LMFDB - Embedded newform 4020.2.q.m.841.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.10
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(1.00432 - 1.73954i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(1.00432 - 1.73954i) q^{7} +1.00000 q^{9} +(0.449173 - 0.777991i) q^{11} +(1.97093 + 3.41375i) q^{13} +1.00000 q^{15} +(0.257734 + 0.446409i) q^{17} +(-0.443489 - 0.768146i) q^{19} +(1.00432 - 1.73954i) q^{21} +(3.81397 + 6.60599i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-1.58144 + 2.73914i) q^{29} +(3.37847 - 5.85168i) q^{31} +(0.449173 - 0.777991i) q^{33} +(1.00432 - 1.73954i) q^{35} +(2.59934 + 4.50219i) q^{37} +(1.97093 + 3.41375i) q^{39} +(2.35166 - 4.07319i) q^{41} -8.28809 q^{43} +1.00000 q^{45} +(-2.65239 + 4.59408i) q^{47} +(1.48267 + 2.56805i) q^{49} +(0.257734 + 0.446409i) q^{51} +9.38940 q^{53} +(0.449173 - 0.777991i) q^{55} +(-0.443489 - 0.768146i) q^{57} +8.88190 q^{59} +(-0.714054 - 1.23678i) q^{61} +(1.00432 - 1.73954i) q^{63} +(1.97093 + 3.41375i) q^{65} +(-7.15136 + 3.98222i) q^{67} +(3.81397 + 6.60599i) q^{69} +(2.30559 - 3.99341i) q^{71} +(1.17004 + 2.02657i) q^{73} +1.00000 q^{75} +(-0.902231 - 1.56271i) q^{77} +(1.31656 - 2.28035i) q^{79} +1.00000 q^{81} +(-2.20208 - 3.81411i) q^{83} +(0.257734 + 0.446409i) q^{85} +(-1.58144 + 2.73914i) q^{87} -5.68320 q^{89} +7.91782 q^{91} +(3.37847 - 5.85168i) q^{93} +(-0.443489 - 0.768146i) q^{95} +(-1.26978 - 2.19933i) q^{97} +(0.449173 - 0.777991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	1.00432	−	1.73954i	0.379599	−	0.657484i	−0.611405	−	0.791318i	$-0.709395\pi$
$7$	1.00432	−	1.73954i	0.379599	−	0.657484i	0.991004	+	0.133833i	$0.0427287\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.449173	−	0.777991i	0.135431	−	0.234573i	−0.790331	−	0.612680i	$-0.790091\pi$
$11$	0.449173	−	0.777991i	0.135431	−	0.234573i	0.925762	+	0.378107i	$0.123425\pi$
$12$		0			0
$13$	1.97093	+	3.41375i	0.546638	+	0.946805i	0.998502	+	0.0547180i	$0.0174260\pi$
$13$	1.97093	+	3.41375i	0.546638	+	0.946805i	−0.451864	+	0.892087i	$0.649241\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.257734	+	0.446409i	0.0625097	+	0.108270i	0.895587	−	0.444887i	$-0.146756\pi$
$17$	0.257734	+	0.446409i	0.0625097	+	0.108270i	−0.833077	+	0.553157i	$0.813423\pi$
$18$		0			0
$19$	−0.443489	−	0.768146i	−0.101743	−	0.176225i	0.810660	−	0.585518i	$-0.199109\pi$
$19$	−0.443489	−	0.768146i	−0.101743	−	0.176225i	−0.912403	+	0.409293i	$0.865775\pi$
$20$		0			0
$21$	1.00432	−	1.73954i	0.219161	−	0.379599i
$22$		0			0
$23$	3.81397	+	6.60599i	0.795268	+	1.37744i	0.922669	+	0.385593i	$0.126003\pi$
$23$	3.81397	+	6.60599i	0.795268	+	1.37744i	−0.127401	+	0.991851i	$0.540663\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.58144	+	2.73914i	−0.293667	+	0.508646i	−0.974674	−	0.223631i	$-0.928209\pi$
$29$	−1.58144	+	2.73914i	−0.293667	+	0.508646i	0.681007	+	0.732277i	$0.261542\pi$
$30$		0			0
$31$	3.37847	−	5.85168i	0.606790	−	1.05099i	−0.384975	−	0.922927i	$-0.625790\pi$
$31$	3.37847	−	5.85168i	0.606790	−	1.05099i	0.991766	−	0.128065i	$-0.0408766\pi$
$32$		0			0
$33$	0.449173	−	0.777991i	0.0781910	−	0.135431i
$34$		0			0
$35$	1.00432	−	1.73954i	0.169762	−	0.294036i
$36$		0			0
$37$	2.59934	+	4.50219i	0.427329	+	0.740155i	0.996635	−	0.0819704i	$-0.0261213\pi$
$37$	2.59934	+	4.50219i	0.427329	+	0.740155i	−0.569306	+	0.822126i	$0.692788\pi$
$38$		0			0
$39$	1.97093	+	3.41375i	0.315602	+	0.546638i
$40$		0			0
$41$	2.35166	−	4.07319i	0.367268	−	0.636126i	−0.621870	−	0.783121i	$-0.713627\pi$
$41$	2.35166	−	4.07319i	0.367268	−	0.636126i	0.989137	+	0.146995i	$0.0469600\pi$
$42$		0			0
$43$	−8.28809			−1.26392			−0.631961	−	0.775000i	$-0.717750\pi$
$43$	−8.28809			−1.26392			−0.631961	+	0.775000i	$0.717750\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−2.65239	+	4.59408i	−0.386891	+	0.670115i	−0.992030	−	0.126005i	$-0.959784\pi$
$47$	−2.65239	+	4.59408i	−0.386891	+	0.670115i	0.605139	+	0.796120i	$0.293118\pi$
$48$		0			0
$49$	1.48267	+	2.56805i	0.211809	+	0.366865i
$50$		0			0
$51$	0.257734	+	0.446409i	0.0360900	+	0.0625097i
$52$		0			0
$53$	9.38940			1.28973			0.644867	−	0.764295i	$-0.276913\pi$
$53$	9.38940			1.28973			0.644867	+	0.764295i	$0.276913\pi$
$54$		0			0
$55$	0.449173	−	0.777991i	0.0605665	−	0.104904i
$56$		0			0
$57$	−0.443489	−	0.768146i	−0.0587416	−	0.101743i
$58$		0			0
$59$	8.88190			1.15633			0.578163	−	0.815922i	$-0.303770\pi$
$59$	8.88190			1.15633			0.578163	+	0.815922i	$0.303770\pi$
$60$		0			0
$61$	−0.714054	−	1.23678i	−0.0914253	−	0.158353i	0.816686	−	0.577083i	$-0.195809\pi$
$61$	−0.714054	−	1.23678i	−0.0914253	−	0.158353i	−0.908111	+	0.418729i	$0.862476\pi$
$62$		0			0
$63$	1.00432	−	1.73954i	0.126533	−	0.219161i
$64$		0			0
$65$	1.97093	+	3.41375i	0.244464	+	0.423424i
$66$		0			0
$67$	−7.15136	+	3.98222i	−0.873677	+	0.486506i
$67$	−7.15136	+	3.98222i	−0.873677	+	0.486506i
$68$		0			0
$69$	3.81397	+	6.60599i	0.459148	+	0.795268i
$70$		0			0
$71$	2.30559	−	3.99341i	0.273624	−	0.473930i	−0.696163	−	0.717883i	$-0.745111\pi$
$71$	2.30559	−	3.99341i	0.273624	−	0.473930i	0.969787	+	0.243953i	$0.0784444\pi$
$72$		0			0
$73$	1.17004	+	2.02657i	0.136943	+	0.237192i	0.926338	−	0.376693i	$-0.122939\pi$
$73$	1.17004	+	2.02657i	0.136943	+	0.237192i	−0.789395	+	0.613886i	$0.789606\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−0.902231	−	1.56271i	−0.102819	−	0.178087i
$78$		0			0
$79$	1.31656	−	2.28035i	0.148125	−	0.256560i	−0.782410	−	0.622764i	$-0.786010\pi$
$79$	1.31656	−	2.28035i	0.148125	−	0.256560i	0.930534	+	0.366204i	$0.119343\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−2.20208	−	3.81411i	−0.241709	−	0.418653i	0.719492	−	0.694501i	$-0.244375\pi$
$83$	−2.20208	−	3.81411i	−0.241709	−	0.418653i	−0.961201	+	0.275848i	$0.911041\pi$
$84$		0			0
$85$	0.257734	+	0.446409i	0.0279552	+	0.0484198i
$86$		0			0
$87$	−1.58144	+	2.73914i	−0.169549	+	0.293667i
$88$		0			0
$89$	−5.68320			−0.602418			−0.301209	−	0.953558i	$-0.597390\pi$
$89$	−5.68320			−0.602418			−0.301209	+	0.953558i	$0.597390\pi$
$90$		0			0
$91$	7.91782			0.830013
$92$		0			0
