LMFDB - Embedded newform 4020.2.q.i.841.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.i.3781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} -1.00000 q^{5} +(-1.68614 + 2.92048i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.68614 + 2.92048i) q^{7} +1.00000 q^{9} +(-0.686141 + 1.18843i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(-3.68614 - 6.38458i) q^{17} +(-0.313859 - 0.543620i) q^{19} +(-1.68614 + 2.92048i) q^{21} +(-3.68614 - 6.38458i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(0.686141 - 1.18843i) q^{29} +(1.87228 - 3.24289i) q^{31} +(-0.686141 + 1.18843i) q^{33} +(1.68614 - 2.92048i) q^{35} +(4.05842 + 7.02939i) q^{37} +(0.500000 + 0.866025i) q^{39} +(2.31386 - 4.00772i) q^{41} -2.37228 q^{43} -1.00000 q^{45} +(3.68614 - 6.38458i) q^{47} +(-2.18614 - 3.78651i) q^{49} +(-3.68614 - 6.38458i) q^{51} +2.74456 q^{53} +(0.686141 - 1.18843i) q^{55} +(-0.313859 - 0.543620i) q^{57} +8.74456 q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.68614 + 2.92048i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(7.55842 + 3.14170i) q^{67} +(-3.68614 - 6.38458i) q^{69} +(2.05842 - 3.56529i) q^{71} +(6.50000 + 11.2583i) q^{73} +1.00000 q^{75} +(-2.31386 - 4.00772i) q^{77} +(7.87228 - 13.6352i) q^{79} +1.00000 q^{81} +(5.05842 + 8.76144i) q^{83} +(3.68614 + 6.38458i) q^{85} +(0.686141 - 1.18843i) q^{87} +11.4891 q^{89} -3.37228 q^{91} +(1.87228 - 3.24289i) q^{93} +(0.313859 + 0.543620i) q^{95} +(0.500000 + 0.866025i) q^{97} +(-0.686141 + 1.18843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{5} - q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^5 - q^7 + 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{5} - q^{7} + 4 q^{9} + 3 q^{11} + 2 q^{13} - 4 q^{15} - 9 q^{17} - 7 q^{19} - q^{21} - 9 q^{23} + 4 q^{25} + 4 q^{27} - 3 q^{29} - 4 q^{31} + 3 q^{33} + q^{35} - q^{37} + 2 q^{39} + 15 q^{41} + 2 q^{43} - 4 q^{45} + 9 q^{47} - 3 q^{49} - 9 q^{51} - 12 q^{53} - 3 q^{55} - 7 q^{57} + 12 q^{59} - 22 q^{61} - q^{63} - 2 q^{65} + 13 q^{67} - 9 q^{69} - 9 q^{71} + 26 q^{73} + 4 q^{75} - 15 q^{77} + 20 q^{79} + 4 q^{81} + 3 q^{83} + 9 q^{85} - 3 q^{87} - 2 q^{91} - 4 q^{93} + 7 q^{95} + 2 q^{97} + 3 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^5 - q^7 + 4 * q^9 + 3 * q^11 + 2 * q^13 - 4 * q^15 - 9 * q^17 - 7 * q^19 - q^21 - 9 * q^23 + 4 * q^25 + 4 * q^27 - 3 * q^29 - 4 * q^31 + 3 * q^33 + q^35 - q^37 + 2 * q^39 + 15 * q^41 + 2 * q^43 - 4 * q^45 + 9 * q^47 - 3 * q^49 - 9 * q^51 - 12 * q^53 - 3 * q^55 - 7 * q^57 + 12 * q^59 - 22 * q^61 - q^63 - 2 * q^65 + 13 * q^67 - 9 * q^69 - 9 * q^71 + 26 * q^73 + 4 * q^75 - 15 * q^77 + 20 * q^79 + 4 * q^81 + 3 * q^83 + 9 * q^85 - 3 * q^87 - 2 * q^91 - 4 * q^93 + 7 * q^95 + 2 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.68614	+	2.92048i	−0.637301	+	1.10384i	0.348721	+	0.937226i	$0.386616\pi$
$7$	−1.68614	+	2.92048i	−0.637301	+	1.10384i	−0.986023	+	0.166612i	$0.946717\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	−0.950730	−	0.310021i	$-0.899664\pi$
$11$	−0.686141	+	1.18843i	−0.206879	+	0.358325i	0.743851	+	0.668346i	$0.232997\pi$
$12$		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
$17$	−3.68614	−	6.38458i	−0.894020	−	1.54849i	−0.835012	−	0.550231i	$-0.814540\pi$
$17$	−3.68614	−	6.38458i	−0.894020	−	1.54849i	−0.0590081	−	0.998258i	$-0.518794\pi$
$18$		0			0
$19$	−0.313859	−	0.543620i	−0.0720043	−	0.124715i	0.827775	−	0.561060i	$-0.189606\pi$
$19$	−0.313859	−	0.543620i	−0.0720043	−	0.124715i	−0.899780	+	0.436345i	$0.856273\pi$
$20$		0			0
$21$	−1.68614	+	2.92048i	−0.367946	+	0.637301i
$22$		0			0
$23$	−3.68614	−	6.38458i	−0.768613	−	1.33128i	−0.938315	−	0.345782i	$-0.887614\pi$
$23$	−3.68614	−	6.38458i	−0.768613	−	1.33128i	0.169701	−	0.985496i	$-0.445720\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	−0.795261	−	0.606268i	$-0.792666\pi$
$29$	0.686141	−	1.18843i	0.127413	−	0.220686i	0.922674	+	0.385582i	$0.125999\pi$
$30$		0			0
$31$	1.87228	−	3.24289i	0.336272	−	0.582440i	−0.647457	−	0.762102i	$-0.724167\pi$
$31$	1.87228	−	3.24289i	0.336272	−	0.582440i	0.983728	+	0.179663i	$0.0575006\pi$
$32$		0			0
$33$	−0.686141	+	1.18843i	−0.119442	+	0.206879i
$34$		0			0
$35$	1.68614	−	2.92048i	0.285010	−	0.493651i
$36$		0			0
$37$	4.05842	+	7.02939i	0.667200	+	1.15563i	0.978684	+	0.205373i	$0.0658409\pi$
$37$	4.05842	+	7.02939i	0.667200	+	1.15563i	−0.311483	+	0.950252i	$0.600826\pi$
$38$		0			0
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$		0			0
$41$	2.31386	−	4.00772i	0.361364	−	0.625901i	−0.626821	−	0.779163i	$-0.715644\pi$
$41$	2.31386	−	4.00772i	0.361364	−	0.625901i	0.988186	+	0.153262i	$0.0489778\pi$
$42$		0			0
$43$	−2.37228			−0.361770			−0.180885	−	0.983504i	$-0.557896\pi$
$43$	−2.37228			−0.361770			−0.180885	+	0.983504i	$0.557896\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	3.68614	−	6.38458i	0.537679	−	0.931287i	−0.461350	−	0.887218i	$-0.652635\pi$
$47$	3.68614	−	6.38458i	0.537679	−	0.931287i	0.999029	−	0.0440687i	$-0.0140321\pi$
$48$		0			0
$49$	−2.18614	−	3.78651i	−0.312306	−	0.540930i
$50$		0			0
$51$	−3.68614	−	6.38458i	−0.516163	−	0.894020i
$52$		0			0
$53$	2.74456			0.376995			0.188497	−	0.982074i	$-0.439638\pi$
$53$	2.74456			0.376995			0.188497	+	0.982074i	$0.439638\pi$
$54$		0			0
$55$	0.686141	−	1.18843i	0.0925192	−	0.160248i
$56$		0			0
$57$	−0.313859	−	0.543620i	−0.0415717	−	0.0720043i
$58$		0			0
$59$	8.74456			1.13845			0.569223	−	0.822183i	$-0.307244\pi$
$59$	8.74456			1.13845			0.569223	+	0.822183i	$0.307244\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$		0			0
$63$	−1.68614	+	2.92048i	−0.212434	+	0.367946i
$64$		0			0
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		0			0
$67$	7.55842	+	3.14170i	0.923408	+	0.383819i
$67$	7.55842	+	3.14170i	0.923408	+	0.383819i
$68$		0			0
$69$	−3.68614	−	6.38458i	−0.443759	−	0.768613i
$70$		0			0
$71$	2.05842	−	3.56529i	0.244290	−	0.423122i	−0.717642	−	0.696412i	$-0.754779\pi$
$71$	2.05842	−	3.56529i	0.244290	−	0.423122i	0.961932	+	0.273290i	$0.0881119\pi$
$72$		0			0
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−2.31386	−	4.00772i	−0.263689	−	0.456722i
$78$		0			0
$79$	7.87228	−	13.6352i	0.885701	−	1.53408i	0.0407926	−	0.999168i	$-0.487012\pi$
