LMFDB - Embedded newform 1248.2.ca.b.49.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(49,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("1248.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not 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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.12
Character	$\chi$	$=$	1248.49
Dual form			1248.2.ca.b.433.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +3.13862 q^{5} +(3.44764 + 1.99050i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.10717 + 3.64973i) q^{11} +(3.58133 - 0.417261i) q^{13} +(-2.71813 + 1.56931i) q^{15} +(0.962941 - 1.66786i) q^{17} +(-1.67206 + 2.89609i) q^{19} -3.98099 q^{21} +(-1.84982 - 3.20398i) q^{23} +4.85094 q^{25} +1.00000i q^{27} +(-5.70476 + 3.29364i) q^{29} -6.35042i q^{31} +(-3.64973 - 2.10717i) q^{33} +(10.8208 + 6.24741i) q^{35} +(-0.708429 - 1.22703i) q^{37} +(-2.89289 + 2.15202i) q^{39} +(-2.47794 + 1.43064i) q^{41} +(-10.0697 - 5.81376i) q^{43} +(1.56931 - 2.71813i) q^{45} -9.74759i q^{47} +(4.42415 + 7.66285i) q^{49} +1.92588i q^{51} +2.32264i q^{53} +(6.61361 + 11.4551i) q^{55} -3.34412i q^{57} +(0.0313645 - 0.0543248i) q^{59} +(6.32541 + 3.65198i) q^{61} +(3.44764 - 1.99050i) q^{63} +(11.2404 - 1.30962i) q^{65} +(5.97751 + 10.3534i) q^{67} +(3.20398 + 1.84982i) q^{69} +(-5.28850 - 3.05332i) q^{71} -9.02220i q^{73} +(-4.20104 + 2.42547i) q^{75} +16.7773i q^{77} -12.0869 q^{79} +(-0.500000 - 0.866025i) q^{81} -5.10910 q^{83} +(3.02231 - 5.23479i) q^{85} +(3.29364 - 5.70476i) q^{87} +(1.29475 - 0.747522i) q^{89} +(13.1777 + 5.69005i) q^{91} +(3.17521 + 5.49962i) q^{93} +(-5.24796 + 9.08974i) q^{95} +(5.07484 + 2.92996i) q^{97} +4.21434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) $ 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	3.13862			1.40363			0.701817	−	0.712357i	$-0.252372\pi$
$5$	3.13862			1.40363			0.701817	+	0.712357i	$0.252372\pi$
$6$		0			0
$7$	3.44764	+	1.99050i	1.30309	+	0.752337i	0.980932	−	0.194351i	$-0.0622599\pi$
$7$	3.44764	+	1.99050i	1.30309	+	0.752337i	0.322154	+	0.946687i	$0.395593\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	2.10717	+	3.64973i	0.635336	+	1.10043i	0.986444	+	0.164100i	$0.0524718\pi$
$11$	2.10717	+	3.64973i	0.635336	+	1.10043i	−0.351108	+	0.936335i	$0.614195\pi$
$12$		0			0
$13$	3.58133	−	0.417261i	0.993281	−	0.115727i
$13$	3.58133	−	0.417261i	0.993281	−	0.115727i
$14$		0			0
$15$	−2.71813	+	1.56931i	−0.701817	+	0.405194i
$16$		0			0
$17$	0.962941	−	1.66786i	0.233547	−	0.404516i	−0.725302	−	0.688431i	$-0.758300\pi$
$17$	0.962941	−	1.66786i	0.233547	−	0.404516i	0.958850	+	0.283915i	$0.0916333\pi$
$18$		0			0
$19$	−1.67206	+	2.89609i	−0.383597	+	0.664409i	−0.991573	−	0.129546i	$-0.958648\pi$
$19$	−1.67206	+	2.89609i	−0.383597	+	0.664409i	0.607977	+	0.793955i	$0.291981\pi$
$20$		0			0
$21$	−3.98099			−0.868724
$22$		0			0
$23$	−1.84982	−	3.20398i	−0.385714	−	0.668077i	0.606154	−	0.795348i	$-0.292712\pi$
$23$	−1.84982	−	3.20398i	−0.385714	−	0.668077i	−0.991868	+	0.127271i	$0.959378\pi$
$24$		0			0
$25$	4.85094			0.970188
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−5.70476	+	3.29364i	−1.05935	+	0.611614i	−0.925251	−	0.379354i	$-0.876146\pi$
$29$	−5.70476	+	3.29364i	−1.05935	+	0.611614i	−0.134095	+	0.990968i	$0.542813\pi$
$30$		0			0
$31$		−	6.35042i		−	1.14057i	−0.821447	−	0.570285i	$-0.806833\pi$
$31$		−	6.35042i		−	1.14057i	0.821447	−	0.570285i	$-0.193167\pi$
$32$		0			0
$33$	−3.64973	−	2.10717i	−0.635336	−	0.366812i
$34$		0			0
$35$	10.8208	+	6.24741i	1.82906	+	1.05601i
$36$		0			0
$37$	−0.708429	−	1.22703i	−0.116465	−	0.201723i	0.801899	−	0.597459i	$-0.203823\pi$
$37$	−0.708429	−	1.22703i	−0.116465	−	0.201723i	−0.918364	+	0.395736i	$0.870490\pi$
$38$		0			0
$39$	−2.89289	+	2.15202i	−0.463233	+	0.344599i
$40$		0			0
$41$	−2.47794	+	1.43064i	−0.386989	+	0.223428i	−0.680855	−	0.732418i	$-0.738392\pi$
$41$	−2.47794	+	1.43064i	−0.386989	+	0.223428i	0.293866	+	0.955847i	$0.405058\pi$
$42$		0			0
$43$	−10.0697	−	5.81376i	−1.53562	−	0.886590i	−0.999088	−	0.0427087i	$-0.986401\pi$
$43$	−10.0697	−	5.81376i	−1.53562	−	0.886590i	−0.536531	−	0.843881i	$-0.680265\pi$
$44$		0			0
$45$	1.56931	−	2.71813i	0.233939	−	0.405194i
$46$		0			0
$47$		−	9.74759i		−	1.42183i	−0.703277	−	0.710916i	$-0.748280\pi$
$47$		−	9.74759i		−	1.42183i	0.703277	−	0.710916i	$-0.251720\pi$
$48$		0			0
$49$	4.42415	+	7.66285i	0.632021	+	1.09469i
$50$		0			0
$51$			1.92588i			0.269677i
$52$		0			0
$53$			2.32264i			0.319039i	0.987195	+	0.159519i	$0.0509944\pi$
$53$			2.32264i			0.319039i	−0.987195	+	0.159519i	$0.949006\pi$
$54$		0			0
$55$	6.61361	+	11.4551i	0.891780	+	1.54461i
$56$		0			0
$57$		−	3.34412i		−	0.442939i
$58$		0			0
$59$	0.0313645	−	0.0543248i	0.00408331	−	0.00707249i	−0.863977	−	0.503532i	$-0.832034\pi$
$59$	0.0313645	−	0.0543248i	0.00408331	−	0.00707249i	0.868060	+	0.496460i	$0.165367\pi$
$60$		0			0
$61$	6.32541	+	3.65198i	0.809885	+	0.467588i	0.846916	−	0.531727i	$-0.178457\pi$
$61$	6.32541	+	3.65198i	0.809885	+	0.467588i	−0.0370307	+	0.999314i	$0.511790\pi$
$62$		0			0
$63$	3.44764	−	1.99050i	0.434362	−	0.250779i
$64$		0			0
$65$	11.2404	−	1.30962i	1.39420	−	0.162439i
$66$		0			0
$67$	5.97751	+	10.3534i	0.730269	+	1.26486i	0.956768	+	0.290852i	$0.0939388\pi$
$67$	5.97751	+	10.3534i	0.730269	+	1.26486i	−0.226498	+	0.974012i	$0.572728\pi$
$68$		0			0
$69$	3.20398	+	1.84982i	0.385714	+	0.222692i
$70$		0			0
$71$	−5.28850	−	3.05332i	−0.627630	−	0.362362i	0.152204	−	0.988349i	$-0.451363\pi$
$71$	−5.28850	−	3.05332i	−0.627630	−	0.362362i	−0.779834	+	0.625987i	$0.784696\pi$
$72$		0			0
$73$		−	9.02220i		−	1.05597i	−0.849254	−	0.527984i	$-0.822948\pi$
$73$		−	9.02220i		−	1.05597i	0.849254	−	0.527984i	$-0.177052\pi$
$74$		0			0
$75$	−4.20104	+	2.42547i	−0.485094	+	0.280069i
$76$		0			0
$77$			16.7773i			1.91195i
$78$		0			0
$79$	−12.0869			−1.35989			−0.679943	−	0.733265i	$-0.737995\pi$
$79$	−12.0869			−1.35989			−0.679943	+	0.733265i	$0.737995\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−5.10910			−0.560797			−0.280398	−	0.959884i	$-0.590467\pi$
$83$	−5.10910			−0.560797			−0.280398	+	0.959884i	$0.590467\pi$
$84$		0			0
$85$	3.02231	−	5.23479i	0.327815	−	0.567792i
$86$		0			0
$87$	3.29364	−	5.70476i	0.353116	−	0.611614i
$88$		0			0
