LMFDB - Embedded newform 1323.2.h.d.802.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.d.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.239123 q^{2} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +O(q^{10})$	\(q+0.239123 q^{2} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +(0.141315 - 0.244765i) q^{10} +(-1.85185 - 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +3.66019 q^{16} +(-3.47141 + 6.01266i) q^{17} +(-0.971410 - 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(-2.80150 + 4.85235i) q^{23} +(1.80150 + 3.12030i) q^{25} +(-0.119562 - 0.207087i) q^{26} +(0.119562 - 0.207087i) q^{29} +1.66019 q^{31} +2.76088 q^{32} +(-0.830095 + 1.43777i) q^{34} +(4.77292 + 8.26693i) q^{37} +(-0.232287 - 0.402332i) q^{38} +(-0.557180 + 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(3.59781 + 6.23159i) q^{44} +(-0.669905 + 1.16031i) q^{46} -5.82846 q^{47} +(0.430782 + 0.746136i) q^{50} +(0.971410 + 1.68253i) q^{52} +(-5.80150 + 10.0485i) q^{53} -4.37756 q^{55} +(0.0285900 - 0.0495193i) q^{58} -2.60301 q^{59} -7.60301 q^{61} +0.396990 q^{62} -6.66019 q^{64} -1.18194 q^{65} +3.50808 q^{67} +(6.74433 - 11.6815i) q^{68} -8.60301 q^{71} +(-7.57442 + 13.1193i) q^{73} +(1.14132 + 1.97682i) q^{74} +(1.88727 + 3.26886i) q^{76} +7.37756 q^{79} +(2.16307 - 3.74654i) q^{80} +(-1.21737 - 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(-0.266078 + 0.460861i) q^{86} +(1.74596 + 3.02409i) q^{88} +(1.37360 + 2.37915i) q^{89} +(5.44282 - 9.42724i) q^{92} -1.39372 q^{94} -2.29630 q^{95} +(-3.58414 + 6.20790i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8	$ 6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8} - 2 q^{11} - 3 q^{13} + 6 q^{16} - 12 q^{17} + 3 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} - q^{26} + q^{29} - 6 q^{31} + 16 q^{32} + 3 q^{34} + 3 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} + 18 q^{47} + 10 q^{50} - 3 q^{52} - 18 q^{53} - 12 q^{55} + 9 q^{58} + 18 q^{59} - 12 q^{61} + 36 q^{62} - 24 q^{64} + 10 q^{65} + 6 q^{68} - 18 q^{71} - 3 q^{73} + 6 q^{74} + 21 q^{76} + 30 q^{79} + 11 q^{80} - 9 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} - 2 q^{89} + 15 q^{92} + 48 q^{94} - 32 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8 - 2 * q^11 - 3 * q^13 + 6 * q^16 - 12 * q^17 + 3 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 - q^26 + q^29 - 6 * q^31 + 16 * q^32 + 3 * q^34 + 3 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 + 18 * q^47 + 10 * q^50 - 3 * q^52 - 18 * q^53 - 12 * q^55 + 9 * q^58 + 18 * q^59 - 12 * q^61 + 36 * q^62 - 24 * q^64 + 10 * q^65 + 6 * q^68 - 18 * q^71 - 3 * q^73 + 6 * q^74 + 21 * q^76 + 30 * q^79 + 11 * q^80 - 9 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 - 2 * q^89 + 15 * q^92 + 48 * q^94 - 32 * q^95 - 3 * 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 $

$2$	0.239123			0.169086			0.0845428	−	0.996420i	$-0.473057\pi$
$2$	0.239123			0.169086			0.0845428	+	0.996420i	$0.473057\pi$
$3$		0			0
$3$		0			0
$4$	−1.94282			−0.971410
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	−0.703087	−	0.711104i	$-0.748196\pi$
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	0.967378	+	0.253339i	$0.0815289\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.942820			−0.333337
$9$		0			0
$10$	0.141315	−	0.244765i	0.0446878	−	0.0774015i
$11$	−1.85185	−	3.20750i	−0.558353	−	0.967096i	−0.997634	−	0.0687465i	$-0.978100\pi$
$11$	−1.85185	−	3.20750i	−0.558353	−	0.967096i	0.439281	−	0.898350i	$-0.355233\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$	3.66019			0.915047
$17$	−3.47141	+	6.01266i	−0.841941	+	1.45828i	0.0463112	+	0.998927i	$0.485253\pi$
$17$	−3.47141	+	6.01266i	−0.841941	+	1.45828i	−0.888252	+	0.459357i	$0.848080\pi$
$18$		0			0
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	0.732818	−	0.680425i	$-0.238205\pi$
$19$	−0.971410	−	1.68253i	−0.222857	−	0.385999i	−0.955674	+	0.294426i	$0.904872\pi$
$20$	−1.14815	+	1.98866i	−0.256735	+	0.444677i
$21$		0			0
$22$	−0.442820	−	0.766987i	−0.0944096	−	0.163522i
$23$	−2.80150	+	4.85235i	−0.584154	+	1.01178i	0.410826	+	0.911714i	$0.365240\pi$
$23$	−2.80150	+	4.85235i	−0.584154	+	1.01178i	−0.994980	+	0.100071i	$0.968093\pi$
$24$		0			0
$25$	1.80150	+	3.12030i	0.360301	+	0.624060i
$26$	−0.119562	−	0.207087i	−0.0234480	−	0.0406131i
$27$		0			0
$28$		0			0
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	−0.854711	−	0.519104i	$-0.826266\pi$
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	0.876913	+	0.480649i	$0.159599\pi$
$30$		0			0
$31$	1.66019			0.298179			0.149089	−	0.988824i	$-0.452366\pi$
$31$	1.66019			0.298179			0.149089	+	0.988824i	$0.452366\pi$
$32$	2.76088			0.488059
$33$		0			0
$34$	−0.830095	+	1.43777i	−0.142360	+	0.246575i
$35$		0			0
$36$		0			0
$37$	4.77292	+	8.26693i	0.784662	+	1.35908i	0.929201	+	0.369576i	$0.120497\pi$
$37$	4.77292	+	8.26693i	0.784662	+	1.35908i	−0.144538	+	0.989499i	$0.546170\pi$
$38$	−0.232287	−	0.402332i	−0.0376819	−	0.0652669i
$39$		0			0
$40$	−0.557180	+	0.965064i	−0.0880979	+	0.152590i
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	−0.922791	−	0.385301i	$-0.874097\pi$
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	0.127715	−	0.991811i	$-0.459236\pi$
$42$		0			0
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	−0.938311	−	0.345794i	$-0.887610\pi$
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	0.768622	+	0.639704i	$0.220943\pi$
$44$	3.59781	+	6.23159i	0.542390	+	0.939447i
$45$		0			0
$46$	−0.669905	+	1.16031i	−0.0987721	+	0.171078i
$47$	−5.82846			−0.850168			−0.425084	−	0.905154i	$-0.639755\pi$
$47$	−5.82846			−0.850168			−0.425084	+	0.905154i	$0.639755\pi$
$48$		0			0
$49$		0			0
$50$	0.430782	+	0.746136i	0.0609217	+	0.105520i
$51$		0			0
$52$	0.971410	+	1.68253i	0.134710	+	0.233325i
$53$	−5.80150	+	10.0485i	−0.796898	+	1.38027i	0.124729	+	0.992191i	$0.460194\pi$
$53$	−5.80150	+	10.0485i	−0.796898	+	1.38027i	−0.921627	+	0.388077i	$0.873139\pi$
$54$		0			0
$55$	−4.37756			−0.590270
$56$		0			0
$57$		0			0
$58$	0.0285900	−	0.0495193i	0.00375405	−	0.00650220i
$59$	−2.60301			−0.338883			−0.169442	−	0.985540i	$-0.554196\pi$
$59$	−2.60301			−0.338883			−0.169442	+	0.985540i	$0.554196\pi$
$60$		0			0
$61$	−7.60301			−0.973466			−0.486733	−	0.873551i	$-0.661811\pi$
$61$	−7.60301			−0.973466			−0.486733	+	0.873551i	$0.661811\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−1.18194			−0.146602
$66$		0			0
$67$	3.50808			0.428580			0.214290	−	0.976770i	$-0.431256\pi$
$67$	3.50808			0.428580			0.214290	+	0.976770i	$0.431256\pi$
$68$	6.74433	−	11.6815i	0.817870	−	1.41659i
$69$		0			0
$70$		0			0
$71$	−8.60301			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$71$	−8.60301			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$72$		0			0
$73$	−7.57442	+	13.1193i	−0.886519	+	1.53550i	−0.0425559	+	0.999094i	$0.513550\pi$
$73$	−7.57442	+	13.1193i	−0.886519	+	1.53550i	−0.843963	+	0.536402i	$0.819783\pi$
$74$	1.14132	+	1.97682i	0.132675	+	0.229800i
$75$		0			0
$76$	1.88727	+	3.26886i	0.216485	+	0.374963i