$79$	7.87228	−	13.6352i	0.885701	−	1.53408i	0.844908	−	0.534911i	$-0.179655\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	5.05842	+	8.76144i	0.555234	+	0.961693i	0.997885	+	0.0649996i	$0.0207046\pi$
$83$	5.05842	+	8.76144i	0.555234	+	0.961693i	−0.442651	+	0.896694i	$0.645962\pi$
$84$		0			0
$85$	3.68614	+	6.38458i	0.399818	+	0.692505i
$86$		0			0
$87$	0.686141	−	1.18843i	0.0735620	−	0.127413i
$88$		0			0
$89$	11.4891			1.21784			0.608922	−	0.793230i	$-0.291602\pi$
$89$	11.4891			1.21784			0.608922	+	0.793230i	$0.291602\pi$
$90$		0			0
$91$	−3.37228			−0.353511
$92$		0			0
$93$	1.87228	−	3.24289i	0.194147	−	0.336272i
$94$		0			0
$95$	0.313859	+	0.543620i	0.0322013	+	0.0557743i
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$		0			0
$99$	−0.686141	+	1.18843i	−0.0689597	+	0.119442i
$100$		0			0
$101$	−6.43070	+	11.1383i	−0.639879	+	1.10830i	0.345580	+	0.938389i	$0.387682\pi$
$101$	−6.43070	+	11.1383i	−0.639879	+	1.10830i	−0.985459	+	0.169913i	$0.945651\pi$
$102$		0			0
$103$	1.05842	−	1.83324i	0.104289	−	0.180635i	−0.809158	−	0.587591i	$-0.800077\pi$
$103$	1.05842	−	1.83324i	0.104289	−	0.180635i	0.913448	+	0.406956i	$0.133410\pi$
$104$		0			0
$105$	1.68614	−	2.92048i	0.164550	−	0.285010i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−5.11684			−0.490105			−0.245052	−	0.969510i	$-0.578805\pi$
$109$	−5.11684			−0.490105			−0.245052	+	0.969510i	$0.578805\pi$
$110$		0			0
$111$	4.05842	+	7.02939i	0.385208	+	0.667200i
$112$		0			0
$113$	−2.05842	+	3.56529i	−0.193640	+	0.335394i	−0.946454	−	0.322839i	$-0.895363\pi$
$113$	−2.05842	+	3.56529i	−0.193640	+	0.335394i	0.752814	+	0.658234i	$0.228696\pi$
$114$		0			0
$115$	3.68614	+	6.38458i	0.343734	+	0.595365i
$116$		0			0
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$		0			0
$119$	24.8614			2.27904
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$		0			0
$123$	2.31386	−	4.00772i	0.208634	−	0.361364i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.87228	−	13.6352i	0.698552	−	1.20993i	−0.270417	−	0.962743i	$-0.587161\pi$
$127$	7.87228	−	13.6352i	0.698552	−	1.20993i	0.968969	−	0.247184i	$-0.0795053\pi$
$128$		0			0
$129$	−2.37228			−0.208868
$130$		0			0
$131$	−5.48913			−0.479587			−0.239794	−	0.970824i	$-0.577080\pi$
$131$	−5.48913			−0.479587			−0.239794	+	0.970824i	$0.577080\pi$
$132$		0			0
$133$	2.11684			0.183554
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−9.25544			−0.790745			−0.395373	−	0.918521i	$-0.629385\pi$
$137$	−9.25544			−0.790745			−0.395373	+	0.918521i	$0.629385\pi$
$138$		0			0
$139$	6.37228			0.540490			0.270245	−	0.962792i	$-0.412895\pi$
$139$	6.37228			0.540490			0.270245	+	0.962792i	$0.412895\pi$
$140$		0			0
$141$	3.68614	−	6.38458i	0.310429	−	0.537679i
$142$		0			0
$143$	−1.37228			−0.114756
$144$		0			0
$145$	−0.686141	+	1.18843i	−0.0569809	+	0.0986938i
$146$		0			0
$147$	−2.18614	−	3.78651i	−0.180310	−	0.312306i
$148$		0			0
$149$	2.74456			0.224843			0.112422	−	0.993661i	$-0.464139\pi$
$149$	2.74456			0.224843			0.112422	+	0.993661i	$0.464139\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$		0			0
$153$	−3.68614	−	6.38458i	−0.298007	−	0.516163i
$154$		0			0
$155$	−1.87228	+	3.24289i	−0.150385	+	0.260475i
$156$		0			0
$157$	−4.68614	−	8.11663i	−0.373995	−	0.647778i	0.616181	−	0.787604i	$-0.288679\pi$
$157$	−4.68614	−	8.11663i	−0.373995	−	0.647778i	−0.990176	+	0.139826i	$0.955346\pi$
$158$		0			0
$159$	2.74456			0.217658
$160$		0			0
$161$	24.8614			1.95935
$162$		0			0
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	−0.695777	−	0.718258i	$-0.744940\pi$
$163$	3.50000	−	6.06218i	0.274141	−	0.474826i	0.969918	+	0.243432i	$0.0782731\pi$
$164$		0			0
$165$	0.686141	−	1.18843i	0.0534160	−	0.0925192i
$166$		0			0
$167$	9.68614	−	16.7769i	0.749536	−	1.29823i	−0.198509	−	0.980099i	$-0.563610\pi$
$167$	9.68614	−	16.7769i	0.749536	−	1.29823i	0.948045	−	0.318136i	$-0.103057\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	−0.313859	−	0.543620i	−0.0240014	−	0.0415717i
$172$		0			0
$173$	−8.05842	−	13.9576i	−0.612670	−	1.06118i	−0.990788	−	0.135419i	$-0.956762\pi$
$173$	−8.05842	−	13.9576i	−0.612670	−	1.06118i	0.378118	−	0.925757i	$-0.376571\pi$
$174$		0			0
$175$	−1.68614	+	2.92048i	−0.127460	+	0.220768i
$176$		0			0
$177$	8.74456			0.657282
$178$		0			0
$179$	−3.25544			−0.243323			−0.121661	−	0.992572i	$-0.538822\pi$
$179$	−3.25544			−0.243323			−0.121661	+	0.992572i	$0.538822\pi$
$180$		0			0
$181$	−1.12772	+	1.95327i	−0.0838227	+	0.145185i	−0.904889	−	0.425648i	$-0.860046\pi$
$181$	−1.12772	+	1.95327i	−0.0838227	+	0.145185i	0.821066	+	0.570833i	$0.193380\pi$
$182$		0			0
$183$	−5.50000	−	9.52628i	−0.406572	−	0.704203i
$184$		0			0
$185$	−4.05842	−	7.02939i	−0.298381	−	0.516811i
$186$		0			0
$187$	10.1168			0.739817
$188$		0			0
$189$	−1.68614	+	2.92048i	−0.122649	+	0.212434i
$190$		0			0
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	0.829948	−	0.557841i	$-0.188370\pi$
$191$	−0.941578	−	1.63086i	−0.0681302	−	0.118005i	−0.898078	+	0.439836i	$0.855037\pi$
$192$		0			0
$193$	−17.1168			−1.23210			−0.616049	−	0.787708i	$-0.711268\pi$
$193$	−17.1168			−1.23210			−0.616049	+	0.787708i	$0.711268\pi$
$194$		0			0
$195$	−0.500000	−	0.866025i	−0.0358057	−	0.0620174i
$196$		0			0
$197$	2.31386	−	4.00772i	0.164856	−	0.285538i	−0.771748	−	0.635928i	$-0.780618\pi$
$197$	2.31386	−	4.00772i	0.164856	−	0.285538i	0.936604	+	0.350390i	$0.113951\pi$
$198$		0			0
$199$	−3.87228	−	6.70699i	−0.274499	−	0.475446i	0.695510	−	0.718517i	$-0.255179\pi$
$199$	−3.87228	−	6.70699i	−0.274499	−	0.475446i	−0.970009	+	0.243071i	$0.921845\pi$
$200$		0			0
$201$	7.55842	+	3.14170i	0.533130	+	0.221598i
$202$		0			0
$203$	2.31386	+	4.00772i	0.162401	+	0.281287i
$204$		0			0
$205$	−2.31386	+	4.00772i	−0.161607	+	0.279911i
$206$		0			0
$207$	−3.68614	−	6.38458i	−0.256204	−	0.443759i
$208$		0			0
$209$	0.861407			0.0595847
$210$		0			0
$211$	−3.87228	−	6.70699i	−0.266579	−	0.461728i	0.701397	−	0.712771i	$-0.252560\pi$
$211$	−3.87228	−	6.70699i	−0.266579	−	0.461728i	−0.967976	+	0.251043i	$0.919227\pi$
$212$		0			0
$213$	2.05842	−	3.56529i	0.141041	−	0.244290i
$214$		0			0
$215$	2.37228			0.161788
$216$		0			0
