LMFDB - Embedded newform 4020.2.q.l.3781.5

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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.5
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.l.841.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(-0.533315 - 0.923729i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.533315 - 0.923729i) q^{7} +1.00000 q^{9} +(-2.16674 - 3.75291i) q^{11} +(0.803167 - 1.39113i) q^{13} +1.00000 q^{15} +(0.990595 - 1.71576i) q^{17} +(-1.89307 + 3.27889i) q^{19} +(0.533315 + 0.923729i) q^{21} +(-0.666244 + 1.15397i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.0815690 + 0.141282i) q^{29} +(-2.43547 - 4.21836i) q^{31} +(2.16674 + 3.75291i) q^{33} +(0.533315 + 0.923729i) q^{35} +(-0.247813 + 0.429225i) q^{37} +(-0.803167 + 1.39113i) q^{39} +(-1.78987 - 3.10014i) q^{41} -8.04481 q^{43} -1.00000 q^{45} +(-5.89637 - 10.2128i) q^{47} +(2.93115 - 5.07690i) q^{49} +(-0.990595 + 1.71576i) q^{51} +11.9905 q^{53} +(2.16674 + 3.75291i) q^{55} +(1.89307 - 3.27889i) q^{57} +7.23368 q^{59} +(-4.37004 + 7.56912i) q^{61} +(-0.533315 - 0.923729i) q^{63} +(-0.803167 + 1.39113i) q^{65} +(2.49766 + 7.79498i) q^{67} +(0.666244 - 1.15397i) q^{69} +(0.647635 + 1.12174i) q^{71} +(4.34664 - 7.52860i) q^{73} -1.00000 q^{75} +(-2.31111 + 4.00296i) q^{77} +(7.53219 + 13.0461i) q^{79} +1.00000 q^{81} +(-5.30202 + 9.18337i) q^{83} +(-0.990595 + 1.71576i) q^{85} +(-0.0815690 - 0.141282i) q^{87} -0.177574 q^{89} -1.71336 q^{91} +(2.43547 + 4.21836i) q^{93} +(1.89307 - 3.27889i) q^{95} +(-8.71138 + 15.0885i) q^{97} +(-2.16674 - 3.75291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$7$	−0.533315	−	0.923729i	−0.201574	−	0.349137i	0.747462	−	0.664305i	$-0.231272\pi$
$7$	−0.533315	−	0.923729i	−0.201574	−	0.349137i	−0.949036	+	0.315168i	$0.897939\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.16674	−	3.75291i	−0.653297	−	1.13154i	−0.982318	−	0.187221i	$-0.940052\pi$
$11$	−2.16674	−	3.75291i	−0.653297	−	1.13154i	0.329020	−	0.944323i	$-0.393281\pi$
$12$		0			0
$13$	0.803167	−	1.39113i	0.222758	−	0.385829i	−0.732886	−	0.680351i	$-0.761827\pi$
$13$	0.803167	−	1.39113i	0.222758	−	0.385829i	0.955645	+	0.294522i	$0.0951606\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.990595	−	1.71576i	0.240254	−	0.416133i	−0.720532	−	0.693421i	$-0.756102\pi$
$17$	0.990595	−	1.71576i	0.240254	−	0.416133i	0.960787	+	0.277289i	$0.0894358\pi$
$18$		0			0
$19$	−1.89307	+	3.27889i	−0.434300	+	0.752229i	−0.997238	−	0.0742695i	$-0.976337\pi$
$19$	−1.89307	+	3.27889i	−0.434300	+	0.752229i	0.562938	+	0.826499i	$0.309671\pi$
$20$		0			0
$21$	0.533315	+	0.923729i	0.116379	+	0.201574i
$22$		0			0
$23$	−0.666244	+	1.15397i	−0.138921	+	0.240619i	−0.927089	−	0.374842i	$-0.877697\pi$
$23$	−0.666244	+	1.15397i	−0.138921	+	0.240619i	0.788167	+	0.615461i	$0.211030\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.0815690	+	0.141282i	0.0151470	+	0.0262353i	0.873500	−	0.486825i	$-0.161845\pi$
$29$	0.0815690	+	0.141282i	0.0151470	+	0.0262353i	−0.858353	+	0.513060i	$0.828512\pi$
$30$		0			0
$31$	−2.43547	−	4.21836i	−0.437424	−	0.757640i	0.560066	−	0.828448i	$-0.310776\pi$
$31$	−2.43547	−	4.21836i	−0.437424	−	0.757640i	−0.997490	+	0.0708075i	$0.977442\pi$
$32$		0			0
$33$	2.16674	+	3.75291i	0.377181	+	0.653297i
$34$		0			0
$35$	0.533315	+	0.923729i	0.0901467	+	0.156139i
$36$		0			0
$37$	−0.247813	+	0.429225i	−0.0407402	+	0.0705641i	−0.885677	−	0.464303i	$-0.846305\pi$
$37$	−0.247813	+	0.429225i	−0.0407402	+	0.0705641i	0.844936	+	0.534867i	$0.179638\pi$
$38$		0			0
$39$	−0.803167	+	1.39113i	−0.128610	+	0.222758i
$40$		0			0
$41$	−1.78987	−	3.10014i	−0.279530	−	0.484161i	0.691738	−	0.722149i	$-0.256845\pi$
$41$	−1.78987	−	3.10014i	−0.279530	−	0.484161i	−0.971268	+	0.237988i	$0.923512\pi$
$42$		0			0
$43$	−8.04481			−1.22682			−0.613411	−	0.789764i	$-0.710203\pi$
$43$	−8.04481			−1.22682			−0.613411	+	0.789764i	$0.710203\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−5.89637	−	10.2128i	−0.860074	−	1.48969i	−0.871856	−	0.489762i	$-0.837084\pi$
$47$	−5.89637	−	10.2128i	−0.860074	−	1.48969i	0.0117820	−	0.999931i	$-0.496250\pi$
$48$		0			0
$49$	2.93115	−	5.07690i	0.418736	−	0.725272i
$50$		0			0
$51$	−0.990595	+	1.71576i	−0.138711	+	0.240254i
$52$		0			0
$53$	11.9905			1.64703			0.823514	−	0.567296i	$-0.192010\pi$
$53$	11.9905			1.64703			0.823514	+	0.567296i	$0.192010\pi$
$54$		0			0
$55$	2.16674	+	3.75291i	0.292163	+	0.506042i
$56$		0			0
$57$	1.89307	−	3.27889i	0.250743	−	0.434300i
$58$		0			0
$59$	7.23368			0.941745			0.470873	−	0.882201i	$-0.343939\pi$
$59$	7.23368			0.941745			0.470873	+	0.882201i	$0.343939\pi$
$60$		0			0
$61$	−4.37004	+	7.56912i	−0.559526	+	0.969127i	0.438010	+	0.898970i	$0.355683\pi$
$61$	−4.37004	+	7.56912i	−0.559526	+	0.969127i	−0.997536	+	0.0701570i	$0.977650\pi$
$62$		0			0
$63$	−0.533315	−	0.923729i	−0.0671914	−	0.116379i
$64$		0			0
$65$	−0.803167	+	1.39113i	−0.0996206	+	0.172548i
$66$		0			0
$67$	2.49766	+	7.79498i	0.305137	+	0.952308i
$67$	2.49766	+	7.79498i	0.305137	+	0.952308i
$68$		0			0
$69$	0.666244	−	1.15397i	0.0802064	−	0.138921i
$70$		0			0
$71$	0.647635	+	1.12174i	0.0768602	+	0.133126i	0.901894	−	0.431958i	$-0.142177\pi$
$71$	0.647635	+	1.12174i	0.0768602	+	0.133126i	−0.825034	+	0.565084i	$0.808844\pi$
$72$		0			0
$73$	4.34664	−	7.52860i	0.508736	−	0.881156i	−0.491213	−	0.871039i	$-0.663446\pi$
$73$	4.34664	−	7.52860i	0.508736	−	0.881156i	0.999949	−	0.0101166i	$-0.00322028\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−2.31111	+	4.00296i	−0.263376	+	0.456180i
$78$		0			0
$79$	7.53219	+	13.0461i	0.847438	+	1.46781i	0.883487	+	0.468455i	$0.155189\pi$
$79$	7.53219	+	13.0461i	0.847438	+	1.46781i	−0.0360493	+	0.999350i	$0.511477\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.30202	+	9.18337i	−0.581972	+	1.00801i	0.413273	+	0.910607i	$0.364385\pi$
$83$	−5.30202	+	9.18337i	−0.581972	+	1.00801i	−0.995245	+	0.0973984i	$0.968948\pi$
$84$		0			0
$85$	−0.990595	+	1.71576i	−0.107445	+	0.186100i
$86$		0			0
$87$	−0.0815690	−	0.141282i	−0.00874511	−	0.0151470i
$88$		0			0
$89$	−0.177574			−0.0188228			−0.00941141	−	0.999956i	$-0.502996\pi$
