LMFDB - Embedded newform 4020.2.q.j.841.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 30 x^{10} - 53 x^{9} + 798 x^{8} - 1096 x^{7} + 4060 x^{6} - 915 x^{5} + 10392 x^{4} + \cdots + 81 $ x^12 - x^11 + 30x^10 - 53x^9 + 798x^8 - 1096x^7 + 4060x^6 - 915x^5 + 10392x^4 - 7038x^3 + 4869x^2 - 675x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.5
Root			$0.0725333 - 0.125631i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.j.3781.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(2.26952 - 3.93092i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.26952 - 3.93092i) q^{7} +1.00000 q^{9} +(-2.47783 + 4.29172i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(0.378275 + 0.655192i) q^{17} +(2.83524 + 4.91078i) q^{19} +(2.26952 - 3.93092i) q^{21} +(4.02702 + 6.97500i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(0.975100 - 1.68892i) q^{29} +(-4.04355 + 7.00363i) q^{31} +(-2.47783 + 4.29172i) q^{33} +(-2.26952 + 3.93092i) q^{35} +(-2.35705 - 4.08253i) q^{37} +(0.500000 + 0.866025i) q^{39} +(0.516533 - 0.894661i) q^{41} -8.67048 q^{43} -1.00000 q^{45} +(-5.48755 + 9.50471i) q^{47} +(-6.80141 - 11.7804i) q^{49} +(0.378275 + 0.655192i) q^{51} -9.08710 q^{53} +(2.47783 - 4.29172i) q^{55} +(2.83524 + 4.91078i) q^{57} +14.5020 q^{59} +(-1.14098 - 1.97624i) q^{61} +(2.26952 - 3.93092i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(1.85934 - 7.97138i) q^{67} +(4.02702 + 6.97500i) q^{69} +(-2.10228 + 3.64125i) q^{71} +(7.29245 + 12.6309i) q^{73} +1.00000 q^{75} +(11.2469 + 19.4803i) q^{77} +(5.59391 - 9.68893i) q^{79} +1.00000 q^{81} +(5.15183 + 8.92324i) q^{83} +(-0.378275 - 0.655192i) q^{85} +(0.975100 - 1.68892i) q^{87} +14.1104 q^{89} +4.53903 q^{91} +(-4.04355 + 7.00363i) q^{93} +(-2.83524 - 4.91078i) q^{95} +(8.53303 + 14.7796i) q^{97} +(-2.47783 + 4.29172i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * 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
$7$	2.26952	−	3.93092i	0.857797	−	1.48575i	−0.0162291	−	0.999868i	$-0.505166\pi$
$7$	2.26952	−	3.93092i	0.857797	−	1.48575i	0.874026	−	0.485879i	$-0.161501\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.47783	+	4.29172i	−0.747093	+	1.29400i	0.202118	+	0.979361i	$0.435218\pi$
$11$	−2.47783	+	4.29172i	−0.747093	+	1.29400i	−0.949211	+	0.314641i	$0.898116\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	0.378275	+	0.655192i	0.0917452	+	0.158907i	0.908246	−	0.418438i	$-0.137422\pi$
$17$	0.378275	+	0.655192i	0.0917452	+	0.158907i	−0.816500	+	0.577345i	$0.804089\pi$
$18$		0			0
$19$	2.83524	+	4.91078i	0.650449	+	1.12661i	0.983014	+	0.183530i	$0.0587526\pi$
$19$	2.83524	+	4.91078i	0.650449	+	1.12661i	−0.332565	+	0.943080i	$0.607914\pi$
$20$		0			0
$21$	2.26952	−	3.93092i	0.495249	−	0.857797i
$22$		0			0
$23$	4.02702	+	6.97500i	0.839691	+	1.45439i	0.890153	+	0.455662i	$0.150597\pi$
$23$	4.02702	+	6.97500i	0.839691	+	1.45439i	−0.0504618	+	0.998726i	$0.516069\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	0.975100	−	1.68892i	0.181072	−	0.313625i	−0.761174	−	0.648548i	$-0.775377\pi$
$29$	0.975100	−	1.68892i	0.181072	−	0.313625i	0.942246	+	0.334922i	$0.108710\pi$
$30$		0			0
$31$	−4.04355	+	7.00363i	−0.726243	+	1.25789i	0.232217	+	0.972664i	$0.425402\pi$
$31$	−4.04355	+	7.00363i	−0.726243	+	1.25789i	−0.958460	+	0.285226i	$0.907931\pi$
$32$		0			0
$33$	−2.47783	+	4.29172i	−0.431334	+	0.747093i
$34$		0			0
$35$	−2.26952	+	3.93092i	−0.383618	+	0.664447i
$36$		0			0
$37$	−2.35705	−	4.08253i	−0.387497	−	0.671164i	0.604615	−	0.796518i	$-0.293327\pi$
$37$	−2.35705	−	4.08253i	−0.387497	−	0.671164i	−0.992112	+	0.125353i	$0.959994\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	0.516533	−	0.894661i	0.0806688	−	0.139723i	−0.822869	−	0.568232i	$-0.807628\pi$
$41$	0.516533	−	0.894661i	0.0806688	−	0.139723i	0.903537	+	0.428509i	$0.140961\pi$
$42$		0			0
$43$	−8.67048			−1.32224			−0.661118	−	0.750282i	$-0.729918\pi$
$43$	−8.67048			−1.32224			−0.661118	+	0.750282i	$0.729918\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−5.48755	+	9.50471i	−0.800441	+	1.38641i	0.118885	+	0.992908i	$0.462068\pi$
$47$	−5.48755	+	9.50471i	−0.800441	+	1.38641i	−0.919326	+	0.393497i	$0.871265\pi$
$48$		0			0
$49$	−6.80141	−	11.7804i	−0.971631	−	1.68291i
$50$		0			0
$51$	0.378275	+	0.655192i	0.0529691	+	0.0917452i
$52$		0			0
$53$	−9.08710			−1.24821			−0.624105	−	0.781341i	$-0.714536\pi$
$53$	−9.08710			−1.24821			−0.624105	+	0.781341i	$0.714536\pi$
$54$		0			0
$55$	2.47783	−	4.29172i	0.334110	−	0.578695i
$56$		0			0
$57$	2.83524	+	4.91078i	0.375537	+	0.650449i
$58$		0			0
$59$	14.5020			1.88800			0.944002	−	0.329939i	$-0.107028\pi$
$59$	14.5020			1.88800			0.944002	+	0.329939i	$0.107028\pi$
$60$		0			0
$61$	−1.14098	−	1.97624i	−0.146088	−	0.253032i	0.783690	−	0.621152i	$-0.213335\pi$
$61$	−1.14098	−	1.97624i	−0.146088	−	0.253032i	−0.929778	+	0.368120i	$0.880002\pi$
$62$		0			0
$63$	2.26952	−	3.93092i	0.285932	−	0.495249i
$64$		0			0
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	1.85934	−	7.97138i	0.227155	−	0.973859i
$67$	1.85934	−	7.97138i	0.227155	−	0.973859i
$68$		0			0
$69$	4.02702	+	6.97500i	0.484796	+	0.839691i
$70$		0			0
$71$	−2.10228	+	3.64125i	−0.249494	+	0.432137i	−0.963386	−	0.268120i	$-0.913598\pi$
$71$	−2.10228	+	3.64125i	−0.249494	+	0.432137i	0.713891	+	0.700257i	$0.246931\pi$
$72$		0			0
$73$	7.29245	+	12.6309i	0.853517	+	1.47833i	0.878014	+	0.478635i	$0.158868\pi$
$73$	7.29245	+	12.6309i	0.853517	+	1.47833i	−0.0244973	+	0.999700i	$0.507799\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	11.2469	+	19.4803i	1.28171	+	2.21998i
$78$		0			0
$79$	5.59391	−	9.68893i	0.629364	−	1.09009i	−0.358316	−	0.933601i	$-0.616649\pi$
$79$	5.59391	−	9.68893i	0.629364	−	1.09009i	0.987680	−	0.156490i	$-0.0500178\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	5.15183	+	8.92324i	0.565487	+	0.979452i	0.997004	+	0.0773476i	$0.0246451\pi$
$83$	5.15183	+	8.92324i	0.565487	+	0.979452i	−0.431517	+	0.902105i	$0.642022\pi$
$84$		0			0
$85$	−0.378275	−	0.655192i	−0.0410297	−	0.0710655i
$86$		0			0
$87$	0.975100	−	1.68892i	0.104542	−	0.181072i
$88$		0			0
$89$	14.1104			1.49570			0.747850	−	0.663868i	$-0.231086\pi$
$89$	14.1104			1.49570			0.747850	+	0.663868i	$0.231086\pi$
