LMFDB - Embedded newform 4020.2.q.m.841.6

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			841.6
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-0.388910 + 0.673613i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.388910 + 0.673613i) q^{7} +1.00000 q^{9} +(-2.02292 + 3.50381i) q^{11} +(-1.61408 - 2.79568i) q^{13} +1.00000 q^{15} +(1.72569 + 2.98898i) q^{17} +(0.784100 + 1.35810i) q^{19} +(-0.388910 + 0.673613i) q^{21} +(-0.0608178 - 0.105339i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.58802 - 7.94668i) q^{29} +(3.20627 - 5.55342i) q^{31} +(-2.02292 + 3.50381i) q^{33} +(-0.388910 + 0.673613i) q^{35} +(2.07970 + 3.60215i) q^{37} +(-1.61408 - 2.79568i) q^{39} +(-5.36270 + 9.28847i) q^{41} +11.3172 q^{43} +1.00000 q^{45} +(-2.40319 + 4.16244i) q^{47} +(3.19750 + 5.53823i) q^{49} +(1.72569 + 2.98898i) q^{51} -6.61886 q^{53} +(-2.02292 + 3.50381i) q^{55} +(0.784100 + 1.35810i) q^{57} +13.5775 q^{59} +(-2.09348 - 3.62601i) q^{61} +(-0.388910 + 0.673613i) q^{63} +(-1.61408 - 2.79568i) q^{65} +(-1.35538 + 8.07236i) q^{67} +(-0.0608178 - 0.105339i) q^{69} +(-4.29099 + 7.43221i) q^{71} +(0.944715 + 1.63629i) q^{73} +1.00000 q^{75} +(-1.57347 - 2.72533i) q^{77} +(-8.70442 + 15.0765i) q^{79} +1.00000 q^{81} +(7.60268 + 13.1682i) q^{83} +(1.72569 + 2.98898i) q^{85} +(4.58802 - 7.94668i) q^{87} -6.89644 q^{89} +2.51094 q^{91} +(3.20627 - 5.55342i) q^{93} +(0.784100 + 1.35810i) q^{95} +(1.00651 + 1.74332i) q^{97} +(-2.02292 + 3.50381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−0.388910	+	0.673613i	−0.146994	+	0.254602i	−0.930115	−	0.367268i	$-0.880293\pi$
$7$	−0.388910	+	0.673613i	−0.146994	+	0.254602i	0.783121	+	0.621869i	$0.213627\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.02292	+	3.50381i	−0.609934	+	1.05644i	0.381316	+	0.924445i	$0.375471\pi$
$11$	−2.02292	+	3.50381i	−0.609934	+	1.05644i	−0.991251	+	0.131993i	$0.957862\pi$
$12$		0			0
$13$	−1.61408	−	2.79568i	−0.447667	−	0.775381i	0.550567	−	0.834791i	$-0.314411\pi$
$13$	−1.61408	−	2.79568i	−0.447667	−	0.775381i	−0.998234	+	0.0594097i	$0.981078\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.72569	+	2.98898i	0.418540	+	0.724933i	0.995793	−	0.0916326i	$-0.0292085\pi$
$17$	1.72569	+	2.98898i	0.418540	+	0.724933i	−0.577253	+	0.816566i	$0.695875\pi$
$18$		0			0
$19$	0.784100	+	1.35810i	0.179885	+	0.311570i	0.941841	−	0.336059i	$-0.109094\pi$
$19$	0.784100	+	1.35810i	0.179885	+	0.311570i	−0.761956	+	0.647629i	$0.775761\pi$
$20$		0			0
$21$	−0.388910	+	0.673613i	−0.0848672	+	0.146994i
$22$		0			0
$23$	−0.0608178	−	0.105339i	−0.0126814	−	0.0219648i	0.859615	−	0.510942i	$-0.170703\pi$
$23$	−0.0608178	−	0.105339i	−0.0126814	−	0.0219648i	−0.872296	+	0.488977i	$0.837370\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.58802	−	7.94668i	0.851973	−	1.47566i	−0.0274516	−	0.999623i	$-0.508739\pi$
$29$	4.58802	−	7.94668i	0.851973	−	1.47566i	0.879425	−	0.476038i	$-0.157927\pi$
$30$		0			0
$31$	3.20627	−	5.55342i	0.575863	−	0.997424i	−0.420084	−	0.907485i	$-0.638000\pi$
$31$	3.20627	−	5.55342i	0.575863	−	0.997424i	0.995947	−	0.0899389i	$-0.0286672\pi$
$32$		0			0
$33$	−2.02292	+	3.50381i	−0.352146	+	0.609934i
$34$		0			0
$35$	−0.388910	+	0.673613i	−0.0657379	+	0.113861i
$36$		0			0
$37$	2.07970	+	3.60215i	0.341901	+	0.592190i	0.984786	−	0.173773i	$-0.0555959\pi$
$37$	2.07970	+	3.60215i	0.341901	+	0.592190i	−0.642885	+	0.765963i	$0.722263\pi$
$38$		0			0
$39$	−1.61408	−	2.79568i	−0.258460	−	0.447667i
$40$		0			0
$41$	−5.36270	+	9.28847i	−0.837513	+	1.45061i	0.0544550	+	0.998516i	$0.482658\pi$
$41$	−5.36270	+	9.28847i	−0.837513	+	1.45061i	−0.891968	+	0.452099i	$0.850675\pi$
$42$		0			0
$43$	11.3172			1.72585			0.862926	−	0.505330i	$-0.168629\pi$
$43$	11.3172			1.72585			0.862926	+	0.505330i	$0.168629\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−2.40319	+	4.16244i	−0.350541	+	0.607154i	−0.986344	−	0.164697i	$-0.947335\pi$
$47$	−2.40319	+	4.16244i	−0.350541	+	0.607154i	0.635804	+	0.771851i	$0.280669\pi$
$48$		0			0
$49$	3.19750	+	5.53823i	0.456785	+	0.791175i
$50$		0			0
$51$	1.72569	+	2.98898i	0.241644	+	0.418540i
$52$		0			0
$53$	−6.61886			−0.909171			−0.454586	−	0.890703i	$-0.650213\pi$
$53$	−6.61886			−0.909171			−0.454586	+	0.890703i	$0.650213\pi$
$54$		0			0
$55$	−2.02292	+	3.50381i	−0.272771	+	0.472453i
$56$		0			0
$57$	0.784100	+	1.35810i	0.103857	+	0.179885i
$58$		0			0
$59$	13.5775			1.76764			0.883820	−	0.467826i	$-0.154963\pi$
$59$	13.5775			1.76764			0.883820	+	0.467826i	$0.154963\pi$
$60$		0			0
$61$	−2.09348	−	3.62601i	−0.268043	−	0.464263i	0.700314	−	0.713835i	$-0.253043\pi$
$61$	−2.09348	−	3.62601i	−0.268043	−	0.464263i	−0.968356	+	0.249572i	$0.919710\pi$
$62$		0			0
$63$	−0.388910	+	0.673613i	−0.0489981	+	0.0848672i
$64$		0			0
$65$	−1.61408	−	2.79568i	−0.200203	−	0.346761i
$66$		0			0
$67$	−1.35538	+	8.07236i	−0.165586	+	0.986195i
$67$	−1.35538	+	8.07236i	−0.165586	+	0.986195i
$68$		0			0
$69$	−0.0608178	−	0.105339i	−0.00732160	−	0.0126814i
$70$		0			0
$71$	−4.29099	+	7.43221i	−0.509246	+	0.882040i	0.490696	+	0.871331i	$0.336742\pi$
$71$	−4.29099	+	7.43221i	−0.509246	+	0.882040i	−0.999943	+	0.0107098i	$0.996591\pi$
$72$		0			0
$73$	0.944715	+	1.63629i	0.110571	+	0.191514i	0.916000	−	0.401177i	$-0.131399\pi$
$73$	0.944715	+	1.63629i	0.110571	+	0.191514i	−0.805430	+	0.592691i	$0.798066\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−1.57347	−	2.72533i	−0.179314	−	0.310581i
$78$		0			0
$79$	−8.70442	+	15.0765i	−0.979324	+	1.69624i	−0.314465	+	0.949269i	$0.601825\pi$
$79$	−8.70442	+	15.0765i	−0.979324	+	1.69624i	−0.664859	+	0.746969i	$0.731508\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	7.60268	+	13.1682i	0.834502	+	1.44540i	0.894435	+	0.447198i	$0.147578\pi$
$83$	7.60268	+	13.1682i	0.834502	+	1.44540i	−0.0599324	+	0.998202i	$0.519089\pi$
$84$		0			0
$85$	1.72569	+	2.98898i	0.187177	+	0.324200i
$86$		0			0
$87$	4.58802	−	7.94668i	0.491887	−	0.851973i
$88$		0			0
$89$	−6.89644			−0.731022			−0.365511	−	0.930807i	$-0.619106\pi$
$89$	−6.89644			−0.731022			−0.365511	+	0.930807i	$0.619106\pi$
$90$		0			0
$91$	2.51094			0.263218
