LMFDB - Embedded newform 1078.2.e.q.177.1

Newspace parameters

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.q.67.1

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.618034 - 1.07047i) q^{5} +1.23607 q^{6} +1.00000 q^{8} +(0.736068 - 1.27491i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.618034 - 1.07047i) q^{5} +1.23607 q^{6} +1.00000 q^{8} +(0.736068 - 1.27491i) q^{9} +(0.618034 + 1.07047i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.618034 + 1.07047i) q^{12} -3.23607 q^{13} -1.52786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.23607 - 2.14093i) q^{17} +(0.736068 + 1.27491i) q^{18} +(3.61803 - 6.26662i) q^{19} -1.23607 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.618034 - 1.07047i) q^{24} +(1.73607 + 3.00696i) q^{25} +(1.61803 - 2.80252i) q^{26} -5.52786 q^{27} +4.47214 q^{29} +(0.763932 - 1.32317i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.618034 + 1.07047i) q^{33} +2.47214 q^{34} -1.47214 q^{36} +(-3.47214 + 6.01392i) q^{37} +(3.61803 + 6.26662i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.618034 - 1.07047i) q^{40} -2.47214 q^{41} -10.4721 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.909830 - 1.57587i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.23607 q^{48} -3.47214 q^{50} +(-1.52786 + 2.64634i) q^{51} +(1.61803 + 2.80252i) q^{52} +(-4.23607 - 7.33708i) q^{53} +(2.76393 - 4.78727i) q^{54} -1.23607 q^{55} -8.94427 q^{57} +(-2.23607 + 3.87298i) q^{58} +(-1.38197 - 2.39364i) q^{59} +(0.763932 + 1.32317i) q^{60} +(0.381966 - 0.661585i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-0.618034 - 1.07047i) q^{66} +(-5.70820 - 9.88690i) q^{67} +(-1.23607 + 2.14093i) q^{68} +4.94427 q^{69} +6.47214 q^{71} +(0.736068 - 1.27491i) q^{72} +(-6.47214 - 11.2101i) q^{73} +(-3.47214 - 6.01392i) q^{74} +(2.14590 - 3.71680i) q^{75} -7.23607 q^{76} -4.00000 q^{78} +(0.618034 + 1.07047i) q^{80} +(1.20820 + 2.09267i) q^{81} +(1.23607 - 2.14093i) q^{82} -12.1803 q^{83} -3.05573 q^{85} +(5.23607 - 9.06914i) q^{86} +(-2.76393 - 4.78727i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +1.81966 q^{90} +4.00000 q^{92} +(-1.23607 + 2.14093i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-4.47214 - 7.74597i) q^{95} +(-0.618034 + 1.07047i) q^{96} +12.4721 q^{97} -1.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 24 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} + 10 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 40 q^{27} + 12 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 10 q^{38} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 24 q^{43} - 2 q^{44} - 26 q^{45} - 8 q^{46} + 4 q^{47} - 4 q^{48} + 4 q^{50} - 24 q^{51} + 2 q^{52} - 8 q^{53} + 20 q^{54} + 4 q^{55} - 10 q^{59} + 12 q^{60} + 6 q^{61} + 8 q^{62} + 4 q^{64} - 8 q^{65} + 2 q^{66} + 4 q^{67} + 4 q^{68} - 16 q^{69} + 8 q^{71} - 6 q^{72} - 8 q^{73} + 4 q^{74} + 22 q^{75} - 20 q^{76} - 16 q^{78} - 2 q^{80} - 22 q^{81} - 4 q^{82} - 4 q^{83} - 48 q^{85} + 12 q^{86} - 20 q^{87} - 2 q^{88} - 20 q^{89} + 52 q^{90} + 16 q^{92} + 4 q^{93} + 4 q^{94} + 2 q^{96} + 32 q^{97} + 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 24 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 + 10 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 40 * q^27 + 12 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 + 12 * q^36 + 4 * q^37 + 10 * q^38 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 24 * q^43 - 2 * q^44 - 26 * q^45 - 8 * q^46 + 4 * q^47 - 4 * q^48 + 4 * q^50 - 24 * q^51 + 2 * q^52 - 8 * q^53 + 20 * q^54 + 4 * q^55 - 10 * q^59 + 12 * q^60 + 6 * q^61 + 8 * q^62 + 4 * q^64 - 8 * q^65 + 2 * q^66 + 4 * q^67 + 4 * q^68 - 16 * q^69 + 8 * q^71 - 6 * q^72 - 8 * q^73 + 4 * q^74 + 22 * q^75 - 20 * q^76 - 16 * q^78 - 2 * q^80 - 22 * q^81 - 4 * q^82 - 4 * q^83 - 48 * q^85 + 12 * q^86 - 20 * q^87 - 2 * q^88 - 20 * q^89 + 52 * q^90 + 16 * q^92 + 4 * q^93 + 4 * q^94 + 2 * q^96 + 32 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.618034	−	1.07047i	−0.356822	−	0.618034i	0.630606	−	0.776103i	$-0.282806\pi$
$3$	−0.618034	−	1.07047i	−0.356822	−	0.618034i	−0.987428	+	0.158069i	$0.949473\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	−0.694092	−	0.719886i	$-0.744194\pi$
$5$	0.618034	−	1.07047i	0.276393	−	0.478727i	0.970486	+	0.241159i	$0.0775275\pi$
$6$	1.23607			0.504623
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	0.736068	−	1.27491i	0.245356	−	0.424969i
$10$	0.618034	+	1.07047i	0.195440	+	0.338511i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−0.618034	+	1.07047i	−0.178411	+	0.309017i
$13$	−3.23607			−0.897524			−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607			−0.897524			−0.448762	+	0.893651i	$0.648135\pi$
$14$		0			0
$15$	−1.52786			−0.394493
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.23607	−	2.14093i	−0.299791	−	0.519252i	0.676297	−	0.736629i	$-0.263583\pi$
$17$	−1.23607	−	2.14093i	−0.299791	−	0.519252i	−0.976088	+	0.217376i	$0.930250\pi$
$18$	0.736068	+	1.27491i	0.173493	+	0.300498i
$19$	3.61803	−	6.26662i	0.830034	−	1.43766i	−0.0679766	−	0.997687i	$-0.521654\pi$
$19$	3.61803	−	6.26662i	0.830034	−	1.43766i	0.898011	−	0.439974i	$-0.145012\pi$
$20$	−1.23607			−0.276393
$21$		0			0
$22$	1.00000			0.213201
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	−0.618034	−	1.07047i	−0.126156	−	0.218508i
$25$	1.73607	+	3.00696i	0.347214	+	0.601392i
$26$	1.61803	−	2.80252i	0.317323	−	0.549619i
$27$	−5.52786			−1.06384
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	0.763932	−	1.32317i	0.139474	−	0.241577i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.618034	+	1.07047i	−0.107586	+	0.186344i
$34$	2.47214			0.423968
$35$		0			0
$36$	−1.47214			−0.245356
$37$	−3.47214	+	6.01392i	−0.570816	+	0.988682i	0.425667	+	0.904880i	$0.360040\pi$
$37$	−3.47214	+	6.01392i	−0.570816	+	0.988682i	−0.996482	+	0.0838017i	$0.973294\pi$
$38$	3.61803	+	6.26662i	0.586923	+	1.01658i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	0.618034	−	1.07047i	0.0977198	−	0.169256i
$41$	−2.47214			−0.386083			−0.193041	−	0.981191i	$-0.561835\pi$
$41$	−2.47214			−0.386083			−0.193041	+	0.981191i	$0.561835\pi$
$42$		0			0
$43$	−10.4721			−1.59699			−0.798493	−	0.602004i	$-0.794369\pi$
