LMFDB - Embedded newform 484.2.e.e.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,2,Mod(9,484)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("484.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,4,0,-2,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	484.9
Dual form			484.2.e.e.269.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11803 - 1.53884i) q^{3} +(-0.500000 - 1.53884i) q^{5} +(3.11803 + 2.26538i) q^{7} +(1.19098 - 3.66547i) q^{9} +(0.736068 - 2.26538i) q^{13} +(-3.42705 - 2.48990i) q^{15} +(0.736068 + 2.26538i) q^{17} +(-3.11803 + 2.26538i) q^{19} +10.0902 q^{21} -2.47214 q^{23} +(1.92705 - 1.40008i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-6.97214 - 5.06555i) q^{29} +(0.263932 - 0.812299i) q^{31} +(1.92705 - 5.93085i) q^{35} +(1.50000 + 1.08981i) q^{37} +(-1.92705 - 5.93085i) q^{39} +(-6.97214 + 5.06555i) q^{41} -6.23607 q^{45} +(-1.11803 + 0.812299i) q^{47} +(2.42705 + 7.46969i) q^{49} +(5.04508 + 3.66547i) q^{51} +(-1.26393 + 3.88998i) q^{53} +(-3.11803 + 9.59632i) q^{57} +(-0.881966 - 0.640786i) q^{59} +(0.736068 + 2.26538i) q^{61} +(12.0172 - 8.73102i) q^{63} -3.85410 q^{65} +12.9443 q^{67} +(-5.23607 + 3.80423i) q^{69} +(-1.97214 - 6.06961i) q^{71} +(0.736068 + 0.534785i) q^{73} +(1.92705 - 5.93085i) q^{75} +(-2.20820 + 6.79615i) q^{79} +(4.61803 + 3.35520i) q^{81} +(4.02786 + 12.3965i) q^{83} +(3.11803 - 2.26538i) q^{85} -22.5623 q^{87} +0.472136 q^{89} +(7.42705 - 5.39607i) q^{91} +(-0.690983 - 2.12663i) q^{93} +(5.04508 + 3.66547i) q^{95} +(-4.50000 + 13.8496i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{5} + 8 q^{7} + 7 q^{9} - 6 q^{13} - 7 q^{15} - 6 q^{17} - 8 q^{19} + 18 q^{21} + 8 q^{23} + q^{25} - 5 q^{27} - 10 q^{29} + 10 q^{31} + q^{35} + 6 q^{37} - q^{39} - 10 q^{41} - 16 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^5 + 8 * q^7 + 7 * q^9 - 6 * q^13 - 7 * q^15 - 6 * q^17 - 8 * q^19 + 18 * q^21 + 8 * q^23 + q^25 - 5 * q^27 - 10 * q^29 + 10 * q^31 + q^35 + 6 * q^37 - q^39 - 10 * q^41 - 16 * q^45 + 3 * q^49 + 9 * q^51 - 14 * q^53 - 8 * q^57 - 8 * q^59 - 6 * q^61 + 19 * q^63 - 2 * q^65 + 16 * q^67 - 12 * q^69 + 10 * q^71 - 6 * q^73 + q^75 + 18 * q^79 + 14 * q^81 + 34 * q^83 + 8 * q^85 - 50 * q^87 - 16 * q^89 + 23 * q^91 - 5 * q^93 + 9 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.226514	−	0.974008i	$-0.427267\pi$
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.996333	+	0.0855571i	$0.0272670\pi$
$4$		0			0
$5$	−0.500000	−	1.53884i	−0.223607	−	0.688191i	−0.998430	−	0.0560130i	$-0.982161\pi$
$5$	−0.500000	−	1.53884i	−0.223607	−	0.688191i	0.774823	−	0.632178i	$-0.217839\pi$
$6$		0			0
$7$	3.11803	+	2.26538i	1.17851	+	0.856235i	0.992002	−	0.126219i	$-0.0402844\pi$
$7$	3.11803	+	2.26538i	1.17851	+	0.856235i	0.186504	+	0.982454i	$0.440284\pi$
$8$		0			0
$9$	1.19098	−	3.66547i	0.396994	−	1.22182i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	−0.795599	−	0.605824i	$-0.792844\pi$
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	0.999747	−	0.0224806i	$-0.00715641\pi$
$14$		0			0
$15$	−3.42705	−	2.48990i	−0.884861	−	0.642889i
$16$		0			0
$17$	0.736068	+	2.26538i	0.178523	+	0.549436i	0.999777	−	0.0211262i	$-0.00672518\pi$
$17$	0.736068	+	2.26538i	0.178523	+	0.549436i	−0.821254	+	0.570563i	$0.806725\pi$
$18$		0			0
$19$	−3.11803	+	2.26538i	−0.715326	+	0.519715i	−0.884887	−	0.465805i	$-0.845765\pi$
$19$	−3.11803	+	2.26538i	−0.715326	+	0.519715i	0.169561	+	0.985520i	$0.445765\pi$
$20$		0			0
$21$	10.0902			2.20186
$22$		0			0
$23$	−2.47214			−0.515476			−0.257738	−	0.966215i	$-0.582977\pi$
$23$	−2.47214			−0.515476			−0.257738	+	0.966215i	$0.582977\pi$
$24$		0			0
$25$	1.92705	−	1.40008i	0.385410	−	0.280017i
$26$		0			0
$27$	−0.690983	−	2.12663i	−0.132980	−	0.409270i
$28$		0			0
$29$	−6.97214	−	5.06555i	−1.29469	−	0.940650i	−0.294804	−	0.955558i	$-0.595254\pi$
$29$	−6.97214	−	5.06555i	−1.29469	−	0.940650i	−0.999889	+	0.0149080i	$0.995254\pi$
$30$		0			0
$31$	0.263932	−	0.812299i	0.0474036	−	0.145893i	−0.924553	−	0.381053i	$-0.875561\pi$
$31$	0.263932	−	0.812299i	0.0474036	−	0.145893i	0.971957	+	0.235160i	$0.0755614\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.92705	−	5.93085i	0.325731	−	1.00250i
$36$		0			0
$37$	1.50000	+	1.08981i	0.246598	+	0.179164i	0.704218	−	0.709984i	$-0.251298\pi$
$37$	1.50000	+	1.08981i	0.246598	+	0.179164i	−0.457619	+	0.889148i	$0.651298\pi$
$38$		0			0
$39$	−1.92705	−	5.93085i	−0.308575	−	0.949697i
$40$		0			0
$41$	−6.97214	+	5.06555i	−1.08886	+	0.791107i	−0.979207	−	0.202863i	$-0.934975\pi$
$41$	−6.97214	+	5.06555i	−1.08886	+	0.791107i	−0.109658	+	0.993969i	$0.534975\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−6.23607			−0.929618
$46$		0			0
$47$	−1.11803	+	0.812299i	−0.163082	+	0.118486i	−0.666333	−	0.745654i	$-0.732137\pi$
$47$	−1.11803	+	0.812299i	−0.163082	+	0.118486i	0.503251	+	0.864140i	$0.332137\pi$
$48$		0			0
$49$	2.42705	+	7.46969i	0.346722	+	1.06710i
$50$		0			0
$51$	5.04508	+	3.66547i	0.706453	+	0.513268i
$52$		0			0
$53$	−1.26393	+	3.88998i	−0.173614	+	0.534330i	−0.999567	−	0.0294087i	$-0.990638\pi$
$53$	−1.26393	+	3.88998i	−0.173614	+	0.534330i	0.825953	+	0.563739i	$0.190638\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.11803	+	9.59632i	−0.412994	+	1.27106i
$58$		0			0
$59$	−0.881966	−	0.640786i	−0.114822	−	0.0834232i	0.528892	−	0.848689i	$-0.322608\pi$
$59$	−0.881966	−	0.640786i	−0.114822	−	0.0834232i	−0.643714	+	0.765266i	$0.722608\pi$
$60$		0			0
$61$	0.736068	+	2.26538i	0.0942438	+	0.290053i	0.987056	−	0.160377i	$-0.0512709\pi$
$61$	0.736068	+	2.26538i	0.0942438	+	0.290053i	−0.892812	+	0.450429i	$0.851271\pi$
$62$		0			0
$63$	12.0172	−	8.73102i	1.51403	−	1.10001i
$64$		0			0
$65$	−3.85410			−0.478043
$66$		0			0
$67$	12.9443			1.58139			0.790697	−	0.612207i	$-0.209718\pi$
$67$	12.9443			1.58139			0.790697	+	0.612207i	$0.209718\pi$
$68$		0			0
$69$	−5.23607	+	3.80423i	−0.630349	+	0.457975i
$70$		0			0
$71$	−1.97214	−	6.06961i	−0.234049	−	0.720330i	−0.997246	−	0.0741639i	$-0.976371\pi$
$71$	−1.97214	−	6.06961i	−0.234049	−	0.720330i	0.763197	−	0.646166i	$-0.223629\pi$
$72$		0			0
$73$	0.736068	+	0.534785i	0.0861502	+	0.0625918i	0.630027	−	0.776574i	$-0.283044\pi$
$73$	0.736068	+	0.534785i	0.0861502	+	0.0625918i	−0.543876	+	0.839165i	$0.683044\pi$
$74$		0			0
$75$	1.92705	−	5.93085i	0.222517	−	0.684836i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.20820	+	6.79615i	−0.248442	+	0.764627i	0.746609	+	0.665263i	$0.231681\pi$
