LMFDB - Embedded newform 1344.2.q.z.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1344,2,Mod(193,1344)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1344.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1344, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,3,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 2.43956i$ of defining polynomial
Character	$\chi$	$=$	1344.193
Dual form			1344.2.q.z.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} +(-1.60074 - 2.77256i) q^{5} +(-1.02398 + 2.43956i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12471 - 3.68011i) q^{11} +3.15352 q^{13} -3.20147 q^{15} +(2.20147 - 3.81306i) q^{17} +(1.57676 + 2.73103i) q^{19} +(1.60074 + 2.10657i) q^{21} +(-2.20147 - 3.81306i) q^{23} +(-2.62471 + 4.54614i) q^{25} -1.00000 q^{27} -7.20147 q^{29} +(-1.02398 + 1.77358i) q^{31} +(-2.12471 - 3.68011i) q^{33} +(8.40294 - 1.06607i) q^{35} +(-4.82618 - 8.35920i) q^{37} +(1.57676 - 2.73103i) q^{39} -10.4989 q^{41} -0.750575 q^{43} +(-1.60074 + 2.77256i) q^{45} +(1.20147 + 2.08101i) q^{47} +(-4.90294 - 4.99611i) q^{49} +(-2.20147 - 3.81306i) q^{51} +(-1.64869 + 2.85561i) q^{53} -13.6044 q^{55} +3.15352 q^{57} +(4.12471 - 7.14421i) q^{59} +(-4.04795 - 7.01126i) q^{61} +(2.62471 - 0.332992i) q^{63} +(-5.04795 - 8.74331i) q^{65} +(2.57676 - 4.46308i) q^{67} -4.40294 q^{69} +6.40294 q^{71} +(-7.62471 + 13.2064i) q^{73} +(2.62471 + 4.54614i) q^{75} +(6.80221 + 8.95172i) q^{77} +(8.22545 + 14.2469i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.5565 q^{83} -14.0959 q^{85} +(-3.60074 + 6.23666i) q^{87} +(-1.20147 - 2.08101i) q^{89} +(-3.22913 + 7.69321i) q^{91} +(1.02398 + 1.77358i) q^{93} +(5.04795 - 8.74331i) q^{95} +4.24943 q^{97} -4.24943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 6 q^{27} - 24 q^{29} - 3 q^{31} + 12 q^{35} + 3 q^{37} + 3 q^{39} - 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49}+ \cdots + 24 q^{95}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 6 * q^27 - 24 * q^29 - 3 * q^31 + 12 * q^35 + 3 * q^37 + 3 * q^39 - 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^51 + 6 * q^53 - 24 * q^55 + 6 * q^57 + 12 * q^59 - 18 * q^61 + 3 * q^63 - 24 * q^65 + 9 * q^67 + 12 * q^69 - 33 * q^73 + 3 * q^75 + 12 * q^77 + 27 * q^79 - 3 * q^81 - 36 * q^83 - 72 * q^85 - 12 * q^87 + 12 * q^89 + 51 * q^91 + 3 * q^93 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−1.60074	−	2.77256i	−0.715871	−	1.23992i	−0.962623	−	0.270846i	$-0.912697\pi$
$5$	−1.60074	−	2.77256i	−0.715871	−	1.23992i	0.246752	−	0.969079i	$-0.420637\pi$
$6$		0			0
$7$	−1.02398	+	2.43956i	−0.387027	+	0.922069i
$7$	−1.02398	+	2.43956i	−0.387027	+	0.922069i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.12471	−	3.68011i	0.640625	−	1.10959i	−0.344669	−	0.938724i	$-0.612009\pi$
$11$	2.12471	−	3.68011i	0.640625	−	1.10959i	0.985293	−	0.170871i	$-0.0546580\pi$
$12$		0			0
$13$	3.15352			0.874629			0.437314	−	0.899309i	$-0.355930\pi$
$13$	3.15352			0.874629			0.437314	+	0.899309i	$0.355930\pi$
$14$		0			0
$15$	−3.20147			−0.826617
$16$		0			0
$17$	2.20147	−	3.81306i	0.533935	−	0.924803i	−0.465279	−	0.885164i	$-0.654046\pi$
$17$	2.20147	−	3.81306i	0.533935	−	0.924803i	0.999214	−	0.0396391i	$-0.0126208\pi$
$18$		0			0
$19$	1.57676	+	2.73103i	0.361734	+	0.626541i	0.988246	−	0.152870i	$-0.0488517\pi$
$19$	1.57676	+	2.73103i	0.361734	+	0.626541i	−0.626513	+	0.779411i	$0.715518\pi$
$20$		0			0
$21$	1.60074	+	2.10657i	0.349309	+	0.459692i
$22$		0			0
$23$	−2.20147	−	3.81306i	−0.459039	−	0.795078i	0.539872	−	0.841747i	$-0.318473\pi$
$23$	−2.20147	−	3.81306i	−0.459039	−	0.795078i	−0.998910	+	0.0466689i	$0.985139\pi$
$24$		0			0
$25$	−2.62471	+	4.54614i	−0.524943	+	0.909227i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−7.20147			−1.33728			−0.668640	−	0.743586i	$-0.733123\pi$
$29$	−7.20147			−1.33728			−0.668640	+	0.743586i	$0.733123\pi$
$30$		0			0
$31$	−1.02398	+	1.77358i	−0.183912	+	0.318544i	−0.943209	−	0.332199i	$-0.892209\pi$
$31$	−1.02398	+	1.77358i	−0.183912	+	0.318544i	0.759298	+	0.650744i	$0.225543\pi$
$32$		0			0
$33$	−2.12471	−	3.68011i	−0.369865	−	0.640625i
$34$		0			0
$35$	8.40294	−	1.06607i	1.42036	−	0.180198i
$36$		0			0
$37$	−4.82618	−	8.35920i	−0.793420	−	1.37424i	−0.923838	−	0.382784i	$-0.874965\pi$
$37$	−4.82618	−	8.35920i	−0.793420	−	1.37424i	0.130418	−	0.991459i	$-0.458368\pi$
$38$		0			0
$39$	1.57676	−	2.73103i	0.252484	−	0.437314i
$40$		0			0
$41$	−10.4989			−1.63964			−0.819822	−	0.572618i	$-0.805928\pi$
$41$	−10.4989			−1.63964			−0.819822	+	0.572618i	$0.805928\pi$
$42$		0			0
$43$	−0.750575			−0.114462			−0.0572308	−	0.998361i	$-0.518227\pi$
$43$	−0.750575			−0.114462			−0.0572308	+	0.998361i	$0.518227\pi$
$44$		0			0
$45$	−1.60074	+	2.77256i	−0.238624	+	0.413308i
$46$		0			0
$47$	1.20147	+	2.08101i	0.175253	+	0.303547i	0.940249	−	0.340488i	$-0.110592\pi$
$47$	1.20147	+	2.08101i	0.175253	+	0.303547i	−0.764996	+	0.644035i	$0.777259\pi$
$48$		0			0
$49$	−4.90294	−	4.99611i	−0.700421	−	0.713730i
$50$		0			0
$51$	−2.20147	−	3.81306i	−0.308268	−	0.533935i
$52$		0			0
$53$	−1.64869	+	2.85561i	−0.226465	+	0.392249i	−0.956758	−	0.290885i	$-0.906050\pi$
$53$	−1.64869	+	2.85561i	−0.226465	+	0.392249i	0.730293	+	0.683134i	$0.239384\pi$
$54$		0			0
$55$	−13.6044			−1.83442
$56$		0			0
$57$	3.15352			0.417694
$58$		0			0
$59$	4.12471	−	7.14421i	0.536992	−	0.930097i	−0.462072	−	0.886842i	$-0.652894\pi$
$59$	4.12471	−	7.14421i	0.536992	−	0.930097i	0.999064	−	0.0432549i	$-0.0137727\pi$
$60$		0			0
$61$	−4.04795	−	7.01126i	−0.518287	−	0.897700i	−0.999774	−	0.0212466i	$-0.993236\pi$
$61$	−4.04795	−	7.01126i	−0.518287	−	0.897700i	0.481487	−	0.876453i	$-0.340097\pi$
$62$		0			0
$63$	2.62471	−	0.332992i	0.330683	−	0.0419531i
$64$		0			0
$65$	−5.04795	−	8.74331i	−0.626121	−	1.08447i
$66$		0			0
$67$	2.57676	−	4.46308i	0.314801	−	0.545252i	−0.664594	−	0.747205i	$-0.731395\pi$
$67$	2.57676	−	4.46308i	0.314801	−	0.545252i	0.979395	+	0.201953i	$0.0647288\pi$
$68$		0			0
$69$	−4.40294			−0.530052
$70$		0			0
$71$	6.40294			0.759890			0.379945	−	0.925009i	$-0.375943\pi$
$71$	6.40294			0.759890			0.379945	+	0.925009i	$0.375943\pi$
$72$		0			0
$73$	−7.62471	+	13.2064i	−0.892405	+	1.54569i	−0.0554215	+	0.998463i	$0.517650\pi$
$73$	−7.62471	+	13.2064i	−0.892405	+	1.54569i	−0.836984	+	0.547228i	$0.815683\pi$
$74$		0			0
$75$	2.62471	+	4.54614i	0.303076	+	0.524943i
$76$		0			0
$77$	6.80221	+	8.95172i	0.775184	+	1.02014i
$78$		0			0