$77$		0			0
$78$		0			0
$79$	7.37756			0.830040			0.415020	−	0.909812i	$-0.363775\pi$
$79$	7.37756			0.830040			0.415020	+	0.909812i	$0.363775\pi$
$80$	2.16307	−	3.74654i	0.241838	−	0.418876i
$81$		0			0
$82$	−1.21737	−	2.10855i	−0.134436	−	0.232850i
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	−0.991211	−	0.132292i	$-0.957766\pi$
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	0.610174	+	0.792267i	$0.291100\pi$
$84$		0			0
$85$	4.10301	+	7.10662i	0.445034	+	0.770821i
$86$	−0.266078	+	0.460861i	−0.0286920	+	0.0496960i
$87$		0			0
$88$	1.74596	+	3.02409i	0.186120	+	0.322369i
$89$	1.37360	+	2.37915i	0.145602	+	0.252189i	0.929597	−	0.368577i	$-0.120155\pi$
$89$	1.37360	+	2.37915i	0.145602	+	0.252189i	−0.783996	+	0.620766i	$0.786822\pi$
$90$		0			0
$91$		0			0
$92$	5.44282	−	9.42724i	0.567453	−	0.982858i
$93$		0			0
$94$	−1.39372			−0.143751
$95$	−2.29630			−0.235596
$96$		0			0
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	−0.988601	−	0.150558i	$-0.951893\pi$
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	0.624687	+	0.780875i	$0.285226\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	−0.986286	−	0.165044i	$-0.947223\pi$
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	0.350211	−	0.936671i	$-0.386110\pi$
$102$		0			0
$103$	2.19850	−	3.80791i	0.216624	−	0.375204i	−0.737150	−	0.675730i	$-0.763829\pi$
$103$	2.19850	−	3.80791i	0.216624	−	0.375204i	0.953774	+	0.300526i	$0.0971621\pi$
$104$	0.471410	+	0.816506i	0.0462256	+	0.0800650i
$105$		0			0
$106$	−1.38727	+	2.40283i	−0.134744	+	0.233384i
$107$	6.86389	+	11.8886i	0.663557	+	1.14931i	0.979674	+	0.200594i	$0.0642873\pi$
$107$	6.86389	+	11.8886i	0.663557	+	1.14931i	−0.316117	+	0.948720i	$0.602379\pi$
$108$		0			0
$109$	−0.631600	+	1.09396i	−0.0604963	+	0.104783i	−0.894687	−	0.446693i	$-0.852602\pi$
$109$	−0.631600	+	1.09396i	−0.0604963	+	0.104783i	0.834191	+	0.551476i	$0.185935\pi$
$110$	−1.04678			−0.0998062
$111$		0			0
$112$		0			0
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	0.996353	+	0.0853326i	$0.0271953\pi$
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	−0.424276	+	0.905533i	$0.639471\pi$
$114$		0			0
$115$	3.31122	+	5.73520i	0.308773	+	0.534810i
$116$	−0.232287	+	0.402332i	−0.0215673	+	0.0373556i
$117$		0			0
$118$	−0.622440			−0.0573003
$119$		0			0
$120$		0			0
$121$	−1.35868	+	2.35331i	−0.123517	+	0.213937i
$122$	−1.81806			−0.164599
$123$		0			0
$124$	−3.22545			−0.289654
$125$	10.1683			0.909478
$126$		0			0
$127$	1.33981			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$127$	1.33981			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$128$	−7.11436			−0.628827
$129$		0			0
$130$	−0.282630			−0.0247883
$131$	−2.48345	+	4.30146i	−0.216980	+	0.375820i	−0.953883	−	0.300178i	$-0.902954\pi$
$131$	−2.48345	+	4.30146i	−0.216980	+	0.375820i	0.736903	+	0.675998i	$0.236287\pi$
$132$		0			0
$133$		0			0
$134$	0.838864			0.0724668
$135$		0			0
$136$	3.27292	−	5.66886i	0.280650	−	0.486100i
$137$	−2.16991	−	3.75839i	−0.185387	−	0.321101i	0.758320	−	0.651883i	$-0.226021\pi$
$137$	−2.16991	−	3.75839i	−0.185387	−	0.321101i	−0.943707	+	0.330782i	$0.892687\pi$
$138$		0			0
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	0.770226	−	0.637771i	$-0.220143\pi$
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	−0.937439	+	0.348150i	$0.886810\pi$
$140$		0			0
$141$		0			0
$142$	−2.05718			−0.172635
$143$	−1.85185	+	3.20750i	−0.154859	+	0.268224i
$144$		0			0
$145$	−0.141315	−	0.244765i	−0.0117356	−	0.0203266i
$146$	−1.81122	+	3.13713i	−0.149898	+	0.259630i
$147$		0			0
$148$	−9.27292	−	16.0612i	−0.762229	−	1.32022i
$149$	5.55555	−	9.62249i	0.455128	−	0.788305i	−0.543568	−	0.839365i	$-0.682927\pi$
$149$	5.55555	−	9.62249i	0.455128	−	0.788305i	0.998696	+	0.0510606i	$0.0162602\pi$
$150$		0			0
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	−0.996905	−	0.0786145i	$-0.974950\pi$
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	0.430370	−	0.902652i	$-0.358383\pi$
$152$	0.915865	+	1.58632i	0.0742864	+	0.128668i
$153$		0			0
$154$		0			0
$155$	0.981125	−	1.69936i	0.0788059	−	0.136496i
$156$		0			0
$157$	0.0571799			0.00456346			0.00228173	−	0.999997i	$-0.499274\pi$
$157$	0.0571799			0.00456346			0.00228173	+	0.999997i	$0.499274\pi$
$158$	1.76415			0.140348
$159$		0			0
$160$	1.63160	−	2.82601i	0.128989	−	0.223416i
$161$		0			0
$162$		0			0
$163$	0.754040	+	1.30604i	0.0590610	+	0.102297i	0.894044	−	0.447979i	$-0.147856\pi$
$163$	0.754040	+	1.30604i	0.0590610	+	0.102297i	−0.834983	+	0.550276i	$0.814523\pi$
$164$	9.89084	+	17.1314i	0.772345	+	1.33774i
$165$		0			0
$166$	−0.830095	+	1.43777i	−0.0644279	+	0.111592i
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	−0.996749	−	0.0805714i	$-0.974325\pi$
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	0.428598	−	0.903496i	$-0.359008\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	0.981125	+	1.69936i	0.0752489	+	0.130335i
$171$		0			0
$172$	2.16182	−	3.74439i	0.164838	−	0.285507i
$173$	−0.252796			−0.0192197			−0.00960987	−	0.999954i	$-0.503059\pi$
$173$	−0.252796			−0.0192197			−0.00960987	+	0.999954i	$0.503059\pi$
$174$		0			0
$175$		0			0
$176$	−6.77812	−	11.7400i	−0.510920	−	0.884939i
$177$		0			0
$178$	0.328460	+	0.568910i	0.0246191	+	0.0426416i
$179$	7.09617	−	12.2909i	0.530393	−	0.918667i	−0.468978	−	0.883210i	$-0.655378\pi$
$179$	7.09617	−	12.2909i	0.530393	−	0.918667i	0.999371	−	0.0354578i	$-0.0112889\pi$
$180$		0			0
$181$	−1.43147			−0.106400			−0.0532002	−	0.998584i	$-0.516942\pi$
$181$	−1.43147			−0.106400			−0.0532002	+	0.998584i	$0.516942\pi$
$182$		0			0
$183$		0			0
$184$	2.64132	−	4.57489i	0.194720	−	0.337266i
$185$	11.2826			0.829515
$186$		0			0
$187$	25.7141			1.88040
$188$	11.3236			0.825862
$189$		0			0
$190$	−0.549100			−0.0398359
$191$	−15.0676			−1.09025			−0.545126	−	0.838354i	$-0.683518\pi$
$191$	−15.0676			−1.09025			−0.545126	+	0.838354i	$0.683518\pi$
$192$		0			0
$193$	−7.84789			−0.564904			−0.282452	−	0.959282i	$-0.591148\pi$
$193$	−7.84789			−0.564904			−0.282452	+	0.959282i	$0.591148\pi$
$194$	−0.857050	+	1.48445i	−0.0615326	+	0.106578i
$195$		0			0
$196$		0			0
$197$	−6.69002			−0.476644			−0.238322	−	0.971186i	$-0.576597\pi$
$197$	−6.69002			−0.476644			−0.238322	+	0.971186i	$0.576597\pi$
$198$		0			0
$199$	9.96978	−	17.2682i	0.706739	−	1.22411i	−0.259322	−	0.965791i	$-0.583499\pi$
$199$	9.96978	−	17.2682i	0.706739	−	1.22411i	0.966060	−	0.258316i	$-0.0831677\pi$
$200$	−1.69850	−	2.94188i	−0.120102	−	0.208022i
$201$		0			0
$202$	−1.52859	−	2.64760i	−0.107551	−	0.186284i
$203$		0			0
$204$		0			0
$205$	−12.0345			−0.840525
$206$	0.525711	−	0.910559i	0.0366280	−	0.0634416i
$207$		0			0
$208$	−1.83009	−	3.16982i	−0.126894	−	0.219787i
$209$	−3.59781	+	6.23159i	−0.248866	+	0.431048i
$210$		0			0
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	0.988973	+	0.148095i	$0.0473141\pi$
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	−0.366233	+	0.930523i	$0.619353\pi$
$212$	11.2713	−	19.5224i	0.774115	−	1.34081i
