LMFDB - Embedded newform 1323.2.f.f.883.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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:	$\Z[a_1, \ldots, a_{4}]$
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			883.4
Root			$-0.335166 + 0.580525i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.f.442.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 - 1.23403i) q^{5} +2.38012 q^{8} +O(q^{10})$	\(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 - 1.23403i) q^{5} +2.38012 q^{8} -0.955182 q^{10} +(-2.46539 + 4.27018i) q^{11} +(1.37730 + 2.38556i) q^{13} +(-0.752918 + 1.30409i) q^{16} -1.11968 q^{17} -4.01505 q^{19} +(1.10479 - 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 + 4.70824i) q^{23} +(1.48478 - 2.57171i) q^{25} +1.84650 q^{26} +(-3.40555 + 5.89858i) q^{29} +(1.25292 + 2.17012i) q^{31} +(2.88483 + 4.99666i) q^{32} +(-0.375279 + 0.650002i) q^{34} -1.41957 q^{37} +(-1.34571 + 2.33083i) q^{38} +(-1.69576 - 2.93714i) q^{40} +(0.124384 + 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} -7.64592 q^{44} +3.64434 q^{46} +(4.73790 - 8.20628i) q^{47} +(-0.995294 - 1.72390i) q^{50} +(-2.13572 + 3.69917i) q^{52} -0.820458 q^{53} +7.02604 q^{55} +(2.28285 + 3.95401i) q^{58} +(3.29204 + 5.70197i) q^{59} +(0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +0.855913 q^{64} +(1.96257 - 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +(-0.868117 - 1.50362i) q^{68} -0.0804951 q^{71} +10.6910 q^{73} +(-0.475793 + 0.824098i) q^{74} +(-3.11297 - 5.39183i) q^{76} +(0.922457 - 1.59774i) q^{79} +2.14572 q^{80} +0.166758 q^{82} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 + 0.578567i) q^{86} +(-5.86792 + 10.1635i) q^{88} -13.5258 q^{89} +(-4.21515 + 7.30085i) q^{92} +(-3.17597 - 5.50094i) q^{94} +(2.86059 + 4.95469i) q^{95} +(-2.70160 + 4.67930i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8} - 14 q^{10} - 4 q^{11} + 8 q^{13} + 2 q^{16} - 24 q^{17} + 2 q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 22 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} + 27 q^{47} - 19 q^{50} + 10 q^{52} - 42 q^{53} - 4 q^{55} - 10 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 27 q^{68} + 6 q^{71} + 30 q^{73} + 36 q^{74} - 5 q^{76} - 4 q^{79} - 40 q^{80} - 10 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 56 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8 - 14 * q^10 - 4 * q^11 + 8 * q^13 + 2 * q^16 - 24 * q^17 + 2 * q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 - 22 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 + 27 * q^47 - 19 * q^50 + 10 * q^52 - 42 * q^53 - 4 * q^55 - 10 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 27 * q^68 + 6 * q^71 + 30 * q^73 + 36 * q^74 - 5 * q^76 - 4 * q^79 - 40 * q^80 - 10 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 56 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.335166	−	0.580525i	0.236998	−	0.410493i	−0.722853	−	0.691002i	$-0.757170\pi$
$2$	0.335166	−	0.580525i	0.236998	−	0.410493i	0.959852	+	0.280508i	$0.0905031\pi$
$3$		0			0
$3$		0			0
$4$	0.775327	+	1.34291i	0.387664	+	0.671453i
$5$	−0.712469	−	1.23403i	−0.318626	−	0.551876i	0.661576	−	0.749878i	$-0.269888\pi$
$5$	−0.712469	−	1.23403i	−0.318626	−	0.551876i	−0.980202	+	0.198002i	$0.936555\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.38012			0.841499
$9$		0			0
$10$	−0.955182			−0.302055
$11$	−2.46539	+	4.27018i	−0.743342	+	1.28751i	0.207623	+	0.978209i	$0.433427\pi$
$11$	−2.46539	+	4.27018i	−0.743342	+	1.28751i	−0.950965	+	0.309297i	$0.899906\pi$
$12$		0			0
$13$	1.37730	+	2.38556i	0.381995	+	0.661635i	0.991347	−	0.131265i	$-0.0419038\pi$
$13$	1.37730	+	2.38556i	0.381995	+	0.661635i	−0.609352	+	0.792900i	$0.708571\pi$
$14$		0			0
$15$		0			0
$16$	−0.752918	+	1.30409i	−0.188230	+	0.326023i
$17$	−1.11968			−0.271562			−0.135781	−	0.990739i	$-0.543354\pi$
$17$	−1.11968			−0.271562			−0.135781	+	0.990739i	$0.543354\pi$
$18$		0			0
$19$	−4.01505			−0.921115			−0.460557	−	0.887630i	$-0.652350\pi$
$19$	−4.01505			−0.921115			−0.460557	+	0.887630i	$0.652350\pi$
$20$	1.10479	−	1.91356i	0.247039	−	0.427884i
$21$		0			0
$22$	1.65263	+	2.86244i	0.352342	+	0.610274i
$23$	2.71830	+	4.70824i	0.566806	+	0.981736i	0.996879	+	0.0789424i	$0.0251543\pi$
$23$	2.71830	+	4.70824i	0.566806	+	0.981736i	−0.430073	+	0.902794i	$0.641512\pi$
$24$		0			0
$25$	1.48478	−	2.57171i	0.296955	−	0.514342i
$26$	1.84650			0.362129
$27$		0			0
$28$		0			0
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	0.354667	+	0.934993i	$0.384594\pi$
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	−0.987061	+	0.160346i	$0.948739\pi$
$30$		0			0
$31$	1.25292	+	2.17012i	0.225031	+	0.389765i	0.956329	−	0.292294i	$-0.0944184\pi$
$31$	1.25292	+	2.17012i	0.225031	+	0.389765i	−0.731298	+	0.682058i	$0.761085\pi$
$32$	2.88483	+	4.99666i	0.509970	+	0.883294i
$33$		0			0
$34$	−0.375279	+	0.650002i	−0.0643597	+	0.111474i
$35$		0			0
$36$		0			0
$37$	−1.41957			−0.233376			−0.116688	−	0.993169i	$-0.537228\pi$
$37$	−1.41957			−0.233376			−0.116688	+	0.993169i	$0.537228\pi$
$38$	−1.34571	+	2.33083i	−0.218303	+	0.378111i
$39$		0			0
$40$	−1.69576	−	2.93714i	−0.268123	−	0.464403i
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	0.875575	−	0.483083i	$-0.160483\pi$
$41$	0.124384	+	0.215440i	0.0194256	+	0.0336460i	−0.856149	+	0.516729i	$0.827150\pi$
$42$		0			0
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	−0.901517	−	0.432743i	$-0.857546\pi$
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	0.825525	+	0.564365i	$0.190879\pi$
$44$	−7.64592			−1.15267
$45$		0			0
$46$	3.64434			0.537328
$47$	4.73790	−	8.20628i	0.691093	−	1.19701i	−0.280387	−	0.959887i	$-0.590463\pi$
$47$	4.73790	−	8.20628i	0.691093	−	1.19701i	0.971480	−	0.237122i	$-0.0762040\pi$
$48$		0			0
$49$		0			0
$50$	−0.995294	−	1.72390i	−0.140756	−	0.243796i
$51$		0			0
$52$	−2.13572	+	3.69917i	−0.296171	+	0.512983i
$53$	−0.820458			−0.112699			−0.0563493	−	0.998411i	$-0.517946\pi$
$53$	−0.820458			−0.112699			−0.0563493	+	0.998411i	$0.517946\pi$
$54$		0			0
$55$	7.02604			0.947392
$56$		0			0
$57$		0			0
$58$	2.28285	+	3.95401i	0.299753	+	0.519187i
$59$	3.29204	+	5.70197i	0.428586	+	0.742334i	0.996748	−	0.0805836i	$-0.0256784\pi$
$59$	3.29204	+	5.70197i	0.428586	+	0.742334i	−0.568161	+	0.822917i	$0.692345\pi$
$60$		0			0
$61$	0.0376322	−	0.0651809i	0.00481831	−	0.00834556i	−0.863606	−	0.504167i	$-0.831800\pi$
$61$	0.0376322	−	0.0651809i	0.00481831	−	0.00834556i	0.868425	+	0.495821i	$0.165133\pi$
$62$	1.67974			0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	1.96257	−	3.39927i	0.243427	−	0.421628i
$66$		0			0
$67$	6.29385	+	10.9013i	0.768916	+	1.33180i	0.938151	+	0.346226i	$0.112537\pi$
$67$	6.29385	+	10.9013i	0.768916	+	1.33180i	−0.169235	+	0.985576i	$0.554130\pi$
$68$	−0.868117	−	1.50362i	−0.105275	−	0.182341i
$69$		0			0
$70$		0			0