$89$	−0.177574			−0.0188228			−0.00941141	+	0.999956i	$0.502996\pi$
$90$		0			0
$91$	−1.71336			−0.179609
$92$		0			0
$93$	2.43547	+	4.21836i	0.252547	+	0.437424i
$94$		0			0
$95$	1.89307	−	3.27889i	0.194225	−	0.336407i
$96$		0			0
$97$	−8.71138	+	15.0885i	−0.884506	+	1.53201i	−0.0382281	+	0.999269i	$0.512171\pi$
$97$	−8.71138	+	15.0885i	−0.884506	+	1.53201i	−0.846278	+	0.532741i	$0.821162\pi$
$98$		0			0
$99$	−2.16674	−	3.75291i	−0.217766	−	0.377181i
$100$		0			0
$101$	2.04586	+	3.54354i	0.203571	+	0.352596i	0.949677	−	0.313232i	$-0.101412\pi$
$101$	2.04586	+	3.54354i	0.203571	+	0.352596i	−0.746105	+	0.665828i	$0.768079\pi$
$102$		0			0
$103$	3.50973	+	6.07903i	0.345824	+	0.598984i	0.985503	−	0.169658i	$-0.0542662\pi$
$103$	3.50973	+	6.07903i	0.345824	+	0.598984i	−0.639679	+	0.768642i	$0.720933\pi$
$104$		0			0
$105$	−0.533315	−	0.923729i	−0.0520462	−	0.0901467i
$106$		0			0
$107$	5.34145			0.516378			0.258189	−	0.966094i	$-0.416874\pi$
$107$	5.34145			0.516378			0.258189	+	0.966094i	$0.416874\pi$
$108$		0			0
$109$	−19.3589			−1.85424			−0.927121	−	0.374762i	$-0.877724\pi$
$109$	−19.3589			−1.85424			−0.927121	+	0.374762i	$0.877724\pi$
$110$		0			0
$111$	0.247813	−	0.429225i	0.0235214	−	0.0407402i
$112$		0			0
$113$	−0.730292	−	1.26490i	−0.0687001	−	0.118992i	0.829629	−	0.558315i	$-0.188552\pi$
$113$	−0.730292	−	1.26490i	−0.0687001	−	0.118992i	−0.898329	+	0.439323i	$0.855218\pi$
$114$		0			0
$115$	0.666244	−	1.15397i	0.0621276	−	0.107608i
$116$		0			0
$117$	0.803167	−	1.39113i	0.0742528	−	0.128610i
$118$		0			0
$119$	−2.11320			−0.193716
$120$		0			0
$121$	−3.88954	+	6.73688i	−0.353595	+	0.612444i
$122$		0			0
$123$	1.78987	+	3.10014i	0.161387	+	0.279530i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.14155	−	14.1016i	−0.722445	−	1.25131i	−0.960017	−	0.279942i	$-0.909685\pi$
$127$	−8.14155	−	14.1016i	−0.722445	−	1.25131i	0.237571	−	0.971370i	$-0.423649\pi$
$128$		0			0
$129$	8.04481			0.708306
$130$		0			0
$131$	−11.0681			−0.967028			−0.483514	−	0.875337i	$-0.660640\pi$
$131$	−11.0681			−0.967028			−0.483514	+	0.875337i	$0.660640\pi$
$132$		0			0
$133$	4.03841			0.350174
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	4.08629			0.349115			0.174558	−	0.984647i	$-0.444150\pi$
$137$	4.08629			0.349115			0.174558	+	0.984647i	$0.444150\pi$
$138$		0			0
$139$	−5.49985			−0.466491			−0.233246	−	0.972418i	$-0.574935\pi$
$139$	−5.49985			−0.466491			−0.233246	+	0.972418i	$0.574935\pi$
$140$		0			0
$141$	5.89637	+	10.2128i	0.496564	+	0.860074i
$142$		0			0
$143$	−6.96102			−0.582110
$144$		0			0
$145$	−0.0815690	−	0.141282i	−0.00677393	−	0.0117328i
$146$		0			0
$147$	−2.93115	+	5.07690i	−0.241757	+	0.418736i
$148$		0			0
$149$	−5.06272			−0.414754			−0.207377	−	0.978261i	$-0.566493\pi$
$149$	−5.06272			−0.414754			−0.207377	+	0.978261i	$0.566493\pi$
$150$		0			0
$151$	−6.78345	+	11.7493i	−0.552029	+	0.956143i	0.446099	+	0.894984i	$0.352813\pi$
$151$	−6.78345	+	11.7493i	−0.552029	+	0.956143i	−0.998128	+	0.0611589i	$0.980520\pi$
$152$		0			0
$153$	0.990595	−	1.71576i	0.0800848	−	0.138711i
$154$		0			0
$155$	2.43547	+	4.21836i	0.195622	+	0.338827i
$156$		0			0
$157$	8.27605	−	14.3345i	0.660501	−	1.14402i	−0.319984	−	0.947423i	$-0.603677\pi$
$157$	8.27605	−	14.3345i	0.660501	−	1.14402i	0.980484	−	0.196598i	$-0.0629892\pi$
$158$		0			0
$159$	−11.9905			−0.950912
$160$		0			0
$161$	1.42127			0.112012
$162$		0			0
$163$	−2.52843	−	4.37936i	−0.198042	−	0.343018i	0.749852	−	0.661606i	$-0.230125\pi$
$163$	−2.52843	−	4.37936i	−0.198042	−	0.343018i	−0.947893	+	0.318588i	$0.896791\pi$
$164$		0			0
$165$	−2.16674	−	3.75291i	−0.168681	−	0.292163i
$166$		0			0
$167$	−3.50365	−	6.06851i	−0.271121	−	0.469595i	0.698028	−	0.716070i	$-0.254061\pi$
$167$	−3.50365	−	6.06851i	−0.271121	−	0.469595i	−0.969149	+	0.246475i	$0.920728\pi$
$168$		0			0
$169$	5.20985	+	9.02372i	0.400757	+	0.694132i
$170$		0			0
$171$	−1.89307	+	3.27889i	−0.144767	+	0.250743i
$172$		0			0
$173$	−1.22910	+	2.12886i	−0.0934467	+	0.161854i	−0.908959	−	0.416885i	$-0.863122\pi$
$173$	−1.22910	+	2.12886i	−0.0934467	+	0.161854i	0.815513	+	0.578739i	$0.196455\pi$
$174$		0			0
$175$	−0.533315	−	0.923729i	−0.0403148	−	0.0698273i
$176$		0			0
$177$	−7.23368			−0.543717
$178$		0			0
$179$	−5.88750			−0.440053			−0.220026	−	0.975494i	$-0.570614\pi$
$179$	−5.88750			−0.440053			−0.220026	+	0.975494i	$0.570614\pi$
$180$		0			0
$181$	−1.27218	−	2.20347i	−0.0945601	−	0.163783i	0.814865	−	0.579651i	$-0.196811\pi$
$181$	−1.27218	−	2.20347i	−0.0945601	−	0.163783i	−0.909425	+	0.415868i	$0.863478\pi$
$182$		0			0
$183$	4.37004	−	7.56912i	0.323042	−	0.559526i
$184$		0			0
$185$	0.247813	−	0.429225i	0.0182196	−	0.0315572i
$186$		0			0
$187$	−8.58545			−0.627830
$188$		0			0
$189$	0.533315	+	0.923729i	0.0387930	+	0.0671914i
$190$		0			0
$191$	−10.3249	+	17.8832i	−0.747083	+	1.29399i	0.202133	+	0.979358i	$0.435213\pi$
$191$	−10.3249	+	17.8832i	−0.747083	+	1.29399i	−0.949215	+	0.314627i	$0.898121\pi$
$192$		0			0
$193$	−25.2981			−1.82099			−0.910497	−	0.413516i	$-0.864301\pi$
$193$	−25.2981			−1.82099			−0.910497	+	0.413516i	$0.864301\pi$
$194$		0			0
$195$	0.803167	−	1.39113i	0.0575160	−	0.0996206i
$196$		0			0
$197$	12.0728	+	20.9107i	0.860149	+	1.48982i	0.871784	+	0.489890i	$0.162963\pi$
$197$	12.0728	+	20.9107i	0.860149	+	1.48982i	−0.0116347	+	0.999932i	$0.503704\pi$
$198$		0			0
$199$	−12.5371	+	21.7150i	−0.888735	+	1.53933i	−0.0473623	+	0.998878i	$0.515082\pi$
$199$	−12.5371	+	21.7150i	−0.888735	+	1.53933i	−0.841372	+	0.540456i	$0.818252\pi$
$200$		0			0
$201$	−2.49766	−	7.79498i	−0.176171	−	0.549815i
$202$		0			0
$203$	0.0870039	−	0.150695i	0.00610648	−	0.0105767i
$204$		0			0
$205$	1.78987	+	3.10014i	0.125010	+	0.216523i
$206$		0			0
$207$	−0.666244	+	1.15397i	−0.0463072	+	0.0802064i
$208$		0			0
$209$	16.4072			1.13491
$210$		0			0
$211$	2.48257	−	4.29993i	0.170907	−	0.296020i	−0.767830	−	0.640653i	$-0.778664\pi$
$211$	2.48257	−	4.29993i	0.170907	−	0.296020i	0.938737	+	0.344634i	$0.111997\pi$
$212$		0			0
$213$	−0.647635	−	1.12174i	−0.0443752	−	0.0768602i
$214$		0			0
$215$	8.04481			0.548651
