LMFDB - Embedded newform 1323.2.f.f.442.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			442.1
Root			$1.19343 + 2.06709i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.f.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.886585	−	0.462565i	$-0.846929\pi$
$2$	−1.19343	−	2.06709i	−0.843886	−	1.46165i	0.0426999	−	0.999088i	$-0.486404\pi$
$3$		0			0
$3$		0			0
$4$	−1.84857	+	3.20182i	−0.924286	+	1.60091i
$5$	1.46043	−	2.52954i	0.653125	−	1.13125i	−0.329235	−	0.944248i	$-0.606791\pi$
$5$	1.46043	−	2.52954i	0.653125	−	1.13125i	0.982360	−	0.186998i	$-0.0598759\pi$
$6$		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	0.745759	−	0.666216i	$-0.232087\pi$
$11$	−0.676857	−	1.17235i	−0.204080	−	0.353477i	−0.949839	+	0.312738i	$0.898754\pi$
$12$		0			0
$13$	0.733001	−	1.26960i	0.203298	−	0.352123i	−0.746291	−	0.665620i	$-0.768167\pi$
$13$	0.733001	−	1.26960i	0.203298	−	0.352123i	0.949589	+	0.313497i	$0.101501\pi$
$14$		0			0
$15$		0			0
$16$	−1.13729	−	1.96984i	−0.284323	−	0.492461i
$17$	−3.31027			−0.802859			−0.401430	−	0.915890i	$-0.631487\pi$
$17$	−3.31027			−0.802859			−0.401430	+	0.915890i	$0.631487\pi$
$18$		0			0
$19$	−2.20659			−0.506226			−0.253113	−	0.967437i	$-0.581454\pi$
$19$	−2.20659			−0.506226			−0.253113	+	0.967437i	$0.581454\pi$
$20$	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	−0.695868	−	0.718169i	$-0.744980\pi$
$23$	1.31415	−	2.27617i	0.274019	−	0.474614i	0.969887	+	0.243555i	$0.0783136\pi$
$24$		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	0.813511	−	0.581549i	$-0.197553\pi$
$29$	−0.521720	−	0.903646i	−0.0968810	−	0.167803i	−0.910392	+	0.413747i	$0.864220\pi$
$30$		0			0
$31$	1.63729	−	2.83587i	0.294066	−	0.509337i	−0.680701	−	0.732561i	$-0.738325\pi$
$31$	1.63729	−	2.83587i	0.294066	−	0.509337i	0.974767	+	0.223224i	$0.0716581\pi$
$32$	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	$-0.878438\pi$
$41$	−0.904289	+	1.56627i	−0.141226	+	0.244611i	0.786732	+	0.617294i	$0.211771\pi$
$42$		0			0
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	0.651613	−	0.758551i	$-0.274093\pi$
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	−0.982731	+	0.185038i	$0.940759\pi$
$44$	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	$-0.260391\pi$
$47$	−1.98957	−	3.44604i	−0.290209	−	0.502656i	−0.973859	+	0.227154i	$0.927058\pi$
$48$		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	−0.127735	−	0.991808i	$-0.540771\pi$
$59$	6.10700	−	10.5776i	0.795064	−	1.37709i	0.922799	−	0.385283i	$-0.125896\pi$
$60$		0			0
$61$	0.279867	+	0.484744i	0.0358333	+	0.0620651i	0.883386	−	0.468646i	$-0.155258\pi$
$61$	0.279867	+	0.484744i	0.0358333	+	0.0620651i	−0.847553	+	0.530711i	$0.821925\pi$
$62$	−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	0.147817	+	0.989015i	$0.452775\pi$
$67$	−6.40588	+	11.0953i	−0.782603	+	1.35551i	−0.930420	+	0.366494i	$0.880558\pi$
$68$	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	$-0.290422\pi$
$73$	10.4554			1.22372			0.611858	+	0.790968i	$0.290422\pi$
$74$	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	0.843625	−	0.536933i	$-0.180417\pi$
$79$	−0.383838	−	0.664827i	−0.0431852	−	0.0747989i	−0.886810	+	0.462134i	$0.847084\pi$
$80$	−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	$-0.201104\pi$
$83$	−0.983707	−	1.70383i	−0.107976	−	0.187020i	−0.914950	+	0.403567i	$0.867770\pi$