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	10.6910			1.25129			0.625644	−	0.780109i	$-0.284836\pi$
$73$	10.6910			1.25129			0.625644	+	0.780109i	$0.284836\pi$
$74$	−0.475793	+	0.824098i	−0.0553098	+	0.0957995i
$75$		0			0
$76$	−3.11297	−	5.39183i	−0.357083	−	0.618485i
$77$		0			0
$78$		0			0
$79$	0.922457	−	1.59774i	0.103785	−	0.179760i	−0.809456	−	0.587180i	$-0.800238\pi$
$79$	0.922457	−	1.59774i	0.103785	−	0.179760i	0.913241	+	0.407420i	$0.133571\pi$
$80$	2.14572			0.239899
$81$		0			0
$82$	0.166758			0.0184153
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	0.129088	+	0.991633i	$0.458795\pi$
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	−0.923323	+	0.384023i	$0.874538\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$	0.334036	+	0.578567i	0.0360200	+	0.0623885i
$87$		0			0
$88$	−5.86792	+	10.1635i	−0.625522	+	1.08344i
$89$	−13.5258			−1.43374			−0.716868	−	0.697209i	$-0.754425\pi$
$89$	−13.5258			−1.43374			−0.716868	+	0.697209i	$0.754425\pi$
$90$		0			0
$91$		0			0
$92$	−4.21515	+	7.30085i	−0.439460	+	0.761167i
$93$		0			0
$94$	−3.17597	−	5.50094i	−0.327576	−	0.567378i
$95$	2.86059	+	4.95469i	0.293491	+	0.508341i
$96$		0			0
$97$	−2.70160	+	4.67930i	−0.274306	+	0.475111i	−0.969960	−	0.243266i	$-0.921781\pi$
$97$	−2.70160	+	4.67930i	−0.274306	+	0.475111i	0.695654	+	0.718377i	$0.255115\pi$
$98$		0			0
$99$		0			0
$100$	4.60475			0.460475
$101$	2.56770	−	4.44739i	0.255496	−	0.442531i	−0.709534	−	0.704671i	$-0.751095\pi$
$101$	2.56770	−	4.44739i	0.255496	−	0.442531i	0.965030	+	0.262139i	$0.0844280\pi$
$102$		0			0
$103$	−7.10561	−	12.3073i	−0.700137	−	1.21267i	−0.968418	−	0.249332i	$-0.919789\pi$
$103$	−7.10561	−	12.3073i	−0.700137	−	1.21267i	0.268282	−	0.963341i	$-0.413544\pi$
$104$	3.27814	+	5.67791i	0.321448	+	0.556765i
$105$		0			0
$106$	−0.274990	+	0.476296i	−0.0267094	+	0.0462620i
$107$	7.66030			0.740549			0.370274	−	0.928922i	$-0.379264\pi$
$107$	7.66030			0.740549			0.370274	+	0.928922i	$0.379264\pi$
$108$		0			0
$109$	1.69879			0.162714			0.0813572	−	0.996685i	$-0.474075\pi$
$109$	1.69879			0.162714			0.0813572	+	0.996685i	$0.474075\pi$
$110$	2.35489	−	4.07880i	0.224530	−	0.388898i
$111$		0			0
$112$		0			0
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	0.879807	−	0.475331i	$-0.157672\pi$
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	−0.851552	+	0.524270i	$0.824338\pi$
$114$		0			0
$115$	3.87341	−	6.70895i	0.361198	−	0.625613i
$116$	−10.5617			−0.980625
$117$		0			0
$118$	4.41352			0.406297
$119$		0			0
$120$		0			0
$121$	−6.65626	−	11.5290i	−0.605115	−	1.04809i
$122$	−0.0252261	−	0.0436929i	−0.00228386	−	0.00395577i
$123$		0			0
$124$	−1.94284	+	3.36510i	−0.174472	+	0.302195i
$125$	−11.3561			−1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	−5.48278	+	9.49645i	−0.484614	+	0.839375i
$129$		0			0
$130$	−1.31557	−	2.27864i	−0.115384	−	0.199850i
$131$	10.2265	+	17.7128i	0.893492	+	1.54757i	0.835660	+	0.549248i	$0.185086\pi$
$131$	10.2265	+	17.7128i	0.893492	+	1.54757i	0.0578326	+	0.998326i	$0.481581\pi$
$132$		0			0
$133$		0			0
$134$	8.43794			0.728927
$135$		0			0
$136$	−2.66497			−0.228519
$137$	6.10581	−	10.5756i	0.521655	−	0.903532i	−0.478028	−	0.878345i	$-0.658648\pi$
$137$	6.10581	−	10.5756i	0.521655	−	0.903532i	0.999683	−	0.0251879i	$-0.00801840\pi$
$138$		0			0
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	0.913842	−	0.406071i	$-0.133101\pi$
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	−0.808588	+	0.588375i	$0.799768\pi$
$140$		0			0
$141$		0			0
$142$	−0.0269793	+	0.0467294i	−0.00226405	+	0.00392145i
$143$	−13.5823			−1.13581
$144$		0			0
$145$	9.70538			0.805988
$146$	3.58327	−	6.20640i	0.296553	−	0.513645i
$147$		0			0
$148$	−1.10063	−	1.90635i	−0.0904715	−	0.156701i
$149$	−4.27797	−	7.40966i	−0.350465	−	0.607023i	0.635866	−	0.771799i	$-0.280643\pi$
$149$	−4.27797	−	7.40966i	−0.350465	−	0.607023i	−0.986331	+	0.164777i	$0.947310\pi$
$150$		0			0
$151$	8.82962	−	15.2933i	0.718544	−	1.24455i	−0.243033	−	0.970018i	$-0.578142\pi$
$151$	8.82962	−	15.2933i	0.718544	−	1.24455i	0.961577	−	0.274537i	$-0.0885244\pi$
$152$	−9.55629			−0.775117
$153$		0			0
$154$		0			0
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	3.16074	+	5.47457i	0.252255	+	0.436918i	0.964146	−	0.265371i	$-0.0854946\pi$
$157$	3.16074	+	5.47457i	0.252255	+	0.436918i	−0.711891	+	0.702289i	$0.752161\pi$
$158$	−0.618353	−	1.07102i	−0.0491936	−	0.0852057i
$159$		0			0
$160$	4.11070	−	7.11993i	0.324979	−	0.562880i
$161$		0			0
$162$		0			0
$163$	8.02267			0.628384			0.314192	−	0.949359i	$-0.398266\pi$
$163$	8.02267			0.628384			0.314192	+	0.949359i	$0.398266\pi$
$164$	−0.192877	+	0.334073i	−0.0150612	+	0.0260867i
$165$		0			0
$166$	4.85041	+	8.40116i	0.376465	+	0.652057i
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	0.904132	−	0.427253i	$-0.140518\pi$
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	−0.822078	+	0.569375i	$0.807185\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$	1.06950			0.0820267
$171$		0			0
$172$	−1.54542			−0.117837
$173$	9.14404	−	15.8379i	0.695208	−	1.20414i	−0.274902	−	0.961472i	$-0.588646\pi$
$173$	9.14404	−	15.8379i	0.695208	−	1.20414i	0.970110	−	0.242664i	$-0.0780212\pi$
$174$		0			0
$175$		0			0
$176$	−3.71247	−	6.43018i	−0.279838	−	0.484693i
$177$		0			0
$178$	−4.53341	+	7.85209i	−0.339793	+	0.588539i
$179$	7.62551			0.569958			0.284979	−	0.958534i	$-0.408013\pi$
$179$	7.62551			0.569958			0.284979	+	0.958534i	$0.408013\pi$
$180$		0			0
$181$	−15.5305			−1.15438			−0.577188	−	0.816611i	$-0.695850\pi$
$181$	−15.5305			−1.15438			−0.577188	+	0.816611i	$0.695850\pi$
$182$		0			0
$183$		0			0
$184$	6.46989	+	11.2062i	0.476967	+	0.826130i
$185$	1.01140	+	1.75180i	0.0743597	+	0.128795i
$186$		0			0
$187$	2.76044	−	4.78122i	0.201863	−	0.349638i
$188$	14.6937			1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	7.41624	−	12.8453i	0.536620	−	0.929454i	−0.462463	−	0.886639i	$-0.653034\pi$
$191$	7.41624	−	12.8453i	0.536620	−	0.929454i	0.999083	−	0.0428150i	$-0.0136326\pi$
$192$		0			0
$193$	−8.28387	−	14.3481i	−0.596286	−	1.03280i	−0.993364	−	0.115013i	$-0.963309\pi$
$193$	−8.28387	−	14.3481i	−0.596286	−	1.03280i	0.397078	−	0.917785i	$-0.370024\pi$
$194$	1.81097	+	3.13669i	0.130020	+	0.225201i
$195$		0			0
$196$		0			0
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	−25.2814			−1.79215			−0.896076	−	0.443901i	$-0.853594\pi$
$199$	−25.2814			−1.79215			−0.896076	+	0.443901i	$0.853594\pi$
$200$	3.53395	−	6.12097i	0.249888	−	0.432818i
$201$		0			0
$202$	−1.72121	−	2.98123i	−0.121104	−	0.209758i
$203$		0			0
$204$		0			0
$205$	0.177240	−	0.306988i	0.0123790	−	0.0214410i
$206$	−9.52625			−0.663725
$207$		0			0
$208$	−4.14798			−0.287611
$209$	9.89864	−	17.1449i	0.684703	−	1.18594i
$210$		0			0
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	0.706961	−	0.707253i	$-0.250066\pi$
