LMFDB - Embedded newform 441.2.h.b.214.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.b.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.239123 q^{2} +(1.09097 + 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})$	\(q-0.239123 q^{2} +(1.09097 + 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 + 2.93533i) q^{9} +(-0.141315 + 0.244765i) q^{10} +(1.85185 + 3.20750i) q^{11} +(-2.11956 - 2.61364i) q^{12} +(0.500000 + 0.866025i) q^{13} +(2.02175 - 0.321688i) q^{15} +3.66019 q^{16} +(-3.47141 + 6.01266i) q^{17} +(0.148152 - 0.701905i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(1.02859 + 1.26836i) q^{24} +(1.80150 + 3.12030i) q^{25} +(-0.119562 - 0.207087i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-0.119562 + 0.207087i) q^{29} +(-0.483448 + 0.0769231i) q^{30} -1.66019 q^{31} -2.76088 q^{32} +(-2.29467 + 5.99054i) q^{33} +(0.830095 - 1.43777i) q^{34} +(1.20370 - 5.70281i) q^{36} +(4.77292 + 8.26693i) q^{37} +(-0.232287 - 0.402332i) q^{38} +(-0.619562 + 1.61745i) q^{39} +(0.557180 - 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(-3.59781 - 6.23159i) q^{44} +(2.63844 + 2.36887i) q^{45} +(-0.669905 + 1.16031i) q^{46} -5.82846 q^{47} +(3.99316 + 4.92398i) q^{48} +(-0.430782 - 0.746136i) q^{50} +(-11.8759 + 1.88962i) q^{51} +(-0.971410 - 1.68253i) q^{52} +(5.80150 - 10.0485i) q^{53} +(1.10589 - 0.566453i) q^{54} +4.37756 q^{55} +(-1.20370 + 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} -2.60301 q^{59} +(-3.92790 + 0.624982i) q^{60} +7.60301 q^{61} +0.396990 q^{62} -6.66019 q^{64} +1.18194 q^{65} +(0.548709 - 1.43248i) q^{66} +3.50808 q^{67} +(6.74433 - 11.6815i) q^{68} +(9.58414 - 1.52496i) q^{69} +8.60301 q^{71} +(-0.584135 + 2.76748i) q^{72} +(7.57442 - 13.1193i) q^{73} +(-1.14132 - 1.97682i) q^{74} +(-2.23229 + 5.82769i) q^{75} +(-1.88727 - 3.26886i) q^{76} +(0.148152 - 0.386770i) q^{78} +7.37756 q^{79} +(2.16307 - 3.74654i) q^{80} +(-8.23229 - 3.63723i) q^{81} +(1.21737 + 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(-0.409028 + 0.0650819i) q^{87} +(1.74596 + 3.02409i) q^{88} +(1.37360 + 2.37915i) q^{89} +(-0.630912 - 0.566453i) q^{90} +(-5.44282 + 9.42724i) q^{92} +(-1.81122 - 2.23342i) q^{93} +1.39372 q^{94} +2.29630 q^{95} +(-3.01204 - 3.71415i) q^{96} +(3.58414 - 6.20790i) q^{97} +(-10.5624 + 3.44854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.239123			−0.169086			−0.0845428	−	0.996420i	$-0.526943\pi$
$2$	−0.239123			−0.169086			−0.0845428	+	0.996420i	$0.526943\pi$
$3$	1.09097	+	1.34528i	0.629873	+	0.776698i
$3$	1.09097	+	1.34528i	0.629873	+	0.776698i
$4$	−1.94282			−0.971410
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	−0.703087	−	0.711104i	$-0.748196\pi$
$5$	0.590972	−	1.02359i	0.264291	−	0.457765i	0.967378	+	0.253339i	$0.0815289\pi$
$6$	−0.260877	−	0.321688i	−0.106502	−	0.131329i
$7$		0			0
$7$		0			0
$8$	0.942820			0.333337
$9$	−0.619562	+	2.93533i	−0.206521	+	0.978442i
$10$	−0.141315	+	0.244765i	−0.0446878	+	0.0774015i
$11$	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	$0.644767\pi$
$12$	−2.11956	−	2.61364i	−0.611865	−	0.754493i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	2.02175	−	0.321688i	0.522014	−	0.0830595i
$16$	3.66019			0.915047
$17$	−3.47141	+	6.01266i	−0.841941	+	1.45828i	0.0463112	+	0.998927i	$0.485253\pi$
$17$	−3.47141	+	6.01266i	−0.841941	+	1.45828i	−0.888252	+	0.459357i	$0.848080\pi$
$18$	0.148152	−	0.701905i	0.0349197	−	0.165441i
$19$	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
$23$	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	$-0.0319070\pi$
$24$	1.02859	+	1.26836i	0.209960	+	0.258902i
$25$	1.80150	+	3.12030i	0.360301	+	0.624060i
$26$	−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	−0.876913	−	0.480649i	$-0.840401\pi$
$29$	−0.119562	+	0.207087i	−0.0222020	+	0.0384551i	0.854711	+	0.519104i	$0.173734\pi$
$30$	−0.483448	+	0.0769231i	−0.0882652	+	0.0140442i
$31$	−1.66019			−0.298179			−0.149089	−	0.988824i	$-0.547634\pi$
$31$	−1.66019			−0.298179			−0.149089	+	0.988824i	$0.547634\pi$
$32$	−2.76088			−0.488059
$33$	−2.29467	+	5.99054i	−0.399451	+	1.04282i
$34$	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	$0.546170\pi$
$38$	−0.232287	−	0.402332i	−0.0376819	−	0.0652669i
$39$	−0.619562	+	1.61745i	−0.0992093	+	0.258999i
$40$	0.557180	−	0.965064i	0.0880979	−	0.152590i
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	−0.922791	−	0.385301i	$-0.874097\pi$
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	0.127715	−	0.991811i	$-0.459236\pi$
$42$		0			0
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	−0.938311	−	0.345794i	$-0.887610\pi$
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	0.768622	+	0.639704i	$0.220943\pi$
$44$	−3.59781	−	6.23159i	−0.542390	−	0.939447i
$45$	2.63844	+	2.36887i	0.393315	+	0.353131i
$46$	−0.669905	+	1.16031i	−0.0987721	+	0.171078i
$47$	−5.82846			−0.850168			−0.425084	−	0.905154i	$-0.639755\pi$
$47$	−5.82846			−0.850168			−0.425084	+	0.905154i	$0.639755\pi$
$48$	3.99316	+	4.92398i	0.576364	+	0.710716i
$49$		0			0
$50$	−0.430782	−	0.746136i	−0.0609217	−	0.105520i
$51$	−11.8759	+	1.88962i	−1.66296	+	0.264599i
$52$	−0.971410	−	1.68253i	−0.134710	−	0.233325i
$53$	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	$-0.126861\pi$
$54$	1.10589	−	0.566453i	0.150492	−	0.0770845i
$55$	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
$59$	−2.60301			−0.338883			−0.169442	−	0.985540i	$-0.554196\pi$
$59$	−2.60301			−0.338883			−0.169442	+	0.985540i	$0.554196\pi$
$60$	−3.92790	+	0.624982i	−0.507090	+	0.0806848i
$61$	7.60301			0.973466			0.486733	−	0.873551i	$-0.338189\pi$
$61$	7.60301			0.973466			0.486733	+	0.873551i	$0.338189\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	1.18194			0.146602
$66$	0.548709	−	1.43248i	0.0675414	−	0.176326i
$67$	3.50808			0.428580			0.214290	−	0.976770i	$-0.431256\pi$
$67$	3.50808			0.428580			0.214290	+	0.976770i	$0.431256\pi$
$68$	6.74433	−	11.6815i	0.817870	−	1.41659i
$69$	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	$0.329462\pi$
$72$	−0.584135	+	2.76748i	−0.0688410	+	0.326151i
$73$	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	$-0.180217\pi$
$74$	−1.14132	−	1.97682i	−0.132675	−	0.229800i
$75$	−2.23229	+	5.82769i	−0.257762	+	0.672923i
$76$	−1.88727	−	3.26886i	−0.216485	−	0.374963i
$77$		0			0
$78$	0.148152	−	0.386770i	0.0167749	−	0.0437931i
$79$	7.37756			0.830040			0.415020	−	0.909812i	$-0.363775\pi$
$79$	7.37756			0.830040			0.415020	+	0.909812i	$0.363775\pi$
$80$	2.16307	−	3.74654i	0.241838	−	0.418876i
$81$	−8.23229	−	3.63723i	−0.914699	−	0.404137i
$82$	1.21737	+	2.10855i	0.134436	+	0.232850i
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	−0.991211	−	0.132292i	$-0.957766\pi$
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	0.610174	+	0.792267i	$0.291100\pi$
$84$		0			0
