LMFDB - Embedded newform 4020.2.q.l.841.2

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			841.2
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.l.3781.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(-1.77038 + 3.06640i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.77038 + 3.06640i) q^{7} +1.00000 q^{9} +(2.11772 - 3.66799i) q^{11} +(-1.76727 - 3.06101i) q^{13} +1.00000 q^{15} +(0.838031 + 1.45151i) q^{17} +(0.842285 + 1.45888i) q^{19} +(1.77038 - 3.06640i) q^{21} +(0.974890 + 1.68856i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-0.599657 + 1.03864i) q^{29} +(-0.178436 + 0.309060i) q^{31} +(-2.11772 + 3.66799i) q^{33} +(1.77038 - 3.06640i) q^{35} +(2.07455 + 3.59322i) q^{37} +(1.76727 + 3.06101i) q^{39} +(-5.74935 + 9.95817i) q^{41} -8.94175 q^{43} -1.00000 q^{45} +(2.77545 - 4.80722i) q^{47} +(-2.76852 - 4.79522i) q^{49} +(-0.838031 - 1.45151i) q^{51} -5.36916 q^{53} +(-2.11772 + 3.66799i) q^{55} +(-0.842285 - 1.45888i) q^{57} +5.02789 q^{59} +(-6.51830 - 11.2900i) q^{61} +(-1.77038 + 3.06640i) q^{63} +(1.76727 + 3.06101i) q^{65} +(-6.10237 - 5.45537i) q^{67} +(-0.974890 - 1.68856i) q^{69} +(3.35178 - 5.80545i) q^{71} +(1.14027 + 1.97501i) q^{73} -1.00000 q^{75} +(7.49834 + 12.9875i) q^{77} +(3.42355 - 5.92977i) q^{79} +1.00000 q^{81} +(-8.45371 - 14.6423i) q^{83} +(-0.838031 - 1.45151i) q^{85} +(0.599657 - 1.03864i) q^{87} +2.17767 q^{89} +12.5150 q^{91} +(0.178436 - 0.309060i) q^{93} +(-0.842285 - 1.45888i) q^{95} +(0.667481 + 1.15611i) q^{97} +(2.11772 - 3.66799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

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

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
$7$	−1.77038	+	3.06640i	−0.669142	+	1.15899i	0.309002	+	0.951061i	$0.400005\pi$
$7$	−1.77038	+	3.06640i	−0.669142	+	1.15899i	−0.978144	+	0.207927i	$0.933328\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.11772	−	3.66799i	0.638515	−	1.10594i	−0.347243	−	0.937775i	$-0.612882\pi$
$11$	2.11772	−	3.66799i	0.638515	−	1.10594i	0.985759	−	0.168166i	$-0.0537845\pi$
$12$		0			0
$13$	−1.76727	−	3.06101i	−0.490154	−	0.848971i	0.509782	−	0.860304i	$-0.329726\pi$
$13$	−1.76727	−	3.06101i	−0.490154	−	0.848971i	−0.999936	+	0.0113324i	$0.996393\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.838031	+	1.45151i	0.203252	+	0.352043i	0.949574	−	0.313542i	$-0.101516\pi$
$17$	0.838031	+	1.45151i	0.203252	+	0.352043i	−0.746322	+	0.665585i	$0.768182\pi$
$18$		0			0
$19$	0.842285	+	1.45888i	0.193233	+	0.334690i	0.946320	−	0.323231i	$-0.104769\pi$
$19$	0.842285	+	1.45888i	0.193233	+	0.334690i	−0.753087	+	0.657922i	$0.771436\pi$
$20$		0			0
$21$	1.77038	−	3.06640i	0.386330	−	0.669142i
$22$		0			0
$23$	0.974890	+	1.68856i	0.203279	+	0.352089i	0.949583	−	0.313516i	$-0.101507\pi$
$23$	0.974890	+	1.68856i	0.203279	+	0.352089i	−0.746304	+	0.665605i	$0.768174\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−0.599657	+	1.03864i	−0.111354	+	0.192870i	−0.916316	−	0.400455i	$-0.868852\pi$
$29$	−0.599657	+	1.03864i	−0.111354	+	0.192870i	0.804963	+	0.593325i	$0.202185\pi$
$30$		0			0
$31$	−0.178436	+	0.309060i	−0.0320480	+	0.0555088i	−0.881605	−	0.471989i	$-0.843536\pi$
$31$	−0.178436	+	0.309060i	−0.0320480	+	0.0555088i	0.849557	+	0.527498i	$0.176870\pi$
$32$		0			0
$33$	−2.11772	+	3.66799i	−0.368647	+	0.638515i
$34$		0			0
$35$	1.77038	−	3.06640i	0.299250	−	0.518315i
$36$		0			0
$37$	2.07455	+	3.59322i	0.341053	+	0.590722i	0.984629	−	0.174661i	$-0.0558829\pi$
$37$	2.07455	+	3.59322i	0.341053	+	0.590722i	−0.643575	+	0.765383i	$0.722550\pi$
$38$		0			0
$39$	1.76727	+	3.06101i	0.282990	+	0.490154i
$40$		0			0
$41$	−5.74935	+	9.95817i	−0.897898	+	1.55520i	−0.0677210	+	0.997704i	$0.521573\pi$
$41$	−5.74935	+	9.95817i	−0.897898	+	1.55520i	−0.830177	+	0.557500i	$0.811761\pi$
$42$		0			0
$43$	−8.94175			−1.36360			−0.681802	−	0.731537i	$-0.738803\pi$
$43$	−8.94175			−1.36360			−0.681802	+	0.731537i	$0.738803\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	2.77545	−	4.80722i	0.404841	−	0.701205i	−0.589462	−	0.807796i	$-0.700660\pi$
$47$	2.77545	−	4.80722i	0.404841	−	0.701205i	0.994303	+	0.106591i	$0.0339937\pi$
$48$		0			0
$49$	−2.76852	−	4.79522i	−0.395503	−	0.685031i
$50$		0			0
$51$	−0.838031	−	1.45151i	−0.117348	−	0.203252i
$52$		0			0
$53$	−5.36916			−0.737511			−0.368755	−	0.929526i	$-0.620216\pi$
$53$	−5.36916			−0.737511			−0.368755	+	0.929526i	$0.620216\pi$
$54$		0			0
$55$	−2.11772	+	3.66799i	−0.285553	+	0.494592i
$56$		0			0
$57$	−0.842285	−	1.45888i	−0.111563	−	0.193233i
$58$		0			0
$59$	5.02789			0.654576			0.327288	−	0.944925i	$-0.393865\pi$
$59$	5.02789			0.654576			0.327288	+	0.944925i	$0.393865\pi$
$60$		0			0
$61$	−6.51830	−	11.2900i	−0.834583	−	1.44554i	−0.894369	−	0.447329i	$-0.852375\pi$
$61$	−6.51830	−	11.2900i	−0.834583	−	1.44554i	0.0597861	−	0.998211i	$-0.480958\pi$
$62$		0			0
$63$	−1.77038	+	3.06640i	−0.223047	+	0.386330i
$64$		0			0
$65$	1.76727	+	3.06101i	0.219203	+	0.379671i
$66$		0			0
$67$	−6.10237	−	5.45537i	−0.745523	−	0.666480i
$67$	−6.10237	−	5.45537i	−0.745523	−	0.666480i
$68$		0			0
$69$	−0.974890	−	1.68856i	−0.117363	−	0.203279i
$70$		0			0
$71$	3.35178	−	5.80545i	0.397783	−	0.688980i	−0.595669	−	0.803230i	$-0.703113\pi$
$71$	3.35178	−	5.80545i	0.397783	−	0.688980i	0.993452	+	0.114250i	$0.0364465\pi$
$72$		0			0
$73$	1.14027	+	1.97501i	0.133459	+	0.231158i	0.925008	−	0.379948i	$-0.124058\pi$
$73$	1.14027	+	1.97501i	0.133459	+	0.231158i	−0.791549	+	0.611106i	$0.790725\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	7.49834	+	12.9875i	0.854516	+	1.48006i
$78$		0			0
$79$	3.42355	−	5.92977i	0.385180	−	0.667151i	−0.606614	−	0.794996i	$-0.707473\pi$
$79$	3.42355	−	5.92977i	0.385180	−	0.667151i	0.991794	+	0.127845i	$0.0408060\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−8.45371	−	14.6423i	−0.927916	−	1.60720i	−0.786804	−	0.617203i	$-0.788266\pi$
$83$	−8.45371	−	14.6423i	−0.927916	−	1.60720i	−0.141112	−	0.989994i	$-0.545068\pi$
$84$		0			0
$85$	−0.838031	−	1.45151i	−0.0908972	−	0.157439i
$86$		0			0
$87$	0.599657	−	1.03864i	0.0642900	−	0.111354i
$88$		0			0