$79$	8.22545	+	14.2469i	0.925435	+	1.60290i	0.790860	+	0.611998i	$0.209634\pi$
$79$	8.22545	+	14.2469i	0.925435	+	1.60290i	0.134576	+	0.990903i	$0.457033\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−14.5565			−1.59778			−0.798890	−	0.601477i	$-0.794579\pi$
$83$	−14.5565			−1.59778			−0.798890	+	0.601477i	$0.794579\pi$
$84$		0			0
$85$	−14.0959			−1.52892
$86$		0			0
$87$	−3.60074	+	6.23666i	−0.386039	+	0.668640i
$88$		0			0
$89$	−1.20147	−	2.08101i	−0.127356	−	0.220587i	0.795296	−	0.606222i	$-0.207316\pi$
$89$	−1.20147	−	2.08101i	−0.127356	−	0.220587i	−0.922651	+	0.385635i	$0.873982\pi$
$90$		0			0
$91$	−3.22913	+	7.69321i	−0.338505	+	0.806468i
$92$		0			0
$93$	1.02398	+	1.77358i	0.106181	+	0.183912i
$94$		0			0
$95$	5.04795	−	8.74331i	0.517909	−	0.897045i
$96$		0			0
$97$	4.24943			0.431464			0.215732	−	0.976453i	$-0.430786\pi$
$97$	4.24943			0.431464			0.215732	+	0.976453i	$0.430786\pi$
$98$		0			0
$99$	−4.24943			−0.427083
$100$		0			0
$101$	1.95205	−	3.38104i	0.194236	−	0.336427i	−0.752414	−	0.658691i	$-0.771111\pi$
$101$	1.95205	−	3.38104i	0.194236	−	0.336427i	0.946650	+	0.322264i	$0.104444\pi$
$102$		0			0
$103$	−4.62471	−	8.01024i	−0.455686	−	0.789272i	0.543041	−	0.839706i	$-0.317273\pi$
$103$	−4.62471	−	8.01024i	−0.455686	−	0.789272i	−0.998727	+	0.0504341i	$0.983940\pi$
$104$		0			0
$105$	3.27823	−	7.81020i	0.319923	−	0.762197i
$106$		0			0
$107$	8.27823	+	14.3383i	0.800287	+	1.38614i	0.919427	+	0.393260i	$0.128653\pi$
$107$	8.27823	+	14.3383i	0.800287	+	1.38614i	−0.119140	+	0.992877i	$0.538014\pi$
$108$		0			0
$109$	10.0277	−	17.3684i	0.960475	−	1.66359i	0.239167	−	0.970979i	$-0.423126\pi$
$109$	10.0277	−	17.3684i	0.960475	−	1.66359i	0.721309	−	0.692614i	$-0.243541\pi$
$110$		0			0
$111$	−9.65237			−0.916162
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$		0			0
$115$	−7.04795	+	12.2074i	−0.657225	+	1.13835i
$116$		0			0
$117$	−1.57676	−	2.73103i	−0.145771	−	0.252484i
$118$		0			0
$119$	7.04795	+	9.27512i	0.646085	+	0.850249i
$120$		0			0
$121$	−3.52881	−	6.11207i	−0.320801	−	0.555643i
$122$		0			0
$123$	−5.24943	+	9.09227i	−0.473325	+	0.819822i
$124$		0			0
$125$	0.798528			0.0714225
$126$		0			0
$127$	12.4509			1.10484			0.552419	−	0.833566i	$-0.313705\pi$
$127$	12.4509			1.10484			0.552419	+	0.833566i	$0.313705\pi$
$128$		0			0
$129$	−0.375287	+	0.650017i	−0.0330422	+	0.0572308i
$130$		0			0
$131$	2.12471	+	3.68011i	0.185637	+	0.321533i	0.943791	−	0.330543i	$-0.107232\pi$
$131$	2.12471	+	3.68011i	0.185637	+	0.321533i	−0.758154	+	0.652076i	$0.773898\pi$
$132$		0			0
$133$	−8.27708	+	1.05010i	−0.717714	+	0.0910551i
$134$		0			0
$135$	1.60074	+	2.77256i	0.137769	+	0.238624i
$136$		0			0
$137$	5.20147	−	9.00921i	0.444392	−	0.769709i	−0.553618	−	0.832771i	$-0.686753\pi$
$137$	5.20147	−	9.00921i	0.444392	−	0.769709i	0.998010	+	0.0630617i	$0.0200865\pi$
$138$		0			0
$139$	−11.6524			−0.988341			−0.494171	−	0.869365i	$-0.664528\pi$
$139$	−11.6524			−0.988341			−0.494171	+	0.869365i	$0.664528\pi$
$140$		0			0
$141$	2.40294			0.202364
$142$		0			0
$143$	6.70032	−	11.6053i	0.560309	−	0.970484i
$144$		0			0
$145$	11.5277	+	19.9665i	0.957320	+	1.65813i
$146$		0			0
$147$	−6.77823	+	1.74802i	−0.559059	+	0.144174i
$148$		0			0
$149$	5.20147	+	9.00921i	0.426121	+	0.738064i	0.996524	−	0.0833012i	$-0.0265464\pi$
$149$	5.20147	+	9.00921i	0.426121	+	0.738064i	−0.570403	+	0.821365i	$0.693213\pi$
$150$		0			0
$151$	10.0037	−	17.3269i	0.814088	−	1.41004i	−0.0958929	−	0.995392i	$-0.530571\pi$
$151$	10.0037	−	17.3269i	0.814088	−	1.41004i	0.909981	−	0.414650i	$-0.136096\pi$
$152$		0			0
$153$	−4.40294			−0.355957
$154$		0			0
$155$	6.55646			0.526628
$156$		0			0
$157$	7.24943	−	12.5564i	0.578567	−	1.00211i	−0.417077	−	0.908871i	$-0.636945\pi$
$157$	7.24943	−	12.5564i	0.578567	−	1.00211i	0.995644	−	0.0932364i	$-0.0297212\pi$
$158$		0			0
$159$	1.64869	+	2.85561i	0.130750	+	0.226465i
$160$		0			0
$161$	11.5565	−	1.46615i	0.910777	−	0.115549i
$162$		0			0
$163$	−5.35499	−	9.27512i	−0.419435	−	0.726483i	0.576447	−	0.817134i	$-0.304439\pi$
$163$	−5.35499	−	9.27512i	−0.419435	−	0.726483i	−0.995883	+	0.0906510i	$0.971105\pi$
$164$		0			0
$165$	−6.80221	+	11.7818i	−0.529551	+	0.917210i
$166$		0			0
$167$	17.3047			1.33908			0.669540	−	0.742776i	$-0.266491\pi$
$167$	17.3047			1.33908			0.669540	+	0.742776i	$0.266491\pi$
$168$		0			0
$169$	−3.05531			−0.235024
$170$		0			0
$171$	1.57676	−	2.73103i	0.120578	−	0.208847i
$172$		0			0
$173$	−1.95205	−	3.38104i	−0.148411	−	0.257056i	0.782229	−	0.622991i	$-0.214083\pi$
$173$	−1.95205	−	3.38104i	−0.148411	−	0.257056i	−0.930640	+	0.365935i	$0.880749\pi$
$174$		0			0
$175$	−8.40294	−	11.0583i	−0.635203	−	0.835928i
$176$		0			0
$177$	−4.12471	−	7.14421i	−0.310032	−	0.536992i
$178$		0			0
$179$	10.4029	−	18.0184i	0.777553	−	1.34676i	−0.155796	−	0.987789i	$-0.549794\pi$
$179$	10.4029	−	18.0184i	0.777553	−	1.34676i	0.933349	−	0.358971i	$-0.116872\pi$
$180$		0			0
$181$	13.2494			0.984822			0.492411	−	0.870363i	$-0.336116\pi$
$181$	13.2494			0.984822			0.492411	+	0.870363i	$0.336116\pi$
$182$		0			0
$183$	−8.09591			−0.598467
$184$		0			0
$185$	−15.4509	+	26.7617i	−1.13597	+	1.96756i
$186$		0			0
$187$	−9.35499	−	16.2033i	−0.684105	−	1.18490i
$188$		0			0
$189$	1.02398	−	2.43956i	0.0744833	−	0.177452i
$190$		0			0
$191$	−2.09591	−	3.63021i	−0.151654	−	0.262673i	0.780181	−	0.625553i	$-0.215127\pi$
$191$	−2.09591	−	3.63021i	−0.151654	−	0.262673i	−0.931836	+	0.362880i	$0.881793\pi$
$192$		0			0
$193$	9.15237	−	15.8524i	0.658802	−	1.14108i	−0.322124	−	0.946697i	$-0.604397\pi$
$193$	9.15237	−	15.8524i	0.658802	−	1.14108i	0.980926	−	0.194381i	$-0.0622698\pi$
$194$		0			0
$195$	−10.0959			−0.722983
$196$		0			0
$197$	−11.9041			−0.848132			−0.424066	−	0.905631i	$-0.639397\pi$
$197$	−11.9041			−0.848132			−0.424066	+	0.905631i	$0.639397\pi$
$198$		0			0
$199$	−0.402945	+	0.697921i	−0.0285640	+	0.0494743i	−0.879954	−	0.475059i	$-0.842427\pi$
$199$	−0.402945	+	0.697921i	−0.0285640	+	0.0494743i	0.851390	+	0.524533i	$0.175760\pi$
$200$		0			0
$201$	−2.57676	−	4.46308i	−0.181751	−	0.314801i
$202$		0			0
$203$	7.37414	−	17.5685i	0.517563	−	1.23306i
$204$		0			0
$205$	16.8059	+	29.1087i	1.17377	+	2.03304i
$206$		0			0
$207$	−2.20147	+	3.81306i	−0.153013	+	0.265026i
$208$		0			0
$209$	13.4006			0.926942
$210$		0			0
$211$	−8.49885			−0.585085			−0.292542	−	0.956253i	$-0.594501\pi$
$211$	−8.49885			−0.585085			−0.292542	+	0.956253i	$0.594501\pi$
$212$		0			0
$213$	3.20147	−	5.54511i	0.219361	−	0.379945i
