LMFDB - Embedded newform 1512.2.j.c.323.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.13
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.481042 - 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} -0.436221 q^{5} +1.00000i q^{7} +(2.44100 + 1.42882i) q^{8} +O(q^{10})$	\(q+(-0.481042 - 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} -0.436221 q^{5} +1.00000i q^{7} +(2.44100 + 1.42882i) q^{8} +(0.209841 + 0.580125i) q^{10} +2.73863i q^{11} -1.64657i q^{13} +(1.32989 - 0.481042i) q^{14} +(0.725955 - 3.93357i) q^{16} -5.22231i q^{17} -5.99963 q^{19} +(0.670559 - 0.558129i) q^{20} +(3.64206 - 1.31739i) q^{22} +7.68296 q^{23} -4.80971 q^{25} +(-2.18975 + 0.792068i) q^{26} +(-1.27946 - 1.53720i) q^{28} +4.94791 q^{29} +9.77950i q^{31} +(-5.58042 + 0.926774i) q^{32} +(-6.94508 + 2.51215i) q^{34} -0.436221i q^{35} +3.81676i q^{37} +(2.88607 + 7.97883i) q^{38} +(-1.06481 - 0.623284i) q^{40} +9.74668i q^{41} -8.84195 q^{43} +(-3.50397 - 4.20981i) q^{44} +(-3.69582 - 10.2175i) q^{46} -4.54668 q^{47} -1.00000 q^{49} +(2.31367 + 6.39637i) q^{50} +(2.10672 + 2.53110i) q^{52} -9.94845 q^{53} -1.19465i q^{55} +(-1.42882 + 2.44100i) q^{56} +(-2.38015 - 6.58016i) q^{58} +13.2892i q^{59} +6.26145i q^{61} +(13.0056 - 4.70435i) q^{62} +(3.91692 + 6.97551i) q^{64} +0.718269i q^{65} +9.42171 q^{67} +(6.68175 + 8.02773i) q^{68} +(-0.580125 + 0.209841i) q^{70} +9.76751 q^{71} -9.14079 q^{73} +(5.07586 - 1.83602i) q^{74} +(9.22262 - 7.67629i) q^{76} -2.73863 q^{77} -5.19984i q^{79} +(-0.316677 + 1.71591i) q^{80} +(12.9620 - 4.68856i) q^{82} -0.227071i q^{83} +2.27808i q^{85} +(4.25335 + 11.7588i) q^{86} +(-3.91302 + 6.68497i) q^{88} +2.46567i q^{89} +1.64657 q^{91} +(-11.8102 + 9.83005i) q^{92} +(2.18714 + 6.04657i) q^{94} +2.61717 q^{95} -3.37287 q^{97} +(0.481042 + 1.32989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.481042	−	1.32989i	−0.340148	−	0.940372i
$2$	−0.481042	−	1.32989i	−0.340148	−	0.940372i
$3$		0			0
$3$		0			0
$4$	−1.53720	+	1.27946i	−0.768599	+	0.639731i
$5$	−0.436221			−0.195084			−0.0975421	−	0.995231i	$-0.531098\pi$
$5$	−0.436221			−0.195084			−0.0975421	+	0.995231i	$0.531098\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.44100	+	1.42882i	0.863022	+	0.505166i
$9$		0			0
$10$	0.209841	+	0.580125i	0.0663575	+	0.183452i
$11$			2.73863i			0.825727i	0.910793	+	0.412863i	$0.135471\pi$
$11$			2.73863i			0.825727i	−0.910793	+	0.412863i	$0.864529\pi$
$12$		0			0
$13$		−	1.64657i		−	0.456676i	−0.973582	−	0.228338i	$-0.926671\pi$
$13$		−	1.64657i		−	0.456676i	0.973582	−	0.228338i	$-0.0733291\pi$
$14$	1.32989	−	0.481042i	0.355427	−	0.128564i
$15$		0			0
$16$	0.725955	−	3.93357i	0.181489	−	0.983393i
$17$		−	5.22231i		−	1.26660i	−0.773908	−	0.633298i	$-0.781701\pi$
$17$		−	5.22231i		−	1.26660i	0.773908	−	0.633298i	$-0.218299\pi$
$18$		0			0
$19$	−5.99963			−1.37641			−0.688204	−	0.725517i	$-0.741601\pi$
$19$	−5.99963			−1.37641			−0.688204	+	0.725517i	$0.741601\pi$
$20$	0.670559	−	0.558129i	0.149942	−	0.124801i
$21$		0			0
$22$	3.64206	−	1.31739i	0.776490	−	0.280869i
$23$	7.68296			1.60201			0.801004	−	0.598659i	$-0.204300\pi$
$23$	7.68296			1.60201			0.801004	+	0.598659i	$0.204300\pi$
$24$		0			0
$25$	−4.80971			−0.961942
$26$	−2.18975	+	0.792068i	−0.429445	+	0.155337i
$27$		0			0
$28$	−1.27946	−	1.53720i	−0.241796	−	0.290503i
$29$	4.94791			0.918804			0.459402	−	0.888228i	$-0.348064\pi$
$29$	4.94791			0.918804			0.459402	+	0.888228i	$0.348064\pi$
$30$		0			0
$31$			9.77950i			1.75645i	0.478248	+	0.878225i	$0.341272\pi$
$31$			9.77950i			1.75645i	−0.478248	+	0.878225i	$0.658728\pi$
$32$	−5.58042	+	0.926774i	−0.986488	+	0.163832i
$33$		0			0
$34$	−6.94508	+	2.51215i	−1.19107	+	0.430830i
$35$		−	0.436221i		−	0.0737349i
$36$		0			0
$37$			3.81676i			0.627472i	0.949510	+	0.313736i	$0.101581\pi$
$37$			3.81676i			0.627472i	−0.949510	+	0.313736i	$0.898419\pi$
$38$	2.88607	+	7.97883i	0.468182	+	1.29434i
$39$		0			0
$40$	−1.06481	−	0.623284i	−0.168362	−	0.0985499i
$41$			9.74668i			1.52218i	0.648649	+	0.761088i	$0.275334\pi$
$41$			9.74668i			1.52218i	−0.648649	+	0.761088i	$0.724666\pi$
$42$		0			0
$43$	−8.84195			−1.34838			−0.674192	−	0.738556i	$-0.735508\pi$
$43$	−8.84195			−1.34838			−0.674192	+	0.738556i	$0.735508\pi$
$44$	−3.50397	−	4.20981i	−0.528243	−	0.634653i
$45$		0			0
$46$	−3.69582	−	10.2175i	−0.544919	−	1.50648i
$47$	−4.54668			−0.663202			−0.331601	−	0.943420i	$-0.607589\pi$
$47$	−4.54668			−0.663202			−0.331601	+	0.943420i	$0.607589\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	2.31367	+	6.39637i	0.327202	+	0.904583i
$51$		0			0
$52$	2.10672	+	2.53110i	0.292150	+	0.351001i
$53$	−9.94845			−1.36652			−0.683262	−	0.730173i	$-0.739439\pi$
$53$	−9.94845			−1.36652			−0.683262	+	0.730173i	$0.739439\pi$
$54$		0			0
$55$		−	1.19465i		−	0.161086i
$56$	−1.42882	+	2.44100i	−0.190935	+	0.326192i
$57$		0			0
$58$	−2.38015	−	6.58016i	−0.312529	−	0.864018i
$59$			13.2892i			1.73011i	0.501681	+	0.865053i	$0.332715\pi$
$59$			13.2892i			1.73011i	−0.501681	+	0.865053i	$0.667285\pi$
$60$		0			0
$61$			6.26145i			0.801696i	0.916145	+	0.400848i	$0.131284\pi$
$61$			6.26145i			0.801696i	−0.916145	+	0.400848i	$0.868716\pi$
$62$	13.0056	−	4.70435i	1.65172	−	0.597453i
$63$		0			0
$64$	3.91692	+	6.97551i	0.489615	+	0.871939i
$65$			0.718269i			0.0890903i
$66$		0			0
$67$	9.42171			1.15104			0.575522	−	0.817786i	$-0.304799\pi$
$67$	9.42171			1.15104			0.575522	+	0.817786i	$0.304799\pi$
$68$	6.68175	+	8.02773i	0.810281	+	0.973505i
$69$		0			0
$70$	−0.580125	+	0.209841i	−0.0693382	+	0.0250808i
$71$	9.76751			1.15919			0.579595	−	0.814905i	$-0.303211\pi$
$71$	9.76751			1.15919			0.579595	+	0.814905i	$0.303211\pi$
$72$		0			0
$73$	−9.14079			−1.06985			−0.534924	−	0.844900i	$-0.679660\pi$
$73$	−9.14079			−1.06985			−0.534924	+	0.844900i	$0.679660\pi$
$74$	5.07586	−	1.83602i	0.590057	−	0.213433i
$75$		0			0
$76$	9.22262	−	7.67629i	1.05791	−	0.880531i
$77$	−2.73863			−0.312095
$78$		0			0
$79$		−	5.19984i		−	0.585028i	−0.956261	−	0.292514i	$-0.905508\pi$
$79$		−	5.19984i		−	0.585028i	0.956261	−	0.292514i	$-0.0944917\pi$
$80$	−0.316677	+	1.71591i	−0.0354056	+	0.191844i
$81$		0			0
$82$	12.9620	−	4.68856i	1.43141	−	0.517764i
$83$		−	0.227071i		−	0.0249243i	−0.999922	−	0.0124622i	$-0.996033\pi$
$83$		−	0.227071i		−	0.0249243i	0.999922	−	0.0124622i	$-0.00396693\pi$
$84$		0			0
