LMFDB - Embedded newform 588.2.x.a.55.4

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			55.4
Character	$\chi$	$=$	588.55
Dual form			588.2.x.a.139.4

$q$-expansion

$f(q)$	$=$	$q+(-1.27947 + 0.602464i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.27407 - 1.54167i) q^{4} +(0.0432081 - 0.0897226i) q^{5} +(1.41416 + 0.0123389i) q^{6} +(0.103018 + 2.64374i) q^{7} +(-0.701339 + 2.74010i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-1.27947 + 0.602464i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.27407 - 1.54167i) q^{4} +(0.0432081 - 0.0897226i) q^{5} +(1.41416 + 0.0123389i) q^{6} +(0.103018 + 2.64374i) q^{7} +(-0.701339 + 2.74010i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.00122877 + 0.140828i) q^{10} +(-2.51790 - 2.00796i) q^{11} +(-1.81681 + 0.836193i) q^{12} +(0.338941 + 0.270296i) q^{13} +(-1.72457 - 3.32052i) q^{14} +(-0.0778583 + 0.0620899i) q^{15} +(-0.753469 - 3.92839i) q^{16} +(1.76286 + 0.402362i) q^{17} +(-1.26876 - 0.624698i) q^{18} +0.291299 q^{19} +(-0.0832719 - 0.180926i) q^{20} +(1.05426 - 2.42663i) q^{21} +(4.43130 + 1.05217i) q^{22} +(-8.74008 + 1.99487i) q^{23} +(1.82077 - 2.16444i) q^{24} +(3.11127 + 3.90140i) q^{25} +(-0.596507 - 0.141636i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(4.20703 + 3.20951i) q^{28} +(0.201203 - 0.881528i) q^{29} +(0.0622102 - 0.126349i) q^{30} -2.49658 q^{31} +(3.33075 + 4.57232i) q^{32} +(1.39733 + 2.90159i) q^{33} +(-2.49793 + 0.547252i) q^{34} +(0.241655 + 0.104988i) q^{35} +(1.99970 + 0.0348984i) q^{36} +(-0.872620 + 3.82320i) q^{37} +(-0.372708 + 0.175497i) q^{38} +(-0.188098 - 0.390589i) q^{39} +(0.215545 + 0.181320i) q^{40} +(-4.00391 + 8.31420i) q^{41} +(0.113064 + 3.73995i) q^{42} +(4.80724 + 9.98234i) q^{43} +(-6.30360 + 1.32347i) q^{44} +(0.0970877 - 0.0221596i) q^{45} +(9.98081 - 7.81795i) q^{46} +(-3.95275 + 4.95659i) q^{47} +(-1.02561 + 3.86628i) q^{48} +(-6.97877 + 0.544709i) q^{49} +(-6.33122 - 3.11729i) q^{50} +(-1.41371 - 1.12739i) q^{51} +(0.848542 - 0.178156i) q^{52} +(-1.58701 - 6.95314i) q^{53} +(0.872067 + 1.11333i) q^{54} +(-0.288953 + 0.139152i) q^{55} +(-7.31636 - 1.57188i) q^{56} +(-0.262452 - 0.126390i) q^{57} +(0.273656 + 1.24910i) q^{58} +(-10.7197 + 5.16235i) q^{59} +(-0.00347534 + 0.199139i) q^{60} +(-0.494137 - 0.112783i) q^{61} +(3.19430 - 1.50410i) q^{62} +(-2.00273 + 1.72889i) q^{63} +(-7.01625 - 3.84347i) q^{64} +(0.0388966 - 0.0187316i) q^{65} +(-3.53594 - 2.87064i) q^{66} -7.57742i q^{67} +(2.86633 - 2.20511i) q^{68} +(8.74008 + 1.99487i) q^{69} +(-0.372441 + 0.0112594i) q^{70} +(1.74261 - 0.397740i) q^{71} +(-2.57957 + 1.16009i) q^{72} +(-11.1695 + 8.90740i) q^{73} +(-1.18685 - 5.41738i) q^{74} +(-1.11040 - 4.86497i) q^{75} +(0.371137 - 0.449086i) q^{76} +(5.04914 - 6.86355i) q^{77} +(0.475981 + 0.386424i) q^{78} -4.06437i q^{79} +(-0.385022 - 0.102135i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.113864 - 13.0500i) q^{82} +(9.81797 + 12.3113i) q^{83} +(-2.39785 - 4.71703i) q^{84} +(0.112271 - 0.140783i) q^{85} +(-12.1647 - 9.87589i) q^{86} +(-0.563758 + 0.706930i) q^{87} +(7.26791 - 5.49103i) q^{88} +(3.04839 - 2.43101i) q^{89} +(-0.110870 + 0.0868444i) q^{90} +(-0.679677 + 0.923918i) q^{91} +(-8.06009 + 16.0159i) q^{92} +(2.24934 + 1.08323i) q^{93} +(2.07125 - 8.72319i) q^{94} +(0.0125865 - 0.0261361i) q^{95} +(-1.01705 - 5.56467i) q^{96} +4.63664i q^{97} +(8.60095 - 4.90140i) q^{98} -3.22052i 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 $

$2$	−1.27947	+	0.602464i	−0.904720	+	0.426006i
$2$	−1.27947	+	0.602464i	−0.904720	+	0.426006i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	1.27407	−	1.54167i	0.637037	−	0.770833i
$5$	0.0432081	−	0.0897226i	0.0193233	−	0.0401251i	−0.891084	−	0.453839i	$-0.850054\pi$
$5$	0.0432081	−	0.0897226i	0.0193233	−	0.0401251i	0.910407	+	0.413714i	$0.135769\pi$
$6$	1.41416	+	0.0123389i	0.577328	+	0.00503734i
$7$	0.103018	+	2.64374i	0.0389373	+	0.999242i
$7$	0.103018	+	2.64374i	0.0389373	+	0.999242i
$8$	−0.701339	+	2.74010i	−0.247961	+	0.968770i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−0.00122877	+	0.140828i	−0.000388570	+	0.0445339i
$11$	−2.51790	−	2.00796i	−0.759176	−	0.605423i	0.165486	−	0.986212i	$-0.447081\pi$
$11$	−2.51790	−	2.00796i	−0.759176	−	0.605423i	−0.924662	+	0.380789i	$0.875652\pi$
$12$	−1.81681	+	0.836193i	−0.524466	+	0.241388i
$13$	0.338941	+	0.270296i	0.0940052	+	0.0749667i	0.669365	−	0.742934i	$-0.266566\pi$
$13$	0.338941	+	0.270296i	0.0940052	+	0.0749667i	−0.575359	+	0.817901i	$0.695138\pi$
$14$	−1.72457	−	3.32052i	−0.460911	−	0.887447i
$15$	−0.0778583	+	0.0620899i	−0.0201029	+	0.0160316i
$16$	−0.753469	−	3.92839i	−0.188367	−	0.982099i
$17$	1.76286	+	0.402362i	0.427557	+	0.0975871i	0.430884	−	0.902407i	$-0.358202\pi$
$17$	1.76286	+	0.402362i	0.427557	+	0.0975871i	−0.00332696	+	0.999994i	$0.501059\pi$
$18$	−1.26876	−	0.624698i	−0.299050	−	0.147243i
$19$	0.291299			0.0668286			0.0334143	−	0.999442i	$-0.489362\pi$
$19$	0.291299			0.0668286			0.0334143	+	0.999442i	$0.489362\pi$
$20$	−0.0832719	−	0.180926i	−0.0186202	−	0.0404562i
$21$	1.05426	−	2.42663i	0.230059	−	0.529534i
$22$	4.43130	+	1.05217i	0.944756	+	0.224324i
$23$	−8.74008	+	1.99487i	−1.82243	+	0.415958i	−0.990338	−	0.138676i	$-0.955715\pi$
$23$	−8.74008	+	1.99487i	−1.82243	+	0.415958i	−0.832094	+	0.554634i	$0.812858\pi$
$24$	1.82077	−	2.16444i	0.371663	−	0.441815i
$25$	3.11127	+	3.90140i	0.622253	+	0.780281i
$26$	−0.596507	−	0.141636i	−0.116985	−	0.0277770i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	4.20703	+	3.20951i	0.795053	+	0.606540i
$29$	0.201203	−	0.881528i	0.0373624	−	0.163696i	−0.952805	−	0.303583i	$-0.901817\pi$
$29$	0.201203	−	0.881528i	0.0373624	−	0.163696i	0.990167	+	0.139888i	$0.0446741\pi$
$30$	0.0622102	−	0.126349i	0.0113580	−	0.0230680i
$31$	−2.49658			−0.448399			−0.224200	−	0.974543i	$-0.571977\pi$
$31$	−2.49658			−0.448399			−0.224200	+	0.974543i	$0.571977\pi$
$32$	3.33075	+	4.57232i	0.588800	+	0.808279i
$33$	1.39733	+	2.90159i	0.243244	+	0.505101i
$34$	−2.49793	+	0.547252i	−0.428392	+	0.0938529i
$35$	0.241655	+	0.104988i	0.0408471	+	0.0177462i
$36$	1.99970	+	0.0348984i	0.333283	+	0.00581640i
$37$	−0.872620	+	3.82320i	−0.143458	+	0.628530i	0.851159	+	0.524908i	$0.175900\pi$
$37$	−0.872620	+	3.82320i	−0.143458	+	0.628530i	−0.994617	+	0.103622i	$0.966957\pi$
$38$	−0.372708	+	0.175497i	−0.0604612	+	0.0284694i
$39$	−0.188098	−	0.390589i	−0.0301198	−	0.0625443i
$40$	0.215545	+	0.181320i	0.0340806	+	0.0286692i
$41$	−4.00391	+	8.31420i	−0.625305	+	1.29846i	0.312043	+	0.950068i	$0.398987\pi$
$41$	−4.00391	+	8.31420i	−0.625305	+	1.29846i	−0.937349	+	0.348392i	$0.886728\pi$
$42$	0.113064	+	3.73995i	0.0174461	+	0.577087i
$43$	4.80724	+	9.98234i	0.733097	+	1.52229i	0.848629	+	0.528989i	$0.177429\pi$
$43$	4.80724	+	9.98234i	0.733097	+	1.52229i	−0.115532	+	0.993304i	$0.536857\pi$
$44$	−6.30360	+	1.32347i	−0.950303	+	0.199521i
$45$	0.0970877	−	0.0221596i	0.0144730	−	0.00330336i
$46$	9.98081	−	7.81795i	1.47159	−	1.15269i
$47$	−3.95275	+	4.95659i	−0.576568	+	0.722993i	−0.981523	−	0.191343i	$-0.938716\pi$
$47$	−3.95275	+	4.95659i	−0.576568	+	0.722993i	0.404955	+	0.914336i	$0.367287\pi$
$48$	−1.02561	+	3.86628i	−0.148035	+	0.558049i
$49$	−6.97877	+	0.544709i	−0.996968	+	0.0778155i
$50$	−6.33122	−	3.11729i	−0.895370	−	0.440852i
$51$	−1.41371	−	1.12739i	−0.197958	−	0.157867i
$52$	0.848542	−	0.178156i	0.117672	−	0.0247058i
