LMFDB - Embedded newform 1323.2.h.f.802.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.4
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.f.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +O(q^{10})$	\(q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +(-1.22880 + 2.12835i) q^{10} +(0.756508 + 1.31031i) q^{11} +(2.58800 + 4.48254i) q^{13} -4.84777 q^{16} +(0.774463 - 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(-0.927765 + 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(-3.68039 + 6.37463i) q^{23} +(1.60922 + 2.78725i) q^{25} +(4.76513 + 8.25344i) q^{26} +(0.0309713 - 0.0536439i) q^{29} +3.84777 q^{31} -6.68021 q^{32} +(1.42597 - 2.46986i) q^{34} +(-0.281608 - 0.487760i) q^{37} +(2.30543 + 3.99313i) q^{38} +(0.749363 - 1.29794i) q^{40} +(4.51188 + 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +(1.05167 + 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} -9.51851 q^{47} +(2.96296 + 5.13199i) q^{50} +(3.59775 + 6.23148i) q^{52} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(0.0570257 - 0.0987714i) q^{58} -8.44331 q^{59} -3.23917 q^{61} +7.08467 q^{62} -2.60434 q^{64} -6.90868 q^{65} +6.93339 q^{67} +(1.07663 - 1.86478i) q^{68} +12.3304 q^{71} +(1.37936 - 2.38912i) q^{73} +(-0.518508 - 0.898083i) q^{74} +(1.74064 + 3.01488i) q^{76} -5.91938 q^{79} +(3.23529 - 5.60368i) q^{80} +(8.30746 + 14.3889i) q^{82} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(9.39010 - 16.2641i) q^{86} +(-0.849444 - 1.47128i) q^{88} +(0.703287 + 1.21813i) q^{89} +(-5.11636 + 8.86180i) q^{92} -17.5259 q^{94} -3.34251 q^{95} +(6.09713 - 10.5605i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8 + 7 * q^10 - 4 * q^11 + 8 * q^13 - 4 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 + 11 * q^26 - 7 * q^29 - 6 * q^31 - 4 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 54 * q^47 - 19 * q^50 + 10 * q^52 + 21 * q^53 - 4 * q^55 - 10 * q^58 - 60 * q^59 - 28 * q^61 - 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 + 27 * q^68 + 6 * q^71 - 15 * q^73 + 36 * q^74 - 5 * q^76 + 8 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 28 * q^89 - 27 * q^92 - 6 * q^94 - 28 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.84124			1.30195			0.650977	−	0.759098i	$-0.274359\pi$
$2$	1.84124			1.30195			0.650977	+	0.759098i	$0.274359\pi$
$3$		0			0
$3$		0			0
$4$	1.39017			0.695084
$5$	−0.667377	+	1.15593i	−0.298460	+	0.516948i	−0.975784	−	0.218737i	$-0.929806\pi$
$5$	−0.667377	+	1.15593i	−0.298460	+	0.516948i	0.677324	+	0.735685i	$0.263140\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.12285			−0.396987
$9$		0			0
$10$	−1.22880	+	2.12835i	−0.388581	+	0.673042i
$11$	0.756508	+	1.31031i	0.228096	+	0.395073i	0.957244	−	0.289283i	$-0.0934167\pi$
$11$	0.756508	+	1.31031i	0.228096	+	0.395073i	−0.729148	+	0.684356i	$0.760083\pi$
$12$		0			0
$13$	2.58800	+	4.48254i	0.717781	+	1.24323i	0.961877	+	0.273482i	$0.0881755\pi$
$13$	2.58800	+	4.48254i	0.717781	+	1.24323i	−0.244096	+	0.969751i	$0.578491\pi$
$14$		0			0
$15$		0			0
$16$	−4.84777			−1.21194
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	−0.756693	−	0.653770i	$-0.773186\pi$
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	0.944528	+	0.328430i	$0.106520\pi$
$18$		0			0
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	0.973153	−	0.230158i	$-0.0739244\pi$
$19$	1.25211	+	2.16872i	0.287254	+	0.497538i	−0.685900	+	0.727696i	$0.740591\pi$
$20$	−0.927765	+	1.60694i	−0.207455	+	0.359322i
$21$		0			0
$22$	1.39291	+	2.41260i	0.296970	+	0.514367i
$23$	−3.68039	+	6.37463i	−0.767415	+	1.32920i	0.171545	+	0.985176i	$0.445124\pi$
$23$	−3.68039	+	6.37463i	−0.767415	+	1.32920i	−0.938960	+	0.344025i	$0.888209\pi$
$24$		0			0
$25$	1.60922	+	2.78725i	0.321843	+	0.557449i
$26$	4.76513	+	8.25344i	0.934518	+	1.61863i
$27$		0			0
$28$		0			0
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	−0.863135	−	0.504972i	$-0.831503\pi$
$29$	0.0309713	−	0.0536439i	0.00575123	−	0.00996143i	0.868887	+	0.495011i	$0.164836\pi$
$30$		0			0
$31$	3.84777			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$31$	3.84777			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$32$	−6.68021			−1.18091
$33$		0			0
$34$	1.42597	−	2.46986i	0.244552	−	0.423577i
$35$		0			0
$36$		0			0
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	0.841949	−	0.539557i	$-0.181408\pi$
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	−0.888245	+	0.459370i	$0.848075\pi$
$38$	2.30543	+	3.99313i	0.373991	+	0.647771i
$39$		0			0
$40$	0.749363	−	1.29794i	0.118485	−	0.205222i
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	0.966822	+	0.255450i	$0.0822237\pi$
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	−0.262185	+	0.965018i	$0.584443\pi$
$42$		0			0
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	−0.155526	−	0.987832i	$-0.549707\pi$
$43$	5.09988	−	8.83325i	0.777724	−	1.34706i	0.933251	−	0.359226i	$-0.116959\pi$
$44$	1.05167	+	1.82155i	0.158546	+	0.274609i
$45$		0			0
$46$	−6.77649	+	11.7372i	−0.999139	+	1.73056i
$47$	−9.51851			−1.38842			−0.694209	−	0.719774i	$-0.744245\pi$
$47$	−9.51851			−1.38842			−0.694209	+	0.719774i	$0.744245\pi$
$48$		0			0
$49$		0			0
$50$	2.96296	+	5.13199i	0.419025	+	0.725773i
$51$		0			0
$52$	3.59775	+	6.23148i	0.498918	+	0.864151i
$53$	−0.755374	+	1.30835i	−0.103759	+	0.179715i	−0.913230	−	0.407444i	$-0.866420\pi$
$53$	−0.755374	+	1.30835i	−0.103759	+	0.179715i	0.809472	+	0.587159i	$0.199754\pi$
$54$		0			0
$55$	−2.01950			−0.272310
$56$		0			0
$57$		0			0
$58$	0.0570257	−	0.0987714i	0.00748784	−	0.0129693i
$59$	−8.44331			−1.09923			−0.549613	−	0.835419i	$-0.685225\pi$
$59$	−8.44331			−1.09923			−0.549613	+	0.835419i	$0.685225\pi$
$60$		0			0
$61$	−3.23917			−0.414733			−0.207367	−	0.978263i	$-0.566489\pi$
$61$	−3.23917			−0.414733			−0.207367	+	0.978263i	$0.566489\pi$
$62$	7.08467			0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	−6.90868			−0.856916
$66$		0			0
$67$	6.93339			0.847049			0.423524	−	0.905885i	$-0.360793\pi$
$67$	6.93339			0.847049			0.423524	+	0.905885i	$0.360793\pi$
$68$	1.07663	−	1.86478i	0.130561	−	0.226138i
$69$		0			0
$70$		0			0
$71$	12.3304			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$71$	12.3304			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$72$		0			0
$73$	1.37936	−	2.38912i	0.161442	−	0.279625i	−0.773944	−	0.633254i	$-0.781719\pi$
$73$	1.37936	−	2.38912i	0.161442	−	0.279625i	0.935386	+	0.353629i	$0.115052\pi$
$74$	−0.518508	−	0.898083i	−0.0602754	−	0.104400i
$75$		0			0
$76$	1.74064	+	3.01488i	0.199665	+	0.345830i
$77$		0			0
$78$		0			0
$79$	−5.91938			−0.665982			−0.332991	−	0.942930i	$-0.608058\pi$
$79$	−5.91938			−0.665982			−0.332991	+	0.942930i	$0.608058\pi$
$80$	3.23529	−	5.60368i	0.361716	−	0.626511i
$81$		0			0
$82$	8.30746	+	14.3889i	0.917406	+	1.58899i
