LMFDB - Embedded newform 1110.2.x.d.841.7

Newspace parameters

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
Defining polynomial:	$x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.7
Root			$2.16125i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.d.751.7

$q$-expansion

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(1.08063 + 1.87170i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(1.08063 + 1.87170i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +4.64319 q^{11} +(0.500000 - 0.866025i) q^{12} +(-4.51941 + 2.60928i) q^{13} +2.16125i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73772 + 1.58063i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.178213 - 0.102891i) q^{19} +(0.866025 + 0.500000i) q^{20} +(1.08063 - 1.87170i) q^{21} +(4.02112 + 2.32159i) q^{22} -3.48652i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.21857 q^{26} +1.00000 q^{27} +(-1.08063 + 1.87170i) q^{28} +6.44199i q^{29} +(-0.500000 - 0.866025i) q^{30} +6.19187i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.32159 - 4.02112i) q^{33} +(1.58063 + 2.73772i) q^{34} +(1.87170 + 1.08063i) q^{35} -1.00000 q^{36} +(2.83833 - 5.37995i) q^{37} +0.205782 q^{38} +(4.51941 + 2.60928i) q^{39} +(0.500000 + 0.866025i) q^{40} +(1.61696 + 2.80066i) q^{41} +(1.87170 - 1.08063i) q^{42} -2.70535i q^{43} +(2.32159 + 4.02112i) q^{44} +1.00000i q^{45} +(1.74326 - 3.01941i) q^{46} +0.834167 q^{47} +1.00000 q^{48} +(1.16450 - 2.01696i) q^{49} +(0.866025 - 0.500000i) q^{50} -3.16125i q^{51} +(-4.51941 - 2.60928i) q^{52} +(0.578919 - 1.00272i) q^{53} +(0.866025 + 0.500000i) q^{54} +(4.02112 - 2.32159i) q^{55} +(-1.87170 + 1.08063i) q^{56} +(-0.178213 - 0.102891i) q^{57} +(-3.22099 + 5.57892i) q^{58} +(3.94537 + 2.27786i) q^{59} -1.00000i q^{60} +(9.21562 - 5.32064i) q^{61} +(-3.09594 + 5.36232i) q^{62} -2.16125 q^{63} -1.00000 q^{64} +(-2.60928 + 4.51941i) q^{65} -4.64319i q^{66} +(0.180274 + 0.312243i) q^{67} +3.16125i q^{68} +(-3.01941 + 1.74326i) q^{69} +(1.08063 + 1.87170i) q^{70} +(2.26228 + 3.91838i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.91562 q^{73} +(5.14804 - 3.24001i) q^{74} -1.00000 q^{75} +(0.178213 + 0.102891i) q^{76} +(5.01755 + 8.69065i) q^{77} +(2.60928 + 4.51941i) q^{78} +(2.06361 - 1.19143i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +3.23393i q^{82} +(-6.98079 + 12.0911i) q^{83} +2.16125 q^{84} +3.16125 q^{85} +(1.35268 - 2.34291i) q^{86} +(5.57892 - 3.22099i) q^{87} +4.64319i q^{88} +(-13.4453 - 7.76267i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-9.76759 - 5.63932i) q^{91} +(3.01941 - 1.74326i) q^{92} +(5.36232 - 3.09594i) q^{93} +(0.722410 + 0.417084i) q^{94} +(0.102891 - 0.178213i) q^{95} +(0.866025 + 0.500000i) q^{96} -0.153047i q^{97} +(2.01696 - 1.16450i) q^{98} +(-2.32159 + 4.02112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) $	$ 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	1.08063	+	1.87170i	0.408438	+	0.707436i	0.994715	−	0.102675i	$-0.0327402\pi$
$7$	1.08063	+	1.87170i	0.408438	+	0.707436i	−0.586277	+	0.810111i	$0.699407\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000			0.316228
$11$	4.64319			1.39997			0.699987	−	0.714156i	$-0.253189\pi$
$11$	4.64319			1.39997			0.699987	+	0.714156i	$0.253189\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−4.51941	+	2.60928i	−1.25346	+	0.723685i	−0.971795	−	0.235828i	$-0.924220\pi$
$13$	−4.51941	+	2.60928i	−1.25346	+	0.723685i	−0.281664	+	0.959513i	$0.590886\pi$
$14$			2.16125i			0.577619i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.73772	+	1.58063i	0.663996	+	0.383358i	0.793798	−	0.608182i	$-0.208101\pi$
$17$	2.73772	+	1.58063i	0.663996	+	0.383358i	−0.129802	+	0.991540i	$0.541434\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	0.178213	−	0.102891i	0.0408848	−	0.0236048i	−0.479418	−	0.877587i	$-0.659152\pi$
$19$	0.178213	−	0.102891i	0.0408848	−	0.0236048i	0.520303	+	0.853982i	$0.325819\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	1.08063	−	1.87170i	0.235812	−	0.408438i
$22$	4.02112	+	2.32159i	0.857305	+	0.494965i
$23$		−	3.48652i		−	0.726989i	−0.931596	−	0.363494i	$-0.881584\pi$
$23$		−	3.48652i		−	0.726989i	0.931596	−	0.363494i	$-0.118416\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−5.21857			−1.02345
$27$	1.00000			0.192450
$28$	−1.08063	+	1.87170i	−0.204219	+	0.353718i
$29$			6.44199i			1.19625i	0.801404	+	0.598123i	$0.204087\pi$
$29$			6.44199i			1.19625i	−0.801404	+	0.598123i	$0.795913\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			6.19187i			1.11209i	0.831151	+	0.556046i	$0.187682\pi$
$31$			6.19187i			1.11209i	−0.831151	+	0.556046i	$0.812318\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.32159	−	4.02112i	−0.404138	−	0.699987i
$34$	1.58063	+	2.73772i	0.271075	+	0.469516i
$35$	1.87170	+	1.08063i	0.316375	+	0.182659i
$36$	−1.00000			−0.166667
$37$	2.83833	−	5.37995i	0.466618	−	0.884459i
$37$	2.83833	−	5.37995i	0.466618	−	0.884459i
$38$	0.205782			0.0333823
$39$	4.51941	+	2.60928i	0.723685	+	0.417820i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	1.61696	+	2.80066i	0.252527	+	0.437390i	0.964221	−	0.265100i	$-0.0854050\pi$
$41$	1.61696	+	2.80066i	0.252527	+	0.437390i	−0.711694	+	0.702490i	$0.752072\pi$
$42$	1.87170	−	1.08063i	0.288809	−	0.166744i
$43$		−	2.70535i		−	0.412563i	−0.978493	−	0.206281i	$-0.933864\pi$
$43$		−	2.70535i		−	0.412563i	0.978493	−	0.206281i	$-0.0661362\pi$
$44$	2.32159	+	4.02112i	0.349993	+	0.606206i
$45$			1.00000i			0.149071i
$46$	1.74326	−	3.01941i	0.257029	−	0.445188i
$47$	0.834167			0.121676			0.0608379	−	0.998148i	$-0.480623\pi$
$47$	0.834167			0.121676			0.0608379	+	0.998148i	$0.480623\pi$
$48$	1.00000			0.144338
$49$	1.16450	−	2.01696i	0.166356	−	0.288138i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	3.16125i		−	0.442664i
$52$	−4.51941	−	2.60928i	−0.626730	−	0.361843i
$53$	0.578919	−	1.00272i	0.0795207	−	0.137734i	−0.823523	−	0.567284i	$-0.807994\pi$
$53$	0.578919	−	1.00272i	0.0795207	−	0.137734i	0.903043	+	0.429550i	$0.141328\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	4.02112	−	2.32159i	0.542207	−	0.313044i
$56$	−1.87170	+	1.08063i	−0.250116	+	0.144405i
$57$	−0.178213	−	0.102891i	−0.0236048	−	0.0136283i
$58$	−3.22099	+	5.57892i	−0.422937	+	0.732549i
$59$	3.94537	+	2.27786i	0.513643	+	0.296552i	0.734330	−	0.678793i	$-0.237496\pi$
$59$	3.94537	+	2.27786i	0.513643	+	0.296552i	−0.220687	+	0.975345i	$0.570830\pi$
$60$		−	1.00000i		−	0.129099i
$61$	9.21562	−	5.32064i	1.17994	−	0.681238i	0.223939	−	0.974603i	$-0.428108\pi$
$61$	9.21562	−	5.32064i	1.17994	−	0.681238i	0.956001	+	0.293365i	$0.0947751\pi$
