LMFDB - Embedded newform 484.2.c.d.483.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(483,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("484.483");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.c (of order $2$, degree $1$, 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			483.4
Root			$1.40958 + 0.114404i$ of defining polynomial
Character	$\chi$	$=$	484.483
Dual form			484.2.c.d.483.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20762 + 0.735975i) q^{2} +0.740676i q^{3} +(0.916683 - 1.77755i) q^{4} -1.34841 q^{5} +(-0.545118 - 0.894453i) q^{6} -1.62837 q^{7} +(0.201231 + 2.82126i) q^{8} +2.45140 q^{9} +(1.62837 - 0.992398i) q^{10} +(1.31659 + 0.678965i) q^{12} +3.55723i q^{13} +(1.96645 - 1.19844i) q^{14} -0.998737i q^{15} +(-2.31939 - 3.25890i) q^{16} -0.0699655i q^{17} +(-2.96035 + 1.80417i) q^{18} -7.95154 q^{19} +(-1.23607 + 2.39688i) q^{20} -1.20609i q^{21} +5.30988i q^{23} +(-2.08964 + 0.149047i) q^{24} -3.18178 q^{25} +(-2.61803 - 4.29578i) q^{26} +4.03772i q^{27} +(-1.49270 + 2.89451i) q^{28} +3.93630i q^{29} +(0.735045 + 1.20609i) q^{30} -3.69389i q^{31} +(5.19940 + 2.22850i) q^{32} +(0.0514928 + 0.0844916i) q^{34} +2.19572 q^{35} +(2.24716 - 4.35749i) q^{36} -6.87861 q^{37} +(9.60242 - 5.85213i) q^{38} -2.63476 q^{39} +(-0.271342 - 3.80423i) q^{40} -5.78625i q^{41} +(0.887654 + 1.45650i) q^{42} -1.89516 q^{43} -3.30550 q^{45} +(-3.90793 - 6.41230i) q^{46} +9.80536i q^{47} +(2.41379 - 1.71791i) q^{48} -4.34841 q^{49} +(3.84237 - 2.34171i) q^{50} +0.0518217 q^{51} +(6.32317 + 3.26086i) q^{52} -3.88765 q^{53} +(-2.97166 - 4.87602i) q^{54} +(-0.327678 - 4.59405i) q^{56} -5.88951i q^{57} +(-2.89701 - 4.75354i) q^{58} +4.86161i q^{59} +(-1.77531 - 0.915525i) q^{60} +1.34602i q^{61} +(2.71861 + 4.46080i) q^{62} -3.99178 q^{63} +(-7.91901 + 1.13545i) q^{64} -4.79662i q^{65} -4.91303i q^{67} +(-0.124367 - 0.0641362i) q^{68} -3.93290 q^{69} +(-2.65159 + 1.61599i) q^{70} +6.97557i q^{71} +(0.493297 + 6.91604i) q^{72} -10.1222i q^{73} +(8.30673 - 5.06248i) q^{74} -2.35667i q^{75} +(-7.28904 + 14.1343i) q^{76} +(3.18178 - 1.93911i) q^{78} +6.00456 q^{79} +(3.12749 + 4.39435i) q^{80} +4.36356 q^{81} +(4.25853 + 6.98758i) q^{82} +3.61193 q^{83} +(-2.14389 - 1.10560i) q^{84} +0.0943425i q^{85} +(2.28863 - 1.39479i) q^{86} -2.91552 q^{87} -5.39711 q^{89} +(3.99178 - 2.43277i) q^{90} -5.79249i q^{91} +(9.43858 + 4.86747i) q^{92} +2.73597 q^{93} +(-7.21649 - 11.8411i) q^{94} +10.7220 q^{95} +(-1.65060 + 3.85107i) q^{96} +7.32624 q^{97} +(5.25122 - 3.20032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5} - 22 q^{12} - 12 q^{14} - 12 q^{16} + 16 q^{20} - 4 q^{25} - 24 q^{26} - 6 q^{34} + 50 q^{36} - 12 q^{37} + 42 q^{38} + 4 q^{42} + 40 q^{45} + 74 q^{48} - 44 q^{49} - 52 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 - 22 * q^12 - 12 * q^14 - 12 * q^16 + 16 * q^20 - 4 * q^25 - 24 * q^26 - 6 * q^34 + 50 * q^36 - 12 * q^37 + 42 * q^38 + 4 * q^42 + 40 * q^45 + 74 * q^48 - 44 * q^49 - 52 * q^53 - 12 * q^56 - 60 * q^58 - 8 * q^60 + 28 * q^64 + 24 * q^69 - 68 * q^70 + 4 * q^78 - 8 * q^80 - 24 * q^81 + 26 * q^82 - 14 * q^86 - 36 * q^89 + 36 * q^92 + 72 * q^93 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.20762	+	0.735975i	−0.853915	+	0.520413i
$2$	−1.20762	+	0.735975i	−0.853915	+	0.520413i
$3$			0.740676i			0.427629i	0.976874	+	0.213815i	$0.0685889\pi$
$3$			0.740676i			0.427629i	−0.976874	+	0.213815i	$0.931411\pi$
$4$	0.916683	−	1.77755i	0.458341	−	0.888776i
$5$	−1.34841			−0.603029			−0.301515	−	0.953462i	$-0.597492\pi$
$5$	−1.34841			−0.603029			−0.301515	+	0.953462i	$0.597492\pi$
$6$	−0.545118	−	0.894453i	−0.222544	−	0.365159i
$7$	−1.62837			−0.615466			−0.307733	−	0.951473i	$-0.599570\pi$
$7$	−1.62837			−0.615466			−0.307733	+	0.951473i	$0.599570\pi$
$8$	0.201231	+	2.82126i	0.0711458	+	0.997466i
$9$	2.45140			0.817133
$10$	1.62837	−	0.992398i	0.514936	−	0.313824i
$11$		0			0
$11$		0			0
$12$	1.31659	+	0.678965i	0.380067	+	0.196000i
$13$			3.55723i			0.986599i	0.869859	+	0.493300i	$0.164209\pi$
$13$			3.55723i			0.986599i	−0.869859	+	0.493300i	$0.835791\pi$
$14$	1.96645	−	1.19844i	0.525555	−	0.320296i
$15$		−	0.998737i		−	0.257873i
$16$	−2.31939	−	3.25890i	−0.579846	−	0.814726i
$17$		−	0.0699655i		−	0.0169691i	−0.999964	−	0.00848456i	$-0.997299\pi$
$17$		−	0.0699655i		−	0.0169691i	0.999964	−	0.00848456i	$-0.00270075\pi$
$18$	−2.96035	+	1.80417i	−0.697762	+	0.425246i
$19$	−7.95154			−1.82421			−0.912104	−	0.409959i	$-0.865543\pi$
$19$	−7.95154			−1.82421			−0.912104	+	0.409959i	$0.865543\pi$
$20$	−1.23607	+	2.39688i	−0.276393	+	0.535958i
$21$		−	1.20609i		−	0.263191i
$22$		0			0
$23$			5.30988i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$23$			5.30988i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$24$	−2.08964	+	0.149047i	−0.426546	+	0.0304240i
$25$	−3.18178			−0.636356
$26$	−2.61803	−	4.29578i	−0.513439	−	0.842472i
$27$			4.03772i			0.777059i
$28$	−1.49270	+	2.89451i	−0.282093	+	0.547011i
$29$			3.93630i			0.730952i	0.930821	+	0.365476i	$0.119094\pi$
$29$			3.93630i			0.730952i	−0.930821	+	0.365476i	$0.880906\pi$
$30$	0.735045	+	1.20609i	0.134200	+	0.220201i
$31$		−	3.69389i		−	0.663441i	−0.943378	−	0.331721i	$-0.892371\pi$
$31$		−	3.69389i		−	0.663441i	0.943378	−	0.331721i	$-0.107629\pi$
$32$	5.19940	+	2.22850i	0.919133	+	0.393947i
$33$		0			0
$34$	0.0514928	+	0.0844916i	0.00883095	+	0.0144902i
$35$	2.19572			0.371144
$36$	2.24716	−	4.35749i	0.374526	−	0.726249i
$37$	−6.87861			−1.13084			−0.565418	−	0.824804i	$-0.691285\pi$
$37$	−6.87861			−1.13084			−0.565418	+	0.824804i	$0.691285\pi$
$38$	9.60242	−	5.85213i	1.55772	−	0.949341i
$39$	−2.63476			−0.421899
$40$	−0.271342	−	3.80423i	−0.0429030	−	0.601501i
$41$		−	5.78625i		−	0.903660i	−0.892104	−	0.451830i	$-0.850771\pi$
$41$		−	5.78625i		−	0.903660i	0.892104	−	0.451830i	$-0.149229\pi$
$42$	0.887654	+	1.45650i	0.136968	+	0.224743i
$43$	−1.89516			−0.289009			−0.144505	−	0.989504i	$-0.546159\pi$
$43$	−1.89516			−0.289009			−0.144505	+	0.989504i	$0.546159\pi$
$44$		0			0
$45$	−3.30550			−0.492755
$46$	−3.90793	−	6.41230i	−0.576193	−	0.945442i
$47$			9.80536i			1.43026i	0.698992	+	0.715129i	$0.253632\pi$
$47$			9.80536i			1.43026i	−0.698992	+	0.715129i	$0.746368\pi$
$48$	2.41379	−	1.71791i	0.348401	−	0.247959i
$49$	−4.34841			−0.621202
$50$	3.84237	−	2.34171i	0.543394	−	0.331168i
$51$	0.0518217			0.00725650
$52$	6.32317	+	3.26086i	0.876866	+	0.452199i
$53$	−3.88765			−0.534010			−0.267005	−	0.963695i	$-0.586034\pi$
$53$	−3.88765			−0.534010			−0.267005	+	0.963695i	$0.586034\pi$
$54$	−2.97166	−	4.87602i	−0.404391	−	0.663543i
$55$		0			0
$56$	−0.327678	−	4.59405i	−0.0437878	−	0.613906i
$57$		−	5.88951i		−	0.780085i
$58$	−2.89701	−	4.75354i	−0.380397	−	0.624171i
$59$			4.86161i			0.632927i	0.948605	+	0.316464i	$0.102496\pi$
$59$			4.86161i			0.632927i	−0.948605	+	0.316464i	$0.897504\pi$
$60$	−1.77531	−	0.915525i	−0.229191	−	0.118194i
$61$			1.34602i			0.172341i	0.996280	+	0.0861704i	$0.0274629\pi$
$61$			1.34602i			0.172341i	−0.996280	+	0.0861704i	$0.972537\pi$
$62$	2.71861	+	4.46080i	0.345263	+	0.566523i
$63$	−3.99178			−0.502917
$64$	−7.91901	+	1.13545i	−0.989877	+	0.141931i
$65$		−	4.79662i		−	0.594948i
$66$		0			0
$67$		−	4.91303i		−	0.600223i	−0.953904	−	0.300111i	$-0.902976\pi$
$67$		−	4.91303i		−	0.600223i	0.953904	−	0.300111i	$-0.0970238\pi$
$68$	−0.124367	−	0.0641362i	−0.0150818	−	0.00777765i
$69$	−3.93290			−0.473465
$70$	−2.65159	+	1.61599i	−0.316925	+	0.193148i
$71$			6.97557i			0.827848i	0.910311	+	0.413924i	$0.135842\pi$
$71$			6.97557i			0.827848i	−0.910311	+	0.413924i	$0.864158\pi$