$93$	3.37847	−	5.85168i	0.350331	−	0.606790i
$94$		0			0
$95$	−0.443489	−	0.768146i	−0.0455010	−	0.0788101i
$96$		0			0
$97$	−1.26978	−	2.19933i	−0.128927	−	0.223308i	0.794334	−	0.607481i	$-0.207820\pi$
$97$	−1.26978	−	2.19933i	−0.128927	−	0.223308i	−0.923261	+	0.384173i	$0.874487\pi$
$98$		0			0
$99$	0.449173	−	0.777991i	0.0451436	−	0.0781910i
$100$		0			0
$101$	2.08447	−	3.61040i	0.207412	−	0.359249i	−0.743486	−	0.668751i	$-0.766829\pi$
$101$	2.08447	−	3.61040i	0.207412	−	0.359249i	0.950899	+	0.309502i	$0.100162\pi$
$102$		0			0
$103$	4.17423	−	7.22998i	0.411299	−	0.712391i	−0.583733	−	0.811946i	$-0.698408\pi$
$103$	4.17423	−	7.22998i	0.411299	−	0.712391i	0.995032	+	0.0995545i	$0.0317418\pi$
$104$		0			0
$105$	1.00432	−	1.73954i	0.0980120	−	0.169762i
$106$		0			0
$107$	4.22998			0.408928			0.204464	−	0.978874i	$-0.434455\pi$
$107$	4.22998			0.408928			0.204464	+	0.978874i	$0.434455\pi$
$108$		0			0
$109$	11.8304			1.13315			0.566575	−	0.824010i	$-0.308268\pi$
$109$	11.8304			1.13315			0.566575	+	0.824010i	$0.308268\pi$
$110$		0			0
$111$	2.59934	+	4.50219i	0.246718	+	0.427329i
$112$		0			0
$113$	4.32509	−	7.49128i	0.406871	−	0.704721i	−0.587667	−	0.809103i	$-0.699953\pi$
$113$	4.32509	−	7.49128i	0.406871	−	0.704721i	0.994537	+	0.104383i	$0.0332866\pi$
$114$		0			0
$115$	3.81397	+	6.60599i	0.355655	+	0.616012i
$116$		0			0
$117$	1.97093	+	3.41375i	0.182213	+	0.315602i
$118$		0			0
$119$	1.03539			0.0949144
$120$		0			0
$121$	5.09649	+	8.82737i	0.463317	+	0.802489i
$122$		0			0
$123$	2.35166	−	4.07319i	0.212042	−	0.367268i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.17191	−	10.6901i	0.547668	−	0.948589i	−0.450765	−	0.892642i	$-0.648849\pi$
$127$	6.17191	−	10.6901i	0.547668	−	0.948589i	0.998434	−	0.0559469i	$-0.0178178\pi$
$128$		0			0
$129$	−8.28809			−0.729726
$130$		0			0
$131$	−5.77449			−0.504520			−0.252260	−	0.967660i	$-0.581174\pi$
$131$	−5.77449			−0.504520			−0.252260	+	0.967660i	$0.581174\pi$
$132$		0			0
$133$	−1.78163			−0.154487
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−8.34696			−0.713129			−0.356565	−	0.934271i	$-0.616052\pi$
$137$	−8.34696			−0.713129			−0.356565	+	0.934271i	$0.616052\pi$
$138$		0			0
$139$	−23.1591			−1.96433			−0.982164	−	0.188029i	$-0.939790\pi$
$139$	−23.1591			−1.96433			−0.982164	+	0.188029i	$0.939790\pi$
$140$		0			0
$141$	−2.65239	+	4.59408i	−0.223372	+	0.386891i
$142$		0			0
$143$	3.54116			0.296127
$144$		0			0
$145$	−1.58144	+	2.73914i	−0.131332	+	0.227473i
$146$		0			0
$147$	1.48267	+	2.56805i	0.122288	+	0.211809i
$148$		0			0
$149$	−5.74171			−0.470379			−0.235190	−	0.971949i	$-0.575571\pi$
$149$	−5.74171			−0.470379			−0.235190	+	0.971949i	$0.575571\pi$
$150$		0			0
$151$	−10.7365	−	18.5962i	−0.873723	−	1.51333i	−0.858116	−	0.513455i	$-0.828365\pi$
$151$	−10.7365	−	18.5962i	−0.873723	−	1.51333i	−0.0156070	−	0.999878i	$-0.504968\pi$
$152$		0			0
$153$	0.257734	+	0.446409i	0.0208366	+	0.0360900i
$154$		0			0
$155$	3.37847	−	5.85168i	0.271365	−	0.470018i
$156$		0			0
$157$	4.04085	+	6.99896i	0.322495	+	0.558578i	0.981002	−	0.193997i	$-0.0621451\pi$
$157$	4.04085	+	6.99896i	0.322495	+	0.558578i	−0.658507	+	0.752574i	$0.728812\pi$
$158$		0			0
$159$	9.38940			0.744628
$160$		0			0
$161$	15.3219			1.20753
$162$		0			0
$163$	4.08651	−	7.07804i	0.320080	−	0.554395i	−0.660424	−	0.750893i	$-0.729624\pi$
$163$	4.08651	−	7.07804i	0.320080	−	0.554395i	0.980504	+	0.196498i	$0.0629569\pi$
$164$		0			0
$165$	0.449173	−	0.777991i	0.0349681	−	0.0605665i
$166$		0			0
$167$	4.32150	−	7.48506i	0.334408	−	0.579212i	−0.648963	−	0.760820i	$-0.724797\pi$
$167$	4.32150	−	7.48506i	0.334408	−	0.579212i	0.983371	+	0.181608i	$0.0581303\pi$
$168$		0			0
$169$	−1.26914	+	2.19822i	−0.0976265	+	0.169094i
$170$		0			0
$171$	−0.443489	−	0.768146i	−0.0339145	−	0.0587416i
$172$		0			0
$173$	5.01325	+	8.68320i	0.381150	+	0.660171i	0.991227	−	0.132171i	$-0.0421948\pi$
$173$	5.01325	+	8.68320i	0.381150	+	0.660171i	−0.610077	+	0.792342i	$0.708861\pi$
$174$		0			0
$175$	1.00432	−	1.73954i	0.0759198	−	0.131497i
$176$		0			0
$177$	8.88190			0.667605
$178$		0			0
$179$	14.4986			1.08368			0.541838	−	0.840483i	$-0.317729\pi$
$179$	14.4986			1.08368			0.541838	+	0.840483i	$0.317729\pi$
$180$		0			0
$181$	−2.95494	+	5.11811i	−0.219639	+	0.380426i	−0.954698	−	0.297578i	$-0.903821\pi$
$181$	−2.95494	+	5.11811i	−0.219639	+	0.380426i	0.735059	+	0.678004i	$0.237155\pi$
$182$		0			0
$183$	−0.714054	−	1.23678i	−0.0527844	−	0.0914253i
$184$		0			0
$185$	2.59934	+	4.50219i	0.191107	+	0.331008i
$186$		0			0
$187$	0.463069			0.0338630
$188$		0			0
$189$	1.00432	−	1.73954i	0.0730538	−	0.126533i
$190$		0			0
$191$	8.95850	+	15.5166i	0.648214	+	1.12274i	0.983549	+	0.180641i	$0.0578173\pi$
$191$	8.95850	+	15.5166i	0.648214	+	1.12274i	−0.335335	+	0.942099i	$0.608849\pi$
$192$		0			0
$193$	−8.52514			−0.613653			−0.306827	−	0.951765i	$-0.599267\pi$
$193$	−8.52514			−0.613653			−0.306827	+	0.951765i	$0.599267\pi$
$194$		0			0
$195$	1.97093	+	3.41375i	0.141141	+	0.244464i
$196$		0			0
$197$	0.730109	−	1.26459i	0.0520181	−	0.0900980i	−0.838844	−	0.544372i	$-0.816768\pi$
$197$	0.730109	−	1.26459i	0.0520181	−	0.0900980i	0.890862	+	0.454274i	$0.150101\pi$
$198$		0			0
$199$	0.385440	+	0.667601i	0.0273231	+	0.0473250i	0.879364	−	0.476151i	$-0.157968\pi$
$199$	0.385440	+	0.667601i	0.0273231	+	0.0473250i	−0.852041	+	0.523476i	$0.824635\pi$
$200$		0			0
$201$	−7.15136	+	3.98222i	−0.504418	+	0.280884i
$202$		0			0
$203$	3.17656	+	5.50197i	0.222951	+	0.386163i
$204$		0			0
$205$	2.35166	−	4.07319i	0.164247	−	0.284484i
$206$		0			0
$207$	3.81397	+	6.60599i	0.265089	+	0.459148i
$208$		0			0
$209$	−0.796814			−0.0551168
$210$		0			0
$211$	1.46317	+	2.53428i	0.100729	+	0.174467i	0.911985	−	0.410223i	$-0.134549\pi$
$211$	1.46317	+	2.53428i	0.100729	+	0.174467i	−0.811256	+	0.584691i	$0.801216\pi$
$212$		0			0
$213$	2.30559	−	3.99341i	0.157977	−	0.273624i
$214$		0			0
$215$	−8.28809			−0.565243
$216$		0			0
$217$	−6.78615	−	11.7540i	−0.460674	−	0.797911i
$218$		0			0
$219$	1.17004	+	2.02657i	0.0790641	+	0.136943i
$220$		0			0
$221$	−1.01595	+	1.75968i	−0.0683404	+	0.118369i
