LMFDB - Embedded newform 765.2.k.b.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(361,765)] 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("765.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			361.1
Root			$-0.254679i$ of defining polynomial
Character	$\chi$	$=$	765.361
Dual form			765.2.k.b.676.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.51230i q^{2} -4.31167 q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.14187 + 1.14187i) q^{7} +5.80761i q^{8} +(1.77647 + 1.77647i) q^{10} +(2.32404 + 2.32404i) q^{11} +6.35524 q^{13} +(2.86872 - 2.86872i) q^{14} +5.96715 q^{16} +(0.768287 - 4.05089i) q^{17} -0.747167i q^{19} +(3.04881 - 3.04881i) q^{20} +(5.83869 - 5.83869i) q^{22} +(-0.101240 - 0.101240i) q^{23} -1.00000i q^{25} -15.9663i q^{26} +(-4.92337 - 4.92337i) q^{28} +(-6.22477 + 6.22477i) q^{29} +(5.10259 - 5.10259i) q^{31} -3.37606i q^{32} +(-10.1771 - 1.93017i) q^{34} -1.61485 q^{35} +(-0.439195 + 0.439195i) q^{37} -1.87711 q^{38} +(-4.10660 - 4.10660i) q^{40} +(4.49889 + 4.49889i) q^{41} +2.74801i q^{43} +(-10.0205 - 10.0205i) q^{44} +(-0.254346 + 0.254346i) q^{46} +11.9308 q^{47} -4.39226i q^{49} -2.51230 q^{50} -27.4017 q^{52} -2.71404i q^{53} -3.28669 q^{55} +(-6.63154 + 6.63154i) q^{56} +(15.6385 + 15.6385i) q^{58} -12.6815i q^{59} +(0.328162 + 0.328162i) q^{61} +(-12.8193 - 12.8193i) q^{62} +3.45261 q^{64} +(-4.49384 + 4.49384i) q^{65} +1.81686 q^{67} +(-3.31260 + 17.4661i) q^{68} +4.05699i q^{70} +(3.01043 - 3.01043i) q^{71} +(-0.856488 + 0.856488i) q^{73} +(1.10339 + 1.10339i) q^{74} +3.22154i q^{76} +5.30750i q^{77} +(-3.57000 - 3.57000i) q^{79} +(-4.21941 + 4.21941i) q^{80} +(11.3026 - 11.3026i) q^{82} +3.58494i q^{83} +(2.32115 + 3.40767i) q^{85} +6.90384 q^{86} +(-13.4971 + 13.4971i) q^{88} +10.5906 q^{89} +(7.25687 + 7.25687i) q^{91} +(0.436515 + 0.436515i) q^{92} -29.9739i q^{94} +(0.528327 + 0.528327i) q^{95} +(-4.92762 + 4.92762i) q^{97} -11.0347 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{10} + 4 q^{11} + 4 q^{14} + 4 q^{16} - 12 q^{17} + 8 q^{20} + 20 q^{22} - 12 q^{23} + 4 q^{28} + 12 q^{29} - 12 q^{34} - 16 q^{35} + 12 q^{37} - 24 q^{38} - 8 q^{40} + 24 q^{41} - 8 q^{44}+ \cdots - 44 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^10 + 4 * q^11 + 4 * q^14 + 4 * q^16 - 12 * q^17 + 8 * q^20 + 20 * q^22 - 12 * q^23 + 4 * q^28 + 12 * q^29 - 12 * q^34 - 16 * q^35 + 12 * q^37 - 24 * q^38 - 8 * q^40 + 24 * q^41 - 8 * q^44 - 24 * q^46 + 48 * q^47 - 4 * q^50 - 56 * q^52 - 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 + 28 * q^64 - 4 * q^65 - 8 * q^67 + 40 * q^68 - 28 * q^71 - 48 * q^73 - 28 * q^74 - 8 * q^79 - 16 * q^80 + 40 * q^82 - 4 * q^85 + 96 * q^86 - 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 + 8 * q^95 + 4 * q^97 - 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	2.51230i		−	1.77647i	−0.459392	−	0.888233i	$-0.651933\pi$
$2$		−	2.51230i		−	1.77647i	0.459392	−	0.888233i	$-0.348067\pi$
$3$		0			0
$3$		0			0
$4$	−4.31167			−2.15583
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	1.14187	+	1.14187i	0.431586	+	0.431586i	0.889168	−	0.457581i	$-0.151284\pi$
$7$	1.14187	+	1.14187i	0.431586	+	0.431586i	−0.457581	+	0.889168i	$0.651284\pi$
$8$			5.80761i			2.05330i
$9$		0			0
$10$	1.77647	+	1.77647i	0.561768	+	0.561768i
$11$	2.32404	+	2.32404i	0.700724	+	0.700724i	0.964566	−	0.263842i	$-0.0849897\pi$
$11$	2.32404	+	2.32404i	0.700724	+	0.700724i	−0.263842	+	0.964566i	$0.584990\pi$
$12$		0			0
$13$	6.35524			1.76263			0.881314	−	0.472531i	$-0.156660\pi$
$13$	6.35524			1.76263			0.881314	+	0.472531i	$0.156660\pi$
$14$	2.86872	−	2.86872i	0.766699	−	0.766699i
$15$		0			0
$16$	5.96715			1.49179
$17$	0.768287	−	4.05089i	0.186337	−	0.982486i
$17$	0.768287	−	4.05089i	0.186337	−	0.982486i
$18$		0			0
$19$		−	0.747167i		−	0.171412i	−0.996320	−	0.0857059i	$-0.972685\pi$
$19$		−	0.747167i		−	0.171412i	0.996320	−	0.0857059i	$-0.0273145\pi$
$20$	3.04881	−	3.04881i	0.681735	−	0.681735i
$21$		0			0
$22$	5.83869	−	5.83869i	1.24481	−	1.24481i
$23$	−0.101240	−	0.101240i	−0.0211101	−	0.0211101i	0.696473	−	0.717583i	$-0.254752\pi$
$23$	−0.101240	−	0.101240i	−0.0211101	−	0.0211101i	−0.717583	+	0.696473i	$0.754752\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		−	15.9663i		−	3.13125i
$27$		0			0
$28$	−4.92337	−	4.92337i	−0.930429	−	0.930429i
$29$	−6.22477	+	6.22477i	−1.15591	+	1.15591i	−0.170565	+	0.985346i	$0.554559\pi$
$29$	−6.22477	+	6.22477i	−1.15591	+	1.15591i	−0.985346	+	0.170565i	$0.945441\pi$
$30$		0			0
$31$	5.10259	−	5.10259i	0.916452	−	0.916452i	−0.0803174	−	0.996769i	$-0.525593\pi$
$31$	5.10259	−	5.10259i	0.916452	−	0.916452i	0.996769	+	0.0803174i	$0.0255934\pi$
$32$		−	3.37606i		−	0.596809i
$33$		0			0
$34$	−10.1771	−	1.93017i	−1.74535	−	0.331021i
$35$	−1.61485			−0.272959
$36$		0			0
$37$	−0.439195	+	0.439195i	−0.0722032	+	0.0722032i	−0.742286	−	0.670083i	$-0.766258\pi$
$37$	−0.439195	+	0.439195i	−0.0722032	+	0.0722032i	0.670083	+	0.742286i	$0.266258\pi$
$38$	−1.87711			−0.304507
$39$		0			0
$40$	−4.10660	−	4.10660i	−0.649311	−	0.649311i
$41$	4.49889	+	4.49889i	0.702609	+	0.702609i	0.964970	−	0.262361i	$-0.0845012\pi$
$41$	4.49889	+	4.49889i	0.702609	+	0.702609i	−0.262361	+	0.964970i	$0.584501\pi$
$42$		0			0
$43$			2.74801i			0.419068i	0.977801	+	0.209534i	$0.0671947\pi$
$43$			2.74801i			0.419068i	−0.977801	+	0.209534i	$0.932805\pi$
$44$	−10.0205	−	10.0205i	−1.51064	−	1.51064i
$45$		0			0
$46$	−0.254346	+	0.254346i	−0.0375013	+	0.0375013i
$47$	11.9308			1.74029			0.870146	−	0.492794i	$-0.164024\pi$
$47$	11.9308			1.74029			0.870146	+	0.492794i	$0.164024\pi$
$48$		0			0
$49$		−	4.39226i		−	0.627466i
$50$	−2.51230			−0.355293
$51$		0			0
$52$	−27.4017			−3.79993
$53$		−	2.71404i		−	0.372802i	−0.982474	−	0.186401i	$-0.940318\pi$
$53$		−	2.71404i		−	0.372802i	0.982474	−	0.186401i	$-0.0596823\pi$
$54$		0			0
$55$	−3.28669			−0.443177
$56$	−6.63154	+	6.63154i	−0.886177	+	0.886177i
$57$		0			0
$58$	15.6385	+	15.6385i	2.05344	+	2.05344i
$59$		−	12.6815i		−	1.65099i	−0.564413	−	0.825493i	$-0.690897\pi$
$59$		−	12.6815i		−	1.65099i	0.564413	−	0.825493i	$-0.309103\pi$
$60$		0			0
$61$	0.328162	+	0.328162i	0.0420168	+	0.0420168i	0.727803	−	0.685786i	$-0.240542\pi$
$61$	0.328162	+	0.328162i	0.0420168	+	0.0420168i	−0.685786	+	0.727803i	$0.740542\pi$
$62$	−12.8193	−	12.8193i	−1.62805	−	1.62805i
$63$		0			0
$64$	3.45261			0.431576
$65$	−4.49384	+	4.49384i	−0.557392	+	0.557392i
$66$		0			0
$67$	1.81686			0.221965			0.110982	−	0.993822i	$-0.464600\pi$
$67$	1.81686			0.221965			0.110982	+	0.993822i	$0.464600\pi$
$68$	−3.31260	+	17.4661i	−0.401712	+	2.11808i
$69$		0			0
$70$			4.05699i			0.484903i
$71$	3.01043	−	3.01043i	0.357272	−	0.357272i	−0.505535	−	0.862806i	$-0.668705\pi$
$71$	3.01043	−	3.01043i	0.357272	−	0.357272i	0.862806	+	0.505535i	$0.168705\pi$
$72$		0			0
$73$	−0.856488	+	0.856488i	−0.100244	+	0.100244i	−0.755450	−	0.655206i	$-0.772582\pi$