$214$		0			0
$215$	1.20147	+	2.08101i	0.0819397	+	0.141924i
$216$		0			0
$217$	−3.27823	−	4.31416i	−0.222541	−	0.292864i
$218$		0			0
$219$	7.62471	+	13.2064i	0.515230	+	0.892405i
$220$		0			0
$221$	6.94239	−	12.0246i	0.466995	−	0.808860i
$222$		0			0
$223$	−16.7985			−1.12491			−0.562456	−	0.826827i	$-0.690144\pi$
$223$	−16.7985			−1.12491			−0.562456	+	0.826827i	$0.690144\pi$
$224$		0			0
$225$	5.24943			0.349962
$226$		0			0
$227$	−8.43175	+	14.6042i	−0.559635	+	0.969316i	0.437892	+	0.899028i	$0.355725\pi$
$227$	−8.43175	+	14.6042i	−0.559635	+	0.969316i	−0.997527	+	0.0702885i	$0.977608\pi$
$228$		0			0
$229$	10.2771	+	17.8004i	0.679129	+	1.17629i	0.975244	+	0.221133i	$0.0709755\pi$
$229$	10.2771	+	17.8004i	0.679129	+	1.17629i	−0.296115	+	0.955152i	$0.595691\pi$
$230$		0			0
$231$	11.1535	−	1.41503i	0.733848	−	0.0931019i
$232$		0			0
$233$	−4.95205	−	8.57720i	−0.324419	−	0.561911i	0.656975	−	0.753912i	$-0.271836\pi$
$233$	−4.95205	−	8.57720i	−0.324419	−	0.561911i	−0.981395	+	0.192001i	$0.938502\pi$
$234$		0			0
$235$	3.84648	−	6.66230i	0.250917	−	0.434601i
$236$		0			0
$237$	16.4509			1.06860
$238$		0			0
$239$	4.40294			0.284803			0.142401	−	0.989809i	$-0.454518\pi$
$239$	4.40294			0.284803			0.142401	+	0.989809i	$0.454518\pi$
$240$		0			0
$241$	−10.4318	+	18.0683i	−0.671968	+	1.16388i	0.305377	+	0.952232i	$0.401218\pi$
$241$	−10.4318	+	18.0683i	−0.671968	+	1.16388i	−0.977345	+	0.211652i	$0.932116\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−6.00368	+	21.5911i	−0.383561	+	1.37941i
$246$		0			0
$247$	4.97234	+	8.61235i	0.316383	+	0.547991i
$248$		0			0
$249$	−7.27823	+	12.6063i	−0.461239	+	0.798890i
$250$		0			0
$251$	−3.44354			−0.217354			−0.108677	−	0.994077i	$-0.534661\pi$
$251$	−3.44354			−0.217354			−0.108677	+	0.994077i	$0.534661\pi$
$252$		0			0
$253$	−18.7100			−1.17629
$254$		0			0
$255$	−7.04795	+	12.2074i	−0.441360	+	0.764458i
$256$		0			0
$257$	2.79853	+	4.84719i	0.174567	+	0.302360i	0.940011	−	0.341143i	$-0.110814\pi$
$257$	2.79853	+	4.84719i	0.174567	+	0.302360i	−0.765444	+	0.643502i	$0.777481\pi$
$258$		0			0
$259$	25.3347	−	3.21417i	1.57422	−	0.199719i
$260$		0			0
$261$	3.60074	+	6.23666i	0.222880	+	0.386039i
$262$		0			0
$263$	0.798528	−	1.38309i	0.0492393	−	0.0852850i	−0.840355	−	0.542036i	$-0.817654\pi$
$263$	0.798528	−	1.38309i	0.0492393	−	0.0852850i	0.889595	+	0.456751i	$0.150987\pi$
$264$		0			0
$265$	10.5565			0.648478
$266$		0			0
$267$	−2.40294			−0.147058
$268$		0			0
$269$	8.85016	−	15.3289i	0.539604	−	0.934621i	−0.459321	−	0.888270i	$-0.651907\pi$
$269$	8.85016	−	15.3289i	0.539604	−	0.934621i	0.998925	−	0.0463511i	$-0.0147593\pi$
$270$		0			0
$271$	1.19779	+	2.07464i	0.0727607	+	0.126025i	0.900110	−	0.435662i	$-0.143486\pi$
$271$	1.19779	+	2.07464i	0.0727607	+	0.126025i	−0.827350	+	0.561687i	$0.810152\pi$
$272$		0			0
$273$	5.04795	+	6.64311i	0.305516	+	0.402060i
$274$		0			0
$275$	11.1535	+	19.3185i	0.672583	+	1.16495i
$276$		0			0
$277$	−2.62471	+	4.54614i	−0.157704	+	0.273151i	−0.934040	−	0.357168i	$-0.883742\pi$
$277$	−2.62471	+	4.54614i	−0.157704	+	0.273151i	0.776337	+	0.630319i	$0.217076\pi$
$278$		0			0
$279$	2.04795			0.122608
$280$		0			0
$281$	20.0959			1.19882			0.599411	−	0.800442i	$-0.295402\pi$
$281$	20.0959			1.19882			0.599411	+	0.800442i	$0.295402\pi$
$282$		0			0
$283$	−11.6247	+	20.1346i	−0.691017	+	1.19688i	0.280487	+	0.959858i	$0.409504\pi$
$283$	−11.6247	+	20.1346i	−0.691017	+	1.19688i	−0.971505	+	0.237020i	$0.923829\pi$
$284$		0			0
$285$	−5.04795	−	8.74331i	−0.299015	−	0.517909i
$286$		0			0
$287$	10.7506	−	25.6126i	0.634586	−	1.51186i
$288$		0			0
$289$	−1.19296	−	2.06627i	−0.0701742	−	0.121545i
$290$		0			0
$291$	2.12471	−	3.68011i	0.124553	−	0.215732i
$292$		0			0
$293$	−11.2015			−0.654397			−0.327199	−	0.944956i	$-0.606105\pi$
$293$	−11.2015			−0.654397			−0.327199	+	0.944956i	$0.606105\pi$
$294$		0			0
$295$	−26.4103			−1.53767
$296$		0			0
$297$	−2.12471	+	3.68011i	−0.123288	+	0.213542i
$298$		0			0
$299$	−6.94239	−	12.0246i	−0.401489	−	0.695399i
$300$		0			0
$301$	0.768571	−	1.83108i	0.0442997	−	0.105541i
$302$		0			0
$303$	−1.95205	−	3.38104i	−0.112142	−	0.194236i
$304$		0			0
$305$	−12.9594	+	22.4464i	−0.742054	+	1.28527i
$306$		0			0
$307$	28.9571			1.65267			0.826335	−	0.563179i	$-0.190422\pi$
$307$	28.9571			1.65267			0.826335	+	0.563179i	$0.190422\pi$
$308$		0			0
$309$	−9.24943			−0.526181
$310$		0			0
$311$	−13.6524	+	23.6466i	−0.774155	+	1.34088i	0.161113	+	0.986936i	$0.448492\pi$
$311$	−13.6524	+	23.6466i	−0.774155	+	1.34088i	−0.935268	+	0.353940i	$0.884842\pi$
$312$		0			0
$313$	2.74943	+	4.76214i	0.155407	+	0.269172i	0.933207	−	0.359339i	$-0.116998\pi$
$313$	2.74943	+	4.76214i	0.155407	+	0.269172i	−0.777800	+	0.628511i	$0.783665\pi$
$314$		0			0
$315$	−5.12471	−	6.74413i	−0.288745	−	0.379989i
$316$		0			0
$317$	−4.80221	−	8.31767i	−0.269719	−	0.467167i	0.699070	−	0.715053i	$-0.253597\pi$
$317$	−4.80221	−	8.31767i	−0.269719	−	0.467167i	−0.968789	+	0.247886i	$0.920264\pi$
$318$		0			0
$319$	−15.3011	+	26.5022i	−0.856695	+	1.48384i
$320$		0			0
$321$	16.5565			0.924092
$322$		0			0
$323$	13.8848			0.772569
$324$		0			0
$325$	−8.27708	+	14.3363i	−0.459130	+	0.795236i
$326$		0			0
$327$	−10.0277	−	17.3684i	−0.554531	−	0.960475i
$328$		0			0
$329$	−6.30704	+	0.800162i	−0.347718	+	0.0441144i
$330$		0			0
$331$	7.77823	+	13.4723i	0.427530	+	0.740504i	0.996653	−	0.0817484i	$-0.0260504\pi$
$331$	7.77823	+	13.4723i	0.427530	+	0.740504i	−0.569123	+	0.822253i	$0.692717\pi$
$332$		0			0
$333$	−4.82618	+	8.35920i	−0.264473	+	0.458081i
$334$		0			0
$335$	−16.4989			−0.901428
$336$		0			0
$337$	17.9977			0.980397			0.490199	−	0.871611i	$-0.336924\pi$
$337$	17.9977			0.980397			0.490199	+	0.871611i	$0.336924\pi$
$338$		0			0
$339$	4.00000	−	6.92820i	0.217250	−	0.376288i
$340$		0			0
$341$	4.35131	+	7.53669i	0.235637	+	0.408135i
$342$		0			0
$343$	17.2088	−	6.84515i	0.929190	−	0.369603i
$344$		0			0
$345$	7.04795	+	12.2074i	0.379449	+	0.657225i
$346$		0			0
$347$	2.84648	−	4.93025i	0.152807	−	0.264670i	−0.779451	−	0.626463i	$-0.784502\pi$
$347$	2.84648	−	4.93025i	0.152807	−	0.264670i	0.932258	+	0.361793i	$0.117835\pi$
$348$		0			0
$349$	18.1918			0.973785			0.486893	−	0.873462i	$-0.338130\pi$
$349$	18.1918			0.973785			0.486893	+	0.873462i	$0.338130\pi$
$350$		0			0
$351$	−3.15352			−0.168322
$352$		0			0
$353$	10.4989	−	18.1845i	0.558797	−	0.967866i	−0.438800	−	0.898585i	$-0.644596\pi$