$84$		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	$-0.610284\pi$
$89$	−6.40711			−0.679153			−0.339576	+	0.940579i	$0.610284\pi$
$90$		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	$-0.0285220\pi$
$97$	4.14143	+	7.17316i	0.420498	+	0.728324i	−0.575490	+	0.817809i	$0.695189\pi$
$98$		0			0
$99$		0			0
$100$	13.0563			1.30563
$101$	8.11331	+	14.0527i	0.807305	+	1.39829i	0.914724	+	0.404079i	$0.132408\pi$
$101$	8.11331	+	14.0527i	0.807305	+	1.39829i	−0.107419	+	0.994214i	$0.534259\pi$
$102$		0			0
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	−0.915652	−	0.401972i	$-0.868325\pi$
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	0.805944	+	0.591992i	$0.201658\pi$
$104$	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	−0.823563	−	0.567224i	$-0.808017\pi$
$113$	0.844555	−	1.46281i	0.0794491	−	0.137610i	0.903012	+	0.429615i	$0.141351\pi$
$114$		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	$-0.908116\pi$
$131$	−2.66432	+	4.61473i	−0.232782	+	0.403191i	0.725844	+	0.687860i	$0.241450\pi$
$132$		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	0.660338	−	0.750969i	$-0.270413\pi$
$137$	−3.74772	−	6.49124i	−0.320189	−	0.554584i	−0.980527	+	0.196385i	$0.937080\pi$
$138$		0			0
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	0.396812	+	0.917900i	$0.370116\pi$
$139$	−7.03285	+	12.1812i	−0.596518	+	1.03320i	−0.993331	+	0.115300i	$0.963217\pi$
$140$		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	−0.817924	−	0.575326i	$-0.804875\pi$
$149$	1.08986	−	1.88769i	0.0892846	−	0.154645i	0.907209	+	0.420680i	$0.138209\pi$
$150$		0			0
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	−0.996486	−	0.0837595i	$-0.973307\pi$
$151$	−7.01387	−	12.1484i	−0.570781	−	0.988621i	0.425705	−	0.904862i	$-0.360026\pi$
$152$	−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	$-0.795568\pi$
$157$	1.48312	−	2.56883i	0.118365	−	0.205015i	0.919120	+	0.393978i	$0.128901\pi$
$158$	−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	$-0.742216\pi$
$167$	3.64889	−	6.32006i	0.282360	−	0.489061i	0.971965	+	0.235124i	$0.0755496\pi$
$168$		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	$-0.117402\pi$
$173$	2.02754	+	3.51181i	0.154151	+	0.266998i	−0.778598	+	0.627522i	$0.784069\pi$
$174$		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	$-0.239713\pi$
$181$	19.6312			1.45917			0.729586	+	0.683889i	$0.239713\pi$
$182$		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	0.976094	−	0.217348i	$-0.0697406\pi$
$191$	4.14357	+	7.17688i	0.299818	+	0.519301i	−0.676276	+	0.736648i	$0.736407\pi$
$192$		0			0
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	−0.300070	−	0.953917i	$-0.597010\pi$
$193$	9.39242	−	16.2682i	0.676082	−	1.17101i	0.976152	−	0.217090i	$-0.0696566\pi$
$194$	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	$-0.329385\pi$
$199$	14.4087			1.02140			0.510702	+	0.859758i	$0.329385\pi$
$200$	−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	−0.999643	−	0.0267212i	$-0.991493\pi$
$211$	−6.92418	+	11.9930i	−0.476680	+	0.825634i	0.522963	+	0.852356i	$0.324827\pi$
$212$	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	$-0.216699\pi$
$223$	−2.33756	−	4.04878i	−0.156535	−	0.271126i	−0.933617	+	0.358273i	$0.883366\pi$
$224$		0			0
$225$		0			0
$226$	−4.03169			−0.268184
$227$	−9.85631	−	17.0716i	−0.654187	−	1.13308i	−0.982097	−	0.188376i	$-0.939678\pi$
