LMFDB - Embedded newform 240.2.bl.a.229.18

Newspace parameters

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.18
Character	$\chi$	$=$	240.229
Dual form			240.2.bl.a.109.18

$q$-expansion

$f(q)$	$=$	$q+(0.903247 + 1.08818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.368289 + 1.96580i) q^{4} +(-2.09919 + 0.770325i) q^{5} +(-0.130770 + 1.40815i) q^{6} +3.05002 q^{7} +(-2.47181 + 1.37484i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.903247 + 1.08818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.368289 + 1.96580i) q^{4} +(-2.09919 + 0.770325i) q^{5} +(-0.130770 + 1.40815i) q^{6} +3.05002 q^{7} +(-2.47181 + 1.37484i) q^{8} +1.00000i q^{9} +(-2.73434 - 1.58851i) q^{10} +(-1.80989 - 1.80989i) q^{11} +(-1.65045 + 1.12961i) q^{12} +(2.47057 + 2.47057i) q^{13} +(2.75492 + 3.31898i) q^{14} +(-2.02905 - 0.939649i) q^{15} +(-3.72873 - 1.44796i) q^{16} -3.66653i q^{17} +(-1.08818 + 0.903247i) q^{18} +(-2.31596 + 2.31596i) q^{19} +(-0.741196 - 4.41029i) q^{20} +(2.15669 + 2.15669i) q^{21} +(0.334715 - 3.60427i) q^{22} +4.86336 q^{23} +(-2.71999 - 0.775675i) q^{24} +(3.81320 - 3.23412i) q^{25} +(-0.456900 + 4.91998i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.12329 + 5.99573i) q^{28} +(4.74672 - 4.74672i) q^{29} +(-0.810226 - 3.05672i) q^{30} +1.86172 q^{31} +(-1.79231 - 5.36541i) q^{32} -2.55957i q^{33} +(3.98986 - 3.31179i) q^{34} +(-6.40257 + 2.34951i) q^{35} +(-1.96580 - 0.368289i) q^{36} +(5.40092 - 5.40092i) q^{37} +(-4.61208 - 0.428306i) q^{38} +3.49392i q^{39} +(4.12972 - 4.79014i) q^{40} -6.47424i q^{41} +(-0.398851 + 4.29490i) q^{42} +(-4.19382 + 4.19382i) q^{43} +(4.22444 - 2.89131i) q^{44} +(-0.770325 - 2.09919i) q^{45} +(4.39282 + 5.29223i) q^{46} +8.24387i q^{47} +(-1.61274 - 3.66047i) q^{48} +2.30263 q^{49} +(6.96358 + 1.22825i) q^{50} +(2.59263 - 2.59263i) q^{51} +(-5.76653 + 3.94676i) q^{52} +(-9.99761 + 9.99761i) q^{53} +(-1.40815 - 0.130770i) q^{54} +(5.19350 + 2.40510i) q^{55} +(-7.53906 + 4.19328i) q^{56} -3.27526 q^{57} +(9.45277 + 0.877843i) q^{58} +(-2.47155 - 2.47155i) q^{59} +(2.59444 - 3.64265i) q^{60} +(8.01822 - 8.01822i) q^{61} +(1.68160 + 2.02590i) q^{62} +3.05002i q^{63} +(4.21965 - 6.79666i) q^{64} +(-7.08935 - 3.28306i) q^{65} +(2.78528 - 2.31192i) q^{66} +(-8.60064 - 8.60064i) q^{67} +(7.20766 + 1.35034i) q^{68} +(3.43891 + 3.43891i) q^{69} +(-8.33981 - 4.84499i) q^{70} -6.63653i q^{71} +(-1.37484 - 2.47181i) q^{72} +2.70041 q^{73} +(10.7556 + 0.998828i) q^{74} +(4.98321 + 0.409472i) q^{75} +(-3.69977 - 5.40565i) q^{76} +(-5.52020 - 5.52020i) q^{77} +(-3.80203 + 3.15587i) q^{78} -10.9690 q^{79} +(8.94271 + 0.167218i) q^{80} -1.00000 q^{81} +(7.04516 - 5.84784i) q^{82} +(3.65688 + 3.65688i) q^{83} +(-5.03390 + 3.44533i) q^{84} +(2.82442 + 7.69675i) q^{85} +(-8.35170 - 0.775591i) q^{86} +6.71288 q^{87} +(6.96199 + 1.98539i) q^{88} +13.1530i q^{89} +(1.58851 - 2.73434i) q^{90} +(7.53530 + 7.53530i) q^{91} +(-1.79112 + 9.56038i) q^{92} +(1.31644 + 1.31644i) q^{93} +(-8.97085 + 7.44625i) q^{94} +(3.07760 - 6.64569i) q^{95} +(2.52656 - 5.06127i) q^{96} -12.4932i q^{97} +(2.07985 + 2.50569i) q^{98} +(1.80989 - 1.80989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.903247	+	1.08818i	0.638692	+	0.769462i
$2$	0.903247	+	1.08818i	0.638692	+	0.769462i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−0.368289	+	1.96580i	−0.184144	+	0.982899i
$5$	−2.09919	+	0.770325i	−0.938786	+	0.344500i
$5$	−2.09919	+	0.770325i	−0.938786	+	0.344500i
$6$	−0.130770	+	1.40815i	−0.0533866	+	0.574877i
$7$	3.05002			1.15280			0.576400	−	0.817168i	$-0.304457\pi$
$7$	3.05002			1.15280			0.576400	+	0.817168i	$0.304457\pi$
$8$	−2.47181	+	1.37484i	−0.873915	+	0.486078i
$9$			1.00000i			0.333333i
$10$	−2.73434	−	1.58851i	−0.864675	−	0.502331i
$11$	−1.80989	−	1.80989i	−0.545702	−	0.545702i	0.379493	−	0.925195i	$-0.376099\pi$
$11$	−1.80989	−	1.80989i	−0.545702	−	0.545702i	−0.925195	+	0.379493i	$0.876099\pi$
$12$	−1.65045	+	1.12961i	−0.476444	+	0.326090i
$13$	2.47057	+	2.47057i	0.685214	+	0.685214i	0.961170	−	0.275956i	$-0.0889946\pi$
$13$	2.47057	+	2.47057i	0.685214	+	0.685214i	−0.275956	+	0.961170i	$0.588995\pi$
$14$	2.75492	+	3.31898i	0.736284	+	0.887036i
$15$	−2.02905	−	0.939649i	−0.523899	−	0.242616i
$16$	−3.72873	−	1.44796i	−0.932182	−	0.361991i
$17$		−	3.66653i		−	0.889265i	−0.895713	−	0.444632i	$-0.853334\pi$
$17$		−	3.66653i		−	0.889265i	0.895713	−	0.444632i	$-0.146666\pi$
$18$	−1.08818	+	0.903247i	−0.256487	+	0.212897i
$19$	−2.31596	+	2.31596i	−0.531318	+	0.531318i	−0.920964	−	0.389647i	$-0.872597\pi$
$19$	−2.31596	+	2.31596i	−0.531318	+	0.531318i	0.389647	+	0.920964i	$0.372597\pi$
$20$	−0.741196	−	4.41029i	−0.165736	−	0.986170i
$21$	2.15669	+	2.15669i	0.470629	+	0.470629i
$22$	0.334715	−	3.60427i	0.0713615	−	0.768433i
$23$	4.86336			1.01408			0.507040	−	0.861922i	$-0.330740\pi$
$23$	4.86336			1.01408			0.507040	+	0.861922i	$0.330740\pi$
$24$	−2.71999	−	0.775675i	−0.555215	−	0.158334i
$25$	3.81320	−	3.23412i	0.762640	−	0.646824i
$26$	−0.456900	+	4.91998i	−0.0896054	+	0.964887i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.12329	+	5.99573i	−0.212282	+	1.13309i
$29$	4.74672	−	4.74672i	0.881444	−	0.881444i	−0.112237	−	0.993681i	$-0.535802\pi$
$29$	4.74672	−	4.74672i	0.881444	−	0.881444i	0.993681	+	0.112237i	$0.0358017\pi$
$30$	−0.810226	−	3.05672i	−0.147926	−	0.558078i
$31$	1.86172			0.334375			0.167188	−	0.985925i	$-0.446531\pi$
$31$	1.86172			0.334375			0.167188	+	0.985925i	$0.446531\pi$
$32$	−1.79231	−	5.36541i	−0.316839	−	0.948479i
$33$		−	2.55957i		−	0.445564i
$34$	3.98986	−	3.31179i	0.684256	−	0.567966i
$35$	−6.40257	+	2.34951i	−1.08223	+	0.397139i
$36$	−1.96580	−	0.368289i	−0.327633	−	0.0613815i
$37$	5.40092	−	5.40092i	0.887905	−	0.887905i	−0.106416	−	0.994322i	$-0.533938\pi$
$37$	5.40092	−	5.40092i	0.887905	−	0.887905i	0.994322	+	0.106416i	$0.0339376\pi$
$38$	−4.61208	−	0.428306i	−0.748178	−	0.0694804i
$39$			3.49392i			0.559475i
$40$	4.12972	−	4.79014i	0.652966	−	0.757387i
$41$		−	6.47424i		−	1.01111i	−0.862796	−	0.505553i	$-0.831288\pi$
$41$		−	6.47424i		−	1.01111i	0.862796	−	0.505553i	$-0.168712\pi$
$42$	−0.398851	+	4.29490i	−0.0615441	+	0.662718i
$43$	−4.19382	+	4.19382i	−0.639551	+	0.639551i	−0.950445	−	0.310893i	$-0.899372\pi$
$43$	−4.19382	+	4.19382i	−0.639551	+	0.639551i	0.310893	+	0.950445i	$0.399372\pi$
$44$	4.22444	−	2.89131i	0.636858	−	0.435882i
$45$	−0.770325	−	2.09919i	−0.114833	−	0.312929i
$46$	4.39282	+	5.29223i	0.647685	+	0.780297i
$47$			8.24387i			1.20249i	0.799064	+	0.601246i	$0.205329\pi$
$47$			8.24387i			1.20249i	−0.799064	+	0.601246i	$0.794671\pi$
$48$	−1.61274	−	3.66047i	−0.232779	−	0.528344i
$49$	2.30263			0.328947
$50$	6.96358	+	1.22825i	0.984798	+	0.173701i
$51$	2.59263	−	2.59263i	0.363041	−	0.363041i
$52$	−5.76653	+	3.94676i	−0.799674	+	0.547318i
$53$	−9.99761	+	9.99761i	−1.37328	+	1.37328i	−0.517739	+	0.855539i	$0.673226\pi$