$53$	−1.58701	−	6.95314i	−0.217993	−	0.955088i	−0.958959	−	0.283546i	$-0.908489\pi$
$53$	−1.58701	−	6.95314i	−0.217993	−	0.955088i	0.740966	−	0.671542i	$-0.234368\pi$
$54$	0.872067	+	1.11333i	0.118673	+	0.151505i
$55$	−0.288953	+	0.139152i	−0.0389624	+	0.0187633i
$56$	−7.31636	−	1.57188i	−0.977690	−	0.210051i
$57$	−0.262452	−	0.126390i	−0.0347626	−	0.0167408i
$58$	0.273656	+	1.24910i	0.0359328	+	0.164015i
$59$	−10.7197	+	5.16235i	−1.39559	+	0.672081i	−0.972262	−	0.233895i	$-0.924853\pi$
$59$	−10.7197	+	5.16235i	−1.39559	+	0.672081i	−0.423329	+	0.905976i	$0.639138\pi$
$60$	−0.00347534	+	0.199139i	−0.000448665	+	0.0257087i
$61$	−0.494137	−	0.112783i	−0.0632677	−	0.0144404i	0.190770	−	0.981635i	$-0.438902\pi$
$61$	−0.494137	−	0.112783i	−0.0632677	−	0.0144404i	−0.254038	+	0.967194i	$0.581759\pi$
$62$	3.19430	−	1.50410i	0.405676	−	0.191021i
$63$	−2.00273	+	1.72889i	−0.252321	+	0.217820i
$64$	−7.01625	−	3.84347i	−0.877031	−	0.480434i
$65$	0.0388966	−	0.0187316i	0.00482453	−	0.00232337i
$66$	−3.53594	−	2.87064i	−0.435244	−	0.353352i
$67$		−	7.57742i		−	0.925729i	−0.886429	−	0.462864i	$-0.846822\pi$
$67$		−	7.57742i		−	0.925729i	0.886429	−	0.462864i	$-0.153178\pi$
$68$	2.86633	−	2.20511i	0.347593	−	0.267408i
$69$	8.74008	+	1.99487i	1.05218	+	0.240154i
$70$	−0.372441	+	0.0112594i	−0.0445152	+	0.00134575i
$71$	1.74261	−	0.397740i	0.206810	−	0.0472031i	−0.117861	−	0.993030i	$-0.537604\pi$
$71$	1.74261	−	0.397740i	0.206810	−	0.0472031i	0.324671	+	0.945827i	$0.394746\pi$
$72$	−2.57957	+	1.16009i	−0.304005	+	0.136718i
$73$	−11.1695	+	8.90740i	−1.30729	+	1.04253i	−0.311564	+	0.950225i	$0.600853\pi$
$73$	−11.1695	+	8.90740i	−1.30729	+	1.04253i	−0.995731	+	0.0923076i	$0.970576\pi$
$74$	−1.18685	−	5.41738i	−0.137969	−	0.629758i
$75$	−1.11040	−	4.86497i	−0.128218	−	0.561758i
$76$	0.371137	−	0.449086i	0.0425723	−	0.0515137i
$77$	5.04914	−	6.86355i	0.575403	−	0.782174i
$78$	0.475981	+	0.386424i	0.0538942	+	0.0437539i
$79$		−	4.06437i		−	0.457278i	−0.973511	−	0.228639i	$-0.926573\pi$
$79$		−	4.06437i		−	0.457278i	0.973511	−	0.228639i	$-0.0734275\pi$
$80$	−0.385022	−	0.102135i	−0.0430467	−	0.0114191i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	0.113864	−	13.0500i	0.0125742	−	1.44113i
$83$	9.81797	+	12.3113i	1.07766	+	1.35135i	0.932184	+	0.361984i	$0.117900\pi$
$83$	9.81797	+	12.3113i	1.07766	+	1.35135i	0.145477	+	0.989362i	$0.453528\pi$
$84$	−2.39785	−	4.71703i	−0.261626	−	0.514670i
$85$	0.112271	−	0.140783i	0.0121775	−	0.0152701i
$86$	−12.1647	−	9.87589i	−1.31175	−	1.06494i
$87$	−0.563758	+	0.706930i	−0.0604412	+	0.0757909i
$88$	7.26791	−	5.49103i	0.774761	−	0.585346i
$89$	3.04839	−	2.43101i	0.323129	−	0.257687i	−0.448467	−	0.893799i	$-0.648030\pi$
$89$	3.04839	−	2.43101i	0.323129	−	0.257687i	0.771596	+	0.636112i	$0.219459\pi$
$90$	−0.110870	+	0.0868444i	−0.0116867	+	0.00915420i
$91$	−0.679677	+	0.923918i	−0.0712495	+	0.0968529i
$92$	−8.06009	+	16.0159i	−0.840323	+	1.66977i
$93$	2.24934	+	1.08323i	0.233246	+	0.112325i
$94$	2.07125	−	8.72319i	0.213633	−	0.899728i
$95$	0.0125865	−	0.0261361i	0.00129135	−	0.00268151i
$96$	−1.01705	−	5.56467i	−0.103803	−	0.567942i
$97$			4.63664i			0.470780i	0.971901	+	0.235390i	$0.0756367\pi$
$97$			4.63664i			0.470780i	−0.971901	+	0.235390i	$0.924363\pi$
$98$	8.60095	−	4.90140i	0.868827	−	0.495116i
$99$		−	3.22052i		−	0.323674i
$100$	9.97865	+	0.174146i	0.997865	+	0.0174146i
$101$	−4.79379	+	9.95441i	−0.477000	+	0.990501i	0.514143	+	0.857704i	$0.328110\pi$
$101$	−4.79379	+	9.95441i	−0.477000	+	0.990501i	−0.991143	+	0.132796i	$0.957604\pi$
$102$	2.48800	+	0.590756i	0.246349	+	0.0584935i
$103$	2.70373	+	1.30205i	0.266407	+	0.128295i	0.562319	−	0.826920i	$-0.309909\pi$
$103$	2.70373	+	1.30205i	0.266407	+	0.128295i	−0.295912	+	0.955215i	$0.595624\pi$
$104$	−0.978349	+	0.739161i	−0.0959351	+	0.0724807i
$105$	−0.172171	−	0.199441i	−0.0168021	−	0.0194635i
$106$	6.21955	+	7.94021i	0.604096	+	0.771221i
$107$	2.92841	−	2.33533i	0.283100	−	0.225765i	−0.471636	−	0.881793i	$-0.656336\pi$
$107$	2.92841	−	2.33533i	0.283100	−	0.225765i	0.754736	+	0.656029i	$0.227765\pi$
$108$	−1.78652	−	0.899078i	−0.171908	−	0.0865138i
$109$	4.13307	−	5.18270i	0.395876	−	0.496413i	−0.543449	−	0.839442i	$-0.682882\pi$
$109$	4.13307	−	5.18270i	0.395876	−	0.496413i	0.939325	+	0.343030i	$0.111453\pi$
$110$	0.285872	−	0.352125i	0.0272568	−	0.0335738i
$111$	2.44503	−	3.06597i	0.232072	−	0.291009i
$112$	10.3081	−	2.39668i	0.974019	−	0.226465i
$113$	2.17341	+	2.72537i	0.204457	+	0.256381i	0.873479	−	0.486862i	$-0.161858\pi$
$113$	2.17341	+	2.72537i	0.204457	+	0.256381i	−0.669022	+	0.743242i	$0.733287\pi$
$114$	0.411944	+	0.00359432i	0.0385821	+	0.000336639i
$115$	−0.198658	+	0.870377i	−0.0185249	+	0.0811630i
$116$	−1.10267	−	1.43332i	−0.102381	−	0.133080i
$117$			0.433521i			0.0400791i
$118$	10.6054	−	13.0633i	0.976308	−	1.20258i
$119$	−0.882135	+	4.70201i	−0.0808652	+	0.431032i
$120$	−0.115527	−	0.256885i	−0.0105462	−	0.0234503i
$121$	−0.139802	−	0.612512i	−0.0127093	−	0.0556829i
$122$	0.700180	−	0.153397i	0.0633913	−	0.0138879i
$123$	7.21479	−	5.75361i	0.650536	−	0.518785i
$124$	−3.18083	+	3.84890i	−0.285647	+	0.345641i
$125$	0.969915	−	0.221377i	0.0867518	−	0.0198005i
$126$	1.52084	−	3.41863i	0.135487	−	0.304556i
$127$	0.415526	+	0.0948410i	0.0368719	+	0.00841578i	0.240917	−	0.970546i	$-0.422552\pi$
$127$	0.415526	+	0.0948410i	0.0368719	+	0.00841578i	−0.204045	+	0.978961i	$0.565409\pi$
$128$	11.2926	+	0.690559i	0.998135	+	0.0610374i
$129$		−	11.0796i		−	0.975501i
$130$	−0.0384819	+	0.0474003i	−0.00337508	+	0.00415729i
$131$	3.08635	−	1.48631i	0.269656	−	0.129859i	−0.294170	−	0.955753i	$-0.595043\pi$
$131$	3.08635	−	1.48631i	0.269656	−	0.129859i	0.563826	+	0.825894i	$0.309329\pi$
$132$	6.25358	+	1.54262i	0.544304	+	0.134268i
$133$	0.0300092	+	0.770121i	0.00260213	+	0.0667779i
$134$	4.56512	+	9.69506i	0.394366	+	0.837525i
$135$	−0.0970877	−	0.0221596i	−0.00835598	−	0.00190720i
$136$	−2.33887	+	4.54822i	−0.200557	+	0.390007i
$137$	13.2872	−	6.39879i	1.13520	−	0.546686i	0.230647	−	0.973037i	$-0.425916\pi$
$137$	13.2872	−	6.39879i	1.13520	−	0.546686i	0.904557	+	0.426352i	$0.140201\pi$
$138$	−12.3845	+	2.71322i	−1.05424	+	0.230964i
$139$	13.6333	+	6.56547i	1.15637	+	0.556876i	0.910940	−	0.412539i	$-0.135358\pi$
$139$	13.6333	+	6.56547i	1.15637	+	0.556876i	0.245425	+	0.969415i	$0.421072\pi$
$140$	0.469743	−	0.238788i	0.0397005	−	0.0201813i
$141$	5.71189	−	2.75070i	0.481028	−	0.231651i
$142$	−1.98999	+	1.55876i	−0.166997	+	0.130808i
$143$	−0.310676	−	1.36116i	−0.0259800	−	0.113826i
$144$	2.60156	−	3.03840i	0.216797	−	0.253200i
$145$	−0.0703993	−	0.0561416i	−0.00584635	−	0.00466231i
$146$	8.92466	−	18.1260i	0.738610	−	1.50012i
$147$	6.52400	+	2.53721i	0.538090	+	0.209266i
$148$	4.78231	+	6.21633i	0.393104	+	0.510979i
$149$	5.80456	−	7.27869i	0.475528	−	0.596293i	−0.484987	−	0.874521i	$-0.661176\pi$
$149$	5.80456	−	7.27869i	0.475528	−	0.596293i	0.960515	+	0.278228i	$0.0897471\pi$
$150$	4.35169	+	5.55560i	0.355314	+	0.453613i
$151$	−12.9126	+	2.94721i	−1.05081	+	0.239840i	−0.712847	−	0.701319i	$-0.752595\pi$
$151$	−12.9126	+	2.94721i	−1.05081	+	0.239840i	−0.337962	+	0.941160i	$0.609738\pi$
$152$	−0.204299	+	0.798188i	−0.0165709	+	0.0647416i
$153$	0.784547	+	1.62913i	0.0634269	+	0.131707i
$154$	−2.32518	+	11.8236i	−0.187368	+	0.952774i
$155$	−0.107873	+	0.224000i	−0.00866453	+	0.0179921i
$156$	−0.841809	−	0.207656i	−0.0673986	−	0.0166258i