$43$	−10.4721			−1.59699			−0.798493	+	0.602004i	$0.794369\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−0.909830	−	1.57587i	−0.135629	−	0.234917i
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	1.23607			0.178411
$49$		0			0
$50$	−3.47214			−0.491034
$51$	−1.52786	+	2.64634i	−0.213944	+	0.370561i
$52$	1.61803	+	2.80252i	0.224381	+	0.388639i
$53$	−4.23607	−	7.33708i	−0.581869	−	1.00783i	−0.995258	−	0.0972717i	$-0.968988\pi$
$53$	−4.23607	−	7.33708i	−0.581869	−	1.00783i	0.413389	−	0.910554i	$-0.364345\pi$
$54$	2.76393	−	4.78727i	0.376124	−	0.651465i
$55$	−1.23607			−0.166671
$56$		0			0
$57$	−8.94427			−1.18470
$58$	−2.23607	+	3.87298i	−0.293610	+	0.508548i
$59$	−1.38197	−	2.39364i	−0.179917	−	0.311625i	0.761935	−	0.647653i	$-0.224249\pi$
$59$	−1.38197	−	2.39364i	−0.179917	−	0.311625i	−0.941852	+	0.336029i	$0.890916\pi$
$60$	0.763932	+	1.32317i	0.0986232	+	0.170820i
$61$	0.381966	−	0.661585i	0.0489057	−	0.0847072i	−0.840536	−	0.541755i	$-0.817760\pi$
$61$	0.381966	−	0.661585i	0.0489057	−	0.0847072i	0.889442	+	0.457048i	$0.151093\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	−0.618034	−	1.07047i	−0.0760747	−	0.131765i
$67$	−5.70820	−	9.88690i	−0.697368	−	1.20788i	−0.969376	−	0.245582i	$-0.921021\pi$
$67$	−5.70820	−	9.88690i	−0.697368	−	1.20788i	0.272008	−	0.962295i	$-0.412312\pi$
$68$	−1.23607	+	2.14093i	−0.149895	+	0.259626i
$69$	4.94427			0.595220
$70$		0			0
$71$	6.47214			0.768101			0.384051	−	0.923312i	$-0.374529\pi$
$71$	6.47214			0.768101			0.384051	+	0.923312i	$0.374529\pi$
$72$	0.736068	−	1.27491i	0.0867464	−	0.150249i
$73$	−6.47214	−	11.2101i	−0.757506	−	1.31204i	−0.944119	−	0.329606i	$-0.893084\pi$
$73$	−6.47214	−	11.2101i	−0.757506	−	1.31204i	0.186612	−	0.982434i	$-0.440249\pi$
$74$	−3.47214	−	6.01392i	−0.403628	−	0.699104i
$75$	2.14590	−	3.71680i	0.247787	−	0.429180i
$76$	−7.23607			−0.830034
$77$		0			0
$78$	−4.00000			−0.452911
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	0.618034	+	1.07047i	0.0690983	+	0.119682i
$81$	1.20820	+	2.09267i	0.134245	+	0.232519i
$82$	1.23607	−	2.14093i	0.136501	−	0.236426i
$83$	−12.1803			−1.33697			−0.668483	−	0.743727i	$-0.733056\pi$
$83$	−12.1803			−1.33697			−0.668483	+	0.743727i	$0.733056\pi$
$84$		0			0
$85$	−3.05573			−0.331440
$86$	5.23607	−	9.06914i	0.564620	−	0.977950i
$87$	−2.76393	−	4.78727i	−0.296325	−	0.513249i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	1.81966			0.191809
$91$		0			0
$92$	4.00000			0.417029
$93$	−1.23607	+	2.14093i	−0.128174	+	0.222004i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	−4.47214	−	7.74597i	−0.458831	−	0.794719i
$96$	−0.618034	+	1.07047i	−0.0630778	+	0.109254i
$97$	12.4721			1.26635			0.633177	−	0.774007i	$-0.281751\pi$
$97$	12.4721			1.26635			0.633177	+	0.774007i	$0.281751\pi$
$98$		0			0
$99$	−1.47214			−0.147955
$100$	1.73607	−	3.00696i	0.173607	−	0.300696i
$101$	−4.09017	−	7.08438i	−0.406987	−	0.704922i	0.587563	−	0.809178i	$-0.300087\pi$
$101$	−4.09017	−	7.08438i	−0.406987	−	0.704922i	−0.994551	+	0.104256i	$0.966754\pi$
$102$	−1.52786	−	2.64634i	−0.151281	−	0.262027i
$103$	7.47214	−	12.9421i	0.736251	−	1.27522i	−0.217921	−	0.975966i	$-0.569927\pi$
$103$	7.47214	−	12.9421i	0.736251	−	1.27522i	0.954172	−	0.299258i	$-0.0967393\pi$
$104$	−3.23607			−0.317323
$105$		0			0
$106$	8.47214			0.822887
$107$	−1.23607	+	2.14093i	−0.119495	+	0.206972i	−0.919568	−	0.392932i	$-0.871461\pi$
$107$	−1.23607	+	2.14093i	−0.119495	+	0.206972i	0.800073	+	0.599903i	$0.204794\pi$
$108$	2.76393	+	4.78727i	0.265959	+	0.460655i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	0.618034	−	1.07047i	0.0589272	−	0.102065i
$111$	8.58359			0.814719
$112$		0			0
$113$	−0.472136			−0.0444148			−0.0222074	−	0.999753i	$-0.507069\pi$
$113$	−0.472136			−0.0444148			−0.0222074	+	0.999753i	$0.507069\pi$
$114$	4.47214	−	7.74597i	0.418854	−	0.725476i
$115$	2.47214	+	4.28187i	0.230528	+	0.399286i
$116$	−2.23607	−	3.87298i	−0.207614	−	0.359597i
$117$	−2.38197	+	4.12569i	−0.220213	+	0.381420i
$118$	2.76393			0.254441
$119$		0			0
$120$	−1.52786			−0.139474
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	0.381966	+	0.661585i	0.0345816	+	0.0598970i
$123$	1.52786	+	2.64634i	0.137763	+	0.238612i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	10.4721			0.936656
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.47214	+	11.2101i	0.569840	+	0.986991i
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	−2.38197	+	4.12569i	−0.208113	+	0.360463i	−0.951120	−	0.308821i	$-0.900066\pi$
$131$	−2.38197	+	4.12569i	−0.208113	+	0.360463i	0.743007	+	0.669284i	$0.233399\pi$
$132$	1.23607			0.107586
$133$		0			0
$134$	11.4164			0.986227
$135$	−3.41641	+	5.91739i	−0.294038	+	0.509288i
$136$	−1.23607	−	2.14093i	−0.105992	−	0.183583i
$137$	9.94427	+	17.2240i	0.849596	+	1.47154i	0.881569	+	0.472056i	$0.156488\pi$
$137$	9.94427	+	17.2240i	0.849596	+	1.47154i	−0.0319723	+	0.999489i	$0.510179\pi$
$138$	−2.47214	+	4.28187i	−0.210442	+	0.364497i
$139$	−21.7082			−1.84127			−0.920633	−	0.390429i	$-0.872327\pi$
$139$	−21.7082			−1.84127			−0.920633	+	0.390429i	$0.872327\pi$
$140$		0			0
$141$	−2.47214			−0.208191
$142$	−3.23607	+	5.60503i	−0.271565	+	0.470364i
$143$	1.61803	+	2.80252i	0.135307	+	0.234358i
$144$	0.736068	+	1.27491i	0.0613390	+	0.106242i
$145$	2.76393	−	4.78727i	0.229532	−	0.397561i
$146$	12.9443			1.07128
$147$		0			0
$148$	6.94427			0.570816
$149$	11.1803	−	19.3649i	0.915929	−	1.58644i	0.110394	−	0.993888i	$-0.464789\pi$
$149$	11.1803	−	19.3649i	0.915929	−	1.58644i	0.805535	−	0.592548i	$-0.201878\pi$
$150$	2.14590	+	3.71680i	0.175212	+	0.303476i
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	3.61803	−	6.26662i	0.293461	−	0.508290i
$153$	−3.63932			−0.294222
$154$		0			0
$155$	−2.47214			−0.198567
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	6.32624	+	10.9574i	0.504889	+	0.874493i	0.999984	+	0.00565427i	$0.00179982\pi$
$157$	6.32624	+	10.9574i	0.504889	+	0.874493i	−0.495095	+	0.868839i	$0.664867\pi$
$158$		0			0
$159$	−5.23607	+	9.06914i	−0.415247	+	0.719229i
$160$	−1.23607			−0.0977198
$161$		0			0
$162$	−2.41641			−0.189851
$163$	9.70820	−	16.8151i	0.760405	−	1.31706i	−0.182237	−	0.983255i	$-0.558334\pi$
