LMFDB - Embedded newform 966.2.i.l.415.1

Newspace parameters

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1768034304.4
Defining polynomial:	$ x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 $ x^8 - 2x^7 - x^6 - 6x^5 + 14x^4 + 18x^3 - 31x^2 - 14x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$-0.885685 - 1.90520i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.l.277.1

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 + 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 + 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.914214 - 1.58346i) q^{10} +(-2.07397 - 3.59222i) q^{11} +(-0.500000 + 0.866025i) q^{12} -2.18558 q^{13} +(-0.840244 - 2.50878i) q^{14} +1.82843 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.67858 + 2.90738i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.66676 - 6.35102i) q^{19} +1.82843 q^{20} +(2.59279 + 0.526718i) q^{21} +4.14794 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.828427 + 1.43488i) q^{25} +(1.09279 - 1.89277i) q^{26} +1.00000 q^{27} +(2.59279 + 0.526718i) q^{28} +5.18558 q^{29} +(-0.914214 + 1.58346i) q^{30} +(-5.25955 - 9.10981i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.07397 + 3.59222i) q^{33} -3.35716 q^{34} +(-1.53633 - 4.58713i) q^{35} +1.00000 q^{36} +(0.518822 - 0.898626i) q^{37} +(3.66676 + 6.35102i) q^{38} +(1.09279 + 1.89277i) q^{39} +(-0.914214 + 1.58346i) q^{40} +7.33352 q^{41} +(-1.75255 + 1.98206i) q^{42} +5.36098 q^{43} +(-2.07397 + 3.59222i) q^{44} +(-0.914214 - 1.58346i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-3.61161 + 6.25550i) q^{47} +1.00000 q^{48} +(-0.857156 - 6.94732i) q^{49} -1.65685 q^{50} +(1.67858 - 2.90738i) q^{51} +(1.09279 + 1.89277i) q^{52} +(-2.27137 - 3.93413i) q^{53} +(-0.500000 + 0.866025i) q^{54} +7.58420 q^{55} +(-1.75255 + 1.98206i) q^{56} -7.33352 q^{57} +(-2.59279 + 4.49085i) q^{58} +(0.235636 + 0.408133i) q^{59} +(-0.914214 - 1.58346i) q^{60} +(7.37117 - 12.7672i) q^{61} +10.5191 q^{62} +(-0.840244 - 2.50878i) q^{63} +1.00000 q^{64} +(1.99809 - 3.46079i) q^{65} +(-2.07397 - 3.59222i) q^{66} +(-6.70249 - 11.6091i) q^{67} +(1.67858 - 2.90738i) q^{68} +1.00000 q^{69} +(4.74073 + 0.963066i) q^{70} +14.1856 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.75955 - 9.97584i) q^{73} +(0.518822 + 0.898626i) q^{74} +(0.828427 - 1.43488i) q^{75} -7.33352 q^{76} +(10.7547 + 2.18480i) q^{77} -2.18558 q^{78} +(2.59279 - 4.49085i) q^{79} +(-0.914214 - 1.58346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.66676 + 6.35102i) q^{82} +5.80479 q^{83} +(-0.840244 - 2.50878i) q^{84} -6.13831 q^{85} +(-2.68049 + 4.64274i) q^{86} +(-2.59279 - 4.49085i) q^{87} +(-2.07397 - 3.59222i) q^{88} +(-3.34725 + 5.79761i) q^{89} +1.82843 q^{90} +(3.83034 - 4.33197i) q^{91} +1.00000 q^{92} +(-5.25955 + 9.10981i) q^{93} +(-3.61161 - 6.25550i) q^{94} +(6.70441 + 11.6124i) q^{95} +(-0.500000 + 0.866025i) q^{96} -4.47127 q^{97} +(6.44514 + 2.73134i) q^{98} +4.14794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	−0.994761	−	0.102228i	$-0.967403\pi$
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	0.585912	+	0.810374i	$0.300736\pi$
$6$	1.00000			0.408248
$7$	−1.75255	+	1.98206i	−0.662401	+	0.749150i
$7$	−1.75255	+	1.98206i	−0.662401	+	0.749150i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.914214	−	1.58346i	−0.289100	−	0.500735i
$11$	−2.07397	−	3.59222i	−0.625325	−	1.08310i	−0.988478	−	0.151366i	$-0.951633\pi$
$11$	−2.07397	−	3.59222i	−0.625325	−	1.08310i	0.363153	−	0.931730i	$-0.381700\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.18558			−0.606172			−0.303086	−	0.952963i	$-0.598017\pi$
$13$	−2.18558			−0.606172			−0.303086	+	0.952963i	$0.598017\pi$
$14$	−0.840244	−	2.50878i	−0.224565	−	0.670500i
$15$	1.82843			0.472098
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.67858	+	2.90738i	0.407115	+	0.705144i	0.994565	−	0.104117i	$-0.0332015\pi$
$17$	1.67858	+	2.90738i	0.407115	+	0.705144i	−0.587450	+	0.809260i	$0.699868\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.66676	−	6.35102i	0.841213	−	1.45702i	−0.0476575	−	0.998864i	$-0.515176\pi$
$19$	3.66676	−	6.35102i	0.841213	−	1.45702i	0.888870	−	0.458159i	$-0.151491\pi$
$20$	1.82843			0.408849
$21$	2.59279	+	0.526718i	0.565793	+	0.114939i
$22$	4.14794			0.884344
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.828427	+	1.43488i	0.165685	+	0.286976i
$26$	1.09279	−	1.89277i	0.214314	−	0.371203i
$27$	1.00000			0.192450
$28$	2.59279	+	0.526718i	0.489992	+	0.0995404i
$29$	5.18558			0.962939			0.481469	−	0.876463i	$-0.340103\pi$
$29$	5.18558			0.962939			0.481469	+	0.876463i	$0.340103\pi$
$30$	−0.914214	+	1.58346i	−0.166912	+	0.289100i
$31$	−5.25955	−	9.10981i	−0.944643	−	1.63617i	−0.756463	−	0.654036i	$-0.773074\pi$
$31$	−5.25955	−	9.10981i	−0.944643	−	1.63617i	−0.188180	−	0.982135i	$-0.560259\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.07397	+	3.59222i	−0.361032	+	0.625325i
$34$	−3.35716			−0.575747
$35$	−1.53633	−	4.58713i	−0.259686	−	0.775366i
$36$	1.00000			0.166667
$37$	0.518822	−	0.898626i	0.0852938	−	0.147733i	−0.820223	−	0.572045i	$-0.806150\pi$
$37$	0.518822	−	0.898626i	0.0852938	−	0.147733i	0.905516	+	0.424311i	$0.139484\pi$
$38$	3.66676	+	6.35102i	0.594827	+	1.03027i
$39$	1.09279	+	1.89277i	0.174987	+	0.303086i
$40$	−0.914214	+	1.58346i	−0.144550	+	0.250368i
$41$	7.33352			1.14530			0.572652	−	0.819799i	$-0.305915\pi$
$41$	7.33352			1.14530			0.572652	+	0.819799i	$0.305915\pi$
$42$	−1.75255	+	1.98206i	−0.270424	+	0.305839i
$43$	5.36098			0.817541			0.408771	−	0.912637i	$-0.365958\pi$
$43$	5.36098			0.817541			0.408771	+	0.912637i	$0.365958\pi$
$44$	−2.07397	+	3.59222i	−0.312663	+	0.541548i
$45$	−0.914214	−	1.58346i	−0.136283	−	0.236049i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−3.61161	+	6.25550i	−0.526808	+	0.912458i	0.472704	+	0.881221i	$0.343278\pi$
$47$	−3.61161	+	6.25550i	−0.526808	+	0.912458i	−0.999512	+	0.0312369i	$0.990055\pi$
$48$	1.00000			0.144338
$49$	−0.857156	−	6.94732i	−0.122451	−	0.992475i
$50$	−1.65685			−0.234315
$51$	1.67858	−	2.90738i	0.235048	−	0.407115i
$52$	1.09279	+	1.89277i	0.151543	+	0.262480i
$53$	−2.27137	−	3.93413i	−0.311997	−	0.540394i	0.666798	−	0.745239i	$-0.267664\pi$
$53$	−2.27137	−	3.93413i	−0.311997	−	0.540394i	−0.978794	+	0.204845i	$0.934331\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	7.58420			1.02265
$56$	−1.75255	+	1.98206i	−0.234194	+	0.264864i
$57$	−7.33352			−0.971349
$58$	−2.59279	+	4.49085i	−0.340450	+	0.589677i
$59$	0.235636	+	0.408133i	0.0306771	+	0.0531344i	0.880956	−	0.473197i	$-0.156900\pi$