$157$	−9.20136	−	19.1068i	−0.734348	−	1.52489i	−0.847198	−	0.531278i	$-0.821712\pi$
$157$	−9.20136	−	19.1068i	−0.734348	−	1.52489i	0.112849	−	0.993612i	$-0.464002\pi$
$158$	2.44864	+	5.20023i	0.194803	+	0.413708i
$159$	−1.58701	+	6.95314i	−0.125858	+	0.551420i
$160$	0.554155	−	0.101283i	0.0438098	−	0.00800710i
$161$	−6.17431	−	22.9010i	−0.486603	−	1.80485i
$162$	−0.302651	−	1.38145i	−0.0237785	−	0.108537i
$163$	−5.23935	−	10.8796i	−0.410378	−	0.852158i	−0.999041	−	0.0437797i	$-0.986060\pi$
$163$	−5.23935	−	10.8796i	−0.410378	−	0.852158i	0.588664	−	0.808378i	$-0.299654\pi$
$164$	7.71644	+	16.7656i	0.602553	+	1.30917i
$165$	0.320714			0.0249675
$166$	−19.9789	−	9.83699i	−1.55066	−	0.763498i
$167$	2.22077	−	9.72981i	0.171848	−	0.752915i	−0.813389	−	0.581720i	$-0.802380\pi$
$167$	2.22077	−	9.72981i	0.171848	−	0.752915i	0.985237	−	0.171195i	$-0.0547629\pi$
$168$	5.90980	+	4.59067i	0.455951	+	0.354178i
$169$	−2.85095	−	12.4908i	−0.219304	−	0.960833i
$170$	−0.0588301	+	0.247767i	−0.00451206	+	0.0190028i
$171$	0.181622	+	0.227747i	0.0138890	+	0.0174162i
$172$	21.5142	+	5.30708i	1.64044	+	0.404661i
$173$	12.3035	−	2.80818i	0.935415	−	0.213502i	0.272465	−	0.962166i	$-0.412161\pi$
$173$	12.3035	−	2.80818i	0.935415	−	0.213502i	0.662950	+	0.748663i	$0.269304\pi$
$174$	0.295410	−	1.24414i	0.0223950	−	0.0943179i
$175$	−9.99380	+	8.62731i	−0.755460	+	0.652163i
$176$	−5.99090	+	11.4042i	−0.451581	+	0.859628i
$177$	11.8980			0.894309
$178$	−2.43572	+	4.94695i	−0.182565	+	0.370789i
$179$	−1.27626	−	0.291299i	−0.0953923	−	0.0217727i	0.174558	−	0.984647i	$-0.444150\pi$
$179$	−1.27626	−	0.291299i	−0.0953923	−	0.0217727i	−0.269951	+	0.962874i	$0.587007\pi$
$180$	0.0895342	−	0.177910i	0.00667349	−	0.0132606i
$181$	−18.1571	+	14.4798i	−1.34961	+	1.07628i	−0.359926	+	0.932981i	$0.617198\pi$
$181$	−18.1571	+	14.4798i	−1.34961	+	1.07628i	−0.989680	+	0.143294i	$0.954230\pi$
$182$	0.312997	−	1.59160i	0.0232009	−	0.117978i
$183$	0.396267	+	0.316012i	0.0292929	+	0.0233603i
$184$	0.663632	−	25.3477i	0.0489236	−	1.86866i
$185$	0.305323	+	0.243487i	0.0224478	+	0.0179015i
$186$	−3.53057	−	0.0308051i	−0.258874	−	0.00225874i
$187$	−3.63079	−	4.55286i	−0.265510	−	0.332938i
$188$	2.60531	+	12.4089i	0.190012	+	0.905011i
$189$	2.55454	−	0.688724i	0.185815	−	0.0500973i
$190$	−0.000357938		0.0410232i	−2.59676e−5		0.00297614i
$191$	5.12907	−	10.6506i	0.371126	−	0.770652i	−0.628850	−	0.777527i	$-0.716474\pi$
$191$	5.12907	−	10.6506i	0.371126	−	0.770652i	0.999976	+	0.00687470i	$0.00218830\pi$
$192$	4.65380	+	6.50708i	0.335859	+	0.469608i
$193$	4.61141	+	2.22074i	0.331937	+	0.159852i	0.592427	−	0.805624i	$-0.298170\pi$
$193$	4.61141	+	2.22074i	0.331937	+	0.159852i	−0.260490	+	0.965477i	$0.583884\pi$
$194$	−2.79341	−	5.93244i	−0.200555	−	0.425924i
$195$	−0.0431720			−0.00309161
$196$	−8.05172	+	11.4529i	−0.575123	+	0.818067i
$197$	−20.4863			−1.45959			−0.729795	−	0.683666i	$-0.760384\pi$
$197$	−20.4863			−1.45959			−0.729795	+	0.683666i	$0.760384\pi$
$198$	1.94025	+	4.12055i	0.137887	+	0.292835i
$199$	16.8766	+	8.12736i	1.19635	+	0.576133i	0.922634	−	0.385677i	$-0.126032\pi$
$199$	16.8766	+	8.12736i	1.19635	+	0.576133i	0.273719	+	0.961810i	$0.411746\pi$
$200$	−12.8723	+	5.78896i	−0.910207	+	0.409341i
$201$	−3.28772	+	6.82702i	−0.231898	+	0.481541i
$202$	0.136327	−	15.6244i	0.00959196	−	1.09933i
$203$	2.35126	+	0.441116i	0.165026	+	0.0309603i
$204$	−3.53923	+	0.743080i	−0.247796	+	0.0520260i
$205$	0.572970	+	0.718482i	0.0400180	+	0.0501809i
$206$	−4.24378	−	0.0370281i	−0.295678	−	0.00257987i
$207$	−7.00900	−	5.58949i	−0.487159	−	0.388496i
$208$	0.806449	−	1.53515i	0.0559172	−	0.106444i
$209$	−0.733463	−	0.584917i	−0.0507347	−	0.0404596i
$210$	0.340443	+	0.151452i	0.0234928	+	0.0104512i
$211$	8.71002	−	6.94601i	0.599623	−	0.478183i	−0.276014	−	0.961154i	$-0.589014\pi$
$211$	8.71002	−	6.94601i	0.599623	−	0.478183i	0.875637	+	0.482971i	$0.160442\pi$
$212$	−12.7414	−	6.41218i	−0.875083	−	0.440391i
$213$	−1.74261	−	0.397740i	−0.119402	−	0.0272527i
$214$	−2.33985	+	4.75223i	−0.159949	+	0.324856i
$215$	1.10335			0.0752480
$216$	2.82746	+	0.0740260i	0.192384	+	0.00503683i
$217$	−0.257194	−	6.60033i	−0.0174595	−	0.448059i
$218$	−2.16573	+	9.12112i	−0.146682	+	0.617760i
$219$	13.9282	−	3.17902i	0.941179	−	0.214818i
$220$	−0.153621	+	0.622760i	−0.0103571	+	0.0419865i
$221$	0.488749	+	0.612872i	0.0328768	+	0.0412262i
$222$	−1.28120	+	5.39585i	−0.0859884	+	0.362145i
$223$	3.75803	+	16.4650i	0.251656	+	1.10258i	0.929921	+	0.367760i	$0.119875\pi$
$223$	3.75803	+	16.4650i	0.251656	+	1.10258i	−0.678264	+	0.734818i	$0.737268\pi$
$224$	−11.7449	+	9.27670i	−0.784740	+	0.619826i
$225$	−1.11040	+	4.86497i	−0.0740265	+	0.324331i
$226$	−4.42274	−	2.17762i	−0.294196	−	0.144853i
$227$	12.9783			0.861398			0.430699	−	0.902496i	$-0.358267\pi$
$227$	12.9783			0.861398			0.430699	+	0.902496i	$0.358267\pi$
$228$	−0.529234	+	0.243582i	−0.0350494	+	0.0161316i
$229$	−3.93075	−	8.16229i	−0.259751	−	0.539379i	0.729783	−	0.683679i	$-0.239621\pi$
$229$	−3.93075	−	8.16229i	−0.259751	−	0.539379i	−0.989534	+	0.144300i	$0.953907\pi$
$230$	−0.270194	−	1.23330i	−0.0178161	−	0.0813216i
$231$	−7.52710	+	3.99310i	−0.495247	+	0.262727i
$232$	2.27436	+	1.16956i	0.149319	+	0.0767857i
$233$	−4.46702	+	19.5713i	−0.292644	+	1.28216i	0.588186	+	0.808725i	$0.299842\pi$
$233$	−4.46702	+	19.5713i	−0.292644	+	1.28216i	−0.880830	+	0.473432i	$0.843015\pi$
$234$	−0.261181	−	0.554676i	−0.0170739	−	0.0362603i
$235$	0.273927	+	0.568816i	0.0178690	+	0.0371054i
$236$	−5.69912	+	23.1035i	−0.370981	+	1.50391i
$237$	−1.76346	+	3.66187i	−0.114549	+	0.237864i
$238$	−1.70413	−	6.54752i	−0.110462	−	0.424413i
$239$	−8.61501	−	17.8893i	−0.557259	−	1.15716i	−0.969274	−	0.245983i	$-0.920889\pi$
$239$	−8.61501	−	17.8893i	−0.557259	−	1.15716i	0.412015	−	0.911177i	$-0.364825\pi$
$240$	0.302578	+	0.259075i	0.0195313	+	0.0167232i
$241$	−25.6883	+	5.86318i	−1.65473	+	0.377680i	−0.945070	−	0.326868i	$-0.894007\pi$
$241$	−25.6883	+	5.86318i	−1.65473	+	0.377680i	−0.709656	+	0.704548i	$0.751150\pi$
$242$	0.547888	+	0.699463i	0.0352196	+	0.0449632i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	−0.803441	+	0.618099i	−0.0514351	+	0.0395697i
$245$	−0.252667	+	0.649689i	−0.0161423	+	0.0415071i
$246$	−5.76475	+	11.7082i	−0.367547	+	0.746488i
$247$	0.0987331	+	0.0787370i	0.00628224	+	0.00500992i
$248$	1.75095	−	6.84087i	0.111185	−	0.434396i
$249$	−3.50399	−	15.3520i	−0.222056	−	0.972893i
$250$	−1.10760	+	0.867583i	−0.0700509	+	0.0548708i
$251$	26.9847	−	12.9951i	1.70326	−	0.820246i	0.710016	−	0.704185i	$-0.248688\pi$
$251$	26.9847	−	12.9951i	1.70326	−	0.820246i	0.993242	−	0.116061i	$-0.0370268\pi$
$252$	0.113743	+	5.29028i	0.00716513	+	0.333256i
$253$	26.0123	+	12.5269i	1.63538	+	0.787556i
$254$	−0.588790	+	0.128993i	−0.0369440	+	0.00809375i
$255$	−0.162236	+	0.0781288i	−0.0101596	+	0.00489261i
$256$	−14.8646	+	5.91984i	−0.929036	+	0.369990i
$257$	19.5395	+	4.45977i	1.21884	+	0.278193i	0.783110	−	0.621883i	$-0.213632\pi$
$257$	19.5395	+	4.45977i	1.21884	+	0.278193i	0.435733	+	0.900076i	$0.356489\pi$
$258$	6.67503	+	14.1759i	0.415570	+	0.882555i
$259$	−10.1975	−	1.91313i	−0.633639	−	0.118876i
$260$	0.0206793	−	0.0838311i	0.00128248	−	0.00519899i
$261$	0.814654	−	0.392317i	0.0504258	−	0.0242838i
$262$	−3.05344	+	3.76110i	−0.188642	+	0.232361i
$263$		−	15.2041i		−	0.937526i	−0.883324	−	0.468763i	$-0.844700\pi$
$263$		−	15.2041i		−	0.937526i	0.883324	−	0.468763i	$-0.155300\pi$