$227$	−9.85631	−	17.0716i	−0.654187	−	1.13308i	0.327910	−	0.944709i	$-0.393656\pi$
$228$		0			0
$229$	14.0364	−	24.3118i	0.927552	−	1.60657i	0.140148	−	0.990131i	$-0.455242\pi$
$229$	14.0364	−	24.3118i	0.927552	−	1.60657i	0.787404	−	0.616437i	$-0.211425\pi$
$230$	−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	−0.987585	−	0.157087i	$-0.949790\pi$
$239$	−5.53069	+	9.57944i	−0.357751	+	0.619642i	0.629834	+	0.776730i	$0.283123\pi$
$240$		0			0
$241$	−11.5849	−	20.0656i	−0.746247	−	1.29254i	−0.949610	−	0.313435i	$-0.898520\pi$
$241$	−11.5849	−	20.0656i	−0.746247	−	1.29254i	0.203362	−	0.979104i	$-0.434813\pi$
$242$	−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	$-0.579005\pi$
$251$	−7.78402			−0.491323			−0.245662	+	0.969356i	$0.579005\pi$
$252$		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	$-0.938232\pi$
$257$	−5.18798	+	8.98585i	−0.323618	+	0.560522i	0.657614	+	0.753355i	$0.271566\pi$
$258$		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	−0.994245	−	0.107128i	$-0.965835\pi$
$263$	−9.56654	−	16.5697i	−0.589898	−	1.02173i	0.404347	−	0.914605i	$-0.367499\pi$
$264$		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	$-0.413176\pi$
$269$	8.83681			0.538790			0.269395	+	0.963030i	$0.413176\pi$
$270$		0			0
$271$	−18.3391			−1.11402			−0.557010	−	0.830506i	$-0.688052\pi$
$271$	−18.3391			−1.11402			−0.557010	+	0.830506i	$0.688052\pi$
$272$	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	0.779101	−	0.626899i	$-0.215676\pi$
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	−0.932460	+	0.361272i	$0.882343\pi$
$278$	33.5730			2.01357
$279$		0			0
$280$		0			0
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	0.890351	−	0.455274i	$-0.150459\pi$
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	−0.839455	+	0.543430i	$0.817125\pi$
$282$		0			0
$283$	−6.24415	+	10.8152i	−0.371176	+	0.642896i	−0.989747	−	0.142833i	$-0.954379\pi$
$283$	−6.24415	+	10.8152i	−0.371176	+	0.642896i	0.618571	+	0.785729i	$0.287712\pi$
$284$	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	$-0.881909\pi$
$293$	−2.60202	+	4.50684i	−0.152012	+	0.263292i	0.779955	+	0.625835i	$0.215242\pi$
$294$		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	$-0.545585\pi$
$307$	−5.00136			−0.285442			−0.142721	+	0.989763i	$0.545585\pi$
$308$		0			0
$309$		0			0
$310$	−11.4147	+	19.7709i	−0.648313	+	1.12291i
$311$	16.1984	−	28.0565i	0.918528	−	1.59094i	0.116876	−	0.993146i	$-0.462712\pi$
$311$	16.1984	−	28.0565i	0.918528	−	1.59094i	0.801652	−	0.597791i	$-0.203955\pi$
$312$		0			0
$313$	0.759535	+	1.31555i	0.0429315	+	0.0743595i	0.886693	−	0.462359i	$-0.152997\pi$
$313$	0.759535	+	1.31555i	0.0429315	+	0.0743595i	−0.843761	+	0.536719i	$0.819664\pi$
$314$	−7.08000			−0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	−10.7544	−	18.6272i	−0.604029	−	1.04621i	−0.992204	−	0.124623i	$-0.960228\pi$
$317$	−10.7544	−	18.6272i	−0.604029	−	1.04621i	0.388175	−	0.921586i	$-0.373106\pi$
$318$		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	−0.999149	−	0.0412580i	$-0.986863\pi$
$331$	−9.73902	−	16.8685i	−0.535305	−	0.927175i	0.463844	−	0.885917i	$-0.346470\pi$
$332$	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	−0.703260	−	0.710933i	$-0.748273\pi$
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	0.967316	+	0.253575i	$0.0816063\pi$
$338$	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	−0.837553	−	0.546356i	$-0.816015\pi$