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	−0.670344	−	0.742050i	$-0.733854\pi$
$83$	2.80111	−	4.85167i	0.307462	−	0.532540i	0.977806	+	0.209510i	$0.0671870\pi$
$84$		0			0
$85$	1.03372	+	1.79045i	0.112122	+	0.194202i
$86$	9.39010	−	16.2641i	1.01256	−	1.75381i
$87$		0			0
$88$	−0.849444	−	1.47128i	−0.0905511	−	0.156839i
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	0.900890	−	0.434048i	$-0.142915\pi$
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	−0.826341	+	0.563169i	$0.809582\pi$
$90$		0			0
$91$		0			0
$92$	−5.11636	+	8.86180i	−0.533418	+	0.923906i
$93$		0			0
$94$	−17.5259			−1.80765
$95$	−3.34251			−0.342935
$96$		0			0
$97$	6.09713	−	10.5605i	0.619070	−	1.07226i	−0.370586	−	0.928798i	$-0.620843\pi$
$97$	6.09713	−	10.5605i	0.619070	−	1.07226i	0.989656	−	0.143462i	$-0.0458236\pi$
$98$		0			0
$99$		0			0
$100$	2.23708	+	3.87474i	0.223708	+	0.387474i
$101$	−0.559336	−	0.968798i	−0.0556560	−	0.0963990i	0.836855	−	0.547425i	$-0.184392\pi$
$101$	−0.559336	−	0.968798i	−0.0556560	−	0.0963990i	−0.892511	+	0.451025i	$0.851058\pi$
$102$		0			0
$103$	0.965224	−	1.67182i	0.0951063	−	0.164729i	−0.814547	−	0.580098i	$-0.803014\pi$
$103$	0.965224	−	1.67182i	0.0951063	−	0.164729i	0.909653	+	0.415369i	$0.136348\pi$
$104$	−2.90593	−	5.03322i	−0.284950	−	0.493548i
$105$		0			0
$106$	−1.39082	+	2.40898i	−0.135089	+	0.233981i
$107$	−2.88969	−	5.00509i	−0.279357	−	0.483860i	0.691868	−	0.722024i	$-0.256788\pi$
$107$	−2.88969	−	5.00509i	−0.279357	−	0.483860i	−0.971225	+	0.238163i	$0.923455\pi$
$108$		0			0
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	−0.993066	−	0.117557i	$-0.962494\pi$
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	0.598340	+	0.801242i	$0.295827\pi$
$110$	−3.71839			−0.354535
$111$		0			0
$112$		0			0
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	−0.974332	−	0.225115i	$-0.927724\pi$
$113$	−7.25105	−	12.5592i	−0.682121	−	1.18147i	0.292211	−	0.956354i	$-0.405609\pi$
$114$		0			0
$115$	−4.91242	−	8.50856i	−0.458085	−	0.793427i
$116$	0.0430553	−	0.0745740i	0.00399759	−	0.00692403i
$117$		0			0
$118$	−15.5462			−1.43114
$119$		0			0
$120$		0			0
$121$	4.35539	−	7.54376i	0.395945	−	0.685796i
$122$	−5.96409			−0.539963
$123$		0			0
$124$	5.34904			0.480358
$125$	−10.9696			−0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	8.56521			0.757065
$129$		0			0
$130$	−12.7205			−1.11566
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	−0.818690	−	0.574236i	$-0.805299\pi$
$131$	1.00673	−	1.74371i	0.0879585	−	0.152349i	0.906648	+	0.421888i	$0.138632\pi$
$132$		0			0
$133$		0			0
$134$	12.7660			1.10282
$135$		0			0
$136$	−0.869605	+	1.50620i	−0.0745680	+	0.129156i
$137$	1.10870	+	1.92032i	0.0947225	+	0.164064i	0.909493	−	0.415720i	$-0.136470\pi$
$137$	1.10870	+	1.92032i	0.0947225	+	0.164064i	−0.814770	+	0.579784i	$0.803137\pi$
$138$		0			0
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	0.849564	−	0.527485i	$-0.176865\pi$
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	−0.881598	+	0.472002i	$0.843532\pi$
$140$		0			0
$141$		0			0
$142$	22.7032			1.90521
$143$	−3.91568	+	6.78216i	−0.327446	+	0.567153i
$144$		0			0
$145$	0.0413391	+	0.0716014i	0.00343303	+	0.00594618i
$146$	2.53973	−	4.39894i	0.210189	−	0.364059i
$147$		0			0
$148$	−0.391482	−	0.678068i	−0.0321797	−	0.0557368i
$149$	3.29249	−	5.70277i	0.269732	−	0.467189i	−0.699061	−	0.715062i	$-0.746398\pi$
$149$	3.29249	−	5.70277i	0.269732	−	0.467189i	0.968792	+	0.247873i	$0.0797317\pi$
$150$		0			0
$151$	−6.33356	−	10.9700i	−0.515417	−	0.892729i	−0.999840	−	0.0178950i	$-0.994304\pi$
$151$	−6.33356	−	10.9700i	−0.515417	−	0.892729i	0.484422	−	0.874834i	$-0.339030\pi$
$152$	−1.40593	−	2.43514i	−0.114036	−	0.197516i
$153$		0			0
$154$		0			0
$155$	−2.56791	+	4.44775i	−0.206260	+	0.357252i
$156$		0			0
$157$	17.3074			1.38128			0.690642	−	0.723197i	$-0.257328\pi$
$157$	17.3074			1.38128			0.690642	+	0.723197i	$0.257328\pi$
$158$	−10.8990			−0.867078
$159$		0			0
$160$	4.45822	−	7.72186i	0.352453	−	0.610467i
$161$		0			0
$162$		0			0
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	0.999697	−	0.0246014i	$-0.00783167\pi$
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	−0.521154	+	0.853463i	$0.674498\pi$
$164$	6.27227	+	10.8639i	0.489782	+	0.848327i
$165$		0			0
$166$	5.15752	−	8.93309i	0.400301	−	0.693342i
$167$	1.76248	+	3.05270i	0.136385	+	0.236225i	0.926126	−	0.377215i	$-0.123118\pi$
$167$	1.76248	+	3.05270i	0.136385	+	0.236225i	−0.789741	+	0.613440i	$0.789785\pi$
$168$		0			0
$169$	−6.89546	+	11.9433i	−0.530420	+	0.918714i
$170$	1.90332	+	3.29665i	0.145978	+	0.252842i
$171$		0			0
$172$	7.08968	−	12.2797i	0.540583	−	0.936318i
$173$	10.1409			0.770999			0.385500	−	0.922708i	$-0.374029\pi$
$173$	10.1409			0.770999			0.385500	+	0.922708i	$0.374029\pi$
$174$		0			0
$175$		0			0
$176$	−3.66738	−	6.35208i	−0.276439	−	0.478806i
$177$		0			0
$178$	1.29492	+	2.24287i	0.0970584	+	0.168110i
$179$	−0.850579	+	1.47325i	−0.0635752	+	0.110116i	−0.896061	−	0.443931i	$-0.853584\pi$
$179$	−0.850579	+	1.47325i	−0.0635752	+	0.110116i	0.832486	+	0.554046i	$0.186917\pi$
$180$		0			0
$181$	16.9941			1.26316			0.631581	−	0.775310i	$-0.282406\pi$
$181$	16.9941			1.26316			0.631581	+	0.775310i	$0.282406\pi$
$182$		0			0
$183$		0			0
$184$	4.13252	−	7.15774i	0.304654	−	0.527676i
$185$	0.751755			0.0552701
$186$		0			0
$187$	2.34355			0.171377
$188$	−13.2323			−0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	−22.6939			−1.64208			−0.821038	−	0.570873i	$-0.806605\pi$
$191$	−22.6939			−1.64208			−0.821038	+	0.570873i	$0.806605\pi$
$192$		0			0
$193$	6.18698			0.445348			0.222674	−	0.974893i	$-0.428521\pi$
$193$	6.18698			0.445348			0.222674	+	0.974893i	$0.428521\pi$
$194$	11.2263	−	19.4445i	0.806001	−	1.39603i
$195$		0			0
$196$		0			0
$197$	−9.77010			−0.696091			−0.348045	−	0.937478i	$-0.613154\pi$
$197$	−9.77010			−0.696091			−0.348045	+	0.937478i	$0.613154\pi$
$198$		0			0
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	−0.670209	−	0.742172i	$-0.733796\pi$
$199$	4.33973	−	7.51664i	0.307636	−	0.532840i	0.977845	+	0.209332i	$0.0671289\pi$
$200$	−1.80691	−	3.12965i	−0.127768	−	0.221300i
$201$		0			0
$202$	−1.02987	−	1.78379i	−0.0724615	−	0.125507i
$203$		0			0
$204$		0			0
$205$	−12.0445			−0.841224
$206$	1.77721	−	3.07822i	0.123824	−	0.214470i
$207$		0			0
$208$	−12.5460	−	21.7303i	−0.869909	−	1.50673i
$209$	−1.89446	+	3.28130i	−0.131043	+	0.226973i
$210$		0			0
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	0.751453	−	0.659786i	$-0.229353\pi$
$211$	−2.84219	−	4.92283i	−0.195665	−	0.338901i	−0.947118	+	0.320885i	$0.896020\pi$
$212$	−1.05010	+	1.81882i	−0.0721209	+	0.124917i
$213$		0			0
$214$	−5.32062	−	9.21558i	−0.363710	−	0.629964i
$215$	6.80708	+	11.7902i	0.464239	+	0.804086i
$216$		0			0
$217$		0			0
$218$	−7.58786	+	13.1426i	−0.513915	+	0.890126i
