LMFDB - Embedded newform 1323.2.f.e.883.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1323,2,Mod(442,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1323.442"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-2,0,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.1
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.e.442.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +4.05086 q^{8} +6.97172 q^{10} +(-0.676857 + 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(-1.13729 + 1.96984i) q^{16} +3.31027 q^{17} +2.20659 q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(1.31415 + 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +3.49916 q^{26} +(-0.521720 + 0.903646i) q^{29} +(-1.63729 - 2.83587i) q^{31} +(1.33629 + 2.31453i) q^{32} +(-3.95060 + 6.84263i) q^{34} -10.8755 q^{37} +(-2.63342 + 4.56121i) q^{38} +(-5.91601 - 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +5.00488 q^{44} -6.27340 q^{46} +(1.98957 - 3.44604i) q^{47} +(-4.21456 - 7.29984i) q^{50} +(-2.71001 + 4.69388i) q^{52} -6.45486 q^{53} +3.95402 q^{55} +(-1.24528 - 2.15688i) q^{58} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(-2.14100 + 3.70832i) q^{65} +(-6.40588 - 11.0953i) q^{67} +(-6.11928 - 10.5989i) q^{68} -12.9177 q^{71} -10.4554 q^{73} +(12.9791 - 22.4805i) q^{74} +(-4.07903 - 7.06509i) q^{76} +(-0.383838 + 0.664827i) q^{79} +6.64375 q^{80} -4.31684 q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(-5.18258 - 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +6.40711 q^{89} +(4.85859 - 8.41533i) q^{92} +(4.74884 + 8.22524i) q^{94} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 + 7.17316i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34}+ \cdots - 12 q^{97}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * q^89 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.19343	+	2.06709i	−0.843886	+	1.46165i	0.0426999	+	0.999088i	$0.486404\pi$
$2$	−1.19343	+	2.06709i	−0.843886	+	1.46165i	−0.886585	+	0.462565i	$0.846929\pi$
$3$		0			0
$3$		0			0
$4$	−1.84857	−	3.20182i	−0.924286	−	1.60091i
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	−0.982360	−	0.186998i	$-0.940124\pi$
$5$	−1.46043	−	2.52954i	−0.653125	−	1.13125i	0.329235	−	0.944248i	$-0.393209\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	4.05086			1.43219
$9$		0			0
$10$	6.97172			2.20465
$11$	−0.676857	+	1.17235i	−0.204080	+	0.353477i	−0.949839	−	0.312738i	$-0.898754\pi$
$11$	−0.676857	+	1.17235i	−0.204080	+	0.353477i	0.745759	+	0.666216i	$0.232087\pi$
$12$		0			0
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	0.746291	−	0.665620i	$-0.231833\pi$
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	−0.949589	+	0.313497i	$0.898499\pi$
$14$		0			0
$15$		0			0
$16$	−1.13729	+	1.96984i	−0.284323	+	0.492461i
$17$	3.31027			0.802859			0.401430	−	0.915890i	$-0.368513\pi$
$17$	3.31027			0.802859			0.401430	+	0.915890i	$0.368513\pi$
$18$		0			0
$19$	2.20659			0.506226			0.253113	−	0.967437i	$-0.418546\pi$
$19$	2.20659			0.506226			0.253113	+	0.967437i	$0.418546\pi$
$20$	−5.39943	+	9.35209i	−1.20735	+	2.09119i
$21$		0			0
$22$	−1.61557	−	2.79825i	−0.344441	−	0.596589i
$23$	1.31415	+	2.27617i	0.274019	+	0.474614i	0.969887	−	0.243555i	$-0.0783136\pi$
$23$	1.31415	+	2.27617i	0.274019	+	0.474614i	−0.695868	+	0.718169i	$0.744980\pi$
$24$		0			0
$25$	−1.76573	+	3.05833i	−0.353146	+	0.611666i
$26$	3.49916			0.686241
$27$		0			0
$28$		0			0
$29$	−0.521720	+	0.903646i	−0.0968810	+	0.167803i	−0.910392	−	0.413747i	$-0.864220\pi$
$29$	−0.521720	+	0.903646i	−0.0968810	+	0.167803i	0.813511	+	0.581549i	$0.197553\pi$
$30$		0			0
$31$	−1.63729	−	2.83587i	−0.294066	−	0.509337i	0.680701	−	0.732561i	$-0.261675\pi$
$31$	−1.63729	−	2.83587i	−0.294066	−	0.509337i	−0.974767	+	0.223224i	$0.928342\pi$
$32$	1.33629	+	2.31453i	0.236226	+	0.409155i
$33$		0			0
$34$	−3.95060	+	6.84263i	−0.677521	+	1.17350i
$35$		0			0
$36$		0			0
$37$	−10.8755			−1.78791			−0.893957	−	0.448153i	$-0.852082\pi$
$37$	−10.8755			−1.78791			−0.893957	+	0.448153i	$0.852082\pi$
$38$	−2.63342	+	4.56121i	−0.427197	+	0.739926i
$39$		0			0
$40$	−5.91601	−	10.2468i	−0.935403	−	1.62017i
$41$	0.904289	+	1.56627i	0.141226	+	0.244611i	0.927959	−	0.372683i	$-0.121562\pi$
$41$	0.904289	+	1.56627i	0.141226	+	0.244611i	−0.786732	+	0.617294i	$0.788229\pi$
$42$		0			0
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	−0.982731	−	0.185038i	$-0.940759\pi$
$43$	−2.17129	+	3.76078i	−0.331118	+	0.573514i	0.651613	+	0.758551i	$0.274093\pi$
$44$	5.00488			0.754514
$45$		0			0
$46$	−6.27340			−0.924962
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	−0.683650	−	0.729810i	$-0.739609\pi$
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	0.973859	+	0.227154i	$0.0729419\pi$
$48$		0			0
$49$		0			0
$50$	−4.21456	−	7.29984i	−0.596029	−	1.03235i
$51$		0			0
$52$	−2.71001	+	4.69388i	−0.375811	+	0.650924i
$53$	−6.45486			−0.886644			−0.443322	−	0.896363i	$-0.646200\pi$
$53$	−6.45486			−0.886644			−0.443322	+	0.896363i	$0.646200\pi$
$54$		0			0
$55$	3.95402			0.533160
$56$		0			0
$57$		0			0
$58$	−1.24528	−	2.15688i	−0.163513	−	0.283213i
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	−0.922799	−	0.385283i	$-0.874104\pi$
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	0.127735	−	0.991808i	$-0.459229\pi$
$60$		0			0
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	−0.883386	−	0.468646i	$-0.844742\pi$
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	0.847553	+	0.530711i	$0.178075\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	−2.14100	+	3.70832i	−0.265558	+	0.459960i
$66$		0			0
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	−0.930420	−	0.366494i	$-0.880558\pi$
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	0.147817	−	0.989015i	$-0.452775\pi$
$68$	−6.11928	−	10.5989i	−0.742072	−	1.28531i
$69$		0			0
$70$		0			0
$71$	−12.9177			−1.53305			−0.766525	−	0.642214i	$-0.778016\pi$
$71$	−12.9177			−1.53305			−0.766525	+	0.642214i	$0.778016\pi$
$72$		0			0
$73$	−10.4554			−1.22372			−0.611858	−	0.790968i	$-0.709578\pi$
$73$	−10.4554			−1.22372			−0.611858	+	0.790968i	$0.709578\pi$
$74$	12.9791	−	22.4805i	1.50879	−	2.61331i
$75$		0			0
$76$	−4.07903	−	7.06509i	−0.467897	−	0.810422i
$77$		0			0
$78$		0			0
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	−0.886810	−	0.462134i	$-0.847084\pi$
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	0.843625	+	0.536933i	$0.180417\pi$
$80$	6.64375			0.742793
$81$		0			0
$82$	−4.31684			−0.476715
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	−0.806974	−	0.590587i	$-0.798896\pi$
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	0.914950	+	0.403567i	$0.132230\pi$