$89$	2.17767			0.230832			0.115416	−	0.993317i	$-0.463180\pi$
$89$	2.17767			0.230832			0.115416	+	0.993317i	$0.463180\pi$
$90$		0			0
$91$	12.5150			1.31193
$92$		0			0
$93$	0.178436	−	0.309060i	0.0185029	−	0.0320480i
$94$		0			0
$95$	−0.842285	−	1.45888i	−0.0864166	−	0.149678i
$96$		0			0
$97$	0.667481	+	1.15611i	0.0677724	+	0.117385i	0.897920	−	0.440158i	$-0.145077\pi$
$97$	0.667481	+	1.15611i	0.0677724	+	0.117385i	−0.830148	+	0.557543i	$0.811744\pi$
$98$		0			0
$99$	2.11772	−	3.66799i	0.212838	−	0.368647i
$100$		0			0
$101$	7.15798	−	12.3980i	0.712245	−	1.23365i	−0.251767	−	0.967788i	$-0.581012\pi$
$101$	7.15798	−	12.3980i	0.712245	−	1.23365i	0.964012	−	0.265857i	$-0.0856550\pi$
$102$		0			0
$103$	−8.48839	+	14.7023i	−0.836386	+	1.44866i	0.0565112	+	0.998402i	$0.482002\pi$
$103$	−8.48839	+	14.7023i	−0.836386	+	1.44866i	−0.892897	+	0.450261i	$0.851331\pi$
$104$		0			0
$105$	−1.77038	+	3.06640i	−0.172772	+	0.299250i
$106$		0			0
$107$	8.72766			0.843734			0.421867	−	0.906658i	$-0.361375\pi$
$107$	8.72766			0.843734			0.421867	+	0.906658i	$0.361375\pi$
$108$		0			0
$109$	19.5468			1.87224			0.936121	−	0.351677i	$-0.114389\pi$
$109$	19.5468			1.87224			0.936121	+	0.351677i	$0.114389\pi$
$110$		0			0
$111$	−2.07455	−	3.59322i	−0.196907	−	0.341053i
$112$		0			0
$113$	−6.00367	+	10.3987i	−0.564778	+	0.978224i	0.432292	+	0.901734i	$0.357705\pi$
$113$	−6.00367	+	10.3987i	−0.564778	+	0.978224i	−0.997070	+	0.0764908i	$0.975628\pi$
$114$		0			0
$115$	−0.974890	−	1.68856i	−0.0909090	−	0.157459i
$116$		0			0
$117$	−1.76727	−	3.06101i	−0.163385	−	0.282990i
$118$		0			0
$119$	−5.93454			−0.544019
$120$		0			0
$121$	−3.46944	−	6.00925i	−0.315404	−	0.546296i
$122$		0			0
$123$	5.74935	−	9.95817i	0.518402	−	0.897898i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.03315	−	10.4497i	0.535355	−	0.927263i	−0.463791	−	0.885945i	$-0.653511\pi$
$127$	6.03315	−	10.4497i	0.535355	−	0.927263i	0.999146	−	0.0413180i	$-0.0131557\pi$
$128$		0			0
$129$	8.94175			0.787277
$130$		0			0
$131$	15.1963			1.32771			0.663853	−	0.747863i	$-0.268920\pi$
$131$	15.1963			1.32771			0.663853	+	0.747863i	$0.268920\pi$
$132$		0			0
$133$	−5.96467			−0.517203
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	6.55731			0.560229			0.280114	−	0.959967i	$-0.409628\pi$
$137$	6.55731			0.560229			0.280114	+	0.959967i	$0.409628\pi$
$138$		0			0
$139$	7.69275			0.652491			0.326245	−	0.945285i	$-0.394216\pi$
$139$	7.69275			0.652491			0.326245	+	0.945285i	$0.394216\pi$
$140$		0			0
$141$	−2.77545	+	4.80722i	−0.233735	+	0.404841i
$142$		0			0
$143$	−14.9703			−1.25188
$144$		0			0
$145$	0.599657	−	1.03864i	0.0497988	−	0.0862541i
$146$		0			0
$147$	2.76852	+	4.79522i	0.228344	+	0.395503i
$148$		0			0
$149$	18.4920			1.51493			0.757463	−	0.652879i	$-0.226439\pi$
$149$	18.4920			1.51493			0.757463	+	0.652879i	$0.226439\pi$
$150$		0			0
$151$	−5.32869	−	9.22956i	−0.433642	−	0.751091i	0.563541	−	0.826088i	$-0.309439\pi$
$151$	−5.32869	−	9.22956i	−0.433642	−	0.751091i	−0.997184	+	0.0749972i	$0.976105\pi$
$152$		0			0
$153$	0.838031	+	1.45151i	0.0677508	+	0.117348i
$154$		0			0
$155$	0.178436	−	0.309060i	0.0143323	−	0.0248243i
$156$		0			0
$157$	−6.40157	−	11.0879i	−0.510901	−	0.884907i	−0.999920	−	0.0126337i	$-0.995978\pi$
$157$	−6.40157	−	11.0879i	−0.510901	−	0.884907i	0.489019	−	0.872273i	$-0.337355\pi$
$158$		0			0
$159$	5.36916			0.425802
$160$		0			0
$161$	−6.90372			−0.544089
$162$		0			0
$163$	8.03386	−	13.9150i	0.629260	−	1.08991i	−0.358440	−	0.933553i	$-0.616691\pi$
$163$	8.03386	−	13.9150i	0.629260	−	1.08991i	0.987700	−	0.156358i	$-0.0499754\pi$
$164$		0			0
$165$	2.11772	−	3.66799i	0.164864	−	0.285553i
$166$		0			0
$167$	4.94195	−	8.55970i	0.382419	−	0.662369i	−0.608988	−	0.793179i	$-0.708424\pi$
$167$	4.94195	−	8.55970i	0.382419	−	0.662369i	0.991407	+	0.130810i	$0.0417577\pi$
$168$		0			0
$169$	0.253483	−	0.439045i	0.0194987	−	0.0337727i
$170$		0			0
$171$	0.842285	+	1.45888i	0.0644112	+	0.111563i
$172$		0			0
$173$	0.717488	+	1.24273i	0.0545496	+	0.0944827i	0.892011	−	0.452014i	$-0.149294\pi$
$173$	0.717488	+	1.24273i	0.0545496	+	0.0944827i	−0.837461	+	0.546497i	$0.815961\pi$
$174$		0			0
$175$	−1.77038	+	3.06640i	−0.133828	+	0.231798i
$176$		0			0
$177$	−5.02789			−0.377919
$178$		0			0
$179$	−5.78384			−0.432305			−0.216152	−	0.976360i	$-0.569351\pi$
$179$	−5.78384			−0.432305			−0.216152	+	0.976360i	$0.569351\pi$
$180$		0			0
$181$	10.7979	−	18.7025i	0.802602	−	1.39015i	−0.115296	−	0.993331i	$-0.536782\pi$
$181$	10.7979	−	18.7025i	0.802602	−	1.39015i	0.917898	−	0.396816i	$-0.129885\pi$
$182$		0			0
$183$	6.51830	+	11.2900i	0.481847	+	0.834583i
$184$		0			0
$185$	−2.07455	−	3.59322i	−0.152524	−	0.264179i
$186$		0			0
$187$	7.09884			0.519119
$188$		0			0
$189$	1.77038	−	3.06640i	0.128777	−	0.223047i
$190$		0			0
$191$	7.64232	+	13.2369i	0.552979	+	0.957788i	0.998058	+	0.0622965i	$0.0198424\pi$
$191$	7.64232	+	13.2369i	0.552979	+	0.957788i	−0.445079	+	0.895492i	$0.646824\pi$
$192$		0			0
$193$	24.2594			1.74623			0.873115	−	0.487514i	$-0.162096\pi$
$193$	24.2594			1.74623			0.873115	+	0.487514i	$0.162096\pi$
$194$		0			0
$195$	−1.76727	−	3.06101i	−0.126557	−	0.219203i
$196$		0			0
$197$	−10.3945	+	18.0037i	−0.740575	+	1.28271i	0.211659	+	0.977344i	$0.432113\pi$
$197$	−10.3945	+	18.0037i	−0.740575	+	1.28271i	−0.952234	+	0.305370i	$0.901220\pi$
$198$		0			0
$199$	−13.1359	−	22.7521i	−0.931180	−	1.61285i	−0.781307	−	0.624147i	$-0.785447\pi$
$199$	−13.1359	−	22.7521i	−0.931180	−	1.61285i	−0.149873	−	0.988705i	$-0.547887\pi$
$200$		0			0
$201$	6.10237	+	5.45537i	0.430428	+	0.384792i
$202$		0			0
$203$	−2.12325	−	3.67757i	−0.149023	−	0.258115i
$204$		0			0
$205$	5.74935	−	9.95817i	0.401552	−	0.695509i
$206$		0			0
$207$	0.974890	+	1.68856i	0.0677595	+	0.117363i
$208$		0			0
$209$	7.13488			0.493530
$210$		0			0
$211$	−11.7661	−	20.3795i	−0.810014	−	1.40299i	−0.912853	−	0.408288i	$-0.866126\pi$
$211$	−11.7661	−	20.3795i	−0.810014	−	1.40299i	0.102839	−	0.994698i	$-0.467207\pi$
$212$		0			0
$213$	−3.35178	+	5.80545i	−0.229660	+	0.397783i
$214$		0			0
$215$	8.94175			0.609822
$216$		0			0
