LMFDB - Embedded newform 867.2.i.c.653.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,-16,0,0,0,0,8,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			653.1
Character	$\chi$	$=$	867.653
Dual form			867.2.i.c.158.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34436 - 0.556851i) q^{2} +(-1.44078 + 0.961322i) q^{3} +(0.0830021 + 0.0830021i) q^{4} +(2.99276 - 0.595296i) q^{5} +(2.47224 - 0.490059i) q^{6} +(0.420765 - 2.11533i) q^{7} +(1.04834 + 2.53091i) q^{8} +(1.15172 - 2.77012i) q^{9} +(-4.35483 - 0.866229i) q^{10} +(-0.915491 - 1.37013i) q^{11} +(-0.199380 - 0.0397964i) q^{12} +(3.12551 - 3.12551i) q^{13} +(-1.74358 + 2.60946i) q^{14} +(-3.73965 + 3.73470i) q^{15} -4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(0.330416 - 0.797694i) q^{19} +(0.297816 + 0.198994i) q^{20} +(1.42728 + 3.45222i) q^{21} +(0.467790 + 2.35174i) q^{22} +(-0.637394 + 0.425893i) q^{23} +(-3.94345 - 2.63871i) q^{24} +(3.98282 - 1.64974i) q^{25} +(-5.94226 + 2.46136i) q^{26} +(1.00359 + 5.09831i) q^{27} +(0.210501 - 0.140652i) q^{28} +(1.55905 + 7.83789i) q^{29} +(7.10709 - 2.93834i) q^{30} +(-2.40167 - 1.60475i) q^{31} +(-0.253786 + 0.612694i) q^{32} +(2.63616 + 1.09398i) q^{33} -6.58114i q^{35} +(0.325520 - 0.134330i) q^{36} +(-1.32318 + 1.98027i) q^{37} +(-0.888394 + 0.888394i) q^{38} +(-1.49857 + 7.50782i) q^{39} +(4.64406 + 6.95033i) q^{40} +(3.02038 + 0.600791i) q^{41} +(0.00359897 - 5.43581i) q^{42} +(-4.38037 - 10.5751i) q^{43} +(0.0377359 - 0.189711i) q^{44} +(1.79778 - 8.97590i) q^{45} +(1.09405 - 0.217619i) q^{46} +(-2.21238 - 2.21238i) q^{47} +(4.05773 + 6.08153i) q^{48} +(2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(5.88369 + 2.43710i) q^{53} +(1.48981 - 7.41281i) q^{54} +(-3.55548 - 3.55548i) q^{55} +(5.79482 - 1.15266i) q^{56} +(0.290783 + 1.46694i) q^{57} +(2.26861 - 11.4051i) q^{58} +(-2.33146 - 5.62864i) q^{59} +(-0.620386 - 0.000410749i) q^{60} +(-5.73423 - 1.14061i) q^{61} +(2.33510 + 3.49473i) q^{62} +(-5.37510 - 3.60183i) q^{63} +(-5.28702 + 5.28702i) q^{64} +(7.49329 - 11.2145i) q^{65} +(-2.93476 - 2.93865i) q^{66} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(-3.66472 + 8.84742i) q^{70} +(-1.80802 - 1.20808i) q^{71} +(8.21831 + 0.0108825i) q^{72} +(-2.45412 - 12.3377i) q^{73} +(2.88154 - 1.92538i) q^{74} +(-4.15245 + 6.20569i) q^{75} +(0.0936354 - 0.0387851i) q^{76} +(-3.28348 + 1.36006i) q^{77} +(6.19535 - 9.25872i) q^{78} +(4.95397 - 3.31013i) q^{79} +(-2.51274 - 12.6324i) q^{80} +(-6.34708 - 6.38079i) q^{81} +(-3.72592 - 2.48958i) q^{82} +(4.96993 - 11.9985i) q^{83} +(-0.168074 + 0.405009i) q^{84} +16.6560i q^{86} +(-9.78099 - 9.79395i) q^{87} +(2.50793 - 3.75339i) q^{88} +(3.42023 - 3.42023i) q^{89} +(-7.41510 + 11.0657i) q^{90} +(-5.29638 - 7.92660i) q^{91} +(-0.0882551 - 0.0175550i) q^{92} +(5.00297 + 0.00331239i) q^{93} +(1.74226 + 4.20619i) q^{94} +(0.513989 - 2.58400i) q^{95} +(-0.223345 - 1.12673i) q^{96} +(-3.47928 + 0.692072i) q^{97} +(-2.41627 - 2.41627i) q^{98} +(-4.84981 + 0.958012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{4} + 8 q^{9} - 32 q^{10} - 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} + 48 q^{22} - 8 q^{24} - 16 q^{25} + 48 q^{27} + 64 q^{28} - 8 q^{30} - 16 q^{31} - 8 q^{36}+ \cdots - 96 q^{97}+O(q^{100}) $ 32 * q - 16 * q^4 + 8 * q^9 - 32 * q^10 - 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 + 48 * q^22 - 8 * q^24 - 16 * q^25 + 48 * q^27 + 64 * q^28 - 8 * q^30 - 16 * q^31 - 8 * q^36 + 32 * q^37 - 8 * q^39 + 64 * q^40 + 56 * q^42 - 16 * q^43 - 24 * q^45 + 80 * q^46 + 72 * q^48 + 48 * q^49 - 96 * q^52 - 48 * q^54 - 48 * q^55 - 24 * q^57 + 32 * q^58 - 32 * q^60 - 64 * q^61 + 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 + 16 * q^78 + 32 * q^79 + 48 * q^81 - 48 * q^82 + 56 * q^87 + 80 * q^88 - 104 * q^90 - 80 * q^91 + 72 * q^93 + 48 * q^94 - 72 * q^96 - 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−1.34436	−	0.556851i	−0.950605	−	0.393753i	−0.147147	−	0.989115i	$-0.547009\pi$
$2$	−1.34436	−	0.556851i	−0.950605	−	0.393753i	−0.803458	+	0.595361i	$0.797009\pi$
$3$	−1.44078	+	0.961322i	−0.831837	+	0.555020i
$3$	−1.44078	+	0.961322i	−0.831837	+	0.555020i
$4$	0.0830021	+	0.0830021i	0.0415010	+	0.0415010i
$5$	2.99276	−	0.595296i	1.33840	−	0.266225i	0.526578	−	0.850127i	$-0.323475\pi$
$5$	2.99276	−	0.595296i	1.33840	−	0.266225i	0.811824	+	0.583902i	$0.198475\pi$
$6$	2.47224	−	0.490059i	1.00929	−	0.200066i
$7$	0.420765	−	2.11533i	0.159034	−	0.799519i	−0.816101	−	0.577909i	$-0.803869\pi$
$7$	0.420765	−	2.11533i	0.159034	−	0.799519i	0.975135	−	0.221610i	$-0.0711312\pi$
$8$	1.04834	+	2.53091i	0.370644	+	0.894813i
$9$	1.15172	−	2.77012i	0.383906	−	0.923372i
$10$	−4.35483	−	0.866229i	−1.37712	−	0.273926i
$11$	−0.915491	−	1.37013i	−0.276031	−	0.413110i	0.667389	−	0.744709i	$-0.267412\pi$
$11$	−0.915491	−	1.37013i	−0.276031	−	0.413110i	−0.943420	+	0.331599i	$0.892412\pi$
$12$	−0.199380	−	0.0397964i	−0.0575560	−	0.0114882i
$13$	3.12551	−	3.12551i	0.866861	−	0.866861i	−0.125262	−	0.992124i	$-0.539977\pi$
$13$	3.12551	−	3.12551i	0.866861	−	0.866861i	0.992124	+	0.125262i	$0.0399772\pi$
$14$	−1.74358	+	2.60946i	−0.465992	+	0.697407i
$15$	−3.73965	+	3.73470i	−0.965572	+	0.964295i
$16$		−	4.22099i		−	1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	+	3.08269i	−0.728524	+	0.726597i
$19$	0.330416	−	0.797694i	0.0758025	−	0.183004i	−0.881436	−	0.472304i	$-0.843423\pi$
$19$	0.330416	−	0.797694i	0.0758025	−	0.183004i	0.957238	+	0.289300i	$0.0934226\pi$
$20$	0.297816	+	0.198994i	0.0665936	+	0.0444964i
$21$	1.42728	+	3.45222i	0.311458	+	0.753337i
$22$	0.467790	+	2.35174i	0.0997331	+	0.501392i
$23$	−0.637394	+	0.425893i	−0.132906	+	0.0888049i	−0.620246	−	0.784407i	$-0.712967\pi$
$23$	−0.637394	+	0.425893i	−0.132906	+	0.0888049i	0.487340	+	0.873212i	$0.337967\pi$
$24$	−3.94345	−	2.63871i	−0.804954	−	0.538624i
$25$	3.98282	−	1.64974i	0.796563	−	0.329947i
$26$	−5.94226	+	2.46136i	−1.16537	+	0.482713i
$27$	1.00359	+	5.09831i	0.193142	+	0.981171i
$28$	0.210501	−	0.140652i	0.0397810	−	0.0265808i
$29$	1.55905	+	7.83789i	0.289509	+	1.45546i	0.802287	+	0.596938i	$0.203616\pi$
$29$	1.55905	+	7.83789i	0.289509	+	1.45546i	−0.512778	+	0.858521i	$0.671384\pi$
$30$	7.10709	−	2.93834i	1.29757	−	0.536466i
$31$	−2.40167	−	1.60475i	−0.431353	−	0.288221i	0.320878	−	0.947121i	$-0.396022\pi$
$31$	−2.40167	−	1.60475i	−0.431353	−	0.288221i	−0.752231	+	0.658900i	$0.771022\pi$
$32$	−0.253786	+	0.612694i	−0.0448635	+	0.108310i
$33$	2.63616	+	1.09398i	0.458897	+	0.190437i
$34$		0			0
$35$		−	6.58114i		−	1.11242i
$36$	0.325520	−	0.134330i	0.0542534	−	0.0223884i
$37$	−1.32318	+	1.98027i	−0.217529	+	0.325555i	−0.924145	−	0.382042i	$-0.875221\pi$
$37$	−1.32318	+	1.98027i	−0.217529	+	0.325555i	0.706616	+	0.707597i	$0.250221\pi$
$38$	−0.888394	+	0.888394i	−0.144117	+	0.144117i
$39$	−1.49857	+	7.50782i	−0.239963	+	1.20221i
$40$	4.64406	+	6.95033i	0.734291	+	1.09894i
$41$	3.02038	+	0.600791i	0.471704	+	0.0938278i	0.425218	−	0.905091i	$-0.360198\pi$
$41$	3.02038	+	0.600791i	0.471704	+	0.0938278i	0.0464865	+	0.998919i	$0.485198\pi$
$42$	0.00359897	−	5.43581i	0.000555333	−	0.838764i
$43$	−4.38037	−	10.5751i	−0.668000	−	1.61269i	−0.784952	−	0.619557i	$-0.787312\pi$
$43$	−4.38037	−	10.5751i	−0.668000	−	1.61269i	0.116952	−	0.993138i	$-0.462688\pi$
$44$	0.0377359	−	0.189711i	0.00568890	−	0.0286000i
$45$	1.79778	−	8.97590i	0.267997	−	1.33805i
$46$	1.09405	−	0.217619i	0.161308	−	0.0320862i
$47$	−2.21238	−	2.21238i	−0.322708	−	0.322708i	0.527097	−	0.849805i	$-0.323281\pi$
$47$	−2.21238	−	2.21238i	−0.322708	−	0.322708i	−0.849805	+	0.527097i	$0.823281\pi$
$48$	4.05773	+	6.08153i	0.585683	+	0.877793i
$49$	2.16958	+	0.898671i	0.309940	+	0.128382i
$50$	−6.27299			−0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	5.88369	+	2.43710i	0.808187	+	0.334762i	0.748230	−	0.663439i	$-0.230904\pi$
$53$	5.88369	+	2.43710i	0.808187	+	0.334762i	0.0599567	+	0.998201i	$0.480904\pi$
$54$	1.48981	−	7.41281i	0.202738	−	1.00876i
$55$	−3.55548	−	3.55548i	−0.479420	−	0.479420i
$56$	5.79482	−	1.15266i	0.774365	−	0.154031i
$57$	0.290783	+	1.46694i	0.0385152	+	0.194301i
$58$	2.26861	−	11.4051i	0.297884	−	1.49756i
$59$	−2.33146	−	5.62864i	−0.303530	−	0.732786i	−0.999886	−	0.0150898i	$-0.995197\pi$
$59$	−2.33146	−	5.62864i	−0.303530	−	0.732786i	0.696356	−	0.717696i	$-0.254803\pi$
$60$	−0.620386		0.000410749i	−0.0800915		5.30274e-5i
$61$	−5.73423	−	1.14061i	−0.734193	−	0.146040i	−0.186187	−	0.982514i	$-0.559613\pi$
$61$	−5.73423	−	1.14061i	−0.734193	−	0.146040i	−0.548006	+	0.836474i	$0.684613\pi$
$62$	2.33510	+	3.49473i	0.296558	+	0.443831i
$63$	−5.37510	−	3.60183i	−0.677199	−	0.453788i
$64$	−5.28702	+	5.28702i	−0.660877	+	0.660877i
$65$	7.49329	−	11.2145i	0.929429	−	1.39099i
$66$	−2.93476	−	2.93865i	−0.361244	−	0.361723i
$67$		−	7.19481i		−	0.878985i	−0.898246	−	0.439493i	$-0.855158\pi$
$67$		−	7.19481i		−	0.878985i	0.898246	−	0.439493i	$-0.144842\pi$
$68$		0			0
$69$	0.508927	−	1.22636i	0.0612676	−	0.147637i
$70$	−3.66472	+	8.84742i	−0.438018	+	1.05747i
$71$	−1.80802	−	1.20808i	−0.214573	−	0.143373i	0.443639	−	0.896205i	$-0.353687\pi$
$71$	−1.80802	−	1.20808i	−0.214573	−	0.143373i	−0.658212	+	0.752832i	$0.728687\pi$
$72$	8.21831	+	0.0108825i	0.968537	+	0.00128251i
