LMFDB - Embedded newform 819.2.bm.e.478.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.5
Root			$1.32725 + 0.488273i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.e.550.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.976547i q^{2} +1.04636 q^{4} +(-0.233786 - 0.134976i) q^{5} +(1.06153 + 2.42346i) q^{7} +2.97491i q^{8} +O(q^{10})$	\(q+0.976547i q^{2} +1.04636 q^{4} +(-0.233786 - 0.134976i) q^{5} +(1.06153 + 2.42346i) q^{7} +2.97491i q^{8} +(0.131811 - 0.228303i) q^{10} +(-0.741794 - 0.428275i) q^{11} +(1.45289 + 3.29986i) q^{13} +(-2.36662 + 1.03663i) q^{14} -0.812427 q^{16} -2.17296 q^{17} +(1.73063 - 0.999181i) q^{19} +(-0.244623 - 0.141233i) q^{20} +(0.418231 - 0.724397i) q^{22} -1.92330 q^{23} +(-2.46356 - 4.26702i) q^{25} +(-3.22247 + 1.41882i) q^{26} +(1.11073 + 2.53580i) q^{28} +(2.97054 + 5.14513i) q^{29} +(-0.0946014 + 0.0546182i) q^{31} +5.15645i q^{32} -2.12200i q^{34} +(0.0789401 - 0.709852i) q^{35} +3.49754i q^{37} +(0.975748 + 1.69004i) q^{38} +(0.401542 - 0.695492i) q^{40} +(7.03015 - 4.05886i) q^{41} +(-1.78890 + 3.09847i) q^{43} +(-0.776181 - 0.448128i) q^{44} -1.87820i q^{46} +(0.592480 + 0.342068i) q^{47} +(-4.74633 + 5.14513i) q^{49} +(4.16694 - 2.40578i) q^{50} +(1.52024 + 3.45283i) q^{52} +(4.21705 + 7.30414i) q^{53} +(0.115614 + 0.200249i) q^{55} +(-7.20958 + 3.15794i) q^{56} +(-5.02446 + 2.90088i) q^{58} -5.00939i q^{59} +(-5.48018 - 9.49195i) q^{61} +(-0.0533372 - 0.0923828i) q^{62} -6.66037 q^{64} +(0.105738 - 0.967568i) q^{65} +(4.83448 + 2.79119i) q^{67} -2.27369 q^{68} +(0.693204 + 0.0770887i) q^{70} +(12.5152 + 7.22567i) q^{71} +(-3.56030 + 2.05554i) q^{73} -3.41551 q^{74} +(1.81086 - 1.04550i) q^{76} +(0.250474 - 2.25233i) q^{77} +(-0.782735 + 1.35574i) q^{79} +(0.189934 + 0.109658i) q^{80} +(3.96367 + 6.86527i) q^{82} -7.98255i q^{83} +(0.508008 + 0.293299i) q^{85} +(-3.02580 - 1.74695i) q^{86} +(1.27408 - 2.20677i) q^{88} -2.71383i q^{89} +(-6.45481 + 7.02392i) q^{91} -2.01246 q^{92} +(-0.334046 + 0.578585i) q^{94} -0.539463 q^{95} +(-8.93689 - 5.15972i) q^{97} +(-5.02446 - 4.63501i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.976547i			0.690523i	0.938507	+	0.345261i	$0.112210\pi$
$2$			0.976547i			0.690523i	−0.938507	+	0.345261i	$0.887790\pi$
$3$		0			0
$3$		0			0
$4$	1.04636			0.523178
$5$	−0.233786	−	0.134976i	−0.104552	−	0.0603632i	0.446812	−	0.894628i	$-0.352559\pi$
$5$	−0.233786	−	0.134976i	−0.104552	−	0.0603632i	−0.551364	+	0.834265i	$0.685893\pi$
$6$		0			0
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$7$	1.06153	+	2.42346i	0.401219	+	0.915982i
$8$			2.97491i			1.05179i
$9$		0			0
$10$	0.131811	−	0.228303i	0.0416822	−	0.0721957i
$11$	−0.741794	−	0.428275i	−0.223659	−	0.129130i	0.383984	−	0.923340i	$-0.374552\pi$
$11$	−0.741794	−	0.428275i	−0.223659	−	0.129130i	−0.607643	+	0.794210i	$0.707885\pi$
$12$		0			0
$13$	1.45289	+	3.29986i	0.402960	+	0.915218i
$13$	1.45289	+	3.29986i	0.402960	+	0.915218i
$14$	−2.36662	+	1.03663i	−0.632507	+	0.277051i
$15$		0			0
$16$	−0.812427			−0.203107
$17$	−2.17296			−0.527021			−0.263510	−	0.964657i	$-0.584880\pi$
$17$	−2.17296			−0.527021			−0.263510	+	0.964657i	$0.584880\pi$
$18$		0			0
$19$	1.73063	−	0.999181i	0.397034	−	0.229228i	−0.288169	−	0.957580i	$-0.593047\pi$
$19$	1.73063	−	0.999181i	0.397034	−	0.229228i	0.685204	+	0.728352i	$0.259713\pi$
$20$	−0.244623	−	0.141233i	−0.0546994	−	0.0315807i
$21$		0			0
$22$	0.418231	−	0.724397i	0.0891671	−	0.154442i
$23$	−1.92330			−0.401037			−0.200518	−	0.979690i	$-0.564263\pi$
$23$	−1.92330			−0.401037			−0.200518	+	0.979690i	$0.564263\pi$
$24$		0			0
$25$	−2.46356	−	4.26702i	−0.492713	−	0.853403i
$26$	−3.22247	+	1.41882i	−0.631979	+	0.278253i
$27$		0			0
$28$	1.11073	+	2.53580i	0.209909	+	0.479222i
$29$	2.97054	+	5.14513i	0.551616	+	0.955427i	0.998158	+	0.0606646i	$0.0193220\pi$
$29$	2.97054	+	5.14513i	0.551616	+	0.955427i	−0.446542	+	0.894763i	$0.647345\pi$
$30$		0			0
$31$	−0.0946014	+	0.0546182i	−0.0169909	+	0.00980971i	−0.508471	−	0.861079i	$-0.669789\pi$
$31$	−0.0946014	+	0.0546182i	−0.0169909	+	0.00980971i	0.491480	+	0.870889i	$0.336456\pi$
$32$			5.15645i			0.911540i
$33$		0			0
$34$		−	2.12200i		−	0.363920i
$35$	0.0789401	−	0.709852i	0.0133433	−	0.119987i
$36$		0			0
$37$			3.49754i			0.574992i	0.957782	+	0.287496i	$0.0928228\pi$
$37$			3.49754i			0.574992i	−0.957782	+	0.287496i	$0.907177\pi$
$38$	0.975748	+	1.69004i	0.158287	+	0.274161i
$39$		0			0
$40$	0.401542	−	0.695492i	0.0634894	−	0.109967i
$41$	7.03015	−	4.05886i	1.09793	−	0.633888i	0.162250	−	0.986750i	$-0.448125\pi$
$41$	7.03015	−	4.05886i	1.09793	−	0.633888i	0.935675	+	0.352862i	$0.114792\pi$
$42$		0			0
$43$	−1.78890	+	3.09847i	−0.272805	+	0.472512i	−0.969579	−	0.244779i	$-0.921285\pi$
$43$	−1.78890	+	3.09847i	−0.272805	+	0.472512i	0.696774	+	0.717291i	$0.254618\pi$
$44$	−0.776181	−	0.448128i	−0.117014	−	0.0675578i
$45$		0			0
$46$		−	1.87820i		−	0.276925i
$47$	0.592480	+	0.342068i	0.0864221	+	0.0498958i	0.542588	−	0.839999i	$-0.317444\pi$
$47$	0.592480	+	0.342068i	0.0864221	+	0.0498958i	−0.456166	+	0.889895i	$0.650778\pi$
$48$		0			0
$49$	−4.74633	+	5.14513i	−0.678046	+	0.735019i
$50$	4.16694	−	2.40578i	0.589295	−	0.340229i
$51$		0			0
$52$	1.52024	+	3.45283i	0.210820	+	0.478822i
$53$	4.21705	+	7.30414i	0.579256	+	1.00330i	0.995565	+	0.0940780i	$0.0299903\pi$
$53$	4.21705	+	7.30414i	0.579256	+	1.00330i	−0.416308	+	0.909223i	$0.636676\pi$
$54$		0			0
$55$	0.115614	+	0.200249i	0.0155894	+	0.0270016i
$56$	−7.20958	+	3.15794i	−0.963420	+	0.421998i
$57$		0			0
$58$	−5.02446	+	2.90088i	−0.659744	+	0.380904i
$59$		−	5.00939i		−	0.652167i	−0.945341	−	0.326084i	$-0.894271\pi$
$59$		−	5.00939i		−	0.652167i	0.945341	−	0.326084i	$-0.105729\pi$
$60$		0			0
$61$	−5.48018	−	9.49195i	−0.701665	−	1.21532i	−0.967882	−	0.251406i	$-0.919107\pi$
$61$	−5.48018	−	9.49195i	−0.701665	−	1.21532i	0.266216	−	0.963913i	$-0.414226\pi$
$62$	−0.0533372	−	0.0923828i	−0.00677383	−	0.0117326i
$63$		0			0
$64$	−6.66037			−0.832546
$65$	0.105738	−	0.967568i	0.0131151	−	0.120012i
$66$		0			0
$67$	4.83448	+	2.79119i	0.590626	+	0.340998i	0.765345	−	0.643620i	$-0.222568\pi$
$67$	4.83448	+	2.79119i	0.590626	+	0.340998i	−0.174719	+	0.984618i	$0.555902\pi$
$68$	−2.27369			−0.275726
$69$		0			0
$70$	0.693204	+	0.0770887i	0.0828537	+	0.00921386i
$71$	12.5152	+	7.22567i	1.48529	+	0.857530i	0.999860	−	0.0167483i	$-0.00533140\pi$
$71$	12.5152	+	7.22567i	1.48529	+	0.857530i	0.485425	+	0.874278i	$0.338665\pi$
$72$		0			0
$73$	−3.56030	+	2.05554i	−0.416701	+	0.240583i	−0.693665	−	0.720298i	$-0.744005\pi$
$73$	−3.56030	+	2.05554i	−0.416701	+	0.240583i	0.276964	+	0.960880i	$0.410672\pi$
$74$	−3.41551			−0.397045
$75$		0			0
$76$	1.81086	−	1.04550i	0.207720	−	0.119927i
$77$	0.250474	−	2.25233i	0.0285442	−	0.256677i
$78$		0			0
$79$	−0.782735	+	1.35574i	−0.0880645	+	0.152532i	−0.906693	−	0.421791i	$-0.861401\pi$
$79$	−0.782735	+	1.35574i	−0.0880645	+	0.152532i	0.818628	+	0.574323i	$0.194735\pi$
$80$	0.189934	+	0.109658i	0.0212353	+	0.0122602i
$81$		0			0
$82$	3.96367	+	6.86527i	0.437714	+	0.758143i
$83$		−	7.98255i		−	0.876198i	−0.898927	−	0.438099i	$-0.855652\pi$