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916732\pi$
$212$	−0.636123	−	1.10180i	−0.0436891	−	0.0756718i
$213$		0			0
$214$	2.56747	−	4.44699i	0.175509	−	0.303990i
$215$	1.42013			0.0968521
$216$		0			0
$217$		0			0
$218$	0.569377	−	0.986190i	0.0385631	−	0.0667932i
$219$		0			0
$220$	5.44748	+	9.43531i	0.367269	+	0.636129i
$221$	−1.54214	−	2.67106i	−0.103735	−	0.179675i
$222$		0			0
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	−0.997276	−	0.0737638i	$-0.976499\pi$
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	0.562519	+	0.826784i	$0.309832\pi$
$224$		0			0
$225$		0			0
$226$	0.402671			0.0267852
$227$	14.4832	−	25.0857i	0.961286	−	1.66500i	0.242009	−	0.970274i	$-0.422194\pi$
$227$	14.4832	−	25.0857i	0.961286	−	1.66500i	0.719277	−	0.694723i	$-0.244473\pi$
$228$		0			0
$229$	7.71790	+	13.3678i	0.510013	+	0.883369i	0.999933	+	0.0116012i	$0.00369285\pi$
$229$	7.71790	+	13.3678i	0.510013	+	0.883369i	−0.489919	+	0.871768i	$0.662974\pi$
$230$	−2.59648	−	4.49723i	−0.171207	−	0.296538i
$231$		0			0
$232$	−8.10561	+	14.0393i	−0.532159	+	0.921727i
$233$	−4.94648			−0.324055			−0.162027	−	0.986786i	$-0.551803\pi$
$233$	−4.94648			−0.324055			−0.162027	+	0.986786i	$0.551803\pi$
$234$		0			0
$235$	−13.5024			−0.880800
$236$	−5.10481	+	8.84179i	−0.332295	+	0.575551i
$237$		0			0
$238$		0			0
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	0.574523	−	0.818489i	$-0.305188\pi$
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	−0.996093	+	0.0883069i	$0.971854\pi$
$240$		0			0
$241$	7.29123	−	12.6288i	0.469670	−	0.813492i	−0.529729	−	0.848167i	$-0.677706\pi$
$241$	7.29123	−	12.6288i	0.469670	−	0.813492i	0.999399	+	0.0346754i	$0.0110397\pi$
$242$	−8.92382			−0.573645
$243$		0			0
$244$	0.116709			0.00747154
$245$		0			0
$246$		0			0
$247$	−5.52993	−	9.57812i	−0.351861	−	0.609441i
$248$	2.98209	+	5.16514i	0.189363	+	0.327987i
$249$		0			0
$250$	−3.80619	+	6.59251i	−0.240724	+	0.416947i
$251$	−14.0715			−0.888187			−0.444094	−	0.895980i	$-0.646474\pi$
$251$	−14.0715			−0.888187			−0.444094	+	0.895980i	$0.646474\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	2.43323	−	4.21448i	0.152674	−	0.264440i
$255$		0			0
$256$	4.53120	+	7.84826i	0.283200	+	0.490517i
$257$	4.18108	+	7.24184i	0.260808	+	0.451733i	0.966457	−	0.256829i	$-0.0826776\pi$
$257$	4.18108	+	7.24184i	0.260808	+	0.451733i	−0.705649	+	0.708562i	$0.749344\pi$
$258$		0			0
$259$		0			0
$260$	6.08653			0.377471
$261$		0			0
$262$	13.7103			0.847025
$263$	1.63533	−	2.83247i	0.100839	−	0.174658i	−0.811192	−	0.584780i	$-0.801181\pi$
$263$	1.63533	−	2.83247i	0.100839	−	0.174658i	0.912030	+	0.410122i	$0.134514\pi$
$264$		0			0
$265$	0.584551	+	1.01247i	0.0359087	+	0.0621956i
$266$		0			0
$267$		0			0
$268$	−9.75958	+	16.9041i	−0.596161	+	1.03258i
$269$	15.3870			0.938161			0.469081	−	0.883155i	$-0.344585\pi$
$269$	15.3870			0.938161			0.469081	+	0.883155i	$0.344585\pi$
$270$		0			0
$271$	8.12617			0.493630			0.246815	−	0.969063i	$-0.420616\pi$
$271$	8.12617			0.493630			0.246815	+	0.969063i	$0.420616\pi$
$272$	0.843026	−	1.46016i	0.0511160	−	0.0885355i
$273$		0			0
$274$	−4.09293	−	7.08915i	−0.247263	−	0.428271i
$275$	7.32110	+	12.6805i	0.441479	+	0.764664i
$276$		0			0
$277$	−6.42287	+	11.1247i	−0.385913	+	0.668421i	−0.991895	−	0.127057i	$-0.959447\pi$
$277$	−6.42287	+	11.1247i	−0.385913	+	0.668421i	0.605982	+	0.795478i	$0.292780\pi$
$278$	1.66365			0.0997793
$279$		0			0
$280$		0			0
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	−0.843620	−	0.536941i	$-0.819580\pi$
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	0.886815	+	0.462125i	$0.152913\pi$
$282$		0			0
$283$	−8.71926	−	15.1022i	−0.518306	−	0.897732i	−0.999774	−	0.0212686i	$-0.993229\pi$
$283$	−8.71926	−	15.1022i	−0.518306	−	0.897732i	0.481468	−	0.876464i	$-0.340104\pi$
$284$	−0.0624100	−	0.108097i	−0.00370335	−	0.00641440i
$285$		0			0
$286$	−4.55234	+	7.88489i	−0.269186	+	0.466243i
$287$		0			0
$288$		0			0
$289$	−15.7463			−0.926254
$290$	3.25292	−	5.63422i	0.191018	−	0.330853i
$291$		0			0
$292$	8.28903	+	14.3570i	0.485079	+	0.840181i
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	0.838537	−	0.544845i	$-0.183412\pi$
$293$	−0.900048	−	1.55893i	−0.0525814	−	0.0910736i	−0.891118	+	0.453772i	$0.850078\pi$
$294$		0			0
$295$	4.69094	−	8.12495i	0.273117	−	0.473053i
$296$	−3.37875			−0.196386
$297$		0			0
$298$	−5.73532			−0.332238
$299$	−7.48786	+	12.9693i	−0.433034	+	0.750037i
$300$		0			0
$301$		0			0
$302$	−5.91878	−	10.2516i	−0.340588	−	0.589915i
$303$		0			0
$304$	3.02300	−	5.23599i	0.173381	−	0.300305i
$305$	−0.107247			−0.00614095
$306$		0			0
$307$	−1.06478			−0.0607699			−0.0303850	−	0.999538i	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$		0			0
$310$	−1.19676	−	2.07286i	−0.0679717	−	0.117730i
$311$	8.46463	+	14.6612i	0.479985	+	0.831359i	0.999736	−	0.0229591i	$-0.00730874\pi$
$311$	8.46463	+	14.6612i	0.479985	+	0.831359i	−0.519751	+	0.854318i	$0.673975\pi$
$312$		0			0
$313$	−4.13928	+	7.16944i	−0.233966	+	0.405241i	−0.958972	−	0.283502i	$-0.908504\pi$
$313$	−4.13928	+	7.16944i	−0.233966	+	0.405241i	0.725006	+	0.688743i	$0.241837\pi$
$314$	4.23750			0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	3.27371	−	5.67023i	0.183870	−	0.318472i	−0.759325	−	0.650711i	$-0.774471\pi$
$317$	3.27371	−	5.67023i	0.183870	−	0.318472i	0.943195	+	0.332239i	$0.107804\pi$
$318$		0			0
$319$	−16.7920	−	29.0846i	−0.940171	−	1.62842i
$320$	−0.609811	−	1.05622i	−0.0340895	−	0.0590447i
$321$		0			0
$322$		0			0
$323$	4.49556			0.250140
$324$		0			0
$325$	8.17995			0.453742
$326$	2.68893	−	4.65736i	0.148926	−	0.257947i
$327$		0			0
$328$	0.296049	+	0.512773i	0.0163466	+	0.0283131i
$329$		0			0
$330$		0			0
$331$	13.3629	−	23.1453i	0.734493	−	1.27218i	−0.220453	−	0.975398i	$-0.570754\pi$
$331$	13.3629	−	23.1453i	0.734493	−	1.27218i	0.954946	−	0.296781i	$-0.0959131\pi$
$332$	−22.4405			−1.23158
$333$		0			0
$334$	1.42161			0.0777872
$335$	8.96834	−	15.5336i	0.489993	−	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$	−1.81397	−	3.14189i	−0.0986670	−	0.170896i
$339$		0			0
$340$	−1.23701	+	2.14257i	−0.0670864	+	0.116197i
$341$	−12.3557			−0.669099
$342$		0			0
$343$		0			0
$344$	−1.18605	+	2.05429i	−0.0639473	+	0.110760i
$345$		0			0
$346$	−6.12955	−	10.6167i	−0.329526	−	0.570757i
$347$	−9.35156	−	16.1974i	−0.502018	−	0.869521i	−0.999997	−	0.00233189i	$-0.999258\pi$
$347$	−9.35156	−	16.1974i	−0.502018	−	0.869521i	0.497979	−	0.867189i	$-0.334076\pi$
$348$		0			0
$349$	15.0542	−	26.0747i	0.805834	−	1.39574i	−0.109893	−	0.993943i	$-0.535051\pi$
$349$	15.0542	−	26.0747i	0.805834	−	1.39574i	0.915727	−	0.401801i	$-0.131616\pi$
$350$		0			0
$351$		0			0
$352$	−28.4488			−1.51633
$353$	−3.12966	+	5.42074i	−0.166575	+	0.288517i	−0.937214	−	0.348756i	$-0.886604\pi$
$353$	−3.12966	+	5.42074i	−0.166575	+	0.288517i	0.770638	+	0.637273i	$0.219938\pi$