$264$	−8.93063	+	1.79382i	−0.549642	+	0.110402i
$265$	−0.692426	−	0.158042i	−0.0425354	−	0.00970842i
$266$	−0.502366	−	0.967265i	−0.0308020	−	0.0593068i
$267$	−3.80128	+	0.867618i	−0.232635	+	0.0530974i
$268$	−11.6818	−	9.65419i	−0.713582	−	0.589724i
$269$	−7.86310	+	6.27061i	−0.479421	+	0.382326i	−0.833172	−	0.553014i	$-0.813478\pi$
$269$	−7.86310	+	6.27061i	−0.479421	+	0.382326i	0.353751	+	0.935340i	$0.384906\pi$
$270$	0.137571	−	0.0301393i	0.00837230	−	0.00183422i
$271$	−2.19942	−	9.63628i	−0.133605	−	0.585363i	−0.996761	−	0.0804244i	$-0.974372\pi$
$271$	−2.19942	−	9.63628i	−0.133605	−	0.585363i	0.863156	−	0.504938i	$-0.168485\pi$
$272$	0.252374	−	7.22839i	0.0153024	−	0.438285i
$273$	1.01324	−	0.537521i	0.0613241	−	0.0325322i
$274$	−13.1455	+	16.1921i	−0.794151	+	0.978202i
$275$		−	16.0707i		−	0.969097i
$276$	14.2109	−	10.9327i	0.855397	−	0.658070i
$277$	−1.83330	+	8.03219i	−0.110152	+	0.482608i	0.889517	+	0.456901i	$0.151041\pi$
$277$	−1.83330	+	8.03219i	−0.110152	+	0.482608i	−0.999670	+	0.0257065i	$0.991816\pi$
$278$	−21.3989	−	0.186711i	−1.28342	−	0.0111982i
$279$	−1.55659	−	1.95191i	−0.0931908	−	0.116858i
$280$	−0.457159	+	0.588525i	−0.0273205	+	0.0351711i
$281$	−3.05972	+	3.83676i	−0.182527	+	0.228882i	−0.864674	−	0.502333i	$-0.832475\pi$
$281$	−3.05972	+	3.83676i	−0.182527	+	0.228882i	0.682147	+	0.731215i	$0.261047\pi$
$282$	−5.65098	+	6.96064i	−0.336511	+	0.414500i
$283$	−6.50037	+	8.15120i	−0.386407	+	0.484539i	−0.936551	−	0.350531i	$-0.886001\pi$
$283$	−6.50037	+	8.15120i	−0.386407	+	0.484539i	0.550144	+	0.835069i	$0.314573\pi$
$284$	1.60704	−	3.19328i	0.0953601	−	0.189486i
$285$	−0.0226801	+	0.0180867i	−0.00134345	+	0.00107137i
$286$	1.21755	+	1.55439i	0.0719951	+	0.0919129i
$287$	−22.3931	−	9.72880i	−1.32182	−	0.574273i
$288$	−1.49809	+	5.45488i	−0.0882757	+	0.321432i
$289$	−12.3707	−	5.95741i	−0.727687	−	0.350436i
$290$	0.123897	+	0.0294183i	0.00727548	+	0.00172750i
$291$	2.01176	−	4.17747i	0.117932	−	0.244888i
$292$	−0.498571	+	28.5684i	−0.0291767	+	1.67184i
$293$		−	7.51453i		−	0.439004i	−0.975612	−	0.219502i	$-0.929557\pi$
$293$		−	7.51453i		−	0.439004i	0.975612	−	0.219502i	$-0.0704432\pi$
$294$	−9.87582	+	0.684195i	−0.575970	+	0.0399030i
$295$			1.18486i			0.0689851i
$296$	−9.86393	−	5.07242i	−0.573329	−	0.294828i
$297$	−1.39733	+	2.90159i	−0.0810813	+	0.168367i
$298$	−3.04160	+	12.8099i	−0.176195	+	0.742056i
$299$	−3.50157	−	1.68627i	−0.202501	−	0.0975194i
$300$	−8.91489	−	4.48647i	−0.514701	−	0.259027i
$301$	−25.8955	+	13.7375i	−1.49259	+	0.791815i
$302$	14.7456	−	11.5502i	0.848515	−	0.664640i
$303$	8.63811	−	6.88867i	0.496247	−	0.395743i
$304$	−0.219485	−	1.14434i	−0.0125883	−	0.0656323i
$305$	−0.0314699	+	0.0394620i	−0.00180196	+	0.00225959i
$306$	−1.98529	−	1.61176i	−0.113492	−	0.0921380i
$307$	4.49049	−	5.63090i	0.256286	−	0.321372i	−0.636998	−	0.770866i	$-0.719824\pi$
$307$	4.49049	−	5.63090i	0.256286	−	0.321372i	0.893284	+	0.449493i	$0.148395\pi$
$308$	−4.14831	−	16.5288i	−0.236372	−	0.941814i
$309$	−1.87104	−	2.34621i	−0.106440	−	0.133471i
$310$	0.00306771	−	0.351590i	0.000174234	−	0.0199690i
$311$	−6.27818	+	27.5065i	−0.356003	+	1.55975i	0.407044	+	0.913409i	$0.366560\pi$
$311$	−6.27818	+	27.5065i	−0.356003	+	1.55975i	−0.763047	+	0.646343i	$0.776298\pi$
$312$	1.20217	−	0.241471i	0.0680596	−	0.0136706i
$313$		−	6.93212i		−	0.391827i	−0.980621	−	0.195913i	$-0.937233\pi$
$313$		−	6.93212i		−	0.391827i	0.980621	−	0.195913i	$-0.0627671\pi$
$314$	23.2840	+	18.9031i	1.31399	+	1.06676i
$315$	0.0685863	+	0.254392i	0.00386440	+	0.0143334i
$316$	−6.26590	−	5.17831i	−0.352485	−	0.291303i
$317$	3.96119	+	17.3551i	0.222483	+	0.974760i	0.955602	+	0.294660i	$0.0952064\pi$
$317$	3.96119	+	17.3551i	0.222483	+	0.974760i	−0.733120	+	0.680100i	$0.761936\pi$
$318$	−2.15849	−	9.85244i	−0.121042	−	0.552497i
$319$	−2.27668	+	1.81559i	−0.127470	+	0.101654i
$320$	−0.648005	+	0.463447i	−0.0362246	+	0.0259075i
$321$	−3.65166	+	0.833468i	−0.203816	+	0.0465197i
$322$	21.6969	+	25.5813i	1.20912	+	1.42559i
$323$	0.513520	+	0.117208i	0.0285730	+	0.00652161i
$324$	1.21951	+	1.58518i	0.0677503	+	0.0880658i
$325$			2.16331i			0.119999i
$326$	13.2582	+	10.7636i	0.734301	+	0.596141i
$327$	−5.97245	+	2.87618i	−0.330277	+	0.159053i
$328$	−19.9736	−	16.8022i	−1.10286	−	0.927744i
$329$	−13.5112	−	9.93944i	−0.744895	−	0.547979i
$330$	−0.410343	+	0.193218i	−0.0225886	+	0.0106363i
$331$	8.13197	+	1.85607i	0.446974	+	0.102019i	0.440082	−	0.897957i	$-0.354949\pi$
$331$	8.13197	+	1.85607i	0.446974	+	0.102019i	0.00689126	+	0.999976i	$0.497806\pi$
$332$	31.4888	+	0.549538i	1.72817	+	0.0301598i
$333$	−3.53317	+	1.70148i	−0.193616	+	0.0932407i
$334$	3.02046	+	13.7869i	0.165272	+	0.754386i
$335$	−0.679865	−	0.327406i	−0.0371450	−	0.0178881i
$336$	−10.3271	−	2.31317i	−0.563390	−	0.126194i
$337$	27.4735	−	13.2305i	1.49657	−	0.720712i	0.506629	−	0.862164i	$-0.330891\pi$
$337$	27.4735	−	13.2305i	1.49657	−	0.720712i	0.989945	+	0.141452i	$0.0451770\pi$
$338$	11.1730	+	14.2640i	0.607730	+	0.775860i
$339$	−0.775680	−	3.39847i	−0.0421291	−	0.184580i
$340$	−0.0739993	−	0.352452i	−0.00401317	−	0.0191144i
$341$	6.28615	+	5.01304i	0.340414	+	0.271471i
$342$	−0.369589	−	0.181974i	−0.0199851	−	0.00984003i
$343$	−2.15901	−	18.3940i	−0.116576	−	0.993182i
$344$	−30.7241	+	6.17130i	−1.65653	+	0.332734i
$345$	0.556627	−	0.697988i	0.0299678	−	0.0375784i
$346$	−14.0501	+	11.0054i	−0.755335	+	0.591653i
$347$	−6.82725	+	1.55827i	−0.366506	+	0.0836525i	−0.401807	−	0.915724i	$-0.631618\pi$
$347$	−6.82725	+	1.55827i	−0.366506	+	0.0836525i	0.0353018	+	0.999377i	$0.488761\pi$
$348$	0.371581	+	1.76981i	0.0199188	+	0.0948717i
$349$	4.60062	+	9.55328i	0.246265	+	0.511375i	0.987059	−	0.160357i	$-0.0512647\pi$
$349$	4.60062	+	9.55328i	0.246265	+	0.511375i	−0.740794	+	0.671733i	$0.765550\pi$
$350$	7.58910	−	17.0593i	0.405654	−	0.911856i
$351$	0.188098	−	0.390589i	0.0100399	−	0.0208481i
$352$	0.794512	−	18.2007i	0.0423477	−	0.970099i
$353$	4.58771	+	9.52648i	0.244179	+	0.507043i	0.986654	−	0.162831i	$-0.0520624\pi$
$353$	4.58771	+	9.52648i	0.244179	+	0.507043i	−0.742475	+	0.669874i	$0.766348\pi$
$354$	−15.2231	+	7.16812i	−0.809099	+	0.380981i
$355$	0.0396088	−	0.173537i	0.00210222	−	0.00921041i
$356$	0.136070	−	7.79690i	0.00721171	−	0.413235i
$357$	2.83490	−	3.85362i	0.150039	−	0.203955i
$358$	1.80843	−	0.396195i	0.0955786	−	0.0209396i
$359$	1.99649	+	4.14575i	0.105371	+	0.218805i	0.946987	−	0.321271i	$-0.104110\pi$
$359$	1.99649	+	4.14575i	0.105371	+	0.218805i	−0.841617	+	0.540075i	$0.818396\pi$
$360$	−0.00737185	+	0.281571i	−0.000388530	+	0.0148401i
$361$	−18.9151			−0.995534
$362$	14.5079	−	29.4654i	0.762516	−	1.54867i
$363$	−0.139802	+	0.612512i	−0.00733769	+	0.0321485i
$364$	0.558414	+	2.22498i	0.0292689	+	0.116620i
$365$	0.316581	+	1.38703i	0.0165706	+	0.0726005i
$366$	−0.697397	−	0.165591i	−0.0364535	−	0.00865558i
$367$	5.06983	+	6.35737i	0.264643	+	0.331852i	0.896343	−	0.443361i	$-0.146214\pi$
$367$	5.06983	+	6.35737i	0.264643	+	0.331852i	−0.631700	+	0.775213i	$0.717643\pi$
$368$	14.4220	+	32.8314i	0.751799	+	1.71146i
$369$	−8.99670	+	2.05344i	−0.468349	+	0.106898i
$370$	−0.537343	−	0.127588i	−0.0279351	−	0.00663296i
$371$	18.2188	−	4.91195i	0.945876	−	0.255016i
$372$	4.53580	−	2.08762i	0.235170	−	0.108238i
$373$	19.3603			1.00244			0.501219	−	0.865321i	$-0.332885\pi$
$373$	19.3603			1.00244			0.501219	+	0.865321i	$0.332885\pi$