$92$		0			0
$93$	3.20627	−	5.55342i	0.332475	−	0.575863i
$94$		0			0
$95$	0.784100	+	1.35810i	0.0804469	+	0.139338i
$96$		0			0
$97$	1.00651	+	1.74332i	0.102195	+	0.177008i	0.912589	−	0.408878i	$-0.134080\pi$
$97$	1.00651	+	1.74332i	0.102195	+	0.177008i	−0.810394	+	0.585886i	$0.800747\pi$
$98$		0			0
$99$	−2.02292	+	3.50381i	−0.203311	+	0.352146i
$100$		0			0
$101$	−5.54767	+	9.60885i	−0.552014	+	0.956117i	0.446115	+	0.894976i	$0.352807\pi$
$101$	−5.54767	+	9.60885i	−0.552014	+	0.956117i	−0.998129	+	0.0611410i	$0.980526\pi$
$102$		0			0
$103$	0.927303	−	1.60614i	0.0913698	−	0.158257i	−0.816718	−	0.577037i	$-0.804209\pi$
$103$	0.927303	−	1.60614i	0.0913698	−	0.158257i	0.908088	+	0.418780i	$0.137542\pi$
$104$		0			0
$105$	−0.388910	+	0.673613i	−0.0379538	+	0.0657379i
$106$		0			0
$107$	10.6658			1.03110			0.515549	−	0.856860i	$-0.327588\pi$
$107$	10.6658			1.03110			0.515549	+	0.856860i	$0.327588\pi$
$108$		0			0
$109$	5.99046			0.573782			0.286891	−	0.957963i	$-0.407378\pi$
$109$	5.99046			0.573782			0.286891	+	0.957963i	$0.407378\pi$
$110$		0			0
$111$	2.07970	+	3.60215i	0.197397	+	0.341901i
$112$		0			0
$113$	1.99102	−	3.44856i	0.187300	−	0.324413i	−0.757049	−	0.653358i	$-0.773360\pi$
$113$	1.99102	−	3.44856i	0.187300	−	0.324413i	0.944349	+	0.328945i	$0.106693\pi$
$114$		0			0
$115$	−0.0608178	−	0.105339i	−0.00567129	−	0.00982296i
$116$		0			0
$117$	−1.61408	−	2.79568i	−0.149222	−	0.258460i
$118$		0			0
$119$	−2.68455			−0.246092
$120$		0			0
$121$	−2.68444	−	4.64958i	−0.244040	−	0.422689i
$122$		0			0
$123$	−5.36270	+	9.28847i	−0.483538	+	0.837513i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.91093	−	3.30983i	0.169568	−	0.293700i	−0.768700	−	0.639609i	$-0.779096\pi$
$127$	1.91093	−	3.30983i	0.169568	−	0.293700i	0.938268	+	0.345909i	$0.112429\pi$
$128$		0			0
$129$	11.3172			0.996421
$130$		0			0
$131$	11.0460			0.965092			0.482546	−	0.875871i	$-0.339712\pi$
$131$	11.0460			0.965092			0.482546	+	0.875871i	$0.339712\pi$
$132$		0			0
$133$	−1.21978			−0.105768
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	4.07308			0.347987			0.173993	−	0.984747i	$-0.444333\pi$
$137$	4.07308			0.347987			0.173993	+	0.984747i	$0.444333\pi$
$138$		0			0
$139$	−2.84340			−0.241174			−0.120587	−	0.992703i	$-0.538478\pi$
$139$	−2.84340			−0.241174			−0.120587	+	0.992703i	$0.538478\pi$
$140$		0			0
$141$	−2.40319	+	4.16244i	−0.202385	+	0.350541i
$142$		0			0
$143$	13.0607			1.09219
$144$		0			0
$145$	4.58802	−	7.94668i	0.381014	−	0.659936i
$146$		0			0
$147$	3.19750	+	5.53823i	0.263725	+	0.456785i
$148$		0			0
$149$	−1.75153			−0.143491			−0.0717457	−	0.997423i	$-0.522857\pi$
$149$	−1.75153			−0.143491			−0.0717457	+	0.997423i	$0.522857\pi$
$150$		0			0
$151$	−3.46264	−	5.99747i	−0.281786	−	0.488067i	0.690039	−	0.723772i	$-0.257593\pi$
$151$	−3.46264	−	5.99747i	−0.281786	−	0.488067i	−0.971825	+	0.235705i	$0.924260\pi$
$152$		0			0
$153$	1.72569	+	2.98898i	0.139513	+	0.241644i
$154$		0			0
$155$	3.20627	−	5.55342i	0.257534	−	0.446062i
$156$		0			0
$157$	−9.82546	−	17.0182i	−0.784157	−	1.35820i	−0.929502	−	0.368818i	$-0.879762\pi$
$157$	−9.82546	−	17.0182i	−0.784157	−	1.35820i	0.145345	−	0.989381i	$-0.453571\pi$
$158$		0			0
$159$	−6.61886			−0.524910
$160$		0			0
$161$	0.0946106			0.00745636
$162$		0			0
$163$	2.27507	−	3.94055i	0.178198	−	0.308647i	−0.763066	−	0.646321i	$-0.776307\pi$
$163$	2.27507	−	3.94055i	0.178198	−	0.308647i	0.941263	+	0.337674i	$0.109640\pi$
$164$		0			0
$165$	−2.02292	+	3.50381i	−0.157484	+	0.272771i
$166$		0			0
$167$	−1.60758	+	2.78441i	−0.124398	+	0.215464i	−0.921498	−	0.388384i	$-0.873033\pi$
$167$	−1.60758	+	2.78441i	−0.124398	+	0.215464i	0.797099	+	0.603848i	$0.206367\pi$
$168$		0			0
$169$	1.28946	−	2.23341i	0.0991894	−	0.171801i
$170$		0			0
$171$	0.784100	+	1.35810i	0.0599616	+	0.103857i
$172$		0			0
$173$	6.18331	+	10.7098i	0.470108	+	0.814251i	0.999416	−	0.0341788i	$-0.0108816\pi$
$173$	6.18331	+	10.7098i	0.470108	+	0.814251i	−0.529308	+	0.848430i	$0.677548\pi$
$174$		0			0
$175$	−0.388910	+	0.673613i	−0.0293989	+	0.0509203i
$176$		0			0
$177$	13.5775			1.02055
$178$		0			0
$179$	−9.94184			−0.743088			−0.371544	−	0.928415i	$-0.621172\pi$
$179$	−9.94184			−0.743088			−0.371544	+	0.928415i	$0.621172\pi$
$180$		0			0
$181$	−9.23966	+	16.0036i	−0.686778	+	1.18953i	0.286096	+	0.958201i	$0.407642\pi$
$181$	−9.23966	+	16.0036i	−0.686778	+	1.18953i	−0.972874	+	0.231334i	$0.925691\pi$
$182$		0			0
$183$	−2.09348	−	3.62601i	−0.154754	−	0.268043i
$184$		0			0
$185$	2.07970	+	3.60215i	0.152903	+	0.264835i
$186$		0			0
$187$	−13.9637			−1.02113
$188$		0			0
$189$	−0.388910	+	0.673613i	−0.0282891	+	0.0489981i
$190$		0			0
$191$	−0.672641	−	1.16505i	−0.0486706	−	0.0842999i	0.840664	−	0.541557i	$-0.182165\pi$
$191$	−0.672641	−	1.16505i	−0.0486706	−	0.0842999i	−0.889334	+	0.457257i	$0.848832\pi$
$192$		0			0
$193$	−5.60599			−0.403528			−0.201764	−	0.979434i	$-0.564667\pi$
$193$	−5.60599			−0.403528			−0.201764	+	0.979434i	$0.564667\pi$
$194$		0			0
$195$	−1.61408	−	2.79568i	−0.115587	−	0.200203i
$196$		0			0
$197$	−4.76907	+	8.26027i	−0.339782	+	0.588520i	−0.984392	−	0.175992i	$-0.943687\pi$
$197$	−4.76907	+	8.26027i	−0.339782	+	0.588520i	0.644610	+	0.764512i	$0.277020\pi$
$198$		0			0
$199$	−9.05298	−	15.6802i	−0.641748	−	1.11154i	−0.985042	−	0.172313i	$-0.944876\pi$
$199$	−9.05298	−	15.6802i	−0.641748	−	1.11154i	0.343294	−	0.939228i	$-0.388457\pi$
$200$		0			0
$201$	−1.35538	+	8.07236i	−0.0956013	+	0.569380i
$202$		0			0
$203$	3.56865	+	6.18109i	0.250470	+	0.433828i
$204$		0			0
$205$	−5.36270	+	9.28847i	−0.374547	+	0.648735i
$206$		0			0
$207$	−0.0608178	−	0.105339i	−0.00422713	−	0.00732160i
$208$		0			0
$209$	−6.34470			−0.438872
$210$		0			0
$211$	7.13049	+	12.3504i	0.490883	+	0.850235i	0.999945	−	0.0104954i	$-0.00334084\pi$
$211$	7.13049	+	12.3504i	0.490883	+	0.850235i	−0.509062	+	0.860730i	$0.670008\pi$
$212$		0			0
$213$	−4.29099	+	7.43221i	−0.294013	+	0.509246i
$214$		0			0
$215$	11.3172			0.771824
$216$		0			0
$217$	2.49390	+	4.31957i	0.169297	+	0.293231i
$218$		0			0
$219$	0.944715	+	1.63629i	0.0638379	+	0.110571i
