LMFDB - Embedded newform 441.2.f.d.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.d.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 + 0.207087i) q^{2} +(0.619562 + 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})$	\(q+(0.119562 + 0.207087i) q^{2} +(0.619562 + 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} +0.282630 q^{10} +(1.85185 + 3.20750i) q^{11} +(3.32326 + 0.528775i) q^{12} +(0.500000 - 0.866025i) q^{13} +(2.02175 + 0.321688i) q^{15} +(-1.83009 - 3.16982i) q^{16} +6.94282 q^{17} +(-0.681943 - 0.222649i) q^{18} -1.94282 q^{19} +(-1.14815 - 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(0.584135 + 1.52496i) q^{24} +(1.80150 + 3.12030i) q^{25} +0.239123 q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.119562 - 0.207087i) q^{29} +(0.175107 + 0.457140i) q^{30} +(0.830095 - 1.43777i) q^{31} +(1.38044 - 2.39099i) q^{32} +(-4.04063 + 4.98251i) q^{33} +(0.830095 + 1.43777i) q^{34} +(1.20370 + 5.70281i) q^{36} -9.54583 q^{37} +(-0.232287 - 0.402332i) q^{38} +(1.71053 + 0.272169i) q^{39} +(0.557180 - 0.965064i) q^{40} +(-5.09097 + 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +7.19562 q^{44} +(0.732287 + 3.46939i) q^{45} +1.33981 q^{46} +(2.91423 + 5.04759i) q^{47} +(3.99316 - 4.92398i) q^{48} +(-0.430782 + 0.746136i) q^{50} +(4.30150 + 11.2297i) q^{51} +(-0.971410 - 1.68253i) q^{52} -11.6030 q^{53} +(-0.0623817 - 1.24095i) q^{54} +4.37756 q^{55} +(-1.20370 - 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} +(1.30150 - 2.25427i) q^{59} +(2.50520 - 3.08917i) q^{60} +(-3.80150 - 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(-0.590972 - 1.02359i) q^{65} +(-1.51492 - 0.241044i) q^{66} +(-1.75404 + 3.03809i) q^{67} +(6.74433 - 11.6815i) q^{68} +(9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(-2.10464 + 1.88962i) q^{72} -15.1488 q^{73} +(-1.14132 - 1.97682i) q^{74} +(-3.93078 + 4.84706i) q^{75} +(-1.88727 + 3.26886i) q^{76} +(0.148152 + 0.386770i) q^{78} +(-3.68878 - 6.38915i) q^{79} -4.32614 q^{80} +(0.966208 - 8.94799i) q^{81} -2.43474 q^{82} +(-3.47141 - 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(0.260877 - 0.321688i) q^{87} +(1.74596 + 3.02409i) q^{88} -2.74720 q^{89} +(-0.630912 + 0.566453i) q^{90} +(-5.44282 - 9.42724i) q^{92} +(2.83981 + 0.451852i) q^{93} +(-0.696860 + 1.20700i) q^{94} +(-1.14815 + 1.98866i) q^{95} +(4.72257 + 0.751424i) 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} + 4 q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	$ 6 q + q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} + 2 q^{12} + 3 q^{13} + 11 q^{15} - 3 q^{16} + 24 q^{17} + 13 q^{18} + 6 q^{19} - 16 q^{20} + 15 q^{22} - 15 q^{24} - 6 q^{25} + 2 q^{26} + 7 q^{27} - q^{29} - 26 q^{30} - 3 q^{31} + 8 q^{32} - 8 q^{33} - 3 q^{34} - 11 q^{36} - 6 q^{37} + 8 q^{38} + 2 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} + 46 q^{44} - 5 q^{45} + 24 q^{46} - 9 q^{47} + 14 q^{48} - 10 q^{50} + 9 q^{51} + 3 q^{52} - 36 q^{53} + 17 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} - 9 q^{59} - 20 q^{60} - 6 q^{61} + 36 q^{62} - 24 q^{64} + 5 q^{65} + 2 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} - 24 q^{72} - 6 q^{73} - 6 q^{74} - 31 q^{75} - 21 q^{76} + 10 q^{78} - 15 q^{79} - 22 q^{80} + 32 q^{81} - 18 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} + q^{87} + 21 q^{88} + 4 q^{89} - 73 q^{90} - 15 q^{92} + 33 q^{93} + 24 q^{94} - 16 q^{95} - 5 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q + q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 + 2 * q^12 + 3 * q^13 + 11 * q^15 - 3 * q^16 + 24 * q^17 + 13 * q^18 + 6 * q^19 - 16 * q^20 + 15 * q^22 - 15 * q^24 - 6 * q^25 + 2 * q^26 + 7 * q^27 - q^29 - 26 * q^30 - 3 * q^31 + 8 * q^32 - 8 * q^33 - 3 * q^34 - 11 * q^36 - 6 * q^37 + 8 * q^38 + 2 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 + 46 * q^44 - 5 * q^45 + 24 * q^46 - 9 * q^47 + 14 * q^48 - 10 * q^50 + 9 * q^51 + 3 * q^52 - 36 * q^53 + 17 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 - 9 * q^59 - 20 * q^60 - 6 * q^61 + 36 * q^62 - 24 * q^64 + 5 * q^65 + 2 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 - 24 * q^72 - 6 * q^73 - 6 * q^74 - 31 * q^75 - 21 * q^76 + 10 * q^78 - 15 * q^79 - 22 * q^80 + 32 * q^81 - 18 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 + q^87 + 21 * q^88 + 4 * q^89 - 73 * q^90 - 15 * q^92 + 33 * q^93 + 24 * q^94 - 16 * q^95 - 5 * q^96 + 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.905196	−	0.424994i	$-0.139724\pi$
$2$	0.119562	+	0.207087i	0.0845428	+	0.146433i	−0.820653	+	0.571426i	$0.806390\pi$
$3$	0.619562	+	1.61745i	0.357704	+	0.933835i
$3$	0.619562	+	1.61745i	0.357704	+	0.933835i
$4$	0.971410	−	1.68253i	0.485705	−	0.841266i
$5$	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	$0.0815289\pi$
$6$	−0.260877	+	0.321688i	−0.106502	+	0.131329i
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$	−2.23229	+	2.00422i	−0.744096	+	0.668073i
$10$	0.282630			0.0893755
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	0.997634	+	0.0687465i	$0.0219000\pi$
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	−0.439281	+	0.898350i	$0.644767\pi$
$12$	3.32326	+	0.528775i	0.959342	+	0.152644i
$13$	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
$17$	6.94282			1.68388			0.841941	−	0.539570i	$-0.181413\pi$
$17$	6.94282			1.68388			0.841941	+	0.539570i	$0.181413\pi$
$18$	−0.681943	−	0.222649i	−0.160736	−	0.0524790i
$19$	−1.94282			−0.445713			−0.222857	−	0.974851i	$-0.571538\pi$
$19$	−1.94282			−0.445713			−0.222857	+	0.974851i	$0.571538\pi$
$20$	−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	$-0.634760\pi$
$23$	2.80150	−	4.85235i	0.584154	−	1.01178i	0.994980	−	0.100071i	$-0.0319070\pi$
$24$	0.584135	+	1.52496i	0.119236	+	0.311282i
$25$	1.80150	+	3.12030i	0.360301	+	0.624060i
$26$	0.239123			0.0468959
$27$	−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	$0.840401\pi$
$30$	0.175107	+	0.457140i	0.0319700	+	0.0834620i
$31$	0.830095	−	1.43777i	0.149089	−	0.258231i	−0.781802	−	0.623527i	$-0.785699\pi$
$31$	0.830095	−	1.43777i	0.149089	−	0.258231i	0.930891	+	0.365297i	$0.119032\pi$
$32$	1.38044	−	2.39099i	0.244029	−	0.422671i
$33$	−4.04063	+	4.98251i	−0.703383	+	0.867344i
$34$	0.830095	+	1.43777i	0.142360	+	0.246575i
$35$		0			0
$36$	1.20370	+	5.70281i	0.200616	+	0.950469i
$37$	−9.54583			−1.56932			−0.784662	−	0.619923i	$-0.787164\pi$
$37$	−9.54583			−1.56932			−0.784662	+	0.619923i	$0.787164\pi$
$38$	−0.232287	−	0.402332i	−0.0376819	−	0.0652669i
$39$	1.71053	+	0.272169i	0.273905	+	0.0435819i
$40$	0.557180	−	0.965064i	0.0880979	−	0.152590i
$41$	−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	$0.887610\pi$
$44$	7.19562			1.08478
