LMFDB - Embedded newform 1323.2.i.d.521.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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([1, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.16
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08430i q^{2} -2.34432 q^{4} +(1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +O(q^{10})$	\(q+2.08430i q^{2} -2.34432 q^{4} +(1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +(5.96509 + 3.44395i) q^{10} +(2.30482 - 1.33069i) q^{11} +(-2.11249 + 1.21964i) q^{13} -3.19280 q^{16} +(3.59017 - 6.21836i) q^{17} +(4.24746 - 2.45227i) q^{19} +(-3.87358 + 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} +(-4.32174 - 2.49516i) q^{23} +(-2.96036 - 5.12749i) q^{25} +(-2.54211 - 4.40306i) q^{26} +(-5.50701 - 3.17947i) q^{29} -2.66543i q^{31} -8.09010i q^{32} +(12.9609 + 7.48301i) q^{34} +(0.844787 + 1.46321i) q^{37} +(5.11128 + 8.85299i) q^{38} +(-2.05391 - 1.18583i) q^{40} +(0.553137 + 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(-5.40324 + 3.11956i) q^{44} +(5.20066 - 9.00781i) q^{46} -4.88196 q^{47} +(10.6873 - 6.17029i) q^{50} +(4.95235 - 2.85924i) q^{52} +(8.94013 + 5.16159i) q^{53} -8.79491i q^{55} +(6.62698 - 11.4783i) q^{58} +5.13640 q^{59} +5.13395i q^{61} +5.55556 q^{62} +10.4766 q^{64} +8.06100i q^{65} +8.33088 q^{67} +(-8.41652 + 14.5778i) q^{68} +2.07026i q^{71} +(6.94112 + 4.00746i) q^{73} +(-3.04978 + 1.76079i) q^{74} +(-9.95741 + 5.74891i) q^{76} +5.01003 q^{79} +(-5.27554 + 9.13750i) q^{80} +(-1.99689 + 1.15291i) q^{82} +(1.04482 - 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} +(10.5950 + 6.11703i) q^{86} +(-0.954997 - 1.65410i) q^{88} +(-0.541267 - 0.937501i) q^{89} +(10.1315 + 5.84945i) q^{92} -10.1755i q^{94} -16.2078i q^{95} +(9.47203 + 5.46868i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			2.08430i			1.47383i	0.675988	+	0.736913i	$0.263717\pi$
$2$			2.08430i			1.47383i	−0.675988	+	0.736913i	$0.736283\pi$
$3$		0			0
$3$		0			0
$4$	−2.34432			−1.17216
$5$	1.65233	−	2.86191i	0.738942	−	1.27989i	−0.214029	−	0.976827i	$-0.568659\pi$
$5$	1.65233	−	2.86191i	0.738942	−	1.27989i	0.952972	−	0.303059i	$-0.0980078\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	0.717672i		−	0.253735i
$9$		0			0
$10$	5.96509	+	3.44395i	1.88633	+	1.08907i
$11$	2.30482	−	1.33069i	0.694929	−	0.401217i	−0.110527	−	0.993873i	$-0.535254\pi$
$11$	2.30482	−	1.33069i	0.694929	−	0.401217i	0.805456	+	0.592656i	$0.201921\pi$
$12$		0			0
$13$	−2.11249	+	1.21964i	−0.585899	+	0.338269i	−0.763474	−	0.645839i	$-0.776508\pi$
$13$	−2.11249	+	1.21964i	−0.585899	+	0.338269i	0.177576	+	0.984107i	$0.443175\pi$
$14$		0			0
$15$		0			0
$16$	−3.19280			−0.798199
$17$	3.59017	−	6.21836i	0.870744	−	1.50817i	0.00951656	−	0.999955i	$-0.496971\pi$
$17$	3.59017	−	6.21836i	0.870744	−	1.50817i	0.861228	−	0.508219i	$-0.169696\pi$
$18$		0			0
$19$	4.24746	−	2.45227i	0.974433	−	0.562589i	0.0738485	−	0.997269i	$-0.476472\pi$
$19$	4.24746	−	2.45227i	0.974433	−	0.562589i	0.900585	+	0.434680i	$0.143139\pi$
$20$	−3.87358	+	6.70924i	−0.866160	+	1.50023i
$21$		0			0
$22$	2.77356	+	4.80394i	0.591324	+	1.02420i
$23$	−4.32174	−	2.49516i	−0.901145	−	0.520276i	−0.0235732	−	0.999722i	$-0.507504\pi$
$23$	−4.32174	−	2.49516i	−0.901145	−	0.520276i	−0.877571	+	0.479446i	$0.840838\pi$
$24$		0			0
$25$	−2.96036	−	5.12749i	−0.592072	−	1.02550i
$26$	−2.54211	−	4.40306i	−0.498549	−	0.863512i
$27$		0			0
$28$		0			0
$29$	−5.50701	−	3.17947i	−1.02263	−	0.590413i	−0.107762	−	0.994177i	$-0.534368\pi$
$29$	−5.50701	−	3.17947i	−1.02263	−	0.590413i	−0.914863	+	0.403764i	$0.867702\pi$
$30$		0			0
$31$		−	2.66543i		−	0.478725i	−0.970930	−	0.239362i	$-0.923062\pi$
$31$		−	2.66543i		−	0.478725i	0.970930	−	0.239362i	$-0.0769384\pi$
$32$		−	8.09010i		−	1.43014i
$33$		0			0
$34$	12.9609	+	7.48301i	2.22278	+	1.28333i
$35$		0			0
$36$		0			0
$37$	0.844787	+	1.46321i	0.138882	+	0.240551i	0.927074	−	0.374879i	$-0.122316\pi$
$37$	0.844787	+	1.46321i	0.138882	+	0.240551i	−0.788192	+	0.615430i	$0.788982\pi$
$38$	5.11128	+	8.85299i	0.829159	+	1.43614i
$39$		0			0
$40$	−2.05391	−	1.18583i	−0.324752	−	0.187496i
$41$	0.553137	+	0.958062i	0.0863855	+	0.149624i	0.905981	−	0.423319i	$-0.139135\pi$
$41$	0.553137	+	0.958062i	0.0863855	+	0.149624i	−0.819595	+	0.572943i	$0.805802\pi$
$42$		0			0
$43$	2.93481	−	5.08323i	0.447554	−	0.775186i	−0.550672	−	0.834721i	$-0.685629\pi$
$43$	2.93481	−	5.08323i	0.447554	−	0.775186i	0.998226	+	0.0595356i	$0.0189620\pi$
$44$	−5.40324	+	3.11956i	−0.814568	+	0.470291i
$45$		0			0
$46$	5.20066	−	9.00781i	0.766796	−	1.32813i
$47$	−4.88196			−0.712107			−0.356053	−	0.934466i	$-0.615878\pi$
$47$	−4.88196			−0.712107			−0.356053	+	0.934466i	$0.615878\pi$
$48$		0			0
$49$		0			0
$50$	10.6873	−	6.17029i	1.51141	−	0.872610i
$51$		0			0
$52$	4.95235	−	2.85924i	0.686767	−	0.396505i
$53$	8.94013	+	5.16159i	1.22802	+	0.708999i	0.966616	−	0.256230i	$-0.0824806\pi$
$53$	8.94013	+	5.16159i	1.22802	+	0.708999i	0.261406	+	0.965229i	$0.415814\pi$
$54$		0			0
$55$		−	8.79491i		−	1.18591i
$56$		0			0
$57$		0			0
$58$	6.62698	−	11.4783i	0.870166	−	1.50717i
$59$	5.13640			0.668703			0.334351	−	0.942448i	$-0.391483\pi$
$59$	5.13640			0.668703			0.334351	+	0.942448i	$0.391483\pi$
$60$		0			0
$61$			5.13395i			0.657335i	0.944446	+	0.328668i	$0.106600\pi$
$61$			5.13395i			0.657335i	−0.944446	+	0.328668i	$0.893400\pi$
$62$	5.55556			0.705556
$63$		0			0
$64$	10.4766			1.30958
$65$			8.06100i			0.999844i
$66$		0			0
$67$	8.33088			1.01778			0.508890	−	0.860832i	$-0.330056\pi$
$67$	8.33088			1.01778			0.508890	+	0.860832i	$0.330056\pi$
$68$	−8.41652	+	14.5778i	−1.02065	+	1.76782i
$69$		0			0
$70$		0			0
$71$			2.07026i			0.245695i	0.992426	+	0.122848i	$0.0392026\pi$
$71$			2.07026i			0.245695i	−0.992426	+	0.122848i	$0.960797\pi$
$72$		0			0
$73$	6.94112	+	4.00746i	0.812396	+	0.469037i	0.847787	−	0.530336i	$-0.177934\pi$
$73$	6.94112	+	4.00746i	0.812396	+	0.469037i	−0.0353910	+	0.999374i	$0.511268\pi$
$74$	−3.04978	+	1.76079i	−0.354530	+	0.204688i
$75$		0			0
$76$	−9.95741	+	5.74891i	−1.14219	+	0.659445i
$77$		0			0
$78$		0			0
$79$	5.01003			0.563672			0.281836	−	0.959463i	$-0.409057\pi$
$79$	5.01003			0.563672			0.281836	+	0.959463i	$0.409057\pi$
$80$	−5.27554	+	9.13750i	−0.589823	+	1.02160i
$81$		0			0
$82$	−1.99689	+	1.15291i	−0.220520	+	0.127317i
$83$	1.04482	−	1.80968i	0.114684	−	0.198638i	−0.802970	−	0.596020i	$-0.796748\pi$
$83$	1.04482	−	1.80968i	0.114684	−	0.198638i	0.917653	+	0.397382i	$0.130081\pi$
$84$		0			0
$85$	−11.8643	−	20.5495i	−1.28686	−	2.22891i
$86$	10.5950	+	6.11703i	1.14249	+	0.659616i
$87$		0			0
$88$	−0.954997	−	1.65410i	−0.101803	−	0.176328i
