LMFDB - Embedded newform 588.2.x.a.55.5

Newspace parameters

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			55.5
Character	$\chi$	$=$	588.55
Dual form			588.2.x.a.139.5

$q$-expansion

$f(q)$	$=$	$q+(-1.20909 + 0.733551i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.923805 - 1.77386i) q^{4} +(-0.0202251 + 0.0419978i) q^{5} +(1.40763 - 0.136302i) q^{6} +(2.50508 - 0.851222i) q^{7} +(0.184253 + 2.82242i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-1.20909 + 0.733551i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.923805 - 1.77386i) q^{4} +(-0.0202251 + 0.0419978i) q^{5} +(1.40763 - 0.136302i) q^{6} +(2.50508 - 0.851222i) q^{7} +(0.184253 + 2.82242i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.00635357 - 0.0656153i) q^{10} +(4.22358 + 3.36820i) q^{11} +(-1.60197 + 1.19737i) q^{12} +(-4.09819 - 3.26819i) q^{13} +(-2.40446 + 2.86681i) q^{14} +(0.0364443 - 0.0290634i) q^{15} +(-2.29317 - 3.27740i) q^{16} +(-1.81779 - 0.414899i) q^{17} +(-1.32737 - 0.487944i) q^{18} -3.64310 q^{19} +(0.0558143 + 0.0746743i) q^{20} +(-2.62633 - 0.319989i) q^{21} +(-7.57745 - 0.974242i) q^{22} +(7.77277 - 1.77408i) q^{23} +(1.05860 - 2.62286i) q^{24} +(3.11609 + 3.90746i) q^{25} +(7.35247 + 0.945317i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(0.804255 - 5.23003i) q^{28} +(0.460848 - 2.01911i) q^{29} +(-0.0227451 + 0.0618741i) q^{30} +6.23384 q^{31} +(5.17679 + 2.28053i) q^{32} +(-2.34391 - 4.86719i) q^{33} +(2.50222 - 0.831791i) q^{34} +(-0.0149160 + 0.122424i) q^{35} +(1.96284 - 0.383725i) q^{36} +(1.79149 - 7.84902i) q^{37} +(4.40485 - 2.67240i) q^{38} +(2.27432 + 4.72268i) q^{39} +(-0.122262 - 0.0493454i) q^{40} +(-1.75191 + 3.63789i) q^{41} +(3.41020 - 1.53965i) q^{42} +(2.31404 + 4.80515i) q^{43} +(9.87648 - 4.38050i) q^{44} +(-0.0454453 + 0.0103726i) q^{45} +(-8.09661 + 7.84675i) q^{46} +(0.371672 - 0.466062i) q^{47} +(0.644061 + 3.94781i) q^{48} +(5.55084 - 4.26476i) q^{49} +(-6.63396 - 2.43866i) q^{50} +(1.45775 + 1.16252i) q^{51} +(-9.58325 + 4.25044i) q^{52} +(0.113587 + 0.497658i) q^{53} +(0.984208 + 1.01555i) q^{54} +(-0.226879 + 0.109259i) q^{55} +(2.86407 + 6.91354i) q^{56} +(3.28232 + 1.58068i) q^{57} +(0.923910 + 2.77934i) q^{58} +(3.00005 - 1.44475i) q^{59} +(-0.0178870 - 0.0914961i) q^{60} +(12.0386 + 2.74773i) q^{61} +(-7.53728 + 4.57284i) q^{62} +(2.22740 + 1.42782i) q^{63} +(-7.93210 + 1.04008i) q^{64} +(0.220143 - 0.106015i) q^{65} +(6.40434 + 4.16549i) q^{66} -9.62227i q^{67} +(-2.41526 + 2.84122i) q^{68} +(-7.77277 - 1.77408i) q^{69} +(-0.0717694 - 0.158963i) q^{70} +(1.82800 - 0.417230i) q^{71} +(-2.09178 + 1.90380i) q^{72} +(7.50927 - 5.98844i) q^{73} +(3.59158 + 10.8043i) q^{74} +(-1.11212 - 4.87252i) q^{75} +(-3.36552 + 6.46236i) q^{76} +(13.4475 + 4.84239i) q^{77} +(-6.21419 - 4.04182i) q^{78} -6.41351i q^{79} +(0.184023 - 0.0300223i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-0.550352 - 5.68366i) q^{82} +(2.99386 + 3.75418i) q^{83} +(-2.99383 + 4.36314i) q^{84} +(0.0541898 - 0.0679518i) q^{85} +(-6.32271 - 4.11240i) q^{86} +(-1.29127 + 1.61920i) q^{87} +(-8.72825 + 12.5413i) q^{88} +(-12.8025 + 10.2097i) q^{89} +(0.0473388 - 0.0458779i) q^{90} +(-13.0482 - 4.69862i) q^{91} +(4.03354 - 15.4267i) q^{92} +(-5.61649 - 2.70476i) q^{93} +(-0.107505 + 0.836153i) q^{94} +(0.0736821 - 0.153002i) q^{95} +(-3.67465 - 4.30081i) q^{96} -6.08284i q^{97} +(-3.58306 + 9.22831i) q^{98} +5.40217i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−1.20909	+	0.733551i	−0.854957	+	0.518699i
$2$	−1.20909	+	0.733551i	−0.854957	+	0.518699i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	0.923805	−	1.77386i	0.461903	−	0.886931i
$5$	−0.0202251	+	0.0419978i	−0.00904493	+	0.0187820i	−0.905442	−	0.424469i	$-0.860461\pi$
$5$	−0.0202251	+	0.0419978i	−0.00904493	+	0.0187820i	0.896397	+	0.443251i	$0.146175\pi$
$6$	1.40763	−	0.136302i	0.574662	−	0.0556449i
$7$	2.50508	−	0.851222i	0.946831	−	0.321732i
$7$	2.50508	−	0.851222i	0.946831	−	0.321732i
$8$	0.184253	+	2.82242i	0.0651434	+	0.997876i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−0.00635357	−	0.0656153i	−0.00200918	−	0.0207494i
$11$	4.22358	+	3.36820i	1.27346	+	1.01555i	0.998536	+	0.0540831i	$0.0172236\pi$
$11$	4.22358	+	3.36820i	1.27346	+	1.01555i	0.274922	+	0.961466i	$0.411348\pi$
$12$	−1.60197	+	1.19737i	−0.462449	+	0.345651i
$13$	−4.09819	−	3.26819i	−1.13663	−	0.906434i	−0.140141	−	0.990132i	$-0.544756\pi$
$13$	−4.09819	−	3.26819i	−1.13663	−	0.906434i	−0.996491	+	0.0836975i	$0.973327\pi$
$14$	−2.40446	+	2.86681i	−0.642618	+	0.766187i
$15$	0.0364443	−	0.0290634i	0.00940989	−	0.00750414i
$16$	−2.29317	−	3.27740i	−0.573292	−	0.819351i
$17$	−1.81779	−	0.414899i	−0.440879	−	0.100628i	−0.00368123	−	0.999993i	$-0.501172\pi$
$17$	−1.81779	−	0.414899i	−0.440879	−	0.100628i	−0.437197	+	0.899366i	$0.644029\pi$
$18$	−1.32737	−	0.487944i	−0.312864	−	0.115010i
$19$	−3.64310			−0.835785			−0.417893	−	0.908496i	$-0.637231\pi$
$19$	−3.64310			−0.835785			−0.417893	+	0.908496i	$0.637231\pi$
$20$	0.0558143	+	0.0746743i	0.0124805	+	0.0166977i
$21$	−2.62633	−	0.319989i	−0.573112	−	0.0698273i
$22$	−7.57745	−	0.974242i	−1.61552	−	0.207709i
$23$	7.77277	−	1.77408i	1.62073	−	0.369922i	0.686654	−	0.726985i	$-0.259079\pi$
$23$	7.77277	−	1.77408i	1.62073	−	0.369922i	0.934080	+	0.357063i	$0.116222\pi$
$24$	1.05860	−	2.62286i	0.216085	−	0.535388i
$25$	3.11609	+	3.90746i	0.623219	+	0.781492i
$26$	7.35247	+	0.945317i	1.44194	+	0.185392i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	0.804255	−	5.23003i	0.151990	−	0.988382i
$29$	0.460848	−	2.01911i	0.0855773	−	0.374938i	−0.913945	−	0.405838i	$-0.866980\pi$
$29$	0.460848	−	2.01911i	0.0855773	−	0.374938i	0.999523	+	0.0308990i	$0.00983703\pi$
$30$	−0.0227451	+	0.0618741i	−0.00415266	+	0.0112966i
$31$	6.23384			1.11963			0.559815	−	0.828618i	$-0.310872\pi$
$31$	6.23384			1.11963			0.559815	+	0.828618i	$0.310872\pi$
$32$	5.17679	+	2.28053i	0.915137	+	0.403144i
$33$	−2.34391	−	4.86719i	−0.408023	−	0.847268i
$34$	2.50222	−	0.831791i	0.429128	−	0.142651i
$35$	−0.0149160	+	0.122424i	−0.00252126	+	0.0206934i
$36$	1.96284	−	0.383725i	0.327141	−	0.0639541i
$37$	1.79149	−	7.84902i	0.294519	−	1.29037i	−0.583645	−	0.812009i	$-0.698374\pi$
$37$	1.79149	−	7.84902i	0.294519	−	1.29037i	0.878163	−	0.478361i	$-0.158769\pi$
$38$	4.40485	−	2.67240i	0.714561	−	0.433521i
$39$	2.27432	+	4.72268i	0.364183	+	0.756234i
$40$	−0.122262	−	0.0493454i	−0.0193313	−	0.00780220i
$41$	−1.75191	+	3.63789i	−0.273603	+	0.568142i	−0.991815	−	0.127682i	$-0.959246\pi$
$41$	−1.75191	+	3.63789i	−0.273603	+	0.568142i	0.718212	+	0.695824i	$0.244961\pi$
$42$	3.41020	−	1.53965i	0.526205	−	0.237573i
$43$	2.31404	+	4.80515i	0.352888	+	0.732779i	0.999550	−	0.0299974i	$-0.00954991\pi$
$43$	2.31404	+	4.80515i	0.352888	+	0.732779i	−0.646662	+	0.762777i	$0.723836\pi$
$44$	9.87648	−	4.38050i	1.48894	−	0.660385i
$45$	−0.0454453	+	0.0103726i	−0.00677459	+	0.00154626i
$46$	−8.09661	+	7.84675i	−1.19378	+	1.15694i
$47$	0.371672	−	0.466062i	0.0542140	−	0.0679822i	−0.753985	−	0.656891i	$-0.771871\pi$
$47$	0.371672	−	0.466062i	0.0542140	−	0.0679822i	0.808199	+	0.588909i	$0.200442\pi$
$48$	0.644061	+	3.94781i	0.0929622	+	0.569817i
$49$	5.55084	−	4.26476i	0.792978	−	0.609251i
$50$	−6.63396	−	2.43866i	−0.938184	−	0.344879i
$51$	1.45775	+	1.16252i	0.204126	+	0.162785i
$52$	−9.58325	+	4.25044i	−1.32896	+	0.589430i