$222$		0			0
$223$	10.5051			0.703471			0.351735	−	0.936099i	$-0.385592\pi$
$223$	10.5051			0.703471			0.351735	+	0.936099i	$0.385592\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	6.70223	−	11.6086i	0.444842	−	0.770490i	−0.553199	−	0.833049i	$-0.686593\pi$
$227$	6.70223	−	11.6086i	0.444842	−	0.770490i	0.998041	+	0.0625596i	$0.0199264\pi$
$228$		0			0
$229$	−4.37210	−	7.57270i	−0.288916	−	0.500418i	0.684635	−	0.728886i	$-0.259962\pi$
$229$	−4.37210	−	7.57270i	−0.288916	−	0.500418i	−0.973551	+	0.228468i	$0.926628\pi$
$230$		0			0
$231$	−0.902231	−	1.56271i	−0.0593624	−	0.102819i
$232$		0			0
$233$	−3.52677	+	6.10855i	−0.231047	+	0.400184i	−0.958116	−	0.286379i	$-0.907548\pi$
$233$	−3.52677	+	6.10855i	−0.231047	+	0.400184i	0.727070	+	0.686564i	$0.240882\pi$
$234$		0			0
$235$	−2.65239	+	4.59408i	−0.173023	+	0.299684i
$236$		0			0
$237$	1.31656	−	2.28035i	0.0855200	−	0.148125i
$238$		0			0
$239$	−6.49940	+	11.2573i	−0.420411	+	0.728174i	−0.995980	−	0.0895800i	$-0.971448\pi$
$239$	−6.49940	+	11.2573i	−0.420411	+	0.728174i	0.575568	+	0.817754i	$0.304781\pi$
$240$		0			0
$241$	0.545924			0.0351661			0.0175830	−	0.999845i	$-0.494403\pi$
$241$	0.545924			0.0351661			0.0175830	+	0.999845i	$0.494403\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.48267	+	2.56805i	0.0947241	+	0.164067i
$246$		0			0
$247$	1.74817	−	3.02793i	0.111234	−	0.192662i
$248$		0			0
$249$	−2.20208	−	3.81411i	−0.139551	−	0.241709i
$250$		0			0
$251$	4.05975	+	7.03169i	0.256249	+	0.443836i	0.965234	−	0.261387i	$-0.0841799\pi$
$251$	4.05975	+	7.03169i	0.256249	+	0.443836i	−0.708985	+	0.705224i	$0.750847\pi$
$252$		0			0
$253$	6.85254			0.430815
$254$		0			0
$255$	0.257734	+	0.446409i	0.0161399	+	0.0279552i
$256$		0			0
$257$	−1.79824	+	3.11464i	−0.112171	+	0.194286i	−0.916645	−	0.399702i	$-0.869114\pi$
$257$	−1.79824	+	3.11464i	−0.112171	+	0.194286i	0.804474	+	0.593987i	$0.202447\pi$
$258$		0			0
$259$	10.4423			0.648854
$260$		0			0
$261$	−1.58144	+	2.73914i	−0.0978889	+	0.169549i
$262$		0			0
$263$	16.9589			1.04573			0.522866	−	0.852415i	$-0.324863\pi$
$263$	16.9589			1.04573			0.522866	+	0.852415i	$0.324863\pi$
$264$		0			0
$265$	9.38940			0.576786
$266$		0			0
$267$	−5.68320			−0.347806
$268$		0			0
$269$	14.6789			0.894990			0.447495	−	0.894286i	$-0.352316\pi$
$269$	14.6789			0.894990			0.447495	+	0.894286i	$0.352316\pi$
$270$		0			0
$271$	−23.3242			−1.41684			−0.708422	−	0.705790i	$-0.750592\pi$
$271$	−23.3242			−1.41684			−0.708422	+	0.705790i	$0.750592\pi$
$272$		0			0
$273$	7.91782			0.479208
$274$		0			0
$275$	0.449173	−	0.777991i	0.0270862	−	0.0469146i
$276$		0			0
$277$	−23.2493			−1.39692			−0.698459	−	0.715650i	$-0.746130\pi$
$277$	−23.2493			−1.39692			−0.698459	+	0.715650i	$0.746130\pi$
$278$		0			0
$279$	3.37847	−	5.85168i	0.202263	−	0.350331i
$280$		0			0
$281$	−1.06574	−	1.84591i	−0.0635765	−	0.110118i	0.832485	−	0.554047i	$-0.186917\pi$
$281$	−1.06574	−	1.84591i	−0.0635765	−	0.110118i	−0.896062	+	0.443930i	$0.853584\pi$
$282$		0			0
$283$	−3.20381			−0.190447			−0.0952233	−	0.995456i	$-0.530357\pi$
$283$	−3.20381			−0.190447			−0.0952233	+	0.995456i	$0.530357\pi$
$284$		0			0
$285$	−0.443489	−	0.768146i	−0.0262700	−	0.0455010i
$286$		0			0
$287$	−4.72366	−	8.18161i	−0.278829	−	0.482945i
$288$		0			0
$289$	8.36715	−	14.4923i	0.492185	−	0.852490i
$290$		0			0
$291$	−1.26978	−	2.19933i	−0.0744359	−	0.128927i
$292$		0			0
$293$	−14.1788			−0.828335			−0.414167	−	0.910201i	$-0.635927\pi$
$293$	−14.1788			−0.828335			−0.414167	+	0.910201i	$0.635927\pi$
$294$		0			0
$295$	8.88190			0.517124
$296$		0			0
$297$	0.449173	−	0.777991i	0.0260637	−	0.0451436i
$298$		0			0
$299$	−15.0342	+	26.0399i	−0.869448	+	1.50593i
$300$		0			0
$301$	−8.32393	+	14.4175i	−0.479783	+	0.831009i
$302$		0			0
$303$	2.08447	−	3.61040i	0.119750	−	0.207412i
$304$		0			0
$305$	−0.714054	−	1.23678i	−0.0408866	−	0.0708177i
$306$		0			0
$307$	0.622679	+	1.07851i	0.0355382	+	0.0615540i	0.883247	−	0.468907i	$-0.155352\pi$
$307$	0.622679	+	1.07851i	0.0355382	+	0.0615540i	−0.847709	+	0.530461i	$0.822019\pi$
$308$		0			0
$309$	4.17423	−	7.22998i	0.237464	−	0.411299i
$310$		0			0
$311$	−16.4403			−0.932245			−0.466122	−	0.884720i	$-0.654349\pi$
$311$	−16.4403			−0.932245			−0.466122	+	0.884720i	$0.654349\pi$
$312$		0			0
$313$	3.05356			0.172598			0.0862988	−	0.996269i	$-0.472496\pi$
$313$	3.05356			0.172598			0.0862988	+	0.996269i	$0.472496\pi$
$314$		0			0
$315$	1.00432	−	1.73954i	0.0565873	−	0.0980120i
$316$		0			0
$317$	6.05978	+	10.4959i	0.340351	+	0.589506i	0.984498	−	0.175396i	$-0.0561206\pi$
$317$	6.05978	+	10.4959i	0.340351	+	0.589506i	−0.644147	+	0.764902i	$0.722787\pi$
$318$		0			0
$319$	1.42068	+	2.46070i	0.0795431	+	0.137773i
$320$		0			0
$321$	4.22998			0.236095
$322$		0			0
$323$	0.228605	−	0.395955i	0.0127199	−	0.0220315i
$324$		0			0
$325$	1.97093	+	3.41375i	0.109328	+	0.189361i
$326$		0			0
$327$	11.8304			0.654225
$328$		0			0
$329$	5.32772	+	9.22788i	0.293727	+	0.508750i
$330$		0			0
$331$	−17.4707	+	30.2601i	−0.960276	+	1.66325i	−0.238472	+	0.971149i	$0.576647\pi$
$331$	−17.4707	+	30.2601i	−0.960276	+	1.66325i	−0.721804	+	0.692098i	$0.756687\pi$
$332$		0			0
$333$	2.59934	+	4.50219i	0.142443	+	0.246718i
$334$		0			0
$335$	−7.15136	+	3.98222i	−0.390720	+	0.217572i
$336$		0			0
$337$	−0.762203	−	1.32017i	−0.0415198	−	0.0719144i	0.844519	−	0.535526i	$-0.179887\pi$
$337$	−0.762203	−	1.32017i	−0.0415198	−	0.0719144i	−0.886039	+	0.463612i	$0.846553\pi$
$338$		0			0
$339$	4.32509	−	7.49128i	0.234907	−	0.406871i
$340$		0			0
$341$	−3.03503	−	5.25683i	−0.164356	−	0.284673i
$342$		0			0
$343$	20.0168			1.08081
$344$		0			0
$345$	3.81397	+	6.60599i	0.205337	+	0.355655i
$346$		0			0
$347$	14.9680	−	25.9253i	0.803523	−	1.39174i	−0.113761	−	0.993508i	$-0.536290\pi$
$347$	14.9680	−	25.9253i	0.803523	−	1.39174i	0.917284	−	0.398235i	$-0.130377\pi$
$348$		0			0
$349$	−4.83666			−0.258901			−0.129450	−	0.991586i	$-0.541321\pi$
$349$	−4.83666			−0.258901			−0.129450	+	0.991586i	$0.541321\pi$
$350$		0			0
$351$	1.97093	+	3.41375i	0.105201	+	0.182213i
$352$		0			0