$89$	−0.541267	−	0.937501i	−0.0573741	−	0.0993749i	0.835912	−	0.548864i	$-0.184939\pi$
$89$	−0.541267	−	0.937501i	−0.0573741	−	0.0993749i	−0.893286	+	0.449489i	$0.851606\pi$
$90$		0			0
$91$		0			0
$92$	10.1315	+	5.84945i	1.05629	+	0.609847i
$93$		0			0
$94$		−	10.1755i		−	1.04952i
$95$		−	16.2078i		−	1.66288i
$96$		0			0
$97$	9.47203	+	5.46868i	0.961739	+	0.555260i	0.896708	−	0.442623i	$-0.145952\pi$
$97$	9.47203	+	5.46868i	0.961739	+	0.555260i	0.0650310	+	0.997883i	$0.479285\pi$
$98$		0			0
$99$		0			0
$100$	6.94004	+	12.0205i	0.694004	+	1.20205i
$101$	−0.263957	−	0.457188i	−0.0262647	−	0.0454919i	0.852594	−	0.522573i	$-0.175028\pi$
$101$	−0.263957	−	0.457188i	−0.0262647	−	0.0454919i	−0.878859	+	0.477082i	$0.841695\pi$
$102$		0			0
$103$	0.678733	+	0.391867i	0.0668775	+	0.0386118i	0.533066	−	0.846074i	$-0.321040\pi$
$103$	0.678733	+	0.391867i	0.0668775	+	0.0386118i	−0.466188	+	0.884685i	$0.654373\pi$
$104$	0.875305	+	1.51607i	0.0858308	+	0.148663i
$105$		0			0
$106$	−10.7583	+	18.6340i	−1.04494	+	1.80989i
$107$	4.63398	−	2.67543i	0.447984	−	0.258644i	−0.258994	−	0.965879i	$-0.583391\pi$
$107$	4.63398	−	2.67543i	0.447984	−	0.258644i	0.706978	+	0.707235i	$0.250058\pi$
$108$		0			0
$109$	−2.98261	+	5.16603i	−0.285682	+	0.494816i	−0.972774	−	0.231754i	$-0.925553\pi$
$109$	−2.98261	+	5.16603i	−0.285682	+	0.494816i	0.687092	+	0.726570i	$0.258887\pi$
$110$	18.3313			1.74782
$111$		0			0
$112$		0			0
$113$	−10.0024	+	5.77487i	−0.940944	+	0.543254i	−0.890256	−	0.455461i	$-0.849475\pi$
$113$	−10.0024	+	5.77487i	−0.940944	+	0.543254i	−0.0506876	+	0.998715i	$0.516141\pi$
$114$		0			0
$115$	−14.2818	+	8.24562i	−1.33179	+	0.768908i
$116$	12.9102	+	7.45371i	1.19868	+	0.692059i
$117$		0			0
$118$			10.7058i			0.985551i
$119$		0			0
$120$		0			0
$121$	−1.95854	+	3.39230i	−0.178049	+	0.308391i
$122$	−10.7007			−0.968797
$123$		0			0
$124$			6.24862i			0.561142i
$125$	−3.04265			−0.272143
$126$		0			0
$127$	−19.0954			−1.69444			−0.847221	−	0.531241i	$-0.821726\pi$
$127$	−19.0954			−1.69444			−0.847221	+	0.531241i	$0.821726\pi$
$128$			5.65629i			0.499950i
$129$		0			0
$130$	−16.8016			−1.47360
$131$	2.07563	−	3.59509i	0.181349	−	0.314105i	−0.760991	−	0.648762i	$-0.775287\pi$
$131$	2.07563	−	3.59509i	0.181349	−	0.314105i	0.942340	+	0.334657i	$0.108620\pi$
$132$		0			0
$133$		0			0
$134$			17.3641i			1.50003i
$135$		0			0
$136$	−4.46274	−	2.57657i	−0.382677	−	0.220939i
$137$	−5.45092	+	3.14709i	−0.465704	+	0.268874i	−0.714440	−	0.699697i	$-0.753318\pi$
$137$	−5.45092	+	3.14709i	−0.465704	+	0.268874i	0.248736	+	0.968571i	$0.419985\pi$
$138$		0			0
$139$	−1.32575	+	0.765423i	−0.112449	+	0.0649223i	−0.555170	−	0.831737i	$-0.687347\pi$
$139$	−1.32575	+	0.765423i	−0.112449	+	0.0649223i	0.442721	+	0.896660i	$0.354013\pi$
$140$		0			0
$141$		0			0
$142$	−4.31506			−0.362112
$143$	−3.24593	+	5.62212i	−0.271438	+	0.470145i
$144$		0			0
$145$	−18.1987	+	10.5070i	−1.51132	+	0.872563i
$146$	−8.35276	+	14.4674i	−0.691279	+	1.19733i
$147$		0			0
$148$	−1.98045	−	3.43025i	−0.162792	−	0.281965i
$149$	−4.63163	−	2.67407i	−0.379438	−	0.219069i	0.298136	−	0.954523i	$-0.403635\pi$
$149$	−4.63163	−	2.67407i	−0.379438	−	0.219069i	−0.677574	+	0.735455i	$0.736969\pi$
$150$		0			0
$151$	−5.74384	−	9.94862i	−0.467427	−	0.809607i	0.531880	−	0.846820i	$-0.321486\pi$
$151$	−5.74384	−	9.94862i	−0.467427	−	0.809607i	−0.999307	+	0.0372121i	$0.988152\pi$
$152$	−1.75993	−	3.04828i	−0.142749	−	0.247248i
$153$		0			0
$154$		0			0
$155$	−7.62821	−	4.40415i	−0.612713	−	0.353750i
$156$		0			0
$157$		−	6.66542i		−	0.531959i	−0.963979	−	0.265979i	$-0.914305\pi$
$157$		−	6.66542i		−	0.531959i	0.963979	−	0.265979i	$-0.0856953\pi$
$158$			10.4424i			0.830754i
$159$		0			0
$160$	−23.1532	−	13.3675i	−1.83042	−	1.05679i
$161$		0			0
$162$		0			0
$163$	11.5460	+	19.9983i	0.904356	+	1.56639i	0.821779	+	0.569807i	$0.192982\pi$
$163$	11.5460	+	19.9983i	0.904356	+	1.56639i	0.0825775	+	0.996585i	$0.473685\pi$
$164$	−1.29673	−	2.24601i	−0.101258	−	0.175384i
$165$		0			0
$166$	3.77192	+	2.17772i	0.292757	+	0.169024i
$167$	−7.95418	−	13.7770i	−0.615513	−	1.06610i	−0.990294	−	0.138986i	$-0.955616\pi$
$167$	−7.95418	−	13.7770i	−0.615513	−	1.06610i	0.374782	−	0.927113i	$-0.377718\pi$
$168$		0			0
$169$	−3.52493	+	6.10536i	−0.271149	+	0.469643i
$170$	42.8314	−	24.7287i	3.28502	−	1.89661i
$171$		0			0
$172$	−6.88013	+	11.9167i	−0.524605	+	0.908643i
$173$	18.6619			1.41884			0.709421	−	0.704785i	$-0.248957\pi$
$173$	18.6619			1.41884			0.709421	+	0.704785i	$0.248957\pi$
$174$		0			0
$175$		0			0
$176$	−7.35882	+	4.24861i	−0.554692	+	0.320251i
$177$		0			0
$178$	1.95404	−	1.12816i	0.146461	−	0.0845595i
$179$	−19.0792	−	11.0154i	−1.42604	−	0.823326i	−0.429237	−	0.903192i	$-0.641218\pi$
$179$	−19.0792	−	11.0154i	−1.42604	−	0.823326i	−0.996806	+	0.0798653i	$0.974551\pi$
$180$		0			0
$181$		−	17.6986i		−	1.31552i	−0.753226	−	0.657762i	$-0.771503\pi$
$181$		−	17.6986i		−	1.31552i	0.753226	−	0.657762i	$-0.228497\pi$
$182$		0			0
$183$		0			0
$184$	−1.79070	+	3.10159i	−0.132012	+	0.228652i
$185$	5.58346			0.410504
$186$		0			0
$187$		−	19.1096i		−	1.39743i
$188$	11.4449			0.834704
$189$		0			0
$190$	33.7820			2.45080
$191$			15.3242i			1.10882i	0.832244	+	0.554409i	$0.187056\pi$
$191$			15.3242i			1.10882i	−0.832244	+	0.554409i	$0.812944\pi$
$192$		0			0
$193$	25.8667			1.86192			0.930962	−	0.365117i	$-0.118971\pi$
$193$	25.8667			1.86192			0.930962	+	0.365117i	$0.118971\pi$
$194$	−11.3984	+	19.7426i	−0.818356	+	1.41744i
$195$		0			0
$196$		0			0
$197$		−	4.18301i		−	0.298027i	−0.988835	−	0.149014i	$-0.952390\pi$
$197$		−	4.18301i		−	0.298027i	0.988835	−	0.149014i	$-0.0476098\pi$
$198$		0			0
$199$	−19.0592	−	11.0038i	−1.35107	−	0.780041i	−0.362671	−	0.931917i	$-0.618135\pi$
$199$	−19.0592	−	11.0038i	−1.35107	−	0.780041i	−0.988399	+	0.151876i	$0.951468\pi$
$200$	−3.67986	+	2.12457i	−0.260205	+	0.150230i
$201$		0			0
$202$	0.952918	−	0.550168i	0.0670471	−	0.0387097i
$203$		0			0
$204$		0			0
$205$	3.65585			0.255336
$206$	−0.816769	+	1.41469i	−0.0569070	+	0.0985658i
$207$		0			0
$208$	6.74474	−	3.89408i	0.467664	−	0.270006i
$209$	6.52641	−	11.3041i	0.451441	−	0.781919i
$210$		0			0
$211$	12.2926	+	21.2914i	0.846257	+	1.46576i	0.884525	+	0.466493i	$0.154483\pi$
$211$	12.2926	+	21.2914i	0.846257	+	1.46576i	−0.0382677	+	0.999268i	$0.512184\pi$
$212$	−20.9586	−	12.1004i	−1.43944	−	0.831061i
$213$		0			0
$214$	5.57641	+	9.65863i	0.381196	+	0.660250i
$215$	−9.69851	−	16.7983i	−0.661433	−	1.14564i
$216$		0			0
$217$		0			0
$218$	−10.7676	−	6.21666i	−0.729272	−	0.421045i
$219$		0			0
$220$			20.6181i			1.39007i
$221$			17.5149i			1.17818i