$62$	−3.09594	+	5.36232i	−0.393184	+	0.681015i
$63$	−2.16125			−0.272292
$64$	−1.00000			−0.125000
$65$	−2.60928	+	4.51941i	−0.323642	+	0.560564i
$66$		−	4.64319i		−	0.571537i
$67$	0.180274	+	0.312243i	0.0220239	+	0.0381465i	0.876827	−	0.480805i	$-0.159656\pi$
$67$	0.180274	+	0.312243i	0.0220239	+	0.0381465i	−0.854803	+	0.518952i	$0.826322\pi$
$68$			3.16125i			0.383358i
$69$	−3.01941	+	1.74326i	−0.363494	+	0.209864i
$70$	1.08063	+	1.87170i	0.129160	+	0.223711i
$71$	2.26228	+	3.91838i	0.268483	+	0.465027i	0.968470	−	0.249129i	$-0.0801443\pi$
$71$	2.26228	+	3.91838i	0.268483	+	0.465027i	−0.699987	+	0.714155i	$0.746811\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	4.91562			0.575329			0.287665	−	0.957731i	$-0.407121\pi$
$73$	4.91562			0.575329			0.287665	+	0.957731i	$0.407121\pi$
$74$	5.14804	−	3.24001i	0.598447	−	0.376644i
$75$	−1.00000			−0.115470
$76$	0.178213	+	0.102891i	0.0204424	+	0.0118024i
$77$	5.01755	+	8.69065i	0.571803	+	0.990391i
$78$	2.60928	+	4.51941i	0.295443	+	0.511723i
$79$	2.06361	−	1.19143i	0.232174	−	0.134046i	−0.379400	−	0.925233i	$-0.623870\pi$
$79$	2.06361	−	1.19143i	0.232174	−	0.134046i	0.611575	+	0.791187i	$0.290536\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			3.23393i			0.357127i
$83$	−6.98079	+	12.0911i	−0.766241	+	1.32717i	0.173347	+	0.984861i	$0.444542\pi$
$83$	−6.98079	+	12.0911i	−0.766241	+	1.32717i	−0.939588	+	0.342308i	$0.888791\pi$
$84$	2.16125			0.235812
$85$	3.16125			0.342886
$86$	1.35268	−	2.34291i	0.145863	−	0.252642i
$87$	5.57892	−	3.22099i	0.598123	−	0.345327i
$88$			4.64319i			0.494965i
$89$	−13.4453	−	7.76267i	−1.42520	−	0.822841i	−0.428466	−	0.903558i	$-0.640946\pi$
$89$	−13.4453	−	7.76267i	−1.42520	−	0.822841i	−0.996737	+	0.0807166i	$0.974279\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−9.76759	−	5.63932i	−1.02392	−	0.591161i
$92$	3.01941	−	1.74326i	0.314795	−	0.181747i
$93$	5.36232	−	3.09594i	0.556046	−	0.321034i
$94$	0.722410	+	0.417084i	0.0745109	+	0.0430189i
$95$	0.102891	−	0.178213i	0.0105564	−	0.0182842i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$		−	0.153047i		−	0.0155396i	−0.999970	−	0.00776981i	$-0.997527\pi$
$97$		−	0.153047i		−	0.0155396i	0.999970	−	0.00776981i	$-0.00247323\pi$
$98$	2.01696	−	1.16450i	0.203744	−	0.117632i
$99$	−2.32159	+	4.02112i	−0.233329	+	0.404138i
$100$	1.00000			0.100000
$101$	8.43932			0.839744			0.419872	−	0.907583i	$-0.362075\pi$
$101$	8.43932			0.839744			0.419872	+	0.907583i	$0.362075\pi$
$102$	1.58063	−	2.73772i	0.156505	−	0.271075i
$103$			4.15256i			0.409164i	0.978849	+	0.204582i	$0.0655834\pi$
$103$			4.15256i			0.409164i	−0.978849	+	0.204582i	$0.934417\pi$
$104$	−2.60928	−	4.51941i	−0.255861	−	0.443165i
$105$		−	2.16125i		−	0.210917i
$106$	1.00272	−	0.578919i	0.0973926	−	0.0562296i
$107$	−8.48343	−	14.6937i	−0.820124	−	1.42050i	−0.905589	−	0.424155i	$-0.860571\pi$
$107$	−8.48343	−	14.6937i	−0.820124	−	1.42050i	0.0854653	−	0.996341i	$-0.472762\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−1.32344	−	0.764087i	−0.126762	−	0.0731863i	0.435278	−	0.900296i	$-0.356650\pi$
$109$	−1.32344	−	0.764087i	−0.126762	−	0.0731863i	−0.562040	+	0.827110i	$0.689983\pi$
$110$	4.64319			0.442711
$111$	−6.07834	+	0.231916i	−0.576930	+	0.0220125i
$112$	−2.16125			−0.204219
$113$	−17.1426	−	9.89727i	−1.61264	−	0.931057i	−0.988756	−	0.149539i	$-0.952221\pi$
$113$	−17.1426	−	9.89727i	−1.61264	−	0.931057i	−0.623883	−	0.781518i	$-0.714446\pi$
$114$	−0.102891	−	0.178213i	−0.00963663	−	0.0166911i
$115$	−1.74326	−	3.01941i	−0.162560	−	0.281562i
$116$	−5.57892	+	3.22099i	−0.517990	+	0.299062i
$117$		−	5.21857i		−	0.482457i
$118$	2.27786	+	3.94537i	0.209694	+	0.363201i
$119$			6.83226i			0.626312i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	10.5592			0.959926
$122$	10.6413			0.963416
$123$	1.61696	−	2.80066i	0.145797	−	0.252527i
$124$	−5.36232	+	3.09594i	−0.481550	+	0.278023i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.87170	−	1.08063i	−0.166744	−	0.0962698i
$127$	−0.713592	+	1.23598i	−0.0633210	+	0.109675i	−0.895948	−	0.444159i	$-0.853503\pi$
$127$	−0.713592	+	1.23598i	−0.0633210	+	0.109675i	0.832627	+	0.553834i	$0.186836\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−2.34291	+	1.35268i	−0.206281	+	0.119097i
$130$	−4.51941	+	2.60928i	−0.396379	+	0.228849i
$131$	−13.7876	−	7.96026i	−1.20463	−	0.695491i	−0.243045	−	0.970015i	$-0.578146\pi$
$131$	−13.7876	−	7.96026i	−1.20463	−	0.695491i	−0.961580	+	0.274524i	$0.911480\pi$
$132$	2.32159	−	4.02112i	0.202069	−	0.349993i
$133$	0.385162	+	0.222373i	0.0333978	+	0.0192822i
$134$			0.360547i			0.0311465i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	−1.58063	+	2.73772i	−0.135538	+	0.234758i
$137$	1.14116			0.0974958			0.0487479	−	0.998811i	$-0.484477\pi$
$137$	1.14116			0.0974958			0.0487479	+	0.998811i	$0.484477\pi$
$138$	−3.48652			−0.296792
$139$	1.38333	−	2.39599i	0.117332	−	0.203225i	−0.801377	−	0.598159i	$-0.795899\pi$
$139$	1.38333	−	2.39599i	0.117332	−	0.203225i	0.918710	+	0.394934i	$0.129232\pi$
$140$			2.16125i			0.182659i
$141$	−0.417084	−	0.722410i	−0.0351248	−	0.0608379i
$142$			4.52456i			0.379693i
$143$	−20.9845	+	12.1154i	−1.75481	+	1.01314i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.22099	+	5.57892i	0.267489	+	0.463304i
$146$	4.25705	+	2.45781i	0.352316	+	0.203410i
$147$	−2.32899			−0.192092
$148$	6.07834	−	0.231916i	0.499636	−	0.0190633i
$149$	10.1666			0.832881			0.416441	−	0.909163i	$-0.363277\pi$
$149$	10.1666			0.832881			0.416441	+	0.909163i	$0.363277\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	−1.21847	−	2.11046i	−0.0991580	−	0.171747i	0.812178	−	0.583409i	$-0.198282\pi$
$151$	−1.21847	−	2.11046i	−0.0991580	−	0.171747i	−0.911336	+	0.411663i	$0.864948\pi$
$152$	0.102891	+	0.178213i	0.00834557	+	0.0144549i
$153$	−2.73772	+	1.58063i	−0.221332	+	0.127786i
$154$			10.0351i			0.808651i
$155$	3.09594	+	5.36232i	0.248672	+	0.430712i
$156$			5.21857i			0.417820i
$157$	−0.705413	+	1.22181i	−0.0562981	+	0.0975111i	−0.892801	−	0.450451i	$-0.851263\pi$
$157$	−0.705413	+	1.22181i	−0.0562981	+	0.0975111i	0.836503	+	0.547963i	$0.184596\pi$
$158$	2.38285			0.189569
$159$	−1.15784			−0.0918226
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	6.52571	−	3.76762i	0.514298	−	0.296930i
$162$		−	1.00000i		−	0.0785674i
$163$	−8.49385	−	4.90393i	−0.665290	−	0.384105i	0.129000	−	0.991645i	$-0.458823\pi$
$163$	−8.49385	−	4.90393i	−0.665290	−	0.384105i	−0.794289	+	0.607539i	$0.792157\pi$
$164$	−1.61696	+	2.80066i	−0.126264	+	0.218695i
$165$	−4.02112	−	2.32159i	−0.313044	−	0.180736i
$166$	−12.0911	+	6.98079i	−0.938450	+	0.541814i