$73$	−2.45412	−	12.3377i	−0.287233	−	1.44402i	−0.807426	−	0.589969i	$-0.799140\pi$
$73$	−2.45412	−	12.3377i	−0.287233	−	1.44402i	0.520193	−	0.854049i	$-0.325860\pi$
$74$	2.88154	−	1.92538i	0.334972	−	0.223821i
$75$	−4.15245	+	6.20569i	−0.479484	+	0.716571i
$76$	0.0936354	−	0.0387851i	0.0107407	−	0.00444895i
$77$	−3.28348	+	1.36006i	−0.374187	+	0.154994i
$78$	6.19535	−	9.25872i	0.701485	−	1.04834i
$79$	4.95397	−	3.31013i	0.557365	−	0.372419i	−0.244753	−	0.969586i	$-0.578707\pi$
$79$	4.95397	−	3.31013i	0.557365	−	0.372419i	0.802117	+	0.597166i	$0.203707\pi$
$80$	−2.51274	−	12.6324i	−0.280933	−	1.41234i
$81$	−6.34708	−	6.38079i	−0.705232	−	0.708977i
$82$	−3.72592	−	2.48958i	−0.411459	−	0.274928i
$83$	4.96993	−	11.9985i	0.545521	−	1.31700i	−0.375258	−	0.926920i	$-0.622446\pi$
$83$	4.96993	−	11.9985i	0.545521	−	1.31700i	0.920779	−	0.390084i	$-0.127554\pi$
$84$	−0.168074	+	0.405009i	−0.0183384	+	0.0441901i
$85$		0			0
$86$			16.6560i			1.79606i
$87$	−9.78099	−	9.79395i	−1.04863	−	1.05002i
$88$	2.50793	−	3.75339i	0.267347	−	0.400112i
$89$	3.42023	−	3.42023i	0.362544	−	0.362544i	−0.502205	−	0.864749i	$-0.667478\pi$
$89$	3.42023	−	3.42023i	0.362544	−	0.362544i	0.864749	+	0.502205i	$0.167478\pi$
$90$	−7.41510	+	11.0657i	−0.781620	+	1.16643i
$91$	−5.29638	−	7.92660i	−0.555212	−	0.830933i
$92$	−0.0882551	−	0.0175550i	−0.00920123	−	0.00183024i
$93$	5.00297	+	0.00331239i	0.518783	+	0.000343479i
$94$	1.74226	+	4.20619i	0.179701	+	0.433836i
$95$	0.513989	−	2.58400i	0.0527342	−	0.265113i
$96$	−0.223345	−	1.12673i	−0.0227951	−	0.114996i
$97$	−3.47928	+	0.692072i	−0.353267	+	0.0702692i	−0.368534	−	0.929614i	$-0.620140\pi$
$97$	−3.47928	+	0.692072i	−0.353267	+	0.0702692i	0.0152668	+	0.999883i	$0.495140\pi$
$98$	−2.41627	−	2.41627i	−0.244080	−	0.244080i
$99$	−4.84981	+	0.958012i	−0.487424	+	0.0962839i
$100$	0.467514	+	0.193650i	0.0467514	+	0.0193650i
$101$	−3.73948			−0.372092			−0.186046	−	0.982541i	$-0.559567\pi$
$101$	−3.73948			−0.372092			−0.186046	+	0.982541i	$0.559567\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	11.1870	+	4.63380i	1.09698	+	0.454382i
$105$	6.32660	+	9.48201i	0.617413	+	0.925350i
$106$	−6.55268	−	6.55268i	−0.636453	−	0.636453i
$107$	−1.85365	+	0.368714i	−0.179199	+	0.0356449i	−0.283874	−	0.958862i	$-0.591620\pi$
$107$	−1.85365	+	0.368714i	−0.179199	+	0.0356449i	0.104675	+	0.994506i	$0.466620\pi$
$108$	−0.339870	+	0.506471i	−0.0327040	+	0.0487352i
$109$	−0.819969	+	4.12226i	−0.0785388	+	0.394841i	0.921441	+	0.388518i	$0.127013\pi$
$109$	−0.819969	+	4.12226i	−0.0785388	+	0.394841i	−0.999980	+	0.00632347i	$0.997987\pi$
$110$	2.79996	+	6.75970i	0.266966	+	0.644513i
$111$	0.00273120	−	4.12515i	0.000259234	−	0.391542i
$112$	−8.92878	−	1.77604i	−0.843690	−	0.167820i
$113$	9.15888	+	13.7072i	0.861595	+	1.28947i	0.955831	+	0.293917i	$0.0949591\pi$
$113$	9.15888	+	13.7072i	0.861595	+	1.28947i	−0.0942363	+	0.995550i	$0.530041\pi$
$114$	0.425951	−	2.13402i	0.0398940	−	0.199869i
$115$	−1.65403	+	1.65403i	−0.154239	+	0.154239i
$116$	−0.521156	+	0.779965i	−0.0483881	+	0.0724180i
$117$	−5.05832	−	12.2577i	−0.467642	−	1.13323i
$118$			8.86518i			0.816106i
$119$		0			0
$120$	−13.3726	−	5.54949i	−1.22075	−	0.506597i
$121$	3.17039	−	7.65399i	0.288217	−	0.695817i
$122$	7.07371	+	4.72650i	0.640424	+	0.427917i
$123$	−4.92927	+	2.03795i	−0.444457	+	0.183756i
$124$	−0.0661465	−	0.332541i	−0.00594013	−	0.0298630i
$125$	−1.74816	+	1.16808i	−0.156360	+	0.104477i
$126$	5.22038	+	7.83529i	0.465068	+	0.698023i
$127$	−11.3753	+	4.71179i	−1.00939	+	0.418104i	−0.825233	−	0.564792i	$-0.808956\pi$
$127$	−11.3753	+	4.71179i	−1.00939	+	0.418104i	−0.184159	+	0.982896i	$0.558956\pi$
$128$	11.2771	−	4.67113i	0.996766	−	0.412874i
$129$	16.4773	+	11.0256i	1.45074	+	0.970746i
$130$	−16.3185	+	10.9037i	−1.43123	+	0.956315i
$131$	0.687984	+	3.45873i	0.0601094	+	0.302191i	0.999132	−	0.0416661i	$-0.0132666\pi$
$131$	0.687984	+	3.45873i	0.0601094	+	0.302191i	−0.939022	+	0.343857i	$0.888267\pi$
$132$	0.128004	+	0.309609i	0.0111413	+	0.0269480i
$133$	−1.54836	−	1.03458i	−0.134260	−	0.0897094i
$134$	−4.00644	+	9.67240i	−0.346103	+	0.835568i
$135$	6.03852	+	14.6606i	0.519713	+	1.26178i
$136$		0			0
$137$		−	14.6484i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$	−1.36708	+	1.36527i	−0.116374	+	0.116220i
$139$	−2.80264	+	4.19445i	−0.237717	+	0.355768i	−0.931077	−	0.364823i	$-0.881130\pi$
$139$	−2.80264	+	4.19445i	−0.237717	+	0.355768i	0.693360	+	0.720591i	$0.256130\pi$
$140$	0.546249	−	0.546249i	0.0461664	−	0.0461664i
$141$	5.31437	+	1.06075i	0.447550	+	0.0893314i
$142$	1.75791	+	2.63090i	0.147520	+	0.220780i
$143$	−7.14374	−	1.42098i	−0.597389	−	0.118828i
$144$	−11.6926	−	4.86139i	−0.974385	−	0.405116i
$145$	9.33173	+	22.5288i	0.774958	+	1.87091i
$146$	−3.57105	+	17.9529i	−0.295542	+	1.48579i
$147$	−3.98981	+	0.790878i	−0.329074	+	0.0652305i
$148$	−0.274193	+	0.0545404i	−0.0225385	+	0.00448319i
$149$	4.44785	+	4.44785i	0.364382	+	0.364382i	0.865423	−	0.501041i	$-0.167050\pi$
$149$	4.44785	+	4.44785i	0.364382	+	0.364382i	−0.501041	+	0.865423i	$0.667050\pi$
$150$	9.03803	−	6.03037i	0.737952	−	0.492377i
$151$	14.0551	+	5.82179i	1.14378	+	0.473771i	0.872445	−	0.488713i	$-0.162533\pi$
$151$	14.0551	+	5.82179i	1.14378	+	0.473771i	0.271339	+	0.962484i	$0.412533\pi$
$152$	2.36528			0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	−8.14291	−	3.37291i	−0.654055	−	0.270918i
$156$	−0.747548	+	0.498780i	−0.0598518	+	0.0399344i
$157$	1.74527	+	1.74527i	0.139287	+	0.139287i	0.773312	−	0.634025i	$-0.218598\pi$
$157$	1.74527	+	1.74527i	0.139287	+	0.139287i	−0.634025	+	0.773312i	$0.718598\pi$
$158$	−8.50316	+	1.69138i	−0.676475	+	0.134559i
$159$	−10.8200	+	2.14478i	−0.858080	+	0.170092i
$160$	−0.394786	+	1.98472i	−0.0312105	+	0.156906i
$161$	0.632711	+	1.52750i	0.0498646	+	0.120384i
$162$	4.97960	+	12.1125i	0.391235	+	0.951644i
$163$	−1.08953	−	0.216722i	−0.0853388	−	0.0169749i	0.152236	−	0.988344i	$-0.451353\pi$
$163$	−1.08953	−	0.216722i	−0.0853388	−	0.0169749i	−0.237575	+	0.971369i	$0.576353\pi$
$164$	0.200831	+	0.300565i	0.0156823	+	0.0234702i
$165$	8.54063	+	1.70472i	0.664887	+	0.132712i
$166$	−13.3627	+	13.3627i	−1.03715	+	1.03715i
$167$	−11.0337	+	16.5131i	−0.853815	+	1.27782i	0.105195	+	0.994452i	$0.466453\pi$
$167$	−11.0337	+	16.5131i	−0.853815	+	1.27782i	−0.959010	+	0.283373i	$0.908547\pi$
$168$	−7.24100	+	7.23142i	−0.558655	+	0.557916i
$169$		−	6.53766i		−	0.502897i
$170$		0			0
$171$	−1.82916	−	1.83401i	−0.139879	−	0.140250i
$172$	0.514179	−	1.24134i	0.0392058	−	0.0946511i
$173$	−9.67520	−	6.46476i	−0.735591	−	0.491507i	0.130465	−	0.991453i	$-0.458353\pi$
$173$	−9.67520	−	6.46476i	−0.735591	−	0.491507i	−0.866056	+	0.499946i	$0.833353\pi$
$174$	7.69538	+	18.6131i	0.583385	+	1.41106i
$175$	−1.81391	−	9.11912i	−0.137118	−	0.689341i
$176$	−5.78330	+	3.86428i	−0.435933	+	0.291281i
$177$	8.77006	+	5.86837i	0.659198	+	0.441094i
$178$	−6.50257	+	2.69345i	−0.487389	+	0.201883i
$179$	0.782216	−	0.324004i	0.0584656	−	0.0242172i	−0.353259	−	0.935526i	$-0.614927\pi$
$179$	0.782216	−	0.324004i	0.0584656	−	0.0242172i	0.411725	+	0.911308i	$0.364927\pi$
$180$	0.894237	−	0.595799i	0.0666525	−	0.0444082i
$181$	1.19220	−	0.796600i	0.0886152	−	0.0592108i	−0.510473	−	0.859894i	$-0.670530\pi$
$181$	1.19220	−	0.796600i	0.0886152	−	0.0592108i	0.599088	+	0.800683i	$0.295530\pi$
$182$	2.70630	+	13.6055i	0.200604	+	1.00851i
$183$	9.35828	−	3.86907i	0.691784	−	0.286010i
$184$	−1.74610	−	1.16671i	−0.128724	−	0.0860109i
$185$	−2.78110	+	6.71416i	−0.204470	+	0.493635i
$186$	−6.72393	−	2.79036i	−0.493023	−	0.204599i
$187$		0			0
$188$		−	0.367264i		−	0.0267855i
$189$	11.2069	+	0.0222598i	0.815181	+	0.00161916i
$190$	−2.12989	+	3.18760i	−0.154518	+	0.231253i
$191$	0.509849	−	0.509849i	0.0368914	−	0.0368914i	−0.688420	−	0.725312i	$-0.741696\pi$
$191$	0.509849	−	0.509849i	0.0368914	−	0.0368914i	0.725312	+	0.688420i	$0.241696\pi$
$192$	2.53493	−	12.7000i	0.182942	−	0.916542i
$193$	−6.45656	−	9.66292i	−0.464753	−	0.695552i	0.522867	−	0.852414i	$-0.324862\pi$
$193$	−6.45656	−	9.66292i	−0.464753	−	0.695552i	−0.987621	+	0.156862i	$0.949862\pi$
$194$	5.06278	+	1.00705i	0.363486	+	0.0723019i
$195$	−0.0154671	+	23.3612i	−0.00110762	+	1.67293i
$196$	0.105488	+	0.254671i	0.00753488	+	0.0181908i
$197$	4.53858	−	22.8170i	0.323360	−	1.62564i	−0.387193	−	0.921999i	$-0.626555\pi$
$197$	4.53858	−	22.8170i	0.323360	−	1.62564i	0.710553	−	0.703643i	$-0.248445\pi$
$198$	7.05335	+	1.41271i	0.501260	+	0.100397i
$199$	23.6514	−	4.70456i	1.67661	−	0.333497i	0.737035	−	0.675854i	$-0.236225\pi$
$199$	23.6514	−	4.70456i	1.67661	−	0.333497i	0.939570	+	0.342357i	$0.111225\pi$
$200$	8.35068	+	8.35068i	0.590482	+	0.590482i
$201$	6.91653	+	10.3662i	0.487854	+	0.731173i
$202$	5.02720	+	2.08233i	0.353712	+	0.146512i
$203$	17.2357			1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	−12.5483	−	5.19767i	−0.874281	−	0.362139i
$207$	0.445674	+	2.25617i	0.0309765	+	0.156814i
$208$	−13.1927	−	13.1927i	−0.914753	−	0.914753i
$209$	−1.39544	+	0.277570i	−0.0965244	+	0.0191999i
$210$	−3.22515	−	16.2702i	−0.222556	−	1.12275i
$211$	−3.04535	+	15.3100i	−0.209651	+	1.05398i	0.722350	+	0.691528i	$0.243062\pi$
$211$	−3.04535	+	15.3100i	−0.209651	+	1.05398i	−0.932000	+	0.362457i	$0.881938\pi$