$216$		0			0
$217$	−2.59775	+	4.49943i	−0.176347	+	0.305441i
$218$		0			0
$219$	−4.34664	+	7.52860i	−0.293719	+	0.508736i
$220$		0			0
$221$	−1.59123	−	2.75608i	−0.107037	−	0.185394i
$222$		0			0
$223$	−22.4992			−1.50666			−0.753330	−	0.657643i	$-0.771554\pi$
$223$	−22.4992			−1.50666			−0.753330	+	0.657643i	$0.771554\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	8.73156	+	15.1235i	0.579534	+	1.00378i	0.995533	+	0.0944174i	$0.0300988\pi$
$227$	8.73156	+	15.1235i	0.579534	+	1.00378i	−0.415998	+	0.909365i	$0.636568\pi$
$228$		0			0
$229$	−7.80114	+	13.5120i	−0.515514	+	0.892896i	0.484324	+	0.874889i	$0.339066\pi$
$229$	−7.80114	+	13.5120i	−0.515514	+	0.892896i	−0.999838	+	0.0180074i	$0.994268\pi$
$230$		0			0
$231$	2.31111	−	4.00296i	0.152060	−	0.263376i
$232$		0			0
$233$	−13.2046	−	22.8711i	−0.865064	−	1.49834i	−0.866983	−	0.498337i	$-0.833944\pi$
$233$	−13.2046	−	22.8711i	−0.865064	−	1.49834i	0.00191883	−	0.999998i	$-0.499389\pi$
$234$		0			0
$235$	5.89637	+	10.2128i	0.384637	+	0.666211i
$236$		0			0
$237$	−7.53219	−	13.0461i	−0.489268	−	0.847438i
$238$		0			0
$239$	−14.5480	−	25.1979i	−0.941033	−	1.62992i	−0.763506	−	0.645801i	$-0.776524\pi$
$239$	−14.5480	−	25.1979i	−0.941033	−	1.62992i	−0.177527	−	0.984116i	$-0.556810\pi$
$240$		0			0
$241$	−10.7913			−0.695131			−0.347566	−	0.937656i	$-0.612992\pi$
$241$	−10.7913			−0.695131			−0.347566	+	0.937656i	$0.612992\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−2.93115	+	5.07690i	−0.187264	+	0.324351i
$246$		0			0
$247$	3.04090	+	5.26699i	0.193488	+	0.335131i
$248$		0			0
$249$	5.30202	−	9.18337i	0.336002	−	0.581972i
$250$		0			0
$251$	−11.0082	+	19.0668i	−0.694833	+	1.20349i	0.275403	+	0.961329i	$0.411189\pi$
$251$	−11.0082	+	19.0668i	−0.694833	+	1.20349i	−0.970237	+	0.242158i	$0.922145\pi$
$252$		0			0
$253$	5.77432			0.363028
$254$		0			0
$255$	0.990595	−	1.71576i	0.0620334	−	0.107445i
$256$		0			0
$257$	0.0523856	+	0.0907344i	0.00326772	+	0.00565986i	0.867655	−	0.497167i	$-0.165627\pi$
$257$	0.0523856	+	0.0907344i	0.00326772	+	0.00565986i	−0.864387	+	0.502827i	$0.832293\pi$
$258$		0			0
$259$	0.528650			0.0328487
$260$		0			0
$261$	0.0815690	+	0.141282i	0.00504899	+	0.00874511i
$262$		0			0
$263$	29.3766			1.81144			0.905719	−	0.423878i	$-0.139331\pi$
$263$	29.3766			1.81144			0.905719	+	0.423878i	$0.139331\pi$
$264$		0			0
$265$	−11.9905			−0.736574
$266$		0			0
$267$	0.177574			0.0108674
$268$		0			0
$269$	10.7472			0.655267			0.327633	−	0.944805i	$-0.393749\pi$
$269$	10.7472			0.655267			0.327633	+	0.944805i	$0.393749\pi$
$270$		0			0
$271$	−26.1552			−1.58881			−0.794407	−	0.607386i	$-0.792218\pi$
$271$	−26.1552			−1.58881			−0.794407	+	0.607386i	$0.792218\pi$
$272$		0			0
$273$	1.71336			0.103697
$274$		0			0
$275$	−2.16674	−	3.75291i	−0.130659	−	0.226309i
$276$		0			0
$277$	12.9346			0.777162			0.388581	−	0.921415i	$-0.372965\pi$
$277$	12.9346			0.777162			0.388581	+	0.921415i	$0.372965\pi$
$278$		0			0
$279$	−2.43547	−	4.21836i	−0.145808	−	0.252547i
$280$		0			0
$281$	−10.0736	+	17.4479i	−0.600939	+	1.04086i	0.391740	+	0.920076i	$0.371873\pi$
$281$	−10.0736	+	17.4479i	−0.600939	+	1.04086i	−0.992679	+	0.120781i	$0.961460\pi$
$282$		0			0
$283$	16.7659			0.996628			0.498314	−	0.866997i	$-0.333953\pi$
$283$	16.7659			0.996628			0.498314	+	0.866997i	$0.333953\pi$
$284$		0			0
$285$	−1.89307	+	3.27889i	−0.112136	+	0.194225i
$286$		0			0
$287$	−1.90913	+	3.30671i	−0.112692	+	0.195189i
$288$		0			0
$289$	6.53744	+	11.3232i	0.384556	+	0.666070i
$290$		0			0
$291$	8.71138	−	15.0885i	0.510670	−	0.884506i
$292$		0			0
$293$	23.0689			1.34770			0.673849	−	0.738869i	$-0.264640\pi$
$293$	23.0689			1.34770			0.673849	+	0.738869i	$0.264640\pi$
$294$		0			0
$295$	−7.23368			−0.421161
$296$		0			0
$297$	2.16674	+	3.75291i	0.125727	+	0.217766i
$298$		0			0
$299$	1.07021	+	1.85366i	0.0618918	+	0.107200i
$300$		0			0
$301$	4.29042	+	7.43122i	0.247296	+	0.428328i
$302$		0			0
$303$	−2.04586	−	3.54354i	−0.117532	−	0.203571i
$304$		0			0
$305$	4.37004	−	7.56912i	0.250228	−	0.433407i
$306$		0			0
$307$	4.93496	−	8.54759i	0.281653	−	0.487837i	−0.690139	−	0.723677i	$-0.742451\pi$
$307$	4.93496	−	8.54759i	0.281653	−	0.487837i	0.971792	+	0.235840i	$0.0757840\pi$
$308$		0			0
$309$	−3.50973	−	6.07903i	−0.199661	−	0.345824i
$310$		0			0
$311$	−24.0360			−1.36296			−0.681479	−	0.731837i	$-0.738663\pi$
$311$	−24.0360			−1.36296			−0.681479	+	0.731837i	$0.738663\pi$
$312$		0			0
$313$	22.7291			1.28472			0.642361	−	0.766402i	$-0.277955\pi$
$313$	22.7291			1.28472			0.642361	+	0.766402i	$0.277955\pi$
$314$		0			0
$315$	0.533315	+	0.923729i	0.0300489	+	0.0520462i
$316$		0			0
$317$	−13.6521	+	23.6460i	−0.766776	+	1.32809i	0.172527	+	0.985005i	$0.444807\pi$
$317$	−13.6521	+	23.6460i	−0.766776	+	1.32809i	−0.939303	+	0.343090i	$0.888527\pi$
$318$		0			0
$319$	0.353478	−	0.612242i	0.0197910	−	0.0342789i
$320$		0			0
$321$	−5.34145			−0.298131
$322$		0			0
$323$	3.75053	+	6.49610i	0.208685	+	0.361453i
$324$		0			0
$325$	0.803167	−	1.39113i	0.0445517	−	0.0771658i
$326$		0			0
$327$	19.3589			1.07055
$328$		0			0
$329$	−6.28925	+	10.8933i	−0.346737	+	0.600567i
$330$		0			0
$331$	14.3698	+	24.8892i	0.789835	+	1.36803i	0.926068	+	0.377357i	$0.123167\pi$
$331$	14.3698	+	24.8892i	0.789835	+	1.36803i	−0.136233	+	0.990677i	$0.543500\pi$
$332$		0			0
$333$	−0.247813	+	0.429225i	−0.0135801	+	0.0235214i
$334$		0			0
$335$	−2.49766	−	7.79498i	−0.136462	−	0.425885i
$336$		0			0
$337$	−10.9431	+	18.9539i	−0.596106	+	1.03249i	0.397283	+	0.917696i	$0.369953\pi$
$337$	−10.9431	+	18.9539i	−0.596106	+	1.03249i	−0.993390	+	0.114790i	$0.963380\pi$
$338$		0			0
$339$	0.730292	+	1.26490i	0.0396640	+	0.0687001i
$340$		0			0
$341$	−10.5541	+	18.2802i	−0.571536	+	0.989929i
$342$		0			0
$343$	−13.7193			−0.740773
$344$		0			0
$345$	−0.666244	+	1.15397i	−0.0358694	+	0.0621276i
$346$		0			0
$347$	−6.85661	−	11.8760i	−0.368082	−	0.637537i	0.621184	−	0.783665i	$-0.286652\pi$
$347$	−6.85661	−	11.8760i	−0.368082	−	0.637537i	−0.989266	+	0.146128i	$0.953319\pi$
$348$		0			0
$349$	9.95719			0.532996			0.266498	−	0.963835i	$-0.414133\pi$