$167$	−13.2273	+	7.63680i	−1.02356	+	0.590953i	−0.915134	−	0.403151i	$-0.867915\pi$
$167$	−13.2273	+	7.63680i	−1.02356	+	0.590953i	−0.108428	+	0.994104i	$0.534582\pi$
$168$	1.87170	+	1.08063i	0.144405	+	0.0833721i
$169$	7.11672	−	12.3265i	0.547440	−	0.948194i
$170$	2.73772	+	1.58063i	0.209974	+	0.121228i
$171$			0.205782i			0.0157366i
$172$	2.34291	−	1.35268i	0.178645	−	0.103141i
$173$	1.38267	−	2.39485i	0.105122	−	0.182077i	−0.808666	−	0.588268i	$-0.799810\pi$
$173$	1.38267	−	2.39485i	0.105122	−	0.182077i	0.913788	+	0.406191i	$0.133143\pi$
$174$	6.44199			0.488366
$175$	2.16125			0.163375
$176$	−2.32159	+	4.02112i	−0.174997	+	0.303103i
$177$		−	4.55572i		−	0.342429i
$178$	−7.76267	−	13.4453i	−0.581837	−	1.00777i
$179$			1.17391i			0.0877424i	0.999037	+	0.0438712i	$0.0139691\pi$
$179$			1.17391i			0.0877424i	−0.999037	+	0.0438712i	$0.986031\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	−10.5795	−	18.3242i	−0.786366	−	1.36203i	−0.928179	−	0.372133i	$-0.878626\pi$
$181$	−10.5795	−	18.3242i	−0.786366	−	1.36203i	0.141813	−	0.989893i	$-0.454707\pi$
$182$	−5.63932	−	9.76759i	−0.418014	−	0.724022i
$183$	−9.21562	−	5.32064i	−0.681238	−	0.393313i
$184$	3.48652			0.257029
$185$	−0.231916	−	6.07834i	−0.0170508	−	0.446888i
$186$	6.19187			0.454010
$187$	12.7118	+	7.33914i	0.929577	+	0.536691i
$188$	0.417084	+	0.722410i	0.0304190	+	0.0526872i
$189$	1.08063	+	1.87170i	0.0786040	+	0.136146i
$190$	0.178213	−	0.102891i	0.0129289	−	0.00746450i
$191$			10.8527i			0.785274i	0.919694	+	0.392637i	$0.128437\pi$
$191$			10.8527i			0.785274i	−0.919694	+	0.392637i	$0.871563\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$		−	22.9744i		−	1.65373i	−0.562399	−	0.826866i	$-0.690122\pi$
$193$		−	22.9744i		−	1.65373i	0.562399	−	0.826866i	$-0.309878\pi$
$194$	0.0765237	−	0.132543i	0.00549408	−	0.00951603i
$195$	5.21857			0.373709
$196$	2.32899			0.166356
$197$	9.19854	−	15.9323i	0.655369	−	1.13513i	−0.326433	−	0.945221i	$-0.605847\pi$
$197$	9.19854	−	15.9323i	0.655369	−	1.13513i	0.981801	−	0.189911i	$-0.0608201\pi$
$198$	−4.02112	+	2.32159i	−0.285768	+	0.164988i
$199$		−	10.9340i		−	0.775090i	−0.921851	−	0.387545i	$-0.873323\pi$
$199$		−	10.9340i		−	0.775090i	0.921851	−	0.387545i	$-0.126677\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	0.180274	−	0.312243i	0.0127155	−	0.0220239i
$202$	7.30867	+	4.21966i	0.514236	+	0.296894i
$203$	−12.0575	+	6.96138i	−0.846268	+	0.488593i
$204$	2.73772	−	1.58063i	0.191679	−	0.110666i
$205$	2.80066	+	1.61696i	0.195607	+	0.112934i
$206$	−2.07628	+	3.59622i	−0.144661	+	0.250561i
$207$	3.01941	+	1.74326i	0.209864	+	0.121165i
$208$		−	5.21857i		−	0.361843i
$209$	0.827474	−	0.477742i	0.0572376	−	0.0330461i
$210$	1.08063	−	1.87170i	0.0745703	−	0.129160i
$211$	−5.36913			−0.369626			−0.184813	−	0.982774i	$-0.559168\pi$
$211$	−5.36913			−0.369626			−0.184813	+	0.982774i	$0.559168\pi$
$212$	1.15784			0.0795207
$213$	2.26228	−	3.91838i	0.155009	−	0.268483i
$214$		−	16.9669i		−	1.15983i
$215$	−1.35268	−	2.34291i	−0.0922518	−	0.159785i
$216$			1.00000i			0.0680414i
$217$	−11.5893	+	6.69110i	−0.786734	+	0.454221i
$218$	−0.764087	−	1.32344i	−0.0517505	−	0.0896345i
$219$	−2.45781	−	4.25705i	−0.166083	−	0.287665i
$220$	4.02112	+	2.32159i	0.271104	+	0.156522i
$221$	−16.4972			−1.10972
$222$	−5.37995	−	2.83833i	−0.361079	−	0.190496i
$223$	−23.1628			−1.55109			−0.775547	−	0.631289i	$-0.782526\pi$
$223$	−23.1628			−1.55109			−0.775547	+	0.631289i	$0.782526\pi$
$224$	−1.87170	−	1.08063i	−0.125058	−	0.0722024i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−9.89727	−	17.1426i	−0.658357	−	1.14031i
$227$	−20.5859	+	11.8853i	−1.36634	+	0.788855i	−0.990458	−	0.137814i	$-0.955992\pi$
$227$	−20.5859	+	11.8853i	−1.36634	+	0.788855i	−0.375879	+	0.926669i	$0.622659\pi$
$228$		−	0.205782i		−	0.0136283i
$229$	−2.27891	−	3.94718i	−0.150594	−	0.260837i	0.780852	−	0.624716i	$-0.214785\pi$
$229$	−2.27891	−	3.94718i	−0.150594	−	0.260837i	−0.931446	+	0.363879i	$0.881452\pi$
$230$		−	3.48652i		−	0.229894i
$231$	5.01755	−	8.69065i	0.330130	−	0.571803i
$232$	−6.44199			−0.422937
$233$	−18.2804			−1.19759			−0.598793	−	0.800904i	$-0.704353\pi$
$233$	−18.2804			−1.19759			−0.598793	+	0.800904i	$0.704353\pi$
$234$	2.60928	−	4.51941i	0.170574	−	0.295443i
$235$	0.722410	−	0.417084i	0.0471248	−	0.0272075i
$236$			4.55572i			0.296552i
$237$	−2.06361	−	1.19143i	−0.134046	−	0.0773914i
$238$	−3.41613	+	5.91691i	−0.221435	+	0.383536i
$239$	17.6319	+	10.1798i	1.14051	+	0.658474i	0.946557	−	0.322537i	$-0.104536\pi$
$239$	17.6319	+	10.1798i	1.14051	+	0.658474i	0.193953	+	0.981011i	$0.437869\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	13.3225	−	7.69174i	0.858176	−	0.495468i	−0.00522493	−	0.999986i	$-0.501663\pi$
$241$	13.3225	−	7.69174i	0.858176	−	0.495468i	0.863401	+	0.504518i	$0.168330\pi$
$242$	9.14453	+	5.27959i	0.587832	+	0.339385i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	9.21562	+	5.32064i	0.589970	+	0.340619i
$245$		−	2.32899i		−	0.148794i
$246$	2.80066	−	1.61696i	0.178564	−	0.103094i
$247$	−0.536944	+	0.930014i	−0.0341649	+	0.0591754i
$248$	−6.19187			−0.393184
$249$	13.9616			0.884779
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$			13.2799i			0.838219i	0.907936	+	0.419110i	$0.137658\pi$
$251$			13.2799i			0.838219i	−0.907936	+	0.419110i	$0.862342\pi$
$252$	−1.08063	−	1.87170i	−0.0680730	−	0.117906i
$253$		−	16.1885i		−	1.01777i
$254$	−1.23598	+	0.713592i	−0.0775521	+	0.0447747i
$255$	−1.58063	−	2.73772i	−0.0989826	−	0.171443i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.52855	−	1.45986i	−0.157727	−	0.0910636i	0.419059	−	0.907959i	$-0.362360\pi$
$257$	−2.52855	−	1.45986i	−0.157727	−	0.0910636i	−0.576786	+	0.816895i	$0.695693\pi$
$258$	−2.70535			−0.168428
$259$	13.1368	−	0.501228i	0.816282	−	0.0311448i
$260$	−5.21857			−0.323642
$261$	−5.57892	−	3.22099i	−0.345327	−	0.199374i
$262$	−7.96026	−	13.7876i	−0.491786	−	0.851799i
$263$	−5.18381	−	8.97862i	−0.319647	−	0.553645i	0.660767	−	0.750591i	$-0.270231\pi$
$263$	−5.18381	−	8.97862i	−0.319647	−	0.553645i	−0.980414	+	0.196946i	$0.936898\pi$
$264$	4.02112	−	2.32159i	0.247483	−	0.142884i
$265$		−	1.15784i		−	0.0711255i
$266$	0.222373	+	0.385162i	0.0136346	+	0.0236158i
$267$			15.5253i			0.950135i
$268$	−0.180274	+	0.312243i	−0.0110120	+	0.0190733i
$269$	25.2440			1.53915			0.769577	−	0.638554i	$-0.220467\pi$
$269$	25.2440			1.53915			0.769577	+	0.638554i	$0.220467\pi$
$270$	1.00000			0.0608581
$271$	−8.17713	+	14.1632i	−0.496725	+	0.860353i	−0.999993	−	0.00377716i	$-0.998798\pi$
$271$	−8.17713	+	14.1632i	−0.496725	+	0.860353i	0.503268	+	0.864131i	$0.332131\pi$