$219$		0			0
$220$	−2.80745			−0.189278
$221$	8.01723			0.539298
$222$		0			0
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	−0.992779	−	0.119957i	$-0.961724\pi$
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	0.600276	+	0.799793i	$0.295058\pi$
$224$		0			0
$225$		0			0
$226$	−13.3509	−	23.1245i	−0.888091	−	1.53822i
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	0.618615	−	0.785694i	$-0.287694\pi$
$227$	−5.59154	−	9.68482i	−0.371123	−	0.642804i	−0.989739	+	0.142890i	$0.954361\pi$
$228$		0			0
$229$	−4.82824	+	8.36275i	−0.319059	+	0.552626i	−0.980292	−	0.197554i	$-0.936700\pi$
$229$	−4.82824	+	8.36275i	−0.319059	+	0.552626i	0.661233	+	0.750181i	$0.270033\pi$
$230$	−9.04494	−	15.6663i	−0.596406	−	1.03301i
$231$		0			0
$232$	−0.0347761	+	0.0602340i	−0.00228317	+	0.00395456i
$233$	9.64492	+	16.7055i	0.631860	+	1.09441i	0.987171	+	0.159666i	$0.0510416\pi$
$233$	9.64492	+	16.7055i	0.631860	+	1.09441i	−0.355311	+	0.934748i	$0.615625\pi$
$234$		0			0
$235$	6.35243	−	11.0027i	0.414387	−	0.717739i
$236$	−11.7376			−0.764054
$237$		0			0
$238$		0			0
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	0.872252	−	0.489057i	$-0.162659\pi$
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	−0.859662	+	0.510864i	$0.829326\pi$
$240$		0			0
$241$	5.31807	+	9.21117i	0.342567	+	0.593344i	0.984909	−	0.173075i	$-0.0553703\pi$
$241$	5.31807	+	9.21117i	0.342567	+	0.593344i	−0.642342	+	0.766419i	$0.722037\pi$
$242$	8.01932	−	13.8899i	0.515502	−	0.892875i
$243$		0			0
$244$	−4.50299			−0.288274
$245$		0			0
$246$		0			0
$247$	−6.48091	+	11.2253i	−0.412370	+	0.714247i
$248$	−4.32046			−0.274350
$249$		0			0
$250$	−20.1976			−1.27741
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	15.6506			0.982007
$255$		0			0
$256$	20.9793			1.31121
$257$	2.34787	−	4.06663i	0.146456	−	0.253669i	−0.783459	−	0.621443i	$-0.786547\pi$
$257$	2.34787	−	4.06663i	0.146456	−	0.253669i	0.929915	+	0.367774i	$0.119880\pi$
$258$		0			0
$259$		0			0
$260$	−9.60421			−0.595628
$261$		0			0
$262$	1.85363	−	3.21059i	0.114518	−	0.198351i
$263$	9.77491	+	16.9306i	0.602747	+	1.04399i	0.992403	+	0.123028i	$0.0392605\pi$
$263$	9.77491	+	16.9306i	0.602747	+	1.04399i	−0.389656	+	0.920960i	$0.627406\pi$
$264$		0			0
$265$	−1.00824	−	1.74632i	−0.0619355	−	0.107276i
$266$		0			0
$267$		0			0
$268$	9.63858			0.588770
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	−0.519079	−	0.854726i	$-0.673725\pi$
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	0.999754	+	0.0221730i	$0.00705846\pi$
$270$		0			0
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	0.548904	−	0.835886i	$-0.315045\pi$
$271$	−7.39882	−	12.8151i	−0.449446	−	0.778464i	−0.998350	+	0.0574218i	$0.981712\pi$
$272$	−3.75442	+	6.50285i	−0.227645	+	0.394293i
$273$		0			0
$274$	2.04138	+	3.53578i	0.123324	+	0.213604i
$275$	−2.43477	+	4.21715i	−0.146822	+	0.254304i
$276$		0			0
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	0.955974	−	0.293452i	$-0.0948040\pi$
$277$	3.72561	+	6.45295i	0.223850	+	0.387720i	−0.732124	+	0.681172i	$0.761471\pi$
$278$	−0.695380	−	1.20443i	−0.0417061	−	0.0722371i
$279$		0			0
$280$		0			0
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	−0.159566	−	0.987187i	$-0.551009\pi$
$281$	12.9938	−	22.5060i	0.775146	−	1.34259i	0.934712	−	0.355406i	$-0.115657\pi$
$282$		0			0
$283$	−18.7554			−1.11489			−0.557445	−	0.830214i	$-0.688218\pi$
$283$	−18.7554			−1.11489			−0.557445	+	0.830214i	$0.688218\pi$
$284$	17.1413			1.01715
$285$		0			0
$286$	−7.20971	+	12.4876i	−0.426319	+	0.738406i
$287$		0			0
$288$		0			0
$289$	7.30041	+	12.6447i	0.429436	+	0.743805i
$290$	0.0761152	+	0.131835i	0.00446964	+	0.00774165i
$291$		0			0
$292$	1.91754	−	3.32127i	0.112215	−	0.194363i
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	0.827829	−	0.560981i	$-0.189576\pi$
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	−0.899738	+	0.436430i	$0.856243\pi$
$294$		0			0
$295$	5.63487	−	9.75988i	0.328075	−	0.568242i
$296$	0.316203	+	0.547680i	0.0183790	+	0.0318333i
$297$		0			0
$298$	6.06227	−	10.5002i	0.351178	−	0.608258i
$299$	−38.0994			−2.20334
$300$		0			0
$301$		0			0
$302$	−11.6616	−	20.1985i	−0.671050	−	1.16229i
$303$		0			0
$304$	−6.06994	−	10.5134i	−0.348135	−	0.602987i
$305$	2.16175	−	3.74425i	0.123781	−	0.214395i
$306$		0			0
$307$	4.66277			0.266118			0.133059	−	0.991108i	$-0.457520\pi$
$307$	4.66277			0.266118			0.133059	+	0.991108i	$0.457520\pi$
$308$		0			0
$309$		0			0
$310$	−4.72814	+	8.18938i	−0.268541	+	0.465126i
$311$	27.4821			1.55837			0.779183	−	0.626797i	$-0.215634\pi$
$311$	27.4821			1.55837			0.779183	+	0.626797i	$0.215634\pi$
$312$		0			0
$313$	−5.49332			−0.310501			−0.155250	−	0.987875i	$-0.549618\pi$
$313$	−5.49332			−0.310501			−0.155250	+	0.987875i	$0.549618\pi$
$314$	31.8671			1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	−9.87758			−0.554780			−0.277390	−	0.960757i	$-0.589469\pi$
$317$	−9.87758			−0.554780			−0.277390	+	0.960757i	$0.589469\pi$
$318$		0			0
$319$	0.0937203			0.00524733
$320$	1.73808	−	3.01044i	0.0971614	−	0.168288i
$321$		0			0
$322$		0			0
$323$	3.87885			0.215825
$324$		0			0
$325$	−8.32930	+	14.4268i	−0.462026	+	0.800253i
$326$	11.2493	+	19.4844i	0.623041	+	1.07914i
$327$		0			0
$328$	−5.06616	−	8.77485i	−0.279732	−	0.484510i
$329$		0			0
$330$		0			0
$331$	−20.6942			−1.13746			−0.568729	−	0.822525i	$-0.692565\pi$
$331$	−20.6942			−1.13746			−0.568729	+	0.822525i	$0.692565\pi$
$332$	3.89401	−	6.74463i	0.213712	−	0.370160i
$333$		0			0
$334$	3.24514	+	5.62076i	0.177566	+	0.307554i
$335$	−4.62718	+	8.01452i	−0.252810	+	0.437880i
$336$		0			0
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	0.885698	−	0.464261i	$-0.153680\pi$
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	−0.844911	+	0.534906i	$0.820347\pi$
$338$	−12.6962	+	21.9905i	−0.690582	+	1.19612i
$339$		0			0
$340$	1.43704	+	2.48903i	0.0779344	+	0.134986i
$341$	2.91087	+	5.04177i	0.157632	+	0.273027i
$342$		0			0
$343$		0			0
$344$	−5.72639	+	9.91840i	−0.308746	+	0.534764i
$345$		0			0
$346$	18.6719			1.00381
$347$	29.5388			1.58572			0.792862	−	0.609401i	$-0.208590\pi$
$347$	29.5388			1.58572			0.792862	+	0.609401i	$0.208590\pi$
$348$		0			0
$349$	−18.0006	+	31.1780i	−0.963551	+	1.66892i	−0.250094	+	0.968222i	$0.580461\pi$
$349$	−18.0006	+	31.1780i	−0.963551	+	1.66892i	−0.713458	+	0.700698i	$0.752872\pi$
$350$		0			0
$351$		0			0
$352$	−5.05363	−	8.75315i	−0.269360	−	0.466545i
$353$	14.7465	+	25.5417i	0.784877	+	1.35945i	0.929073	+	0.369897i	$0.120607\pi$
$353$	14.7465	+	25.5417i	0.784877	+	1.35945i	−0.144196	+	0.989549i	$0.546060\pi$
$354$		0			0
$355$	−8.22900	+	14.2530i	−0.436750	+	0.756473i
$356$	0.977687	+	1.69340i	0.0518173	+	0.0897502i
$357$		0			0
$358$	−1.56612	+	2.71260i	−0.0827720	+	0.143365i
$359$	−2.70535	−	4.68580i	−0.142783	−	0.247307i	0.785761	−	0.618531i	$-0.212272\pi$
