LMFDB - Embedded newform 4020.2.q.m.3781.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.3
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.m.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-1.96234 - 3.39887i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.96234 - 3.39887i) q^{7} +1.00000 q^{9} +(-0.165135 - 0.286022i) q^{11} +(-3.41962 + 5.92295i) q^{13} +1.00000 q^{15} +(1.72717 - 2.99154i) q^{17} +(-3.54303 + 6.13671i) q^{19} +(-1.96234 - 3.39887i) q^{21} +(-0.989388 + 1.71367i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-2.31553 - 4.01062i) q^{29} +(3.25426 + 5.63654i) q^{31} +(-0.165135 - 0.286022i) q^{33} +(-1.96234 - 3.39887i) q^{35} +(-2.28135 + 3.95142i) q^{37} +(-3.41962 + 5.92295i) q^{39} +(3.72148 + 6.44579i) q^{41} +5.35239 q^{43} +1.00000 q^{45} +(4.85734 + 8.41315i) q^{47} +(-4.20152 + 7.27725i) q^{49} +(1.72717 - 2.99154i) q^{51} +13.3034 q^{53} +(-0.165135 - 0.286022i) q^{55} +(-3.54303 + 6.13671i) q^{57} -5.68339 q^{59} +(1.97466 - 3.42021i) q^{61} +(-1.96234 - 3.39887i) q^{63} +(-3.41962 + 5.92295i) q^{65} +(-5.78845 + 5.78738i) q^{67} +(-0.989388 + 1.71367i) q^{69} +(-1.85164 - 3.20713i) q^{71} +(2.79103 - 4.83421i) q^{73} +1.00000 q^{75} +(-0.648100 + 1.12254i) q^{77} +(4.12506 + 7.14481i) q^{79} +1.00000 q^{81} +(-8.83630 + 15.3049i) q^{83} +(1.72717 - 2.99154i) q^{85} +(-2.31553 - 4.01062i) q^{87} -6.96652 q^{89} +26.8418 q^{91} +(3.25426 + 5.63654i) q^{93} +(-3.54303 + 6.13671i) q^{95} +(1.00524 - 1.74112i) q^{97} +(-0.165135 - 0.286022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−1.96234	−	3.39887i	−0.741693	−	1.28465i	−0.951724	−	0.306956i	$-0.900690\pi$
$7$	−1.96234	−	3.39887i	−0.741693	−	1.28465i	0.210031	−	0.977695i	$-0.432644\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.165135	−	0.286022i	−0.0497901	−	0.0862389i	0.840056	−	0.542499i	$-0.182522\pi$
$11$	−0.165135	−	0.286022i	−0.0497901	−	0.0862389i	−0.889846	+	0.456260i	$0.849189\pi$
$12$		0			0
$13$	−3.41962	+	5.92295i	−0.948432	+	1.64273i	−0.199701	+	0.979857i	$0.563997\pi$
$13$	−3.41962	+	5.92295i	−0.948432	+	1.64273i	−0.748730	+	0.662875i	$0.769336\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.72717	−	2.99154i	0.418899	−	0.725555i	−0.576930	−	0.816794i	$-0.695749\pi$
$17$	1.72717	−	2.99154i	0.418899	−	0.725555i	0.995829	+	0.0912387i	$0.0290826\pi$
$18$		0			0
$19$	−3.54303	+	6.13671i	−0.812827	+	1.40786i	0.0980505	+	0.995181i	$0.468739\pi$
$19$	−3.54303	+	6.13671i	−0.812827	+	1.40786i	−0.910878	+	0.412677i	$0.864594\pi$
$20$		0			0
$21$	−1.96234	−	3.39887i	−0.428217	−	0.741693i
$22$		0			0
$23$	−0.989388	+	1.71367i	−0.206302	+	0.357325i	−0.950547	−	0.310582i	$-0.899476\pi$
$23$	−0.989388	+	1.71367i	−0.206302	+	0.357325i	0.744245	+	0.667907i	$0.232809\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.31553	−	4.01062i	−0.429984	−	0.744754i	0.566887	−	0.823795i	$-0.308147\pi$
$29$	−2.31553	−	4.01062i	−0.429984	−	0.744754i	−0.996871	+	0.0790413i	$0.974814\pi$
$30$		0			0
$31$	3.25426	+	5.63654i	0.584482	+	1.01235i	0.994940	+	0.100473i	$0.0320356\pi$
$31$	3.25426	+	5.63654i	0.584482	+	1.01235i	−0.410458	+	0.911880i	$0.634631\pi$
$32$		0			0
$33$	−0.165135	−	0.286022i	−0.0287463	−	0.0497901i
$34$		0			0
$35$	−1.96234	−	3.39887i	−0.331695	−	0.574513i
$36$		0			0
$37$	−2.28135	+	3.95142i	−0.375052	+	0.649609i	−0.990335	−	0.138697i	$-0.955709\pi$
$37$	−2.28135	+	3.95142i	−0.375052	+	0.649609i	0.615283	+	0.788307i	$0.289042\pi$
$38$		0			0
$39$	−3.41962	+	5.92295i	−0.547577	+	0.948432i
$40$		0			0
$41$	3.72148	+	6.44579i	0.581197	+	1.00666i	0.995338	+	0.0964501i	$0.0307488\pi$
$41$	3.72148	+	6.44579i	0.581197	+	1.00666i	−0.414141	+	0.910213i	$0.635918\pi$
$42$		0			0
$43$	5.35239			0.816231			0.408116	−	0.912930i	$-0.366186\pi$
$43$	5.35239			0.816231			0.408116	+	0.912930i	$0.366186\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	4.85734	+	8.41315i	0.708515	+	1.22718i	0.965408	+	0.260745i	$0.0839680\pi$
$47$	4.85734	+	8.41315i	0.708515	+	1.22718i	−0.256893	+	0.966440i	$0.582699\pi$
$48$		0			0
$49$	−4.20152	+	7.27725i	−0.600218	+	1.03961i
$50$		0			0
$51$	1.72717	−	2.99154i	0.241852	−	0.418899i
$52$		0			0
$53$	13.3034			1.82736			0.913682	−	0.406429i	$-0.133226\pi$
$53$	13.3034			1.82736			0.913682	+	0.406429i	$0.133226\pi$
$54$		0			0
$55$	−0.165135	−	0.286022i	−0.0222668	−	0.0385672i
$56$		0			0
$57$	−3.54303	+	6.13671i	−0.469286	+	0.812827i
$58$		0			0
$59$	−5.68339			−0.739915			−0.369957	−	0.929049i	$-0.620628\pi$
$59$	−5.68339			−0.739915			−0.369957	+	0.929049i	$0.620628\pi$
$60$		0			0
$61$	1.97466	−	3.42021i	0.252830	−	0.437914i	−0.711474	−	0.702712i	$-0.751972\pi$
$61$	1.97466	−	3.42021i	0.252830	−	0.437914i	0.964304	+	0.264799i	$0.0853055\pi$
$62$		0			0
$63$	−1.96234	−	3.39887i	−0.247231	−	0.428217i
$64$		0			0
$65$	−3.41962	+	5.92295i	−0.424152	+	0.734652i
$66$		0			0
$67$	−5.78845	+	5.78738i	−0.707172	+	0.707042i
$67$	−5.78845	+	5.78738i	−0.707172	+	0.707042i
$68$		0			0
$69$	−0.989388	+	1.71367i	−0.119108	+	0.206302i
$70$		0			0
$71$	−1.85164	−	3.20713i	−0.219749	−	0.380616i	0.734982	−	0.678086i	$-0.237190\pi$
$71$	−1.85164	−	3.20713i	−0.219749	−	0.380616i	−0.954731	+	0.297470i	$0.903857\pi$
$72$		0			0
$73$	2.79103	−	4.83421i	0.326666	−	0.565801i	−0.655182	−	0.755471i	$-0.727408\pi$
$73$	2.79103	−	4.83421i	0.326666	−	0.565801i	0.981848	+	0.189669i	$0.0607416\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−0.648100	+	1.12254i	−0.0738579	+	0.127926i
$78$		0			0
$79$	4.12506	+	7.14481i	0.464106	+	0.803854i	0.999161	−	0.0409627i	$-0.0130425\pi$
$79$	4.12506	+	7.14481i	0.464106	+	0.803854i	−0.535055	+	0.844817i	$0.679709\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−8.83630	+	15.3049i	−0.969910	+	1.67993i	−0.274107	+	0.961699i	$0.588382\pi$
$83$	−8.83630	+	15.3049i	−0.969910	+	1.67993i	−0.695802	+	0.718233i	$0.744951\pi$
$84$		0			0
$85$	1.72717	−	2.99154i	0.187338	−	0.324478i
$86$		0			0
$87$	−2.31553	−	4.01062i	−0.248251	−	0.429984i
$88$		0			0
$89$	−6.96652			−0.738449			−0.369225	−	0.929340i	$-0.620377\pi$
$89$	−6.96652			−0.738449			−0.369225	+	0.929340i	$0.620377\pi$