$79$	−2.20820	+	6.79615i	−0.248442	+	0.764627i	−0.995051	+	0.0993636i	$0.968319\pi$
$80$		0			0
$81$	4.61803	+	3.35520i	0.513115	+	0.372800i
$82$		0			0
$83$	4.02786	+	12.3965i	0.442116	+	1.36069i	0.885616	+	0.464418i	$0.153736\pi$
$83$	4.02786	+	12.3965i	0.442116	+	1.36069i	−0.443501	+	0.896274i	$0.646264\pi$
$84$		0			0
$85$	3.11803	−	2.26538i	0.338198	−	0.245715i
$86$		0			0
$87$	−22.5623			−2.41893
$88$		0			0
$89$	0.472136			0.0500463			0.0250232	−	0.999687i	$-0.492034\pi$
$89$	0.472136			0.0500463			0.0250232	+	0.999687i	$0.492034\pi$
$90$		0			0
$91$	7.42705	−	5.39607i	0.778566	−	0.565662i
$92$		0			0
$93$	−0.690983	−	2.12663i	−0.0716516	−	0.220521i
$94$		0			0
$95$	5.04508	+	3.66547i	0.517615	+	0.376069i
$96$		0			0
$97$	−4.50000	+	13.8496i	−0.456906	+	1.40621i	0.411977	+	0.911194i	$0.364838\pi$
$97$	−4.50000	+	13.8496i	−0.456906	+	1.40621i	−0.868883	+	0.495017i	$0.835162\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.50000	−	16.9273i	0.547270	−	1.68433i	−0.168259	−	0.985743i	$-0.553815\pi$
$101$	5.50000	−	16.9273i	0.547270	−	1.68433i	0.715530	−	0.698582i	$-0.246185\pi$
$102$		0			0
$103$	6.35410	+	4.61653i	0.626088	+	0.454880i	0.855043	−	0.518557i	$-0.173531\pi$
$103$	6.35410	+	4.61653i	0.626088	+	0.454880i	−0.228955	+	0.973437i	$0.573531\pi$
$104$		0			0
$105$	−5.04508	−	15.5272i	−0.492350	−	1.51530i
$106$		0			0
$107$	9.35410	−	6.79615i	0.904295	−	0.657009i	−0.0352704	−	0.999378i	$-0.511229\pi$
$107$	9.35410	−	6.79615i	0.904295	−	0.657009i	0.939566	+	0.342369i	$0.111229\pi$
$108$		0			0
$109$	−12.4721			−1.19461			−0.597307	−	0.802013i	$-0.703763\pi$
$109$	−12.4721			−1.19461			−0.597307	+	0.802013i	$0.703763\pi$
$110$		0			0
$111$	4.85410			0.460731
$112$		0			0
$113$	−14.2082	+	10.3229i	−1.33660	+	0.971093i	−0.337034	+	0.941493i	$0.609424\pi$
$113$	−14.2082	+	10.3229i	−1.33660	+	0.971093i	−0.999562	+	0.0296008i	$0.990576\pi$
$114$		0			0
$115$	1.23607	+	3.80423i	0.115264	+	0.354746i
$116$		0			0
$117$	−7.42705	−	5.39607i	−0.686631	−	0.498867i
$118$		0			0
$119$	−2.83688	+	8.73102i	−0.260056	+	0.800371i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−6.97214	+	21.4580i	−0.628656	+	1.93481i
$124$		0			0
$125$	−9.66312	−	7.02067i	−0.864296	−	0.627948i
$126$		0			0
$127$	−0.736068	−	2.26538i	−0.0653155	−	0.201020i	0.913073	−	0.407797i	$-0.133703\pi$
$127$	−0.736068	−	2.26538i	−0.0653155	−	0.201020i	−0.978388	+	0.206776i	$0.933703\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.52786			0.832453			0.416227	−	0.909261i	$-0.363352\pi$
$131$	9.52786			0.832453			0.416227	+	0.909261i	$0.363352\pi$
$132$		0			0
$133$	−14.8541			−1.28801
$134$		0			0
$135$	−2.92705	+	2.12663i	−0.251920	+	0.183031i
$136$		0			0
$137$	4.26393	+	13.1230i	0.364292	+	1.12118i	0.950423	+	0.310960i	$0.100650\pi$
$137$	4.26393	+	13.1230i	0.364292	+	1.12118i	−0.586131	+	0.810216i	$0.699350\pi$
$138$		0			0
$139$	−9.35410	−	6.79615i	−0.793405	−	0.576442i	0.115567	−	0.993300i	$-0.463131\pi$
$139$	−9.35410	−	6.79615i	−0.793405	−	0.576442i	−0.908972	+	0.416857i	$0.863131\pi$
$140$		0			0
$141$	−1.11803	+	3.44095i	−0.0941554	+	0.289781i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−4.30902	+	13.2618i	−0.357844	+	1.10133i
$146$		0			0
$147$	16.6353	+	12.0862i	1.37205	+	0.996855i
$148$		0			0
$149$	0.736068	+	2.26538i	0.0603010	+	0.185588i	0.976669	−	0.214749i	$-0.0688933\pi$
$149$	0.736068	+	2.26538i	0.0603010	+	0.185588i	−0.916368	+	0.400336i	$0.868893\pi$
$150$		0			0
$151$	−15.5902	+	11.3269i	−1.26871	+	0.921772i	−0.999150	−	0.0412119i	$-0.986878\pi$
$151$	−15.5902	+	11.3269i	−1.26871	+	0.921772i	−0.269560	+	0.962984i	$0.586878\pi$
$152$		0			0
$153$	9.18034			0.742186
$154$		0			0
$155$	−1.38197			−0.111002
$156$		0			0
$157$	−14.2082	+	10.3229i	−1.13394	+	0.823854i	−0.986263	−	0.165182i	$-0.947179\pi$
$157$	−14.2082	+	10.3229i	−1.13394	+	0.823854i	−0.147675	+	0.989036i	$0.547179\pi$
$158$		0			0
$159$	3.30902	+	10.1841i	0.262422	+	0.807652i
$160$		0			0
$161$	−7.70820	−	5.60034i	−0.607492	−	0.441368i
$162$		0			0
$163$	3.50000	−	10.7719i	0.274141	−	0.843720i	−0.715304	−	0.698813i	$-0.753712\pi$
$163$	3.50000	−	10.7719i	0.274141	−	0.843720i	0.989445	−	0.144907i	$-0.0462881\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.50000	−	16.9273i	0.425603	−	1.30987i	−0.476813	−	0.879005i	$-0.658208\pi$
$167$	5.50000	−	16.9273i	0.425603	−	1.30987i	0.902416	−	0.430866i	$-0.141792\pi$
$168$		0			0
$169$	5.92705	+	4.30625i	0.455927	+	0.331250i
$170$		0			0
$171$	4.59017	+	14.1271i	0.351019	+	1.08033i
$172$		0			0
$173$	5.50000	−	3.99598i	0.418157	−	0.303809i	−0.358739	−	0.933438i	$-0.616793\pi$
$173$	5.50000	−	3.99598i	0.418157	−	0.303809i	0.776896	+	0.629629i	$0.216793\pi$
$174$		0			0
$175$	9.18034			0.693968
$176$		0			0
$177$	−2.85410			−0.214527
$178$		0			0
$179$	2.11803	−	1.53884i	0.158309	−	0.115018i	−0.505810	−	0.862645i	$-0.668806\pi$
$179$	2.11803	−	1.53884i	0.158309	−	0.115018i	0.664120	+	0.747626i	$0.268806\pi$
$180$		0			0
$181$	−0.500000	−	1.53884i	−0.0371647	−	0.114381i	0.930753	−	0.365648i	$-0.119153\pi$
$181$	−0.500000	−	1.53884i	−0.0371647	−	0.114381i	−0.967918	+	0.251267i	$0.919153\pi$
$182$		0			0
$183$	5.04508	+	3.66547i	0.372943	+	0.270959i
$184$		0			0
$185$	0.927051	−	2.85317i	0.0681581	−	0.209769i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.66312	−	8.19624i	0.193713	−	0.596189i
$190$		0			0
$191$	−21.0623	−	15.3027i	−1.52401	−	1.10726i	−0.959452	−	0.281872i	$-0.909045\pi$
$191$	−21.0623	−	15.3027i	−1.52401	−	1.10726i	−0.564563	−	0.825390i	$-0.690955\pi$
$192$		0			0
$193$	−6.97214	−	21.4580i	−0.501865	−	1.54458i	−0.805977	−	0.591946i	$-0.798360\pi$
$193$	−6.97214	−	21.4580i	−0.501865	−	1.54458i	0.304112	−	0.952636i	$-0.401640\pi$
$194$		0			0
$195$	−8.16312	+	5.93085i	−0.584573	+	0.424717i
$196$		0			0
$197$	−2.94427			−0.209771			−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427			−0.209771			−0.104885	+	0.994484i	$0.533448\pi$
$198$		0			0
$199$	−0.944272			−0.0669377			−0.0334688	−	0.999440i	$-0.510655\pi$
$199$	−0.944272			−0.0669377			−0.0334688	+	0.999440i	$0.510655\pi$
$200$		0			0
$201$	27.4164	−	19.9192i	1.93380	−	1.40499i
$202$		0			0
$203$	−10.2639	−	31.5891i	−0.720387	−	2.21712i
$204$		0			0
$205$	11.2812	+	8.19624i	0.787910	+	0.572450i
$206$		0			0
$207$	−2.94427	+	9.06154i	−0.204641	+	0.629820i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	3.68034	−	11.3269i	0.253365	−	0.779777i	−0.740782	−	0.671745i	$-0.765545\pi$
$211$	3.68034	−	11.3269i	0.253365	−	0.779777i	0.994147	−	0.108032i	$-0.0344550\pi$
