LMFDB - Embedded newform 441.2.g.d.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (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:	$3.52140272914$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.d.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 - 0.207087i) q^{2} +(-1.71053 - 0.272169i) q^{3} +(0.971410 + 1.68253i) q^{4} -1.18194 q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 + 0.931107i) q^{9} +O(q^{10})$	\(q+(0.119562 - 0.207087i) q^{2} +(-1.71053 - 0.272169i) q^{3} +(0.971410 + 1.68253i) q^{4} -1.18194 q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 + 0.931107i) q^{9} +(-0.141315 + 0.244765i) q^{10} -3.70370 q^{11} +(-1.20370 - 3.14241i) q^{12} +(0.500000 - 0.866025i) q^{13} +(2.02175 + 0.321688i) q^{15} +(-1.83009 + 3.16982i) q^{16} +(-3.47141 + 6.01266i) q^{17} +(0.533792 - 0.479256i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-1.14815 - 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} -5.60301 q^{23} +(-1.61273 - 0.256606i) q^{24} -3.60301 q^{25} +(-0.119562 - 0.207087i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.119562 - 0.207087i) q^{29} +(0.308342 - 0.380217i) q^{30} +(0.830095 + 1.43777i) q^{31} +(1.38044 + 2.39099i) q^{32} +(6.33530 + 1.00803i) q^{33} +(0.830095 + 1.43777i) q^{34} +(1.20370 + 5.70281i) q^{36} +(4.77292 + 8.26693i) q^{37} +0.464574 q^{38} +(-1.09097 + 1.34528i) q^{39} -1.11436 q^{40} +(-5.09097 + 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +(-3.59781 - 6.23159i) q^{44} +(-3.37072 - 1.10052i) q^{45} +(-0.669905 + 1.16031i) q^{46} +(2.91423 - 5.04759i) q^{47} +(3.99316 - 4.92398i) q^{48} +(-0.430782 + 0.746136i) q^{50} +(7.57442 - 9.34004i) q^{51} +1.94282 q^{52} +(5.80150 - 10.0485i) q^{53} +(-1.04351 + 0.674501i) q^{54} +4.37756 q^{55} +(-1.20370 - 3.14241i) q^{57} -0.0571799 q^{58} +(1.30150 + 2.25427i) q^{59} +(1.42270 + 3.71415i) q^{60} +(-3.80150 + 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(-0.590972 + 1.02359i) q^{65} +(0.966208 - 1.19143i) q^{66} +(-1.75404 - 3.03809i) q^{67} -13.4887 q^{68} +(9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(2.68878 + 0.877867i) q^{72} +(7.57442 - 13.1193i) q^{73} +2.28263 q^{74} +(6.16307 + 0.980627i) q^{75} +(-1.88727 + 3.26886i) q^{76} +(0.148152 + 0.386770i) q^{78} +(-3.68878 + 6.38915i) q^{79} +(2.16307 - 3.74654i) q^{80} +(7.26608 + 5.31075i) q^{81} +(1.21737 + 2.10855i) q^{82} +(-3.47141 - 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} -0.532157 q^{86} +(0.148152 + 0.386770i) q^{87} -3.49192 q^{88} +(1.37360 + 2.37915i) q^{89} +(-0.630912 + 0.566453i) q^{90} +(-5.44282 - 9.42724i) q^{92} +(-1.02859 - 2.68527i) q^{93} +(-0.696860 - 1.20700i) q^{94} +(-1.14815 - 1.98866i) q^{95} +(-1.71053 - 4.46558i) q^{96} +(3.58414 + 6.20790i) q^{97} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + q^2 - 2 * q^3 - 3 * q^4 + 10 * q^5 - q^6 - 12 * q^8 + 8 * q^9	$ 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 11 q^{12} + 3 q^{13} + 11 q^{15} - 3 q^{16} - 12 q^{17} - 23 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 12 q^{25} - q^{26} + 7 q^{27} - q^{29} - 5 q^{30} - 3 q^{31} + 8 q^{32} - 5 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} - 16 q^{38} + 2 q^{39} - 42 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + 4 q^{45} - 12 q^{46} - 9 q^{47} + 14 q^{48} - 10 q^{50} + 3 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} + 12 q^{55} + 11 q^{57} - 18 q^{58} - 9 q^{59} + 37 q^{60} - 6 q^{61} + 36 q^{62} - 24 q^{64} + 5 q^{65} + 32 q^{66} - 12 q^{68} + 39 q^{69} + 18 q^{71} + 9 q^{72} + 3 q^{73} + 12 q^{74} + 35 q^{75} - 21 q^{76} + 10 q^{78} - 15 q^{79} + 11 q^{80} + 8 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} + 68 q^{86} + 10 q^{87} - 42 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 15 q^{93} + 24 q^{94} - 16 q^{95} - 2 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q + q^2 - 2 * q^3 - 3 * q^4 + 10 * q^5 - q^6 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 11 * q^12 + 3 * q^13 + 11 * q^15 - 3 * q^16 - 12 * q^17 - 23 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 12 * q^25 - q^26 + 7 * q^27 - q^29 - 5 * q^30 - 3 * q^31 + 8 * q^32 - 5 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 - 16 * q^38 + 2 * q^39 - 42 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + 4 * q^45 - 12 * q^46 - 9 * q^47 + 14 * q^48 - 10 * q^50 + 3 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 + 12 * q^55 + 11 * q^57 - 18 * q^58 - 9 * q^59 + 37 * q^60 - 6 * q^61 + 36 * q^62 - 24 * q^64 + 5 * q^65 + 32 * q^66 - 12 * q^68 + 39 * q^69 + 18 * q^71 + 9 * q^72 + 3 * q^73 + 12 * q^74 + 35 * q^75 - 21 * q^76 + 10 * q^78 - 15 * q^79 + 11 * q^80 + 8 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 + 68 * q^86 + 10 * q^87 - 42 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 15 * q^93 + 24 * q^94 - 16 * q^95 - 2 * q^96 + 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	−0.820653	−	0.571426i	$-0.806390\pi$
$2$	0.119562	−	0.207087i	0.0845428	−	0.146433i	0.905196	+	0.424994i	$0.139724\pi$
$3$	−1.71053	−	0.272169i	−0.987577	−	0.157137i
$3$	−1.71053	−	0.272169i	−0.987577	−	0.157137i
$4$	0.971410	+	1.68253i	0.485705	+	0.841266i
$5$	−1.18194			−0.528581			−0.264291	−	0.964443i	$-0.585138\pi$
$5$	−1.18194			−0.528581			−0.264291	+	0.964443i	$0.585138\pi$
$6$	−0.260877	+	0.321688i	−0.106502	+	0.131329i
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$	2.85185	+	0.931107i	0.950616	+	0.310369i
$10$	−0.141315	+	0.244765i	−0.0446878	+	0.0774015i
$11$	−3.70370			−1.11671			−0.558353	−	0.829603i	$-0.688567\pi$
$11$	−3.70370			−1.11671			−0.558353	+	0.829603i	$0.688567\pi$
$12$	−1.20370	−	3.14241i	−0.347477	−	0.907137i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	2.02175	+	0.321688i	0.522014	+	0.0830595i
$16$	−1.83009	+	3.16982i	−0.457524	+	0.792454i
$17$	−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	$0.848080\pi$
$18$	0.533792	−	0.479256i	0.125816	−	0.112962i
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	0.955674	−	0.294426i	$-0.0951285\pi$
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	−0.732818	+	0.680425i	$0.761795\pi$
$20$	−1.14815	−	1.98866i	−0.256735	−	0.444677i
$21$		0			0
$22$	−0.442820	+	0.766987i	−0.0944096	+	0.163522i
$23$	−5.60301			−1.16831			−0.584154	−	0.811643i	$-0.698574\pi$
$23$	−5.60301			−1.16831			−0.584154	+	0.811643i	$0.698574\pi$
$24$	−1.61273	−	0.256606i	−0.329196	−	0.0523795i
$25$	−3.60301			−0.720602
$26$	−0.119562	−	0.207087i	−0.0234480	−	0.0406131i
$27$	−4.62476	−	2.36887i	−0.890036	−	0.455890i
$28$		0			0
$29$	−0.119562	−	0.207087i	−0.0222020	−	0.0384551i	0.854711	−	0.519104i	$-0.173734\pi$
$29$	−0.119562	−	0.207087i	−0.0222020	−	0.0384551i	−0.876913	+	0.480649i	$0.840401\pi$
$30$	0.308342	−	0.380217i	0.0562952	−	0.0694178i
$31$	0.830095	+	1.43777i	0.149089	+	0.258231i	0.930891	−	0.365297i	$-0.119032\pi$
$31$	0.830095	+	1.43777i	0.149089	+	0.258231i	−0.781802	+	0.623527i	$0.785699\pi$
$32$	1.38044	+	2.39099i	0.244029	+	0.422671i
$33$	6.33530	+	1.00803i	1.10283	+	0.175476i
$34$	0.830095	+	1.43777i	0.142360	+	0.246575i
$35$		0			0
$36$	1.20370	+	5.70281i	0.200616	+	0.950469i
$37$	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	$0.546170\pi$
$38$	0.464574			0.0753638
$39$	−1.09097	+	1.34528i	−0.174695	+	0.215417i
$40$	−1.11436			−0.176196
$41$	−5.09097	+	8.81782i	−0.795076	+	1.37711i	0.127715	+	0.991811i	$0.459236\pi$
$41$	−5.09097	+	8.81782i	−0.795076	+	1.37711i	−0.922791	+	0.385301i	$0.874097\pi$
$42$		0			0
$43$	−1.11273	−	1.92730i	−0.169689	−	0.293910i	0.768622	−	0.639704i	$-0.220943\pi$
$43$	−1.11273	−	1.92730i	−0.169689	−	0.293910i	−0.938311	+	0.345794i	$0.887610\pi$
$44$	−3.59781	−	6.23159i	−0.542390	−	0.939447i
$45$	−3.37072	−	1.10052i	−0.502478	−	0.164055i
$46$	−0.669905	+	1.16031i	−0.0987721	+	0.171078i
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	−0.571344	−	0.820711i	$-0.693578\pi$
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	0.996428	+	0.0844432i	$0.0269112\pi$
$48$	3.99316	−	4.92398i	0.576364	−	0.710716i
$49$		0			0
$50$	−0.430782	+	0.746136i	−0.0609217	+	0.105520i
$51$	7.57442	−	9.34004i	1.06063	−	1.30787i
$52$	1.94282			0.269421