$73$	−0.856488	+	0.856488i	−0.100244	+	0.100244i	0.655206	+	0.755450i	$0.272582\pi$
$74$	1.10339	+	1.10339i	0.128267	+	0.128267i
$75$		0			0
$76$			3.22154i			0.369535i
$77$			5.30750i			0.604846i
$78$		0			0
$79$	−3.57000	−	3.57000i	−0.401656	−	0.401656i	0.477160	−	0.878816i	$-0.341666\pi$
$79$	−3.57000	−	3.57000i	−0.401656	−	0.401656i	−0.878816	+	0.477160i	$0.841666\pi$
$80$	−4.21941	+	4.21941i	−0.471744	+	0.471744i
$81$		0			0
$82$	11.3026	−	11.3026i	1.24816	−	1.24816i
$83$			3.58494i			0.393498i	0.980454	+	0.196749i	$0.0630385\pi$
$83$			3.58494i			0.393498i	−0.980454	+	0.196749i	$0.936962\pi$
$84$		0			0
$85$	2.32115	+	3.40767i	0.251764	+	0.369614i
$86$	6.90384			0.744460
$87$		0			0
$88$	−13.4971	+	13.4971i	−1.43880	+	1.43880i
$89$	10.5906			1.12260			0.561300	−	0.827613i	$-0.310302\pi$
$89$	10.5906			1.12260			0.561300	+	0.827613i	$0.310302\pi$
$90$		0			0
$91$	7.25687	+	7.25687i	0.760726	+	0.760726i
$92$	0.436515	+	0.436515i	0.0455098	+	0.0455098i
$93$		0			0
$94$		−	29.9739i		−	3.09157i
$95$	0.528327	+	0.528327i	0.0542052	+	0.0542052i
$96$		0			0
$97$	−4.92762	+	4.92762i	−0.500324	+	0.500324i	−0.911539	−	0.411215i	$-0.865105\pi$
$97$	−4.92762	+	4.92762i	−0.500324	+	0.500324i	0.411215	+	0.911539i	$0.365105\pi$
$98$	−11.0347			−1.11467
$99$		0			0
$100$			4.31167i			0.431167i
$101$	0.679421			0.0676049			0.0338025	−	0.999429i	$-0.489238\pi$
$101$	0.679421			0.0676049			0.0338025	+	0.999429i	$0.489238\pi$
$102$		0			0
$103$	−0.156455			−0.0154160			−0.00770798	−	0.999970i	$-0.502454\pi$
$103$	−0.156455			−0.0154160			−0.00770798	+	0.999970i	$0.502454\pi$
$104$			36.9088i			3.61921i
$105$		0			0
$106$	−6.81849			−0.662270
$107$	−12.7033	+	12.7033i	−1.22807	+	1.22807i	−0.263382	+	0.964692i	$0.584838\pi$
$107$	−12.7033	+	12.7033i	−1.22807	+	1.22807i	−0.964692	+	0.263382i	$0.915162\pi$
$108$		0			0
$109$	4.10981	+	4.10981i	0.393649	+	0.393649i	0.875986	−	0.482337i	$-0.160212\pi$
$109$	4.10981	+	4.10981i	0.393649	+	0.393649i	−0.482337	+	0.875986i	$0.660212\pi$
$110$			8.25715i			0.787289i
$111$		0			0
$112$	6.81371	+	6.81371i	0.643835	+	0.643835i
$113$	6.57408	+	6.57408i	0.618438	+	0.618438i	0.945131	−	0.326693i	$-0.105934\pi$
$113$	6.57408	+	6.57408i	0.618438	+	0.618438i	−0.326693	+	0.945131i	$0.605934\pi$
$114$		0			0
$115$	0.143175			0.0133512
$116$	26.8392	−	26.8392i	2.49195	−	2.49195i
$117$		0			0
$118$	−31.8597			−2.93292
$119$	5.50288	−	3.74831i	0.504448	−	0.343607i
$120$		0			0
$121$		−	0.197689i		−	0.0179717i
$122$	0.824442	−	0.824442i	0.0746414	−	0.0746414i
$123$		0			0
$124$	−22.0007	+	22.0007i	−1.97572	+	1.97572i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$			15.1796i			1.34698i	0.739198	+	0.673488i	$0.235205\pi$
$127$			15.1796i			1.34698i	−0.739198	+	0.673488i	$0.764795\pi$
$128$		−	15.4261i		−	1.36349i
$129$		0			0
$130$	11.2899	+	11.2899i	0.990188	+	0.990188i
$131$	−1.40184	+	1.40184i	−0.122480	+	0.122480i	−0.765690	−	0.643210i	$-0.777602\pi$
$131$	−1.40184	+	1.40184i	−0.122480	+	0.122480i	0.643210	+	0.765690i	$0.277602\pi$
$132$		0			0
$133$	0.853168	−	0.853168i	0.0739790	−	0.0739790i
$134$		−	4.56450i		−	0.394313i
$135$		0			0
$136$	23.5260	+	4.46191i	2.01734	+	0.382606i
$137$	−19.6088			−1.67530			−0.837648	−	0.546211i	$-0.816070\pi$
$137$	−19.6088			−1.67530			−0.837648	+	0.546211i	$0.816070\pi$
$138$		0			0
$139$	−2.55364	+	2.55364i	−0.216597	+	0.216597i	−0.807063	−	0.590466i	$-0.798944\pi$
$139$	−2.55364	+	2.55364i	−0.216597	+	0.216597i	0.590466	+	0.807063i	$0.298944\pi$
$140$	6.96269			0.588455
$141$		0			0
$142$	−7.56310	−	7.56310i	−0.634681	−	0.634681i
$143$	14.7698	+	14.7698i	1.23512	+	1.23512i
$144$		0			0
$145$		−	8.80316i		−	0.731062i
$146$	2.15176	+	2.15176i	0.178081	+	0.178081i
$147$		0			0
$148$	1.89366	−	1.89366i	0.155658	−	0.155658i
$149$	1.26402			0.103553			0.0517763	−	0.998659i	$-0.483512\pi$
$149$	1.26402			0.103553			0.0517763	+	0.998659i	$0.483512\pi$
$150$		0			0
$151$		−	16.2206i		−	1.32002i	−0.751258	−	0.660009i	$-0.770553\pi$
$151$		−	16.2206i		−	1.32002i	0.751258	−	0.660009i	$-0.229447\pi$
$152$	4.33926			0.351960
$153$		0			0
$154$	13.3341			1.07449
$155$			7.21615i			0.579615i
$156$		0			0
$157$	−8.52619			−0.680464			−0.340232	−	0.940341i	$-0.610506\pi$
$157$	−8.52619			−0.680464			−0.340232	+	0.940341i	$0.610506\pi$
$158$	−8.96892	+	8.96892i	−0.713529	+	0.713529i
$159$		0			0
$160$	2.38723	+	2.38723i	0.188727	+	0.188727i
$161$		−	0.231207i		−	0.0182216i
$162$		0			0
$163$	−10.9321	−	10.9321i	−0.856267	−	0.856267i	0.134629	−	0.990896i	$-0.457016\pi$
$163$	−10.9321	−	10.9321i	−0.856267	−	0.856267i	−0.990896	+	0.134629i	$0.957016\pi$
$164$	−19.3977	−	19.3977i	−1.51471	−	1.51471i
$165$		0			0
$166$	9.00646			0.699037
$167$	2.59558	−	2.59558i	0.200852	−	0.200852i	−0.599513	−	0.800365i	$-0.704639\pi$
$167$	2.59558	−	2.59558i	0.200852	−	0.200852i	0.800365	+	0.599513i	$0.204639\pi$
$168$		0			0
$169$	27.3891			2.10686
$170$	8.56111	−	5.83144i	0.656607	−	0.447251i
$171$		0			0
$172$		−	11.8485i		−	0.903441i
$173$	6.46394	−	6.46394i	0.491444	−	0.491444i	−0.417317	−	0.908761i	$-0.637030\pi$
$173$	6.46394	−	6.46394i	0.491444	−	0.491444i	0.908761	+	0.417317i	$0.137030\pi$
$174$		0			0
$175$	1.14187	−	1.14187i	0.0863173	−	0.0863173i
$176$	13.8679	+	13.8679i	1.04533	+	1.04533i
$177$		0			0
$178$		−	26.6067i		−	1.99426i
$179$		−	8.76138i		−	0.654857i	−0.944876	−	0.327428i	$-0.893818\pi$
$179$		−	8.76138i		−	0.654857i	0.944876	−	0.327428i	$-0.106182\pi$
$180$		0			0
$181$	3.44161	+	3.44161i	0.255813	+	0.255813i	0.823349	−	0.567536i	$-0.192103\pi$
$181$	3.44161	+	3.44161i	0.255813	+	0.255813i	−0.567536	+	0.823349i	$0.692103\pi$
$182$	18.2314	−	18.2314i	1.35140	−	1.35140i
$183$		0			0
$184$	0.587964	−	0.587964i	0.0433453	−	0.0433453i
$185$		−	0.621115i		−	0.0456653i
$186$		0			0
$187$	11.2000	−	7.62890i	0.819022	−	0.557881i
$188$	−51.4418			−3.75178
$189$		0			0
$190$	1.32732	−	1.32732i	0.0962937	−	0.0962937i
$191$	−11.2751			−0.815838			−0.407919	−	0.913018i	$-0.633745\pi$
$191$	−11.2751			−0.815838			−0.407919	+	0.913018i	$0.633745\pi$
$192$		0			0
$193$	3.23976	+	3.23976i	0.233203	+	0.233203i	0.814028	−	0.580825i	$-0.197270\pi$
$193$	3.23976	+	3.23976i	0.233203	+	0.233203i	−0.580825	+	0.814028i	$0.697270\pi$
$194$	12.3797	+	12.3797i	0.888809	+	0.888809i
$195$		0			0
$196$			18.9380i			1.35271i
$197$	9.36781	+	9.36781i	0.667429	+	0.667429i	0.957120	−	0.289691i	$-0.0935526\pi$
$197$	9.36781	+	9.36781i	0.667429	+	0.667429i	−0.289691	+	0.957120i	$0.593553\pi$
$198$		0			0
$199$	−1.86562	+	1.86562i	−0.132251	+	0.132251i	−0.770133	−	0.637883i	$-0.779810\pi$
$199$	−1.86562	+	1.86562i	−0.132251	+	0.132251i	0.637883	+	0.770133i	$0.279810\pi$
$200$	5.80761			0.410660
$201$		0			0
$202$		−	1.70691i		−	0.120098i
$203$	−14.2158			−0.997751
$204$		0			0
$205$	−6.36239			−0.444369
$206$			0.393062i			0.0273860i
$207$		0			0