$217$	6.31386	+	10.9359i	0.428613	+	0.742379i
$218$		0			0
$219$	6.50000	+	11.2583i	0.439229	+	0.760767i
$220$		0			0
$221$	3.68614	−	6.38458i	0.247957	−	0.429474i
$222$		0			0
$223$	−23.1168			−1.54802			−0.774009	−	0.633174i	$-0.781752\pi$
$223$	−23.1168			−1.54802			−0.774009	+	0.633174i	$0.781752\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−3.43070	+	5.94215i	−0.227704	+	0.394395i	−0.957127	−	0.289668i	$-0.906455\pi$
$227$	−3.43070	+	5.94215i	−0.227704	+	0.394395i	0.729423	+	0.684062i	$0.239788\pi$
$228$		0			0
$229$	7.61684	+	13.1928i	0.503335	+	0.871802i	0.999993	+	0.00385547i	$0.00122724\pi$
$229$	7.61684	+	13.1928i	0.503335	+	0.871802i	−0.496657	+	0.867947i	$0.665439\pi$
$230$		0			0
$231$	−2.31386	−	4.00772i	−0.152241	−	0.263689i
$232$		0			0
$233$	6.68614	−	11.5807i	0.438024	−	0.758679i	−0.559513	−	0.828821i	$-0.689012\pi$
$233$	6.68614	−	11.5807i	0.438024	−	0.758679i	0.997537	+	0.0701421i	$0.0223453\pi$
$234$		0			0
$235$	−3.68614	+	6.38458i	−0.240457	+	0.416484i
$236$		0			0
$237$	7.87228	−	13.6352i	0.511360	−	0.885701i
$238$		0			0
$239$	14.0584	−	24.3499i	0.909364	−	1.57506i	0.0944136	−	0.995533i	$-0.469902\pi$
$239$	14.0584	−	24.3499i	0.909364	−	1.57506i	0.814950	−	0.579531i	$-0.196764\pi$
$240$		0			0
$241$	6.88316			0.443383			0.221692	−	0.975117i	$-0.428842\pi$
$241$	6.88316			0.443383			0.221692	+	0.975117i	$0.428842\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	2.18614	+	3.78651i	0.139667	+	0.241911i
$246$		0			0
$247$	0.313859	−	0.543620i	0.0199704	−	0.0345897i
$248$		0			0
$249$	5.05842	+	8.76144i	0.320564	+	0.555234i
$250$		0			0
$251$	−0.941578	−	1.63086i	−0.0594319	−	0.102939i	0.834779	−	0.550586i	$-0.185596\pi$
$251$	−0.941578	−	1.63086i	−0.0594319	−	0.102939i	−0.894211	+	0.447647i	$0.852262\pi$
$252$		0			0
$253$	10.1168			0.636041
$254$		0			0
$255$	3.68614	+	6.38458i	0.230835	+	0.399818i
$256$		0			0
$257$	2.31386	−	4.00772i	0.144335	−	0.249995i	−0.784790	−	0.619762i	$-0.787229\pi$
$257$	2.31386	−	4.00772i	0.144335	−	0.249995i	0.929124	+	0.369767i	$0.120563\pi$
$258$		0			0
$259$	−27.3723			−1.70083
$260$		0			0
$261$	0.686141	−	1.18843i	0.0424710	−	0.0735620i
$262$		0			0
$263$	−17.4891			−1.07843			−0.539213	−	0.842170i	$-0.681278\pi$
$263$	−17.4891			−1.07843			−0.539213	+	0.842170i	$0.681278\pi$
$264$		0			0
$265$	−2.74456			−0.168597
$266$		0			0
$267$	11.4891			0.703123
$268$		0			0
$269$	9.25544			0.564314			0.282157	−	0.959368i	$-0.408950\pi$
$269$	9.25544			0.564314			0.282157	+	0.959368i	$0.408950\pi$
$270$		0			0
$271$	−8.88316			−0.539613			−0.269807	−	0.962915i	$-0.586960\pi$
$271$	−8.88316			−0.539613			−0.269807	+	0.962915i	$0.586960\pi$
$272$		0			0
$273$	−3.37228			−0.204100
$274$		0			0
$275$	−0.686141	+	1.18843i	−0.0413758	+	0.0716651i
$276$		0			0
$277$	−13.8614			−0.832851			−0.416426	−	0.909170i	$-0.636717\pi$
$277$	−13.8614			−0.832851			−0.416426	+	0.909170i	$0.636717\pi$
$278$		0			0
$279$	1.87228	−	3.24289i	0.112091	−	0.194147i
$280$		0			0
$281$	−9.68614	−	16.7769i	−0.577827	−	1.00083i	−0.995728	−	0.0923329i	$-0.970568\pi$
$281$	−9.68614	−	16.7769i	−0.577827	−	1.00083i	0.417901	−	0.908492i	$-0.362766\pi$
$282$		0			0
$283$	−9.48913			−0.564070			−0.282035	−	0.959404i	$-0.591009\pi$
$283$	−9.48913			−0.564070			−0.282035	+	0.959404i	$0.591009\pi$
$284$		0			0
$285$	0.313859	+	0.543620i	0.0185914	+	0.0322013i
$286$		0			0
$287$	7.80298	+	13.5152i	0.460596	+	0.797775i
$288$		0			0
$289$	−18.6753	+	32.3465i	−1.09855	+	1.90274i
$290$		0			0
$291$	0.500000	+	0.866025i	0.0293105	+	0.0507673i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−8.74456			−0.509128
$296$		0			0
$297$	−0.686141	+	1.18843i	−0.0398139	+	0.0689597i
$298$		0			0
$299$	3.68614	−	6.38458i	0.213175	−	0.369230i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$		0			0
$303$	−6.43070	+	11.1383i	−0.369434	+	0.639879i
$304$		0			0
$305$	5.50000	+	9.52628i	0.314929	+	0.545473i
$306$		0			0
$307$	0.500000	+	0.866025i	0.0285365	+	0.0494267i	0.879941	−	0.475083i	$-0.157582\pi$
$307$	0.500000	+	0.866025i	0.0285365	+	0.0494267i	−0.851404	+	0.524510i	$0.824249\pi$
$308$		0			0
$309$	1.05842	−	1.83324i	0.0602115	−	0.104289i
$310$		0			0
$311$	−14.2337			−0.807118			−0.403559	−	0.914954i	$-0.632227\pi$
$311$	−14.2337			−0.807118			−0.403559	+	0.914954i	$0.632227\pi$
$312$		0			0
$313$	−3.48913			−0.197217			−0.0986085	−	0.995126i	$-0.531439\pi$
$313$	−3.48913			−0.197217			−0.0986085	+	0.995126i	$0.531439\pi$
$314$		0			0
$315$	1.68614	−	2.92048i	0.0950033	−	0.164550i
$316$		0			0
$317$	−8.05842	−	13.9576i	−0.452606	−	0.783937i	0.545941	−	0.837824i	$-0.316172\pi$
$317$	−8.05842	−	13.9576i	−0.452606	−	0.783937i	−0.998547	+	0.0538869i	$0.982839\pi$
$318$		0			0
$319$	0.941578	+	1.63086i	0.0527182	+	0.0913107i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.31386	+	4.00772i	−0.128747	+	0.222996i
$324$		0			0
$325$	0.500000	+	0.866025i	0.0277350	+	0.0480384i
$326$		0			0
$327$	−5.11684			−0.282962
$328$		0			0
$329$	12.4307	+	21.5306i	0.685327	+	1.18702i
$330$		0			0
$331$	14.9891	−	25.9619i	0.823877	−	1.42700i	−0.0788978	−	0.996883i	$-0.525140\pi$
$331$	14.9891	−	25.9619i	0.823877	−	1.42700i	0.902775	−	0.430114i	$-0.141527\pi$
$332$		0			0
$333$	4.05842	+	7.02939i	0.222400	+	0.385208i
$334$		0			0
$335$	−7.55842	−	3.14170i	−0.412961	−	0.171649i
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$		0			0
$339$	−2.05842	+	3.56529i	−0.111798	+	0.193640i
$340$		0			0
$341$	2.56930	+	4.45015i	0.139135	+	0.240989i
$342$		0			0
$343$	−8.86141			−0.478471
$344$		0			0
$345$	3.68614	+	6.38458i	0.198455	+	0.343734i
$346$		0			0
$347$	8.05842	−	13.9576i	0.432599	−	0.749283i	−0.564497	−	0.825435i	$-0.690930\pi$
$347$	8.05842	−	13.9576i	0.432599	−	0.749283i	0.997096	+	0.0761518i	$0.0242633\pi$
$348$		0			0
$349$	−8.37228			−0.448158			−0.224079	−	0.974571i	$-0.571937\pi$
$349$	−8.37228			−0.448158			−0.224079	+	0.974571i	$0.571937\pi$
$350$		0			0
$351$	0.500000	+	0.866025i	0.0266880	+	0.0462250i
$352$		0			0
$353$	−9.17527	−	15.8920i	−0.488350	−	0.845847i	0.511560	−	0.859248i	$-0.329068\pi$
$353$	−9.17527	−	15.8920i	−0.488350	−	0.845847i	−0.999910	+	0.0134003i	$0.995734\pi$
$354$		0			0