$53$	5.80150	−	10.0485i	0.796898	−	1.38027i	−0.124729	−	0.992191i	$-0.539806\pi$
$53$	5.80150	−	10.0485i	0.796898	−	1.38027i	0.921627	−	0.388077i	$-0.126861\pi$
$54$	−1.04351	+	0.674501i	−0.142003	+	0.0917880i
$55$	4.37756			0.590270
$56$		0			0
$57$	−1.20370	−	3.14241i	−0.159434	−	0.416223i
$58$	−0.0571799			−0.00750809
$59$	1.30150	+	2.25427i	0.169442	+	0.293481i	0.938224	−	0.346029i	$-0.112470\pi$
$59$	1.30150	+	2.25427i	0.169442	+	0.293481i	−0.768782	+	0.639511i	$0.779137\pi$
$60$	1.42270	+	3.71415i	0.183670	+	0.479495i
$61$	−3.80150	+	6.58440i	−0.486733	+	0.843046i	−0.999884	−	0.0152524i	$-0.995145\pi$
$61$	−3.80150	+	6.58440i	−0.486733	+	0.843046i	0.513151	+	0.858298i	$0.328478\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−0.590972	+	1.02359i	−0.0733010	+	0.126961i
$66$	0.966208	−	1.19143i	0.118932	−	0.146655i
$67$	−1.75404	−	3.03809i	−0.214290	−	0.371161i	0.738763	−	0.673966i	$-0.235410\pi$
$67$	−1.75404	−	3.03809i	−0.214290	−	0.371161i	−0.953053	+	0.302804i	$0.902077\pi$
$68$	−13.4887			−1.63574
$69$	9.58414	+	1.52496i	1.15379	+	0.183584i
$70$		0			0
$71$	8.60301			1.02099			0.510495	−	0.859881i	$-0.329462\pi$
$71$	8.60301			1.02099			0.510495	+	0.859881i	$0.329462\pi$
$72$	2.68878	+	0.877867i	0.316876	+	0.103458i
$73$	7.57442	−	13.1193i	0.886519	−	1.53550i	0.0425559	−	0.999094i	$-0.486450\pi$
$73$	7.57442	−	13.1193i	0.886519	−	1.53550i	0.843963	−	0.536402i	$-0.180217\pi$
$74$	2.28263			0.265350
$75$	6.16307	+	0.980627i	0.711650	+	0.113233i
$76$	−1.88727	+	3.26886i	−0.216485	+	0.374963i
$77$		0			0
$78$	0.148152	+	0.386770i	0.0167749	+	0.0437931i
$79$	−3.68878	+	6.38915i	−0.415020	+	0.718836i	−0.995431	−	0.0954881i	$-0.969559\pi$
$79$	−3.68878	+	6.38915i	−0.415020	+	0.718836i	0.580410	+	0.814324i	$0.302892\pi$
$80$	2.16307	−	3.74654i	0.241838	−	0.418876i
$81$	7.26608	+	5.31075i	0.807342	+	0.590084i
$82$	1.21737	+	2.10855i	0.134436	+	0.232850i
$83$	−3.47141	−	6.01266i	−0.381037	−	0.659975i	0.610174	−	0.792267i	$-0.291100\pi$
$83$	−3.47141	−	6.01266i	−0.381037	−	0.659975i	−0.991211	+	0.132292i	$0.957766\pi$
$84$		0			0
$85$	4.10301	−	7.10662i	0.445034	−	0.770821i
$86$	−0.532157			−0.0573840
$87$	0.148152	+	0.386770i	0.0158835	+	0.0414661i
$88$	−3.49192			−0.372240
$89$	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	$0.786822\pi$
$90$	−0.630912	+	0.566453i	−0.0665039	+	0.0597094i
$91$		0			0
$92$	−5.44282	−	9.42724i	−0.567453	−	0.982858i
$93$	−1.02859	−	2.68527i	−0.106660	−	0.278450i
$94$	−0.696860	−	1.20700i	−0.0718756	−	0.124492i
$95$	−1.14815	−	1.98866i	−0.117798	−	0.204032i
$96$	−1.71053	−	4.46558i	−0.174581	−	0.455766i
$97$	3.58414	+	6.20790i	0.363914	+	0.630317i	0.988601	−	0.150558i	$-0.0481069\pi$
$97$	3.58414	+	6.20790i	0.363914	+	0.630317i	−0.624687	+	0.780875i	$0.714774\pi$
$98$		0			0
$99$	−10.5624	−	3.44854i	−1.06156	−	0.346591i
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	12.7850			1.27215			0.636075	−	0.771627i	$-0.280557\pi$
$101$	12.7850			1.27215			0.636075	+	0.771627i	$0.280557\pi$
$102$	−1.02859	−	2.68527i	−0.101846	−	0.265882i
$103$	4.39699			0.433248			0.216624	−	0.976255i	$-0.430495\pi$
$103$	4.39699			0.433248			0.216624	+	0.976255i	$0.430495\pi$
$104$	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	$-0.935713\pi$
$107$	−6.86389	−	11.8886i	−0.663557	−	1.14931i	0.316117	−	0.948720i	$-0.397621\pi$
$108$	−0.506837	−	10.0825i	−0.0487704	−	0.970185i
$109$	−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	$0.185935\pi$
$110$	0.523388	−	0.906535i	0.0499031	−	0.0864347i
$111$	−5.91423	−	15.4399i	−0.561354	−	1.46549i
$112$		0			0
$113$	−6.08126	+	10.5330i	−0.572076	+	0.990866i	0.424276	+	0.905533i	$0.360529\pi$
$113$	−6.08126	+	10.5330i	−0.572076	+	0.990866i	−0.996353	+	0.0853326i	$0.972805\pi$
$114$	−0.794668	−	0.126442i	−0.0744275	−	0.0118424i
$115$	6.62244			0.617546
$116$	0.232287	−	0.402332i	0.0215673	−	0.0373556i
$117$	2.23229	−	2.00422i	0.206375	−	0.185290i
$118$	0.622440			0.0573003
$119$		0			0
$120$	1.90615	+	0.303294i	0.174007	+	0.0276868i
$121$	2.71737			0.247034
$122$	0.909028	+	1.57448i	0.0822996	+	0.142547i
$123$	11.1082	−	13.6976i	1.00159	−	1.23507i
$124$	−1.61273	+	2.79332i	−0.144827	+	0.250848i
$125$	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	$0.481067\pi$
$128$	−3.55718	+	6.16122i	−0.314413	+	0.544580i
$129$	1.37880	+	3.59955i	0.121397	+	0.316923i
$130$	0.141315	+	0.244765i	0.0123942	+	0.0214673i
$131$	4.96690			0.433960			0.216980	−	0.976176i	$-0.430379\pi$
$131$	4.96690			0.433960			0.216980	+	0.976176i	$0.430379\pi$
$132$	4.45813	+	11.6385i	0.388030	+	1.01301i
$133$		0			0
$134$	−0.838864			−0.0724668
$135$	5.46621	+	2.79987i	0.470456	+	0.240975i
$136$	−3.27292	+	5.66886i	−0.280650	+	0.486100i
$137$	−4.33981			−0.370775			−0.185387	−	0.982665i	$-0.559354\pi$
$137$	−4.33981			−0.370775			−0.185387	+	0.982665i	$0.559354\pi$
$138$	1.46169	−	1.80242i	0.124428	−	0.153432i
$139$	1.97141	−	3.41458i	0.167213	−	0.289621i	−0.770226	−	0.637771i	$-0.779857\pi$
$139$	1.97141	−	3.41458i	0.167213	−	0.289621i	0.937439	+	0.348150i	$0.113190\pi$
$140$		0			0
$141$	−6.35868	+	7.84092i	−0.535498	+	0.660324i
$142$	1.02859	−	1.78157i	0.0863174	−	0.149506i
$143$	−1.85185	+	3.20750i	−0.154859	+	0.268224i
$144$	−8.17059	+	7.33582i	−0.680883	+	0.611319i
$145$	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
$149$	11.1111			0.910256			0.455128	−	0.890426i	$-0.349594\pi$
$149$	11.1111			0.910256			0.455128	+	0.890426i	$0.349594\pi$
$150$	0.939941	−	1.15905i	0.0767459	−	0.0946356i
$151$	13.9234			1.13307			0.566535	−	0.824038i	$-0.308284\pi$
$151$	13.9234			1.13307			0.566535	+	0.824038i	$0.308284\pi$
$152$	0.915865	+	1.58632i	0.0742864	+	0.128668i
$153$	−15.4984	+	13.9149i	−1.25297	+	1.12496i
$154$		0			0
$155$	−0.981125	−	1.69936i	−0.0788059	−	0.136496i
$156$	−3.32326	−	0.528775i	−0.266074	−	0.0423359i
$157$	0.0285900	+	0.0495193i	0.00228173	+	0.00395207i	0.867164	−	0.498023i	$-0.165940\pi$
$157$	0.0285900	+	0.0495193i	0.00228173	+	0.00395207i	−0.864882	+	0.501975i	$0.832607\pi$
$158$	0.882073	+	1.52780i	0.0701740	+	0.121545i
$159$	−12.6586	+	15.6093i	−1.00389	+	1.23790i
$160$	−1.63160	−	2.82601i	−0.128989	−	0.223416i
$161$		0			0
$162$	1.96853	−	0.869747i	0.154662	−	0.0683338i
$163$	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	$0.814523\pi$
$164$	−19.7817			−1.54469
$165$	−7.48796	−	1.19143i	−0.582937	−	0.0927531i
$166$	−1.66019			−0.128856
$167$	−7.34213	+	12.7169i	−0.568151	+	0.984067i	0.428598	+	0.903496i	$0.359008\pi$
$167$	−7.34213	+	12.7169i	−0.568151	+	0.984067i	−0.996749	+	0.0805714i	$0.974325\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−0.981125	−	1.69936i	−0.0752489	−	0.130335i
$171$	1.20370	+	5.70281i	0.0920490	+	0.436105i
$172$	2.16182	−	3.74439i	0.164838	−	0.285507i
$173$	0.126398	−	0.218928i	0.00960987	−	0.0166448i	−0.861180	−	0.508299i	$-0.830274\pi$
$173$	0.126398	−	0.218928i	0.00960987	−	0.0166448i	0.870790	+	0.491655i	$0.163608\pi$
$174$	0.0978082	+	0.0155626i	0.00741482	+	0.00117980i
$175$		0			0
$176$	6.77812	−	11.7400i	0.510920	−	0.884939i
$177$	−1.61273	−	4.21024i	−0.121220	−	0.316461i
$178$	0.656920			0.0492383
$179$	−7.09617	+	12.2909i	−0.530393	+	0.918667i	0.468978	+	0.883210i	$0.344622\pi$
$179$	−7.09617	+	12.2909i	−0.530393	+	0.918667i	−0.999371	+	0.0354578i	$0.988711\pi$
$180$	−1.42270	−	6.74040i	−0.106042	−	0.502400i
$181$	1.43147			0.106400			0.0532002	−	0.998584i	$-0.483058\pi$
$181$	1.43147			0.106400			0.0532002	+	0.998584i	$0.483058\pi$
$182$		0			0
$183$	8.29467	−	10.2282i	0.613160	−	0.756089i
$184$	−5.28263			−0.389441
$185$	−5.64132	−	9.77104i	−0.414758	−	0.718381i
$186$	−0.679065	−	0.108048i	−0.0497914	−	0.00792248i
$187$	12.8571	−	22.2691i	0.940201	−	1.62848i
$188$	11.3236			0.825862
$189$		0			0
$190$	−0.549100			−0.0398359
$191$	−7.53379	+	13.0489i	−0.545126	+	0.944186i	0.453473	+	0.891270i	$0.350185\pi$
$191$	−7.53379	+	13.0489i	−0.545126	+	0.944186i	−0.998599	+	0.0529159i	$0.983148\pi$
$192$	11.3925	+	1.81270i	0.822181	+	0.130820i
$193$	3.92395	+	6.79647i	0.282452	+	0.489221i	0.971988	−	0.235030i	$-0.0755190\pi$
$193$	3.92395	+	6.79647i	0.282452	+	0.489221i	−0.689536	+	0.724251i	$0.742186\pi$
$194$	1.71410			0.123065
$195$	1.28947	−	1.59005i	0.0923406	−	0.113866i
