LMFDB - Embedded newform 4020.2.q.m.841.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			841.5
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-0.436767 + 0.756503i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.436767 + 0.756503i) q^{7} +1.00000 q^{9} +(1.09530 - 1.89712i) q^{11} +(-1.27391 - 2.20647i) q^{13} +1.00000 q^{15} +(-3.07842 - 5.33199i) q^{17} +(-1.66901 - 2.89081i) q^{19} +(-0.436767 + 0.756503i) q^{21} +(-2.10244 - 3.64153i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-0.323233 + 0.559856i) q^{29} +(0.579844 - 1.00432i) q^{31} +(1.09530 - 1.89712i) q^{33} +(-0.436767 + 0.756503i) q^{35} +(-2.36632 - 4.09859i) q^{37} +(-1.27391 - 2.20647i) q^{39} +(-4.00304 + 6.93346i) q^{41} -9.15156 q^{43} +1.00000 q^{45} +(-6.21127 + 10.7582i) q^{47} +(3.11847 + 5.40135i) q^{49} +(-3.07842 - 5.33199i) q^{51} -8.66314 q^{53} +(1.09530 - 1.89712i) q^{55} +(-1.66901 - 2.89081i) q^{57} -3.64380 q^{59} +(-2.99641 - 5.18993i) q^{61} +(-0.436767 + 0.756503i) q^{63} +(-1.27391 - 2.20647i) q^{65} +(1.38723 - 8.06694i) q^{67} +(-2.10244 - 3.64153i) q^{69} +(5.31716 - 9.20959i) q^{71} +(-0.0239280 - 0.0414445i) q^{73} +1.00000 q^{75} +(0.956786 + 1.65720i) q^{77} +(-1.57787 + 2.73295i) q^{79} +1.00000 q^{81} +(-2.29548 - 3.97588i) q^{83} +(-3.07842 - 5.33199i) q^{85} +(-0.323233 + 0.559856i) q^{87} -3.07807 q^{89} +2.22560 q^{91} +(0.579844 - 1.00432i) q^{93} +(-1.66901 - 2.89081i) q^{95} +(1.76819 + 3.06259i) q^{97} +(1.09530 - 1.89712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−0.436767	+	0.756503i	−0.165083	+	0.285931i	−0.936685	−	0.350174i	$-0.886122\pi$
$7$	−0.436767	+	0.756503i	−0.165083	+	0.285931i	0.771602	+	0.636106i	$0.219456\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.09530	−	1.89712i	0.330247	−	0.572004i	−0.652313	−	0.757949i	$-0.726201\pi$
$11$	1.09530	−	1.89712i	0.330247	−	0.572004i	0.982560	+	0.185945i	$0.0595347\pi$
$12$		0			0
$13$	−1.27391	−	2.20647i	−0.353318	−	0.611964i	0.633511	−	0.773734i	$-0.281613\pi$
$13$	−1.27391	−	2.20647i	−0.353318	−	0.611964i	−0.986829	+	0.161769i	$0.948280\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.07842	−	5.33199i	−0.746628	−	1.29320i	−0.949431	−	0.313977i	$-0.898338\pi$
$17$	−3.07842	−	5.33199i	−0.746628	−	1.29320i	0.202803	−	0.979220i	$-0.434995\pi$
$18$		0			0
$19$	−1.66901	−	2.89081i	−0.382897	−	0.663198i	0.608578	−	0.793494i	$-0.291740\pi$
$19$	−1.66901	−	2.89081i	−0.382897	−	0.663198i	−0.991475	+	0.130297i	$0.958407\pi$
$20$		0			0
$21$	−0.436767	+	0.756503i	−0.0953104	+	0.165083i
$22$		0			0
$23$	−2.10244	−	3.64153i	−0.438389	−	0.759312i	0.559177	−	0.829049i	$-0.311117\pi$
$23$	−2.10244	−	3.64153i	−0.438389	−	0.759312i	−0.997565	+	0.0697369i	$0.977784\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.323233	+	0.559856i	−0.0600228	+	0.103963i	−0.894475	−	0.447117i	$-0.852451\pi$
$29$	−0.323233	+	0.559856i	−0.0600228	+	0.103963i	0.834453	+	0.551080i	$0.185784\pi$
$30$		0			0
$31$	0.579844	−	1.00432i	0.104143	−	0.180381i	−0.809245	−	0.587472i	$-0.800123\pi$
$31$	0.579844	−	1.00432i	0.104143	−	0.180381i	0.913388	+	0.407091i	$0.133457\pi$
$32$		0			0
$33$	1.09530	−	1.89712i	0.190668	−	0.330247i
$34$		0			0
$35$	−0.436767	+	0.756503i	−0.0738271	+	0.127872i
$36$		0			0
$37$	−2.36632	−	4.09859i	−0.389021	−	0.673805i	0.603297	−	0.797517i	$-0.293853\pi$
$37$	−2.36632	−	4.09859i	−0.389021	−	0.673805i	−0.992318	+	0.123712i	$0.960520\pi$
$38$		0			0
$39$	−1.27391	−	2.20647i	−0.203988	−	0.353318i
$40$		0			0
$41$	−4.00304	+	6.93346i	−0.625169	+	1.08283i	0.363339	+	0.931657i	$0.381637\pi$
$41$	−4.00304	+	6.93346i	−0.625169	+	1.08283i	−0.988508	+	0.151168i	$0.951697\pi$
$42$		0			0
$43$	−9.15156			−1.39560			−0.697800	−	0.716293i	$-0.745837\pi$
$43$	−9.15156			−1.39560			−0.697800	+	0.716293i	$0.745837\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−6.21127	+	10.7582i	−0.906006	+	1.56925i	−0.0864453	+	0.996257i	$0.527551\pi$
$47$	−6.21127	+	10.7582i	−0.906006	+	1.56925i	−0.819561	+	0.572992i	$0.805783\pi$
$48$		0			0
$49$	3.11847	+	5.40135i	0.445496	+	0.771621i
$50$		0			0
$51$	−3.07842	−	5.33199i	−0.431066	−	0.746628i
$52$		0			0
$53$	−8.66314			−1.18997			−0.594987	−	0.803735i	$-0.702843\pi$
$53$	−8.66314			−1.18997			−0.594987	+	0.803735i	$0.702843\pi$
$54$		0			0
$55$	1.09530	−	1.89712i	0.147691	−	0.255808i
$56$		0			0
$57$	−1.66901	−	2.89081i	−0.221066	−	0.382897i
$58$		0			0
$59$	−3.64380			−0.474382			−0.237191	−	0.971463i	$-0.576227\pi$
$59$	−3.64380			−0.474382			−0.237191	+	0.971463i	$0.576227\pi$
$60$		0			0
$61$	−2.99641	−	5.18993i	−0.383651	−	0.664502i	0.607930	−	0.793990i	$-0.292000\pi$
$61$	−2.99641	−	5.18993i	−0.383651	−	0.664502i	−0.991581	+	0.129488i	$0.958667\pi$
$62$		0			0
$63$	−0.436767	+	0.756503i	−0.0550275	+	0.0953104i
$64$		0			0
$65$	−1.27391	−	2.20647i	−0.158009	−	0.273679i
$66$		0			0
$67$	1.38723	−	8.06694i	0.169477	−	0.985534i
$67$	1.38723	−	8.06694i	0.169477	−	0.985534i
$68$		0			0
$69$	−2.10244	−	3.64153i	−0.253104	−	0.438389i
$70$		0			0
$71$	5.31716	−	9.20959i	0.631031	−	1.09298i	−0.356311	−	0.934368i	$-0.615965\pi$
$71$	5.31716	−	9.20959i	0.631031	−	1.09298i	0.987341	−	0.158610i	$-0.0507012\pi$
$72$		0			0
$73$	−0.0239280	−	0.0414445i	−0.00280056	−	0.00485071i	0.864622	−	0.502423i	$-0.167558\pi$
$73$	−0.0239280	−	0.0414445i	−0.00280056	−	0.00485071i	−0.867422	+	0.497573i	$0.834225\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	0.956786	+	1.65720i	0.109036	+	0.188856i
$78$		0			0
$79$	−1.57787	+	2.73295i	−0.177524	+	0.307481i	−0.941032	−	0.338318i	$-0.890142\pi$
$79$	−1.57787	+	2.73295i	−0.177524	+	0.307481i	0.763508	+	0.645799i	$0.223475\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−2.29548	−	3.97588i	−0.251961	−	0.436409i	0.712105	−	0.702073i	$-0.247742\pi$
$83$	−2.29548	−	3.97588i	−0.251961	−	0.436409i	−0.964066	+	0.265664i	$0.914409\pi$
$84$		0			0
$85$	−3.07842	−	5.33199i	−0.333902	−	0.578335i
$86$		0			0
$87$	−0.323233	+	0.559856i	−0.0346542	+	0.0600228i
$88$		0			0
$89$	−3.07807			−0.326275			−0.163137	−	0.986603i	$-0.552161\pi$
$89$	−3.07807			−0.326275			−0.163137	+	0.986603i	$0.552161\pi$