$208$	37.9227			2.62946
$209$	1.73644	−	1.73644i	0.120112	−	0.120112i
$210$		0			0
$211$	5.04513	+	5.04513i	0.347321	+	0.347321i	0.859111	−	0.511790i	$-0.171017\pi$
$211$	5.04513	+	5.04513i	0.347321	+	0.347321i	−0.511790	+	0.859111i	$0.671017\pi$
$212$			11.7020i			0.803699i
$213$		0			0
$214$	31.9145	+	31.9145i	2.18163	+	2.18163i
$215$	−1.94314	−	1.94314i	−0.132521	−	0.132521i
$216$		0			0
$217$	11.6530			0.791057
$218$	10.3251	−	10.3251i	0.699304	−	0.699304i
$219$		0			0
$220$	14.1711			0.955416
$221$	4.88265	−	25.7444i	0.328443	−	1.73176i
$222$		0			0
$223$			12.1709i			0.815025i	0.913200	+	0.407512i	$0.133604\pi$
$223$			12.1709i			0.815025i	−0.913200	+	0.407512i	$0.866396\pi$
$224$	3.85502	−	3.85502i	0.257575	−	0.257575i
$225$		0			0
$226$	16.5161	−	16.5161i	1.09863	−	1.09863i
$227$	0.590883	+	0.590883i	0.0392183	+	0.0392183i	0.726444	−	0.687226i	$-0.241172\pi$
$227$	0.590883	+	0.590883i	0.0392183	+	0.0392183i	−0.687226	+	0.726444i	$0.741172\pi$
$228$		0			0
$229$		−	6.13420i		−	0.405360i	−0.979245	−	0.202680i	$-0.935035\pi$
$229$		−	6.13420i		−	0.405360i	0.979245	−	0.202680i	$-0.0649651\pi$
$230$		−	0.359700i		−	0.0237179i
$231$		0			0
$232$	−36.1511	−	36.1511i	−2.37343	−	2.37343i
$233$	11.9056	−	11.9056i	0.779962	−	0.779962i	−0.199862	−	0.979824i	$-0.564049\pi$
$233$	11.9056	−	11.9056i	0.779962	−	0.779962i	0.979824	+	0.199862i	$0.0640494\pi$
$234$		0			0
$235$	−8.43638	+	8.43638i	−0.550329	+	0.550329i
$236$			54.6783i			3.55925i
$237$		0			0
$238$	−9.41689	−	13.8249i	−0.610407	−	0.896135i
$239$	−6.95301			−0.449753			−0.224876	−	0.974387i	$-0.572198\pi$
$239$	−6.95301			−0.449753			−0.224876	+	0.974387i	$0.572198\pi$
$240$		0			0
$241$	−21.7234	+	21.7234i	−1.39933	+	1.39933i	−0.597335	+	0.801992i	$0.703774\pi$
$241$	−21.7234	+	21.7234i	−1.39933	+	1.39933i	−0.801992	+	0.597335i	$0.796226\pi$
$242$	−0.496655			−0.0319262
$243$		0			0
$244$	−1.41492	−	1.41492i	−0.0905812	−	0.0905812i
$245$	3.10580	+	3.10580i	0.198422	+	0.198422i
$246$		0			0
$247$		−	4.74843i		−	0.302135i
$248$	29.6339	+	29.6339i	1.88175	+	1.88175i
$249$		0			0
$250$	1.77647	−	1.77647i	0.112354	−	0.112354i
$251$	−22.5294			−1.42204			−0.711021	−	0.703171i	$-0.751767\pi$
$251$	−22.5294			−1.42204			−0.711021	+	0.703171i	$0.751767\pi$
$252$		0			0
$253$		−	0.470573i		−	0.0295846i
$254$	38.1359			2.39286
$255$		0			0
$256$	−31.8499			−1.99062
$257$			1.90476i			0.118816i	0.998234	+	0.0594079i	$0.0189212\pi$
$257$			1.90476i			0.118816i	−0.998234	+	0.0594079i	$0.981079\pi$
$258$		0			0
$259$	−1.00301			−0.0623238
$260$	19.3759	−	19.3759i	1.20164	−	1.20164i
$261$		0			0
$262$	3.52186	+	3.52186i	0.217581	+	0.217581i
$263$			7.80192i			0.481087i	0.970638	+	0.240543i	$0.0773256\pi$
$263$			7.80192i			0.481087i	−0.970638	+	0.240543i	$0.922674\pi$
$264$		0			0
$265$	1.91912	+	1.91912i	0.117890	+	0.117890i
$266$	−2.14342	−	2.14342i	−0.131421	−	0.131421i
$267$		0			0
$268$	−7.83369			−0.478519
$269$	−9.71848	+	9.71848i	−0.592546	+	0.592546i	−0.938318	−	0.345772i	$-0.887617\pi$
$269$	−9.71848	+	9.71848i	−0.592546	+	0.592546i	0.345772	+	0.938318i	$0.387617\pi$
$270$		0			0
$271$	−12.4855			−0.758438			−0.379219	−	0.925307i	$-0.623807\pi$
$271$	−12.4855			−0.758438			−0.379219	+	0.925307i	$0.623807\pi$
$272$	4.58448	−	24.1723i	0.277975	−	1.46566i
$273$		0			0
$274$			49.2633i			2.97611i
$275$	2.32404	−	2.32404i	0.140145	−	0.140145i
$276$		0			0
$277$	−18.9930	+	18.9930i	−1.14118	+	1.14118i	−0.152944	+	0.988235i	$0.548875\pi$
$277$	−18.9930	+	18.9930i	−1.14118	+	1.14118i	−0.988235	+	0.152944i	$0.951125\pi$
$278$	6.41552	+	6.41552i	0.384777	+	0.384777i
$279$		0			0
$280$		−	9.37841i		−	0.560467i
$281$			15.5290i			0.926385i	0.886258	+	0.463193i	$0.153296\pi$
$281$			15.5290i			0.926385i	−0.886258	+	0.463193i	$0.846704\pi$
$282$		0			0
$283$	−7.38186	−	7.38186i	−0.438806	−	0.438806i	0.452804	−	0.891610i	$-0.350424\pi$
$283$	−7.38186	−	7.38186i	−0.438806	−	0.438806i	−0.891610	+	0.452804i	$0.850424\pi$
$284$	−12.9800	+	12.9800i	−0.770219	+	0.770219i
$285$		0			0
$286$	37.1063	−	37.1063i	2.19414	−	2.19414i
$287$			10.2743i			0.606473i
$288$		0			0
$289$	−15.8195	−	6.22450i	−0.930557	−	0.366147i
$290$	−22.1162			−1.29871
$291$		0			0
$292$	3.69289	−	3.69289i	0.216110	−	0.216110i
$293$	−7.10645			−0.415163			−0.207581	−	0.978218i	$-0.566559\pi$
$293$	−7.10645			−0.415163			−0.207581	+	0.978218i	$0.566559\pi$
$294$		0			0
$295$	8.96715	+	8.96715i	0.522087	+	0.522087i
$296$	−2.55067	−	2.55067i	−0.148255	−	0.148255i
$297$		0			0
$298$		−	3.17560i		−	0.183958i
$299$	−0.643407	−	0.643407i	−0.0372092	−	0.0372092i
$300$		0			0
$301$	−3.13787	+	3.13787i	−0.180864	+	0.180864i
$302$	−40.7512			−2.34497
$303$		0			0
$304$		−	4.45845i		−	0.255710i
$305$	−0.464091			−0.0265738
$306$		0			0
$307$	4.80512			0.274243			0.137121	−	0.990554i	$-0.456215\pi$
$307$	4.80512			0.274243			0.137121	+	0.990554i	$0.456215\pi$
$308$		−	22.8842i		−	1.30395i
$309$		0			0
$310$	18.1292			1.02967
$311$	5.67759	−	5.67759i	0.321947	−	0.321947i	−0.527567	−	0.849514i	$-0.676896\pi$
$311$	5.67759	−	5.67759i	0.321947	−	0.321947i	0.849514	+	0.527567i	$0.176896\pi$
$312$		0			0
$313$	15.6285	+	15.6285i	0.883374	+	0.883374i	0.993876	−	0.110502i	$-0.0352458\pi$
$313$	15.6285	+	15.6285i	0.883374	+	0.883374i	−0.110502	+	0.993876i	$0.535246\pi$
$314$			21.4204i			1.20882i
$315$		0			0
$316$	15.3927	+	15.3927i	0.865905	+	0.865905i
$317$	11.2888	+	11.2888i	0.634041	+	0.634041i	0.949079	−	0.315038i	$-0.102017\pi$
$317$	11.2888	+	11.2888i	0.634041	+	0.634041i	−0.315038	+	0.949079i	$0.602017\pi$
$318$		0			0
$319$	−28.9332			−1.61995
$320$	−2.44136	+	2.44136i	−0.136476	+	0.136476i
$321$		0			0
$322$	−0.580861			−0.0323701
$323$	−3.02669	−	0.574039i	−0.168410	−	0.0319404i
$324$		0			0
$325$		−	6.35524i		−	0.352526i
$326$	−27.4647	+	27.4647i	−1.52113	+	1.52113i
$327$		0			0
$328$	−26.1278	+	26.1278i	−1.44267	+	1.44267i
$329$	13.6235	+	13.6235i	0.751086	+	0.751086i
$330$		0			0
$331$		−	3.87911i		−	0.213215i	−0.994301	−	0.106608i	$-0.966001\pi$
$331$		−	3.87911i		−	0.213215i	0.994301	−	0.106608i	$-0.0339989\pi$
$332$		−	15.4571i		−	0.848317i
$333$		0			0
$334$	−6.52088	−	6.52088i	−0.356807	−	0.356807i
$335$	−1.28471	+	1.28471i	−0.0701914	+	0.0701914i
$336$		0			0
$337$	−17.2431	+	17.2431i	−0.939290	+	0.939290i	−0.998260	−	0.0589698i	$-0.981218\pi$
$337$	−17.2431	+	17.2431i	−0.939290	+	0.939290i	0.0589698	+	0.998260i	$0.481218\pi$
$338$		−	68.8098i		−	3.74276i
$339$		0			0
$340$	−10.0080	−	14.6928i	−0.542762	−	0.796827i
$341$	23.7172			1.28436
$342$		0			0
$343$	13.0085	−	13.0085i	0.702392	−	0.702392i
$344$	−15.9594			−0.860473
$345$		0			0
$346$	−16.2394	−	16.2394i	−0.873034	−	0.873034i
$347$	−7.51698	−	7.51698i	−0.403532	−	0.403532i	0.475943	−	0.879476i	$-0.342107\pi$
$347$	−7.51698	−	7.51698i	−0.403532	−	0.403532i	−0.879476	+	0.475943i	$0.842107\pi$
$348$		0			0