$45$	0.732287	+	3.46939i	0.109163	+	0.517186i
$46$	1.33981			0.197544
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$	3.99316	−	4.92398i	0.576364	−	0.710716i
$49$		0			0
$50$	−0.430782	+	0.746136i	−0.0609217	+	0.105520i
$51$	4.30150	+	11.2297i	0.602331	+	1.57247i
$52$	−0.971410	−	1.68253i	−0.134710	−	0.233325i
$53$	−11.6030			−1.59380			−0.796898	−	0.604114i	$-0.793527\pi$
$53$	−11.6030			−1.59380			−0.796898	+	0.604114i	$0.793527\pi$
$54$	−0.0623817	−	1.24095i	−0.00848907	−	0.168872i
$55$	4.37756			0.590270
$56$		0			0
$57$	−1.20370	−	3.14241i	−0.159434	−	0.416223i
$58$	0.0285900	−	0.0495193i	0.00375405	−	0.00650220i
$59$	1.30150	−	2.25427i	0.169442	−	0.293481i	−0.768782	−	0.639511i	$-0.779137\pi$
$59$	1.30150	−	2.25427i	0.169442	−	0.293481i	0.938224	+	0.346029i	$0.112470\pi$
$60$	2.50520	−	3.08917i	0.323420	−	0.398811i
$61$	−3.80150	−	6.58440i	−0.486733	−	0.843046i	0.513151	−	0.858298i	$-0.328478\pi$
$61$	−3.80150	−	6.58440i	−0.486733	−	0.843046i	−0.999884	+	0.0152524i	$0.995145\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	−0.590972	−	1.02359i	−0.0733010	−	0.126961i
$66$	−1.51492	−	0.241044i	−0.186473	−	0.0296704i
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	−0.953053	−	0.302804i	$-0.902077\pi$
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	0.738763	+	0.673966i	$0.235410\pi$
$68$	6.74433	−	11.6815i	0.817870	−	1.41659i
$69$	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	$0.329462\pi$
$72$	−2.10464	+	1.88962i	−0.248035	+	0.222694i
$73$	−15.1488			−1.77304			−0.886519	−	0.462693i	$-0.846883\pi$
$73$	−15.1488			−1.77304			−0.886519	+	0.462693i	$0.846883\pi$
$74$	−1.14132	−	1.97682i	−0.132675	−	0.229800i
$75$	−3.93078	+	4.84706i	−0.453888	+	0.559690i
$76$	−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	0.580410	−	0.814324i	$-0.302892\pi$
$79$	−3.68878	−	6.38915i	−0.415020	−	0.718836i	−0.995431	+	0.0954881i	$0.969559\pi$
$80$	−4.32614			−0.483677
$81$	0.966208	−	8.94799i	0.107356	−	0.994221i
$82$	−2.43474			−0.268872
$83$	−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
$86$	0.266078	−	0.460861i	0.0286920	−	0.0496960i
$87$	0.260877	−	0.321688i	0.0279689	−	0.0344886i
$88$	1.74596	+	3.02409i	0.186120	+	0.322369i
$89$	−2.74720			−0.291203			−0.145602	−	0.989343i	$-0.546512\pi$
$89$	−2.74720			−0.291203			−0.145602	+	0.989343i	$0.546512\pi$
$90$	−0.630912	+	0.566453i	−0.0665039	+	0.0597094i
$91$		0			0
$92$	−5.44282	−	9.42724i	−0.567453	−	0.982858i
$93$	2.83981	+	0.451852i	0.294475	+	0.0468548i
$94$	−0.696860	+	1.20700i	−0.0718756	+	0.124492i
$95$	−1.14815	+	1.98866i	−0.117798	+	0.204032i
$96$	4.72257	+	0.751424i	0.481995	+	0.0766919i
$97$	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
$100$	7.00000			0.700000
$101$	−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	$-0.386110\pi$
$102$	−1.81122	+	2.23342i	−0.179338	+	0.221142i
$103$	−2.19850	+	3.80791i	−0.216624	+	0.375204i	−0.953774	−	0.300526i	$-0.902838\pi$
$103$	−2.19850	+	3.80791i	−0.216624	+	0.375204i	0.737150	+	0.675730i	$0.236171\pi$
$104$	0.471410	−	0.816506i	0.0462256	−	0.0800650i
$105$		0			0
$106$	−1.38727	−	2.40283i	−0.134744	−	0.233384i
$107$	13.7278			1.32711			0.663557	−	0.748126i	$-0.269046\pi$
$107$	13.7278			1.32711			0.663557	+	0.748126i	$0.269046\pi$
$108$	−8.47825	+	5.48016i	−0.815820	+	0.527329i
$109$	1.26320			0.120993			0.0604963	−	0.998168i	$-0.480732\pi$
$109$	1.26320			0.120993			0.0604963	+	0.998168i	$0.480732\pi$
$110$	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	$0.972805\pi$
$114$	0.506837	−	0.624982i	0.0474696	−	0.0585349i
$115$	−3.31122	−	5.73520i	−0.308773	−	0.534810i
$116$	−0.464574			−0.0431346
$117$	0.619562	+	2.93533i	0.0572785	+	0.271371i
$118$	0.622440			0.0573003
$119$		0			0
$120$	1.90615	+	0.303294i	0.174007	+	0.0276868i
$121$	−1.35868	+	2.35331i	−0.123517	+	0.213937i
$122$	0.909028	−	1.57448i	0.0822996	−	0.142547i
$123$	−17.4166	−	2.77121i	−1.57040	−	0.249871i
$124$	−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
$129$	2.42790	−	2.99386i	0.213765	−	0.263594i
$130$	0.141315	−	0.244765i	0.0123942	−	0.0214673i
$131$	−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	$0.236287\pi$
$132$	4.45813	+	11.6385i	0.388030	+	1.01301i
$133$		0			0
$134$	−0.838864			−0.0724668
$135$	−5.15787	+	3.33394i	−0.443918	+	0.286940i
$136$	6.54583			0.561300
$137$	2.16991	+	3.75839i	0.185387	+	0.321101i	0.943707	−	0.330782i	$-0.107313\pi$
$137$	2.16991	+	3.75839i	0.185387	+	0.321101i	−0.758320	+	0.651883i	$0.773979\pi$
$138$	0.830095	+	2.16708i	0.0706624	+	0.184474i
$139$	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
$143$	3.70370			0.309719
$144$	10.4383	+	3.40803i	0.869859	+	0.284002i
$145$	−0.282630			−0.0234712
$146$	−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	−0.998696	−	0.0510606i	$-0.983740\pi$
$149$	−5.55555	+	9.62249i	−0.455128	+	0.788305i	0.543568	+	0.839365i	$0.317073\pi$
$150$	−1.47373	−	0.234491i	−0.120330	−	0.0191461i
$151$	−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	$-0.358383\pi$
$152$	−1.83173			−0.148573
$153$	−15.4984	+	13.9149i	−1.25297	+	1.12496i
$154$		0			0
$155$	−0.981125	−	1.69936i	−0.0788059	−	0.136496i
$156$	2.11956	−	2.61364i	0.169701	−	0.209259i
$157$	0.0285900	−	0.0495193i	0.00228173	−	0.00395207i	−0.864882	−	0.501975i	$-0.832607\pi$
$157$	0.0285900	−	0.0495193i	0.00228173	−	0.00395207i	0.867164	+	0.498023i	$0.165940\pi$
$158$	0.882073	−	1.52780i	0.0701740	−	0.121545i
$159$	−7.18878	−	18.7673i	−0.570107	−	1.48834i
$160$	−1.63160	−	2.82601i	−0.128989	−	0.223416i
$161$		0			0
$162$	1.96853	−	0.869747i	0.154662	−	0.0683338i
$163$	−1.50808			−0.118122			−0.0590610	−	0.998254i	$-0.518811\pi$
$163$	−1.50808			−0.118122			−0.0590610	+	0.998254i	$0.518811\pi$
$164$	9.89084	+	17.1314i	0.772345	+	1.33774i
$165$	2.71217	+	7.08048i	0.211142	+	0.551215i
$166$	0.830095	−	1.43777i	0.0644279	−	0.111592i
$167$	−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
$170$	1.96225			0.150498
$171$	4.33693	−	3.89384i	0.331653	−	0.297769i
$172$	−4.32365			−0.329675
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	0.870790	−	0.491655i	$-0.163608\pi$
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	−0.861180	+	0.508299i	$0.830274\pi$
$174$	0.0978082	+	0.0155626i	0.00741482	+	0.00117980i
$175$		0			0
$176$	6.77812	−	11.7400i	0.510920	−	0.884939i
$177$	4.45254	+	0.708458i	0.334673	+	0.0532510i
$178$	−0.328460	−	0.568910i	−0.0246191	−	0.0426416i
$179$	14.1923			1.06079			0.530393	−	0.847752i	$-0.322044\pi$
$179$	14.1923			1.06079			0.530393	+	0.847752i	$0.322044\pi$
$180$	6.54871	+	2.13810i	0.488112	+	0.159365i
$181$	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
$184$	2.64132	−	4.57489i	0.194720	−	0.337266i