$85$			2.27808i			0.247093i
$86$	4.25335	+	11.7588i	0.458650	+	1.26798i
$87$		0			0
$88$	−3.91302	+	6.68497i	−0.417129	+	0.712621i
$89$			2.46567i			0.261360i	0.991425	+	0.130680i	$0.0417161\pi$
$89$			2.46567i			0.261360i	−0.991425	+	0.130680i	$0.958284\pi$
$90$		0			0
$91$	1.64657			0.172607
$92$	−11.8102	+	9.83005i	−1.23130	+	1.02485i
$93$		0			0
$94$	2.18714	+	6.04657i	0.225587	+	0.623657i
$95$	2.61717			0.268516
$96$		0			0
$97$	−3.37287			−0.342463			−0.171232	−	0.985231i	$-0.554775\pi$
$97$	−3.37287			−0.342463			−0.171232	+	0.985231i	$0.554775\pi$
$98$	0.481042	+	1.32989i	0.0485925	+	0.134339i
$99$		0			0
$100$	7.39348	−	6.15384i	0.739348	−	0.615384i
$101$	1.20021			0.119425			0.0597125	−	0.998216i	$-0.480982\pi$
$101$	1.20021			0.119425			0.0597125	+	0.998216i	$0.480982\pi$
$102$		0			0
$103$		−	10.7004i		−	1.05434i	−0.849761	−	0.527169i	$-0.823254\pi$
$103$		−	10.7004i		−	1.05434i	0.849761	−	0.527169i	$-0.176746\pi$
$104$	2.35266	−	4.01927i	0.230697	−	0.394122i
$105$		0			0
$106$	4.78562	+	13.2303i	0.464820	+	1.28504i
$107$			1.49655i			0.144676i	0.997380	+	0.0723382i	$0.0230461\pi$
$107$			1.49655i			0.144676i	−0.997380	+	0.0723382i	$0.976954\pi$
$108$		0			0
$109$			18.4352i			1.76578i	0.469583	+	0.882888i	$0.344404\pi$
$109$			18.4352i			1.76578i	−0.469583	+	0.882888i	$0.655596\pi$
$110$	−1.58875	+	0.574675i	−0.151481	+	0.0547931i
$111$		0			0
$112$	3.93357	+	0.725955i	0.371688	+	0.0685963i
$113$		−	5.25692i		−	0.494529i	−0.968948	−	0.247265i	$-0.920468\pi$
$113$		−	5.25692i		−	0.494529i	0.968948	−	0.247265i	$-0.0795317\pi$
$114$		0			0
$115$	−3.35147			−0.312526
$116$	−7.60592	+	6.33066i	−0.706192	+	0.587787i
$117$		0			0
$118$	17.6731	−	6.39266i	1.62694	−	0.588492i
$119$	5.22231			0.478729
$120$		0			0
$121$	3.49993			0.318175
$122$	8.32702	−	3.01202i	0.753893	−	0.272695i
$123$		0			0
$124$	−12.5125	−	15.0330i	−1.12366	−	1.35001i
$125$	4.27921			0.382744
$126$		0			0
$127$			19.7677i			1.75410i	0.480396	+	0.877051i	$0.340493\pi$
$127$			19.7677i			1.75410i	−0.480396	+	0.877051i	$0.659507\pi$
$128$	7.39244	−	8.56457i	0.653405	−	0.757008i
$129$		0			0
$130$	0.955216	−	0.345517i	0.0837780	−	0.0303039i
$131$			9.25252i			0.808397i	0.914671	+	0.404198i	$0.132449\pi$
$131$			9.25252i			0.808397i	−0.914671	+	0.404198i	$0.867551\pi$
$132$		0			0
$133$		−	5.99963i		−	0.520234i
$134$	−4.53223	−	12.5298i	−0.391525	−	1.08241i
$135$		0			0
$136$	7.46177	−	12.7476i	0.639842	−	1.09310i
$137$			2.53255i			0.216370i	0.994131	+	0.108185i	$0.0345039\pi$
$137$			2.53255i			0.216370i	−0.994131	+	0.108185i	$0.965496\pi$
$138$		0			0
$139$	−19.7831			−1.67798			−0.838991	−	0.544146i	$-0.816854\pi$
$139$	−19.7831			−1.67798			−0.838991	+	0.544146i	$0.816854\pi$
$140$	0.558129	+	0.670559i	0.0471705	+	0.0566726i
$141$		0			0
$142$	−4.69858	−	12.9897i	−0.394296	−	1.09007i
$143$	4.50934			0.377090
$144$		0			0
$145$	−2.15839			−0.179244
$146$	4.39710	+	12.1562i	0.363906	+	1.00606i
$147$		0			0
$148$	−4.88340	−	5.86712i	−0.401413	−	0.482274i
$149$	−8.16461			−0.668871			−0.334435	−	0.942419i	$-0.608546\pi$
$149$	−8.16461			−0.668871			−0.334435	+	0.942419i	$0.608546\pi$
$150$		0			0
$151$			14.8741i			1.21044i	0.796058	+	0.605220i	$0.206915\pi$
$151$			14.8741i			1.21044i	−0.796058	+	0.605220i	$0.793085\pi$
$152$	−14.6451	−	8.57242i	−1.18787	−	0.695315i
$153$		0			0
$154$	1.31739	+	3.64206i	0.106159	+	0.293486i
$155$		−	4.26603i		−	0.342656i
$156$		0			0
$157$			4.92207i			0.392824i	0.980521	+	0.196412i	$0.0629290\pi$
$157$			4.92207i			0.392824i	−0.980521	+	0.196412i	$0.937071\pi$
$158$	−6.91520	+	2.50134i	−0.550144	+	0.198996i
$159$		0			0
$160$	2.43430	−	0.404279i	0.192448	−	0.0319610i
$161$			7.68296i			0.605502i
$162$		0			0
$163$	−5.87250			−0.459970			−0.229985	−	0.973194i	$-0.573868\pi$
$163$	−5.87250			−0.459970			−0.229985	+	0.973194i	$0.573868\pi$
$164$	−12.4705	−	14.9826i	−0.973782	−	1.16994i
$165$		0			0
$166$	−0.301979	+	0.109231i	−0.0234381	+	0.00847795i
$167$	22.1181			1.71155			0.855777	−	0.517345i	$-0.173080\pi$
$167$	22.1181			1.71155			0.855777	+	0.517345i	$0.173080\pi$
$168$		0			0
$169$	10.2888			0.791447
$170$	3.02960	−	1.09585i	0.232359	−	0.0840481i
$171$		0			0
$172$	13.5918	−	11.3129i	1.03637	−	0.862603i
$173$	−24.1920			−1.83928			−0.919642	−	0.392758i	$-0.871521\pi$
$173$	−24.1920			−1.83928			−0.919642	+	0.392758i	$0.871521\pi$
$174$		0			0
$175$		−	4.80971i		−	0.363580i
$176$	10.7726	+	1.98812i	0.812014	+	0.149860i
$177$		0			0
$178$	3.27906	−	1.18609i	0.245776	−	0.0889010i
$179$		−	5.41287i		−	0.404577i	−0.979326	−	0.202288i	$-0.935162\pi$
$179$		−	5.41287i		−	0.404577i	0.979326	−	0.202288i	$-0.0648378\pi$
$180$		0			0
$181$		−	6.19672i		−	0.460598i	−0.973120	−	0.230299i	$-0.926030\pi$
$181$		−	6.19672i		−	0.460598i	0.973120	−	0.230299i	$-0.0739705\pi$
$182$	−0.792068	−	2.18975i	−0.0587120	−	0.162315i
$183$		0			0
$184$	18.7541	+	10.9776i	1.38257	+	0.809280i
$185$		−	1.66495i		−	0.122410i
$186$		0			0
$187$	14.3020			1.04586
$188$	6.98915	−	5.81731i	0.509736	−	0.424271i
$189$		0			0
$190$	−1.25897	−	3.48054i	−0.0913350	−	0.252505i
$191$	13.6191			0.985444			0.492722	−	0.870187i	$-0.336002\pi$
$191$	13.6191			0.985444			0.492722	+	0.870187i	$0.336002\pi$
$192$		0			0
$193$	5.89278			0.424172			0.212086	−	0.977251i	$-0.431974\pi$
$193$	5.89278			0.424172			0.212086	+	0.977251i	$0.431974\pi$
$194$	1.62249	+	4.48554i	0.116488	+	0.322043i
$195$		0			0
$196$	1.53720	−	1.27946i	0.109800	−	0.0913901i
$197$	−19.0323			−1.35600			−0.677998	−	0.735064i	$-0.737152\pi$
$197$	−19.0323			−1.35600			−0.677998	+	0.735064i	$0.737152\pi$
$198$		0			0
$199$		−	5.91398i		−	0.419231i	−0.977784	−	0.209616i	$-0.932779\pi$
$199$		−	5.91398i		−	0.419231i	0.977784	−	0.209616i	$-0.0672212\pi$
$200$	−11.7405	−	6.87223i	−0.830177	−	0.485940i
$201$		0			0
$202$	−0.577349	−	1.59614i	−0.0406221	−	0.112304i
$203$			4.94791i			0.347275i
$204$		0			0
$205$		−	4.25171i		−	0.296952i
$206$	−14.2303	+	5.14732i	−0.991469	+	0.358631i
$207$		0			0
$208$	−6.47690	−	1.19534i	−0.449092	−	0.0828816i
$209$		−	16.4307i		−	1.13654i
$210$		0			0
$211$	12.9334			0.890369			0.445185	−	0.895439i	$-0.353138\pi$
$211$	12.9334			0.890369			0.445185	+	0.895439i	$0.353138\pi$
$212$	15.2927	−	12.7287i	1.05031	−	0.874208i
$213$		0			0
$214$	1.99024	−	0.719901i	0.136050	−	0.0492114i
$215$	3.85705			0.263049
$216$		0			0
$217$	−9.77950			−0.663876