$196$		0			0
$197$	6.69002			0.476644			0.238322	−	0.971186i	$-0.423403\pi$
$197$	6.69002			0.476644			0.238322	+	0.971186i	$0.423403\pi$
$198$	−1.97700	+	1.77502i	−0.140499	+	0.126145i
$199$	−9.96978	+	17.2682i	−0.706739	+	1.22411i	0.259322	+	0.965791i	$0.416501\pi$
$199$	−9.96978	+	17.2682i	−0.706739	+	1.22411i	−0.966060	+	0.258316i	$0.916832\pi$
$200$	−3.39699			−0.240203
$201$	2.17347	+	5.67414i	0.153305	+	0.400223i
$202$	1.52859	−	2.64760i	0.107551	−	0.186284i
$203$		0			0
$204$	23.0728	+	3.67119i	1.61542	+	0.257035i
$205$	6.01724	−	10.4222i	0.420262	−	0.727916i
$206$	0.525711	−	0.910559i	0.0366280	−	0.0634416i
$207$	−15.9789	−	5.21700i	−1.11061	−	0.362607i
$208$	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	−0.366233	−	0.930523i	$-0.619353\pi$
$211$	9.04583	−	15.6678i	0.622741	−	1.07862i	0.988973	−	0.148095i	$-0.0473141\pi$
$212$	22.5426			1.54823
$213$	−14.7157	−	2.34147i	−1.00831	−	0.160435i
$214$	−3.28263			−0.224396
$215$	1.31518	+	2.27796i	0.0896944	+	0.155355i
$216$	−4.36032	−	2.23342i	−0.296682	−	0.151965i
$217$		0			0
$218$	0.151030	+	0.261592i	0.0102291	+	0.0177172i
$219$	−16.5270	+	20.3794i	−1.11679	+	1.37712i
$220$	4.25241	+	7.36538i	0.286697	+	0.496574i
$221$	3.47141	+	6.01266i	0.233512	+	0.404455i
$222$	−3.90451	−	0.621261i	−0.262054	−	0.0416963i
$223$	−11.3285	−	19.6215i	−0.758610	−	1.31395i	−0.943560	−	0.331203i	$-0.892546\pi$
$223$	−11.3285	−	19.6215i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$224$		0			0
$225$	−10.2752	−	3.35479i	−0.685016	−	0.223653i
$226$	1.45417	+	2.51870i	0.0967299	+	0.167541i
$227$	5.28263			0.350620			0.175310	−	0.984513i	$-0.443907\pi$
$227$	5.28263			0.350620			0.175310	+	0.984513i	$0.443907\pi$
$228$	4.11793	−	5.07783i	0.272716	−	0.336287i
$229$	−19.3365			−1.27779			−0.638897	−	0.769292i	$-0.720609\pi$
$229$	−19.3365			−1.27779			−0.638897	+	0.769292i	$0.720609\pi$
$230$	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	$0.0210810\pi$
$233$	8.49028	+	14.7056i	0.556217	+	0.963396i	−0.441591	+	0.897217i	$0.645586\pi$
$234$	−0.148152	−	0.701905i	−0.00968497	−	0.0458850i
$235$	−3.44445	+	5.96597i	−0.224691	+	0.389177i
$236$	−2.52859	+	4.37965i	−0.164597	+	0.285091i
$237$	8.04871	−	9.92489i	0.522820	−	0.644691i
$238$		0			0
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	0.452415	+	0.891808i	$0.350563\pi$
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	−0.998535	+	0.0541011i	$0.982771\pi$
$240$	−4.71969	+	5.81987i	−0.304655	+	0.375671i
$241$	−27.1456			−1.74860			−0.874300	−	0.485386i	$-0.838679\pi$
$241$	−27.1456			−1.74860			−0.874300	+	0.485386i	$0.838679\pi$
$242$	0.324893	−	0.562732i	0.0208849	−	0.0361738i
$243$	−10.9834	−	11.0618i	−0.704589	−	0.709616i
$244$	−14.7713			−0.945634
$245$		0			0
$246$	−1.50847	−	3.93807i	−0.0961766	−	0.251082i
$247$	1.94282			0.123619
$248$	0.782630	+	1.35556i	0.0496971	+	0.0860778i
$249$	4.30150	+	11.2297i	0.272597	+	0.711651i
$250$	1.21574	−	2.10571i	0.0768898	−	0.133177i
$251$	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
$254$	0.160190	−	0.277457i	0.0100512	−	0.0174092i
$255$	−8.95254	+	11.0394i	−0.560630	+	0.691314i
$256$	−5.80959	−	10.0625i	−0.363099	−	0.628906i
$257$	14.8421			0.925827			0.462913	−	0.886404i	$-0.346804\pi$
$257$	14.8421			0.925827			0.462913	+	0.886404i	$0.346804\pi$
$258$	0.910272	+	0.144836i	0.0566711	+	0.00901712i
$259$		0			0
$260$	−2.29630			−0.142411
$261$	−0.148152	−	0.701905i	−0.00917035	−	0.0434468i
$262$	0.593850	−	1.02858i	0.0366882	−	0.0635458i
$263$	−7.74145			−0.477358			−0.238679	−	0.971099i	$-0.576714\pi$
$263$	−7.74145			−0.477358			−0.238679	+	0.971099i	$0.576714\pi$
$264$	5.97304	+	0.950391i	0.367615	+	0.0584925i
$265$	−6.85705	+	11.8768i	−0.421225	+	0.729584i
$266$		0			0
$267$	−1.70206	−	4.44346i	−0.104165	−	0.271936i
$268$	3.40778	−	5.90246i	0.208164	−	0.360550i
$269$	−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	$0.181338\pi$
$270$	1.23337	−	0.797222i	0.0750603	−	0.0485174i
$271$	−10.9903	−	19.0357i	−0.667612	−	1.15634i	−0.978570	−	0.205915i	$-0.933983\pi$
$271$	−10.9903	−	19.0357i	−0.667612	−	1.15634i	0.310958	−	0.950424i	$-0.399350\pi$
$272$	−12.7060	−	22.0075i	−0.770416	−	1.33440i
$273$		0			0
$274$	−0.518875	+	0.898718i	−0.0313464	+	0.0542935i
$275$	13.3445			0.804701
$276$	6.74433	+	17.6070i	0.405961	+	1.05982i
$277$	−10.8285			−0.650619			−0.325310	−	0.945608i	$-0.605469\pi$
$277$	−10.8285			−0.650619			−0.325310	+	0.945608i	$0.605469\pi$
$278$	−0.471410	−	0.816506i	−0.0282733	−	0.0489708i
$279$	1.02859	+	4.87320i	0.0615801	+	0.291751i
$280$		0			0
$281$	8.43831	+	14.6156i	0.503387	+	0.871892i	0.999992	+	0.00391559i	$0.00124638\pi$
$281$	8.43831	+	14.6156i	0.503387	+	0.871892i	−0.496605	+	0.867977i	$0.665420\pi$
$282$	0.863496	+	2.25427i	0.0514204	+	0.134240i
$283$	−7.65856	−	13.2650i	−0.455254	−	0.788523i	0.543449	−	0.839442i	$-0.317118\pi$
$283$	−7.65856	−	13.2650i	−0.455254	−	0.788523i	−0.998703	+	0.0509194i	$0.983785\pi$
$284$	8.35705	+	14.4748i	0.495900	+	0.858923i
$285$	1.42270	+	3.71415i	0.0842736	+	0.220008i
$286$	0.442820	+	0.766987i	0.0261845	+	0.0453529i
$287$		0			0
$288$	1.71053	+	8.10408i	0.100794	+	0.477537i
$289$	−15.6014	−	27.0224i	−0.917728	−	1.58955i
$290$	0.0675835			0.00396864
$291$	−4.44119	−	11.5943i	−0.260347	−	0.679671i
$292$	29.4315			1.72235
$293$	−4.68482	+	8.11435i	−0.273690	+	0.474045i	−0.969804	−	0.243886i	$-0.921578\pi$
$293$	−4.68482	+	8.11435i	−0.273690	+	0.474045i	0.696114	+	0.717932i	$0.254911\pi$
$294$		0			0
$295$	−1.53831	−	2.66442i	−0.0895636	−	0.155129i
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$	17.1287	+	8.77359i	0.993909	+	0.509095i
$298$	1.32846	−	2.30096i	0.0769556	−	0.133291i
$299$	−2.80150	+	4.85235i	−0.162015	+	0.280619i
$300$	4.33693	+	11.3221i	0.250393	+	0.653684i
$301$		0			0
$302$	1.66470	−	2.88335i	0.0957929	−	0.165918i
$303$	−21.8691	−	3.47966i	−1.25635	−	0.199901i
$304$	−7.11109			−0.407849
$305$	4.49316	−	7.78239i	0.257278	−	0.445618i
$306$	1.02859	+	4.87320i	0.0588006	+	0.278582i
$307$	−2.71410			−0.154902			−0.0774509	−	0.996996i	$-0.524678\pi$
$307$	−2.71410			−0.154902			−0.0774509	+	0.996996i	$0.524678\pi$
$308$		0			0
$309$	−7.52120	−	1.19672i	−0.427866	−	0.0680792i
$310$	−0.469220			−0.0266499
$311$	−6.99028	−	12.1075i	−0.396383	−	0.686555i	0.596894	−	0.802320i	$-0.296401\pi$
$311$	−6.99028	−	12.1075i	−0.396383	−	0.686555i	−0.993277	+	0.115765i	$0.963068\pi$
$312$	−1.02859	+	1.26836i	−0.0582324	+	0.0718066i
$313$	−9.52696	+	16.5012i	−0.538495	+	0.932701i	0.460490	+	0.887665i	$0.347674\pi$
$313$	−9.52696	+	16.5012i	−0.538495	+	0.932701i	−0.998985	+	0.0450364i	$0.985660\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	2.00972	−	3.48093i	0.112877	−	0.195508i	−0.804052	−	0.594559i	$-0.797327\pi$
$317$	2.00972	−	3.48093i	0.112877	−	0.195508i	0.916929	+	0.399050i	$0.130660\pi$
$318$	1.71900	+	4.48769i	0.0963970	+	0.251657i
$319$	0.442820	+	0.766987i	0.0247932	+	0.0429430i
$320$	7.87197			0.440056
$321$	8.50520	+	22.2040i	0.474714	+	1.23931i
$322$		0			0
$323$	−13.4887			−0.750529
$324$	−1.87717	+	17.3843i	−0.104287	+	0.965796i
$325$	−1.80150	+	3.12030i	−0.0999295	+	0.173083i
$326$	0.360617			0.0199727
$327$	1.37812	−	1.69936i	0.0762099	−	0.0939747i
$328$	−4.79987	+	8.31362i	−0.265028	+	0.459043i
$329$		0			0
$330$	−1.14200	+	1.40821i	−0.0628652	+	0.0775193i
$331$	6.18878	−	10.7193i	0.340166	−	0.589185i	−0.644297	−	0.764775i	$-0.722850\pi$
$331$	6.18878	−	10.7193i	0.340166	−	0.589185i	0.984463	+	0.175590i	$0.0561834\pi$
$332$	6.74433	−	11.6815i	0.370143	−	0.641106i
$333$	5.91423	+	28.0201i	0.324098	+	1.53549i
$334$	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	−0.983277	−	0.182117i	$-0.941705\pi$
$337$	−6.12997	+	10.6174i	−0.333920	+	0.578367i	0.649356	+	0.760484i	$0.275038\pi$
$338$	2.86948			0.156079
$339$	13.2690	−	16.3620i	0.720671	−	0.888662i
$340$	15.9428			0.864621
$341$	−3.07442	−	5.32505i	−0.166489	−	0.288368i
$342$	1.32489	+	0.432568i	0.0716420	+	0.0233906i
$343$		0			0
$344$	−1.04910	−	1.81709i	−0.0565637	−	0.0979711i
$345$	−11.3279	−	1.80242i	−0.609874	−	0.0970391i
$346$	−0.0302247	−	0.0523508i	−0.00162489	−	0.00281440i
$347$	−3.32489	−	5.75888i	−0.178490	−	0.309153i	0.762874	−	0.646547i	$-0.223788\pi$
