	−	0.994668i	$-0.532886\pi$
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	0.684184	+	0.729310i	$0.260159\pi$
$200$	3.36432	+	3.69883i	0.237893	+	0.261547i
$201$	−0.697248	−	0.0967381i	−0.0491801	−	0.00682338i
$202$	4.21978	+	3.65646i	0.296903	+	0.257268i
$203$	6.25667	+	21.3083i	0.439132	+	1.49555i
$204$	−2.88215	−	0.830841i	−0.201791	−	0.0581705i
$205$	−0.602306	−	0.376912i	−0.0420669	−	0.0263247i
$206$	18.3173			1.27622
$207$	2.44766	−	14.1778i	0.170124	−	0.985423i
$208$		−	1.47595i		−	0.102338i
$209$	−4.24492	+	0.610327i	−0.293627	+	0.0422172i
$210$	10.5242	−	7.01875i	0.726242	−	0.484340i
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.765907	−	0.642951i	$-0.777710\pi$
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.296716	+	0.954966i	$0.595892\pi$
$212$	1.85884	+	1.61069i	0.127666	+	0.110623i
$213$	−1.91975	+	13.8367i	−0.131539	+	0.948078i
$214$	5.55231	+	8.63957i	0.379548	+	0.590589i
$215$	5.60350	−	19.9699i	0.382155	−	1.36194i
$216$	4.75804	+	2.08832i	0.323743	+	0.142092i
$217$	−10.7097	−	6.88270i	−0.727021	−	0.467228i
$218$	12.1003	+	1.73975i	0.819533	+	0.117831i
$219$	−4.96843	+	0.0245299i	−0.335735	+	0.00165758i
$220$	0.476897	+	1.55468i	0.0321524	+	0.104817i
$221$	−1.67382	−	1.93169i	−0.112594	−	0.129940i
$222$	10.4971	+	16.1579i	0.704521	+	1.08445i
$223$	−1.88085	−	2.92665i	−0.125951	−	0.195983i	0.772551	−	0.634952i	$-0.218980\pi$
$223$	−1.88085	−	2.92665i	−0.125951	−	0.195983i	−0.898502	+	0.438969i	$0.855344\pi$
$224$	−3.13391	−	0.920200i	−0.209393	−	0.0614834i
$225$	−14.5275	−	3.73504i	−0.968503	−	0.249002i
$226$	2.66234	+	9.06711i	0.177097	+	0.603135i
$227$	−18.4257	−	8.41476i	−1.22296	−	0.558507i	−0.303930	−	0.952695i	$-0.598299\pi$
$227$	−18.4257	−	8.41476i	−1.22296	−	0.558507i	−0.919030	+	0.394188i	$0.871026\pi$
$228$	−9.78579	+	2.92592i	−0.648080	+	0.193774i
$229$			9.44144i			0.623908i	0.950097	+	0.311954i	$0.100983\pi$
$229$			9.44144i			0.623908i	−0.950097	+	0.311954i	$0.899017\pi$
$230$	8.28429	−	6.80959i	0.546250	−	0.449011i
$231$	4.06942	−	0.605616i	0.267748	−	0.0398466i
$232$	−6.73005	+	0.967635i	−0.441850	+	0.0635284i
$233$	−4.97061	+	10.8841i	−0.325636	+	0.713042i	−0.999671	−	0.0256568i	$-0.991832\pi$
$233$	−4.97061	+	10.8841i	−0.325636	+	0.713042i	0.674035	+	0.738699i	$0.264560\pi$
$234$	2.43053	+	3.70112i	0.158889	+	0.241950i
$235$	0.653995	−	0.102080i	0.0426619	−	0.00665895i
$236$	−2.41806	+	8.23516i	−0.157402	+	0.536063i
$237$	−3.76978	−	4.30740i	−0.244873	−	0.279796i
$238$	−5.14518	+	2.34973i	−0.333513	+	0.152310i
$239$	−15.5939	+	13.5122i	−1.00869	+	0.874034i	−0.992052	−	0.125828i	$-0.959841\pi$
$239$	−15.5939	+	13.5122i	−1.00869	+	0.874034i	−0.0166366	+	0.999862i	$0.505296\pi$
$240$	1.66846	+	3.49517i	0.107699	+	0.225612i
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.163647	−	0.986519i	$-0.552326\pi$
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.434953	+	0.900453i	$0.643235\pi$
$242$	1.49019	−	10.3645i	0.0957933	−	0.666257i
$243$	−15.3703	+	2.59865i	−0.986007	+	0.166703i
$244$	−3.51024	+	3.04164i	−0.224720	+	0.194721i
$245$	2.21595	−	7.89727i	0.141572	−	0.504538i
$246$	−0.362461	−	0.414153i	−0.0231097	−	0.0264054i
$247$	−8.35105	−	2.45209i	−0.531365	−	0.156023i
$248$	2.55243	−	2.94566i	0.162079	−	0.187050i
$249$	−11.5336	−	24.9286i	−0.730913	−	1.57979i
$250$	−6.38019	−	9.18113i	−0.403519	−	0.580666i
$251$	−3.51524	−	24.4491i	−0.221880	−	1.54321i	−0.730917	−	0.682466i	$-0.760908\pi$
$251$	−3.51524	−	24.4491i	−0.221880	−	1.54321i	0.509037	−	0.860745i	$-0.330002\pi$
$252$	9.37402	−	2.85330i	0.590508	−	0.179741i
$253$	3.38143	−	0.854670i	0.212589	−	0.0537327i
$254$			11.1184i			0.697628i
$255$	6.14742	+	2.68228i	0.384966	+	0.167971i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	1.94338	−	0.570628i	0.121225	−	0.0355948i	−0.220557	−	0.975374i	$-0.570788\pi$
$257$	1.94338	−	0.570628i	0.121225	−	0.0355948i	0.341782	+	0.939779i	$0.388969\pi$
$258$	8.61914	−	13.5584i	0.536604	−	0.844106i
$259$	34.8634	+	10.2368i	2.16630	+	0.636084i
$260$	−0.430328	+	3.27214i	−0.0266878	+	0.202930i
$261$	15.2830	−	13.5093i	0.945992	−	0.836203i
$262$	−9.80767	+	8.49840i	−0.605920	+	0.525033i
$263$	−10.8582	+	16.8957i	−0.669547	+	1.04184i	0.325796	+	0.945440i	$0.394368\pi$
$263$	−10.8582	+	16.8957i	−0.669547	+	1.04184i	−0.995343	+	0.0963952i	$0.969269\pi$
$264$	0.00621893	+	1.25962i	0.000382749	+	0.0775242i
$265$	−3.65139	−	4.11284i	−0.224303	−	0.252650i
$266$	−10.4132	+	16.2032i	−0.638472	+	0.993481i
$267$	11.2730	+	9.67106i	0.689895	+	0.591859i
$268$	−0.168830	−	0.369686i	−0.0103129	−	0.0225822i
$269$	7.98286	+	12.4216i	0.486723	+	0.757356i	0.994568	−	0.104093i	$-0.0331938\pi$
$269$	7.98286	+	12.4216i	0.486723	+	0.757356i	−0.507844	+	0.861449i	$0.669557\pi$
$270$	−9.93960	−	6.01701i	−0.604905	−	0.366184i
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	−0.905519	−	0.424305i	$-0.860518\pi$
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	0.548855	+	0.835918i	$0.315064\pi$
$272$	−0.487896	−	1.66162i	−0.0295830	−	0.100751i
$273$	8.02310	+	2.31283i	0.485580	+	0.139979i
$274$	2.32595	−	0.334422i	0.140516	−	0.0202032i
$275$	−0.603986	−	3.58574i	−0.0364217	−	0.216228i
$276$	7.66601	−	3.19880i	0.461439	−	0.192545i
$277$		−	32.6649i		−	1.96264i	−0.192377	−	0.981321i	$-0.561620\pi$