$218$	24.5168	−	8.86812i	1.66049	−	0.600625i
$219$		0			0
$220$	1.52851	+	1.83641i	0.103052	+	0.123811i
$221$	−8.59890			−0.578424
$222$		0			0
$223$		−	0.758557i		−	0.0507967i	−0.999677	−	0.0253984i	$-0.991915\pi$
$223$		−	0.758557i		−	0.0507967i	0.999677	−	0.0253984i	$-0.00808542\pi$
$224$	−0.926774	−	5.58042i	−0.0619227	−	0.372858i
$225$		0			0
$226$	−6.99111	+	2.52880i	−0.465042	+	0.168213i
$227$			3.60986i			0.239595i	0.992798	+	0.119797i	$0.0382245\pi$
$227$			3.60986i			0.239595i	−0.992798	+	0.119797i	$0.961776\pi$
$228$		0			0
$229$		−	3.47625i		−	0.229717i	−0.993382	−	0.114859i	$-0.963358\pi$
$229$		−	3.47625i		−	0.229717i	0.993382	−	0.114859i	$-0.0366415\pi$
$230$	1.61220	+	4.45708i	0.106305	+	0.293891i
$231$		0			0
$232$	12.0778	+	7.06970i	0.792949	+	0.464149i
$233$		−	22.9786i		−	1.50538i	−0.658376	−	0.752689i	$-0.728756\pi$
$233$		−	22.9786i		−	1.50538i	0.658376	−	0.752689i	$-0.271244\pi$
$234$		0			0
$235$	1.98336			0.129380
$236$	−17.0030	−	20.4281i	−1.10680	−	1.32976i
$237$		0			0
$238$	−2.51215	−	6.94508i	−0.162838	−	0.450183i
$239$	10.4478			0.675813			0.337906	−	0.941180i	$-0.390281\pi$
$239$	10.4478			0.675813			0.337906	+	0.941180i	$0.390281\pi$
$240$		0			0
$241$	−10.0939			−0.650208			−0.325104	−	0.945678i	$-0.605399\pi$
$241$	−10.0939			−0.650208			−0.325104	+	0.945678i	$0.605399\pi$
$242$	−1.68361	−	4.65450i	−0.108227	−	0.299203i
$243$		0			0
$244$	−8.01128	−	9.62508i	−0.512870	−	0.616183i
$245$	0.436221			0.0278692
$246$		0			0
$247$			9.87880i			0.628573i
$248$	−13.9732	+	23.8717i	−0.887299	+	1.51586i
$249$		0			0
$250$	−2.05848	−	5.69086i	−0.130189	−	0.359922i
$251$		−	18.0568i		−	1.13974i	−0.821736	−	0.569868i	$-0.806994\pi$
$251$		−	18.0568i		−	1.13974i	0.821736	−	0.569868i	$-0.193006\pi$
$252$		0			0
$253$			21.0408i			1.32282i
$254$	26.2889	−	9.50910i	1.64951	−	0.596654i
$255$		0			0
$256$	−14.9460	−	5.71119i	−0.934124	−	0.356950i
$257$		−	3.77643i		−	0.235567i	−0.993039	−	0.117784i	$-0.962421\pi$
$257$		−	3.77643i		−	0.235567i	0.993039	−	0.117784i	$-0.0375789\pi$
$258$		0			0
$259$	−3.81676			−0.237162
$260$	−0.918997	−	1.10412i	−0.0569938	−	0.0684747i
$261$		0			0
$262$	12.3048	−	4.45085i	0.760194	−	0.274974i
$263$	−19.1460			−1.18060			−0.590298	−	0.807185i	$-0.700990\pi$
$263$	−19.1460			−1.18060			−0.590298	+	0.807185i	$0.700990\pi$
$264$		0			0
$265$	4.33973			0.266587
$266$	−7.97883	+	2.88607i	−0.489213	+	0.176956i
$267$		0			0
$268$	−14.4830	+	12.0547i	−0.884692	+	0.736359i
$269$	−11.9031			−0.725747			−0.362873	−	0.931838i	$-0.618204\pi$
$269$	−11.9031			−0.725747			−0.362873	+	0.931838i	$0.618204\pi$
$270$		0			0
$271$			26.4765i			1.60833i	0.594403	+	0.804167i	$0.297388\pi$
$271$			26.4765i			1.60833i	−0.594403	+	0.804167i	$0.702612\pi$
$272$	−20.5423	−	3.79116i	−1.24556	−	0.229873i
$273$		0			0
$274$	3.36800	−	1.21826i	0.203469	−	0.0735979i
$275$		−	13.1720i		−	0.794302i
$276$		0			0
$277$		−	9.49587i		−	0.570552i	−0.958445	−	0.285276i	$-0.907915\pi$
$277$		−	9.49587i		−	0.570552i	0.958445	−	0.285276i	$-0.0920852\pi$
$278$	9.51650	+	26.3093i	0.570762	+	1.57793i
$279$		0			0
$280$	0.623284	−	1.06481i	0.0372484	−	0.0636349i
$281$		−	16.7754i		−	1.00073i	−0.865813	−	0.500367i	$-0.833198\pi$
$281$		−	16.7754i		−	1.00073i	0.865813	−	0.500367i	$-0.166802\pi$
$282$		0			0
$283$	13.6841			0.813437			0.406719	−	0.913554i	$-0.366673\pi$
$283$	13.6841			0.813437			0.406719	+	0.913554i	$0.366673\pi$
$284$	−15.0146	+	12.4972i	−0.890952	+	0.741569i
$285$		0			0
$286$	−2.16918	−	5.99691i	−0.128266	−	0.354605i
$287$	−9.74668			−0.575328
$288$		0			0
$289$	−10.2725			−0.604268
$290$	1.03827	+	2.87041i	0.0609695	+	0.168556i
$291$		0			0
$292$	14.0512	−	11.6953i	0.822284	−	0.684415i
$293$	−9.46088			−0.552710			−0.276355	−	0.961056i	$-0.589127\pi$
$293$	−9.46088			−0.552710			−0.276355	+	0.961056i	$0.589127\pi$
$294$		0			0
$295$		−	5.79703i		−	0.337516i
$296$	−5.45348	+	9.31670i	−0.316977	+	0.541522i
$297$		0			0
$298$	3.92752	+	10.8580i	0.227515	+	0.628987i
$299$		−	12.6505i		−	0.731599i
$300$		0			0
$301$		−	8.84195i		−	0.509641i
$302$	19.7809	−	7.15508i	1.13826	−	0.411728i
$303$		0			0
$304$	−4.35546	+	23.6000i	−0.249803	+	1.35355i
$305$		−	2.73138i		−	0.156398i
$306$		0			0
$307$	−12.4055			−0.708019			−0.354009	−	0.935242i	$-0.615182\pi$
$307$	−12.4055			−0.708019			−0.354009	+	0.935242i	$0.615182\pi$
$308$	4.20981	−	3.50397i	0.239876	−	0.199657i
$309$		0			0
$310$	−5.67333	+	2.05214i	−0.322224	+	0.116554i
$311$	−1.70862			−0.0968870			−0.0484435	−	0.998826i	$-0.515426\pi$
$311$	−1.70862			−0.0968870			−0.0484435	+	0.998826i	$0.515426\pi$
$312$		0			0
$313$	11.9889			0.677652			0.338826	−	0.940849i	$-0.389970\pi$
$313$	11.9889			0.677652			0.338826	+	0.940849i	$0.389970\pi$
$314$	6.54580	−	2.36772i	0.369401	−	0.133618i
$315$		0			0
$316$	6.65300	+	7.99318i	0.374260	+	0.449652i
$317$	24.6470			1.38431			0.692155	−	0.721748i	$-0.256661\pi$
$317$	24.6470			1.38431			0.692155	+	0.721748i	$0.256661\pi$
$318$		0			0
$319$			13.5505i			0.758681i
$320$	−1.70864	−	3.04287i	−0.0955161	−	0.170101i
$321$		0			0
$322$	10.2175	−	3.69582i	0.569397	−	0.205960i
$323$			31.3319i			1.74336i
$324$		0			0
$325$			7.91952i			0.439296i
$326$	2.82492	+	7.80976i	0.156458	+	0.432543i
$327$		0			0
$328$	−13.9263	+	23.7916i	−0.768951	+	1.31367i
$329$		−	4.54668i		−	0.250667i
$330$		0			0
$331$	−5.66221			−0.311223			−0.155612	−	0.987818i	$-0.549735\pi$
$331$	−5.66221			−0.311223			−0.155612	+	0.987818i	$0.549735\pi$
$332$	0.290529	+	0.349054i	0.0159449	+	0.0191568i
$333$		0			0
$334$	−10.6397	−	29.4146i	−0.582181	−	1.60950i
$335$	−4.10995			−0.224551
$336$		0			0
$337$	−32.2480			−1.75666			−0.878331	−	0.478053i	$-0.841343\pi$
$337$	−32.2480			−1.75666			−0.878331	+	0.478053i	$0.841343\pi$
$338$	−4.94935	−	13.6830i	−0.269209	−	0.744255i
$339$		0			0
$340$	−2.91472	−	3.50187i	−0.158073	−	0.189915i
$341$	−26.7824			−1.45035
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−21.5832	−	12.6336i	−1.16369	−	0.681158i
$345$		0			0
$346$	11.6374	+	32.1726i	0.625628	+	1.72961i
$347$			20.3357i			1.09168i	0.837889	+	0.545840i	$0.183789\pi$
$347$			20.3357i			1.09168i	−0.837889	+	0.545840i	$0.816211\pi$
$348$		0			0
$349$		−	8.27539i		−	0.442971i	−0.975164	−	0.221486i	$-0.928909\pi$
$349$		−	8.27539i		−	0.442971i	0.975164	−	0.221486i	$-0.0710906\pi$
$350$	−6.39637	+	2.31367i	−0.341900	+	0.123671i