$53$	−9.99761	+	9.99761i	−1.37328	+	1.37328i	−0.855539	+	0.517739i	$0.826774\pi$
$54$	−1.40815	−	0.130770i	−0.191626	−	0.0177955i
$55$	5.19350	+	2.40510i	0.700292	+	0.324303i
$56$	−7.53906	+	4.19328i	−1.00745	+	0.560351i
$57$	−3.27526			−0.433819
$58$	9.45277	+	0.877843i	1.24121	+	0.115266i
$59$	−2.47155	−	2.47155i	−0.321769	−	0.321769i	0.527676	−	0.849445i	$-0.323063\pi$
$59$	−2.47155	−	2.47155i	−0.321769	−	0.321769i	−0.849445	+	0.527676i	$0.823063\pi$
$60$	2.59444	−	3.64265i	0.334941	−	0.470264i
$61$	8.01822	−	8.01822i	1.02663	−	1.02663i	0.0269927	−	0.999636i	$-0.491407\pi$
$61$	8.01822	−	8.01822i	1.02663	−	1.02663i	0.999636	−	0.0269927i	$-0.00859310\pi$
$62$	1.68160	+	2.02590i	0.213563	+	0.257289i
$63$			3.05002i			0.384267i
$64$	4.21965	−	6.79666i	0.527456	−	0.849582i
$65$	−7.08935	−	3.28306i	−0.879325	−	0.407213i
$66$	2.78528	−	2.31192i	0.342845	−	0.284578i
$67$	−8.60064	−	8.60064i	−1.05074	−	1.05074i	−0.998642	−	0.0520936i	$-0.983411\pi$
$67$	−8.60064	−	8.60064i	−1.05074	−	1.05074i	−0.0520936	−	0.998642i	$-0.516589\pi$
$68$	7.20766	+	1.35034i	0.874058	+	0.163753i
$69$	3.43891	+	3.43891i	0.413997	+	0.413997i
$70$	−8.33981	−	4.84499i	−0.996797	−	0.579087i
$71$		−	6.63653i		−	0.787611i	−0.919194	−	0.393806i	$-0.871158\pi$
$71$		−	6.63653i		−	0.787611i	0.919194	−	0.393806i	$-0.128842\pi$
$72$	−1.37484	−	2.47181i	−0.162026	−	0.291305i
$73$	2.70041			0.316059			0.158030	−	0.987434i	$-0.449486\pi$
$73$	2.70041			0.316059			0.158030	+	0.987434i	$0.449486\pi$
$74$	10.7556	+	0.998828i	1.25031	+	0.116111i
$75$	4.98321	+	0.409472i	0.575411	+	0.0472817i
$76$	−3.69977	−	5.40565i	−0.424393	−	0.620071i
$77$	−5.52020	−	5.52020i	−0.629085	−	0.629085i
$78$	−3.80203	+	3.15587i	−0.430495	+	0.357332i
$79$	−10.9690			−1.23411			−0.617054	−	0.786921i	$-0.711674\pi$
$79$	−10.9690			−1.23411			−0.617054	+	0.786921i	$0.711674\pi$
$80$	8.94271	+	0.167218i	0.999825	+	0.0186955i
$81$	−1.00000			−0.111111
$82$	7.04516	−	5.84784i	0.778008	−	0.645786i
$83$	3.65688	+	3.65688i	0.401395	+	0.401395i	0.878724	−	0.477330i	$-0.158395\pi$
$83$	3.65688	+	3.65688i	0.401395	+	0.401395i	−0.477330	+	0.878724i	$0.658395\pi$
$84$	−5.03390	+	3.44533i	−0.549244	+	0.375917i
$85$	2.82442	+	7.69675i	0.306352	+	0.834830i
$86$	−8.35170	−	0.775591i	−0.900587	−	0.0836341i
$87$	6.71288			0.719696
$88$	6.96199	+	1.98539i	0.742151	+	0.211644i
$89$			13.1530i			1.39421i	0.716968	+	0.697106i	$0.245529\pi$
$89$			13.1530i			1.39421i	−0.716968	+	0.697106i	$0.754471\pi$
$90$	1.58851	−	2.73434i	0.167444	−	0.288225i
$91$	7.53530	+	7.53530i	0.789914	+	0.789914i
$92$	−1.79112	+	9.56038i	−0.186737	+	0.996739i
$93$	1.31644	+	1.31644i	0.136508	+	0.136508i
$94$	−8.97085	+	7.44625i	−0.925272	+	0.768022i
$95$	3.07760	−	6.64569i	0.315755	−	0.681833i
$96$	2.52656	−	5.06127i	0.257866	−	0.516564i
$97$		−	12.4932i		−	1.26849i	−0.773131	−	0.634247i	$-0.781310\pi$
$97$		−	12.4932i		−	1.26849i	0.773131	−	0.634247i	$-0.218690\pi$
$98$	2.07985	+	2.50569i	0.210096	+	0.253113i
$99$	1.80989	−	1.80989i	0.181901	−	0.181901i
$100$	4.95327	+	8.68707i	0.495327	+	0.868707i
$101$	0.569518	+	0.569518i	0.0566692	+	0.0566692i	0.734873	−	0.678204i	$-0.237242\pi$
$101$	0.569518	+	0.569518i	0.0566692	+	0.0566692i	−0.678204	+	0.734873i	$0.737242\pi$
$102$	5.16304	+	0.479473i	0.511218	+	0.0474749i
$103$	−12.2060			−1.20269			−0.601345	−	0.798989i	$-0.705368\pi$
$103$	−12.2060			−1.20269			−0.601345	+	0.798989i	$0.705368\pi$
$104$	−9.50341	−	2.71014i	−0.931886	−	0.265752i
$105$	−6.18866	−	2.86595i	−0.603951	−	0.279688i
$106$	−19.9096	−	1.84893i	−1.93379	−	0.179584i
$107$	−7.99550	+	7.99550i	−0.772955	+	0.772955i	−0.978622	−	0.205667i	$-0.934063\pi$
$107$	−7.99550	+	7.99550i	−0.772955	+	0.772955i	0.205667	+	0.978622i	$0.434063\pi$
$108$	−1.12961	−	1.65045i	−0.108697	−	0.158815i
$109$	−7.07511	+	7.07511i	−0.677672	+	0.677672i	−0.959473	−	0.281801i	$-0.909068\pi$
$109$	−7.07511	+	7.07511i	−0.677672	+	0.677672i	0.281801	+	0.959473i	$0.409068\pi$
$110$	2.07383	+	7.82388i	0.197732	+	0.745978i
$111$	7.63805			0.724972
$112$	−11.3727	−	4.41632i	−1.07462	−	0.417303i
$113$		−	6.25105i		−	0.588050i	−0.955798	−	0.294025i	$-0.905005\pi$
$113$		−	6.25105i		−	0.588050i	0.955798	−	0.294025i	$-0.0949948\pi$
$114$	−2.95837	−	3.56409i	−0.277077	−	0.333808i
$115$	−10.2091	+	3.74637i	−0.952005	+	0.349351i
$116$	7.58293	+	11.0793i	0.704058	+	1.02868i
$117$	−2.47057	+	2.47057i	−0.228405	+	0.228405i
$118$	0.457081	−	4.92193i	0.0420777	−	0.453100i
$119$		−	11.1830i		−	1.02514i
$120$	6.30729	−	0.466985i	0.575774	−	0.0426297i
$121$		−	4.44861i		−	0.404419i
$122$	15.9677	+	1.48286i	1.44565	+	0.134252i
$123$	4.57798	−	4.57798i	0.412782	−	0.412782i
$124$	−0.685652	+	3.65977i	−0.0615734	+	0.328657i
$125$	−5.51331	+	9.72643i	−0.493125	+	0.869958i
$126$	−3.31898	+	2.75492i	−0.295679	+	0.245428i
$127$			14.1884i			1.25902i	0.776993	+	0.629509i	$0.216744\pi$
$127$			14.1884i			1.25902i	−0.776993	+	0.629509i	$0.783256\pi$
$128$	11.2074	−	1.54730i	0.990604	−	0.136764i
$129$	−5.93095			−0.522191
$130$	−2.83086	−	10.6799i	−0.248283	−	0.936692i
$131$	−12.5522	+	12.5522i	−1.09669	+	1.09669i	−0.101896	+	0.994795i	$0.532491\pi$
$131$	−12.5522	+	12.5522i	−1.09669	+	1.09669i	−0.994795	+	0.101896i	$0.967509\pi$
$132$	5.03160	+	0.942661i	0.437944	+	0.0820481i
$133$	−7.06373	+	7.06373i	−0.612503	+	0.612503i
$134$	1.59057	−	17.1276i	0.137405	−	1.47960i
$135$	0.939649	−	2.02905i	0.0808721	−	0.174633i
$136$	5.04088	+	9.06296i	0.432252	+	0.777142i
$137$	4.88336			0.417214			0.208607	−	0.978000i	$-0.433107\pi$
$137$	4.88336			0.417214			0.208607	+	0.978000i	$0.433107\pi$
$138$	−0.635982	+	6.84836i	−0.0541383	+	0.582971i
$139$	5.84556	+	5.84556i	0.495814	+	0.495814i	0.910132	−	0.414318i	$-0.135980\pi$
$139$	5.84556	+	5.84556i	0.495814	+	0.495814i	−0.414318	+	0.910132i	$0.635980\pi$
$140$	−2.26066	−	13.4515i	−0.191061	−	1.13686i
$141$	−5.82930	+	5.82930i	−0.490915	+	0.490915i
$142$	7.22177	−	5.99443i	0.606037	−	0.503041i
$143$		−	8.94292i		−	0.747845i
$144$	1.44796	−	3.72873i	0.120664	−	0.310727i
$145$	−6.30775	+	13.6208i	−0.523830	+	1.13115i
$146$	2.43914	+	2.93855i	0.201865	+	0.243196i
$147$	1.62821	+	1.62821i	0.134292	+	0.134292i
$148$	8.62802	+	12.6062i	0.709219	+	1.03622i
$149$	−15.1483	−	15.1483i	−1.24100	−	1.24100i	−0.959587	−	0.281412i	$-0.909197\pi$
$149$	−15.1483	−	15.1483i	−1.24100	−	1.24100i	−0.281412	−	0.959587i	$-0.590803\pi$
$150$	4.05549	+	5.79250i	0.331129	+	0.472956i
$151$		−	4.02031i		−	0.327168i	−0.986529	−	0.163584i	$-0.947694\pi$
$151$		−	4.02031i		−	0.327168i	0.986529	−	0.163584i	$-0.0523056\pi$
$152$	2.54054	−	8.90867i	0.206065	−	0.722589i
$153$	3.66653			0.296422
$154$	1.02089	−	10.9931i	0.0822655	−	0.885849i
$155$	−3.90811	+	1.43413i	−0.313907	+	0.115192i
$156$	−6.86834	−	1.28677i	−0.549907	−	0.103024i
$157$	9.86041	+	9.86041i	0.786946	+	0.786946i	0.980992	−	0.194046i	$-0.0621612\pi$