$359$	−2.70535	−	4.68580i	−0.142783	−	0.247307i	−0.928544	+	0.371224i	$0.878938\pi$
$360$		0			0
$361$	6.36444	−	11.0235i	0.334971	−	0.580186i
$362$	31.2902			1.64458
$363$		0			0
$364$		0			0
$365$	1.84110	+	3.18888i	0.0963676	+	0.166914i
$366$		0			0
$367$	−11.5422	−	19.9916i	−0.602496	−	1.04355i	−0.992442	−	0.122715i	$-0.960840\pi$
$367$	−11.5422	−	19.9916i	−0.602496	−	1.04355i	0.389946	−	0.920838i	$-0.372494\pi$
$368$	17.8417	−	30.9027i	0.930063	−	1.61092i
$369$		0			0
$370$	1.38416			0.0719591
$371$		0			0
$372$		0			0
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	0.441078	+	0.897469i	$0.354596\pi$
$373$	−10.7515	+	18.6222i	−0.556692	+	0.964219i	−0.997770	+	0.0667498i	$0.978737\pi$
$374$	4.31504			0.223125
$375$		0			0
$376$	10.6878			0.551184
$377$	0.320615			0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	−4.64665			−0.238368
$381$		0			0
$382$	−41.7850			−2.13791
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.0549390	−	0.998490i	$-0.482504\pi$
$383$	17.4604	−	30.2424i	0.892187	−	1.54531i	0.837248	−	0.546823i	$-0.184163\pi$
$384$		0			0
$385$		0			0
$386$	11.3917			0.579823
$387$		0			0
$388$	8.47603	−	14.6809i	0.430305	−	0.745311i
$389$	−14.4411	−	25.0127i	−0.732192	−	1.26819i	−0.955944	−	0.293548i	$-0.905164\pi$
$389$	−14.4411	−	25.0127i	−0.732192	−	1.26819i	0.223752	−	0.974646i	$-0.428169\pi$
$390$		0			0
$391$	5.70066	+	9.87383i	0.288295	+	0.499341i
$392$		0			0
$393$		0			0
$394$	−17.9891			−0.906278
$395$	3.95046	−	6.84239i	0.198769	−	0.344278i
$396$		0			0
$397$	−5.59226	−	9.68607i	−0.280667	−	0.486130i	0.690882	−	0.722968i	$-0.257222\pi$
$397$	−5.59226	−	9.68607i	−0.280667	−	0.486130i	−0.971549	+	0.236838i	$0.923889\pi$
$398$	7.99049	−	13.8399i	0.400527	−	0.693734i
$399$		0			0
$400$	−7.80111	−	13.5119i	−0.390056	−	0.675596i
$401$	−0.541061	+	0.937146i	−0.0270193	+	0.0467988i	−0.879219	−	0.476418i	$-0.841935\pi$
$401$	−0.541061	+	0.937146i	−0.0270193	+	0.0467988i	0.852200	+	0.523217i	$0.175268\pi$
$402$		0			0
$403$	9.95802	+	17.2478i	0.496044	+	0.859174i
$404$	−0.777570	−	1.34679i	−0.0386856	−	0.0670054i
$405$		0			0
$406$		0			0
$407$	0.426078	−	0.737988i	0.0211199	−	0.0365807i
$408$		0			0
$409$	21.7349			1.07472			0.537360	−	0.843353i	$-0.319422\pi$
$409$	21.7349			1.07472			0.537360	+	0.843353i	$0.319422\pi$
$410$	−22.1768			−1.09524
$411$		0			0
$412$	1.34182	−	2.32410i	0.0661069	−	0.114500i
$413$		0			0
$414$		0			0
$415$	3.73879	+	6.47578i	0.183530	+	0.317884i
$416$	−17.2884	−	29.9443i	−0.847632	−	1.46814i
$417$		0			0
$418$	−3.48816	+	6.04167i	−0.170611	+	0.295508i
$419$	12.5906	+	21.8075i	0.615090	+	1.06537i	0.990369	+	0.138455i	$0.0442135\pi$
$419$	12.5906	+	21.8075i	0.615090	+	1.06537i	−0.375279	+	0.926912i	$0.622453\pi$
$420$		0			0
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	0.237090	+	0.971488i	$0.423806\pi$
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	−0.959878	+	0.280418i	$0.909527\pi$
$422$	−5.23316	−	9.06411i	−0.254746	−	0.441234i
$423$		0			0
$424$	0.848171	−	1.46907i	0.0411908	−	0.0713446i
$425$	4.98512			0.241814
$426$		0			0
$427$		0			0
$428$	−4.01715	−	6.95791i	−0.194176	−	0.336323i
$429$		0			0
$430$	12.5335	+	21.7086i	0.604418	+	1.04688i
$431$	−2.44517	+	4.23516i	−0.117780	+	0.204000i	−0.918887	−	0.394520i	$-0.870911\pi$
$431$	−2.44517	+	4.23516i	−0.117780	+	0.204000i	0.801108	+	0.598520i	$0.204244\pi$
$432$		0			0
$433$	−9.71430			−0.466839			−0.233420	−	0.972376i	$-0.574992\pi$
$433$	−9.71430			−0.466839			−0.233420	+	0.972376i	$0.574992\pi$
$434$		0			0
$435$		0			0
$436$	−5.72896	+	9.92285i	−0.274367	+	0.475218i
$437$	−18.4330			−0.881771
$438$		0			0
$439$	14.8235			0.707488			0.353744	−	0.935342i	$-0.384908\pi$
$439$	14.8235			0.707488			0.353744	+	0.935342i	$0.384908\pi$
$440$	2.26760			0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	21.9020			1.04059			0.520297	−	0.853986i	$-0.325821\pi$
$443$	21.9020			1.04059			0.520297	+	0.853986i	$0.325821\pi$
$444$		0			0
$445$	−1.87743			−0.0889987
$446$	−10.7921	+	18.6925i	−0.511021	+	0.885115i
$447$		0			0
$448$		0			0
$449$	−21.4952			−1.01442			−0.507212	−	0.861822i	$-0.669324\pi$
$449$	−21.4952			−1.01442			−0.507212	+	0.861822i	$0.669324\pi$
$450$		0			0
$451$	−6.82655	+	11.8239i	−0.321450	+	0.556767i
$452$	−10.0802	−	17.4594i	−0.474131	−	0.821220i
$453$		0			0
$454$	−10.2954	−	17.8321i	−0.483185	−	0.836902i
$455$		0			0
$456$		0			0
$457$	40.6255			1.90038			0.950190	−	0.311670i	$-0.100888\pi$
$457$	40.6255			1.90038			0.950190	+	0.311670i	$0.100888\pi$
$458$	−8.88995	+	15.3978i	−0.415400	+	0.719494i
$459$		0			0
$460$	−6.82908	−	11.8283i	−0.318408	−	0.551498i
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	−0.831181	−	0.556003i	$-0.812334\pi$
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	0.897103	+	0.441822i	$0.145668\pi$
$462$		0			0
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	−0.983719	−	0.179711i	$-0.942484\pi$
$463$	−13.9324	−	24.1317i	−0.647494	−	1.12149i	0.336225	−	0.941782i	$-0.390850\pi$
$464$	−0.150142	+	0.260053i	−0.00697016	+	0.0120727i
$465$		0			0
$466$	17.7586	+	30.7588i	0.822653	+	1.42488i
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	−0.990126	−	0.140182i	$-0.955231\pi$
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	0.373661	−	0.927565i	$-0.378102\pi$
$468$		0			0
$469$		0			0
$470$	11.6964	−	20.2587i	0.539513	−	0.934463i
$471$		0			0
$472$	9.48056			0.436378
$473$	15.4324			0.709582
$474$		0			0
$475$	−4.02983	+	6.97987i	−0.184901	+	0.320258i
$476$		0			0
$477$		0			0
$478$	0.358381	+	0.620734i	0.0163920	+	0.0283917i
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	0.960422	+	0.278551i	$0.0898540\pi$
$479$	15.7895	+	27.3483i	0.721443	+	1.24958i	−0.238979	+	0.971025i	$0.576813\pi$
$480$		0			0
$481$	1.45760	−	2.52464i	0.0664609	−	0.115114i
$482$	9.79185	+	16.9600i	0.446007	+	0.772506i
$483$		0			0
$484$	6.05472	−	10.4871i	0.275215	−	0.476686i
$485$	8.13817	+	14.0957i	0.369535	+	0.640054i
$486$		0			0
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	−0.869473	−	0.493980i	$-0.835541\pi$
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	0.862536	+	0.505996i	$0.168875\pi$
$488$	3.63710			0.164644
$489$		0			0
$490$		0			0
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	0.994813	−	0.101720i	$-0.0324345\pi$
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	−0.585498	+	0.810674i	$0.699101\pi$
$492$		0			0
$493$	−0.0479723	−	0.0830905i	−0.00216057	−	0.00374221i
$494$	−11.9329	+	20.6684i	−0.536887	+	0.929916i
$495$		0			0
$496$	−18.6531			−0.837549
$497$		0			0
$498$		0			0
$499$	10.6546	−	18.4543i	0.476964	−	0.826126i	−0.522687	−	0.852524i	$-0.675070\pi$
$499$	10.6546	−	18.4543i	0.476964	−	0.826126i	0.999652	+	0.0263983i	$0.00840381\pi$
$500$	−15.2496			−0.681981
$501$		0			0
