LMFDB - Embedded newform 1440.2.cc.b.911.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(911,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1440.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.cc (of order $6$, degree $2$, not 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			911.1
Character	$\chi$	$=$	1440.911
Dual form			1440.2.cc.b.1391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72054 + 0.199393i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(2.92049 - 0.686124i) q^{9} +O(q^{10})$	\(q+(-1.72054 + 0.199393i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(2.92049 - 0.686124i) q^{9} +(4.08838 + 2.36043i) q^{11} +(-1.87107 + 1.08026i) q^{13} +(-1.03295 - 1.39033i) q^{15} -1.23675i q^{17} -4.35920 q^{19} +(7.29129 + 3.15363i) q^{21} +(0.117833 + 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.88799 + 1.76282i) q^{27} +(-2.84210 + 4.92266i) q^{29} +(4.06804 - 2.34868i) q^{31} +(-7.50485 - 3.24600i) q^{33} -4.58651i q^{35} -9.91926i q^{37} +(3.00385 - 2.23171i) q^{39} +(6.34052 - 3.66070i) q^{41} +(2.62545 - 4.54741i) q^{43} +(2.05444 + 2.18615i) q^{45} +(1.05958 - 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(0.246600 + 2.12788i) q^{51} +7.92028 q^{53} +4.72085i q^{55} +(7.50016 - 0.869192i) q^{57} +(10.1979 - 5.88778i) q^{59} +(-6.27586 - 3.62337i) q^{61} +(-13.1737 - 3.97211i) q^{63} +(-1.87107 - 1.08026i) q^{65} +(7.51856 + 13.0225i) q^{67} +(-0.243430 - 0.327653i) q^{69} +0.851441 q^{71} +10.6769 q^{73} +(0.687589 - 1.58972i) q^{75} +(-10.8261 - 18.7514i) q^{77} +(10.0179 + 5.78381i) q^{79} +(8.05847 - 4.00763i) q^{81} +(2.35035 + 1.35698i) q^{83} +(1.07106 - 0.618377i) q^{85} +(3.90839 - 9.03630i) q^{87} -12.9321i q^{89} +9.90928 q^{91} +(-6.53089 + 4.85213i) q^{93} +(-2.17960 - 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(13.5596 + 4.08846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5}+O(q^{10}) $ 48 * q + 24 * q^5	$ 48 q + 24 q^{5} + 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} + 16 q^{39} + 12 q^{41} + 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} - 12 q^{61} + 56 q^{63} + 40 q^{69} - 8 q^{81} + 60 q^{83} + 36 q^{87} + 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 + 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 + 16 * q^39 + 12 * q^41 + 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 - 12 * q^61 + 56 * q^63 + 40 * q^69 - 8 * q^81 + 60 * q^83 + 36 * q^87 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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
$3$	−1.72054	+	0.199393i	−0.993352	+	0.115119i
$3$	−1.72054	+	0.199393i	−0.993352	+	0.115119i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−3.97204	−	2.29326i	−1.50129	−	0.866769i	−0.999999	−	0.00148944i	$-0.999526\pi$
$7$	−3.97204	−	2.29326i	−1.50129	−	0.866769i	−0.501289	−	0.865280i	$-0.667141\pi$
$8$		0			0
$9$	2.92049	−	0.686124i	0.973495	−	0.228708i
$10$		0			0
$11$	4.08838	+	2.36043i	1.23269	+	0.711695i	0.967590	−	0.252525i	$-0.0812610\pi$
$11$	4.08838	+	2.36043i	1.23269	+	0.711695i	0.265102	+	0.964220i	$0.414594\pi$
$12$		0			0
$13$	−1.87107	+	1.08026i	−0.518942	+	0.299611i	−0.736501	−	0.676436i	$-0.763524\pi$
$13$	−1.87107	+	1.08026i	−0.518942	+	0.299611i	0.217560	+	0.976047i	$0.430190\pi$
$14$		0			0
$15$	−1.03295	−	1.39033i	−0.266706	−	0.358982i
$16$		0			0
$17$		−	1.23675i		−	0.299957i	−0.988689	−	0.149978i	$-0.952080\pi$
$17$		−	1.23675i		−	0.299957i	0.988689	−	0.149978i	$-0.0479204\pi$
$18$		0			0
$19$	−4.35920			−1.00007			−0.500034	−	0.866005i	$-0.666679\pi$
$19$	−4.35920			−1.00007			−0.500034	+	0.866005i	$0.666679\pi$
$20$		0			0
$21$	7.29129	+	3.15363i	1.59109	+	0.688179i
$22$		0			0
$23$	0.117833	+	0.204092i	0.0245698	+	0.0425562i	0.878049	−	0.478571i	$-0.158845\pi$
$23$	0.117833	+	0.204092i	0.0245698	+	0.0425562i	−0.853479	+	0.521127i	$0.825512\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−4.88799	+	1.76282i	−0.940694	+	0.339256i
$28$		0			0
$29$	−2.84210	+	4.92266i	−0.527764	+	0.914114i	0.471712	+	0.881753i	$0.343636\pi$
$29$	−2.84210	+	4.92266i	−0.527764	+	0.914114i	−0.999476	+	0.0323617i	$0.989697\pi$
$30$		0			0
$31$	4.06804	−	2.34868i	0.730641	−	0.421836i	−0.0880155	−	0.996119i	$-0.528053\pi$
$31$	4.06804	−	2.34868i	0.730641	−	0.421836i	0.818657	+	0.574283i	$0.194719\pi$
$32$		0			0
$33$	−7.50485	−	3.24600i	−1.30643	−	0.565057i
$34$		0			0
$35$		−	4.58651i		−	0.775262i
$36$		0			0
$37$		−	9.91926i		−	1.63072i	−0.578957	−	0.815358i	$-0.696540\pi$
$37$		−	9.91926i		−	1.63072i	0.578957	−	0.815358i	$-0.303460\pi$
$38$		0			0
$39$	3.00385	−	2.23171i	0.481000	−	0.357359i
$40$		0			0
$41$	6.34052	−	3.66070i	0.990222	−	0.571705i	0.0848815	−	0.996391i	$-0.472949\pi$
$41$	6.34052	−	3.66070i	0.990222	−	0.571705i	0.905341	+	0.424686i	$0.139616\pi$
$42$		0			0
$43$	2.62545	−	4.54741i	0.400377	−	0.693473i	−0.593394	−	0.804912i	$-0.702212\pi$
