LMFDB - Embedded newform 4020.2.q.l.841.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.7
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.l.3781.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(0.479055 - 0.829747i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.479055 - 0.829747i) q^{7} +1.00000 q^{9} +(2.72246 - 4.71544i) q^{11} +(-0.313643 - 0.543246i) q^{13} +1.00000 q^{15} +(0.164969 + 0.285735i) q^{17} +(-1.58583 - 2.74674i) q^{19} +(-0.479055 + 0.829747i) q^{21} +(2.10690 + 3.64927i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.47619 - 6.02093i) q^{29} +(-0.592977 + 1.02707i) q^{31} +(-2.72246 + 4.71544i) q^{33} +(-0.479055 + 0.829747i) q^{35} +(-0.869283 - 1.50564i) q^{37} +(0.313643 + 0.543246i) q^{39} +(4.61489 - 7.99323i) q^{41} +5.91727 q^{43} -1.00000 q^{45} +(-5.13709 + 8.89769i) q^{47} +(3.04101 + 5.26719i) q^{49} +(-0.164969 - 0.285735i) q^{51} -8.34914 q^{53} +(-2.72246 + 4.71544i) q^{55} +(1.58583 + 2.74674i) q^{57} -5.10894 q^{59} +(-3.31870 - 5.74815i) q^{61} +(0.479055 - 0.829747i) q^{63} +(0.313643 + 0.543246i) q^{65} +(0.549606 - 8.16688i) q^{67} +(-2.10690 - 3.64927i) q^{69} +(1.82911 - 3.16812i) q^{71} +(-3.21378 - 5.56643i) q^{73} -1.00000 q^{75} +(-2.60842 - 4.51791i) q^{77} +(-6.94398 + 12.0273i) q^{79} +1.00000 q^{81} +(5.70265 + 9.87728i) q^{83} +(-0.164969 - 0.285735i) q^{85} +(-3.47619 + 6.02093i) q^{87} +13.4182 q^{89} -0.601009 q^{91} +(0.592977 - 1.02707i) q^{93} +(1.58583 + 2.74674i) q^{95} +(1.57581 + 2.72938i) q^{97} +(2.72246 - 4.71544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.479055	−	0.829747i	0.181066	−	0.313615i	−0.761178	−	0.648543i	$-0.775379\pi$
$7$	0.479055	−	0.829747i	0.181066	−	0.313615i	0.942244	+	0.334928i	$0.108712\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.72246	−	4.71544i	0.820853	−	1.42176i	−0.0841949	−	0.996449i	$-0.526832\pi$
$11$	2.72246	−	4.71544i	0.820853	−	1.42176i	0.905048	−	0.425310i	$-0.139835\pi$
$12$		0			0
$13$	−0.313643	−	0.543246i	−0.0869890	−	0.150669i	0.819248	−	0.573439i	$-0.194391\pi$
$13$	−0.313643	−	0.543246i	−0.0869890	−	0.150669i	−0.906237	+	0.422770i	$0.861058\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.164969	+	0.285735i	0.0400110	+	0.0693010i	0.885337	−	0.464949i	$-0.153927\pi$
$17$	0.164969	+	0.285735i	0.0400110	+	0.0693010i	−0.845326	+	0.534250i	$0.820594\pi$
$18$		0			0
$19$	−1.58583	−	2.74674i	−0.363815	−	0.630146i	0.624770	−	0.780809i	$-0.285193\pi$
$19$	−1.58583	−	2.74674i	−0.363815	−	0.630146i	−0.988585	+	0.150663i	$0.951859\pi$
$20$		0			0
$21$	−0.479055	+	0.829747i	−0.104538	+	0.181066i
$22$		0			0
$23$	2.10690	+	3.64927i	0.439320	+	0.760925i	0.997637	−	0.0687031i	$-0.0218861\pi$
$23$	2.10690	+	3.64927i	0.439320	+	0.760925i	−0.558317	+	0.829628i	$0.688553\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.47619	−	6.02093i	0.645512	−	1.11806i	−0.338671	−	0.940905i	$-0.609977\pi$
$29$	3.47619	−	6.02093i	0.645512	−	1.11806i	0.984183	−	0.177155i	$-0.0566893\pi$
$30$		0			0
$31$	−0.592977	+	1.02707i	−0.106502	+	0.184467i	−0.914351	−	0.404923i	$-0.867298\pi$
$31$	−0.592977	+	1.02707i	−0.106502	+	0.184467i	0.807849	+	0.589390i	$0.200632\pi$
$32$		0			0
$33$	−2.72246	+	4.71544i	−0.473920	+	0.820853i
$34$		0			0
$35$	−0.479055	+	0.829747i	−0.0809750	+	0.140253i
$36$		0			0
$37$	−0.869283	−	1.50564i	−0.142909	−	0.247526i	0.785682	−	0.618631i	$-0.212312\pi$
$37$	−0.869283	−	1.50564i	−0.142909	−	0.247526i	−0.928591	+	0.371105i	$0.878979\pi$
$38$		0			0
$39$	0.313643	+	0.543246i	0.0502231	+	0.0869890i
$40$		0			0
$41$	4.61489	−	7.99323i	0.720725	−	1.24833i	−0.239984	−	0.970777i	$-0.577142\pi$
$41$	4.61489	−	7.99323i	0.720725	−	1.24833i	0.960709	−	0.277556i	$-0.0895244\pi$
$42$		0			0
$43$	5.91727			0.902375			0.451188	−	0.892429i	$-0.351000\pi$
$43$	5.91727			0.902375			0.451188	+	0.892429i	$0.351000\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−5.13709	+	8.89769i	−0.749321	+	1.29786i	0.198828	+	0.980034i	$0.436287\pi$
$47$	−5.13709	+	8.89769i	−0.749321	+	1.29786i	−0.948149	+	0.317828i	$0.897047\pi$
$48$		0			0
$49$	3.04101	+	5.26719i	0.434430	+	0.752456i
$50$		0			0
$51$	−0.164969	−	0.285735i	−0.0231003	−	0.0400110i
$52$		0			0
$53$	−8.34914			−1.14684			−0.573421	−	0.819261i	$-0.694384\pi$
$53$	−8.34914			−1.14684			−0.573421	+	0.819261i	$0.694384\pi$
$54$		0			0
$55$	−2.72246	+	4.71544i	−0.367097	+	0.635830i
$56$		0			0
$57$	1.58583	+	2.74674i	0.210049	+	0.363815i
$58$		0			0
$59$	−5.10894			−0.665127			−0.332564	−	0.943081i	$-0.607914\pi$
$59$	−5.10894			−0.665127			−0.332564	+	0.943081i	$0.607914\pi$
$60$		0			0
$61$	−3.31870	−	5.74815i	−0.424916	−	0.735976i	0.571497	−	0.820604i	$-0.306363\pi$
$61$	−3.31870	−	5.74815i	−0.424916	−	0.735976i	−0.996413	+	0.0846287i	$0.973030\pi$
$62$		0			0
$63$	0.479055	−	0.829747i	0.0603552	−	0.104538i
$64$		0			0
$65$	0.313643	+	0.543246i	0.0389027	+	0.0673814i
$66$		0			0
$67$	0.549606	−	8.16688i	0.0671450	−	0.997743i
$67$	0.549606	−	8.16688i	0.0671450	−	0.997743i
$68$		0			0
$69$	−2.10690	−	3.64927i	−0.253642	−	0.439320i
$70$		0			0
$71$	1.82911	−	3.16812i	0.217076	−	0.375987i	−0.736837	−	0.676071i	$-0.763681\pi$
$71$	1.82911	−	3.16812i	0.217076	−	0.375987i	0.953913	+	0.300084i	$0.0970147\pi$
$72$		0			0
$73$	−3.21378	−	5.56643i	−0.376145	−	0.651502i	0.614353	−	0.789031i	$-0.289417\pi$
$73$	−3.21378	−	5.56643i	−0.376145	−	0.651502i	−0.990498	+	0.137530i	$0.956084\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−2.60842	−	4.51791i	−0.297257	−	0.514864i
$78$		0			0
$79$	−6.94398	+	12.0273i	−0.781259	+	1.35318i	0.149949	+	0.988694i	$0.452089\pi$
$79$	−6.94398	+	12.0273i	−0.781259	+	1.35318i	−0.931208	+	0.364487i	$0.881244\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	5.70265	+	9.87728i	0.625947	+	1.08417i	0.988357	+	0.152153i	$0.0486207\pi$
$83$	5.70265	+	9.87728i	0.625947	+	1.08417i	−0.362410	+	0.932019i	$0.618046\pi$
$84$		0			0
$85$	−0.164969	−	0.285735i	−0.0178934	−	0.0309924i
$86$		0			0
$87$	−3.47619	+	6.02093i	−0.372686	+	0.645512i
$88$		0			0
$89$	13.4182			1.42232			0.711162	−	0.703028i	$-0.248169\pi$