$90$		0			0
$91$	26.8418			2.81378
$92$		0			0
$93$	3.25426	+	5.63654i	0.337451	+	0.584482i
$94$		0			0
$95$	−3.54303	+	6.13671i	−0.363507	+	0.629613i
$96$		0			0
$97$	1.00524	−	1.74112i	0.102066	−	0.176784i	−0.810470	−	0.585781i	$-0.800788\pi$
$97$	1.00524	−	1.74112i	0.102066	−	0.176784i	0.912536	+	0.408997i	$0.134121\pi$
$98$		0			0
$99$	−0.165135	−	0.286022i	−0.0165967	−	0.0287463i
$100$		0			0
$101$	−5.57733	−	9.66022i	−0.554965	−	0.961228i	−0.997906	−	0.0646774i	$-0.979398\pi$
$101$	−5.57733	−	9.66022i	−0.554965	−	0.961228i	0.442941	−	0.896551i	$-0.353935\pi$
$102$		0			0
$103$	1.32048	+	2.28713i	0.130110	+	0.225358i	0.923719	−	0.383071i	$-0.125133\pi$
$103$	1.32048	+	2.28713i	0.130110	+	0.225358i	−0.793609	+	0.608429i	$0.791800\pi$
$104$		0			0
$105$	−1.96234	−	3.39887i	−0.191504	−	0.331695i
$106$		0			0
$107$	13.6421			1.31883			0.659417	−	0.751777i	$-0.270803\pi$
$107$	13.6421			1.31883			0.659417	+	0.751777i	$0.270803\pi$
$108$		0			0
$109$	−7.18360			−0.688064			−0.344032	−	0.938958i	$-0.611793\pi$
$109$	−7.18360			−0.688064			−0.344032	+	0.938958i	$0.611793\pi$
$110$		0			0
$111$	−2.28135	+	3.95142i	−0.216536	+	0.375052i
$112$		0			0
$113$	−1.53376	−	2.65655i	−0.144284	−	0.249908i	0.784821	−	0.619722i	$-0.212755\pi$
$113$	−1.53376	−	2.65655i	−0.144284	−	0.249908i	−0.929106	+	0.369814i	$0.879421\pi$
$114$		0			0
$115$	−0.989388	+	1.71367i	−0.0922609	+	0.159801i
$116$		0			0
$117$	−3.41962	+	5.92295i	−0.316144	+	0.547577i
$118$		0			0
$119$	−13.5571			−1.24278
$120$		0			0
$121$	5.44546	−	9.43181i	0.495042	−	0.857438i
$122$		0			0
$123$	3.72148	+	6.44579i	0.335554	+	0.581197i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.68246	+	15.0385i	0.770444	+	1.33445i	0.937320	+	0.348470i	$0.113299\pi$
$127$	8.68246	+	15.0385i	0.770444	+	1.33445i	−0.166876	+	0.985978i	$0.553368\pi$
$128$		0			0
$129$	5.35239			0.471251
$130$		0			0
$131$	17.5299			1.53159			0.765796	−	0.643084i	$-0.222345\pi$
$131$	17.5299			1.53159			0.765796	+	0.643084i	$0.222345\pi$
$132$		0			0
$133$	27.8105			2.41147
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	10.6390			0.908952			0.454476	−	0.890759i	$-0.349827\pi$
$137$	10.6390			0.908952			0.454476	+	0.890759i	$0.349827\pi$
$138$		0			0
$139$	7.57810			0.642766			0.321383	−	0.946949i	$-0.395852\pi$
$139$	7.57810			0.642766			0.321383	+	0.946949i	$0.395852\pi$
$140$		0			0
$141$	4.85734	+	8.41315i	0.409062	+	0.708515i
$142$		0			0
$143$	2.25879			0.188890
$144$		0			0
$145$	−2.31553	−	4.01062i	−0.192295	−	0.333064i
$146$		0			0
$147$	−4.20152	+	7.27725i	−0.346536	+	0.600218i
$148$		0			0
$149$	−8.11024			−0.664417			−0.332208	−	0.943206i	$-0.607794\pi$
$149$	−8.11024			−0.664417			−0.332208	+	0.943206i	$0.607794\pi$
$150$		0			0
$151$	−1.77250	+	3.07006i	−0.144244	+	0.249838i	−0.929091	−	0.369852i	$-0.879408\pi$
$151$	−1.77250	+	3.07006i	−0.144244	+	0.249838i	0.784847	+	0.619690i	$0.212742\pi$
$152$		0			0
$153$	1.72717	−	2.99154i	0.139633	−	0.241852i
$154$		0			0
$155$	3.25426	+	5.63654i	0.261388	+	0.452738i
$156$		0			0
$157$	4.46681	−	7.73673i	0.356490	−	0.617459i	−0.630882	−	0.775879i	$-0.717307\pi$
$157$	4.46681	−	7.73673i	0.356490	−	0.617459i	0.987372	+	0.158420i	$0.0506401\pi$
$158$		0			0
$159$	13.3034			1.05503
$160$		0			0
$161$	7.76604			0.612050
$162$		0			0
$163$	1.54635	+	2.67836i	0.121119	+	0.209785i	0.920209	−	0.391426i	$-0.128018\pi$
$163$	1.54635	+	2.67836i	0.121119	+	0.209785i	−0.799090	+	0.601211i	$0.794685\pi$
$164$		0			0
$165$	−0.165135	−	0.286022i	−0.0128557	−	0.0222668i
$166$		0			0
$167$	−5.19651	−	9.00062i	−0.402118	−	0.696489i	0.591863	−	0.806038i	$-0.298392\pi$
$167$	−5.19651	−	9.00062i	−0.402118	−	0.696489i	−0.993981	+	0.109550i	$0.965059\pi$
$168$		0			0
$169$	−16.8876	−	29.2502i	−1.29904	−	2.25001i
$170$		0			0
$171$	−3.54303	+	6.13671i	−0.270942	+	0.469286i
$172$		0			0
$173$	−6.08629	+	10.5418i	−0.462732	+	0.801475i	−0.999096	−	0.0425114i	$-0.986464\pi$
$173$	−6.08629	+	10.5418i	−0.462732	+	0.801475i	0.536364	+	0.843987i	$0.319797\pi$
$174$		0			0
$175$	−1.96234	−	3.39887i	−0.148339	−	0.256930i
$176$		0			0
$177$	−5.68339			−0.427190
$178$		0			0
$179$	16.3168			1.21957			0.609787	−	0.792566i	$-0.291255\pi$
$179$	16.3168			1.21957			0.609787	+	0.792566i	$0.291255\pi$
$180$		0			0
$181$	−9.25502	−	16.0302i	−0.687920	−	1.19151i	−0.972510	−	0.232863i	$-0.925191\pi$
$181$	−9.25502	−	16.0302i	−0.687920	−	1.19151i	0.284590	−	0.958649i	$-0.408143\pi$
$182$		0			0
$183$	1.97466	−	3.42021i	0.145971	−	0.252830i
$184$		0			0
$185$	−2.28135	+	3.95142i	−0.167728	+	0.290514i
$186$		0			0
$187$	−1.14086			−0.0834281
$188$		0			0
$189$	−1.96234	−	3.39887i	−0.142739	−	0.247231i
$190$		0			0
$191$	−12.1060	+	20.9682i	−0.875958	+	1.51720i	−0.0202194	+	0.999796i	$0.506436\pi$
$191$	−12.1060	+	20.9682i	−0.875958	+	1.51720i	−0.855739	+	0.517408i	$0.826897\pi$
$192$		0			0
$193$	−1.99202			−0.143388			−0.0716942	−	0.997427i	$-0.522841\pi$
$193$	−1.99202			−0.143388			−0.0716942	+	0.997427i	$0.522841\pi$
$194$		0			0
$195$	−3.41962	+	5.92295i	−0.244884	+	0.424152i
$196$		0			0
$197$	−3.12651	−	5.41527i	−0.222755	−	0.385822i	0.732889	−	0.680348i	$-0.238172\pi$
$197$	−3.12651	−	5.41527i	−0.222755	−	0.385822i	−0.955643	+	0.294526i	$0.904838\pi$
$198$		0			0
$199$	11.7627	−	20.3736i	0.833836	−	1.44425i	−0.0611384	−	0.998129i	$-0.519473\pi$
$199$	11.7627	−	20.3736i	0.833836	−	1.44425i	0.894975	−	0.446117i	$-0.147194\pi$
$200$		0			0
$201$	−5.78845	+	5.78738i	−0.408286	+	0.408211i
$202$		0			0
$203$	−9.08771	+	15.7404i	−0.637832	+	1.10476i
$204$		0			0
$205$	3.72148	+	6.44579i	0.259919	+	0.450193i
$206$		0			0
$207$	−0.989388	+	1.71367i	−0.0687672	+	0.119108i
$208$		0			0
$209$	2.34031			0.161883
$210$		0			0
$211$	−13.4174	+	23.2396i	−0.923692	+	1.59988i	−0.130041	+	0.991509i	$0.541511\pi$
$211$	−13.4174	+	23.2396i	−0.923692	+	1.59988i	−0.793651	+	0.608373i	$0.791823\pi$
$212$		0			0
$213$	−1.85164	−	3.20713i	−0.126872	−	0.219749i
$214$		0			0
$215$	5.35239			0.365030
$216$		0			0
$217$	12.7719	−	22.1216i	0.867013	−	1.50171i
$218$		0			0