$347$	−3.32489	−	5.75888i	−0.178490	−	0.309153i	−0.941363	+	0.337394i	$0.890454\pi$
$348$	−0.506837	+	0.624982i	−0.0271693	+	0.0335025i
$349$	5.71737	+	9.90278i	0.306044	+	0.530083i	0.977493	−	0.210967i	$-0.0676613\pi$
$349$	5.71737	+	9.90278i	0.306044	+	0.530083i	−0.671449	+	0.741050i	$0.734328\pi$
$350$		0			0
$351$	−4.36389	+	2.82073i	−0.232927	+	0.150559i
$352$	−5.11273	−	8.85550i	−0.272509	−	0.472000i
$353$	22.1956			1.18135			0.590677	−	0.806908i	$-0.298861\pi$
$353$	22.1956			1.18135			0.590677	+	0.806908i	$0.298861\pi$
$354$	−1.06470	−	0.169409i	−0.0565884	−	0.00900397i
$355$	−10.1683			−0.539676
$356$	−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	0.948334	−	0.317272i	$-0.102767\pi$
$359$	3.77812	+	6.54389i	0.199401	+	0.345373i	−0.748933	+	0.662646i	$0.769434\pi$
$360$	−3.17799	−	1.03759i	−0.167495	−	0.0546857i
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	0.171149	−	0.296439i	0.00899539	−	0.0155805i
$363$	−4.64815	−	0.739583i	−0.243965	−	0.0388180i
$364$		0			0
$365$	−8.95254	+	15.5062i	−0.468597	+	0.811634i
$366$	−1.12640	−	2.94062i	−0.0588778	−	0.153708i
$367$	18.5231			0.966900			0.483450	−	0.875372i	$-0.339384\pi$
$367$	18.5231			0.966900			0.483450	+	0.875372i	$0.339384\pi$
$368$	10.2540	−	17.7605i	0.534529	−	0.925831i
$369$	−22.7290	+	20.4068i	−1.18323	+	1.06234i
$370$	−2.69794			−0.140259
$371$		0			0
$372$	3.51887	−	4.33914i	0.182445	−	0.224974i
$373$	15.6602			0.810854			0.405427	−	0.914127i	$-0.367123\pi$
$373$	15.6602			0.810854			0.405427	+	0.914127i	$0.367123\pi$
$374$	−3.07442	−	5.32505i	−0.158974	−	0.275352i
$375$	−17.3932	−	2.76748i	−0.898179	−	0.142912i
$376$	2.74759	−	4.75897i	0.141696	−	0.245425i
$377$	−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	$0.466931\pi$
$380$	2.23065	−	3.86360i	0.114430	−	0.198199i
$381$	−2.29179	−	0.364654i	−0.117412	−	0.0186818i
$382$	1.80150	+	3.12030i	0.0921730	+	0.159648i
$383$	−0.225450			−0.0115200			−0.00575998	−	0.999983i	$-0.501833\pi$
$383$	−0.225450			−0.0115200			−0.00575998	+	0.999983i	$0.501833\pi$
$384$	7.76157	−	9.57081i	0.396081	−	0.488408i
$385$		0			0
$386$	1.87661			0.0955171
$387$	−1.37880	−	6.53242i	−0.0700885	−	0.332062i
$388$	−6.96333	+	12.0608i	−0.353510	+	0.612296i
$389$	25.2632			1.28090			0.640448	−	0.768002i	$-0.278749\pi$
$389$	25.2632			1.28090			0.640448	+	0.768002i	$0.278749\pi$
$390$	−0.175107	−	0.457140i	−0.00886688	−	0.0231482i
$391$	19.4503	−	33.6890i	0.983646	−	1.70373i
$392$		0			0
$393$	−8.49604	−	1.35183i	−0.428569	−	0.0681910i
$394$	0.799870	−	1.38542i	0.0402969	−	0.0697962i
$395$	4.35993	−	7.55162i	0.219372	−	0.379963i
$396$	−4.45813	−	21.1215i	−0.224029	−	1.06139i
$397$	−10.1505	−	17.5811i	−0.509438	−	0.882372i	−0.999940	−	0.0109322i	$-0.996520\pi$
$397$	−10.1505	−	17.5811i	−0.509438	−	0.882372i	0.490503	−	0.871440i	$-0.336813\pi$
$398$	2.38401	+	4.12922i	0.119499	+	0.206979i
$399$		0			0
$400$	6.59385	−	11.4209i	0.329693	−	0.571044i
$401$	−15.2255			−0.760323			−0.380161	−	0.924920i	$-0.624132\pi$
$401$	−15.2255			−0.760323			−0.380161	+	0.924920i	$0.624132\pi$
$402$	1.43490	+	0.228312i	0.0715665	+	0.0113872i
$403$	1.66019			0.0826999
$404$	12.4194	+	21.5111i	0.617890	+	1.07022i
$405$	−8.58809	−	6.27701i	−0.426746	−	0.311907i
$406$		0			0
$407$	−17.6774	−	30.6182i	−0.876238	−	1.51769i
$408$	7.14132	−	8.80598i	0.353548	−	0.435961i
$409$	0.828460	+	1.43494i	0.0409647	+	0.0709530i	0.885781	−	0.464104i	$-0.153624\pi$
$409$	0.828460	+	1.43494i	0.0409647	+	0.0709530i	−0.844816	+	0.535057i	$0.820290\pi$
$410$	−1.43886	−	2.49218i	−0.0710603	−	0.123080i
$411$	7.42339	+	1.18116i	0.366169	+	0.0582624i
$412$	4.27128	+	7.39807i	0.210431	+	0.364477i
$413$		0			0
$414$	−2.99084	+	2.68527i	−0.146992	+	0.131974i
$415$	4.10301	+	7.10662i	0.201409	+	0.348850i
$416$	2.76088			0.135363
$417$	−4.30150	+	5.30420i	−0.210646	+	0.259748i
$418$	−1.72064			−0.0841592
$419$	16.6871	−	28.9030i	0.815220	−	1.41200i	−0.0939492	−	0.995577i	$-0.529949\pi$
$419$	16.6871	−	28.9030i	0.815220	−	1.41200i	0.909170	−	0.416426i	$-0.136718\pi$
$420$		0			0
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	0.553523	−	0.832834i	$-0.313283\pi$
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	−0.998017	+	0.0629481i	$0.979950\pi$
$422$	−2.16307	−	3.74654i	−0.105297	−	0.182379i
$423$	13.0108	−	11.6815i	0.632606	−	0.567975i
$424$	5.46978	−	9.47393i	0.265636	−	0.460095i
$425$	12.5075	−	21.6637i	0.606704	−	1.05084i
$426$	−2.24433	+	2.76748i	−0.108738	+	0.134085i
$427$		0			0
$428$	13.3353	−	23.0974i	0.644586	−	1.11646i
$429$	4.04063	−	4.98251i	0.195083	−	0.240558i
$430$	0.628979			0.0303321
$431$	−14.6413	+	25.3595i	−0.705247	+	1.22152i	0.261355	+	0.965243i	$0.415831\pi$
$431$	−14.6413	+	25.3595i	−0.705247	+	1.22152i	−0.966602	+	0.256281i	$0.917503\pi$
$432$	15.9727	−	10.3244i	0.768485	−	0.496733i
$433$	12.2449			0.588451			0.294226	−	0.955736i	$-0.404938\pi$
$433$	12.2449			0.588451			0.294226	+	0.955736i	$0.404938\pi$
$434$		0			0
$435$	−0.175107	−	0.457140i	−0.00839573	−	0.0219182i
$436$	−2.45417			−0.117533
$437$	−5.44282	−	9.42724i	−0.260365	−	0.450966i
$438$	2.24433	+	5.85911i	0.107238	+	0.279959i
$439$	−2.41586	+	4.18440i	−0.115303	+	0.199711i	−0.917901	−	0.396810i	$-0.870117\pi$
$439$	−2.41586	+	4.18440i	−0.115303	+	0.199711i	0.802598	+	0.596520i	$0.203451\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	−0.622440	+	1.07810i	−0.0295730	+	0.0512220i	−0.880433	−	0.474170i	$-0.842748\pi$
$443$	−0.622440	+	1.07810i	−0.0295730	+	0.0512220i	0.850860	+	0.525392i	$0.176081\pi$
$444$	20.2330	−	24.9494i	0.960215	−	1.18404i
$445$	−1.62352	−	2.81202i	−0.0769622	−	0.133302i
$446$	−5.41780			−0.256540
$447$	−19.0059	−	3.02409i	−0.898948	−	0.143035i
$448$		0			0
$449$	8.82846			0.416641			0.208320	−	0.978061i	$-0.433200\pi$
$449$	8.82846			0.416641			0.208320	+	0.978061i	$0.433200\pi$
$450$	−1.92326	+	1.72676i	−0.0906632	+	0.0814004i
$451$	18.8554	−	32.6585i	0.887867	−	1.53783i
$452$	−23.6296			−1.11144
$453$	−23.8164	−	3.78951i	−1.11899	−	0.178047i
$454$	0.631600	−	1.09396i	0.0296425	−	0.0513422i
$455$		0			0
$456$	−1.13487	−	2.96273i	−0.0531451	−	0.138743i
$457$	5.25404	−	9.10026i	0.245774	−	0.425692i	−0.716575	−	0.697510i	$-0.754291\pi$
$457$	5.25404	−	9.10026i	0.245774	−	0.425692i	0.962349	+	0.271817i	$0.0876247\pi$
$458$	−2.31191	+	4.00434i	−0.108028	+	0.187111i
$459$	30.2977	−	19.5838i	1.41417	−	0.914093i
$460$	6.43310	+	11.1425i	0.299945	+	0.519520i
$461$	11.2758	+	19.5302i	0.525166	+	0.909614i	0.999570	+	0.0293073i	$0.00933013\pi$
$461$	11.2758	+	19.5302i	0.525166	+	0.909614i	−0.474404	+	0.880307i	$0.657337\pi$
$462$		0			0
$463$	−5.19850	+	9.00406i	−0.241595	+	0.418454i	−0.961169	−	0.275962i	$-0.911004\pi$
$463$	−5.19850	+	9.00406i	−0.241595	+	0.418454i	0.719574	+	0.694416i	$0.244337\pi$
$464$	0.875237			0.0406318
$465$	1.21574	+	3.17384i	0.0563784	+	0.147183i
$466$	4.06045			0.188097
$467$	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	$0.733633\pi$
$468$	5.54063	+	1.80897i	0.256116	+	0.0836198i
$469$		0			0
$470$	0.823649	+	1.42660i	0.0379921	+	0.0658043i
$471$	−0.0354265	−	0.0924857i	−0.00163237	−	0.00426152i
$472$	1.22708	+	2.12537i	0.0564812	+	0.0978282i
$473$	4.12120	+	7.13812i	0.189493	+	0.328211i
$474$	−1.09300	−	2.85342i	−0.0502030	−	0.131062i
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	25.9012	−	23.2550i	1.18594	−	1.06477i
$478$	2.01887	+	3.49679i	0.0923412	+	0.159940i
$479$	−14.5354			−0.664141			−0.332070	−	0.943255i	$-0.607747\pi$
$479$	−14.5354			−0.664141			−0.332070	+	0.943255i	$0.607747\pi$
$480$	2.02175	+	5.27806i	0.0922800	+	0.240909i
$481$	9.54583			0.435252
$482$	−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
$486$	−3.60396	+	0.951958i	−0.163479	+	0.0431817i
$487$	−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	$0.262241\pi$
$488$	−3.58414	+	6.20790i	−0.162246	+	0.281019i
$489$	−0.934349	−	2.43924i	−0.0422527	−	0.110306i
$490$		0			0
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	−0.997417	−	0.0718303i	$-0.977116\pi$
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	0.560915	+	0.827873i	$0.310449\pi$
$492$	33.8372	+	5.38396i	1.52550	+	0.242727i
$493$	1.66019			0.0747712