$157$	9.86041	+	9.86041i	0.786946	+	0.786946i	−0.194046	+	0.980992i	$0.562161\pi$
$158$	−9.90771	−	11.9363i	−0.788215	−	0.949600i
$159$	−14.1388			−1.12128
$160$	7.89551	+	9.88235i	0.624195	+	0.781268i
$161$	14.8333			1.16903
$162$	−0.903247	−	1.08818i	−0.0709658	−	0.0854958i
$163$	−13.1713	−	13.1713i	−1.03165	−	1.03165i	−0.999482	−	0.0321718i	$-0.989758\pi$
$163$	−13.1713	−	13.1713i	−1.03165	−	1.03165i	−0.0321718	−	0.999482i	$-0.510242\pi$
$164$	12.7270	+	2.38439i	0.993815	+	0.186190i
$165$	1.97170	+	5.37302i	0.153497	+	0.418289i
$166$	−0.676291	+	7.28242i	−0.0524904	+	0.565226i
$167$	0.0610761			0.00472621			0.00236311	−	0.999997i	$-0.499248\pi$
$167$	0.0610761			0.00472621			0.00236311	+	0.999997i	$0.499248\pi$
$168$	−8.29602	−	2.36583i	−0.640052	−	0.182527i
$169$		−	0.792537i		−	0.0609644i
$170$	−5.82433	+	10.0256i	−0.446705	+	0.768925i
$171$	−2.31596	−	2.31596i	−0.177106	−	0.177106i
$172$	−6.69966	−	9.78874i	−0.510845	−	0.746384i
$173$	8.01622	+	8.01622i	0.609462	+	0.609462i	0.942805	−	0.333343i	$-0.108177\pi$
$173$	8.01622	+	8.01622i	0.609462	+	0.609462i	−0.333343	+	0.942805i	$0.608177\pi$
$174$	6.06339	+	7.30485i	0.459664	+	0.553779i
$175$	11.6303	−	9.86413i	0.879171	−	0.745658i
$176$	4.12793	+	9.36923i	0.311154	+	0.706232i
$177$		−	3.49531i		−	0.262723i
$178$	−14.3128	+	11.8804i	−1.07279	+	0.890472i
$179$	11.8352	−	11.8352i	0.884607	−	0.884607i	−0.109392	−	0.993999i	$-0.534890\pi$
$179$	11.8352	−	11.8352i	0.884607	−	0.884607i	0.993999	+	0.109392i	$0.0348903\pi$
$180$	4.41029	−	0.741196i	0.328723	−	0.0552455i
$181$	3.63391	+	3.63391i	0.270106	+	0.270106i	0.829143	−	0.559037i	$-0.188829\pi$
$181$	3.63391	+	3.63391i	0.270106	+	0.270106i	−0.559037	+	0.829143i	$0.688829\pi$
$182$	−1.39355	+	15.0060i	−0.103297	+	1.11232i
$183$	11.3395			0.838239
$184$	−12.0213	+	6.68632i	−0.886221	+	0.492922i
$185$	−7.17709	+	15.4980i	−0.527670	+	1.13944i
$186$	−0.243458	+	2.62159i	−0.0178512	+	0.192225i
$187$	−6.63602	+	6.63602i	−0.485274	+	0.485274i
$188$	−16.2058	−	3.03612i	−1.18193	−	0.221432i
$189$	−2.15669	+	2.15669i	−0.156876	+	0.156876i
$190$	10.0116	−	2.65370i	0.726315	−	0.192520i
$191$	19.0823			1.38074			0.690372	−	0.723455i	$-0.257447\pi$
$191$	19.0823			1.38074			0.690372	+	0.723455i	$0.257447\pi$
$192$	7.78971	−	1.82222i	0.562174	−	0.131507i
$193$		−	2.99015i		−	0.215236i	−0.994192	−	0.107618i	$-0.965678\pi$
$193$		−	2.99015i		−	0.215236i	0.994192	−	0.107618i	$-0.0343223\pi$
$194$	13.5949	−	11.2845i	0.976058	−	0.810177i
$195$	−2.69145	−	7.33440i	−0.192739	−	0.525227i
$196$	−0.848033	+	4.52651i	−0.0605738	+	0.323322i
$197$	1.37271	−	1.37271i	0.0978016	−	0.0978016i	−0.656513	−	0.754315i	$-0.727969\pi$
$197$	1.37271	−	1.37271i	0.0978016	−	0.0978016i	0.754315	+	0.656513i	$0.227969\pi$
$198$	3.60427	+	0.334715i	0.256144	+	0.0237872i
$199$			15.7129i			1.11386i	0.830560	+	0.556930i	$0.188021\pi$
$199$			15.7129i			1.11386i	−0.830560	+	0.556930i	$0.811979\pi$
$200$	−4.97911	+	13.2366i	−0.352076	+	0.935971i
$201$		−	12.1631i		−	0.857922i
$202$	−0.105325	+	1.13416i	−0.00741063	+	0.0797989i
$203$	14.4776	−	14.4776i	1.01613	−	1.01613i
$204$	4.14175	+	6.05142i	0.289981	+	0.423684i
$205$	4.98727	+	13.5907i	0.348326	+	0.949213i
$206$	−11.0250	−	13.2823i	−0.768149	−	0.925425i
$207$			4.86336i			0.338027i
$208$	−5.63479	−	12.7894i	−0.390703	−	0.886785i
$209$	8.38326			0.579882
$210$	−2.47121	−	9.32306i	−0.170529	−	0.643352i
$211$	16.8391	−	16.8391i	1.15925	−	1.15925i	0.174614	−	0.984637i	$-0.444132\pi$
$211$	16.8391	−	16.8391i	1.15925	−	1.15925i	0.984637	−	0.174614i	$-0.0558679\pi$
$212$	−15.9713	−	23.3353i	−1.09691	−	1.60267i
$213$	4.69274	−	4.69274i	0.321541	−	0.321541i
$214$	−15.9225	−	1.47866i	−1.08844	−	0.101079i
$215$	5.57302	−	12.0342i	0.380077	−	0.820727i
$216$	0.775675	−	2.71999i	0.0527780	−	0.185072i
$217$	5.67830			0.385468
$218$	−14.0896	−	1.30845i	−0.954267	−	0.0886192i
$219$	1.90948	+	1.90948i	0.129031	+	0.129031i
$220$	−6.64065	+	9.32361i	−0.447712	+	0.628598i
$221$	9.05844	−	9.05844i	0.609336	−	0.609336i
$222$	6.89905	+	8.31160i	0.463034	+	0.557838i
$223$		−	10.6893i		−	0.715809i	−0.933758	−	0.357905i	$-0.883491\pi$
$223$		−	10.6893i		−	0.715809i	0.933758	−	0.357905i	$-0.116509\pi$
$224$	−5.46659	−	16.3646i	−0.365252	−	1.09341i
$225$	3.23412	+	3.81320i	0.215608	+	0.254213i
$226$	6.80230	−	5.64625i	0.452482	−	0.375583i
$227$	15.0722	+	15.0722i	1.00037	+	1.00037i	1.00000		0.000374434i	$0.000119186\pi$
$227$	15.0722	+	15.0722i	1.00037	+	1.00037i	0.000374434		1.00000i	$0.499881\pi$
$228$	1.20624	−	6.43851i	0.0798854	−	0.426401i
$229$	−3.23629	−	3.23629i	−0.213860	−	0.213860i	0.592045	−	0.805905i	$-0.298321\pi$
$229$	−3.23629	−	3.23629i	−0.213860	−	0.213860i	−0.805905	+	0.592045i	$0.798321\pi$
$230$	−13.2981	−	7.72550i	−0.876850	−	0.509404i
$231$		−	7.80674i		−	0.513646i
$232$	−5.20701	+	18.2589i	−0.341857	+	1.19876i
$233$	4.75428			0.311463			0.155732	−	0.987799i	$-0.450227\pi$
$233$	4.75428			0.311463			0.155732	+	0.987799i	$0.450227\pi$
$234$	−4.91998	−	0.456900i	−0.321629	−	0.0298685i
$235$	−6.35046	−	17.3054i	−0.414258	−	1.12888i
$236$	5.76882	−	3.94833i	0.375518	−	0.257015i
$237$	−7.75625	−	7.75625i	−0.503823	−	0.503823i
$238$	12.1692	−	10.1010i	0.788810	−	0.654752i
$239$	11.9224			0.771196			0.385598	−	0.922667i	$-0.373995\pi$
$239$	11.9224			0.771196			0.385598	+	0.922667i	$0.373995\pi$
$240$	6.20521	+	6.44169i	0.400545	+	0.415809i
$241$	−28.2991			−1.82291			−0.911453	−	0.411403i	$-0.865039\pi$
$241$	−28.2991			−1.82291			−0.911453	+	0.411403i	$0.865039\pi$
$242$	4.84090	−	4.01819i	0.311185	−	0.258299i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	12.8092	+	18.7152i	0.820024	+	1.19812i
$245$	−4.83366	+	1.77377i	−0.308811	+	0.113322i
$246$	9.11673	+	0.846636i	0.581261	+	0.0539796i
$247$	−11.4435			−0.728133
$248$	−4.60182	+	2.55956i	−0.292216	+	0.162533i
$249$			5.17161i			0.327737i
$250$	−15.5640	+	2.78588i	−0.984355	+	0.176195i
$251$	−4.39215	−	4.39215i	−0.277230	−	0.277230i	0.554772	−	0.832002i	$-0.312805\pi$
$251$	−4.39215	−	4.39215i	−0.277230	−	0.277230i	−0.832002	+	0.554772i	$0.812805\pi$
$252$	−5.99573	−	1.12329i	−0.377695	−	0.0707605i
$253$	−8.80214	−	8.80214i	−0.553386	−	0.553386i
$254$	−15.4396	+	12.8156i	−0.968767	+	0.804125i
$255$	−3.44526	+	7.43959i	−0.215750	+	0.465885i
$256$	11.8068	+	10.7981i	0.737925	+	0.674882i
$257$		−	2.53050i		−	0.157849i	−0.996881	−	0.0789243i	$-0.974851\pi$
$257$		−	2.53050i		−	0.157849i	0.996881	−	0.0789243i	$-0.0251485\pi$
$258$	−5.35712	−	6.45397i	−0.333520	−	0.401807i
$259$	16.4729	−	16.4729i	1.02358	−	1.02358i
$260$	9.06476	−	12.7271i	0.562172	−	0.789302i
$261$	4.74672	+	4.74672i	0.293815	+	0.293815i
$262$	−24.9969	−	2.32136i	−1.54431	−	0.143414i
$263$	−0.540983			−0.0333584			−0.0166792	−	0.999861i	$-0.505309\pi$
$263$	−0.540983			−0.0333584			−0.0166792	+	0.999861i	$0.505309\pi$
$264$	3.51899	+	6.32676i	0.216579	+	0.389385i
$265$	13.2855	−	28.6883i	0.816120	−	1.76231i