$349$	9.95719			0.532996			0.266498	+	0.963835i	$0.414133\pi$
$350$		0			0
$351$	−0.803167	+	1.39113i	−0.0428699	+	0.0742528i
$352$		0			0
$353$	−3.47663	+	6.02170i	−0.185042	+	0.320503i	−0.943591	−	0.331114i	$-0.892576\pi$
$353$	−3.47663	+	6.02170i	−0.185042	+	0.320503i	0.758548	+	0.651617i	$0.225909\pi$
$354$		0			0
$355$	−0.647635	−	1.12174i	−0.0343729	−	0.0595356i
$356$		0			0
$357$	2.11320			0.111842
$358$		0			0
$359$	−1.76364			−0.0930812			−0.0465406	−	0.998916i	$-0.514820\pi$
$359$	−1.76364			−0.0930812			−0.0465406	+	0.998916i	$0.514820\pi$
$360$		0			0
$361$	2.33258	+	4.04015i	0.122767	+	0.212639i
$362$		0			0
$363$	3.88954	−	6.73688i	0.204148	−	0.353595i
$364$		0			0
$365$	−4.34664	+	7.52860i	−0.227514	+	0.394065i
$366$		0			0
$367$	2.45501	+	4.25219i	0.128150	+	0.221963i	0.922960	−	0.384896i	$-0.125763\pi$
$367$	2.45501	+	4.25219i	0.128150	+	0.221963i	−0.794810	+	0.606859i	$0.792429\pi$
$368$		0			0
$369$	−1.78987	−	3.10014i	−0.0931768	−	0.161387i
$370$		0			0
$371$	−6.39474	−	11.0760i	−0.331998	−	0.575038i
$372$		0			0
$373$	8.01627	+	13.8846i	0.415066	+	0.718916i	0.995435	−	0.0954374i	$-0.0304250\pi$
$373$	8.01627	+	13.8846i	0.415066	+	0.718916i	−0.580369	+	0.814354i	$0.697092\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	0.262054			0.0134965
$378$		0			0
$379$	−18.0088	+	31.1921i	−0.925049	+	1.60223i	−0.133566	+	0.991040i	$0.542643\pi$
$379$	−18.0088	+	31.1921i	−0.925049	+	1.60223i	−0.791483	+	0.611191i	$0.790691\pi$
$380$		0			0
$381$	8.14155	+	14.1016i	0.417104	+	0.722445i
$382$		0			0
$383$	10.1527	−	17.5850i	0.518779	−	0.898552i	−0.480983	−	0.876730i	$-0.659720\pi$
$383$	10.1527	−	17.5850i	0.518779	−	0.898552i	0.999762	−	0.0218219i	$-0.00694667\pi$
$384$		0			0
$385$	2.31111	−	4.00296i	0.117785	−	0.204010i
$386$		0			0
$387$	−8.04481			−0.408941
$388$		0			0
$389$	18.0599	−	31.2806i	0.915672	−	1.58599i	0.109758	−	0.993958i	$-0.464992\pi$
$389$	18.0599	−	31.2806i	0.915672	−	1.58599i	0.805914	−	0.592033i	$-0.201674\pi$
$390$		0			0
$391$	1.31996	+	2.28623i	0.0667530	+	0.115620i
$392$		0			0
$393$	11.0681			0.558314
$394$		0			0
$395$	−7.53219	−	13.0461i	−0.378986	−	0.656423i
$396$		0			0
$397$	−19.7459			−0.991017			−0.495509	−	0.868603i	$-0.665018\pi$
$397$	−19.7459			−0.991017			−0.495509	+	0.868603i	$0.665018\pi$
$398$		0			0
$399$	−4.03841			−0.202173
$400$		0			0
$401$	−13.7036			−0.684325			−0.342162	−	0.939641i	$-0.611159\pi$
$401$	−13.7036			−0.684325			−0.342162	+	0.939641i	$0.611159\pi$
$402$		0			0
$403$	−7.82437			−0.389759
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	2.14779			0.106462
$408$		0			0
$409$	−6.58503	−	11.4056i	−0.325609	−	0.563971i	0.656026	−	0.754738i	$-0.272236\pi$
$409$	−6.58503	−	11.4056i	−0.325609	−	0.563971i	−0.981635	+	0.190767i	$0.938903\pi$
$410$		0			0
$411$	−4.08629			−0.201562
$412$		0			0
$413$	−3.85783	−	6.68196i	−0.189831	−	0.328798i
$414$		0			0
$415$	5.30202	−	9.18337i	0.260266	−	0.450794i
$416$		0			0
$417$	5.49985			0.269329
$418$		0			0
$419$	−5.79245	+	10.0328i	−0.282979	+	0.490135i	−0.972117	−	0.234496i	$-0.924656\pi$
$419$	−5.79245	+	10.0328i	−0.282979	+	0.490135i	0.689138	+	0.724630i	$0.257990\pi$
$420$		0			0
$421$	−14.7309	+	25.5146i	−0.717938	+	1.24351i	0.243877	+	0.969806i	$0.421581\pi$
$421$	−14.7309	+	25.5146i	−0.717938	+	1.24351i	−0.961815	+	0.273699i	$0.911753\pi$
$422$		0			0
$423$	−5.89637	−	10.2128i	−0.286691	−	0.496564i
$424$		0			0
$425$	0.990595	−	1.71576i	0.0480509	−	0.0832266i
$426$		0			0
$427$	9.32242			0.451144
$428$		0			0
$429$	6.96102			0.336081
$430$		0			0
$431$	−0.533246	−	0.923609i	−0.0256856	−	0.0444887i	0.852897	−	0.522079i	$-0.174844\pi$
$431$	−0.533246	−	0.923609i	−0.0256856	−	0.0444887i	−0.878582	+	0.477591i	$0.841510\pi$
$432$		0			0
$433$	−10.7829	−	18.6765i	−0.518193	−	0.897536i	−0.999777	−	0.0211360i	$-0.993272\pi$
$433$	−10.7829	−	18.6765i	−0.518193	−	0.897536i	0.481584	−	0.876400i	$-0.340062\pi$
$434$		0			0
$435$	0.0815690	+	0.141282i	0.00391093	+	0.00677393i
$436$		0			0
$437$	−2.52249	−	4.36908i	−0.120667	−	0.209002i
$438$		0			0
$439$	6.93786	−	12.0167i	0.331126	−	0.573527i	−0.651607	−	0.758557i	$-0.725905\pi$
$439$	6.93786	−	12.0167i	0.331126	−	0.573527i	0.982733	+	0.185030i	$0.0592381\pi$
$440$		0			0
$441$	2.93115	−	5.07690i	0.139579	−	0.241757i
$442$		0			0
$443$	−15.8007	−	27.3677i	−0.750716	−	1.30028i	−0.947476	−	0.319827i	$-0.896375\pi$
$443$	−15.8007	−	27.3677i	−0.750716	−	1.30028i	0.196760	−	0.980452i	$-0.436958\pi$
$444$		0			0
$445$	0.177574			0.00841782
$446$		0			0
$447$	5.06272			0.239458
$448$		0			0
$449$	−4.55570	−	7.89070i	−0.214997	−	0.372385i	0.738275	−	0.674500i	$-0.235641\pi$
$449$	−4.55570	−	7.89070i	−0.214997	−	0.372385i	−0.953272	+	0.302115i	$0.902307\pi$
$450$		0			0
$451$	−7.75637	+	13.4344i	−0.365233	+	0.632602i
$452$		0			0
$453$	6.78345	−	11.7493i	0.318714	−	0.552029i
$454$		0			0
$455$	1.71336			0.0803237
$456$		0			0
$457$	−13.9725	−	24.2011i	−0.653606	−	1.13208i	−0.982241	−	0.187622i	$-0.939922\pi$
$457$	−13.9725	−	24.2011i	−0.653606	−	1.13208i	0.328635	−	0.944457i	$-0.393411\pi$
$458$		0			0
$459$	−0.990595	+	1.71576i	−0.0462370	+	0.0800848i
$460$		0			0
$461$	35.3854			1.64806			0.824031	−	0.566545i	$-0.191720\pi$
$461$	35.3854			1.64806			0.824031	+	0.566545i	$0.191720\pi$
$462$		0			0
$463$	12.5154	−	21.6773i	0.581639	−	1.00743i	−0.413647	−	0.910437i	$-0.635745\pi$
$463$	12.5154	−	21.6773i	0.581639	−	1.00743i	0.995285	−	0.0969901i	$-0.0309215\pi$
$464$		0			0
$465$	−2.43547	−	4.21836i	−0.112942	−	0.195622i
$466$		0			0
$467$	7.97146	−	13.8070i	0.368875	−	0.638910i	−0.620515	−	0.784195i	$-0.713076\pi$
$467$	7.97146	−	13.8070i	0.368875	−	0.638910i	0.989390	+	0.145284i	$0.0464097\pi$
$468$		0			0
$469$	5.86841	−	6.46434i	0.270978	−	0.298495i
$470$		0			0
$471$	−8.27605	+	14.3345i	−0.381340	+	0.660501i
$472$		0			0
$473$	17.4310	+	30.1914i	0.801479	+	1.38820i
$474$		0			0
$475$	−1.89307	+	3.27889i	−0.0868600	+	0.150446i
$476$		0			0
$477$	11.9905			0.549010
$478$		0			0
$479$	21.0748	−	36.5025i	0.962930	−	1.66784i	0.247853	−	0.968798i	$-0.420275\pi$
$479$	21.0748	−	36.5025i	0.962930	−	1.66784i	0.715077	−	0.699046i	$-0.246392\pi$