$355$	−2.05842	+	3.56529i	−0.109250	+	0.189226i
$356$		0			0
$357$	24.8614			1.31581
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	9.30298	−	16.1132i	0.489631	−	0.848065i
$362$		0			0
$363$	4.55842	+	7.89542i	0.239255	+	0.414402i
$364$		0			0
$365$	−6.50000	−	11.2583i	−0.340226	−	0.589288i
$366$		0			0
$367$	1.05842	−	1.83324i	0.0552492	−	0.0956944i	−0.837078	−	0.547083i	$-0.815738\pi$
$367$	1.05842	−	1.83324i	0.0552492	−	0.0956944i	0.892327	+	0.451389i	$0.149071\pi$
$368$		0			0
$369$	2.31386	−	4.00772i	0.120455	−	0.208634i
$370$		0			0
$371$	−4.62772	+	8.01544i	−0.240259	+	0.416141i
$372$		0			0
$373$	−6.61684	+	11.4607i	−0.342607	+	0.593413i	−0.984916	−	0.173033i	$-0.944643\pi$
$373$	−6.61684	+	11.4607i	−0.342607	+	0.593413i	0.642309	+	0.766446i	$0.277977\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	1.37228			0.0706761
$378$		0			0
$379$	3.75544	+	6.50461i	0.192904	+	0.334119i	0.946211	−	0.323549i	$-0.104876\pi$
$379$	3.75544	+	6.50461i	0.192904	+	0.334119i	−0.753307	+	0.657668i	$0.771543\pi$
$380$		0			0
$381$	7.87228	−	13.6352i	0.403309	−	0.698552i
$382$		0			0
$383$	17.0584	+	29.5461i	0.871645	+	1.50973i	0.860295	+	0.509797i	$0.170280\pi$
$383$	17.0584	+	29.5461i	0.871645	+	1.50973i	0.0113501	+	0.999936i	$0.496387\pi$
$384$		0			0
$385$	2.31386	+	4.00772i	0.117925	+	0.204252i
$386$		0			0
$387$	−2.37228			−0.120590
$388$		0			0
$389$	−12.4307	−	21.5306i	−0.630262	−	1.09165i	−0.987498	−	0.157631i	$-0.949614\pi$
$389$	−12.4307	−	21.5306i	−0.630262	−	1.09165i	0.357236	−	0.934014i	$-0.383719\pi$
$390$		0			0
$391$	−27.1753	+	47.0689i	−1.37431	+	2.38038i
$392$		0			0
$393$	−5.48913			−0.276890
$394$		0			0
$395$	−7.87228	+	13.6352i	−0.396097	+	0.686061i
$396$		0			0
$397$	−29.1168			−1.46133			−0.730666	−	0.682735i	$-0.760790\pi$
$397$	−29.1168			−1.46133			−0.730666	+	0.682735i	$0.760790\pi$
$398$		0			0
$399$	2.11684			0.105975
$400$		0			0
$401$	25.7228			1.28454			0.642268	−	0.766480i	$-0.277994\pi$
$401$	25.7228			1.28454			0.642268	+	0.766480i	$0.277994\pi$
$402$		0			0
$403$	3.74456			0.186530
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−11.1386			−0.552120
$408$		0			0
$409$	6.80298	−	11.7831i	0.336386	−	0.582638i	−0.647364	−	0.762181i	$-0.724129\pi$
$409$	6.80298	−	11.7831i	0.336386	−	0.582638i	0.983750	+	0.179543i	$0.0574620\pi$
$410$		0			0
$411$	−9.25544			−0.456537
$412$		0			0
$413$	−14.7446	+	25.5383i	−0.725532	+	1.25666i
$414$		0			0
$415$	−5.05842	−	8.76144i	−0.248308	−	0.430082i
$416$		0			0
$417$	6.37228			0.312052
$418$		0			0
$419$	18.1753	+	31.4805i	0.887920	+	1.53792i	0.842330	+	0.538962i	$0.181183\pi$
$419$	18.1753	+	31.4805i	0.887920	+	1.53792i	0.0455898	+	0.998960i	$0.485483\pi$
$420$		0			0
$421$	8.12772	+	14.0776i	0.396121	+	0.686101i	0.993244	−	0.116049i	$-0.0370228\pi$
$421$	8.12772	+	14.0776i	0.396121	+	0.686101i	−0.597123	+	0.802150i	$0.703689\pi$
$422$		0			0
$423$	3.68614	−	6.38458i	0.179226	−	0.310429i
$424$		0			0
$425$	−3.68614	−	6.38458i	−0.178804	−	0.309698i
$426$		0			0
$427$	37.0951			1.79516
$428$		0			0
$429$	−1.37228			−0.0662544
$430$		0			0
$431$	13.5475	−	23.4650i	0.652562	−	1.13027i	−0.329937	−	0.944003i	$-0.607027\pi$
$431$	13.5475	−	23.4650i	0.652562	−	1.13027i	0.982499	−	0.186268i	$-0.0596393\pi$
$432$		0			0
$433$	−10.6861	+	18.5089i	−0.513543	+	0.889483i	0.486333	+	0.873773i	$0.338334\pi$
$433$	−10.6861	+	18.5089i	−0.513543	+	0.889483i	−0.999877	+	0.0157095i	$0.994999\pi$
$434$		0			0
$435$	−0.686141	+	1.18843i	−0.0328979	+	0.0569809i
$436$		0			0
$437$	−2.31386	+	4.00772i	−0.110687	+	0.191715i
$438$		0			0
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$	−2.18614	−	3.78651i	−0.104102	−	0.180310i
$442$		0			0
$443$	6.43070	−	11.1383i	0.305532	−	0.529197i	−0.671848	−	0.740689i	$-0.734499\pi$
$443$	6.43070	−	11.1383i	0.305532	−	0.529197i	0.977380	+	0.211492i	$0.0678324\pi$
$444$		0			0
$445$	−11.4891			−0.544637
$446$		0			0
$447$	2.74456			0.129813
$448$		0			0
$449$	5.56930	−	9.64630i	0.262831	−	0.455237i	−0.704162	−	0.710040i	$-0.748677\pi$
$449$	5.56930	−	9.64630i	0.262831	−	0.455237i	0.966993	+	0.254802i	$0.0820104\pi$
$450$		0			0
$451$	3.17527	+	5.49972i	0.149517	+	0.258972i
$452$		0			0
$453$	0.500000	+	0.866025i	0.0234920	+	0.0406894i
$454$		0			0
$455$	3.37228			0.158095
$456$		0			0
$457$	−4.98913	+	8.64142i	−0.233381	+	0.404229i	−0.958801	−	0.284078i	$-0.908312\pi$
$457$	−4.98913	+	8.64142i	−0.233381	+	0.404229i	0.725420	+	0.688307i	$0.241646\pi$
$458$		0			0
$459$	−3.68614	−	6.38458i	−0.172054	−	0.298007i
$460$		0			0
$461$	23.4891			1.09400			0.546999	−	0.837133i	$-0.315770\pi$
$461$	23.4891			1.09400			0.546999	+	0.837133i	$0.315770\pi$
$462$		0			0
$463$	−3.05842	−	5.29734i	−0.142137	−	0.246188i	0.786164	−	0.618018i	$-0.212064\pi$
$463$	−3.05842	−	5.29734i	−0.142137	−	0.246188i	−0.928301	+	0.371829i	$0.878731\pi$
$464$		0			0
$465$	−1.87228	+	3.24289i	−0.0868250	+	0.150385i
$466$		0			0
$467$	−12.4307	−	21.5306i	−0.575224	−	0.996318i	−0.996017	−	0.0891611i	$-0.971581\pi$
$467$	−12.4307	−	21.5306i	−0.575224	−	0.996318i	0.420793	−	0.907157i	$-0.361752\pi$
$468$		0			0
$469$	−21.9198	+	16.7769i	−1.01216	+	0.774685i
$470$		0			0
$471$	−4.68614	−	8.11663i	−0.215926	−	0.373995i
$472$		0			0
$473$	1.62772	−	2.81929i	0.0748426	−	0.129631i
$474$		0			0
$475$	−0.313859	−	0.543620i	−0.0144009	−	0.0249430i
$476$		0			0
$477$	2.74456			0.125665
$478$		0			0
$479$	−21.1753	−	36.6766i	−0.967523	−	1.67580i	−0.702679	−	0.711507i	$-0.748013\pi$
$479$	−21.1753	−	36.6766i	−0.967523	−	1.67580i	−0.264843	−	0.964291i	$-0.585320\pi$
$480$		0			0
$481$	−4.05842	+	7.02939i	−0.185048	+	0.320513i
$482$		0			0
$483$	24.8614			1.13123
$484$		0			0
$485$	−0.500000	−	0.866025i	−0.0227038	−	0.0393242i
$486$		0			0
$487$	15.2446	+	26.4044i	0.690797	+	1.19650i	0.971577	+	0.236723i	$0.0760735\pi$
$487$	15.2446	+	26.4044i	0.690797	+	1.19650i	−0.280780	+	0.959772i	$0.590593\pi$
$488$		0			0
$489$	3.50000	−	6.06218i	0.158275	−	0.274141i
$490$		0			0
$491$	−8.74456			−0.394637			−0.197318	−	0.980339i	$-0.563223\pi$
$491$	−8.74456			−0.394637			−0.197318	+	0.980339i	$0.563223\pi$
$492$		0			0
$493$	−10.1168			−0.455640
$494$		0			0
$495$	0.686141	−	1.18843i	0.0308397	−	0.0534160i