$353$	14.0900	+	24.4046i	0.749935	+	1.29892i	0.947853	+	0.318706i	$0.103248\pi$
$353$	14.0900	+	24.4046i	0.749935	+	1.29892i	−0.197919	+	0.980218i	$0.563418\pi$
$354$		0			0
$355$	2.30559	−	3.99341i	0.122368	−	0.211948i
$356$		0			0
$357$	1.03539			0.0547989
$358$		0			0
$359$	−4.27740			−0.225753			−0.112876	−	0.993609i	$-0.536006\pi$
$359$	−4.27740			−0.225753			−0.112876	+	0.993609i	$0.536006\pi$
$360$		0			0
$361$	9.10663	−	15.7732i	0.479297	−	0.830166i
$362$		0			0
$363$	5.09649	+	8.82737i	0.267496	+	0.463317i
$364$		0			0
$365$	1.17004	+	2.02657i	0.0612428	+	0.106076i
$366$		0			0
$367$	−13.6776	+	23.6903i	−0.713965	+	1.23662i	0.249392	+	0.968403i	$0.419769\pi$
$367$	−13.6776	+	23.6903i	−0.713965	+	1.23662i	−0.963357	+	0.268221i	$0.913564\pi$
$368$		0			0
$369$	2.35166	−	4.07319i	0.122423	−	0.212042i
$370$		0			0
$371$	9.43000	−	16.3332i	0.489581	−	0.847979i
$372$		0			0
$373$	−6.11683	+	10.5947i	−0.316717	+	0.548571i	−0.979801	−	0.199975i	$-0.935914\pi$
$373$	−6.11683	+	10.5947i	−0.316717	+	0.548571i	0.663084	+	0.748545i	$0.269247\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−12.4677			−0.642118
$378$		0			0
$379$	0.378326	+	0.655279i	0.0194333	+	0.0336594i	0.875579	−	0.483076i	$-0.160480\pi$
$379$	0.378326	+	0.655279i	0.0194333	+	0.0336594i	−0.856145	+	0.516735i	$0.827147\pi$
$380$		0			0
$381$	6.17191	−	10.6901i	0.316196	−	0.547668i
$382$		0			0
$383$	9.00803	+	15.6024i	0.460289	+	0.797244i	0.998975	−	0.0452628i	$-0.0144125\pi$
$383$	9.00803	+	15.6024i	0.460289	+	0.797244i	−0.538686	+	0.842506i	$0.681079\pi$
$384$		0			0
$385$	−0.902231	−	1.56271i	−0.0459820	−	0.0796431i
$386$		0			0
$387$	−8.28809			−0.421307
$388$		0			0
$389$	−9.61562	−	16.6547i	−0.487531	−	0.844429i	0.512366	−	0.858767i	$-0.328769\pi$
$389$	−9.61562	−	16.6547i	−0.487531	−	0.844429i	−0.999897	+	0.0143381i	$0.995436\pi$
$390$		0			0
$391$	−1.96598	+	3.40518i	−0.0994239	+	0.172207i
$392$		0			0
$393$	−5.77449			−0.291285
$394$		0			0
$395$	1.31656	−	2.28035i	0.0662435	−	0.114737i
$396$		0			0
$397$	−36.7701			−1.84544			−0.922718	−	0.385475i	$-0.874038\pi$
$397$	−36.7701			−1.84544			−0.922718	+	0.385475i	$0.874038\pi$
$398$		0			0
$399$	−1.78163			−0.0891929
$400$		0			0
$401$	14.5326			0.725726			0.362863	−	0.931843i	$-0.381799\pi$
$401$	14.5326			0.725726			0.362863	+	0.931843i	$0.381799\pi$
$402$		0			0
$403$	26.6349			1.32678
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	4.67022			0.231494
$408$		0			0
$409$	−8.98300	+	15.5590i	−0.444181	+	0.769343i	−0.997995	−	0.0632969i	$-0.979838\pi$
$409$	−8.98300	+	15.5590i	−0.444181	+	0.769343i	0.553814	+	0.832640i	$0.313172\pi$
$410$		0			0
$411$	−8.34696			−0.411725
$412$		0			0
$413$	8.92031	−	15.4504i	0.438940	−	0.760266i
$414$		0			0
$415$	−2.20208	−	3.81411i	−0.108096	−	0.187227i
$416$		0			0
$417$	−23.1591			−1.13410
$418$		0			0
$419$	8.24996	+	14.2894i	0.403037	+	0.698081i	0.994091	−	0.108551i	$-0.0346212\pi$
$419$	8.24996	+	14.2894i	0.403037	+	0.698081i	−0.591054	+	0.806632i	$0.701288\pi$
$420$		0			0
$421$	−10.9666	−	18.9946i	−0.534478	−	0.925742i	−0.999188	−	0.0402798i	$-0.987175\pi$
$421$	−10.9666	−	18.9946i	−0.534478	−	0.925742i	0.464711	−	0.885462i	$-0.346158\pi$
$422$		0			0
$423$	−2.65239	+	4.59408i	−0.128964	+	0.223372i
$424$		0			0
$425$	0.257734	+	0.446409i	0.0125019	+	0.0216540i
$426$		0			0
$427$	−2.86857			−0.138820
$428$		0			0
$429$	3.54116			0.170969
$430$		0			0
$431$	9.68750	−	16.7792i	0.466630	−	0.808228i	−0.532643	−	0.846340i	$-0.678801\pi$
$431$	9.68750	−	16.7792i	0.466630	−	0.808228i	0.999273	+	0.0381123i	$0.0121345\pi$
$432$		0			0
$433$	−7.55103	+	13.0788i	−0.362879	+	0.628525i	−0.988433	−	0.151656i	$-0.951540\pi$
$433$	−7.55103	+	13.0788i	−0.362879	+	0.628525i	0.625554	+	0.780181i	$0.284873\pi$
$434$		0			0
$435$	−1.58144	+	2.73914i	−0.0758244	+	0.131332i
$436$		0			0
$437$	3.38291	−	5.85937i	0.161827	−	0.280292i
$438$		0			0
$439$	1.12731	+	1.95256i	0.0538035	+	0.0931904i	0.891673	−	0.452681i	$-0.149532\pi$
$439$	1.12731	+	1.95256i	0.0538035	+	0.0931904i	−0.837869	+	0.545871i	$0.816199\pi$
$440$		0			0
$441$	1.48267	+	2.56805i	0.0706031	+	0.122288i
$442$		0			0
$443$	12.8491	−	22.2553i	0.610478	−	1.05738i	−0.380682	−	0.924706i	$-0.624311\pi$
$443$	12.8491	−	22.2553i	0.610478	−	1.05738i	0.991160	−	0.132673i	$-0.0423561\pi$
$444$		0			0
$445$	−5.68320			−0.269410
$446$		0			0
$447$	−5.74171			−0.271574
$448$		0			0
$449$	10.6364	−	18.4229i	0.501965	−	0.869429i	−0.498032	−	0.867158i	$-0.665944\pi$
$449$	10.6364	−	18.4229i	0.501965	−	0.869429i	0.999997	−	0.00227049i	$-0.000722720\pi$
$450$		0			0
$451$	−2.11261	−	3.65914i	−0.0994787	−	0.172302i
$452$		0			0
$453$	−10.7365	−	18.5962i	−0.504444	−	0.873723i
$454$		0			0
$455$	7.91782			0.371193
$456$		0			0
$457$	−4.36693	+	7.56374i	−0.204276	+	0.353817i	−0.949902	−	0.312548i	$-0.898817\pi$
$457$	−4.36693	+	7.56374i	−0.204276	+	0.353817i	0.745626	+	0.666365i	$0.232151\pi$
$458$		0			0
$459$	0.257734	+	0.446409i	0.0120300	+	0.0208366i
$460$		0			0
$461$	−12.4832			−0.581402			−0.290701	−	0.956814i	$-0.593888\pi$
$461$	−12.4832			−0.581402			−0.290701	+	0.956814i	$0.593888\pi$
$462$		0			0
$463$	−12.2900	−	21.2869i	−0.571165	−	0.989286i	−0.996447	−	0.0842253i	$-0.973158\pi$
$463$	−12.2900	−	21.2869i	−0.571165	−	0.989286i	0.425282	−	0.905061i	$-0.360175\pi$
$464$		0			0
$465$	3.37847	−	5.85168i	0.156673	−	0.271365i
$466$		0			0
$467$	−9.09618	−	15.7550i	−0.420921	−	0.729057i	0.575109	−	0.818077i	$-0.304960\pi$
$467$	−9.09618	−	15.7550i	−0.420921	−	0.729057i	−0.996030	+	0.0890204i	$0.971626\pi$
$468$		0			0
$469$	−0.255039	+	16.4395i	−0.0117766	+	0.759106i
$470$		0			0
$471$	4.04085	+	6.99896i	0.186193	+	0.322495i
$472$		0			0
$473$	−3.72279	+	6.44806i	−0.171174	+	0.296482i
$474$		0			0
$475$	−0.443489	−	0.768146i	−0.0203487	−	0.0352449i
$476$		0			0
$477$	9.38940			0.429911
$478$		0			0
$479$	−9.53078	−	16.5078i	−0.435473	−	0.754261i	0.561862	−	0.827231i	$-0.310085\pi$
$479$	−9.53078	−	16.5078i	−0.435473	−	0.754261i	−0.997334	+	0.0729707i	$0.976752\pi$
$480$		0			0
$481$	−10.2462	+	17.7470i	−0.467189	+	0.809194i
$482$		0			0