$85$	4.10301	+	7.10662i	0.445034	+	0.770821i
$86$	0.266078	−	0.460861i	0.0286920	−	0.0496960i
$87$	−0.409028	+	0.0650819i	−0.0438524	+	0.00697751i
$88$	1.74596	+	3.02409i	0.186120	+	0.322369i
$89$	1.37360	+	2.37915i	0.145602	+	0.252189i	0.929597	−	0.368577i	$-0.120155\pi$
$89$	1.37360	+	2.37915i	0.145602	+	0.252189i	−0.783996	+	0.620766i	$0.786822\pi$
$90$	−0.630912	−	0.566453i	−0.0665039	−	0.0597094i
$91$		0			0
$92$	−5.44282	+	9.42724i	−0.567453	+	0.982858i
$93$	−1.81122	−	2.23342i	−0.187815	−	0.231595i
$94$	1.39372			0.143751
$95$	2.29630			0.235596
$96$	−3.01204	−	3.71415i	−0.307415	−	0.379074i
$97$	3.58414	−	6.20790i	0.363914	−	0.630317i	−0.624687	−	0.780875i	$-0.714774\pi$
$97$	3.58414	−	6.20790i	0.363914	−	0.630317i	0.988601	+	0.150558i	$0.0481069\pi$
$98$		0			0
$99$	−10.5624	+	3.44854i	−1.06156	+	0.346591i
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	−0.986286	−	0.165044i	$-0.947223\pi$
$101$	−6.39248	−	11.0721i	−0.636075	−	1.10171i	0.350211	−	0.936671i	$-0.386110\pi$
$102$	2.83981	−	0.451852i	0.281183	−	0.0447400i
$103$	−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
$107$	−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	$-0.397621\pi$
$108$	8.98508	−	4.60230i	0.864590	−	0.442856i
$109$	−0.631600	+	1.09396i	−0.0604963	+	0.104783i	−0.894687	−	0.446693i	$-0.852602\pi$
$109$	−0.631600	+	1.09396i	−0.0604963	+	0.104783i	0.834191	+	0.551476i	$0.185935\pi$
$110$	−1.04678			−0.0998062
$111$	−5.91423	+	15.4399i	−0.561354	+	1.46549i
$112$		0			0
$113$	−6.08126	−	10.5330i	−0.572076	−	0.990866i	−0.996353	−	0.0853326i	$-0.972805\pi$
$113$	−6.08126	−	10.5330i	−0.572076	−	0.990866i	0.424276	−	0.905533i	$-0.360529\pi$
$114$	0.287832	−	0.751424i	0.0269579	−	0.0703773i
$115$	−3.31122	−	5.73520i	−0.308773	−	0.534810i
$116$	0.232287	−	0.402332i	0.0215673	−	0.0373556i
$117$	−2.85185	+	0.931107i	−0.263653	+	0.0860809i
$118$	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
$122$	−1.81806			−0.164599
$123$	6.30834	−	16.4688i	0.568804	−	1.48494i
$124$	3.22545			0.289654
$125$	10.1683			0.909478
$126$		0			0
$127$	1.33981			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$127$	1.33981			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$128$	7.11436			0.628827
$129$	−3.80671	+	0.605698i	−0.335162	+	0.0533287i
$130$	−0.282630			−0.0247883
$131$	−2.48345	+	4.30146i	−0.216980	+	0.375820i	−0.953883	−	0.300178i	$-0.902954\pi$
$131$	−2.48345	+	4.30146i	−0.216980	+	0.375820i	0.736903	+	0.675998i	$0.236287\pi$
$132$	4.45813	−	11.6385i	0.388030	−	1.01301i
$133$		0			0
$134$	−0.838864			−0.0724668
$135$	−0.308342	+	6.13381i	−0.0265378	+	0.527915i
$136$	−3.27292	+	5.66886i	−0.280650	+	0.486100i
$137$	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	$0.773979\pi$
$138$	−2.29179	+	0.364654i	−0.195090	+	0.0310414i
$139$	1.97141	+	3.41458i	0.167213	+	0.289621i	0.937439	−	0.348150i	$-0.113190\pi$
$139$	1.97141	+	3.41458i	0.167213	+	0.289621i	−0.770226	+	0.637771i	$0.779857\pi$
$140$		0			0
$141$	−6.35868	−	7.84092i	−0.535498	−	0.660324i
$142$	−2.05718			−0.172635
$143$	−1.85185	+	3.20750i	−0.154859	+	0.268224i
$144$	−2.26771	+	10.7439i	−0.188976	+	0.895321i
$145$	0.141315	+	0.244765i	0.0117356	+	0.0203266i
$146$	−1.81122	+	3.13713i	−0.149898	+	0.259630i
$147$		0			0
$148$	−9.27292	−	16.0612i	−0.762229	−	1.32022i
$149$	−5.55555	+	9.62249i	−0.455128	+	0.788305i	−0.998696	−	0.0510606i	$-0.983740\pi$
$149$	−5.55555	+	9.62249i	−0.455128	+	0.788305i	0.543568	+	0.839365i	$0.317073\pi$
$150$	0.533792	−	1.39354i	0.0435839	−	0.113782i
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	−0.996905	−	0.0786145i	$-0.974950\pi$
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	0.430370	−	0.902652i	$-0.358383\pi$
$152$	0.915865	+	1.58632i	0.0742864	+	0.128668i
$153$	−15.4984	−	13.9149i	−1.25297	−	1.12496i
$154$		0			0
$155$	−0.981125	+	1.69936i	−0.0788059	+	0.136496i
$156$	1.20370	−	3.14241i	0.0963729	−	0.251594i
$157$	−0.0571799			−0.00456346			−0.00228173	−	0.999997i	$-0.500726\pi$
$157$	−0.0571799			−0.00456346			−0.00228173	+	0.999997i	$0.500726\pi$
$158$	−1.76415			−0.140348
$159$	19.8473	−	3.15798i	1.57400	−	0.250444i
$160$	−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	$0.814523\pi$
$164$	9.89084	+	17.1314i	0.772345	+	1.33774i
$165$	4.77579	+	5.88905i	0.371795	+	0.458462i
$166$	0.830095	−	1.43777i	0.0644279	−	0.111592i
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	−0.996749	−	0.0805714i	$-0.974325\pi$
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	0.428598	−	0.903496i	$-0.359008\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−0.981125	−	1.69936i	−0.0752489	−	0.130335i
$171$	−5.54063	+	1.80897i	−0.423702	+	0.138336i
$172$	2.16182	−	3.74439i	0.164838	−	0.285507i
$173$	−0.252796			−0.0192197			−0.00960987	−	0.999954i	$-0.503059\pi$
$173$	−0.252796			−0.0192197			−0.00960987	+	0.999954i	$0.503059\pi$
$174$	0.0978082	−	0.0155626i	0.00741482	−	0.00117980i
$175$		0			0
$176$	6.77812	+	11.7400i	0.510920	+	0.884939i
$177$	−2.83981	−	3.50178i	−0.213453	−	0.263210i
$178$	−0.328460	−	0.568910i	−0.0246191	−	0.0426416i
$179$	−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	$0.988711\pi$
$180$	−5.12601	−	4.60230i	−0.382070	−	0.343035i
$181$	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
$185$	11.2826			0.829515
$186$	0.433105	+	0.534063i	0.0317568	+	0.0391594i
$187$	−25.7141			−1.88040
$188$	11.3236			0.825862
$189$		0			0
$190$	−0.549100			−0.0398359
$191$	15.0676			1.09025			0.545126	−	0.838354i	$-0.316482\pi$
$191$	15.0676			1.09025			0.545126	+	0.838354i	$0.316482\pi$
$192$	−7.26608	−	8.95983i	−0.524384	−	0.646620i
$193$	−7.84789			−0.564904			−0.282452	−	0.959282i	$-0.591148\pi$
$193$	−7.84789			−0.564904			−0.282452	+	0.959282i	$0.591148\pi$
$194$	−0.857050	+	1.48445i	−0.0615326	+	0.106578i
$195$	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	$0.423403\pi$
$198$	2.52571	−	0.824626i	0.179494	−	0.0586036i
$199$	−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	$0.916832\pi$
$200$	1.69850	+	2.94188i	0.120102	+	0.208022i
$201$	3.82722	+	4.71935i	0.269951	+	0.332878i
$202$	1.52859	+	2.64760i	0.107551	+	0.186284i
$203$		0			0
$204$	23.0728	−	3.67119i	1.61542	−	0.257035i
$205$	−12.0345			−0.840525
$206$	0.525711	−	0.910559i	0.0366280	−	0.0634416i
$207$	12.5075	+	11.2297i	0.869333	+	0.780515i
$208$	1.83009	+	3.16982i	0.126894	+	0.219787i
$209$	−3.59781	+	6.23159i	−0.248866	+	0.431048i
$210$		0			0
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	0.988973	+	0.148095i	$0.0473141\pi$
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	−0.366233	+	0.930523i	$0.619353\pi$
$212$	−11.2713	+	19.5224i	−0.774115	+	1.34081i
$213$	9.38564	+	11.5735i	0.643093	+	0.793001i
$214$	1.64132	+	2.84284i	0.112198	+	0.194333i
$215$	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
