LMFDB - Embedded newform 845.2.k.e.268.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (of order $4$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			268.5
Root			$0.274809i$ of defining polynomial
Character	$\chi$	$=$	845.268
Dual form			845.2.k.e.577.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.274809 q^{2} +(1.67095 + 1.67095i) q^{3} -1.92448 q^{4} +(1.69883 + 1.45395i) q^{5} +(0.459191 + 0.459191i) q^{6} -0.386104i q^{7} -1.07848 q^{8} +2.58414i q^{9} +(0.466854 + 0.399558i) q^{10} +(-3.08375 + 3.08375i) q^{11} +(-3.21571 - 3.21571i) q^{12} -0.106105i q^{14} +(0.409188 + 5.26814i) q^{15} +3.55258 q^{16} +(1.39475 + 1.39475i) q^{17} +0.710144i q^{18} +(-3.54274 + 3.54274i) q^{19} +(-3.26937 - 2.79810i) q^{20} +(0.645159 - 0.645159i) q^{21} +(-0.847442 + 0.847442i) q^{22} +(0.235896 - 0.235896i) q^{23} +(-1.80209 - 1.80209i) q^{24} +(0.772064 + 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +0.743049i q^{28} +8.16410i q^{29} +(0.112448 + 1.44773i) q^{30} +(-2.54187 - 2.54187i) q^{31} +3.13324 q^{32} -10.3056 q^{33} +(0.383290 + 0.383290i) q^{34} +(0.561375 - 0.655925i) q^{35} -4.97313i q^{36} -4.82502i q^{37} +(-0.973575 + 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(-3.29253 - 3.29253i) q^{41} +(0.177295 - 0.177295i) q^{42} +(4.82129 - 4.82129i) q^{43} +(5.93462 - 5.93462i) q^{44} +(-3.75721 + 4.39002i) q^{45} +(0.0648264 - 0.0648264i) q^{46} +9.83310i q^{47} +(5.93619 + 5.93619i) q^{48} +6.85092 q^{49} +(0.212170 + 1.35756i) q^{50} +4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(0.190959 - 0.190959i) q^{54} +(-9.72240 + 0.755161i) q^{55} +0.416405i q^{56} -11.8395 q^{57} +2.24356i q^{58} +(1.71630 + 1.71630i) q^{59} +(-0.787474 - 10.1384i) q^{60} +10.6468 q^{61} +(-0.698529 - 0.698529i) q^{62} +0.997746 q^{63} -6.24413 q^{64} -2.83207 q^{66} -6.37591 q^{67} +(-2.68417 - 2.68417i) q^{68} +0.788342 q^{69} +(0.154271 - 0.180254i) q^{70} +(-3.07858 - 3.07858i) q^{71} -2.78695i q^{72} +6.08593 q^{73} -1.32596i q^{74} +(-6.96446 + 9.54462i) q^{75} +(6.81793 - 6.81793i) q^{76} +(1.19065 + 1.19065i) q^{77} +3.34944i q^{79} +(6.03525 + 5.16528i) q^{80} +10.0746 q^{81} +(-0.904815 - 0.904815i) q^{82} +5.18834i q^{83} +(-1.24160 + 1.24160i) q^{84} +(0.341552 + 4.39735i) q^{85} +(1.32493 - 1.32493i) q^{86} +(-13.6418 + 13.6418i) q^{87} +(3.32577 - 3.32577i) q^{88} +(3.53455 + 3.53455i) q^{89} +(-1.03251 + 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} -8.49469i q^{93} +2.70222i q^{94} +(-11.1695 + 0.867558i) q^{95} +(5.23549 + 5.23549i) q^{96} +14.7480 q^{97} +1.88269 q^{98} +(-7.96886 - 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.274809			0.194319			0.0971595	−	0.995269i	$-0.469024\pi$
$2$	0.274809			0.194319			0.0971595	+	0.995269i	$0.469024\pi$
$3$	1.67095	+	1.67095i	0.964723	+	0.964723i	0.999399	−	0.0346758i	$-0.0110399\pi$
$3$	1.67095	+	1.67095i	0.964723	+	0.964723i	−0.0346758	+	0.999399i	$0.511040\pi$
$4$	−1.92448			−0.962240
$5$	1.69883	+	1.45395i	0.759741	+	0.650226i
$5$	1.69883	+	1.45395i	0.759741	+	0.650226i
$6$	0.459191	+	0.459191i	0.187464	+	0.187464i
$7$		−	0.386104i		−	0.145933i	−0.997334	−	0.0729667i	$-0.976753\pi$
$7$		−	0.386104i		−	0.145933i	0.997334	−	0.0729667i	$-0.0232467\pi$
$8$	−1.07848			−0.381301
$9$			2.58414i			0.861380i
$10$	0.466854	+	0.399558i	0.147632	+	0.126351i
$11$	−3.08375	+	3.08375i	−0.929787	+	0.929787i	−0.997692	−	0.0679048i	$-0.978369\pi$
$11$	−3.08375	+	3.08375i	−0.929787	+	0.929787i	0.0679048	+	0.997692i	$0.478369\pi$
$12$	−3.21571	−	3.21571i	−0.928295	−	0.928295i
$13$		0			0
$13$		0			0
$14$		−	0.106105i		−	0.0283576i
$15$	0.409188	+	5.26814i	0.105652	+	1.36023i
$16$	3.55258			0.888146
$17$	1.39475	+	1.39475i	0.338277	+	0.338277i	0.855719	−	0.517442i	$-0.173116\pi$
$17$	1.39475	+	1.39475i	0.338277	+	0.338277i	−0.517442	+	0.855719i	$0.673116\pi$
$18$			0.710144i			0.167383i
$19$	−3.54274	+	3.54274i	−0.812760	+	0.812760i	−0.985047	−	0.172287i	$-0.944884\pi$
$19$	−3.54274	+	3.54274i	−0.812760	+	0.812760i	0.172287	+	0.985047i	$0.444884\pi$
$20$	−3.26937	−	2.79810i	−0.731053	−	0.625673i
$21$	0.645159	−	0.645159i	0.140785	−	0.140785i
$22$	−0.847442	+	0.847442i	−0.180675	+	0.180675i
$23$	0.235896	−	0.235896i	0.0491878	−	0.0491878i	−0.682085	−	0.731273i	$-0.738927\pi$
$23$	0.235896	−	0.235896i	0.0491878	−	0.0491878i	0.731273	+	0.682085i	$0.238927\pi$
$24$	−1.80209	−	1.80209i	−0.367849	−	0.367849i
$25$	0.772064	+	4.94003i	0.154413	+	0.988006i
$26$		0			0
$27$	0.694880	−	0.694880i	0.133730	−	0.133730i
$28$			0.743049i			0.140423i
$29$			8.16410i			1.51603i	0.652235	+	0.758017i	$0.273832\pi$
$29$			8.16410i			1.51603i	−0.652235	+	0.758017i	$0.726168\pi$
$30$	0.112448	+	1.44773i	0.0205302	+	0.264318i
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	0.440982	−	0.897516i	$-0.354630\pi$
$31$	−2.54187	−	2.54187i	−0.456534	−	0.456534i	−0.897516	+	0.440982i	$0.854630\pi$
$32$	3.13324			0.553884
$33$	−10.3056			−1.79397
$34$	0.383290	+	0.383290i	0.0657336	+	0.0657336i
$35$	0.561375	−	0.655925i	0.0948897	−	0.110872i
$36$		−	4.97313i		−	0.828855i
$37$		−	4.82502i		−	0.793229i	−0.917985	−	0.396614i	$-0.870185\pi$
$37$		−	4.82502i		−	0.793229i	0.917985	−	0.396614i	$-0.129815\pi$
$38$	−0.973575	+	0.973575i	−0.157935	+	0.157935i
$39$		0			0
$40$	−1.83216	−	1.56806i	−0.289690	−	0.247931i
$41$	−3.29253	−	3.29253i	−0.514207	−	0.514207i	0.401606	−	0.915813i	$-0.368452\pi$
$41$	−3.29253	−	3.29253i	−0.514207	−	0.514207i	−0.915813	+	0.401606i	$0.868452\pi$
$42$	0.177295	−	0.177295i	0.0273573	−	0.0273573i
$43$	4.82129	−	4.82129i	0.735240	−	0.735240i	−0.236413	−	0.971653i	$-0.575972\pi$
$43$	4.82129	−	4.82129i	0.735240	−	0.735240i	0.971653	+	0.236413i	$0.0759718\pi$
$44$	5.93462	−	5.93462i	0.894678	−	0.894678i
$45$	−3.75721	+	4.39002i	−0.560092	+	0.654426i
$46$	0.0648264	−	0.0648264i	0.00955813	−	0.00955813i
$47$			9.83310i			1.43430i	0.696917	+	0.717152i	$0.254555\pi$
$47$			9.83310i			1.43430i	−0.696917	+	0.717152i	$0.745445\pi$
$48$	5.93619	+	5.93619i	0.856815	+	0.856815i
$49$	6.85092			0.978703
$50$	0.212170	+	1.35756i	0.0300054	+	0.191988i
$51$			4.66112i			0.652687i
$52$		0			0
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	0.0148021	−	0.999890i	$-0.495288\pi$
$53$	−7.17155	−	7.17155i	−0.985088	−	0.985088i	−0.999890	+	0.0148021i	$0.995288\pi$
$54$	0.190959	−	0.190959i	0.0259862	−	0.0259862i
$55$	−9.72240	+	0.755161i	−1.31097	+	0.101826i
$56$			0.416405i			0.0556445i
$57$	−11.8395			−1.56818
$58$			2.24356i			0.294594i
$59$	1.71630	+	1.71630i	0.223443	+	0.223443i	0.809947	−	0.586504i	$-0.199496\pi$
$59$	1.71630	+	1.71630i	0.223443	+	0.223443i	−0.586504	+	0.809947i	$0.699496\pi$
$60$	−0.787474	−	10.1384i	−0.101662	−	1.30887i
$61$	10.6468			1.36318			0.681589	−	0.731735i	$-0.261289\pi$
$61$	10.6468			1.36318			0.681589	+	0.731735i	$0.261289\pi$
$62$	−0.698529	−	0.698529i	−0.0887133	−	0.0887133i
$63$	0.997746			0.125704
$64$	−6.24413			−0.780516
$65$		0			0
$66$	−2.83207			−0.348603
$67$	−6.37591			−0.778942			−0.389471	−	0.921039i	$-0.627342\pi$
$67$	−6.37591			−0.778942			−0.389471	+	0.921039i	$0.627342\pi$
$68$	−2.68417	−	2.68417i	−0.325504	−	0.325504i
$69$	0.788342			0.0949052
$70$	0.154271	−	0.180254i	0.0184389	−	0.0215445i
$71$	−3.07858	−	3.07858i	−0.365360	−	0.365360i	0.500422	−	0.865782i	$-0.333178\pi$
$71$	−3.07858	−	3.07858i	−0.365360	−	0.365360i	−0.865782	+	0.500422i	$0.833178\pi$
$72$		−	2.78695i		−	0.328445i
$73$	6.08593			0.712304			0.356152	−	0.934428i	$-0.384088\pi$
$73$	6.08593			0.712304			0.356152	+	0.934428i	$0.384088\pi$
$74$		−	1.32596i		−	0.154139i
$75$	−6.96446	+	9.54462i	−0.804187	+	1.10212i
$76$	6.81793	−	6.81793i	0.782070	−	0.782070i
$77$	1.19065	+	1.19065i	0.135687	+	0.135687i
$78$		0			0
$79$			3.34944i			0.376842i	0.982088	+	0.188421i	$0.0603369\pi$
$79$			3.34944i			0.376842i	−0.982088	+	0.188421i	$0.939663\pi$
$80$	6.03525	+	5.16528i	0.674761	+	0.577496i
$81$	10.0746			1.11940
$82$	−0.904815	−	0.904815i	−0.0999202	−	0.0999202i
$83$			5.18834i			0.569494i	0.958603	+	0.284747i	$0.0919096\pi$