$502$	−6.01401			−0.268418
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	−20.5059			−0.911597
$507$		0			0
$508$	11.8165			0.524271
$509$	−18.3868	+	31.8468i	−0.814979	+	1.41159i	0.0943635	+	0.995538i	$0.469918\pi$
$509$	−18.3868	+	31.8468i	−0.814979	+	1.41159i	−0.909343	+	0.416048i	$0.863415\pi$
$510$		0			0
$511$		0			0
$512$	21.4975			0.950065
$513$		0			0
$514$	4.32299	−	7.48764i	0.190679	−	0.330265i
$515$	1.28834	+	2.23146i	0.0567709	+	0.0983300i
$516$		0			0
$517$	−7.20083	−	12.4722i	−0.316692	−	0.548527i
$518$		0			0
$519$		0			0
$520$	7.75740			0.340184
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	−0.995890	−	0.0905758i	$-0.971129\pi$
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	0.576386	+	0.817178i	$0.304463\pi$
$522$		0			0
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.803920	+	0.594737i	$0.202744\pi$
$523$	20.9715	+	36.3236i	0.917018	+	1.58832i	0.113097	+	0.993584i	$0.463923\pi$
$524$	1.39952	−	2.42405i	0.0611385	−	0.105895i
$525$		0			0
$526$	17.9980	+	31.1734i	0.784749	+	1.35922i
$527$	2.97996	−	5.16144i	0.129809	−	0.224836i
$528$		0			0
$529$	−15.5906	−	27.0037i	−0.677851	−	1.17407i
$530$	−1.85641	−	3.21539i	−0.0806372	−	0.139668i
$531$		0			0
$532$		0			0
$533$	−23.3535	+	40.4494i	−1.01155	+	1.75206i
$534$		0			0
$535$	7.71405			0.333507
$536$	−7.78515			−0.336267
$537$		0			0
$538$	14.5157	−	25.1419i	0.625816	−	1.08395i
$539$		0			0
$540$		0			0
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	0.833344	−	0.552754i	$-0.186423\pi$
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	−0.895371	+	0.445320i	$0.853090\pi$
$542$	−13.6230	−	23.5957i	−0.585158	−	1.01352i
$543$		0			0
$544$	−5.17358	+	8.96090i	−0.221815	+	0.384196i
$545$	−5.50059	−	9.52731i	−0.235620	−	0.408105i
$546$		0			0
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	−0.834840	−	0.550492i	$-0.814440\pi$
$547$	1.38738	−	2.40301i	0.0593201	−	0.102745i	0.894160	+	0.447747i	$0.147773\pi$
$548$	1.54128	+	2.66957i	0.0658401	+	0.114038i
$549$		0			0
$550$	−4.48300	+	7.76478i	−0.191156	+	0.331091i
$551$	0.155118			0.00660825
$552$		0			0
$553$		0			0
$554$	6.85975	+	11.8814i	0.291443	+	0.504794i
$555$		0			0
$556$	−0.525024	−	0.909368i	−0.0222660	−	0.0385658i
$557$	−15.5344	+	26.9064i	−0.658214	+	1.14006i	0.322864	+	0.946445i	$0.395354\pi$
$557$	−15.5344	+	26.9064i	−0.658214	+	1.14006i	−0.981078	+	0.193614i	$0.937979\pi$
$558$		0			0
$559$	52.7939			2.23294
$560$		0			0
$561$		0			0
$562$	23.9248	−	41.4389i	1.00920	−	1.74799i
$563$	0.288041			0.0121395			0.00606973	−	0.999982i	$-0.498068\pi$
$563$	0.288041			0.0121395			0.00606973	+	0.999982i	$0.498068\pi$
$564$		0			0
$565$	19.3567			0.814344
$566$	−34.5331			−1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	16.0801			0.674112			0.337056	−	0.941485i	$-0.390569\pi$
$569$	16.0801			0.674112			0.337056	+	0.941485i	$0.390569\pi$
$570$		0			0
$571$	−15.2858			−0.639690			−0.319845	−	0.947470i	$-0.603631\pi$
$571$	−15.2858			−0.639690			−0.319845	+	0.947470i	$0.603631\pi$
$572$	−5.44345	+	9.42834i	−0.227602	+	0.394218i
$573$		0			0
$574$		0			0
$575$	−23.6902			−0.987950
$576$		0			0
$577$	−12.0812	+	20.9253i	−0.502949	+	0.871133i	0.497045	+	0.867725i	$0.334418\pi$
$577$	−12.0812	+	20.9253i	−0.502949	+	0.871133i	−0.999994	+	0.00340833i	$0.998915\pi$
$578$	13.4418	+	23.2819i	0.559106	+	0.968400i
$579$		0			0
$580$	0.0574683	+	0.0995380i	0.00238624	+	0.00413309i
$581$		0			0
$582$		0			0
$583$	−2.28579			−0.0946676
$584$	−1.54881	+	2.68262i	−0.0640902	+	0.111007i
$585$		0			0
$586$	−2.26636	−	3.92546i	−0.0936226	−	0.162159i
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	−0.207339	−	0.978269i	$-0.566480\pi$
$587$	18.0145	−	31.2020i	0.743537	−	1.28784i	0.950875	−	0.309574i	$-0.100186\pi$
$588$		0			0
$589$	4.81783	+	8.34472i	0.198515	+	0.343838i
$590$	10.3752	−	17.9703i	0.427138	−	0.739825i
$591$		0			0
$592$	1.36517	+	2.36455i	0.0561082	+	0.0971823i
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	0.999904	+	0.0138558i	$0.00441057\pi$
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	−0.487953	+	0.872870i	$0.662256\pi$
$594$		0			0
$595$		0			0
$596$	4.57712	−	7.92780i	0.187486	−	0.324735i
$597$		0			0
$598$	−70.1501			−2.86865
$599$	−39.5283			−1.61508			−0.807542	−	0.589810i	$-0.799203\pi$
$599$	−39.5283			−1.61508			−0.807542	+	0.589810i	$0.799203\pi$
$600$		0			0
$601$	−1.86447	+	3.22936i	−0.0760534	+	0.131728i	−0.901544	−	0.432688i	$-0.857565\pi$
$601$	−1.86447	+	3.22936i	−0.0760534	+	0.131728i	0.825490	+	0.564416i	$0.190899\pi$
$602$		0			0
$603$		0			0
$604$	−8.80470	−	15.2502i	−0.358258	−	0.620521i
$605$	5.81337	+	10.0691i	0.236347	+	0.409365i
$606$		0			0
$607$	11.8264	−	20.4839i	0.480018	−	0.831415i	−0.519719	−	0.854337i	$-0.673964\pi$
$607$	11.8264	−	20.4839i	0.480018	−	0.831415i	0.999737	+	0.0229218i	$0.00729686\pi$
$608$	−8.36436	−	14.4875i	−0.339219	−	0.587545i
$609$		0			0
$610$	3.98029	−	6.89407i	0.161157	−	0.279133i
$611$	−24.6339	−	42.6671i	−0.996580	−	1.72613i
$612$		0			0
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	0.901833	+	0.432084i	$0.142222\pi$
$614$	8.58528			0.346474
$615$		0			0
$616$		0			0
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	0.965965	+	0.258672i	$0.0832849\pi$
$617$	17.5615	+	30.4174i	0.706999	+	1.22456i	−0.258966	+	0.965886i	$0.583382\pi$
$618$		0			0
$619$	−10.5816	−	18.3279i	−0.425311	−	0.736660i	0.571138	−	0.820854i	$-0.306502\pi$
$619$	−10.5816	−	18.3279i	−0.425311	−	0.736660i	−0.996449	+	0.0841934i	$0.973169\pi$
$620$	−3.56983	+	6.18312i	−0.143368	+	0.248320i
$621$		0			0
$622$	50.6011			2.02892
$623$		0			0
$624$		0			0
$625$	−0.725240	+	1.25615i	−0.0290096	+	0.0502461i
$626$	−10.1145			−0.404257
$627$		0			0
$628$	24.0602			0.960107
$629$	−0.872381			−0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	6.64657			0.264386
$633$		0			0
$634$	−18.1870			−0.722298
$635$	−5.67273	+	9.82546i	−0.225115	+	0.389911i
$636$		0			0
$637$		0			0
$638$	0.172562			0.00683178
$639$		0			0
$640$	−5.71622	+	9.90078i	−0.225953	+	0.391363i
$641$	−4.93735	−	8.55174i	−0.195013	−	0.337773i	0.751891	−	0.659287i	$-0.229142\pi$
$641$	−4.93735	−	8.55174i	−0.195013	−	0.337773i	−0.946905	+	0.321514i	$0.895808\pi$
$642$		0			0
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.865448	−	0.501000i	$-0.832966\pi$
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.00115462	−	0.999999i	$-0.500368\pi$
$644$		0			0
$645$		0			0
$646$	7.14190			0.280994
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.0131398	−	0.999914i	$-0.495817\pi$
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.859381	−	0.511336i	$-0.170849\pi$
$648$		0			0
$649$	−6.38743	−	11.0634i	−0.250729	−	0.434275i
$650$	−15.3362	+	26.5631i	−0.601537	+	1.04189i
$651$		0			0
$652$	8.49341	+	14.7110i	0.332628	+	0.576128i
