LMFDB - Embedded newform 4020.2.q.k.841.2

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:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.2
Root			$-0.288886 + 0.500366i$ of defining polynomial
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.k.3781.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +(1.34203 - 2.32447i) q^{11} +(-0.0777729 - 0.134707i) q^{13} -1.00000 q^{15} +(-0.386637 - 0.669675i) q^{17} +(-0.333089 - 0.576927i) q^{19} +(1.13810 - 1.97125i) q^{21} +(-2.24130 - 3.88205i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.790296 - 1.36883i) q^{29} +(-2.92455 + 5.06547i) q^{31} +(-1.34203 + 2.32447i) q^{33} +(-1.13810 + 1.97125i) q^{35} +(-4.60808 - 7.98142i) q^{37} +(0.0777729 + 0.134707i) q^{39} +(-4.88835 + 8.46687i) q^{41} -4.88135 q^{43} +1.00000 q^{45} +(4.20309 - 7.27996i) q^{47} +(0.909436 + 1.57519i) q^{49} +(0.386637 + 0.669675i) q^{51} +7.78200 q^{53} +(1.34203 - 2.32447i) q^{55} +(0.333089 + 0.576927i) q^{57} -10.5918 q^{59} +(1.14396 + 1.98139i) q^{61} +(-1.13810 + 1.97125i) q^{63} +(-0.0777729 - 0.134707i) q^{65} +(-1.48295 + 8.04990i) q^{67} +(2.24130 + 3.88205i) q^{69} +(6.37678 - 11.0449i) q^{71} +(-3.73675 - 6.47224i) q^{73} -1.00000 q^{75} +(3.05474 + 5.29097i) q^{77} +(-6.85569 + 11.8744i) q^{79} +1.00000 q^{81} +(-4.19414 - 7.26447i) q^{83} +(-0.386637 - 0.669675i) q^{85} +(-0.790296 + 1.36883i) q^{87} +5.03057 q^{89} +0.354055 q^{91} +(2.92455 - 5.06547i) q^{93} +(-0.333089 - 0.576927i) q^{95} +(-5.24485 - 9.08435i) q^{97} +(1.34203 - 2.32447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.13810	+	1.97125i	−0.430163	+	0.745064i	−0.996887	−	0.0788435i	$-0.974877\pi$
$7$	−1.13810	+	1.97125i	−0.430163	+	0.745064i	0.566724	+	0.823908i	$0.308211\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.34203	−	2.32447i	0.404638	−	0.700853i	−0.589642	−	0.807665i	$-0.700731\pi$
$11$	1.34203	−	2.32447i	0.404638	−	0.700853i	0.994279	+	0.106812i	$0.0340643\pi$
$12$		0			0
$13$	−0.0777729	−	0.134707i	−0.0215703	−	0.0373609i	0.855039	−	0.518564i	$-0.173533\pi$
$13$	−0.0777729	−	0.134707i	−0.0215703	−	0.0373609i	−0.876609	+	0.481203i	$0.840200\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−0.386637	−	0.669675i	−0.0937732	−	0.162420i	0.815323	−	0.579007i	$-0.196560\pi$
$17$	−0.386637	−	0.669675i	−0.0937732	−	0.162420i	−0.909096	+	0.416587i	$0.863226\pi$
$18$		0			0
$19$	−0.333089	−	0.576927i	−0.0764159	−	0.132356i	0.825285	−	0.564716i	$-0.191014\pi$
$19$	−0.333089	−	0.576927i	−0.0764159	−	0.132356i	−0.901701	+	0.432360i	$0.857681\pi$
$20$		0			0
$21$	1.13810	−	1.97125i	0.248355	−	0.430163i
$22$		0			0
$23$	−2.24130	−	3.88205i	−0.467344	−	0.809464i	0.531960	−	0.846770i	$-0.321456\pi$
$23$	−2.24130	−	3.88205i	−0.467344	−	0.809464i	−0.999304	+	0.0373060i	$0.988122\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	0.790296	−	1.36883i	0.146754	−	0.254186i	−0.783272	−	0.621679i	$-0.786451\pi$
$29$	0.790296	−	1.36883i	0.146754	−	0.254186i	0.930026	+	0.367494i	$0.119784\pi$
$30$		0			0
$31$	−2.92455	+	5.06547i	−0.525265	+	0.909786i	0.474302	+	0.880362i	$0.342700\pi$
$31$	−2.92455	+	5.06547i	−0.525265	+	0.909786i	−0.999567	+	0.0294235i	$0.990633\pi$
$32$		0			0
$33$	−1.34203	+	2.32447i	−0.233618	+	0.404638i
$34$		0			0
$35$	−1.13810	+	1.97125i	−0.192375	+	0.333203i
$36$		0			0
$37$	−4.60808	−	7.98142i	−0.757563	−	1.31214i	−0.944090	−	0.329688i	$-0.893057\pi$
$37$	−4.60808	−	7.98142i	−0.757563	−	1.31214i	0.186527	−	0.982450i	$-0.440277\pi$
$38$		0			0
$39$	0.0777729	+	0.134707i	0.0124536	+	0.0215703i
$40$		0			0
$41$	−4.88835	+	8.46687i	−0.763432	+	1.32230i	0.177640	+	0.984096i	$0.443154\pi$
$41$	−4.88835	+	8.46687i	−0.763432	+	1.32230i	−0.941072	+	0.338207i	$0.890179\pi$
$42$		0			0
$43$	−4.88135			−0.744399			−0.372199	−	0.928153i	$-0.621396\pi$
$43$	−4.88135			−0.744399			−0.372199	+	0.928153i	$0.621396\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	4.20309	−	7.27996i	0.613083	−	1.06189i	−0.377634	−	0.925955i	$-0.623262\pi$
$47$	4.20309	−	7.27996i	0.613083	−	1.06189i	0.990718	−	0.135936i	$-0.0434043\pi$
$48$		0			0
$49$	0.909436	+	1.57519i	0.129919	+	0.225027i
$50$		0			0
$51$	0.386637	+	0.669675i	0.0541400	+	0.0937732i
$52$		0			0
$53$	7.78200			1.06894			0.534470	−	0.845188i	$-0.320511\pi$
$53$	7.78200			1.06894			0.534470	+	0.845188i	$0.320511\pi$
$54$		0			0
$55$	1.34203	−	2.32447i	0.180959	−	0.313431i
$56$		0			0
$57$	0.333089	+	0.576927i	0.0441187	+	0.0764159i
$58$		0			0
$59$	−10.5918			−1.37893			−0.689465	−	0.724319i	$-0.742154\pi$
$59$	−10.5918			−1.37893			−0.689465	+	0.724319i	$0.742154\pi$
$60$		0			0
$61$	1.14396	+	1.98139i	0.146468	+	0.253691i	0.929920	−	0.367762i	$-0.119876\pi$
$61$	1.14396	+	1.98139i	0.146468	+	0.253691i	−0.783451	+	0.621453i	$0.786543\pi$
$62$		0			0
$63$	−1.13810	+	1.97125i	−0.143388	+	0.248355i
$64$		0			0
$65$	−0.0777729	−	0.134707i	−0.00964654	−	0.0167083i
$66$		0			0
$67$	−1.48295	+	8.04990i	−0.181172	+	0.983451i
$67$	−1.48295	+	8.04990i	−0.181172	+	0.983451i
$68$		0			0
$69$	2.24130	+	3.88205i	0.269821	+	0.467344i
$70$		0			0
$71$	6.37678	−	11.0449i	0.756785	−	1.31079i	−0.187697	−	0.982227i	$-0.560102\pi$
$71$	6.37678	−	11.0449i	0.756785	−	1.31079i	0.944482	−	0.328563i	$-0.106564\pi$
$72$		0			0
$73$	−3.73675	−	6.47224i	−0.437353	−	0.757518i	0.560131	−	0.828404i	$-0.310751\pi$
$73$	−3.73675	−	6.47224i	−0.437353	−	0.757518i	−0.997484	+	0.0708858i	$0.977417\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	3.05474	+	5.29097i	0.348120	+	0.602962i
$78$		0			0
$79$	−6.85569	+	11.8744i	−0.771326	+	1.33598i	0.165511	+	0.986208i	$0.447073\pi$
$79$	−6.85569	+	11.8744i	−0.771326	+	1.33598i	−0.936836	+	0.349768i	$0.886261\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−4.19414	−	7.26447i	−0.460367	−	0.797379i	0.538612	−	0.842554i	$-0.318949\pi$
$83$	−4.19414	−	7.26447i	−0.460367	−	0.797379i	−0.998979	+	0.0451747i	$0.985616\pi$
$84$		0			0
$85$	−0.386637	−	0.669675i	−0.0419367	−	0.0726364i
$86$		0			0
$87$	−0.790296	+	1.36883i	−0.0847286	+	0.146754i
$88$		0			0
$89$	5.03057			0.533239			0.266619	−	0.963802i	$-0.414093\pi$