$83$			5.18834i			0.569494i	−0.958603	+	0.284747i	$0.908090\pi$
$84$	−1.24160	+	1.24160i	−0.135469	+	0.135469i
$85$	0.341552	+	4.39735i	0.0370465	+	0.476959i
$86$	1.32493	−	1.32493i	0.142871	−	0.142871i
$87$	−13.6418	+	13.6418i	−1.46255	+	1.46255i
$88$	3.32577	−	3.32577i	0.354528	−	0.354528i
$89$	3.53455	+	3.53455i	0.374662	+	0.374662i	0.869172	−	0.494510i	$-0.164652\pi$
$89$	3.53455	+	3.53455i	0.374662	+	0.374662i	−0.494510	+	0.869172i	$0.664652\pi$
$90$	−1.03251	+	1.20642i	−0.108836	+	0.127167i
$91$		0			0
$92$	−0.453978	+	0.453978i	−0.0473305	+	0.0473305i
$93$		−	8.49469i		−	0.880858i
$94$			2.70222i			0.278713i
$95$	−11.1695	+	0.867558i	−1.14596	+	0.0890096i
$96$	5.23549	+	5.23549i	0.534345	+	0.534345i
$97$	14.7480			1.49744			0.748718	−	0.662889i	$-0.230670\pi$
$97$	14.7480			1.49744			0.748718	+	0.662889i	$0.230670\pi$
$98$	1.88269			0.190181
$99$	−7.96886	−	7.96886i	−0.800900	−	0.800900i
$100$	−1.48582	−	9.50699i	−0.148582	−	0.950699i
$101$		−	5.27950i		−	0.525329i	−0.964887	−	0.262665i	$-0.915399\pi$
$101$		−	5.27950i		−	0.525329i	0.964887	−	0.262665i	$-0.0846013\pi$
$102$			1.28092i			0.126829i
$103$	1.21001	−	1.21001i	0.119226	−	0.119226i	−0.644976	−	0.764203i	$-0.723133\pi$
$103$	1.21001	−	1.21001i	0.119226	−	0.119226i	0.764203	+	0.644976i	$0.223133\pi$
$104$		0			0
$105$	2.03405	−	0.157989i	0.198503	−	0.0154181i
$106$	−1.97080	−	1.97080i	−0.191421	−	0.191421i
$107$	2.86583	−	2.86583i	0.277050	−	0.277050i	−0.554880	−	0.831930i	$-0.687236\pi$
$107$	2.86583	−	2.86583i	0.277050	−	0.277050i	0.831930	+	0.554880i	$0.187236\pi$
$108$	−1.33728	+	1.33728i	−0.128680	+	0.128680i
$109$	5.02898	−	5.02898i	0.481689	−	0.481689i	−0.423982	−	0.905671i	$-0.639368\pi$
$109$	5.02898	−	5.02898i	0.481689	−	0.481689i	0.905671	+	0.423982i	$0.139368\pi$
$110$	−2.67180	+	0.207525i	−0.254746	+	0.0197867i
$111$	8.06237	−	8.06237i	0.765246	−	0.765246i
$112$		−	1.37167i		−	0.129610i
$113$	−2.81027	−	2.81027i	−0.264368	−	0.264368i	0.562458	−	0.826826i	$-0.309856\pi$
$113$	−2.81027	−	2.81027i	−0.264368	−	0.264368i	−0.826826	+	0.562458i	$0.809856\pi$
$114$	−3.25359			−0.304726
$115$	0.743730	−	0.0577672i	0.0693532	−	0.00538682i
$116$		−	15.7116i		−	1.45879i
$117$		0			0
$118$	0.471653	+	0.471653i	0.0434192	+	0.0434192i
$119$	0.538519	−	0.538519i	0.0493659	−	0.0493659i
$120$	−0.441301	−	5.68159i	−0.0402851	−	0.518655i
$121$		−	8.01908i		−	0.729008i
$122$	2.92582			0.264892
$123$		−	11.0033i		−	0.992134i
$124$	4.89179	+	4.89179i	0.439296	+	0.439296i
$125$	−5.87095	+	9.51483i	−0.525113	+	0.851032i
$126$	0.274189			0.0244267
$127$	8.06380	+	8.06380i	0.715547	+	0.715547i	0.967690	−	0.252143i	$-0.0811354\pi$
$127$	8.06380	+	8.06380i	0.715547	+	0.715547i	−0.252143	+	0.967690i	$0.581135\pi$
$128$	−7.98243			−0.705553
$129$	16.1123			1.41860
$130$		0			0
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	19.8329			1.72623
$133$	1.36786	+	1.36786i	0.118609	+	0.118609i
$134$	−1.75216			−0.151363
$135$	2.19080	−	0.170165i	0.188554	−	0.0146454i
$136$	−1.50421	−	1.50421i	−0.128985	−	0.128985i
$137$			0.243949i			0.0208420i	0.999946	+	0.0104210i	$0.00331717\pi$
$137$			0.243949i			0.0208420i	−0.999946	+	0.0104210i	$0.996683\pi$
$138$	0.216643			0.0184419
$139$		−	11.6840i		−	0.991027i	−0.868600	−	0.495514i	$-0.834980\pi$
$139$		−	11.6840i		−	0.991027i	0.868600	−	0.495514i	$-0.165020\pi$
$140$	−1.08036	+	1.26232i	−0.0913067	+	0.106685i
$141$	−16.4306	+	16.4306i	−1.38371	+	1.38371i
$142$	−0.846020	−	0.846020i	−0.0709965	−	0.0709965i
$143$		0			0
$144$			9.18038i			0.765032i
$145$	−11.8702	+	13.8694i	−0.985765	+	1.15179i
$146$	1.67247			0.138414
$147$	11.4475	+	11.4475i	0.944178	+	0.944178i
$148$			9.28566i			0.763277i
$149$	−1.79074	+	1.79074i	−0.146703	+	0.146703i	−0.776644	−	0.629940i	$-0.783079\pi$
$149$	−1.79074	+	1.79074i	−0.146703	+	0.146703i	0.629940	+	0.776644i	$0.283079\pi$
$150$	−1.91389	+	2.62294i	−0.156269	+	0.214162i
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	−0.594059	−	0.804421i	$-0.702475\pi$
$151$	2.58498	−	2.58498i	0.210362	−	0.210362i	0.804421	+	0.594059i	$0.202475\pi$
$152$	3.82078	−	3.82078i	0.309906	−	0.309906i
$153$	−3.60423	+	3.60423i	−0.291385	+	0.291385i
$154$	0.327201	+	0.327201i	0.0263666	+	0.0263666i
$155$	−0.622463	−	8.01398i	−0.0499974	−	0.643698i
$156$		0			0
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	−0.790042	−	0.613053i	$-0.789941\pi$
$157$	−2.21767	+	2.21767i	−0.176990	+	0.176990i	0.613053	+	0.790042i	$0.289941\pi$
$158$			0.920455i			0.0732275i
$159$		−	23.9666i		−	1.90067i
$160$	5.32285	+	4.55558i	0.420809	+	0.360150i
$161$	−0.0910805	−	0.0910805i	−0.00717815	−	0.00717815i
$162$	2.76860			0.217522
$163$	14.8128			1.16023			0.580116	−	0.814534i	$-0.303007\pi$
$163$	14.8128			1.16023			0.580116	+	0.814534i	$0.303007\pi$
$164$	6.33641	+	6.33641i	0.494790	+	0.494790i
$165$	−17.5075	−	14.9838i	−1.36296	−	1.16649i
$166$			1.42580i			0.110664i
$167$		−	3.46812i		−	0.268372i	−0.990956	−	0.134186i	$-0.957158\pi$
$167$		−	3.46812i		−	0.268372i	0.990956	−	0.134186i	$-0.0428419\pi$
$168$	−0.695792	+	0.695792i	−0.0536815	+	0.0536815i
$169$		0			0
$170$	0.0938613	+	1.20843i	0.00719883	+	0.0926823i
$171$	−9.15493	−	9.15493i	−0.700095	−	0.700095i
$172$	−9.27848	+	9.27848i	−0.707477	+	0.707477i
$173$	2.76467	−	2.76467i	0.210194	−	0.210194i	−0.594156	−	0.804350i	$-0.702514\pi$
$173$	2.76467	−	2.76467i	0.210194	−	0.210194i	0.804350	+	0.594156i	$0.202514\pi$
$174$	−3.74888	+	3.74888i	−0.284202	+	0.284202i
$175$	1.90736	−	0.298097i	0.144183	−	0.0225340i
$176$	−10.9553	+	10.9553i	−0.825787	+	0.825787i
$177$			5.73569i			0.431121i
$178$	0.971326	+	0.971326i	0.0728040	+	0.0728040i
$179$	−6.49760			−0.485653			−0.242827	−	0.970070i	$-0.578075\pi$
$179$	−6.49760			−0.485653			−0.242827	+	0.970070i	$0.578075\pi$
$180$	7.23067	−	8.44851i	0.538943	−	0.629715i
$181$			11.9845i			0.890802i	0.895331	+	0.445401i	$0.146939\pi$
$181$			11.9845i			0.890802i	−0.895331	+	0.445401i	$0.853061\pi$
$182$		0			0
$183$	17.7902	+	17.7902i	1.31509	+	1.31509i
$184$	−0.254410	+	0.254410i	−0.0187553	+	0.0187553i
$185$	7.01534	−	8.19691i	0.515778	−	0.602649i
$186$		−	2.33441i		−	0.171167i
$187$	−8.60214			−0.629051
$188$		−	18.9236i		−	1.38015i
$189$	−0.268296	−	0.268296i	−0.0195156	−	0.0195156i
$190$	−3.06947	+	0.238412i	−0.222683	+	0.0172963i
$191$	−5.19291			−0.375746			−0.187873	−	0.982193i	$-0.560159\pi$
$191$	−5.19291			−0.375746			−0.187873	+	0.982193i	$0.560159\pi$
$192$	−10.4336	−	10.4336i	−0.752981	−	0.752981i
$193$	6.67413			0.480414			0.240207	−	0.970722i	$-0.422785\pi$
$193$	6.67413			0.480414			0.240207	+	0.970722i	$0.422785\pi$
$194$	4.05289			0.290980
$195$		0			0
$196$	−13.1845			−0.941748
$197$	19.5971			1.39624			0.698119	−	0.715982i	$-0.254021\pi$
$197$	19.5971			1.39624			0.698119	+	0.715982i	$0.254021\pi$
$198$	−2.18991	−	2.18991i	−0.155630	−	0.155630i
$199$	−14.7060			−1.04248			−0.521242	−	0.853409i	$-0.674531\pi$
$199$	−14.7060			−1.04248			−0.521242	+	0.853409i	$0.674531\pi$
$200$	−0.832657	−	5.32773i	−0.0588777	−	0.376727i
$201$	−10.6538	−	10.6538i	−0.751463	−	0.751463i
$202$		−	1.45085i		−	0.102082i
$203$	3.15219			0.221240
$204$		−	8.97023i		−	0.628042i
$205$	−0.806286	−	10.3806i	−0.0563135	−	0.725014i
$206$	0.332522	−	0.332522i	0.0231679	−	0.0231679i
$207$	0.609590	+	0.609590i	0.0423694	+	0.0423694i
$208$		0			0
$209$		−	21.8499i		−	1.51139i
$210$	0.558974	−	0.0434167i	0.0385728	−	0.00299604i
$211$	−21.4143			−1.47422			−0.737111	−	0.675771i	$-0.763811\pi$
$211$	−21.4143			−1.47422			−0.737111	+	0.675771i	$0.763811\pi$
$212$	13.8015	+	13.8015i	0.947892	+	0.947892i
$213$		−	10.2883i		−	0.704943i
$214$	0.787555	−	0.787555i	0.0538362	−	0.0538362i
$215$	15.2005	−	1.18065i	1.03666	−	0.0805199i
$216$	−0.749414	+	0.749414i	−0.0509912	+	0.0509912i
$217$	−0.981427	+	0.981427i	−0.0666236	+	0.0666236i
$218$	1.38201	−	1.38201i	0.0936014	−	0.0936014i
$219$	10.1693	+	10.1693i	0.687176	+	0.687176i
$220$	18.7106	−	1.45329i	1.26147	−	0.0979809i