$212$		0			0
$213$	−13.5172	−	9.82084i	−0.926185	−	0.672913i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.66312	−	1.93487i	0.180784	−	0.131347i
$218$		0			0
$219$	2.38197			0.160958
$220$		0			0
$221$	5.67376			0.381659
$222$		0			0
$223$	9.82624	−	7.13918i	0.658014	−	0.478075i	−0.207978	−	0.978134i	$-0.566688\pi$
$223$	9.82624	−	7.13918i	0.658014	−	0.478075i	0.865992	+	0.500059i	$0.166688\pi$
$224$		0			0
$225$	−2.83688	−	8.73102i	−0.189125	−	0.582068i
$226$		0			0
$227$	−4.59017	−	3.33495i	−0.304660	−	0.221349i	0.424942	−	0.905221i	$-0.360295\pi$
$227$	−4.59017	−	3.33495i	−0.304660	−	0.221349i	−0.729602	+	0.683872i	$0.760295\pi$
$228$		0			0
$229$	5.02786	−	15.4742i	0.332251	−	1.02256i	−0.635810	−	0.771846i	$-0.719334\pi$
$229$	5.02786	−	15.4742i	0.332251	−	1.02256i	0.968061	−	0.250717i	$-0.0806662\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.736068	−	2.26538i	0.0482214	−	0.148410i	−0.924047	−	0.382280i	$-0.875139\pi$
$233$	0.736068	−	2.26538i	0.0482214	−	0.148410i	0.972268	+	0.233870i	$0.0751390\pi$
$234$		0			0
$235$	1.80902	+	1.31433i	0.118007	+	0.0857373i
$236$		0			0
$237$	5.78115	+	17.7926i	0.375526	+	1.15575i
$238$		0			0
$239$	9.35410	−	6.79615i	0.605067	−	0.439607i	−0.242607	−	0.970125i	$-0.578003\pi$
$239$	9.35410	−	6.79615i	0.605067	−	0.439607i	0.847674	+	0.530518i	$0.178003\pi$
$240$		0			0
$241$	12.4721			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$241$	12.4721			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$242$		0			0
$243$	21.6525			1.38901
$244$		0			0
$245$	10.2812	−	7.46969i	0.656839	−	0.477221i
$246$		0			0
$247$	2.83688	+	8.73102i	0.180506	+	0.555542i
$248$		0			0
$249$	27.6074	+	20.0579i	1.74955	+	1.27112i
$250$		0			0
$251$	7.97214	−	24.5357i	0.503197	−	1.54868i	−0.300584	−	0.953755i	$-0.597182\pi$
$251$	7.97214	−	24.5357i	0.503197	−	1.54868i	0.803781	−	0.594925i	$-0.202818\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	3.11803	−	9.59632i	0.195259	−	0.600945i
$256$		0			0
$257$	3.97214	+	2.88593i	0.247775	+	0.180019i	0.704740	−	0.709466i	$-0.251064\pi$
$257$	3.97214	+	2.88593i	0.247775	+	0.180019i	−0.456965	+	0.889485i	$0.651064\pi$
$258$		0			0
$259$	2.20820	+	6.79615i	0.137211	+	0.422292i
$260$		0			0
$261$	−26.8713	+	19.5232i	−1.66329	+	1.20845i
$262$		0			0
$263$	5.88854			0.363103			0.181552	−	0.983381i	$-0.441888\pi$
$263$	5.88854			0.363103			0.181552	+	0.983381i	$0.441888\pi$
$264$		0			0
$265$	6.61803			0.406543
$266$		0			0
$267$	1.00000	−	0.726543i	0.0611990	−	0.0444637i
$268$		0			0
$269$	−7.44427	−	22.9111i	−0.453885	−	1.39692i	−0.872439	−	0.488723i	$-0.837463\pi$
$269$	−7.44427	−	22.9111i	−0.453885	−	1.39692i	0.418554	−	0.908192i	$-0.362537\pi$
$270$		0			0
$271$	15.5902	+	11.3269i	0.947035	+	0.688061i	0.950104	−	0.311934i	$-0.100977\pi$
$271$	15.5902	+	11.3269i	0.947035	+	0.688061i	−0.00306845	+	0.999995i	$0.500977\pi$
$272$		0			0
$273$	7.42705	−	22.8581i	0.449506	−	1.38344i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.97214	+	21.4580i	−0.418915	+	1.28929i	0.489787	+	0.871842i	$0.337075\pi$
$277$	−6.97214	+	21.4580i	−0.418915	+	1.28929i	−0.908702	+	0.417446i	$0.862925\pi$
$278$		0			0
$279$	−2.66312	−	1.93487i	−0.159437	−	0.115838i
$280$		0			0
$281$	8.44427	+	25.9888i	0.503743	+	1.55036i	0.802874	+	0.596149i	$0.203303\pi$
$281$	8.44427	+	25.9888i	0.503743	+	1.55036i	−0.299130	+	0.954212i	$0.596697\pi$
$282$		0			0
$283$	9.35410	−	6.79615i	0.556044	−	0.403989i	−0.273965	−	0.961740i	$-0.588335\pi$
$283$	9.35410	−	6.79615i	0.556044	−	0.403989i	0.830009	+	0.557750i	$0.188335\pi$
$284$		0			0
$285$	16.3262			0.967083
$286$		0			0
$287$	−33.2148			−1.96061
$288$		0			0
$289$	9.16312	−	6.65740i	0.539007	−	0.391612i
$290$		0			0
$291$	11.7812	+	36.2587i	0.690623	+	2.12552i
$292$		0			0
$293$	−6.97214	−	5.06555i	−0.407317	−	0.295933i	0.365198	−	0.930930i	$-0.381001\pi$
$293$	−6.97214	−	5.06555i	−0.407317	−	0.295933i	−0.772515	+	0.634997i	$0.781001\pi$
$294$		0			0
$295$	−0.545085	+	1.67760i	−0.0317361	+	0.0976736i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.81966	+	5.60034i	−0.105234	+	0.323876i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−14.3992	−	44.3161i	−0.827212	−	2.54590i
$304$		0			0
$305$	3.11803	−	2.26538i	0.178538	−	0.129716i
$306$		0			0
$307$	9.52786			0.543784			0.271892	−	0.962328i	$-0.412351\pi$
$307$	9.52786			0.543784			0.271892	+	0.962328i	$0.412351\pi$
$308$		0			0
$309$	20.5623			1.16975
$310$		0			0
$311$	−13.5902	+	9.87384i	−0.770628	+	0.559894i	−0.902152	−	0.431419i	$-0.858013\pi$
$311$	−13.5902	+	9.87384i	−0.770628	+	0.559894i	0.131524	+	0.991313i	$0.458013\pi$
$312$		0			0
$313$	−2.31966	−	7.13918i	−0.131115	−	0.403530i	0.863851	−	0.503748i	$-0.168046\pi$
$313$	−2.31966	−	7.13918i	−0.131115	−	0.403530i	−0.994966	+	0.100218i	$0.968046\pi$
$314$		0			0
$315$	−19.4443	−	14.1271i	−1.09556	−	0.795971i
$316$		0			0
$317$	−4.50000	+	13.8496i	−0.252745	+	0.777870i	0.741520	+	0.670930i	$0.234105\pi$
$317$	−4.50000	+	13.8496i	−0.252745	+	0.777870i	−0.994266	+	0.106939i	$0.965895\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	9.35410	−	28.7890i	0.522095	−	1.60684i
$322$		0			0
$323$	−7.42705	−	5.39607i	−0.413252	−	0.300245i
$324$		0			0
$325$	−1.75329	−	5.39607i	−0.0972550	−	0.299320i
$326$		0			0
$327$	−26.4164	+	19.1926i	−1.46083	+	1.06136i
$328$		0			0
$329$	−5.32624			−0.293645
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	5.78115	−	4.20025i	0.316805	−	0.230172i
$334$		0			0
$335$	−6.47214	−	19.9192i	−0.353611	−	1.08830i
$336$		0			0
$337$	−19.4443	−	14.1271i	−1.05920	−	0.769552i	−0.0852573	−	0.996359i	$-0.527171\pi$
$337$	−19.4443	−	14.1271i	−1.05920	−	0.769552i	−0.973940	+	0.226807i	$0.927171\pi$
$338$		0			0
$339$	−14.2082	+	43.7284i	−0.771684	+	2.37500i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−1.01722	+	3.13068i	−0.0549248	+	0.169041i
$344$		0			0
$345$	8.47214	+	6.15537i	0.456124	+	0.331394i
$346$		0			0
$347$	−5.50000	−	16.9273i	−0.295255	−	0.908703i	−0.983136	−	0.182879i	$-0.941458\pi$
$347$	−5.50000	−	16.9273i	−0.295255	−	0.908703i	0.687880	−	0.725824i	$-0.258542\pi$
$348$		0			0
$349$	13.2082	−	9.59632i	0.707019	−	0.513679i	−0.175192	−	0.984534i	$-0.556055\pi$
$349$	13.2082	−	9.59632i	0.707019	−	0.513679i	0.882211	+	0.470855i	$0.156055\pi$
$350$		0			0
$351$	−5.32624			−0.284294
$352$		0			0
$353$	−14.9443			−0.795403			−0.397702	−	0.917515i	$-0.630192\pi$
$353$	−14.9443			−0.795403			−0.397702	+	0.917515i	$0.630192\pi$
$354$		0			0