$89$	1.29475	−	0.747522i	0.137243	−	0.0792372i	−0.429806	−	0.902921i	$-0.641418\pi$
$89$	1.29475	−	0.747522i	0.137243	−	0.0792372i	0.567049	+	0.823684i	$0.308085\pi$
$90$		0			0
$91$	13.1777	+	5.69005i	1.38140	+	0.596479i
$92$		0			0
$93$	3.17521	+	5.49962i	0.329254	+	0.570285i
$94$		0			0
$95$	−5.24796	+	9.08974i	−0.538429	+	0.932587i
$96$		0			0
$97$	5.07484	+	2.92996i	0.515272	+	0.297492i	0.734998	−	0.678069i	$-0.237183\pi$
$97$	5.07484	+	2.92996i	0.515272	+	0.297492i	−0.219726	+	0.975562i	$0.570516\pi$
$98$		0			0
$99$	4.21434			0.423557
$100$		0			0
$101$	−6.98634	+	4.03356i	−0.695166	+	0.401355i	−0.805545	−	0.592535i	$-0.798127\pi$
$101$	−6.98634	+	4.03356i	−0.695166	+	0.401355i	0.110378	+	0.993890i	$0.464794\pi$
$102$		0			0
$103$	19.0873			1.88073			0.940363	−	0.340172i	$-0.110485\pi$
$103$	19.0873			1.88073			0.940363	+	0.340172i	$0.110485\pi$
$104$		0			0
$105$	−12.4948			−1.21937
$106$		0			0
$107$	5.69031	−	3.28530i	0.550103	−	0.317602i	−0.199060	−	0.979987i	$-0.563789\pi$
$107$	5.69031	−	3.28530i	0.550103	−	0.317602i	0.749164	+	0.662385i	$0.230456\pi$
$108$		0			0
$109$	12.1256			1.16142			0.580710	−	0.814110i	$-0.302775\pi$
$109$	12.1256			1.16142			0.580710	+	0.814110i	$0.302775\pi$
$110$		0			0
$111$	1.22703	+	0.708429i	0.116465	+	0.0672411i
$112$		0			0
$113$	−9.34914	+	16.1932i	−0.879493	+	1.52333i	−0.0275947	+	0.999619i	$0.508785\pi$
$113$	−9.34914	+	16.1932i	−0.879493	+	1.52333i	−0.851898	+	0.523707i	$0.824549\pi$
$114$		0			0
$115$	−5.80589	−	10.0561i	−0.541402	−	0.937735i
$116$		0			0
$117$	1.42930	−	3.31015i	0.132139	−	0.306023i
$118$		0			0
$119$	6.63975	−	3.83346i	0.608665	−	0.351413i
$120$		0			0
$121$	−3.38035	+	5.85493i	−0.307304	+	0.532267i
$122$		0			0
$123$	1.43064	−	2.47794i	0.128996	−	0.223428i
$124$		0			0
$125$	−0.467837			−0.0418446
$126$		0			0
$127$	0.445189	+	0.771090i	0.0395041	+	0.0684231i	0.885101	−	0.465398i	$-0.154089\pi$
$127$	0.445189	+	0.771090i	0.0395041	+	0.0684231i	−0.845597	+	0.533821i	$0.820756\pi$
$128$		0			0
$129$	11.6275			1.02375
$130$		0			0
$131$		−	3.32094i		−	0.290152i	−0.989421	−	0.145076i	$-0.953657\pi$
$131$		−	3.32094i		−	0.290152i	0.989421	−	0.145076i	$-0.0463426\pi$
$132$		0			0
$133$	−11.5293	+	6.65646i	−0.999719	+	0.577188i
$134$		0			0
$135$			3.13862i			0.270129i
$136$		0			0
$137$	−5.97444	−	3.44934i	−0.510431	−	0.294697i	0.222580	−	0.974914i	$-0.428552\pi$
$137$	−5.97444	−	3.44934i	−0.510431	−	0.294697i	−0.733011	+	0.680217i	$0.761885\pi$
$138$		0			0
$139$	4.32371	+	2.49629i	0.366732	+	0.211733i	0.672030	−	0.740524i	$-0.265423\pi$
$139$	4.32371	+	2.49629i	0.366732	+	0.211733i	−0.305298	+	0.952257i	$0.598756\pi$
$140$		0			0
$141$	4.87380	+	8.44166i	0.410448	+	0.710916i
$142$		0			0
$143$	9.06936	+	12.1916i	0.758418	+	1.01952i
$144$		0			0
$145$	−17.9051	+	10.3375i	−1.48693	+	0.858482i
$146$		0			0
$147$	−7.66285	−	4.42415i	−0.632021	−	0.364898i
$148$		0			0
$149$	10.5148	−	18.2122i	0.861409	−	1.49200i	−0.00916087	−	0.999958i	$-0.502916\pi$
$149$	10.5148	−	18.2122i	0.861409	−	1.49200i	0.870569	−	0.492045i	$-0.163751\pi$
$150$		0			0
$151$			15.5772i			1.26765i	0.773475	+	0.633827i	$0.218517\pi$
$151$			15.5772i			1.26765i	−0.773475	+	0.633827i	$0.781483\pi$
$152$		0			0
$153$	−0.962941	−	1.66786i	−0.0778491	−	0.134839i
$154$		0			0
$155$		−	19.9316i		−	1.60094i
$156$		0			0
$157$			13.5871i			1.08437i	0.840260	+	0.542184i	$0.182402\pi$
$157$			13.5871i			1.08437i	−0.840260	+	0.542184i	$0.817598\pi$
$158$		0			0
$159$	−1.16132	−	2.01146i	−0.0920985	−	0.159519i
$160$		0			0
$161$		−	14.7282i		−	1.16075i
$162$		0			0
$163$	5.85529	−	10.1417i	0.458622	−	0.794356i	−0.540266	−	0.841494i	$-0.681677\pi$
$163$	5.85529	−	10.1417i	0.458622	−	0.794356i	0.998888	+	0.0471375i	$0.0150099\pi$
$164$		0			0
$165$	−11.4551	−	6.61361i	−0.891780	−	0.514869i
$166$		0			0
$167$	−0.133302	+	0.0769619i	−0.0103152	+	0.00595549i	−0.505149	−	0.863032i	$-0.668562\pi$
$167$	−0.133302	+	0.0769619i	−0.0103152	+	0.00595549i	0.494834	+	0.868988i	$0.335229\pi$
$168$		0			0
$169$	12.6518	−	2.98869i	0.973214	−	0.229900i
$170$		0			0
$171$	1.67206	+	2.89609i	0.127866	+	0.221470i
$172$		0			0
$173$	−22.4496	−	12.9613i	−1.70681	−	0.985428i	−0.938452	−	0.345408i	$-0.887740\pi$
$173$	−22.4496	−	12.9613i	−1.70681	−	0.985428i	−0.768359	−	0.640019i	$-0.778926\pi$
$174$		0			0
$175$	16.7243	+	9.65578i	1.26424	+	0.729908i
$176$		0			0
$177$			0.0627289i			0.00471500i
$178$		0			0
$179$	−10.9372	+	6.31460i	−0.817485	+	0.471975i	−0.849549	−	0.527510i	$-0.823126\pi$
$179$	−10.9372	+	6.31460i	−0.817485	+	0.471975i	0.0320632	+	0.999486i	$0.489792\pi$
$180$		0			0
$181$		−	18.4603i		−	1.37215i	−0.727533	−	0.686073i	$-0.759333\pi$
$181$		−	18.4603i		−	1.37215i	0.727533	−	0.686073i	$-0.240667\pi$
$182$		0			0
$183$	−7.30395			−0.539924
$184$		0			0
$185$	−2.22349	−	3.85120i	−0.163474	−	0.283146i
$186$		0			0
$187$	8.11633			0.593525
$188$		0			0
$189$	−1.99050	+	3.44764i	−0.144787	+	0.250779i
$190$		0			0
$191$	2.75962	−	4.77980i	0.199679	−	0.345854i	−0.748745	−	0.662858i	$-0.769343\pi$
$191$	2.75962	−	4.77980i	0.199679	−	0.345854i	0.948424	+	0.317004i	$0.102677\pi$
$192$		0			0
$193$	0.109080	−	0.0629771i	0.00785172	−	0.00453319i	−0.496069	−	0.868283i	$-0.665224\pi$
$193$	0.109080	−	0.0629771i	0.00785172	−	0.00453319i	0.503921	+	0.863750i	$0.331890\pi$
$194$		0			0
$195$	−9.07968	+	6.75438i	−0.650209	+	0.483691i
$196$		0			0
$197$	−4.66226	−	8.07527i	−0.332172	−	0.575339i	0.650765	−	0.759279i	$-0.274448\pi$
$197$	−4.66226	−	8.07527i	−0.332172	−	0.575339i	−0.982938	+	0.183940i	$0.941115\pi$
$198$		0			0
$199$	7.90454	−	13.6911i	0.560338	−	0.970534i	−0.437128	−	0.899399i	$-0.644004\pi$
$199$	7.90454	−	13.6911i	0.560338	−	0.970534i	0.997467	−	0.0711353i	$-0.0226622\pi$
$200$		0			0
$201$	−10.3534	−	5.97751i	−0.730269	−	0.421621i
$202$		0			0
$203$	−26.2239			−1.84056
$204$		0			0
$205$	−7.77732	+	4.49024i	−0.543191	+	0.313612i
$206$		0			0
$207$	−3.69964			−0.257143
$208$		0			0
$209$	−14.0933			−0.974852
$210$		0			0
$211$	−16.2882	+	9.40397i	−1.12132	+	0.647396i	−0.941738	−	0.336346i	$-0.890809\pi$
$211$	−16.2882	+	9.40397i	−1.12132	+	0.647396i	−0.179585	+	0.983742i	$0.557475\pi$
$212$		0			0
$213$	6.10664			0.418420
$214$		0			0
$215$	−31.6050	−	18.2472i	−2.15545	−	1.24445i
$216$		0			0
$217$	12.6405	−	21.8940i	0.858092	−	1.48626i