$351$		0			0
$352$	−2.53809	−	15.2827i	−0.135280	−	0.814570i
$353$			8.23298i			0.438197i	0.975703	+	0.219099i	$0.0703117\pi$
$353$			8.23298i			0.438197i	−0.975703	+	0.219099i	$0.929688\pi$
$354$		0			0
$355$	−4.26080			−0.226140
$356$	−3.15473	−	3.79022i	−0.167200	−	0.200881i
$357$		0			0
$358$	−7.19850	+	2.60381i	−0.380453	+	0.137616i
$359$	10.5802			0.558403			0.279202	−	0.960232i	$-0.409930\pi$
$359$	10.5802			0.558403			0.279202	+	0.960232i	$0.409930\pi$
$360$		0			0
$361$	16.9955			0.894502
$362$	−8.24093	+	2.98088i	−0.433134	+	0.156672i
$363$		0			0
$364$	−2.53110	+	2.10672i	−0.132666	+	0.110422i
$365$	3.98741			0.208710
$366$		0			0
$367$		−	23.7595i		−	1.24023i	−0.784509	−	0.620117i	$-0.787085\pi$
$367$		−	23.7595i		−	1.24023i	0.784509	−	0.620117i	$-0.212915\pi$
$368$	5.57748	−	30.2215i	0.290746	−	1.57540i
$369$		0			0
$370$	−2.21420	+	0.800912i	−0.115111	+	0.0416374i
$371$		−	9.94845i		−	0.516498i
$372$		0			0
$373$			12.1442i			0.628802i	0.949290	+	0.314401i	$0.101804\pi$
$373$			12.1442i			0.628802i	−0.949290	+	0.314401i	$0.898196\pi$
$374$	−6.87984	−	19.0200i	−0.355748	−	0.983500i
$375$		0			0
$376$	−11.0984	−	6.49642i	−0.572358	−	0.335027i
$377$		−	8.14708i		−	0.419596i
$378$		0			0
$379$	−32.1386			−1.65085			−0.825426	−	0.564511i	$-0.809065\pi$
$379$	−32.1386			−1.65085			−0.825426	+	0.564511i	$0.809065\pi$
$380$	−4.02310	+	3.34856i	−0.206381	+	0.171778i
$381$		0			0
$382$	−6.55136	−	18.1119i	−0.335197	−	0.926684i
$383$	30.0530			1.53564			0.767819	−	0.640667i	$-0.221342\pi$
$383$	30.0530			1.53564			0.767819	+	0.640667i	$0.221342\pi$
$384$		0			0
$385$	1.19465			0.0608849
$386$	−2.83467	−	7.83673i	−0.144281	−	0.398879i
$387$		0			0
$388$	5.18477	−	4.31546i	0.263217	−	0.219084i
$389$	12.8723			0.652652			0.326326	−	0.945257i	$-0.394189\pi$
$389$	12.8723			0.652652			0.326326	+	0.945257i	$0.394189\pi$
$390$		0			0
$391$		−	40.1228i		−	2.02910i
$392$	−2.44100	−	1.42882i	−0.123289	−	0.0721666i
$393$		0			0
$394$	9.15533	+	25.3108i	0.461239	+	1.27514i
$395$			2.26828i			0.114130i
$396$		0			0
$397$		−	20.8323i		−	1.04554i	−0.852473	−	0.522771i	$-0.824898\pi$
$397$		−	20.8323i		−	1.04554i	0.852473	−	0.522771i	$-0.175102\pi$
$398$	−7.86493	+	2.84487i	−0.394233	+	0.142601i
$399$		0			0
$400$	−3.49163	+	18.9193i	−0.174582	+	0.945967i
$401$			15.8270i			0.790361i	0.918604	+	0.395180i	$0.129318\pi$
$401$			15.8270i			0.790361i	−0.918604	+	0.395180i	$0.870682\pi$
$402$		0			0
$403$	16.1026			0.802129
$404$	−1.84495	+	1.53562i	−0.0917899	+	0.0763998i
$405$		0			0
$406$	6.58016	−	2.38015i	0.326568	−	0.118125i
$407$	−10.4527			−0.518120
$408$		0			0
$409$	−3.95136			−0.195382			−0.0976910	−	0.995217i	$-0.531146\pi$
$409$	−3.95136			−0.195382			−0.0976910	+	0.995217i	$0.531146\pi$
$410$	−5.65429	+	2.04525i	−0.279246	+	0.101008i
$411$		0			0
$412$	13.6907	+	16.4486i	0.674492	+	0.810363i
$413$	−13.2892			−0.653919
$414$		0			0
$415$			0.0990534i			0.00486234i
$416$	1.52600	+	9.18855i	0.0748181	+	0.450506i
$417$		0			0
$418$	−21.8510	+	7.90387i	−1.06877	+	0.386591i
$419$		−	3.56977i		−	0.174395i	−0.996191	−	0.0871974i	$-0.972209\pi$
$419$		−	3.56977i		−	0.174395i	0.996191	−	0.0871974i	$-0.0277911\pi$
$420$		0			0
$421$			16.3767i			0.798152i	0.916918	+	0.399076i	$0.130669\pi$
$421$			16.3767i			0.798152i	−0.916918	+	0.399076i	$0.869331\pi$
$422$	−6.22148	−	17.1999i	−0.302857	−	0.837278i
$423$		0			0
$424$	−24.2841	−	14.2146i	−1.17934	−	0.690321i
$425$			25.1178i			1.21839i
$426$		0			0
$427$	−6.26145			−0.303013
$428$	−1.91477	−	2.30049i	−0.0925540	−	0.111198i
$429$		0			0
$430$	−1.85540	−	5.12944i	−0.0894754	−	0.247363i
$431$	28.7503			1.38485			0.692426	−	0.721489i	$-0.256542\pi$
$431$	28.7503			1.38485			0.692426	+	0.721489i	$0.256542\pi$
$432$		0			0
$433$	−23.6276			−1.13547			−0.567735	−	0.823212i	$-0.692180\pi$
$433$	−23.6276			−1.13547			−0.567735	+	0.823212i	$0.692180\pi$
$434$	4.70435	+	13.0056i	0.225816	+	0.624290i
$435$		0			0
$436$	−23.5872	−	28.3386i	−1.12962	−	1.35717i
$437$	−46.0949			−2.20502
$438$		0			0
$439$		−	15.4891i		−	0.739255i	−0.929180	−	0.369628i	$-0.879485\pi$
$439$		−	15.4891i		−	0.739255i	0.929180	−	0.369628i	$-0.120515\pi$
$440$	1.70694	−	2.91613i	0.0813753	−	0.139021i
$441$		0			0
$442$	4.13643	+	11.4356i	0.196750	+	0.543934i
$443$		−	21.7640i		−	1.03404i	−0.855974	−	0.517019i	$-0.827042\pi$
$443$		−	21.7640i		−	1.03404i	0.855974	−	0.517019i	$-0.172958\pi$
$444$		0			0
$445$		−	1.07558i		−	0.0509872i
$446$	−1.00879	+	0.364897i	−0.0477678	+	0.0172784i
$447$		0			0
$448$	−6.97551	+	3.91692i	−0.329562	+	0.185057i
$449$		−	28.9358i		−	1.36557i	−0.730621	−	0.682783i	$-0.760769\pi$
$449$		−	28.9358i		−	1.36557i	0.730621	−	0.682783i	$-0.239231\pi$
$450$		0			0
$451$	−26.6925			−1.25690
$452$	6.72603	+	8.08093i	0.316366	+	0.380095i
$453$		0			0
$454$	4.80070	−	1.73649i	0.225308	−	0.0814976i
$455$	−0.718269			−0.0336730
$456$		0			0
$457$	26.2466			1.22776			0.613882	−	0.789397i	$-0.289607\pi$
$457$	26.2466			1.22776			0.613882	+	0.789397i	$0.289607\pi$
$458$	−4.62302	+	1.67222i	−0.216020	+	0.0781378i
$459$		0			0
$460$	5.15188	−	4.28808i	0.240207	−	0.199933i
$461$	−7.47471			−0.348132			−0.174066	−	0.984734i	$-0.555691\pi$
$461$	−7.47471			−0.348132			−0.174066	+	0.984734i	$0.555691\pi$
$462$		0			0
$463$		−	8.09410i		−	0.376165i	−0.982153	−	0.188082i	$-0.939773\pi$
$463$		−	8.09410i		−	0.376165i	0.982153	−	0.188082i	$-0.0602272\pi$
$464$	3.59196	−	19.4630i	0.166753	−	0.903546i
$465$		0			0
$466$	−30.5590	+	11.0537i	−1.41562	+	0.512051i
$467$		−	16.0617i		−	0.743246i	−0.928384	−	0.371623i	$-0.878801\pi$
$467$		−	16.0617i		−	0.743246i	0.928384	−	0.371623i	$-0.121199\pi$
$468$		0			0
$469$			9.42171i			0.435054i
$470$	−0.954079	−	2.63765i	−0.0440084	−	0.121666i
$471$		0			0
$472$	−18.9879	+	32.4389i	−0.873991	+	1.49312i
$473$		−	24.2148i		−	1.11340i
$474$		0			0
$475$	28.8565			1.32403
$476$	−8.02773	+	6.68175i	−0.367950	+	0.306257i
$477$		0			0
$478$	−5.02583	−	13.8944i	−0.229876	−	0.635515i
$479$	−31.6989			−1.44836			−0.724181	−	0.689610i	$-0.757782\pi$
$479$	−31.6989			−1.44836			−0.724181	+	0.689610i	$0.757782\pi$
$480$		0			0
$481$	6.28456			0.286551
$482$	4.85561	+	13.4238i	0.221167	+	0.611437i
$483$		0			0
$484$	−5.38008	+	4.47802i	−0.244549	+	0.203546i
$485$	1.47132			0.0668092
$486$		0			0
$487$			30.5363i			1.38373i	0.722025	+	0.691867i	$0.243211\pi$
