LMFDB - Embedded newform 1224.2.l.d.1189.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (of order $2$, degree $1$, 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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.8
Root			$-0.410541 - 1.35331i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.d.1189.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.410541 + 1.35331i) q^{2} +(-1.66291 - 1.11118i) q^{4} -1.09133 q^{5} -4.50716i q^{7} +(2.18647 - 1.79426i) q^{8} +(0.448036 - 1.47691i) q^{10} +2.15194 q^{11} +0.937317i q^{13} +(6.09960 + 1.85037i) q^{14} +(1.53056 + 3.69559i) q^{16} +(-3.95062 + 1.18007i) q^{17} +0.902826i q^{19} +(1.81479 + 1.21267i) q^{20} +(-0.883460 + 2.91225i) q^{22} +2.09199i q^{23} -3.80899 q^{25} +(-1.26848 - 0.384807i) q^{26} +(-5.00826 + 7.49501i) q^{28} -5.32633 q^{29} -6.09729i q^{31} +(-5.62965 + 0.554135i) q^{32} +(0.0248832 - 5.83090i) q^{34} +4.91881i q^{35} -3.32532 q^{37} +(-1.22181 - 0.370647i) q^{38} +(-2.38616 + 1.95813i) q^{40} -4.72595i q^{41} +10.1644i q^{43} +(-3.57849 - 2.39120i) q^{44} +(-2.83111 - 0.858845i) q^{46} -11.3283 q^{47} -13.3145 q^{49} +(1.56375 - 5.15476i) q^{50} +(1.04153 - 1.55868i) q^{52} -9.56417i q^{53} -2.34849 q^{55} +(-8.08700 - 9.85475i) q^{56} +(2.18668 - 7.20820i) q^{58} -5.57204i q^{59} +12.3069 q^{61} +(8.25154 + 2.50318i) q^{62} +(1.56128 - 7.84617i) q^{64} -1.02292i q^{65} -1.17928i q^{67} +(7.88082 + 2.42750i) q^{68} +(-6.65669 - 2.01937i) q^{70} +1.79316i q^{71} +12.8058i q^{73} +(1.36518 - 4.50020i) q^{74} +(1.00320 - 1.50132i) q^{76} -9.69915i q^{77} -2.60982i q^{79} +(-1.67035 - 4.03312i) q^{80} +(6.39569 + 1.94019i) q^{82} +12.8147i q^{83} +(4.31145 - 1.28785i) q^{85} +(-13.7557 - 4.17291i) q^{86} +(4.70515 - 3.86114i) q^{88} -10.1783 q^{89} +4.22464 q^{91} +(2.32457 - 3.47879i) q^{92} +(4.65074 - 15.3308i) q^{94} -0.985283i q^{95} -2.93381i q^{97} +(5.46613 - 18.0186i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.410541	+	1.35331i	−0.290296	+	0.956937i
$2$	−0.410541	+	1.35331i	−0.290296	+	0.956937i
$3$		0			0
$3$		0			0
$4$	−1.66291	−	1.11118i	−0.831456	−	0.555590i
$5$	−1.09133			−0.488059			−0.244029	−	0.969768i	$-0.578469\pi$
$5$	−1.09133			−0.488059			−0.244029	+	0.969768i	$0.578469\pi$
$6$		0			0
$7$		−	4.50716i		−	1.70355i	−0.523911	−	0.851773i	$-0.675528\pi$
$7$		−	4.50716i		−	1.70355i	0.523911	−	0.851773i	$-0.324472\pi$
$8$	2.18647	−	1.79426i	0.773033	−	0.634366i
$9$		0			0
$10$	0.448036	−	1.47691i	0.141682	−	0.467042i
$11$	2.15194			0.648835			0.324418	−	0.945914i	$-0.394832\pi$
$11$	2.15194			0.648835			0.324418	+	0.945914i	$0.394832\pi$
$12$		0			0
$13$			0.937317i			0.259965i	0.991516	+	0.129982i	$0.0414921\pi$
$13$			0.937317i			0.259965i	−0.991516	+	0.129982i	$0.958508\pi$
$14$	6.09960	+	1.85037i	1.63019	+	0.494532i
$15$		0			0
$16$	1.53056	+	3.69559i	0.382640	+	0.923898i
$17$	−3.95062	+	1.18007i	−0.958167	+	0.286210i
$17$	−3.95062	+	1.18007i	−0.958167	+	0.286210i
$18$		0			0
$19$			0.902826i			0.207122i	0.994623	+	0.103561i	$0.0330238\pi$
$19$			0.902826i			0.207122i	−0.994623	+	0.103561i	$0.966976\pi$
$20$	1.81479	+	1.21267i	0.405800	+	0.271161i
$21$		0			0
$22$	−0.883460	+	2.91225i	−0.188354	+	0.620895i
$23$			2.09199i			0.436209i	0.975925	+	0.218105i	$0.0699874\pi$
$23$			2.09199i			0.436209i	−0.975925	+	0.218105i	$0.930013\pi$
$24$		0			0
$25$	−3.80899			−0.761799
$26$	−1.26848	−	0.384807i	−0.248770	−	0.0754668i
$27$		0			0
$28$	−5.00826	+	7.49501i	−0.946473	+	1.41642i
$29$	−5.32633			−0.989075			−0.494538	−	0.869156i	$-0.664663\pi$
$29$	−5.32633			−0.989075			−0.494538	+	0.869156i	$0.664663\pi$
$30$		0			0
$31$		−	6.09729i		−	1.09511i	−0.836771	−	0.547553i	$-0.815560\pi$
$31$		−	6.09729i		−	1.09511i	0.836771	−	0.547553i	$-0.184440\pi$
$32$	−5.62965	+	0.554135i	−0.995191	+	0.0979582i
$33$		0			0
$34$	0.0248832	−	5.83090i	0.00426744	−	0.999991i
$35$			4.91881i			0.831430i
$36$		0			0
$37$	−3.32532			−0.546679			−0.273340	−	0.961918i	$-0.588128\pi$
$37$	−3.32532			−0.546679			−0.273340	+	0.961918i	$0.588128\pi$
$38$	−1.22181	−	0.370647i	−0.198203	−	0.0601268i
$39$		0			0
$40$	−2.38616	+	1.95813i	−0.377286	+	0.309608i
$41$		−	4.72595i		−	0.738069i	−0.929416	−	0.369035i	$-0.879688\pi$
$41$		−	4.72595i		−	0.738069i	0.929416	−	0.369035i	$-0.120312\pi$
$42$		0			0
$43$			10.1644i			1.55006i	0.631924	+	0.775030i	$0.282266\pi$
$43$			10.1644i			1.55006i	−0.631924	+	0.775030i	$0.717734\pi$
$44$	−3.57849	−	2.39120i	−0.539478	−	0.360486i
$45$		0			0
$46$	−2.83111	−	0.858845i	−0.417425	−	0.126630i
$47$	−11.3283			−1.65241			−0.826204	−	0.563371i	$-0.809504\pi$
$47$	−11.3283			−1.65241			−0.826204	+	0.563371i	$0.809504\pi$
$48$		0			0
$49$	−13.3145			−1.90207
$50$	1.56375	−	5.15476i	0.221147	−	0.728993i
$51$		0			0
$52$	1.04153	−	1.55868i	0.144434	−	0.216150i
$53$		−	9.56417i		−	1.31374i	−0.754004	−	0.656870i	$-0.771880\pi$
$53$		−	9.56417i		−	1.31374i	0.754004	−	0.656870i	$-0.228120\pi$
$54$		0			0
$55$	−2.34849			−0.316670
$56$	−8.08700	−	9.85475i	−1.08067	−	1.31690i
$57$		0			0
$58$	2.18668	−	7.20820i	0.287125	−	0.946482i
$59$		−	5.57204i		−	0.725418i	−0.931903	−	0.362709i	$-0.881852\pi$
$59$		−	5.57204i		−	0.725418i	0.931903	−	0.362709i	$-0.118148\pi$
$60$		0			0
$61$	12.3069			1.57574			0.787869	−	0.615843i	$-0.211184\pi$
$61$	12.3069			1.57574			0.787869	+	0.615843i	$0.211184\pi$
$62$	8.25154	+	2.50318i	1.04795	+	0.317905i
$63$		0			0
$64$	1.56128	−	7.84617i	0.195160	−	0.980771i
$65$		−	1.02292i		−	0.126878i
$66$		0			0
$67$		−	1.17928i		−	0.144072i	−0.997402	−	0.0720359i	$-0.977050\pi$
$67$		−	1.17928i		−	0.144072i	0.997402	−	0.0720359i	$-0.0229496\pi$
$68$	7.88082	+	2.42750i	0.955689	+	0.294377i
$69$		0			0
$70$	−6.65669	−	2.01937i	−0.795626	−	0.241361i
$71$			1.79316i			0.212809i	0.994323	+	0.106405i	$0.0339339\pi$
$71$			1.79316i			0.212809i	−0.994323	+	0.106405i	$0.966066\pi$
$72$		0			0
$73$			12.8058i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$73$			12.8058i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$74$	1.36518	−	4.50020i	0.158699	−	0.523137i
$75$		0			0
$76$	1.00320	−	1.50132i	0.115075	−	0.172213i
$77$		−	9.69915i		−	1.10532i
$78$		0			0
$79$		−	2.60982i		−	0.293628i	−0.989164	−	0.146814i	$-0.953098\pi$
$79$		−	2.60982i		−	0.293628i	0.989164	−	0.146814i	$-0.0469019\pi$
$80$	−1.67035	−	4.03312i	−0.186751	−	0.450916i
$81$		0			0
$82$	6.39569	+	1.94019i	0.706286	+	0.214259i
$83$			12.8147i			1.40660i	0.710895	+	0.703298i	$0.248290\pi$
$83$			12.8147i			1.40660i	−0.710895	+	0.703298i	$0.751710\pi$