$272$	−2.73772	+	1.58063i	−0.165999	+	0.0958395i
$273$			11.2786i			0.682614i
$274$	0.988273	+	0.570579i	0.0597037	+	0.0344700i
$275$	2.32159	−	4.02112i	0.139997	−	0.242483i
$276$	−3.01941	−	1.74326i	−0.181747	−	0.104932i
$277$	2.90340	−	1.67628i	0.174448	−	0.100718i	−0.410233	−	0.911981i	$-0.634553\pi$
$277$	2.90340	−	1.67628i	0.174448	−	0.100718i	0.584682	+	0.811263i	$0.301219\pi$
$278$	2.39599	−	1.38333i	0.143702	−	0.0829664i
$279$	−5.36232	−	3.09594i	−0.321034	−	0.185349i
$280$	−1.08063	+	1.87170i	−0.0645798	+	0.111855i
$281$	−2.92257	−	1.68735i	−0.174346	−	0.100659i	0.410287	−	0.911956i	$-0.365428\pi$
$281$	−2.92257	−	1.68735i	−0.174346	−	0.100659i	−0.584634	+	0.811297i	$0.698762\pi$
$282$		−	0.834167i		−	0.0496740i
$283$	18.0520	−	10.4223i	1.07308	−	0.619543i	0.144059	−	0.989569i	$-0.453984\pi$
$283$	18.0520	−	10.4223i	1.07308	−	0.619543i	0.929022	+	0.370026i	$0.120651\pi$
$284$	−2.26228	+	3.91838i	−0.134242	+	0.232513i
$285$	−0.205782			−0.0121895
$286$	−24.2308			−1.43280
$287$	−3.49466	+	6.05294i	−0.206283	+	0.357293i
$288$		−	1.00000i		−	0.0589256i
$289$	−3.50324	−	6.06780i	−0.206073	−	0.356929i
$290$			6.44199i			0.378286i
$291$	−0.132543	+	0.0765237i	−0.00776981	+	0.00448590i
$292$	2.45781	+	4.25705i	0.143832	+	0.249125i
$293$	1.12816	+	1.95403i	0.0659077	+	0.114156i	0.897096	−	0.441835i	$-0.145672\pi$
$293$	1.12816	+	1.95403i	0.0659077	+	0.114156i	−0.831189	+	0.555991i	$0.812339\pi$
$294$	−2.01696	−	1.16450i	−0.117632	−	0.0679147i
$295$	4.55572			0.265244
$296$	5.37995	+	2.83833i	0.312704	+	0.164974i
$297$	4.64319			0.269425
$298$	8.80454	+	5.08331i	0.510034	+	0.294468i
$299$	9.09731	+	15.7570i	0.526111	+	0.911251i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	5.06361	−	2.92348i	0.291862	−	0.168506i
$302$		−	2.43695i		−	0.140231i
$303$	−4.21966	−	7.30867i	−0.242413	−	0.419872i
$304$			0.205782i			0.0118024i
$305$	5.32064	−	9.21562i	0.304659	−	0.527685i
$306$	−3.16125			−0.180717
$307$	14.0079			0.799474			0.399737	−	0.916630i	$-0.369101\pi$
$307$	14.0079			0.799474			0.399737	+	0.916630i	$0.369101\pi$
$308$	−5.01755	+	8.69065i	−0.285901	+	0.495196i
$309$	3.59622	−	2.07628i	0.204582	−	0.118115i
$310$			6.19187i			0.351675i
$311$	17.2177	+	9.94062i	0.976323	+	0.563681i	0.901158	−	0.433490i	$-0.142718\pi$
$311$	17.2177	+	9.94062i	0.976323	+	0.563681i	0.0751653	+	0.997171i	$0.476052\pi$
$312$	−2.60928	+	4.51941i	−0.147722	+	0.255861i
$313$	−21.0731	−	12.1665i	−1.19112	−	0.687694i	−0.232560	−	0.972582i	$-0.574710\pi$
$313$	−21.0731	−	12.1665i	−1.19112	−	0.687694i	−0.958561	+	0.284888i	$0.908043\pi$
$314$	−1.22181	+	0.705413i	−0.0689508	+	0.0398087i
$315$	−1.87170	+	1.08063i	−0.105458	+	0.0608864i
$316$	2.06361	+	1.19143i	0.116087	+	0.0670229i
$317$	2.30160	−	3.98649i	0.129271	−	0.223903i	−0.794124	−	0.607756i	$-0.792070\pi$
$317$	2.30160	−	3.98649i	0.129271	−	0.223903i	0.923394	+	0.383853i	$0.125403\pi$
$318$	−1.00272	−	0.578919i	−0.0562296	−	0.0324642i
$319$			29.9113i			1.67471i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−8.48343	+	14.6937i	−0.473499	+	0.820124i
$322$	7.53524			0.419922
$323$	0.650529			0.0361964
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			5.21857i			0.289474i
$326$	−4.90393	−	8.49385i	−0.271603	−	0.470431i
$327$			1.52817i			0.0845083i
$328$	−2.80066	+	1.61696i	−0.154641	+	0.0892818i
$329$	0.901423	+	1.56131i	0.0496971	+	0.0860778i
$330$	−2.32159	−	4.02112i	−0.127800	−	0.221355i
$331$	−22.7234	−	13.1193i	−1.24899	−	0.721105i	−0.278082	−	0.960557i	$-0.589699\pi$
$331$	−22.7234	−	13.1193i	−1.24899	−	0.721105i	−0.970908	+	0.239453i	$0.923032\pi$
$332$	−13.9616			−0.766241
$333$	3.24001	+	5.14804i	0.177552	+	0.282111i
$334$	−15.2736			−0.835734
$335$	0.312243	+	0.180274i	0.0170597	+	0.00984940i
$336$	1.08063	+	1.87170i	0.0589530	+	0.102110i
$337$	4.83436	+	8.37335i	0.263344	+	0.456126i	0.967129	−	0.254288i	$-0.0818412\pi$
$337$	4.83436	+	8.37335i	0.263344	+	0.456126i	−0.703784	+	0.710414i	$0.748508\pi$
$338$	12.3265	−	7.11672i	0.670474	−	0.387099i
$339$			19.7945i			1.07509i
$340$	1.58063	+	2.73772i	0.0857215	+	0.148474i
$341$			28.7500i			1.55690i
$342$	−0.102891	+	0.178213i	−0.00556371	+	0.00963663i
$343$	20.1623			1.08866
$344$	2.70535			0.145863
$345$	−1.74326	+	3.01941i	−0.0938539	+	0.162560i
$346$	2.39485	−	1.38267i	0.128748	−	0.0743327i
$347$		−	36.2192i		−	1.94435i	−0.234259	−	0.972174i	$-0.575266\pi$
$347$		−	36.2192i		−	1.94435i	0.234259	−	0.972174i	$-0.424734\pi$
$348$	5.57892	+	3.22099i	0.299062	+	0.172663i
$349$	4.27797	−	7.40967i	0.228995	−	0.396630i	−0.728516	−	0.685029i	$-0.759789\pi$
$349$	4.27797	−	7.40967i	0.228995	−	0.396630i	0.957510	+	0.288399i	$0.0931228\pi$
$350$	1.87170	+	1.08063i	0.100047	+	0.0577619i
$351$	−4.51941	+	2.60928i	−0.241228	+	0.139273i
$352$	−4.02112	+	2.32159i	−0.214326	+	0.123741i
$353$	29.7047	+	17.1500i	1.58102	+	0.912804i	0.994710	+	0.102719i	$0.0327542\pi$
$353$	29.7047	+	17.1500i	1.58102	+	0.912804i	0.586312	+	0.810085i	$0.300579\pi$
$354$	2.27786	−	3.94537i	0.121067	−	0.209694i
$355$	3.91838	+	2.26228i	0.207966	+	0.120069i
$356$		−	15.5253i		−	0.822841i
$357$	5.91691	−	3.41613i	0.313156	−	0.180801i
$358$	−0.586956	+	1.01664i	−0.0310216	+	0.0537310i
$359$	−0.531359			−0.0280441			−0.0140220	−	0.999902i	$-0.504464\pi$
$359$	−0.531359			−0.0280441			−0.0140220	+	0.999902i	$0.504464\pi$
$360$	−1.00000			−0.0527046
$361$	−9.47883	+	16.4178i	−0.498886	+	0.864095i
$362$		−	21.1590i		−	1.11209i
$363$	−5.27959	−	9.14453i	−0.277107	−	0.479963i
$364$		−	11.2786i		−	0.591161i
$365$	4.25705	−	2.45781i	0.222824	−	0.128648i
$366$	−5.32064	−	9.21562i	−0.278114	−	0.481708i
$367$	10.6682	+	18.4778i	0.556873	+	0.964533i	0.997755	+	0.0669678i	$0.0213325\pi$
$367$	10.6682	+	18.4778i	0.556873	+	0.964533i	−0.440882	+	0.897565i	$0.645334\pi$
$368$	3.01941	+	1.74326i	0.157398	+	0.0908736i
$369$	−3.23393			−0.168351
$370$	2.83833	−	5.37995i	0.147557	−	0.279691i
$371$	2.50238			0.129917
$372$	5.36232	+	3.09594i	0.278023	+	0.160517i
$373$	−12.0963	−	20.9513i	−0.626320	−	1.08482i	−0.988284	−	0.152626i	$-0.951227\pi$
$373$	−12.0963	−	20.9513i	−0.626320	−	1.08482i	0.361964	−	0.932192i	$-0.382106\pi$
$374$	7.33914	+	12.7118i	0.379498	+	0.657310i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$			0.834167i			0.0430189i
$377$	−16.8090	−	29.1140i	−0.865706	−	1.49945i
$378$			2.16125i			0.111163i
$379$	12.1357	−	21.0196i	0.623367	−	1.07970i	−0.365488	−	0.930816i	$-0.619098\pi$
$379$	12.1357	−	21.0196i	0.623367	−	1.07970i	0.988854	−	0.148886i	$-0.0475689\pi$
$380$	0.205782			0.0105564
$381$	1.42718			0.0731169