$487$			30.5363i			1.38373i	−0.722025	+	0.691867i	$0.756789\pi$
$488$	−8.94651	+	15.2842i	−0.404990	+	0.691882i
$489$		0			0
$490$	−0.209841	−	0.580125i	−0.00947964	−	0.0262074i
$491$			41.2201i			1.86024i	0.367259	+	0.930119i	$0.380296\pi$
$491$			41.2201i			1.86024i	−0.367259	+	0.930119i	$0.619704\pi$
$492$		0			0
$493$		−	25.8395i		−	1.16375i
$494$	13.1377	−	4.75211i	0.591092	−	0.213808i
$495$		0			0
$496$	38.4684	+	7.09948i	1.72728	+	0.318776i
$497$			9.76751i			0.438133i
$498$		0			0
$499$	4.03676			0.180710			0.0903552	−	0.995910i	$-0.471200\pi$
$499$	4.03676			0.180710			0.0903552	+	0.995910i	$0.471200\pi$
$500$	−6.57799	+	5.47508i	−0.294177	+	0.244853i
$501$		0			0
$502$	−24.0135	+	8.68608i	−1.07178	+	0.387679i
$503$	40.2393			1.79418			0.897092	−	0.441845i	$-0.145676\pi$
$503$	40.2393			1.79418			0.897092	+	0.441845i	$0.145676\pi$
$504$		0			0
$505$	−0.523556			−0.0232979
$506$	27.9818	−	10.1215i	1.24394	−	0.449955i
$507$		0			0
$508$	−25.2921	−	30.3869i	−1.12215	−	1.34820i
$509$	−9.68050			−0.429081			−0.214540	−	0.976715i	$-0.568825\pi$
$509$	−9.68050			−0.429081			−0.214540	+	0.976715i	$0.568825\pi$
$510$		0			0
$511$		−	9.14079i		−	0.404365i
$512$	−0.405604	+	22.6238i	−0.0179253	+	0.999839i
$513$		0			0
$514$	−5.02222	+	1.81662i	−0.221521	+	0.0801276i
$515$			4.66773i			0.205685i
$516$		0			0
$517$		−	12.4517i		−	0.547624i
$518$	1.83602	+	5.07586i	0.0806701	+	0.223020i
$519$		0			0
$520$	−1.02628	+	1.75329i	−0.0450054	+	0.0768869i
$521$		−	3.92629i		−	0.172014i	−0.996295	−	0.0860069i	$-0.972589\pi$
$521$		−	3.92629i		−	0.172014i	0.996295	−	0.0860069i	$-0.0274107\pi$
$522$		0			0
$523$	20.8709			0.912623			0.456311	−	0.889820i	$-0.349170\pi$
$523$	20.8709			0.912623			0.456311	+	0.889820i	$0.349170\pi$
$524$	−11.8382	−	14.2230i	−0.517156	−	0.621333i
$525$		0			0
$526$	9.21005	+	25.4621i	0.401577	+	1.11020i
$527$	51.0716			2.22471
$528$		0			0
$529$	36.0279			1.56643
$530$	−2.08759	−	5.77134i	−0.0906791	−	0.250691i
$531$		0			0
$532$	7.67629	+	9.22262i	0.332810	+	0.399851i
$533$	16.0486			0.695141
$534$		0			0
$535$		−	0.652825i		−	0.0282241i
$536$	22.9983	+	13.4620i	0.993377	+	0.581469i
$537$		0			0
$538$	5.72590	+	15.8298i	0.246861	+	0.682472i
$539$		−	2.73863i		−	0.117961i
$540$		0			0
$541$		−	3.18975i		−	0.137138i	−0.997646	−	0.0685691i	$-0.978157\pi$
$541$		−	3.18975i		−	0.137138i	0.997646	−	0.0685691i	$-0.0218434\pi$
$542$	35.2108	−	12.7363i	1.51243	−	0.547071i
$543$		0			0
$544$	4.83990	+	29.1427i	0.207509	+	1.24948i
$545$		−	8.04185i		−	0.344475i
$546$		0			0
$547$	27.9137			1.19350			0.596751	−	0.802426i	$-0.296458\pi$
$547$	27.9137			1.19350			0.596751	+	0.802426i	$0.296458\pi$
$548$	−3.24030	−	3.89303i	−0.138419	−	0.166302i
$549$		0			0
$550$	−17.5173	+	6.33628i	−0.746939	+	0.270180i
$551$	−29.6856			−1.26465
$552$		0			0
$553$	5.19984			0.221120
$554$	−12.6284	+	4.56791i	−0.536531	+	0.194072i
$555$		0			0
$556$	30.4106	−	25.3117i	1.28970	−	1.07346i
$557$	−14.0025			−0.593304			−0.296652	−	0.954986i	$-0.595870\pi$
$557$	−14.0025			−0.593304			−0.296652	+	0.954986i	$0.595870\pi$
$558$		0			0
$559$			14.5589i			0.615775i
$560$	−1.71591	−	0.316677i	−0.0725104	−	0.0133821i
$561$		0			0
$562$	−22.3093	+	8.06965i	−0.941063	+	0.340398i
$563$		−	13.8839i		−	0.585137i	−0.956245	−	0.292569i	$-0.905490\pi$
$563$		−	13.8839i		−	0.585137i	0.956245	−	0.292569i	$-0.0945100\pi$
$564$		0			0
$565$			2.29318i			0.0964749i
$566$	−6.58264	−	18.1983i	−0.276689	−	0.764933i
$567$		0			0
$568$	23.8424	+	13.9561i	1.00041	+	0.585583i
$569$		−	14.7512i		−	0.618401i	−0.950997	−	0.309200i	$-0.899939\pi$
$569$		−	14.7512i		−	0.618401i	0.950997	−	0.309200i	$-0.100061\pi$
$570$		0			0
$571$	4.28135			0.179169			0.0895845	−	0.995979i	$-0.471446\pi$
$571$	4.28135			0.179169			0.0895845	+	0.995979i	$0.471446\pi$
$572$	−6.93174	+	5.76952i	−0.289831	+	0.241236i
$573$		0			0
$574$	4.68856	+	12.9620i	0.195697	+	0.541022i
$575$	−36.9528			−1.54104
$576$		0			0
$577$	11.1951			0.466059			0.233030	−	0.972470i	$-0.425136\pi$
$577$	11.1951			0.466059			0.233030	+	0.972470i	$0.425136\pi$
$578$	4.94152	+	13.6613i	0.205540	+	0.568236i
$579$		0			0
$580$	3.31787	−	2.76157i	0.137767	−	0.114668i
$581$	0.227071			0.00942051
$582$		0			0
$583$		−	27.2451i		−	1.12838i
$584$	−22.3126	−	13.0606i	−0.923303	−	0.540451i
$585$		0			0
$586$	4.55107	+	12.5819i	0.188003	+	0.519753i
$587$		−	1.45377i		−	0.0600035i	−0.999550	−	0.0300018i	$-0.990449\pi$
$587$		−	1.45377i		−	0.0600035i	0.999550	−	0.0300018i	$-0.00955129\pi$
$588$		0			0
$589$		−	58.6733i		−	2.41759i
$590$	−7.70940	+	2.78861i	−0.317391	+	0.114805i
$591$		0			0
$592$	15.0135	+	2.77080i	0.617051	+	0.113879i
$593$			13.1827i			0.541347i	0.962671	+	0.270674i	$0.0872464\pi$
$593$			13.1827i			0.541347i	−0.962671	+	0.270674i	$0.912754\pi$
$594$		0			0
$595$	−2.27808			−0.0933924
$596$	12.5506	−	10.4463i	0.514093	−	0.427897i
$597$		0			0
$598$	−16.8238	+	6.08543i	−0.687975	+	0.248852i
$599$	−14.4852			−0.591848			−0.295924	−	0.955211i	$-0.595628\pi$
$599$	−14.4852			−0.591848			−0.295924	+	0.955211i	$0.595628\pi$
$600$		0			0
$601$	−27.7364			−1.13139			−0.565695	−	0.824614i	$-0.691392\pi$
$601$	−27.7364			−1.13139			−0.565695	+	0.824614i	$0.691392\pi$
$602$	−11.7588	+	4.25335i	−0.479253	+	0.173353i
$603$		0			0
$604$	−19.0309	−	22.8645i	−0.774356	−	0.930343i
$605$	−1.52674			−0.0620709
$606$		0			0
$607$			18.5137i			0.751447i	0.926732	+	0.375723i	$0.122606\pi$
$607$			18.5137i			0.751447i	−0.926732	+	0.375723i	$0.877394\pi$
$608$	33.4804	−	5.56030i	1.35781	−	0.225500i
$609$		0			0
$610$	−3.63242	+	1.31391i	−0.147073	+	0.0531985i
$611$			7.48643i			0.302868i
$612$		0			0
$613$			25.3069i			1.02213i	0.859541	+	0.511067i	$0.170750\pi$
$613$			25.3069i			1.02213i	−0.859541	+	0.511067i	$0.829250\pi$
$614$	5.96756	+	16.4979i	0.240831	+	0.665801i
$615$		0			0
$616$	−6.68497	−	3.91302i	−0.269345	−	0.157660i
$617$		−	47.8249i		−	1.92536i	−0.270647	−	0.962679i	$-0.587238\pi$
$617$		−	47.8249i		−	1.92536i	0.270647	−	0.962679i	$-0.412762\pi$
$618$		0			0
$619$	3.22411			0.129588			0.0647939	−	0.997899i	$-0.479361\pi$
$619$	3.22411			0.129588			0.0647939	+	0.997899i	$0.479361\pi$
$620$	5.45822	+	6.55773i	0.219207	+	0.263365i
$621$		0			0
$622$	0.821918	+	2.27227i	0.0329559	+	0.0911098i
$623$	−2.46567			−0.0987848
$624$		0			0
$625$	22.1819			0.887275
$626$	−5.76715	−	15.9439i	−0.230502	−	0.637245i