$90$		0			0
$91$	2.22560			0.233306
$92$		0			0
$93$	0.579844	−	1.00432i	0.0601270	−	0.104143i
$94$		0			0
$95$	−1.66901	−	2.89081i	−0.171237	−	0.296591i
$96$		0			0
$97$	1.76819	+	3.06259i	0.179532	+	0.310959i	0.941720	−	0.336397i	$-0.109208\pi$
$97$	1.76819	+	3.06259i	0.179532	+	0.310959i	−0.762188	+	0.647355i	$0.775875\pi$
$98$		0			0
$99$	1.09530	−	1.89712i	0.110082	−	0.190668i
$100$		0			0
$101$	−1.45576	+	2.52145i	−0.144853	+	0.250894i	−0.929318	−	0.369280i	$-0.879604\pi$
$101$	−1.45576	+	2.52145i	−0.144853	+	0.250894i	0.784465	+	0.620173i	$0.212938\pi$
$102$		0			0
$103$	3.42216	−	5.92736i	0.337196	−	0.584040i	−0.646708	−	0.762737i	$-0.723855\pi$
$103$	3.42216	−	5.92736i	0.337196	−	0.584040i	0.983904	+	0.178697i	$0.0571883\pi$
$104$		0			0
$105$	−0.436767	+	0.756503i	−0.0426241	+	0.0738271i
$106$		0			0
$107$	10.6982			1.03423			0.517115	−	0.855916i	$-0.327006\pi$
$107$	10.6982			1.03423			0.517115	+	0.855916i	$0.327006\pi$
$108$		0			0
$109$	5.25484			0.503323			0.251661	−	0.967815i	$-0.419023\pi$
$109$	5.25484			0.503323			0.251661	+	0.967815i	$0.419023\pi$
$110$		0			0
$111$	−2.36632	−	4.09859i	−0.224602	−	0.389021i
$112$		0			0
$113$	9.32036	−	16.1433i	0.876786	−	1.51864i	0.0219375	−	0.999759i	$-0.493017\pi$
$113$	9.32036	−	16.1433i	0.876786	−	1.51864i	0.854848	−	0.518878i	$-0.173650\pi$
$114$		0			0
$115$	−2.10244	−	3.64153i	−0.196053	−	0.339575i
$116$		0			0
$117$	−1.27391	−	2.20647i	−0.117773	−	0.203988i
$118$		0			0
$119$	5.37822			0.493021
$120$		0			0
$121$	3.10062	+	5.37042i	0.281874	+	0.488220i
$122$		0			0
$123$	−4.00304	+	6.93346i	−0.360942	+	0.625169i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−9.10885	+	15.7770i	−0.808279	+	1.39998i	0.105775	+	0.994390i	$0.466268\pi$
$127$	−9.10885	+	15.7770i	−0.808279	+	1.39998i	−0.914055	+	0.405591i	$0.867066\pi$
$128$		0			0
$129$	−9.15156			−0.805750
$130$		0			0
$131$	−6.92110			−0.604699			−0.302350	−	0.953197i	$-0.597771\pi$
$131$	−6.92110			−0.604699			−0.302350	+	0.953197i	$0.597771\pi$
$132$		0			0
$133$	2.91588			0.252839
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	3.08824			0.263846			0.131923	−	0.991260i	$-0.457885\pi$
$137$	3.08824			0.263846			0.131923	+	0.991260i	$0.457885\pi$
$138$		0			0
$139$	2.25892			0.191599			0.0957995	−	0.995401i	$-0.469459\pi$
$139$	2.25892			0.191599			0.0957995	+	0.995401i	$0.469459\pi$
$140$		0			0
$141$	−6.21127	+	10.7582i	−0.523083	+	0.906006i
$142$		0			0
$143$	−5.58126			−0.466728
$144$		0			0
$145$	−0.323233	+	0.559856i	−0.0268430	+	0.0464935i
$146$		0			0
$147$	3.11847	+	5.40135i	0.257207	+	0.445496i
$148$		0			0
$149$	12.7007			1.04049			0.520243	−	0.854019i	$-0.325842\pi$
$149$	12.7007			1.04049			0.520243	+	0.854019i	$0.325842\pi$
$150$		0			0
$151$	−1.02601	−	1.77710i	−0.0834955	−	0.144618i	0.821254	−	0.570563i	$-0.193275\pi$
$151$	−1.02601	−	1.77710i	−0.0834955	−	0.144618i	−0.904749	+	0.425945i	$0.859942\pi$
$152$		0			0
$153$	−3.07842	−	5.33199i	−0.248876	−	0.431066i
$154$		0			0
$155$	0.579844	−	1.00432i	0.0465742	−	0.0806689i
$156$		0			0
$157$	−1.88957	−	3.27283i	−0.150804	−	0.261200i	0.780719	−	0.624882i	$-0.214853\pi$
$157$	−1.88957	−	3.27283i	−0.150804	−	0.261200i	−0.931523	+	0.363682i	$0.881520\pi$
$158$		0			0
$159$	−8.66314			−0.687032
$160$		0			0
$161$	3.67311			0.289481
$162$		0			0
$163$	7.92924	−	13.7338i	0.621066	−	1.07572i	−0.368222	−	0.929738i	$-0.620033\pi$
$163$	7.92924	−	13.7338i	0.621066	−	1.07572i	0.989288	−	0.145979i	$-0.0466334\pi$
$164$		0			0
$165$	1.09530	−	1.89712i	0.0852693	−	0.147691i
$166$		0			0
$167$	9.55406	−	16.5481i	0.739315	−	1.28053i	−0.213489	−	0.976945i	$-0.568483\pi$
$167$	9.55406	−	16.5481i	0.739315	−	1.28053i	0.952804	−	0.303586i	$-0.0981839\pi$
$168$		0			0
$169$	3.25433	−	5.63666i	0.250333	−	0.433590i
$170$		0			0
$171$	−1.66901	−	2.89081i	−0.127632	−	0.221066i
$172$		0			0
$173$	−4.12739	−	7.14884i	−0.313799	−	0.543517i	0.665382	−	0.746503i	$-0.268269\pi$
$173$	−4.12739	−	7.14884i	−0.313799	−	0.543517i	−0.979182	+	0.202986i	$0.934935\pi$
$174$		0			0
$175$	−0.436767	+	0.756503i	−0.0330165	+	0.0571863i
$176$		0			0
$177$	−3.64380			−0.273885
$178$		0			0
$179$	−1.75612			−0.131259			−0.0656293	−	0.997844i	$-0.520905\pi$
$179$	−1.75612			−0.131259			−0.0656293	+	0.997844i	$0.520905\pi$
$180$		0			0
$181$	−1.58843	+	2.75125i	−0.118067	+	0.204499i	−0.919002	−	0.394253i	$-0.871003\pi$
$181$	−1.58843	+	2.75125i	−0.118067	+	0.204499i	0.800934	+	0.598752i	$0.204337\pi$
$182$		0			0
$183$	−2.99641	−	5.18993i	−0.221501	−	0.383651i
$184$		0			0
$185$	−2.36632	−	4.09859i	−0.173976	−	0.301335i
$186$		0			0
$187$	−13.4872			−0.986285
$188$		0			0
$189$	−0.436767	+	0.756503i	−0.0317701	+	0.0550275i
$190$		0			0
$191$	−6.01274	−	10.4144i	−0.435067	−	0.753557i	0.562234	−	0.826978i	$-0.309942\pi$
$191$	−6.01274	−	10.4144i	−0.435067	−	0.753557i	−0.997301	+	0.0734204i	$0.976609\pi$
$192$		0			0
$193$	21.9520			1.58014			0.790069	−	0.613017i	$-0.210044\pi$
$193$	21.9520			1.58014			0.790069	+	0.613017i	$0.210044\pi$
$194$		0			0
$195$	−1.27391	−	2.20647i	−0.0912263	−	0.158009i
$196$		0			0
$197$	8.82749	−	15.2897i	0.628933	−	1.08934i	−0.358834	−	0.933402i	$-0.616825\pi$
$197$	8.82749	−	15.2897i	0.628933	−	1.08934i	0.987766	−	0.155942i	$-0.0498412\pi$
$198$		0			0
$199$	−2.39395	−	4.14645i	−0.169703	−	0.293934i	0.768612	−	0.639715i	$-0.220947\pi$
$199$	−2.39395	−	4.14645i	−0.169703	−	0.293934i	−0.938315	+	0.345781i	$0.887614\pi$
$200$		0			0
$201$	1.38723	−	8.06694i	0.0978475	−	0.568998i
$202$		0			0
$203$	−0.282355	−	0.489053i	−0.0198174	−	0.0343248i
$204$		0			0
$205$	−4.00304	+	6.93346i	−0.279584	+	0.484254i
$206$		0			0
$207$	−2.10244	−	3.64153i	−0.146130	−	0.253104i
$208$		0			0
$209$	−7.31230			−0.505802
$210$		0			0
$211$	1.86531	+	3.23081i	0.128413	+	0.222418i	0.923062	−	0.384651i	$-0.125678\pi$
$211$	1.86531	+	3.23081i	0.128413	+	0.222418i	−0.794649	+	0.607070i	$0.792345\pi$
$212$		0			0
$213$	5.31716	−	9.20959i	0.364326	−	0.631031i
$214$		0			0
$215$	−9.15156			−0.624131
$216$		0			0
$217$	0.506514	+	0.877308i	0.0343844	+	0.0595555i
$218$		0			0