$496$		0			0
$497$	6.94158	+	12.0232i	0.311372	+	0.539313i
$498$		0			0
$499$	−15.0584	−	26.0820i	−0.674108	−	1.16759i	−0.976729	−	0.214478i	$-0.931195\pi$
$499$	−15.0584	−	26.0820i	−0.674108	−	1.16759i	0.302621	−	0.953111i	$-0.402138\pi$
$500$		0			0
$501$	9.68614	−	16.7769i	0.432745	−	0.749536i
$502$		0			0
$503$	−11.0584	+	19.1537i	−0.493071	+	0.854023i	−0.999968	−	0.00798291i	$-0.997459\pi$
$503$	−11.0584	+	19.1537i	−0.493071	+	0.854023i	0.506897	+	0.862006i	$0.330792\pi$
$504$		0			0
$505$	6.43070	−	11.1383i	0.286163	−	0.495648i
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$		0			0
$509$	9.25544			0.410240			0.205120	−	0.978737i	$-0.434242\pi$
$509$	9.25544			0.410240			0.205120	+	0.978737i	$0.434242\pi$
$510$		0			0
$511$	−43.8397			−1.93935
$512$		0			0
$513$	−0.313859	−	0.543620i	−0.0138572	−	0.0240014i
$514$		0			0
$515$	−1.05842	+	1.83324i	−0.0466396	+	0.0807822i
$516$		0			0
$517$	5.05842	+	8.76144i	0.222469	+	0.385328i
$518$		0			0
$519$	−8.05842	−	13.9576i	−0.353725	−	0.612670i
$520$		0			0
$521$	25.7228			1.12694			0.563468	−	0.826138i	$-0.309467\pi$
$521$	25.7228			1.12694			0.563468	+	0.826138i	$0.309467\pi$
$522$		0			0
$523$	2.94158	+	5.09496i	0.128626	+	0.222787i	0.923145	−	0.384453i	$-0.125610\pi$
$523$	2.94158	+	5.09496i	0.128626	+	0.222787i	−0.794518	+	0.607240i	$0.792277\pi$
$524$		0			0
$525$	−1.68614	+	2.92048i	−0.0735892	+	0.127460i
$526$		0			0
$527$	−27.6060			−1.20253
$528$		0			0
$529$	−15.6753	+	27.1504i	−0.681533	+	1.18045i
$530$		0			0
$531$	8.74456			0.379482
$532$		0			0
$533$	4.62772			0.200449
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.25544			−0.140482
$538$		0			0
$539$	6.00000			0.258438
$540$		0			0
$541$	−10.6060			−0.455986			−0.227993	−	0.973663i	$-0.573216\pi$
$541$	−10.6060			−0.455986			−0.227993	+	0.973663i	$0.573216\pi$
$542$		0			0
$543$	−1.12772	+	1.95327i	−0.0483950	+	0.0838227i
$544$		0			0
$545$	5.11684			0.219182
$546$		0			0
$547$	21.5000	−	37.2391i	0.919274	−	1.59223i	0.118753	−	0.992924i	$-0.462110\pi$
$547$	21.5000	−	37.2391i	0.919274	−	1.59223i	0.800521	−	0.599305i	$-0.204556\pi$
$548$		0			0
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$	−0.861407			−0.0366972
$552$		0			0
$553$	26.5475	+	45.9817i	1.12892	+	1.95534i
$554$		0			0
$555$	−4.05842	−	7.02939i	−0.172270	−	0.298381i
$556$		0			0
$557$	6.68614	−	11.5807i	0.283301	−	0.490692i	−0.688895	−	0.724861i	$-0.741904\pi$
$557$	6.68614	−	11.5807i	0.283301	−	0.490692i	0.972196	+	0.234170i	$0.0752372\pi$
$558$		0			0
$559$	−1.18614	−	2.05446i	−0.0501684	−	0.0868942i
$560$		0			0
$561$	10.1168			0.427133
$562$		0			0
$563$	31.7228			1.33696			0.668479	−	0.743731i	$-0.266946\pi$
$563$	31.7228			1.33696			0.668479	+	0.743731i	$0.266946\pi$
$564$		0			0
$565$	2.05842	−	3.56529i	0.0865985	−	0.149993i
$566$		0			0
$567$	−1.68614	+	2.92048i	−0.0708113	+	0.122649i
$568$		0			0
$569$	−18.4307	+	31.9229i	−0.772655	+	1.33828i	0.163448	+	0.986552i	$0.447739\pi$
$569$	−18.4307	+	31.9229i	−0.772655	+	1.33828i	−0.936103	+	0.351726i	$0.885595\pi$
$570$		0			0
$571$	18.2446	−	31.6005i	0.763511	−	1.32244i	−0.177519	−	0.984117i	$-0.556807\pi$
$571$	18.2446	−	31.6005i	0.763511	−	1.32244i	0.941030	−	0.338323i	$-0.109860\pi$
$572$		0			0
$573$	−0.941578	−	1.63086i	−0.0393350	−	0.0681302i
$574$		0			0
$575$	−3.68614	−	6.38458i	−0.153723	−	0.266256i
$576$		0			0
$577$	−4.38316	+	7.59185i	−0.182473	+	0.316053i	−0.942722	−	0.333579i	$-0.891744\pi$
$577$	−4.38316	+	7.59185i	−0.182473	+	0.316053i	0.760249	+	0.649632i	$0.225077\pi$
$578$		0			0
$579$	−17.1168			−0.711352
$580$		0			0
$581$	−34.1168			−1.41541
$582$		0			0
$583$	−1.88316	+	3.26172i	−0.0779924	+	0.135087i
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$		0			0
$587$	19.8030	+	34.2998i	0.817357	+	1.41570i	0.907623	+	0.419786i	$0.137895\pi$
$587$	19.8030	+	34.2998i	0.817357	+	1.41570i	−0.0902666	+	0.995918i	$0.528772\pi$
$588$		0			0
$589$	−2.35053			−0.0968520
$590$		0			0
$591$	2.31386	−	4.00772i	0.0951795	−	0.164856i
$592$		0			0
$593$	8.31386	+	14.4000i	0.341409	+	0.591338i	0.984695	−	0.174288i	$-0.0557625\pi$
$593$	8.31386	+	14.4000i	0.341409	+	0.591338i	−0.643285	+	0.765626i	$0.722429\pi$
$594$		0			0
$595$	−24.8614			−1.01922
$596$		0			0
$597$	−3.87228	−	6.70699i	−0.158482	−	0.274499i
$598$		0			0
$599$	−5.05842	+	8.76144i	−0.206682	+	0.357983i	−0.950667	−	0.310213i	$-0.899600\pi$
$599$	−5.05842	+	8.76144i	−0.206682	+	0.357983i	0.743986	+	0.668196i	$0.232933\pi$
$600$		0			0
$601$	−2.75544	−	4.77256i	−0.112397	−	0.194677i	0.804339	−	0.594170i	$-0.202519\pi$
$601$	−2.75544	−	4.77256i	−0.112397	−	0.194677i	−0.916736	+	0.399493i	$0.869186\pi$
$602$		0			0
$603$	7.55842	+	3.14170i	0.307803	+	0.127940i
$604$		0			0
$605$	−4.55842	−	7.89542i	−0.185326	−	0.320994i
$606$		0			0
$607$	2.98913	−	5.17732i	0.121325	−	0.210141i	−0.798966	−	0.601377i	$-0.794619\pi$
$607$	2.98913	−	5.17732i	0.121325	−	0.210141i	0.920290	+	0.391236i	$0.127952\pi$
$608$		0			0
$609$	2.31386	+	4.00772i	0.0937623	+	0.162401i
$610$		0			0
$611$	7.37228			0.298251
$612$		0			0
$613$	−0.616844	−	1.06841i	−0.0249141	−	0.0431525i	0.853300	−	0.521421i	$-0.174598\pi$
$613$	−0.616844	−	1.06841i	−0.0249141	−	0.0431525i	−0.878214	+	0.478269i	$0.841265\pi$
$614$		0			0
$615$	−2.31386	+	4.00772i	−0.0933038	+	0.161607i
$616$		0			0
$617$	40.9783			1.64972			0.824861	−	0.565335i	$-0.191253\pi$
$617$	40.9783			1.64972			0.824861	+	0.565335i	$0.191253\pi$
$618$		0			0
$619$	−24.6168	−	42.6376i	−0.989434	−	1.71375i	−0.620274	−	0.784385i	$-0.712979\pi$
$619$	−24.6168	−	42.6376i	−0.989434	−	1.71375i	−0.369160	−	0.929366i	$-0.620355\pi$
$620$		0			0
$621$	−3.68614	−	6.38458i	−0.147920	−	0.256204i
$622$		0			0
$623$	−19.3723	+	33.5538i	−0.776134	+	1.34430i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	0.861407			0.0344013
$628$		0			0
$629$	29.9198	−	51.8227i	1.19298	−	2.06630i
$630$		0			0
$631$	13.9198	+	24.1099i	0.554140	+	0.959798i	0.997970	+	0.0636871i	$0.0202860\pi$
$631$	13.9198	+	24.1099i	0.554140	+	0.959798i	−0.443830	+	0.896111i	$0.646381\pi$
$632$		0			0
$633$	−3.87228	−	6.70699i	−0.153909	−	0.266579i
$634$		0			0
$635$	−7.87228	+	13.6352i	−0.312402	+	0.541096i