$219$	2.79103	−	4.83421i	0.188600	−	0.326666i
$220$		0			0
$221$	11.8125	+	20.4599i	0.794595	+	1.37628i
$222$		0			0
$223$	−2.59113			−0.173515			−0.0867576	−	0.996229i	$-0.527651\pi$
$223$	−2.59113			−0.173515			−0.0867576	+	0.996229i	$0.527651\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	1.43559	+	2.48652i	0.0952836	+	0.165036i	0.909727	−	0.415207i	$-0.136291\pi$
$227$	1.43559	+	2.48652i	0.0952836	+	0.165036i	−0.814443	+	0.580243i	$0.802958\pi$
$228$		0			0
$229$	−9.08469	+	15.7351i	−0.600333	+	1.03981i	0.392437	+	0.919779i	$0.371632\pi$
$229$	−9.08469	+	15.7351i	−0.600333	+	1.03981i	−0.992770	+	0.120029i	$0.961701\pi$
$230$		0			0
$231$	−0.648100	+	1.12254i	−0.0426419	+	0.0738579i
$232$		0			0
$233$	14.1180	+	24.4530i	0.924899	+	1.60197i	0.791723	+	0.610880i	$0.209184\pi$
$233$	14.1180	+	24.4530i	0.924899	+	1.60197i	0.133176	+	0.991092i	$0.457483\pi$
$234$		0			0
$235$	4.85734	+	8.41315i	0.316858	+	0.548814i
$236$		0			0
$237$	4.12506	+	7.14481i	0.267951	+	0.464106i
$238$		0			0
$239$	−4.12717	−	7.14847i	−0.266964	−	0.462396i	0.701112	−	0.713051i	$-0.252687\pi$
$239$	−4.12717	−	7.14847i	−0.266964	−	0.462396i	−0.968076	+	0.250655i	$0.919354\pi$
$240$		0			0
$241$	−17.4156			−1.12184			−0.560918	−	0.827871i	$-0.689552\pi$
$241$	−17.4156			−1.12184			−0.560918	+	0.827871i	$0.689552\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−4.20152	+	7.27725i	−0.268425	+	0.464927i
$246$		0			0
$247$	−24.2316	−	41.9704i	−1.54182	−	2.67051i
$248$		0			0
$249$	−8.83630	+	15.3049i	−0.559978	+	0.969910i
$250$		0			0
$251$	4.86501	−	8.42645i	0.307077	−	0.531873i	−0.670645	−	0.741779i	$-0.733982\pi$
$251$	4.86501	−	8.42645i	0.307077	−	0.531873i	0.977722	+	0.209906i	$0.0673158\pi$
$252$		0			0
$253$	0.653530			0.0410871
$254$		0			0
$255$	1.72717	−	2.99154i	0.108159	−	0.187338i
$256$		0			0
$257$	3.29008	+	5.69859i	0.205230	+	0.355468i	0.950206	−	0.311623i	$-0.100873\pi$
$257$	3.29008	+	5.69859i	0.205230	+	0.355468i	−0.744976	+	0.667091i	$0.767539\pi$
$258$		0			0
$259$	17.9071			1.11269
$260$		0			0
$261$	−2.31553	−	4.01062i	−0.143328	−	0.248251i
$262$		0			0
$263$	−9.58787			−0.591213			−0.295607	−	0.955310i	$-0.595522\pi$
$263$	−9.58787			−0.591213			−0.295607	+	0.955310i	$0.595522\pi$
$264$		0			0
$265$	13.3034			0.817222
$266$		0			0
$267$	−6.96652			−0.426344
$268$		0			0
$269$	−2.74795			−0.167545			−0.0837727	−	0.996485i	$-0.526697\pi$
$269$	−2.74795			−0.167545			−0.0837727	+	0.996485i	$0.526697\pi$
$270$		0			0
$271$	−23.4576			−1.42494			−0.712472	−	0.701700i	$-0.752425\pi$
$271$	−23.4576			−1.42494			−0.712472	+	0.701700i	$0.752425\pi$
$272$		0			0
$273$	26.8418			1.62454
$274$		0			0
$275$	−0.165135	−	0.286022i	−0.00995801	−	0.0172478i
$276$		0			0
$277$	−23.0593			−1.38550			−0.692749	−	0.721179i	$-0.743601\pi$
$277$	−23.0593			−1.38550			−0.692749	+	0.721179i	$0.743601\pi$
$278$		0			0
$279$	3.25426	+	5.63654i	0.194827	+	0.337451i
$280$		0			0
$281$	−3.37254	+	5.84141i	−0.201189	+	0.348469i	−0.948912	−	0.315542i	$-0.897814\pi$
$281$	−3.37254	+	5.84141i	−0.201189	+	0.348469i	0.747723	+	0.664011i	$0.231147\pi$
$282$		0			0
$283$	−15.3983			−0.915334			−0.457667	−	0.889124i	$-0.651315\pi$
$283$	−15.3983			−0.915334			−0.457667	+	0.889124i	$0.651315\pi$
$284$		0			0
$285$	−3.54303	+	6.13671i	−0.209871	+	0.363507i
$286$		0			0
$287$	14.6056	−	25.2976i	0.862140	−	1.49327i
$288$		0			0
$289$	2.53379	+	4.38865i	0.149046	+	0.258156i
$290$		0			0
$291$	1.00524	−	1.74112i	0.0589280	−	0.102066i
$292$		0			0
$293$	5.62807			0.328796			0.164398	−	0.986394i	$-0.447432\pi$
$293$	5.62807			0.328796			0.164398	+	0.986394i	$0.447432\pi$
$294$		0			0
$295$	−5.68339			−0.330900
$296$		0			0
$297$	−0.165135	−	0.286022i	−0.00958210	−	0.0165967i
$298$		0			0
$299$	−6.76666	−	11.7202i	−0.391326	−	0.677796i
$300$		0			0
$301$	−10.5032	−	18.1920i	−0.605393	−	1.04857i
$302$		0			0
$303$	−5.57733	−	9.66022i	−0.320409	−	0.554965i
$304$		0			0
$305$	1.97466	−	3.42021i	0.113069	−	0.195841i
$306$		0			0
$307$	−15.4529	+	26.7652i	−0.881942	+	1.52757i	−0.0327629	+	0.999463i	$0.510431\pi$
$307$	−15.4529	+	26.7652i	−0.881942	+	1.52757i	−0.849179	+	0.528105i	$0.822903\pi$
$308$		0			0
$309$	1.32048	+	2.28713i	0.0751193	+	0.130110i
$310$		0			0
$311$	−23.4156			−1.32778			−0.663888	−	0.747832i	$-0.731095\pi$
$311$	−23.4156			−1.32778			−0.663888	+	0.747832i	$0.731095\pi$
$312$		0			0
$313$	8.71922			0.492840			0.246420	−	0.969163i	$-0.420746\pi$
$313$	8.71922			0.492840			0.246420	+	0.969163i	$0.420746\pi$
$314$		0			0
$315$	−1.96234	−	3.39887i	−0.110565	−	0.191504i
$316$		0			0
$317$	−9.78814	+	16.9535i	−0.549756	+	0.952206i	0.448534	+	0.893766i	$0.351946\pi$
$317$	−9.78814	+	16.9535i	−0.549756	+	0.952206i	−0.998291	+	0.0584406i	$0.981387\pi$
$318$		0			0
$319$	−0.764751	+	1.32459i	−0.0428178	+	0.0741627i
$320$		0			0
$321$	13.6421			0.761429
$322$		0			0
$323$	12.2388	+	21.1982i	0.680986	+	1.17950i
$324$		0			0
$325$	−3.41962	+	5.92295i	−0.189686	+	0.328546i
$326$		0			0
$327$	−7.18360			−0.397254
$328$		0			0
$329$	19.0634	−	33.0189i	1.05100	−	1.82039i
$330$		0			0
$331$	9.68919	+	16.7822i	0.532566	+	0.922432i	0.999277	+	0.0380218i	$0.0121056\pi$
$331$	9.68919	+	16.7822i	0.532566	+	0.922432i	−0.466711	+	0.884410i	$0.654561\pi$
$332$		0			0
$333$	−2.28135	+	3.95142i	−0.125017	+	0.216536i
$334$		0			0
$335$	−5.78845	+	5.78738i	−0.316257	+	0.316199i
$336$		0			0
$337$	0.495420	−	0.858092i	0.0269872	−	0.0467433i	−0.852216	−	0.523190i	$-0.824742\pi$
$337$	0.495420	−	0.858092i	0.0269872	−	0.0467433i	0.879204	+	0.476446i	$0.158075\pi$
$338$		0			0
$339$	−1.53376	−	2.65655i	−0.0833025	−	0.144284i
$340$		0			0
$341$	1.07478	−	1.86158i	0.0582028	−	0.100810i
$342$		0			0
$343$	5.50650			0.297323
$344$		0			0
$345$	−0.989388	+	1.71367i	−0.0532669	+	0.0922609i
$346$		0			0
$347$	5.11776	+	8.86421i	0.274736	+	0.475856i	0.970068	−	0.242832i	$-0.0780763\pi$
$347$	5.11776	+	8.86421i	0.274736	+	0.475856i	−0.695333	+	0.718688i	$0.744743\pi$
$348$		0			0
$349$	−6.41054			−0.343148			−0.171574	−	0.985171i	$-0.554885\pi$
$349$	−6.41054			−0.343148			−0.171574	+	0.985171i	$0.554885\pi$