$212$	0.286074	+	0.690643i	0.0196476	+	0.0474336i
$213$	3.76633	+	0.00249363i	0.258065	+	0.000170861i
$214$	2.69729	+	0.536524i	0.184383	+	0.0366760i
$215$	−19.4047	−	29.0412i	−1.32339	−	1.98059i
$216$	−11.8513	+	7.88477i	−0.806377	+	0.536490i
$217$	−4.40510	+	4.40510i	−0.299038	+	0.299038i
$218$	3.39782	−	5.08520i	0.230130	−	0.344413i
$219$	15.3964	+	15.4168i	1.04039	+	1.04177i
$220$		−	0.590224i		−	0.0397929i
$221$		0			0
$222$	−2.30077	+	5.54415i	−0.154417	+	0.372099i
$223$	−0.930718	+	2.24695i	−0.0623255	+	0.150467i	−0.951974	−	0.306179i	$-0.900949\pi$
$223$	−0.930718	+	2.24695i	−0.0623255	+	0.150467i	0.889648	+	0.456646i	$0.150949\pi$
$224$	1.18926	+	0.794641i	0.0794611	+	0.0530942i
$225$	0.0171254	−	12.9329i	0.00114169	−	0.862193i
$226$	−4.67992	−	23.5276i	−0.311304	−	1.56503i
$227$	1.16773	−	0.780250i	0.0775048	−	0.0517870i	−0.516214	−	0.856460i	$-0.672659\pi$
$227$	1.16773	−	0.780250i	0.0775048	−	0.0517870i	0.593719	+	0.804673i	$0.297659\pi$
$228$	−0.0976235	+	0.145895i	−0.00646527	+	0.00966211i
$229$	10.0488	−	4.16234i	0.664043	−	0.275055i	−0.0250960	−	0.999685i	$-0.507989\pi$
$229$	10.0488	−	4.16234i	0.664043	−	0.275055i	0.689139	+	0.724630i	$0.257989\pi$
$230$	3.14466	−	1.30256i	0.207353	−	0.0858884i
$231$	3.42333	−	5.11604i	0.225239	−	0.336611i
$232$	−18.2026	+	12.1626i	−1.19506	+	0.798513i
$233$	−2.79686	−	14.0608i	−0.183228	−	0.921151i	−0.957530	−	0.288334i	$-0.906899\pi$
$233$	−2.79686	−	14.0608i	−0.183228	−	0.921151i	0.774302	−	0.632817i	$-0.218101\pi$
$234$	−0.0255506	+	19.2955i	−0.00167030	+	1.26139i
$235$	−7.93813	−	5.30409i	−0.517826	−	0.346000i
$236$	0.273673	−	0.660704i	0.0178146	−	0.0430082i
$237$	−3.95549	+	9.53155i	−0.256937	+	0.619140i
$238$		0			0
$239$			23.7093i			1.53362i	0.641872	+	0.766812i	$0.278158\pi$
$239$			23.7093i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$240$	15.7641	+	15.7850i	1.01757	+	1.01892i
$241$	1.56359	−	2.34007i	0.100719	−	0.150737i	−0.777687	−	0.628652i	$-0.783607\pi$
$241$	1.56359	−	2.34007i	0.100719	−	0.150737i	0.878406	+	0.477914i	$0.158607\pi$
$242$	−8.52427	+	8.52427i	−0.547961	+	0.547961i
$243$	15.2788	+	3.09175i	0.980134	+	0.198336i
$244$	−0.381280	−	0.570626i	−0.0244090	−	0.0365306i
$245$	7.02801	+	1.39796i	0.449003	+	0.0893123i
$246$	7.76154	+	0.00513881i	0.494858	+	0.000327638i
$247$	−1.46048	−	3.52592i	−0.0929284	−	0.224349i
$248$	1.54371	−	7.76073i	0.0980254	−	0.492807i
$249$	4.37380	+	22.0649i	0.277178	+	1.39831i
$250$	3.00061	−	0.596858i	0.189775	−	0.0377486i
$251$	10.7058	+	10.7058i	0.675745	+	0.675745i	0.959034	−	0.283289i	$-0.0914257\pi$
$251$	10.7058	+	10.7058i	0.675745	+	0.675745i	−0.283289	+	0.959034i	$0.591426\pi$
$252$	−0.147185	−	0.745104i	−0.00927179	−	0.0469372i
$253$	1.16706	+	0.483411i	0.0733723	+	0.0303918i
$254$	17.9162			1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	−18.3799	−	7.61319i	−1.14650	−	0.474898i	−0.273145	−	0.961973i	$-0.588064\pi$
$257$	−18.3799	−	7.61319i	−1.14650	−	0.474898i	−0.873360	+	0.487075i	$0.838064\pi$
$258$	−16.0118	−	23.9977i	−0.996850	−	1.49403i
$259$	3.63218	+	3.63218i	0.225693	+	0.225693i
$260$	1.55279	−	0.308868i	0.0962997	−	0.0191552i
$261$	23.5074	+	4.70829i	1.45507	+	0.291436i
$262$	1.00110	−	5.03288i	0.0618482	−	0.310932i
$263$	0.0501727	+	0.121128i	0.00309378	+	0.00746905i	0.925419	−	0.378946i	$-0.123713\pi$
$263$	0.0501727	+	0.121128i	0.00309378	+	0.00746905i	−0.922325	+	0.386415i	$0.873713\pi$
$264$	−0.00517669	+	7.81875i	−0.000318603	+	0.481211i
$265$	19.0593	+	3.79112i	1.17080	+	0.232887i
$266$	1.50544	+	2.25305i	0.0923045	+	0.138143i
$267$	−1.63987	+	8.21576i	−0.100358	+	0.502796i
$268$	0.597184	−	0.597184i	0.0364788	−	0.0364788i
$269$	3.30317	−	4.94355i	0.201398	−	0.301413i	−0.716999	−	0.697075i	$-0.754485\pi$
$269$	3.30317	−	4.94355i	0.201398	−	0.301413i	0.918396	+	0.395661i	$0.129485\pi$
$270$	0.0458262	−	23.0716i	0.00278890	−	1.40409i
$271$			6.87483i			0.417616i	0.977957	+	0.208808i	$0.0669584\pi$
$271$			6.87483i			0.417616i	−0.977957	+	0.208808i	$0.933042\pi$
$272$		0			0
$273$	15.2510	+	6.32899i	0.923030	+	0.383048i
$274$	−8.15697	+	19.6927i	−0.492781	+	1.18968i
$275$	−5.90659	−	3.94666i	−0.356181	−	0.237992i
$276$	0.144033	−	0.0595485i	0.00866974	−	0.00358440i
$277$	1.61874	+	8.13797i	0.0972608	+	0.488963i	0.998456	+	0.0555495i	$0.0176911\pi$
$277$	1.61874	+	8.13797i	0.0972608	+	0.488963i	−0.901195	+	0.433414i	$0.857309\pi$
$278$	6.10344	−	4.07818i	0.366060	−	0.244593i
$279$	−7.21138	+	4.80469i	−0.431734	+	0.287649i
$280$	16.6563	−	6.89927i	0.995404	−	0.412310i
$281$	12.2411	−	5.07041i	0.730240	−	0.302475i	0.0135893	−	0.999908i	$-0.495674\pi$
$281$	12.2411	−	5.07041i	0.730240	−	0.302475i	0.716651	+	0.697432i	$0.245674\pi$
$282$	−6.55373	−	4.38534i	−0.390269	−	0.261143i
$283$	11.6680	−	7.79633i	0.693593	−	0.463444i	−0.158142	−	0.987416i	$-0.550550\pi$
$283$	11.6680	−	7.79633i	0.693593	−	0.463444i	0.851735	+	0.523972i	$0.175550\pi$
$284$	−0.0497963	−	0.250343i	−0.00295487	−	0.0148551i
$285$	1.74351	+	4.21709i	0.103276	+	0.249799i
$286$	8.81247	+	5.88830i	0.521092	+	0.348183i
$287$	2.54174	−	6.13631i	0.150034	−	0.362215i
$288$	1.40494	+	1.40867i	0.0827870	+	0.0830066i
$289$		0			0
$290$		−	35.4832i		−	2.08364i
$291$	4.34759	−	4.34183i	0.254860	−	0.254523i
$292$	0.820357	−	1.22775i	0.0480078	−	0.0718487i
$293$	−18.6721	+	18.6721i	−1.09083	+	1.09083i	−0.0953949	+	0.995440i	$0.530411\pi$
$293$	−18.6721	+	18.6721i	−1.09083	+	1.09083i	−0.995440	+	0.0953949i	$0.969589\pi$
$294$	5.80414	+	1.15851i	0.338504	+	0.0675657i
$295$	−10.3282	−	15.4572i	−0.601331	−	0.899955i
$296$	−6.39904	−	1.27285i	−0.371936	−	0.0739827i
$297$	6.06657	−	6.04252i	0.352018	−	0.350622i
$298$	−3.50271	−	8.45629i	−0.202907	−	0.489860i
$299$	−0.661049	+	3.32332i	−0.0382295	+	0.192193i
$300$	−0.859747	+	0.170423i	−0.0496375	+	0.00983935i
$301$	−24.2130	+	4.81627i	−1.39561	+	0.277605i
$302$	−15.6531	−	15.6531i	−0.900738	−	0.900738i
$303$	5.38778	−	3.59484i	0.309520	−	0.206518i
$304$	−3.36705	−	1.39468i	−0.193114	−	0.0799904i
$305$	−17.8402			−1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	−0.385424	−	0.159648i	−0.0219616	−	0.00909677i
$309$	−13.4483	+	8.97302i	−0.765049	+	0.510457i
$310$	9.06879	+	9.06879i	0.515073	+	0.515073i
$311$	−22.8877	+	4.55265i	−1.29784	+	0.258157i	−0.795206	−	0.606340i	$-0.792637\pi$
$311$	−22.8877	+	4.55265i	−1.29784	+	0.258157i	−0.502638	+	0.864497i	$0.667637\pi$
$312$	−20.5726	+	4.07799i	−1.16470	+	0.230871i
$313$	−0.314998	+	1.58360i	−0.0178048	+	0.0895106i	−0.988666	−	0.150132i	$-0.952030\pi$
$313$	−0.314998	+	1.58360i	−0.0178048	+	0.0895106i	0.970861	+	0.239642i	$0.0770302\pi$
$314$	−1.37441	−	3.31812i	−0.0775624	−	0.187252i
$315$	−18.2305	−	7.57963i	−1.02717	−	0.427064i
$316$	0.685937	+	0.136441i	0.0385870	+	0.00767543i
$317$	−13.5476	−	20.2754i	−0.760908	−	1.13878i	−0.986372	−	0.164528i	$-0.947390\pi$
$317$	−13.5476	−	20.2754i	−0.760908	−	1.13878i	0.225464	−	0.974251i	$-0.427610\pi$
$318$	15.7402	+	3.14176i	0.882669	+	0.176181i
$319$	9.31162	−	9.31162i	0.521351	−	0.521351i
$320$	−12.6754	+	18.9701i	−0.708577	+	1.06046i
$321$	2.31626	−	2.31319i	0.129281	−	0.129110i
$322$		−	2.40583i		−	0.134072i
$323$		0			0
$324$	0.00279782	−	1.05644i	0.000155435	−	0.0586911i
$325$	7.29207	−	17.6046i	0.404491	−	0.976529i
$326$	1.34404	+	0.898060i	0.0744396	+	0.0497389i
$327$	−2.78143	−	6.72755i	−0.153813	−	0.372034i
$328$	1.64583	+	8.27415i	0.0908758	+	0.456863i
$329$	−5.61080	+	3.74901i	−0.309333	+	0.206690i
$330$	−10.5324	−	7.04761i	−0.579789	−	0.387958i
$331$	−28.1459	+	11.6584i	−1.54704	+	0.640804i	−0.982777	−	0.184793i	$-0.940839\pi$
$331$	−28.1459	+	11.6584i	−1.54704	+	0.640804i	−0.564260	+	0.825597i	$0.690839\pi$
$332$	1.40841	−	0.583384i	0.0772967	−	0.0320173i
$333$	3.96166	+	5.94607i	0.217098	+	0.325843i
$334$	24.0286	−	16.0554i	1.31479	−	0.878514i
$335$	−4.28304	−	21.5323i	−0.234008	−	1.17644i
$336$	14.5718	−	6.02453i	0.794956	−	0.328665i
$337$	14.3229	+	9.57025i	0.780218	+	0.521325i	0.880734	−	0.473611i	$-0.157050\pi$
$337$	14.3229	+	9.57025i	0.780218	+	0.521325i	−0.100517	+	0.994935i	$0.532050\pi$
$338$	−3.64051	+	8.78896i	−0.198018	+	0.478057i
$339$	−26.3730	−	10.9445i	−1.43239	−	0.594425i
$340$		0			0
$341$			4.75973i			0.257754i
$342$	1.43777	+	3.48413i	0.0777459	+	0.188400i
$343$	11.2015	−	16.7643i	0.604826	−	0.905186i
$344$	22.1727	−	22.1727i	1.19547	−	1.19547i
$345$	0.793047	−	3.97317i	0.0426962	−	0.213908i
$346$	9.40702	+	14.0786i	0.505724	+	0.756870i
$347$	19.8459	+	3.94759i	1.06538	+	0.211918i	0.696499	−	0.717558i	$-0.254740\pi$
$347$	19.8459	+	3.94759i	1.06538	+	0.211918i	0.368884	+	0.929476i	$0.379740\pi$
$348$	0.00107573	−	1.62476i	5.76652e−5	−	0.0870963i
$349$	2.90948	+	7.02410i	0.155741	+	0.375992i	0.982421	−	0.186681i	$-0.0597731\pi$
$349$	2.90948	+	7.02410i	0.155741	+	0.375992i	−0.826680	+	0.562673i	$0.809773\pi$
$350$	−2.63946	+	13.2694i	−0.141085	+	0.709281i
$351$	19.0716	+	12.7981i	1.01797	+	0.683112i
$352$	1.07181	−	0.213196i	0.0571276	−	0.0113634i
$353$	−8.44344	−	8.44344i	−0.449399	−	0.449399i	0.445756	−	0.895155i	$-0.352935\pi$
$353$	−8.44344	−	8.44344i	−0.449399	−	0.449399i	−0.895155	+	0.445756i	$0.852935\pi$
$354$	−8.52230	−	12.7728i	−0.452955	−	0.678867i