$354$		0			0
$355$	0.0573502	+	0.0993335i	0.00304383	+	0.00527208i
$356$	−10.4870	−	18.1639i	−0.555807	−	0.962686i
$357$		0			0
$358$	2.55582	−	4.42680i	0.135079	−	0.233964i
$359$	−10.1951			−0.538077			−0.269038	−	0.963129i	$-0.586706\pi$
$359$	−10.1951			−0.538077			−0.269038	+	0.963129i	$0.586706\pi$
$360$		0			0
$361$	−2.87941			−0.151548
$362$	−5.20532	+	9.01587i	−0.273585	+	0.473864i
$363$		0			0
$364$		0			0
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	−14.3278	+	24.8165i	−0.747906	+	1.29541i	0.200918	+	0.979608i	$0.435608\pi$
$367$	−14.3278	+	24.8165i	−0.747906	+	1.29541i	−0.948824	+	0.315804i	$0.897726\pi$
$368$	−8.18664			−0.426758
$369$		0			0
$370$	1.35595			0.0704926
$371$		0			0
$372$		0			0
$373$	8.03670	+	13.9200i	0.416124	+	0.720749i	0.995546	−	0.0942796i	$-0.0300548\pi$
$373$	8.03670	+	13.9200i	0.416124	+	0.720749i	−0.579421	+	0.815028i	$0.696721\pi$
$374$	−1.85041	−	3.20501i	−0.0956826	−	0.165727i
$375$		0			0
$376$	11.2768	−	19.5319i	0.581555	−	1.00728i
$377$	−18.7619			−0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	−4.43579	+	7.68302i	−0.227551	+	0.394130i
$381$		0			0
$382$	−4.97135	−	8.61063i	−0.254356	−	0.440558i
$383$	5.79327	+	10.0342i	0.296022	+	0.512725i	0.975222	−	0.221228i	$-0.0710065\pi$
$383$	5.79327	+	10.0342i	0.296022	+	0.512725i	−0.679200	+	0.733953i	$0.737673\pi$
$384$		0			0
$385$		0			0
$386$	−11.1059			−0.565275
$387$		0			0
$388$	−8.37848			−0.425353
$389$	8.90675	−	15.4270i	0.451590	−	0.782178i	−0.546895	−	0.837201i	$-0.684190\pi$
$389$	8.90675	−	15.4270i	0.451590	−	0.782178i	0.998485	+	0.0550239i	$0.0175235\pi$
$390$		0			0
$391$	−3.04363	−	5.27172i	−0.153923	−	0.266602i
$392$		0			0
$393$		0			0
$394$	1.35320	−	2.34381i	0.0681732	−	0.118079i
$395$	−2.62889			−0.132274
$396$		0			0
$397$	−13.0846			−0.656696			−0.328348	−	0.944557i	$-0.606492\pi$
$397$	−13.0846			−0.656696			−0.328348	+	0.944557i	$0.606492\pi$
$398$	−8.47348	+	14.6765i	−0.424737	+	0.735666i
$399$		0			0
$400$	2.23583	+	3.87257i	0.111792	+	0.193629i
$401$	7.05165	+	12.2138i	0.352143	+	0.609929i	0.986625	−	0.163009i	$-0.0521199\pi$
$401$	7.05165	+	12.2138i	0.352143	+	0.609929i	−0.634482	+	0.772938i	$0.718787\pi$
$402$		0			0
$403$	−3.45129	+	5.97782i	−0.171921	+	0.297776i
$404$	7.96323			0.396185
$405$		0			0
$406$		0			0
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	−1.32300	−	2.29150i	−0.0654179	−	0.113307i	0.831461	−	0.555583i	$-0.187505\pi$
$409$	−1.32300	−	2.29150i	−0.0654179	−	0.113307i	−0.896879	+	0.442275i	$0.854171\pi$
$410$	−0.118810	−	0.205784i	−0.00586759	−	0.0101630i
$411$		0			0
$412$	11.0183	−	19.0843i	0.542835	−	0.940217i
$413$		0			0
$414$		0			0
$415$	20.6212			1.01226
$416$	−7.94655	+	13.7638i	−0.389612	+	0.674827i
$417$		0			0
$418$	−6.63538	−	11.4928i	−0.324547	−	0.562132i
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	0.906700	+	0.421776i	$0.138593\pi$
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	−0.0880816	+	0.996113i	$0.528074\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$	−5.04421			−0.245548
$423$		0			0
$424$	−1.95279			−0.0948358
$425$	−1.66247	+	2.87949i	−0.0806418	+	0.139676i
$426$		0			0
$427$		0			0
$428$	5.93923	+	10.2871i	0.287084	+	0.497244i
$429$		0			0
$430$	0.475980	−	0.824422i	0.0229538	−	0.0397571i
$431$	35.3285			1.70172			0.850858	−	0.525396i	$-0.176083\pi$
$431$	35.3285			1.70172			0.850858	+	0.525396i	$0.176083\pi$
$432$		0			0
$433$	−5.47404			−0.263066			−0.131533	−	0.991312i	$-0.541990\pi$
$433$	−5.47404			−0.263066			−0.131533	+	0.991312i	$0.541990\pi$
$434$		0			0
$435$		0			0
$436$	1.31712	+	2.28131i	0.0630785	+	0.109255i
$437$	−10.9141	−	18.9038i	−0.522093	−	0.904292i
$438$		0			0
$439$	3.19906	−	5.54093i	0.152683	−	0.264454i	−0.779530	−	0.626365i	$-0.784542\pi$
$439$	3.19906	−	5.54093i	0.152683	−	0.264454i	0.932213	+	0.361911i	$0.117875\pi$
$440$	16.7228			0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	−3.19341	+	5.53115i	−0.151723	+	0.262793i	−0.931861	−	0.362815i	$-0.881816\pi$
$443$	−3.19341	+	5.53115i	−0.151723	+	0.262793i	0.780138	+	0.625608i	$0.215149\pi$
$444$		0			0
$445$	9.63674	+	16.6913i	0.456825	+	0.791245i
$446$	4.35200	+	7.53789i	0.206073	+	0.356929i
$447$		0			0
$448$		0			0
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	−1.22662			−0.0577593
$452$	−0.465741	+	0.806687i	−0.0219066	+	0.0379434i
$453$		0			0
$454$	−9.70859	−	16.8158i	−0.455647	−	0.789203i
$455$		0			0
$456$		0			0
$457$	−5.26120	+	9.11266i	−0.246108	+	0.426272i	−0.962443	−	0.271485i	$-0.912485\pi$
$457$	−5.26120	+	9.11266i	−0.246108	+	0.426272i	0.716334	+	0.697757i	$0.245819\pi$
$458$	10.3471			0.483489
$459$		0			0
$460$	12.0127			0.560093
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	−0.936657	−	0.350249i	$-0.886097\pi$
$461$	−3.54278	+	6.13627i	−0.165004	+	0.285794i	0.771653	+	0.636044i	$0.219430\pi$
$462$		0			0
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108654\pi$
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	−0.181246	+	0.983438i	$0.558013\pi$
$464$	−5.12820	−	8.88230i	−0.238071	−	0.412350i
$465$		0			0
$466$	−1.65789	+	2.87156i	−0.0768004	+	0.133022i
$467$	−3.92431			−0.181596			−0.0907978	−	0.995869i	$-0.528942\pi$
$467$	−3.92431			−0.181596			−0.0907978	+	0.995869i	$0.528942\pi$
$468$		0			0
$469$		0			0
$470$	−4.52555	+	7.83849i	−0.208748	+	0.361563i
$471$		0			0
$472$	7.83544	+	13.5714i	0.360655	+	0.624673i
$473$	−2.45707	−	4.25577i	−0.112976	−	0.195681i
$474$		0			0
$475$	−5.96145	+	10.3255i	−0.273530	+	0.473768i
$476$		0			0
$477$		0			0
$478$	−8.73755			−0.399646
$479$	−8.04324	+	13.9313i	−0.367505	+	0.636537i	−0.989175	−	0.146742i	$-0.953121\pi$
$479$	−8.04324	+	13.9313i	−0.367505	+	0.636537i	0.621670	+	0.783279i	$0.286455\pi$
$480$		0			0
$481$	−1.95518	−	3.38647i	−0.0891486	−	0.154410i
$482$	−4.88755	−	8.46549i	−0.222622	−	0.385592i
$483$		0			0
$484$	10.3216	−	17.8775i	0.469162	−	0.812612i
$485$	7.69921			0.349603
$486$		0			0
$487$	3.50344			0.158756			0.0793781	−	0.996845i	$-0.474707\pi$
$487$	3.50344			0.158756			0.0793781	+	0.996845i	$0.474707\pi$
$488$	0.0895692	−	0.155138i	0.00405461	−	0.00702279i
$489$		0			0
$490$		0			0
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.787296	+	0.616575i	$0.211480\pi$
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.140321	+	0.990106i	$0.455186\pi$
$492$		0			0
$493$	3.81312	−	6.60452i	0.171734	−	0.297452i
$494$	−7.41379			−0.333562
$495$		0			0
$496$	−3.77338			−0.169430
$497$		0			0
$498$		0			0
$499$	−5.91486	−	10.2448i	−0.264785	−	0.458622i	0.702722	−	0.711465i	$-0.251968\pi$
$499$	−5.91486	−	10.2448i	−0.264785	−	0.458622i	−0.967507	+	0.252843i	$0.918634\pi$
$500$	−8.80470	−	15.2502i	−0.393758	−	0.682009i
$501$		0			0
$502$	−4.71631	+	8.16888i	−0.210499	+	0.364595i
$503$	21.8595			0.974665			0.487332	−	0.873217i	$-0.337970\pi$