$84$		0			0
$85$	4.31145	−	1.28785i	0.467642	−	0.139687i
$86$	−13.7557	−	4.17291i	−1.48331	−	0.449977i
$87$		0			0
$88$	4.70515	−	3.86114i	0.501571	−	0.411599i
$89$	−10.1783			−1.07890			−0.539448	−	0.842019i	$-0.681367\pi$
$89$	−10.1783			−1.07890			−0.539448	+	0.842019i	$0.681367\pi$
$90$		0			0
$91$	4.22464			0.442862
$92$	2.32457	−	3.47879i	0.242353	−	0.362689i
$93$		0			0
$94$	4.65074	−	15.3308i	0.479688	−	1.58125i
$95$		−	0.985283i		−	0.101088i
$96$		0			0
$97$		−	2.93381i		−	0.297884i	−0.988846	−	0.148942i	$-0.952413\pi$
$97$		−	2.93381i		−	0.297884i	0.988846	−	0.148942i	$-0.0475867\pi$
$98$	5.46613	−	18.0186i	0.552162	−	1.82016i
$99$		0			0
$100$	6.33402	+	4.23248i	0.633402	+	0.423248i
$101$			7.76557i			0.772704i	0.922352	+	0.386352i	$0.126265\pi$
$101$			7.76557i			0.772704i	−0.922352	+	0.386352i	$0.873735\pi$
$102$		0			0
$103$	−15.3040			−1.50795			−0.753975	−	0.656903i	$-0.771866\pi$
$103$	−15.3040			−1.50795			−0.753975	+	0.656903i	$0.771866\pi$
$104$	1.68179	+	2.04941i	0.164913	+	0.200962i
$105$		0			0
$106$	12.9433	+	3.92648i	1.25717	+	0.381374i
$107$	−2.59291			−0.250666			−0.125333	−	0.992115i	$-0.540000\pi$
$107$	−2.59291			−0.250666			−0.125333	+	0.992115i	$0.540000\pi$
$108$		0			0
$109$	−6.45422			−0.618202			−0.309101	−	0.951029i	$-0.600028\pi$
$109$	−6.45422			−0.618202			−0.309101	+	0.951029i	$0.600028\pi$
$110$	0.964149	−	3.17824i	0.0919280	−	0.303033i
$111$		0			0
$112$	16.6566	−	6.89847i	1.57390	−	0.651844i
$113$		−	17.8899i		−	1.68294i	−0.540306	−	0.841468i	$-0.681692\pi$
$113$		−	17.8899i		−	1.68294i	0.540306	−	0.841468i	$-0.318308\pi$
$114$		0			0
$115$		−	2.28305i		−	0.212896i
$116$	8.85723	+	5.91851i	0.822373	+	0.549520i
$117$		0			0
$118$	7.54071	+	2.28755i	0.694179	+	0.210586i
$119$	5.31877	+	17.8061i	0.487571	+	1.63228i
$120$		0			0
$121$	−6.36914			−0.579013
$122$	−5.05249	+	16.6551i	−0.457431	+	1.50788i
$123$		0			0
$124$	−6.77518	+	10.1393i	−0.608429	+	0.910532i
$125$	9.61354			0.859861
$126$		0			0
$127$	8.08668			0.717577			0.358788	−	0.933419i	$-0.383190\pi$
$127$	8.08668			0.717577			0.358788	+	0.933419i	$0.383190\pi$
$128$	9.97736	+	5.33407i	0.881882	+	0.471470i
$129$		0			0
$130$	1.38434	+	0.419952i	0.121414	+	0.0368322i
$131$	−15.3668			−1.34260			−0.671302	−	0.741184i	$-0.734265\pi$
$131$	−15.3668			−1.34260			−0.671302	+	0.741184i	$0.734265\pi$
$132$		0			0
$133$	4.06918			0.352843
$134$	1.59593	+	0.484141i	0.137868	+	0.0418234i
$135$		0			0
$136$	−6.52056	+	9.66863i	−0.559133	+	0.829078i
$137$	−6.06055			−0.517788			−0.258894	−	0.965906i	$-0.583358\pi$
$137$	−6.06055			−0.517788			−0.258894	+	0.965906i	$0.583358\pi$
$138$		0			0
$139$	−18.5205			−1.57089			−0.785444	−	0.618933i	$-0.787565\pi$
$139$	−18.5205			−1.57089			−0.785444	+	0.618933i	$0.787565\pi$
$140$	5.46568	−	8.17955i	0.461934	−	0.691298i
$141$		0			0
$142$	−2.42671	−	0.736166i	−0.203645	−	0.0617777i
$143$			2.01705i			0.168674i
$144$		0			0
$145$	5.81280			0.482727
$146$	−17.3303	−	5.25730i	−1.43426	−	0.435097i
$147$		0			0
$148$	5.52972	+	3.69503i	0.454540	+	0.303729i
$149$		−	13.2018i		−	1.08153i	−0.841173	−	0.540766i	$-0.818134\pi$
$149$		−	13.2018i		−	1.08153i	0.841173	−	0.540766i	$-0.181866\pi$
$150$		0			0
$151$	−2.14998			−0.174963			−0.0874816	−	0.996166i	$-0.527882\pi$
$151$	−2.14998			−0.174963			−0.0874816	+	0.996166i	$0.527882\pi$
$152$	1.61990	+	1.97400i	0.131391	+	0.160112i
$153$		0			0
$154$	13.1260	+	3.98189i	1.05772	+	0.320870i
$155$			6.65417i			0.534476i
$156$		0			0
$157$		−	1.15615i		−	0.0922710i	−0.998935	−	0.0461355i	$-0.985309\pi$
$157$		−	1.15615i		−	0.0922710i	0.998935	−	0.0461355i	$-0.0146906\pi$
$158$	3.53191	+	1.07144i	0.280983	+	0.0852390i
$159$		0			0
$160$	6.14382	−	0.604746i	0.485712	−	0.0478094i
$161$	9.42891			0.743102
$162$		0			0
$163$	−0.0884470			−0.00692770			−0.00346385	−	0.999994i	$-0.501103\pi$
$163$	−0.0884470			−0.00692770			−0.00346385	+	0.999994i	$0.501103\pi$
$164$	−5.25138	+	7.85884i	−0.410064	+	0.613672i
$165$		0			0
$166$	−17.3423	−	5.26095i	−1.34602	−	0.408329i
$167$		−	12.8349i		−	0.993194i	−0.867981	−	0.496597i	$-0.834583\pi$
$167$		−	12.8349i		−	0.993194i	0.867981	−	0.496597i	$-0.165417\pi$
$168$		0			0
$169$	12.1214			0.932418
$170$	−0.0271559	+	6.36345i	−0.00208276	+	0.488054i
$171$		0			0
$172$	11.2945	−	16.9026i	0.861198	−	1.28881i
$173$	11.4693			0.871994			0.435997	−	0.899948i	$-0.356396\pi$
$173$	11.4693			0.871994			0.435997	+	0.899948i	$0.356396\pi$
$174$		0			0
$175$			17.1677i			1.29776i
$176$	3.29368	+	7.95270i	0.248270	+	0.599458i
$177$		0			0
$178$	4.17860	−	13.7744i	0.313199	−	1.03243i
$179$			5.52123i			0.412676i	0.978481	+	0.206338i	$0.0661547\pi$
$179$			5.52123i			0.412676i	−0.978481	+	0.206338i	$0.933845\pi$
$180$		0			0
$181$	−20.5464			−1.52720			−0.763599	−	0.645691i	$-0.776570\pi$
$181$	−20.5464			−1.52720			−0.763599	+	0.645691i	$0.776570\pi$
$182$	−1.73438	+	5.71725i	−0.128561	+	0.423791i
$183$		0			0
$184$	3.75356	+	4.57406i	0.276716	+	0.337204i
$185$	3.62903			0.266812
$186$		0			0
$187$	−8.50152	+	2.53945i	−0.621693	+	0.185703i
$188$	18.8380	+	12.5878i	1.37391	+	0.918062i
$189$		0			0
$190$	1.33340	+	0.404499i	0.0967348	+	0.0293454i
$191$	5.54627			0.401314			0.200657	−	0.979662i	$-0.435692\pi$
$191$	5.54627			0.401314			0.200657	+	0.979662i	$0.435692\pi$
$192$		0			0
$193$		−	11.5593i		−	0.832057i	−0.909352	−	0.416028i	$-0.863422\pi$
$193$		−	11.5593i		−	0.832057i	0.909352	−	0.416028i	$-0.136578\pi$
$194$	3.97037	+	1.20445i	0.285056	+	0.0864744i
$195$		0			0
$196$	22.1408	+	14.7948i	1.58149	+	1.05677i
$197$	17.2128			1.22636			0.613182	−	0.789942i	$-0.289889\pi$
$197$	17.2128			1.22636			0.613182	+	0.789942i	$0.289889\pi$
$198$		0			0
$199$		−	10.1130i		−	0.716890i	−0.933551	−	0.358445i	$-0.883307\pi$
$199$		−	10.1130i		−	0.716890i	0.933551	−	0.358445i	$-0.116693\pi$
$200$	−8.32824	+	6.83431i	−0.588895	+	0.483259i
$201$		0			0
$202$	−10.5093	−	3.18808i	−0.739429	−	0.224313i
$203$			24.0066i			1.68493i
$204$		0			0
$205$			5.15758i			0.360221i
$206$	6.28292	−	20.7111i	0.437752	−	1.44301i
$207$		0			0
$208$	−3.46394	+	1.43462i	−0.240181	+	0.0994729i
$209$			1.94283i			0.134388i
$210$		0			0
$211$	−16.4992			−1.13585			−0.567925	−	0.823080i	$-0.692254\pi$
$211$	−16.4992			−1.13585			−0.567925	+	0.823080i	$0.692254\pi$
$212$	−10.6275	+	15.9044i	−0.729901	+	1.09232i
$213$		0			0
$214$	1.06450	−	3.50902i	0.0727675	−	0.239872i
$215$		−	11.0928i		−	0.756521i
$216$		0			0
$217$	−27.4814			−1.86556