$219$	−0.0239280	−	0.0414445i	−0.00161690	−	0.00280056i
$220$		0			0
$221$	−7.84324	+	13.5849i	−0.527594	+	0.913819i
$222$		0			0
$223$	−18.6541			−1.24917			−0.624584	−	0.780958i	$-0.714731\pi$
$223$	−18.6541			−1.24917			−0.624584	+	0.780958i	$0.714731\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−8.43267	+	14.6058i	−0.559696	+	0.969422i	0.437825	+	0.899060i	$0.355749\pi$
$227$	−8.43267	+	14.6058i	−0.559696	+	0.969422i	−0.997522	+	0.0703622i	$0.977585\pi$
$228$		0			0
$229$	4.04145	+	6.99999i	0.267066	+	0.462573i	0.968103	−	0.250553i	$-0.0806124\pi$
$229$	4.04145	+	6.99999i	0.267066	+	0.462573i	−0.701037	+	0.713125i	$0.747279\pi$
$230$		0			0
$231$	0.956786	+	1.65720i	0.0629519	+	0.109036i
$232$		0			0
$233$	−2.70411	+	4.68365i	−0.177152	+	0.306836i	−0.940904	−	0.338674i	$-0.890022\pi$
$233$	−2.70411	+	4.68365i	−0.177152	+	0.306836i	0.763752	+	0.645510i	$0.223355\pi$
$234$		0			0
$235$	−6.21127	+	10.7582i	−0.405178	+	0.701789i
$236$		0			0
$237$	−1.57787	+	2.73295i	−0.102494	+	0.177524i
$238$		0			0
$239$	−9.54264	+	16.5283i	−0.617262	+	1.06913i	0.372721	+	0.927943i	$0.378425\pi$
$239$	−9.54264	+	16.5283i	−0.617262	+	1.06913i	−0.989983	+	0.141186i	$0.954909\pi$
$240$		0			0
$241$	7.37395			0.474998			0.237499	−	0.971388i	$-0.423672\pi$
$241$	7.37395			0.474998			0.237499	+	0.971388i	$0.423672\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	3.11847	+	5.40135i	0.199232	+	0.345079i
$246$		0			0
$247$	−4.25232	+	7.36524i	−0.270569	+	0.468639i
$248$		0			0
$249$	−2.29548	−	3.97588i	−0.145470	−	0.251961i
$250$		0			0
$251$	−7.20657	−	12.4821i	−0.454874	−	0.787866i	0.543807	−	0.839211i	$-0.316983\pi$
$251$	−7.20657	−	12.4821i	−0.454874	−	0.787866i	−0.998681	+	0.0513449i	$0.983649\pi$
$252$		0			0
$253$	−9.21124			−0.579106
$254$		0			0
$255$	−3.07842	−	5.33199i	−0.192778	−	0.333902i
$256$		0			0
$257$	11.0017	−	19.0555i	0.686268	−	1.18865i	−0.286769	−	0.958000i	$-0.592581\pi$
$257$	11.0017	−	19.0555i	0.686268	−	1.18865i	0.973037	−	0.230651i	$-0.0740854\pi$
$258$		0			0
$259$	4.13413			0.256883
$260$		0			0
$261$	−0.323233	+	0.559856i	−0.0200076	+	0.0346542i
$262$		0			0
$263$	−5.51723			−0.340207			−0.170104	−	0.985426i	$-0.554410\pi$
$263$	−5.51723			−0.340207			−0.170104	+	0.985426i	$0.554410\pi$
$264$		0			0
$265$	−8.66314			−0.532173
$266$		0			0
$267$	−3.07807			−0.188375
$268$		0			0
$269$	−4.05203			−0.247057			−0.123528	−	0.992341i	$-0.539421\pi$
$269$	−4.05203			−0.247057			−0.123528	+	0.992341i	$0.539421\pi$
$270$		0			0
$271$	22.3639			1.35851			0.679256	−	0.733902i	$-0.262303\pi$
$271$	22.3639			1.35851			0.679256	+	0.733902i	$0.262303\pi$
$272$		0			0
$273$	2.22560			0.134700
$274$		0			0
$275$	1.09530	−	1.89712i	0.0660493	−	0.114401i
$276$		0			0
$277$	−0.341518			−0.0205198			−0.0102599	−	0.999947i	$-0.503266\pi$
$277$	−0.341518			−0.0205198			−0.0102599	+	0.999947i	$0.503266\pi$
$278$		0			0
$279$	0.579844	−	1.00432i	0.0347144	−	0.0601270i
$280$		0			0
$281$	−6.37905	−	11.0488i	−0.380542	−	0.659118i	0.610598	−	0.791941i	$-0.290929\pi$
$281$	−6.37905	−	11.0488i	−0.380542	−	0.659118i	−0.991140	+	0.132823i	$0.957596\pi$
$282$		0			0
$283$	18.8010			1.11760			0.558802	−	0.829301i	$-0.311261\pi$
$283$	18.8010			1.11760			0.558802	+	0.829301i	$0.311261\pi$
$284$		0			0
$285$	−1.66901	−	2.89081i	−0.0988636	−	0.171237i
$286$		0			0
$287$	−3.49679	−	6.05662i	−0.206409	−	0.357511i
$288$		0			0
$289$	−10.4534	+	18.1058i	−0.614905	+	1.06505i
$290$		0			0
$291$	1.76819	+	3.06259i	0.103653	+	0.179532i
$292$		0			0
$293$	−17.9116			−1.04641			−0.523204	−	0.852207i	$-0.675263\pi$
$293$	−17.9116			−1.04641			−0.523204	+	0.852207i	$0.675263\pi$
$294$		0			0
$295$	−3.64380			−0.212150
$296$		0			0
$297$	1.09530	−	1.89712i	0.0635560	−	0.110082i
$298$		0			0
$299$	−5.35662	+	9.27793i	−0.309781	+	0.536557i
$300$		0			0
$301$	3.99710	−	6.92318i	0.230389	−	0.399046i
$302$		0			0
$303$	−1.45576	+	2.52145i	−0.0836312	+	0.144853i
$304$		0			0
$305$	−2.99641	−	5.18993i	−0.171574	−	0.297174i
$306$		0			0
$307$	11.6094	+	20.1080i	0.662581	+	1.14762i	0.979935	+	0.199317i	$0.0638722\pi$
$307$	11.6094	+	20.1080i	0.662581	+	1.14762i	−0.317354	+	0.948307i	$0.602794\pi$
$308$		0			0
$309$	3.42216	−	5.92736i	0.194680	−	0.337196i
$310$		0			0
$311$	−0.428849			−0.0243178			−0.0121589	−	0.999926i	$-0.503870\pi$
$311$	−0.428849			−0.0243178			−0.0121589	+	0.999926i	$0.503870\pi$
$312$		0			0
$313$	26.4449			1.49475			0.747377	−	0.664401i	$-0.231313\pi$
$313$	26.4449			1.49475			0.747377	+	0.664401i	$0.231313\pi$
$314$		0			0
$315$	−0.436767	+	0.756503i	−0.0246090	+	0.0426241i
$316$		0			0
$317$	13.5428	+	23.4567i	0.760637	+	1.31746i	0.942523	+	0.334142i	$0.108446\pi$
$317$	13.5428	+	23.4567i	0.760637	+	1.31746i	−0.181886	+	0.983320i	$0.558220\pi$
$318$		0			0
$319$	0.708077	+	1.22643i	0.0396447	+	0.0686666i
$320$		0			0
$321$	10.6982			0.597113
$322$		0			0
$323$	−10.2758	+	17.7983i	−0.571763	+	0.990323i
$324$		0			0
$325$	−1.27391	−	2.20647i	−0.0706636	−	0.122393i
$326$		0			0
$327$	5.25484			0.290593
$328$		0			0
$329$	−5.42576	−	9.39768i	−0.299132	−	0.518111i
$330$		0			0
$331$	−4.07232	+	7.05347i	−0.223835	+	0.387694i	−0.955969	−	0.293467i	$-0.905191\pi$
$331$	−4.07232	+	7.05347i	−0.223835	+	0.387694i	0.732134	+	0.681160i	$0.238524\pi$
$332$		0			0
$333$	−2.36632	−	4.09859i	−0.129674	−	0.224602i
$334$		0			0
$335$	1.38723	−	8.06694i	0.0757923	−	0.440744i
$336$		0			0
$337$	13.1864	+	22.8395i	0.718307	+	1.24414i	0.961670	+	0.274209i	$0.0884160\pi$
$337$	13.1864	+	22.8395i	0.718307	+	1.24414i	−0.243363	+	0.969935i	$0.578251\pi$
$338$		0			0
$339$	9.32036	−	16.1433i	0.506212	−	0.876786i
$340$		0			0
$341$	−1.27021	−	2.20007i	−0.0687858	−	0.119141i
$342$		0			0
$343$	−11.5629			−0.624339
$344$		0			0
$345$	−2.10244	−	3.64153i	−0.113192	−	0.196053i
$346$		0			0
$347$	5.76820	−	9.99082i	0.309653	−	0.536335i	−0.668633	−	0.743592i	$-0.733120\pi$
$347$	5.76820	−	9.99082i	0.309653	−	0.536335i	0.978287	+	0.207257i	$0.0664536\pi$
$348$		0			0
$349$	16.7299			0.895528			0.447764	−	0.894152i	$-0.352220\pi$
$349$	16.7299			0.895528			0.447764	+	0.894152i	$0.352220\pi$
$350$		0			0