$277$		−	32.6649i		−	1.96264i	0.192377	−	0.981321i	$-0.438380\pi$
$278$	−0.130513	−	0.907741i	−0.00782767	−	0.0544427i
$279$	−1.54972	+	11.5899i	−0.0927796	+	0.693866i
$280$	6.67952	+	2.95379i	0.399178	+	0.176523i
$281$	−3.24036	+	3.73957i	−0.193304	+	0.223084i	−0.844125	−	0.536147i	$-0.819879\pi$
$281$	−3.24036	+	3.73957i	−0.193304	+	0.223084i	0.650821	+	0.759231i	$0.274425\pi$
$282$	0.507851	+	0.0704607i	0.0302421	+	0.00419587i
$283$	7.79627	−	5.01036i	0.463440	−	0.297835i	−0.288007	−	0.957628i	$-0.592993\pi$
$283$	7.79627	−	5.01036i	0.463440	−	0.297835i	0.751447	+	0.659793i	$0.229356\pi$
$284$	−7.33634	+	3.35039i	−0.435332	+	0.198809i
$285$	22.5480	−	3.63355i	1.33563	−	0.215233i
$286$	−0.580315	+	0.902987i	−0.0343147	+	0.0533948i
$287$	−1.02729	−	0.147702i	−0.0606388	−	0.00871854i
$288$	0.456244	+	2.96510i	0.0268845	+	0.174720i
$289$	11.7784	+	7.56950i	0.692845	+	0.445265i
$290$	15.2025	−	0.183009i	0.892722	−	0.0107466i
$291$	−12.6028	−	19.3991i	−0.738789	−	1.13719i
$292$	−1.55086	−	2.41319i	−0.0907572	−	0.141221i
$293$	−6.42750	+	21.8900i	−0.375498	+	1.27883i	0.527636	+	0.849471i	$0.323079\pi$
$293$	−6.42750	+	21.8900i	−0.375498	+	1.27883i	−0.903134	+	0.429359i	$0.858740\pi$
$294$	3.40851	−	5.36176i	0.198788	−	0.312704i
$295$	7.76184	−	17.5522i	0.451912	−	1.02193i
$296$	−4.62131	+	10.1192i	−0.268608	+	0.588169i
$297$	−2.08989	−	3.14841i	−0.121268	−	0.182689i
$298$	10.1916			0.590383
$299$	6.96298	+	1.27302i	0.402679	+	0.0736207i
$300$	−2.67989	−	8.23518i	−0.154723	−	0.475458i
$301$	−4.31165	−	29.9882i	−0.248520	−	1.72849i
$302$	−8.77208	+	19.2082i	−0.504776	+	1.10531i
$303$	−4.06087	−	8.77713i	−0.233291	−	0.504233i
$304$	−4.45663	−	3.86169i	−0.255605	−	0.221483i
$305$	8.66894	−	5.71980i	0.496382	−	0.327515i
$306$	3.95975	+	3.36327i	0.226364	+	0.192265i
$307$	16.0568	−	7.33288i	0.916408	−	0.418509i	0.0993417	−	0.995053i	$-0.468326\pi$
$307$	16.0568	−	7.33288i	0.916408	−	0.418509i	0.817066	+	0.576544i	$0.195599\pi$
$308$	1.55553	+	1.79518i	0.0886344	+	0.102290i
$309$	−28.9241	−	13.0370i	−1.64543	−	0.741648i
$310$	−6.51752	+	5.78628i	−0.370170	+	0.328638i
$311$	22.4582	+	3.22901i	1.27349	+	0.183100i	0.745704	−	0.666277i	$-0.232113\pi$
$311$	22.4582	+	3.22901i	1.27349	+	0.183100i	0.527786	+	0.849377i	$0.323022\pi$
$312$	−1.05048	+	2.33061i	−0.0594717	+	0.131945i
$313$	6.80241	+	7.85039i	0.384495	+	0.443731i	0.914697	−	0.404141i	$-0.132429\pi$
$313$	6.80241	+	7.85039i	0.384495	+	0.443731i	−0.530202	+	0.847871i	$0.677884\pi$
$314$	−6.66696	−	14.5986i	−0.376238	−	0.823847i
$315$	−21.6139	+	3.59260i	−1.21781	+	0.202420i
$316$	0.931067	−	3.17092i	0.0523766	−	0.178378i
$317$	−1.99686	+	2.30450i	−0.112155	+	0.129434i	−0.809051	−	0.587738i	$-0.800018\pi$
$317$	−1.99686	+	2.30450i	−0.112155	+	0.129434i	0.696896	+	0.717172i	$0.254564\pi$
$318$	−1.78884	−	3.86638i	−0.100313	−	0.216816i
$319$	4.49791	+	2.05413i	0.251835	+	0.115009i
$320$	−1.18618	+	1.89552i	−0.0663094	+	0.105963i
$321$	−2.61838	−	17.5942i	−0.146144	−	0.982011i
$322$	7.04420	−	13.9910i	0.392558	−	0.779686i
$323$	−10.2122			−0.568221
$324$	−6.02691	−	6.68404i	−0.334828	−	0.371335i
$325$	1.90806	−	7.12880i	0.105840	−	0.395435i
$326$	−4.13752	−	14.0911i	−0.229156	−	0.780433i
$327$	−17.8688	−	11.3593i	−0.988148	−	0.628172i
$328$	0.0895214	−	0.304882i	0.00494299	−	0.0168343i
$329$	0.813370	−	0.522721i	0.0448425	−	0.0288186i
$330$	0.353468	−	2.79436i	0.0194578	−	0.153825i
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.955753	−	0.294172i	$-0.904956\pi$
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.155160	−	0.987889i	$-0.549589\pi$
$332$	8.57367	−	13.3409i	0.470541	−	0.732176i
$333$	−5.07551	−	32.9855i	−0.278136	−	1.80759i
$334$	0.611894	−	4.25582i	0.0334814	−	0.232868i
$335$	0.266506	+	0.868810i	0.0145608	+	0.0474681i
$336$	4.29370	+	3.68356i	0.234241	+	0.200955i
$337$	6.43537	+	14.0915i	0.350557	+	0.767613i	0.999974	+	0.00718065i	$0.00228569\pi$
$337$	6.43537	+	14.0915i	0.350557	+	0.767613i	−0.649417	+	0.760432i	$0.724987\pi$
$338$	9.10369	−	5.85059i	0.495176	−	0.318230i
$339$	2.24935	−	16.2124i	0.122168	−	0.880537i
$340$	0.597191	+	3.82603i	0.0323872	+	0.207495i
$341$	−2.71976	+	0.798593i	−0.147283	+	0.0432463i
$342$	17.5348	+	2.34465i	0.948175	+	0.126784i
$343$	1.54874	+	10.7717i	0.0836240	+	0.581618i
$344$	9.27575			0.500115
$345$	−17.9280	+	4.85657i	−0.965212	+	0.261469i
$346$	−15.9827			−0.859233
$347$	3.43226	+	23.8719i	0.184254	+	1.28151i	0.846566	+	0.532284i	$0.178666\pi$
$347$	3.43226	+	23.8719i	0.184254	+	1.28151i	−0.662312	+	0.749228i	$0.730425\pi$
$348$	11.3159	+	3.26204i	0.606594	+	0.174864i
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	−0.408619	−	0.912705i	$-0.633990\pi$
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	0.149693	+	0.988733i	$0.452171\pi$
$350$	−13.9471	−	8.49597i	−0.745506	−	0.454129i
$351$	−1.20376	−	7.57419i	−0.0642519	−	0.404280i
$352$	−0.611802	+	0.393181i	−0.0326092	+	0.0209566i
$353$	−6.56143	−	14.3675i	−0.349230	−	0.764707i	−0.999985	−	0.00541925i	$-0.998275\pi$
$353$	−6.56143	−	14.3675i	−0.349230	−	0.764707i	0.650756	−	0.759287i	$-0.274452\pi$
$354$	9.67950	−	11.2828i	0.514460	−	0.599675i
$355$	17.2413	−	5.28876i	0.915076	−	0.280698i
$356$	−1.22040	+	8.48806i	−0.0646810	+	0.449866i
$357$	9.79693	−	0.0483690i	0.518509	−	0.00255996i