$220$		0			0
$221$	5.57081	−	9.64892i	0.374733	−	0.649056i
$222$		0			0
$223$	−6.84704			−0.458512			−0.229256	−	0.973366i	$-0.573629\pi$
$223$	−6.84704			−0.458512			−0.229256	+	0.973366i	$0.573629\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	4.24144	−	7.34639i	0.281514	−	0.487597i	−0.690244	−	0.723577i	$-0.742497\pi$
$227$	4.24144	−	7.34639i	0.281514	−	0.487597i	0.971758	+	0.235980i	$0.0758300\pi$
$228$		0			0
$229$	−2.36664	−	4.09913i	−0.156392	−	0.270878i	0.777173	−	0.629287i	$-0.216653\pi$
$229$	−2.36664	−	4.09913i	−0.156392	−	0.270878i	−0.933565	+	0.358408i	$0.883320\pi$
$230$		0			0
$231$	−1.57347	−	2.72533i	−0.103527	−	0.179314i
$232$		0			0
$233$	−5.52791	+	9.57462i	−0.362145	+	0.627254i	−0.988314	−	0.152434i	$-0.951289\pi$
$233$	−5.52791	+	9.57462i	−0.362145	+	0.627254i	0.626168	+	0.779688i	$0.284622\pi$
$234$		0			0
$235$	−2.40319	+	4.16244i	−0.156767	+	0.271528i
$236$		0			0
$237$	−8.70442	+	15.0765i	−0.565413	+	0.979324i
$238$		0			0
$239$	11.0356	−	19.1143i	0.713836	−	1.23640i	−0.249571	−	0.968356i	$-0.580290\pi$
$239$	11.0356	−	19.1143i	0.713836	−	1.23640i	0.963407	−	0.268043i	$-0.0863769\pi$
$240$		0			0
$241$	18.7368			1.20694			0.603471	−	0.797385i	$-0.293784\pi$
$241$	18.7368			1.20694			0.603471	+	0.797385i	$0.293784\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	3.19750	+	5.53823i	0.204281	+	0.353824i
$246$		0			0
$247$	2.53121	−	4.38418i	0.161057	−	0.278959i
$248$		0			0
$249$	7.60268	+	13.1682i	0.481800	+	0.834502i
$250$		0			0
$251$	−11.1549	−	19.3209i	−0.704092	−	1.21952i	−0.967018	−	0.254708i	$-0.918021\pi$
$251$	−11.1549	−	19.3209i	−0.704092	−	1.21952i	0.262926	−	0.964816i	$-0.415313\pi$
$252$		0			0
$253$	0.492119			0.0309392
$254$		0			0
$255$	1.72569	+	2.98898i	0.108067	+	0.187177i
$256$		0			0
$257$	6.83867	−	11.8449i	0.426584	−	0.738866i	−0.569983	−	0.821657i	$-0.693050\pi$
$257$	6.83867	−	11.8449i	0.426584	−	0.738866i	0.996567	+	0.0827910i	$0.0263834\pi$
$258$		0			0
$259$	−3.23527			−0.201030
$260$		0			0
$261$	4.58802	−	7.94668i	0.283991	−	0.491887i
$262$		0			0
$263$	17.8436			1.10028			0.550141	−	0.835072i	$-0.314574\pi$
$263$	17.8436			1.10028			0.550141	+	0.835072i	$0.314574\pi$
$264$		0			0
$265$	−6.61886			−0.406594
$266$		0			0
$267$	−6.89644			−0.422056
$268$		0			0
$269$	6.61717			0.403456			0.201728	−	0.979442i	$-0.435344\pi$
$269$	6.61717			0.403456			0.201728	+	0.979442i	$0.435344\pi$
$270$		0			0
$271$	3.41260			0.207301			0.103650	−	0.994614i	$-0.466948\pi$
$271$	3.41260			0.207301			0.103650	+	0.994614i	$0.466948\pi$
$272$		0			0
$273$	2.51094			0.151969
$274$		0			0
$275$	−2.02292	+	3.50381i	−0.121987	+	0.211287i
$276$		0			0
$277$	−20.2164			−1.21469			−0.607344	−	0.794439i	$-0.707765\pi$
$277$	−20.2164			−1.21469			−0.607344	+	0.794439i	$0.707765\pi$
$278$		0			0
$279$	3.20627	−	5.55342i	0.191954	−	0.332475i
$280$		0			0
$281$	−5.54229	−	9.59953i	−0.330625	−	0.572660i	0.652009	−	0.758211i	$-0.273926\pi$
$281$	−5.54229	−	9.59953i	−0.330625	−	0.572660i	−0.982635	+	0.185551i	$0.940593\pi$
$282$		0			0
$283$	26.5624			1.57897			0.789486	−	0.613769i	$-0.210347\pi$
$283$	26.5624			1.57897			0.789486	+	0.613769i	$0.210347\pi$
$284$		0			0
$285$	0.784100	+	1.35810i	0.0464461	+	0.0804469i
$286$		0			0
$287$	−4.17122	−	7.22476i	−0.246219	−	0.426464i
$288$		0			0
$289$	2.54402	−	4.40637i	0.149648	−	0.259198i
$290$		0			0
$291$	1.00651	+	1.74332i	0.0590025	+	0.102195i
$292$		0			0
$293$	19.3768			1.13201			0.566003	−	0.824403i	$-0.308489\pi$
$293$	19.3768			1.13201			0.566003	+	0.824403i	$0.308489\pi$
$294$		0			0
$295$	13.5775			0.790513
$296$		0			0
$297$	−2.02292	+	3.50381i	−0.117382	+	0.203311i
$298$		0			0
$299$	−0.196330	+	0.340054i	−0.0113541	+	0.0196658i
$300$		0			0
$301$	−4.40136	+	7.62339i	−0.253690	+	0.439405i
$302$		0			0
$303$	−5.54767	+	9.60885i	−0.318706	+	0.552014i
$304$		0			0
$305$	−2.09348	−	3.62601i	−0.119872	−	0.207625i
$306$		0			0
$307$	−6.02352	−	10.4330i	−0.343781	−	0.595445i	0.641351	−	0.767248i	$-0.278374\pi$
$307$	−6.02352	−	10.4330i	−0.343781	−	0.595445i	−0.985131	+	0.171802i	$0.945041\pi$
$308$		0			0
$309$	0.927303	−	1.60614i	0.0527524	−	0.0913698i
$310$		0			0
$311$	11.4317			0.648234			0.324117	−	0.946017i	$-0.394933\pi$
$311$	11.4317			0.648234			0.324117	+	0.946017i	$0.394933\pi$
$312$		0			0
$313$	−13.3601			−0.755158			−0.377579	−	0.925977i	$-0.623243\pi$
$313$	−13.3601			−0.755158			−0.377579	+	0.925977i	$0.623243\pi$
$314$		0			0
$315$	−0.388910	+	0.673613i	−0.0219126	+	0.0379538i
$316$		0			0
$317$	−3.83349	−	6.63980i	−0.215310	−	0.372928i	0.738058	−	0.674737i	$-0.235743\pi$
$317$	−3.83349	−	6.63980i	−0.215310	−	0.372928i	−0.953369	+	0.301809i	$0.902410\pi$
$318$		0			0
$319$	18.5624	+	32.1510i	1.03930	+	1.80011i
$320$		0			0
$321$	10.6658			0.595305
$322$		0			0
$323$	−2.70622	+	4.68731i	−0.150578	+	0.260809i
$324$		0			0
$325$	−1.61408	−	2.79568i	−0.0895333	−	0.155076i
$326$		0			0
$327$	5.99046			0.331273
$328$		0			0
$329$	−1.86925	−	3.23763i	−0.103055	−	0.178496i
$330$		0			0
$331$	8.48244	−	14.6920i	0.466237	−	0.807547i	−0.533019	−	0.846103i	$-0.678943\pi$
$331$	8.48244	−	14.6920i	0.466237	−	0.807547i	0.999256	+	0.0385566i	$0.0122760\pi$
$332$		0			0
$333$	2.07970	+	3.60215i	0.113967	+	0.197397i
$334$		0			0
$335$	−1.35538	+	8.07236i	−0.0740524	+	0.441040i
$336$		0			0
$337$	−16.6555	−	28.8482i	−0.907284	−	1.57146i	−0.817822	−	0.575471i	$-0.804819\pi$
$337$	−16.6555	−	28.8482i	−0.907284	−	1.57146i	−0.0894616	−	0.995990i	$-0.528515\pi$
$338$		0			0
$339$	1.99102	−	3.44856i	0.108138	−	0.187300i
$340$		0			0
$341$	12.9721	+	22.4683i	0.702477	+	1.21673i
$342$		0			0
$343$	−10.4189			−0.562568
$344$		0			0
$345$	−0.0608178	−	0.105339i	−0.00327432	−	0.00567129i
$346$		0			0
$347$	−14.7518	+	25.5509i	−0.791918	+	1.37164i	0.132861	+	0.991135i	$0.457584\pi$
$347$	−14.7518	+	25.5509i	−0.791918	+	1.37164i	−0.924778	+	0.380507i	$0.875750\pi$
$348$		0			0
$349$	−15.2694			−0.817355			−0.408677	−	0.912679i	$-0.634010\pi$
$349$	−15.2694			−0.817355			−0.408677	+	0.912679i	$0.634010\pi$
$350$		0			0