$59$	0.235636	+	0.408133i	0.0306771	+	0.0531344i	−0.850279	+	0.526332i	$0.823567\pi$
$60$	−0.914214	−	1.58346i	−0.118024	−	0.204424i
$61$	7.37117	−	12.7672i	0.943781	−	1.63468i	0.185608	−	0.982624i	$-0.440575\pi$
$61$	7.37117	−	12.7672i	0.943781	−	1.63468i	0.758174	−	0.652053i	$-0.226092\pi$
$62$	10.5191			1.33593
$63$	−0.840244	−	2.50878i	−0.105861	−	0.316077i
$64$	1.00000			0.125000
$65$	1.99809	−	3.46079i	0.247833	−	0.429259i
$66$	−2.07397	−	3.59222i	−0.255288	−	0.442172i
$67$	−6.70249	−	11.6091i	−0.818840	−	1.41827i	−0.906537	−	0.422125i	$-0.861284\pi$
$67$	−6.70249	−	11.6091i	−0.818840	−	1.41827i	0.0876974	−	0.996147i	$-0.472049\pi$
$68$	1.67858	−	2.90738i	0.203557	−	0.352572i
$69$	1.00000			0.120386
$70$	4.74073	+	0.963066i	0.566626	+	0.115108i
$71$	14.1856			1.68352			0.841759	−	0.539853i	$-0.181520\pi$
$71$	14.1856			1.68352			0.841759	+	0.539853i	$0.181520\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−5.75955	−	9.97584i	−0.674105	−	1.16758i	−0.976730	−	0.214474i	$-0.931196\pi$
$73$	−5.75955	−	9.97584i	−0.674105	−	1.16758i	0.302625	−	0.953110i	$-0.402137\pi$
$74$	0.518822	+	0.898626i	0.0603118	+	0.104463i
$75$	0.828427	−	1.43488i	0.0956585	−	0.165685i
$76$	−7.33352			−0.841213
$77$	10.7547	+	2.18480i	1.22562	+	0.248981i
$78$	−2.18558			−0.247469
$79$	2.59279	−	4.49085i	0.291712	−	0.505260i	−0.682503	−	0.730883i	$-0.739109\pi$
$79$	2.59279	−	4.49085i	0.291712	−	0.505260i	0.974215	+	0.225623i	$0.0724418\pi$
$80$	−0.914214	−	1.58346i	−0.102212	−	0.177037i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.66676	+	6.35102i	−0.404926	+	0.701352i
$83$	5.80479			0.637159			0.318579	−	0.947896i	$-0.396794\pi$
$83$	5.80479			0.637159			0.318579	+	0.947896i	$0.396794\pi$
$84$	−0.840244	−	2.50878i	−0.0916782	−	0.273731i
$85$	−6.13831			−0.665794
$86$	−2.68049	+	4.64274i	−0.289044	+	0.500640i
$87$	−2.59279	−	4.49085i	−0.277976	−	0.481469i
$88$	−2.07397	−	3.59222i	−0.221086	−	0.382932i
$89$	−3.34725	+	5.79761i	−0.354808	+	0.614545i	−0.987085	−	0.160197i	$-0.948787\pi$
$89$	−3.34725	+	5.79761i	−0.354808	+	0.614545i	0.632277	+	0.774742i	$0.282120\pi$
$90$	1.82843			0.192733
$91$	3.83034	−	4.33197i	0.401528	−	0.454113i
$92$	1.00000			0.104257
$93$	−5.25955	+	9.10981i	−0.545390	+	0.944643i
$94$	−3.61161	−	6.25550i	−0.372509	−	0.645205i
$95$	6.70441	+	11.6124i	0.687857	+	1.19140i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−4.47127			−0.453989			−0.226994	−	0.973896i	$-0.572890\pi$
$97$	−4.47127			−0.453989			−0.226994	+	0.973896i	$0.572890\pi$
$98$	6.44514	+	2.73134i	0.651057	+	0.275907i
$99$	4.14794			0.416884
$100$	0.828427	−	1.43488i	0.0828427	−	0.143488i
$101$	−7.65303	−	13.2554i	−0.761505	−	1.31897i	−0.942075	−	0.335404i	$-0.891127\pi$
$101$	−7.65303	−	13.2554i	−0.761505	−	1.31897i	0.180569	−	0.983562i	$-0.442206\pi$
$102$	1.67858	+	2.90738i	0.166204	+	0.287874i
$103$	−3.70249	+	6.41291i	−0.364818	+	0.631883i	−0.988747	−	0.149598i	$-0.952202\pi$
$103$	−3.70249	+	6.41291i	−0.364818	+	0.631883i	0.623929	+	0.781481i	$0.285535\pi$
$104$	−2.18558			−0.214314
$105$	−3.20441	+	3.62406i	−0.312718	+	0.353672i
$106$	4.54274			0.441230
$107$	2.75064	−	4.76424i	0.265914	−	0.460577i	−0.701889	−	0.712287i	$-0.747660\pi$
$107$	2.75064	−	4.76424i	0.265914	−	0.460577i	0.967803	+	0.251710i	$0.0809929\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.34753	+	16.1904i	0.895331	+	1.55076i	0.833394	+	0.552679i	$0.186394\pi$
$109$	9.34753	+	16.1904i	0.895331	+	1.55076i	0.0619370	+	0.998080i	$0.480272\pi$
$110$	−3.79210	+	6.56811i	−0.361563	+	0.626245i
$111$	−1.03764			−0.0984888
$112$	−0.840244	−	2.50878i	−0.0793956	−	0.237058i
$113$	5.28187			0.496876			0.248438	−	0.968648i	$-0.420083\pi$
$113$	5.28187			0.496876			0.248438	+	0.968648i	$0.420083\pi$
$114$	3.66676	−	6.35102i	0.343424	−	0.594827i
$115$	−0.914214	−	1.58346i	−0.0852509	−	0.147659i
$116$	−2.59279	−	4.49085i	−0.240735	−	0.416965i
$117$	1.09279	−	1.89277i	0.101029	−	0.174987i
$118$	−0.471271			−0.0433840
$119$	−8.70441	−	1.76828i	−0.797932	−	0.162098i
$120$	1.82843			0.166912
$121$	−3.10270	+	5.37403i	−0.282063	+	0.488548i
$122$	7.37117	+	12.7672i	0.667354	+	1.15589i
$123$	−3.66676	−	6.35102i	−0.330621	−	0.572652i
$124$	−5.25955	+	9.10981i	−0.472322	+	0.818085i
$125$	−12.1716			−1.08866
$126$	2.59279	+	0.526718i	0.230984	+	0.0469238i
$127$	6.49108			0.575991			0.287995	−	0.957632i	$-0.407011\pi$
$127$	6.49108			0.575991			0.287995	+	0.957632i	$0.407011\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.68049	−	4.64274i	−0.236004	−	0.408771i
$130$	1.99809	+	3.46079i	0.175244	+	0.303532i
$131$	2.20441	−	3.81814i	0.192600	−	0.333593i	−0.753511	−	0.657435i	$-0.771641\pi$
$131$	2.20441	−	3.81814i	0.192600	−	0.333593i	0.946111	+	0.323842i	$0.104975\pi$
$132$	4.14794			0.361032
$133$	6.16195	+	18.3982i	0.534309	+	1.59533i
$134$	13.4050			1.15801
$135$	−0.914214	+	1.58346i	−0.0786830	+	0.136283i
$136$	1.67858	+	2.90738i	0.143937	+	0.249306i
$137$	−0.840244	−	1.45535i	−0.0717869	−	0.124339i	0.827898	−	0.560879i	$-0.189537\pi$
$137$	−0.840244	−	1.45535i	−0.0717869	−	0.124339i	−0.899685	+	0.436541i	$0.856203\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	−13.3137			−1.12925			−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137			−1.12925			−0.564627	+	0.825346i	$0.690980\pi$
$140$	−3.20441	+	3.62406i	−0.270822	+	0.306289i
$141$	7.22323			0.608305
$142$	−7.09279	+	12.2851i	−0.595214	+	1.03094i
$143$	4.53283	+	7.85110i	0.379054	+	0.656542i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.74073	+	8.21119i	−0.393696	+	0.681902i
$146$	11.5191			0.953328
$147$	−5.58798	+	4.21598i	−0.460889	+	0.347728i
$148$	−1.03764			−0.0852938
$149$	−9.67886	+	16.7643i	−0.792923	+	1.37338i	0.131226	+	0.991352i	$0.458108\pi$
$149$	−9.67886	+	16.7643i	−0.792923	+	1.37338i	−0.924150	+	0.382031i	$0.875225\pi$
$150$	0.828427	+	1.43488i	0.0676408	+	0.117157i
$151$	−2.79210	−	4.83606i	−0.227218	−	0.393553i	0.729765	−	0.683699i	$-0.239630\pi$
$151$	−2.79210	−	4.83606i	−0.227218	−	0.393553i	−0.956983	+	0.290145i	$0.906296\pi$
$152$	3.66676	−	6.35102i	0.297414	−	0.515135i
$153$	−3.35716			−0.271410
$154$	−7.26946	+	8.22148i	−0.585790	+	0.662506i
$155$	19.2334			1.54487
$156$	1.09279	−	1.89277i	0.0874933	−	0.151543i
$157$	11.3951	+	19.7369i	0.909427	+	1.57517i	0.814862	+	0.579654i	$0.196812\pi$
$157$	11.3951	+	19.7369i	0.909427	+	1.57517i	0.0945641	+	0.995519i	$0.469854\pi$
$158$	2.59279	+	4.49085i	0.206271	+	0.357273i
$159$	−2.27137	+	3.93413i	−0.180131	+	0.311997i
$160$	1.82843			0.144550
$161$	−0.840244	−	2.50878i	−0.0662205	−	0.197720i
$162$	1.00000			0.0785674
$163$	12.7184	−	22.0289i	0.996183	−	1.72544i	0.422498	−	0.906364i	$-0.361153\pi$