$355$	−6.13014	−	2.53919i	−0.325354	−	0.134766i
$356$	0.567772			0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	21.2469	+	8.80076i	1.12137	+	0.464487i	0.864839	−	0.502049i	$-0.167420\pi$
$359$	21.2469	+	8.80076i	1.12137	+	0.464487i	0.256531	+	0.966536i	$0.417420\pi$
$360$	24.6019	−	4.85976i	1.29663	−	0.256132i
$361$	12.9079	+	12.9079i	0.679363	+	0.679363i
$362$	−2.04633	+	0.407040i	−0.107553	+	0.0213935i
$363$	2.79011	+	14.0755i	0.146443	+	0.738773i
$364$	0.218313	−	1.09753i	0.0114427	−	0.0575264i
$365$	−14.6892	−	35.4628i	−0.768866	−	1.85621i
$366$	−14.7354	−	0.00975609i	−0.770231	−	0.000509959i
$367$	−16.0952	−	3.20154i	−0.840163	−	0.167119i	−0.243792	−	0.969828i	$-0.578391\pi$
$367$	−16.0952	−	3.20154i	−0.840163	−	0.167119i	−0.596371	+	0.802709i	$0.703391\pi$
$368$	1.79769	+	2.69043i	0.0937111	+	0.140249i
$369$	5.14289	−	7.67486i	0.267728	−	0.399537i
$370$	7.47758	−	7.47758i	0.388741	−	0.388741i
$371$	7.63093	−	11.4205i	0.396178	−	0.592923i
$372$	0.414982	+	0.415531i	0.0215158	+	0.0215443i
$373$		−	1.61824i		−	0.0837894i	−0.999122	−	0.0418947i	$-0.986661\pi$
$373$		−	1.61824i		−	0.0837894i	0.999122	−	0.0418947i	$-0.0133394\pi$
$374$		0			0
$375$	1.39582	−	3.36351i	0.0720798	−	0.173691i
$376$	3.28001	−	7.91865i	0.169154	−	0.408373i
$377$	29.3703	+	19.6246i	1.51265	+	1.01072i
$378$	−15.0537	−	6.27050i	−0.774278	−	0.322520i
$379$	3.02965	+	15.2311i	0.155623	+	0.782368i	0.977208	+	0.212283i	$0.0680898\pi$
$379$	3.02965	+	15.2311i	0.155623	+	0.782368i	−0.821586	+	0.570085i	$0.806910\pi$
$380$	0.257139	−	0.171815i	0.0131910	−	0.00881393i
$381$	11.8598	−	17.7240i	0.607594	−	0.908027i
$382$	−0.969330	+	0.401510i	−0.0495952	+	0.0205430i
$383$	−20.4588	+	8.47433i	−1.04540	+	0.433018i	−0.838247	−	0.545291i	$-0.816419\pi$
$383$	−20.4588	+	8.47433i	−1.04540	+	0.433018i	−0.207151	+	0.978309i	$0.566419\pi$
$384$	−11.7574	+	17.5710i	−0.599994	+	0.896668i
$385$	−9.01702	+	6.02498i	−0.459550	+	0.307061i
$386$	3.29912	+	16.5858i	0.167921	+	0.844194i
$387$	−34.3393	−	0.0454712i	−1.74557	−	0.00231143i
$388$	−0.346231	−	0.231344i	−0.0175772	−	0.0117447i
$389$	−5.80572	+	14.0162i	−0.294362	+	0.710652i	0.705636	+	0.708574i	$0.250661\pi$
$389$	−5.80572	+	14.0162i	−0.294362	+	0.710652i	−0.999998	+	0.00207747i	$0.999339\pi$
$390$	13.0295	−	31.3972i	0.659774	−	1.58986i
$391$		0			0
$392$			6.43314i			0.324922i
$393$	−4.31619	−	4.32191i	−0.217723	−	0.218011i
$394$	−18.8071	+	28.1469i	−0.947490	+	1.41802i
$395$	12.8555	−	12.8555i	0.646831	−	0.646831i
$396$	−0.482061	−	0.323027i	−0.0242245	−	0.0162327i
$397$	20.9101	+	31.2942i	1.04945	+	1.57061i	0.797922	+	0.602760i	$0.205932\pi$
$397$	20.9101	+	31.2942i	1.04945	+	1.57061i	0.251526	+	0.967850i	$0.419068\pi$
$398$	−34.4157	−	6.84571i	−1.72510	−	0.343145i
$399$	3.22541	+	0.00213550i	0.161473	+	0.000106909i
$400$	−6.96352	−	16.8114i	−0.348176	−	0.840571i
$401$	−0.689420	+	3.46595i	−0.0344280	+	0.173081i	−0.994174	−	0.107789i	$-0.965623\pi$
$401$	−0.689420	+	3.46595i	−0.0344280	+	0.173081i	0.959746	+	0.280870i	$0.0906230\pi$
$402$	−3.52588	−	17.7873i	−0.175855	−	0.887151i
$403$	−12.5221	+	2.49080i	−0.623770	+	0.124076i
$404$	−0.310384	−	0.310384i	−0.0154422	−	0.0154422i
$405$	−22.7937	−	15.3178i	−1.13263	−	0.761146i
$406$	−23.1710	−	9.59773i	−1.14996	−	0.476327i
$407$	3.92459			0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	−12.6328	−	5.23268i	−0.623890	−	0.258424i
$411$	14.0818	+	21.1052i	0.694605	+	1.04104i
$412$	0.774744	+	0.774744i	0.0381689	+	0.0381689i
$413$	−12.8874	+	2.56347i	−0.634148	+	0.126140i
$414$	0.657203	−	3.28127i	0.0322998	−	0.161266i
$415$	7.73115	−	38.8671i	0.379507	−	1.90791i
$416$	1.12177	+	2.70819i	0.0549993	+	0.132780i
$417$	0.00578500	−	8.73753i	0.000283293	−	0.427879i
$418$	2.03053	+	0.403898i	0.0993165	+	0.0197553i
$419$	17.4409	+	26.1021i	0.852042	+	1.27517i	0.959712	+	0.280985i	$0.0906611\pi$
$419$	17.4409	+	26.1021i	0.852042	+	1.27517i	−0.107670	+	0.994187i	$0.534339\pi$
$420$	−0.261906	+	1.31215i	−0.0127797	+	0.0640262i
$421$	10.7245	−	10.7245i	0.522682	−	0.522682i	−0.395699	−	0.918380i	$-0.629498\pi$
$421$	10.7245	−	10.7245i	0.522682	−	0.522682i	0.918380	+	0.395699i	$0.129498\pi$
$422$	12.6194	−	18.8863i	0.614305	−	0.919373i
$423$	−8.67658	+	3.58050i	−0.421870	+	0.174090i
$424$			17.4460i			0.847253i
$425$		0			0
$426$	−5.06191	−	2.10064i	−0.245250	−	0.101776i
$427$	−4.82553	+	11.6499i	−0.233524	+	0.563776i
$428$	−0.184461	−	0.123253i	−0.00891625	−	0.00595764i
$429$	11.6586	−	4.82011i	0.562883	−	0.232717i
$430$	9.91525	+	49.8473i	0.478156	+	2.40385i
$431$	9.52337	−	6.36331i	0.458724	−	0.306510i	−0.304652	−	0.952464i	$-0.598540\pi$
$431$	9.52337	−	6.36331i	0.458724	−	0.306510i	0.763376	+	0.645954i	$0.223540\pi$
$432$	21.5199	−	4.23616i	1.03538	−	0.203812i
$433$	24.7526	−	10.2528i	1.18953	−	0.492720i	0.301930	−	0.953330i	$-0.402369\pi$
$433$	24.7526	−	10.2528i	1.18953	−	0.492720i	0.887603	+	0.460610i	$0.152369\pi$
$434$	8.37502	−	3.46905i	0.402014	−	0.166520i
$435$	−35.1024	−	23.4883i	−1.68303	−	1.12618i
$436$	−0.410216	+	0.274097i	−0.0196458	+	0.0131269i
$437$	0.129127	+	0.649167i	0.00617700	+	0.0310539i
$438$	−12.1134	−	29.2991i	−0.578799	−	1.39997i
$439$	−7.08940	−	4.73699i	−0.338359	−	0.226084i	0.374769	−	0.927118i	$-0.377722\pi$
$439$	−7.08940	−	4.73699i	−0.338359	−	0.226084i	−0.713128	+	0.701034i	$0.752722\pi$
$440$	5.27126	−	12.7259i	0.251297	−	0.606685i
$441$	4.98817	−	4.97498i	0.237532	−	0.236904i
$442$		0			0
$443$			18.8773i			0.896886i	0.893811	+	0.448443i	$0.148021\pi$
$443$			18.8773i			0.896886i	−0.893811	+	0.448443i	$0.851979\pi$
$444$	0.342622	−	0.342169i	0.0162601	−	0.0162386i
$445$	8.19987	−	12.2720i	0.388711	−	0.581747i
$446$	2.50244	−	2.50244i	0.118494	−	0.118494i
$447$	−10.6842	−	2.13257i	−0.505345	−	0.100867i
$448$	8.95919	+	13.4084i	0.423282	+	0.633486i
$449$	−26.7408	−	5.31908i	−1.26198	−	0.251023i	−0.481633	−	0.876373i	$-0.659956\pi$
$449$	−26.7408	−	5.31908i	−1.26198	−	0.251023i	−0.780345	+	0.625350i	$0.784956\pi$
$450$	−7.22473	+	17.3769i	−0.340577	+	0.819156i
$451$	−1.94197	−	4.68833i	−0.0914438	−	0.220765i
$452$	−0.377522	+	1.89793i	−0.0177572	+	0.0892713i
$453$	−25.8469	+	5.12348i	−1.21439	+	0.240722i
$454$	−2.00433	+	0.398685i	−0.0940677	+	0.0187112i
$455$	−20.5695	−	20.5695i	−0.964311	−	0.964311i
$456$	−3.40786	+	2.27380i	−0.159588	+	0.106480i
$457$	−9.73907	−	4.03405i	−0.455574	−	0.188705i	0.143082	−	0.989711i	$-0.454299\pi$
$457$	−9.73907	−	4.03405i	−0.455574	−	0.188705i	−0.598657	+	0.801006i	$0.704299\pi$
$458$	−15.8270			−0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	9.13414	+	3.78349i	0.425419	+	0.176215i	0.585112	−	0.810952i	$-0.301050\pi$
$461$	9.13414	+	3.78349i	0.425419	+	0.176215i	−0.159693	+	0.987167i	$0.551050\pi$
$462$	−7.45106	+	4.97150i	−0.346655	+	0.231295i
$463$	−16.2123	−	16.2123i	−0.753448	−	0.753448i	0.221673	−	0.975121i	$-0.428848\pi$
$463$	−16.2123	−	16.2123i	−0.753448	−	0.753448i	−0.975121	+	0.221673i	$0.928848\pi$
$464$	33.0836	−	6.58074i	1.53587	−	0.305503i
$465$	14.9746	−	2.96833i	0.694432	−	0.137653i
$466$	−4.06977	+	20.4601i	−0.188529	+	0.947797i
$467$	9.89105	+	23.8791i	0.457703	+	1.10499i	0.969325	+	0.245783i	$0.0790450\pi$
$467$	9.89105	+	23.8791i	0.457703	+	1.10499i	−0.511621	+	0.859211i	$0.670955\pi$
$468$	0.597567	−	1.43727i	0.0276226	−	0.0664378i
$469$	−15.2194	−	3.02732i	−0.702766	−	0.139789i
$470$	7.71810	+	11.5509i	0.356009	+	0.532806i
$471$	−4.19231	−	0.836789i	−0.193172	−	0.0385572i
$472$	11.8014	−	11.8014i	0.543205	−	0.543205i
$473$	−10.4791	+	15.6831i	−0.481831	+	0.721111i
$474$	10.6253	−	10.6112i	0.488034	−	0.487388i
$475$		−	3.72217i		−	0.170785i
$476$		0			0
$477$	13.5274	−	13.4916i	0.619378	−	0.617740i
$478$	13.2025	−	31.8737i	0.603870	−	1.45787i
$479$	−7.20443	−	4.81385i	−0.329179	−	0.219950i	0.379987	−	0.924992i	$-0.375928\pi$
$479$	−7.20443	−	4.81385i	−0.329179	−	0.219950i	−0.709166	+	0.705041i	$0.750928\pi$
$480$	−1.33916	−	3.23907i	−0.0611238	−	0.147843i
$481$	2.05377	+	10.3250i	0.0936437	+	0.470778i
$482$	−3.40509	+	2.27521i	−0.155098	+	0.103633i
$483$	−2.38002	−	1.59256i	−0.108295	−	0.0724639i
$484$	0.898446	−	0.372148i	0.0408384	−	0.0169158i
$485$	−10.0006	+	4.14240i	−0.454106	+	0.188097i
$486$	−18.8185	−	12.6644i	−0.853625	−	0.574470i
$487$	32.2752	−	21.5656i	1.46253	−	0.977229i	0.466851	−	0.884336i	$-0.345389\pi$
$487$	32.2752	−	21.5656i	1.46253	−	0.977229i	0.995676	−	0.0928931i	$-0.0296115\pi$
$488$	−3.12463	−	15.7086i	−0.141445	−	0.711094i
$489$	1.77812	−	0.735143i	0.0804094	−	0.0332443i
$490$	−8.66971	−	5.79291i	−0.391658	−	0.261697i
$491$	4.84934	−	11.7073i	0.218848	−	0.528345i	−0.775882	−	0.630878i	$-0.782695\pi$
$491$	4.84934	−	11.7073i	0.218848	−	0.528345i	0.994730	+	0.102533i	$0.0326948\pi$
$492$	−0.578293	−	0.239986i	−0.0260715	−	0.0108194i
$493$		0			0
$494$			5.55337i			0.249858i
$495$	−13.9440	+	5.75417i	−0.626736	+	0.258631i
$496$	−6.77361	+	10.1374i	−0.304144	+	0.455184i
$497$	−3.31625	+	3.31625i	−0.148754	+	0.148754i
$498$	6.40693	−	32.0987i	0.287101	−	1.43838i
$499$	−20.6206	−	30.8610i	−0.923106	−	1.38153i	−0.924358	−	0.381527i	$-0.875398\pi$
$499$	−20.6206	−	30.8610i	−0.923106	−	1.38153i	0.00125143	−	0.999999i	$-0.499602\pi$
$500$	−0.242054	−	0.0481476i	−0.0108250	−	0.00215323i