$358$	−9.55675	+	14.8706i	−0.505090	+	0.785935i
$359$	−1.03639	−	1.19605i	−0.0546984	−	0.0631254i	0.727741	−	0.685852i	$-0.240570\pi$
$359$	−1.03639	−	1.19605i	−0.0546984	−	0.0631254i	−0.782439	+	0.622727i	$0.786025\pi$
$360$	−0.146976	−	6.70659i	−0.00774633	−	0.353469i
$361$	−13.2701	+	8.52818i	−0.698427	+	0.448852i
$362$	−5.71171	+	19.4523i	−0.300201	+	1.02239i
$363$	−9.72988	+	15.3056i	−0.510686	+	0.803336i
$364$	1.35817	+	4.62549i	0.0711872	+	0.242441i
$365$	2.73463	+	5.80215i	0.143137	+	0.303698i
$366$	7.70771	−	2.30458i	0.402889	−	0.120463i
$367$	34.0866			1.77931			0.889653	−	0.456637i	$-0.150946\pi$
$367$	34.0866			1.77931			0.889653	+	0.456637i	$0.150946\pi$
$368$	3.93301	+	2.74434i	0.205022	+	0.143059i
$369$	0.277582	+	0.911949i	0.0144504	+	0.0474742i
$370$	13.1957	−	21.0868i	0.686012	−	1.09625i
$371$	−7.30760	−	3.33727i	−0.379392	−	0.173262i
$372$	−6.12697	+	2.83473i	−0.317668	+	0.146974i
$373$	−7.49073	+	8.64477i	−0.387855	+	0.447609i	−0.915779	−	0.401683i	$-0.868425\pi$
$373$	−7.49073	+	8.64477i	−0.387855	+	0.447609i	0.527923	+	0.849292i	$0.322971\pi$
$374$	−0.354822	+	1.20841i	−0.0183474	+	0.0624856i
$375$	3.54020	+	19.0386i	0.182815	+	0.983147i
$376$	0.122970	+	0.269266i	0.00634168	+	0.0138863i
$377$	6.57175	+	7.58421i	0.338462	+	0.390607i
$378$	−16.8329	−	2.16626i	−0.865793	−	0.111420i
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.782858	−	0.622200i	$-0.213761\pi$
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.575853	+	0.817553i	$0.304670\pi$
$380$	8.75433	+	9.86066i	0.449088	+	0.505841i
$381$	7.91330	−	17.5566i	0.405410	−	0.899451i
$382$	0.312184	+	0.360280i	0.0159727	+	0.0184335i
$383$	−11.7553	+	5.36847i	−0.600668	+	0.274316i	−0.692453	−	0.721463i	$-0.743470\pi$
$383$	−11.7553	+	5.36847i	−0.600668	+	0.274316i	0.0917849	+	0.995779i	$0.470743\pi$
$384$	−1.30338	+	1.14070i	−0.0665129	+	0.0582111i
$385$	−2.92517	−	4.43340i	−0.149080	−	0.225947i
$386$	2.50162	+	2.16767i	0.127329	+	0.110331i
$387$	−23.2601	+	15.2750i	−1.18238	+	0.776470i
$388$	5.54831	−	12.1491i	0.281673	−	0.616778i
$389$	−3.82143	−	26.5786i	−0.193754	−	1.34759i	−0.821962	−	0.569543i	$-0.807120\pi$
$389$	−3.82143	−	26.5786i	−0.193754	−	1.34759i	0.628208	−	0.778046i	$-0.283789\pi$
$390$	3.00840	−	4.86064i	0.152336	−	0.246128i
$391$	8.25973	−	0.868547i	0.417713	−	0.0439243i
$392$	3.66817			0.185271
$393$	21.5355	−	6.43905i	1.08632	−	0.324807i
$394$	1.06740	−	2.33727i	0.0537746	−	0.117750i
$395$	−2.98867	+	6.75840i	−0.150376	+	0.340052i
$396$	0.886692	−	1.99344i	0.0445580	−	0.100174i
$397$	−6.70727	+	22.8429i	−0.336628	+	1.14645i	0.601127	+	0.799154i	$0.294719\pi$
$397$	−6.70727	+	22.8429i	−0.336628	+	1.14645i	−0.937755	+	0.347297i	$0.887099\pi$
$398$	−4.87176	−	7.58060i	−0.244199	−	0.379981i
$399$	27.9754	−	18.1745i	1.40052	−	0.909861i
$400$	3.18239	−	3.85647i	0.159120	−	0.192824i
$401$	−27.8844	−	17.9202i	−1.39248	−	0.894893i	−0.392787	−	0.919629i	$-0.628489\pi$
$401$	−27.8844	−	17.9202i	−1.39248	−	0.894893i	−0.999694	+	0.0247360i	$0.992125\pi$
$402$	0.00347535	+	0.703919i	0.000173335	+	0.0351083i
$403$	−5.69419	−	0.818702i	−0.283648	−	0.0407824i
$404$	3.01870	−	4.69720i	0.150186	−	0.233694i
$405$	11.4127	+	16.5756i	0.567103	+	0.823647i
$406$	20.2010	−	9.22547i	1.00256	−	0.457853i
$407$	6.80602	−	4.37397i	0.337362	−	0.216809i
$408$	−0.412212	+	2.97105i	−0.0204075	+	0.147089i
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	−0.766227	−	0.642570i	$-0.777868\pi$
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	0.745075	+	0.666980i	$0.232414\pi$
$410$	−0.287359	+	0.649816i	−0.0141916	+	0.0320921i
$411$	−3.91085	−	1.12739i	−0.192908	−	0.0556098i
$412$	−2.60682	−	18.1308i	−0.128429	−	0.893241i
$413$		−	28.0334i		−	1.37943i
$414$	−14.3818	−	0.405043i	−0.706827	−	0.0199068i
$415$	−22.8973	+	27.0767i	−1.12398	+	1.32914i
$416$	−1.46092	+	0.210049i	−0.0716277	+	0.0102985i
$417$	−0.439980	+	1.52627i	−0.0215459	+	0.0747417i
$418$	1.20823	+	4.11485i	0.0590965	+	0.201264i
$419$	−17.0320	+	19.6560i	−0.832069	+	0.960259i	−0.999672	−	0.0255957i	$-0.991852\pi$
$419$	−17.0320	+	19.6560i	−0.832069	+	0.960259i	0.167603	+	0.985855i	$0.446397\pi$
$420$	−8.44507	−	9.41825i	−0.412077	−	0.459563i
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	0.803300	−	0.595574i	$-0.203075\pi$
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	−0.875456	+	0.483297i	$0.839439\pi$
$422$	6.68284	+	14.6334i	0.325315	+	0.712342i
$423$	−0.751780	−	0.472716i	−0.0365528	−	0.0229842i
$424$	1.32976	−	2.06915i	0.0645788	−	0.100487i
$425$	−0.208441	−	8.65633i	−0.0101109	−	0.419894i
$426$	13.9691	−	0.0689676i	0.676806	−	0.00334149i
$427$	8.20186	−	12.7623i	0.396916	−	0.617613i
$428$	7.76145	−	6.72534i	0.375164	−	0.325081i
$429$	1.55904	−	1.01284i	0.0752711	−	0.0489006i
$430$	−20.5641	−	2.70444i	−0.991690	−	0.130420i
$431$	−3.54845	−	1.04192i	−0.170923	−	0.0501875i	0.195151	−	0.980773i	$-0.437480\pi$
$431$	−3.54845	−	1.04192i	−0.170923	−	0.0501875i	−0.366074	+	0.930586i	$0.619298\pi$
$432$	1.38992	−	5.00681i	0.0668727	−	0.240890i
$433$	26.7068	−	7.84183i	1.28345	−	0.376854i	0.432276	−	0.901742i	$-0.357711\pi$
$433$	26.7068	−	7.84183i	1.28345	−	0.376854i	0.851172	+	0.524887i	$0.175893\pi$
$434$	−5.28849	+	11.5802i	−0.253856	+	0.555867i