$53$	0.113587	+	0.497658i	0.0156024	+	0.0683586i	0.982130	−	0.188205i	$-0.0602669\pi$
$53$	0.113587	+	0.497658i	0.0156024	+	0.0683586i	−0.966527	+	0.256563i	$0.917410\pi$
$54$	0.984208	+	1.01555i	0.133934	+	0.138198i
$55$	−0.226879	+	0.109259i	−0.0305924	+	0.0147325i
$56$	2.86407	+	6.91354i	0.382728	+	0.923861i
$57$	3.28232	+	1.58068i	0.434754	+	0.209367i
$58$	0.923910	+	2.77934i	0.121315	+	0.364945i
$59$	3.00005	−	1.44475i	0.390573	−	0.188090i	−0.228282	−	0.973595i	$-0.573311\pi$
$59$	3.00005	−	1.44475i	0.390573	−	0.188090i	0.618856	+	0.785505i	$0.287597\pi$
$60$	−0.0178870	−	0.0914961i	−0.00230920	−	0.0118121i
$61$	12.0386	+	2.74773i	1.54138	+	0.351811i	0.906974	−	0.421187i	$-0.138386\pi$
$61$	12.0386	+	2.74773i	1.54138	+	0.351811i	0.634409	+	0.772998i	$0.281244\pi$
$62$	−7.53728	+	4.57284i	−0.957235	+	0.580751i
$63$	2.22740	+	1.42782i	0.280626	+	0.179889i
$64$	−7.93210	+	1.04008i	−0.991513	+	0.130010i
$65$	0.220143	−	0.106015i	0.0273054	−	0.0131496i
$66$	6.40434	+	4.16549i	0.788319	+	0.512737i
$67$		−	9.62227i		−	1.17555i	−0.809025	−	0.587774i	$-0.800004\pi$
$67$		−	9.62227i		−	1.17555i	0.809025	−	0.587774i	$-0.199996\pi$
$68$	−2.41526	+	2.84122i	−0.292893	+	0.344549i
$69$	−7.77277	−	1.77408i	−0.935731	−	0.213575i
$70$	−0.0717694	−	0.158963i	−0.00857809	−	0.0189998i
$71$	1.82800	−	0.417230i	0.216944	−	0.0495161i	−0.112667	−	0.993633i	$-0.535939\pi$
$71$	1.82800	−	0.417230i	0.216944	−	0.0495161i	0.329611	+	0.944117i	$0.393082\pi$
$72$	−2.09178	+	1.90380i	−0.246518	+	0.224366i
$73$	7.50927	−	5.98844i	0.878894	−	0.700894i	−0.0762337	−	0.997090i	$-0.524290\pi$
$73$	7.50927	−	5.98844i	0.878894	−	0.700894i	0.955127	+	0.296196i	$0.0957181\pi$
$74$	3.59158	+	10.8043i	0.417513	+	1.25598i
$75$	−1.11212	−	4.87252i	−0.128417	−	0.562630i
$76$	−3.36552	+	6.46236i	−0.386051	+	0.741284i
$77$	13.4475	+	4.84239i	1.53248	+	0.551842i
$78$	−6.21419	−	4.04182i	−0.703618	−	0.457646i
$79$		−	6.41351i		−	0.721576i	−0.932648	−	0.360788i	$-0.882508\pi$
$79$		−	6.41351i		−	0.721576i	0.932648	−	0.360788i	$-0.117492\pi$
$80$	0.184023	−	0.0300223i	0.0205744	−	0.00335660i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−0.550352	−	5.68366i	−0.0607762	−	0.627655i
$83$	2.99386	+	3.75418i	0.328619	+	0.412075i	0.918504	−	0.395412i	$-0.129398\pi$
$83$	2.99386	+	3.75418i	0.328619	+	0.412075i	−0.589885	+	0.807487i	$0.700827\pi$
$84$	−2.99383	+	4.36314i	−0.326654	+	0.476057i
$85$	0.0541898	−	0.0679518i	0.00587771	−	0.00737041i
$86$	−6.32271	−	4.11240i	−0.681796	−	0.443452i
$87$	−1.29127	+	1.61920i	−0.138438	+	0.173596i
$88$	−8.72825	+	12.5413i	−0.930435	+	1.33691i
$89$	−12.8025	+	10.2097i	−1.35706	+	1.08222i	−0.368794	+	0.929511i	$0.620229\pi$
$89$	−12.8025	+	10.2097i	−1.35706	+	1.08222i	−0.988271	+	0.152712i	$0.951199\pi$
$90$	0.0473388	−	0.0458779i	0.00498994	−	0.00483596i
$91$	−13.0482	−	4.69862i	−1.36783	−	0.492549i
$92$	4.03354	−	15.4267i	0.420526	−	1.60835i
$93$	−5.61649	−	2.70476i	−0.582403	−	0.280471i
$94$	−0.107505	+	0.836153i	−0.0110883	+	0.0862426i
$95$	0.0736821	−	0.153002i	0.00755962	−	0.0156977i
$96$	−3.67465	−	4.30081i	−0.375042	−	0.438950i
$97$		−	6.08284i		−	0.617618i	−0.951124	−	0.308809i	$-0.900070\pi$
$97$		−	6.08284i		−	0.617618i	0.951124	−	0.308809i	$-0.0999305\pi$
$98$	−3.58306	+	9.22831i	−0.361944	+	0.932200i
$99$			5.40217i			0.542938i
$100$	9.80995	−	1.91779i	0.980995	−	0.191779i
$101$	2.27205	−	4.71797i	0.226078	−	0.469455i	−0.756816	−	0.653628i	$-0.773246\pi$
$101$	2.27205	−	4.71797i	0.226078	−	0.469455i	0.982894	+	0.184173i	$0.0589605\pi$
$102$	−2.61533	−	0.336256i	−0.258956	−	0.0332943i
$103$	15.4641	+	7.44714i	1.52373	+	0.733788i	0.993475	−	0.114052i	$-0.0363830\pi$
$103$	15.4641	+	7.44714i	1.52373	+	0.733788i	0.530252	+	0.847840i	$0.322097\pi$
$104$	8.46911	−	12.1690i	0.830465	−	1.19327i
$105$	0.0665566	−	0.103828i	0.00649526	−	0.0101326i
$106$	−0.502395	−	0.518392i	−0.0487969	−	0.0503507i
$107$	4.24003	−	3.38131i	0.409899	−	0.326883i	−0.396737	−	0.917932i	$-0.629857\pi$
$107$	4.24003	−	3.38131i	0.409899	−	0.326883i	0.806636	+	0.591049i	$0.201286\pi$
$108$	−1.93495	−	0.505922i	−0.186191	−	0.0486824i
$109$	−10.5405	+	13.2174i	−1.00960	+	1.26600i	−0.0459163	+	0.998945i	$0.514621\pi$
$109$	−10.5405	+	13.2174i	−1.00960	+	1.26600i	−0.963682	+	0.267051i	$0.913951\pi$
$110$	0.194171	−	0.298532i	0.0185134	−	0.0284639i
$111$	−5.01963	+	6.29442i	−0.476443	+	0.597440i
$112$	−8.53437	−	6.25816i	−0.806422	−	0.591341i
$113$	−8.37381	−	10.5004i	−0.787742	−	0.987797i	−0.999944	−	0.0105709i	$-0.996635\pi$
$113$	−8.37381	−	10.5004i	−0.787742	−	0.987797i	0.212203	−	0.977226i	$-0.431936\pi$
$114$	−5.12814	+	0.496561i	−0.480295	+	0.0465072i
$115$	−0.0826972	+	0.362320i	−0.00771156	+	0.0337865i
$116$	−3.15588	−	2.68274i	−0.293016	−	0.249086i
$117$		−	5.24178i		−	0.484602i
$118$	−2.56754	+	3.94752i	−0.236361	+	0.363399i
$119$	−4.90688	+	0.507988i	−0.449813	+	0.0465672i
$120$	0.0887441	+	0.0975062i	0.00810119	+	0.00890106i
$121$	4.04619	+	17.7275i	0.367836	+	1.61159i
$122$	−16.5714	+	5.50866i	−1.50030	+	0.498731i
$123$	3.15684	−	2.51750i	0.284643	−	0.226995i
$124$	5.75885	−	11.0580i	0.517160	−	0.993034i
$125$	−0.454355	+	0.103704i	−0.0406387	+	0.00927552i
$126$	−3.74052	−	0.0924527i	−0.333232	−	0.00823635i
$127$	−16.5222	−	3.77108i	−1.46611	−	0.334629i	−0.586352	−	0.810057i	$-0.699436\pi$
$127$	−16.5222	−	3.77108i	−1.46611	−	0.334629i	−0.879755	+	0.475427i	$0.842293\pi$
$128$	8.82768	−	7.07616i	0.780264	−	0.625450i
$129$		−	5.33332i		−	0.469573i
$130$	−0.188406	+	0.289669i	−0.0165243	+	0.0254056i
$131$	0.352038	−	0.169532i	0.0307577	−	0.0148121i	−0.418442	−	0.908244i	$-0.637424\pi$
$131$	0.352038	−	0.169532i	0.0307577	−	0.0148121i	0.449199	+	0.893432i	$0.351709\pi$
$132$	−10.7990	−	0.338554i	−0.939935	−	0.0294673i
$133$	−9.12626	+	3.10109i	−0.791348	+	0.268899i
$134$	7.05843	+	11.6342i	0.609756	+	1.00504i
$135$	0.0454453	+	0.0103726i	0.00391131	+	0.000892732i
$136$	0.836084	−	5.20701i	0.0716936	−	0.446497i
$137$	4.71687	−	2.27152i	0.402989	−	0.194069i	−0.221399	−	0.975183i	$-0.571062\pi$
$137$	4.71687	−	2.27152i	0.402989	−	0.194069i	0.624389	+	0.781114i	$0.285348\pi$
$138$	10.6994	−	3.55669i	0.910791	−	0.302766i
$139$	−10.8589	−	5.22936i	−0.921039	−	0.443549i	−0.0875968	−	0.996156i	$-0.527919\pi$
$139$	−10.8589	−	5.22936i	−0.921039	−	0.443549i	−0.833442	+	0.552607i	$0.813633\pi$
$140$	0.203384	+	0.139555i	0.0171890	+	0.0117945i
$141$	−0.537082	+	0.258645i	−0.0452305	+	0.0217818i
$142$	−1.90416	+	1.84540i	−0.159794	+	0.154863i
$143$	−6.30112	−	27.6070i	−0.526926	−	2.30861i
$144$	1.13261	−	3.83630i	0.0943842	−	0.319692i
$145$	0.0754773	+	0.0601912i	0.00626805	+	0.00499860i
$146$	−4.68657	+	12.7490i	−0.387863	+	1.05512i
$147$	−6.85155	+	1.43399i	−0.565106	+	0.118274i
$148$	−12.2681	−	10.4288i	−1.00843	−	0.857243i
$149$	−12.8149	+	16.0694i	−1.04984	+	1.31646i	−0.103024	+	0.994679i	$0.532852\pi$
$149$	−12.8149	+	16.0694i	−1.04984	+	1.31646i	−0.946815	+	0.321778i	$0.895720\pi$
$150$	4.91890	+	5.07553i	0.401627	+	0.414415i
$151$	12.4520	−	2.84209i	1.01333	−	0.231286i	0.316554	−	0.948574i	$-0.397474\pi$
$151$	12.4520	−	2.84209i	1.01333	−	0.231286i	0.696776	+	0.717288i	$0.254617\pi$
$152$	−0.671254	−	10.2824i	−0.0544459	−	0.834010i
$153$	−0.808992	−	1.67989i	−0.0654032	−	0.135811i
$154$	−19.8114	+	4.00953i	−1.59645	+	0.323097i
$155$	−0.126080	+	0.261807i	−0.0101270	+	0.0210289i
$156$	10.4784	+	0.328502i	0.838944	+	0.0263012i