$218$	2.64972	−	8.73458i	0.179462	−	0.591580i
$219$		0			0
$220$	3.90533	+	2.60959i	0.263297	+	0.175939i
$221$	−1.10610	−	3.70299i	−0.0744045	−	0.249090i
$222$		0			0
$223$	12.3236			0.825248			0.412624	−	0.910901i	$-0.364612\pi$
$223$	12.3236			0.825248			0.412624	+	0.910901i	$0.364612\pi$
$224$	2.49757	+	25.3737i	0.166876	+	1.69535i
$225$		0			0
$226$	24.2106	+	7.34451i	1.61046	+	0.488550i
$227$	16.6910			1.10782			0.553910	−	0.832576i	$-0.313135\pi$
$227$	16.6910			1.10782			0.553910	+	0.832576i	$0.313135\pi$
$228$		0			0
$229$		−	22.4230i		−	1.48175i	−0.671641	−	0.740876i	$-0.734410\pi$
$229$		−	22.4230i		−	1.48175i	0.671641	−	0.740876i	$-0.265590\pi$
$230$	3.08969	+	0.937286i	0.203728	+	0.0618028i
$231$		0			0
$232$	−11.6459	+	9.55681i	−0.764588	+	0.627435i
$233$			3.16889i			0.207601i	0.994598	+	0.103800i	$0.0331003\pi$
$233$			3.16889i			0.207601i	−0.994598	+	0.103800i	$0.966900\pi$
$234$		0			0
$235$	12.3630			0.806473
$236$	−6.19154	+	9.26582i	−0.403035	+	0.603153i
$237$		0			0
$238$	−26.2808	−	0.112153i	−1.70353	−	0.00726977i
$239$	23.4480			1.51672			0.758362	−	0.651833i	$-0.226000\pi$
$239$	23.4480			1.51672			0.758362	+	0.651833i	$0.226000\pi$
$240$		0			0
$241$		−	18.4921i		−	1.19118i	−0.803287	−	0.595592i	$-0.796918\pi$
$241$		−	18.4921i		−	1.19118i	0.803287	−	0.595592i	$-0.203082\pi$
$242$	2.61479	−	8.61944i	0.168085	−	0.554079i
$243$		0			0
$244$	−20.4653	−	13.6752i	−1.31016	−	0.875464i
$245$	14.5305			0.928321
$246$		0			0
$247$	−0.846234			−0.0538446
$248$	−10.9401	−	13.3315i	−0.694697	−	0.846552i
$249$		0			0
$250$	−3.94675	+	13.0101i	−0.249614	+	0.822833i
$251$			9.97157i			0.629400i	0.949191	+	0.314700i	$0.101904\pi$
$251$			9.97157i			0.629400i	−0.949191	+	0.314700i	$0.898096\pi$
$252$		0			0
$253$			4.50184i			0.283028i
$254$	−3.31991	+	10.9438i	−0.208310	+	0.686676i
$255$		0			0
$256$	−11.3148	+	11.3126i	−0.707174	+	0.707040i
$257$	11.4103			0.711756			0.355878	−	0.934533i	$-0.384182\pi$
$257$	11.4103			0.711756			0.355878	+	0.934533i	$0.384182\pi$
$258$		0			0
$259$			14.9877i			0.931293i
$260$	−1.13665	+	1.70103i	−0.0704923	+	0.105494i
$261$		0			0
$262$	6.30869	−	20.7961i	0.389752	−	1.28479i
$263$	3.52123			0.217128			0.108564	−	0.994089i	$-0.465375\pi$
$263$	3.52123			0.217128			0.108564	+	0.994089i	$0.465375\pi$
$264$		0			0
$265$			10.4377i			0.641182i
$266$	−1.67056	+	5.50687i	−0.102429	+	0.337648i
$267$		0			0
$268$	−1.31039	+	1.96104i	−0.0800448	+	0.119789i
$269$	−16.1868			−0.986927			−0.493464	−	0.869766i	$-0.664269\pi$
$269$	−16.1868			−0.986927			−0.493464	+	0.869766i	$0.664269\pi$
$270$		0			0
$271$	3.71581			0.225720			0.112860	−	0.993611i	$-0.463999\pi$
$271$	3.71581			0.225720			0.112860	+	0.993611i	$0.463999\pi$
$272$	−10.4077	−	12.7937i	−0.631061	−	0.775733i
$273$		0			0
$274$	2.48810	−	8.20182i	0.150312	−	0.495490i
$275$	−8.19674			−0.494282
$276$		0			0
$277$	−23.2136			−1.39477			−0.697384	−	0.716698i	$-0.745653\pi$
$277$	−23.2136			−1.39477			−0.697384	+	0.716698i	$0.745653\pi$
$278$	7.60342	−	25.0640i	0.456023	−	1.50324i
$279$		0			0
$280$	8.82561	+	10.7548i	0.527431	+	0.642723i
$281$	−7.49035			−0.446837			−0.223419	−	0.974723i	$-0.571722\pi$
$281$	−7.49035			−0.446837			−0.223419	+	0.974723i	$0.571722\pi$
$282$		0			0
$283$	10.4614			0.621865			0.310933	−	0.950432i	$-0.399359\pi$
$283$	10.4614			0.621865			0.310933	+	0.950432i	$0.399359\pi$
$284$	1.99253	−	2.98187i	0.118235	−	0.176942i
$285$		0			0
$286$	−2.72970	−	0.828082i	−0.161411	−	0.0489655i
$287$	−21.3006			−1.25733
$288$		0			0
$289$	14.2149	−	9.32405i	0.836168	−	0.548473i
$290$	−2.38639	+	7.86654i	−0.140134	+	0.461939i
$291$		0			0
$292$	14.2296	−	21.2949i	0.832722	−	1.24619i
$293$			18.5453i			1.08343i	0.840563	+	0.541714i	$0.182224\pi$
$293$			18.5453i			1.08343i	−0.840563	+	0.541714i	$0.817776\pi$
$294$		0			0
$295$			6.08095i			0.354047i
$296$	−7.27070	+	5.96648i	−0.422601	+	0.346795i
$297$		0			0
$298$	17.8661	+	5.41987i	1.03496	+	0.313964i
$299$	−1.96085			−0.113399
$300$		0			0
$301$	45.8127			2.64060
$302$	0.882655	−	2.90960i	0.0507911	−	0.167429i
$303$		0			0
$304$	−3.33647	+	1.38183i	−0.191360	+	0.0792533i
$305$	−13.4309			−0.769053
$306$		0			0
$307$			26.1750i			1.49389i	0.664888	+	0.746943i	$0.268479\pi$
$307$			26.1750i			1.49389i	−0.664888	+	0.746943i	$0.731521\pi$
$308$	−10.7775	+	16.1288i	−0.614105	+	0.919026i
$309$		0			0
$310$	−9.00517	−	2.73181i	−0.511460	−	0.155156i
$311$		−	6.77320i		−	0.384073i	−0.981388	−	0.192037i	$-0.938491\pi$
$311$		−	6.77320i		−	0.384073i	0.981388	−	0.192037i	$-0.0615092\pi$
$312$		0			0
$313$			19.5423i			1.10460i	0.833647	+	0.552298i	$0.186249\pi$
$313$			19.5423i			1.10460i	−0.833647	+	0.552298i	$0.813751\pi$
$314$	1.56464	+	0.474647i	0.0882975	+	0.0267859i
$315$		0			0
$316$	−2.89998	+	4.33991i	−0.163137	+	0.244139i
$317$	−25.1958			−1.41514			−0.707569	−	0.706644i	$-0.750208\pi$
$317$	−25.1958			−1.41514			−0.707569	+	0.706644i	$0.750208\pi$
$318$		0			0
$319$	−11.4620			−0.641747
$320$	−1.70388	+	8.56278i	−0.0952496	+	0.478674i
$321$		0			0
$322$	−3.87095	+	12.7603i	−0.215720	+	0.711102i
$323$	−1.06540	−	3.56673i	−0.0592805	−	0.198458i
$324$		0			0
$325$		−	3.57023i		−	0.198041i
$326$	0.0363111	−	0.119696i	0.00201108	−	0.00662937i
$327$		0			0
$328$	−8.47957	−	10.3331i	−0.468206	−	0.570552i
$329$			51.0586i			2.81495i
$330$		0			0
$331$			31.3229i			1.72166i	0.508892	+	0.860830i	$0.330055\pi$
$331$			31.3229i			1.72166i	−0.508892	+	0.860830i	$0.669945\pi$
$332$	14.2394	−	21.3097i	0.781491	−	1.16952i
$333$		0			0
$334$	17.3696	+	5.26925i	0.950424	+	0.288320i
$335$			1.28698i			0.0703155i
$336$		0			0
$337$		−	26.9846i		−	1.46995i	−0.678096	−	0.734973i	$-0.737195\pi$
$337$		−	26.9846i		−	1.46995i	0.678096	−	0.734973i	$-0.262805\pi$
$338$	−4.97634	+	16.4041i	−0.270677	+	0.892265i
$339$		0			0
$340$	−8.60059	−	2.64921i	−0.466433	−	0.143673i
$341$		−	13.1210i		−	0.710543i
$342$		0			0
$343$			28.4603i			1.53671i
$344$	18.2376	+	22.2242i	0.983306	+	1.19825i
$345$		0			0
$346$	−4.70861	+	15.5215i	−0.253136	+	0.834443i
$347$	21.7482			1.16750			0.583752	−	0.811932i	$-0.301584\pi$
$347$	21.7482			1.16750			0.583752	+	0.811932i	$0.301584\pi$
$348$		0			0
$349$		−	10.6762i		−	0.571484i	−0.958307	−	0.285742i	$-0.907760\pi$
$349$		−	10.6762i		−	0.571484i	0.958307	−	0.285742i	$-0.0922400\pi$
$350$	−23.2333	−	7.04805i	−1.24187	−	0.376734i
$351$		0			0
$352$	−12.1147	+	1.19247i	−0.645715	+	0.0635587i
$353$	−9.76739			−0.519866			−0.259933	−	0.965627i	$-0.583700\pi$