$84$		0			0
$85$	−4.83443	−	8.37348i	−0.524368	−	0.908232i
$86$	−5.18258	−	8.97649i	−0.558852	−	0.967960i
$87$		0			0
$88$	−2.74185	+	4.74903i	−0.292283	+	0.506248i
$89$	6.40711			0.679153			0.339576	−	0.940579i	$-0.389716\pi$
$89$	6.40711			0.679153			0.339576	+	0.940579i	$0.389716\pi$
$90$		0			0
$91$		0			0
$92$	4.85859	−	8.41533i	0.506543	−	0.877359i
$93$		0			0
$94$	4.74884	+	8.22524i	0.489806	+	0.848369i
$95$	−3.22257	−	5.58166i	−0.330629	−	0.572666i
$96$		0			0
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	−0.995988	−	0.0894847i	$-0.971478\pi$
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	0.575490	+	0.817809i	$0.304811\pi$
$98$		0			0
$99$		0			0
$100$	13.0563			1.30563
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	0.107419	+	0.994214i	$0.465741\pi$
$101$	−8.11331	+	14.0527i	−0.807305	+	1.39829i	−0.914724	+	0.404079i	$0.867592\pi$
$102$		0			0
$103$	1.11342	+	1.92849i	0.109708	+	0.190020i	0.915652	−	0.401972i	$-0.131675\pi$
$103$	1.11342	+	1.92849i	0.109708	+	0.190020i	−0.805944	+	0.591992i	$0.798342\pi$
$104$	−2.96929	−	5.14295i	−0.291162	−	0.504308i
$105$		0			0
$106$	7.70346	−	13.3428i	0.748226	−	1.29597i
$107$	−17.5081			−1.69257			−0.846284	−	0.532732i	$-0.821165\pi$
$107$	−17.5081			−1.69257			−0.846284	+	0.532732i	$0.821165\pi$
$108$		0			0
$109$	15.5983			1.49405			0.747025	−	0.664796i	$-0.231482\pi$
$109$	15.5983			1.49405			0.747025	+	0.664796i	$0.231482\pi$
$110$	−4.71886	+	8.17331i	−0.449926	+	0.779295i
$111$		0			0
$112$		0			0
$113$	0.844555	+	1.46281i	0.0794491	+	0.137610i	0.903012	−	0.429615i	$-0.141351\pi$
$113$	0.844555	+	1.46281i	0.0794491	+	0.137610i	−0.823563	+	0.567224i	$0.808017\pi$
$114$		0			0
$115$	3.83845	−	6.64839i	0.357937	−	0.619966i
$116$	3.85775			0.358183
$117$		0			0
$118$	29.1532			2.68377
$119$		0			0
$120$		0			0
$121$	4.58373	+	7.93925i	0.416703	+	0.721750i
$122$	−0.668005	−	1.15702i	−0.0604784	−	0.104752i
$123$		0			0
$124$	−6.05330	+	10.4846i	−0.543602	+	0.941546i
$125$	−4.28942			−0.383657
$126$		0			0
$127$	−3.96918			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$127$	−3.96918			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$128$	10.3696	−	17.9607i	0.916552	−	1.58751i
$129$		0			0
$130$	−5.11028	−	8.85127i	−0.448202	−	0.776308i
$131$	2.66432	+	4.61473i	0.232782	+	0.403191i	0.958626	−	0.284669i	$-0.0918837\pi$
$131$	2.66432	+	4.61473i	0.232782	+	0.403191i	−0.725844	+	0.687860i	$0.758550\pi$
$132$		0			0
$133$		0			0
$134$	30.5800			2.64171
$135$		0			0
$136$	13.4095			1.14985
$137$	−3.74772	+	6.49124i	−0.320189	+	0.554584i	−0.980527	−	0.196385i	$-0.937080\pi$
$137$	−3.74772	+	6.49124i	−0.320189	+	0.554584i	0.660338	+	0.750969i	$0.270413\pi$
$138$		0			0
$139$	7.03285	+	12.1812i	0.596518	+	1.03320i	0.993331	+	0.115300i	$0.0367830\pi$
$139$	7.03285	+	12.1812i	0.596518	+	1.03320i	−0.396812	+	0.917900i	$0.629884\pi$
$140$		0			0
$141$		0			0
$142$	15.4164	−	26.7021i	1.29372	−	2.24079i
$143$	1.98455			0.165956
$144$		0			0
$145$	3.04775			0.253102
$146$	12.4779	−	21.6123i	1.03268	−	1.78865i
$147$		0			0
$148$	20.1041	+	34.8212i	1.65254	+	2.86229i
$149$	1.08986	+	1.88769i	0.0892846	+	0.154645i	0.907209	−	0.420680i	$-0.138209\pi$
$149$	1.08986	+	1.88769i	0.0892846	+	0.154645i	−0.817924	+	0.575326i	$0.804875\pi$
$150$		0			0
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	0.425705	+	0.904862i	$0.360026\pi$
$151$	−7.01387	+	12.1484i	−0.570781	+	0.988621i	−0.996486	+	0.0837595i	$0.973307\pi$
$152$	8.93857			0.725014
$153$		0			0
$154$		0			0
$155$	−4.78231	+	8.28320i	−0.384124	+	0.665322i
$156$		0			0
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	0.800755	−	0.598993i	$-0.204432\pi$
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	−0.919120	+	0.393978i	$0.871099\pi$
$158$	−0.916172	−	1.58686i	−0.0728867	−	0.126243i
$159$		0			0
$160$	3.90314	−	6.76043i	0.308570	−	0.534459i
$161$		0			0
$162$		0			0
$163$	0.388555			0.0304340			0.0152170	−	0.999884i	$-0.495156\pi$
$163$	0.388555			0.0304340			0.0152170	+	0.999884i	$0.495156\pi$
$164$	3.34329	−	5.79074i	0.261067	−	0.452181i
$165$		0			0
$166$	2.34798	+	4.06682i	0.182239	+	0.315646i
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	0.689606	−	0.724185i	$-0.257784\pi$
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	−0.971965	+	0.235124i	$0.924450\pi$
$168$		0			0
$169$	5.42542	−	9.39710i	0.417340	−	0.722854i
$170$	23.0783			1.77003
$171$		0			0
$172$	16.0551			1.22419
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	−0.932750	−	0.360525i	$-0.882598\pi$
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	0.778598	+	0.627522i	$0.215931\pi$
$174$		0			0
$175$		0			0
$176$	−1.53957	−	2.66661i	−0.116049	−	0.201003i
$177$		0			0
$178$	−7.64647	+	13.2441i	−0.573127	+	0.992685i
$179$	10.5849			0.791149			0.395575	−	0.918434i	$-0.370545\pi$
$179$	10.5849			0.791149			0.395575	+	0.918434i	$0.370545\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$		0			0
$183$		0			0
$184$	5.32343	+	9.22045i	0.392448	+	0.679740i
$185$	15.8829	+	27.5099i	1.16773	+	2.02257i
$186$		0			0
$187$	−2.24058	+	3.88081i	−0.163848	+	0.283793i
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	−0.676276	−	0.736648i	$-0.736407\pi$
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	0.976094	+	0.217348i	$0.0697406\pi$
$192$		0			0
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$	−9.88504	−	17.1214i	−0.709705	−	1.22924i
$195$		0			0
$196$		0			0
$197$	−5.99634			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$197$	−5.99634			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$198$		0			0
$199$	−14.4087			−1.02140			−0.510702	−	0.859758i	$-0.670615\pi$
$199$	−14.4087			−1.02140			−0.510702	+	0.859758i	$0.670615\pi$
$200$	−7.15272	+	12.3889i	−0.505773	+	0.876025i
$201$		0			0
$202$	−19.3654	−	33.5419i	−1.36255	−	2.36000i
$203$		0			0
$204$		0			0
$205$	2.64131	−	4.57488i	0.184477	−	0.319523i
$206$	−5.31515			−0.370324
$207$		0			0
$208$	3.33454			0.231209
$209$	−1.49354	+	2.58690i	−0.103311	+	0.178939i
$210$		0			0
$211$	−6.92418	−	11.9930i	−0.476680	−	0.825634i	0.522963	−	0.852356i	$-0.324827\pi$
$211$	−6.92418	−	11.9930i	−0.476680	−	0.825634i	−0.999643	+	0.0267212i	$0.991493\pi$
$212$	11.9323	+	20.6673i	0.819512	+	1.41944i
$213$		0			0
$214$	20.8947	−	36.1907i	1.42833	−	2.47395i
$215$	12.6841			0.865047
$216$		0			0
$217$		0			0
$218$	−18.6156	+	32.2431i	−1.26081	+	2.18378i
$219$		0			0
$220$	−7.30929	−	12.6601i	−0.492792	−	0.853541i
$221$	−2.42644	−	4.20271i	−0.163220	−	0.282705i
$222$		0			0
$223$	2.33756	−	4.04878i	0.156535	−	0.271126i	−0.777082	−	0.629399i	$-0.783301\pi$