$217$	−0.631800	−	1.09431i	−0.0428894	−	0.0742865i
$218$		0			0
$219$	−1.14027	−	1.97501i	−0.0770525	−	0.133459i
$220$		0			0
$221$	2.96206	−	5.13044i	0.199250	−	0.345111i
$222$		0			0
$223$	18.2423			1.22159			0.610797	−	0.791787i	$-0.290849\pi$
$223$	18.2423			1.22159			0.610797	+	0.791787i	$0.290849\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−2.91120	+	5.04234i	−0.193223	+	0.334672i	−0.946317	−	0.323241i	$-0.895227\pi$
$227$	−2.91120	+	5.04234i	−0.193223	+	0.334672i	0.753094	+	0.657913i	$0.228561\pi$
$228$		0			0
$229$	−0.619049	−	1.07222i	−0.0409079	−	0.0708546i	0.844847	−	0.535009i	$-0.179692\pi$
$229$	−0.619049	−	1.07222i	−0.0409079	−	0.0708546i	−0.885754	+	0.464154i	$0.846358\pi$
$230$		0			0
$231$	−7.49834	−	12.9875i	−0.493355	−	0.854516i
$232$		0			0
$233$	6.68989	−	11.5872i	0.438269	−	0.759105i	−0.559287	−	0.828974i	$-0.688925\pi$
$233$	6.68989	−	11.5872i	0.438269	−	0.759105i	0.997556	+	0.0698696i	$0.0222583\pi$
$234$		0			0
$235$	−2.77545	+	4.80722i	−0.181050	+	0.313588i
$236$		0			0
$237$	−3.42355	+	5.92977i	−0.222384	+	0.385180i
$238$		0			0
$239$	−2.35410	+	4.07743i	−0.152274	+	0.263747i	−0.932063	−	0.362296i	$-0.881993\pi$
$239$	−2.35410	+	4.07743i	−0.152274	+	0.263747i	0.779789	+	0.626043i	$0.215326\pi$
$240$		0			0
$241$	26.6832			1.71881			0.859407	−	0.511292i	$-0.170833\pi$
$241$	26.6832			1.71881			0.859407	+	0.511292i	$0.170833\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.76852	+	4.79522i	0.176874	+	0.306355i
$246$		0			0
$247$	2.97710	−	5.15649i	0.189428	−	0.328099i
$248$		0			0
$249$	8.45371	+	14.6423i	0.535732	+	0.927916i
$250$		0			0
$251$	−9.22375	−	15.9760i	−0.582198	−	1.00840i	−0.995218	−	0.0976749i	$-0.968859\pi$
$251$	−9.22375	−	15.9760i	−0.582198	−	1.00840i	0.413020	−	0.910722i	$-0.364474\pi$
$252$		0			0
$253$	8.25816			0.519186
$254$		0			0
$255$	0.838031	+	1.45151i	0.0524795	+	0.0908972i
$256$		0			0
$257$	6.01811	−	10.4237i	0.375399	−	0.650210i	−0.614988	−	0.788537i	$-0.710839\pi$
$257$	6.01811	−	10.4237i	0.375399	−	0.650210i	0.990387	+	0.138326i	$0.0441723\pi$
$258$		0			0
$259$	−14.6910			−0.912853
$260$		0			0
$261$	−0.599657	+	1.03864i	−0.0371178	+	0.0642900i
$262$		0			0
$263$	−7.69307			−0.474375			−0.237188	−	0.971464i	$-0.576226\pi$
$263$	−7.69307			−0.474375			−0.237188	+	0.971464i	$0.576226\pi$
$264$		0			0
$265$	5.36916			0.329825
$266$		0			0
$267$	−2.17767			−0.133271
$268$		0			0
$269$	−32.5624			−1.98536			−0.992682	−	0.120761i	$-0.961467\pi$
$269$	−32.5624			−1.98536			−0.992682	+	0.120761i	$0.961467\pi$
$270$		0			0
$271$	−7.11931			−0.432467			−0.216234	−	0.976342i	$-0.569377\pi$
$271$	−7.11931			−0.432467			−0.216234	+	0.976342i	$0.569377\pi$
$272$		0			0
$273$	−12.5150			−0.757443
$274$		0			0
$275$	2.11772	−	3.66799i	0.127703	−	0.221188i
$276$		0			0
$277$	−16.2722			−0.977703			−0.488851	−	0.872367i	$-0.662584\pi$
$277$	−16.2722			−0.977703			−0.488851	+	0.872367i	$0.662584\pi$
$278$		0			0
$279$	−0.178436	+	0.309060i	−0.0106827	+	0.0185029i
$280$		0			0
$281$	3.16694	+	5.48530i	0.188924	+	0.327225i	0.944892	−	0.327383i	$-0.106167\pi$
$281$	3.16694	+	5.48530i	0.188924	+	0.327225i	−0.755968	+	0.654609i	$0.772833\pi$
$282$		0			0
$283$	15.9720			0.949434			0.474717	−	0.880138i	$-0.342550\pi$
$283$	15.9720			0.949434			0.474717	+	0.880138i	$0.342550\pi$
$284$		0			0
$285$	0.842285	+	1.45888i	0.0498927	+	0.0864166i
$286$		0			0
$287$	−20.3571	−	35.2596i	−1.20164	−	2.08131i
$288$		0			0
$289$	7.09541	−	12.2896i	0.417377	−	0.722918i
$290$		0			0
$291$	−0.667481	−	1.15611i	−0.0391284	−	0.0677724i
$292$		0			0
$293$	−24.3375			−1.42181			−0.710906	−	0.703287i	$-0.751715\pi$
$293$	−24.3375			−1.42181			−0.710906	+	0.703287i	$0.751715\pi$
$294$		0			0
$295$	−5.02789			−0.292735
$296$		0			0
$297$	−2.11772	+	3.66799i	−0.122882	+	0.212838i
$298$		0			0
$299$	3.44580	−	5.96829i	0.199276	−	0.345155i
$300$		0			0
$301$	15.8303	−	27.4189i	0.912445	−	1.58040i
$302$		0			0
$303$	−7.15798	+	12.3980i	−0.411215	+	0.712245i
$304$		0			0
$305$	6.51830	+	11.2900i	0.373237	+	0.646465i
$306$		0			0
$307$	−7.29569	−	12.6365i	−0.416387	−	0.721204i	0.579186	−	0.815195i	$-0.303371\pi$
$307$	−7.29569	−	12.6365i	−0.416387	−	0.721204i	−0.995573	+	0.0939920i	$0.970037\pi$
$308$		0			0
$309$	8.48839	−	14.7023i	0.482888	−	0.836386i
$310$		0			0
$311$	−31.9348			−1.81086			−0.905428	−	0.424500i	$-0.860450\pi$
$311$	−31.9348			−1.81086			−0.905428	+	0.424500i	$0.860450\pi$
$312$		0			0
$313$	5.27372			0.298088			0.149044	−	0.988831i	$-0.452380\pi$
$313$	5.27372			0.298088			0.149044	+	0.988831i	$0.452380\pi$
$314$		0			0
$315$	1.77038	−	3.06640i	0.0997499	−	0.172772i
$316$		0			0
$317$	−7.47026	−	12.9389i	−0.419572	−	0.726719i	0.576325	−	0.817221i	$-0.304486\pi$
$317$	−7.47026	−	12.9389i	−0.419572	−	0.726719i	−0.995896	+	0.0905015i	$0.971153\pi$
$318$		0			0
$319$	2.53981	+	4.39908i	0.142202	+	0.246301i
$320$		0			0
$321$	−8.72766			−0.487130
$322$		0			0
$323$	−1.41172	+	2.44517i	−0.0785503	+	0.136053i
$324$		0			0
$325$	−1.76727	−	3.06101i	−0.0980307	−	0.169794i
$326$		0			0
$327$	−19.5468			−1.08094
$328$		0			0
$329$	9.82722	+	17.0212i	0.541792	+	0.938411i
$330$		0			0
$331$	2.69650	−	4.67048i	0.148213	−	0.256713i	−0.782354	−	0.622834i	$-0.785981\pi$
$331$	2.69650	−	4.67048i	0.148213	−	0.256713i	0.930567	+	0.366121i	$0.119314\pi$
$332$		0			0
$333$	2.07455	+	3.59322i	0.113684	+	0.196907i
$334$		0			0
$335$	6.10237	+	5.45537i	0.333408	+	0.298059i
$336$		0			0
$337$	10.8579	+	18.8065i	0.591469	+	1.02445i	0.994035	+	0.109063i	$0.0347852\pi$
$337$	10.8579	+	18.8065i	0.591469	+	1.02445i	−0.402566	+	0.915391i	$0.631882\pi$
$338$		0			0
$339$	6.00367	−	10.3987i	0.326075	−	0.564778i
$340$		0			0
$341$	0.755753	+	1.30900i	0.0409263	+	0.0708864i
$342$		0			0
$343$	−5.17999			−0.279693
$344$		0			0
$345$	0.974890	+	1.68856i	0.0524863	+	0.0909090i
$346$		0			0
$347$	3.18885	−	5.52325i	0.171186	−	0.296503i	−0.767649	−	0.640871i	$-0.778573\pi$
$347$	3.18885	−	5.52325i	0.171186	−	0.296503i	0.938835	+	0.344368i	$0.111907\pi$
$348$		0			0
$349$	−22.7930			−1.22008			−0.610039	−	0.792371i	$-0.708846\pi$
$349$	−22.7930			−1.22008			−0.610039	+	0.792371i	$0.708846\pi$