$382$	−5.42635	+	9.39872i	−0.277636	+	0.480880i
$383$	−11.1983	+	6.46534i	−0.572206	+	0.330363i	−0.758030	−	0.652220i	$-0.773838\pi$
$383$	−11.1983	+	6.46534i	−0.572206	+	0.330363i	0.185824	+	0.982583i	$0.440505\pi$
$384$			1.00000i			0.0510310i
$385$	8.69065	+	5.01755i	0.442917	+	0.255718i
$386$	11.4872	−	19.8964i	0.584682	−	1.01270i
$387$	2.34291	+	1.35268i	0.119097	+	0.0687605i
$388$	0.132543	−	0.0765237i	0.00672885	−	0.00388490i
$389$	−10.9293	+	6.31001i	−0.554136	+	0.319930i	−0.750788	−	0.660543i	$-0.770326\pi$
$389$	−10.9293	+	6.31001i	−0.554136	+	0.319930i	0.196653	+	0.980473i	$0.436993\pi$
$390$	4.51941	+	2.60928i	0.228849	+	0.132126i
$391$	5.51088	−	9.54512i	0.278697	−	0.482718i
$392$	2.01696	+	1.16450i	0.101872	+	0.0588159i
$393$			15.9205i			0.803084i
$394$	15.9323	−	9.19854i	0.802659	−	0.463416i
$395$	1.19143	−	2.06361i	0.0599471	−	0.103831i
$396$	−4.64319			−0.233329
$397$	1.44241			0.0723926			0.0361963	−	0.999345i	$-0.488476\pi$
$397$	1.44241			0.0723926			0.0361963	+	0.999345i	$0.488476\pi$
$398$	5.46700	−	9.46911i	0.274036	−	0.474644i
$399$		−	0.444747i		−	0.0222652i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			19.5163i			0.974597i	0.873235	+	0.487299i	$0.162018\pi$
$401$			19.5163i			0.974597i	−0.873235	+	0.487299i	$0.837982\pi$
$402$	0.312243	−	0.180274i	0.0155733	−	0.00899123i
$403$	−16.1563	−	27.9836i	−0.804805	−	1.39396i
$404$	4.21966	+	7.30867i	0.209936	+	0.363620i
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$	−13.9228			−0.690975
$407$	13.1789	−	24.9801i	0.653253	−	1.23822i
$408$	3.16125			0.156505
$409$	−8.91730	−	5.14840i	−0.440932	−	0.254572i	0.263061	−	0.964779i	$-0.415268\pi$
$409$	−8.91730	−	5.14840i	−0.440932	−	0.254572i	−0.703993	+	0.710207i	$0.748601\pi$
$410$	1.61696	+	2.80066i	0.0798561	+	0.138315i
$411$	−0.570579	−	0.988273i	−0.0281446	−	0.0487479i
$412$	−3.59622	+	2.07628i	−0.177173	+	0.102291i
$413$			9.84606i			0.484493i
$414$	1.74326	+	3.01941i	0.0856765	+	0.148396i
$415$			13.9616i			0.685347i
$416$	2.60928	−	4.51941i	0.127931	−	0.221582i
$417$	−2.76665			−0.135484
$418$	0.955485			0.0467343
$419$	−3.05527	+	5.29188i	−0.149260	+	0.258525i	−0.930954	−	0.365136i	$-0.881022\pi$
$419$	−3.05527	+	5.29188i	−0.149260	+	0.258525i	0.781694	+	0.623662i	$0.214356\pi$
$420$	1.87170	−	1.08063i	0.0913296	−	0.0527291i
$421$		−	28.0074i		−	1.36500i	−0.730888	−	0.682498i	$-0.760894\pi$
$421$		−	28.0074i		−	1.36500i	0.730888	−	0.682498i	$-0.239106\pi$
$422$	−4.64980	−	2.68456i	−0.226349	−	0.130683i
$423$	−0.417084	+	0.722410i	−0.0202793	+	0.0351248i
$424$	1.00272	+	0.578919i	0.0486963	+	0.0281148i
$425$	2.73772	−	1.58063i	0.132799	−	0.0766716i
$426$	3.91838	−	2.26228i	0.189846	−	0.109608i
$427$	19.9173	+	11.4992i	0.963865	+	0.556487i
$428$	8.48343	−	14.6937i	0.410062	−	0.710248i
$429$	20.9845	+	12.1154i	1.01314	+	0.584937i
$430$		−	2.70535i		−	0.130464i
$431$	−13.3803	+	7.72513i	−0.644507	+	0.372106i	−0.786348	−	0.617783i	$-0.788031\pi$
$431$	−13.3803	+	7.72513i	−0.644507	+	0.372106i	0.141842	+	0.989889i	$0.454698\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	17.9207			0.861215			0.430607	−	0.902539i	$-0.358299\pi$
$433$	17.9207			0.861215			0.430607	+	0.902539i	$0.358299\pi$
$434$	−13.3822			−0.642366
$435$	3.22099	−	5.57892i	0.154435	−	0.267489i
$436$		−	1.52817i		−	0.0731863i
$437$	−0.358731	−	0.621341i	−0.0171604	−	0.0297228i
$438$		−	4.91562i		−	0.234877i
$439$	−3.25893	+	1.88155i	−0.155540	+	0.0898013i	−0.575750	−	0.817626i	$-0.695290\pi$
$439$	−3.25893	+	1.88155i	−0.155540	+	0.0898013i	0.420210	+	0.907427i	$0.361957\pi$
$440$	2.32159	+	4.02112i	0.110678	+	0.191699i
$441$	1.16450	+	2.01696i	0.0554522	+	0.0960460i
$442$	−14.2870	−	8.24860i	−0.679563	−	0.392346i
$443$	39.4966			1.87654			0.938271	−	0.345902i	$-0.112427\pi$
$443$	39.4966			1.87654			0.938271	+	0.345902i	$0.112427\pi$
$444$	−3.24001	−	5.14804i	−0.153764	−	0.244315i
$445$	−15.5253			−0.735972
$446$	−20.0596	−	11.5814i	−0.949848	−	0.548395i
$447$	−5.08331	−	8.80454i	−0.240432	−	0.416441i
$448$	−1.08063	−	1.87170i	−0.0510548	−	0.0884295i
$449$	−3.39675	+	1.96112i	−0.160303	+	0.0925508i	−0.578005	−	0.816033i	$-0.696169\pi$
$449$	−3.39675	+	1.96112i	−0.160303	+	0.0925508i	0.417703	+	0.908584i	$0.362835\pi$
$450$			1.00000i			0.0471405i
$451$	7.50786	+	13.0040i	0.353531	+	0.612334i
$452$		−	19.7945i		−	0.931057i
$453$	−1.21847	+	2.11046i	−0.0572489	+	0.0991580i
$454$	−23.7706			−1.11561
$455$	−11.2786			−0.528751
$456$	0.102891	−	0.178213i	0.00481831	−	0.00834557i
$457$	−4.62565	+	2.67062i	−0.216379	+	0.124926i	−0.604272	−	0.796778i	$-0.706536\pi$
$457$	−4.62565	+	2.67062i	−0.216379	+	0.124926i	0.387894	+	0.921704i	$0.373203\pi$
$458$		−	4.55782i		−	0.212973i
$459$	2.73772	+	1.58063i	0.127786	+	0.0737773i
$460$	1.74326	−	3.01941i	0.0812798	−	0.140781i
$461$	22.9413	+	13.2452i	1.06848	+	0.616889i	0.927767	−	0.373161i	$-0.121726\pi$
$461$	22.9413	+	13.2452i	1.06848	+	0.616889i	0.140716	+	0.990050i	$0.455059\pi$
$462$	8.69065	−	5.01755i	0.404326	−	0.233437i
$463$	−29.0544	+	16.7746i	−1.35027	+	0.779580i	−0.988287	−	0.152604i	$-0.951234\pi$
$463$	−29.0544	+	16.7746i	−1.35027	+	0.779580i	−0.361984	+	0.932184i	$0.617901\pi$
$464$	−5.57892	−	3.22099i	−0.258995	−	0.149531i
$465$	3.09594	−	5.36232i	0.143571	−	0.248672i
$466$	−15.8313	−	9.14018i	−0.733369	−	0.423411i
$467$			19.4765i			0.901265i	0.892709	+	0.450633i	$0.148802\pi$
$467$			19.4765i			0.901265i	−0.892709	+	0.450633i	$0.851198\pi$
$468$	4.51941	−	2.60928i	0.208910	−	0.120614i
$469$	−0.389617	+	0.674836i	−0.0179908	+	0.0311610i
$470$	0.834167			0.0384773
$471$	1.41083			0.0650074
$472$	−2.27786	+	3.94537i	−0.104847	+	0.181600i
$473$		−	12.5615i		−	0.577577i
$474$	−1.19143	−	2.06361i	−0.0547240	−	0.0947847i
$475$		−	0.205782i		−	0.00944193i
$476$	−5.91691	+	3.41613i	−0.271201	+	0.156578i
$477$	0.578919	+	1.00272i	0.0265069	+	0.0459113i
$478$	10.1798	+	17.6319i	0.465611	+	0.806462i
$479$	11.0157	+	6.35989i	0.503318	+	0.290591i	0.730083	−	0.683359i	$-0.239482\pi$
$479$	11.0157	+	6.35989i	0.503318	+	0.290591i	−0.226765	+	0.973950i	$0.572815\pi$
$480$	1.00000			0.0456435
$481$	1.21027	+	31.7202i	0.0551834	+	1.44632i
$482$	15.3835			0.700698
$483$	−6.52571	−	3.76762i	−0.296930	−	0.171433i
$484$	5.27959	+	9.14453i	0.239982	+	0.415660i
$485$	−0.0765237	−	0.132543i	−0.00347476	−	0.00601847i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$			33.0632i			1.49824i	0.662435	+	0.749119i	$0.269523\pi$
$487$			33.0632i			1.49824i	−0.662435	+	0.749119i	$0.730477\pi$
$488$	5.32064	+	9.21562i	0.240854	+	0.417172i
$489$			9.80785i			0.443526i