$213$		0			0
$214$	1.64132	+	2.84284i	0.112198	+	0.194333i
$215$	1.31518	+	2.27796i	0.0896944	+	0.155355i
$216$		0			0
$217$		0			0
$218$	−0.151030	+	0.261592i	−0.0102291	+	0.0177172i
$219$		0			0
$220$	8.50481			0.573394
$221$	6.94282			0.467025
$222$		0			0
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	0.943560	−	0.331203i	$-0.107454\pi$
$224$		0			0
$225$		0			0
$226$	1.45417	+	2.51870i	0.0967299	+	0.167541i
$227$	−2.64132	−	4.57489i	−0.175310	−	0.303646i	0.764958	−	0.644080i	$-0.222760\pi$
$227$	−2.64132	−	4.57489i	−0.175310	−	0.303646i	−0.940269	+	0.340433i	$0.889426\pi$
$228$		0			0
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	0.346778	+	0.937947i	$0.387276\pi$
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	−0.985675	+	0.168655i	$0.946058\pi$
$230$	0.791790	+	1.37142i	0.0522091	+	0.0904288i
$231$		0			0
$232$	−0.112725	+	0.195246i	−0.00740077	+	0.0128185i
$233$	−8.49028	−	14.7056i	−0.556217	−	0.963396i	−0.997808	−	0.0661796i	$-0.978919\pi$
$233$	−8.49028	−	14.7056i	−0.556217	−	0.963396i	0.441591	−	0.897217i	$-0.354414\pi$
$234$		0			0
$235$	−3.44445	+	5.96597i	−0.224691	+	0.389177i
$236$	5.05718			0.329194
$237$		0			0
$238$		0			0
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	0.998535	+	0.0541011i	$0.0172293\pi$
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	−0.452415	+	0.891808i	$0.649437\pi$
$240$		0			0
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.857507	−	0.514473i	$-0.827988\pi$
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.0167933	−	0.999859i	$-0.505346\pi$
$242$	−0.324893	+	0.562732i	−0.0208849	+	0.0361738i
$243$		0			0
$244$	14.7713			0.945634
$245$		0			0
$246$		0			0
$247$	−0.971410	+	1.68253i	−0.0618093	+	0.107057i
$248$	−1.56526			−0.0993941
$249$		0			0
$250$	2.43147			0.153780
$251$	19.0780			1.20419			0.602096	−	0.798424i	$-0.294332\pi$
$251$	19.0780			1.20419			0.602096	+	0.798424i	$0.294332\pi$
$252$		0			0
$253$	20.7518			1.30466
$254$	0.320380			0.0201024
$255$		0			0
$256$	11.6192			0.726198
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	−0.999105	−	0.0423070i	$-0.986529\pi$
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	0.536191	+	0.844097i	$0.319863\pi$
$258$		0			0
$259$		0			0
$260$	2.29630			0.142411
$261$		0			0
$262$	−0.593850	+	1.02858i	−0.0366882	+	0.0635458i
$263$	−3.87072	−	6.70429i	−0.238679	−	0.413404i	0.721656	−	0.692251i	$-0.243381\pi$
$263$	−3.87072	−	6.70429i	−0.238679	−	0.413404i	−0.960335	+	0.278847i	$0.910048\pi$
$264$		0			0
$265$	6.85705	+	11.8768i	0.421225	+	0.729584i
$266$		0			0
$267$		0			0
$268$	−6.81557			−0.416327
$269$	−0.755675	+	1.30887i	−0.0460743	+	0.0798031i	−0.888143	−	0.459567i	$-0.848004\pi$
$269$	−0.755675	+	1.30887i	−0.0460743	+	0.0798031i	0.842069	+	0.539371i	$0.181338\pi$
$270$		0			0
$271$	10.9903	+	19.0357i	0.667612	+	1.15634i	0.978570	+	0.205915i	$0.0660169\pi$
$271$	10.9903	+	19.0357i	0.667612	+	1.15634i	−0.310958	+	0.950424i	$0.600650\pi$
$272$	−12.7060	+	22.0075i	−0.770416	+	1.33440i
$273$		0			0
$274$	−0.518875	−	0.898718i	−0.0313464	−	0.0542935i
$275$	6.67223	−	11.5566i	0.402350	−	0.696892i
$276$		0			0
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	0.981575	−	0.191077i	$-0.0611982\pi$
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	−0.656265	+	0.754530i	$0.727865\pi$
$278$	−0.471410	−	0.816506i	−0.0282733	−	0.0489708i
$279$		0			0
$280$		0			0
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	0.496605	+	0.867977i	$0.334580\pi$
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	−0.999992	+	0.00391559i	$0.998754\pi$
$282$		0			0
$283$	−15.3171			−0.910508			−0.455254	−	0.890362i	$-0.650451\pi$
$283$	−15.3171			−0.910508			−0.455254	+	0.890362i	$0.650451\pi$
$284$	16.7141			0.991799
$285$		0			0
$286$	−0.442820	+	0.766987i	−0.0261845	+	0.0453529i
$287$		0			0
$288$		0			0
$289$	−15.6014	−	27.0224i	−0.917728	−	1.58955i
$290$	−0.0337917	−	0.0585290i	−0.00198432	−	0.00343694i
$291$		0			0
$292$	14.7157	−	25.4884i	0.861173	−	1.49160i
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	0.696114	−	0.717932i	$-0.254911\pi$
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	−0.969804	+	0.243886i	$0.921578\pi$
$294$		0			0
$295$	−1.53831	+	2.66442i	−0.0895636	+	0.155129i
$296$	−4.50000	−	7.79423i	−0.261557	−	0.453030i
$297$		0			0
$298$	1.32846	−	2.30096i	0.0769556	−	0.133291i
$299$	5.60301			0.324030
$300$		0			0
$301$		0			0
$302$	−1.66470	−	2.88335i	−0.0957929	−	0.165918i
$303$		0			0
$304$	−3.55555	−	6.15838i	−0.203925	−	0.353208i
$305$	−4.49316	+	7.78239i	−0.257278	+	0.445618i
$306$		0			0
$307$	2.71410			0.154902			0.0774509	−	0.996996i	$-0.475322\pi$
$307$	2.71410			0.154902			0.0774509	+	0.996996i	$0.475322\pi$
$308$		0			0
$309$		0			0
$310$	0.234610	−	0.406356i	0.0133249	−	0.0230795i
$311$	13.9806			0.792765			0.396383	−	0.918085i	$-0.370265\pi$
$311$	13.9806			0.792765			0.396383	+	0.918085i	$0.370265\pi$
$312$		0			0
$313$	−19.0539			−1.07699			−0.538495	−	0.842628i	$-0.681007\pi$
$313$	−19.0539			−1.07699			−0.538495	+	0.842628i	$0.681007\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	4.01943			0.225754			0.112877	−	0.993609i	$-0.463993\pi$
$317$	4.01943			0.225754			0.112877	+	0.993609i	$0.463993\pi$
$318$		0			0
$319$	−0.885640			−0.0495863
$320$	−3.93598	+	6.81732i	−0.220028	+	0.381100i
$321$		0			0
$322$		0			0
$323$	13.4887			0.750529
$324$		0			0
$325$	1.80150	−	3.12030i	0.0999295	−	0.173083i
$326$	0.180309	+	0.312304i	0.00998637	+	0.0172969i
$327$		0			0
$328$	4.79987	+	8.31362i	0.265028	+	0.459043i
$329$		0			0
$330$		0			0
$331$	−12.3776			−0.680332			−0.340166	−	0.940365i	$-0.610483\pi$
$331$	−12.3776			−0.680332			−0.340166	+	0.940365i	$0.610483\pi$
$332$	6.74433	−	11.6815i	0.370143	−	0.641106i
$333$		0			0
$334$	−1.75567	−	3.04092i	−0.0960663	−	0.166392i
$335$	2.07318	−	3.59085i	0.113270	−	0.196189i
$336$		0			0
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	0.649356	−	0.760484i	$-0.275038\pi$
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	−0.983277	+	0.182117i	$0.941705\pi$
$338$	1.43474	−	2.48504i	0.0780395	−	0.135168i
$339$		0			0
$340$	−7.97141	−	13.8069i	−0.432310	−	0.748784i
$341$	−3.07442	−	5.32505i	−0.166489	−	0.288368i
$342$		0			0
$343$		0			0
$344$	1.04910	−	1.81709i	0.0565637	−	0.0979711i
$345$		0			0
$346$	−0.0604495			−0.00324978
$347$	−6.64979			−0.356979			−0.178490	−	0.983942i	$-0.557121\pi$
$347$	−6.64979			−0.356979			−0.178490	+	0.983942i	$0.557121\pi$
$348$		0			0
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	−0.977493	−	0.210967i	$-0.932339\pi$
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	0.671449	+	0.741050i	$0.265672\pi$
$350$		0			0
$351$		0			0
$352$	−5.11273	−	8.85550i	−0.272509	−	0.472000i
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	−0.994141	−	0.108087i	$-0.965528\pi$
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	0.403465	−	0.914995i	$-0.367806\pi$
$354$		0			0
$355$	−5.08414	+	8.80598i	−0.269838	+	0.467373i
$356$	−2.66866	−	4.62226i	−0.141439	−	0.244979i