$350$		0			0
$351$	1.76727	+	3.06101i	0.0943301	+	0.163385i
$352$		0			0
$353$	10.2530	+	17.7587i	0.545713	+	0.945202i	0.998562	+	0.0536150i	$0.0170744\pi$
$353$	10.2530	+	17.7587i	0.545713	+	0.945202i	−0.452849	+	0.891587i	$0.649592\pi$
$354$		0			0
$355$	−3.35178	+	5.80545i	−0.177894	+	0.308121i
$356$		0			0
$357$	5.93454			0.314089
$358$		0			0
$359$	−20.8861			−1.10232			−0.551162	−	0.834398i	$-0.685816\pi$
$359$	−20.8861			−1.10232			−0.551162	+	0.834398i	$0.685816\pi$
$360$		0			0
$361$	8.08111	−	13.9969i	0.425322	−	0.736679i
$362$		0			0
$363$	3.46944	+	6.00925i	0.182099	+	0.315404i
$364$		0			0
$365$	−1.14027	−	1.97501i	−0.0596846	−	0.103377i
$366$		0			0
$367$	5.61631	−	9.72773i	0.293169	−	0.507783i	−0.681388	−	0.731922i	$-0.738624\pi$
$367$	5.61631	−	9.72773i	0.293169	−	0.507783i	0.974557	+	0.224139i	$0.0719569\pi$
$368$		0			0
$369$	−5.74935	+	9.95817i	−0.299299	+	0.518402i
$370$		0			0
$371$	9.50548	−	16.4640i	0.493500	−	0.854767i
$372$		0			0
$373$	−1.01629	+	1.76027i	−0.0526215	+	0.0911431i	−0.891136	−	0.453736i	$-0.850091\pi$
$373$	−1.01629	+	1.76027i	−0.0526215	+	0.0911431i	0.838515	+	0.544879i	$0.183424\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	4.23904			0.218321
$378$		0			0
$379$	−11.7529	−	20.3566i	−0.603706	−	1.04565i	−0.992255	−	0.124221i	$-0.960357\pi$
$379$	−11.7529	−	20.3566i	−0.603706	−	1.04565i	0.388549	−	0.921428i	$-0.372976\pi$
$380$		0			0
$381$	−6.03315	+	10.4497i	−0.309088	+	0.535355i
$382$		0			0
$383$	−0.746923	−	1.29371i	−0.0381660	−	0.0661054i	0.846311	−	0.532688i	$-0.178818\pi$
$383$	−0.746923	−	1.29371i	−0.0381660	−	0.0661054i	−0.884477	+	0.466583i	$0.845485\pi$
$384$		0			0
$385$	−7.49834	−	12.9875i	−0.382151	−	0.661905i
$386$		0			0
$387$	−8.94175			−0.454535
$388$		0			0
$389$	4.15369	+	7.19440i	0.210600	+	0.364771i	0.951903	−	0.306401i	$-0.0991248\pi$
$389$	4.15369	+	7.19440i	0.210600	+	0.364771i	−0.741302	+	0.671171i	$0.765791\pi$
$390$		0			0
$391$	−1.63398	+	2.83013i	−0.0826337	+	0.143126i
$392$		0			0
$393$	−15.1963			−0.766552
$394$		0			0
$395$	−3.42355	+	5.92977i	−0.172258	+	0.298359i
$396$		0			0
$397$	2.88761			0.144925			0.0724624	−	0.997371i	$-0.476914\pi$
$397$	2.88761			0.144925			0.0724624	+	0.997371i	$0.476914\pi$
$398$		0			0
$399$	5.96467			0.298607
$400$		0			0
$401$	−27.6874			−1.38264			−0.691321	−	0.722548i	$-0.742971\pi$
$401$	−27.6874			−1.38264			−0.691321	+	0.722548i	$0.742971\pi$
$402$		0			0
$403$	1.26138			0.0628338
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	17.5732			0.871072
$408$		0			0
$409$	−2.79682	+	4.84424i	−0.138294	+	0.239532i	−0.926851	−	0.375430i	$-0.877495\pi$
$409$	−2.79682	+	4.84424i	−0.138294	+	0.239532i	0.788557	+	0.614962i	$0.210829\pi$
$410$		0			0
$411$	−6.55731			−0.323448
$412$		0			0
$413$	−8.90130	+	15.4175i	−0.438004	+	0.758646i
$414$		0			0
$415$	8.45371	+	14.6423i	0.414977	+	0.718760i
$416$		0			0
$417$	−7.69275			−0.376716
$418$		0			0
$419$	11.3010	+	19.5739i	0.552090	+	0.956248i	0.998124	+	0.0612317i	$0.0195029\pi$
$419$	11.3010	+	19.5739i	0.552090	+	0.956248i	−0.446034	+	0.895016i	$0.647164\pi$
$420$		0			0
$421$	12.8570	+	22.2689i	0.626611	+	1.08532i	0.988227	+	0.152995i	$0.0488917\pi$
$421$	12.8570	+	22.2689i	0.626611	+	1.08532i	−0.361616	+	0.932327i	$0.617775\pi$
$422$		0			0
$423$	2.77545	−	4.80722i	0.134947	−	0.233735i
$424$		0			0
$425$	0.838031	+	1.45151i	0.0406505	+	0.0704086i
$426$		0			0
$427$	46.1596			2.23382
$428$		0			0
$429$	14.9703			0.722775
$430$		0			0
$431$	13.4999	−	23.3825i	0.650268	−	1.12630i	−0.332790	−	0.943001i	$-0.607990\pi$
$431$	13.4999	−	23.3825i	0.650268	−	1.12630i	0.983058	−	0.183296i	$-0.0586766\pi$
$432$		0			0
$433$	0.388933	−	0.673651i	0.0186909	−	0.0323736i	−0.856529	−	0.516099i	$-0.827383\pi$
$433$	0.388933	−	0.673651i	0.0186909	−	0.0323736i	0.875220	+	0.483726i	$0.160717\pi$
$434$		0			0
$435$	−0.599657	+	1.03864i	−0.0287514	+	0.0497988i
$436$		0			0
$437$	−1.64227	+	2.84450i	−0.0785605	+	0.136071i
$438$		0			0
$439$	−8.92447	−	15.4576i	−0.425942	−	0.737753i	0.570566	−	0.821252i	$-0.306724\pi$
$439$	−8.92447	−	15.4576i	−0.425942	−	0.737753i	−0.996508	+	0.0834991i	$0.973390\pi$
$440$		0			0
$441$	−2.76852	−	4.79522i	−0.131834	−	0.228344i
$442$		0			0
$443$	1.25093	−	2.16668i	0.0594337	−	0.102942i	−0.834778	−	0.550587i	$-0.814404\pi$
$443$	1.25093	−	2.16668i	0.0594337	−	0.102942i	0.894211	+	0.447645i	$0.147737\pi$
$444$		0			0
$445$	−2.17767			−0.103231
$446$		0			0
$447$	−18.4920			−0.874642
$448$		0			0
$449$	−9.67340	+	16.7548i	−0.456516	+	0.790709i	−0.998774	−	0.0495034i	$-0.984236\pi$
$449$	−9.67340	+	16.7548i	−0.456516	+	0.790709i	0.542258	+	0.840212i	$0.317569\pi$
$450$		0			0
$451$	24.3510	+	42.1771i	1.14664	+	1.98604i
$452$		0			0
$453$	5.32869	+	9.22956i	0.250364	+	0.433642i
$454$		0			0
$455$	−12.5150			−0.586713
$456$		0			0
$457$	−6.83187	+	11.8331i	−0.319581	+	0.553531i	−0.980401	−	0.197014i	$-0.936876\pi$
$457$	−6.83187	+	11.8331i	−0.319581	+	0.553531i	0.660819	+	0.750545i	$0.270209\pi$
$458$		0			0
$459$	−0.838031	−	1.45151i	−0.0391159	−	0.0677508i
$460$		0			0
$461$	21.1405			0.984612			0.492306	−	0.870422i	$-0.336154\pi$
$461$	21.1405			0.984612			0.492306	+	0.870422i	$0.336154\pi$
$462$		0			0
$463$	1.26171	+	2.18535i	0.0586369	+	0.101562i	0.893854	−	0.448359i	$-0.147991\pi$
$463$	1.26171	+	2.18535i	0.0586369	+	0.101562i	−0.835217	+	0.549921i	$0.814658\pi$
$464$		0			0
$465$	−0.178436	+	0.309060i	−0.00827476	+	0.0143323i
$466$		0			0
$467$	6.82022	+	11.8130i	0.315602	+	0.546639i	0.979565	−	0.201126i	$-0.0644602\pi$
$467$	6.82022	+	11.8130i	0.315602	+	0.546639i	−0.663963	+	0.747765i	$0.731127\pi$
$468$		0			0
$469$	27.5319	−	9.05417i	1.27130	−	0.418083i
$470$		0			0
$471$	6.40157	+	11.0879i	0.294969	+	0.510901i
$472$		0			0
$473$	−18.9361	+	32.7983i	−0.870682	+	1.50807i
$474$		0			0
$475$	0.842285	+	1.45888i	0.0386467	+	0.0669380i
$476$		0			0
$477$	−5.36916			−0.245837
$478$		0			0
$479$	−12.1283	−	21.0069i	−0.554158	−	0.959829i	−0.997969	−	0.0637086i	$-0.979707\pi$
$479$	−12.1283	−	21.0069i	−0.554158	−	0.959829i	0.443811	−	0.896120i	$-0.353626\pi$