$349$		−	11.5579i		−	0.618682i	−0.950951	−	0.309341i	$-0.899892\pi$
$349$		−	11.5579i		−	0.618682i	0.950951	−	0.309341i	$-0.100108\pi$
$350$	−2.86872	−	2.86872i	−0.153340	−	0.153340i
$351$		0			0
$352$	7.84609	−	7.84609i	0.418198	−	0.418198i
$353$	11.3682			0.605070			0.302535	−	0.953138i	$-0.402167\pi$
$353$	11.3682			0.605070			0.302535	+	0.953138i	$0.402167\pi$
$354$		0			0
$355$			4.25738i			0.225958i
$356$	−45.6631			−2.42014
$357$		0			0
$358$	−22.0113			−1.16333
$359$		−	32.1310i		−	1.69581i	−0.530147	−	0.847906i	$-0.677863\pi$
$359$		−	32.1310i		−	1.69581i	0.530147	−	0.847906i	$-0.322137\pi$
$360$		0			0
$361$	18.4417			0.970618
$362$	8.64637	−	8.64637i	0.454443	−	0.454443i
$363$		0			0
$364$	−31.2892	−	31.2892i	−1.64000	−	1.64000i
$365$		−	1.21126i		−	0.0634001i
$366$		0			0
$367$	−13.6155	−	13.6155i	−0.710723	−	0.710723i	0.255964	−	0.966686i	$-0.417607\pi$
$367$	−13.6155	−	13.6155i	−0.710723	−	0.710723i	−0.966686	+	0.255964i	$0.917607\pi$
$368$	−0.604116	−	0.604116i	−0.0314917	−	0.0314917i
$369$		0			0
$370$	−1.56043			−0.0811229
$371$	3.09908	−	3.09908i	0.160896	−	0.160896i
$372$		0			0
$373$	−20.3136			−1.05180			−0.525900	−	0.850547i	$-0.676271\pi$
$373$	−20.3136			−1.05180			−0.525900	+	0.850547i	$0.676271\pi$
$374$	−19.1661	−	28.1377i	−0.991056	−	1.45497i
$375$		0			0
$376$			69.2897i			3.57334i
$377$	−39.5599	+	39.5599i	−2.03744	+	2.03744i
$378$		0			0
$379$	24.2540	−	24.2540i	1.24585	−	1.24585i	0.288308	−	0.957538i	$-0.406907\pi$
$379$	24.2540	−	24.2540i	1.24585	−	1.24585i	0.957538	−	0.288308i	$-0.0930928\pi$
$380$	−2.27797	−	2.27797i	−0.116857	−	0.116857i
$381$		0			0
$382$			28.3265i			1.44931i
$383$		−	21.3225i		−	1.08953i	−0.838589	−	0.544764i	$-0.816619\pi$
$383$		−	21.3225i		−	1.08953i	0.838589	−	0.544764i	$-0.183381\pi$
$384$		0			0
$385$	−3.75297	−	3.75297i	−0.191269	−	0.191269i
$386$	8.13925	−	8.13925i	0.414277	−	0.414277i
$387$		0			0
$388$	21.2463	−	21.2463i	1.07862	−	1.07862i
$389$			11.7682i			0.596672i	0.954461	+	0.298336i	$0.0964316\pi$
$389$			11.7682i			0.596672i	−0.954461	+	0.298336i	$0.903568\pi$
$390$		0			0
$391$	−0.487895	+	0.332332i	−0.0246739	+	0.0168067i
$392$	25.5086			1.28838
$393$		0			0
$394$	23.5348	−	23.5348i	1.18567	−	1.18567i
$395$	5.04874			0.254030
$396$		0			0
$397$	2.37514	+	2.37514i	0.119205	+	0.119205i	0.764193	−	0.644988i	$-0.223138\pi$
$397$	2.37514	+	2.37514i	0.119205	+	0.119205i	−0.644988	+	0.764193i	$0.723138\pi$
$398$	4.68701	+	4.68701i	0.234939	+	0.234939i
$399$		0			0
$400$		−	5.96715i		−	0.298357i
$401$	1.83450	+	1.83450i	0.0916105	+	0.0916105i	0.751427	−	0.659816i	$-0.229366\pi$
$401$	1.83450	+	1.83450i	0.0916105	+	0.0916105i	−0.659816	+	0.751427i	$0.729366\pi$
$402$		0			0
$403$	32.4282	−	32.4282i	1.61536	−	1.61536i
$404$	−2.92944			−0.145745
$405$		0			0
$406$			35.7143i			1.77247i
$407$	−2.04141			−0.101189
$408$		0			0
$409$	−30.8364			−1.52476			−0.762381	−	0.647129i	$-0.775970\pi$
$409$	−30.8364			−1.52476			−0.762381	+	0.647129i	$0.775970\pi$
$410$			15.9843i			0.789406i
$411$		0			0
$412$	0.674582			0.0332343
$413$	14.4806	−	14.4806i	0.712543	−	0.712543i
$414$		0			0
$415$	−2.53494	−	2.53494i	−0.124435	−	0.124435i
$416$		−	21.4557i		−	1.05195i
$417$		0			0
$418$	−4.36248	−	4.36248i	−0.213376	−	0.213376i
$419$	−13.1997	−	13.1997i	−0.644849	−	0.644849i	0.306894	−	0.951744i	$-0.400710\pi$
$419$	−13.1997	−	13.1997i	−0.644849	−	0.644849i	−0.951744	+	0.306894i	$0.900710\pi$
$420$		0			0
$421$	−29.5695			−1.44113			−0.720565	−	0.693388i	$-0.756117\pi$
$421$	−29.5695			−1.44113			−0.720565	+	0.693388i	$0.756117\pi$
$422$	12.6749	−	12.6749i	0.617004	−	0.617004i
$423$		0			0
$424$	15.7621			0.765475
$425$	−4.05089	−	0.768287i	−0.196497	−	0.0372674i
$426$		0			0
$427$			0.749436i			0.0362678i
$428$	54.7724	−	54.7724i	2.64752	−	2.64752i
$429$		0			0
$430$	−4.88175	+	4.88175i	−0.235419	+	0.235419i
$431$	−11.5583	−	11.5583i	−0.556744	−	0.556744i	0.371635	−	0.928379i	$-0.378797\pi$
$431$	−11.5583	−	11.5583i	−0.556744	−	0.556744i	−0.928379	+	0.371635i	$0.878797\pi$
$432$		0			0
$433$			14.3256i			0.688446i	0.938888	+	0.344223i	$0.111858\pi$
$433$			14.3256i			0.688446i	−0.938888	+	0.344223i	$0.888142\pi$
$434$		−	29.2758i		−	1.40529i
$435$		0			0
$436$	−17.7202	−	17.7202i	−0.848641	−	0.848641i
$437$	−0.0756434	+	0.0756434i	−0.00361851	+	0.00361851i
$438$		0			0
$439$	−21.5167	+	21.5167i	−1.02694	+	1.02694i	−0.0273099	+	0.999627i	$0.508694\pi$
$439$	−21.5167	+	21.5167i	−1.02694	+	1.02694i	−0.999627	+	0.0273099i	$0.991306\pi$
$440$		−	19.0878i		−	0.909975i
$441$		0			0
$442$	−64.6778	−	12.2667i	−3.07641	−	0.583468i
$443$	−26.5036			−1.25922			−0.629612	−	0.776909i	$-0.716786\pi$
$443$	−26.5036			−1.25922			−0.629612	+	0.776909i	$0.716786\pi$
$444$		0			0
$445$	−7.48867	+	7.48867i	−0.354997	+	0.354997i
$446$	30.5770			1.44786
$447$		0			0
$448$	3.94243	+	3.94243i	0.186262	+	0.186262i
$449$	−11.1999	−	11.1999i	−0.528556	−	0.528556i	0.391585	−	0.920142i	$-0.371927\pi$
$449$	−11.1999	−	11.1999i	−0.528556	−	0.528556i	−0.920142	+	0.391585i	$0.871927\pi$
$450$		0			0
$451$			20.9112i			0.984669i
$452$	−28.3453	−	28.3453i	−1.33325	−	1.33325i
$453$		0			0
$454$	1.48448	−	1.48448i	0.0696700	−	0.0696700i
$455$	−10.2628			−0.481126
$456$		0			0
$457$		−	4.25348i		−	0.198969i	−0.995039	−	0.0994847i	$-0.968281\pi$
$457$		−	4.25348i		−	0.198969i	0.995039	−	0.0994847i	$-0.0317194\pi$
$458$	−15.4110			−0.720108
$459$		0			0
$460$	−0.617325			−0.0287829
$461$			23.9740i			1.11658i	0.829646	+	0.558290i	$0.188542\pi$
$461$			23.9740i			1.11658i	−0.829646	+	0.558290i	$0.811458\pi$
$462$		0			0
$463$	23.0127			1.06949			0.534746	−	0.845013i	$-0.320407\pi$
$463$	23.0127			1.06949			0.534746	+	0.845013i	$0.320407\pi$
$464$	−37.1441	+	37.1441i	−1.72437	+	1.72437i
$465$		0			0
$466$	−29.9105	−	29.9105i	−1.38558	−	1.38558i
$467$			21.7845i			1.00807i	0.863684	+	0.504033i	$0.168151\pi$
$467$			21.7845i			1.00807i	−0.863684	+	0.504033i	$0.831849\pi$
$468$		0			0
$469$	2.07462	+	2.07462i	0.0957969	+	0.0957969i
$470$	21.1947	+	21.1947i	0.977640	+	0.977640i
$471$		0			0
$472$	73.6490			3.38997
$473$	−6.38649	+	6.38649i	−0.293651	+	0.293651i
$474$		0			0
$475$	−0.747167			−0.0342824
$476$	−23.7266	+	16.1615i	−1.08751	+	0.740760i
$477$		0			0
$478$			17.4681i			0.798971i
$479$	23.2853	−	23.2853i	1.06393	−	1.06393i	0.0661200	−	0.997812i	$-0.478938\pi$
$479$	23.2853	−	23.2853i	1.06393	−	1.06393i	0.997812	−	0.0661200i	$-0.0210620\pi$
$480$		0			0
$481$	−2.79119	+	2.79119i	−0.127267	+	0.127267i
$482$	54.5758	+	54.5758i	2.48586	+	2.48586i
$483$		0			0
$484$			0.852369i			0.0387441i
$485$		−	6.96870i		−	0.316433i
$486$		0			0
$487$	−13.1864	−	13.1864i	−0.597535	−	0.597535i	0.342121	−	0.939656i	$-0.388855\pi$
$487$	−13.1864	−	13.1864i	−0.597535	−	0.597535i	−0.939656	+	0.342121i	$0.888855\pi$
$488$	−1.90584	+	1.90584i	−0.0862731	+	0.0862731i
$489$		0			0
$490$	7.80271	−	7.80271i	0.352491	−	0.352491i