$266$	−14.0669	−	1.30634i	−0.862499	−	0.0800970i
$267$	−9.30055	+	9.30055i	−0.569184	+	0.569184i
$268$	20.0747	−	13.7396i	1.22625	−	0.839280i
$269$	−3.00188	+	3.00188i	−0.183028	+	0.183028i	−0.792674	−	0.609646i	$-0.791312\pi$
$269$	−3.00188	+	3.00188i	−0.183028	+	0.183028i	0.609646	+	0.792674i	$0.291312\pi$
$270$	3.05672	−	0.810226i	0.186026	−	0.0493088i
$271$	−8.44312			−0.512883			−0.256442	−	0.966560i	$-0.582550\pi$
$271$	−8.44312			−0.512883			−0.256442	+	0.966560i	$0.582550\pi$
$272$	−5.30900	+	13.6715i	−0.321906	+	0.828956i
$273$			10.6565i			0.644962i
$274$	4.41089	+	5.31400i	0.266471	+	0.321030i
$275$	−12.7549	−	1.04807i	−0.769147	−	0.0632011i
$276$	−8.02673	+	5.49370i	−0.483152	+	0.330682i
$277$	12.2494	−	12.2494i	0.735992	−	0.735992i	−0.235807	−	0.971800i	$-0.575773\pi$
$277$	12.2494	−	12.2494i	0.735992	−	0.735992i	0.971800	+	0.235807i	$0.0757735\pi$
$278$	−1.08106	+	11.6410i	−0.0648376	+	0.698182i
$279$			1.86172i			0.111458i
$280$	12.5957	−	14.6100i	0.752739	−	0.873116i
$281$			16.6912i			0.995715i	0.867259	+	0.497857i	$0.165880\pi$
$281$			16.6912i			0.995715i	−0.867259	+	0.497857i	$0.834120\pi$
$282$	−11.6086	−	1.07805i	−0.691285	−	0.0641970i
$283$	1.25800	−	1.25800i	0.0747802	−	0.0747802i	−0.668727	−	0.743508i	$-0.733161\pi$
$283$	1.25800	−	1.25800i	0.0747802	−	0.0747802i	0.743508	+	0.668727i	$0.233161\pi$
$284$	13.0461	+	2.44416i	0.774143	+	0.145034i
$285$	6.87540	−	2.52302i	0.407264	−	0.149451i
$286$	9.73155	−	8.07767i	0.575438	−	0.477643i
$287$		−	19.7466i		−	1.16560i
$288$	5.36541	−	1.79231i	0.316160	−	0.105613i
$289$	3.55654			0.209208
$290$	−20.5194	+	5.43895i	−1.20494	+	0.319386i
$291$	8.83403	−	8.83403i	0.517860	−	0.517860i
$292$	−0.994532	+	5.30847i	−0.0582006	+	0.310655i
$293$	12.4197	−	12.4197i	0.725564	−	0.725564i	−0.244169	−	0.969733i	$-0.578515\pi$
$293$	12.4197	−	12.4197i	0.725564	−	0.725564i	0.969733	+	0.244169i	$0.0785151\pi$
$294$	−0.301115	+	3.24246i	−0.0175614	+	0.189104i
$295$	7.09216	+	3.28436i	0.412922	+	0.191223i
$296$	−5.92464	+	20.7754i	−0.344363	+	1.20755i
$297$	2.55957			0.148521
$298$	2.80148	−	30.1669i	0.162285	−	1.74752i
$299$	12.0153	+	12.0153i	0.694862	+	0.694862i
$300$	−2.64020	+	9.64517i	−0.152432	+	0.556864i
$301$	−12.7912	+	12.7912i	−0.737275	+	0.737275i
$302$	4.37484	−	3.63134i	0.251744	−	0.208960i
$303$			0.805420i			0.0462702i
$304$	11.9890	−	5.28216i	0.687617	−	0.302953i
$305$	−10.6551	+	23.0084i	−0.610111	+	1.31746i
$306$	3.31179	+	3.98986i	0.189322	+	0.228085i
$307$	21.6994	+	21.6994i	1.23845	+	1.23845i	0.960634	+	0.277816i	$0.0896107\pi$
$307$	21.6994	+	21.6994i	1.23845	+	1.23845i	0.277816	+	0.960634i	$0.410389\pi$
$308$	12.8846	−	8.81857i	0.734170	−	0.502485i
$309$	−8.63093	−	8.63093i	−0.490996	−	0.490996i
$310$	−5.09059	−	2.95737i	−0.289126	−	0.167967i
$311$			13.6575i			0.774447i	0.921986	+	0.387224i	$0.126566\pi$
$311$			13.6575i			0.774447i	−0.921986	+	0.387224i	$0.873434\pi$
$312$	−4.80356	−	8.63629i	−0.271948	−	0.488934i
$313$	−13.7537			−0.777403			−0.388701	−	0.921364i	$-0.627076\pi$
$313$	−13.7537			−0.777403			−0.388701	+	0.921364i	$0.627076\pi$
$314$	−1.82355	+	19.6363i	−0.102909	+	1.10814i
$315$	−2.34951	−	6.40257i	−0.132380	−	0.360744i
$316$	4.03976	−	21.5628i	0.227254	−	1.21300i
$317$	−16.5311	−	16.5311i	−0.928477	−	0.928477i	0.0691306	−	0.997608i	$-0.477977\pi$
$317$	−16.5311	−	16.5311i	−0.928477	−	0.928477i	−0.997608	+	0.0691306i	$0.977977\pi$
$318$	−12.7708	−	15.3856i	−0.716151	−	0.862780i
$319$	−17.1821			−0.962012
$320$	−3.62222	+	17.5180i	−0.202488	+	0.979285i
$321$	−11.3073			−0.631115
$322$	13.3982	+	16.1414i	0.746651	+	0.899526i
$323$	8.49155	+	8.49155i	0.472482	+	0.472482i
$324$	0.368289	−	1.96580i	0.0204605	−	0.109211i
$325$	17.4109	+	1.43066i	0.965784	+	0.0793588i
$326$	2.43585	−	26.2297i	0.134909	−	1.45273i
$327$	−10.0057			−0.553317
$328$	8.90102	+	16.0031i	0.491476	+	0.883621i
$329$			25.1440i			1.38623i
$330$	−4.06590	+	6.99874i	−0.223821	+	0.385268i
$331$	−8.05179	−	8.05179i	−0.442566	−	0.442566i	0.450307	−	0.892874i	$-0.351314\pi$
$331$	−8.05179	−	8.05179i	−0.442566	−	0.442566i	−0.892874	+	0.450307i	$0.851314\pi$
$332$	−8.53547	+	5.84190i	−0.468445	+	0.320616i
$333$	5.40092	+	5.40092i	0.295968	+	0.295968i
$334$	0.0551668	+	0.0664621i	0.00301859	+	0.00363664i
$335$	24.6797	+	11.4291i	1.34839	+	0.624438i
$336$	−4.91890	−	11.1645i	−0.268348	−	0.609074i
$337$			4.77730i			0.260236i	0.991499	+	0.130118i	$0.0415356\pi$
$337$			4.77730i			0.260236i	−0.991499	+	0.130118i	$0.958464\pi$
$338$	0.862426	−	0.715857i	0.0469098	−	0.0389375i
$339$	4.42016	−	4.42016i	0.240070	−	0.240070i
$340$	−16.1705	+	2.71762i	−0.876966	+	0.147384i
$341$	−3.36951	−	3.36951i	−0.182469	−	0.182469i
$342$	0.428306	−	4.61208i	0.0231601	−	0.249393i
$343$	−14.3271			−0.773589
$344$	4.60049	−	16.1321i	0.248042	−	0.869785i
$345$	−9.86802	−	4.56985i	−0.531276	−	0.246033i
$346$	−1.48249	+	15.9638i	−0.0796994	+	0.858217i
$347$	−3.32673	+	3.32673i	−0.178588	+	0.178588i	−0.790740	−	0.612152i	$-0.790304\pi$
$347$	−3.32673	+	3.32673i	−0.178588	+	0.178588i	0.612152	+	0.790740i	$0.290304\pi$
$348$	−2.47228	+	13.1962i	−0.132528	+	0.707389i
$349$	21.8586	−	21.8586i	1.17007	−	1.17007i	0.187872	−	0.982194i	$-0.439841\pi$
$349$	21.8586	−	21.8586i	1.17007	−	1.17007i	0.982194	−	0.187872i	$-0.0601590\pi$
$350$	21.2391	+	3.74620i	1.13528	+	0.200243i
$351$	−3.49392			−0.186492
$352$	−6.46691	+	12.9547i	−0.344687	+	0.690487i
$353$			5.19436i			0.276468i	0.990400	+	0.138234i	$0.0441426\pi$
$353$			5.19436i			0.276468i	−0.990400	+	0.138234i	$0.955857\pi$
$354$	3.80354	−	3.15713i	0.202156	−	0.167799i
$355$	5.11229	+	13.9313i	0.271332	+	0.739399i
$356$	−25.8561	−	4.84409i	−1.37037	−	0.256736i
$357$	7.90758	−	7.90758i	0.418513	−	0.418513i
$358$	23.5691	+	2.18877i	1.24566	+	0.115680i
$359$			21.0115i			1.10894i	0.832203	+	0.554472i	$0.187080\pi$
$359$			21.0115i			1.10894i	−0.832203	+	0.554472i	$0.812920\pi$
$360$	4.79014	+	4.12972i	0.252462	+	0.217655i
$361$			8.27265i			0.435403i
$362$	−0.672044	+	7.23668i	−0.0353218	+	0.380352i
$363$	3.14564	−	3.14564i	0.165103	−	0.165103i
$364$	−17.5880	+	12.0377i	−0.921864	+	0.630948i
$365$	−5.66868	+	2.08020i	−0.296712	+	0.108882i
$366$	10.2424	+	12.3394i	0.535376	+	0.644993i
$367$			24.5855i			1.28335i	0.766976	+	0.641676i	$0.221760\pi$
$367$			24.5855i			1.28335i	−0.766976	+	0.641676i	$0.778240\pi$
$368$	−18.1341	−	7.04196i	−0.945307	−	0.367088i
$369$	6.47424			0.337035
$370$	−23.3474	+	6.18854i	−1.21377	+	0.321727i
$371$	−30.4929	+	30.4929i	−1.58311	+	1.58311i
$372$	−3.07268	+	2.10302i	−0.159311	+	0.109037i
$373$	−1.00389	+	1.00389i	−0.0519795	+	0.0519795i	−0.732619	−	0.680639i	$-0.761702\pi$
$373$	−1.00389	+	1.00389i	−0.0519795	+	0.0519795i	0.680639	+	0.732619i	$0.261702\pi$
$374$	−13.2152	−	1.22724i	−0.683340	−	0.0634592i
$375$	−10.7761	+	2.97913i	−0.556477	+	0.153842i
$376$	−11.3340	−	20.3772i	−0.584505	−	1.05088i
$377$	23.4542			1.20796