$374$	7.38841	+	3.63782i	0.382046	+	0.188107i
$375$	−0.969915	−	0.221377i	−0.0500862	−	0.0114318i
$376$	−10.8093	−	14.3072i	−0.557448	−	0.737835i
$377$	0.306469	−	0.244401i	0.0157840	−	0.0125873i
$378$	−2.85352	+	2.42022i	−0.146769	+	0.124483i
$379$	21.8478	+	17.4231i	1.12225	+	0.894963i	0.995290	−	0.0969453i	$-0.0309072\pi$
$379$	21.8478	+	17.4231i	1.12225	+	0.894963i	0.126958	+	0.991908i	$0.459479\pi$
$380$	−0.0242570	−	0.0527035i	−0.00124436	−	0.00270363i
$381$	−0.333226	−	0.265739i	−0.0170717	−	0.0136142i
$382$	−0.145862	+	16.7172i	−0.00746295	+	0.855327i
$383$	−1.53609	−	1.92620i	−0.0784907	−	0.0984242i	0.741036	−	0.671466i	$-0.234335\pi$
$383$	−1.53609	−	1.92620i	−0.0784907	−	0.0984242i	−0.819526	+	0.573041i	$0.805763\pi$
$384$	−9.87467	−	5.52185i	−0.503915	−	0.281786i
$385$	−0.397651	−	0.749583i	−0.0202662	−	0.0382023i
$386$	−7.23807	−	0.0631541i	−0.368408	−	0.00321446i
$387$	−4.80724	+	9.98234i	−0.244366	+	0.507431i
$388$	7.14816	+	5.90743i	0.362893	+	0.299904i
$389$	11.5003	+	5.53824i	0.583088	+	0.280800i	0.702084	−	0.712095i	$-0.252253\pi$
$389$	11.5003	+	5.53824i	0.583088	+	0.280800i	−0.118996	+	0.992895i	$0.537968\pi$
$390$	0.0552372	−	0.0260096i	0.00279704	−	0.00131705i
$391$	−16.2102			−0.819786
$392$	3.40193	−	19.5045i	0.171823	−	0.985128i
$393$	−3.42559			−0.172798
$394$	26.2116	−	12.3423i	1.32052	−	0.621794i
$395$	−0.364666	−	0.175614i	−0.0183483	−	0.00883609i
$396$	−4.96496	−	4.10318i	−0.249499	−	0.206193i
$397$	−1.18100	+	2.45238i	−0.0592728	+	0.123081i	−0.928501	−	0.371330i	$-0.878902\pi$
$397$	−1.18100	+	2.45238i	−0.0592728	+	0.123081i	0.869228	+	0.494411i	$0.164616\pi$
$398$	−26.4895	−	0.231128i	−1.32780	−	0.0115854i
$399$	0.307106	−	0.706875i	0.0153745	−	0.0353880i
$400$	12.9820	−	15.1619i	0.649101	−	0.758093i
$401$	15.0268	+	18.8430i	0.750402	+	0.940974i	0.999623	−	0.0274725i	$-0.00874588\pi$
$401$	15.0268	+	18.8430i	0.750402	+	0.940974i	−0.249221	+	0.968447i	$0.580174\pi$
$402$	0.0934971	−	10.7157i	0.00466321	−	0.534449i
$403$	−0.846193	−	0.674816i	−0.0421519	−	0.0336150i
$404$	9.23873	+	20.0731i	0.459644	+	0.998673i
$405$	0.0778583	+	0.0620899i	0.00386881	+	0.00308527i
$406$	−3.27412	+	0.852157i	−0.162492	+	0.0422919i
$407$	9.87400	−	7.87425i	0.489436	−	0.390312i
$408$	4.08065	−	3.08300i	0.202022	−	0.152631i
$409$	−23.5080	−	5.36555i	−1.16240	−	0.265309i	−0.402541	−	0.915402i	$-0.631873\pi$
$409$	−23.5080	−	5.36555i	−1.16240	−	0.265309i	−0.759855	+	0.650092i	$0.774730\pi$
$410$	−1.16596	−	0.574080i	−0.0575825	−	0.0283518i
$411$	−14.7477			−0.727451
$412$	5.45208	−	2.50935i	0.268605	−	0.123627i
$413$	−14.7523	−	27.8084i	−0.725912	−	1.36836i
$414$	12.3353	+	2.92890i	0.606245	+	0.143948i
$415$	1.52882	−	0.348943i	0.0750469	−	0.0171290i
$416$	−0.106951	+	2.45003i	−0.00524371	+	0.120123i
$417$	−9.43457	−	11.8306i	−0.462013	−	0.579346i
$418$	1.29083	+	0.306498i	0.0631367	+	0.0149913i
$419$	−1.89739	−	8.31300i	−0.0926934	−	0.406116i	0.907200	−	0.420699i	$-0.138215\pi$
$419$	−1.89739	−	8.31300i	−0.0926934	−	0.406116i	−0.999894	+	0.0145827i	$0.995358\pi$
$420$	−0.526830	+	0.0113270i	−0.0257067	+	0.000552703i
$421$	4.12697	−	18.0814i	0.201136	−	0.881236i	−0.769110	−	0.639116i	$-0.779300\pi$
$421$	4.12697	−	18.0814i	0.201136	−	0.881236i	0.970246	−	0.242119i	$-0.0778426\pi$
$422$	−6.95947	+	14.1347i	−0.338782	+	0.688065i
$423$	−6.33972			−0.308248
$424$	20.1653	+	0.527950i	0.979314	+	0.0256395i
$425$	3.91496	+	8.12949i	0.189903	+	0.394338i
$426$	2.46924	−	0.540966i	0.119635	−	0.0262099i
$427$	0.247266	−	1.31799i	0.0119660	−	0.0637820i
$428$	0.130715	−	7.49001i	0.00631833	−	0.362043i
$429$	−0.310676	+	1.36116i	−0.0149996	+	0.0657174i
$430$	−1.41170	+	0.664730i	−0.0680784	+	0.0320561i
$431$	7.43353	+	15.4359i	0.358061	+	0.743521i	0.999725	−	0.0234652i	$-0.00746989\pi$
$431$	7.43353	+	15.4359i	0.358061	+	0.743521i	−0.641664	+	0.766986i	$0.721756\pi$
$432$	−3.66224	+	1.60873i	−0.176200	+	0.0773999i
$433$	−11.8997	+	24.7100i	−0.571863	+	1.18748i	0.391723	+	0.920083i	$0.371879\pi$
$433$	−11.8997	+	24.7100i	−0.571863	+	1.18748i	−0.963585	+	0.267402i	$0.913835\pi$
$434$	4.30553	+	8.28995i	0.206672	+	0.397930i
$435$	0.0390687	+	0.0811269i	0.00187320	+	0.00388974i
$436$	−2.72416	−	12.9750i	−0.130464	−	0.621388i
$437$	−2.54598	+	0.581103i	−0.121791	+	0.0277979i
$438$	−15.9054	+	12.4587i	−0.759990	+	0.595298i
$439$	3.77614	−	4.73513i	0.180225	−	0.225995i	−0.683510	−	0.729941i	$-0.739547\pi$
$439$	3.77614	−	4.73513i	0.180225	−	0.225995i	0.863735	+	0.503946i	$0.168119\pi$
$440$	−0.178637	−	0.889352i	−0.00851619	−	0.0423982i
$441$	−4.77707	−	5.11661i	−0.227479	−	0.243648i
$442$	−0.994571	−	0.489696i	−0.0473069	−	0.0232925i
$443$	17.8627	+	14.2450i	0.848681	+	0.676800i	0.948005	−	0.318255i	$-0.103097\pi$
$443$	17.8627	+	14.2450i	0.848681	+	0.676800i	−0.0993245	+	0.995055i	$0.531668\pi$
$444$	−1.61155	−	7.67569i	−0.0764808	−	0.364272i
$445$	−0.0864014	−	0.378549i	−0.00409582	−	0.0179449i
$446$	−14.7278	−	18.8024i	−0.697384	−	0.890317i
$447$	−8.38783	+	4.03937i	−0.396731	+	0.191055i
$448$	9.43835	−	18.9451i	0.445920	−	0.895073i
$449$	28.7190	+	13.8303i	1.35533	+	0.652694i	0.963591	−	0.267382i	$-0.0861584\pi$
$449$	28.7190	+	13.8303i	1.35533	+	0.652694i	0.391742	+	0.920075i	$0.371873\pi$
$450$	−1.51025	−	6.89355i	−0.0711939	−	0.324965i
$451$	26.7760	−	12.8947i	1.26083	−	0.607186i
$452$	6.97068	+	0.121651i	0.327873	+	0.00572200i
$453$	12.9126	+	2.94721i	0.606685	+	0.138472i
$454$	−16.6053	+	7.81894i	−0.779324	+	0.366961i
$455$	0.0535287	+	0.100903i	0.00250947	+	0.00473041i
$456$	0.530388	−	0.630500i	0.0248377	−	0.0295259i
$457$	−17.0128	+	8.19293i	−0.795825	+	0.383249i	−0.787188	−	0.616714i	$-0.788464\pi$
$457$	−17.0128	+	8.19293i	−0.795825	+	0.383249i	−0.00863743	+	0.999963i	$0.502749\pi$
$458$	9.94675	+	8.07525i	0.464781	+	0.377332i
$459$		−	1.80820i		−	0.0843994i
$460$	1.08873	+	1.41519i	0.0507621	+	0.0659835i
$461$	−8.87806	−	2.02636i	−0.413492	−	0.0943769i	0.0107137	−	0.999943i	$-0.496590\pi$
$461$	−8.87806	−	2.02636i	−0.413492	−	0.0943769i	−0.424206	+	0.905566i	$0.639447\pi$
$462$	7.22499	−	9.64385i	0.336137	−	0.448673i
$463$	−28.1302	+	6.42053i	−1.30732	+	0.298387i	−0.818756	−	0.574141i	$-0.805336\pi$
$463$	−28.1302	+	6.42053i	−1.30732	+	0.298387i	−0.488563	+	0.872528i	$0.662479\pi$
$464$	−3.61459	−	0.126201i	−0.167803	−	0.00585874i
$465$	0.194380	−	0.155013i	0.00901414	−	0.00718854i
$466$	−6.07559	−	27.7320i	−0.281446	−	1.28466i
$467$	5.51726	+	24.1727i	0.255309	+	1.11858i	0.926203	+	0.377026i	$0.123053\pi$
$467$	5.51726	+	24.1727i	0.255309	+	1.11858i	−0.670894	+	0.741553i	$0.734089\pi$
$468$	0.668345	+	0.552338i	0.0308943	+	0.0255319i
$469$	20.0328	−	0.780613i	0.925027	−	0.0360454i
$470$	−0.693172	−	0.562750i	−0.0319736	−	0.0259577i
$471$			21.2070i			0.977165i
$472$	−6.62717	−	32.9937i	−0.305040	−	1.51866i
$473$	7.93997	−	34.7873i	0.365080	−	1.59952i
$474$	0.0501500	−	5.74767i	0.00230346	−	0.263999i
$475$	0.906309	+	1.13648i	0.0415843	+	0.0521451i
$476$	6.12502	+	7.35067i	0.280740	+	0.336917i
$477$	4.44670	−	5.57599i	0.203601	−	0.255307i
$478$	21.8003	+	17.6985i	0.997121	+	0.809510i
$479$	−7.52756	+	9.43927i	−0.343943	+	0.431291i	−0.923475	−	0.383659i	$-0.874664\pi$
$479$	−7.52756	+	9.43927i	−0.343943	+	0.431291i	0.579532	+	0.814950i	$0.303235\pi$
$480$	−0.543222	−	0.149186i	−0.0247946	−	0.00680940i
$481$	−1.32916	+	1.05997i	−0.0606046	+	0.0483305i
$482$	29.3349	−	22.9780i	1.33617	−	1.04662i
$483$	−4.37353	+	23.3120i	−0.199002	+	1.06073i