$636$		0			0
$637$	2.18614	−	3.78651i	0.0866180	−	0.150027i
$638$		0			0
$639$	2.05842	−	3.56529i	0.0814299	−	0.141041i
$640$		0			0
$641$	−3.17527	+	5.49972i	−0.125415	+	0.217226i	−0.921895	−	0.387439i	$-0.873360\pi$
$641$	−3.17527	+	5.49972i	−0.125415	+	0.217226i	0.796480	+	0.604665i	$0.206693\pi$
$642$		0			0
$643$	−32.4674			−1.28039			−0.640194	−	0.768213i	$-0.721146\pi$
$643$	−32.4674			−1.28039			−0.640194	+	0.768213i	$0.721146\pi$
$644$		0			0
$645$	2.37228			0.0934085
$646$		0			0
$647$	7.80298	+	13.5152i	0.306767	+	0.531336i	0.977653	−	0.210224i	$-0.0674194\pi$
$647$	7.80298	+	13.5152i	0.306767	+	0.531336i	−0.670886	+	0.741560i	$0.734086\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$		0			0
$651$	6.31386	+	10.9359i	0.247460	+	0.428613i
$652$		0			0
$653$	23.0584	+	39.9384i	0.902346	+	1.56291i	0.824441	+	0.565948i	$0.191490\pi$
$653$	23.0584	+	39.9384i	0.902346	+	1.56291i	0.0779048	+	0.996961i	$0.475177\pi$
$654$		0			0
$655$	5.48913			0.214478
$656$		0			0
$657$	6.50000	+	11.2583i	0.253589	+	0.439229i
$658$		0			0
$659$	9.68614	−	16.7769i	0.377318	−	0.653535i	−0.613353	−	0.789809i	$-0.710180\pi$
$659$	9.68614	−	16.7769i	0.377318	−	0.653535i	0.990671	+	0.136274i	$0.0435129\pi$
$660$		0			0
$661$	33.1168			1.28810			0.644048	−	0.764985i	$-0.277254\pi$
$661$	33.1168			1.28810			0.644048	+	0.764985i	$0.277254\pi$
$662$		0			0
$663$	3.68614	−	6.38458i	0.143158	−	0.247957i
$664$		0			0
$665$	−2.11684			−0.0820877
$666$		0			0
$667$	−10.1168			−0.391726
$668$		0			0
$669$	−23.1168			−0.893749
$670$		0			0
$671$	15.0951			0.582740
$672$		0			0
$673$	−10.6060			−0.408830			−0.204415	−	0.978884i	$-0.565529\pi$
$673$	−10.6060			−0.408830			−0.204415	+	0.978884i	$0.565529\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−3.17527	+	5.49972i	−0.122035	+	0.211371i	−0.920570	−	0.390577i	$-0.872275\pi$
$677$	−3.17527	+	5.49972i	−0.122035	+	0.211371i	0.798535	+	0.601949i	$0.205609\pi$
$678$		0			0
$679$	−3.37228			−0.129416
$680$		0			0
$681$	−3.43070	+	5.94215i	−0.131465	+	0.227704i
$682$		0			0
$683$	23.0584	+	39.9384i	0.882306	+	1.52820i	0.848771	+	0.528761i	$0.177343\pi$
$683$	23.0584	+	39.9384i	0.882306	+	1.52820i	0.0335354	+	0.999438i	$0.489323\pi$
$684$		0			0
$685$	9.25544			0.353632
$686$		0			0
$687$	7.61684	+	13.1928i	0.290601	+	0.503335i
$688$		0			0
$689$	1.37228	+	2.37686i	0.0522798	+	0.0905512i
$690$		0			0
$691$	−7.17527	+	12.4279i	−0.272960	+	0.472781i	−0.969618	−	0.244622i	$-0.921336\pi$
$691$	−7.17527	+	12.4279i	−0.272960	+	0.472781i	0.696658	+	0.717403i	$0.254669\pi$
$692$		0			0
$693$	−2.31386	−	4.00772i	−0.0878962	−	0.152241i
$694$		0			0
$695$	−6.37228			−0.241714
$696$		0			0
$697$	−34.1168			−1.29227
$698$		0			0
$699$	6.68614	−	11.5807i	0.252893	−	0.438024i
$700$		0			0
$701$	−9.68614	+	16.7769i	−0.365840	+	0.633654i	−0.988911	−	0.148512i	$-0.952552\pi$
$701$	−9.68614	+	16.7769i	−0.365840	+	0.633654i	0.623070	+	0.782166i	$0.285885\pi$
$702$		0			0
$703$	2.54755	−	4.41248i	0.0960826	−	0.166420i
$704$		0			0
$705$	−3.68614	+	6.38458i	−0.138828	+	0.240457i
$706$		0			0
$707$	−21.6861	−	37.5615i	−0.815591	−	1.41265i
$708$		0			0
$709$	24.8030	+	42.9600i	0.931496	+	1.61340i	0.780767	+	0.624823i	$0.214829\pi$
$709$	24.8030	+	42.9600i	0.931496	+	1.61340i	0.150729	+	0.988575i	$0.451838\pi$
$710$		0			0
$711$	7.87228	−	13.6352i	0.295234	−	0.511360i
$712$		0			0
$713$	−27.6060			−1.03385
$714$		0			0
$715$	1.37228			0.0513204
$716$		0			0
$717$	14.0584	−	24.3499i	0.525021	−	0.909364i
$718$		0			0
$719$	−26.0584	−	45.1345i	−0.971815	−	1.68323i	−0.690068	−	0.723745i	$-0.742419\pi$
$719$	−26.0584	−	45.1345i	−0.971815	−	1.68323i	−0.281747	−	0.959489i	$-0.590914\pi$
$720$		0			0
$721$	3.56930	+	6.18220i	0.132928	+	0.230237i
$722$		0			0
$723$	6.88316			0.255987
$724$		0			0
$725$	0.686141	−	1.18843i	0.0254826	−	0.0441372i
$726$		0			0
$727$	−6.61684	−	11.4607i	−0.245405	−	0.425054i	0.716840	−	0.697237i	$-0.245588\pi$
$727$	−6.61684	−	11.4607i	−0.245405	−	0.425054i	−0.962245	+	0.272183i	$0.912254\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.74456	+	15.1460i	0.323429	+	0.560196i
$732$		0			0
$733$	−13.9416	+	24.1475i	−0.514944	+	0.891909i	0.484906	+	0.874566i	$0.338854\pi$
$733$	−13.9416	+	24.1475i	−0.514944	+	0.891909i	−0.999850	+	0.0173426i	$0.994479\pi$
$734$		0			0
$735$	2.18614	+	3.78651i	0.0806370	+	0.139667i
$736$		0			0
$737$	−8.91983	+	6.82701i	−0.328566	+	0.251476i
$738$		0			0
$739$	9.24456	+	16.0121i	0.340067	+	0.589013i	0.984445	−	0.175694i	$-0.0562170\pi$
$739$	9.24456	+	16.0121i	0.340067	+	0.589013i	−0.644378	+	0.764707i	$0.722884\pi$
$740$		0			0
$741$	0.313859	−	0.543620i	0.0115299	−	0.0199704i
$742$		0			0
$743$	−10.8030	−	18.7113i	−0.396323	−	0.686452i	0.596946	−	0.802281i	$-0.296381\pi$
$743$	−10.8030	−	18.7113i	−0.396323	−	0.686452i	−0.993269	+	0.115830i	$0.963047\pi$
$744$		0			0
$745$	−2.74456			−0.100553
$746$		0			0
$747$	5.05842	+	8.76144i	0.185078	+	0.320564i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	48.4674			1.76860			0.884300	−	0.466919i	$-0.154636\pi$
$751$	48.4674			1.76860			0.884300	+	0.466919i	$0.154636\pi$
$752$		0			0
$753$	−0.941578	−	1.63086i	−0.0343130	−	0.0594319i
$754$		0			0
$755$	−0.500000	−	0.866025i	−0.0181969	−	0.0315179i
$756$		0			0
$757$	20.7337	−	35.9118i	0.753579	−	1.30524i	−0.192499	−	0.981297i	$-0.561659\pi$
$757$	20.7337	−	35.9118i	0.753579	−	1.30524i	0.946078	−	0.323939i	$-0.105007\pi$
$758$		0			0
$759$	10.1168			0.367218
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	8.62772	−	14.9436i	0.312344	−	0.540996i
$764$		0			0
$765$	3.68614	+	6.38458i	0.133273	+	0.230835i
$766$		0			0
$767$	4.37228	+	7.57301i	0.157874	+	0.273446i
$768$		0			0
$769$	−10.9891	+	19.0337i	−0.396278	+	0.686374i	−0.993263	−	0.115878i	$-0.963032\pi$
$769$	−10.9891	+	19.0337i	−0.396278	+	0.686374i	0.596985	+	0.802252i	$0.296365\pi$
$770$		0			0
$771$	2.31386	−	4.00772i	0.0833316	−	0.144335i
$772$		0			0
$773$	−11.3139	+	19.5962i	−0.406931	+	0.704826i	−0.994544	−	0.104317i	$-0.966734\pi$
$773$	−11.3139	+	19.5962i	−0.406931	+	0.704826i	0.587613	+	0.809142i	$0.300068\pi$
$774$		0			0
$775$	1.87228	−	3.24289i	0.0672543	−	0.116488i
$776$		0			0