$483$	15.3219			0.697168
$484$		0			0
$485$	−1.26978	−	2.19933i	−0.0576578	−	0.0998663i
$486$		0			0
$487$	5.18998	+	8.98931i	0.235180	+	0.407344i	0.959325	−	0.282304i	$-0.0910986\pi$
$487$	5.18998	+	8.98931i	0.235180	+	0.407344i	−0.724145	+	0.689648i	$0.757765\pi$
$488$		0			0
$489$	4.08651	−	7.07804i	0.184798	−	0.320080i
$490$		0			0
$491$	34.2726			1.54670			0.773350	−	0.633979i	$-0.218580\pi$
$491$	34.2726			1.54670			0.773350	+	0.633979i	$0.218580\pi$
$492$		0			0
$493$	−1.63037			−0.0734281
$494$		0			0
$495$	0.449173	−	0.777991i	0.0201888	−	0.0349681i
$496$		0			0
$497$	−4.63113	−	8.02135i	−0.207734	−	0.359807i
$498$		0			0
$499$	−18.3681	−	31.8145i	−0.822269	−	1.42421i	−0.903989	−	0.427556i	$-0.859375\pi$
$499$	−18.3681	−	31.8145i	−0.822269	−	1.42421i	0.0817198	−	0.996655i	$-0.473959\pi$
$500$		0			0
$501$	4.32150	−	7.48506i	0.193071	−	0.334408i
$502$		0			0
$503$	12.9332	−	22.4010i	0.576664	−	0.998811i	−0.419195	−	0.907896i	$-0.637688\pi$
$503$	12.9332	−	22.4010i	0.576664	−	0.998811i	0.995859	−	0.0909149i	$-0.0289791\pi$
$504$		0			0
$505$	2.08447	−	3.61040i	0.0927576	−	0.160661i
$506$		0			0
$507$	−1.26914	+	2.19822i	−0.0563647	+	0.0976265i
$508$		0			0
$509$	−25.3104			−1.12186			−0.560932	−	0.827862i	$-0.689557\pi$
$509$	−25.3104			−1.12186			−0.560932	+	0.827862i	$0.689557\pi$
$510$		0			0
$511$	4.70041			0.207934
$512$		0			0
$513$	−0.443489	−	0.768146i	−0.0195805	−	0.0339145i
$514$		0			0
$515$	4.17423	−	7.22998i	0.183939	−	0.318591i
$516$		0			0
$517$	2.38277	+	4.12707i	0.104794	+	0.181508i
$518$		0			0
$519$	5.01325	+	8.68320i	0.220057	+	0.381150i
$520$		0			0
$521$	7.89460			0.345869			0.172934	−	0.984933i	$-0.444675\pi$
$521$	7.89460			0.345869			0.172934	+	0.984933i	$0.444675\pi$
$522$		0			0
$523$	5.70501	+	9.88137i	0.249463	+	0.432082i	0.963377	−	0.268151i	$-0.0864127\pi$
$523$	5.70501	+	9.88137i	0.249463	+	0.432082i	−0.713914	+	0.700233i	$0.753079\pi$
$524$		0			0
$525$	1.00432	−	1.73954i	0.0438323	−	0.0759198i
$526$		0			0
$527$	3.48298			0.151721
$528$		0			0
$529$	−17.5928	+	30.4715i	−0.764902	+	1.32485i
$530$		0			0
$531$	8.88190			0.385442
$532$		0			0
$533$	18.5398			0.803050
$534$		0			0
$535$	4.22998			0.182878
$536$		0			0
$537$	14.4986			0.625660
$538$		0			0
$539$	2.66390			0.114742
$540$		0			0
$541$	−32.9188			−1.41529			−0.707644	−	0.706569i	$-0.750242\pi$
$541$	−32.9188			−1.41529			−0.707644	+	0.706569i	$0.750242\pi$
$542$		0			0
$543$	−2.95494	+	5.11811i	−0.126809	+	0.219639i
$544$		0			0
$545$	11.8304			0.506760
$546$		0			0
$547$	−6.67910	+	11.5685i	−0.285578	+	0.494635i	−0.972749	−	0.231860i	$-0.925519\pi$
$547$	−6.67910	+	11.5685i	−0.285578	+	0.494635i	0.687172	+	0.726495i	$0.258852\pi$
$548$		0			0
$549$	−0.714054	−	1.23678i	−0.0304751	−	0.0527844i
$550$		0			0
$551$	2.80541			0.119515
$552$		0			0
$553$	−2.64451	−	4.58043i	−0.112456	−	0.194780i
$554$		0			0
$555$	2.59934	+	4.50219i	0.110336	+	0.191107i
$556$		0			0
$557$	−10.2829	+	17.8106i	−0.435702	+	0.754658i	−0.997353	−	0.0727166i	$-0.976833\pi$
$557$	−10.2829	+	17.8106i	−0.435702	+	0.754658i	0.561651	+	0.827374i	$0.310166\pi$
$558$		0			0
$559$	−16.3353	−	28.2935i	−0.690908	−	1.19669i
$560$		0			0
$561$	0.463069			0.0195508
$562$		0			0
$563$	21.7874			0.918230			0.459115	−	0.888377i	$-0.348167\pi$
$563$	21.7874			0.918230			0.459115	+	0.888377i	$0.348167\pi$
$564$		0			0
$565$	4.32509	−	7.49128i	0.181958	−	0.315161i
$566$		0			0
$567$	1.00432	−	1.73954i	0.0421776	−	0.0730538i
$568$		0			0
$569$	8.38004	−	14.5147i	0.351310	−	0.608486i	−0.635170	−	0.772373i	$-0.719070\pi$
$569$	8.38004	−	14.5147i	0.351310	−	0.608486i	0.986479	+	0.163887i	$0.0524032\pi$
$570$		0			0
$571$	0.926564	−	1.60486i	0.0387755	−	0.0671612i	−0.845986	−	0.533205i	$-0.820988\pi$
$571$	0.926564	−	1.60486i	0.0387755	−	0.0671612i	0.884762	+	0.466043i	$0.154321\pi$
$572$		0			0
$573$	8.95850	+	15.5166i	0.374247	+	0.648214i
$574$		0			0
$575$	3.81397	+	6.60599i	0.159054	+	0.275489i
$576$		0			0
$577$	−3.77114	+	6.53180i	−0.156995	+	0.271922i	−0.933783	−	0.357839i	$-0.883514\pi$
$577$	−3.77114	+	6.53180i	−0.156995	+	0.271922i	0.776789	+	0.629761i	$0.216847\pi$
$578$		0			0
$579$	−8.52514			−0.354293
$580$		0			0
$581$	−8.84639			−0.367010
$582$		0			0
$583$	4.21747	−	7.30487i	0.174670	−	0.302537i
$584$		0			0
$585$	1.97093	+	3.41375i	0.0814880	+	0.141141i
$586$		0			0
$587$	6.88159	+	11.9193i	0.284033	+	0.491960i	0.972374	−	0.233427i	$-0.0749940\pi$
$587$	6.88159	+	11.9193i	0.284033	+	0.491960i	−0.688341	+	0.725387i	$0.741661\pi$
$588$		0			0
$589$	−5.99325			−0.246948
$590$		0			0
$591$	0.730109	−	1.26459i	0.0300327	−	0.0520181i
$592$		0			0
$593$	−2.36910	−	4.10340i	−0.0972873	−	0.168507i	0.813274	−	0.581881i	$-0.197683\pi$
$593$	−2.36910	−	4.10340i	−0.0972873	−	0.168507i	−0.910561	+	0.413375i	$0.864350\pi$
$594$		0			0
$595$	1.03539			0.0424470
$596$		0			0
$597$	0.385440	+	0.667601i	0.0157750	+	0.0273231i
$598$		0			0
$599$	0.371400	−	0.643283i	0.0151750	−	0.0262838i	−0.858338	−	0.513084i	$-0.828503\pi$
$599$	0.371400	−	0.643283i	0.0151750	−	0.0262838i	0.873513	+	0.486801i	$0.161836\pi$
$600$		0			0
$601$	7.07042	+	12.2463i	0.288409	+	0.499538i	0.973430	−	0.228985i	$-0.0735405\pi$
$601$	7.07042	+	12.2463i	0.288409	+	0.499538i	−0.685021	+	0.728523i	$0.740207\pi$
$602$		0			0
$603$	−7.15136	+	3.98222i	−0.291226	+	0.162169i
$604$		0			0
$605$	5.09649	+	8.82737i	0.207202	+	0.358884i
$606$		0			0
$607$	6.33085	−	10.9654i	0.256961	−	0.445070i	−0.708465	−	0.705746i	$-0.750612\pi$
$607$	6.33085	−	10.9654i	0.256961	−	0.445070i	0.965426	+	0.260676i	$0.0839454\pi$
$608$		0			0
$609$	3.17656	+	5.50197i	0.128721	+	0.222951i
$610$		0			0
$611$	−20.9107			−0.845957
$612$		0			0
$613$	−5.00548	−	8.66975i	−0.202169	−	0.350168i	0.747058	−	0.664759i	$-0.231466\pi$
$613$	−5.00548	−	8.66975i	−0.202169	−	0.350168i	−0.949227	+	0.314591i	$0.898133\pi$
$614$		0			0
$615$	2.35166	−	4.07319i	0.0948281	−	0.164247i
$616$		0			0
$617$	−38.3374			−1.54340			−0.771702	−	0.635984i	$-0.780594\pi$
$617$	−38.3374			−1.54340			−0.771702	+	0.635984i	$0.780594\pi$
$618$		0			0