$491$			3.97306i			0.179302i	0.995973	+	0.0896508i	$0.0285751\pi$
$491$			3.97306i			0.179302i	−0.995973	+	0.0896508i	$0.971425\pi$
$492$		0			0
$493$	20.4335	+	29.9983i	0.920277	+	1.35106i
$494$	−11.9295			−0.536733
$495$		0			0
$496$	30.4479	−	30.4479i	1.36715	−	1.36715i
$497$	6.87503			0.308387
$498$		0			0
$499$	−24.1326	−	24.1326i	−1.08032	−	1.08032i	−0.996479	−	0.0838426i	$-0.973281\pi$
$499$	−24.1326	−	24.1326i	−1.08032	−	1.08032i	−0.0838426	−	0.996479i	$-0.526719\pi$
$500$	−3.04881	−	3.04881i	−0.136347	−	0.136347i
$501$		0			0
$502$			56.6007i			2.52621i
$503$	−27.8677	−	27.8677i	−1.24256	−	1.24256i	−0.958935	−	0.283626i	$-0.908463\pi$
$503$	−27.8677	−	27.8677i	−1.24256	−	1.24256i	−0.283626	−	0.958935i	$-0.591537\pi$
$504$		0			0
$505$	−0.480423	+	0.480423i	−0.0213785	+	0.0213785i
$506$	−1.18222			−0.0525561
$507$		0			0
$508$		−	65.4496i		−	2.90386i
$509$	−8.87274			−0.393277			−0.196639	−	0.980476i	$-0.563003\pi$
$509$	−8.87274			−0.393277			−0.196639	+	0.980476i	$0.563003\pi$
$510$		0			0
$511$	−1.95600			−0.0865282
$512$			49.1643i			2.17278i
$513$		0			0
$514$	4.78534			0.211072
$515$	0.110630	−	0.110630i	0.00487496	−	0.00487496i
$516$		0			0
$517$	27.7277	+	27.7277i	1.21946	+	1.21946i
$518$			2.51986i			0.110716i
$519$		0			0
$520$	−26.0985	−	26.0985i	−1.14449	−	1.14449i
$521$	−12.4387	−	12.4387i	−0.544948	−	0.544948i	0.380027	−	0.924975i	$-0.375915\pi$
$521$	−12.4387	−	12.4387i	−0.544948	−	0.544948i	−0.924975	+	0.380027i	$0.875915\pi$
$522$		0			0
$523$	−20.1681			−0.881892			−0.440946	−	0.897534i	$-0.645357\pi$
$523$	−20.1681			−0.881892			−0.440946	+	0.897534i	$0.645357\pi$
$524$	6.04428	−	6.04428i	0.264046	−	0.264046i
$525$		0			0
$526$	19.6008			0.854635
$527$	−16.7498	−	24.5903i	−0.729632	−	1.07117i
$528$		0			0
$529$		−	22.9795i		−	0.999109i
$530$	4.82140	−	4.82140i	0.209428	−	0.209428i
$531$		0			0
$532$	−3.67858	+	3.67858i	−0.159487	+	0.159487i
$533$	28.5915	+	28.5915i	1.23844	+	1.23844i
$534$		0			0
$535$		−	17.9652i		−	0.776702i
$536$			10.5516i			0.455760i
$537$		0			0
$538$	24.4158	+	24.4158i	1.05264	+	1.05264i
$539$	10.2078	−	10.2078i	0.439681	−	0.439681i
$540$		0			0
$541$	30.2202	−	30.2202i	1.29927	−	1.29927i	0.370391	−	0.928876i	$-0.379224\pi$
$541$	30.2202	−	30.2202i	1.29927	−	1.29927i	0.928876	−	0.370391i	$-0.120776\pi$
$542$			31.3673i			1.34734i
$543$		0			0
$544$	−13.6761	−	2.59378i	−0.586356	−	0.111208i
$545$	−5.81215			−0.248965
$546$		0			0
$547$	10.0510	−	10.0510i	0.429751	−	0.429751i	−0.458792	−	0.888544i	$-0.651718\pi$
$547$	10.0510	−	10.0510i	0.429751	−	0.429751i	0.888544	+	0.458792i	$0.151718\pi$
$548$	84.5468			3.61166
$549$		0			0
$550$	−5.83869	−	5.83869i	−0.248963	−	0.248963i
$551$	4.65094	+	4.65094i	0.198137	+	0.198137i
$552$		0			0
$553$		−	8.15295i		−	0.346699i
$554$	47.7162	+	47.7162i	2.02727	+	2.02727i
$555$		0			0
$556$	11.0105	−	11.0105i	0.466947	−	0.466947i
$557$	4.00971			0.169897			0.0849484	−	0.996385i	$-0.472927\pi$
$557$	4.00971			0.169897			0.0849484	+	0.996385i	$0.472927\pi$
$558$		0			0
$559$			17.4643i			0.738661i
$560$	−9.63604			−0.407197
$561$		0			0
$562$	39.0137			1.64569
$563$		−	5.66772i		−	0.238866i	−0.992842	−	0.119433i	$-0.961892\pi$
$563$		−	5.66772i		−	0.238866i	0.992842	−	0.119433i	$-0.0381077\pi$
$564$		0			0
$565$	−9.29716			−0.391134
$566$	−18.5455	+	18.5455i	−0.779524	+	0.779524i
$567$		0			0
$568$	17.4834	+	17.4834i	0.733586	+	0.733586i
$569$		−	0.249161i		−	0.0104454i	−0.999986	−	0.00522269i	$-0.998338\pi$
$569$		−	0.249161i		−	0.0104454i	0.999986	−	0.00522269i	$-0.00166244\pi$
$570$		0			0
$571$	24.1579	+	24.1579i	1.01098	+	1.01098i	0.999939	+	0.0110385i	$0.00351375\pi$
$571$	24.1579	+	24.1579i	1.01098	+	1.01098i	0.0110385	+	0.999939i	$0.496486\pi$
$572$	−63.6826	−	63.6826i	−2.66270	−	2.66270i
$573$		0			0
$574$	25.8122			1.07738
$575$	−0.101240	+	0.101240i	−0.00422201	+	0.00422201i
$576$		0			0
$577$	28.3587			1.18059			0.590295	−	0.807188i	$-0.299011\pi$
$577$	28.3587			1.18059			0.590295	+	0.807188i	$0.299011\pi$
$578$	−15.6378	+	39.7433i	−0.650448	+	1.65310i
$579$		0			0
$580$			37.9563i			1.57605i
$581$	−4.09354	+	4.09354i	−0.169829	+	0.169829i
$582$		0			0
$583$	6.30753	−	6.30753i	0.261231	−	0.261231i
$584$	−4.97415	−	4.97415i	−0.205832	−	0.205832i
$585$		0			0
$586$			17.8535i			0.737523i
$587$			22.8461i			0.942960i	0.881877	+	0.471480i	$0.156280\pi$
$587$			22.8461i			0.942960i	−0.881877	+	0.471480i	$0.843720\pi$
$588$		0			0
$589$	−3.81249	−	3.81249i	−0.157091	−	0.157091i
$590$	22.5282	−	22.5282i	0.927471	−	0.927471i
$591$		0			0
$592$	−2.62074	+	2.62074i	−0.107712	+	0.107712i
$593$			10.3077i			0.423285i	0.977347	+	0.211642i	$0.0678812\pi$
$593$			10.3077i			0.423285i	−0.977347	+	0.211642i	$0.932119\pi$
$594$		0			0
$595$	−1.24067	+	6.54158i	−0.0508624	+	0.268179i
$596$	−5.45004			−0.223242
$597$		0			0
$598$	−1.61643	+	1.61643i	−0.0661009	+	0.0661009i
$599$	−25.2157			−1.03028			−0.515142	−	0.857105i	$-0.672261\pi$
$599$	−25.2157			−1.03028			−0.515142	+	0.857105i	$0.672261\pi$
$600$		0			0
$601$	−6.05550	−	6.05550i	−0.247009	−	0.247009i	0.572733	−	0.819742i	$-0.305883\pi$
$601$	−6.05550	−	6.05550i	−0.247009	−	0.247009i	−0.819742	+	0.572733i	$0.805883\pi$
$602$	7.88329	+	7.88329i	0.321299	+	0.321299i
$603$		0			0
$604$			69.9380i			2.84574i
$605$	0.139787	+	0.139787i	0.00568316	+	0.00568316i
$606$		0			0
$607$	6.94394	−	6.94394i	0.281846	−	0.281846i	−0.551999	−	0.833845i	$-0.686135\pi$
$607$	6.94394	−	6.94394i	0.281846	−	0.281846i	0.833845	+	0.551999i	$0.186135\pi$
$608$	−2.52248			−0.102300
$609$		0			0
$610$			1.16594i			0.0472074i
$611$	75.8234			3.06749
$612$		0			0
$613$	22.3926			0.904427			0.452214	−	0.891910i	$-0.350635\pi$
$613$	22.3926			0.904427			0.452214	+	0.891910i	$0.350635\pi$
$614$		−	12.0719i		−	0.487183i
$615$		0			0
$616$	−30.8239			−1.24193
$617$	15.0930	−	15.0930i	0.607620	−	0.607620i	−0.334704	−	0.942323i	$-0.608636\pi$
$617$	15.0930	−	15.0930i	0.607620	−	0.607620i	0.942323	+	0.334704i	$0.108636\pi$
$618$		0			0
$619$	−10.6460	−	10.6460i	−0.427900	−	0.427900i	0.460013	−	0.887912i	$-0.347845\pi$
$619$	−10.6460	−	10.6460i	−0.427900	−	0.427900i	−0.887912	+	0.460013i	$0.847845\pi$
$620$		−	31.1136i		−	1.24955i
$621$		0			0
$622$	−14.2638	−	14.2638i	−0.571928	−	0.571928i
$623$	12.0931	+	12.0931i	0.484499	+	0.484499i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	39.2635	−	39.2635i	1.56928	−	1.56928i
$627$		0			0
$628$	36.7621			1.46697
$629$	1.44170	+	2.11656i	0.0574845	+	0.0843928i
$630$		0			0
$631$		−	41.6046i		−	1.65625i	−0.560540	−	0.828127i	$-0.689406\pi$
$631$		−	41.6046i		−	1.65625i	0.560540	−	0.828127i	$-0.310594\pi$
$632$	20.7332	−	20.7332i	0.824721	−	0.824721i
$633$		0			0
$634$	28.3608	−	28.3608i	1.12635	−	1.12635i
$635$	−10.7336	−	10.7336i	−0.425951	−	0.425951i
$636$		0			0
$637$		−	27.9139i		−	1.10599i
$638$			72.6890i			2.87779i