$435$	−24.1359	−	10.5311i	−1.15723	−	0.504929i
$436$		−	12.2247i		−	0.585456i
$437$	22.0619	−	17.6940i	1.05537	−	0.846419i
$438$	0.731361	+	4.91437i	0.0349458	+	0.234818i
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	0.810978	+	0.585077i	$0.198936\pi$
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	−0.613292	+	0.789856i	$0.710155\pi$
$440$	1.47099	−	0.693297i	0.0701266	−	0.0330516i
$441$	−9.19839	+	6.04061i	−0.438018	+	0.287648i
$442$	−1.67382	+	1.93169i	−0.0796156	+	0.0918814i
$443$	32.1145	+	9.42968i	1.52581	+	0.448017i	0.933764	−	0.357889i	$-0.116503\pi$
$443$	32.1145	+	9.42968i	1.52581	+	0.448017i	0.592043	+	0.805906i	$0.298321\pi$
$444$	14.4995	−	12.6898i	0.688117	−	0.602231i
$445$	5.18038	−	18.4620i	0.245574	−	0.875184i
$446$	−2.62919	+	2.27821i	−0.124496	+	0.107876i
$447$	−16.0932	−	7.25369i	−0.761180	−	0.343088i
$448$	−0.464831	+	3.23297i	−0.0219612	+	0.152744i
$449$	38.0510	+	5.47090i	1.79574	+	0.258188i	0.957770	−	0.287534i	$-0.0928354\pi$
$449$	38.0510	+	5.47090i	1.79574	+	0.258188i	0.837966	+	0.545722i	$0.183745\pi$
$450$	−1.62954	+	14.9112i	−0.0768170	+	0.702922i
$451$	−0.174643	+	0.151329i	−0.00822363	+	0.00712581i
$452$	8.59593	−	3.92563i	0.404319	−	0.184646i
$453$	27.5227	−	24.0875i	1.29313	−	1.13173i
$454$	−5.70685	+	19.4357i	−0.267836	+	0.912164i
$455$	−1.66241	−	10.6506i	−0.0779352	−	0.499307i
$456$	4.28880	+	9.26978i	0.200842	+	0.434097i
$457$	−3.10118	+	6.79064i	−0.145067	+	0.317653i	−0.968192	−	0.250207i	$-0.919501\pi$
$457$	−3.10118	+	6.79064i	−0.145067	+	0.317653i	0.823125	+	0.567860i	$0.192229\pi$
$458$	9.34534	−	1.34366i	0.436679	−	0.0627850i
$459$	−3.85895	−	8.12909i	−0.180120	−	0.379434i
$460$	−7.91926	−	7.23086i	−0.369237	−	0.337141i
$461$			23.1040i			1.07606i	0.842925	+	0.538030i	$0.180831\pi$
$461$			23.1040i			1.07606i	−0.842925	+	0.538030i	$0.819169\pi$
$462$	−1.17859	−	3.94181i	−0.0548330	−	0.183390i
$463$	−9.46248	−	4.32137i	−0.439759	−	0.200831i	0.183217	−	0.983073i	$-0.441349\pi$
$463$	−9.46248	−	4.32137i	−0.439759	−	0.200831i	−0.622975	+	0.782242i	$0.714076\pi$
$464$	1.91557	+	6.52384i	0.0889282	+	0.302862i
$465$	14.4098	−	4.49816i	0.668241	−	0.208597i
$466$	11.4807	+	3.37105i	0.531834	+	0.156161i
$467$	−16.4551	−	25.6047i	−0.761453	−	1.18484i	−0.978007	−	0.208573i	$-0.933118\pi$
$467$	−16.4551	−	25.6047i	−0.761453	−	1.18484i	0.216554	−	0.976271i	$-0.430518\pi$
$468$	3.31754	−	2.93252i	0.153354	−	0.135556i
$469$	0.869283	+	1.00321i	0.0401397	+	0.0463237i
$470$	−0.194114	−	0.632811i	−0.00895381	−	0.0291894i
$471$	0.137239	+	27.7972i	0.00632364	+	1.28083i
$472$	8.49547	+	1.22146i	0.391036	+	0.0562224i
$473$	−5.67492	−	3.64705i	−0.260933	−	0.167692i
$474$	−3.72706	+	4.34441i	−0.171190	+	0.199545i
$475$	−16.5332	−	24.4133i	−0.758595	−	1.12016i
$476$	3.05804	+	4.75841i	0.140165	+	0.218101i
$477$	0.0728587	+	7.37843i	0.00333597	+	0.337835i
$478$	15.5939	+	13.5122i	0.713251	+	0.618035i
$479$	11.3558	−	3.33437i	0.518861	−	0.152351i	−0.0118082	−	0.999930i	$-0.503759\pi$
$479$	11.3558	−	3.33437i	0.518861	−	0.152351i	0.530669	+	0.847579i	$0.321941\pi$
$480$	3.22215	−	2.14889i	0.147070	−	0.0980832i
$481$	16.2521	−	2.33670i	0.741033	−	0.106544i
$482$			9.38833i			0.427627i
$483$	−21.0811	+	17.0790i	−0.959221	+	0.777122i
$484$	−10.4711			−0.475959
$485$	−15.8427	+	25.3166i	−0.719380	+	1.14957i
$486$	4.75962	+	14.8441i	0.215901	+	0.673340i
$487$	0.399122	+	1.35928i	0.0180859	+	0.0615951i	0.968042	−	0.250790i	$-0.0806903\pi$
$487$	0.399122	+	1.35928i	0.0180859	+	0.0615951i	−0.949956	+	0.312385i	$0.898872\pi$
$488$	3.51024	+	3.04164i	0.158901	+	0.137688i
$489$	−3.49569	+	25.1955i	−0.158081	+	1.13938i
$490$	−8.13225	−	1.06949i	−0.367378	−	0.0483148i
$491$	−12.9167	+	5.89886i	−0.582922	+	0.266212i	−0.684974	−	0.728567i	$-0.740187\pi$
$491$	−12.9167	+	5.89886i	−0.582922	+	0.266212i	0.102052	+	0.994779i	$0.467459\pi$
$492$	−0.358354	+	0.417712i	−0.0161559	+	0.0188319i
$493$	9.90554	+	6.36591i	0.446123	+	0.286706i
$494$	−1.23865	+	8.61502i	−0.0557296	+	0.387608i
$495$	−2.54699	+	4.16090i	−0.114479	+	0.187018i
$496$	−3.27893	−	2.10724i	−0.147228	−	0.0946178i
$497$	19.9084	−	17.2507i	0.893014	−	0.773801i
$498$	−23.0335	+	14.9639i	−1.03216	+	0.670550i
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.231536	−	0.972826i	$-0.425625\pi$
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.981098	+	0.193514i	$0.0619885\pi$
$500$	−8.17969	+	7.62186i	−0.365807	+	0.340860i
$501$	−3.99522	+	6.28470i	−0.178493	+	0.280779i
$502$	−23.6999	+	6.95893i	−1.05778	+	0.310592i
$503$	36.7413	+	16.7792i	1.63821	+	0.748146i	0.999768	−	0.0215221i	$-0.00685123\pi$
$503$	36.7413	+	16.7792i	1.63821	+	0.748146i	0.638444	+	0.769669i	$0.279579\pi$
$504$	−4.15832	−	8.87254i	−0.185226	−	0.395214i
$505$	−8.06192	+	9.53345i	−0.358751	+	0.424233i
$506$	−1.32720	−	3.22538i	−0.0590012	−	0.143386i
$507$	−18.5394	+	2.75905i	−0.823361	+	0.122534i
$508$	11.0052	−	1.58231i	0.488276	−	0.0702035i
$509$	17.8004	+	8.12919i	0.788991	+	0.360320i	0.768811	−	0.639476i	$-0.220849\pi$
$509$	17.8004	+	8.12919i	0.788991	+	0.360320i	0.0201799	+	0.999796i	$0.493576\pi$
$510$	1.78011	−	6.46657i	0.0788244	−	0.286345i
$511$	7.08087	+	6.13561i	0.313239	+	0.271423i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−26.0198	−	16.1825i	−1.14880	−	0.714473i