$89$	5.03057			0.533239			0.266619	+	0.963802i	$0.414093\pi$
$90$		0			0
$91$	0.354055			0.0371150
$92$		0			0
$93$	2.92455	−	5.06547i	0.303262	−	0.525265i
$94$		0			0
$95$	−0.333089	−	0.576927i	−0.0341742	−	0.0591915i
$96$		0			0
$97$	−5.24485	−	9.08435i	−0.532534	−	0.922376i	−0.999278	−	0.0379835i	$-0.987907\pi$
$97$	−5.24485	−	9.08435i	−0.532534	−	0.922376i	0.466745	−	0.884392i	$-0.345427\pi$
$98$		0			0
$99$	1.34203	−	2.32447i	0.134879	−	0.233618i
$100$		0			0
$101$	0.530519	−	0.918886i	0.0527886	−	0.0914326i	−0.838424	−	0.545019i	$-0.816522\pi$
$101$	0.530519	−	0.918886i	0.0527886	−	0.0914326i	0.891212	+	0.453587i	$0.149856\pi$
$102$		0			0
$103$	6.85611	−	11.8751i	0.675553	−	1.17009i	−0.300754	−	0.953702i	$-0.597238\pi$
$103$	6.85611	−	11.8751i	0.675553	−	1.17009i	0.976307	−	0.216390i	$-0.0694284\pi$
$104$		0			0
$105$	1.13810	−	1.97125i	0.111068	−	0.192375i
$106$		0			0
$107$	−18.1522			−1.75484			−0.877420	−	0.479723i	$-0.840737\pi$
$107$	−18.1522			−1.75484			−0.877420	+	0.479723i	$0.840737\pi$
$108$		0			0
$109$	−1.05330			−0.100887			−0.0504437	−	0.998727i	$-0.516064\pi$
$109$	−1.05330			−0.100887			−0.0504437	+	0.998727i	$0.516064\pi$
$110$		0			0
$111$	4.60808	+	7.98142i	0.437379	+	0.757563i
$112$		0			0
$113$	7.44853	−	12.9012i	0.700698	−	1.21365i	−0.267523	−	0.963551i	$-0.586205\pi$
$113$	7.44853	−	12.9012i	0.700698	−	1.21365i	0.968222	−	0.250094i	$-0.0804614\pi$
$114$		0			0
$115$	−2.24130	−	3.88205i	−0.209003	−	0.362003i
$116$		0			0
$117$	−0.0777729	−	0.134707i	−0.00719011	−	0.0124536i
$118$		0			0
$119$	1.76013			0.161351
$120$		0			0
$121$	1.89790	+	3.28727i	0.172537	+	0.298842i
$122$		0			0
$123$	4.88835	−	8.46687i	0.440768	−	0.763432i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	5.45909	−	9.45542i	0.484416	−	0.839033i	−0.515424	−	0.856935i	$-0.672366\pi$
$127$	5.45909	−	9.45542i	0.484416	−	0.839033i	0.999840	+	0.0179027i	$0.00569891\pi$
$128$		0			0
$129$	4.88135			0.429779
$130$		0			0
$131$	−4.93164			−0.430880			−0.215440	−	0.976517i	$-0.569119\pi$
$131$	−4.93164			−0.430880			−0.215440	+	0.976517i	$0.569119\pi$
$132$		0			0
$133$	1.51636			0.131485
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	9.40754			0.803741			0.401870	−	0.915697i	$-0.368360\pi$
$137$	9.40754			0.803741			0.401870	+	0.915697i	$0.368360\pi$
$138$		0			0
$139$	−9.64017			−0.817668			−0.408834	−	0.912609i	$-0.634065\pi$
$139$	−9.64017			−0.817668			−0.408834	+	0.912609i	$0.634065\pi$
$140$		0			0
$141$	−4.20309	+	7.27996i	−0.353964	+	0.613083i
$142$		0			0
$143$	−0.417495			−0.0349127
$144$		0			0
$145$	0.790296	−	1.36883i	0.0656305	−	0.113675i
$146$		0			0
$147$	−0.909436	−	1.57519i	−0.0750090	−	0.129919i
$148$		0			0
$149$	−12.3962			−1.01554			−0.507769	−	0.861493i	$-0.669530\pi$
$149$	−12.3962			−1.01554			−0.507769	+	0.861493i	$0.669530\pi$
$150$		0			0
$151$	−2.27804	−	3.94569i	−0.185385	−	0.321095i	0.758321	−	0.651881i	$-0.226020\pi$
$151$	−2.27804	−	3.94569i	−0.185385	−	0.321095i	−0.943706	+	0.330785i	$0.892686\pi$
$152$		0			0
$153$	−0.386637	−	0.669675i	−0.0312577	−	0.0541400i
$154$		0			0
$155$	−2.92455	+	5.06547i	−0.234906	+	0.406869i
$156$		0			0
$157$	1.44535	+	2.50342i	0.115352	+	0.199795i	0.917920	−	0.396765i	$-0.129867\pi$
$157$	1.44535	+	2.50342i	0.115352	+	0.199795i	−0.802569	+	0.596560i	$0.796534\pi$
$158$		0			0
$159$	−7.78200			−0.617152
$160$		0			0
$161$	10.2033			0.804137
$162$		0			0
$163$	7.15348	−	12.3902i	0.560304	−	0.970475i	−0.437166	−	0.899381i	$-0.644018\pi$
$163$	7.15348	−	12.3902i	0.560304	−	0.970475i	0.997470	−	0.0710940i	$-0.0226490\pi$
$164$		0			0
$165$	−1.34203	+	2.32447i	−0.104477	+	0.180959i
$166$		0			0
$167$	−12.0904	+	20.9412i	−0.935584	+	1.62048i	−0.161994	+	0.986792i	$0.551793\pi$
$167$	−12.0904	+	20.9412i	−0.935584	+	1.62048i	−0.773590	+	0.633687i	$0.781541\pi$
$168$		0			0
$169$	6.48790	−	11.2374i	0.499069	−	0.864414i
$170$		0			0
$171$	−0.333089	−	0.576927i	−0.0254720	−	0.0441187i
$172$		0			0
$173$	−11.6805	−	20.2313i	−0.888054	−	1.53815i	−0.842173	−	0.539208i	$-0.818724\pi$
$173$	−11.6805	−	20.2313i	−0.888054	−	1.53815i	−0.0458811	−	0.998947i	$-0.514610\pi$
$174$		0			0
$175$	−1.13810	+	1.97125i	−0.0860326	+	0.149013i
$176$		0			0
$177$	10.5918			0.796125
$178$		0			0
$179$	−7.46602			−0.558036			−0.279018	−	0.960286i	$-0.590009\pi$
$179$	−7.46602			−0.558036			−0.279018	+	0.960286i	$0.590009\pi$
$180$		0			0
$181$	−4.45233	+	7.71165i	−0.330939	+	0.573203i	−0.982696	−	0.185225i	$-0.940699\pi$
$181$	−4.45233	+	7.71165i	−0.330939	+	0.573203i	0.651757	+	0.758427i	$0.274032\pi$
$182$		0			0
$183$	−1.14396	−	1.98139i	−0.0845636	−	0.146468i
$184$		0			0
$185$	−4.60808	−	7.98142i	−0.338792	−	0.586806i
$186$		0			0
$187$	−2.07552			−0.151777
$188$		0			0
$189$	1.13810	−	1.97125i	0.0827849	−	0.143388i
$190$		0			0
$191$	9.74545	+	16.8796i	0.705156	+	1.22137i	0.966635	+	0.256157i	$0.0824563\pi$
$191$	9.74545	+	16.8796i	0.705156	+	1.22137i	−0.261479	+	0.965209i	$0.584210\pi$
$192$		0			0
$193$	9.62585			0.692884			0.346442	−	0.938071i	$-0.387390\pi$
$193$	9.62585			0.692884			0.346442	+	0.938071i	$0.387390\pi$
$194$		0			0
$195$	0.0777729	+	0.134707i	0.00556943	+	0.00964654i
$196$		0			0
$197$	1.58812	−	2.75070i	0.113149	−	0.195979i	−0.803889	−	0.594779i	$-0.797240\pi$
$197$	1.58812	−	2.75070i	0.113149	−	0.195979i	0.917038	+	0.398799i	$0.130573\pi$
$198$		0			0
$199$	−3.11819	−	5.40087i	−0.221043	−	0.382858i	0.734082	−	0.679061i	$-0.237613\pi$
$199$	−3.11819	−	5.40087i	−0.221043	−	0.382858i	−0.955125	+	0.296203i	$0.904279\pi$
$200$		0			0
$201$	1.48295	−	8.04990i	0.104600	−	0.567796i
$202$		0			0
$203$	1.79888	+	3.11575i	0.126257	+	0.218683i
$204$		0			0
$205$	−4.88835	+	8.46687i	−0.341417	+	0.591352i
$206$		0			0
$207$	−2.24130	−	3.88205i	−0.155781	−	0.269821i
$208$		0			0
$209$	−1.78806			−0.123683
$210$		0			0
$211$	−10.5562	−	18.2838i	−0.726718	−	1.25871i	−0.958263	−	0.285888i	$-0.907712\pi$
$211$	−10.5562	−	18.2838i	−0.726718	−	1.25871i	0.231545	−	0.972824i	$-0.425622\pi$
$212$		0			0
$213$	−6.37678	+	11.0449i	−0.436930	+	0.756785i
$214$		0			0
$215$	−4.88135			−0.332905
$216$		0			0