$501$	0.0227750	−	34.3988i	0.00101751	−	1.53683i
$502$	−8.43090	−	20.3540i	−0.376290	−	0.908444i
$503$	−6.23297	+	31.3353i	−0.277914	+	1.39717i	0.549460	+	0.835520i	$0.314833\pi$
$503$	−6.23297	+	31.3353i	−0.277914	+	1.39717i	−0.827375	+	0.561650i	$0.810167\pi$
$504$	3.48100	−	17.3799i	0.155056	−	0.774160i
$505$	−11.1913	+	2.22610i	−0.498008	+	0.0990600i
$506$	−1.29976	−	1.29976i	−0.0577812	−	0.0577812i
$507$	6.28480	+	9.41937i	0.279118	+	0.418329i
$508$	−1.33526	−	0.553083i	−0.0592426	−	0.0245391i
$509$	2.30289			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$509$	2.30289			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	−18.7797	−	7.77882i	−0.829954	−	0.343778i
$513$	4.39850	+	0.884001i	0.194198	+	0.0390296i
$514$	20.4697	+	20.4697i	0.902880	+	0.902880i
$515$	27.9345	−	5.55652i	1.23094	−	0.244849i
$516$	0.452505	+	2.28279i	0.0199204	+	0.100494i
$517$	−1.00583	+	5.05666i	−0.0442364	+	0.222391i
$518$	−2.86037	−	6.90554i	−0.125677	−	0.303412i
$519$	20.1546	+	0.0133441i	0.884688	+	0.000585740i
$520$	36.2384	+	7.20827i	1.58916	+	0.316104i
$521$	1.52929	+	2.28875i	0.0669995	+	0.100272i	0.863456	−	0.504423i	$-0.168295\pi$
$521$	1.52929	+	2.28875i	0.0669995	+	0.100272i	−0.796457	+	0.604695i	$0.793295\pi$
$522$	−28.9806	−	19.4198i	−1.26845	−	0.849981i
$523$	29.8001	−	29.8001i	1.30307	−	1.30307i	0.376755	−	0.926313i	$-0.377040\pi$
$523$	29.8001	−	29.8001i	1.30307	−	1.30307i	0.926313	−	0.376755i	$-0.122960\pi$
$524$	−0.229978	+	0.344186i	−0.0100466	+	0.0150358i
$525$	11.3799	+	11.3949i	0.496658	+	0.497316i
$526$		−	0.190778i		−	0.00831830i
$527$		0			0
$528$	4.61767	−	11.1272i	0.200958	−	0.484249i
$529$	−8.57683	+	20.7063i	−0.372906	+	0.900274i
$530$	−23.5114	−	15.7098i	−1.02127	−	0.682390i
$531$	−18.2772	−	0.0242021i	−0.793161	−	0.00105028i
$532$	−0.0426446	−	0.214389i	−0.00184888	−	0.00929494i
$533$	11.3180	−	7.56246i	0.490238	−	0.327566i
$534$	6.77953	−	10.1318i	0.293379	−	0.438444i
$535$	−5.32803	+	2.20694i	−0.230351	+	0.0954144i
$536$	18.2094	−	7.54259i	0.786527	−	0.325790i
$537$	−0.815532	+	1.21878i	−0.0351928	+	0.0525943i
$538$	−7.19347	+	4.80652i	−0.310132	+	0.207224i
$539$	−0.754939	−	3.79534i	−0.0325175	−	0.163477i
$540$	−0.715648	+	1.71807i	−0.0307966	+	0.0739339i
$541$	12.1699	+	8.13164i	0.523223	+	0.349606i	0.788965	−	0.614438i	$-0.210617\pi$
$541$	12.1699	+	8.13164i	0.523223	+	0.349606i	−0.265742	+	0.964044i	$0.585617\pi$
$542$	3.82826	−	9.24223i	0.164438	−	0.396988i
$543$	−0.951908	+	2.29381i	−0.0408503	+	0.0984369i
$544$		0			0
$545$			12.8251i			0.549365i
$546$	−16.9784	−	17.0009i	−0.726610	−	0.727573i
$547$	15.2378	−	22.8049i	0.651520	−	0.975068i	−0.347777	−	0.937577i	$-0.613063\pi$
$547$	15.2378	−	22.8049i	0.651520	−	0.975068i	0.999297	−	0.0374912i	$-0.0119366\pi$
$548$	1.21585	−	1.21585i	0.0519384	−	0.0519384i
$549$	−9.76385	+	14.5708i	−0.416711	+	0.621868i
$550$	5.74287	+	8.59481i	0.244877	+	0.366484i
$551$	6.76737	+	1.34611i	0.288300	+	0.0573464i
$552$	3.63734	+	0.00240823i	0.154816	+	0.000102501i
$553$	−4.91757	−	11.8721i	−0.209116	−	0.504851i
$554$	2.35547	−	11.8417i	0.100074	−	0.503107i
$555$	−2.44751	−	12.3472i	−0.103891	−	0.524109i
$556$	−0.580773	+	0.115523i	−0.0246302	+	0.00489926i
$557$	31.0707	+	31.0707i	1.31651	+	1.31651i	0.916522	+	0.399984i	$0.130984\pi$
$557$	31.0707	+	31.0707i	1.31651	+	1.31651i	0.399984	+	0.916522i	$0.369016\pi$
$558$	12.3702	−	2.44356i	0.523671	−	0.103444i
$559$	−46.7436	−	19.3619i	−1.97705	−	0.818919i
$560$	−27.7789			−1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	33.9044	+	14.0437i	1.42890	+	0.591870i	0.957080	−	0.289825i	$-0.0935970\pi$
$563$	33.9044	+	14.0437i	1.42890	+	0.591870i	0.471821	+	0.881695i	$0.343597\pi$
$564$	0.353059	+	0.529148i	0.0148665	+	0.0222811i
$565$	35.5701	+	35.5701i	1.49645	+	1.49645i
$566$	−20.0274	+	3.98370i	−0.841815	+	0.167448i
$567$	−16.1681	+	10.7414i	−0.678997	+	0.451095i
$568$	1.16213	−	5.84243i	0.0487620	−	0.245143i
$569$	9.46803	+	22.8578i	0.396920	+	0.958251i	0.988392	+	0.151925i	$0.0485472\pi$
$569$	9.46803	+	22.8578i	0.396920	+	0.958251i	−0.591472	+	0.806326i	$0.701453\pi$
$570$	0.00439636	−	6.64016i	0.000184143	−	0.278126i
$571$	1.93303	+	0.384503i	0.0808947	+	0.0160910i	0.235372	−	0.971905i	$-0.424369\pi$
$571$	1.93303	+	0.384503i	0.0808947	+	0.0160910i	−0.154477	+	0.987996i	$0.549369\pi$
$572$	−0.475001	−	0.710889i	−0.0198608	−	0.0297238i
$573$	−0.244453	+	1.22471i	−0.0102122	+	0.0511631i
$574$	−6.83402	+	6.83402i	−0.285247	+	0.285247i
$575$	−1.83601	+	2.74779i	−0.0765671	+	0.114591i
$576$	8.55649	+	20.7348i	0.356520	+	0.863951i
$577$		−	26.8179i		−	1.11645i	−0.829691	−	0.558223i	$-0.811483\pi$
$577$		−	26.8179i		−	1.11645i	0.829691	−	0.558223i	$-0.188517\pi$
$578$		0			0
$579$	18.5917	+	7.71536i	0.772644	+	0.320639i
$580$	−1.09538	+	2.64449i	−0.0454833	+	0.109806i
$581$	−23.2896	−	15.5616i	−0.966214	−	0.645603i
$582$	−8.26247	+	3.41602i	−0.342490	+	0.141599i
$583$	−2.04732	−	10.2926i	−0.0847913	−	0.426275i
$584$	28.6529	−	19.1452i	1.18566	−	0.792235i
$585$	−22.4353	−	33.6733i	−0.927586	−	1.39222i
$586$	35.4995	−	14.7044i	1.46647	−	0.607433i
$587$	−41.3023	+	17.1080i	−1.70473	+	0.706122i	−0.999994	−	0.00334911i	$-0.998934\pi$
$587$	−41.3023	+	17.1080i	−1.70473	+	0.706122i	−0.704735	+	0.709471i	$0.748934\pi$
$588$	−0.396807	−	0.265518i	−0.0163641	−	0.0109498i
$589$	−2.07364	+	1.38557i	−0.0854430	+	0.0570912i
$590$	5.27741	+	26.5313i	0.217268	+	1.09228i
$591$	15.3953	+	37.2374i	0.633280	+	1.53174i
$592$	8.35871	+	5.58511i	0.343541	+	0.229547i
$593$	−8.44534	+	20.3889i	−0.346809	+	0.837270i	0.650184	+	0.759777i	$0.274692\pi$
$593$	−8.44534	+	20.3889i	−0.346809	+	0.837270i	−0.996993	+	0.0774935i	$0.975308\pi$
$594$	−11.5204	+	4.74513i	−0.472689	+	0.194695i
$595$		0			0
$596$			0.738361i			0.0302444i
$597$	−29.5540	+	29.5149i	−1.20956	+	1.20796i
$598$	2.73928	−	4.09963i	0.112018	−	0.167646i
$599$	−16.9345	+	16.9345i	−0.691926	+	0.691926i	−0.962655	−	0.270729i	$-0.912735\pi$
$599$	−16.9345	+	16.9345i	−0.691926	+	0.691926i	0.270729	+	0.962655i	$0.412735\pi$
$600$	−20.0592	−	4.00384i	−0.818914	−	0.163456i
$601$	1.46551	+	2.19329i	0.0597794	+	0.0894662i	0.860155	−	0.510033i	$-0.170367\pi$
$601$	1.46551	+	2.19329i	0.0597794	+	0.0894662i	−0.800376	+	0.599499i	$0.795367\pi$
$602$	35.2329	+	7.00826i	1.43599	+	0.285635i
$603$	−19.9304	−	8.28640i	−0.811630	−	0.337448i
$604$	0.683377	+	1.64982i	0.0278062	+	0.0671302i
$605$	4.93180	−	24.7939i	0.200506	−	1.00801i
$606$	−9.24490	+	1.83256i	−0.375548	+	0.0744428i
$607$	35.5752	−	7.07635i	1.44395	−	0.287220i	0.589930	−	0.807454i	$-0.299155\pi$
$607$	35.5752	−	7.07635i	1.44395	−	0.287220i	0.854024	+	0.520234i	$0.174155\pi$
$608$	0.404887	+	0.404887i	0.0164203	+	0.0164203i
$609$	−24.8329	+	16.5691i	−1.00628	+	0.671412i
$610$	23.9836	+	9.93432i	0.971066	+	0.402229i
$611$	−13.8296			−0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	32.8447	+	13.6047i	1.32550	+	0.549041i
$615$	−13.5389	+	9.03346i	−0.545942	+	0.364264i
$616$	−6.88440	−	6.88440i	−0.277380	−	0.277380i
$617$	9.68025	−	1.92552i	0.389712	−	0.0775186i	0.00365472	−	0.999993i	$-0.498837\pi$
$617$	9.68025	−	1.92552i	0.389712	−	0.0775186i	0.386057	+	0.922475i	$0.373837\pi$
$618$	23.0760	−	4.57422i	0.928253	−	0.184002i
$619$	−6.30326	+	31.6886i	−0.253349	+	1.27367i	0.619233	+	0.785207i	$0.287443\pi$
$619$	−6.30326	+	31.6886i	−0.253349	+	1.27367i	−0.872583	+	0.488466i	$0.837557\pi$
$620$	−0.395921	−	0.955837i	−0.0159006	−	0.0383873i
$621$	−2.81102	−	2.82221i	−0.112802	−	0.113251i
$622$	33.3044	+	6.62467i	1.33539	+	0.265625i
$623$	−5.79580	−	8.67402i	−0.232204	−	0.347517i
$624$	31.6904	+	6.32543i	1.26863	+	0.253220i
$625$	−19.7780	+	19.7780i	−0.791122	+	0.791122i
$626$	1.30530	−	1.95352i	0.0521704	−	0.0780785i
$627$	1.74369	−	1.74138i	0.0696362	−	0.0695441i
$628$			0.289721i			0.0115611i
$629$		0			0
$630$	20.2876	+	20.3414i	0.808279	+	0.810422i
$631$	1.47845	−	3.56930i	0.0588563	−	0.142092i	−0.891716	−	0.452596i	$-0.850498\pi$
$631$	1.47845	−	3.56930i	0.0588563	−	0.142092i	0.950572	+	0.310504i	$0.100498\pi$
$632$	13.5711	+	9.06791i	0.539829	+	0.360702i
$633$	−10.3302	−	24.9860i	−0.410587	−	0.993104i
$634$	6.92242	+	34.8014i	0.274925	+	1.38214i
$635$	−31.2385	+	20.8729i	−1.23966	+	0.828316i
$636$	−1.07610	−	0.720059i	−0.0426702	−	0.0285522i
$637$	9.58987	−	3.97225i	0.379964	−	0.157386i
$638$	−17.7033	+	7.33297i	−0.700882	+	0.290315i
$639$	−5.42887	+	3.61706i	−0.214763	+	0.143089i
$640$	30.9690	−	20.6928i	1.22416	−	0.817955i
$641$	7.30038	+	36.7015i	0.288348	+	1.44962i	0.804922	+	0.593380i	$0.202207\pi$
$641$	7.30038	+	36.7015i	0.288348	+	1.44962i	−0.516575	+	0.856242i	$0.672793\pi$
$642$	−4.40198	+	1.81995i	−0.173732	+	0.0718276i
$643$	35.3195	+	23.5997i	1.39286	+	0.930682i	0.999938	+	0.0111111i	$0.00353683\pi$
$643$	35.3195	+	23.5997i	1.39286	+	0.930682i	0.392925	+	0.919570i	$0.371463\pi$
$644$	−0.0742693	+	0.179302i	−0.00292662	+	0.00706549i
$645$	55.8760	+	23.1879i	2.20011	+	0.913024i
$646$		0			0
$647$		−	48.3331i		−	1.90017i	−0.311989	−	0.950086i	$-0.600995\pi$
$647$		−	48.3331i		−	1.90017i	0.311989	−	0.950086i	$-0.399005\pi$
$648$	9.49533	−	22.7531i	0.373012	−	0.893828i
$649$	−5.57753	+	8.34737i	−0.218937	+	0.327663i
$650$	−19.6063	+	19.6063i	−0.769023	+	0.769023i