$514$	−0.841392	−	1.84239i	−0.0371122	−	0.0812644i
$515$	0.493027	+	40.9557i	0.0217253	+	1.80472i
$516$	−14.6470	−	6.60185i	−0.644797	−	0.290630i
$517$	0.0306373	−	0.213087i	0.00134743	−	0.00937156i
$518$	5.17104	−	35.9654i	0.227202	−	1.58023i
$519$	25.2376	+	11.3754i	1.10781	+	0.499324i
$520$	3.30008	−	0.0397265i	0.144718	−	0.00174212i
$521$	13.6630	+	29.9179i	0.598588	+	1.31073i	0.930111	+	0.367279i	$0.119710\pi$
$521$	13.6630	+	29.9179i	0.598588	+	1.31073i	−0.331522	+	0.943447i	$0.607562\pi$
$522$	−15.5468	−	13.2048i	−0.680463	−	0.577960i
$523$	−25.0573	−	7.35747i	−1.09568	−	0.321720i	−0.316544	−	0.948578i	$-0.602522\pi$
$523$	−25.0573	−	7.35747i	−1.09568	−	0.321720i	−0.779134	+	0.626858i	$0.784341\pi$
$524$	9.80767	+	8.49840i	0.428450	+	0.371254i
$525$	15.9765	+	23.3423i	0.697274	+	1.01874i
$526$	18.2690	+	8.34319i	0.796568	+	0.363780i
$527$	−6.68115	+	0.960605i	−0.291036	+	0.0418446i
$528$	1.24591	−	0.185418i	0.0542214	−	0.00806929i
$529$	−16.3391	+	16.1875i	−0.710395	+	0.703803i
$530$	−3.55133	+	4.19954i	−0.154260	+	0.182417i
$531$	−23.3149	+	10.9271i	−1.01178	+	0.474194i
$532$	17.5202	+	8.00121i	0.759597	+	0.346897i
$533$	−0.449989	+	0.132129i	−0.0194912	+	0.00572313i
$534$	7.96831	−	12.5346i	0.344823	−	0.542424i
$535$	−19.1678	+	12.6470i	−0.828697	+	0.546777i
$536$	−0.341896	+	0.219723i	−0.0147677	+	0.00949060i
$537$	25.6746	−	16.6797i	1.10794	−	0.719784i
$538$	11.1591	−	9.66937i	0.481101	−	0.416876i
$539$	−2.24419	−	1.44226i	−0.0966643	−	0.0621224i
$540$	−4.54122	+	10.6947i	−0.195423	+	0.460228i
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	0.857030	+	0.515267i	$0.172307\pi$
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	−0.967481	+	0.252942i	$0.918602\pi$
$542$	7.54262	+	4.84735i	0.323983	+	0.208212i
$543$	22.8640	−	26.6512i	0.981187	−	1.14371i
$544$	−1.57527	+	0.719403i	−0.0675392	+	0.0308441i
$545$	−3.56424	+	27.1019i	−0.152675	+	1.16092i
$546$	1.14748	−	8.27058i	0.0491077	−	0.353948i
$547$	8.62440	+	7.47309i	0.368753	+	0.319526i	0.819450	−	0.573151i	$-0.194279\pi$
$547$	8.62440	+	7.47309i	0.368753	+	0.319526i	−0.450697	+	0.892677i	$0.648825\pi$
$548$	−0.662036	−	2.25469i	−0.0282808	−	0.0963154i
$549$	−13.8112	−	1.84675i	−0.589448	−	0.0788174i
$550$	−3.46329	+	1.10814i	−0.147675	+	0.0472513i
$551$	40.0950			1.70810
$552$	−4.25723	−	7.13274i	−0.181200	−	0.303590i
$553$			10.7942i			0.459014i
$554$	−32.3324	+	4.64870i	−1.37367	+	0.197504i
$555$	−35.8450	+	23.9055i	−1.52153	+	1.01473i
$556$	−0.879927	+	0.258370i	−0.0373172	+	0.0109573i
$557$	−15.3807	−	13.3275i	−0.651703	−	0.564704i	0.265012	−	0.964245i	$-0.414624\pi$
$557$	−15.3807	−	13.3275i	−0.651703	−	0.564704i	−0.916715	+	0.399541i	$0.869169\pi$
$558$	11.6924	−	0.115457i	0.494980	−	0.00488770i
$559$	−7.40165	−	11.5172i	−0.313056	−	0.487125i
$560$	1.97313	−	7.03190i	0.0833798	−	0.297152i
$561$	1.42035	−	1.65562i	0.0599674	−	0.0699004i
$562$	4.16266	+	2.67518i	0.175591	+	0.112846i
$563$	−10.7639	−	1.54761i	−0.453643	−	0.0652241i	−0.0882938	−	0.996094i	$-0.528141\pi$
$563$	−10.7639	−	1.54761i	−0.453643	−	0.0652241i	−0.365350	+	0.930870i	$0.619051\pi$
$564$	−0.00253133	−	0.512710i	−0.000106588	−	0.0215890i
$565$	−20.2016	+	6.19680i	−0.849886	+	0.260701i
$566$	−6.06889	−	7.00387i	−0.255094	−	0.294395i
$567$	25.0385	+	15.4012i	1.05152	+	0.646790i
$568$	4.36036	+	6.78485i	0.182957	+	0.284686i
$569$	−25.0014	−	7.34108i	−1.04811	−	0.307754i	−0.288059	−	0.957613i	$-0.593010\pi$
$569$	−25.0014	−	7.34108i	−1.04811	−	0.307754i	−0.760055	+	0.649859i	$0.774828\pi$
$570$	−6.80548	−	21.8013i	−0.285050	−	0.913158i
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	0.936607	−	0.350383i	$-0.113949\pi$
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	−0.977355	+	0.211607i	$0.932130\pi$
$572$	0.976383	+	0.445899i	0.0408246	+	0.0186440i
$573$	−0.236535	−	0.791095i	−0.00988140	−	0.0330485i
$574$			1.03785i			0.0433190i
$575$	15.4486	+	18.3396i	0.644251	+	0.764815i
$576$	2.86999	−	0.873579i	0.119583	−	0.0363991i
$577$	−28.9240	+	4.15865i	−1.20412	+	0.173127i	−0.715023	−	0.699101i	$-0.753584\pi$
$577$	−28.9240	+	4.15865i	−1.20412	+	0.173127i	−0.489100	+	0.872227i	$0.662675\pi$
$578$	5.81622	−	12.7357i	0.241923	−	0.529737i
$579$	−2.40741	−	5.20336i	−0.100049	−	0.216244i
$580$	−2.34469	−	15.0217i	−0.0973578	−	0.623743i
$581$	−14.5928	+	49.6987i	−0.605413	+	2.06185i
$582$	−17.4081	+	15.2353i	−0.721587	+	0.631523i
$583$	−1.62710	+	0.743071i	−0.0673875	+	0.0307749i
$584$	−2.16791	+	1.87851i	−0.0897088	+	0.0777331i
$585$	−8.20993	+	5.53407i	−0.339439	+	0.228805i
$586$	22.5820	+	3.24680i	0.932852	+	0.134124i
$587$	0.787458	−	5.47689i	0.0325019	−	0.226056i	−0.967096	−	0.254412i	$-0.918118\pi$
$587$	0.787458	−	5.47689i	0.0325019	−	0.226056i	0.999598	+	0.0283562i	$0.00902727\pi$
$588$	−5.79227	−	2.61076i	−0.238869	−	0.107666i
$589$	−17.3705	+	15.0516i	−0.715737	+	0.620190i
$590$	−18.4781	−	5.18490i	−0.760733	−	0.213459i
$591$	−3.34900	+	2.93100i	−0.137759	+	0.120565i
$592$	10.6739	+	3.13415i	0.438696	+	0.128813i
$593$	21.7749	−	25.1296i	0.894189	−	1.03195i	−0.105108	−	0.994461i	$-0.533519\pi$
$593$	21.7749	−	25.1296i	0.894189	−	1.03195i	0.999297	−	0.0374879i	$-0.0119356\pi$
$594$	−2.81894	+	2.51668i	−0.115663	+	0.103261i
$595$	−5.39225	−	11.4409i	−0.221061	−	0.469031i