$357$		0			0
$358$	1.69686	−	2.93905i	0.0896819	−	0.155334i
$359$	−3.77812	−	6.54389i	−0.199401	−	0.345373i	0.748933	−	0.662646i	$-0.230566\pi$
$359$	−3.77812	−	6.54389i	−0.199401	−	0.345373i	−0.948334	+	0.317272i	$0.897233\pi$
$360$		0			0
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	−0.342298			−0.0179908
$363$		0			0
$364$		0			0
$365$	8.95254	+	15.5062i	0.468597	+	0.811634i
$366$		0			0
$367$	9.26157	+	16.0415i	0.483450	+	0.837360i	0.999819	−	0.0190063i	$-0.00605025\pi$
$367$	9.26157	+	16.0415i	0.483450	+	0.837360i	−0.516370	+	0.856366i	$0.672717\pi$
$368$	−10.2540	+	17.7605i	−0.534529	+	0.925831i
$369$		0			0
$370$	2.69794			0.140259
$371$		0			0
$372$		0			0
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	−0.994371	−	0.105954i	$-0.966210\pi$
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	0.588944	+	0.808174i	$0.299544\pi$
$374$	6.14884			0.317949
$375$		0			0
$376$	5.49519			0.283393
$377$	−0.239123			−0.0123155
$378$		0			0
$379$	4.03775			0.207405			0.103703	−	0.994608i	$-0.466931\pi$
$379$	4.03775			0.207405			0.103703	+	0.994608i	$0.466931\pi$
$380$	4.46130			0.228860
$381$		0			0
$382$	−3.60301			−0.184346
$383$	0.112725	−	0.195246i	0.00575998	−	0.00997659i	−0.863131	−	0.504980i	$-0.831500\pi$
$383$	0.112725	−	0.195246i	0.00575998	−	0.00997659i	0.868891	+	0.495003i	$0.164833\pi$
$384$		0			0
$385$		0			0
$386$	−1.87661			−0.0955171
$387$		0			0
$388$	6.96333	−	12.0608i	0.353510	−	0.612296i
$389$	12.6316	+	21.8786i	0.640448	+	1.10929i	0.985333	+	0.170643i	$0.0545844\pi$
$389$	12.6316	+	21.8786i	0.640448	+	1.10929i	−0.344885	+	0.938645i	$0.612082\pi$
$390$		0			0
$391$	−19.4503	−	33.6890i	−0.983646	−	1.70373i
$392$		0			0
$393$		0			0
$394$	−1.59974			−0.0805938
$395$	4.35993	−	7.55162i	0.219372	−	0.379963i
$396$		0			0
$397$	10.1505	+	17.5811i	0.509438	+	0.882372i	0.999940	+	0.0109322i	$0.00347991\pi$
$397$	10.1505	+	17.5811i	0.509438	+	0.882372i	−0.490503	+	0.871440i	$0.663187\pi$
$398$	2.38401	−	4.12922i	0.119499	−	0.206979i
$399$		0			0
$400$	6.59385	+	11.4209i	0.329693	+	0.571044i
$401$	−7.61273	+	13.1856i	−0.380161	+	0.658459i	−0.991085	−	0.133231i	$-0.957465\pi$
$401$	−7.61273	+	13.1856i	−0.380161	+	0.658459i	0.610924	+	0.791689i	$0.290798\pi$
$402$		0			0
$403$	−0.830095	−	1.43777i	−0.0413500	−	0.0716203i
$404$	12.4194	+	21.5111i	0.617890	+	1.07022i
$405$		0			0
$406$		0			0
$407$	17.6774	−	30.6182i	0.876238	−	1.51769i
$408$		0			0
$409$	1.65692			0.0819294			0.0409647	−	0.999161i	$-0.486957\pi$
$409$	1.65692			0.0819294			0.0409647	+	0.999161i	$0.486957\pi$
$410$	−2.87772			−0.142121
$411$		0			0
$412$	−4.27128	+	7.39807i	−0.210431	+	0.364477i
$413$		0			0
$414$		0			0
$415$	4.10301	+	7.10662i	0.201409	+	0.348850i
$416$	−1.38044	−	2.39099i	−0.0676816	−	0.117228i
$417$		0			0
$418$	−0.860320	+	1.49012i	−0.0420796	+	0.0728840i
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	0.909170	+	0.416426i	$0.136718\pi$
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	−0.0939492	+	0.995577i	$0.529949\pi$
$420$		0			0
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	−0.998017	−	0.0629481i	$-0.979950\pi$
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	0.553523	+	0.832834i	$0.313283\pi$
$422$	2.16307	+	3.74654i	0.105297	+	0.182379i
$423$		0			0
$424$	5.46978	−	9.47393i	0.265636	−	0.460095i
$425$	−25.0150			−1.21341
$426$		0			0
$427$		0			0
$428$	−13.3353	−	23.0974i	−0.644586	−	1.11646i
$429$		0			0
$430$	0.314490	+	0.544712i	0.0151660	+	0.0262684i
$431$	14.6413	−	25.3595i	0.705247	−	1.22152i	−0.261355	−	0.965243i	$-0.584169\pi$
$431$	14.6413	−	25.3595i	0.705247	−	1.22152i	0.966602	−	0.256281i	$-0.0824974\pi$
$432$		0			0
$433$	−12.2449			−0.588451			−0.294226	−	0.955736i	$-0.595062\pi$
$433$	−12.2449			−0.588451			−0.294226	+	0.955736i	$0.595062\pi$
$434$		0			0
$435$		0			0
$436$	1.22708	−	2.12537i	0.0587667	−	0.101787i
$437$	10.8856			0.520731
$438$		0			0
$439$	−4.83173			−0.230606			−0.115303	−	0.993330i	$-0.536784\pi$
$439$	−4.83173			−0.230606			−0.115303	+	0.993330i	$0.536784\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	−1.24488			−0.0591461			−0.0295730	−	0.999563i	$-0.509415\pi$
$443$	−1.24488			−0.0591461			−0.0295730	+	0.999563i	$0.509415\pi$
$444$		0			0
$445$	3.24704			0.153924
$446$	2.70890	−	4.69195i	0.128270	−	0.222170i
$447$		0			0
$448$		0			0
$449$	−8.82846			−0.416641			−0.208320	−	0.978061i	$-0.566800\pi$
$449$	−8.82846			−0.416641			−0.208320	+	0.978061i	$0.566800\pi$
$450$		0			0
$451$	−18.8554	+	32.6585i	−0.887867	+	1.53783i
$452$	−11.8148	−	20.4638i	−0.555721	−	0.962537i
$453$		0			0
$454$	−0.631600	−	1.09396i	−0.0296425	−	0.0513422i
$455$		0			0
$456$		0			0
$457$	−10.5081			−0.491547			−0.245774	−	0.969327i	$-0.579042\pi$
$457$	−10.5081			−0.491547			−0.245774	+	0.969327i	$0.579042\pi$
$458$	−2.31191	+	4.00434i	−0.108028	+	0.187111i
$459$		0			0
$460$	−6.43310	−	11.1425i	−0.299945	−	0.519520i
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	−0.474404	−	0.880307i	$-0.657337\pi$
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	0.999570	−	0.0293073i	$-0.00933013\pi$
$462$		0			0
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	0.719574	−	0.694416i	$-0.244337\pi$
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	−0.961169	+	0.275962i	$0.911004\pi$
$464$	0.437618	−	0.757977i	0.0203159	−	0.0351882i
$465$		0			0
$466$	−2.03022	−	3.51645i	−0.0940483	−	0.162897i
$467$	6.65856	+	11.5330i	0.308121	+	0.533682i	0.977951	−	0.208833i	$-0.0669664\pi$
$467$	6.65856	+	11.5330i	0.308121	+	0.533682i	−0.669830	+	0.742514i	$0.733633\pi$
$468$		0			0
$469$		0			0
$470$	−0.823649	+	1.42660i	−0.0379921	+	0.0658043i
$471$		0			0
$472$	2.45417			0.112962
$473$	8.24239			0.378986
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$	2.01887	+	3.49679i	0.0923412	+	0.159940i
$479$	7.26771	+	12.5880i	0.332070	+	0.575163i	0.982918	−	0.184046i	$-0.0589195\pi$
$479$	7.26771	+	12.5880i	0.332070	+	0.575163i	−0.650847	+	0.759209i	$0.725586\pi$
$480$		0			0
$481$	4.77292	−	8.26693i	0.217626	−	0.376940i
$482$	−3.24557	−	5.62149i	−0.147832	−	0.256052i
$483$		0			0
$484$	2.63968	−	4.57206i	0.119985	−	0.207821i
$485$	4.23624	+	7.33739i	0.192358	+	0.333174i
$486$		0			0
$487$	−6.52696	+	11.3050i	−0.295765	+	0.512279i	−0.975162	−	0.221491i	$-0.928908\pi$
$487$	−6.52696	+	11.3050i	−0.295765	+	0.512279i	0.679398	+	0.733770i	$0.262241\pi$
$488$	7.16827			0.324492
$489$		0			0
$490$		0			0
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	0.997417	−	0.0718303i	$-0.0228840\pi$
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	−0.560915	+	0.827873i	$0.689551\pi$
$492$		0			0
$493$	0.830095	+	1.43777i	0.0373856	+	0.0647538i
$494$	−0.232287	+	0.402332i	−0.0104511	+	0.0181018i
$495$		0			0
$496$	6.07661			0.272848
$497$		0			0
$498$		0			0
$499$	18.1111	−	31.3693i	0.810764	−	1.40428i	−0.101566	−	0.994829i	$-0.532385\pi$
$499$	18.1111	−	31.3693i	0.810764	−	1.40428i	0.912330	−	0.409455i	$-0.134281\pi$
$500$	−19.7551			−0.883476
$501$		0			0
$502$	4.56199			0.203612