$218$		0			0
$219$	4.51110	+	7.81345i	0.304832	+	0.527984i
$220$		0			0
$221$	2.75267	−	6.37496i	0.185165	−	0.428826i
$222$		0			0
$223$	0.888282	−	0.512850i	0.0594838	−	0.0343430i	−0.469963	−	0.882686i	$-0.655733\pi$
$223$	0.888282	−	0.512850i	0.0594838	−	0.0343430i	0.529447	+	0.848343i	$0.322399\pi$
$224$		0			0
$225$	2.42547	−	4.20104i	0.161698	−	0.280069i
$226$		0			0
$227$	3.67251	−	6.36098i	0.243753	−	0.422193i	−0.718027	−	0.696015i	$-0.754955\pi$
$227$	3.67251	−	6.36098i	0.243753	−	0.422193i	0.961780	+	0.273822i	$0.0882879\pi$
$228$		0			0
$229$	−2.10642			−0.139196			−0.0695982	−	0.997575i	$-0.522172\pi$
$229$	−2.10642			−0.139196			−0.0695982	+	0.997575i	$0.522172\pi$
$230$		0			0
$231$	−8.38864	−	14.5295i	−0.551932	−	0.955974i
$232$		0			0
$233$	−30.1894			−1.97777			−0.988886	−	0.148674i	$-0.952500\pi$
$233$	−30.1894			−1.97777			−0.988886	+	0.148674i	$0.952500\pi$
$234$		0			0
$235$		−	30.5940i		−	1.99573i
$236$		0			0
$237$	10.4676	−	6.04346i	0.679943	−	0.392565i
$238$		0			0
$239$		−	18.4895i		−	1.19598i	−0.801502	−	0.597992i	$-0.795966\pi$
$239$		−	18.4895i		−	1.19598i	0.801502	−	0.597992i	$-0.204034\pi$
$240$		0			0
$241$	8.80353	+	5.08272i	0.567086	+	0.327407i	0.755984	−	0.654590i	$-0.227159\pi$
$241$	8.80353	+	5.08272i	0.567086	+	0.327407i	−0.188899	+	0.981997i	$0.560492\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	13.8857	+	24.0508i	0.887127	+	1.53655i
$246$		0			0
$247$	−4.77976	+	11.0695i	−0.304129	+	0.704338i
$248$		0			0
$249$	4.42461	−	2.55455i	0.280398	−	0.161888i
$250$		0			0
$251$	1.44560	+	0.834618i	0.0912455	+	0.0526806i	0.544928	−	0.838483i	$-0.316557\pi$
$251$	1.44560	+	0.834618i	0.0912455	+	0.0526806i	−0.453683	+	0.891163i	$0.649890\pi$
$252$		0			0
$253$	7.79578	−	13.5027i	0.490117	−	0.848907i
$254$		0			0
$255$			6.04461i			0.378528i
$256$		0			0
$257$	15.8839	+	27.5117i	0.990809	+	1.71613i	0.612553	+	0.790430i	$0.290143\pi$
$257$	15.8839	+	27.5117i	0.990809	+	1.71613i	0.378256	+	0.925701i	$0.376524\pi$
$258$		0			0
$259$		−	5.64050i		−	0.350483i
$260$		0			0
$261$			6.58728i			0.407743i
$262$		0			0
$263$	−1.42242	−	2.46371i	−0.0877102	−	0.151919i	0.818833	−	0.574032i	$-0.194622\pi$
$263$	−1.42242	−	2.46371i	−0.0877102	−	0.151919i	−0.906543	+	0.422114i	$0.861288\pi$
$264$		0			0
$265$			7.28988i			0.447813i
$266$		0			0
$267$	−0.747522	+	1.29475i	−0.0457476	+	0.0792372i
$268$		0			0
$269$	−7.47092	−	4.31334i	−0.455510	−	0.262989i	0.254644	−	0.967035i	$-0.418042\pi$
$269$	−7.47092	−	4.31334i	−0.455510	−	0.262989i	−0.710155	+	0.704046i	$0.751375\pi$
$270$		0			0
$271$	−0.896928	+	0.517842i	−0.0544845	+	0.0314566i	−0.526995	−	0.849869i	$-0.676681\pi$
$271$	−0.896928	+	0.517842i	−0.0544845	+	0.0314566i	0.472510	+	0.881325i	$0.343348\pi$
$272$		0			0
$273$	−14.2572	+	1.66111i	−0.862887	+	0.100535i
$274$		0			0
$275$	10.2218	+	17.7046i	0.616396	+	1.06763i
$276$		0			0
$277$	−14.5234	−	8.38507i	−0.872625	−	0.503810i	−0.00440514	−	0.999990i	$-0.501402\pi$
$277$	−14.5234	−	8.38507i	−0.872625	−	0.503810i	−0.868220	+	0.496180i	$0.834736\pi$
$278$		0			0
$279$	−5.49962	−	3.17521i	−0.329254	−	0.190095i
$280$		0			0
$281$		−	17.7570i		−	1.05930i	−0.848217	−	0.529648i	$-0.822324\pi$
$281$		−	17.7570i		−	1.05930i	0.848217	−	0.529648i	$-0.177676\pi$
$282$		0			0
$283$	10.5921	−	6.11533i	0.629633	−	0.363519i	−0.150977	−	0.988537i	$-0.548242\pi$
$283$	10.5921	−	6.11533i	0.629633	−	0.363519i	0.780610	+	0.625019i	$0.214909\pi$
$284$		0			0
$285$		−	10.4959i		−	0.621725i
$286$		0			0
$287$	−11.3907			−0.672374
$288$		0			0
$289$	6.64549	+	11.5103i	0.390911	+	0.677078i
$290$		0			0
$291$	−5.85992			−0.343514
$292$		0			0
$293$	−6.17354	+	10.6929i	−0.360662	+	0.624686i	−0.988070	−	0.154005i	$-0.950783\pi$
$293$	−6.17354	+	10.6929i	−0.360662	+	0.624686i	0.627408	+	0.778691i	$0.284116\pi$
$294$		0			0
$295$	0.0984412	−	0.170505i	0.00573147	−	0.00992719i
$296$		0			0
$297$	−3.64973	+	2.10717i	−0.211779	+	0.122271i
$298$		0			0
$299$	−7.96171	−	10.7027i	−0.460437	−	0.618950i
$300$		0			0
$301$	−23.1445	−	40.0875i	−1.33403	−	2.31060i
$302$		0			0
$303$	4.03356	−	6.98634i	0.231722	−	0.401355i
$304$		0			0
$305$	19.8531	+	11.4622i	1.13678	+	0.656322i
$306$		0			0
$307$	15.8252			0.903189			0.451595	−	0.892223i	$-0.350855\pi$
$307$	15.8252			0.903189			0.451595	+	0.892223i	$0.350855\pi$
$308$		0			0
$309$	−16.5301	+	9.54365i	−0.940363	+	0.542919i
$310$		0			0
$311$	−17.0009			−0.964030			−0.482015	−	0.876163i	$-0.660095\pi$
$311$	−17.0009			−0.964030			−0.482015	+	0.876163i	$0.660095\pi$
$312$		0			0
$313$	3.56281			0.201382			0.100691	−	0.994918i	$-0.467895\pi$
$313$	3.56281			0.201382			0.100691	+	0.994918i	$0.467895\pi$
$314$		0			0
$315$	10.8208	−	6.24741i	0.609685	−	0.352002i
$316$		0			0
$317$	6.07202			0.341039			0.170519	−	0.985354i	$-0.445455\pi$
$317$	6.07202			0.341039			0.170519	+	0.985354i	$0.445455\pi$
$318$		0			0
$319$	−24.0418	−	13.8805i	−1.34608	−	0.777161i
$320$		0			0
$321$	−3.28530	+	5.69031i	−0.183368	+	0.317602i
$322$		0			0
$323$	3.22019	+	5.57753i	0.179176	+	0.310342i
$324$		0			0
$325$	17.3728	−	2.02411i	0.963670	−	0.112277i
$326$		0			0
$327$	−10.5011	+	6.06280i	−0.580710	+	0.335273i
$328$		0			0
$329$	19.4025	−	33.6062i	1.06970	−	1.85277i
$330$		0			0
$331$	−8.39629	+	14.5428i	−0.461502	+	0.799345i	−0.999036	−	0.0438972i	$-0.986023\pi$
$331$	−8.39629	+	14.5428i	−0.461502	+	0.799345i	0.537534	+	0.843242i	$0.319356\pi$
$332$		0			0
$333$	−1.41686			−0.0776433
$334$		0			0
$335$	18.7611	+	32.4953i	1.02503	+	1.77541i
$336$		0			0
$337$	28.8880			1.57363			0.786815	−	0.617189i	$-0.211729\pi$
$337$	28.8880			1.57363			0.786815	+	0.617189i	$0.211729\pi$
$338$		0			0
$339$		−	18.6983i		−	1.01555i
$340$		0			0
$341$	23.1773	−	13.3814i	1.25512	−	0.724645i
$342$		0			0
$343$			7.35807i			0.397299i
$344$		0			0
$345$	10.0561	+	5.80589i	0.541402	+	0.312578i
$346$		0			0
$347$	3.63911	+	2.10104i	0.195358	+	0.112790i	0.594488	−	0.804104i	$-0.297355\pi$
$347$	3.63911	+	2.10104i	0.195358	+	0.112790i	−0.399131	+	0.916894i	$0.630688\pi$
$348$		0			0
$349$	−3.16574	−	5.48322i	−0.169458	−	0.293510i	0.768771	−	0.639524i	$-0.220868\pi$
$349$	−3.16574	−	5.48322i	−0.169458	−	0.293510i	−0.938229	+	0.346014i	$0.887535\pi$
$350$		0			0
$351$	0.417261	+	3.58133i	0.0222717	+	0.191157i
$352$		0			0