$351$	−1.61408	−	2.79568i	−0.0861535	−	0.149222i
$352$		0			0
$353$	14.1559	+	24.5188i	0.753444	+	1.30500i	0.946144	+	0.323745i	$0.104942\pi$
$353$	14.1559	+	24.5188i	0.753444	+	1.30500i	−0.192701	+	0.981258i	$0.561725\pi$
$354$		0			0
$355$	−4.29099	+	7.43221i	−0.227742	+	0.394460i
$356$		0			0
$357$	−2.68455			−0.142081
$358$		0			0
$359$	−17.4267			−0.919747			−0.459873	−	0.887985i	$-0.652105\pi$
$359$	−17.4267			−0.919747			−0.459873	+	0.887985i	$0.652105\pi$
$360$		0			0
$361$	8.27038	−	14.3247i	0.435283	−	0.753932i
$362$		0			0
$363$	−2.68444	−	4.64958i	−0.140896	−	0.244040i
$364$		0			0
$365$	0.944715	+	1.63629i	0.0494486	+	0.0856476i
$366$		0			0
$367$	15.7476	−	27.2756i	0.822018	−	1.42378i	−0.0821598	−	0.996619i	$-0.526182\pi$
$367$	15.7476	−	27.2756i	0.822018	−	1.42378i	0.904177	−	0.427157i	$-0.140485\pi$
$368$		0			0
$369$	−5.36270	+	9.28847i	−0.279171	+	0.483538i
$370$		0			0
$371$	2.57415	−	4.45855i	0.133643	−	0.231476i
$372$		0			0
$373$	−0.559763	+	0.969539i	−0.0289835	+	0.0502008i	−0.880153	−	0.474690i	$-0.842560\pi$
$373$	−0.559763	+	0.969539i	−0.0289835	+	0.0502008i	0.851170	+	0.524890i	$0.175894\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−29.6218			−1.52560
$378$		0			0
$379$	1.57644	+	2.73047i	0.0809762	+	0.140255i	0.903669	−	0.428231i	$-0.140863\pi$
$379$	1.57644	+	2.73047i	0.0809762	+	0.140255i	−0.822693	+	0.568485i	$0.807530\pi$
$380$		0			0
$381$	1.91093	−	3.30983i	0.0979000	−	0.169568i
$382$		0			0
$383$	15.0905	+	26.1375i	0.771087	+	1.33556i	0.936968	+	0.349416i	$0.113620\pi$
$383$	15.0905	+	26.1375i	0.771087	+	1.33556i	−0.165881	+	0.986146i	$0.553047\pi$
$384$		0			0
$385$	−1.57347	−	2.72533i	−0.0801916	−	0.138896i
$386$		0			0
$387$	11.3172			0.575284
$388$		0			0
$389$	−5.26974	−	9.12746i	−0.267187	−	0.462781i	0.700948	−	0.713213i	$-0.252761\pi$
$389$	−5.26974	−	9.12746i	−0.267187	−	0.462781i	−0.968134	+	0.250432i	$0.919427\pi$
$390$		0			0
$391$	0.209905	−	0.363566i	0.0106153	−	0.0183863i
$392$		0			0
$393$	11.0460			0.557196
$394$		0			0
$395$	−8.70442	+	15.0765i	−0.437967	+	0.758581i
$396$		0			0
$397$	6.06775			0.304532			0.152266	−	0.988340i	$-0.451343\pi$
$397$	6.06775			0.304532			0.152266	+	0.988340i	$0.451343\pi$
$398$		0			0
$399$	−1.21978			−0.0610653
$400$		0			0
$401$	18.3786			0.917784			0.458892	−	0.888492i	$-0.348247\pi$
$401$	18.3786			0.917784			0.458892	+	0.888492i	$0.348247\pi$
$402$		0			0
$403$	−20.7008			−1.03118
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−16.8283			−0.834149
$408$		0			0
$409$	6.75296	−	11.6965i	0.333913	−	0.578353i	−0.649363	−	0.760479i	$-0.724964\pi$
$409$	6.75296	−	11.6965i	0.333913	−	0.578353i	0.983275	+	0.182125i	$0.0582977\pi$
$410$		0			0
$411$	4.07308			0.200910
$412$		0			0
$413$	−5.28043	+	9.14598i	−0.259833	+	0.450044i
$414$		0			0
$415$	7.60268	+	13.1682i	0.373201	+	0.646403i
$416$		0			0
$417$	−2.84340			−0.139242
$418$		0			0
$419$	12.4022	+	21.4813i	0.605888	+	1.04943i	0.991911	+	0.126939i	$0.0405152\pi$
$419$	12.4022	+	21.4813i	0.605888	+	1.04943i	−0.386023	+	0.922489i	$0.626151\pi$
$420$		0			0
$421$	−11.7334	−	20.3229i	−0.571853	−	0.990478i	−0.996376	−	0.0850612i	$-0.972891\pi$
$421$	−11.7334	−	20.3229i	−0.571853	−	0.990478i	0.424523	−	0.905417i	$-0.360442\pi$
$422$		0			0
$423$	−2.40319	+	4.16244i	−0.116847	+	0.202385i
$424$		0			0
$425$	1.72569	+	2.98898i	0.0837081	+	0.144987i
$426$		0			0
$427$	3.25670			0.157603
$428$		0			0
$429$	13.0607			0.630575
$430$		0			0
$431$	7.18798	−	12.4500i	0.346233	−	0.599693i	−0.639344	−	0.768921i	$-0.720794\pi$
$431$	7.18798	−	12.4500i	0.346233	−	0.599693i	0.985577	+	0.169228i	$0.0541273\pi$
$432$		0			0
$433$	−16.2571	+	28.1582i	−0.781269	+	1.35320i	0.149935	+	0.988696i	$0.452094\pi$
$433$	−16.2571	+	28.1582i	−0.781269	+	1.35320i	−0.931203	+	0.364501i	$0.881240\pi$
$434$		0			0
$435$	4.58802	−	7.94668i	0.219979	−	0.381014i
$436$		0			0
$437$	0.0953744	−	0.165193i	0.00456238	−	0.00790227i
$438$		0			0
$439$	−13.0548	−	22.6115i	−0.623071	−	1.07919i	−0.988911	−	0.148513i	$-0.952551\pi$
$439$	−13.0548	−	22.6115i	−0.623071	−	1.07919i	0.365840	−	0.930678i	$-0.380782\pi$
$440$		0			0
$441$	3.19750	+	5.53823i	0.152262	+	0.263725i
$442$		0			0
$443$	−6.07535	+	10.5228i	−0.288649	+	0.499954i	−0.973487	−	0.228741i	$-0.926539\pi$
$443$	−6.07535	+	10.5228i	−0.288649	+	0.499954i	0.684839	+	0.728695i	$0.259873\pi$
$444$		0			0
$445$	−6.89644			−0.326923
$446$		0			0
$447$	−1.75153			−0.0828448
$448$		0			0
$449$	−19.3366	+	33.4919i	−0.912548	+	1.58058i	−0.102097	+	0.994774i	$0.532555\pi$
$449$	−19.3366	+	33.4919i	−0.912548	+	1.58058i	−0.810452	+	0.585806i	$0.800778\pi$
$450$		0			0
$451$	−21.6967	−	37.5797i	−1.02166	−	1.76956i
$452$		0			0
$453$	−3.46264	−	5.99747i	−0.162689	−	0.281786i
$454$		0			0
$455$	2.51094			0.117715
$456$		0			0
$457$	0.145978	−	0.252841i	0.00682857	−	0.0118274i	−0.862591	−	0.505902i	$-0.831160\pi$
$457$	0.145978	−	0.252841i	0.00682857	−	0.0118274i	0.869419	+	0.494075i	$0.164493\pi$
$458$		0			0
$459$	1.72569	+	2.98898i	0.0805481	+	0.139513i
$460$		0			0
$461$	−13.3668			−0.622552			−0.311276	−	0.950320i	$-0.600756\pi$
$461$	−13.3668			−0.622552			−0.311276	+	0.950320i	$0.600756\pi$
$462$		0			0
$463$	0.324433	+	0.561935i	0.0150777	+	0.0261153i	0.873466	−	0.486886i	$-0.161867\pi$
$463$	0.324433	+	0.561935i	0.0150777	+	0.0261153i	−0.858388	+	0.513001i	$0.828534\pi$
$464$		0			0
$465$	3.20627	−	5.55342i	0.148687	−	0.257534i
$466$		0			0
$467$	17.3568	+	30.0629i	0.803177	+	1.39114i	0.917515	+	0.397702i	$0.130192\pi$
$467$	17.3568	+	30.0629i	0.803177	+	1.39114i	−0.114337	+	0.993442i	$0.536474\pi$
$468$		0			0
$469$	−4.91052	−	4.05243i	−0.226747	−	0.187124i
$470$		0			0
$471$	−9.82546	−	17.0182i	−0.452733	−	0.784157i
$472$		0			0
$473$	−22.8938	+	39.6532i	−1.05266	+	1.82325i
$474$		0			0
$475$	0.784100	+	1.35810i	0.0359770	+	0.0623139i
$476$		0			0
$477$	−6.61886			−0.303057
$478$		0			0
$479$	−21.3393	−	36.9607i	−0.975017	−	1.68878i	−0.679878	−	0.733325i	$-0.737967\pi$
$479$	−21.3393	−	36.9607i	−0.975017	−	1.68878i	−0.295139	−	0.955454i	$-0.595366\pi$
$480$		0			0
$481$	6.71363	−	11.6284i	0.306115	−	0.530207i