$490$	1.16450	−	2.01696i	0.0526065	−	0.0911172i
$491$	18.4326			0.831853			0.415927	−	0.909398i	$-0.363457\pi$
$491$	18.4326			0.831853			0.415927	+	0.909398i	$0.363457\pi$
$492$	3.23393			0.145797
$493$	−10.1824	+	17.6364i	−0.458591	+	0.794303i
$494$	−0.930014	+	0.536944i	−0.0418433	+	0.0241582i
$495$			4.64319i			0.208696i
$496$	−5.36232	−	3.09594i	−0.240775	−	0.139012i
$497$	−4.88936	+	8.46861i	−0.219318	+	0.379869i
$498$	12.0911	+	6.98079i	0.541814	+	0.312817i
$499$	34.0311	−	19.6479i	1.52344	−	0.879559i	0.523826	−	0.851825i	$-0.324504\pi$
$499$	34.0311	−	19.6479i	1.52344	−	0.879559i	0.999615	−	0.0277344i	$-0.00882925\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	13.2273	+	7.63680i	0.590953	+	0.341187i
$502$	−6.63994	+	11.5007i	−0.296355	+	0.513302i
$503$	−25.6760	−	14.8240i	−1.14483	−	0.660970i	−0.197211	−	0.980361i	$-0.563188\pi$
$503$	−25.6760	−	14.8240i	−1.14483	−	0.660970i	−0.947623	+	0.319391i	$0.896522\pi$
$504$		−	2.16125i		−	0.0962698i
$505$	7.30867	−	4.21966i	0.325231	−	0.187772i
$506$	8.09427	−	14.0197i	0.359834	−	0.623251i
$507$	−14.2334			−0.632129
$508$	−1.42718			−0.0633210
$509$	−17.2652	+	29.9043i	−0.765268	+	1.32548i	0.174836	+	0.984598i	$0.444060\pi$
$509$	−17.2652	+	29.9043i	−0.765268	+	1.32548i	−0.940105	+	0.340886i	$0.889273\pi$
$510$		−	3.16125i		−	0.139983i
$511$	5.31194	+	9.20055i	0.234986	+	0.407008i
$512$		−	1.00000i		−	0.0441942i
$513$	0.178213	−	0.102891i	0.00786828	−	0.00454275i
$514$	−1.45986	−	2.52855i	−0.0643917	−	0.111530i
$515$	2.07628	+	3.59622i	0.0914918	+	0.158468i
$516$	−2.34291	−	1.35268i	−0.103141	−	0.0595483i
$517$	3.87320			0.170343
$518$	11.6274	+	6.13434i	0.510880	+	0.269527i
$519$	−2.76534			−0.121385
$520$	−4.51941	−	2.60928i	−0.198189	−	0.114425i
$521$	21.9354	+	37.9932i	0.961006	+	1.66451i	0.719983	+	0.693992i	$0.244150\pi$
$521$	21.9354	+	37.9932i	0.961006	+	1.66451i	0.241023	+	0.970519i	$0.422517\pi$
$522$	−3.22099	−	5.57892i	−0.140979	−	0.244183i
$523$	24.1241	−	13.9281i	1.05487	−	0.609031i	0.130864	−	0.991400i	$-0.458225\pi$
$523$	24.1241	−	13.9281i	1.05487	−	0.609031i	0.924010	+	0.382369i	$0.124892\pi$
$524$		−	15.9205i		−	0.695491i
$525$	−1.08063	−	1.87170i	−0.0471624	−	0.0816876i
$526$		−	10.3676i		−	0.452049i
$527$	−9.78703	+	16.9516i	−0.426330	+	0.738425i
$528$	4.64319			0.202069
$529$	10.8442			0.471487
$530$	0.578919	−	1.00272i	0.0251466	−	0.0435553i
$531$	−3.94537	+	2.27786i	−0.171214	+	0.0988507i
$532$			0.444747i			0.0192822i
$533$	−14.6154	−	8.43823i	−0.633065	−	0.365500i
$534$	−7.76267	+	13.4453i	−0.335924	+	0.581837i
$535$	−14.6937	−	8.48343i	−0.635265	−	0.366771i
$536$	−0.312243	+	0.180274i	−0.0134868	+	0.00778663i
$537$	1.01664	−	0.586956i	0.0438712	−	0.0253290i
$538$	21.8620	+	12.6220i	0.942536	+	0.544173i
$539$	5.40697	−	9.36515i	0.232895	−	0.403385i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$			9.84613i			0.423318i	0.977344	+	0.211659i	$0.0678866\pi$
$541$			9.84613i			0.423318i	−0.977344	+	0.211659i	$0.932113\pi$
$542$	−14.1632	+	8.17713i	−0.608362	+	0.351238i
$543$	−10.5795	+	18.3242i	−0.454009	+	0.786366i
$544$	−3.16125			−0.135538
$545$	−1.52817			−0.0654598
$546$	−5.63932	+	9.76759i	−0.241341	+	0.418014i
$547$			22.3203i			0.954348i	0.878809	+	0.477174i	$0.158339\pi$
$547$			22.3203i			0.954348i	−0.878809	+	0.477174i	$0.841661\pi$
$548$	0.570579	+	0.988273i	0.0243739	+	0.0422169i
$549$			10.6413i			0.454159i
$550$	4.02112	−	2.32159i	0.171461	−	0.0989931i
$551$	0.662823	+	1.14804i	0.0282372	+	0.0489083i
$552$	−1.74326	−	3.01941i	−0.0741980	−	0.128515i
$553$	4.45998	+	2.57497i	0.189658	+	0.109499i
$554$	3.35255			0.142436
$555$	−5.14804	+	3.24001i	−0.218522	+	0.137531i
$556$	2.76665			0.117332
$557$	−6.99456	−	4.03831i	−0.296369	−	0.171109i	0.344441	−	0.938808i	$-0.388068\pi$
$557$	−6.99456	−	4.03831i	−0.296369	−	0.171109i	−0.640811	+	0.767699i	$0.721402\pi$
$558$	−3.09594	−	5.36232i	−0.131061	−	0.227005i
$559$	7.05904	+	12.2266i	0.298565	+	0.517131i
$560$	−1.87170	+	1.08063i	−0.0790937	+	0.0456648i
$561$		−	14.6783i		−	0.619718i
$562$	−1.68735	−	2.92257i	−0.0711765	−	0.123281i
$563$			14.8077i			0.624069i	0.950071	+	0.312034i	$0.101010\pi$
$563$			14.8077i			0.624069i	−0.950071	+	0.312034i	$0.898990\pi$
$564$	0.417084	−	0.722410i	0.0175624	−	0.0304190i
$565$	−19.7945			−0.832763
$566$	20.8447			0.876167
$567$	1.08063	−	1.87170i	0.0453820	−	0.0786040i
$568$	−3.91838	+	2.26228i	−0.164412	+	0.0949232i
$569$		−	25.6916i		−	1.07705i	−0.842611	−	0.538523i	$-0.818982\pi$
$569$		−	25.6916i		−	1.07705i	0.842611	−	0.538523i	$-0.181018\pi$
$570$	−0.178213	−	0.102891i	−0.00746450	−	0.00430963i
$571$	−2.31582	+	4.01112i	−0.0969142	+	0.167860i	−0.910406	−	0.413716i	$-0.864231\pi$
$571$	−2.31582	+	4.01112i	−0.0969142	+	0.167860i	0.813492	+	0.581576i	$0.197564\pi$
$572$	−20.9845	−	12.1154i	−0.877405	−	0.506570i
$573$	9.39872	−	5.42635i	0.392637	−	0.226689i
$574$	−6.05294	+	3.49466i	−0.252645	+	0.145864i
$575$	−3.01941	−	1.74326i	−0.125918	−	0.0726989i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−26.8227	−	15.4861i	−1.11664	−	0.644694i	−0.176101	−	0.984372i	$-0.556349\pi$
$577$	−26.8227	−	15.4861i	−1.11664	−	0.644694i	−0.940542	+	0.339678i	$0.889682\pi$
$578$		−	7.00649i		−	0.291431i
$579$	−19.8964	+	11.4872i	−0.826866	+	0.477391i
$580$	−3.22099	+	5.57892i	−0.133744	+	0.231652i
$581$	−30.1745			−1.25185
$582$	−0.153047			−0.00634402
$583$	2.68803	−	4.65581i	0.111327	−	0.192824i
$584$			4.91562i			0.203410i
$585$	−2.60928	−	4.51941i	−0.107881	−	0.186855i
$586$			2.25632i			0.0932076i
$587$	−32.3952	+	18.7033i	−1.33709	+	0.771970i	−0.986375	−	0.164512i	$-0.947395\pi$
$587$	−32.3952	+	18.7033i	−1.33709	+	0.771970i	−0.350716	+	0.936482i	$0.614062\pi$
$588$	−1.16450	−	2.01696i	−0.0480230	−	0.0831782i
$589$	0.637088	+	1.10347i	0.0262508	+	0.0454676i
$590$	3.94537	+	2.27786i	0.162428	+	0.0937780i
$591$	−18.3971			−0.756755
$592$	3.24001	+	5.14804i	0.133164	+	0.211583i
$593$	−10.9308			−0.448876			−0.224438	−	0.974488i	$-0.572055\pi$
$593$	−10.9308			−0.448876			−0.224438	+	0.974488i	$0.572055\pi$
$594$	4.02112	+	2.32159i	0.164988	+	0.0952561i
$595$	3.41613	+	5.91691i	0.140048	+	0.242570i
$596$	5.08331	+	8.80454i	0.208220	+	0.360648i
$597$	−9.46911	+	5.46700i	−0.387545	+	0.223749i
$598$			18.1946i			0.744033i
$599$	−22.6620	−	39.2517i	−0.925943	−	1.60378i	−0.790037	−	0.613059i	$-0.789939\pi$
$599$	−22.6620	−	39.2517i	−0.925943	−	1.60378i	−0.135906	−	0.990722i	$-0.543394\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	19.7964	−	34.2884i	0.807514	−	1.39865i	−0.107067	−	0.994252i	$-0.534146\pi$
$601$	19.7964	−	34.2884i	0.807514	−	1.39865i	0.914581	−	0.404403i	$-0.132521\pi$