$596$	−1.45041	−	10.0879i	−0.0594113	−	0.413215i
$597$	2.29745	+	15.4376i	0.0940282	+	0.631820i
$598$	0.269129	−	7.07327i	0.0110055	−	0.289248i
$599$			17.0942i			0.698449i	0.937039	+	0.349224i	$0.113555\pi$
$599$			17.0942i			0.698449i	−0.937039	+	0.349224i	$0.886445\pi$
$600$	−7.76997	+	3.82460i	−0.317208	+	0.156139i
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	−0.794246	−	0.607597i	$-0.792134\pi$
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	0.979311	+	0.202359i	$0.0648609\pi$
$602$	−29.0694	+	8.53554i	−1.18478	+	0.347883i
$603$	0.495514	−	1.11400i	0.0201789	−	0.0453658i
$604$	20.2611	+	5.94918i	0.824411	+	0.242069i
$605$	23.2142	+	3.05296i	0.943792	+	0.124121i
$606$	−8.10987	+	5.26865i	−0.329441	+	0.214024i
$607$	−13.4570	+	11.6605i	−0.546202	+	0.473287i	−0.883709	−	0.468036i	$-0.844962\pi$
$607$	−13.4570	+	11.6605i	−0.546202	+	0.473287i	0.337507	+	0.941323i	$0.390416\pi$
$608$	−3.18814	+	4.96084i	−0.129296	+	0.201189i
$609$	−38.4647	+	0.189906i	−1.55867	+	0.00769537i
$610$	−6.89530	−	7.76669i	−0.279182	−	0.314464i
$611$	0.236209	−	0.367548i	0.00955598	−	0.0148694i
$612$	2.76550	−	4.39809i	0.111789	−	0.177782i
$613$	−16.4861	−	36.0995i	−0.665867	−	1.45805i	−0.876952	−	0.480577i	$-0.840427\pi$
$613$	−16.4861	−	36.0995i	−0.665867	−	1.45805i	0.211085	−	0.977468i	$-0.432300\pi$
$614$	−9.54336	−	14.8498i	−0.385138	−	0.599287i
$615$	0.916252	−	0.821577i	0.0369468	−	0.0331292i
$616$	1.55553	−	1.79518i	0.0626740	−	0.0723297i
$617$	7.78003	+	26.4963i	0.313212	+	1.06670i	0.954205	+	0.299155i	$0.0967048\pi$
$617$	7.78003	+	26.4963i	0.313212	+	1.06670i	−0.640992	+	0.767547i	$0.721477\pi$
$618$	−8.78797	+	30.4850i	−0.353504	+	1.22629i
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.113045	−	0.993590i	$-0.463940\pi$
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.388392	+	0.921494i	$0.373030\pi$
$620$	6.65492	+	5.62771i	0.267268	+	0.226014i
$621$	22.4215	+	10.8756i	0.899742	+	0.436422i
$622$		−	22.6892i		−	0.909754i
$623$	−3.98609	−	27.7238i	−0.159699	−	1.11073i
$624$	2.45639	+	0.708107i	0.0983342	+	0.0283469i
$625$	20.3564	−	14.5126i	0.814257	−	0.580505i
$626$	6.80241	−	7.85039i	0.271879	−	0.313765i
$627$	1.02081	−	7.35755i	0.0407670	−	0.293832i
$628$	−13.5012	+	8.67670i	−0.538757	+	0.346238i
$629$	17.5242	−	8.00303i	0.698736	−	0.319102i
$630$	6.63202	+	20.8826i	0.264226	+	0.831984i
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.126872	−	0.991919i	$-0.459506\pi$
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.849577	−	0.527465i	$-0.176857\pi$
$632$	−3.27115	−	0.470321i	−0.130119	−	0.0187083i
$633$	−0.137566	−	27.8634i	−0.00546775	−	1.10747i
$634$	2.56523	+	1.64857i	0.101878	+	0.0654731i
$635$	−24.8596	+	0.299261i	−0.986523	+	0.0118758i
$636$	−3.57245	+	2.32088i	−0.141657	+	0.0920287i
$637$	−2.92704	−	4.55457i	−0.115974	−	0.180459i
$638$	1.39310	−	4.74447i	0.0551534	−	0.187835i
$639$	−22.1072	−	9.83337i	−0.874547	−	0.389002i
$640$	2.04503	+	0.904345i	0.0808370	+	0.0357474i
$641$	15.0340	−	32.9199i	0.593808	−	1.30026i	−0.339305	−	0.940676i	$-0.610192\pi$
$641$	15.0340	−	32.9199i	0.593808	−	1.30026i	0.933113	−	0.359582i	$-0.117081\pi$
$642$	−17.0425	+	5.09564i	−0.672612	+	0.201109i
$643$	−21.0704			−0.830935			−0.415468	−	0.909608i	$-0.636382\pi$
$643$	−21.0704			−0.830935			−0.415468	+	0.909608i	$0.636382\pi$
$644$	−14.8511	−	4.98138i	−0.585213	−	0.196294i
$645$	30.5472	+	18.9066i	1.20279	+	0.744448i
$646$	1.45335	+	10.1082i	0.0571811	+	0.397703i
$647$	11.0528	−	24.2022i	0.434530	−	0.951487i	−0.558040	−	0.829814i	$-0.688447\pi$
$647$	11.0528	−	24.2022i	0.434530	−	0.951487i	0.992570	−	0.121674i	$-0.0388261\pi$
$648$	−5.75828	+	6.91680i	−0.226207	+	0.271718i
$649$	−4.71729	−	4.08755i	−0.185170	−	0.160450i
$650$	−7.32778	−	0.874100i	−0.287419	−	0.0342850i
$651$	16.5929	−	14.5218i	0.650325	−	0.569156i
$652$	−13.3588	+	6.10077i	−0.523172	+	0.238925i
$653$	24.4803	+	28.2518i	0.957989	+	1.10558i	0.994341	+	0.106239i	$0.0338807\pi$
$653$	24.4803	+	28.2518i	0.957989	+	1.10558i	−0.0363521	+	0.999339i	$0.511574\pi$
$654$	−8.70071	+	19.3035i	−0.340225	+	0.754828i
$655$	−19.2656	−	21.7003i	−0.752769	−	0.847900i
$656$	−0.314519	−	0.0452210i	−0.0122799	−	0.00176558i
$657$	2.34285	−	8.28062i	0.0914033	−	0.323058i
$658$	−0.633155	−	0.730700i	−0.0246830	−	0.0284857i
$659$	−3.52585	−	7.72053i	−0.137347	−	0.300749i	0.828443	−	0.560074i	$-0.189227\pi$
$659$	−3.52585	−	7.72053i	−0.137347	−	0.300749i	−0.965790	+	0.259325i	$0.916500\pi$
$660$	−2.81622	+	0.0478088i	−0.109621	+	0.00186096i
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.0781093	+	0.996945i	$0.524888\pi$
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.473279	+	0.880912i	$0.656930\pi$
$662$	−20.2113	+	23.3251i	−0.785534	+	0.906554i
$663$	4.01792	−	1.85895i	0.156043	−	0.0721957i
$664$	−14.4253	−	6.58779i	−0.559809	−	0.255656i
$665$	−36.5091	−	22.8467i	−1.41576	−	0.885958i
$666$	−31.9274	+	9.71817i	−1.23716	+	0.376572i
$667$	−32.4293	+	3.41008i	−1.25567	+	0.132039i
$668$	−4.29958			−0.166356
$669$	5.77313	−	1.72615i	0.223202	−	0.0667368i
$670$	0.822039	−	0.387438i	0.0317581	−	0.0149680i
$671$	−0.951655	−	3.24104i	−0.0367382	−	0.125119i
$672$	3.03501	−	4.77423i	0.117078	−	0.184170i
$673$	−10.3983	+	35.4134i	−0.400825	+	1.36509i	0.473948	+	0.880553i	$0.342828\pi$