$223$	2.33756	−	4.04878i	0.156535	−	0.271126i	0.933617	+	0.358273i	$0.116634\pi$
$224$		0			0
$225$		0			0
$226$	−4.03169			−0.268184
$227$	9.85631	−	17.0716i	0.654187	−	1.13308i	−0.327910	−	0.944709i	$-0.606344\pi$
$227$	9.85631	−	17.0716i	0.654187	−	1.13308i	0.982097	−	0.188376i	$-0.0603222\pi$
$228$		0			0
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.787404	−	0.616437i	$-0.788575\pi$
$229$	−14.0364	−	24.3118i	−0.927552	−	1.60657i	−0.140148	−	0.990131i	$-0.544758\pi$
$230$	9.16188	+	15.8688i	0.604116	+	1.04636i
$231$		0			0
$232$	−2.11342	+	3.66054i	−0.138753	+	0.240326i
$233$	−13.8023			−0.904216			−0.452108	−	0.891963i	$-0.649328\pi$
$233$	−13.8023			−0.904216			−0.452108	+	0.891963i	$0.649328\pi$
$234$		0			0
$235$	−11.6225			−0.758171
$236$	−22.5785	+	39.1070i	−1.46973	+	2.54565i
$237$		0			0
$238$		0			0
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	0.629834	−	0.776730i	$-0.283123\pi$
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	−0.987585	+	0.157087i	$0.949790\pi$
$240$		0			0
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	−0.203362	−	0.979104i	$-0.565187\pi$
$241$	11.5849	−	20.0656i	0.746247	−	1.29254i	0.949610	−	0.313435i	$-0.101480\pi$
$242$	−21.8815			−1.40660
$243$		0			0
$244$	2.06942			0.132481
$245$		0			0
$246$		0			0
$247$	−1.61743	−	2.80147i	−0.102915	−	0.178253i
$248$	−6.63243	−	11.4877i	−0.421160	−	0.729470i
$249$		0			0
$250$	5.11914	−	8.86660i	0.323763	−	0.560773i
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$	4.73696	−	8.20466i	0.297223	−	0.514806i
$255$		0			0
$256$	13.8226	+	23.9414i	0.863912	+	1.49634i
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	0.981232	−	0.192833i	$-0.0617676\pi$
$257$	5.18798	+	8.98585i	0.323618	+	0.560522i	−0.657614	+	0.753355i	$0.728434\pi$
$258$		0			0
$259$		0			0
$260$	15.8312			0.981807
$261$		0			0
$262$	−12.7187			−0.785767
$263$	−9.56654	+	16.5697i	−0.589898	+	1.02173i	0.404347	+	0.914605i	$0.367499\pi$
$263$	−9.56654	+	16.5697i	−0.589898	+	1.02173i	−0.994245	+	0.107128i	$0.965835\pi$
$264$		0			0
$265$	9.42689	+	16.3279i	0.579090	+	1.00301i
$266$		0			0
$267$		0			0
$268$	−23.6835	+	41.0210i	−1.44670	+	2.50576i
$269$	−8.83681			−0.538790			−0.269395	−	0.963030i	$-0.586824\pi$
$269$	−8.83681			−0.538790			−0.269395	+	0.963030i	$0.586824\pi$
$270$		0			0
$271$	18.3391			1.11402			0.557010	−	0.830506i	$-0.311948\pi$
$271$	18.3391			1.11402			0.557010	+	0.830506i	$0.311948\pi$
$272$	−3.76474	+	6.52073i	−0.228271	+	0.395377i
$273$		0			0
$274$	−8.94531	−	15.4937i	−0.540406	−	0.936010i
$275$	−2.39029	−	4.14011i	−0.144140	−	0.249658i
$276$		0			0
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	−0.932460	−	0.361272i	$-0.882343\pi$
$277$	−2.55241	+	4.42091i	−0.153360	+	0.265627i	0.779101	+	0.626899i	$0.215676\pi$
$278$	−33.5730			−2.01357
$279$		0			0
$280$		0			0
$281$	0.853180	−	1.47775i	0.0508964	−	0.0881552i	−0.839455	−	0.543430i	$-0.817125\pi$
$281$	0.853180	−	1.47775i	0.0508964	−	0.0881552i	0.890351	+	0.455274i	$0.150459\pi$
$282$		0			0
$283$	6.24415	+	10.8152i	0.371176	+	0.642896i	0.989747	−	0.142833i	$-0.0456213\pi$
$283$	6.24415	+	10.8152i	0.371176	+	0.642896i	−0.618571	+	0.785729i	$0.712288\pi$
$284$	23.8793	+	41.3602i	1.41698	+	2.45428i
$285$		0			0
$286$	−2.36843	+	4.10224i	−0.140048	+	0.242571i
$287$		0			0
$288$		0			0
$289$	−6.04208			−0.355417
$290$	−3.63729	+	6.29997i	−0.213589	+	0.369947i
$291$		0			0
$292$	19.3276	+	33.4764i	1.13106	+	1.95906i
$293$	2.60202	+	4.50684i	0.152012	+	0.263292i	0.931967	−	0.362543i	$-0.118091\pi$
$293$	2.60202	+	4.50684i	0.152012	+	0.263292i	−0.779955	+	0.625835i	$0.784758\pi$
$294$		0			0
$295$	−17.8377	+	30.8959i	−1.03855	+	1.79883i
$296$	−44.0549			−2.56064
$297$		0			0
$298$	−5.20269			−0.301384
$299$	1.92654	−	3.33687i	0.111415	−	0.192976i
$300$		0			0
$301$		0			0
$302$	−16.7412	−	28.9966i	−0.963347	−	1.66857i
$303$		0			0
$304$	−2.50953	+	4.34663i	−0.143931	+	0.249297i
$305$	1.63491			0.0936145
$306$		0			0
$307$	5.00136			0.285442			0.142721	−	0.989763i	$-0.454415\pi$
$307$	5.00136			0.285442			0.142721	+	0.989763i	$0.454415\pi$
$308$		0			0
$309$		0			0
$310$	−11.4147	−	19.7709i	−0.648313	−	1.12291i
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.801652	−	0.597791i	$-0.796045\pi$
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.116876	−	0.993146i	$-0.537288\pi$
$312$		0			0
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	−0.886693	−	0.462359i	$-0.847003\pi$
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	0.843761	+	0.536719i	$0.180336\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	0.388175	+	0.921586i	$0.373106\pi$
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	−0.992204	+	0.124623i	$0.960228\pi$
$318$		0			0
$319$	−0.706261	−	1.22328i	−0.0395430	−	0.0684905i
$320$	15.9600	+	27.6436i	0.892193	+	1.54532i
$321$		0			0
$322$		0			0
$323$	7.30441			0.406428
$324$		0			0
$325$	5.17713			0.287175
$326$	−0.463715	+	0.803178i	−0.0256828	+	0.0444839i
$327$		0			0
$328$	3.66315	+	6.34476i	0.202263	+	0.350330i
$329$		0			0
$330$		0			0
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	0.463844	+	0.885917i	$0.346470\pi$
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	−0.999149	+	0.0412580i	$0.986863\pi$
$332$	−7.27381			−0.399202
$333$		0			0
$334$	17.4188			0.953116
$335$	−18.7107	+	32.4079i	−1.02228	+	1.77063i
$336$		0			0
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	0.967316	−	0.253575i	$-0.0816063\pi$
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	−0.703260	+	0.710933i	$0.748273\pi$
$338$	12.9498	+	22.4296i	0.704374	+	1.22001i
$339$		0			0
$340$	−17.8736	+	30.9580i	−0.969332	+	1.67893i
$341$	4.43285			0.240052
$342$		0			0
$343$		0			0
$344$	−8.79558	+	15.2344i	−0.474226	+	0.821383i
$345$		0			0
$346$	−4.83948	−	8.38222i	−0.260172	−	0.450631i
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	0.891935	−	0.452164i	$-0.149348\pi$
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	−0.837553	+	0.546356i	$0.816015\pi$
$348$		0			0
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	−0.561346	−	0.827581i	$-0.689716\pi$
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	0.997379	+	0.0723497i	$0.0230498\pi$
$350$		0			0
$351$		0			0
$352$	−3.61792			−0.192836
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	−0.544588	−	0.838704i	$-0.683314\pi$
$353$	8.53072	−	14.7756i	0.454045	−	0.786428i	0.998633	+	0.0522753i	$0.0166473\pi$
$354$		0			0
$355$	18.8655	+	32.6759i	1.00127	+	1.73426i
$356$	−11.8440	−	20.5144i	−0.627731	−	1.08726i
$357$		0			0
$358$	−12.6323	+	21.8798i	−0.667639	+	1.15639i