$163$	12.7184	−	22.0289i	0.996183	−	1.72544i	0.573685	−	0.819076i	$-0.305513\pi$
$164$	−3.66676	−	6.35102i	−0.286326	−	0.495931i
$165$	−3.79210	−	6.56811i	−0.295215	−	0.511327i
$166$	−2.90240	+	5.02710i	−0.225270	+	0.390178i
$167$	−22.1185			−1.71158			−0.855791	−	0.517323i	$-0.826929\pi$
$167$	−22.1185			−1.71158			−0.855791	+	0.517323i	$0.826929\pi$
$168$	2.59279	+	0.526718i	0.200038	+	0.0406372i
$169$	−8.22323			−0.632556
$170$	3.06916	−	5.31594i	0.235394	−	0.407714i
$171$	3.66676	+	6.35102i	0.280404	+	0.485674i
$172$	−2.68049	−	4.64274i	−0.204385	−	0.354006i
$173$	6.84244	−	11.8514i	0.520221	−	0.901049i	−0.479503	−	0.877540i	$-0.659183\pi$
$173$	6.84244	−	11.8514i	0.520221	−	0.901049i	0.999724	−	0.0235086i	$-0.00748371\pi$
$174$	5.18558			0.393118
$175$	−4.29588	−	0.872696i	−0.324738	−	0.0659696i
$176$	4.14794			0.312663
$177$	0.235636	−	0.408133i	0.0177115	−	0.0306771i
$178$	−3.34725	−	5.79761i	−0.250887	−	0.434549i
$179$	1.38839	+	2.40476i	0.103773	+	0.179740i	0.913236	−	0.407431i	$-0.133575\pi$
$179$	1.38839	+	2.40476i	0.103773	+	0.179740i	−0.809463	+	0.587170i	$0.800242\pi$
$180$	−0.914214	+	1.58346i	−0.0681415	+	0.118024i
$181$	−20.9629			−1.55816			−0.779081	−	0.626923i	$-0.784314\pi$
$181$	−20.9629			−1.55816			−0.779081	+	0.626923i	$0.784314\pi$
$182$	1.83642	+	5.48315i	0.136125	+	0.406438i
$183$	−14.7423			−1.08978
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	0.948628	+	1.64307i	0.0697445	+	0.120801i
$186$	−5.25955	−	9.10981i	−0.385649	−	0.667964i
$187$	6.96264	−	12.0596i	0.509159	−	0.881888i
$188$	7.22323			0.526808
$189$	−1.75255	+	1.98206i	−0.127479	+	0.144174i
$190$	−13.4088			−0.972777
$191$	4.48118	−	7.76163i	0.324247	−	0.561612i	−0.657113	−	0.753792i	$-0.728223\pi$
$191$	4.48118	−	7.76163i	0.324247	−	0.561612i	0.981360	+	0.192180i	$0.0615559\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−5.81951	−	10.0797i	−0.418898	−	0.725552i	0.576931	−	0.816793i	$-0.304250\pi$
$193$	−5.81951	−	10.0797i	−0.418898	−	0.725552i	−0.995829	+	0.0912408i	$0.970917\pi$
$194$	2.23564	−	3.87223i	0.160509	−	0.278010i
$195$	−3.99618			−0.286172
$196$	−5.58798	+	4.21598i	−0.399141	+	0.301141i
$197$	9.58157			0.682658			0.341329	−	0.939944i	$-0.389123\pi$
$197$	9.58157			0.682658			0.341329	+	0.939944i	$0.389123\pi$
$198$	−2.07397	+	3.59222i	−0.147391	+	0.255288i
$199$	4.97637	+	8.61932i	0.352765	+	0.611007i	0.986733	−	0.162352i	$-0.0519081\pi$
$199$	4.97637	+	8.61932i	0.352765	+	0.611007i	−0.633968	+	0.773360i	$0.718575\pi$
$200$	0.828427	+	1.43488i	0.0585786	+	0.101461i
$201$	−6.70249	+	11.6091i	−0.472758	+	0.818840i
$202$	15.3061			1.07693
$203$	−9.08798	+	10.2782i	−0.637851	+	0.721385i
$204$	−3.35716			−0.235048
$205$	−6.70441	+	11.6124i	−0.468256	+	0.811043i
$206$	−3.70249	−	6.41291i	−0.257965	−	0.446809i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	1.09279	−	1.89277i	0.0757715	−	0.131240i
$209$	−30.4190			−2.10413
$210$	−1.53633	−	4.58713i	−0.106017	−	0.316542i
$211$	0.303519			0.0208951			0.0104476	−	0.999945i	$-0.496674\pi$
$211$	0.303519			0.0208951			0.0104476	+	0.999945i	$0.496674\pi$
$212$	−2.27137	+	3.93413i	−0.155998	+	0.270197i
$213$	−7.09279	−	12.2851i	−0.485990	−	0.841759i
$214$	2.75064	+	4.76424i	0.188030	+	0.325677i
$215$	−4.90108	+	8.48892i	−0.334251	+	0.578939i
$216$	1.00000			0.0680414
$217$	27.2738	+	5.54061i	1.85147	+	0.376121i
$218$	−18.6951			−1.26619
$219$	−5.75955	+	9.97584i	−0.389194	+	0.674105i
$220$	−3.79210	−	6.56811i	−0.255663	−	0.442822i
$221$	−3.66867	−	6.35433i	−0.246782	−	0.427438i
$222$	0.518822	−	0.898626i	0.0348211	−	0.0603118i
$223$	−16.9375			−1.13422			−0.567111	−	0.823642i	$-0.691939\pi$
$223$	−16.9375			−1.13422			−0.567111	+	0.823642i	$0.691939\pi$
$224$	2.59279	+	0.526718i	0.173238	+	0.0351929i
$225$	−1.65685			−0.110457
$226$	−2.64093	+	4.57423i	−0.175672	+	0.304273i
$227$	10.7685	+	18.6515i	0.714728	+	1.23795i	0.963064	+	0.269272i	$0.0867830\pi$
$227$	10.7685	+	18.6515i	0.714728	+	1.23795i	−0.248336	+	0.968674i	$0.579884\pi$
$228$	3.66676	+	6.35102i	0.242837	+	0.420606i
$229$	0.333239	−	0.577187i	0.0220211	−	0.0381416i	−0.854805	−	0.518950i	$-0.826323\pi$
$229$	0.333239	−	0.577187i	0.0220211	−	0.0381416i	0.876826	+	0.480808i	$0.159657\pi$
$230$	1.82843			0.120563
$231$	−3.48528	−	10.4063i	−0.229315	−	0.684683i
$232$	5.18558			0.340450
$233$	0.838334	−	1.45204i	0.0549211	−	0.0951261i	−0.837258	−	0.546808i	$-0.815843\pi$
$233$	0.838334	−	1.45204i	0.0549211	−	0.0951261i	0.892179	+	0.451682i	$0.149176\pi$
$234$	1.09279	+	1.89277i	0.0714380	+	0.123734i
$235$	−6.60357	−	11.4377i	−0.430770	−	0.746115i
$236$	0.235636	−	0.408133i	0.0153386	−	0.0265672i
$237$	−5.18558			−0.336840
$238$	5.88357	−	6.65410i	0.381375	−	0.431321i
$239$	10.7220			0.693546			0.346773	−	0.937949i	$-0.387278\pi$
$239$	10.7220			0.693546			0.346773	+	0.937949i	$0.387278\pi$
$240$	−0.914214	+	1.58346i	−0.0590122	+	0.102212i
$241$	−9.10171	−	15.7646i	−0.586292	−	1.01549i	−0.994713	−	0.102694i	$-0.967254\pi$
$241$	−9.10171	−	15.7646i	−0.586292	−	1.01549i	0.408420	−	0.912794i	$-0.366080\pi$
$242$	−3.10270	−	5.37403i	−0.199449	−	0.345456i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−14.7423			−0.943781
$245$	11.7845	+	4.99406i	0.752882	+	0.319059i
$246$	7.33352			0.467568
$247$	−8.01401	+	13.8807i	−0.509919	+	0.883206i
$248$	−5.25955	−	9.10981i	−0.333982	−	0.578474i
$249$	−2.90240	−	5.02710i	−0.183932	−	0.318579i
$250$	6.08579	−	10.5409i	0.384899	−	0.666665i
$251$	−0.794604			−0.0501549			−0.0250775	−	0.999686i	$-0.507983\pi$
$251$	−0.794604			−0.0501549			−0.0250775	+	0.999686i	$0.507983\pi$
$252$	−1.75255	+	1.98206i	−0.110400	+	0.124858i
$253$	4.14794			0.260779
$254$	−3.24554	+	5.62144i	−0.203643	+	0.352721i
$255$	3.06916	+	5.31594i	0.192198	+	0.332897i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.295595	−	0.511985i	0.0184387	−	0.0319368i	−0.856659	−	0.515883i	$-0.827464\pi$
$257$	0.295595	−	0.511985i	0.0184387	−	0.0319368i	0.875098	+	0.483947i	$0.160797\pi$
$258$	5.36098			0.333760
$259$	0.871874	+	2.60322i	0.0541756	+	0.161756i
$260$	−3.99618			−0.247833
$261$	−2.59279	+	4.49085i	−0.160490	+	0.277976i
$262$	2.20441	+	3.81814i	0.136189	+	0.235886i
$263$	−1.43363	−	2.48312i	−0.0884012	−	0.153115i	0.818434	−	0.574600i	$-0.194842\pi$
$263$	−1.43363	−	2.48312i	−0.0884012	−	0.153115i	−0.906835	+	0.421485i	$0.861509\pi$
$264$	−2.07397	+	3.59222i	−0.127644	+	0.221086i
$265$	8.30607			0.510238
$266$	−19.0143	−	3.86270i	−1.16584	−	0.236837i
$267$	6.69450			0.409697
$268$	−6.70249	+	11.6091i	−0.409420	+	0.709136i
$269$	3.58897	+	6.21628i	0.218823	+	0.379013i	0.954449	−	0.298376i	$-0.0964448\pi$