$222$		0			0
$223$	7.31908	+	4.22567i	0.490122	+	0.282972i	0.724625	−	0.689143i	$-0.242013\pi$
$223$	7.31908	+	4.22567i	0.490122	+	0.282972i	−0.234503	+	0.972115i	$0.575346\pi$
$224$		0			0
$225$		0			0
$226$	−12.0366	−	20.8480i	−0.800662	−	1.38679i
$227$	−2.91475	−	5.04849i	−0.193458	−	0.335080i	0.752936	−	0.658094i	$-0.228637\pi$
$227$	−2.91475	−	5.04849i	−0.193458	−	0.335080i	−0.946394	+	0.323014i	$0.895304\pi$
$228$		0			0
$229$	4.15541	+	2.39913i	0.274597	+	0.158539i	0.630975	−	0.775803i	$-0.282655\pi$
$229$	4.15541	+	2.39913i	0.274597	+	0.158539i	−0.356378	+	0.934342i	$0.615988\pi$
$230$	−17.1864	−	29.7677i	−1.13324	−	1.96282i
$231$		0			0
$232$	−2.28182	+	3.95223i	−0.149809	+	0.259476i
$233$	−19.9587	+	11.5232i	−1.30754	+	0.754907i	−0.981685	−	0.190513i	$-0.938985\pi$
$233$	−19.9587	+	11.5232i	−1.30754	+	0.754907i	−0.325853	+	0.945420i	$0.605652\pi$
$234$		0			0
$235$	−8.06659	+	13.9717i	−0.526206	+	0.911416i
$236$	−12.0414			−0.783828
$237$		0			0
$238$		0			0
$239$	−5.91972	+	3.41775i	−0.382915	+	0.221076i	−0.679086	−	0.734059i	$-0.737624\pi$
$239$	−5.91972	+	3.41775i	−0.382915	+	0.221076i	0.296171	+	0.955135i	$0.404290\pi$
$240$		0			0
$241$	−3.89112	+	2.24654i	−0.250649	+	0.144712i	−0.620061	−	0.784553i	$-0.712892\pi$
$241$	−3.89112	+	2.24654i	−0.250649	+	0.144712i	0.369412	+	0.929266i	$0.379559\pi$
$242$	−7.07058	−	4.08220i	−0.454514	−	0.262414i
$243$		0			0
$244$		−	12.0356i		−	0.770503i
$245$		0			0
$246$		0			0
$247$	−5.98180	+	10.3608i	−0.380613	+	0.659241i
$248$	−1.91290			−0.121469
$249$		0			0
$250$		−	6.34181i		−	0.401092i
$251$	−0.467438			−0.0295044			−0.0147522	−	0.999891i	$-0.504696\pi$
$251$	−0.467438			−0.0295044			−0.0147522	+	0.999891i	$0.504696\pi$
$252$		0			0
$253$	−13.2811			−0.834975
$254$		−	39.8006i		−	2.49731i
$255$		0			0
$256$	9.16385			0.572741
$257$	−10.7433	+	18.6079i	−0.670146	+	1.16073i	0.307716	+	0.951478i	$0.400435\pi$
$257$	−10.7433	+	18.6079i	−0.670146	+	1.16073i	−0.977862	+	0.209249i	$0.932898\pi$
$258$		0			0
$259$		0			0
$260$		−	18.8976i		−	1.17198i
$261$		0			0
$262$	7.49327	+	4.32624i	0.462936	+	0.267276i
$263$	9.60394	−	5.54484i	0.592205	−	0.341909i	−0.173764	−	0.984787i	$-0.555593\pi$
$263$	9.60394	−	5.54484i	0.592205	−	0.341909i	0.765969	+	0.642878i	$0.222260\pi$
$264$		0			0
$265$	29.5440	−	17.0572i	1.81487	−	1.04782i
$266$		0			0
$267$		0			0
$268$	−19.5303			−1.19300
$269$	11.0288	−	19.1024i	0.672435	−	1.16469i	−0.304776	−	0.952424i	$-0.598582\pi$
$269$	11.0288	−	19.1024i	0.672435	−	1.16469i	0.977212	−	0.212268i	$-0.0680850\pi$
$270$		0			0
$271$	4.10874	−	2.37218i	0.249588	−	0.144100i	−0.369988	−	0.929037i	$-0.620638\pi$
$271$	4.10874	−	2.37218i	0.249588	−	0.144100i	0.619576	+	0.784937i	$0.287305\pi$
$272$	−11.4627	+	19.8540i	−0.695028	+	1.20382i
$273$		0			0
$274$	−6.55950	−	11.3614i	−0.396274	−	0.686366i
$275$	−13.6462	−	7.87862i	−0.822895	−	0.475099i
$276$		0			0
$277$	3.21329	+	5.56558i	0.193068	+	0.334404i	0.946265	−	0.323391i	$-0.104823\pi$
$277$	3.21329	+	5.56558i	0.193068	+	0.334404i	−0.753197	+	0.657794i	$0.771490\pi$
$278$	−1.59537	−	2.76327i	−0.0956842	−	0.165730i
$279$		0			0
$280$		0			0
$281$	17.0883	+	9.86595i	1.01940	+	0.588553i	0.913931	−	0.405869i	$-0.133031\pi$
$281$	17.0883	+	9.86595i	1.01940	+	0.588553i	0.105473	+	0.994422i	$0.466364\pi$
$282$		0			0
$283$		−	5.60130i		−	0.332963i	−0.986045	−	0.166481i	$-0.946759\pi$
$283$		−	5.60130i		−	0.332963i	0.986045	−	0.166481i	$-0.0532406\pi$
$284$		−	4.85336i		−	0.287994i
$285$		0			0
$286$	−11.7182	−	6.76551i	−0.692912	−	0.400053i
$287$		0			0
$288$		0			0
$289$	−17.2787	−	29.9275i	−1.01639	−	1.76044i
$290$	−21.8999	−	37.9317i	−1.28600	−	2.22743i
$291$		0			0
$292$	−16.2722	−	9.39477i	−0.952260	−	0.549787i
$293$	15.0393	+	26.0488i	0.878603	+	1.52178i	0.852875	+	0.522115i	$0.174857\pi$
$293$	15.0393	+	26.0488i	0.878603	+	1.52178i	0.0257278	+	0.999669i	$0.491810\pi$
$294$		0			0
$295$	8.48701	−	14.6999i	0.494133	−	0.855863i
$296$	1.05011	−	0.606281i	0.0610363	−	0.0352393i
$297$		0			0
$298$	5.57358	−	9.65373i	0.322869	−	0.559225i
$299$	12.1728			0.703972
$300$		0			0
$301$		0			0
$302$	20.7360	−	11.9719i	1.19322	−	0.688906i
$303$		0			0
$304$	−13.5613	+	7.82960i	−0.777792	+	0.449059i
$305$	14.6929	+	8.48296i	0.841314	+	0.485733i
$306$		0			0
$307$			23.4497i			1.33835i	0.743106	+	0.669173i	$0.233352\pi$
$307$			23.4497i			1.33835i	−0.743106	+	0.669173i	$0.766648\pi$
$308$		0			0
$309$		0			0
$310$	9.17959	−	15.8995i	0.521366	−	0.903032i
$311$	−16.7101			−0.947546			−0.473773	−	0.880647i	$-0.657108\pi$
$311$	−16.7101			−0.947546			−0.473773	+	0.880647i	$0.657108\pi$
$312$		0			0
$313$			14.8675i			0.840363i	0.907440	+	0.420182i	$0.138034\pi$
$313$			14.8675i			0.840363i	−0.907440	+	0.420182i	$0.861966\pi$
$314$	13.8928			0.784014
$315$		0			0
$316$	−11.7451			−0.660715
$317$			2.27199i			0.127608i	0.997962	+	0.0638040i	$0.0203232\pi$
$317$			2.27199i			0.127608i	−0.997962	+	0.0638040i	$0.979677\pi$
$318$		0			0
$319$	−16.9235			−0.947536
$320$	17.3108	−	29.9832i	0.967704	−	1.67611i
$321$		0			0
$322$		0			0
$323$		−	35.2163i		−	1.95949i
$324$		0			0
$325$	12.5074	+	7.22117i	0.693788	+	0.400559i
$326$	−41.6826	+	24.0655i	−2.30859	+	1.33286i
$327$		0			0
$328$	0.687575	−	0.396971i	0.0379650	−	0.0219191i
$329$		0			0
$330$		0			0
$331$	−11.9488			−0.656765			−0.328383	−	0.944545i	$-0.606504\pi$
$331$	−11.9488			−0.656765			−0.328383	+	0.944545i	$0.606504\pi$
$332$	−2.44939	+	4.24247i	−0.134428	+	0.232836i
$333$		0			0
$334$	28.7155	−	16.5789i	1.57124	−	0.907158i
$335$	13.7653	−	23.8423i	0.752080	−	1.30264i
$336$		0			0
$337$	2.34636	+	4.06402i	0.127815	+	0.221381i	0.922830	−	0.385208i	$-0.125870\pi$
$337$	2.34636	+	4.06402i	0.127815	+	0.221381i	−0.795015	+	0.606590i	$0.792537\pi$
$338$	−12.7254	−	7.34703i	−0.692172	−	0.399626i
$339$		0			0
$340$	27.8137	+	48.1747i	1.50841	+	2.61264i
$341$	−3.54685	−	6.14332i	−0.192073	−	0.332679i
$342$		0			0
$343$		0			0
$344$	−3.64810	−	2.10623i	−0.196692	−	0.113560i
$345$		0			0
$346$			38.8972i			2.09112i
$347$		−	7.39619i		−	0.397048i	−0.980096	−	0.198524i	$-0.936385\pi$
$347$		−	7.39619i		−	0.397048i	0.980096	−	0.198524i	$-0.0636148\pi$
$348$		0			0
$349$	−18.0496	−	10.4209i	−0.966171	−	0.557819i	−0.0681042	−	0.997678i	$-0.521695\pi$
$349$	−18.0496	−	10.4209i	−0.966171	−	0.557819i	−0.898067	+	0.439859i	$0.855028\pi$
$350$		0			0
$351$		0			0
$352$	−10.7654	−	18.6462i	−0.573798	−	0.993847i
$353$	3.54953	+	6.14797i	0.188923	+	0.327224i	0.944891	−	0.327384i	$-0.106167\pi$
$353$	3.54953	+	6.14797i	0.188923	+	0.327224i	−0.755969	+	0.654608i	$0.772834\pi$
$354$		0			0
$355$	5.92491	+	3.42075i	0.314462	+	0.181554i