$90$		0			0
$91$	4.53903			0.475820
$92$		0			0
$93$	−4.04355	+	7.00363i	−0.419297	+	0.726243i
$94$		0			0
$95$	−2.83524	−	4.91078i	−0.290890	−	0.503836i
$96$		0			0
$97$	8.53303	+	14.7796i	0.866398	+	1.50064i	0.865653	+	0.500645i	$0.166904\pi$
$97$	8.53303	+	14.7796i	0.866398	+	1.50064i	0.000745111		1.00000i	$0.499763\pi$
$98$		0			0
$99$	−2.47783	+	4.29172i	−0.249031	+	0.431334i
$100$		0			0
$101$	−2.96053	+	5.12779i	−0.294584	+	0.510234i	−0.974888	−	0.222696i	$-0.928514\pi$
$101$	−2.96053	+	5.12779i	−0.294584	+	0.510234i	0.680304	+	0.732930i	$0.261848\pi$
$102$		0			0
$103$	1.44768	−	2.50745i	0.142644	−	0.247066i	−0.785848	−	0.618420i	$-0.787773\pi$
$103$	1.44768	−	2.50745i	0.142644	−	0.247066i	0.928491	+	0.371354i	$0.121106\pi$
$104$		0			0
$105$	−2.26952	+	3.93092i	−0.221482	+	0.383618i
$106$		0			0
$107$	−13.2240			−1.27841			−0.639206	−	0.769035i	$-0.720737\pi$
$107$	−13.2240			−1.27841			−0.639206	+	0.769035i	$0.720737\pi$
$108$		0			0
$109$	7.70282			0.737796			0.368898	−	0.929470i	$-0.379735\pi$
$109$	7.70282			0.737796			0.368898	+	0.929470i	$0.379735\pi$
$110$		0			0
$111$	−2.35705	−	4.08253i	−0.223721	−	0.387497i
$112$		0			0
$113$	−3.04355	+	5.27158i	−0.286313	+	0.495909i	−0.972927	−	0.231114i	$-0.925763\pi$
$113$	−3.04355	+	5.27158i	−0.286313	+	0.495909i	0.686614	+	0.727022i	$0.259096\pi$
$114$		0			0
$115$	−4.02702	−	6.97500i	−0.375521	−	0.650422i
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	3.43401			0.314795
$120$		0			0
$121$	−6.77924	−	11.7420i	−0.616295	−	1.06745i
$122$		0			0
$123$	0.516533	−	0.894661i	0.0465742	−	0.0806688i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.09663	−	12.2917i	0.629724	−	1.09071i	−0.357882	−	0.933767i	$-0.616501\pi$
$127$	7.09663	−	12.2917i	0.629724	−	1.09071i	0.987607	−	0.156948i	$-0.0501655\pi$
$128$		0			0
$129$	−8.67048			−0.763393
$130$		0			0
$131$	19.2328			1.68038			0.840190	−	0.542293i	$-0.182444\pi$
$131$	19.2328			1.68038			0.840190	+	0.542293i	$0.182444\pi$
$132$		0			0
$133$	25.7385			2.23181
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	7.77825			0.664541			0.332270	−	0.943184i	$-0.392185\pi$
$137$	7.77825			0.664541			0.332270	+	0.943184i	$0.392185\pi$
$138$		0			0
$139$	2.51375			0.213214			0.106607	−	0.994301i	$-0.466001\pi$
$139$	2.51375			0.213214			0.106607	+	0.994301i	$0.466001\pi$
$140$		0			0
$141$	−5.48755	+	9.50471i	−0.462135	+	0.800441i
$142$		0			0
$143$	−4.95565			−0.414412
$144$		0			0
$145$	−0.975100	+	1.68892i	−0.0809777	+	0.140257i
$146$		0			0
$147$	−6.80141	−	11.7804i	−0.560971	−	0.971631i
$148$		0			0
$149$	−15.3260			−1.25555			−0.627776	−	0.778394i	$-0.716035\pi$
$149$	−15.3260			−1.25555			−0.627776	+	0.778394i	$0.716035\pi$
$150$		0			0
$151$	−2.20012	−	3.81071i	−0.179043	−	0.310111i	0.762510	−	0.646976i	$-0.223967\pi$
$151$	−2.20012	−	3.81071i	−0.179043	−	0.310111i	−0.941553	+	0.336865i	$0.890633\pi$
$152$		0			0
$153$	0.378275	+	0.655192i	0.0305817	+	0.0529691i
$154$		0			0
$155$	4.04355	−	7.00363i	0.324786	−	0.562545i
$156$		0			0
$157$	−3.43967	−	5.95769i	−0.274516	−	0.475475i	0.695497	−	0.718529i	$-0.255184\pi$
$157$	−3.43967	−	5.95769i	−0.274516	−	0.475475i	−0.970013	+	0.243054i	$0.921851\pi$
$158$		0			0
$159$	−9.08710			−0.720654
$160$		0			0
$161$	36.5575			2.88114
$162$		0			0
$163$	−6.57930	+	11.3957i	−0.515330	+	0.892579i	0.484511	+	0.874785i	$0.338997\pi$
$163$	−6.57930	+	11.3957i	−0.515330	+	0.892579i	−0.999842	+	0.0177935i	$0.994336\pi$
$164$		0			0
$165$	2.47783	−	4.29172i	0.192898	−	0.334110i
$166$		0			0
$167$	−8.25685	+	14.3013i	−0.638934	+	1.10667i	0.346733	+	0.937964i	$0.387291\pi$
$167$	−8.25685	+	14.3013i	−0.638934	+	1.10667i	−0.985667	+	0.168703i	$0.946042\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	2.83524	+	4.91078i	0.216816	+	0.375537i
$172$		0			0
$173$	−3.71676	−	6.43762i	−0.282580	−	0.489443i	0.689439	−	0.724343i	$-0.257857\pi$
$173$	−3.71676	−	6.43762i	−0.282580	−	0.489443i	−0.972019	+	0.234900i	$0.924524\pi$
$174$		0			0
$175$	2.26952	−	3.93092i	0.171559	−	0.297150i
$176$		0			0
$177$	14.5020			1.09004
$178$		0			0
$179$	22.4972			1.68152			0.840761	−	0.541406i	$-0.182108\pi$
$179$	22.4972			1.68152			0.840761	+	0.541406i	$0.182108\pi$
$180$		0			0
$181$	−6.14619	+	10.6455i	−0.456843	+	0.791275i	−0.998792	−	0.0491363i	$-0.984353\pi$
$181$	−6.14619	+	10.6455i	−0.456843	+	0.791275i	0.541949	+	0.840411i	$0.317686\pi$
$182$		0			0
$183$	−1.14098	−	1.97624i	−0.0843439	−	0.146088i
$184$		0			0
$185$	2.35705	+	4.08253i	0.173294	+	0.300154i
$186$		0			0
$187$	−3.74920			−0.274169
$188$		0			0
$189$	2.26952	−	3.93092i	0.165083	−	0.285932i
$190$		0			0
$191$	−4.36109	−	7.55363i	−0.315558	−	0.546562i	0.663998	−	0.747734i	$-0.268858\pi$
$191$	−4.36109	−	7.55363i	−0.315558	−	0.546562i	−0.979556	+	0.201172i	$0.935525\pi$
$192$		0			0
$193$	−19.3169			−1.39046			−0.695229	−	0.718788i	$-0.744697\pi$
$193$	−19.3169			−1.39046			−0.695229	+	0.718788i	$0.744697\pi$
$194$		0			0
$195$	−0.500000	−	0.866025i	−0.0358057	−	0.0620174i
$196$		0			0
$197$	9.80950	−	16.9906i	0.698898	−	1.21053i	−0.269951	−	0.962874i	$-0.587007\pi$
$197$	9.80950	−	16.9906i	0.698898	−	1.21053i	0.968849	−	0.247653i	$-0.0796592\pi$
$198$		0			0
$199$	0.348098	+	0.602923i	0.0246760	+	0.0427401i	0.878100	−	0.478478i	$-0.158811\pi$
$199$	0.348098	+	0.602923i	0.0246760	+	0.0427401i	−0.853424	+	0.521218i	$0.825478\pi$
$200$		0			0
$201$	1.85934	−	7.97138i	0.131148	−	0.562258i
$202$		0			0
$203$	−4.42601	−	7.66608i	−0.310645	−	0.538053i
$204$		0			0
$205$	−0.516533	+	0.894661i	−0.0360762	+	0.0624858i
$206$		0			0
$207$	4.02702	+	6.97500i	0.279897	+	0.484796i
$208$		0			0
$209$	−28.1009			−1.94378
$210$		0			0
$211$	−0.0968252	−	0.167706i	−0.00666572	−	0.0115454i	0.862673	−	0.505762i	$-0.168788\pi$
$211$	−0.0968252	−	0.167706i	−0.00666572	−	0.0115454i	−0.869339	+	0.494216i	$0.835455\pi$
$212$		0			0
$213$	−2.10228	+	3.64125i	−0.144046	+	0.249494i
$214$		0			0
$215$	8.67048			0.591322
$216$		0			0
$217$	18.3538	+	31.7897i	1.24594	+	2.15803i
$218$		0			0
$219$	7.29245	+	12.6309i	0.492778	+	0.853517i
$220$		0			0
$221$	−0.378275	+	0.655192i	−0.0254455	+	0.0440729i
$222$		0			0
$223$	−10.3477			−0.692934			−0.346467	−	0.938062i	$-0.612619\pi$