$653$	20.9956	−	36.3655i	0.821622	−	1.42309i	−0.0828523	−	0.996562i	$-0.526403\pi$
$653$	20.9956	−	36.3655i	0.821622	−	1.42309i	0.904474	−	0.426529i	$-0.140264\pi$
$654$		0			0
$655$	1.34374	+	2.32742i	0.0525042	+	0.0909399i
$656$	−21.8726	−	37.8844i	−0.853980	−	1.47914i
$657$		0			0
$658$		0			0
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	−0.175356	−	0.984505i	$-0.556108\pi$
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	0.940284	−	0.340390i	$-0.110559\pi$
$660$		0			0
$661$	0.186739			0.00726330			0.00363165	−	0.999993i	$-0.498844\pi$
$661$	0.186739			0.00726330			0.00363165	+	0.999993i	$0.498844\pi$
$662$	−38.1030			−1.48092
$663$		0			0
$664$	−3.14522	+	5.44769i	−0.122058	+	0.211411i
$665$		0			0
$666$		0			0
$667$	0.227973	+	0.394862i	0.00882717	+	0.0152891i
$668$	2.45014	+	4.24376i	0.0947987	+	0.164196i
$669$		0			0
$670$	−8.51976	+	14.7567i	−0.329147	+	0.570099i
$671$	−2.45046	−	4.24432i	−0.0945989	−	0.163850i
$672$		0			0
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	−0.951544	−	0.307512i	$-0.900503\pi$
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	0.742086	+	0.670305i	$0.233837\pi$
$674$	1.37862	+	2.38785i	0.0531026	+	0.0919764i
$675$		0			0
$676$	−9.58584	+	16.6032i	−0.368686	+	0.638583i
$677$	28.3901			1.09112			0.545560	−	0.838072i	$-0.316317\pi$
$677$	28.3901			1.09112			0.545560	+	0.838072i	$0.316317\pi$
$678$		0			0
$679$		0			0
$680$	−1.16071	−	2.01041i	−0.0445111	−	0.0770956i
$681$		0			0
$682$	5.35961	+	9.28312i	0.205230	+	0.355469i
$683$	−5.92034	+	10.2543i	−0.226536	+	0.392371i	−0.956779	−	0.290816i	$-0.906073\pi$
$683$	−5.92034	+	10.2543i	−0.226536	+	0.392371i	0.730243	+	0.683187i	$0.239407\pi$
$684$		0			0
$685$	−2.95968			−0.113083
$686$		0			0
$687$		0			0
$688$	−24.7230	+	42.8216i	−0.942557	+	1.63256i
$689$	−7.81962			−0.297904
$690$		0			0
$691$	−11.9083			−0.453014			−0.226507	−	0.974010i	$-0.572731\pi$
$691$	−11.9083			−0.453014			−0.226507	+	0.974010i	$0.572731\pi$
$692$	14.0976			0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	1.00819			0.0382429
$696$		0			0
$697$	13.9771			0.529422
$698$	−33.1435	+	57.4062i	−1.25450	+	2.17286i
$699$		0			0
$700$		0			0
$701$	31.3902			1.18559			0.592795	−	0.805353i	$-0.298024\pi$
$701$	31.3902			1.18559			0.592795	+	0.805353i	$0.298024\pi$
$702$		0			0
$703$	0.705208	−	1.22146i	0.0265974	−	0.0460681i
$704$	−1.97020	−	3.41249i	−0.0742549	−	0.128613i
$705$		0			0
$706$	27.1518	+	47.0284i	1.02187	+	1.76994i
$707$		0			0
$708$		0			0
$709$	0.625218			0.0234806			0.0117403	−	0.999931i	$-0.496263\pi$
$709$	0.625218			0.0234806			0.0117403	+	0.999931i	$0.496263\pi$
$710$	−15.1516	+	26.2433i	−0.568628	+	0.984893i
$711$		0			0
$712$	−0.789685	−	1.36777i	−0.0295947	−	0.0512595i
$713$	−14.1613	+	24.5281i	−0.530345	+	0.918584i
$714$		0			0
$715$	−5.22647	−	9.05251i	−0.195459	−	0.338545i
$716$	−1.18245	+	2.04806i	−0.0441901	+	0.0765395i
$717$		0			0
$718$	−4.98119	−	8.62768i	−0.185897	−	0.321982i
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	0.998681	−	0.0513506i	$-0.0163526\pi$
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$720$		0			0
$721$		0			0
$722$	11.7185	−	20.2970i	0.436116	−	0.755376i
$723$		0			0
$724$	23.6246			0.878003
$725$	0.199358			0.00740399
$726$		0			0
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	−0.265899	−	0.964001i	$-0.585669\pi$
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	0.967799	−	0.251726i	$-0.0809980\pi$
$728$		0			0
$729$		0			0
$730$	3.38991	+	5.87150i	0.125466	+	0.217314i
$731$	−7.89934	−	13.6821i	−0.292168	−	0.506049i
$732$		0			0
$733$	1.20077	−	2.07980i	0.0443516	−	0.0768193i	−0.842997	−	0.537918i	$-0.819211\pi$
$733$	1.20077	−	2.07980i	0.0443516	−	0.0768193i	0.887349	+	0.461098i	$0.152544\pi$
$734$	−21.2519	−	36.8093i	−0.784421	−	1.35866i
$735$		0			0
$736$	24.5858	−	42.5839i	0.906245	−	1.56966i
$737$	5.24517	+	9.08490i	0.193208	+	0.334646i
$738$		0			0
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	0.438667	+	0.898650i	$0.355451\pi$
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	−0.997587	+	0.0694277i	$0.977883\pi$
$740$	1.04507			0.0384174
$741$		0			0
$742$		0			0
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	0.908970	−	0.416862i	$-0.136870\pi$
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	−0.815498	+	0.578760i	$0.803537\pi$
$744$		0			0
$745$	4.39467	+	7.61179i	0.161008	+	0.278874i
$746$	−19.7961	+	34.2879i	−0.724787	+	1.25537i
$747$		0			0
$748$	3.25793			0.119122
$749$		0			0
$750$		0			0
$751$	0.487506	−	0.844384i	0.0177893	−	0.0308120i	−0.856994	−	0.515327i	$-0.827671\pi$
$751$	0.487506	−	0.844384i	0.0177893	−	0.0308120i	0.874783	+	0.484515i	$0.161004\pi$
$752$	46.1435			1.68268
$753$		0			0
$754$	0.590329			0.0214985
$755$	16.9075			0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	10.5350			0.382648
$759$		0			0
$760$	3.75314			0.136141
$761$	27.0875	−	46.9169i	0.981920	−	1.70073i	0.327023	−	0.945016i	$-0.393955\pi$
$761$	27.0875	−	46.9169i	0.981920	−	1.70073i	0.654897	−	0.755718i	$-0.272712\pi$
$762$		0			0
$763$		0			0
$764$	−31.5484			−1.14138
$765$		0			0
$766$	32.1489	−	55.6835i	1.16159	−	2.01193i
$767$	−21.8513	−	37.8475i	−0.789004	−	1.36659i
$768$		0			0
$769$	10.4326	+	18.0698i	0.376208	+	0.651612i	0.990507	−	0.137462i	$-0.0438943\pi$
$769$	10.4326	+	18.0698i	0.376208	+	0.651612i	−0.614299	+	0.789074i	$0.710561\pi$
$770$		0			0
$771$		0			0
$772$	8.60094			0.309554
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.366447	+	0.930439i	$0.619426\pi$
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.622561	+	0.782572i	$0.713908\pi$
$774$		0			0
$775$	6.19189	+	10.7247i	0.222419	+	0.385242i
$776$	−6.84616	+	11.8579i	−0.245763	+	0.425674i
$777$		0			0
$778$	−26.5895	−	46.0544i	−0.953281	−	1.65113i
$779$	−11.2987	+	19.5700i	−0.404819	+	0.701168i
$780$		0			0
$781$	9.32802	+	16.1566i	0.333783	+	0.578129i
$782$	10.4963	+	18.1801i	0.375346	+	0.650119i
$783$		0			0
$784$		0			0
$785$	−11.5506	+	20.0062i	−0.412258	+	0.714051i
$786$		0			0
$787$	−9.18949			−0.327570			−0.163785	−	0.986496i	$-0.552370\pi$
$787$	−9.18949			−0.327570			−0.163785	+	0.986496i	$0.552370\pi$
$788$	−13.5821			−0.483841
$789$		0			0
$790$	7.27374	−	12.5985i	0.258788	−	0.448234i
$791$		0			0
$792$		0			0
$793$	−8.38296	−	14.5197i	−0.297688	−	0.515610i
$794$	−10.2967	−	17.8344i	−0.365416	−	0.632919i
$795$		0			0
$796$	6.03296	−	10.4494i	0.213832	−	0.370369i
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	0.921855	−	0.387534i	$-0.126673\pi$
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	−0.796542	+	0.604583i	$0.793340\pi$
$798$		0			0
$799$	−7.37174	+	12.7682i	−0.260793	+	0.451707i
$800$	−10.7499	−	18.6194i	−0.380067	−	0.658295i
$801$		0			0
$802$	−0.996224	+	1.72551i	−0.0351779	+	0.0609299i
$803$	4.17398			0.147297
$804$		0			0
$805$		0			0