$351$	−1.27391	−	2.20647i	−0.0679960	−	0.117773i
$352$		0			0
$353$	−14.8770	−	25.7678i	−0.791825	−	1.37148i	−0.924836	−	0.380367i	$-0.875798\pi$
$353$	−14.8770	−	25.7678i	−0.791825	−	1.37148i	0.133011	−	0.991115i	$-0.457536\pi$
$354$		0			0
$355$	5.31716	−	9.20959i	0.282206	−	0.488794i
$356$		0			0
$357$	5.37822			0.284646
$358$		0			0
$359$	24.6130			1.29902			0.649511	−	0.760352i	$-0.274974\pi$
$359$	24.6130			1.29902			0.649511	+	0.760352i	$0.274974\pi$
$360$		0			0
$361$	3.92881	−	6.80490i	0.206779	−	0.358152i
$362$		0			0
$363$	3.10062	+	5.37042i	0.162740	+	0.281874i
$364$		0			0
$365$	−0.0239280	−	0.0414445i	−0.00125245	−	0.00216930i
$366$		0			0
$367$	−6.33883	+	10.9792i	−0.330884	+	0.573108i	−0.982685	−	0.185282i	$-0.940680\pi$
$367$	−6.33883	+	10.9792i	−0.330884	+	0.573108i	0.651801	+	0.758390i	$0.274014\pi$
$368$		0			0
$369$	−4.00304	+	6.93346i	−0.208390	+	0.360942i
$370$		0			0
$371$	3.78378	−	6.55369i	0.196444	−	0.340251i
$372$		0			0
$373$	−7.10934	+	12.3137i	−0.368108	+	0.637581i	−0.989270	−	0.146101i	$-0.953328\pi$
$373$	−7.10934	+	12.3137i	−0.368108	+	0.637581i	0.621162	+	0.783682i	$0.286661\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	1.64707			0.0848286
$378$		0			0
$379$	−10.7582	−	18.6337i	−0.552610	−	0.957148i	−0.998085	−	0.0618542i	$-0.980299\pi$
$379$	−10.7582	−	18.6337i	−0.552610	−	0.957148i	0.445475	−	0.895294i	$-0.353035\pi$
$380$		0			0
$381$	−9.10885	+	15.7770i	−0.466660	+	0.808279i
$382$		0			0
$383$	−13.2051	−	22.8719i	−0.674750	−	1.16870i	−0.976542	−	0.215328i	$-0.930918\pi$
$383$	−13.2051	−	22.8719i	−0.674750	−	1.16870i	0.301792	−	0.953374i	$-0.402415\pi$
$384$		0			0
$385$	0.956786	+	1.65720i	0.0487623	+	0.0844589i
$386$		0			0
$387$	−9.15156			−0.465200
$388$		0			0
$389$	−8.88730	−	15.3933i	−0.450604	−	0.780469i	0.547820	−	0.836596i	$-0.315458\pi$
$389$	−8.88730	−	15.3933i	−0.450604	−	0.780469i	−0.998424	+	0.0561275i	$0.982125\pi$
$390$		0			0
$391$	−12.9444	+	22.4204i	−0.654626	+	1.13385i
$392$		0			0
$393$	−6.92110			−0.349123
$394$		0			0
$395$	−1.57787	+	2.73295i	−0.0793912	+	0.137510i
$396$		0			0
$397$	14.2842			0.716906			0.358453	−	0.933548i	$-0.383304\pi$
$397$	14.2842			0.716906			0.358453	+	0.933548i	$0.383304\pi$
$398$		0			0
$399$	2.91588			0.145976
$400$		0			0
$401$	26.0441			1.30058			0.650291	−	0.759686i	$-0.274647\pi$
$401$	26.0441			1.30058			0.650291	+	0.759686i	$0.274647\pi$
$402$		0			0
$403$	−2.95467			−0.147182
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−10.3674			−0.513892
$408$		0			0
$409$	−15.7417	+	27.2654i	−0.778376	+	1.34819i	0.154502	+	0.987993i	$0.450623\pi$
$409$	−15.7417	+	27.2654i	−0.778376	+	1.34819i	−0.932878	+	0.360194i	$0.882711\pi$
$410$		0			0
$411$	3.08824			0.152332
$412$		0			0
$413$	1.59149	−	2.75655i	0.0783122	−	0.135641i
$414$		0			0
$415$	−2.29548	−	3.97588i	−0.112680	−	0.195168i
$416$		0			0
$417$	2.25892			0.110620
$418$		0			0
$419$	−8.07225	−	13.9815i	−0.394355	−	0.683043i	0.598664	−	0.801001i	$-0.295699\pi$
$419$	−8.07225	−	13.9815i	−0.394355	−	0.683043i	−0.993019	+	0.117958i	$0.962365\pi$
$420$		0			0
$421$	−9.98072	−	17.2871i	−0.486430	−	0.842522i	0.513448	−	0.858121i	$-0.328368\pi$
$421$	−9.98072	−	17.2871i	−0.486430	−	0.842522i	−0.999878	+	0.0155985i	$0.995035\pi$
$422$		0			0
$423$	−6.21127	+	10.7582i	−0.302002	+	0.523083i
$424$		0			0
$425$	−3.07842	−	5.33199i	−0.149326	−	0.258639i
$426$		0			0
$427$	5.23493			0.253336
$428$		0			0
$429$	−5.58126			−0.269466
$430$		0			0
$431$	−5.43435	+	9.41257i	−0.261763	+	0.453387i	−0.966711	−	0.255872i	$-0.917637\pi$
$431$	−5.43435	+	9.41257i	−0.261763	+	0.453387i	0.704947	+	0.709260i	$0.250971\pi$
$432$		0			0
$433$	2.47684	−	4.29001i	0.119029	−	0.206165i	−0.800354	−	0.599528i	$-0.795355\pi$
$433$	2.47684	−	4.29001i	0.119029	−	0.206165i	0.919383	+	0.393363i	$0.128688\pi$
$434$		0			0
$435$	−0.323233	+	0.559856i	−0.0154978	+	0.0268430i
$436$		0			0
$437$	−7.01799	+	12.1555i	−0.335716	+	0.581477i
$438$		0			0
$439$	6.54614	+	11.3382i	0.312430	+	0.541145i	0.978888	−	0.204398i	$-0.0655237\pi$
$439$	6.54614	+	11.3382i	0.312430	+	0.541145i	−0.666458	+	0.745543i	$0.732190\pi$
$440$		0			0
$441$	3.11847	+	5.40135i	0.148499	+	0.257207i
$442$		0			0
$443$	2.60200	−	4.50680i	0.123625	−	0.214125i	−0.797570	−	0.603227i	$-0.793881\pi$
$443$	2.60200	−	4.50680i	0.123625	−	0.214125i	0.921195	+	0.389102i	$0.127215\pi$
$444$		0			0
$445$	−3.07807			−0.145915
$446$		0			0
$447$	12.7007			0.600724
$448$		0			0
$449$	8.41212	−	14.5702i	0.396992	−	0.687611i	−0.596361	−	0.802717i	$-0.703387\pi$
$449$	8.41212	−	14.5702i	0.396992	−	0.687611i	0.993353	+	0.115105i	$0.0367206\pi$
$450$		0			0
$451$	8.76909	+	15.1885i	0.412920	+	0.715199i
$452$		0			0
$453$	−1.02601	−	1.77710i	−0.0482062	−	0.0834955i
$454$		0			0
$455$	2.22560			0.104338
$456$		0			0
$457$	10.9881	−	19.0320i	0.514003	−	0.890280i	−0.485865	−	0.874034i	$-0.661495\pi$
$457$	10.9881	−	19.0320i	0.514003	−	0.890280i	0.999868	−	0.0162456i	$-0.00517137\pi$
$458$		0			0
$459$	−3.07842	−	5.33199i	−0.143689	−	0.248876i
$460$		0			0
$461$	−22.4235			−1.04437			−0.522184	−	0.852833i	$-0.674883\pi$
$461$	−22.4235			−1.04437			−0.522184	+	0.852833i	$0.674883\pi$
$462$		0			0
$463$	−8.98973	−	15.5707i	−0.417788	−	0.723630i	0.577929	−	0.816087i	$-0.303861\pi$
$463$	−8.98973	−	15.5707i	−0.417788	−	0.723630i	−0.995717	+	0.0924571i	$0.970528\pi$
$464$		0			0
$465$	0.579844	−	1.00432i	0.0268896	−	0.0465742i
$466$		0			0
$467$	7.89466	+	13.6740i	0.365321	+	0.632755i	0.988828	−	0.149063i	$-0.0476258\pi$
$467$	7.89466	+	13.6740i	0.365321	+	0.632755i	−0.623506	+	0.781818i	$0.714292\pi$
$468$		0			0
$469$	5.49677	+	4.57282i	0.253817	+	0.211153i
$470$		0			0
$471$	−1.88957	−	3.27283i	−0.0870667	−	0.150804i
$472$		0			0
$473$	−10.0237	+	17.3616i	−0.460892	+	0.798288i
$474$		0			0
$475$	−1.66901	−	2.89081i	−0.0765795	−	0.132640i
$476$		0			0
$477$	−8.66314			−0.396658
$478$		0			0
$479$	12.0622	+	20.8924i	0.551137	+	0.954597i	0.998193	+	0.0600909i	$0.0191391\pi$
$479$	12.0622	+	20.8924i	0.551137	+	0.954597i	−0.447056	+	0.894506i	$0.647528\pi$
$480$		0			0