$72$	0.493297	+	6.91604i	0.0581356	+	0.815063i
$73$		−	10.1222i		−	1.18471i	−0.805676	−	0.592356i	$-0.798198\pi$
$73$		−	10.1222i		−	1.18471i	0.805676	−	0.592356i	$-0.201802\pi$
$74$	8.30673	−	5.06248i	0.965638	−	0.588501i
$75$		−	2.35667i		−	0.272124i
$76$	−7.28904	+	14.1343i	−0.836110	+	1.62131i
$77$		0			0
$78$	3.18178	−	1.93911i	0.360266	−	0.219561i
$79$	6.00456			0.675566			0.337783	−	0.941224i	$-0.390323\pi$
$79$	6.00456			0.675566			0.337783	+	0.941224i	$0.390323\pi$
$80$	3.12749	+	4.39435i	0.349664	+	0.491303i
$81$	4.36356			0.484840
$82$	4.25853	+	6.98758i	0.470276	+	0.771649i
$83$	3.61193			0.396461			0.198230	−	0.980155i	$-0.436481\pi$
$83$	3.61193			0.396461			0.198230	+	0.980155i	$0.436481\pi$
$84$	−2.14389	−	1.10560i	−0.233918	−	0.120631i
$85$			0.0943425i			0.0102329i
$86$	2.28863	−	1.39479i	0.246789	−	0.150404i
$87$	−2.91552			−0.312576
$88$		0			0
$89$	−5.39711			−0.572093			−0.286046	−	0.958216i	$-0.592341\pi$
$89$	−5.39711			−0.572093			−0.286046	+	0.958216i	$0.592341\pi$
$90$	3.99178	−	2.43277i	0.420771	−	0.256436i
$91$		−	5.79249i		−	0.607218i
$92$	9.43858	+	4.86747i	0.984040	+	0.507469i
$93$	2.73597			0.283707
$94$	−7.21649	−	11.8411i	−0.744325	−	1.22132i
$95$	10.7220			1.10005
$96$	−1.65060	+	3.85107i	−0.168463	+	0.393048i
$97$	7.32624			0.743867			0.371933	−	0.928259i	$-0.378695\pi$
$97$	7.32624			0.743867			0.371933	+	0.928259i	$0.378695\pi$
$98$	5.25122	−	3.20032i	0.530454	−	0.323281i
$99$		0			0
$100$	−2.91668	+	5.65578i	−0.291668	+	0.565578i
$101$			9.57267i			0.952516i	0.879306	+	0.476258i	$0.158007\pi$
$101$			9.57267i			0.952516i	−0.879306	+	0.476258i	$0.841993\pi$
$102$	−0.0625809	+	0.0381395i	−0.00619643	+	0.00377637i
$103$			10.3215i			1.01701i	0.861060	+	0.508503i	$0.169801\pi$
$103$			10.3215i			1.01701i	−0.861060	+	0.508503i	$0.830199\pi$
$104$	−10.0359	+	0.715824i	−0.984099	+	0.0701924i
$105$			1.62631i			0.158712i
$106$	4.69480	−	2.86121i	0.455999	−	0.277906i
$107$	11.0772			1.07087			0.535435	−	0.844577i	$-0.320148\pi$
$107$	11.0772			1.07087			0.535435	+	0.844577i	$0.320148\pi$
$108$	7.17726	+	3.70131i	0.690632	+	0.356158i
$109$			8.95933i			0.858149i	0.903269	+	0.429074i	$0.141160\pi$
$109$			8.95933i			0.858149i	−0.903269	+	0.429074i	$0.858840\pi$
$110$		0			0
$111$		−	5.09482i		−	0.483579i
$112$	3.77682	+	5.30670i	0.356875	+	0.501436i
$113$	11.0231			1.03696			0.518481	−	0.855089i	$-0.326498\pi$
$113$	11.0231			1.03696			0.518481	+	0.855089i	$0.326498\pi$
$114$	4.33453	+	7.11228i	0.405966	+	0.666126i
$115$		−	7.15991i		−	0.667665i
$116$	6.99697	+	3.60834i	0.649653	+	0.335026i
$117$			8.72020i			0.806183i
$118$	−3.57802	−	5.87096i	−0.329383	−	0.540466i
$119$			0.113930i			0.0104439i
$120$	2.81770	−	0.200977i	0.257219	−	0.0183466i
$121$		0			0
$122$	−0.990640	−	1.62548i	−0.0896883	−	0.147164i
$123$	4.28573			0.386432
$124$	−6.56608	−	3.38612i	−0.589651	−	0.304083i
$125$	11.0324			0.986770
$126$	4.82055	−	2.93785i	0.429449	−	0.261725i
$127$	10.2923			0.913298			0.456649	−	0.889647i	$-0.349050\pi$
$127$	10.2923			0.913298			0.456649	+	0.889647i	$0.349050\pi$
$128$	8.72748	−	7.19938i	0.771408	−	0.636341i
$129$		−	1.40370i		−	0.123589i
$130$	3.53019	+	5.79249i	0.309618	+	0.508035i
$131$	−1.86768			−0.163180			−0.0815901	−	0.996666i	$-0.526000\pi$
$131$	−1.86768			−0.163180			−0.0815901	+	0.996666i	$0.526000\pi$
$132$		0			0
$133$	12.9480			1.12274
$134$	3.61587	+	5.93307i	0.312363	+	0.512539i
$135$		−	5.44452i		−	0.468589i
$136$	0.197391	−	0.0140792i	0.0169261	−	0.00120728i
$137$	−1.25447			−0.107177			−0.0535885	−	0.998563i	$-0.517066\pi$
$137$	−1.25447			−0.107177			−0.0535885	+	0.998563i	$0.517066\pi$
$138$	4.74944	−	2.89451i	0.404299	−	0.246397i
$139$	−6.29114			−0.533608			−0.266804	−	0.963751i	$-0.585968\pi$
$139$	−6.29114			−0.533608			−0.266804	+	0.963751i	$0.585968\pi$
$140$	2.01277	−	3.90300i	0.170111	−	0.329864i
$141$	−7.26259			−0.611620
$142$	−5.13384	−	8.42382i	−0.430822	−	0.706912i
$143$		0			0
$144$	−5.68574	−	7.98888i	−0.473812	−	0.665740i
$145$		−	5.30776i		−	0.440785i
$146$	7.44967	+	12.2237i	0.616539	+	1.01164i
$147$		−	3.22076i		−	0.265644i
$148$	−6.30550	+	12.2271i	−0.518309	+	1.00506i
$149$		−	17.1557i		−	1.40545i	−0.711462	−	0.702724i	$-0.751967\pi$
$149$		−	17.1557i		−	1.40545i	0.711462	−	0.702724i	$-0.248033\pi$
$150$	1.73445	+	2.84595i	0.141617	+	0.232371i
$151$	12.1583			0.989428			0.494714	−	0.869056i	$-0.335273\pi$
$151$	12.1583			0.989428			0.494714	+	0.869056i	$0.335273\pi$
$152$	−1.60009	−	22.4334i	−0.129785	−	1.81959i
$153$		−	0.171513i		−	0.0138660i
$154$		0			0
$155$			4.98089i			0.400074i
$156$	−2.41524	+	4.68342i	−0.193374	+	0.374974i
$157$	−5.30173			−0.423124			−0.211562	−	0.977365i	$-0.567855\pi$
$157$	−5.30173			−0.423124			−0.211562	+	0.977365i	$0.567855\pi$
$158$	−7.25121	+	4.41920i	−0.576876	+	0.351573i
$159$		−	2.87949i		−	0.228358i
$160$	−7.01095	−	3.00494i	−0.554264	−	0.237562i
$161$		−	8.64644i		−	0.681435i
$162$	−5.26951	+	3.21147i	−0.414012	+	0.252317i
$163$			10.0576i			0.787768i	0.919160	+	0.393884i	$0.128869\pi$
$163$			10.0576i			0.787768i	−0.919160	+	0.393884i	$0.871131\pi$
$164$	−10.2854	−	5.30415i	−0.803152	−	0.414185i
$165$		0			0
$166$	−4.36183	+	2.65829i	−0.338544	+	0.206323i
$167$	−21.9076			−1.69526			−0.847632	−	0.530585i	$-0.821972\pi$
$167$	−21.9076			−1.69526			−0.847632	+	0.530585i	$0.821972\pi$
$168$	3.40270	−	0.242703i	0.262524	−	0.0187249i
$169$	0.346084			0.0266219
$170$	−0.0694337	−	0.113930i	−0.00532532	−	0.00873801i
$171$	−19.4924			−1.49062
$172$	−1.73726	+	3.36874i	−0.132465	+	0.256864i
$173$			11.8322i			0.899586i	0.893133	+	0.449793i	$0.148502\pi$
$173$			11.8322i			0.899586i	−0.893133	+	0.449793i	$0.851498\pi$
$174$	3.52083	−	2.14575i	0.266914	−	0.162669i
$175$	5.18111			0.391655
$176$		0			0
$177$	−3.60087			−0.270658
$178$	6.51765	−	3.97214i	0.488518	−	0.297724i
$179$			0.933676i			0.0697862i	0.999391	+	0.0348931i	$0.0111091\pi$
$179$			0.933676i			0.0697862i	−0.999391	+	0.0348931i	$0.988891\pi$
$180$	−3.03010	+	5.87570i	−0.225850	+	0.437949i
$181$	18.8395			1.40033			0.700163	−	0.713983i	$-0.253111\pi$
$181$	18.8395			1.40033			0.700163	+	0.713983i	$0.253111\pi$
$182$	4.26313	+	6.99512i	0.316004	+	0.518513i
$183$	−0.996967			−0.0736979
$184$	−14.9805	+	1.06851i	−1.10438	+	0.0787716i
$185$	9.27521			0.681927
$186$	−3.30401	+	2.01361i	−0.242262	+	0.147645i
$187$		0			0
$188$	17.4295	+	8.98840i	1.27118	+	0.655547i
$189$		−	6.57490i		−	0.478253i
$190$	−12.9480	+	7.89110i	−0.939350	+	0.572480i
$191$		−	20.4441i		−	1.47928i	−0.673001	−	0.739641i	$-0.734995\pi$
$191$		−	20.4441i		−	1.47928i	0.673001	−	0.739641i	$-0.265005\pi$
$192$	−0.840998	−	5.86542i	−0.0606938	−	0.423300i
$193$			17.3409i			1.24823i	0.781333	+	0.624114i	$0.214540\pi$
$193$			17.3409i			1.24823i	−0.781333	+	0.624114i	$0.785460\pi$
$194$	−8.84730	+	5.39192i	−0.635199	+	0.387118i
$195$	3.55274			0.254417
$196$	−3.98612	+	7.72953i	−0.284723	+	0.552110i
$197$			3.49133i			0.248747i	0.992235	+	0.124374i	$0.0396921\pi$
$197$			3.49133i			0.248747i	−0.992235	+	0.124374i	$0.960308\pi$
$198$		0			0
$199$		−	11.2660i		−	0.798625i	−0.916815	−	0.399313i	$-0.869249\pi$
$199$		−	11.2660i		−	0.798625i	0.916815	−	0.399313i	$-0.130751\pi$
$200$	−0.640271	−	8.97663i	−0.0452740	−	0.634743i
$201$	3.63896			0.256673
$202$	−7.04524	−	11.5601i	−0.495701	−	0.813368i
$203$		−	6.40974i		−	0.449876i
$204$	0.0475041	−	0.0921159i	0.00332595	−	0.00644940i
$205$			7.80226i			0.544933i
$206$	−7.59635	−	12.4644i	−0.529263	−	0.868436i
$207$			13.0166i			0.904718i
$208$	11.5927	−	8.25060i	0.803808	−	0.572076i
$209$		0			0
$210$	−1.19693	−	1.96397i	−0.0825957	−	0.135526i