$350$		0			0
$351$	−3.41962	+	5.92295i	−0.182526	+	0.316144i
$352$		0			0
$353$	7.31382	−	12.6679i	0.389275	−	0.674245i	−0.603077	−	0.797683i	$-0.706059\pi$
$353$	7.31382	−	12.6679i	0.389275	−	0.674245i	0.992352	+	0.123438i	$0.0393922\pi$
$354$		0			0
$355$	−1.85164	−	3.20713i	−0.0982746	−	0.170217i
$356$		0			0
$357$	−13.5571			−0.717519
$358$		0			0
$359$	−31.6722			−1.67160			−0.835798	−	0.549037i	$-0.814994\pi$
$359$	−31.6722			−1.67160			−0.835798	+	0.549037i	$0.814994\pi$
$360$		0			0
$361$	−15.6061	−	27.0306i	−0.821376	−	1.42267i
$362$		0			0
$363$	5.44546	−	9.43181i	0.285813	−	0.495042i
$364$		0			0
$365$	2.79103	−	4.83421i	0.146089	−	0.253034i
$366$		0			0
$367$	−14.7023	−	25.4651i	−0.767454	−	1.32927i	−0.938939	−	0.344083i	$-0.888190\pi$
$367$	−14.7023	−	25.4651i	−0.767454	−	1.32927i	0.171485	−	0.985187i	$-0.445143\pi$
$368$		0			0
$369$	3.72148	+	6.44579i	0.193732	+	0.335554i
$370$		0			0
$371$	−26.1058	−	45.2165i	−1.35534	−	2.34752i
$372$		0			0
$373$	15.2527	+	26.4185i	0.789756	+	1.36790i	0.926116	+	0.377238i	$0.123126\pi$
$373$	15.2527	+	26.4185i	0.789756	+	1.36790i	−0.136361	+	0.990659i	$0.543541\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	31.6730			1.63124
$378$		0			0
$379$	−5.29067	+	9.16371i	−0.271764	+	0.470708i	−0.969313	−	0.245828i	$-0.920940\pi$
$379$	−5.29067	+	9.16371i	−0.271764	+	0.470708i	0.697550	+	0.716536i	$0.254274\pi$
$380$		0			0
$381$	8.68246	+	15.0385i	0.444816	+	0.770444i
$382$		0			0
$383$	−13.6989	+	23.7272i	−0.699980	+	1.21240i	0.268492	+	0.963282i	$0.413475\pi$
$383$	−13.6989	+	23.7272i	−0.699980	+	1.21240i	−0.968473	+	0.249120i	$0.919859\pi$
$384$		0			0
$385$	−0.648100	+	1.12254i	−0.0330303	+	0.0572101i
$386$		0			0
$387$	5.35239			0.272077
$388$		0			0
$389$	−8.60121	+	14.8977i	−0.436099	+	0.755345i	−0.997385	−	0.0722770i	$-0.976973\pi$
$389$	−8.60121	+	14.8977i	−0.436099	+	0.755345i	0.561286	+	0.827622i	$0.310307\pi$
$390$		0			0
$391$	3.41768	+	5.91959i	0.172839	+	0.299366i
$392$		0			0
$393$	17.5299			0.884265
$394$		0			0
$395$	4.12506	+	7.14481i	0.207554	+	0.359495i
$396$		0			0
$397$	22.4688			1.12768			0.563838	−	0.825885i	$-0.309324\pi$
$397$	22.4688			1.12768			0.563838	+	0.825885i	$0.309324\pi$
$398$		0			0
$399$	27.8105			1.39226
$400$		0			0
$401$	13.2250			0.660427			0.330213	−	0.943906i	$-0.392879\pi$
$401$	13.2250			0.660427			0.330213	+	0.943906i	$0.392879\pi$
$402$		0			0
$403$	−44.5133			−2.21736
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	1.50692			0.0746955
$408$		0			0
$409$	−1.22967	−	2.12986i	−0.0608035	−	0.105315i	0.834021	−	0.551732i	$-0.186033\pi$
$409$	−1.22967	−	2.12986i	−0.0608035	−	0.105315i	−0.894825	+	0.446418i	$0.852700\pi$
$410$		0			0
$411$	10.6390			0.524783
$412$		0			0
$413$	11.1527	+	19.3171i	0.548790	+	0.950532i
$414$		0			0
$415$	−8.83630	+	15.3049i	−0.433757	+	0.751289i
$416$		0			0
$417$	7.57810			0.371101
$418$		0			0
$419$	−1.29623	+	2.24513i	−0.0633249	+	0.109682i	−0.895950	−	0.444156i	$-0.853504\pi$
$419$	−1.29623	+	2.24513i	−0.0633249	+	0.109682i	0.832625	+	0.553837i	$0.186837\pi$
$420$		0			0
$421$	−8.70135	+	15.0712i	−0.424078	+	0.734524i	−0.996334	−	0.0855509i	$-0.972735\pi$
$421$	−8.70135	+	15.0712i	−0.424078	+	0.734524i	0.572256	+	0.820075i	$0.306068\pi$
$422$		0			0
$423$	4.85734	+	8.41315i	0.236172	+	0.409062i
$424$		0			0
$425$	1.72717	−	2.99154i	0.0837799	−	0.145111i
$426$		0			0
$427$	−15.4998			−0.750088
$428$		0			0
$429$	2.25879			0.109056
$430$		0			0
$431$	15.1339	+	26.2128i	0.728976	+	1.26262i	0.957316	+	0.289042i	$0.0933368\pi$
$431$	15.1339	+	26.2128i	0.728976	+	1.26262i	−0.228340	+	0.973581i	$0.573330\pi$
$432$		0			0
$433$	−17.5768	−	30.4439i	−0.844687	−	1.46304i	−0.885893	−	0.463890i	$-0.846453\pi$
$433$	−17.5768	−	30.4439i	−0.844687	−	1.46304i	0.0412060	−	0.999151i	$-0.486880\pi$
$434$		0			0
$435$	−2.31553	−	4.01062i	−0.111021	−	0.192295i
$436$		0			0
$437$	−7.01087	−	12.1432i	−0.335375	−	0.580887i
$438$		0			0
$439$	11.7722	−	20.3900i	0.561855	−	0.973162i	−0.435479	−	0.900199i	$-0.643421\pi$
$439$	11.7722	−	20.3900i	0.561855	−	0.973162i	0.997335	−	0.0729634i	$-0.0232456\pi$
$440$		0			0
$441$	−4.20152	+	7.27725i	−0.200073	+	0.346536i
$442$		0			0
$443$	13.5982	+	23.5527i	0.646068	+	1.11902i	0.984054	+	0.177872i	$0.0569212\pi$
$443$	13.5982	+	23.5527i	0.646068	+	1.11902i	−0.337986	+	0.941151i	$0.609746\pi$
$444$		0			0
$445$	−6.96652			−0.330245
$446$		0			0
$447$	−8.11024			−0.383601
$448$		0			0
$449$	3.98678	+	6.90531i	0.188148	+	0.325882i	0.944633	−	0.328129i	$-0.106418\pi$
$449$	3.98678	+	6.90531i	0.188148	+	0.325882i	−0.756485	+	0.654011i	$0.773085\pi$
$450$		0			0
$451$	1.22909	−	2.12885i	0.0578757	−	0.100244i
$452$		0			0
$453$	−1.77250	+	3.07006i	−0.0832792	+	0.144244i
$454$		0			0
$455$	26.8418			1.25836
$456$		0			0
$457$	0.221554	+	0.383743i	0.0103639	+	0.0179507i	0.871161	−	0.490998i	$-0.163368\pi$
$457$	0.221554	+	0.383743i	0.0103639	+	0.0179507i	−0.860797	+	0.508949i	$0.830034\pi$
$458$		0			0
$459$	1.72717	−	2.99154i	0.0806172	−	0.139633i
$460$		0			0
$461$	−4.10322			−0.191106			−0.0955530	−	0.995424i	$-0.530462\pi$
$461$	−4.10322			−0.191106			−0.0955530	+	0.995424i	$0.530462\pi$
$462$		0			0
$463$	14.5920	−	25.2740i	0.678146	−	1.17458i	−0.297393	−	0.954755i	$-0.596117\pi$
$463$	14.5920	−	25.2740i	0.678146	−	1.17458i	0.975539	−	0.219828i	$-0.0705495\pi$
$464$		0			0
$465$	3.25426	+	5.63654i	0.150913	+	0.261388i
$466$		0			0
$467$	19.7034	−	34.1272i	0.911763	−	1.57922i	0.100190	−	0.994968i	$-0.468055\pi$
$467$	19.7034	−	34.1272i	0.911763	−	1.57922i	0.811573	−	0.584252i	$-0.198612\pi$
$468$		0			0
$469$	31.0294	+	8.31738i	1.43281	+	0.384061i
$470$		0			0
$471$	4.46681	−	7.73673i	0.205820	−	0.356490i
$472$		0			0
$473$	−0.883866	−	1.53090i	−0.0406402	−	0.0703909i
$474$		0			0
$475$	−3.54303	+	6.13671i	−0.162565	+	0.281572i
$476$		0			0
$477$	13.3034			0.609122
$478$		0			0
$479$	5.69448	−	9.86313i	0.260187	−	0.450658i	−0.706104	−	0.708108i	$-0.749549\pi$
$479$	5.69448	−	9.86313i	0.260187	−	0.450658i	0.966292	+	0.257450i	$0.0828823\pi$
$480$		0			0