$480$		0			0
$481$	7.33259	−	12.7004i	0.334337	−	0.579089i
$482$		0			0
$483$	6.90372			0.314130
$484$		0			0
$485$	−0.667481	−	1.15611i	−0.0303087	−	0.0524963i
$486$		0			0
$487$	−8.94569	−	15.4944i	−0.405368	−	0.702118i	0.588996	−	0.808136i	$-0.299523\pi$
$487$	−8.94569	−	15.4944i	−0.405368	−	0.702118i	−0.994364	+	0.106018i	$0.966190\pi$
$488$		0			0
$489$	−8.03386	+	13.9150i	−0.363304	+	0.629260i
$490$		0			0
$491$	7.18456			0.324234			0.162117	−	0.986772i	$-0.448168\pi$
$491$	7.18456			0.324234			0.162117	+	0.986772i	$0.448168\pi$
$492$		0			0
$493$	−2.01012			−0.0905314
$494$		0			0
$495$	−2.11772	+	3.66799i	−0.0951843	+	0.164864i
$496$		0			0
$497$	11.8679	+	20.5557i	0.532346	+	0.922051i
$498$		0			0
$499$	7.70306	+	13.3421i	0.344837	+	0.597274i	0.985324	−	0.170694i	$-0.0546010\pi$
$499$	7.70306	+	13.3421i	0.344837	+	0.597274i	−0.640488	+	0.767969i	$0.721268\pi$
$500$		0			0
$501$	−4.94195	+	8.55970i	−0.220790	+	0.382419i
$502$		0			0
$503$	1.96640	−	3.40590i	0.0876773	−	0.151861i	−0.818852	−	0.574005i	$-0.805389\pi$
$503$	1.96640	−	3.40590i	0.0876773	−	0.151861i	0.906529	+	0.422144i	$0.138722\pi$
$504$		0			0
$505$	−7.15798	+	12.3980i	−0.318526	+	0.551703i
$506$		0			0
$507$	−0.253483	+	0.439045i	−0.0112576	+	0.0194987i
$508$		0			0
$509$	−26.4409			−1.17197			−0.585987	−	0.810321i	$-0.699293\pi$
$509$	−26.4409			−1.17197			−0.585987	+	0.810321i	$0.699293\pi$
$510$		0			0
$511$	−8.07489			−0.357212
$512$		0			0
$513$	−0.842285	−	1.45888i	−0.0371878	−	0.0644112i
$514$		0			0
$515$	8.48839	−	14.7023i	0.374043	−	0.647862i
$516$		0			0
$517$	−11.7552	−	20.3606i	−0.516994	−	0.895460i
$518$		0			0
$519$	−0.717488	−	1.24273i	−0.0314942	−	0.0545496i
$520$		0			0
$521$	32.4156			1.42015			0.710076	−	0.704125i	$-0.248661\pi$
$521$	32.4156			1.42015			0.710076	+	0.704125i	$0.248661\pi$
$522$		0			0
$523$	−1.41886	−	2.45753i	−0.0620423	−	0.107460i	0.833336	−	0.552767i	$-0.186428\pi$
$523$	−1.41886	−	2.45753i	−0.0620423	−	0.107460i	−0.895378	+	0.445307i	$0.853095\pi$
$524$		0			0
$525$	1.77038	−	3.06640i	0.0772659	−	0.133828i
$526$		0			0
$527$	−0.598138			−0.0260553
$528$		0			0
$529$	9.59918	−	16.6263i	0.417356	−	0.722881i
$530$		0			0
$531$	5.02789			0.218192
$532$		0			0
$533$	40.6427			1.76043
$534$		0			0
$535$	−8.72766			−0.377329
$536$		0			0
$537$	5.78384			0.249591
$538$		0			0
$539$	−23.4518			−1.01014
$540$		0			0
$541$	22.9583			0.987052			0.493526	−	0.869731i	$-0.335708\pi$
$541$	22.9583			0.987052			0.493526	+	0.869731i	$0.335708\pi$
$542$		0			0
$543$	−10.7979	+	18.7025i	−0.463383	+	0.802602i
$544$		0			0
$545$	−19.5468			−0.837292
$546$		0			0
$547$	11.2670	−	19.5151i	0.481743	−	0.834403i	−0.518037	−	0.855358i	$-0.673337\pi$
$547$	11.2670	−	19.5151i	0.481743	−	0.834403i	0.999780	+	0.0209545i	$0.00667052\pi$
$548$		0			0
$549$	−6.51830	−	11.2900i	−0.278194	−	0.481847i
$550$		0			0
$551$	−2.02033			−0.0860689
$552$		0			0
$553$	12.1220	+	20.9959i	0.515480	+	0.892838i
$554$		0			0
$555$	2.07455	+	3.59322i	0.0880596	+	0.152524i
$556$		0			0
$557$	19.6584	−	34.0493i	0.832952	−	1.44272i	−0.0627342	−	0.998030i	$-0.519982\pi$
$557$	19.6584	−	34.0493i	0.832952	−	1.44272i	0.895687	−	0.444686i	$-0.146685\pi$
$558$		0			0
$559$	15.8025	+	27.3708i	0.668376	+	1.15766i
$560$		0			0
$561$	−7.09884			−0.299713
$562$		0			0
$563$	9.20286			0.387854			0.193927	−	0.981016i	$-0.437877\pi$
$563$	9.20286			0.387854			0.193927	+	0.981016i	$0.437877\pi$
$564$		0			0
$565$	6.00367	−	10.3987i	0.252576	−	0.437475i
$566$		0			0
$567$	−1.77038	+	3.06640i	−0.0743492	+	0.128777i
$568$		0			0
$569$	0.902901	−	1.56387i	0.0378516	−	0.0655609i	−0.846479	−	0.532422i	$-0.821282\pi$
$569$	0.902901	−	1.56387i	0.0378516	−	0.0655609i	0.884331	+	0.466861i	$0.154615\pi$
$570$		0			0
$571$	1.32456	−	2.29420i	0.0554309	−	0.0960092i	−0.836978	−	0.547236i	$-0.815680\pi$
$571$	1.32456	−	2.29420i	0.0554309	−	0.0960092i	0.892409	+	0.451227i	$0.149013\pi$
$572$		0			0
$573$	−7.64232	−	13.2369i	−0.319263	−	0.552979i
$574$		0			0
$575$	0.974890	+	1.68856i	0.0406557	+	0.0704178i
$576$		0			0
$577$	6.80774	−	11.7913i	0.283410	−	0.490880i	−0.688812	−	0.724940i	$-0.741868\pi$
$577$	6.80774	−	11.7913i	0.283410	−	0.490880i	0.972222	+	0.234059i	$0.0752010\pi$
$578$		0			0
$579$	−24.2594			−1.00819
$580$		0			0
$581$	59.8653			2.48363
$582$		0			0
$583$	−11.3704	+	19.6940i	−0.470912	+	0.815644i
$584$		0			0
$585$	1.76727	+	3.06101i	0.0730678	+	0.126557i
$586$		0			0
$587$	4.65500	+	8.06270i	0.192132	+	0.332783i	0.945957	−	0.324293i	$-0.105126\pi$
$587$	4.65500	+	8.06270i	0.192132	+	0.332783i	−0.753824	+	0.657076i	$0.771793\pi$
$588$		0			0
$589$	−0.601175			−0.0247710
$590$		0			0
$591$	10.3945	−	18.0037i	0.427571	−	0.740575i
$592$		0			0
$593$	7.36439	+	12.7555i	0.302419	+	0.523806i	0.976683	−	0.214685i	$-0.0688724\pi$
$593$	7.36439	+	12.7555i	0.302419	+	0.523806i	−0.674264	+	0.738490i	$0.735539\pi$
$594$		0			0
$595$	5.93454			0.243293
$596$		0			0
$597$	13.1359	+	22.7521i	0.537617	+	0.931180i
$598$		0			0
$599$	−9.82402	+	17.0157i	−0.401399	+	0.695243i	−0.993895	−	0.110330i	$-0.964809\pi$
$599$	−9.82402	+	17.0157i	−0.401399	+	0.695243i	0.592496	+	0.805573i	$0.298142\pi$
$600$		0			0
$601$	−14.4777	−	25.0761i	−0.590558	−	1.02288i	−0.994157	−	0.107941i	$-0.965574\pi$
$601$	−14.4777	−	25.0761i	−0.590558	−	1.02288i	0.403599	−	0.914936i	$-0.367759\pi$
$602$		0			0
$603$	−6.10237	−	5.45537i	−0.248508	−	0.222160i
$604$		0			0
$605$	3.46944	+	6.00925i	0.141053	+	0.244311i
$606$		0			0
$607$	−18.6693	+	32.3362i	−0.757764	+	1.31249i	0.186225	+	0.982507i	$0.440375\pi$
$607$	−18.6693	+	32.3362i	−0.757764	+	1.31249i	−0.943988	+	0.329978i	$0.892959\pi$
$608$		0			0
$609$	2.12325	+	3.67757i	0.0860383	+	0.149023i
$610$		0			0
$611$	−19.6199			−0.793737
$612$		0			0
$613$	−9.82934	−	17.0249i	−0.397003	−	0.687630i	0.596351	−	0.802724i	$-0.296617\pi$
$613$	−9.82934	−	17.0249i	−0.397003	−	0.687630i	−0.993355	+	0.115093i	$0.963283\pi$
$614$		0			0
$615$	−5.74935	+	9.95817i	−0.231836	+	0.401552i
$616$		0			0
$617$	42.1396			1.69648			0.848239	−	0.529614i	$-0.177663\pi$
$617$	42.1396			1.69648			0.848239	+	0.529614i	$0.177663\pi$