$494$	0.232287	−	0.402332i	0.0104511	−	0.0181018i
$495$	12.4841	+	4.07598i	0.561120	+	0.183202i
$496$	−6.07661			−0.272848
$497$		0			0
$498$	2.83981	+	0.451852i	0.127255	+	0.0202480i
$499$	−36.2222			−1.62153			−0.810764	−	0.585374i	$-0.800948\pi$
$499$	−36.2222			−1.62153			−0.810764	+	0.585374i	$0.800948\pi$
$500$	9.87756	+	17.1084i	0.441738	+	0.765112i
$501$	16.0201	−	19.7545i	0.715726	−	0.882564i
$502$	2.28100	−	3.95080i	0.101806	−	0.176333i
$503$	−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
$506$	2.48113	−	4.29743i	0.110299	−	0.191044i
$507$	−7.43474	−	19.4094i	−0.330188	−	0.862002i
$508$	1.30150	+	2.25427i	0.0577449	+	0.100017i
$509$	−34.3034			−1.52047			−0.760237	−	0.649646i	$-0.774917\pi$
$509$	−34.3034			−1.52047			−0.760237	+	0.649646i	$0.774917\pi$
$510$	1.21574	+	3.17384i	0.0538337	+	0.140540i
$511$		0			0
$512$	−17.0071			−0.751616
$513$	−0.506837	−	10.0825i	−0.0223774	−	0.445151i
$514$	1.77455	−	3.07361i	0.0782720	−	0.135571i
$515$	−5.19699			−0.229007
$516$	−4.71698	+	5.81652i	−0.207653	+	0.256058i
$517$	−10.7934	+	18.6948i	−0.474694	+	0.822195i
$518$		0			0
$519$	−0.275794	+	0.340082i	−0.0121060	+	0.0149279i
$520$	−0.557180	+	0.965064i	−0.0244340	+	0.0423209i
$521$	−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	$0.238715\pi$
$522$	−0.163069	−	0.0532407i	−0.00713732	−	0.00233028i
$523$	15.3015	+	26.5030i	0.669088	+	1.15889i	0.978159	+	0.207856i	$0.0666485\pi$
$523$	15.3015	+	26.5030i	0.669088	+	1.15889i	−0.309071	+	0.951039i	$0.600018\pi$
$524$	4.82489	+	8.35696i	0.210776	+	0.365075i
$525$		0			0
$526$	−0.925580	+	1.60315i	−0.0403572	+	0.0699007i
$527$	−11.5264			−0.502098
$528$	−14.7895	+	18.2369i	−0.643629	+	0.793661i
$529$	8.39372			0.364944
$530$	1.63968	+	2.84001i	0.0712232	+	0.123362i
$531$	1.61273	+	7.64068i	0.0699863	+	0.331577i
$532$		0			0
$533$	5.09097	+	8.81782i	0.220514	+	0.381942i
$534$	−1.12368	−	0.178793i	−0.0486266	−	0.00773714i
$535$	8.11273	+	14.0517i	0.350744	+	0.607506i
$536$	−1.65374	−	2.86437i	−0.0714309	−	0.123722i
$537$	15.4834	−	19.0927i	0.668160	−	0.823911i
$538$	0.180699	+	0.312981i	0.00779051	+	0.0134936i
$539$		0			0
$540$	0.599052	+	11.9169i	0.0257791	+	0.512821i
$541$	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	$0.643795\pi$
$542$	−5.25607			−0.225767
$543$	−2.44858	−	0.389601i	−0.105079	−	0.0167194i
$544$	−19.1683			−0.821833
$545$	0.746515	−	1.29300i	0.0319772	−	0.0553861i
$546$		0			0
$547$	5.46169	+	9.45993i	0.233525	+	0.404478i	0.958843	−	0.283937i	$-0.0916405\pi$
$547$	5.46169	+	9.45993i	0.233525	+	0.404478i	−0.725318	+	0.688414i	$0.758307\pi$
$548$	−4.21574	−	7.30187i	−0.180087	−	0.311920i
$549$	−16.9721	+	15.2381i	−0.724352	+	0.650346i
$550$	1.59549	−	2.76346i	0.0680317	−	0.117834i
$551$	0.232287	−	0.402332i	0.00989575	−	0.0171399i
$552$	9.03611	+	1.43777i	0.384603	+	0.0611954i
$553$		0			0
$554$	−1.29467	+	2.24243i	−0.0550052	+	0.0952718i
$555$	6.99028	+	18.2491i	0.296721	+	0.774631i
$556$	7.66019			0.324864
$557$	6.97210	−	12.0760i	0.295417	−	0.511678i	−0.679665	−	0.733523i	$-0.737875\pi$
$557$	6.97210	−	12.0760i	0.295417	−	0.511678i	0.975082	+	0.221845i	$0.0712080\pi$
$558$	1.13216	+	0.369640i	0.0479280	+	0.0156481i
$559$	−2.22545			−0.0941265
$560$		0			0
$561$	−28.0534	+	34.5927i	−1.18441	+	1.46050i
$562$	4.03559			0.170231
$563$	15.1287	+	26.2037i	0.637600	+	1.10435i	0.985958	+	0.166993i	$0.0534059\pi$
$563$	15.1287	+	26.2037i	0.637600	+	1.10435i	−0.348358	+	0.937361i	$0.613261\pi$
$564$	−19.3695	−	3.08194i	−0.815602	−	0.129773i
$565$	7.18770	−	12.4495i	0.302389	−	0.523753i
$566$	−3.66268			−0.153954
$567$		0			0
$568$	8.11109			0.340334
$569$	10.5676	−	18.3036i	0.443016	−	0.767326i	−0.554896	−	0.831920i	$-0.687242\pi$
$569$	10.5676	−	18.3036i	0.443016	−	0.767326i	0.997912	+	0.0645936i	$0.0205751\pi$
$570$	0.939253	+	0.149448i	0.0393410	+	0.00625968i
$571$	16.3932	+	28.3938i	0.686033	+	1.18824i	0.973111	+	0.230336i	$0.0739826\pi$
$571$	16.3932	+	28.3938i	0.686033	+	1.18824i	−0.287078	+	0.957907i	$0.592684\pi$
$572$	−7.19562			−0.300864
$573$	16.4383	−	20.2701i	0.686720	−	0.846797i
$574$		0			0
$575$	20.1877			0.841885
$576$	−18.9939	−	6.20135i	−0.791410	−	0.258390i
$577$	−8.68715	+	15.0466i	−0.361651	+	0.626397i	−0.988233	−	0.152958i	$-0.951120\pi$
$577$	−8.68715	+	15.0466i	−0.361651	+	0.626397i	0.626582	+	0.779355i	$0.284453\pi$
$578$	−7.46130			−0.310349
$579$	−4.86225	−	12.6936i	−0.202068	−	0.527527i
$580$	−0.274550	+	0.475534i	−0.0114001	+	0.0197455i
$581$		0			0
$582$	−2.93203	−	0.466524i	−0.121536	−	0.0193381i
$583$	−21.4870	+	37.2166i	−0.889901	+	1.54135i
$584$	7.14132	−	12.3691i	0.295510	−	0.511838i
$585$	−2.63844	+	2.36887i	−0.109086	+	0.0979409i
$586$	1.12025	+	1.94033i	0.0462771	+	0.0801543i
$587$	8.48796	+	14.7016i	0.350336	+	0.606799i	0.986308	−	0.164913i	$-0.0527342\pi$
$587$	8.48796	+	14.7016i	0.350336	+	0.606799i	−0.635973	+	0.771712i	$0.719401\pi$
$588$		0			0
$589$	−1.61273	+	2.79332i	−0.0664512	+	0.115097i
$590$	−0.735689			−0.0302878
$591$	−11.4435	−	1.82082i	−0.470723	−	0.0748983i
$592$	−34.9396			−1.43601
$593$	−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	$0.919838\pi$
$594$	3.86483	−	2.49815i	0.158576	−	0.102500i
$595$		0			0
$596$	10.7934	+	18.6948i	0.442116	+	0.765767i
$597$	21.7535	−	26.8243i	0.890311	−	1.09785i
$598$	0.669905	+	1.16031i	0.0273945	+	0.0474486i
$599$	−14.6030	−	25.2932i	−0.596663	−	1.03345i	−0.993310	−	0.115479i	$-0.963160\pi$
$599$	−14.6030	−	25.2932i	−0.596663	−	1.03345i	0.396647	−	0.917971i	$-0.370174\pi$
$600$	5.81066	+	0.924554i	0.237219	+	0.0377448i
$601$	3.89536	+	6.74695i	0.158895	+	0.275214i	0.934470	−	0.356041i	$-0.115874\pi$
$601$	3.89536	+	6.74695i	0.158895	+	0.275214i	−0.775576	+	0.631255i	$0.782540\pi$
$602$		0			0
$603$	−2.17347	−	10.2974i	−0.0885106	−	0.419341i
$604$	13.5253	+	23.4265i	0.550337	+	0.953212i
$605$	−3.21178			−0.130577
$606$	−3.33530	+	4.11277i	−0.135487	+	0.167070i
$607$	19.6408			0.797194			0.398597	−	0.917126i	$-0.369497\pi$
$607$	19.6408			0.797194			0.398597	+	0.917126i	$0.369497\pi$
$608$	−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
$612$	−38.4676	−	12.5594i	−1.55496	−	0.507683i
$613$	−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	$0.324543\pi$
$614$	−0.324502	+	0.562054i	−0.0130958	+	0.0226827i
$615$	−13.1293	+	16.1898i	−0.529424	+	0.652834i
$616$		0			0
$617$	5.33009	−	9.23200i	0.214582	−	0.371666i	−0.738562	−	0.674186i	$-0.764495\pi$
$617$	5.33009	−	9.23200i	0.214582	−	0.371666i	0.953143	+	0.302520i	$0.0978279\pi$
$618$	−1.14707	+	1.41446i	−0.0461420	+	0.0568979i
$619$	18.0150			0.724086			0.362043	−	0.932161i	$-0.382079\pi$
$619$	18.0150			0.724086			0.362043	+	0.932161i	$0.382079\pi$
$620$	1.90615	−	3.30155i	0.0765528	−	0.132593i
$621$	25.9126	+	13.2728i	1.03984	+	0.532620i
$622$	−3.34308			−0.134045
$623$		0			0
$624$	−2.26771	−	5.92017i	−0.0907812	−	0.236997i
$625$	5.99673			0.239869
$626$	2.27812	+	3.94581i	0.0910519	+	0.157706i
$627$	4.45813	+	11.6385i	0.178040	+	0.464799i
$628$	−0.0555452	+	0.0962071i	−0.00221649	+	0.00383908i
$629$	−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	$0.420155\pi$
$632$	−3.47786	+	6.02382i	−0.138342	+	0.239615i
$633$	−19.7375	+	24.3384i	−0.784495	+	0.967363i
$634$	−0.480570	−	0.832371i	−0.0190859	−	0.0330577i
$635$	−1.58358			−0.0628424
$636$	−38.5598	−	6.13538i	−1.52900	−	0.243284i
$637$		0			0
$638$	0.211777			0.00838434
$639$	24.5345	+	8.01033i	0.970569	+	0.316884i
$640$	4.20439	−	7.28221i	0.166193	−	0.287855i
$641$	19.1456			0.756205			0.378102	−	0.925764i	$-0.376577\pi$
$641$	19.1456			0.756205			0.378102	+	0.925764i	$0.376577\pi$
$642$	5.61505	+	0.893429i	0.221608	+	0.0352608i
$643$	3.24433	−	5.61934i	0.127944	−	0.221605i	−0.794936	−	0.606693i	$-0.792496\pi$
$643$	3.24433	−	5.61934i	0.127944	−	0.221605i	0.922880	+	0.385088i	$0.125829\pi$
$644$		0			0
$645$	−1.62967	−	4.25447i	−0.0641681	−	0.167520i
$646$	−1.61273	+	2.79332i	−0.0634518	+	0.109902i
$647$	−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	$0.772261\pi$
$648$	6.85060	+	5.00708i	0.269117	+	0.196697i
$649$	−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
$653$	−43.2405			−1.69213			−0.846066	−	0.533079i	$-0.821035\pi$