$353$	−9.76739			−0.519866			−0.259933	+	0.965627i	$0.583700\pi$
$354$		0			0
$355$		−	1.95694i		−	0.103863i
$356$	16.9256	+	11.3099i	0.897055	+	0.599424i
$357$		0			0
$358$	−7.47195	−	2.26669i	−0.394905	−	0.119798i
$359$	16.3621			0.863558			0.431779	−	0.901979i	$-0.357886\pi$
$359$	16.3621			0.863558			0.431779	+	0.901979i	$0.357886\pi$
$360$		0			0
$361$	18.1849			0.957100
$362$	8.43511	−	27.8057i	0.443340	−	1.46143i
$363$		0			0
$364$	−7.02520	−	4.69433i	−0.368221	−	0.246050i
$365$		−	13.9754i		−	0.731506i
$366$		0			0
$367$			27.3487i			1.42759i	0.700354	+	0.713795i	$0.253025\pi$
$367$			27.3487i			1.42759i	−0.700354	+	0.713795i	$0.746975\pi$
$368$	−7.73112	+	3.20191i	−0.403013	+	0.166911i
$369$		0			0
$370$	−1.48986	+	4.91121i	−0.0774543	+	0.255322i
$371$	−43.1072			−2.23802
$372$		0			0
$373$			28.5136i			1.47638i	0.674595	+	0.738188i	$0.264318\pi$
$373$			28.5136i			1.47638i	−0.674595	+	0.738188i	$0.735682\pi$
$374$	0.0535473	−	12.5478i	0.00276886	−	0.648830i
$375$		0			0
$376$	−24.7691	+	20.3260i	−1.27737	+	1.04823i
$377$		−	4.99246i		−	0.257125i
$378$		0			0
$379$	38.4761			1.97638			0.988191	−	0.153225i	$-0.0489658\pi$
$379$	38.4761			1.97638			0.988191	+	0.153225i	$0.0489658\pi$
$380$	−1.09483	+	1.63844i	−0.0561634	+	0.0840502i
$381$		0			0
$382$	−2.27697	+	7.50584i	−0.116500	+	0.384032i
$383$	29.0247			1.48309			0.741546	−	0.670902i	$-0.234093\pi$
$383$	29.0247			1.48309			0.741546	+	0.670902i	$0.234093\pi$
$384$		0			0
$385$			10.5850i			0.539461i
$386$	15.6434	+	4.74556i	0.796226	+	0.241543i
$387$		0			0
$388$	−3.25999	+	4.87868i	−0.165501	+	0.247677i
$389$		−	1.95561i		−	0.0991536i	−0.998770	−	0.0495768i	$-0.984213\pi$
$389$		−	1.95561i		−	0.0991536i	0.998770	−	0.0495768i	$-0.0157873\pi$
$390$		0			0
$391$	−2.46870	−	8.26465i	−0.124847	−	0.417961i
$392$	−29.1117	+	23.8896i	−1.47036	+	1.20661i
$393$		0			0
$394$	−7.06657	+	23.2943i	−0.356008	+	1.17355i
$395$			2.84818i			0.143308i
$396$		0			0
$397$	−19.8933			−0.998415			−0.499208	−	0.866482i	$-0.666375\pi$
$397$	−19.8933			−0.998415			−0.499208	+	0.866482i	$0.666375\pi$
$398$	13.6860	+	4.15179i	0.686019	+	0.208110i
$399$		0			0
$400$	−5.82989	−	14.0765i	−0.291494	−	0.703824i
$401$		−	5.41196i		−	0.270261i	−0.990828	−	0.135130i	$-0.956855\pi$
$401$		−	5.41196i		−	0.270261i	0.990828	−	0.135130i	$-0.0431453\pi$
$402$		0			0
$403$	5.71509			0.284689
$404$	8.62895	−	12.9135i	0.429306	−	0.642469i
$405$		0			0
$406$	−32.4885	−	9.85569i	−1.61238	−	0.489130i
$407$	−7.15590			−0.354705
$408$		0			0
$409$	12.7442			0.630160			0.315080	−	0.949065i	$-0.397969\pi$
$409$	12.7442			0.630160			0.315080	+	0.949065i	$0.397969\pi$
$410$	−6.97982	−	2.11740i	−0.344709	−	0.104571i
$411$		0			0
$412$	25.4493	+	17.0055i	1.25380	+	0.837802i
$413$	−25.1141			−1.23578
$414$		0			0
$415$		−	13.9851i		−	0.686502i
$416$	−0.519400	−	5.27676i	−0.0254657	−	0.258715i
$417$		0			0
$418$	−2.62926	−	0.797611i	−0.128601	−	0.0390124i
$419$	6.65318			0.325029			0.162514	−	0.986706i	$-0.448040\pi$
$419$	6.65318			0.325029			0.162514	+	0.986706i	$0.448040\pi$
$420$		0			0
$421$		−	32.3311i		−	1.57572i	−0.615853	−	0.787861i	$-0.711188\pi$
$421$		−	32.3311i		−	1.57572i	0.615853	−	0.787861i	$-0.288812\pi$
$422$	6.77358	−	22.3286i	0.329733	−	1.08694i
$423$		0			0
$424$	−17.1606	−	20.9118i	−0.833392	−	1.01556i
$425$	15.0479	−	4.49489i	0.729930	−	0.218034i
$426$		0			0
$427$		−	55.4692i		−	2.68434i
$428$	4.31179	+	2.88119i	0.208418	+	0.139268i
$429$		0			0
$430$	15.0120	+	4.55403i	0.723943	+	0.219615i
$431$		−	1.48678i		−	0.0716157i	−0.999359	−	0.0358079i	$-0.988600\pi$
$431$		−	1.48678i		−	0.0716157i	0.999359	−	0.0358079i	$-0.0114004\pi$
$432$		0			0
$433$	9.04590			0.434718			0.217359	−	0.976092i	$-0.430256\pi$
$433$	9.04590			0.434718			0.217359	+	0.976092i	$0.430256\pi$
$434$	11.2822	−	37.1910i	0.541565	−	1.78522i
$435$		0			0
$436$	10.7328	+	7.17180i	0.514008	+	0.343467i
$437$	−1.88870			−0.0903487
$438$		0			0
$439$			16.2737i			0.776704i	0.921511	+	0.388352i	$0.126955\pi$
$439$			16.2737i			0.776704i	−0.921511	+	0.388352i	$0.873045\pi$
$440$	−5.13489	+	4.21379i	−0.244796	+	0.200885i
$441$		0			0
$442$	5.46540	+	0.0233235i	0.259963	+	0.00110938i
$443$			25.0216i			1.18881i	0.804164	+	0.594407i	$0.202613\pi$
$443$			25.0216i			1.18881i	−0.804164	+	0.594407i	$0.797387\pi$
$444$		0			0
$445$	11.1079			0.526565
$446$	−5.05933	+	16.6777i	−0.239566	+	0.789711i
$447$		0			0
$448$	−35.3639	−	7.03694i	−1.67079	−	0.332464i
$449$			20.5388i			0.969288i	0.874712	+	0.484644i	$0.161051\pi$
$449$			20.5388i			0.969288i	−0.874712	+	0.484644i	$0.838949\pi$
$450$		0			0
$451$		−	10.1700i		−	0.478885i
$452$	−19.8789	+	29.7493i	−0.935023	+	1.39929i
$453$		0			0
$454$	−6.85233	+	22.5882i	−0.321596	+	1.06011i
$455$	−4.61048			−0.216143
$456$		0			0
$457$	−1.97960			−0.0926019			−0.0463010	−	0.998928i	$-0.514743\pi$
$457$	−1.97960			−0.0926019			−0.0463010	+	0.998928i	$0.514743\pi$
$458$	30.3453	+	9.20555i	1.41794	+	0.430147i
$459$		0			0
$460$	−2.53688	+	3.79652i	−0.118283	+	0.177014i
$461$		−	30.0835i		−	1.40113i	−0.713591	−	0.700563i	$-0.752932\pi$
$461$		−	30.0835i		−	1.40113i	0.713591	−	0.700563i	$-0.247068\pi$
$462$		0			0
$463$	14.7207			0.684129			0.342065	−	0.939676i	$-0.388874\pi$
$463$	14.7207			0.684129			0.342065	+	0.939676i	$0.388874\pi$
$464$	−8.15226	−	19.6839i	−0.378459	−	0.913804i
$465$		0			0
$466$	−4.28850	−	1.30096i	−0.198661	−	0.0602657i
$467$			2.03739i			0.0942793i	0.998888	+	0.0471396i	$0.0150106\pi$
$467$			2.03739i			0.0942793i	−0.998888	+	0.0471396i	$0.984989\pi$
$468$		0			0
$469$	−5.31519			−0.245433
$470$	−5.07551	+	16.7310i	−0.234116	+	0.771743i
$471$		0			0
$472$	−9.99767	−	12.1831i	−0.460180	−	0.560772i
$473$			21.8733i			1.00573i
$474$		0			0
$475$		−	3.43886i		−	0.157786i
$476$	10.9411	−	35.5201i	0.501485	−	1.62806i
$477$		0			0
$478$	−9.62635	+	31.7325i	−0.440299	+	1.45141i
$479$		−	36.4905i		−	1.66729i	−0.552298	−	0.833647i	$-0.686249\pi$
$479$		−	36.4905i		−	1.66729i	0.552298	−	0.833647i	$-0.313751\pi$
$480$		0			0
$481$		−	3.11688i		−	0.142117i
$482$	25.0257	+	7.59177i	1.13989	+	0.345796i
$483$		0			0
$484$	10.5913	+	7.07726i	0.481424	+	0.321694i
$485$			3.20177i			0.145385i
$486$		0			0
$487$		−	30.8474i		−	1.39783i	−0.715205	−	0.698914i	$-0.753667\pi$
$487$		−	30.8474i		−	1.39783i	0.715205	−	0.698914i	$-0.246333\pi$
$488$	26.9087	−	22.0818i	1.21810	−	0.999595i
$489$		0			0
$490$	−5.96537	+	19.6643i	−0.269488	+	0.888344i