$157$	−7.88108	−	16.3652i	−0.628978	−	1.30609i	−0.935198	−	0.354126i	$-0.884778\pi$
$157$	−7.88108	−	16.3652i	−0.628978	−	1.30609i	0.306219	−	0.951961i	$-0.400936\pi$
$158$	4.70464	+	7.75452i	0.374281	+	0.616917i
$159$	0.113587	−	0.497658i	0.00900805	−	0.0394669i
$160$	−0.200478	+	0.171290i	−0.0158492	+	0.0135417i
$161$	17.9613	−	11.0606i	1.41555	−	0.871695i
$162$	−0.446111	−	1.34201i	−0.0350498	−	0.105438i
$163$	0.749849	+	1.55708i	0.0587327	+	0.121960i	0.928269	−	0.371909i	$-0.121297\pi$
$163$	0.749849	+	1.55708i	0.0587327	+	0.121960i	−0.869537	+	0.493869i	$0.835582\pi$
$164$	4.83468	+	6.46835i	0.377525	+	0.505093i
$165$	0.251817			0.0196039
$166$	−6.37374	−	2.34300i	−0.494698	−	0.181852i
$167$	−5.01762	+	21.9836i	−0.388275	+	1.70114i	0.282320	+	0.959320i	$0.408896\pi$
$167$	−5.01762	+	21.9836i	−0.388275	+	1.70114i	−0.670595	+	0.741823i	$0.733961\pi$
$168$	0.419233	−	7.47156i	0.0323445	−	0.576444i
$169$	3.22126	+	14.1133i	0.247789	+	1.08564i
$170$	−0.0156743	+	0.121911i	−0.00120216	+	0.00935014i
$171$	−2.27144	−	2.84829i	−0.173701	−	0.217814i
$172$	10.6614	+	0.334239i	0.812924	+	0.0254855i
$173$	−15.7733	+	3.60016i	−1.19922	+	0.273715i	−0.775070	−	0.631875i	$-0.782286\pi$
$173$	−15.7733	+	3.60016i	−1.19922	+	0.273715i	−0.424154	+	0.905590i	$0.639429\pi$
$174$	0.373495	−	2.90497i	0.0283146	−	0.220225i
$175$	11.1322	+	7.13601i	0.841513	+	0.539431i
$176$	1.35355	−	21.5662i	0.102028	−	1.62562i
$177$	−3.32980			−0.250283
$178$	7.99011	−	21.7357i	0.598884	−	1.62916i
$179$	0.240257	+	0.0548370i	0.0179576	+	0.00409871i	0.231490	−	0.972837i	$-0.425640\pi$
$179$	0.240257	+	0.0548370i	0.0179576	+	0.00409871i	−0.213533	+	0.976936i	$0.568497\pi$
$180$	−0.0235831	+	0.0901960i	−0.00175778	+	0.00672281i
$181$	−5.83782	+	4.65550i	−0.433921	+	0.346041i	−0.815963	−	0.578104i	$-0.803793\pi$
$181$	−5.83782	+	4.65550i	−0.433921	+	0.346041i	0.382041	+	0.924145i	$0.375221\pi$
$182$	19.2232	−	3.89049i	1.42492	−	0.288382i
$183$	−9.65420	−	7.69896i	−0.713659	−	0.569124i
$184$	6.43937	+	21.6111i	0.474716	+	1.59319i
$185$	0.293409	+	0.233986i	0.0215718	+	0.0172030i
$186$	8.77493	−	0.849682i	0.643409	−	0.0623017i
$187$	−6.28013	−	7.87503i	−0.459248	−	0.575879i
$188$	−0.483377	−	1.08985i	−0.0352539	−	0.0794852i
$189$	−1.38731	−	2.25286i	−0.100912	−	0.163871i
$190$	0.0231467	+	0.239044i	0.00167924	+	0.0173420i
$191$	−0.526785	+	1.09388i	−0.0381168	+	0.0791504i	−0.919158	−	0.393890i	$-0.871129\pi$
$191$	−0.526785	+	1.09388i	−0.0381168	+	0.0791504i	0.881041	+	0.473040i	$0.156843\pi$
$192$	7.59785	+	2.50453i	0.548328	+	0.180749i
$193$	9.04236	+	4.35457i	0.650884	+	0.313449i	0.730031	−	0.683414i	$-0.239506\pi$
$193$	9.04236	+	4.35457i	0.650884	+	0.313449i	−0.0791475	+	0.996863i	$0.525220\pi$
$194$	4.46207	+	7.35471i	0.320358	+	0.528037i
$195$	−0.244340			−0.0174976
$196$	−2.43719	−	13.7862i	−0.174085	−	0.984731i
$197$	−11.0226			−0.785329			−0.392664	−	0.919682i	$-0.628447\pi$
$197$	−11.0226			−0.785329			−0.392664	+	0.919682i	$0.628447\pi$
$198$	−3.96277	−	6.53172i	−0.281622	−	0.464189i
$199$	−7.21398	−	3.47407i	−0.511386	−	0.246270i	0.160351	−	0.987060i	$-0.448737\pi$
$199$	−7.21398	−	3.47407i	−0.511386	−	0.246270i	−0.671737	+	0.740790i	$0.734452\pi$
$200$	−10.4543	+	9.51489i	−0.739233	+	0.672804i
$201$	−4.17495	+	8.66937i	−0.294478	+	0.611490i
$202$	0.713750	+	7.37112i	0.0502193	+	0.518630i
$203$	−0.564247	−	5.45030i	−0.0396023	−	0.382536i
$204$	3.40883	−	1.51191i	0.238666	−	0.105855i
$205$	−0.117351	−	0.147153i	−0.00819613	−	0.0102776i
$206$	−24.1604	+	2.33947i	−1.68334	+	0.162998i
$207$	6.23328	+	4.97087i	0.433243	+	0.345499i
$208$	−1.31336	+	20.9259i	−0.0910653	+	1.45095i
$209$	−15.3870	−	12.2707i	−1.06434	−	0.848781i
$210$	−0.00430960	+	0.174361i	−0.000297391	+	0.0120320i
$211$	−2.57719	+	2.05524i	−0.177421	+	0.141489i	−0.708174	−	0.706038i	$-0.750481\pi$
$211$	−2.57719	+	2.05524i	−0.177421	+	0.141489i	0.530753	+	0.847527i	$0.321909\pi$
$212$	0.987709	+	0.258251i	0.0678361	+	0.0177368i
$213$	−1.82800	−	0.417230i	−0.125253	−	0.0285881i
$214$	−2.64622	+	7.19859i	−0.180892	+	0.492085i
$215$	−0.248608			−0.0169549
$216$	2.71066	−	0.807681i	0.184437	−	0.0549557i
$217$	15.6163	−	5.30638i	1.06010	−	0.360220i
$218$	3.04882	−	23.7131i	0.206492	−	1.60605i
$219$	−9.36391	+	2.13725i	−0.632754	+	0.144422i
$220$	−0.0157814	+	0.503387i	−0.00106398	+	0.0339383i
$221$	6.09367	+	7.64122i	0.409905	+	0.514004i
$222$	1.45192	−	11.2927i	0.0974462	−	0.757916i
$223$	3.49760	+	15.3240i	0.234217	+	1.02617i	0.946100	+	0.323874i	$0.104985\pi$
$223$	3.49760	+	15.3240i	0.234217	+	1.02617i	−0.711883	+	0.702298i	$0.752158\pi$
$224$	14.9095	+	1.30630i	0.996184	+	0.0872806i
$225$	−1.11212	+	4.87252i	−0.0741414	+	0.324835i
$226$	17.8273	+	6.55336i	1.18585	+	0.435923i
$227$	−14.8216			−0.983742			−0.491871	−	0.870668i	$-0.663687\pi$
$227$	−14.8216			−0.983742			−0.491871	+	0.870668i	$0.663687\pi$
$228$	5.83614	−	4.36214i	0.386508	−	0.288890i
$229$	5.04858	+	10.4835i	0.333619	+	0.692768i	0.998533	−	0.0541526i	$-0.0172458\pi$
$229$	5.04858	+	10.4835i	0.333619	+	0.692768i	−0.664913	+	0.746921i	$0.731531\pi$
$230$	−0.165792	−	0.498741i	−0.0109320	−	0.0328860i
$231$	−10.0147	−	10.1975i	−0.658922	−	0.670946i
$232$	5.78368	+	0.928678i	0.379717	+	0.0609707i
$233$	−2.35978	+	10.3389i	−0.154594	+	0.677322i	0.836920	+	0.547325i	$0.184354\pi$
$233$	−2.35978	+	10.3389i	−0.154594	+	0.677322i	−0.991514	+	0.129997i	$0.958503\pi$
$234$	3.84511	+	6.33779i	0.251363	+	0.414314i
$235$	0.0120565	+	0.0250356i	0.000786479	+	0.00163314i
$236$	0.208679	−	6.65634i	0.0135838	−	0.433291i
$237$	−2.78272	+	5.77837i	−0.180757	+	0.375346i
$238$	5.56023	−	4.21365i	0.360416	−	0.273130i
$239$	8.65838	+	17.9793i	0.560064	+	1.16299i	0.968226	+	0.250076i	$0.0804555\pi$
$239$	8.65838	+	17.9793i	0.560064	+	1.16299i	−0.408162	+	0.912909i	$0.633830\pi$
$240$	−0.178825	−	0.0527956i	−0.0115431	−	0.00340794i
$241$	18.2252	−	4.15979i	1.17399	−	0.267956i	0.409329	−	0.912387i	$-0.365763\pi$
$241$	18.2252	−	4.15979i	1.17399	−	0.267956i	0.764662	+	0.644431i	$0.222906\pi$
$242$	−17.8963	−	18.4661i	−1.15042	−	1.18705i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	15.9954	−	18.8164i	1.02400	−	1.20460i
$245$	0.0668442	+	0.319378i	0.00427052	+	0.0204043i
$246$	−1.97020	+	5.35959i	−0.125615	+	0.341715i
$247$	14.9301	+	11.9064i	0.949981	+	0.757584i
$248$	1.14861	+	17.5945i	0.0729365	+	1.11725i
$249$	−1.06850	−	4.68139i	−0.0677132	−	0.296671i
$250$	0.473285	−	0.458680i	0.0299331	−	0.0290094i
$251$	−14.3874	+	6.92863i	−0.908127	+	0.437331i	−0.828818	−	0.559519i	$-0.810986\pi$
$251$	−14.3874	+	6.92863i	−0.908127	+	0.437331i	−0.0793098	+	0.996850i	$0.525272\pi$
$252$	4.59044	−	2.63208i	0.289171	−	0.165805i
$253$	38.8044	+	18.6872i	2.43961	+	1.17486i
$254$	22.7431	−	7.56029i	1.42703	−	0.474375i
$255$	−0.0783065	+	0.0377104i	−0.00490374	+	0.00236152i
$256$	−5.48276	+	15.0313i	−0.342672	+	0.939455i
$257$	13.7431	+	3.13677i	0.857270	+	0.195666i	0.628495	−	0.777813i	$-0.283671\pi$
$257$	13.7431	+	3.13677i	0.857270	+	0.195666i	0.228774	+	0.973480i	$0.426528\pi$
$258$	3.91226	+	6.44847i	0.243567	+	0.401464i
$259$	−2.19344	−	21.1874i	−0.136294	−	1.31652i
$260$	0.0153128	−	0.488441i	0.000949660	−	0.0302918i
$261$	1.86593	−	0.898587i	0.115498	−	0.0556211i
$262$	−0.301285	+	0.463218i	−0.0186135	+	0.0286177i
$263$		−	17.2157i		−	1.06156i	−0.847509	−	0.530781i	$-0.821898\pi$