$482$		0			0
$483$	0.0946106			0.00430493
$484$		0			0
$485$	1.00651	+	1.74332i	0.0457032	+	0.0791602i
$486$		0			0
$487$	16.6988	+	28.9232i	0.756696	+	1.31064i	0.944527	+	0.328435i	$0.106521\pi$
$487$	16.6988	+	28.9232i	0.756696	+	1.31064i	−0.187831	+	0.982201i	$0.560146\pi$
$488$		0			0
$489$	2.27507	−	3.94055i	0.102882	−	0.178198i
$490$		0			0
$491$	−30.9827			−1.39823			−0.699114	−	0.715010i	$-0.746422\pi$
$491$	−30.9827			−1.39823			−0.699114	+	0.715010i	$0.746422\pi$
$492$		0			0
$493$	31.6699			1.42634
$494$		0			0
$495$	−2.02292	+	3.50381i	−0.0909236	+	0.157484i
$496$		0			0
$497$	−3.33762	−	5.78092i	−0.149713	−	0.259310i
$498$		0			0
$499$	0.722460	+	1.25134i	0.0323417	+	0.0560175i	0.881743	−	0.471730i	$-0.156370\pi$
$499$	0.722460	+	1.25134i	0.0323417	+	0.0560175i	−0.849401	+	0.527747i	$0.823037\pi$
$500$		0			0
$501$	−1.60758	+	2.78441i	−0.0718214	+	0.124398i
$502$		0			0
$503$	16.4059	−	28.4159i	0.731505	−	1.26700i	−0.224736	−	0.974420i	$-0.572152\pi$
$503$	16.4059	−	28.4159i	0.731505	−	1.26700i	0.956240	−	0.292583i	$-0.0945149\pi$
$504$		0			0
$505$	−5.54767	+	9.60885i	−0.246868	+	0.427588i
$506$		0			0
$507$	1.28946	−	2.23341i	0.0572670	−	0.0991894i
$508$		0			0
$509$	38.7233			1.71638			0.858190	−	0.513333i	$-0.171589\pi$
$509$	38.7233			1.71638			0.858190	+	0.513333i	$0.171589\pi$
$510$		0			0
$511$	−1.46964			−0.0650130
$512$		0			0
$513$	0.784100	+	1.35810i	0.0346188	+	0.0599616i
$514$		0			0
$515$	0.927303	−	1.60614i	0.0408618	−	0.0707748i
$516$		0			0
$517$	−9.72292	−	16.8406i	−0.427614	−	0.740648i
$518$		0			0
$519$	6.18331	+	10.7098i	0.271417	+	0.470108i
$520$		0			0
$521$	−5.46616			−0.239477			−0.119738	−	0.992805i	$-0.538206\pi$
$521$	−5.46616			−0.239477			−0.119738	+	0.992805i	$0.538206\pi$
$522$		0			0
$523$	−13.6610	−	23.6615i	−0.597353	−	1.03464i	−0.993210	−	0.116333i	$-0.962886\pi$
$523$	−13.6610	−	23.6615i	−0.597353	−	1.03464i	0.395858	−	0.918312i	$-0.370447\pi$
$524$		0			0
$525$	−0.388910	+	0.673613i	−0.0169734	+	0.0293989i
$526$		0			0
$527$	22.1321			0.964087
$528$		0			0
$529$	11.4926	−	19.9058i	0.499678	−	0.865468i
$530$		0			0
$531$	13.5775			0.589214
$532$		0			0
$533$	34.6234			1.49971
$534$		0			0
$535$	10.6658			0.461121
$536$		0			0
$537$	−9.94184			−0.429022
$538$		0			0
$539$	−25.8732			−1.11444
$540$		0			0
$541$	−21.4370			−0.921647			−0.460823	−	0.887492i	$-0.652446\pi$
$541$	−21.4370			−0.921647			−0.460823	+	0.887492i	$0.652446\pi$
$542$		0			0
$543$	−9.23966	+	16.0036i	−0.396512	+	0.686778i
$544$		0			0
$545$	5.99046			0.256603
$546$		0			0
$547$	18.1221	−	31.3884i	0.774845	−	1.34207i	−0.160037	−	0.987111i	$-0.551161\pi$
$547$	18.1221	−	31.3884i	0.774845	−	1.34207i	0.934882	−	0.354959i	$-0.115505\pi$
$548$		0			0
$549$	−2.09348	−	3.62601i	−0.0893475	−	0.154754i
$550$		0			0
$551$	14.3898			0.613028
$552$		0			0
$553$	−6.77048	−	11.7268i	−0.287910	−	0.498675i
$554$		0			0
$555$	2.07970	+	3.60215i	0.0882785	+	0.152903i
$556$		0			0
$557$	15.9211	−	27.5762i	0.674599	−	1.16844i	−0.301987	−	0.953312i	$-0.597650\pi$
$557$	15.9211	−	27.5762i	0.674599	−	1.16844i	0.976586	−	0.215127i	$-0.0690167\pi$
$558$		0			0
$559$	−18.2669	−	31.6391i	−0.772606	−	1.33819i
$560$		0			0
$561$	−13.9637			−0.589549
$562$		0			0
$563$	−32.8884			−1.38608			−0.693041	−	0.720898i	$-0.743730\pi$
$563$	−32.8884			−1.38608			−0.693041	+	0.720898i	$0.743730\pi$
$564$		0			0
$565$	1.99102	−	3.44856i	0.0837630	−	0.145082i
$566$		0			0
$567$	−0.388910	+	0.673613i	−0.0163327	+	0.0282891i
$568$		0			0
$569$	7.46086	−	12.9226i	0.312776	−	0.541743i	−0.666186	−	0.745785i	$-0.732075\pi$
$569$	7.46086	−	12.9226i	0.312776	−	0.541743i	0.978962	+	0.204042i	$0.0654078\pi$
$570$		0			0
$571$	−5.28221	+	9.14906i	−0.221054	+	0.382876i	−0.955128	−	0.296193i	$-0.904283\pi$
$571$	−5.28221	+	9.14906i	−0.221054	+	0.382876i	0.734074	+	0.679069i	$0.237616\pi$
$572$		0			0
$573$	−0.672641	−	1.16505i	−0.0281000	−	0.0486706i
$574$		0			0
$575$	−0.0608178	−	0.105339i	−0.00253628	−	0.00439296i
$576$		0			0
$577$	−8.08784	+	14.0086i	−0.336701	+	0.583184i	−0.983810	−	0.179214i	$-0.942645\pi$
$577$	−8.08784	+	14.0086i	−0.336701	+	0.583184i	0.647109	+	0.762398i	$0.275978\pi$
$578$		0			0
$579$	−5.60599			−0.232977
$580$		0			0
$581$	−11.8270			−0.490668
$582$		0			0
$583$	13.3895	−	23.1912i	0.554535	−	0.960482i
$584$		0			0
$585$	−1.61408	−	2.79568i	−0.0667342	−	0.115587i
$586$		0			0
$587$	−7.54095	−	13.0613i	−0.311248	−	0.539098i	0.667385	−	0.744713i	$-0.267414\pi$
$587$	−7.54095	−	13.0613i	−0.311248	−	0.539098i	−0.978633	+	0.205615i	$0.934080\pi$
$588$		0			0
$589$	10.0561			0.414356
$590$		0			0
$591$	−4.76907	+	8.26027i	−0.196173	+	0.339782i
$592$		0			0
$593$	−11.1109	−	19.2446i	−0.456270	−	0.790282i	0.542491	−	0.840062i	$-0.317481\pi$
$593$	−11.1109	−	19.2446i	−0.456270	−	0.790282i	−0.998760	+	0.0497796i	$0.984148\pi$
$594$		0			0
$595$	−2.68455			−0.110056
$596$		0			0
$597$	−9.05298	−	15.6802i	−0.370514	−	0.641748i
$598$		0			0
$599$	−2.37543	+	4.11436i	−0.0970573	+	0.168108i	−0.910465	−	0.413585i	$-0.864276\pi$
$599$	−2.37543	+	4.11436i	−0.0970573	+	0.168108i	0.813408	+	0.581693i	$0.197610\pi$
$600$		0			0
$601$	−18.8283	−	32.6115i	−0.768020	−	1.33025i	−0.938635	−	0.344913i	$-0.887909\pi$
$601$	−18.8283	−	32.6115i	−0.768020	−	1.33025i	0.170614	−	0.985338i	$-0.445425\pi$
$602$		0			0
$603$	−1.35538	+	8.07236i	−0.0551954	+	0.328732i
$604$		0			0
$605$	−2.68444	−	4.64958i	−0.109138	−	0.189032i
$606$		0			0
$607$	19.2458	−	33.3347i	0.781164	−	1.35302i	−0.150100	−	0.988671i	$-0.547960\pi$
$607$	19.2458	−	33.3347i	0.781164	−	1.35302i	0.931264	−	0.364345i	$-0.118707\pi$
$608$		0			0
$609$	3.56865	+	6.18109i	0.144609	+	0.250470i
$610$		0			0
$611$	15.5158			0.627701
$612$		0			0
$613$	24.3592	+	42.1914i	0.983861	+	1.70410i	0.646894	+	0.762580i	$0.276068\pi$
$613$	24.3592	+	42.1914i	0.983861	+	1.70410i	0.336967	+	0.941517i	$0.390599\pi$
$614$		0			0
$615$	−5.36270	+	9.28847i	−0.216245	+	0.374547i
$616$		0			0
$617$	−10.2055			−0.410860			−0.205430	−	0.978672i	$-0.565859\pi$
$617$	−10.2055			−0.410860			−0.205430	+	0.978672i	$0.565859\pi$