$83$		−	7.98255i		−	0.876198i	0.898927	−	0.438099i	$-0.144348\pi$
$84$		0			0
$85$	0.508008	+	0.293299i	0.0551012	+	0.0318127i
$86$	−3.02580	−	1.74695i	−0.326280	−	0.188378i
$87$		0			0
$88$	1.27408	−	2.20677i	0.135817	−	0.235242i
$89$		−	2.71383i		−	0.287665i	−0.989602	−	0.143833i	$-0.954057\pi$
$89$		−	2.71383i		−	0.287665i	0.989602	−	0.143833i	$-0.0459427\pi$
$90$		0			0
$91$	−6.45481	+	7.02392i	−0.676648	+	0.736307i
$92$	−2.01246			−0.209814
$93$		0			0
$94$	−0.334046	+	0.578585i	−0.0344542	+	0.0596764i
$95$	−0.539463			−0.0553478
$96$		0			0
$97$	−8.93689	−	5.15972i	−0.907404	−	0.523890i	−0.0278089	−	0.999613i	$-0.508853\pi$
$97$	−8.93689	−	5.15972i	−0.907404	−	0.523890i	−0.879595	+	0.475723i	$0.842186\pi$
$98$	−5.02446	−	4.63501i	−0.507548	−	0.468207i
$99$		0			0
$100$	−2.57776	−	4.46482i	−0.257776	−	0.446482i
$101$	5.65484	−	9.79447i	0.562678	−	0.974586i	−0.434584	−	0.900631i	$-0.643105\pi$
$101$	5.65484	−	9.79447i	0.562678	−	0.974586i	0.997262	−	0.0739548i	$-0.0235621\pi$
$102$		0			0
$103$	7.93581	−	13.7452i	0.781938	−	1.35436i	−0.148873	−	0.988856i	$-0.547564\pi$
$103$	7.93581	−	13.7452i	0.781938	−	1.35436i	0.930811	−	0.365501i	$-0.119102\pi$
$104$	−9.81680	+	4.32223i	−0.962616	+	0.423829i
$105$		0			0
$106$	−7.13284	+	4.11815i	−0.692803	+	0.399990i
$107$	−11.0959			−1.07268			−0.536341	−	0.844001i	$-0.680194\pi$
$107$	−11.0959			−1.07268			−0.536341	+	0.844001i	$0.680194\pi$
$108$		0			0
$109$	6.15552	−	3.55389i	0.589592	−	0.340401i	−0.175344	−	0.984507i	$-0.556104\pi$
$109$	6.15552	−	3.55389i	0.589592	−	0.340401i	0.764936	+	0.644106i	$0.222770\pi$
$110$	−0.195553	+	0.112902i	−0.0186452	+	0.0107648i
$111$		0			0
$112$	−0.862412	−	1.96889i	−0.0814903	−	0.186042i
$113$	−7.53381	+	13.0489i	−0.708721	+	1.22754i	0.256610	+	0.966515i	$0.417394\pi$
$113$	−7.53381	+	13.0489i	−0.708721	+	1.22754i	−0.965332	+	0.261026i	$0.915939\pi$
$114$		0			0
$115$	0.449641	+	0.259601i	0.0419293	+	0.0242079i
$116$	3.10825	+	5.38364i	0.288593	+	0.499859i
$117$		0			0
$118$	4.89191			0.450336
$119$	−2.30666	−	5.26609i	−0.211451	−	0.482742i
$120$		0			0
$121$	−5.13316	−	8.89090i	−0.466651	−	0.808263i
$122$	9.26934	−	5.35165i	0.839206	−	0.484516i
$123$		0			0
$124$	−0.0989868	+	0.0571501i	−0.00888928	+	0.00513223i
$125$			2.67985i			0.239693i
$126$		0			0
$127$	0.799919	+	1.38550i	0.0709813	+	0.122943i	0.899332	−	0.437267i	$-0.144054\pi$
$127$	0.799919	+	1.38550i	0.0709813	+	0.122943i	−0.828350	+	0.560210i	$0.810720\pi$
$128$			3.80873i			0.336648i
$129$		0			0
$130$	0.944875	+	0.103258i	0.0828710	+	0.00905630i
$131$	−6.29272	+	10.8993i	−0.549797	+	0.952277i	0.448491	+	0.893788i	$0.351962\pi$
$131$	−6.29272	+	10.8993i	−0.549797	+	0.952277i	−0.998288	+	0.0584895i	$0.981372\pi$
$132$		0			0
$133$	4.25859	+	3.13346i	0.369266	+	0.271706i
$134$	−2.72573	+	4.72110i	−0.235467	+	0.407841i
$135$		0			0
$136$		−	6.46437i		−	0.554315i
$137$		−	17.7573i		−	1.51711i	−0.651611	−	0.758553i	$-0.725907\pi$
$137$		−	17.7573i		−	1.51711i	0.651611	−	0.758553i	$-0.274093\pi$
$138$		0			0
$139$	11.4869	−	19.8959i	0.974308	−	1.68755i	0.292107	−	0.956386i	$-0.405644\pi$
$139$	11.4869	−	19.8959i	0.974308	−	1.68755i	0.682201	−	0.731165i	$-0.261023\pi$
$140$	0.0825995	−	0.742758i	0.00698093	−	0.0627745i
$141$		0			0
$142$	−7.05621	+	12.2217i	−0.592144	+	1.02562i
$143$	0.335502	−	3.07006i	0.0280561	−	0.256731i
$144$		0			0
$145$		−	1.60381i		−	0.133189i
$146$	−2.00733	−	3.47680i	−0.166128	−	0.287742i
$147$		0			0
$148$			3.65967i			0.300823i
$149$	11.1178	−	6.41884i	0.910803	−	0.525852i	0.0301133	−	0.999546i	$-0.490413\pi$
$149$	11.1178	−	6.41884i	0.910803	−	0.525852i	0.880689	+	0.473694i	$0.157080\pi$
$150$		0			0
$151$	7.32362	−	4.22830i	0.595988	−	0.344094i	−0.171474	−	0.985189i	$-0.554853\pi$
$151$	7.32362	−	4.22830i	0.595988	−	0.344094i	0.767462	+	0.641095i	$0.221520\pi$
$152$	2.97247	+	5.14848i	0.241100	+	0.417597i
$153$		0			0
$154$	2.19951	+	0.244600i	0.177242	+	0.0197104i
$155$	0.0294886			0.00236858
$156$		0			0
$157$	8.35754	+	14.4757i	0.667004	+	1.15529i	0.978738	+	0.205116i	$0.0657571\pi$
$157$	8.35754	+	14.4757i	0.667004	+	1.15529i	−0.311733	+	0.950170i	$0.600910\pi$
$158$	−1.32394	−	0.764377i	−0.105327	−	0.0608106i
$159$		0			0
$160$	0.695998	−	1.20550i	0.0550235	−	0.0953035i
$161$	−2.04164	−	4.66105i	−0.160904	−	0.367342i
$162$		0			0
$163$	18.7003	−	10.7966i	1.46472	−	0.845656i	0.465496	−	0.885050i	$-0.345876\pi$
$163$	18.7003	−	10.7966i	1.46472	−	0.845656i	0.999224	+	0.0393940i	$0.0125427\pi$
$164$	7.35604	−	4.24701i	0.574410	−	0.331636i
$165$		0			0
$166$	7.79533			0.605035
$167$	10.3948	−	6.00144i	0.804373	−	0.464405i	−0.0406249	−	0.999174i	$-0.512935\pi$
$167$	10.3948	−	6.00144i	0.804373	−	0.464405i	0.844998	+	0.534769i	$0.179602\pi$
$168$		0			0
$169$	−8.77820	+	9.58870i	−0.675246	+	0.737592i
$170$	−0.286420	+	0.496094i	−0.0219674	+	0.0380487i
$171$		0			0
$172$	−1.87183	+	3.24210i	−0.142725	+	0.247208i
$173$	3.54154	+	6.13414i	0.269259	+	0.466370i	0.968671	−	0.248349i	$-0.0798880\pi$
$173$	3.54154	+	6.13414i	0.269259	+	0.466370i	−0.699412	+	0.714719i	$0.746555\pi$
$174$		0			0
$175$	7.72581	−	10.4999i	0.584016	−	0.793718i
$176$	0.602654	+	0.347942i	0.0454267	+	0.0262271i
$177$		0			0
$178$	2.65018			0.198640
$179$	6.80438	−	11.7855i	0.508583	−	0.880892i	−0.491368	−	0.870952i	$-0.663503\pi$
$179$	6.80438	−	11.7855i	0.508583	−	0.880892i	0.999951	−	0.00993940i	$-0.00316386\pi$
$180$		0			0
$181$	−10.9994			−0.817576			−0.408788	−	0.912629i	$-0.634048\pi$
$181$	−10.9994			−0.817576			−0.408788	+	0.912629i	$0.634048\pi$
$182$	−6.85919	−	6.30342i	−0.508437	−	0.467241i
$183$		0			0
$184$		−	5.72166i		−	0.421806i
$185$	0.472085	−	0.817675i	0.0347084	−	0.0601167i
$186$		0			0
$187$	1.61189	+	0.930626i	0.117873	+	0.0680541i
$188$	0.619945	+	0.357925i	0.0452141	+	0.0261044i
$189$		0			0
$190$		−	0.526811i		−	0.0382189i
$191$	−6.32207	−	10.9501i	−0.457449	−	0.792325i	0.541376	−	0.840780i	$-0.317903\pi$
$191$	−6.32207	−	10.9501i	−0.457449	−	0.792325i	−0.998825	+	0.0484554i	$0.984570\pi$
$192$		0			0
$193$	14.7814	+	8.53405i	1.06399	+	0.614295i	0.926533	−	0.376213i	$-0.122774\pi$
$193$	14.7814	+	8.53405i	1.06399	+	0.614295i	0.137456	+	0.990508i	$0.456107\pi$
$194$	5.03871	−	8.72729i	0.361758	−	0.626583i
$195$		0			0
$196$	−4.96635	+	5.38364i	−0.354739	+	0.384546i
$197$	−7.05210	+	4.07153i	−0.502442	+	0.290085i	−0.729721	−	0.683745i	$-0.760350\pi$
$197$	−7.05210	+	4.07153i	−0.502442	+	0.290085i	0.227280	+	0.973830i	$0.427017\pi$
$198$		0			0
$199$	9.84965			0.698223			0.349112	−	0.937081i	$-0.386483\pi$
$199$	9.84965			0.698223			0.349112	+	0.937081i	$0.386483\pi$
$200$	12.6940	−	7.32888i	0.897600	−	0.518230i
$201$		0			0
$202$	9.56476	+	5.52222i	0.672974	+	0.388542i
$203$	−9.31572	+	12.6607i	−0.653835	+	0.888606i
$204$		0			0
$205$	−2.19140			−0.153054
$206$	13.4229	+	7.74969i	0.935215	+	0.539947i
$207$		0			0
$208$	−1.18037	−	2.68090i	−0.0818439	−	0.185887i
$209$	−1.71170			−0.118401
$210$		0			0
$211$	2.89735	+	5.01836i	0.199462	+	0.345478i	0.948354	−	0.317214i	$-0.102747\pi$
$211$	2.89735	+	5.01836i	0.199462	+	0.345478i	−0.748892	+	0.662692i	$0.769414\pi$