$185$	−5.64132	+	9.77104i	−0.414758	+	0.718381i
$186$	0.245960	+	0.642111i	0.0180346	+	0.0470819i
$187$	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	−0.998599	−	0.0529159i	$-0.983148\pi$
$191$	−7.53379	−	13.0489i	−0.545126	−	0.944186i	0.453473	−	0.891270i	$-0.350185\pi$
$192$	−4.12640	−	10.7725i	−0.297797	−	0.777440i
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	−0.689536	−	0.724251i	$-0.742186\pi$
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	0.971988	+	0.235030i	$0.0755190\pi$
$194$	−0.857050	+	1.48445i	−0.0615326	+	0.106578i
$195$	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	$0.423403\pi$
$198$	−0.548709	−	2.59964i	−0.0389950	−	0.184749i
$199$	19.9396			1.41348			0.706739	−	0.707475i	$-0.250166\pi$
$199$	19.9396			1.41348			0.706739	+	0.707475i	$0.250166\pi$
$200$	1.69850	+	2.94188i	0.120102	+	0.208022i
$201$	−6.00069	−	0.954790i	−0.423256	−	0.0673457i
$202$	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
$206$	−1.05142			−0.0732561
$207$	3.47141	+	16.4467i	0.241280	+	1.14312i
$208$	−3.66019			−0.253789
$209$	−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	$-0.0473141\pi$
$212$	−11.2713	+	19.5224i	−0.774115	+	1.34081i
$213$	5.33009	+	13.9149i	0.365212	+	0.953436i
$214$	1.64132	+	2.84284i	0.112198	+	0.194333i
$215$	−2.63036			−0.179389
$216$	−4.36032	−	2.23342i	−0.296682	−	0.151965i
$217$		0			0
$218$	0.151030	+	0.261592i	0.0102291	+	0.0177172i
$219$	−9.38564	−	24.5025i	−0.634223	−	1.65572i
$220$	4.25241	−	7.36538i	0.286697	−	0.496574i
$221$	3.47141	−	6.01266i	0.233512	−	0.404455i
$222$	2.49028	−	3.07078i	0.167137	−	0.206097i
$223$	−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
$226$	−2.90834			−0.193460
$227$	−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	$0.889426\pi$
$228$	−6.45649	−	1.02731i	−0.427592	−	0.0680356i
$229$	9.66827	−	16.7459i	0.638897	−	1.10660i	−0.346778	−	0.937947i	$-0.612724\pi$
$229$	9.66827	−	16.7459i	0.638897	−	1.10660i	0.985675	−	0.168655i	$-0.0539425\pi$
$230$	0.791790	−	1.37142i	0.0522091	−	0.0904288i
$231$		0			0
$232$	−0.112725	−	0.195246i	−0.00740077	−	0.0128185i
$233$	−16.9806			−1.11243			−0.556217	−	0.831037i	$-0.687748\pi$
$233$	−16.9806			−1.11243			−0.556217	+	0.831037i	$0.687748\pi$
$234$	−0.533792	+	0.479256i	−0.0348951	+	0.0313299i
$235$	6.88891			0.449383
$236$	−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	$0.982771\pi$
$240$	−2.68031	−	6.99731i	−0.173013	−	0.451674i
$241$	13.5728	+	23.5088i	0.874300	+	1.51433i	0.857507	+	0.514473i	$0.172012\pi$
$241$	13.5728	+	23.5088i	0.874300	+	1.51433i	0.0167933	+	0.999859i	$0.494654\pi$
$242$	−0.649786			−0.0417699
$243$	15.0715	−	3.98104i	0.966840	−	0.255384i
$244$	−14.7713			−0.945634
$245$		0			0
$246$	−1.50847	−	3.93807i	−0.0961766	−	0.251082i
$247$	−0.971410	+	1.68253i	−0.0618093	+	0.107057i
$248$	0.782630	−	1.35556i	0.0496971	−	0.0860778i
$249$	7.57442	−	9.34004i	0.480009	−	0.591901i
$250$	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
$255$	14.0367	+	2.23342i	0.879010	+	0.139862i
$256$	−5.80959	+	10.0625i	−0.363099	+	0.628906i
$257$	−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	$0.319863\pi$
$258$	0.910272	+	0.144836i	0.0566711	+	0.00901712i
$259$		0			0
$260$	−2.29630			−0.142411
$261$	0.681943	+	0.222649i	0.0422112	+	0.0137817i
$262$	−1.18770			−0.0733764
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	0.960335	−	0.278847i	$-0.0899523\pi$
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	−0.721656	+	0.692251i	$0.756619\pi$
$264$	−3.80959	+	4.69761i	−0.234464	+	0.289118i
$265$	−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
$269$	1.51135			0.0921486			0.0460743	−	0.998938i	$-0.485329\pi$
$269$	1.51135			0.0921486			0.0460743	+	0.998938i	$0.485329\pi$
$270$	−1.30710	−	0.669515i	−0.0795474	−	0.0407454i
$271$	21.9806			1.33522			0.667612	−	0.744509i	$-0.267316\pi$
$271$	21.9806			1.33522			0.667612	+	0.744509i	$0.267316\pi$
$272$	−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
$276$	11.8759	−	14.6442i	0.714847	−	0.881480i
$277$	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	$0.727865\pi$
$278$	0.942820			0.0565466
$279$	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	$0.665420\pi$
$282$	−2.38401	−	0.379327i	−0.141965	−	0.0225886i
$283$	−7.65856	+	13.2650i	−0.455254	+	0.788523i	−0.998703	−	0.0509194i	$-0.983785\pi$
$283$	−7.65856	+	13.2650i	−0.455254	+	0.788523i	0.543449	+	0.839442i	$0.317118\pi$
$284$	8.35705	−	14.4748i	0.495900	−	0.858923i
$285$	−3.92790	−	0.624982i	−0.232669	−	0.0370207i
$286$	0.442820	+	0.766987i	0.0261845	+	0.0453529i
$287$		0			0
$288$	1.71053	+	8.10408i	0.100794	+	0.477537i
$289$	31.2028			1.83546
$290$	−0.0337917	−	0.0585290i	−0.00198432	−	0.00343694i
$291$	−7.82038	+	9.64334i	−0.458439	+	0.565302i
$292$	−14.7157	+	25.4884i	−0.861173	+	1.49160i
$293$	−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
$296$	−9.00000			−0.523114
$297$	−0.966208	−	19.2207i	−0.0560651	−	1.11530i
$298$	−2.65692			−0.153911
$299$	−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
$303$	13.9480	−	17.1994i	0.801293	−	0.988077i
$304$	3.55555	+	6.15838i	0.203925	+	0.353208i
$305$	−8.98633			−0.514556
$306$	−4.73461	−	1.54581i	−0.270660	−	0.0883684i
$307$	−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
$310$	0.234610	−	0.406356i	0.0133249	−	0.0230795i
$311$	−6.99028	+	12.1075i	−0.396383	+	0.686555i	−0.993277	−	0.115765i	$-0.963068\pi$
$311$	−6.99028	+	12.1075i	−0.396383	+	0.686555i	0.596894	+	0.802320i	$0.296401\pi$
$312$	1.61273	+	0.256606i	0.0913026	+	0.0145275i
$313$	−9.52696	−	16.5012i	−0.538495	−	0.932701i	−0.998985	−	0.0450364i	$-0.985660\pi$
$313$	−9.52696	−	16.5012i	−0.538495	−	0.932701i	0.460490	−	0.887665i	$-0.347674\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	2.00972	+	3.48093i	0.112877	+	0.195508i	0.916929	−	0.399050i	$-0.130660\pi$
$317$	2.00972	+	3.48093i	0.112877	+	0.195508i	−0.804052	+	0.594559i	$0.797327\pi$
$318$	3.02696	−	3.73255i	0.169743	−	0.209311i
$319$	0.442820	−	0.766987i	0.0247932	−	0.0429430i
$320$	−3.93598	+	6.81732i	−0.220028	+	0.381100i
$321$	8.50520	+	22.2040i	0.474714	+	1.23931i
$322$		0			0
$323$	−13.4887			−0.750529
$324$	−14.1167	−	10.3178i	−0.784260	−	0.573213i
$325$	3.60301			0.199859
$326$	−0.180309	−	0.312304i	−0.00998637	−	0.0172969i
$327$	0.782630	+	2.04316i	0.0432795	+	0.112987i
$328$	−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	0.984463	−	0.175590i	$-0.0561834\pi$
$331$	6.18878	+	10.7193i	0.340166	+	0.589185i	−0.644297	+	0.764775i	$0.722850\pi$
$332$	−13.4887			−0.740286
$333$	21.3090	−	19.1319i	1.16773	−	1.04842i
$334$	−3.51135			−0.192133
$335$	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	$0.275038\pi$