$378$	−4.29490	−	0.398851i	−0.220906	−	0.0205147i
$379$	−4.93721	−	4.93721i	−0.253607	−	0.253607i	0.568841	−	0.822448i	$-0.307392\pi$
$379$	−4.93721	−	4.93721i	−0.253607	−	0.253607i	−0.822448	+	0.568841i	$0.807392\pi$
$380$	11.9306	+	8.49747i	0.612029	+	0.435911i
$381$	−10.0327	+	10.0327i	−0.513992	+	0.513992i
$382$	17.2360	+	20.7650i	0.881870	+	1.06243i
$383$		−	4.25312i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$383$		−	4.25312i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$384$	9.01894	+	6.83072i	0.460246	+	0.348579i
$385$	15.8403	+	7.33560i	0.807296	+	0.373857i
$386$	3.25383	−	2.70085i	0.165616	−	0.137469i
$387$	−4.19382	−	4.19382i	−0.213184	−	0.213184i
$388$	24.5591	+	4.60111i	1.24680	+	0.233586i
$389$	−15.1555	−	15.1555i	−0.768414	−	0.768414i	0.209413	−	0.977827i	$-0.432845\pi$
$389$	−15.1555	−	15.1555i	−0.768414	−	0.768414i	−0.977827	+	0.209413i	$0.932845\pi$
$390$	5.55013	−	9.55357i	0.281042	−	0.483764i
$391$		−	17.8317i		−	0.901786i
$392$	−5.69166	+	3.16574i	−0.287472	+	0.159894i
$393$	−17.7515			−0.895445
$394$	2.73366	+	0.253865i	0.137720	+	0.0127895i
$395$	23.0260	−	8.44969i	1.15856	−	0.425150i
$396$	2.89131	+	4.22444i	0.145294	+	0.212286i
$397$	2.06126	+	2.06126i	0.103451	+	0.103451i	0.756938	−	0.653487i	$-0.226694\pi$
$397$	2.06126	+	2.06126i	0.103451	+	0.103451i	−0.653487	+	0.756938i	$0.726694\pi$
$398$	−17.0985	+	14.1927i	−0.857073	+	0.711413i
$399$	−9.98962			−0.500107
$400$	−18.9013	+	6.53777i	−0.945063	+	0.326889i
$401$	10.1012			0.504431			0.252215	−	0.967671i	$-0.418841\pi$
$401$	10.1012			0.504431			0.252215	+	0.967671i	$0.418841\pi$
$402$	13.2357	−	10.9863i	0.660139	−	0.547948i
$403$	4.59952	+	4.59952i	0.229119	+	0.229119i
$404$	−1.32930	+	0.909811i	−0.0661354	+	0.0452648i
$405$	2.09919	−	0.770325i	0.104310	−	0.0382778i
$406$	28.8312	+	2.67744i	1.43087	+	0.132879i
$407$	−19.5501			−0.969063
$408$	−2.84404	+	9.97292i	−0.140801	+	0.493733i
$409$			15.5464i			0.768720i	0.923183	+	0.384360i	$0.125578\pi$
$409$			15.5464i			0.768720i	−0.923183	+	0.384360i	$0.874422\pi$
$410$	−10.2844	+	17.7028i	−0.507910	+	0.874278i
$411$	3.45306	+	3.45306i	0.170327	+	0.170327i
$412$	4.49532	−	23.9945i	0.221469	−	1.18212i
$413$	−7.53829	−	7.53829i	−0.370935	−	0.370935i
$414$	−5.29223	+	4.39282i	−0.260099	+	0.215895i
$415$	−10.4935	−	4.85950i	−0.515104	−	0.238543i
$416$	8.82760	−	17.6837i	0.432809	−	0.867013i
$417$			8.26686i			0.404830i
$418$	7.57216	+	9.12253i	0.370366	+	0.446198i
$419$	0.811206	−	0.811206i	0.0396300	−	0.0396300i	−0.687014	−	0.726644i	$-0.741079\pi$
$419$	0.811206	−	0.811206i	0.0396300	−	0.0396300i	0.726644	+	0.687014i	$0.241079\pi$
$420$	7.91310	−	11.1102i	0.386120	−	0.542120i
$421$	6.67755	+	6.67755i	0.325444	+	0.325444i	0.850851	−	0.525407i	$-0.176087\pi$
$421$	6.67755	+	6.67755i	0.325444	+	0.325444i	−0.525407	+	0.850851i	$0.676087\pi$
$422$	33.5339	+	3.11417i	1.63241	+	0.151595i
$423$	−8.24387			−0.400831
$424$	10.9671	−	38.4572i	0.532609	−	1.86765i
$425$	−11.8580	−	13.9812i	−0.575197	−	0.678189i
$426$	9.34526	+	0.867859i	0.452779	+	0.0420479i
$427$	24.4558	−	24.4558i	1.18350	−	1.18350i
$428$	−12.7729	−	18.6622i	−0.617401	−	0.902072i
$429$	6.32360	−	6.32360i	0.305306	−	0.305306i
$430$	18.1293	−	4.80541i	0.874271	−	0.231738i
$431$	−20.8900			−1.00623			−0.503117	−	0.864218i	$-0.667814\pi$
$431$	−20.8900			−1.00623			−0.503117	+	0.864218i	$0.667814\pi$
$432$	3.66047	−	1.61274i	0.176115	−	0.0775932i
$433$			21.0344i			1.01085i	0.862870	+	0.505426i	$0.168664\pi$
$433$			21.0344i			1.01085i	−0.862870	+	0.505426i	$0.831336\pi$
$434$	5.12891	+	6.17903i	0.246195	+	0.296603i
$435$	−14.0916	+	5.17110i	−0.675641	+	0.247935i
$436$	−11.3025	−	16.5139i	−0.541294	−	0.790873i
$437$	−11.2633	+	11.2633i	−0.538799	+	0.538799i
$438$	−0.353133	+	3.80260i	−0.0168734	+	0.181695i
$439$			27.5268i			1.31378i	0.753986	+	0.656891i	$0.228129\pi$
$439$			27.5268i			1.31378i	−0.753986	+	0.656891i	$0.771871\pi$
$440$	−16.1439	+	1.19528i	−0.769633	+	0.0569827i
$441$			2.30263i			0.109649i
$442$	18.0393	+	1.67524i	0.858040	+	0.0796829i
$443$	−15.3577	+	15.3577i	−0.729667	+	0.729667i	−0.970553	−	0.240886i	$-0.922562\pi$
$443$	−15.3577	+	15.3577i	−0.729667	+	0.729667i	0.240886	+	0.970553i	$0.422562\pi$
$444$	−2.81301	+	15.0149i	−0.133499	+	0.712574i
$445$	−10.1321	−	27.6106i	−0.480306	−	1.30887i
$446$	11.6319	−	9.65509i	0.550788	−	0.457182i
$447$		−	21.4230i		−	1.01327i
$448$	12.8700	−	20.7299i	0.608052	−	0.979398i
$449$	34.2343			1.61562			0.807808	−	0.589445i	$-0.200654\pi$
$449$	34.2343			1.61562			0.807808	+	0.589445i	$0.200654\pi$
$450$	−1.22825	+	6.96358i	−0.0579004	+	0.328266i
$451$	−11.7177	+	11.7177i	−0.551763	+	0.551763i
$452$	12.2883	+	2.30219i	0.577993	+	0.108286i
$453$	2.84279	−	2.84279i	0.133566	−	0.133566i
$454$	−2.78740	+	30.0152i	−0.130819	+	1.40868i
$455$	−21.6227	−	10.0134i	−1.01369	−	0.469435i
$456$	8.09582	−	4.50295i	0.379121	−	0.210870i
$457$	−37.3287			−1.74616			−0.873081	−	0.487575i	$-0.837881\pi$
$457$	−37.3287			−1.74616			−0.873081	+	0.487575i	$0.837881\pi$
$458$	0.598509	−	6.44485i	0.0279665	−	0.301148i
$459$	2.59263	+	2.59263i	0.121014	+	0.121014i
$460$	−3.60470	−	21.4488i	−0.168070	−	1.00006i
$461$	4.31480	−	4.31480i	0.200960	−	0.200960i	−0.599451	−	0.800411i	$-0.704614\pi$
$461$	4.31480	−	4.31480i	0.200960	−	0.200960i	0.800411	+	0.599451i	$0.204614\pi$
$462$	8.49517	−	7.05142i	0.395231	−	0.328062i
$463$		−	12.6151i		−	0.586272i	−0.956071	−	0.293136i	$-0.905301\pi$
$463$		−	12.6151i		−	0.586272i	0.956071	−	0.293136i	$-0.0946988\pi$
$464$	−24.5723	+	10.8262i	−1.14074	+	0.502591i
$465$	−3.77754	−	1.74937i	−0.175179	−	0.0811250i
$466$	4.29429	+	5.17353i	0.198929	+	0.239659i
$467$	−3.20222	−	3.20222i	−0.148181	−	0.148181i	0.629124	−	0.777305i	$-0.283414\pi$
$467$	−3.20222	−	3.20222i	−0.148181	−	0.148181i	−0.777305	+	0.629124i	$0.783414\pi$
$468$	−3.94676	−	5.76653i	−0.182439	−	0.266558i
$469$	−26.2321	−	26.2321i	−1.21129	−	1.21129i
$470$	13.0955	−	22.5416i	0.604049	−	1.03977i
$471$			13.9447i			0.642539i
$472$	9.50719	+	2.71122i	0.437604	+	0.124794i
$473$	15.1807			0.698009
$474$	1.43442	−	15.4460i	0.0658849	−	0.709460i
$475$	−1.34113	+	16.3213i	−0.0615352	+	0.748873i
$476$	21.9835	+	4.11857i	1.00761	+	0.188775i
$477$	−9.99761	−	9.99761i	−0.457759	−	0.457759i
$478$	10.7689	+	12.9738i	0.492557	+	0.593406i
$479$	−9.07562			−0.414676			−0.207338	−	0.978269i	$-0.566480\pi$
$479$	−9.07562			−0.414676			−0.207338	+	0.978269i	$0.566480\pi$
$480$	−1.40491	+	12.5708i	−0.0641249	+	0.573778i
$481$	26.6867			1.21681
$482$	−25.5611	−	30.7947i	−1.16428	−	1.40266i
$483$	10.4888	+	10.4888i	0.477255	+	0.477255i
$484$	8.74506	+	1.63837i	0.397503	+	0.0744714i
$485$	9.62383	+	26.2256i	0.436996	+	1.19084i
$486$	0.130770	−	1.40815i	0.00593185	−	0.0638752i
$487$	−1.02703			−0.0465390			−0.0232695	−	0.999729i	$-0.507408\pi$
$487$	−1.02703			−0.0465390			−0.0232695	+	0.999729i	$0.507408\pi$