$223$	−10.3477			−0.692934			−0.346467	+	0.938062i	$0.612619\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−12.4708	+	21.6001i	−0.827718	+	1.43365i	0.0721066	+	0.997397i	$0.477028\pi$
$227$	−12.4708	+	21.6001i	−0.827718	+	1.43365i	−0.899824	+	0.436252i	$0.856306\pi$
$228$		0			0
$229$	9.55619	+	16.5518i	0.631491	+	1.09377i	0.987247	+	0.159195i	$0.0508900\pi$
$229$	9.55619	+	16.5518i	0.631491	+	1.09377i	−0.355756	+	0.934579i	$0.615777\pi$
$230$		0			0
$231$	11.2469	+	19.4803i	0.739994	+	1.28171i
$232$		0			0
$233$	2.65828	−	4.60427i	0.174150	−	0.301636i	−0.765717	−	0.643178i	$-0.777616\pi$
$233$	2.65828	−	4.60427i	0.174150	−	0.301636i	0.939867	+	0.341542i	$0.110949\pi$
$234$		0			0
$235$	5.48755	−	9.50471i	0.357968	−	0.620019i
$236$		0			0
$237$	5.59391	−	9.68893i	0.363363	−	0.629364i
$238$		0			0
$239$	10.1157	−	17.5209i	0.654331	−	1.13334i	−0.327729	−	0.944772i	$-0.606283\pi$
$239$	10.1157	−	17.5209i	0.654331	−	1.13334i	0.982061	−	0.188564i	$-0.0603832\pi$
$240$		0			0
$241$	0.318963			0.0205462			0.0102731	−	0.999947i	$-0.496730\pi$
$241$	0.318963			0.0205462			0.0102731	+	0.999947i	$0.496730\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	6.80141	+	11.7804i	0.434526	+	0.752622i
$246$		0			0
$247$	−2.83524	+	4.91078i	−0.180402	+	0.312466i
$248$		0			0
$249$	5.15183	+	8.92324i	0.326484	+	0.565487i
$250$		0			0
$251$	5.20630	+	9.01758i	0.328619	+	0.569185i	0.982238	−	0.187639i	$-0.0600835\pi$
$251$	5.20630	+	9.01758i	0.328619	+	0.569185i	−0.653619	+	0.756824i	$0.726750\pi$
$252$		0			0
$253$	−39.9130			−2.50931
$254$		0			0
$255$	−0.378275	−	0.655192i	−0.0236885	−	0.0410297i
$256$		0			0
$257$	1.24152	−	2.15038i	0.0774440	−	0.134137i	−0.824702	−	0.565567i	$-0.808657\pi$
$257$	1.24152	−	2.15038i	0.0774440	−	0.134137i	0.902146	+	0.431430i	$0.141991\pi$
$258$		0			0
$259$	−21.3975			−1.32957
$260$		0			0
$261$	0.975100	−	1.68892i	0.0603572	−	0.104542i
$262$		0			0
$263$	13.0244			0.803120			0.401560	−	0.915833i	$-0.368468\pi$
$263$	13.0244			0.803120			0.401560	+	0.915833i	$0.368468\pi$
$264$		0			0
$265$	9.08710			0.558216
$266$		0			0
$267$	14.1104			0.863543
$268$		0			0
$269$	−16.7861			−1.02346			−0.511732	−	0.859145i	$-0.670996\pi$
$269$	−16.7861			−1.02346			−0.511732	+	0.859145i	$0.670996\pi$
$270$		0			0
$271$	3.17156			0.192659			0.0963293	−	0.995350i	$-0.469290\pi$
$271$	3.17156			0.192659			0.0963293	+	0.995350i	$0.469290\pi$
$272$		0			0
$273$	4.53903			0.274715
$274$		0			0
$275$	−2.47783	+	4.29172i	−0.149419	+	0.258800i
$276$		0			0
$277$	−24.2309			−1.45589			−0.727946	−	0.685635i	$-0.759525\pi$
$277$	−24.2309			−1.45589			−0.727946	+	0.685635i	$0.759525\pi$
$278$		0			0
$279$	−4.04355	+	7.00363i	−0.242081	+	0.419297i
$280$		0			0
$281$	−2.49665	−	4.32433i	−0.148938	−	0.257968i	0.781897	−	0.623407i	$-0.214252\pi$
$281$	−2.49665	−	4.32433i	−0.148938	−	0.257968i	−0.930835	+	0.365439i	$0.880919\pi$
$282$		0			0
$283$	18.0921			1.07546			0.537731	−	0.843117i	$-0.319282\pi$
$283$	18.0921			1.07546			0.537731	+	0.843117i	$0.319282\pi$
$284$		0			0
$285$	−2.83524	−	4.91078i	−0.167945	−	0.290890i
$286$		0			0
$287$	−2.34456	−	4.06090i	−0.138395	−	0.239707i
$288$		0			0
$289$	8.21382	−	14.2267i	0.483166	−	0.836867i
$290$		0			0
$291$	8.53303	+	14.7796i	0.500215	+	0.866398i
$292$		0			0
$293$	−5.62583			−0.328665			−0.164332	−	0.986405i	$-0.552547\pi$
$293$	−5.62583			−0.328665			−0.164332	+	0.986405i	$0.552547\pi$
$294$		0			0
$295$	−14.5020			−0.844341
$296$		0			0
$297$	−2.47783	+	4.29172i	−0.143778	+	0.249031i
$298$		0			0
$299$	−4.02702	+	6.97500i	−0.232888	+	0.403375i
$300$		0			0
$301$	−19.6778	+	34.0830i	−1.13421	+	1.96451i
$302$		0			0
$303$	−2.96053	+	5.12779i	−0.170078	+	0.294584i
$304$		0			0
$305$	1.14098	+	1.97624i	0.0653325	+	0.113159i
$306$		0			0
$307$	−8.78733	−	15.2201i	−0.501519	−	0.868657i	−0.999998	−	0.00175518i	$-0.999441\pi$
$307$	−8.78733	−	15.2201i	−0.501519	−	0.868657i	0.498479	−	0.866902i	$-0.333892\pi$
$308$		0			0
$309$	1.44768	−	2.50745i	0.0823554	−	0.142644i
$310$		0			0
$311$	24.6522			1.39790			0.698949	−	0.715171i	$-0.253651\pi$
$311$	24.6522			1.39790			0.698949	+	0.715171i	$0.253651\pi$
$312$		0			0
$313$	28.6093			1.61709			0.808547	−	0.588432i	$-0.200254\pi$
$313$	28.6093			1.61709			0.808547	+	0.588432i	$0.200254\pi$
$314$		0			0
$315$	−2.26952	+	3.93092i	−0.127873	+	0.221482i
$316$		0			0
$317$	12.5304	+	21.7033i	0.703779	+	1.21898i	0.967130	+	0.254281i	$0.0818390\pi$
$317$	12.5304	+	21.7033i	0.703779	+	1.21898i	−0.263351	+	0.964700i	$0.584828\pi$
$318$		0			0
$319$	4.83226	+	8.36971i	0.270554	+	0.468614i
$320$		0			0
$321$	−13.2240			−0.738092
$322$		0			0
$323$	−2.14500	+	3.71525i	−0.119351	+	0.206722i
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$		0			0
$327$	7.70282			0.425967
$328$		0			0
$329$	24.9082	+	43.1422i	1.37323	+	2.37851i
$330$		0			0
$331$	−5.02203	+	8.69841i	−0.276036	+	0.478108i	−0.970396	−	0.241520i	$-0.922354\pi$
$331$	−5.02203	+	8.69841i	−0.276036	+	0.478108i	0.694360	+	0.719628i	$0.255687\pi$
$332$		0			0
$333$	−2.35705	−	4.08253i	−0.129166	−	0.223721i
$334$		0			0
$335$	−1.85934	+	7.97138i	−0.101587	+	0.435523i
$336$		0			0
$337$	17.1096	+	29.6347i	0.932019	+	1.61430i	0.779865	+	0.625948i	$0.215288\pi$
$337$	17.1096	+	29.6347i	0.932019	+	1.61430i	0.152155	+	0.988357i	$0.451379\pi$
$338$		0			0
$339$	−3.04355	+	5.27158i	−0.165303	+	0.286313i
$340$		0			0
$341$	−20.0384	−	34.7076i	−1.08514	−	1.87952i
$342$		0			0
$343$	−29.9705			−1.61825
$344$		0			0
$345$	−4.02702	−	6.97500i	−0.216807	−	0.375521i
$346$		0			0
$347$	1.18632	−	2.05477i	0.0636852	−	0.110306i	−0.832425	−	0.554138i	$-0.813048\pi$
$347$	1.18632	−	2.05477i	0.0636852	−	0.110306i	0.896110	+	0.443832i	$0.146381\pi$
$348$		0			0
$349$	−19.1818			−1.02678			−0.513390	−	0.858155i	$-0.671611\pi$
$349$	−19.1818			−1.02678			−0.513390	+	0.858155i	$0.671611\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	−11.5296	−	19.9698i	−0.613656	−	1.06288i	−0.990619	−	0.136655i	$-0.956365\pi$
$353$	−11.5296	−	19.9698i	−0.613656	−	1.06288i	0.376963	−	0.926229i	$-0.376969\pi$
$354$		0			0
$355$	2.10228	−	3.64125i	0.111577	−	0.193257i
$356$		0			0
$357$	3.43401			0.181747
$358$		0			0
$359$	3.08984			0.163075			0.0815377	−	0.996670i	$-0.474017\pi$