$503$	21.8595			0.974665			0.487332	+	0.873217i	$0.337970\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	−8.98470	+	15.5620i	−0.399419	+	0.691813i
$507$		0			0
$508$	5.62869	+	9.74918i	0.249733	+	0.432550i
$509$	−8.44831	−	14.6329i	−0.374465	−	0.648592i	0.615782	−	0.787917i	$-0.288840\pi$
$509$	−8.44831	−	14.6329i	−0.374465	−	0.648592i	−0.990247	+	0.139324i	$0.955507\pi$
$510$		0			0
$511$		0			0
$512$	−15.8563			−0.700756
$513$		0			0
$514$	5.60542			0.247245
$515$	−10.1250	+	17.5371i	−0.446163	+	0.772777i
$516$		0			0
$517$	23.3615	+	40.4633i	1.02744	+	1.77957i
$518$		0			0
$519$		0			0
$520$	4.67115	−	8.09067i	0.204843	−	0.354799i
$521$	34.4932			1.51117			0.755587	−	0.655048i	$-0.227352\pi$
$521$	34.4932			1.51117			0.755587	+	0.655048i	$0.227352\pi$
$522$		0			0
$523$	1.99123			0.0870704			0.0435352	−	0.999052i	$-0.486138\pi$
$523$	1.99123			0.0870704			0.0435352	+	0.999052i	$0.486138\pi$
$524$	−15.8577	+	27.4664i	−0.692749	+	1.19988i
$525$		0			0
$526$	−1.09622	−	1.89870i	−0.0477972	−	0.0827873i
$527$	−1.40287	−	2.42983i	−0.0611098	−	0.105845i
$528$		0			0
$529$	−3.27836	+	5.67829i	−0.142538	+	0.246882i
$530$	0.783687			0.0340412
$531$		0			0
$532$		0			0
$533$	−0.342629	+	0.593452i	−0.0148409	+	0.0257052i
$534$		0			0
$535$	−5.45772	−	9.45305i	−0.235958	−	0.408691i
$536$	14.9801	+	25.9463i	0.647042	+	1.12071i
$537$		0			0
$538$	5.15720	−	8.93253i	0.222343	−	0.385109i
$539$		0			0
$540$		0			0
$541$	30.1363			1.29566			0.647830	−	0.761785i	$-0.275677\pi$
$541$	30.1363			1.29566			0.647830	+	0.761785i	$0.275677\pi$
$542$	2.72362	−	4.71745i	0.116989	−	0.202632i
$543$		0			0
$544$	−3.23008	−	5.59466i	−0.138488	−	0.239869i
$545$	−1.21033	−	2.09636i	−0.0518450	−	0.0897982i
$546$		0			0
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	−0.653792	−	0.756674i	$-0.726823\pi$
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	0.982195	+	0.187864i	$0.0601563\pi$
$548$	18.9360			0.808906
$549$		0			0
$550$	9.81514			0.418519
$551$	13.6734	−	23.6831i	0.582508	−	1.00893i
$552$		0			0
$553$		0			0
$554$	4.30546	+	7.45728i	0.182921	+	0.316829i
$555$		0			0
$556$	−1.92423	+	3.33287i	−0.0816056	+	0.141345i
$557$	−23.2823			−0.986504			−0.493252	−	0.869886i	$-0.664192\pi$
$557$	−23.2823			−0.986504			−0.493252	+	0.869886i	$0.664192\pi$
$558$		0			0
$559$	−2.74531			−0.116114
$560$		0			0
$561$		0			0
$562$	−0.485375	−	0.840695i	−0.0204743	−	0.0354626i
$563$	−2.27942	−	3.94808i	−0.0960663	−	0.166392i	0.813987	−	0.580883i	$-0.197293\pi$
$563$	−2.27942	−	3.94808i	−0.0960663	−	0.166392i	−0.910053	+	0.414492i	$0.863959\pi$
$564$		0			0
$565$	0.427982	−	0.741286i	0.0180053	−	0.0311861i
$566$	−11.6896			−0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	9.09976	−	15.7612i	0.381482	−	0.660746i	−0.609793	−	0.792561i	$-0.708747\pi$
$569$	9.09976	−	15.7612i	0.381482	−	0.660746i	0.991274	+	0.131815i	$0.0420806\pi$
$570$		0			0
$571$	8.52275	+	14.7618i	0.356666	+	0.617763i	0.987402	−	0.158234i	$-0.0505801\pi$
$571$	8.52275	+	14.7618i	0.356666	+	0.617763i	−0.630736	+	0.775998i	$0.717247\pi$
$572$	−10.5307	−	18.2398i	−0.440313	−	0.762644i
$573$		0			0
$574$		0			0
$575$	16.1443			0.673264
$576$		0			0
$577$	−11.4095			−0.474982			−0.237491	−	0.971390i	$-0.576325\pi$
$577$	−11.4095			−0.474982			−0.237491	+	0.971390i	$0.576325\pi$
$578$	−5.27764	+	9.14113i	−0.219521	+	0.380221i
$579$		0			0
$580$	7.52485	+	13.0334i	0.312452	+	0.541183i
$581$		0			0
$582$		0			0
$583$	2.02275	−	3.50350i	0.0837736	−	0.145100i
$584$	25.4459			1.05296
$585$		0			0
$586$	−1.20666			−0.0498468
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	−0.809190	−	0.587548i	$-0.800094\pi$
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	0.913426	+	0.407005i	$0.133427\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$	−3.14449	−	5.44642i	−0.129457	−	0.224226i
$591$		0			0
$592$	1.06882	−	1.85126i	0.0439283	−	0.0760861i
$593$	19.9778			0.820391			0.410196	−	0.911998i	$-0.365460\pi$
$593$	19.9778			0.820391			0.410196	+	0.911998i	$0.365460\pi$
$594$		0			0
$595$		0			0
$596$	6.63365	−	11.4898i	0.271725	−	0.470641i
$597$		0			0
$598$	5.01935	+	8.69378i	0.205257	+	0.355515i
$599$	2.19660	+	3.80463i	0.0897508	+	0.155453i	0.907406	−	0.420256i	$-0.138060\pi$
$599$	2.19660	+	3.80463i	0.0897508	+	0.155453i	−0.817655	+	0.575709i	$0.804726\pi$
$600$		0			0
$601$	−12.1778	+	21.0926i	−0.496743	+	0.860385i	−0.999993	−	0.00375637i	$-0.998804\pi$
$601$	−12.1778	+	21.0926i	−0.496743	+	0.860385i	0.503250	+	0.864141i	$0.332138\pi$
$602$		0			0
$603$		0			0
$604$	27.3834			1.11421
$605$	−9.48476	+	16.4281i	−0.385610	+	0.667897i
$606$		0			0
$607$	6.56281	+	11.3671i	0.266376	+	0.461377i	0.967923	−	0.251246i	$-0.0808403\pi$
$607$	6.56281	+	11.3671i	0.266376	+	0.461377i	−0.701547	+	0.712623i	$0.747507\pi$
$608$	−11.5827	−	20.0618i	−0.469741	−	0.813615i
$609$		0			0
$610$	−0.0359456	+	0.0622597i	−0.00145540	+	0.00252082i
$611$	26.1021			1.05598
$612$		0			0
$613$	46.4806			1.87733			0.938667	−	0.344825i	$-0.112062\pi$
$613$	46.4806			1.87733			0.938667	+	0.344825i	$0.112062\pi$
$614$	−0.356877	+	0.618129i	−0.0144024	+	0.0249456i
$615$		0			0
$616$		0			0
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	−0.996416	−	0.0845873i	$-0.973043\pi$
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$618$		0			0
$619$	15.9606	−	27.6446i	0.641511	−	1.11113i	−0.343585	−	0.939122i	$-0.611641\pi$
$619$	15.9606	−	27.6446i	0.641511	−	1.11113i	0.985096	−	0.172008i	$-0.0550254\pi$
$620$	5.53686			0.222366
$621$		0			0
$622$	11.3482			0.455023
$623$		0			0
$624$		0			0
$625$	0.666993	+	1.15527i	0.0266797	+	0.0462106i
$626$	2.77469	+	4.80591i	0.110899	+	0.192083i
$627$		0			0
$628$	−4.90122	+	8.48916i	−0.195580	+	0.338754i
$629$	1.58947			0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	2.19556	−	3.80282i	0.0873346	−	0.151268i
$633$		0			0
$634$	−2.19447	−	3.80094i	−0.0871537	−	0.150955i
$635$	−5.17236	−	8.95878i	−0.205259	−	0.355519i
$636$		0			0
$637$		0			0
$638$	−22.5124			−0.891276
$639$		0			0
$640$	15.6252			0.617641
$641$	−20.2001	+	34.9875i	−0.797854	+	1.38192i	0.123157	+	0.992387i	$0.460698\pi$
$641$	−20.2001	+	34.9875i	−0.797854	+	1.38192i	−0.921011	+	0.389537i	$0.872635\pi$
$642$		0			0
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	0.715400	−	0.698715i	$-0.246244\pi$
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$644$		0			0
$645$		0			0
$646$	1.50676	−	2.60979i	0.0592827	−	0.102681i
$647$	−34.5548			−1.35849			−0.679245	−	0.733912i	$-0.737692\pi$
$647$	−34.5548			−1.35849			−0.679245	+	0.733912i	$0.737692\pi$
$648$		0			0
$649$	−32.4646			−1.27435
$650$	2.74164	−	4.74866i	0.107536	−	0.186258i
$651$		0			0
$652$	6.22019	+	10.7737i	0.243602	+	0.421930i
$653$	−11.1472	−	19.3075i	−0.436223	−	0.755560i	0.561172	−	0.827699i	$-0.310351\pi$
$653$	−11.1472	−	19.3075i	−0.436223	−	0.755560i	−0.997395	+	0.0721392i	$0.977017\pi$