$491$		−	25.3599i		−	1.14448i	−0.820087	−	0.572239i	$-0.806075\pi$
$491$		−	25.3599i		−	1.14448i	0.820087	−	0.572239i	$-0.193925\pi$
$492$		0			0
$493$	21.0423	−	6.28546i	0.947699	−	0.283083i
$494$	0.347413	−	1.14522i	0.0156309	−	0.0515259i
$495$		0			0
$496$	22.5331	−	9.33226i	1.01177	−	0.419031i
$497$	8.08207			0.362530
$498$		0			0
$499$	42.5600			1.90525			0.952624	−	0.304151i	$-0.0983728\pi$
$499$	42.5600			1.90525			0.952624	+	0.304151i	$0.0983728\pi$
$500$	−15.9865	−	10.6824i	−0.714937	−	0.477730i
$501$		0			0
$502$	−13.4947	−	4.09373i	−0.602296	−	0.182712i
$503$			1.06763i			0.0476032i	0.999717	+	0.0238016i	$0.00757699\pi$
$503$			1.06763i			0.0476032i	−0.999717	+	0.0238016i	$0.992423\pi$
$504$		0			0
$505$		−	8.47483i		−	0.377125i
$506$	−6.09239	−	1.84819i	−0.270840	−	0.0821619i
$507$		0			0
$508$	−13.4474	−	8.98576i	−0.596634	−	0.398679i
$509$		−	22.2695i		−	0.987078i	−0.869724	−	0.493539i	$-0.835703\pi$
$509$		−	22.2695i		−	0.987078i	0.869724	−	0.493539i	$-0.164297\pi$
$510$		0			0
$511$	57.7178			2.55328
$512$	−10.6644	−	19.9567i	−0.471303	−	0.881972i
$513$		0			0
$514$	−4.68439	+	15.4417i	−0.206620	+	0.681105i
$515$	16.7018			0.735969
$516$		0			0
$517$	−24.3780			−1.07214
$518$	−20.2831	−	6.15307i	−0.891188	−	0.270351i
$519$		0			0
$520$	−1.83539	−	2.23659i	−0.0804872	−	0.0980810i
$521$		−	34.2365i		−	1.49993i	−0.661477	−	0.749965i	$-0.730070\pi$
$521$		−	34.2365i		−	1.49993i	0.661477	−	0.749965i	$-0.269930\pi$
$522$		0			0
$523$		−	13.3460i		−	0.583580i	−0.956482	−	0.291790i	$-0.905749\pi$
$523$		−	13.3460i		−	0.583580i	0.956482	−	0.291790i	$-0.0942508\pi$
$524$	25.5536	+	17.0753i	1.11632	+	0.745937i
$525$		0			0
$526$	−1.44561	+	4.76533i	−0.0630315	+	0.207778i
$527$	7.19524	+	24.0881i	0.313430	+	1.04929i
$528$		0			0
$529$	18.6236			0.809722
$530$	−14.1255	−	4.28510i	−0.613571	−	0.186133i
$531$		0			0
$532$	−6.76669	−	4.52159i	−0.293373	−	0.196036i
$533$	4.42971			0.191872
$534$		0			0
$535$	2.82973			0.122340
$536$	−2.11593	−	2.57845i	−0.0913942	−	0.111372i
$537$		0			0
$538$	6.64534	−	21.9058i	0.286501	−	0.944427i
$539$	−28.6520			−1.23413
$540$		0			0
$541$	7.80167			0.335420			0.167710	−	0.985836i	$-0.446363\pi$
$541$	7.80167			0.335420			0.167710	+	0.985836i	$0.446363\pi$
$542$	−1.52549	+	5.02866i	−0.0655255	+	0.215999i
$543$		0			0
$544$	21.5867	−	8.83257i	0.925522	−	0.378693i
$545$	7.04370			0.301719
$546$		0			0
$547$	−41.8604			−1.78982			−0.894912	−	0.446243i	$-0.852762\pi$
$547$	−41.8604			−1.78982			−0.894912	+	0.446243i	$0.852762\pi$
$548$	10.0782	+	6.73436i	0.430518	+	0.287678i
$549$		0			0
$550$	3.36509	−	11.0928i	0.143488	−	0.472997i
$551$		−	4.80875i		−	0.204860i
$552$		0			0
$553$	−11.7629			−0.500209
$554$	9.53011	−	31.4152i	0.404895	−	1.33470i
$555$		0			0
$556$	30.7980	+	20.5796i	1.30613	+	0.872770i
$557$			13.9855i			0.592585i	0.955097	+	0.296293i	$0.0957503\pi$
$557$			13.9855i			0.592585i	−0.955097	+	0.296293i	$0.904250\pi$
$558$		0			0
$559$	−9.52729			−0.402962
$560$	−18.1779	+	7.52852i	−0.768157	+	0.318138i
$561$		0			0
$562$	3.07509	−	10.1368i	0.129715	−	0.427595i
$563$		−	41.3480i		−	1.74261i	−0.490740	−	0.871306i	$-0.663274\pi$
$563$		−	41.3480i		−	1.74261i	0.490740	−	0.871306i	$-0.336726\pi$
$564$		0			0
$565$			19.5238i			0.821372i
$566$	−4.29483	+	14.1575i	−0.180525	+	0.595086i
$567$		0			0
$568$	3.21740	+	3.92069i	0.134999	+	0.164509i
$569$	10.7561			0.450918			0.225459	−	0.974253i	$-0.427612\pi$
$569$	10.7561			0.450918			0.225459	+	0.974253i	$0.427612\pi$
$570$		0			0
$571$	−25.8339			−1.08111			−0.540557	−	0.841308i	$-0.681786\pi$
$571$	−25.8339			−1.08111			−0.540557	+	0.841308i	$0.681786\pi$
$572$	2.24131	−	3.35418i	0.0937138	−	0.140245i
$573$		0			0
$574$	8.74476	−	28.8264i	0.364999	−	1.20319i
$575$		−	7.96836i		−	0.332304i
$576$		0			0
$577$	−2.24890			−0.0936230			−0.0468115	−	0.998904i	$-0.514906\pi$
$577$	−2.24890			−0.0936230			−0.0468115	+	0.998904i	$0.514906\pi$
$578$	6.78258	+	23.0651i	0.282118	+	0.959380i
$579$		0			0
$580$	−9.66618	−	6.45907i	−0.401366	−	0.268198i
$581$	57.7579			2.39620
$582$		0			0
$583$		−	20.5816i		−	0.852401i
$584$	22.9769	+	27.9995i	0.950791	+	1.15863i
$585$		0			0
$586$	−25.0976	−	7.61360i	−1.03677	−	0.314515i
$587$			5.73170i			0.236573i	0.992980	+	0.118286i	$0.0377401\pi$
$587$			5.73170i			0.236573i	−0.992980	+	0.118286i	$0.962260\pi$
$588$		0			0
$589$	5.50479			0.226821
$590$	−8.22943	−	2.49648i	−0.338800	−	0.102778i
$591$		0			0
$592$	−5.08960	−	12.2890i	−0.209181	−	0.505076i
$593$	−38.1021			−1.56467			−0.782333	−	0.622860i	$-0.785971\pi$
$593$	−38.1021			−1.56467			−0.782333	+	0.622860i	$0.785971\pi$
$594$		0			0
$595$	−5.80455	−	19.4324i	−0.237963	−	0.796649i
$596$	−14.6696	+	21.9534i	−0.600888	+	0.899247i
$597$		0			0
$598$	0.805010	−	2.65365i	0.0329193	−	0.108516i
$599$	−35.5413			−1.45218			−0.726089	−	0.687601i	$-0.758664\pi$
$599$	−35.5413			−1.45218			−0.726089	+	0.687601i	$0.758664\pi$
$600$		0			0
$601$		−	23.1587i		−	0.944662i	−0.881421	−	0.472331i	$-0.843413\pi$
$601$		−	23.1587i		−	0.944662i	0.881421	−	0.472331i	$-0.156587\pi$
$602$	−18.8080	+	61.9989i	−0.766555	+	2.52689i
$603$		0			0
$604$	3.57523	+	2.38902i	0.145474	+	0.0972078i
$605$	6.95085			0.282592
$606$		0			0
$607$		−	10.3420i		−	0.419769i	−0.977726	−	0.209885i	$-0.932691\pi$
$607$		−	10.3420i		−	0.419769i	0.977726	−	0.209885i	$-0.0673089\pi$
$608$	−0.500288	−	5.08259i	−0.0202893	−	0.206126i
$609$		0			0
$610$	5.51394	−	18.1763i	0.223253	−	0.735935i
$611$		−	10.6182i		−	0.429568i
$612$		0			0
$613$		−	4.02328i		−	0.162499i	−0.996694	−	0.0812494i	$-0.974109\pi$
$613$		−	4.02328i		−	0.162499i	0.996694	−	0.0812494i	$-0.0258910\pi$
$614$	−35.4230	−	10.7459i	−1.42955	−	0.433669i
$615$		0			0
$616$	−17.4028	−	21.2069i	−0.701178	−	0.854449i
$617$			12.5655i			0.505868i	0.967483	+	0.252934i	$0.0813956\pi$
$617$			12.5655i			0.505868i	−0.967483	+	0.252934i	$0.918604\pi$
$618$		0			0
$619$	−10.5183			−0.422765			−0.211383	−	0.977403i	$-0.567797\pi$
$619$	−10.5183			−0.422765			−0.211383	+	0.977403i	$0.567797\pi$
$620$	7.39398	−	11.0653i	0.296949	−	0.444393i
$621$		0			0
$622$	9.16626	+	2.78067i	0.367534	+	0.111495i
$623$			45.8751i			1.83795i
$624$		0			0
$625$	8.55339			0.342136
$626$	−26.4468	−	8.02291i	−1.05703	−	0.320660i
$627$		0			0
$628$	−1.28469	+	1.92258i	−0.0512648	+	0.0767193i
$629$	13.1371	−	3.92412i	0.523810	−	0.156465i
$630$		0			0
$631$	−21.0598			−0.838377			−0.419188	−	0.907899i	$-0.637685\pi$
$631$	−21.0598			−0.838377			−0.419188	+	0.907899i	$0.637685\pi$