$263$		−	17.2157i		−	1.06156i	0.847509	−	0.530781i	$-0.178102\pi$
$264$	13.3054	−	7.51230i	0.818889	−	0.462350i
$265$	−0.0231979	−	0.00529476i	−0.00142503	−	0.000325255i
$266$	8.75968	−	10.4441i	0.537091	−	0.640368i
$267$	15.9645	−	3.64379i	0.977011	−	0.222996i
$268$	−17.0686	−	8.88910i	−1.04263	−	0.542988i
$269$	−0.966429	+	0.770701i	−0.0589242	+	0.0469905i	−0.652509	−	0.757781i	$-0.726284\pi$
$269$	−0.966429	+	0.770701i	−0.0589242	+	0.0469905i	0.593585	+	0.804771i	$0.297712\pi$
$270$	−0.0625564	+	0.0207951i	−0.00380706	+	0.00126555i
$271$	1.98137	+	8.68095i	0.120360	+	0.527330i	0.998777	+	0.0494363i	$0.0157425\pi$
$271$	1.98137	+	8.68095i	0.120360	+	0.527330i	−0.878418	+	0.477894i	$0.841400\pi$
$272$	2.80871	+	6.90906i	0.170303	+	0.418923i
$273$	9.71740	+	9.89473i	0.588124	+	0.598856i
$274$	−4.03685	+	6.20655i	−0.243875	+	0.374951i
$275$			26.9991i			1.62811i
$276$	−10.3275	+	12.1489i	−0.621642	+	0.731278i
$277$	−0.652312	+	2.85797i	−0.0391937	+	0.171719i	−0.990737	−	0.135797i	$-0.956640\pi$
$277$	−0.652312	+	2.85797i	−0.0391937	+	0.171719i	0.951543	+	0.307516i	$0.0994976\pi$
$278$	16.9654	−	1.64277i	1.01752	−	0.0985268i
$279$	3.88673	+	4.87381i	0.232693	+	0.291787i
$280$	−0.348280	−	0.0195421i	−0.0208137	−	0.00116787i
$281$	2.02682	−	2.54155i	0.120910	−	0.151616i	−0.717693	−	0.696360i	$-0.754802\pi$
$281$	2.02682	−	2.54155i	0.120910	−	0.151616i	0.838602	+	0.544744i	$0.183373\pi$
$282$	0.459652	−	0.706703i	0.0273719	−	0.0420835i
$283$	−15.0553	+	18.8788i	−0.894946	+	1.12223i	0.0969649	+	0.995288i	$0.469087\pi$
$283$	−15.0553	+	18.8788i	−0.894946	+	1.12223i	−0.991911	+	0.126939i	$0.959485\pi$
$284$	0.948611	−	3.62806i	0.0562897	−	0.215286i
$285$	−0.132771	+	0.105881i	−0.00786465	+	0.00627185i
$286$	27.8698	+	28.7572i	1.64797	+	1.70045i
$287$	−1.29203	+	10.6045i	−0.0762664	+	0.625961i
$288$	1.44469	+	5.46927i	0.0851293	+	0.322280i
$289$	−12.1843	−	5.86763i	−0.716721	−	0.345155i
$290$	−0.135412	−	0.0174101i	−0.00795169	−	0.00102236i
$291$	−2.63924	+	5.48045i	−0.154715	+	0.321269i
$292$	−3.68557	−	18.8526i	−0.215681	−	1.10326i
$293$		−	21.4997i		−	1.25603i	−0.778202	−	0.628014i	$-0.783868\pi$
$293$		−	21.4997i		−	1.25603i	0.778202	−	0.628014i	$-0.216132\pi$
$294$	7.23224	−	6.75979i	0.421793	−	0.394239i
$295$			0.155216i			0.00903701i
$296$	22.4833	+	3.61012i	1.30682	+	0.209834i
$297$	2.34391	−	4.86719i	0.136008	−	0.282423i
$298$	3.70668	−	28.8298i	0.214722	−	1.67006i
$299$	−37.6523	−	18.1324i	−2.17749	−	1.04862i
$300$	−9.67056	−	2.52851i	−0.558330	−	0.145984i
$301$	9.88711	+	10.0675i	0.569883	+	0.580283i
$302$	−12.9708	+	12.5705i	−0.746386	+	0.723353i
$303$	−4.09410	+	3.26493i	−0.235200	+	0.187566i
$304$	8.35425	+	11.9399i	0.479149	+	0.684802i
$305$	−0.358880	+	0.450021i	−0.0205494	+	0.0257681i
$306$	2.21043	+	1.43770i	0.126362	+	0.0821880i
$307$	1.05044	−	1.31721i	0.0599516	−	0.0751769i	−0.750952	−	0.660357i	$-0.770405\pi$
$307$	1.05044	−	1.31721i	0.0599516	−	0.0751769i	0.810903	+	0.585180i	$0.198976\pi$
$308$	21.0126	−	19.3806i	1.19730	−	1.10431i
$309$	−10.7015	−	13.4193i	−0.608788	−	0.763396i
$310$	−0.0396071	−	0.409035i	−0.00224953	−	0.0232316i
$311$	−6.08177	+	26.6460i	−0.344865	+	1.51095i	0.443797	+	0.896127i	$0.353631\pi$
$311$	−6.08177	+	26.6460i	−0.344865	+	1.51095i	−0.788662	+	0.614827i	$0.789226\pi$
$312$	−12.9103	+	7.28926i	−0.730903	+	0.412673i
$313$		−	16.2824i		−	0.920338i	−0.887831	−	0.460169i	$-0.847789\pi$
$313$		−	16.2824i		−	0.920338i	0.887831	−	0.460169i	$-0.152211\pi$
$314$	21.5337	+	14.0059i	1.21522	+	0.790397i
$315$	−0.105015	+	0.0646683i	−0.00591691	+	0.00364364i
$316$	−11.3767	−	5.92483i	−0.639988	−	0.333298i
$317$	−3.86046	−	16.9138i	−0.216825	−	0.949971i	−0.959807	−	0.280660i	$-0.909447\pi$
$317$	−3.86046	−	16.9138i	−0.216825	−	0.949971i	0.742982	−	0.669311i	$-0.233411\pi$
$318$	0.227720	+	0.685036i	0.0127699	+	0.0384149i
$319$	8.74717	−	6.97564i	0.489748	−	0.390561i
$320$	0.116746	−	0.354167i	0.00652632	−	0.0197985i
$321$	−5.28722	+	1.20677i	−0.295104	+	0.0673556i
$322$	−13.6033	+	26.5487i	−0.758083	+	1.47950i
$323$	6.62240	+	1.51152i	0.368480	+	0.0841032i
$324$	1.52382	+	1.29536i	0.0846567	+	0.0719647i
$325$		−	26.1975i		−	1.45318i
$326$	−2.04883	−	1.33260i	−0.113474	−	0.0738057i
$327$	15.2315	−	7.33510i	0.842303	−	0.405632i
$328$	−10.5904	−	4.27434i	−0.584759	−	0.236011i
$329$	0.534346	−	1.48390i	0.0294595	−	0.0818100i
$330$	−0.304470	+	0.184721i	−0.0167605	+	0.0101685i
$331$	15.6987	+	3.58313i	0.862879	+	0.196947i	0.630986	−	0.775794i	$-0.282651\pi$
$331$	15.6987	+	3.58313i	0.862879	+	0.196947i	0.231894	+	0.972741i	$0.425508\pi$
$332$	9.42514	−	1.84256i	0.517272	−	0.101124i
$333$	7.25358	−	3.49314i	0.397494	−	0.191423i
$334$	−10.0594	−	30.2609i	−0.550423	−	1.65580i
$335$	0.404114	+	0.194611i	0.0220791	+	0.0106327i
$336$	4.97388	+	9.34133i	0.271348	+	0.509611i
$337$	−29.1283	+	14.0275i	−1.58672	+	0.764124i	−0.998990	−	0.0449324i	$-0.985693\pi$
$337$	−29.1283	+	14.0275i	−1.58672	+	0.764124i	−0.587730	+	0.809057i	$0.699978\pi$
$338$	−14.2476	−	14.7013i	−0.774968	−	0.799644i
$339$	2.98858	+	13.0938i	0.162317	+	0.711158i
$340$	−0.0704763	−	0.158899i	−0.00382212	−	0.00861753i
$341$	26.3291	+	20.9968i	1.42580	+	1.13704i
$342$	4.83575	+	1.77763i	0.261487	+	0.0961233i
$343$	10.2750	−	15.4085i	0.554801	−	0.831983i
$344$	−13.1358	+	7.41656i	−0.708234	+	0.399874i
$345$	0.231712	−	0.290558i	0.0124750	−	0.0156431i
$346$	16.4305	−	15.9235i	0.883310	−	0.856051i
$347$	−22.3555	+	5.10249i	−1.20010	+	0.273916i	−0.775432	−	0.631431i	$-0.782468\pi$
$347$	−22.3555	+	5.10249i	−1.20010	+	0.273916i	−0.424672	+	0.905347i	$0.639611\pi$
$348$	1.67935	+	3.78635i	0.0900227	+	0.202970i
$349$	−7.36603	−	15.2957i	−0.394295	−	0.818762i	−0.999738	−	0.0228733i	$-0.992719\pi$
$349$	−7.36603	−	15.2957i	−0.394295	−	0.818762i	0.605444	−	0.795888i	$-0.292996\pi$
$350$	−18.6944	−	0.462063i	−0.999260	−	0.0246983i
$351$	−2.27432	+	4.72268i	−0.121394	+	0.252078i
$352$	14.1834	+	27.0685i	0.755976	+	1.44275i
$353$	−12.0111	−	24.9414i	−0.639288	−	1.32750i	−0.928893	−	0.370349i	$-0.879238\pi$
$353$	−12.0111	−	24.9414i	−0.639288	−	1.32750i	0.289604	−	0.957146i	$-0.406476\pi$
$354$	4.02604	−	2.44258i	0.213981	−	0.129822i
$355$	−0.0194488	+	0.0852107i	−0.00103223	+	0.00452251i
$356$	6.28351	+	32.1416i	0.333025	+	1.70350i
$357$	4.64135	+	1.67133i	0.245646	+	0.0884563i
$358$	−0.330718	+	0.109938i	−0.0174790	+	0.00581039i
$359$	−12.7529	−	26.4817i	−0.673074	−	1.39765i	−0.905208	−	0.424969i	$-0.860285\pi$
$359$	−12.7529	−	26.4817i	−0.673074	−	1.39765i	0.232134	−	0.972684i	$-0.425429\pi$
$360$	−0.0376493	−	0.126355i	−0.00198429	−	0.00665947i
$361$	−5.72779			−0.301463
$362$	3.64340	−	9.91127i	0.191493	−	0.520925i
$363$	4.04619	−	17.7275i	0.212370	−	0.930454i
$364$	−20.3887	+	18.8052i	−1.06866	+	0.985658i
$365$	0.0996259	+	0.436490i	0.00521466	+	0.0228469i
$366$	17.3204	+	2.22691i	0.905351	+	0.116402i
$367$	3.58881	+	4.50022i	0.187334	+	0.234910i	0.866626	−	0.498959i	$-0.166284\pi$
$367$	3.58881	+	4.50022i	0.187334	+	0.234910i	−0.679291	+	0.733869i	$0.737713\pi$
$368$	−23.6387	−	21.4062i	−1.23225	−	1.11588i
$369$	−3.93651	+	0.898484i	−0.204927	+	0.0467732i
$370$	−0.526398	−	0.0676797i	−0.0273661	−	0.00351850i
$371$	0.708162	+	1.14998i	0.0367660	+	0.0597042i
$372$	−9.98641	+	7.46421i	−0.517771	+	0.387001i
$373$	16.7948			0.869600			0.434800	−	0.900527i	$-0.356819\pi$
$373$	16.7948			0.869600			0.434800	+	0.900527i	$0.356819\pi$