$212$	4.41254	+	7.64274i	0.303054	+	0.524905i
$213$		0			0
$214$		−	10.8357i		−	0.740712i
$215$	0.836439	−	0.482919i	0.0570447	−	0.0329348i
$216$		0			0
$217$	−0.232787	−	0.171284i	−0.0158026	−	0.0116275i
$218$	3.47054	+	6.01116i	0.235055	+	0.407127i
$219$		0			0
$220$	0.120973	+	0.209532i	0.00815602	+	0.0141266i
$221$	−3.15708	−	7.17048i	−0.212368	−	0.482339i
$222$		0			0
$223$	−19.1896	+	11.0791i	−1.28503	+	0.741911i	−0.977763	−	0.209713i	$-0.932747\pi$
$223$	−19.1896	+	11.0791i	−1.28503	+	0.741911i	−0.307265	+	0.951624i	$0.599414\pi$
$224$	−12.4964	+	5.47370i	−0.834954	+	0.365727i
$225$		0			0
$226$	−12.7429	−	7.35712i	−0.847645	−	0.489388i
$227$		−	27.1745i		−	1.80363i	−0.432120	−	0.901816i	$-0.642234\pi$
$227$		−	27.1745i		−	1.80363i	0.432120	−	0.901816i	$-0.357766\pi$
$228$		0			0
$229$	1.14109	+	0.658811i	0.0754056	+	0.0435354i	0.537229	−	0.843437i	$-0.319471\pi$
$229$	1.14109	+	0.658811i	0.0754056	+	0.0435354i	−0.461823	+	0.886972i	$0.652805\pi$
$230$	−0.253512	+	0.439096i	−0.0167161	+	0.0289531i
$231$		0			0
$232$	−15.3063	+	8.83710i	−1.00491	+	0.580184i
$233$	9.48801	−	16.4337i	0.621580	−	1.07661i	−0.367611	−	0.929980i	$-0.619824\pi$
$233$	9.48801	−	16.4337i	0.621580	−	1.07661i	0.989192	−	0.146629i	$-0.0468425\pi$
$234$		0			0
$235$	−0.0923423	−	0.159942i	−0.00602375	−	0.0104334i
$236$		−	5.24161i		−	0.341200i
$237$		0			0
$238$	5.14259	−	2.25256i	0.333344	−	0.146012i
$239$		−	11.7016i		−	0.756912i	−0.925619	−	0.378456i	$-0.876455\pi$
$239$		−	11.7016i		−	0.756912i	0.925619	−	0.378456i	$-0.123545\pi$
$240$		0			0
$241$		−	21.4556i		−	1.38208i	−0.722817	−	0.691039i	$-0.757153\pi$
$241$		−	21.4556i		−	1.38208i	0.722817	−	0.691039i	$-0.242847\pi$
$242$	8.68238	−	5.01277i	0.558124	−	0.322233i
$243$		0			0
$244$	−5.73422	−	9.93196i	−0.367096	−	0.635829i
$245$	1.80409	−	0.562218i	0.115259	−	0.0359188i
$246$		0			0
$247$	5.81159	+	4.25915i	0.369782	+	0.271003i
$248$	−0.162484	−	0.281431i	−0.0103178	−	0.0178709i
$249$		0			0
$250$	−2.61700			−0.165514
$251$	6.14063	−	10.6359i	0.387593	−	0.671331i	−0.604532	−	0.796581i	$-0.706640\pi$
$251$	6.14063	−	10.6359i	0.387593	−	0.671331i	0.992125	+	0.125250i	$0.0399731\pi$
$252$		0			0
$253$	1.42670	+	0.823703i	0.0896956	+	0.0517858i
$254$	−1.35301	+	0.781158i	−0.0848951	+	0.0490142i
$255$		0			0
$256$	−17.0401			−1.06501
$257$	0.990284			0.0617722			0.0308861	−	0.999523i	$-0.490167\pi$
$257$	0.990284			0.0617722			0.0308861	+	0.999523i	$0.490167\pi$
$258$		0			0
$259$	−8.47615	+	3.71273i	−0.526682	+	0.230698i
$260$	0.110639	−	1.01242i	0.00686155	−	0.0627876i
$261$		0			0
$262$	−10.6437	−	6.14514i	−0.657569	−	0.379648i
$263$	0.187525	−	0.324803i	0.0115633	−	0.0200282i	−0.860186	−	0.509981i	$-0.829653\pi$
$263$	0.187525	−	0.324803i	0.0115633	−	0.0200282i	0.871749	+	0.489952i	$0.162986\pi$
$264$		0			0
$265$		−	2.27681i		−	0.139863i
$266$	−3.05998	+	4.15871i	−0.187619	+	0.254987i
$267$		0			0
$268$	5.05859	+	2.92058i	0.309002	+	0.178403i
$269$	−17.0590			−1.04010			−0.520051	−	0.854135i	$-0.674087\pi$
$269$	−17.0590			−1.04010			−0.520051	+	0.854135i	$0.674087\pi$
$270$		0			0
$271$			13.3623i			0.811701i	0.913939	+	0.405850i	$0.133025\pi$
$271$			13.3623i			0.811701i	−0.913939	+	0.405850i	$0.866975\pi$
$272$	1.76537			0.107042
$273$		0			0
$274$	17.3408			1.04760
$275$			4.22033i			0.254495i
$276$		0			0
$277$	−4.70390			−0.282630			−0.141315	−	0.989965i	$-0.545133\pi$
$277$	−4.70390			−0.282630			−0.141315	+	0.989965i	$0.545133\pi$
$278$	19.4293	+	11.2175i	1.16529	+	0.672782i
$279$		0			0
$280$	2.11174	+	0.234840i	0.126201	+	0.0140344i
$281$			31.2950i			1.86691i	0.358700	+	0.933453i	$0.383220\pi$
$281$			31.2950i			1.86691i	−0.358700	+	0.933453i	$0.616780\pi$
$282$		0			0
$283$	7.76972	−	13.4575i	0.461862	−	0.799968i	−0.537192	−	0.843460i	$-0.680515\pi$
$283$	7.76972	−	13.4575i	0.461862	−	0.799968i	0.999054	+	0.0434919i	$0.0138483\pi$
$284$	13.0954	+	7.56063i	0.777069	+	0.448641i
$285$		0			0
$286$	2.99805	+	0.327633i	0.177279	+	0.0193733i
$287$	17.2992	+	12.7287i	1.02114	+	0.751352i
$288$		0			0
$289$	−12.2782			−0.722249
$290$	1.56620			0.0919703
$291$		0			0
$292$	−3.72534	+	2.15082i	−0.218009	+	0.125867i
$293$	5.22137	+	3.01456i	0.305036	+	0.176113i	0.644703	−	0.764433i	$-0.276981\pi$
$293$	5.22137	+	3.01456i	0.305036	+	0.176113i	−0.339667	+	0.940546i	$0.610314\pi$
$294$		0			0
$295$	−0.676149	+	1.17112i	−0.0393669	+	0.0681855i
$296$	−10.4049			−0.604770
$297$		0			0
$298$	6.26830	+	10.8570i	0.363113	+	0.628930i
$299$	−2.79436	−	6.34664i	−0.161602	−	0.367036i
$300$		0			0
$301$	−9.40798	−	1.04623i	−0.542267	−	0.0603036i
$302$	4.12913	+	7.15186i	0.237605	+	0.411543i
$303$		0			0
$304$	−1.40601	+	0.811762i	−0.0806404	+	0.0465577i
$305$			2.95878i			0.169419i
$306$		0			0
$307$		−	13.7607i		−	0.785363i	−0.919675	−	0.392681i	$-0.871547\pi$
$307$		−	13.7607i		−	0.785363i	0.919675	−	0.392681i	$-0.128453\pi$
$308$	0.262085	−	2.35674i	0.0149337	−	0.134288i
$309$		0			0
$310$			0.0287970i			0.00163556i
$311$	14.0828	+	24.3920i	0.798560	+	1.38315i	0.920554	+	0.390615i	$0.127738\pi$
$311$	14.0828	+	24.3920i	0.798560	+	1.38315i	−0.121995	+	0.992531i	$0.538929\pi$
$312$		0			0
$313$	−6.10426	+	10.5729i	−0.345033	+	0.597615i	−0.985360	−	0.170488i	$-0.945466\pi$
$313$	−6.10426	+	10.5729i	−0.345033	+	0.597615i	0.640327	+	0.768103i	$0.278799\pi$
$314$	−14.1362	+	8.16153i	−0.797751	+	0.460582i
$315$		0			0
$316$	−0.819019	+	1.41858i	−0.0460734	+	0.0798015i
$317$	−11.1776	−	6.45338i	−0.627795	−	0.362458i	0.152103	−	0.988365i	$-0.451396\pi$
$317$	−11.1776	−	6.45338i	−0.627795	−	0.362458i	−0.779898	+	0.625907i	$0.784729\pi$
$318$		0			0
$319$		−	5.08884i		−	0.284920i
$320$	1.55710	+	0.898992i	0.0870445	+	0.0502552i
$321$		0			0
$322$	4.55174	−	1.99375i	0.253658	−	0.111108i
$323$	−3.76060	+	2.17118i	−0.209245	+	0.120808i
$324$		0			0
$325$	10.5013	−	14.3289i	0.582506	−	0.794827i
$326$	10.5434	+	18.2617i	0.583945	+	1.01142i
$327$		0			0
$328$	12.0747	+	20.9141i	0.666716	+	1.15479i
$329$	−0.200057	+	1.79897i	−0.0110295	+	0.0991802i
$330$		0			0
$331$	−13.4228	+	7.74964i	−0.737782	+	0.425958i	−0.821262	−	0.570551i	$-0.806730\pi$
$331$	−13.4228	+	7.74964i	−0.737782	+	0.425958i	0.0834805	+	0.996509i	$0.473396\pi$
$332$		−	8.35259i		−	0.458408i
$333$		0			0
$334$	5.86068	+	10.1510i	0.320682	+	0.555438i
$335$	−0.753489	−	1.30508i	−0.0411675	−	0.0713042i
$336$		0			0
$337$	34.6418			1.88706			0.943528	−	0.331292i	$-0.107484\pi$
$337$	34.6418			1.88706			0.943528	+	0.331292i	$0.107484\pi$
$338$	−9.36382	−	8.57233i	−0.509324	−	0.466273i
$339$		0			0
$340$	0.531557	+	0.306895i	0.0288277	+	0.0166437i
$341$	0.0935664			0.00506690
$342$		0			0
$343$	−17.5074	−	6.04084i	−0.945309	−	0.326175i
$344$	−9.21766	−	5.32182i	−0.496983	−	0.286933i
$345$		0			0
$346$	−5.99027	+	3.45848i	−0.322039	+	0.185929i
$347$	−30.8011			−1.65349			−0.826746	−	0.562575i	$-0.809811\pi$
$347$	−30.8011			−1.65349			−0.826746	+	0.562575i	$0.809811\pi$
$348$		0			0
$349$	−10.6230	+	6.13321i	−0.568638	+	0.328303i	−0.756605	−	0.653872i	$-0.773144\pi$