$353$	7.42833	−	4.28875i	0.395370	−	0.228267i	−0.289114	−	0.957295i	$-0.593361\pi$
$353$	7.42833	−	4.28875i	0.395370	−	0.228267i	0.684484	+	0.729028i	$0.260027\pi$
$354$		0			0
$355$	−16.5986	−	9.58321i	−0.880962	−	0.508624i
$356$		0			0
$357$	−3.83346	+	6.63975i	−0.202888	+	0.351413i
$358$		0			0
$359$			25.9007i			1.36699i	0.729956	+	0.683494i	$0.239541\pi$
$359$			25.9007i			1.36699i	−0.729956	+	0.683494i	$0.760459\pi$
$360$		0			0
$361$	3.90843	+	6.76961i	0.205707	+	0.356295i
$362$		0			0
$363$		−	6.76069i		−	0.354844i
$364$		0			0
$365$		−	28.3173i		−	1.48219i
$366$		0			0
$367$	11.2481	+	19.4823i	0.587148	+	1.01697i	0.994604	+	0.103745i	$0.0330826\pi$
$367$	11.2481	+	19.4823i	0.587148	+	1.01697i	−0.407456	+	0.913225i	$0.633584\pi$
$368$		0			0
$369$			2.86128i			0.148952i
$370$		0			0
$371$	−4.62320	+	8.00762i	−0.240025	+	0.415735i
$372$		0			0
$373$	7.64709	+	4.41505i	0.395951	+	0.228603i	0.684736	−	0.728792i	$-0.259918\pi$
$373$	7.64709	+	4.41505i	0.395951	+	0.228603i	−0.288784	+	0.957394i	$0.593251\pi$
$374$		0			0
$375$	0.405159	−	0.233919i	0.0209223	−	0.0120795i
$376$		0			0
$377$	−19.0563	+	14.1760i	−0.981448	+	0.730100i
$378$		0			0
$379$	2.94384	+	5.09888i	0.151215	+	0.261912i	0.931674	−	0.363294i	$-0.118348\pi$
$379$	2.94384	+	5.09888i	0.151215	+	0.261912i	−0.780459	+	0.625206i	$0.785015\pi$
$380$		0			0
$381$	−0.771090	−	0.445189i	−0.0395041	−	0.0228077i
$382$		0			0
$383$	10.8164	+	6.24483i	0.552691	+	0.319096i	0.750207	−	0.661204i	$-0.229954\pi$
$383$	10.8164	+	6.24483i	0.552691	+	0.319096i	−0.197516	+	0.980300i	$0.563287\pi$
$384$		0			0
$385$			52.6575i			2.68367i
$386$		0			0
$387$	−10.0697	+	5.81376i	−0.511873	+	0.295530i
$388$		0			0
$389$			7.83635i			0.397319i	0.980069	+	0.198659i	$0.0636587\pi$
$389$			7.83635i			0.397319i	−0.980069	+	0.198659i	$0.936341\pi$
$390$		0			0
$391$	−7.12507			−0.360330
$392$		0			0
$393$	1.66047	+	2.87602i	0.0837595	+	0.145076i
$394$		0			0
$395$	−37.9363			−1.90878
$396$		0			0
$397$	−4.81455	+	8.33904i	−0.241635	+	0.418524i	−0.961180	−	0.275921i	$-0.911017\pi$
$397$	−4.81455	+	8.33904i	−0.241635	+	0.418524i	0.719545	+	0.694446i	$0.244350\pi$
$398$		0			0
$399$	6.65646	−	11.5293i	0.333240	−	0.577188i
$400$		0			0
$401$	−32.5570	+	18.7968i	−1.62582	+	0.938666i	−0.640494	+	0.767963i	$0.721271\pi$
$401$	−32.5570	+	18.7968i	−1.62582	+	0.938666i	−0.985323	+	0.170703i	$0.945396\pi$
$402$		0			0
$403$	−2.64978	−	22.7429i	−0.131995	−	1.13291i
$404$		0			0
$405$	−1.56931	−	2.71813i	−0.0779797	−	0.135065i
$406$		0			0
$407$	2.98556	−	5.17114i	0.147989	−	0.256324i
$408$		0			0
$409$	−30.8797	−	17.8284i	−1.52690	−	0.881557i	−0.999490	−	0.0319469i	$-0.989829\pi$
$409$	−30.8797	−	17.8284i	−1.52690	−	0.881557i	−0.527412	−	0.849610i	$-0.676837\pi$
$410$		0			0
$411$	6.89869			0.340287
$412$		0			0
$413$	0.216267	−	0.124862i	0.0106418	−	0.00614404i
$414$		0			0
$415$	−16.0355			−0.787153
$416$		0			0
$417$	−4.99259			−0.244488
$418$		0			0
$419$	11.0423	−	6.37526i	0.539450	−	0.311452i	−0.205406	−	0.978677i	$-0.565851\pi$
$419$	11.0423	−	6.37526i	0.539450	−	0.311452i	0.744856	+	0.667225i	$0.232518\pi$
$420$		0			0
$421$	−7.12038			−0.347026			−0.173513	−	0.984832i	$-0.555512\pi$
$421$	−7.12038			−0.347026			−0.173513	+	0.984832i	$0.555512\pi$
$422$		0			0
$423$	−8.44166	−	4.87380i	−0.410448	−	0.236972i
$424$		0			0
$425$	4.67117	−	8.09070i	0.226585	−	0.392457i
$426$		0			0
$427$	14.5385	+	25.1814i	0.703567	+	1.21861i
$428$		0			0
$429$	−13.9501	−	6.02358i	−0.673518	−	0.290821i
$430$		0			0
$431$	−0.125387	+	0.0723921i	−0.00603967	+	0.00348700i	−0.503017	−	0.864277i	$-0.667777\pi$
$431$	−0.125387	+	0.0723921i	−0.00603967	+	0.00348700i	0.496977	+	0.867764i	$0.334443\pi$
$432$		0			0
$433$	10.4272	−	18.0604i	0.501097	−	0.867925i	−0.498902	−	0.866658i	$-0.666263\pi$
$433$	10.4272	−	18.0604i	0.501097	−	0.867925i	0.999999	−	0.00126704i	$-0.000403311\pi$
$434$		0			0
$435$	10.3375	−	17.9051i	0.495645	−	0.858482i
$436$		0			0
$437$	12.3720			0.591835
$438$		0			0
$439$	−12.9810	−	22.4838i	−0.619550	−	1.07309i	−0.989568	−	0.144068i	$-0.953982\pi$
$439$	−12.9810	−	22.4838i	−0.619550	−	1.07309i	0.370018	−	0.929025i	$-0.379352\pi$
$440$		0			0
$441$	8.84830			0.421348
$442$		0			0
$443$			5.43334i			0.258146i	0.991635	+	0.129073i	$0.0412001\pi$
$443$			5.43334i			0.258146i	−0.991635	+	0.129073i	$0.958800\pi$
$444$		0			0
$445$	4.06372	−	2.34619i	0.192639	−	0.111220i
$446$		0			0
$447$			21.0297i			0.994669i
$448$		0			0
$449$	−6.29523	−	3.63455i	−0.297090	−	0.171525i	0.344045	−	0.938953i	$-0.388203\pi$
$449$	−6.29523	−	3.63455i	−0.297090	−	0.171525i	−0.641135	+	0.767428i	$0.721536\pi$
$450$		0			0
$451$	−10.4429	−	6.02921i	−0.491737	−	0.283904i
$452$		0			0
$453$	−7.78860	−	13.4902i	−0.365940	−	0.633827i
$454$		0			0
$455$	41.3597	+	17.8589i	1.93897	+	0.837239i
$456$		0			0
$457$	−21.6279	+	12.4869i	−1.01171	+	0.584111i	−0.911692	−	0.410875i	$-0.865223\pi$
$457$	−21.6279	+	12.4869i	−1.01171	+	0.584111i	−0.100018	+	0.994986i	$0.531890\pi$
$458$		0			0
$459$	1.66786	+	0.962941i	0.0778491	+	0.0449462i
$460$		0			0
$461$	9.23732	−	15.9995i	0.430225	−	0.745171i	−0.566667	−	0.823947i	$-0.691768\pi$
$461$	9.23732	−	15.9995i	0.430225	−	0.745171i	0.996892	+	0.0787751i	$0.0251009\pi$
$462$		0			0
$463$		−	5.51017i		−	0.256079i	−0.991769	−	0.128040i	$-0.959131\pi$
$463$		−	5.51017i		−	0.256079i	0.991769	−	0.128040i	$-0.0408685\pi$
$464$		0			0
$465$	9.96578	+	17.2612i	0.462152	+	0.800471i
$466$		0			0
$467$			28.3047i			1.30979i	0.755722	+	0.654893i	$0.227286\pi$
$467$			28.3047i			1.30979i	−0.755722	+	0.654893i	$0.772714\pi$
$468$		0			0
$469$			47.5929i			2.19763i
$470$		0			0
$471$	−6.79355	−	11.7668i	−0.313030	−	0.542184i
$472$		0			0
$473$		−	49.0023i		−	2.25313i
$474$		0			0
$475$	−8.11106	+	14.0488i	−0.372161	+	0.644602i
$476$		0			0
$477$	2.01146	+	1.16132i	0.0920985	+	0.0531731i
$478$		0			0
$479$	0.857951	−	0.495338i	0.0392008	−	0.0226326i	−0.480272	−	0.877120i	$-0.659462\pi$
$479$	0.857951	−	0.495338i	0.0392008	−	0.0226326i	0.519472	+	0.854487i	$0.326129\pi$
$480$		0			0
$481$	−3.04911	−	4.09881i	−0.139027	−	0.186890i
$482$		0			0
$483$	7.36412	+	12.7550i	0.335079	+	0.580374i
$484$		0			0
$485$	15.9280	+	9.19603i	0.723253	+	0.417570i
$486$		0			0
$487$	17.0470	+	9.84212i	0.772476	+	0.445989i	0.833757	−	0.552132i	$-0.186185\pi$