$618$		0			0
$619$	16.6432	+	28.8268i	0.668946	+	1.15865i	0.978199	+	0.207668i	$0.0665874\pi$
$619$	16.6432	+	28.8268i	0.668946	+	1.15865i	−0.309254	+	0.950980i	$0.600079\pi$
$620$		0			0
$621$	−0.0608178	−	0.105339i	−0.00244053	−	0.00422713i
$622$		0			0
$623$	2.68210	−	4.64553i	0.107456	−	0.186119i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−6.34470			−0.253383
$628$		0			0
$629$	−7.17783	+	12.4324i	−0.286199	+	0.495711i
$630$		0			0
$631$	1.71576	+	2.97179i	0.0683035	+	0.118305i	0.898155	−	0.439680i	$-0.144908\pi$
$631$	1.71576	+	2.97179i	0.0683035	+	0.118305i	−0.829851	+	0.557985i	$0.811575\pi$
$632$		0			0
$633$	7.13049	+	12.3504i	0.283412	+	0.490883i
$634$		0			0
$635$	1.91093	−	3.30983i	0.0758330	−	0.131347i
$636$		0			0
$637$	10.3221	−	17.8783i	0.408975	−	0.708365i
$638$		0			0
$639$	−4.29099	+	7.43221i	−0.169749	+	0.294013i
$640$		0			0
$641$	−7.33336	+	12.7018i	−0.289650	+	0.501689i	−0.973726	−	0.227722i	$-0.926872\pi$
$641$	−7.33336	+	12.7018i	−0.289650	+	0.501689i	0.684076	+	0.729411i	$0.260206\pi$
$642$		0			0
$643$	24.1621			0.952861			0.476431	−	0.879212i	$-0.341930\pi$
$643$	24.1621			0.952861			0.476431	+	0.879212i	$0.341930\pi$
$644$		0			0
$645$	11.3172			0.445613
$646$		0			0
$647$	19.5556	+	33.8713i	0.768810	+	1.33162i	0.938208	+	0.346071i	$0.112484\pi$
$647$	19.5556	+	33.8713i	0.768810	+	1.33162i	−0.169398	+	0.985548i	$0.554182\pi$
$648$		0			0
$649$	−27.4663	+	47.5729i	−1.07814	+	1.86740i
$650$		0			0
$651$	2.49390	+	4.31957i	0.0977438	+	0.169297i
$652$		0			0
$653$	−0.113368	−	0.196359i	−0.00443643	−	0.00768412i	0.863799	−	0.503837i	$-0.168079\pi$
$653$	−0.113368	−	0.196359i	−0.00443643	−	0.00768412i	−0.868235	+	0.496153i	$0.834745\pi$
$654$		0			0
$655$	11.0460			0.431602
$656$		0			0
$657$	0.944715	+	1.63629i	0.0368568	+	0.0638379i
$658$		0			0
$659$	18.9488	−	32.8203i	0.738140	−	1.27850i	−0.215192	−	0.976572i	$-0.569038\pi$
$659$	18.9488	−	32.8203i	0.738140	−	1.27850i	0.953332	−	0.301925i	$-0.0976291\pi$
$660$		0			0
$661$	−45.0290			−1.75143			−0.875713	−	0.482832i	$-0.839608\pi$
$661$	−45.0290			−1.75143			−0.875713	+	0.482832i	$0.839608\pi$
$662$		0			0
$663$	5.57081	−	9.64892i	0.216352	−	0.374733i
$664$		0			0
$665$	−1.21978			−0.0473010
$666$		0			0
$667$	−1.11613			−0.0432168
$668$		0			0
$669$	−6.84704			−0.264722
$670$		0			0
$671$	16.9398			0.653953
$672$		0			0
$673$	−4.50744			−0.173749			−0.0868745	−	0.996219i	$-0.527688\pi$
$673$	−4.50744			−0.173749			−0.0868745	+	0.996219i	$0.527688\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	10.0989	−	17.4919i	0.388134	−	0.672268i	−0.604065	−	0.796935i	$-0.706453\pi$
$677$	10.0989	−	17.4919i	0.388134	−	0.672268i	0.992199	+	0.124668i	$0.0397865\pi$
$678$		0			0
$679$	−1.56576			−0.0600885
$680$		0			0
$681$	4.24144	−	7.34639i	0.162532	−	0.281514i
$682$		0			0
$683$	16.7633	+	29.0349i	0.641429	+	1.11099i	0.985114	+	0.171903i	$0.0549916\pi$
$683$	16.7633	+	29.0349i	0.641429	+	1.11099i	−0.343684	+	0.939085i	$0.611675\pi$
$684$		0			0
$685$	4.07308			0.155624
$686$		0			0
$687$	−2.36664	−	4.09913i	−0.0902928	−	0.156392i
$688$		0			0
$689$	10.6834	+	18.5042i	0.407005	+	0.704954i
$690$		0			0
$691$	−11.7209	+	20.3012i	−0.445884	+	0.772293i	−0.998113	−	0.0613990i	$-0.980444\pi$
$691$	−11.7209	+	20.3012i	−0.445884	+	0.772293i	0.552230	+	0.833692i	$0.313777\pi$
$692$		0			0
$693$	−1.57347	−	2.72533i	−0.0597713	−	0.103527i
$694$		0			0
$695$	−2.84340			−0.107856
$696$		0			0
$697$	−37.0173			−1.40213
$698$		0			0
$699$	−5.52791	+	9.57462i	−0.209085	+	0.362145i
$700$		0			0
$701$	−2.80551	+	4.85928i	−0.105963	+	0.183533i	−0.914131	−	0.405419i	$-0.867126\pi$
$701$	−2.80551	+	4.85928i	−0.105963	+	0.183533i	0.808169	+	0.588951i	$0.200459\pi$
$702$		0			0
$703$	−3.26139	+	5.64889i	−0.123006	+	0.213052i
$704$		0			0
$705$	−2.40319	+	4.16244i	−0.0905092	+	0.156767i
$706$		0			0
$707$	−4.31510	−	7.47397i	−0.162286	−	0.281087i
$708$		0			0
$709$	−5.28170	−	9.14817i	−0.198358	−	0.343567i	0.749638	−	0.661848i	$-0.230228\pi$
$709$	−5.28170	−	9.14817i	−0.198358	−	0.343567i	−0.947996	+	0.318281i	$0.896894\pi$
$710$		0			0
$711$	−8.70442	+	15.0765i	−0.326441	+	0.565413i
$712$		0			0
$713$	−0.779993			−0.0292110
$714$		0			0
$715$	13.0607			0.488442
$716$		0			0
$717$	11.0356	−	19.1143i	0.412133	−	0.713836i
$718$		0			0
$719$	2.87175	+	4.97402i	0.107098	+	0.185499i	0.914594	−	0.404374i	$-0.132511\pi$
$719$	2.87175	+	4.97402i	0.107098	+	0.185499i	−0.807495	+	0.589874i	$0.799177\pi$
$720$		0			0
$721$	0.721275	+	1.24929i	0.0268617	+	0.0465258i
$722$		0			0
$723$	18.7368			0.696829
$724$		0			0
$725$	4.58802	−	7.94668i	0.170395	−	0.295132i
$726$		0			0
$727$	−16.9503	−	29.3589i	−0.628653	−	1.08886i	−0.987822	−	0.155587i	$-0.950273\pi$
$727$	−16.9503	−	29.3589i	−0.628653	−	1.08886i	0.359169	−	0.933273i	$-0.383060\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	19.5299	+	33.8267i	0.722339	+	1.25113i
$732$		0			0
$733$	10.3756	−	17.9710i	0.383230	−	0.663774i	−0.608292	−	0.793714i	$-0.708145\pi$
$733$	10.3756	−	17.9710i	0.383230	−	0.663774i	0.991522	+	0.129939i	$0.0414782\pi$
$734$		0			0
$735$	3.19750	+	5.53823i	0.117941	+	0.204281i
$736$		0			0
$737$	−25.5421	−	21.0788i	−0.940857	−	0.776446i
$738$		0			0
$739$	−6.07751	−	10.5266i	−0.223565	−	0.387226i	0.732323	−	0.680957i	$-0.238436\pi$
$739$	−6.07751	−	10.5266i	−0.223565	−	0.387226i	−0.955888	+	0.293732i	$0.905103\pi$
$740$		0			0
$741$	2.53121	−	4.38418i	0.0929862	−	0.161057i
$742$		0			0
$743$	18.1645	+	31.4619i	0.666392	+	1.15422i	0.978906	+	0.204312i	$0.0654956\pi$
$743$	18.1645	+	31.4619i	0.666392	+	1.15422i	−0.312514	+	0.949913i	$0.601171\pi$
$744$		0			0
$745$	−1.75153			−0.0641713
$746$		0			0
$747$	7.60268	+	13.1682i	0.278167	+	0.481800i
$748$		0			0
$749$	−4.14802	+	7.18459i	−0.151566	+	0.262519i
$750$		0			0
$751$	−14.0234			−0.511723			−0.255861	−	0.966713i	$-0.582359\pi$
$751$	−14.0234			−0.511723			−0.255861	+	0.966713i	$0.582359\pi$
$752$		0			0
$753$	−11.1549	−	19.3209i	−0.406508	−	0.704092i
$754$		0			0
$755$	−3.46264	−	5.99747i	−0.126018	−	0.218270i
$756$		0			0