$349$	−10.6230	+	6.13321i	−0.568638	+	0.328303i	0.187967	+	0.982175i	$0.439810\pi$
$350$	10.2536	+	7.54462i	0.548080	+	0.403277i
$351$		0			0
$352$	2.20838	−	3.82502i	0.117707	−	0.203874i
$353$	3.36012	+	1.93996i	0.178841	+	0.103254i	0.586748	−	0.809770i	$-0.300408\pi$
$353$	3.36012	+	1.93996i	0.178841	+	0.103254i	−0.407907	+	0.913023i	$0.633741\pi$
$354$		0			0
$355$	−1.95059	−	3.37852i	−0.103527	−	0.179313i
$356$		−	2.83963i		−	0.150500i
$357$		0			0
$358$	11.5091	+	6.64479i	0.608276	+	0.351188i
$359$	−32.2363	−	18.6117i	−1.70137	−	0.982286i	−0.944379	−	0.328859i	$-0.893336\pi$
$359$	−32.2363	−	18.6117i	−1.70137	−	0.982286i	−0.756990	−	0.653427i	$-0.773331\pi$
$360$		0			0
$361$	−7.50327	+	12.9961i	−0.394909	+	0.684003i
$362$		−	10.7414i		−	0.564555i
$363$		0			0
$364$	−6.75403	+	7.34952i	−0.354007	+	0.385220i
$365$	1.10980			0.0580894
$366$		0			0
$367$	−8.57322	+	14.8492i	−0.447518	+	0.775124i	−0.998224	−	0.0595753i	$-0.981025\pi$
$367$	−8.57322	+	14.8492i	−0.447518	+	0.775124i	0.550706	+	0.834700i	$0.314359\pi$
$368$	1.56254			0.0814533
$369$		0			0
$370$	0.798498	+	0.461013i	0.0415120	+	0.0239669i
$371$	−13.2248	+	17.9734i	−0.686597	+	0.933132i
$372$		0			0
$373$	−5.67303	−	9.82597i	−0.293738	−	0.508770i	0.680952	−	0.732328i	$-0.261566\pi$
$373$	−5.67303	−	9.82597i	−0.293738	−	0.508770i	−0.974691	+	0.223558i	$0.928233\pi$
$374$	−0.908800	+	1.57409i	−0.0469929	+	0.0813941i
$375$		0			0
$376$	−1.01762	+	1.76257i	−0.0524799	+	0.0908978i
$377$	−12.6624	+	17.2777i	−0.652144	+	0.889848i
$378$		0			0
$379$	18.3332	−	10.5847i	0.941713	−	0.543698i	0.0512161	−	0.998688i	$-0.483690\pi$
$379$	18.3332	−	10.5847i	0.941713	−	0.543698i	0.890497	+	0.454989i	$0.150357\pi$
$380$	−0.564471			−0.0289567
$381$		0			0
$382$	10.6933	−	6.17380i	0.547119	−	0.315879i
$383$	18.5097	−	10.6866i	0.945803	−	0.546060i	0.0540285	−	0.998539i	$-0.482794\pi$
$383$	18.5097	−	10.6866i	0.945803	−	0.546060i	0.891775	+	0.452480i	$0.149460\pi$
$384$		0			0
$385$	−0.362569	+	0.492756i	−0.0184782	+	0.0251132i
$386$	−8.33390	+	14.4347i	−0.424184	+	0.734709i
$387$		0			0
$388$	−9.35117	−	5.39890i	−0.474734	−	0.274088i
$389$	−1.28830	−	2.23141i	−0.0653195	−	0.113137i	0.831516	−	0.555501i	$-0.187473\pi$
$389$	−1.28830	−	2.23141i	−0.0653195	−	0.113137i	−0.896836	+	0.442364i	$0.854140\pi$
$390$		0			0
$391$	4.17927			0.211355
$392$	−15.3063	−	14.1199i	−0.773085	−	0.713162i
$393$		0			0
$394$	−3.97604	−	6.88671i	−0.200310	−	0.346948i
$395$	0.365985	−	0.211301i	0.0184147	−	0.0106317i
$396$		0			0
$397$	−10.1386	+	5.85352i	−0.508842	+	0.293780i	−0.732357	−	0.680921i	$-0.761580\pi$
$397$	−10.1386	+	5.85352i	−0.508842	+	0.293780i	0.223516	+	0.974700i	$0.428247\pi$
$398$			9.61865i			0.482139i
$399$		0			0
$400$	2.00147	+	3.46664i	0.100073	+	0.173332i
$401$			37.5533i			1.87532i	0.347549	+	0.937662i	$0.387014\pi$
$401$			37.5533i			1.87532i	−0.347549	+	0.937662i	$0.612986\pi$
$402$		0			0
$403$	−0.317678	−	0.232818i	−0.0158247	−	0.0115975i
$404$	5.91697	−	10.2485i	0.294380	−	0.509882i
$405$		0			0
$406$	−12.3638	−	9.09724i	−0.613603	−	0.451488i
$407$	1.49791	−	2.59445i	0.0742486	−	0.128602i
$408$		0			0
$409$			8.89957i			0.440055i	0.975494	+	0.220028i	$0.0706148\pi$
$409$			8.89957i			0.440055i	−0.975494	+	0.220028i	$0.929385\pi$
$410$		−	2.14001i		−	0.105687i
$411$		0			0
$412$	8.30368	−	14.3824i	0.409093	−	0.708570i
$413$	12.1401	−	5.31760i	0.597373	−	0.261662i
$414$		0			0
$415$	−1.07746	+	1.86621i	−0.0528902	+	0.0916085i
$416$	−17.0156	+	7.49177i	−0.834257	+	0.367314i
$417$		0			0
$418$		−	1.67155i		−	0.0817583i
$419$	−16.0435	−	27.7881i	−0.783775	−	1.35754i	−0.929728	−	0.368247i	$-0.879958\pi$
$419$	−16.0435	−	27.7881i	−0.783775	−	1.35754i	0.145953	−	0.989292i	$-0.453375\pi$
$420$		0			0
$421$			10.0906i			0.491785i	0.969297	+	0.245892i	$0.0790810\pi$
$421$			10.0906i			0.491785i	−0.969297	+	0.245892i	$0.920919\pi$
$422$	−4.90067	+	2.82940i	−0.238561	+	0.137733i
$423$		0			0
$424$	−21.7292	+	12.5453i	−1.05526	+	0.609256i
$425$	5.35323	+	9.27207i	0.259670	+	0.449761i
$426$		0			0
$427$	17.1860	−	23.3570i	0.831690	−	1.13032i
$428$	−11.6103			−0.561204
$429$		0			0
$430$	0.471593	+	0.816822i	0.0227422	+	0.0393907i
$431$	−0.967588	−	0.558637i	−0.0466071	−	0.0269086i	0.476515	−	0.879166i	$-0.341900\pi$
$431$	−0.967588	−	0.558637i	−0.0466071	−	0.0269086i	−0.523122	+	0.852258i	$0.675233\pi$
$432$		0			0
$433$	−14.9651	+	25.9203i	−0.719176	+	1.24565i	0.242151	+	0.970239i	$0.422147\pi$
$433$	−14.9651	+	25.9203i	−0.719176	+	1.24565i	−0.961327	+	0.275410i	$0.911186\pi$
$434$	0.167267	−	0.227327i	0.00802908	−	0.0109121i
$435$		0			0
$436$	6.44087	−	3.71864i	0.308462	−	0.178090i
$437$	−3.32853	+	1.92173i	−0.159225	+	0.0919288i
$438$		0			0
$439$	−19.1161			−0.912360			−0.456180	−	0.889887i	$-0.650783\pi$
$439$	−19.1161			−0.912360			−0.456180	+	0.889887i	$0.650783\pi$
$440$	−0.595723	+	0.343941i	−0.0284000	+	0.0163967i
$441$		0			0
$442$	7.00231	−	3.08304i	0.333066	−	0.146645i
$443$	−6.70719	+	11.6172i	−0.318668	+	0.551950i	−0.980210	−	0.197958i	$-0.936569\pi$
$443$	−6.70719	+	11.6172i	−0.318668	+	0.551950i	0.661542	+	0.749908i	$0.269902\pi$
$444$		0			0
$445$	−0.366303	+	0.634455i	−0.0173644	+	0.0300761i
$446$	−10.8193	−	18.7395i	−0.512307	−	0.887341i
$447$		0			0
$448$	−7.07015	−	16.1411i	−0.334033	−	0.762597i
$449$	13.9832	+	8.07323i	0.659910	+	0.380999i	0.792243	−	0.610206i	$-0.208913\pi$
$449$	13.9832	+	8.07323i	0.659910	+	0.380999i	−0.132333	+	0.991205i	$0.542247\pi$
$450$		0			0
$451$	−6.95323			−0.327415
$452$	−7.88305	+	13.6538i	−0.370787	+	0.642223i
$453$		0			0
$454$	26.5371			1.24545
$455$	2.45711	−	0.770847i	0.115191	−	0.0361379i
$456$		0			0
$457$		−	7.65880i		−	0.358264i	−0.983825	−	0.179132i	$-0.942671\pi$
$457$		−	7.65880i		−	0.358264i	0.983825	−	0.179132i	$-0.0573289\pi$
$458$	−0.643360	+	1.11433i	−0.0300622	+	0.0520693i
$459$		0			0
$460$	0.470485	+	0.271635i	0.0219365	+	0.0126650i
$461$	−26.3366	−	15.2054i	−1.22662	−	0.708187i	−0.260295	−	0.965529i	$-0.583820\pi$
$461$	−26.3366	−	15.2054i	−1.22662	−	0.708187i	−0.966320	+	0.257342i	$0.917153\pi$
$462$		0			0
$463$			0.0512983i			0.00238403i	0.999999	+	0.00119202i	$0.000379431\pi$
$463$			0.0512983i			0.00238403i	−0.999999	+	0.00119202i	$0.999621\pi$
$464$	−2.41335	−	4.18005i	−0.112037	−	0.194054i
$465$		0			0
$466$	16.0483	+	9.26549i	0.743423	+	0.429216i
$467$	−11.2666	+	19.5143i	−0.521356	+	0.903015i	0.478335	+	0.878177i	$0.341240\pi$
$467$	−11.2666	+	19.5143i	−0.521356	+	0.903015i	−0.999691	+	0.0248380i	$0.992093\pi$
$468$		0			0
$469$	−1.63241	+	14.6791i	−0.0753777	+	0.677818i
$470$	0.156190	−	0.0901766i	0.00720453	−	0.00415954i
$471$		0			0
$472$	14.9025			0.685943
$473$	2.65399	−	1.53228i	0.122031	−	0.0704544i
$474$		0			0
$475$	−8.52705	−	4.92309i	−0.391248	−	0.225887i
$476$	−2.41358	−	5.51021i	−0.110626	−	0.252560i
$477$		0			0
$478$	11.4271			0.522665
$479$	25.7792	+	14.8836i	1.17788	+	0.680049i	0.955523	−	0.294916i	$-0.0952917\pi$
$479$	25.7792	+	14.8836i	1.17788	+	0.680049i	0.222357	+	0.974965i	$0.428625\pi$
$480$		0			0
$481$	−11.5414	+	5.08155i	−0.526243	+	0.231699i
$482$	20.9524			0.954357
$483$		0			0