$219$	25.9126	−	4.12304i	1.75101	−	0.278609i
$220$	−8.50481			−0.573394
$221$	−6.94282			−0.467025
$222$	1.41423	−	3.69204i	0.0949169	−	0.247793i
$223$	−11.3285	+	19.6215i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$223$	−11.3285	+	19.6215i	−0.758610	+	1.31395i	−0.943560	+	0.331203i	$0.892546\pi$
$224$		0			0
$225$	−10.2752	+	3.35479i	−0.685016	+	0.223653i
$226$	1.45417	+	2.51870i	0.0967299	+	0.167541i
$227$	−2.64132	−	4.57489i	−0.175310	−	0.303646i	0.764958	−	0.644080i	$-0.222760\pi$
$227$	−2.64132	−	4.57489i	−0.175310	−	0.303646i	−0.940269	+	0.340433i	$0.889426\pi$
$228$	2.33857	−	6.10514i	0.154875	−	0.404323i
$229$	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
$233$	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	$0.645586\pi$
$234$	0.681943	−	0.222649i	0.0445800	−	0.0145550i
$235$	−3.44445	+	5.96597i	−0.224691	+	0.389177i
$236$	5.05718			0.329194
$237$	8.04871	+	9.92489i	0.522820	+	0.644691i
$238$		0			0
$239$	−8.44282	−	14.6234i	−0.546121	−	0.945909i	−0.998535	−	0.0541011i	$-0.982771\pi$
$239$	−8.44282	−	14.6234i	−0.546121	−	0.945909i	0.452415	−	0.891808i	$-0.350563\pi$
$240$	7.40000	−	1.17744i	0.477668	−	0.0760034i
$241$	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	$0.494654\pi$
$242$	0.324893	−	0.562732i	0.0208849	−	0.0361738i
$243$	−4.08809	−	15.0429i	−0.262251	−	0.965000i
$244$	−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
$248$	−1.56526			−0.0993941
$249$	−11.8759	+	1.88962i	−0.752606	+	0.119750i
$250$	−2.43147			−0.153780
$251$	19.0780			1.20419			0.602096	−	0.798424i	$-0.294332\pi$
$251$	19.0780			1.20419			0.602096	+	0.798424i	$0.294332\pi$
$252$		0			0
$253$	20.7518			1.30466
$254$	−0.320380			−0.0201024
$255$	−5.08414	+	13.2728i	−0.318381	+	0.831176i
$256$	11.6192			0.726198
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	−0.999105	−	0.0423070i	$-0.986529\pi$
$257$	−7.42107	+	12.8537i	−0.462913	+	0.801790i	0.536191	+	0.844097i	$0.319863\pi$
$258$	0.910272	−	0.144836i	0.0566711	−	0.00901712i
$259$		0			0
$260$	−2.29630			−0.142411
$261$	−0.533792	−	0.479256i	−0.0330409	−	0.0296652i
$262$	0.593850	−	1.02858i	0.0366882	−	0.0635458i
$263$	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	$0.756619\pi$
$264$	−2.16346	+	5.64800i	−0.133152	+	0.347611i
$265$	−6.85705	−	11.8768i	−0.421225	−	0.729584i
$266$		0			0
$267$	−1.70206	+	4.44346i	−0.104165	+	0.271936i
$268$	−6.81557			−0.416327
$269$	−0.755675	+	1.30887i	−0.0460743	+	0.0798031i	−0.888143	−	0.459567i	$-0.848004\pi$
$269$	−0.755675	+	1.30887i	−0.0460743	+	0.0798031i	0.842069	+	0.539371i	$0.181338\pi$
$270$	0.0737316	−	1.46674i	0.00448716	−	0.0892628i
$271$	−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
$275$	−6.67223	+	11.5566i	−0.402350	+	0.696892i
$276$	−18.6202	+	2.96273i	−1.12081	+	0.178335i
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	0.981575	−	0.191077i	$-0.0611982\pi$
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	−0.656265	+	0.754530i	$0.727865\pi$
$278$	−0.471410	−	0.816506i	−0.0282733	−	0.0489708i
$279$	1.02859	−	4.87320i	0.0615801	−	0.291751i
$280$		0			0
$281$	8.43831	−	14.6156i	0.503387	−	0.871892i	−0.496605	−	0.867977i	$-0.665420\pi$
$281$	8.43831	−	14.6156i	0.503387	−	0.871892i	0.999992	−	0.00391559i	$-0.00124638\pi$
$282$	1.52051	+	1.87495i	0.0905450	+	0.111651i
$283$	15.3171			0.910508			0.455254	−	0.890362i	$-0.349549\pi$
$283$	15.3171			0.910508			0.455254	+	0.890362i	$0.349549\pi$
$284$	−16.7141			−0.991799
$285$	2.50520	+	3.08917i	0.148395	+	0.182987i
$286$	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
$290$	−0.0337917	−	0.0585290i	−0.00198432	−	0.00343694i
$291$	12.2616	−	1.95098i	0.718786	−	0.114368i
$292$	−14.7157	+	25.4884i	−0.861173	+	1.49160i
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	0.696114	−	0.717932i	$-0.254911\pi$
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	−0.969804	+	0.243886i	$0.921578\pi$
$294$		0			0
$295$	−1.53831	+	2.66442i	−0.0895636	+	0.155129i
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$	−16.1625	−	10.4471i	−0.937844	−	0.606203i
$298$	1.32846	−	2.30096i	0.0769556	−	0.133291i
$299$	5.60301			0.324030
$300$	4.33693	−	11.3221i	0.250393	−	0.653684i
$301$		0			0
$302$	1.66470	+	2.88335i	0.0957929	+	0.165918i
$303$	7.92107	−	20.6790i	0.455053	−	1.18798i
$304$	3.55555	+	6.15838i	0.203925	+	0.353208i
$305$	4.49316	−	7.78239i	0.257278	−	0.445618i
$306$	3.70602	+	3.32738i	0.211859	+	0.190214i
$307$	−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
$311$	13.9806			0.792765			0.396383	−	0.918085i	$-0.370265\pi$
$311$	13.9806			0.792765			0.396383	+	0.918085i	$0.370265\pi$
$312$	−0.584135	+	1.52496i	−0.0330701	+	0.0863341i
$313$	19.0539			1.07699			0.538495	−	0.842628i	$-0.318993\pi$
$313$	19.0539			1.07699			0.538495	+	0.842628i	$0.318993\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	−4.01943			−0.225754			−0.112877	−	0.993609i	$-0.536007\pi$
$317$	−4.01943			−0.225754			−0.112877	+	0.993609i	$0.536007\pi$
$318$	−4.74596	+	0.755146i	−0.266140	+	0.0423465i
$319$	−0.885640			−0.0495863
$320$	−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
$324$	15.9939	+	7.06649i	0.888547	+	0.392583i
$325$	−1.80150	+	3.12030i	−0.0999295	+	0.173083i
$326$	−0.180309	−	0.312304i	−0.00998637	−	0.0172969i
$327$	−2.16075	+	0.343803i	−0.119489	+	0.0190124i
$328$	−4.79987	−	8.31362i	−0.265028	−	0.459043i
$329$		0			0
$330$	−1.14200	−	1.40821i	−0.0628652	−	0.0775193i
$331$	−12.3776			−0.680332			−0.340166	−	0.940365i	$-0.610483\pi$
$331$	−12.3776			−0.680332			−0.340166	+	0.940365i	$0.610483\pi$
$332$	6.74433	−	11.6815i	0.370143	−	0.641106i
$333$	−27.2233	+	8.88819i	−1.49183	+	0.487070i
$334$	1.75567	+	3.04092i	0.0960663	+	0.166392i
$335$	2.07318	−	3.59085i	0.113270	−	0.196189i
$336$		0			0
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	0.649356	−	0.760484i	$-0.275038\pi$
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	−0.983277	+	0.182117i	$0.941705\pi$
$338$	−1.43474	+	2.48504i	−0.0780395	+	0.135168i
$339$	7.53543	−	19.6723i	0.409268	−	1.06845i
$340$	−7.97141	−	13.8069i	−0.432310	−	0.748784i
$341$	−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
$345$	4.10301	−	10.7115i	0.220899	−	0.576686i
$346$	0.0604495			0.00324978
$347$	6.64979			0.356979			0.178490	−	0.983942i	$-0.442879\pi$
$347$	6.64979			0.356979			0.178490	+	0.983942i	$0.442879\pi$
$348$	0.794668	−	0.126442i	0.0425987	−	0.00677802i
$349$	5.71737	−	9.90278i	0.306044	−	0.530083i	−0.671449	−	0.741050i	$-0.734328\pi$
$349$	5.71737	−	9.90278i	0.306044	−	0.530083i	0.977493	+	0.210967i	$0.0676613\pi$
$350$		0			0
$351$	−4.36389	−	2.82073i	−0.232927	−	0.150559i
$352$	−5.11273	−	8.85550i	−0.272509	−	0.472000i
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	−0.994141	−	0.108087i	$-0.965528\pi$
$353$	−11.0978	−	19.2220i	−0.590677	−	1.02308i	0.403465	−	0.914995i	$-0.367806\pi$