$481$	−15.6027	−	27.0247i	−0.711423	−	1.23222i
$482$		0			0
$483$	7.76604			0.353367
$484$		0			0
$485$	1.00524	−	1.74112i	0.0456454	−	0.0790602i
$486$		0			0
$487$	9.35600	−	16.2051i	0.423961	−	0.734321i	−0.572362	−	0.820001i	$-0.693973\pi$
$487$	9.35600	−	16.2051i	0.423961	−	0.734321i	0.996323	+	0.0856796i	$0.0273061\pi$
$488$		0			0
$489$	1.54635	+	2.67836i	0.0699283	+	0.121119i
$490$		0			0
$491$	2.82238			0.127372			0.0636861	−	0.997970i	$-0.479714\pi$
$491$	2.82238			0.127372			0.0636861	+	0.997970i	$0.479714\pi$
$492$		0			0
$493$	−15.9973			−0.720480
$494$		0			0
$495$	−0.165135	−	0.286022i	−0.00742226	−	0.0128557i
$496$		0			0
$497$	−7.26706	+	12.5869i	−0.325972	+	0.564600i
$498$		0			0
$499$	9.88528	−	17.1218i	0.442526	−	0.766477i	−0.555350	−	0.831616i	$-0.687416\pi$
$499$	9.88528	−	17.1218i	0.442526	−	0.766477i	0.997876	+	0.0651394i	$0.0207492\pi$
$500$		0			0
$501$	−5.19651	−	9.00062i	−0.232163	−	0.402118i
$502$		0			0
$503$	−5.35919	−	9.28239i	−0.238954	−	0.413881i	0.721460	−	0.692456i	$-0.243471\pi$
$503$	−5.35919	−	9.28239i	−0.238954	−	0.413881i	−0.960415	+	0.278575i	$0.910138\pi$
$504$		0			0
$505$	−5.57733	−	9.66022i	−0.248188	−	0.429874i
$506$		0			0
$507$	−16.8876	−	29.2502i	−0.750004	−	1.29904i
$508$		0			0
$509$	34.9880			1.55082			0.775408	−	0.631461i	$-0.217544\pi$
$509$	34.9880			1.55082			0.775408	+	0.631461i	$0.217544\pi$
$510$		0			0
$511$	−21.9078			−0.969143
$512$		0			0
$513$	−3.54303	+	6.13671i	−0.156429	+	0.270942i
$514$		0			0
$515$	1.32048	+	2.28713i	0.0581872	+	0.100783i
$516$		0			0
$517$	1.60423	−	2.77861i	0.0705540	−	0.122203i
$518$		0			0
$519$	−6.08629	+	10.5418i	−0.267158	+	0.462732i
$520$		0			0
$521$	10.7534			0.471114			0.235557	−	0.971861i	$-0.424309\pi$
$521$	10.7534			0.471114			0.235557	+	0.971861i	$0.424309\pi$
$522$		0			0
$523$	−16.6674	+	28.8688i	−0.728815	+	1.26235i	0.228569	+	0.973528i	$0.426595\pi$
$523$	−16.6674	+	28.8688i	−0.728815	+	1.26235i	−0.957384	+	0.288817i	$0.906738\pi$
$524$		0			0
$525$	−1.96234	−	3.39887i	−0.0856434	−	0.148339i
$526$		0			0
$527$	22.4826			0.979357
$528$		0			0
$529$	9.54222	+	16.5276i	0.414879	+	0.718592i
$530$		0			0
$531$	−5.68339			−0.246638
$532$		0			0
$533$	−50.9041			−2.20490
$534$		0			0
$535$	13.6421			0.589801
$536$		0			0
$537$	16.3168			0.704121
$538$		0			0
$539$	2.77527			0.119539
$540$		0			0
$541$	22.1659			0.952985			0.476492	−	0.879179i	$-0.341908\pi$
$541$	22.1659			0.952985			0.476492	+	0.879179i	$0.341908\pi$
$542$		0			0
$543$	−9.25502	−	16.0302i	−0.397171	−	0.687920i
$544$		0			0
$545$	−7.18360			−0.307711
$546$		0			0
$547$	2.97141	+	5.14663i	0.127048	+	0.220054i	0.922532	−	0.385921i	$-0.126116\pi$
$547$	2.97141	+	5.14663i	0.127048	+	0.220054i	−0.795483	+	0.605975i	$0.792783\pi$
$548$		0			0
$549$	1.97466	−	3.42021i	0.0842765	−	0.145971i
$550$		0			0
$551$	32.8160			1.39801
$552$		0			0
$553$	16.1895	−	28.0411i	0.688448	−	1.19243i
$554$		0			0
$555$	−2.28135	+	3.95142i	−0.0968380	+	0.167728i
$556$		0			0
$557$	−0.0179960	−	0.0311700i	−0.000762515	−	0.00132071i	0.865644	−	0.500660i	$-0.166909\pi$
$557$	−0.0179960	−	0.0311700i	−0.000762515	−	0.00132071i	−0.866406	+	0.499339i	$0.833576\pi$
$558$		0			0
$559$	−18.3031	+	31.7019i	−0.774140	+	1.34085i
$560$		0			0
$561$	−1.14086			−0.0481672
$562$		0			0
$563$	0.972741			0.0409961			0.0204981	−	0.999790i	$-0.493475\pi$
$563$	0.972741			0.0409961			0.0204981	+	0.999790i	$0.493475\pi$
$564$		0			0
$565$	−1.53376	−	2.65655i	−0.0645259	−	0.111762i
$566$		0			0
$567$	−1.96234	−	3.39887i	−0.0824104	−	0.142739i
$568$		0			0
$569$	−1.37956	−	2.38946i	−0.0578341	−	0.100172i	0.835659	−	0.549249i	$-0.185086\pi$
$569$	−1.37956	−	2.38946i	−0.0578341	−	0.100172i	−0.893493	+	0.449077i	$0.851753\pi$
$570$		0			0
$571$	5.13282	+	8.89031i	0.214802	+	0.372048i	0.953211	−	0.302305i	$-0.0977561\pi$
$571$	5.13282	+	8.89031i	0.214802	+	0.372048i	−0.738409	+	0.674353i	$0.764423\pi$
$572$		0			0
$573$	−12.1060	+	20.9682i	−0.505735	+	0.875958i
$574$		0			0
$575$	−0.989388	+	1.71367i	−0.0412603	+	0.0714650i
$576$		0			0
$577$	−6.03772	−	10.4576i	−0.251354	−	0.435357i	0.712545	−	0.701626i	$-0.247542\pi$
$577$	−6.03772	−	10.4576i	−0.251354	−	0.435357i	−0.963899	+	0.266269i	$0.914209\pi$
$578$		0			0
$579$	−1.99202			−0.0827854
$580$		0			0
$581$	69.3591			2.87750
$582$		0			0
$583$	−2.19686	−	3.80507i	−0.0909846	−	0.157590i
$584$		0			0
$585$	−3.41962	+	5.92295i	−0.141384	+	0.244884i
$586$		0			0
$587$	5.54727	−	9.60815i	0.228960	−	0.396571i	−0.728540	−	0.685003i	$-0.759801\pi$
$587$	5.54727	−	9.60815i	0.228960	−	0.396571i	0.957500	+	0.288432i	$0.0931341\pi$
$588$		0			0
$589$	−46.1198			−1.90033
$590$		0			0
$591$	−3.12651	−	5.41527i	−0.128607	−	0.222755i
$592$		0			0
$593$	2.25996	−	3.91436i	0.0928054	−	0.160744i	−0.815885	−	0.578214i	$-0.803750\pi$
$593$	2.25996	−	3.91436i	0.0928054	−	0.160744i	0.908691	+	0.417470i	$0.137083\pi$
$594$		0			0
$595$	−13.5571			−0.555788
$596$		0			0
$597$	11.7627	−	20.3736i	0.481415	−	0.833836i
$598$		0			0
$599$	17.4955	+	30.3031i	0.714848	+	1.23815i	0.963018	+	0.269436i	$0.0868374\pi$
$599$	17.4955	+	30.3031i	0.714848	+	1.23815i	−0.248170	+	0.968716i	$0.579829\pi$
$600$		0			0
$601$	19.1833	−	33.2265i	0.782504	−	1.35534i	−0.147975	−	0.988991i	$-0.547275\pi$
$601$	19.1833	−	33.2265i	0.782504	−	1.35534i	0.930479	−	0.366346i	$-0.119391\pi$
$602$		0			0
$603$	−5.78845	+	5.78738i	−0.235724	+	0.235681i
$604$		0			0
$605$	5.44546	−	9.43181i	0.221389	−	0.383458i
$606$		0			0
$607$	−11.7172	−	20.2948i	−0.475586	−	0.823739i	0.524023	−	0.851704i	$-0.324431\pi$
$607$	−11.7172	−	20.2948i	−0.475586	−	0.823739i	−0.999609	+	0.0279648i	$0.991097\pi$
$608$		0			0
$609$	−9.08771	+	15.7404i	−0.368253	+	0.637832i
$610$		0			0
$611$	−66.4410			−2.68791
$612$		0			0
$613$	−5.02798	+	8.70871i	−0.203078	+	0.351742i	−0.949519	−	0.313710i	$-0.898428\pi$
$613$	−5.02798	+	8.70871i	−0.203078	+	0.351742i	0.746441	+	0.665452i	$0.231761\pi$
$614$		0			0
$615$	3.72148	+	6.44579i	0.150064	+	0.259919i
$616$		0			0
$617$	−4.63280			−0.186510			−0.0932548	−	0.995642i	$-0.529727\pi$