$89$	13.4182			1.42232			0.711162	+	0.703028i	$0.248169\pi$
$90$		0			0
$91$	−0.601009			−0.0630029
$92$		0			0
$93$	0.592977	−	1.02707i	0.0614889	−	0.106502i
$94$		0			0
$95$	1.58583	+	2.74674i	0.162703	+	0.281810i
$96$		0			0
$97$	1.57581	+	2.72938i	0.159999	+	0.277126i	0.934868	−	0.354996i	$-0.115518\pi$
$97$	1.57581	+	2.72938i	0.159999	+	0.277126i	−0.774869	+	0.632122i	$0.782184\pi$
$98$		0			0
$99$	2.72246	−	4.71544i	0.273618	−	0.473920i
$100$		0			0
$101$	−5.36992	+	9.30097i	−0.534327	+	0.925481i	0.464869	+	0.885380i	$0.346101\pi$
$101$	−5.36992	+	9.30097i	−0.534327	+	0.925481i	−0.999196	+	0.0401016i	$0.987232\pi$
$102$		0			0
$103$	4.49317	−	7.78240i	0.442725	−	0.766823i	−0.555165	−	0.831740i	$-0.687345\pi$
$103$	4.49317	−	7.78240i	0.442725	−	0.766823i	0.997891	+	0.0649173i	$0.0206784\pi$
$104$		0			0
$105$	0.479055	−	0.829747i	0.0467510	−	0.0809750i
$106$		0			0
$107$	−3.71894			−0.359524			−0.179762	−	0.983710i	$-0.557533\pi$
$107$	−3.71894			−0.359524			−0.179762	+	0.983710i	$0.557533\pi$
$108$		0			0
$109$	−11.8845			−1.13833			−0.569164	−	0.822224i	$-0.692733\pi$
$109$	−11.8845			−1.13833			−0.569164	+	0.822224i	$0.692733\pi$
$110$		0			0
$111$	0.869283	+	1.50564i	0.0825087	+	0.142909i
$112$		0			0
$113$	−1.39249	+	2.41187i	−0.130995	+	0.226890i	−0.924060	−	0.382247i	$-0.875150\pi$
$113$	−1.39249	+	2.41187i	−0.130995	+	0.226890i	0.793066	+	0.609136i	$0.208484\pi$
$114$		0			0
$115$	−2.10690	−	3.64927i	−0.196470	−	0.340296i
$116$		0			0
$117$	−0.313643	−	0.543246i	−0.0289963	−	0.0502231i
$118$		0			0
$119$	0.316118			0.0289784
$120$		0			0
$121$	−9.32359	−	16.1489i	−0.847599	−	1.46808i
$122$		0			0
$123$	−4.61489	+	7.99323i	−0.416111	+	0.720725i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	6.54597	−	11.3380i	0.580861	−	1.00608i	−0.414516	−	0.910042i	$-0.636049\pi$
$127$	6.54597	−	11.3380i	0.580861	−	1.00608i	0.995378	−	0.0960394i	$-0.0306175\pi$
$128$		0			0
$129$	−5.91727			−0.520987
$130$		0			0
$131$	−16.1701			−1.41279			−0.706396	−	0.707817i	$-0.749680\pi$
$131$	−16.1701			−1.41279			−0.706396	+	0.707817i	$0.749680\pi$
$132$		0			0
$133$	−3.03880			−0.263498
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	19.5894			1.67363			0.836817	−	0.547482i	$-0.184414\pi$
$137$	19.5894			1.67363			0.836817	+	0.547482i	$0.184414\pi$
$138$		0			0
$139$	−13.4935			−1.14450			−0.572251	−	0.820079i	$-0.693930\pi$
$139$	−13.4935			−1.14450			−0.572251	+	0.820079i	$0.693930\pi$
$140$		0			0
$141$	5.13709	−	8.89769i	0.432621	−	0.749321i
$142$		0			0
$143$	−3.41553			−0.285621
$144$		0			0
$145$	−3.47619	+	6.02093i	−0.288682	+	0.500011i
$146$		0			0
$147$	−3.04101	−	5.26719i	−0.250819	−	0.434430i
$148$		0			0
$149$	2.97628			0.243826			0.121913	−	0.992541i	$-0.461097\pi$
$149$	2.97628			0.243826			0.121913	+	0.992541i	$0.461097\pi$
$150$		0			0
$151$	−5.57259	−	9.65202i	−0.453491	−	0.785470i	0.545109	−	0.838365i	$-0.316488\pi$
$151$	−5.57259	−	9.65202i	−0.453491	−	0.785470i	−0.998600	+	0.0528953i	$0.983155\pi$
$152$		0			0
$153$	0.164969	+	0.285735i	0.0133370	+	0.0231003i
$154$		0			0
$155$	0.592977	−	1.02707i	0.0476291	−	0.0824960i
$156$		0			0
$157$	−5.96656	−	10.3344i	−0.476183	−	0.824773i	0.523445	−	0.852060i	$-0.324647\pi$
$157$	−5.96656	−	10.3344i	−0.476183	−	0.824773i	−0.999628	+	0.0272864i	$0.991313\pi$
$158$		0			0
$159$	8.34914			0.662130
$160$		0			0
$161$	4.03729			0.318183
$162$		0			0
$163$	2.63583	−	4.56539i	0.206454	−	0.357589i	−0.744141	−	0.668023i	$-0.767141\pi$
$163$	2.63583	−	4.56539i	0.206454	−	0.357589i	0.950595	+	0.310434i	$0.100474\pi$
$164$		0			0
$165$	2.72246	−	4.71544i	0.211943	−	0.367097i
$166$		0			0
$167$	6.42358	−	11.1260i	0.497071	−	0.860953i	−0.502923	−	0.864331i	$-0.667742\pi$
$167$	6.42358	−	11.1260i	0.497071	−	0.860953i	0.999994	+	0.00337830i	$0.00107535\pi$
$168$		0			0
$169$	6.30326	−	10.9176i	0.484866	−	0.839812i
$170$		0			0
$171$	−1.58583	−	2.74674i	−0.121272	−	0.210049i
$172$		0			0
$173$	1.06558	+	1.84564i	0.0810145	+	0.140321i	0.903686	−	0.428196i	$-0.140851\pi$
$173$	1.06558	+	1.84564i	0.0810145	+	0.140321i	−0.822671	+	0.568517i	$0.807517\pi$
$174$		0			0
$175$	0.479055	−	0.829747i	0.0362131	−	0.0627230i
$176$		0			0
$177$	5.10894			0.384011
$178$		0			0
$179$	5.26883			0.393811			0.196906	−	0.980422i	$-0.436911\pi$
$179$	5.26883			0.393811			0.196906	+	0.980422i	$0.436911\pi$
$180$		0			0
$181$	13.0998	−	22.6896i	0.973703	−	1.68650i	0.289551	−	0.957163i	$-0.406494\pi$
$181$	13.0998	−	22.6896i	0.973703	−	1.68650i	0.684152	−	0.729340i	$-0.260173\pi$
$182$		0			0
$183$	3.31870	+	5.74815i	0.245325	+	0.424916i
$184$		0			0
$185$	0.869283	+	1.50564i	0.0639110	+	0.110697i
$186$		0			0
$187$	1.79649			0.131372
$188$		0			0
$189$	−0.479055	+	0.829747i	−0.0348461	+	0.0603552i
$190$		0			0
$191$	−11.2775	−	19.5332i	−0.816011	−	1.41337i	−0.908600	−	0.417668i	$-0.862847\pi$
$191$	−11.2775	−	19.5332i	−0.816011	−	1.41337i	0.0925883	−	0.995704i	$-0.470486\pi$
$192$		0			0
$193$	2.84675			0.204914			0.102457	−	0.994737i	$-0.467330\pi$
$193$	2.84675			0.204914			0.102457	+	0.994737i	$0.467330\pi$
$194$		0			0
$195$	−0.313643	−	0.543246i	−0.0224605	−	0.0389027i
$196$		0			0
$197$	1.94350	−	3.36624i	0.138469	−	0.239835i	−0.788448	−	0.615101i	$-0.789115\pi$
$197$	1.94350	−	3.36624i	0.138469	−	0.239835i	0.926917	+	0.375266i	$0.122449\pi$
$198$		0			0
$199$	−5.90353	−	10.2252i	−0.418490	−	0.724847i	0.577297	−	0.816534i	$-0.304107\pi$
$199$	−5.90353	−	10.2252i	−0.418490	−	0.724847i	−0.995788	+	0.0916873i	$0.970774\pi$
$200$		0			0
$201$	−0.549606	+	8.16688i	−0.0387662	+	0.576047i
$202$		0			0
$203$	−3.33057	−	5.76871i	−0.233760	−	0.404884i
$204$		0			0
$205$	−4.61489	+	7.99323i	−0.322318	+	0.558271i
$206$		0			0
$207$	2.10690	+	3.64927i	0.146440	+	0.253642i
$208$		0			0
$209$	−17.2695			−1.19455
$210$		0			0
$211$	−5.55464	−	9.62092i	−0.382397	−	0.662331i	0.609007	−	0.793165i	$-0.291568\pi$
$211$	−5.55464	−	9.62092i	−0.382397	−	0.662331i	−0.991404	+	0.130833i	$0.958235\pi$
$212$		0			0
$213$	−1.82911	+	3.16812i	−0.125329	+	0.217076i
$214$		0			0
$215$	−5.91727			−0.403555
$216$		0			0
$217$	0.568137	+	0.984043i	0.0385677	+	0.0668012i