$221$		0			0
$222$	2.21561	−	2.21561i	0.148702	−	0.148702i
$223$		−	27.3356i		−	1.83053i	−0.402855	−	0.915264i	$-0.631982\pi$
$223$		−	27.3356i		−	1.83053i	0.402855	−	0.915264i	$-0.368018\pi$
$224$		−	1.20976i		−	0.0808302i
$225$	−12.7657	+	1.99512i	−0.851049	+	0.133008i
$226$	−0.772287	−	0.772287i	−0.0513718	−	0.0513718i
$227$	6.92738			0.459786			0.229893	−	0.973216i	$-0.426162\pi$
$227$	6.92738			0.459786			0.229893	+	0.973216i	$0.426162\pi$
$228$	22.7848			1.50896
$229$	−4.56825	−	4.56825i	−0.301879	−	0.301879i	0.539870	−	0.841749i	$-0.318473\pi$
$229$	−4.56825	−	4.56825i	−0.301879	−	0.301879i	−0.841749	+	0.539870i	$0.818473\pi$
$230$	0.204383	−	0.0158749i	0.0134766	−	0.00104676i
$231$			3.97903i			0.261801i
$232$		−	8.80482i		−	0.578065i
$233$	−5.49074	+	5.49074i	−0.359711	+	0.359711i	−0.863706	−	0.503996i	$-0.831863\pi$
$233$	−5.49074	+	5.49074i	−0.359711	+	0.359711i	0.503996	+	0.863706i	$0.331863\pi$
$234$		0			0
$235$	−14.2968	+	16.7048i	−0.932622	+	1.08970i
$236$	−3.30298	−	3.30298i	−0.215006	−	0.215006i
$237$	−5.59674	+	5.59674i	−0.363548	+	0.363548i
$238$	0.147990	−	0.147990i	0.00959274	−	0.00959274i
$239$	−8.33949	+	8.33949i	−0.539437	+	0.539437i	−0.923363	−	0.383927i	$-0.874571\pi$
$239$	−8.33949	+	8.33949i	−0.539437	+	0.539437i	0.383927	+	0.923363i	$0.374571\pi$
$240$	1.45367	+	18.7155i	0.0938343	+	1.20808i
$241$	1.03184	−	1.03184i	0.0664667	−	0.0664667i	−0.673092	−	0.739559i	$-0.735034\pi$
$241$	1.03184	−	1.03184i	0.0664667	−	0.0664667i	0.739559	+	0.673092i	$0.235034\pi$
$242$		−	2.20371i		−	0.141660i
$243$	14.7496	+	14.7496i	0.946185	+	0.946185i
$244$	−20.4895			−1.31171
$245$	11.6386	+	9.96089i	0.743561	+	0.636378i
$246$		−	3.02380i		−	0.192791i
$247$		0			0
$248$	2.74136	+	2.74136i	0.174077	+	0.174077i
$249$	−8.66945	+	8.66945i	−0.549404	+	0.549404i
$250$	−1.61339	+	2.61476i	−0.102040	+	0.165372i
$251$		−	13.0098i		−	0.821169i	−0.911823	−	0.410585i	$-0.865325\pi$
$251$		−	13.0098i		−	0.821169i	0.911823	−	0.410585i	$-0.134675\pi$
$252$	−1.92014			−0.120958
$253$			1.45489i			0.0914684i
$254$	2.21600	+	2.21600i	0.139044	+	0.139044i
$255$	−6.77703	+	7.91846i	−0.424394	+	0.495873i
$256$	10.2946			0.643413
$257$	20.8324	+	20.8324i	1.29949	+	1.29949i	0.928729	+	0.370760i	$0.120903\pi$
$257$	20.8324	+	20.8324i	1.29949	+	1.29949i	0.370760	+	0.928729i	$0.379097\pi$
$258$	4.42779			0.275662
$259$	−1.86296			−0.115759
$260$		0			0
$261$	−21.0972			−1.30588
$262$	5.73326			0.354202
$263$	−3.57265	−	3.57265i	−0.220299	−	0.220299i	0.588325	−	0.808624i	$-0.299788\pi$
$263$	−3.57265	−	3.57265i	−0.220299	−	0.220299i	−0.808624	+	0.588325i	$0.799788\pi$
$264$	11.1144			0.684043
$265$	−1.75619	−	22.6103i	−0.107882	−	1.38894i
$266$	0.375901	+	0.375901i	0.0230480	+	0.0230480i
$267$			11.8121i			0.722890i
$268$	12.2703			0.749529
$269$		−	8.64999i		−	0.527399i	−0.964605	−	0.263699i	$-0.915057\pi$
$269$		−	8.64999i		−	0.527399i	0.964605	−	0.263699i	$-0.0849427\pi$
$270$	0.602052	−	0.0467627i	0.0366397	−	0.00284589i
$271$	16.2843	−	16.2843i	0.989201	−	0.989201i	−0.0107409	−	0.999942i	$-0.503419\pi$
$271$	16.2843	−	16.2843i	0.989201	−	0.989201i	0.999942	+	0.0107409i	$0.00341900\pi$
$272$	4.95497	+	4.95497i	0.300439	+	0.300439i
$273$		0			0
$274$			0.0670394i			0.00405000i
$275$	−17.6147	−	12.8530i	−1.06221	−	0.775064i
$276$	−1.51715			−0.0913216
$277$	−15.3026	−	15.3026i	−0.919444	−	0.919444i	0.0775451	−	0.996989i	$-0.475292\pi$
$277$	−15.3026	−	15.3026i	−0.919444	−	0.919444i	−0.996989	+	0.0775451i	$0.975292\pi$
$278$		−	3.21087i		−	0.192575i
$279$	6.56856	−	6.56856i	0.393250	−	0.393250i
$280$	−0.605432	+	0.707403i	−0.0361815	+	0.0422754i
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	−0.419805	−	0.907614i	$-0.637902\pi$
$281$	8.17717	−	8.17717i	0.487809	−	0.487809i	0.907614	+	0.419805i	$0.137902\pi$
$282$	−4.51527	+	4.51527i	−0.268880	+	0.268880i
$283$	−3.18152	+	3.18152i	−0.189122	+	0.189122i	−0.795316	−	0.606195i	$-0.792695\pi$
$283$	−3.18152	+	3.18152i	−0.189122	+	0.189122i	0.606195	+	0.795316i	$0.292695\pi$
$284$	5.92467	+	5.92467i	0.351564	+	0.351564i
$285$	−20.1133	−	17.2140i	−1.19141	−	1.01967i
$286$		0			0
$287$	−1.27126	+	1.27126i	−0.0750400	+	0.0750400i
$288$			8.09674i			0.477105i
$289$		−	13.1093i		−	0.771137i
$290$	−3.26203	+	3.81144i	−0.191553	+	0.223815i
$291$	24.6432	+	24.6432i	1.44461	+	1.44461i
$292$	−11.7123			−0.685408
$293$	−13.1055			−0.765631			−0.382815	−	0.923825i	$-0.625045\pi$
$293$	−13.1055			−0.765631			−0.382815	+	0.923825i	$0.625045\pi$
$294$	3.14588	+	3.14588i	0.183472	+	0.183472i
$295$	0.420293	+	5.41111i	0.0244704	+	0.315047i
$296$			5.20370i			0.302459i
$297$			4.28568i			0.248680i
$298$	−0.492111	+	0.492111i	−0.0285072	+	0.0285072i
$299$		0			0
$300$	13.4030	−	18.3684i	0.773821	−	1.06050i
$301$	−1.86152	−	1.86152i	−0.107296	−	0.107296i
$302$	0.710373	−	0.710373i	0.0408774	−	0.0408774i
$303$	8.82177	−	8.82177i	0.506797	−	0.506797i
$304$	−12.5859	+	12.5859i	−0.721849	+	0.721849i
$305$	18.0871	+	15.4799i	1.03566	+	0.886374i
$306$	−0.990475	+	0.990475i	−0.0566217	+	0.0566217i
$307$		−	7.75447i		−	0.442571i	−0.975209	−	0.221285i	$-0.928975\pi$
$307$		−	7.75447i		−	0.442571i	0.975209	−	0.221285i	$-0.0710252\pi$
$308$	−2.29138	−	2.29138i	−0.130564	−	0.130564i
$309$	4.04374			0.230040
$310$	−0.171058	−	2.20231i	−0.00971546	−	0.125083i
$311$			11.6030i			0.657947i	0.944339	+	0.328974i	$0.106703\pi$
$311$			11.6030i			0.657947i	−0.944339	+	0.328974i	$0.893297\pi$
$312$		0			0
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	0.359188	−	0.933265i	$-0.383054\pi$
$313$	−10.1565	−	10.1565i	−0.574078	−	0.574078i	−0.933265	+	0.359188i	$0.883054\pi$
$314$	−0.609436	+	0.609436i	−0.0343924	+	0.0343924i
$315$	1.69500	+	1.45067i	0.0955026	+	0.0817361i
$316$		−	6.44593i		−	0.362612i
$317$	21.7686			1.22265			0.611323	−	0.791381i	$-0.290638\pi$
$317$	21.7686			1.22265			0.611323	+	0.791381i	$0.290638\pi$
$318$		−	6.58623i		−	0.369337i
$319$	−25.1761	−	25.1761i	−1.40959	−	1.40959i
$320$	−10.6077	−	9.07864i	−0.592990	−	0.507512i
$321$	9.57732			0.534554
$322$	−0.0250297	−	0.0250297i	−0.00139485	−	0.00139485i
$323$	−9.88248			−0.549876
$324$	−19.3884			−1.07714
$325$		0			0
$326$	4.07070			0.225455
$327$	16.8064			0.929393
$328$	3.55093	+	3.55093i	0.196067	+	0.196067i
$329$	3.79659			0.209313
$330$	−4.81121	−	4.11768i	−0.264848	−	0.226671i
$331$	−13.8731	−	13.8731i	−0.762536	−	0.762536i	0.214244	−	0.976780i	$-0.431271\pi$
$331$	−13.8731	−	13.8731i	−0.762536	−	0.762536i	−0.976780	+	0.214244i	$0.931271\pi$
$332$		−	9.98485i		−	0.547990i
$333$	12.4685			0.683272
$334$		−	0.953071i		−	0.0521497i
$335$	−10.8316	−	9.27025i	−0.591794	−	0.506488i
$336$	2.29198	−	2.29198i	0.125038	−	0.125038i
$337$	9.35946	+	9.35946i	0.509842	+	0.509842i	0.914478	−	0.404636i	$-0.132602\pi$
$337$	9.35946	+	9.35946i	0.509842	+	0.509842i	−0.404636	+	0.914478i	$0.632602\pi$
$338$		0			0
$339$		−	9.39165i		−	0.510084i
$340$	−0.657309	−	8.46261i	−0.0356476	−	0.458949i
$341$	15.6770			0.848959
$342$	−2.51585	−	2.51585i	−0.136042	−	0.136042i
$343$		−	5.34789i		−	0.288759i
$344$	−5.19967	+	5.19967i	−0.280347	+	0.280347i
$345$	1.33926	+	1.14621i	0.0721034	+	0.0617098i
$346$	0.759754	−	0.759754i	0.0408446	−	0.0408446i
$347$	−19.5532	+	19.5532i	−1.04967	+	1.04967i	−0.0509719	+	0.998700i	$0.516232\pi$
$347$	−19.5532	+	19.5532i	−1.04967	+	1.04967i	−0.998700	+	0.0509719i	$0.983768\pi$
$348$	26.2533	−	26.2533i	1.40733	−	1.40733i
$349$	−20.8717	−	20.8717i	−1.11724	−	1.11724i	−0.992145	−	0.125093i	$-0.960077\pi$
$349$	−20.8717	−	20.8717i	−1.11724	−	1.11724i	−0.125093	−	0.992145i	$-0.539923\pi$
$350$	0.524160	−	0.0819196i	0.0280175	−	0.00437878i
$351$		0			0
$352$	−9.66215	+	9.66215i	−0.514994	+	0.514994i
$353$			15.6355i			0.832195i	0.909320	+	0.416098i	$0.136603\pi$
$353$			15.6355i			0.832195i	−0.909320	+	0.416098i	$0.863397\pi$
$354$			1.57622i			0.0837750i
$355$	−0.753894	−	9.70609i	−0.0400125	−	0.515146i
$356$	−6.80218	−	6.80218i	−0.360515	−	0.360515i
$357$	1.79967			0.0952489