$347$	1.01302	−	1.75460i	0.0543817	−	0.0941919i	0.891935	+	0.452164i	$0.149348\pi$
$348$		0			0
$349$	−8.14577	−	14.1089i	−0.436033	−	0.755231i	0.561346	−	0.827581i	$-0.310284\pi$
$349$	−8.14577	−	14.1089i	−0.436033	−	0.755231i	−0.997379	+	0.0723497i	$0.976950\pi$
$350$		0			0
$351$		0			0
$352$	−3.61792			−0.192836
$353$	−8.53072	−	14.7756i	−0.454045	−	0.786428i	0.544588	−	0.838704i	$-0.316686\pi$
$353$	−8.53072	−	14.7756i	−0.454045	−	0.786428i	−0.998633	+	0.0522753i	$0.983353\pi$
$354$		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	$-0.252074\pi$
$367$	−5.07874	−	8.79664i	−0.265108	−	0.459181i	−0.967592	+	0.252519i	$0.918741\pi$
$368$	−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	−0.320904	−	0.947112i	$-0.603987\pi$
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	0.980675	−	0.195645i	$-0.0626799\pi$
$374$	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	−0.271419	−	0.962461i	$-0.587493\pi$
$383$	13.6563	−	23.6535i	0.697806	−	1.20864i	0.969225	−	0.246175i	$-0.0791737\pi$
$384$		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	0.914179	−	0.405311i	$-0.132837\pi$
$389$	2.09223	+	3.62385i	0.106080	+	0.183736i	−0.808099	+	0.589047i	$0.799503\pi$
$390$		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	$-0.220424\pi$
$397$	30.6709			1.53933			0.769664	+	0.638450i	$0.220424\pi$
$398$	−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	−0.938765	−	0.344557i	$-0.888029\pi$
$401$	−3.42402	+	5.93057i	−0.170987	+	0.296158i	0.767778	+	0.640716i	$0.221362\pi$
$402$		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	$-0.982513\pi$
$409$	−9.13490	+	15.8221i	−0.451692	+	0.782353i	0.546799	+	0.837264i	$0.315846\pi$
$410$	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	−0.449698	−	0.893181i	$-0.648468\pi$
$419$	11.2310	−	19.4526i	0.548669	−	0.950322i	0.998366	−	0.0571410i	$-0.0181984\pi$
$420$		0			0
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	0.999960	+	0.00894684i	$0.00284791\pi$
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	−0.492232	+	0.870464i	$0.663819\pi$
$422$	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	$-0.325615\pi$
$433$	21.6764			1.04170			0.520851	+	0.853648i	$0.325615\pi$
$434$		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	−0.884191	−	0.467126i	$-0.845289\pi$
$439$	−17.7390	−	30.7249i	−0.846639	−	1.46642i	0.0375520	−	0.999295i	$-0.488044\pi$
$440$	−16.0172			−0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	−9.60313	−	16.6331i	−0.456258	−	0.790263i	0.542501	−	0.840055i	$-0.317477\pi$
$443$	−9.60313	−	16.6331i	−0.456258	−	0.790263i	−0.998760	+	0.0497923i	$0.984144\pi$
$444$		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	0.955912	−	0.293653i	$-0.0948711\pi$
$457$	4.78098	+	8.28090i	0.223645	+	0.387364i	−0.732267	+	0.681017i	$0.761538\pi$
$458$	−67.0062			−3.13099
$459$		0			0
$460$	28.3826			1.32335
$461$	10.9187	+	18.9118i	0.508536	+	0.880809i	0.999951	+	0.00988416i	$0.00314628\pi$
$461$	10.9187	+	18.9118i	0.508536	+	0.880809i	−0.491416	+	0.870925i	$0.663520\pi$
$462$		0			0
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	−0.384010	−	0.923329i	$-0.625457\pi$
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	0.991631	−	0.129102i	$-0.0412094\pi$
$464$	−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	$-0.200167\pi$