$488$	−8.79575	+	30.8432i	−0.398165	+	1.39621i
$489$		−	18.6270i		−	0.842342i
$490$	−6.29618	−	3.65775i	−0.284433	−	0.165241i
$491$	−20.0654	−	20.0654i	−0.905539	−	0.905539i	0.0903689	−	0.995908i	$-0.471195\pi$
$491$	−20.0654	−	20.0654i	−0.905539	−	0.905539i	−0.995908	+	0.0903689i	$0.971195\pi$
$492$	7.31336	+	10.6854i	0.329712	+	0.481735i
$493$	−17.4040	−	17.4040i	−0.783837	−	0.783837i
$494$	−10.3363	−	12.4526i	−0.465053	−	0.560271i
$495$	−2.40510	+	5.19350i	−0.108101	+	0.233431i
$496$	−6.94186	−	2.69571i	−0.311699	−	0.121041i
$497$		−	20.2416i		−	0.907958i
$498$	−5.62766	+	4.67124i	−0.252181	+	0.209323i
$499$	15.1622	−	15.1622i	0.678752	−	0.678752i	−0.280966	−	0.959718i	$-0.590655\pi$
$499$	15.1622	−	15.1622i	0.678752	−	0.678752i	0.959718	+	0.280966i	$0.0906547\pi$
$500$	−17.0897	−	14.4202i	−0.764275	−	0.644890i
$501$	0.0431873	+	0.0431873i	0.00192947	+	0.00192947i
$502$	0.812271	−	8.74667i	0.0362534	−	0.390383i
$503$	−15.6071			−0.695885			−0.347942	−	0.937516i	$-0.613120\pi$
$503$	−15.6071			−0.695885			−0.347942	+	0.937516i	$0.613120\pi$
$504$	−4.19328	−	7.53906i	−0.186784	−	0.335817i
$505$	−1.63424	−	0.756813i	−0.0727228	−	0.0336777i
$506$	1.62784	−	17.5289i	0.0723663	−	0.779253i
$507$	0.560408	−	0.560408i	0.0248886	−	0.0248886i
$508$	−27.8916	−	5.22543i	−1.23749	−	0.231841i
$509$	10.8076	−	10.8076i	0.479040	−	0.479040i	−0.425785	−	0.904824i	$-0.640002\pi$
$509$	10.8076	−	10.8076i	0.479040	−	0.479040i	0.904824	+	0.425785i	$0.140002\pi$
$510$	−11.2076	+	2.97072i	−0.496279	+	0.131546i
$511$	8.23632			0.364353
$512$	−1.08587	+	22.6013i	−0.0479893	+	0.998848i
$513$		−	3.27526i		−	0.144606i
$514$	2.75365	−	2.28567i	0.121458	−	0.100817i
$515$	25.6227	−	9.40257i	1.12907	−	0.414327i
$516$	2.18430	−	11.6591i	0.0961586	−	0.513262i
$517$	14.9205	−	14.9205i	0.656202	−	0.656202i
$518$	32.8047	+	3.04645i	1.44135	+	0.133853i
$519$			11.3367i			0.497624i
$520$	22.0372	−	1.63161i	0.966393	−	0.0715507i
$521$		−	32.1238i		−	1.40737i	−0.710513	−	0.703684i	$-0.751537\pi$
$521$		−	32.1238i		−	1.40737i	0.710513	−	0.703684i	$-0.248463\pi$
$522$	−0.877843	+	9.45277i	−0.0384222	+	0.413737i
$523$	−3.26553	+	3.26553i	−0.142792	+	0.142792i	−0.774889	−	0.632097i	$-0.782194\pi$
$523$	−3.26553	+	3.26553i	−0.142792	+	0.142792i	0.632097	+	0.774889i	$0.282194\pi$
$524$	−20.0523	−	29.2979i	−0.875987	−	1.27989i
$525$	15.1989	+	1.24890i	0.663334	+	0.0545064i
$526$	−0.488641	−	0.588689i	−0.0213058	−	0.0256681i
$527$		−	6.82607i		−	0.297348i
$528$	−3.70616	+	9.54393i	−0.161290	+	0.415346i
$529$	0.652259			0.0283591
$530$	43.2182	−	11.4556i	1.87728	−	0.497599i
$531$	2.47155	−	2.47155i	0.107256	−	0.107256i
$532$	−11.2844	−	16.4874i	−0.489240	−	0.714818i
$533$	15.9951	−	15.9951i	0.692824	−	0.692824i
$534$	−18.5214	−	1.72001i	−0.801499	−	0.0744322i
$535$	10.6249	−	22.9432i	0.459356	−	0.991922i
$536$	33.0836	+	9.43465i	1.42899	+	0.407515i
$537$	16.7375			0.722278
$538$	−5.97805	−	0.555159i	−0.257732	−	0.0239346i
$539$	−4.16751	−	4.16751i	−0.179507	−	0.179507i
$540$	3.64265	+	2.59444i	0.156755	+	0.111647i
$541$	−25.5767	+	25.5767i	−1.09963	+	1.09963i	−0.105176	+	0.994454i	$0.533541\pi$
$541$	−25.5767	+	25.5767i	−1.09963	+	1.09963i	−0.994454	+	0.105176i	$0.966459\pi$
$542$	−7.62623	−	9.18767i	−0.327574	−	0.394644i
$543$			5.13913i			0.220541i
$544$	−19.6724	+	6.57157i	−0.843449	+	0.281754i
$545$	9.40186	−	20.3021i	0.402731	−	0.869647i
$546$	−11.5963	+	9.62548i	−0.496274	+	0.411932i
$547$	−6.44163	−	6.44163i	−0.275424	−	0.275424i	0.555855	−	0.831279i	$-0.312391\pi$
$547$	−6.44163	−	6.44163i	−0.275424	−	0.275424i	−0.831279	+	0.555855i	$0.812391\pi$
$548$	−1.79849	+	9.59971i	−0.0768276	+	0.410079i
$549$	8.01822	+	8.01822i	0.342209	+	0.342209i
$550$	−10.3803	−	14.8263i	−0.442617	−	0.632196i
$551$			21.9864i			0.936654i
$552$	−13.2283	−	3.77239i	−0.563033	−	0.160563i
$553$	−33.4557			−1.42268
$554$	24.3937	+	2.26536i	1.03639	+	0.0962457i
$555$	−16.0337	+	5.88378i	−0.680594	+	0.249753i
$556$	−13.6440	+	9.33833i	−0.578636	+	0.396033i
$557$	1.38276	+	1.38276i	0.0585893	+	0.0585893i	0.735794	−	0.677205i	$-0.236809\pi$
$557$	1.38276	+	1.38276i	0.0585893	+	0.0585893i	−0.677205	+	0.735794i	$0.736809\pi$
$558$	−2.02590	+	1.68160i	−0.0857631	+	0.0711877i
$559$	−20.7223			−0.876459
$560$	27.2755	+	0.510018i	1.15260	+	0.0215522i
$561$	−9.38474			−0.396224
$562$	−18.1631	+	15.0763i	−0.766165	+	0.635955i
$563$	−4.13198	−	4.13198i	−0.174142	−	0.174142i	0.614654	−	0.788797i	$-0.289296\pi$
$563$	−4.13198	−	4.13198i	−0.174142	−	0.174142i	−0.788797	+	0.614654i	$0.789296\pi$
$564$	−9.31236	−	13.6061i	−0.392121	−	0.572920i
$565$	4.81534	+	13.1221i	0.202583	+	0.552053i
$566$	2.50522	+	0.232650i	0.105302	+	0.00977900i
$567$	−3.05002			−0.128089
$568$	9.12414	+	16.4042i	0.382840	+	0.688306i
$569$			14.2348i			0.596755i	0.954448	+	0.298378i	$0.0964455\pi$
$569$			14.2348i			0.596755i	−0.954448	+	0.298378i	$0.903554\pi$
$570$	8.95569	+	5.20279i	0.375113	+	0.217921i
$571$	14.6986	+	14.6986i	0.615116	+	0.615116i	0.944275	−	0.329158i	$-0.106765\pi$
$571$	14.6986	+	14.6986i	0.615116	+	0.615116i	−0.329158	+	0.944275i	$0.606765\pi$
$572$	17.5800	+	3.29358i	0.735056	+	0.137711i
$573$	13.4932	+	13.4932i	0.563686	+	0.563686i
$574$	21.4879	−	17.8360i	0.896887	−	0.744462i
$575$	18.5450	−	15.7287i	0.773378	−	0.655931i
$576$	6.79666	+	4.21965i	0.283194	+	0.175819i
$577$			8.52221i			0.354784i	0.984140	+	0.177392i	$0.0567661\pi$
$577$			8.52221i			0.354784i	−0.984140	+	0.177392i	$0.943234\pi$
$578$	3.21244	+	3.87017i	0.133620	+	0.160978i
$579$	2.11436	−	2.11436i	0.0878696	−	0.0878696i
$580$	−24.4527	−	17.4162i	−1.01534	−	0.723167i
$581$	11.1536	+	11.1536i	0.462728	+	0.462728i
$582$	17.5924	+	1.63374i	0.729227	+	0.0677206i
$583$	36.1891			1.49880
$584$	−6.67490	+	3.71263i	−0.276209	+	0.153630i
$585$	3.28306	−	7.08935i	0.135738	−	0.293108i
$586$	24.7329	+	2.29685i	1.02171	+	0.0948820i
$587$	−13.9568	+	13.9568i	−0.576057	+	0.576057i	−0.933815	−	0.357757i	$-0.883541\pi$
$587$	−13.9568	+	13.9568i	−0.576057	+	0.576057i	0.357757	+	0.933815i	$0.383541\pi$
$588$	−3.80037	+	2.60107i	−0.156725	+	0.107267i
$589$	−4.31168	+	4.31168i	−0.177660	+	0.177660i
$590$	2.83199	+	10.6842i	0.116591	+	0.439860i
$591$	1.94131			0.0798547
$592$	−27.9589	+	12.3182i	−1.14910	+	0.506276i
$593$			22.9285i			0.941561i	0.882250	+	0.470781i	$0.156028\pi$
$593$			22.9285i			0.941561i	−0.882250	+	0.470781i	$0.843972\pi$
$594$	2.31192	+	2.78528i	0.0948594	+	0.114282i
$595$	8.61455	+	23.4752i	0.353162	+	0.962391i
$596$	35.3575	−	24.1996i	1.44830	−	0.991254i
$597$	−11.1107	+	11.1107i	−0.454731	+	0.454731i
$598$	−2.22207	+	23.9276i	−0.0908671	+	0.978473i
$599$		−	15.8822i		−	0.648928i	−0.945898	−	0.324464i	$-0.894816\pi$
$599$		−	15.8822i		−	0.648928i	0.945898	−	0.324464i	$-0.105184\pi$
$600$	−12.8805	+	5.83895i	−0.525843	+	0.238374i
$601$		−	4.12190i		−	0.168136i	−0.996460	−	0.0840680i	$-0.973209\pi$