$354$	0.679065	+	0.837357i	0.0360919	+	0.0445050i
$355$	5.08414	−	8.80598i	0.269838	−	0.467373i
$356$	−2.66866	−	4.62226i	−0.141439	−	0.244979i
$357$		0			0
$358$	1.69686	−	2.93905i	0.0896819	−	0.155334i
$359$	3.77812	+	6.54389i	0.199401	+	0.345373i	0.948334	−	0.317272i	$-0.102767\pi$
$359$	3.77812	+	6.54389i	0.199401	+	0.345373i	−0.748933	+	0.662646i	$0.769434\pi$
$360$	2.48757	+	2.23342i	0.131106	+	0.117712i
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	−0.342298			−0.0179908
$363$	−4.64815	+	0.739583i	−0.243965	+	0.0388180i
$364$		0			0
$365$	−8.95254	−	15.5062i	−0.468597	−	0.811634i
$366$	−1.98345	−	2.44580i	−0.103677	−	0.127844i
$367$	−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	$0.993950\pi$
$368$	10.2540	−	17.7605i	0.534529	−	0.925831i
$369$	29.0374	−	9.48048i	1.51162	−	0.493534i
$370$	−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	$0.299544\pi$
$374$	6.14884			0.317949
$375$	11.0933	+	13.6792i	0.572855	+	0.706390i
$376$	−5.49519			−0.283393
$377$	−0.239123			−0.0123155
$378$		0			0
$379$	4.03775			0.207405			0.103703	−	0.994608i	$-0.466931\pi$
$379$	4.03775			0.207405			0.103703	+	0.994608i	$0.466931\pi$
$380$	−4.46130			−0.228860
$381$	1.46169	+	1.80242i	0.0748849	+	0.0923408i
$382$	−3.60301			−0.184346
$383$	0.112725	−	0.195246i	0.00575998	−	0.00997659i	−0.863131	−	0.504980i	$-0.831500\pi$
$383$	0.112725	−	0.195246i	0.00575998	−	0.00997659i	0.868891	+	0.495003i	$0.164833\pi$
$384$	7.76157	+	9.57081i	0.396081	+	0.488408i
$385$		0			0
$386$	1.87661			0.0955171
$387$	−4.96784	−	4.46029i	−0.252530	−	0.226729i
$388$	−6.96333	+	12.0608i	−0.353510	+	0.612296i
$389$	−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	$-0.387918\pi$
$390$	−0.308342	−	0.380217i	−0.0156135	−	0.0192530i
$391$	19.4503	+	33.6890i	0.983646	+	1.70373i
$392$		0			0
$393$	−8.49604	+	1.35183i	−0.428569	+	0.0681910i
$394$	−1.59974			−0.0805938
$395$	4.35993	−	7.55162i	0.219372	−	0.379963i
$396$	20.5208	−	6.69989i	1.03121	−	0.336682i
$397$	−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
$401$	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	$0.0425351\pi$
$402$	−0.915177	−	1.12851i	−0.0456449	−	0.0562848i
$403$	−0.830095	−	1.43777i	−0.0413500	−	0.0716203i
$404$	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
$408$	−11.1969	+	1.78157i	−0.554327	+	0.0882009i
$409$	−1.65692			−0.0819294			−0.0409647	−	0.999161i	$-0.513043\pi$
$409$	−1.65692			−0.0819294			−0.0409647	+	0.999161i	$0.513043\pi$
$410$	2.87772			0.142121
$411$	−2.68878	+	7.01942i	−0.132628	+	0.346243i
$412$	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
$416$	−1.38044	−	2.39099i	−0.0676816	−	0.117228i
$417$	−2.44282	+	6.37731i	−0.119625	+	0.312298i
$418$	0.860320	−	1.49012i	0.0420796	−	0.0728840i
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	0.909170	+	0.416426i	$0.136718\pi$
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	−0.0939492	+	0.995577i	$0.529949\pi$
$420$		0			0
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	−0.998017	−	0.0629481i	$-0.979950\pi$
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	0.553523	+	0.832834i	$0.313283\pi$
$422$	−2.16307	−	3.74654i	−0.105297	−	0.182379i
$423$	3.61109	−	17.1084i	0.175577	−	0.831841i
$424$	5.46978	−	9.47393i	0.265636	−	0.460095i
$425$	−25.0150			−1.21341
$426$	−2.24433	−	2.76748i	−0.108738	−	0.134085i
$427$		0			0
$428$	13.3353	+	23.0974i	0.644586	+	1.11646i
$429$	−6.33530	+	1.00803i	−0.305871	+	0.0486682i
$430$	−0.314490	−	0.544712i	−0.0151660	−	0.0262684i
$431$	−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	$0.917503\pi$
$432$	−16.9275	+	8.67053i	−0.814425	+	0.417161i
$433$	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
$437$	10.8856			0.520731
$438$	−6.19630	+	0.985915i	−0.296071	+	0.0471088i
$439$	4.83173			0.230606			0.115303	−	0.993330i	$-0.463216\pi$
$439$	4.83173			0.230606			0.115303	+	0.993330i	$0.463216\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	1.24488			0.0591461			0.0295730	−	0.999563i	$-0.490585\pi$
$443$	1.24488			0.0591461			0.0295730	+	0.999563i	$0.490585\pi$
$444$	11.4903	−	29.9969i	0.545305	−	1.42359i
$445$	3.24704			0.153924
$446$	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	$0.433200\pi$
$450$	2.45705	−	0.802208i	0.115826	−	0.0378165i
$451$	18.8554	−	32.6585i	0.887867	−	1.53783i
$452$	11.8148	+	20.4638i	0.555721	+	0.962537i
$453$	8.62640	−	22.5204i	0.405304	−	1.05810i
$454$	0.631600	+	1.09396i	0.0296425	+	0.0513422i
$455$		0			0
$456$	−1.13487	+	2.96273i	−0.0531451	+	0.138743i
$457$	−10.5081			−0.491547			−0.245774	−	0.969327i	$-0.579042\pi$
$457$	−10.5081			−0.491547			−0.245774	+	0.969327i	$0.579042\pi$
$458$	−2.31191	+	4.00434i	−0.108028	+	0.187111i
$459$	1.81122	−	36.0305i	0.0845405	−	1.68176i
$460$	6.43310	+	11.1425i	0.299945	+	0.519520i
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	−0.474404	−	0.880307i	$-0.657337\pi$
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	0.999570	−	0.0293073i	$-0.00933013\pi$
$462$		0			0
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	0.719574	−	0.694416i	$-0.244337\pi$
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	−0.961169	+	0.275962i	$0.911004\pi$
$464$	−0.437618	+	0.757977i	−0.0203159	+	0.0351882i
$465$	−3.35649	+	0.534063i	−0.155654	+	0.0247666i
$466$	−2.03022	−	3.51645i	−0.0940483	−	0.162897i
$467$	6.65856	+	11.5330i	0.308121	+	0.533682i	0.977951	−	0.208833i	$-0.0669664\pi$
$467$	6.65856	+	11.5330i	0.308121	+	0.533682i	−0.669830	+	0.742514i	$0.733633\pi$
$468$	5.54063	−	1.80897i	0.256116	−	0.0836198i
$469$		0			0
$470$	0.823649	−	1.42660i	0.0379921	−	0.0658043i
$471$	−0.0623817	−	0.0769231i	−0.00287440	−	0.00354443i
$472$	−2.45417			−0.112962
$473$	−8.24239			−0.378986
$474$	−1.92463	−	2.37327i	−0.0884013	−	0.109008i
$475$	−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
$479$	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	$0.725586\pi$
$480$	−5.58181	+	0.888141i	−0.254774	+	0.0405379i
$481$	−4.77292	+	8.26693i	−0.217626	+	0.376940i
$482$	−3.24557	−	5.62149i	−0.147832	−	0.256052i
$483$		0			0
$484$	2.63968	−	4.57206i	0.119985	−	0.207821i
$485$	−4.23624	−	7.33739i	−0.192358	−	0.333174i
$486$	0.977558	+	3.59710i	0.0443429	+	0.163168i
$487$	−6.52696	+	11.3050i	−0.295765	+	0.512279i	−0.975162	−	0.221491i	$-0.928908\pi$
$487$	−6.52696	+	11.3050i	−0.295765	+	0.512279i	0.679398	+	0.733770i	$0.262241\pi$
$488$	7.16827			0.324492
$489$	−0.934349	+	2.43924i	−0.0422527	+	0.110306i
$490$		0			0
$491$	−9.67223	−	16.7528i	−0.436502	−	0.756043i	0.560915	−	0.827873i	$-0.310449\pi$
$491$	−9.67223	−	16.7528i	−0.436502	−	0.756043i	−0.997417	+	0.0718303i	$0.977116\pi$
$492$	−12.2560	+	31.9959i	−0.552542	+	1.44249i
$493$	−0.830095	−	1.43777i	−0.0373856	−	0.0647538i
$494$	0.232287	−	0.402332i	0.0104511	−	0.0181018i