$632$	−4.68269	−	5.70629i	−0.186268	−	0.226984i
$633$		0			0
$634$	10.3439	−	34.0978i	0.410809	−	1.35420i
$635$	−8.82526			−0.350220
$636$		0			0
$637$		−	12.4799i		−	0.494471i
$638$	4.70560	−	15.5116i	0.186297	−	0.614111i
$639$		0			0
$640$	−10.8886	−	5.82125i	−0.430410	−	0.230105i
$641$		−	24.0196i		−	0.948716i	−0.880332	−	0.474358i	$-0.842680\pi$
$641$		−	24.0196i		−	0.948716i	0.880332	−	0.474358i	$-0.157320\pi$
$642$		0			0
$643$	−23.7076			−0.934937			−0.467469	−	0.884010i	$-0.654834\pi$
$643$	−23.7076			−0.934937			−0.467469	+	0.884010i	$0.654834\pi$
$644$	−15.6795	−	10.4772i	−0.617857	−	0.412860i
$645$		0			0
$646$	5.26429	+	0.0224652i	0.207121	+	0.000883882i
$647$	−18.2996			−0.719430			−0.359715	−	0.933062i	$-0.617126\pi$
$647$	−18.2996			−0.719430			−0.359715	+	0.933062i	$0.617126\pi$
$648$		0			0
$649$		−	11.9907i		−	0.470677i
$650$	4.83164	+	1.46573i	0.189513	+	0.0574905i
$651$		0			0
$652$	0.147080	+	0.0982805i	0.00576008	+	0.00384896i
$653$	−8.49676			−0.332504			−0.166252	−	0.986083i	$-0.553166\pi$
$653$	−8.49676			−0.332504			−0.166252	+	0.986083i	$0.553166\pi$
$654$		0			0
$655$	16.7703			0.655270
$656$	17.4652	−	7.23334i	0.681900	−	0.282415i
$657$		0			0
$658$	−69.0983	−	20.9616i	−2.69373	−	0.817170i
$659$		−	24.5353i		−	0.955760i	−0.878425	−	0.477880i	$-0.841405\pi$
$659$		−	24.5353i		−	0.955760i	0.878425	−	0.477880i	$-0.158595\pi$
$660$		0			0
$661$		−	40.1736i		−	1.56257i	−0.624172	−	0.781287i	$-0.714564\pi$
$661$		−	40.1736i		−	1.56257i	0.624172	−	0.781287i	$-0.285436\pi$
$662$	−42.3896	−	12.8593i	−1.64752	−	0.499791i
$663$		0			0
$664$	22.9929	+	28.0189i	0.892296	+	1.08735i
$665$	−4.44083			−0.172208
$666$		0			0
$667$		−	11.1426i		−	0.431444i
$668$	−14.2619	+	21.3433i	−0.551809	+	0.825798i
$669$		0			0
$670$	−1.74169	−	0.528359i	−0.0672875	−	0.0204123i
$671$	26.4838			1.02239
$672$		0			0
$673$			28.1852i			1.08646i	0.839584	+	0.543230i	$0.182799\pi$
$673$			28.1852i			1.08646i	−0.839584	+	0.543230i	$0.817201\pi$
$674$	36.5186	+	11.0783i	1.40665	+	0.426719i
$675$		0			0
$676$	−20.1569	−	13.4691i	−0.775265	−	0.518042i
$677$	−6.02100			−0.231406			−0.115703	−	0.993284i	$-0.536912\pi$
$677$	−6.02100			−0.231406			−0.115703	+	0.993284i	$0.536912\pi$
$678$		0			0
$679$	−13.2232			−0.507458
$680$	7.11610	−	10.5517i	0.272890	−	0.404639i
$681$		0			0
$682$	17.7568	+	5.38671i	0.679945	+	0.206268i
$683$	13.1925			0.504797			0.252399	−	0.967623i	$-0.418781\pi$
$683$	13.1925			0.504797			0.252399	+	0.967623i	$0.418781\pi$
$684$		0			0
$685$	6.61408			0.252711
$686$	−38.5157	−	11.6841i	−1.47054	−	0.446101i
$687$		0			0
$688$	−37.5636	+	15.5573i	−1.43210	+	0.593115i
$689$	8.96466			0.341526
$690$		0			0
$691$	14.1826			0.539532			0.269766	−	0.962926i	$-0.413054\pi$
$691$	14.1826			0.539532			0.269766	+	0.962926i	$0.413054\pi$
$692$	−19.0724	−	12.7444i	−0.725025	−	0.484471i
$693$		0			0
$694$	−8.92852	+	29.4321i	−0.338922	+	1.11723i
$695$	20.2120			0.766686
$696$		0			0
$697$	5.57696	+	18.6704i	0.211243	+	0.707194i
$698$	14.4482	+	4.38301i	0.546874	+	0.165899i
$699$		0			0
$700$	19.0764	−	28.5484i	0.721022	−	1.07903i
$701$			34.7929i			1.31411i	0.753843	+	0.657054i	$0.228198\pi$
$701$			34.7929i			1.31411i	−0.753843	+	0.657054i	$0.771802\pi$
$702$		0			0
$703$		−	3.00218i		−	0.113230i
$704$	3.35979	−	16.8845i	0.126627	−	0.636359i
$705$		0			0
$706$	4.00991	−	13.2183i	0.150915	−	0.497479i
$707$	35.0007			1.31634
$708$		0			0
$709$	31.5333			1.18426			0.592129	−	0.805843i	$-0.298288\pi$
$709$	31.5333			1.18426			0.592129	+	0.805843i	$0.298288\pi$
$710$	2.64835	+	0.803402i	0.0993908	+	0.0301512i
$711$		0			0
$712$	−22.2545	+	18.2625i	−0.834022	+	0.684414i
$713$	12.7554			0.477695
$714$		0			0
$715$		−	2.20128i		−	0.0823231i
$716$	6.13508	−	9.18133i	0.229279	−	0.343122i
$717$		0			0
$718$	−6.71730	+	22.1430i	−0.250688	+	0.826371i
$719$		−	1.51558i		−	0.0565215i	−0.999601	−	0.0282607i	$-0.991003\pi$
$719$		−	1.51558i		−	0.0565215i	0.999601	−	0.0282607i	$-0.00899687\pi$
$720$		0			0
$721$			68.9777i			2.56886i
$722$	−7.46564	+	24.6099i	−0.277842	+	0.915885i
$723$		0			0
$724$	34.1668	+	22.8307i	1.26980	+	0.848496i
$725$	20.2880			0.753476
$726$		0			0
$727$	−45.8675			−1.70113			−0.850566	−	0.525868i	$-0.823741\pi$
$727$	−45.8675			−1.70113			−0.850566	+	0.525868i	$0.823741\pi$
$728$	9.23703	−	7.58008i	0.342347	−	0.280937i
$729$		0			0
$730$	18.9131	+	5.73747i	0.700005	+	0.212353i
$731$	−11.9948	−	40.1558i	−0.443642	−	1.48522i
$732$		0			0
$733$		−	3.07515i		−	0.113583i	−0.998386	−	0.0567916i	$-0.981913\pi$
$733$		−	3.07515i		−	0.113583i	0.998386	−	0.0567916i	$-0.0180871\pi$
$734$	−37.0114	−	11.2278i	−1.36611	−	0.414424i
$735$		0			0
$736$	−1.15924	−	11.7771i	−0.0427303	−	0.434111i
$737$		−	2.53774i		−	0.0934788i
$738$		0			0
$739$		−	45.3607i		−	1.66862i	−0.551296	−	0.834309i	$-0.685867\pi$
$739$		−	45.3607i		−	1.66862i	0.551296	−	0.834309i	$-0.314133\pi$
$740$	−6.03476	−	4.03251i	−0.221842	−	0.148238i
$741$		0			0
$742$	17.6973	−	58.3376i	0.649687	−	2.14164i
$743$			25.7594i			0.945021i	0.881325	+	0.472511i	$0.156652\pi$
$743$			25.7594i			0.945021i	−0.881325	+	0.472511i	$0.843348\pi$
$744$		0			0
$745$			14.4075i			0.527851i
$746$	−38.5878	−	11.7060i	−1.41280	−	0.428586i
$747$		0			0
$748$	16.9591	+	5.22383i	0.620085	+	0.191002i
$749$			11.6867i			0.427022i
$750$		0			0
$751$			38.9213i			1.42026i	0.704072	+	0.710128i	$0.251363\pi$
$751$			38.9213i			1.42026i	−0.704072	+	0.710128i	$0.748637\pi$
$752$	−17.3387	−	41.8649i	−0.632277	−	1.52666i
$753$		0			0
$754$	6.75636	+	2.04961i	0.246052	+	0.0746423i
$755$	2.34635			0.0853923
$756$		0			0
$757$			0.841416i			0.0305818i	0.999883	+	0.0152909i	$0.00486743\pi$
$757$			0.841416i			0.0305818i	−0.999883	+	0.0152909i	$0.995133\pi$
$758$	−15.7960	+	52.0702i	−0.573736	+	1.89127i
$759$		0			0
$760$	−1.76785	−	2.15429i	−0.0641267	−	0.0781443i
$761$	−25.2293			−0.914562			−0.457281	−	0.889322i	$-0.651177\pi$
$761$	−25.2293			−0.914562			−0.457281	+	0.889322i	$0.651177\pi$
$762$		0			0
$763$			29.0902i			1.05313i
$764$	−9.22297	−	6.16291i	−0.333675	−	0.222966i
$765$		0			0
$766$	−11.9158	+	39.2795i	−0.430536	+	1.41923i
$767$	5.22277			0.188583
$768$		0			0
$769$	−15.0970			−0.544413			−0.272207	−	0.962239i	$-0.587753\pi$
$769$	−15.0970			−0.544413			−0.272207	+	0.962239i	$0.587753\pi$
$770$	−14.3248	−	4.34557i	−0.516231	−	0.156604i
$771$		0			0
$772$	−12.8445	+	19.2221i	−0.462282	+	0.691819i
$773$			13.4587i			0.484077i	0.970267	+	0.242038i	$0.0778160\pi$