$374$	13.3700	+	4.91484i	0.691346	+	0.254140i
$375$	0.454355	+	0.103704i	0.0234628	+	0.00535523i
$376$	1.38391	+	0.963142i	0.0713695	+	0.0496702i
$377$	−8.48747	+	6.76853i	−0.437127	+	0.348597i
$378$	3.32997	+	1.70625i	0.171275	+	0.0877598i
$379$	−4.38597	−	3.49770i	−0.225292	−	0.179665i	0.504338	−	0.863506i	$-0.331737\pi$
$379$	−4.38597	−	3.49770i	−0.225292	−	0.179665i	−0.729631	+	0.683842i	$0.760308\pi$
$380$	−0.203337	−	0.272046i	−0.0104310	−	0.0139557i
$381$	13.2498	+	10.5663i	0.678806	+	0.541330i
$382$	−0.165486	−	1.70903i	−0.00846700	−	0.0874413i
$383$	9.06944	+	11.3727i	0.463427	+	0.581119i	0.957548	−	0.288274i	$-0.0930815\pi$
$383$	9.06944	+	11.3727i	0.463427	+	0.581119i	−0.494121	+	0.869393i	$0.664510\pi$
$384$	−11.0237	+	2.54521i	−0.562551	+	0.129885i
$385$	−0.475347	+	0.466828i	−0.0242259	+	0.0237917i
$386$	−14.1273	+	1.36796i	−0.719063	+	0.0696273i
$387$	−2.31404	+	4.80515i	−0.117629	+	0.244260i
$388$	−10.7901	−	5.61935i	−0.547785	−	0.285280i
$389$	23.2981	+	11.2198i	1.18126	+	0.568866i	0.918279	−	0.395934i	$-0.129579\pi$
$389$	23.2981	+	11.2198i	1.18126	+	0.568866i	0.262984	+	0.964800i	$0.415293\pi$
$390$	0.295430	−	0.179236i	0.0149597	−	0.00907598i
$391$	−14.8653			−0.751771
$392$	13.0597	+	14.8810i	0.659614	+	0.751605i
$393$	−0.390732			−0.0197098
$394$	13.3274	−	8.08565i	0.671422	−	0.407349i
$395$	0.269353	+	0.129714i	0.0135526	+	0.00652661i
$396$	9.58270	+	4.99055i	0.481549	+	0.250785i
$397$	−0.931072	+	1.93339i	−0.0467292	+	0.0970341i	−0.923026	−	0.384737i	$-0.874292\pi$
$397$	−0.931072	+	1.93339i	−0.0467292	+	0.0970341i	0.876297	+	0.481771i	$0.160006\pi$
$398$	11.2708	−	1.09136i	0.564953	−	0.0547048i
$399$	9.56799	+	1.16575i	0.478999	+	0.0583606i
$400$	5.66059	−	19.1732i	0.283030	−	0.958658i
$401$	−24.4998	−	30.7218i	−1.22346	−	1.53417i	−0.762853	−	0.646573i	$-0.776202\pi$
$401$	−24.4998	−	30.7218i	−1.22346	−	1.53417i	−0.460611	−	0.887602i	$-0.652370\pi$
$402$	−1.31153	−	13.5446i	−0.0654133	−	0.675543i
$403$	−25.5474	−	20.3734i	−1.27261	−	1.01487i
$404$	−6.27008	−	8.38879i	−0.311948	−	0.417358i
$405$	−0.0364443	−	0.0290634i	−0.00181093	−	0.00144417i
$406$	4.68030	+	6.17601i	0.232280	+	0.306510i
$407$	34.0035	−	27.1169i	1.68549	−	1.34414i
$408$	−3.01252	+	4.32859i	−0.149142	+	0.214297i
$409$	17.6336	+	4.02476i	0.871928	+	0.199012i	0.634997	−	0.772515i	$-0.281001\pi$
$409$	17.6336	+	4.02476i	0.871928	+	0.199012i	0.236931	+	0.971527i	$0.423859\pi$
$410$	0.249832	+	0.0918388i	0.0123383	+	0.00453560i
$411$	−5.23533			−0.258240
$412$	27.4960	−	20.5515i	1.35463	−	1.01250i
$413$	6.28556	−	6.17291i	0.309292	−	0.303749i
$414$	−11.1830	−	1.43781i	−0.549614	−	0.0706646i
$415$	−0.218219	+	0.0498070i	−0.0107119	+	0.00244493i
$416$	−13.7623	−	26.2648i	−0.674751	−	1.28774i
$417$	7.51458	+	9.42299i	0.367991	+	0.461446i
$418$	27.6054	+	3.54927i	1.35023	+	0.173600i
$419$	0.546483	+	2.39430i	0.0266974	+	0.116969i	0.986521	−	0.163636i	$-0.0523221\pi$
$419$	0.546483	+	2.39430i	0.0266974	+	0.116969i	−0.959823	+	0.280605i	$0.909465\pi$
$420$	−0.122692	−	0.213979i	−0.00598674	−	0.0104411i
$421$	−5.92496	+	25.9589i	−0.288765	+	1.26516i	0.597457	+	0.801901i	$0.296178\pi$
$421$	−5.92496	+	25.9589i	−0.288765	+	1.26516i	−0.886222	+	0.463261i	$0.846679\pi$
$422$	1.60844	−	4.37548i	0.0782975	−	0.212995i
$423$	0.596116			0.0289842
$424$	−1.38367	+	0.412286i	−0.0671970	+	0.0200224i
$425$	−4.04320	−	8.39580i	−0.196124	−	0.407256i
$426$	2.51628	−	0.836465i	0.121914	−	0.0405269i
$427$	32.4965	−	3.36423i	1.57262	−	0.162806i
$428$	−2.08101	−	10.6449i	−0.100590	−	0.514540i
$429$	−6.30112	+	27.6070i	−0.304221	+	1.33288i
$430$	0.300589	−	0.182366i	0.0144957	−	0.00879449i
$431$	10.0519	+	20.8729i	0.484181	+	1.00541i	0.989775	+	0.142641i	$0.0455593\pi$
$431$	10.0519	+	20.8729i	0.484181	+	1.00541i	−0.505593	+	0.862772i	$0.668726\pi$
$432$	−2.68495	+	2.96497i	−0.129180	+	0.142652i
$433$	−0.810188	+	1.68237i	−0.0389351	+	0.0808497i	−0.919529	−	0.393022i	$-0.871430\pi$
$433$	−0.810188	+	1.68237i	−0.0389351	+	0.0808497i	0.880594	+	0.473872i	$0.157144\pi$
$434$	−14.9890	+	17.8712i	−0.719494	+	0.857846i
$435$	−0.0418868	−	0.0869788i	−0.00200832	−	0.00417031i
$436$	13.7084	+	30.9077i	0.656515	+	1.48021i
$437$	−28.3170	+	6.46317i	−1.35459	+	0.309175i
$438$	9.75404	−	9.45304i	0.466066	−	0.451684i
$439$	−3.20537	+	4.01940i	−0.152984	+	0.191836i	−0.852417	−	0.522862i	$-0.824864\pi$
$439$	−3.20537	+	4.01940i	−0.152984	+	0.191836i	0.699434	+	0.714698i	$0.253436\pi$
$440$	−0.350179	−	0.620217i	−0.0166941	−	0.0295677i
$441$	6.79521	+	1.68079i	0.323582	+	0.0800377i
$442$	−12.9730	−	4.76892i	−0.617064	−	0.226834i
$443$	3.10497	+	2.47613i	0.147522	+	0.117645i	0.694470	−	0.719522i	$-0.255639\pi$
$443$	3.10497	+	2.47613i	0.147522	+	0.117645i	−0.546948	+	0.837167i	$0.684210\pi$
$444$	6.52827	+	14.7190i	0.309818	+	0.698531i
$445$	−0.169852	−	0.744169i	−0.00805175	−	0.0352770i
$446$	−15.4699	−	15.9625i	−0.732520	−	0.755844i
$447$	18.5181	−	8.91784i	0.875876	−	0.421800i
$448$	−18.9852	+	9.35746i	−0.896967	+	0.442098i
$449$	10.3399	+	4.97945i	0.487972	+	0.234995i	0.661657	−	0.749806i	$-0.269853\pi$
$449$	10.3399	+	4.97945i	0.487972	+	0.234995i	−0.173686	+	0.984801i	$0.555568\pi$
$450$	−2.22959	−	6.70712i	−0.105104	−	0.316177i
$451$	−19.6525	+	9.46413i	−0.925399	+	0.445649i
$452$	−26.3621	+	5.15363i	−1.23997	+	0.242406i
$453$	−12.4520	−	2.84209i	−0.585047	−	0.133533i
$454$	17.9206	−	10.8724i	0.841057	−	0.510266i
$455$	0.461233	−	0.452968i	0.0216230	−	0.0212354i
$456$	−3.85657	+	9.55534i	−0.180601	+	0.447470i
$457$	−28.5171	+	13.7331i	−1.33397	+	0.642408i	−0.958677	−	0.284496i	$-0.908174\pi$
$457$	−28.5171	+	13.7331i	−1.33397	+	0.642408i	−0.375297	+	0.926904i	$0.622459\pi$
$458$	−13.7944	−	8.97210i	−0.644568	−	0.419239i
$459$			1.86454i			0.0870291i
$460$	0.566310	+	0.481407i	0.0264043	+	0.0224457i
$461$	20.9740	+	4.78718i	0.976857	+	0.222961i	0.681010	−	0.732274i	$-0.261541\pi$
$461$	20.9740	+	4.78718i	0.976857	+	0.222961i	0.295847	+	0.955235i	$0.404398\pi$
$462$	19.5891	+	4.98338i	0.911369	+	0.231848i
$463$	−23.9768	+	5.47256i	−1.11430	+	0.254331i	−0.739754	−	0.672877i	$-0.765058\pi$
$463$	−23.9768	+	5.47256i	−1.11430	+	0.254331i	−0.374545	+	0.927209i	$0.622201\pi$
$464$	−7.67423	+	3.11977i	−0.356267	+	0.144831i
$465$	0.227188	−	0.181176i	0.0105356	−	0.00840185i
$466$	−4.73090	−	14.2317i	−0.219155	−	0.659269i
$467$	1.15321	+	5.05255i	0.0533643	+	0.233804i	0.994576	−	0.104013i	$-0.0331684\pi$
$467$	1.15321	+	5.05255i	0.0533643	+	0.233804i	−0.941212	+	0.337818i	$0.890311\pi$
$468$	−9.29819	−	4.84238i	−0.429809	−	0.223839i
$469$	−8.19069	−	24.1046i	−0.378211	−	1.11304i
$470$	−0.0329423	−	0.0214262i	−0.00151951	−	0.000988319i
$471$			18.1640i			0.836954i
$472$	4.63045	+	8.20120i	0.213134	+	0.377491i
$473$	−6.41116	+	28.0891i	−0.294785	+	1.29154i
$474$	−0.874172	−	9.02785i	−0.0401521	−	0.414663i
$475$	−11.3523	−	14.2353i	−0.520877	−	0.653159i
$476$	−3.63190	+	9.17340i	−0.166468	+	0.420462i
$477$	−0.318264	+	0.399091i	−0.0145723	+	0.0182731i
$478$	−23.6575	−	15.3873i	−1.08207	−	0.703797i
$479$	7.24551	−	9.08558i	0.331056	−	0.415131i	−0.588247	−	0.808681i	$-0.700182\pi$
$479$	7.24551	−	9.08558i	0.331056	−	0.415131i	0.919303	+	0.393550i	$0.128753\pi$
$480$	0.254945	−	0.0673430i	0.0116366	−	0.00307377i
$481$	−32.9940	+	26.3118i	−1.50440	+	1.19972i
$482$	−18.9846	+	18.3987i	−0.864723	+	0.838039i
$483$	−20.9815	+	2.17213i	−0.954693	+	0.0988353i