$43$	2.62545	−	4.54741i	0.400377	−	0.693473i	0.993771	+	0.111439i	$0.0355458\pi$
$44$		0			0
$45$	2.05444	+	2.18615i	0.306258	+	0.325892i
$46$		0			0
$47$	1.05958	−	1.83524i	0.154555	−	0.267698i	−0.778342	−	0.627841i	$-0.783939\pi$
$47$	1.05958	−	1.83524i	0.154555	−	0.267698i	0.932897	+	0.360143i	$0.117272\pi$
$48$		0			0
$49$	7.01804	+	12.1556i	1.00258	+	1.73652i
$50$		0			0
$51$	0.246600	+	2.12788i	0.0345308	+	0.297963i
$52$		0			0
$53$	7.92028			1.08793			0.543967	−	0.839107i	$-0.316922\pi$
$53$	7.92028			1.08793			0.543967	+	0.839107i	$0.316922\pi$
$54$		0			0
$55$			4.72085i			0.636560i
$56$		0			0
$57$	7.50016	−	0.869192i	0.993420	−	0.115127i
$58$		0			0
$59$	10.1979	−	5.88778i	1.32766	−	0.766524i	0.342722	−	0.939437i	$-0.388651\pi$
$59$	10.1979	−	5.88778i	1.32766	−	0.766524i	0.984937	+	0.172913i	$0.0553179\pi$
$60$		0			0
$61$	−6.27586	−	3.62337i	−0.803541	−	0.463925i	0.0411667	−	0.999152i	$-0.486893\pi$
$61$	−6.27586	−	3.62337i	−0.803541	−	0.463925i	−0.844708	+	0.535228i	$0.820226\pi$
$62$		0			0
$63$	−13.1737	−	3.97211i	−1.65973	−	0.500439i
$64$		0			0
$65$	−1.87107	−	1.08026i	−0.232078	−	0.133990i
$66$		0			0
$67$	7.51856	+	13.0225i	0.918538	+	1.59095i	0.801637	+	0.597811i	$0.203962\pi$
$67$	7.51856	+	13.0225i	0.918538	+	1.59095i	0.116900	+	0.993144i	$0.462704\pi$
$68$		0			0
$69$	−0.243430	−	0.327653i	−0.0293055	−	0.0394448i
$70$		0			0
$71$	0.851441			0.101047			0.0505237	−	0.998723i	$-0.483911\pi$
$71$	0.851441			0.101047			0.0505237	+	0.998723i	$0.483911\pi$
$72$		0			0
$73$	10.6769			1.24964			0.624819	−	0.780770i	$-0.285173\pi$
$73$	10.6769			1.24964			0.624819	+	0.780770i	$0.285173\pi$
$74$		0			0
$75$	0.687589	−	1.58972i	0.0793959	−	0.183565i
$76$		0			0
$77$	−10.8261	−	18.7514i	−1.23375	−	2.13692i
$78$		0			0
$79$	10.0179	+	5.78381i	1.12710	+	0.650730i	0.943203	−	0.332217i	$-0.107796\pi$
$79$	10.0179	+	5.78381i	1.12710	+	0.650730i	0.183894	+	0.982946i	$0.441130\pi$
$80$		0			0
$81$	8.05847	−	4.00763i	0.895385	−	0.445292i
$82$		0			0
$83$	2.35035	+	1.35698i	0.257985	+	0.148948i	0.623415	−	0.781891i	$-0.285745\pi$
$83$	2.35035	+	1.35698i	0.257985	+	0.148948i	−0.365430	+	0.930839i	$0.619078\pi$
$84$		0			0
$85$	1.07106	−	0.618377i	0.116173	−	0.0670724i
$86$		0			0
$87$	3.90839	−	9.03630i	0.419023	−	0.968793i
$88$		0			0
$89$		−	12.9321i		−	1.37080i	−0.728166	−	0.685401i	$-0.759627\pi$
$89$		−	12.9321i		−	1.37080i	0.728166	−	0.685401i	$-0.240373\pi$
$90$		0			0
$91$	9.90928			1.03877
$92$		0			0
$93$	−6.53089	+	4.85213i	−0.677222	+	0.503142i
$94$		0			0
$95$	−2.17960	−	3.77518i	−0.223622	−	0.387325i
$96$		0			0
$97$	−0.816409	+	1.41406i	−0.0828938	+	0.143576i	−0.904492	−	0.426491i	$-0.859750\pi$
$97$	−0.816409	+	1.41406i	−0.0828938	+	0.143576i	0.821598	+	0.570067i	$0.193083\pi$
$98$		0			0
$99$	13.5596	+	4.08846i	1.36279	+	0.410905i
$100$		0			0
$101$	−1.28871	+	2.23211i	−0.128231	+	0.222103i	−0.922991	−	0.384820i	$-0.874263\pi$
$101$	−1.28871	+	2.23211i	−0.128231	+	0.222103i	0.794760	+	0.606924i	$0.207597\pi$
$102$		0			0
$103$	8.62567	−	4.98003i	0.849913	−	0.490697i	−0.0107087	−	0.999943i	$-0.503409\pi$
$103$	8.62567	−	4.98003i	0.849913	−	0.490697i	0.860621	+	0.509245i	$0.170075\pi$
$104$		0			0
$105$	0.914516	+	7.89126i	0.0892476	+	0.770108i
$106$		0			0
$107$			7.28403i			0.704173i	0.935967	+	0.352087i	$0.114528\pi$
$107$			7.28403i			0.704173i	−0.935967	+	0.352087i	$0.885472\pi$
$108$		0			0
$109$		−	2.56505i		−	0.245687i	−0.992426	−	0.122844i	$-0.960799\pi$
$109$		−	2.56505i		−	0.245687i	0.992426	−	0.122844i	$-0.0392014\pi$
$110$		0			0
$111$	1.97783	+	17.0664i	0.187727	+	1.61987i
$112$		0			0
$113$	0.311444	−	0.179812i	0.0292981	−	0.0169153i	−0.485279	−	0.874359i	$-0.661282\pi$
$113$	0.311444	−	0.179812i	0.0292981	−	0.0169153i	0.514578	+	0.857444i	$0.327949\pi$
$114$		0			0
$115$	−0.117833	+	0.204092i	−0.0109880	+	0.0190317i
$116$		0			0
$117$	−4.72324	+	4.43868i	−0.436664	+	0.410356i
$118$		0			0
$119$	−2.83619	+	4.91243i	−0.259993	+	0.450322i
$120$		0			0
$121$	5.64322	+	9.77435i	0.513020	+	0.888577i
$122$		0			0
$123$	−10.1792	+	7.56261i	−0.917825	+	0.681898i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	9.02927i		−	0.801218i	−0.916249	−	0.400609i	$-0.868799\pi$
$127$		−	9.02927i		−	0.801218i	0.916249	−	0.400609i	$-0.131201\pi$
$128$		0			0
$129$	−3.61046	+	8.34747i	−0.317883	+	0.734954i
$130$		0			0
$131$	0.986098	−	0.569324i	0.0861558	−	0.0497421i	−0.456303	−	0.889824i	$-0.650827\pi$
$131$	0.986098	−	0.569324i	0.0861558	−	0.0497421i	0.542459	+	0.840082i	$0.317493\pi$
$132$		0			0
$133$	17.3149	+	9.99676i	1.50139	+	0.866829i
$134$		0			0
$135$	−3.97065	−	3.35171i	−0.341739	−	0.288469i
$136$		0			0
$137$	−3.39260	−	1.95872i	−0.289850	−	0.167345i	0.348024	−	0.937485i	$-0.386853\pi$
$137$	−3.39260	−	1.95872i	−0.289850	−	0.167345i	−0.637874	+	0.770141i	$0.720186\pi$
$138$		0			0
$139$	−5.70435	−	9.88022i	−0.483836	−	0.838029i	0.515991	−	0.856594i	$-0.327424\pi$