$484$	−5.37111	−	9.30304i	−0.244142	−	0.422866i
$485$	1.39288	+	2.41254i	0.0632474	+	0.109548i
$486$		0			0
$487$			7.87082i			0.356661i	0.983971	+	0.178330i	$0.0570696\pi$
$487$			7.87082i			0.356661i	−0.983971	+	0.178330i	$0.942930\pi$
$488$	28.2377	−	16.3030i	1.27826	−	0.738004i
$489$		0			0
$490$	0.549032	+	1.76178i	0.0248027	+	0.0795893i
$491$	−11.3549	−	19.6673i	−0.512441	−	0.887574i	−0.999896	−	0.0144261i	$-0.995408\pi$
$491$	−11.3549	−	19.6673i	−0.512441	−	0.887574i	0.487455	−	0.873148i	$-0.337925\pi$
$492$		0			0
$493$	−6.45488	−	11.1802i	−0.290713	−	0.503530i
$494$	−4.15926	+	5.67529i	−0.187134	+	0.255343i
$495$		0			0
$496$	0.0768568	−	0.0443733i	0.00345097	−	0.00199242i
$497$	−4.22589	+	38.0004i	−0.189557	+	1.70455i
$498$		0			0
$499$	20.7627	+	11.9874i	0.929467	+	0.536628i	0.886643	−	0.462455i	$-0.153031\pi$
$499$	20.7627	+	11.9874i	0.929467	+	0.536628i	0.0428241	+	0.999083i	$0.486365\pi$
$500$			2.80408i			0.125402i
$501$		0			0
$502$	10.3864	+	5.99662i	0.463570	+	0.267642i
$503$	8.75880	−	15.1707i	0.390535	−	0.676427i	−0.601985	−	0.798508i	$-0.705623\pi$
$503$	8.75880	−	15.1707i	0.390535	−	0.676427i	0.992520	+	0.122080i	$0.0389566\pi$
$504$		0			0
$505$	−2.64404	+	1.52654i	−0.117658	+	0.0679301i
$506$	−0.804385	+	1.39324i	−0.0357593	+	0.0619369i
$507$		0			0
$508$	0.837000	+	1.44973i	0.0371359	+	0.0643212i
$509$			14.5540i			0.645095i	0.946553	+	0.322548i	$0.104539\pi$
$509$			14.5540i			0.645095i	−0.946553	+	0.322548i	$0.895461\pi$
$510$		0			0
$511$	−8.76086	−	6.44623i	−0.387558	−	0.285165i
$512$		−	9.02303i		−	0.398765i
$513$		0			0
$514$			0.967059i			0.0426551i
$515$	−3.71056	+	2.14229i	−0.163507	+	0.0944007i
$516$		0			0
$517$	−0.292999	−	0.507489i	−0.0128861	−	0.0223193i
$518$	−3.62565	−	8.27736i	−0.159302	−	0.363686i
$519$		0			0
$520$	2.87843	+	0.314560i	0.126227	+	0.0137944i
$521$	14.8659	+	25.7484i	0.651286	+	1.12806i	0.982811	+	0.184614i	$0.0591033\pi$
$521$	14.8659	+	25.7484i	0.651286	+	1.12806i	−0.331526	+	0.943446i	$0.607563\pi$
$522$		0			0
$523$	−8.39584			−0.367125			−0.183562	−	0.983008i	$-0.558763\pi$
$523$	−8.39584			−0.367125			−0.183562	+	0.983008i	$0.558763\pi$
$524$	−6.58442	+	11.4046i	−0.287642	+	0.498210i
$525$		0			0
$526$	0.317186	+	0.183127i	0.0138300	+	0.00798473i
$527$	0.205565	−	0.118683i	0.00895457	−	0.00516992i
$528$		0			0
$529$	−19.3009			−0.839170
$530$	2.22341			0.0965787
$531$		0			0
$532$	4.45600	+	3.27872i	0.193192	+	0.142151i
$533$	23.6077	+	17.3015i	1.02257	+	0.749409i
$534$		0			0
$535$	2.59407	+	1.49769i	0.112151	+	0.0647506i
$536$	−8.30354	+	14.3821i	−0.358658	+	0.621214i
$537$		0			0
$538$		−	16.6589i		−	0.718215i
$539$	5.72433	−	1.78390i	0.246564	−	0.0768379i
$540$		0			0
$541$	38.2304	+	22.0723i	1.64365	+	0.948964i	0.979519	+	0.201350i	$0.0645328\pi$
$541$	38.2304	+	22.0723i	1.64365	+	0.948964i	0.664134	+	0.747614i	$0.268801\pi$
$542$	−13.0489			−0.560498
$543$		0			0
$544$		−	11.2048i		−	0.480400i
$545$	−1.91877			−0.0821909
$546$		0			0
$547$	3.55444			0.151977			0.0759885	−	0.997109i	$-0.475789\pi$
$547$	3.55444			0.151977			0.0759885	+	0.997109i	$0.475789\pi$
$548$		−	18.5804i		−	0.793717i
$549$		0			0
$550$	−4.12135			−0.175735
$551$	10.2818	+	5.93622i	0.438021	+	0.252892i
$552$		0			0
$553$	−4.11647	−	0.457778i	−0.175050	−	0.0194667i
$554$		−	4.59358i		−	0.195163i
$555$		0			0
$556$	12.0194	−	20.8182i	0.509736	−	0.882889i
$557$	−21.1719	−	12.2236i	−0.897083	−	0.517931i	−0.0208303	−	0.999783i	$-0.506631\pi$
$557$	−21.1719	−	12.2236i	−0.897083	−	0.517931i	−0.876253	+	0.481852i	$0.839964\pi$
$558$		0			0
$559$	−12.8236	−	1.40139i	−0.542381	−	0.0592724i
$560$	−0.0641331	+	0.576703i	−0.00271012	+	0.0243701i
$561$		0			0
$562$	−30.5611			−1.28914
$563$	13.6017			0.573245			0.286622	−	0.958044i	$-0.407468\pi$
$563$	13.6017			0.573245			0.286622	+	0.958044i	$0.407468\pi$
$564$		0			0
$565$	3.52260	−	2.03377i	0.148197	−	0.0855614i
$566$	13.1419	+	7.58749i	0.552396	+	0.318926i
$567$		0			0
$568$	−21.4957	+	37.2317i	−0.901941	+	1.56221i
$569$	−0.836836			−0.0350820			−0.0175410	−	0.999846i	$-0.505584\pi$
$569$	−0.836836			−0.0350820			−0.0175410	+	0.999846i	$0.505584\pi$
$570$		0			0
$571$	−14.1413	−	24.4935i	−0.591796	−	1.02502i	−0.993990	−	0.109467i	$-0.965086\pi$
$571$	−14.1413	−	24.4935i	−0.591796	−	1.02502i	0.402194	−	0.915554i	$-0.368248\pi$
$572$	0.351054	−	3.21237i	0.0146783	−	0.134316i
$573$		0			0
$574$	−12.4302	+	16.8935i	−0.518826	+	0.705119i
$575$	4.73818	+	8.20677i	0.197596	+	0.342246i
$576$		0			0
$577$	23.7679	−	13.7224i	0.989472	−	0.571272i	0.0843557	−	0.996436i	$-0.473117\pi$
$577$	23.7679	−	13.7224i	0.989472	−	0.571272i	0.905116	+	0.425164i	$0.139783\pi$
$578$		−	11.9903i		−	0.498729i
$579$		0			0
$580$		−	1.67816i		−	0.0696818i
$581$	19.3454	−	8.47368i	0.802582	−	0.351548i
$582$		0			0
$583$		−	7.22423i		−	0.299197i
$584$	−6.11504	−	10.5916i	−0.253042	−	0.438282i
$585$		0			0
$586$	−2.94386	+	5.09892i	−0.121610	+	0.210634i
$587$	4.70300	−	2.71528i	0.194113	−	0.112071i	−0.399793	−	0.916605i	$-0.630918\pi$
$587$	4.70300	−	2.71528i	0.194113	−	0.112071i	0.593907	+	0.804534i	$0.297585\pi$
$588$		0			0
$589$	−0.109147	+	0.189048i	−0.00449732	+	0.00778959i
$590$	−1.14366	−	0.660292i	−0.0470837	−	0.0271838i
$591$		0			0
$592$		−	2.84150i		−	0.116785i
$593$	21.9497	+	12.6726i	0.901364	+	0.520403i	0.877643	−	0.479316i	$-0.159115\pi$
$593$	21.9497	+	12.6726i	0.901364	+	0.520403i	0.0237218	+	0.999719i	$0.492448\pi$
$594$		0			0
$595$	−0.171534	+	1.54248i	−0.00703221	+	0.0632356i
$596$	11.6331	−	6.71640i	0.476512	−	0.275114i
$597$		0			0
$598$	6.19779	−	2.72882i	0.253447	−	0.111590i
$599$	10.4813	+	18.1541i	0.428253	+	0.741756i	0.996718	−	0.0809515i	$-0.0257959\pi$
$599$	10.4813	+	18.1541i	0.428253	+	0.741756i	−0.568465	+	0.822707i	$0.692463\pi$
$600$		0			0
$601$	15.7239	+	27.2345i	0.641390	+	1.11092i	0.985123	+	0.171852i	$0.0549752\pi$
$601$	15.7239	+	27.2345i	0.641390	+	1.11092i	−0.343733	+	0.939067i	$0.611691\pi$
$602$	1.02169	−	9.18733i	0.0416410	−	0.374448i
$603$		0			0
$604$	7.66312	−	4.42430i	0.311808	−	0.180022i
$605$			2.77142i			0.112674i
$606$		0			0
$607$	9.97909	+	17.2843i	0.405039	+	0.701548i	0.994326	−	0.106376i	$-0.0339247\pi$
$607$	9.97909	+	17.2843i	0.405039	+	0.701548i	−0.589287	+	0.807924i	$0.700591\pi$
$608$	5.15223	+	8.92392i	0.208950	+	0.361913i
$609$		0			0
$610$	−2.88939			−0.116988
$611$	−0.267969	+	2.45209i	−0.0108409	+	0.0992010i
$612$		0			0
$613$	4.21477	+	2.43340i	0.170233	+	0.0982841i	0.582696	−	0.812690i	$-0.301998\pi$
$613$	4.21477	+	2.43340i	0.170233	+	0.0982841i	−0.412463	+	0.910974i	$0.635331\pi$
$614$	13.4379			0.542311
$615$		0			0
$616$	6.70049	+	0.745138i	0.269970	+	0.0300225i
$617$	−21.6231	−	12.4841i	−0.870512	−	0.502590i	−0.00299347	−	0.999996i	$-0.500953\pi$
$617$	−21.6231	−	12.4841i	−0.870512	−	0.502590i	−0.867518	+	0.497405i	$0.834286\pi$
$618$		0			0
$619$	−17.1875	+	9.92322i	−0.690825	+	0.398848i	−0.803921	−	0.594736i	$-0.797257\pi$
$619$	−17.1875	+	9.92322i	−0.690825	+	0.398848i	0.113096	+	0.993584i	$0.463923\pi$
$620$	0.0308556			0.00123919
$621$		0			0
$622$	−23.8200	+	13.7525i	−0.955094	+	0.551424i