$353$	10.4989	−	18.1845i	0.558797	−	0.967866i	0.997597	−	0.0692807i	$-0.0220704\pi$
$354$		0			0
$355$	−10.2494	−	17.7525i	−0.543983	−	0.942206i
$356$		0			0
$357$	11.5565	−	1.46615i	0.611633	−	0.0775967i
$358$		0			0
$359$	12.3453	+	21.3827i	0.651562	+	1.12854i	0.982744	+	0.184971i	$0.0592191\pi$
$359$	12.3453	+	21.3827i	0.651562	+	1.12854i	−0.331182	+	0.943567i	$0.607448\pi$
$360$		0			0
$361$	4.52766	−	7.84213i	0.238298	−	0.412744i
$362$		0			0
$363$	−7.05761			−0.370429
$364$		0			0
$365$	48.8206			2.55539
$366$		0			0
$367$	2.92807	−	5.07157i	0.152844	−	0.264734i	−0.779428	−	0.626492i	$-0.784490\pi$
$367$	2.92807	−	5.07157i	0.152844	−	0.264734i	0.932272	+	0.361758i	$0.117823\pi$
$368$		0			0
$369$	5.24943	+	9.09227i	0.273274	+	0.473325i
$370$		0			0
$371$	−5.27823	−	6.94616i	−0.274032	−	0.360627i
$372$		0			0
$373$	0.317673	+	0.550227i	0.0164485	+	0.0284897i	0.874132	−	0.485688i	$-0.161431\pi$
$373$	0.317673	+	0.550227i	0.0164485	+	0.0284897i	−0.857684	+	0.514177i	$0.828097\pi$
$374$		0			0
$375$	0.399264	−	0.691545i	0.0206179	−	0.0357112i
$376$		0			0
$377$	−22.7100			−1.16962
$378$		0			0
$379$	−10.7506			−0.552220			−0.276110	−	0.961126i	$-0.589045\pi$
$379$	−10.7506			−0.552220			−0.276110	+	0.961126i	$0.589045\pi$
$380$		0			0
$381$	6.22545	−	10.7828i	0.318939	−	0.552419i
$382$		0			0
$383$	−7.49885	−	12.9884i	−0.383173	−	0.663676i	0.608341	−	0.793676i	$-0.291835\pi$
$383$	−7.49885	−	12.9884i	−0.383173	−	0.663676i	−0.991514	+	0.130000i	$0.958502\pi$
$384$		0			0
$385$	13.9306	−	33.1888i	0.709969	−	1.69146i
$386$		0			0
$387$	0.375287	+	0.650017i	0.0190769	+	0.0330422i
$388$		0			0
$389$	3.10557	−	5.37900i	0.157458	−	0.272726i	−0.776493	−	0.630126i	$-0.783003\pi$
$389$	3.10557	−	5.37900i	0.157458	−	0.272726i	0.933952	+	0.357400i	$0.116337\pi$
$390$		0			0
$391$	−19.3859			−0.980388
$392$		0			0
$393$	4.24943			0.214355
$394$		0			0
$395$	26.3335	−	45.6110i	1.32498	−	2.29494i
$396$		0			0
$397$	0.624713	+	1.08203i	0.0313534	+	0.0543057i	0.881276	−	0.472601i	$-0.156685\pi$
$397$	0.624713	+	1.08203i	0.0313534	+	0.0543057i	−0.849923	+	0.526907i	$0.823352\pi$
$398$		0			0
$399$	−3.22913	+	7.69321i	−0.161659	+	0.385142i
$400$		0			0
$401$	−1.05761	−	1.83184i	−0.0528147	−	0.0914778i	0.838409	−	0.545041i	$-0.183486\pi$
$401$	−1.05761	−	1.83184i	−0.0528147	−	0.0914778i	−0.891224	+	0.453563i	$0.850153\pi$
$402$		0			0
$403$	−3.22913	+	5.59302i	−0.160854	+	0.278608i
$404$		0			0
$405$	3.20147			0.159082
$406$		0			0
$407$	−41.0170			−2.03314
$408$		0			0
$409$	8.05646	−	13.9542i	0.398367	−	0.689991i	−0.595158	−	0.803609i	$-0.702911\pi$
$409$	8.05646	−	13.9542i	0.398367	−	0.689991i	0.993525	+	0.113618i	$0.0362439\pi$
$410$		0			0
$411$	−5.20147	−	9.00921i	−0.256570	−	0.444392i
$412$		0			0
$413$	13.2052	+	17.3780i	0.649783	+	0.855116i
$414$		0			0
$415$	23.3011	+	40.3586i	1.14380	+	1.98113i
$416$		0			0
$417$	−5.82618	+	10.0912i	−0.285310	+	0.494171i
$418$		0			0
$419$	20.1106			0.982469			0.491234	−	0.871027i	$-0.336546\pi$
$419$	20.1106			0.982469			0.491234	+	0.871027i	$0.336546\pi$
$420$		0			0
$421$	−4.96171			−0.241819			−0.120909	−	0.992664i	$-0.538581\pi$
$421$	−4.96171			−0.241819			−0.120909	+	0.992664i	$0.538581\pi$
$422$		0			0
$423$	1.20147	−	2.08101i	0.0584176	−	0.101182i
$424$		0			0
$425$	11.5565	+	20.0164i	0.560571	+	0.970937i
$426$		0			0
$427$	21.2494	−	2.69588i	1.02833	−	0.130463i
$428$		0			0
$429$	−6.70032	−	11.6053i	−0.323495	−	0.560309i
$430$		0			0
$431$	10.4029	−	18.0184i	0.501092	−	0.867917i	−0.498907	−	0.866656i	$-0.666265\pi$
$431$	10.4029	−	18.0184i	0.501092	−	0.867917i	0.999999	−	0.00126164i	$-0.000401592\pi$
$432$		0			0
$433$	−8.05531			−0.387114			−0.193557	−	0.981089i	$-0.562002\pi$
$433$	−8.05531			−0.387114			−0.193557	+	0.981089i	$0.562002\pi$
$434$		0			0
$435$	23.0553			1.10542
$436$		0			0
$437$	6.94239	−	12.0246i	0.332099	−	0.575213i
$438$		0			0
$439$	8.09959	+	14.0289i	0.386572	+	0.669563i	0.991986	−	0.126348i	$-0.0403257\pi$
$439$	8.09959	+	14.0289i	0.386572	+	0.669563i	−0.605414	+	0.795911i	$0.706992\pi$
$440$		0			0
$441$	−1.87529	+	6.74413i	−0.0892994	+	0.321149i
$442$		0			0
$443$	7.72177	+	13.3745i	0.366872	+	0.635441i	0.989075	−	0.147415i	$-0.0470953\pi$
$443$	7.72177	+	13.3745i	0.366872	+	0.635441i	−0.622202	+	0.782856i	$0.713762\pi$
$444$		0			0
$445$	−3.84648	+	6.66230i	−0.182341	+	0.315823i
$446$		0			0
$447$	10.4029			0.492042
$448$		0			0
$449$	31.5159			1.48733			0.743663	−	0.668555i	$-0.233087\pi$
$449$	31.5159			1.48733			0.743663	+	0.668555i	$0.233087\pi$
$450$		0			0
$451$	−22.3070	+	38.6369i	−1.05040	+	1.81934i
$452$		0			0
$453$	−10.0037	−	17.3269i	−0.470014	−	0.814088i
$454$		0			0
$455$	26.4989	−	3.36186i	1.24229	−	0.157606i
$456$		0			0
$457$	5.55761	+	9.62607i	0.259974	+	0.450289i	0.966235	−	0.257664i	$-0.0829526\pi$
$457$	5.55761	+	9.62607i	0.259974	+	0.450289i	−0.706260	+	0.707952i	$0.749619\pi$
$458$		0			0
$459$	−2.20147	+	3.81306i	−0.102756	+	0.177978i
$460$		0			0
$461$	−13.5971			−0.633278			−0.316639	−	0.948546i	$-0.602554\pi$
$461$	−13.5971			−0.633278			−0.316639	+	0.948546i	$0.602554\pi$
$462$		0			0
$463$	2.55876			0.118916			0.0594579	−	0.998231i	$-0.481063\pi$
$463$	2.55876			0.118916			0.0594579	+	0.998231i	$0.481063\pi$
$464$		0			0
$465$	3.27823	−	5.67806i	0.152024	−	0.263314i
$466$		0			0
$467$	−0.307039	−	0.531807i	−0.0142081	−	0.0246091i	0.858834	−	0.512254i	$-0.171189\pi$
$467$	−0.307039	−	0.531807i	−0.0142081	−	0.0246091i	−0.873042	+	0.487645i	$0.837856\pi$
$468$		0			0
$469$	8.24943	+	10.8563i	0.380923	+	0.501295i
$470$		0			0
$471$	−7.24943	−	12.5564i	−0.334036	−	0.578567i
$472$		0			0
$473$	−1.59476	+	2.76220i	−0.0733270	+	0.127006i
$474$		0			0
$475$	−16.5542			−0.759557
$476$		0			0
$477$	3.29738			0.150977
$478$		0			0
$479$	−10.0480	+	17.4036i	−0.459103	+	0.795189i	−0.998914	−	0.0465970i	$-0.985162\pi$
$479$	−10.0480	+	17.4036i	−0.459103	+	0.795189i	0.539811	+	0.841786i	$0.318496\pi$
$480$		0			0
$481$	−15.2195	−	26.3609i	−0.693948	−	1.20195i
$482$		0			0
$483$	4.50851	−	10.7413i	0.205144	−	0.488744i
$484$		0			0
$485$	−6.80221	−	11.7818i	−0.308872	−	0.534983i
$486$		0			0
$487$	−11.6860	+	20.2408i	−0.529544	+	0.917196i	0.469863	+	0.882740i	$0.344303\pi$
$487$	−11.6860	+	20.2408i	−0.529544	+	0.917196i	−0.999406	+	0.0344568i	$0.989030\pi$
$488$		0			0
$489$	−10.7100			−0.484322
$490$		0			0
$491$	−22.7483			−1.02662			−0.513308	−	0.858205i	$-0.671580\pi$
$491$	−22.7483			−1.02662			−0.513308	+	0.858205i	$0.671580\pi$