$355$	−8.35410	+	6.06961i	−0.443390	+	0.322141i
$356$		0			0
$357$	7.42705	+	22.8581i	0.393081	+	1.20978i
$358$		0			0
$359$	−9.35410	−	6.79615i	−0.493691	−	0.358687i	0.312911	−	0.949782i	$-0.398696\pi$
$359$	−9.35410	−	6.79615i	−0.493691	−	0.358687i	−0.806602	+	0.591095i	$0.798696\pi$
$360$		0			0
$361$	−1.28115	+	3.94298i	−0.0674291	+	0.207525i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.454915	−	1.40008i	0.0238113	−	0.0732838i
$366$		0			0
$367$	−16.2984	−	11.8415i	−0.850768	−	0.618119i	0.0745895	−	0.997214i	$-0.476235\pi$
$367$	−16.2984	−	11.8415i	−0.850768	−	0.618119i	−0.925358	+	0.379095i	$0.876235\pi$
$368$		0			0
$369$	10.2639	+	31.5891i	0.534319	+	1.64446i
$370$		0			0
$371$	−12.7533	+	9.26581i	−0.662118	+	0.481057i
$372$		0			0
$373$	−6.58359			−0.340885			−0.170443	−	0.985368i	$-0.554520\pi$
$373$	−6.58359			−0.340885			−0.170443	+	0.985368i	$0.554520\pi$
$374$		0			0
$375$	−31.2705			−1.61480
$376$		0			0
$377$	−16.6074	+	12.0660i	−0.855324	+	0.621429i
$378$		0			0
$379$	0.972136	+	2.99193i	0.0499353	+	0.153685i	0.972915	−	0.231164i	$-0.0742535\pi$
$379$	0.972136	+	2.99193i	0.0499353	+	0.153685i	−0.922979	+	0.384849i	$0.874253\pi$
$380$		0			0
$381$	−5.04508	−	3.66547i	−0.258468	−	0.187788i
$382$		0			0
$383$	6.15248	−	18.9354i	0.314377	−	0.967552i	−0.661633	−	0.749828i	$-0.730136\pi$
$383$	6.15248	−	18.9354i	0.314377	−	0.967552i	0.976010	−	0.217725i	$-0.0698636\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	21.6803	+	15.7517i	1.09924	+	0.798642i	0.980935	−	0.194335i	$-0.0622550\pi$
$389$	21.6803	+	15.7517i	1.09924	+	0.798642i	0.118302	+	0.992978i	$0.462255\pi$
$390$		0			0
$391$	−1.81966	−	5.60034i	−0.0920242	−	0.283221i
$392$		0			0
$393$	20.1803	−	14.6619i	1.01796	−	0.739594i
$394$		0			0
$395$	11.5623			0.581763
$396$		0			0
$397$	32.8328			1.64783			0.823916	−	0.566712i	$-0.191785\pi$
$397$	32.8328			1.64783			0.823916	+	0.566712i	$0.191785\pi$
$398$		0			0
$399$	−31.4615	+	22.8581i	−1.57504	+	1.14434i
$400$		0			0
$401$	2.08359	+	6.41264i	0.104050	+	0.320232i	0.989506	−	0.144490i	$-0.0461542\pi$
$401$	2.08359	+	6.41264i	0.104050	+	0.320232i	−0.885457	+	0.464722i	$0.846154\pi$
$402$		0			0
$403$	−1.64590	−	1.19581i	−0.0819880	−	0.0595678i
$404$		0			0
$405$	2.85410	−	8.78402i	0.141821	−	0.436482i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−2.20820	+	6.79615i	−0.109189	+	0.336048i	−0.990691	−	0.136132i	$-0.956533\pi$
$409$	−2.20820	+	6.79615i	−0.109189	+	0.336048i	0.881502	+	0.472180i	$0.156533\pi$
$410$		0			0
$411$	29.2254	+	21.2335i	1.44158	+	1.04737i
$412$		0			0
$413$	−1.29837	−	3.99598i	−0.0638888	−	0.196630i
$414$		0			0
$415$	17.0623	−	12.3965i	0.837556	−	0.608520i
$416$		0			0
$417$	−30.2705			−1.48235
$418$		0			0
$419$	−4.58359			−0.223923			−0.111962	−	0.993713i	$-0.535713\pi$
$419$	−4.58359			−0.223923			−0.111962	+	0.993713i	$0.535713\pi$
$420$		0			0
$421$	7.50000	−	5.44907i	0.365528	−	0.265571i	−0.389826	−	0.920888i	$-0.627465\pi$
$421$	7.50000	−	5.44907i	0.365528	−	0.265571i	0.755354	+	0.655317i	$0.227465\pi$
$422$		0			0
$423$	1.64590	+	5.06555i	0.0800263	+	0.246296i
$424$		0			0
$425$	4.59017	+	3.33495i	0.222656	+	0.161769i
$426$		0			0
$427$	−2.83688	+	8.73102i	−0.137286	+	0.422524i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.15248	+	15.8577i	−0.248186	+	0.763838i	0.746910	+	0.664925i	$0.231537\pi$
$431$	−5.15248	+	15.8577i	−0.248186	+	0.763838i	−0.995096	+	0.0989130i	$0.968463\pi$
$432$		0			0
$433$	−15.7361	−	11.4329i	−0.756227	−	0.549431i	0.141524	−	0.989935i	$-0.454800\pi$
$433$	−15.7361	−	11.4329i	−0.756227	−	0.549431i	−0.897751	+	0.440504i	$0.854800\pi$
$434$		0			0
$435$	11.2812	+	34.7198i	0.540890	+	1.66469i
$436$		0			0
$437$	7.70820	−	5.60034i	0.368733	−	0.267900i
$438$		0			0
$439$	−15.4164			−0.735785			−0.367893	−	0.929868i	$-0.619921\pi$
$439$	−15.4164			−0.735785			−0.367893	+	0.929868i	$0.619921\pi$
$440$		0			0
$441$	30.2705			1.44145
$442$		0			0
$443$	−2.64590	+	1.92236i	−0.125710	+	0.0913340i	−0.648864	−	0.760905i	$-0.724755\pi$
$443$	−2.64590	+	1.92236i	−0.125710	+	0.0913340i	0.523153	+	0.852239i	$0.324755\pi$
$444$		0			0
$445$	−0.236068	−	0.726543i	−0.0111907	−	0.0344414i
$446$		0			0
$447$	5.04508	+	3.66547i	0.238624	+	0.173371i
$448$		0			0
$449$	−4.50000	+	13.8496i	−0.212368	+	0.653602i	0.786962	+	0.617002i	$0.211653\pi$
$449$	−4.50000	+	13.8496i	−0.212368	+	0.653602i	−0.999330	+	0.0366002i	$0.988347\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−15.5902	+	47.9816i	−0.732490	+	2.25437i
$454$		0			0
$455$	−12.0172	−	8.73102i	−0.563376	−	0.409317i
$456$		0			0
$457$	−2.20820	−	6.79615i	−0.103295	−	0.317911i	0.886031	−	0.463626i	$-0.153452\pi$
$457$	−2.20820	−	6.79615i	−0.103295	−	0.317911i	−0.989327	+	0.145715i	$0.953452\pi$
$458$		0			0
$459$	4.30902	−	3.13068i	0.201128	−	0.146128i
$460$		0			0
$461$	−33.7771			−1.57316			−0.786578	−	0.617491i	$-0.788149\pi$
$461$	−33.7771			−1.57316			−0.786578	+	0.617491i	$0.788149\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$	−2.92705	+	2.12663i	−0.135739	+	0.0986200i
$466$		0			0
$467$	3.91641	+	12.0535i	0.181230	+	0.557768i	0.999863	−	0.0165487i	$-0.00526787\pi$
$467$	3.91641	+	12.0535i	0.181230	+	0.557768i	−0.818633	+	0.574317i	$0.805268\pi$
$468$		0			0
$469$	40.3607	+	29.3238i	1.86368	+	1.35404i
$470$		0			0
$471$	−14.2082	+	43.7284i	−0.654679	+	2.01490i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−2.83688	+	8.73102i	−0.130165	+	0.400607i
$476$		0			0
$477$	12.7533	+	9.26581i	0.583933	+	0.424252i
$478$		0			0
$479$	−8.44427	−	25.9888i	−0.385829	−	1.18746i	−0.935877	−	0.352326i	$-0.885391\pi$
$479$	−8.44427	−	25.9888i	−0.385829	−	1.18746i	0.550049	−	0.835133i	$-0.314609\pi$
$480$		0			0
$481$	3.57295	−	2.59590i	0.162912	−	0.118363i
$482$		0			0
$483$	−24.9443			−1.13500
$484$		0			0
$485$	23.5623			1.06991
$486$		0			0
$487$	14.5902	−	10.6004i	0.661144	−	0.480349i	−0.205905	−	0.978572i	$-0.566014\pi$
$487$	14.5902	−	10.6004i	0.661144	−	0.480349i	0.867049	+	0.498223i	$0.166014\pi$
$488$		0			0
$489$	−9.16312	−	28.2012i	−0.414371	−	1.27530i
$490$		0			0
$491$	−9.35410	−	6.79615i	−0.422145	−	0.306706i	0.356355	−	0.934350i	$-0.384019\pi$
$491$	−9.35410	−	6.79615i	−0.422145	−	0.306706i	−0.778500	+	0.627644i	$0.784019\pi$
$492$		0			0
$493$	6.34346	−	19.5232i	0.285695	−	0.879279i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.60081	−	23.3929i	0.340943	−	1.04931i
$498$		0			0
$499$	18.8262	+	13.6781i	0.842778	+	0.612314i	0.923145	−	0.384451i	$-0.125609\pi$