$359$	2.96726			0.156606			0.0783030	−	0.996930i	$-0.475050\pi$
$359$	2.96726			0.156606			0.0783030	+	0.996930i	$0.475050\pi$
$360$		0			0
$361$	−14.1310			−0.743736
$362$	23.4285	−	40.5794i	1.23137	−	2.13280i
$363$		0			0
$364$		0			0
$365$	15.2695	+	26.4475i	0.799240	+	1.38432i
$366$		0			0
$367$	5.07874	−	8.79664i	0.265108	−	0.459181i	−0.702484	−	0.711700i	$-0.747926\pi$
$367$	5.07874	−	8.79664i	0.265108	−	0.459181i	0.967592	+	0.252519i	$0.0812590\pi$
$368$	−5.97827			−0.311639
$369$		0			0
$370$	−75.8207			−3.94173
$371$		0			0
$372$		0			0
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	0.980675	+	0.195645i	$0.0626799\pi$
$373$	12.7423	+	22.0703i	0.659771	+	1.14276i	−0.320904	+	0.947112i	$0.603987\pi$
$374$	−5.34798	−	9.26297i	−0.276537	−	0.478977i
$375$		0			0
$376$	8.05947	−	13.9594i	0.415635	−	0.719902i
$377$	1.52969			0.0787829
$378$		0			0
$379$	9.85497			0.506216			0.253108	−	0.967438i	$-0.418547\pi$
$379$	9.85497			0.506216			0.253108	+	0.967438i	$0.418547\pi$
$380$	−11.9143	+	20.6362i	−0.611191	+	1.05861i
$381$		0			0
$382$	9.89016	+	17.1303i	0.506025	+	0.876460i
$383$	−13.6563	−	23.6535i	−0.697806	−	1.20864i	−0.969225	−	0.246175i	$-0.920826\pi$
$383$	−13.6563	−	23.6535i	−0.697806	−	1.20864i	0.271419	−	0.962461i	$-0.412507\pi$
$384$		0			0
$385$		0			0
$386$	−44.8370			−2.28214
$387$		0			0
$388$	30.6229			1.55464
$389$	2.09223	−	3.62385i	0.106080	−	0.183736i	−0.808099	−	0.589047i	$-0.799503\pi$
$389$	2.09223	−	3.62385i	0.106080	−	0.183736i	0.914179	+	0.405311i	$0.132837\pi$
$390$		0			0
$391$	4.35019	+	7.53475i	0.219999	+	0.381049i
$392$		0			0
$393$		0			0
$394$	7.15624	−	12.3950i	0.360526	−	0.624450i
$395$	2.24228			0.112821
$396$		0			0
$397$	−30.6709			−1.53933			−0.769664	−	0.638450i	$-0.779576\pi$
$397$	−30.6709			−1.53933			−0.769664	+	0.638450i	$0.779576\pi$
$398$	17.1958	−	29.7840i	0.861948	−	1.49294i
$399$		0			0
$400$	−4.01629	−	6.95642i	−0.200815	−	0.347821i
$401$	−3.42402	−	5.93057i	−0.170987	−	0.296158i	0.767778	−	0.640716i	$-0.221362\pi$
$401$	−3.42402	−	5.93057i	−0.170987	−	0.296158i	−0.938765	+	0.344557i	$0.888029\pi$
$402$		0			0
$403$	−2.40027	+	4.15739i	−0.119566	+	0.207095i
$404$	59.9922			2.98472
$405$		0			0
$406$		0			0
$407$	7.36113	−	12.7499i	0.364878	−	0.631987i
$408$		0			0
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	0.998491	−	0.0549104i	$-0.0174873\pi$
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	−0.546799	+	0.837264i	$0.684154\pi$
$410$	6.30445	+	10.9196i	0.311355	+	0.539282i
$411$		0			0
$412$	4.11646	−	7.12991i	0.202803	−	0.351265i
$413$		0			0
$414$		0			0
$415$	−5.74655			−0.282087
$416$	1.95901	−	3.39311i	0.0960485	−	0.166361i
$417$		0			0
$418$	−3.56490	−	6.17458i	−0.174365	−	0.302009i
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	−0.998366	−	0.0571410i	$-0.981802\pi$
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	0.449698	−	0.893181i	$-0.351532\pi$
$420$		0			0
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	−0.492232	−	0.870464i	$-0.663819\pi$
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	0.999960	−	0.00894684i	$-0.00284791\pi$
$422$	33.0542			1.60905
$423$		0			0
$424$	−26.1477			−1.26985
$425$	−5.84505	+	10.1239i	−0.283526	+	0.491082i
$426$		0			0
$427$		0			0
$428$	32.3649	+	56.0577i	1.56442	+	2.70965i
$429$		0			0
$430$	−15.1376	+	26.2191i	−0.730001	+	1.26440i
$431$	−20.2427			−0.975055			−0.487527	−	0.873108i	$-0.662101\pi$
$431$	−20.2427			−0.975055			−0.487527	+	0.873108i	$0.662101\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$		0			0
$435$		0			0
$436$	−28.8346	−	49.9431i	−1.38093	−	2.39184i
$437$	2.89978	+	5.02257i	0.138715	+	0.240262i
$438$		0			0
$439$	17.7390	−	30.7249i	0.846639	−	1.46642i	−0.0375520	−	0.999295i	$-0.511956\pi$
$439$	17.7390	−	30.7249i	0.846639	−	1.46642i	0.884191	−	0.467126i	$-0.154711\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	−0.998760	−	0.0497923i	$-0.984144\pi$
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	0.542501	+	0.840055i	$0.317477\pi$
$444$		0			0
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$	5.57946	+	9.66391i	0.264195	+	0.457599i
$447$		0			0
$448$		0			0
$449$	29.6082			1.39730			0.698648	−	0.715465i	$-0.253785\pi$
$449$	29.6082			1.39730			0.698648	+	0.715465i	$0.253785\pi$
$450$		0			0
$451$	−2.44830			−0.115286
$452$	3.12244	−	5.40823i	0.146867	−	0.254382i
$453$		0			0
$454$	23.5257	+	40.7478i	1.10412	+	1.91239i
$455$		0			0
$456$		0			0
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$	67.0062			3.13099
$459$		0			0
$460$	−28.3826			−1.32335
$461$	−10.9187	+	18.9118i	−0.508536	+	0.880809i	0.491416	+	0.870925i	$0.336480\pi$
$461$	−10.9187	+	18.9118i	−0.508536	+	0.880809i	−0.999951	+	0.00988416i	$0.996854\pi$
$462$		0			0
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	0.991631	+	0.129102i	$0.0412094\pi$
$463$	13.0744	+	22.6456i	0.607621	+	1.05243i	−0.384010	+	0.923329i	$0.625457\pi$
$464$	−1.18670	−	2.05542i	−0.0550909	−	0.0954203i
$465$		0			0
$466$	16.4721	−	28.5305i	0.763054	−	1.32165i
$467$	−34.9527			−1.61742			−0.808709	−	0.588209i	$-0.799833\pi$
$467$	−34.9527			−1.61742			−0.808709	+	0.588209i	$0.799833\pi$
$468$		0			0
$469$		0			0
$470$	13.8707	−	24.0248i	0.639809	−	1.10818i
$471$		0			0
$472$	−24.7386	−	42.8485i	−1.13869	−	1.97226i
$473$	−2.93930	−	5.09102i	−0.135149	−	0.234086i
$474$		0			0
$475$	−3.89623	+	6.74848i	−0.178771	+	0.309641i
$476$		0			0
$477$		0			0
$478$	26.4021			1.20760
$479$	−14.9054	+	25.8170i	−0.681047	+	1.17961i	0.293615	+	0.955924i	$0.405142\pi$
$479$	−14.9054	+	25.8170i	−0.681047	+	1.17961i	−0.974662	+	0.223684i	$0.928192\pi$
$480$		0			0
$481$	7.97172	+	13.8074i	0.363479	+	0.629565i
$482$	27.6516	+	47.8939i	1.25949	+	2.18151i
$483$		0			0
$484$	16.9467	−	29.3525i	0.770304	−	1.33421i
$485$	24.1931			1.09855
$486$		0			0
$487$	22.4506			1.01733			0.508667	−	0.860964i	$-0.330139\pi$
$487$	22.4506			1.01733			0.508667	+	0.860964i	$0.330139\pi$
$488$	−1.13370	+	1.96363i	−0.0513202	+	0.0888892i
$489$		0			0
$490$		0			0
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	−0.925493	−	0.378765i	$-0.876349\pi$
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	0.134726	−	0.990883i	$-0.456984\pi$
$492$		0			0
$493$	−1.72704	+	2.99132i	−0.0777819	+	0.134722i
$494$	7.72119			0.347393
$495$		0			0
$496$	7.44830			0.334438
$497$		0			0
$498$		0			0
$499$	4.46760	+	7.73811i	0.199997	+	0.346405i	0.948527	−	0.316696i	$-0.102573\pi$
$499$	4.46760	+	7.73811i	0.199997	+	0.346405i	−0.748530	+	0.663101i	$0.769240\pi$
$500$	7.92929	+	13.7339i	0.354609	+	0.614200i
$501$		0			0
$502$	−9.28972	+	16.0903i	−0.414621	+	0.718144i