$673$	−10.3983	+	35.4134i	−0.400825	+	1.36509i	−0.874773	+	0.484532i	$0.838990\pi$
$674$	13.0322	−	8.37530i	0.501982	−	0.322605i
$675$	13.1859	−	22.3860i	0.507527	−	0.861636i
$676$	−7.08663	−	8.17841i	−0.272563	−	0.314554i
$677$	−8.84282	+	13.7597i	−0.339857	+	0.528828i	−0.968548	−	0.248827i	$-0.919955\pi$
$677$	−8.84282	+	13.7597i	−0.339857	+	0.528828i	0.628691	+	0.777656i	$0.283591\pi$
$678$	−16.3675	+	0.0808089i	−0.628590	+	0.00310345i
$679$	−6.20832	+	43.1798i	−0.238253	+	1.65709i
$680$	3.70209	−	1.13561i	0.141969	−	0.0435488i
$681$	22.8445	−	26.6285i	0.875404	−	1.02041i
$682$	1.17753	+	2.57842i	0.0450898	+	0.0987330i
$683$	−11.3707	+	7.30751i	−0.435088	+	0.279614i	−0.739795	−	0.672832i	$-0.765078\pi$
$683$	−11.3707	+	7.30751i	−0.435088	+	0.279614i	0.304707	+	0.952446i	$0.401441\pi$
$684$	−0.174681	−	17.6900i	−0.00667910	−	0.676395i
$685$	0.810341	+	5.19161i	0.0309615	+	0.198361i
$686$	10.4417	−	3.06595i	0.398664	−	0.117058i
$687$	−15.7132	−	4.52967i	−0.599496	−	0.172818i
$688$	−1.32008	−	9.18133i	−0.0503274	−	0.350035i
$689$	−3.63024			−0.138301
$690$	7.35856	+	17.0544i	0.280135	+	0.649249i
$691$	22.9769			0.874082			0.437041	−	0.899442i	$-0.356027\pi$
$691$	22.9769			0.874082			0.437041	+	0.899442i	$0.356027\pi$
$692$	2.27457	+	15.8200i	0.0864661	+	0.601385i
$693$	−0.944449	+	7.06321i	−0.0358767	+	0.268309i
$694$	23.1405	−	6.79466i	0.878401	−	0.257922i
$695$	2.02611	−	0.316248i	0.0768547	−	0.0119960i
$696$	1.61842	−	11.6649i	0.0613461	−	0.442158i
$697$	−0.462921	+	0.297501i	−0.0175344	+	0.0112687i
$698$	2.09425	+	4.58577i	0.0792686	+	0.173574i
$699$	−15.7295	−	13.4943i	−0.594944	−	0.510401i
$700$	−6.42461	+	15.0143i	−0.242827	+	0.567487i
$701$	2.66198	−	18.5145i	0.100542	−	0.699283i	−0.875741	−	0.482782i	$-0.839626\pi$
$701$	2.66198	−	18.5145i	0.100542	−	0.699283i	0.976282	−	0.216501i	$-0.0694645\pi$
$702$	−7.32578	+	2.26943i	−0.276494	+	0.0856539i
$703$	35.4666	−	55.1872i	1.33765	−	2.08142i
$704$	0.476248	+	0.549619i	0.0179493	+	0.0207146i
$705$	−0.143874	+	1.13740i	−0.00541861	+	0.0428371i
$706$	−13.2875	+	8.53936i	−0.500082	+	0.321383i
$707$	−5.13800	+	17.4984i	−0.193234	+	0.658095i
$708$	−12.5455	−	7.97527i	−0.471489	−	0.299729i
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	−0.975960	−	0.217950i	$-0.930063\pi$
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	0.703197	−	0.710995i	$-0.251755\pi$
$710$	−7.68863	−	16.3132i	−0.288549	−	0.612223i
$711$	8.97732	−	4.20742i	0.336676	−	0.157791i
$712$	8.57534			0.321375
$713$	12.7693	−	13.6513i	0.478214	−	0.511244i
$714$	−1.44213	−	9.69033i	−0.0539702	−	0.362652i
$715$	−2.03461	−	1.27322i	−0.0760903	−	0.0476159i
$716$	16.0793	+	7.34317i	0.600912	+	0.274427i
$717$	−15.0067	−	32.4354i	−0.560436	−	1.21132i
$718$	−1.03639	+	1.19605i	−0.0386776	+	0.0446364i
$719$	−9.22894	+	31.4309i	−0.344181	+	1.17217i	0.587599	+	0.809152i	$0.300073\pi$
$719$	−9.22894	+	31.4309i	−0.344181	+	1.17217i	−0.931781	+	0.363022i	$0.881745\pi$
$720$	−6.61741	+	1.09993i	−0.246616	+	0.0409919i
$721$	24.8535	+	54.4216i	0.925593	+	2.02677i
$722$	10.3299	+	11.9214i	0.384439	+	0.443667i
$723$	6.68198	−	14.8248i	0.248506	−	0.551339i
$724$	20.0672	+	2.88522i	0.745790	+	0.107228i
$725$	0.818380	+	33.9864i	0.0303939	+	1.26222i
$726$	16.5345	+	7.45263i	0.613654	+	0.276593i
$727$	7.08273	+	8.17391i	0.262684	+	0.303154i	0.871735	−	0.489977i	$-0.162995\pi$
$727$	7.08273	+	8.17391i	0.262684	+	0.303154i	−0.609051	+	0.793131i	$0.708450\pi$
$728$	4.38512	−	2.00262i	0.162523	−	0.0742219i
$729$	3.04926	−	26.8273i	0.112936	−	0.993602i
$730$	5.35391	−	3.53253i	0.198157	−	0.130745i
$731$	−12.1399	−	10.5193i	−0.449012	−	0.389071i
$732$	−3.37805	−	7.30128i	−0.124856	−	0.269863i
$733$	−1.90844	+	4.17890i	−0.0704898	+	0.154351i	−0.941597	−	0.336742i	$-0.890675\pi$
$733$	−1.90844	+	4.17890i	−0.0704898	+	0.154351i	0.871107	+	0.491093i	$0.163402\pi$
$734$	−4.85103	−	33.7397i	−0.179055	−	1.24535i
$735$	12.0801	+	7.47679i	0.445583	+	0.275785i
$736$	2.15669	−	4.28354i	0.0794965	−	0.157893i
$737$	0.295564			0.0108872
$738$	0.863163	−	0.404541i	0.0317735	−	0.0148914i
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	−0.991043	−	0.133543i	$-0.957365\pi$
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	0.749920	+	0.661529i	$0.230092\pi$
$740$	−22.7501	−	10.0604i	−0.836309	−	0.369829i
$741$	8.08750	−	12.7221i	0.297102	−	0.467356i
$742$	−2.26332	+	7.70816i	−0.0830891	+	0.282976i
$743$	−11.1301	−	17.3188i	−0.408324	−	0.635364i	0.574802	−	0.818292i	$-0.305079\pi$
$743$	−11.1301	−	17.3188i	−0.408324	−	0.635364i	−0.983126	+	0.182928i	$0.941443\pi$
$744$	3.67784	+	5.66118i	0.134836	+	0.207549i
$745$	0.274316	+	22.7874i	0.0100502	+	0.834867i
$746$	9.62282	+	6.18421i	0.352316	+	0.226420i
$747$	47.0216	−	7.23528i	1.72043	−	0.264725i
$748$	1.24661	+	0.179236i	0.0455806	+	0.00655350i
$749$	−18.1351	+	28.2187i	−0.662640	+	1.03109i
$750$	18.3410	−	6.21364i	0.669717	−	0.226890i
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	−0.473176	−	0.880968i	$-0.656892\pi$
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	0.355927	+	0.934514i	$0.384165\pi$
$752$	0.249025	−	0.160039i	0.00908101	−	0.00583601i
$753$	42.3765	+	5.87943i	1.54429	+	0.214258i
$754$	6.57175	−	7.58421i	0.239329	−	0.276201i
$755$	−43.1838	−	19.0965i	−1.57162	−	0.694994i