$218$		0			0
$219$	3.21378	+	5.56643i	0.217167	+	0.376145i
$220$		0			0
$221$	0.103483	−	0.179238i	0.00696102	−	0.0120568i
$222$		0			0
$223$	−25.8108			−1.72842			−0.864209	−	0.503133i	$-0.832181\pi$
$223$	−25.8108			−1.72842			−0.864209	+	0.503133i	$0.832181\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	7.29379	−	12.6332i	0.484106	−	0.838496i	−0.515727	−	0.856753i	$-0.672478\pi$
$227$	7.29379	−	12.6332i	0.484106	−	0.838496i	0.999833	+	0.0182567i	$0.00581162\pi$
$228$		0			0
$229$	−2.40699	−	4.16903i	−0.159058	−	0.275497i	0.775471	−	0.631383i	$-0.217513\pi$
$229$	−2.40699	−	4.16903i	−0.159058	−	0.275497i	−0.934529	+	0.355886i	$0.884179\pi$
$230$		0			0
$231$	2.60842	+	4.51791i	0.171621	+	0.297257i
$232$		0			0
$233$	2.64495	−	4.58119i	0.173276	−	0.300123i	−0.766287	−	0.642498i	$-0.777898\pi$
$233$	2.64495	−	4.58119i	0.173276	−	0.300123i	0.939563	+	0.342375i	$0.111231\pi$
$234$		0			0
$235$	5.13709	−	8.89769i	0.335107	−	0.580422i
$236$		0			0
$237$	6.94398	−	12.0273i	0.451060	−	0.781259i
$238$		0			0
$239$	−4.30266	+	7.45243i	−0.278316	+	0.482057i	−0.970966	−	0.239216i	$-0.923110\pi$
$239$	−4.30266	+	7.45243i	−0.278316	+	0.482057i	0.692650	+	0.721274i	$0.256443\pi$
$240$		0			0
$241$	−25.8114			−1.66266			−0.831329	−	0.555780i	$-0.812420\pi$
$241$	−25.8114			−1.66266			−0.831329	+	0.555780i	$0.812420\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−3.04101	−	5.26719i	−0.194283	−	0.336508i
$246$		0			0
$247$	−0.994771	+	1.72299i	−0.0632958	+	0.109631i
$248$		0			0
$249$	−5.70265	−	9.87728i	−0.361391	−	0.625947i
$250$		0			0
$251$	−10.1160	−	17.5214i	−0.638514	−	1.10594i	−0.985759	−	0.168164i	$-0.946216\pi$
$251$	−10.1160	−	17.5214i	−0.638514	−	1.10594i	0.347246	−	0.937774i	$-0.387117\pi$
$252$		0			0
$253$	22.9439			1.44247
$254$		0			0
$255$	0.164969	+	0.285735i	0.0103308	+	0.0178934i
$256$		0			0
$257$	−14.8987	+	25.8052i	−0.929352	+	1.60969i	−0.144945	+	0.989440i	$0.546300\pi$
$257$	−14.8987	+	25.8052i	−0.929352	+	1.60969i	−0.784408	+	0.620246i	$0.787033\pi$
$258$		0			0
$259$	−1.66574			−0.103504
$260$		0			0
$261$	3.47619	−	6.02093i	0.215171	−	0.372686i
$262$		0			0
$263$	−29.5465			−1.82192			−0.910958	−	0.412499i	$-0.864656\pi$
$263$	−29.5465			−1.82192			−0.910958	+	0.412499i	$0.864656\pi$
$264$		0			0
$265$	8.34914			0.512883
$266$		0			0
$267$	−13.4182			−0.821179
$268$		0			0
$269$	20.6672			1.26010			0.630050	−	0.776555i	$-0.283034\pi$
$269$	20.6672			1.26010			0.630050	+	0.776555i	$0.283034\pi$
$270$		0			0
$271$	9.26385			0.562739			0.281369	−	0.959600i	$-0.409211\pi$
$271$	9.26385			0.562739			0.281369	+	0.959600i	$0.409211\pi$
$272$		0			0
$273$	0.601009			0.0363747
$274$		0			0
$275$	2.72246	−	4.71544i	0.164171	−	0.284352i
$276$		0			0
$277$	−7.05965			−0.424173			−0.212087	−	0.977251i	$-0.568026\pi$
$277$	−7.05965			−0.424173			−0.212087	+	0.977251i	$0.568026\pi$
$278$		0			0
$279$	−0.592977	+	1.02707i	−0.0355006	+	0.0614889i
$280$		0			0
$281$	1.94383	+	3.36681i	0.115959	+	0.200847i	0.918163	−	0.396204i	$-0.129673\pi$
$281$	1.94383	+	3.36681i	0.115959	+	0.200847i	−0.802204	+	0.597050i	$0.796339\pi$
$282$		0			0
$283$	17.9566			1.06741			0.533706	−	0.845670i	$-0.320799\pi$
$283$	17.9566			1.06741			0.533706	+	0.845670i	$0.320799\pi$
$284$		0			0
$285$	−1.58583	−	2.74674i	−0.0939366	−	0.162703i
$286$		0			0
$287$	−4.42157	−	7.65839i	−0.260997	−	0.452061i
$288$		0			0
$289$	8.44557	−	14.6282i	0.496798	−	0.860480i
$290$		0			0
$291$	−1.57581	−	2.72938i	−0.0923754	−	0.159999i
$292$		0			0
$293$	15.1831			0.887005			0.443503	−	0.896273i	$-0.353736\pi$
$293$	15.1831			0.887005			0.443503	+	0.896273i	$0.353736\pi$
$294$		0			0
$295$	5.10894			0.297454
$296$		0			0
$297$	−2.72246	+	4.71544i	−0.157973	+	0.273618i
$298$		0			0
$299$	1.32163	−	2.28914i	0.0764320	−	0.132384i
$300$		0			0
$301$	2.83470	−	4.90984i	0.163389	−	0.282998i
$302$		0			0
$303$	5.36992	−	9.30097i	0.308494	−	0.534327i
$304$		0			0
$305$	3.31870	+	5.74815i	0.190028	+	0.329138i
$306$		0			0
$307$	−16.1191	−	27.9191i	−0.919964	−	1.59343i	−0.799466	−	0.600712i	$-0.794884\pi$
$307$	−16.1191	−	27.9191i	−0.919964	−	1.59343i	−0.120499	−	0.992713i	$-0.538449\pi$
$308$		0			0
$309$	−4.49317	+	7.78240i	−0.255608	+	0.442725i
$310$		0			0
$311$	−24.7103			−1.40119			−0.700595	−	0.713559i	$-0.747082\pi$
$311$	−24.7103			−1.40119			−0.700595	+	0.713559i	$0.747082\pi$
$312$		0			0
$313$	−5.31424			−0.300378			−0.150189	−	0.988657i	$-0.547988\pi$
$313$	−5.31424			−0.300378			−0.150189	+	0.988657i	$0.547988\pi$
$314$		0			0
$315$	−0.479055	+	0.829747i	−0.0269917	+	0.0467510i
$316$		0			0
$317$	14.2119	+	24.6157i	0.798219	+	1.38256i	0.920775	+	0.390095i	$0.127558\pi$
$317$	14.2119	+	24.6157i	0.798219	+	1.38256i	−0.122556	+	0.992462i	$0.539109\pi$
$318$		0			0
$319$	−18.9276	−	32.7835i	−1.05974	−	1.83552i
$320$		0			0
$321$	3.71894			0.207571
$322$		0			0
$323$	0.523228	−	0.906257i	0.0291132	−	0.0504255i
$324$		0			0
$325$	−0.313643	−	0.543246i	−0.0173978	−	0.0301339i
$326$		0			0
$327$	11.8845			0.657214
$328$		0			0
$329$	4.92189	+	8.52497i	0.271353	+	0.469997i
$330$		0			0
$331$	−1.90532	+	3.30011i	−0.104726	+	0.181391i	−0.913626	−	0.406555i	$-0.866730\pi$
$331$	−1.90532	+	3.30011i	−0.104726	+	0.181391i	0.808900	+	0.587946i	$0.200063\pi$
$332$		0			0
$333$	−0.869283	−	1.50564i	−0.0476364	−	0.0825087i
$334$		0			0
$335$	−0.549606	+	8.16688i	−0.0300282	+	0.446204i
$336$		0			0
$337$	−2.79279	−	4.83726i	−0.152133	−	0.263502i	0.779878	−	0.625931i	$-0.215281\pi$
$337$	−2.79279	−	4.83726i	−0.152133	−	0.263502i	−0.932011	+	0.362429i	$0.881948\pi$
$338$		0			0
$339$	1.39249	−	2.41187i	0.0756298	−	0.130995i
$340$		0			0
$341$	3.22872	+	5.59230i	0.174845	+	0.302840i
$342$		0			0
$343$	12.5340			0.676773
$344$		0			0
$345$	2.10690	+	3.64927i	0.113432	+	0.196470i
$346$		0			0
$347$	−13.2731	+	22.9897i	−0.712539	+	1.23415i	0.251363	+	0.967893i	$0.419121\pi$
$347$	−13.2731	+	22.9897i	−0.712539	+	1.23415i	−0.963901	+	0.266260i	$0.914212\pi$
$348$		0			0
$349$	−16.7469			−0.896438			−0.448219	−	0.893924i	$-0.647942\pi$
$349$	−16.7469			−0.896438			−0.448219	+	0.893924i	$0.647942\pi$