$269$	3.58897	+	6.21628i	0.218823	+	0.379013i	−0.735625	+	0.677389i	$0.763111\pi$
$270$	−0.914214	−	1.58346i	−0.0556373	−	0.0963666i
$271$	5.25955	−	9.10981i	0.319495	−	0.553382i	−0.660888	−	0.750485i	$-0.729820\pi$
$271$	5.25955	−	9.10981i	0.319495	−	0.553382i	0.980383	+	0.197103i	$0.0631534\pi$
$272$	−3.35716			−0.203557
$273$	−5.66676	−	1.15119i	−0.342968	−	0.0696730i
$274$	1.68049			0.101522
$275$	3.43627	−	5.95179i	0.207215	−	0.358906i
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	15.4642	+	26.7848i	0.929156	+	1.60935i	0.784737	+	0.619829i	$0.212798\pi$
$277$	15.4642	+	26.7848i	0.929156	+	1.60935i	0.144419	+	0.989517i	$0.453869\pi$
$278$	6.65685	−	11.5300i	0.399252	−	0.691524i
$279$	10.5191			0.629762
$280$	−1.53633	−	4.58713i	−0.0918130	−	0.274133i
$281$	−2.09949			−0.125245			−0.0626225	−	0.998037i	$-0.519946\pi$
$281$	−2.09949			−0.125245			−0.0626225	+	0.998037i	$0.519946\pi$
$282$	−3.61161	+	6.25550i	−0.215068	+	0.372509i
$283$	−10.1738	−	17.6215i	−0.604768	−	1.04749i	−0.992088	−	0.125543i	$-0.959933\pi$
$283$	−10.1738	−	17.6215i	−0.604768	−	1.04749i	0.387321	−	0.921945i	$-0.373401\pi$
$284$	−7.09279	−	12.2851i	−0.420880	−	0.728985i
$285$	6.70441	−	11.6124i	0.397135	−	0.687857i
$286$	−9.06566			−0.536064
$287$	−12.8523	+	14.5355i	−0.758650	+	0.858004i
$288$	1.00000			0.0589256
$289$	2.86475	−	4.96190i	0.168515	−	0.291876i
$290$	−4.74073	−	8.21119i	−0.278385	−	0.482177i
$291$	2.23564	+	3.87223i	0.131055	+	0.226994i
$292$	−5.75955	+	9.97584i	−0.337052	+	0.583792i
$293$	−31.4853			−1.83939			−0.919695	−	0.392634i	$-0.871564\pi$
$293$	−31.4853			−1.83939			−0.919695	+	0.392634i	$0.871564\pi$
$294$	−0.857156	−	6.94732i	−0.0499903	−	0.405176i
$295$	−0.861685			−0.0501693
$296$	0.518822	−	0.898626i	0.0301559	−	0.0522316i
$297$	−2.07397	−	3.59222i	−0.120344	−	0.208442i
$298$	−9.67886	−	16.7643i	−0.560681	−	0.971129i
$299$	1.09279	−	1.89277i	0.0631978	−	0.109462i
$300$	−1.65685			−0.0956585
$301$	−9.39537	+	10.6258i	−0.541540	+	0.612461i
$302$	5.58420			0.321335
$303$	−7.65303	+	13.2554i	−0.439655	+	0.761505i
$304$	3.66676	+	6.35102i	0.210303	+	0.364256i
$305$	13.4776	+	23.3440i	0.771727	+	1.33667i
$306$	1.67858	−	2.90738i	0.0959579	−	0.166204i
$307$	1.64865			0.0940933			0.0470466	−	0.998893i	$-0.485019\pi$
$307$	1.64865			0.0940933			0.0470466	+	0.998893i	$0.485019\pi$
$308$	−3.48528	−	10.4063i	−0.198592	−	0.592953i
$309$	7.40499			0.421255
$310$	−9.61671	+	16.6566i	−0.546192	+	0.946033i
$311$	−6.08897	−	10.5464i	−0.345274	−	0.598032i	0.640130	−	0.768267i	$-0.278881\pi$
$311$	−6.08897	−	10.5464i	−0.345274	−	0.598032i	−0.985403	+	0.170235i	$0.945547\pi$
$312$	1.09279	+	1.89277i	0.0618671	+	0.107157i
$313$	−6.28347	+	10.8833i	−0.355163	+	0.615160i	−0.987146	−	0.159822i	$-0.948908\pi$
$313$	−6.28347	+	10.8833i	−0.355163	+	0.615160i	0.631983	+	0.774982i	$0.282241\pi$
$314$	−22.7902			−1.28612
$315$	4.74073	+	0.963066i	0.267110	+	0.0542626i
$316$	−5.18558			−0.291712
$317$	4.58897	−	7.94833i	0.257742	−	0.446423i	−0.707894	−	0.706318i	$-0.750355\pi$
$317$	4.58897	−	7.94833i	0.257742	−	0.446423i	0.965637	+	0.259895i	$0.0836881\pi$
$318$	−2.27137	−	3.93413i	−0.127372	−	0.220615i
$319$	−10.7547	−	18.6278i	−0.602150	−	1.04295i
$320$	−0.914214	+	1.58346i	−0.0511061	+	0.0885183i
$321$	−5.50127			−0.307051
$322$	2.59279	+	0.526718i	0.144491	+	0.0293529i
$323$	24.6198			1.36988
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.81060	−	3.13604i	−0.100434	−	0.173956i
$326$	12.7184	+	22.0289i	0.704408	+	1.22007i
$327$	9.34753	−	16.1904i	0.516920	−	0.895331i
$328$	7.33352			0.404926
$329$	−6.06927	−	18.1215i	−0.334610	−	0.999071i
$330$	7.58420			0.417497
$331$	14.6948	−	25.4521i	0.807698	−	1.39897i	−0.106756	−	0.994285i	$-0.534046\pi$
$331$	14.6948	−	25.4521i	0.807698	−	1.39897i	0.914454	−	0.404689i	$-0.132620\pi$
$332$	−2.90240	−	5.02710i	−0.159290	−	0.275898i
$333$	0.518822	+	0.898626i	0.0284313	+	0.0492444i
$334$	11.0593	−	19.1552i	0.605135	−	1.04813i
$335$	24.5100			1.33913
$336$	−1.75255	+	1.98206i	−0.0956093	+	0.108130i
$337$	8.12048			0.442351			0.221175	−	0.975234i	$-0.429011\pi$
$337$	8.12048			0.442351			0.221175	+	0.975234i	$0.429011\pi$
$338$	4.11161	−	7.12152i	0.223642	−	0.387360i
$339$	−2.64093	−	4.57423i	−0.143436	−	0.248438i
$340$	3.06916	+	5.31594i	0.166448	+	0.288297i
$341$	−21.8163	+	37.7869i	−1.18142	+	2.04628i
$342$	−7.33352			−0.396551
$343$	15.2722	+	10.4766i	0.824624	+	0.565682i
$344$	5.36098			0.289044
$345$	−0.914214	+	1.58346i	−0.0492196	+	0.0852509i
$346$	6.84244	+	11.8514i	0.367852	+	0.637138i
$347$	−14.1307	−	24.4751i	−0.758577	−	1.31389i	−0.943576	−	0.331155i	$-0.892562\pi$
$347$	−14.1307	−	24.4751i	−0.758577	−	1.31389i	0.185000	−	0.982739i	$-0.440772\pi$
$348$	−2.59279	+	4.49085i	−0.138988	+	0.240735i
$349$	24.1307			1.29169			0.645843	−	0.763471i	$-0.276506\pi$
$349$	24.1307			1.29169			0.645843	+	0.763471i	$0.276506\pi$
$350$	2.90372	−	3.28399i	0.155210	−	0.175537i
$351$	−2.18558			−0.116658
$352$	−2.07397	+	3.59222i	−0.110543	+	0.191466i
$353$	−6.70441	−	11.6124i	−0.356839	−	0.618064i	0.630592	−	0.776115i	$-0.282812\pi$
$353$	−6.70441	−	11.6124i	−0.356839	−	0.618064i	−0.987431	+	0.158051i	$0.949479\pi$
$354$	0.235636	+	0.408133i	0.0125239	+	0.0216920i
$355$	−12.9687	+	22.4624i	−0.688305	+	1.19218i
$356$	6.69450			0.354808
$357$	2.82083	+	8.42237i	0.149294	+	0.445759i
$358$	−2.77677			−0.146757
$359$	1.94254	−	3.36458i	0.102523	−	0.177576i	−0.810200	−	0.586153i	$-0.800642\pi$
$359$	1.94254	−	3.36458i	0.102523	−	0.177576i	0.912724	+	0.408577i	$0.133975\pi$
$360$	−0.914214	−	1.58346i	−0.0481833	−	0.0834559i
$361$	−17.3903	−	30.1208i	−0.915277	−	1.58531i
$362$	10.4815	−	18.1544i	0.550893	−	0.954175i
$363$	6.20540			0.325699
$364$	−5.66676	−	1.15119i	−0.297019	−	0.0603386i
$365$	21.0618			1.10243
$366$	7.37117	−	12.7672i	0.385297	−	0.667354i
$367$	0.718724	+	1.24487i	0.0375171	+	0.0649815i	0.884174	−	0.467157i	$-0.154722\pi$
$367$	0.718724	+	1.24487i	0.0375171	+	0.0649815i	−0.846657	+	0.532139i	$0.821388\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	−3.66676	+	6.35102i	−0.190884	+	0.330621i
$370$	−1.89726			−0.0986337
$371$	11.7784	+	2.39274i	0.611503	+	0.124225i
$372$	10.5191			0.545390
$373$	−9.14794	+	15.8447i	−0.473662	+	0.820407i	−0.999545	−	0.0301497i	$-0.990402\pi$
$373$	−9.14794	+	15.8447i	−0.473662	+	0.820407i	0.525883	+	0.850557i	$0.323735\pi$
$374$	6.96264	+	12.0596i	0.360029	+	0.623589i
$375$	6.08579	+	10.5409i	0.314269	+	0.544329i
$376$	−3.61161	+	6.25550i	−0.186255	+	0.322603i
$377$	−11.3335			−0.583706
$378$	−0.840244	−	2.50878i	−0.0432175	−	0.129038i