$777$	−27.3723			−0.981975
$778$		0			0
$779$	−2.90491			−0.104079
$780$		0			0
$781$	2.82473	+	4.89258i	0.101077	+	0.175070i
$782$		0			0
$783$	0.686141	−	1.18843i	0.0245207	−	0.0424710i
$784$		0			0
$785$	4.68614	+	8.11663i	0.167256	+	0.289695i
$786$		0			0
$787$	−3.05842	−	5.29734i	−0.109021	−	0.188830i	0.806353	−	0.591435i	$-0.201438\pi$
$787$	−3.05842	−	5.29734i	−0.109021	−	0.188830i	−0.915374	+	0.402605i	$0.868105\pi$
$788$		0			0
$789$	−17.4891			−0.622629
$790$		0			0
$791$	−6.94158	−	12.0232i	−0.246814	−	0.427495i
$792$		0			0
$793$	5.50000	−	9.52628i	0.195311	−	0.338288i
$794$		0			0
$795$	−2.74456			−0.0973396
$796$		0			0
$797$	15.4307	−	26.7268i	0.546584	−	0.946710i	−0.451922	−	0.892058i	$-0.649261\pi$
$797$	15.4307	−	26.7268i	0.546584	−	0.946710i	0.998505	−	0.0546530i	$-0.0174052\pi$
$798$		0			0
$799$	−54.3505			−1.92278
$800$		0			0
$801$	11.4891			0.405948
$802$		0			0
$803$	−17.8397			−0.629548
$804$		0			0
$805$	−24.8614			−0.876249
$806$		0			0
$807$	9.25544			0.325807
$808$		0			0
$809$	−0.510875			−0.0179614			−0.00898070	−	0.999960i	$-0.502859\pi$
$809$	−0.510875			−0.0179614			−0.00898070	+	0.999960i	$0.502859\pi$
$810$		0			0
$811$	2.98913	−	5.17732i	0.104962	−	0.181800i	−0.808760	−	0.588138i	$-0.799861\pi$
$811$	2.98913	−	5.17732i	0.104962	−	0.181800i	0.913723	+	0.406338i	$0.133194\pi$
$812$		0			0
$813$	−8.88316			−0.311546
$814$		0			0
$815$	−3.50000	+	6.06218i	−0.122600	+	0.212349i
$816$		0			0
$817$	0.744563	+	1.28962i	0.0260489	+	0.0451181i
$818$		0			0
$819$	−3.37228			−0.117837
$820$		0			0
$821$	−2.05842	−	3.56529i	−0.0718394	−	0.124430i	0.827868	−	0.560923i	$-0.189554\pi$
$821$	−2.05842	−	3.56529i	−0.0718394	−	0.124430i	−0.899707	+	0.436493i	$0.856220\pi$
$822$		0			0
$823$	2.12772	+	3.68532i	0.0741676	+	0.128462i	0.900724	−	0.434392i	$-0.143037\pi$
$823$	2.12772	+	3.68532i	0.0741676	+	0.128462i	−0.826556	+	0.562854i	$0.809703\pi$
$824$		0			0
$825$	−0.686141	+	1.18843i	−0.0238884	+	0.0413758i
$826$		0			0
$827$	−10.8030	−	18.7113i	−0.375657	−	0.650656i	0.614768	−	0.788708i	$-0.289249\pi$
$827$	−10.8030	−	18.7113i	−0.375657	−	0.650656i	−0.990425	+	0.138051i	$0.955916\pi$
$828$		0			0
$829$	1.39403			0.0484167			0.0242083	−	0.999707i	$-0.492293\pi$
$829$	1.39403			0.0484167			0.0242083	+	0.999707i	$0.492293\pi$
$830$		0			0
$831$	−13.8614			−0.480847
$832$		0			0
$833$	−16.1168	+	27.9152i	−0.558416	+	0.967204i
$834$		0			0
$835$	−9.68614	+	16.7769i	−0.335203	+	0.580588i
$836$		0			0
$837$	1.87228	−	3.24289i	0.0647155	−	0.112091i
$838$		0			0
$839$	10.8030	−	18.7113i	0.372960	−	0.645986i	−0.617059	−	0.786917i	$-0.711676\pi$
$839$	10.8030	−	18.7113i	0.372960	−	0.645986i	0.990020	+	0.140930i	$0.0450094\pi$
$840$		0			0
$841$	13.5584	+	23.4839i	0.467532	+	0.809789i
$842$		0			0
$843$	−9.68614	−	16.7769i	−0.333608	−	0.577827i
$844$		0			0
$845$	−6.00000	+	10.3923i	−0.206406	+	0.357506i
$846$		0			0
$847$	−30.7446			−1.05640
$848$		0			0
$849$	−9.48913			−0.325666
$850$		0			0
$851$	29.9198	−	51.8227i	1.02564	−	1.77646i
$852$		0			0
$853$	19.6168	+	33.9774i	0.671668	+	1.16336i	0.977431	+	0.211255i	$0.0677552\pi$
$853$	19.6168	+	33.9774i	0.671668	+	1.16336i	−0.305763	+	0.952108i	$0.598912\pi$
$854$		0			0
$855$	0.313859	+	0.543620i	0.0107338	+	0.0185914i
$856$		0			0
$857$	−20.2337			−0.691170			−0.345585	−	0.938388i	$-0.612319\pi$
$857$	−20.2337			−0.691170			−0.345585	+	0.938388i	$0.612319\pi$
$858$		0			0
$859$	−4.12772	+	7.14942i	−0.140836	+	0.243935i	−0.927812	−	0.373049i	$-0.878312\pi$
$859$	−4.12772	+	7.14942i	−0.140836	+	0.243935i	0.786976	+	0.616984i	$0.211646\pi$
$860$		0			0
$861$	7.80298	+	13.5152i	0.265925	+	0.460596i
$862$		0			0
$863$	−49.2119			−1.67519			−0.837597	−	0.546289i	$-0.816040\pi$
$863$	−49.2119			−1.67519			−0.837597	+	0.546289i	$0.816040\pi$
$864$		0			0
$865$	8.05842	+	13.9576i	0.273995	+	0.474573i
$866$		0			0
$867$	−18.6753	+	32.3465i	−0.634245	+	1.09855i
$868$		0			0
$869$	10.8030	+	18.7113i	0.366466	+	0.634738i
$870$		0			0
$871$	1.05842	+	8.11663i	0.0358633	+	0.275022i
$872$		0			0
$873$	0.500000	+	0.866025i	0.0169224	+	0.0293105i
$874$		0			0
$875$	1.68614	−	2.92048i	0.0570020	−	0.0987303i
$876$		0			0
$877$	10.3614	+	17.9465i	0.349880	+	0.606010i	0.986228	−	0.165392i	$-0.0528891\pi$
$877$	10.3614	+	17.9465i	0.349880	+	0.606010i	−0.636348	+	0.771402i	$0.719556\pi$
$878$		0			0
$879$	−6.00000			−0.202375
$880$		0			0
$881$	−11.3139	−	19.5962i	−0.381174	−	0.660212i	0.610057	−	0.792358i	$-0.291147\pi$
$881$	−11.3139	−	19.5962i	−0.381174	−	0.660212i	−0.991230	+	0.132146i	$0.957813\pi$
$882$		0			0
$883$	3.80298	−	6.58696i	0.127981	−	0.221669i	−0.794913	−	0.606723i	$-0.792484\pi$
$883$	3.80298	−	6.58696i	0.127981	−	0.221669i	0.922894	+	0.385054i	$0.125817\pi$
$884$		0			0
$885$	−8.74456			−0.293945
$886$		0			0
$887$	−13.5475	−	23.4650i	−0.454882	−	0.787879i	0.543799	−	0.839215i	$-0.316985\pi$
$887$	−13.5475	−	23.4650i	−0.454882	−	0.787879i	−0.998681	+	0.0513364i	$0.983652\pi$
$888$		0			0
$889$	26.5475	+	45.9817i	0.890376	+	1.54218i
$890$		0			0
$891$	−0.686141	+	1.18843i	−0.0229866	+	0.0398139i
$892$		0			0
$893$	−4.62772			−0.154861
$894$		0			0
$895$	3.25544			0.108817
$896$		0			0
$897$	3.68614	−	6.38458i	0.123077	−	0.213175i
$898$		0			0
$899$	−2.56930	−	4.45015i	−0.0856908	−	0.148421i
$900$		0			0
$901$	−10.1168	−	17.5229i	−0.337041	−	0.583772i
$902$		0			0
$903$	4.00000	−	6.92820i	0.133112	−	0.230556i
$904$		0			0
$905$	1.12772	−	1.95327i	0.0374866	−	0.0649288i
$906$		0			0
$907$	−13.1753	+	22.8202i	−0.437478	+	0.757733i	−0.997494	−	0.0707480i	$-0.977461\pi$
$907$	−13.1753	+	22.8202i	−0.437478	+	0.757733i	0.560017	+	0.828481i	$0.310795\pi$
$908$		0			0
$909$	−6.43070	+	11.1383i	−0.213293	+	0.369434i
$910$		0			0
$911$	13.0217			0.431430			0.215715	−	0.976456i	$-0.430792\pi$
$911$	13.0217			0.431430			0.215715	+	0.976456i	$0.430792\pi$
$912$		0			0
$913$	−13.8832			−0.459465
$914$		0			0
$915$	5.50000	+	9.52628i	0.181824	+	0.314929i
$916$		0			0
$917$	9.25544	−	16.0309i	0.305641	−	0.529387i
$918$		0			0
$919$	−9.05842	−	15.6896i	−0.298810	−	0.517554i	0.677054	−	0.735933i	$-0.263256\pi$
$919$	−9.05842	−	15.6896i	−0.298810	−	0.517554i	−0.975864	+	0.218379i	$0.929923\pi$