$467$	34.9527			1.61742			0.808709	+	0.588209i	$0.200167\pi$
$468$		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	0.974662	+	0.223684i	$0.0718083\pi$
$479$	14.9054	+	25.8170i	0.681047	+	1.17961i	−0.293615	+	0.955924i	$0.594858\pi$
$480$		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	0.134726	+	0.990883i	$0.456984\pi$
$491$	−17.5222	+	30.3494i	−0.790767	+	1.36965i	−0.925493	+	0.378765i	$0.876349\pi$
$492$		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	−0.748530	−	0.663101i	$-0.769240\pi$
$499$	4.46760	−	7.73811i	0.199997	−	0.346405i	0.948527	+	0.316696i	$0.102573\pi$
$500$	−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	$-0.590932\pi$
$503$	−12.6403			−0.563603			−0.281802	+	0.959473i	$0.590932\pi$
$504$		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	−0.365924	−	0.930645i	$-0.619247\pi$
$509$	14.0555	−	24.3449i	0.623000	−	1.07907i	0.988924	−	0.148423i	$-0.0474196\pi$
$510$		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	$-0.559441\pi$
$521$	−8.47536			−0.371312			−0.185656	+	0.982615i	$0.559441\pi$
$522$		0			0
$523$	33.4473			1.46255			0.731273	−	0.682085i	$-0.238926\pi$
$523$	33.4473			1.46255			0.731273	+	0.682085i	$0.238926\pi$
$524$	−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	0.797709	−	0.603043i	$-0.206045\pi$
$547$	−2.88599	−	4.99869i	−0.123396	−	0.213728i	−0.921105	+	0.389315i	$0.872712\pi$
$548$	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	$-0.848037\pi$
$563$	−1.09566	+	1.89773i	−0.0461764	+	0.0799799i	0.842013	+	0.539457i	$0.181370\pi$
$564$		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	0.993475	−	0.114049i	$-0.0363822\pi$
$569$	9.49302	+	16.4424i	0.397968	+	0.689301i	−0.595507	+	0.803350i	$0.703049\pi$
$570$		0			0
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	−0.543825	−	0.839198i	$-0.683025\pi$
$571$	10.8690	−	18.8257i	0.454854	−	0.787831i	0.998680	+	0.0513674i	$0.0163580\pi$
$572$	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	$-0.722418\pi$
$577$	−30.9032			−1.28652			−0.643258	+	0.765649i	$0.722418\pi$
$578$	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	$-0.290411\pi$
$587$	−9.18332	−	15.9060i	−0.379036	−	0.656510i	−0.990922	+	0.134436i	$0.957078\pi$
$588$		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	$-0.693010\pi$
$593$	−27.7550			−1.13976			−0.569880	+	0.821728i	$0.693010\pi$
$594$		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	−0.861881	−	0.507110i	$-0.830714\pi$
$599$	0.201412	−	0.348855i	0.00822945	−	0.0142538i	0.870111	+	0.492856i	$0.164047\pi$
$600$		0			0
$601$	−12.3733	−	21.4312i	−0.504717	−	0.874196i	−0.999985	−	0.00545577i	$-0.998263\pi$
$601$	−12.3733	−	21.4312i	−0.504717	−	0.874196i	0.495268	−	0.868740i	$-0.335070\pi$
$602$		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	$-0.670885\pi$
$607$	12.0348	−	20.8449i	0.488479	−	0.846070i	0.999912	+	0.0132531i	$0.00421872\pi$
$608$	−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	−0.0449604	−	0.998989i	$-0.514316\pi$
$617$	20.9315	−	36.2544i	0.842669	−	1.45955i	0.887630	−	0.460558i	$-0.152350\pi$
$618$		0			0
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	0.975649	−	0.219339i	$-0.0703900\pi$
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	−0.677777	+	0.735267i	$0.737057\pi$
$620$	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	0.959458	−	0.281850i	$-0.0909481\pi$