$338$	−1.43474	+	2.48504i	−0.0780395	+	0.135168i
$339$	−20.8044	−	3.31026i	−1.12994	−	0.179788i
$340$	−7.97141	−	13.8069i	−0.432310	−	0.748784i
$341$	6.14884			0.332978
$342$	1.32489	+	0.432568i	0.0716420	+	0.0233906i
$343$		0			0
$344$	−1.04910	−	1.81709i	−0.0565637	−	0.0979711i
$345$	7.22489	−	8.90904i	0.388975	−	0.479647i
$346$	−0.0302247	+	0.0523508i	−0.00162489	+	0.00281440i
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	−0.941363	−	0.337394i	$-0.890454\pi$
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	0.762874	+	0.646547i	$0.223788\pi$
$348$	−0.287832	−	0.751424i	−0.0154294	−	0.0402806i
$349$	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
$352$	10.2255			0.545018
$353$	−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	$-0.367806\pi$
$354$	0.385640	+	1.00677i	0.0204965	+	0.0535090i
$355$	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
$359$	−7.55623			−0.398803			−0.199401	−	0.979918i	$-0.563900\pi$
$359$	−7.55623			−0.398803			−0.199401	+	0.979918i	$0.563900\pi$
$360$	0.690415	+	3.27101i	0.0363880	+	0.172397i
$361$	−15.2255			−0.801339
$362$	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
$366$	3.10985	+	0.494818i	0.162554	+	0.0258646i
$367$	−9.26157	−	16.0415i	−0.483450	−	0.837360i	0.516370	−	0.856366i	$-0.327283\pi$
$367$	−9.26157	−	16.0415i	−0.483450	−	0.837360i	−0.999819	+	0.0190063i	$0.993950\pi$
$368$	−20.5081			−1.06906
$369$	−6.30834	−	29.8873i	−0.328399	−	1.55587i
$370$	−2.69794			−0.140259
$371$		0			0
$372$	3.51887	−	4.33914i	0.182445	−	0.224974i
$373$	−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	$0.299544\pi$
$374$	−3.07442	+	5.32505i	−0.158974	+	0.275352i
$375$	6.29987	+	16.4467i	0.325324	+	0.849302i
$376$	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
$381$	0.830095	+	2.16708i	0.0425271	+	0.111023i
$382$	1.80150	−	3.12030i	0.0921730	−	0.159648i
$383$	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	$0.164833\pi$
$384$	7.76157	−	9.57081i	0.396081	−	0.488408i
$385$		0			0
$386$	1.87661			0.0955171
$387$	6.34665	+	2.07213i	0.322618	+	0.105332i
$388$	13.9267			0.707019
$389$	−12.6316	−	21.8786i	−0.640448	−	1.10929i	−0.985333	−	0.170643i	$-0.945416\pi$
$389$	−12.6316	−	21.8786i	−0.640448	−	1.10929i	0.344885	−	0.938645i	$-0.387918\pi$
$390$	0.483448	+	0.0769231i	0.0244804	+	0.00389515i
$391$	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
$395$	−8.71986			−0.438744
$396$	−16.0627	+	14.4216i	−0.807180	+	0.724712i
$397$	20.3009			1.01888			0.509438	−	0.860508i	$-0.329853\pi$
$397$	20.3009			1.01888			0.509438	+	0.860508i	$0.329853\pi$
$398$	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	−0.610924	−	0.791689i	$-0.709202\pi$
$401$	7.61273	−	13.1856i	0.380161	−	0.658459i	0.991085	+	0.133231i	$0.0425351\pi$
$402$	−0.519728	−	1.35682i	−0.0259217	−	0.0676720i
$403$	−0.830095	−	1.43777i	−0.0413500	−	0.0716203i
$404$	−24.8389			−1.23578
$405$	−8.58809	−	6.27701i	−0.426746	−	0.311907i
$406$		0			0
$407$	−17.6774	−	30.6182i	−0.876238	−	1.51769i
$408$	4.05555	+	10.5876i	0.200779	+	0.524162i
$409$	0.828460	−	1.43494i	0.0409647	−	0.0709530i	−0.844816	−	0.535057i	$-0.820290\pi$
$409$	0.828460	−	1.43494i	0.0409647	−	0.0709530i	0.885781	+	0.464104i	$0.153624\pi$
$410$	−1.43886	+	2.49218i	−0.0710603	+	0.123080i
$411$	−4.73461	+	5.83826i	−0.233541	+	0.287980i
$412$	4.27128	+	7.39807i	0.210431	+	0.364477i
$413$		0			0
$414$	−2.99084	+	2.68527i	−0.146992	+	0.131974i
$415$	−8.20602			−0.402818
$416$	−1.38044	−	2.39099i	−0.0676816	−	0.117228i
$417$	6.74433	+	1.07311i	0.330271	+	0.0525505i
$418$	0.860320	−	1.49012i	0.0420796	−	0.0728840i
$419$	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	$0.979950\pi$
$422$	4.32614			0.210593
$423$	−16.6219	−	5.42692i	−0.808184	−	0.263866i
$424$	−10.9396			−0.531272
$425$	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
$429$	2.29467	+	5.99054i	0.110788	+	0.289226i
$430$	−0.314490	−	0.544712i	−0.0151660	−	0.0262684i
$431$	29.2826			1.41049			0.705247	−	0.708961i	$-0.250836\pi$
$431$	29.2826			1.41049			0.705247	+	0.708961i	$0.250836\pi$
$432$	0.954858	+	18.9949i	0.0459406	+	0.913894i
$433$	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
$436$	1.22708	−	2.12537i	0.0587667	−	0.101787i
$437$	−5.44282	+	9.42724i	−0.260365	+	0.450966i
$438$	3.95198	−	4.87320i	0.188833	−	0.232850i
$439$	−2.41586	−	4.18440i	−0.115303	−	0.199711i	0.802598	−	0.596520i	$-0.203451\pi$
$439$	−2.41586	−	4.18440i	−0.115303	−	0.199711i	−0.917901	+	0.396810i	$0.870117\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	0.850860	−	0.525392i	$-0.176081\pi$
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	−0.880433	+	0.474170i	$0.842748\pi$
$444$	−31.7233	−	5.04759i	−1.50552	−	0.239548i
$445$	−1.62352	+	2.81202i	−0.0769622	+	0.133302i
$446$	2.70890	−	4.69195i	0.128270	−	0.222170i
$447$	−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	$0.433200\pi$
$450$	−0.533792	−	2.52897i	−0.0251632	−	0.119217i
$451$	−37.7108			−1.77573
$452$	11.8148	+	20.4638i	0.555721	+	0.962537i
$453$	15.1900	−	18.7309i	0.713690	−	0.880053i
$454$	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	0.962349	−	0.271817i	$-0.0876247\pi$
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	−0.716575	+	0.697510i	$0.754291\pi$
$458$	4.62382			0.216057
$459$	−32.1089	−	16.4467i	−1.49872	−	0.767665i
$460$	−12.8662			−0.599890
$461$	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	$0.244337\pi$
$464$	−0.437618	+	0.757977i	−0.0203159	+	0.0351882i
$465$	2.14076	−	2.63978i	0.0992753	−	0.122417i
$466$	−2.03022	−	3.51645i	−0.0940483	−	0.162897i
$467$	−13.3171			−0.616242			−0.308121	−	0.951347i	$-0.599700\pi$
$467$	−13.3171			−0.616242			−0.308121	+	0.951347i	$0.599700\pi$
$468$	5.54063	+	1.80897i	0.256116	+	0.0836198i
$469$		0			0
$470$	0.823649	+	1.42660i	0.0379921	+	0.0658043i
$471$	0.0978082	+	0.0155626i	0.00450676	+	0.000717086i
$472$	1.22708	−	2.12537i	0.0564812	−	0.0978282i
$473$	4.12120	−	7.13812i	0.189493	−	0.328211i
$474$	3.01763	+	0.480145i	0.138604	+	0.0220538i
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	25.9012	−	23.2550i	1.18594	−	1.06477i
$478$	−4.03775			−0.184682
$479$	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	$0.725586\pi$
$480$	3.56006	−	4.38992i	0.162494	−	0.200372i
$481$	−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
$485$	8.47249			0.384716
$486$	2.62640	+	2.64514i	0.119136	+	0.119986i
$487$	13.0539			0.591529			0.295765	−	0.955261i	$-0.404426\pi$
$487$	13.0539			0.591529			0.295765	+	0.955261i	$0.404426\pi$
$488$	−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	$0.310449\pi$
$492$	−21.5813	+	26.6119i	−0.972958	+	1.19976i
$493$	−0.830095	−	1.43777i	−0.0373856	−	0.0647538i
$494$	−0.464574			−0.0209022