$920$		0			0
$921$	0.500000	+	0.866025i	0.0164756	+	0.0285365i
$922$		0			0
$923$	4.11684			0.135508
$924$		0			0
$925$	4.05842	+	7.02939i	0.133440	+	0.231125i
$926$		0			0
$927$	1.05842	−	1.83324i	0.0347631	−	0.0602115i
$928$		0			0
$929$	15.7663			0.517276			0.258638	−	0.965974i	$-0.416726\pi$
$929$	15.7663			0.517276			0.258638	+	0.965974i	$0.416726\pi$
$930$		0			0
$931$	−1.37228	+	2.37686i	−0.0449747	+	0.0778985i
$932$		0			0
$933$	−14.2337			−0.465990
$934$		0			0
$935$	−10.1168			−0.330856
$936$		0			0
$937$	6.88316			0.224863			0.112431	−	0.993659i	$-0.464136\pi$
$937$	6.88316			0.224863			0.112431	+	0.993659i	$0.464136\pi$
$938$		0			0
$939$	−3.48913			−0.113863
$940$		0			0
$941$	−35.4891			−1.15691			−0.578456	−	0.815713i	$-0.696345\pi$
$941$	−35.4891			−1.15691			−0.578456	+	0.815713i	$0.696345\pi$
$942$		0			0
$943$	−34.1168			−1.11100
$944$		0			0
$945$	1.68614	−	2.92048i	0.0548502	−	0.0950033i
$946$		0			0
$947$	−33.9565			−1.10344			−0.551719	−	0.834030i	$-0.686028\pi$
$947$	−33.9565			−1.10344			−0.551719	+	0.834030i	$0.686028\pi$
$948$		0			0
$949$	−6.50000	+	11.2583i	−0.210999	+	0.365461i
$950$		0			0
$951$	−8.05842	−	13.9576i	−0.261312	−	0.452606i
$952$		0			0
$953$	−14.7446			−0.477623			−0.238812	−	0.971066i	$-0.576758\pi$
$953$	−14.7446			−0.477623			−0.238812	+	0.971066i	$0.576758\pi$
$954$		0			0
$955$	0.941578	+	1.63086i	0.0304687	+	0.0527734i
$956$		0			0
$957$	0.941578	+	1.63086i	0.0304369	+	0.0527182i
$958$		0			0
$959$	15.6060	−	27.0303i	0.503943	−	0.872855i
$960$		0			0
$961$	8.48913	+	14.7036i	0.273843	+	0.474310i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	17.1168			0.551011
$966$		0			0
$967$	11.7337	−	20.3233i	0.377330	−	0.653555i	−0.613343	−	0.789817i	$-0.710176\pi$
$967$	11.7337	−	20.3233i	0.377330	−	0.653555i	0.990673	+	0.136262i	$0.0435089\pi$
$968$		0			0
$969$	−2.31386	+	4.00772i	−0.0743319	+	0.128747i
$970$		0			0
$971$	−0.686141	+	1.18843i	−0.0220193	+	0.0381385i	−0.876825	−	0.480809i	$-0.840343\pi$
$971$	−0.686141	+	1.18843i	−0.0220193	+	0.0381385i	0.854806	+	0.518948i	$0.173676\pi$
$972$		0			0
$973$	−10.7446	+	18.6101i	−0.344455	+	0.596613i
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	3.43070	+	5.94215i	0.109758	+	0.190106i	0.915672	−	0.401926i	$-0.131659\pi$
$977$	3.43070	+	5.94215i	0.109758	+	0.190106i	−0.805914	+	0.592032i	$0.798326\pi$
$978$		0			0
$979$	−7.88316	+	13.6540i	−0.251947	+	0.436385i
$980$		0			0
$981$	−5.11684			−0.163368
$982$		0			0
$983$	−58.9783			−1.88111			−0.940557	−	0.339636i	$-0.889696\pi$
$983$	−58.9783			−1.88111			−0.940557	+	0.339636i	$0.889696\pi$
$984$		0			0
$985$	−2.31386	+	4.00772i	−0.0737257	+	0.127697i
$986$		0			0
$987$	12.4307	+	21.5306i	0.395674	+	0.685327i
$988$		0			0
$989$	8.74456	+	15.1460i	0.278061	+	0.481616i
$990$		0			0
$991$	12.4674			0.396039			0.198020	−	0.980198i	$-0.436549\pi$
$991$	12.4674			0.396039			0.198020	+	0.980198i	$0.436549\pi$
$992$		0			0
$993$	14.9891	−	25.9619i	0.475666	−	0.823877i
$994$		0			0
$995$	3.87228	+	6.70699i	0.122760	+	0.212626i
$996$		0			0
$997$	30.4674			0.964911			0.482456	−	0.875920i	$-0.339745\pi$
$997$	30.4674			0.964911			0.482456	+	0.875920i	$0.339745\pi$
$998$		0			0
$999$	4.05842	+	7.02939i	0.128403	+	0.222400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.i.841.1	✓	4
67.29	even	3	inner	4020.2.q.i.3781.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.i.841.1	✓	4	1.1	even	1	trivial
4020.2.q.i.3781.1	yes	4	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.68614 + 2.92048i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} -1.00000 q^{5} +(-1.68614 + 2.92048i) q^{7} +1.00000 q^{9} +(-0.686141 + 1.18843i) q^{11} +(0.500000 + 0.866025i) q^{13} -1.00000 q^{15} +(-3.68614 - 6.38458i) q^{17} +(-0.313859 - 0.543620i) q^{19} +(-1.68614 + 2.92048i) q^{21} +(-3.68614 - 6.38458i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(0.686141 - 1.18843i) q^{29} +(1.87228 - 3.24289i) q^{31} +(-0.686141 + 1.18843i) q^{33} +(1.68614 - 2.92048i) q^{35} +(4.05842 + 7.02939i) q^{37} +(0.500000 + 0.866025i) q^{39} +(2.31386 - 4.00772i) q^{41} -2.37228 q^{43} -1.00000 q^{45} +(3.68614 - 6.38458i) q^{47} +(-2.18614 - 3.78651i) q^{49} +(-3.68614 - 6.38458i) q^{51} +2.74456 q^{53} +(0.686141 - 1.18843i) q^{55} +(-0.313859 - 0.543620i) q^{57} +8.74456 q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.68614 + 2.92048i) q^{63} +(-0.500000 - 0.866025i) q^{65} +(7.55842 + 3.14170i) q^{67} +(-3.68614 - 6.38458i) q^{69} +(2.05842 - 3.56529i) q^{71} +(6.50000 + 11.2583i) q^{73} +1.00000 q^{75} +(-2.31386 - 4.00772i) q^{77} +(7.87228 - 13.6352i) q^{79} +1.00000 q^{81} +(5.05842 + 8.76144i) q^{83} +(3.68614 + 6.38458i) q^{85} +(0.686141 - 1.18843i) q^{87} +11.4891 q^{89} -3.37228 q^{91} +(1.87228 - 3.24289i) q^{93} +(0.313859 + 0.543620i) q^{95} +(0.500000 + 0.866025i) q^{97} +(-0.686141 + 1.18843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} - q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^5 - q^7 + 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{5} - q^{7} + 4 q^{9} + 3 q^{11} + 2 q^{13} - 4 q^{15} - 9 q^{17} - 7 q^{19} - q^{21} - 9 q^{23} + 4 q^{25} + 4 q^{27} - 3 q^{29} - 4 q^{31} + 3 q^{33} + q^{35} - q^{37} + 2 q^{39} + 15 q^{41} + 2 q^{43} - 4 q^{45} + 9 q^{47} - 3 q^{49} - 9 q^{51} - 12 q^{53} - 3 q^{55} - 7 q^{57} + 12 q^{59} - 22 q^{61} - q^{63} - 2 q^{65} + 13 q^{67} - 9 q^{69} - 9 q^{71} + 26 q^{73} + 4 q^{75} - 15 q^{77} + 20 q^{79} + 4 q^{81} + 3 q^{83} + 9 q^{85} - 3 q^{87} - 2 q^{91} - 4 q^{93} + 7 q^{95} + 2 q^{97} + 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^5 - q^7 + 4 * q^9 + 3 * q^11 + 2 * q^13 - 4 * q^15 - 9 * q^17 - 7 * q^19 - q^21 - 9 * q^23 + 4 * q^25 + 4 * q^27 - 3 * q^29 - 4 * q^31 + 3 * q^33 + q^35 - q^37 + 2 * q^39 + 15 * q^41 + 2 * q^43 - 4 * q^45 + 9 * q^47 - 3 * q^49 - 9 * q^51 - 12 * q^53 - 3 * q^55 - 7 * q^57 + 12 * q^59 - 22 * q^61 - q^63 - 2 * q^65 + 13 * q^67 - 9 * q^69 - 9 * q^71 + 26 * q^73 + 4 * q^75 - 15 * q^77 + 20 * q^79 + 4 * q^81 + 3 * q^83 + 9 * q^85 - 3 * q^87 - 2 * q^91 - 4 * q^93 + 7 * q^95 + 2 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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