$641$	5.96592	+	10.3333i	0.235640	+	0.408140i	−0.723819	+	0.689990i	$0.757615\pi$
$642$		0			0
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	−0.140072	−	0.990141i	$-0.544733\pi$
$643$	19.9678	−	34.5852i	0.787452	−	1.36391i	0.927524	−	0.373765i	$-0.121933\pi$
$644$		0			0
$645$		0			0
$646$	−8.71733	−	15.0989i	−0.342979	−	0.594057i
$647$	−0.988954			−0.0388798			−0.0194399	−	0.999811i	$-0.506188\pi$
$647$	−0.988954			−0.0388798			−0.0194399	+	0.999811i	$0.506188\pi$
$648$		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	−0.553567	−	0.832805i	$-0.686734\pi$
$653$	11.3573	−	19.6715i	0.444447	−	0.769804i	0.998014	+	0.0630004i	$0.0200669\pi$
$654$		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	0.948922	+	0.315512i	$0.102176\pi$
$659$	19.1943	+	33.2454i	0.747702	+	1.29506i	−0.201220	+	0.979546i	$0.564491\pi$
$660$		0			0
$661$	16.9629	−	29.3806i	0.659780	−	1.14277i	−0.320892	−	0.947116i	$-0.603983\pi$
$661$	16.9629	−	29.3806i	0.659780	−	1.14277i	0.980672	−	0.195657i	$-0.0626839\pi$
$662$	−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	−0.989351	−	0.145549i	$-0.953505\pi$
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	0.368626	−	0.929578i	$-0.379828\pi$
$674$	−23.1403			−0.891332
$675$		0			0
$676$	−40.1171			−1.54297
$677$	18.9842	+	32.8816i	0.729622	+	1.26374i	0.957043	+	0.289946i	$0.0936375\pi$
$677$	18.9842	+	32.8816i	0.729622	+	1.26374i	−0.227421	+	0.973797i	$0.573029\pi$
$678$		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	$-0.150364\pi$
$691$	1.34574	+	2.33089i	0.0511943	+	0.0886711i	−0.839293	+	0.543680i	$0.817031\pi$
$692$	−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	0.937278	+	0.348582i	$0.113337\pi$
$709$	20.5167	+	35.5359i	0.770520	+	1.33458i	−0.166759	+	0.985998i	$0.553330\pi$
$710$	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	$-0.627498\pi$
$719$	−20.9109			−0.779845			−0.389923	+	0.920848i	$0.627498\pi$
$720$		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	$-0.182276\pi$
$727$	−1.32165	−	2.28917i	−0.0490173	−	0.0849005i	−0.889493	+	0.456949i	$0.848942\pi$
$728$		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	$-0.749182\pi$
$733$	7.07446	−	12.2533i	0.261301	−	0.452587i	0.966588	+	0.256335i	$0.0825151\pi$
$734$	−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	−0.992048	−	0.125861i	$-0.959831\pi$
$743$	−10.5496	+	18.2724i	−0.387026	+	0.670348i	0.605022	+	0.796208i	$0.293164\pi$
$744$		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	−0.960101	−	0.279654i	$-0.909780\pi$
$751$	−6.51848	+	11.2903i	−0.237863	+	0.411990i	0.722238	+	0.691644i	$0.243113\pi$
$752$	−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	$-0.798412\pi$
$761$	3.02038	−	5.23146i	0.109489	−	0.189640i	0.915563	+	0.402174i	$0.131745\pi$
$762$		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	$-0.834575\pi$
$769$	−0.108129	+	0.187285i	−0.00389924	+	0.00675368i	0.864069	+	0.503373i	$0.167908\pi$
$770$		0			0
$771$		0			0
$772$	34.7251	+	60.1457i	1.24979	+	2.16469i
$773$	−37.6264			−1.35333			−0.676663	−	0.736293i	$-0.736575\pi$
$773$	−37.6264			−1.35333			−0.676663	+	0.736293i	$0.736575\pi$
$774$		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	−0.449139	−	0.893462i	$-0.648269\pi$
$787$	15.4067	−	26.6853i	0.549191	−	0.951226i	0.998330	−	0.0577648i	$-0.0183973\pi$
$788$	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	0.349264	+	0.937024i	$0.386431\pi$