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$	4.24620	−	7.35463i	0.188766	−	0.326953i
$507$		0			0
$508$	7.33732	+	12.7086i	0.325541	+	0.563854i
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	−0.988924	−	0.148423i	$-0.952580\pi$
$509$	−14.0555	−	24.3449i	−0.623000	−	1.07907i	0.365924	−	0.930645i	$-0.380753\pi$
$510$		0			0
$511$		0			0
$512$	−24.5070			−1.08307
$513$		0			0
$514$	−24.7661			−1.09238
$515$	3.25214	−	5.63287i	0.143306	−	0.248214i
$516$		0			0
$517$	2.69331	+	4.66495i	0.118452	+	0.205164i
$518$		0			0
$519$		0			0
$520$	−8.67288	+	15.0219i	−0.380331	+	0.658753i
$521$	8.47536			0.371312			0.185656	−	0.982615i	$-0.440559\pi$
$521$	8.47536			0.371312			0.185656	+	0.982615i	$0.440559\pi$
$522$		0			0
$523$	−33.4473			−1.46255			−0.731273	−	0.682085i	$-0.761074\pi$
$523$	−33.4473			−1.46255			−0.731273	+	0.682085i	$0.761074\pi$
$524$	9.85035	−	17.0613i	0.430315	−	0.745327i
$525$		0			0
$526$	−22.8341	−	39.5498i	−0.995613	−	1.72445i
$527$	−5.41988	−	9.38751i	−0.236094	−	0.408926i
$528$		0			0
$529$	8.04603	−	13.9361i	0.349827	−	0.605919i
$530$	−45.0015			−1.95474
$531$		0			0
$532$		0			0
$533$	1.32569	−	2.29616i	0.0574220	−	0.0994579i
$534$		0			0
$535$	25.5693	+	44.2874i	1.10546	+	1.91471i
$536$	−25.9493	−	44.9456i	−1.12084	−	1.94135i
$537$		0			0
$538$	10.5461	−	18.2665i	0.454677	−	0.787523i
$539$		0			0
$540$		0			0
$541$	18.2586			0.784998			0.392499	−	0.919752i	$-0.371611\pi$
$541$	18.2586			0.784998			0.392499	+	0.919752i	$0.371611\pi$
$542$	−21.8865	+	37.9085i	−0.940106	+	1.62831i
$543$		0			0
$544$	4.42350	+	7.66173i	0.189656	+	0.328494i
$545$	−22.7803	−	39.4567i	−0.975802	−	1.69014i
$546$		0			0
$547$	−2.88599	+	4.99869i	−0.123396	+	0.213728i	−0.921105	−	0.389315i	$-0.872712\pi$
$547$	−2.88599	+	4.99869i	−0.123396	+	0.213728i	0.797709	+	0.603043i	$0.206045\pi$
$548$	27.7117			1.18378
$549$		0			0
$550$	11.4106			0.486551
$551$	−1.15122	+	1.99397i	−0.0490437	+	0.0849461i
$552$		0			0
$553$		0			0
$554$	−6.09227	−	10.5521i	−0.258836	−	0.448317i
$555$		0			0
$556$	26.0014	−	45.0358i	1.10271	−	1.90994i
$557$	33.3821			1.41445			0.707223	−	0.706991i	$-0.249948\pi$
$557$	33.3821			1.41445			0.707223	+	0.706991i	$0.249948\pi$
$558$		0			0
$559$	6.36623			0.269263
$560$		0			0
$561$		0			0
$562$	2.03643	+	3.52720i	0.0859015	+	0.148786i
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	0.888190	−	0.459477i	$-0.151963\pi$
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	−0.842013	+	0.539457i	$0.818630\pi$
$564$		0			0
$565$	2.46683	−	4.27268i	0.103780	−	0.179753i
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	−0.595507	−	0.803350i	$-0.703049\pi$
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	0.993475	+	0.114049i	$0.0363822\pi$
$570$		0			0
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	0.998680	−	0.0513674i	$-0.0163580\pi$
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	−0.543825	+	0.839198i	$0.683025\pi$
$572$	−3.66858	−	6.35417i	−0.153391	−	0.265681i
$573$		0			0
$574$		0			0
$575$	−9.28172			−0.387074
$576$		0			0
$577$	30.9032			1.28652			0.643258	−	0.765649i	$-0.277582\pi$
$577$	30.9032			1.28652			0.643258	+	0.765649i	$0.277582\pi$
$578$	7.21083	−	12.4895i	0.299931	−	0.519496i
$579$		0			0
$580$	−5.63398	−	9.75835i	−0.233938	−	0.405193i
$581$		0			0
$582$		0			0
$583$	4.36902	−	7.56737i	0.180946	−	0.313408i
$584$	−42.3535			−1.75260
$585$		0			0
$586$	−12.4214			−0.513122
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	−0.611886	−	0.790946i	$-0.709589\pi$
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	0.990922	+	0.134436i	$0.0429222\pi$
$588$		0			0
$589$	−3.61282	−	6.25759i	−0.148864	−	0.257840i
$590$	−42.5763	−	73.7444i	−1.75284	−	3.03601i
$591$		0			0
$592$	12.3685	−	21.4230i	0.508344	−	0.880478i
$593$	27.7550			1.13976			0.569880	−	0.821728i	$-0.306990\pi$
$593$	27.7550			1.13976			0.569880	+	0.821728i	$0.306990\pi$
$594$		0			0
$595$		0			0
$596$	4.02936	−	6.97905i	0.165049	−	0.285873i
$597$		0			0
$598$	4.59841	+	7.96468i	0.188043	+	0.325700i
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	0.870111	−	0.492856i	$-0.164047\pi$
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	−0.861881	+	0.507110i	$0.830714\pi$
$600$		0			0
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	−0.495268	−	0.868740i	$-0.664930\pi$
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	0.999985	−	0.00545577i	$-0.00173663\pi$
$602$		0			0
$603$		0			0
$604$	51.8626			2.11026
$605$	13.3885	−	23.1895i	0.544318	−	0.942787i
$606$		0			0
$607$	−12.0348	−	20.8449i	−0.488479	−	0.846070i	0.511434	−	0.859323i	$-0.329115\pi$
$607$	−12.0348	−	20.8449i	−0.488479	−	0.846070i	−0.999912	+	0.0132531i	$0.995781\pi$
$608$	2.94865	+	5.10721i	0.119584	+	0.207125i
$609$		0			0
$610$	−1.95115	+	3.37950i	−0.0789999	+	0.136832i
$611$	−5.83343			−0.235995
$612$		0			0
$613$	−20.3815			−0.823200			−0.411600	−	0.911365i	$-0.635030\pi$
$613$	−20.3815			−0.823200			−0.411600	+	0.911365i	$0.635030\pi$
$614$	−5.96879	+	10.3382i	−0.240881	+	0.417218i
$615$		0			0
$616$		0			0
$617$	20.9315	+	36.2544i	0.842669	+	1.45955i	0.887630	+	0.460558i	$0.152350\pi$
$617$	20.9315	+	36.2544i	0.842669	+	1.45955i	−0.0449604	+	0.998989i	$0.514316\pi$
$618$		0			0
$619$	−7.41095	+	12.8361i	−0.297871	+	0.515928i	−0.975649	−	0.219339i	$-0.929610\pi$
$619$	−7.41095	+	12.8361i	−0.297871	+	0.515928i	0.677777	+	0.735267i	$0.262943\pi$
$620$	35.3617			1.42016
$621$		0			0
$622$	77.3270			3.10053
$623$		0			0
$624$		0			0
$625$	15.0930	+	26.1419i	0.603722	+	1.04568i
$626$	−1.81291	−	3.14005i	−0.0724585	−	0.125502i
$627$		0			0
$628$	−5.48329	+	9.49734i	−0.218807	+	0.378985i
$629$	−36.0007			−1.43544
$630$		0			0
$631$	−21.0294			−0.837169			−0.418585	−	0.908178i	$-0.637474\pi$
$631$	−21.0294			−0.837169			−0.418585	+	0.908178i	$0.637474\pi$
$632$	−1.55487	+	2.69312i	−0.0618496	+	0.107127i
$633$		0			0
$634$	−25.6694	−	44.4607i	−1.01946	−	1.76576i
$635$	5.79673	+	10.0402i	0.230036	+	0.398434i
$636$		0			0
$637$		0			0
$638$	3.37150			0.133479
$639$		0			0
$640$	−60.5764			−2.39449
$641$	5.96592	−	10.3333i	0.235640	−	0.408140i	−0.723819	−	0.689990i	$-0.757615\pi$
$641$	5.96592	−	10.3333i	0.235640	−	0.408140i	0.959458	+	0.281850i	$0.0909481\pi$
$642$		0			0
$643$	−19.9678	−	34.5852i	−0.787452	−	1.36391i	−0.927524	−	0.373765i	$-0.878067\pi$
$643$	−19.9678	−	34.5852i	−0.787452	−	1.36391i	0.140072	−	0.990141i	$-0.455267\pi$
$644$		0			0
$645$		0			0
$646$	−8.71733	+	15.0989i	−0.342979	+	0.594057i
$647$	0.988954			0.0388798			0.0194399	−	0.999811i	$-0.493812\pi$
$647$	0.988954			0.0388798			0.0194399	+	0.999811i	$0.493812\pi$
$648$		0			0
$649$	16.5343			0.649027