$651$	2.11208	−	10.5815i	0.0827790	−	0.414723i
$652$	−0.0724451	−	0.108422i	−0.00283717	−	0.00424613i
$653$	−6.34586	−	1.26227i	−0.248333	−	0.0493965i	0.0693542	−	0.997592i	$-0.477906\pi$
$653$	−6.34586	−	1.26227i	−0.248333	−	0.0493965i	−0.317687	+	0.948196i	$0.602906\pi$
$654$	−0.00701353	+	10.5931i	−0.000274251	+	0.414222i
$655$	4.11794	+	9.94158i	0.160901	+	0.388450i
$656$	2.53593	−	12.7490i	0.0990114	−	0.497764i
$657$	−37.0033	−	7.41136i	−1.44364	−	0.289145i
$658$	9.63056	−	1.91564i	0.375439	−	0.0746794i
$659$	17.7005	+	17.7005i	0.689515	+	0.689515i	0.962125	−	0.272610i	$-0.0878869\pi$
$659$	17.7005	+	17.7005i	0.689515	+	0.689515i	−0.272610	+	0.962125i	$0.587887\pi$
$660$	0.567395	+	0.850385i	0.0220858	+	0.0331012i
$661$	23.0223	+	9.53615i	0.895464	+	0.370913i	0.782474	−	0.622683i	$-0.213957\pi$
$661$	23.0223	+	9.53615i	0.895464	+	0.370913i	0.112990	+	0.993596i	$0.463957\pi$
$662$	44.3302			1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	−5.24974	−	2.17451i	−0.203576	−	0.0843240i
$666$	−2.01481	−	10.1997i	−0.0780723	−	0.395231i
$667$	−4.33184	−	4.33184i	−0.167729	−	0.167729i
$668$	−2.28645	+	0.454802i	−0.0884652	+	0.0175968i
$669$	−0.819081	−	4.13210i	−0.0316675	−	0.159756i
$670$	−6.23235	+	31.3321i	−0.240777	+	1.21047i
$671$	3.68686	+	8.90086i	0.142329	+	0.343614i
$672$	−2.47738	−	0.00164024i	−0.0955670	−	6.32736e-5i
$673$	18.4220	+	3.66436i	0.710115	+	0.141251i	0.536915	−	0.843636i	$-0.319589\pi$
$673$	18.4220	+	3.66436i	0.710115	+	0.141251i	0.173200	+	0.984887i	$0.444589\pi$
$674$	−13.9259	−	20.8416i	−0.536405	−	0.802787i
$675$	12.4080	+	18.6500i	0.477584	+	0.717838i
$676$	0.542640	−	0.542640i	0.0208708	−	0.0208708i
$677$	5.50607	−	8.24041i	0.211615	−	0.316705i	−0.710444	−	0.703754i	$-0.751506\pi$
$677$	5.50607	−	8.24041i	0.211615	−	0.316705i	0.922059	+	0.387049i	$0.126506\pi$
$678$	29.3603	+	29.3992i	1.12758	+	1.12907i
$679$			7.65102i			0.293619i
$680$		0			0
$681$	−0.932371	+	2.24673i	−0.0357285	+	0.0860950i
$682$	2.65046	−	6.39878i	0.101491	−	0.245022i
$683$	−1.98540	−	1.32660i	−0.0759692	−	0.0507610i	0.517006	−	0.855982i	$-0.327047\pi$
$683$	−1.98540	−	1.32660i	−0.0759692	−	0.0507610i	−0.592975	+	0.805221i	$0.702047\pi$
$684$	0.000402615	−	0.304050i	1.53944e−5	−	0.0116257i
$685$	−8.72013	−	43.8391i	−0.333179	−	1.67500i
$686$	−24.3941	+	16.2996i	−0.931370	+	0.622322i
$687$	−10.4768	+	15.6572i	−0.399714	+	0.597358i
$688$	−44.6375	+	18.4895i	−1.70179	+	0.704905i
$689$	26.0068	−	10.7724i	0.990779	−	0.410394i
$690$	−3.27860	+	4.89975i	−0.124814	+	0.186530i
$691$	−27.1095	+	18.1140i	−1.03129	+	0.689088i	−0.951476	−	0.307722i	$-0.900433\pi$
$691$	−27.1095	+	18.1140i	−1.03129	+	0.689088i	−0.0798165	+	0.996810i	$0.525433\pi$
$692$	−0.266473	−	1.33965i	−0.0101298	−	0.0509258i
$693$	−0.0141184	+	10.6620i	−0.000536313	+	0.405017i
$694$	−24.4818	−	16.3582i	−0.929315	−	0.620948i
$695$	−5.89068	+	14.2214i	−0.223446	+	0.539447i
$696$	14.5338	−	35.0222i	0.550904	−	1.32751i
$697$		0			0
$698$		−	11.0631i		−	0.418743i
$699$	17.5466	+	17.5698i	0.663673	+	0.664552i
$700$	0.606348	−	0.907464i	0.0229178	−	0.0342989i
$701$	31.7150	−	31.7150i	1.19786	−	1.19786i	0.223051	−	0.974807i	$-0.428398\pi$
$701$	31.7150	−	31.7150i	1.19786	−	1.19786i	0.974807	−	0.223051i	$-0.0716016\pi$
$702$	−18.5124	−	27.8253i	−0.698706	−	1.05020i
$703$	1.14245	+	1.70980i	0.0430885	+	0.0644864i
$704$	12.0841	+	2.40368i	0.455437	+	0.0905921i
$705$	16.5361	+	0.0109483i	0.622784	+	0.000412337i
$706$	6.64926	+	16.0527i	0.250248	+	0.604153i
$707$	−1.57344	+	7.91022i	−0.0591753	+	0.297495i
$708$	0.240846	+	1.21502i	0.00905156	+	0.0456633i
$709$	−38.7263	+	7.70314i	−1.45440	+	0.289297i	−0.858106	−	0.513472i	$-0.828359\pi$
$709$	−38.7263	+	7.70314i	−1.45440	+	0.289297i	−0.596290	+	0.802769i	$0.703359\pi$
$710$	6.82716	+	6.82716i	0.256219	+	0.256219i
$711$	−3.46388	−	17.5354i	−0.129906	−	0.657629i
$712$	12.2419	+	5.07074i	0.458783	+	0.190034i
$713$	2.21426			0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	0.0918186	+	0.0380325i	0.00343142	+	0.00142134i
$717$	−22.7922	−	34.1599i	−0.851191	−	1.27573i
$718$	−23.6628	−	23.6628i	−0.883086	−	0.883086i
$719$	43.1030	−	8.57373i	1.60747	−	0.319746i	0.691929	−	0.721966i	$-0.256761\pi$
$719$	43.1030	−	8.57373i	1.60747	−	0.319746i	0.915543	+	0.402220i	$0.131761\pi$
$720$	−37.8871	−	7.58839i	−1.41197	−	0.282803i
$721$	3.92744	−	19.7446i	0.146265	−	0.735326i
$722$	−10.1650	−	24.5406i	−0.378304	−	0.913307i
$723$	−0.00322743	+	4.87465i	−0.000120030	+	0.181290i
$724$	0.165074	+	0.0328353i	0.00613493	+	0.00122031i
$725$	19.1399	+	28.6448i	0.710837	+	1.06384i
$726$	4.08707	−	20.4762i	0.151685	−	0.759943i
$727$	−0.0802760	+	0.0802760i	−0.00297727	+	0.00297727i	−0.708594	−	0.705617i	$-0.750670\pi$
$727$	−0.0802760	+	0.0802760i	−0.00297727	+	0.00297727i	0.705617	+	0.708594i	$0.250670\pi$
$728$	14.5091	−	21.7144i	0.537744	−	0.804790i
$729$	−24.9856	+	10.2333i	−0.925392	+	0.379010i
$730$			55.8544i			2.06726i
$731$		0			0
$732$	1.09790	+	0.455616i	0.0405795	+	0.0168400i
$733$	3.12587	−	7.54651i	0.115457	−	0.278737i	−0.855579	−	0.517673i	$-0.826799\pi$
$733$	3.12587	−	7.54651i	0.115457	−	0.278737i	0.971035	+	0.238936i	$0.0767986\pi$
$734$	19.8549	+	13.2667i	0.732860	+	0.489681i
$735$	−11.4697	+	4.74203i	−0.423068	+	0.174912i
$736$	−0.0991804	−	0.498613i	−0.00365584	−	0.0183791i
$737$	−9.85781	+	6.58678i	−0.363117	+	0.242627i
$738$	−11.1876	+	7.45394i	−0.411823	+	0.274383i
$739$	10.8531	−	4.49550i	0.399237	−	0.165370i	−0.174025	−	0.984741i	$-0.555677\pi$
$739$	10.8531	−	4.49550i	0.399237	−	0.165370i	0.573263	+	0.819372i	$0.305677\pi$
$740$	−0.788126	+	0.326452i	−0.0289721	+	0.0120006i
$741$	5.49379	+	3.67610i	0.201819	+	0.135045i
$742$	−16.6182	+	11.1039i	−0.610074	+	0.407639i
$743$	8.00737	+	40.2557i	0.293762	+	1.47684i	0.792385	+	0.610021i	$0.208839\pi$
$743$	8.00737	+	40.2557i	0.293762	+	1.47684i	−0.498623	+	0.866819i	$0.666161\pi$
$744$	5.23642	+	12.6655i	0.191976	+	0.464341i
$745$	15.9591	+	10.6635i	0.584697	+	0.390682i
$746$	−0.901121	+	2.17550i	−0.0329924	+	0.0796507i
$747$	−27.5132	−	27.5862i	−1.00666	−	1.00933i
$748$		0			0
$749$			4.07622i			0.148942i
$750$	−3.74945	+	3.74449i	−0.136911	+	0.136730i
$751$	−0.938366	+	1.40436i	−0.0342414	+	0.0512460i	−0.848195	−	0.529683i	$-0.822311\pi$
$751$	−0.938366	+	1.40436i	−0.0342414	+	0.0512460i	0.813954	+	0.580929i	$0.197311\pi$
$752$	−9.33841	+	9.33841i	−0.340537	+	0.340537i
$753$	−25.7165	−	5.13303i	−0.937162	−	0.187058i
$754$	−28.5562	−	42.7373i	−1.03995	−	1.55640i
$755$	45.5290	+	9.05629i	1.65697	+	0.329592i
$756$	0.928347	+	0.932042i	0.0337637	+	0.0338980i
$757$	20.8300	+	50.2881i	0.757080	+	1.82775i	0.514126	+	0.857715i	$0.328116\pi$
$757$	20.8300	+	50.2881i	0.757080	+	1.82775i	0.242954	+	0.970038i	$0.421884\pi$
$758$	4.40851	−	22.1631i	0.160124	−	0.805000i
$759$	−2.14619	+	0.425427i	−0.0779019	+	0.0154420i
$760$	7.07871	−	1.40804i	0.256772	−	0.0510751i
$761$	−24.1395	−	24.1395i	−0.875055	−	0.875055i	0.117963	−	0.993018i	$-0.462364\pi$
$761$	−24.1395	−	24.1395i	−0.875055	−	0.875055i	−0.993018	+	0.117963i	$0.962364\pi$
$762$	−25.8134	+	17.2233i	−0.935121	+	0.623933i
$763$	8.37493	+	3.46901i	0.303193	+	0.125587i
$764$	0.0846370			0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	−24.8794	−	10.3054i	−0.898343	−	0.372106i
$768$	4.04525	−	2.69907i	0.145970	−	0.0973944i
$769$	31.3211	+	31.3211i	1.12947	+	1.12947i	0.990264	+	0.139204i	$0.0444544\pi$
$769$	31.3211	+	31.3211i	1.12947	+	1.12947i	0.139204	+	0.990264i	$0.455546\pi$
$770$	15.4771	−	3.07859i	0.557757	−	0.110945i
$771$	33.8002	−	6.70001i	1.21728	−	0.241295i
$772$	0.266135	−	1.33795i	0.00957840	−	0.0481539i
$773$	5.31114	+	12.8222i	0.191028	+	0.461184i	0.990154	−	0.139980i	$-0.0447039\pi$
$773$	5.31114	+	12.8222i	0.191028	+	0.461184i	−0.799126	+	0.601164i	$0.794704\pi$
$774$	46.1390	+	19.1830i	1.65843	+	0.689520i
$775$	−12.2128	−	2.42928i	−0.438698	−	0.0872624i
$776$	−5.39903	−	8.08023i	−0.193814	−	0.290063i
$777$	−8.72489	−	1.74150i	−0.313004	−	0.0624758i
$778$	15.6099	−	15.6099i	0.559643	−	0.559643i
$779$	1.47723	−	2.21083i	0.0529272	−	0.0792111i
$780$	−1.94031	+	1.93774i	−0.0694742	+	0.0693822i
$781$			3.58322i			0.128218i
$782$		0			0
$783$	−38.3954	+	15.8146i	−1.37214	+	0.565168i
$784$	3.79328	−	9.15778i	0.135474	−	0.327064i
$785$	6.26211	+	4.18421i	0.223504	+	0.149341i
$786$	3.39584	+	8.21367i	0.121126	+	0.292972i
$787$	4.67010	+	23.4782i	0.166471	+	0.836907i	0.970274	+	0.242011i	$0.0778069\pi$
$787$	4.67010	+	23.4782i	0.166471	+	0.836907i	−0.803802	+	0.594896i	$0.797193\pi$
$788$	2.27057	−	1.51714i	0.0808856	−	0.0540460i
$789$	−0.188731	−	0.126287i	−0.00671899	−	0.00449593i
$790$	−24.4410	+	10.1238i	−0.869572	+	0.360189i
$791$	32.8490	−	13.6065i	1.16798	−	0.483792i
$792$	−7.50888	−	11.2701i	−0.266817	−	0.400466i
$793$	−21.4874	+	14.3574i	−0.763040	+	0.509847i
$794$	−10.6845	−	53.7144i	−0.379178	−	1.90625i
$795$	−31.1048	+	12.8599i	−1.10317	+	0.456094i
$796$	2.35361	+	1.57263i	0.0834213	+	0.0557403i
$797$	17.9210	−	43.2651i	0.634795	−	1.53253i	−0.198734	−	0.980053i	$-0.563683\pi$
$797$	17.9210	−	43.2651i	0.634795	−	1.53253i	0.833529	−	0.552476i	$-0.186317\pi$
$798$	−4.33492	−	1.79895i	−0.153455	−	0.0636820i
$799$		0			0
$800$			2.85893i			0.101078i