$359$	3.08984			0.163075			0.0815377	+	0.996670i	$0.474017\pi$
$360$		0			0
$361$	−6.57719	+	11.3920i	−0.346168	+	0.599580i
$362$		0			0
$363$	−6.77924	−	11.7420i	−0.355818	−	0.616295i
$364$		0			0
$365$	−7.29245	−	12.6309i	−0.381704	−	0.661131i
$366$		0			0
$367$	11.9937	−	20.7738i	0.626068	−	1.08438i	−0.362265	−	0.932075i	$-0.617997\pi$
$367$	11.9937	−	20.7738i	0.626068	−	1.08438i	0.988333	−	0.152306i	$-0.0486701\pi$
$368$		0			0
$369$	0.516533	−	0.894661i	0.0268896	−	0.0465742i
$370$		0			0
$371$	−20.6233	+	35.7207i	−1.07071	+	1.85452i
$372$		0			0
$373$	−12.9157	+	22.3706i	−0.668749	+	1.15831i	0.309505	+	0.950898i	$0.399837\pi$
$373$	−12.9157	+	22.3706i	−0.668749	+	1.15831i	−0.978254	+	0.207409i	$0.933497\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	1.95020			0.100440
$378$		0			0
$379$	−16.6869	−	28.9026i	−0.857149	−	1.48463i	−0.874637	−	0.484778i	$-0.838900\pi$
$379$	−16.6869	−	28.9026i	−0.857149	−	1.48463i	0.0174881	−	0.999847i	$-0.494433\pi$
$380$		0			0
$381$	7.09663	−	12.2917i	0.363572	−	0.629724i
$382$		0			0
$383$	−15.6281	−	27.0686i	−0.798558	−	1.38314i	−0.920555	−	0.390613i	$-0.872263\pi$
$383$	−15.6281	−	27.0686i	−0.798558	−	1.38314i	0.121997	−	0.992530i	$-0.461070\pi$
$384$		0			0
$385$	−11.2469	−	19.4803i	−0.573197	−	0.992806i
$386$		0			0
$387$	−8.67048			−0.440745
$388$		0			0
$389$	2.86565	+	4.96345i	0.145294	+	0.251657i	0.929483	−	0.368866i	$-0.120254\pi$
$389$	2.86565	+	4.96345i	0.145294	+	0.251657i	−0.784188	+	0.620523i	$0.786920\pi$
$390$		0			0
$391$	−3.04664	+	5.27694i	−0.154075	+	0.266866i
$392$		0			0
$393$	19.2328			0.970167
$394$		0			0
$395$	−5.59391	+	9.68893i	−0.281460	+	0.487503i
$396$		0			0
$397$	12.4332			0.624007			0.312003	−	0.950081i	$-0.399000\pi$
$397$	12.4332			0.624007			0.312003	+	0.950081i	$0.399000\pi$
$398$		0			0
$399$	25.7385			1.28854
$400$		0			0
$401$	4.05317			0.202406			0.101203	−	0.994866i	$-0.467731\pi$
$401$	4.05317			0.202406			0.101203	+	0.994866i	$0.467731\pi$
$402$		0			0
$403$	−8.08710			−0.402847
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	23.3614			1.15798
$408$		0			0
$409$	14.6794	−	25.4254i	0.725848	−	1.25721i	−0.232776	−	0.972530i	$-0.574781\pi$
$409$	14.6794	−	25.4254i	0.725848	−	1.25721i	0.958624	−	0.284675i	$-0.0918857\pi$
$410$		0			0
$411$	7.77825			0.383673
$412$		0			0
$413$	32.9126	−	57.0063i	1.61952	−	2.80510i
$414$		0			0
$415$	−5.15183	−	8.92324i	−0.252894	−	0.438024i
$416$		0			0
$417$	2.51375			0.123099
$418$		0			0
$419$	−4.13787	−	7.16700i	−0.202148	−	0.350131i	0.747072	−	0.664743i	$-0.231459\pi$
$419$	−4.13787	−	7.16700i	−0.202148	−	0.350131i	−0.949220	+	0.314612i	$0.898126\pi$
$420$		0			0
$421$	−14.4288	−	24.9914i	−0.703216	−	1.21801i	−0.967332	−	0.253515i	$-0.918413\pi$
$421$	−14.4288	−	24.9914i	−0.703216	−	1.21801i	0.264116	−	0.964491i	$-0.414920\pi$
$422$		0			0
$423$	−5.48755	+	9.50471i	−0.266814	+	0.462135i
$424$		0			0
$425$	0.378275	+	0.655192i	0.0183490	+	0.0317815i
$426$		0			0
$427$	−10.3579			−0.501255
$428$		0			0
$429$	−4.95565			−0.239261
$430$		0			0
$431$	−0.828840	+	1.43559i	−0.0399238	+	0.0691501i	−0.885297	−	0.465026i	$-0.846045\pi$
$431$	−0.828840	+	1.43559i	−0.0399238	+	0.0691501i	0.845373	+	0.534176i	$0.179378\pi$
$432$		0			0
$433$	3.78997	−	6.56442i	0.182134	−	0.315466i	−0.760473	−	0.649370i	$-0.775033\pi$
$433$	3.78997	−	6.56442i	0.182134	−	0.315466i	0.942607	+	0.333904i	$0.108366\pi$
$434$		0			0
$435$	−0.975100	+	1.68892i	−0.0467525	+	0.0809777i
$436$		0			0
$437$	−22.8351	+	39.5516i	−1.09235	+	1.89201i
$438$		0			0
$439$	8.29811	+	14.3727i	0.396047	+	0.685974i	0.993234	−	0.116128i	$-0.0370484\pi$
$439$	8.29811	+	14.3727i	0.396047	+	0.685974i	−0.597187	+	0.802102i	$0.703715\pi$
$440$		0			0
$441$	−6.80141	−	11.7804i	−0.323877	−	0.560971i
$442$		0			0
$443$	−5.11469	+	8.85890i	−0.243006	+	0.420899i	−0.961569	−	0.274563i	$-0.911467\pi$
$443$	−5.11469	+	8.85890i	−0.243006	+	0.420899i	0.718563	+	0.695462i	$0.244800\pi$
$444$		0			0
$445$	−14.1104			−0.668897
$446$		0			0
$447$	−15.3260			−0.724893
$448$		0			0
$449$	−2.99876	+	5.19401i	−0.141520	+	0.245120i	−0.928069	−	0.372407i	$-0.878532\pi$
$449$	−2.99876	+	5.19401i	−0.141520	+	0.245120i	0.786549	+	0.617528i	$0.211866\pi$
$450$		0			0
$451$	2.55976	+	4.43363i	0.120534	+	0.208771i
$452$		0			0
$453$	−2.20012	−	3.81071i	−0.103370	−	0.179043i
$454$		0			0
$455$	−4.53903			−0.212793
$456$		0			0
$457$	−3.57130	+	6.18567i	−0.167058	+	0.289353i	−0.937384	−	0.348297i	$-0.886760\pi$
$457$	−3.57130	+	6.18567i	−0.167058	+	0.289353i	0.770326	+	0.637650i	$0.220093\pi$
$458$		0			0
$459$	0.378275	+	0.655192i	0.0176564	+	0.0305817i
$460$		0			0
$461$	−24.5110			−1.14159			−0.570796	−	0.821092i	$-0.693365\pi$
$461$	−24.5110			−1.14159			−0.570796	+	0.821092i	$0.693365\pi$
$462$		0			0
$463$	−4.19450	−	7.26509i	−0.194935	−	0.337637i	0.751944	−	0.659227i	$-0.229116\pi$
$463$	−4.19450	−	7.26509i	−0.194935	−	0.337637i	−0.946879	+	0.321589i	$0.895783\pi$
$464$		0			0
$465$	4.04355	−	7.00363i	0.187515	−	0.324786i
$466$		0			0
$467$	6.43427	+	11.1445i	0.297743	+	0.515705i	0.975619	−	0.219470i	$-0.0704329\pi$
$467$	6.43427	+	11.1445i	0.297743	+	0.515705i	−0.677876	+	0.735176i	$0.737100\pi$
$468$		0			0
$469$	−27.1150	−	25.4001i	−1.25206	−	1.17287i
$470$		0			0
$471$	−3.43967	−	5.95769i	−0.158492	−	0.274516i
$472$		0			0
$473$	21.4839	−	37.2113i	0.987833	−	1.71098i
$474$		0			0
$475$	2.83524	+	4.91078i	0.130090	+	0.225322i
$476$		0			0
$477$	−9.08710			−0.416070
$478$		0			0
$479$	2.15912	+	3.73970i	0.0986526	+	0.170871i	0.911127	−	0.412125i	$-0.135213\pi$
$479$	2.15912	+	3.73970i	0.0986526	+	0.170871i	−0.812475	+	0.582997i	$0.801880\pi$
$480$		0			0
$481$	2.35705	−	4.08253i	0.107472	−	0.186147i
$482$		0			0
$483$	36.5575			1.66343
$484$		0			0
$485$	−8.53303	−	14.7796i	−0.387465	−	0.671109i
$486$		0			0
$487$	12.0604	+	20.8892i	0.546507	+	0.946579i	0.998510	+	0.0545621i	$0.0173763\pi$
$487$	12.0604	+	20.8892i	0.546507	+	0.946579i	−0.452003	+	0.892016i	$0.649290\pi$
$488$		0			0
$489$	−6.57930	+	11.3957i	−0.297526	+	0.515330i
$490$		0			0
$491$	−37.0736			−1.67311			−0.836553	−	0.547886i	$-0.815433\pi$
$491$	−37.0736			−1.67311			−0.836553	+	0.547886i	$0.815433\pi$
$492$		0			0