$358$	−1.78560			−0.0943716
$359$	−14.0592	−	14.0592i	−0.742017	−	0.742017i	0.230949	−	0.972966i	$-0.425817\pi$
$359$	−14.0592	−	14.0592i	−0.742017	−	0.742017i	−0.972966	+	0.230949i	$0.925817\pi$
$360$	4.05208	−	4.73456i	0.213563	−	0.249533i
$361$		−	6.10198i		−	0.321157i
$362$			3.29345i			0.173100i
$363$	13.3995	−	13.3995i	0.703290	−	0.703290i
$364$		0			0
$365$	10.3390	+	8.84863i	0.541167	+	0.463159i
$366$	4.88890	+	4.88890i	0.255547	+	0.255547i
$367$	−15.5741	+	15.5741i	−0.812963	+	0.812963i	−0.985077	−	0.172114i	$-0.944940\pi$
$367$	−15.5741	+	15.5741i	−0.812963	+	0.812963i	0.172114	+	0.985077i	$0.444940\pi$
$368$	0.838042	−	0.838042i	0.0436860	−	0.0436860i
$369$	8.50836	−	8.50836i	0.442928	−	0.442928i
$370$	1.92788	−	2.25258i	0.100225	−	0.117106i
$371$	−2.76896	+	2.76896i	−0.143757	+	0.143757i
$372$			16.3479i			0.847597i
$373$	−0.824171	−	0.824171i	−0.0426740	−	0.0426740i	0.685448	−	0.728122i	$-0.259606\pi$
$373$	−0.824171	−	0.824171i	−0.0426740	−	0.0426740i	−0.728122	+	0.685448i	$0.759606\pi$
$374$	−2.36394			−0.122237
$375$	−25.7088	+	6.08874i	−1.32760	+	0.314421i
$376$		−	10.6048i		−	0.546901i
$377$		0			0
$378$	−0.0737299	−	0.0737299i	−0.00379226	−	0.00379226i
$379$	−18.6501	+	18.6501i	−0.957990	+	0.957990i	−0.999152	−	0.0411628i	$-0.986894\pi$
$379$	−18.6501	+	18.6501i	−0.957990	+	0.957990i	0.0411628	+	0.999152i	$0.486894\pi$
$380$	21.4954	−	1.66960i	1.10269	−	0.0856486i
$381$			26.9484i			1.38061i
$382$	−1.42706			−0.0730146
$383$			32.8001i			1.67601i	0.545664	+	0.838004i	$0.316278\pi$
$383$			32.8001i			1.67601i	−0.545664	+	0.838004i	$0.683722\pi$
$384$	−13.3382	−	13.3382i	−0.680663	−	0.680663i
$385$	0.291570	+	3.75386i	0.0148598	+	0.191314i
$386$	1.83411			0.0933536
$387$	12.4589	+	12.4589i	0.633321	+	0.633321i
$388$	−28.3823			−1.44089
$389$	−9.36826			−0.474989			−0.237495	−	0.971389i	$-0.576326\pi$
$389$	−9.36826			−0.474989			−0.237495	+	0.971389i	$0.576326\pi$
$390$		0			0
$391$	0.658034			0.0332782
$392$	−7.38859			−0.373180
$393$	34.8606	+	34.8606i	1.75848	+	1.75848i
$394$	5.38546			0.271316
$395$	−4.86992	+	5.69014i	−0.245032	+	0.286302i
$396$	15.3359	+	15.3359i	0.770658	+	0.770658i
$397$			11.6520i			0.584797i	0.956297	+	0.292399i	$0.0944534\pi$
$397$			11.6520i			0.584797i	−0.956297	+	0.292399i	$0.905547\pi$
$398$	−4.04135			−0.202574
$399$			4.57126i			0.228849i
$400$	2.74282	+	17.5499i	0.137141	+	0.877494i
$401$	−14.5782	+	14.5782i	−0.728002	+	0.728002i	−0.970221	−	0.242220i	$-0.922124\pi$
$401$	−14.5782	+	14.5782i	−0.728002	+	0.728002i	0.242220	+	0.970221i	$0.422124\pi$
$402$	−2.92776	−	2.92776i	−0.146024	−	0.146024i
$403$		0			0
$404$			10.1603i			0.505493i
$405$	17.1151	+	14.6480i	0.850457	+	0.727866i
$406$	0.866248			0.0429912
$407$	14.8792	+	14.8792i	0.737534	+	0.737534i
$408$		−	5.02693i		−	0.248870i
$409$	3.22285	−	3.22285i	0.159360	−	0.159360i	−0.622923	−	0.782283i	$-0.714055\pi$
$409$	3.22285	−	3.22285i	0.159360	−	0.159360i	0.782283	+	0.622923i	$0.214055\pi$
$410$	−0.221574	−	2.85269i	−0.0109428	−	0.140884i
$411$	−0.407627	+	0.407627i	−0.0201067	+	0.0201067i
$412$	−2.32865	+	2.32865i	−0.114724	+	0.114724i
$413$	0.662669	−	0.662669i	0.0326078	−	0.0326078i
$414$	0.167521	+	0.167521i	0.00823318	+	0.00823318i
$415$	−7.54358	+	8.81412i	−0.370300	+	0.432668i
$416$		0			0
$417$	19.5234	−	19.5234i	0.956067	−	0.956067i
$418$		−	6.00453i		−	0.293691i
$419$			0.652044i			0.0318545i	0.999873	+	0.0159272i	$0.00507001\pi$
$419$			0.652044i			0.0318545i	−0.999873	+	0.0159272i	$0.994930\pi$
$420$	−3.91448	+	0.304047i	−0.191007	+	0.0148360i
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	0.557906	−	0.829904i	$-0.311605\pi$
$421$	−5.58095	−	5.58095i	−0.271999	−	0.271999i	−0.829904	+	0.557906i	$0.811605\pi$
$422$	−5.88484			−0.286470
$423$	−25.4101			−1.23548
$424$	7.73438	+	7.73438i	0.375615	+	0.375615i
$425$	−5.81328	+	7.96695i	−0.281985	+	0.386454i
$426$		−	2.82731i		−	0.136984i
$427$		−	4.11075i		−	0.198933i
$428$	−5.51524	+	5.51524i	−0.266589	+	0.266589i
$429$		0			0
$430$	4.17722	−	0.324454i	0.201443	−	0.0156466i
$431$	25.2795	+	25.2795i	1.21767	+	1.21767i	0.968445	+	0.249227i	$0.0801767\pi$
$431$	25.2795	+	25.2795i	1.21767	+	1.21767i	0.249227	+	0.968445i	$0.419823\pi$
$432$	2.46862	−	2.46862i	0.118771	−	0.118771i
$433$	−18.6534	+	18.6534i	−0.896424	+	0.896424i	−0.995118	−	0.0986941i	$-0.968533\pi$
$433$	−18.6534	+	18.6534i	−0.896424	+	0.896424i	0.0986941	+	0.995118i	$0.468533\pi$
$434$	−0.269705	+	0.269705i	−0.0129462	+	0.0129462i
$435$	−43.0096	+	3.34065i	−2.06215	+	0.160172i
$436$	−9.67818	+	9.67818i	−0.463501	+	0.463501i
$437$			1.67144i			0.0799558i
$438$	2.79461	+	2.79461i	0.133531	+	0.133531i
$439$	−1.72935			−0.0825374			−0.0412687	−	0.999148i	$-0.513140\pi$
$439$	−1.72935			−0.0825374			−0.0412687	+	0.999148i	$0.513140\pi$
$440$	10.4854	−	0.814426i	0.499873	−	0.0388263i
$441$			17.7038i			0.843036i
$442$		0			0
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	0.771935	−	0.635702i	$-0.219289\pi$
$443$	2.86737	+	2.86737i	0.136233	+	0.136233i	−0.635702	+	0.771935i	$0.719289\pi$
$444$	−15.5159	+	15.5159i	−0.736350	+	0.736350i
$445$	0.865554	+	11.1437i	0.0410312	+	0.528261i
$446$		−	7.51206i		−	0.355706i
$447$	−5.98448			−0.283056
$448$			2.41088i			0.113903i
$449$	14.2752	+	14.2752i	0.673687	+	0.673687i	0.958564	−	0.284877i	$-0.0919527\pi$
$449$	14.2752	+	14.2752i	0.673687	+	0.673687i	−0.284877	+	0.958564i	$0.591953\pi$
$450$	−3.50813	+	0.548277i	−0.165375	+	0.0258460i
$451$	20.3067			0.956205
$452$	5.40832	+	5.40832i	0.254386	+	0.254386i
$453$	8.63872			0.405883
$454$	1.90370			0.0893452
$455$		0			0
$456$	12.7686			0.597946
$457$	−14.7816			−0.691454			−0.345727	−	0.938335i	$-0.612368\pi$
$457$	−14.7816			−0.691454			−0.345727	+	0.938335i	$0.612368\pi$
$458$	−1.25540	−	1.25540i	−0.0586608	−	0.0586608i
$459$	1.93837			0.0904753
$460$	−1.43129	+	0.111172i	−0.0667344	+	0.00518341i
$461$	−4.29491	−	4.29491i	−0.200034	−	0.200034i	0.599981	−	0.800015i	$-0.295175\pi$
$461$	−4.29491	−	4.29491i	−0.200034	−	0.200034i	−0.800015	+	0.599981i	$0.795175\pi$
$462$			1.09347i			0.0508729i
$463$	−36.0148			−1.67375			−0.836874	−	0.547396i	$-0.815619\pi$
$463$	−36.0148			−1.67375			−0.836874	+	0.547396i	$0.815619\pi$
$464$			29.0036i			1.34646i
$465$	12.3508	−	14.4310i	0.572757	−	0.669224i
$466$	−1.50890	+	1.50890i	−0.0698986	+	0.0698986i
$467$	−7.68952	−	7.68952i	−0.355829	−	0.355829i	0.506444	−	0.862273i	$-0.330960\pi$
$467$	−7.68952	−	7.68952i	−0.355829	−	0.355829i	−0.862273	+	0.506444i	$0.830960\pi$
$468$		0			0
$469$			2.46176i			0.113674i
$470$	−3.92889	+	4.59062i	−0.181226	+	0.211749i
$471$	−7.41124			−0.341492
$472$	−1.85099	−	1.85099i	−0.0851989	−	0.0851989i
$473$			29.7353i			1.36723i
$474$	−1.53803	+	1.53803i	−0.0706442	+	0.0706442i
$475$	−20.2365	−	14.7660i	−0.928512	−	0.677511i
$476$	−1.03637	+	1.03637i	−0.0475019	+	0.0475019i
$477$	18.5323	−	18.5323i	0.848536	−	0.848536i
$478$	−2.29176	+	2.29176i	−0.104823	+	0.104823i
$479$	−6.49399	−	6.49399i	−0.296718	−	0.296718i	0.543009	−	0.839727i	$-0.317285\pi$
$479$	−6.49399	−	6.49399i	−0.296718	−	0.296718i	−0.839727	+	0.543009i	$0.817285\pi$
$480$	1.28208	+	16.5064i	0.0585189	+	0.753408i
$481$		0			0
$482$	0.283559	−	0.283559i	0.0129157	−	0.0129157i
$483$		−	0.304382i		−	0.0138498i
$484$			15.4326i			0.701480i
$485$	25.0544	+	21.4429i	1.13766	+	0.973672i
$486$	4.05331	+	4.05331i	0.183862	+	0.183862i
$487$	25.7313			1.16600			0.582998	−	0.812473i	$-0.301879\pi$
$487$	25.7313			1.16600			0.582998	+	0.812473i	$0.301879\pi$
$488$	−11.4823			−0.519781
$489$	24.7515	+	24.7515i	1.11930	+	1.11930i
$490$	3.19838	+	2.73734i	0.144488	+	0.123660i
$491$		−	13.1972i		−	0.595581i	−0.954631	−	0.297790i	$-0.903750\pi$
$491$		−	13.1972i		−	0.595581i	0.954631	−	0.297790i	$-0.0962497\pi$
$492$			21.1756i			0.954671i
$493$	−11.3869	+	11.3869i	−0.512839	+	0.512839i
$494$		0			0
$495$	−1.95144	−	25.1241i	−0.0877108	−	1.12924i
$496$	−9.03023	−	9.03023i	−0.405469	−	0.405469i
$497$	−1.18865	+	1.18865i	−0.0533183	+	0.0533183i