$619$	−10.2608	−	17.7722i	−0.412415	−	0.714324i	0.582738	−	0.812660i	$-0.301981\pi$
$619$	−10.2608	−	17.7722i	−0.412415	−	0.714324i	−0.995153	+	0.0983361i	$0.968648\pi$
$620$		0			0
$621$	3.81397	+	6.60599i	0.153049	+	0.265089i
$622$		0			0
$623$	−5.70778	+	9.88616i	−0.228677	+	0.396081i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−0.796814			−0.0318217
$628$		0			0
$629$	−1.33988	+	2.32074i	−0.0534244	+	0.0925338i
$630$		0			0
$631$	−11.6628	−	20.2005i	−0.464288	−	0.804171i	0.534881	−	0.844927i	$-0.320356\pi$
$631$	−11.6628	−	20.2005i	−0.464288	−	0.804171i	−0.999169	+	0.0407567i	$0.987023\pi$
$632$		0			0
$633$	1.46317	+	2.53428i	0.0581558	+	0.100729i
$634$		0			0
$635$	6.17191	−	10.6901i	0.244925	−	0.424222i
$636$		0			0
$637$	−5.84447	+	10.1229i	−0.231566	+	0.401084i
$638$		0			0
$639$	2.30559	−	3.99341i	0.0912079	−	0.157977i
$640$		0			0
$641$	−10.3018	+	17.8432i	−0.406896	+	0.704764i	−0.994540	−	0.104355i	$-0.966722\pi$
$641$	−10.3018	+	17.8432i	−0.406896	+	0.704764i	0.587644	+	0.809119i	$0.300055\pi$
$642$		0			0
$643$	−32.4204			−1.27854			−0.639268	−	0.768984i	$-0.720762\pi$
$643$	−32.4204			−1.27854			−0.639268	+	0.768984i	$0.720762\pi$
$644$		0			0
$645$	−8.28809			−0.326343
$646$		0			0
$647$	−16.9438	−	29.3474i	−0.666128	−	1.15377i	−0.978978	−	0.203965i	$-0.934617\pi$
$647$	−16.9438	−	29.3474i	−0.666128	−	1.15377i	0.312851	−	0.949802i	$-0.398716\pi$
$648$		0			0
$649$	3.98951	−	6.91004i	0.156602	−	0.271243i
$650$		0			0
$651$	−6.78615	−	11.7540i	−0.265970	−	0.460674i
$652$		0			0
$653$	13.5962	+	23.5494i	0.532061	+	0.921557i	0.999299	+	0.0374258i	$0.0119158\pi$
$653$	13.5962	+	23.5494i	0.532061	+	0.921557i	−0.467238	+	0.884132i	$0.654751\pi$
$654$		0			0
$655$	−5.77449			−0.225628
$656$		0			0
$657$	1.17004	+	2.02657i	0.0456477	+	0.0790641i
$658$		0			0
$659$	−8.44291	+	14.6236i	−0.328889	+	0.569653i	−0.982292	−	0.187358i	$-0.940008\pi$
$659$	−8.44291	+	14.6236i	−0.328889	+	0.569653i	0.653403	+	0.757011i	$0.273341\pi$
$660$		0			0
$661$	−33.5897			−1.30649			−0.653243	−	0.757148i	$-0.726592\pi$
$661$	−33.5897			−1.30649			−0.653243	+	0.757148i	$0.726592\pi$
$662$		0			0
$663$	−1.01595	+	1.75968i	−0.0394563	+	0.0683404i
$664$		0			0
$665$	−1.78163			−0.0690886
$666$		0			0
$667$	−24.1263			−0.934175
$668$		0			0
$669$	10.5051			0.406149
$670$		0			0
$671$	−1.28294			−0.0495272
$672$		0			0
$673$	−0.462042			−0.0178104			−0.00890520	−	0.999960i	$-0.502835\pi$
$673$	−0.462042			−0.0178104			−0.00890520	+	0.999960i	$0.502835\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−15.5433	+	26.9217i	−0.597376	+	1.03469i	0.395831	+	0.918323i	$0.370457\pi$
$677$	−15.5433	+	26.9217i	−0.597376	+	1.03469i	−0.993207	+	0.116362i	$0.962877\pi$
$678$		0			0
$679$	−5.10109			−0.195762
$680$		0			0
$681$	6.70223	−	11.6086i	0.256830	−	0.444842i
$682$		0			0
$683$	25.3011	+	43.8229i	0.968121	+	1.67683i	0.700985	+	0.713176i	$0.252744\pi$
$683$	25.3011	+	43.8229i	0.968121	+	1.67683i	0.267136	+	0.963659i	$0.413923\pi$
$684$		0			0
$685$	−8.34696			−0.318921
$686$		0			0
$687$	−4.37210	−	7.57270i	−0.166806	−	0.288916i
$688$		0			0
$689$	18.5059	+	32.0531i	0.705017	+	1.22113i
$690$		0			0
$691$	−10.9731	+	19.0060i	−0.417438	+	0.723023i	−0.995681	−	0.0928411i	$-0.970405\pi$
$691$	−10.9731	+	19.0060i	−0.417438	+	0.723023i	0.578243	+	0.815864i	$0.303738\pi$
$692$		0			0
$693$	−0.902231	−	1.56271i	−0.0342729	−	0.0593624i
$694$		0			0
$695$	−23.1591			−0.878474
$696$		0			0
$697$	2.42441			0.0918311
$698$		0			0
$699$	−3.52677	+	6.10855i	−0.133395	+	0.231047i
$700$		0			0
$701$	−18.6162	+	32.2442i	−0.703124	+	1.21785i	0.264240	+	0.964457i	$0.414879\pi$
$701$	−18.6162	+	32.2442i	−0.703124	+	1.21785i	−0.967364	+	0.253390i	$0.918454\pi$
$702$		0			0
$703$	2.30556	−	3.99334i	0.0869558	−	0.150612i
$704$		0			0
$705$	−2.65239	+	4.59408i	−0.0998948	+	0.173023i
$706$		0			0
$707$	−4.18696	−	7.25203i	−0.157467	−	0.272741i
$708$		0			0
$709$	−1.23558	−	2.14008i	−0.0464031	−	0.0803726i	0.841891	−	0.539648i	$-0.181443\pi$
$709$	−1.23558	−	2.14008i	−0.0464031	−	0.0803726i	−0.888294	+	0.459275i	$0.848109\pi$
$710$		0			0
$711$	1.31656	−	2.28035i	0.0493750	−	0.0855200i
$712$		0			0
$713$	51.5415			1.93024
$714$		0			0
$715$	3.54116			0.132432
$716$		0			0
$717$	−6.49940	+	11.2573i	−0.242725	+	0.420411i
$718$		0			0
$719$	−19.3472	−	33.5103i	−0.721528	−	1.24972i	−0.960387	−	0.278670i	$-0.910107\pi$
$719$	−19.3472	−	33.5103i	−0.721528	−	1.24972i	0.238859	−	0.971054i	$-0.423227\pi$
$720$		0			0
$721$	−8.38457	−	14.5225i	−0.312258	−	0.540846i
$722$		0			0
$723$	0.545924			0.0203031
$724$		0			0
$725$	−1.58144	+	2.73914i	−0.0587334	+	0.101729i
$726$		0			0
$727$	5.43301	+	9.41024i	0.201499	+	0.349007i	0.949012	−	0.315241i	$-0.102085\pi$
$727$	5.43301	+	9.41024i	0.201499	+	0.349007i	−0.747513	+	0.664248i	$0.768752\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.13612	−	3.69988i	−0.0790074	−	0.136845i
$732$		0			0
$733$	−11.0079	+	19.0662i	−0.406585	+	0.704226i	−0.994505	−	0.104693i	$-0.966614\pi$
$733$	−11.0079	+	19.0662i	−0.406585	+	0.704226i	0.587919	+	0.808920i	$0.299947\pi$
$734$		0			0
$735$	1.48267	+	2.56805i	0.0546890	+	0.0947241i
$736$		0			0
$737$	−0.114064	+	7.35240i	−0.00420159	+	0.270829i
$738$		0			0
$739$	−1.58197	−	2.74005i	−0.0581936	−	0.100794i	0.835461	−	0.549550i	$-0.185201\pi$
$739$	−1.58197	−	2.74005i	−0.0581936	−	0.100794i	−0.893655	+	0.448756i	$0.851867\pi$
$740$		0			0
$741$	1.74817	−	3.02793i	0.0642208	−	0.111234i
$742$		0			0
$743$	5.08319	+	8.80434i	0.186484	+	0.323000i	0.944076	−	0.329729i	$-0.106957\pi$
$743$	5.08319	+	8.80434i	0.186484	+	0.323000i	−0.757591	+	0.652729i	$0.773624\pi$
$744$		0			0
$745$	−5.74171			−0.210360
$746$		0			0
$747$	−2.20208	−	3.81411i	−0.0805697	−	0.139551i
$748$		0			0
$749$	4.24828	−	7.35823i	0.155229	−	0.268864i
$750$		0			0
$751$	−29.5949			−1.07993			−0.539966	−	0.841687i	$-0.681563\pi$
$751$	−29.5949			−1.07993			−0.539966	+	0.841687i	$0.681563\pi$
$752$		0			0
$753$	4.05975	+	7.03169i	0.147945	+	0.256249i
$754$		0			0
$755$	−10.7365	−	18.5962i	−0.390741	−	0.676783i
$756$		0			0
$757$	−9.04419	+	15.6650i	−0.328717	+	0.569354i	−0.982257	−	0.187537i	$-0.939949\pi$