$627$		0			0
$628$	−6.29760	−	7.56620i	−0.251302	−	0.301924i
$629$	19.9323			0.794754
$630$		0			0
$631$		−	22.6025i		−	0.899791i	−0.893081	−	0.449896i	$-0.851461\pi$
$631$		−	22.6025i		−	0.899791i	0.893081	−	0.449896i	$-0.148539\pi$
$632$	7.42966	−	12.6928i	0.295536	−	0.504892i
$633$		0			0
$634$	−11.8562	−	32.7777i	−0.470870	−	1.30177i
$635$		−	8.62311i		−	0.342198i
$636$		0			0
$637$			1.64657i			0.0652394i
$638$	18.0206	−	6.51835i	0.713443	−	0.258064i
$639$		0			0
$640$	−3.22474	+	3.73605i	−0.127469	+	0.147680i
$641$			15.4383i			0.609775i	0.952388	+	0.304888i	$0.0986189\pi$
$641$			15.4383i			0.609775i	−0.952388	+	0.304888i	$0.901381\pi$
$642$		0			0
$643$	1.41036			0.0556191			0.0278095	−	0.999613i	$-0.491147\pi$
$643$	1.41036			0.0556191			0.0278095	+	0.999613i	$0.491147\pi$
$644$	−9.83005	−	11.8102i	−0.387358	−	0.465388i
$645$		0			0
$646$	41.6679	−	15.0720i	1.63940	−	0.592998i
$647$	−0.811574			−0.0319063			−0.0159531	−	0.999873i	$-0.505078\pi$
$647$	−0.811574			−0.0319063			−0.0159531	+	0.999873i	$0.505078\pi$
$648$		0			0
$649$	−36.3941			−1.42860
$650$	10.5321	−	3.80962i	0.413102	−	0.149426i
$651$		0			0
$652$	9.02719	−	7.51364i	0.353532	−	0.294257i
$653$	9.82168			0.384352			0.192176	−	0.981360i	$-0.438446\pi$
$653$	9.82168			0.384352			0.192176	+	0.981360i	$0.438446\pi$
$654$		0			0
$655$		−	4.03615i		−	0.157705i
$656$	38.3393	+	7.07565i	1.49690	+	0.276258i
$657$		0			0
$658$	−6.04657	+	2.18714i	−0.235720	+	0.0852637i
$659$			11.1456i			0.434170i	0.976153	+	0.217085i	$0.0696548\pi$
$659$			11.1456i			0.434170i	−0.976153	+	0.217085i	$0.930345\pi$
$660$		0			0
$661$			15.3989i			0.598947i	0.954105	+	0.299474i	$0.0968111\pi$
$661$			15.3989i			0.598947i	−0.954105	+	0.299474i	$0.903189\pi$
$662$	2.72376	+	7.53010i	0.105862	+	0.292666i
$663$		0			0
$664$	0.324445	−	0.554280i	0.0125909	−	0.0215102i
$665$			2.61717i			0.101489i
$666$		0			0
$667$	38.0146			1.47193
$668$	−34.0000	+	28.2993i	−1.31550	+	1.09493i
$669$		0			0
$670$	1.97706	+	5.46577i	0.0763804	+	0.211161i
$671$	−17.1478			−0.661982
$672$		0			0
$673$	20.4112			0.786795			0.393398	−	0.919368i	$-0.371300\pi$
$673$	20.4112			0.786795			0.393398	+	0.919368i	$0.371300\pi$
$674$	15.5126	+	42.8862i	0.597525	+	1.65192i
$675$		0			0
$676$	−15.8159	+	13.1641i	−0.608305	+	0.506313i
$677$	50.5124			1.94135			0.970674	−	0.240401i	$-0.0772789\pi$
$677$	50.5124			1.94135			0.970674	+	0.240401i	$0.0772789\pi$
$678$		0			0
$679$		−	3.37287i		−	0.129439i
$680$	−3.25498	+	5.56080i	−0.124823	+	0.213247i
$681$		0			0
$682$	12.8834	+	35.6176i	0.493333	+	1.36387i
$683$			33.3625i			1.27658i	0.769796	+	0.638291i	$0.220358\pi$
$683$			33.3625i			1.27658i	−0.769796	+	0.638291i	$0.779642\pi$
$684$		0			0
$685$		−	1.10475i		−	0.0422104i
$686$	−1.32989	+	0.481042i	−0.0507753	+	0.0183663i
$687$		0			0
$688$	−6.41886	+	34.7804i	−0.244717	+	1.32599i
$689$			16.3808i			0.624059i
$690$		0			0
$691$	24.3714			0.927133			0.463567	−	0.886062i	$-0.346569\pi$
$691$	24.3714			0.927133			0.463567	+	0.886062i	$0.346569\pi$
$692$	37.1879	−	30.9527i	1.41367	−	1.17665i
$693$		0			0
$694$	27.0442	−	9.78234i	1.02659	−	0.371333i
$695$	8.62982			0.327348
$696$		0			0
$697$	50.9002			1.92798
$698$	−11.0053	+	3.98081i	−0.416558	+	0.150676i
$699$		0			0
$700$	6.15384	+	7.39348i	0.232593	+	0.279447i
$701$	34.1271			1.28896			0.644481	−	0.764620i	$-0.277073\pi$
$701$	34.1271			1.28896			0.644481	+	0.764620i	$0.277073\pi$
$702$		0			0
$703$		−	22.8991i		−	0.863658i
$704$	−19.1033	+	10.7270i	−0.719983	+	0.404288i
$705$		0			0
$706$	10.9489	−	3.96041i	0.412069	−	0.149052i
$707$			1.20021i			0.0451384i
$708$		0			0
$709$		−	22.8145i		−	0.856818i	−0.903585	−	0.428409i	$-0.859074\pi$
$709$		−	22.8145i		−	0.856818i	0.903585	−	0.428409i	$-0.140926\pi$
$710$	2.04962	+	5.66638i	0.0769209	+	0.212655i
$711$		0			0
$712$	−3.52300	+	6.01868i	−0.132030	+	0.225560i
$713$			75.1355i			2.81385i
$714$		0			0
$715$	−1.96707			−0.0735642
$716$	6.92556	+	8.32065i	0.258820	+	0.310957i
$717$		0			0
$718$	−5.08953	−	14.0705i	−0.189940	−	0.525107i
$719$	2.18175			0.0813654			0.0406827	−	0.999172i	$-0.487047\pi$
$719$	2.18175			0.0813654			0.0406827	+	0.999172i	$0.487047\pi$
$720$		0			0
$721$	10.7004			0.398502
$722$	−8.17556	−	22.6021i	−0.304263	−	0.841164i
$723$		0			0
$724$	7.92846	+	9.52558i	0.294659	+	0.354015i
$725$	−23.7980			−0.883837
$726$		0			0
$727$		−	15.3017i		−	0.567507i	−0.958897	−	0.283754i	$-0.908420\pi$
$727$		−	15.3017i		−	0.567507i	0.958897	−	0.283754i	$-0.0915798\pi$
$728$	4.01927	+	2.35266i	0.148964	+	0.0871953i
$729$		0			0
$730$	−1.91811	−	5.30280i	−0.0709924	−	0.196265i
$731$			46.1754i			1.70786i
$732$		0			0
$733$			15.8711i			0.586213i	0.956080	+	0.293106i	$0.0946890\pi$
$733$			15.8711i			0.586213i	−0.956080	+	0.293106i	$0.905311\pi$
$734$	−31.5974	+	11.4293i	−1.16628	+	0.421863i
$735$		0			0
$736$	−42.8741	+	7.12036i	−1.58036	+	0.262460i
$737$			25.8025i			0.950449i
$738$		0			0
$739$	31.1319			1.14521			0.572603	−	0.819833i	$-0.305934\pi$
$739$	31.1319			1.14521			0.572603	+	0.819833i	$0.305934\pi$
$740$	2.13024	+	2.55936i	0.0783093	+	0.0940840i
$741$		0			0
$742$	−13.2303	+	4.78562i	−0.485700	+	0.175686i
$743$	14.6629			0.537930			0.268965	−	0.963150i	$-0.413318\pi$
$743$	14.6629			0.537930			0.268965	+	0.963150i	$0.413318\pi$
$744$		0			0
$745$	3.56158			0.130486
$746$	16.1504	−	5.84186i	0.591308	−	0.213886i
$747$		0			0
$748$	−21.9849	+	18.2988i	−0.803849	+	0.669071i
$749$	−1.49655			−0.0546826
$750$		0			0
$751$			8.46100i			0.308746i	0.988013	+	0.154373i	$0.0493358\pi$
$751$			8.46100i			0.308746i	−0.988013	+	0.154373i	$0.950664\pi$
$752$	−3.30069	+	17.8847i	−0.120364	+	0.652188i
$753$		0			0
$754$	−10.8347	+	3.91908i	−0.394576	+	0.142725i
$755$		−	6.48842i		−	0.236138i
$756$		0			0
$757$		−	39.6473i		−	1.44101i	−0.693451	−	0.720504i	$-0.743911\pi$
$757$		−	39.6473i		−	1.44101i	0.693451	−	0.720504i	$-0.256089\pi$
$758$	15.4600	+	42.7408i	0.561533	+	1.55241i
$759$		0			0
$760$	6.38849	+	3.73947i	0.231735	+	0.135645i
$761$			49.7301i			1.80271i	0.433076	+	0.901357i	$0.357428\pi$
$761$			49.7301i			1.80271i	−0.433076	+	0.901357i	$0.642572\pi$
$762$		0			0
$763$	−18.4352			−0.667401
$764$	−20.9353	+	17.4251i	−0.757411	+	0.630419i
$765$		0			0
$766$	−14.4568	−	39.9671i	−0.522344	−	1.44407i
$767$	21.8816			0.790098
$768$		0			0