$495$	−2.71217	+	12.8496i	−0.121903	+	0.577545i
$496$	−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	$-0.134281\pi$
$500$	−19.7551			−0.883476
$501$	9.09781	−	23.7511i	0.406460	−	1.06112i
$502$	−4.56199			−0.203612
$503$	−15.6764			−0.698974			−0.349487	−	0.936941i	$-0.613644\pi$
$503$	−15.6764			−0.698974			−0.349487	+	0.936941i	$0.613644\pi$
$504$		0			0
$505$	−15.1111			−0.672435
$506$	−4.96225			−0.220599
$507$	20.5264	−	3.26602i	0.911609	−	0.145049i
$508$	−2.60301			−0.115490
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	−0.182492	−	0.983207i	$-0.558416\pi$
$509$	17.1517	−	29.7076i	0.760237	−	1.31677i	0.942729	−	0.333561i	$-0.108250\pi$
$510$	1.21574	−	3.17384i	0.0538337	−	0.140540i
$511$		0			0
$512$	−17.0071			−0.751616
$513$	−8.47825	−	5.48016i	−0.374324	−	0.241955i
$514$	1.77455	−	3.07361i	0.0782720	−	0.135571i
$515$	2.59850	+	4.50073i	0.114503	+	0.198326i
$516$	7.39575	−	1.17676i	0.325580	−	0.0518041i
$517$	−10.7934	−	18.6948i	−0.474694	−	0.822195i
$518$		0			0
$519$	−0.275794	−	0.340082i	−0.0121060	−	0.0149279i
$520$	1.11436			0.0488679
$521$	−5.12244	+	8.87233i	−0.224418	+	0.388704i	−0.956145	−	0.292895i	$-0.905381\pi$
$521$	−5.12244	+	8.87233i	−0.224418	+	0.388704i	0.731727	+	0.681598i	$0.238715\pi$
$522$	0.127642	+	0.114601i	0.00558674	+	0.00501596i
$523$	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
$527$	5.76320	−	9.98215i	0.251049	−	0.434829i
$528$	−8.39892	+	21.9265i	−0.365516	+	0.954230i
$529$	−4.19686	−	7.26918i	−0.182472	−	0.316051i
$530$	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
$534$	0.407003	−	1.06254i	0.0176127	−	0.0459804i
$535$	−16.2255			−0.701487
$536$	3.30749			0.142862
$537$	−24.2765	+	3.86271i	−1.04761	+	0.166688i
$538$	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	$0.643795\pi$
$542$	2.62803	+	4.55189i	0.112884	+	0.195520i
$543$	1.56169	+	1.92573i	0.0670187	+	0.0826410i
$544$	9.58414	−	16.6002i	0.410916	−	0.711728i
$545$	0.746515	+	1.29300i	0.0319772	+	0.0553861i
$546$		0			0
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	−0.725318	−	0.688414i	$-0.758307\pi$
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	0.958843	+	0.283937i	$0.0916405\pi$
$548$	−4.21574	−	7.30187i	−0.180087	−	0.311920i
$549$	−4.71053	+	22.3173i	−0.201041	+	0.952480i
$550$	1.59549	−	2.76346i	0.0680317	−	0.117834i
$551$	−0.464574			−0.0197915
$552$	9.03611	−	1.43777i	0.384603	−	0.0611954i
$553$		0			0
$554$	−1.29467	−	2.24243i	−0.0550052	−	0.0952718i
$555$	12.3090	+	15.1783i	0.522489	+	0.644283i
$556$	−3.83009	−	6.63392i	−0.162432	−	0.281341i
$557$	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	$0.0712080\pi$
$558$	−0.245960	+	1.16530i	−0.0104123	+	0.0493309i
$559$	−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
$563$	−30.2574			−1.27520			−0.637600	−	0.770368i	$-0.720073\pi$
$563$	−30.2574			−1.27520			−0.637600	+	0.770368i	$0.720073\pi$
$564$	12.3538	+	15.2335i	0.520188	+	0.641446i
$565$	−14.3754			−0.604778
$566$	−3.66268			−0.153954
$567$		0			0
$568$	8.11109			0.340334
$569$	−21.1352			−0.886032			−0.443016	−	0.896514i	$-0.646092\pi$
$569$	−21.1352			−0.886032			−0.443016	+	0.896514i	$0.646092\pi$
$570$	−0.599052	−	0.738693i	−0.0250915	−	0.0309405i
$571$	−32.7863			−1.37207			−0.686033	−	0.727571i	$-0.740649\pi$
$571$	−32.7863			−1.37207			−0.686033	+	0.727571i	$0.740649\pi$
$572$	3.59781	−	6.23159i	0.150432	−	0.260556i
$573$	16.4383	+	20.2701i	0.686720	+	0.846797i
$574$		0			0
$575$	20.1877			0.841885
$576$	4.12640	−	19.5498i	0.171933	−	0.814576i
$577$	−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	$0.284453\pi$
$578$	3.73065	+	6.46168i	0.155175	+	0.268770i
$579$	−8.56183	−	10.5576i	−0.355817	−	0.438760i
$580$	−0.274550	−	0.475534i	−0.0114001	−	0.0197455i
$581$		0			0
$582$	−2.93203	+	0.466524i	−0.121536	+	0.0193381i
$583$	42.9740			1.77980
$584$	7.14132	−	12.3691i	0.295510	−	0.511838i
$585$	−0.732287	+	3.46939i	−0.0302763	+	0.143442i
$586$	1.12025	+	1.94033i	0.0462771	+	0.0801543i
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	−0.635973	−	0.771712i	$-0.719401\pi$
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	0.986308	+	0.164913i	$0.0527342\pi$
$588$		0			0
$589$	−1.61273	−	2.79332i	−0.0664512	−	0.115097i
$590$	0.367845	−	0.637125i	0.0151439	−	0.0262300i
$591$	7.29863	+	8.99996i	0.300225	+	0.370209i
$592$	17.4698	+	30.2585i	0.718003	+	1.24362i
$593$	−6.53667	−	11.3218i	−0.268429	−	0.464932i	0.700027	−	0.714116i	$-0.253171\pi$
$593$	−6.53667	−	11.3218i	−0.268429	−	0.464932i	−0.968456	+	0.249184i	$0.919838\pi$
$594$	3.86483	+	2.49815i	0.158576	+	0.102500i
$595$		0			0
$596$	10.7934	−	18.6948i	0.442116	−	0.765767i
$597$	−34.1073	+	5.42692i	−1.39592	+	0.222109i
$598$	−1.33981			−0.0547889
$599$	29.2060			1.19333			0.596663	−	0.802492i	$-0.296493\pi$
$599$	29.2060			1.19333			0.596663	+	0.802492i	$0.296493\pi$
$600$	−2.10464	+	5.49446i	−0.0859218	+	0.224310i
$601$	3.89536	−	6.74695i	0.158895	−	0.275214i	−0.775576	−	0.631255i	$-0.782540\pi$
$601$	3.89536	−	6.74695i	0.158895	−	0.275214i	0.934470	+	0.356041i	$0.115874\pi$
$602$		0			0
$603$	−2.17347	+	10.2974i	−0.0885106	+	0.419341i
$604$	13.5253	+	23.4265i	0.550337	+	0.953212i
$605$	1.60589	+	2.78148i	0.0652887	+	0.113083i
$606$	−1.89411	+	4.94483i	−0.0769430	+	0.200870i
$607$	−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
$611$	−2.91423	−	5.04759i	−0.117897	−	0.204204i
$612$	30.1105	+	27.0342i	1.21715	+	1.09279i
$613$	−11.7826	+	20.4081i	−0.475896	+	0.824276i	−0.999619	−	0.0276128i	$-0.991209\pi$
$613$	−11.7826	+	20.4081i	−0.475896	+	0.824276i	0.523723	+	0.851889i	$0.324543\pi$
$614$	0.649005			0.0261917
$615$	−13.1293	−	16.1898i	−0.529424	−	0.652834i
$616$		0			0
$617$	5.33009	+	9.23200i	0.214582	+	0.371666i	0.953143	−	0.302520i	$-0.0978279\pi$
$617$	5.33009	+	9.23200i	0.214582	+	0.371666i	−0.738562	+	0.674186i	$0.764495\pi$
$618$	1.79849	−	0.286164i	0.0723460	−	0.0115112i
$619$	−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	$0.951254\pi$
$620$	1.90615	−	3.30155i	0.0765528	−	0.132593i
$621$	−1.46169	+	29.0774i	−0.0586558	+	1.16683i
$622$	−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
$626$	−4.55623			−0.182104
$627$	−12.3083	+	1.95842i	−0.491548	+	0.0782118i
$628$	0.111090			0.00443299
$629$	−66.2750			−2.64256
$630$		0			0
$631$	12.4703			0.496436			0.248218	−	0.968704i	$-0.420155\pi$
$631$	12.4703			0.496436			0.248218	+	0.968704i	$0.420155\pi$
$632$	6.95571			0.276683
$633$	−11.2089	+	29.2623i	−0.445514	+	1.16307i
$634$	0.961139			0.0381717
$635$	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
$639$	−5.33009	+	25.2526i	−0.210855	+	0.998979i
$640$	4.20439	−	7.28221i	0.166193	−	0.287855i
$641$	−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	$0.956757\pi$
$642$	−2.03379	+	5.30949i	−0.0802674	+	0.209549i