$350$		0			0
$351$	0.313643	+	0.543246i	0.0167410	+	0.0289963i
$352$		0			0
$353$	16.9615	+	29.3782i	0.902770	+	1.56364i	0.823883	+	0.566760i	$0.191803\pi$
$353$	16.9615	+	29.3782i	0.902770	+	1.56364i	0.0788866	+	0.996884i	$0.474864\pi$
$354$		0			0
$355$	−1.82911	+	3.16812i	−0.0970793	+	0.168146i
$356$		0			0
$357$	−0.316118			−0.0167307
$358$		0			0
$359$	−25.7990			−1.36162			−0.680810	−	0.732461i	$-0.738372\pi$
$359$	−25.7990			−1.36162			−0.680810	+	0.732461i	$0.738372\pi$
$360$		0			0
$361$	4.47027	−	7.74274i	0.235278	−	0.407513i
$362$		0			0
$363$	9.32359	+	16.1489i	0.489362	+	0.847599i
$364$		0			0
$365$	3.21378	+	5.56643i	0.168217	+	0.291360i
$366$		0			0
$367$	−18.6285	+	32.2655i	−0.972398	+	1.68424i	−0.284131	+	0.958785i	$0.591705\pi$
$367$	−18.6285	+	32.2655i	−0.972398	+	1.68424i	−0.688267	+	0.725458i	$0.741628\pi$
$368$		0			0
$369$	4.61489	−	7.99323i	0.240242	−	0.416111i
$370$		0			0
$371$	−3.99969	+	6.92767i	−0.207654	+	0.359667i
$372$		0			0
$373$	3.73860	−	6.47545i	0.193578	−	0.335286i	−0.752856	−	0.658186i	$-0.771324\pi$
$373$	3.73860	−	6.47545i	0.193578	−	0.335286i	0.946433	+	0.322899i	$0.104658\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−4.36113			−0.224610
$378$		0			0
$379$	13.9264	+	24.1212i	0.715350	+	1.23902i	0.962824	+	0.270128i	$0.0870660\pi$
$379$	13.9264	+	24.1212i	0.715350	+	1.23902i	−0.247475	+	0.968894i	$0.579601\pi$
$380$		0			0
$381$	−6.54597	+	11.3380i	−0.335360	+	0.580861i
$382$		0			0
$383$	−7.38438	−	12.7901i	−0.377324	−	0.653545i	0.613348	−	0.789813i	$-0.289822\pi$
$383$	−7.38438	−	12.7901i	−0.377324	−	0.653545i	−0.990672	+	0.136268i	$0.956489\pi$
$384$		0			0
$385$	2.60842	+	4.51791i	0.132937	+	0.230254i
$386$		0			0
$387$	5.91727			0.300792
$388$		0			0
$389$	−12.8027	−	22.1749i	−0.649122	−	1.12431i	−0.983333	−	0.181814i	$-0.941803\pi$
$389$	−12.8027	−	22.1749i	−0.649122	−	1.12431i	0.334211	−	0.942498i	$-0.391530\pi$
$390$		0			0
$391$	−0.695150	+	1.20403i	−0.0351552	+	0.0608906i
$392$		0			0
$393$	16.1701			0.815676
$394$		0			0
$395$	6.94398	−	12.0273i	0.349390	−	0.605161i
$396$		0			0
$397$	−15.0861			−0.757149			−0.378575	−	0.925571i	$-0.623586\pi$
$397$	−15.0861			−0.757149			−0.378575	+	0.925571i	$0.623586\pi$
$398$		0			0
$399$	3.03880			0.152130
$400$		0			0
$401$	13.7112			0.684705			0.342352	−	0.939572i	$-0.388776\pi$
$401$	13.7112			0.684705			0.342352	+	0.939572i	$0.388776\pi$
$402$		0			0
$403$	0.743933			0.0370580
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−9.46636			−0.469230
$408$		0			0
$409$	−6.47370	+	11.2128i	−0.320104	+	0.554436i	−0.980509	−	0.196473i	$-0.937051\pi$
$409$	−6.47370	+	11.2128i	−0.320104	+	0.554436i	0.660405	+	0.750909i	$0.270385\pi$
$410$		0			0
$411$	−19.5894			−0.966274
$412$		0			0
$413$	−2.44746	+	4.23913i	−0.120432	+	0.208594i
$414$		0			0
$415$	−5.70265	−	9.87728i	−0.279932	−	0.484856i
$416$		0			0
$417$	13.4935			0.660778
$418$		0			0
$419$	16.5722	+	28.7039i	0.809605	+	1.40228i	0.913138	+	0.407651i	$0.133652\pi$
$419$	16.5722	+	28.7039i	0.809605	+	1.40228i	−0.103533	+	0.994626i	$0.533015\pi$
$420$		0			0
$421$	−3.32304	−	5.75567i	−0.161955	−	0.280514i	0.773615	−	0.633656i	$-0.218447\pi$
$421$	−3.32304	−	5.75567i	−0.161955	−	0.280514i	−0.935570	+	0.353142i	$0.885113\pi$
$422$		0			0
$423$	−5.13709	+	8.89769i	−0.249774	+	0.432621i
$424$		0			0
$425$	0.164969	+	0.285735i	0.00800219	+	0.0138602i
$426$		0			0
$427$	−6.35935			−0.307751
$428$		0			0
$429$	3.41553			0.164903
$430$		0			0
$431$	8.58443	−	14.8687i	0.413498	−	0.716199i	−0.581772	−	0.813352i	$-0.697640\pi$
$431$	8.58443	−	14.8687i	0.413498	−	0.716199i	0.995269	+	0.0971532i	$0.0309737\pi$
$432$		0			0
$433$	8.82418	−	15.2839i	0.424063	−	0.734499i	−0.572269	−	0.820066i	$-0.693937\pi$
$433$	8.82418	−	15.2839i	0.424063	−	0.734499i	0.996332	+	0.0855667i	$0.0272701\pi$
$434$		0			0
$435$	3.47619	−	6.02093i	0.166670	−	0.288682i
$436$		0			0
$437$	6.68239	−	11.5742i	0.319662	−	0.553671i
$438$		0			0
$439$	20.4335	+	35.3919i	0.975239	+	1.68916i	0.679144	+	0.734005i	$0.262351\pi$
$439$	20.4335	+	35.3919i	0.975239	+	1.68916i	0.296095	+	0.955159i	$0.404316\pi$
$440$		0			0
$441$	3.04101	+	5.26719i	0.144810	+	0.250819i
$442$		0			0
$443$	20.6967	−	35.8478i	0.983331	−	1.70318i	0.334203	−	0.942501i	$-0.391533\pi$
$443$	20.6967	−	35.8478i	0.983331	−	1.70318i	0.649128	−	0.760679i	$-0.275134\pi$
$444$		0			0
$445$	−13.4182			−0.636083
$446$		0			0
$447$	−2.97628			−0.140773
$448$		0			0
$449$	−0.662031	+	1.14667i	−0.0312432	+	0.0541147i	−0.881224	−	0.472699i	$-0.843280\pi$
$449$	−0.662031	+	1.14667i	−0.0312432	+	0.0541147i	0.849981	+	0.526813i	$0.176613\pi$
$450$		0			0
$451$	−25.1277	−	43.5225i	−1.18322	−	2.04940i
$452$		0			0
$453$	5.57259	+	9.65202i	0.261823	+	0.453491i
$454$		0			0
$455$	0.601009			0.0281757
$456$		0			0
$457$	6.77703	−	11.7382i	0.317016	−	0.549088i	−0.662848	−	0.748754i	$-0.730652\pi$
$457$	6.77703	−	11.7382i	0.317016	−	0.549088i	0.979864	+	0.199666i	$0.0639857\pi$
$458$		0			0
$459$	−0.164969	−	0.285735i	−0.00770011	−	0.0133370i
$460$		0			0
$461$	16.9085			0.787506			0.393753	−	0.919216i	$-0.371176\pi$
$461$	16.9085			0.787506			0.393753	+	0.919216i	$0.371176\pi$
$462$		0			0
$463$	8.10997	+	14.0469i	0.376902	+	0.652814i	0.990610	−	0.136720i	$-0.0436559\pi$
$463$	8.10997	+	14.0469i	0.376902	+	0.652814i	−0.613708	+	0.789533i	$0.710323\pi$
$464$		0			0
$465$	−0.592977	+	1.02707i	−0.0274987	+	0.0476291i
$466$		0			0
$467$	−13.3352	−	23.0972i	−0.617078	−	1.06881i	−0.990016	−	0.140954i	$-0.954983\pi$
$467$	−13.3352	−	23.0972i	−0.617078	−	1.06881i	0.372939	−	0.927856i	$-0.378350\pi$
$468$		0			0
$469$	−6.51316	−	4.36842i	−0.300750	−	0.201715i
$470$		0			0
$471$	5.96656	+	10.3344i	0.274924	+	0.476183i
$472$		0			0
$473$	16.1095	−	27.9025i	0.740718	−	1.28296i
$474$		0			0
$475$	−1.58583	−	2.74674i	−0.0727630	−	0.126029i
$476$		0			0
$477$	−8.34914			−0.382281
$478$		0			0
$479$	11.7407	+	20.3354i	0.536445	+	0.929150i	0.999092	+	0.0426076i	$0.0135665\pi$
$479$	11.7407	+	20.3354i	0.536445	+	0.929150i	−0.462647	+	0.886543i	$0.653100\pi$
$480$		0			0