$163$	9.70820	−	16.8151i	0.760405	−	1.31706i	0.942642	−	0.333806i	$-0.108333\pi$
$164$	1.23607	+	2.14093i	0.0965207	+	0.167179i
$165$	0.763932	+	1.32317i	0.0594720	+	0.103009i
$166$	6.09017	−	10.5485i	0.472689	−	0.818721i
$167$	11.4164			0.883428			0.441714	−	0.897156i	$-0.354371\pi$
$167$	11.4164			0.883428			0.441714	+	0.897156i	$0.354371\pi$
$168$		0			0
$169$	−2.52786			−0.194451
$170$	1.52786	−	2.64634i	0.117182	−	0.202965i
$171$	−5.32624	−	9.22531i	−0.407308	−	0.705477i
$172$	5.23607	+	9.06914i	0.399246	+	0.691515i
$173$	1.61803	−	2.80252i	0.123017	−	0.213071i	−0.797939	−	0.602738i	$-0.794076\pi$
$173$	1.61803	−	2.80252i	0.123017	−	0.213071i	0.920956	+	0.389667i	$0.127410\pi$
$174$	5.52786			0.419066
$175$		0			0
$176$	1.00000			0.0753778
$177$	−1.70820	+	2.95870i	−0.128396	+	0.222389i
$178$	−5.00000	−	8.66025i	−0.374766	−	0.649113i
$179$	4.47214	+	7.74597i	0.334263	+	0.578961i	0.983343	−	0.181760i	$-0.0581792\pi$
$179$	4.47214	+	7.74597i	0.334263	+	0.578961i	−0.649080	+	0.760720i	$0.724846\pi$
$180$	−0.909830	+	1.57587i	−0.0678147	+	0.117459i
$181$	9.23607			0.686512			0.343256	−	0.939242i	$-0.388470\pi$
$181$	9.23607			0.686512			0.343256	+	0.939242i	$0.388470\pi$
$182$		0			0
$183$	−0.944272			−0.0698026
$184$	−2.00000	+	3.46410i	−0.147442	+	0.255377i
$185$	4.29180	+	7.43361i	0.315539	+	0.546530i
$186$	−1.23607	−	2.14093i	−0.0906329	−	0.156981i
$187$	−1.23607	+	2.14093i	−0.0903902	+	0.156560i
$188$	−2.00000			−0.145865
$189$		0			0
$190$	8.94427			0.648886
$191$	1.23607	−	2.14093i	0.0894387	−	0.154912i	−0.817835	−	0.575452i	$-0.804826\pi$
$191$	1.23607	−	2.14093i	0.0894387	−	0.154912i	0.907274	+	0.420540i	$0.138159\pi$
$192$	−0.618034	−	1.07047i	−0.0446028	−	0.0772542i
$193$	7.47214	+	12.9421i	0.537856	+	0.931594i	0.999019	+	0.0442787i	$0.0140990\pi$
$193$	7.47214	+	12.9421i	0.537856	+	0.931594i	−0.461163	+	0.887315i	$0.652568\pi$
$194$	−6.23607	+	10.8012i	−0.447724	+	0.775480i
$195$	4.94427			0.354067
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	0.736068	−	1.27491i	0.0523101	−	0.0906037i
$199$	−9.47214	−	16.4062i	−0.671462	−	1.16301i	−0.977490	−	0.210984i	$-0.932333\pi$
$199$	−9.47214	−	16.4062i	−0.671462	−	1.16301i	0.306028	−	0.952023i	$-0.401000\pi$
$200$	1.73607	+	3.00696i	0.122759	+	0.212624i
$201$	−7.05573	+	12.2209i	−0.497673	+	0.861994i
$202$	8.18034			0.575567
$203$		0			0
$204$	3.05573			0.213944
$205$	−1.52786	+	2.64634i	−0.106711	+	0.184828i
$206$	7.47214	+	12.9421i	0.520608	+	0.901720i
$207$	2.94427	+	5.09963i	0.204641	+	0.354449i
$208$	1.61803	−	2.80252i	0.112190	−	0.194320i
$209$	−7.23607			−0.500529
$210$		0			0
$211$	−13.5279			−0.931297			−0.465648	−	0.884970i	$-0.654179\pi$
$211$	−13.5279			−0.931297			−0.465648	+	0.884970i	$0.654179\pi$
$212$	−4.23607	+	7.33708i	−0.290934	+	0.503913i
$213$	−4.00000	−	6.92820i	−0.274075	−	0.474713i
$214$	−1.23607	−	2.14093i	−0.0844959	−	0.146351i
$215$	−6.47214	+	11.2101i	−0.441396	+	0.764520i
$216$	−5.52786			−0.376124
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−8.00000	+	13.8564i	−0.540590	+	0.936329i
$220$	0.618034	+	1.07047i	0.0416678	+	0.0721708i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	−4.29180	+	7.43361i	−0.288046	+	0.498911i
$223$	−0.472136			−0.0316166			−0.0158083	−	0.999875i	$-0.505032\pi$
$223$	−0.472136			−0.0316166			−0.0158083	+	0.999875i	$0.505032\pi$
$224$		0			0
$225$	5.11146			0.340764
$226$	0.236068	−	0.408882i	0.0157030	−	0.0271984i
$227$	9.61803	+	16.6589i	0.638371	+	1.10569i	0.985790	+	0.167982i	$0.0537249\pi$
$227$	9.61803	+	16.6589i	0.638371	+	1.10569i	−0.347419	+	0.937710i	$0.612942\pi$
$228$	4.47214	+	7.74597i	0.296174	+	0.512989i
$229$	−8.61803	+	14.9269i	−0.569496	+	0.986396i	0.427120	+	0.904195i	$0.359528\pi$
$229$	−8.61803	+	14.9269i	−0.569496	+	0.986396i	−0.996616	+	0.0822006i	$0.973805\pi$
$230$	−4.94427			−0.326016
$231$		0			0
$232$	4.47214			0.293610
$233$	7.47214	−	12.9421i	0.489516	−	0.847866i	−0.510411	−	0.859930i	$-0.670507\pi$
$233$	7.47214	−	12.9421i	0.489516	−	0.847866i	0.999927	+	0.0120640i	$0.00384018\pi$
$234$	−2.38197	−	4.12569i	−0.155714	−	0.269705i
$235$	−1.23607	−	2.14093i	−0.0806322	−	0.139659i
$236$	−1.38197	+	2.39364i	−0.0899583	+	0.155812i
$237$		0			0
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$	0.763932	−	1.32317i	0.0493116	−	0.0854102i
$241$	−7.70820	−	13.3510i	−0.496529	−	0.860014i	0.503463	−	0.864017i	$-0.332059\pi$
$241$	−7.70820	−	13.3510i	−0.496529	−	0.860014i	−0.999992	+	0.00400327i	$0.998726\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	−6.79837	+	11.7751i	−0.436116	+	0.755375i
$244$	−0.763932			−0.0489057
$245$		0			0
$246$	−3.05573			−0.194826
$247$	−11.7082	+	20.2792i	−0.744975	+	1.29033i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	7.52786	+	13.0386i	0.477059	+	0.826290i
$250$	−5.23607	+	9.06914i	−0.331158	+	0.573583i
$251$	29.2361			1.84536			0.922682	−	0.385562i	$-0.125992\pi$
$251$	29.2361			1.84536			0.922682	+	0.385562i	$0.125992\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	1.88854	+	3.27105i	0.118265	+	0.204841i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.47214	+	6.01392i	−0.216586	+	0.375138i	−0.953762	−	0.300563i	$-0.902825\pi$
$257$	−3.47214	+	6.01392i	−0.216586	+	0.375138i	0.737176	+	0.675701i	$0.236159\pi$
$258$	−12.9443			−0.805875
$259$		0			0
$260$	4.00000			0.248069
$261$	3.29180	−	5.70156i	0.203757	−	0.352918i
$262$	−2.38197	−	4.12569i	−0.147158	−	0.254886i
$263$	2.47214	+	4.28187i	0.152438	+	0.264031i	0.932123	−	0.362141i	$-0.117954\pi$
$263$	2.47214	+	4.28187i	0.152438	+	0.264031i	−0.779685	+	0.626172i	$0.784621\pi$
$264$	−0.618034	+	1.07047i	−0.0380374	+	0.0658826i
$265$	−10.4721			−0.643298
$266$		0			0
$267$	12.3607			0.756461
$268$	−5.70820	+	9.88690i	−0.348684	+	0.603938i
$269$	11.3820	+	19.7141i	0.693971	+	1.20199i	0.970526	+	0.240995i	$0.0774736\pi$
$269$	11.3820	+	19.7141i	0.693971	+	1.20199i	−0.276556	+	0.960998i	$0.589193\pi$
$270$	−3.41641	−	5.91739i	−0.207916	−	0.360121i
$271$	−0.472136	+	0.817763i	−0.0286802	+	0.0496756i	−0.880009	−	0.474957i	$-0.842464\pi$
$271$	−0.472136	+	0.817763i	−0.0286802	+	0.0496756i	0.851329	+	0.524632i	$0.175797\pi$
$272$	2.47214			0.149895
$273$		0			0
$274$	−19.8885			−1.20151