$211$	−2.74295			−0.188833			−0.0944163	−	0.995533i	$-0.530098\pi$
$211$	−2.74295			−0.188833			−0.0944163	+	0.995533i	$0.530098\pi$
$212$	−3.56375	+	6.91051i	−0.244759	+	0.474616i
$213$	−5.16663			−0.354012
$214$	−13.3770	+	8.15251i	−0.914431	+	0.557294i
$215$	2.55546			0.174281
$216$	−11.3915	+	0.812513i	−0.775090	+	0.0552845i
$217$			6.01501i			0.408325i
$218$	−6.59384	−	10.8195i	−0.446591	−	0.732786i
$219$	7.49726			0.506618
$220$		0			0
$221$	0.248884			0.0167417
$222$	3.74966	+	6.15259i	0.251660	+	0.412935i
$223$		−	23.7258i		−	1.58880i	−0.607398	−	0.794398i	$-0.707787\pi$
$223$		−	23.7258i		−	1.58880i	0.607398	−	0.794398i	$-0.292213\pi$
$224$	−8.46655	−	3.62882i	−0.565695	−	0.242461i
$225$	−7.79981			−0.519988
$226$	−13.3117	+	8.11270i	−0.885478	+	0.539649i
$227$	−0.800839			−0.0531536			−0.0265768	−	0.999647i	$-0.508461\pi$
$227$	−0.800839			−0.0531536			−0.0265768	+	0.999647i	$0.508461\pi$
$228$	−10.4689	−	5.39881i	−0.693321	−	0.357545i
$229$	−23.5889			−1.55880			−0.779401	−	0.626526i	$-0.784476\pi$
$229$	−23.5889			−1.55880			−0.779401	+	0.626526i	$0.784476\pi$
$230$	5.26951	+	8.64644i	0.347461	+	0.570129i
$231$		0			0
$232$	−11.1053	+	0.792103i	−0.729100	+	0.0520041i
$233$		−	17.4915i		−	1.14591i	−0.819588	−	0.572953i	$-0.805798\pi$
$233$		−	17.4915i		−	1.14591i	0.819588	−	0.572953i	$-0.194202\pi$
$234$	−6.41785	−	10.5307i	−0.419548	−	0.688412i
$235$		−	13.2217i		−	0.862487i
$236$	8.64176	+	4.45655i	0.562531	+	0.290097i
$237$			4.44743i			0.288892i
$238$	−0.0838493	−	0.137584i	−0.00543515	−	0.00891822i
$239$	6.68497			0.432415			0.216207	−	0.976347i	$-0.430631\pi$
$239$	6.68497			0.432415			0.216207	+	0.976347i	$0.430631\pi$
$240$	−3.25479	+	2.31646i	−0.210096	+	0.149527i
$241$		−	4.28655i		−	0.276121i	−0.990424	−	0.138061i	$-0.955913\pi$
$241$		−	4.28655i		−	0.276121i	0.990424	−	0.138061i	$-0.0440868\pi$
$242$		0			0
$243$			15.3451i			0.984391i
$244$	2.39263	+	1.23388i	0.153172	+	0.0789909i
$245$	5.86346			0.374603
$246$	−5.17553	+	3.15419i	−0.329980	+	0.201104i
$247$		−	28.2855i		−	1.79976i
$248$	10.4214	−	0.743323i	0.661760	−	0.0472010i
$249$			2.67527i			0.169538i
$250$	−13.3230	+	8.11959i	−0.842618	+	0.513528i
$251$		−	4.89768i		−	0.309139i	−0.987982	−	0.154569i	$-0.950601\pi$
$251$		−	4.89768i		−	0.309139i	0.987982	−	0.154569i	$-0.0493990\pi$
$252$	−3.65920	+	7.09560i	−0.230508	+	0.446981i
$253$		0			0
$254$	−12.4292	+	7.57491i	−0.779879	+	0.475292i
$255$	−0.0698772			−0.00437588
$256$	−5.24091	+	15.1173i	−0.327557	+	0.944832i
$257$	−12.3843			−0.772511			−0.386256	−	0.922392i	$-0.626232\pi$
$257$	−12.3843			−0.772511			−0.386256	+	0.922392i	$0.626232\pi$
$258$	1.03309	+	1.69513i	0.0643171	+	0.105534i
$259$	11.2009			0.695991
$260$	−8.52625	−	4.39698i	−0.528776	−	0.272689i
$261$			9.64944i			0.597285i
$262$	2.25545	−	1.37457i	0.139342	−	0.0849211i
$263$	16.9489			1.04511			0.522556	−	0.852605i	$-0.324979\pi$
$263$	16.9489			1.04511			0.522556	+	0.852605i	$0.324979\pi$
$264$		0			0
$265$	5.24217			0.322024
$266$	−15.6363	+	9.52943i	−0.958722	+	0.584287i
$267$		−	3.99751i		−	0.244644i
$268$	−8.73318	−	4.50369i	−0.533464	−	0.275107i
$269$	3.95476			0.241126			0.120563	−	0.992706i	$-0.461530\pi$
$269$	3.95476			0.241126			0.120563	+	0.992706i	$0.461530\pi$
$270$	4.00703	+	6.57490i	0.243860	+	0.400135i
$271$	−23.7375			−1.44195			−0.720974	−	0.692962i	$-0.756305\pi$
$271$	−23.7375			−1.44195			−0.720974	+	0.692962i	$0.756305\pi$
$272$	−0.228011	+	0.162277i	−0.0138252	+	0.00983949i
$273$	4.29036			0.259664
$274$	1.51493	−	0.923261i	0.0915200	−	0.0557763i
$275$		0			0
$276$	−3.60522	+	6.99093i	−0.217009	+	0.420804i
$277$			15.0111i			0.901928i	0.892542	+	0.450964i	$0.148920\pi$
$277$			15.0111i			0.901928i	−0.892542	+	0.450964i	$0.851080\pi$
$278$	7.59730	−	4.63012i	0.455656	−	0.277696i
$279$		−	9.05519i		−	0.542120i
$280$	0.441845	+	6.19468i	0.0264053	+	0.370203i
$281$			5.74135i			0.342500i	0.985228	+	0.171250i	$0.0547806\pi$
$281$			5.74135i			0.342500i	−0.985228	+	0.171250i	$0.945219\pi$
$282$	8.77043	−	5.34508i	0.522272	−	0.318295i
$283$	−11.1948			−0.665460			−0.332730	−	0.943022i	$-0.607970\pi$
$283$	−11.1948			−0.665460			−0.332730	+	0.943022i	$0.607970\pi$
$284$	12.3994	+	6.39439i	0.735771	+	0.379437i
$285$			7.94150i			0.470414i
$286$		0			0
$287$			9.42215i			0.556172i
$288$	12.7458	+	5.46295i	0.751054	+	0.321907i
$289$	16.9951			0.999712
$290$	3.90637	+	6.40974i	0.229390	+	0.376393i
$291$			5.42637i			0.318099i
$292$	−17.9927	−	9.27883i	−1.05294	−	0.543003i
$293$			5.30290i			0.309799i	0.987930	+	0.154899i	$0.0495053\pi$
$293$			5.30290i			0.309799i	−0.987930	+	0.154899i	$0.950495\pi$
$294$	2.37040	+	3.88945i	0.138245	+	0.226838i
$295$		−	6.55546i		−	0.381674i
$296$	−1.38419	−	19.4063i	−0.0804542	−	1.12797i
$297$		0			0
$298$	12.6261	+	20.7175i	0.731413	+	1.20013i
$299$	−18.8885			−1.09235
$300$	−4.18910	−	2.16032i	−0.241858	−	0.124726i
$301$	3.08602			0.177875
$302$	−14.6826	+	8.94819i	−0.844887	+	0.514911i
$303$	−7.09024			−0.407324
$304$	18.4427	+	25.9133i	1.05776	+	1.48623i
$305$		−	1.81500i		−	0.103926i
$306$	0.126230	+	0.207123i	0.00721606	+	0.0118404i
$307$	2.27014			0.129564			0.0647820	−	0.997899i	$-0.479365\pi$
$307$	2.27014			0.129564			0.0647820	+	0.997899i	$0.479365\pi$
$308$		0			0
$309$	−7.64487			−0.434901
$310$	−3.66581	−	6.01501i	−0.208204	−	0.341630i
$311$			20.1665i			1.14354i	0.820414	+	0.571770i	$0.193743\pi$
$311$			20.1665i			1.14354i	−0.820414	+	0.571770i	$0.806257\pi$
$312$	−0.530194	−	7.43333i	−0.0300163	−	0.420830i
$313$	1.54188			0.0871524			0.0435762	−	0.999050i	$-0.486125\pi$
$313$	1.54188			0.0871524			0.0435762	+	0.999050i	$0.486125\pi$
$314$	6.40247	−	3.90194i	0.361312	−	0.220199i
$315$	5.38258			0.303274
$316$	5.50428	−	10.6734i	0.309640	−	0.600427i
$317$	−16.8622			−0.947076			−0.473538	−	0.880773i	$-0.657023\pi$
$317$	−16.8622			−0.947076			−0.473538	+	0.880773i	$0.657023\pi$
$318$	2.11923	+	3.47732i	0.118841	+	0.194999i
$319$		0			0
$320$	10.6781	−	1.53105i	0.596924	−	0.0855885i
$321$			8.20458i			0.457935i
$322$	6.36356	+	10.4416i	0.354627	+	0.581887i
$323$			0.556334i			0.0309552i
$324$	4.00000	−	7.75646i	0.222222	−	0.430914i
$325$		−	11.3183i		−	0.627828i
$326$	−7.40210	−	12.1457i	−0.409965	−	0.672687i
$327$	−6.63596			−0.366969
$328$	16.3245	−	1.16437i	0.901370	−	0.0642916i
$329$		−	15.9667i		−	0.880275i
$330$		0			0
$331$		−	33.9735i		−	1.86735i	−0.358115	−	0.933677i	$-0.616581\pi$
$331$		−	33.9735i		−	1.86735i	0.358115	−	0.933677i	$-0.383419\pi$
$332$	3.31099	−	6.42039i	0.181714	−	0.352365i
$333$	−16.8622			−0.924044
$334$	26.4561	−	16.1235i	1.44761	−	0.882237i
$335$			6.62480i			0.361952i
$336$	−3.93054	+	2.79739i	−0.214429	+	0.152610i
$337$		−	17.0957i		−	0.931262i	−0.884979	−	0.465631i	$-0.845827\pi$
$337$		−	17.0957i		−	0.931262i	0.884979	−	0.465631i	$-0.154173\pi$
$338$	−0.417938	+	0.254709i	−0.0227328	+	0.0138544i
$339$			8.16452i			0.443436i
$340$	0.167699	+	0.0864821i	0.00909474	+	0.00469015i
$341$		0			0
$342$	23.5394	−	14.3459i	1.27286	−	0.775738i
$343$	18.4794			0.997794
$344$	−0.381364	−	5.34674i	−0.0205618	−	0.288277i
$345$	5.30317			0.285513
$346$	−8.70820	−	14.2888i	−0.468156	−	0.768170i
$347$	−2.49909			−0.134158			−0.0670790	−	0.997748i	$-0.521368\pi$
$347$	−2.49909			−0.134158			−0.0670790	+	0.997748i	$0.521368\pi$
$348$	−2.67261	+	5.18249i	−0.143267	+	0.277810i
$349$			7.01126i			0.375304i	0.982236	+	0.187652i	$0.0600878\pi$
$349$			7.01126i			0.375304i	−0.982236	+	0.187652i	$0.939912\pi$
$350$	−6.25680	+	3.81317i	−0.334440	+	0.203822i
$351$	−14.3631			−0.766646
$352$		0			0
$353$	17.9431			0.955017			0.477509	−	0.878627i	$-0.341540\pi$