$602$	5.84695			0.238304
$603$	−0.360547			−0.0146826
$604$	1.21847	−	2.11046i	0.0495790	−	0.0858733i
$605$	9.14453	−	5.27959i	0.371778	−	0.214646i
$606$		−	8.43932i		−	0.342824i
$607$	35.1813	+	20.3119i	1.42796	+	0.824435i	0.996960	−	0.0779145i	$-0.0248261\pi$
$607$	35.1813	+	20.3119i	1.42796	+	0.824435i	0.431004	+	0.902350i	$0.358159\pi$
$608$	−0.102891	+	0.178213i	−0.00417278	+	0.00722747i
$609$	12.0575	+	6.96138i	0.488593	+	0.282089i
$610$	9.21562	−	5.32064i	0.373130	−	0.215426i
$611$	−3.76995	+	2.17658i	−0.152516	+	0.0880550i
$612$	−2.73772	−	1.58063i	−0.110666	−	0.0638930i
$613$	−7.78583	+	13.4855i	−0.314467	+	0.544672i	−0.979324	−	0.202298i	$-0.935159\pi$
$613$	−7.78583	+	13.4855i	−0.314467	+	0.544672i	0.664857	+	0.746970i	$0.268492\pi$
$614$	12.1312	+	7.00396i	0.489576	+	0.282657i
$615$		−	3.23393i		−	0.130404i
$616$	−8.69065	+	5.01755i	−0.350156	+	0.202163i
$617$	10.5032	−	18.1921i	0.422843	−	0.732386i	−0.573373	−	0.819295i	$-0.694365\pi$
$617$	10.5032	−	18.1921i	0.422843	−	0.732386i	0.996216	+	0.0869081i	$0.0276987\pi$
$618$	4.15256			0.167040
$619$	−29.8151			−1.19837			−0.599186	−	0.800610i	$-0.704509\pi$
$619$	−29.8151			−1.19837			−0.599186	+	0.800610i	$0.704509\pi$
$620$	−3.09594	+	5.36232i	−0.124336	+	0.215356i
$621$		−	3.48652i		−	0.139909i
$622$	9.94062	+	17.2177i	0.398582	+	0.690365i
$623$		−	33.5542i		−	1.34432i
$624$	−4.51941	+	2.60928i	−0.180921	+	0.104455i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.1665	−	21.0731i	−0.486273	−	0.842249i
$627$	−0.827474	−	0.477742i	−0.0330461	−	0.0190792i
$628$	−1.41083			−0.0562981
$629$	16.2742	−	10.2425i	0.648897	−	0.408395i
$630$	−2.16125			−0.0861063
$631$	−19.1456	−	11.0537i	−0.762173	−	0.440041i	0.0679026	−	0.997692i	$-0.478369\pi$
$631$	−19.1456	−	11.0537i	−0.762173	−	0.440041i	−0.830075	+	0.557651i	$0.811703\pi$
$632$	1.19143	+	2.06361i	0.0473924	+	0.0820860i
$633$	2.68456	+	4.64980i	0.106702	+	0.184813i
$634$	3.98649	−	2.30160i	0.158324	−	0.0914081i
$635$			1.42718i			0.0566361i
$636$	−0.578919	−	1.00272i	−0.0229556	−	0.0397603i
$637$			12.1540i			0.481559i
$638$	−14.9557	+	25.9040i	−0.592101	+	1.02555i
$639$	−4.52456			−0.178989
$640$	−1.00000			−0.0395285
$641$	−2.21636	+	3.83886i	−0.0875411	+	0.151626i	−0.906471	−	0.422268i	$-0.861234\pi$
$641$	−2.21636	+	3.83886i	−0.0875411	+	0.151626i	0.818930	+	0.573893i	$0.194568\pi$
$642$	−14.6937	+	8.48343i	−0.579915	+	0.334814i
$643$		−	44.3817i		−	1.75024i	−0.483902	−	0.875122i	$-0.660781\pi$
$643$		−	44.3817i		−	1.75024i	0.483902	−	0.875122i	$-0.339219\pi$
$644$	6.52571	+	3.76762i	0.257149	+	0.148465i
$645$	−1.35268	+	2.34291i	−0.0532616	+	0.0922518i
$646$	0.563375	+	0.325265i	0.0221657	+	0.0127974i
$647$	−36.1565	+	20.8750i	−1.42146	+	0.820681i	−0.996424	−	0.0844957i	$-0.973072\pi$
$647$	−36.1565	+	20.8750i	−1.42146	+	0.820681i	−0.425037	+	0.905176i	$0.639739\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	18.3191	+	10.5765i	0.719087	+	0.415165i
$650$	−2.60928	+	4.51941i	−0.102345	+	0.177266i
$651$	11.5893	+	6.69110i	0.454221	+	0.262245i
$652$		−	9.80785i		−	0.384105i
$653$	15.9953	−	9.23488i	0.625944	−	0.361389i	−0.153236	−	0.988190i	$-0.548969\pi$
$653$	15.9953	−	9.23488i	0.625944	−	0.361389i	0.779179	+	0.626801i	$0.215636\pi$
$654$	−0.764087	+	1.32344i	−0.0298782	+	0.0517505i
$655$	−15.9205			−0.622066
$656$	−3.23393			−0.126264
$657$	−2.45781	+	4.25705i	−0.0958882	+	0.166083i
$658$			1.80285i			0.0702823i
$659$	3.89081	+	6.73909i	0.151565	+	0.262518i	0.931803	−	0.362965i	$-0.118236\pi$
$659$	3.89081	+	6.73909i	0.151565	+	0.262518i	−0.780238	+	0.625482i	$0.784902\pi$
$660$		−	4.64319i		−	0.180736i
$661$	24.6064	−	14.2065i	0.957077	−	0.552569i	0.0618049	−	0.998088i	$-0.480314\pi$
$661$	24.6064	−	14.2065i	0.957077	−	0.552569i	0.895272	+	0.445520i	$0.146981\pi$
$662$	−13.1193	−	22.7234i	−0.509898	−	0.883169i
$663$	8.24860	+	14.2870i	0.320349	+	0.554861i
$664$	−12.0911	−	6.98079i	−0.469225	−	0.270907i
$665$	0.444747			0.0172465
$666$	0.231916	+	6.07834i	0.00898655	+	0.235531i
$667$	22.4601			0.869658
$668$	−13.2273	−	7.63680i	−0.511781	−	0.295477i
$669$	11.5814	+	20.0596i	0.447763	+	0.775547i
$670$	0.180274	+	0.312243i	0.00696457	+	0.0120630i
$671$	42.7899	−	24.7047i	1.65188	−	0.953716i
$672$			2.16125i			0.0833721i
$673$	−11.5000	−	19.9185i	−0.443291	−	0.767803i	0.554640	−	0.832090i	$-0.312856\pi$
$673$	−11.5000	−	19.9185i	−0.443291	−	0.767803i	−0.997931	+	0.0642874i	$0.979523\pi$
$674$			9.66872i			0.372425i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	14.2334			0.547440
$677$	41.5752			1.59786			0.798932	−	0.601422i	$-0.205399\pi$
$677$	41.5752			1.59786			0.798932	+	0.601422i	$0.205399\pi$
$678$	−9.89727	+	17.1426i	−0.380103	+	0.658357i
$679$	0.286459	−	0.165387i	0.0109933	−	0.00634697i
$680$			3.16125i			0.121228i
$681$	20.5859	+	11.8853i	0.788855	+	0.455446i
$682$	−14.3750	+	24.8982i	−0.550448	+	0.953403i
$683$	−8.30680	−	4.79594i	−0.317851	−	0.183511i	0.332583	−	0.943074i	$-0.392080\pi$
$683$	−8.30680	−	4.79594i	−0.317851	−	0.183511i	−0.650434	+	0.759563i	$0.725413\pi$
$684$	−0.178213	+	0.102891i	−0.00681413	+	0.00393414i
$685$	0.988273	−	0.570579i	0.0377600	−	0.0218007i
$686$	17.4611	+	10.0811i	0.666666	+	0.384900i
$687$	−2.27891	+	3.94718i	−0.0869458	+	0.150594i
$688$	2.34291	+	1.35268i	0.0893224	+	0.0515703i
$689$			6.04226i			0.230192i
$690$	−3.01941	+	1.74326i	−0.114947	+	0.0663647i
$691$	−14.0821	+	24.3909i	−0.535709	+	0.927875i	0.463420	+	0.886139i	$0.346622\pi$
$691$	−14.0821	+	24.3909i	−0.535709	+	0.927875i	−0.999129	+	0.0417362i	$0.986711\pi$
$692$	2.76534			0.105122
$693$	−10.0351			−0.381202
$694$	18.1096	−	31.3667i	0.687431	−	1.19067i
$695$		−	2.76665i		−	0.104945i
$696$	3.22099	+	5.57892i	0.122091	+	0.211469i
$697$			10.2233i			0.387233i
$698$	7.40967	−	4.27797i	0.280460	−	0.161924i
$699$	9.14018	+	15.8313i	0.345713	+	0.598793i
$700$	1.08063	+	1.87170i	0.0408438	+	0.0707436i
$701$	23.6784	+	13.6707i	0.894319	+	0.516335i	0.875353	−	0.483485i	$-0.160629\pi$
$701$	23.6784	+	13.6707i	0.894319	+	0.516335i	0.0189664	+	0.999820i	$0.493962\pi$
$702$	−5.21857			−0.196962
$703$	−0.0477241	−	1.25081i	−0.00179995	−	0.0471753i
$704$	−4.64319			−0.174997
$705$	−0.722410	−	0.417084i	−0.0272075	−	0.0157083i
$706$	17.1500	+	29.7047i	0.645450	+	1.11795i
$707$	9.11975	+	15.7959i	0.342983	+	0.594065i
$708$	3.94537	−	2.27786i	0.148276	−	0.0856072i
$709$		−	1.92294i		−	0.0722174i	−0.999348	−	0.0361087i	$-0.988504\pi$
$709$		−	1.92294i		−	0.0722174i	0.999348	−	0.0361087i	$-0.0114963\pi$
$710$	2.26228	+	3.91838i	0.0849019	+	0.147054i
$711$			2.38285i			0.0893639i