$275$	1.73607	−	3.00696i	0.104689	−	0.181326i
$276$	−2.47214	−	4.28187i	−0.148805	−	0.257738i
$277$	−1.76393	−	3.05522i	−0.105984	−	0.183570i	0.808156	−	0.588969i	$-0.200466\pi$
$277$	−1.76393	−	3.05522i	−0.105984	−	0.183570i	−0.914140	+	0.405399i	$0.867133\pi$
$278$	10.8541	−	18.7999i	0.650986	−	1.12754i
$279$	−2.94427			−0.176269
$280$		0			0
$281$	28.8328			1.72002			0.860011	−	0.510276i	$-0.170457\pi$
$281$	28.8328			1.72002			0.860011	+	0.510276i	$0.170457\pi$
$282$	1.23607	−	2.14093i	0.0736068	−	0.127491i
$283$	−7.32624	−	12.6894i	−0.435500	−	0.754308i	0.561837	−	0.827248i	$-0.310095\pi$
$283$	−7.32624	−	12.6894i	−0.435500	−	0.754308i	−0.997336	+	0.0729407i	$0.976762\pi$
$284$	−3.23607	−	5.60503i	−0.192025	−	0.332598i
$285$	−5.52786	+	9.57454i	−0.327442	+	0.567147i
$286$	−3.23607			−0.191353
$287$		0			0
$288$	−1.47214			−0.0867464
$289$	5.44427	−	9.42976i	0.320251	−	0.554692i
$290$	2.76393	+	4.78727i	0.162304	+	0.281118i
$291$	−7.70820	−	13.3510i	−0.451863	−	0.782650i
$292$	−6.47214	+	11.2101i	−0.378753	+	0.656020i
$293$	−26.6525			−1.55705			−0.778527	−	0.627611i	$-0.784033\pi$
$293$	−26.6525			−1.55705			−0.778527	+	0.627611i	$0.784033\pi$
$294$		0			0
$295$	−3.41641			−0.198911
$296$	−3.47214	+	6.01392i	−0.201814	+	0.349552i
$297$	2.76393	+	4.78727i	0.160380	+	0.277786i
$298$	11.1803	+	19.3649i	0.647660	+	1.12178i
$299$	6.47214	−	11.2101i	0.374293	−	0.648295i
$300$	−4.29180			−0.247787
$301$		0			0
$302$	12.0000			0.690522
$303$	−5.05573	+	8.75678i	−0.290444	+	0.503064i
$304$	3.61803	+	6.26662i	0.207508	+	0.359415i
$305$	−0.472136	−	0.817763i	−0.0270344	−	0.0468250i
$306$	1.81966	−	3.15174i	0.104023	−	0.180173i
$307$	−26.0689			−1.48783			−0.743915	−	0.668274i	$-0.767033\pi$
$307$	−26.0689			−1.48783			−0.743915	+	0.668274i	$0.767033\pi$
$308$		0			0
$309$	−18.4721			−1.05084
$310$	1.23607	−	2.14093i	0.0702039	−	0.121597i
$311$	10.7082	+	18.5472i	0.607207	+	1.05171i	0.991699	+	0.128584i	$0.0410433\pi$
$311$	10.7082	+	18.5472i	0.607207	+	1.05171i	−0.384492	+	0.923128i	$0.625623\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	−9.76393	+	16.9116i	−0.551890	+	0.955902i	0.446248	+	0.894909i	$0.352760\pi$
$313$	−9.76393	+	16.9116i	−0.551890	+	0.955902i	−0.998138	+	0.0609924i	$0.980573\pi$
$314$	−12.6525			−0.714021
$315$		0			0
$316$		0			0
$317$	15.4721	−	26.7985i	0.869002	−	1.50516i	0.00598366	−	0.999982i	$-0.498095\pi$
$317$	15.4721	−	26.7985i	0.869002	−	1.50516i	0.863018	−	0.505173i	$-0.168571\pi$
$318$	−5.23607	−	9.06914i	−0.293624	−	0.508572i
$319$	−2.23607	−	3.87298i	−0.125196	−	0.216845i
$320$	0.618034	−	1.07047i	0.0345492	−	0.0598409i
$321$	3.05573			0.170554
$322$		0			0
$323$	−17.8885			−0.995345
$324$	1.20820	−	2.09267i	0.0671224	−	0.116259i
$325$	−5.61803	−	9.73072i	−0.311632	−	0.539763i
$326$	9.70820	+	16.8151i	0.537688	+	0.931302i
$327$	6.18034	−	10.7047i	0.341774	−	0.591969i
$328$	−2.47214			−0.136501
$329$		0			0
$330$	−1.52786			−0.0841061
$331$	8.47214	−	14.6742i	0.465671	−	0.806565i	−0.533561	−	0.845762i	$-0.679146\pi$
$331$	8.47214	−	14.6742i	0.465671	−	0.806565i	0.999232	+	0.0391964i	$0.0124798\pi$
$332$	6.09017	+	10.5485i	0.334241	+	0.578923i
$333$	5.11146	+	8.85330i	0.280106	+	0.485158i
$334$	−5.70820	+	9.88690i	−0.312339	+	0.540987i
$335$	−14.1115			−0.770991
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	1.26393	−	2.18919i	0.0687488	−	0.119076i
$339$	0.291796	+	0.505406i	0.0158482	+	0.0274499i
$340$	1.52786	+	2.64634i	0.0828601	+	0.143518i
$341$	−1.00000	+	1.73205i	−0.0541530	+	0.0937958i
$342$	10.6525			0.576020
$343$		0			0
$344$	−10.4721			−0.564620
$345$	3.05573	−	5.29268i	0.164515	−	0.284948i
$346$	1.61803	+	2.80252i	0.0869860	+	0.150664i
$347$	−1.23607	−	2.14093i	−0.0663556	−	0.114931i	0.830939	−	0.556364i	$-0.187804\pi$
$347$	−1.23607	−	2.14093i	−0.0663556	−	0.114931i	−0.897295	+	0.441432i	$0.854471\pi$
$348$	−2.76393	+	4.78727i	−0.148162	+	0.256625i
$349$	21.7082			1.16201			0.581007	−	0.813899i	$-0.302659\pi$
$349$	21.7082			1.16201			0.581007	+	0.813899i	$0.302659\pi$
$350$		0			0
$351$	17.8885			0.954820
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	8.52786	+	14.7707i	0.453892	+	0.786165i	0.998624	−	0.0524459i	$-0.0167017\pi$
$353$	8.52786	+	14.7707i	0.453892	+	0.786165i	−0.544731	+	0.838611i	$0.683368\pi$
$354$	−1.70820	−	2.95870i	−0.0907900	−	0.157253i
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	10.0000			0.529999
$357$		0			0
$358$	−8.94427			−0.472719
$359$	−13.4164	+	23.2379i	−0.708091	+	1.22645i	0.257473	+	0.966285i	$0.417110\pi$
$359$	−13.4164	+	23.2379i	−0.708091	+	1.22645i	−0.965564	+	0.260164i	$0.916223\pi$
$360$	−0.909830	−	1.57587i	−0.0479523	−	0.0830557i
$361$	−16.6803	−	28.8912i	−0.877913	−	1.52059i
$362$	−4.61803	+	7.99867i	−0.242718	+	0.420401i
$363$	1.23607			0.0648767
$364$		0			0
$365$	−16.0000			−0.837478
$366$	0.472136	−	0.817763i	0.0246789	−	0.0427452i
$367$	2.70820	+	4.69075i	0.141367	+	0.244855i	0.928012	−	0.372551i	$-0.121517\pi$
$367$	2.70820	+	4.69075i	0.141367	+	0.244855i	−0.786645	+	0.617406i	$0.788184\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$	−1.81966	+	3.15174i	−0.0947277	+	0.164073i
$370$	−8.58359			−0.446240
$371$		0			0
$372$	2.47214			0.128174
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$	−1.23607	−	2.14093i	−0.0639156	−	0.110705i
$375$	−6.47214	−	11.2101i	−0.334220	−	0.578885i
$376$	1.00000	−	1.73205i	0.0515711	−	0.0893237i
$377$	−14.4721			−0.745353
$378$		0			0
$379$	14.4721			0.743384			0.371692	−	0.928356i	$-0.378778\pi$
$379$	14.4721			0.743384			0.371692	+	0.928356i	$0.378778\pi$
$380$	−4.47214	+	7.74597i	−0.229416	+	0.397360i
$381$	7.41641	+	12.8456i	0.379954	+	0.658100i
$382$	1.23607	+	2.14093i	0.0632427	+	0.109540i
$383$	11.9443	−	20.6881i	0.610324	−	1.05711i	−0.380862	−	0.924632i	$-0.624373\pi$
$383$	11.9443	−	20.6881i	0.610324	−	1.05711i	0.991186	−	0.132480i	$-0.0422940\pi$
$384$	1.23607			0.0630778
$385$		0			0
$386$	−14.9443			−0.760643
$387$	−7.70820	+	13.3510i	−0.391830	+	0.678670i
$388$	−6.23607	−	10.8012i	−0.316588	−	0.548347i
$389$	−16.7082	−	28.9395i	−0.847140	−	1.46729i	−0.883750	−	0.467959i	$-0.844989\pi$
$389$	−16.7082	−	28.9395i	−0.847140	−	1.46729i	0.0366105	−	0.999330i	$-0.488344\pi$