$797$	−17.9792	+	31.1408i	−0.636855	+	1.10306i	−0.986119	+	0.166040i	$0.946902\pi$
$798$		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	$-0.334603\pi$
$811$	28.2811			0.993082			0.496541	+	0.868013i	$0.334603\pi$
$812$		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	0.958712	+	0.284378i	$0.0917872\pi$
$821$	20.7917	+	36.0123i	0.725635	+	1.25684i	−0.233077	+	0.972458i	$0.574879\pi$
$822$		0			0
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	−0.930284	−	0.366841i	$-0.880439\pi$
$823$	−4.22999	+	7.32656i	−0.147448	+	0.255388i	0.782835	+	0.622229i	$0.213773\pi$
$824$	−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	$-0.593269\pi$
$829$	−16.6327			−0.577679			−0.288839	+	0.957378i	$0.593269\pi$
$830$	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	0.999919	+	0.0127182i	$0.00404843\pi$
$839$	14.8006	+	25.6354i	0.510974	+	0.885033i	−0.488945	+	0.872314i	$0.662618\pi$
$840$		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	0.999834	+	0.0182366i	$0.00580520\pi$
$853$	15.0619	+	26.0880i	0.515710	+	0.893236i	−0.484124	+	0.875000i	$0.660861\pi$
$854$		0			0
$855$		0			0
$856$	−70.9227			−2.42409
$857$	−18.5447	−	32.1204i	−0.633475	−	1.09721i	−0.986836	−	0.161724i	$-0.948295\pi$
$857$	−18.5447	−	32.1204i	−0.633475	−	1.09721i	0.353361	−	0.935487i	$-0.385039\pi$
$858$		0			0
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	−0.896491	−	0.443062i	$-0.853892\pi$
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	0.831948	+	0.554853i	$0.187226\pi$
$860$	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	−0.945291	−	0.326228i	$-0.894222\pi$
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	0.755167	+	0.655532i	$0.227556\pi$
$878$	−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	$-0.703916\pi$
$881$	−35.4810			−1.19538			−0.597692	+	0.801726i	$0.703916\pi$
$882$		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	−0.260767	+	0.965402i	$0.583975\pi$
$887$	−28.7832	+	49.8540i	−0.966446	+	1.67393i	−0.705679	+	0.708532i	$0.749358\pi$
$888$		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	0.638765	−	0.769402i	$-0.279446\pi$
$907$	−10.4486	−	18.0975i	−0.346939	−	0.600917i	−0.985704	+	0.168485i	$0.946112\pi$
$908$	72.8804			2.41862
$909$		0			0
$910$		0			0
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	0.613539	−	0.789665i	$-0.289746\pi$
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	−0.990639	+	0.136508i	$0.956412\pi$
$912$		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	$-0.196302\pi$
$929$	−2.83363	−	4.90799i	−0.0929683	−	0.161026i	−0.908759	+	0.417322i	$0.862969\pi$
$930$		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	$-0.460134\pi$
$937$	7.64754			0.249834			0.124917	+	0.992167i	$0.460134\pi$
$938$		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	$-0.941533\pi$
$941$	−10.2276	+	17.7147i	−0.333410	+	0.577483i	0.649768	+	0.760132i	$0.274866\pi$
$942$		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	0.824698	−	0.565573i	$-0.191345\pi$
$947$	−2.38343	−	4.12823i	−0.0774512	−	0.134149i	−0.902150	+	0.431423i	$0.858012\pi$
$948$		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	−0.909667	−	0.415337i	$-0.863664\pi$
$967$	−2.95856	+	5.12438i	−0.0951409	+	0.164789i	0.814526	+	0.580126i	$0.196997\pi$
$968$	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	$-0.653934\pi$