$356$	1.26890	+	2.19780i	0.0672517	+	0.116483i
$357$		0			0
$358$	22.9593	−	39.7668i	1.21344	−	2.10174i
$359$	−8.56701	+	4.94616i	−0.452149	+	0.261049i	−0.708737	−	0.705472i	$-0.750735\pi$
$359$	−8.56701	+	4.94616i	−0.452149	+	0.261049i	0.256588	+	0.966521i	$0.417402\pi$
$360$		0			0
$361$	2.52726	−	4.37734i	0.133014	−	0.230386i
$362$	36.8892			1.93885
$363$		0			0
$364$		0			0
$365$	22.9380	−	13.2432i	1.20063	−	0.693183i
$366$		0			0
$367$	27.0321	−	15.6070i	1.41107	−	0.814680i	0.415578	−	0.909558i	$-0.363579\pi$
$367$	27.0321	−	15.6070i	1.41107	−	0.814680i	0.995489	+	0.0948779i	$0.0302461\pi$
$368$	13.7984	+	7.96653i	0.719293	+	0.415284i
$369$		0			0
$370$			11.6376i			0.605011i
$371$		0			0
$372$		0			0
$373$	−14.5232	+	25.1549i	−0.751981	+	1.30247i	0.194881	+	0.980827i	$0.437568\pi$
$373$	−14.5232	+	25.1549i	−0.751981	+	1.30247i	−0.946861	+	0.321642i	$0.895765\pi$
$374$	39.8302			2.05957
$375$		0			0
$376$			3.50365i			0.180687i
$377$	15.5113			0.798873
$378$		0			0
$379$	−0.518354			−0.0266261			−0.0133130	−	0.999911i	$-0.504238\pi$
$379$	−0.518354			−0.0266261			−0.0133130	+	0.999911i	$0.504238\pi$
$380$			37.9963i			1.94917i
$381$		0			0
$382$	−31.9402			−1.63420
$383$	6.60511	−	11.4404i	0.337505	−	0.584576i	−0.646458	−	0.762950i	$-0.723750\pi$
$383$	6.60511	−	11.4404i	0.337505	−	0.584576i	0.983963	+	0.178374i	$0.0570836\pi$
$384$		0			0
$385$		0			0
$386$			53.9140i			2.74415i
$387$		0			0
$388$	−22.2055	−	12.8203i	−1.12731	−	0.650854i
$389$	−29.2921	+	16.9118i	−1.48517	+	0.857461i	−0.999857	−	0.0168815i	$-0.994626\pi$
$389$	−29.2921	+	16.9118i	−1.48517	+	0.857461i	−0.485309	+	0.874343i	$0.661293\pi$
$390$		0			0
$391$	−31.0316	+	17.9161i	−1.56933	+	0.906055i
$392$		0			0
$393$		0			0
$394$	8.71867			0.439240
$395$	8.27820	−	14.3383i	0.416521	−	0.721436i
$396$		0			0
$397$	−7.42483	+	4.28673i	−0.372641	+	0.215145i	−0.674612	−	0.738173i	$-0.735689\pi$
$397$	−7.42483	+	4.28673i	−0.372641	+	0.215145i	0.301970	+	0.953317i	$0.402356\pi$
$398$	22.9353	−	39.7251i	1.14964	−	1.99124i
$399$		0			0
$400$	9.45183	+	16.3710i	0.472591	+	0.818552i
$401$	13.9743	+	8.06808i	0.697844	+	0.402900i	0.806544	−	0.591174i	$-0.201335\pi$
$401$	13.9743	+	8.06808i	0.697844	+	0.402900i	−0.108700	+	0.994075i	$0.534669\pi$
$402$		0			0
$403$	3.25087	+	5.63068i	0.161938	+	0.280484i
$404$	0.618801	+	1.07180i	0.0307865	+	0.0533238i
$405$		0			0
$406$		0			0
$407$	3.89416	+	2.24830i	0.193026	+	0.111444i
$408$		0			0
$409$		−	16.3233i		−	0.807135i	−0.914950	−	0.403568i	$-0.867770\pi$
$409$		−	16.3233i		−	0.807135i	0.914950	−	0.403568i	$-0.132230\pi$
$410$			7.61991i			0.376320i
$411$		0			0
$412$	−1.59117	−	0.918662i	−0.0783913	−	0.0452592i
$413$		0			0
$414$		0			0
$415$	−3.45276	−	5.98035i	−0.169489	−	0.293564i
$416$	9.86706	+	17.0902i	0.483772	+	0.837918i
$417$		0			0
$418$	23.5611	+	13.6030i	1.15241	+	0.665345i
$419$	−0.589031	−	1.02023i	−0.0287760	−	0.0498415i	0.851279	−	0.524714i	$-0.175828\pi$
$419$	−0.589031	−	1.02023i	−0.0287760	−	0.0498415i	−0.880055	+	0.474872i	$0.842494\pi$
$420$		0			0
$421$	3.43544	−	5.95035i	0.167433	−	0.290002i	−0.770084	−	0.637943i	$-0.779786\pi$
$421$	3.43544	−	5.95035i	0.167433	−	0.290002i	0.937517	+	0.347941i	$0.113119\pi$
$422$	−44.3777	+	25.6215i	−2.16027	+	1.24724i
$423$		0			0
$424$	3.70433	−	6.41609i	0.179898	−	0.311593i
$425$	−42.5128			−2.06217
$426$		0			0
$427$		0			0
$428$	−10.8636	+	6.27208i	−0.525110	+	0.303172i
$429$		0			0
$430$	35.0128	−	20.2146i	1.68847	−	0.974837i
$431$	−0.702488	−	0.405582i	−0.0338377	−	0.0195362i	0.482986	−	0.875628i	$-0.339552\pi$
$431$	−0.702488	−	0.405582i	−0.0338377	−	0.0195362i	−0.516823	+	0.856092i	$0.672886\pi$
$432$		0			0
$433$			8.59662i			0.413127i	0.978433	+	0.206564i	$0.0662280\pi$
$433$			8.59662i			0.413127i	−0.978433	+	0.206564i	$0.933772\pi$
$434$		0			0
$435$		0			0
$436$	6.99219	−	12.1108i	0.334865	−	0.580004i
$437$	−24.4752			−1.17081
$438$		0			0
$439$		−	27.5936i		−	1.31697i	−0.752593	−	0.658486i	$-0.771197\pi$
$439$		−	27.5936i		−	1.31697i	0.752593	−	0.658486i	$-0.228803\pi$
$440$	−6.31186			−0.300906
$441$		0			0
$442$	−36.5065			−1.73643
$443$		−	12.2457i		−	0.581812i	−0.956752	−	0.290906i	$-0.906043\pi$
$443$		−	12.2457i		−	0.581812i	0.956752	−	0.290906i	$-0.0939567\pi$
$444$		0			0
$445$	−3.57739			−0.169585
$446$	−8.80759	+	15.2552i	−0.417051	+	0.722354i
$447$		0			0
$448$		0			0
$449$		−	22.0163i		−	1.03901i	−0.854466	−	0.519507i	$-0.826116\pi$
$449$		−	22.0163i		−	1.03901i	0.854466	−	0.519507i	$-0.173884\pi$
$450$		0			0
$451$	2.54976	+	1.47211i	0.120064	+	0.0693187i
$452$	23.4488	−	13.5382i	1.10294	−	0.636781i
$453$		0			0
$454$	10.5226	−	6.07522i	0.493849	−	0.285124i
$455$		0			0
$456$		0			0
$457$	24.1559			1.12997			0.564983	−	0.825103i	$-0.308883\pi$
$457$	24.1559			1.12997			0.564983	+	0.825103i	$0.308883\pi$
$458$	−5.00051	+	8.66114i	−0.233659	+	0.404709i
$459$		0			0
$460$	33.4812	−	19.3304i	1.56107	−	0.901284i
$461$	−16.3899	+	28.3881i	−0.763352	+	1.32216i	0.177762	+	0.984074i	$0.443114\pi$
$461$	−16.3899	+	28.3881i	−0.763352	+	1.32216i	−0.941114	+	0.338091i	$0.890219\pi$
$462$		0			0
$463$	15.7659	+	27.3074i	0.732704	+	1.26908i	0.955723	+	0.294266i	$0.0950753\pi$
$463$	15.7659	+	27.3074i	0.732704	+	1.26908i	−0.223020	+	0.974814i	$0.571591\pi$
$464$	17.5828	+	10.1514i	0.816259	+	0.471267i
$465$		0			0
$466$	−24.0178	−	41.6000i	−1.11260	−	1.92708i
$467$	−16.5765	−	28.7114i	−0.767070	−	1.32860i	−0.939145	−	0.343521i	$-0.888380\pi$
$467$	−16.5765	−	28.7114i	−0.767070	−	1.32860i	0.172075	−	0.985084i	$-0.444953\pi$
$468$		0			0
$469$		0			0
$470$	−29.1213	−	16.8132i	−1.34327	−	0.775536i
$471$		0			0
$472$		−	3.68626i		−	0.169674i
$473$		−	15.6212i		−	0.718265i
$474$		0			0
$475$	−25.1480	−	14.5192i	−1.15387	−	0.666187i
$476$		0			0
$477$		0			0
$478$	−7.12364	−	12.3385i	−0.325828	−	0.564350i
$479$	11.3972	+	19.7406i	0.520754	+	0.901972i	0.999709	+	0.0241323i	$0.00768229\pi$
$479$	11.3972	+	19.7406i	0.520754	+	0.901972i	−0.478955	+	0.877839i	$0.658984\pi$
$480$		0			0
$481$	−3.56921	−	2.06068i	−0.162742	−	0.0939590i
$482$	−4.68247	−	8.11027i	−0.213281	−	0.369413i
$483$		0			0
$484$	4.59146	−	7.95264i	0.208703	−	0.361484i
$485$	31.3017	−	18.0721i	1.42134	−	0.820611i
$486$		0			0
$487$	1.36560	−	2.36528i	0.0618811	−	0.107181i	−0.833425	−	0.552632i	$-0.813623\pi$
$487$	1.36560	−	2.36528i	0.0618811	−	0.107181i	0.895306	+	0.445451i	$0.146957\pi$
$488$	3.68449			0.166789
$489$		0			0
$490$		0			0
$491$	−21.6775	+	12.5155i	−0.978291	+	0.564817i	−0.901754	−	0.432250i	$-0.857720\pi$
$491$	−21.6775	+	12.5155i	−0.978291	+	0.564817i	−0.0765375	+	0.997067i	$0.524387\pi$