$639$		0			0
$640$	10.9079	+	10.9079i	0.431173	+	0.431173i
$641$	−6.26768	+	6.26768i	−0.247559	+	0.247559i	−0.819968	−	0.572409i	$-0.806009\pi$
$641$	−6.26768	+	6.26768i	−0.247559	+	0.247559i	0.572409	+	0.819968i	$0.306009\pi$
$642$		0			0
$643$	−21.2314	+	21.2314i	−0.837285	+	0.837285i	−0.988501	−	0.151216i	$-0.951681\pi$
$643$	−21.2314	+	21.2314i	−0.837285	+	0.837285i	0.151216	+	0.988501i	$0.451681\pi$
$644$			0.996886i			0.0392828i
$645$		0			0
$646$	−1.44216	+	7.60397i	−0.0567410	+	0.299174i
$647$	−0.383859			−0.0150911			−0.00754553	−	0.999972i	$-0.502402\pi$
$647$	−0.383859			−0.0150911			−0.00754553	+	0.999972i	$0.502402\pi$
$648$		0			0
$649$	29.4722	−	29.4722i	1.15689	−	1.15689i
$650$	−15.9663			−0.626250
$651$		0			0
$652$	47.1355	+	47.1355i	1.84597	+	1.84597i
$653$	−1.02342	−	1.02342i	−0.0400497	−	0.0400497i	0.686798	−	0.726848i	$-0.259016\pi$
$653$	−1.02342	−	1.02342i	−0.0400497	−	0.0400497i	−0.726848	+	0.686798i	$0.759016\pi$
$654$		0			0
$655$		−	1.98251i		−	0.0774629i
$656$	26.8455	+	26.8455i	1.04814	+	1.04814i
$657$		0			0
$658$	34.2263	−	34.2263i	1.33428	−	1.33428i
$659$	21.8603			0.851555			0.425777	−	0.904828i	$-0.360001\pi$
$659$	21.8603			0.851555			0.425777	+	0.904828i	$0.360001\pi$
$660$		0			0
$661$			40.5201i			1.57605i	0.615644	+	0.788024i	$0.288896\pi$
$661$			40.5201i			1.57605i	−0.615644	+	0.788024i	$0.711104\pi$
$662$	−9.74551			−0.378770
$663$		0			0
$664$	−20.8200			−0.807971
$665$			1.20656i			0.0467884i
$666$		0			0
$667$	1.26040			0.0488027
$668$	−11.1913	+	11.1913i	−0.433004	+	0.433004i
$669$		0			0
$670$	3.22759	+	3.22759i	0.124693	+	0.124693i
$671$			1.52532i			0.0588844i
$672$		0			0
$673$	−5.61265	−	5.61265i	−0.216352	−	0.216352i	0.590607	−	0.806959i	$-0.298888\pi$
$673$	−5.61265	−	5.61265i	−0.216352	−	0.216352i	−0.806959	+	0.590607i	$0.798888\pi$
$674$	43.3198	+	43.3198i	1.66862	+	1.66862i
$675$		0			0
$676$	−118.093			−4.54203
$677$	1.81406	−	1.81406i	0.0697200	−	0.0697200i	−0.671387	−	0.741107i	$-0.734301\pi$
$677$	1.81406	−	1.81406i	0.0697200	−	0.0697200i	0.741107	+	0.671387i	$0.234301\pi$
$678$		0			0
$679$	−11.2534			−0.431866
$680$	−19.7905	+	13.4804i	−0.758929	+	0.516948i
$681$		0			0
$682$		−	59.5849i		−	2.28162i
$683$	10.2987	−	10.2987i	0.394070	−	0.394070i	−0.482065	−	0.876135i	$-0.660113\pi$
$683$	10.2987	−	10.2987i	0.394070	−	0.394070i	0.876135	+	0.482065i	$0.160113\pi$
$684$		0			0
$685$	13.8655	−	13.8655i	0.529775	−	0.529775i
$686$	−32.6813	−	32.6813i	−1.24778	−	1.24778i
$687$		0			0
$688$			16.3978i			0.625160i
$689$		−	17.2484i		−	0.657111i
$690$		0			0
$691$	30.3791	+	30.3791i	1.15567	+	1.15567i	0.985396	+	0.170278i	$0.0544665\pi$
$691$	30.3791	+	30.3791i	1.15567	+	1.15567i	0.170278	+	0.985396i	$0.445533\pi$
$692$	−27.8703	+	27.8703i	−1.05947	+	1.05947i
$693$		0			0
$694$	−18.8849	+	18.8849i	−0.716862	+	0.716862i
$695$		−	3.61139i		−	0.136988i
$696$		0			0
$697$	21.6810	−	14.7681i	0.821225	−	0.559381i
$698$	−29.0370			−1.09907
$699$		0			0
$700$	−4.92337	+	4.92337i	−0.186086	+	0.186086i
$701$	−46.4002			−1.75251			−0.876256	−	0.481846i	$-0.839967\pi$
$701$	−46.4002			−1.75251			−0.876256	+	0.481846i	$0.839967\pi$
$702$		0			0
$703$	0.328152	+	0.328152i	0.0123765	+	0.0123765i
$704$	8.02400	+	8.02400i	0.302416	+	0.302416i
$705$		0			0
$706$		−	28.5605i		−	1.07489i
$707$	0.775811	+	0.775811i	0.0291774	+	0.0291774i
$708$		0			0
$709$	−29.3677	+	29.3677i	−1.10293	+	1.10293i	−0.108871	+	0.994056i	$0.534724\pi$
$709$	−29.3677	+	29.3677i	−1.10293	+	1.10293i	−0.994056	+	0.108871i	$0.965276\pi$
$710$	10.6958			0.401408
$711$		0			0
$712$			61.5060i			2.30503i
$713$	−1.03317			−0.0386927
$714$		0			0
$715$	−20.8877			−0.781156
$716$			37.7762i			1.41176i
$717$		0			0
$718$	−80.7229			−3.01255
$719$	0.455602	−	0.455602i	0.0169911	−	0.0169911i	−0.698560	−	0.715551i	$-0.746176\pi$
$719$	0.455602	−	0.455602i	0.0169911	−	0.0169911i	0.715551	+	0.698560i	$0.246176\pi$
$720$		0			0
$721$	−0.178651	−	0.178651i	−0.00665332	−	0.00665332i
$722$		−	46.3313i		−	1.72427i
$723$		0			0
$724$	−14.8391	−	14.8391i	−0.551490	−	0.551490i
$725$	6.22477	+	6.22477i	0.231182	+	0.231182i
$726$		0			0
$727$	−42.4141			−1.57305			−0.786525	−	0.617558i	$-0.788122\pi$
$727$	−42.4141			−1.57305			−0.786525	+	0.617558i	$0.788122\pi$
$728$	−42.1451	+	42.1451i	−1.56200	+	1.56200i
$729$		0			0
$730$	−3.04305			−0.112628
$731$	11.1319	+	2.11126i	0.411728	+	0.0780879i
$732$		0			0
$733$		−	43.4227i		−	1.60386i	−0.597421	−	0.801928i	$-0.703808\pi$
$733$		−	43.4227i		−	1.60386i	0.597421	−	0.801928i	$-0.296192\pi$
$734$	−34.2062	+	34.2062i	−1.26258	+	1.26258i
$735$		0			0
$736$	−0.341793	+	0.341793i	−0.0125987	+	0.0125987i
$737$	4.22245	+	4.22245i	0.155536	+	0.155536i
$738$		0			0
$739$			28.0864i			1.03318i	0.856234	+	0.516588i	$0.172798\pi$
$739$			28.0864i			1.03318i	−0.856234	+	0.516588i	$0.827202\pi$
$740$			2.67804i			0.0984468i
$741$		0			0
$742$	−7.78583	−	7.78583i	−0.285827	−	0.285827i
$743$	31.9613	−	31.9613i	1.17254	−	1.17254i	0.190944	−	0.981601i	$-0.438845\pi$
$743$	31.9613	−	31.9613i	1.17254	−	1.17254i	0.981601	−	0.190944i	$-0.0611547\pi$
$744$		0			0
$745$	−0.893798	+	0.893798i	−0.0327462	+	0.0327462i
$746$			51.0340i			1.86849i
$747$		0			0
$748$	−48.2905	+	32.8933i	−1.76568	+	1.20270i
$749$	−29.0110			−1.06004
$750$		0			0
$751$	17.0168	−	17.0168i	0.620952	−	0.620952i	−0.324823	−	0.945775i	$-0.605305\pi$
$751$	17.0168	−	17.0168i	0.620952	−	0.620952i	0.945775	+	0.324823i	$0.105305\pi$
$752$	71.1931			2.59614
$753$		0			0
$754$	99.3866	+	99.3866i	3.61945	+	3.61945i
$755$	11.4697	+	11.4697i	0.417426	+	0.417426i
$756$		0			0
$757$			18.0018i			0.654285i	0.944975	+	0.327143i	$0.106086\pi$
$757$			18.0018i			0.654285i	−0.944975	+	0.327143i	$0.893914\pi$
$758$	−60.9335	−	60.9335i	−2.21320	−	2.21320i
$759$		0			0
$760$	−3.06832	+	3.06832i	−0.111300	+	0.111300i
$761$	−23.4172			−0.848874			−0.424437	−	0.905458i	$-0.639528\pi$
$761$	−23.4172			−0.848874			−0.424437	+	0.905458i	$0.639528\pi$
$762$		0			0
$763$			9.38575i			0.339787i
$764$	48.6145			1.75881
$765$		0			0
$766$	−53.5685			−1.93551
$767$		−	80.5938i		−	2.91007i
$768$		0			0
$769$	9.52627			0.343526			0.171763	−	0.985138i	$-0.445054\pi$
$769$	9.52627			0.343526			0.171763	+	0.985138i	$0.445054\pi$
$770$	−9.42860	+	9.42860i	−0.339783	+	0.339783i
$771$		0			0
$772$	−13.9688	−	13.9688i	−0.502746	−	0.502746i
$773$			20.0047i			0.719519i	0.933045	+	0.359759i	$0.117141\pi$
$773$			20.0047i			0.719519i	−0.933045	+	0.359759i	$0.882859\pi$
$774$		0			0
$775$	−5.10259	−	5.10259i	−0.183290	−	0.183290i
$776$	−28.6177	−	28.6177i	−1.02732	−	1.02732i
$777$		0			0
$778$	29.5653			1.05997
$779$	3.36142	−	3.36142i	0.120435	−	0.120435i
$780$		0			0
$781$	13.9927			0.500698
$782$	0.834919	+	1.22574i	0.0298566	+	0.0438324i
$783$		0			0
$784$		−	26.2093i		−	0.936046i
$785$	6.02893	−	6.02893i	0.215182	−	0.215182i
$786$		0			0