$495$	−9.77197	+	8.77359i	−0.439217	+	0.394344i
$496$	−6.07661			−0.272848
$497$		0			0
$498$	2.83981	+	0.451852i	0.127255	+	0.0202480i
$499$	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	$-0.134281\pi$
$500$	9.87756	−	17.1084i	0.441738	−	0.765112i
$501$	−25.1179	−	3.99660i	−1.12219	−	0.178555i
$502$	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
$507$	−13.0917	+	16.1434i	−0.581421	+	0.716952i
$508$	1.30150	−	2.25427i	0.0577449	−	0.100017i
$509$	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	$-0.108250\pi$
$510$	1.21574	+	3.17384i	0.0538337	+	0.140540i
$511$		0			0
$512$	−17.0071			−0.751616
$513$	8.98508	+	4.60230i	0.396701	+	0.203196i
$514$	−3.54910			−0.156544
$515$	2.59850	+	4.50073i	0.114503	+	0.198326i
$516$	−2.67877	−	6.99329i	−0.117926	−	0.307862i
$517$	−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
$521$	10.2449			0.448836			0.224418	−	0.974493i	$-0.427952\pi$
$521$	10.2449			0.448836			0.224418	+	0.974493i	$0.427952\pi$
$522$	0.0354265	+	0.167842i	0.00155058	+	0.00734624i
$523$	−30.6030			−1.33818			−0.669088	−	0.743183i	$-0.733315\pi$
$523$	−30.6030			−1.33818			−0.669088	+	0.743183i	$0.733315\pi$
$524$	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
$528$	23.1884	+	3.68958i	1.00915	+	0.160568i
$529$	−4.19686	−	7.26918i	−0.182472	−	0.316051i
$530$	−3.27936			−0.142446
$531$	1.61273	+	7.64068i	0.0699863	+	0.331577i
$532$		0			0
$533$	5.09097	+	8.81782i	0.220514	+	0.381942i
$534$	0.716681	−	0.883742i	0.0310138	−	0.0382433i
$535$	8.11273	−	14.0517i	0.350744	−	0.607506i
$536$	−1.65374	+	2.86437i	−0.0714309	+	0.123722i
$537$	8.79303	+	22.9554i	0.379447	+	0.990599i
$538$	0.180699	+	0.312981i	0.00779051	+	0.0134936i
$539$		0			0
$540$	0.599052	+	11.9169i	0.0257791	+	0.512821i
$541$	−26.0917			−1.12177			−0.560884	−	0.827894i	$-0.689539\pi$
$541$	−26.0917			−1.12177			−0.560884	+	0.827894i	$0.689539\pi$
$542$	2.62803	+	4.55189i	0.112884	+	0.195520i
$543$	0.886884	+	2.31533i	0.0380598	+	0.0993604i
$544$	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	0.958843	−	0.283937i	$-0.0916405\pi$
$547$	5.46169	+	9.45993i	0.233525	+	0.404478i	−0.725318	+	0.688414i	$0.758307\pi$
$548$	8.43147			0.360175
$549$	21.6826	+	7.07922i	0.925392	+	0.302134i
$550$	−3.19097			−0.136063
$551$	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
$555$	−19.2993	−	3.07078i	−0.819210	−	0.130347i
$556$	−3.83009	−	6.63392i	−0.162432	−	0.281341i
$557$	−13.9442			−0.590835			−0.295417	−	0.955368i	$-0.595459\pi$
$557$	−13.9442			−0.590835			−0.295417	+	0.955368i	$0.595459\pi$
$558$	−0.886196	+	0.795655i	−0.0375157	+	0.0336828i
$559$	−2.22545			−0.0941265
$560$		0			0
$561$	−28.0534	+	34.5927i	−1.18441	+	1.46050i
$562$	−2.01780	+	3.49492i	−0.0851156	+	0.147424i
$563$	15.1287	−	26.2037i	0.637600	−	1.10435i	−0.348358	−	0.937361i	$-0.613261\pi$
$563$	15.1287	−	26.2037i	0.637600	−	1.10435i	0.985958	−	0.166993i	$-0.0534059\pi$
$564$	7.01570	+	18.3154i	0.295414	+	0.771219i
$565$	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	0.997912	−	0.0645936i	$-0.0205751\pi$
$569$	10.5676	+	18.3036i	0.443016	+	0.767326i	−0.554896	+	0.831920i	$0.687242\pi$
$570$	−0.340201	−	0.888141i	−0.0142495	−	0.0372001i
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	−0.287078	−	0.957907i	$-0.592684\pi$
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	0.973111	−	0.230336i	$-0.0739826\pi$
$572$	3.59781	−	6.23159i	0.150432	−	0.260556i
$573$	16.4383	−	20.2701i	0.686720	−	0.846797i
$574$		0			0
$575$	20.1877			0.841885
$576$	14.8675	−	13.3485i	0.619477	−	0.556187i
$577$	17.3743			0.723301			0.361651	−	0.932314i	$-0.382213\pi$
$577$	17.3743			0.723301			0.361651	+	0.932314i	$0.382213\pi$
$578$	3.73065	+	6.46168i	0.155175	+	0.268770i
$579$	13.4241	+	2.13595i	0.557886	+	0.0887671i
$580$	−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
$584$	−14.2826			−0.591019
$585$	3.37072	+	1.10052i	0.139362	+	0.0455007i
$586$	−2.24050			−0.0925542
$587$	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
$590$	0.367845	−	0.637125i	0.0151439	−	0.0262300i
$591$	4.14488	+	10.8208i	0.170498	+	0.445107i
$592$	17.4698	+	30.2585i	0.718003	+	1.24362i
$593$	13.0733			0.536858			0.268429	−	0.963300i	$-0.413496\pi$
$593$	13.0733			0.536858			0.268429	+	0.963300i	$0.413496\pi$
$594$	3.86483	−	2.49815i	0.158576	−	0.102500i
$595$		0			0
$596$	10.7934	+	18.6948i	0.442116	+	0.765767i
$597$	12.3538	+	32.2512i	0.505607	+	1.31995i
$598$	0.669905	−	1.16031i	0.0273945	−	0.0474486i
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	0.396647	+	0.917971i	$0.370174\pi$
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	−0.993310	+	0.115479i	$0.963160\pi$
$600$	−3.70602	+	4.56991i	−0.151298	+	0.186566i
$601$	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
$604$	−27.0506			−1.10067
$605$	1.60589	+	2.78148i	0.0652887	+	0.113083i
$606$	5.22941	+	0.832069i	0.212430	+	0.0338005i
$607$	−9.82038	+	17.0094i	−0.398597	+	0.690390i	−0.993553	−	0.113368i	$-0.963836\pi$
$607$	−9.82038	+	17.0094i	−0.398597	+	0.690390i	0.594956	+	0.803758i	$0.297169\pi$
$608$	−2.68194	+	4.64526i	−0.108767	+	0.188390i
$609$		0			0
$610$	−1.07442	−	1.86095i	−0.0435020	−	0.0753477i
$611$	5.82846			0.235794
$612$	8.35705	+	39.5936i	0.337814	+	1.60048i
$613$	23.5653			0.951792			0.475896	−	0.879502i	$-0.342124\pi$
$613$	23.5653			0.951792			0.475896	+	0.879502i	$0.342124\pi$
$614$	−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	$0.0978279\pi$
$618$	−0.651421	−	1.70062i	−0.0262040	−	0.0684091i
$619$	−9.00752	−	15.6015i	−0.362043	−	0.627077i	0.626254	−	0.779619i	$-0.284587\pi$
$619$	−9.00752	−	15.6015i	−0.362043	−	0.627077i	−0.988297	+	0.152542i	$0.951254\pi$
$620$	−3.81230			−0.153106
$621$	−24.4509	+	15.8046i	−0.981181	+	0.634215i
$622$	−3.34308			−0.134045
$623$		0			0
$624$	−2.26771	−	5.92017i	−0.0907812	−	0.236997i
$625$	−2.99837	+	5.19332i	−0.119935	+	0.207733i
$626$	2.27812	−	3.94581i	0.0910519	−	0.157706i
$627$	7.85021	−	9.68013i	0.313507	−	0.386587i
$628$	−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
$633$	30.9464	+	4.92398i	1.23001	+	0.195711i
$634$	−0.480570	+	0.832371i	−0.0190859	+	0.0330577i
$635$	0.791790	−	1.37142i	0.0314212	−	0.0544232i
$636$	−38.5598	−	6.13538i	−1.52900	−	0.243284i
$637$		0			0
$638$	0.211777			0.00838434
$639$	−19.2044	+	17.2423i	−0.759714	+	0.682096i
$640$	−8.40877			−0.332386
$641$	−9.57279	−	16.5806i	−0.378102	−	0.654892i	0.612684	−	0.790328i	$-0.290090\pi$
$641$	−9.57279	−	16.5806i	−0.378102	−	0.654892i	−0.990786	+	0.135436i	$0.956757\pi$
$642$	−3.58126	+	4.41606i	−0.141341	+	0.174288i
$643$	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
$647$	48.0988			1.89096			0.945479	−	0.325682i	$-0.105594\pi$