$492$		0			0
$493$	−39.5422	+	22.8297i	−1.78089	+	1.02820i
$494$	−21.5950	−	12.4679i	−0.971605	−	0.560957i
$495$		0			0
$496$			8.51016i			0.382118i
$497$		0			0
$498$		0			0
$499$	−4.29981	+	7.44749i	−0.192486	+	0.333395i	−0.946073	−	0.323952i	$-0.894988\pi$
$499$	−4.29981	+	7.44749i	−0.192486	+	0.333395i	0.753588	+	0.657348i	$0.228322\pi$
$500$	7.13296			0.318996
$501$		0			0
$502$		−	0.974283i		−	0.0434844i
$503$	−39.0362			−1.74054			−0.870269	−	0.492577i	$-0.836055\pi$
$503$	−39.0362			−1.74054			−0.870269	+	0.492577i	$0.836055\pi$
$504$		0			0
$505$	−1.74457			−0.0776325
$506$		−	27.6818i		−	1.23061i
$507$		0			0
$508$	44.7657			1.98616
$509$	16.2909	−	28.2167i	0.722083	−	1.25068i	−0.238080	−	0.971245i	$-0.576518\pi$
$509$	16.2909	−	28.2167i	0.722083	−	1.25068i	0.960163	−	0.279439i	$-0.0901485\pi$
$510$		0			0
$511$		0			0
$512$			30.4128i			1.34407i
$513$		0			0
$514$	−38.7845	−	22.3922i	−1.71071	−	0.987679i
$515$	2.24298	−	1.29498i	0.0988373	−	0.0570638i
$516$		0			0
$517$	−11.2520	+	6.49636i	−0.494864	+	0.285710i
$518$		0			0
$519$		0			0
$520$	5.78516			0.253696
$521$	−3.68456	+	6.38185i	−0.161424	+	0.279594i	−0.935379	−	0.353646i	$-0.884942\pi$
$521$	−3.68456	+	6.38185i	−0.161424	+	0.279594i	0.773956	+	0.633240i	$0.218275\pi$
$522$		0			0
$523$	−37.5991	+	21.7078i	−1.64409	+	0.949217i	−0.664735	+	0.747079i	$0.731455\pi$
$523$	−37.5991	+	21.7078i	−1.64409	+	0.949217i	−0.979357	+	0.202138i	$0.935211\pi$
$524$	−4.86594	+	8.42806i	−0.212570	+	0.368181i
$525$		0			0
$526$	11.5571	+	20.0175i	0.503915	+	0.872806i
$527$	−16.5746	−	9.56933i	−0.722000	−	0.416847i
$528$		0			0
$529$	0.951610	+	1.64824i	0.0413744	+	0.0716625i
$530$	35.5525	+	61.5787i	1.54430	+	2.67481i
$531$		0			0
$532$		0			0
$533$	−2.33699	−	1.34926i	−0.101226	−	0.0584430i
$534$		0			0
$535$		−	17.6827i		−	0.764491i
$536$		−	5.97884i		−	0.258247i
$537$		0			0
$538$	39.8151	+	22.9873i	1.71655	+	0.991052i
$539$		0			0
$540$		0			0
$541$	10.8221	+	18.7444i	0.465278	+	0.805884i	0.999214	−	0.0396402i	$-0.0126212\pi$
$541$	10.8221	+	18.7444i	0.465278	+	0.805884i	−0.533936	+	0.845525i	$0.679288\pi$
$542$	4.94434	+	8.56385i	0.212378	+	0.367849i
$543$		0			0
$544$	−50.3072	−	29.0449i	−2.15690	−	1.24529i
$545$	9.85648	+	17.0719i	0.422205	+	0.731281i
$546$		0			0
$547$	−11.9092	+	20.6273i	−0.509200	+	0.881960i	0.490743	+	0.871304i	$0.336725\pi$
$547$	−11.9092	+	20.6273i	−0.509200	+	0.881960i	−0.999943	+	0.0106561i	$0.996608\pi$
$548$	12.7787	−	7.37780i	0.545880	−	0.315164i
$549$		0			0
$550$	16.4214	−	28.4428i	0.700213	−	1.21280i
$551$	−31.1877			−1.32864
$552$		0			0
$553$		0			0
$554$	−11.6004	+	6.69748i	−0.492852	+	0.284548i
$555$		0			0
$556$	3.10799	−	1.79440i	0.131808	−	0.0760994i
$557$	−9.42040	−	5.43887i	−0.399155	−	0.230452i	0.286964	−	0.957941i	$-0.407354\pi$
$557$	−9.42040	−	5.43887i	−0.399155	−	0.230452i	−0.686119	+	0.727489i	$0.740687\pi$
$558$		0			0
$559$			14.3177i			0.605574i
$560$		0			0
$561$		0			0
$562$	−20.5636	+	35.6173i	−0.867425	+	1.50242i
$563$	−13.3552			−0.562853			−0.281427	−	0.959583i	$-0.590808\pi$
$563$	−13.3552			−0.562853			−0.281427	+	0.959583i	$0.590808\pi$
$564$		0			0
$565$			38.1679i			1.60573i
$566$	11.6748			0.490729
$567$		0			0
$568$	1.48577			0.0623415
$569$			9.63862i			0.404072i	0.979378	+	0.202036i	$0.0647558\pi$
$569$			9.63862i			0.404072i	−0.979378	+	0.202036i	$0.935244\pi$
$570$		0			0
$571$	−34.4062			−1.43985			−0.719926	−	0.694050i	$-0.755824\pi$
$571$	−34.4062			−1.43985			−0.719926	+	0.694050i	$0.755824\pi$
$572$	7.60951	−	13.1801i	0.318170	−	0.551086i
$573$		0			0
$574$		0			0
$575$			29.5462i			1.23216i
$576$		0			0
$577$	20.9017	+	12.0676i	0.870149	+	0.502381i	0.867398	−	0.497616i	$-0.165791\pi$
$577$	20.9017	+	12.0676i	0.870149	+	0.502381i	0.00275107	+	0.999996i	$0.499124\pi$
$578$	62.3780	−	36.0140i	2.59458	−	1.49798i
$579$		0			0
$580$	42.6637	−	24.6319i	1.77151	−	1.02278i
$581$		0			0
$582$		0			0
$583$	27.4738			1.13785
$584$	2.87604	−	4.98145i	0.119011	−	0.206134i
$585$		0			0
$586$	−54.2935	+	31.3464i	−2.24284	+	1.29491i
$587$	−3.96848	+	6.87362i	−0.163797	+	0.283704i	−0.936227	−	0.351395i	$-0.885707\pi$
$587$	−3.96848	+	6.87362i	−0.163797	+	0.283704i	0.772431	+	0.635099i	$0.219041\pi$
$588$		0			0
$589$	−6.53634	−	11.3213i	−0.269325	−	0.466485i
$590$	30.6391	+	17.6895i	1.26139	+	0.728266i
$591$		0			0
$592$	−2.69724	−	4.67175i	−0.110856	−	0.192008i
$593$	20.9147	+	36.2252i	0.858862	+	1.48759i	0.873015	+	0.487693i	$0.162161\pi$
$593$	20.9147	+	36.2252i	0.858862	+	1.48759i	−0.0141532	+	0.999900i	$0.504505\pi$
$594$		0			0
$595$		0			0
$596$	10.8580	+	6.26889i	0.444763	+	0.256784i
$597$		0			0
$598$			25.3719i			1.03753i
$599$			8.74505i			0.357313i	0.983911	+	0.178657i	$0.0571751\pi$
$599$			8.74505i			0.357313i	−0.983911	+	0.178657i	$0.942825\pi$
$600$		0			0
$601$	−12.6427	−	7.29924i	−0.515705	−	0.297742i	0.219471	−	0.975619i	$-0.429567\pi$
$601$	−12.6427	−	7.29924i	−0.515705	−	0.297742i	−0.735176	+	0.677877i	$0.762900\pi$
$602$		0			0
$603$		0			0
$604$	13.4654	+	23.3228i	0.547900	+	0.948990i
$605$	6.47230	+	11.2104i	0.263137	+	0.455766i
$606$		0			0
$607$	−9.51436	−	5.49312i	−0.386176	−	0.222959i	0.294326	−	0.955705i	$-0.404905\pi$
$607$	−9.51436	−	5.49312i	−0.386176	−	0.222959i	−0.680502	+	0.732746i	$0.738238\pi$
$608$	−19.8391	−	34.3624i	−0.804583	−	1.39358i
$609$		0			0
$610$	−17.6811	+	30.6245i	−0.715885	+	1.23995i
$611$	10.3131	−	5.95426i	0.417222	−	0.240883i
$612$		0			0
$613$	−11.9068	+	20.6231i	−0.480909	+	0.832959i	−0.999760	−	0.0219056i	$-0.993027\pi$
$613$	−11.9068	+	20.6231i	−0.480909	+	0.832959i	0.518851	+	0.854865i	$0.326360\pi$
$614$	−48.8763			−1.97249
$615$		0			0
$616$		0			0
$617$	36.5255	−	21.0880i	1.47046	−	0.848971i	0.471011	−	0.882127i	$-0.343889\pi$
$617$	36.5255	−	21.0880i	1.47046	−	0.848971i	0.999450	+	0.0331557i	$0.0105557\pi$
$618$		0			0
$619$	22.6532	−	13.0789i	0.910511	−	0.525683i	0.0299151	−	0.999552i	$-0.490476\pi$
$619$	22.6532	−	13.0789i	0.910511	−	0.525683i	0.880595	+	0.473869i	$0.157143\pi$
$620$	17.8830	+	10.3247i	0.718198	+	0.414652i
$621$		0			0
$622$		−	34.8290i		−	1.39652i
$623$		0			0
$624$		0			0
$625$	9.77434	−	16.9297i	0.390974	−	0.677186i
$626$	−30.9885			−1.23855
$627$		0			0
$628$			15.6259i			0.623541i
$629$	12.1317			0.483724
$630$		0			0
$631$	−19.2419			−0.766009			−0.383004	−	0.923746i	$-0.625111\pi$
$631$	−19.2419			−0.766009			−0.383004	+	0.923746i	$0.625111\pi$
$632$		−	3.59556i		−	0.143024i
$633$		0			0
$634$	−4.73553			−0.188072
$635$	−31.5518	+	54.6493i	−1.25209	+	2.16869i
$636$		0			0
$637$		0			0
$638$		−	35.2738i		−	1.39650i
$639$		0			0
$640$	16.1878	+	9.34604i	0.639879	+	0.369435i