$481$	−6.02895	+	10.4424i	−0.274896	+	0.476134i
$482$		0			0
$483$	3.67311			0.167132
$484$		0			0
$485$	1.76819	+	3.06259i	0.0802892	+	0.139065i
$486$		0			0
$487$	7.00357	+	12.1305i	0.317362	+	0.549687i	0.979937	−	0.199309i	$-0.0638697\pi$
$487$	7.00357	+	12.1305i	0.317362	+	0.549687i	−0.662575	+	0.748996i	$0.730536\pi$
$488$		0			0
$489$	7.92924	−	13.7338i	0.358572	−	0.621066i
$490$		0			0
$491$	−21.1879			−0.956196			−0.478098	−	0.878307i	$-0.658674\pi$
$491$	−21.1879			−0.956196			−0.478098	+	0.878307i	$0.658674\pi$
$492$		0			0
$493$	3.98019			0.179259
$494$		0			0
$495$	1.09530	−	1.89712i	0.0492303	−	0.0852693i
$496$		0			0
$497$	4.64472	+	8.04490i	0.208344	+	0.360863i
$498$		0			0
$499$	−3.14567	−	5.44846i	−0.140820	−	0.243907i	0.786986	−	0.616971i	$-0.211640\pi$
$499$	−3.14567	−	5.44846i	−0.140820	−	0.243907i	−0.927805	+	0.373064i	$0.878307\pi$
$500$		0			0
$501$	9.55406	−	16.5481i	0.426844	−	0.739315i
$502$		0			0
$503$	4.41870	−	7.65342i	0.197020	−	0.341249i	−0.750541	−	0.660824i	$-0.770207\pi$
$503$	4.41870	−	7.65342i	0.197020	−	0.341249i	0.947561	+	0.319575i	$0.103540\pi$
$504$		0			0
$505$	−1.45576	+	2.52145i	−0.0647804	+	0.112203i
$506$		0			0
$507$	3.25433	−	5.63666i	0.144530	−	0.250333i
$508$		0			0
$509$	−2.59211			−0.114893			−0.0574466	−	0.998349i	$-0.518296\pi$
$509$	−2.59211			−0.114893			−0.0574466	+	0.998349i	$0.518296\pi$
$510$		0			0
$511$	0.0418039			0.00184929
$512$		0			0
$513$	−1.66901	−	2.89081i	−0.0736886	−	0.127632i
$514$		0			0
$515$	3.42216	−	5.92736i	0.150798	−	0.261191i
$516$		0			0
$517$	13.6065	+	23.5671i	0.598411	+	1.03648i
$518$		0			0
$519$	−4.12739	−	7.14884i	−0.181172	−	0.313799i
$520$		0			0
$521$	41.4807			1.81730			0.908650	−	0.417558i	$-0.137114\pi$
$521$	41.4807			1.81730			0.908650	+	0.417558i	$0.137114\pi$
$522$		0			0
$523$	−18.4360	−	31.9321i	−0.806151	−	1.39629i	−0.915511	−	0.402293i	$-0.868213\pi$
$523$	−18.4360	−	31.9321i	−0.806151	−	1.39629i	0.109360	−	0.994002i	$-0.465120\pi$
$524$		0			0
$525$	−0.436767	+	0.756503i	−0.0190621	+	0.0330165i
$526$		0			0
$527$	−7.14002			−0.311024
$528$		0			0
$529$	2.65950	−	4.60639i	0.115630	−	0.200278i
$530$		0			0
$531$	−3.64380			−0.158127
$532$		0			0
$533$	20.3980			0.883534
$534$		0			0
$535$	10.6982			0.462522
$536$		0			0
$537$	−1.75612			−0.0757822
$538$		0			0
$539$	13.6627			0.588494
$540$		0			0
$541$	−6.44614			−0.277141			−0.138571	−	0.990353i	$-0.544251\pi$
$541$	−6.44614			−0.277141			−0.138571	+	0.990353i	$0.544251\pi$
$542$		0			0
$543$	−1.58843	+	2.75125i	−0.0681663	+	0.118067i
$544$		0			0
$545$	5.25484			0.225093
$546$		0			0
$547$	−4.64619	+	8.04744i	−0.198657	+	0.344084i	−0.948093	−	0.317993i	$-0.896991\pi$
$547$	−4.64619	+	8.04744i	−0.198657	+	0.344084i	0.749436	+	0.662076i	$0.230325\pi$
$548$		0			0
$549$	−2.99641	−	5.18993i	−0.127884	−	0.221501i
$550$		0			0
$551$	2.15792			0.0919303
$552$		0			0
$553$	−1.37832	−	2.38733i	−0.0586123	−	0.101519i
$554$		0			0
$555$	−2.36632	−	4.09859i	−0.100445	−	0.173976i
$556$		0			0
$557$	0.592099	−	1.02555i	0.0250880	−	0.0434538i	−0.853209	−	0.521570i	$-0.825347\pi$
$557$	0.592099	−	1.02555i	0.0250880	−	0.0434538i	0.878297	+	0.478116i	$0.158680\pi$
$558$		0			0
$559$	11.6582	+	20.1926i	0.493090	+	0.854057i
$560$		0			0
$561$	−13.4872			−0.569432
$562$		0			0
$563$	−29.1492			−1.22849			−0.614245	−	0.789115i	$-0.710540\pi$
$563$	−29.1492			−1.22849			−0.614245	+	0.789115i	$0.710540\pi$
$564$		0			0
$565$	9.32036	−	16.1433i	0.392111	−	0.679155i
$566$		0			0
$567$	−0.436767	+	0.756503i	−0.0183425	+	0.0317701i
$568$		0			0
$569$	−0.105593	+	0.182893i	−0.00442670	+	0.00766727i	−0.868230	−	0.496161i	$-0.834742\pi$
$569$	−0.105593	+	0.182893i	−0.00442670	+	0.00766727i	0.863804	+	0.503829i	$0.168076\pi$
$570$		0			0
$571$	−11.6012	+	20.0939i	−0.485495	+	0.840902i	−0.999861	−	0.0166686i	$-0.994694\pi$
$571$	−11.6012	+	20.0939i	−0.485495	+	0.840902i	0.514366	+	0.857571i	$0.328027\pi$
$572$		0			0
$573$	−6.01274	−	10.4144i	−0.251186	−	0.435067i
$574$		0			0
$575$	−2.10244	−	3.64153i	−0.0876778	−	0.151862i
$576$		0			0
$577$	−3.98263	+	6.89812i	−0.165799	+	0.287173i	−0.936939	−	0.349493i	$-0.886354\pi$
$577$	−3.98263	+	6.89812i	−0.165799	+	0.287173i	0.771140	+	0.636666i	$0.219687\pi$
$578$		0			0
$579$	21.9520			0.912294
$580$		0			0
$581$	4.01035			0.166378
$582$		0			0
$583$	−9.48878	+	16.4350i	−0.392985	+	0.680670i
$584$		0			0
$585$	−1.27391	−	2.20647i	−0.0526695	−	0.0912263i
$586$		0			0
$587$	−16.9774	−	29.4058i	−0.700734	−	1.21371i	−0.968209	−	0.250142i	$-0.919523\pi$
$587$	−16.9774	−	29.4058i	−0.700734	−	1.21371i	0.267476	−	0.963565i	$-0.413810\pi$
$588$		0			0
$589$	−3.87106			−0.159504
$590$		0			0
$591$	8.82749	−	15.2897i	0.363114	−	0.628933i
$592$		0			0
$593$	−3.56903	−	6.18174i	−0.146563	−	0.253854i	0.783392	−	0.621528i	$-0.213488\pi$
$593$	−3.56903	−	6.18174i	−0.146563	−	0.253854i	−0.929955	+	0.367674i	$0.880154\pi$
$594$		0			0
$595$	5.37822			0.220486
$596$		0			0
$597$	−2.39395	−	4.14645i	−0.0979780	−	0.169703i
$598$		0			0
$599$	0.738992	−	1.27997i	0.0301944	−	0.0522982i	−0.850533	−	0.525921i	$-0.823721\pi$
$599$	0.738992	−	1.27997i	0.0301944	−	0.0522982i	0.880728	+	0.473623i	$0.157054\pi$
$600$		0			0
$601$	20.3549	+	35.2556i	0.830292	+	1.43811i	0.897807	+	0.440390i	$0.145160\pi$
$601$	20.3549	+	35.2556i	0.830292	+	1.43811i	−0.0675147	+	0.997718i	$0.521507\pi$
$602$		0			0
$603$	1.38723	−	8.06694i	0.0564923	−	0.328511i
$604$		0			0
$605$	3.10062	+	5.37042i	0.126058	+	0.218339i
$606$		0			0
$607$	10.1173	−	17.5237i	0.410649	−	0.711265i	−0.584312	−	0.811529i	$-0.698635\pi$
$607$	10.1173	−	17.5237i	0.410649	−	0.711265i	0.994961	+	0.100264i	$0.0319688\pi$
$608$		0			0
$609$	−0.282355	−	0.489053i	−0.0114416	−	0.0198174i
$610$		0			0
$611$	31.6503			1.28043
$612$		0			0
$613$	12.2177	+	21.1617i	0.493469	+	0.854714i	0.999972	−	0.00752486i	$-0.00239526\pi$
$613$	12.2177	+	21.1617i	0.493469	+	0.854714i	−0.506503	+	0.862238i	$0.669062\pi$
$614$		0			0
$615$	−4.00304	+	6.93346i	−0.161418	+	0.279584i
$616$		0			0
$617$	−7.97216			−0.320947			−0.160473	−	0.987040i	$-0.551302\pi$