$647$	48.0988			1.89096			0.945479	+	0.325682i	$0.105594\pi$
$648$	0.910961	−	8.43634i	0.0357859	−	0.331411i
$649$	9.64076			0.378433
$650$	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	$-0.512298\pi$
$653$	21.6202	−	37.4474i	0.846066	−	1.46543i	0.884692	−	0.466175i	$-0.154368\pi$
$654$	−0.329539	+	0.406356i	−0.0128860	+	0.0158898i
$655$	2.93530	+	5.08408i	0.114691	+	0.198651i
$656$	37.2678			1.45506
$657$	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	$0.817778\pi$
$660$	14.5478	+	2.31474i	0.566271	+	0.0901013i
$661$	−21.1677	+	36.6636i	−0.823329	+	1.42605i	0.0798613	+	0.996806i	$0.474552\pi$
$661$	−21.1677	+	36.6636i	−0.823329	+	1.42605i	−0.903190	+	0.429241i	$0.858781\pi$
$662$	−1.47988	+	2.56323i	−0.0575172	+	0.0996227i
$663$	11.8759	+	1.88962i	0.461223	+	0.0733867i
$664$	−3.27292	−	5.66886i	−0.127014	−	0.219994i
$665$		0			0
$666$	6.50972	+	2.12537i	0.252246	+	0.0823566i
$667$	−1.33981			−0.0518777
$668$	14.2644	+	24.7067i	0.551908	+	0.955933i
$669$	24.7181	−	30.4799i	0.955655	−	1.17842i
$670$	−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	0.707296	−	0.706918i	$-0.249915\pi$
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	−0.965857	+	0.259077i	$0.916582\pi$
$674$	−2.93163			−0.112922
$675$	−0.939941	−	18.6982i	−0.0361784	−	0.719693i
$676$	23.3138			0.896686
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	0.884263	−	0.466989i	$-0.154661\pi$
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	−0.846556	+	0.532300i	$0.821328\pi$
$678$	−1.80190	−	4.70409i	−0.0692014	−	0.180660i
$679$		0			0
$680$	3.86840	−	6.70027i	0.148346	−	0.256943i
$681$	5.76320	−	7.10662i	0.220846	−	0.272326i
$682$	0.735165	+	1.27334i	0.0281509	+	0.0487589i
$683$	27.1672			1.03952			0.519761	−	0.854312i	$-0.326021\pi$
$683$	27.1672			1.03952			0.519761	+	0.854312i	$0.326021\pi$
$684$	−2.33857	−	11.0795i	−0.0894173	−	0.423637i
$685$	5.12941			0.195985
$686$		0			0
$687$	33.0758	+	5.26280i	1.26192	+	0.200788i
$688$	−4.07279	+	7.05427i	−0.155273	+	0.268942i
$689$	−5.80150	+	10.0485i	−0.221020	+	0.382817i
$690$	2.70877	+	0.431001i	0.103121	+	0.0164079i
$691$	−25.1586	−	43.5759i	−0.957077	−	1.65771i	−0.729543	−	0.683935i	$-0.760267\pi$
$691$	−25.1586	−	43.5759i	−0.957077	−	1.65771i	−0.227534	−	0.973770i	$-0.573066\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	−2.33009	−	4.03584i	−0.0883855	−	0.153088i
$696$	0.245960	−	0.303294i	0.00932308	−	0.0114963i
$697$	−35.3457	+	61.2205i	−1.33881	+	2.31889i
$698$	−1.36716	+	2.36798i	−0.0517476	+	0.0896295i
$699$	−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	$0.174799\pi$
$702$	−1.10589	−	0.566453i	−0.0417391	−	0.0213794i
$703$	18.5458			0.699469
$704$	−12.3337	−	21.3625i	−0.464842	−	0.805131i
$705$	4.26810	+	11.1425i	0.160746	+	0.419649i
$706$	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	−0.950687	−	0.310153i	$-0.899620\pi$
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	0.206743	−	0.978395i	$-0.433714\pi$
$710$	2.43147			0.0912514
$711$	21.0397	+	6.86930i	0.789050	+	0.257619i
$712$	−2.59012			−0.0970688
$713$	−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
$717$	−28.8834	−	4.59574i	−1.07867	−	0.171631i
$718$	−0.903436	−	1.56480i	−0.0337159	−	0.0583977i
$719$	22.0377			0.821869			0.410935	−	0.911665i	$-0.365202\pi$
$719$	22.0377			0.821869			0.410935	+	0.911665i	$0.365202\pi$
$720$	9.65718	−	8.67053i	0.359902	−	0.323132i
$721$		0			0
$722$	−1.82038	−	3.15299i	−0.0677475	−	0.117342i
$723$	−29.6150	+	36.5184i	−1.10140	+	1.35813i
$724$	1.39054	−	2.40849i	0.0516792	−	0.0895110i
$725$	0.430782	−	0.746136i	0.0159988	−	0.0277108i
$726$	−0.402583	−	1.05100i	−0.0149412	−	0.0390061i
$727$	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
$730$	−4.28152			−0.158466
$731$	−7.72545	−	13.3809i	−0.285736	−	0.494909i
$732$	−9.15172	−	23.8918i	−0.338257	−	0.883066i
$733$	5.93474	−	10.2793i	0.219205	−	0.379674i	−0.735360	−	0.677676i	$-0.762987\pi$
$733$	5.93474	−	10.2793i	0.219205	−	0.379674i	0.954565	+	0.298003i	$0.0963204\pi$
$734$	2.21466	−	3.83590i	0.0817444	−	0.141586i
$735$		0			0
$736$	−7.73461	−	13.3967i	−0.285102	−	0.493810i
$737$	−12.9929			−0.478598
$738$	5.43504	−	4.87975i	0.200066	−	0.179626i
$739$	−12.1844			−0.448212			−0.224106	−	0.974565i	$-0.571946\pi$
$739$	−12.1844			−0.448212			−0.224106	+	0.974565i	$0.571946\pi$
$740$	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	$-0.137149\pi$
$744$	2.67743	+	0.426015i	0.0981593	+	0.0156185i
$745$	6.56634	+	11.3732i	0.240572	+	0.416683i
$746$	−3.74472			−0.137104
$747$	19.7999	+	6.46451i	0.724439	+	0.236524i
$748$	49.9579			1.82664
$749$		0			0
$750$	−2.65267	+	3.27101i	−0.0968616	+	0.119440i
$751$	−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	$0.881375\pi$
$752$	10.6666	−	18.4752i	0.388972	−	0.673720i
$753$	11.8200	+	30.8577i	0.430744	+	1.12452i
$754$	−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
$759$	12.8571	+	33.5651i	0.466681	+	1.21833i
$760$	−1.08250	+	1.87495i	−0.0392664	+	0.0680114i
$761$	−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	$0.250340\pi$
$762$	−0.349525	+	0.431001i	−0.0126620	+	0.0156135i
$763$		0			0
$764$	−29.2736			−1.05908
$765$	5.08414	+	24.0874i	0.183817	+	0.870880i
$766$	0.0539104			0.00194786
$767$	−1.30150	−	2.25427i	−0.0469946	−	0.0813971i
$768$	−19.8750	−	3.16237i	−0.717177	−	0.114112i
$769$	−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
$773$	−4.38005			−0.157539			−0.0787697	−	0.996893i	$-0.525099\pi$
$773$	−4.38005			−0.157539			−0.0787697	+	0.996893i	$0.525099\pi$
$774$	0.329704	+	1.56205i	0.0118510	+	0.0561469i
$775$	5.98168			0.214868
$776$	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
$780$	−1.42270	−	3.71415i	−0.0509409	−	0.132988i
$781$	15.9315	+	27.5941i	0.570073	+	0.987395i
$782$	9.30206			0.332641
$783$	0.0623817	+	1.24095i	0.00222934	+	0.0443481i
$784$		0			0
$785$	−0.0337917	−	0.0585290i	−0.00120608	−	0.00208899i
$786$	−0.735854	−	1.92105i	−0.0262470	−	0.0685214i
$787$	13.8107	−	23.9208i	0.492297	−	0.852683i	−0.507664	−	0.861555i	$-0.669491\pi$
$787$	13.8107	−	23.9208i	0.492297	−	0.852683i	0.999961	+	0.00887191i	$0.00282405\pi$
$788$	6.49876	−	11.2562i	0.231509	−	0.400985i
$789$	−8.44570	+	10.4144i	−0.300675	+	0.370763i
$790$	−1.04256	−	1.80577i	−0.0370926	−	0.0642463i
$791$		0			0
$792$	−9.95843	−	3.25135i	−0.353857	−	0.115532i
$793$	−7.60301			−0.269991
$794$	2.42721	+	4.20406i	0.0861386	+	0.149196i
$795$	−23.4584	−	3.73255i	−0.831985	−	0.132380i
$796$	19.3695	−	33.5489i	0.686533	−	1.18911i
$797$	−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
$800$	9.94747			0.351696
$801$	6.13255	−	5.50600i	0.216683	−	0.194545i
$802$	3.64076			0.128560
$803$	−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