$503$	−15.6764			−0.698974			−0.349487	−	0.936941i	$-0.613644\pi$
$503$	−15.6764			−0.698974			−0.349487	+	0.936941i	$0.613644\pi$
$504$		0			0
$505$	−15.1111			−0.672435
$506$	4.96225			0.220599
$507$		0			0
$508$	−2.60301			−0.115490
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	−0.182492	−	0.983207i	$-0.558416\pi$
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	0.942729	−	0.333561i	$-0.108250\pi$
$510$		0			0
$511$		0			0
$512$	17.0071			0.751616
$513$		0			0
$514$	−1.77455	+	3.07361i	−0.0782720	+	0.135571i
$515$	−2.59850	−	4.50073i	−0.114503	−	0.198326i
$516$		0			0
$517$	10.7934	+	18.6948i	0.474694	+	0.822195i
$518$		0			0
$519$		0			0
$520$	1.11436			0.0488679
$521$	−5.12244	+	8.87233i	−0.224418	+	0.388704i	−0.956145	−	0.292895i	$-0.905381\pi$
$521$	−5.12244	+	8.87233i	−0.224418	+	0.388704i	0.731727	+	0.681598i	$0.238715\pi$
$522$		0			0
$523$	−15.3015	−	26.5030i	−0.669088	−	1.15889i	−0.978159	−	0.207856i	$-0.933352\pi$
$523$	−15.3015	−	26.5030i	−0.669088	−	1.15889i	0.309071	−	0.951039i	$-0.399982\pi$
$524$	4.82489	−	8.35696i	0.210776	−	0.365075i
$525$		0			0
$526$	−0.925580	−	1.60315i	−0.0403572	−	0.0699007i
$527$	−5.76320	+	9.98215i	−0.251049	+	0.434829i
$528$		0			0
$529$	−4.19686	−	7.26918i	−0.182472	−	0.316051i
$530$	1.63968	+	2.84001i	0.0712232	+	0.123362i
$531$		0			0
$532$		0			0
$533$	−5.09097	+	8.81782i	−0.220514	+	0.381942i
$534$		0			0
$535$	16.2255			0.701487
$536$	−3.30749			−0.142862
$537$		0			0
$538$	−0.180699	+	0.312981i	−0.00779051	+	0.0134936i
$539$		0			0
$540$		0			0
$541$	13.0458	+	22.5960i	0.560884	+	0.971480i	0.997420	+	0.0717926i	$0.0228720\pi$
$541$	13.0458	+	22.5960i	0.560884	+	0.971480i	−0.436536	+	0.899687i	$0.643795\pi$
$542$	2.62803	+	4.55189i	0.112884	+	0.195520i
$543$		0			0
$544$	−9.58414	+	16.6002i	−0.410916	+	0.711728i
$545$	0.746515	+	1.29300i	0.0319772	+	0.0553861i
$546$		0			0
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	−0.725318	−	0.688414i	$-0.758307\pi$
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	0.958843	+	0.283937i	$0.0916405\pi$
$548$	4.21574	+	7.30187i	0.180087	+	0.311920i
$549$		0			0
$550$	1.59549	−	2.76346i	0.0680317	−	0.117834i
$551$	−0.464574			−0.0197915
$552$		0			0
$553$		0			0
$554$	1.29467	+	2.24243i	0.0550052	+	0.0952718i
$555$		0			0
$556$	3.83009	+	6.63392i	0.162432	+	0.281341i
$557$	−6.97210	+	12.0760i	−0.295417	+	0.511678i	−0.975082	−	0.221845i	$-0.928792\pi$
$557$	−6.97210	+	12.0760i	−0.295417	+	0.511678i	0.679665	+	0.733523i	$0.262125\pi$
$558$		0			0
$559$	2.22545			0.0941265
$560$		0			0
$561$		0			0
$562$	−2.01780	+	3.49492i	−0.0851156	+	0.147424i
$563$	−30.2574			−1.27520			−0.637600	−	0.770368i	$-0.720073\pi$
$563$	−30.2574			−1.27520			−0.637600	+	0.770368i	$0.720073\pi$
$564$		0			0
$565$	14.3754			0.604778
$566$	−3.66268			−0.153954
$567$		0			0
$568$	8.11109			0.340334
$569$	21.1352			0.886032			0.443016	−	0.896514i	$-0.353908\pi$
$569$	21.1352			0.886032			0.443016	+	0.896514i	$0.353908\pi$
$570$		0			0
$571$	−32.7863			−1.37207			−0.686033	−	0.727571i	$-0.740649\pi$
$571$	−32.7863			−1.37207			−0.686033	+	0.727571i	$0.740649\pi$
$572$	3.59781	−	6.23159i	0.150432	−	0.260556i
$573$		0			0
$574$		0			0
$575$	−20.1877			−0.841885
$576$		0			0
$577$	8.68715	−	15.0466i	0.361651	−	0.626397i	−0.626582	−	0.779355i	$-0.715547\pi$
$577$	8.68715	−	15.0466i	0.361651	−	0.626397i	0.988233	+	0.152958i	$0.0488800\pi$
$578$	−3.73065	−	6.46168i	−0.155175	−	0.268770i
$579$		0			0
$580$	0.274550	+	0.475534i	0.0114001	+	0.0197455i
$581$		0			0
$582$		0			0
$583$	42.9740			1.77980
$584$	7.14132	−	12.3691i	0.295510	−	0.511838i
$585$		0			0
$586$	−1.12025	−	1.94033i	−0.0462771	−	0.0801543i
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	−0.635973	−	0.771712i	$-0.719401\pi$
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	0.986308	+	0.164913i	$0.0527342\pi$
$588$		0			0
$589$	−1.61273	−	2.79332i	−0.0664512	−	0.115097i
$590$	−0.367845	+	0.637125i	−0.0151439	+	0.0262300i
$591$		0			0
$592$	17.4698	+	30.2585i	0.718003	+	1.24362i
$593$	−6.53667	−	11.3218i	−0.268429	−	0.464932i	0.700027	−	0.714116i	$-0.253171\pi$
$593$	−6.53667	−	11.3218i	−0.268429	−	0.464932i	−0.968456	+	0.249184i	$0.919838\pi$
$594$		0			0
$595$		0			0
$596$	−10.7934	+	18.6948i	−0.442116	+	0.765767i
$597$		0			0
$598$	1.33981			0.0547889
$599$	−29.2060			−1.19333			−0.596663	−	0.802492i	$-0.703507\pi$
$599$	−29.2060			−1.19333			−0.596663	+	0.802492i	$0.703507\pi$
$600$		0			0
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	−0.934470	−	0.356041i	$-0.884126\pi$
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	0.775576	+	0.631255i	$0.217460\pi$
$602$		0			0
$603$		0			0
$604$	13.5253	+	23.4265i	0.550337	+	0.953212i
$605$	1.60589	+	2.78148i	0.0652887	+	0.113083i
$606$		0			0
$607$	9.82038	−	17.0094i	0.398597	−	0.690390i	−0.594956	−	0.803758i	$-0.702831\pi$
$607$	9.82038	−	17.0094i	0.398597	−	0.690390i	0.993553	+	0.113368i	$0.0361639\pi$
$608$	−2.68194	−	4.64526i	−0.108767	−	0.188390i
$609$		0			0
$610$	−1.07442	+	1.86095i	−0.0435020	+	0.0753477i
$611$	2.91423	+	5.04759i	0.117897	+	0.204204i
$612$		0			0
$613$	−11.7826	+	20.4081i	−0.475896	+	0.824276i	−0.999619	−	0.0276128i	$-0.991209\pi$
$613$	−11.7826	+	20.4081i	−0.475896	+	0.824276i	0.523723	+	0.851889i	$0.324543\pi$
$614$	0.649005			0.0261917
$615$		0			0
$616$		0			0
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	0.738562	−	0.674186i	$-0.235505\pi$
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	−0.953143	+	0.302520i	$0.902172\pi$
$618$		0			0
$619$	9.00752	+	15.6015i	0.362043	+	0.627077i	0.988297	−	0.152542i	$-0.0487460\pi$
$619$	9.00752	+	15.6015i	0.362043	+	0.627077i	−0.626254	+	0.779619i	$0.715413\pi$
$620$	−1.90615	+	3.30155i	−0.0765528	+	0.132593i
$621$		0			0
$622$	3.34308			0.134045
$623$		0			0
$624$		0			0
$625$	−2.99837	+	5.19332i	−0.119935	+	0.207733i
$626$	−4.55623			−0.182104
$627$		0			0
$628$	−0.111090			−0.00443299
$629$	−66.2750			−2.64256
$630$		0			0
$631$	12.4703			0.496436			0.248218	−	0.968704i	$-0.420155\pi$
$631$	12.4703			0.496436			0.248218	+	0.968704i	$0.420155\pi$
$632$	−6.95571			−0.276683
$633$		0			0
$634$	0.961139			0.0381717
$635$	0.791790	−	1.37142i	0.0314212	−	0.0544232i
$636$		0			0
$637$		0			0
$638$	−0.211777			−0.00838434
$639$		0			0
$640$	−4.20439	+	7.28221i	−0.166193	+	0.287855i
$641$	9.57279	+	16.5806i	0.378102	+	0.654892i	0.990786	−	0.135436i	$-0.0432434\pi$
$641$	9.57279	+	16.5806i	0.378102	+	0.654892i	−0.612684	+	0.790328i	$0.709910\pi$
$642$		0			0
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	0.794936	−	0.606693i	$-0.207504\pi$
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	−0.922880	+	0.385088i	$0.874171\pi$
$644$		0			0
$645$		0			0
$646$	3.22545			0.126904
$647$	−24.0494	+	41.6548i	−0.945479	+	1.63762i	−0.190691	+	0.981650i	$0.561073\pi$
$647$	−24.0494	+	41.6548i	−0.945479	+	1.63762i	−0.754789	+	0.655968i	$0.772261\pi$
$648$		0			0
$649$	4.82038	+	8.34914i	0.189216	+	0.327733i
$650$	0.430782	−	0.746136i	0.0168967	−	0.0292659i
$651$		0			0