$498$	−2.38244	+	2.38244i	−0.106760	+	0.106760i
$499$	−16.7683	+	16.7683i	−0.750650	+	0.750650i	−0.974601	−	0.223950i	$-0.928105\pi$
$499$	−16.7683	+	16.7683i	−0.750650	+	0.750650i	0.223950	+	0.974601i	$0.428105\pi$
$500$	11.2985	−	18.3111i	0.505285	−	0.818897i
$501$	5.79506	−	5.79506i	0.258904	−	0.258904i
$502$		−	3.57520i		−	0.159569i
$503$	5.33090	+	5.33090i	0.237693	+	0.237693i	0.815894	−	0.578201i	$-0.196245\pi$
$503$	5.33090	+	5.33090i	0.237693	+	0.237693i	−0.578201	+	0.815894i	$0.696245\pi$
$504$	−1.07605			−0.0479311
$505$	7.67612	−	8.96898i	0.341583	−	0.399114i
$506$			0.399817i			0.0177740i
$507$		0			0
$508$	−15.5186	−	15.5186i	−0.688528	−	0.688528i
$509$	21.6741	−	21.6741i	0.960687	−	0.960687i	−0.0385690	−	0.999256i	$-0.512280\pi$
$509$	21.6741	−	21.6741i	0.960687	−	0.960687i	0.999256	+	0.0385690i	$0.0122799\pi$
$510$	−1.86239	+	2.17606i	−0.0824678	+	0.0963576i
$511$		−	2.34980i		−	0.103949i
$512$	18.7939			0.830581
$513$			4.92355i			0.217380i
$514$	5.72492	+	5.72492i	0.252515	+	0.252515i
$515$	3.81491	−	0.296312i	0.168105	−	0.0130571i
$516$	−31.0077			−1.36504
$517$	−30.3229	−	30.3229i	−1.33360	−	1.33360i
$518$	−0.511957			−0.0224941
$519$	9.23923			0.405557
$520$		0			0
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	−5.79768			−0.253758
$523$	7.60576	+	7.60576i	0.332576	+	0.332576i	0.853564	−	0.520988i	$-0.174436\pi$
$523$	7.60576	+	7.60576i	0.332576	+	0.332576i	−0.520988	+	0.853564i	$0.674436\pi$
$524$	−40.1499			−1.75396
$525$	3.68521	+	2.68900i	0.160836	+	0.117358i
$526$	−0.981796	−	0.981796i	−0.0428083	−	0.0428083i
$527$		−	7.09057i		−	0.308870i
$528$	−36.6115			−1.59331
$529$			22.8887i			0.995161i
$530$	−0.482617	−	6.21351i	−0.0209636	−	0.269898i
$531$	−4.43516	+	4.43516i	−0.192469	+	0.192469i
$532$	−2.63243	−	2.63243i	−0.114130	−	0.114130i
$533$		0			0
$534$			3.24607i			0.140471i
$535$	9.03534	−	0.701795i	0.390632	−	0.0303412i
$536$	6.87630			0.297011
$537$	−10.8572	−	10.8572i	−0.468521	−	0.468521i
$538$		−	2.37709i		−	0.102484i
$539$	−21.1266	+	21.1266i	−0.909986	+	0.909986i
$540$	−4.21616	+	0.327478i	−0.181435	+	0.0140924i
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	−0.424135	−	0.905599i	$-0.639422\pi$
$541$	11.1986	−	11.1986i	0.481464	−	0.481464i	0.905599	+	0.424135i	$0.139422\pi$
$542$	4.47507	−	4.47507i	0.192221	−	0.192221i
$543$	−20.0255	+	20.0255i	−0.859377	+	0.859377i
$544$	4.37009	+	4.37009i	0.187366	+	0.187366i
$545$	15.8553	−	1.23152i	0.679166	−	0.0527523i
$546$		0			0
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.00999077	+	0.999950i	$0.503180\pi$
$547$	−23.6205	+	23.6205i	−1.00994	+	1.00994i	−0.999950	+	0.00999077i	$0.996820\pi$
$548$		−	0.469476i		−	0.0200550i
$549$			27.5127i			1.17422i
$550$	−4.84067	−	3.53211i	−0.206407	−	0.150610i
$551$	−28.9232	−	28.9232i	−1.23217	−	1.23217i
$552$	−0.850212			−0.0361874
$553$	1.29323			0.0549938
$554$	−4.20528	−	4.20528i	−0.178665	−	0.178665i
$555$	25.4189	−	1.97434i	1.07897	−	0.0838061i
$556$			22.4857i			0.953606i
$557$		−	31.1464i		−	1.31972i	−0.751390	−	0.659859i	$-0.770616\pi$
$557$		−	31.1464i		−	1.31972i	0.751390	−	0.659859i	$-0.229384\pi$
$558$	1.80510	−	1.80510i	0.0764159	−	0.0764159i
$559$		0			0
$560$	1.99433	−	2.33023i	0.0842759	−	0.0984702i
$561$	−14.3737	−	14.3737i	−0.606860	−	0.606860i
$562$	2.24716	−	2.24716i	0.0947906	−	0.0947906i
$563$	14.7397	−	14.7397i	0.621203	−	0.621203i	−0.324636	−	0.945839i	$-0.605242\pi$
$563$	14.7397	−	14.7397i	0.621203	−	0.621203i	0.945839	+	0.324636i	$0.105242\pi$
$564$	31.6204	−	31.6204i	1.33146	−	1.33146i
$565$	−0.688190	−	8.86018i	−0.0289524	−	0.372751i
$566$	−0.874308	+	0.874308i	−0.0367499	+	0.0367499i
$567$		−	3.88985i		−	0.163359i
$568$	3.32019	+	3.32019i	0.139312	+	0.139312i
$569$	41.7455			1.75006			0.875031	−	0.484066i	$-0.160841\pi$
$569$	41.7455			1.75006			0.875031	+	0.484066i	$0.160841\pi$
$570$	−5.52730	−	4.73055i	−0.231513	−	0.198141i
$571$		−	19.2151i		−	0.804127i	−0.915612	−	0.402064i	$-0.868293\pi$
$571$		−	19.2151i		−	0.804127i	0.915612	−	0.402064i	$-0.131707\pi$
$572$		0			0
$573$	−8.67709	−	8.67709i	−0.362491	−	0.362491i
$574$	−0.349353	+	0.349353i	−0.0145817	+	0.0145817i
$575$	1.34746	+	0.983209i	0.0561931	+	0.0410027i
$576$		−	16.1357i		−	0.672321i
$577$	−21.8168			−0.908243			−0.454122	−	0.890940i	$-0.650047\pi$
$577$	−21.8168			−0.908243			−0.454122	+	0.890940i	$0.650047\pi$
$578$		−	3.60256i		−	0.149847i
$579$	11.1521	+	11.1521i	0.463466	+	0.463466i
$580$	22.8439	−	26.6914i	0.948542	−	1.10830i
$581$	2.00324			0.0831082
$582$	6.77217	+	6.77217i	0.280715	+	0.280715i
$583$	44.2306			1.83184
$584$	−6.56356			−0.271602
$585$		0			0
$586$	−3.60150			−0.148777
$587$	−5.85530			−0.241674			−0.120837	−	0.992672i	$-0.538558\pi$
$587$	−5.85530			−0.241674			−0.120837	+	0.992672i	$0.538558\pi$
$588$	−22.0306	−	22.0306i	−0.908525	−	0.908525i
$589$	18.0104			0.742105
$590$	0.115500	+	1.48702i	0.00475507	+	0.0612197i
$591$	32.7458	+	32.7458i	1.34698	+	1.34698i
$592$		−	17.1413i		−	0.704503i
$593$	45.6277			1.87370			0.936852	−	0.349727i	$-0.113726\pi$
$593$	45.6277			1.87370			0.936852	+	0.349727i	$0.113726\pi$
$594$			1.17774i			0.0483233i
$595$	1.69783	−	0.131874i	0.0696043	−	0.00540632i
$596$	3.44625	−	3.44625i	0.141164	−	0.141164i
$597$	−24.5730	−	24.5730i	−1.00571	−	1.00571i
$598$		0			0
$599$			12.7240i			0.519888i	0.965624	+	0.259944i	$0.0837041\pi$
$599$			12.7240i			0.519888i	−0.965624	+	0.259944i	$0.916296\pi$
$600$	7.51104	−	10.2937i	0.306637	−	0.420238i
$601$	−24.7272			−1.00864			−0.504321	−	0.863516i	$-0.668257\pi$
$601$	−24.7272			−1.00864			−0.504321	+	0.863516i	$0.668257\pi$
$602$	−0.511561	−	0.511561i	−0.0208497	−	0.0208497i
$603$		−	16.4763i		−	0.670965i
$604$	−4.97473	+	4.97473i	−0.202419	+	0.202419i
$605$	11.6593	−	13.6231i	0.474020	−	0.553857i
$606$	2.42430	−	2.42430i	0.0984804	−	0.0984804i
$607$	3.11245	−	3.11245i	0.126331	−	0.126331i	−0.641115	−	0.767445i	$-0.721528\pi$
$607$	3.11245	−	3.11245i	0.126331	−	0.126331i	0.767445	+	0.641115i	$0.221528\pi$
$608$	−11.1003	+	11.1003i	−0.450175	+	0.450175i
$609$	5.26714	+	5.26714i	0.213435	+	0.213435i
$610$	4.97048	+	4.25400i	0.201249	+	0.172239i
$611$		0			0
$612$	6.93628	−	6.93628i	0.280382	−	0.280382i
$613$			1.16058i			0.0468752i	0.999725	+	0.0234376i	$0.00746111\pi$
$613$			1.16058i			0.0468752i	−0.999725	+	0.0234376i	$0.992539\pi$
$614$		−	2.13099i		−	0.0859999i
$615$	15.9982	−	18.6928i	0.645111	−	0.753765i
$616$	−1.28409	−	1.28409i	−0.0517375	−	0.0517375i
$617$	−38.4760			−1.54899			−0.774493	−	0.632583i	$-0.781995\pi$
$617$	−38.4760			−1.54899			−0.774493	+	0.632583i	$0.781995\pi$
$618$	1.11126			0.0447012
$619$	−24.7229	−	24.7229i	−0.993698	−	0.993698i	0.00628240	−	0.999980i	$-0.498000\pi$
$619$	−24.7229	−	24.7229i	−0.993698	−	0.993698i	−0.999980	+	0.00628240i	$0.998000\pi$
$620$	1.19792	+	15.4227i	0.0481096	+	0.619392i
$621$		−	0.327839i		−	0.0131557i
$622$			3.18861i			0.127852i
$623$	1.36470	−	1.36470i	0.0546757	−	0.0546757i
$624$		0			0
$625$	−23.8078	+	7.62804i	−0.952313	+	0.305122i
$626$	−2.79109	−	2.79109i	−0.111554	−	0.111554i
$627$	36.5100	−	36.5100i	1.45807	−	1.45807i
$628$	4.26787	−	4.26787i	0.170306	−	0.170306i
$629$	6.72971	−	6.72971i	0.268331	−	0.268331i
$630$	0.465802	+	0.398657i	0.0185580	+	0.0158829i
$631$	5.16604	−	5.16604i	0.205657	−	0.205657i	−0.596762	−	0.802419i	$-0.703546\pi$
$631$	5.16604	−	5.16604i	0.205657	−	0.205657i	0.802419	+	0.596762i	$0.203546\pi$
$632$		−	3.61231i		−	0.143690i
$633$	−35.7822	−	35.7822i	−1.42222	−	1.42222i
$634$	5.98220			0.237583
$635$	1.97469	+	25.4234i	0.0783633	+	1.00890i
$636$			46.1232i			1.82891i
$637$		0			0
$638$	−6.91860	−	6.91860i	−0.273910	−	0.273910i
$639$	7.95548	−	7.95548i	0.314714	−	0.314714i
$640$	−13.5608	−	11.6060i	−0.536038	−	0.458769i
$641$		−	8.31220i		−	0.328312i	−0.986434	−	0.164156i	$-0.947510\pi$
$641$		−	8.31220i		−	0.328312i	0.986434	−	0.164156i	$-0.0524901\pi$
$642$	2.63193			0.103874
$643$			11.1556i			0.439933i	0.975507	+	0.219967i	$0.0705948\pi$