$650$	−6.17856	+	10.7016i	−0.242343	+	0.419751i
$651$		0			0
$652$	−0.718272	−	1.24408i	−0.0281297	−	0.0487221i
$653$	11.3573	+	19.6715i	0.444447	+	0.769804i	0.998014	−	0.0630004i	$-0.0200669\pi$
$653$	11.3573	+	19.6715i	0.444447	+	0.769804i	−0.553567	+	0.832805i	$0.686734\pi$
$654$		0			0
$655$	7.78211	−	13.4790i	0.304072	−	0.526668i
$656$	−4.11376			−0.160615
$657$		0			0
$658$		0			0
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	−0.201220	−	0.979546i	$-0.564491\pi$
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	0.948922	−	0.315512i	$-0.102176\pi$
$660$		0			0
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	−0.980672	−	0.195657i	$-0.937316\pi$
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	0.320892	−	0.947116i	$-0.396017\pi$
$662$	−23.2458	−	40.2628i	−0.903472	−	1.56486i
$663$		0			0
$664$	3.98486	−	6.90198i	0.154642	−	0.267849i
$665$		0			0
$666$		0			0
$667$	−2.74247			−0.106189
$668$	−13.4905	+	23.3662i	−0.521962	+	0.904064i
$669$		0			0
$670$	−44.6601	−	77.3535i	−1.72537	−	2.98843i
$671$	−0.378860	−	0.656205i	−0.0146257	−	0.0253325i
$672$		0			0
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	0.368626	+	0.929578i	$0.379828\pi$
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	−0.989351	+	0.145549i	$0.953505\pi$
$674$	−23.1403			−0.891332
$675$		0			0
$676$	−40.1171			−1.54297
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	0.227421	+	0.973797i	$0.426971\pi$
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	−0.957043	+	0.289946i	$0.906363\pi$
$678$		0			0
$679$		0			0
$680$	−19.5836	−	33.9198i	−0.750997	−	1.30076i
$681$		0			0
$682$	−5.29031	+	9.16309i	−0.202577	+	0.350873i
$683$	15.1871			0.581120			0.290560	−	0.956857i	$-0.406158\pi$
$683$	15.1871			0.581120			0.290560	+	0.956857i	$0.406158\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$		0			0
$687$		0			0
$688$	−4.93877	−	8.55420i	−0.188289	−	0.326126i
$689$	4.73142	+	8.19507i	0.180253	+	0.312207i
$690$		0			0
$691$	−1.34574	+	2.33089i	−0.0511943	+	0.0886711i	−0.890487	−	0.455009i	$-0.849636\pi$
$691$	−1.34574	+	2.33089i	−0.0511943	+	0.0886711i	0.839293	+	0.543680i	$0.182969\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	20.5420	−	35.5798i	0.779203	−	1.34962i
$696$		0			0
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$	19.4429	+	33.6761i	0.735924	+	1.27466i
$699$		0			0
$700$		0			0
$701$	11.8515			0.447625			0.223813	−	0.974632i	$-0.428150\pi$
$701$	11.8515			0.447625			0.223813	+	0.974632i	$0.428150\pi$
$702$		0			0
$703$	−23.9976			−0.905088
$704$	7.39689	−	12.8118i	0.278781	−	0.482862i
$705$		0			0
$706$	20.3617	+	35.2675i	0.766323	+	1.32731i
$707$		0			0
$708$		0			0
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$	−90.0587			−3.37984
$711$		0			0
$712$	25.9543			0.972679
$713$	4.30328	−	7.45351i	0.161159	−	0.279136i
$714$		0			0
$715$	−2.89830	−	5.02001i	−0.108390	−	0.187738i
$716$	−19.5669	−	33.8908i	−0.731248	−	1.26656i
$717$		0			0
$718$	−3.54123	+	6.13359i	−0.132158	+	0.228904i
$719$	20.9109			0.779845			0.389923	−	0.920848i	$-0.372502\pi$
$719$	20.9109			0.779845			0.389923	+	0.920848i	$0.372502\pi$
$720$		0			0
$721$		0			0
$722$	16.8644	−	29.2100i	0.627628	−	1.08708i
$723$		0			0
$724$	36.2896	+	62.8554i	1.34869	+	2.33600i
$725$	−1.84243	−	3.19119i	−0.0684263	−	0.118518i
$726$		0			0
$727$	1.32165	−	2.28917i	0.0490173	−	0.0849005i	−0.840476	−	0.541849i	$-0.817724\pi$
$727$	1.32165	−	2.28917i	0.0490173	−	0.0849005i	0.889493	+	0.456949i	$0.151058\pi$
$728$		0			0
$729$		0			0
$730$	−72.8924			−2.69787
$731$	−7.18756	+	12.4492i	−0.265841	+	0.460451i
$732$		0			0
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	0.705287	−	0.708922i	$-0.250818\pi$
$733$	−7.07446	−	12.2533i	−0.261301	−	0.452587i	−0.966588	+	0.256335i	$0.917485\pi$
$734$	12.1223	+	20.9964i	0.447442	+	0.774992i
$735$		0			0
$736$	−3.51218	+	6.08327i	−0.129461	+	0.224232i
$737$	17.3435			0.638855
$738$		0			0
$739$	15.7181			0.578200			0.289100	−	0.957299i	$-0.406644\pi$
$739$	15.7181			0.578200			0.289100	+	0.957299i	$0.406644\pi$
$740$	58.7212	−	101.708i	2.15864	−	3.73887i
$741$		0			0
$742$		0			0
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	0.605022	−	0.796208i	$-0.293164\pi$
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	−0.992048	+	0.125861i	$0.959831\pi$
$744$		0			0
$745$	3.18333	−	5.51368i	0.116628	−	0.202006i
$746$	−60.8283			−2.22708
$747$		0			0
$748$	16.5675			0.605768
$749$		0			0
$750$		0			0
$751$	−6.51848	−	11.2903i	−0.237863	−	0.411990i	0.722238	−	0.691644i	$-0.243113\pi$
$751$	−6.51848	−	11.2903i	−0.237863	−	0.411990i	−0.960101	+	0.279654i	$0.909780\pi$
$752$	4.52544	+	7.83829i	0.165026	+	0.285833i
$753$		0			0
$754$	−1.82558	+	3.16200i	−0.0664838	+	0.115153i
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$	−11.7613	+	20.3711i	−0.427188	+	0.739912i
$759$		0			0
$760$	−13.0542	−	22.6105i	−0.473525	−	0.820169i
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	0.806074	−	0.591814i	$-0.201588\pi$
$761$	−3.02038	−	5.23146i	−0.109489	−	0.189640i	−0.915563	+	0.402174i	$0.868255\pi$
$762$		0			0
$763$		0			0
$764$	−30.6388			−1.10847
$765$		0			0
$766$	65.1918			2.35547
$767$	−8.95288	+	15.5068i	−0.323270	+	0.559920i
$768$		0			0
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	0.867968	−	0.496619i	$-0.165425\pi$
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	−0.864069	+	0.503373i	$0.832092\pi$
$770$		0			0
$771$		0			0
$772$	34.7251	−	60.1457i	1.24979	−	2.16469i
$773$	37.6264			1.35333			0.676663	−	0.736293i	$-0.263425\pi$
$773$	37.6264			1.35333			0.676663	+	0.736293i	$0.263425\pi$
$774$		0			0
$775$	11.5640			0.415393
$776$	−16.7763	+	29.0575i	−0.602235	+	1.04310i
$777$		0			0
$778$	4.99388	+	8.64965i	0.179039	+	0.310105i
$779$	1.99539	+	3.45612i	0.0714923	+	0.123828i
$780$		0			0
$781$	8.74345	−	15.1441i	0.312865	−	0.541898i
$782$	−20.7667			−0.742614
$783$		0			0
$784$		0			0
$785$	−4.33198	+	7.50321i	−0.154615	+	0.267801i
$786$		0			0
$787$	−15.4067	−	26.6853i	−0.549191	−	0.951226i	−0.998330	−	0.0577648i	$-0.981603\pi$
$787$	−15.4067	−	26.6853i	−0.549191	−	0.951226i	0.449139	−	0.893462i	$-0.351731\pi$
$788$	11.0847	+	19.1992i	0.394875	+	0.683943i
$789$		0			0
$790$	−2.67601	+	4.63499i	−0.0952083	+	0.164906i
$791$		0			0
$792$		0			0
$793$	0.820571			0.0291393
$794$	36.6037	−	63.3994i	1.29902	−	2.24996i
$795$		0			0
$796$	26.6355	+	46.1340i	0.944070	+	1.63518i
$797$	17.9792	+	31.1408i	0.636855	+	1.10306i	0.986119	+	0.166040i	$0.0530981\pi$
$797$	17.9792	+	31.1408i	0.636855	+	1.10306i	−0.349264	+	0.937024i	$0.613569\pi$
$798$		0			0
$799$	6.58602	−	11.4073i	0.232997	−	0.403562i