$618$		0			0
$619$	6.01300	+	10.4148i	0.241683	+	0.418607i	0.961194	−	0.275874i	$-0.0889673\pi$
$619$	6.01300	+	10.4148i	0.241683	+	0.418607i	−0.719511	+	0.694481i	$0.755634\pi$
$620$		0			0
$621$	−0.974890	−	1.68856i	−0.0391210	−	0.0677595i
$622$		0			0
$623$	−3.85531	+	6.67759i	−0.154460	+	0.267532i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.13488			−0.284940
$628$		0			0
$629$	−3.47707	+	6.02246i	−0.138640	+	0.240131i
$630$		0			0
$631$	1.59076	+	2.75528i	0.0633273	+	0.109686i	0.895951	−	0.444153i	$-0.146495\pi$
$631$	1.59076	+	2.75528i	0.0633273	+	0.109686i	−0.832623	+	0.553839i	$0.813162\pi$
$632$		0			0
$633$	11.7661	+	20.3795i	0.467662	+	0.810014i
$634$		0			0
$635$	−6.03315	+	10.4497i	−0.239418	+	0.414685i
$636$		0			0
$637$	−9.78548	+	16.9489i	−0.387715	+	0.671541i
$638$		0			0
$639$	3.35178	−	5.80545i	0.132594	−	0.229660i
$640$		0			0
$641$	22.1513	−	38.3671i	0.874923	−	1.51541i	0.0180781	−	0.999837i	$-0.494245\pi$
$641$	22.1513	−	38.3671i	0.874923	−	1.51541i	0.856845	−	0.515574i	$-0.172421\pi$
$642$		0			0
$643$	14.6350			0.577149			0.288574	−	0.957458i	$-0.406819\pi$
$643$	14.6350			0.577149			0.288574	+	0.957458i	$0.406819\pi$
$644$		0			0
$645$	−8.94175			−0.352081
$646$		0			0
$647$	0.585486	+	1.01409i	0.0230178	+	0.0398680i	0.877305	−	0.479934i	$-0.159339\pi$
$647$	0.585486	+	1.01409i	0.0230178	+	0.0398680i	−0.854287	+	0.519802i	$0.826006\pi$
$648$		0			0
$649$	10.6476	−	18.4423i	0.417957	−	0.723922i
$650$		0			0
$651$	0.631800	+	1.09431i	0.0247622	+	0.0428894i
$652$		0			0
$653$	12.4745	+	21.6065i	0.488166	+	0.845528i	0.999907	−	0.0136116i	$-0.00433284\pi$
$653$	12.4745	+	21.6065i	0.488166	+	0.845528i	−0.511742	+	0.859139i	$0.671000\pi$
$654$		0			0
$655$	−15.1963			−0.593768
$656$		0			0
$657$	1.14027	+	1.97501i	0.0444863	+	0.0770525i
$658$		0			0
$659$	−11.0968	+	19.2201i	−0.432268	+	0.748711i	−0.997068	−	0.0765172i	$-0.975620\pi$
$659$	−11.0968	+	19.2201i	−0.432268	+	0.748711i	0.564800	+	0.825228i	$0.308953\pi$
$660$		0			0
$661$	−37.7355			−1.46774			−0.733870	−	0.679290i	$-0.762288\pi$
$661$	−37.7355			−1.46774			−0.733870	+	0.679290i	$0.762288\pi$
$662$		0			0
$663$	−2.96206	+	5.13044i	−0.115037	+	0.199250i
$664$		0			0
$665$	5.96467			0.231300
$666$		0			0
$667$	−2.33840			−0.0905432
$668$		0			0
$669$	−18.2423			−0.705287
$670$		0			0
$671$	−55.2157			−2.13158
$672$		0			0
$673$	20.2660			0.781196			0.390598	−	0.920561i	$-0.372268\pi$
$673$	20.2660			0.781196			0.390598	+	0.920561i	$0.372268\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−18.6753	+	32.3466i	−0.717750	+	1.24318i	0.244139	+	0.969740i	$0.421495\pi$
$677$	−18.6753	+	32.3466i	−0.717750	+	1.24318i	−0.961889	+	0.273440i	$0.911839\pi$
$678$		0			0
$679$	−4.72679			−0.181398
$680$		0			0
$681$	2.91120	−	5.04234i	0.111557	−	0.193223i
$682$		0			0
$683$	−14.2364	−	24.6582i	−0.544741	−	0.943520i	−0.998623	−	0.0524577i	$-0.983295\pi$
$683$	−14.2364	−	24.6582i	−0.544741	−	0.943520i	0.453882	−	0.891062i	$-0.350039\pi$
$684$		0			0
$685$	−6.55731			−0.250542
$686$		0			0
$687$	0.619049	+	1.07222i	0.0236182	+	0.0409079i
$688$		0			0
$689$	9.48878	+	16.4350i	0.361494	+	0.626125i
$690$		0			0
$691$	10.1727	−	17.6197i	0.386989	−	0.670285i	−0.605054	−	0.796185i	$-0.706848\pi$
$691$	10.1727	−	17.6197i	0.386989	−	0.670285i	0.992043	+	0.125900i	$0.0401817\pi$
$692$		0			0
$693$	7.49834	+	12.9875i	0.284839	+	0.493355i
$694$		0			0
$695$	−7.69275			−0.291803
$696$		0			0
$697$	−19.2725			−0.729999
$698$		0			0
$699$	−6.68989	+	11.5872i	−0.253035	+	0.438269i
$700$		0			0
$701$	−0.365832	+	0.633640i	−0.0138173	+	0.0239323i	−0.872851	−	0.487986i	$-0.837732\pi$
$701$	−0.365832	+	0.633640i	−0.0138173	+	0.0239323i	0.859034	+	0.511918i	$0.171065\pi$
$702$		0			0
$703$	−3.49472	+	6.05303i	−0.131806	+	0.228295i
$704$		0			0
$705$	2.77545	−	4.80722i	0.104529	−	0.181050i
$706$		0			0
$707$	25.3447	+	43.8984i	0.953187	+	1.65097i
$708$		0			0
$709$	0.484267	+	0.838776i	0.0181870	+	0.0315009i	0.874976	−	0.484167i	$-0.160877\pi$
$709$	0.484267	+	0.838776i	0.0181870	+	0.0315009i	−0.856789	+	0.515668i	$0.827544\pi$
$710$		0			0
$711$	3.42355	−	5.92977i	0.128393	−	0.222384i
$712$		0			0
$713$	−0.695821			−0.0260587
$714$		0			0
$715$	14.9703			0.559859
$716$		0			0
$717$	2.35410	−	4.07743i	0.0879156	−	0.152274i
$718$		0			0
$719$	−1.34247	−	2.32522i	−0.0500656	−	0.0867162i	0.839907	−	0.542731i	$-0.182610\pi$
$719$	−1.34247	−	2.32522i	−0.0500656	−	0.0867162i	−0.889972	+	0.456015i	$0.849276\pi$
$720$		0			0
$721$	−30.0554	−	52.0575i	−1.11932	−	1.93872i
$722$		0			0
$723$	−26.6832			−0.992358
$724$		0			0
$725$	−0.599657	+	1.03864i	−0.0222707	+	0.0385740i
$726$		0			0
$727$	−24.9178	−	43.1589i	−0.924150	−	1.60067i	−0.792923	−	0.609322i	$-0.791442\pi$
$727$	−24.9178	−	43.1589i	−0.924150	−	1.60067i	−0.131227	−	0.991352i	$-0.541892\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−7.49346	−	12.9791i	−0.277156	−	0.480048i
$732$		0			0
$733$	−2.18656	+	3.78724i	−0.0807625	+	0.139885i	−0.903578	−	0.428424i	$-0.859069\pi$
$733$	−2.18656	+	3.78724i	−0.0807625	+	0.139885i	0.822815	+	0.568309i	$0.192402\pi$
$734$		0			0
$735$	−2.76852	−	4.79522i	−0.102118	−	0.176874i
$736$		0			0
$737$	−32.9334	+	10.8305i	−1.21312	+	0.398947i
$738$		0			0
$739$	9.46206	+	16.3888i	0.348067	+	0.602871i	0.985906	−	0.167299i	$-0.0535047\pi$
$739$	9.46206	+	16.3888i	0.348067	+	0.602871i	−0.637839	+	0.770170i	$0.720171\pi$
$740$		0			0
$741$	−2.97710	+	5.15649i	−0.109366	+	0.189428i
$742$		0			0
$743$	−0.139459	−	0.241549i	−0.00511624	−	0.00886159i	0.863456	−	0.504424i	$-0.168295\pi$
$743$	−0.139459	−	0.241549i	−0.00511624	−	0.00886159i	−0.868572	+	0.495563i	$0.834962\pi$
$744$		0			0
$745$	−18.4920			−0.677495
$746$		0			0
$747$	−8.45371	−	14.6423i	−0.309305	−	0.535732i
$748$		0			0
$749$	−15.4513	+	26.7624i	−0.564578	+	0.977879i
$750$		0			0
$751$	4.42245			0.161377			0.0806887	−	0.996739i	$-0.474288\pi$
$751$	4.42245			0.161377			0.0806887	+	0.996739i	$0.474288\pi$
$752$		0			0
$753$	9.22375	+	15.9760i	0.336132	+	0.582198i
$754$		0			0
$755$	5.32869	+	9.22956i	0.193931	+	0.335898i
$756$		0			0