$379$	−5.97637			−0.306985			−0.153493	−	0.988150i	$-0.549052\pi$
$379$	−5.97637			−0.306985			−0.153493	+	0.988150i	$0.549052\pi$
$380$	6.70441	−	11.6124i	0.343929	−	0.595702i
$381$	−3.24554	−	5.62144i	−0.166274	−	0.287995i
$382$	4.48118	+	7.76163i	0.229277	+	0.397119i
$383$	2.94863	−	5.10717i	0.150668	−	0.260964i	−0.780805	−	0.624774i	$-0.785191\pi$
$383$	2.94863	−	5.10717i	0.150668	−	0.260964i	0.931473	+	0.363810i	$0.118524\pi$
$384$	1.00000			0.0510310
$385$	−13.2917	+	15.0324i	−0.677407	+	0.766121i
$386$	11.6390			0.592411
$387$	−2.68049	+	4.64274i	−0.136257	+	0.236004i
$388$	2.23564	+	3.87223i	0.113497	+	0.196583i
$389$	8.55675	+	14.8207i	0.433844	+	0.751441i	0.997201	−	0.0747736i	$-0.0238234\pi$
$389$	8.55675	+	14.8207i	0.433844	+	0.751441i	−0.563356	+	0.826214i	$0.690490\pi$
$390$	1.99809	−	3.46079i	0.101177	−	0.175244i
$391$	−3.35716			−0.169779
$392$	−0.857156	−	6.94732i	−0.0432929	−	0.350893i
$393$	−4.40881			−0.222395
$394$	−4.79078	+	8.29788i	−0.241356	+	0.418041i
$395$	4.74073	+	8.21119i	0.238532	+	0.413150i
$396$	−2.07397	−	3.59222i	−0.104221	−	0.180516i
$397$	6.42249	−	11.1241i	0.322336	−	0.558302i	−0.658634	−	0.752464i	$-0.728865\pi$
$397$	6.42249	−	11.1241i	0.322336	−	0.558302i	0.980970	+	0.194162i	$0.0621987\pi$
$398$	−9.95273			−0.498885
$399$	12.8523	−	14.5355i	0.643422	−	0.727686i
$400$	−1.65685			−0.0828427
$401$	−8.71650	+	15.0974i	−0.435281	+	0.753930i	−0.997319	−	0.0731824i	$-0.976684\pi$
$401$	−8.71650	+	15.0974i	−0.435281	+	0.753930i	0.562037	+	0.827112i	$0.310018\pi$
$402$	−6.70249	−	11.6091i	−0.334290	−	0.579007i
$403$	11.4952	+	19.9102i	0.572616	+	0.991800i
$404$	−7.65303	+	13.2554i	−0.380753	+	0.659483i
$405$	1.82843			0.0908553
$406$	−4.35716	−	13.0095i	−0.216242	−	0.645651i
$407$	−4.30408			−0.213346
$408$	1.67858	−	2.90738i	0.0831020	−	0.143937i
$409$	4.53382	+	7.85281i	0.224183	+	0.388297i	0.956074	−	0.293125i	$-0.0946953\pi$
$409$	4.53382	+	7.85281i	0.224183	+	0.388297i	−0.731891	+	0.681422i	$0.761362\pi$
$410$	−6.70441	−	11.6124i	−0.331107	−	0.573494i
$411$	−0.840244	+	1.45535i	−0.0414462	+	0.0717869i
$412$	7.40499			0.364818
$413$	−1.22191	−	0.248227i	−0.0601262	−	0.0122145i
$414$	1.00000			0.0491473
$415$	−5.30682	+	9.19168i	−0.260502	+	0.451202i
$416$	1.09279	+	1.89277i	0.0535785	+	0.0928007i
$417$	6.65685	+	11.5300i	0.325988	+	0.564627i
$418$	15.2095	−	26.3436i	0.743921	−	1.28851i
$419$	−6.63902			−0.324338			−0.162169	−	0.986763i	$-0.551849\pi$
$419$	−6.63902			−0.324338			−0.162169	+	0.986763i	$0.551849\pi$
$420$	4.74073	+	0.963066i	0.231324	+	0.0469928i
$421$	−0.942543			−0.0459367			−0.0229684	−	0.999736i	$-0.507312\pi$
$421$	−0.942543			−0.0459367			−0.0229684	+	0.999736i	$0.507312\pi$
$422$	−0.151760	+	0.262855i	−0.00738754	+	0.0127956i
$423$	−3.61161	−	6.25550i	−0.175603	−	0.304153i
$424$	−2.27137	−	3.93413i	−0.110307	−	0.191058i
$425$	−2.78116	+	4.81711i	−0.134906	+	0.233664i
$426$	14.1856			0.687294
$427$	12.3872	+	36.9853i	0.599457	+	1.78984i
$428$	−5.50127			−0.265914
$429$	4.53283	−	7.85110i	0.218847	−	0.379054i
$430$	−4.90108	−	8.48892i	−0.236351	−	0.409372i
$431$	17.6849	+	30.6311i	0.851850	+	1.47545i	0.879536	+	0.475832i	$0.157853\pi$
$431$	17.6849	+	30.6311i	0.851850	+	1.47545i	−0.0276860	+	0.999617i	$0.508814\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	32.7627			1.57448			0.787238	−	0.616650i	$-0.211510\pi$
$433$	32.7627			1.57448			0.787238	+	0.616650i	$0.211510\pi$
$434$	−18.4352	+	20.8495i	−0.884919	+	1.00081i
$435$	9.48146			0.454601
$436$	9.34753	−	16.1904i	0.447666	−	0.775380i
$437$	3.66676	+	6.35102i	0.175405	+	0.303810i
$438$	−5.75955	−	9.97584i	−0.275202	−	0.476664i
$439$	9.65817	−	16.7284i	0.460959	−	0.798405i	−0.538050	−	0.842913i	$-0.680839\pi$
$439$	9.65817	−	16.7284i	0.460959	−	0.798405i	0.999009	+	0.0445080i	$0.0141720\pi$
$440$	7.58420			0.361563
$441$	6.44514	+	2.73134i	0.306911	+	0.130064i
$442$	7.33734			0.349002
$443$	−7.20441	+	12.4784i	−0.342292	+	0.592866i	−0.984858	−	0.173364i	$-0.944536\pi$
$443$	−7.20441	+	12.4784i	−0.342292	+	0.592866i	0.642566	+	0.766230i	$0.277870\pi$
$444$	0.518822	+	0.898626i	0.0246222	+	0.0426469i
$445$	−6.12020	−	10.6005i	−0.290125	−	0.502512i
$446$	8.46877	−	14.6683i	0.401008	−	0.694566i
$447$	19.3577			0.915589
$448$	−1.75255	+	1.98206i	−0.0828001	+	0.0936437i
$449$	−11.0580			−0.521860			−0.260930	−	0.965358i	$-0.584029\pi$
$449$	−11.0580			−0.521860			−0.260930	+	0.965358i	$0.584029\pi$
$450$	0.828427	−	1.43488i	0.0390524	−	0.0676408i
$451$	−15.2095	−	26.3436i	−0.716187	−	1.24047i
$452$	−2.64093	−	4.57423i	−0.124219	−	0.215154i
$453$	−2.79210	+	4.83606i	−0.131184	+	0.227218i
$454$	−21.5369			−1.01078
$455$	3.35777	+	10.0255i	0.157415	+	0.470005i
$456$	−7.33352			−0.343424
$457$	12.9225	−	22.3824i	0.604489	−	1.04701i	−0.387643	−	0.921809i	$-0.626711\pi$
$457$	12.9225	−	22.3824i	0.604489	−	1.04701i	0.992132	−	0.125196i	$-0.0399559\pi$
$458$	0.333239	+	0.577187i	0.0155712	+	0.0269702i
$459$	1.67858	+	2.90738i	0.0783493	+	0.135705i
$460$	−0.914214	+	1.58346i	−0.0426254	+	0.0738294i
$461$	−39.3341			−1.83197			−0.915986	−	0.401211i	$-0.868589\pi$
$461$	−39.3341			−1.83197			−0.915986	+	0.401211i	$0.868589\pi$
$462$	10.7547	+	2.18480i	0.500356	+	0.101646i
$463$	25.0778			1.16547			0.582733	−	0.812664i	$-0.301983\pi$
$463$	25.0778			1.16547			0.582733	+	0.812664i	$0.301983\pi$
$464$	−2.59279	+	4.49085i	−0.120367	+	0.208482i
$465$	−9.61671	−	16.6566i	−0.445964	−	0.772433i
$466$	0.838334	+	1.45204i	0.0388351	+	0.0672643i
$467$	11.4815	−	19.8865i	0.531299	−	0.920236i	−0.468034	−	0.883710i	$-0.655038\pi$
$467$	11.4815	−	19.8865i	0.531299	−	0.920236i	0.999333	−	0.0365258i	$-0.0116291\pi$
$468$	−2.18558			−0.101029
$469$	34.7563	+	7.06066i	1.60490	+	0.326031i
$470$	13.2071			0.609200
$471$	11.3951	−	19.7369i	0.525058	−	0.909427i
$472$	0.235636	+	0.408133i	0.0108460	+	0.0187858i
$473$	−11.1185	−	19.2578i	−0.511229	−	0.885475i
$474$	2.59279	−	4.49085i	0.119091	−	0.206271i
$475$	12.1506			0.557507
$476$	2.82083	+	8.42237i	0.129293	+	0.386039i
$477$	4.54274			0.207998
$478$	−5.36098	+	9.28548i	−0.245205	+	0.424708i
$479$	8.30578	+	14.3860i	0.379501	+	0.657315i	0.990990	−	0.133938i	$-0.0427624\pi$
$479$	8.30578	+	14.3860i	0.379501	+	0.657315i	−0.611489	+	0.791253i	$0.709429\pi$
$480$	−0.914214	−	1.58346i	−0.0417279	−	0.0722749i
$481$	−1.13393	+	1.96402i	−0.0517027	+	0.0895517i
$482$	18.2034			0.829143
$483$	−1.75255	+	1.98206i	−0.0797437	+	0.0901870i
$484$	6.20540			0.282063
$485$	4.08770	−	7.08010i	0.185613	−	0.321491i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	7.41131	+	12.8368i	0.335839	+	0.581690i	0.983646	−	0.180115i	$-0.0576470\pi$