$806$	18.3351	+	31.7573i	0.645827	+	1.11860i
$807$		0			0
$808$	0.628050	+	1.08781i	0.0220947	+	0.0382692i
$809$	2.97060	−	5.14522i	0.104441	−	0.180896i	−0.809069	−	0.587714i	$-0.800028\pi$
$809$	2.97060	−	5.14522i	0.104441	−	0.180896i	0.913510	+	0.406817i	$0.133361\pi$
$810$		0			0
$811$	−44.4139			−1.55958			−0.779791	−	0.626039i	$-0.784675\pi$
$811$	−44.4139			−1.55958			−0.779791	+	0.626039i	$0.784675\pi$
$812$		0			0
$813$		0			0
$814$	0.784512	−	1.35881i	0.0274971	−	0.0476264i
$815$	−16.3097			−0.571304
$816$		0			0
$817$	25.5424			0.893616
$818$	40.0191			1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	−6.35522			−0.221799			−0.110899	−	0.993832i	$-0.535373\pi$
$821$	−6.35522			−0.221799			−0.110899	+	0.993832i	$0.535373\pi$
$822$		0			0
$823$	−9.46433			−0.329906			−0.164953	−	0.986301i	$-0.552747\pi$
$823$	−9.46433			−0.329906			−0.164953	+	0.986301i	$0.552747\pi$
$824$	−1.08380	+	1.87720i	−0.0377560	+	0.0653953i
$825$		0			0
$826$		0			0
$827$	4.86261			0.169090			0.0845448	−	0.996420i	$-0.473056\pi$
$827$	4.86261			0.169090			0.0845448	+	0.996420i	$0.473056\pi$
$828$		0			0
$829$	−20.3926	+	35.3211i	−0.708266	+	1.22675i	0.257234	+	0.966349i	$0.417189\pi$
$829$	−20.3926	+	35.3211i	−0.708266	+	1.22675i	−0.965500	+	0.260403i	$0.916145\pi$
$830$	6.88402	+	11.9235i	0.238948	+	0.413870i
$831$		0			0
$832$	−6.74003	−	11.6741i	−0.233668	−	0.404725i
$833$		0			0
$834$		0			0
$835$	−4.70494			−0.162821
$836$	−2.63362	+	4.56156i	−0.0910856	+	0.157765i
$837$		0			0
$838$	23.1823	+	40.1529i	0.800818	+	1.38706i
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	−0.651316	−	0.758807i	$-0.725783\pi$
$839$	9.60171	−	16.6307i	0.331488	−	0.574154i	0.982804	+	0.184653i	$0.0591161\pi$
$840$		0			0
$841$	14.4981	+	25.1114i	0.499934	+	0.865911i
$842$	−27.3063	+	47.2959i	−0.941036	+	1.62992i
$843$		0			0
$844$	−3.95113	−	6.84355i	−0.136003	−	0.235565i
$845$	−9.20374	−	15.9413i	−0.316618	−	0.548399i
$846$		0			0
$847$		0			0
$848$	3.66188	−	6.34256i	0.125749	−	0.217804i
$849$		0			0
$850$	9.17880			0.314830
$851$	4.14571			0.142113
$852$		0			0
$853$	6.95055	−	12.0387i	0.237982	−	0.412198i	−0.722153	−	0.691734i	$-0.756847\pi$
$853$	6.95055	−	12.0387i	0.237982	−	0.412198i	0.960135	+	0.279536i	$0.0901806\pi$
$854$		0			0
$855$		0			0
$856$	3.24469	+	5.61996i	0.110901	+	0.192086i
$857$	−28.4919	−	49.3494i	−0.973265	−	1.68574i	−0.685547	−	0.728029i	$-0.740437\pi$
$857$	−28.4919	−	49.3494i	−0.973265	−	1.68574i	−0.287718	−	0.957715i	$-0.592897\pi$
$858$		0			0
$859$	−10.0501	+	17.4073i	−0.342905	+	0.593929i	−0.984971	−	0.172721i	$-0.944744\pi$
$859$	−10.0501	+	17.4073i	−0.342905	+	0.593929i	0.642066	+	0.766650i	$0.278078\pi$
$860$	9.46298	+	16.3904i	0.322685	+	0.558907i
$861$		0			0
$862$	−4.50214	+	7.79794i	−0.153344	+	0.265599i
$863$	3.08893	+	5.35018i	0.105148	+	0.182122i	0.913799	−	0.406167i	$-0.133135\pi$
$863$	3.08893	+	5.35018i	0.105148	+	0.182122i	−0.808650	+	0.588289i	$0.799802\pi$
$864$		0			0
$865$	−6.76781	+	11.7222i	−0.230112	+	0.398566i
$866$	−17.8864			−0.607803
$867$		0			0
$868$		0			0
$869$	−4.47806	−	7.75623i	−0.151908	−	0.263112i
$870$		0			0
$871$	17.9436	+	31.0792i	0.607996	+	1.05308i
$872$	4.62732	−	8.01476i	0.156701	−	0.271414i
$873$		0			0
$874$	−33.9396			−1.14802
$875$		0			0
$876$		0			0
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	−0.358697	−	0.933454i	$-0.616779\pi$
$877$	18.6287	−	32.2658i	0.629046	−	1.08954i	0.987743	−	0.156086i	$-0.0498877\pi$
$878$	27.2937			0.921117
$879$		0			0
$880$	9.79009			0.330024
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	11.1453			0.374857
$885$		0			0
$886$	40.3268			1.35480
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	−0.999703	−	0.0243782i	$-0.992239\pi$
$887$	−14.2581	+	24.6957i	−0.478739	+	0.829201i	0.520964	+	0.853579i	$0.325573\pi$
$888$		0			0
$889$		0			0
$890$	−3.45680			−0.115872
$891$		0			0
$892$	−8.14822	+	14.1131i	−0.272823	+	0.472543i
$893$	−11.9182	−	20.6430i	−0.398828	−	0.690790i
$894$		0			0
$895$	−1.13531	−	1.96642i	−0.0379493	−	0.0657301i
$896$		0			0
$897$		0			0
$898$	−39.5779			−1.32073
$899$	0.119171	−	0.206410i	0.00397456	−	0.00688414i
$900$		0			0
$901$	1.17002	+	2.02653i	0.0389790	+	0.0675135i
$902$	−12.5693	+	21.7707i	−0.418513	+	0.724885i
$903$		0			0
$904$	8.14183	+	14.1021i	0.270793	+	0.469028i
$905$	−11.3415	+	19.6440i	−0.377003	+	0.652989i
$906$		0			0
$907$	3.94577	+	6.83428i	0.131017	+	0.226929i	0.924069	−	0.382226i	$-0.124842\pi$
$907$	3.94577	+	6.83428i	0.131017	+	0.226929i	−0.793052	+	0.609154i	$0.791509\pi$
$908$	−7.77317	−	13.4635i	−0.257962	−	0.446803i
$909$		0			0
$910$		0			0
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	−0.528306	−	0.849054i	$-0.677173\pi$
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	0.999455	+	0.0329991i	$0.0105058\pi$
$912$		0			0
$913$	8.47625			0.280523
$914$	74.8013			2.47421
$915$		0			0
$916$	−6.71206	+	11.6256i	−0.221773	+	0.384121i
$917$		0			0
$918$		0			0
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	0.924335	−	0.381582i	$-0.124621\pi$
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	−0.792627	+	0.609706i	$0.791287\pi$
$920$	5.51590	+	9.55382i	0.181854	+	0.314980i
$921$		0			0
$922$	2.60610	−	4.51390i	0.0858274	−	0.148657i
$923$	31.9110	+	55.2714i	1.05036	+	1.81928i
$924$		0			0
$925$	0.906337	−	1.56982i	0.0298002	−	0.0516154i
$926$	−25.6529	−	44.4322i	−0.843008	−	1.46013i
$927$		0			0
$928$	−0.206895	+	0.358353i	−0.00679167	+	0.0117635i
$929$	18.8006			0.616829			0.308414	−	0.951252i	$-0.400202\pi$
$929$	18.8006			0.616829			0.308414	+	0.951252i	$0.400202\pi$
$930$		0			0
$931$		0			0
$932$	13.4081	+	23.2234i	0.439196	+	0.760709i
$933$		0			0
$934$	−24.5288	−	42.4852i	−0.802608	−	1.39016i
$935$	−1.56403	+	2.70898i	−0.0511493	+	0.0885932i
$936$		0			0
$937$	−48.5788			−1.58700			−0.793500	−	0.608570i	$-0.791744\pi$
$937$	−48.5788			−1.58700			−0.793500	+	0.608570i	$0.791744\pi$
$938$		0			0
$939$		0			0
$940$	8.83094	−	15.2956i	0.288034	−	0.498889i
$941$	20.4851			0.667795			0.333898	−	0.942609i	$-0.391636\pi$
$941$	20.4851			0.667795			0.333898	+	0.942609i	$0.391636\pi$
$942$		0			0
$943$	−66.4220			−2.16300
$944$	40.9312			1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	14.8505			0.482576			0.241288	−	0.970454i	$-0.422430\pi$
$947$	14.8505			0.482576			0.241288	+	0.970454i	$0.422430\pi$
$948$		0			0
$949$	14.2791			0.463519
$950$	−7.41989	+	12.8516i	−0.240733	+	0.416962i
$951$		0			0
$952$		0			0
$953$	−46.4678			−1.50524			−0.752620	−	0.658456i	$-0.771210\pi$
$953$	−46.4678			−1.50524			−0.752620	+	0.658456i	$0.771210\pi$
$954$		0			0
$955$	15.1454	−	26.2326i	0.490094	−	0.848868i
$956$	0.270584	+	0.468665i	0.00875130	+	0.0151577i
$957$		0			0
$958$	29.0724	+	50.3548i	0.939285	+	1.62689i
$959$		0			0
$960$		0			0
$961$	−16.1947			−0.522409