$807$	0.936374	+	2.44453i	0.0329619	+	0.0860516i
$808$	−6.02696	−	10.4390i	−0.212028	−	0.367242i
$809$	−24.7896			−0.871556			−0.435778	−	0.900054i	$-0.643527\pi$
$809$	−24.7896			−0.871556			−0.435778	+	0.900054i	$0.643527\pi$
$810$	0.273080	−	2.52897i	0.00959504	−	0.0888590i
$811$	−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
$814$	4.22708	−	7.32153i	0.148159	−	0.256619i
$815$	−0.891233	+	1.54366i	−0.0312185	+	0.0540721i
$816$	27.7238	−	34.1863i	0.970528	−	1.19676i
$817$	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	0.999988	+	0.00496829i	$0.00158146\pi$
$821$	14.4497	+	25.0275i	0.504296	+	0.873467i	−0.495691	+	0.868499i	$0.665085\pi$
$822$	−1.77511	−	0.282443i	−0.0619139	−	0.00985133i
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	−2.07279	+	3.59017i	−0.0722089	+	0.125069i
$825$	−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	$0.843597\pi$
$828$	31.0442	+	10.1357i	1.07886	+	0.352240i
$829$	−14.8123			−0.514452			−0.257226	−	0.966351i	$-0.582809\pi$
$829$	−14.8123			−0.514452			−0.257226	+	0.966351i	$0.582809\pi$
$830$	−0.981125	−	1.69936i	−0.0340554	−	0.0589856i
$831$	−11.8135	+	14.5673i	−0.409807	+	0.505335i
$832$	−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
$836$	−13.9798			−0.483501
$837$	−7.24488	+	4.68294i	−0.250420	+	0.161866i
$838$	7.98057			0.275684
$839$	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
$842$	2.18086	−	3.77737i	0.0751575	−	0.130177i
$843$	−18.4119	+	22.7038i	−0.634140	+	0.781960i
$844$	−17.5744	−	30.4398i	−0.604936	−	1.04778i
$845$	14.1833			0.487921
$846$	−0.863496	−	4.09103i	−0.0296876	−	0.140652i
$847$		0			0
$848$	21.2346	+	36.7794i	0.729199	+	1.26301i
$849$	−26.2004	−	4.16884i	−0.899196	−	0.143074i
$850$	−2.99084	+	5.18029i	−0.102585	+	0.177682i
$851$	−26.7427	+	46.3197i	−0.916728	+	1.58782i
$852$	28.5900	+	4.54906i	0.979478	+	0.155848i
$853$	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
$856$	12.9428			0.442376
$857$	−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	$-0.346370\pi$
$858$	−0.966208	+	1.19143i	−0.0329858	+	0.0406749i
$859$	−25.1947	+	43.6384i	−0.859631	+	1.48892i	0.0126501	+	0.999920i	$0.495973\pi$
$859$	−25.1947	+	43.6384i	−0.859631	+	1.48892i	−0.872281	+	0.489005i	$0.837360\pi$
$860$	−2.55515	+	4.42566i	−0.0871300	+	0.150914i
$861$		0			0
$862$	3.50108	+	6.06405i	0.119247	+	0.206542i
$863$	1.13268			0.0385568			0.0192784	−	0.999814i	$-0.493863\pi$
$863$	1.13268			0.0385568			0.0192784	+	0.999814i	$0.493863\pi$
$864$	−12.0482	+	7.78768i	−0.409886	+	0.264942i
$865$	0.298791			0.0101592
$866$	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
$870$	0.0737316	−	0.0909187i	0.00249974	−	0.00308243i
$871$	1.75404	+	3.03809i	0.0594334	+	0.102942i
$872$	1.19097			0.0403313
$873$	−20.4428	−	6.67443i	−0.691885	−	0.225895i
$874$	−2.60301			−0.0880481
$875$		0			0
$876$	−50.3435	−	8.01033i	−1.70095	−	0.270644i
$877$	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	$0.0136156\pi$
$878$	0.577690	−	1.00059i	0.0194961	−	0.0337682i
$879$	−16.0271	−	2.55012i	−0.540580	−	0.0860135i
$880$	−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
$885$	3.35649	−	4.13891i	0.112827	−	0.139128i
$886$	0.148840	−	0.257798i	0.00500038	−	0.00866091i
$887$	−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	$0.920746\pi$
$888$	−5.57605	−	14.5570i	−0.187120	−	0.488503i
$889$		0			0
$890$	−0.776443			−0.0260264
$891$	30.4899	−	13.4712i	1.02145	−	0.451302i
$892$	−44.0183			−1.47384
$893$	−5.66182	−	9.80657i	−0.189466	−	0.328164i
$894$	−1.64613	−	4.29743i	−0.0550547	−	0.143728i
$895$	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
$899$	−0.396990			−0.0132404
$900$	−15.6260	+	14.0295i	−0.520867	+	0.467651i
$901$	−80.5576			−2.68376
$902$	−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
$906$	5.69506	+	0.906160i	0.189206	+	0.0301052i
$907$	−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	$-0.366973\pi$
$908$	−10.2632			−0.340596
$909$	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	$0.721860\pi$
$912$	−7.75800	+	9.56641i	−0.256893	+	0.316776i
$913$	12.8571	−	22.2691i	0.425506	−	0.736998i
$914$	−1.25636	+	2.17609i	−0.0415568	+	0.0719785i
$915$	−5.56758	−	14.5349i	−0.184059	−	0.480510i
$916$	−18.7837	−	32.5343i	−0.620631	−	1.07496i
$917$		0			0
$918$	−0.433105	−	8.61572i	−0.0142946	−	0.284361i
$919$	14.3926			0.474768			0.237384	−	0.971416i	$-0.423710\pi$
$919$	14.3926			0.474768			0.237384	+	0.971416i	$0.423710\pi$
$920$	−3.12188	−	5.40726i	−0.102925	−	0.178272i
$921$	−1.68155	−	4.38992i	−0.0554090	−	0.144653i
$922$	−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
$926$	−2.48616			−0.0817004
$927$	−2.72421	−	12.9066i	−0.0894747	−	0.423908i
$928$	−0.660190			−0.0216718
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	−0.973509	−	0.228647i	$-0.926570\pi$
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	0.288741	−	0.957407i	$-0.406763\pi$
$930$	0.802616	+	0.127707i	0.0263188	+	0.00418768i
$931$		0			0
$932$	−16.4951	+	28.5703i	−0.540315	+	0.935853i
$933$	−23.9142	−	3.80507i	−0.782917	−	0.124573i
$934$	−1.59222	−	2.75780i	−0.0520989	−	0.0902379i
$935$	30.3926			0.993945
$936$	0.584135	+	2.76748i	0.0190931	+	0.0904581i
$937$	−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
$940$	6.69196	−	11.5908i	0.218268	−	0.378050i
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	−0.891080	−	0.453846i	$-0.850052\pi$
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	0.838582	+	0.544775i	$0.183385\pi$
$942$	0.00847130	+	0.0221155i	0.000276010	+	0.000720561i
$943$	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	0.953934	+	0.300016i	$0.0969922\pi$
$947$	22.6735	+	39.2716i	0.736789	+	1.27616i	−0.217145	+	0.976139i	$0.569675\pi$
$948$	−8.88034	−	23.1833i	−0.288420	−	0.752960i
$949$	−7.57442	+	13.1193i	−0.245876	+	0.425870i
$950$	0.836931	−	1.44961i	0.0271536	−	0.0470315i
$951$	−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	$0.841785\pi$
$954$	7.91260	+	2.58340i	0.256180	+	0.0836408i
$955$	−17.8090			−0.576287
$956$	16.4029	+	28.4106i	0.530507	+	0.918865i
$957$	1.51492	+	0.241044i	0.0489703	+	0.00779183i
$958$	−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
$962$	−2.28263			−0.0735950
$963$	−30.6443	+	27.5135i	−0.987500	+	0.886609i
$964$	52.7390			1.69861
$965$	−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	$0.302036\pi$
$968$	−1.28100	+	2.21875i	−0.0411728	+	0.0713133i
$969$	−8.35705	−	21.8172i	−0.268467	−	0.700870i
$970$	1.01298	+	1.75454i	0.0325250	+	0.0563349i
$971$	21.0183			0.674510			0.337255	−	0.941413i	$-0.390502\pi$
$971$	21.0183			0.674510			0.337255	+	0.941413i	$0.390502\pi$
$972$	7.94243	−	29.2256i	0.254754	−	0.937410i
$973$		0			0