$480$		0			0
$481$	0.398070	+	0.689478i	0.0181504	+	0.0314375i
$482$		0			0
$483$	−1.42127			−0.0646701
$484$		0			0
$485$	8.71138	−	15.0885i	0.395563	−	0.685136i
$486$		0			0
$487$	−3.27309	+	5.66915i	−0.148318	+	0.256894i	−0.930606	−	0.366023i	$-0.880719\pi$
$487$	−3.27309	+	5.66915i	−0.148318	+	0.256894i	0.782288	+	0.622917i	$0.214053\pi$
$488$		0			0
$489$	2.52843	+	4.37936i	0.114339	+	0.198042i
$490$		0			0
$491$	14.2575			0.643431			0.321716	−	0.946836i	$-0.395741\pi$
$491$	14.2575			0.643431			0.321716	+	0.946836i	$0.395741\pi$
$492$		0			0
$493$	0.323207			0.0145565
$494$		0			0
$495$	2.16674	+	3.75291i	0.0973878	+	0.168681i
$496$		0			0
$497$	0.690787	−	1.19648i	0.0309860	−	0.0536694i
$498$		0			0
$499$	−7.10745	+	12.3105i	−0.318173	+	0.551092i	−0.980107	−	0.198470i	$-0.936403\pi$
$499$	−7.10745	+	12.3105i	−0.318173	+	0.551092i	0.661934	+	0.749562i	$0.269736\pi$
$500$		0			0
$501$	3.50365	+	6.06851i	0.156532	+	0.271121i
$502$		0			0
$503$	3.08313	+	5.34015i	0.137470	+	0.238105i	0.926538	−	0.376200i	$-0.122770\pi$
$503$	3.08313	+	5.34015i	0.137470	+	0.238105i	−0.789068	+	0.614306i	$0.789436\pi$
$504$		0			0
$505$	−2.04586	−	3.54354i	−0.0910398	−	0.157686i
$506$		0			0
$507$	−5.20985	−	9.02372i	−0.231377	−	0.400757i
$508$		0			0
$509$	18.3740			0.814411			0.407206	−	0.913336i	$-0.366503\pi$
$509$	18.3740			0.814411			0.407206	+	0.913336i	$0.366503\pi$
$510$		0			0
$511$	−9.27251			−0.410192
$512$		0			0
$513$	1.89307	−	3.27889i	0.0835810	−	0.144767i
$514$		0			0
$515$	−3.50973	−	6.07903i	−0.154657	−	0.267874i
$516$		0			0
$517$	−25.5518	+	44.2571i	−1.12377	+	1.94642i
$518$		0			0
$519$	1.22910	−	2.12886i	0.0539515	−	0.0934467i
$520$		0			0
$521$	0.796816			0.0349091			0.0174546	−	0.999848i	$-0.494444\pi$
$521$	0.796816			0.0349091			0.0174546	+	0.999848i	$0.494444\pi$
$522$		0			0
$523$	10.9202	−	18.9143i	0.477505	−	0.827063i	−0.522162	−	0.852846i	$-0.674874\pi$
$523$	10.9202	−	18.9143i	0.477505	−	0.827063i	0.999668	+	0.0257827i	$0.00820781\pi$
$524$		0			0
$525$	0.533315	+	0.923729i	0.0232758	+	0.0403148i
$526$		0			0
$527$	−9.65027			−0.420372
$528$		0			0
$529$	10.6122	+	18.3809i	0.461402	+	0.799171i
$530$		0			0
$531$	7.23368			0.313915
$532$		0			0
$533$	−5.75025			−0.249071
$534$		0			0
$535$	−5.34145			−0.230931
$536$		0			0
$537$	5.88750			0.254065
$538$		0			0
$539$	−25.4042			−1.09424
$540$		0			0
$541$	12.4373			0.534723			0.267361	−	0.963596i	$-0.413848\pi$
$541$	12.4373			0.534723			0.267361	+	0.963596i	$0.413848\pi$
$542$		0			0
$543$	1.27218	+	2.20347i	0.0545943	+	0.0945601i
$544$		0			0
$545$	19.3589			0.829242
$546$		0			0
$547$	5.41456	+	9.37830i	0.231510	+	0.400987i	0.958253	−	0.285923i	$-0.0923000\pi$
$547$	5.41456	+	9.37830i	0.231510	+	0.400987i	−0.726743	+	0.686910i	$0.758967\pi$
$548$		0			0
$549$	−4.37004	+	7.56912i	−0.186509	+	0.323042i
$550$		0			0
$551$	−0.617663			−0.0263133
$552$		0			0
$553$	8.03406	−	13.9154i	0.341643	−	0.591743i
$554$		0			0
$555$	−0.247813	+	0.429225i	−0.0105191	+	0.0182196i
$556$		0			0
$557$	0.791619	+	1.37112i	0.0335420	+	0.0580964i	0.882309	−	0.470670i	$-0.155988\pi$
$557$	0.791619	+	1.37112i	0.0335420	+	0.0580964i	−0.848767	+	0.528767i	$0.822655\pi$
$558$		0			0
$559$	−6.46132	+	11.1913i	−0.273285	+	0.473343i
$560$		0			0
$561$	8.58545			0.362478
$562$		0			0
$563$	−23.2453			−0.979673			−0.489837	−	0.871814i	$-0.662944\pi$
$563$	−23.2453			−0.979673			−0.489837	+	0.871814i	$0.662944\pi$
$564$		0			0
$565$	0.730292	+	1.26490i	0.0307236	+	0.0532149i
$566$		0			0
$567$	−0.533315	−	0.923729i	−0.0223971	−	0.0387930i
$568$		0			0
$569$	−4.35265	−	7.53901i	−0.182473	−	0.316052i	0.760249	−	0.649631i	$-0.225077\pi$
$569$	−4.35265	−	7.53901i	−0.182473	−	0.316052i	−0.942722	+	0.333580i	$0.891743\pi$
$570$		0			0
$571$	−6.65788	−	11.5318i	−0.278624	−	0.482590i	0.692419	−	0.721495i	$-0.256545\pi$
$571$	−6.65788	−	11.5318i	−0.278624	−	0.482590i	−0.971043	+	0.238905i	$0.923212\pi$
$572$		0			0
$573$	10.3249	−	17.8832i	0.431328	−	0.747083i
$574$		0			0
$575$	−0.666244	+	1.15397i	−0.0277843	+	0.0481238i
$576$		0			0
$577$	19.8043	+	34.3021i	0.824464	+	1.42801i	0.902328	+	0.431050i	$0.141857\pi$
$577$	19.8043	+	34.3021i	0.824464	+	1.42801i	−0.0778640	+	0.996964i	$0.524810\pi$
$578$		0			0
$579$	25.2981			1.05135
$580$		0			0
$581$	11.3106			0.469242
$582$		0			0
$583$	−25.9804	−	44.9994i	−1.07600	−	1.86369i
$584$		0			0
$585$	−0.803167	+	1.39113i	−0.0332069	+	0.0575160i
$586$		0			0
$587$	−17.3644	+	30.0760i	−0.716706	+	1.24137i	0.245592	+	0.969373i	$0.421018\pi$
$587$	−17.3644	+	30.0760i	−0.716706	+	1.24137i	−0.962298	+	0.271998i	$0.912316\pi$
$588$		0			0
$589$	18.4421			0.759892
$590$		0			0
$591$	−12.0728	−	20.9107i	−0.496608	−	0.860149i
$592$		0			0
$593$	7.12725	−	12.3448i	0.292681	−	0.506938i	−0.681762	−	0.731574i	$-0.738786\pi$
$593$	7.12725	−	12.3448i	0.292681	−	0.506938i	0.974443	+	0.224636i	$0.0721193\pi$
$594$		0			0
$595$	2.11320			0.0866326
$596$		0			0
$597$	12.5371	−	21.7150i	0.513111	−	0.888735i
$598$		0			0
$599$	−3.57473	−	6.19162i	−0.146060	−	0.252983i	0.783708	−	0.621129i	$-0.213326\pi$
$599$	−3.57473	−	6.19162i	−0.146060	−	0.252983i	−0.929768	+	0.368147i	$0.879992\pi$
$600$		0			0
$601$	−10.5096	+	18.2031i	−0.428694	+	0.742520i	−0.996757	−	0.0804652i	$-0.974359\pi$
$601$	−10.5096	+	18.2031i	−0.428694	+	0.742520i	0.568064	+	0.822985i	$0.307693\pi$
$602$		0			0
$603$	2.49766	+	7.79498i	0.101712	+	0.317436i
$604$		0			0
$605$	3.88954	−	6.73688i	0.158132	−	0.273893i
$606$		0			0
$607$	−5.99837	−	10.3895i	−0.243466	−	0.421696i	0.718233	−	0.695803i	$-0.244951\pi$
$607$	−5.99837	−	10.3895i	−0.243466	−	0.421696i	−0.961699	+	0.274107i	$0.911618\pi$
$608$		0			0
$609$	−0.0870039	+	0.150695i	−0.00352558	+	0.00610648i
$610$		0			0
$611$	−18.9431			−0.766355
$612$		0			0
$613$	8.76632	−	15.1837i	0.354068	−	0.613265i	−0.632890	−	0.774242i	$-0.718131\pi$
$613$	8.76632	−	15.1837i	0.354068	−	0.613265i	0.986958	+	0.160977i	$0.0514646\pi$
$614$		0			0
$615$	−1.78987	−	3.10014i	−0.0721745	−	0.125010i
$616$		0			0
$617$	12.4758			0.502255			0.251128	−	0.967954i	$-0.419199\pi$