$487$	7.41131	+	12.8368i	0.335839	+	0.581690i	−0.647807	+	0.761805i	$0.724314\pi$
$488$	7.37117	−	12.7672i	0.333677	−	0.577946i
$489$	−25.4368			−1.15029
$490$	−10.2172	+	7.70861i	−0.461567	+	0.348240i
$491$	22.2466			1.00398			0.501988	−	0.864875i	$-0.332602\pi$
$491$	22.2466			1.00398			0.501988	+	0.864875i	$0.332602\pi$
$492$	−3.66676	+	6.35102i	−0.165310	+	0.286326i
$493$	8.70441	+	15.0765i	0.392027	+	0.679010i
$494$	−8.01401	−	13.8807i	−0.360567	−	0.624521i
$495$	−3.79210	+	6.56811i	−0.170442	+	0.295215i
$496$	10.5191			0.472322
$497$	−24.8609	+	28.1167i	−1.11516	+	1.26121i
$498$	5.80479			0.260119
$499$	5.64284	−	9.77369i	0.252608	−	0.437531i	−0.711635	−	0.702550i	$-0.752045\pi$
$499$	5.64284	−	9.77369i	0.252608	−	0.437531i	0.964243	+	0.265019i	$0.0853782\pi$
$500$	6.08579	+	10.5409i	0.272165	+	0.471403i
$501$	11.0593	+	19.1552i	0.494091	+	0.855791i
$502$	0.397302	−	0.688147i	0.0177325	−	0.0307135i
$503$	27.1339			1.20984			0.604920	−	0.796286i	$-0.293205\pi$
$503$	27.1339			1.20984			0.604920	+	0.796286i	$0.293205\pi$
$504$	−0.840244	−	2.50878i	−0.0374274	−	0.111750i
$505$	27.9860			1.24536
$506$	−2.07397	+	3.59222i	−0.0921992	+	0.159694i
$507$	4.11161	+	7.12152i	0.182603	+	0.316278i
$508$	−3.24554	−	5.62144i	−0.143998	−	0.249411i
$509$	19.3976	−	33.5976i	0.859783	−	1.48919i	−0.0123530	−	0.999924i	$-0.503932\pi$
$509$	19.3976	−	33.5976i	0.859783	−	1.48919i	0.872136	−	0.489264i	$-0.162734\pi$
$510$	−6.13831			−0.271809
$511$	29.8666	+	6.06733i	1.32122	+	0.268403i
$512$	1.00000			0.0441942
$513$	3.66676	−	6.35102i	0.161891	−	0.280404i
$514$	0.295595	+	0.511985i	0.0130381	+	0.0225827i
$515$	−6.76974	−	11.7255i	−0.298310	−	0.516689i
$516$	−2.68049	+	4.64274i	−0.118002	+	0.204385i
$517$	29.9615			1.31771
$518$	−2.69039	−	0.546546i	−0.118209	−	0.0240139i
$519$	−13.6849			−0.600699
$520$	1.99809	−	3.46079i	0.0876220	−	0.151766i
$521$	−0.764956	−	1.32494i	−0.0335133	−	0.0580468i	0.848782	−	0.528743i	$-0.177336\pi$
$521$	−0.764956	−	1.32494i	−0.0335133	−	0.0580468i	−0.882296	+	0.470696i	$0.844003\pi$
$522$	−2.59279	−	4.49085i	−0.113483	−	0.196559i
$523$	−4.21141	+	7.29438i	−0.184152	+	0.318961i	−0.943290	−	0.331968i	$-0.892287\pi$
$523$	−4.21141	+	7.29438i	−0.184152	+	0.318961i	0.759138	+	0.650929i	$0.225621\pi$
$524$	−4.40881			−0.192600
$525$	1.39216	+	4.15669i	0.0607589	+	0.181413i
$526$	2.86725			0.125018
$527$	17.6571	−	30.5831i	0.769157	−	1.33222i
$528$	−2.07397	−	3.59222i	−0.0902579	−	0.156331i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−4.15303	+	7.19326i	−0.180396	+	0.312455i
$531$	−0.471271			−0.0204514
$532$	12.8523	−	14.5355i	0.557220	−	0.630194i
$533$	−16.0280			−0.694251
$534$	−3.34725	+	5.79761i	−0.144850	+	0.250887i
$535$	5.02934	+	8.71107i	0.217437	+	0.376612i
$536$	−6.70249	−	11.6091i	−0.289504	−	0.501435i
$537$	1.38839	−	2.40476i	0.0599133	−	0.103773i
$538$	−7.17794			−0.309463
$539$	−23.1786	+	17.4876i	−0.998373	+	0.753245i
$540$	1.82843			0.0786830
$541$	2.82692	−	4.89636i	0.121539	−	0.210511i	−0.798836	−	0.601549i	$-0.794551\pi$
$541$	2.82692	−	4.89636i	0.121539	−	0.210511i	0.920375	+	0.391038i	$0.127884\pi$
$542$	5.25955	+	9.10981i	0.225917	+	0.391300i
$543$	10.4815	+	18.1544i	0.449803	+	0.779081i
$544$	1.67858	−	2.90738i	0.0719684	−	0.124653i
$545$	−34.1826			−1.46422
$546$	3.83034	−	4.33197i	0.163923	−	0.185391i
$547$	−26.2480			−1.12229			−0.561143	−	0.827719i	$-0.689638\pi$
$547$	−26.2480			−1.12229			−0.561143	+	0.827719i	$0.689638\pi$
$548$	−0.840244	+	1.45535i	−0.0358935	+	0.0621693i
$549$	7.37117	+	12.7672i	0.314594	+	0.544892i
$550$	3.43627	+	5.95179i	0.146523	+	0.253785i
$551$	19.0143	−	32.9337i	0.810036	−	1.40302i
$552$	1.00000			0.0425628
$553$	4.35716	+	13.0095i	0.185285	+	0.553220i
$554$	−30.9285			−1.31403
$555$	0.948628	−	1.64307i	0.0402670	−	0.0697445i
$556$	6.65685	+	11.5300i	0.282314	+	0.488981i
$557$	−18.6211	−	32.2527i	−0.789001	−	1.36659i	−0.926579	−	0.376099i	$-0.877265\pi$
$557$	−18.6211	−	32.2527i	−0.789001	−	1.36659i	0.137578	−	0.990491i	$-0.456068\pi$
$558$	−5.25955	+	9.10981i	−0.222655	+	0.385649i
$559$	−11.7169			−0.495570
$560$	4.74073	+	0.963066i	0.200332	+	0.0406970i
$561$	−13.9253			−0.587926
$562$	1.04974	−	1.81821i	0.0442808	−	0.0766965i
$563$	−6.74483	−	11.6824i	−0.284261	−	0.492354i	0.688169	−	0.725551i	$-0.258415\pi$
$563$	−6.74483	−	11.6824i	−0.284261	−	0.492354i	−0.972430	+	0.233196i	$0.925082\pi$
$564$	−3.61161	−	6.25550i	−0.152076	−	0.263404i
$565$	−4.82875	+	8.36365i	−0.203147	+	0.351861i
$566$	20.3475			0.855271
$567$	2.59279	+	0.526718i	0.108887	+	0.0221201i
$568$	14.1856			0.595214
$569$	8.36897	−	14.4955i	0.350846	−	0.607682i	−0.635552	−	0.772058i	$-0.719228\pi$
$569$	8.36897	−	14.4955i	0.350846	−	0.607682i	0.986398	+	0.164375i	$0.0525609\pi$
$570$	6.70441	+	11.6124i	0.280817	+	0.486389i
$571$	13.0836	+	22.6614i	0.547530	+	0.948350i	0.998443	+	0.0557822i	$0.0177652\pi$
$571$	13.0836	+	22.6614i	0.547530	+	0.948350i	−0.450913	+	0.892568i	$0.648901\pi$
$572$	4.53283	−	7.85110i	0.189527	−	0.328271i
$573$	−8.96236			−0.374408
$574$	−6.16195	−	18.3982i	−0.257195	−	0.767926i
$575$	−1.65685			−0.0690956
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−9.89858	−	17.1448i	−0.412083	−	0.713749i	0.583034	−	0.812448i	$-0.301865\pi$
$577$	−9.89858	−	17.1448i	−0.412083	−	0.713749i	−0.995117	+	0.0986987i	$0.968532\pi$
$578$	2.86475	+	4.96190i	0.119158	+	0.206388i
$579$	−5.81951	+	10.0797i	−0.241851	+	0.418898i
$580$	9.48146			0.393696
$581$	−10.1732	+	11.5055i	−0.422054	+	0.477327i
$582$	−4.47127			−0.185340
$583$	−9.42150	+	16.3185i	−0.390199	+	0.675844i
$584$	−5.75955	−	9.97584i	−0.238332	−	0.412803i
$585$	1.99809	+	3.46079i	0.0826108	+	0.143086i
$586$	15.7426	−	27.2671i	0.650322	−	1.12639i
$587$	−3.20078			−0.132110			−0.0660551	−	0.997816i	$-0.521041\pi$
$587$	−3.20078			−0.132110			−0.0660551	+	0.997816i	$0.521041\pi$
$588$	6.44514	+	2.73134i	0.265793	+	0.112639i
$589$	−77.1421			−3.17858
$590$	0.430843	−	0.746241i	0.0177375	−	0.0307223i
$591$	−4.79078	−	8.29788i	−0.197066	−	0.341329i
$592$	0.518822	+	0.898626i	0.0213235	+	0.0369333i
$593$	16.0517	−	27.8023i	0.659162	−	1.14170i	−0.321670	−	0.946852i	$-0.604244\pi$
$593$	16.0517	−	27.8023i	0.659162	−	1.14170i	0.980833	−	0.194851i	$-0.0624224\pi$
$594$	4.14794			0.170192
$595$	10.7577	−	12.1665i	0.441022	−	0.498779i
$596$	19.3577			0.792923
$597$	4.97637	−	8.61932i	0.203669	−	0.352765i
$598$	1.09279	+	1.89277i	0.0446876	+	0.0774011i
$599$	−22.5921	−	39.1306i	−0.923087	−	1.59883i	−0.794608	−	0.607122i	$-0.792324\pi$