$484$	−1.12241	−	0.564858i	−0.0510185	−	0.0256754i
$485$	0.416012	+	0.200341i	0.0188901	+	0.00909700i
$486$	−0.326710	+	1.37596i	−0.0148199	+	0.0624147i
$487$	−13.4428	+	27.9143i	−0.609153	+	1.26492i	0.337093	+	0.941471i	$0.390556\pi$
$487$	−13.4428	+	27.9143i	−0.609153	+	1.26492i	−0.946246	+	0.323448i	$0.895158\pi$
$488$	0.655595	−	1.27488i	0.0296774	−	0.0577112i
$489$			12.0755i			0.546072i
$490$	−0.0681352	−	0.983479i	−0.00307803	−	0.0444291i
$491$		−	21.2953i		−	0.961042i	−0.876983	−	0.480521i	$-0.840448\pi$
$491$		−	21.2953i		−	0.961042i	0.876983	−	0.480521i	$-0.159552\pi$
$492$	0.322045	−	18.4533i	0.0145189	−	0.831940i
$493$	0.709386	−	1.47306i	0.0319491	−	0.0663431i
$494$	−0.173762	−	0.0412583i	−0.00781792	−	0.00185630i
$495$	−0.288953	−	0.139152i	−0.0129875	−	0.00625444i
$496$	1.88110	+	9.80756i	0.0844637	+	0.440372i
$497$	1.23105	+	4.56605i	0.0552199	+	0.204815i
$498$	13.7323	+	17.5313i	0.615357	+	0.785598i
$499$	2.87794	−	2.29508i	0.128834	−	0.102742i	−0.556953	−	0.830544i	$-0.688030\pi$
$499$	2.87794	−	2.29508i	0.128834	−	0.102742i	0.685787	+	0.727802i	$0.259458\pi$
$500$	0.894454	−	1.77733i	0.0400012	−	0.0794848i
$501$	−6.22245	+	7.80270i	−0.277998	+	0.348599i
$502$	−26.6969	+	32.8842i	−1.19154	+	1.46769i
$503$	−2.69326	+	3.37725i	−0.120087	+	0.150584i	−0.838241	−	0.545300i	$-0.816416\pi$
$503$	−2.69326	+	3.37725i	−0.120087	+	0.150584i	0.718154	+	0.695884i	$0.244987\pi$
$504$	−3.33273	−	6.70022i	−0.148452	−	0.298451i
$505$	0.686004	+	0.860222i	0.0305268	+	0.0382794i
$506$	−40.8288	−	0.356243i	−1.81506	−	0.0158369i
$507$	−2.85095	+	12.4908i	−0.126615	+	0.554737i
$508$	0.675624	−	0.519767i	0.0299760	−	0.0230609i
$509$		−	15.9436i		−	0.706688i	−0.935493	−	0.353344i	$-0.885045\pi$
$509$		−	15.9436i		−	0.706688i	0.935493	−	0.353344i	$-0.114955\pi$
$510$	0.160506	−	0.197705i	0.00710733	−	0.00875451i
$511$	−24.6996	−	28.6118i	−1.09264	−	1.26571i
$512$	15.4522	−	16.5296i	0.682899	−	0.730513i
$513$	−0.0648202	−	0.283996i	−0.00286188	−	0.0125387i
$514$	−27.6871	+	6.06574i	−1.22122	+	0.267548i
$515$	0.233646	−	0.186327i	0.0102957	−	0.00821054i
$516$	−17.0810	−	14.1162i	−0.751948	−	0.621430i
$517$	19.9053	−	4.54325i	0.875433	−	0.199812i
$518$	14.1999	−	3.69582i	0.623908	−	0.162385i
$519$	−12.3035	−	2.80818i	−0.540062	−	0.123266i
$520$	0.0240468	+	0.119718i	0.00105452	+	0.00524997i
$521$		−	16.7274i		−	0.732841i	−0.930449	−	0.366420i	$-0.880583\pi$
$521$		−	16.7274i		−	0.732841i	0.930449	−	0.366420i	$-0.119417\pi$
$522$	−0.805967	+	0.992756i	−0.0352762	+	0.0434518i
$523$	38.0435	−	18.3208i	1.66352	−	0.801111i	0.664998	−	0.746845i	$-0.268432\pi$
$523$	38.0435	−	18.3208i	1.66352	−	0.801111i	0.998527	−	0.0542658i	$-0.0172818\pi$
$524$	1.64085	−	6.65179i	0.0716808	−	0.290585i
$525$	12.7474	−	3.43679i	0.556340	−	0.149994i
$526$	9.15993	+	19.4532i	0.399392	+	0.848198i
$527$	−4.40113	−	1.00453i	−0.191716	−	0.0437580i
$528$	10.3457	−	7.67552i	0.450240	−	0.334034i
$529$	51.6872	−	24.8912i	2.24727	−	1.08223i
$530$	0.981150	−	0.214952i	0.0426185	−	0.00933693i
$531$	−10.7197	−	5.16235i	−0.465197	−	0.224027i
$532$	1.22550	+	0.934927i	0.0531323	+	0.0405342i
$533$	−3.60438	+	1.73578i	−0.156123	+	0.0751850i
$534$	4.34091	−	3.40023i	0.187850	−	0.147142i
$535$	−0.0830006	−	0.363649i	−0.00358843	−	0.0157219i
$536$	20.7628	+	5.31434i	0.896818	+	0.229544i
$537$	1.02348	+	0.816200i	0.0441665	+	0.0352216i
$538$	6.28276	−	12.7603i	0.270869	−	0.550134i
$539$	18.6656	+	12.6416i	0.803985	+	0.544511i
$540$	−0.157860	+	0.121444i	−0.00679320	+	0.00522611i
$541$	15.4158	−	19.3309i	0.662779	−	0.831098i	−0.330864	−	0.943678i	$-0.607340\pi$
$541$	15.4158	−	19.3309i	0.662779	−	0.831098i	0.993643	+	0.112580i	$0.0359116\pi$
$542$	8.61960	+	11.0042i	0.370243	+	0.472673i
$543$	22.6415	−	5.16778i	0.971641	−	0.221771i
$544$	4.03194	+	9.40053i	0.172868	+	0.403044i
$545$	−0.286423	−	0.594764i	−0.0122690	−	0.0254769i
$546$	−0.972572	+	1.29818i	−0.0416222	+	0.0555570i
$547$	5.35169	−	11.1129i	0.228822	−	0.475154i	−0.754670	−	0.656104i	$-0.772203\pi$
$547$	5.35169	−	11.1129i	0.228822	−	0.475154i	0.983492	+	0.180951i	$0.0579174\pi$
$548$	7.06412	−	28.6370i	0.301764	−	1.22331i
$549$	−0.219912	−	0.456651i	−0.00938559	−	0.0194894i
$550$	9.68199	+	20.5619i	0.412841	+	0.876761i
$551$	0.0586103	−	0.256788i	0.00249688	−	0.0109395i
$552$	−11.5959	+	22.5496i	−0.493553	+	0.959774i
$553$	10.7452	−	0.418705i	0.456931	−	0.0178052i
$554$	−2.49346	−	11.3814i	−0.105937	−	0.483550i
$555$	−0.169441	−	0.351849i	−0.00719239	−	0.0149351i
$556$	27.4917	−	12.6532i	1.16591	−	0.536614i
$557$	−18.4403			−0.781339			−0.390670	−	0.920531i	$-0.627756\pi$
$557$	−18.4403			−0.781339			−0.390670	+	0.920531i	$0.627756\pi$
$558$	3.16756	+	1.55961i	0.134094	+	0.0660235i
$559$	−1.06882	+	4.68280i	−0.0452062	+	0.198061i
$560$	0.230356	−	1.02842i	0.00973430	−	0.0434587i
$561$	1.29581	+	5.67733i	0.0547093	+	0.239697i
$562$	1.60330	−	6.75238i	0.0676310	−	0.284832i
$563$	−18.8789	−	23.6734i	−0.795649	−	0.997713i	−0.999824	−	0.0187783i	$-0.994022\pi$
$563$	−18.8789	−	23.6734i	−0.795649	−	0.997713i	0.204174	−	0.978935i	$-0.434549\pi$
$564$	3.03671	−	12.3104i	0.127869	−	0.518362i
$565$	0.338436	−	0.0772457i	0.0142381	−	0.00324975i
$566$	3.40620	−	14.3454i	0.143173	−	0.602984i
$567$	−2.60038	−	0.487853i	−0.109206	−	0.0204879i
$568$	−0.132316	+	5.05388i	−0.00555187	+	0.212056i
$569$	38.9896			1.63453			0.817265	−	0.576262i	$-0.195489\pi$
$569$	38.9896			1.63453			0.817265	+	0.576262i	$0.195489\pi$
$570$	0.0181218	−	0.0368053i	0.000759038	−	0.00154161i
$571$	−33.2694	−	7.59351i	−1.39228	−	0.317779i	−0.540352	−	0.841439i	$-0.681709\pi$
$571$	−33.2694	−	7.59351i	−1.39228	−	0.317779i	−0.851927	+	0.523660i	$0.824566\pi$
$572$	−2.49428	−	1.25526i	−0.104291	−	0.0524850i
$573$	−9.24226	+	7.37046i	−0.386101	+	0.307905i
$574$	34.5125	−	1.04336i	1.44052	−	0.0435489i
$575$	−34.9755	−	27.8920i	−1.45858	−	1.16318i
$576$	−1.36961	−	7.88189i	−0.0570672	−	0.328412i
$577$	14.4450	+	11.5195i	0.601352	+	0.479562i	0.876215	−	0.481921i	$-0.160061\pi$
$577$	14.4450	+	11.5195i	0.601352	+	0.479562i	−0.274862	+	0.961484i	$0.588632\pi$
$578$	19.4170	+	0.169419i	0.807641	+	0.00704688i
$579$	−3.19120	−	4.00164i	−0.132622	−	0.166302i
$580$	−0.176246	+	0.0370037i	−0.00731820	+	0.00153649i
$581$	−31.5366	+	27.2245i	−1.30836	+	1.12946i
$582$	−0.0572112	+	6.55696i	−0.00237148	+	0.271795i
$583$	−9.96570	+	20.6940i	−0.412737	+	0.857058i
$584$	−16.5735	−	36.8527i	−0.685817	−	1.52498i
$585$	0.0388966	+	0.0187316i	0.00160818	+	0.000774458i
$586$	4.52723	+	9.61460i	0.187018	+	0.397175i
$587$	−27.3889			−1.13046			−0.565230	−	0.824934i	$-0.691212\pi$
$587$	−27.3889			−1.13046			−0.565230	+	0.824934i	$0.691212\pi$
$588$	12.2236	−	6.82523i	0.504092	−	0.281468i
$589$	−0.727252			−0.0299659
$590$	−0.713834	−	1.51599i	−0.0293881	−	0.0624122i
$591$	18.4575	+	8.88868i	0.759241	+	0.365631i
$592$	15.6765	+	0.547336i	0.644301	+	0.0224954i
$593$	−2.01452	+	4.18319i	−0.0827263	+	0.171783i	−0.938229	−	0.346016i	$-0.887534\pi$
$593$	−2.01452	+	4.18319i	−0.0827263	+	0.171783i	0.855502	+	0.517799i	$0.173249\pi$
$594$	0.0397377	−	4.55433i	0.00163046	−	0.186866i
$595$	0.383761	+	0.282312i	0.0157327	+	0.0115737i
$596$	−3.82586	−	18.2223i	−0.156714	−	0.746414i
$597$	−11.6790	−	14.6450i	−0.477989	−	0.599380i
$598$	5.49606	+	0.0479546i	0.224751	+	0.00196101i
$599$	35.1376	+	28.0213i	1.43568	+	1.14492i	0.964883	+	0.262678i	$0.0846058\pi$