$481$	−0.545290	+	0.944470i	−0.0248631	+	0.0430641i
$482$		0			0
$483$	−4.03729			−0.183703
$484$		0			0
$485$	−1.57581	−	2.72938i	−0.0715536	−	0.123935i
$486$		0			0
$487$	−12.9081	−	22.3575i	−0.584921	−	1.01311i	−0.994885	−	0.101012i	$-0.967792\pi$
$487$	−12.9081	−	22.3575i	−0.584921	−	1.01311i	0.409964	−	0.912102i	$-0.365541\pi$
$488$		0			0
$489$	−2.63583	+	4.56539i	−0.119196	+	0.206454i
$490$		0			0
$491$	14.4535			0.652276			0.326138	−	0.945322i	$-0.394253\pi$
$491$	14.4535			0.652276			0.326138	+	0.945322i	$0.394253\pi$
$492$		0			0
$493$	2.29386			0.103310
$494$		0			0
$495$	−2.72246	+	4.71544i	−0.122366	+	0.211943i
$496$		0			0
$497$	−1.75249	−	3.03541i	−0.0786100	−	0.136157i
$498$		0			0
$499$	−2.32326	−	4.02401i	−0.104004	−	0.180139i	0.809327	−	0.587358i	$-0.199832\pi$
$499$	−2.32326	−	4.02401i	−0.104004	−	0.180139i	−0.913331	+	0.407219i	$0.866499\pi$
$500$		0			0
$501$	−6.42358	+	11.1260i	−0.286984	+	0.497071i
$502$		0			0
$503$	−16.7226	+	28.9643i	−0.745623	+	1.29146i	0.204281	+	0.978912i	$0.434514\pi$
$503$	−16.7226	+	28.9643i	−0.745623	+	1.29146i	−0.949903	+	0.312544i	$0.898819\pi$
$504$		0			0
$505$	5.36992	−	9.30097i	0.238958	−	0.413888i
$506$		0			0
$507$	−6.30326	+	10.9176i	−0.279937	+	0.484866i
$508$		0			0
$509$	15.6351			0.693014			0.346507	−	0.938047i	$-0.387368\pi$
$509$	15.6351			0.693014			0.346507	+	0.938047i	$0.387368\pi$
$510$		0			0
$511$	−6.15831			−0.272428
$512$		0			0
$513$	1.58583	+	2.74674i	0.0700162	+	0.121272i
$514$		0			0
$515$	−4.49317	+	7.78240i	−0.197993	+	0.342934i
$516$		0			0
$517$	27.9710	+	48.4473i	1.23016	+	2.13071i
$518$		0			0
$519$	−1.06558	−	1.84564i	−0.0467738	−	0.0810145i
$520$		0			0
$521$	−29.1688			−1.27791			−0.638954	−	0.769245i	$-0.720633\pi$
$521$	−29.1688			−1.27791			−0.638954	+	0.769245i	$0.720633\pi$
$522$		0			0
$523$	−2.00502	−	3.47280i	−0.0876734	−	0.151855i	0.818854	−	0.574002i	$-0.194610\pi$
$523$	−2.00502	−	3.47280i	−0.0876734	−	0.151855i	−0.906527	+	0.422147i	$0.861277\pi$
$524$		0			0
$525$	−0.479055	+	0.829747i	−0.0209077	+	0.0362131i
$526$		0			0
$527$	−0.391293			−0.0170450
$528$		0			0
$529$	2.62191	−	4.54127i	0.113996	−	0.197447i
$530$		0			0
$531$	−5.10894			−0.221709
$532$		0			0
$533$	−5.78972			−0.250781
$534$		0			0
$535$	3.71894			0.160784
$536$		0			0
$537$	−5.26883			−0.227367
$538$		0			0
$539$	33.1162			1.42641
$540$		0			0
$541$	25.9321			1.11491			0.557454	−	0.830208i	$-0.311778\pi$
$541$	25.9321			1.11491			0.557454	+	0.830208i	$0.311778\pi$
$542$		0			0
$543$	−13.0998	+	22.6896i	−0.562167	+	0.973703i
$544$		0			0
$545$	11.8845			0.509076
$546$		0			0
$547$	3.88351	−	6.72644i	0.166047	−	0.287602i	−0.770980	−	0.636860i	$-0.780233\pi$
$547$	3.88351	−	6.72644i	0.166047	−	0.287602i	0.937027	+	0.349258i	$0.113566\pi$
$548$		0			0
$549$	−3.31870	−	5.74815i	−0.141639	−	0.245325i
$550$		0			0
$551$	−22.0506			−0.939387
$552$		0			0
$553$	6.65310	+	11.5235i	0.282918	+	0.490029i
$554$		0			0
$555$	−0.869283	−	1.50564i	−0.0368990	−	0.0639110i
$556$		0			0
$557$	−1.04610	+	1.81189i	−0.0443245	+	0.0767723i	−0.887337	−	0.461122i	$-0.847447\pi$
$557$	−1.04610	+	1.81189i	−0.0443245	+	0.0767723i	0.843012	+	0.537895i	$0.180780\pi$
$558$		0			0
$559$	−1.85591	−	3.21453i	−0.0784967	−	0.135960i
$560$		0			0
$561$	−1.79649			−0.0758479
$562$		0			0
$563$	32.9318			1.38791			0.693954	−	0.720019i	$-0.255867\pi$
$563$	32.9318			1.38791			0.693954	+	0.720019i	$0.255867\pi$
$564$		0			0
$565$	1.39249	−	2.41187i	0.0585826	−	0.101468i
$566$		0			0
$567$	0.479055	−	0.829747i	0.0201184	−	0.0348461i
$568$		0			0
$569$	19.9082	−	34.4820i	0.834595	−	1.44556i	−0.0597654	−	0.998212i	$-0.519035\pi$
$569$	19.9082	−	34.4820i	0.834595	−	1.44556i	0.894360	−	0.447348i	$-0.147631\pi$
$570$		0			0
$571$	−17.7542	+	30.7512i	−0.742992	+	1.28690i	0.208135	+	0.978100i	$0.433261\pi$
$571$	−17.7542	+	30.7512i	−0.742992	+	1.28690i	−0.951127	+	0.308800i	$0.900073\pi$
$572$		0			0
$573$	11.2775	+	19.5332i	0.471124	+	0.816011i
$574$		0			0
$575$	2.10690	+	3.64927i	0.0878640	+	0.152185i
$576$		0			0
$577$	−7.83771	+	13.5753i	−0.326288	+	0.565147i	−0.981772	−	0.190061i	$-0.939131\pi$
$577$	−7.83771	+	13.5753i	−0.326288	+	0.565147i	0.655484	+	0.755209i	$0.272465\pi$
$578$		0			0
$579$	−2.84675			−0.118307
$580$		0			0
$581$	10.9275			0.453350
$582$		0			0
$583$	−22.7302	+	39.3699i	−0.941389	+	1.63053i
$584$		0			0
$585$	0.313643	+	0.543246i	0.0129676	+	0.0224605i
$586$		0			0
$587$	−9.98340	−	17.2918i	−0.412059	−	0.713707i	0.583056	−	0.812432i	$-0.301857\pi$
$587$	−9.98340	−	17.2918i	−0.412059	−	0.713707i	−0.995115	+	0.0987251i	$0.968524\pi$
$588$		0			0
$589$	3.76145			0.154988
$590$		0			0
$591$	−1.94350	+	3.36624i	−0.0799450	+	0.138469i
$592$		0			0
$593$	22.2369	+	38.5154i	0.913158	+	1.58164i	0.809576	+	0.587016i	$0.199697\pi$
$593$	22.2369	+	38.5154i	0.913158	+	1.58164i	0.103583	+	0.994621i	$0.466969\pi$
$594$		0			0
$595$	−0.316118			−0.0129596
$596$		0			0
$597$	5.90353	+	10.2252i	0.241616	+	0.418490i
$598$		0			0
$599$	−4.83770	+	8.37914i	−0.197663	+	0.342363i	−0.947770	−	0.318954i	$-0.896669\pi$
$599$	−4.83770	+	8.37914i	−0.197663	+	0.342363i	0.750107	+	0.661316i	$0.230002\pi$
$600$		0			0
$601$	−1.10904	−	1.92091i	−0.0452386	−	0.0783556i	0.842519	−	0.538666i	$-0.181071\pi$
$601$	−1.10904	−	1.92091i	−0.0452386	−	0.0783556i	−0.887758	+	0.460310i	$0.847738\pi$
$602$		0			0
$603$	0.549606	−	8.16688i	0.0223817	−	0.332581i
$604$		0			0
$605$	9.32359	+	16.1489i	0.379058	+	0.656548i
$606$		0			0
$607$	13.5923	−	23.5426i	0.551696	−	0.955565i	−0.446457	−	0.894805i	$-0.647314\pi$
$607$	13.5923	−	23.5426i	0.551696	−	0.955565i	0.998152	−	0.0607597i	$-0.0193523\pi$
$608$		0			0
$609$	3.33057	+	5.76871i	0.134961	+	0.233760i
$610$		0			0
$611$	6.44485			0.260731
$612$		0			0
$613$	−1.16400	−	2.01610i	−0.0470134	−	0.0814296i	0.841561	−	0.540162i	$-0.181637\pi$
$613$	−1.16400	−	2.01610i	−0.0470134	−	0.0814296i	−0.888574	+	0.458732i	$0.848304\pi$
$614$		0			0
$615$	4.61489	−	7.99323i	0.186090	−	0.322318i
$616$		0			0
$617$	−20.0025			−0.805271			−0.402636	−	0.915360i	$-0.631906\pi$
$617$	−20.0025			−0.805271			−0.402636	+	0.915360i	$0.631906\pi$