$499$	18.8262	+	13.6781i	0.842778	+	0.612314i	−0.0803672	+	0.996765i	$0.525609\pi$
$500$		0			0
$501$	−14.3992	−	44.3161i	−0.643308	−	1.97990i
$502$		0			0
$503$	29.5344	−	21.4580i	1.31688	−	0.956766i	0.316910	−	0.948456i	$-0.397355\pi$
$503$	29.5344	−	21.4580i	1.31688	−	0.956766i	0.999965	−	0.00831064i	$-0.00264539\pi$
$504$		0			0
$505$	−28.7984			−1.28151
$506$		0			0
$507$	19.1803			0.851829
$508$		0			0
$509$	23.2082	−	16.8617i	1.02869	−	0.747384i	0.0606404	−	0.998160i	$-0.480686\pi$
$509$	23.2082	−	16.8617i	1.02869	−	0.747384i	0.968045	+	0.250776i	$0.0806857\pi$
$510$		0			0
$511$	1.08359	+	3.33495i	0.0479353	+	0.147530i
$512$		0			0
$513$	6.97214	+	5.06555i	0.307827	+	0.223650i
$514$		0			0
$515$	3.92705	−	12.0862i	0.173047	−	0.532582i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	5.50000	−	16.9273i	0.241423	−	0.743024i
$520$		0			0
$521$	−6.20820	−	4.51052i	−0.271986	−	0.197610i	0.443428	−	0.896310i	$-0.353762\pi$
$521$	−6.20820	−	4.51052i	−0.271986	−	0.197610i	−0.715415	+	0.698700i	$0.753762\pi$
$522$		0			0
$523$	8.79180	+	27.0584i	0.384438	+	1.18318i	0.936887	+	0.349633i	$0.113694\pi$
$523$	8.79180	+	27.0584i	0.384438	+	1.18318i	−0.552448	+	0.833547i	$0.686306\pi$
$524$		0			0
$525$	19.4443	−	14.1271i	0.848618	−	0.616557i
$526$		0			0
$527$	2.03444			0.0886217
$528$		0			0
$529$	−16.8885			−0.734285
$530$		0			0
$531$	−3.39919	+	2.46965i	−0.147512	+	0.107174i
$532$		0			0
$533$	6.34346	+	19.5232i	0.274766	+	0.845642i
$534$		0			0
$535$	−15.1353	−	10.9964i	−0.654354	−	0.475416i
$536$		0			0
$537$	2.11803	−	6.51864i	0.0913999	−	0.281300i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.55573	−	7.86572i	0.109879	−	0.338174i	−0.880965	−	0.473181i	$-0.843106\pi$
$541$	2.55573	−	7.86572i	0.109879	−	0.338174i	0.990845	+	0.135007i	$0.0431057\pi$
$542$		0			0
$543$	−3.42705	−	2.48990i	−0.147069	−	0.106852i
$544$		0			0
$545$	6.23607	+	19.1926i	0.267124	+	0.822123i
$546$		0			0
$547$	−31.0066	+	22.5276i	−1.32575	+	0.963211i	−0.325904	+	0.945403i	$0.605669\pi$
$547$	−31.0066	+	22.5276i	−1.32575	+	0.963211i	−0.999841	+	0.0178077i	$0.994331\pi$
$548$		0			0
$549$	9.18034			0.391807
$550$		0			0
$551$	33.2148			1.41500
$552$		0			0
$553$	−22.2812	+	16.1882i	−0.947491	+	0.688393i
$554$		0			0
$555$	−2.42705	−	7.46969i	−0.103023	−	0.317071i
$556$		0			0
$557$	25.6803	+	18.6579i	1.08811	+	0.790559i	0.979079	−	0.203479i	$-0.0652250\pi$
$557$	25.6803	+	18.6579i	1.08811	+	0.790559i	0.109032	+	0.994038i	$0.465225\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.02786	+	12.3965i	−0.169754	+	0.522450i	−0.999355	−	0.0359070i	$-0.988568\pi$
$563$	−4.02786	+	12.3965i	−0.169754	+	0.522450i	0.829601	+	0.558357i	$0.188568\pi$
$564$		0			0
$565$	22.9894	+	16.7027i	0.967170	+	0.702690i
$566$		0			0
$567$	6.79837	+	20.9232i	0.285505	+	0.878694i
$568$		0			0
$569$	−24.2082	+	17.5883i	−1.01486	+	0.737339i	−0.965223	−	0.261428i	$-0.915807\pi$
$569$	−24.2082	+	17.5883i	−1.01486	+	0.737339i	−0.0496377	+	0.998767i	$0.515807\pi$
$570$		0			0
$571$	9.52786			0.398729			0.199364	−	0.979925i	$-0.436112\pi$
$571$	9.52786			0.398729			0.199364	+	0.979925i	$0.436112\pi$
$572$		0			0
$573$	−68.1591			−2.84739
$574$		0			0
$575$	−4.76393	+	3.46120i	−0.198670	+	0.144342i
$576$		0			0
$577$	−11.1525	−	34.3238i	−0.464284	−	1.42892i	−0.859881	−	0.510494i	$-0.829462\pi$
$577$	−11.1525	−	34.3238i	−0.464284	−	1.42892i	0.395598	−	0.918424i	$-0.370538\pi$
$578$		0			0
$579$	−47.7877	−	34.7198i	−1.98599	−	1.44291i
$580$		0			0
$581$	−15.5238	+	47.7773i	−0.644036	+	1.98214i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−4.59017	+	14.1271i	−0.189780	+	0.584083i
$586$		0			0
$587$	6.35410	+	4.61653i	0.262262	+	0.190544i	0.711144	−	0.703047i	$-0.248178\pi$
$587$	6.35410	+	4.61653i	0.262262	+	0.190544i	−0.448882	+	0.893591i	$0.648178\pi$
$588$		0			0
$589$	1.01722	+	3.13068i	0.0419139	+	0.128998i
$590$		0			0
$591$	−6.23607	+	4.53077i	−0.256518	+	0.186371i
$592$		0			0
$593$	37.4164			1.53651			0.768254	−	0.640145i	$-0.221126\pi$
$593$	37.4164			1.53651			0.768254	+	0.640145i	$0.221126\pi$
$594$		0			0
$595$	14.8541			0.608959
$596$		0			0
$597$	−2.00000	+	1.45309i	−0.0818546	+	0.0594708i
$598$		0			0
$599$	14.2082	+	43.7284i	0.580531	+	1.78669i	0.616519	+	0.787340i	$0.288542\pi$
$599$	14.2082	+	43.7284i	0.580531	+	1.78669i	−0.0359877	+	0.999352i	$0.511458\pi$
$600$		0			0
$601$	−27.1525	−	19.7274i	−1.10757	−	0.804699i	−0.125293	−	0.992120i	$-0.539987\pi$
$601$	−27.1525	−	19.7274i	−1.10757	−	0.804699i	−0.982280	+	0.187421i	$0.939987\pi$
$602$		0			0
$603$	15.4164	−	47.4468i	0.627805	−	1.93218i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.62461	−	20.3885i	0.268885	−	0.827542i	−0.721888	−	0.692010i	$-0.756726\pi$
$607$	6.62461	−	20.3885i	0.268885	−	0.827542i	0.990773	−	0.135532i	$-0.0432745\pi$
$608$		0			0
$609$	−70.3500	−	51.1123i	−2.85073	−	2.07117i
$610$		0			0
$611$	1.01722	+	3.13068i	0.0411524	+	0.126654i
$612$		0			0
$613$	8.44427	−	6.13512i	0.341061	−	0.247795i	−0.404048	−	0.914738i	$-0.632397\pi$
$613$	8.44427	−	6.13512i	0.341061	−	0.247795i	0.745109	+	0.666942i	$0.232397\pi$
$614$		0			0
$615$	36.5066			1.47209
$616$		0			0
$617$	−7.52786			−0.303060			−0.151530	−	0.988453i	$-0.548420\pi$
$617$	−7.52786			−0.303060			−0.151530	+	0.988453i	$0.548420\pi$
$618$		0			0
$619$	−18.0623	+	13.1230i	−0.725985	+	0.527459i	−0.888291	−	0.459281i	$-0.848107\pi$
$619$	−18.0623	+	13.1230i	−0.725985	+	0.527459i	0.162306	+	0.986741i	$0.448107\pi$
$620$		0			0
$621$	1.70820	+	5.25731i	0.0685479	+	0.210969i
$622$		0			0
$623$	1.47214	+	1.06957i	0.0589799	+	0.0428514i
$624$		0			0
$625$	−2.29180	+	7.05342i	−0.0916718	+	0.282137i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.36475	+	4.20025i	−0.0544160	+	0.167475i
$630$		0			0
$631$	19.2984	+	14.0211i	0.768256	+	0.558171i	0.901432	−	0.432922i	$-0.142517\pi$
$631$	19.2984	+	14.0211i	0.768256	+	0.558171i	−0.133175	+	0.991092i	$0.542517\pi$
$632$		0			0
$633$	−9.63525	−	29.6543i	−0.382967	−	1.17865i
$634$		0			0
$635$	−3.11803	+	2.26538i	−0.123735	+	0.0898990i
$636$		0			0
$637$	18.7082			0.741246
$638$		0			0
$639$	−24.5967			−0.973032
$640$		0			0
$641$	−21.9164	+	15.9232i	−0.865646	+	0.628929i	−0.929415	−	0.369036i	$-0.879688\pi$
$641$	−21.9164	+	15.9232i	−0.865646	+	0.628929i	0.0637690	+	0.997965i	$0.479688\pi$
$642$		0			0
$643$	−3.79180	−	11.6699i	−0.149534	−	0.460218i	0.848032	−	0.529945i	$-0.177787\pi$