$353$	17.9431			0.955017			0.477509	+	0.878627i	$0.341540\pi$
$354$	4.34848	−	2.65015i	0.231119	−	0.140854i
$355$		−	9.40596i		−	0.499216i
$356$	−4.94744	+	9.59365i	−0.262214	+	0.508462i
$357$	−0.0843849			−0.00446612
$358$	−0.687162	−	1.12752i	−0.0363176	−	0.0595915i
$359$	9.67947			0.510863			0.255431	−	0.966827i	$-0.417783\pi$
$359$	9.67947			0.510863			0.255431	+	0.966827i	$0.417783\pi$
$360$	−0.665168	−	9.32568i	−0.0350574	−	0.491506i
$361$	44.2270			2.32774
$362$	−22.7509	+	13.8654i	−1.19576	+	0.728748i
$363$		0			0
$364$	−10.2965	−	5.30988i	−0.539681	−	0.278313i
$365$			13.6489i			0.714416i
$366$	1.20396	−	0.733743i	0.0629318	−	0.0383533i
$367$			30.9471i			1.61543i	0.589575	+	0.807713i	$0.299295\pi$
$367$			30.9471i			1.61543i	−0.589575	+	0.807713i	$0.700705\pi$
$368$	17.3044	−	12.3156i	0.902053	−	0.641998i
$369$		−	14.1844i		−	0.738411i
$370$	−11.2009	+	6.82632i	−0.582308	+	0.354883i
$371$	6.33054			0.328665
$372$	2.50802	−	4.86333i	0.130035	−	0.252152i
$373$		−	4.92658i		−	0.255088i	−0.991833	−	0.127544i	$-0.959291\pi$
$373$		−	4.92658i		−	0.255088i	0.991833	−	0.127544i	$-0.0407095\pi$
$374$		0			0
$375$			8.17145i			0.421972i
$376$	−27.6635	+	1.97314i	−1.42663	+	0.101757i
$377$	−14.0023			−0.721157
$378$	4.83896	+	7.93996i	0.248889	+	0.408388i
$379$			4.02515i			0.206758i	0.994642	+	0.103379i	$0.0329655\pi$
$379$			4.02515i			0.206758i	−0.994642	+	0.103379i	$0.967035\pi$
$380$	9.82864	−	19.0589i	0.504199	−	0.977699i
$381$			7.62329i			0.390553i
$382$	15.0463	+	24.6887i	0.769837	+	1.26318i
$383$		−	11.9889i		−	0.612604i	−0.951934	−	0.306302i	$-0.900908\pi$
$383$		−	11.9889i		−	0.612604i	0.951934	−	0.306302i	$-0.0990918\pi$
$384$	5.33240	+	6.46423i	0.272118	+	0.329877i
$385$		0			0
$386$	−12.7625	−	20.9412i	−0.649594	−	1.06588i
$387$	−4.64579			−0.236159
$388$	6.71584	−	13.0228i	0.340945	−	0.661131i
$389$	13.7371			0.696496			0.348248	−	0.937402i	$-0.386777\pi$
$389$	13.7371			0.696496			0.348248	+	0.937402i	$0.386777\pi$
$390$	−4.29036	+	2.61473i	−0.217251	+	0.132402i
$391$	0.371508			0.0187880
$392$	−0.875034	−	12.2680i	−0.0441959	−	0.619628i
$393$		−	1.38335i		−	0.0697807i
$394$	−2.56953	−	4.21619i	−0.129451	−	0.212409i
$395$	−8.09663			−0.407386
$396$		0			0
$397$	−12.1547			−0.610027			−0.305014	−	0.952348i	$-0.598661\pi$
$397$	−12.1547			−0.610027			−0.305014	+	0.952348i	$0.598661\pi$
$398$	8.29149	+	13.6050i	0.415615	+	0.681958i
$399$			9.59030i			0.480115i
$400$	7.37977	+	10.3691i	0.368989	+	0.518456i
$401$	−28.7805			−1.43723			−0.718614	−	0.695409i	$-0.755223\pi$
$401$	−28.7805			−1.43723			−0.718614	+	0.695409i	$0.755223\pi$
$402$	−4.39448	+	2.67819i	−0.219177	+	0.133576i
$403$	13.1400			0.654551
$404$	17.0159	+	8.77510i	0.846574	+	0.436578i
$405$	−5.88388			−0.292373
$406$	4.71741	+	7.74052i	0.234121	+	0.384156i
$407$		0			0
$408$	0.0104281	+	0.146203i	0.000516269	+	0.00723811i
$409$		−	18.9552i		−	0.937276i	−0.883390	−	0.468638i	$-0.844745\pi$
$409$		−	18.9552i		−	0.937276i	0.883390	−	0.468638i	$-0.155255\pi$
$410$	−5.74226	−	9.42215i	−0.283590	−	0.465327i
$411$		−	0.929159i		−	0.0458320i
$412$	18.3470	+	9.46152i	0.903891	+	0.466136i
$413$		−	7.91649i		−	0.389545i
$414$	−9.57991	−	15.7191i	−0.470827	−	0.772552i
$415$	−4.87038			−0.239077
$416$	−7.92731	+	18.4955i	−0.388668	+	0.906816i
$417$		−	4.65970i		−	0.228186i
$418$		0			0
$419$			15.3705i			0.750898i	0.926843	+	0.375449i	$0.122512\pi$
$419$			15.3705i			0.750898i	−0.926843	+	0.375449i	$0.877488\pi$
$420$	2.89086	+	1.49081i	0.141059	+	0.0727442i
$421$	19.3208			0.941640			0.470820	−	0.882229i	$-0.343958\pi$
$421$	19.3208			0.941640			0.470820	+	0.882229i	$0.343958\pi$
$422$	3.31244	−	2.01874i	0.161247	−	0.0982709i
$423$			24.0369i			1.16871i
$424$	−0.782315	−	10.9681i	−0.0379926	−	0.532657i
$425$			0.222615i			0.0107984i
$426$	6.23932	−	3.80251i	0.302296	−	0.184232i
$427$		−	2.19182i		−	0.106070i
$428$	10.1542	−	19.6902i	0.490824	−	0.951763i
$429$		0			0
$430$	−3.08602	+	1.88075i	−0.148821	+	0.0906980i
$431$	27.1040			1.30555			0.652777	−	0.757550i	$-0.273604\pi$
$431$	27.1040			1.30555			0.652777	+	0.757550i	$0.273604\pi$
$432$	13.1585	−	9.36502i	0.633090	−	0.450575i
$433$	4.35614			0.209343			0.104671	−	0.994507i	$-0.466621\pi$
$433$	4.35614			0.209343			0.104671	+	0.994507i	$0.466621\pi$
$434$	−4.42689	−	7.26383i	−0.212498	−	0.348675i
$435$	3.93133			0.188493
$436$	15.9257	+	8.21287i	0.762702	+	0.393325i
$437$		−	42.2217i		−	2.01974i
$438$	−9.05382	+	5.51779i	−0.432608	+	0.263650i
$439$	−24.0996			−1.15021			−0.575105	−	0.818080i	$-0.695039\pi$
$439$	−24.0996			−1.15021			−0.575105	+	0.818080i	$0.695039\pi$
$440$		0			0
$441$	−10.6597			−0.507605
$442$	−0.300556	+	0.183172i	−0.0142960	+	0.00871261i
$443$			23.0448i			1.09489i	0.836841	+	0.547446i	$0.184400\pi$
$443$			23.0448i			1.09489i	−0.836841	+	0.547446i	$0.815600\pi$
$444$	−9.05630	−	4.67033i	−0.429793	−	0.221644i
$445$	7.27754			0.344989
$446$	17.4616	+	28.6517i	0.826829	+	1.35670i
$447$	12.7068			0.601011
$448$	12.8951	−	1.84893i	0.609235	−	0.0873536i
$449$	−3.77349			−0.178082			−0.0890409	−	0.996028i	$-0.528380\pi$
$449$	−3.77349			−0.178082			−0.0890409	+	0.996028i	$0.528380\pi$
$450$	9.41920	−	5.74046i	0.444025	−	0.270608i
$451$		0			0
$452$	10.1047	−	19.5941i	0.475283	−	0.921628i
$453$			9.00535i			0.423108i
$454$	0.967108	−	0.589397i	0.0453886	−	0.0276618i
$455$			7.81068i			0.366170i
$456$	16.6158	−	1.18515i	0.778108	−	0.0554997i
$457$			35.2571i			1.64926i	0.565674	+	0.824629i	$0.308616\pi$
$457$			35.2571i			1.64926i	−0.565674	+	0.824629i	$0.691384\pi$
$458$	28.4864	−	17.3609i	1.33108	−	0.811220i
$459$	0.282501			0.0131860
$460$	−12.7271	−	6.56337i	−0.593405	−	0.306019i
$461$			38.5074i			1.79347i	0.442571	+	0.896734i	$0.354067\pi$
$461$			38.5074i			1.79347i	−0.442571	+	0.896734i	$0.645933\pi$
$462$		0			0
$463$			10.7672i			0.500394i	0.968195	+	0.250197i	$0.0804954\pi$
$463$			10.7672i			0.500394i	−0.968195	+	0.250197i	$0.919505\pi$
$464$	12.8280	−	9.12979i	0.595525	−	0.423840i
$465$	−3.68922			−0.171084
$466$	12.8733	+	21.1231i	0.596344	+	0.978507i
$467$			20.6799i			0.956950i	0.878101	+	0.478475i	$0.158810\pi$
$467$			20.6799i			0.956950i	−0.878101	+	0.478475i	$0.841190\pi$
$468$	15.5006	+	7.99366i	0.716516	+	0.369507i
$469$			8.00023i			0.369416i
$470$	9.73082	+	15.9667i	0.448849	+	0.736491i
$471$		−	3.92686i		−	0.180940i
$472$	−13.7159	+	0.978304i	−0.631323	+	0.0450301i
$473$		0			0
$474$	−3.27320	−	5.37080i	−0.150343	−	0.246689i
$475$	25.3000			1.16085
$476$	0.202516	+	0.104437i	0.00928230	+	0.00478688i
$477$	−9.53019			−0.436358
$478$	−8.07289	+	4.91997i	−0.369245	+	0.225034i
$479$	−11.4138			−0.521511			−0.260756	−	0.965405i	$-0.583972\pi$
$479$	−11.4138			−0.521511			−0.260756	+	0.965405i	$0.583972\pi$
$480$	2.22569	−	5.19284i	0.101588	−	0.237019i
$481$		−	24.4688i		−	1.11568i
$482$	3.15479	+	5.17652i	0.143697	+	0.235784i
$483$	6.40421			0.291401
$484$		0			0
$485$	−9.87880			−0.448573
$486$	−11.2936	−	18.5311i	−0.512290	−	0.840586i
$487$			4.00496i			0.181482i	0.995875	+	0.0907410i	$0.0289235\pi$
$487$			4.00496i			0.181482i	−0.995875	+	0.0907410i	$0.971076\pi$
$488$	−3.79748	+	0.270861i	−0.171904	+	0.0122613i
$489$	−7.44938			−0.336873
$490$	−7.08082	+	4.31536i	−0.319879	+	0.194948i
$491$	11.1940			0.505179			0.252589	−	0.967574i	$-0.418718\pi$
$491$	11.1940			0.505179			0.252589	+	0.967574i	$0.418718\pi$
$492$	3.92866	−	7.61812i	0.177118	−	0.343451i
$493$	0.275405			0.0124036
$494$	20.8174	+	34.1581i	0.936619	+	1.53684i
$495$		0			0
$496$	−12.0380	+	8.56754i	−0.540523	+	0.384694i
$497$		−	11.3588i		−	0.509512i