$773$			13.4587i			0.484077i	−0.970267	+	0.242038i	$0.922184\pi$
$774$		0			0
$775$			23.2245i			0.834250i
$776$	−5.26402	−	6.41469i	−0.188967	−	0.230274i
$777$		0			0
$778$	2.64656	+	0.802859i	0.0948837	+	0.0287839i
$779$	4.26671			0.152871
$780$		0			0
$781$			3.85879i			0.138078i
$782$	12.1982	+	0.0520553i	0.436205	+	0.00186150i
$783$		0			0
$784$	−20.3786	−	49.2048i	−0.727806	−	1.75732i
$785$			1.26175i			0.0450337i
$786$		0			0
$787$	35.0623			1.24984			0.624918	−	0.780690i	$-0.285132\pi$
$787$	35.0623			1.24984			0.624918	+	0.780690i	$0.285132\pi$
$788$	−28.6234	−	19.1266i	−1.01967	−	0.681355i
$789$		0			0
$790$	−3.85449	−	1.16930i	−0.137136	−	0.0416017i
$791$	−80.6324			−2.86696
$792$		0			0
$793$			11.5355i			0.409637i
$794$	8.16700	−	26.9218i	0.289836	−	0.955420i
$795$		0			0
$796$	−11.2373	+	16.8170i	−0.398297	+	0.596063i
$797$			18.2020i			0.644746i	0.946613	+	0.322373i	$0.104481\pi$
$797$			18.2020i			0.644746i	−0.946613	+	0.322373i	$0.895519\pi$
$798$		0			0
$799$	44.7540	−	13.3683i	1.58328	−	0.472935i
$800$	21.4433	−	2.11070i	0.758135	−	0.0746244i
$801$		0			0
$802$	7.32408	+	2.22183i	0.258622	+	0.0784556i
$803$			27.5574i			0.972478i
$804$		0			0
$805$	−10.2901			−0.362678
$806$	−2.34628	+	7.73431i	−0.0826441	+	0.272429i
$807$		0			0
$808$	13.9334	+	16.9792i	0.490177	+	0.597325i
$809$		−	54.0320i		−	1.89966i	−0.312762	−	0.949831i	$-0.601254\pi$
$809$		−	54.0320i		−	1.89966i	0.312762	−	0.949831i	$-0.398746\pi$
$810$		0			0
$811$	−22.5517			−0.791896			−0.395948	−	0.918273i	$-0.629584\pi$
$811$	−22.5517			−0.791896			−0.395948	+	0.918273i	$0.629584\pi$
$812$	26.6757	−	39.9209i	0.936133	−	1.40095i
$813$		0			0
$814$	2.93779	−	9.68417i	0.102969	−	0.339430i
$815$	0.0965251			0.00338113
$816$		0			0
$817$	−9.17671			−0.321052
$818$	−5.23201	+	17.2469i	−0.182933	+	0.603023i
$819$		0			0
$820$	5.73100	−	8.57661i	0.200135	−	0.299508i
$821$	−2.49637			−0.0871238			−0.0435619	−	0.999051i	$-0.513871\pi$
$821$	−2.49637			−0.0871238			−0.0435619	+	0.999051i	$0.513871\pi$
$822$		0			0
$823$		−	46.3364i		−	1.61519i	−0.589740	−	0.807593i	$-0.700770\pi$
$823$		−	46.3364i		−	1.61519i	0.589740	−	0.807593i	$-0.299230\pi$
$824$	−33.4618	+	27.4594i	−1.16570	+	0.956592i
$825$		0			0
$826$	10.3103	−	33.9872i	0.358743	−	1.18257i
$827$	56.3590			1.95979			0.979897	−	0.199506i	$-0.0639336\pi$
$827$	56.3590			1.95979			0.979897	+	0.199506i	$0.0639336\pi$
$828$		0			0
$829$			34.4237i			1.19558i	0.801651	+	0.597792i	$0.203955\pi$
$829$			34.4237i			1.19558i	−0.801651	+	0.597792i	$0.796045\pi$
$830$	18.9262	+	5.74145i	0.656939	+	0.199289i
$831$		0			0
$832$	7.35435	+	1.46341i	0.254966	+	0.0507348i
$833$	52.6005	−	15.7120i	1.82250	−	0.544390i
$834$		0			0
$835$			14.0071i			0.484737i
$836$	2.15883	−	3.23076i	0.0746648	−	0.111738i
$837$		0			0
$838$	−2.73140	+	9.00383i	−0.0943546	+	0.311032i
$839$		−	38.7295i		−	1.33709i	−0.743672	−	0.668545i	$-0.766918\pi$
$839$		−	38.7295i		−	1.33709i	0.743672	−	0.668545i	$-0.233082\pi$
$840$		0			0
$841$	−0.630187			−0.0217306
$842$	43.7541	+	13.2732i	1.50787	+	0.457426i
$843$		0			0
$844$	27.4367	+	18.3336i	0.944410	+	0.631067i
$845$	−13.2285			−0.455075
$846$		0			0
$847$			28.7067i			0.986374i
$848$	35.3453	−	14.6385i	1.21376	−	0.502689i
$849$		0			0
$850$	−0.0947800	+	22.2099i	−0.00325093	+	0.761792i
$851$		−	6.95652i		−	0.238466i
$852$		0			0
$853$	−21.7832			−0.745842			−0.372921	−	0.927863i	$-0.621644\pi$
$853$	−21.7832			−0.745842			−0.372921	+	0.927863i	$0.621644\pi$
$854$	75.0672	+	22.7724i	2.56875	+	0.779254i
$855$		0			0
$856$	−5.66932	+	4.65236i	−0.193773	+	0.159014i
$857$		−	57.2834i		−	1.95677i	−0.206803	−	0.978383i	$-0.566306\pi$
$857$		−	57.2834i		−	1.95677i	0.206803	−	0.978383i	$-0.433694\pi$
$858$		0			0
$859$			26.9367i			0.919068i	0.888160	+	0.459534i	$0.151984\pi$
$859$			26.9367i			0.919068i	−0.888160	+	0.459534i	$0.848016\pi$
$860$	−12.3261	+	18.4463i	−0.420315	+	0.629014i
$861$		0			0
$862$	2.01208	+	0.610384i	0.0685317	+	0.0207898i
$863$	−9.72421			−0.331016			−0.165508	−	0.986208i	$-0.552926\pi$
$863$	−9.72421			−0.331016			−0.165508	+	0.986208i	$0.552926\pi$
$864$		0			0
$865$	−12.5168			−0.425584
$866$	−3.71371	+	12.2419i	−0.126197	+	0.415998i
$867$		0			0
$868$	45.6992	+	30.5368i	1.55113	+	1.03649i
$869$		−	5.61619i		−	0.190516i
$870$		0			0
$871$	1.10536			0.0374536
$872$	−14.1119	+	11.5805i	−0.477890	+	0.392166i
$873$		0			0
$874$	0.775388	−	2.55600i	0.0262279	−	0.0864580i
$875$		−	43.3297i		−	1.46481i
$876$		0			0
$877$	−23.9282			−0.808000			−0.404000	−	0.914759i	$-0.632380\pi$
$877$	−23.9282			−0.808000			−0.404000	+	0.914759i	$0.632380\pi$
$878$	−22.0235	−	6.68103i	−0.743256	−	0.225474i
$879$		0			0
$880$	−3.59450	−	8.67904i	−0.121170	−	0.292571i
$881$			14.6254i			0.492741i	0.969176	+	0.246371i	$0.0792381\pi$
$881$			14.6254i			0.492741i	−0.969176	+	0.246371i	$0.920762\pi$
$882$		0			0
$883$		−	16.5291i		−	0.556248i	−0.960545	−	0.278124i	$-0.910287\pi$
$883$		−	16.5291i		−	0.556248i	0.960545	−	0.278124i	$-0.0897126\pi$
$884$	−2.27533	+	7.38682i	−0.0765277	+	0.248446i
$885$		0			0
$886$	−33.8621	−	10.2724i	−1.13762	−	0.345108i
$887$		−	37.7524i		−	1.26760i	−0.773496	−	0.633801i	$-0.781494\pi$
$887$		−	37.7524i		−	1.26760i	0.773496	−	0.633801i	$-0.218506\pi$
$888$		0			0
$889$		−	36.4479i		−	1.22242i
$890$	−4.56024	+	15.0325i	−0.152860	+	0.503889i
$891$		0			0
$892$	−20.4931	−	13.6937i	−0.686158	−	0.458500i
$893$		−	10.2275i		−	0.342251i
$894$		0			0
$895$		−	6.02550i		−	0.201410i
$896$	24.0415	−	44.9695i	0.803170	−	1.50233i
$897$		0			0
$898$	−27.7955	−	8.43203i	−0.927547	−	0.281380i
$899$			32.4762i			1.08314i
$900$		0			0
$901$	11.2864	+	37.7844i	0.376005	+	1.25878i
$902$	13.7632	+	4.17519i	0.458263	+	0.139019i
$903$		0			0
$904$	−32.0990	−	39.1156i	−1.06760	−	1.30097i
$905$	22.4229			0.745363
$906$		0			0
$907$	5.93020			0.196909			0.0984545	−	0.995142i	$-0.468610\pi$
$907$	5.93020			0.196909			0.0984545	+	0.995142i	$0.468610\pi$
$908$	−27.7557	−	18.5467i	−0.921105	−	0.615494i
$909$		0			0
$910$	1.89279	−	6.23943i	0.0627454	−	0.206835i
$911$			6.91945i			0.229252i	0.993409	+	0.114626i	$0.0365669\pi$
$911$			6.91945i			0.229252i	−0.993409	+	0.114626i	$0.963433\pi$
$912$		0			0
$913$			27.5765i			0.912649i
$914$	0.812707	−	2.67902i	0.0268820	−	0.0886142i
$915$		0			0
$916$	−24.9160	+	37.2875i	−0.823247	+	1.23201i
$917$			69.2606i			2.28719i
$918$		0			0
$919$	11.0028			0.362948			0.181474	−	0.983396i	$-0.441913\pi$
$919$	11.0028			0.362948			0.181474	+	0.983396i	$0.441913\pi$