$599$	35.1376	+	28.0213i	1.43568	+	1.14492i	0.470799	+	0.882240i	$0.343966\pi$
$600$	14.1093	+	0.369396i	0.576008	+	0.0150805i
$601$	−20.5040	−	16.3514i	−0.836374	−	0.666986i	0.108616	−	0.994084i	$-0.465358\pi$
$601$	−20.5040	−	16.3514i	−0.836374	−	0.666986i	−0.944991	+	0.327098i	$0.893929\pi$
$602$	24.8561	−	33.1778i	1.01306	−	1.35223i
$603$	5.92426	−	4.72444i	0.241255	−	0.192394i
$604$	−11.9080	+	23.6618i	−0.484528	+	0.962786i
$605$	−0.0609967	−	0.0139221i	−0.00247987	−	0.000566014i
$606$	−6.90201	+	14.0180i	−0.280375	+	0.569441i
$607$	−3.05315			−0.123923			−0.0619617	−	0.998079i	$-0.519736\pi$
$607$	−3.05315			−0.123923			−0.0619617	+	0.998079i	$0.519736\pi$
$608$	0.970246	+	1.33191i	0.0393487	+	0.0540162i
$609$	−1.92702	−	1.41761i	−0.0780868	−	0.0574443i
$610$	0.0164903	−	0.0694499i	0.000667673	−	0.00281194i
$611$	−2.67949	+	0.611577i	−0.108401	+	0.0247418i
$612$	3.51115	+	0.866122i	0.141930	+	0.0350109i
$613$	−9.63884	−	12.0867i	−0.389309	−	0.488178i	0.548098	−	0.836414i	$-0.315352\pi$
$613$	−9.63884	−	12.0867i	−0.389309	−	0.488178i	−0.937407	+	0.348236i	$0.886781\pi$
$614$	−2.35302	+	9.90991i	−0.0949603	+	0.399931i
$615$	−0.204491	−	0.895932i	−0.00824586	−	0.0361275i
$616$	15.2656	+	18.6488i	0.615069	+	0.751382i
$617$	−1.71172	+	7.49954i	−0.0689113	+	0.301920i	−0.997625	−	0.0688771i	$-0.978058\pi$
$617$	−1.71172	+	7.49954i	−0.0689113	+	0.301920i	0.928714	+	0.370797i	$0.120915\pi$
$618$	3.80745	+	1.87467i	0.153158	+	0.0754102i
$619$	44.4332			1.78592			0.892961	−	0.450135i	$-0.148624\pi$
$619$	44.4332			1.78592			0.892961	+	0.450135i	$0.148624\pi$
$620$	0.207895	+	0.451696i	0.00834927	+	0.0181405i
$621$	3.88970	+	8.07705i	0.156088	+	0.324121i
$622$	−8.53895	−	38.9761i	−0.342381	−	1.56280i
$623$	6.74102	+	7.80874i	0.270073	+	0.312850i
$624$	−1.39266	+	1.03322i	−0.0557511	+	0.0413619i
$625$	−5.52994	+	24.2283i	−0.221198	+	0.969131i
$626$	4.17635	+	8.86942i	0.166921	+	0.354493i
$627$	0.407041	+	0.845230i	0.0162557	+	0.0337552i
$628$	−41.1795	−	10.1581i	−1.64324	−	0.405352i
$629$	−3.07662	+	6.38866i	−0.122673	+	0.254733i
$630$	−0.241016	−	0.284166i	−0.00960231	−	0.0113214i
$631$	12.4745	+	25.9036i	0.496604	+	1.03121i	0.987151	+	0.159793i	$0.0510827\pi$
$631$	12.4745	+	25.9036i	0.496604	+	1.03121i	−0.490547	+	0.871415i	$0.663203\pi$
$632$	11.1368	+	2.85050i	0.442997	+	0.113387i
$633$	−10.8612	+	2.47900i	−0.431695	+	0.0985315i
$634$	−15.5240	−	19.8188i	−0.616538	−	0.787106i
$635$	0.0264635	−	0.0331841i	0.00105017	−	0.00131687i
$636$	8.69746	+	11.3055i	0.344877	+	0.448291i
$637$	−2.51262	−	1.70171i	−0.0995537	−	0.0674243i
$638$	1.81911	−	3.69461i	0.0720193	−	0.146271i
$639$	1.39747	+	1.11444i	0.0552830	+	0.0440867i
$640$	0.549891	−	0.983364i	0.0217364	−	0.0388709i
$641$	−0.540475	−	2.36798i	−0.0213475	−	0.0935295i	0.963132	−	0.269030i	$-0.0867029\pi$
$641$	−0.540475	−	2.36798i	−0.0213475	−	0.0935295i	−0.984479	+	0.175500i	$0.943846\pi$
$642$	4.17005	−	3.26639i	0.164579	−	0.128914i
$643$	−39.3033	+	18.9275i	−1.54997	+	0.746427i	−0.996270	−	0.0862874i	$-0.972500\pi$
$643$	−39.3033	+	18.9275i	−1.54997	+	0.746427i	−0.553702	+	0.832715i	$0.686785\pi$
$644$	−43.1723	−	19.6589i	−1.70123	−	0.774669i
$645$	−0.994086	−	0.478727i	−0.0391421	−	0.0188498i
$646$	−0.727646	+	0.159414i	−0.0286288	+	0.00627206i
$647$	−27.7425	+	13.3601i	−1.09067	+	0.525240i	−0.890714	−	0.454565i	$-0.849795\pi$
$647$	−27.7425	+	13.3601i	−1.09067	+	0.525240i	−0.199958	+	0.979804i	$0.564081\pi$
$648$	−2.51533	−	1.29348i	−0.0988116	−	0.0508128i
$649$	37.3570	+	8.52650i	1.46639	+	0.334694i
$650$	−1.30331	−	2.76788i	−0.0511202	−	0.108565i
$651$	−2.63205	+	6.05828i	−0.103158	+	0.237443i
$652$	−23.4481	−	5.78412i	−0.918297	−	0.226524i
$653$	−36.1076	+	17.3885i	−1.41300	+	0.680465i	−0.975753	−	0.218876i	$-0.929761\pi$
$653$	−36.1076	+	17.3885i	−1.41300	+	0.680465i	−0.437247	+	0.899341i	$0.644047\pi$
$654$	5.90877	−	7.27817i	0.231051	−	0.284599i
$655$		−	0.341136i		−	0.0133293i
$656$	35.6783	+	9.46444i	1.39300	+	0.369524i
$657$	−13.9282	−	3.17902i	−0.543390	−	0.124025i
$658$	23.2753	+	4.57720i	0.907364	+	0.178438i
$659$	4.05205	−	0.924854i	0.157846	−	0.0360272i	−0.142868	−	0.989742i	$-0.545632\pi$
$659$	4.05205	−	0.924854i	0.157846	−	0.0360272i	0.300713	+	0.953715i	$0.402775\pi$
$660$	0.408613	−	0.494434i	0.0159052	−	0.0192458i
$661$	5.87709	−	4.68682i	0.228592	−	0.182296i	−0.502495	−	0.864580i	$-0.667585\pi$
$661$	5.87709	−	4.68682i	0.228592	−	0.182296i	0.731087	+	0.682284i	$0.239013\pi$
$662$	−11.5228	+	2.52444i	−0.447847	+	0.0981151i
$663$	−0.174432	−	0.764238i	−0.00677439	−	0.0296806i
$664$	−40.6200	+	18.2677i	−1.57636	+	0.708926i
$665$	0.0703938	+	0.0305830i	0.00272976	+	0.00118596i
$666$	3.49549	−	4.30560i	0.135447	−	0.166839i
$667$			8.10599i			0.313865i
$668$	−12.1707	−	15.8202i	−0.470898	−	0.612101i
$669$	3.75803	−	16.4650i	0.145294	−	0.636574i
$670$	1.06712	+	0.00931087i	0.0412263	+	0.000359710i
$671$	1.01772	+	1.27618i	0.0392888	+	0.0492666i
$672$	14.6068	−	3.26209i	0.563470	−	0.125838i
$673$	29.3544	−	36.8092i	1.13153	−	1.41889i	0.237209	−	0.971459i	$-0.423767\pi$
$673$	29.3544	−	36.8092i	1.13153	−	1.41889i	0.894318	−	0.447432i	$-0.147661\pi$
$674$	−27.1805	+	33.4798i	−1.04695	+	1.28959i
$675$	3.11127	−	3.90140i	0.119753	−	0.150165i
$676$	−22.8890	−	11.5190i	−0.880347	−	0.443040i
$677$	−10.2151	+	8.14623i	−0.392596	+	0.313085i	−0.799816	−	0.600245i	$-0.795070\pi$
$677$	−10.2151	+	8.14623i	−0.392596	+	0.313085i	0.407220	+	0.913330i	$0.366498\pi$
$678$	3.03992	+	3.88092i	0.116747	+	0.149046i
$679$	−12.2581	+	0.477660i	−0.470423	+	0.0183309i
$680$	0.307020	+	0.406370i	0.0117737	+	0.0155836i
$681$	−11.6930	−	5.63106i	−0.448077	−	0.215783i
$682$	−11.0631	−	2.62684i	−0.423628	−	0.100587i
$683$	−12.7595	+	26.4953i	−0.488227	+	1.01381i	0.500729	+	0.865604i	$0.333065\pi$
$683$	−12.7595	+	26.4953i	−0.488227	+	1.01381i	−0.988956	+	0.148209i	$0.952649\pi$
$684$	0.582510	+	0.0101659i	0.0222728	+	0.000388702i
$685$		−	1.46864i		−	0.0561140i
$686$	13.8441	+	22.2338i	0.528570	+	0.848890i
$687$			9.05946i			0.345640i
$688$	35.5925	−	26.4061i	1.35695	−	1.00672i
$689$	1.34151	−	2.78567i	0.0511073	−	0.106125i
$690$	−0.291673	+	1.22840i	−0.0111038	+	0.0467644i
$691$	−12.9649	−	6.24354i	−0.493206	−	0.237516i	0.170712	−	0.985321i	$-0.445393\pi$
$691$	−12.9649	−	6.24354i	−0.493206	−	0.237516i	−0.663918	+	0.747805i	$0.731108\pi$
$692$	11.3462	−	22.5457i	0.431319	−	0.857058i
$693$	8.51423	−	0.331773i	0.323429	−	0.0126030i
$694$	7.79643	−	6.10693i	0.295949	−	0.231816i
$695$	1.17814	−	0.939537i	0.0446895	−	0.0356387i
$696$	−1.54167	−	2.04055i	−0.0584369	−	0.0773468i
$697$	−10.4037	+	13.0458i	−0.394067	+	0.494144i
$698$	−11.6418	−	9.45140i	−0.440650	−	0.357741i
$699$	12.5163	−	15.6949i	0.473410	−	0.593637i
$700$	0.567587	+	26.3989i	0.0214528	+	0.997786i
$701$	−28.2283	−	35.3971i	−1.06617	−	1.33693i	−0.938564	−	0.345106i	$-0.887843\pi$
$701$	−28.2283	−	35.3971i	−1.06617	−	1.33693i	−0.127603	−	0.991825i	$-0.540728\pi$
$702$	−0.00534919	+	0.613068i	−0.000201892	+	0.0231388i
$703$	−0.254194	+	1.11369i	−0.00958709	+	0.0420038i
$704$	9.94869	+	23.7658i	0.374955	+	0.895708i
$705$		−	0.631338i		−	0.0237776i
$706$	−11.6092	−	9.42489i	−0.436918	−	0.354710i
$707$	−26.8108	−	11.6481i	−1.00832	−	0.438071i
$708$	15.1589	−	18.3428i	0.569708	−	0.689363i
$709$	6.02683	+	26.4053i	0.226342	+	0.991670i	0.952595	+	0.304242i	$0.0984032\pi$
$709$	6.02683	+	26.4053i	0.226342	+	0.991670i	−0.726253	+	0.687428i	$0.758740\pi$