$623$	6.57686	−	2.88080i	0.263496	−	0.115417i
$624$		0			0
$625$	−11.9561	+	20.7086i	−0.478244	+	0.828343i
$626$	−10.3249	−	5.96109i	−0.412667	−	0.238253i
$627$		0			0
$628$	8.74496	+	15.1467i	0.348962	+	0.604420i
$629$		−	7.60002i		−	0.303033i
$630$		0			0
$631$	−34.8669	−	20.1304i	−1.38803	−	0.801380i	−0.394937	−	0.918708i	$-0.629234\pi$
$631$	−34.8669	−	20.1304i	−1.38803	−	0.801380i	−0.993093	+	0.117329i	$0.962567\pi$
$632$	−4.03319	−	2.32856i	−0.160432	−	0.0926253i
$633$		0			0
$634$	6.30202	−	10.9154i	0.250285	−	0.433507i
$635$		−	0.431880i		−	0.0171387i
$636$		0			0
$637$	−23.8741	−	8.18690i	−0.945928	−	0.324377i
$638$	4.96949			0.196744
$639$		0			0
$640$	0.514089	−	0.890428i	0.0203211	−	0.0351972i
$641$	−17.8340			−0.704400			−0.352200	−	0.935925i	$-0.614566\pi$
$641$	−17.8340			−0.704400			−0.352200	+	0.935925i	$0.614566\pi$
$642$		0			0
$643$	30.6543	+	17.6983i	1.20889	+	0.697953i	0.962517	−	0.271222i	$-0.0874279\pi$
$643$	30.6543	+	17.6983i	1.20889	+	0.697953i	0.246373	+	0.969175i	$0.420761\pi$
$644$	−2.13628	−	4.87712i	−0.0841812	−	0.192185i
$645$		0			0
$646$	−2.12026	−	3.67240i	−0.0834207	−	0.144489i
$647$	18.5936	−	32.2050i	0.730988	−	1.26611i	−0.225473	−	0.974249i	$-0.572393\pi$
$647$	18.5936	−	32.2050i	0.730988	−	1.26611i	0.956461	−	0.291860i	$-0.0942740\pi$
$648$		0			0
$649$	−2.14540	+	3.71594i	−0.0842142	+	0.145863i
$650$	13.9929	+	10.2550i	0.548846	+	0.402234i
$651$		0			0
$652$	19.5672	−	11.2971i	0.766309	−	0.442429i
$653$	48.8766			1.91269			0.956344	−	0.292243i	$-0.0944017\pi$
$653$	48.8766			1.91269			0.956344	+	0.292243i	$0.0944017\pi$
$654$		0			0
$655$	2.94230	−	1.69874i	0.114965	−	0.0663751i
$656$	−5.71149	+	3.29753i	−0.222996	+	0.128747i
$657$		0			0
$658$	−1.75678	−	0.195365i	−0.0684862	−	0.00761611i
$659$	4.54386	−	7.87020i	0.177004	−	0.306579i	−0.763849	−	0.645395i	$-0.776693\pi$
$659$	4.54386	−	7.87020i	0.177004	−	0.306579i	0.940853	+	0.338815i	$0.110026\pi$
$660$		0			0
$661$	−0.714628	−	0.412591i	−0.0277958	−	0.0160479i	0.486038	−	0.873938i	$-0.338442\pi$
$661$	−0.714628	−	0.412591i	−0.0277958	−	0.0160479i	−0.513834	+	0.857890i	$0.671775\pi$
$662$	−7.56788	−	13.1080i	−0.294134	−	0.509455i
$663$		0			0
$664$	23.7474			0.921576
$665$	−0.572654	−	1.30737i	−0.0222066	−	0.0506976i
$666$		0			0
$667$	−5.71326	−	9.89566i	−0.221218	−	0.383161i
$668$	10.8767	−	6.27964i	0.420830	−	0.242966i
$669$		0			0
$670$	1.27447	−	0.735817i	0.0492372	−	0.0284271i
$671$			9.38809i			0.362423i
$672$		0			0
$673$	−4.51142	−	7.81401i	−0.173903	−	0.301208i	0.765878	−	0.642985i	$-0.222304\pi$
$673$	−4.51142	−	7.81401i	−0.173903	−	0.301208i	−0.939781	+	0.341777i	$0.888971\pi$
$674$			33.8293i			1.30306i
$675$		0			0
$676$	−9.18513	+	10.0332i	−0.353274	+	0.385892i
$677$	−17.0440	+	29.5211i	−0.655055	+	1.13459i	0.326825	+	0.945085i	$0.394021\pi$
$677$	−17.0440	+	29.5211i	−0.655055	+	1.13459i	−0.981880	+	0.189503i	$0.939312\pi$
$678$		0			0
$679$	3.01763	−	27.1354i	0.115806	−	1.04136i
$680$	−0.872537	+	1.51128i	−0.0334603	+	0.0579549i
$681$		0			0
$682$			0.0913720i			0.00349881i
$683$		−	45.1344i		−	1.72702i	−0.504333	−	0.863509i	$-0.668262\pi$
$683$		−	45.1344i		−	1.72702i	0.504333	−	0.863509i	$-0.331738\pi$
$684$		0			0
$685$	−2.39681	+	4.15140i	−0.0915775	+	0.158617i
$686$	5.89917	−	17.0968i	0.225231	−	0.652758i
$687$		0			0
$688$	1.45335	−	2.51728i	0.0554085	−	0.0959704i
$689$	−17.9758	+	24.5278i	−0.684822	+	0.934436i
$690$		0			0
$691$			1.12706i			0.0428753i	0.999770	+	0.0214376i	$0.00682433\pi$
$691$			1.12706i			0.0428753i	−0.999770	+	0.0214376i	$0.993176\pi$
$692$	3.70572	+	6.41849i	0.140870	+	0.243994i
$693$		0			0
$694$		−	30.0788i		−	1.14177i
$695$	−5.37096	+	3.10092i	−0.203732	+	0.117625i
$696$		0			0
$697$	−15.2763	+	8.81975i	−0.578630	+	0.334072i
$698$	−5.98937	−	10.3739i	−0.226701	−	0.392658i
$699$		0			0
$700$	8.08395	−	10.9866i	0.305545	−	0.415256i
$701$	−27.0972			−1.02345			−0.511723	−	0.859151i	$-0.670993\pi$
$701$	−27.0972			−1.02345			−0.511723	+	0.859151i	$0.670993\pi$
$702$		0			0
$703$	3.49468	+	6.05296i	0.131804	+	0.228292i
$704$	4.94062	+	2.85247i	0.186207	+	0.107506i
$705$		0			0
$706$	−1.89447	+	3.28131i	−0.0712992	+	0.123494i
$707$	29.7393	+	3.30720i	1.11846	+	0.124380i
$708$		0			0
$709$	1.88215	−	1.08666i	0.0706856	−	0.0408103i	−0.464241	−	0.885709i	$-0.653673\pi$
$709$	1.88215	−	1.08666i	0.0706856	−	0.0408103i	0.534926	+	0.844899i	$0.320339\pi$
$710$	3.29928	−	1.90484i	0.123820	−	0.0714875i
$711$		0			0
$712$	8.07340			0.302563
$713$	0.181947	−	0.105047i	0.00681398	−	0.00393405i
$714$		0			0
$715$	−0.492821	+	0.672451i	−0.0184304	+	0.0251482i
$716$	7.11980	−	12.3319i	0.266079	−	0.460863i
$717$		0			0
$718$	18.1752	−	31.4803i	0.678291	−	1.17483i
$719$	−18.7379	−	32.4550i	−0.698805	−	1.21037i	−0.968881	−	0.247527i	$-0.920382\pi$
$719$	−18.7379	−	32.4550i	−0.698805	−	1.21037i	0.270076	−	0.962839i	$-0.412951\pi$
$720$		0			0
$721$	41.7351	+	4.64121i	1.55430	+	0.172848i
$722$	−12.6913	−	7.32730i	−0.472320	−	0.272694i
$723$		0			0
$724$	−11.5092			−0.427738
$725$	14.6362	−	25.3507i	0.543576	−	0.941502i
$726$		0			0
$727$	−17.7356			−0.657775			−0.328888	−	0.944369i	$-0.606674\pi$
$727$	−17.7356			−0.657775			−0.328888	+	0.944369i	$0.606674\pi$
$728$	−20.8955	−	19.2025i	−0.774440	−	0.711691i
$729$		0			0
$730$			1.08377i			0.0401121i
$731$	3.88722	−	6.73285i	0.143774	−	0.249024i
$732$		0			0
$733$	26.7507	+	15.4445i	0.988058	+	0.570456i	0.904693	−	0.426063i	$-0.140100\pi$
$733$	26.7507	+	15.4445i	0.988058	+	0.570456i	0.0833651	+	0.996519i	$0.473433\pi$
$734$	−14.5010	−	8.37215i	−0.535241	−	0.309022i
$735$		0			0
$736$		−	9.91741i		−	0.365561i
$737$	−2.39079	−	4.14097i	−0.0880660	−	0.152535i
$738$		0			0
$739$	37.1382	+	21.4417i	1.36615	+	0.788748i	0.990434	−	0.137987i	$-0.0440632\pi$
$739$	37.1382	+	21.4417i	1.36615	+	0.788748i	0.375717	+	0.926735i	$0.377397\pi$
$740$	0.493969	−	0.855579i	0.0181587	−	0.0314517i
$741$		0			0
$742$	−17.5519	−	12.9146i	−0.644349	−	0.474111i
$743$	7.88851	−	4.55444i	0.289401	−	0.167086i	−0.348270	−	0.937394i	$-0.613231\pi$
$743$	7.88851	−	4.55444i	0.289401	−	0.167086i	0.637672	+	0.770308i	$0.279898\pi$
$744$		0			0
$745$	−3.46557			−0.126969
$746$	9.59552	−	5.53998i	0.351317	−	0.202833i
$747$		0			0
$748$	1.68661	+	0.973766i	0.0616686	+	0.0356044i
$749$	−11.7786	−	26.8905i	−0.430381	−	0.982558i
$750$		0			0
$751$	−24.3205			−0.887469			−0.443734	−	0.896158i	$-0.646347\pi$
$751$	−24.3205			−0.887469			−0.443734	+	0.896158i	$0.646347\pi$
$752$	−0.481347	−	0.277906i	−0.0175529	−	0.0101342i
$753$		0			0
$754$	−16.8725	−	12.3654i	−0.614460	−	0.450321i
$755$	−2.28288			−0.0830825
$756$		0			0
$757$	−8.95806	−	15.5158i	−0.325586	−	0.563932i	0.656045	−	0.754722i	$-0.272228\pi$
$757$	−8.95806	−	15.5158i	−0.325586	−	0.563932i	−0.981631	+	0.190790i	$0.938895\pi$
$758$	10.3364	+	17.9032i	0.375436	+	0.650274i
$759$		0			0
$760$		−	1.60485i		−	0.0582142i
$761$	−43.6045	+	25.1751i	−1.58066	+	0.912596i	−0.585901	+	0.810383i	$0.699259\pi$
$761$	−43.6045	+	25.1751i	−1.58066	+	0.912596i	−0.994763	+	0.102213i	$0.967408\pi$
$762$		0			0
$763$	15.1470	+	11.1451i	0.548357	+	0.403481i