$390$	−2.47214	+	4.28187i	−0.125181	+	0.216821i
$391$	9.88854			0.500085
$392$		0			0
$393$	5.88854			0.297038
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$	0.736068	+	1.27491i	0.0369888	+	0.0640665i
$397$	11.8541	−	20.5319i	0.594940	−	1.03047i	−0.398615	−	0.917118i	$-0.630509\pi$
$397$	11.8541	−	20.5319i	0.594940	−	1.03047i	0.993555	−	0.113348i	$-0.0361577\pi$
$398$	18.9443			0.949591
$399$		0			0
$400$	−3.47214			−0.173607
$401$	−7.18034	+	12.4367i	−0.358569	+	0.621060i	−0.987722	−	0.156222i	$-0.950069\pi$
$401$	−7.18034	+	12.4367i	−0.358569	+	0.621060i	0.629153	+	0.777282i	$0.283402\pi$
$402$	−7.05573	−	12.2209i	−0.351908	−	0.609522i
$403$	3.23607	+	5.60503i	0.161200	+	0.279207i
$404$	−4.09017	+	7.08438i	−0.203494	+	0.352461i
$405$	2.98684			0.148417
$406$		0			0
$407$	6.94427			0.344215
$408$	−1.52786	+	2.64634i	−0.0756405	+	0.131013i
$409$	−1.70820	−	2.95870i	−0.0844652	−	0.146298i	0.820698	−	0.571362i	$-0.193585\pi$
$409$	−1.70820	−	2.95870i	−0.0844652	−	0.146298i	−0.905163	+	0.425064i	$0.860252\pi$
$410$	−1.52786	−	2.64634i	−0.0754558	−	0.130693i
$411$	12.2918	−	21.2900i	0.606310	−	1.05016i
$412$	−14.9443			−0.736251
$413$		0			0
$414$	−5.88854			−0.289406
$415$	−7.52786	+	13.0386i	−0.369528	+	0.640042i
$416$	1.61803	+	2.80252i	0.0793306	+	0.137405i
$417$	13.4164	+	23.2379i	0.657004	+	1.13796i
$418$	3.61803	−	6.26662i	0.176964	−	0.306510i
$419$	17.2361			0.842037			0.421019	−	0.907052i	$-0.361673\pi$
$419$	17.2361			0.842037			0.421019	+	0.907052i	$0.361673\pi$
$420$		0			0
$421$	16.4721			0.802803			0.401401	−	0.915902i	$-0.368523\pi$
$421$	16.4721			0.802803			0.401401	+	0.915902i	$0.368523\pi$
$422$	6.76393	−	11.7155i	0.329263	−	0.570300i
$423$	−1.47214	−	2.54981i	−0.0715777	−	0.123976i
$424$	−4.23607	−	7.33708i	−0.205722	−	0.356320i
$425$	4.29180	−	7.43361i	0.208183	−	0.360583i
$426$	8.00000			0.387601
$427$		0			0
$428$	2.47214			0.119495
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$	−6.47214	−	11.2101i	−0.312114	−	0.540597i
$431$	−11.5279	−	19.9668i	−0.555278	−	0.961769i	−0.997882	−	0.0650521i	$-0.979279\pi$
$431$	−11.5279	−	19.9668i	−0.555278	−	0.961769i	0.442604	−	0.896717i	$-0.354055\pi$
$432$	2.76393	−	4.78727i	0.132980	−	0.230328i
$433$	28.4721			1.36828			0.684142	−	0.729349i	$-0.260177\pi$
$433$	28.4721			1.36828			0.684142	+	0.729349i	$0.260177\pi$
$434$		0			0
$435$	−6.83282			−0.327608
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	14.4721	+	25.0665i	0.692296	+	1.19909i
$438$	−8.00000	−	13.8564i	−0.382255	−	0.662085i
$439$	−4.47214	+	7.74597i	−0.213443	+	0.369695i	−0.952790	−	0.303630i	$-0.901801\pi$
$439$	−4.47214	+	7.74597i	−0.213443	+	0.369695i	0.739347	+	0.673325i	$0.235135\pi$
$440$	−1.23607			−0.0589272
$441$		0			0
$442$	−8.00000			−0.380521
$443$	12.4721	−	21.6024i	0.592569	−	1.02636i	−0.401316	−	0.915940i	$-0.631447\pi$
$443$	12.4721	−	21.6024i	0.592569	−	1.02636i	0.993885	−	0.110420i	$-0.0352196\pi$
$444$	−4.29180	−	7.43361i	−0.203680	−	0.352783i
$445$	6.18034	+	10.7047i	0.292976	+	0.507450i
$446$	0.236068	−	0.408882i	0.0111781	−	0.0193611i
$447$	−27.6393			−1.30729
$448$		0			0
$449$	18.9443			0.894035			0.447018	−	0.894525i	$-0.352486\pi$
$449$	18.9443			0.894035			0.447018	+	0.894525i	$0.352486\pi$
$450$	−2.55573	+	4.42665i	−0.120478	+	0.208674i
$451$	1.23607	+	2.14093i	0.0582042	+	0.100813i
$452$	0.236068	+	0.408882i	0.0111037	+	0.0192322i
$453$	−7.41641	+	12.8456i	−0.348453	+	0.603539i
$454$	−19.2361			−0.902793
$455$		0			0
$456$	−8.94427			−0.418854
$457$	−13.4721	+	23.3344i	−0.630200	+	1.09154i	0.357311	+	0.933986i	$0.383694\pi$
$457$	−13.4721	+	23.3344i	−0.630200	+	1.09154i	−0.987511	+	0.157553i	$0.949640\pi$
$458$	−8.61803	−	14.9269i	−0.402694	−	0.697487i
$459$	6.83282	+	11.8348i	0.318929	+	0.552400i
$460$	2.47214	−	4.28187i	0.115264	−	0.199643i
$461$	24.7639			1.15337			0.576686	−	0.816966i	$-0.304346\pi$
$461$	24.7639			1.15337			0.576686	+	0.816966i	$0.304346\pi$
$462$		0			0
$463$	−30.4721			−1.41616			−0.708080	−	0.706132i	$-0.750438\pi$
$463$	−30.4721			−1.41616			−0.708080	+	0.706132i	$0.750438\pi$
$464$	−2.23607	+	3.87298i	−0.103807	+	0.179799i
$465$	1.52786	+	2.64634i	0.0708530	+	0.122721i
$466$	7.47214	+	12.9421i	0.346140	+	0.599532i
$467$	13.5623	−	23.4906i	0.627589	−	1.08702i	−0.360445	−	0.932780i	$-0.617375\pi$
$467$	13.5623	−	23.4906i	0.627589	−	1.08702i	0.988034	−	0.154235i	$-0.0492913\pi$
$468$	4.76393			0.220213
$469$		0			0
$470$	2.47214			0.114031
$471$	7.81966	−	13.5440i	0.360311	−	0.624077i
$472$	−1.38197	−	2.39364i	−0.0636101	−	0.110176i
$473$	5.23607	+	9.06914i	0.240755	+	0.416999i
$474$		0			0
$475$	25.1246			1.15280
$476$		0			0
$477$	−12.4721			−0.571060
$478$	−10.0000	+	17.3205i	−0.457389	+	0.792222i
$479$	−6.18034	−	10.7047i	−0.282387	−	0.489109i	0.689585	−	0.724205i	$-0.257793\pi$
$479$	−6.18034	−	10.7047i	−0.282387	−	0.489109i	−0.971972	+	0.235096i	$0.924460\pi$
$480$	0.763932	+	1.32317i	0.0348686	+	0.0603941i
$481$	11.2361	−	19.4614i	0.512321	−	0.887365i
$482$	15.4164			0.702198
$483$		0			0
$484$	1.00000			0.0454545
$485$	7.70820	−	13.3510i	0.350012	−	0.606238i
$486$	−6.79837	−	11.7751i	−0.308381	−	0.534131i
$487$	−8.47214	−	14.6742i	−0.383909	−	0.664950i	0.607708	−	0.794160i	$-0.292089\pi$
$487$	−8.47214	−	14.6742i	−0.383909	−	0.664950i	−0.991617	+	0.129210i	$0.958756\pi$
$488$	0.381966	−	0.661585i	0.0172908	−	0.0299485i
$489$	−24.0000			−1.08532
$490$		0			0
$491$	−16.9443			−0.764684			−0.382342	−	0.924021i	$-0.624882\pi$
$491$	−16.9443			−0.764684			−0.382342	+	0.924021i	$0.624882\pi$
$492$	1.52786	−	2.64634i	0.0688814	−	0.119306i
$493$	−5.52786	−	9.57454i	−0.248962	−	0.431216i
$494$	−11.7082	−	20.2792i	−0.526777	−	0.912405i
$495$	−0.909830	+	1.57587i	−0.0408938	+	0.0708302i
$496$	2.00000			0.0898027
$497$		0			0
$498$	−15.0557			−0.674663
$499$	16.1803	−	28.0252i	0.724331	−	1.25458i	−0.234917	−	0.972015i	$-0.575482\pi$
$499$	16.1803	−	28.0252i	0.724331	−	1.25458i	0.959249	−	0.282564i	$-0.0911848\pi$
$500$	−5.23607	−	9.06914i	−0.234164	−	0.405584i
$501$	−7.05573	−	12.2209i	−0.315227	−	0.545989i
$502$	−14.6180	+	25.3192i	−0.652435	+	1.13005i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$		0			0
$505$	−10.1115			−0.449954