$217$	−6.65689	−	11.5301i	−0.451899	−	0.782712i
$218$		0			0
$219$	3.73675	+	6.47224i	0.252506	+	0.437353i
$220$		0			0
$221$	−0.0601397	+	0.104165i	−0.00404544	+	0.00700690i
$222$		0			0
$223$	−25.1746			−1.68581			−0.842906	−	0.538060i	$-0.819157\pi$
$223$	−25.1746			−1.68581			−0.842906	+	0.538060i	$0.819157\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	14.8271	−	25.6813i	0.984110	−	1.70453i	0.338284	−	0.941044i	$-0.390153\pi$
$227$	14.8271	−	25.6813i	0.984110	−	1.70453i	0.645826	−	0.763485i	$-0.276513\pi$
$228$		0			0
$229$	−12.8348	−	22.2305i	−0.848148	−	1.46904i	−0.882859	−	0.469638i	$-0.844384\pi$
$229$	−12.8348	−	22.2305i	−0.848148	−	1.46904i	0.0347106	−	0.999397i	$-0.488949\pi$
$230$		0			0
$231$	−3.05474	−	5.29097i	−0.200987	−	0.348120i
$232$		0			0
$233$	−10.4330	+	18.0706i	−0.683492	+	1.18384i	0.290417	+	0.956900i	$0.406206\pi$
$233$	−10.4330	+	18.0706i	−0.683492	+	1.18384i	−0.973908	+	0.226942i	$0.927127\pi$
$234$		0			0
$235$	4.20309	−	7.27996i	0.274179	−	0.474892i
$236$		0			0
$237$	6.85569	−	11.8744i	0.445325	−	0.771326i
$238$		0			0
$239$	8.15344	−	14.1222i	0.527402	−	0.913488i	−0.472087	−	0.881552i	$-0.656499\pi$
$239$	8.15344	−	14.1222i	0.527402	−	0.913488i	0.999490	−	0.0319362i	$-0.0101673\pi$
$240$		0			0
$241$	5.68032			0.365902			0.182951	−	0.983122i	$-0.441435\pi$
$241$	5.68032			0.365902			0.182951	+	0.983122i	$0.441435\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.909436	+	1.57519i	0.0581018	+	0.100635i
$246$		0			0
$247$	−0.0518106	+	0.0897386i	−0.00329663	+	0.00570993i
$248$		0			0
$249$	4.19414	+	7.26447i	0.265793	+	0.460367i
$250$		0			0
$251$	−7.53313	−	13.0478i	−0.475487	−	0.823568i	0.524119	−	0.851645i	$-0.324395\pi$
$251$	−7.53313	−	13.0478i	−0.475487	−	0.823568i	−0.999606	+	0.0280776i	$0.991061\pi$
$252$		0			0
$253$	−12.0316			−0.756420
$254$		0			0
$255$	0.386637	+	0.669675i	0.0242121	+	0.0419367i
$256$		0			0
$257$	−3.23525	+	5.60361i	−0.201809	+	0.349544i	−0.949111	−	0.314941i	$-0.898015\pi$
$257$	−3.23525	+	5.60361i	−0.201809	+	0.349544i	0.747302	+	0.664484i	$0.231349\pi$
$258$		0			0
$259$	20.9779			1.30350
$260$		0			0
$261$	0.790296	−	1.36883i	0.0489181	−	0.0847286i
$262$		0			0
$263$	−15.6255			−0.963511			−0.481755	−	0.876306i	$-0.660001\pi$
$263$	−15.6255			−0.963511			−0.481755	+	0.876306i	$0.660001\pi$
$264$		0			0
$265$	7.78200			0.478044
$266$		0			0
$267$	−5.03057			−0.307866
$268$		0			0
$269$	15.9632			0.973296			0.486648	−	0.873598i	$-0.338219\pi$
$269$	15.9632			0.973296			0.486648	+	0.873598i	$0.338219\pi$
$270$		0			0
$271$	−27.7137			−1.68349			−0.841745	−	0.539876i	$-0.818471\pi$
$271$	−27.7137			−1.68349			−0.841745	+	0.539876i	$0.818471\pi$
$272$		0			0
$273$	−0.354055			−0.0214284
$274$		0			0
$275$	1.34203	−	2.32447i	0.0809275	−	0.140171i
$276$		0			0
$277$	0.357694			0.0214918			0.0107459	−	0.999942i	$-0.496579\pi$
$277$	0.357694			0.0214918			0.0107459	+	0.999942i	$0.496579\pi$
$278$		0			0
$279$	−2.92455	+	5.06547i	−0.175088	+	0.303262i
$280$		0			0
$281$	11.6739	+	20.2197i	0.696405	+	1.20621i	0.969705	+	0.244280i	$0.0785515\pi$
$281$	11.6739	+	20.2197i	0.696405	+	1.20621i	−0.273300	+	0.961929i	$0.588115\pi$
$282$		0			0
$283$	−14.7440			−0.876443			−0.438221	−	0.898867i	$-0.644391\pi$
$283$	−14.7440			−0.876443			−0.438221	+	0.898867i	$0.644391\pi$
$284$		0			0
$285$	0.333089	+	0.576927i	0.0197305	+	0.0341742i
$286$		0			0
$287$	−11.1269	−	19.2724i	−0.656800	−	1.13761i
$288$		0			0
$289$	8.20102	−	14.2046i	0.482413	−	0.835564i
$290$		0			0
$291$	5.24485	+	9.08435i	0.307459	+	0.532534i
$292$		0			0
$293$	8.24349			0.481590			0.240795	−	0.970576i	$-0.422592\pi$
$293$	8.24349			0.481590			0.240795	+	0.970576i	$0.422592\pi$
$294$		0			0
$295$	−10.5918			−0.616676
$296$		0			0
$297$	−1.34203	+	2.32447i	−0.0778726	+	0.134879i
$298$		0			0
$299$	−0.348625	+	0.603837i	−0.0201615	+	0.0349208i
$300$		0			0
$301$	5.55549	−	9.62239i	0.320213	−	0.554625i
$302$		0			0
$303$	−0.530519	+	0.918886i	−0.0304775	+	0.0527886i
$304$		0			0
$305$	1.14396	+	1.98139i	0.0655027	+	0.113454i
$306$		0			0
$307$	1.12893	+	1.95537i	0.0644316	+	0.111599i	0.896442	−	0.443162i	$-0.146143\pi$
$307$	1.12893	+	1.95537i	0.0644316	+	0.111599i	−0.832010	+	0.554760i	$0.812810\pi$
$308$		0			0
$309$	−6.85611	+	11.8751i	−0.390031	+	0.675553i
$310$		0			0
$311$	16.7611			0.950433			0.475216	−	0.879869i	$-0.342370\pi$
$311$	16.7611			0.950433			0.475216	+	0.879869i	$0.342370\pi$
$312$		0			0
$313$	−17.9458			−1.01436			−0.507179	−	0.861841i	$-0.669312\pi$
$313$	−17.9458			−1.01436			−0.507179	+	0.861841i	$0.669312\pi$
$314$		0			0
$315$	−1.13810	+	1.97125i	−0.0641249	+	0.111068i
$316$		0			0
$317$	4.65490	+	8.06252i	0.261445	+	0.452836i	0.966626	−	0.256191i	$-0.0824676\pi$
$317$	4.65490	+	8.06252i	0.261445	+	0.452836i	−0.705181	+	0.709027i	$0.749134\pi$
$318$		0			0
$319$	−2.12120	−	3.67403i	−0.118765	−	0.205706i
$320$		0			0
$321$	18.1522			1.01316
$322$		0			0
$323$	−0.257569	+	0.446123i	−0.0143315	+	0.0248229i
$324$		0			0
$325$	−0.0777729	−	0.134707i	−0.00431406	−	0.00747218i
$326$		0			0
$327$	1.05330			0.0582474
$328$		0			0
$329$	9.56710	+	16.5707i	0.527451	+	0.913573i
$330$		0			0
$331$	5.34083	−	9.25059i	0.293559	−	0.508458i	−0.681090	−	0.732200i	$-0.738494\pi$
$331$	5.34083	−	9.25059i	0.293559	−	0.508458i	0.974649	+	0.223741i	$0.0718271\pi$
$332$		0			0
$333$	−4.60808	−	7.98142i	−0.252521	−	0.437379i
$334$		0			0
$335$	−1.48295	+	8.04990i	−0.0810225	+	0.439813i
$336$		0			0
$337$	−10.6164	−	18.3881i	−0.578311	−	1.00166i	−0.995673	−	0.0929234i	$-0.970379\pi$
$337$	−10.6164	−	18.3881i	−0.578311	−	1.00166i	0.417363	−	0.908740i	$-0.362954\pi$
$338$		0			0
$339$	−7.44853	+	12.9012i	−0.404548	+	0.700698i
$340$		0			0
$341$	7.84968	+	13.5960i	0.425084	+	0.736267i
$342$		0			0
$343$	−20.0736			−1.08387
$344$		0			0
$345$	2.24130	+	3.88205i	0.120668	+	0.209003i
$346$		0			0
$347$	−16.0343	+	27.7723i	−0.860768	+	1.49089i	0.0104202	+	0.999946i	$0.496683\pi$
$347$	−16.0343	+	27.7723i	−0.860768	+	1.49089i	−0.871188	+	0.490949i	$0.836650\pi$
$348$		0			0
$349$	−25.2370			−1.35091			−0.675453	−	0.737403i	$-0.736052\pi$