$643$			11.1556i			0.439933i	−0.975507	+	0.219967i	$0.929405\pi$
$644$	0.175283	+	0.175283i	0.00690710	+	0.00690710i
$645$	27.3720	+	23.4264i	1.07777	+	0.922414i
$646$	−2.71579			−0.106851
$647$	−29.7686	−	29.7686i	−1.17033	−	1.17033i	−0.982132	−	0.188194i	$-0.939736\pi$
$647$	−29.7686	−	29.7686i	−1.17033	−	1.17033i	−0.188194	−	0.982132i	$-0.560264\pi$
$648$	−10.8653			−0.426830
$649$	−10.5853			−0.415509
$650$		0			0
$651$	−3.27983			−0.128547
$652$	−28.5070			−1.11642
$653$	−30.2101	−	30.2101i	−1.18221	−	1.18221i	−0.979169	−	0.203045i	$-0.934916\pi$
$653$	−30.2101	−	30.2101i	−1.18221	−	1.18221i	−0.203045	−	0.979169i	$-0.565084\pi$
$654$	4.61853			0.180599
$655$	35.4423	+	30.3334i	1.38485	+	1.18522i
$656$	−11.6970	−	11.6970i	−0.456691	−	0.456691i
$657$			15.7269i			0.613565i
$658$	1.04334			0.0406735
$659$		−	17.6082i		−	0.685916i	−0.939351	−	0.342958i	$-0.888571\pi$
$659$		−	17.6082i		−	0.685916i	0.939351	−	0.342958i	$-0.111429\pi$
$660$	33.6928	+	28.8360i	1.31149	+	1.12244i
$661$	19.7044	−	19.7044i	0.766413	−	0.766413i	−0.211060	−	0.977473i	$-0.567692\pi$
$661$	19.7044	−	19.7044i	0.766413	−	0.766413i	0.977473	+	0.211060i	$0.0676915\pi$
$662$	−3.81246	−	3.81246i	−0.148175	−	0.148175i
$663$		0			0
$664$		−	5.59552i		−	0.217148i
$665$	0.334967	+	4.31258i	0.0129895	+	0.167235i
$666$	3.42646			0.132773
$667$	1.92588	+	1.92588i	0.0745704	+	0.0745704i
$668$			6.67434i			0.258238i
$669$	45.6764	−	45.6764i	1.76595	−	1.76595i
$670$	−2.97662	−	2.54754i	−0.114997	−	0.0984202i
$671$	−32.8320	+	32.8320i	−1.26747	+	1.26747i
$672$	2.02144	−	2.02144i	0.0779788	−	0.0779788i
$673$	5.16432	−	5.16432i	0.199070	−	0.199070i	−0.600531	−	0.799601i	$-0.705044\pi$
$673$	5.16432	−	5.16432i	0.199070	−	0.199070i	0.799601	+	0.600531i	$0.205044\pi$
$674$	2.57206	+	2.57206i	0.0990721	+	0.0990721i
$675$	3.96922	+	2.89624i	0.152775	+	0.111476i
$676$		0			0
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	−0.641473	−	0.767145i	$-0.721677\pi$
$677$	3.26988	−	3.26988i	0.125672	−	0.125672i	0.767145	+	0.641473i	$0.221677\pi$
$678$		−	2.58091i		−	0.0991191i
$679$		−	5.69427i		−	0.218526i
$680$	−0.368357	−	4.74245i	−0.0141258	−	0.181865i
$681$	11.5753	+	11.5753i	0.443566	+	0.443566i
$682$	4.30818			0.164969
$683$	−27.0952			−1.03677			−0.518384	−	0.855148i	$-0.673466\pi$
$683$	−27.0952			−1.03677			−0.518384	+	0.855148i	$0.673466\pi$
$684$	17.6185	+	17.6185i	0.673660	+	0.673660i
$685$	−0.354690	+	0.414429i	−0.0135520	+	0.0158345i
$686$		−	1.46965i		−	0.0561114i
$687$		−	15.2666i		−	0.582458i
$688$	17.1280	−	17.1280i	0.653000	−	0.653000i
$689$		0			0
$690$	0.368040	+	0.314988i	0.0140111	+	0.0119914i
$691$	8.88521	+	8.88521i	0.338009	+	0.338009i	0.855618	−	0.517608i	$-0.173178\pi$
$691$	8.88521	+	8.88521i	0.338009	+	0.338009i	−0.517608	+	0.855618i	$0.673178\pi$
$692$	−5.32055	+	5.32055i	−0.202257	+	0.202257i
$693$	−3.07680	+	3.07680i	−0.116878	+	0.116878i
$694$	−5.37339	+	5.37339i	−0.203971	+	0.203971i
$695$	16.9880	−	19.8492i	0.644392	−	0.752924i
$696$	14.7124	−	14.7124i	0.557672	−	0.557672i
$697$		−	9.18452i		−	0.347889i
$698$	−5.73573	−	5.73573i	−0.217101	−	0.217101i
$699$	−18.3495			−0.694042
$700$	−3.67068	+	0.573681i	−0.138739	+	0.0216831i
$701$		−	39.3955i		−	1.48795i	−0.668208	−	0.743974i	$-0.732938\pi$
$701$		−	39.3955i		−	1.48795i	0.668208	−	0.743974i	$-0.267062\pi$
$702$		0			0
$703$	17.0938	+	17.0938i	0.644705	+	0.644705i
$704$	19.2554	−	19.2554i	0.725714	−	0.725714i
$705$	−51.8021	+	4.02358i	−1.95098	+	0.151537i
$706$			4.29678i			0.161711i
$707$	−2.03843			−0.0766631
$708$		−	11.0382i		−	0.414842i
$709$	18.0945	+	18.0945i	0.679552	+	0.679552i	0.959899	−	0.280347i	$-0.0904495\pi$
$709$	18.0945	+	18.0945i	0.679552	+	0.679552i	−0.280347	+	0.959899i	$0.590450\pi$
$710$	−0.207176	−	2.66732i	−0.00777519	−	0.100103i
$711$	−8.65543			−0.324604
$712$	−3.81195	−	3.81195i	−0.142859	−	0.142859i
$713$	−1.19924			−0.0449118
$714$	0.494566			0.0185087
$715$		0			0
$716$	12.5045			0.467315
$717$	−27.8697			−1.04081
$718$	−3.86359	−	3.86359i	−0.144188	−	0.144188i
$719$	8.68536			0.323909			0.161955	−	0.986798i	$-0.448220\pi$
$719$	8.68536			0.323909			0.161955	+	0.986798i	$0.448220\pi$
$720$	−13.3478	+	15.5959i	−0.497443	+	0.581226i
$721$	−0.467191	−	0.467191i	−0.0173991	−	0.0173991i
$722$		−	1.67688i		−	0.0624069i
$723$	3.44830			0.128244
$724$		−	23.0640i		−	0.857166i
$725$	−40.3309	+	6.30321i	−1.49785	+	0.234095i
$726$	3.68229	−	3.68229i	0.136663	−	0.136663i
$727$	17.4677	+	17.4677i	0.647841	+	0.647841i	0.952471	−	0.304630i	$-0.0985327\pi$
$727$	17.4677	+	17.4677i	0.647841	+	0.647841i	−0.304630	+	0.952471i	$0.598533\pi$
$728$		0			0
$729$			19.0676i			0.706209i
$730$	2.84124	+	2.43168i	0.105159	+	0.0900005i
$731$	13.4490			0.497429
$732$	−34.2369	−	34.2369i	−1.26543	−	1.26543i
$733$		−	34.2413i		−	1.26473i	−0.774670	−	0.632365i	$-0.782084\pi$
$733$		−	34.2413i		−	1.26473i	0.774670	−	0.632365i	$-0.217916\pi$
$734$	−4.27990	+	4.27990i	−0.157974	+	0.157974i
$735$	2.80331	+	36.0916i	0.103402	+	1.33126i
$736$	0.739121	−	0.739121i	0.0272444	−	0.0272444i
$737$	19.6617	−	19.6617i	0.724250	−	0.724250i
$738$	2.33817	−	2.33817i	0.0860692	−	0.0860692i
$739$	−19.9754	−	19.9754i	−0.734807	−	0.734807i	0.236761	−	0.971568i	$-0.423914\pi$
$739$	−19.9754	−	19.9754i	−0.734807	−	0.734807i	−0.971568	+	0.236761i	$0.923914\pi$
$740$	−13.5009	+	15.7748i	−0.496302	+	0.579893i
$741$		0			0
$742$	−0.760935	+	0.760935i	−0.0279348	+	0.0279348i
$743$			31.6768i			1.16211i	0.813864	+	0.581055i	$0.197360\pi$
$743$			31.6768i			1.16211i	−0.813864	+	0.581055i	$0.802640\pi$
$744$			9.16136i			0.335872i
$745$	−5.64582	+	0.438523i	−0.206847	+	0.0160662i
$746$	−0.226489	−	0.226489i	−0.00829237	−	0.00829237i
$747$	−13.4074			−0.490551
$748$	16.5547			0.605298
$749$	−1.10651	−	1.10651i	−0.0404309	−	0.0404309i
$750$	−7.06501	+	1.67324i	−0.257978	+	0.0610980i
$751$		−	2.44047i		−	0.0890541i	−0.999008	−	0.0445271i	$-0.985822\pi$
$751$		−	2.44047i		−	0.0890541i	0.999008	−	0.0445271i	$-0.0141781\pi$
$752$			34.9329i			1.27387i
$753$	21.7387	−	21.7387i	0.792201	−	0.792201i
$754$		0			0
$755$	8.14986	−	0.633018i	0.296604	−	0.0230379i
$756$	0.516329	+	0.516329i	0.0187787	+	0.0187787i
$757$	30.1874	−	30.1874i	1.09718	−	1.09718i	0.102439	−	0.994739i	$-0.467335\pi$
$757$	30.1874	−	30.1874i	1.09718	−	1.09718i	0.994739	−	0.102439i	$-0.0326646\pi$
$758$	−5.12520	+	5.12520i	−0.186156	+	0.186156i
$759$	−2.43105	+	2.43105i	−0.0882416	+	0.0882416i
$760$	12.0461	−	0.935645i	0.436957	−	0.0339394i
$761$	28.2568	−	28.2568i	1.02431	−	1.02431i	0.0246125	−	0.999697i	$-0.492165\pi$
$761$	28.2568	−	28.2568i	1.02431	−	1.02431i	0.999697	−	0.0246125i	$-0.00783521\pi$
$762$			7.40565i			0.268279i
$763$	−1.94171	−	1.94171i	−0.0702946	−	0.0702946i
$764$	9.99366			0.361558
$765$	−11.3634	+	0.882617i	−0.410843	+	0.0319111i
$766$			9.01376i			0.325680i
$767$		0			0
$768$	17.2018	+	17.2018i	0.620716	+	0.620716i
$769$	27.1011	−	27.1011i	0.977291	−	0.977291i	−0.0224570	−	0.999748i	$-0.507149\pi$
$769$	27.1011	−	27.1011i	0.977291	−	0.977291i	0.999748	+	0.0224570i	$0.00714888\pi$
$770$	0.0801260	+	1.03159i	0.00288754	+	0.0371760i
$771$			69.6197i			2.50729i
$772$	−12.8442			−0.462274
$773$		−	14.5788i		−	0.524363i	−0.965019	−	0.262181i	$-0.915558\pi$
$773$		−	14.5788i		−	0.524363i	0.965019	−	0.262181i	$-0.0844419\pi$
$774$	3.42381	+	3.42381i	0.123066	+	0.123066i
$775$	10.5945	−	14.5194i	0.380564	−	0.521553i
$776$	−15.9055			−0.570973
$777$	−3.11291	−	3.11291i	−0.111675	−	0.111675i
$778$	−2.57448			−0.0922995
$779$	23.3291			0.835853
$780$		0			0
$781$	18.9872			0.679414
$782$	0.180833			0.00646659
$783$	5.67306	+	5.67306i	0.202739	+	0.202739i
$784$	24.3385			0.869232
$785$	−6.99184	+	0.543072i	−0.249549	+	0.0193831i
$786$	9.57999	+	9.57999i	0.341707	+	0.341707i
$787$		−	0.947805i		−	0.0337856i	−0.999857	−	0.0168928i	$-0.994623\pi$
$787$		−	0.947805i		−	0.0337856i	0.999857	−	0.0168928i	$-0.00537740\pi$
$788$	−37.7143			−1.34352
$789$		−	11.9394i		−	0.425056i
$790$	−1.33829	+	1.56370i	−0.0476144	+	0.0556339i