$962$	2.68380	−	4.64847i	0.0865291	−	0.149873i
$963$		0			0
$964$	7.39301	+	12.8051i	0.238113	+	0.412423i
$965$	−4.12905	+	7.15172i	−0.132919	+	0.230222i
$966$		0			0
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	0.879578	−	0.475754i	$-0.157825\pi$
$967$	0.863670	+	1.49592i	0.0277738	+	0.0481056i	−0.851804	+	0.523860i	$0.824492\pi$
$968$	−4.89045	+	8.47050i	−0.157185	+	0.272252i
$969$		0			0
$970$	14.9843	+	25.9536i	0.481118	+	0.833320i
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	0.798960	−	0.601384i	$-0.205384\pi$
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	−0.920294	+	0.391228i	$0.872050\pi$
$972$		0			0
$973$		0			0
$974$	−0.281870	+	0.488213i	−0.00903169	+	0.0156434i
$975$		0			0
$976$	15.7027			0.502633
$977$	56.6202			1.81144			0.905721	−	0.423875i	$-0.139330\pi$
$977$	56.6202			1.81144			0.905721	+	0.423875i	$0.139330\pi$
$978$		0			0
$979$	−1.06408	+	1.84305i	−0.0340083	+	0.0589041i
$980$		0			0
$981$		0			0
$982$	16.6997	+	28.9247i	0.532909	+	0.923025i
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	−0.999847	−	0.0174790i	$-0.994436\pi$
$983$	−16.1486	−	27.9702i	−0.515061	−	0.892112i	0.484786	−	0.874633i	$-0.338897\pi$
$984$		0			0
$985$	6.52033	−	11.2936i	0.207755	−	0.359842i
$986$	−0.0883286	−	0.152990i	−0.00281296	−	0.00487218i
$987$		0			0
$988$	−9.00955	+	15.6050i	−0.286632	+	0.496461i
$989$	37.5391	+	65.0197i	1.19367	+	2.06750i
$990$		0			0
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	−0.957003	−	0.290078i	$-0.906319\pi$
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	0.729716	+	0.683750i	$0.239652\pi$
$992$	−25.7039			−0.816100
$993$		0			0
$994$		0			0
$995$	5.79247	+	10.0329i	0.183634	+	0.318063i
$996$		0			0
$997$	28.1262	+	48.7160i	0.890765	+	1.54285i	0.838960	+	0.544194i	$0.183164\pi$
$997$	28.1262	+	48.7160i	0.890765	+	1.54285i	0.0518058	+	0.998657i	$0.483502\pi$
$998$	19.6176	−	33.9787i	0.620985	−	1.07558i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.f.802.4		10
3.2	odd	2		441.2.h.f.214.2		10
7.2	even	3		1323.2.g.f.667.2		10
7.3	odd	6		1323.2.f.e.883.2		10
7.4	even	3		1323.2.f.f.883.2		10
7.5	odd	6		189.2.g.b.100.2		10
7.6	odd	2		189.2.h.b.46.4		10
9.4	even	3		1323.2.g.f.361.2		10
9.5	odd	6		441.2.g.f.67.4		10
21.2	odd	6		441.2.g.f.79.4		10
21.5	even	6		63.2.g.b.16.4	yes	10
21.11	odd	6		441.2.f.f.295.4		10
21.17	even	6		441.2.f.e.295.4		10
21.20	even	2		63.2.h.b.25.2	yes	10
28.19	even	6		3024.2.t.i.289.2		10
28.27	even	2		3024.2.q.i.2881.4		10
63.4	even	3		1323.2.f.f.442.2		10
63.5	even	6		63.2.h.b.58.2	yes	10
63.11	odd	6		3969.2.a.ba.1.2		5
63.13	odd	6		189.2.g.b.172.2		10
63.20	even	6		567.2.e.f.487.4		10
63.23	odd	6		441.2.h.f.373.2		10
63.25	even	3		3969.2.a.bb.1.4		5
63.31	odd	6		1323.2.f.e.442.2		10
63.32	odd	6		441.2.f.f.148.4		10
63.34	odd	6		567.2.e.e.487.2		10
63.38	even	6		3969.2.a.z.1.2		5
63.40	odd	6		189.2.h.b.37.4		10
63.41	even	6		63.2.g.b.4.4	✓	10
63.47	even	6		567.2.e.f.163.4		10
63.52	odd	6		3969.2.a.bc.1.4		5
63.58	even	3	inner	1323.2.h.f.226.4		10
63.59	even	6		441.2.f.e.148.4		10
63.61	odd	6		567.2.e.e.163.2		10
84.47	odd	6		1008.2.t.i.961.5		10
84.83	odd	2		1008.2.q.i.529.2		10
252.103	even	6		3024.2.q.i.2305.4		10
252.131	odd	6		1008.2.q.i.625.2		10
252.139	even	6		3024.2.t.i.1873.2		10
252.167	odd	6		1008.2.t.i.193.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	63.41	even	6
63.2.g.b.16.4	yes	10	21.5	even	6
63.2.h.b.25.2	yes	10	21.20	even	2
63.2.h.b.58.2	yes	10	63.5	even	6
189.2.g.b.100.2		10	7.5	odd	6
189.2.g.b.172.2		10	63.13	odd	6
189.2.h.b.37.4		10	63.40	odd	6
189.2.h.b.46.4		10	7.6	odd	2
441.2.f.e.148.4		10	63.59	even	6
441.2.f.e.295.4		10	21.17	even	6
441.2.f.f.148.4		10	63.32	odd	6
441.2.f.f.295.4		10	21.11	odd	6
441.2.g.f.67.4		10	9.5	odd	6
441.2.g.f.79.4		10	21.2	odd	6
441.2.h.f.214.2		10	3.2	odd	2
441.2.h.f.373.2		10	63.23	odd	6
567.2.e.e.163.2		10	63.61	odd	6
567.2.e.e.487.2		10	63.34	odd	6
567.2.e.f.163.4		10	63.47	even	6
567.2.e.f.487.4		10	63.20	even	6
1008.2.q.i.529.2		10	84.83	odd	2
1008.2.q.i.625.2		10	252.131	odd	6
1008.2.t.i.193.5		10	252.167	odd	6
1008.2.t.i.961.5		10	84.47	odd	6
1323.2.f.e.442.2		10	63.31	odd	6
1323.2.f.e.883.2		10	7.3	odd	6
1323.2.f.f.442.2		10	63.4	even	3
1323.2.f.f.883.2		10	7.4	even	3
1323.2.g.f.361.2		10	9.4	even	3
1323.2.g.f.667.2		10	7.2	even	3
1323.2.h.f.226.4		10	63.58	even	3	inner
1323.2.h.f.802.4		10	1.1	even	1	trivial
3024.2.q.i.2305.4		10	252.103	even	6
3024.2.q.i.2881.4		10	28.27	even	2
3024.2.t.i.289.2		10	28.19	even	6
3024.2.t.i.1873.2		10	252.139	even	6
3969.2.a.z.1.2		5	63.38	even	6
3969.2.a.ba.1.2		5	63.11	odd	6
3969.2.a.bb.1.4		5	63.25	even	3
3969.2.a.bc.1.4		5	63.52	odd	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +O(q^{10})\)	\(q+1.84124 q^{2} +1.39017 q^{4} +(-0.667377 + 1.15593i) q^{5} -1.12285 q^{8} +(-1.22880 + 2.12835i) q^{10} +(0.756508 + 1.31031i) q^{11} +(2.58800 + 4.48254i) q^{13} -4.84777 q^{16} +(0.774463 - 1.34141i) q^{17} +(1.25211 + 2.16872i) q^{19} +(-0.927765 + 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(-3.68039 + 6.37463i) q^{23} +(1.60922 + 2.78725i) q^{25} +(4.76513 + 8.25344i) q^{26} +(0.0309713 - 0.0536439i) q^{29} +3.84777 q^{31} -6.68021 q^{32} +(1.42597 - 2.46986i) q^{34} +(-0.281608 - 0.487760i) q^{37} +(2.30543 + 3.99313i) q^{38} +(0.749363 - 1.29794i) q^{40} +(4.51188 + 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +(1.05167 + 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} -9.51851 q^{47} +(2.96296 + 5.13199i) q^{50} +(3.59775 + 6.23148i) q^{52} +(-0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(0.0570257 - 0.0987714i) q^{58} -8.44331 q^{59} -3.23917 q^{61} +7.08467 q^{62} -2.60434 q^{64} -6.90868 q^{65} +6.93339 q^{67} +(1.07663 - 1.86478i) q^{68} +12.3304 q^{71} +(1.37936 - 2.38912i) q^{73} +(-0.518508 - 0.898083i) q^{74} +(1.74064 + 3.01488i) q^{76} -5.91938 q^{79} +(3.23529 - 5.60368i) q^{80} +(8.30746 + 14.3889i) q^{82} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(9.39010 - 16.2641i) q^{86} +(-0.849444 - 1.47128i) q^{88} +(0.703287 + 1.21813i) q^{89} +(-5.11636 + 8.86180i) q^{92} -17.5259 q^{94} -3.34251 q^{95} +(6.09713 - 10.5605i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 + 6 * q^8 + 7 * q^10 - 4 * q^11 + 8 * q^13 - 4 * q^16 + 12 * q^17 - q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 + 11 * q^26 - 7 * q^29 - 6 * q^31 - 4 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 54 * q^47 - 19 * q^50 + 10 * q^52 + 21 * q^53 - 4 * q^55 - 10 * q^58 - 60 * q^59 - 28 * q^61 - 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 + 27 * q^68 + 6 * q^71 - 15 * q^73 + 36 * q^74 - 5 * q^76 + 8 * q^79 + 20 * q^80 + 5 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 28 * q^89 - 27 * q^92 - 6 * q^94 - 28 * q^95 + 12 * q^97

Introduction

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