$618$		0			0
$619$	−16.5668	−	28.6945i	−0.665876	−	1.15333i	−0.979047	−	0.203634i	$-0.934725\pi$
$619$	−16.5668	−	28.6945i	−0.665876	−	1.15333i	0.313171	−	0.949697i	$-0.398609\pi$
$620$		0			0
$621$	−2.10690	−	3.64927i	−0.0845472	−	0.146440i
$622$		0			0
$623$	6.42804	−	11.1337i	0.257534	−	0.446062i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	17.2695			0.689676
$628$		0			0
$629$	0.286810	−	0.496770i	0.0114359	−	0.0198075i
$630$		0			0
$631$	−0.251748	−	0.436040i	−0.0100219	−	0.0173585i	0.860971	−	0.508654i	$-0.169857\pi$
$631$	−0.251748	−	0.436040i	−0.0100219	−	0.0173585i	−0.870993	+	0.491296i	$0.836523\pi$
$632$		0			0
$633$	5.55464	+	9.62092i	0.220777	+	0.382397i
$634$		0			0
$635$	−6.54597	+	11.3380i	−0.259769	+	0.449933i
$636$		0			0
$637$	1.90759	−	3.30404i	0.0755813	−	0.130911i
$638$		0			0
$639$	1.82911	−	3.16812i	0.0723587	−	0.125329i
$640$		0			0
$641$	−0.426891	+	0.739397i	−0.0168612	+	0.0292044i	−0.874333	−	0.485327i	$-0.838701\pi$
$641$	−0.426891	+	0.739397i	−0.0168612	+	0.0292044i	0.857472	+	0.514531i	$0.172034\pi$
$642$		0			0
$643$	−40.9137			−1.61348			−0.806739	−	0.590908i	$-0.798770\pi$
$643$	−40.9137			−1.61348			−0.806739	+	0.590908i	$0.798770\pi$
$644$		0			0
$645$	5.91727			0.232992
$646$		0			0
$647$	13.3045	+	23.0441i	0.523055	+	0.905957i	0.999640	+	0.0268290i	$0.00854095\pi$
$647$	13.3045	+	23.0441i	0.523055	+	0.905957i	−0.476585	+	0.879128i	$0.658126\pi$
$648$		0			0
$649$	−13.9089	+	24.0909i	−0.545972	+	0.945651i
$650$		0			0
$651$	−0.568137	−	0.984043i	−0.0222671	−	0.0385677i
$652$		0			0
$653$	−0.987507	−	1.71041i	−0.0386441	−	0.0669336i	0.846056	−	0.533093i	$-0.178971\pi$
$653$	−0.987507	−	1.71041i	−0.0386441	−	0.0669336i	−0.884701	+	0.466160i	$0.845637\pi$
$654$		0			0
$655$	16.1701			0.631820
$656$		0			0
$657$	−3.21378	−	5.56643i	−0.125382	−	0.217167i
$658$		0			0
$659$	2.70454	−	4.68440i	0.105354	−	0.182478i	−0.808529	−	0.588457i	$-0.799736\pi$
$659$	2.70454	−	4.68440i	0.105354	−	0.182478i	0.913883	+	0.405978i	$0.133069\pi$
$660$		0			0
$661$	−15.6953			−0.610478			−0.305239	−	0.952276i	$-0.598736\pi$
$661$	−15.6953			−0.610478			−0.305239	+	0.952276i	$0.598736\pi$
$662$		0			0
$663$	−0.103483	+	0.179238i	−0.00401895	+	0.00696102i
$664$		0			0
$665$	3.03880			0.117840
$666$		0			0
$667$	29.2960			1.13435
$668$		0			0
$669$	25.8108			0.997903
$670$		0			0
$671$	−36.1401			−1.39517
$672$		0			0
$673$	5.89364			0.227183			0.113592	−	0.993528i	$-0.463764\pi$
$673$	5.89364			0.227183			0.113592	+	0.993528i	$0.463764\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	12.4536	−	21.5702i	0.478630	−	0.829011i	−0.521070	−	0.853514i	$-0.674467\pi$
$677$	12.4536	−	21.5702i	0.478630	−	0.829011i	0.999700	+	0.0245028i	$0.00780026\pi$
$678$		0			0
$679$	3.01959			0.115881
$680$		0			0
$681$	−7.29379	+	12.6332i	−0.279499	+	0.484106i
$682$		0			0
$683$	22.8706	+	39.6131i	0.875121	+	1.51575i	0.856634	+	0.515925i	$0.172552\pi$
$683$	22.8706	+	39.6131i	0.875121	+	1.51575i	0.0184869	+	0.999829i	$0.494115\pi$
$684$		0			0
$685$	−19.5894			−0.748472
$686$		0			0
$687$	2.40699	+	4.16903i	0.0918325	+	0.159058i
$688$		0			0
$689$	2.61865	+	4.53564i	0.0997626	+	0.172794i
$690$		0			0
$691$	10.6974	−	18.5285i	0.406950	−	0.704857i	−0.587597	−	0.809154i	$-0.699926\pi$
$691$	10.6974	−	18.5285i	0.406950	−	0.704857i	0.994546	+	0.104297i	$0.0332591\pi$
$692$		0			0
$693$	−2.60842	−	4.51791i	−0.0990855	−	0.171621i
$694$		0			0
$695$	13.4935			0.511837
$696$		0			0
$697$	3.04526			0.115348
$698$		0			0
$699$	−2.64495	+	4.58119i	−0.100041	+	0.173276i
$700$		0			0
$701$	20.0754	−	34.7716i	0.758238	−	1.31331i	−0.185511	−	0.982642i	$-0.559394\pi$
$701$	20.0754	−	34.7716i	0.758238	−	1.31331i	0.943749	−	0.330664i	$-0.107273\pi$
$702$		0			0
$703$	−2.75708	+	4.77539i	−0.103985	+	0.180107i
$704$		0			0
$705$	−5.13709	+	8.89769i	−0.193474	+	0.335107i
$706$		0			0
$707$	5.14497	+	8.91135i	0.193497	+	0.335146i
$708$		0			0
$709$	1.92621	+	3.33630i	0.0723404	+	0.125297i	0.899927	−	0.436041i	$-0.143620\pi$
$709$	1.92621	+	3.33630i	0.0723404	+	0.125297i	−0.827586	+	0.561339i	$0.810287\pi$
$710$		0			0
$711$	−6.94398	+	12.0273i	−0.260420	+	0.451060i
$712$		0			0
$713$	−4.99739			−0.187154
$714$		0			0
$715$	3.41553			0.127733
$716$		0			0
$717$	4.30266	−	7.45243i	0.160686	−	0.278316i
$718$		0			0
$719$	2.96895	+	5.14237i	0.110723	+	0.191778i	0.916062	−	0.401037i	$-0.131350\pi$
$719$	2.96895	+	5.14237i	0.110723	+	0.191778i	−0.805339	+	0.592815i	$0.798017\pi$
$720$		0			0
$721$	−4.30495	−	7.45639i	−0.160325	−	0.277691i
$722$		0			0
$723$	25.8114			0.959936
$724$		0			0
$725$	3.47619	−	6.02093i	0.129102	−	0.223612i
$726$		0			0
$727$	−3.53480	−	6.12245i	−0.131098	−	0.227069i	0.793002	−	0.609219i	$-0.208517\pi$
$727$	−3.53480	−	6.12245i	−0.131098	−	0.227069i	−0.924100	+	0.382150i	$0.875184\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.976169	+	1.69077i	0.0361049	+	0.0625355i
$732$		0			0
$733$	−20.1649	+	34.9267i	−0.744809	+	1.29005i	0.205475	+	0.978662i	$0.434126\pi$
$733$	−20.1649	+	34.9267i	−0.744809	+	1.29005i	−0.950284	+	0.311385i	$0.899207\pi$
$734$		0			0
$735$	3.04101	+	5.26719i	0.112169	+	0.194283i
$736$		0			0
$737$	−37.0142	−	24.8256i	−1.36343	−	0.914465i
$738$		0			0
$739$	−1.87442	−	3.24658i	−0.0689515	−	0.119428i	0.829489	−	0.558524i	$-0.188632\pi$
$739$	−1.87442	−	3.24658i	−0.0689515	−	0.119428i	−0.898440	+	0.439096i	$0.855299\pi$
$740$		0			0
$741$	0.994771	−	1.72299i	0.0365438	−	0.0632958i
$742$		0			0
$743$	20.1669	+	34.9301i	0.739852	+	1.28146i	0.952561	+	0.304346i	$0.0984380\pi$
$743$	20.1669	+	34.9301i	0.739852	+	1.28146i	−0.212709	+	0.977116i	$0.568229\pi$
$744$		0			0
$745$	−2.97628			−0.109043
$746$		0			0
$747$	5.70265	+	9.87728i	0.208649	+	0.361391i
$748$		0			0
$749$	−1.78158	+	3.08578i	−0.0650974	+	0.112752i
$750$		0			0
$751$	32.9690			1.20306			0.601528	−	0.798851i	$-0.294559\pi$
$751$	32.9690			1.20306			0.601528	+	0.798851i	$0.294559\pi$
$752$		0			0
$753$	10.1160	+	17.5214i	0.368646	+	0.638514i
$754$		0			0
$755$	5.57259	+	9.65202i	0.202807	+	0.351273i
$756$		0			0