$920$	−4.09638	−	4.99182i	−0.135054	−	0.164575i
$921$		0			0
$922$	40.7123	+	12.3505i	1.34079	+	0.406741i
$923$	−1.68076			−0.0553230
$924$		0			0
$925$	12.6661			0.416459
$926$	−6.04345	+	19.9217i	−0.198600	+	0.654669i
$927$		0			0
$928$	29.9854	−	2.95151i	0.984318	−	0.0968880i
$929$			23.4763i			0.770234i	0.922868	+	0.385117i	$0.125839\pi$
$929$			23.4763i			0.770234i	−0.922868	+	0.385117i	$0.874161\pi$
$930$		0			0
$931$		−	12.0206i		−	0.393961i
$932$	3.52120	−	5.26958i	0.115341	−	0.172611i
$933$		0			0
$934$	−2.75723	−	0.836432i	−0.0902193	−	0.0273689i
$935$	9.27799	−	2.77139i	0.303423	−	0.0906340i
$936$		0			0
$937$	10.9870			0.358931			0.179466	−	0.983764i	$-0.442563\pi$
$937$	10.9870			0.358931			0.179466	+	0.983764i	$0.442563\pi$
$938$	2.18210	−	7.19312i	0.0712481	−	0.234864i
$939$		0			0
$940$	−20.5586	−	13.7375i	−0.670547	−	0.448068i
$941$	−52.9233			−1.72525			−0.862625	−	0.505844i	$-0.831181\pi$
$941$	−52.9233			−1.72525			−0.862625	+	0.505844i	$0.831181\pi$
$942$		0			0
$943$	9.88662			0.321953
$944$	20.5920	−	8.52833i	0.670212	−	0.277574i
$945$		0			0
$946$	−29.6014	−	8.97987i	−0.962424	−	0.291961i
$947$	19.3112			0.627528			0.313764	−	0.949501i	$-0.398410\pi$
$947$	19.3112			0.627528			0.313764	+	0.949501i	$0.398410\pi$
$948$		0			0
$949$	−12.0031			−0.389637
$950$	4.65385	+	1.41179i	0.150991	+	0.0458045i
$951$		0			0
$952$	43.5780	+	29.3892i	1.41237	+	0.952509i
$953$	42.6147			1.38043			0.690213	−	0.723606i	$-0.257517\pi$
$953$	42.6147			1.38043			0.690213	+	0.723606i	$0.257517\pi$
$954$		0			0
$955$	−6.05283			−0.195865
$956$	−38.9920	−	26.0549i	−1.26109	−	0.842677i
$957$		0			0
$958$	49.3831	+	14.9808i	1.59549	+	0.484009i
$959$			27.3159i			0.882075i
$960$		0			0
$961$	−6.17691			−0.199255
$962$	4.21811	+	1.27961i	0.135997	+	0.0412561i
$963$		0			0
$964$	−20.5481	+	30.7508i	−0.661809	+	0.990417i
$965$			12.6150i			0.406093i
$966$		0			0
$967$	−34.0443			−1.09479			−0.547396	−	0.836874i	$-0.684381\pi$
$967$	−34.0443			−1.09479			−0.547396	+	0.836874i	$0.684381\pi$
$968$	−13.9259	+	11.4279i	−0.447596	+	0.367306i
$969$		0			0
$970$	−4.33299	−	1.31445i	−0.139124	−	0.0422046i
$971$		−	14.1122i		−	0.452881i	−0.974025	−	0.226440i	$-0.927291\pi$
$971$		−	14.1122i		−	0.452881i	0.974025	−	0.226440i	$-0.0727088\pi$
$972$		0			0
$973$			83.4748i			2.67608i
$974$	41.7462	+	12.6641i	1.33763	+	0.405784i
$975$		0			0
$976$	18.8364	+	45.4813i	0.602940	+	1.45582i
$977$	−13.3995			−0.428687			−0.214344	−	0.976758i	$-0.568761\pi$
$977$	−13.3995			−0.428687			−0.214344	+	0.976758i	$0.568761\pi$
$978$		0			0
$979$	−21.9031			−0.700026
$980$	−24.1630	−	16.1460i	−0.771858	−	0.515766i
$981$		0			0
$982$	34.3199	+	10.4113i	1.09519	+	0.332237i
$983$			35.0579i			1.11817i	0.829110	+	0.559086i	$0.188848\pi$
$983$			35.0579i			1.11817i	−0.829110	+	0.559086i	$0.811152\pi$
$984$		0			0
$985$	−18.7849			−0.598538
$986$	−0.132536	+	31.0573i	−0.00422082	+	0.989066i
$987$		0			0
$988$	1.40721	+	0.940318i	0.0447694	+	0.0299155i
$989$	−21.2638			−0.676151
$990$		0			0
$991$		−	34.1550i		−	1.08497i	−0.840066	−	0.542485i	$-0.817484\pi$
$991$		−	34.1550i		−	1.08497i	0.840066	−	0.542485i	$-0.182516\pi$
$992$	3.37872	+	34.3256i	0.107275	+	1.08984i
$993$		0			0
$994$	−3.31802	+	10.9376i	−0.105241	+	0.346919i
$995$			11.0366i			0.349885i
$996$		0			0
$997$	−25.0001			−0.791762			−0.395881	−	0.918302i	$-0.629561\pi$
$997$	−25.0001			−0.791762			−0.395881	+	0.918302i	$0.629561\pi$
$998$	−17.4726	+	57.5970i	−0.553086	+	1.82320i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.d.1189.8		18
3.2	odd	2		408.2.l.b.373.11	yes	18
4.3	odd	2		4896.2.l.d.3025.8		18
8.3	odd	2		4896.2.l.c.3025.12		18
8.5	even	2		1224.2.l.c.1189.7		18
12.11	even	2		1632.2.l.a.1393.12		18
17.16	even	2		1224.2.l.c.1189.8		18
24.5	odd	2		408.2.l.a.373.12	yes	18
24.11	even	2		1632.2.l.b.1393.8		18
51.50	odd	2		408.2.l.a.373.11	✓	18
68.67	odd	2		4896.2.l.c.3025.11		18
136.67	odd	2		4896.2.l.d.3025.7		18
136.101	even	2	inner	1224.2.l.d.1189.7		18
204.203	even	2		1632.2.l.b.1393.7		18
408.101	odd	2		408.2.l.b.373.12	yes	18
408.203	even	2		1632.2.l.a.1393.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.11	✓	18	51.50	odd	2
408.2.l.a.373.12	yes	18	24.5	odd	2
408.2.l.b.373.11	yes	18	3.2	odd	2
408.2.l.b.373.12	yes	18	408.101	odd	2
1224.2.l.c.1189.7		18	8.5	even	2
1224.2.l.c.1189.8		18	17.16	even	2
1224.2.l.d.1189.7		18	136.101	even	2	inner
1224.2.l.d.1189.8		18	1.1	even	1	trivial
1632.2.l.a.1393.11		18	408.203	even	2
1632.2.l.a.1393.12		18	12.11	even	2
1632.2.l.b.1393.7		18	204.203	even	2
1632.2.l.b.1393.8		18	24.11	even	2
4896.2.l.c.3025.11		18	68.67	odd	2
4896.2.l.c.3025.12		18	8.3	odd	2
4896.2.l.d.3025.7		18	136.67	odd	2
4896.2.l.d.3025.8		18	4.3	odd	2

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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.410541 + 1.35331i) q^{2} +(-1.66291 - 1.11118i) q^{4} -1.09133 q^{5} -4.50716i q^{7} +(2.18647 - 1.79426i) q^{8} +(0.448036 - 1.47691i) q^{10} +2.15194 q^{11} +0.937317i q^{13} +(6.09960 + 1.85037i) q^{14} +(1.53056 + 3.69559i) q^{16} +(-3.95062 + 1.18007i) q^{17} +0.902826i q^{19} +(1.81479 + 1.21267i) q^{20} +(-0.883460 + 2.91225i) q^{22} +2.09199i q^{23} -3.80899 q^{25} +(-1.26848 - 0.384807i) q^{26} +(-5.00826 + 7.49501i) q^{28} -5.32633 q^{29} -6.09729i q^{31} +(-5.62965 + 0.554135i) q^{32} +(0.0248832 - 5.83090i) q^{34} +4.91881i q^{35} -3.32532 q^{37} +(-1.22181 - 0.370647i) q^{38} +(-2.38616 + 1.95813i) q^{40} -4.72595i q^{41} +10.1644i q^{43} +(-3.57849 - 2.39120i) q^{44} +(-2.83111 - 0.858845i) q^{46} -11.3283 q^{47} -13.3145 q^{49} +(1.56375 - 5.15476i) q^{50} +(1.04153 - 1.55868i) q^{52} -9.56417i q^{53} -2.34849 q^{55} +(-8.08700 - 9.85475i) q^{56} +(2.18668 - 7.20820i) q^{58} -5.57204i q^{59} +12.3069 q^{61} +(8.25154 + 2.50318i) q^{62} +(1.56128 - 7.84617i) q^{64} -1.02292i q^{65} -1.17928i q^{67} +(7.88082 + 2.42750i) q^{68} +(-6.65669 - 2.01937i) q^{70} +1.79316i q^{71} +12.8058i q^{73} +(1.36518 - 4.50020i) q^{74} +(1.00320 - 1.50132i) q^{76} -9.69915i q^{77} -2.60982i q^{79} +(-1.67035 - 4.03312i) q^{80} +(6.39569 + 1.94019i) q^{82} +12.8147i q^{83} +(4.31145 - 1.28785i) q^{85} +(-13.7557 - 4.17291i) q^{86} +(4.70515 - 3.86114i) q^{88} -10.1783 q^{89} +4.22464 q^{91} +(2.32457 - 3.47879i) q^{92} +(4.65074 - 15.3308i) q^{94} -0.985283i q^{95} -2.93381i q^{97} +(5.46613 - 18.0186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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