$764$	−6.61514	−	11.4578i	−0.239327	−	0.414527i
$765$		0			0
$766$	10.4360	+	18.0756i	0.377067	+	0.653099i
$767$	16.5303	−	7.27811i	0.596875	−	0.262797i
$768$		0			0
$769$	8.74545	−	5.04919i	0.315369	−	0.182078i	−0.333958	−	0.942588i	$-0.608384\pi$
$769$	8.74545	−	5.04919i	0.315369	−	0.182078i	0.649326	+	0.760510i	$0.275051\pi$
$770$	−0.481199	−	0.354066i	−0.0173412	−	0.0127596i
$771$		0			0
$772$	15.4666	+	8.92966i	0.556656	+	0.321385i
$773$		−	20.0887i		−	0.722540i	−0.932461	−	0.361270i	$-0.882343\pi$
$773$		−	20.0887i		−	0.722540i	0.932461	−	0.361270i	$-0.117657\pi$
$774$		0			0
$775$	0.466113	+	0.269111i	0.0167433	+	0.00966674i
$776$	15.3497	−	26.5864i	0.551022	−	0.954398i
$777$		0			0
$778$	2.17907	−	1.25809i	0.0781235	−	0.0451046i
$779$	8.11108	−	14.0488i	0.290609	−	0.503350i
$780$		0			0
$781$	−6.18915	−	10.7199i	−0.221465	−	0.383589i
$782$			4.08125i			0.145945i
$783$		0			0
$784$	3.85604	−	4.18005i	0.137716	−	0.149287i
$785$		−	4.51228i		−	0.161050i
$786$		0			0
$787$			27.4272i			0.977673i	0.872375	+	0.488837i	$0.162579\pi$
$787$			27.4272i			0.977673i	−0.872375	+	0.488837i	$0.837421\pi$
$788$	−7.37901	+	4.26027i	−0.262866	+	0.151766i
$789$		0			0
$790$	0.206346	+	0.357401i	0.00734145	+	0.0127158i
$791$	−39.6209	−	4.40610i	−1.40876	−	0.156663i
$792$		0			0
$793$	23.3600	−	31.8746i	0.829539	−	1.13190i
$794$	−5.71624	−	9.90082i	−0.202862	−	0.351367i
$795$		0			0
$796$	10.3062			0.365295
$797$	−5.27175	+	9.13093i	−0.186735	+	0.323434i	−0.944160	−	0.329488i	$-0.893124\pi$
$797$	−5.27175	+	9.13093i	−0.186735	+	0.323434i	0.757425	+	0.652922i	$0.226457\pi$
$798$		0			0
$799$	−1.28744	−	0.743302i	−0.0455463	−	0.0262961i
$800$	22.0026	−	12.7032i	0.777911	−	0.449127i
$801$		0			0
$802$	−36.6726			−1.29495
$803$	3.52134			0.124265
$804$		0			0
$805$	−0.151826	+	1.36526i	−0.00535116	+	0.0481191i
$806$	0.227357	−	0.310228i	0.00800832	−	0.0109273i
$807$		0			0
$808$	29.1377	+	16.8226i	1.02506	+	0.591818i
$809$	−22.5557	+	39.0675i	−0.793015	+	1.37354i	0.131078	+	0.991372i	$0.458156\pi$
$809$	−22.5557	+	39.0675i	−0.793015	+	1.37354i	−0.924092	+	0.382170i	$0.875177\pi$
$810$		0			0
$811$		−	47.4243i		−	1.66529i	−0.553806	−	0.832646i	$-0.686825\pi$
$811$		−	47.4243i		−	1.66529i	0.553806	−	0.832646i	$-0.313175\pi$
$812$	−9.74756	+	13.2476i	−0.342072	+	0.464899i
$813$		0			0
$814$	2.53361	+	1.46278i	0.0888028	+	0.0512703i
$815$	−5.82915			−0.204186
$816$		0			0
$817$			7.14975i			0.250138i
$818$	−8.69085			−0.303868
$819$		0			0
$820$	−2.29298			−0.0800745
$821$			2.29657i			0.0801508i	0.999197	+	0.0400754i	$0.0127598\pi$
$821$			2.29657i			0.0801508i	−0.999197	+	0.0400754i	$0.987240\pi$
$822$		0			0
$823$	−13.9893			−0.487636			−0.243818	−	0.969821i	$-0.578400\pi$
$823$	−13.9893			−0.487636			−0.243818	+	0.969821i	$0.578400\pi$
$824$	40.8908	+	23.6083i	1.42450	+	0.822435i
$825$		0			0
$826$	5.19288	+	11.8553i	0.180684	+	0.412500i
$827$		−	24.9362i		−	0.867115i	−0.901126	−	0.433558i	$-0.857258\pi$
$827$		−	24.9362i		−	0.867115i	0.901126	−	0.433558i	$-0.142742\pi$
$828$		0			0
$829$	20.3143	−	35.1854i	0.705546	−	1.22204i	−0.260949	−	0.965353i	$-0.584035\pi$
$829$	20.3143	−	35.1854i	0.705546	−	1.22204i	0.966494	−	0.256688i	$-0.0826314\pi$
$830$	−1.82244	−	1.05219i	−0.0632578	−	0.0365219i
$831$		0			0
$832$	−9.67680	−	21.9783i	−0.335483	−	0.761961i
$833$	10.3136	−	11.1802i	0.357345	−	0.387370i
$834$		0			0
$835$	−3.24021			−0.112132
$836$	−1.79104			−0.0619446
$837$		0			0
$838$	27.1364	−	15.6672i	0.937412	−	0.541215i
$839$	13.2505	+	7.65020i	0.457459	+	0.264114i	0.710975	−	0.703217i	$-0.248254\pi$
$839$	13.2505	+	7.65020i	0.457459	+	0.264114i	−0.253516	+	0.967331i	$0.581587\pi$
$840$		0			0
$841$	−3.14826	+	5.45295i	−0.108561	+	0.188033i
$842$	−9.85393			−0.339589
$843$		0			0
$844$	3.03166	+	5.25099i	0.104354	+	0.180747i
$845$	3.34647	−	1.05685i	0.115122	−	0.0363568i
$846$		0			0
$847$	16.0978	−	21.8779i	0.553125	−	0.751735i
$848$	−3.42605	−	5.93409i	−0.117651	−	0.203777i
$849$		0			0
$850$	−9.05461	+	5.22768i	−0.310571	+	0.179308i
$851$		−	6.72683i		−	0.230593i
$852$		0			0
$853$		−	10.9869i		−	0.376183i	−0.982151	−	0.188092i	$-0.939770\pi$
$853$		−	10.9869i		−	0.376183i	0.982151	−	0.188092i	$-0.0602302\pi$
$854$	22.8092	+	16.7830i	0.780513	+	0.574301i
$855$		0			0
$856$		−	33.0094i		−	1.12824i
$857$	7.19211	+	12.4571i	0.245678	+	0.425526i	0.962322	−	0.271913i	$-0.0876561\pi$
$857$	7.19211	+	12.4571i	0.245678	+	0.425526i	−0.716644	+	0.697439i	$0.754323\pi$
$858$		0			0
$859$	12.9855	−	22.4915i	0.443058	−	0.767399i	−0.554857	−	0.831946i	$-0.687227\pi$
$859$	12.9855	−	22.4915i	0.443058	−	0.767399i	0.997915	+	0.0645470i	$0.0205602\pi$
$860$	0.875213	−	0.505305i	0.0298445	−	0.0172307i
$861$		0			0
$862$	0.545536	−	0.944895i	0.0185810	−	0.0321833i
$863$	35.9901	+	20.7789i	1.22512	+	0.707322i	0.966004	−	0.258525i	$-0.0832366\pi$
$863$	35.9901	+	20.7789i	1.22512	+	0.707322i	0.259113	+	0.965847i	$0.416570\pi$
$864$		0			0
$865$		−	1.91210i		−	0.0650133i
$866$	−25.3124	−	14.6141i	−0.860149	−	0.496607i
$867$		0			0
$868$	−0.243578	−	0.179224i	−0.00826757	−	0.00608327i
$869$	1.16126	−	0.670451i	0.0393929	−	0.0227435i
$870$		0			0
$871$	−2.18656	+	20.0084i	−0.0740887	+	0.677960i
$872$	10.5725	+	18.3121i	0.358030	+	0.620127i
$873$		0			0
$874$	−1.87666	−	3.25047i	−0.0634789	−	0.109949i
$875$	−6.49452	+	2.84473i	−0.219555	+	0.0961696i
$876$		0			0
$877$	−25.9308	+	14.9712i	−0.875621	+	0.505540i	−0.869212	−	0.494440i	$-0.835373\pi$
$877$	−25.9308	+	14.9712i	−0.875621	+	0.505540i	−0.00640883	+	0.999979i	$0.502040\pi$
$878$		−	18.6677i		−	0.630006i
$879$		0			0
$880$	−0.0939279	−	0.162688i	−0.00316631	−	0.00548421i
$881$	−10.5608	−	18.2919i	−0.355803	−	0.616269i	0.631452	−	0.775415i	$-0.282459\pi$
$881$	−10.5608	−	18.2919i	−0.355803	−	0.616269i	−0.987255	+	0.159146i	$0.949126\pi$
$882$		0			0
$883$	20.7966			0.699862			0.349931	−	0.936775i	$-0.386205\pi$
$883$	20.7966			0.699862			0.349931	+	0.936775i	$0.386205\pi$
$884$	−3.30343	−	7.50288i	−0.111106	−	0.252349i
$885$		0			0
$886$	−11.3447	−	6.54989i	−0.381134	−	0.220048i
$887$	−30.1149			−1.01116			−0.505580	−	0.862780i	$-0.668721\pi$
$887$	−30.1149			−1.01116			−0.505580	+	0.862780i	$0.668721\pi$
$888$		0			0
$889$	−2.50857	+	3.40932i	−0.0841348	+	0.114345i
$890$	−0.619575	−	0.357712i	−0.0207682	−	0.0119905i
$891$		0			0
$892$	−20.0791	+	11.5927i	−0.672298	+	0.388152i
$893$	1.36715			0.0457501
$894$		0			0
$895$	−3.18153	+	1.83686i	−0.106347	+	0.0613995i
$896$	−9.23031	+	4.04307i	−0.308363	+	0.135069i
$897$		0			0
$898$	−7.88389	+	13.6553i	−0.263089	+	0.455683i
$899$	−0.562036	−	0.324491i	−0.0187449	−	0.0108224i
$900$		0			0
$901$	−9.16349	−	15.8716i	−0.305280	−	0.528761i
$902$		−	6.79016i		−	0.226088i
$903$		0			0
$904$	−38.8194	−	22.4124i	−1.29111	−	0.745425i
$905$	2.57149	+	1.48465i	0.0854794	+	0.0493515i
$906$		0			0
$907$	−11.6388	+	20.1590i	−0.386460	+	0.669369i	−0.991971	−	0.126469i	$-0.959636\pi$
$907$	−11.6388	+	20.1590i	−0.386460	+	0.669369i	0.605510	+	0.795837i	$0.292969\pi$
$908$		−	28.4342i		−	0.943620i
$909$		0			0
$910$	0.752769	+	2.39948i	0.0249540	+	0.0795420i