$349$	−25.2370			−1.35091			−0.675453	+	0.737403i	$0.736052\pi$
$350$		0			0
$351$	0.0777729	+	0.134707i	0.00415121	+	0.00719011i
$352$		0			0
$353$	−5.05164	−	8.74969i	−0.268872	−	0.465699i	0.699699	−	0.714438i	$-0.253317\pi$
$353$	−5.05164	−	8.74969i	−0.268872	−	0.465699i	−0.968571	+	0.248738i	$0.919984\pi$
$354$		0			0
$355$	6.37678	−	11.0449i	0.338444	−	0.586203i
$356$		0			0
$357$	−1.76013			−0.0931561
$358$		0			0
$359$	−11.1318			−0.587513			−0.293757	−	0.955880i	$-0.594905\pi$
$359$	−11.1318			−0.587513			−0.293757	+	0.955880i	$0.594905\pi$
$360$		0			0
$361$	9.27810	−	16.0701i	0.488321	−	0.845797i
$362$		0			0
$363$	−1.89790	−	3.28727i	−0.0996141	−	0.172537i
$364$		0			0
$365$	−3.73675	−	6.47224i	−0.195590	−	0.338772i
$366$		0			0
$367$	8.67010	−	15.0170i	0.452575	−	0.783883i	−0.545970	−	0.837805i	$-0.683839\pi$
$367$	8.67010	−	15.0170i	0.452575	−	0.783883i	0.998545	+	0.0539214i	$0.0171720\pi$
$368$		0			0
$369$	−4.88835	+	8.46687i	−0.254477	+	0.440768i
$370$		0			0
$371$	−8.85672	+	15.3403i	−0.459818	+	0.796429i
$372$		0			0
$373$	7.58109	−	13.1308i	0.392534	−	0.679889i	−0.600249	−	0.799813i	$-0.704932\pi$
$373$	7.58109	−	13.1308i	0.392534	−	0.679889i	0.992783	+	0.119924i	$0.0382652\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−0.245854			−0.0126621
$378$		0			0
$379$	6.59791	+	11.4279i	0.338912	+	0.587012i	0.984228	−	0.176903i	$-0.0566078\pi$
$379$	6.59791	+	11.4279i	0.338912	+	0.587012i	−0.645317	+	0.763915i	$0.723275\pi$
$380$		0			0
$381$	−5.45909	+	9.45542i	−0.279678	+	0.484416i
$382$		0			0
$383$	10.0816	+	17.4619i	0.515147	+	0.892260i	0.999845	+	0.0175790i	$0.00559585\pi$
$383$	10.0816	+	17.4619i	0.515147	+	0.892260i	−0.484699	+	0.874681i	$0.661071\pi$
$384$		0			0
$385$	3.05474	+	5.29097i	0.155684	+	0.269653i
$386$		0			0
$387$	−4.88135			−0.248133
$388$		0			0
$389$	−8.55329	−	14.8147i	−0.433669	−	0.751137i	0.563517	−	0.826105i	$-0.309448\pi$
$389$	−8.55329	−	14.8147i	−0.433669	−	0.751137i	−0.997186	+	0.0749675i	$0.976115\pi$
$390$		0			0
$391$	−1.73314	+	3.00189i	−0.0876487	+	0.151812i
$392$		0			0
$393$	4.93164			0.248769
$394$		0			0
$395$	−6.85569	+	11.8744i	−0.344947	+	0.597466i
$396$		0			0
$397$	−3.18544			−0.159873			−0.0799364	−	0.996800i	$-0.525472\pi$
$397$	−3.18544			−0.159873			−0.0799364	+	0.996800i	$0.525472\pi$
$398$		0			0
$399$	−1.51636			−0.0759130
$400$		0			0
$401$	13.3423			0.666283			0.333142	−	0.942877i	$-0.391891\pi$
$401$	13.3423			0.666283			0.333142	+	0.942877i	$0.391891\pi$
$402$		0			0
$403$	0.909803			0.0453205
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−24.7367			−1.22615
$408$		0			0
$409$	9.68190	−	16.7695i	0.478739	−	0.829201i	−0.520964	−	0.853579i	$-0.674427\pi$
$409$	9.68190	−	16.7695i	0.478739	−	0.829201i	0.999703	+	0.0243783i	$0.00776063\pi$
$410$		0			0
$411$	−9.40754			−0.464040
$412$		0			0
$413$	12.0545	−	20.8791i	0.593165	−	1.02739i
$414$		0			0
$415$	−4.19414	−	7.26447i	−0.205882	−	0.356599i
$416$		0			0
$417$	9.64017			0.472081
$418$		0			0
$419$	−17.1638	−	29.7286i	−0.838507	−	1.45234i	−0.891143	−	0.453722i	$-0.850096\pi$
$419$	−17.1638	−	29.7286i	−0.838507	−	1.45234i	0.0526366	−	0.998614i	$-0.483237\pi$
$420$		0			0
$421$	16.4008	+	28.4070i	0.799324	+	1.38447i	0.920057	+	0.391785i	$0.128142\pi$
$421$	16.4008	+	28.4070i	0.799324	+	1.38447i	−0.120732	+	0.992685i	$0.538524\pi$
$422$		0			0
$423$	4.20309	−	7.27996i	0.204361	−	0.353964i
$424$		0			0
$425$	−0.386637	−	0.669675i	−0.0187546	−	0.0324840i
$426$		0			0
$427$	−5.20776			−0.252021
$428$		0			0
$429$	0.417495			0.0201568
$430$		0			0
$431$	−13.6080	+	23.5698i	−0.655476	+	1.13532i	0.326298	+	0.945267i	$0.394199\pi$
$431$	−13.6080	+	23.5698i	−0.655476	+	1.13532i	−0.981774	+	0.190051i	$0.939135\pi$
$432$		0			0
$433$	1.39442	−	2.41520i	0.0670114	−	0.116067i	−0.830573	−	0.556910i	$-0.811987\pi$
$433$	1.39442	−	2.41520i	0.0670114	−	0.116067i	0.897584	+	0.440843i	$0.145320\pi$
$434$		0			0
$435$	−0.790296	+	1.36883i	−0.0378918	+	0.0656305i
$436$		0			0
$437$	−1.49311	+	2.58614i	−0.0714250	+	0.123712i
$438$		0			0
$439$	−12.1856	−	21.1060i	−0.581586	−	1.00734i	−0.995292	−	0.0969252i	$-0.969099\pi$
$439$	−12.1856	−	21.1060i	−0.581586	−	1.00734i	0.413706	−	0.910410i	$-0.364234\pi$
$440$		0			0
$441$	0.909436	+	1.57519i	0.0433065	+	0.0750090i
$442$		0			0
$443$	17.4251	−	30.1812i	0.827893	−	1.43395i	−0.0717957	−	0.997419i	$-0.522873\pi$
$443$	17.4251	−	30.1812i	0.827893	−	1.43395i	0.899688	−	0.436533i	$-0.143794\pi$
$444$		0			0
$445$	5.03057			0.238472
$446$		0			0
$447$	12.3962			0.586321
$448$		0			0
$449$	−0.512740	+	0.888091i	−0.0241977	+	0.0419116i	−0.877871	−	0.478898i	$-0.841036\pi$
$449$	−0.512740	+	0.888091i	−0.0241977	+	0.0419116i	0.853673	+	0.520809i	$0.174370\pi$
$450$		0			0
$451$	13.1206	+	22.7256i	0.617827	+	1.07011i
$452$		0			0
$453$	2.27804	+	3.94569i	0.107032	+	0.185385i
$454$		0			0
$455$	0.354055			0.0165983
$456$		0			0
$457$	5.04794	−	8.74328i	0.236132	−	0.408993i	−0.723469	−	0.690357i	$-0.757453\pi$
$457$	5.04794	−	8.74328i	0.236132	−	0.408993i	0.959601	+	0.281364i	$0.0907867\pi$
$458$		0			0
$459$	0.386637	+	0.669675i	0.0180467	+	0.0312577i
$460$		0			0
$461$	−15.8337			−0.737447			−0.368723	−	0.929539i	$-0.620205\pi$
$461$	−15.8337			−0.737447			−0.368723	+	0.929539i	$0.620205\pi$
$462$		0			0
$463$	−16.9607	−	29.3768i	−0.788230	−	1.36525i	−0.927050	−	0.374937i	$-0.877664\pi$
$463$	−16.9607	−	29.3768i	−0.788230	−	1.36525i	0.138820	−	0.990318i	$-0.455669\pi$
$464$		0			0
$465$	2.92455	−	5.06547i	0.135623	−	0.234906i
$466$		0			0
$467$	17.2039	+	29.7981i	0.796103	+	1.37889i	0.922137	+	0.386864i	$0.126442\pi$
$467$	17.2039	+	29.7981i	0.796103	+	1.37889i	−0.126034	+	0.992026i	$0.540225\pi$
$468$		0			0
$469$	−14.1806	−	12.0849i	−0.654801	−	0.558029i
$470$		0			0
$471$	−1.44535	−	2.50342i	−0.0665982	−	0.115352i
$472$		0			0
$473$	−6.55093	+	11.3465i	−0.301212	+	0.521714i
$474$		0			0
$475$	−0.333089	−	0.576927i	−0.0152832	−	0.0264712i
$476$		0			0
$477$	7.78200			0.356313
$478$		0			0
$479$	−5.27156	−	9.13061i	−0.240864	−	0.417188i	0.720097	−	0.693874i	$-0.244097\pi$