$654$		0			0
$655$	14.5721	−	25.2396i	0.569379	−	0.986194i
$656$	−0.374605			−0.0146259
$657$		0			0
$658$		0			0
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	−0.927217	−	0.374526i	$-0.877806\pi$
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	0.787957	+	0.615730i	$0.211139\pi$
$660$		0			0
$661$	21.4530	+	37.1577i	0.834425	+	1.44527i	0.894498	+	0.447072i	$0.147533\pi$
$661$	21.4530	+	37.1577i	0.834425	+	1.44527i	−0.0600736	+	0.998194i	$0.519134\pi$
$662$	−8.95760	−	15.5150i	−0.348147	−	0.603008i
$663$		0			0
$664$	−17.2221	+	29.8296i	−0.668349	+	1.15761i
$665$		0			0
$666$		0			0
$667$	−37.0293			−1.43378
$668$	−1.64428	+	2.84798i	−0.0636191	+	0.110192i
$669$		0			0
$670$	−6.01177	−	10.4127i	−0.232255	−	0.402277i
$671$	0.185556	+	0.321392i	0.00716331	+	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$	−6.38376			−0.245893
$675$		0			0
$676$	8.39238			0.322784
$677$	13.1808	−	22.8298i	0.506580	−	0.877422i	−0.493391	−	0.869808i	$-0.664243\pi$
$677$	13.1808	−	22.8298i	0.506580	−	0.877422i	0.999971	−	0.00761453i	$-0.00242380\pi$
$678$		0			0
$679$		0			0
$680$	1.89871	+	3.28866i	0.0728121	+	0.126114i
$681$		0			0
$682$	−4.14122	+	7.17280i	−0.158575	+	0.274661i
$683$	3.93175			0.150444			0.0752222	−	0.997167i	$-0.476033\pi$
$683$	3.93175			0.150444			0.0752222	+	0.997167i	$0.476033\pi$
$684$		0			0
$685$	−17.4008			−0.664850
$686$		0			0
$687$		0			0
$688$	−0.750378	−	1.29969i	−0.0286079	−	0.0495503i
$689$	−1.13002	−	1.95725i	−0.0430503	−	0.0745653i
$690$		0			0
$691$	9.95052	−	17.2348i	0.378536	−	0.655643i	−0.612314	−	0.790615i	$-0.709761\pi$
$691$	9.95052	−	17.2348i	0.378536	−	0.655643i	0.990849	+	0.134972i	$0.0430944\pi$
$692$	28.3585			1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	1.76823	−	3.06266i	0.0670727	−	0.116173i
$696$		0			0
$697$	−0.139270	−	0.241223i	−0.00527524	−	0.00913699i
$698$	−10.0913	−	17.4787i	−0.381963	−	0.661579i
$699$		0			0
$700$		0			0
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	5.69965			0.214966
$704$	−2.11016	+	3.65490i	−0.0795295	+	0.137749i
$705$		0			0
$706$	2.09792	+	3.63370i	0.0789561	+	0.136756i
$707$		0			0
$708$		0			0
$709$	−22.3172	+	38.6545i	−0.838139	+	1.45170i	0.0533097	+	0.998578i	$0.483023\pi$
$709$	−22.3172	+	38.6545i	−0.838139	+	1.45170i	−0.891449	+	0.453121i	$0.850310\pi$
$710$	0.0768875			0.00288554
$711$		0			0
$712$	−32.1931			−1.20649
$713$	−6.81163	+	11.7981i	−0.255097	+	0.441842i
$714$		0			0
$715$	9.67699	+	16.7610i	0.361899	+	0.626827i
$716$	5.91227	+	10.2403i	0.220952	+	0.382700i
$717$		0			0
$718$	−3.41705	+	5.91851i	−0.127523	+	0.220877i
$719$	39.0192			1.45517			0.727586	−	0.686016i	$-0.240642\pi$
$719$	39.0192			1.45517			0.727586	+	0.686016i	$0.240642\pi$
$720$		0			0
$721$		0			0
$722$	−0.965081	+	1.67157i	−0.0359166	+	0.0622094i
$723$		0			0
$724$	−12.0413	−	20.8561i	−0.447510	−	0.775109i
$725$	10.1130	+	17.5162i	0.375586	+	0.650534i
$726$		0			0
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	−0.578242	−	0.815865i	$-0.696261\pi$
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	0.995681	+	0.0928402i	$0.0295946\pi$
$728$		0			0
$729$		0			0
$730$	−10.2119			−0.377958
$731$	0.557951	−	0.966399i	0.0206366	−	0.0357436i
$732$		0			0
$733$	−0.448519	−	0.776858i	−0.0165664	−	0.0286939i	0.857623	−	0.514278i	$-0.171940\pi$
$733$	−0.448519	−	0.776858i	−0.0165664	−	0.0286939i	−0.874190	+	0.485584i	$0.838607\pi$
$734$	9.60441	+	16.6353i	0.354505	+	0.614021i
$735$		0			0
$736$	−15.6837	+	27.1649i	−0.578108	+	1.00131i
$737$	−62.0671			−2.28627
$738$		0			0
$739$	−3.58063			−0.131716			−0.0658578	−	0.997829i	$-0.520978\pi$
$739$	−3.58063			−0.131716			−0.0658578	+	0.997829i	$0.520978\pi$
$740$	−1.56833	+	2.71643i	−0.0576531	+	0.0998581i
$741$		0			0
$742$		0			0
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.814493	+	0.580173i	$0.197015\pi$
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.0951977	+	0.995458i	$0.469652\pi$
$744$		0			0
$745$	−6.09583	+	10.5583i	−0.223334	+	0.386826i
$746$	10.7745			0.394483
$747$		0			0
$748$	8.56098			0.313020
$749$		0			0
$750$		0			0
$751$	21.4515	+	37.1551i	0.782776	+	1.35581i	0.930319	+	0.366752i	$0.119530\pi$
$751$	21.4515	+	37.1551i	0.782776	+	1.35581i	−0.147543	+	0.989056i	$0.547136\pi$
$752$	7.13450	+	12.3573i	0.260168	+	0.450625i
$753$		0			0
$754$	−6.28835	+	10.8917i	−0.229008	+	0.396654i
$755$	−25.1633			−0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	−0.341510	+	0.591513i	−0.0124042	+	0.0214847i
$759$		0			0
$760$	6.80856	+	11.7928i	0.246972	+	0.427769i
$761$	−20.3599	−	35.2643i	−0.738044	−	1.27833i	−0.953375	−	0.301789i	$-0.902416\pi$
$761$	−20.3599	−	35.2643i	−0.738044	−	1.27833i	0.215330	−	0.976541i	$-0.430917\pi$
$762$		0			0
$763$		0			0
$764$	23.0001			0.832113
$765$		0			0
$766$	7.76683			0.280627
$767$	−9.06826	+	15.7067i	−0.327436	+	0.567135i
$768$		0			0
$769$	−5.57381	−	9.65413i	−0.200997	−	0.348137i	0.747853	−	0.663864i	$-0.231085\pi$
$769$	−5.57381	−	9.65413i	−0.200997	−	0.348137i	−0.948850	+	0.315728i	$0.897751\pi$
$770$		0			0
$771$		0			0
$772$	12.8454	−	22.2489i	0.462317	−	0.800756i
$773$	0.925662			0.0332937			0.0166469	−	0.999861i	$-0.494701\pi$
$773$	0.925662			0.0332937			0.0166469	+	0.999861i	$0.494701\pi$
$774$		0			0
$775$	7.44121			0.267296
$776$	−6.43012	+	11.1373i	−0.230828	+	0.399806i
$777$		0			0
$778$	−5.97049	−	10.3412i	−0.214052	−	0.370750i
$779$	−0.499408	−	0.865001i	−0.0178932	−	0.0309919i
$780$		0			0
$781$	0.198452	−	0.343728i	0.00710116	−	0.0122996i
$782$	−4.08049			−0.145918
$783$		0			0
$784$		0			0
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	11.5120	+	19.9393i	0.410358	+	0.710761i	0.994929	−	0.100582i	$-0.0320704\pi$
$787$	11.5120	+	19.9393i	0.410358	+	0.710761i	−0.584571	+	0.811343i	$0.698737\pi$
$788$	3.13030	+	5.42184i	0.111512	+	0.193145i
$789$		0			0
$790$	−0.881115	+	1.52614i	−0.0313487	+	0.0542975i
$791$		0			0
$792$		0			0
$793$	0.207324			0.00736228
$794$	−4.38551	+	7.59592i	−0.155636	+	0.269569i
$795$		0			0
$796$	−19.6014	−	33.9505i	−0.694752	−	1.20335i
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	0.994151	−	0.108000i	$-0.0344447\pi$
$797$	11.3925	+	19.7325i	0.403544	+	0.698960i	−0.590606	+	0.806960i	$0.701111\pi$
$798$		0			0
$799$	−5.30492	+	9.18839i	−0.187675	+	0.325062i
$800$	17.1333			0.605753
$801$		0			0
$802$	9.45390			0.333829
$803$	−26.3575	+	45.6525i	−0.930135	+	1.61104i
$804$		0			0
$805$		0			0
$806$	2.31352	+	4.00713i	0.0814901	+	0.141145i
$807$		0			0
$808$	6.11143	−	10.5853i	0.214999	−	0.372390i
$809$	13.4751			0.473758			0.236879	−	0.971539i	$-0.423876\pi$
$809$	13.4751			0.473758			0.236879	+	0.971539i	$0.423876\pi$
$810$		0			0
$811$	30.7348			1.07924			0.539622	−	0.841907i	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$		0			0
$814$	−2.34603	−	4.06344i	−0.0822283	−	0.142424i