$787$	−12.8060	+	12.8060i	−0.456484	+	0.456484i	−0.897500	−	0.441015i	$-0.854618\pi$
$787$	−12.8060	+	12.8060i	−0.456484	+	0.456484i	0.441015	+	0.897500i	$0.354618\pi$
$788$	−40.3909	−	40.3909i	−1.43887	−	1.43887i
$789$		0			0
$790$		−	12.6840i		−	0.451275i
$791$			15.0135i			0.533819i
$792$		0			0
$793$	2.08555	+	2.08555i	0.0740600	+	0.0740600i
$794$	5.96708	−	5.96708i	0.211764	−	0.211764i
$795$		0			0
$796$	8.04395	−	8.04395i	0.285110	−	0.285110i
$797$		−	44.1981i		−	1.56558i	−0.622289	−	0.782788i	$-0.713797\pi$
$797$		−	44.1981i		−	1.56558i	0.622289	−	0.782788i	$-0.286203\pi$
$798$		0			0
$799$	9.16631	−	48.3306i	0.324281	−	1.70981i
$800$	−3.37606			−0.119362
$801$		0			0
$802$	4.60882	−	4.60882i	0.162743	−	0.162743i
$803$	−3.98102			−0.140487
$804$		0			0
$805$	0.163488	+	0.163488i	0.00576219	+	0.00576219i
$806$	−81.4695	−	81.4695i	−2.86964	−	2.86964i
$807$		0			0
$808$			3.94581i			0.138813i
$809$	14.4229	+	14.4229i	0.507083	+	0.507083i	0.913630	−	0.406547i	$-0.133267\pi$
$809$	14.4229	+	14.4229i	0.507083	+	0.507083i	−0.406547	+	0.913630i	$0.633267\pi$
$810$		0			0
$811$	−1.48389	+	1.48389i	−0.0521064	+	0.0521064i	−0.732680	−	0.680573i	$-0.761731\pi$
$811$	−1.48389	+	1.48389i	−0.0521064	+	0.0521064i	0.680573	+	0.732680i	$0.261731\pi$
$812$	61.2937			2.15099
$813$		0			0
$814$			5.12865i			0.179759i
$815$	15.4603			0.541551
$816$		0			0
$817$	2.05322			0.0718332
$818$			77.4704i			2.70869i
$819$		0			0
$820$	27.4325			0.957985
$821$	3.49477	−	3.49477i	0.121968	−	0.121968i	−0.643488	−	0.765456i	$-0.722513\pi$
$821$	3.49477	−	3.49477i	0.121968	−	0.121968i	0.765456	+	0.643488i	$0.222513\pi$
$822$		0			0
$823$	8.09920	+	8.09920i	0.282320	+	0.282320i	0.834034	−	0.551713i	$-0.186026\pi$
$823$	8.09920	+	8.09920i	0.282320	+	0.282320i	−0.551713	+	0.834034i	$0.686026\pi$
$824$		−	0.908630i		−	0.0316536i
$825$		0			0
$826$	−36.3796	−	36.3796i	−1.26581	−	1.26581i
$827$	13.6785	+	13.6785i	0.475647	+	0.475647i	0.903736	−	0.428090i	$-0.140813\pi$
$827$	13.6785	+	13.6785i	0.475647	+	0.475647i	−0.428090	+	0.903736i	$0.640813\pi$
$828$		0			0
$829$	26.7634			0.929530			0.464765	−	0.885434i	$-0.346139\pi$
$829$	26.7634			0.929530			0.464765	+	0.885434i	$0.346139\pi$
$830$	−6.36853	+	6.36853i	−0.221055	+	0.221055i
$831$		0			0
$832$	21.9422			0.760708
$833$	−17.7926	−	3.37452i	−0.616477	−	0.116920i
$834$		0			0
$835$			3.67070i			0.127030i
$836$	−7.48697	+	7.48697i	−0.258942	+	0.258942i
$837$		0			0
$838$	−33.1617	+	33.1617i	−1.14555	+	1.14555i
$839$	−37.0327	−	37.0327i	−1.27851	−	1.27851i	−0.941502	−	0.337008i	$-0.890585\pi$
$839$	−37.0327	−	37.0327i	−1.27851	−	1.27851i	−0.337008	−	0.941502i	$-0.609415\pi$
$840$		0			0
$841$		−	48.4956i		−	1.67226i
$842$			74.2876i			2.56012i
$843$		0			0
$844$	−21.7529	−	21.7529i	−0.748766	−	0.748766i
$845$	−19.3670	+	19.3670i	−0.666247	+	0.666247i
$846$		0			0
$847$	0.225735	−	0.225735i	0.00775635	−	0.00775635i
$848$		−	16.1951i		−	0.556141i
$849$		0			0
$850$	−1.93017	+	10.1771i	−0.0662043	+	0.349071i
$851$	0.0889284			0.00304843
$852$		0			0
$853$	0.0880569	−	0.0880569i	0.00301501	−	0.00301501i	−0.705598	−	0.708613i	$-0.749321\pi$
$853$	0.0880569	−	0.0880569i	0.00301501	−	0.00301501i	0.708613	+	0.705598i	$0.249321\pi$
$854$	1.88281			0.0644285
$855$		0			0
$856$	−73.7758	−	73.7758i	−2.52160	−	2.52160i
$857$	15.9912	+	15.9912i	0.546249	+	0.546249i	0.925354	−	0.379104i	$-0.123768\pi$
$857$	15.9912	+	15.9912i	0.546249	+	0.546249i	−0.379104	+	0.925354i	$0.623768\pi$
$858$		0			0
$859$			38.2254i			1.30423i	0.758118	+	0.652117i	$0.226119\pi$
$859$			38.2254i			1.30423i	−0.758118	+	0.652117i	$0.773881\pi$
$860$	8.37817	+	8.37817i	0.285693	+	0.285693i
$861$		0			0
$862$	−29.0380	+	29.0380i	−0.989037	+	0.989037i
$863$	22.1777			0.754939			0.377469	−	0.926022i	$-0.376794\pi$
$863$	22.1777			0.754939			0.377469	+	0.926022i	$0.376794\pi$
$864$		0			0
$865$			9.14139i			0.310816i
$866$	35.9904			1.22300
$867$		0			0
$868$	−50.2438			−1.70539
$869$		−	16.5936i		−	0.562901i
$870$		0			0
$871$	11.5466			0.391241
$872$	−23.8682	+	23.8682i	−0.808279	+	0.808279i
$873$		0			0
$874$	0.190039	+	0.190039i	0.00642817	+	0.00642817i
$875$			1.61485i			0.0545918i
$876$		0			0
$877$	19.1327	+	19.1327i	0.646067	+	0.646067i	0.952040	−	0.305973i	$-0.0989819\pi$
$877$	19.1327	+	19.1327i	0.646067	+	0.646067i	−0.305973	+	0.952040i	$0.598982\pi$
$878$	54.0565	+	54.0565i	1.82432	+	1.82432i
$879$		0			0
$880$	−19.6121			−0.661125
$881$	26.0576	−	26.0576i	0.877903	−	0.877903i	−0.115414	−	0.993317i	$-0.536820\pi$
$881$	26.0576	−	26.0576i	0.877903	−	0.877903i	0.993317	+	0.115414i	$0.0368195\pi$
$882$		0			0
$883$	20.6901			0.696277			0.348138	−	0.937443i	$-0.386814\pi$
$883$	20.6901			0.696277			0.348138	+	0.937443i	$0.386814\pi$
$884$	−21.0524	+	111.001i	−0.708068	+	3.73338i
$885$		0			0
$886$			66.5851i			2.23697i
$887$	10.5540	−	10.5540i	0.354368	−	0.354368i	−0.507364	−	0.861732i	$-0.669380\pi$
$887$	10.5540	−	10.5540i	0.354368	−	0.354368i	0.861732	+	0.507364i	$0.169380\pi$
$888$		0			0
$889$	−17.3332	+	17.3332i	−0.581336	+	0.581336i
$890$	18.8138	+	18.8138i	0.630640	+	0.630640i
$891$		0			0
$892$		−	52.4770i		−	1.75706i
$893$		−	8.91433i		−	0.298307i
$894$		0			0
$895$	6.19523	+	6.19523i	0.207084	+	0.207084i
$896$	17.6146	−	17.6146i	0.588463	−	0.588463i
$897$		0			0
$898$	−28.1376	+	28.1376i	−0.938963	+	0.938963i
$899$			63.5249i			2.11867i
$900$		0			0
$901$	−10.9943	−	2.08516i	−0.366273	−	0.0694668i
$902$	52.5352			1.74923
$903$		0			0
$904$	−38.1797	+	38.1797i	−1.26984	+	1.26984i
$905$	−4.86717			−0.161790
$906$		0			0
$907$	−19.3243	−	19.3243i	−0.641653	−	0.641653i	0.309309	−	0.950962i	$-0.399902\pi$
$907$	−19.3243	−	19.3243i	−0.641653	−	0.641653i	−0.950962	+	0.309309i	$0.899902\pi$
$908$	−2.54769	−	2.54769i	−0.0845481	−	0.0845481i
$909$		0			0
$910$			25.7832i			0.854703i
$911$	−33.4927	−	33.4927i	−1.10966	−	1.10966i	−0.993194	−	0.116469i	$-0.962843\pi$
$911$	−33.4927	−	33.4927i	−1.10966	−	1.10966i	−0.116469	−	0.993194i	$-0.537157\pi$
$912$		0			0
$913$	−8.33154	+	8.33154i	−0.275734	+	0.275734i
$914$	−10.6860			−0.353463
$915$		0			0
$916$			26.4486i			0.873888i
$917$	−3.20145			−0.105721
$918$		0			0
$919$	25.7946			0.850884			0.425442	−	0.904986i	$-0.360119\pi$
$919$	25.7946			0.850884			0.425442	+	0.904986i	$0.360119\pi$
$920$			0.831507i			0.0274140i
$921$		0			0
$922$	60.2300			1.98357
$923$	19.1320	−	19.1320i	0.629737	−	0.629737i
$924$		0			0
$925$	0.439195	+	0.439195i	0.0144406	+	0.0144406i
$926$		−	57.8150i		−	1.89992i
$927$		0			0
$928$	21.0152	+	21.0152i	0.689858	+	0.689858i
$929$	17.4671	+	17.4671i	0.573076	+	0.573076i	0.932987	−	0.359911i	$-0.117193\pi$
$929$	17.4671	+	17.4671i	0.573076	+	0.573076i	−0.359911	+	0.932987i	$0.617193\pi$
$930$		0			0
$931$	−3.28175			−0.107555
$932$	−51.3330	+	51.3330i	−1.68147	+	1.68147i
$933$		0			0
$934$	54.7292			1.79080
$935$	−2.52512	+	13.3140i	−0.0825802	+	0.435415i