$139$	−5.70435	−	9.88022i	−0.483836	−	0.838029i	−0.999828	+	0.0185646i	$0.994090\pi$
$140$		0			0
$141$	−1.45711	+	3.36887i	−0.122711	+	0.283710i
$142$		0			0
$143$	−10.1995			−0.852927
$144$		0			0
$145$	−5.68419			−0.472047
$146$		0			0
$147$	−14.4985	−	19.5148i	−1.19582	−	1.60955i
$148$		0			0
$149$	−9.86802	−	17.0919i	−0.808420	−	1.40022i	−0.913958	−	0.405809i	$-0.866990\pi$
$149$	−9.86802	−	17.0919i	−0.808420	−	1.40022i	0.105538	−	0.994415i	$-0.466344\pi$
$150$		0			0
$151$	5.32377	+	3.07368i	0.433243	+	0.250133i	0.700727	−	0.713429i	$-0.252859\pi$
$151$	5.32377	+	3.07368i	0.433243	+	0.250133i	−0.267484	+	0.963562i	$0.586192\pi$
$152$		0			0
$153$	−0.848567	−	3.61192i	−0.0686025	−	0.292007i
$154$		0			0
$155$	4.06804	+	2.34868i	0.326753	+	0.188651i
$156$		0			0
$157$	−0.339511	+	0.196017i	−0.0270959	+	0.0156438i	−0.513487	−	0.858098i	$-0.671646\pi$
$157$	−0.339511	+	0.196017i	−0.0270959	+	0.0156438i	0.486391	+	0.873741i	$0.338313\pi$
$158$		0			0
$159$	−13.6271	+	1.57924i	−1.08070	+	0.125242i
$160$		0			0
$161$		−	1.08088i		−	0.0851855i
$162$		0			0
$163$	24.6306			1.92922			0.964609	−	0.263683i	$-0.0849374\pi$
$163$	24.6306			1.92922			0.964609	+	0.263683i	$0.0849374\pi$
$164$		0			0
$165$	−0.941303	−	8.12239i	−0.0732803	−	0.632328i
$166$		0			0
$167$	−1.50486	−	2.60649i	−0.116450	−	0.201697i	0.801909	−	0.597447i	$-0.203818\pi$
$167$	−1.50486	−	2.60649i	−0.116450	−	0.201697i	−0.918358	+	0.395750i	$0.870485\pi$
$168$		0			0
$169$	−4.16606	+	7.21583i	−0.320466	+	0.555064i
$170$		0			0
$171$	−12.7310	+	2.99095i	−0.973562	+	0.228724i
$172$		0			0
$173$	4.98815	−	8.63974i	0.379242	−	0.656867i	−0.611710	−	0.791082i	$-0.709518\pi$
$173$	4.98815	−	8.63974i	0.379242	−	0.656867i	0.990952	+	0.134215i	$0.0428513\pi$
$174$		0			0
$175$	3.97204	−	2.29326i	0.300258	−	0.173354i
$176$		0			0
$177$	−16.3719	+	12.1635i	−1.23059	+	0.914267i
$178$		0			0
$179$		−	11.1600i		−	0.834136i	−0.908875	−	0.417068i	$-0.863058\pi$
$179$		−	11.1600i		−	0.834136i	0.908875	−	0.417068i	$-0.136942\pi$
$180$		0			0
$181$			4.80407i			0.357083i	0.983932	+	0.178542i	$0.0571379\pi$
$181$			4.80407i			0.357083i	−0.983932	+	0.178542i	$0.942862\pi$
$182$		0			0
$183$	11.5203	+	4.98277i	0.851606	+	0.368337i
$184$		0			0
$185$	8.59033	−	4.95963i	0.631574	−	0.364639i
$186$		0			0
$187$	2.91927	−	5.05632i	0.213478	−	0.369755i
$188$		0			0
$189$	23.4579	+	4.20741i	1.70631	+	0.306044i
$190$		0			0
$191$	0.143662	−	0.248830i	0.0103950	−	0.0180047i	−0.860781	−	0.508975i	$-0.830024\pi$
$191$	0.143662	−	0.248830i	0.0103950	−	0.0180047i	0.871176	+	0.490971i	$0.163358\pi$
$192$		0			0
$193$	1.19503	+	2.06986i	0.0860204	+	0.148992i	0.905826	−	0.423651i	$-0.139252\pi$
$193$	1.19503	+	2.06986i	0.0860204	+	0.148992i	−0.819805	+	0.572643i	$0.805918\pi$
$194$		0			0
$195$	3.43464	+	1.48555i	0.245960	+	0.106383i
$196$		0			0
$197$	10.8177			0.770732			0.385366	−	0.922764i	$-0.374075\pi$
$197$	10.8177			0.770732			0.385366	+	0.922764i	$0.374075\pi$
$198$		0			0
$199$		−	5.10541i		−	0.361913i	−0.983491	−	0.180957i	$-0.942081\pi$
$199$		−	5.10541i		−	0.361913i	0.983491	−	0.180957i	$-0.0579193\pi$
$200$		0			0
$201$	−15.5325	−	20.9066i	−1.09558	−	1.47464i
$202$		0			0
$203$	22.5778	−	13.0353i	1.58465	−	0.914899i
$204$		0			0
$205$	6.34052	+	3.66070i	0.442841	+	0.255674i
$206$		0			0
$207$	0.484161	+	0.515201i	0.0336515	+	0.0358089i
$208$		0			0
$209$	−17.8221	−	10.2896i	−1.23278	−	0.711744i
$210$		0			0
$211$	−0.491584	−	0.851449i	−0.0338420	−	0.0586161i	0.848608	−	0.529022i	$-0.177441\pi$
$211$	−0.491584	−	0.851449i	−0.0338420	−	0.0586161i	−0.882450	+	0.470406i	$0.844108\pi$
$212$		0			0
$213$	−1.46493	+	0.169771i	−0.100376	+	0.0116325i
$214$		0			0
$215$	5.25090			0.358108
$216$		0			0
$217$	−21.5445			−1.46254
$218$		0			0
$219$	−18.3700	+	2.12890i	−1.24133	+	0.143857i
$220$		0			0
$221$	1.33602	+	2.31405i	0.0898704	+	0.155660i
$222$		0			0
$223$	−10.3531	−	5.97739i	−0.693297	−	0.400275i	0.111549	−	0.993759i	$-0.464419\pi$
$223$	−10.3531	−	5.97739i	−0.693297	−	0.400275i	−0.804846	+	0.593484i	$0.797752\pi$
$224$		0			0
$225$	−0.866042	+	2.87228i	−0.0577361	+	0.191485i
$226$		0			0
$227$	−17.0870	−	9.86519i	−1.13410	−	0.654775i	−0.189140	−	0.981950i	$-0.560570\pi$
$227$	−17.0870	−	9.86519i	−1.13410	−	0.654775i	−0.944964	+	0.327175i	$0.893903\pi$
$228$		0			0
$229$	−0.735791	+	0.424809i	−0.0486225	+	0.0280722i	−0.524114	−	0.851648i	$-0.675603\pi$
$229$	−0.735791	+	0.424809i	−0.0486225	+	0.0280722i	0.475492	+	0.879720i	$0.342270\pi$
$230$		0			0
$231$	22.3656	+	30.1038i	1.47155	+	1.98068i
$232$		0			0
$233$			26.9773i			1.76734i	0.468111	+	0.883670i	$0.344935\pi$
$233$			26.9773i			1.76734i	−0.468111	+	0.883670i	$0.655065\pi$
$234$		0			0
$235$	2.11916			0.138239
$236$		0			0
$237$	−18.3893	−	7.95377i	−1.19452	−	0.516653i
$238$		0			0
$239$	−6.98946	−	12.1061i	−0.452111	−	0.783079i	0.546406	−	0.837520i	$-0.315995\pi$
$239$	−6.98946	−	12.1061i	−0.452111	−	0.783079i	−0.998517	+	0.0544415i	$0.982662\pi$