$617$	−4.63280			−0.186510			−0.0932548	+	0.995642i	$0.529727\pi$
$618$		0			0
$619$	22.3070	−	38.6369i	0.896596	−	1.55295i	0.0647782	−	0.997900i	$-0.479366\pi$
$619$	22.3070	−	38.6369i	0.896596	−	1.55295i	0.831817	−	0.555049i	$-0.187301\pi$
$620$		0			0
$621$	−0.989388	+	1.71367i	−0.0397028	+	0.0687672i
$622$		0			0
$623$	13.6706	+	23.6782i	0.547703	+	0.948649i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	2.34031			0.0934631
$628$		0			0
$629$	7.88055	+	13.6495i	0.314218	+	0.544242i
$630$		0			0
$631$	2.02341	−	3.50464i	0.0805505	−	0.139518i	−0.822936	−	0.568134i	$-0.807666\pi$
$631$	2.02341	−	3.50464i	0.0805505	−	0.139518i	0.903487	+	0.428616i	$0.140999\pi$
$632$		0			0
$633$	−13.4174	+	23.2396i	−0.533294	+	0.923692i
$634$		0			0
$635$	8.68246	+	15.0385i	0.344553	+	0.596783i
$636$		0			0
$637$	−28.7352	−	49.7709i	−1.13853	−	1.97199i
$638$		0			0
$639$	−1.85164	−	3.20713i	−0.0732496	−	0.126872i
$640$		0			0
$641$	−20.1961	−	34.9807i	−0.797699	−	1.38165i	−0.921111	−	0.389299i	$-0.872717\pi$
$641$	−20.1961	−	34.9807i	−0.797699	−	1.38165i	0.123413	−	0.992355i	$-0.460616\pi$
$642$		0			0
$643$	20.4876			0.807952			0.403976	−	0.914770i	$-0.367628\pi$
$643$	20.4876			0.807952			0.403976	+	0.914770i	$0.367628\pi$
$644$		0			0
$645$	5.35239			0.210750
$646$		0			0
$647$	−17.3160	+	29.9922i	−0.680763	+	1.17912i	0.293985	+	0.955810i	$0.405018\pi$
$647$	−17.3160	+	29.9922i	−0.680763	+	1.17912i	−0.974748	+	0.223306i	$0.928315\pi$
$648$		0			0
$649$	0.938527	+	1.62558i	0.0368404	+	0.0638094i
$650$		0			0
$651$	12.7719	−	22.1216i	0.500570	−	0.867013i
$652$		0			0
$653$	−15.6884	+	27.1731i	−0.613935	+	1.06337i	0.376635	+	0.926362i	$0.377081\pi$
$653$	−15.6884	+	27.1731i	−0.613935	+	1.06337i	−0.990570	+	0.137005i	$0.956252\pi$
$654$		0			0
$655$	17.5299			0.684949
$656$		0			0
$657$	2.79103	−	4.83421i	0.108889	−	0.188600i
$658$		0			0
$659$	−14.4688	−	25.0606i	−0.563623	−	0.976224i	−0.997176	−	0.0750957i	$-0.976074\pi$
$659$	−14.4688	−	25.0606i	−0.563623	−	0.976224i	0.433553	−	0.901128i	$-0.357260\pi$
$660$		0			0
$661$	−31.6814			−1.23226			−0.616132	−	0.787643i	$-0.711301\pi$
$661$	−31.6814			−1.23226			−0.616132	+	0.787643i	$0.711301\pi$
$662$		0			0
$663$	11.8125	+	20.4599i	0.458760	+	0.794595i
$664$		0			0
$665$	27.8105			1.07844
$666$		0			0
$667$	9.16385			0.354826
$668$		0			0
$669$	−2.59113			−0.100179
$670$		0			0
$671$	−1.30434			−0.0503536
$672$		0			0
$673$	22.1781			0.854901			0.427451	−	0.904039i	$-0.359412\pi$
$673$	22.1781			0.854901			0.427451	+	0.904039i	$0.359412\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−0.377326	−	0.653547i	−0.0145018	−	0.0251179i	0.858683	−	0.512506i	$-0.171283\pi$
$677$	−0.377326	−	0.653547i	−0.0145018	−	0.0251179i	−0.873185	+	0.487388i	$0.837950\pi$
$678$		0			0
$679$	−7.89044			−0.302807
$680$		0			0
$681$	1.43559	+	2.48652i	0.0550120	+	0.0952836i
$682$		0			0
$683$	14.8316	−	25.6891i	0.567516	−	0.982967i	−0.429294	−	0.903165i	$-0.641238\pi$
$683$	14.8316	−	25.6891i	0.567516	−	0.982967i	0.996811	−	0.0798026i	$-0.0254290\pi$
$684$		0			0
$685$	10.6390			0.406495
$686$		0			0
$687$	−9.08469	+	15.7351i	−0.346603	+	0.600333i
$688$		0			0
$689$	−45.4926	+	78.7955i	−1.73313	+	3.00187i
$690$		0			0
$691$	−6.44570	−	11.1643i	−0.245206	−	0.424709i	0.716984	−	0.697090i	$-0.245522\pi$
$691$	−6.44570	−	11.1643i	−0.245206	−	0.424709i	−0.962190	+	0.272381i	$0.912189\pi$
$692$		0			0
$693$	−0.648100	+	1.12254i	−0.0246193	+	0.0426419i
$694$		0			0
$695$	7.57810			0.287454
$696$		0			0
$697$	25.7104			0.973853
$698$		0			0
$699$	14.1180	+	24.4530i	0.533991	+	0.924899i
$700$		0			0
$701$	−5.49541	−	9.51834i	−0.207559	−	0.359503i	0.743386	−	0.668863i	$-0.233219\pi$
$701$	−5.49541	−	9.51834i	−0.207559	−	0.359503i	−0.950945	+	0.309360i	$0.899885\pi$
$702$		0			0
$703$	−16.1658	−	28.0000i	−0.609705	−	1.05604i
$704$		0			0
$705$	4.85734	+	8.41315i	0.182938	+	0.316858i
$706$		0			0
$707$	−21.8892	+	37.9132i	−0.823228	+	1.42587i
$708$		0			0
$709$	4.22007	−	7.30937i	0.158488	−	0.274509i	−0.775836	−	0.630935i	$-0.782671\pi$
$709$	4.22007	−	7.30937i	0.158488	−	0.274509i	0.934324	+	0.356426i	$0.116005\pi$
$710$		0			0
$711$	4.12506	+	7.14481i	0.154702	+	0.267951i
$712$		0			0
$713$	−12.8789			−0.482318
$714$		0			0
$715$	2.25879			0.0844741
$716$		0			0
$717$	−4.12717	−	7.14847i	−0.154132	−	0.266964i
$718$		0			0
$719$	1.29459	−	2.24229i	0.0482800	−	0.0836234i	−0.840875	−	0.541229i	$-0.817959\pi$
$719$	1.29459	−	2.24229i	0.0482800	−	0.0836234i	0.889155	+	0.457605i	$0.151293\pi$
$720$		0			0
$721$	5.18244	−	8.97625i	0.193004	−	0.334293i
$722$		0			0
$723$	−17.4156			−0.647693
$724$		0			0
$725$	−2.31553	−	4.01062i	−0.0859968	−	0.148951i
$726$		0			0
$727$	−20.3933	+	35.3221i	−0.756344	+	1.31003i	0.188360	+	0.982100i	$0.439683\pi$
$727$	−20.3933	+	35.3221i	−0.756344	+	1.31003i	−0.944703	+	0.327926i	$0.893650\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	9.24447	−	16.0119i	0.341919	−	0.592221i
$732$		0			0
$733$	3.06661	+	5.31153i	0.113268	+	0.196186i	0.917086	−	0.398689i	$-0.130535\pi$
$733$	3.06661	+	5.31153i	0.113268	+	0.196186i	−0.803818	+	0.594875i	$0.797201\pi$
$734$		0			0
$735$	−4.20152	+	7.27725i	−0.154976	+	0.268425i
$736$		0			0
$737$	2.61120	+	0.699926i	0.0961846	+	0.0257821i
$738$		0			0
$739$	9.57005	−	16.5758i	0.352040	−	0.609751i	−0.634567	−	0.772868i	$-0.718822\pi$
$739$	9.57005	−	16.5758i	0.352040	−	0.609751i	0.986607	+	0.163117i	$0.0521548\pi$
$740$		0			0
$741$	−24.2316	−	41.9704i	−0.890171	−	1.54182i
$742$		0			0
$743$	−19.5801	+	33.9137i	−0.718324	+	1.24417i	0.243340	+	0.969941i	$0.421757\pi$
$743$	−19.5801	+	33.9137i	−0.718324	+	1.24417i	−0.961664	+	0.274232i	$0.911576\pi$
$744$		0			0
$745$	−8.11024			−0.297136
$746$		0			0
$747$	−8.83630	+	15.3049i	−0.323303	+	0.559978i
$748$		0			0
$749$	−26.7704	−	46.3677i	−0.978170	−	1.69424i
$750$		0			0
$751$	30.8337			1.12514			0.562570	−	0.826750i	$-0.309813\pi$
$751$	30.8337			1.12514			0.562570	+	0.826750i	$0.309813\pi$
$752$		0			0
$753$	4.86501	−	8.42645i	0.177291	−	0.307077i
$754$		0			0
$755$	−1.77250	+	3.07006i	−0.0645078	+	0.111731i
$756$		0			0