$493$	1.47542			0.0664498
$494$		0			0
$495$	2.47783	−	4.29172i	0.111370	−	0.192898i
$496$		0			0
$497$	9.54230	+	16.5278i	0.428031	+	0.741371i
$498$		0			0
$499$	17.8167	+	30.8594i	0.797584	+	1.38146i	0.921185	+	0.389124i	$0.127222\pi$
$499$	17.8167	+	30.8594i	0.797584	+	1.38146i	−0.123602	+	0.992332i	$0.539444\pi$
$500$		0			0
$501$	−8.25685	+	14.3013i	−0.368889	+	0.638934i
$502$		0			0
$503$	9.97159	−	17.2713i	0.444611	−	0.770089i	−0.553414	−	0.832906i	$-0.686675\pi$
$503$	9.97159	−	17.2713i	0.444611	−	0.770089i	0.998025	+	0.0628173i	$0.0200086\pi$
$504$		0			0
$505$	2.96053	−	5.12779i	0.131742	−	0.228184i
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	14.8777			0.659441			0.329720	−	0.944079i	$-0.393046\pi$
$509$	14.8777			0.659441			0.329720	+	0.944079i	$0.393046\pi$
$510$		0			0
$511$	66.2014			2.92858
$512$		0			0
$513$	2.83524	+	4.91078i	0.125179	+	0.216816i
$514$		0			0
$515$	−1.44768	+	2.50745i	−0.0637922	+	0.110491i
$516$		0			0
$517$	−27.1944	−	47.1021i	−1.19601	−	2.07155i
$518$		0			0
$519$	−3.71676	−	6.43762i	−0.163148	−	0.282580i
$520$		0			0
$521$	−25.4853			−1.11653			−0.558267	−	0.829662i	$-0.688533\pi$
$521$	−25.4853			−1.11653			−0.558267	+	0.829662i	$0.688533\pi$
$522$		0			0
$523$	−19.2335	−	33.3135i	−0.841024	−	1.45670i	−0.889030	−	0.457849i	$-0.848620\pi$
$523$	−19.2335	−	33.3135i	−0.841024	−	1.45670i	0.0480063	−	0.998847i	$-0.484713\pi$
$524$		0			0
$525$	2.26952	−	3.93092i	0.0990498	−	0.171559i
$526$		0			0
$527$	−6.11830			−0.266517
$528$		0			0
$529$	−20.9337	+	36.2583i	−0.910163	+	1.57645i
$530$		0			0
$531$	14.5020			0.629335
$532$		0			0
$533$	1.03307			0.0447470
$534$		0			0
$535$	13.2240			0.571723
$536$		0			0
$537$	22.4972			0.970828
$538$		0			0
$539$	67.4109			2.90359
$540$		0			0
$541$	34.8739			1.49935			0.749673	−	0.661808i	$-0.230211\pi$
$541$	34.8739			1.49935			0.749673	+	0.661808i	$0.230211\pi$
$542$		0			0
$543$	−6.14619	+	10.6455i	−0.263758	+	0.456843i
$544$		0			0
$545$	−7.70282			−0.329953
$546$		0			0
$547$	1.10632	−	1.91620i	0.0473027	−	0.0819307i	−0.841405	−	0.540406i	$-0.818271\pi$
$547$	1.10632	−	1.91620i	0.0473027	−	0.0819307i	0.888707	+	0.458475i	$0.151604\pi$
$548$		0			0
$549$	−1.14098	−	1.97624i	−0.0486960	−	0.0843439i
$550$		0			0
$551$	11.0586			0.471111
$552$		0			0
$553$	−25.3909	−	43.9784i	−1.07973	−	1.87015i
$554$		0			0
$555$	2.35705	+	4.08253i	0.100051	+	0.173294i
$556$		0			0
$557$	−0.766829	+	1.32819i	−0.0324916	+	0.0562771i	−0.881814	−	0.471597i	$-0.843678\pi$
$557$	−0.766829	+	1.32819i	−0.0324916	+	0.0562771i	0.849322	+	0.527875i	$0.177011\pi$
$558$		0			0
$559$	−4.33524	−	7.50886i	−0.183361	−	0.317591i
$560$		0			0
$561$	−3.74920			−0.158291
$562$		0			0
$563$	30.5580			1.28787			0.643933	−	0.765082i	$-0.277302\pi$
$563$	30.5580			1.28787			0.643933	+	0.765082i	$0.277302\pi$
$564$		0			0
$565$	3.04355	−	5.27158i	0.128043	−	0.221777i
$566$		0			0
$567$	2.26952	−	3.93092i	0.0953108	−	0.165083i
$568$		0			0
$569$	4.19357	−	7.26347i	0.175803	−	0.304501i	−0.764636	−	0.644463i	$-0.777081\pi$
$569$	4.19357	−	7.26347i	0.175803	−	0.304501i	0.940439	+	0.339962i	$0.110414\pi$
$570$		0			0
$571$	−12.3849	+	21.4513i	−0.518292	+	0.897709i	0.481482	+	0.876456i	$0.340099\pi$
$571$	−12.3849	+	21.4513i	−0.518292	+	0.897709i	−0.999774	+	0.0212527i	$0.993235\pi$
$572$		0			0
$573$	−4.36109	−	7.55363i	−0.182187	−	0.315558i
$574$		0			0
$575$	4.02702	+	6.97500i	0.167938	+	0.290878i
$576$		0			0
$577$	−12.4083	+	21.4918i	−0.516564	+	0.894715i	0.483251	+	0.875482i	$0.339456\pi$
$577$	−12.4083	+	21.4918i	−0.516564	+	0.894715i	−0.999815	+	0.0192332i	$0.993878\pi$
$578$		0			0
$579$	−19.3169			−0.802781
$580$		0			0
$581$	46.7687			1.94029
$582$		0			0
$583$	22.5163	−	38.9993i	0.932528	−	1.61519i
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$		0			0
$587$	−12.5358	−	21.7127i	−0.517409	−	0.896179i	−0.999796	−	0.0202207i	$-0.993563\pi$
$587$	−12.5358	−	21.7127i	−0.517409	−	0.896179i	0.482386	−	0.875959i	$-0.339770\pi$
$588$		0			0
$589$	−45.8578			−1.88954
$590$		0			0
$591$	9.80950	−	16.9906i	0.403509	−	0.698898i
$592$		0			0
$593$	−6.70135	−	11.6071i	−0.275191	−	0.476645i	0.694992	−	0.719017i	$-0.255408\pi$
$593$	−6.70135	−	11.6071i	−0.275191	−	0.476645i	−0.970183	+	0.242372i	$0.922075\pi$
$594$		0			0
$595$	−3.43401			−0.140781
$596$		0			0
$597$	0.348098	+	0.602923i	0.0142467	+	0.0246760i
$598$		0			0
$599$	−6.86643	+	11.8930i	−0.280555	+	0.485935i	−0.971522	−	0.236951i	$-0.923852\pi$
$599$	−6.86643	+	11.8930i	−0.280555	+	0.485935i	0.690967	+	0.722887i	$0.257185\pi$
$600$		0			0
$601$	−9.51169	−	16.4747i	−0.387990	−	0.672018i	0.604189	−	0.796841i	$-0.293497\pi$
$601$	−9.51169	−	16.4747i	−0.387990	−	0.672018i	−0.992179	+	0.124823i	$0.960164\pi$
$602$		0			0
$603$	1.85934	−	7.97138i	0.0757183	−	0.324620i
$604$		0			0
$605$	6.77924	+	11.7420i	0.275615	+	0.477380i
$606$		0			0
$607$	20.8046	−	36.0347i	0.844433	−	1.46260i	−0.0416788	−	0.999131i	$-0.513271\pi$
$607$	20.8046	−	36.0347i	0.844433	−	1.46260i	0.886112	−	0.463471i	$-0.153396\pi$
$608$		0			0
$609$	−4.42601	−	7.66608i	−0.179351	−	0.310645i
$610$		0			0
$611$	−10.9751			−0.444005
$612$		0			0
$613$	−24.2793	−	42.0530i	−0.980633	−	1.69851i	−0.659931	−	0.751326i	$-0.729415\pi$
$613$	−24.2793	−	42.0530i	−0.980633	−	1.69851i	−0.320702	−	0.947180i	$-0.603919\pi$
$614$		0			0
$615$	−0.516533	+	0.894661i	−0.0208286	+	0.0360762i
$616$		0			0
$617$	3.84758			0.154898			0.0774489	−	0.996996i	$-0.475323\pi$
$617$	3.84758			0.154898			0.0774489	+	0.996996i	$0.475323\pi$
$618$		0			0
$619$	−4.18886	−	7.25532i	−0.168364	−	0.291616i	0.769480	−	0.638670i	$-0.220515\pi$
$619$	−4.18886	−	7.25532i	−0.168364	−	0.291616i	−0.937845	+	0.347054i	$0.887182\pi$
$620$		0			0
$621$	4.02702	+	6.97500i	0.161599	+	0.279897i
$622$		0			0
$623$	32.0238	−	55.4669i	1.28301	−	2.22223i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−28.1009			−1.12224
$628$		0			0
$629$	1.78323	−	3.08864i	0.0711019	−	0.123152i
$630$		0			0
$631$	7.54675	+	13.0714i	0.300431	+	0.520362i	0.976234	−	0.216720i	$-0.0695360\pi$
$631$	7.54675	+	13.0714i	0.300431	+	0.520362i	−0.675802	+	0.737083i	$0.736203\pi$
$632$		0			0
$633$	−0.0968252	−	0.167706i	−0.00384846	−	0.00666572i
$634$		0			0