$791$	−1.08506	+	1.08506i	−0.0385802	+	0.0385802i
$792$	8.59426	+	8.59426i	0.305384	+	0.305384i
$793$		0			0
$794$			3.20207i			0.113637i
$795$	34.8462	−	40.7152i	1.23587	−	1.44402i
$796$	28.3015			1.00312
$797$	−3.30722	−	3.30722i	−0.117148	−	0.117148i	0.646103	−	0.763250i	$-0.276398\pi$
$797$	−3.30722	−	3.30722i	−0.117148	−	0.117148i	−0.763250	+	0.646103i	$0.776398\pi$
$798$			1.25622i			0.0444698i
$799$	−13.7147	+	13.7147i	−0.485192	+	0.485192i
$800$	2.41906	+	15.4783i	0.0855268	+	0.547241i
$801$	−9.13379	+	9.13379i	−0.322726	+	0.322726i
$802$	−4.00622	+	4.00622i	−0.141465	+	0.141465i
$803$	−18.7675	+	18.7675i	−0.662291	+	0.662291i
$804$	20.5031	+	20.5031i	0.723088	+	0.723088i
$805$	−0.0223041	−	0.287157i	−0.000786117	−	0.0101210i
$806$		0			0
$807$	14.4537	−	14.4537i	0.508794	−	0.508794i
$808$			5.69384i			0.200308i
$809$			24.4365i			0.859143i	0.903033	+	0.429572i	$0.141335\pi$
$809$			24.4365i			0.859143i	−0.903033	+	0.429572i	$0.858665\pi$
$810$	4.70338	+	4.02540i	0.165260	+	0.141438i
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	0.523670	−	0.851921i	$-0.324562\pi$
$811$	−9.34795	−	9.34795i	−0.328251	−	0.328251i	−0.851921	+	0.523670i	$0.824562\pi$
$812$	−6.06632			−0.212886
$813$	54.4205			1.90861
$814$	4.08893	+	4.08893i	0.143317	+	0.143317i
$815$	25.1645	+	21.5371i	0.881475	+	0.754412i
$816$			16.5590i			0.579681i
$817$			34.1611i			1.19515i
$818$	0.885667	−	0.885667i	0.0309666	−	0.0309666i
$819$		0			0
$820$	1.55168	+	19.9773i	0.0541871	+	0.697638i
$821$	1.38999	+	1.38999i	0.0485110	+	0.0485110i	0.730946	−	0.682435i	$-0.239079\pi$
$821$	1.38999	+	1.38999i	0.0485110	+	0.0485110i	−0.682435	+	0.730946i	$0.739079\pi$
$822$	−0.112019	+	0.112019i	−0.00390712	+	0.00390712i
$823$	−11.6284	+	11.6284i	−0.405339	+	0.405339i	−0.880110	−	0.474771i	$-0.842531\pi$
$823$	−11.6284	+	11.6284i	−0.405339	+	0.405339i	0.474771	+	0.880110i	$0.342531\pi$
$824$	−1.30498	+	1.30498i	−0.0454610	+	0.0454610i
$825$	−7.95658	−	50.9100i	−0.277013	−	1.77246i
$826$	0.182107	−	0.182107i	0.00633632	−	0.00633632i
$827$		−	27.3262i		−	0.950225i	−0.879925	−	0.475113i	$-0.842407\pi$
$827$		−	27.3262i		−	0.950225i	0.879925	−	0.475113i	$-0.157593\pi$
$828$	−1.17314	−	1.17314i	−0.0407696	−	0.0407696i
$829$	14.5553			0.505526			0.252763	−	0.967528i	$-0.418661\pi$
$829$	14.5553			0.505526			0.252763	+	0.967528i	$0.418661\pi$
$830$	−2.07304	+	2.42219i	−0.0719563	+	0.0840756i
$831$		−	51.1397i		−	1.77402i
$832$		0			0
$833$	9.55534	+	9.55534i	0.331073	+	0.331073i
$834$	5.36521	−	5.36521i	0.185782	−	0.185782i
$835$	5.04248	−	5.89176i	0.174502	−	0.203893i
$836$			42.0496i			1.45432i
$837$	−3.53259			−0.122104
$838$			0.179187i			0.00618993i
$839$	17.2947	+	17.2947i	0.597079	+	0.597079i	0.939534	−	0.342455i	$-0.111258\pi$
$839$	17.2947	+	17.2947i	0.597079	+	0.597079i	−0.342455	+	0.939534i	$0.611258\pi$
$840$	−2.19368	+	0.170388i	−0.0756892	+	0.00587895i
$841$	−37.6525			−1.29836
$842$	−1.53369	−	1.53369i	−0.0528545	−	0.0528545i
$843$	27.3273			0.941201
$844$	41.2114			1.41856
$845$		0			0
$846$	−6.98292			−0.240078
$847$	−3.09620			−0.106387
$848$	−25.4775	−	25.4775i	−0.874902	−	0.874902i
$849$	−10.6323			−0.364900
$850$	−1.59754	+	2.18939i	−0.0547951	+	0.0750954i
$851$	−1.13821	−	1.13821i	−0.0390172	−	0.0390172i
$852$			19.7996i			0.678324i
$853$	2.94669			0.100893			0.0504464	−	0.998727i	$-0.483936\pi$
$853$	2.94669			0.100893			0.0504464	+	0.998727i	$0.483936\pi$
$854$		−	1.12967i		−	0.0386565i
$855$	−2.24189	−	28.8635i	−0.0766711	−	0.987111i
$856$	−3.09075	+	3.09075i	−0.105640	+	0.105640i
$857$	13.0632	+	13.0632i	0.446229	+	0.446229i	0.894099	−	0.447870i	$-0.147817\pi$
$857$	13.0632	+	13.0632i	0.446229	+	0.446229i	−0.447870	+	0.894099i	$0.647817\pi$
$858$		0			0
$859$			3.08382i			0.105219i	0.998615	+	0.0526093i	$0.0167538\pi$
$859$			3.08382i			0.105219i	−0.998615	+	0.0526093i	$0.983246\pi$
$860$	−29.2530	+	2.27215i	−0.997519	+	0.0774795i
$861$	−4.24841			−0.144786
$862$	6.94703	+	6.94703i	0.236617	+	0.236617i
$863$			50.9818i			1.73544i	0.497053	+	0.867720i	$0.334415\pi$
$863$			50.9818i			1.73544i	−0.497053	+	0.867720i	$0.665585\pi$
$864$	2.17723	−	2.17723i	0.0740708	−	0.0740708i
$865$	8.71639	−	0.677021i	0.296366	−	0.0230194i
$866$	−5.12611	+	5.12611i	−0.174192	+	0.174192i
$867$	21.9050	−	21.9050i	0.743934	−	0.743934i
$868$	1.88874	−	1.88874i	0.0641079	−	0.0641079i
$869$	−10.3289	−	10.3289i	−0.350382	−	0.350382i
$870$	−11.8194	+	0.918039i	−0.400715	+	0.0311244i
$871$		0			0
$872$	−5.42366	+	5.42366i	−0.183668	+	0.183668i
$873$			38.1110i			1.28986i
$874$			0.459326i			0.0155369i
$875$	3.67371	+	2.26679i	0.124194	+	0.0766316i
$876$	−19.5706	−	19.5706i	−0.661228	−	0.661228i
$877$	−26.7687			−0.903916			−0.451958	−	0.892039i	$-0.649274\pi$
$877$	−26.7687			−0.903916			−0.451958	+	0.892039i	$0.649274\pi$
$878$	−0.475240			−0.0160386
$879$	−21.8986	−	21.8986i	−0.738621	−	0.738621i
$880$	−34.5397	+	2.68277i	−1.16433	+	0.0904362i
$881$		−	31.4805i		−	1.06061i	−0.847808	−	0.530303i	$-0.822078\pi$
$881$		−	31.4805i		−	1.06061i	0.847808	−	0.530303i	$-0.177922\pi$
$882$			4.86514i			0.163818i
$883$	−27.3576	+	27.3576i	−0.920657	+	0.920657i	−0.997076	−	0.0764191i	$-0.975651\pi$
$883$	−27.3576	+	27.3576i	−0.920657	+	0.920657i	0.0764191	+	0.997076i	$0.475651\pi$
$884$		0			0
$885$	−8.33941	+	9.74398i	−0.280326	+	0.327540i
$886$	0.787978	+	0.787978i	0.0264726	+	0.0264726i
$887$	−0.971214	+	0.971214i	−0.0326102	+	0.0326102i	−0.723224	−	0.690614i	$-0.757341\pi$
$887$	−0.971214	+	0.971214i	−0.0326102	+	0.0326102i	0.690614	+	0.723224i	$0.257341\pi$
$888$	−8.69511	+	8.69511i	−0.291789	+	0.291789i
$889$	3.11346	−	3.11346i	0.104422	−	0.104422i
$890$	0.237862	+	3.06238i	0.00797314	+	0.102651i
$891$	−31.0677	+	31.0677i	−1.04081	+	1.04081i
$892$			52.6068i			1.76141i
$893$	−34.8361	−	34.8361i	−1.16575	−	1.16575i
$894$	−1.64459			−0.0550032
$895$	−11.0383	−	9.44717i	−0.368971	−	0.315784i
$896$			3.08204i			0.102964i
$897$		0			0
$898$	3.92294	+	3.92294i	0.130910	+	0.130910i
$899$	20.7521	−	20.7521i	0.692122	−	0.692122i
$900$	24.5674	−	3.83957i	0.818914	−	0.127986i
$901$		−	20.0051i		−	0.666465i
$902$	5.58046			0.185809
$903$		−	6.22100i		−	0.207022i
$904$	3.03083	+	3.03083i	0.100804	+	0.100804i
$905$	−17.4249	+	20.3597i	−0.579223	+	0.676779i
$906$	2.37400			0.0788707
$907$	16.4640	+	16.4640i	0.546679	+	0.546679i	0.925479	−	0.378800i	$-0.123663\pi$
$907$	16.4640	+	16.4640i	0.546679	+	0.546679i	−0.378800	+	0.925479i	$0.623663\pi$
$908$	−13.3316			−0.442425
$909$	13.6430			0.452508
$910$		0			0
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	−42.0607			−1.39277
$913$	−15.9996	−	15.9996i	−0.529508	−	0.529508i
$914$	−4.06211			−0.134363
$915$	4.35653	+	56.0886i	0.144022	+	1.85423i
$916$	8.79151	+	8.79151i	0.290480	+	0.290480i
$917$		−	8.05518i		−	0.266006i
$918$	0.532680			0.0175811
$919$			16.6099i			0.547909i	0.961743	+	0.273955i	$0.0883318\pi$
$919$			16.6099i			0.547909i	−0.961743	+	0.273955i	$0.911668\pi$
$920$	−0.802099	+	0.0623008i	−0.0264444	+	0.00205400i
$921$	12.9573	−	12.9573i	0.426958	−	0.426958i
$922$	−1.18028	−	1.18028i	−0.0388704	−	0.0388704i
$923$		0			0
$924$		−	7.65756i		−	0.251915i
$925$	23.8358	−	3.72523i	0.783715	−	0.122485i
$926$	−9.89717			−0.325241
$927$	3.12685	+	3.12685i	0.102699	+	0.102699i
$928$			25.5801i			0.839708i
$929$	30.2829	−	30.2829i	0.993548	−	0.993548i	−0.00643095	−	0.999979i	$-0.502047\pi$
$929$	30.2829	−	30.2829i	0.993548	−	0.993548i	0.999979	+	0.00643095i	$0.00204705\pi$
$930$	3.39412	−	3.96578i	0.111297	−	0.130043i
$931$	−24.2710	+	24.2710i	−0.795451	+	0.795451i
$932$	10.5668	−	10.5668i	0.346128	−	0.346128i
$933$	−19.3881	+	19.3881i	−0.634737	+	0.634737i
$934$	−2.11315	−	2.11315i	−0.0691443	−	0.0691443i
$935$	−14.6136	−	12.5071i	−0.477916	−	0.409025i
$936$		0			0
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	−0.0822783	−	0.996609i	$-0.526220\pi$
$937$	27.9881	−	27.9881i	0.914331	−	0.914331i	0.996609	+	0.0822783i	$0.0262196\pi$
$938$			0.676514i			0.0220890i