$484$	35.1841	+	9.19939i	1.59928	+	0.418154i
$485$	0.255466	+	0.123026i	0.0116001	+	0.00558632i
$486$	−0.180343	+	1.40267i	−0.00818052	+	0.0636263i
$487$	−4.05232	+	8.41473i	−0.183628	+	0.381308i	−0.972380	−	0.233404i	$-0.925013\pi$
$487$	−4.05232	+	8.41473i	−0.183628	+	0.381308i	0.788752	+	0.614712i	$0.210728\pi$
$488$	−5.53709	+	34.4842i	−0.250652	+	1.56103i
$489$		−	1.72823i		−	0.0781531i
$490$	−0.315101	−	0.337124i	−0.0142348	−	0.0152297i
$491$		−	28.7183i		−	1.29604i	−0.761623	−	0.648020i	$-0.775597\pi$
$491$		−	28.7183i		−	1.29604i	0.761623	−	0.648020i	$-0.224403\pi$
$492$	−1.54938	−	7.92547i	−0.0698516	−	0.357308i
$493$	−1.67545	+	3.47910i	−0.0754584	+	0.156691i
$494$	−26.7858	−	3.44389i	−1.20515	−	0.154948i
$495$	−0.226879	−	0.109259i	−0.0101975	−	0.00491084i
$496$	−14.2952	−	20.4308i	−0.641875	−	0.917370i
$497$	4.22414	−	2.60123i	0.189479	−	0.116681i
$498$	4.72595	+	4.87643i	0.211775	+	0.218518i
$499$	−7.47416	+	5.96044i	−0.334589	+	0.266826i	−0.776343	−	0.630310i	$-0.782928\pi$
$499$	−7.47416	+	5.96044i	−0.334589	+	0.266826i	0.441754	+	0.897136i	$0.354356\pi$
$500$	−0.235780	+	0.901764i	−0.0105444	+	0.0403281i
$501$	14.0591	−	17.6295i	0.628112	−	0.787628i
$502$	12.3132	−	18.9313i	0.549567	−	0.844944i
$503$	24.9628	−	31.3024i	1.11304	−	1.39570i	0.204008	−	0.978969i	$-0.434603\pi$
$503$	24.9628	−	31.3024i	1.11304	−	1.39570i	0.909028	−	0.416735i	$-0.136826\pi$
$504$	−3.61950	+	6.54975i	−0.161226	+	0.291749i
$505$	0.152192	+	0.190842i	0.00677245	+	0.00849238i
$506$	−60.6261	+	5.87046i	−2.69516	+	0.260974i
$507$	3.22126	−	14.1133i	0.143061	−	0.626792i
$508$	−21.9526	+	25.8243i	−0.973991	+	1.14577i
$509$		−	21.8877i		−	0.970156i	−0.874471	−	0.485078i	$-0.838791\pi$
$509$		−	21.8877i		−	0.970156i	0.874471	−	0.485078i	$-0.161209\pi$
$510$	0.0670172	−	0.103037i	0.00296757	−	0.00456256i
$511$	13.7138	−	21.3936i	0.606664	−	0.946396i
$512$	−4.39706	−	22.1961i	−0.194324	−	0.980937i
$513$	0.810667	+	3.55176i	0.0357918	+	0.156814i
$514$	−18.9176	+	6.28861i	−0.834420	+	0.277379i
$515$	−0.625527	+	0.498841i	−0.0275640	+	0.0219816i
$516$	−9.46057	−	4.92695i	−0.416478	−	0.216897i
$517$	3.13958	−	0.716588i	0.138079	−	0.0315155i
$518$	18.1941	+	24.0085i	0.799402	+	1.05487i
$519$	15.7733	+	3.60016i	0.692373	+	0.158030i
$520$	0.339782	+	0.601803i	0.0149004	+	0.0263908i
$521$		−	23.6652i		−	1.03679i	−0.855141	−	0.518395i	$-0.826530\pi$
$521$		−	23.6652i		−	1.03679i	0.855141	−	0.518395i	$-0.173470\pi$
$522$	−1.59693	+	2.45523i	−0.0698956	+	0.107463i
$523$	13.4207	−	6.46306i	0.586846	−	0.282610i	−0.116806	−	0.993155i	$-0.537266\pi$
$523$	13.4207	−	6.46306i	0.586846	−	0.282610i	0.703652	+	0.710545i	$0.251551\pi$
$524$	0.0244872	−	0.781081i	0.00106973	−	0.0341217i
$525$	−6.93355	−	11.2594i	−0.302605	−	0.491400i
$526$	12.6286	+	20.8153i	0.550632	+	0.907591i
$527$	−11.3318	−	2.58641i	−0.493621	−	0.112666i
$528$	−10.5767	+	18.8432i	−0.460294	+	0.820046i
$529$	36.5463	−	17.5997i	1.58897	−	0.765206i
$530$	0.0319323	−	0.0106150i	0.00138705	−	0.000461085i
$531$	3.00005	+	1.44475i	0.130191	+	0.0626967i
$532$	−2.92999	+	19.0535i	−0.127031	+	0.826075i
$533$	19.0690	−	9.18314i	0.825969	−	0.397766i
$534$	−16.6296	+	16.1164i	−0.719634	+	0.697427i
$535$	0.0562527	+	0.246459i	0.00243201	+	0.0106554i
$536$	27.1581	−	1.77294i	1.17305	−	0.0765792i
$537$	−0.192671	−	0.153650i	−0.00831437	−	0.00663049i
$538$	0.603152	−	1.64077i	0.0260037	−	0.0707388i
$539$	37.8090	+	0.683774i	1.62855	+	0.0294522i
$540$	0.0603822	−	0.0710315i	0.00259844	−	0.00305671i
$541$	16.8716	−	21.1564i	0.725368	−	0.909583i	−0.273261	−	0.961940i	$-0.588102\pi$
$541$	16.8716	−	21.1564i	0.725368	−	0.909583i	0.998628	+	0.0523575i	$0.0166735\pi$
$542$	−8.76358	−	9.04263i	−0.376428	−	0.388414i
$543$	7.27964	−	1.66153i	0.312399	−	0.0713031i
$544$	−8.46414	−	6.29336i	−0.362897	−	0.269826i
$545$	−0.341919	−	0.710002i	−0.0146462	−	0.0304131i
$546$	−19.0075	−	4.83542i	−0.813447	−	0.206937i
$547$	−17.0893	+	35.4864i	−0.730687	+	1.51729i	0.120665	+	0.992693i	$0.461497\pi$
$547$	−17.0893	+	35.4864i	−0.730687	+	1.51729i	−0.851352	+	0.524595i	$0.824217\pi$
$548$	0.328098	−	10.4655i	0.0140156	−	0.447065i
$549$	5.35767	+	11.1253i	0.228660	+	0.474817i
$550$	−19.8052	−	32.6444i	−0.844498	−	1.39196i
$551$	−1.67892	+	7.35581i	−0.0715242	+	0.313368i
$552$	3.57505	−	22.2649i	0.152164	−	0.947657i
$553$	−5.45932	−	16.0664i	−0.232154	−	0.683211i
$554$	−1.30776	−	3.93405i	−0.0555614	−	0.167142i
$555$	−0.162829	−	0.338119i	−0.00691173	−	0.0143523i
$556$	−19.3077	+	14.4312i	−0.818827	+	0.612021i
$557$	−16.4411			−0.696631			−0.348315	−	0.937377i	$-0.613246\pi$
$557$	−16.4411			−0.696631			−0.348315	+	0.937377i	$0.613246\pi$
$558$	−8.27460	−	3.04176i	−0.350292	−	0.128768i
$559$	6.22081	−	27.2551i	0.263112	−	1.15277i
$560$	0.435437	−	0.231853i	0.0184006	−	0.00979757i
$561$	2.24135	+	9.82000i	0.0946299	+	0.414601i
$562$	−0.586252	+	4.55974i	−0.0247295	+	0.192341i
$563$	−23.6382	−	29.6414i	−0.996231	−	1.24923i	−0.968343	−	0.249623i	$-0.919693\pi$
$563$	−23.6382	−	29.6414i	−0.996231	−	1.24923i	−0.0278882	−	0.999611i	$-0.508878\pi$
$564$	−0.0373586	+	1.19165i	−0.00157308	+	0.0501774i
$565$	0.610356	−	0.139310i	0.0256779	−	0.00586080i
$566$	4.35471	−	33.8700i	0.183042	−	1.42366i
$567$	0.272447	+	2.63169i	0.0114417	+	0.110520i
$568$	1.51441	+	5.08252i	0.0635434	+	0.213258i
$569$	−22.9076			−0.960337			−0.480168	−	0.877176i	$-0.659424\pi$
$569$	−22.9076			−0.960337			−0.480168	+	0.877176i	$0.659424\pi$
$570$	0.0828626	−	0.225414i	0.00347073	−	0.00944154i
$571$	−9.81062	−	2.23921i	−0.410562	−	0.0937080i	0.0122513	−	0.999925i	$-0.496100\pi$
$571$	−9.81062	−	2.23921i	−0.410562	−	0.0937080i	−0.422813	+	0.906217i	$0.638957\pi$
$572$	−54.7920	−	14.3262i	−2.29097	−	0.599007i
$573$	0.949234	−	0.756989i	0.0396548	−	0.0316237i
$574$	−6.21673	−	13.7695i	−0.259481	−	0.574729i
$575$	31.1528	+	24.8436i	1.29916	+	1.03605i
$576$	−5.75875	−	5.55309i	−0.239948	−	0.231379i
$577$	−1.75522	−	1.39974i	−0.0730708	−	0.0582720i	0.586273	−	0.810113i	$-0.300594\pi$
$577$	−1.75522	−	1.39974i	−0.0730708	−	0.0582720i	−0.659344	+	0.751841i	$0.729166\pi$
$578$	19.0361	−	1.84328i	0.791797	−	0.0766702i
$579$	−6.25751	−	7.84667i	−0.260053	−	0.326096i
$580$	0.176497	−	0.0782814i	0.00732865	−	0.00325046i
$581$	10.6955	+	6.85609i	0.443724	+	0.284438i
$582$	−0.829101	−	8.56238i	−0.0343673	−	0.354922i
$583$	−1.19646	+	2.48449i	−0.0495525	+	0.102897i
$584$	18.2855	+	20.0909i	0.756660	+	0.831368i
$585$	0.220143	+	0.106015i	0.00910180	+	0.00438320i
$586$	15.7712	+	25.9951i	0.651500	+	1.07385i
$587$	−26.2199			−1.08221			−0.541105	−	0.840955i	$-0.681994\pi$
$587$	−26.2199			−1.08221			−0.541105	+	0.840955i	$0.681994\pi$
$588$	−3.78579	+	13.4784i	−0.156123	+	0.555841i
$589$	−22.7105			−0.935770
$590$	−0.113859	−	0.187670i	−0.00468749	−	0.00772625i
$591$	9.93103	+	4.78253i	0.408508	+	0.196727i
$592$	−29.8326	+	12.1277i	−1.22611	+	0.498445i
$593$	−17.4668	+	36.2702i	−0.717276	+	1.48944i	0.148450	+	0.988920i	$0.452572\pi$
$593$	−17.4668	+	36.2702i	−0.717276	+	1.48944i	−0.865726	+	0.500519i	$0.833143\pi$
$594$	0.736325	+	7.60425i	0.0302118	+	0.312006i
$595$	0.0779076	−	0.216352i	0.00319390	−	0.00886958i
$596$	16.6664	+	37.5769i	0.682682	+	1.53921i
$597$	4.99223	+	6.26006i	0.204318	+	0.256207i
$598$	58.8261	−	5.69617i	2.40558	−	0.232934i
$599$	1.44658	+	1.15361i	0.0591057	+	0.0471352i	0.652597	−	0.757705i	$-0.273679\pi$