$635$	−7.09663	+	12.2917i	−0.281621	+	0.487782i
$636$		0			0
$637$	6.80141	−	11.7804i	0.269482	−	0.466756i
$638$		0			0
$639$	−2.10228	+	3.64125i	−0.0831648	+	0.144046i
$640$		0			0
$641$	4.88599	−	8.46279i	0.192985	−	0.334260i	−0.753253	−	0.657731i	$-0.771516\pi$
$641$	4.88599	−	8.46279i	0.192985	−	0.334260i	0.946238	+	0.323471i	$0.104850\pi$
$642$		0			0
$643$	−16.4978			−0.650611			−0.325305	−	0.945609i	$-0.605467\pi$
$643$	−16.4978			−0.650611			−0.325305	+	0.945609i	$0.605467\pi$
$644$		0			0
$645$	8.67048			0.341400
$646$		0			0
$647$	−5.29123	−	9.16468i	−0.208020	−	0.360301i	0.743071	−	0.669213i	$-0.233368\pi$
$647$	−5.29123	−	9.16468i	−0.208020	−	0.360301i	−0.951091	+	0.308912i	$0.900035\pi$
$648$		0			0
$649$	−35.9335	+	62.2387i	−1.41051	+	2.44308i
$650$		0			0
$651$	18.3538	+	31.7897i	0.719343	+	1.24594i
$652$		0			0
$653$	−13.9788	−	24.2119i	−0.547032	−	0.947487i	−0.998476	−	0.0551874i	$-0.982424\pi$
$653$	−13.9788	−	24.2119i	−0.547032	−	0.947487i	0.451444	−	0.892299i	$-0.350909\pi$
$654$		0			0
$655$	−19.2328			−0.751489
$656$		0			0
$657$	7.29245	+	12.6309i	0.284506	+	0.492778i
$658$		0			0
$659$	−23.4251	+	40.5734i	−0.912511	+	1.58052i	−0.102006	+	0.994784i	$0.532526\pi$
$659$	−23.4251	+	40.5734i	−0.912511	+	1.58052i	−0.810505	+	0.585732i	$0.800807\pi$
$660$		0			0
$661$	27.6521			1.07554			0.537770	−	0.843091i	$-0.319267\pi$
$661$	27.6521			1.07554			0.537770	+	0.843091i	$0.319267\pi$
$662$		0			0
$663$	−0.378275	+	0.655192i	−0.0146910	+	0.0254455i
$664$		0			0
$665$	−25.7385			−0.998097
$666$		0			0
$667$	15.7070			0.608177
$668$		0			0
$669$	−10.3477			−0.400066
$670$		0			0
$671$	11.3086			0.436565
$672$		0			0
$673$	−12.5347			−0.483176			−0.241588	−	0.970379i	$-0.577668\pi$
$673$	−12.5347			−0.483176			−0.241588	+	0.970379i	$0.577668\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−15.4863	+	26.8231i	−0.595188	+	1.03090i	0.398332	+	0.917241i	$0.369589\pi$
$677$	−15.4863	+	26.8231i	−0.595188	+	1.03090i	−0.993520	+	0.113655i	$0.963744\pi$
$678$		0			0
$679$	77.4634			2.97277
$680$		0			0
$681$	−12.4708	+	21.6001i	−0.477883	+	0.827718i
$682$		0			0
$683$	−0.377653	−	0.654114i	−0.0144505	−	0.0250290i	0.858710	−	0.512462i	$-0.171267\pi$
$683$	−0.377653	−	0.654114i	−0.0144505	−	0.0250290i	−0.873160	+	0.487433i	$0.837933\pi$
$684$		0			0
$685$	−7.77825			−0.297192
$686$		0			0
$687$	9.55619	+	16.5518i	0.364591	+	0.631491i
$688$		0			0
$689$	−4.54355	−	7.86966i	−0.173095	−	0.299810i
$690$		0			0
$691$	22.1077	−	38.2917i	0.841017	−	1.45668i	−0.0480193	−	0.998846i	$-0.515291\pi$
$691$	22.1077	−	38.2917i	0.841017	−	1.45668i	0.889036	−	0.457837i	$-0.151376\pi$
$692$		0			0
$693$	11.2469	+	19.4803i	0.427236	+	0.739994i
$694$		0			0
$695$	−2.51375			−0.0953521
$696$		0			0
$697$	0.781565			0.0296039
$698$		0			0
$699$	2.65828	−	4.60427i	0.100545	−	0.174150i
$700$		0			0
$701$	−19.8712	+	34.4180i	−0.750526	+	1.29995i	0.197042	+	0.980395i	$0.436866\pi$
$701$	−19.8712	+	34.4180i	−0.750526	+	1.29995i	−0.947568	+	0.319554i	$0.896467\pi$
$702$		0			0
$703$	13.3656	−	23.1499i	0.504094	−	0.873116i
$704$		0			0
$705$	5.48755	−	9.50471i	0.206673	−	0.357968i
$706$		0			0
$707$	13.4380	+	23.2752i	0.505386	+	0.875355i
$708$		0			0
$709$	−10.8541	−	18.7998i	−0.407633	−	0.706040i	0.586991	−	0.809593i	$-0.300312\pi$
$709$	−10.8541	−	18.7998i	−0.407633	−	0.706040i	−0.994624	+	0.103553i	$0.966979\pi$
$710$		0			0
$711$	5.59391	−	9.68893i	0.209788	−	0.363363i
$712$		0			0
$713$	−65.1338			−2.43928
$714$		0			0
$715$	4.95565			0.185331
$716$		0			0
$717$	10.1157	−	17.5209i	0.377778	−	0.654331i
$718$		0			0
$719$	−21.4111	−	37.0851i	−0.798499	−	1.38304i	−0.920594	−	0.390522i	$-0.872295\pi$
$719$	−21.4111	−	37.0851i	−0.798499	−	1.38304i	0.122095	−	0.992518i	$-0.461039\pi$
$720$		0			0
$721$	−6.57105	−	11.3814i	−0.244719	−	0.423865i
$722$		0			0
$723$	0.318963			0.0118624
$724$		0			0
$725$	0.975100	−	1.68892i	0.0362143	−	0.0627250i
$726$		0			0
$727$	8.76712	+	15.1851i	0.325154	+	0.563184i	0.981544	−	0.191239i	$-0.0612504\pi$
$727$	8.76712	+	15.1851i	0.325154	+	0.563184i	−0.656389	+	0.754422i	$0.727917\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.27983	−	5.68083i	−0.121309	−	0.210113i
$732$		0			0
$733$	−19.9070	+	34.4799i	−0.735281	+	1.27354i	0.219320	+	0.975653i	$0.429616\pi$
$733$	−19.9070	+	34.4799i	−0.735281	+	1.27354i	−0.954600	+	0.297890i	$0.903717\pi$
$734$		0			0
$735$	6.80141	+	11.7804i	0.250874	+	0.434526i
$736$		0			0
$737$	29.6038	+	27.7315i	1.09047	+	1.02150i
$738$		0			0
$739$	−1.80641	−	3.12880i	−0.0664499	−	0.115095i	0.830886	−	0.556442i	$-0.187834\pi$
$739$	−1.80641	−	3.12880i	−0.0664499	−	0.115095i	−0.897336	+	0.441348i	$0.854501\pi$
$740$		0			0
$741$	−2.83524	+	4.91078i	−0.104155	+	0.180402i
$742$		0			0
$743$	15.9058	+	27.5497i	0.583529	+	1.01070i	0.995057	+	0.0993047i	$0.0316618\pi$
$743$	15.9058	+	27.5497i	0.583529	+	1.01070i	−0.411528	+	0.911397i	$0.635005\pi$
$744$		0			0
$745$	15.3260			0.561500
$746$		0			0
$747$	5.15183	+	8.92324i	0.188496	+	0.326484i
$748$		0			0
$749$	−30.0121	+	51.9825i	−1.09662	+	1.89940i
$750$		0			0
$751$	−0.173048			−0.00631460			−0.00315730	−	0.999995i	$-0.501005\pi$
$751$	−0.173048			−0.00631460			−0.00315730	+	0.999995i	$0.501005\pi$
$752$		0			0
$753$	5.20630	+	9.01758i	0.189728	+	0.328619i
$754$		0			0
$755$	2.20012	+	3.81071i	0.0800704	+	0.138686i
$756$		0			0
$757$	4.81499	−	8.33981i	0.175004	−	0.303115i	−0.765159	−	0.643842i	$-0.777340\pi$
$757$	4.81499	−	8.33981i	0.175004	−	0.303115i	0.940163	+	0.340726i	$0.110673\pi$
$758$		0			0
$759$	−39.9130			−1.44875
$760$		0			0
$761$	−29.2173			−1.05913			−0.529564	−	0.848270i	$-0.677644\pi$
$761$	−29.2173			−1.05913			−0.529564	+	0.848270i	$0.677644\pi$
$762$		0			0
$763$	17.4817	−	30.2792i	0.632879	−	1.09618i
$764$		0			0
$765$	−0.378275	−	0.655192i	−0.0136766	−	0.0236885i
$766$		0			0
$767$	7.25102	+	12.5591i	0.261819	+	0.453484i
$768$		0			0
$769$	10.0505	−	17.4079i	0.362430	−	0.627746i	−0.625931	−	0.779879i	$-0.715281\pi$
$769$	10.0505	−	17.4079i	0.362430	−	0.627746i	0.988360	+	0.152132i	$0.0486140\pi$
$770$		0			0
$771$	1.24152	−	2.15038i	0.0447123	−	0.0774440i
$772$		0			0
$773$	−20.1518	+	34.9039i	−0.724809	+	1.25541i	0.234243	+	0.972178i	$0.424739\pi$