$911$	44.5525			1.47609			0.738044	−	0.674752i	$-0.235749\pi$
$911$	44.5525			1.47609			0.738044	+	0.674752i	$0.235749\pi$
$912$		0			0
$913$	−3.41873	+	5.92141i	−0.113143	+	0.195970i
$914$	7.47918			0.247389
$915$		0			0
$916$	1.19399	+	0.689351i	0.0394506	+	0.0227768i
$917$	−33.0939	−	3.68026i	−1.09286	−	0.121533i
$918$		0			0
$919$	24.9437	+	43.2037i	0.822815	+	1.42516i	0.903578	+	0.428424i	$0.140931\pi$
$919$	24.9437	+	43.2037i	0.822815	+	1.42516i	−0.0807626	+	0.996733i	$0.525736\pi$
$920$	−0.772288	+	1.33764i	−0.0254616	+	0.0441008i
$921$		0			0
$922$	14.8488	−	25.7189i	0.489019	−	0.847006i
$923$	−5.66044	+	51.7967i	−0.186316	+	1.70491i
$924$		0			0
$925$	14.9241	−	8.61641i	0.490700	−	0.283306i
$926$	−0.0500952			−0.00164623
$927$		0			0
$928$	−26.5306	+	15.3175i	−0.870910	+	0.502820i
$929$	−33.8457	+	19.5408i	−1.11044	+	0.641113i	−0.938943	−	0.344071i	$-0.888194\pi$
$929$	−33.8457	+	19.5408i	−1.11044	+	0.641113i	−0.171497	+	0.985185i	$0.554860\pi$
$930$		0			0
$931$	−3.07323	+	13.6468i	−0.100721	+	0.447255i
$932$	9.92784	−	17.1955i	0.325197	−	0.563258i
$933$		0			0
$934$	−19.0567	−	11.0024i	−0.623553	−	0.360008i
$935$	−0.251225	−	0.435134i	−0.00821593	−	0.0142304i
$936$		0			0
$937$	−38.4496			−1.25610			−0.628048	−	0.778175i	$-0.716146\pi$
$937$	−38.4496			−1.25610			−0.628048	+	0.778175i	$0.716146\pi$
$938$	−14.3348	−	1.59413i	−0.468049	−	0.0520500i
$939$		0			0
$940$	−0.0966229	−	0.167356i	−0.00315149	−	0.00545854i
$941$	−51.4932	+	29.7296i	−1.67863	+	0.969158i	−0.716095	+	0.698003i	$0.754072\pi$
$941$	−51.4932	+	29.7296i	−1.67863	+	0.969158i	−0.962536	+	0.271155i	$0.912594\pi$
$942$		0			0
$943$	−13.5211	+	7.80642i	−0.440308	+	0.254212i
$944$			4.06977i			0.132460i
$945$		0			0
$946$	1.49635	+	2.59175i	0.0486504	+	0.0842650i
$947$			34.9364i			1.13528i	0.823277	+	0.567639i	$0.192143\pi$
$947$			34.9364i			1.13528i	−0.823277	+	0.567639i	$0.807857\pi$
$948$		0			0
$949$	−11.9557	−	8.76202i	−0.388099	−	0.284427i
$950$	4.80763	−	8.32706i	0.155980	−	0.270166i
$951$		0			0
$952$	15.6661	−	6.86210i	0.507743	−	0.222402i
$953$	11.3153	−	19.5987i	0.366540	−	0.634865i	−0.622482	−	0.782634i	$-0.713876\pi$
$953$	11.3153	−	19.5987i	0.366540	−	0.634865i	0.989022	+	0.147769i	$0.0472091\pi$
$954$		0			0
$955$			3.41332i			0.110452i
$956$		−	12.2440i		−	0.396000i
$957$		0			0
$958$	−14.5345	+	25.1746i	−0.469590	+	0.813353i
$959$	43.0341	−	18.8498i	1.38964	−	0.608692i
$960$		0			0
$961$	−15.4940	+	26.8365i	−0.499808	+	0.865692i
$962$	−4.96237	−	11.2707i	−0.159993	−	0.363383i
$963$		0			0
$964$		−	22.4502i		−	0.723073i
$965$	−2.30379	−	3.99028i	−0.0741616	−	0.128452i
$966$		0			0
$967$			0.0768624i			0.00247173i	0.999999	+	0.00123586i	$0.000393388\pi$
$967$			0.0768624i			0.00247173i	−0.999999	+	0.00123586i	$0.999607\pi$
$968$	26.4496	−	15.2707i	0.850123	−	0.490819i
$969$		0			0
$970$	−2.35596	+	1.36021i	−0.0756452	+	0.0436738i
$971$	−1.39708	−	2.41982i	−0.0448345	−	0.0776557i	0.842737	−	0.538325i	$-0.180943\pi$
$971$	−1.39708	−	2.41982i	−0.0448345	−	0.0776557i	−0.887572	+	0.460669i	$0.847609\pi$
$972$		0			0
$973$	60.4107	+	6.71806i	1.93668	+	0.215371i
$974$	−7.68622			−0.246283
$975$		0			0
$976$	4.45225	+	7.71152i	0.142513	+	0.246840i
$977$	2.83594	+	1.63733i	0.0907298	+	0.0523829i	0.544678	−	0.838645i	$-0.316652\pi$
$977$	2.83594	+	1.63733i	0.0907298	+	0.0523829i	−0.453949	+	0.891028i	$0.649985\pi$
$978$		0			0
$979$	−1.16227	+	2.01310i	−0.0371462	+	0.0643390i
$980$	1.88773	−	0.588280i	0.0603012	−	0.0187919i
$981$		0			0
$982$	19.2061	−	11.0886i	0.612891	−	0.353853i
$983$	−4.04611	+	2.33602i	−0.129051	+	0.0745076i	−0.563136	−	0.826364i	$-0.690405\pi$
$983$	−4.04611	+	2.33602i	−0.129051	+	0.0745076i	0.434085	+	0.900872i	$0.357072\pi$
$984$		0			0
$985$	2.19824			0.0700419
$986$	10.9180	−	6.30350i	0.347699	−	0.200744i
$987$		0			0
$988$	6.08099	+	4.45659i	0.193462	+	0.141783i
$989$	3.44060	−	5.95929i	0.109405	−	0.189495i
$990$		0			0
$991$	3.31788	−	5.74673i	0.105396	−	0.182551i	−0.808504	−	0.588491i	$-0.799722\pi$
$991$	3.31788	−	5.74673i	0.105396	−	0.182551i	0.913900	+	0.405940i	$0.133056\pi$
$992$	−0.281636	−	0.487807i	−0.00894194	−	0.0154879i
$993$		0			0
$994$	−37.1092	−	4.12678i	−1.17703	−	0.130894i
$995$	−2.30271	−	1.32947i	−0.0730008	−	0.0421470i
$996$		0			0
$997$	−13.4800			−0.426915			−0.213457	−	0.976952i	$-0.568472\pi$
$997$	−13.4800			−0.426915			−0.213457	+	0.976952i	$0.568472\pi$
$998$	−11.7062	+	20.2758i	−0.370554	+	0.641818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.e.478.5		12
3.2	odd	2		273.2.t.c.205.2	yes	12
7.4	even	3		819.2.do.f.361.2		12
13.4	even	6		819.2.do.f.667.2		12
21.11	odd	6		273.2.bl.c.88.5	yes	12
39.17	odd	6		273.2.bl.c.121.5	yes	12
91.4	even	6	inner	819.2.bm.e.550.2		12
273.95	odd	6		273.2.t.c.4.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.5	✓	12	273.95	odd	6
273.2.t.c.205.2	yes	12	3.2	odd	2
273.2.bl.c.88.5	yes	12	21.11	odd	6
273.2.bl.c.121.5	yes	12	39.17	odd	6
819.2.bm.e.478.5		12	1.1	even	1	trivial
819.2.bm.e.550.2		12	91.4	even	6	inner
819.2.do.f.361.2		12	7.4	even	3
819.2.do.f.667.2		12	13.4	even	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.976547i q^{2} +1.04636 q^{4} +(-0.233786 - 0.134976i) q^{5} +(1.06153 + 2.42346i) q^{7} +2.97491i q^{8} +O(q^{10})\)	\(q+0.976547i q^{2} +1.04636 q^{4} +(-0.233786 - 0.134976i) q^{5} +(1.06153 + 2.42346i) q^{7} +2.97491i q^{8} +(0.131811 - 0.228303i) q^{10} +(-0.741794 - 0.428275i) q^{11} +(1.45289 + 3.29986i) q^{13} +(-2.36662 + 1.03663i) q^{14} -0.812427 q^{16} -2.17296 q^{17} +(1.73063 - 0.999181i) q^{19} +(-0.244623 - 0.141233i) q^{20} +(0.418231 - 0.724397i) q^{22} -1.92330 q^{23} +(-2.46356 - 4.26702i) q^{25} +(-3.22247 + 1.41882i) q^{26} +(1.11073 + 2.53580i) q^{28} +(2.97054 + 5.14513i) q^{29} +(-0.0946014 + 0.0546182i) q^{31} +5.15645i q^{32} -2.12200i q^{34} +(0.0789401 - 0.709852i) q^{35} +3.49754i q^{37} +(0.975748 + 1.69004i) q^{38} +(0.401542 - 0.695492i) q^{40} +(7.03015 - 4.05886i) q^{41} +(-1.78890 + 3.09847i) q^{43} +(-0.776181 - 0.448128i) q^{44} -1.87820i q^{46} +(0.592480 + 0.342068i) q^{47} +(-4.74633 + 5.14513i) q^{49} +(4.16694 - 2.40578i) q^{50} +(1.52024 + 3.45283i) q^{52} +(4.21705 + 7.30414i) q^{53} +(0.115614 + 0.200249i) q^{55} +(-7.20958 + 3.15794i) q^{56} +(-5.02446 + 2.90088i) q^{58} -5.00939i q^{59} +(-5.48018 - 9.49195i) q^{61} +(-0.0533372 - 0.0923828i) q^{62} -6.66037 q^{64} +(0.105738 - 0.967568i) q^{65} +(4.83448 + 2.79119i) q^{67} -2.27369 q^{68} +(0.693204 + 0.0770887i) q^{70} +(12.5152 + 7.22567i) q^{71} +(-3.56030 + 2.05554i) q^{73} -3.41551 q^{74} +(1.81086 - 1.04550i) q^{76} +(0.250474 - 2.25233i) q^{77} +(-0.782735 + 1.35574i) q^{79} +(0.189934 + 0.109658i) q^{80} +(3.96367 + 6.86527i) q^{82} -7.98255i q^{83} +(0.508008 + 0.293299i) q^{85} +(-3.02580 - 1.74695i) q^{86} +(1.27408 - 2.20677i) q^{88} -2.71383i q^{89} +(-6.45481 + 7.02392i) q^{91} -2.01246 q^{92} +(-0.334046 + 0.578585i) q^{94} -0.539463 q^{95} +(-8.93689 - 5.15972i) q^{97} +(-5.02446 - 4.63501i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

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