$800$	−9.43814			−0.333689
$801$		0			0
$802$	16.3454			0.577174
$803$	7.07684	−	12.2574i	0.249736	−	0.432556i
$804$		0			0
$805$		0			0
$806$	−5.72914	−	9.92315i	−0.201800	−	0.349528i
$807$		0			0
$808$	−32.8659	+	56.9254i	−1.15622	+	2.00263i
$809$	−38.9636			−1.36989			−0.684943	−	0.728596i	$-0.740173\pi$
$809$	−38.9636			−1.36989			−0.684943	+	0.728596i	$0.740173\pi$
$810$		0			0
$811$	−28.2811			−0.993082			−0.496541	−	0.868013i	$-0.665397\pi$
$811$	−28.2811			−0.993082			−0.496541	+	0.868013i	$0.665397\pi$
$812$		0			0
$813$		0			0
$814$	17.5701	+	30.4322i	0.615830	+	1.06665i
$815$	−0.567459	−	0.982867i	−0.0198772	−	0.0344283i
$816$		0			0
$817$	−4.79113	+	8.29849i	−0.167621	+	0.290327i
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	−0.233077	−	0.972458i	$-0.574879\pi$
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	0.958712	−	0.284378i	$-0.0917872\pi$
$822$		0			0
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	0.782835	−	0.622229i	$-0.213773\pi$
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	−0.930284	+	0.366841i	$0.880439\pi$
$824$	4.51029	+	7.81205i	0.157123	+	0.272146i
$825$		0			0
$826$		0			0
$827$	−44.2823			−1.53985			−0.769923	−	0.638137i	$-0.779706\pi$
$827$	−44.2823			−1.53985			−0.769923	+	0.638137i	$0.779706\pi$
$828$		0			0
$829$	16.6327			0.577679			0.288839	−	0.957378i	$-0.406731\pi$
$829$	16.6327			0.577679			0.288839	+	0.957378i	$0.406731\pi$
$830$	6.85813	−	11.8786i	0.238049	−	0.412314i
$831$		0			0
$832$	8.01045	+	13.8745i	0.277712	+	0.481012i
$833$		0			0
$834$		0			0
$835$	−10.6579	+	18.4601i	−0.368832	+	0.638836i
$836$	11.0437			0.381954
$837$		0			0
$838$	53.6137			1.85205
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	0.488945	+	0.872314i	$0.337382\pi$
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	−0.999919	+	0.0127182i	$0.995952\pi$
$840$		0			0
$841$	13.9556	+	24.1718i	0.481228	+	0.833512i
$842$	24.8657	+	43.0687i	0.856929	+	1.48424i
$843$		0			0
$844$	−25.5997	+	44.3400i	−0.881178	+	1.52624i
$845$	−31.6938			−1.09030
$846$		0			0
$847$		0			0
$848$	7.34105	−	12.7151i	0.252093	−	0.436638i
$849$		0			0
$850$	−13.9514	−	24.1645i	−0.478528	−	0.828834i
$851$	−14.2920	−	24.7544i	−0.489922	−	0.848570i
$852$		0			0
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	0.484124	+	0.875000i	$0.339139\pi$
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	−0.999834	+	0.0182366i	$0.994195\pi$
$854$		0			0
$855$		0			0
$856$	−70.9227			−2.42409
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	−0.353361	−	0.935487i	$-0.614961\pi$
$857$	18.5447	−	32.1204i	0.633475	−	1.09721i	0.986836	−	0.161724i	$-0.0517053\pi$
$858$		0			0
$859$	1.89166	+	3.27646i	0.0645427	+	0.111791i	0.896491	−	0.443062i	$-0.146108\pi$
$859$	1.89166	+	3.27646i	0.0645427	+	0.111791i	−0.831948	+	0.554853i	$0.812774\pi$
$860$	−23.4474	−	40.6121i	−0.799551	−	1.38486i
$861$		0			0
$862$	24.1583	−	41.8434i	0.822835	−	1.42519i
$863$	0.427118			0.0145393			0.00726963	−	0.999974i	$-0.497686\pi$
$863$	0.427118			0.0145393			0.00726963	+	0.999974i	$0.497686\pi$
$864$		0			0
$865$	11.8444			0.402720
$866$	25.8694	−	44.8071i	0.879077	−	1.52261i
$867$		0			0
$868$		0			0
$869$	−0.519608	−	0.899987i	−0.0176265	−	0.0305300i
$870$		0			0
$871$	−9.39105	+	16.2658i	−0.318203	+	0.551145i
$872$	63.1866			2.13977
$873$		0			0
$874$	−13.8428			−0.468240
$875$		0			0
$876$		0			0
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	0.755167	−	0.655532i	$-0.227556\pi$
$877$	−5.63038	−	9.75210i	−0.190124	−	0.329305i	−0.945291	+	0.326228i	$0.894222\pi$
$878$	42.3408	+	73.3364i	1.42893	+	2.47498i
$879$		0			0
$880$	−4.49687	+	7.78881i	−0.151589	+	0.262561i
$881$	35.4810			1.19538			0.597692	−	0.801726i	$-0.296084\pi$
$881$	35.4810			1.19538			0.597692	+	0.801726i	$0.296084\pi$
$882$		0			0
$883$	−5.30092			−0.178390			−0.0891952	−	0.996014i	$-0.528429\pi$
$883$	−5.30092			−0.178390			−0.0891952	+	0.996014i	$0.528429\pi$
$884$	−8.97088	+	15.5380i	−0.301723	+	0.522600i
$885$		0			0
$886$	−22.9214	−	39.7010i	−0.770060	−	1.33378i
$887$	28.7832	+	49.8540i	0.966446	+	1.67393i	0.705679	+	0.708532i	$0.250642\pi$
$887$	28.7832	+	49.8540i	0.966446	+	1.67393i	0.260767	+	0.965402i	$0.416025\pi$
$888$		0			0
$889$		0			0
$890$	44.6686			1.49730
$891$		0			0
$892$	−17.2846			−0.578732
$893$	4.39016	−	7.60398i	0.146911	−	0.254458i
$894$		0			0
$895$	−15.4585	−	26.7749i	−0.516720	−	0.894985i
$896$		0			0
$897$		0			0
$898$	−35.3354	+	61.2027i	−1.17916	+	2.04236i
$899$	3.41683			0.113958
$900$		0			0
$901$	−21.3674			−0.711850
$902$	2.92188	−	5.06085i	0.0972881	−	0.168508i
$903$		0			0
$904$	3.42117	+	5.92565i	0.113787	+	0.197084i
$905$	28.6700	+	49.6579i	0.953023	+	1.65068i
$906$		0			0
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	−0.985704	−	0.168485i	$-0.946112\pi$
$907$	−10.4486	+	18.0975i	−0.346939	+	0.600917i	0.638765	+	0.769402i	$0.279446\pi$
$908$	−72.8804			−2.41862
$909$		0			0
$910$		0			0
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	−0.990639	−	0.136508i	$-0.956412\pi$
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	0.613539	+	0.789665i	$0.289746\pi$
$912$		0			0
$913$	1.33166	+	2.30650i	0.0440715	+	0.0763340i
$914$	11.4116	+	19.7654i	0.377461	+	0.653782i
$915$		0			0
$916$	−51.8946	+	89.8841i	−1.71465	+	2.96986i
$917$		0			0
$918$		0			0
$919$	−37.3030			−1.23051			−0.615257	−	0.788327i	$-0.710948\pi$
$919$	−37.3030			−1.23051			−0.615257	+	0.788327i	$0.710948\pi$
$920$	15.5490	−	26.9317i	0.512636	−	0.887911i
$921$		0			0
$922$	−26.0616	−	45.1399i	−0.858292	−	1.48660i
$923$	9.46870	+	16.4003i	0.311666	+	0.539822i
$924$		0			0
$925$	19.2031	−	33.2607i	0.631394	−	1.09361i
$926$	−62.4140			−2.05105
$927$		0			0
$928$	−2.78869			−0.0915432
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	−0.815791	−	0.578347i	$-0.803698\pi$
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	0.908759	+	0.417322i	$0.137031\pi$
$930$		0			0
$931$		0			0
$932$	25.5145	+	44.1923i	0.835754	+	1.44757i
$933$		0			0
$934$	41.7138	−	72.2503i	1.36492	−	2.36410i
$935$	13.0889			0.428052
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$		0			0
$939$		0			0
$940$	21.4851	+	37.2133i	0.700766	+	1.21376i
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	0.983178	−	0.182650i	$-0.0584674\pi$
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	−0.649768	+	0.760132i	$0.725134\pi$
$942$		0			0
$943$	−2.37674	+	4.11663i	−0.0773973	+	0.134056i
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	−0.902150	−	0.431423i	$-0.858012\pi$
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	0.824698	+	0.565573i	$0.191345\pi$
$948$		0			0