$479$	−5.27156	−	9.13061i	−0.240864	−	0.417188i	−0.960961	+	0.276685i	$0.910764\pi$
$480$		0			0
$481$	−0.716767	+	1.24148i	−0.0326818	+	0.0566065i
$482$		0			0
$483$	−10.2033			−0.464268
$484$		0			0
$485$	−5.24485	−	9.08435i	−0.238156	−	0.412499i
$486$		0			0
$487$	14.2516	+	24.6845i	0.645802	+	1.11856i	0.984116	+	0.177529i	$0.0568102\pi$
$487$	14.2516	+	24.6845i	0.645802	+	1.11856i	−0.338314	+	0.941033i	$0.609856\pi$
$488$		0			0
$489$	−7.15348	+	12.3902i	−0.323492	+	0.560304i
$490$		0			0
$491$	27.4994			1.24103			0.620515	−	0.784195i	$-0.286924\pi$
$491$	27.4994			1.24103			0.620515	+	0.784195i	$0.286924\pi$
$492$		0			0
$493$	−1.22223			−0.0550465
$494$		0			0
$495$	1.34203	−	2.32447i	0.0603198	−	0.104477i
$496$		0			0
$497$	14.5149	+	25.1405i	0.651082	+	1.12771i
$498$		0			0
$499$	14.1244	+	24.4641i	0.632294	+	1.09517i	0.987082	+	0.160218i	$0.0512198\pi$
$499$	14.1244	+	24.4641i	0.632294	+	1.09517i	−0.354788	+	0.934947i	$0.615447\pi$
$500$		0			0
$501$	12.0904	−	20.9412i	0.540160	−	0.935584i
$502$		0			0
$503$	−12.4351	+	21.5382i	−0.554454	+	0.960342i	0.443492	+	0.896278i	$0.353739\pi$
$503$	−12.4351	+	21.5382i	−0.554454	+	0.960342i	−0.997946	+	0.0640637i	$0.979594\pi$
$504$		0			0
$505$	0.530519	−	0.918886i	0.0236078	−	0.0408899i
$506$		0			0
$507$	−6.48790	+	11.2374i	−0.288138	+	0.499069i
$508$		0			0
$509$	37.5674			1.66514			0.832572	−	0.553917i	$-0.186867\pi$
$509$	37.5674			1.66514			0.832572	+	0.553917i	$0.186867\pi$
$510$		0			0
$511$	17.0112			0.752533
$512$		0			0
$513$	0.333089	+	0.576927i	0.0147062	+	0.0254720i
$514$		0			0
$515$	6.85611	−	11.8751i	0.302116	−	0.523281i
$516$		0			0
$517$	−11.2813	−	19.5399i	−0.496153	−	0.859362i
$518$		0			0
$519$	11.6805	+	20.2313i	0.512718	+	0.888054i
$520$		0			0
$521$	4.44091			0.194560			0.0972800	−	0.995257i	$-0.468986\pi$
$521$	4.44091			0.194560			0.0972800	+	0.995257i	$0.468986\pi$
$522$		0			0
$523$	7.35695	+	12.7426i	0.321697	+	0.557196i	0.980838	−	0.194823i	$-0.0624134\pi$
$523$	7.35695	+	12.7426i	0.321697	+	0.557196i	−0.659141	+	0.752019i	$0.729080\pi$
$524$		0			0
$525$	1.13810	−	1.97125i	0.0496710	−	0.0860326i
$526$		0			0
$527$	4.52296			0.197023
$528$		0			0
$529$	1.45312	−	2.51688i	0.0631791	−	0.109429i
$530$		0			0
$531$	−10.5918			−0.459643
$532$		0			0
$533$	1.52072			0.0658699
$534$		0			0
$535$	−18.1522			−0.784789
$536$		0			0
$537$	7.46602			0.322182
$538$		0			0
$539$	4.88197			0.210281
$540$		0			0
$541$	−8.90460			−0.382839			−0.191419	−	0.981508i	$-0.561309\pi$
$541$	−8.90460			−0.382839			−0.191419	+	0.981508i	$0.561309\pi$
$542$		0			0
$543$	4.45233	−	7.71165i	0.191068	−	0.330939i
$544$		0			0
$545$	−1.05330			−0.0451183
$546$		0			0
$547$	14.6728	−	25.4140i	0.627363	−	1.08663i	−0.360715	−	0.932676i	$-0.617467\pi$
$547$	14.6728	−	25.4140i	0.627363	−	1.08663i	0.988079	−	0.153949i	$-0.0491992\pi$
$548$		0			0
$549$	1.14396	+	1.98139i	0.0488228	+	0.0845636i
$550$		0			0
$551$	−1.05296			−0.0448574
$552$		0			0
$553$	−15.6050	−	27.0286i	−0.663592	−	1.14937i
$554$		0			0
$555$	4.60808	+	7.98142i	0.195602	+	0.338792i
$556$		0			0
$557$	2.59596	−	4.49633i	0.109994	−	0.190516i	−0.805773	−	0.592224i	$-0.798250\pi$
$557$	2.59596	−	4.49633i	0.109994	−	0.190516i	0.915768	+	0.401708i	$0.131583\pi$
$558$		0			0
$559$	0.379637	+	0.657550i	0.0160569	+	0.0278114i
$560$		0			0
$561$	2.07552			0.0876283
$562$		0			0
$563$	10.9825			0.462859			0.231430	−	0.972852i	$-0.425660\pi$
$563$	10.9825			0.462859			0.231430	+	0.972852i	$0.425660\pi$
$564$		0			0
$565$	7.44853	−	12.9012i	0.313362	−	0.542759i
$566$		0			0
$567$	−1.13810	+	1.97125i	−0.0477959	+	0.0827849i
$568$		0			0
$569$	3.96707	−	6.87116i	0.166308	−	0.288054i	−0.770811	−	0.637064i	$-0.780149\pi$
$569$	3.96707	−	6.87116i	0.166308	−	0.288054i	0.937119	+	0.349010i	$0.113482\pi$
$570$		0			0
$571$	16.8047	−	29.1067i	0.703257	−	1.21808i	−0.264060	−	0.964506i	$-0.585062\pi$
$571$	16.8047	−	29.1067i	0.703257	−	1.21808i	0.967317	−	0.253570i	$-0.0816049\pi$
$572$		0			0
$573$	−9.74545	−	16.8796i	−0.407122	−	0.705156i
$574$		0			0
$575$	−2.24130	−	3.88205i	−0.0934688	−	0.161893i
$576$		0			0
$577$	0.0491809	−	0.0851838i	0.00204743	−	0.00354625i	−0.865000	−	0.501772i	$-0.832682\pi$
$577$	0.0491809	−	0.0851838i	0.00204743	−	0.00354625i	0.867047	+	0.498226i	$0.166015\pi$
$578$		0			0
$579$	−9.62585			−0.400037
$580$		0			0
$581$	19.0935			0.792132
$582$		0			0
$583$	10.4437	−	18.0890i	0.432533	−	0.749169i
$584$		0			0
$585$	−0.0777729	−	0.134707i	−0.00321551	−	0.00556943i
$586$		0			0
$587$	11.6866	+	20.2417i	0.482356	+	0.835465i	0.999795	−	0.0202548i	$-0.00644776\pi$
$587$	11.6866	+	20.2417i	0.482356	+	0.835465i	−0.517439	+	0.855720i	$0.673114\pi$
$588$		0			0
$589$	3.89655			0.160554
$590$		0			0
$591$	−1.58812	+	2.75070i	−0.0653265	+	0.113149i
$592$		0			0
$593$	−10.1112	−	17.5130i	−0.415215	−	0.719174i	0.580236	−	0.814449i	$-0.302960\pi$
$593$	−10.1112	−	17.5130i	−0.415215	−	0.719174i	−0.995451	+	0.0952746i	$0.969627\pi$
$594$		0			0
$595$	1.76013			0.0721584
$596$		0			0
$597$	3.11819	+	5.40087i	0.127619	+	0.221043i
$598$		0			0
$599$	0.326232	−	0.565051i	0.0133295	−	0.0230874i	−0.859284	−	0.511499i	$-0.829090\pi$
$599$	0.326232	−	0.565051i	0.0133295	−	0.0230874i	0.872613	+	0.488412i	$0.162424\pi$
$600$		0			0
$601$	12.7792	+	22.1342i	0.521275	+	0.902874i	0.999694	+	0.0247426i	$0.00787662\pi$
$601$	12.7792	+	22.1342i	0.521275	+	0.902874i	−0.478419	+	0.878132i	$0.658790\pi$
$602$		0			0
$603$	−1.48295	+	8.04990i	−0.0603906	+	0.327817i
$604$		0			0
$605$	1.89790	+	3.28727i	0.0771608	+	0.133646i
$606$		0			0
$607$	−6.76139	+	11.7111i	−0.274436	+	0.475338i	−0.969993	−	0.243134i	$-0.921825\pi$
$607$	−6.76139	+	11.7111i	−0.274436	+	0.475338i	0.695556	+	0.718471i	$0.255158\pi$
$608$		0			0
$609$	−1.79888	−	3.11575i	−0.0728942	−	0.126257i
$610$		0			0
$611$	−1.30754			−0.0528976
$612$		0			0
$613$	−1.81636	−	3.14602i	−0.0733620	−	0.127067i	0.827011	−	0.562186i	$-0.190040\pi$
$613$	−1.81636	−	3.14602i	−0.0733620	−	0.127067i	−0.900373	+	0.435119i	$0.856706\pi$
$614$		0			0
$615$	4.88835	−	8.46687i	0.197117	−	0.341417i
$616$		0			0