$757$	−9.04419	+	15.6650i	−0.328717	+	0.569354i	0.653541	+	0.756891i	$0.273283\pi$
$758$		0			0
$759$	6.85254			0.248731
$760$		0			0
$761$	−19.7840			−0.717171			−0.358585	−	0.933497i	$-0.616741\pi$
$761$	−19.7840			−0.717171			−0.358585	+	0.933497i	$0.616741\pi$
$762$		0			0
$763$	11.8816	−	20.5795i	0.430143	−	0.745029i
$764$		0			0
$765$	0.257734	+	0.446409i	0.00931840	+	0.0161399i
$766$		0			0
$767$	17.5056	+	30.3206i	0.632091	+	1.09481i
$768$		0			0
$769$	12.5298	−	21.7023i	0.451837	−	0.782605i	−0.546663	−	0.837353i	$-0.684102\pi$
$769$	12.5298	−	21.7023i	0.451837	−	0.782605i	0.998500	+	0.0547478i	$0.0174355\pi$
$770$		0			0
$771$	−1.79824	+	3.11464i	−0.0647619	+	0.112171i
$772$		0			0
$773$	18.7446	−	32.4666i	0.674197	−	1.16774i	−0.302506	−	0.953147i	$-0.597823\pi$
$773$	18.7446	−	32.4666i	0.674197	−	1.16774i	0.976703	−	0.214596i	$-0.0688434\pi$
$774$		0			0
$775$	3.37847	−	5.85168i	0.121358	−	0.210198i
$776$		0			0
$777$	10.4423			0.374616
$778$		0			0
$779$	−4.17174			−0.149468
$780$		0			0
$781$	−2.07122	−	3.58746i	−0.0741142	−	0.128370i
$782$		0			0
$783$	−1.58144	+	2.73914i	−0.0565162	+	0.0978889i
$784$		0			0
$785$	4.04085	+	6.99896i	0.144224	+	0.249804i
$786$		0			0
$787$	−17.4852	−	30.2853i	−0.623282	−	1.07956i	−0.988870	−	0.148779i	$-0.952466\pi$
$787$	−17.4852	−	30.2853i	−0.623282	−	1.07956i	0.365589	−	0.930777i	$-0.380868\pi$
$788$		0			0
$789$	16.9589			0.603754
$790$		0			0
$791$	−8.68759	−	15.0474i	−0.308895	−	0.535022i
$792$		0			0
$793$	2.81470	−	4.87521i	0.0999531	−	0.173124i
$794$		0			0
$795$	9.38940			0.333008
$796$		0			0
$797$	19.8435	−	34.3699i	0.702892	−	1.21744i	−0.264555	−	0.964371i	$-0.585225\pi$
$797$	19.8435	−	34.3699i	0.702892	−	1.21744i	0.967447	−	0.253074i	$-0.0814417\pi$
$798$		0			0
$799$	−2.73445			−0.0967377
$800$		0			0
$801$	−5.68320			−0.200806
$802$		0			0
$803$	2.10221			0.0741853
$804$		0			0
$805$	15.3219			0.540024
$806$		0			0
$807$	14.6789			0.516723
$808$		0			0
$809$	−54.6646			−1.92191			−0.960953	−	0.276711i	$-0.910756\pi$
$809$	−54.6646			−1.92191			−0.960953	+	0.276711i	$0.910756\pi$
$810$		0			0
$811$	15.1885	−	26.3073i	0.533341	−	0.923773i	−0.465901	−	0.884837i	$-0.654270\pi$
$811$	15.1885	−	26.3073i	0.533341	−	0.923773i	0.999242	−	0.0389361i	$-0.0123969\pi$
$812$		0			0
$813$	−23.3242			−0.818015
$814$		0			0
$815$	4.08651	−	7.07804i	0.143144	−	0.247933i
$816$		0			0
$817$	3.67568	+	6.36646i	0.128596	+	0.222734i
$818$		0			0
$819$	7.91782			0.276671
$820$		0			0
$821$	−0.380717	−	0.659422i	−0.0132871	−	0.0230140i	0.859305	−	0.511463i	$-0.170896\pi$
$821$	−0.380717	−	0.659422i	−0.0132871	−	0.0230140i	−0.872593	+	0.488449i	$0.837563\pi$
$822$		0			0
$823$	0.294522	+	0.510126i	0.0102664	+	0.0177819i	0.871113	−	0.491083i	$-0.163399\pi$
$823$	0.294522	+	0.510126i	0.0102664	+	0.0177819i	−0.860847	+	0.508865i	$0.830065\pi$
$824$		0			0
$825$	0.449173	−	0.777991i	0.0156382	−	0.0270862i
$826$		0			0
$827$	−6.91107	−	11.9703i	−0.240321	−	0.416249i	0.720484	−	0.693471i	$-0.243919\pi$
$827$	−6.91107	−	11.9703i	−0.240321	−	0.416249i	−0.960806	+	0.277222i	$0.910586\pi$
$828$		0			0
$829$	29.3493			1.01934			0.509671	−	0.860369i	$-0.329767\pi$
$829$	29.3493			1.01934			0.509671	+	0.860369i	$0.329767\pi$
$830$		0			0
$831$	−23.2493			−0.806510
$832$		0			0
$833$	−0.764267	+	1.32375i	−0.0264803	+	0.0458652i
$834$		0			0
$835$	4.32150	−	7.48506i	0.149552	−	0.259031i
$836$		0			0
$837$	3.37847	−	5.85168i	0.116777	−	0.202263i
$838$		0			0
$839$	−4.79382	+	8.30314i	−0.165501	+	0.286656i	−0.936833	−	0.349777i	$-0.886257\pi$
$839$	−4.79382	+	8.30314i	−0.165501	+	0.286656i	0.771332	+	0.636433i	$0.219591\pi$
$840$		0			0
$841$	9.49807	+	16.4511i	0.327520	+	0.567281i
$842$		0			0
$843$	−1.06574	−	1.84591i	−0.0367059	−	0.0635765i
$844$		0			0
$845$	−1.26914	+	2.19822i	−0.0436599	+	0.0756212i
$846$		0			0
$847$	20.4741			0.703498
$848$		0			0
$849$	−3.20381			−0.109954
$850$		0			0
$851$	−19.8276	+	34.3424i	−0.679682	+	1.17724i
$852$		0			0
$853$	−4.38041	−	7.58710i	−0.149982	−	0.259777i	0.781238	−	0.624233i	$-0.214588\pi$
$853$	−4.38041	−	7.58710i	−0.149982	−	0.259777i	−0.931221	+	0.364456i	$0.881255\pi$
$854$		0			0
$855$	−0.443489	−	0.768146i	−0.0151670	−	0.0262700i
$856$		0			0
$857$	7.21838			0.246575			0.123288	−	0.992371i	$-0.460656\pi$
$857$	7.21838			0.246575			0.123288	+	0.992371i	$0.460656\pi$
$858$		0			0
$859$	−7.38318	+	12.7880i	−0.251911	+	0.436322i	−0.964052	−	0.265714i	$-0.914392\pi$
$859$	−7.38318	+	12.7880i	−0.251911	+	0.436322i	0.712141	+	0.702036i	$0.247726\pi$
$860$		0			0
$861$	−4.72366	−	8.18161i	−0.160982	−	0.278829i
$862$		0			0
$863$	25.3765			0.863825			0.431913	−	0.901916i	$-0.357839\pi$
$863$	25.3765			0.863825			0.431913	+	0.901916i	$0.357839\pi$
$864$		0			0
$865$	5.01325	+	8.68320i	0.170455	+	0.295238i
$866$		0			0
$867$	8.36715	−	14.4923i	0.284163	−	0.492185i
$868$		0			0
$869$	−1.18273	−	2.04855i	−0.0401214	−	0.0694922i
$870$		0			0
$871$	−27.6892	−	16.5643i	−0.938212	−	0.561259i
$872$		0			0
$873$	−1.26978	−	2.19933i	−0.0429756	−	0.0744359i
$874$		0			0
$875$	1.00432	−	1.73954i	0.0339524	−	0.0588072i
$876$		0			0
$877$	−16.7747	−	29.0546i	−0.566440	−	0.981103i	−0.996914	−	0.0785000i	$-0.974987\pi$
$877$	−16.7747	−	29.0546i	−0.566440	−	0.981103i	0.430474	−	0.902603i	$-0.358346\pi$
$878$		0			0
$879$	−14.1788			−0.478239
$880$		0			0
$881$	−6.85434	−	11.8721i	−0.230929	−	0.399980i	0.727153	−	0.686475i	$-0.240843\pi$
$881$	−6.85434	−	11.8721i	−0.230929	−	0.399980i	−0.958082	+	0.286495i	$0.907510\pi$
$882$		0			0
$883$	−16.4728	+	28.5317i	−0.554353	+	0.960168i	0.443600	+	0.896225i	$0.353701\pi$
$883$	−16.4728	+	28.5317i	−0.554353	+	0.960168i	−0.997954	+	0.0639433i	$0.979632\pi$
$884$		0			0
$885$	8.88190			0.298562
$886$		0			0
$887$	−2.14141	−	3.70903i	−0.0719014	−	0.124537i	0.827833	−	0.560974i	$-0.189573\pi$
$887$	−2.14141	−	3.70903i	−0.0719014	−	0.124537i	−0.899735	+	0.436437i	$0.856240\pi$
$888$		0			0
$889$	−12.3972	−	21.4726i	−0.415789	−	0.720167i
$890$		0			0
$891$	0.449173	−	0.777991i	0.0150479	−	0.0260637i
$892$		0			0
$893$	4.70523			0.157454