$599$	1.44658	+	1.15361i	0.0591057	+	0.0471352i	−0.593491	+	0.804840i	$0.702251\pi$
$600$	13.5474	−	4.03665i	0.553070	−	0.164796i
$601$	−22.6368	−	18.0522i	−0.923373	−	0.736365i	0.0414847	−	0.999139i	$-0.486791\pi$
$601$	−22.6368	−	18.0522i	−0.923373	−	0.736365i	−0.964857	+	0.262774i	$0.915363\pi$
$602$	−19.3395	−	4.91987i	−0.788218	−	0.200519i
$603$	7.52300	−	5.99939i	0.306360	−	0.244314i
$604$	6.46176	−	24.7137i	0.262925	−	1.00559i
$605$	−0.826352	−	0.188609i	−0.0335960	−	0.00766806i
$606$	2.55514	−	6.95083i	0.103796	−	0.282358i
$607$	14.8862			0.604213			0.302107	−	0.953274i	$-0.402310\pi$
$607$	14.8862			0.604213			0.302107	+	0.953274i	$0.402310\pi$
$608$	−18.8596	−	8.30819i	−0.764858	−	0.336942i
$609$	−1.85643	+	5.15537i	−0.0752263	+	0.208906i
$610$	0.103805	−	0.807374i	0.00420295	−	0.0326896i
$611$	−3.04636	+	0.695313i	−0.123243	+	0.0281293i
$612$	−3.72724	−	0.116850i	−0.150665	−	0.00472340i
$613$	−17.9532	−	22.5126i	−0.725122	−	0.909275i	0.273493	−	0.961874i	$-0.411821\pi$
$613$	−17.9532	−	22.5126i	−0.725122	−	0.909275i	−0.998616	+	0.0525992i	$0.983249\pi$
$614$	−0.303836	+	2.36317i	−0.0122618	+	0.0953698i
$615$	0.0418820	+	0.183497i	0.00168884	+	0.00739931i
$616$	−11.1895	+	38.8467i	−0.450838	+	1.56518i
$617$	−2.68207	+	11.7509i	−0.107976	+	0.473074i	0.891810	+	0.452410i	$0.149435\pi$
$617$	−2.68207	+	11.7509i	−0.107976	+	0.473074i	−0.999786	+	0.0206649i	$0.993422\pi$
$618$	22.7828	+	8.37502i	0.916460	+	0.336893i
$619$	31.9913			1.28584			0.642919	−	0.765934i	$-0.277723\pi$
$619$	31.9913			1.28584			0.642919	+	0.765934i	$0.277723\pi$
$620$	0.347937	+	0.465507i	0.0139735	+	0.0186952i
$621$	−3.45921	−	7.18312i	−0.138813	−	0.288249i
$622$	−12.1928	−	36.6787i	−0.488885	−	1.47068i
$623$	−23.3806	+	36.4738i	−0.936726	+	1.46129i
$624$	10.2627	−	18.2838i	0.410838	−	0.731936i
$625$	−5.55577	+	24.3414i	−0.222231	+	0.973657i
$626$	11.9440	+	19.6870i	0.477379	+	0.786849i
$627$	8.53912	+	17.7317i	0.341020	+	0.708134i
$628$	−36.3102	−	1.13834i	−1.44894	−	0.0454247i
$629$	−6.51309	+	13.5246i	−0.259694	+	0.539260i
$630$	0.0795350	−	0.155224i	0.00316875	−	0.00618426i
$631$	−0.432844	−	0.898809i	−0.0172312	−	0.0357810i	0.892176	−	0.451689i	$-0.149178\pi$
$631$	−0.432844	−	0.898809i	−0.0172312	−	0.0357810i	−0.909407	+	0.415908i	$0.863464\pi$
$632$	18.1016	−	1.18171i	0.720044	−	0.0470059i
$633$	3.21371	−	0.733508i	0.127733	−	0.0291543i
$634$	17.0748	+	17.6184i	0.678125	+	0.699718i
$635$	0.492540	−	0.617625i	0.0195458	−	0.0245097i
$636$	−0.777844	−	0.661227i	−0.0308435	−	0.0262194i
$637$	−36.6864	−	0.663473i	−1.45357	−	0.0262878i
$638$	−5.45915	+	14.8507i	−0.216130	+	0.587944i
$639$	1.46595	+	1.16905i	0.0579919	+	0.0462470i
$640$	0.118642	+	0.513859i	0.00468975	+	0.0203121i
$641$	−1.09975	−	4.81831i	−0.0434374	−	0.190312i	0.948554	−	0.316614i	$-0.102546\pi$
$641$	−1.09975	−	4.81831i	−0.0434374	−	0.190312i	−0.991992	+	0.126303i	$0.959689\pi$
$642$	5.50751	−	5.33755i	0.217364	−	0.210656i
$643$	10.1570	−	4.89137i	0.400555	−	0.192897i	−0.222751	−	0.974875i	$-0.571504\pi$
$643$	10.1570	−	4.89137i	0.400555	−	0.192897i	0.623305	+	0.781978i	$0.285789\pi$
$644$	−3.02721	−	42.0786i	−0.119289	−	1.65813i
$645$	0.223988	+	0.107867i	0.00881951	+	0.00424725i
$646$	−9.11586	+	3.03030i	−0.358659	+	0.119226i
$647$	20.6885	−	9.96305i	0.813349	−	0.391688i	0.0195048	−	0.999810i	$-0.493791\pi$
$647$	20.6885	−	9.96305i	0.813349	−	0.391688i	0.793844	+	0.608122i	$0.208077\pi$
$648$	−2.79266	−	0.448414i	−0.109706	−	0.0176154i
$649$	17.5372	+	4.00274i	0.688394	+	0.157121i
$650$	19.2172	+	31.6752i	0.753761	+	1.24240i
$651$	−16.3721	−	1.99476i	−0.641673	−	0.0781807i
$652$	3.45475	+	0.108308i	0.135299	+	0.00424166i
$653$	−30.0701	+	14.4810i	−1.17673	+	0.566685i	−0.916958	−	0.398985i	$-0.869363\pi$
$653$	−30.0701	+	14.4810i	−1.17673	+	0.566685i	−0.259775	+	0.965669i	$0.583648\pi$
$654$	−13.0356	+	20.0419i	−0.509732	+	0.783700i
$655$			0.0182136i			0.000711665i
$656$	15.9403	−	2.60056i	0.622362	−	0.101535i
$657$	9.36391	+	2.13725i	0.365321	+	0.0833821i
$658$	0.442442	+	2.18614i	0.0172482	+	0.0852246i
$659$	−16.5044	+	3.76703i	−0.642922	+	0.146743i	−0.531537	−	0.847035i	$-0.678386\pi$
$659$	−16.5044	+	3.76703i	−0.642922	+	0.146743i	−0.111384	+	0.993777i	$0.535528\pi$
$660$	0.232630	−	0.446688i	0.00905510	−	0.0173873i
$661$	−17.1836	+	13.7034i	−0.668364	+	0.533002i	−0.897845	−	0.440311i	$-0.854868\pi$
$661$	−17.1836	+	13.7034i	−0.668364	+	0.533002i	0.229482	+	0.973313i	$0.426297\pi$
$662$	−21.6096	+	7.18348i	−0.839881	+	0.279194i
$663$	−2.17481	−	9.52845i	−0.0844625	−	0.370054i
$664$	−10.0443	+	9.14165i	−0.389792	+	0.354765i
$665$	0.0543405	−	0.446003i	0.00210723	−	0.0172953i
$666$	−6.20785	+	9.54440i	−0.240549	+	0.369838i
$667$		−	16.5116i		−	0.639332i
$668$	34.3606	+	29.2091i	1.32945	+	1.13014i
$669$	3.49760	−	15.3240i	0.135225	−	0.592460i
$670$	−0.631369	+	0.0611358i	−0.0243919	+	0.00236188i
$671$	41.5911	+	52.1536i	1.60561	+	2.01337i
$672$	−12.8662	−	7.64593i	−0.496325	−	0.294948i
$673$	−13.2490	+	16.6138i	−0.510713	+	0.640414i	−0.968608	−	0.248592i	$-0.920032\pi$
$673$	−13.2490	+	16.6138i	−0.510713	+	0.640414i	0.457895	+	0.889006i	$0.348604\pi$
$674$	24.9289	−	38.3276i	0.960227	−	1.47632i
$675$	3.11609	−	3.90746i	0.119939	−	0.150398i
$676$	28.0108	+	7.32384i	1.07734	+	0.281686i
$677$	4.67935	−	3.73166i	0.179842	−	0.143419i	−0.529431	−	0.848353i	$-0.677595\pi$
$677$	4.67935	−	3.73166i	0.179842	−	0.143419i	0.709273	+	0.704934i	$0.249023\pi$
$678$	−13.2184	−	13.6393i	−0.507651	−	0.523816i
$679$	−5.17784	−	15.2380i	−0.198707	−	0.584780i
$680$	0.201773	+	0.140426i	0.00773765	+	0.00538509i
$681$	13.3538	+	6.43084i	0.511718	+	0.246430i
$682$	−47.2366	−	6.07326i	−1.80878	−	0.232557i
$683$	−7.36978	+	15.3035i	−0.281997	+	0.585573i	−0.993067	−	0.117548i	$-0.962496\pi$
$683$	−7.36978	+	15.3035i	−0.281997	+	0.585573i	0.711070	+	0.703121i	$0.248211\pi$
$684$	−7.15084	+	1.39795i	−0.273419	+	0.0534519i
$685$			0.244040i			0.00932429i
$686$	−1.12052	+	26.1676i	−0.0427815	+	0.999084i
$687$		−	11.6358i		−	0.443933i
$688$	10.4419	−	18.6031i	0.398096	−	0.709236i
$689$	1.16094	−	2.41072i	0.0442284	−	0.0918411i
$690$	−0.0670222	+	0.521285i	−0.00255149	+	0.0198450i
$691$	45.7148	+	22.0151i	1.73907	+	0.837494i	0.983142	+	0.182845i	$0.0585306\pi$
$691$	45.7148	+	22.0151i	1.73907	+	0.837494i	0.755933	+	0.654649i	$0.227184\pi$
$692$	−8.18530	+	31.3056i	−0.311158	+	1.19006i
$693$	4.59844	+	13.5329i	0.174680	+	0.514071i
$694$	23.2869	−	22.5682i	0.883957	−	0.856679i
$695$	0.439244	−	0.350285i	0.0166615	−	0.0132871i
$696$	−4.80797	−	3.34615i	−0.182246	−	0.126836i
$697$	4.69396	−	5.88604i	0.177797	−	0.222950i
$698$	20.1264	+	13.0906i	0.761796	+	0.495485i
$699$	6.61196	−	8.29113i	0.250087	−	0.313599i
$700$	22.9422	−	13.1547i	0.867135	−	0.497199i
$701$	23.1859	+	29.0742i	0.875719	+	1.09812i	0.994452	+	0.105191i	$0.0335453\pi$
$701$	23.1859	+	29.0742i	0.875719	+	1.09812i	−0.118733	+	0.992926i	$0.537883\pi$
$702$	−0.714463	−	7.37848i	−0.0269657	−	0.278483i
$703$	−6.52657	+	28.5948i	−0.246154	+	1.07847i
$704$	−37.0051	−	22.3240i	−1.39468	−	0.841368i
$705$		−	0.0277874i		−	0.00104653i
$706$	32.8183	+	21.3456i	1.23513	+	0.803353i
$707$	1.67564	−	13.7529i	0.0630188	−	0.517231i
$708$	−3.07609	+	5.90661i	−0.115607	+	0.221984i
$709$	0.372392	+	1.63155i	0.0139855	+	0.0612743i	0.981439	−	0.191774i	$-0.0614240\pi$
$709$	0.372392	+	1.63155i	0.0139855	+	0.0612743i	−0.967454	+	0.253048i	$0.918567\pi$