$492$		0			0
$493$	−15.8538	+	27.4597i	−0.714021	+	1.23672i
$494$		0			0
$495$	6.80221	+	11.7818i	0.305737	+	0.529551i
$496$		0			0
$497$	−6.55646	+	15.6204i	−0.294098	+	0.700670i
$498$		0			0
$499$	−4.26972	−	7.39537i	−0.191139	−	0.331062i	0.754489	−	0.656313i	$-0.227885\pi$
$499$	−4.26972	−	7.39537i	−0.191139	−	0.331062i	−0.945628	+	0.325250i	$0.894551\pi$
$500$		0			0
$501$	8.65237	−	14.9863i	0.386559	−	0.669540i
$502$		0			0
$503$	7.59706			0.338736			0.169368	−	0.985553i	$-0.445827\pi$
$503$	7.59706			0.338736			0.169368	+	0.985553i	$0.445827\pi$
$504$		0			0
$505$	−12.4989			−0.556192
$506$		0			0
$507$	−1.52766	+	2.64598i	−0.0678456	+	0.117512i
$508$		0			0
$509$	−2.49517	−	4.32176i	−0.110596	−	0.191559i	0.805414	−	0.592712i	$-0.201943\pi$
$509$	−2.49517	−	4.32176i	−0.110596	−	0.191559i	−0.916011	+	0.401153i	$0.868609\pi$
$510$		0			0
$511$	−24.4103	−	32.1240i	−1.07985	−	1.42108i
$512$		0			0
$513$	−1.57676	−	2.73103i	−0.0696156	−	0.120578i
$514$		0			0
$515$	−14.8059	+	25.6446i	−0.652425	+	1.13003i
$516$		0			0
$517$	10.2111			0.449085
$518$		0			0
$519$	−3.90409			−0.171371
$520$		0			0
$521$	6.24943	−	10.8243i	0.273792	−	0.474222i	−0.696037	−	0.718005i	$-0.745055\pi$
$521$	6.24943	−	10.8243i	0.273792	−	0.474222i	0.969830	+	0.243783i	$0.0783886\pi$
$522$		0			0
$523$	22.1309	+	38.3319i	0.967718	+	1.67614i	0.702129	+	0.712050i	$0.252233\pi$
$523$	22.1309	+	38.3319i	0.967718	+	1.67614i	0.265589	+	0.964086i	$0.414434\pi$
$524$		0			0
$525$	−13.7782	+	1.74802i	−0.601331	+	0.0762898i
$526$		0			0
$527$	4.50851	+	7.80897i	0.196394	+	0.340164i
$528$		0			0
$529$	1.80704	−	3.12988i	0.0785669	−	0.136082i
$530$		0			0
$531$	−8.24943			−0.357995
$532$		0			0
$533$	−33.1083			−1.43408
$534$		0			0
$535$	26.5025	−	45.9037i	1.14580	−	1.98459i
$536$		0			0
$537$	−10.4029	−	18.0184i	−0.448920	−	0.777553i
$538$		0			0
$539$	−28.8036	+	7.42807i	−1.24066	+	0.319950i
$540$		0			0
$541$	12.9797	+	22.4815i	0.558041	+	0.966556i	0.997660	+	0.0683711i	$0.0217802\pi$
$541$	12.9797	+	22.4815i	0.558041	+	0.966556i	−0.439619	+	0.898184i	$0.644886\pi$
$542$		0			0
$543$	6.62471	−	11.4743i	0.284294	−	0.492411i
$544$		0			0
$545$	−64.2065			−2.75031
$546$		0			0
$547$	−22.9018			−0.979210			−0.489605	−	0.871944i	$-0.662859\pi$
$547$	−22.9018			−0.979210			−0.489605	+	0.871944i	$0.662859\pi$
$548$		0			0
$549$	−4.04795	+	7.01126i	−0.172762	+	0.299233i
$550$		0			0
$551$	−11.3550	−	19.6674i	−0.483739	−	0.837860i
$552$		0			0
$553$	−43.1789	+	5.47802i	−1.83615	+	0.232949i
$554$		0			0
$555$	15.4509	+	26.7617i	0.655854	+	1.13597i
$556$		0			0
$557$	−3.25311	+	5.63454i	−0.137839	+	0.238743i	−0.926678	−	0.375856i	$-0.877349\pi$
$557$	−3.25311	+	5.63454i	−0.137839	+	0.238743i	0.788840	+	0.614599i	$0.210682\pi$
$558$		0			0
$559$	−2.36695			−0.100111
$560$		0			0
$561$	−18.7100			−0.789936
$562$		0			0
$563$	−22.1224	+	38.3171i	−0.932349	+	1.61488i	−0.153053	+	0.988218i	$0.548911\pi$
$563$	−22.1224	+	38.3171i	−0.932349	+	1.61488i	−0.779295	+	0.626657i	$0.784423\pi$
$564$		0			0
$565$	−12.8059	−	22.1805i	−0.538748	−	0.933139i
$566$		0			0
$567$	−1.60074	−	2.10657i	−0.0672246	−	0.0884677i
$568$		0			0
$569$	6.50851	+	11.2731i	0.272851	+	0.472592i	0.969591	−	0.244732i	$-0.0787001\pi$
$569$	6.50851	+	11.2731i	0.272851	+	0.472592i	−0.696740	+	0.717324i	$0.745367\pi$
$570$		0			0
$571$	15.0853	−	26.1285i	0.631299	−	1.09344i	−0.355987	−	0.934491i	$-0.615855\pi$
$571$	15.0853	−	26.1285i	0.631299	−	1.09344i	0.987286	−	0.158951i	$-0.0508112\pi$
$572$		0			0
$573$	−4.19181			−0.175115
$574$		0			0
$575$	23.1129			0.963876
$576$		0			0
$577$	14.9029	−	25.8127i	0.620418	−	1.07459i	−0.368990	−	0.929433i	$-0.620296\pi$
$577$	14.9029	−	25.8127i	0.620418	−	1.07459i	0.989408	−	0.145162i	$-0.0463702\pi$
$578$		0			0
$579$	−9.15237	−	15.8524i	−0.380360	−	0.658802i
$580$		0			0
$581$	14.9055	−	35.5114i	0.618383	−	1.47326i
$582$		0			0
$583$	7.00598	+	12.1347i	0.290158	+	0.502568i
$584$		0			0
$585$	−5.04795	+	8.74331i	−0.208707	+	0.361491i
$586$		0			0
$587$	−18.2494			−0.753234			−0.376617	−	0.926369i	$-0.622913\pi$
$587$	−18.2494			−0.753234			−0.376617	+	0.926369i	$0.622913\pi$
$588$		0			0
$589$	−6.45826			−0.266108
$590$		0			0
$591$	−5.95205	+	10.3092i	−0.244835	+	0.424066i
$592$		0			0
$593$	11.8944	+	20.6018i	0.488446	+	0.846013i	0.999912	−	0.0132906i	$-0.00423066\pi$
$593$	11.8944	+	20.6018i	0.488446	+	0.846013i	−0.511466	+	0.859304i	$0.670897\pi$
$594$		0			0
$595$	14.4339	−	34.3879i	0.591731	−	1.40976i
$596$		0			0
$597$	0.402945	+	0.697921i	0.0164914	+	0.0285640i
$598$		0			0
$599$	7.75057	−	13.4244i	0.316680	−	0.548506i	−0.663113	−	0.748519i	$-0.730765\pi$
$599$	7.75057	−	13.4244i	0.316680	−	0.548506i	0.979793	+	0.200013i	$0.0640986\pi$
$600$		0			0
$601$	15.8059			0.644736			0.322368	−	0.946614i	$-0.395521\pi$
$601$	15.8059			0.644736			0.322368	+	0.946614i	$0.395521\pi$
$602$		0			0
$603$	−5.15352			−0.209868
$604$		0			0
$605$	−11.2974	+	19.5676i	−0.459304	+	0.795537i
$606$		0			0
$607$	−2.97602	−	5.15462i	−0.120793	−	0.209220i	0.799288	−	0.600949i	$-0.205210\pi$
$607$	−2.97602	−	5.15462i	−0.120793	−	0.209220i	−0.920081	+	0.391729i	$0.871877\pi$
$608$		0			0
$609$	−11.5277	−	15.1704i	−0.467124	−	0.614736i
$610$		0			0
$611$	3.78887	+	6.56251i	0.153281	+	0.265491i
$612$		0			0
$613$	−14.2015	+	24.5977i	−0.573592	+	0.993491i	0.422601	+	0.906316i	$0.361117\pi$
$613$	−14.2015	+	24.5977i	−0.573592	+	0.993491i	−0.996193	+	0.0871747i	$0.972216\pi$
$614$		0			0
$615$	33.6118			1.35536
$616$		0			0
$617$	−10.1918			−0.410307			−0.205153	−	0.978730i	$-0.565769\pi$
$617$	−10.1918			−0.410307			−0.205153	+	0.978730i	$0.565769\pi$
$618$		0			0
$619$	10.4306	−	18.0663i	0.419241	−	0.726147i	−0.576622	−	0.817011i	$-0.695629\pi$
$619$	10.4306	−	18.0663i	0.419241	−	0.726147i	0.995863	+	0.0908638i	$0.0289628\pi$
$620$		0			0
$621$	2.20147	+	3.81306i	0.0883420	+	0.153013i
$622$		0			0
$623$	6.30704	−	0.800162i	0.252686	−	0.0320578i
$624$		0			0
$625$	11.8453	+	20.5167i	0.473813	+	0.820669i
$626$		0			0
$627$	6.70032	−	11.6053i	0.267585	−	0.463471i
$628$		0			0
$629$	−42.4989			−1.69454
$630$		0			0
$631$	41.6191			1.65683			0.828416	−	0.560113i	$-0.189242\pi$
$631$	41.6191			1.65683			0.828416	+	0.560113i	$0.189242\pi$
$632$		0			0
$633$	−4.24943	+	7.36022i	−0.168899	+	0.292542i
$634$		0			0
$635$	−19.9306	−	34.5208i	−0.790922	−	1.36992i
$636$		0			0
$637$	−15.4615	−	15.7553i	−0.612608	−	0.624249i
$638$		0			0
$639$	−3.20147	−	5.54511i	−0.126648	−	0.219361i