$710$	0.0538719	+	0.245898i	0.00202178	+	0.00922840i
$711$	3.17765	−	2.53409i	0.119171	−	0.0950360i
$712$	4.52325	+	10.0579i	0.169516	+	0.376934i
$713$	21.8203	−	4.98035i	0.817178	−	0.186515i
$714$	−1.30550	+	6.63851i	−0.0488570	+	0.248440i
$715$	−0.135550	−	0.0309385i	−0.00506929	−	0.00115703i
$716$	−2.07514	+	1.59643i	−0.0775516	+	0.0596615i
$717$			19.8556i			0.741520i
$718$	−5.05211	−	4.10154i	−0.188543	−	0.153068i
$719$	−15.2099	+	7.32469i	−0.567233	+	0.273165i	−0.695442	−	0.718582i	$-0.744791\pi$
$719$	−15.2099	+	7.32469i	−0.567233	+	0.273165i	0.128209	+	0.991747i	$0.459077\pi$
$720$	−0.160204	−	0.364702i	−0.00597047	−	0.0135917i
$721$	−3.16375	+	7.28212i	−0.117824	+	0.271200i
$722$	24.2013	−	11.3957i	0.900680	−	0.424104i
$723$	25.6883	+	5.86318i	0.955357	+	0.218054i
$724$	−0.810474	+	46.4405i	−0.0301210	+	1.72595i
$725$	4.06519	−	1.95769i	0.150977	−	0.0727069i
$726$	−0.190144	−	0.867914i	−0.00705692	−	0.0322113i
$727$	−19.0828	−	9.18981i	−0.707744	−	0.340831i	0.0451440	−	0.998980i	$-0.485625\pi$
$727$	−19.0828	−	9.18981i	−0.707744	−	0.340831i	−0.752888	+	0.658149i	$0.771340\pi$
$728$	−2.05494	−	2.51036i	−0.0761611	−	0.0930401i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	−1.24069	−	1.58393i	−0.0459200	−	0.0586240i
$731$	4.45799	+	19.5317i	0.164885	+	0.722407i
$732$	0.992059	−	0.208288i	0.0366676	−	0.00769855i
$733$	−4.30833	−	3.43578i	−0.159132	−	0.126903i	0.540687	−	0.841224i	$-0.318164\pi$
$733$	−4.30833	−	3.43578i	−0.159132	−	0.126903i	−0.699819	+	0.714321i	$0.746736\pi$
$734$	−10.3168	−	5.07965i	−0.380799	−	0.187493i
$735$	0.509535	−	0.475722i	0.0187945	−	0.0175473i
$736$	−38.2322	−	33.3180i	−1.40926	−	1.22812i
$737$	−15.2152	+	19.0792i	−0.560457	+	0.702791i
$738$	10.2739	−	8.04749i	0.378186	−	0.296232i
$739$	20.2802	−	4.62883i	0.746020	−	0.170274i	0.167420	−	0.985886i	$-0.446456\pi$
$739$	20.2802	−	4.62883i	0.746020	−	0.170274i	0.578600	+	0.815612i	$0.303599\pi$
$740$	0.764379	−	0.160486i	0.0280991	−	0.00589957i
$741$	−0.0547928	−	0.113778i	−0.00201286	−	0.00417975i
$742$	−20.3512	+	17.2609i	−0.747114	+	0.633667i
$743$	−11.3040	+	23.4731i	−0.414705	+	0.861143i	0.584072	+	0.811702i	$0.301458\pi$
$743$	−11.3040	+	23.4731i	−0.414705	+	0.861143i	−0.998777	+	0.0494416i	$0.984256\pi$
$744$	−4.54569	+	5.40371i	−0.166653	+	0.198109i
$745$	−0.402258	−	0.835298i	−0.0147376	−	0.0306030i
$746$	−24.7709	+	11.6639i	−0.906926	+	0.427045i
$747$	−3.50399	+	15.3520i	−0.128204	+	0.561700i
$748$	−11.6449	−	0.203225i	−0.425779	−	0.00743064i
$749$	6.47569	+	7.50138i	0.236616	+	0.274094i
$750$	1.37435	−	0.301094i	0.0501840	−	0.0109944i
$751$	−19.4347	−	40.3566i	−0.709184	−	1.47264i	−0.873804	−	0.486278i	$-0.838354\pi$
$751$	−19.4347	−	40.3566i	−0.709184	−	1.47264i	0.164620	−	0.986357i	$-0.447360\pi$
$752$	22.4497	+	11.7933i	0.818657	+	0.430058i
$753$	−29.9507			−1.09147
$754$	−0.244875	+	0.497340i	−0.00891781	+	0.0181121i
$755$	−0.293496	+	1.28589i	−0.0106814	+	0.0467984i
$756$	2.19289	−	4.81573i	0.0797546	−	0.175146i
$757$	2.00781	+	8.79680i	0.0729752	+	0.319725i	0.998220	−	0.0596464i	$-0.0189973\pi$
$757$	2.00781	+	8.79680i	0.0729752	+	0.319725i	−0.925244	+	0.379372i	$0.876140\pi$
$758$	−38.4504	−	9.12972i	−1.39658	−	0.331606i
$759$	−18.0011	−	22.5726i	−0.653397	−	0.819334i
$760$	0.0627880	+	0.0528184i	0.00227756	+	0.00191593i
$761$	5.13003	−	1.17090i	0.185964	−	0.0424450i	−0.128525	−	0.991706i	$-0.541024\pi$
$761$	5.13003	−	1.17090i	0.185964	−	0.0424450i	0.314488	+	0.949261i	$0.398167\pi$
$762$	0.586449	+	0.139247i	0.0212448	+	0.00504440i
$763$	14.1275	+	10.3929i	0.511451	+	0.376247i
$764$	−9.88489	−	21.4770i	−0.357623	−	0.777011i
$765$	0.180068			0.00651039
$766$	3.12585	+	1.53907i	0.112941	+	0.0556089i
$767$	−5.02872	−	1.14777i	−0.181576	−	0.0414436i
$768$	15.9610	+	1.11590i	0.575944	+	0.0402665i
$769$	3.70432	−	2.95409i	0.133581	−	0.106527i	−0.554420	−	0.832237i	$-0.687060\pi$
$769$	3.70432	−	2.95409i	0.133581	−	0.106527i	0.688001	+	0.725710i	$0.258488\pi$
$770$	0.960379	+	0.719497i	0.0346096	+	0.0259289i

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)

\(f(q)\)	\(=\)	\(q+(-1.27947 + 0.602464i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.27407 - 1.54167i) q^{4} +(0.0432081 - 0.0897226i) q^{5} +(1.41416 + 0.0123389i) q^{6} +(0.103018 + 2.64374i) q^{7} +(-0.701339 + 2.74010i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-1.27947 + 0.602464i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(1.27407 - 1.54167i) q^{4} +(0.0432081 - 0.0897226i) q^{5} +(1.41416 + 0.0123389i) q^{6} +(0.103018 + 2.64374i) q^{7} +(-0.701339 + 2.74010i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.00122877 + 0.140828i) q^{10} +(-2.51790 - 2.00796i) q^{11} +(-1.81681 + 0.836193i) q^{12} +(0.338941 + 0.270296i) q^{13} +(-1.72457 - 3.32052i) q^{14} +(-0.0778583 + 0.0620899i) q^{15} +(-0.753469 - 3.92839i) q^{16} +(1.76286 + 0.402362i) q^{17} +(-1.26876 - 0.624698i) q^{18} +0.291299 q^{19} +(-0.0832719 - 0.180926i) q^{20} +(1.05426 - 2.42663i) q^{21} +(4.43130 + 1.05217i) q^{22} +(-8.74008 + 1.99487i) q^{23} +(1.82077 - 2.16444i) q^{24} +(3.11127 + 3.90140i) q^{25} +(-0.596507 - 0.141636i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(4.20703 + 3.20951i) q^{28} +(0.201203 - 0.881528i) q^{29} +(0.0622102 - 0.126349i) q^{30} -2.49658 q^{31} +(3.33075 + 4.57232i) q^{32} +(1.39733 + 2.90159i) q^{33} +(-2.49793 + 0.547252i) q^{34} +(0.241655 + 0.104988i) q^{35} +(1.99970 + 0.0348984i) q^{36} +(-0.872620 + 3.82320i) q^{37} +(-0.372708 + 0.175497i) q^{38} +(-0.188098 - 0.390589i) q^{39} +(0.215545 + 0.181320i) q^{40} +(-4.00391 + 8.31420i) q^{41} +(0.113064 + 3.73995i) q^{42} +(4.80724 + 9.98234i) q^{43} +(-6.30360 + 1.32347i) q^{44} +(0.0970877 - 0.0221596i) q^{45} +(9.98081 - 7.81795i) q^{46} +(-3.95275 + 4.95659i) q^{47} +(-1.02561 + 3.86628i) q^{48} +(-6.97877 + 0.544709i) q^{49} +(-6.33122 - 3.11729i) q^{50} +(-1.41371 - 1.12739i) q^{51} +(0.848542 - 0.178156i) q^{52} +(-1.58701 - 6.95314i) q^{53} +(0.872067 + 1.11333i) q^{54} +(-0.288953 + 0.139152i) q^{55} +(-7.31636 - 1.57188i) q^{56} +(-0.262452 - 0.126390i) q^{57} +(0.273656 + 1.24910i) q^{58} +(-10.7197 + 5.16235i) q^{59} +(-0.00347534 + 0.199139i) q^{60} +(-0.494137 - 0.112783i) q^{61} +(3.19430 - 1.50410i) q^{62} +(-2.00273 + 1.72889i) q^{63} +(-7.01625 - 3.84347i) q^{64} +(0.0388966 - 0.0187316i) q^{65} +(-3.53594 - 2.87064i) q^{66} -7.57742i q^{67} +(2.86633 - 2.20511i) q^{68} +(8.74008 + 1.99487i) q^{69} +(-0.372441 + 0.0112594i) q^{70} +(1.74261 - 0.397740i) q^{71} +(-2.57957 + 1.16009i) q^{72} +(-11.1695 + 8.90740i) q^{73} +(-1.18685 - 5.41738i) q^{74} +(-1.11040 - 4.86497i) q^{75} +(0.371137 - 0.449086i) q^{76} +(5.04914 - 6.86355i) q^{77} +(0.475981 + 0.386424i) q^{78} -4.06437i q^{79} +(-0.385022 - 0.102135i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.113864 - 13.0500i) q^{82} +(9.81797 + 12.3113i) q^{83} +(-2.39785 - 4.71703i) q^{84} +(0.112271 - 0.140783i) q^{85} +(-12.1647 - 9.87589i) q^{86} +(-0.563758 + 0.706930i) q^{87} +(7.26791 - 5.49103i) q^{88} +(3.04839 - 2.43101i) q^{89} +(-0.110870 + 0.0868444i) q^{90} +(-0.679677 + 0.923918i) q^{91} +(-8.06009 + 16.0159i) q^{92} +(2.24934 + 1.08323i) q^{93} +(2.07125 - 8.72319i) q^{94} +(0.0125865 - 0.0261361i) q^{95} +(-1.01705 - 5.56467i) q^{96} +4.63664i q^{97} +(8.60095 - 4.90140i) q^{98} -3.22052i 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