$652$	−1.46496	−	2.53739i	−0.0573724	−	0.0993720i
$653$	−21.6202	+	37.4474i	−0.846066	+	1.46543i	0.0386267	+	0.999254i	$0.487702\pi$
$653$	−21.6202	+	37.4474i	−0.846066	+	1.46543i	−0.884692	+	0.466175i	$0.845632\pi$
$654$		0			0
$655$	2.93530	+	5.08408i	0.114691	+	0.198651i
$656$	−18.6339	−	32.2749i	−0.727532	−	1.26012i
$657$		0			0
$658$		0			0
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	−0.889417	−	0.457097i	$-0.848889\pi$
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	0.840566	+	0.541709i	$0.182222\pi$
$660$		0			0
$661$	−42.3354			−1.64666			−0.823329	−	0.567565i	$-0.807886\pi$
$661$	−42.3354			−1.64666			−0.823329	+	0.567565i	$0.807886\pi$
$662$	−2.95976			−0.115034
$663$		0			0
$664$	3.27292	−	5.66886i	0.127014	−	0.219994i
$665$		0			0
$666$		0			0
$667$	0.669905	+	1.16031i	0.0259388	+	0.0449274i
$668$	14.2644	+	24.7067i	0.551908	+	0.955933i
$669$		0			0
$670$	0.495745	−	0.858655i	0.0191523	−	0.0331727i
$671$	14.0796	+	24.3866i	0.543538	+	0.941435i
$672$		0			0
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	−0.965857	−	0.259077i	$-0.916582\pi$
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	0.707296	+	0.706918i	$0.249915\pi$
$674$	−1.46582	−	2.53887i	−0.0564612	−	0.0977936i
$675$		0			0
$676$	−11.6569	+	20.1904i	−0.448343	+	0.776553i
$677$	−1.96225			−0.0754154			−0.0377077	−	0.999289i	$-0.512006\pi$
$677$	−1.96225			−0.0754154			−0.0377077	+	0.999289i	$0.512006\pi$
$678$		0			0
$679$		0			0
$680$	−3.86840	−	6.70027i	−0.148346	−	0.256943i
$681$		0			0
$682$	−0.735165	−	1.27334i	−0.0281509	−	0.0487589i
$683$	13.5836	−	23.5275i	0.519761	−	0.900253i	−0.479975	−	0.877282i	$-0.659354\pi$
$683$	13.5836	−	23.5275i	0.519761	−	0.900253i	0.999736	−	0.0229706i	$-0.00731243\pi$
$684$		0			0
$685$	−5.12941			−0.195985
$686$		0			0
$687$		0			0
$688$	−4.07279	+	7.05427i	−0.155273	+	0.268942i
$689$	11.6030			0.442039
$690$		0			0
$691$	−50.3171			−1.91415			−0.957077	−	0.289835i	$-0.906399\pi$
$691$	−50.3171			−1.91415			−0.957077	+	0.289835i	$0.906399\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	−4.66019			−0.176771
$696$		0			0
$697$	70.6914			2.67763
$698$	−1.36716	+	2.36798i	−0.0517476	+	0.0896295i
$699$		0			0
$700$		0			0
$701$	−45.1672			−1.70594			−0.852970	−	0.521960i	$-0.825201\pi$
$701$	−45.1672			−1.70594			−0.852970	+	0.521960i	$0.825201\pi$
$702$		0			0
$703$	9.27292	−	16.0612i	0.349735	−	0.605758i
$704$	12.3337	+	21.3625i	0.464842	+	0.805131i
$705$		0			0
$706$	−2.65374	−	4.59642i	−0.0998750	−	0.172989i
$707$		0			0
$708$		0			0
$709$	39.6181			1.48789			0.743944	−	0.668242i	$-0.232953\pi$
$709$	39.6181			1.48789			0.743944	+	0.668242i	$0.232953\pi$
$710$	−1.21574	+	2.10571i	−0.0456257	+	0.0790261i
$711$		0			0
$712$	−1.29506	−	2.24311i	−0.0485344	−	0.0840640i
$713$	−4.65103	+	8.05582i	−0.174182	+	0.301693i
$714$		0			0
$715$	2.18878	+	3.79108i	0.0818557	+	0.141778i
$716$	−13.7866	+	23.8791i	−0.515229	+	0.892403i
$717$		0			0
$718$	−0.903436	−	1.56480i	−0.0337159	−	0.0583977i
$719$	−11.0189	−	19.0853i	−0.410935	−	0.711760i	0.584058	−	0.811712i	$-0.301464\pi$
$719$	−11.0189	−	19.0853i	−0.410935	−	0.711760i	−0.994992	+	0.0999525i	$0.968131\pi$
$720$		0			0
$721$		0			0
$722$	1.82038	−	3.15299i	0.0677475	−	0.117342i
$723$		0			0
$724$	2.78109			0.103358
$725$	0.861564			0.0319977
$726$		0			0
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	0.478402	+	0.878141i	$0.341216\pi$
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	−0.999693	+	0.0247621i	$0.992117\pi$
$728$		0			0
$729$		0			0
$730$	2.14076	+	3.70790i	0.0792331	+	0.137236i
$731$	−7.72545	−	13.3809i	−0.285736	−	0.494909i
$732$		0			0
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	−0.954565	−	0.298003i	$-0.903680\pi$
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	0.735360	+	0.677676i	$0.237013\pi$
$734$	2.21466	+	3.83590i	0.0817444	+	0.141586i
$735$		0			0
$736$	−7.73461	+	13.3967i	−0.285102	+	0.493810i
$737$	−6.49643	−	11.2522i	−0.239299	−	0.414478i
$738$		0			0
$739$	6.09222	−	10.5520i	0.224106	−	0.388163i	−0.731945	−	0.681364i	$-0.761387\pi$
$739$	6.09222	−	10.5520i	0.224106	−	0.388163i	0.956051	+	0.293201i	$0.0947206\pi$
$740$	−21.9201			−0.805800
$741$		0			0
$742$		0			0
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	−0.908604	−	0.417659i	$-0.862851\pi$
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	0.0925987	−	0.995704i	$-0.470483\pi$
$744$		0			0
$745$	−6.56634	−	11.3732i	−0.240572	−	0.416683i
$746$	−1.87236	+	3.24302i	−0.0685519	+	0.118735i
$747$		0			0
$748$	−49.9579			−1.82664
$749$		0			0
$750$		0			0
$751$	−21.4029	+	37.0709i	−0.781002	+	1.35274i	0.150356	+	0.988632i	$0.451958\pi$
$751$	−21.4029	+	37.0709i	−0.781002	+	1.35274i	−0.931358	+	0.364104i	$0.881375\pi$
$752$	−21.3333			−0.777944
$753$		0			0
$754$	−0.0571799			−0.00208237
$755$	−16.4567			−0.598919
$756$		0			0
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$	0.965520			0.0350693
$759$		0			0
$760$	2.16500			0.0785328
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	−0.966201	−	0.257788i	$-0.917006\pi$
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	0.706352	+	0.707861i	$0.250340\pi$
$762$		0			0
$763$		0			0
$764$	29.2736			1.05908
$765$		0			0
$766$	0.0269552	−	0.0466878i	0.000973931	−	0.00168690i
$767$	1.30150	+	2.25427i	0.0469946	+	0.0813971i
$768$		0			0
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	0.997239	+	0.0742597i	$0.0236594\pi$
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	−0.434309	+	0.900764i	$0.643007\pi$
$770$		0			0
$771$		0			0
$772$	15.2470			0.548753
$773$	2.19002	−	3.79323i	0.0787697	−	0.136433i	−0.823950	−	0.566663i	$-0.808234\pi$
$773$	2.19002	−	3.79323i	0.0787697	−	0.136433i	0.902719	+	0.430230i	$0.141567\pi$
$774$		0			0
$775$	2.99084	+	5.18029i	0.107434	+	0.186081i
$776$	3.37919	−	5.85294i	0.121306	−	0.210108i
$777$		0			0
$778$	3.02051	+	5.23168i	0.108291	+	0.187565i
$779$	−9.89084	+	17.1314i	−0.354376	+	0.613798i
$780$		0			0
$781$	15.9315	+	27.5941i	0.570073	+	0.987395i
$782$	−4.65103	−	8.05582i	−0.166321	−	0.288076i
$783$		0			0
$784$		0			0
$785$	0.0337917	−	0.0585290i	0.00120608	−	0.00208899i
$786$		0			0
$787$	27.6213			0.984594			0.492297	−	0.870427i	$-0.336157\pi$
$787$	27.6213			0.984594			0.492297	+	0.870427i	$0.336157\pi$
$788$	12.9975			0.463017
$789$		0			0
$790$	1.04256	−	1.80577i	0.0370926	−	0.0642463i
$791$		0			0
$792$		0			0
$793$	3.80150	+	6.58440i	0.134995	+	0.233819i
$794$	2.42721	+	4.20406i	0.0861386	+	0.149196i
$795$		0			0
$796$	−19.3695	+	33.5489i	−0.686533	+	1.18911i
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	0.838587	−	0.544767i	$-0.183382\pi$
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	−0.891076	+	0.453854i	$0.850049\pi$
$798$		0			0
$799$	20.2330	−	35.0445i	0.715791	−	1.23979i
$800$	4.97373	+	8.61476i	0.175848	+	0.304578i
$801$		0			0
$802$	−1.82038	+	3.15299i	−0.0642798	+	0.111336i
$803$	56.1067			1.97996
$804$		0			0
$805$		0			0
$806$	−0.198495	−	0.343803i	−0.00699169	−	0.0121100i
$807$		0			0