$617$	12.4758			0.502255			0.251128	+	0.967954i	$0.419199\pi$
$618$		0			0
$619$	16.3378	−	28.2979i	0.656672	−	1.13739i	−0.324800	−	0.945783i	$-0.605297\pi$
$619$	16.3378	−	28.2979i	0.656672	−	1.13739i	0.981472	−	0.191606i	$-0.0613696\pi$
$620$		0			0
$621$	0.666244	−	1.15397i	0.0267355	−	0.0463072i
$622$		0			0
$623$	0.0947030	+	0.164030i	0.00379419	+	0.00657174i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−16.4072			−0.655239
$628$		0			0
$629$	0.490964	+	0.850375i	0.0195760	+	0.0339067i
$630$		0			0
$631$	−11.2078	+	19.4125i	−0.446176	+	0.772799i	−0.998133	−	0.0610732i	$-0.980548\pi$
$631$	−11.2078	+	19.4125i	−0.446176	+	0.772799i	0.551958	+	0.833872i	$0.313881\pi$
$632$		0			0
$633$	−2.48257	+	4.29993i	−0.0986732	+	0.170907i
$634$		0			0
$635$	8.14155	+	14.1016i	0.323087	+	0.559604i
$636$		0			0
$637$	−4.70840	−	8.15520i	−0.186554	−	0.323121i
$638$		0			0
$639$	0.647635	+	1.12174i	0.0256201	+	0.0443752i
$640$		0			0
$641$	20.3201	+	35.1955i	0.802596	+	1.39014i	0.917902	+	0.396808i	$0.129882\pi$
$641$	20.3201	+	35.1955i	0.802596	+	1.39014i	−0.115305	+	0.993330i	$0.536785\pi$
$642$		0			0
$643$	40.4888			1.59672			0.798361	−	0.602180i	$-0.205701\pi$
$643$	40.4888			1.59672			0.798361	+	0.602180i	$0.205701\pi$
$644$		0			0
$645$	−8.04481			−0.316764
$646$		0			0
$647$	12.5564	−	21.7482i	0.493641	−	0.855012i	−0.506332	−	0.862339i	$-0.668999\pi$
$647$	12.5564	−	21.7482i	0.493641	−	0.855012i	0.999973	+	0.00732683i	$0.00233222\pi$
$648$		0			0
$649$	−15.6735	−	27.1473i	−0.615240	−	1.06563i
$650$		0			0
$651$	2.59775	−	4.49943i	0.101814	−	0.176347i
$652$		0			0
$653$	23.9503	−	41.4831i	0.937246	−	1.62336i	0.166668	−	0.986013i	$-0.446699\pi$
$653$	23.9503	−	41.4831i	0.937246	−	1.62336i	0.770578	−	0.637345i	$-0.219967\pi$
$654$		0			0
$655$	11.0681			0.432468
$656$		0			0
$657$	4.34664	−	7.52860i	0.169579	−	0.293719i
$658$		0			0
$659$	−5.37402	−	9.30808i	−0.209342	−	0.362591i	0.742165	−	0.670217i	$-0.233799\pi$
$659$	−5.37402	−	9.30808i	−0.209342	−	0.362591i	−0.951507	+	0.307626i	$0.900466\pi$
$660$		0			0
$661$	−41.0323			−1.59597			−0.797985	−	0.602677i	$-0.794101\pi$
$661$	−41.0323			−1.59597			−0.797985	+	0.602677i	$0.794101\pi$
$662$		0			0
$663$	1.59123	+	2.75608i	0.0617981	+	0.107037i
$664$		0			0
$665$	−4.03841			−0.156603
$666$		0			0
$667$	−0.217379			−0.00841696
$668$		0			0
$669$	22.4992			0.869870
$670$		0			0
$671$	37.8750			1.46215
$672$		0			0
$673$	24.5007			0.944431			0.472216	−	0.881483i	$-0.343454\pi$
$673$	24.5007			0.944431			0.472216	+	0.881483i	$0.343454\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−13.1437	−	22.7656i	−0.505155	−	0.874954i	−0.999982	−	0.00596294i	$-0.998102\pi$
$677$	−13.1437	−	22.7656i	−0.505155	−	0.874954i	0.494827	−	0.868991i	$-0.335231\pi$
$678$		0			0
$679$	18.5836			0.713175
$680$		0			0
$681$	−8.73156	−	15.1235i	−0.334594	−	0.579534i
$682$		0			0
$683$	5.83585	−	10.1080i	0.223302	−	0.386771i	−0.732506	−	0.680760i	$-0.761650\pi$
$683$	5.83585	−	10.1080i	0.223302	−	0.386771i	0.955809	+	0.293989i	$0.0949829\pi$
$684$		0			0
$685$	−4.08629			−0.156129
$686$		0			0
$687$	7.80114	−	13.5120i	0.297632	−	0.515514i
$688$		0			0
$689$	9.63041	−	16.6804i	0.366889	−	0.635471i
$690$		0			0
$691$	−12.2738	−	21.2588i	−0.466917	−	0.808725i	0.532368	−	0.846513i	$-0.321302\pi$
$691$	−12.2738	−	21.2588i	−0.466917	−	0.808725i	−0.999286	+	0.0377882i	$0.987969\pi$
$692$		0			0
$693$	−2.31111	+	4.00296i	−0.0877919	+	0.152060i
$694$		0			0
$695$	5.49985			0.208621
$696$		0			0
$697$	−7.09214			−0.268634
$698$		0			0
$699$	13.2046	+	22.8711i	0.499445	+	0.865064i
$700$		0			0
$701$	−4.90180	−	8.49017i	−0.185139	−	0.320669i	0.758485	−	0.651691i	$-0.225940\pi$
$701$	−4.90180	−	8.49017i	−0.185139	−	0.320669i	−0.943623	+	0.331022i	$0.892607\pi$
$702$		0			0
$703$	−0.938254	−	1.62510i	−0.0353869	−	0.0612919i
$704$		0			0
$705$	−5.89637	−	10.2128i	−0.222070	−	0.384637i
$706$		0			0
$707$	2.18218	−	3.77965i	0.0820694	−	0.142148i
$708$		0			0
$709$	−25.3875	+	43.9725i	−0.953449	+	1.65142i	−0.215572	+	0.976488i	$0.569162\pi$
$709$	−25.3875	+	43.9725i	−0.953449	+	1.65142i	−0.737877	+	0.674935i	$0.764172\pi$
$710$		0			0
$711$	7.53219	+	13.0461i	0.282479	+	0.489268i
$712$		0			0
$713$	6.49048			0.243070
$714$		0			0
$715$	6.96102			0.260327
$716$		0			0
$717$	14.5480	+	25.1979i	0.543306	+	0.941033i
$718$		0			0
$719$	5.17918	−	8.97060i	0.193151	−	0.334547i	−0.753142	−	0.657858i	$-0.771463\pi$
$719$	5.17918	−	8.97060i	0.193151	−	0.334547i	0.946293	+	0.323311i	$0.104796\pi$
$720$		0			0
$721$	3.74358	−	6.48407i	0.139418	−	0.241479i
$722$		0			0
$723$	10.7913			0.401334
$724$		0			0
$725$	0.0815690	+	0.141282i	0.00302940	+	0.00524707i
$726$		0			0
$727$	−12.9887	+	22.4971i	−0.481725	+	0.834373i	−0.999780	−	0.0209746i	$-0.993323\pi$
$727$	−12.9887	+	22.4971i	−0.481725	+	0.834373i	0.518055	+	0.855348i	$0.326656\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−7.96914	+	13.8030i	−0.294749	+	0.510521i
$732$		0			0
$733$	16.6979	+	28.9215i	0.616749	+	1.06824i	0.990075	+	0.140541i	$0.0448841\pi$
$733$	16.6979	+	28.9215i	0.616749	+	1.06824i	−0.373326	+	0.927700i	$0.621783\pi$
$734$		0			0
$735$	2.93115	−	5.07690i	0.108117	−	0.187264i
$736$		0			0
$737$	23.8421	−	26.2632i	0.878233	−	0.967417i
$738$		0			0
$739$	−5.43367	+	9.41140i	−0.199881	+	0.346204i	−0.948490	−	0.316808i	$-0.897389\pi$
$739$	−5.43367	+	9.41140i	−0.199881	+	0.346204i	0.748609	+	0.663012i	$0.230722\pi$
$740$		0			0
$741$	−3.04090	−	5.26699i	−0.111710	−	0.193488i
$742$		0			0
$743$	−13.6430	+	23.6304i	−0.500514	+	0.866916i	0.499486	+	0.866322i	$0.333522\pi$
$743$	−13.6430	+	23.6304i	−0.500514	+	0.866916i	−1.00000		0.000593660i	$0.999811\pi$
$744$		0			0
$745$	5.06272			0.185484
$746$		0			0
$747$	−5.30202	+	9.18337i	−0.193991	+	0.336002i
$748$		0			0
$749$	−2.84868	−	4.93405i	−0.104088	−	0.180286i
$750$		0			0
$751$	−40.8075			−1.48909			−0.744543	−	0.667574i	$-0.767333\pi$
$751$	−40.8075			−1.48909			−0.744543	+	0.667574i	$0.767333\pi$
$752$		0			0
$753$	11.0082	−	19.0668i	0.401162	−	0.694833i
$754$		0			0
$755$	6.78345	−	11.7493i	0.246875	−	0.427600i
$756$		0			0