$653$	−43.2405			−1.69213			−0.846066	+	0.533079i	$0.821035\pi$
$654$	−0.187145	−	0.488568i	−0.00731795	−	0.0191045i
$655$	−5.87059			−0.229383
$656$	−18.6339	−	32.2749i	−0.727532	−	1.26012i
$657$	33.8166	−	30.3616i	1.31931	−	1.18452i
$658$		0			0
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	0.889417	−	0.457097i	$-0.151111\pi$
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	−0.840566	+	0.541709i	$0.817778\pi$
$660$	−5.26925	−	13.7561i	−0.205105	−	0.535456i
$661$	−21.1677	−	36.6636i	−0.823329	−	1.42605i	−0.903190	−	0.429241i	$-0.858781\pi$
$661$	−21.1677	−	36.6636i	−0.823329	−	1.42605i	0.0798613	−	0.996806i	$-0.474552\pi$
$662$	−1.47988	−	2.56323i	−0.0575172	−	0.0996227i
$663$	−4.30150	−	11.2297i	−0.167057	−	0.436124i
$664$	−3.27292	−	5.66886i	−0.127014	−	0.219994i
$665$		0			0
$666$	6.50972	+	2.12537i	0.252246	+	0.0823566i
$667$	0.669905	+	1.16031i	0.0259388	+	0.0449274i
$668$	−28.5289			−1.10382
$669$	14.0374	+	36.6464i	0.542716	+	1.41683i
$670$	0.991489			0.0383046
$671$	14.0796	−	24.3866i	0.543538	−	0.941435i
$672$		0			0
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	0.707296	−	0.706918i	$-0.249915\pi$
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	−0.965857	+	0.259077i	$0.916582\pi$
$674$	1.46582	+	2.53887i	0.0564612	+	0.0977936i
$675$	16.6631	+	8.53508i	0.641362	+	0.328515i
$676$	−11.6569	+	20.1904i	−0.448343	+	0.776553i
$677$	0.981125	−	1.69936i	0.0377077	−	0.0653117i	−0.846556	−	0.532300i	$-0.821328\pi$
$677$	0.981125	−	1.69936i	0.0377077	−	0.0653117i	0.884263	+	0.466989i	$0.154661\pi$
$678$	−1.80190	−	4.70409i	−0.0692014	−	0.180660i
$679$		0			0
$680$	3.86840	−	6.70027i	0.148346	−	0.256943i
$681$	−9.03611	−	1.43777i	−0.346265	−	0.0550953i
$682$	−1.47033			−0.0563019
$683$	−13.5836	+	23.5275i	−0.519761	+	0.900253i	0.479975	+	0.877282i	$0.340646\pi$
$683$	−13.5836	+	23.5275i	−0.519761	+	0.900253i	−0.999736	+	0.0229706i	$0.992688\pi$
$684$	−8.42588	+	7.56503i	−0.322171	+	0.289256i
$685$	5.12941			0.195985
$686$		0			0
$687$	33.0758	+	5.26280i	1.26192	+	0.200788i
$688$	8.14557			0.310547
$689$	−5.80150	−	10.0485i	−0.221020	−	0.382817i
$690$	−1.72764	+	2.13036i	−0.0657702	+	0.0811014i
$691$	−25.1586	+	43.5759i	−0.957077	+	1.65771i	−0.227534	+	0.973770i	$0.573066\pi$
$691$	−25.1586	+	43.5759i	−0.957077	+	1.65771i	−0.729543	+	0.683935i	$0.760267\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	−2.33009	+	4.03584i	−0.0883855	+	0.153088i
$696$	0.139680	+	0.364654i	0.00529457	+	0.0138222i
$697$	−35.3457	−	61.2205i	−1.33881	−	2.31889i
$698$	2.73431			0.103495
$699$	−10.5205	−	27.4652i	−0.397922	−	1.03883i
$700$		0			0
$701$	45.1672			1.70594			0.852970	−	0.521960i	$-0.174799\pi$
$701$	45.1672			1.70594			0.852970	+	0.521960i	$0.174799\pi$
$702$	0.0623817	+	1.24095i	0.00235445	+	0.0468368i
$703$	−9.27292	+	16.0612i	−0.349735	+	0.605758i
$704$	24.6673			0.929685
$705$	7.51561	−	9.26752i	0.283054	−	0.349035i
$706$	2.65374	−	4.59642i	0.0998750	−	0.172989i
$707$		0			0
$708$	5.51724	−	6.80333i	0.207351	−	0.255685i
$709$	−19.8090	+	34.3102i	−0.743944	+	1.28855i	0.206743	+	0.978395i	$0.433714\pi$
$709$	−19.8090	+	34.3102i	−0.743944	+	1.28855i	−0.950687	+	0.310153i	$0.899620\pi$
$710$	−1.21574	+	2.10571i	−0.0456257	+	0.0790261i
$711$	−16.4688	+	14.7862i	−0.617629	+	0.554528i
$712$	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
$716$	−27.5732			−1.03046
$717$	18.4218	−	22.7159i	0.687973	−	0.848342i
$718$	1.80687			0.0674318
$719$	−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	$0.968131\pi$
$720$	9.65718	−	8.67053i	0.359902	−	0.323132i
$721$		0			0
$722$	−1.82038	−	3.15299i	−0.0677475	−	0.117342i
$723$	46.4334	+	7.38817i	1.72688	+	0.274769i
$724$	1.39054	+	2.40849i	0.0516792	+	0.0895110i
$725$	0.430782	+	0.746136i	0.0159988	+	0.0277108i
$726$	−0.708899	+	0.874145i	−0.0263097	+	0.0324426i
$727$	14.0555	+	24.3449i	0.521291	+	0.902903i	0.999693	+	0.0247621i	$0.00788284\pi$
$727$	14.0555	+	24.3449i	0.521291	+	0.902903i	−0.478402	+	0.878141i	$0.658784\pi$
$728$		0			0
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	2.14076	+	3.70790i	0.0792331	+	0.137236i
$731$	15.4509			0.571472
$732$	25.2668	+	4.02028i	0.933887	+	0.148594i
$733$	−11.8695			−0.438409			−0.219205	−	0.975679i	$-0.570346\pi$
$733$	−11.8695			−0.438409			−0.219205	+	0.975679i	$0.570346\pi$
$734$	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
$738$	1.50847	+	7.14676i	0.0555276	+	0.263076i
$739$	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	$0.0947206\pi$
$740$	10.9601	−	18.9834i	0.402900	−	0.697843i
$741$	−3.32326	−	0.528775i	−0.122083	−	0.0194250i
$742$		0			0
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	−0.0925987	−	0.995704i	$-0.529517\pi$
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	0.908604	−	0.417659i	$-0.137149\pi$
$744$	−0.969775	−	2.53173i	−0.0355537	−	0.0928177i
$745$	−13.1327			−0.481144
$746$	1.87236	−	3.24302i	0.0685519	−	0.118735i
$747$	−4.30150	−	20.3794i	−0.157384	−	0.745645i
$748$	49.9579			1.82664
$749$		0			0
$750$	−2.65267	+	3.27101i	−0.0968616	+	0.119440i
$751$	42.8058			1.56200			0.781002	−	0.624528i	$-0.214709\pi$
$751$	42.8058			1.56200			0.781002	+	0.624528i	$0.214709\pi$
$752$	10.6666	+	18.4752i	0.388972	+	0.673720i
$753$	−32.6335	−	5.19243i	−1.18923	−	0.189223i
$754$	−0.0285900	+	0.0495193i	−0.00104119	+	0.00180339i
$755$	−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	$0.634032\pi$
$758$	0.482760	−	0.836165i	0.0175346	−	0.0303709i
$759$	−35.4967	−	5.64800i	−1.28845	−	0.205010i
$760$	−1.08250	−	1.87495i	−0.0392664	−	0.0680114i
$761$	14.3365			0.519699			0.259850	−	0.965649i	$-0.416327\pi$
$761$	14.3365			0.519699			0.259850	+	0.965649i	$0.416327\pi$
$762$	−0.349525	+	0.431001i	−0.0126620	+	0.0156135i
$763$		0			0
$764$	−29.2736			−1.05908
$765$	18.3182	−	16.4467i	0.662296	−	0.594630i
$766$	−0.0269552	+	0.0466878i	−0.000973931	+	0.00168690i
$767$	2.60301			0.0939892
$768$	7.19879	+	18.7934i	0.259764	+	0.678149i
$769$	−15.6105	+	27.0382i	−0.562930	+	0.975024i	0.434309	+	0.900764i	$0.356993\pi$
$769$	−15.6105	+	27.0382i	−0.562930	+	0.975024i	−0.997239	+	0.0742597i	$0.976341\pi$
$770$		0			0
$771$	−25.3880	−	4.03956i	−0.914325	−	0.145481i
$772$	−7.62352	+	13.2043i	−0.274376	+	0.475234i
$773$	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	$0.141567\pi$
$774$	−1.51763	−	0.495495i	−0.0545501	−	0.0178102i
$775$	−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
$779$	−19.7817			−0.708752
$780$	3.92790	+	0.624982i	0.140641	+	0.0223779i
$781$	−31.8629			−1.14015
$782$	−4.65103	−	8.05582i	−0.166321	−	0.288076i
$783$	0.0623817	+	1.24095i	0.00222934	+	0.0443481i
$784$		0			0
$785$	−0.0337917	−	0.0585290i	−0.00120608	−	0.00208899i
$786$	−1.29575	+	1.59779i	−0.0462178	+	0.0569913i
$787$	13.8107	+	23.9208i	0.492297	+	0.852683i	0.999961	−	0.00887191i	$-0.00282405\pi$
$787$	13.8107	+	23.9208i	0.492297	+	0.852683i	−0.507664	+	0.861555i	$0.669491\pi$
$788$	6.49876	+	11.2562i	0.231509	+	0.400985i
$789$	13.2420	+	2.10698i	0.471428	+	0.0750105i
$790$	−1.04256	−	1.80577i	−0.0370926	−	0.0642463i
$791$		0			0
$792$	−9.95843	−	3.25135i	−0.353857	−	0.115532i
$793$	3.80150	+	6.58440i	0.134995	+	0.233819i
$794$	−4.85443			−0.172277
$795$	14.9617	−	18.4493i	0.530637	−	0.654330i
$796$	−38.7390			−1.37307
$797$	−1.48181	+	2.56658i	−0.0524885	+	0.0909128i	−0.891076	−	0.453854i	$-0.850049\pi$
$797$	−1.48181	+	2.56658i	−0.0524885	+	0.0909128i	0.838587	+	0.544767i	$0.183382\pi$
$798$		0			0
$799$	20.2330	+	35.0445i	0.715791	+	1.23979i
$800$	−4.97373	−	8.61476i	−0.175848	−	0.304578i
$801$	1.70206	+	8.06394i	0.0601394	+	0.284925i
$802$	−1.82038	+	3.15299i	−0.0642798	+	0.111336i
$803$	−28.0534	+	48.5898i	−0.989981	+	1.71470i
$804$	−7.43559	+	9.16886i	−0.262233	+	0.323361i
$805$		0			0
$806$	0.198495	−	0.343803i	0.00699169	−	0.0121100i
$807$	1.64884	−	2.03319i	0.0580419	−	0.0715717i
$808$	12.0539			0.424055
$809$	12.3948	−	21.4684i	0.435778	−	0.754790i	−0.561581	−	0.827422i	$-0.689807\pi$
$809$	12.3948	−	21.4684i	0.435778	−	0.754790i	0.997359	+	0.0726323i	$0.0231400\pi$
$810$	−2.32669	+	1.02799i	−0.0817516	+	0.0361199i
$811$	−8.24377			−0.289478			−0.144739	−	0.989470i	$-0.546234\pi$
$811$	−8.24377			−0.289478			−0.144739	+	0.989470i	$0.546234\pi$