$617$	−17.7653			−0.715203			−0.357602	−	0.933874i	$-0.616405\pi$
$617$	−17.7653			−0.715203			−0.357602	+	0.933874i	$0.616405\pi$
$618$		0			0
$619$	−9.77863	−	16.9371i	−0.393036	−	0.680759i	0.599812	−	0.800141i	$-0.295242\pi$
$619$	−9.77863	−	16.9371i	−0.393036	−	0.680759i	−0.992848	+	0.119382i	$0.961909\pi$
$620$		0			0
$621$	2.24130	+	3.88205i	0.0899404	+	0.155781i
$622$		0			0
$623$	−5.72531	+	9.91653i	−0.229380	+	0.397297i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	1.78806			0.0714084
$628$		0			0
$629$	−3.56330	+	6.17182i	−0.142078	+	0.246087i
$630$		0			0
$631$	15.6938	+	27.1824i	0.624759	+	1.08211i	0.988587	+	0.150648i	$0.0481360\pi$
$631$	15.6938	+	27.1824i	0.624759	+	1.08211i	−0.363829	+	0.931466i	$0.618531\pi$
$632$		0			0
$633$	10.5562	+	18.2838i	0.419571	+	0.726718i
$634$		0			0
$635$	5.45909	−	9.45542i	0.216637	−	0.375227i
$636$		0			0
$637$	0.141459	−	0.245014i	0.00560481	−	0.00970781i
$638$		0			0
$639$	6.37678	−	11.0449i	0.252262	−	0.436930i
$640$		0			0
$641$	0.370192	−	0.641191i	0.0146217	−	0.0253255i	−0.858622	−	0.512609i	$-0.828679\pi$
$641$	0.370192	−	0.641191i	0.0146217	−	0.0253255i	0.873244	+	0.487284i	$0.162012\pi$
$642$		0			0
$643$	−47.8156			−1.88566			−0.942832	−	0.333268i	$-0.891848\pi$
$643$	−47.8156			−1.88566			−0.942832	+	0.333268i	$0.891848\pi$
$644$		0			0
$645$	4.88135			0.192203
$646$		0			0
$647$	18.8521	+	32.6527i	0.741151	+	1.28371i	0.951972	+	0.306186i	$0.0990531\pi$
$647$	18.8521	+	32.6527i	0.741151	+	1.28371i	−0.210821	+	0.977525i	$0.567614\pi$
$648$		0			0
$649$	−14.2145	+	24.6202i	−0.557967	+	0.966427i
$650$		0			0
$651$	6.65689	+	11.5301i	0.260904	+	0.451899i
$652$		0			0
$653$	16.7316	+	28.9800i	0.654759	+	1.13408i	0.981954	+	0.189119i	$0.0605633\pi$
$653$	16.7316	+	28.9800i	0.654759	+	1.13408i	−0.327195	+	0.944957i	$0.606103\pi$
$654$		0			0
$655$	−4.93164			−0.192695
$656$		0			0
$657$	−3.73675	−	6.47224i	−0.145784	−	0.252506i
$658$		0			0
$659$	17.0677	−	29.5620i	0.664861	−	1.15157i	−0.314461	−	0.949270i	$-0.601824\pi$
$659$	17.0677	−	29.5620i	0.664861	−	1.15157i	0.979323	−	0.202303i	$-0.0648427\pi$
$660$		0			0
$661$	−29.4211			−1.14435			−0.572175	−	0.820132i	$-0.693900\pi$
$661$	−29.4211			−1.14435			−0.572175	+	0.820132i	$0.693900\pi$
$662$		0			0
$663$	0.0601397	−	0.104165i	0.00233563	−	0.00404544i
$664$		0			0
$665$	1.51636			0.0588020
$666$		0			0
$667$	−7.08517			−0.274339
$668$		0			0
$669$	25.1746			0.973305
$670$		0			0
$671$	6.14090			0.237067
$672$		0			0
$673$	−45.3295			−1.74733			−0.873663	−	0.486532i	$-0.838262\pi$
$673$	−45.3295			−1.74733			−0.873663	+	0.486532i	$0.838262\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	7.56313	−	13.0997i	0.290675	−	0.503464i	−0.683295	−	0.730143i	$-0.739454\pi$
$677$	7.56313	−	13.0997i	0.290675	−	0.503464i	0.973969	+	0.226679i	$0.0727869\pi$
$678$		0			0
$679$	23.8767			0.916306
$680$		0			0
$681$	−14.8271	+	25.6813i	−0.568176	+	0.984110i
$682$		0			0
$683$	15.0573	+	26.0800i	0.576151	+	0.997923i	0.995916	+	0.0902896i	$0.0287793\pi$
$683$	15.0573	+	26.0800i	0.576151	+	0.997923i	−0.419765	+	0.907633i	$0.637887\pi$
$684$		0			0
$685$	9.40754			0.359444
$686$		0			0
$687$	12.8348	+	22.2305i	0.489679	+	0.848148i
$688$		0			0
$689$	−0.605228	−	1.04829i	−0.0230574	−	0.0399365i
$690$		0			0
$691$	−23.7019	+	41.0528i	−0.901661	+	1.56172i	−0.0763236	+	0.997083i	$0.524318\pi$
$691$	−23.7019	+	41.0528i	−0.901661	+	1.56172i	−0.825337	+	0.564640i	$0.809015\pi$
$692$		0			0
$693$	3.05474	+	5.29097i	0.116040	+	0.200987i
$694$		0			0
$695$	−9.64017			−0.365672
$696$		0			0
$697$	7.56007			0.286358
$698$		0			0
$699$	10.4330	−	18.0706i	0.394614	−	0.683492i
$700$		0			0
$701$	−22.2350	+	38.5122i	−0.839805	+	1.45459i	0.0502518	+	0.998737i	$0.483998\pi$
$701$	−22.2350	+	38.5122i	−0.839805	+	1.45459i	−0.890057	+	0.455849i	$0.849336\pi$
$702$		0			0
$703$	−3.06980	+	5.31705i	−0.115780	+	0.200536i
$704$		0			0
$705$	−4.20309	+	7.27996i	−0.158297	+	0.274179i
$706$		0			0
$707$	1.20757	+	2.09158i	0.0454154	+	0.0786618i
$708$		0			0
$709$	22.8950	+	39.6552i	0.859838	+	1.48928i	0.872083	+	0.489359i	$0.162769\pi$
$709$	22.8950	+	39.6552i	0.859838	+	1.48928i	−0.0122444	+	0.999925i	$0.503898\pi$
$710$		0			0
$711$	−6.85569	+	11.8744i	−0.257109	+	0.445325i
$712$		0			0
$713$	26.2192			0.981918
$714$		0			0
$715$	−0.417495			−0.0156134
$716$		0			0
$717$	−8.15344	+	14.1222i	−0.304496	+	0.527402i
$718$		0			0
$719$	−5.56816	−	9.64434i	−0.207657	−	0.359673i	0.743319	−	0.668937i	$-0.233251\pi$
$719$	−5.56816	−	9.64434i	−0.207657	−	0.359673i	−0.950976	+	0.309264i	$0.899917\pi$
$720$		0			0
$721$	15.6059	+	27.0303i	0.581196	+	1.00666i
$722$		0			0
$723$	−5.68032			−0.211254
$724$		0			0
$725$	0.790296	−	1.36883i	0.0293509	−	0.0508372i
$726$		0			0
$727$	3.06823	+	5.31433i	0.113794	+	0.197098i	0.917297	−	0.398203i	$-0.130366\pi$
$727$	3.06823	+	5.31433i	0.113794	+	0.197098i	−0.803503	+	0.595301i	$0.797033\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.88731	+	3.26892i	0.0698047	+	0.120905i
$732$		0			0
$733$	8.05415	−	13.9502i	0.297487	−	0.515262i	−0.678074	−	0.734994i	$-0.737185\pi$
$733$	8.05415	−	13.9502i	0.297487	−	0.515262i	0.975560	+	0.219732i	$0.0705183\pi$
$734$		0			0
$735$	−0.909436	−	1.57519i	−0.0335451	−	0.0581018i
$736$		0			0
$737$	16.7215	+	14.2503i	0.615946	+	0.524916i
$738$		0			0
$739$	−2.96273	−	5.13160i	−0.108986	−	0.188769i	0.806374	−	0.591406i	$-0.201427\pi$
$739$	−2.96273	−	5.13160i	−0.108986	−	0.188769i	−0.915360	+	0.402637i	$0.868094\pi$
$740$		0			0
$741$	0.0518106	−	0.0897386i	0.00190331	−	0.00329663i
$742$		0			0
$743$	4.76725	+	8.25711i	0.174893	+	0.302924i	0.940124	−	0.340832i	$-0.110709\pi$
$743$	4.76725	+	8.25711i	0.174893	+	0.302924i	−0.765231	+	0.643756i	$0.777375\pi$
$744$		0			0
$745$	−12.3962			−0.454163
$746$		0			0
$747$	−4.19414	−	7.26447i	−0.153456	−	0.265793i
$748$		0			0
$749$	20.6591	−	35.7826i	0.754868	−	1.30747i
$750$		0			0
$751$	25.5634			0.932820			0.466410	−	0.884569i	$-0.345547\pi$
$751$	25.5634			0.932820			0.466410	+	0.884569i	$0.345547\pi$
$752$		0			0
$753$	7.53313	+	13.0478i	0.274523	+	0.475487i
$754$		0			0