$757$	−22.3746	−	38.7540i	−0.813220	−	1.40854i	−0.910599	−	0.413291i	$-0.864379\pi$
$757$	−22.3746	−	38.7540i	−0.813220	−	1.40854i	0.0973785	−	0.995247i	$-0.468954\pi$
$758$		0			0
$759$	0.653530			0.0237216
$760$		0			0
$761$	−50.7359			−1.83918			−0.919588	−	0.392885i	$-0.871477\pi$
$761$	−50.7359			−1.83918			−0.919588	+	0.392885i	$0.871477\pi$
$762$		0			0
$763$	14.0966	+	24.4161i	0.510332	+	0.883921i
$764$		0			0
$765$	1.72717	−	2.99154i	0.0624458	−	0.108159i
$766$		0			0
$767$	19.4350	−	33.6625i	0.701759	−	1.21548i
$768$		0			0
$769$	0.384834	+	0.666552i	0.0138775	+	0.0240365i	0.872881	−	0.487934i	$-0.162249\pi$
$769$	0.384834	+	0.666552i	0.0138775	+	0.0240365i	−0.859003	+	0.511970i	$0.828916\pi$
$770$		0			0
$771$	3.29008	+	5.69859i	0.118489	+	0.205230i
$772$		0			0
$773$	−14.9745	−	25.9365i	−0.538594	−	0.932871i	−0.998980	−	0.0451529i	$-0.985623\pi$
$773$	−14.9745	−	25.9365i	−0.538594	−	0.932871i	0.460387	−	0.887719i	$-0.347711\pi$
$774$		0			0
$775$	3.25426	+	5.63654i	0.116896	+	0.202470i
$776$		0			0
$777$	17.9071			0.642414
$778$		0			0
$779$	−52.7412			−1.88965
$780$		0			0
$781$	−0.611539	+	1.05922i	−0.0218826	+	0.0379018i
$782$		0			0
$783$	−2.31553	−	4.01062i	−0.0827504	−	0.143328i
$784$		0			0
$785$	4.46681	−	7.73673i	0.159427	−	0.276136i
$786$		0			0
$787$	5.28487	−	9.15366i	0.188385	−	0.326293i	−0.756327	−	0.654194i	$-0.773008\pi$
$787$	5.28487	−	9.15366i	0.188385	−	0.326293i	0.944712	+	0.327901i	$0.106341\pi$
$788$		0			0
$789$	−9.58787			−0.341337
$790$		0			0
$791$	−6.01951	+	10.4261i	−0.214029	+	0.370710i
$792$		0			0
$793$	13.5052	+	23.3917i	0.479583	+	0.830662i
$794$		0			0
$795$	13.3034			0.471824
$796$		0			0
$797$	7.97783	+	13.8180i	0.282589	+	0.489459i	0.972022	−	0.234891i	$-0.0754734\pi$
$797$	7.97783	+	13.8180i	0.282589	+	0.489459i	−0.689433	+	0.724350i	$0.742140\pi$
$798$		0			0
$799$	33.5577			1.18719
$800$		0			0
$801$	−6.96652			−0.246150
$802$		0			0
$803$	−1.84359			−0.0650588
$804$		0			0
$805$	7.76604			0.273717
$806$		0			0
$807$	−2.74795			−0.0967323
$808$		0			0
$809$	28.3639			0.997221			0.498610	−	0.866826i	$-0.333844\pi$
$809$	28.3639			0.997221			0.498610	+	0.866826i	$0.333844\pi$
$810$		0			0
$811$	−17.9447	−	31.0811i	−0.630122	−	1.09140i	−0.987526	−	0.157454i	$-0.949672\pi$
$811$	−17.9447	−	31.0811i	−0.630122	−	1.09140i	0.357404	−	0.933950i	$-0.383662\pi$
$812$		0			0
$813$	−23.4576			−0.822692
$814$		0			0
$815$	1.54635	+	2.67836i	0.0541662	+	0.0938187i
$816$		0			0
$817$	−18.9637	+	32.8461i	−0.663455	+	1.14914i
$818$		0			0
$819$	26.8418			0.937927
$820$		0			0
$821$	−15.6488	+	27.1045i	−0.546147	+	0.945954i	0.452387	+	0.891822i	$0.350573\pi$
$821$	−15.6488	+	27.1045i	−0.546147	+	0.945954i	−0.998534	+	0.0541320i	$0.982761\pi$
$822$		0			0
$823$	−8.85570	+	15.3385i	−0.308690	+	0.534667i	−0.978076	−	0.208248i	$-0.933224\pi$
$823$	−8.85570	+	15.3385i	−0.308690	+	0.534667i	0.669386	+	0.742915i	$0.266557\pi$
$824$		0			0
$825$	−0.165135	−	0.286022i	−0.00574926	−	0.00995801i
$826$		0			0
$827$	−10.2628	+	17.7757i	−0.356873	+	0.618122i	−0.987437	−	0.158015i	$-0.949490\pi$
$827$	−10.2628	+	17.7757i	−0.356873	+	0.618122i	0.630564	+	0.776138i	$0.282824\pi$
$828$		0			0
$829$	22.0274			0.765042			0.382521	−	0.923947i	$-0.375056\pi$
$829$	22.0274			0.765042			0.382521	+	0.923947i	$0.375056\pi$
$830$		0			0
$831$	−23.0593			−0.799917
$832$		0			0
$833$	14.5135	+	25.1381i	0.502862	+	0.870982i
$834$		0			0
$835$	−5.19651	−	9.00062i	−0.179833	−	0.311479i
$836$		0			0
$837$	3.25426	+	5.63654i	0.112484	+	0.194827i
$838$		0			0
$839$	−26.7015	−	46.2484i	−0.921838	−	1.59667i	−0.796568	−	0.604548i	$-0.793354\pi$
$839$	−26.7015	−	46.2484i	−0.921838	−	1.59667i	−0.125270	−	0.992123i	$-0.539980\pi$
$840$		0			0
$841$	3.77660	−	6.54127i	0.130228	−	0.225561i
$842$		0			0
$843$	−3.37254	+	5.84141i	−0.116156	+	0.201189i
$844$		0			0
$845$	−16.8876	−	29.2502i	−0.580951	−	1.00624i
$846$		0			0
$847$	−42.7433			−1.46868
$848$		0			0
$849$	−15.3983			−0.528468
$850$		0			0
$851$	−4.51429	−	7.81897i	−0.154748	−	0.268031i
$852$		0			0
$853$	28.2407	−	48.9144i	0.966944	−	1.67480i	0.262645	−	0.964893i	$-0.415405\pi$
$853$	28.2407	−	48.9144i	0.966944	−	1.67480i	0.704299	−	0.709903i	$-0.251261\pi$
$854$		0			0
$855$	−3.54303	+	6.13671i	−0.121169	+	0.209871i
$856$		0			0
$857$	−32.4080			−1.10704			−0.553519	−	0.832837i	$-0.686715\pi$
$857$	−32.4080			−1.10704			−0.553519	+	0.832837i	$0.686715\pi$
$858$		0			0
$859$	−5.99668	−	10.3865i	−0.204604	−	0.354384i	0.745403	−	0.666615i	$-0.232257\pi$
$859$	−5.99668	−	10.3865i	−0.204604	−	0.354384i	−0.950006	+	0.312230i	$0.898924\pi$
$860$		0			0
$861$	14.6056	−	25.2976i	0.497757	−	0.862140i
$862$		0			0
$863$	51.5899			1.75614			0.878070	−	0.478532i	$-0.158831\pi$
$863$	51.5899			1.75614			0.878070	+	0.478532i	$0.158831\pi$
$864$		0			0
$865$	−6.08629	+	10.5418i	−0.206940	+	0.358431i
$866$		0			0
$867$	2.53379	+	4.38865i	0.0860520	+	0.149046i
$868$		0			0
$869$	1.36238	−	2.35972i	0.0462157	−	0.0800479i
$870$		0			0
$871$	−14.4841	−	54.0754i	−0.490775	−	1.83227i
$872$		0			0
$873$	1.00524	−	1.74112i	0.0340221	−	0.0589280i
$874$		0			0
$875$	−1.96234	−	3.39887i	−0.0663391	−	0.114903i
$876$		0			0
$877$	9.61392	−	16.6518i	0.324639	−	0.562291i	−0.656800	−	0.754065i	$-0.728091\pi$
$877$	9.61392	−	16.6518i	0.324639	−	0.562291i	0.981439	+	0.191773i	$0.0614239\pi$
$878$		0			0
$879$	5.62807			0.189830
$880$		0			0
$881$	28.2969	−	49.0116i	0.953346	−	1.65124i	0.215236	−	0.976562i	$-0.430948\pi$
$881$	28.2969	−	49.0116i	0.953346	−	1.65124i	0.738109	−	0.674681i	$-0.235719\pi$
$882$		0			0
$883$	−0.951717	−	1.64842i	−0.0320278	−	0.0554738i	0.849567	−	0.527480i	$-0.176863\pi$
$883$	−0.951717	−	1.64842i	−0.0320278	−	0.0554738i	−0.881595	+	0.472007i	$0.843530\pi$
$884$		0			0
$885$	−5.68339			−0.191045
$886$		0			0
$887$	−14.3744	+	24.8972i	−0.482645	+	0.835966i	−0.999801	−	0.0199249i	$-0.993657\pi$
$887$	−14.3744	+	24.8972i	−0.482645	+	0.835966i	0.517156	+	0.855891i	$0.326991\pi$
$888$		0			0
$889$	34.0758	−	59.0210i	1.14287	−	1.97950i
$890$		0			0