$757$	−6.06818	+	10.5104i	−0.220552	+	0.382007i	−0.954976	−	0.296684i	$-0.904119\pi$
$757$	−6.06818	+	10.5104i	−0.220552	+	0.382007i	0.734424	+	0.678691i	$0.237452\pi$
$758$		0			0
$759$	−8.25816			−0.299752
$760$		0			0
$761$	−49.4892			−1.79398			−0.896990	−	0.442050i	$-0.854251\pi$
$761$	−49.4892			−1.79398			−0.896990	+	0.442050i	$0.854251\pi$
$762$		0			0
$763$	−34.6053	+	59.9382i	−1.25280	+	2.16991i
$764$		0			0
$765$	−0.838031	−	1.45151i	−0.0302991	−	0.0524795i
$766$		0			0
$767$	−8.88566	−	15.3904i	−0.320843	−	0.555716i
$768$		0			0
$769$	−15.1464	+	26.2344i	−0.546194	+	0.946036i	0.452337	+	0.891847i	$0.350591\pi$
$769$	−15.1464	+	26.2344i	−0.546194	+	0.946036i	−0.998531	+	0.0541885i	$0.982743\pi$
$770$		0			0
$771$	−6.01811	+	10.4237i	−0.216737	+	0.375399i
$772$		0			0
$773$	−6.78582	+	11.7534i	−0.244069	+	0.422740i	−0.961869	−	0.273509i	$-0.911816\pi$
$773$	−6.78582	+	11.7534i	−0.244069	+	0.422740i	0.717801	+	0.696249i	$0.245149\pi$
$774$		0			0
$775$	−0.178436	+	0.309060i	−0.00640960	+	0.0111018i
$776$		0			0
$777$	14.6910			0.527036
$778$		0			0
$779$	−19.3704			−0.694016
$780$		0			0
$781$	−14.1962	−	24.5886i	−0.507981	−	0.879848i
$782$		0			0
$783$	0.599657	−	1.03864i	0.0214300	−	0.0371178i
$784$		0			0
$785$	6.40157	+	11.0879i	0.228482	+	0.395742i
$786$		0			0
$787$	−9.29532	−	16.1000i	−0.331342	−	0.573902i	0.651433	−	0.758706i	$-0.274168\pi$
$787$	−9.29532	−	16.1000i	−0.331342	−	0.573902i	−0.982775	+	0.184805i	$0.940835\pi$
$788$		0			0
$789$	7.69307			0.273881
$790$		0			0
$791$	−21.2576	−	36.8193i	−0.755834	−	1.30914i
$792$		0			0
$793$	−23.0393	+	39.9052i	−0.818148	+	1.41707i
$794$		0			0
$795$	−5.36916			−0.190424
$796$		0			0
$797$	23.4363	−	40.5929i	0.830156	−	1.43787i	−0.0677578	−	0.997702i	$-0.521585\pi$
$797$	23.4363	−	40.5929i	0.830156	−	1.43787i	0.897914	−	0.440171i	$-0.145082\pi$
$798$		0			0
$799$	9.30364			0.329139
$800$		0			0
$801$	2.17767			0.0769441
$802$		0			0
$803$	9.65910			0.340862
$804$		0			0
$805$	6.90372			0.243324
$806$		0			0
$807$	32.5624			1.14625
$808$		0			0
$809$	−14.7158			−0.517381			−0.258690	−	0.965960i	$-0.583291\pi$
$809$	−14.7158			−0.517381			−0.258690	+	0.965960i	$0.583291\pi$
$810$		0			0
$811$	5.54863	−	9.61051i	0.194839	−	0.337471i	−0.752009	−	0.659153i	$-0.770915\pi$
$811$	5.54863	−	9.61051i	0.194839	−	0.337471i	0.946848	+	0.321682i	$0.104248\pi$
$812$		0			0
$813$	7.11931			0.249685
$814$		0			0
$815$	−8.03386	+	13.9150i	−0.281414	+	0.487423i
$816$		0			0
$817$	−7.53150	−	13.0449i	−0.263494	−	0.456385i
$818$		0			0
$819$	12.5150			0.437310
$820$		0			0
$821$	8.16952	+	14.1500i	0.285118	+	0.493839i	0.972638	−	0.232326i	$-0.0746338\pi$
$821$	8.16952	+	14.1500i	0.285118	+	0.493839i	−0.687520	+	0.726166i	$0.741300\pi$
$822$		0			0
$823$	−16.6328	−	28.8088i	−0.579782	−	1.00421i	−0.995504	−	0.0947206i	$-0.969804\pi$
$823$	−16.6328	−	28.8088i	−0.579782	−	1.00421i	0.415722	−	0.909492i	$-0.363529\pi$
$824$		0			0
$825$	−2.11772	+	3.66799i	−0.0737294	+	0.127703i
$826$		0			0
$827$	8.36856	+	14.4948i	0.291003	+	0.504032i	0.974047	−	0.226345i	$-0.0726776\pi$
$827$	8.36856	+	14.4948i	0.291003	+	0.504032i	−0.683044	+	0.730377i	$0.739344\pi$
$828$		0			0
$829$	−18.9972			−0.659798			−0.329899	−	0.944016i	$-0.607015\pi$
$829$	−18.9972			−0.659798			−0.329899	+	0.944016i	$0.607015\pi$
$830$		0			0
$831$	16.2722			0.564477
$832$		0			0
$833$	4.64021	−	8.03708i	0.160774	−	0.278468i
$834$		0			0
$835$	−4.94195	+	8.55970i	−0.171023	+	0.296221i
$836$		0			0
$837$	0.178436	−	0.309060i	0.00616764	−	0.0106827i
$838$		0			0
$839$	−19.5372	+	33.8393i	−0.674497	+	1.16826i	0.302118	+	0.953271i	$0.402306\pi$
$839$	−19.5372	+	33.8393i	−0.674497	+	1.16826i	−0.976616	+	0.214993i	$0.931027\pi$
$840$		0			0
$841$	13.7808	+	23.8691i	0.475201	+	0.823072i
$842$		0			0
$843$	−3.16694	−	5.48530i	−0.109075	−	0.188924i
$844$		0			0
$845$	−0.253483	+	0.439045i	−0.00872007	+	0.0151036i
$846$		0			0
$847$	24.5690			0.844201
$848$		0			0
$849$	−15.9720			−0.548156
$850$		0			0
$851$	−4.04491	+	7.00599i	−0.138658	+	0.240162i
$852$		0			0
$853$	−8.66811	−	15.0136i	−0.296791	−	0.514056i	0.678609	−	0.734499i	$-0.262583\pi$
$853$	−8.66811	−	15.0136i	−0.296791	−	0.514056i	−0.975400	+	0.220443i	$0.929250\pi$
$854$		0			0
$855$	−0.842285	−	1.45888i	−0.0288055	−	0.0498927i
$856$		0			0
$857$	−19.0041			−0.649166			−0.324583	−	0.945857i	$-0.605224\pi$
$857$	−19.0041			−0.649166			−0.324583	+	0.945857i	$0.605224\pi$
$858$		0			0
$859$	22.1605	−	38.3831i	0.756105	−	1.30961i	−0.188718	−	0.982031i	$-0.560433\pi$
$859$	22.1605	−	38.3831i	0.756105	−	1.30961i	0.944823	−	0.327581i	$-0.106234\pi$
$860$		0			0
$861$	20.3571	+	35.2596i	0.693769	+	1.20164i
$862$		0			0
$863$	29.1742			0.993101			0.496551	−	0.868008i	$-0.334600\pi$
$863$	29.1742			0.993101			0.496551	+	0.868008i	$0.334600\pi$
$864$		0			0
$865$	−0.717488	−	1.24273i	−0.0243953	−	0.0422540i
$866$		0			0
$867$	−7.09541	+	12.2896i	−0.240973	+	0.417377i
$868$		0			0
$869$	−14.5002	−	25.1151i	−0.491887	−	0.851973i
$870$		0			0
$871$	−5.91439	+	28.3205i	−0.200401	+	0.959605i
$872$		0			0
$873$	0.667481	+	1.15611i	0.0225908	+	0.0391284i
$874$		0			0
$875$	1.77038	−	3.06640i	0.0598499	−	0.103663i
$876$		0			0
$877$	26.3584	+	45.6540i	0.890059	+	1.54163i	0.839803	+	0.542891i	$0.182670\pi$
$877$	26.3584	+	45.6540i	0.890059	+	1.54163i	0.0502562	+	0.998736i	$0.483996\pi$
$878$		0			0
$879$	24.3375			0.820884
$880$		0			0
$881$	14.0381	+	24.3148i	0.472957	+	0.819185i	0.999521	−	0.0309504i	$-0.00985339\pi$
$881$	14.0381	+	24.3148i	0.472957	+	0.819185i	−0.526564	+	0.850135i	$0.676520\pi$
$882$		0			0
$883$	−14.8494	+	25.7200i	−0.499723	+	0.865545i	−1.00000		0.000320025i	$-0.999898\pi$
$883$	−14.8494	+	25.7200i	−0.499723	+	0.865545i	0.500277	+	0.865865i	$0.333231\pi$
$884$		0			0
$885$	5.02789			0.169011
$886$		0			0
$887$	9.95499	+	17.2426i	0.334256	+	0.578948i	0.983342	−	0.181767i	$-0.0581817\pi$
$887$	9.95499	+	17.2426i	0.334256	+	0.578948i	−0.649086	+	0.760715i	$0.724848\pi$
$888$		0			0
$889$	21.3620	+	37.0000i	0.716458	+	1.24094i
$890$		0			0
$891$	2.11772	−	3.66799i	0.0709462	−	0.122882i