$498$	−1.96893	−	3.23070i	−0.0882298	−	0.144771i
$499$			39.3656i			1.76224i	0.472888	+	0.881122i	$0.343211\pi$
$499$			39.3656i			1.76224i	−0.472888	+	0.881122i	$0.656789\pi$
$500$	10.1132	−	19.6107i	0.452278	−	0.877018i
$501$		−	16.2265i		−	0.724944i
$502$	3.60456	+	5.91452i	0.160880	+	0.263978i
$503$	−19.3369			−0.862191			−0.431096	−	0.902306i	$-0.641873\pi$
$503$	−19.3369			−0.862191			−0.431096	+	0.902306i	$0.641873\pi$
$504$	−0.803269	−	11.2619i	−0.0357804	−	0.501643i
$505$		−	12.9079i		−	0.574395i
$506$		0			0
$507$			0.256336i			0.0113843i
$508$	9.43482	−	18.2952i	0.418602	−	0.811718i
$509$	−42.9965			−1.90579			−0.952893	−	0.303306i	$-0.901910\pi$
$509$	−42.9965			−1.90579			−0.952893	+	0.303306i	$0.901910\pi$
$510$	0.0843849	−	0.0514278i	0.00373663	−	0.00227726i
$511$			16.4827i			0.729150i
$512$	−4.79694	−	22.1131i	−0.211997	−	0.977270i
$513$		−	32.1061i		−	1.41752i
$514$	14.9555	−	9.11453i	0.659659	−	0.402025i
$515$		−	13.9176i		−	0.613284i
$516$	−2.49515	−	1.28675i	−0.109843	−	0.0566458i
$517$		0			0
$518$	−13.5264	+	8.24359i	−0.594317	+	0.362202i
$519$	−8.76383			−0.384689
$520$	13.5325	−	0.965228i	0.593440	−	0.0423280i
$521$	−14.7313			−0.645389			−0.322694	−	0.946503i	$-0.604589\pi$
$521$	−14.7313			−0.645389			−0.322694	+	0.946503i	$0.604589\pi$
$522$	−7.10174	−	11.6528i	−0.310835	−	0.510031i
$523$	40.4528			1.76888			0.884440	−	0.466655i	$-0.154541\pi$
$523$	40.4528			1.76888			0.884440	+	0.466655i	$0.154541\pi$
$524$	−1.71207	+	3.31991i	−0.0747923	+	0.145031i
$525$			3.83752i			0.167483i
$526$	−20.4677	+	12.4739i	−0.892436	+	0.543889i
$527$	−0.258445			−0.0112580
$528$		0			0
$529$	−5.19479			−0.225860
$530$	−6.33054	+	3.85810i	−0.274981	+	0.167585i
$531$			11.9177i			0.517186i
$532$	11.8692	−	23.0158i	0.514597	−	0.997862i
$533$	20.5830			0.891551
$534$	2.94206	+	4.82746i	0.127316	+	0.208905i
$535$	−14.9366			−0.645765
$536$	13.8609	−	0.988653i	0.598702	−	0.0427033i
$537$	−0.691551			−0.0298426
$538$	−4.77584	+	2.91060i	−0.205901	+	0.125485i
$539$		0			0
$540$	−9.67791	−	4.99089i	−0.416471	−	0.214774i
$541$			16.7350i			0.719496i	0.933050	+	0.359748i	$0.117137\pi$
$541$			16.7350i			0.719496i	−0.933050	+	0.359748i	$0.882863\pi$
$542$	28.6658	−	17.4702i	1.23130	−	0.750408i
$543$			13.9539i			0.598821i
$544$	0.155918	−	0.363779i	0.00668494	−	0.0155969i
$545$		−	12.0809i		−	0.517489i
$546$	−5.18111	+	3.15759i	−0.221731	+	0.135133i
$547$	−9.29004			−0.397214			−0.198607	−	0.980079i	$-0.563642\pi$
$547$	−9.29004			−0.397214			−0.198607	+	0.980079i	$0.563642\pi$
$548$	−1.14996	+	2.22989i	−0.0491237	+	0.0952564i
$549$			3.29964i			0.140825i
$550$		0			0
$551$		−	31.2996i		−	1.33341i
$552$	−0.791419	−	11.0957i	−0.0336850	−	0.472265i
$553$	−9.77764			−0.415787
$554$	−11.0478	−	18.1276i	−0.469375	−	0.770170i
$555$			6.86992i			0.291612i
$556$	−5.76698	+	11.1828i	−0.244575	+	0.474258i
$557$			13.2620i			0.561928i	0.959718	+	0.280964i	$0.0906541\pi$
$557$			13.2620i			0.561928i	−0.959718	+	0.280964i	$0.909346\pi$
$558$	6.66439	+	10.9352i	0.282126	+	0.462924i
$559$		−	6.74153i		−	0.285136i
$560$	−5.09271	−	7.15563i	−0.215206	−	0.302380i
$561$		0			0
$562$	−4.22549	−	6.93336i	−0.178241	−	0.292466i
$563$	23.5044			0.990594			0.495297	−	0.868724i	$-0.335059\pi$
$563$	23.5044			0.990594			0.495297	+	0.868724i	$0.335059\pi$
$564$	−6.65749	+	12.9096i	−0.280331	+	0.543594i
$565$	−14.8637			−0.625319
$566$	13.5190	−	8.23907i	0.568246	−	0.346314i
$567$	−7.10549			−0.298402
$568$	−19.6799	+	1.40370i	−0.825750	+	0.0588979i
$569$			12.8798i			0.539950i	0.962867	+	0.269975i	$0.0870154\pi$
$569$			12.8798i			0.539950i	−0.962867	+	0.269975i	$0.912985\pi$
$570$	−5.84474	−	9.59030i	−0.244809	−	0.401693i
$571$	−20.4261			−0.854806			−0.427403	−	0.904061i	$-0.640571\pi$
$571$	−20.4261			−0.854806			−0.427403	+	0.904061i	$0.640571\pi$
$572$		0			0
$573$	15.1424			0.632585
$574$	−6.93446	−	11.3784i	−0.289439	−	0.474923i
$575$		−	16.8949i		−	0.704564i
$576$	−19.4127	+	2.78344i	−0.808861	+	0.115976i
$577$	6.84506			0.284963			0.142482	−	0.989797i	$-0.454492\pi$
$577$	6.84506			0.284963			0.142482	+	0.989797i	$0.454492\pi$
$578$	−20.5236	+	12.5080i	−0.853669	+	0.520263i
$579$	−12.8440			−0.533779
$580$	−9.43482	−	4.86553i	−0.391759	−	0.202030i
$581$	−5.88155			−0.244008
$582$	−3.99367	−	6.55298i	−0.165543	−	0.271630i
$583$		0			0
$584$	28.5573	−	2.03689i	1.18171	−	0.0842873i
$585$		−	11.7584i		−	0.486152i
$586$	−3.90280	−	6.40388i	−0.161223	−	0.264542i
$587$			0.638798i			0.0263660i	0.999913	+	0.0131830i	$0.00419640\pi$
$587$			0.638798i			0.0263660i	−0.999913	+	0.0131830i	$0.995804\pi$
$588$	−5.72508	−	2.95242i	−0.236098	−	0.121756i
$589$			29.3721i			1.21026i
$590$	4.82465	+	7.91649i	0.198628	+	0.325917i
$591$	−2.58594			−0.106372
$592$	15.9541	+	22.4167i	0.655711	+	0.921321i
$593$		−	17.0480i		−	0.700077i	−0.936735	−	0.350039i	$-0.886168\pi$
$593$		−	17.0480i		−	0.700077i	0.936735	−	0.350039i	$-0.113832\pi$
$594$		0			0
$595$		−	0.153624i		−	0.00629799i
$596$	−30.4951	−	15.7263i	−1.24913	−	0.644175i
$597$	8.34445			0.341516
$598$	22.8101	−	13.9014i	0.932773	−	0.568472i
$599$			1.98468i			0.0810916i	0.999178	+	0.0405458i	$0.0129097\pi$
$599$			1.98468i			0.0810916i	−0.999178	+	0.0405458i	$0.987090\pi$
$600$	6.64877	−	0.474233i	0.271435	−	0.0193605i
$601$			16.4628i			0.671532i	0.941945	+	0.335766i	$0.108995\pi$
$601$			16.4628i			0.671532i	−0.941945	+	0.335766i	$0.891005\pi$
$602$	−3.72673	+	2.27123i	−0.151890	+	0.0925685i
$603$		−	12.0438i		−	0.490462i
$604$	11.1453	−	21.6120i	0.453496	−	0.879380i
$605$		0			0
$606$	8.56231	−	5.21824i	0.347820	−	0.211976i
$607$	−28.7204			−1.16573			−0.582863	−	0.812571i	$-0.698067\pi$
$607$	−28.7204			−1.16573			−0.582863	+	0.812571i	$0.698067\pi$
$608$	−41.3432	−	17.7200i	−1.67669	−	0.718642i
$609$	4.74754			0.192380
$610$	1.33579	+	2.19182i	0.0540847	+	0.0887444i
$611$	−34.8800			−1.41109
$612$	−0.304874	−	0.157223i	−0.0123238	−	0.00635538i
$613$		−	6.65378i		−	0.268744i	−0.990931	−	0.134372i	$-0.957098\pi$
$613$		−	6.65378i		−	0.268744i	0.990931	−	0.134372i	$-0.0429017\pi$
$614$	−2.74147	+	1.67077i	−0.110637	+	0.0674267i
$615$	−5.77894			−0.233029
$616$		0			0
$617$	−17.8948			−0.720416			−0.360208	−	0.932872i	$-0.617294\pi$
$617$	−17.8948			−0.720416			−0.360208	+	0.932872i	$0.617294\pi$
$618$	9.23208	−	5.62643i	0.371369	−	0.226328i
$619$			23.2378i			0.934007i	0.884256	+	0.467003i	$0.154666\pi$
$619$			23.2378i			0.934007i	−0.884256	+	0.467003i	$0.845334\pi$
$620$	8.85379	+	4.56589i	0.355577	+	0.183371i
$621$	−21.4398			−0.860349
$622$	−14.8421	−	24.3535i	−0.595112	−	0.976485i
$623$	8.78849			0.352103
$624$	6.11102	+	8.58642i	0.244636	+	0.343732i
$625$	1.03262			0.0413048
$626$	−1.86201	+	1.13479i	−0.0744208	+	0.0453552i
$627$		0			0
$628$	−4.86001	+	9.42411i	−0.193935	+	0.376063i
$629$			0.481265i			0.0191893i
$630$	−6.50010	+	3.96144i	−0.258970	+	0.157828i
$631$		−	46.3216i		−	1.84404i	−0.387148	−	0.922018i	$-0.626540\pi$
$631$		−	46.3216i		−	1.84404i	0.387148	−	0.922018i	$-0.373460\pi$
$632$	1.20830	+	16.9404i	0.0480636	+	0.673854i
$633$		−	2.03164i		−	0.0807503i
$634$	20.3631	−	12.4102i	0.808723	−	0.492871i
$635$	−13.8783			−0.550745
$636$	−5.11845	−	2.63958i	−0.202960	−	0.104666i
$637$		−	15.4683i		−	0.612877i
$638$		0			0
$639$			17.0999i			0.676462i
$640$	−11.7683	+	9.70774i	−0.465181	+	0.383732i
$641$	27.1756			1.07337			0.536687	−	0.843782i	$-0.319676\pi$
$641$	27.1756			1.07337			0.536687	+	0.843782i	$0.319676\pi$
$642$	−6.03836	−	9.90800i	−0.238315	−	0.391038i
$643$		−	31.0236i		−	1.22345i	−0.791069	−	0.611726i	$-0.790475\pi$
$643$		−	31.0236i		−	1.22345i	0.791069	−	0.611726i	$-0.209525\pi$