$240$		0			0
$241$	7.14583	−	12.3769i	0.460303	−	0.797269i	−0.538673	−	0.842515i	$-0.681074\pi$
$241$	7.14583	−	12.3769i	0.460303	−	0.797269i	0.998976	+	0.0452465i	$0.0144073\pi$
$242$		0			0
$243$	−13.0658	+	8.50207i	−0.838171	+	0.545408i
$244$		0			0
$245$	−7.01804	+	12.1556i	−0.448366	+	0.776593i
$246$		0			0
$247$	8.15637	−	4.70908i	0.518977	−	0.299632i
$248$		0			0
$249$	−4.31444	−	1.86609i	−0.273417	−	0.118258i
$250$		0			0
$251$		−	9.70630i		−	0.612656i	−0.951926	−	0.306328i	$-0.900900\pi$
$251$		−	9.70630i		−	0.612656i	0.951926	−	0.306328i	$-0.0991004\pi$
$252$		0			0
$253$			1.11254i			0.0699449i
$254$		0			0
$255$	−1.71950	+	1.27750i	−0.107679	+	0.0800002i
$256$		0			0
$257$	16.4543	−	9.49991i	1.02639	−	0.592588i	0.110444	−	0.993882i	$-0.464773\pi$
$257$	16.4543	−	9.49991i	1.02639	−	0.592588i	0.915949	+	0.401294i	$0.131439\pi$
$258$		0			0
$259$	−22.7474	+	39.3996i	−1.41345	+	2.44817i
$260$		0			0
$261$	−4.92275	+	16.3266i	−0.304711	+	1.01059i
$262$		0			0
$263$	−12.6788	+	21.9603i	−0.781806	+	1.35413i	0.149083	+	0.988825i	$0.452368\pi$
$263$	−12.6788	+	21.9603i	−0.781806	+	1.35413i	−0.930889	+	0.365303i	$0.880965\pi$
$264$		0			0
$265$	3.96014	+	6.85916i	0.243269	+	0.421355i
$266$		0			0
$267$	2.57857	+	22.2502i	0.157806	+	1.36169i
$268$		0			0
$269$	−10.6387			−0.648652			−0.324326	−	0.945945i	$-0.605138\pi$
$269$	−10.6387			−0.648652			−0.324326	+	0.945945i	$0.605138\pi$
$270$		0			0
$271$			22.9127i			1.39185i	0.718115	+	0.695924i	$0.245005\pi$
$271$			22.9127i			1.39185i	−0.718115	+	0.695924i	$0.754995\pi$
$272$		0			0
$273$	−17.0493	+	1.97584i	−1.03187	+	0.119583i
$274$		0			0
$275$	−4.08838	+	2.36043i	−0.246538	+	0.142339i
$276$		0			0
$277$	−13.2767	−	7.66533i	−0.797722	−	0.460565i	0.0449517	−	0.998989i	$-0.485687\pi$
$277$	−13.2767	−	7.66533i	−0.797722	−	0.460565i	−0.842674	+	0.538424i	$0.819020\pi$
$278$		0			0
$279$	10.2692	−	9.65047i	0.614798	−	0.577759i
$280$		0			0
$281$	−9.30426	−	5.37182i	−0.555046	−	0.320456i	0.196109	−	0.980582i	$-0.437169\pi$
$281$	−9.30426	−	5.37182i	−0.555046	−	0.320456i	−0.751155	+	0.660126i	$0.770503\pi$
$282$		0			0
$283$	−8.88802	−	15.3945i	−0.528338	−	0.915108i	−0.999454	−	0.0330371i	$-0.989482\pi$
$283$	−8.88802	−	15.3945i	−0.528338	−	0.915108i	0.471116	−	0.882071i	$-0.343851\pi$
$284$		0			0
$285$	4.50282	+	6.06073i	0.266724	+	0.359007i
$286$		0			0
$287$	−33.5797			−1.98215
$288$		0			0
$289$	15.4704			0.910026
$290$		0			0
$291$	1.12271	−	2.59573i	0.0658143	−	0.152164i
$292$		0			0
$293$	13.9870	+	24.2262i	0.817129	+	1.41531i	0.907789	+	0.419428i	$0.137769\pi$
$293$	13.9870	+	24.2262i	0.817129	+	1.41531i	−0.0906593	+	0.995882i	$0.528897\pi$
$294$		0			0
$295$	10.1979	+	5.88778i	0.593747	+	0.342800i
$296$		0			0
$297$	−24.1450	−	4.33065i	−1.40103	−	0.251290i
$298$		0			0
$299$	−0.440947	−	0.254581i	−0.0255006	−	0.0147228i
$300$		0			0
$301$	−20.8567	+	12.0416i	−1.20216	+	0.694069i
$302$		0			0
$303$	1.77221	−	4.09739i	0.101811	−	0.235389i
$304$		0			0
$305$		−	7.24674i		−	0.414947i
$306$		0			0
$307$	−15.3914			−0.878434			−0.439217	−	0.898381i	$-0.644744\pi$
$307$	−15.3914			−0.878434			−0.439217	+	0.898381i	$0.644744\pi$
$308$		0			0
$309$	−13.8478	+	10.2882i	−0.787773	+	0.585276i
$310$		0			0
$311$	9.87577	+	17.1053i	0.560004	+	0.969955i	0.997495	+	0.0707323i	$0.0225336\pi$
$311$	9.87577	+	17.1053i	0.560004	+	0.969955i	−0.437492	+	0.899222i	$0.644133\pi$
$312$		0			0
$313$	−8.85105	+	15.3305i	−0.500291	+	0.866529i	0.499709	+	0.866193i	$0.333440\pi$
$313$	−8.85105	+	15.3305i	−0.500291	+	0.866529i	−1.00000		0.000335911i	$0.999893\pi$
$314$		0			0
$315$	−3.14692	−	13.3948i	−0.177309	−	0.754714i
$316$		0			0
$317$	−2.67910	+	4.64033i	−0.150473	+	0.260627i	−0.931401	−	0.363994i	$-0.881413\pi$
$317$	−2.67910	+	4.64033i	−0.150473	+	0.260627i	0.780928	+	0.624621i	$0.214746\pi$
$318$		0			0
$319$	−23.2391	+	13.4171i	−1.30114	+	0.751214i
$320$		0			0
$321$	−1.45238	−	12.5324i	−0.0810640	−	0.699492i
$322$		0			0
$323$			5.39126i			0.299978i
$324$		0			0
$325$		−	2.16053i		−	0.119844i
$326$		0			0
$327$	0.511452	+	4.41326i	0.0282834	+	0.244054i
$328$		0			0
$329$	−8.41736	+	4.85977i	−0.464064	+	0.267928i
$330$		0			0
$331$	−12.9222	+	22.3818i	−0.710266	+	1.23022i	0.254491	+	0.967075i	$0.418092\pi$
$331$	−12.9222	+	22.3818i	−0.710266	+	1.23022i	−0.964757	+	0.263142i	$0.915241\pi$
$332$		0			0
$333$	−6.80584	−	28.9690i	−0.372958	−	1.58749i
$334$		0			0
$335$	−7.51856	+	13.0225i	−0.410783	+	0.711496i
$336$		0			0
$337$	8.23294	+	14.2599i	0.448477	+	0.776784i	0.998287	−	0.0585051i	$-0.0186334\pi$
$337$	8.23294	+	14.2599i	0.448477	+	0.776784i	−0.549810	+	0.835289i	$0.685300\pi$
$338$		0			0
$339$	−0.499997	+	0.371473i	−0.0271561	+	0.0201756i
$340$		0			0
$341$	22.1756			1.20087
$342$		0			0
$343$		−	32.2711i		−	1.74247i
$344$		0			0
$345$	0.162041	−	0.374643i	0.00872399	−	0.0201701i
$346$		0			0