$769$	5.62877			0.202979			0.101489	−	0.994837i	$-0.467639\pi$
$769$	5.62877			0.202979			0.101489	+	0.994837i	$0.467639\pi$
$770$	−0.574675	−	1.58875i	−0.0207099	−	0.0572544i
$771$		0			0
$772$	−9.05837	+	7.53959i	−0.326018	+	0.271356i
$773$	25.3999			0.913570			0.456785	−	0.889577i	$-0.349001\pi$
$773$	25.3999			0.913570			0.456785	+	0.889577i	$0.349001\pi$
$774$		0			0
$775$		−	47.0366i		−	1.68960i
$776$	−8.23317	−	4.81924i	−0.295553	−	0.173001i
$777$		0			0
$778$	−6.19211	−	17.1187i	−0.221998	−	0.613736i
$779$		−	58.4764i		−	2.09514i
$780$		0			0
$781$			26.7495i			0.957174i
$782$	−53.3588	+	19.3007i	−1.90811	+	0.690193i
$783$		0			0
$784$	−0.725955	+	3.93357i	−0.0259270	+	0.140485i
$785$		−	2.14711i		−	0.0766338i
$786$		0			0
$787$	−31.5311			−1.12396			−0.561982	−	0.827150i	$-0.689961\pi$
$787$	−31.5311			−1.12396			−0.561982	+	0.827150i	$0.689961\pi$
$788$	29.2564	−	24.3511i	1.04222	−	0.867472i
$789$		0			0
$790$	3.01656	−	1.09114i	0.107324	−	0.0388209i
$791$	5.25692			0.186915
$792$		0			0
$793$	10.3099			0.366115
$794$	−27.7046	+	10.0212i	−0.983199	+	0.355639i
$795$		0			0
$796$	7.56671	+	9.09096i	0.268195	+	0.322221i
$797$	−37.3724			−1.32380			−0.661899	−	0.749593i	$-0.730249\pi$
$797$	−37.3724			−1.32380			−0.661899	+	0.749593i	$0.730249\pi$
$798$		0			0
$799$			23.7442i			0.840010i
$800$	26.8402	−	4.45751i	0.948945	−	0.157597i
$801$		0			0
$802$	21.0481	−	7.61343i	0.743233	−	0.268840i
$803$		−	25.0332i		−	0.883402i
$804$		0			0
$805$		−	3.35147i		−	0.118124i
$806$	−7.74603	−	21.4147i	−0.272842	−	0.754299i
$807$		0			0
$808$	2.92970	+	1.71488i	0.103066	+	0.0603294i
$809$		−	4.37230i		−	0.153722i	−0.997042	−	0.0768610i	$-0.975510\pi$
$809$		−	4.37230i		−	0.153722i	0.997042	−	0.0768610i	$-0.0244898\pi$
$810$		0			0
$811$	−29.1067			−1.02208			−0.511038	−	0.859558i	$-0.670739\pi$
$811$	−29.1067			−1.02208			−0.511038	+	0.859558i	$0.670739\pi$
$812$	−6.33066	−	7.60592i	−0.222163	−	0.266915i
$813$		0			0
$814$	5.02817	+	13.9009i	0.176237	+	0.487226i
$815$	2.56171			0.0897328
$816$		0			0
$817$	53.0484			1.85593
$818$	1.90077	+	5.25486i	0.0664587	+	0.183732i
$819$		0			0
$820$	5.43990	+	6.53572i	0.189970	+	0.228237i
$821$	45.1785			1.57674			0.788370	−	0.615201i	$-0.210925\pi$
$821$	45.1785			1.57674			0.788370	+	0.615201i	$0.210925\pi$
$822$		0			0
$823$		−	30.6242i		−	1.06749i	−0.845644	−	0.533747i	$-0.820783\pi$
$823$		−	30.6242i		−	1.06749i	0.845644	−	0.533747i	$-0.179217\pi$
$824$	15.2889	−	26.1195i	0.532615	−	0.909917i
$825$		0			0
$826$	6.39266	+	17.6731i	0.222429	+	0.614927i
$827$		−	12.0993i		−	0.420734i	−0.977623	−	0.210367i	$-0.932534\pi$
$827$		−	12.0993i		−	0.420734i	0.977623	−	0.210367i	$-0.0674658\pi$
$828$		0			0
$829$		−	15.2105i		−	0.528283i	−0.964484	−	0.264142i	$-0.914911\pi$
$829$		−	15.2105i		−	0.528283i	0.964484	−	0.264142i	$-0.0850886\pi$
$830$	0.131730	−	0.0476488i	0.00457241	−	0.00165391i
$831$		0			0
$832$	11.4857	−	6.44948i	0.398194	−	0.223595i
$833$			5.22231i			0.180942i
$834$		0			0
$835$	−9.64841			−0.333897
$836$	21.0225	+	25.2573i	0.727078	+	0.873542i
$837$		0			0
$838$	−4.74739	+	1.71721i	−0.163996	+	0.0593200i
$839$	−42.2155			−1.45744			−0.728721	−	0.684811i	$-0.759885\pi$
$839$	−42.2155			−1.45744			−0.728721	+	0.684811i	$0.759885\pi$
$840$		0			0
$841$	−4.51816			−0.155799
$842$	21.7792	−	7.87788i	0.750560	−	0.271490i
$843$		0			0
$844$	−19.8811	+	16.5477i	−0.684337	+	0.569597i
$845$	−4.48820			−0.154399
$846$		0			0
$847$			3.49993i			0.120259i
$848$	−7.22213	+	39.1329i	−0.248009	+	1.34383i
$849$		0			0
$850$	33.4038	−	12.0827i	1.14574	−	0.414434i
$851$			29.3240i			1.00521i
$852$		0			0
$853$		−	49.2536i		−	1.68641i	−0.537592	−	0.843205i	$-0.680666\pi$
$853$		−	49.2536i		−	1.68641i	0.537592	−	0.843205i	$-0.319334\pi$
$854$	3.01202	+	8.32702i	0.103069	+	0.284945i
$855$		0			0
$856$	−2.13830	+	3.65306i	−0.0730856	+	0.124859i
$857$		−	25.9243i		−	0.885557i	−0.896631	−	0.442779i	$-0.853993\pi$
$857$		−	25.9243i		−	0.885557i	0.896631	−	0.442779i	$-0.146007\pi$
$858$		0			0
$859$	9.25940			0.315927			0.157963	−	0.987445i	$-0.449507\pi$
$859$	9.25940			0.315927			0.157963	+	0.987445i	$0.449507\pi$
$860$	−5.92905	+	4.93495i	−0.202179	+	0.168280i
$861$		0			0
$862$	−13.8301	−	38.2346i	−0.471055	−	1.30228i
$863$	−6.21443			−0.211542			−0.105771	−	0.994391i	$-0.533731\pi$
$863$	−6.21443			−0.211542			−0.105771	+	0.994391i	$0.533731\pi$
$864$		0			0
$865$	10.5531			0.358815
$866$	11.3659	+	31.4220i	0.386227	+	1.06776i
$867$		0			0
$868$	15.0330	−	12.5125i	0.510254	−	0.424702i
$869$	14.2404			0.483073
$870$		0			0
$871$		−	15.5135i		−	0.525655i
$872$	−26.3407	+	45.0004i	−0.892010	+	1.52390i
$873$		0			0
$874$	22.1736	+	61.3010i	0.750032	+	2.07354i
$875$			4.27921i			0.144664i
$876$		0			0
$877$			15.1038i			0.510020i	0.966938	+	0.255010i	$0.0820787\pi$
$877$			15.1038i			0.510020i	−0.966938	+	0.255010i	$0.917921\pi$
$878$	−20.5988	+	7.45091i	−0.695175	+	0.251456i
$879$		0			0
$880$	−4.69923	−	0.867261i	−0.158411	−	0.0292354i
$881$			2.59677i			0.0874874i	0.999043	+	0.0437437i	$0.0139285\pi$
$881$			2.59677i			0.0874874i	−0.999043	+	0.0437437i	$0.986072\pi$
$882$		0			0
$883$	11.0661			0.372404			0.186202	−	0.982511i	$-0.440382\pi$
$883$	11.0661			0.372404			0.186202	+	0.982511i	$0.440382\pi$
$884$	13.2182	−	11.0020i	0.444576	−	0.370036i
$885$		0			0
$886$	−28.9436	+	10.4694i	−0.972380	+	0.351726i
$887$	−7.38595			−0.247996			−0.123998	−	0.992282i	$-0.539572\pi$
$887$	−7.38595			−0.247996			−0.123998	+	0.992282i	$0.539572\pi$
$888$		0			0
$889$	−19.7677			−0.662989
$890$	−1.43039	+	0.517397i	−0.0479469	+	0.0173432i
$891$		0			0
$892$	0.970544	+	1.16605i	0.0324962	+	0.0390423i
$893$	27.2784			0.912837
$894$		0			0
$895$			2.36121i			0.0789265i
$896$	8.56457	+	7.39244i	0.286122	+	0.246964i
$897$		0			0
$898$	−38.4814	+	13.9193i	−1.28414	+	0.464494i
$899$			48.3881i			1.61383i
$900$		0			0
$901$			51.9539i			1.73084i
$902$	12.8402	+	35.4980i	0.427532	+	1.18195i
$903$		0			0
$904$	7.51122	−	12.8321i	0.249819	−	0.426790i
$905$			2.70314i			0.0898555i
$906$		0			0
$907$	5.58114			0.185319			0.0926594	−	0.995698i	$-0.470463\pi$
$907$	5.58114			0.185319			0.0926594	+	0.995698i	$0.470463\pi$
$908$	−4.61867	−	5.54906i	−0.153276	−	0.184152i
$909$		0			0
$910$	0.345517	+	0.955216i	0.0114538	+	0.0316651i
$911$	−7.02450			−0.232732			−0.116366	−	0.993206i	$-0.537125\pi$