$808$	6.02696	+	10.4390i	0.212028	+	0.367242i
$809$	−12.3948	+	21.4684i	−0.435778	+	0.754790i	−0.997359	−	0.0726323i	$-0.976860\pi$
$809$	−12.3948	+	21.4684i	−0.435778	+	0.754790i	0.561581	+	0.827422i	$0.310193\pi$
$810$		0			0
$811$	8.24377			0.289478			0.144739	−	0.989470i	$-0.453766\pi$
$811$	8.24377			0.289478			0.144739	+	0.989470i	$0.453766\pi$
$812$		0			0
$813$		0			0
$814$	4.22708	−	7.32153i	0.148159	−	0.256619i
$815$	1.78247			0.0624370
$816$		0			0
$817$	4.32365			0.151265
$818$	0.396208			0.0138531
$819$		0			0
$820$	23.3808			0.816494
$821$	28.8993			1.00859			0.504296	−	0.863531i	$-0.331752\pi$
$821$	28.8993			1.00859			0.504296	+	0.863531i	$0.331752\pi$
$822$		0			0
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	−2.07279	+	3.59017i	−0.0722089	+	0.125069i
$825$		0			0
$826$		0			0
$827$	50.7108			1.76339			0.881694	−	0.471821i	$-0.156403\pi$
$827$	50.7108			1.76339			0.881694	+	0.471821i	$0.156403\pi$
$828$		0			0
$829$	−7.40615	+	12.8278i	−0.257226	+	0.445529i	−0.965498	−	0.260411i	$-0.916142\pi$
$829$	−7.40615	+	12.8278i	−0.257226	+	0.445529i	0.708272	+	0.705940i	$0.249475\pi$
$830$	0.981125	+	1.69936i	0.0340554	+	0.0589856i
$831$		0			0
$832$	3.33009	+	5.76789i	0.115450	+	0.199966i
$833$		0			0
$834$		0			0
$835$	−17.3560			−0.600628
$836$	6.98989	−	12.1069i	0.241751	−	0.418724i
$837$		0			0
$838$	3.99028	+	6.91138i	0.137842	+	0.238750i
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	−0.413138	−	0.910669i	$-0.635567\pi$
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	0.995231	−	0.0975464i	$-0.0310994\pi$
$840$		0			0
$841$	14.4714	+	25.0652i	0.499014	+	0.864318i
$842$	−2.18086	+	3.77737i	−0.0751575	+	0.130177i
$843$		0			0
$844$	−17.5744	−	30.4398i	−0.604936	−	1.04778i
$845$	−7.09166	−	12.2831i	−0.243961	−	0.422552i
$846$		0			0
$847$		0			0
$848$	−21.2346	+	36.7794i	−0.729199	+	1.26301i
$849$		0			0
$850$	−5.98168			−0.205170
$851$	−53.4854			−1.83346
$852$		0			0
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	−0.949119	−	0.314916i	$-0.898024\pi$
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	0.747285	+	0.664503i	$0.231357\pi$
$854$		0			0
$855$		0			0
$856$	−6.47141	−	11.2088i	−0.221188	−	0.383109i
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	−0.999161	−	0.0409451i	$-0.986963\pi$
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	0.464121	−	0.885772i	$-0.346370\pi$
$858$		0			0
$859$	25.1947	−	43.6384i	0.859631	−	1.48892i	−0.0126501	−	0.999920i	$-0.504027\pi$
$859$	25.1947	−	43.6384i	0.859631	−	1.48892i	0.872281	−	0.489005i	$-0.162640\pi$
$860$	−2.55515	−	4.42566i	−0.0871300	−	0.150914i
$861$		0			0
$862$	3.50108	−	6.06405i	0.119247	−	0.206542i
$863$	0.566340	+	0.980929i	0.0192784	+	0.0333912i	0.875504	−	0.483211i	$-0.160530\pi$
$863$	0.566340	+	0.980929i	0.0192784	+	0.0333912i	−0.856225	+	0.516603i	$0.827196\pi$
$864$		0			0
$865$	−0.149395	+	0.258761i	−0.00507960	+	0.00879812i
$866$	−2.92804			−0.0994987
$867$		0			0
$868$		0			0
$869$	−13.6621	−	23.6635i	−0.463456	−	0.802729i
$870$		0			0
$871$	−1.75404	−	3.03809i	−0.0594334	−	0.102942i
$872$	0.595485	−	1.03141i	0.0201657	−	0.0349280i
$873$		0			0
$874$	2.60301			0.0880481
$875$		0			0
$876$		0			0
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	−0.536575	−	0.843853i	$-0.680282\pi$
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	0.999085	+	0.0427615i	$0.0136156\pi$
$878$	−1.15538			−0.0389922
$879$		0			0
$880$	−16.0227			−0.540125
$881$	−1.20929			−0.0407420			−0.0203710	−	0.999792i	$-0.506485\pi$
$881$	−1.20929			−0.0407420			−0.0203710	+	0.999792i	$0.506485\pi$
$882$		0			0
$883$	−51.0884			−1.71926			−0.859631	−	0.510916i	$-0.829306\pi$
$883$	−51.0884			−1.71926			−0.859631	+	0.510916i	$0.829306\pi$
$884$	−13.4887			−0.453672
$885$		0			0
$886$	−0.297680			−0.0100008
$887$	−20.7878	+	36.0056i	−0.697987	+	1.20895i	0.271176	+	0.962530i	$0.412587\pi$
$887$	−20.7878	+	36.0056i	−0.697987	+	1.20895i	−0.969163	+	0.246419i	$0.920746\pi$
$888$		0			0
$889$		0			0
$890$	0.776443			0.0260264
$891$		0			0
$892$	−22.0092	+	38.1210i	−0.736921	+	1.27638i
$893$	5.66182	+	9.80657i	0.189466	+	0.328164i
$894$		0			0
$895$	−8.38727	−	14.5272i	−0.280356	−	0.485590i
$896$		0			0
$897$		0			0
$898$	−2.11109			−0.0704480
$899$	0.198495	−	0.343803i	0.00662018	−	0.0114665i
$900$		0			0
$901$	−40.2788	−	69.7649i	−1.34188	−	2.32421i
$902$	−4.50877	+	7.80942i	−0.150126	+	0.260025i
$903$		0			0
$904$	−5.73353	−	9.93077i	−0.190694	−	0.330292i
$905$	−0.845958	+	1.46524i	−0.0281206	+	0.0487063i
$906$		0			0
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	−0.994421	−	0.105486i	$-0.966360\pi$
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	0.405857	−	0.913937i	$-0.366973\pi$
$908$	5.13160	+	8.88819i	0.170298	+	0.294965i
$909$		0			0
$910$		0			0
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	−0.985005	−	0.172526i	$-0.944807\pi$
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	0.641915	+	0.766776i	$0.278140\pi$
$912$		0			0
$913$	25.7141			0.851013
$914$	−2.51273			−0.0831136
$915$		0			0
$916$	18.7837	−	32.5343i	0.620631	−	1.07496i
$917$		0			0
$918$		0			0
$919$	−7.19630	−	12.4644i	−0.237384	−	0.411161i	0.722579	−	0.691289i	$-0.242957\pi$
$919$	−7.19630	−	12.4644i	−0.237384	−	0.411161i	−0.959963	+	0.280127i	$0.909623\pi$
$920$	−3.12188	−	5.40726i	−0.102925	−	0.178272i
$921$		0			0
$922$	2.69630	−	4.67014i	0.0887981	−	0.153803i
$923$	4.30150	+	7.45043i	0.141586	+	0.245234i
$924$		0			0
$925$	−17.1969	+	29.7858i	−0.565429	+	0.979352i
$926$	−1.24308	−	2.15308i	−0.0408502	−	0.0707546i
$927$		0			0
$928$	0.330095	−	0.571741i	0.0108359	−	0.0187683i
$929$	41.7428			1.36954			0.684769	−	0.728760i	$-0.259903\pi$
$929$	41.7428			1.36954			0.684769	+	0.728760i	$0.259903\pi$
$930$		0			0
$931$		0			0
$932$	16.4951	+	28.5703i	0.540315	+	0.935853i
$933$		0			0
$934$	1.59222	+	2.75780i	0.0520989	+	0.0902379i
$935$	15.1963	−	26.3208i	0.496972	−	0.860781i
$936$		0			0
$937$	3.17154			0.103610			0.0518048	−	0.998657i	$-0.483503\pi$
$937$	3.17154			0.103610			0.0518048	+	0.998657i	$0.483503\pi$
$938$		0			0
$939$		0			0
$940$	6.69196	−	11.5908i	0.218268	−	0.378050i
$941$	3.22080			0.104995			0.0524976	−	0.998621i	$-0.483282\pi$
$941$	3.22080			0.104995			0.0524976	+	0.998621i	$0.483282\pi$
$942$		0			0
$943$	57.0495			1.85779
$944$	−9.52751			−0.310094
$945$		0			0
$946$	1.97095			0.0640810
$947$	45.3469			1.47358			0.736789	−	0.676123i	$-0.236341\pi$
$947$	45.3469			1.47358			0.736789	+	0.676123i	$0.236341\pi$
$948$		0			0
$949$	15.1488			0.491752
$950$	0.836931	−	1.44961i	0.0271536	−	0.0470315i
$951$		0			0
$952$		0			0
$953$	54.2703			1.75799			0.878994	−	0.476832i	$-0.158215\pi$
$953$	54.2703			1.75799			0.878994	+	0.476832i	$0.158215\pi$
$954$		0			0
$955$	−8.90451	+	15.4231i	−0.288143	+	0.499079i
$956$	−16.4029	−	28.4106i	−0.530507	−	0.918865i
$957$		0			0
$958$	1.73788	+	3.01010i	0.0561483	+	0.0972518i
$959$		0			0
$960$		0			0
$961$	−28.2438			−0.911089
$962$	1.14132	−	1.97682i	0.0367975	−	0.0637351i
$963$		0			0