$347$	−13.0391	+	7.52814i	−0.699976	+	0.404132i	−0.807339	−	0.590088i	$-0.799093\pi$
$347$	−13.0391	+	7.52814i	−0.699976	+	0.404132i	0.107362	+	0.994220i	$0.465760\pi$
$348$		0			0
$349$	7.00796	+	4.04605i	0.375128	+	0.216580i	0.675696	−	0.737180i	$-0.263843\pi$
$349$	7.00796	+	4.04605i	0.375128	+	0.216580i	−0.300569	+	0.953760i	$0.597176\pi$
$350$		0			0
$351$	7.24146	−	8.57868i	0.386521	−	0.457896i
$352$		0			0
$353$	8.16936	+	4.71658i	0.434811	+	0.251038i	0.701394	−	0.712774i	$-0.252561\pi$
$353$	8.16936	+	4.71658i	0.434811	+	0.251038i	−0.266583	+	0.963812i	$0.585895\pi$
$354$		0			0
$355$	0.425720	+	0.737369i	0.0225949	+	0.0391355i
$356$		0			0
$357$	3.90027	−	9.01753i	0.206424	−	0.477258i
$358$		0			0
$359$	28.9175			1.52621			0.763103	−	0.646277i	$-0.223675\pi$
$359$	28.9175			1.52621			0.763103	+	0.646277i	$0.223675\pi$
$360$		0			0
$361$	0.00262185			0.000137992
$362$		0			0
$363$	−11.6583	−	15.6919i	−0.611902	−	0.823611i
$364$		0			0
$365$	5.33845	+	9.24648i	0.279428	+	0.483983i
$366$		0			0
$367$	−27.0895	−	15.6401i	−1.41406	−	0.816407i	−0.418291	−	0.908313i	$-0.637371\pi$
$367$	−27.0895	−	15.6401i	−1.41406	−	0.816407i	−0.995768	+	0.0919062i	$0.970704\pi$
$368$		0			0
$369$	16.0057	−	15.0414i	0.833223	−	0.783024i
$370$		0			0
$371$	−31.4596	−	18.1632i	−1.63330	−	0.942988i
$372$		0			0
$373$	17.8238	−	10.2906i	0.922882	−	0.532826i	0.0383285	−	0.999265i	$-0.487797\pi$
$373$	17.8238	−	10.2906i	0.922882	−	0.532826i	0.884553	+	0.466439i	$0.154463\pi$
$374$		0			0
$375$	1.72054	−	0.199393i	0.0888481	−	0.0102966i
$376$		0			0
$377$		−	12.2808i		−	0.632496i
$378$		0			0
$379$	−1.15098			−0.0591219			−0.0295609	−	0.999563i	$-0.509411\pi$
$379$	−1.15098			−0.0591219			−0.0295609	+	0.999563i	$0.509411\pi$
$380$		0			0
$381$	1.80037	+	15.5352i	0.0922357	+	0.795892i
$382$		0			0
$383$	0.0240645	+	0.0416809i	0.00122964	+	0.00212979i	0.866640	−	0.498935i	$-0.166275\pi$
$383$	0.0240645	+	0.0416809i	0.00122964	+	0.00212979i	−0.865410	+	0.501065i	$0.832942\pi$
$384$		0			0
$385$	10.8261	−	18.7514i	0.551750	−	0.955659i
$386$		0			0
$387$	4.54750	−	15.0820i	0.231162	−	0.766662i
$388$		0			0
$389$	−10.1379	+	17.5594i	−0.514012	+	0.890294i	0.485856	+	0.874039i	$0.338508\pi$
$389$	−10.1379	+	17.5594i	−0.514012	+	0.890294i	−0.999868	+	0.0162556i	$0.994825\pi$
$390$		0			0
$391$	0.252412	−	0.145730i	0.0127650	−	0.00736989i
$392$		0			0
$393$	−1.58310	+	1.17616i	−0.0798567	+	0.0593296i
$394$		0			0
$395$			11.5676i			0.582030i
$396$		0			0
$397$			16.5809i			0.832169i	0.909326	+	0.416085i	$0.136598\pi$
$397$			16.5809i			0.832169i	−0.909326	+	0.416085i	$0.863402\pi$
$398$		0			0
$399$	−31.7842	−	13.7473i	−1.59120	−	0.688227i
$400$		0			0
$401$	18.1229	−	10.4632i	0.905013	−	0.522510i	0.0261899	−	0.999657i	$-0.491663\pi$
$401$	18.1229	−	10.4632i	0.905013	−	0.522510i	0.878823	+	0.477147i	$0.158329\pi$
$402$		0			0
$403$	−5.07439	+	8.78910i	−0.252773	+	0.437816i
$404$		0			0
$405$	7.49994	+	4.97502i	0.372675	+	0.247211i
$406$		0			0
$407$	23.4137	−	40.5537i	1.16057	−	2.01017i
$408$		0			0
$409$	−8.62868	−	14.9453i	−0.426661	−	0.738998i	0.569913	−	0.821705i	$-0.306977\pi$
$409$	−8.62868	−	14.9453i	−0.426661	−	0.738998i	−0.996574	+	0.0827069i	$0.973643\pi$
$410$		0			0
$411$	6.22765	+	2.69359i	0.307187	+	0.132865i
$412$		0			0
$413$	−54.0088			−2.65760
$414$		0			0
$415$			2.71396i			0.133223i
$416$		0			0
$417$	11.7846	+	15.8619i	0.577093	+	0.776759i
$418$		0			0
$419$	12.4910	−	7.21167i	0.610224	−	0.352313i	−0.162829	−	0.986654i	$-0.552062\pi$
$419$	12.4910	−	7.21167i	0.610224	−	0.352313i	0.773053	+	0.634341i	$0.218729\pi$
$420$		0			0
$421$	23.2632	+	13.4310i	1.13378	+	0.654588i	0.944883	−	0.327409i	$-0.106175\pi$
$421$	23.2632	+	13.4310i	1.13378	+	0.654588i	0.188897	+	0.981997i	$0.439509\pi$
$422$		0			0
$423$	1.83528	−	6.08680i	0.0892343	−	0.295951i
$424$		0			0
$425$	1.07106	+	0.618377i	0.0519541	+	0.0299957i
$426$		0			0
$427$	16.6186	+	28.7843i	0.804231	+	1.39297i
$428$		0			0
$429$	17.5486	−	2.03371i	0.847256	−	0.0981884i
$430$		0			0
$431$	12.6429			0.608988			0.304494	−	0.952514i	$-0.401513\pi$
$431$	12.6429			0.608988			0.304494	+	0.952514i	$0.401513\pi$
$432$		0			0
$433$	−28.3673			−1.36324			−0.681622	−	0.731705i	$-0.738725\pi$
$433$	−28.3673			−1.36324			−0.681622	+	0.731705i	$0.738725\pi$
$434$		0			0
$435$	9.77986	−	1.13339i	0.468908	−	0.0543417i
$436$		0			0
$437$	−0.513656	−	0.889679i	−0.0245715	−	0.0425591i
$438$		0			0
$439$	1.62013	+	0.935382i	0.0773246	+	0.0446434i	0.538164	−	0.842840i	$-0.319118\pi$
$439$	1.62013	+	0.935382i	0.0773246	+	0.0446434i	−0.460839	+	0.887484i	$0.652452\pi$
$440$		0			0
$441$	28.8363	+	30.6850i	1.37316	+	1.46119i
$442$		0			0
$443$	−32.9508	−	19.0242i	−1.56554	−	0.903866i	−0.996679	−	0.0814332i	$-0.974050\pi$
$443$	−32.9508	−	19.0242i	−1.56554	−	0.903866i	−0.568863	−	0.822433i	$-0.692616\pi$
$444$		0			0
$445$	11.1995	−	6.46606i	0.530909	−	0.306521i