$894$		0			0
$895$	14.4986			0.484634
$896$		0			0
$897$	−15.0342	+	26.0399i	−0.501976	+	0.869448i
$898$		0			0
$899$	10.6857	+	18.5082i	0.356388	+	0.617283i
$900$		0			0
$901$	2.41997	+	4.19151i	0.0806208	+	0.139639i
$902$		0			0
$903$	−8.32393	+	14.4175i	−0.277003	+	0.479783i
$904$		0			0
$905$	−2.95494	+	5.11811i	−0.0982256	+	0.170132i
$906$		0			0
$907$	5.61708	−	9.72907i	0.186512	−	0.323048i	−0.757573	−	0.652751i	$-0.773615\pi$
$907$	5.61708	−	9.72907i	0.186512	−	0.323048i	0.944085	+	0.329702i	$0.106948\pi$
$908$		0			0
$909$	2.08447	−	3.61040i	0.0691374	−	0.119750i
$910$		0			0
$911$	−44.7593			−1.48294			−0.741471	−	0.670985i	$-0.765871\pi$
$911$	−44.7593			−1.48294			−0.741471	+	0.670985i	$0.765871\pi$
$912$		0			0
$913$	−3.95645			−0.130940
$914$		0			0
$915$	−0.714054	−	1.23678i	−0.0236059	−	0.0408866i
$916$		0			0
$917$	−5.79946	+	10.0450i	−0.191515	+	0.331714i
$918$		0			0
$919$	−1.87120	−	3.24101i	−0.0617252	−	0.106911i	0.833511	−	0.552502i	$-0.186327\pi$
$919$	−1.87120	−	3.24101i	−0.0617252	−	0.106911i	−0.895237	+	0.445591i	$0.852994\pi$
$920$		0			0
$921$	0.622679	+	1.07851i	0.0205180	+	0.0355382i
$922$		0			0
$923$	18.1767			0.598293
$924$		0			0
$925$	2.59934	+	4.50219i	0.0854658	+	0.148031i
$926$		0			0
$927$	4.17423	−	7.22998i	0.137100	−	0.237464i
$928$		0			0
$929$	−28.2045			−0.925359			−0.462679	−	0.886526i	$-0.653112\pi$
$929$	−28.2045			−0.925359			−0.462679	+	0.886526i	$0.653112\pi$
$930$		0			0
$931$	1.31509	−	2.27781i	0.0431004	−	0.0746521i
$932$		0			0
$933$	−16.4403			−0.538232
$934$		0			0
$935$	0.463069			0.0151440
$936$		0			0
$937$	−24.2594			−0.792520			−0.396260	−	0.918138i	$-0.629692\pi$
$937$	−24.2594			−0.792520			−0.396260	+	0.918138i	$0.629692\pi$
$938$		0			0
$939$	3.05356			0.0996492
$940$		0			0
$941$	−6.44570			−0.210124			−0.105062	−	0.994466i	$-0.533504\pi$
$941$	−6.44570			−0.210124			−0.105062	+	0.994466i	$0.533504\pi$
$942$		0			0
$943$	35.8767			1.16830
$944$		0			0
$945$	1.00432	−	1.73954i	0.0326707	−	0.0565873i
$946$		0			0
$947$	−29.6988			−0.965081			−0.482541	−	0.875874i	$-0.660286\pi$
$947$	−29.6988			−0.965081			−0.482541	+	0.875874i	$0.660286\pi$
$948$		0			0
$949$	−4.61215	+	7.98847i	−0.149717	+	0.259317i
$950$		0			0
$951$	6.05978	+	10.4959i	0.196502	+	0.340351i
$952$		0			0
$953$	26.6073			0.861895			0.430948	−	0.902377i	$-0.358179\pi$
$953$	26.6073			0.861895			0.430948	+	0.902377i	$0.358179\pi$
$954$		0			0
$955$	8.95850	+	15.5166i	0.289890	+	0.502105i
$956$		0			0
$957$	1.42068	+	2.46070i	0.0459242	+	0.0795431i
$958$		0			0
$959$	−8.38306	+	14.5199i	−0.270703	+	0.468871i
$960$		0			0
$961$	−7.32807	−	12.6926i	−0.236389	−	0.409438i
$962$		0			0
$963$	4.22998			0.136309
$964$		0			0
$965$	−8.52514			−0.274434
$966$		0			0
$967$	27.5540	−	47.7249i	0.886077	−	1.53473i	0.0416021	−	0.999134i	$-0.486754\pi$
$967$	27.5540	−	47.7249i	0.886077	−	1.53473i	0.844475	−	0.535596i	$-0.179913\pi$
$968$		0			0
$969$	0.228605	−	0.395955i	0.00734384	−	0.0127199i
$970$		0			0
$971$	−1.37903	+	2.38854i	−0.0442551	+	0.0766520i	−0.887304	−	0.461184i	$-0.847425\pi$
$971$	−1.37903	+	2.38854i	−0.0442551	+	0.0766520i	0.843049	+	0.537836i	$0.180758\pi$
$972$		0			0
$973$	−23.2592	+	40.2861i	−0.745656	+	1.29151i
$974$		0			0
$975$	1.97093	+	3.41375i	0.0631203	+	0.109328i
$976$		0			0
$977$	28.9598	+	50.1598i	0.926506	+	1.60476i	0.789121	+	0.614238i	$0.210537\pi$
$977$	28.9598	+	50.1598i	0.926506	+	1.60476i	0.137385	+	0.990518i	$0.456130\pi$
$978$		0			0
$979$	−2.55274	+	4.42148i	−0.0815860	+	0.141311i
$980$		0			0
$981$	11.8304			0.377717
$982$		0			0
$983$	−20.2479			−0.645809			−0.322904	−	0.946432i	$-0.604659\pi$
$983$	−20.2479			−0.645809			−0.322904	+	0.946432i	$0.604659\pi$
$984$		0			0
$985$	0.730109	−	1.26459i	0.0232632	−	0.0402931i
$986$		0			0
$987$	5.32772	+	9.22788i	0.169583	+	0.293727i
$988$		0			0
$989$	−31.6105	−	54.7511i	−1.00516	−	1.74098i
$990$		0			0
$991$	−24.6481			−0.782972			−0.391486	−	0.920184i	$-0.628039\pi$
$991$	−24.6481			−0.782972			−0.391486	+	0.920184i	$0.628039\pi$
$992$		0			0
$993$	−17.4707	+	30.2601i	−0.554416	+	0.960276i
$994$		0			0
$995$	0.385440	+	0.667601i	0.0122193	+	0.0211644i
$996$		0			0
$997$	−48.4724			−1.53514			−0.767568	−	0.640967i	$-0.778534\pi$
$997$	−48.4724			−1.53514			−0.767568	+	0.640967i	$0.778534\pi$
$998$		0			0
$999$	2.59934	+	4.50219i	0.0822395	+	0.142443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.10	✓	24
67.29	even	3	inner	4020.2.q.m.3781.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.10	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.10	yes	24	67.29	even	3	inner

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(1.00432 - 1.73954i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(1.00432 - 1.73954i) q^{7} +1.00000 q^{9} +(0.449173 - 0.777991i) q^{11} +(1.97093 + 3.41375i) q^{13} +1.00000 q^{15} +(0.257734 + 0.446409i) q^{17} +(-0.443489 - 0.768146i) q^{19} +(1.00432 - 1.73954i) q^{21} +(3.81397 + 6.60599i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-1.58144 + 2.73914i) q^{29} +(3.37847 - 5.85168i) q^{31} +(0.449173 - 0.777991i) q^{33} +(1.00432 - 1.73954i) q^{35} +(2.59934 + 4.50219i) q^{37} +(1.97093 + 3.41375i) q^{39} +(2.35166 - 4.07319i) q^{41} -8.28809 q^{43} +1.00000 q^{45} +(-2.65239 + 4.59408i) q^{47} +(1.48267 + 2.56805i) q^{49} +(0.257734 + 0.446409i) q^{51} +9.38940 q^{53} +(0.449173 - 0.777991i) q^{55} +(-0.443489 - 0.768146i) q^{57} +8.88190 q^{59} +(-0.714054 - 1.23678i) q^{61} +(1.00432 - 1.73954i) q^{63} +(1.97093 + 3.41375i) q^{65} +(-7.15136 + 3.98222i) q^{67} +(3.81397 + 6.60599i) q^{69} +(2.30559 - 3.99341i) q^{71} +(1.17004 + 2.02657i) q^{73} +1.00000 q^{75} +(-0.902231 - 1.56271i) q^{77} +(1.31656 - 2.28035i) q^{79} +1.00000 q^{81} +(-2.20208 - 3.81411i) q^{83} +(0.257734 + 0.446409i) q^{85} +(-1.58144 + 2.73914i) q^{87} -5.68320 q^{89} +7.91782 q^{91} +(3.37847 - 5.85168i) q^{93} +(-0.443489 - 0.768146i) q^{95} +(-1.26978 - 2.19933i) q^{97} +(0.449173 - 0.777991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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