$892$		0			0
$893$	9.35087			0.312915
$894$		0			0
$895$	5.78384			0.193333
$896$		0			0
$897$	−3.44580	+	5.96829i	−0.115052	+	0.199276i
$898$		0			0
$899$	−0.214001	−	0.370660i	−0.00713732	−	0.0123622i
$900$		0			0
$901$	−4.49952	−	7.79340i	−0.149901	−	0.259636i
$902$		0			0
$903$	−15.8303	+	27.4189i	−0.526801	+	0.912445i
$904$		0			0
$905$	−10.7979	+	18.7025i	−0.358935	+	0.621693i
$906$		0			0
$907$	1.40093	−	2.42648i	0.0465170	−	0.0805698i	−0.841829	−	0.539744i	$-0.818521\pi$
$907$	1.40093	−	2.42648i	0.0465170	−	0.0805698i	0.888346	+	0.459174i	$0.151854\pi$
$908$		0			0
$909$	7.15798	−	12.3980i	0.237415	−	0.411215i
$910$		0			0
$911$	26.2479			0.869631			0.434815	−	0.900520i	$-0.356814\pi$
$911$	26.2479			0.869631			0.434815	+	0.900520i	$0.356814\pi$
$912$		0			0
$913$	−71.6103			−2.36995
$914$		0			0
$915$	−6.51830	−	11.2900i	−0.215488	−	0.373237i
$916$		0			0
$917$	−26.9033	+	46.5979i	−0.888425	+	1.53880i
$918$		0			0
$919$	−24.2744	−	42.0445i	−0.800738	−	1.38692i	−0.919131	−	0.393952i	$-0.871108\pi$
$919$	−24.2744	−	42.0445i	−0.800738	−	1.38692i	0.118393	−	0.992967i	$-0.462226\pi$
$920$		0			0
$921$	7.29569	+	12.6365i	0.240401	+	0.416387i
$922$		0			0
$923$	−23.6940			−0.779898
$924$		0			0
$925$	2.07455	+	3.59322i	0.0682107	+	0.118144i
$926$		0			0
$927$	−8.48839	+	14.7023i	−0.278795	+	0.482888i
$928$		0			0
$929$	13.1121			0.430194			0.215097	−	0.976593i	$-0.430993\pi$
$929$	13.1121			0.430194			0.215097	+	0.976593i	$0.430993\pi$
$930$		0			0
$931$	4.66377	−	8.07789i	0.152849	−	0.264742i
$932$		0			0
$933$	31.9348			1.04550
$934$		0			0
$935$	−7.09884			−0.232157
$936$		0			0
$937$	−21.0327			−0.687107			−0.343554	−	0.939133i	$-0.611631\pi$
$937$	−21.0327			−0.687107			−0.343554	+	0.939133i	$0.611631\pi$
$938$		0			0
$939$	−5.27372			−0.172101
$940$		0			0
$941$	12.7165			0.414546			0.207273	−	0.978283i	$-0.433541\pi$
$941$	12.7165			0.414546			0.207273	+	0.978283i	$0.433541\pi$
$942$		0			0
$943$	−22.4199			−0.730094
$944$		0			0
$945$	−1.77038	+	3.06640i	−0.0575906	+	0.0997499i
$946$		0			0
$947$	42.3458			1.37605			0.688027	−	0.725685i	$-0.258477\pi$
$947$	42.3458			1.37605			0.688027	+	0.725685i	$0.258477\pi$
$948$		0			0
$949$	4.03035	−	6.98077i	0.130831	−	0.226605i
$950$		0			0
$951$	7.47026	+	12.9389i	0.242240	+	0.419572i
$952$		0			0
$953$	12.5553			0.406705			0.203353	−	0.979106i	$-0.434816\pi$
$953$	12.5553			0.406705			0.203353	+	0.979106i	$0.434816\pi$
$954$		0			0
$955$	−7.64232	−	13.2369i	−0.247300	−	0.428336i
$956$		0			0
$957$	−2.53981	−	4.39908i	−0.0821003	−	0.142202i
$958$		0			0
$959$	−11.6090	+	20.1073i	−0.374873	+	0.649299i
$960$		0			0
$961$	15.4363	+	26.7365i	0.497946	+	0.862468i
$962$		0			0
$963$	8.72766			0.281245
$964$		0			0
$965$	−24.2594			−0.780938
$966$		0			0
$967$	10.9614	−	18.9857i	0.352494	−	0.610538i	−0.634192	−	0.773176i	$-0.718667\pi$
$967$	10.9614	−	18.9857i	0.352494	−	0.610538i	0.986686	+	0.162638i	$0.0520003\pi$
$968$		0			0
$969$	1.41172	−	2.44517i	0.0453510	−	0.0785503i
$970$		0			0
$971$	−13.5042	+	23.3899i	−0.433369	+	0.750617i	−0.997161	−	0.0752996i	$-0.976009\pi$
$971$	−13.5042	+	23.3899i	−0.433369	+	0.750617i	0.563792	+	0.825917i	$0.309342\pi$
$972$		0			0
$973$	−13.6191	+	23.5890i	−0.436609	+	0.756230i
$974$		0			0
$975$	1.76727	+	3.06101i	0.0565981	+	0.0980307i
$976$		0			0
$977$	−7.68156	−	13.3048i	−0.245755	−	0.425660i	0.716589	−	0.697496i	$-0.245702\pi$
$977$	−7.68156	−	13.3048i	−0.245755	−	0.425660i	−0.962344	+	0.271836i	$0.912369\pi$
$978$		0			0
$979$	4.61168	−	7.98766i	0.147390	−	0.255287i
$980$		0			0
$981$	19.5468			0.624081
$982$		0			0
$983$	−40.0542			−1.27753			−0.638766	−	0.769401i	$-0.720555\pi$
$983$	−40.0542			−1.27753			−0.638766	+	0.769401i	$0.720555\pi$
$984$		0			0
$985$	10.3945	−	18.0037i	0.331195	−	0.573647i
$986$		0			0
$987$	−9.82722	−	17.0212i	−0.312804	−	0.541792i
$988$		0			0
$989$	−8.71722	−	15.0987i	−0.277192	−	0.480110i
$990$		0			0
$991$	20.2046			0.641821			0.320910	−	0.947110i	$-0.396011\pi$
$991$	20.2046			0.641821			0.320910	+	0.947110i	$0.396011\pi$
$992$		0			0
$993$	−2.69650	+	4.67048i	−0.0855709	+	0.148213i
$994$		0			0
$995$	13.1359	+	22.7521i	0.416437	+	0.721289i
$996$		0			0
$997$	−61.2878			−1.94100			−0.970502	−	0.241093i	$-0.922494\pi$
$997$	−61.2878			−1.94100			−0.970502	+	0.241093i	$0.922494\pi$
$998$		0			0
$999$	−2.07455	−	3.59322i	−0.0656358	−	0.113684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.841.2	✓	22
67.29	even	3	inner	4020.2.q.l.3781.2	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.2	✓	22	1.1	even	1	trivial
4020.2.q.l.3781.2	yes	22	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.77038 + 3.06640i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-1.77038 + 3.06640i) q^{7} +1.00000 q^{9} +(2.11772 - 3.66799i) q^{11} +(-1.76727 - 3.06101i) q^{13} +1.00000 q^{15} +(0.838031 + 1.45151i) q^{17} +(0.842285 + 1.45888i) q^{19} +(1.77038 - 3.06640i) q^{21} +(0.974890 + 1.68856i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-0.599657 + 1.03864i) q^{29} +(-0.178436 + 0.309060i) q^{31} +(-2.11772 + 3.66799i) q^{33} +(1.77038 - 3.06640i) q^{35} +(2.07455 + 3.59322i) q^{37} +(1.76727 + 3.06101i) q^{39} +(-5.74935 + 9.95817i) q^{41} -8.94175 q^{43} -1.00000 q^{45} +(2.77545 - 4.80722i) q^{47} +(-2.76852 - 4.79522i) q^{49} +(-0.838031 - 1.45151i) q^{51} -5.36916 q^{53} +(-2.11772 + 3.66799i) q^{55} +(-0.842285 - 1.45888i) q^{57} +5.02789 q^{59} +(-6.51830 - 11.2900i) q^{61} +(-1.77038 + 3.06640i) q^{63} +(1.76727 + 3.06101i) q^{65} +(-6.10237 - 5.45537i) q^{67} +(-0.974890 - 1.68856i) q^{69} +(3.35178 - 5.80545i) q^{71} +(1.14027 + 1.97501i) q^{73} -1.00000 q^{75} +(7.49834 + 12.9875i) q^{77} +(3.42355 - 5.92977i) q^{79} +1.00000 q^{81} +(-8.45371 - 14.6423i) q^{83} +(-0.838031 - 1.45151i) q^{85} +(0.599657 - 1.03864i) q^{87} +2.17767 q^{89} +12.5150 q^{91} +(0.178436 - 0.309060i) q^{93} +(-0.842285 - 1.45888i) q^{95} +(0.667481 + 1.15611i) q^{97} +(2.11772 - 3.66799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 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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