$641$	15.2483	−	8.80362i	0.602272	−	0.347722i	−0.167663	−	0.985844i	$-0.553622\pi$
$641$	15.2483	−	8.80362i	0.602272	−	0.347722i	0.769935	+	0.638122i	$0.220289\pi$
$642$		0			0
$643$	43.1158	−	24.8929i	1.70032	−	0.981680i	0.754893	−	0.655848i	$-0.227689\pi$
$643$	43.1158	−	24.8929i	1.70032	−	0.981680i	0.945428	−	0.325832i	$-0.105645\pi$
$644$		0			0
$645$		0			0
$646$	73.4014			2.88794
$647$	5.77035	−	9.99454i	0.226856	−	0.392926i	−0.730019	−	0.683427i	$-0.760489\pi$
$647$	5.77035	−	9.99454i	0.226856	−	0.392926i	0.956875	+	0.290501i	$0.0938221\pi$
$648$		0			0
$649$	11.8385	−	6.83495i	0.464701	−	0.268295i
$650$	−15.0511	+	26.0693i	−0.590354	+	1.02252i
$651$		0			0
$652$	−27.0677	−	46.8826i	−1.06005	−	1.83606i
$653$	18.2249	+	10.5222i	0.713197	+	0.411765i	0.812244	−	0.583318i	$-0.198246\pi$
$653$	18.2249	+	10.5222i	0.713197	+	0.411765i	−0.0990464	+	0.995083i	$0.531579\pi$
$654$		0			0
$655$	−6.85923	−	11.8805i	−0.268012	−	0.464211i
$656$	−1.76606	−	3.05890i	−0.0689529	−	0.119430i
$657$		0			0
$658$		0			0
$659$	31.8016	+	18.3607i	1.23881	+	0.715230i	0.968852	−	0.247641i	$-0.0796555\pi$
$659$	31.8016	+	18.3607i	1.23881	+	0.715230i	0.269962	+	0.962871i	$0.412989\pi$
$660$		0			0
$661$		−	23.0731i		−	0.897439i	−0.893673	−	0.448719i	$-0.851880\pi$
$661$		−	23.0731i		−	0.897439i	0.893673	−	0.448719i	$-0.148120\pi$
$662$		−	24.9049i		−	0.967957i
$663$		0			0
$664$	−1.29875	−	0.749836i	−0.0504015	−	0.0290993i
$665$		0			0
$666$		0			0
$667$	15.8666	+	27.4817i	0.614356	+	1.06410i
$668$	18.6472	+	32.2978i	0.721480	+	1.24964i
$669$		0			0
$670$	49.6945	+	28.6911i	1.91987	+	1.10844i
$671$	6.83168	+	11.8328i	0.263734	+	0.456801i
$672$		0			0
$673$	24.7594	−	42.8846i	0.954406	−	1.65308i	0.218684	−	0.975796i	$-0.429824\pi$
$673$	24.7594	−	42.8846i	0.954406	−	1.65308i	0.735722	−	0.677284i	$-0.236843\pi$
$674$	−8.47065	+	4.89053i	−0.326277	+	0.188376i
$675$		0			0
$676$	8.26358	−	14.3129i	0.317830	−	0.550498i
$677$	29.8153			1.14590			0.572948	−	0.819592i	$-0.305800\pi$
$677$	29.8153			1.14590			0.572948	+	0.819592i	$0.305800\pi$
$678$		0			0
$679$		0			0
$680$	−14.7478	+	8.51465i	−0.565553	+	0.326522i
$681$		0			0
$682$	12.8045	−	7.39271i	0.490311	−	0.283081i
$683$	26.1841	+	15.1174i	1.00191	+	0.578451i	0.908812	−	0.417207i	$-0.136991\pi$
$683$	26.1841	+	15.1174i	1.00191	+	0.578451i	0.0930943	+	0.995657i	$0.470324\pi$
$684$		0			0
$685$			20.8001i			0.794731i
$686$		0			0
$687$		0			0
$688$	−9.37024	+	16.2297i	−0.357237	+	0.618753i
$689$	−25.1812			−0.959328
$690$		0			0
$691$		−	30.8945i		−	1.17528i	−0.809121	−	0.587642i	$-0.800056\pi$
$691$		−	30.8945i		−	1.17528i	0.809121	−	0.587642i	$-0.199944\pi$
$692$	−43.7496			−1.66311
$693$		0			0
$694$	15.4159			0.585180
$695$			5.05891i			0.191896i
$696$		0			0
$697$	7.94343			0.300879
$698$	21.7204	−	37.6208i	0.822128	−	1.42397i
$699$		0			0
$700$		0			0
$701$			0.757329i			0.0286039i	0.999898	+	0.0143020i	$0.00455261\pi$
$701$			0.757329i			0.0286039i	−0.999898	+	0.0143020i	$0.995447\pi$
$702$		0			0
$703$	7.17640	+	4.14329i	0.270663	+	0.156267i
$704$	24.1467	−	13.9411i	0.910065	−	0.525426i
$705$		0			0
$706$	−12.8142	+	7.39831i	−0.482270	+	0.278439i
$707$		0			0
$708$		0			0
$709$	−21.5087			−0.807778			−0.403889	−	0.914808i	$-0.632342\pi$
$709$	−21.5087			−0.807778			−0.403889	+	0.914808i	$0.632342\pi$
$710$	−7.12988	+	12.3493i	−0.267580	+	0.463461i
$711$		0			0
$712$	−0.672819	+	0.388452i	−0.0252149	+	0.0145579i
$713$	−6.65065	+	11.5193i	−0.249069	+	0.431400i
$714$		0			0
$715$	10.7267	+	18.5791i	0.401155	+	0.694820i
$716$	44.7277	+	25.8235i	1.67155	+	0.965071i
$717$		0			0
$718$	−10.3093	−	17.8562i	−0.384740	−	0.666389i
$719$	22.1254	+	38.3224i	0.825140	+	1.42918i	0.901813	+	0.432127i	$0.142237\pi$
$719$	22.1254	+	38.3224i	0.825140	+	1.42918i	−0.0766729	+	0.997056i	$0.524430\pi$
$720$		0			0
$721$		0			0
$722$	9.12371	+	5.26758i	0.339549	+	0.196039i
$723$		0			0
$724$			41.4911i			1.54201i
$725$			37.6495i			1.39827i
$726$		0			0
$727$	−2.95166	−	1.70414i	−0.109471	−	0.0632031i	0.444265	−	0.895895i	$-0.353465\pi$
$727$	−2.95166	−	1.70414i	−0.109471	−	0.0632031i	−0.553736	+	0.832692i	$0.686798\pi$
$728$		0			0
$729$		0			0
$730$	27.6029	+	47.8097i	1.02163	+	1.76952i
$731$	−21.0729	−	36.4994i	−0.779410	−	1.34998i
$732$		0			0
$733$	5.46407	+	3.15468i	0.201820	+	0.116521i	0.597504	−	0.801866i	$-0.296159\pi$
$733$	5.46407	+	3.15468i	0.201820	+	0.116521i	−0.395684	+	0.918387i	$0.629492\pi$
$734$	32.5298	+	56.3432i	1.20070	+	2.07967i
$735$		0			0
$736$	−20.1861	+	34.9633i	−0.744069	+	1.28876i
$737$	19.2012	−	11.0858i	0.707284	−	0.408351i
$738$		0			0
$739$	2.45388	−	4.25024i	0.0902674	−	0.156348i	−0.817356	−	0.576133i	$-0.804561\pi$
$739$	2.45388	−	4.25024i	0.0902674	−	0.156348i	0.907624	+	0.419785i	$0.137895\pi$
$740$	−13.0894			−0.481177
$741$		0			0
$742$		0			0
$743$	−26.1921	+	15.1220i	−0.960895	+	0.554773i	−0.896448	−	0.443148i	$-0.853862\pi$
$743$	−26.1921	+	15.1220i	−0.960895	+	0.554773i	−0.0644465	+	0.997921i	$0.520528\pi$
$744$		0			0
$745$	−15.3059	+	8.83688i	−0.560766	+	0.323758i
$746$	−52.4304	−	30.2707i	−1.91961	−	1.10829i
$747$		0			0
$748$			44.7990i			1.63801i
$749$		0			0
$750$		0			0
$751$	25.0321	−	43.3569i	0.913435	−	1.58212i	0.104257	−	0.994550i	$-0.466753\pi$
$751$	25.0321	−	43.3569i	0.913435	−	1.58212i	0.809177	−	0.587565i	$-0.199913\pi$
$752$	15.5871			0.568403
$753$		0			0
$754$			32.3303i			1.17740i
$755$	−37.9628			−1.38161
$756$		0			0
$757$	37.2695			1.35458			0.677291	−	0.735716i	$-0.263154\pi$
$757$	37.2695			1.35458			0.677291	+	0.735716i	$0.263154\pi$
$758$		−	1.08041i		−	0.0392422i
$759$		0			0
$760$	−11.6319			−0.421933
$761$	−5.27174	+	9.13092i	−0.191100	+	0.330996i	−0.945615	−	0.325287i	$-0.894539\pi$
$761$	−5.27174	+	9.13092i	−0.191100	+	0.330996i	0.754515	+	0.656283i	$0.227872\pi$
$762$		0			0
$763$		0			0
$764$		−	35.9248i		−	1.29971i
$765$		0			0
$766$	23.8452	+	13.7671i	0.861563	+	0.497424i
$767$	−10.8506	+	6.26459i	−0.391792	+	0.226201i
$768$		0			0
$769$	12.4720	−	7.20070i	0.449751	−	0.259664i	−0.257974	−	0.966152i	$-0.583055\pi$
$769$	12.4720	−	7.20070i	0.449751	−	0.259664i	0.707725	+	0.706488i	$0.249722\pi$
$770$		0			0
$771$		0			0
$772$	−60.6398			−2.18247
$773$	−10.9386	+	18.9462i	−0.393433	+	0.681446i	−0.992900	−	0.118954i	$-0.962046\pi$
$773$	−10.9386	+	18.9462i	−0.393433	+	0.681446i	0.599467	+	0.800400i	$0.295379\pi$
$774$		0			0
$775$	−13.6669	+	7.89062i	−0.490931	+	0.283439i
$776$	3.92472	−	6.79781i	0.140889	−	0.244027i
$777$		0			0
$778$	−35.2493	−	61.0536i	−1.26375	−	2.18888i
$779$	4.69885	+	2.71288i	0.168354	+	0.0971992i
$780$		0			0