$801$	−5.53529	−	13.4136i	−0.195580	−	0.473945i
$802$	2.85685	−	4.27557i	0.100879	−	0.150976i
$803$	−14.6575	+	14.6575i	−0.517252	+	0.517252i
$804$	−0.286327	+	1.43450i	−0.0100980	+	0.0505909i
$805$	2.80287	+	4.19478i	0.0987880	+	0.147847i
$806$	18.2212	+	3.62442i	0.641814	+	0.127665i
$807$	−0.00681816	+	10.2980i	−0.000240011	+	0.362507i
$808$	−3.92024	−	9.46429i	−0.137913	−	0.332952i
$809$	−2.28565	+	11.4907i	−0.0803592	+	0.403993i	0.919579	+	0.392904i	$0.128530\pi$
$809$	−2.28565	+	11.4907i	−0.0803592	+	0.403993i	−0.999939	+	0.0110886i	$0.996470\pi$
$810$	22.1132	+	33.2853i	0.776980	+	1.16953i
$811$	18.4661	−	3.67314i	0.648434	−	0.128982i	0.140094	−	0.990138i	$-0.455259\pi$
$811$	18.4661	−	3.67314i	0.648434	−	0.128982i	0.508340	+	0.861157i	$0.330259\pi$
$812$	1.43060	+	1.43060i	0.0502042	+	0.0502042i
$813$	−6.60892	−	9.90514i	−0.231785	−	0.347389i
$814$	−5.27605	−	2.18541i	−0.184926	−	0.0765987i
$815$	−3.38972			−0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	−16.4118	−	6.79797i	−0.573824	−	0.237686i
$819$	−28.0575	+	5.54238i	−0.980410	+	0.193666i
$820$	0.779963	+	0.779963i	0.0272375	+	0.0272375i
$821$	−29.7119	+	5.91006i	−1.03695	+	0.206263i	−0.684079	−	0.729408i	$-0.739795\pi$
$821$	−29.7119	+	5.91006i	−1.03695	+	0.206263i	−0.352874	+	0.935671i	$0.614795\pi$
$822$	−7.17857	−	36.2144i	−0.250381	−	1.26312i
$823$	−4.47717	+	22.5083i	−0.156064	+	0.784589i	0.820881	+	0.571099i	$0.193483\pi$
$823$	−4.47717	+	22.5083i	−0.156064	+	0.784589i	−0.976945	+	0.213489i	$0.931517\pi$
$824$	9.78523	+	23.6236i	0.340884	+	0.822968i
$825$	12.3041	+	0.00814639i	0.428375	+	0.000283621i
$826$	18.7528	+	3.73016i	0.652493	+	0.129789i
$827$	9.72768	+	14.5585i	0.338265	+	0.506249i	0.961136	−	0.276076i	$-0.0890340\pi$
$827$	9.72768	+	14.5585i	0.338265	+	0.506249i	−0.622871	+	0.782324i	$0.714034\pi$
$828$	−0.150275	+	0.224258i	−0.00522240	+	0.00779351i
$829$	−31.1358	+	31.1358i	−1.08139	+	1.08139i	−0.0850121	+	0.996380i	$0.527093\pi$
$829$	−31.1358	+	31.1358i	−1.08139	+	1.08139i	−0.996380	+	0.0850121i	$0.972907\pi$
$830$	−32.0366	+	47.9462i	−1.11201	+	1.66424i
$831$	−10.1555	−	10.1689i	−0.352289	−	0.352756i
$832$			33.0493i			1.14578i
$833$		0			0
$834$	−4.87328	+	11.7432i	−0.168748	+	0.406632i
$835$	−23.1910	+	55.9881i	−0.802559	+	1.93755i
$836$	−0.138863	−	0.0927852i	−0.00480267	−	0.00320904i
$837$	5.77119	−	13.8550i	0.199481	−	0.478898i
$838$	−8.91178	−	44.8026i	−0.307852	−	1.54768i
$839$	16.4446	−	10.9879i	0.567731	−	0.379346i	−0.238325	−	0.971186i	$-0.576598\pi$
$839$	16.4446	−	10.9879i	0.567731	−	0.379346i	0.806056	+	0.591840i	$0.201598\pi$
$840$	−17.3657	+	25.9524i	−0.599174	+	0.895444i
$841$	−32.2093	+	13.3415i	−1.11067	+	0.460053i
$842$	−20.3896	+	8.44564i	−0.702671	+	0.291056i
$843$	−12.7624	+	19.0730i	−0.439561	+	0.656908i
$844$	−1.52353	+	1.01799i	−0.0524422	+	0.0350407i
$845$	−3.89185	−	19.5656i	−0.133884	−	0.673078i
$846$	13.6582	+	0.0180859i	0.469580	+	0.000621805i
$847$	−14.8567	−	9.92694i	−0.510483	−	0.341094i
$848$	10.2870	−	24.8350i	0.353257	−	0.852837i
$849$	−9.31634	+	22.4496i	−0.319736	+	0.770468i
$850$		0			0
$851$		−	1.82575i		−	0.0625858i
$852$	0.312406	+	0.312820i	0.0107029	+	0.0107170i
$853$	−3.43080	+	5.13456i	−0.117469	+	0.175804i	−0.885544	−	0.464555i	$-0.846214\pi$
$853$	−3.43080	+	5.13456i	−0.117469	+	0.175804i	0.768076	+	0.640359i	$0.221214\pi$
$854$	12.9745	−	12.9745i	0.443977	−	0.443977i
$855$	−6.56600	−	4.39985i	−0.224553	−	0.150472i
$856$	−2.87643	−	4.30489i	−0.0983145	−	0.147138i
$857$	−25.5035	−	5.07296i	−0.871184	−	0.173289i	−0.260798	−	0.965393i	$-0.583986\pi$
$857$	−25.5035	−	5.07296i	−0.871184	−	0.173289i	−0.610386	+	0.792104i	$0.708986\pi$
$858$	−18.3574	−	0.0121542i	−0.626712	−	0.000414937i
$859$	1.25664	+	3.03380i	0.0428761	+	0.103512i	0.943867	−	0.330326i	$-0.107159\pi$
$859$	1.25664	+	3.03380i	0.0428761	+	0.103512i	−0.900991	+	0.433838i	$0.857159\pi$
$860$	0.799849	−	4.02111i	0.0272746	−	0.137119i
$861$	2.23687	+	11.2845i	0.0762322	+	0.384576i
$862$	−16.3462	+	3.25147i	−0.556755	+	0.110745i
$863$	−10.3922	−	10.3922i	−0.353754	−	0.353754i	0.507750	−	0.861504i	$-0.330477\pi$
$863$	−10.3922	−	10.3922i	−0.353754	−	0.353754i	−0.861504	+	0.507750i	$0.830477\pi$
$864$	−3.37840	−	0.678985i	−0.114936	−	0.0230995i
$865$	−32.8040	−	13.5878i	−1.11537	−	0.462000i
$866$	−38.9856			−1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	−9.07062	−	3.75718i	−0.307700	−	0.127453i
$870$	34.1107	+	51.1236i	1.15646	+	1.73325i
$871$	−22.4875	−	22.4875i	−0.761958	−	0.761958i
$872$	−11.2927	+	2.24626i	−0.382419	+	0.0760679i
$873$	−2.09003	+	10.4351i	−0.0707370	+	0.353174i
$874$	0.187896	−	0.944618i	0.00635569	−	0.0319522i
$875$	1.73532	+	4.18943i	0.0586644	+	0.141629i
$876$	−0.00169332	+	2.55755i	−5.72119e−5	+	0.0864117i
$877$	13.0801	+	2.60180i	0.441684	+	0.0878565i	0.410923	−	0.911670i	$-0.365207\pi$
$877$	13.0801	+	2.60180i	0.441684	+	0.0878565i	0.0307618	+	0.999527i	$0.490207\pi$
$878$	6.89290	+	10.3160i	0.232624	+	0.348146i
$879$	8.95256	−	44.8523i	0.301962	−	1.51283i
$880$	−15.0076	+	15.0076i	−0.505907	+	0.505907i
$881$	10.9553	−	16.3958i	0.369094	−	0.552389i	−0.599709	−	0.800218i	$-0.704717\pi$
$881$	10.9553	−	16.3958i	0.369094	−	0.552389i	0.968804	+	0.247829i	$0.0797172\pi$
$882$	−9.47622	+	3.91048i	−0.319081	+	0.131673i
$883$			44.5932i			1.50068i	0.661051	+	0.750341i	$0.270111\pi$
$883$			44.5932i			1.50068i	−0.661051	+	0.750341i	$0.729889\pi$
$884$		0			0
$885$	29.7401	+	12.3418i	0.999702	+	0.414866i
$886$	10.5118	−	25.3778i	0.353152	−	0.852584i
$887$	13.8993	+	9.28722i	0.466693	+	0.311834i	0.766590	−	0.642137i	$-0.221952\pi$
$887$	13.8993	+	9.28722i	0.466693	+	0.311834i	−0.299896	+	0.953972i	$0.596952\pi$
$888$	10.4432	−	4.31764i	0.350452	−	0.144890i
$889$	5.18067	+	26.0450i	0.173754	+	0.873522i
$890$	−17.8572	+	11.9318i	−0.598575	+	0.399955i
$891$	−2.93181	+	14.5379i	−0.0982194	+	0.487038i
$892$	−0.263753	+	0.109250i	−0.00883111	+	0.00365797i
$893$	−2.49580	+	1.03380i	−0.0835189	+	0.0345947i
$894$	13.1759	+	8.81646i	0.440667	+	0.294866i
$895$	2.14810	−	1.43532i	0.0718032	−	0.0479773i
$896$	−5.13597	−	25.8203i	−0.171581	−	0.862594i
$897$	−2.24235	−	5.42367i	−0.0748699	−	0.181091i
$898$	32.9873	+	22.0414i	1.10080	+	0.735532i
$899$	8.83348	−	21.3259i	0.294613	−	0.711259i
$900$	1.07488	−	1.07204i	0.0358293	−	0.0357345i
$901$		0			0
$902$			7.38418i			0.245866i
$903$	30.2557	−	30.2157i	1.00685	−	1.00552i
$904$	−25.0902	+	37.5501i	−0.834487	+	1.24890i
$905$	3.09374	−	3.09374i	0.102839	−	0.102839i
$906$	37.6005	+	7.50509i	1.24919	+	0.249340i
$907$	5.11877	+	7.66078i	0.169966	+	0.254372i	0.906668	−	0.421846i	$-0.138618\pi$
$907$	5.11877	+	7.66078i	0.169966	+	0.254372i	−0.736702	+	0.676218i	$0.763618\pi$
$908$	0.161686	+	0.0321614i	0.00536574	+	0.00106731i
$909$	−4.30683	+	10.3588i	−0.142848	+	0.343579i
$910$	16.1986	+	39.1068i	0.536978	+	1.29638i
$911$	0.391215	−	1.96677i	0.0129615	−	0.0651621i	−0.973763	−	0.227564i	$-0.926924\pi$
$911$	0.391215	−	1.96677i	0.0129615	−	0.0651621i	0.986725	+	0.162402i	$0.0519240\pi$
$912$	6.19194	−	1.22739i	0.205036	−	0.0406430i
$913$	−20.9894	+	4.17505i	−0.694648	+	0.138174i
$914$	10.8464	+	10.8464i	0.358768	+	0.358768i
$915$	25.7038	−	17.1501i	0.849742	−	0.566966i
$916$	1.17955	+	0.488587i	0.0389735	+	0.0161434i
$917$	7.60583			0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	−5.92020	−	2.45223i	−0.195183	−	0.0808475i
$921$	35.2005	−	23.4865i	1.15990	−	0.773907i
$922$	−10.1727	−	10.1727i	−0.335021	−	0.335021i
$923$	−9.42688	+	1.87512i	−0.310290	+	0.0617204i
$924$	0.708785	−	0.140498i	0.0233173	−	0.00462206i
$925$	−2.00304	+	10.0700i	−0.0658595	+	0.331098i
$926$	12.7673	+	30.8229i	0.419558	+	1.01290i
$927$	10.7502	−	25.8564i	0.353083	−	0.849234i
$928$	−5.19789	−	1.03392i	−0.170629	−	0.0339402i
$929$	13.5854	+	20.3321i	0.445724	+	0.667073i	0.984502	−	0.175375i	$-0.0561137\pi$
$929$	13.5854	+	20.3321i	0.445724	+	0.667073i	−0.538778	+	0.842448i	$0.681114\pi$
$930$	−21.7842	−	4.34814i	−0.714332	−	0.142581i
$931$	1.43373	−	1.43373i	0.0469885	−	0.0469885i
$932$	0.934927	−	1.39922i	0.0306245	−	0.0458329i
$933$	28.5997	−	28.5619i	0.936312	−	0.935073i
$934$		−	37.6099i		−	1.23063i
$935$		0			0
$936$	25.7205	−	25.6524i	0.840699	−	0.838476i
$937$	19.3663	−	46.7545i	0.632671	−	1.52740i	−0.203582	−	0.979058i	$-0.565258\pi$
$937$	19.3663	−	46.7545i	0.632671	−	1.52740i	0.836252	−	0.548345i	$-0.184742\pi$
$938$	18.7745	+	12.5447i	0.613010	+	0.409600i
$939$	−1.06851	−	2.58445i	−0.0348695	−	0.0843403i
$940$	−0.218631	−	1.09913i	−0.00713095	−	0.0358497i
$941$	−2.99651	+	2.00221i	−0.0976836	+	0.0652701i	−0.603453	−	0.797399i	$-0.706209\pi$
$941$	−2.99651	+	2.00221i	−0.0976836	+	0.0652701i	0.505769	+	0.862669i	$0.331209\pi$
$942$	5.17001	+	3.45944i	0.168448	+	0.112715i
$943$	−2.18105	+	0.903419i	−0.0710246	+	0.0294194i
$944$	−23.7584	+	9.84105i	−0.773270	+	0.320299i
$945$	33.5527	−	6.60480i	1.09147	−	0.214854i
$946$	22.8209	−	15.2484i	0.741970	−	0.495769i
$947$	−5.22957	−	26.2908i	−0.169938	−	0.854336i	−0.967843	−	0.251554i	$-0.919059\pi$
$947$	−5.22957	−	26.2908i	−0.169938	−	0.854336i	0.797905	−	0.602783i	$-0.205941\pi$
$948$	−1.11945	+	0.462824i	−0.0363581	+	0.0150318i
$949$	−46.2320	−	30.8912i	−1.50075	−	1.00277i
$950$	−2.07269	+	5.00393i	−0.0672471	+	0.162349i