$487$	17.0470	+	9.84212i	0.772476	+	0.445989i	−0.0612815	+	0.998121i	$0.519519\pi$
$488$		0			0
$489$			11.7106i			0.529571i
$490$		0			0
$491$	25.6962	−	14.8357i	1.15966	−	0.669527i	0.208434	−	0.978036i	$-0.433163\pi$
$491$	25.6962	−	14.8357i	1.15966	−	0.669527i	0.951221	+	0.308509i	$0.0998301\pi$
$492$		0			0
$493$			12.6863i			0.571364i
$494$		0			0
$495$	13.2272			0.594520
$496$		0			0
$497$	−12.1552	−	21.0535i	−0.545237	−	0.944378i
$498$		0			0
$499$	6.24154			0.279410			0.139705	−	0.990193i	$-0.455385\pi$
$499$	6.24154			0.279410			0.139705	+	0.990193i	$0.455385\pi$
$500$		0			0
$501$	0.0769619	−	0.133302i	0.00343840	−	0.00595549i
$502$		0			0
$503$	−3.85799	+	6.68224i	−0.172019	+	0.297946i	−0.939126	−	0.343574i	$-0.888363\pi$
$503$	−3.85799	+	6.68224i	−0.172019	+	0.297946i	0.767106	+	0.641520i	$0.221696\pi$
$504$		0			0
$505$	−21.9275	+	12.6598i	−0.975759	+	0.563355i
$506$		0			0
$507$	−9.46242	+	8.91418i	−0.420241	+	0.395893i
$508$		0			0
$509$	8.96597	+	15.5295i	0.397409	+	0.688333i	0.993405	−	0.114654i	$-0.0365759\pi$
$509$	8.96597	+	15.5295i	0.397409	+	0.688333i	−0.595996	+	0.802987i	$0.703243\pi$
$510$		0			0
$511$	17.9587	−	31.1053i	0.794444	−	1.37602i
$512$		0			0
$513$	−2.89609	−	1.67206i	−0.127866	−	0.0738232i
$514$		0			0
$515$	59.9078			2.63985
$516$		0			0
$517$	35.5761	−	20.5399i	1.56463	−	0.903342i
$518$		0			0
$519$	25.9226			1.13787
$520$		0			0
$521$	30.0883			1.31819			0.659096	−	0.752059i	$-0.270939\pi$
$521$	30.0883			1.31819			0.659096	+	0.752059i	$0.270939\pi$
$522$		0			0
$523$	−31.8942	+	18.4142i	−1.39464	+	0.805195i	−0.993824	−	0.110965i	$-0.964606\pi$
$523$	−31.8942	+	18.4142i	−1.39464	+	0.805195i	−0.400814	+	0.916160i	$0.631273\pi$
$524$		0			0
$525$	−19.3116			−0.842826
$526$		0			0
$527$	−10.5916	−	6.11508i	−0.461378	−	0.266377i
$528$		0			0
$529$	4.65633	−	8.06499i	0.202449	−	0.350652i
$530$		0			0
$531$	−0.0313645	−	0.0543248i	−0.00136110	−	0.00235750i
$532$		0			0
$533$	−8.27736	+	6.15753i	−0.358532	+	0.266712i
$534$		0			0
$535$	17.8597	−	10.3113i	0.772144	−	0.445797i
$536$		0			0
$537$	6.31460	−	10.9372i	0.272495	−	0.471975i
$538$		0			0
$539$	−18.6449	+	32.2939i	−0.803092	+	1.39100i
$540$		0			0
$541$	−3.36378			−0.144620			−0.0723100	−	0.997382i	$-0.523037\pi$
$541$	−3.36378			−0.144620			−0.0723100	+	0.997382i	$0.523037\pi$
$542$		0			0
$543$	9.23017	+	15.9871i	0.396104	+	0.686073i
$544$		0			0
$545$	38.0576			1.63021
$546$		0			0
$547$			29.3993i			1.25702i	0.777801	+	0.628511i	$0.216335\pi$
$547$			29.3993i			1.25702i	−0.777801	+	0.628511i	$0.783665\pi$
$548$		0			0
$549$	6.32541	−	3.65198i	0.269962	−	0.155863i
$550$		0			0
$551$		−	22.0287i		−	0.938453i
$552$		0			0
$553$	−41.6714	−	24.0590i	−1.77205	−	1.02309i
$554$		0			0
$555$	3.85120	+	2.22349i	0.163474	+	0.0943818i
$556$		0			0
$557$	9.16684	+	15.8774i	0.388412	+	0.672749i	0.992236	−	0.124369i	$-0.0396905\pi$
$557$	9.16684	+	15.8774i	0.388412	+	0.672749i	−0.603824	+	0.797117i	$0.706357\pi$
$558$		0			0
$559$	−38.4888	−	16.6193i	−1.62790	−	0.702920i
$560$		0			0
$561$	−7.02895	+	4.05816i	−0.296762	+	0.171336i
$562$		0			0
$563$	−0.0171903	−	0.00992482i	−0.000724485	−	0.000418281i	0.499638	−	0.866234i	$-0.333466\pi$
$563$	−0.0171903	−	0.00992482i	−0.000724485	−	0.000418281i	−0.500362	+	0.865816i	$0.666800\pi$
$564$		0			0
$565$	−29.3434	+	50.8243i	−1.23449	+	2.13819i
$566$		0			0
$567$		−	3.98099i		−	0.167186i
$568$		0			0
$569$	4.01749	+	6.95849i	0.168422	+	0.291715i	0.937865	−	0.347000i	$-0.112800\pi$
$569$	4.01749	+	6.95849i	0.168422	+	0.291715i	−0.769443	+	0.638715i	$0.779466\pi$
$570$		0			0
$571$		−	43.0575i		−	1.80190i	−0.433922	−	0.900950i	$-0.642871\pi$
$571$		−	43.0575i		−	1.80190i	0.433922	−	0.900950i	$-0.357129\pi$
$572$		0			0
$573$			5.51923i			0.230569i
$574$		0			0
$575$	−8.97337	−	15.5423i	−0.374216	−	0.648160i
$576$		0			0
$577$		−	27.1370i		−	1.12973i	−0.825184	−	0.564864i	$-0.808929\pi$
$577$		−	27.1370i		−	1.12973i	0.825184	−	0.564864i	$-0.191071\pi$
$578$		0			0
$579$	−0.0629771	+	0.109080i	−0.00261724	+	0.00453319i
$580$		0			0
$581$	−17.6143	−	10.1696i	−0.730766	−	0.421908i
$582$		0			0
$583$	−8.47699	+	4.89419i	−0.351081	+	0.202697i
$584$		0			0
$585$	4.48604	−	10.3893i	0.185475	−	0.429545i
$586$		0			0
$587$	−12.4090	−	21.4930i	−0.512175	−	0.887113i	−0.999900	−	0.0141157i	$-0.995507\pi$
$587$	−12.4090	−	21.4930i	−0.512175	−	0.887113i	0.487726	−	0.872997i	$-0.337827\pi$
$588$		0			0
$589$	18.3914	+	10.6183i	0.757804	+	0.437519i
$590$		0			0
$591$	8.07527	+	4.66226i	0.332172	+	0.191780i
$592$		0			0
$593$			21.5232i			0.883852i	0.897051	+	0.441926i	$0.145705\pi$
$593$			21.5232i			0.883852i	−0.897051	+	0.441926i	$0.854295\pi$
$594$		0			0
$595$	20.8396	−	12.0318i	0.854342	−	0.493255i
$596$		0			0
$597$			15.8091i			0.647023i
$598$		0			0
$599$	17.8112			0.727744			0.363872	−	0.931449i	$-0.381455\pi$
$599$	17.8112			0.727744			0.363872	+	0.931449i	$0.381455\pi$
$600$		0			0
$601$	−9.07847	−	15.7244i	−0.370319	−	0.641411i	0.619296	−	0.785158i	$-0.287418\pi$
$601$	−9.07847	−	15.7244i	−0.370319	−	0.641411i	−0.989614	+	0.143747i	$0.954085\pi$
$602$		0			0
$603$	11.9550			0.486846
$604$		0			0
$605$	−10.6096	+	18.3764i	−0.431343	+	0.747108i
$606$		0			0
$607$	8.39617	−	14.5426i	0.340790	−	0.590265i	−0.643790	−	0.765202i	$-0.722639\pi$
$607$	8.39617	−	14.5426i	0.340790	−	0.590265i	0.984580	+	0.174937i	$0.0559722\pi$
$608$		0			0
$609$	22.7106	−	13.1120i	0.920279	−	0.531324i
$610$		0			0
$611$	−4.06729	−	34.9093i	−0.164545	−	1.41228i
$612$		0			0
$613$	6.93552	+	12.0127i	0.280123	+	0.485187i	0.971415	−	0.237388i	$-0.0762914\pi$
$613$	6.93552	+	12.0127i	0.280123	+	0.485187i	−0.691292	+	0.722576i	$0.742958\pi$
$614$		0			0
$615$	4.49024	−	7.77732i	0.181064	−	0.313612i
$616$		0			0
$617$	13.9565	+	8.05780i	0.561868	+	0.324395i	0.753895	−	0.656995i	$-0.228173\pi$
$617$	13.9565	+	8.05780i	0.561868	+	0.324395i	−0.192027	+	0.981390i	$0.561506\pi$
$618$		0			0
$619$	−24.5032			−0.984866			−0.492433	−	0.870350i	$-0.663892\pi$
$619$	−24.5032			−0.984866			−0.492433	+	0.870350i	$0.663892\pi$
$620$		0			0
$621$	3.20398	−	1.84982i	0.128571	−	0.0742308i
$622$		0			0
$623$	5.95176			0.238452
$624$		0			0
$625$	−25.7231			−1.02892
$626$		0			0
$627$	12.2051	−	7.04663i	0.487426	−	0.281415i