$971$	−28.9775			−0.929933			−0.464966	+	0.885328i	$0.653934\pi$
$972$		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	−0.623401	−	0.781902i	$-0.714250\pi$
$977$	11.4228	−	19.7848i	0.365447	−	0.632972i	0.988848	+	0.148930i	$0.0475830\pi$
$978$		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	$-0.000483619\pi$
$983$	15.6351	+	27.0809i	0.498684	+	0.863745i	−0.501315	+	0.865265i	$0.667150\pi$
$984$		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	$-0.276111\pi$
$997$	−10.6439	−	18.4358i	−0.337095	−	0.583866i	−0.983885	+	0.178802i	$0.942778\pi$
$998$	−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.f.442.1		10
3.2	odd	2		441.2.f.f.148.5		10
7.2	even	3		1323.2.g.f.361.1		10
7.3	odd	6		189.2.h.b.37.5		10
7.4	even	3		1323.2.h.f.226.5		10
7.5	odd	6		189.2.g.b.172.1		10
7.6	odd	2		1323.2.f.e.442.1		10
9.2	odd	6		441.2.f.f.295.5		10
9.4	even	3		3969.2.a.bb.1.5		5
9.5	odd	6		3969.2.a.ba.1.1		5
9.7	even	3	inner	1323.2.f.f.883.1		10
21.2	odd	6		441.2.g.f.67.5		10
21.5	even	6		63.2.g.b.4.5	✓	10
21.11	odd	6		441.2.h.f.373.1		10
21.17	even	6		63.2.h.b.58.1	yes	10
21.20	even	2		441.2.f.e.148.5		10
28.3	even	6		3024.2.q.i.2305.2		10
28.19	even	6		3024.2.t.i.1873.4		10
63.2	odd	6		441.2.h.f.214.1		10
63.5	even	6		567.2.e.f.487.5		10
63.11	odd	6		441.2.g.f.79.5		10
63.13	odd	6		3969.2.a.bc.1.5		5
63.16	even	3		1323.2.h.f.802.5		10
63.20	even	6		441.2.f.e.295.5		10
63.25	even	3		1323.2.g.f.667.1		10
63.31	odd	6		567.2.e.e.163.1		10
63.34	odd	6		1323.2.f.e.883.1		10
63.38	even	6		63.2.g.b.16.5	yes	10
63.40	odd	6		567.2.e.e.487.1		10
63.41	even	6		3969.2.a.z.1.1		5
63.47	even	6		63.2.h.b.25.1	yes	10
63.52	odd	6		189.2.g.b.100.1		10
63.59	even	6		567.2.e.f.163.5		10
63.61	odd	6		189.2.h.b.46.5		10
84.47	odd	6		1008.2.t.i.193.3		10
84.59	odd	6		1008.2.q.i.625.4		10
252.47	odd	6		1008.2.q.i.529.4		10
252.115	even	6		3024.2.t.i.289.4		10
252.187	even	6		3024.2.q.i.2881.2		10
252.227	odd	6		1008.2.t.i.961.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	21.5	even	6
63.2.g.b.16.5	yes	10	63.38	even	6
63.2.h.b.25.1	yes	10	63.47	even	6
63.2.h.b.58.1	yes	10	21.17	even	6
189.2.g.b.100.1		10	63.52	odd	6
189.2.g.b.172.1		10	7.5	odd	6
189.2.h.b.37.5		10	7.3	odd	6
189.2.h.b.46.5		10	63.61	odd	6
441.2.f.e.148.5		10	21.20	even	2
441.2.f.e.295.5		10	63.20	even	6
441.2.f.f.148.5		10	3.2	odd	2
441.2.f.f.295.5		10	9.2	odd	6
441.2.g.f.67.5		10	21.2	odd	6
441.2.g.f.79.5		10	63.11	odd	6
441.2.h.f.214.1		10	63.2	odd	6
441.2.h.f.373.1		10	21.11	odd	6
567.2.e.e.163.1		10	63.31	odd	6
567.2.e.e.487.1		10	63.40	odd	6
567.2.e.f.163.5		10	63.59	even	6
567.2.e.f.487.5		10	63.5	even	6
1008.2.q.i.529.4		10	252.47	odd	6
1008.2.q.i.625.4		10	84.59	odd	6
1008.2.t.i.193.3		10	84.47	odd	6
1008.2.t.i.961.3		10	252.227	odd	6
1323.2.f.e.442.1		10	7.6	odd	2
1323.2.f.e.883.1		10	63.34	odd	6
1323.2.f.f.442.1		10	1.1	even	1	trivial
1323.2.f.f.883.1		10	9.7	even	3	inner
1323.2.g.f.361.1		10	7.2	even	3
1323.2.g.f.667.1		10	63.25	even	3
1323.2.h.f.226.5		10	7.4	even	3
1323.2.h.f.802.5		10	63.16	even	3
3024.2.q.i.2305.2		10	28.3	even	6
3024.2.q.i.2881.2		10	252.187	even	6
3024.2.t.i.289.4		10	252.115	even	6
3024.2.t.i.1873.4		10	28.19	even	6
3969.2.a.z.1.1		5	63.41	even	6
3969.2.a.ba.1.1		5	9.5	odd	6
3969.2.a.bb.1.5		5	9.4	even	3
3969.2.a.bc.1.5		5	63.13	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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