$643$	−3.79180	−	11.6699i	−0.149534	−	0.460218i	−0.997566	+	0.0697267i	$0.977787\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.08359	−	6.41264i	0.0819145	−	0.252107i	−0.901709	−	0.432344i	$-0.857687\pi$
$647$	2.08359	−	6.41264i	0.0819145	−	0.252107i	0.983623	+	0.180237i	$0.0576866\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	2.66312	−	8.19624i	0.104376	−	0.321236i
$652$		0			0
$653$	−6.20820	−	4.51052i	−0.242946	−	0.176510i	0.459649	−	0.888101i	$-0.347975\pi$
$653$	−6.20820	−	4.51052i	−0.242946	−	0.176510i	−0.702595	+	0.711590i	$0.747975\pi$
$654$		0			0
$655$	−4.76393	−	14.6619i	−0.186142	−	0.572887i
$656$		0			0
$657$	2.83688	−	2.06111i	0.110677	−	0.0804117i
$658$		0			0
$659$	40.3607			1.57223			0.786114	−	0.618081i	$-0.212090\pi$
$659$	40.3607			1.57223			0.786114	+	0.618081i	$0.212090\pi$
$660$		0			0
$661$	−30.3607			−1.18089			−0.590447	−	0.807077i	$-0.701048\pi$
$661$	−30.3607			−1.18089			−0.590447	+	0.807077i	$0.701048\pi$
$662$		0			0
$663$	12.0172	−	8.73102i	0.466710	−	0.339085i
$664$		0			0
$665$	7.42705	+	22.8581i	0.288009	+	0.886400i
$666$		0			0
$667$	17.2361	+	12.5227i	0.667383	+	0.484882i
$668$		0			0
$669$	9.82624	−	30.2421i	0.379904	−	1.16923i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	11.3885	−	35.0503i	0.438996	−	1.35109i	−0.449940	−	0.893059i	$-0.648554\pi$
$673$	11.3885	−	35.0503i	0.438996	−	1.35109i	0.888936	−	0.458032i	$-0.151446\pi$
$674$		0			0
$675$	−4.30902	−	3.13068i	−0.165854	−	0.120500i
$676$		0			0
$677$	−1.08359	−	3.33495i	−0.0416458	−	0.128173i	0.928072	−	0.372401i	$-0.121465\pi$
$677$	−1.08359	−	3.33495i	−0.0416458	−	0.128173i	−0.969718	+	0.244228i	$0.921465\pi$
$678$		0			0
$679$	−45.4058	+	32.9892i	−1.74251	+	1.26601i
$680$		0			0
$681$	−14.8541			−0.569210
$682$		0			0
$683$	−0.944272			−0.0361316			−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272			−0.0361316			−0.0180658	+	0.999837i	$0.505751\pi$
$684$		0			0
$685$	18.0623	−	13.1230i	0.690125	−	0.501405i
$686$		0			0
$687$	−13.1631	−	40.5119i	−0.502204	−	1.54563i
$688$		0			0
$689$	7.88197	+	5.72658i	0.300279	+	0.218165i
$690$		0			0
$691$	−7.44427	+	22.9111i	−0.283193	+	0.871580i	0.703741	+	0.710457i	$0.251512\pi$
$691$	−7.44427	+	22.9111i	−0.283193	+	0.871580i	−0.986934	+	0.161123i	$0.948488\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.78115	+	17.7926i	−0.219292	+	0.674910i
$696$		0			0
$697$	−16.6074	−	12.0660i	−0.629050	−	0.457031i
$698$		0			0
$699$	−1.92705	−	5.93085i	−0.0728878	−	0.224325i
$700$		0			0
$701$	−39.6246	+	28.7890i	−1.49660	+	1.08734i	−0.524890	+	0.851170i	$0.675894\pi$
$701$	−39.6246	+	28.7890i	−1.49660	+	1.08734i	−0.971711	+	0.236174i	$0.924106\pi$
$702$		0			0
$703$	−7.14590			−0.269513
$704$		0			0
$705$	5.85410			0.220478
$706$		0			0
$707$	55.4959	−	40.3202i	2.08714	−	1.51640i
$708$		0			0
$709$	7.20820	+	22.1846i	0.270710	+	0.833159i	0.990323	+	0.138784i	$0.0443193\pi$
$709$	7.20820	+	22.1846i	0.270710	+	0.833159i	−0.719613	+	0.694375i	$0.755681\pi$
$710$		0			0
$711$	22.2812	+	16.1882i	0.835609	+	0.607105i
$712$		0			0
$713$	−0.652476	+	2.00811i	−0.0244354	+	0.0752045i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.35410	−	28.7890i	0.349335	−	1.07514i
$718$		0			0
$719$	31.7705	+	23.0826i	1.18484	+	0.860837i	0.992709	−	0.120533i	$-0.0384602\pi$
$719$	31.7705	+	23.0826i	1.18484	+	0.860837i	0.192131	+	0.981369i	$0.438460\pi$
$720$		0			0
$721$	9.35410	+	28.7890i	0.348365	+	1.07216i
$722$		0			0
$723$	26.4164	−	19.1926i	0.982437	−	0.713782i
$724$		0			0
$725$	−20.5279			−0.762386
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	32.0066	−	23.2541i	1.18543	−	0.861264i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−27.1525	−	19.7274i	−1.00290	−	0.728649i	−0.0401916	−	0.999192i	$-0.512797\pi$
$733$	−27.1525	−	19.7274i	−1.00290	−	0.728649i	−0.962708	+	0.270543i	$0.912797\pi$
$734$		0			0
$735$	10.2812	−	31.6421i	0.379226	−	1.16714i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	7.31966	−	22.5276i	0.269258	−	0.828691i	−0.721424	−	0.692494i	$-0.756512\pi$
$739$	7.31966	−	22.5276i	0.269258	−	0.828691i	0.990682	−	0.136197i	$-0.0434881\pi$
$740$		0			0
$741$	19.4443	+	14.1271i	0.714303	+	0.518972i
$742$		0			0
$743$	1.08359	+	3.33495i	0.0397531	+	0.122348i	0.968964	−	0.247203i	$-0.0795115\pi$
$743$	1.08359	+	3.33495i	0.0397531	+	0.122348i	−0.929210	+	0.369551i	$0.879512\pi$
$744$		0			0
$745$	3.11803	−	2.26538i	0.114236	−	0.0829973i
$746$		0			0
$747$	50.2361			1.83804
$748$		0			0
$749$	44.5623			1.62827
$750$		0			0
$751$	−5.59017	+	4.06150i	−0.203988	+	0.148206i	−0.685089	−	0.728459i	$-0.740237\pi$
$751$	−5.59017	+	4.06150i	−0.203988	+	0.148206i	0.481101	+	0.876665i	$0.340237\pi$
$752$		0			0
$753$	−20.8713	−	64.2353i	−0.760593	−	2.34087i
$754$		0			0
$755$	25.2254	+	18.3273i	0.918047	+	0.667000i
$756$		0			0
$757$	8.26393	−	25.4338i	0.300358	−	0.924406i	−0.681011	−	0.732273i	$-0.738460\pi$
$757$	8.26393	−	25.4338i	0.300358	−	0.924406i	0.981369	−	0.192133i	$-0.0615405\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.84752	+	17.9968i	−0.211973	+	0.652385i	0.787382	+	0.616465i	$0.211436\pi$
$761$	−5.84752	+	17.9968i	−0.211973	+	0.652385i	−0.999355	+	0.0359193i	$0.988564\pi$
$762$		0			0
$763$	−38.8885	−	28.2542i	−1.40786	−	1.02287i
$764$		0			0
$765$	−4.59017	−	14.1271i	−0.165958	−	0.510766i
$766$		0			0
$767$	−2.10081	+	1.52633i	−0.0758560	+	0.0551126i
$768$		0			0
$769$	37.4164			1.34927			0.674635	−	0.738151i	$-0.264301\pi$
$769$	37.4164			1.34927			0.674635	+	0.738151i	$0.264301\pi$
$770$		0			0
$771$	12.8541			0.462929
$772$		0			0
$773$	22.9164	−	16.6497i	0.824246	−	0.598850i	−0.0936796	−	0.995602i	$-0.529863\pi$
$773$	22.9164	−	16.6497i	0.824246	−	0.598850i	0.917926	+	0.396753i	$0.129863\pi$
$774$		0			0
$775$	−0.628677	−	1.93487i	−0.0225827	−	0.0695026i
$776$		0			0
$777$	15.1353	+	10.9964i	0.542974	+	0.394494i
$778$		0			0
$779$	10.2639	−	31.5891i	0.367744	−	1.13180i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−5.95492	+	18.3273i	−0.212811	+	0.654966i
$784$		0			0
$785$	22.9894	+	16.7027i	0.820525	+	0.596147i
$786$		0			0
$787$	5.15248	+	15.8577i	0.183666	+	0.565266i	0.999923	−	0.0124235i	$-0.00395462\pi$
$787$	5.15248	+	15.8577i	0.183666	+	0.565266i	−0.816257	+	0.577689i	$0.803955\pi$
$788$		0			0
$789$	12.4721	−	9.06154i	0.444020	−	0.322599i
$790$		0			0
$791$	−67.6869			−2.40667
$792$		0			0
$793$	5.67376			0.201481
$794$		0			0
$795$	14.0172	−	10.1841i	0.497140	−	0.361193i
$796$		0			0
$797$	4.26393	+	13.1230i	0.151036	+	0.464842i	0.997738	−	0.0672265i	$-0.0214150\pi$