$815$	−5.71590	−	9.90023i	−0.200219	−	0.346790i
$816$		0			0
$817$	2.00075	−	3.46540i	0.0699974	−	0.121239i
$818$	−1.77369			−0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	−8.49319	+	14.7106i	−0.296414	+	0.513405i	−0.975313	−	0.220827i	$-0.929124\pi$
$821$	−8.49319	+	14.7106i	−0.296414	+	0.513405i	0.678899	+	0.734232i	$0.262458\pi$
$822$		0			0
$823$	9.29157	+	16.0935i	0.323884	+	0.560983i	0.981286	−	0.192557i	$-0.0616780\pi$
$823$	9.29157	+	16.0935i	0.323884	+	0.560983i	−0.657402	+	0.753540i	$0.728345\pi$
$824$	−16.9122	−	29.2928i	−0.589164	−	1.02046i
$825$		0			0
$826$		0			0
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	9.57433			0.332530			0.166265	−	0.986081i	$-0.446829\pi$
$829$	9.57433			0.332530			0.166265	+	0.986081i	$0.446829\pi$
$830$	6.91154	−	11.9711i	0.239903	−	0.415524i
$831$		0			0
$832$	1.17885	+	2.04183i	0.0408693	+	0.0707877i
$833$		0			0
$834$		0			0
$835$	1.51097	−	2.61708i	0.0522894	−	0.0905678i
$836$	30.6987			1.06174
$837$		0			0
$838$	22.4651			0.776045
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	−0.222664	−	0.974895i	$-0.571475\pi$
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	0.955616	−	0.294615i	$-0.0951913\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$	1.62187	+	2.80917i	0.0558934	+	0.0968103i
$843$		0			0
$844$	5.83428	−	10.1053i	0.200824	−	0.347838i
$845$	−7.71198			−0.265300
$846$		0			0
$847$		0			0
$848$	0.617738	−	1.06995i	0.0212132	−	0.0367423i
$849$		0			0
$850$	1.11441	+	1.93021i	0.0382239	+	0.0662058i
$851$	−3.85883	−	6.68370i	−0.132279	−	0.229114i
$852$		0			0
$853$	−7.14039	+	12.3675i	−0.244482	+	0.423456i	−0.961986	−	0.273099i	$-0.911951\pi$
$853$	−7.14039	+	12.3675i	−0.244482	+	0.423456i	0.717504	+	0.696555i	$0.245285\pi$
$854$		0			0
$855$		0			0
$856$	18.2324			0.623171
$857$	−17.3895	+	30.1195i	−0.594013	+	1.02886i	0.399672	+	0.916658i	$0.369124\pi$
$857$	−17.3895	+	30.1195i	−0.594013	+	1.02886i	−0.993685	+	0.112203i	$0.964209\pi$
$858$		0			0
$859$	−6.32429	−	10.9540i	−0.215782	−	0.373745i	0.737732	−	0.675093i	$-0.235897\pi$
$859$	−6.32429	−	10.9540i	−0.215782	−	0.373745i	−0.953514	+	0.301348i	$0.902563\pi$
$860$	1.10107	+	1.90710i	0.0375460	+	0.0650316i
$861$		0			0
$862$	11.8409	−	20.5091i	0.403304	−	0.698543i
$863$	26.4797			0.901379			0.450690	−	0.892681i	$-0.351178\pi$
$863$	26.4797			0.901379			0.450690	+	0.892681i	$0.351178\pi$
$864$		0			0
$865$	−26.0594			−0.886045
$866$	−1.83471	+	3.17782i	−0.0623461	+	0.107987i
$867$		0			0
$868$		0			0
$869$	4.54843	+	7.87811i	0.154295	+	0.267247i
$870$		0			0
$871$	−17.3371	+	30.0287i	−0.587444	+	1.01748i
$872$	4.04332			0.136924
$873$		0			0
$874$	−14.6322			−0.494941
$875$		0			0
$876$		0			0
$877$	−14.2267	−	24.6414i	−0.480402	−	0.832081i	0.519345	−	0.854565i	$-0.326176\pi$
$877$	−14.2267	−	24.6414i	−0.480402	−	0.832081i	−0.999747	+	0.0224835i	$0.992843\pi$
$878$	−2.14443	−	3.71427i	−0.0723711	−	0.125350i
$879$		0			0
$880$	−5.29004	+	9.16261i	−0.178327	+	0.308872i
$881$	−20.3637			−0.686071			−0.343036	−	0.939322i	$-0.611455\pi$
$881$	−20.3637			−0.686071			−0.343036	+	0.939322i	$0.611455\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	2.39132	−	4.14189i	0.0804288	−	0.139307i
$885$		0			0
$886$	2.14065	+	3.70771i	0.0719164	+	0.124563i
$887$	2.10846	+	3.65196i	0.0707952	+	0.122621i	0.899250	−	0.437435i	$-0.144113\pi$
$887$	2.10846	+	3.65196i	0.0707952	+	0.122621i	−0.828455	+	0.560056i	$0.810780\pi$
$888$		0			0
$889$		0			0
$890$	12.9196			0.433067
$891$		0			0
$892$	−20.1346			−0.674157
$893$	−19.0229	+	32.9486i	−0.636576	+	1.10258i
$894$		0			0
$895$	−5.43294	−	9.41013i	−0.181603	−	0.314546i
$896$		0			0
$897$		0			0
$898$	3.93685	−	6.81883i	0.131375	−	0.227547i
$899$	−17.0675			−0.569233
$900$		0			0
$901$	0.918649			0.0306046
$902$	−0.411122	+	0.712084i	−0.0136889	+	0.0237098i
$903$		0			0
$904$	0.714872	+	1.23819i	0.0237763	+	0.0411817i
$905$	11.0650	+	19.1652i	0.367814	+	0.637072i
$906$		0			0
$907$	−23.9925	+	41.5563i	−0.796659	+	1.37985i	0.125121	+	0.992142i	$0.460068\pi$
$907$	−23.9925	+	41.5563i	−0.796659	+	1.37985i	−0.921780	+	0.387713i	$0.873265\pi$
$908$	44.9170			1.49062
$909$		0			0
$910$		0			0
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	−0.570247	−	0.821474i	$-0.693152\pi$
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	0.996540	+	0.0831113i	$0.0264857\pi$
$912$		0			0
$913$	−35.6782	−	61.7965i	−1.18078	−	2.04517i
$914$	3.52675	+	6.10852i	0.116655	+	0.202052i
$915$		0			0
$916$	−11.9678	+	20.7288i	−0.395427	+	0.684900i
$917$		0			0
$918$		0			0
$919$	−2.26957			−0.0748661			−0.0374330	−	0.999299i	$-0.511918\pi$
$919$	−2.26957			−0.0748661			−0.0374330	+	0.999299i	$0.511918\pi$
$920$	9.21919	−	15.9681i	0.303948	−	0.526453i
$921$		0			0
$922$	2.37484	+	4.11334i	0.0782111	+	0.135466i
$923$	−0.110866	−	0.192026i	−0.00364920	−	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$	21.9548			0.721479
$927$		0			0
$928$	−39.2976			−1.29001
$929$	−22.9248	+	39.7069i	−0.752138	+	1.30274i	0.194647	+	0.980873i	$0.437644\pi$
$929$	−22.9248	+	39.7069i	−0.752138	+	1.30274i	−0.946785	+	0.321868i	$0.895689\pi$
$930$		0			0
$931$		0			0
$932$	−3.83514	−	6.64266i	−0.125624	−	0.217587i
$933$		0			0
$934$	−1.31530	+	2.27816i	−0.0430379	+	0.0745438i
$935$	−7.86691			−0.257275
$936$		0			0
$937$	56.2075			1.83622			0.918110	−	0.396325i	$-0.129715\pi$
$937$	56.2075			1.83622			0.918110	+	0.396325i	$0.129715\pi$
$938$		0			0
$939$		0			0
$940$	−10.4688	−	18.1325i	−0.341454	−	0.591416i
$941$	17.6402	+	30.5536i	0.575053	+	0.996020i	0.996036	+	0.0889519i	$0.0283517\pi$
$941$	17.6402	+	30.5536i	0.575053	+	0.996020i	−0.420983	+	0.907068i	$0.638315\pi$
$942$		0			0
$943$	−0.676229	+	1.17126i	−0.0220210	+	0.0381415i
$944$	−9.91453			−0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	−25.3565	+	43.9188i	−0.823976	+	1.42717i	0.0787236	+	0.996896i	$0.474916\pi$
$947$	−25.3565	+	43.9188i	−0.823976	+	1.42717i	−0.902699	+	0.430272i	$0.858418\pi$
$948$		0			0
$949$	14.7248	+	25.5040i	0.477986	+	0.827896i
$950$	3.99615	+	6.92154i	0.129652	+	0.224564i
$951$		0			0
$952$		0			0
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	−21.1354			−0.683924
$956$	10.1061	−	17.5043i	0.326855	−	0.566130i
$957$		0			0
$958$	5.39165	+	9.33861i	0.174196	+	0.301717i
$959$		0			0
$960$		0			0
$961$	12.3604	−	21.4088i	0.398722	−	0.690607i
$962$	−2.62125			−0.0845123
$963$		0			0
$964$	22.6124			0.728295
$965$	−11.8040	+	20.4451i	−0.379984	+	0.658152i
$966$		0			0
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	0.578239	−	0.815867i	$-0.303740\pi$
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	−0.995681	+	0.0928360i	$0.970407\pi$
$968$	−15.8427	−	27.4404i	−0.509204	−	0.881967i
$969$		0			0
$970$	2.58052	−	4.46959i	0.0828554	−	0.143510i
$971$	7.94412			0.254939			0.127469	−	0.991843i	$-0.459315\pi$
$971$	7.94412			0.254939			0.127469	+	0.991843i	$0.459315\pi$