$781$	2.75487	+	4.77158i	0.0985771	+	0.170740i
$782$	−37.3425	−	64.6792i	−1.33537	−	2.31292i
$783$		0			0
$784$		0			0
$785$	−19.0759	−	11.0135i	−0.680847	−	0.393087i
$786$		0			0
$787$			27.6901i			0.987046i	0.869733	+	0.493523i	$0.164291\pi$
$787$			27.6901i			0.987046i	−0.869733	+	0.493523i	$0.835709\pi$
$788$			9.80633i			0.349336i
$789$		0			0
$790$	29.8853	+	17.2543i	1.06327	+	0.613880i
$791$		0			0
$792$		0			0
$793$	−6.26160	−	10.8454i	−0.222356	−	0.385132i
$794$	−8.93484	−	15.4756i	−0.317086	−	0.549208i
$795$		0			0
$796$	44.6809	+	25.7965i	1.58367	+	0.914334i
$797$	21.3285	+	36.9420i	0.755493	+	1.30855i	0.945129	+	0.326697i	$0.105936\pi$
$797$	21.3285	+	36.9420i	0.755493	+	1.30855i	−0.189636	+	0.981854i	$0.560731\pi$
$798$		0			0
$799$	−17.5271	+	30.3578i	−0.620063	+	1.07398i
$800$	−41.4820	+	23.9496i	−1.46661	+	0.846747i
$801$		0			0
$802$	−16.8163	+	29.1267i	−0.593805	+	1.02850i
$803$	21.3307			0.752743
$804$		0			0
$805$		0			0
$806$	−11.7360	+	6.77581i	−0.413384	+	0.238668i
$807$		0			0
$808$	−0.328111	+	0.189435i	−0.0115429	+	0.00666430i
$809$	30.9391	+	17.8627i	1.08776	+	0.628019i	0.932979	−	0.359930i	$-0.117199\pi$
$809$	30.9391	+	17.8627i	1.08776	+	0.628019i	0.154781	+	0.987949i	$0.450533\pi$
$810$		0			0
$811$			5.85377i			0.205554i	0.994704	+	0.102777i	$0.0327728\pi$
$811$			5.85377i			0.205554i	−0.994704	+	0.102777i	$0.967227\pi$
$812$		0			0
$813$		0			0
$814$	−4.68613	+	8.11662i	−0.164249	+	0.284487i
$815$	76.3113			2.67307
$816$		0			0
$817$		−	28.7878i		−	1.00716i
$818$	34.0227			1.18958
$819$		0			0
$820$	−8.57050			−0.299295
$821$			17.5768i			0.613436i	0.951801	+	0.306718i	$0.0992308\pi$
$821$			17.5768i			0.613436i	−0.951801	+	0.306718i	$0.900769\pi$
$822$		0			0
$823$	30.3785			1.05893			0.529465	−	0.848332i	$-0.322393\pi$
$823$	30.3785			1.05893			0.529465	+	0.848332i	$0.322393\pi$
$824$	0.281232	−	0.487108i	0.00979717	−	0.0169692i
$825$		0			0
$826$		0			0
$827$			15.4454i			0.537089i	0.963267	+	0.268545i	$0.0865426\pi$
$827$			15.4454i			0.537089i	−0.963267	+	0.268545i	$0.913457\pi$
$828$		0			0
$829$	−35.4158	−	20.4473i	−1.23004	−	0.710164i	−0.263002	−	0.964795i	$-0.584713\pi$
$829$	−35.4158	−	20.4473i	−1.23004	−	0.710164i	−0.967038	+	0.254631i	$0.918046\pi$
$830$	12.4649	−	7.19659i	0.432662	−	0.249797i
$831$		0			0
$832$	−22.1318	+	12.7778i	−0.767281	+	0.442990i
$833$		0			0
$834$		0			0
$835$	−52.5716			−1.81931
$836$	−15.3000	+	26.5004i	−0.529162	+	0.916535i
$837$		0			0
$838$	2.12647	−	1.22772i	0.0734577	−	0.0424108i
$839$	16.8620	−	29.2058i	0.582140	−	1.00830i	−0.413086	−	0.910692i	$-0.635549\pi$
$839$	16.8620	−	29.2058i	0.582140	−	1.00830i	0.995225	−	0.0976035i	$-0.0311177\pi$
$840$		0			0
$841$	5.71808	+	9.90401i	0.197175	+	0.341517i
$842$	12.4023	+	7.16049i	0.427413	+	0.246767i
$843$		0			0
$844$	−28.8178	−	49.9139i	−0.991950	−	1.71811i
$845$	11.6487	+	20.1761i	0.400726	+	0.694079i
$846$		0			0
$847$		0			0
$848$	−28.5440	−	16.4799i	−0.980206	−	0.565922i
$849$		0			0
$850$		−	88.6096i		−	3.03928i
$851$		−	8.43151i		−	0.289028i
$852$		0			0
$853$	37.6715	+	21.7497i	1.28985	+	0.744694i	0.978627	−	0.205643i	$-0.0659286\pi$
$853$	37.6715	+	21.7497i	1.28985	+	0.744694i	0.311221	+	0.950337i	$0.399262\pi$
$854$		0			0
$855$		0			0
$856$	−1.92008	−	3.32568i	−0.0656271	−	0.113669i
$857$	4.21534	+	7.30118i	0.143993	+	0.249404i	0.928997	−	0.370088i	$-0.120672\pi$
$857$	4.21534	+	7.30118i	0.143993	+	0.249404i	−0.785004	+	0.619491i	$0.787339\pi$
$858$		0			0
$859$	−2.07929	−	1.20048i	−0.0709445	−	0.0409598i	0.464108	−	0.885779i	$-0.346375\pi$
$859$	−2.07929	−	1.20048i	−0.0709445	−	0.0409598i	−0.535053	+	0.844819i	$0.679708\pi$
$860$	22.7364	+	39.3807i	0.775306	+	1.34287i
$861$		0			0
$862$	0.845356	−	1.46420i	0.0287929	−	0.0498708i
$863$	−8.12017	+	4.68818i	−0.276414	+	0.159588i	−0.631799	−	0.775132i	$-0.717683\pi$
$863$	−8.12017	+	4.68818i	−0.276414	+	0.159588i	0.355385	+	0.934720i	$0.384350\pi$
$864$		0			0
$865$	30.8356	−	53.4089i	1.04844	−	1.81596i
$866$	−17.9180			−0.608877
$867$		0			0
$868$		0			0
$869$	11.5472	−	6.66678i	0.391712	−	0.226155i
$870$		0			0
$871$	−17.5989	+	10.1607i	−0.596316	+	0.344283i
$872$	3.70751	+	2.14053i	0.125552	+	0.0724877i
$873$		0			0
$874$		−	51.0137i		−	1.72557i
$875$		0			0
$876$		0			0
$877$	−1.71542	+	2.97119i	−0.0579256	+	0.100330i	−0.893534	−	0.448995i	$-0.851782\pi$
$877$	−1.71542	+	2.97119i	−0.0579256	+	0.100330i	0.835608	+	0.549326i	$0.185115\pi$
$878$	57.5135			1.94099
$879$		0			0
$880$			28.0804i			0.946589i
$881$	−43.4962			−1.46542			−0.732712	−	0.680539i	$-0.761746\pi$
$881$	−43.4962			−1.46542			−0.732712	+	0.680539i	$0.761746\pi$
$882$		0			0
$883$	49.6074			1.66942			0.834711	−	0.550688i	$-0.185635\pi$
$883$	49.6074			1.66942			0.834711	+	0.550688i	$0.185635\pi$
$884$		−	41.0607i		−	1.38102i
$885$		0			0
$886$	25.5238			0.857489
$887$	17.5766	−	30.4436i	0.590164	−	1.02219i	−0.404045	−	0.914739i	$-0.632396\pi$
$887$	17.5766	−	30.4436i	0.590164	−	1.02219i	0.994210	−	0.107456i	$-0.0342704\pi$
$888$		0			0
$889$		0			0
$890$		−	7.45638i		−	0.249938i
$891$		0			0
$892$	−17.1583	−	9.90634i	−0.574502	−	0.331689i
$893$	−20.7359	+	11.9719i	−0.693901	+	0.400624i
$894$		0			0
$895$	−63.0500	+	36.4019i	−2.10753	+	1.21678i
$896$		0			0
$897$		0			0
$898$	45.8887			1.53132
$899$	−8.47464	+	14.6785i	−0.282645	+	0.489556i
$900$		0			0
$901$	64.1932	−	37.0620i	2.13859	−	1.23471i
$902$	−3.06832	+	5.31448i	−0.102164	+	0.176953i
$903$		0			0
$904$	4.14446	+	7.17842i	0.137843	+	0.238751i
$905$	−50.6517	−	29.2438i	−1.68372	−	0.972097i
$906$		0			0
$907$	−19.0816	−	33.0504i	−0.633596	−	1.09742i	−0.986811	−	0.161878i	$-0.948245\pi$
$907$	−19.0816	−	33.0504i	−0.633596	−	1.09742i	0.353215	−	0.935542i	$-0.385088\pi$
$908$	6.83310	+	11.8353i	0.226765	+	0.392768i
$909$		0			0
$910$		0			0
$911$	39.9027	+	23.0378i	1.32203	+	0.763277i	0.984053	−	0.177876i	$-0.0569226\pi$
$911$	39.9027	+	23.0378i	1.32203	+	0.763277i	0.337981	+	0.941153i	$0.390256\pi$
$912$		0			0
$913$		−	5.56130i		−	0.184052i
$914$			50.3482i			1.66537i
$915$		0			0
$916$	−9.74163	−	5.62433i	−0.321872	−	0.185833i
$917$		0			0
$918$		0			0
$919$	−5.27574	−	9.13785i	−0.174031	−	0.301430i	0.765795	−	0.643085i	$-0.222346\pi$
$919$	−5.27574	−	9.13785i	−0.174031	−	0.301430i	−0.939825	+	0.341655i	$0.889013\pi$
$920$	5.91765	+	10.2497i	0.195099	+	0.337922i
$921$		0			0
$922$	−59.1694	−	34.1615i	−1.94864	−	1.12505i
$923$	−2.52499	−	4.37340i	−0.0831109	−	0.143952i
$924$		0			0
$925$	5.00175	−	8.66328i	0.164456	−	0.284847i
$926$	−56.9168	+	32.8609i	−1.87040	+	1.07988i
$927$		0			0
$928$	−25.7223	+	44.5523i	−0.844375	+	1.46250i
$929$	−52.9029			−1.73569			−0.867843	−	0.496838i	$-0.834494\pi$