$757$	25.3380	−	43.8866i	0.920924	−	1.59509i	0.122935	−	0.992415i	$-0.460769\pi$
$757$	25.3380	−	43.8866i	0.920924	−	1.59509i	0.797989	−	0.602672i	$-0.205897\pi$
$758$		0			0
$759$	−22.9439			−0.832810
$760$		0			0
$761$	28.2597			1.02441			0.512207	−	0.858862i	$-0.328828\pi$
$761$	28.2597			1.02441			0.512207	+	0.858862i	$0.328828\pi$
$762$		0			0
$763$	−5.69333	+	9.86113i	−0.206112	+	0.356997i
$764$		0			0
$765$	−0.164969	−	0.285735i	−0.00596448	−	0.0103308i
$766$		0			0
$767$	1.60238	+	2.77541i	0.0578587	+	0.100214i
$768$		0			0
$769$	3.62275	−	6.27478i	0.130640	−	0.226275i	−0.793284	−	0.608852i	$-0.791630\pi$
$769$	3.62275	−	6.27478i	0.130640	−	0.226275i	0.923923	+	0.382578i	$0.124964\pi$
$770$		0			0
$771$	14.8987	−	25.8052i	0.536562	−	0.929352i
$772$		0			0
$773$	−20.0968	+	34.8087i	−0.722832	+	1.25198i	0.237028	+	0.971503i	$0.423827\pi$
$773$	−20.0968	+	34.8087i	−0.722832	+	1.25198i	−0.959860	+	0.280479i	$0.909507\pi$
$774$		0			0
$775$	−0.592977	+	1.02707i	−0.0213004	+	0.0368933i
$776$		0			0
$777$	1.66574			0.0597580
$778$		0			0
$779$	−29.2738			−1.04884
$780$		0			0
$781$	−9.95939	−	17.2502i	−0.356375	−	0.617259i
$782$		0			0
$783$	−3.47619	+	6.02093i	−0.124229	+	0.215171i
$784$		0			0
$785$	5.96656	+	10.3344i	0.212956	+	0.368850i
$786$		0			0
$787$	6.15509	+	10.6609i	0.219405	+	0.380021i	0.954626	−	0.297806i	$-0.0962550\pi$
$787$	6.15509	+	10.6609i	0.219405	+	0.380021i	−0.735221	+	0.677827i	$0.762922\pi$
$788$		0			0
$789$	29.5465			1.05188
$790$		0			0
$791$	1.33416	+	2.31083i	0.0474373	+	0.0821638i
$792$		0			0
$793$	−2.08177	+	3.60574i	−0.0739260	+	0.128044i
$794$		0			0
$795$	−8.34914			−0.296113
$796$		0			0
$797$	5.71388	−	9.89672i	0.202396	−	0.350560i	−0.746904	−	0.664932i	$-0.768461\pi$
$797$	5.71388	−	9.89672i	0.202396	−	0.350560i	0.949300	+	0.314372i	$0.101794\pi$
$798$		0			0
$799$	−3.38985			−0.119924
$800$		0			0
$801$	13.4182			0.474108
$802$		0			0
$803$	−34.9976			−1.23504
$804$		0			0
$805$	−4.03729			−0.142296
$806$		0			0
$807$	−20.6672			−0.727519
$808$		0			0
$809$	2.21775			0.0779719			0.0389860	−	0.999240i	$-0.487587\pi$
$809$	2.21775			0.0779719			0.0389860	+	0.999240i	$0.487587\pi$
$810$		0			0
$811$	−9.60235	+	16.6318i	−0.337184	+	0.584020i	−0.983902	−	0.178709i	$-0.942808\pi$
$811$	−9.60235	+	16.6318i	−0.337184	+	0.584020i	0.646718	+	0.762729i	$0.276141\pi$
$812$		0			0
$813$	−9.26385			−0.324897
$814$		0			0
$815$	−2.63583	+	4.56539i	−0.0923291	+	0.159919i
$816$		0			0
$817$	−9.38380	−	16.2532i	−0.328298	−	0.568628i
$818$		0			0
$819$	−0.601009			−0.0210010
$820$		0			0
$821$	−0.784249	−	1.35836i	−0.0273705	−	0.0474071i	0.852016	−	0.523516i	$-0.175380\pi$
$821$	−0.784249	−	1.35836i	−0.0273705	−	0.0474071i	−0.879386	+	0.476109i	$0.842047\pi$
$822$		0			0
$823$	13.5234	+	23.4233i	0.471397	+	0.816484i	0.999465	−	0.0327184i	$-0.0104164\pi$
$823$	13.5234	+	23.4233i	0.471397	+	0.816484i	−0.528067	+	0.849203i	$0.677083\pi$
$824$		0			0
$825$	−2.72246	+	4.71544i	−0.0947839	+	0.164171i
$826$		0			0
$827$	16.5255	+	28.6230i	0.574648	+	0.995320i	0.996080	+	0.0884599i	$0.0281945\pi$
$827$	16.5255	+	28.6230i	0.574648	+	0.995320i	−0.421431	+	0.906860i	$0.638472\pi$
$828$		0			0
$829$	8.50334			0.295333			0.147667	−	0.989037i	$-0.452824\pi$
$829$	8.50334			0.295333			0.147667	+	0.989037i	$0.452824\pi$
$830$		0			0
$831$	7.05965			0.244896
$832$		0			0
$833$	−1.00335	+	1.73785i	−0.0347640	+	0.0602129i
$834$		0			0
$835$	−6.42358	+	11.1260i	−0.222297	+	0.385030i
$836$		0			0
$837$	0.592977	−	1.02707i	0.0204963	−	0.0355006i
$838$		0			0
$839$	−28.3255	+	49.0612i	−0.977905	+	1.69378i	−0.307910	+	0.951415i	$0.599630\pi$
$839$	−28.3255	+	49.0612i	−0.977905	+	1.69378i	−0.669995	+	0.742366i	$0.733704\pi$
$840$		0			0
$841$	−9.66777	−	16.7451i	−0.333371	−	0.577416i
$842$		0			0
$843$	−1.94383	−	3.36681i	−0.0669489	−	0.115959i
$844$		0			0
$845$	−6.30326	+	10.9176i	−0.216839	+	0.375575i
$846$		0			0
$847$	−17.8660			−0.613885
$848$		0			0
$849$	−17.9566			−0.616270
$850$		0			0
$851$	3.66299	−	6.34449i	0.125566	−	0.217486i
$852$		0			0
$853$	12.7699	+	22.1181i	0.437233	+	0.757310i	0.997475	−	0.0710191i	$-0.0226251\pi$
$853$	12.7699	+	22.1181i	0.437233	+	0.757310i	−0.560242	+	0.828329i	$0.689292\pi$
$854$		0			0
$855$	1.58583	+	2.74674i	0.0542343	+	0.0939366i
$856$		0			0
$857$	8.93414			0.305184			0.152592	−	0.988289i	$-0.451238\pi$
$857$	8.93414			0.305184			0.152592	+	0.988289i	$0.451238\pi$
$858$		0			0
$859$	5.05627	−	8.75771i	0.172518	−	0.298809i	−0.766782	−	0.641908i	$-0.778143\pi$
$859$	5.05627	−	8.75771i	0.172518	−	0.298809i	0.939299	+	0.343099i	$0.111476\pi$
$860$		0			0
$861$	4.42157	+	7.65839i	0.150687	+	0.260997i
$862$		0			0
$863$	−42.6588			−1.45212			−0.726061	−	0.687630i	$-0.758651\pi$
$863$	−42.6588			−1.45212			−0.726061	+	0.687630i	$0.758651\pi$
$864$		0			0
$865$	−1.06558	−	1.84564i	−0.0362308	−	0.0627536i
$866$		0			0
$867$	−8.44557	+	14.6282i	−0.286827	+	0.496798i
$868$		0			0
$869$	37.8095	+	65.4879i	1.28260	+	2.22152i
$870$		0			0
$871$	−4.60901	+	2.26292i	−0.156170	+	0.0766760i
$872$		0			0
$873$	1.57581	+	2.72938i	0.0533329	+	0.0923754i
$874$		0			0
$875$	−0.479055	+	0.829747i	−0.0161950	+	0.0280506i
$876$		0			0
$877$	2.61730	+	4.53329i	0.0883798	+	0.153078i	0.906826	−	0.421504i	$-0.138498\pi$
$877$	2.61730	+	4.53329i	0.0883798	+	0.153078i	−0.818447	+	0.574583i	$0.805164\pi$
$878$		0			0
$879$	−15.1831			−0.512113
$880$		0			0
$881$	−10.5005	−	18.1873i	−0.353769	−	0.612746i	0.633137	−	0.774040i	$-0.281767\pi$
$881$	−10.5005	−	18.1873i	−0.353769	−	0.612746i	−0.986907	+	0.161293i	$0.948434\pi$
$882$		0			0
$883$	−14.7526	+	25.5523i	−0.496465	+	0.859903i	−0.999992	−	0.00407655i	$-0.998702\pi$
$883$	−14.7526	+	25.5523i	−0.496465	+	0.859903i	0.503526	+	0.863980i	$0.332036\pi$
$884$		0			0
$885$	−5.10894			−0.171735
$886$		0			0
$887$	10.2102	+	17.6845i	0.342824	+	0.593789i	0.984956	−	0.172805i	$-0.0552832\pi$
$887$	10.2102	+	17.6845i	0.342824	+	0.593789i	−0.642132	+	0.766594i	$0.721950\pi$
$888$		0			0
$889$	−6.27176	−	10.8630i	−0.210348	−	0.364334i
$890$		0			0
$891$	2.72246	−	4.71544i	0.0912059	−	0.157973i