$506$	−2.00000	+	3.46410i	−0.0889108	+	0.153998i
$507$	1.56231	+	2.70599i	0.0693844	+	0.120177i
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	−12.0344	+	20.8443i	−0.533417	+	0.923906i	0.465821	+	0.884879i	$0.345759\pi$
$509$	−12.0344	+	20.8443i	−0.533417	+	0.923906i	−0.999238	+	0.0390268i	$0.987574\pi$
$510$	−3.77709			−0.167252
$511$		0			0
$512$	1.00000			0.0441942
$513$	−20.0000	+	34.6410i	−0.883022	+	1.52944i
$514$	−3.47214	−	6.01392i	−0.153149	−	0.265262i
$515$	−9.23607	−	15.9973i	−0.406990	−	0.704927i
$516$	6.47214	−	11.2101i	0.284920	−	0.493496i
$517$	−2.00000			−0.0879599
$518$		0			0
$519$	−4.00000			−0.175581
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	5.18034	+	8.97261i	0.226955	+	0.393097i	0.956904	−	0.290404i	$-0.0937897\pi$
$521$	5.18034	+	8.97261i	0.226955	+	0.393097i	−0.729949	+	0.683501i	$0.760456\pi$
$522$	3.29180	+	5.70156i	0.144078	+	0.249550i
$523$	7.14590	−	12.3771i	0.312468	−	0.541211i	−0.666428	−	0.745570i	$-0.732178\pi$
$523$	7.14590	−	12.3771i	0.312468	−	0.541211i	0.978896	+	0.204359i	$0.0655109\pi$
$524$	4.76393			0.208113
$525$		0			0
$526$	−4.94427			−0.215580
$527$	−2.47214	+	4.28187i	−0.107688	+	0.186521i
$528$	−0.618034	−	1.07047i	−0.0268965	−	0.0465861i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	5.23607	−	9.06914i	0.227440	−	0.393938i
$531$	−4.06888			−0.176575
$532$		0			0
$533$	8.00000			0.346518
$534$	−6.18034	+	10.7047i	−0.267449	+	0.463236i
$535$	1.52786	+	2.64634i	0.0660553	+	0.114411i
$536$	−5.70820	−	9.88690i	−0.246557	−	0.427049i
$537$	5.52786	−	9.57454i	0.238545	−	0.413172i
$538$	−22.7639			−0.981423
$539$		0			0
$540$	6.83282			0.294038
$541$	13.4721	−	23.3344i	0.579212	−	1.00323i	−0.416358	−	0.909201i	$-0.636694\pi$
$541$	13.4721	−	23.3344i	0.579212	−	1.00323i	0.995570	−	0.0940243i	$-0.0299731\pi$
$542$	−0.472136	−	0.817763i	−0.0202800	−	0.0351259i
$543$	−5.70820	−	9.88690i	−0.244962	−	0.424287i
$544$	−1.23607	+	2.14093i	−0.0529960	+	0.0917917i
$545$	12.3607			0.529473
$546$		0			0
$547$	−0.944272			−0.0403742			−0.0201871	−	0.999796i	$-0.506426\pi$
$547$	−0.944272			−0.0403742			−0.0201871	+	0.999796i	$0.506426\pi$
$548$	9.94427	−	17.2240i	0.424798	−	0.735772i
$549$	−0.562306	−	0.973942i	−0.0239986	−	0.0415668i
$550$	1.73607	+	3.00696i	0.0740262	+	0.128217i
$551$	16.1803	−	28.0252i	0.689306	−	1.19391i
$552$	4.94427			0.210442
$553$		0			0
$554$	3.52786			0.149885
$555$	5.30495	−	9.18845i	0.225183	−	0.390028i
$556$	10.8541	+	18.7999i	0.460316	+	0.797291i
$557$	−12.4164	−	21.5058i	−0.526100	−	0.911232i	−0.999538	−	0.0304047i	$-0.990320\pi$
$557$	−12.4164	−	21.5058i	−0.526100	−	0.911232i	0.473438	−	0.880827i	$-0.343013\pi$
$558$	1.47214	−	2.54981i	0.0623205	−	0.107942i
$559$	33.8885			1.43333
$560$		0			0
$561$	3.05573			0.129013
$562$	−14.4164	+	24.9700i	−0.608119	+	1.05329i
$563$	−15.6180	−	27.0512i	−0.658222	−	1.14007i	−0.981076	−	0.193625i	$-0.937976\pi$
$563$	−15.6180	−	27.0512i	−0.658222	−	1.14007i	0.322854	−	0.946449i	$-0.395358\pi$
$564$	1.23607	+	2.14093i	0.0520479	+	0.0901495i
$565$	−0.291796	+	0.505406i	−0.0122760	+	0.0212626i
$566$	14.6525			0.615889
$567$		0			0
$568$	6.47214			0.271565
$569$	18.4164	−	31.8982i	0.772056	−	1.33724i	−0.164378	−	0.986397i	$-0.552562\pi$
$569$	18.4164	−	31.8982i	0.772056	−	1.33724i	0.936434	−	0.350843i	$-0.114105\pi$
$570$	−5.52786	−	9.57454i	−0.231537	−	0.401033i
$571$	5.05573	+	8.75678i	0.211576	+	0.366460i	0.952208	−	0.305451i	$-0.0988072\pi$
$571$	5.05573	+	8.75678i	0.211576	+	0.366460i	−0.740632	+	0.671911i	$0.765474\pi$
$572$	1.61803	−	2.80252i	0.0676534	−	0.117179i
$573$	−3.05573			−0.127655
$574$		0			0
$575$	−13.8885			−0.579192
$576$	0.736068	−	1.27491i	0.0306695	−	0.0531211i
$577$	−13.4721	−	23.3344i	−0.560852	−	0.971425i	−0.997422	−	0.0717545i	$-0.977140\pi$
$577$	−13.4721	−	23.3344i	−0.560852	−	0.971425i	0.436570	−	0.899670i	$-0.356193\pi$
$578$	5.44427	+	9.42976i	0.226452	+	0.392226i
$579$	9.23607	−	15.9973i	0.383838	−	0.664827i
$580$	−5.52786			−0.229532
$581$		0			0
$582$	15.4164			0.639031
$583$	−4.23607	+	7.33708i	−0.175440	+	0.303871i
$584$	−6.47214	−	11.2101i	−0.267819	−	0.463876i
$585$	2.94427	+	5.09963i	0.121731	+	0.210844i
$586$	13.3262	−	23.0817i	0.550502	−	0.953497i
$587$	−5.81966			−0.240203			−0.120102	−	0.992762i	$-0.538322\pi$
$587$	−5.81966			−0.240203			−0.120102	+	0.992762i	$0.538322\pi$
$588$		0			0
$589$	−14.4721			−0.596314
$590$	1.70820	−	2.95870i	0.0703256	−	0.121808i
$591$	−11.1246	−	19.2684i	−0.457605	−	0.792596i
$592$	−3.47214	−	6.01392i	−0.142704	−	0.247170i
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	−0.999965	−	0.00831589i	$-0.997353\pi$
$593$	−12.0000	+	20.7846i	−0.492781	+	0.853522i	0.507184	+	0.861838i	$0.330686\pi$
$594$	−5.52786			−0.226811
$595$		0			0
$596$	−22.3607			−0.915929
$597$	−11.7082	+	20.2792i	−0.479185	+	0.829973i
$598$	6.47214	+	11.2101i	0.264665	+	0.458414i
$599$	16.1803	+	28.0252i	0.661111	+	1.14508i	0.980324	+	0.197395i	$0.0632480\pi$
$599$	16.1803	+	28.0252i	0.661111	+	1.14508i	−0.319213	+	0.947683i	$0.603419\pi$
$600$	2.14590	−	3.71680i	0.0876059	−	0.151738i
$601$	−34.8328			−1.42086			−0.710430	−	0.703768i	$-0.751500\pi$
$601$	−34.8328			−1.42086			−0.710430	+	0.703768i	$0.751500\pi$
$602$		0			0
$603$	−16.8065			−0.684414
$604$	−6.00000	+	10.3923i	−0.244137	+	0.422857i
$605$	0.618034	+	1.07047i	0.0251267	+	0.0435206i
$606$	−5.05573	−	8.75678i	−0.205375	−	0.355720i
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	−7.23607			−0.293461
$609$		0			0
$610$	0.944272			0.0382325
$611$	−3.23607	+	5.60503i	−0.130917	+	0.226755i
$612$	1.81966	+	3.15174i	0.0735554	+	0.127402i
$613$	−14.2361	−	24.6576i	−0.574989	−	0.995911i	−0.996043	−	0.0888750i	$-0.971673\pi$
$613$	−14.2361	−	24.6576i	−0.574989	−	0.995911i	0.421053	−	0.907036i	$-0.361660\pi$
$614$	13.0344	−	22.5763i	0.526027	−	0.911106i
$615$	3.77709			0.152307
$616$		0			0
$617$	21.4164			0.862192			0.431096	−	0.902306i	$-0.358127\pi$
$617$	21.4164			0.862192			0.431096	+	0.902306i	$0.358127\pi$
$618$	9.23607	−	15.9973i	0.371529	−	0.643507i
$619$	−9.27051	−	16.0570i	−0.372613	−	0.645385i	0.617353	−	0.786686i	$-0.288205\pi$
$619$	−9.27051	−	16.0570i	−0.372613	−	0.645385i	−0.989967	+	0.141301i	$0.954872\pi$