$929$	−52.9029			−1.73569			−0.867843	+	0.496838i	$0.834494\pi$
$930$		0			0
$931$		0			0
$932$	46.7896	−	27.0140i	1.53265	−	0.884873i
$933$		0			0
$934$	59.8433	−	34.5505i	1.95813	−	1.13053i
$935$	−54.6899	−	31.5752i	−1.78855	−	1.03262i
$936$		0			0
$937$		−	10.3265i		−	0.337353i	−0.985671	−	0.168676i	$-0.946051\pi$
$937$		−	10.3265i		−	0.337353i	0.985671	−	0.168676i	$-0.0539493\pi$
$938$		0			0
$939$		0			0
$940$	18.9107	−	32.7543i	0.616798	−	1.06833i
$941$	1.01067			0.0329470			0.0164735	−	0.999864i	$-0.494756\pi$
$941$	1.01067			0.0329470			0.0164735	+	0.999864i	$0.494756\pi$
$942$		0			0
$943$		−	5.52066i		−	0.179777i
$944$	−16.3995			−0.533758
$945$		0			0
$946$	32.5594			1.05860
$947$			10.8132i			0.351383i	0.984445	+	0.175692i	$0.0562162\pi$
$947$			10.8132i			0.351383i	−0.984445	+	0.175692i	$0.943784\pi$
$948$		0			0
$949$	−19.5507			−0.634642
$950$	30.2624	−	52.4161i	0.981843	−	1.70060i
$951$		0			0
$952$		0			0
$953$		−	26.7466i		−	0.866408i	−0.901296	−	0.433204i	$-0.857383\pi$
$953$		−	26.7466i		−	0.866408i	0.901296	−	0.433204i	$-0.142617\pi$
$954$		0			0
$955$	43.8564	+	25.3205i	1.41916	+	0.819353i
$956$	13.8777	−	8.01232i	0.448838	−	0.259137i
$957$		0			0
$958$	−41.1454	+	23.7553i	−1.32935	+	0.767500i
$959$		0			0
$960$		0			0
$961$	23.8955			0.770823
$962$	4.29509	−	7.43931i	0.138479	−	0.239853i
$963$		0			0
$964$	9.12204	−	5.26661i	0.293801	−	0.169626i
$965$	42.7402	−	74.0281i	1.37585	−	2.38305i
$966$		0			0
$967$	1.62313	+	2.81134i	0.0521962	+	0.0904065i	0.890943	−	0.454115i	$-0.150045\pi$
$967$	1.62313	+	2.81134i	0.0521962	+	0.0904065i	−0.838747	+	0.544522i	$0.816711\pi$
$968$	2.43456	+	1.40559i	0.0782497	+	0.0451775i
$969$		0			0
$970$	37.6677	+	65.2424i	1.20944	+	2.09481i
$971$	−4.41423	−	7.64567i	−0.141659	−	0.245361i	0.786462	−	0.617638i	$-0.211910\pi$
$971$	−4.41423	−	7.64567i	−0.141659	−	0.245361i	−0.928122	+	0.372277i	$0.878577\pi$
$972$		0			0
$973$		0			0
$974$	4.92997	+	2.84632i	0.157966	+	0.0912019i
$975$		0			0
$976$		−	16.3917i		−	0.524685i
$977$		−	41.8866i		−	1.34007i	−0.742330	−	0.670035i	$-0.766279\pi$
$977$		−	41.8866i		−	1.34007i	0.742330	−	0.670035i	$-0.233721\pi$
$978$		0			0
$979$	−2.49504	−	1.44051i	−0.0797419	−	0.0460390i
$980$		0			0
$981$		0			0
$982$	−26.0861	−	45.1825i	−0.832441	−	1.44183i
$983$	2.35194	+	4.07368i	0.0750153	+	0.129930i	0.901093	−	0.433626i	$-0.142766\pi$
$983$	2.35194	+	4.07368i	0.0750153	+	0.129930i	−0.826078	+	0.563556i	$0.809433\pi$
$984$		0			0
$985$	−11.9714	−	6.91170i	−0.381441	−	0.220225i
$986$	−47.5840	−	82.4179i	−1.51538	−	2.62472i
$987$		0			0
$988$	14.0233	−	24.2890i	0.446139	−	0.772736i
$989$	−25.3669	+	14.6456i	−0.806621	+	0.465703i
$990$		0			0
$991$	−18.9327	+	32.7924i	−0.601418	+	1.04169i	0.391189	+	0.920310i	$0.372064\pi$
$991$	−18.9327	+	32.7924i	−0.601418	+	1.04169i	−0.992607	+	0.121375i	$0.961269\pi$
$992$	−21.5636			−0.684644
$993$		0			0
$994$		0			0
$995$	−62.9840	+	36.3638i	−1.99673	+	1.15281i
$996$		0			0
$997$	−3.18336	+	1.83791i	−0.100818	+	0.0582073i	−0.549561	−	0.835453i	$-0.685205\pi$
$997$	−3.18336	+	1.83791i	−0.100818	+	0.0582073i	0.448743	+	0.893661i	$0.351872\pi$
$998$	−15.5228	−	8.96211i	−0.491367	−	0.283691i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.d.521.16		48
3.2	odd	2		441.2.i.d.227.4		48
7.2	even	3		1323.2.s.d.656.21		48
7.3	odd	6		1323.2.o.e.440.3		48
7.4	even	3		1323.2.o.e.440.4		48
7.5	odd	6		1323.2.s.d.656.22		48
7.6	odd	2	inner	1323.2.i.d.521.23		48
9.4	even	3		441.2.s.d.374.4		48
9.5	odd	6		1323.2.s.d.962.22		48
21.2	odd	6		441.2.s.d.362.3		48
21.5	even	6		441.2.s.d.362.4		48
21.11	odd	6		441.2.o.e.146.22	yes	48
21.17	even	6		441.2.o.e.146.21	✓	48
21.20	even	2		441.2.i.d.227.3		48
63.4	even	3		441.2.o.e.293.21	yes	48
63.5	even	6	inner	1323.2.i.d.1097.16		48
63.13	odd	6		441.2.s.d.374.3		48
63.23	odd	6	inner	1323.2.i.d.1097.23		48
63.31	odd	6		441.2.o.e.293.22	yes	48
63.32	odd	6		1323.2.o.e.881.3		48
63.40	odd	6		441.2.i.d.68.22		48
63.41	even	6		1323.2.s.d.962.21		48
63.58	even	3		441.2.i.d.68.21		48
63.59	even	6		1323.2.o.e.881.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.21		48	63.58	even	3
441.2.i.d.68.22		48	63.40	odd	6
441.2.i.d.227.3		48	21.20	even	2
441.2.i.d.227.4		48	3.2	odd	2
441.2.o.e.146.21	✓	48	21.17	even	6
441.2.o.e.146.22	yes	48	21.11	odd	6
441.2.o.e.293.21	yes	48	63.4	even	3
441.2.o.e.293.22	yes	48	63.31	odd	6
441.2.s.d.362.3		48	21.2	odd	6
441.2.s.d.362.4		48	21.5	even	6
441.2.s.d.374.3		48	63.13	odd	6
441.2.s.d.374.4		48	9.4	even	3
1323.2.i.d.521.16		48	1.1	even	1	trivial
1323.2.i.d.521.23		48	7.6	odd	2	inner
1323.2.i.d.1097.16		48	63.5	even	6	inner
1323.2.i.d.1097.23		48	63.23	odd	6	inner
1323.2.o.e.440.3		48	7.3	odd	6
1323.2.o.e.440.4		48	7.4	even	3
1323.2.o.e.881.3		48	63.32	odd	6
1323.2.o.e.881.4		48	63.59	even	6
1323.2.s.d.656.21		48	7.2	even	3
1323.2.s.d.656.22		48	7.5	odd	6
1323.2.s.d.962.21		48	63.41	even	6
1323.2.s.d.962.22		48	9.5	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.08430i q^{2} -2.34432 q^{4} +(1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +O(q^{10})\)	\(q+2.08430i q^{2} -2.34432 q^{4} +(1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +(5.96509 + 3.44395i) q^{10} +(2.30482 - 1.33069i) q^{11} +(-2.11249 + 1.21964i) q^{13} -3.19280 q^{16} +(3.59017 - 6.21836i) q^{17} +(4.24746 - 2.45227i) q^{19} +(-3.87358 + 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} +(-4.32174 - 2.49516i) q^{23} +(-2.96036 - 5.12749i) q^{25} +(-2.54211 - 4.40306i) q^{26} +(-5.50701 - 3.17947i) q^{29} -2.66543i q^{31} -8.09010i q^{32} +(12.9609 + 7.48301i) q^{34} +(0.844787 + 1.46321i) q^{37} +(5.11128 + 8.85299i) q^{38} +(-2.05391 - 1.18583i) q^{40} +(0.553137 + 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} +(-5.40324 + 3.11956i) q^{44} +(5.20066 - 9.00781i) q^{46} -4.88196 q^{47} +(10.6873 - 6.17029i) q^{50} +(4.95235 - 2.85924i) q^{52} +(8.94013 + 5.16159i) q^{53} -8.79491i q^{55} +(6.62698 - 11.4783i) q^{58} +5.13640 q^{59} +5.13395i q^{61} +5.55556 q^{62} +10.4766 q^{64} +8.06100i q^{65} +8.33088 q^{67} +(-8.41652 + 14.5778i) q^{68} +2.07026i q^{71} +(6.94112 + 4.00746i) q^{73} +(-3.04978 + 1.76079i) q^{74} +(-9.95741 + 5.74891i) q^{76} +5.01003 q^{79} +(-5.27554 + 9.13750i) q^{80} +(-1.99689 + 1.15291i) q^{82} +(1.04482 - 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} +(10.5950 + 6.11703i) q^{86} +(-0.954997 - 1.65410i) q^{88} +(-0.541267 - 0.937501i) q^{89} +(10.1315 + 5.84945i) q^{92} -10.1755i q^{94} -16.2078i q^{95} +(9.47203 + 5.46868i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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