$757$	−11.0738	+	19.1804i	−0.402485	+	0.697125i	−0.994025	−	0.109151i	$-0.965187\pi$
$757$	−11.0738	+	19.1804i	−0.402485	+	0.697125i	0.591540	+	0.806276i	$0.298520\pi$
$758$		0			0
$759$	0.492119			0.0178628
$760$		0			0
$761$	15.2791			0.553865			0.276933	−	0.960889i	$-0.410682\pi$
$761$	15.2791			0.553865			0.276933	+	0.960889i	$0.410682\pi$
$762$		0			0
$763$	−2.32975	+	4.03525i	−0.0843427	+	0.146086i
$764$		0			0
$765$	1.72569	+	2.98898i	0.0623923	+	0.108067i
$766$		0			0
$767$	−21.9152	−	37.9583i	−0.791314	−	1.37060i
$768$		0			0
$769$	8.10208	−	14.0332i	0.292169	−	0.506051i	−0.682154	−	0.731209i	$-0.738957\pi$
$769$	8.10208	−	14.0332i	0.292169	−	0.506051i	0.974322	+	0.225158i	$0.0722898\pi$
$770$		0			0
$771$	6.83867	−	11.8449i	0.246289	−	0.426584i
$772$		0			0
$773$	4.05947	−	7.03121i	0.146009	−	0.252895i	−0.783740	−	0.621089i	$-0.786690\pi$
$773$	4.05947	−	7.03121i	0.146009	−	0.252895i	0.929749	+	0.368194i	$0.120024\pi$
$774$		0			0
$775$	3.20627	−	5.55342i	0.115173	−	0.199485i
$776$		0			0
$777$	−3.23527			−0.116065
$778$		0			0
$779$	−16.8196			−0.602623
$780$		0			0
$781$	−17.3607	−	30.0696i	−0.621214	−	1.07597i
$782$		0			0
$783$	4.58802	−	7.94668i	0.163962	−	0.283991i
$784$		0			0
$785$	−9.82546	−	17.0182i	−0.350686	−	0.607405i
$786$		0			0
$787$	−19.3112	−	33.4480i	−0.688370	−	1.19229i	−0.972365	−	0.233466i	$-0.924993\pi$
$787$	−19.3112	−	33.4480i	−0.688370	−	1.19229i	0.283995	−	0.958826i	$-0.408340\pi$
$788$		0			0
$789$	17.8436			0.635248
$790$		0			0
$791$	1.54866	+	2.68236i	0.0550640	+	0.0953737i
$792$		0			0
$793$	−6.75810	+	11.7054i	−0.239987	+	0.415670i
$794$		0			0
$795$	−6.61886			−0.234747
$796$		0			0
$797$	−14.1507	+	24.5097i	−0.501243	+	0.868178i	0.498756	+	0.866742i	$0.333790\pi$
$797$	−14.1507	+	24.5097i	−0.501243	+	0.868178i	−0.999999	+	0.00143588i	$0.999543\pi$
$798$		0			0
$799$	−16.5886			−0.586862
$800$		0			0
$801$	−6.89644			−0.243674
$802$		0			0
$803$	−7.64435			−0.269763
$804$		0			0
$805$	0.0946106			0.00333459
$806$		0			0
$807$	6.61717			0.232935
$808$		0			0
$809$	47.2214			1.66022			0.830108	−	0.557602i	$-0.188279\pi$
$809$	47.2214			1.66022			0.830108	+	0.557602i	$0.188279\pi$
$810$		0			0
$811$	−8.98162	+	15.5566i	−0.315387	+	0.546267i	−0.979520	−	0.201348i	$-0.935468\pi$
$811$	−8.98162	+	15.5566i	−0.315387	+	0.546267i	0.664132	+	0.747615i	$0.268801\pi$
$812$		0			0
$813$	3.41260			0.119685
$814$		0			0
$815$	2.27507	−	3.94055i	0.0796924	−	0.138031i
$816$		0			0
$817$	8.87379	+	15.3699i	0.310455	+	0.537723i
$818$		0			0
$819$	2.51094			0.0877392
$820$		0			0
$821$	−16.8767	−	29.2312i	−0.588999	−	1.02018i	−0.994364	−	0.106022i	$-0.966189\pi$
$821$	−16.8767	−	29.2312i	−0.588999	−	1.02018i	0.405365	−	0.914155i	$-0.367145\pi$
$822$		0			0
$823$	−16.2070	−	28.0714i	−0.564942	−	0.978508i	−0.997055	−	0.0766885i	$-0.975565\pi$
$823$	−16.2070	−	28.0714i	−0.564942	−	0.978508i	0.432113	−	0.901819i	$-0.357768\pi$
$824$		0			0
$825$	−2.02292	+	3.50381i	−0.0704292	+	0.121987i
$826$		0			0
$827$	13.1395	+	22.7583i	0.456905	+	0.791382i	0.998795	−	0.0490669i	$-0.0156247\pi$
$827$	13.1395	+	22.7583i	0.456905	+	0.791382i	−0.541891	+	0.840449i	$0.682291\pi$
$828$		0			0
$829$	−41.1950			−1.43076			−0.715380	−	0.698735i	$-0.753746\pi$
$829$	−41.1950			−1.43076			−0.715380	+	0.698735i	$0.753746\pi$
$830$		0			0
$831$	−20.2164			−0.701300
$832$		0			0
$833$	−11.0358	+	19.1145i	−0.382366	+	0.662278i
$834$		0			0
$835$	−1.60758	+	2.78441i	−0.0556327	+	0.0963586i
$836$		0			0
$837$	3.20627	−	5.55342i	0.110825	−	0.191954i
$838$		0			0
$839$	−17.1743	+	29.7467i	−0.592922	+	1.02697i	0.400914	+	0.916115i	$0.368692\pi$
$839$	−17.1743	+	29.7467i	−0.592922	+	1.02697i	−0.993837	+	0.110856i	$0.964641\pi$
$840$		0			0
$841$	−27.5998	−	47.8042i	−0.951717	−	1.64842i
$842$		0			0
$843$	−5.54229	−	9.59953i	−0.190887	−	0.330625i
$844$		0			0
$845$	1.28946	−	2.23341i	0.0443588	−	0.0768318i
$846$		0			0
$847$	4.17602			0.143490
$848$		0			0
$849$	26.5624			0.911620
$850$		0			0
$851$	0.252966	−	0.438150i	0.00867155	−	0.0150196i
$852$		0			0
$853$	2.99100	+	5.18057i	0.102410	+	0.177379i	0.912677	−	0.408681i	$-0.134011\pi$
$853$	2.99100	+	5.18057i	0.102410	+	0.177379i	−0.810267	+	0.586061i	$0.800678\pi$
$854$		0			0
$855$	0.784100	+	1.35810i	0.0268156	+	0.0464461i
$856$		0			0
$857$	−2.68570			−0.0917419			−0.0458710	−	0.998947i	$-0.514606\pi$
$857$	−2.68570			−0.0917419			−0.0458710	+	0.998947i	$0.514606\pi$
$858$		0			0
$859$	9.17219	−	15.8867i	0.312951	−	0.542047i	−0.666049	−	0.745908i	$-0.732016\pi$
$859$	9.17219	−	15.8867i	0.312951	−	0.542047i	0.979000	+	0.203861i	$0.0653491\pi$
$860$		0			0
$861$	−4.17122	−	7.22476i	−0.142155	−	0.246219i
$862$		0			0
$863$	45.0419			1.53324			0.766622	−	0.642099i	$-0.221936\pi$
$863$	45.0419			1.53324			0.766622	+	0.642099i	$0.221936\pi$
$864$		0			0
$865$	6.18331	+	10.7098i	0.210239	+	0.364144i
$866$		0			0
$867$	2.54402	−	4.40637i	0.0863994	−	0.149648i
$868$		0			0
$869$	−35.2167	−	60.9972i	−1.19465	−	2.06919i
$870$		0			0
$871$	24.7554	−	9.24026i	0.838805	−	0.313094i
$872$		0			0
$873$	1.00651	+	1.74332i	0.0340651	+	0.0590025i
$874$		0			0
$875$	−0.388910	+	0.673613i	−0.0131476	+	0.0227723i
$876$		0			0
$877$	−5.22351	−	9.04738i	−0.176385	−	0.305508i	0.764254	−	0.644915i	$-0.223107\pi$
$877$	−5.22351	−	9.04738i	−0.176385	−	0.305508i	−0.940640	+	0.339406i	$0.889774\pi$
$878$		0			0
$879$	19.3768			0.653565
$880$		0			0
$881$	−15.4797	−	26.8116i	−0.521524	−	0.903305i	−0.999687	−	0.0250343i	$-0.992031\pi$
$881$	−15.4797	−	26.8116i	−0.521524	−	0.903305i	0.478163	−	0.878271i	$-0.341303\pi$
$882$		0			0
$883$	20.6010	−	35.6819i	0.693278	−	1.20079i	−0.277480	−	0.960731i	$-0.589499\pi$
$883$	20.6010	−	35.6819i	0.693278	−	1.20079i	0.970758	−	0.240061i	$-0.0771673\pi$
$884$		0			0
$885$	13.5775			0.456403
$886$		0			0
$887$	23.5613	+	40.8093i	0.791110	+	1.37024i	0.925280	+	0.379284i	$0.123830\pi$
$887$	23.5613	+	40.8093i	0.791110	+	1.37024i	−0.134170	+	0.990958i	$0.542837\pi$
$888$		0			0
$889$	1.48636	+	2.57446i	0.0498510	+	0.0863445i
$890$		0			0
$891$	−2.02292	+	3.50381i	−0.0677705	+	0.117382i
$892$		0			0