$599$	−22.5921	−	39.1306i	−0.923087	−	1.59883i	−0.128479	−	0.991712i	$-0.541009\pi$
$600$	0.828427	−	1.43488i	0.0338204	−	0.0585786i
$601$	15.5166			0.632934			0.316467	−	0.948604i	$-0.397503\pi$
$601$	15.5166			0.632934			0.316467	+	0.948604i	$0.397503\pi$
$602$	−4.50453	−	13.4495i	−0.183591	−	0.548162i
$603$	13.4050			0.545893
$604$	−2.79210	+	4.83606i	−0.113609	+	0.196777i
$605$	−5.67306	−	9.82602i	−0.230643	−	0.399485i
$606$	−7.65303	−	13.2554i	−0.310883	−	0.538466i
$607$	−2.43113	+	4.21083i	−0.0986763	+	0.170912i	−0.911137	−	0.412104i	$-0.864794\pi$
$607$	−2.43113	+	4.21083i	−0.0986763	+	0.170912i	0.812461	+	0.583016i	$0.198128\pi$
$608$	−7.33352			−0.297414
$609$	13.4451	+	2.73134i	0.544824	+	0.110680i
$610$	−26.9553			−1.09139
$611$	7.89348	−	13.6719i	0.319336	−	0.553106i
$612$	1.67858	+	2.90738i	0.0678525	+	0.117524i
$613$	−3.40499	−	5.89761i	−0.137526	−	0.238202i	0.789033	−	0.614350i	$-0.210582\pi$
$613$	−3.40499	−	5.89761i	−0.137526	−	0.238202i	−0.926560	+	0.376148i	$0.877248\pi$
$614$	−0.824324	+	1.42777i	−0.0332670	+	0.0576201i
$615$	13.4088			0.540695
$616$	10.7547	+	2.18480i	0.433321	+	0.0880279i
$617$	7.70087			0.310025			0.155013	−	0.987912i	$-0.450458\pi$
$617$	7.70087			0.310025			0.155013	+	0.987912i	$0.450458\pi$
$618$	−3.70249	+	6.41291i	−0.148936	+	0.257965i
$619$	−1.56828	−	2.71635i	−0.0630346	−	0.109179i	0.832786	−	0.553595i	$-0.186745\pi$
$619$	−1.56828	−	2.71635i	−0.0630346	−	0.109179i	−0.895820	+	0.444416i	$0.853411\pi$
$620$	−9.61671	−	16.6566i	−0.386216	−	0.668946i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	12.1779			0.488291
$623$	−5.62501	−	16.7950i	−0.225361	−	0.672879i
$624$	−2.18558			−0.0874933
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	−6.28347	−	10.8833i	−0.251138	−	0.434984i
$627$	15.2095	+	26.3436i	0.607409	+	1.05206i
$628$	11.3951	−	19.7369i	0.454713	−	0.787587i
$629$	3.48353			0.138898
$630$	−3.20441	+	3.62406i	−0.127667	+	0.144386i
$631$	−22.1045			−0.879966			−0.439983	−	0.898006i	$-0.645016\pi$
$631$	−22.1045			−0.879966			−0.439983	+	0.898006i	$0.645016\pi$
$632$	2.59279	−	4.49085i	0.103136	−	0.178636i
$633$	−0.151760	−	0.262855i	−0.00603190	−	0.0104476i
$634$	4.58897	+	7.94833i	0.182251	+	0.315669i
$635$	−5.93424	+	10.2784i	−0.235493	+	0.407886i
$636$	4.54274			0.180131
$637$	1.87339	+	15.1839i	0.0742262	+	0.601610i
$638$	21.5095			0.851568
$639$	−7.09279	+	12.2851i	−0.280586	+	0.485990i
$640$	−0.914214	−	1.58346i	−0.0361375	−	0.0625919i
$641$	9.27415	+	16.0633i	0.366307	+	0.634462i	0.988985	−	0.148016i	$-0.0472886\pi$
$641$	9.27415	+	16.0633i	0.366307	+	0.634462i	−0.622678	+	0.782478i	$0.713955\pi$
$642$	2.75064	−	4.76424i	0.108559	−	0.188030i
$643$	−12.4114			−0.489456			−0.244728	−	0.969592i	$-0.578699\pi$
$643$	−12.4114			−0.489456			−0.244728	+	0.969592i	$0.578699\pi$
$644$	−1.75255	+	1.98206i	−0.0690600	+	0.0781043i
$645$	9.80216			0.385959
$646$	−12.3099	+	21.3214i	−0.484326	+	0.838877i
$647$	−18.9101	−	32.7532i	−0.743432	−	1.28766i	−0.950924	−	0.309425i	$-0.899863\pi$
$647$	−18.9101	−	32.7532i	−0.743432	−	1.28766i	0.207492	−	0.978237i	$-0.433470\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	0.977402	−	1.69291i	0.0383664	−	0.0664525i
$650$	3.62119			0.142035
$651$	−8.83862	−	26.3901i	−0.346413	−	1.03431i
$652$	−25.4368			−0.996183
$653$	−9.75474	+	16.8957i	−0.381732	+	0.661180i	−0.991310	−	0.131546i	$-0.958006\pi$
$653$	−9.75474	+	16.8957i	−0.381732	+	0.661180i	0.609578	+	0.792726i	$0.291339\pi$
$654$	9.34753	+	16.1904i	0.365517	+	0.633095i
$655$	4.03059	+	6.98119i	0.157488	+	0.272778i
$656$	−3.66676	+	6.35102i	−0.143163	+	0.247966i
$657$	11.5191			0.449403
$658$	18.7283	+	3.80461i	0.730106	+	0.148319i
$659$	−33.6772			−1.31188			−0.655939	−	0.754814i	$-0.727727\pi$
$659$	−33.6772			−1.31188			−0.655939	+	0.754814i	$0.727727\pi$
$660$	−3.79210	+	6.56811i	−0.147607	+	0.255663i
$661$	−13.6983	−	23.7262i	−0.532803	−	0.922842i	−0.999266	−	0.0383011i	$-0.987805\pi$
$661$	−13.6983	−	23.7262i	−0.532803	−	0.922842i	0.466463	−	0.884541i	$-0.345528\pi$
$662$	14.6948	+	25.4521i	0.571129	+	0.989224i
$663$	−3.66867	+	6.35433i	−0.142479	+	0.246782i
$664$	5.80479			0.225270
$665$	−34.7662	−	7.06267i	−1.34818	−	0.273879i
$666$	−1.03764			−0.0402079
$667$	−2.59279	+	4.49085i	−0.100393	+	0.173886i
$668$	11.0593	+	19.1552i	0.427895	+	0.741136i
$669$	8.46877	+	14.6683i	0.327422	+	0.567111i
$670$	−12.2550	+	21.2263i	−0.473453	+	0.820044i
$671$	−61.1503			−2.36068
$672$	−0.840244	−	2.50878i	−0.0324131	−	0.0967784i
$673$	7.79715			0.300558			0.150279	−	0.988644i	$-0.451983\pi$
$673$	7.79715			0.300558			0.150279	+	0.988644i	$0.451983\pi$
$674$	−4.06024	+	7.03255i	−0.156395	+	0.270884i
$675$	0.828427	+	1.43488i	0.0318862	+	0.0552285i
$676$	4.11161	+	7.12152i	0.158139	+	0.273905i
$677$	0.0283290	−	0.0490673i	0.00108877	−	0.00188581i	−0.865481	−	0.500943i	$-0.832987\pi$
$677$	0.0283290	−	0.0490673i	0.00108877	−	0.00188581i	0.866569	+	0.499057i	$0.166320\pi$
$678$	5.28187			0.202849
$679$	7.83611	−	8.86235i	0.300722	−	0.340106i
$680$	−6.13831			−0.235394
$681$	10.7685	−	18.6515i	0.412649	−	0.714728i
$682$	−21.8163	−	37.7869i	−0.835389	−	1.44694i
$683$	17.9817	+	31.1453i	0.688052	+	1.19174i	0.972467	+	0.233040i	$0.0748674\pi$
$683$	17.9817	+	31.1453i	0.688052	+	1.19174i	−0.284415	+	0.958701i	$0.591799\pi$
$684$	3.66676	−	6.35102i	0.140202	−	0.242837i
$685$	3.07265			0.117400
$686$	−16.7091	+	7.98786i	−0.637956	+	0.304978i
$687$	−0.666478			−0.0254277
$688$	−2.68049	+	4.64274i	−0.102193	+	0.177003i
$689$	4.96427	+	8.59836i	0.189123	+	0.327571i
$690$	−0.914214	−	1.58346i	−0.0348035	−	0.0602815i
$691$	11.0181	−	19.0839i	0.419149	−	0.725987i	−0.576705	−	0.816952i	$-0.695662\pi$
$691$	11.0181	−	19.0839i	0.419149	−	0.725987i	0.995854	+	0.0909653i	$0.0289952\pi$
$692$	−13.6849			−0.520221
$693$	−7.26946	+	8.22148i	−0.276144	+	0.312308i
$694$	28.2614			1.07279
$695$	12.1716	−	21.0818i	0.461694	−	0.799678i
$696$	−2.59279	−	4.49085i	−0.0982795	−	0.170225i
$697$	12.3099	+	21.3214i	0.466270	+	0.807604i
$698$	−12.0653	+	20.8978i	−0.456680	+	0.790992i
$699$	−1.67667			−0.0634174
$700$	1.39216	+	4.15669i	0.0526188	+	0.157108i
$701$	37.5337			1.41763			0.708814	−	0.705396i	$-0.249231\pi$
$701$	37.5337			1.41763			0.708814	+	0.705396i	$0.249231\pi$
$702$	1.09279	−	1.89277i	0.0412448	−	0.0714380i
$703$	−3.80479	−	6.59009i	−0.143500	−	0.248550i
$704$	−2.07397	−	3.59222i	−0.0781657	−	0.135387i
$705$	−6.60357	+	11.4377i	−0.248705	+	0.430770i
$706$	13.4088			0.504647
$707$	39.6854	+	8.06199i	1.49252	+	0.303202i
$708$	−0.471271			−0.0177115
$709$	−20.4894	+	35.4887i	−0.769495	+	1.33280i	0.168342	+	0.985729i	$0.446159\pi$