$891$	−0.165135	−	0.286022i	−0.00553223	−	0.00958210i
$892$		0			0
$893$	−68.8388			−2.30360
$894$		0			0
$895$	16.3168			0.545410
$896$		0			0
$897$	−6.76666	−	11.7202i	−0.225932	−	0.391326i
$898$		0			0
$899$	15.0707	−	26.1032i	0.502636	−	0.870590i
$900$		0			0
$901$	22.9772	−	39.7977i	0.765482	−	1.32585i
$902$		0			0
$903$	−10.5032	−	18.1920i	−0.349524	−	0.605393i
$904$		0			0
$905$	−9.25502	−	16.0302i	−0.307647	−	0.532860i
$906$		0			0
$907$	17.7120	+	30.6782i	0.588119	+	1.01865i	0.994479	+	0.104939i	$0.0334646\pi$
$907$	17.7120	+	30.6782i	0.588119	+	1.01865i	−0.406360	+	0.913713i	$0.633202\pi$
$908$		0			0
$909$	−5.57733	−	9.66022i	−0.184988	−	0.320409i
$910$		0			0
$911$	5.19893			0.172248			0.0861241	−	0.996284i	$-0.472552\pi$
$911$	5.19893			0.172248			0.0861241	+	0.996284i	$0.472552\pi$
$912$		0			0
$913$	5.83672			0.193167
$914$		0			0
$915$	1.97466	−	3.42021i	0.0652803	−	0.113069i
$916$		0			0
$917$	−34.3995	−	59.5817i	−1.13597	−	1.96756i
$918$		0			0
$919$	−24.8423	+	43.0281i	−0.819472	+	1.41937i	0.0865995	+	0.996243i	$0.472400\pi$
$919$	−24.8423	+	43.0281i	−0.819472	+	1.41937i	−0.906072	+	0.423124i	$0.860933\pi$
$920$		0			0
$921$	−15.4529	+	26.7652i	−0.509189	+	0.881942i
$922$		0			0
$923$	25.3275			0.833666
$924$		0			0
$925$	−2.28135	+	3.95142i	−0.0750104	+	0.129922i
$926$		0			0
$927$	1.32048	+	2.28713i	0.0433702	+	0.0751193i
$928$		0			0
$929$	5.73579			0.188185			0.0940927	−	0.995563i	$-0.470005\pi$
$929$	5.73579			0.188185			0.0940927	+	0.995563i	$0.470005\pi$
$930$		0			0
$931$	−29.7723	−	51.5671i	−0.975746	−	1.69004i
$932$		0			0
$933$	−23.4156			−0.766592
$934$		0			0
$935$	−1.14086			−0.0373102
$936$		0			0
$937$	29.9157			0.977303			0.488651	−	0.872479i	$-0.337489\pi$
$937$	29.9157			0.977303			0.488651	+	0.872479i	$0.337489\pi$
$938$		0			0
$939$	8.71922			0.284541
$940$		0			0
$941$	−40.5427			−1.32166			−0.660828	−	0.750538i	$-0.729795\pi$
$941$	−40.5427			−1.32166			−0.660828	+	0.750538i	$0.729795\pi$
$942$		0			0
$943$	−14.7279			−0.479608
$944$		0			0
$945$	−1.96234	−	3.39887i	−0.0638348	−	0.110565i
$946$		0			0
$947$	−7.97412			−0.259124			−0.129562	−	0.991571i	$-0.541357\pi$
$947$	−7.97412			−0.259124			−0.129562	+	0.991571i	$0.541357\pi$
$948$		0			0
$949$	19.0885	+	33.0623i	0.619640	+	1.07325i
$950$		0			0
$951$	−9.78814	+	16.9535i	−0.317402	+	0.549756i
$952$		0			0
$953$	60.5601			1.96173			0.980867	−	0.194681i	$-0.0623672\pi$
$953$	60.5601			1.96173			0.980867	+	0.194681i	$0.0623672\pi$
$954$		0			0
$955$	−12.1060	+	20.9682i	−0.391740	+	0.678514i
$956$		0			0
$957$	−0.764751	+	1.32459i	−0.0247209	+	0.0428178i
$958$		0			0
$959$	−20.8773	−	36.1605i	−0.674163	−	1.16768i
$960$		0			0
$961$	−5.68039	+	9.83872i	−0.183238	+	0.317378i
$962$		0			0
$963$	13.6421			0.439611
$964$		0			0
$965$	−1.99202			−0.0641253
$966$		0			0
$967$	−18.4756	−	32.0006i	−0.594134	−	1.02907i	−0.993668	−	0.112353i	$-0.964161\pi$
$967$	−18.4756	−	32.0006i	−0.594134	−	1.02907i	0.399534	−	0.916718i	$-0.369172\pi$
$968$		0			0
$969$	12.2388	+	21.1982i	0.393167	+	0.680986i
$970$		0			0
$971$	6.97807	+	12.0864i	0.223937	+	0.387870i	0.956000	−	0.293367i	$-0.0947757\pi$
$971$	6.97807	+	12.0864i	0.223937	+	0.387870i	−0.732063	+	0.681237i	$0.761442\pi$
$972$		0			0
$973$	−14.8708	−	25.7569i	−0.476735	−	0.825729i
$974$		0			0
$975$	−3.41962	+	5.92295i	−0.109515	+	0.189686i
$976$		0			0
$977$	−9.48733	+	16.4325i	−0.303527	+	0.525724i	−0.976932	−	0.213550i	$-0.931497\pi$
$977$	−9.48733	+	16.4325i	−0.303527	+	0.525724i	0.673406	+	0.739273i	$0.264831\pi$
$978$		0			0
$979$	1.15042	+	1.99258i	0.0367674	+	0.0636831i
$980$		0			0
$981$	−7.18360			−0.229355
$982$		0			0
$983$	39.6782			1.26554			0.632770	−	0.774340i	$-0.281918\pi$
$983$	39.6782			1.26554			0.632770	+	0.774340i	$0.281918\pi$
$984$		0			0
$985$	−3.12651	−	5.41527i	−0.0996189	−	0.172545i
$986$		0			0
$987$	19.0634	−	33.0189i	0.606796	−	1.05100i
$988$		0			0
$989$	−5.29559	+	9.17223i	−0.168390	+	0.291660i
$990$		0			0
$991$	10.1444			0.322249			0.161124	−	0.986934i	$-0.448488\pi$
$991$	10.1444			0.322249			0.161124	+	0.986934i	$0.448488\pi$
$992$		0			0
$993$	9.68919	+	16.7822i	0.307477	+	0.532566i
$994$		0			0
$995$	11.7627	−	20.3736i	0.372903	−	0.645887i
$996$		0			0
$997$	50.4488			1.59773			0.798865	−	0.601510i	$-0.205434\pi$
$997$	50.4488			1.59773			0.798865	+	0.601510i	$0.205434\pi$
$998$		0			0
$999$	−2.28135	+	3.95142i	−0.0721788	+	0.125017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.3781.3	yes	24
67.37	even	3	inner	4020.2.q.m.841.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.3	✓	24	67.37	even	3	inner
4020.2.q.m.3781.3	yes	24	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.96234 - 3.39887i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.96234 - 3.39887i) q^{7} +1.00000 q^{9} +(-0.165135 - 0.286022i) q^{11} +(-3.41962 + 5.92295i) q^{13} +1.00000 q^{15} +(1.72717 - 2.99154i) q^{17} +(-3.54303 + 6.13671i) q^{19} +(-1.96234 - 3.39887i) q^{21} +(-0.989388 + 1.71367i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-2.31553 - 4.01062i) q^{29} +(3.25426 + 5.63654i) q^{31} +(-0.165135 - 0.286022i) q^{33} +(-1.96234 - 3.39887i) q^{35} +(-2.28135 + 3.95142i) q^{37} +(-3.41962 + 5.92295i) q^{39} +(3.72148 + 6.44579i) q^{41} +5.35239 q^{43} +1.00000 q^{45} +(4.85734 + 8.41315i) q^{47} +(-4.20152 + 7.27725i) q^{49} +(1.72717 - 2.99154i) q^{51} +13.3034 q^{53} +(-0.165135 - 0.286022i) q^{55} +(-3.54303 + 6.13671i) q^{57} -5.68339 q^{59} +(1.97466 - 3.42021i) q^{61} +(-1.96234 - 3.39887i) q^{63} +(-3.41962 + 5.92295i) q^{65} +(-5.78845 + 5.78738i) q^{67} +(-0.989388 + 1.71367i) q^{69} +(-1.85164 - 3.20713i) q^{71} +(2.79103 - 4.83421i) q^{73} +1.00000 q^{75} +(-0.648100 + 1.12254i) q^{77} +(4.12506 + 7.14481i) q^{79} +1.00000 q^{81} +(-8.83630 + 15.3049i) q^{83} +(1.72717 - 2.99154i) q^{85} +(-2.31553 - 4.01062i) q^{87} -6.96652 q^{89} +26.8418 q^{91} +(3.25426 + 5.63654i) q^{93} +(-3.54303 + 6.13671i) q^{95} +(1.00524 - 1.74112i) q^{97} +(-0.165135 - 0.286022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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