$710$	−0.0389910	−	0.117294i	−0.00146331	−	0.00440197i
$711$	5.01428	−	3.99876i	0.188050	−	0.149965i
$712$	−31.1749	−	34.2529i	−1.16833	−	1.28368i
$713$	48.4541	−	11.0593i	1.81462	−	0.414176i
$714$	−6.83783	+	1.38387i	−0.255899	+	0.0517902i
$715$	1.28687	+	0.293721i	0.0481264	+	0.0109845i
$716$	0.319224	−	0.375523i	0.0119299	−	0.0140340i
$717$		−	19.9555i		−	0.745253i
$718$	34.8452	+	22.6639i	1.30041	+	0.845810i
$719$	−22.6809	+	10.9226i	−0.845856	+	0.407343i	−0.806038	−	0.591864i	$-0.798392\pi$
$719$	−22.6809	+	10.9226i	−0.845856	+	0.407343i	−0.0398186	+	0.999207i	$0.512678\pi$
$720$	0.138209	+	0.125157i	0.00515075	+	0.00466431i
$721$	45.0781	+	5.49226i	1.67879	+	0.204542i
$722$	6.92542	−	4.20163i	0.257738	−	0.156368i
$723$	−18.2252	−	4.15979i	−0.677804	−	0.154704i
$724$	2.86521	+	14.6563i	0.106485	+	0.544695i
$725$	9.32562	−	4.49098i	0.346345	−	0.166791i
$726$	8.11183	+	24.4023i	0.301058	+	0.905654i
$727$	6.48005	+	3.12063i	0.240332	+	0.115738i	0.550173	−	0.835051i	$-0.314562\pi$
$727$	6.48005	+	3.12063i	0.240332	+	0.115738i	−0.309842	+	0.950788i	$0.600276\pi$
$728$	10.8573	−	37.6933i	0.402398	−	1.39701i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−0.440644	−	0.454675i	−0.0163090	−	0.0168283i
$731$	−2.21279	−	9.69485i	−0.0818429	−	0.358577i
$732$	−22.5755	+	10.0129i	−0.834414	+	0.370086i
$733$	−15.3744	−	12.2607i	−0.567868	−	0.452859i	0.296987	−	0.954881i	$-0.404018\pi$
$733$	−15.3744	−	12.2607i	−0.567868	−	0.452859i	−0.864855	+	0.502022i	$0.832590\pi$
$734$	−7.64034	−	2.80861i	−0.282010	−	0.103668i
$735$	0.0783486	−	0.316753i	0.00288993	−	0.0116836i
$736$	44.2839	+	8.54193i	1.63232	+	0.314860i
$737$	32.4097	−	40.6405i	1.19383	−	1.49701i
$738$	4.10052	−	3.97398i	0.150942	−	0.146284i
$739$	24.7658	−	5.65262i	0.911023	−	0.207935i	0.258772	−	0.965938i	$-0.416682\pi$
$739$	24.7658	−	5.65262i	0.911023	−	0.207935i	0.652251	+	0.758003i	$0.273825\pi$
$740$	0.686110	−	0.304309i	0.0252219	−	0.0111866i
$741$	−8.28559	−	17.2052i	−0.304379	−	0.632049i
$742$	−1.69981	−	0.870964i	−0.0624018	−	0.0319741i
$743$	17.6325	−	36.6143i	0.646874	−	1.34325i	−0.277117	−	0.960836i	$-0.589379\pi$
$743$	17.6325	−	36.6143i	0.646874	−	1.34325i	0.923992	−	0.382413i	$-0.124907\pi$
$744$	6.59911	−	16.3505i	0.241935	−	0.599437i
$745$	−0.415697	−	0.863204i	−0.0152300	−	0.0316253i
$746$	−20.3064	+	12.3198i	−0.743470	+	0.451060i
$747$	−1.06850	+	4.68139i	−0.0390942	+	0.171283i
$748$	−19.7708	+	3.86508i	−0.722893	+	0.141321i
$749$	7.74336	−	12.0796i	0.282936	−	0.441381i
$750$	−0.625428	+	0.207905i	−0.0228374	+	0.00759163i
$751$	−11.5481	−	23.9798i	−0.421396	−	0.875037i	−0.998303	−	0.0582276i	$-0.981455\pi$
$751$	−11.5481	−	23.9798i	−0.421396	−	0.875037i	0.576908	−	0.816809i	$-0.304259\pi$
$752$	−2.37978	−	0.149361i	−0.0867817	−	0.00544663i
$753$	15.9689			0.581938
$754$	5.29706	−	14.4098i	0.192908	−	0.524773i
$755$	−0.132481	+	0.580439i	−0.00482149	+	0.0211243i
$756$	−5.27786	+	0.379699i	−0.191954	+	0.0138095i
$757$	−6.96186	−	30.5019i	−0.253033	−	1.10861i	−0.928533	−	0.371250i	$-0.878929\pi$
$757$	−6.96186	−	30.5019i	−0.253033	−	1.10861i	0.675500	−	0.737360i	$-0.263928\pi$
$758$	7.86878	+	1.01170i	0.285807	+	0.0367466i
$759$	−26.8535	−	33.6732i	−0.974720	−	1.22226i
$760$	0.445413	+	0.179771i	0.0161568	+	0.00652096i
$761$	8.29894	−	1.89418i	0.300836	−	0.0686639i	−0.0694384	−	0.997586i	$-0.522121\pi$
$761$	8.29894	−	1.89418i	0.300836	−	0.0686639i	0.370275	+	0.928922i	$0.379264\pi$
$762$	−23.7711	−	3.05628i	−0.861137	−	0.110717i
$763$	−15.1539	+	42.0829i	−0.548608	+	1.52350i
$764$	1.45375	+	1.94498i	0.0525947	+	0.0703668i
$765$	0.0869137			0.00314237
$766$	−19.3083	−	7.09776i	−0.697636	−	0.256453i
$767$	−17.0165	−	3.88390i	−0.614429	−	0.140239i
$768$	11.4616	−	11.1638i	0.413586	−	0.402840i
$769$	−1.66663	+	1.32909i	−0.0601002	+	0.0479283i	−0.653079	−	0.757290i	$-0.726523\pi$
$769$	−1.66663	+	1.32909i	−0.0601002	+	0.0479283i	0.592979	+	0.805218i	$0.297952\pi$
$770$	0.232296	−	0.913129i	0.00837135	−	0.0329069i
$771$	−11.0211	−	8.7890

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20909 + 0.733551i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.923805 - 1.77386i) q^{4} +(-0.0202251 + 0.0419978i) q^{5} +(1.40763 - 0.136302i) q^{6} +(2.50508 - 0.851222i) q^{7} +(0.184253 + 2.82242i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-1.20909 + 0.733551i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(0.923805 - 1.77386i) q^{4} +(-0.0202251 + 0.0419978i) q^{5} +(1.40763 - 0.136302i) q^{6} +(2.50508 - 0.851222i) q^{7} +(0.184253 + 2.82242i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.00635357 - 0.0656153i) q^{10} +(4.22358 + 3.36820i) q^{11} +(-1.60197 + 1.19737i) q^{12} +(-4.09819 - 3.26819i) q^{13} +(-2.40446 + 2.86681i) q^{14} +(0.0364443 - 0.0290634i) q^{15} +(-2.29317 - 3.27740i) q^{16} +(-1.81779 - 0.414899i) q^{17} +(-1.32737 - 0.487944i) q^{18} -3.64310 q^{19} +(0.0558143 + 0.0746743i) q^{20} +(-2.62633 - 0.319989i) q^{21} +(-7.57745 - 0.974242i) q^{22} +(7.77277 - 1.77408i) q^{23} +(1.05860 - 2.62286i) q^{24} +(3.11609 + 3.90746i) q^{25} +(7.35247 + 0.945317i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(0.804255 - 5.23003i) q^{28} +(0.460848 - 2.01911i) q^{29} +(-0.0227451 + 0.0618741i) q^{30} +6.23384 q^{31} +(5.17679 + 2.28053i) q^{32} +(-2.34391 - 4.86719i) q^{33} +(2.50222 - 0.831791i) q^{34} +(-0.0149160 + 0.122424i) q^{35} +(1.96284 - 0.383725i) q^{36} +(1.79149 - 7.84902i) q^{37} +(4.40485 - 2.67240i) q^{38} +(2.27432 + 4.72268i) q^{39} +(-0.122262 - 0.0493454i) q^{40} +(-1.75191 + 3.63789i) q^{41} +(3.41020 - 1.53965i) q^{42} +(2.31404 + 4.80515i) q^{43} +(9.87648 - 4.38050i) q^{44} +(-0.0454453 + 0.0103726i) q^{45} +(-8.09661 + 7.84675i) q^{46} +(0.371672 - 0.466062i) q^{47} +(0.644061 + 3.94781i) q^{48} +(5.55084 - 4.26476i) q^{49} +(-6.63396 - 2.43866i) q^{50} +(1.45775 + 1.16252i) q^{51} +(-9.58325 + 4.25044i) q^{52} +(0.113587 + 0.497658i) q^{53} +(0.984208 + 1.01555i) q^{54} +(-0.226879 + 0.109259i) q^{55} +(2.86407 + 6.91354i) q^{56} +(3.28232 + 1.58068i) q^{57} +(0.923910 + 2.77934i) q^{58} +(3.00005 - 1.44475i) q^{59} +(-0.0178870 - 0.0914961i) q^{60} +(12.0386 + 2.74773i) q^{61} +(-7.53728 + 4.57284i) q^{62} +(2.22740 + 1.42782i) q^{63} +(-7.93210 + 1.04008i) q^{64} +(0.220143 - 0.106015i) q^{65} +(6.40434 + 4.16549i) q^{66} -9.62227i q^{67} +(-2.41526 + 2.84122i) q^{68} +(-7.77277 - 1.77408i) q^{69} +(-0.0717694 - 0.158963i) q^{70} +(1.82800 - 0.417230i) q^{71} +(-2.09178 + 1.90380i) q^{72} +(7.50927 - 5.98844i) q^{73} +(3.59158 + 10.8043i) q^{74} +(-1.11212 - 4.87252i) q^{75} +(-3.36552 + 6.46236i) q^{76} +(13.4475 + 4.84239i) q^{77} +(-6.21419 - 4.04182i) q^{78} -6.41351i q^{79} +(0.184023 - 0.0300223i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-0.550352 - 5.68366i) q^{82} +(2.99386 + 3.75418i) q^{83} +(-2.99383 + 4.36314i) q^{84} +(0.0541898 - 0.0679518i) q^{85} +(-6.32271 - 4.11240i) q^{86} +(-1.29127 + 1.61920i) q^{87} +(-8.72825 + 12.5413i) q^{88} +(-12.8025 + 10.2097i) q^{89} +(0.0473388 - 0.0458779i) q^{90} +(-13.0482 - 4.69862i) q^{91} +(4.03354 - 15.4267i) q^{92} +(-5.61649 - 2.70476i) q^{93} +(-0.107505 + 0.836153i) q^{94} +(0.0736821 - 0.153002i) q^{95} +(-3.67465 - 4.30081i) q^{96} -6.08284i q^{97} +(-3.58306 + 9.22831i) q^{98} +5.40217i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more