$643$	3.24433	+	5.61934i	0.127944	+	0.221605i	0.922880	−	0.385088i	$-0.125829\pi$
$643$	3.24433	+	5.61934i	0.127944	+	0.221605i	−0.794936	+	0.606693i	$0.792496\pi$
$644$		0			0
$645$	−1.62967	+	4.25447i	−0.0641681	+	0.167520i
$646$	3.22545			0.126904
$647$	−24.0494	+	41.6548i	−0.945479	+	1.63762i	−0.190691	+	0.981650i	$0.561073\pi$
$647$	−24.0494	+	41.6548i	−0.945479	+	1.63762i	−0.754789	+	0.655968i	$0.772261\pi$
$648$	−7.76157	−	3.42926i	−0.304903	−	0.134714i
$649$	−4.82038	−	8.34914i	−0.189216	−	0.327733i
$650$	0.430782	−	0.746136i	0.0168967	−	0.0292659i
$651$		0			0
$652$	−1.46496	−	2.53739i	−0.0573724	−	0.0993720i
$653$	21.6202	−	37.4474i	0.846066	−	1.46543i	−0.0386267	−	0.999254i	$-0.512298\pi$
$653$	21.6202	−	37.4474i	0.846066	−	1.46543i	0.884692	−	0.466175i	$-0.154368\pi$
$654$	0.516685	−	0.0822114i	0.0202040	−	0.00321472i
$655$	2.93530	+	5.08408i	0.114691	+	0.198651i
$656$	−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	−0.840566	−	0.541709i	$-0.817778\pi$
$659$	1.25404	−	2.17206i	0.0488505	−	0.0846115i	0.889417	+	0.457097i	$0.151111\pi$
$660$	−9.27851	−	11.4414i	−0.361165	−	0.445354i
$661$	42.3354			1.64666			0.823329	−	0.567565i	$-0.192114\pi$
$661$	42.3354			1.64666			0.823329	+	0.567565i	$0.192114\pi$
$662$	2.95976			0.115034
$663$	−7.57442	−	9.34004i	−0.294166	−	0.362737i
$664$	−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
$668$	14.2644	+	24.7067i	0.551908	+	0.955933i
$669$	−38.7554	+	6.16650i	−1.49837	+	0.238411i
$670$	−0.495745	+	0.858655i	−0.0191523	+	0.0331727i
$671$	14.0796	+	24.3866i	0.543538	+	0.941435i
$672$		0			0
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	−0.965857	−	0.259077i	$-0.916582\pi$
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	0.707296	+	0.706918i	$0.249915\pi$
$674$	1.46582	+	2.53887i	0.0564612	+	0.0977936i
$675$	−15.7231	−	10.1631i	−0.605183	−	0.391178i
$676$	−11.6569	+	20.1904i	−0.448343	+	0.776553i
$677$	−1.96225			−0.0754154			−0.0377077	−	0.999289i	$-0.512006\pi$
$677$	−1.96225			−0.0754154			−0.0377077	+	0.999289i	$0.512006\pi$
$678$	−1.80190	+	4.70409i	−0.0692014	+	0.180660i
$679$		0			0
$680$	3.86840	+	6.70027i	0.148346	+	0.256943i
$681$	3.27292	−	8.54439i	0.125418	−	0.327422i
$682$	0.735165	+	1.27334i	0.0281509	+	0.0487589i
$683$	−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	$0.992688\pi$
$684$	10.7644	−	3.51451i	0.411589	−	0.134381i
$685$	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
$689$	11.6030			0.442039
$690$	−0.981125	+	2.56136i	−0.0373508	+	0.0975093i
$691$	50.3171			1.91415			0.957077	−	0.289835i	$-0.0936005\pi$
$691$	50.3171			1.91415			0.957077	+	0.289835i	$0.0936005\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	4.66019			0.176771
$696$	−0.385640	+	0.0613605i	−0.0146177	+	0.00232586i
$697$	70.6914			2.67763
$698$	−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	$0.174799\pi$
$702$	1.04351	+	0.674501i	0.0393846	+	0.0254574i
$703$	−9.27292	+	16.0612i	−0.349735	+	0.605758i
$704$	−12.3337	−	21.3625i	−0.464842	−	0.805131i
$705$	−11.7837	+	1.87495i	−0.443800	+	0.0706145i
$706$	2.65374	+	4.59642i	0.0998750	+	0.172989i
$707$		0			0
$708$	5.51724	+	6.80333i	0.207351	+	0.255685i
$709$	39.6181			1.48789			0.743944	−	0.668242i	$-0.232953\pi$
$709$	39.6181			1.48789			0.743944	+	0.668242i	$0.232953\pi$
$710$	−1.21574	+	2.10571i	−0.0456257	+	0.0790261i
$711$	−4.57085	+	21.6555i	−0.171420	+	0.812147i
$712$	1.29506	+	2.24311i	0.0485344	+	0.0840640i
$713$	−4.65103	+	8.05582i	−0.174182	+	0.301693i
$714$		0			0
$715$	2.18878	+	3.79108i	0.0818557	+	0.141778i
$716$	13.7866	−	23.8791i	0.515229	−	0.892403i
$717$	10.4617	−	27.3117i	0.390699	−	1.01997i
$718$	−0.903436	−	1.56480i	−0.0337159	−	0.0583977i
$719$	−11.0189	−	19.0853i	−0.410935	−	0.711760i	0.584058	−	0.811712i	$-0.301464\pi$
$719$	−11.0189	−	19.0853i	−0.410935	−	0.711760i	−0.994992	+	0.0999525i	$0.968131\pi$
$720$	9.65718	+	8.67053i	0.359902	+	0.323132i
$721$		0			0
$722$	−1.82038	+	3.15299i	−0.0677475	+	0.117342i
$723$	−16.8184	+	43.9066i	−0.625481	+	1.63290i
$724$	−2.78109			−0.103358
$725$	−0.861564			−0.0319977
$726$	1.11148	−	0.176852i	0.0412509	−	0.00656358i
$727$	14.0555	−	24.3449i	0.521291	−	0.902903i	−0.478402	−	0.878141i	$-0.658784\pi$
$727$	14.0555	−	24.3449i	0.521291	−	0.902903i	0.999693	−	0.0247621i	$-0.00788284\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$	2.14076	+	3.70790i	0.0792331	+	0.137236i
$731$	−7.72545	−	13.3809i	−0.285736	−	0.494909i
$732$	−16.1150	−	19.8715i	−0.595629	−	0.734473i
$733$	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
$737$	6.49643	+	11.2522i	0.239299	+	0.414478i
$738$	−6.94351	+	2.26700i	−0.255594	+	0.0834496i
$739$	6.09222	−	10.5520i	0.224106	−	0.388163i	−0.731945	−	0.681364i	$-0.761387\pi$
$739$	6.09222	−	10.5520i	0.224106	−	0.388163i	0.956051	+	0.293201i	$0.0947206\pi$
$740$	−21.9201			−0.805800
$741$	−3.32326	+	0.528775i	−0.122083	+	0.0194250i
$742$		0			0
$743$	22.2427	+	38.5255i	0.816005	+	1.41336i	0.908604	+	0.417659i	$0.137149\pi$
$743$	22.2427	+	38.5255i	0.816005	+	1.41336i	−0.0925987	+	0.995704i	$0.529517\pi$
$744$	−1.70765	−	2.10571i	−0.0626057	−	0.0771993i
$745$	6.56634	+	11.3732i	0.240572	+	0.416683i
$746$	1.87236	−	3.24302i	0.0685519	−	0.118735i
$747$	−15.4984	−	13.9149i	−0.567056	−	0.509121i
$748$	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	$0.881375\pi$
$752$	−21.3333			−0.777944
$753$	20.8135	+	25.6653i	0.758488	+	0.935294i
$754$	0.0571799			0.00208237
$755$	−16.4567			−0.598919
$756$		0			0
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$	−0.965520			−0.0350693
$759$	22.6397	+	27.9171i	0.821768	+	1.01333i
$760$	2.16500			0.0785328
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	−0.966201	−	0.257788i	$-0.917006\pi$
$761$	−7.16827	+	12.4158i	−0.259850	+	0.450073i	0.706352	+	0.707861i	$0.250340\pi$
$762$	−0.349525	−	0.431001i	−0.0126620	−	0.0156135i
$763$		0			0
$764$	−29.2736			−1.05908
$765$	−23.4023	+	7.64068i	−0.846113	+	0.276250i
$766$	−0.0269552	+	0.0466878i	−0.000973931	+	0.00168690i
$767$	−1.30150	−	2.25427i	−0.0469946	−	0.0813971i
$768$	12.6762	+	15.6310i	0.457412	+	0.564037i
$769$	−15.6105	−	27.0382i	−0.562930	−	0.975024i	−0.997239	−	0.0742597i	$-0.976341\pi$
$769$	−15.6105	−	27.0382i	−0.562930	−	0.975024i	0.434309	−	0.900764i	$-0.356993\pi$
$770$		0			0
$771$	−25.3880	+	4.03956i	−0.914325	+	0.145481i
$772$	15.2470			0.548753
$773$	2.19002	−	3.79323i	0.0787697	−	0.136433i	−0.823950	−	0.566663i	$-0.808234\pi$
$773$	2.19002	−	3.79323i	0.0787697	−	0.136433i	0.902719	+	0.430230i	$0.141567\pi$
$774$	1.18793	+	1.06656i	0.0426992	+	0.0383367i
$775$	−2.99084	−	5.18029i	−0.107434	−	0.186081i
$776$	3.37919	−	5.85294i	0.121306	−	0.210108i
$777$		0			0
$778$	3.02051	+	5.23168i	0.108291	+	0.187565i
$779$	9.89084	−	17.1314i	0.354376	−	0.613798i
$780$	−2.50520	−	3.08917i	−0.0897006	−	0.110610i