$972$		0			0
$973$		0			0
$974$	1.17424	−	2.03384i	0.0376249	−	0.0651683i
$975$		0			0
$976$	0.0566680	+	0.0981518i	0.00181390	+	0.00314176i
$977$	−26.1274	−	45.2540i	−0.835889	−	1.44780i	−0.893304	−	0.449452i	$-0.851619\pi$
$977$	−26.1274	−	45.2540i	−0.835889	−	1.44780i	0.0574149	−	0.998350i	$-0.481714\pi$
$978$		0			0
$979$	33.3464	−	57.7577i	1.06576	−	1.84594i
$980$		0			0
$981$		0			0
$982$	27.5569			0.879376
$983$	19.4190	−	33.6346i	0.619369	−	1.07278i	−0.370232	−	0.928939i	$-0.620722\pi$
$983$	19.4190	−	33.6346i	0.619369	−	1.07278i	0.989601	−	0.143839i	$-0.0459448\pi$
$984$		0			0
$985$	−2.87652	−	4.98228i	−0.0916535	−	0.158749i
$986$	−2.55606	−	4.42722i	−0.0814015	−	0.140991i
$987$		0			0
$988$	8.57501	−	14.8524i	0.272807	−	0.472516i
$989$	−5.41827			−0.172291
$990$		0			0
$991$	30.9378			0.982771			0.491385	−	0.870942i	$-0.336491\pi$
$991$	30.9378			0.982771			0.491385	+	0.870942i	$0.336491\pi$
$992$	−7.22890	+	12.5208i	−0.229518	+	0.397536i
$993$		0			0
$994$		0			0
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	23.5335	−	40.7612i	0.745313	−	1.29092i	−0.204735	−	0.978817i	$-0.565633\pi$
$997$	23.5335	−	40.7612i	0.745313	−	1.29092i	0.950048	−	0.312103i	$-0.101033\pi$
$998$	−7.92985			−0.251015
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.f.883.4		10
3.2	odd	2		441.2.f.f.295.2		10
7.2	even	3		1323.2.h.f.802.2		10
7.3	odd	6		189.2.g.b.100.4		10
7.4	even	3		1323.2.g.f.667.4		10
7.5	odd	6		189.2.h.b.46.2		10
7.6	odd	2		1323.2.f.e.883.4		10
9.2	odd	6		3969.2.a.ba.1.4		5
9.4	even	3	inner	1323.2.f.f.442.4		10
9.5	odd	6		441.2.f.f.148.2		10
9.7	even	3		3969.2.a.bb.1.2		5
21.2	odd	6		441.2.h.f.214.4		10
21.5	even	6		63.2.h.b.25.4	yes	10
21.11	odd	6		441.2.g.f.79.2		10
21.17	even	6		63.2.g.b.16.2	yes	10
21.20	even	2		441.2.f.e.295.2		10
28.3	even	6		3024.2.t.i.289.1		10
28.19	even	6		3024.2.q.i.2881.5		10
63.4	even	3		1323.2.h.f.226.2		10
63.5	even	6		63.2.g.b.4.2	✓	10
63.13	odd	6		1323.2.f.e.442.4		10
63.20	even	6		3969.2.a.z.1.4		5
63.23	odd	6		441.2.g.f.67.2		10
63.31	odd	6		189.2.h.b.37.2		10
63.32	odd	6		441.2.h.f.373.4		10
63.34	odd	6		3969.2.a.bc.1.2		5
63.38	even	6		567.2.e.f.163.2		10
63.40	odd	6		189.2.g.b.172.4		10
63.41	even	6		441.2.f.e.148.2		10
63.47	even	6		567.2.e.f.487.2		10
63.52	odd	6		567.2.e.e.163.4		10
63.58	even	3		1323.2.g.f.361.4		10
63.59	even	6		63.2.h.b.58.4	yes	10
63.61	odd	6		567.2.e.e.487.4		10
84.47	odd	6		1008.2.q.i.529.1		10
84.59	odd	6		1008.2.t.i.961.4		10
252.31	even	6		3024.2.q.i.2305.5		10
252.59	odd	6		1008.2.q.i.625.1		10
252.103	even	6		3024.2.t.i.1873.1		10
252.131	odd	6		1008.2.t.i.193.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	63.5	even	6
63.2.g.b.16.2	yes	10	21.17	even	6
63.2.h.b.25.4	yes	10	21.5	even	6
63.2.h.b.58.4	yes	10	63.59	even	6
189.2.g.b.100.4		10	7.3	odd	6
189.2.g.b.172.4		10	63.40	odd	6
189.2.h.b.37.2		10	63.31	odd	6
189.2.h.b.46.2		10	7.5	odd	6
441.2.f.e.148.2		10	63.41	even	6
441.2.f.e.295.2		10	21.20	even	2
441.2.f.f.148.2		10	9.5	odd	6
441.2.f.f.295.2		10	3.2	odd	2
441.2.g.f.67.2		10	63.23	odd	6
441.2.g.f.79.2		10	21.11	odd	6
441.2.h.f.214.4		10	21.2	odd	6
441.2.h.f.373.4		10	63.32	odd	6
567.2.e.e.163.4		10	63.52	odd	6
567.2.e.e.487.4		10	63.61	odd	6
567.2.e.f.163.2		10	63.38	even	6
567.2.e.f.487.2		10	63.47	even	6
1008.2.q.i.529.1		10	84.47	odd	6
1008.2.q.i.625.1		10	252.59	odd	6
1008.2.t.i.193.4		10	252.131	odd	6
1008.2.t.i.961.4		10	84.59	odd	6
1323.2.f.e.442.4		10	63.13	odd	6
1323.2.f.e.883.4		10	7.6	odd	2
1323.2.f.f.442.4		10	9.4	even	3	inner
1323.2.f.f.883.4		10	1.1	even	1	trivial
1323.2.g.f.361.4		10	63.58	even	3
1323.2.g.f.667.4		10	7.4	even	3
1323.2.h.f.226.2		10	63.4	even	3
1323.2.h.f.802.2		10	7.2	even	3
3024.2.q.i.2305.5		10	252.31	even	6
3024.2.q.i.2881.5		10	28.19	even	6
3024.2.t.i.289.1		10	28.3	even	6
3024.2.t.i.1873.1		10	252.103	even	6
3969.2.a.z.1.4		5	63.20	even	6
3969.2.a.ba.1.4		5	9.2	odd	6
3969.2.a.bb.1.2		5	9.7	even	3
3969.2.a.bc.1.2		5	63.34	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 - 1.23403i) q^{5} +2.38012 q^{8} +O(q^{10})\)	\(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +(-0.712469 - 1.23403i) q^{5} +2.38012 q^{8} -0.955182 q^{10} +(-2.46539 + 4.27018i) q^{11} +(1.37730 + 2.38556i) q^{13} +(-0.752918 + 1.30409i) q^{16} -1.11968 q^{17} -4.01505 q^{19} +(1.10479 - 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 + 4.70824i) q^{23} +(1.48478 - 2.57171i) q^{25} +1.84650 q^{26} +(-3.40555 + 5.89858i) q^{29} +(1.25292 + 2.17012i) q^{31} +(2.88483 + 4.99666i) q^{32} +(-0.375279 + 0.650002i) q^{34} -1.41957 q^{37} +(-1.34571 + 2.33083i) q^{38} +(-1.69576 - 2.93714i) q^{40} +(0.124384 + 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} -7.64592 q^{44} +3.64434 q^{46} +(4.73790 - 8.20628i) q^{47} +(-0.995294 - 1.72390i) q^{50} +(-2.13572 + 3.69917i) q^{52} -0.820458 q^{53} +7.02604 q^{55} +(2.28285 + 3.95401i) q^{58} +(3.29204 + 5.70197i) q^{59} +(0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +0.855913 q^{64} +(1.96257 - 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +(-0.868117 - 1.50362i) q^{68} -0.0804951 q^{71} +10.6910 q^{73} +(-0.475793 + 0.824098i) q^{74} +(-3.11297 - 5.39183i) q^{76} +(0.922457 - 1.59774i) q^{79} +2.14572 q^{80} +0.166758 q^{82} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 + 0.578567i) q^{86} +(-5.86792 + 10.1635i) q^{88} -13.5258 q^{89} +(-4.21515 + 7.30085i) q^{92} +(-3.17597 - 5.50094i) q^{94} +(2.86059 + 4.95469i) q^{95} +(-2.70160 + 4.67930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} + 4 q^{5} + 6 q^{8} - 14 q^{10} - 4 q^{11} + 8 q^{13} + 2 q^{16} - 24 q^{17} + 2 q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 22 q^{26} - 7 q^{29} + 3 q^{31} + 2 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} + 27 q^{47} - 19 q^{50} + 10 q^{52} - 42 q^{53} - 4 q^{55} - 10 q^{58} + 30 q^{59} + 14 q^{61} - 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 27 q^{68} + 6 q^{71} + 30 q^{73} + 36 q^{74} - 5 q^{76} - 4 q^{79} - 40 q^{80} - 10 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 56 q^{89} - 27 q^{92} + 3 q^{94} + 14 q^{95} + 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 + 6 * q^8 - 14 * q^10 - 4 * q^11 + 8 * q^13 + 2 * q^16 - 24 * q^17 + 2 * q^19 + 5 * q^20 - q^22 - 3 * q^23 - q^25 - 22 * q^26 - 7 * q^29 + 3 * q^31 + 2 * q^32 - 3 * q^34 + 20 * q^38 + 3 * q^40 + 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 + 27 * q^47 - 19 * q^50 + 10 * q^52 - 42 * q^53 - 4 * q^55 - 10 * q^58 + 30 * q^59 + 14 * q^61 - 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 27 * q^68 + 6 * q^71 + 30 * q^73 + 36 * q^74 - 5 * q^76 - 4 * q^79 - 40 * q^80 - 10 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 56 * q^89 - 27 * q^92 + 3 * q^94 + 14 * q^95 + 12 * q^97

Introduction

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