$628$		0			0
$629$	−2.72870			−0.108800
$630$		0			0
$631$	−10.2300	−	5.90627i	−0.407248	−	0.235125i	0.282358	−	0.959309i	$-0.408883\pi$
$631$	−10.2300	−	5.90627i	−0.407248	−	0.235125i	−0.689607	+	0.724184i	$0.742217\pi$
$632$		0			0
$633$	9.40397	−	16.2882i	0.373774	−	0.647396i
$634$		0			0
$635$	1.39728	+	2.42016i	0.0554493	+	0.0960410i
$636$		0			0
$637$	19.0417	+	25.5971i	0.754461	+	1.01420i
$638$		0			0
$639$	−5.28850	+	3.05332i	−0.209210	+	0.120787i
$640$		0			0
$641$	14.1841	−	24.5677i	0.560240	−	0.970364i	−0.437235	−	0.899347i	$-0.644042\pi$
$641$	14.1841	−	24.5677i	0.560240	−	0.970364i	0.997475	−	0.0710170i	$-0.0226244\pi$
$642$		0			0
$643$	−6.21913	+	10.7718i	−0.245258	+	0.424800i	−0.962204	−	0.272329i	$-0.912206\pi$
$643$	−6.21913	+	10.7718i	−0.245258	+	0.424800i	0.716946	+	0.697129i	$0.245539\pi$
$644$		0			0
$645$	36.4944			1.43696
$646$		0			0
$647$	3.30728	+	5.72838i	0.130023	+	0.225206i	0.923685	−	0.383153i	$-0.125162\pi$
$647$	3.30728	+	5.72838i	0.130023	+	0.225206i	−0.793662	+	0.608358i	$0.791828\pi$
$648$		0			0
$649$	0.264361			0.0103771
$650$		0			0
$651$			25.2810i			0.990839i
$652$		0			0
$653$	−23.5353	+	13.5881i	−0.921009	+	0.531745i	−0.883957	−	0.467569i	$-0.845130\pi$
$653$	−23.5353	+	13.5881i	−0.921009	+	0.531745i	−0.0370519	+	0.999313i	$0.511797\pi$
$654$		0			0
$655$		−	10.4232i		−	0.407267i
$656$		0			0
$657$	−7.81345	−	4.51110i	−0.304832	−	0.175995i
$658$		0			0
$659$	−13.1651	−	7.60087i	−0.512839	−	0.296088i	0.221161	−	0.975237i	$-0.429015\pi$
$659$	−13.1651	−	7.60087i	−0.512839	−	0.296088i	−0.734000	+	0.679150i	$0.762349\pi$
$660$		0			0
$661$	−10.5180	−	18.2177i	−0.409102	−	0.708585i	0.585688	−	0.810537i	$-0.300825\pi$
$661$	−10.5180	−	18.2177i	−0.409102	−	0.708585i	−0.994789	+	0.101952i	$0.967491\pi$
$662$		0			0
$663$	0.803595	+	6.89721i	0.0312091	+	0.267865i
$664$		0			0
$665$	−36.1862	+	20.8921i	−1.40324	+	0.810161i
$666$		0			0
$667$	21.1056	+	12.1853i	0.817210	+	0.471817i
$668$		0			0
$669$	−0.512850	+	0.888282i	−0.0198279	+	0.0343430i
$670$		0			0
$671$			30.7814i			1.18830i
$672$		0			0
$673$	−1.24365	−	2.15406i	−0.0479391	−	0.0830329i	0.841060	−	0.540942i	$-0.181932\pi$
$673$	−1.24365	−	2.15406i	−0.0479391	−	0.0830329i	−0.888999	+	0.457909i	$0.848599\pi$
$674$		0			0
$675$			4.85094i			0.186713i
$676$		0			0
$677$		−	3.55109i		−	0.136479i	−0.997669	−	0.0682397i	$-0.978262\pi$
$677$		−	3.55109i		−	0.136479i	0.997669	−	0.0682397i	$-0.0217383\pi$
$678$		0			0
$679$	11.6641	+	20.2029i	0.447629	+	0.775316i
$680$		0			0
$681$			7.34503i			0.281462i
$682$		0			0
$683$	7.60672	−	13.1752i	0.291063	−	0.504136i	−0.682998	−	0.730420i	$-0.739324\pi$
$683$	7.60672	−	13.1752i	0.291063	−	0.504136i	0.974061	+	0.226284i	$0.0726577\pi$
$684$		0			0
$685$	−18.7515	−	10.8262i	−0.716458	−	0.413647i
$686$		0			0
$687$	1.82422	−	1.05321i	0.0695982	−	0.0401825i
$688$		0			0
$689$	0.969146	+	8.31812i	0.0369215	+	0.316895i
$690$		0			0
$691$	−11.4909	−	19.9028i	−0.437134	−	0.757137i	0.560334	−	0.828267i	$-0.310673\pi$
$691$	−11.4909	−	19.9028i	−0.437134	−	0.757137i	−0.997467	+	0.0711296i	$0.977340\pi$
$692$		0			0
$693$	14.5295	+	8.38864i	0.551932	+	0.318658i
$694$		0			0
$695$	13.5705	+	7.83492i	0.514758	+	0.297196i
$696$		0			0
$697$			5.51049i			0.208725i
$698$		0			0
$699$	26.1448	−	15.0947i	0.988886	−	0.570934i
$700$		0			0
$701$		−	13.4528i		−	0.508105i	−0.967190	−	0.254053i	$-0.918236\pi$
$701$		−	13.4528i		−	0.508105i	0.967190	−	0.254053i	$-0.0817636\pi$
$702$		0			0
$703$	4.73814			0.178702
$704$		0			0
$705$	15.2970	+	26.4952i	0.576118	+	0.997866i
$706$		0			0
$707$	−32.1152			−1.20782
$708$		0			0
$709$	−17.8824	+	30.9732i	−0.671587	+	1.16322i	0.305866	+	0.952074i	$0.401054\pi$
$709$	−17.8824	+	30.9732i	−0.671587	+	1.16322i	−0.977454	+	0.211149i	$0.932279\pi$
$710$		0			0
$711$	−6.04346	+	10.4676i	−0.226648	+	0.392565i
$712$		0			0
$713$	−20.3466	+	11.7471i	−0.761988	+	0.439934i
$714$		0			0
$715$	28.4653	+	38.2649i	1.06454	+	1.43103i
$716$		0			0
$717$	9.24473	+	16.0123i	0.345251	+	0.597992i
$718$		0			0
$719$	6.16811	−	10.6835i	0.230032	−	0.398427i	−0.727785	−	0.685805i	$-0.759450\pi$
$719$	6.16811	−	10.6835i	0.230032	−	0.398427i	0.957817	+	0.287378i	$0.0927837\pi$
$720$		0			0
$721$	65.8061	+	37.9932i	2.45075	+	1.41494i
$722$		0			0
$723$	−10.1654			−0.378057
$724$		0			0
$725$	−27.6734	+	15.9773i	−1.02777	+	0.593381i
$726$		0			0
$727$	−37.8521			−1.40386			−0.701928	−	0.712247i	$-0.747677\pi$
$727$	−37.8521			−1.40386			−0.701928	+	0.712247i	$0.747677\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−19.3931	+	11.1966i	−0.717279	+	0.414121i
$732$		0			0
$733$	6.75241			0.249406			0.124703	−	0.992194i	$-0.460202\pi$
$733$	6.75241			0.249406			0.124703	+	0.992194i	$0.460202\pi$
$734$		0			0
$735$	−24.0508	−	13.8857i	−0.887127	−	0.512183i
$736$		0			0
$737$	−25.1913	+	43.6326i	−0.927933	+	1.60723i
$738$		0			0
$739$	−0.391736	−	0.678507i	−0.0144103	−	0.0249593i	0.858730	−	0.512428i	$-0.171254\pi$
$739$	−0.391736	−	0.678507i	−0.0144103	−	0.0249593i	−0.873141	+	0.487468i	$0.837920\pi$
$740$		0			0
$741$	−1.39537	−	11.9764i	−0.0512602	−	0.439963i
$742$		0			0
$743$	41.1541	−	23.7603i	1.50980	−	0.871683i	0.509864	−	0.860255i	$-0.329696\pi$
$743$	41.1541	−	23.7603i	1.50980	−	0.871683i	0.999935	−	0.0114275i	$-0.00363755\pi$
$744$		0			0
$745$	33.0021	−	57.1613i	1.20910	−	2.09423i
$746$		0			0
$747$	−2.55455	+	4.42461i	−0.0934661	+	0.161888i
$748$		0			0
$749$	26.1575			0.955776
$750$		0			0
$751$	19.5727	+	33.9009i	0.714218	+	1.23706i	0.963260	+	0.268570i	$0.0865510\pi$
$751$	19.5727	+	33.9009i	0.714218	+	1.23706i	−0.249042	+	0.968493i	$0.580116\pi$
$752$		0			0
$753$	−1.66924			−0.0608303
$754$		0			0
$755$			48.8909i			1.77932i
$756$		0			0
$757$	13.8830	−	8.01535i	0.504586	−	0.291323i	−0.226019	−	0.974123i	$-0.572571\pi$
$757$	13.8830	−	8.01535i	0.504586	−	0.291323i	0.730605	+	0.682800i	$0.239238\pi$
$758$		0			0
$759$			15.5916i			0.565938i
$760$		0			0
$761$	18.3101	+	10.5714i	0.663742	+	0.383212i	0.793701	−	0.608308i	$-0.208151\pi$
$761$	18.3101	+	10.5714i	0.663742	+	0.383212i	−0.129959	+	0.991519i	$0.541485\pi$
$762$		0			0
$763$	41.8047	+	24.1359i	1.51343	+	0.873780i
$764$		0			0
$765$	−3.02231	−	5.23479i	−0.109272	−	0.189264i
$766$		0			0
$767$	0.0896587	−	0.207642i	0.00323739	−	0.00749752i