$773$	−20.1518	+	34.9039i	−0.724809	+	1.25541i	−0.959052	+	0.283228i	$0.908595\pi$
$774$		0			0
$775$	−4.04355	+	7.00363i	−0.145249	+	0.251578i
$776$		0			0
$777$	−21.3975			−0.767630
$778$		0			0
$779$	5.85798			0.209884
$780$		0			0
$781$	−10.4181	−	18.0448i	−0.372791	−	0.645692i
$782$		0			0
$783$	0.975100	−	1.68892i	0.0348472	−	0.0603572i
$784$		0			0
$785$	3.43967	+	5.95769i	0.122767	+	0.212639i
$786$		0			0
$787$	−4.87435	−	8.44261i	−0.173752	−	0.300947i	0.765977	−	0.642868i	$-0.222256\pi$
$787$	−4.87435	−	8.44261i	−0.173752	−	0.300947i	−0.939729	+	0.341921i	$0.888922\pi$
$788$		0			0
$789$	13.0244			0.463681
$790$		0			0
$791$	13.8148	+	23.9279i	0.491197	+	0.850778i
$792$		0			0
$793$	1.14098	−	1.97624i	0.0405175	−	0.0701784i
$794$		0			0
$795$	9.08710			0.322286
$796$		0			0
$797$	1.34081	−	2.32236i	0.0474940	−	0.0822621i	−0.841301	−	0.540567i	$-0.818210\pi$
$797$	1.34081	−	2.32236i	0.0474940	−	0.0822621i	0.888795	+	0.458305i	$0.151543\pi$
$798$		0			0
$799$	−8.30321			−0.293746
$800$		0			0
$801$	14.1104			0.498567
$802$		0			0
$803$	−72.2777			−2.55062
$804$		0			0
$805$	−36.5575			−1.28848
$806$		0			0
$807$	−16.7861			−0.590897
$808$		0			0
$809$	1.52230			0.0535213			0.0267607	−	0.999642i	$-0.491481\pi$
$809$	1.52230			0.0535213			0.0267607	+	0.999642i	$0.491481\pi$
$810$		0			0
$811$	−13.9995	+	24.2478i	−0.491588	+	0.851456i	−0.999953	−	0.00968576i	$-0.996917\pi$
$811$	−13.9995	+	24.2478i	−0.491588	+	0.851456i	0.508365	+	0.861142i	$0.330250\pi$
$812$		0			0
$813$	3.17156			0.111232
$814$		0			0
$815$	6.57930	−	11.3957i	0.230463	−	0.399173i
$816$		0			0
$817$	−24.5829	−	42.5789i	−0.860047	−	1.48965i
$818$		0			0
$819$	4.53903			0.158607
$820$		0			0
$821$	11.0047	+	19.0607i	0.384067	+	0.665223i	0.991639	−	0.129041i	$-0.0411899\pi$
$821$	11.0047	+	19.0607i	0.384067	+	0.665223i	−0.607572	+	0.794264i	$0.707857\pi$
$822$		0			0
$823$	21.8420	+	37.8315i	0.761364	+	1.31872i	0.942147	+	0.335199i	$0.108804\pi$
$823$	21.8420	+	37.8315i	0.761364	+	1.31872i	−0.180783	+	0.983523i	$0.557863\pi$
$824$		0			0
$825$	−2.47783	+	4.29172i	−0.0862668	+	0.149419i
$826$		0			0
$827$	9.24918	+	16.0200i	0.321625	+	0.557072i	0.980824	−	0.194898i	$-0.0624375\pi$
$827$	9.24918	+	16.0200i	0.321625	+	0.557072i	−0.659198	+	0.751969i	$0.729104\pi$
$828$		0			0
$829$	15.9522			0.554042			0.277021	−	0.960864i	$-0.410653\pi$
$829$	15.9522			0.554042			0.277021	+	0.960864i	$0.410653\pi$
$830$		0			0
$831$	−24.2309			−0.840559
$832$		0			0
$833$	5.14561	−	8.91246i	0.178285	−	0.308798i
$834$		0			0
$835$	8.25685	−	14.3013i	0.285740	−	0.494916i
$836$		0			0
$837$	−4.04355	+	7.00363i	−0.139766	+	0.242081i
$838$		0			0
$839$	3.34548	−	5.79455i	0.115499	−	0.200050i	−0.802480	−	0.596679i	$-0.796487\pi$
$839$	3.34548	−	5.79455i	0.115499	−	0.200050i	0.917979	+	0.396629i	$0.129820\pi$
$840$		0			0
$841$	12.5984	+	21.8210i	0.434426	+	0.752448i
$842$		0			0
$843$	−2.49665	−	4.32433i	−0.0859892	−	0.148938i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	−61.5424			−2.11462
$848$		0			0
$849$	18.0921			0.620918
$850$		0			0
$851$	18.9838	−	32.8809i	0.650755	−	1.12714i
$852$		0			0
$853$	12.3059	+	21.3144i	0.421346	+	0.729792i	0.996071	−	0.0885539i	$-0.0282245\pi$
$853$	12.3059	+	21.3144i	0.421346	+	0.729792i	−0.574726	+	0.818346i	$0.694891\pi$
$854$		0			0
$855$	−2.83524	−	4.91078i	−0.0969632	−	0.167945i
$856$		0			0
$857$	−29.1629			−0.996187			−0.498093	−	0.867123i	$-0.665966\pi$
$857$	−29.1629			−0.996187			−0.498093	+	0.867123i	$0.665966\pi$
$858$		0			0
$859$	−12.0933	+	20.9461i	−0.412616	+	0.714673i	−0.995175	−	0.0981161i	$-0.968718\pi$
$859$	−12.0933	+	20.9461i	−0.412616	+	0.714673i	0.582559	+	0.812789i	$0.302052\pi$
$860$		0			0
$861$	−2.34456	−	4.06090i	−0.0799024	−	0.138395i
$862$		0			0
$863$	−34.9525			−1.18980			−0.594898	−	0.803801i	$-0.702807\pi$
$863$	−34.9525			−1.18980			−0.594898	+	0.803801i	$0.702807\pi$
$864$		0			0
$865$	3.71676	+	6.43762i	0.126374	+	0.218886i
$866$		0			0
$867$	8.21382	−	14.2267i	0.278956	−	0.483166i
$868$		0			0
$869$	27.7215	+	48.0150i	0.940386	+	1.62880i
$870$		0			0
$871$	7.83309	−	2.37545i	0.265414	−	0.0804890i
$872$		0			0
$873$	8.53303	+	14.7796i	0.288799	+	0.500215i
$874$		0			0
$875$	−2.26952	+	3.93092i	−0.0767237	+	0.132889i
$876$		0			0
$877$	−10.0717	−	17.4447i	−0.340098	−	0.589067i	0.644353	−	0.764728i	$-0.277127\pi$
$877$	−10.0717	−	17.4447i	−0.340098	−	0.589067i	−0.984451	+	0.175662i	$0.943794\pi$
$878$		0			0
$879$	−5.62583			−0.189755
$880$		0			0
$881$	−6.89329	−	11.9395i	−0.232241	−	0.402253i	0.726226	−	0.687456i	$-0.241272\pi$
$881$	−6.89329	−	11.9395i	−0.232241	−	0.402253i	−0.958467	+	0.285203i	$0.907939\pi$
$882$		0			0
$883$	16.0354	−	27.7742i	0.539635	−	0.934676i	−0.459288	−	0.888287i	$-0.651895\pi$
$883$	16.0354	−	27.7742i	0.539635	−	0.934676i	0.998923	−	0.0463883i	$-0.0147712\pi$
$884$		0			0
$885$	−14.5020			−0.487481
$886$		0			0
$887$	−2.06743	−	3.58090i	−0.0694177	−	0.120235i	0.829227	−	0.558911i	$-0.188781\pi$
$887$	−2.06743	−	3.58090i	−0.0694177	−	0.120235i	−0.898645	+	0.438676i	$0.855447\pi$
$888$		0			0
$889$	−32.2119	−	55.7926i	−1.08035	−	1.87122i
$890$		0			0
$891$	−2.47783	+	4.29172i	−0.0830103	+	0.143778i
$892$		0			0
$893$	−62.2341			−2.08259
$894$		0			0
$895$	−22.4972			−0.752000
$896$		0			0
$897$	−4.02702	+	6.97500i	−0.134458	+	0.232888i
$898$		0			0
$899$	7.88573	+	13.6585i	0.263004	+	0.455536i
$900$		0			0
$901$	−3.43742	−	5.95379i	−0.114517	−	0.198350i
$902$		0			0
$903$	−19.6778	+	34.0830i	−0.654836	+	1.13421i
$904$		0			0
$905$	6.14619	−	10.6455i	0.204306	−	0.353869i
$906$		0			0
$907$	−16.9808	+	29.4116i	−0.563837	+	0.976595i	0.433320	+	0.901240i	$0.357342\pi$
$907$	−16.9808	+	29.4116i	−0.563837	+	0.976595i	−0.997157	+	0.0753543i	$0.975991\pi$
$908$		0			0
$909$	−2.96053	+	5.12779i	−0.0981946	+	0.170078i
$910$		0			0
$911$	8.72053			0.288924			0.144462	−	0.989510i	$-0.453855\pi$
$911$	8.72053			0.288924			0.144462	+	0.989510i	$0.453855\pi$
$912$		0			0
$913$	−51.0614			−1.68988
$914$		0			0
$915$	1.14098	+	1.97624i	0.0377197	+	0.0653325i
$916$		0			0
$917$	43.6492	−	75.6027i	1.44142	−	2.49662i
$918$		0			0
$919$	−7.00107	−	12.1262i	−0.230944	−	0.400007i	0.727142	−	0.686487i	$-0.240848\pi$