$797$	4.26393	+	13.1230i	0.151036	+	0.464842i	−0.846702	+	0.532068i	$0.821415\pi$
$798$		0			0
$799$	−2.66312	−	1.93487i	−0.0942144	−	0.0684508i
$800$		0			0
$801$	0.562306	−	1.73060i	0.0198681	−	0.0611477i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−4.76393	+	14.6619i	−0.167907	+	0.516763i
$806$		0			0
$807$	−51.0238	−	37.0710i	−1.79612	−	1.30496i
$808$		0			0
$809$	−5.84752	−	17.9968i	−0.205588	−	0.632735i	−0.999689	−	0.0249486i	$-0.992058\pi$
$809$	−5.84752	−	17.9968i	−0.205588	−	0.632735i	0.794101	−	0.607786i	$-0.207942\pi$
$810$		0			0
$811$	24.7705	−	17.9968i	0.869810	−	0.631954i	−0.0607258	−	0.998154i	$-0.519342\pi$
$811$	24.7705	−	17.9968i	0.869810	−	0.631954i	0.930536	+	0.366200i	$0.119342\pi$
$812$		0			0
$813$	50.4508			1.76939
$814$		0			0
$815$	−18.3262			−0.641940
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−10.9336	−	33.6502i	−0.382052	−	1.17583i
$820$		0			0
$821$	20.9164	+	15.1967i	0.729988	+	0.530367i	0.889560	−	0.456819i	$-0.151011\pi$
$821$	20.9164	+	15.1967i	0.729988	+	0.530367i	−0.159572	+	0.987186i	$0.551011\pi$
$822$		0			0
$823$	−12.2082	+	37.5730i	−0.425551	+	1.30971i	0.476914	+	0.878950i	$0.341755\pi$
$823$	−12.2082	+	37.5730i	−0.425551	+	1.30971i	−0.902465	+	0.430762i	$0.858245\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.02786	+	12.3965i	−0.140063	+	0.431068i	−0.996343	−	0.0854428i	$-0.972769\pi$
$827$	−4.02786	+	12.3965i	−0.140063	+	0.431068i	0.856281	+	0.516511i	$0.172769\pi$
$828$		0			0
$829$	−28.2082	−	20.4945i	−0.979711	−	0.711802i	−0.0220673	−	0.999756i	$-0.507025\pi$
$829$	−28.2082	−	20.4945i	−0.979711	−	0.711802i	−0.957644	+	0.287954i	$0.907025\pi$
$830$		0			0
$831$	18.2533	+	56.1778i	0.633200	+	1.94879i
$832$		0			0
$833$	−15.1353	+	10.9964i	−0.524406	+	0.381003i
$834$		0			0
$835$	−28.7984			−0.996609
$836$		0			0
$837$	−1.90983			−0.0660134
$838$		0			0
$839$	2.11803	−	1.53884i	0.0731227	−	0.0531267i	−0.550623	−	0.834754i	$-0.685610\pi$
$839$	2.11803	−	1.53884i	0.0731227	−	0.0531267i	0.623746	+	0.781627i	$0.285610\pi$
$840$		0			0
$841$	13.9894	+	43.0548i	0.482392	+	1.48465i
$842$		0			0
$843$	57.8779	+	42.0508i	1.99342	+	1.44830i
$844$		0			0
$845$	3.66312	−	11.2739i	0.126015	−	0.387835i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	9.35410	−	28.7890i	0.321032	−	0.988035i
$850$		0			0
$851$	−3.70820	−	2.69417i	−0.127116	−	0.0923549i
$852$		0			0
$853$	5.50000	+	16.9273i	0.188316	+	0.579578i	0.999990	−	0.00453334i	$-0.00144301\pi$
$853$	5.50000	+	16.9273i	0.188316	+	0.579578i	−0.811673	+	0.584112i	$0.801443\pi$
$854$		0			0
$855$	19.4443	−	14.1271i	0.664980	−	0.483136i
$856$		0			0
$857$	2.94427			0.100574			0.0502872	−	0.998735i	$-0.483986\pi$
$857$	2.94427			0.100574			0.0502872	+	0.998735i	$0.483986\pi$
$858$		0			0
$859$	−31.0557			−1.05961			−0.529804	−	0.848120i	$-0.677734\pi$
$859$	−31.0557			−1.05961			−0.529804	+	0.848120i	$0.677734\pi$
$860$		0			0
$861$	−70.3500	+	51.1123i	−2.39752	+	1.74190i
$862$		0			0
$863$	−7.79180	−	23.9807i	−0.265236	−	0.816312i	−0.991639	−	0.129043i	$-0.958809\pi$
$863$	−7.79180	−	23.9807i	−0.265236	−	0.816312i	0.726403	−	0.687269i	$-0.241191\pi$
$864$		0			0
$865$	−8.89919	−	6.46564i	−0.302581	−	0.219838i
$866$		0			0
$867$	9.16312	−	28.2012i	0.311196	−	0.957762i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	9.52786	−	29.3238i	0.322839	−	0.993597i
$872$		0			0
$873$	45.4058	+	32.9892i	1.53675	+	1.11652i
$874$		0			0
$875$	−14.2254	−	43.7814i	−0.480907	−	1.48008i
$876$		0			0
$877$	−22.3885	+	16.2662i	−0.756007	+	0.549272i	−0.897683	−	0.440642i	$-0.854751\pi$
$877$	−22.3885	+	16.2662i	−0.756007	+	0.549272i	0.141676	+	0.989913i	$0.454751\pi$
$878$		0			0
$879$	−22.5623			−0.761008
$880$		0			0
$881$	15.8885			0.535299			0.267649	−	0.963516i	$-0.413753\pi$
$881$	15.8885			0.535299			0.267649	+	0.963516i	$0.413753\pi$
$882$		0			0
$883$	−4.06231	+	2.95144i	−0.136707	+	0.0993238i	−0.654037	−	0.756462i	$-0.726926\pi$
$883$	−4.06231	+	2.95144i	−0.136707	+	0.0993238i	0.517330	+	0.855786i	$0.326926\pi$
$884$		0			0
$885$	1.42705	+	4.39201i	0.0479698	+	0.147636i
$886$		0			0
$887$	−1.64590	−	1.19581i	−0.0552638	−	0.0401515i	0.559810	−	0.828621i	$-0.310874\pi$
$887$	−1.64590	−	1.19581i	−0.0552638	−	0.0401515i	−0.615074	+	0.788469i	$0.710874\pi$
$888$		0			0
$889$	2.83688	−	8.73102i	0.0951459	−	0.292829i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.64590	−	5.06555i	0.0550779	−	0.169512i
$894$		0			0
$895$	−3.42705	−	2.48990i	−0.114554	−	0.0832281i
$896$		0			0
$897$	4.76393	+	14.6619i	0.159063	+	0.489546i
$898$		0			0
$899$	−5.95492	+	4.32650i	−0.198608	+	0.144297i
$900$		0			0
$901$	−9.74265			−0.324575
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.11803	+	1.53884i	−0.0704058	+	0.0511528i
$906$		0			0
$907$	0.611456	+	1.88187i	0.0203031	+	0.0624864i	0.960695	−	0.277607i	$-0.0895413\pi$
$907$	0.611456	+	1.88187i	0.0203031	+	0.0624864i	−0.940392	+	0.340093i	$0.889541\pi$
$908$		0			0
$909$	−55.4959	−	40.3202i	−1.84068	−	1.33734i
$910$		0			0
$911$	−6.02786	+	18.5519i	−0.199712	+	0.614650i	0.800177	+	0.599764i	$0.204739\pi$
$911$	−6.02786	+	18.5519i	−0.199712	+	0.614650i	−0.999889	+	0.0148867i	$0.995261\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	3.11803	−	9.59632i	0.103079	−	0.317245i
$916$		0			0
$917$	29.7082	+	21.5843i	0.981051	+	0.712776i
$918$		0			0
$919$	−6.62461	−	20.3885i	−0.218526	−	0.672553i	−0.998884	−	0.0472210i	$-0.984963\pi$
$919$	−6.62461	−	20.3885i	−0.218526	−	0.672553i	0.780359	−	0.625332i	$-0.215037\pi$
$920$		0			0
$921$	20.1803	−	14.6619i	0.664965	−	0.483125i
$922$		0			0
$923$	−15.2016			−0.500368
$924$		0			0
$925$	4.41641			0.145211
$926$		0			0
$927$	24.4894	−	17.7926i	0.804336	−	0.584384i
$928$		0			0
$929$	6.15248	+	18.9354i	0.201856	+	0.621249i	0.999828	+	0.0185545i	$0.00590642\pi$
$929$	6.15248	+	18.9354i	0.201856	+	0.621249i	−0.797972	+	0.602695i	$0.794094\pi$
$930$		0			0
$931$	−24.4894	−	17.7926i	−0.802606	−	0.583128i
$932$		0			0
$933$	−13.5902	+	41.8262i	−0.444922	+	1.36933i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.20820	+	6.79615i	−0.0721389	+	0.222021i	−0.980625	−	0.195894i	$-0.937239\pi$
$937$	−2.20820	+	6.79615i	−0.0721389	+	0.222021i	0.908486	+	0.417915i	$0.137239\pi$
$938$		0			0
$939$	−15.8992	−	11.5514i	−0.518850	−	0.376967i
$940$		0			0
$941$	3.68034	+	11.3269i	0.119976	+	0.369247i	0.992952	−	0.118515i	$-0.0378134\pi$
$941$	3.68034	+	11.3269i	0.119976	+	0.369247i	−0.872977	+	0.487762i	$0.837813\pi$
$942$		0			0