$812$		0			0
$813$	13.6183	+	35.5525i	0.477615	+	1.24688i
$814$	−8.45417			−0.296319
$815$	−0.891233	−	1.54366i	−0.0312185	−	0.0540721i
$816$	15.7443	+	41.1027i	0.551162	+	1.43888i
$817$	2.16182	−	3.74439i	0.0756327	−	0.131000i
$818$	0.396208			0.0138531
$819$		0			0
$820$	23.3808			0.816494
$821$	14.4497	−	25.0275i	0.504296	−	0.873467i	−0.495691	−	0.868499i	$-0.665085\pi$
$821$	14.4497	−	25.0275i	0.504296	−	0.873467i	0.999988	−	0.00496829i	$-0.00158146\pi$
$822$	1.13216	−	1.39606i	0.0394885	−	0.0486934i
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	4.14557			0.144418
$825$	−22.8261	−	3.63194i	−0.794704	−	0.126448i
$826$		0			0
$827$	−50.7108			−1.76339			−0.881694	−	0.471821i	$-0.843597\pi$
$827$	−50.7108			−1.76339			−0.881694	+	0.471821i	$0.843597\pi$
$828$	−6.74433	−	31.9529i	−0.234381	−	1.11044i
$829$	7.40615	−	12.8278i	0.257226	−	0.445529i	−0.708272	−	0.705940i	$-0.750525\pi$
$829$	7.40615	−	12.8278i	0.257226	−	0.445529i	0.965498	+	0.260411i	$0.0838581\pi$
$830$	1.96225			0.0681107
$831$	18.5224	+	2.94717i	0.642536	+	0.102236i
$832$	−3.33009	+	5.76789i	−0.115450	+	0.199966i
$833$		0			0
$834$	0.584135	+	1.52496i	0.0202269	+	0.0528052i
$835$	8.67799	−	15.0307i	0.300314	−	0.520159i
$836$	6.98989	−	12.1069i	0.241751	−	0.418724i
$837$	−0.433105	−	8.61572i	−0.0149703	−	0.297803i
$838$	−3.99028	−	6.91138i	−0.137842	−	0.238750i
$839$	16.8606	+	29.2034i	0.582093	+	1.00821i	0.995231	+	0.0975464i	$0.0310994\pi$
$839$	16.8606	+	29.2034i	0.582093	+	1.00821i	−0.413138	+	0.910669i	$0.635567\pi$
$840$		0			0
$841$	14.4714	−	25.0652i	0.499014	−	0.864318i
$842$	−4.36173			−0.150315
$843$	−10.4561	−	27.2971i	−0.360127	−	0.940161i
$844$	35.1488			1.20987
$845$	−7.09166	−	12.2831i	−0.243961	−	0.422552i
$846$	−0.863496	−	4.09103i	−0.0296876	−	0.140652i
$847$		0			0
$848$	21.2346	+	36.7794i	0.729199	+	1.26301i
$849$	9.48989	+	24.7747i	0.325692	+	0.850264i
$850$	−2.99084	−	5.18029i	−0.102585	−	0.177682i
$851$	−26.7427	−	46.3197i	−0.916728	−	1.58782i
$852$	−10.3554	−	27.0342i	−0.354771	−	0.926177i
$853$	5.89480	+	10.2101i	0.201834	+	0.349587i	0.949119	−	0.314916i	$-0.101976\pi$
$853$	5.89480	+	10.2101i	0.201834	+	0.349587i	−0.747285	+	0.664503i	$0.768643\pi$
$854$		0			0
$855$	−1.42270	−	6.74040i	−0.0486554	−	0.230517i
$856$	−6.47141	−	11.2088i	−0.221188	−	0.383109i
$857$	31.3261			1.07008			0.535040	−	0.844827i	$-0.320296\pi$
$857$	31.3261			1.07008			0.535040	+	0.844827i	$0.320296\pi$
$858$	−0.548709	−	1.43248i	−0.0187326	−	0.0489040i
$859$	50.3893			1.71926			0.859631	−	0.510915i	$-0.170693\pi$
$859$	50.3893			1.71926			0.859631	+	0.510915i	$0.170693\pi$
$860$	−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	0.856225	−	0.516603i	$-0.172804\pi$
$863$	−0.566340	−	0.980929i	−0.0192784	−	0.0333912i	−0.875504	+	0.483211i	$0.839470\pi$
$864$	−0.720248	−	14.3278i	−0.0245034	−	0.487443i
$865$	−0.149395	+	0.258761i	−0.00507960	+	0.00879812i
$866$	1.46402	−	2.53575i	0.0497494	−	0.0861684i
$867$	19.3320	+	50.4689i	0.656550	+	1.71401i
$868$		0			0
$869$	13.6621	−	23.6635i	0.463456	−	0.802729i
$870$	−0.115604	−	0.0183941i	−0.00391933	−	0.000623618i
$871$	−3.50808			−0.118867
$872$	−0.595485	+	1.03141i	−0.0201657	+	0.0349280i
$873$	4.44119	+	21.0412i	0.150311	+	0.712137i
$874$	−2.60301			−0.0880481
$875$		0			0
$876$	−50.3435	−	8.01033i	−1.70095	−	0.270644i
$877$	−27.3937			−0.925020			−0.462510	−	0.886614i	$-0.653051\pi$
$877$	−27.3937			−0.925020			−0.462510	+	0.886614i	$0.653051\pi$
$878$	0.577690	+	1.00059i	0.0194961	+	0.0337682i
$879$	10.2220	−	12.6048i	0.344780	−	0.425149i
$880$	−8.01135	+	13.8761i	−0.270063	+	0.467762i
$881$	−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	$0.829306\pi$
$884$	−6.74433	+	11.6815i	−0.226836	+	0.392892i
$885$	1.90615	+	4.97626i	0.0640745	+	0.167275i
$886$	0.148840	+	0.257798i	0.00500038	+	0.00866091i
$887$	41.5757			1.39597			0.697987	−	0.716110i	$-0.254079\pi$
$887$	41.5757			1.39597			0.697987	+	0.716110i	$0.254079\pi$
$888$	−5.57605	−	14.5570i	−0.187120	−	0.488503i
$889$		0			0
$890$	−0.776443			−0.0260264
$891$	−26.9114	−	19.6694i	−0.901564	−	0.658950i
$892$	22.0092	−	38.1210i	0.736921	−	1.27638i
$893$	11.3236			0.378931
$894$	−2.89862	+	3.57430i	−0.0969445	+	0.119543i
$895$	8.38727	−	14.5272i	0.280356	−	0.485590i
$896$		0			0
$897$	6.11273	−	7.53762i	0.204098	−	0.251674i
$898$	1.05555	−	1.82826i	0.0352240	−	0.0610098i
$899$	0.198495	−	0.343803i	0.00662018	−	0.0114665i
$900$	−4.33693	−	20.5473i	−0.144564	−	0.684910i
$901$	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
$905$	−1.69192			−0.0562412
$906$	−3.63229	+	4.47899i	−0.120675	+	0.148804i
$907$	35.4509			1.17713			0.588564	−	0.808451i	$-0.299694\pi$
$907$	35.4509			1.17713			0.588564	+	0.808451i	$0.299694\pi$
$908$	5.13160	+	8.88819i	0.170298	+	0.294965i
$909$	36.4607	+	11.9042i	1.20933	+	0.394836i
$910$		0			0
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	0.985005	−	0.172526i	$-0.0551930\pi$
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	−0.641915	+	0.766776i	$0.721860\pi$
$912$	12.1638	+	1.93542i	0.402782	+	0.0640880i
$913$	12.8571	+	22.2691i	0.425506	+	0.736998i
$914$	−1.25636	−	2.17609i	−0.0415568	−	0.0719785i
$915$	−9.80383	+	12.0891i	−0.324105	+	0.399654i
$916$	−18.7837	−	32.5343i	−0.620631	−	1.07496i
$917$		0			0
$918$	−0.433105	−	8.61572i	−0.0142946	−	0.284361i
$919$	−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	$0.909623\pi$
$920$	6.24377			0.205851
$921$	4.64256	+	0.738693i	0.152978	+	0.0243408i
$922$	5.39261			0.177596
$923$	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
$927$	12.5395	+	4.09407i	0.411853	+	0.134467i
$928$	0.330095	−	0.571741i	0.0108359	−	0.0187683i
$929$	−20.8714	+	36.1503i	−0.684769	+	1.18605i	0.288741	+	0.957407i	$0.406763\pi$
$929$	−20.8714	+	36.1503i	−0.684769	+	1.18605i	−0.973509	+	0.228647i	$0.926570\pi$
$930$	0.802616	+	0.127707i	0.0263188	+	0.00418768i
$931$		0			0
$932$	−16.4951	+	28.5703i	−0.540315	+	0.935853i
$933$	8.66182	+	22.6129i	0.283575	+	0.740312i
$934$	3.18443			0.104198
$935$	−15.1963	+	26.3208i	−0.496972	+	0.860781i
$936$	2.10464	−	1.88962i	0.0687925	−	0.0617641i
$937$	−3.17154			−0.103610			−0.0518048	−	0.998657i	$-0.516497\pi$
$937$	−3.17154			−0.103610			−0.0518048	+	0.998657i	$0.516497\pi$
$938$		0			0
$939$	20.7873	−	25.6329i	0.678367	−	0.836497i
$940$	−13.3839			−0.436535
$941$	−1.61040	−	2.78930i	−0.0524976	−	0.0909285i	0.838582	−	0.544775i	$-0.183385\pi$
$941$	−1.61040	−	2.78930i	−0.0524976	−	0.0909285i	−0.891080	+	0.453846i	$0.850052\pi$
$942$	−0.0233882	−	0.00372138i	−0.000762029	−	0.000121249i
$943$	28.5248	−	49.4063i	0.928894	−	1.60889i
$944$	−9.52751			−0.310094
$945$		0			0
$946$	1.97095			0.0640810
$947$	22.6735	−	39.2716i	0.736789	−	1.27616i	−0.217145	−	0.976139i	$-0.569675\pi$
$947$	22.6735	−	39.2716i	0.736789	−	1.27616i	0.953934	−	0.300016i	$-0.0969922\pi$
$948$	24.5175	+	3.90107i	0.796293	+	0.126701i
$949$	−7.57442	−	13.1193i	−0.245876	−	0.425870i
$950$	−1.67386			−0.0543073
$951$	−4.38508	+	5.40726i	−0.142196	+	0.175343i
$952$		0			0
$953$	−54.2703			−1.75799			−0.878994	−	0.476832i	$-0.841785\pi$
$953$	−54.2703			−1.75799			−0.878994	+	0.476832i	$0.841785\pi$
$954$	−1.71900	−	8.14421i	−0.0556548	−	0.263679i
$955$	8.90451	−	15.4231i	0.288143	−	0.499079i
$956$	−32.8058			−1.06101
$957$	−0.548709	−	1.43248i	−0.0177372	−	0.0463054i
$958$	−1.73788	+	3.01010i	−0.0561483	+	0.0972518i
$959$		0			0
$960$	−13.4653	−	2.14250i	−0.434589	−	0.0691490i
$961$	14.1219	−	24.4598i	0.455545	−	0.789027i
$962$	1.14132	−	1.97682i	0.0367975	−	0.0637351i
$963$	−8.50520	−	40.2955i	−0.274076	−	1.29850i
$964$	−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	−0.995170	−	0.0981667i	$-0.968702\pi$
$967$	−12.8295	+	22.2214i	−0.412570	+	0.714593i	0.582600	+	0.812759i	$0.302036\pi$
$968$	2.56199			0.0823455
$969$	23.0728	+	3.67119i	0.741205	+	0.117936i
$970$	−2.02597			−0.0650500
$971$	−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	$0.942832\pi$
$972$	7.94243	−	29.2256i	0.254754	−	0.937410i
$973$		0			0
$974$	1.56075	+	2.70329i	0.0500096	+	0.0866191i
$975$	3.93078	−	4.84706i	0.125886	−	0.155230i
$976$	−13.9142	−	24.1002i	−0.445384	−	0.771427i