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$	−9.29980	−	16.1077i	−0.301725	−	0.522604i
$951$		0			0
$952$		0			0
$953$	48.9412			1.58536			0.792680	−	0.609638i	$-0.208685\pi$
$953$	48.9412			1.58536			0.792680	+	0.609638i	$0.208685\pi$
$954$		0			0
$955$	−24.2056			−0.783276
$956$	−20.4478	+	35.4166i	−0.661328	+	1.14545i
$957$		0			0
$958$	−35.5773	−	61.6217i	−1.14945	−	1.99091i
$959$		0			0
$960$		0			0
$961$	10.1386	−	17.5605i	0.327050	−	0.566468i
$962$	−38.0549			−1.22694
$963$		0			0
$964$	−85.6619			−2.75898
$965$	27.4340	−	47.5171i	0.883132	−	1.52963i
$966$		0			0
$967$	−2.95856	−	5.12438i	−0.0951409	−	0.164789i	0.814526	−	0.580126i	$-0.196997\pi$
$967$	−2.95856	−	5.12438i	−0.0951409	−	0.164789i	−0.909667	+	0.415337i	$0.863664\pi$
$968$	18.5680	+	32.1608i	0.596799	+	1.03369i
$969$		0			0
$970$	−28.8729	+	50.0093i	−0.927052	+	1.60570i
$971$	28.9775			0.929933			0.464966	−	0.885328i	$-0.346066\pi$
$971$	28.9775			0.929933			0.464966	+	0.885328i	$0.346066\pi$
$972$		0			0
$973$		0			0
$974$	−26.7933	+	46.4074i	−0.858513	+	1.48699i
$975$		0			0
$976$	−0.636580	−	1.10259i	−0.0203764	−	0.0352930i
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	0.988848	−	0.148930i	$-0.0475830\pi$
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	−0.623401	+	0.781902i	$0.714250\pi$
$978$		0			0
$979$	−4.33670	+	7.51139i	−0.138602	+	0.240065i
$980$		0			0
$981$		0			0
$982$	83.6465			2.66927
$983$	−15.6351	+	27.0809i	−0.498684	+	0.863745i	−0.999999	−	0.00151933i	$-0.999516\pi$
$983$	−15.6351	+	27.0809i	−0.498684	+	0.863745i	0.501315	+	0.865265i	$0.332850\pi$
$984$		0			0
$985$	8.75726	+	15.1680i	0.279029	+	0.483293i
$986$	−4.12221	−	7.13988i	−0.131278	−	0.227380i
$987$		0			0
$988$	−5.97988	+	10.3574i	−0.190245	+	0.329514i
$989$	−11.4136			−0.362930
$990$		0			0
$991$	−7.01463			−0.222827			−0.111414	−	0.993774i	$-0.535538\pi$
$991$	−7.01463			−0.222827			−0.111414	+	0.993774i	$0.535538\pi$
$992$	4.37581	−	7.57912i	0.138932	−	0.240637i
$993$		0			0
$994$		0			0
$995$	21.0429	+	36.4474i	0.667105	+	1.15546i
$996$		0			0
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	−0.646790	−	0.762668i	$-0.723889\pi$
$997$	10.6439	−	18.4358i	0.337095	−	0.583866i	0.983885	+	0.178802i	$0.0572222\pi$
$998$	−21.3271			−0.675099
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.e.883.1		10
3.2	odd	2		441.2.f.e.295.5		10
7.2	even	3		189.2.h.b.46.5		10
7.3	odd	6		1323.2.g.f.667.1		10
7.4	even	3		189.2.g.b.100.1		10
7.5	odd	6		1323.2.h.f.802.5		10
7.6	odd	2		1323.2.f.f.883.1		10
9.2	odd	6		3969.2.a.z.1.1		5
9.4	even	3	inner	1323.2.f.e.442.1		10
9.5	odd	6		441.2.f.e.148.5		10
9.7	even	3		3969.2.a.bc.1.5		5
21.2	odd	6		63.2.h.b.25.1	yes	10
21.5	even	6		441.2.h.f.214.1		10
21.11	odd	6		63.2.g.b.16.5	yes	10
21.17	even	6		441.2.g.f.79.5		10
21.20	even	2		441.2.f.f.295.5		10
28.11	odd	6		3024.2.t.i.289.4		10
28.23	odd	6		3024.2.q.i.2881.2		10
63.2	odd	6		567.2.e.f.487.5		10
63.4	even	3		189.2.h.b.37.5		10
63.5	even	6		441.2.g.f.67.5		10
63.11	odd	6		567.2.e.f.163.5		10
63.13	odd	6		1323.2.f.f.442.1		10
63.16	even	3		567.2.e.e.487.1		10
63.20	even	6		3969.2.a.ba.1.1		5
63.23	odd	6		63.2.g.b.4.5	✓	10
63.25	even	3		567.2.e.e.163.1		10
63.31	odd	6		1323.2.h.f.226.5		10
63.32	odd	6		63.2.h.b.58.1	yes	10
63.34	odd	6		3969.2.a.bb.1.5		5
63.40	odd	6		1323.2.g.f.361.1		10
63.41	even	6		441.2.f.f.148.5		10
63.58	even	3		189.2.g.b.172.1		10
63.59	even	6		441.2.h.f.373.1		10
84.11	even	6		1008.2.t.i.961.3		10
84.23	even	6		1008.2.q.i.529.4		10
252.23	even	6		1008.2.t.i.193.3		10
252.67	odd	6		3024.2.q.i.2305.2		10
252.95	even	6		1008.2.q.i.625.4		10
252.247	odd	6		3024.2.t.i.1873.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	63.23	odd	6
63.2.g.b.16.5	yes	10	21.11	odd	6
63.2.h.b.25.1	yes	10	21.2	odd	6
63.2.h.b.58.1	yes	10	63.32	odd	6
189.2.g.b.100.1		10	7.4	even	3
189.2.g.b.172.1		10	63.58	even	3
189.2.h.b.37.5		10	63.4	even	3
189.2.h.b.46.5		10	7.2	even	3
441.2.f.e.148.5		10	9.5	odd	6
441.2.f.e.295.5		10	3.2	odd	2
441.2.f.f.148.5		10	63.41	even	6
441.2.f.f.295.5		10	21.20	even	2
441.2.g.f.67.5		10	63.5	even	6
441.2.g.f.79.5		10	21.17	even	6
441.2.h.f.214.1		10	21.5	even	6
441.2.h.f.373.1		10	63.59	even	6
567.2.e.e.163.1		10	63.25	even	3
567.2.e.e.487.1		10	63.16	even	3
567.2.e.f.163.5		10	63.11	odd	6
567.2.e.f.487.5		10	63.2	odd	6
1008.2.q.i.529.4		10	84.23	even	6
1008.2.q.i.625.4		10	252.95	even	6
1008.2.t.i.193.3		10	252.23	even	6
1008.2.t.i.961.3		10	84.11	even	6
1323.2.f.e.442.1		10	9.4	even	3	inner
1323.2.f.e.883.1		10	1.1	even	1	trivial
1323.2.f.f.442.1		10	63.13	odd	6
1323.2.f.f.883.1		10	7.6	odd	2
1323.2.g.f.361.1		10	63.40	odd	6
1323.2.g.f.667.1		10	7.3	odd	6
1323.2.h.f.226.5		10	63.31	odd	6
1323.2.h.f.802.5		10	7.5	odd	6
3024.2.q.i.2305.2		10	252.67	odd	6
3024.2.q.i.2881.2		10	28.23	odd	6
3024.2.t.i.289.4		10	28.11	odd	6
3024.2.t.i.1873.4		10	252.247	odd	6
3969.2.a.z.1.1		5	9.2	odd	6
3969.2.a.ba.1.1		5	63.20	even	6
3969.2.a.bb.1.5		5	63.34	odd	6
3969.2.a.bc.1.5		5	9.7	even	3

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +(-1.46043 - 2.52954i) q^{5} +4.05086 q^{8} +6.97172 q^{10} +(-0.676857 + 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(-1.13729 + 1.96984i) q^{16} +3.31027 q^{17} +2.20659 q^{19} +(-5.39943 + 9.35209i) q^{20} +(-1.61557 - 2.79825i) q^{22} +(1.31415 + 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +3.49916 q^{26} +(-0.521720 + 0.903646i) q^{29} +(-1.63729 - 2.83587i) q^{31} +(1.33629 + 2.31453i) q^{32} +(-3.95060 + 6.84263i) q^{34} -10.8755 q^{37} +(-2.63342 + 4.56121i) q^{38} +(-5.91601 - 10.2468i) q^{40} +(0.904289 + 1.56627i) q^{41} +(-2.17129 + 3.76078i) q^{43} +5.00488 q^{44} -6.27340 q^{46} +(1.98957 - 3.44604i) q^{47} +(-4.21456 - 7.29984i) q^{50} +(-2.71001 + 4.69388i) q^{52} -6.45486 q^{53} +3.95402 q^{55} +(-1.24528 - 2.15688i) q^{58} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(-2.14100 + 3.70832i) q^{65} +(-6.40588 - 11.0953i) q^{67} +(-6.11928 - 10.5989i) q^{68} -12.9177 q^{71} -10.4554 q^{73} +(12.9791 - 22.4805i) q^{74} +(-4.07903 - 7.06509i) q^{76} +(-0.383838 + 0.664827i) q^{79} +6.64375 q^{80} -4.31684 q^{82} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(-5.18258 - 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +6.40711 q^{89} +(4.85859 - 8.41533i) q^{92} +(4.74884 + 8.22524i) q^{94} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 + 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34}+ \cdots - 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * q^89 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97

Introduction

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