$893$	−7.53735			−0.252228
$894$		0			0
$895$	−9.94184			−0.332319
$896$		0			0
$897$	−0.196330	+	0.340054i	−0.00655527	+	0.0113541i
$898$		0			0
$899$	−29.4208	−	50.9584i	−0.981240	−	1.69956i
$900$		0			0
$901$	−11.4221	−	19.7836i	−0.380525	−	0.659088i
$902$		0			0
$903$	−4.40136	+	7.62339i	−0.146468	+	0.253690i
$904$		0			0
$905$	−9.23966	+	16.0036i	−0.307137	+	0.531976i
$906$		0			0
$907$	−2.41483	+	4.18260i	−0.0801830	+	0.138881i	−0.903328	−	0.428950i	$-0.858884\pi$
$907$	−2.41483	+	4.18260i	−0.0801830	+	0.138881i	0.823145	+	0.567831i	$0.192217\pi$
$908$		0			0
$909$	−5.54767	+	9.60885i	−0.184005	+	0.318706i
$910$		0			0
$911$	−16.2265			−0.537607			−0.268804	−	0.963195i	$-0.586628\pi$
$911$	−16.2265			−0.537607			−0.268804	+	0.963195i	$0.586628\pi$
$912$		0			0
$913$	−61.5186			−2.03597
$914$		0			0
$915$	−2.09348	−	3.62601i	−0.0692083	−	0.119872i
$916$		0			0
$917$	−4.29590	+	7.44071i	−0.141863	+	0.245714i
$918$		0			0
$919$	10.9490	+	18.9642i	0.361173	+	0.625571i	0.988154	−	0.153464i	$-0.0490429\pi$
$919$	10.9490	+	18.9642i	0.361173	+	0.625571i	−0.626981	+	0.779035i	$0.715710\pi$
$920$		0			0
$921$	−6.02352	−	10.4330i	−0.198482	−	0.343781i
$922$		0			0
$923$	27.7041			0.911890
$924$		0			0
$925$	2.07970	+	3.60215i	0.0683802	+	0.118438i
$926$		0			0
$927$	0.927303	−	1.60614i	0.0304566	−	0.0527524i
$928$		0			0
$929$	41.0571			1.34704			0.673521	−	0.739169i	$-0.264781\pi$
$929$	41.0571			1.34704			0.673521	+	0.739169i	$0.264781\pi$
$930$		0			0
$931$	−5.01431	+	8.68505i	−0.164337	+	0.284641i
$932$		0			0
$933$	11.4317			0.374258
$934$		0			0
$935$	−13.9637			−0.456663
$936$		0			0
$937$	−45.4009			−1.48318			−0.741592	−	0.670852i	$-0.765929\pi$
$937$	−45.4009			−1.48318			−0.741592	+	0.670852i	$0.765929\pi$
$938$		0			0
$939$	−13.3601			−0.435991
$940$		0			0
$941$	−41.8665			−1.36481			−0.682404	−	0.730975i	$-0.739065\pi$
$941$	−41.8665			−1.36481			−0.682404	+	0.730975i	$0.739065\pi$
$942$		0			0
$943$	1.30459			0.0424833
$944$		0			0
$945$	−0.388910	+	0.673613i	−0.0126513	+	0.0219126i
$946$		0			0
$947$	2.67193			0.0868262			0.0434131	−	0.999057i	$-0.486177\pi$
$947$	2.67193			0.0868262			0.0434131	+	0.999057i	$0.486177\pi$
$948$		0			0
$949$	3.04970	−	5.28224i	0.0989975	−	0.171469i
$950$		0			0
$951$	−3.83349	−	6.63980i	−0.124309	−	0.215310i
$952$		0			0
$953$	−33.2824			−1.07812			−0.539061	−	0.842267i	$-0.681221\pi$
$953$	−33.2824			−1.07812			−0.539061	+	0.842267i	$0.681221\pi$
$954$		0			0
$955$	−0.672641	−	1.16505i	−0.0217661	−	0.0377001i
$956$		0			0
$957$	18.5624	+	32.1510i	0.600038	+	1.03930i
$958$		0			0
$959$	−1.58406	+	2.74368i	−0.0511521	+	0.0885980i
$960$		0			0
$961$	−5.06033	−	8.76474i	−0.163236	−	0.282734i
$962$		0			0
$963$	10.6658			0.343699
$964$		0			0
$965$	−5.60599			−0.180463
$966$		0			0
$967$	−24.4371	+	42.3262i	−0.785843	+	1.36112i	0.142651	+	0.989773i	$0.454437\pi$
$967$	−24.4371	+	42.3262i	−0.785843	+	1.36112i	−0.928494	+	0.371347i	$0.878896\pi$
$968$		0			0
$969$	−2.70622	+	4.68731i	−0.0869363	+	0.150578i
$970$		0			0
$971$	5.43413	−	9.41220i	0.174390	−	0.302052i	−0.765560	−	0.643364i	$-0.777538\pi$
$971$	5.43413	−	9.41220i	0.174390	−	0.302052i	0.939950	+	0.341312i	$0.110871\pi$
$972$		0			0
$973$	1.10583	−	1.91535i	0.0354512	−	0.0614033i
$974$		0			0
$975$	−1.61408	−	2.79568i	−0.0516921	−	0.0895333i
$976$		0			0
$977$	−5.65761	−	9.79927i	−0.181003	−	0.313506i	0.761219	−	0.648494i	$-0.224601\pi$
$977$	−5.65761	−	9.79927i	−0.181003	−	0.313506i	−0.942222	+	0.334988i	$0.891268\pi$
$978$		0			0
$979$	13.9510	−	24.1638i	0.445875	−	0.772279i
$980$		0			0
$981$	5.99046			0.191261
$982$		0			0
$983$	−27.7090			−0.883780			−0.441890	−	0.897069i	$-0.645692\pi$
$983$	−27.7090			−0.883780			−0.441890	+	0.897069i	$0.645692\pi$
$984$		0			0
$985$	−4.76907	+	8.26027i	−0.151955	+	0.263194i
$986$		0			0
$987$	−1.86925	−	3.23763i	−0.0594988	−	0.103055i
$988$		0			0
$989$	−0.688285	−	1.19214i	−0.0218862	−	0.0379080i
$990$		0			0
$991$	9.40449			0.298743			0.149372	−	0.988781i	$-0.452275\pi$
$991$	9.40449			0.298743			0.149372	+	0.988781i	$0.452275\pi$
$992$		0			0
$993$	8.48244	−	14.6920i	0.269182	−	0.466237i
$994$		0			0
$995$	−9.05298	−	15.6802i	−0.286999	−	0.497096i
$996$		0			0
$997$	−28.8267			−0.912952			−0.456476	−	0.889736i	$-0.650889\pi$
$997$	−28.8267			−0.912952			−0.456476	+	0.889736i	$0.650889\pi$
$998$		0			0
$999$	2.07970	+	3.60215i	0.0657989	+	0.113967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.6	✓	24
67.29	even	3	inner	4020.2.q.m.3781.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.6	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.388910 + 0.673613i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-0.388910 + 0.673613i) q^{7} +1.00000 q^{9} +(-2.02292 + 3.50381i) q^{11} +(-1.61408 - 2.79568i) q^{13} +1.00000 q^{15} +(1.72569 + 2.98898i) q^{17} +(0.784100 + 1.35810i) q^{19} +(-0.388910 + 0.673613i) q^{21} +(-0.0608178 - 0.105339i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(4.58802 - 7.94668i) q^{29} +(3.20627 - 5.55342i) q^{31} +(-2.02292 + 3.50381i) q^{33} +(-0.388910 + 0.673613i) q^{35} +(2.07970 + 3.60215i) q^{37} +(-1.61408 - 2.79568i) q^{39} +(-5.36270 + 9.28847i) q^{41} +11.3172 q^{43} +1.00000 q^{45} +(-2.40319 + 4.16244i) q^{47} +(3.19750 + 5.53823i) q^{49} +(1.72569 + 2.98898i) q^{51} -6.61886 q^{53} +(-2.02292 + 3.50381i) q^{55} +(0.784100 + 1.35810i) q^{57} +13.5775 q^{59} +(-2.09348 - 3.62601i) q^{61} +(-0.388910 + 0.673613i) q^{63} +(-1.61408 - 2.79568i) q^{65} +(-1.35538 + 8.07236i) q^{67} +(-0.0608178 - 0.105339i) q^{69} +(-4.29099 + 7.43221i) q^{71} +(0.944715 + 1.63629i) q^{73} +1.00000 q^{75} +(-1.57347 - 2.72533i) q^{77} +(-8.70442 + 15.0765i) q^{79} +1.00000 q^{81} +(7.60268 + 13.1682i) q^{83} +(1.72569 + 2.98898i) q^{85} +(4.58802 - 7.94668i) q^{87} -6.89644 q^{89} +2.51094 q^{91} +(3.20627 - 5.55342i) q^{93} +(0.784100 + 1.35810i) q^{95} +(1.00651 + 1.74332i) q^{97} +(-2.02292 + 3.50381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 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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