$640$		0			0
$641$	24.4006	−	42.2632i	0.963768	−	1.66929i	0.250877	−	0.968019i	$-0.419281\pi$
$641$	24.4006	−	42.2632i	0.963768	−	1.66929i	0.712890	−	0.701275i	$-0.247386\pi$
$642$		0			0
$643$	−11.8442			−0.467089			−0.233544	−	0.972346i	$-0.575032\pi$
$643$	−11.8442			−0.467089			−0.233544	+	0.972346i	$0.575032\pi$
$644$		0			0
$645$	2.40294			0.0946159
$646$		0			0
$647$	−16.7579	+	29.0256i	−0.658822	+	1.14111i	0.322098	+	0.946706i	$0.395612\pi$
$647$	−16.7579	+	29.0256i	−0.658822	+	1.14111i	−0.980921	+	0.194408i	$0.937722\pi$
$648$		0			0
$649$	−17.5277	−	30.3588i	−0.688021	−	1.19169i
$650$		0			0
$651$	−5.37529	+	0.681953i	−0.210674	+	0.0267278i
$652$		0			0
$653$	−23.2531	−	40.2756i	−0.909964	−	1.57610i	−0.814111	−	0.580709i	$-0.802775\pi$
$653$	−23.2531	−	40.2756i	−0.909964	−	1.57610i	−0.0958532	−	0.995395i	$-0.530558\pi$
$654$		0			0
$655$	6.80221	−	11.7818i	0.265784	−	0.460352i
$656$		0			0
$657$	15.2494			0.594937
$658$		0			0
$659$	10.1152			0.394033			0.197017	−	0.980400i	$-0.436875\pi$
$659$	10.1152			0.394033			0.197017	+	0.980400i	$0.436875\pi$
$660$		0			0
$661$	16.6321	−	28.8076i	0.646913	−	1.12049i	−0.336943	−	0.941525i	$-0.609393\pi$
$661$	16.6321	−	28.8076i	0.646913	−	1.12049i	0.983856	−	0.178961i	$-0.0572735\pi$
$662$		0			0
$663$	−6.94239	−	12.0246i	−0.269620	−	0.466995i
$664$		0			0
$665$	16.1609	+	21.2677i	0.626692	+	0.824728i
$666$		0			0
$667$	15.8538	+	27.4597i	0.613863	+	1.06324i
$668$		0			0
$669$	−8.39926	+	14.5480i	−0.324734	+	0.562456i
$670$		0			0
$671$	−34.4029			−1.32811
$672$		0			0
$673$	−50.4966			−1.94650			−0.973249	−	0.229751i	$-0.926209\pi$
$673$	−50.4966			−1.94650			−0.973249	+	0.229751i	$0.926209\pi$
$674$		0			0
$675$	2.62471	−	4.54614i	0.101025	−	0.174981i
$676$		0			0
$677$	14.3993	+	24.9403i	0.553409	+	0.958532i	0.998025	+	0.0628110i	$0.0200065\pi$
$677$	14.3993	+	24.9403i	0.553409	+	0.958532i	−0.444617	+	0.895721i	$0.646660\pi$
$678$		0			0
$679$	−4.35131	+	10.3667i	−0.166988	+	0.397839i
$680$		0			0
$681$	8.43175	+	14.6042i	0.323105	+	0.559635i
$682$		0			0
$683$	−6.62356	+	11.4723i	−0.253444	+	0.438977i	−0.964472	−	0.264186i	$-0.914897\pi$
$683$	−6.62356	+	11.4723i	−0.253444	+	0.438977i	0.711028	+	0.703164i	$0.248230\pi$
$684$		0			0
$685$	−33.3047			−1.27251
$686$		0			0
$687$	20.5542			0.784190
$688$		0			0
$689$	−5.19917	+	9.00523i	−0.198073	+	0.343072i
$690$		0			0
$691$	−19.8335	−	34.3527i	−0.754504	−	1.30684i	−0.945621	−	0.325271i	$-0.894544\pi$
$691$	−19.8335	−	34.3527i	−0.754504	−	1.30684i	0.191117	−	0.981567i	$-0.438789\pi$
$692$		0			0
$693$	4.35131	−	10.3667i	0.165293	−	0.393800i
$694$		0			0
$695$	18.6524	+	32.3069i	0.707525	+	1.22547i
$696$		0			0
$697$	−23.1129	+	40.0328i	−0.875465	+	1.51635i
$698$		0			0
$699$	−9.90409			−0.374607
$700$		0			0
$701$	2.10787			0.0796130			0.0398065	−	0.999207i	$-0.487326\pi$
$701$	2.10787			0.0796130			0.0398065	+	0.999207i	$0.487326\pi$
$702$		0			0
$703$	15.2195	−	26.3609i	0.574013	−	0.994220i
$704$		0			0
$705$	−3.84648	−	6.66230i	−0.144867	−	0.250917i
$706$		0			0
$707$	6.24943	+	8.22425i	0.235034	+	0.309305i
$708$		0			0
$709$	−7.49885	−	12.9884i	−0.281625	−	0.487789i	0.690160	−	0.723657i	$-0.257540\pi$
$709$	−7.49885	−	12.9884i	−0.281625	−	0.487789i	−0.971785	+	0.235868i	$0.924207\pi$
$710$		0			0
$711$	8.22545	−	14.2469i	0.308478	−	0.534300i
$712$		0			0
$713$	9.01702			0.337690
$714$		0			0
$715$	−42.9018			−1.60444
$716$		0			0
$717$	2.20147	−	3.81306i	0.0822155	−	0.142401i
$718$		0			0
$719$	−11.4029	−	19.7505i	−0.425258	−	0.736569i	0.571186	−	0.820820i	$-0.306483\pi$
$719$	−11.4029	−	19.7505i	−0.425258	−	0.736569i	−0.996444	+	0.0842518i	$0.973150\pi$
$720$		0			0
$721$	24.2771	−	3.07999i	0.904126	−	0.114705i
$722$		0			0
$723$	10.4318	+	18.0683i	0.387961	+	0.671968i
$724$		0			0
$725$	18.9018	−	32.7389i	0.701995	−	1.21589i
$726$		0			0
$727$	16.9691			0.629348			0.314674	−	0.949200i	$-0.398105\pi$
$727$	16.9691			0.629348			0.314674	+	0.949200i	$0.398105\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−1.65237	+	2.86199i	−0.0611151	+	0.105854i
$732$		0			0
$733$	0.672665	+	1.16509i	0.0248455	+	0.0430336i	0.878181	−	0.478329i	$-0.158757\pi$
$733$	0.672665	+	1.16509i	0.0248455	+	0.0430336i	−0.853335	+	0.521362i	$0.825424\pi$
$734$		0			0
$735$	15.6966	+	15.9949i	0.578979	+	0.589981i
$736$		0			0
$737$	−10.9497	−	18.9655i	−0.403339	−	0.698604i
$738$		0			0
$739$	22.6321	−	39.1999i	0.832534	−	1.44199i	−0.0634880	−	0.997983i	$-0.520222\pi$
$739$	22.6321	−	39.1999i	0.832534	−	1.44199i	0.896022	−	0.444009i	$-0.146444\pi$
$740$		0			0
$741$	9.94469			0.365327
$742$		0			0
$743$	−27.8036			−1.02001			−0.510007	−	0.860170i	$-0.670357\pi$
$743$	−27.8036			−1.02001			−0.510007	+	0.860170i	$0.670357\pi$
$744$		0			0
$745$	16.6524	−	28.8428i	0.610096	−	1.05672i
$746$		0			0
$747$	7.27823	+	12.6063i	0.266297	+	0.461239i
$748$		0			0
$749$	−43.4560	+	5.51318i	−1.58785	+	0.201447i
$750$		0			0
$751$	−15.0313	−	26.0350i	−0.548501	−	0.950032i	−0.998378	−	0.0569412i	$-0.981865\pi$
$751$	−15.0313	−	26.0350i	−0.548501	−	0.950032i	0.449876	−	0.893091i	$-0.351468\pi$
$752$		0			0
$753$	−1.72177	+	2.98219i	−0.0627447	+	0.108677i
$754$		0			0
$755$	−64.0530			−2.33113
$756$		0			0
$757$	17.3241			0.629654			0.314827	−	0.949149i	$-0.398054\pi$
$757$	17.3241			0.629654			0.314827	+	0.949149i	$0.398054\pi$
$758$		0			0
$759$	−9.35499	+	16.2033i	−0.339565	+	0.588143i
$760$		0			0
$761$	−6.10557	−	10.5752i	−0.221327	−	0.383349i	0.733884	−	0.679274i	$-0.237705\pi$
$761$	−6.10557	−	10.5752i	−0.221327	−	0.383349i	−0.955211	+	0.295925i	$0.904372\pi$
$762$		0			0
$763$	32.1033	+	42.2480i	1.16222	+	1.52948i
$764$		0			0
$765$	7.04795	+	12.2074i	0.254819	+	0.441360i
$766$		0			0
$767$	13.0074	−	22.5294i	0.469669	−	0.813490i
$768$		0			0
$769$	11.1152			0.400825			0.200413	−	0.979712i	$-0.435772\pi$
$769$	11.1152			0.400825			0.200413	+	0.979712i	$0.435772\pi$
$770$		0			0
$771$	5.59706			0.201573
$772$		0			0
$773$	−0.143858	+	0.249170i	−0.00517423	+	0.00896202i	−0.868601	−	0.495512i	$-0.834980\pi$
$773$	−0.143858	+	0.249170i	−0.00517423	+	0.00896202i	0.863427	+	0.504474i	$0.168314\pi$
$774$		0			0
$775$	−5.37529	−	9.31027i	−0.193086	−	0.334435i
$776$		0			0
$777$	9.88380	−	23.5476i	0.354579	−	0.844764i
$778$		0			0
$779$	−16.5542	−	28.6727i	−0.593115	−	1.02730i
$780$		0			0
$781$	13.6044	−	23.5635i	0.486804	−	0.843170i
$782$		0			0
$783$	7.20147			0.257360
$784$		0			0
$785$	−46.4177			−1.65672