$712$	7.76267	−	13.4453i	0.290918	−	0.503885i
$713$	21.5881			0.808479
$714$	6.83226			0.255691
$715$	−12.1154	+	20.9845i	−0.453090	+	0.784775i
$716$	−1.01664	+	0.586956i	−0.0379936	+	0.0219356i
$717$		−	20.3595i		−	0.760340i
$718$	−0.460171	−	0.265680i	−0.0171734	−	0.00991508i
$719$	10.1641	−	17.6047i	0.379056	−	0.656544i	−0.611869	−	0.790959i	$-0.709582\pi$
$719$	10.1641	−	17.6047i	0.379056	−	0.656544i	0.990925	+	0.134415i	$0.0429155\pi$
$720$	−0.866025	−	0.500000i	−0.0322749	−	0.0186339i
$721$	−7.77234	+	4.48736i	−0.289457	+	0.167118i
$722$	−16.4178	+	9.47883i	−0.611008	+	0.352765i
$723$	−13.3225	−	7.69174i	−0.495468	−	0.286059i
$724$	10.5795	−	18.3242i	0.393183	−	0.681013i
$725$	5.57892	+	3.22099i	0.207196	+	0.119625i
$726$		−	10.5592i		−	0.391888i
$727$	−35.6599	+	20.5883i	−1.32255	+	0.763576i	−0.984135	−	0.177420i	$-0.943225\pi$
$727$	−35.6599	+	20.5883i	−1.32255	+	0.763576i	−0.338418	+	0.940996i	$0.609892\pi$
$728$	5.63932	−	9.76759i	0.209007	−	0.362011i
$729$	1.00000			0.0370370
$730$	4.91562			0.181935
$731$	4.27615	−	7.40652i	0.158159	−	0.273940i
$732$		−	10.6413i		−	0.393313i
$733$	17.2131	+	29.8140i	0.635782	+	1.10121i	0.986349	+	0.164669i	$0.0526556\pi$
$733$	17.2131	+	29.8140i	0.635782	+	1.10121i	−0.350567	+	0.936538i	$0.614011\pi$
$734$			21.3363i			0.787538i
$735$	−2.01696	+	1.16450i	−0.0743969	+	0.0429531i
$736$	1.74326	+	3.01941i	0.0642573	+	0.111297i
$737$	0.837044	+	1.44980i	0.0308329	+	0.0534042i
$738$	−2.80066	−	1.61696i	−0.103094	−	0.0595212i
$739$	29.2229			1.07498			0.537490	−	0.843270i	$-0.319372\pi$
$739$	29.2229			1.07498			0.537490	+	0.843270i	$0.319372\pi$
$740$	5.14804	−	3.24001i	0.189246	−	0.119105i
$741$	1.07389			0.0394503
$742$	2.16713	+	1.25119i	0.0795577	+	0.0459326i
$743$	12.0985	+	20.9553i	0.443852	+	0.768774i	0.997971	−	0.0636630i	$-0.0202783\pi$
$743$	12.0985	+	20.9553i	0.443852	+	0.768774i	−0.554119	+	0.832437i	$0.686945\pi$
$744$	3.09594	+	5.36232i	0.113503	+	0.196592i
$745$	8.80454	−	5.08331i	0.322574	−	0.186238i
$746$		−	24.1925i		−	0.885750i
$747$	−6.98079	−	12.0911i	−0.255414	−	0.442390i
$748$			14.6783i			0.536691i
$749$	18.3348	−	31.7569i	0.669940	−	1.16037i
$750$	−1.00000			−0.0365148
$751$	17.0205			0.621085			0.310543	−	0.950559i	$-0.399489\pi$
$751$	17.0205			0.621085			0.310543	+	0.950559i	$0.399489\pi$
$752$	−0.417084	+	0.722410i	−0.0152095	+	0.0263436i
$753$	11.5007	−	6.63994i	0.419110	−	0.241973i
$754$		−	33.6179i		−	1.22429i
$755$	−2.11046	−	1.21847i	−0.0768074	−	0.0443448i
$756$	−1.08063	+	1.87170i	−0.0393020	+	0.0680730i
$757$	43.0684	+	24.8655i	1.56535	+	0.903753i	0.996700	+	0.0811706i	$0.0258659\pi$
$757$	43.0684	+	24.8655i	1.56535	+	0.903753i	0.568646	+	0.822582i	$0.307467\pi$
$758$	21.0196	−	12.1357i	0.763465	−	0.440787i
$759$	−14.0197	+	8.09427i	−0.508883	+	0.293804i
$760$	0.178213	+	0.102891i	0.00646445	+	0.00373225i
$761$	−2.37295	+	4.11007i	−0.0860193	+	0.148990i	−0.905825	−	0.423652i	$-0.860748\pi$
$761$	−2.37295	+	4.11007i	−0.0860193	+	0.148990i	0.819806	+	0.572642i	$0.194081\pi$
$762$	1.23598	+	0.713592i	0.0447747	+	0.0258507i
$763$		−	3.30277i		−	0.119568i
$764$	−9.39872	+	5.42635i	−0.340034	+	0.196319i
$765$	−1.58063	+	2.73772i	−0.0571477	+	0.0989826i
$766$	−12.9307			−0.467204
$767$	−23.7743			−0.858441
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$			35.1897i			1.26897i	0.772934	+	0.634486i	$0.218788\pi$
$769$			35.1897i			1.26897i	−0.772934	+	0.634486i	$0.781212\pi$
$770$	5.01755	+	8.69065i	0.180820	+	0.313189i
$771$			2.91972i			0.105151i
$772$	19.8964	−	11.4872i	0.716087	−	0.413433i
$773$	−1.01203	−	1.75289i	−0.0364003	−	0.0630471i	0.847251	−	0.531192i	$-0.178256\pi$
$773$	−1.01203	−	1.75289i	−0.0364003	−	0.0630471i	−0.883652	+	0.468145i	$0.844922\pi$
$774$	1.35268	+	2.34291i	0.0486210	+	0.0842140i
$775$	5.36232	+	3.09594i	0.192620	+	0.111209i
$776$	0.153047			0.00549408
$777$	−7.00249	−	11.1262i

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(1.08063 + 1.87170i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(1.08063 + 1.87170i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +1.00000 q^{10} +4.64319 q^{11} +(0.500000 - 0.866025i) q^{12} +(-4.51941 + 2.60928i) q^{13} +2.16125i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.73772 + 1.58063i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.178213 - 0.102891i) q^{19} +(0.866025 + 0.500000i) q^{20} +(1.08063 - 1.87170i) q^{21} +(4.02112 + 2.32159i) q^{22} -3.48652i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.21857 q^{26} +1.00000 q^{27} +(-1.08063 + 1.87170i) q^{28} +6.44199i q^{29} +(-0.500000 - 0.866025i) q^{30} +6.19187i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.32159 - 4.02112i) q^{33} +(1.58063 + 2.73772i) q^{34} +(1.87170 + 1.08063i) q^{35} -1.00000 q^{36} +(2.83833 - 5.37995i) q^{37} +0.205782 q^{38} +(4.51941 + 2.60928i) q^{39} +(0.500000 + 0.866025i) q^{40} +(1.61696 + 2.80066i) q^{41} +(1.87170 - 1.08063i) q^{42} -2.70535i q^{43} +(2.32159 + 4.02112i) q^{44} +1.00000i q^{45} +(1.74326 - 3.01941i) q^{46} +0.834167 q^{47} +1.00000 q^{48} +(1.16450 - 2.01696i) q^{49} +(0.866025 - 0.500000i) q^{50} -3.16125i q^{51} +(-4.51941 - 2.60928i) q^{52} +(0.578919 - 1.00272i) q^{53} +(0.866025 + 0.500000i) q^{54} +(4.02112 - 2.32159i) q^{55} +(-1.87170 + 1.08063i) q^{56} +(-0.178213 - 0.102891i) q^{57} +(-3.22099 + 5.57892i) q^{58} +(3.94537 + 2.27786i) q^{59} -1.00000i q^{60} +(9.21562 - 5.32064i) q^{61} +(-3.09594 + 5.36232i) q^{62} -2.16125 q^{63} -1.00000 q^{64} +(-2.60928 + 4.51941i) q^{65} -4.64319i q^{66} +(0.180274 + 0.312243i) q^{67} +3.16125i q^{68} +(-3.01941 + 1.74326i) q^{69} +(1.08063 + 1.87170i) q^{70} +(2.26228 + 3.91838i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.91562 q^{73} +(5.14804 - 3.24001i) q^{74} -1.00000 q^{75} +(0.178213 + 0.102891i) q^{76} +(5.01755 + 8.69065i) q^{77} +(2.60928 + 4.51941i) q^{78} +(2.06361 - 1.19143i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +3.23393i q^{82} +(-6.98079 + 12.0911i) q^{83} +2.16125 q^{84} +3.16125 q^{85} +(1.35268 - 2.34291i) q^{86} +(5.57892 - 3.22099i) q^{87} +4.64319i q^{88} +(-13.4453 - 7.76267i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(-9.76759 - 5.63932i) q^{91} +(3.01941 - 1.74326i) q^{92} +(5.36232 - 3.09594i) q^{93} +(0.722410 + 0.417084i) q^{94} +(0.102891 - 0.178213i) q^{95} +(0.866025 + 0.500000i) q^{96} -0.153047i q^{97} +(2.01696 - 1.16450i) q^{98} +(-2.32159 + 4.02112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \)	\( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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