$951$	39.0103	+	16.1889i	1.26500	+	0.524960i
$952$		0			0
$953$		−	24.2594i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$	−25.6985	+	10.6048i	−0.832021	+	0.343344i
$955$	1.22234	−	1.82937i	0.0395541	−	0.0591969i
$956$	−1.96792	+	1.96792i	−0.0636470	+	0.0636470i
$957$	−4.46457	+	22.3675i	−0.144319	+	0.723039i
$958$	7.00474	+	10.4833i	0.226313	+	0.338701i
$959$	−30.9862	−	6.16353i	−1.00060	−	0.199031i
$960$	0.0261636	−	39.5170i	0.000844428	−	1.27541i
$961$	−8.67037	−	20.9321i	−0.279689	−	0.675230i
$962$	2.98848	−	15.0241i	0.0963525	−	0.484397i
$963$	−1.11350	+	5.55948i	−0.0358822	+	0.179152i
$964$	0.324012	−	0.0644499i	0.0104357	−	0.00207579i
$965$	−25.0752	−	25.0752i	−0.807200	−	0.807200i
$966$	2.31278	+	3.46629i	0.0744125	+	0.111526i
$967$	12.2636	+	5.07976i	0.394372	+	0.163354i	0.571051	−	0.820914i	$-0.306536\pi$
$967$	12.2636	+	5.07976i	0.394372	+	0.163354i	−0.176680	+	0.984268i	$0.556536\pi$
$968$	22.6952			0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	14.2905	+	5.91933i	0.458605	+	0.189960i	0.600012	−	0.799991i	$-0.295163\pi$
$971$	14.2905	+	5.91933i	0.458605	+	0.189960i	−0.141407	+	0.989952i	$0.545163\pi$
$972$	1.01155	+	1.52479i	0.0324454	+	0.0489077i
$973$	7.69338	+	7.69338i	0.246638	+	0.246638i
$974$	−55.3982	+	11.0194i	−1.77507	+	0.353084i
$975$	6.41741	+	32.3745i	0.205522	+	1.03681i
$976$	−4.81450	+	24.2041i	−0.154108	+	0.774755i
$977$	−7.72995	−	18.6618i	−0.247303	−	0.597042i	0.750670	−	0.660677i	$-0.229731\pi$
$977$	−7.72995	−	18.6618i	−0.247303	−	0.597042i	−0.997973	+	0.0636347i	$0.979731\pi$
$978$	−2.79980	−	0.00185371i	−0.0895277	−	5.92750e-5i
$979$	−7.81735	−	1.55497i	−0.249844	−	0.0496970i
$980$	0.467306	+	0.699373i	0.0149275	+	0.0223406i
$981$	10.4748	+	7.01910i	0.334434	+	0.224103i
$982$	−13.0385	+	13.0385i	−0.416075	+	0.416075i
$983$	14.4927	−	21.6898i	0.462244	−	0.691797i	−0.524984	−	0.851112i	$-0.675929\pi$
$983$	14.4927	−	21.6898i	0.462244	−	0.691797i	0.987228	+	0.159315i	$0.0509286\pi$
$984$	−10.3254	−	10.3391i	−0.329162	−	0.329598i
$985$		−	70.9874i		−	2.26185i
$986$		0			0
$987$	4.47994	−	10.7953i	0.142598	−	0.343618i
$988$	0.171435	−	0.413882i	0.00545409	−	0.0131673i
$989$	7.29590	+	4.87497i	0.231996	+	0.155015i
$990$	21.9499	+	0.0290655i	0.697615	+	0.000923762i
$991$	−7.04470	−	35.4161i	−0.223782	−	1.12503i	−0.915332	−	0.402701i	$-0.868072\pi$
$991$	−7.04470	−	35.4161i	−0.223782	−	1.12503i	0.691549	−	0.722329i	$-0.256928\pi$
$992$	1.59273	−	1.06423i	0.0505692	−	0.0337892i
$993$	29.3447	−	43.8545i	0.931225	−	1.39168i
$994$	6.30488	−	2.61157i	0.199979	−	0.0828339i
$995$	67.9824	−	28.1592i	2.15519	−	0.892707i
$996$	−1.46840	+	2.19447i	−0.0465280	+	0.0695344i
$997$	−12.2838	+	8.20777i	−0.389032	+	0.259943i	−0.734669	−	0.678425i	$-0.762663\pi$
$997$	−12.2838	+	8.20777i	−0.389032	+	0.259943i	0.345638	+	0.938368i	$0.387663\pi$
$998$	10.5365	+	52.9708i	0.333529	+	1.67676i
$999$	−11.4240	−	4.75858i	−0.361439	−	0.150555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.c.653.1		32
3.2	odd	2	inner	867.2.i.c.653.4		32
17.2	even	8		867.2.i.b.827.4		32
17.3	odd	16		51.2.i.a.29.1	✓	32
17.4	even	4		867.2.i.h.503.4		32
17.5	odd	16	inner	867.2.i.c.158.4		32
17.6	odd	16		867.2.i.i.65.1		32
17.7	odd	16		867.2.i.f.224.4		32
17.8	even	8		867.2.i.f.329.1		32
17.9	even	8		867.2.i.g.329.1		32
17.10	odd	16		867.2.i.g.224.4		32
17.11	odd	16		867.2.i.b.65.1		32
17.12	odd	16		867.2.i.d.158.4		32
17.13	even	4		51.2.i.a.44.4	yes	32
17.14	odd	16		867.2.i.h.131.1		32
17.15	even	8		867.2.i.i.827.4		32
17.16	even	2		867.2.i.d.653.1		32
51.2	odd	8		867.2.i.b.827.1		32
51.5	even	16	inner	867.2.i.c.158.1		32
51.8	odd	8		867.2.i.f.329.4		32
51.11	even	16		867.2.i.b.65.4		32
51.14	even	16		867.2.i.h.131.4		32
51.20	even	16		51.2.i.a.29.4	yes	32
51.23	even	16		867.2.i.i.65.4		32
51.26	odd	8		867.2.i.g.329.4		32
51.29	even	16		867.2.i.d.158.1		32
51.32	odd	8		867.2.i.i.827.1		32
51.38	odd	4		867.2.i.h.503.1		32
51.41	even	16		867.2.i.f.224.1		32
51.44	even	16		867.2.i.g.224.1		32
51.47	odd	4		51.2.i.a.44.1	yes	32
51.50	odd	2		867.2.i.d.653.4		32
68.3	even	16		816.2.cj.c.641.4		32
68.47	odd	4		816.2.cj.c.401.3		32
204.47	even	4		816.2.cj.c.401.4		32
204.71	odd	16		816.2.cj.c.641.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	17.3	odd	16
51.2.i.a.29.4	yes	32	51.20	even	16
51.2.i.a.44.1	yes	32	51.47	odd	4
51.2.i.a.44.4	yes	32	17.13	even	4
816.2.cj.c.401.3		32	68.47	odd	4
816.2.cj.c.401.4		32	204.47	even	4
816.2.cj.c.641.3		32	204.71	odd	16
816.2.cj.c.641.4		32	68.3	even	16
867.2.i.b.65.1		32	17.11	odd	16
867.2.i.b.65.4		32	51.11	even	16
867.2.i.b.827.1		32	51.2	odd	8
867.2.i.b.827.4		32	17.2	even	8
867.2.i.c.158.1		32	51.5	even	16	inner
867.2.i.c.158.4		32	17.5	odd	16	inner
867.2.i.c.653.1		32	1.1	even	1	trivial
867.2.i.c.653.4		32	3.2	odd	2	inner
867.2.i.d.158.1		32	51.29	even	16
867.2.i.d.158.4		32	17.12	odd	16
867.2.i.d.653.1		32	17.16	even	2
867.2.i.d.653.4		32	51.50	odd	2
867.2.i.f.224.1		32	51.41	even	16
867.2.i.f.224.4		32	17.7	odd	16
867.2.i.f.329.1		32	17.8	even	8
867.2.i.f.329.4		32	51.8	odd	8
867.2.i.g.224.1		32	51.44	even	16
867.2.i.g.224.4		32	17.10	odd	16
867.2.i.g.329.1		32	17.9	even	8
867.2.i.g.329.4		32	51.26	odd	8
867.2.i.h.131.1		32	17.14	odd	16
867.2.i.h.131.4		32	51.14	even	16
867.2.i.h.503.1		32	51.38	odd	4
867.2.i.h.503.4		32	17.4	even	4
867.2.i.i.65.1		32	17.6	odd	16
867.2.i.i.65.4		32	51.23	even	16
867.2.i.i.827.1		32	51.32	odd	8
867.2.i.i.827.4		32	17.15	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34436 - 0.556851i) q^{2} +(-1.44078 + 0.961322i) q^{3} +(0.0830021 + 0.0830021i) q^{4} +(2.99276 - 0.595296i) q^{5} +(2.47224 - 0.490059i) q^{6} +(0.420765 - 2.11533i) q^{7} +(1.04834 + 2.53091i) q^{8} +(1.15172 - 2.77012i) q^{9} +(-4.35483 - 0.866229i) q^{10} +(-0.915491 - 1.37013i) q^{11} +(-0.199380 - 0.0397964i) q^{12} +(3.12551 - 3.12551i) q^{13} +(-1.74358 + 2.60946i) q^{14} +(-3.73965 + 3.73470i) q^{15} -4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(0.330416 - 0.797694i) q^{19} +(0.297816 + 0.198994i) q^{20} +(1.42728 + 3.45222i) q^{21} +(0.467790 + 2.35174i) q^{22} +(-0.637394 + 0.425893i) q^{23} +(-3.94345 - 2.63871i) q^{24} +(3.98282 - 1.64974i) q^{25} +(-5.94226 + 2.46136i) q^{26} +(1.00359 + 5.09831i) q^{27} +(0.210501 - 0.140652i) q^{28} +(1.55905 + 7.83789i) q^{29} +(7.10709 - 2.93834i) q^{30} +(-2.40167 - 1.60475i) q^{31} +(-0.253786 + 0.612694i) q^{32} +(2.63616 + 1.09398i) q^{33} -6.58114i q^{35} +(0.325520 - 0.134330i) q^{36} +(-1.32318 + 1.98027i) q^{37} +(-0.888394 + 0.888394i) q^{38} +(-1.49857 + 7.50782i) q^{39} +(4.64406 + 6.95033i) q^{40} +(3.02038 + 0.600791i) q^{41} +(0.00359897 - 5.43581i) q^{42} +(-4.38037 - 10.5751i) q^{43} +(0.0377359 - 0.189711i) q^{44} +(1.79778 - 8.97590i) q^{45} +(1.09405 - 0.217619i) q^{46} +(-2.21238 - 2.21238i) q^{47} +(4.05773 + 6.08153i) q^{48} +(2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(5.88369 + 2.43710i) q^{53} +(1.48981 - 7.41281i) q^{54} +(-3.55548 - 3.55548i) q^{55} +(5.79482 - 1.15266i) q^{56} +(0.290783 + 1.46694i) q^{57} +(2.26861 - 11.4051i) q^{58} +(-2.33146 - 5.62864i) q^{59} +(-0.620386 - 0.000410749i) q^{60} +(-5.73423 - 1.14061i) q^{61} +(2.33510 + 3.49473i) q^{62} +(-5.37510 - 3.60183i) q^{63} +(-5.28702 + 5.28702i) q^{64} +(7.49329 - 11.2145i) q^{65} +(-2.93476 - 2.93865i) q^{66} -7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(-3.66472 + 8.84742i) q^{70} +(-1.80802 - 1.20808i) q^{71} +(8.21831 + 0.0108825i) q^{72} +(-2.45412 - 12.3377i) q^{73} +(2.88154 - 1.92538i) q^{74} +(-4.15245 + 6.20569i) q^{75} +(0.0936354 - 0.0387851i) q^{76} +(-3.28348 + 1.36006i) q^{77} +(6.19535 - 9.25872i) q^{78} +(4.95397 - 3.31013i) q^{79} +(-2.51274 - 12.6324i) q^{80} +(-6.34708 - 6.38079i) q^{81} +(-3.72592 - 2.48958i) q^{82} +(4.96993 - 11.9985i) q^{83} +(-0.168074 + 0.405009i) q^{84} +16.6560i q^{86} +(-9.78099 - 9.79395i) q^{87} +(2.50793 - 3.75339i) q^{88} +(3.42023 - 3.42023i) q^{89} +(-7.41510 + 11.0657i) q^{90} +(-5.29638 - 7.92660i) q^{91} +(-0.0882551 - 0.0175550i) q^{92} +(5.00297 + 0.00331239i) q^{93} +(1.74226 + 4.20619i) q^{94} +(0.513989 - 2.58400i) q^{95} +(-0.223345 - 1.12673i) q^{96} +(-3.47928 + 0.692072i) q^{97} +(-2.41627 - 2.41627i) q^{98} +(-4.84981 + 0.958012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{4} + 8 q^{9} - 32 q^{10} - 24 q^{12} - 16 q^{13} - 16 q^{15} + 16 q^{18} + 16 q^{19} + 16 q^{21} + 48 q^{22} - 8 q^{24} - 16 q^{25} + 48 q^{27} + 64 q^{28} - 8 q^{30} - 16 q^{31} - 8 q^{36}+ \cdots - 96 q^{97}+O(q^{100}) \) 32 * q - 16 * q^4 + 8 * q^9 - 32 * q^10 - 24 * q^12 - 16 * q^13 - 16 * q^15 + 16 * q^18 + 16 * q^19 + 16 * q^21 + 48 * q^22 - 8 * q^24 - 16 * q^25 + 48 * q^27 + 64 * q^28 - 8 * q^30 - 16 * q^31 - 8 * q^36 + 32 * q^37 - 8 * q^39 + 64 * q^40 + 56 * q^42 - 16 * q^43 - 24 * q^45 + 80 * q^46 + 72 * q^48 + 48 * q^49 - 96 * q^52 - 48 * q^54 - 48 * q^55 - 24 * q^57 + 32 * q^58 - 32 * q^60 - 64 * q^61 + 16 * q^63 + 16 * q^64 - 72 * q^66 + 80 * q^69 - 48 * q^70 + 64 * q^72 - 48 * q^76 + 16 * q^78 + 32 * q^79 + 48 * q^81 - 48 * q^82 + 56 * q^87 + 80 * q^88 - 104 * q^90 - 80 * q^91 + 72 * q^93 + 48 * q^94 - 72 * q^96 - 96 * q^97

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