$768$		0			0
$769$	−23.6873	+	13.6759i	−0.854185	+	0.493164i	−0.862061	−	0.506805i	$-0.830826\pi$
$769$	−23.6873	+	13.6759i	−0.854185	+	0.493164i	0.00787567	+	0.999969i	$0.497493\pi$
$770$		0			0
$771$	−27.5117	−	15.8839i	−0.990809	−	0.572044i
$772$		0			0
$773$	−8.48123	+	14.6899i	−0.305049	+	0.528360i	−0.977272	−	0.211989i	$-0.932006\pi$
$773$	−8.48123	+	14.6899i	−0.305049	+	0.528360i	0.672224	+	0.740348i	$0.265339\pi$
$774$		0			0
$775$		−	30.8055i		−	1.10657i
$776$		0			0
$777$	2.82025	+	4.88481i	0.101176	+	0.175242i
$778$		0			0
$779$		−	9.56846i		−	0.342826i
$780$		0			0
$781$		−	25.7355i		−	0.920887i
$782$		0			0
$783$	−3.29364	−	5.70476i	−0.117705	−	0.203871i
$784$		0			0
$785$			42.6447i			1.52206i
$786$		0			0
$787$	−11.0502	+	19.1396i	−0.393899	+	0.682252i	−0.992960	−	0.118451i	$-0.962207\pi$
$787$	−11.0502	+	19.1396i	−0.393899	+	0.682252i	0.599061	+	0.800703i	$0.295541\pi$
$788$		0			0
$789$	2.46371	+	1.42242i	0.0877102	+	0.0506395i
$790$		0			0
$791$	−64.4649	+	37.2188i	−2.29211	+	1.32335i
$792$		0			0
$793$	24.1772	+	10.4396i	0.858556	+	0.370720i
$794$		0			0
$795$	−3.64494	−	6.31322i	−0.129273	−	0.223907i
$796$		0			0
$797$	1.98959	+	1.14869i	0.0704748	+	0.0406886i	0.534823	−	0.844964i	$-0.320378\pi$
$797$	1.98959	+	1.14869i	0.0704748	+	0.0406886i	−0.464349	+	0.885653i	$0.653711\pi$
$798$		0			0
$799$	−16.2576	−	9.38635i	−0.575154	−	0.332065i
$800$		0			0
$801$		−	1.49504i		−	0.0528248i
$802$		0			0
$803$	32.9286	−	19.0113i	1.16202	−	0.670895i
$804$		0			0
$805$		−	46.2264i		−	1.62927i
$806$		0			0
$807$	8.62668			0.303673
$808$		0			0
$809$	3.89606	+	6.74818i	0.136978	+	0.237253i	0.926351	−	0.376660i	$-0.122928\pi$
$809$	3.89606	+	6.74818i	0.136978	+	0.237253i	−0.789373	+	0.613914i	$0.789594\pi$
$810$		0			0
$811$	17.0777			0.599679			0.299840	−	0.953990i	$-0.403067\pi$
$811$	17.0777			0.599679			0.299840	+	0.953990i	$0.403067\pi$
$812$		0			0
$813$	0.517842	−	0.896928i	0.0181615	−	0.0314566i
$814$		0			0
$815$	18.3775	−	31.8308i	0.643737	−	1.11499i
$816$		0			0
$817$	33.6743	−	19.4419i	1.17812	−	0.680186i
$818$		0			0
$819$	11.5166	−	8.56718i	0.402421	−	0.299362i
$820$		0			0
$821$	−11.0400	−	19.1218i	−0.385297	−	0.667354i	0.606513	−	0.795073i	$-0.292568\pi$
$821$	−11.0400	−	19.1218i	−0.385297	−	0.667354i	−0.991810	+	0.127719i	$0.959234\pi$
$822$		0			0
$823$	17.9141	−	31.0281i	0.624447	−	1.08157i	−0.364201	−	0.931320i	$-0.618658\pi$
$823$	17.9141	−	31.0281i	0.624447	−	1.08157i	0.988648	−	0.150253i	$-0.0480087\pi$
$824$		0			0
$825$	−17.7046	−	10.2218i	−0.616396	−	0.355876i
$826$		0			0
$827$	17.0225			0.591929			0.295964	−	0.955199i	$-0.404359\pi$
$827$	17.0225			0.591929			0.295964	+	0.955199i	$0.404359\pi$
$828$		0			0
$829$	−15.3179	+	8.84379i	−0.532013	+	0.307158i	−0.741836	−	0.670582i	$-0.766045\pi$
$829$	−15.3179	+	8.84379i	−0.532013	+	0.307158i	0.209823	+	0.977739i	$0.432711\pi$
$830$		0			0
$831$	16.7701			0.581750
$832$		0			0
$833$	17.0408			0.590428
$834$		0			0
$835$	−0.418384	+	0.241554i	−0.0144788	+	0.00835933i
$836$		0			0
$837$	6.35042			0.219503
$838$		0			0
$839$	21.4773	+	12.3999i	0.741478	+	0.428093i	0.822606	−	0.568611i	$-0.192519\pi$
$839$	21.4773	+	12.3999i	0.741478	+	0.428093i	−0.0811284	+	0.996704i	$0.525852\pi$
$840$		0			0
$841$	7.19616	−	12.4641i	0.248143	−	0.429797i
$842$		0			0
$843$	8.87852	+	15.3781i	0.305793	+	0.529648i
$844$		0			0
$845$	39.7092	−	9.38038i	1.36604	−	0.322695i
$846$		0			0
$847$	−23.3084	+	13.4571i	−0.800888	+	0.462393i
$848$		0			0
$849$	−6.11533	+	10.5921i	−0.209878	+	0.363519i
$850$		0			0
$851$	−2.62093	+	4.53959i	−0.0898444	+	0.155615i
$852$		0			0
$853$	42.6375			1.45988			0.729941	−	0.683510i	$-0.239548\pi$
$853$	42.6375			1.45988			0.729941	+	0.683510i	$0.239548\pi$
$854$		0			0
$855$	5.24796	+	9.08974i	0.179476	+	0.310862i
$856$		0			0
$857$	18.8716			0.644640			0.322320	−	0.946631i	$-0.395537\pi$
$857$	18.8716			0.644640			0.322320	+	0.946631i	$0.395537\pi$
$858$		0			0
$859$			34.5624i			1.17926i	0.807675	+	0.589628i	$0.200726\pi$
$859$			34.5624i			1.17926i	−0.807675	+	0.589628i	$0.799274\pi$
$860$		0			0
$861$	9.86466	−	5.69537i	0.336187	−	0.194098i
$862$		0			0
$863$		−	13.9874i		−	0.476136i	−0.971249	−	0.238068i	$-0.923486\pi$
$863$		−	13.9874i		−	0.476136i	0.971249	−	0.238068i	$-0.0765141\pi$
$864$		0			0
$865$	−70.4608	−	40.6805i	−2.39574	−	1.38318i
$866$		0			0
$867$	−11.5103	−	6.64549i	−0.390911	−	0.225693i
$868$		0			0
$869$	−25.4692	−	44.1140i	−0.863985	−	1.49647i
$870$		0			0
$871$	25.7275	+	34.5846i	0.871742	+	1.17185i
$872$		0			0
$873$	5.07484	−	2.92996i	0.171757	−	0.0991641i
$874$		0			0
$875$	−1.61293	−	0.931228i	−0.0545271	−	0.0314812i
$876$		0			0
$877$	−25.6958	+	44.5064i	−0.867686	+	1.50288i	−0.00332994	+	0.999994i	$0.501060\pi$
$877$	−25.6958	+	44.5064i	−0.867686	+	1.50288i	−0.864356	+	0.502881i	$0.832273\pi$
$878$		0			0
$879$		−	12.3471i		−	0.416457i
$880$		0			0
$881$	−12.8416	−	22.2423i	−0.432644	−	0.749362i	0.564456	−	0.825463i	$-0.309086\pi$
$881$	−12.8416	−	22.2423i	−0.432644	−	0.749362i	−0.997100	+	0.0761015i	$0.975753\pi$
$882$		0			0
$883$			1.54889i			0.0521242i	0.999660	+	0.0260621i	$0.00829676\pi$
$883$			1.54889i			0.0521242i	−0.999660	+	0.0260621i	$0.991703\pi$
$884$		0			0
$885$			0.196882i			0.00661813i
$886$		0			0
$887$	−1.64662	−	2.85204i	−0.0552883	−	0.0957621i	0.837057	−	0.547116i	$-0.184274\pi$
$887$	−1.64662	−	2.85204i	−0.0552883	−	0.0957621i	−0.892345	+	0.451354i	$0.850941\pi$
$888$		0			0
$889$			3.54459i			0.118882i
$890$		0			0
$891$	2.10717	−	3.64973i	0.0705929	−	0.122271i
$892$		0			0
$893$	28.2299	+	16.2986i	0.944679	+	0.545410i
$894$		0			0
$895$	−34.3278	+	19.8191i	−1.14745	+	0.662481i
$896$		0			0
$897$	12.2464	+	5.28791i	0.408894	+	0.176558i
$898$		0			0
$899$	20.9160	+	36.2276i	0.697588	+	1.20826i
$900$		0			0
$901$	3.87384	+	2.23656i	0.129056	+	0.0745107i
$902$		0			0
$903$	40.0875	+	23.1445i	1.33403	+	0.770201i
$904$		0			0
$905$		−	57.9400i		−	1.92599i
$906$		0			0
$907$	9.53698	−	5.50618i	0.316670	−	0.182830i	−0.333237	−	0.942843i	$-0.608141\pi$
$907$	9.53698	−	5.50618i	0.316670	−	0.182830i	0.649907	+	0.760013i	$0.274808\pi$
$908$		0			0
$909$			8.06713i			0.267570i
$910$		0			0
$911$	−57.1333			−1.89291			−0.946456	−	0.322833i	$-0.895365\pi$