$757$	−21.9565	−	38.0298i	−0.798023	−	1.38222i	−0.920902	−	0.389794i	$-0.872546\pi$
$757$	−21.9565	−	38.0298i	−0.798023	−	1.38222i	0.122879	−	0.992422i	$-0.460787\pi$
$758$		0			0
$759$	−5.77432			−0.209594
$760$		0			0
$761$	7.74216			0.280653			0.140327	−	0.990105i	$-0.455185\pi$
$761$	7.74216			0.280653			0.140327	+	0.990105i	$0.455185\pi$
$762$		0			0
$763$	10.3244	+	17.8823i	0.373767	+	0.647384i
$764$		0			0
$765$	−0.990595	+	1.71576i	−0.0358150	+	0.0620334i
$766$		0			0
$767$	5.80985	−	10.0630i	0.209782	−	0.363352i
$768$		0			0
$769$	0.437877	+	0.758425i	0.0157902	+	0.0273495i	0.873813	−	0.486263i	$-0.161640\pi$
$769$	0.437877	+	0.758425i	0.0157902	+	0.0273495i	−0.858022	+	0.513612i	$0.828307\pi$
$770$		0			0
$771$	−0.0523856	−	0.0907344i	−0.00188662	−	0.00326772i
$772$		0			0
$773$	7.04211	+	12.1973i	0.253287	+	0.438706i	0.964429	−	0.264342i	$-0.0851549\pi$
$773$	7.04211	+	12.1973i	0.253287	+	0.438706i	−0.711142	+	0.703049i	$0.751822\pi$
$774$		0			0
$775$	−2.43547	−	4.21836i	−0.0874848	−	0.151528i
$776$		0			0
$777$	−0.528650			−0.0189652
$778$		0			0
$779$	13.5534			0.485600
$780$		0			0
$781$	2.80652	−	4.86103i	0.100425	−	0.173941i
$782$		0			0
$783$	−0.0815690	−	0.141282i	−0.00291504	−	0.00504899i
$784$		0			0
$785$	−8.27605	+	14.3345i	−0.295385	+	0.511622i
$786$		0			0
$787$	1.35079	−	2.33964i	0.0481505	−	0.0833991i	−0.840946	−	0.541120i	$-0.818001\pi$
$787$	1.35079	−	2.33964i	0.0481505	−	0.0833991i	0.889096	+	0.457721i	$0.151334\pi$
$788$		0			0
$789$	−29.3766			−1.04583
$790$		0			0
$791$	−0.778952	+	1.34918i	−0.0276963	+	0.0479715i
$792$		0			0
$793$	7.01973	+	12.1585i	0.249278	+	0.431762i
$794$		0			0
$795$	11.9905			0.425261
$796$		0			0
$797$	−12.6333	−	21.8815i	−0.447493	−	0.775081i	0.550729	−	0.834684i	$-0.314350\pi$
$797$	−12.6333	−	21.8815i	−0.447493	−	0.775081i	−0.998222	+	0.0596029i	$0.981017\pi$
$798$		0			0
$799$	−23.3637			−0.826547
$800$		0			0
$801$	−0.177574			−0.00627427
$802$		0			0
$803$	−37.6722			−1.32942
$804$		0			0
$805$	−1.42127			−0.0500933
$806$		0			0
$807$	−10.7472			−0.378318
$808$		0			0
$809$	51.6700			1.81662			0.908310	−	0.418299i	$-0.137373\pi$
$809$	51.6700			1.81662			0.908310	+	0.418299i	$0.137373\pi$
$810$		0			0
$811$	20.4218	+	35.3716i	0.717106	+	1.24206i	0.962142	+	0.272549i	$0.0878668\pi$
$811$	20.4218	+	35.3716i	0.717106	+	1.24206i	−0.245036	+	0.969514i	$0.578800\pi$
$812$		0			0
$813$	26.1552			0.917302
$814$		0			0
$815$	2.52843	+	4.37936i	0.0885670	+	0.153402i
$816$		0			0
$817$	15.2294	−	26.3780i	0.532808	−	0.922851i
$818$		0			0
$819$	−1.71336			−0.0598698
$820$		0			0
$821$	−7.87403	+	13.6382i	−0.274806	+	0.475977i	−0.970086	−	0.242761i	$-0.921947\pi$
$821$	−7.87403	+	13.6382i	−0.274806	+	0.475977i	0.695280	+	0.718739i	$0.255280\pi$
$822$		0			0
$823$	8.78977	−	15.2243i	0.306392	−	0.530687i	−0.671178	−	0.741296i	$-0.734211\pi$
$823$	8.78977	−	15.2243i	0.306392	−	0.530687i	0.977570	+	0.210609i	$0.0675448\pi$
$824$		0			0
$825$	2.16674	+	3.75291i	0.0754363	+	0.130659i
$826$		0			0
$827$	−26.3049	+	45.5614i	−0.914710	+	1.58432i	−0.107385	+	0.994217i	$0.534248\pi$
$827$	−26.3049	+	45.5614i	−0.914710	+	1.58432i	−0.807325	+	0.590107i	$0.799086\pi$
$828$		0			0
$829$	−12.5790			−0.436887			−0.218443	−	0.975850i	$-0.570098\pi$
$829$	−12.5790			−0.436887			−0.218443	+	0.975850i	$0.570098\pi$
$830$		0			0
$831$	−12.9346			−0.448695
$832$		0			0
$833$	−5.80716	−	10.0583i	−0.201206	−	0.348499i
$834$		0			0
$835$	3.50365	+	6.06851i	0.121249	+	0.210009i
$836$		0			0
$837$	2.43547	+	4.21836i	0.0841823	+	0.145808i
$838$		0			0
$839$	7.09738	+	12.2930i	0.245029	+	0.424402i	0.962140	−	0.272557i	$-0.0878692\pi$
$839$	7.09738	+	12.2930i	0.245029	+	0.424402i	−0.717111	+	0.696959i	$0.754536\pi$
$840$		0			0
$841$	14.4867	−	25.0917i	0.499541	−	0.865231i
$842$		0			0
$843$	10.0736	−	17.4479i	0.346952	−	0.600939i
$844$		0			0
$845$	−5.20985	−	9.02372i	−0.179224	−	0.310425i
$846$		0			0
$847$	8.29741			0.285102
$848$		0			0
$849$	−16.7659			−0.575404
$850$		0			0
$851$	−0.330208	−	0.571937i	−0.0113194	−	0.0196057i
$852$		0			0
$853$	2.25392	−	3.90390i	0.0771727	−	0.133667i	−0.824856	−	0.565342i	$-0.808744\pi$
$853$	2.25392	−	3.90390i	0.0771727	−	0.133667i	0.902029	+	0.431675i	$0.142077\pi$
$854$		0			0
$855$	1.89307	−	3.27889i	0.0647416	−	0.112136i
$856$		0			0
$857$	2.19611			0.0750176			0.0375088	−	0.999296i	$-0.488058\pi$
$857$	2.19611			0.0750176			0.0375088	+	0.999296i	$0.488058\pi$
$858$		0			0
$859$	−14.3704	−	24.8903i	−0.490313	−	0.849246i	0.509625	−	0.860397i	$-0.329784\pi$
$859$	−14.3704	−	24.8903i	−0.490313	−	0.849246i	−0.999938	+	0.0111501i	$0.996451\pi$
$860$		0			0
$861$	1.90913	−	3.30671i	0.0650629	−	0.112692i
$862$		0			0
$863$	−20.1376			−0.685492			−0.342746	−	0.939428i	$-0.611357\pi$
$863$	−20.1376			−0.685492			−0.342746	+	0.939428i	$0.611357\pi$
$864$		0			0
$865$	1.22910	−	2.12886i	0.0417906	−	0.0723835i
$866$		0			0
$867$	−6.53744	−	11.3232i	−0.222023	−	0.384556i
$868$		0			0
$869$	32.6406	−	56.5352i	1.10726	−	1.91783i
$870$		0			0
$871$	12.8498	+	2.78611i	0.435400	+	0.0944039i
$872$		0			0
$873$	−8.71138	+	15.0885i	−0.294835	+	0.510670i
$874$		0			0
$875$	0.533315	+	0.923729i	0.0180293	+	0.0312277i
$876$		0			0
$877$	−14.2506	+	24.6827i	−0.481207	+	0.833476i	−0.999767	−	0.0215655i	$-0.993135\pi$
$877$	−14.2506	+	24.6827i	−0.481207	+	0.833476i	0.518560	+	0.855041i	$0.326468\pi$
$878$		0			0
$879$	−23.0689			−0.778094
$880$		0			0
$881$	15.5244	−	26.8891i	0.523031	−	0.905917i	−0.476610	−	0.879115i	$-0.658134\pi$
$881$	15.5244	−	26.8891i	0.523031	−	0.905917i	0.999641	−	0.0268015i	$-0.00853221\pi$
$882$		0			0
$883$	14.4827	+	25.0849i	0.487383	+	0.844173i	0.999895	−	0.0145078i	$-0.00461812\pi$
$883$	14.4827	+	25.0849i	0.487383	+	0.844173i	−0.512511	+	0.858680i	$0.671285\pi$
$884$		0			0
$885$	7.23368			0.243158
$886$		0			0
$887$	10.2370	−	17.7310i	0.343724	−	0.595347i	−0.641397	−	0.767209i	$-0.721645\pi$
$887$	10.2370	−	17.7310i	0.343724	−	0.595347i	0.985121	+	0.171862i	$0.0549782\pi$
$888$		0			0
$889$	−8.68402	+	15.0412i	−0.291253	+	0.504464i
$890$		0			0
$891$	−2.16674	−	3.75291i	−0.0725886	−	0.125727i