$786$		0			0
$787$	−5.75057	+	9.96029i	−0.204986	+	0.355046i	−0.950128	−	0.311860i	$-0.899048\pi$
$787$	−5.75057	+	9.96029i	−0.204986	+	0.355046i	0.745142	+	0.666905i	$0.232382\pi$
$788$		0			0
$789$	−0.798528	−	1.38309i	−0.0284283	−	0.0492393i
$790$		0			0
$791$	−8.19181	+	19.5165i	−0.291267	+	0.693927i
$792$		0			0
$793$	−12.7653	−	22.1101i	−0.453309	−	0.785154i
$794$		0			0
$795$	5.27823	−	9.14217i	0.187200	−	0.324239i
$796$		0			0
$797$	18.6980			0.662318			0.331159	−	0.943575i	$-0.392560\pi$
$797$	18.6980			0.662318			0.331159	+	0.943575i	$0.392560\pi$
$798$		0			0
$799$	10.5800			0.374295
$800$		0			0
$801$	−1.20147	+	2.08101i	−0.0424519	+	0.0735289i
$802$		0			0
$803$	32.4006	+	56.1196i	1.14339	+	1.98042i
$804$		0			0
$805$	−22.5638	−	29.6940i	−0.795270	−	1.04658i
$806$		0			0
$807$	−8.85016	−	15.3289i	−0.311540	−	0.539604i
$808$		0			0
$809$	26.9018	−	46.5953i	0.945817	−	1.63820i	0.191709	−	0.981452i	$-0.438597\pi$
$809$	26.9018	−	46.5953i	0.945817	−	1.63820i	0.754108	−	0.656751i	$-0.228070\pi$
$810$		0			0
$811$	34.7866			1.22152			0.610761	−	0.791815i	$-0.290864\pi$
$811$	34.7866			1.22152			0.610761	+	0.791815i	$0.290864\pi$
$812$		0			0
$813$	2.39558			0.0840168
$814$		0			0
$815$	−17.1439	+	29.6940i	−0.600523	+	1.04014i
$816$		0			0
$817$	−1.18348	−	2.04984i	−0.0414046	−	0.0717149i
$818$		0			0
$819$	8.27708	−	1.05010i	0.289225	−	0.0366934i
$820$		0			0
$821$	18.9055	+	32.7452i	0.659806	+	1.14282i	0.980666	+	0.195690i	$0.0626947\pi$
$821$	18.9055	+	32.7452i	0.659806	+	1.14282i	−0.320860	+	0.947127i	$0.603972\pi$
$822$		0			0
$823$	27.2088	−	47.1271i	0.948440	−	1.64275i	0.199728	−	0.979851i	$-0.435994\pi$
$823$	27.2088	−	47.1271i	0.948440	−	1.64275i	0.748712	−	0.662896i	$-0.230673\pi$
$824$		0			0
$825$	22.3070			0.776631
$826$		0			0
$827$	7.86120			0.273361			0.136680	−	0.990615i	$-0.456357\pi$
$827$	7.86120			0.273361			0.136680	+	0.990615i	$0.456357\pi$
$828$		0			0
$829$	3.22913	−	5.59302i	0.112152	−	0.194253i	−0.804486	−	0.593972i	$-0.797559\pi$
$829$	3.22913	−	5.59302i	0.112152	−	0.194253i	0.916638	+	0.399719i	$0.130892\pi$
$830$		0			0
$831$	2.62471	+	4.54614i	0.0910503	+	0.157704i
$832$		0			0
$833$	−29.8442	+	7.69643i	−1.03404	+	0.266665i
$834$		0			0
$835$	−27.7003	−	47.9784i	−0.958609	−	1.66036i
$836$		0			0
$837$	1.02398	−	1.77358i	0.0353938	−	0.0613039i
$838$		0			0
$839$	−28.3218			−0.977776			−0.488888	−	0.872347i	$-0.662597\pi$
$839$	−28.3218			−0.977776			−0.488888	+	0.872347i	$0.662597\pi$
$840$		0			0
$841$	22.8612			0.788317
$842$		0			0
$843$	10.0480	−	17.4036i	0.346070	−	0.599411i
$844$		0			0
$845$	4.89075	+	8.47103i	0.168247	+	0.291412i
$846$		0			0
$847$	18.5242	−	2.35013i	0.636499	−	0.0807515i
$848$		0			0
$849$	11.6247	+	20.1346i	0.398959	+	0.691017i
$850$		0			0
$851$	−21.2494	+	36.8051i	−0.728421	+	1.26166i
$852$		0			0
$853$	−8.75057			−0.299614			−0.149807	−	0.988715i	$-0.547865\pi$
$853$	−8.75057			−0.299614			−0.149807	+	0.988715i	$0.547865\pi$
$854$		0			0
$855$	−10.0959			−0.345273
$856$		0			0
$857$	12.3453	−	21.3827i	0.421708	−	0.730420i	−0.574398	−	0.818576i	$-0.694764\pi$
$857$	12.3453	−	21.3827i	0.421708	−	0.730420i	0.996107	+	0.0881555i	$0.0280972\pi$
$858$		0			0
$859$	−4.24943	−	7.36022i	−0.144989	−	0.251127i	0.784380	−	0.620280i	$-0.212981\pi$
$859$	−4.24943	−	7.36022i	−0.144989	−	0.251127i	−0.929369	+	0.369153i	$0.879648\pi$
$860$		0			0
$861$	−16.8059	−	22.1166i	−0.572743	−	0.753731i
$862$		0			0
$863$	−9.30704	−	16.1203i	−0.316815	−	0.548740i	0.663006	−	0.748614i	$-0.269280\pi$
$863$	−9.30704	−	16.1203i	−0.316815	−	0.548740i	−0.979822	+	0.199874i	$0.935947\pi$
$864$		0			0
$865$	−6.24943	+	10.8243i	−0.212487	+	0.368038i
$866$		0			0
$867$	−2.38592			−0.0810302
$868$		0			0
$869$	69.9069			2.37143
$870$		0			0
$871$	8.12586	−	14.0744i	0.275334	−	0.476893i
$872$		0			0
$873$	−2.12471	−	3.68011i	−0.0719106	−	0.124553i
$874$		0			0
$875$	−0.817673	+	1.94806i	−0.0276424	+	0.0658564i
$876$		0			0
$877$	−22.0553	−	38.2009i	−0.744755	−	1.28995i	−0.950309	−	0.311308i	$-0.899233\pi$
$877$	−22.0553	−	38.2009i	−0.744755	−	1.28995i	0.205554	−	0.978646i	$-0.434100\pi$
$878$		0			0
$879$	−5.60074	+	9.70076i	−0.188908	+	0.327199i
$880$		0			0
$881$	−11.2900			−0.380370			−0.190185	−	0.981748i	$-0.560909\pi$
$881$	−11.2900			−0.380370			−0.190185	+	0.981748i	$0.560909\pi$
$882$		0			0
$883$	42.2471			1.42173			0.710864	−	0.703329i	$-0.248304\pi$
$883$	42.2471			1.42173			0.710864	+	0.703329i	$0.248304\pi$
$884$		0			0
$885$	−13.2052	+	22.8720i	−0.443886	+	0.768834i
$886$		0			0
$887$	1.99034	+	3.44737i	0.0668290	+	0.115751i	0.897504	−	0.441007i	$-0.145378\pi$
$887$	1.99034	+	3.44737i	0.0668290	+	0.115751i	−0.830675	+	0.556758i	$0.812045\pi$
$888$		0			0
$889$	−12.7494	+	30.3748i	−0.427602	+	1.01874i
$890$		0			0
$891$	2.12471	+	3.68011i	0.0711805	+	0.123288i
$892$		0			0
$893$	−3.78887	+	6.56251i	−0.126790	+	0.219606i
$894$		0			0
$895$	−66.6095			−2.22651
$896$		0			0
$897$	−13.8848			−0.463599
$898$		0			0
$899$	7.37414	−	12.7724i	0.245941	−	0.425983i
$900$		0			0
$901$	7.25909	+	12.5731i	0.241835	+	0.418871i
$902$		0			0
$903$	−1.20147	−	1.58114i	−0.0399825	−	0.0526170i
$904$		0			0
$905$	−21.2088	−	36.7348i	−0.705005	−	1.22111i
$906$		0			0
$907$	−6.28674	+	10.8890i	−0.208748	+	0.361562i	−0.951320	−	0.308204i	$-0.900272\pi$
$907$	−6.28674	+	10.8890i	−0.208748	+	0.361562i	0.742572	+	0.669766i	$0.233605\pi$
$908$		0			0
$909$	−3.90409			−0.129491
$910$		0			0
$911$	7.09821			0.235174			0.117587	−	0.993063i	$-0.462484\pi$
$911$	7.09821			0.235174			0.117587	+	0.993063i	$0.462484\pi$
$912$		0			0
$913$	−30.9283	+	53.5694i	−1.02358	+	1.77289i
$914$		0			0
$915$	12.9594	+	22.4464i	0.428425	+	0.742054i
$916$		0			0
$917$	−11.1535	+	1.41503i	−0.368322	+	0.0467283i
$918$		0			0
$919$	18.7206	+	32.4251i	0.617536	+	1.06960i	0.989934	+	0.141531i	$0.0452024\pi$
$919$	18.7206	+	32.4251i	0.617536	+	1.06960i	−0.372398	+	0.928073i	$0.621464\pi$
$920$		0			0
$921$	14.4786	−	25.0776i	0.477085	−	0.826335i
$922$		0			0
$923$	20.1918			0.664622
$924$		0			0
$925$	50.6694			1.66600
$926$		0			0
$927$	−4.62471	+	8.01024i	−0.151895	+	0.263091i
$928$		0			0
$929$	−3.94239	−	6.82841i	−0.129345	−	0.224033i	0.794078	−	0.607816i	$-0.207954\pi$
$929$	−3.94239	−	6.82841i	−0.129345	−	0.224033i	−0.923423	+	0.383783i	$0.874621\pi$
$930$		0			0
$931$	5.91376	−	21.2677i	0.193816	−	0.697022i
$932$		0			0
$933$	13.6524	+	23.6466i	0.446959	+	0.774155i
$934$		0			0