$446$		0			0
$447$	20.3863	+	27.4396i	0.964238	+	1.29785i
$448$		0			0
$449$			4.53199i			0.213878i	0.994266	+	0.106939i	$0.0341049\pi$
$449$			4.53199i			0.213878i	−0.994266	+	0.106939i	$0.965895\pi$
$450$		0			0
$451$	34.5632			1.62752
$452$		0			0
$453$	−9.77261	−	4.22686i	−0.459157	−	0.198595i
$454$		0			0
$455$	4.95464	+	8.58169i	0.232277	+	0.402316i
$456$		0			0
$457$	6.38333	−	11.0562i	0.298599	−	0.517189i	−0.677216	−	0.735784i	$-0.736814\pi$
$457$	6.38333	−	11.0562i	0.298599	−	0.517189i	0.975816	+	0.218595i	$0.0701472\pi$
$458$		0			0
$459$	2.18018	+	6.04524i	0.101762	+	0.282168i
$460$		0			0
$461$	17.8836	−	30.9753i	0.832923	−	1.44266i	−0.0627876	−	0.998027i	$-0.519999\pi$
$461$	17.8836	−	30.9753i	0.832923	−	1.44266i	0.895710	−	0.444638i	$-0.146668\pi$
$462$		0			0
$463$	27.6653	−	15.9726i	1.28572	−	0.742309i	0.307829	−	0.951442i	$-0.400398\pi$
$463$	27.6653	−	15.9726i	1.28572	−	0.742309i	0.977887	+	0.209133i	$0.0670642\pi$
$464$		0			0
$465$	−7.46751	−	3.22986i	−0.346298	−	0.149781i
$466$		0			0
$467$			0.817062i			0.0378091i	0.999821	+	0.0189046i	$0.00601787\pi$
$467$			0.817062i			0.0378091i	−0.999821	+	0.0189046i	$0.993982\pi$
$468$		0			0
$469$		−	68.9679i		−	3.18464i
$470$		0			0
$471$	0.545056	−	0.404950i	0.0251149	−	0.0186591i
$472$		0			0
$473$	21.4676	−	12.3944i	0.987083	−	0.569893i
$474$		0			0
$475$	2.17960	−	3.77518i	0.100007	−	0.173217i
$476$		0			0
$477$	23.1311	−	5.43429i	1.05910	−	0.248819i
$478$		0			0
$479$	17.3720	−	30.0891i	0.793746	−	1.37481i	−0.129887	−	0.991529i	$-0.541461\pi$
$479$	17.3720	−	30.0891i	0.793746	−	1.37481i	0.923633	−	0.383279i	$-0.125205\pi$
$480$		0			0
$481$	10.7154	+	18.5596i	0.488581	+	0.846246i
$482$		0			0
$483$	0.215520	+	1.85970i	0.00980650	+	0.0846191i
$484$		0			0
$485$	−1.63282			−0.0741425
$486$		0			0
$487$			39.8130i			1.80410i	0.431630	+	0.902051i	$0.357939\pi$
$487$			39.8130i			1.80410i	−0.431630	+	0.902051i	$0.642061\pi$
$488$		0			0
$489$	−42.3778	+	4.91116i	−1.91639	+	0.222090i
$490$		0			0
$491$	21.9098	−	12.6496i	0.988775	−	0.570870i	0.0838674	−	0.996477i	$-0.473273\pi$
$491$	21.9098	−	12.6496i	0.988775	−	0.570870i	0.904908	+	0.425607i	$0.139939\pi$
$492$		0			0
$493$	6.08812	+	3.51498i	0.274195	+	0.158307i
$494$		0			0
$495$	3.23909	+	13.7872i	0.145586	+	0.619688i
$496$		0			0
$497$	−3.38195	−	1.95257i	−0.151701	−	0.0875848i
$498$		0			0
$499$	−5.75232	−	9.96331i	−0.257509	−	0.446019i	0.708065	−	0.706147i	$-0.249568\pi$
$499$	−5.75232	−	9.96331i	−0.257509	−	0.446019i	−0.965574	+	0.260128i	$0.916235\pi$
$500$		0			0
$501$	3.10888	+	4.18451i	0.138895	+	0.186950i
$502$		0			0
$503$	−16.2502			−0.724561			−0.362281	−	0.932069i	$-0.618002\pi$
$503$	−16.2502			−0.724561			−0.362281	+	0.932069i	$0.618002\pi$
$504$		0			0
$505$	−2.57742			−0.114694
$506$		0			0
$507$	5.72908	−	13.2458i	0.254437	−	0.588266i
$508$		0			0
$509$	2.87628	+	4.98186i	0.127489	+	0.220817i	0.922703	−	0.385512i	$-0.125975\pi$
$509$	2.87628	+	4.98186i	0.127489	+	0.220817i	−0.795214	+	0.606328i	$0.792642\pi$
$510$		0			0
$511$	−42.4091	−	24.4849i	−1.87607	−	1.08315i
$512$		0			0
$513$	21.3077	−	7.68450i	0.940759	−	0.339279i
$514$		0			0
$515$	8.62567	+	4.98003i	0.380093	+	0.219447i
$516$		0			0
$517$	8.66391	−	5.00211i	0.381038	−	0.219993i
$518$		0			0
$519$	−6.85960	+	15.8596i	−0.301103	+	0.696158i
$520$		0			0
$521$			30.4544i			1.33423i	0.744953	+	0.667117i	$0.232472\pi$
$521$			30.4544i			1.33423i	−0.744953	+	0.667117i	$0.767528\pi$
$522$		0			0
$523$	−18.7457			−0.819694			−0.409847	−	0.912154i	$-0.634418\pi$
$523$	−18.7457			−0.819694			−0.409847	+	0.912154i	$0.634418\pi$
$524$		0			0
$525$	−6.37677	+	4.73762i	−0.278305	+	0.206767i
$526$		0			0
$527$	−2.90474	−	5.03116i	−0.126533	−	0.219161i
$528$		0			0
$529$	11.4722	−	19.8705i	0.498793	−	0.863934i
$530$		0			0
$531$	25.7432	−	24.1922i	1.11716	−	1.04985i
$532$		0			0
$533$	−7.90903	+	13.6988i	−0.342578	+	0.593363i
$534$		0			0
$535$	−6.30815	+	3.64201i	−0.272725	+	0.157458i
$536$		0			0
$537$	2.22522	+	19.2011i	0.0960251	+	0.828590i
$538$		0			0
$539$			66.2623i			2.85412i
$540$		0			0
$541$			28.8219i			1.23915i	0.784938	+	0.619575i	$0.212695\pi$
$541$			28.8219i			1.23915i	−0.784938	+	0.619575i	$0.787305\pi$
$542$		0			0
$543$	−0.957895	−	8.26557i	−0.0411072	−	0.354709i
$544$		0			0
$545$	2.22140	−	1.28253i	0.0951543	−	0.0549373i
$546$		0			0
$547$	8.43142	−	14.6036i	0.360502	−	0.624407i	−0.627542	−	0.778583i	$-0.715939\pi$
$547$	8.43142	−	14.6036i	0.360502	−	0.624407i	0.988043	+	0.154176i	$0.0492722\pi$
$548$		0			0
$549$	−20.8146	−	6.27598i	−0.888347	−	0.267852i
$550$		0			0
$551$	12.3893	−	21.4588i	0.527801	−	0.914177i
$552$		0			0
$553$	−26.5275	−	45.9470i	−1.12806	−	1.95387i
$554$		0			0
$555$	−13.7911	+	10.2461i	−0.585398	+	0.434921i
$556$		0			0
$557$	20.1743			0.854811			0.427406	−	0.904060i	$-0.359428\pi$
$557$	20.1743			0.854811			0.427406	+	0.904060i	$0.359428\pi$