$919$	−7.00107	−	12.1262i	−0.230944	−	0.400007i	−0.958086	+	0.286480i	$0.907515\pi$
$920$		0			0
$921$	−8.78733	−	15.2201i	−0.289552	−	0.501519i
$922$		0			0
$923$	−4.20455			−0.138395
$924$		0			0
$925$	−2.35705	−	4.08253i	−0.0774994	−	0.134233i
$926$		0			0
$927$	1.44768	−	2.50745i	0.0475479	−	0.0823554i
$928$		0			0
$929$	55.7898			1.83041			0.915203	−	0.402994i	$-0.132031\pi$
$929$	55.7898			1.83041			0.915203	+	0.402994i	$0.132031\pi$
$930$		0			0
$931$	38.5673	−	66.8005i	1.26399	−	2.18930i
$932$		0			0
$933$	24.6522			0.807077
$934$		0			0
$935$	3.74920			0.122612
$936$		0			0
$937$	26.1013			0.852693			0.426347	−	0.904560i	$-0.359800\pi$
$937$	26.1013			0.852693			0.426347	+	0.904560i	$0.359800\pi$
$938$		0			0
$939$	28.6093			0.933630
$940$		0			0
$941$	41.4730			1.35198			0.675990	−	0.736910i	$-0.263716\pi$
$941$	41.4730			1.35198			0.675990	+	0.736910i	$0.263716\pi$
$942$		0			0
$943$	8.32034			0.270948
$944$		0			0
$945$	−2.26952	+	3.93092i	−0.0738274	+	0.127873i
$946$		0			0
$947$	26.0803			0.847496			0.423748	−	0.905780i	$-0.360714\pi$
$947$	26.0803			0.847496			0.423748	+	0.905780i	$0.360714\pi$
$948$		0			0
$949$	−7.29245	+	12.6309i	−0.236723	+	0.410016i
$950$		0			0
$951$	12.5304	+	21.7033i	0.406327	+	0.703779i
$952$		0			0
$953$	−0.466122			−0.0150992			−0.00754958	−	0.999972i	$-0.502403\pi$
$953$	−0.466122			−0.0150992			−0.00754958	+	0.999972i	$0.502403\pi$
$954$		0			0
$955$	4.36109	+	7.55363i	0.141122	+	0.244430i
$956$		0			0
$957$	4.83226	+	8.36971i	0.156205	+	0.270554i
$958$		0			0
$959$	17.6529	−	30.5757i	0.570041	−	0.987340i
$960$		0			0
$961$	−17.2006	−	29.7923i	−0.554858	−	0.961042i
$962$		0			0
$963$	−13.2240			−0.426137
$964$		0			0
$965$	19.3169			0.621832
$966$		0			0
$967$	13.2485	−	22.9471i	0.426043	−	0.737929i	−0.570474	−	0.821316i	$-0.693240\pi$
$967$	13.2485	−	22.9471i	0.426043	−	0.737929i	0.996517	+	0.0833871i	$0.0265738\pi$
$968$		0			0
$969$	−2.14500	+	3.71525i	−0.0689074	+	0.119351i
$970$		0			0
$971$	10.7785	−	18.6688i	0.345897	−	0.599111i	−0.639619	−	0.768692i	$-0.720908\pi$
$971$	10.7785	−	18.6688i	0.345897	−	0.599111i	0.985516	+	0.169580i	$0.0542413\pi$
$972$		0			0
$973$	5.70501	−	9.88136i	0.182894	−	0.316782i
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	−0.950508	−	1.64633i	−0.0304094	−	0.0526707i	0.850420	−	0.526104i	$-0.176348\pi$
$977$	−0.950508	−	1.64633i	−0.0304094	−	0.0526707i	−0.880830	+	0.473433i	$0.843014\pi$
$978$		0			0
$979$	−34.9631	+	60.5579i	−1.11743	+	1.93544i
$980$		0			0
$981$	7.70282			0.245932
$982$		0			0
$983$	−10.7477			−0.342798			−0.171399	−	0.985202i	$-0.554829\pi$
$983$	−10.7477			−0.342798			−0.171399	+	0.985202i	$0.554829\pi$
$984$		0			0
$985$	−9.80950	+	16.9906i	−0.312557	+	0.541364i
$986$		0			0
$987$	24.9082	+	43.1422i	0.792836	+	1.37323i
$988$		0			0
$989$	−34.9162	−	60.4766i	−1.11027	−	1.92304i
$990$		0			0
$991$	7.64972			0.243001			0.121501	−	0.992591i	$-0.461229\pi$
$991$	7.64972			0.243001			0.121501	+	0.992591i	$0.461229\pi$
$992$		0			0
$993$	−5.02203	+	8.69841i	−0.159369	+	0.276036i
$994$		0			0
$995$	−0.348098	−	0.602923i	−0.0110354	−	0.0191140i
$996$		0			0
$997$	−22.4291			−0.710336			−0.355168	−	0.934803i	$-0.615576\pi$
$997$	−22.4291			−0.710336			−0.355168	+	0.934803i	$0.615576\pi$
$998$		0			0
$999$	−2.35705	−	4.08253i	−0.0745738	−	0.129166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.j.841.5	✓	12
67.29	even	3	inner	4020.2.q.j.3781.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.j.841.5	✓	12	1.1	even	1	trivial
4020.2.q.j.3781.5	yes	12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.26952 - 3.93092i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(2.26952 - 3.93092i) q^{7} +1.00000 q^{9} +(-2.47783 + 4.29172i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(0.378275 + 0.655192i) q^{17} +(2.83524 + 4.91078i) q^{19} +(2.26952 - 3.93092i) q^{21} +(4.02702 + 6.97500i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(0.975100 - 1.68892i) q^{29} +(-4.04355 + 7.00363i) q^{31} +(-2.47783 + 4.29172i) q^{33} +(-2.26952 + 3.93092i) q^{35} +(-2.35705 - 4.08253i) q^{37} +(0.500000 + 0.866025i) q^{39} +(0.516533 - 0.894661i) q^{41} -8.67048 q^{43} -1.00000 q^{45} +(-5.48755 + 9.50471i) q^{47} +(-6.80141 - 11.7804i) q^{49} +(0.378275 + 0.655192i) q^{51} -9.08710 q^{53} +(2.47783 - 4.29172i) q^{55} +(2.83524 + 4.91078i) q^{57} +14.5020 q^{59} +(-1.14098 - 1.97624i) q^{61} +(2.26952 - 3.93092i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(1.85934 - 7.97138i) q^{67} +(4.02702 + 6.97500i) q^{69} +(-2.10228 + 3.64125i) q^{71} +(7.29245 + 12.6309i) q^{73} +1.00000 q^{75} +(11.2469 + 19.4803i) q^{77} +(5.59391 - 9.68893i) q^{79} +1.00000 q^{81} +(5.15183 + 8.92324i) q^{83} +(-0.378275 - 0.655192i) q^{85} +(0.975100 - 1.68892i) q^{87} +14.1104 q^{89} +4.53903 q^{91} +(-4.04355 + 7.00363i) q^{93} +(-2.83524 - 4.91078i) q^{95} +(8.53303 + 14.7796i) q^{97} +(-2.47783 + 4.29172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} - 12 q^{5} + 2 q^{7} + 12 q^{9} - 5 q^{11} + 6 q^{13} - 12 q^{15} + 9 q^{17} - 11 q^{19} + 2 q^{21} + 19 q^{23} + 12 q^{25} + 12 q^{27} + 8 q^{29} - 4 q^{31} - 5 q^{33} - 2 q^{35} + 5 q^{37} + 6 q^{39} - 9 q^{41} - 14 q^{43} - 12 q^{45} - 6 q^{47} - 46 q^{49} + 9 q^{51} - 20 q^{53} + 5 q^{55} - 11 q^{57} + 6 q^{59} + 27 q^{61} + 2 q^{63} - 6 q^{65} + 3 q^{67} + 19 q^{69} + 25 q^{71} - 8 q^{73} + 12 q^{75} + 10 q^{77} - 2 q^{79} + 12 q^{81} + 20 q^{83} - 9 q^{85} + 8 q^{87} + 12 q^{89} + 4 q^{91} - 4 q^{93} + 11 q^{95} - q^{97} - 5 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 - 12 * q^5 + 2 * q^7 + 12 * q^9 - 5 * q^11 + 6 * q^13 - 12 * q^15 + 9 * q^17 - 11 * q^19 + 2 * q^21 + 19 * q^23 + 12 * q^25 + 12 * q^27 + 8 * q^29 - 4 * q^31 - 5 * q^33 - 2 * q^35 + 5 * q^37 + 6 * q^39 - 9 * q^41 - 14 * q^43 - 12 * q^45 - 6 * q^47 - 46 * q^49 + 9 * q^51 - 20 * q^53 + 5 * q^55 - 11 * q^57 + 6 * q^59 + 27 * q^61 + 2 * q^63 - 6 * q^65 + 3 * q^67 + 19 * q^69 + 25 * q^71 - 8 * q^73 + 12 * q^75 + 10 * q^77 - 2 * q^79 + 12 * q^81 + 20 * q^83 - 9 * q^85 + 8 * q^87 + 12 * q^89 + 4 * q^91 - 4 * q^93 + 11 * q^95 - q^97 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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