$620$	1.23607	+	2.14093i	0.0496417	+	0.0859819i
$621$	11.0557	−	19.1491i	0.443651	−	0.768426i
$622$	−21.4164			−0.858720
$623$		0			0
$624$	−4.00000			−0.160128
$625$	−2.20820	+	3.82472i	−0.0883282	+	0.152989i
$626$	−9.76393	−	16.9116i	−0.390245	−	0.675925i
$627$	4.47214	+	7.74597i	0.178600	+	0.309344i
$628$	6.32624	−	10.9574i	0.252444	−	0.437246i
$629$	17.1672			0.684500
$630$		0			0
$631$	−31.4164			−1.25067			−0.625334	−	0.780357i	$-0.715037\pi$
$631$	−31.4164			−1.25067			−0.625334	+	0.780357i	$0.715037\pi$
$632$		0			0
$633$	8.36068	+	14.4811i	0.332307	+	0.575573i
$634$	15.4721	+	26.7985i	0.614477	+	1.06431i
$635$	−7.41641	+	12.8456i	−0.294311	+	0.509762i
$636$	10.4721			0.415247
$637$		0			0
$638$	4.47214			0.177054
$639$	4.76393	−	8.25137i	0.188458	−	0.326419i
$640$	0.618034	+	1.07047i	0.0244299	+	0.0423139i
$641$	−13.7639	−	23.8398i	−0.543643	−	0.941617i	−0.998691	−	0.0511499i	$-0.983711\pi$
$641$	−13.7639	−	23.8398i	−0.543643	−	0.941617i	0.455048	−	0.890467i	$-0.349622\pi$
$642$	−1.52786	+	2.64634i	−0.0603000	+	0.104443i
$643$	−18.7639			−0.739977			−0.369989	−	0.929036i	$-0.620638\pi$
$643$	−18.7639			−0.739977			−0.369989	+	0.929036i	$0.620638\pi$
$644$		0			0
$645$	16.0000			0.629999
$646$	8.94427	−	15.4919i	0.351908	−	0.609522i
$647$	14.4164	+	24.9700i	0.566767	+	0.981670i	0.996883	+	0.0788961i	$0.0251395\pi$
$647$	14.4164	+	24.9700i	0.566767	+	0.981670i	−0.430115	+	0.902774i	$0.641527\pi$
$648$	1.20820	+	2.09267i	0.0474627	+	0.0822079i
$649$	−1.38197	+	2.39364i	−0.0542469	+	0.0939584i
$650$	11.2361			0.440715
$651$		0			0
$652$	−19.4164			−0.760405
$653$	−23.1803	+	40.1495i	−0.907117	+	1.57117i	−0.0890665	+	0.996026i	$0.528388\pi$
$653$	−23.1803	+	40.1495i	−0.907117	+	1.57117i	−0.818050	+	0.575147i	$0.804945\pi$
$654$	6.18034	+	10.7047i	0.241670	+	0.418585i
$655$	2.94427	+	5.09963i	0.115042	+	0.199259i
$656$	1.23607	−	2.14093i	0.0482603	−	0.0835894i
$657$	−19.0557			−0.743435
$658$		0			0
$659$	16.5836			0.646005			0.323003	−	0.946398i	$-0.395308\pi$
$659$	16.5836			0.646005			0.323003	+	0.946398i	$0.395308\pi$
$660$	0.763932	−	1.32317i	0.0297360	−	0.0515043i
$661$	1.56231	+	2.70599i	0.0607667	+	0.105251i	0.894808	−	0.446451i	$-0.147312\pi$
$661$	1.56231	+	2.70599i	0.0607667	+	0.105251i	−0.834042	+	0.551701i	$0.813979\pi$
$662$	8.47214	+	14.6742i	0.329279	+	0.570328i
$663$	4.94427	−	8.56373i	0.192020	−	0.332588i
$664$	−12.1803			−0.472689
$665$		0			0
$666$	−10.2229			−0.396130
$667$	−8.94427	+	15.4919i	−0.346324	+	0.599850i
$668$	−5.70820	−	9.88690i	−0.220857	−	0.382536i
$669$	0.291796	+	0.505406i	0.0112815	+	0.0195401i
$670$	7.05573	−	12.2209i	0.272587	−	0.472134i
$671$	−0.763932			−0.0294913
$672$		0			0
$673$	−3.88854			−0.149892			−0.0749462	−	0.997188i	$-0.523878\pi$
$673$	−3.88854			−0.149892			−0.0749462	+	0.997188i	$0.523878\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$	−9.59675	−	16.6221i	−0.369379	−	0.639783i
$676$	1.26393	+	2.18919i	0.0486128	+	0.0841998i
$677$	13.0344	−	22.5763i	0.500954	−	0.867678i	−0.499045	−	0.866576i	$-0.666316\pi$
$677$	13.0344	−	22.5763i	0.500954	−	0.867678i	0.999999	−	0.00110228i	$-0.000350865\pi$
$678$	−0.583592			−0.0224127
$679$		0			0
$680$	−3.05573			−0.117182
$681$	11.8885	−	20.5916i	0.455570	−	0.789070i
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$	−16.4721	−	28.5306i	−0.630289	−	1.09169i	−0.987493	−	0.157666i	$-0.949603\pi$
$683$	−16.4721	−	28.5306i	−0.630289	−	1.09169i	0.357204	−	0.934026i	$-0.383730\pi$
$684$	−5.32624	+	9.22531i	−0.203654	+	0.352739i
$685$	24.5836			0.939291
$686$		0			0
$687$	21.3050			0.812835
$688$	5.23607	−	9.06914i	0.199623	−	0.345758i
$689$	13.7082	+	23.7433i	0.522241	+	0.904548i
$690$	3.05573	+	5.29268i	0.116330	+	0.201489i
$691$	−6.32624	+	10.9574i	−0.240661	+	0.416838i	−0.960903	−	0.276886i	$-0.910698\pi$
$691$	−6.32624	+	10.9574i	−0.240661	+	0.416838i	0.720241	+	0.693723i	$0.244031\pi$
$692$	−3.23607			−0.123017
$693$		0			0
$694$	2.47214			0.0938410
$695$	−13.4164	+	23.2379i	−0.508913	+	0.881464i
$696$	−2.76393	−	4.78727i	−0.104767	−	0.181461i
$697$	3.05573	+	5.29268i	0.115744	+	0.200474i
$698$	−10.8541	+	18.7999i	−0.410834	+	0.711585i
$699$	−18.4721			−0.698680
$700$		0			0
$701$	−42.7214			−1.61356			−0.806782	−	0.590850i	$-0.798793\pi$
$701$	−42.7214			−1.61356			−0.806782	+	0.590850i	$0.798793\pi$
$702$	−8.94427	+	15.4919i	−0.337580	+	0.584705i
$703$	25.1246	+	43.5171i	0.947593	+	1.64128i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−1.52786	+	2.64634i	−0.0575427	+	0.0996669i
$706$	−17.0557			−0.641901
$707$		0			0
$708$	3.41641			0.128396
$709$	−2.23607	+	3.87298i	−0.0839773	+	0.145453i	−0.904955	−	0.425507i	$-0.860096\pi$
$709$	−2.23607	+	3.87298i	−0.0839773	+	0.145453i	0.820978	+	0.570960i	$0.193429\pi$
$710$	4.00000	+	6.92820i	0.150117	+	0.260011i
$711$		0			0
$712$	−5.00000	+	8.66025i	−0.187383	+	0.324557i
$713$	8.00000			0.299602
$714$		0			0
$715$	4.00000			0.149592
$716$	4.47214	−	7.74597i	0.167132	−	0.289480i
$717$	−12.3607	−	21.4093i	−0.461618	−	0.799546i
$718$	−13.4164	−	23.2379i	−0.500696	−	0.867231i
$719$	−8.41641	+	14.5776i	−0.313879	+	0.543654i	−0.979199	−	0.202904i	$-0.934962\pi$
$719$	−8.41641	+	14.5776i	−0.313879	+	0.543654i	0.665320	+	0.746559i	$0.268295\pi$
$720$	1.81966			0.0678147
$721$		0			0
$722$	33.3607			1.24156
$723$	−9.52786	+	16.5027i	−0.354345	+	0.613744i
$724$	−4.61803	−	7.99867i	−0.171628	−	0.297268i
$725$	7.76393	+	13.4475i	0.288345	+	0.499429i
$726$	−0.618034	+	1.07047i	−0.0229374	+	0.0397287i
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$		0			0
$729$	24.0557			0.890953
$730$	8.00000	−	13.8564i	0.296093	−	0.512849i
$731$	12.9443	+	22.4201i	0.478761	+	0.829239i
$732$	0.472136	+	0.817763i	0.0174506	+	0.0302254i
$733$	−24.5623	+	42.5432i	−0.907229	+	1.57137i	−0.0893332	+	0.996002i	$0.528474\pi$
$733$	−24.5623	+	42.5432i	−0.907229	+	1.57137i	−0.817896	+	0.575366i	$0.804860\pi$
$734$	−5.41641			−0.199923
$735$		0			0
$736$	4.00000			0.147442
$737$	−5.70820	+	9.88690i	−0.210264	+	0.364189i
$738$	−1.81966	−	3.15174i	−0.0669826	−	0.116017i
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	4.29180	−	7.43361i	0.157770	−	0.273265i
$741$	28.9443			1.06329
$742$		0			0