$617$	−7.97216			−0.320947			−0.160473	+	0.987040i	$0.551302\pi$
$618$		0			0
$619$	−7.20120	−	12.4728i	−0.289441	−	0.501326i	0.684236	−	0.729261i	$-0.260136\pi$
$619$	−7.20120	−	12.4728i	−0.289441	−	0.501326i	−0.973676	+	0.227935i	$0.926803\pi$
$620$		0			0
$621$	−2.10244	−	3.64153i	−0.0843680	−	0.146130i
$622$		0			0
$623$	1.34440	−	2.32857i	0.0538623	−	0.0932922i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−7.31230			−0.292025
$628$		0			0
$629$	−14.5691	+	25.2344i	−0.580908	+	1.00616i
$630$		0			0
$631$	8.54690	+	14.8037i	0.340247	+	0.589325i	0.984478	−	0.175506i	$-0.0561561\pi$
$631$	8.54690	+	14.8037i	0.340247	+	0.589325i	−0.644232	+	0.764830i	$0.722823\pi$
$632$		0			0
$633$	1.86531	+	3.23081i	0.0741395	+	0.128413i
$634$		0			0
$635$	−9.10885	+	15.7770i	−0.361474	+	0.626091i
$636$		0			0
$637$	7.94527	−	13.7616i	0.314803	−	0.545255i
$638$		0			0
$639$	5.31716	−	9.20959i	0.210344	−	0.364326i
$640$		0			0
$641$	8.37426	−	14.5046i	0.330763	−	0.572899i	−0.651898	−	0.758306i	$-0.726027\pi$
$641$	8.37426	−	14.5046i	0.330763	−	0.572899i	0.982662	+	0.185407i	$0.0593604\pi$
$642$		0			0
$643$	10.9880			0.433324			0.216662	−	0.976247i	$-0.430483\pi$
$643$	10.9880			0.433324			0.216662	+	0.976247i	$0.430483\pi$
$644$		0			0
$645$	−9.15156			−0.360342
$646$		0			0
$647$	−1.75088	−	3.03261i	−0.0688342	−	0.119224i	0.829554	−	0.558426i	$-0.188595\pi$
$647$	−1.75088	−	3.03261i	−0.0688342	−	0.119224i	−0.898388	+	0.439202i	$0.855261\pi$
$648$		0			0
$649$	−3.99107	+	6.91274i	−0.156663	+	0.271349i
$650$		0			0
$651$	0.506514	+	0.877308i	0.0198518	+	0.0343844i
$652$		0			0
$653$	−20.0009	−	34.6426i	−0.782695	−	1.35567i	−0.930366	−	0.366632i	$-0.880511\pi$
$653$	−20.0009	−	34.6426i	−0.782695	−	1.35567i	0.147671	−	0.989037i	$-0.452822\pi$
$654$		0			0
$655$	−6.92110			−0.270430
$656$		0			0
$657$	−0.0239280	−	0.0414445i	−0.000933520	−	0.00161690i
$658$		0			0
$659$	9.22357	−	15.9757i	0.359299	−	0.622324i	−0.628545	−	0.777773i	$-0.716349\pi$
$659$	9.22357	−	15.9757i	0.359299	−	0.622324i	0.987844	+	0.155449i	$0.0496824\pi$
$660$		0			0
$661$	47.6127			1.85192			0.925961	−	0.377620i	$-0.123258\pi$
$661$	47.6127			1.85192			0.925961	+	0.377620i	$0.123258\pi$
$662$		0			0
$663$	−7.84324	+	13.5849i	−0.304606	+	0.527594i
$664$		0			0
$665$	2.91588			0.113073
$666$		0			0
$667$	2.71831			0.105253
$668$		0			0
$669$	−18.6541			−0.721208
$670$		0			0
$671$	−13.1279			−0.506797
$672$		0			0
$673$	1.55614			0.0599848			0.0299924	−	0.999550i	$-0.490452\pi$
$673$	1.55614			0.0599848			0.0299924	+	0.999550i	$0.490452\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−19.3586	+	33.5302i	−0.744013	+	1.28867i	0.206641	+	0.978417i	$0.433747\pi$
$677$	−19.3586	+	33.5302i	−0.744013	+	1.28867i	−0.950654	+	0.310252i	$0.899587\pi$
$678$		0			0
$679$	−3.08914			−0.118550
$680$		0			0
$681$	−8.43267	+	14.6058i	−0.323141	+	0.559696i
$682$		0			0
$683$	−18.5183	−	32.0747i	−0.708583	−	1.22730i	−0.965383	−	0.260838i	$-0.916001\pi$
$683$	−18.5183	−	32.0747i	−0.708583	−	1.22730i	0.256799	−	0.966465i	$-0.417332\pi$
$684$		0			0
$685$	3.08824			0.117996
$686$		0			0
$687$	4.04145	+	6.99999i	0.154191	+	0.267066i
$688$		0			0
$689$	11.0360	+	19.1150i	0.420439	+	0.728222i
$690$		0			0
$691$	−14.3993	+	24.9404i	−0.547776	+	0.948776i	0.450650	+	0.892701i	$0.351192\pi$
$691$	−14.3993	+	24.9404i	−0.547776	+	0.948776i	−0.998427	+	0.0560758i	$0.982141\pi$
$692$		0			0
$693$	0.956786	+	1.65720i	0.0363453	+	0.0629519i
$694$		0			0
$695$	2.25892			0.0856857
$696$		0			0
$697$	49.2922			1.86707
$698$		0			0
$699$	−2.70411	+	4.68365i	−0.102279	+	0.177152i
$700$		0			0
$701$	6.38903	−	11.0661i	0.241311	−	0.417962i	−0.719777	−	0.694205i	$-0.755756\pi$
$701$	6.38903	−	11.0661i	0.241311	−	0.417962i	0.961088	+	0.276243i	$0.0890894\pi$
$702$		0			0
$703$	−7.89884	+	13.6812i	−0.297910	+	0.515996i
$704$		0			0
$705$	−6.21127	+	10.7582i	−0.233930	+	0.405178i
$706$		0			0
$707$	−1.27166	−	2.20257i	−0.0478255	−	0.0828363i
$708$		0			0
$709$	8.87848	+	15.3780i	0.333438	+	0.577532i	0.983184	−	0.182620i	$-0.0584578\pi$
$709$	8.87848	+	15.3780i	0.333438	+	0.577532i	−0.649745	+	0.760152i	$0.725124\pi$
$710$		0			0
$711$	−1.57787	+	2.73295i	−0.0591747	+	0.102494i
$712$		0			0
$713$	−4.87635			−0.182621
$714$		0			0
$715$	−5.58126			−0.208727
$716$		0			0
$717$	−9.54264	+	16.5283i	−0.356376	+	0.617262i
$718$		0			0
$719$	19.8214	+	34.3317i	0.739215	+	1.28036i	0.952849	+	0.303444i	$0.0981365\pi$
$719$	19.8214	+	34.3317i	0.739215	+	1.28036i	−0.213634	+	0.976914i	$0.568530\pi$
$720$		0			0
$721$	2.98938	+	5.17775i	0.111330	+	0.192830i
$722$		0			0
$723$	7.37395			0.274240
$724$		0			0
$725$	−0.323233	+	0.559856i	−0.0120046	+	0.0207925i
$726$		0			0
$727$	16.9401	+	29.3411i	0.628274	+	1.08820i	0.987898	+	0.155106i	$0.0495718\pi$
$727$	16.9401	+	29.3411i	0.628274	+	1.08820i	−0.359624	+	0.933097i	$0.617095\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	28.1724	+	48.7960i	1.04199	+	1.80478i
$732$		0			0
$733$	−17.3172	+	29.9943i	−0.639625	+	1.10786i	0.345890	+	0.938275i	$0.387577\pi$
$733$	−17.3172	+	29.9943i	−0.639625	+	1.10786i	−0.985515	+	0.169588i	$0.945756\pi$
$734$		0			0
$735$	3.11847	+	5.40135i	0.115026	+	0.199232i
$736$		0			0
$737$	−13.7846	−	11.4675i	−0.507760	−	0.422411i
$738$		0			0
$739$	−10.1097	−	17.5106i	−0.371893	−	0.644137i	0.617964	−	0.786206i	$-0.287958\pi$
$739$	−10.1097	−	17.5106i	−0.371893	−	0.644137i	−0.989857	+	0.142069i	$0.954624\pi$
$740$		0			0
$741$	−4.25232	+	7.36524i	−0.156213	+	0.270569i
$742$		0			0
$743$	−20.1138	−	34.8381i	−0.737904	−	1.27809i	−0.953437	−	0.301591i	$-0.902482\pi$
$743$	−20.1138	−	34.8381i	−0.737904	−	1.27809i	0.215533	−	0.976496i	$-0.430851\pi$
$744$		0			0
$745$	12.7007			0.465319
$746$		0			0
$747$	−2.29548	−	3.97588i	−0.0839870	−	0.145470i
$748$		0			0
$749$	−4.67261	+	8.09319i	−0.170733	+	0.295719i
$750$		0			0
$751$	−6.40388			−0.233681			−0.116840	−	0.993151i	$-0.537277\pi$
$751$	−6.40388			−0.233681			−0.116840	+	0.993151i	$0.537277\pi$
$752$		0			0
$753$	−7.20657	−	12.4821i	−0.262622	−	0.454874i
$754$		0			0
$755$	−1.02601	−	1.77710i	−0.0373403	−	0.0646754i
$756$		0			0