$755$	−2.27804	−	3.94569i	−0.0829065	−	0.143598i
$756$		0			0
$757$	−6.43229	+	11.1410i	−0.233785	+	0.404928i	−0.958919	−	0.283680i	$-0.908445\pi$
$757$	−6.43229	+	11.1410i	−0.233785	+	0.404928i	0.725134	+	0.688608i	$0.241778\pi$
$758$		0			0
$759$	12.0316			0.436719
$760$		0			0
$761$	41.3565			1.49917			0.749585	−	0.661908i	$-0.230253\pi$
$761$	41.3565			1.49917			0.749585	+	0.661908i	$0.230253\pi$
$762$		0			0
$763$	1.19876	−	2.07632i	0.0433981	−	0.0751677i
$764$		0			0
$765$	−0.386637	−	0.669675i	−0.0139789	−	0.0242121i
$766$		0			0
$767$	0.823752	+	1.42678i	0.0297439	+	0.0515180i
$768$		0			0
$769$	−20.4554	+	35.4298i	−0.737640	+	1.27763i	0.215915	+	0.976412i	$0.430727\pi$
$769$	−20.4554	+	35.4298i	−0.737640	+	1.27763i	−0.953555	+	0.301218i	$0.902607\pi$
$770$		0			0
$771$	3.23525	−	5.60361i	0.116515	−	0.201809i
$772$		0			0
$773$	−16.4205	+	28.4412i	−0.590605	+	1.02296i	0.403546	+	0.914960i	$0.367778\pi$
$773$	−16.4205	+	28.4412i	−0.590605	+	1.02296i	−0.994151	+	0.107999i	$0.965556\pi$
$774$		0			0
$775$	−2.92455	+	5.06547i	−0.105053	+	0.181957i
$776$		0			0
$777$	−20.9779			−0.752578
$778$		0			0
$779$	6.51303			0.233353
$780$		0			0
$781$	−17.1157	−	29.6452i	−0.612447	−	1.06079i
$782$		0			0
$783$	−0.790296	+	1.36883i	−0.0282429	+	0.0489181i
$784$		0			0
$785$	1.44535	+	2.50342i	0.0515868	+	0.0893509i
$786$		0			0
$787$	6.21479	+	10.7643i	0.221533	+	0.383707i	0.955274	−	0.295723i	$-0.0955605\pi$
$787$	6.21479	+	10.7643i	0.221533	+	0.383707i	−0.733740	+	0.679430i	$0.762227\pi$
$788$		0			0
$789$	15.6255			0.556283
$790$		0			0
$791$	16.9544	+	29.3659i	0.602829	+	1.04413i
$792$		0			0
$793$	0.177937	−	0.308197i	0.00631874	−	0.0109444i
$794$		0			0
$795$	−7.78200			−0.275999
$796$		0			0
$797$	0.212702	−	0.368411i	0.00753429	−	0.0130498i	−0.862234	−	0.506511i	$-0.830935\pi$
$797$	0.212702	−	0.368411i	0.00753429	−	0.0130498i	0.869768	+	0.493461i	$0.164268\pi$
$798$		0			0
$799$	−6.50027			−0.229963
$800$		0			0
$801$	5.03057			0.177746
$802$		0			0
$803$	−20.0593			−0.707879
$804$		0			0
$805$	10.2033			0.359621
$806$		0			0
$807$	−15.9632			−0.561933
$808$		0			0
$809$	−25.9056			−0.910792			−0.455396	−	0.890289i	$-0.650502\pi$
$809$	−25.9056			−0.910792			−0.455396	+	0.890289i	$0.650502\pi$
$810$		0			0
$811$	13.0245	−	22.5591i	0.457353	−	0.792158i	−0.541467	−	0.840722i	$-0.682131\pi$
$811$	13.0245	−	22.5591i	0.457353	−	0.792158i	0.998820	+	0.0485636i	$0.0154644\pi$
$812$		0			0
$813$	27.7137			0.971963
$814$		0			0
$815$	7.15348	−	12.3902i	0.250576	−	0.434010i
$816$		0			0
$817$	1.62593	+	2.81619i	0.0568839	+	0.0985258i
$818$		0			0
$819$	0.354055			0.0123717
$820$		0			0
$821$	−1.38469	−	2.39836i	−0.0483261	−	0.0837032i	0.840851	−	0.541267i	$-0.182055\pi$
$821$	−1.38469	−	2.39836i	−0.0483261	−	0.0837032i	−0.889177	+	0.457564i	$0.848722\pi$
$822$		0			0
$823$	15.6250	+	27.0632i	0.544652	+	0.943366i	0.998629	+	0.0523518i	$0.0166717\pi$
$823$	15.6250	+	27.0632i	0.544652	+	0.943366i	−0.453976	+	0.891014i	$0.649995\pi$
$824$		0			0
$825$	−1.34203	+	2.32447i	−0.0467235	+	0.0809275i
$826$		0			0
$827$	−11.4717	−	19.8695i	−0.398909	−	0.690931i	0.594682	−	0.803961i	$-0.297278\pi$
$827$	−11.4717	−	19.8695i	−0.398909	−	0.690931i	−0.993592	+	0.113029i	$0.963945\pi$
$828$		0			0
$829$	42.3864			1.47214			0.736071	−	0.676904i	$-0.236679\pi$
$829$	42.3864			1.47214			0.736071	+	0.676904i	$0.236679\pi$
$830$		0			0
$831$	−0.357694			−0.0124083
$832$		0			0
$833$	0.703243	−	1.21805i	0.0243659	−	0.0422030i
$834$		0			0
$835$	−12.0904	+	20.9412i	−0.418406	+	0.724700i
$836$		0			0
$837$	2.92455	−	5.06547i	0.101087	−	0.175088i
$838$		0			0
$839$	−10.4241	+	18.0551i	−0.359880	+	0.623330i	−0.987940	−	0.154834i	$-0.950516\pi$
$839$	−10.4241	+	18.0551i	−0.359880	+	0.623330i	0.628061	+	0.778164i	$0.283849\pi$
$840$		0			0
$841$	13.2509	+	22.9512i	0.456926	+	0.791420i
$842$		0			0
$843$	−11.6739	−	20.2197i	−0.402069	−	0.696405i
$844$		0			0
$845$	6.48790	−	11.2374i	0.223191	−	0.386578i
$846$		0			0
$847$	−8.64005			−0.296876
$848$		0			0
$849$	14.7440			0.506014
$850$		0			0
$851$	−20.6562	+	35.7776i	−0.708085	+	1.22644i
$852$		0			0
$853$	−24.8234	−	42.9953i	−0.849936	−	1.47213i	−0.881265	−	0.472623i	$-0.843307\pi$
$853$	−24.8234	−	42.9953i	−0.849936	−	1.47213i	0.0313285	−	0.999509i	$-0.490026\pi$
$854$		0			0
$855$	−0.333089	−	0.576927i	−0.0113914	−	0.0197305i
$856$		0			0
$857$	41.1807			1.40670			0.703352	−	0.710841i	$-0.251686\pi$
$857$	41.1807			1.40670			0.703352	+	0.710841i	$0.251686\pi$
$858$		0			0
$859$	−25.0265	+	43.3472i	−0.853894	+	1.47899i	0.0237727	+	0.999717i	$0.492432\pi$
$859$	−25.0265	+	43.3472i	−0.853894	+	1.47899i	−0.877667	+	0.479271i	$0.840901\pi$
$860$		0			0
$861$	11.1269	+	19.2724i	0.379204	+	0.656800i
$862$		0			0
$863$	−7.49286			−0.255060			−0.127530	−	0.991835i	$-0.540705\pi$
$863$	−7.49286			−0.255060			−0.127530	+	0.991835i	$0.540705\pi$
$864$		0			0
$865$	−11.6805	−	20.2313i	−0.397150	−	0.687884i
$866$		0			0
$867$	−8.20102	+	14.2046i	−0.278521	+	0.482413i
$868$		0			0
$869$	18.4011	+	31.8717i	0.624215	+	1.08117i
$870$		0			0
$871$	1.19971	−	0.426300i	0.0406506	−	0.0144446i
$872$		0			0
$873$	−5.24485	−	9.08435i	−0.177511	−	0.307459i
$874$		0			0
$875$	−1.13810	+	1.97125i	−0.0384750	+	0.0666406i
$876$		0			0
$877$	14.6108	+	25.3066i	0.493371	+	0.854544i	0.999971	−	0.00763710i	$-0.00243099\pi$
$877$	14.6108	+	25.3066i	0.493371	+	0.854544i	−0.506599	+	0.862182i	$0.669098\pi$
$878$		0			0
$879$	−8.24349			−0.278046
$880$		0			0
$881$	24.8344	+	43.0144i	0.836692	+	1.44919i	0.892645	+	0.450760i	$0.148847\pi$
$881$	24.8344	+	43.0144i	0.836692	+	1.44919i	−0.0559527	+	0.998433i	$0.517820\pi$
$882$		0			0
$883$	28.7036	−	49.7160i	0.965952	−	1.67308i	0.258917	−	0.965900i	$-0.416634\pi$
$883$	28.7036	−	49.7160i	0.965952	−	1.67308i	0.707035	−	0.707179i	$-0.250032\pi$
$884$		0			0
$885$	10.5918			0.356038
$886$		0			0
$887$	20.7819	+	35.9954i	0.697789	+	1.20861i	0.969231	+	0.246151i	$0.0791659\pi$
$887$	20.7819	+	35.9954i	0.697789	+	1.20861i	−0.271443	+	0.962455i	$0.587501\pi$
$888$		0			0
$889$	12.4260	+	21.5225i	0.416755	+	0.721842i