$756$	0.251365	+	16.9699i	0.00914206	+	0.617189i
$757$	−3.07665	−	21.3986i	−0.111823	−	0.777745i	−0.966145	−	0.258000i	$-0.916936\pi$
$757$	−3.07665	−	21.3986i	−0.111823	−	0.777745i	0.854322	−	0.519744i	$-0.173973\pi$
$758$		−	26.7233i		−	0.970633i
$759$	−0.199880	+	6.03769i	−0.00725517	+	0.219154i
$760$	8.51442	−	10.0685i	0.308851	−	0.365225i
$761$	−20.1120	+	2.89166i	−0.729058	+	0.104823i	−0.496841	−	0.867841i	$-0.665507\pi$
$761$	−20.1120	+	2.89166i	−0.729058	+	0.104823i	−0.232217	+	0.972664i	$0.574598\pi$
$762$	−18.5041	−	5.33419i	−0.670331	−	0.193237i
$763$	11.2492	+	38.3111i	0.407247	+	1.38695i
$764$	0.312184	−	0.360280i	0.0112944	−	0.0130345i
$765$	−7.41337	+	8.94416i	−0.268031	+	0.323377i
$766$	6.98678	+	10.8716i	0.252443	+	0.392808i
$767$	−5.26239	−	11.5230i	−0.190014	−	0.416073i
$768$	1.31458	+	1.12778i	0.0474358	+	0.0406951i
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	−0.828164	−	0.560485i	$-0.810615\pi$
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	0.853867	+	0.520491i	$0.174251\pi$
$770$	−3.97197	+	3.52633i	−0.143140	+	0.127080i
$771$	0.0173200	+	3.50810i	0.000623765	+	0.126341i
$772$	1.78958	−	2.78465i	0.0644085	−	0.100222i
$773$	−3.24542	+	2.81217i	−0.116729	+	0.101147i	−0.711270	−	0.702919i	$-0.751880\pi$
$773$	−3.24542	+	2.81217i	−0.116729	+	0.101147i	0.594540	+

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

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.479764 + 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.20932 - 0.344845i) q^{5} +(1.71562 + 0.238029i) q^{6} +(2.74772 - 1.76585i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.479764 + 1.66428i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.20932 - 0.344845i) q^{5} +(1.71562 + 0.238029i) q^{6} +(2.74772 - 1.76585i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-2.53965 - 1.59692i) q^{9} +(-0.655753 - 2.13775i) q^{10} +(0.103499 - 0.719848i) q^{11} +(-0.00855129 - 1.73203i) q^{12} +(0.797957 - 1.24165i) q^{13} +(-2.13892 - 2.46844i) q^{14} +(-0.486034 + 3.84237i) q^{15} +(0.841254 - 0.540641i) q^{16} +(0.487896 - 1.66162i) q^{17} +(-1.21924 + 2.74107i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(-2.02267 + 0.953313i) q^{20} +(1.62061 + 5.42016i) q^{21} -0.727250 q^{22} +(1.82495 + 4.43504i) q^{23} +(-1.71318 + 0.254958i) q^{24} +(4.76216 - 1.52374i) q^{25} +(-1.34257 - 0.613130i) q^{26} +(3.87616 - 3.46054i) q^{27} +(-2.13892 + 2.46844i) q^{28} +(-1.91557 + 6.52384i) q^{29} +(3.87243 - 0.0657391i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.14837 + 0.517608i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(5.46163 - 4.84886i) q^{35} +(2.88668 + 0.816734i) q^{36} +(7.28503 + 8.40738i) q^{37} +(-5.36407 + 2.44969i) q^{38} +(1.68361 + 1.92372i) q^{39} +(1.23147 + 1.86641i) q^{40} +(-0.240142 - 0.208084i) q^{41} +(5.13435 - 2.37549i) q^{42} +(3.85328 - 8.43752i) q^{43} +(0.103499 + 0.719848i) q^{44} +(-6.16159 - 2.65233i) q^{45} +(4.13018 - 2.43755i) q^{46} +0.296017 q^{47} +(0.496174 + 1.65946i) q^{48} +(1.52381 - 3.33668i) q^{49} +(-2.18596 - 4.49684i) q^{50} +(2.53133 + 1.60918i) q^{51} +(-0.415822 + 1.41616i) q^{52} +(-1.32976 - 2.06915i) q^{53} +(-3.97696 - 3.34422i) q^{54} +(-0.0195746 - 1.62606i) q^{55} +(2.74772 + 1.76585i) q^{56} +(10.2137 - 0.0504267i) q^{57} +(6.73005 + 0.967635i) q^{58} +(4.64023 - 7.22033i) q^{59} +(-0.616174 - 3.82365i) q^{60} +(4.22497 - 1.92948i) q^{61} +(-3.27893 + 2.10724i) q^{62} +(-9.79817 + 0.0967525i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.33477 - 3.01836i) q^{65} +(0.348909 - 1.21035i) q^{66} +(0.0578385 + 0.402276i) q^{67} +1.73177i q^{68} +(-8.25669 + 0.909463i) q^{69} +(-5.57677 - 4.71598i) q^{70} +(7.98308 - 1.14779i) q^{71} +(0.397603 - 2.97354i) q^{72} +(0.808166 + 2.75236i) q^{73} +(7.28503 - 8.40738i) q^{74} +(0.251217 + 8.65661i) q^{75} +(3.18814 + 4.96084i) q^{76} +(-0.986759 - 2.16070i) q^{77} +(1.66454 - 1.94025i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(1.67216 - 1.48455i) q^{80} +(3.89967 + 8.11126i) q^{81} +(-0.171790 + 0.267311i) q^{82} +(-11.9849 + 10.3850i) q^{83} +(-3.08200 - 4.74403i) q^{84} +(0.504916 - 3.83929i) q^{85} +(-8.90001 - 2.61328i) q^{86} +(-9.93847 - 6.31795i) q^{87} +(0.697792 - 0.204890i) q^{88} +(3.56233 - 7.80041i) q^{89} +(-1.74844 + 6.47634i) q^{90} -4.82076i q^{91} +(-3.00053 - 3.74124i) q^{92} +(6.67742 - 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(-5.62165 - 11.9276i) q^{95} +(1.57196 - 0.727290i) q^{96} +(-8.74637 + 10.0938i) q^{97} +(-3.51958 - 1.03344i) q^{98} +(-1.41239 + 1.66288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} + O(q^{10}) \)	\( 240q - 24q^{2} + 2q^{3} - 24q^{4} + 2q^{6} - 24q^{8} - 6q^{9} - 9q^{12} + 11q^{15} - 24q^{16} - 6q^{18} - 4q^{23} + 2q^{24} - 12q^{25} + 2q^{27} + 22q^{30} + 28q^{31} - 24q^{32} - 36q^{35} - 6q^{36} - 4q^{46} + 104q^{47} - 9q^{48} + 70q^{49} + 54q^{50} - 9q^{54} - 26q^{55} - 44q^{57} - 11q^{60} + 44q^{61} + 28q^{62} - 121q^{63} - 24q^{64} + 44q^{65} + 44q^{66} - 102q^{69} - 36q^{70} + 16q^{72} - 82q^{75} + 8q^{77} - 44q^{79} + 74q^{81} - 11q^{84} + 22q^{85} - 93q^{87} - 4q^{92} + 172q^{93} + 16q^{94} + 26q^{95} + 2q^{96} + 4q^{98} + O(q^{100}) \)

Introduction

L-functions

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