$757$	10.9984	−	19.0498i	0.399743	−	0.692375i	−0.593951	−	0.804501i	$-0.702433\pi$
$757$	10.9984	−	19.0498i	0.399743	−	0.692375i	0.993694	+	0.112126i	$0.0357661\pi$
$758$		0			0
$759$	−9.21124			−0.334347
$760$		0			0
$761$	−21.3840			−0.775169			−0.387584	−	0.921834i	$-0.626690\pi$
$761$	−21.3840			−0.775169			−0.387584	+	0.921834i	$0.626690\pi$
$762$		0			0
$763$	−2.29514	+	3.97531i	−0.0830898	+	0.143916i
$764$		0			0
$765$	−3.07842	−	5.33199i	−0.111301	−	0.192778i
$766$		0			0
$767$	4.64186	+	8.03993i	0.167608	+	0.290305i
$768$		0			0
$769$	12.0411	−	20.8559i	0.434215	−	0.752082i	−0.563017	−	0.826446i	$-0.690359\pi$
$769$	12.0411	−	20.8559i	0.434215	−	0.752082i	0.997231	+	0.0743638i	$0.0236926\pi$
$770$		0			0
$771$	11.0017	−	19.0555i	0.396217	−	0.686268i
$772$		0			0
$773$	4.30251	−	7.45216i	0.154750	−	0.268036i	−0.778218	−	0.627995i	$-0.783876\pi$
$773$	4.30251	−	7.45216i	0.154750	−	0.268036i	0.932968	+	0.359959i	$0.117209\pi$
$774$		0			0
$775$	0.579844	−	1.00432i	0.0208286	−	0.0360762i
$776$		0			0
$777$	4.13413			0.148311
$778$		0			0
$779$	26.7244			0.957503
$780$		0			0
$781$	−11.6478	−	20.1746i	−0.416792	−	0.721904i
$782$		0			0
$783$	−0.323233	+	0.559856i	−0.0115514	+	0.0200076i
$784$		0			0
$785$	−1.88957	−	3.27283i	−0.0674416	−	0.116812i
$786$		0			0
$787$	−6.89857	−	11.9487i	−0.245907	−	0.425924i	0.716479	−	0.697609i	$-0.245753\pi$
$787$	−6.89857	−	11.9487i	−0.245907	−	0.425924i	−0.962386	+	0.271685i	$0.912419\pi$
$788$		0			0
$789$	−5.51723			−0.196419
$790$		0			0
$791$	8.14166	+	14.1018i	0.289484	+	0.501401i
$792$		0			0
$793$	−7.63428	+	13.2230i	−0.271101	+	0.469561i
$794$		0			0
$795$	−8.66314			−0.307250
$796$		0			0
$797$	4.03228	−	6.98411i	0.142831	−	0.247390i	−0.785731	−	0.618568i	$-0.787713\pi$
$797$	4.03228	−	6.98411i	0.142831	−	0.247390i	0.928561	+	0.371179i	$0.121046\pi$
$798$		0			0
$799$	76.4836			2.70580
$800$		0			0
$801$	−3.07807			−0.108758
$802$		0			0
$803$	−0.104834			−0.00369950
$804$		0			0
$805$	3.67311			0.129460
$806$		0			0
$807$	−4.05203			−0.142638
$808$		0			0
$809$	3.70801			0.130367			0.0651834	−	0.997873i	$-0.479237\pi$
$809$	3.70801			0.130367			0.0651834	+	0.997873i	$0.479237\pi$
$810$		0			0
$811$	1.14352	−	1.98064i	0.0401545	−	0.0695497i	−0.845250	−	0.534372i	$-0.820548\pi$
$811$	1.14352	−	1.98064i	0.0401545	−	0.0695497i	0.885404	+	0.464822i	$0.153882\pi$
$812$		0			0
$813$	22.3639			0.784337
$814$		0			0
$815$	7.92924	−	13.7338i	0.277749	−	0.481075i
$816$		0			0
$817$	15.2740	+	26.4554i	0.534371	+	0.925558i
$818$		0			0
$819$	2.22560			0.0777688
$820$		0			0
$821$	25.2218	+	43.6854i	0.880245	+	1.52463i	0.851068	+	0.525056i	$0.175956\pi$
$821$	25.2218	+	43.6854i	0.880245	+	1.52463i	0.0291776	+	0.999574i	$0.490711\pi$
$822$		0			0
$823$	2.17792	+	3.77226i	0.0759174	+	0.131493i	0.901485	−	0.432811i	$-0.142478\pi$
$823$	2.17792	+	3.77226i	0.0759174	+	0.131493i	−0.825567	+	0.564303i	$0.809145\pi$
$824$		0			0
$825$	1.09530	−	1.89712i	0.0381336	−	0.0660493i
$826$		0			0
$827$	6.15215	+	10.6558i	0.213931	+	0.370540i	0.952941	−	0.303155i	$-0.0980398\pi$
$827$	6.15215	+	10.6558i	0.213931	+	0.370540i	−0.739010	+	0.673694i	$0.764706\pi$
$828$		0			0
$829$	−48.4404			−1.68241			−0.841203	−	0.540720i	$-0.818152\pi$
$829$	−48.4404			−1.68241			−0.841203	+	0.540720i	$0.818152\pi$
$830$		0			0
$831$	−0.341518			−0.0118471
$832$		0			0
$833$	19.1999	−	33.2553i	0.665238	−	1.15223i
$834$		0			0
$835$	9.55406	−	16.5481i	0.330632	−	0.572671i
$836$		0			0
$837$	0.579844	−	1.00432i	0.0200423	−	0.0347144i
$838$		0			0
$839$	−20.0058	+	34.6511i	−0.690678	+	1.19629i	0.280938	+	0.959726i	$0.409354\pi$
$839$	−20.0058	+	34.6511i	−0.690678	+	1.19629i	−0.971616	+	0.236564i	$0.923979\pi$
$840$		0			0
$841$	14.2910	+	24.7528i	0.492795	+	0.853545i
$842$		0			0
$843$	−6.37905	−	11.0488i	−0.219706	−	0.380542i
$844$		0			0
$845$	3.25433	−	5.63666i	0.111952	−	0.193907i
$846$		0			0
$847$	−5.41699			−0.186130
$848$		0			0
$849$	18.8010			0.645249
$850$		0			0
$851$	−9.95011	+	17.2341i	−0.341085	+	0.590777i
$852$		0			0
$853$	−8.94990	−	15.5017i	−0.306439	−	0.530767i	0.671142	−	0.741329i	$-0.265804\pi$
$853$	−8.94990	−	15.5017i	−0.306439	−	0.530767i	−0.977581	+	0.210561i	$0.932471\pi$
$854$		0			0
$855$	−1.66901	−	2.89081i	−0.0570790	−	0.0988636i
$856$		0			0
$857$	2.32144			0.0792990			0.0396495	−	0.999214i	$-0.487376\pi$
$857$	2.32144			0.0792990			0.0396495	+	0.999214i	$0.487376\pi$
$858$		0			0
$859$	−6.11931	+	10.5989i	−0.208788	+	0.361631i	−0.951333	−	0.308165i	$-0.900285\pi$
$859$	−6.11931	+	10.5989i	−0.208788	+	0.361631i	0.742545	+	0.669796i	$0.233619\pi$
$860$		0			0
$861$	−3.49679	−	6.05662i	−0.119170	−	0.206409i
$862$		0			0
$863$	−41.5235			−1.41348			−0.706738	−	0.707476i	$-0.749834\pi$
$863$	−41.5235			−1.41348			−0.706738	+	0.707476i	$0.749834\pi$
$864$		0			0
$865$	−4.12739	−	7.14884i	−0.140335	−	0.243068i
$866$		0			0
$867$	−10.4534	+	18.1058i	−0.355016	+	0.614905i
$868$		0			0
$869$	3.45649	+	5.98682i	0.117254	+	0.203089i
$870$		0			0
$871$	−19.5667	+	7.21565i	−0.662991	+	0.244493i
$872$		0			0
$873$	1.76819	+	3.06259i	0.0598440	+	0.103653i
$874$		0			0
$875$	−0.436767	+	0.756503i	−0.0147654	+	0.0255745i
$876$		0			0
$877$	9.09708	+	15.7566i	0.307187	+	0.532063i	0.977746	−	0.209793i	$-0.0672791\pi$
$877$	9.09708	+	15.7566i	0.307187	+	0.532063i	−0.670559	+	0.741856i	$0.733946\pi$
$878$		0			0
$879$	−17.9116			−0.604144
$880$		0			0
$881$	−4.77004	−	8.26195i	−0.160707	−	0.278352i	0.774416	−	0.632677i	$-0.218044\pi$
$881$	−4.77004	−	8.26195i	−0.160707	−	0.278352i	−0.935122	+	0.354325i	$0.884711\pi$
$882$		0			0
$883$	−23.9079	+	41.4098i	−0.804566	+	1.39355i	0.112017	+	0.993706i	$0.464269\pi$
$883$	−23.9079	+	41.4098i	−0.804566	+	1.39355i	−0.916584	+	0.399843i	$0.869065\pi$
$884$		0			0
$885$	−3.64380			−0.122485
$886$		0			0
$887$	23.6204	+	40.9117i	0.793095	+	1.37368i	0.924042	+	0.382291i	$0.124865\pi$
$887$	23.6204	+	40.9117i	0.793095	+	1.37368i	−0.130947	+	0.991389i	$0.541802\pi$
$888$		0			0
$889$	−7.95689	−	13.7817i	−0.266866	−	0.462225i
$890$		0			0
$891$	1.09530	−	1.89712i	0.0366941	−	0.0635560i