$911$	−57.1333			−1.89291			−0.946456	+	0.322833i	$0.895365\pi$
$912$		0			0
$913$	−10.7658	−	18.6468i	−0.356294	−	0.617120i
$914$		0			0
$915$	−22.9243			−0.757855
$916$		0			0
$917$	6.61031	−	11.4494i	0.218292	−	0.378092i
$918$		0			0
$919$	−1.95754	+	3.39056i	−0.0645734	+	0.111844i	−0.896505	−	0.443034i	$-0.853902\pi$
$919$	−1.95754	+	3.39056i	−0.0645734	+	0.111844i	0.831931	+	0.554879i	$0.187235\pi$
$920$		0			0
$921$	−13.7050	+	7.91258i	−0.451595	+	0.260728i
$922$		0			0
$923$	−20.2139	−	8.72824i	−0.665348	−	0.287293i
$924$		0			0
$925$	−3.43655	−	5.95227i	−0.112993	−	0.195709i
$926$		0			0
$927$	9.54365	−	16.5301i	0.313454	−	0.542919i
$928$		0			0
$929$	23.5063	+	13.5713i	0.771215	+	0.445261i	0.833308	−	0.552809i	$-0.186444\pi$
$929$	23.5063	+	13.5713i	0.771215	+	0.445261i	−0.0620927	+	0.998070i	$0.519777\pi$
$930$		0			0
$931$	−29.5898			−0.969766
$932$		0			0
$933$	14.7232	−	8.50043i	0.482015	−	0.278292i
$934$		0			0
$935$	25.4741			0.833091
$936$		0			0
$937$	−15.1865			−0.496121			−0.248061	−	0.968745i	$-0.579793\pi$
$937$	−15.1865			−0.496121			−0.248061	+	0.968745i	$0.579793\pi$
$938$		0			0
$939$	−3.08549	+	1.78141i	−0.100691	+	0.0581340i
$940$		0			0
$941$	−23.8706			−0.778158			−0.389079	−	0.921204i	$-0.627207\pi$
$941$	−23.8706			−0.778158			−0.389079	+	0.921204i	$0.627207\pi$
$942$		0			0
$943$	9.16749	+	5.29285i	0.298535	+	0.172359i
$944$		0			0
$945$	−6.24741	+	10.8208i	−0.203228	+	0.352002i
$946$		0			0
$947$	−0.105623	−	0.182945i	−0.00343230	−	0.00594492i	0.864304	−	0.502970i	$-0.167759\pi$
$947$	−0.105623	−	0.182945i	−0.00343230	−	0.00594492i	−0.867736	+	0.497025i	$0.834426\pi$
$948$		0			0
$949$	−3.76461	−	32.3114i	−0.122204	−	1.04887i
$950$		0			0
$951$	−5.25852	+	3.03601i	−0.170519	+	0.0984494i
$952$		0			0
$953$	−14.5683	+	25.2330i	−0.471913	+	0.817377i	−0.999484	−	0.0321343i	$-0.989770\pi$
$953$	−14.5683	+	25.2330i	−0.471913	+	0.817377i	0.527571	+	0.849511i	$0.323103\pi$
$954$		0			0
$955$	8.66139	−	15.0020i	0.280276	−	0.485452i
$956$		0			0
$957$	27.7611			0.897388
$958$		0			0
$959$	−13.7318	−	23.7842i	−0.443423	−	0.768031i
$960$		0			0
$961$	−9.32783			−0.300898
$962$		0			0
$963$		−	6.57061i		−	0.211735i
$964$		0			0
$965$	0.342360	−	0.197661i	0.0110209	−	0.00636295i
$966$		0			0
$967$		−	7.86383i		−	0.252884i	−0.991974	−	0.126442i	$-0.959644\pi$
$967$		−	7.86383i		−	0.252884i	0.991974	−	0.126442i	$-0.0403557\pi$
$968$		0			0
$969$	−5.57753	−	3.22019i	−0.179176	−	0.103447i
$970$		0			0
$971$	−45.0181	−	25.9912i	−1.44470	−	0.834098i	−0.446541	−	0.894763i	$-0.647344\pi$
$971$	−45.0181	−	25.9912i	−1.44470	−	0.834098i	−0.998158	+	0.0606655i	$0.980678\pi$
$972$		0			0
$973$	9.93773	+	17.2127i	0.318589	+	0.551812i
$974$		0			0
$975$	−14.0332	+	10.4393i	−0.449423	+	0.334326i
$976$		0			0
$977$	46.1724	−	26.6577i	1.47719	−	0.852854i	0.477519	−	0.878621i	$-0.341536\pi$
$977$	46.1724	−	26.6577i	1.47719	−	0.852854i	0.999668	+	0.0257671i	$0.00820282\pi$
$978$		0			0
$979$	5.45651	+	3.15032i	0.174391	+	0.100685i
$980$		0			0
$981$	6.06280	−	10.5011i	0.193570	−	0.335273i
$982$		0			0
$983$			5.04182i			0.160809i	0.996762	+	0.0804046i	$0.0256212\pi$
$983$			5.04182i			0.160809i	−0.996762	+	0.0804046i	$0.974379\pi$
$984$		0			0
$985$	−14.6331	−	25.3452i	−0.466248	−	0.807566i
$986$		0			0
$987$			38.8051i			1.23518i
$988$		0			0
$989$			43.0176i			1.36788i
$990$		0			0
$991$	−2.07413	−	3.59249i	−0.0658868	−	0.114119i	0.831200	−	0.555973i	$-0.187654\pi$
$991$	−2.07413	−	3.59249i	−0.0658868	−	0.114119i	−0.897087	+	0.441854i	$0.854321\pi$
$992$		0			0
$993$		−	16.7926i		−	0.532897i
$994$		0			0
$995$	24.8094	−	42.9711i	0.786510	−	1.36228i
$996$		0			0
$997$	−26.6284	−	15.3739i	−0.843330	−	0.486897i	0.0150648	−	0.999887i	$-0.495205\pi$
$997$	−26.6284	−	15.3739i	−0.843330	−	0.486897i	−0.858395	+	0.512990i	$0.828538\pi$
$998$		0			0
$999$	1.22703	−	0.708429i	0.0388216	−	0.0224137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.b.49.12		48
4.3	odd	2		312.2.bk.b.205.10	✓	48
8.3	odd	2		312.2.bk.b.205.19	yes	48
8.5	even	2	inner	1248.2.ca.b.49.13		48
12.11	even	2		936.2.dg.e.829.15		48
13.4	even	6	inner	1248.2.ca.b.433.13		48
24.11	even	2		936.2.dg.e.829.6		48
52.43	odd	6		312.2.bk.b.277.19	yes	48
104.43	odd	6		312.2.bk.b.277.10	yes	48
104.69	even	6	inner	1248.2.ca.b.433.12		48
156.95	even	6		936.2.dg.e.901.6		48
312.251	even	6		936.2.dg.e.901.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.10	✓	48	4.3	odd	2
312.2.bk.b.205.19	yes	48	8.3	odd	2
312.2.bk.b.277.10	yes	48	104.43	odd	6
312.2.bk.b.277.19	yes	48	52.43	odd	6
936.2.dg.e.829.6		48	24.11	even	2
936.2.dg.e.829.15		48	12.11	even	2
936.2.dg.e.901.6		48	156.95	even	6
936.2.dg.e.901.15		48	312.251	even	6
1248.2.ca.b.49.12		48	1.1	even	1	trivial
1248.2.ca.b.49.13		48	8.5	even	2	inner
1248.2.ca.b.433.12		48	104.69	even	6	inner
1248.2.ca.b.433.13		48	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +3.13862 q^{5} +(3.44764 + 1.99050i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.10717 + 3.64973i) q^{11} +(3.58133 - 0.417261i) q^{13} +(-2.71813 + 1.56931i) q^{15} +(0.962941 - 1.66786i) q^{17} +(-1.67206 + 2.89609i) q^{19} -3.98099 q^{21} +(-1.84982 - 3.20398i) q^{23} +4.85094 q^{25} +1.00000i q^{27} +(-5.70476 + 3.29364i) q^{29} -6.35042i q^{31} +(-3.64973 - 2.10717i) q^{33} +(10.8208 + 6.24741i) q^{35} +(-0.708429 - 1.22703i) q^{37} +(-2.89289 + 2.15202i) q^{39} +(-2.47794 + 1.43064i) q^{41} +(-10.0697 - 5.81376i) q^{43} +(1.56931 - 2.71813i) q^{45} -9.74759i q^{47} +(4.42415 + 7.66285i) q^{49} +1.92588i q^{51} +2.32264i q^{53} +(6.61361 + 11.4551i) q^{55} -3.34412i q^{57} +(0.0313645 - 0.0543248i) q^{59} +(6.32541 + 3.65198i) q^{61} +(3.44764 - 1.99050i) q^{63} +(11.2404 - 1.30962i) q^{65} +(5.97751 + 10.3534i) q^{67} +(3.20398 + 1.84982i) q^{69} +(-5.28850 - 3.05332i) q^{71} -9.02220i q^{73} +(-4.20104 + 2.42547i) q^{75} +16.7773i q^{77} -12.0869 q^{79} +(-0.500000 - 0.866025i) q^{81} -5.10910 q^{83} +(3.02231 - 5.23479i) q^{85} +(3.29364 - 5.70476i) q^{87} +(1.29475 - 0.747522i) q^{89} +(13.1777 + 5.69005i) q^{91} +(3.17521 + 5.49962i) q^{93} +(-5.24796 + 9.08974i) q^{95} +(5.07484 + 2.92996i) q^{97} +4.21434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) \) 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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