$939$		−	33.9419i		−	1.10765i
$940$	27.5139	−	32.1480i	0.897406	−	1.04855i
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	0.636213	−	0.771513i	$-0.280500\pi$
$941$	−4.15042	−	4.15042i	−0.135300	−	0.135300i	−0.771513	+	0.636213i	$0.780500\pi$
$942$	−2.03667			−0.0663584
$943$	−1.55339			−0.0505854
$944$	6.09729	+	6.09729i	0.198450	+	0.198450i
$945$	−0.0657011	−	0.845877i	−0.00213726	−	0.0275164i
$946$			8.17153i			0.265679i
$947$			24.8598i			0.807836i	0.914795	+	0.403918i	$0.132352\pi$
$947$			24.8598i			0.807836i	−0.914795	+	0.403918i	$0.867648\pi$
$948$	10.7708	−	10.7708i	0.349820	−	0.349820i
$949$		0			0
$950$	−5.56115	−	4.05783i	−0.180428	−	0.131653i
$951$	36.3742	+	36.3742i	1.17951	+	1.17951i
$952$	−0.580782	+	0.580782i	−0.0188233	+	0.0188233i
$953$	−23.1258	+	23.1258i	−0.749118	+	0.749118i	−0.974314	−	0.225196i	$-0.927698\pi$
$953$	−23.1258	+	23.1258i	−0.749118	+	0.749118i	0.225196	+	0.974314i	$0.427698\pi$
$954$	5.09284	−	5.09284i	0.164887	−	0.164887i
$955$	−8.82189	−	7.55023i	−0.285470	−	0.244320i
$956$	16.0492	−	16.0492i	0.519068	−	0.519068i
$957$		−	84.1358i		−	2.71973i
$958$	−1.78460	−	1.78460i	−0.0576580	−	0.0576580i
$959$	0.0941897			0.00304154
$960$	−2.55502	−	32.8949i	−0.0824629	−	1.06168i
$961$		−	18.0777i		−	0.583153i
$962$		0			0
$963$	7.40571	+	7.40571i	0.238646	+	0.238646i
$964$	−1.98576	+	1.98576i	−0.0639569	+	0.0639569i
$965$	11.3382	+	9.70384i	0.364990	+	0.312378i
$966$		−	0.0836467i		−	0.00269129i
$967$	30.0090			0.965023			0.482512	−	0.875890i	$-0.339725\pi$
$967$	30.0090			0.965023			0.482512	+	0.875890i	$0.339725\pi$
$968$			8.64843i			0.277971i
$969$	−16.5131	−	16.5131i	−0.530478	−	0.530478i
$970$	6.88518	+	5.89269i	0.221070	+	0.189203i
$971$	−6.27318			−0.201316			−0.100658	−	0.994921i	$-0.532095\pi$
$971$	−6.27318			−0.201316			−0.100658	+	0.994921i	$0.532095\pi$
$972$	−28.3853	−	28.3853i	−0.910457	−	0.910457i
$973$	−4.51125			−0.144624
$974$	7.07119			0.226575
$975$		0			0
$976$	37.8235			1.21070
$977$	−15.5621			−0.497876			−0.248938	−	0.968519i	$-0.580082\pi$
$977$	−15.5621			−0.497876			−0.248938	+	0.968519i	$0.580082\pi$
$978$	6.80193	+	6.80193i	0.217502	+	0.217502i
$979$	−21.7994			−0.696712
$980$	−22.3982	−	19.1695i	−0.715484	−	0.612349i
$981$	12.9956	+	12.9956i	0.414918	+	0.414918i
$982$		−	3.62670i		−	0.115733i
$983$	53.4558			1.70498			0.852488	−	0.522746i	$-0.175093\pi$
$983$	53.4558			1.70498			0.852488	+	0.522746i	$0.175093\pi$
$984$			11.8668i			0.378301i
$985$	33.2923	+	28.4932i	1.06078	+	0.907870i
$986$	−3.12921	+	3.12921i	−0.0996545	+	0.0996545i
$987$	6.34391	+	6.34391i	0.201929	+	0.201929i
$988$		0			0
$989$		−	2.27465i		−	0.0723297i
$990$	−0.536273	−	6.90431i	−0.0170439	−	0.219433i
$991$	−23.6397			−0.750940			−0.375470	−	0.926835i	$-0.622519\pi$
$991$	−23.6397			−0.750940			−0.375470	+	0.926835i	$0.622519\pi$
$992$	−7.96431	−	7.96431i	−0.252867	−	0.252867i
$993$		−	46.3626i		−	1.47127i
$994$	−0.326652	+	0.326652i	−0.0103608	+	0.0103608i
$995$	−24.9831	−	21.3818i	−0.792018	−	0.677850i
$996$	16.6842	−	16.6842i	0.528658	−	0.528658i
$997$	36.5771	−	36.5771i	1.15841	−	1.15841i	0.173591	−	0.984818i	$-0.444463\pi$
$997$	36.5771	−	36.5771i	1.15841	−	1.15841i	0.984818	−	0.173591i	$-0.0555370\pi$
$998$	−4.60806	+	4.60806i	−0.145866	+	0.145866i
$999$	−3.35281	−	3.35281i	−0.106078	−	0.106078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.e.268.5		20
5.2	odd	4		845.2.f.e.437.5		20
13.2	odd	12		845.2.t.f.188.2		20
13.3	even	3		65.2.o.a.33.4	yes	20
13.4	even	6		845.2.o.f.258.2		20
13.5	odd	4		845.2.f.e.408.6		20
13.6	odd	12		65.2.t.a.28.4	yes	20
13.7	odd	12		845.2.t.g.418.2		20
13.8	odd	4		845.2.f.d.408.5		20
13.9	even	3		845.2.o.e.258.4		20
13.10	even	6		845.2.o.g.488.2		20
13.11	odd	12		845.2.t.e.188.4		20
13.12	even	2		845.2.k.d.268.6		20
39.29	odd	6		585.2.cf.a.163.2		20
39.32	even	12		585.2.dp.a.28.2		20
65.2	even	12		845.2.o.e.357.4		20
65.3	odd	12		325.2.x.b.7.2		20
65.7	even	12		845.2.o.g.587.2		20
65.12	odd	4		845.2.f.d.437.6		20
65.17	odd	12		845.2.t.e.427.4		20
65.19	odd	12		325.2.x.b.93.2		20
65.22	odd	12		845.2.t.f.427.2		20
65.29	even	6		325.2.s.b.293.2		20
65.32	even	12		65.2.o.a.2.4	✓	20
65.37	even	12		845.2.o.f.357.2		20
65.42	odd	12		65.2.t.a.7.4	yes	20
65.47	even	4		845.2.k.d.577.6		20
65.57	even	4	inner	845.2.k.e.577.5		20
65.58	even	12		325.2.s.b.132.2		20
65.62	odd	12		845.2.t.g.657.2		20
195.32	odd	12		585.2.cf.a.262.2		20
195.107	even	12		585.2.dp.a.397.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	65.32	even	12
65.2.o.a.33.4	yes	20	13.3	even	3
65.2.t.a.7.4	yes	20	65.42	odd	12
65.2.t.a.28.4	yes	20	13.6	odd	12
325.2.s.b.132.2		20	65.58	even	12
325.2.s.b.293.2		20	65.29	even	6
325.2.x.b.7.2		20	65.3	odd	12
325.2.x.b.93.2		20	65.19	odd	12
585.2.cf.a.163.2		20	39.29	odd	6
585.2.cf.a.262.2		20	195.32	odd	12
585.2.dp.a.28.2		20	39.32	even	12
585.2.dp.a.397.2		20	195.107	even	12
845.2.f.d.408.5		20	13.8	odd	4
845.2.f.d.437.6		20	65.12	odd	4
845.2.f.e.408.6		20	13.5	odd	4
845.2.f.e.437.5		20	5.2	odd	4
845.2.k.d.268.6		20	13.12	even	2
845.2.k.d.577.6		20	65.47	even	4
845.2.k.e.268.5		20	1.1	even	1	trivial
845.2.k.e.577.5		20	65.57	even	4	inner
845.2.o.e.258.4		20	13.9	even	3
845.2.o.e.357.4		20	65.2	even	12
845.2.o.f.258.2		20	13.4	even	6
845.2.o.f.357.2		20	65.37	even	12
845.2.o.g.488.2		20	13.10	even	6
845.2.o.g.587.2		20	65.7	even	12
845.2.t.e.188.4		20	13.11	odd	12
845.2.t.e.427.4		20	65.17	odd	12
845.2.t.f.188.2		20	13.2	odd	12
845.2.t.f.427.2		20	65.22	odd	12
845.2.t.g.418.2		20	13.7	odd	12
845.2.t.g.657.2		20	65.62	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.274809 q^{2} +(1.67095 + 1.67095i) q^{3} -1.92448 q^{4} +(1.69883 + 1.45395i) q^{5} +(0.459191 + 0.459191i) q^{6} -0.386104i q^{7} -1.07848 q^{8} +2.58414i q^{9} +(0.466854 + 0.399558i) q^{10} +(-3.08375 + 3.08375i) q^{11} +(-3.21571 - 3.21571i) q^{12} -0.106105i q^{14} +(0.409188 + 5.26814i) q^{15} +3.55258 q^{16} +(1.39475 + 1.39475i) q^{17} +0.710144i q^{18} +(-3.54274 + 3.54274i) q^{19} +(-3.26937 - 2.79810i) q^{20} +(0.645159 - 0.645159i) q^{21} +(-0.847442 + 0.847442i) q^{22} +(0.235896 - 0.235896i) q^{23} +(-1.80209 - 1.80209i) q^{24} +(0.772064 + 4.94003i) q^{25} +(0.694880 - 0.694880i) q^{27} +0.743049i q^{28} +8.16410i q^{29} +(0.112448 + 1.44773i) q^{30} +(-2.54187 - 2.54187i) q^{31} +3.13324 q^{32} -10.3056 q^{33} +(0.383290 + 0.383290i) q^{34} +(0.561375 - 0.655925i) q^{35} -4.97313i q^{36} -4.82502i q^{37} +(-0.973575 + 0.973575i) q^{38} +(-1.83216 - 1.56806i) q^{40} +(-3.29253 - 3.29253i) q^{41} +(0.177295 - 0.177295i) q^{42} +(4.82129 - 4.82129i) q^{43} +(5.93462 - 5.93462i) q^{44} +(-3.75721 + 4.39002i) q^{45} +(0.0648264 - 0.0648264i) q^{46} +9.83310i q^{47} +(5.93619 + 5.93619i) q^{48} +6.85092 q^{49} +(0.212170 + 1.35756i) q^{50} +4.66112i q^{51} +(-7.17155 - 7.17155i) q^{53} +(0.190959 - 0.190959i) q^{54} +(-9.72240 + 0.755161i) q^{55} +0.416405i q^{56} -11.8395 q^{57} +2.24356i q^{58} +(1.71630 + 1.71630i) q^{59} +(-0.787474 - 10.1384i) q^{60} +10.6468 q^{61} +(-0.698529 - 0.698529i) q^{62} +0.997746 q^{63} -6.24413 q^{64} -2.83207 q^{66} -6.37591 q^{67} +(-2.68417 - 2.68417i) q^{68} +0.788342 q^{69} +(0.154271 - 0.180254i) q^{70} +(-3.07858 - 3.07858i) q^{71} -2.78695i q^{72} +6.08593 q^{73} -1.32596i q^{74} +(-6.96446 + 9.54462i) q^{75} +(6.81793 - 6.81793i) q^{76} +(1.19065 + 1.19065i) q^{77} +3.34944i q^{79} +(6.03525 + 5.16528i) q^{80} +10.0746 q^{81} +(-0.904815 - 0.904815i) q^{82} +5.18834i q^{83} +(-1.24160 + 1.24160i) q^{84} +(0.341552 + 4.39735i) q^{85} +(1.32493 - 1.32493i) q^{86} +(-13.6418 + 13.6418i) q^{87} +(3.32577 - 3.32577i) q^{88} +(3.53455 + 3.53455i) q^{89} +(-1.03251 + 1.20642i) q^{90} +(-0.453978 + 0.453978i) q^{92} -8.49469i q^{93} +2.70222i q^{94} +(-11.1695 + 0.867558i) q^{95} +(5.23549 + 5.23549i) q^{96} +14.7480 q^{97} +1.88269 q^{98} +(-7.96886 - 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Introduction

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