$558$		0			0
$559$			11.3447i			0.479830i
$560$		0			0
$561$	−4.01451	+	9.28166i	−0.169493	+	0.391872i
$562$		0			0
$563$	−5.22595	+	3.01721i	−0.220248	+	0.127160i	−0.606065	−	0.795415i	$-0.707253\pi$
$563$	−5.22595	+	3.01721i	−0.220248	+	0.127160i	0.385817	+	0.922575i	$0.373920\pi$
$564$		0			0
$565$	0.311444	+	0.179812i	0.0131025	+	0.00756475i
$566$		0			0
$567$	−41.1990	−	2.56168i	−1.73020	−	0.107580i
$568$		0			0
$569$	12.8303	+	7.40759i	0.537875	+	0.310543i	0.744217	−	0.667937i	$-0.232823\pi$
$569$	12.8303	+	7.40759i	0.537875	+	0.310543i	−0.206342	+	0.978480i	$0.566156\pi$
$570$		0			0
$571$	3.96582	+	6.86900i	0.165964	+	0.287459i	0.936997	−	0.349337i	$-0.113593\pi$
$571$	3.96582	+	6.86900i	0.165964	+	0.287459i	−0.771033	+	0.636795i	$0.780260\pi$
$572$		0			0
$573$	−0.197561	+	0.456767i	−0.00825324	+	0.0190817i
$574$		0			0
$575$	−0.235665			−0.00982793
$576$		0			0
$577$	−9.19579			−0.382826			−0.191413	−	0.981510i	$-0.561307\pi$
$577$	−9.19579			−0.382826			−0.191413	+	0.981510i	$0.561307\pi$
$578$		0			0
$579$	−2.46881	−	3.32298i	−0.102600	−	0.138098i
$580$		0			0
$581$	−6.22379	−	10.7799i	−0.258207	−	0.447227i
$582$		0			0
$583$	32.3811	+	18.6952i	1.34109	+	0.774278i
$584$		0			0
$585$	−6.20563	−	1.87111i	−0.256571	−	0.0773607i
$586$		0			0
$587$	−6.45327	−	3.72580i	−0.266355	−	0.153780i	0.360875	−	0.932614i	$-0.382478\pi$
$587$	−6.45327	−	3.72580i	−0.266355	−	0.153780i	−0.627230	+	0.778834i	$0.715811\pi$
$588$		0			0
$589$	−17.7334	+	10.2384i	−0.730692	+	0.421865i
$590$		0			0
$591$	−18.6123	+	2.15698i	−0.765608	+	0.0887261i
$592$		0			0
$593$			5.98713i			0.245862i	0.992415	+	0.122931i	$0.0392294\pi$
$593$			5.98713i			0.245862i	−0.992415	+	0.122931i	$0.960771\pi$
$594$		0			0
$595$	−5.67239			−0.232545
$596$		0			0
$597$	1.01798	+	8.78404i	0.0416632	+	0.359507i
$598$		0			0
$599$	−18.3740	−	31.8246i	−0.750740	−	1.30032i	−0.947465	−	0.319861i	$-0.896364\pi$
$599$	−18.3740	−	31.8246i	−0.750740	−	1.30032i	0.196725	−	0.980459i	$-0.436969\pi$
$600$		0			0
$601$	−5.67611	+	9.83130i	−0.231533	+	0.401027i	−0.958260	−	0.285900i	$-0.907708\pi$
$601$	−5.67611	+	9.83130i	−0.231533	+	0.401027i	0.726726	+	0.686927i	$0.241041\pi$
$602$		0			0
$603$	30.8929	+	32.8734i	1.25806	+	1.33871i
$604$		0			0
$605$	−5.64322	+	9.77435i	−0.229430	+	0.397384i
$606$		0			0
$607$	−5.06707	+	2.92548i	−0.205666	+	0.118741i	−0.599296	−	0.800528i	$-0.704553\pi$
$607$	−5.06707	+	2.92548i	−0.205666	+	0.118741i	0.393630	+	0.919269i	$0.371219\pi$
$608$		0			0
$609$	−36.2468	+	26.9296i	−1.46879	+	1.09124i
$610$		0			0
$611$			4.57849i			0.185226i
$612$		0			0
$613$			18.4132i			0.743703i	0.928292	+	0.371851i	$0.121277\pi$
$613$			18.4132i			0.743703i	−0.928292	+	0.371851i	$0.878723\pi$
$614$		0			0
$615$	−11.6390	−	5.03411i	−0.469330	−	0.202995i
$616$		0			0
$617$	7.12123	−	4.11144i	0.286690	−	0.165520i	−0.349758	−	0.936840i	$-0.613736\pi$
$617$	7.12123	−	4.11144i	0.286690	−	0.165520i	0.636448	+	0.771320i	$0.280403\pi$
$618$		0			0
$619$	22.2663	−	38.5663i	0.894957	−	1.55011i	0.0610991	−	0.998132i	$-0.480539\pi$
$619$	22.2663	−	38.5663i	0.894957	−	1.55011i	0.833858	−	0.551979i	$-0.186127\pi$
$620$		0			0
$621$	−0.935744	−	0.789883i	−0.0375501	−	0.0316969i
$622$		0			0
$623$	−29.6567	+	51.3668i	−1.18817	+	2.05797i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	32.7151	+	14.1500i	1.30652	+	0.565096i
$628$		0			0
$629$	−12.2677			−0.489145
$630$		0			0
$631$			2.02785i			0.0807273i	0.999185	+	0.0403637i	$0.0128516\pi$
$631$			2.02785i			0.0807273i	−0.999185	+	0.0403637i	$0.987148\pi$
$632$		0			0
$633$	1.01556	+	1.36693i	0.0403649	+	0.0543306i
$634$		0			0
$635$	7.81958	−	4.51464i	0.310311	−	0.179158i
$636$		0			0
$637$	−26.2625	−	15.1627i	−1.04056	−	0.600767i
$638$		0			0
$639$	2.48662	−	0.584194i	0.0983692	−	0.0231103i
$640$		0			0
$641$	−22.2376	−	12.8389i	−0.878332	−	0.507105i	−0.00822364	−	0.999966i	$-0.502618\pi$
$641$	−22.2376	−	12.8389i	−0.878332	−	0.507105i	−0.870108	+	0.492861i	$0.835951\pi$
$642$		0			0
$643$	−3.54072	−	6.13270i	−0.139632	−	0.241850i	0.787725	−	0.616027i	$-0.211259\pi$
$643$	−3.54072	−	6.13270i	−0.139632	−	0.241850i	−0.927357	+	0.374177i	$0.877925\pi$
$644$		0			0
$645$	−9.03435	+	1.04699i	−0.355727	+	0.0412252i
$646$		0			0
$647$	48.6780			1.91373			0.956865	−	0.290533i	$-0.0938325\pi$
$647$	48.6780			1.91373			0.956865	+	0.290533i	$0.0938325\pi$
$648$		0			0
$649$	55.5907			2.18213
$650$		0			0
$651$	37.0681	−	4.29582i	1.45281	−	0.168366i
$652$		0			0
$653$	−1.32043	−	2.28705i	−0.0516724	−	0.0894993i	0.839032	−	0.544082i	$-0.183122\pi$
$653$	−1.32043	−	2.28705i	−0.0516724	−	0.0894993i	−0.890705	+	0.454582i	$0.849789\pi$
$654$		0			0
$655$	0.986098	+	0.569324i	0.0385300	+	0.0222453i
$656$		0			0
$657$	31.1818	−	7.32568i	1.21652	−	0.285802i
$658$		0			0
$659$	−3.04662	−	1.75896i	−0.118679	−	0.0685195i	0.439485	−	0.898250i	$-0.355161\pi$
$659$	−3.04662	−	1.75896i	−0.118679	−	0.0685195i	−0.558165	+	0.829730i	$0.688494\pi$