$644$	−15.3695	−	7.92604i	−0.605643	−	0.312330i
$645$			1.89277i			0.0745276i
$646$	−0.409447	−	0.671838i	−0.0161095	−	0.0264331i
$647$			42.1713i			1.65793i	0.559303	+	0.828963i	$0.311069\pi$
$647$			42.1713i			1.65793i	−0.559303	+	0.828963i	$0.688931\pi$
$648$	0.878082	+	12.3107i	0.0344943	+	0.483611i
$649$		0			0
$650$	8.33001	+	13.6682i	0.326730	+	0.536112i
$651$	−4.45517			−0.174612
$652$	17.8778	+	9.21959i	0.700150	+	0.361067i
$653$	−4.04757			−0.158394			−0.0791969	−	0.996859i	$-0.525236\pi$
$653$	−4.04757			−0.158394			−0.0791969	+	0.996859i	$0.525236\pi$
$654$	8.01371	−	4.88390i	0.313361	−	0.190976i
$655$	2.51841			0.0984025
$656$	−18.8568	+	13.4205i	−0.736235	+	0.523984i
$657$		−	24.8135i		−	0.968068i
$658$	11.7511	+	19.2817i	0.458106	+	0.751680i
$659$	6.46292			0.251760			0.125880	−	0.992045i	$-0.459825\pi$
$659$	6.46292			0.251760			0.125880	+	0.992045i	$0.459825\pi$
$660$		0			0
$661$	26.6232			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$661$	26.6232			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$662$	25.0037	+	41.0271i	0.971795	+	1.59456i
$663$			0.184342i			0.00715925i
$664$	0.726831	+	10.1902i	0.0282065	+	0.395456i
$665$	−17.4593			−0.677043
$666$	20.3631	−	12.4102i	0.789055	−	0.480884i
$667$	−20.9012			−0.809300
$668$	−20.0824	+	38.9420i	−0.777010	+	1.50671i
$669$	17.5731			0.679416
$670$	−4.87569	−	8.00023i	−0.188364	−	0.309076i
$671$		0			0
$672$	2.68778	−	6.27096i	0.103683	−	0.241908i
$673$			8.31993i			0.320710i	0.987059	+	0.160355i	$0.0512639\pi$
$673$			8.31993i			0.320710i	−0.987059	+	0.160355i	$0.948736\pi$
$674$	12.5820	+	20.6451i	0.484641	+	0.795219i
$675$		−	12.8471i		−	0.494486i
$676$	0.317250	−	0.615183i	0.0122019	−	0.0236609i
$677$		−	15.2629i		−	0.586602i	−0.956020	−	0.293301i	$-0.905246\pi$
$677$		−	15.2629i		−	0.586602i	0.956020	−	0.293301i	$-0.0947538\pi$
$678$	−6.00888	−	9.85962i	−0.230769	−	0.378656i
$679$	−11.9298			−0.457824
$680$	−0.266165	+	0.0189846i	−0.0102069	+	0.000728026i
$681$		−	0.593162i		−	0.0227300i
$682$		0			0
$683$			32.9156i			1.25948i	0.776806	+	0.629740i	$0.216839\pi$
$683$			32.9156i			1.25948i	−0.776806	+	0.629740i	$0.783161\pi$
$684$	−17.8683	+	34.6488i	−0.683213	+	1.32483i
$685$	1.69155			0.0646308
$686$	−22.3161	+	13.6004i	−0.852031	+	0.519265i
$687$		−	17.4718i		−	0.666589i
$688$	4.39560	+	6.17614i	0.167581	+	0.235463i
$689$		−	13.8293i		−	0.526854i
$690$	−6.40421	+	3.90300i	−0.243804	+	0.148585i
$691$		−	45.5175i		−	1.73157i	−0.500419	−	0.865783i	$-0.666821\pi$
$691$		−	45.5175i		−	1.73157i	0.500419	−	0.865783i	$-0.333179\pi$
$692$	21.0324	+	10.8464i	0.799531	+	0.412318i
$693$		0			0
$694$	3.01794	−	1.83926i	0.114559	−	0.0698175i
$695$	8.48306			0.321781
$696$	−0.586692	−	8.22544i	−0.0222385	−	0.311784i
$697$	−0.404838			−0.0153343
$698$	−5.16011	−	8.46693i	−0.195313	−	0.320478i
$699$	12.9555			0.490023
$700$	4.74944	−	9.20970i	0.179512	−	0.348094i
$701$			50.0843i			1.89166i	0.324665	+	0.945829i	$0.394748\pi$
$701$			50.0843i			1.89166i	−0.324665	+	0.945829i	$0.605252\pi$
$702$	17.3452	−	10.5709i	0.654651	−	0.398972i
$703$	54.6955			2.06288
$704$		0			0
$705$	9.79298			0.368825
$706$	−21.6685	+	13.2057i	−0.815504	+	0.497003i
$707$		−	15.5878i		−	0.586241i
$708$	−3.30086	+	6.40074i	−0.124054	+	0.240555i
$709$	−8.49866			−0.319174			−0.159587	−	0.987184i	$-0.551016\pi$
$709$	−8.49866			−0.319174			−0.159587	+	0.987184i	$0.551016\pi$
$710$	6.92254	+	11.3588i	0.259798	+	0.426288i
$711$	14.7196			0.552027
$712$	−1.08606	−	15.2267i	−0.0407020	−	0.570643i
$713$	19.6141			0.734553
$714$	0.101905	−	0.0621052i	0.00381369	−	0.00232423i
$715$		0			0
$716$	1.65966	+	0.855885i	0.0620243	+	0.0319859i
$717$			4.95139i			0.184913i
$718$	−11.6891	+	7.12384i	−0.436233	+	0.265859i
$719$		−	7.29734i		−	0.272145i	−0.990699	−	0.136072i	$-0.956552\pi$
$719$		−	7.29734i		−	0.272145i	0.990699	−	0.136072i	$-0.0434480\pi$
$720$	7.66673	+	10.7723i	0.285722	+	0.401460i
$721$		−	16.8072i		−	0.625932i
$722$	−53.4093	+	32.5499i	−1.98769	+	1.21138i
$723$	3.17494			0.118077
$724$	17.2698	−	33.4881i	0.641828	−	1.24458i
$725$		−	12.5244i		−	0.465146i
$726$		0			0
$727$			1.85004i			0.0686140i	0.999411	+	0.0343070i	$0.0109224\pi$
$727$			1.85004i			0.0686140i	−0.999411	+	0.0343070i	$0.989078\pi$
$728$	16.3421	−	1.16563i	0.605679	−	0.0432010i
$729$	1.72491			0.0638855
$730$	−10.0452	−	16.4827i	−0.371791	−	0.610050i
$731$			0.132596i			0.00490423i
$732$	−0.913903	+	1.77216i	−0.0337788	+	0.0655010i
$733$			18.8938i			0.697857i	0.937149	+	0.348928i	$0.113454\pi$
$733$			18.8938i			0.697857i	−0.937149	+	0.348928i	$0.886546\pi$
$734$	−22.7763	−	37.3723i	−0.840689	−	1.37944i
$735$			4.34292i			0.160191i
$736$	−11.8331	+	27.6082i	−0.436173	+	1.01765i
$737$		0			0
$738$	10.4394	+	17.1293i	0.384278	+	0.630540i
$739$	−15.7186			−0.578218			−0.289109	−	0.957296i	$-0.593359\pi$
$739$	−15.7186			−0.578218			−0.289109	+	0.957296i	$0.593359\pi$
$740$	8.50243	−	16.4872i	0.312555	−	0.606081i
$741$	20.9504			0.769631
$742$	−7.64487	+	4.65911i	−0.280652	+	0.171041i
$743$	−5.80638			−0.213015			−0.106508	−	0.994312i	$-0.533967\pi$
$743$	−5.80638			−0.213015			−0.106508	+	0.994312i	$0.533967\pi$
$744$	0.550561	+	7.71888i	0.0201845	+	0.282988i
$745$			23.1330i			0.847526i
$746$	3.62583	+	5.94942i	0.132751	+	0.217824i
$747$	8.85428			0.323961
$748$		0			0
$749$	−18.0377			−0.659083
$750$	−6.01398	−	9.86799i	−0.219599	−	0.360328i
$751$		−	3.00343i		−	0.109597i	−0.998497	−	0.0547983i	$-0.982548\pi$
$751$		−	3.00343i		−	0.109597i	0.998497	−	0.0547983i	$-0.0174516\pi$
$752$	31.9547	−	22.7424i	1.16527	−	0.829330i
$753$	3.62759			0.132197
$754$	16.9095	−	10.3054i	0.615806	−	0.375299i
$755$	−16.3944			−0.596654
$756$	−11.6872	−	6.02709i	−0.425060	−	0.219203i
$757$	−26.0871			−0.948152			−0.474076	−	0.880484i	$-0.657218\pi$
$757$	−26.0871			−0.948152			−0.474076	+	0.880484i	$0.657218\pi$
$758$	−2.96241	−	4.86085i	−0.107600	−	0.176554i
$759$		0			0
$760$	2.15759	+	30.2495i	0.0782639	+	1.09726i
$761$			31.9526i			1.15828i	0.815228	+	0.579140i	$0.196612\pi$
$761$			31.9526i			1.15828i	−0.815228	+	0.579140i	$0.803388\pi$
$762$	−5.61055	−	9.20602i	−0.203249	−	0.333499i
$763$		−	14.5891i		−	0.528161i
$764$	−36.3405	−	18.7408i	−1.31475	−	0.678017i
$765$			0.231271i			0.00836162i
$766$	8.82353	+	14.4780i	0.318807	+	0.523112i
$767$	−17.2939			−0.624446
$768$	−11.1970	−	3.88181i	−0.404038	−	0.140073i
$769$			22.3560i			0.806176i	0.915161	+	0.403088i	$0.132063\pi$
$769$			22.3560i			0.806176i	−0.915161	+	0.403088i	$0.867937\pi$
$770$		0			0
$771$		−	9.17275i		−	0.330348i
$772$	30.8244	+	15.8961i	1.10940	+	0.572115i
$773$	5.07704			0.182608			0.0913042	−	0.995823i	$-0.470896\pi$
$773$	5.07704			0.182608			0.0913042	+	0.995823i	$0.470896\pi$
$774$	5.61034	−	3.41919i	0.201660	−	0.122900i
$775$			11.7531i			0.422185i
$776$	1.47426	+	20.6692i	0.0529230	+	0.741982i
$777$			8.29624i			0.297626i
$778$	−16.5891	+	10.1101i	−0.594749	+	0.362465i
$779$			46.0096i			1.64846i
$780$	3.25674	−	6.31519i	0.116610	−	0.226120i
$781$		0			0
$782$	−0.448640	+	0.273421i	−0.0160433	+	0.00977750i
$783$	−15.8937			−0.567993
$784$	10.0856	+	14.1711i	0.360202	+	0.506109i
$785$	7.14893			0.255156
$786$	1.01811	+	1.67056i	0.0363147	+	0.0595867i
$787$	−2.94375			−0.104933			−0.0524667	−	0.998623i	$-0.516708\pi$
$787$	−2.94375			−0.104933			−0.0524667	+	0.998623i	$0.516708\pi$
$788$	6.20602	+	3.20044i	0.221080	+	0.114011i
$789$			12.5536i			0.446920i
$790$	9.77764	−	5.95891i	0.347873	−	0.212009i
$791$	−17.9496			−0.638215
$792$		0			0
$793$	−4.78812			−0.170031
$794$	14.6782	−	8.94556i	0.520911	−	0.317466i
$795$			3.88275i			0.137707i