$890$		0			0
$891$	1.34203	−	2.32447i	0.0449597	−	0.0778726i
$892$		0			0
$893$	−5.60001			−0.187397
$894$		0			0
$895$	−7.46602			−0.249561
$896$		0			0
$897$	0.348625	−	0.603837i	0.0116403	−	0.0201615i
$898$		0			0
$899$	4.62252	+	8.00644i	0.154170	+	0.267030i
$900$		0			0
$901$	−3.00881	−	5.21141i	−0.100238	−	0.173617i
$902$		0			0
$903$	−5.55549	+	9.62239i	−0.184875	+	0.320213i
$904$		0			0
$905$	−4.45233	+	7.71165i	−0.148000	+	0.256344i
$906$		0			0
$907$	−1.92559	+	3.33523i	−0.0639383	+	0.110744i	−0.896223	−	0.443605i	$-0.853699\pi$
$907$	−1.92559	+	3.33523i	−0.0639383	+	0.110744i	0.832284	+	0.554349i	$0.187033\pi$
$908$		0			0
$909$	0.530519	−	0.918886i	0.0175962	−	0.0304775i
$910$		0			0
$911$	25.2093			0.835223			0.417611	−	0.908626i	$-0.362867\pi$
$911$	25.2093			0.835223			0.417611	+	0.908626i	$0.362867\pi$
$912$		0			0
$913$	−22.5147			−0.745128
$914$		0			0
$915$	−1.14396	−	1.98139i	−0.0378180	−	0.0655027i
$916$		0			0
$917$	5.61273	−	9.72153i	0.185349	−	0.321033i
$918$		0			0
$919$	11.7053	+	20.2741i	0.386122	+	0.668782i	0.991924	−	0.126833i	$-0.0404812\pi$
$919$	11.7053	+	20.2741i	0.386122	+	0.668782i	−0.605802	+	0.795615i	$0.707148\pi$
$920$		0			0
$921$	−1.12893	−	1.95537i	−0.0371996	−	0.0644316i
$922$		0			0
$923$	−1.98376			−0.0652963
$924$		0			0
$925$	−4.60808	−	7.98142i	−0.151513	−	0.262428i
$926$		0			0
$927$	6.85611	−	11.8751i	0.225184	−	0.390031i
$928$		0			0
$929$	−45.0451			−1.47788			−0.738941	−	0.673770i	$-0.764674\pi$
$929$	−45.0451			−1.47788			−0.738941	+	0.673770i	$0.764674\pi$
$930$		0			0
$931$	0.605847	−	1.04936i	0.0198558	−	0.0343913i
$932$		0			0
$933$	−16.7611			−0.548733
$934$		0			0
$935$	−2.07552			−0.0678766
$936$		0			0
$937$	31.2061			1.01946			0.509729	−	0.860335i	$-0.329746\pi$
$937$	31.2061			1.01946			0.509729	+	0.860335i	$0.329746\pi$
$938$		0			0
$939$	17.9458			0.585640
$940$		0			0
$941$	−39.4151			−1.28490			−0.642448	−	0.766329i	$-0.722081\pi$
$941$	−39.4151			−1.28490			−0.642448	+	0.766329i	$0.722081\pi$
$942$		0			0
$943$	43.8251			1.42714
$944$		0			0
$945$	1.13810	−	1.97125i	0.0370225	−	0.0641249i
$946$		0			0
$947$	2.13466			0.0693671			0.0346835	−	0.999398i	$-0.488958\pi$
$947$	2.13466			0.0693671			0.0346835	+	0.999398i	$0.488958\pi$
$948$		0			0
$949$	−0.581235	+	1.00673i	−0.0188677	+	0.0326798i
$950$		0			0
$951$	−4.65490	−	8.06252i	−0.150945	−	0.261445i
$952$		0			0
$953$	3.33558			0.108050			0.0540249	−	0.998540i	$-0.482795\pi$
$953$	3.33558			0.108050			0.0540249	+	0.998540i	$0.482795\pi$
$954$		0			0
$955$	9.74545	+	16.8796i	0.315355	+	0.546211i
$956$		0			0
$957$	2.12120	+	3.67403i	0.0685688	+	0.118765i
$958$		0			0
$959$	−10.7068	+	18.5447i	−0.345739	+	0.598838i
$960$		0			0
$961$	−1.60600	−	2.78168i	−0.0518066	−	0.0897317i
$962$		0			0
$963$	−18.1522			−0.584947
$964$		0			0
$965$	9.62585			0.309867
$966$		0			0
$967$	−23.7597	+	41.1529i	−0.764059	+	1.32339i	0.176683	+	0.984268i	$0.443463\pi$
$967$	−23.7597	+	41.1529i	−0.764059	+	1.32339i	−0.940743	+	0.339122i	$0.889870\pi$
$968$		0			0
$969$	0.257569	−	0.446123i	0.00827431	−	0.0143315i
$970$		0			0
$971$	−10.2235	+	17.7077i	−0.328089	+	0.568266i	−0.982133	−	0.188191i	$-0.939738\pi$
$971$	−10.2235	+	17.7077i	−0.328089	+	0.568266i	0.654044	+	0.756456i	$0.273071\pi$
$972$		0			0
$973$	10.9715	−	19.0032i	0.351731	−	0.609215i
$974$		0			0
$975$	0.0777729	+	0.134707i	0.00249073	+	0.00431406i
$976$		0			0
$977$	23.2695	+	40.3039i	0.744457	+	1.28944i	0.950448	+	0.310883i	$0.100625\pi$
$977$	23.2695	+	40.3039i	0.744457	+	1.28944i	−0.205992	+	0.978554i	$0.566042\pi$
$978$		0			0
$979$	6.75118	−	11.6934i	0.215769	−	0.373722i
$980$		0			0
$981$	−1.05330			−0.0336292
$982$		0			0
$983$	−30.7857			−0.981910			−0.490955	−	0.871185i	$-0.663352\pi$
$983$	−30.7857			−0.981910			−0.490955	+	0.871185i	$0.663352\pi$
$984$		0			0
$985$	1.58812	−	2.75070i	0.0506017	−	0.0876447i
$986$		0			0
$987$	−9.56710	−	16.5707i	−0.304524	−	0.527451i
$988$		0			0
$989$	10.9406	+	18.9496i	0.347890	+	0.602564i
$990$		0			0
$991$	−53.7648			−1.70790			−0.853948	−	0.520359i	$-0.825798\pi$
$991$	−53.7648			−1.70790			−0.853948	+	0.520359i	$0.825798\pi$
$992$		0			0
$993$	−5.34083	+	9.25059i	−0.169486	+	0.293559i
$994$		0			0
$995$	−3.11819	−	5.40087i	−0.0988534	−	0.171219i
$996$		0			0
$997$	35.5827			1.12691			0.563457	−	0.826145i	$-0.309471\pi$
$997$	35.5827			1.12691			0.563457	+	0.826145i	$0.309471\pi$
$998$		0			0
$999$	4.60808	+	7.98142i	0.145793	+	0.252521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.841.2	✓	14
67.29	even	3	inner	4020.2.q.k.3781.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.2	✓	14	1.1	even	1	trivial
4020.2.q.k.3781.2	yes	14	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-1.13810 + 1.97125i) q^{7} +1.00000 q^{9} +(1.34203 - 2.32447i) q^{11} +(-0.0777729 - 0.134707i) q^{13} -1.00000 q^{15} +(-0.386637 - 0.669675i) q^{17} +(-0.333089 - 0.576927i) q^{19} +(1.13810 - 1.97125i) q^{21} +(-2.24130 - 3.88205i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(0.790296 - 1.36883i) q^{29} +(-2.92455 + 5.06547i) q^{31} +(-1.34203 + 2.32447i) q^{33} +(-1.13810 + 1.97125i) q^{35} +(-4.60808 - 7.98142i) q^{37} +(0.0777729 + 0.134707i) q^{39} +(-4.88835 + 8.46687i) q^{41} -4.88135 q^{43} +1.00000 q^{45} +(4.20309 - 7.27996i) q^{47} +(0.909436 + 1.57519i) q^{49} +(0.386637 + 0.669675i) q^{51} +7.78200 q^{53} +(1.34203 - 2.32447i) q^{55} +(0.333089 + 0.576927i) q^{57} -10.5918 q^{59} +(1.14396 + 1.98139i) q^{61} +(-1.13810 + 1.97125i) q^{63} +(-0.0777729 - 0.134707i) q^{65} +(-1.48295 + 8.04990i) q^{67} +(2.24130 + 3.88205i) q^{69} +(6.37678 - 11.0449i) q^{71} +(-3.73675 - 6.47224i) q^{73} -1.00000 q^{75} +(3.05474 + 5.29097i) q^{77} +(-6.85569 + 11.8744i) q^{79} +1.00000 q^{81} +(-4.19414 - 7.26447i) q^{83} +(-0.386637 - 0.669675i) q^{85} +(-0.790296 + 1.36883i) q^{87} +5.03057 q^{89} +0.354055 q^{91} +(2.92455 - 5.06547i) q^{93} +(-0.333089 - 0.576927i) q^{95} +(-5.24485 - 9.08435i) q^{97} +(1.34203 - 2.32447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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