$781$	15.9315	+	27.5941i	0.570073	+	0.987395i
$782$	−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
$786$	2.03160	−	0.323255i	0.0724648	−	0.0115301i
$787$	−27.6213			−0.984594			−0.492297	−	0.870427i	$-0.663843\pi$
$787$	−27.6213			−0.984594			−0.492297	+	0.870427i	$0.663843\pi$
$788$	−12.9975			−0.463017
$789$	−4.79630	+	12.5214i	−0.170753	+	0.445774i
$790$	−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
$794$	2.42721	+	4.20406i	0.0861386	+	0.149196i
$795$	8.49673	−	22.1819i	0.301348	−	0.786710i
$796$	19.3695	−	33.5489i	0.686533	−	1.18911i
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	0.838587	−	0.544767i	$-0.183382\pi$
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	−0.891076	+	0.453854i	$0.850049\pi$
$798$		0			0
$799$	20.2330	−	35.0445i	0.715791	−	1.23979i
$800$	−4.97373	−	8.61476i	−0.175848	−	0.304578i
$801$	−7.83461	+	2.55794i	−0.276822	+	0.0903804i
$802$	−1.82038	+	3.15299i	−0.0642798	+	0.111336i
$803$	56.1067			1.97996
$804$	−7.43559	−	9.16886i	−0.262233	−	0.323361i
$805$		0			0
$806$	0.198495	+	0.343803i	0.00699169	+	0.0121100i
$807$	−2.58521	+	0.411342i	−0.0910039	+	0.0144799i
$808$	−6.02696	−	10.4390i	−0.212028	−	0.367242i
$809$	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	$0.0231400\pi$
$810$	2.05361	−	1.50098i	0.0721566	−	0.0527390i
$811$	−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
$815$	1.78247			0.0624370
$816$	−43.4681	+	6.91636i	−1.52169	+	0.242121i
$817$	−4.32365			−0.151265
$818$	0.396208			0.0138531
$819$		0			0
$820$	23.3808			0.816494
$821$	−28.8993			−1.00859			−0.504296	−	0.863531i	$-0.668248\pi$
$821$	−28.8993			−1.00859			−0.504296	+	0.863531i	$0.668248\pi$
$822$	0.642950	−	1.67851i	0.0224255	−	0.0585447i
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	−2.07279	+	3.59017i	−0.0722089	+	0.125069i
$825$	−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	$0.843597\pi$
$828$	−24.2999	−	21.8172i	−0.844479	−	0.758201i
$829$	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	$0.0838581\pi$
$830$	−0.981125	−	1.69936i	−0.0340554	−	0.0589856i
$831$	−6.70890	+	17.5145i	−0.232729	+	0.607571i
$832$	−3.33009	−	5.76789i	−0.115450	−	0.199966i
$833$		0			0
$834$	0.584135	−	1.52496i	0.0202269	−	0.0528052i
$835$	−17.3560			−0.600628
$836$	6.98989	−	12.1069i	0.241751	−	0.418724i
$837$	7.67799	−	3.93278i	0.265390	−	0.135937i
$838$	−3.99028	−	6.91138i	−0.137842	−	0.238750i
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	−0.413138	−	0.910669i	$-0.635567\pi$
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	0.995231	−	0.0975464i	$-0.0310994\pi$
$840$		0			0
$841$	14.4714	+	25.0652i	0.499014	+	0.864318i
$842$	2.18086	−	3.77737i	0.0751575	−	0.130177i
$843$	28.8680	−	4.59329i	0.994267	−	0.158201i
$844$	−17.5744	−	30.4398i	−0.604936	−	1.04778i
$845$	−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
$849$	16.7105	+	20.6058i	0.573504	+	0.707190i
$850$	5.98168			0.205170
$851$	53.4854			1.83346
$852$	−18.2346	−	22.4852i	−0.624707	−	0.770329i
$853$	5.89480	−	10.2101i	0.201834	−	0.349587i	−0.747285	−	0.664503i	$-0.768643\pi$
$853$	5.89480	−	10.2101i	0.201834	−	0.349587i	0.949119	+	0.314916i	$0.101976\pi$
$854$		0			0
$855$	−1.42270	+	6.74040i	−0.0486554	+	0.230517i
$856$	−6.47141	−	11.2088i	−0.221188	−	0.383109i
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	−0.999161	−	0.0409451i	$-0.986963\pi$
$857$	−15.6631	−	27.1292i	−0.535040	−	0.926717i	0.464121	−	0.885772i	$-0.346370\pi$
$858$	1.51492	−	0.241044i	0.0517184	−	0.00822909i
$859$	−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
$863$	−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	$0.839470\pi$
$864$	12.7684	−	6.54017i	0.434390	−	0.222501i
$865$	−0.149395	+	0.258761i	−0.00507960	+	0.00879812i
$866$	−2.92804			−0.0994987
$867$	19.3320	−	50.4689i	0.656550	−	1.71401i
$868$		0			0
$869$	13.6621	+	23.6635i	0.463456	+	0.802729i
$870$	0.0418721	−	0.109313i	0.00141960	−	0.00370605i
$871$	1.75404	+	3.03809i	0.0594334	+	0.102942i
$872$	−0.595485	+	1.03141i	−0.0201657	+	0.0349280i
$873$	16.0016	+	14.3668i	0.541573	+	0.486242i
$874$	−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	$0.0136156\pi$
$878$	−1.15538			−0.0389922
$879$	5.80507	−	15.1549i	0.195800	−	0.511163i
$880$	16.0227			0.540125
$881$	−1.20929			−0.0407420			−0.0203710	−	0.999792i	$-0.506485\pi$
$881$	−1.20929			−0.0407420			−0.0203710	+	0.999792i	$0.506485\pi$
$882$		0			0
$883$	−51.0884			−1.71926			−0.859631	−	0.510916i	$-0.829306\pi$
$883$	−51.0884			−1.71926			−0.859631	+	0.510916i	$0.829306\pi$
$884$	13.4887			0.453672
$885$	−5.26264	+	0.837357i	−0.176902	+	0.0281474i
$886$	−0.297680			−0.0100008
$887$	−20.7878	+	36.0056i	−0.697987	+	1.20895i	0.271176	+	0.962530i	$0.412587\pi$
$887$	−20.7878	+	36.0056i	−0.697987	+	1.20895i	−0.969163	+	0.246419i	$0.920746\pi$
$888$	−5.57605	+	14.5570i	−0.187120	+	0.488503i
$889$		0			0
$890$	−0.776443			−0.0260264
$891$	−3.57854	−	33.1406i	−0.119886	−	1.11025i
$892$	22.0092	−	38.1210i	0.736921	−	1.27638i
$893$	−5.66182	−	9.80657i	−0.189466	−	0.328164i
$894$	4.54475	−	0.723131i	0.151999	−	0.0241851i
$895$	8.38727	+	14.5272i	0.280356	+	0.485590i
$896$		0			0
$897$	6.11273	+	7.53762i	0.204098	+	0.251674i
$898$	−2.11109			−0.0704480
$899$	0.198495	−	0.343803i	0.00662018	−	0.0114665i
$900$	19.9629	−	6.51775i	0.665431	−	0.217258i
$901$	40.2788	+	69.7649i	1.34188	+	2.32421i
$902$	−4.50877	+	7.80942i	−0.150126	+	0.260025i
$903$		0			0
$904$	−5.73353	−	9.93077i	−0.190694	−	0.330292i
$905$	0.845958	−	1.46524i	0.0281206	−	0.0487063i
$906$	−2.06277	+	5.38515i	−0.0685310	+	0.178910i
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	−0.994421	−	0.105486i	$-0.966360\pi$
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	0.405857	−	0.913937i	$-0.366973\pi$
$908$	5.13160	+	8.88819i	0.170298	+	0.294965i
$909$	36.4607	−	11.9042i	1.20933	−	0.394836i
$910$		0			0
$911$	10.3554	−	17.9361i	0.343090	−	0.594250i	−0.641915	−	0.766776i	$-0.721860\pi$
$911$	10.3554	−	17.9361i	0.343090	−	0.594250i	0.985005	+	0.172526i	$0.0551930\pi$
$912$	−4.40576	+	11.5018i	−0.145889	+	0.380864i
$913$	−25.7141			−0.851013
$914$	2.51273			0.0831136
$915$	15.3714	−	2.44580i	0.508163	−	0.0808556i
$916$	−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	$0.909623\pi$
$920$	−3.12188	−	5.40726i	−0.102925	−	0.178272i
$921$	−2.96101	−	3.65123i	−0.0975685	−	0.120312i
$922$	−2.69630	+	4.67014i	−0.0887981	+	0.153803i
$923$	4.30150	+	7.45043i	0.141586	+	0.245234i
$924$		0			0
$925$	−17.1969	+	29.7858i	−0.565429	+	0.979352i
$926$	1.24308	+	2.15308i	0.0408502	+	0.0707546i
$927$	−9.81534	−	8.81253i	−0.322378	−	0.289442i
$928$	0.330095	−	0.571741i	0.0108359	−	0.0187683i
$929$	41.7428			1.36954			0.684769	−	0.728760i	$-0.259903\pi$
$929$	41.7428			1.36954			0.684769	+	0.728760i	$0.259903\pi$
$930$	0.802616	−	0.127707i	0.0263188	−	0.00418768i