$935$	−29.9497	+	51.8745i	−0.979461	+	1.69648i
$936$		0			0
$937$	36.9954			1.20859			0.604294	−	0.796762i	$-0.293455\pi$
$937$	36.9954			1.20859			0.604294	+	0.796762i	$0.293455\pi$
$938$		0			0
$939$	5.49885			0.179448
$940$		0			0
$941$	−6.35131	+	11.0008i	−0.207047	+	0.358616i	−0.950783	−	0.309858i	$-0.899719\pi$
$941$	−6.35131	+	11.0008i	−0.207047	+	0.358616i	0.743736	+	0.668473i	$0.233052\pi$
$942$		0			0
$943$	23.1129	+	40.0328i	0.752661	+	1.30365i
$944$		0			0
$945$	−8.40294	+	1.06607i	−0.273348	+	0.0346791i
$946$		0			0
$947$	−11.5565	−	20.0164i	−0.375535	−	0.650445i	0.614872	−	0.788627i	$-0.289208\pi$
$947$	−11.5565	−	20.0164i	−0.375535	−	0.650445i	−0.990407	+	0.138182i	$0.955874\pi$
$948$		0			0
$949$	−24.0447	+	41.6466i	−0.780523	+	1.35191i
$950$		0			0
$951$	−9.60442			−0.311445
$952$		0			0
$953$	−43.4200			−1.40651			−0.703255	−	0.710937i	$-0.748271\pi$
$953$	−43.4200			−1.40651			−0.703255	+	0.710937i	$0.748271\pi$
$954$		0			0
$955$	−6.70998	+	11.6220i	−0.217130	+	0.376080i
$956$		0			0
$957$	15.3011	+	26.5022i	0.494613	+	0.856695i
$958$		0			0
$959$	16.6524	+	21.9145i	0.537733	+	0.707658i
$960$		0			0
$961$	13.4029	+	23.2146i	0.432353	+	0.748857i
$962$		0			0
$963$	8.27823	−	14.3383i	0.266762	−	0.462046i
$964$		0			0
$965$	−58.6021			−1.88647
$966$		0			0
$967$	−11.6450			−0.374478			−0.187239	−	0.982314i	$-0.559954\pi$
$967$	−11.6450			−0.374478			−0.187239	+	0.982314i	$0.559954\pi$
$968$		0			0
$969$	6.94239	−	12.0246i	0.223022	−	0.386285i
$970$		0			0
$971$	16.6812	+	28.8926i	0.535324	+	0.927209i	0.999148	+	0.0412813i	$0.0131440\pi$
$971$	16.6812	+	28.8926i	0.535324	+	0.927209i	−0.463823	+	0.885928i	$0.653523\pi$
$972$		0			0
$973$	11.9318	−	28.4267i	0.382514	−	0.911318i
$974$		0			0
$975$	8.27708	+	14.3363i	0.265079	+	0.459130i
$976$		0			0
$977$	−9.59476	+	16.6186i	−0.306963	+	0.531676i	−0.977697	−	0.210023i	$-0.932646\pi$
$977$	−9.59476	+	16.6186i	−0.306963	+	0.531676i	0.670733	+	0.741699i	$0.265980\pi$
$978$		0			0
$979$	−10.2111			−0.326349
$980$		0			0
$981$	−20.0553			−0.640317
$982$		0			0
$983$	−3.03829	+	5.26248i	−0.0969065	+	0.167847i	−0.910403	−	0.413723i	$-0.864228\pi$
$983$	−3.03829	+	5.26248i	−0.0969065	+	0.167847i	0.813496	+	0.581570i	$0.197561\pi$
$984$		0			0
$985$	19.0553	+	33.0048i	0.607153	+	1.05162i
$986$		0			0
$987$	−2.46056	+	5.86214i	−0.0783204	+	0.186594i
$988$		0			0
$989$	1.65237	+	2.86199i	0.0525423	+	0.0910059i
$990$		0			0
$991$	−15.8299	+	27.4181i	−0.502852	+	0.870966i	0.497142	+	0.867669i	$0.334383\pi$
$991$	−15.8299	+	27.4181i	−0.502852	+	0.870966i	−0.999995	+	0.00329664i	$0.998951\pi$
$992$		0			0
$993$	15.5565			0.493669
$994$		0			0
$995$	2.58003			0.0817925
$996$		0			0
$997$	7.68003	−	13.3022i	0.243229	−	0.421285i	−0.718403	−	0.695627i	$-0.755127\pi$
$997$	7.68003	−	13.3022i	0.243229	−	0.421285i	0.961632	+	0.274342i	$0.0884600\pi$
$998$		0			0
$999$	4.82618	+	8.35920i	0.152694	+	0.264473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.q.z.193.1		6
4.3	odd	2		1344.2.q.y.193.1		6
7.2	even	3	inner	1344.2.q.z.961.1		6
7.3	odd	6		9408.2.a.ei.1.1		3
7.4	even	3		9408.2.a.eh.1.3		3
8.3	odd	2		672.2.q.l.193.3	yes	6
8.5	even	2		672.2.q.k.193.3	✓	6
24.5	odd	2		2016.2.s.u.865.1		6
24.11	even	2		2016.2.s.v.865.1		6
28.3	even	6		9408.2.a.eg.1.1		3
28.11	odd	6		9408.2.a.ej.1.3		3
28.23	odd	6		1344.2.q.y.961.1		6
56.3	even	6		4704.2.a.bv.1.3		3
56.11	odd	6		4704.2.a.bs.1.1		3
56.37	even	6		672.2.q.k.289.3	yes	6
56.45	odd	6		4704.2.a.bt.1.3		3
56.51	odd	6		672.2.q.l.289.3	yes	6
56.53	even	6		4704.2.a.bu.1.1		3
168.107	even	6		2016.2.s.v.289.1		6
168.149	odd	6		2016.2.s.u.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.k.193.3	✓	6	8.5	even	2
672.2.q.k.289.3	yes	6	56.37	even	6
672.2.q.l.193.3	yes	6	8.3	odd	2
672.2.q.l.289.3	yes	6	56.51	odd	6
1344.2.q.y.193.1		6	4.3	odd	2
1344.2.q.y.961.1		6	28.23	odd	6
1344.2.q.z.193.1		6	1.1	even	1	trivial
1344.2.q.z.961.1		6	7.2	even	3	inner
2016.2.s.u.289.1		6	168.149	odd	6
2016.2.s.u.865.1		6	24.5	odd	2
2016.2.s.v.289.1		6	168.107	even	6
2016.2.s.v.865.1		6	24.11	even	2
4704.2.a.bs.1.1		3	56.11	odd	6
4704.2.a.bt.1.3		3	56.45	odd	6
4704.2.a.bu.1.1		3	56.53	even	6
4704.2.a.bv.1.3		3	56.3	even	6
9408.2.a.eg.1.1		3	28.3	even	6
9408.2.a.eh.1.3		3	7.4	even	3
9408.2.a.ei.1.1		3	7.3	odd	6
9408.2.a.ej.1.3		3	28.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.60074 - 2.77256i) q^{5} +(-1.02398 + 2.43956i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12471 - 3.68011i) q^{11} +3.15352 q^{13} -3.20147 q^{15} +(2.20147 - 3.81306i) q^{17} +(1.57676 + 2.73103i) q^{19} +(1.60074 + 2.10657i) q^{21} +(-2.20147 - 3.81306i) q^{23} +(-2.62471 + 4.54614i) q^{25} -1.00000 q^{27} -7.20147 q^{29} +(-1.02398 + 1.77358i) q^{31} +(-2.12471 - 3.68011i) q^{33} +(8.40294 - 1.06607i) q^{35} +(-4.82618 - 8.35920i) q^{37} +(1.57676 - 2.73103i) q^{39} -10.4989 q^{41} -0.750575 q^{43} +(-1.60074 + 2.77256i) q^{45} +(1.20147 + 2.08101i) q^{47} +(-4.90294 - 4.99611i) q^{49} +(-2.20147 - 3.81306i) q^{51} +(-1.64869 + 2.85561i) q^{53} -13.6044 q^{55} +3.15352 q^{57} +(4.12471 - 7.14421i) q^{59} +(-4.04795 - 7.01126i) q^{61} +(2.62471 - 0.332992i) q^{63} +(-5.04795 - 8.74331i) q^{65} +(2.57676 - 4.46308i) q^{67} -4.40294 q^{69} +6.40294 q^{71} +(-7.62471 + 13.2064i) q^{73} +(2.62471 + 4.54614i) q^{75} +(6.80221 + 8.95172i) q^{77} +(8.22545 + 14.2469i) q^{79} +(-0.500000 + 0.866025i) q^{81} -14.5565 q^{83} -14.0959 q^{85} +(-3.60074 + 6.23666i) q^{87} +(-1.20147 - 2.08101i) q^{89} +(-3.22913 + 7.69321i) q^{91} +(1.02398 + 1.77358i) q^{93} +(5.04795 - 8.74331i) q^{95} +4.24943 q^{97} -4.24943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{7} - 3 q^{9} + 6 q^{13} - 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 6 q^{27} - 24 q^{29} - 3 q^{31} + 12 q^{35} + 3 q^{37} + 3 q^{39} - 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49}+ \cdots + 24 q^{95}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^7 - 3 * q^9 + 6 * q^13 - 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 6 * q^27 - 24 * q^29 - 3 * q^31 + 12 * q^35 + 3 * q^37 + 3 * q^39 - 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^51 + 6 * q^53 - 24 * q^55 + 6 * q^57 + 12 * q^59 - 18 * q^61 + 3 * q^63 - 24 * q^65 + 9 * q^67 + 12 * q^69 - 33 * q^73 + 3 * q^75 + 12 * q^77 + 27 * q^79 - 3 * q^81 - 36 * q^83 - 72 * q^85 - 12 * q^87 + 12 * q^89 + 51 * q^91 + 3 * q^93 + 24 * q^95

Introduction

L-functions

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