$974$	1.56075	+	2.70329i	0.0500096	+	0.0866191i
$975$	2.23229	+	5.82769i	0.0714904	+	0.186635i
$976$	−13.9142	+	24.1002i	−0.445384	+	0.771427i
$977$	1.04910	−	1.81709i	0.0335637	−	0.0581340i	−0.848756	−	0.528785i	$-0.822648\pi$
$977$	1.04910	−	1.81709i	0.0335637	−	0.0581340i	0.882319	+	0.470651i	$0.155981\pi$
$978$	0.393423	−	0.485131i	0.0125803	−	0.0155128i
$979$	−5.08740	−	8.81164i	−0.162594	−	0.281621i
$980$		0			0
$981$	−2.81982	+	2.53173i	−0.0900301	+	0.0808319i
$982$	−4.62571			−0.147612
$983$	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	$0.592864\pi$
$984$	−16.4207	−	2.61275i	−0.523472	−	0.0832914i
$985$	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
$989$	−12.4692			−0.396498
$990$	−2.98525	−	0.974661i	−0.0948774	−	0.0309768i
$991$	−17.2632			−0.548384			−0.274192	−	0.961675i	$-0.588410\pi$
$991$	−17.2632			−0.548384			−0.274192	+	0.961675i	$0.588410\pi$
$992$	−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
$996$	−8.35705	−	21.8172i	−0.264803	−	0.691305i
$997$	−19.4509	−	33.6899i	−0.616016	−	1.06697i	−0.990205	−	0.139619i	$-0.955412\pi$
$997$	−19.4509	−	33.6899i	−0.616016	−	1.06697i	0.374189	−	0.927352i	$-0.377921\pi$
$998$	8.66157			0.274177
$999$	44.1472	+	22.6129i	1.39676	+	0.715439i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	7.6	odd	2
63.2.f.b.43.2	yes	6	63.34	odd	6
189.2.f.a.64.2		6	21.20	even	2
189.2.f.a.127.2		6	63.20	even	6
441.2.f.d.148.2		6	1.1	even	1	trivial
441.2.f.d.295.2		6	9.7	even	3	inner
441.2.g.d.67.2		6	7.2	even	3
441.2.g.d.79.2		6	63.25	even	3
441.2.g.e.67.2		6	7.5	odd	6
441.2.g.e.79.2		6	63.52	odd	6
441.2.h.b.214.2		6	63.16	even	3
441.2.h.b.373.2		6	7.4	even	3
441.2.h.c.214.2		6	63.61	odd	6
441.2.h.c.373.2		6	7.3	odd	6
567.2.a.d.1.2		3	63.13	odd	6
567.2.a.g.1.2		3	63.41	even	6
1008.2.r.k.337.2		6	28.27	even	2
1008.2.r.k.673.2		6	252.223	even	6
1323.2.f.c.442.2		6	3.2	odd	2
1323.2.f.c.883.2		6	9.2	odd	6
1323.2.g.b.361.2		6	21.2	odd	6
1323.2.g.b.667.2		6	63.11	odd	6
1323.2.g.c.361.2		6	21.5	even	6
1323.2.g.c.667.2		6	63.38	even	6
1323.2.h.d.226.2		6	21.17	even	6
1323.2.h.d.802.2		6	63.47	even	6
1323.2.h.e.226.2		6	21.11	odd	6
1323.2.h.e.802.2		6	63.2	odd	6
3024.2.r.g.1009.3		6	84.83	odd	2
3024.2.r.g.2017.3		6	252.83	odd	6
3969.2.a.m.1.2		3	9.4	even	3
3969.2.a.p.1.2		3	9.5	odd	6
9072.2.a.bq.1.3		3	252.139	even	6
9072.2.a.cd.1.1		3	252.167	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 + 0.207087i) q^{2} +(0.619562 + 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} +O(q^{10})\)	\(q+(0.119562 + 0.207087i) q^{2} +(0.619562 + 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} +0.282630 q^{10} +(1.85185 + 3.20750i) q^{11} +(3.32326 + 0.528775i) q^{12} +(0.500000 - 0.866025i) q^{13} +(2.02175 + 0.321688i) q^{15} +(-1.83009 - 3.16982i) q^{16} +6.94282 q^{17} +(-0.681943 - 0.222649i) q^{18} -1.94282 q^{19} +(-1.14815 - 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(0.584135 + 1.52496i) q^{24} +(1.80150 + 3.12030i) q^{25} +0.239123 q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.119562 - 0.207087i) q^{29} +(0.175107 + 0.457140i) q^{30} +(0.830095 - 1.43777i) q^{31} +(1.38044 - 2.39099i) q^{32} +(-4.04063 + 4.98251i) q^{33} +(0.830095 + 1.43777i) q^{34} +(1.20370 + 5.70281i) q^{36} -9.54583 q^{37} +(-0.232287 - 0.402332i) q^{38} +(1.71053 + 0.272169i) q^{39} +(0.557180 - 0.965064i) q^{40} +(-5.09097 + 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +7.19562 q^{44} +(0.732287 + 3.46939i) q^{45} +1.33981 q^{46} +(2.91423 + 5.04759i) q^{47} +(3.99316 - 4.92398i) q^{48} +(-0.430782 + 0.746136i) q^{50} +(4.30150 + 11.2297i) q^{51} +(-0.971410 - 1.68253i) q^{52} -11.6030 q^{53} +(-0.0623817 - 1.24095i) q^{54} +4.37756 q^{55} +(-1.20370 - 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} +(1.30150 - 2.25427i) q^{59} +(2.50520 - 3.08917i) q^{60} +(-3.80150 - 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(-0.590972 - 1.02359i) q^{65} +(-1.51492 - 0.241044i) q^{66} +(-1.75404 + 3.03809i) q^{67} +(6.74433 - 11.6815i) q^{68} +(9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(-2.10464 + 1.88962i) q^{72} -15.1488 q^{73} +(-1.14132 - 1.97682i) q^{74} +(-3.93078 + 4.84706i) q^{75} +(-1.88727 + 3.26886i) q^{76} +(0.148152 + 0.386770i) q^{78} +(-3.68878 - 6.38915i) q^{79} -4.32614 q^{80} +(0.966208 - 8.94799i) q^{81} -2.43474 q^{82} +(-3.47141 - 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(0.260877 - 0.321688i) q^{87} +(1.74596 + 3.02409i) q^{88} -2.74720 q^{89} +(-0.630912 + 0.566453i) q^{90} +(-5.44282 - 9.42724i) q^{92} +(2.83981 + 0.451852i) q^{93} +(-0.696860 + 1.20700i) q^{94} +(-1.14815 + 1.98866i) q^{95} +(4.72257 + 0.751424i) q^{96} +(3.58414 + 6.20790i) q^{97} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	\( 6 q + q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} + 2 q^{12} + 3 q^{13} + 11 q^{15} - 3 q^{16} + 24 q^{17} + 13 q^{18} + 6 q^{19} - 16 q^{20} + 15 q^{22} - 15 q^{24} - 6 q^{25} + 2 q^{26} + 7 q^{27} - q^{29} - 26 q^{30} - 3 q^{31} + 8 q^{32} - 8 q^{33} - 3 q^{34} - 11 q^{36} - 6 q^{37} + 8 q^{38} + 2 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} + 46 q^{44} - 5 q^{45} + 24 q^{46} - 9 q^{47} + 14 q^{48} - 10 q^{50} + 9 q^{51} + 3 q^{52} - 36 q^{53} + 17 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} - 9 q^{59} - 20 q^{60} - 6 q^{61} + 36 q^{62} - 24 q^{64} + 5 q^{65} + 2 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} - 24 q^{72} - 6 q^{73} - 6 q^{74} - 31 q^{75} - 21 q^{76} + 10 q^{78} - 15 q^{79} - 22 q^{80} + 32 q^{81} - 18 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} + q^{87} + 21 q^{88} + 4 q^{89} - 73 q^{90} - 15 q^{92} + 33 q^{93} + 24 q^{94} - 16 q^{95} - 5 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 + 2 * q^12 + 3 * q^13 + 11 * q^15 - 3 * q^16 + 24 * q^17 + 13 * q^18 + 6 * q^19 - 16 * q^20 + 15 * q^22 - 15 * q^24 - 6 * q^25 + 2 * q^26 + 7 * q^27 - q^29 - 26 * q^30 - 3 * q^31 + 8 * q^32 - 8 * q^33 - 3 * q^34 - 11 * q^36 - 6 * q^37 + 8 * q^38 + 2 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 + 46 * q^44 - 5 * q^45 + 24 * q^46 - 9 * q^47 + 14 * q^48 - 10 * q^50 + 9 * q^51 + 3 * q^52 - 36 * q^53 + 17 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 - 9 * q^59 - 20 * q^60 - 6 * q^61 + 36 * q^62 - 24 * q^64 + 5 * q^65 + 2 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 - 24 * q^72 - 6 * q^73 - 6 * q^74 - 31 * q^75 - 21 * q^76 + 10 * q^78 - 15 * q^79 - 22 * q^80 + 32 * q^81 - 18 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 + q^87 + 21 * q^88 + 4 * q^89 - 73 * q^90 - 15 * q^92 + 33 * q^93 + 24 * q^94 - 16 * q^95 - 5 * q^96 + 3 * q^97 - 46 * q^99

Introduction

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