$931$		0			0
$932$	−16.4951	−	28.5703i	−0.540315	−	0.935853i
$933$	15.2524	+	18.8078i	0.499341	+	0.615740i
$934$	−1.59222	−	2.75780i	−0.0520989	−	0.0902379i
$935$	−15.1963	+	26.3208i	−0.496972	+	0.860781i
$936$	−2.68878	+	0.877867i	−0.0878855	+	0.0286940i
$937$	−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
$941$	3.22080			0.104995			0.0524976	−	0.998621i	$-0.483282\pi$
$941$	3.22080			0.104995			0.0524976	+	0.998621i	$0.483282\pi$
$942$	0.0149169	+	0.0183941i	0.000486019	+	0.000599312i
$943$	−57.0495			−1.85779
$944$	−9.52751			−0.310094
$945$		0			0
$946$	1.97095			0.0640810
$947$	−45.3469			−1.47358			−0.736789	−	0.676123i	$-0.763659\pi$
$947$	−45.3469			−1.47358			−0.736789	+	0.676123i	$0.763659\pi$
$948$	−15.6372	−	19.2823i	−0.507872	−	0.626259i
$949$	15.1488			0.491752
$950$	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	$0.841785\pi$
$954$	−6.19359	−	5.56081i	−0.200525	−	0.180038i
$955$	8.90451	−	15.4231i	0.288143	−	0.499079i
$956$	16.4029	+	28.4106i	0.530507	+	0.918865i
$957$	−0.966208	−	1.19143i	−0.0312331	−	0.0385136i
$958$	−1.73788	−	3.01010i	−0.0561483	−	0.0972518i
$959$		0			0
$960$	−13.4653	+	2.14250i	−0.434589	+	0.0691490i
$961$	−28.2438			−0.911089
$962$	1.14132	−	1.97682i	0.0367975	−	0.0637351i
$963$	39.1495	−	12.7820i	1.26158	−	0.411895i
$964$	−26.3695	−	45.6733i	−0.849304	−	1.47104i
$965$	−4.63788	+	8.03305i	−0.149299	+	0.258593i
$966$		0			0
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	0.582600	−	0.812759i	$-0.302036\pi$
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	−0.995170	+	0.0981667i	$0.968702\pi$
$968$	−1.28100	+	2.21875i	−0.0411728	+	0.0713133i
$969$	−14.7157	−	18.1460i	−0.472738	−	0.582934i
$970$	1.01298	+	1.75454i	0.0325250	+	0.0563349i
$971$	−10.5092	−	18.2024i	−0.337255	−	0.584143i	0.646660	−	0.762778i	$-0.276165\pi$
$971$	−10.5092	−	18.2024i	−0.337255	−	0.584143i	−0.983915	+	0.178635i	$0.942832\pi$
$972$	7.94243	+	29.2256i	0.254754	+	0.937410i
$973$		0			0
$974$	1.56075	−	2.70329i	0.0500096	−	0.0866191i
$975$	−6.16307	+	0.980627i	−0.197376	+	0.0314052i
$976$	27.8285			0.890767
$977$	−2.09820			−0.0671273			−0.0335637	−	0.999437i	$-0.510686\pi$
$977$	−2.09820			−0.0671273			−0.0335637	+	0.999437i	$0.510686\pi$
$978$	0.223425	−	0.583280i	0.00714433	−	0.0186512i
$979$	−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
$983$	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	$0.592864\pi$
$984$	5.94763	−	15.5271i	0.189604	−	0.494986i
$985$	3.95361	−	6.84786i	0.125973	−	0.218191i
$986$	0.198495	+	0.343803i	0.00632137	+	0.0109489i
$987$		0			0
$988$	1.88727	−	3.26886i	0.0600422	−	0.103996i
$989$	6.23461	+	10.7987i	0.198249	+	0.343377i
$990$	0.648543	−	3.07263i	0.0206120	−	0.0976546i
$991$	8.63160	−	14.9504i	0.274192	−	0.474914i	−0.695739	−	0.718295i	$-0.744923\pi$
$991$	8.63160	−	14.9504i	0.274192	−	0.474914i	0.969931	+	0.243380i	$0.0782564\pi$
$992$	4.58358			0.145529
$993$	−13.5036	−	16.6513i	−0.428523	−	0.528413i
$994$		0			0
$995$	11.7837	+	20.4100i	0.373569	+	0.647040i
$996$	23.0728	−	3.67119i	0.731089	−	0.116326i
$997$	−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	$-0.377921\pi$
$998$	−4.33078	+	7.50114i	−0.137089	+	0.237444i
$999$	−41.6569	−	26.9262i	−1.31797	−	0.851906i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	63.31	odd	6
63.2.f.b.43.2	yes	6	7.3	odd	6
189.2.f.a.64.2		6	63.59	even	6
189.2.f.a.127.2		6	21.17	even	6
441.2.f.d.148.2		6	63.4	even	3
441.2.f.d.295.2		6	7.4	even	3
441.2.g.d.67.2		6	9.4	even	3
441.2.g.d.79.2		6	7.2	even	3
441.2.g.e.67.2		6	63.13	odd	6
441.2.g.e.79.2		6	7.5	odd	6
441.2.h.b.214.2		6	1.1	even	1	trivial
441.2.h.b.373.2		6	63.58	even	3	inner
441.2.h.c.214.2		6	7.6	odd	2
441.2.h.c.373.2		6	63.40	odd	6
567.2.a.d.1.2		3	63.52	odd	6
567.2.a.g.1.2		3	63.38	even	6
1008.2.r.k.337.2		6	252.31	even	6
1008.2.r.k.673.2		6	28.3	even	6
1323.2.f.c.442.2		6	63.32	odd	6
1323.2.f.c.883.2		6	21.11	odd	6
1323.2.g.b.361.2		6	9.5	odd	6
1323.2.g.b.667.2		6	21.2	odd	6
1323.2.g.c.361.2		6	63.41	even	6
1323.2.g.c.667.2		6	21.5	even	6
1323.2.h.d.226.2		6	63.5	even	6
1323.2.h.d.802.2		6	21.20	even	2
1323.2.h.e.226.2		6	63.23	odd	6
1323.2.h.e.802.2		6	3.2	odd	2
3024.2.r.g.1009.3		6	252.59	odd	6
3024.2.r.g.2017.3		6	84.59	odd	6
3969.2.a.m.1.2		3	63.25	even	3
3969.2.a.p.1.2		3	63.11	odd	6
9072.2.a.bq.1.3		3	252.115	even	6
9072.2.a.cd.1.1		3	252.227	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.239123 q^{2} +(1.09097 + 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 + 2.93533i) q^{9} +O(q^{10})\)	\(q-0.239123 q^{2} +(1.09097 + 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 - 1.02359i) q^{5} +(-0.260877 - 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 + 2.93533i) q^{9} +(-0.141315 + 0.244765i) q^{10} +(1.85185 + 3.20750i) q^{11} +(-2.11956 - 2.61364i) q^{12} +(0.500000 + 0.866025i) q^{13} +(2.02175 - 0.321688i) q^{15} +3.66019 q^{16} +(-3.47141 + 6.01266i) q^{17} +(0.148152 - 0.701905i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(1.02859 + 1.26836i) q^{24} +(1.80150 + 3.12030i) q^{25} +(-0.119562 - 0.207087i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-0.119562 + 0.207087i) q^{29} +(-0.483448 + 0.0769231i) q^{30} -1.66019 q^{31} -2.76088 q^{32} +(-2.29467 + 5.99054i) q^{33} +(0.830095 - 1.43777i) q^{34} +(1.20370 - 5.70281i) q^{36} +(4.77292 + 8.26693i) q^{37} +(-0.232287 - 0.402332i) q^{38} +(-0.619562 + 1.61745i) q^{39} +(0.557180 - 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(-3.59781 - 6.23159i) q^{44} +(2.63844 + 2.36887i) q^{45} +(-0.669905 + 1.16031i) q^{46} -5.82846 q^{47} +(3.99316 + 4.92398i) q^{48} +(-0.430782 - 0.746136i) q^{50} +(-11.8759 + 1.88962i) q^{51} +(-0.971410 - 1.68253i) q^{52} +(5.80150 - 10.0485i) q^{53} +(1.10589 - 0.566453i) q^{54} +4.37756 q^{55} +(-1.20370 + 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} -2.60301 q^{59} +(-3.92790 + 0.624982i) q^{60} +7.60301 q^{61} +0.396990 q^{62} -6.66019 q^{64} +1.18194 q^{65} +(0.548709 - 1.43248i) q^{66} +3.50808 q^{67} +(6.74433 - 11.6815i) q^{68} +(9.58414 - 1.52496i) q^{69} +8.60301 q^{71} +(-0.584135 + 2.76748i) q^{72} +(7.57442 - 13.1193i) q^{73} +(-1.14132 - 1.97682i) q^{74} +(-2.23229 + 5.82769i) q^{75} +(-1.88727 - 3.26886i) q^{76} +(0.148152 - 0.386770i) q^{78} +7.37756 q^{79} +(2.16307 - 3.74654i) q^{80} +(-8.23229 - 3.63723i) q^{81} +(1.21737 + 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(-0.409028 + 0.0650819i) q^{87} +(1.74596 + 3.02409i) q^{88} +(1.37360 + 2.37915i) q^{89} +(-0.630912 - 0.566453i) q^{90} +(-5.44282 + 9.42724i) q^{92} +(-1.81122 - 2.23342i) q^{93} +1.39372 q^{94} +2.29630 q^{95} +(-3.01204 - 3.71415i) q^{96} +(3.58414 - 6.20790i) q^{97} +(-10.5624 + 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Introduction

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