$892$		0			0
$893$	41.4667			1.38763
$894$		0			0
$895$	−1.75612			−0.0587007
$896$		0			0
$897$	−5.35662	+	9.27793i	−0.178852	+	0.309781i
$898$		0			0
$899$	0.374849	+	0.649258i	0.0125019	+	0.0216540i
$900$		0			0
$901$	26.6688	+	46.1918i	0.888467	+	1.53887i
$902$		0			0
$903$	3.99710	−	6.92318i	0.133015	−	0.230389i
$904$		0			0
$905$	−1.58843	+	2.75125i	−0.0528014	+	0.0914546i
$906$		0			0
$907$	−17.5111	+	30.3302i	−0.581448	+	1.00710i	0.413860	+	0.910341i	$0.364180\pi$
$907$	−17.5111	+	30.3302i	−0.581448	+	1.00710i	−0.995308	+	0.0967570i	$0.969153\pi$
$908$		0			0
$909$	−1.45576	+	2.52145i	−0.0482845	+	0.0836312i
$910$		0			0
$911$	−40.8606			−1.35377			−0.676886	−	0.736088i	$-0.736671\pi$
$911$	−40.8606			−1.35377			−0.676886	+	0.736088i	$0.736671\pi$
$912$		0			0
$913$	−10.0570			−0.332837
$914$		0			0
$915$	−2.99641	−	5.18993i	−0.0990581	−	0.171574i
$916$		0			0
$917$	3.02291	−	5.23583i	0.0998252	−	0.172902i
$918$		0			0
$919$	−20.3055	−	35.1701i	−0.669816	−	1.16016i	−0.977955	−	0.208814i	$-0.933040\pi$
$919$	−20.3055	−	35.1701i	−0.669816	−	1.16016i	0.308139	−	0.951341i	$-0.400294\pi$
$920$		0			0
$921$	11.6094	+	20.1080i	0.382541	+	0.662581i
$922$		0			0
$923$	−27.0942			−0.891818
$924$		0			0
$925$	−2.36632	−	4.09859i	−0.0778043	−	0.134761i
$926$		0			0
$927$	3.42216	−	5.92736i	0.112399	−	0.194680i
$928$		0			0
$929$	35.4723			1.16381			0.581905	−	0.813257i	$-0.302308\pi$
$929$	35.4723			1.16381			0.581905	+	0.813257i	$0.302308\pi$
$930$		0			0
$931$	10.4095	−	18.0298i	0.341158	−	0.590903i
$932$		0			0
$933$	−0.428849			−0.0140399
$934$		0			0
$935$	−13.4872			−0.441080
$936$		0			0
$937$	20.2336			0.661002			0.330501	−	0.943806i	$-0.392782\pi$
$937$	20.2336			0.661002			0.330501	+	0.943806i	$0.392782\pi$
$938$		0			0
$939$	26.4449			0.862996
$940$		0			0
$941$	17.2172			0.561264			0.280632	−	0.959815i	$-0.409456\pi$
$941$	17.2172			0.561264			0.280632	+	0.959815i	$0.409456\pi$
$942$		0			0
$943$	33.6646			1.09627
$944$		0			0
$945$	−0.436767	+	0.756503i	−0.0142080	+	0.0246090i
$946$		0			0
$947$	−49.7168			−1.61558			−0.807789	−	0.589471i	$-0.799336\pi$
$947$	−49.7168			−1.61558			−0.807789	+	0.589471i	$0.799336\pi$
$948$		0			0
$949$	−0.0609640	+	0.105593i	−0.00197898	+	0.00342769i
$950$		0			0
$951$	13.5428	+	23.4567i	0.439154	+	0.760637i
$952$		0			0
$953$	−30.3052			−0.981682			−0.490841	−	0.871249i	$-0.663310\pi$
$953$	−30.3052			−0.981682			−0.490841	+	0.871249i	$0.663310\pi$
$954$		0			0
$955$	−6.01274	−	10.4144i	−0.194568	−	0.337001i
$956$		0			0
$957$	0.708077	+	1.22643i	0.0228889	+	0.0396447i
$958$		0			0
$959$	−1.34884	+	2.33626i	−0.0435564	+	0.0754418i
$960$		0			0
$961$	14.8276	+	25.6821i	0.478308	+	0.828455i
$962$		0			0
$963$	10.6982			0.344743
$964$		0			0
$965$	21.9520			0.706660
$966$		0			0
$967$	−21.0317	+	36.4280i	−0.676334	+	1.17145i	0.299743	+	0.954020i	$0.403099\pi$
$967$	−21.0317	+	36.4280i	−0.676334	+	1.17145i	−0.976077	+	0.217425i	$0.930234\pi$
$968$		0			0
$969$	−10.2758	+	17.7983i	−0.330108	+	0.571763i
$970$		0			0
$971$	20.3806	−	35.3003i	0.654045	−	1.13284i	−0.328087	−	0.944648i	$-0.606404\pi$
$971$	20.3806	−	35.3003i	0.654045	−	1.13284i	0.982132	−	0.188192i	$-0.0602628\pi$
$972$		0			0
$973$	−0.986622	+	1.70888i	−0.0316296	+	0.0547842i
$974$		0			0
$975$	−1.27391	−	2.20647i	−0.0407976	−	0.0706636i
$976$		0			0
$977$	−26.1615	−	45.3131i	−0.836981	−	1.44969i	−0.892407	−	0.451231i	$-0.850985\pi$
$977$	−26.1615	−	45.3131i	−0.836981	−	1.44969i	0.0554256	−	0.998463i	$-0.482348\pi$
$978$		0			0
$979$	−3.37143	+	5.83948i	−0.107751	+	0.186631i
$980$		0			0
$981$	5.25484			0.167774
$982$		0			0
$983$	35.7056			1.13883			0.569416	−	0.822049i	$-0.307169\pi$
$983$	35.7056			1.13883			0.569416	+	0.822049i	$0.307169\pi$
$984$		0			0
$985$	8.82749	−	15.2897i	0.281267	−	0.487169i
$986$		0			0
$987$	−5.42576	−	9.39768i	−0.172704	−	0.299132i
$988$		0			0
$989$	19.2406	+	33.3257i	0.611815	+	1.05969i
$990$		0			0
$991$	−23.6689			−0.751867			−0.375933	−	0.926647i	$-0.622678\pi$
$991$	−23.6689			−0.751867			−0.375933	+	0.926647i	$0.622678\pi$
$992$		0			0
$993$	−4.07232	+	7.05347i	−0.129231	+	0.223835i
$994$		0			0
$995$	−2.39395	−	4.14645i	−0.0758935	−	0.131451i
$996$		0			0
$997$	41.6861			1.32021			0.660106	−	0.751173i	$-0.270511\pi$
$997$	41.6861			1.32021			0.660106	+	0.751173i	$0.270511\pi$
$998$		0			0
$999$	−2.36632	−	4.09859i	−0.0748672	−	0.129674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.5	✓	24
67.29	even	3	inner	4020.2.q.m.3781.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.5	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.5	yes	24	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.436767 + 0.756503i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.436767 + 0.756503i) q^{7} +1.00000 q^{9} +(1.09530 - 1.89712i) q^{11} +(-1.27391 - 2.20647i) q^{13} +1.00000 q^{15} +(-3.07842 - 5.33199i) q^{17} +(-1.66901 - 2.89081i) q^{19} +(-0.436767 + 0.756503i) q^{21} +(-2.10244 - 3.64153i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(-0.323233 + 0.559856i) q^{29} +(0.579844 - 1.00432i) q^{31} +(1.09530 - 1.89712i) q^{33} +(-0.436767 + 0.756503i) q^{35} +(-2.36632 - 4.09859i) q^{37} +(-1.27391 - 2.20647i) q^{39} +(-4.00304 + 6.93346i) q^{41} -9.15156 q^{43} +1.00000 q^{45} +(-6.21127 + 10.7582i) q^{47} +(3.11847 + 5.40135i) q^{49} +(-3.07842 - 5.33199i) q^{51} -8.66314 q^{53} +(1.09530 - 1.89712i) q^{55} +(-1.66901 - 2.89081i) q^{57} -3.64380 q^{59} +(-2.99641 - 5.18993i) q^{61} +(-0.436767 + 0.756503i) q^{63} +(-1.27391 - 2.20647i) q^{65} +(1.38723 - 8.06694i) q^{67} +(-2.10244 - 3.64153i) q^{69} +(5.31716 - 9.20959i) q^{71} +(-0.0239280 - 0.0414445i) q^{73} +1.00000 q^{75} +(0.956786 + 1.65720i) q^{77} +(-1.57787 + 2.73295i) q^{79} +1.00000 q^{81} +(-2.29548 - 3.97588i) q^{83} +(-3.07842 - 5.33199i) q^{85} +(-0.323233 + 0.559856i) q^{87} -3.07807 q^{89} +2.22560 q^{91} +(0.579844 - 1.00432i) q^{93} +(-1.66901 - 2.89081i) q^{95} +(1.76819 + 3.06259i) q^{97} +(1.09530 - 1.89712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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