$796$	−20.0259	−	10.3273i	−0.709799	−	0.366043i
$797$	7.49194			0.265378			0.132689	−	0.991158i	$-0.457639\pi$
$797$	7.49194			0.265378			0.132689	+	0.991158i	$0.457639\pi$
$798$	−7.05822	−	11.5814i	−0.249858	−	0.409978i
$799$	0.686037			0.0242702
$800$	−16.5434	−	7.09060i	−0.584896	−	0.250691i
$801$	−13.2305			−0.467476
$802$	34.7558	−	21.1817i	1.22727	−	0.747952i
$803$		0			0
$804$	3.33578	−	6.46845i	0.117644	−	0.228125i
$805$			11.6590i			0.410925i
$806$	−15.8681	+	9.67072i	−0.558931	+	0.340637i
$807$			2.92919i			0.103112i
$808$	−27.0070	+	1.92631i	−0.950103	+	0.0677675i
$809$			39.8260i			1.40021i	0.714041	+	0.700104i	$0.246863\pi$
$809$			39.8260i			1.40021i	−0.714041	+	0.700104i	$0.753137\pi$
$810$	7.10549	−	4.33039i	0.249661	−	0.152154i
$811$	42.6481			1.49758			0.748788	−	0.662809i	$-0.230636\pi$
$811$	42.6481			1.49758			0.748788	+	0.662809i	$0.230636\pi$
$812$	−11.3937	−	5.87570i	−0.399839	−	0.206197i
$813$		−	17.5818i		−	0.616619i
$814$		0			0
$815$		−	13.5617i		−	0.475047i
$816$	−0.120195	−	0.168882i	−0.00420765	−	0.00591205i
$817$	15.0694			0.527213
$818$	13.9506	+	22.8907i	0.487770	+	0.800354i
$819$		−	14.1997i		−	0.496178i
$820$	13.8689	+	7.15220i	0.484324	+	0.249766i
$821$		−	19.3110i		−	0.673958i	−0.941512	−	0.336979i	$-0.890595\pi$
$821$		−	19.3110i		−	0.673958i	0.941512	−	0.336979i	$-0.109405\pi$
$822$	0.683837	+	1.12207i	0.0238516	+	0.0391366i
$823$			9.91929i			0.345765i	0.984942	+	0.172882i	$0.0553080\pi$
$823$			9.91929i			0.345765i	−0.984942	+	0.172882i	$0.944692\pi$
$824$	−29.1196	+	2.07700i	−1.01443	+	0.0723557i
$825$		0			0
$826$	5.82633	+	9.56010i	0.202724	+	0.332638i
$827$	−43.6308			−1.51719			−0.758596	−	0.651562i	$-0.774114\pi$
$827$	−43.6308			−1.51719			−0.758596	+	0.651562i	$0.774114\pi$
$828$	23.1377	+	11.9321i	0.804092	+	0.414670i
$829$	−28.1496			−0.977677			−0.488838	−	0.872374i	$-0.662579\pi$
$829$	−28.1496			−0.977677			−0.488838	+	0.872374i	$0.662579\pi$
$830$	5.88155	−	3.58447i	0.204152	−	0.124419i
$831$	−11.1183			−0.385691
$832$	−4.03905	−	28.1698i	−0.140029	−	0.976611i
$833$			0.304239i			0.0105413i
$834$	3.42942	+	5.62713i	0.118751	+	0.194852i
$835$	29.5406			1.02229
$836$		0			0
$837$	14.9149			0.515533
$838$	−11.3123	−	18.5617i	−0.390777	−	0.641203i
$839$		−	34.9528i		−	1.20670i	−0.797475	−	0.603352i	$-0.793831\pi$
$839$		−	34.9528i		−	1.20670i	0.797475	−	0.603352i	$-0.206169\pi$
$840$	−4.58825	+	0.327264i	−0.158310	+	0.0112917i
$841$	13.5056			0.465709
$842$	−23.3322	+	14.2196i	−0.804081	+	0.490041i
$843$	−4.25248			−0.146463
$844$	−2.51442	+	4.87574i	−0.0865498	+	0.167830i
$845$	−0.466665			−0.0160538
$846$	−17.6905	−	29.0273i	−0.608212	−	0.997980i
$847$		0			0
$848$	9.01697	+	12.6695i	0.309644	+	0.435072i
$849$		−	8.29170i		−	0.284570i
$850$	−0.163839	−	0.268834i	−0.00561963	−	0.00922092i
$851$		−	36.5246i		−	1.25205i
$852$	−4.73617	+	9.18396i	−0.162258	+	0.314637i
$853$		−	27.2162i		−	0.931864i	−0.884821	−	0.465932i	$-0.845719\pi$
$853$		−	27.2162i		−	0.931864i	0.884821	−	0.465932i	$-0.154281\pi$
$854$	1.61313	+	2.64689i	0.0552001	+	0.0905746i
$855$	26.2838			0.898888
$856$	2.22906	+	31.2515i	0.0761878	+	1.06816i
$857$			37.5541i			1.28282i	0.767197	+	0.641412i	$0.221651\pi$
$857$			37.5541i			1.28282i	−0.767197	+	0.641412i	$0.778349\pi$
$858$		0			0
$859$		−	4.50293i		−	0.153638i	−0.997045	−	0.0768190i	$-0.975524\pi$
$859$		−	4.50293i		−	0.153638i	0.997045	−	0.0768190i	$-0.0244764\pi$
$860$	2.34255	−	4.54246i	0.0798801	−	0.154897i
$861$	−6.97876			−0.237835
$862$	−32.7313	+	19.9478i	−1.11483	+	0.679426i
$863$		−	18.0361i		−	0.613958i	−0.951716	−	0.306979i	$-0.900682\pi$
$863$		−	18.0361i		−	0.613958i	0.951716	−	0.306979i	$-0.0993181\pi$
$864$	−8.99807	+	20.9937i	−0.306120	+	0.714221i
$865$		−	15.9547i		−	0.542477i
$866$	−5.26055	+	3.20601i	−0.178761	+	0.108945i
$867$			12.5879i			0.427506i
$868$	10.6920	+	5.51386i	0.362910	+	0.187152i
$869$		0			0
$870$	−4.74754	+	2.89336i	−0.160957	+	0.0980940i
$871$	17.4768			0.592179
$872$	−25.2766	+	1.80289i	−0.855974	+	0.0610536i
$873$	17.9595			0.607838
$874$	31.0741	+	50.9877i	1.05110	+	1.72468i
$875$	−17.9649			−0.607323
$876$	6.87261	−	13.3268i	0.232204	−	0.450270i
$877$			13.6207i			0.459939i	0.973198	+	0.229970i	$0.0738627\pi$
$877$			13.6207i			0.459939i	−0.973198	+	0.229970i	$0.926137\pi$
$878$	29.1031	−	17.7367i	0.982181	−	0.598583i
$879$	−3.92773			−0.132479
$880$		0			0
$881$	5.44549			0.183463			0.0917317	−	0.995784i	$-0.470760\pi$
$881$	5.44549			0.183463			0.0917317	+	0.995784i	$0.470760\pi$
$882$	12.8728	−	7.84527i	0.433451	−	0.264164i
$883$		−	28.2297i		−	0.950005i	−0.879985	−	0.475002i	$-0.842447\pi$
$883$		−	28.2297i		−	0.950005i	0.879985	−	0.475002i	$-0.157553\pi$
$884$	0.228147	−	0.442404i	0.00767343	−	0.0148797i
$885$	4.85547			0.163215
$886$	−16.9604	−	27.8293i	−0.569796	−	0.934945i
$887$	−42.4394			−1.42498			−0.712488	−	0.701684i	$-0.752432\pi$
$887$	−42.4394			−1.42498			−0.712488	+	0.701684i	$0.752432\pi$
$888$	14.3738	−	1.02523i	0.482353	−	0.0344046i
$889$	−16.7597			−0.562104
$890$	−8.78849	+	5.35608i	−0.294591	+	0.179536i
$891$		0			0
$892$	−42.1738	−	21.7490i	−1.41208	−	0.728211i
$893$		−	77.9677i		−	2.60909i
$894$	−15.3450	+	9.35188i	−0.513212	+	0.312774i
$895$		−	1.25898i		−	0.0420831i
$896$	−14.2116	+	11.7232i	−0.474775	+	0.391646i
$897$		−	13.9902i		−	0.467120i
$898$	4.55693	−	2.77719i	0.152067	−	0.0926760i
$899$	14.5402			0.484944
$900$	−7.14996	+	13.8646i	−0.238332	+	0.462153i
$901$			0.272002i			0.00906169i
$902$		0			0
$903$			2.28574i			0.0760646i
$904$	2.21818	+	31.0989i	0.0737755	+	1.03434i
$905$	−25.4034			−0.844438
$906$	−6.62771	−	10.8750i	−0.220191	−	0.361298i
$907$		−	34.6899i		−	1.15186i	−0.817500	−	0.575929i	$-0.804640\pi$
$907$		−	34.6899i		−	1.15186i	0.817500	−	0.575929i	$-0.195360\pi$
$908$	−0.734116	+	1.42353i	−0.0243625	+	0.0472416i
$909$			23.4664i			0.778333i
$910$	−5.74846	−	9.43231i	−0.190560	−	0.312678i
$911$		−	29.6674i		−	0.982924i	−0.870899	−	0.491462i	$-0.836463\pi$
$911$		−	29.6674i		−	0.982924i	0.870899	−	0.491462i	$-0.163537\pi$
$912$	−19.1933	+	13.6600i	−0.635555	+	0.452329i
$913$		0			0
$914$	−25.9483	−	42.5771i	−0.858294	−	1.40833i
$915$	1.34432			0.0444420
$916$	−21.6236	+	41.9306i	−0.714463	+	1.38543i
$917$	3.04128			0.100432
$918$	−0.341153	+	0.207914i	−0.0112597	+	0.00686217i
$919$	21.6093			0.712825			0.356412	−	0.934329i	$-0.384000\pi$
$919$	21.6093			0.712825			0.356412	+	0.934329i	$0.384000\pi$
$920$	20.2000	−	1.44079i	0.665973	−	0.0475016i
$921$			1.68144i			0.0554054i
$922$	−28.3405	−	46.5022i	−0.933343	−	1.53147i
$923$	−24.8137			−0.816754
$924$		0			0
$925$	21.8862			0.719614
$926$	−7.92438	−	13.0027i	−0.260411	−	0.427294i
$927$			25.3021i			0.831029i
$928$	−8.77205	+	20.4664i	−0.287957	+	0.671842i
$929$	47.2208			1.54926			0.774632	−	0.632412i	$-0.217935\pi$
$929$	47.2208			1.54926			0.774632	+	0.632412i	$0.217935\pi$
$930$	4.45517	−	2.71517i	0.146091	−	0.0890340i
$931$	34.5766			1.13320
$932$	−31.0921	−	16.0342i	−1.01845	−	0.525217i
$933$	−14.9369			−0.489011
$934$	−15.2199	−	24.9734i	−0.498009	−	0.817154i
$935$		0			0
$936$	−24.6020	+	1.75477i	−0.804140	+	0.0573565i
$937$		−	46.3875i		−	1.51541i	−0.652595	−	0.757707i	$-0.726320\pi$
$937$		−	46.3875i		−	1.51541i	0.652595	−	0.757707i	$-0.273680\pi$
$938$	−5.88797	−	9.66123i	−0.192249	−	0.315450i
$939$			1.14204i			0.0372689i
$940$	−23.5022	−	12.1201i	−0.766558	−	0.395314i
$941$			39.4205i			1.28507i	0.766255	+	0.642536i	$0.222118\pi$
$941$			39.4205i			1.28507i	−0.766255	+	0.642536i	$0.777882\pi$
$942$	2.89007	+	4.74215i	0.0941636	+	0.154508i
$943$	30.7243			1.00052