$964$	26.3695	+	45.6733i	0.849304	+	1.47104i
$965$	−4.63788	+	8.03305i	−0.149299	+	0.258593i
$966$		0			0
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	0.582600	−	0.812759i	$-0.302036\pi$
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	−0.995170	+	0.0981667i	$0.968702\pi$
$968$	1.28100	−	2.21875i	0.0411728	−	0.0713133i
$969$		0			0
$970$	1.01298	+	1.75454i	0.0325250	+	0.0563349i
$971$	−10.5092	−	18.2024i	−0.337255	−	0.584143i	0.646660	−	0.762778i	$-0.276165\pi$
$971$	−10.5092	−	18.2024i	−0.337255	−	0.584143i	−0.983915	+	0.178635i	$0.942832\pi$
$972$		0			0
$973$		0			0
$974$	−1.56075	+	2.70329i	−0.0500096	+	0.0866191i
$975$		0			0
$976$	−27.8285			−0.890767
$977$	2.09820			0.0671273			0.0335637	−	0.999437i	$-0.489314\pi$
$977$	2.09820			0.0671273			0.0335637	+	0.999437i	$0.489314\pi$
$978$		0			0
$979$	5.08740	−	8.81164i	0.162594	−	0.281621i
$980$		0			0
$981$		0			0
$982$	2.31285	+	4.00598i	0.0738062	+	0.127836i
$983$	21.4962	+	37.2325i	0.685622	+	1.18753i	0.973241	+	0.229787i	$0.0738028\pi$
$983$	21.4962	+	37.2325i	0.685622	+	1.18753i	−0.287620	+	0.957745i	$0.592864\pi$
$984$		0			0
$985$	−3.95361	+	6.84786i	−0.125973	+	0.218191i
$986$	0.198495	+	0.343803i	0.00632137	+	0.0109489i
$987$		0			0
$988$	1.88727	−	3.26886i	0.0600422	−	0.103996i
$989$	−6.23461	−	10.7987i	−0.198249	−	0.343377i
$990$		0			0
$991$	8.63160	−	14.9504i	0.274192	−	0.474914i	−0.695739	−	0.718295i	$-0.744923\pi$
$991$	8.63160	−	14.9504i	0.274192	−	0.474914i	0.969931	+	0.243380i	$0.0782564\pi$
$992$	4.58358			0.145529
$993$		0			0
$994$		0			0
$995$	−11.7837	−	20.4100i	−0.373569	−	0.647040i
$996$		0			0
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	0.990205	+	0.139619i	$0.0445878\pi$
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	−0.374189	+	0.927352i	$0.622079\pi$
$998$	4.33078	−	7.50114i	0.137089	−	0.237444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.d.802.2		6
3.2	odd	2		441.2.h.c.214.2		6
7.2	even	3		1323.2.g.c.667.2		6
7.3	odd	6		1323.2.f.c.883.2		6
7.4	even	3		189.2.f.a.127.2		6
7.5	odd	6		1323.2.g.b.667.2		6
7.6	odd	2		1323.2.h.e.802.2		6
9.4	even	3		1323.2.g.c.361.2		6
9.5	odd	6		441.2.g.e.67.2		6
21.2	odd	6		441.2.g.e.79.2		6
21.5	even	6		441.2.g.d.79.2		6
21.11	odd	6		63.2.f.b.43.2	yes	6
21.17	even	6		441.2.f.d.295.2		6
21.20	even	2		441.2.h.b.214.2		6
28.11	odd	6		3024.2.r.g.2017.3		6
63.4	even	3		189.2.f.a.64.2		6
63.5	even	6		441.2.h.b.373.2		6
63.11	odd	6		567.2.a.d.1.2		3
63.13	odd	6		1323.2.g.b.361.2		6
63.23	odd	6		441.2.h.c.373.2		6
63.25	even	3		567.2.a.g.1.2		3
63.31	odd	6		1323.2.f.c.442.2		6
63.32	odd	6		63.2.f.b.22.2	✓	6
63.38	even	6		3969.2.a.m.1.2		3
63.40	odd	6		1323.2.h.e.226.2		6
63.41	even	6		441.2.g.d.67.2		6
63.52	odd	6		3969.2.a.p.1.2		3
63.58	even	3	inner	1323.2.h.d.226.2		6
63.59	even	6		441.2.f.d.148.2		6
84.11	even	6		1008.2.r.k.673.2		6
252.11	even	6		9072.2.a.bq.1.3		3
252.67	odd	6		3024.2.r.g.1009.3		6
252.95	even	6		1008.2.r.k.337.2		6
252.151	odd	6		9072.2.a.cd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	63.32	odd	6
63.2.f.b.43.2	yes	6	21.11	odd	6
189.2.f.a.64.2		6	63.4	even	3
189.2.f.a.127.2		6	7.4	even	3
441.2.f.d.148.2		6	63.59	even	6
441.2.f.d.295.2		6	21.17	even	6
441.2.g.d.67.2		6	63.41	even	6
441.2.g.d.79.2		6	21.5	even	6
441.2.g.e.67.2		6	9.5	odd	6
441.2.g.e.79.2		6	21.2	odd	6
441.2.h.b.214.2		6	21.20	even	2
441.2.h.b.373.2		6	63.5	even	6
441.2.h.c.214.2		6	3.2	odd	2
441.2.h.c.373.2		6	63.23	odd	6
567.2.a.d.1.2		3	63.11	odd	6
567.2.a.g.1.2		3	63.25	even	3
1008.2.r.k.337.2		6	252.95	even	6
1008.2.r.k.673.2		6	84.11	even	6
1323.2.f.c.442.2		6	63.31	odd	6
1323.2.f.c.883.2		6	7.3	odd	6
1323.2.g.b.361.2		6	63.13	odd	6
1323.2.g.b.667.2		6	7.5	odd	6
1323.2.g.c.361.2		6	9.4	even	3
1323.2.g.c.667.2		6	7.2	even	3
1323.2.h.d.226.2		6	63.58	even	3	inner
1323.2.h.d.802.2		6	1.1	even	1	trivial
1323.2.h.e.226.2		6	63.40	odd	6
1323.2.h.e.802.2		6	7.6	odd	2
3024.2.r.g.1009.3		6	252.67	odd	6
3024.2.r.g.2017.3		6	28.11	odd	6
3969.2.a.m.1.2		3	63.38	even	6
3969.2.a.p.1.2		3	63.52	odd	6
9072.2.a.bq.1.3		3	252.11	even	6
9072.2.a.cd.1.1		3	252.151	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)

\(f(q)\)	\(=\)	\(q+0.239123 q^{2} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +O(q^{10})\)	\(q+0.239123 q^{2} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +(0.141315 - 0.244765i) q^{10} +(-1.85185 - 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +3.66019 q^{16} +(-3.47141 + 6.01266i) q^{17} +(-0.971410 - 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(-2.80150 + 4.85235i) q^{23} +(1.80150 + 3.12030i) q^{25} +(-0.119562 - 0.207087i) q^{26} +(0.119562 - 0.207087i) q^{29} +1.66019 q^{31} +2.76088 q^{32} +(-0.830095 + 1.43777i) q^{34} +(4.77292 + 8.26693i) q^{37} +(-0.232287 - 0.402332i) q^{38} +(-0.557180 + 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(3.59781 + 6.23159i) q^{44} +(-0.669905 + 1.16031i) q^{46} -5.82846 q^{47} +(0.430782 + 0.746136i) q^{50} +(0.971410 + 1.68253i) q^{52} +(-5.80150 + 10.0485i) q^{53} -4.37756 q^{55} +(0.0285900 - 0.0495193i) q^{58} -2.60301 q^{59} -7.60301 q^{61} +0.396990 q^{62} -6.66019 q^{64} -1.18194 q^{65} +3.50808 q^{67} +(6.74433 - 11.6815i) q^{68} -8.60301 q^{71} +(-7.57442 + 13.1193i) q^{73} +(1.14132 + 1.97682i) q^{74} +(1.88727 + 3.26886i) q^{76} +7.37756 q^{79} +(2.16307 - 3.74654i) q^{80} +(-1.21737 - 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(-0.266078 + 0.460861i) q^{86} +(1.74596 + 3.02409i) q^{88} +(1.37360 + 2.37915i) q^{89} +(5.44282 - 9.42724i) q^{92} -1.39372 q^{94} -2.29630 q^{95} +(-3.58414 + 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8	\( 6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8} - 2 q^{11} - 3 q^{13} + 6 q^{16} - 12 q^{17} + 3 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} - q^{26} + q^{29} - 6 q^{31} + 16 q^{32} + 3 q^{34} + 3 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} + 18 q^{47} + 10 q^{50} - 3 q^{52} - 18 q^{53} - 12 q^{55} + 9 q^{58} + 18 q^{59} - 12 q^{61} + 36 q^{62} - 24 q^{64} + 10 q^{65} + 6 q^{68} - 18 q^{71} - 3 q^{73} + 6 q^{74} + 21 q^{76} + 30 q^{79} + 11 q^{80} - 9 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} - 2 q^{89} + 15 q^{92} + 48 q^{94} - 32 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8 - 2 * q^11 - 3 * q^13 + 6 * q^16 - 12 * q^17 + 3 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 - q^26 + q^29 - 6 * q^31 + 16 * q^32 + 3 * q^34 + 3 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 + 18 * q^47 + 10 * q^50 - 3 * q^52 - 18 * q^53 - 12 * q^55 + 9 * q^58 + 18 * q^59 - 12 * q^61 + 36 * q^62 - 24 * q^64 + 10 * q^65 + 6 * q^68 - 18 * q^71 - 3 * q^73 + 6 * q^74 + 21 * q^76 + 30 * q^79 + 11 * q^80 - 9 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 - 2 * q^89 + 15 * q^92 + 48 * q^94 - 32 * q^95 - 3 * q^97

Introduction

L-functions

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Varieties

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Database

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