$936$		0			0
$937$			37.0383i			1.20999i	0.796230	+	0.604994i	$0.206825\pi$
$937$			37.0383i			1.20999i	−0.796230	+	0.604994i	$0.793175\pi$
$938$	5.21207	−	5.21207i	0.170180	−	0.170180i
$939$		0			0
$940$	36.3749	−	36.3749i	1.18642	−	1.18642i
$941$	−24.2477	−	24.2477i	−0.790452	−	0.790452i	0.191115	−	0.981568i	$-0.438790\pi$
$941$	−24.2477	−	24.2477i	−0.790452	−	0.790452i	−0.981568	+	0.191115i	$0.938790\pi$
$942$		0			0
$943$		−	0.910938i		−	0.0296642i
$944$		−	75.6721i		−	2.46292i
$945$		0			0
$946$	16.0448	+	16.0448i	0.521661	+	0.521661i
$947$	−26.2345	+	26.2345i	−0.852507	+	0.852507i	−0.990441	−	0.137934i	$-0.955954\pi$
$947$	−26.2345	+	26.2345i	−0.852507	+	0.852507i	0.137934	+	0.990441i	$0.455954\pi$
$948$		0			0
$949$	−5.44319	+	5.44319i	−0.176694	+	0.176694i
$950$			1.87711i			0.0609015i
$951$		0			0
$952$	21.7687	+	31.9586i	0.705529	+	1.03578i
$953$	−26.9203			−0.872033			−0.436016	−	0.899939i	$-0.643611\pi$
$953$	−26.9203			−0.872033			−0.436016	+	0.899939i	$0.643611\pi$
$954$		0			0
$955$	7.97270	−	7.97270i	0.257991	−	0.257991i
$956$	29.9791			0.969592
$957$		0			0
$958$	−58.4997	−	58.4997i	−1.89004	−	1.89004i
$959$	−22.3907	−	22.3907i	−0.723035	−	0.723035i
$960$		0			0
$961$		−	21.0728i		−	0.679768i
$962$	7.01232	+	7.01232i	0.226086	+	0.226086i
$963$		0			0
$964$	93.6641	−	93.6641i	3.01672	−	3.01672i
$965$	−4.58171			−0.147490
$966$		0			0
$967$			26.4462i			0.850452i	0.905087	+	0.425226i	$0.139805\pi$
$967$			26.4462i			0.850452i	−0.905087	+	0.425226i	$0.860195\pi$
$968$	1.14810			0.0369014
$969$		0			0
$970$	−17.5075			−0.562132
$971$		−	9.69327i		−	0.311072i	−0.987830	−	0.155536i	$-0.950290\pi$
$971$		−	9.69327i		−	0.311072i	0.987830	−	0.155536i	$-0.0497104\pi$
$972$		0			0
$973$	−5.83185			−0.186961
$974$	−33.1283	+	33.1283i	−1.06150	+	1.06150i
$975$		0			0
$976$	1.95819	+	1.95819i	0.0626801	+	0.0626801i
$977$			5.81399i			0.186006i	0.995666	+	0.0930029i	$0.0296466\pi$
$977$			5.81399i			0.186006i	−0.995666	+	0.0930029i	$0.970353\pi$
$978$		0			0
$979$	24.6129	+	24.6129i	0.786632	+	0.786632i
$980$	−13.3912	−	13.3912i	−0.427765	−	0.427765i
$981$		0			0
$982$	9.98153			0.318523
$983$	−22.4102	+	22.4102i	−0.714776	+	0.714776i	−0.967530	−	0.252755i	$-0.918663\pi$
$983$	−22.4102	+	22.4102i	−0.714776	+	0.714776i	0.252755	+	0.967530i	$0.418663\pi$
$984$		0			0
$985$	−13.2481			−0.422119
$986$	75.3648	−	51.3351i	2.40010	−	1.63484i
$987$		0			0
$988$			20.4736i			0.651353i
$989$	0.278210	−	0.278210i	0.00884655	−	0.00884655i
$990$		0			0
$991$	34.2715	−	34.2715i	1.08867	−	1.08867i	0.0930058	−	0.995666i	$-0.470352\pi$
$991$	34.2715	−	34.2715i	1.08867	−	1.08867i	0.995666	−	0.0930058i	$-0.0296475\pi$
$992$	−17.2266	−	17.2266i	−0.546946	−	0.546946i
$993$		0			0
$994$		−	17.2722i		−	0.547840i
$995$		−	2.63839i		−	0.0836426i
$996$		0			0
$997$	4.30543	+	4.30543i	0.136354	+	0.136354i	0.771990	−	0.635635i	$-0.219262\pi$
$997$	4.30543	+	4.30543i	0.136354	+	0.136354i	−0.635635	+	0.771990i	$0.719262\pi$
$998$	−60.6283	+	60.6283i	−1.91916	+	1.91916i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.k.b.361.1		12
3.2	odd	2		85.2.e.a.21.6	✓	12
12.11	even	2		1360.2.bt.d.1041.4		12
15.2	even	4		425.2.j.b.174.1		12
15.8	even	4		425.2.j.c.174.6		12
15.14	odd	2		425.2.e.f.276.1		12
17.13	even	4	inner	765.2.k.b.676.6		12
51.2	odd	8		1445.2.d.g.866.2		12
51.8	odd	8		1445.2.a.o.1.6		6
51.26	odd	8		1445.2.a.n.1.6		6
51.32	odd	8		1445.2.d.g.866.1		12
51.47	odd	4		85.2.e.a.81.1	yes	12
204.47	even	4		1360.2.bt.d.81.4		12
255.47	even	4		425.2.j.c.149.6		12
255.59	odd	8		7225.2.a.z.1.1		6
255.98	even	4		425.2.j.b.149.1		12
255.149	odd	4		425.2.e.f.251.6		12
255.179	odd	8		7225.2.a.bb.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.6	✓	12	3.2	odd	2
85.2.e.a.81.1	yes	12	51.47	odd	4
425.2.e.f.251.6		12	255.149	odd	4
425.2.e.f.276.1		12	15.14	odd	2
425.2.j.b.149.1		12	255.98	even	4
425.2.j.b.174.1		12	15.2	even	4
425.2.j.c.149.6		12	255.47	even	4
425.2.j.c.174.6		12	15.8	even	4
765.2.k.b.361.1		12	1.1	even	1	trivial
765.2.k.b.676.6		12	17.13	even	4	inner
1360.2.bt.d.81.4		12	204.47	even	4
1360.2.bt.d.1041.4		12	12.11	even	2
1445.2.a.n.1.6		6	51.26	odd	8
1445.2.a.o.1.6		6	51.8	odd	8
1445.2.d.g.866.1		12	51.32	odd	8
1445.2.d.g.866.2		12	51.2	odd	8
7225.2.a.z.1.1		6	255.59	odd	8
7225.2.a.bb.1.1		6	255.179	odd	8

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.51230i q^{2} -4.31167 q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.14187 + 1.14187i) q^{7} +5.80761i q^{8} +(1.77647 + 1.77647i) q^{10} +(2.32404 + 2.32404i) q^{11} +6.35524 q^{13} +(2.86872 - 2.86872i) q^{14} +5.96715 q^{16} +(0.768287 - 4.05089i) q^{17} -0.747167i q^{19} +(3.04881 - 3.04881i) q^{20} +(5.83869 - 5.83869i) q^{22} +(-0.101240 - 0.101240i) q^{23} -1.00000i q^{25} -15.9663i q^{26} +(-4.92337 - 4.92337i) q^{28} +(-6.22477 + 6.22477i) q^{29} +(5.10259 - 5.10259i) q^{31} -3.37606i q^{32} +(-10.1771 - 1.93017i) q^{34} -1.61485 q^{35} +(-0.439195 + 0.439195i) q^{37} -1.87711 q^{38} +(-4.10660 - 4.10660i) q^{40} +(4.49889 + 4.49889i) q^{41} +2.74801i q^{43} +(-10.0205 - 10.0205i) q^{44} +(-0.254346 + 0.254346i) q^{46} +11.9308 q^{47} -4.39226i q^{49} -2.51230 q^{50} -27.4017 q^{52} -2.71404i q^{53} -3.28669 q^{55} +(-6.63154 + 6.63154i) q^{56} +(15.6385 + 15.6385i) q^{58} -12.6815i q^{59} +(0.328162 + 0.328162i) q^{61} +(-12.8193 - 12.8193i) q^{62} +3.45261 q^{64} +(-4.49384 + 4.49384i) q^{65} +1.81686 q^{67} +(-3.31260 + 17.4661i) q^{68} +4.05699i q^{70} +(3.01043 - 3.01043i) q^{71} +(-0.856488 + 0.856488i) q^{73} +(1.10339 + 1.10339i) q^{74} +3.22154i q^{76} +5.30750i q^{77} +(-3.57000 - 3.57000i) q^{79} +(-4.21941 + 4.21941i) q^{80} +(11.3026 - 11.3026i) q^{82} +3.58494i q^{83} +(2.32115 + 3.40767i) q^{85} +6.90384 q^{86} +(-13.4971 + 13.4971i) q^{88} +10.5906 q^{89} +(7.25687 + 7.25687i) q^{91} +(0.436515 + 0.436515i) q^{92} -29.9739i q^{94} +(0.528327 + 0.528327i) q^{95} +(-4.92762 + 4.92762i) q^{97} -11.0347 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{10} + 4 q^{11} + 4 q^{14} + 4 q^{16} - 12 q^{17} + 8 q^{20} + 20 q^{22} - 12 q^{23} + 4 q^{28} + 12 q^{29} - 12 q^{34} - 16 q^{35} + 12 q^{37} - 24 q^{38} - 8 q^{40} + 24 q^{41} - 8 q^{44}+ \cdots - 44 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^10 + 4 * q^11 + 4 * q^14 + 4 * q^16 - 12 * q^17 + 8 * q^20 + 20 * q^22 - 12 * q^23 + 4 * q^28 + 12 * q^29 - 12 * q^34 - 16 * q^35 + 12 * q^37 - 24 * q^38 - 8 * q^40 + 24 * q^41 - 8 * q^44 - 24 * q^46 + 48 * q^47 - 4 * q^50 - 56 * q^52 - 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 + 28 * q^64 - 4 * q^65 - 8 * q^67 + 40 * q^68 - 28 * q^71 - 48 * q^73 - 28 * q^74 - 8 * q^79 - 16 * q^80 + 40 * q^82 - 4 * q^85 + 96 * q^86 - 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 + 8 * q^95 + 4 * q^97 - 44 * q^98

Introduction

L-functions

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