$944$	15.8435	−	11.2759i	0.515662	−	0.367000i
$945$			8.86568i			0.288401i
$946$		0			0
$947$		−	24.9488i		−	0.810725i	−0.914156	−	0.405363i	$-0.867145\pi$
$947$		−	24.9488i		−	0.810725i	0.914156	−	0.405363i	$-0.132855\pi$
$948$	7.90554	+	4.07688i	0.256760	+	0.132411i
$949$	36.0070			1.16884
$950$	−30.5528	+	18.6202i	−0.991264	+	0.604119i
$951$		−	12.4894i		−	0.404998i
$952$	−0.321425	+	0.0229261i	−0.0104175	+	0.000743040i
$953$			40.9113i			1.32525i	0.748952	+	0.662624i	$0.230557\pi$
$953$			40.9113i			1.32525i	−0.748952	+	0.662624i	$0.769443\pi$
$954$	11.5088	−	7.01398i	0.372612	−	0.227086i
$955$			27.5671i			0.892051i
$956$	6.12800	−	11.8829i	0.198194	−	0.384320i
$957$		0			0
$958$	13.7835	−	8.40029i	0.445326	−	0.271401i
$959$	2.04275			0.0659638
$960$	1.13401	+	7.90901i	0.0366001	+	0.255262i
$961$	17.3552			0.559845
$962$	18.0084	+	29.5490i	0.580615	+	0.952698i
$963$	27.1545			0.875043
$964$	−7.61957	−	3.92941i	−0.245410	−	0.126558i
$965$		−	23.3828i		−	0.752718i
$966$	−7.73384	+	4.71333i	−0.248832	+	0.151649i
$967$	−23.6696			−0.761164			−0.380582	−	0.924747i	$-0.624276\pi$
$967$	−23.6696			−0.761164			−0.380582	+	0.924747i	$0.624276\pi$
$968$		0			0
$969$	−0.412063			−0.0132374
$970$	11.9298	−	7.27055i	0.383043	−	0.233443i
$971$		−	53.9321i		−	1.73076i	−0.501112	−	0.865382i	$-0.667076\pi$
$971$		−	53.9321i		−	1.73076i	0.501112	−	0.865382i	$-0.332924\pi$
$972$	27.2768	+	14.0666i	0.874903	+	0.451187i
$973$	10.2443			0.328417
$974$	−2.94755	−	4.83646i	−0.0944455	−	0.154970i
$975$	8.38321			0.268478
$976$	4.38656	−	3.12195i	0.140410	−	0.0999311i
$977$	−9.59586			−0.306999			−0.153499	−	0.988149i	$-0.549054\pi$
$977$	−9.59586			−0.306999			−0.153499	+	0.988149i	$0.549054\pi$
$978$	8.99601	−	5.48256i	0.287661	−	0.175313i
$979$		0			0
$980$	5.37494	−	10.4226i	0.171696	−	0.332938i
$981$			21.9629i			0.701222i
$982$	−13.5181	+	8.23851i	−0.431380	+	0.262901i
$983$			35.3025i			1.12597i	0.826466	+	0.562987i	$0.190348\pi$
$983$			35.3025i			1.12597i	−0.826466	+	0.562987i	$0.809652\pi$
$984$	0.862421	+	12.0912i	0.0274930	+	0.385452i
$985$		−	4.70776i		−	0.150002i
$986$	−0.332584	+	0.202691i	−0.0105916	+	0.00645500i
$987$	11.8262			0.376431
$988$	−50.2789	−	25.9288i	−1.59959	−	0.824906i
$989$		−	10.0631i		−	0.319987i
$990$		0			0
$991$		−	17.8021i		−	0.565502i	−0.959193	−	0.282751i	$-0.908753\pi$
$991$		−	17.8021i		−	0.565502i	0.959193	−	0.282751i	$-0.0912471\pi$
$992$	8.23183	−	19.2060i	0.261361	−	0.609791i
$993$	25.1634			0.798536
$994$	8.35979	+	13.7171i	0.265156	+	0.435080i
$995$			15.1912i			0.481594i
$996$	4.75543	+	2.45237i	0.150682	+	0.0777064i
$997$		−	62.9390i		−	1.99330i	−0.0817877	−	0.996650i	$-0.526063\pi$
$997$		−	62.9390i		−	1.99330i	0.0817877	−	0.996650i	$-0.473937\pi$
$998$	−28.9721	−	47.5386i	−0.917094	−	1.50481i
$999$		−	27.7739i		−	0.878727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.c.d.483.4		16
4.3	odd	2	inner	484.2.c.d.483.14		16
11.2	odd	10		44.2.g.a.7.1	✓	16
11.3	even	5		484.2.g.f.475.3		16
11.4	even	5		484.2.g.j.215.1		16
11.5	even	5		44.2.g.a.19.3	yes	16
11.6	odd	10		484.2.g.i.239.2		16
11.7	odd	10		484.2.g.f.215.4		16
11.8	odd	10		484.2.g.j.475.2		16
11.9	even	5		484.2.g.i.403.4		16
11.10	odd	2	inner	484.2.c.d.483.13		16
33.2	even	10		396.2.r.a.271.4		16
33.5	odd	10		396.2.r.a.19.2		16
44.3	odd	10		484.2.g.f.475.4		16
44.7	even	10		484.2.g.f.215.3		16
44.15	odd	10		484.2.g.j.215.2		16
44.19	even	10		484.2.g.j.475.1		16
44.27	odd	10		44.2.g.a.19.1	yes	16
44.31	odd	10		484.2.g.i.403.2		16
44.35	even	10		44.2.g.a.7.3	yes	16
44.39	even	10		484.2.g.i.239.4		16
44.43	even	2	inner	484.2.c.d.483.3		16
88.5	even	10		704.2.u.c.63.3		16
88.13	odd	10		704.2.u.c.447.2		16
88.27	odd	10		704.2.u.c.63.2		16
88.35	even	10		704.2.u.c.447.3		16
132.35	odd	10		396.2.r.a.271.2		16
132.71	even	10		396.2.r.a.19.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	11.2	odd	10
44.2.g.a.7.3	yes	16	44.35	even	10
44.2.g.a.19.1	yes	16	44.27	odd	10
44.2.g.a.19.3	yes	16	11.5	even	5
396.2.r.a.19.2		16	33.5	odd	10
396.2.r.a.19.4		16	132.71	even	10
396.2.r.a.271.2		16	132.35	odd	10
396.2.r.a.271.4		16	33.2	even	10
484.2.c.d.483.3		16	44.43	even	2	inner
484.2.c.d.483.4		16	1.1	even	1	trivial
484.2.c.d.483.13		16	11.10	odd	2	inner
484.2.c.d.483.14		16	4.3	odd	2	inner
484.2.g.f.215.3		16	44.7	even	10
484.2.g.f.215.4		16	11.7	odd	10
484.2.g.f.475.3		16	11.3	even	5
484.2.g.f.475.4		16	44.3	odd	10
484.2.g.i.239.2		16	11.6	odd	10
484.2.g.i.239.4		16	44.39	even	10
484.2.g.i.403.2		16	44.31	odd	10
484.2.g.i.403.4		16	11.9	even	5
484.2.g.j.215.1		16	11.4	even	5
484.2.g.j.215.2		16	44.15	odd	10
484.2.g.j.475.1		16	44.19	even	10
484.2.g.j.475.2		16	11.8	odd	10
704.2.u.c.63.2		16	88.27	odd	10
704.2.u.c.63.3		16	88.5	even	10
704.2.u.c.447.2		16	88.13	odd	10
704.2.u.c.447.3		16	88.35	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20762 + 0.735975i) q^{2} +0.740676i q^{3} +(0.916683 - 1.77755i) q^{4} -1.34841 q^{5} +(-0.545118 - 0.894453i) q^{6} -1.62837 q^{7} +(0.201231 + 2.82126i) q^{8} +2.45140 q^{9} +(1.62837 - 0.992398i) q^{10} +(1.31659 + 0.678965i) q^{12} +3.55723i q^{13} +(1.96645 - 1.19844i) q^{14} -0.998737i q^{15} +(-2.31939 - 3.25890i) q^{16} -0.0699655i q^{17} +(-2.96035 + 1.80417i) q^{18} -7.95154 q^{19} +(-1.23607 + 2.39688i) q^{20} -1.20609i q^{21} +5.30988i q^{23} +(-2.08964 + 0.149047i) q^{24} -3.18178 q^{25} +(-2.61803 - 4.29578i) q^{26} +4.03772i q^{27} +(-1.49270 + 2.89451i) q^{28} +3.93630i q^{29} +(0.735045 + 1.20609i) q^{30} -3.69389i q^{31} +(5.19940 + 2.22850i) q^{32} +(0.0514928 + 0.0844916i) q^{34} +2.19572 q^{35} +(2.24716 - 4.35749i) q^{36} -6.87861 q^{37} +(9.60242 - 5.85213i) q^{38} -2.63476 q^{39} +(-0.271342 - 3.80423i) q^{40} -5.78625i q^{41} +(0.887654 + 1.45650i) q^{42} -1.89516 q^{43} -3.30550 q^{45} +(-3.90793 - 6.41230i) q^{46} +9.80536i q^{47} +(2.41379 - 1.71791i) q^{48} -4.34841 q^{49} +(3.84237 - 2.34171i) q^{50} +0.0518217 q^{51} +(6.32317 + 3.26086i) q^{52} -3.88765 q^{53} +(-2.97166 - 4.87602i) q^{54} +(-0.327678 - 4.59405i) q^{56} -5.88951i q^{57} +(-2.89701 - 4.75354i) q^{58} +4.86161i q^{59} +(-1.77531 - 0.915525i) q^{60} +1.34602i q^{61} +(2.71861 + 4.46080i) q^{62} -3.99178 q^{63} +(-7.91901 + 1.13545i) q^{64} -4.79662i q^{65} -4.91303i q^{67} +(-0.124367 - 0.0641362i) q^{68} -3.93290 q^{69} +(-2.65159 + 1.61599i) q^{70} +6.97557i q^{71} +(0.493297 + 6.91604i) q^{72} -10.1222i q^{73} +(8.30673 - 5.06248i) q^{74} -2.35667i q^{75} +(-7.28904 + 14.1343i) q^{76} +(3.18178 - 1.93911i) q^{78} +6.00456 q^{79} +(3.12749 + 4.39435i) q^{80} +4.36356 q^{81} +(4.25853 + 6.98758i) q^{82} +3.61193 q^{83} +(-2.14389 - 1.10560i) q^{84} +0.0943425i q^{85} +(2.28863 - 1.39479i) q^{86} -2.91552 q^{87} -5.39711 q^{89} +(3.99178 - 2.43277i) q^{90} -5.79249i q^{91} +(9.43858 + 4.86747i) q^{92} +2.73597 q^{93} +(-7.21649 - 11.8411i) q^{94} +10.7220 q^{95} +(-1.65060 + 3.85107i) q^{96} +7.32624 q^{97} +(5.25122 - 3.20032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5} - 22 q^{12} - 12 q^{14} - 12 q^{16} + 16 q^{20} - 4 q^{25} - 24 q^{26} - 6 q^{34} + 50 q^{36} - 12 q^{37} + 42 q^{38} + 4 q^{42} + 40 q^{45} + 74 q^{48} - 44 q^{49} - 52 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 - 22 * q^12 - 12 * q^14 - 12 * q^16 + 16 * q^20 - 4 * q^25 - 24 * q^26 - 6 * q^34 + 50 * q^36 - 12 * q^37 + 42 * q^38 + 4 * q^42 + 40 * q^45 + 74 * q^48 - 44 * q^49 - 52 * q^53 - 12 * q^56 - 60 * q^58 - 8 * q^60 + 28 * q^64 + 24 * q^69 - 68 * q^70 + 4 * q^78 - 8 * q^80 - 24 * q^81 + 26 * q^82 - 14 * q^86 - 36 * q^89 + 36 * q^92 + 72 * q^93 - 8 * q^97

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