$943$	17.2361	−	12.5227i	0.561284	−	0.407796i
$944$		0			0
$945$	−13.9443			−0.453607
$946$		0			0
$947$	−23.7771			−0.772652			−0.386326	−	0.922362i	$-0.626256\pi$
$947$	−23.7771			−0.772652			−0.386326	+	0.922362i	$0.626256\pi$
$948$		0			0
$949$	1.75329	−	1.27384i	0.0569142	−	0.0413506i
$950$		0			0
$951$	11.7812	+	36.2587i	0.382030	+	1.17577i
$952$		0			0
$953$	−36.6803	−	26.6498i	−1.18819	−	0.863273i	−0.195121	−	0.980779i	$-0.562510\pi$
$953$	−36.6803	−	26.6498i	−1.18819	−	0.863273i	−0.993072	+	0.117507i	$0.962510\pi$
$954$		0			0
$955$	−13.0172	+	40.0629i	−0.421227	+	1.29640i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.4336	+	50.5775i	−0.530670	+	1.63323i
$960$		0			0
$961$	24.4894	+	17.7926i	0.789979	+	0.573954i
$962$		0			0
$963$	−13.7705	−	42.3813i	−0.443748	−	1.36572i
$964$		0			0
$965$	−29.5344	+	21.4580i	−0.950747	+	0.690758i
$966$		0			0
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$		0			0
$969$	−24.0344			−0.772098
$970$		0			0
$971$	−5.59017	+	4.06150i	−0.179397	+	0.130340i	−0.673860	−	0.738859i	$-0.735365\pi$
$971$	−5.59017	+	4.06150i	−0.179397	+	0.130340i	0.494463	+	0.869199i	$0.335365\pi$
$972$		0			0
$973$	−13.7705	−	42.3813i	−0.441462	−	1.35868i
$974$		0			0
$975$	−12.0172	−	8.73102i	−0.384859	−	0.279616i
$976$		0			0
$977$	−6.31966	+	19.4499i	−0.202184	+	0.622258i	0.797633	+	0.603143i	$0.206085\pi$
$977$	−6.31966	+	19.4499i	−0.202184	+	0.622258i	−0.999817	+	0.0191154i	$0.993915\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−14.8541	+	45.7162i	−0.474255	+	1.45961i
$982$		0			0
$983$	31.7705	+	23.0826i	1.01332	+	0.736221i	0.964903	−	0.262606i	$-0.0845818\pi$
$983$	31.7705	+	23.0826i	1.01332	+	0.736221i	0.0484187	+	0.998827i	$0.484582\pi$
$984$		0			0
$985$	1.47214	+	4.53077i	0.0469062	+	0.144362i
$986$		0			0
$987$	−11.2812	+	8.19624i	−0.359083	+	0.260889i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$	−25.4164	+	18.4661i	−0.806565	+	0.586004i
$994$		0			0
$995$	0.472136	+	1.45309i	0.0149677	+	0.0460659i
$996$		0			0
$997$	−24.2082	−	17.5883i	−0.766682	−	0.557027i	0.134271	−	0.990945i	$-0.457131\pi$
$997$	−24.2082	−	17.5883i	−0.766682	−	0.557027i	−0.900952	+	0.433918i	$0.857131\pi$
$998$		0			0
$999$	1.28115	−	3.94298i	0.0405339	−	0.124750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.e.e.9.1		4
11.2	odd	10		484.2.e.c.245.1		4
11.3	even	5		44.2.e.a.37.1	yes	4
11.4	even	5		484.2.a.b.1.1		2
11.5	even	5	inner	484.2.e.e.269.1		4
11.6	odd	10		484.2.e.d.269.1		4
11.7	odd	10		484.2.a.c.1.1		2
11.8	odd	10		484.2.e.c.81.1		4
11.9	even	5		44.2.e.a.25.1	✓	4
11.10	odd	2		484.2.e.d.9.1		4
33.14	odd	10		396.2.j.a.37.1		4
33.20	odd	10		396.2.j.a.289.1		4
33.26	odd	10		4356.2.a.t.1.2		2
33.29	even	10		4356.2.a.u.1.2		2
44.3	odd	10		176.2.m.b.81.1		4
44.7	even	10		1936.2.a.z.1.2		2
44.15	odd	10		1936.2.a.ba.1.2		2
44.31	odd	10		176.2.m.b.113.1		4
55.3	odd	20		1100.2.cb.a.1049.1		8
55.9	even	10		1100.2.n.a.201.1		4
55.14	even	10		1100.2.n.a.301.1		4
55.42	odd	20		1100.2.cb.a.949.1		8
55.47	odd	20		1100.2.cb.a.1049.2		8
55.53	odd	20		1100.2.cb.a.949.2		8
88.3	odd	10		704.2.m.d.257.1		4
88.29	odd	10		7744.2.a.db.1.2		2
88.37	even	10		7744.2.a.da.1.2		2
88.51	even	10		7744.2.a.bo.1.1		2
88.53	even	10		704.2.m.e.641.1		4
88.59	odd	10		7744.2.a.bp.1.1		2
88.69	even	10		704.2.m.e.257.1		4
88.75	odd	10		704.2.m.d.641.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.25.1	✓	4	11.9	even	5
44.2.e.a.37.1	yes	4	11.3	even	5
176.2.m.b.81.1		4	44.3	odd	10
176.2.m.b.113.1		4	44.31	odd	10
396.2.j.a.37.1		4	33.14	odd	10
396.2.j.a.289.1		4	33.20	odd	10
484.2.a.b.1.1		2	11.4	even	5
484.2.a.c.1.1		2	11.7	odd	10
484.2.e.c.81.1		4	11.8	odd	10
484.2.e.c.245.1		4	11.2	odd	10
484.2.e.d.9.1		4	11.10	odd	2
484.2.e.d.269.1		4	11.6	odd	10
484.2.e.e.9.1		4	1.1	even	1	trivial
484.2.e.e.269.1		4	11.5	even	5	inner
704.2.m.d.257.1		4	88.3	odd	10
704.2.m.d.641.1		4	88.75	odd	10
704.2.m.e.257.1		4	88.69	even	10
704.2.m.e.641.1		4	88.53	even	10
1100.2.n.a.201.1		4	55.9	even	10
1100.2.n.a.301.1		4	55.14	even	10
1100.2.cb.a.949.1		8	55.42	odd	20
1100.2.cb.a.949.2		8	55.53	odd	20
1100.2.cb.a.1049.1		8	55.3	odd	20
1100.2.cb.a.1049.2		8	55.47	odd	20
1936.2.a.z.1.2		2	44.7	even	10
1936.2.a.ba.1.2		2	44.15	odd	10
4356.2.a.t.1.2		2	33.26	odd	10
4356.2.a.u.1.2		2	33.29	even	10
7744.2.a.bo.1.1		2	88.51	even	10
7744.2.a.bp.1.1		2	88.59	odd	10
7744.2.a.da.1.2		2	88.37	even	10
7744.2.a.db.1.2		2	88.29	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.11803 - 1.53884i) q^{3} +(-0.500000 - 1.53884i) q^{5} +(3.11803 + 2.26538i) q^{7} +(1.19098 - 3.66547i) q^{9} +(0.736068 - 2.26538i) q^{13} +(-3.42705 - 2.48990i) q^{15} +(0.736068 + 2.26538i) q^{17} +(-3.11803 + 2.26538i) q^{19} +10.0902 q^{21} -2.47214 q^{23} +(1.92705 - 1.40008i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-6.97214 - 5.06555i) q^{29} +(0.263932 - 0.812299i) q^{31} +(1.92705 - 5.93085i) q^{35} +(1.50000 + 1.08981i) q^{37} +(-1.92705 - 5.93085i) q^{39} +(-6.97214 + 5.06555i) q^{41} -6.23607 q^{45} +(-1.11803 + 0.812299i) q^{47} +(2.42705 + 7.46969i) q^{49} +(5.04508 + 3.66547i) q^{51} +(-1.26393 + 3.88998i) q^{53} +(-3.11803 + 9.59632i) q^{57} +(-0.881966 - 0.640786i) q^{59} +(0.736068 + 2.26538i) q^{61} +(12.0172 - 8.73102i) q^{63} -3.85410 q^{65} +12.9443 q^{67} +(-5.23607 + 3.80423i) q^{69} +(-1.97214 - 6.06961i) q^{71} +(0.736068 + 0.534785i) q^{73} +(1.92705 - 5.93085i) q^{75} +(-2.20820 + 6.79615i) q^{79} +(4.61803 + 3.35520i) q^{81} +(4.02786 + 12.3965i) q^{83} +(3.11803 - 2.26538i) q^{85} -22.5623 q^{87} +0.472136 q^{89} +(7.42705 - 5.39607i) q^{91} +(-0.690983 - 2.12663i) q^{93} +(5.04508 + 3.66547i) q^{95} +(-4.50000 + 13.8496i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{5} + 8 q^{7} + 7 q^{9} - 6 q^{13} - 7 q^{15} - 6 q^{17} - 8 q^{19} + 18 q^{21} + 8 q^{23} + q^{25} - 5 q^{27} - 10 q^{29} + 10 q^{31} + q^{35} + 6 q^{37} - q^{39} - 10 q^{41} - 16 q^{45}+ \cdots - 18 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^5 + 8 * q^7 + 7 * q^9 - 6 * q^13 - 7 * q^15 - 6 * q^17 - 8 * q^19 + 18 * q^21 + 8 * q^23 + q^25 - 5 * q^27 - 10 * q^29 + 10 * q^31 + q^35 + 6 * q^37 - q^39 - 10 * q^41 - 16 * q^45 + 3 * q^49 + 9 * q^51 - 14 * q^53 - 8 * q^57 - 8 * q^59 - 6 * q^61 + 19 * q^63 - 2 * q^65 + 16 * q^67 - 12 * q^69 + 10 * q^71 - 6 * q^73 + q^75 + 18 * q^79 + 14 * q^81 + 34 * q^83 + 8 * q^85 - 50 * q^87 - 16 * q^89 + 23 * q^91 - 5 * q^93 + 9 * q^95 - 18 * q^97

Introduction

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