$601$		−	4.12190i		−	0.168136i	0.996460	−	0.0840680i	$-0.0267913\pi$
$602$	−25.4729	−	2.36557i	−1.03820	−	0.0964134i
$603$	8.60064	−	8.60064i	0.350245	−	0.350245i
$604$	7.90313	+	1.48064i	0.321574	+	0.0602462i
$605$	3.42687	+	9.33847i	0.139322	+	0.379663i
$606$	−0.876445	+	0.727494i	−0.0356032	+	0.0295524i
$607$			26.7142i			1.08429i	0.840283	+	0.542147i	$0.182389\pi$
$607$			26.7142i			1.08429i	−0.840283	+	0.542147i	$0.817611\pi$
$608$	16.5770	+	8.27515i	0.672286	+	0.335602i
$609$	20.4744			0.829666
$610$	−34.6616	+	9.18754i	−1.40341	+	0.371993i
$611$	−20.3671	+	20.3671i	−0.823964	+	0.823964i
$612$	−1.35034	+	7.20766i	−0.0545844	+	0.291353i
$613$	−10.0253	+	10.0253i	−0.404918	+	0.404918i	−0.879962	−	0.475044i	$-0.842432\pi$
$613$	−10.0253	+	10.0253i	−0.404918	+	0.404918i	0.475044	+	0.879962i	$0.342432\pi$
$614$	−4.01302	+	43.2129i	−0.161952	+	1.74393i
$615$	−6.08351	+	13.1366i	−0.245311	+	0.529718i
$616$	21.2342	+	6.05549i	0.855552	+	0.243983i
$617$	−26.3757			−1.06185			−0.530923	−	0.847420i	$-0.678155\pi$
$617$	−26.3757			−1.06185			−0.530923	+	0.847420i	$0.678155\pi$
$618$	1.59618	−	17.1879i	0.0642076	−	0.691399i
$619$	−7.39439	−	7.39439i	−0.297206	−	0.297206i	0.542713	−	0.839918i	$-0.317397\pi$
$619$	−7.39439	−	7.39439i	−0.297206	−	0.297206i	−0.839918	+	0.542713i	$0.817397\pi$
$620$	−1.37990	−	8.21073i	−0.0554182	−	0.329751i
$621$	−3.43891	+	3.43891i	−0.137999	+	0.137999i
$622$	−14.8619	+	12.3361i	−0.595908	+	0.494634i
$623$			40.1168i			1.60725i
$624$	5.05906	−	13.0279i	0.202525	−	0.521532i
$625$	4.08096	−	24.6647i	0.163239	−	0.986587i
$626$	−12.4230	−	14.9665i	−0.496521	−	0.598182i
$627$	5.92786	+	5.92786i	0.236736	+	0.236736i
$628$	−23.0150	+	15.7521i	−0.918400	+	0.628577i
$629$	−19.8026	−	19.8026i	−0.789583	−	0.789583i
$630$	4.84499	−	8.33981i	0.193029	−	0.332266i
$631$			34.8730i			1.38827i	0.719844	+	0.694136i	$0.244213\pi$
$631$			34.8730i			1.38827i	−0.719844	+	0.694136i	$0.755787\pi$
$632$	27.1132	−	15.0806i	1.07851	−	0.599873i
$633$	23.8141			0.946525
$634$	3.05720	−	32.9205i	0.121417	−	1.30744i
$635$	−10.9297	−	29.7842i	−0.433732	−	1.18195i
$636$	5.20715	−	27.7939i	0.206477	−	1.10210i
$637$	5.68882	+	5.68882i	0.225399	+	0.225399i
$638$	−15.5197	−	18.6973i	−0.614429	−	0.740232i
$639$	6.63653			0.262537
$640$	−22.3345	+	11.8814i	−0.882850	+	0.469655i
$641$	6.05015			0.238966			0.119483	−	0.992836i	$-0.461876\pi$
$641$	6.05015			0.238966			0.119483	+	0.992836i	$0.461876\pi$
$642$	−10.2133	−	12.3045i	−0.403088	−	0.485619i
$643$	7.52447	+	7.52447i	0.296736	+	0.296736i	0.839734	−	0.542998i	$-0.182711\pi$
$643$	7.52447	+	7.52447i	0.296736	+	0.296736i	−0.542998	+	0.839734i	$0.682711\pi$
$644$	−5.46296	+	29.1594i	−0.215271	+	1.14904i
$645$	12.4502	−	4.56876i	0.490226	−	0.179895i
$646$	−1.57040	+	16.9103i	−0.0617865	+	0.665328i
$647$	24.8356			0.976389			0.488194	−	0.872735i	$-0.337656\pi$
$647$	24.8356			0.976389			0.488194	+	0.872735i	$0.337656\pi$
$648$	2.47181	−	1.37484i	0.0971017	−	0.0540087i
$649$			8.94648i			0.351180i
$650$	14.1695	+	20.2385i	0.555775	+	0.793820i
$651$	4.01516	+	4.01516i	0.157367	+	0.157367i
$652$	30.7429	−	21.0412i	1.20399	−	0.824039i
$653$	20.0550	+	20.0550i	0.784813	+	0.784813i	0.980639	−	0.195826i	$-0.0627386\pi$
$653$	20.0550	+	20.0550i	0.784813	+	0.784813i	−0.195826	+	0.980639i	$0.562739\pi$
$654$	−9.03763	−	10.8881i	−0.353399	−	0.425757i
$655$	16.6802	−	36.0187i	0.651749	−	1.40737i
$656$	−9.37446	+	24.1407i	−0.366011	+	0.942535i
$657$			2.70041i			0.105353i
$658$	−27.3613	+	22.7112i	−1.06665	+	0.885376i
$659$	20.7719	−	20.7719i	0.809158	−	0.809158i	−0.175349	−	0.984506i	$-0.556105\pi$
$659$	20.7719	−	20.7719i	0.809158	−	0.809158i	0.984506	+	0.175349i	$0.0561053\pi$
$660$	−11.2884	+	1.89714i	−0.439402	+	0.0738461i
$661$	−11.2908	−	11.2908i	−0.439161	−	0.439161i	0.452568	−	0.891730i	$-0.350508\pi$
$661$	−11.2908	−	11.2908i	−0.439161	−	0.439161i	−0.891730	+	0.452568i	$0.850508\pi$
$662$	1.48907	−	16.0346i	0.0578744	−	0.623202i
$663$	12.8106			0.497521
$664$	−14.0667	−	4.01149i	−0.545894	−	0.155676i
$665$	9.38674	−	20.2695i	0.364002	−	0.786017i
$666$	−0.998828	+	10.7556i	−0.0387038	+	0.416769i
$667$	23.0850	−	23.0850i	0.893855	−	0.893855i
$668$	−0.0224936	+	0.120063i	−0.000870305	+	0.00464539i
$669$	7.55849	−	7.55849i	0.292228	−	0.292228i
$670$	9.85489	+	37.1793i	0.380728	+	1.43636i
$671$	−29.0242			−1.12047
$672$	7.70607	−	15.4370i	0.297268	−	0.595495i
$673$			1.03722i			0.0399820i	0.999800	+	0.0199910i	$0.00636376\pi$
$673$			1.03722i			0.0399820i	−0.999800	+	0.0199910i	$0.993636\pi$
$674$	−5.19858	+	4.31508i	−0.200242	+	0.166211i
$675$	−0.409472	+	4.98321i	−0.0157606	+	0.191804i
$676$	1.55797	+	0.291882i	0.0599218	+	0.0112262i
$677$	18.4431	−	18.4431i	0.708825	−	0.708825i	−0.257463	−	0.966288i	$-0.582887\pi$
$677$	18.4431	−	18.4431i	0.708825	−	0.708825i	0.966288	+	0.257463i	$0.0828867\pi$
$678$	8.80245	+	0.817450i	0.338056	+	0.0313940i
$679$		−	38.1046i		−	1.46232i
$680$	−17.5632	−	15.1418i	−0.673518	−	0.580660i
$681$			21.3153i			0.816802i
$682$	0.623147	−	6.71015i	0.0238615	−	0.256945i
$683$	0.922102	−	0.922102i	0.0352833	−	0.0352833i	−0.689245	−	0.724528i	$-0.742058\pi$
$683$	0.922102	−	0.922102i	0.0352833	−	0.0352833i	0.724528	+	0.689245i	$0.242058\pi$
$684$	5.40565	−	3.69977i	0.206690	−	0.141464i
$685$	−10.2511	+	3.76178i	−0.391675	+	0.143730i
$686$	−12.9409	−	15.5905i	−0.494086	−	0.595248i
$687$		−	4.57681i		−	0.174616i
$688$	21.7101	−	9.56511i	0.827690	−	0.364666i
$689$	−49.3997			−1.88198
$690$	−3.94042	−	14.8659i	−0.150009	−	0.565936i
$691$	−7.34104	+	7.34104i	−0.279266	+	0.279266i	−0.832816	−	0.553550i	$-0.813273\pi$
$691$	−7.34104	+	7.34104i	−0.279266	+	0.279266i	0.553550	+	0.832816i	$0.313273\pi$
$692$	−18.7106	+	12.8060i	−0.711269	+	0.486811i
$693$	5.52020	−	5.52020i	0.209695	−	0.209695i
$694$	−6.62495	−	0.615235i	−0.251480	−	0.0233540i
$695$	−16.7739	−	7.76795i	−0.636271	−	0.294655i
$696$	−16.5929	+	9.22911i	−0.628954	+	0.349828i
$697$	−23.7380			−0.899141
$698$	43.5300	+	4.04246i	1.64763	+	0.153009i
$699$	3.36178	+	3.36178i	0.127154	+	0.127154i
$700$	15.1076	+	26.4957i	0.571012	+	1.00145i
$701$	25.7637	−	25.7637i	0.973080	−	0.973080i	−0.0265667	−	0.999647i	$-0.508457\pi$
$701$	25.7637	−	25.7637i	0.973080	−	0.973080i	0.999647	+	0.0265667i	$0.00845745\pi$
$702$	−3.15587	−	3.80203i	−0.119111	−	0.143498i
$703$			25.0166i			0.943520i
$704$	−19.9383	+	4.66409i	−0.751453	+	0.175785i
$705$	7.74635	−	16.7273i	0.291744	−	0.629985i
$706$	−5.65242	+	4.69179i	−0.212732	+	0.176578i
$707$	1.73704	+	1.73704i	0.0653282	+	0.0653282i
$708$	6.87107	+	1.28728i	0.258230	+	0.0483790i
$709$	18.8691	+	18.8691i	0.708645	+	0.708645i	0.966250	−	0.257605i	$-0.0829335\pi$
$709$	18.8691	+	18.8691i	0.708645	+	0.708645i	−0.257605	+	0.966250i	$0.582933\pi$
$710$	−10.5422	+	18.1466i	−0.395642	+	0.681028i
$711$		−	10.9690i		−	0.411369i
$712$	−18.0832	−	32.5116i	−0.677695	−	1.21842i
$713$	9.05423			0.339084