$743$	21.8885			0.803013			0.401506	−	0.915856i	$-0.368487\pi$
$743$	21.8885			0.803013			0.401506	+	0.915856i	$0.368487\pi$
$744$	−1.23607	+	2.14093i	−0.0453165	+	0.0784904i
$745$	−13.8197	−	23.9364i	−0.506313	−	0.876960i
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	−8.96556	+	15.5288i	−0.328033	+	0.568169i
$748$	2.47214			0.0903902
$749$		0			0
$750$	12.9443			0.472658
$751$	8.47214	−	14.6742i	0.309153	−	0.535468i	−0.669025	−	0.743240i	$-0.733288\pi$
$751$	8.47214	−	14.6742i	0.309153	−	0.535468i	0.978177	+	0.207772i	$0.0666213\pi$
$752$	1.00000	+	1.73205i	0.0364662	+	0.0631614i
$753$	−18.0689	−	31.2962i	−0.658467	−	1.14050i
$754$	7.23607	−	12.5332i	0.263522	−	0.456434i
$755$	−14.8328			−0.539821
$756$		0			0
$757$	−23.3050			−0.847033			−0.423516	−	0.905888i	$-0.639204\pi$
$757$	−23.3050			−0.847033			−0.423516	+	0.905888i	$0.639204\pi$
$758$	−7.23607	+	12.5332i	−0.262826	+	0.455228i
$759$	−2.47214	−	4.28187i	−0.0897329	−	0.155422i
$760$	−4.47214	−	7.74597i	−0.162221	−	0.280976i
$761$	5.70820	−	9.88690i	0.206922	−	0.358400i	−0.743821	−	0.668379i	$-0.766989\pi$
$761$	5.70820	−	9.88690i	0.206922	−	0.358400i	0.950743	+	0.309979i	$0.100322\pi$
$762$	−14.8328			−0.537336
$763$		0			0
$764$	−2.47214			−0.0894387
$765$	−2.24922	+	3.89577i	−0.0813209	+	0.140852i
$766$	11.9443	+	20.6881i	0.431564	+	0.747491i
$767$	4.47214	+	7.74597i	0.161479	+	0.279691i
$768$	−0.618034	+	1.07047i	−0.0223014	+	0.0386271i
$769$	−43.4164			−1.56564			−0.782818	−	0.622251i	$-0.786218\pi$
$769$	−43.4164			−1.56564			−0.782818	+	0.622251i	$0.786218\pi$
$770$		0			0
$771$	8.58359			0.309131
$772$	7.47214	−	12.9421i	0.268928	−	0.465797i
$773$	−7.85410	−	13.6037i	−0.282492	−	0.489291i	0.689506	−	0.724280i	$-0.257828\pi$
$773$	−7.85410	−	13.6037i	−0.282492	−	0.489291i	−0.971998	+	0.234989i	$0.924495\pi$
$774$	−7.70820	−	13.3510i	−0.277066	−	0.479892i
$775$	3.47214	−	6.01392i	0.124723	−	0.216026i
$776$	12.4721			0.447724
$777$		0			0
$778$	33.4164			1.19804
$779$	−8.94427	+	15.4919i	−0.320462	+	0.555056i
$780$	−2.47214	−	4.28187i	−0.0885167	−	0.153315i
$781$	−3.23607	−	5.60503i	−0.115796	−

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.618034 - 1.07047i) q^{5} +1.23607 q^{6} +1.00000 q^{8} +(0.736068 - 1.27491i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.618034 - 1.07047i) q^{5} +1.23607 q^{6} +1.00000 q^{8} +(0.736068 - 1.27491i) q^{9} +(0.618034 + 1.07047i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.618034 + 1.07047i) q^{12} -3.23607 q^{13} -1.52786 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.23607 - 2.14093i) q^{17} +(0.736068 + 1.27491i) q^{18} +(3.61803 - 6.26662i) q^{19} -1.23607 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.618034 - 1.07047i) q^{24} +(1.73607 + 3.00696i) q^{25} +(1.61803 - 2.80252i) q^{26} -5.52786 q^{27} +4.47214 q^{29} +(0.763932 - 1.32317i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.618034 + 1.07047i) q^{33} +2.47214 q^{34} -1.47214 q^{36} +(-3.47214 + 6.01392i) q^{37} +(3.61803 + 6.26662i) q^{38} +(2.00000 + 3.46410i) q^{39} +(0.618034 - 1.07047i) q^{40} -2.47214 q^{41} -10.4721 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.909830 - 1.57587i) q^{45} +(-2.00000 - 3.46410i) q^{46} +(1.00000 - 1.73205i) q^{47} +1.23607 q^{48} -3.47214 q^{50} +(-1.52786 + 2.64634i) q^{51} +(1.61803 + 2.80252i) q^{52} +(-4.23607 - 7.33708i) q^{53} +(2.76393 - 4.78727i) q^{54} -1.23607 q^{55} -8.94427 q^{57} +(-2.23607 + 3.87298i) q^{58} +(-1.38197 - 2.39364i) q^{59} +(0.763932 + 1.32317i) q^{60} +(0.381966 - 0.661585i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-0.618034 - 1.07047i) q^{66} +(-5.70820 - 9.88690i) q^{67} +(-1.23607 + 2.14093i) q^{68} +4.94427 q^{69} +6.47214 q^{71} +(0.736068 - 1.27491i) q^{72} +(-6.47214 - 11.2101i) q^{73} +(-3.47214 - 6.01392i) q^{74} +(2.14590 - 3.71680i) q^{75} -7.23607 q^{76} -4.00000 q^{78} +(0.618034 + 1.07047i) q^{80} +(1.20820 + 2.09267i) q^{81} +(1.23607 - 2.14093i) q^{82} -12.1803 q^{83} -3.05573 q^{85} +(5.23607 - 9.06914i) q^{86} +(-2.76393 - 4.78727i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +1.81966 q^{90} +4.00000 q^{92} +(-1.23607 + 2.14093i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-4.47214 - 7.74597i) q^{95} +(-0.618034 + 1.07047i) q^{96} +12.4721 q^{97} -1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} - 6 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 24 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{18} + 10 q^{19} + 4 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 40 q^{27} + 12 q^{30} - 4 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} + 12 q^{36} + 4 q^{37} + 10 q^{38} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 24 q^{43} - 2 q^{44} - 26 q^{45} - 8 q^{46} + 4 q^{47} - 4 q^{48} + 4 q^{50} - 24 q^{51} + 2 q^{52} - 8 q^{53} + 20 q^{54} + 4 q^{55} - 10 q^{59} + 12 q^{60} + 6 q^{61} + 8 q^{62} + 4 q^{64} - 8 q^{65} + 2 q^{66} + 4 q^{67} + 4 q^{68} - 16 q^{69} + 8 q^{71} - 6 q^{72} - 8 q^{73} + 4 q^{74} + 22 q^{75} - 20 q^{76} - 16 q^{78} - 2 q^{80} - 22 q^{81} - 4 q^{82} - 4 q^{83} - 48 q^{85} + 12 q^{86} - 20 q^{87} - 2 q^{88} - 20 q^{89} + 52 q^{90} + 16 q^{92} + 4 q^{93} + 4 q^{94} + 2 q^{96} + 32 q^{97} + 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 - 6 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 24 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^18 + 10 * q^19 + 4 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 40 * q^27 + 12 * q^30 - 4 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 + 12 * q^36 + 4 * q^37 + 10 * q^38 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 24 * q^43 - 2 * q^44 - 26 * q^45 - 8 * q^46 + 4 * q^47 - 4 * q^48 + 4 * q^50 - 24 * q^51 + 2 * q^52 - 8 * q^53 + 20 * q^54 + 4 * q^55 - 10 * q^59 + 12 * q^60 + 6 * q^61 + 8 * q^62 + 4 * q^64 - 8 * q^65 + 2 * q^66 + 4 * q^67 + 4 * q^68 - 16 * q^69 + 8 * q^71 - 6 * q^72 - 8 * q^73 + 4 * q^74 + 22 * q^75 - 20 * q^76 - 16 * q^78 - 2 * q^80 - 22 * q^81 - 4 * q^82 - 4 * q^83 - 48 * q^85 + 12 * q^86 - 20 * q^87 - 2 * q^88 - 20 * q^89 + 52 * q^90 + 16 * q^92 + 4 * q^93 + 4 * q^94 + 2 * q^96 + 32 * q^97 + 12 * q^99

Introduction

L-functions

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