$892$		0			0
$893$	44.6490			1.49412
$894$		0			0
$895$	5.88750			0.196798
$896$		0			0
$897$	−1.07021	−	1.85366i	−0.0357333	−	0.0618918i
$898$		0			0
$899$	0.397318	−	0.688175i	0.0132513	−	0.0229519i
$900$		0			0
$901$	11.8778	−	20.5729i	0.395706	−	0.685383i
$902$		0			0
$903$	−4.29042	−	7.43122i	−0.142776	−	0.247296i
$904$		0			0
$905$	1.27218	+	2.20347i	0.0422886	+	0.0732459i
$906$		0			0
$907$	13.9962	+	24.2422i	0.464737	+	0.804948i	0.999190	−	0.0402506i	$-0.0128156\pi$
$907$	13.9962	+	24.2422i	0.464737	+	0.804948i	−0.534453	+	0.845198i	$0.679482\pi$
$908$		0			0
$909$	2.04586	+	3.54354i	0.0678570	+	0.117532i
$910$		0			0
$911$	−22.5750			−0.747944			−0.373972	−	0.927440i	$-0.622004\pi$
$911$	−22.5750			−0.747944			−0.373972	+	0.927440i	$0.622004\pi$
$912$		0			0
$913$	45.9524			1.52080
$914$		0			0
$915$	−4.37004	+	7.56912i	−0.144469	+	0.250228i
$916$		0			0
$917$	5.90280	+	10.2240i	0.194928	+	0.337625i
$918$		0			0
$919$	25.2070	−	43.6599i	0.831503	−	1.44021i	−0.0653430	−	0.997863i	$-0.520814\pi$
$919$	25.2070	−	43.6599i	0.831503	−	1.44021i	0.896846	−	0.442343i	$-0.145853\pi$
$920$		0			0
$921$	−4.93496	+	8.54759i	−0.162612	+	0.281653i
$922$		0			0
$923$	2.08064			0.0684850
$924$		0			0
$925$	−0.247813	+	0.429225i	−0.00814804	+	0.0141128i
$926$		0			0
$927$	3.50973	+	6.07903i	0.115275	+	0.199661i
$928$		0			0
$929$	4.31660			0.141623			0.0708115	−	0.997490i	$-0.477441\pi$
$929$	4.31660			0.141623			0.0708115	+	0.997490i	$0.477441\pi$
$930$		0			0
$931$	11.0977	+	19.2218i	0.363714	+	0.629971i
$932$		0			0
$933$	24.0360			0.786905
$934$		0			0
$935$	8.58545			0.280774
$936$		0			0
$937$	21.2293			0.693531			0.346766	−	0.937952i	$-0.387280\pi$
$937$	21.2293			0.693531			0.346766	+	0.937952i	$0.387280\pi$
$938$		0			0
$939$	−22.7291			−0.741735
$940$		0			0
$941$	9.35916			0.305100			0.152550	−	0.988296i	$-0.451251\pi$
$941$	9.35916			0.305100			0.152550	+	0.988296i	$0.451251\pi$
$942$		0			0
$943$	4.76996			0.155331
$944$		0			0
$945$	−0.533315	−	0.923729i	−0.0173487	−	0.0300489i
$946$		0			0
$947$	−47.4322			−1.54134			−0.770670	−	0.637234i	$-0.780078\pi$
$947$	−47.4322			−1.54134			−0.770670	+	0.637234i	$0.780078\pi$
$948$		0			0
$949$	−6.98215	−	12.0934i	−0.226650	−	0.392570i
$950$		0			0
$951$	13.6521	−	23.6460i	0.442698	−	0.766776i
$952$		0			0
$953$	3.66381			0.118682			0.0593412	−	0.998238i	$-0.481100\pi$
$953$	3.66381			0.118682			0.0593412	+	0.998238i	$0.481100\pi$
$954$		0			0
$955$	10.3249	−	17.8832i	0.334106	−	0.578688i
$956$		0			0
$957$	−0.353478	+	0.612242i	−0.0114263	+	0.0197910i
$958$		0			0
$959$	−2.17928	−	3.77463i	−0.0703726	−	0.121889i
$960$		0			0
$961$	3.63694	−	6.29936i	0.117321	−	0.203205i
$962$		0			0
$963$	5.34145			0.172126
$964$		0			0
$965$	25.2981			0.814373
$966$		0			0
$967$	−19.1349	−	33.1426i	−0.615336	−	1.06579i	−0.990325	−	0.138765i	$-0.955687\pi$
$967$	−19.1349	−	33.1426i	−0.615336	−	1.06579i	0.374989	−	0.927029i	$-0.377646\pi$
$968$		0			0
$969$	−3.75053	−	6.49610i	−0.120484	−	0.208685i
$970$		0			0
$971$	−14.3238	−	24.8095i	−0.459672	−	0.796176i	0.539271	−	0.842132i	$-0.318700\pi$
$971$	−14.3238	−	24.8095i	−0.459672	−	0.796176i	−0.998943	+	0.0459564i	$0.985366\pi$
$972$		0			0
$973$	2.93315	+	5.08037i	0.0940325	+	0.162869i
$974$		0			0
$975$	−0.803167	+	1.39113i	−0.0257219	+	0.0445517i
$976$		0			0
$977$	2.28448	−	3.95683i	0.0730869	−	0.126590i	−0.827166	−	0.561958i	$-0.810048\pi$
$977$	2.28448	−	3.95683i	0.0730869	−	0.126590i	0.900253	+	0.435368i	$0.143382\pi$
$978$		0			0
$979$	0.384757	+	0.666419i	0.0122969	+	0.0212988i
$980$		0			0
$981$	−19.3589			−0.618081
$982$		0			0
$983$	−21.7634			−0.694146			−0.347073	−	0.937838i	$-0.612824\pi$
$983$	−21.7634			−0.694146			−0.347073	+	0.937838i	$0.612824\pi$
$984$		0			0
$985$	−12.0728	−	20.9107i	−0.384671	−	0.666269i
$986$		0			0
$987$	6.28925	−	10.8933i	0.200189	−	0.346737i
$988$		0			0
$989$	5.35980	−	9.28345i	0.170432	−	0.295197i
$990$		0			0
$991$	−26.0754			−0.828312			−0.414156	−	0.910206i	$-0.635923\pi$
$991$	−26.0754			−0.828312			−0.414156	+	0.910206i	$0.635923\pi$
$992$		0			0
$993$	−14.3698	−	24.8892i	−0.456011	−	0.789835i
$994$		0			0
$995$	12.5371	−	21.7150i	0.397454	−	0.688411i
$996$		0			0
$997$	−8.37122			−0.265119			−0.132560	−	0.991175i	$-0.542320\pi$
$997$	−8.37122			−0.265119			−0.132560	+	0.991175i	$0.542320\pi$
$998$		0			0
$999$	0.247813	−	0.429225i	0.00784046	−	0.0135801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.3781.5	yes	22
67.37	even	3	inner	4020.2.q.l.841.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.5	✓	22	67.37	even	3	inner
4020.2.q.l.3781.5	yes	22	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.533315 - 0.923729i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.533315 - 0.923729i) q^{7} +1.00000 q^{9} +(-2.16674 - 3.75291i) q^{11} +(0.803167 - 1.39113i) q^{13} +1.00000 q^{15} +(0.990595 - 1.71576i) q^{17} +(-1.89307 + 3.27889i) q^{19} +(0.533315 + 0.923729i) q^{21} +(-0.666244 + 1.15397i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.0815690 + 0.141282i) q^{29} +(-2.43547 - 4.21836i) q^{31} +(2.16674 + 3.75291i) q^{33} +(0.533315 + 0.923729i) q^{35} +(-0.247813 + 0.429225i) q^{37} +(-0.803167 + 1.39113i) q^{39} +(-1.78987 - 3.10014i) q^{41} -8.04481 q^{43} -1.00000 q^{45} +(-5.89637 - 10.2128i) q^{47} +(2.93115 - 5.07690i) q^{49} +(-0.990595 + 1.71576i) q^{51} +11.9905 q^{53} +(2.16674 + 3.75291i) q^{55} +(1.89307 - 3.27889i) q^{57} +7.23368 q^{59} +(-4.37004 + 7.56912i) q^{61} +(-0.533315 - 0.923729i) q^{63} +(-0.803167 + 1.39113i) q^{65} +(2.49766 + 7.79498i) q^{67} +(0.666244 - 1.15397i) q^{69} +(0.647635 + 1.12174i) q^{71} +(4.34664 - 7.52860i) q^{73} -1.00000 q^{75} +(-2.31111 + 4.00296i) q^{77} +(7.53219 + 13.0461i) q^{79} +1.00000 q^{81} +(-5.30202 + 9.18337i) q^{83} +(-0.990595 + 1.71576i) q^{85} +(-0.0815690 - 0.141282i) q^{87} -0.177574 q^{89} -1.71336 q^{91} +(2.43547 + 4.21836i) q^{93} +(1.89307 - 3.27889i) q^{95} +(-8.71138 + 15.0885i) q^{97} +(-2.16674 - 3.75291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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