$892$		0			0
$893$	32.5862			1.09046
$894$		0			0
$895$	−5.26883			−0.176118
$896$		0			0
$897$	−1.32163	+	2.28914i	−0.0441280	+	0.0764320i
$898$		0			0
$899$	4.12260	+	7.14056i	0.137496	+	0.238151i
$900$		0			0
$901$	−1.37735	−	2.38564i	−0.0458862	−	0.0794773i
$902$		0			0
$903$	−2.83470	+	4.90984i	−0.0943328	+	0.163389i
$904$		0			0
$905$	−13.0998	+	22.6896i	−0.435453	+	0.754227i
$906$		0			0
$907$	2.61745	−	4.53356i	0.0869110	−	0.150534i	−0.819293	−	0.573375i	$-0.805634\pi$
$907$	2.61745	−	4.53356i	0.0869110	−	0.150534i	0.906204	+	0.422841i	$0.138967\pi$
$908$		0			0
$909$	−5.36992	+	9.30097i	−0.178109	+	0.308494i
$910$		0			0
$911$	−56.8162			−1.88240			−0.941202	−	0.337844i	$-0.890302\pi$
$911$	−56.8162			−1.88240			−0.941202	+	0.337844i	$0.890302\pi$
$912$		0			0
$913$	62.1009			2.05524
$914$		0			0
$915$	−3.31870	−	5.74815i	−0.109713	−	0.190028i
$916$		0			0
$917$	−7.74638	+	13.4171i	−0.255808	+	0.443073i
$918$		0			0
$919$	−13.2706	−	22.9853i	−0.437756	−	0.758216i	0.559760	−	0.828655i	$-0.310893\pi$
$919$	−13.2706	−	22.9853i	−0.437756	−	0.758216i	−0.997516	+	0.0704387i	$0.977560\pi$
$920$		0			0
$921$	16.1191	+	27.9191i	0.531142	+	0.919964i
$922$		0			0
$923$	−2.29476			−0.0755329
$924$		0			0
$925$	−0.869283	−	1.50564i	−0.0285819	−	0.0495052i
$926$		0			0
$927$	4.49317	−	7.78240i	0.147575	−	0.255608i
$928$		0			0
$929$	−38.4700			−1.26216			−0.631079	−	0.775718i	$-0.717388\pi$
$929$	−38.4700			−1.26216			−0.631079	+	0.775718i	$0.717388\pi$
$930$		0			0
$931$	9.64507	−	16.7058i	0.316104	−	0.547509i
$932$		0			0
$933$	24.7103			0.808978
$934$		0			0
$935$	−1.79649			−0.0587515
$936$		0			0
$937$	−25.8042			−0.842985			−0.421493	−	0.906832i	$-0.638494\pi$
$937$	−25.8042			−0.842985			−0.421493	+	0.906832i	$0.638494\pi$
$938$		0			0
$939$	5.31424			0.173424
$940$		0			0
$941$	1.40529			0.0458113			0.0229056	−	0.999738i	$-0.492708\pi$
$941$	1.40529			0.0458113			0.0229056	+	0.999738i	$0.492708\pi$
$942$		0			0
$943$	38.8926			1.26652
$944$		0			0
$945$	0.479055	−	0.829747i	0.0155837	−	0.0269917i
$946$		0			0
$947$	−4.08154			−0.132632			−0.0663160	−	0.997799i	$-0.521125\pi$
$947$	−4.08154			−0.132632			−0.0663160	+	0.997799i	$0.521125\pi$
$948$		0			0
$949$	−2.01596	+	3.49175i	−0.0654409	+	0.113347i
$950$		0			0
$951$	−14.2119	−	24.6157i	−0.460852	−	0.798219i
$952$		0			0
$953$	31.7858			1.02964			0.514821	−	0.857297i	$-0.327858\pi$
$953$	31.7858			1.02964			0.514821	+	0.857297i	$0.327858\pi$
$954$		0			0
$955$	11.2775	+	19.5332i	0.364931	+	0.632080i
$956$		0			0
$957$	18.9276	+	32.7835i	0.611842	+	1.05974i
$958$		0			0
$959$	9.38439	−	16.2542i	0.303038	−	0.524877i
$960$		0			0
$961$	14.7968	+	25.6287i	0.477315	+	0.826733i
$962$		0			0
$963$	−3.71894			−0.119841
$964$		0			0
$965$	−2.84675			−0.0916403
$966$		0			0
$967$	14.1752	−	24.5521i	0.455842	−	0.789542i	−0.542894	−	0.839801i	$-0.682671\pi$
$967$	14.1752	−	24.5521i	0.455842	−	0.789542i	0.998736	+	0.0502593i	$0.0160048\pi$
$968$		0			0
$969$	−0.523228	+	0.906257i	−0.0168085	+	0.0291132i
$970$		0			0
$971$	9.42443	−	16.3236i	0.302444	−	0.523849i	−0.674245	−	0.738508i	$-0.735531\pi$
$971$	9.42443	−	16.3236i	0.302444	−	0.523849i	0.976689	+	0.214659i	$0.0688640\pi$
$972$		0			0
$973$	−6.46411	+	11.1962i	−0.207230	+	0.358933i
$974$		0			0
$975$	0.313643	+	0.543246i	0.0100446	+	0.0173978i
$976$		0			0
$977$	−9.78107	−	16.9413i	−0.312924	−	0.542001i	0.666070	−	0.745889i	$-0.267975\pi$
$977$	−9.78107	−	16.9413i	−0.312924	−	0.542001i	−0.978994	+	0.203889i	$0.934642\pi$
$978$		0			0
$979$	36.5305	−	63.2726i	1.16752	−	2.02220i
$980$		0			0
$981$	−11.8845			−0.379443
$982$		0			0
$983$	0.469324			0.0149691			0.00748455	−	0.999972i	$-0.497618\pi$
$983$	0.469324			0.0149691			0.00748455	+	0.999972i	$0.497618\pi$
$984$		0			0
$985$	−1.94350	+	3.36624i	−0.0619251	+	0.107257i
$986$		0			0
$987$	−4.92189	−	8.52497i	−0.156666	−	0.271353i
$988$		0			0
$989$	12.4671	+	21.5937i	0.396432	+	0.686640i
$990$		0			0
$991$	24.5683			0.780439			0.390220	−	0.920722i	$-0.372399\pi$
$991$	24.5683			0.780439			0.390220	+	0.920722i	$0.372399\pi$
$992$		0			0
$993$	1.90532	−	3.30011i	0.0604635	−	0.104726i
$994$		0			0
$995$	5.90353	+	10.2252i	0.187155	+	0.324161i
$996$		0			0
$997$	13.6806			0.433268			0.216634	−	0.976253i	$-0.430492\pi$
$997$	13.6806			0.433268			0.216634	+	0.976253i	$0.430492\pi$
$998$		0			0
$999$	0.869283	+	1.50564i	0.0275029	+	0.0476364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.841.7	✓	22
67.29	even	3	inner	4020.2.q.l.3781.7	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.7	✓	22	1.1	even	1	trivial
4020.2.q.l.3781.7	yes	22	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.479055 - 0.829747i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.479055 - 0.829747i) q^{7} +1.00000 q^{9} +(2.72246 - 4.71544i) q^{11} +(-0.313643 - 0.543246i) q^{13} +1.00000 q^{15} +(0.164969 + 0.285735i) q^{17} +(-1.58583 - 2.74674i) q^{19} +(-0.479055 + 0.829747i) q^{21} +(2.10690 + 3.64927i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(3.47619 - 6.02093i) q^{29} +(-0.592977 + 1.02707i) q^{31} +(-2.72246 + 4.71544i) q^{33} +(-0.479055 + 0.829747i) q^{35} +(-0.869283 - 1.50564i) q^{37} +(0.313643 + 0.543246i) q^{39} +(4.61489 - 7.99323i) q^{41} +5.91727 q^{43} -1.00000 q^{45} +(-5.13709 + 8.89769i) q^{47} +(3.04101 + 5.26719i) q^{49} +(-0.164969 - 0.285735i) q^{51} -8.34914 q^{53} +(-2.72246 + 4.71544i) q^{55} +(1.58583 + 2.74674i) q^{57} -5.10894 q^{59} +(-3.31870 - 5.74815i) q^{61} +(0.479055 - 0.829747i) q^{63} +(0.313643 + 0.543246i) q^{65} +(0.549606 - 8.16688i) q^{67} +(-2.10690 - 3.64927i) q^{69} +(1.82911 - 3.16812i) q^{71} +(-3.21378 - 5.56643i) q^{73} -1.00000 q^{75} +(-2.60842 - 4.51791i) q^{77} +(-6.94398 + 12.0273i) q^{79} +1.00000 q^{81} +(5.70265 + 9.87728i) q^{83} +(-0.164969 - 0.285735i) q^{85} +(-3.47619 + 6.02093i) q^{87} +13.4182 q^{89} -0.601009 q^{91} +(0.592977 - 1.02707i) q^{93} +(1.58583 + 2.74674i) q^{95} +(1.57581 + 2.72938i) q^{97} +(2.72246 - 4.71544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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