$714$	15.7474	+	1.46240i	0.589331	+	0.0547290i
$715$	6.88896	+	18.7729i	0.257632	+	0.702067i
$716$	18.9069	+	27.6245i	0.706584	+	1.03237i
$717$	8.43041	+	8.43041i	0.314839	+	0.314839i
$718$	−22.8644	+	18.9786i	−0.853290	+	0.708274i
$719$	−48.8119			−1.82038			−0.910189	−	0.414194i	$-0.864063\pi$
$719$	−48.8119			−1.82038			−0.910189	+	0.414194i	$0.864063\pi$
$720$	−0.167218	+	8.94271i	−0.00623184	+	0.333275i
$721$	−37.2285			−1.38646
$722$	−9.00217	+	7.47225i	−0.335026	+	0.278088i
$723$	−20.0105	−	20.0105i	−0.744199	−	0.744199i
$724$	−8.48187	+	5.80521i	−0.315226	+	0.215749i
$725$	2.74873	−	33.4517i	0.102085	−	1.24236i
$726$	6.26432	+	0.581744i	0.232491	+	0.0215906i
$727$	20.2737			0.751908			0.375954	−	0.926638i	$-0.377315\pi$
$727$	20.2737			0.751908			0.375954	+	0.926638i	$0.377315\pi$
$728$	−28.9856	−	8.26600i	−1.07428	−	0.306358i
$729$		−	1.00000i		−	0.0370370i
$730$	−7.38386	−	4.28964i	−0.273289	−	0.158767i
$731$	15.3768	+	15.3768i	0.568730	+	0.568730i
$732$	−4.17620	+	22.2911i	−0.154357	+	0.823904i
$733$	−21.1889	−	21.1889i	−0.782631	−	0.782631i	0.197643	−	0.980274i	$-0.436671\pi$
$733$	−21.1889	−	21.1889i	−0.782631	−	0.782631i	−0.980274	+	0.197643i	$0.936671\pi$
$734$	−26.7535	+	22.2068i	−0.987490	+	0.819666i
$735$	−4.67216	−	2.16367i	−0.172335	−	0.0798080i
$736$	−8.71666	−	26.0939i	−0.321300	−	0.961834i
$737$			31.1324i			1.14678i
$738$	5.84784	+	7.04516i	0.215262	+	0.259336i
$739$	−3.65840	+	3.65840i	−0.134576	+	0.134576i	−0.771186	−	0.636610i	$-0.780336\pi$
$739$	−3.65840	+	3.65840i	−0.134576	+	0.134576i	0.636610	+	0.771186i	$0.280336\pi$
$740$	−27.8227	−	19.8165i	−1.02278	−	0.728467i
$741$	−8.09178	−	8.09178i	−0.297259	−	0.297259i
$742$	−60.7246	−	5.63926i	−2.22927	−	0.207024i
$743$	−4.42017			−0.162160			−0.0810802	−	0.996708i	$-0.525837\pi$
$743$	−4.42017			−0.162160			−0.0810802	+	0.996708i	$0.525837\pi$
$744$	−5.06386	−	1.44409i	−0.185650	−	0.0529430i
$745$	43.4684	+	20.1301i	1.59256	+	0.737509i
$746$	−1.99918	−	0.185656i	−0.0731952	−	0.00679736i
$747$	−3.65688	+	3.65688i	−0.133798	+	0.133798i
$748$	−10.6011	−	15.4890i	−0.387615	−	0.566335i
$749$	−24.3865	+	24.3865i	−0.891062	+	0.891062i
$750$	−12.9753	−	9.03551i	−0.473793	−	0.329930i
$751$	30.4414			1.11082			0.555411	−	0.831576i	$-0.312561\pi$
$751$	30.4414			1.11082			0.555411	+	0.831576i	$0.312561\pi$
$752$	11.9368	−	30.7391i	0.435291	−	1.12094i
$753$		−	6.21144i		−	0.226358i
$754$	21.1850	+	25.5225i	0.771512	+	0.929476i
$755$	3.09695	+	8.43940i	0.112710	+	0.307141i
$756$	−3.44533	−	5.03390i	−0.125306	−	0.183081i
$757$	−18.5016	+	18.5016i	−0.672454	+	0.672454i	−0.958281	−	0.285828i	$-0.907732\pi$
$757$	−18.5016	+	18.5016i	−0.672454	+	0.672454i	0.285828	+	0.958281i	$0.407732\pi$
$758$	0.913071	−	9.83211i	0.0331642	−	0.357118i
$759$		−	12.4481i		−	0.451838i
$760$	1.52950	+	20.6580i	0.0554807	+	0.749346i
$761$		−	11.9248i		−	0.432273i	−0.976363	−	0.216137i	$-0.930654\pi$
$761$		−	11.9248i		−	0.432273i	0.976363	−	0.216137i	$-0.0693456\pi$
$762$	−19.9795	−	1.85542i	−0.723780	−	0.0672148i
$763$	−21.5792	+	21.5792i	−0.781220	+	0.781220i
$764$	−7.02778	+	37.5119i	−0.254256	+	1.35713i
$765$	−7.69675	+	2.82442i	−0.278277	+	0.102117i
$766$	4.62817	−	3.84161i	0.167223	−	0.138803i
$767$		−	12.2123i		−	0.440961i
$768$	0.713251	+	15.9841i	0.0257372	+	0.576776i
$769$	51.5679			1.85958			0.929792	−	0.368085i	$-0.119986\pi$
$769$	51.5679			1.85958			0.929792	+	0.368085i	$0.119986\pi$
$770$	6.32522	+	23.8630i	0.227945	+	0.859963i
$771$	1.78934	−	1.78934i	0.0644414	−	0.0644414i
$772$	5.87803	+	1.10124i	0.211555	+	0.0396345i
$773$	−13.7126	+	13.7126i	−0.493209	+	0.493209i	−0.909316	−	0.416107i	$-0.863394\pi$
$773$	−13.7126	+	13.7126i	−0.493209	+	0.493209i	0.416107	+	0.909316i	$0.363394\pi$
$774$	0.775591	−	8.35170i	0.0278780	−	0.300196i
$775$	7.09912	−	6.02103i	0.255008	−	0.216282i

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.903247 + 1.08818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.368289 + 1.96580i) q^{4} +(-2.09919 + 0.770325i) q^{5} +(-0.130770 + 1.40815i) q^{6} +3.05002 q^{7} +(-2.47181 + 1.37484i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.903247 + 1.08818i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.368289 + 1.96580i) q^{4} +(-2.09919 + 0.770325i) q^{5} +(-0.130770 + 1.40815i) q^{6} +3.05002 q^{7} +(-2.47181 + 1.37484i) q^{8} +1.00000i q^{9} +(-2.73434 - 1.58851i) q^{10} +(-1.80989 - 1.80989i) q^{11} +(-1.65045 + 1.12961i) q^{12} +(2.47057 + 2.47057i) q^{13} +(2.75492 + 3.31898i) q^{14} +(-2.02905 - 0.939649i) q^{15} +(-3.72873 - 1.44796i) q^{16} -3.66653i q^{17} +(-1.08818 + 0.903247i) q^{18} +(-2.31596 + 2.31596i) q^{19} +(-0.741196 - 4.41029i) q^{20} +(2.15669 + 2.15669i) q^{21} +(0.334715 - 3.60427i) q^{22} +4.86336 q^{23} +(-2.71999 - 0.775675i) q^{24} +(3.81320 - 3.23412i) q^{25} +(-0.456900 + 4.91998i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.12329 + 5.99573i) q^{28} +(4.74672 - 4.74672i) q^{29} +(-0.810226 - 3.05672i) q^{30} +1.86172 q^{31} +(-1.79231 - 5.36541i) q^{32} -2.55957i q^{33} +(3.98986 - 3.31179i) q^{34} +(-6.40257 + 2.34951i) q^{35} +(-1.96580 - 0.368289i) q^{36} +(5.40092 - 5.40092i) q^{37} +(-4.61208 - 0.428306i) q^{38} +3.49392i q^{39} +(4.12972 - 4.79014i) q^{40} -6.47424i q^{41} +(-0.398851 + 4.29490i) q^{42} +(-4.19382 + 4.19382i) q^{43} +(4.22444 - 2.89131i) q^{44} +(-0.770325 - 2.09919i) q^{45} +(4.39282 + 5.29223i) q^{46} +8.24387i q^{47} +(-1.61274 - 3.66047i) q^{48} +2.30263 q^{49} +(6.96358 + 1.22825i) q^{50} +(2.59263 - 2.59263i) q^{51} +(-5.76653 + 3.94676i) q^{52} +(-9.99761 + 9.99761i) q^{53} +(-1.40815 - 0.130770i) q^{54} +(5.19350 + 2.40510i) q^{55} +(-7.53906 + 4.19328i) q^{56} -3.27526 q^{57} +(9.45277 + 0.877843i) q^{58} +(-2.47155 - 2.47155i) q^{59} +(2.59444 - 3.64265i) q^{60} +(8.01822 - 8.01822i) q^{61} +(1.68160 + 2.02590i) q^{62} +3.05002i q^{63} +(4.21965 - 6.79666i) q^{64} +(-7.08935 - 3.28306i) q^{65} +(2.78528 - 2.31192i) q^{66} +(-8.60064 - 8.60064i) q^{67} +(7.20766 + 1.35034i) q^{68} +(3.43891 + 3.43891i) q^{69} +(-8.33981 - 4.84499i) q^{70} -6.63653i q^{71} +(-1.37484 - 2.47181i) q^{72} +2.70041 q^{73} +(10.7556 + 0.998828i) q^{74} +(4.98321 + 0.409472i) q^{75} +(-3.69977 - 5.40565i) q^{76} +(-5.52020 - 5.52020i) q^{77} +(-3.80203 + 3.15587i) q^{78} -10.9690 q^{79} +(8.94271 + 0.167218i) q^{80} -1.00000 q^{81} +(7.04516 - 5.84784i) q^{82} +(3.65688 + 3.65688i) q^{83} +(-5.03390 + 3.44533i) q^{84} +(2.82442 + 7.69675i) q^{85} +(-8.35170 - 0.775591i) q^{86} +6.71288 q^{87} +(6.96199 + 1.98539i) q^{88} +13.1530i q^{89} +(1.58851 - 2.73434i) q^{90} +(7.53530 + 7.53530i) q^{91} +(-1.79112 + 9.56038i) q^{92} +(1.31644 + 1.31644i) q^{93} +(-8.97085 + 7.44625i) q^{94} +(3.07760 - 6.64569i) q^{95} +(2.52656 - 5.06127i) q^{96} -12.4932i q^{97} +(2.07985 + 2.50569i) q^{98} +(1.80989 - 1.80989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more