$977$	1.04910	+	1.81709i	0.0335637	+	0.0581340i	0.882319	−	0.470651i	$-0.155981\pi$
$977$	1.04910	+	1.81709i	0.0335637	+	0.0581340i	−0.848756	+	0.528785i	$0.822648\pi$
$978$	−0.616848	−	0.0981487i	−0.0197246	−	0.00313845i
$979$	−5.08740	−	8.81164i	−0.162594	−	0.281621i
$980$		0			0
$981$	−2.81982	+	2.53173i	−0.0900301	+	0.0808319i
$982$	2.31285	+	4.00598i	0.0738062	+	0.127836i
$983$	−42.9923			−1.37124			−0.685622	−	0.727958i	$-0.740469\pi$
$983$	−42.9923			−1.37124			−0.685622	+	0.727958i	$0.740469\pi$
$984$	10.4730	−	12.9143i	0.333868	−	0.411694i
$985$	−7.90723			−0.251945
$986$	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
$990$	2.33671	−	2.09797i	0.0742654	−	0.0666779i
$991$	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	$0.0782564\pi$
$992$	−2.29179	+	3.96950i	−0.0727644	+	0.126032i
$993$	−13.5036	+	16.6513i	−0.428523	+	0.528413i
$994$		0			0
$995$	11.7837	−	20.4100i	0.373569	−	0.647040i
$996$	−14.7157	+	18.1460i	−0.466286	+	0.574979i
$997$	38.9018			1.23203			0.616016	−	0.787733i	$-0.288746\pi$
$997$	38.9018			1.23203			0.616016	+	0.787733i	$0.288746\pi$
$998$	−4.33078	+	7.50114i	−0.137089	+	0.237444i
$999$	−2.49028	−	49.5390i	−0.0787891	−	1.56735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.d.67.2		6
3.2	odd	2		1323.2.g.b.361.2		6
7.2	even	3		441.2.h.b.373.2		6
7.3	odd	6		63.2.f.b.22.2	✓	6
7.4	even	3		441.2.f.d.148.2		6
7.5	odd	6		441.2.h.c.373.2		6
7.6	odd	2		441.2.g.e.67.2		6
9.2	odd	6		1323.2.h.e.802.2		6
9.7	even	3		441.2.h.b.214.2		6
21.2	odd	6		1323.2.h.e.226.2		6
21.5	even	6		1323.2.h.d.226.2		6
21.11	odd	6		1323.2.f.c.442.2		6
21.17	even	6		189.2.f.a.64.2		6
21.20	even	2		1323.2.g.c.361.2		6
28.3	even	6		1008.2.r.k.337.2		6
63.2	odd	6		1323.2.g.b.667.2		6
63.4	even	3		3969.2.a.m.1.2		3
63.11	odd	6		1323.2.f.c.883.2		6
63.16	even	3	inner	441.2.g.d.79.2		6
63.20	even	6		1323.2.h.d.802.2		6
63.25	even	3		441.2.f.d.295.2		6
63.31	odd	6		567.2.a.d.1.2		3
63.32	odd	6		3969.2.a.p.1.2		3
63.34	odd	6		441.2.h.c.214.2		6
63.38	even	6		189.2.f.a.127.2		6
63.47	even	6		1323.2.g.c.667.2		6
63.52	odd	6		63.2.f.b.43.2	yes	6
63.59	even	6		567.2.a.g.1.2		3
63.61	odd	6		441.2.g.e.79.2		6
84.59	odd	6		3024.2.r.g.1009.3		6
252.31	even	6		9072.2.a.bq.1.3		3
252.59	odd	6		9072.2.a.cd.1.1		3
252.115	even	6		1008.2.r.k.673.2		6
252.227	odd	6		3024.2.r.g.2017.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	7.3	odd	6
63.2.f.b.43.2	yes	6	63.52	odd	6
189.2.f.a.64.2		6	21.17	even	6
189.2.f.a.127.2		6	63.38	even	6
441.2.f.d.148.2		6	7.4	even	3
441.2.f.d.295.2		6	63.25	even	3
441.2.g.d.67.2		6	1.1	even	1	trivial
441.2.g.d.79.2		6	63.16	even	3	inner
441.2.g.e.67.2		6	7.6	odd	2
441.2.g.e.79.2		6	63.61	odd	6
441.2.h.b.214.2		6	9.7	even	3
441.2.h.b.373.2		6	7.2	even	3
441.2.h.c.214.2		6	63.34	odd	6
441.2.h.c.373.2		6	7.5	odd	6
567.2.a.d.1.2		3	63.31	odd	6
567.2.a.g.1.2		3	63.59	even	6
1008.2.r.k.337.2		6	28.3	even	6
1008.2.r.k.673.2		6	252.115	even	6
1323.2.f.c.442.2		6	21.11	odd	6
1323.2.f.c.883.2		6	63.11	odd	6
1323.2.g.b.361.2		6	3.2	odd	2
1323.2.g.b.667.2		6	63.2	odd	6
1323.2.g.c.361.2		6	21.20	even	2
1323.2.g.c.667.2		6	63.47	even	6
1323.2.h.d.226.2		6	21.5	even	6
1323.2.h.d.802.2		6	63.20	even	6
1323.2.h.e.226.2		6	21.2	odd	6
1323.2.h.e.802.2		6	9.2	odd	6
3024.2.r.g.1009.3		6	84.59	odd	6
3024.2.r.g.2017.3		6	252.227	odd	6
3969.2.a.m.1.2		3	63.4	even	3
3969.2.a.p.1.2		3	63.32	odd	6
9072.2.a.bq.1.3		3	252.31	even	6
9072.2.a.cd.1.1		3	252.59	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 - 0.207087i) q^{2} +(-1.71053 - 0.272169i) q^{3} +(0.971410 + 1.68253i) q^{4} -1.18194 q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 + 0.931107i) q^{9} +O(q^{10})\)	\(q+(0.119562 - 0.207087i) q^{2} +(-1.71053 - 0.272169i) q^{3} +(0.971410 + 1.68253i) q^{4} -1.18194 q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(2.85185 + 0.931107i) q^{9} +(-0.141315 + 0.244765i) q^{10} -3.70370 q^{11} +(-1.20370 - 3.14241i) q^{12} +(0.500000 - 0.866025i) q^{13} +(2.02175 + 0.321688i) q^{15} +(-1.83009 + 3.16982i) q^{16} +(-3.47141 + 6.01266i) q^{17} +(0.533792 - 0.479256i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-1.14815 - 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} -5.60301 q^{23} +(-1.61273 - 0.256606i) q^{24} -3.60301 q^{25} +(-0.119562 - 0.207087i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.119562 - 0.207087i) q^{29} +(0.308342 - 0.380217i) q^{30} +(0.830095 + 1.43777i) q^{31} +(1.38044 + 2.39099i) q^{32} +(6.33530 + 1.00803i) q^{33} +(0.830095 + 1.43777i) q^{34} +(1.20370 + 5.70281i) q^{36} +(4.77292 + 8.26693i) q^{37} +0.464574 q^{38} +(-1.09097 + 1.34528i) q^{39} -1.11436 q^{40} +(-5.09097 + 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +(-3.59781 - 6.23159i) q^{44} +(-3.37072 - 1.10052i) q^{45} +(-0.669905 + 1.16031i) q^{46} +(2.91423 - 5.04759i) q^{47} +(3.99316 - 4.92398i) q^{48} +(-0.430782 + 0.746136i) q^{50} +(7.57442 - 9.34004i) q^{51} +1.94282 q^{52} +(5.80150 - 10.0485i) q^{53} +(-1.04351 + 0.674501i) q^{54} +4.37756 q^{55} +(-1.20370 - 3.14241i) q^{57} -0.0571799 q^{58} +(1.30150 + 2.25427i) q^{59} +(1.42270 + 3.71415i) q^{60} +(-3.80150 + 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(-0.590972 + 1.02359i) q^{65} +(0.966208 - 1.19143i) q^{66} +(-1.75404 - 3.03809i) q^{67} -13.4887 q^{68} +(9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(2.68878 + 0.877867i) q^{72} +(7.57442 - 13.1193i) q^{73} +2.28263 q^{74} +(6.16307 + 0.980627i) q^{75} +(-1.88727 + 3.26886i) q^{76} +(0.148152 + 0.386770i) q^{78} +(-3.68878 + 6.38915i) q^{79} +(2.16307 - 3.74654i) q^{80} +(7.26608 + 5.31075i) q^{81} +(1.21737 + 2.10855i) q^{82} +(-3.47141 - 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} -0.532157 q^{86} +(0.148152 + 0.386770i) q^{87} -3.49192 q^{88} +(1.37360 + 2.37915i) q^{89} +(-0.630912 + 0.566453i) q^{90} +(-5.44282 - 9.42724i) q^{92} +(-1.02859 - 2.68527i) q^{93} +(-0.696860 - 1.20700i) q^{94} +(-1.14815 - 1.98866i) q^{95} +(-1.71053 - 4.46558i) q^{96} +(3.58414 + 6.20790i) q^{97} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + q^2 - 2 * q^3 - 3 * q^4 + 10 * q^5 - q^6 - 12 * q^8 + 8 * q^9	\( 6 q + q^{2} - 2 q^{3} - 3 q^{4} + 10 q^{5} - q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} + 11 q^{12} + 3 q^{13} + 11 q^{15} - 3 q^{16} - 12 q^{17} - 23 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 12 q^{25} - q^{26} + 7 q^{27} - q^{29} - 5 q^{30} - 3 q^{31} + 8 q^{32} - 5 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} - 16 q^{38} + 2 q^{39} - 42 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + 4 q^{45} - 12 q^{46} - 9 q^{47} + 14 q^{48} - 10 q^{50} + 3 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} + 12 q^{55} + 11 q^{57} - 18 q^{58} - 9 q^{59} + 37 q^{60} - 6 q^{61} + 36 q^{62} - 24 q^{64} + 5 q^{65} + 32 q^{66} - 12 q^{68} + 39 q^{69} + 18 q^{71} + 9 q^{72} + 3 q^{73} + 12 q^{74} + 35 q^{75} - 21 q^{76} + 10 q^{78} - 15 q^{79} + 11 q^{80} + 8 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} + 68 q^{86} + 10 q^{87} - 42 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 15 q^{93} + 24 q^{94} - 16 q^{95} - 2 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 - 2 * q^3 - 3 * q^4 + 10 * q^5 - q^6 - 12 * q^8 + 8 * q^9 - 4 * q^11 + 11 * q^12 + 3 * q^13 + 11 * q^15 - 3 * q^16 - 12 * q^17 - 23 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 12 * q^25 - q^26 + 7 * q^27 - q^29 - 5 * q^30 - 3 * q^31 + 8 * q^32 - 5 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 - 16 * q^38 + 2 * q^39 - 42 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + 4 * q^45 - 12 * q^46 - 9 * q^47 + 14 * q^48 - 10 * q^50 + 3 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 + 12 * q^55 + 11 * q^57 - 18 * q^58 - 9 * q^59 + 37 * q^60 - 6 * q^61 + 36 * q^62 - 24 * q^64 + 5 * q^65 + 32 * q^66 - 12 * q^68 + 39 * q^69 + 18 * q^71 + 9 * q^72 + 3 * q^73 + 12 * q^74 + 35 * q^75 - 21 * q^76 + 10 * q^78 - 15 * q^79 + 11 * q^80 + 8 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 + 68 * q^86 + 10 * q^87 - 42 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 15 * q^93 + 24 * q^94 - 16 * q^95 - 2 * q^96 + 3 * q^97 - 46 * q^99

Introduction

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