$709$	−20.4894	+	35.4887i	−0.769495	+	1.33280i	−0.937837	+	0.347076i	$0.887175\pi$
$710$	−12.9687	−	22.4624i	−0.486705	−	0.842998i
$711$	2.59279	+	4.49085i	0.0972373	+	0.168420i
$712$	−3.34725	+	5.79761i	−0.125443	+	0.217274i
$713$	10.5191			0.393944
$714$	−8.70441	−	1.76828i	−0.325754	−	0.0661761i
$715$	−16.5759			−0.619904
$716$	1.38839	−	2.40476i	0.0518864	−	0.0898699i
$717$	−5.36098	−	9.28548i	−0.200209	−	0.346773i
$718$	1.94254	+	3.36458i	0.0724950	+	0.125565i
$719$	−8.86985	+	15.3630i	−0.330789	+	0.572944i	−0.982667	−	0.185380i	$-0.940648\pi$
$719$	−8.86985	+	15.3630i	−0.330789	+	0.572944i	0.651877	+	0.758324i	$0.273982\pi$
$720$	1.82843			0.0681415
$721$	−6.22200	−	18.5775i	−0.231719	−	0.691863i
$722$	34.7805			1.29440
$723$	−9.10171	+	15.7646i	−0.338496	+	0.586292i
$724$	10.4815	+	18.1544i	0.389540	+	0.674704i
$725$	4.29588	+	7.44068i	0.159545	+	0.276340i
$726$	−3.10270	+	5.37403i	−0.115152	+	0.199449i
$727$	14.4240			0.534957			0.267478	−	0.963564i	$-0.413810\pi$
$727$	14.4240			0.534957			0.267478	+	0.963564i	$0.413810\pi$
$728$	3.83034	−	4.33197i	0.141962	−	0.160553i
$729$	1.00000			0.0370370
$730$	−10.5309	+	18.2401i	−0.389767	+	0.675096i
$731$	8.99882	+	15.5864i	0.332833	+	0.576484i
$732$	7.37117	+	12.7672i	0.272446	+	0.471891i
$733$	15.8427	−	27.4404i	0.585164	−	1.01353i	−0.409691	−	0.912224i	$-0.634363\pi$
$733$	15.8427	−	27.4404i	0.585164	−	1.01353i	0.994855	−	0.101310i	$-0.0323033\pi$
$734$	−1.43745			−0.0530572
$735$	−1.56725	−	12.7027i	−0.0578088	−	0.468545i
$736$	1.00000			0.0368605
$737$	−27.8015	+	48.1537i	−1.02408	+	1.77376i
$738$	−3.66676	−	6.35102i	−0.134975	−	0.233784i
$739$	2.10011	+	3.63749i	0.0772536	+	0.133807i	0.902064	−	0.431602i	$-0.142052\pi$
$739$	2.10011	+	3.63749i	0.0772536	+	0.133807i	−0.824810	+	0.565409i	$0.808718\pi$
$740$	0.948628	−	1.64307i	0.0348723	−	0.0604005i
$741$	16.0280			0.588804
$742$	−7.96136	+	9.00400i	−0.292271	+	0.330547i
$743$	−42.3168			−1.55245			−0.776227	−	0.630454i	$-0.782869\pi$
$743$	−42.3168			−1.55245			−0.776227	+	0.630454i	$0.782869\pi$
$744$	−5.25955	+	9.10981i	−0.192825	+	0.333982i
$745$	−17.6971	−	30.6523i	−0.648371	−	1.12301i
$746$	−9.14794	−	15.8447i	−0.334930	−	0.580115i
$747$	−2.90240	+	5.02710i	−0.106193	+	0.183932i
$748$	−13.9253			−0.509159
$749$	4.62241	+	13.8015i	0.168899	+	0.504296i
$750$	−12.1716			−0.444443
$751$	−8.22219	+	14.2413i	−0.300032	+	0.519671i	−0.976143	−	0.217129i	$-0.930331\pi$
$751$	−8.22219	+	14.2413i	−0.300032	+	0.519671i	0.676111	+	0.736800i	$0.263664\pi$
$752$	−3.61161	−	6.25550i	−0.131702	−	0.228115i
$753$	0.397302	+	0.688147i	0.0144785	+	0.0250775i
$754$	5.66676	−	9.81512i	0.206371	−	0.357446i
$755$	10.2103			0.371591
$756$	2.59279	+	0.526718i	0.0942989	+	0.0191566i
$757$	45.4215			1.65087			0.825437	−	0.564494i	$-0.190929\pi$
$757$	45.4215			1.65087			0.825437	+	0.564494i	$0.190929\pi$
$758$	2.98818	−	5.17568i	0.108536	−	0.187989i
$759$	−2.07397	−	3.59222i	−0.0752803	−	0.130389i
$760$	6.70441	+	11.6124i	0.243194	+	0.421225i
$761$	−7.82107	+	13.5465i	−0.283513	+	0.491060i	−0.972248	−	0.233954i	$-0.924833\pi$
$761$	−7.82107	+	13.5465i	−0.283513	+	0.491060i	0.688734	+	0.725014i	$0.258167\pi$
$762$	6.49108			0.235147
$763$	−48.4724	−	9.84704i	−1.75482	−	0.356487i
$764$	−8.96236			−0.324247
$765$	3.06916	−	5.31594i	0.110966	−	0.192198i
$766$	2.94863	+	5.10717i	0.106538	+	0.184530i
$767$	−0.515001	−	0.892008i	−0.0185956	−	0.0322086i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−14.1205			−0.509198			−0.254599	−	0.967047i	$-0.581943\pi$
$769$	−14.1205			−0.509198			−0.254599	+	0.967047i	$0.581943\pi$
$770$	−6.37258	−	19.0271i	−0.229652	−	0.685690i
$771$	−0.591190			−0.0212912
$772$	−5.81951	+	10.0797i	−0.209449	+	0.362776i
$773$	−8.80260	−	15.2466i	−0.316608	−	0.548380i	0.663170	−	0.748468i	$-0.269210\pi$
$773$	−8.80260	−	15.2466i	−0.316608	−	0.548380i	−0.979778	+	0.200088i	$0.935877\pi$
$774$	−2.68049	−

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 + 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(-1.75255 + 1.98206i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.914214 - 1.58346i) q^{10} +(-2.07397 - 3.59222i) q^{11} +(-0.500000 + 0.866025i) q^{12} -2.18558 q^{13} +(-0.840244 - 2.50878i) q^{14} +1.82843 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.67858 + 2.90738i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.66676 - 6.35102i) q^{19} +1.82843 q^{20} +(2.59279 + 0.526718i) q^{21} +4.14794 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.828427 + 1.43488i) q^{25} +(1.09279 - 1.89277i) q^{26} +1.00000 q^{27} +(2.59279 + 0.526718i) q^{28} +5.18558 q^{29} +(-0.914214 + 1.58346i) q^{30} +(-5.25955 - 9.10981i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.07397 + 3.59222i) q^{33} -3.35716 q^{34} +(-1.53633 - 4.58713i) q^{35} +1.00000 q^{36} +(0.518822 - 0.898626i) q^{37} +(3.66676 + 6.35102i) q^{38} +(1.09279 + 1.89277i) q^{39} +(-0.914214 + 1.58346i) q^{40} +7.33352 q^{41} +(-1.75255 + 1.98206i) q^{42} +5.36098 q^{43} +(-2.07397 + 3.59222i) q^{44} +(-0.914214 - 1.58346i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-3.61161 + 6.25550i) q^{47} +1.00000 q^{48} +(-0.857156 - 6.94732i) q^{49} -1.65685 q^{50} +(1.67858 - 2.90738i) q^{51} +(1.09279 + 1.89277i) q^{52} +(-2.27137 - 3.93413i) q^{53} +(-0.500000 + 0.866025i) q^{54} +7.58420 q^{55} +(-1.75255 + 1.98206i) q^{56} -7.33352 q^{57} +(-2.59279 + 4.49085i) q^{58} +(0.235636 + 0.408133i) q^{59} +(-0.914214 - 1.58346i) q^{60} +(7.37117 - 12.7672i) q^{61} +10.5191 q^{62} +(-0.840244 - 2.50878i) q^{63} +1.00000 q^{64} +(1.99809 - 3.46079i) q^{65} +(-2.07397 - 3.59222i) q^{66} +(-6.70249 - 11.6091i) q^{67} +(1.67858 - 2.90738i) q^{68} +1.00000 q^{69} +(4.74073 + 0.963066i) q^{70} +14.1856 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.75955 - 9.97584i) q^{73} +(0.518822 + 0.898626i) q^{74} +(0.828427 - 1.43488i) q^{75} -7.33352 q^{76} +(10.7547 + 2.18480i) q^{77} -2.18558 q^{78} +(2.59279 - 4.49085i) q^{79} +(-0.914214 - 1.58346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.66676 + 6.35102i) q^{82} +5.80479 q^{83} +(-0.840244 - 2.50878i) q^{84} -6.13831 q^{85} +(-2.68049 + 4.64274i) q^{86} +(-2.59279 - 4.49085i) q^{87} +(-2.07397 - 3.59222i) q^{88} +(-3.34725 + 5.79761i) q^{89} +1.82843 q^{90} +(3.83034 - 4.33197i) q^{91} +1.00000 q^{92} +(-5.25955 + 9.10981i) q^{93} +(-3.61161 - 6.25550i) q^{94} +(6.70441 + 11.6124i) q^{95} +(-0.500000 + 0.866025i) q^{96} -4.47127 q^{97} +(6.44514 + 2.73134i) q^{98} +4.14794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

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