$911$	−7.02450			−0.232732			−0.116366	+	0.993206i	$0.537125\pi$
$912$		0			0
$913$	0.621864			0.0205807
$914$	−12.6257	−	34.9050i	−0.417622	−	1.15456i
$915$		0			0
$916$	4.44773	+	5.34369i	0.146957	+	0.176560i
$917$	−9.25252			−0.305545
$918$		0			0
$919$			25.7961i			0.850935i	0.904974	+	0.425468i	$0.139890\pi$
$919$			25.7961i			0.850935i	−0.904974	+	0.425468i	$0.860110\pi$
$920$	−8.18093	−	4.78867i	−0.269717	−	0.157878i
$921$		0			0
$922$	3.59564	+	9.94051i	0.118416	+	0.327373i
$923$		−	16.0829i		−	0.529374i
$924$		0			0
$925$		−	18.3575i		−	0.603591i
$926$	−10.7642	+	3.89360i	−0.353735	+	0.127952i
$927$		0			0
$928$	−27.6114	+	4.58559i	−0.906390	+	0.150530i
$929$		−	10.1558i		−	0.333201i	−0.986024	−	0.166600i	$-0.946721\pi$
$929$		−	10.1558i		−	0.333201i	0.986024	−	0.166600i	$-0.0532790\pi$
$930$		0			0
$931$	5.99963			0.196630
$932$	29.4003	+	35.3227i	0.963037	+	1.15703i
$933$		0			0
$934$	−21.3602	+	7.72633i	−0.698927	+	0.252813i
$935$	−6.23882			−0.204031
$936$		0			0
$937$	19.1504			0.625616			0.312808	−	0.949816i	$-0.398730\pi$
$937$	19.1504			0.625616			0.312808	+	0.949816i	$0.398730\pi$
$938$	12.5298	−	4.53223i	0.409113	−	0.147983i
$939$		0			0
$940$	−3.04882	+	2.53763i	−0.0994415	+	0.0827685i
$941$	14.3260			0.467016			0.233508	−	0.972355i	$-0.424980\pi$
$941$	14.3260			0.467016			0.233508	+	0.972355i	$0.424980\pi$
$942$		0			0
$943$			74.8833i			2.43854i
$944$	52.2740	+	9.64736i	1.70137	+	0.313995i
$945$		0			0
$946$	−32.2029	+	11.6483i	−1.04701	+	0.378720i
$947$		−	7.67662i		−	0.249456i	−0.992191	−	0.124728i	$-0.960194\pi$
$947$		−	7.67662i		−	0.249456i	0.992191	−	0.124728i	$-0.0398059\pi$
$948$		0			0
$949$			15.0509i			0.488574i
$950$	−13.8812	−	38.3758i	−0.450364	−	1.24508i
$951$		0			0
$952$	12.7476	+	7.46177i	0.413153	+	0.241837i
$953$			52.6546i			1.70565i	0.522197	+	0.852825i	$0.325113\pi$
$953$			52.6546i			1.70565i	−0.522197	+	0.852825i	$0.674887\pi$
$954$		0			0
$955$	−5.94095			−0.192245
$956$	−16.0604	+	13.3676i	−0.519429	+	0.432338i
$957$		0			0
$958$	15.2485	+	42.1560i	0.492657	+	1.36200i
$959$	−2.53255			−0.0817803
$960$		0			0
$961$	−64.6386			−2.08512
$962$	−3.02313	−	8.35775i	−0.0974698	−	0.269465i
$963$		0			0
$964$	15.5164	−	12.9148i	0.499749	−	0.415958i
$965$	−2.57056			−0.0827492
$966$		0			0
$967$		−	50.1578i		−	1.61297i	−0.591257	−	0.806483i	$-0.701368\pi$
$967$		−	50.1578i		−	1.61297i	0.591257	−	0.806483i	$-0.298632\pi$
$968$	8.54330	+	5.00078i	0.274592	+	0.160731i
$969$		0			0
$970$	−0.707766	−	1.95669i	−0.0227250	−	0.0628255i
$971$			54.8144i			1.75908i	0.475828	+	0.879538i	$0.342148\pi$
$971$			54.8144i			1.75908i	−0.475828	+	0.879538i	$0.657852\pi$
$972$		0			0
$973$		−	19.7831i		−	0.634217i
$974$	40.6099	−	14.6892i	1.30122	−	0.470674i
$975$		0			0
$976$	24.6299	+	4.54553i	0.788382	+	0.145499i
$977$		−	0.0603583i		−	0.00193103i	−1.00000		0.000965516i	$-0.999693\pi$
$977$		−	0.0603583i		−	0.00193103i	1.00000		0.000965516i	$-0.000307333\pi$
$978$		0			0
$979$	−6.75254			−0.215812
$980$	−0.670559	+	0.558129i	−0.0214202	+	0.0178288i
$981$		0			0
$982$	54.8181	−	19.8286i	1.74932	−	0.632756i
$983$	−7.40354			−0.236136			−0.118068	−	0.993005i	$-0.537670\pi$
$983$	−7.40354			−0.236136			−0.118068	+	0.993005i	$0.537670\pi$
$984$		0			0
$985$	8.30230			0.264533
$986$	−34.3637	+	12.4299i	−1.09436	+	0.395849i
$987$		0			0
$988$	−12.6395	−	15.1857i	−0.402118	−	0.483121i
$989$	−67.9323			−2.16012
$990$		0			0
$991$			35.6861i			1.13361i	0.823853	+	0.566803i	$0.191820\pi$
$991$			35.6861i			1.13361i	−0.823853	+	0.566803i	$0.808180\pi$
$992$	−9.06338	−	54.5737i	−0.287763	−	1.73272i
$993$		0			0
$994$	12.9897	−	4.69858i	0.412008	−	0.149030i
$995$			2.57981i			0.0817853i
$996$		0			0
$997$		−	52.4345i		−	1.66062i	−0.557304	−	0.830308i	$-0.688164\pi$
$997$		−	52.4345i		−	1.66062i	0.557304	−	0.830308i	$-0.311836\pi$
$998$	−1.94185	−	5.36844i	−0.0614682	−	0.169935i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.13	✓	32
3.2	odd	2	inner	1512.2.j.c.323.20	yes	32
4.3	odd	2		6048.2.j.c.5615.12		32
8.3	odd	2	inner	1512.2.j.c.323.19	yes	32
8.5	even	2		6048.2.j.c.5615.22		32
12.11	even	2		6048.2.j.c.5615.21		32
24.5	odd	2		6048.2.j.c.5615.11		32
24.11	even	2	inner	1512.2.j.c.323.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.13	✓	32	1.1	even	1	trivial
1512.2.j.c.323.14	yes	32	24.11	even	2	inner
1512.2.j.c.323.19	yes	32	8.3	odd	2	inner
1512.2.j.c.323.20	yes	32	3.2	odd	2	inner
6048.2.j.c.5615.11		32	24.5	odd	2
6048.2.j.c.5615.12		32	4.3	odd	2
6048.2.j.c.5615.21		32	12.11	even	2
6048.2.j.c.5615.22		32	8.5	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.481042 - 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} -0.436221 q^{5} +1.00000i q^{7} +(2.44100 + 1.42882i) q^{8} +O(q^{10})\)	\(q+(-0.481042 - 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} -0.436221 q^{5} +1.00000i q^{7} +(2.44100 + 1.42882i) q^{8} +(0.209841 + 0.580125i) q^{10} +2.73863i q^{11} -1.64657i q^{13} +(1.32989 - 0.481042i) q^{14} +(0.725955 - 3.93357i) q^{16} -5.22231i q^{17} -5.99963 q^{19} +(0.670559 - 0.558129i) q^{20} +(3.64206 - 1.31739i) q^{22} +7.68296 q^{23} -4.80971 q^{25} +(-2.18975 + 0.792068i) q^{26} +(-1.27946 - 1.53720i) q^{28} +4.94791 q^{29} +9.77950i q^{31} +(-5.58042 + 0.926774i) q^{32} +(-6.94508 + 2.51215i) q^{34} -0.436221i q^{35} +3.81676i q^{37} +(2.88607 + 7.97883i) q^{38} +(-1.06481 - 0.623284i) q^{40} +9.74668i q^{41} -8.84195 q^{43} +(-3.50397 - 4.20981i) q^{44} +(-3.69582 - 10.2175i) q^{46} -4.54668 q^{47} -1.00000 q^{49} +(2.31367 + 6.39637i) q^{50} +(2.10672 + 2.53110i) q^{52} -9.94845 q^{53} -1.19465i q^{55} +(-1.42882 + 2.44100i) q^{56} +(-2.38015 - 6.58016i) q^{58} +13.2892i q^{59} +6.26145i q^{61} +(13.0056 - 4.70435i) q^{62} +(3.91692 + 6.97551i) q^{64} +0.718269i q^{65} +9.42171 q^{67} +(6.68175 + 8.02773i) q^{68} +(-0.580125 + 0.209841i) q^{70} +9.76751 q^{71} -9.14079 q^{73} +(5.07586 - 1.83602i) q^{74} +(9.22262 - 7.67629i) q^{76} -2.73863 q^{77} -5.19984i q^{79} +(-0.316677 + 1.71591i) q^{80} +(12.9620 - 4.68856i) q^{82} -0.227071i q^{83} +2.27808i q^{85} +(4.25335 + 11.7588i) q^{86} +(-3.91302 + 6.68497i) q^{88} +2.46567i q^{89} +1.64657 q^{91} +(-11.8102 + 9.83005i) q^{92} +(2.18714 + 6.04657i) q^{94} +2.61717 q^{95} -3.37287 q^{97} +(0.481042 + 1.32989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

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