$660$		0			0
$661$	3.44771	−	1.99053i	0.134100	−	0.0774228i	−0.431449	−	0.902137i	$-0.641998\pi$
$661$	3.44771	−	1.99053i	0.134100	−	0.0774228i	0.565549	+	0.824715i	$0.308664\pi$
$662$		0			0
$663$	−2.76007	−	3.71502i	−0.107192	−	0.144279i
$664$		0			0
$665$			19.9935i			0.775315i
$666$		0			0
$667$	−1.33957			−0.0518683
$668$		0			0
$669$	19.0048	+	8.21997i	0.734767	+	0.317802i
$670$		0			0
$671$	−17.1054	−	29.6274i	−0.660346	−	1.14375i
$672$		0			0
$673$	8.00949	−	13.8728i	0.308743	−	0.534759i	−0.669345	−	0.742952i	$-0.733425\pi$
$673$	8.00949	−	13.8728i	0.308743	−	0.534759i	0.978088	+	0.208193i	$0.0667583\pi$
$674$		0			0
$675$	0.917345	−	5.11454i	0.0353086	−	0.196859i
$676$		0			0
$677$	−0.225619	+	0.390784i	−0.00867125	+	0.0150190i	−0.870328	−	0.492472i	$-0.836094\pi$
$677$	−0.225619	+	0.390784i	−0.00867125	+	0.0150190i	0.861657	+	0.507491i	$0.169427\pi$
$678$		0			0
$679$	6.48561	−	3.74447i	0.248895	−	0.143700i
$680$		0			0
$681$	31.3658	+	13.5664i	1.20194	+	0.519865i
$682$		0			0
$683$		−	23.3047i		−	0.891728i	−0.895101	−	0.445864i	$-0.852896\pi$
$683$		−	23.3047i		−	0.891728i	0.895101	−	0.445864i	$-0.147104\pi$
$684$		0			0
$685$		−	3.91744i		−	0.149678i
$686$		0			0
$687$	1.18125	−	0.877611i	0.0450676	−	0.0334829i
$688$		0			0
$689$	−14.8194	+	8.55598i	−0.564574	+	0.325957i
$690$		0			0
$691$	4.50424	−	7.80158i	0.171349	−	0.296786i	−0.767542	−	0.640998i	$-0.778521\pi$
$691$	4.50424	−	7.80158i	0.171349	−	0.296786i	0.938892	+	0.344212i	$0.111854\pi$
$692$		0			0
$693$	−44.4833	−	47.3351i	−1.68978	−	1.79811i
$694$		0			0
$695$	5.70435	−	9.88022i	0.216378	−	0.374778i
$696$		0			0
$697$	−4.52738	−	7.84166i	−0.171487	−	0.297024i
$698$		0			0
$699$	−5.37907	−	46.4153i	−0.203455	−	1.75559i
$700$		0			0
$701$	10.3925			0.392520			0.196260	−	0.980552i	$-0.437120\pi$
$701$	10.3925			0.392520			0.196260	+	0.980552i	$0.437120\pi$
$702$		0			0
$703$			43.2400i			1.63083i
$704$		0			0
$705$	−3.64608	+	0.422544i	−0.137319	+	0.0159139i
$706$		0			0
$707$	10.2376	−	5.91068i	0.385025	−	0.222294i
$708$		0			0
$709$	−22.1577	−	12.7927i	−0.832149	−	0.480442i	0.0224386	−	0.999748i	$-0.492857\pi$
$709$	−22.1577	−	12.7927i	−0.832149	−	0.480442i	−0.854588	+	0.519307i	$0.826190\pi$
$710$		0			0
$711$	33.2254	+	10.0180i	1.24605	+	0.375706i
$712$		0			0
$713$	0.958696	+	0.553503i	0.0359035	+	0.0207289i
$714$		0			0
$715$	−5.09976	−	8.83305i	−0.190720	−	0.330337i
$716$		0			0
$717$	14.4395	+	19.4353i	0.539252	+	0.725826i
$718$		0			0
$719$	36.4552			1.35955			0.679774	−	0.733422i	$-0.262078\pi$
$719$	36.4552			1.35955			0.679774	+	0.733422i	$0.262078\pi$
$720$		0			0
$721$	−45.6820			−1.70129
$722$		0			0
$723$	−9.82678	+	22.7198i	−0.365462	+	0.844958i
$724$		0			0
$725$	−2.84210	−	4.92266i	−0.105553	−	0.182823i
$726$		0			0
$727$	21.4834	+	12.4034i	0.796774	+	0.460018i	0.842342	−	0.538943i	$-0.181176\pi$
$727$	21.4834	+	12.4034i	0.796774	+	0.460018i	−0.0455677	+	0.998961i	$0.514510\pi$
$728$		0			0
$729$	20.7849	−	17.2333i	0.769811	−	0.638272i
$730$		0			0
$731$	−5.62403	−	3.24703i	−0.208012	−	0.120096i
$732$		0			0
$733$	27.3108	−	15.7679i	1.00875	−	0.582400i	0.0979219	−	0.995194i	$-0.468780\pi$
$733$	27.3108	−	15.7679i	1.00875	−	0.582400i	0.910824	+	0.412794i	$0.135447\pi$
$734$		0			0
$735$	9.65105	−	22.3135i	0.355985	−	0.823046i
$736$		0			0
$737$			70.9880i			2.61488i
$738$		0			0
$739$	−20.1619			−0.741668			−0.370834	−	0.928699i	$-0.620928\pi$
$739$	−20.1619			−0.741668			−0.370834	+	0.928699i	$0.620928\pi$
$740$		0			0
$741$	−13.0944	+	9.72846i	−0.481034	+	0.357384i
$742$		0			0
$743$	−0.498520	−	0.863461i	−0.0182889	−	0.0316773i	0.856736	−	0.515755i	$-0.172489\pi$
$743$	−0.498520	−	0.863461i	−0.0182889	−	0.0316773i	−0.875025	+	0.484078i	$0.839155\pi$
$744$		0			0
$745$	9.86802	−	17.0919i	0.361536	−	0.626199i
$746$		0			0
$747$	7.79523	+	2.35040i	0.285213	+	0.0859966i
$748$		0			0
$749$	16.7041	−	28.9324i	0.610356	−	1.05717i
$750$		0			0
$751$	−37.7503	+	21.7951i	−1.37753	+	0.795316i	−0.991861	−	0.127323i	$-0.959362\pi$
$751$	−37.7503	+	21.7951i	−1.37753	+	0.795316i	−0.385666	+	0.922639i	$0.626028\pi$
$752$		0			0
$753$	1.93536	+	16.7000i	0.0705286	+	0.608583i
$754$		0			0
$755$			6.14737i			0.223726i
$756$		0			0
$757$			5.54083i			0.201385i	0.994918	+	0.100692i	$0.0321058\pi$
$757$			5.54083i			0.201385i	−0.994918	+	0.100692i	$0.967894\pi$
$758$		0			0
$759$	−0.221833	−	1.91417i	−0.00805201	−	0.0694799i
$760$		0			0
$761$	−23.1798	+	13.3829i	−0.840267	+	0.485128i	−0.857355	−	0.514726i	$-0.827894\pi$
$761$	−23.1798	+	13.3829i	−0.840267	+	0.485128i	0.0170880	+	0.999854i	$0.494560\pi$
$762$		0			0
$763$	−5.88232	+	10.1885i	−0.212954	+	0.368847i
$764$		0			0
$765$	2.70373	−	2.54084i	0.0977537	−	0.0918643i
$766$		0			0
$767$	−12.7207	+	22.0329i	−0.459318	+	0.795562i
$768$		0			0
$769$	−1.93609	−	3.35341i	−0.0698174	−	0.120927i	0.829003	−	0.559244i	$-0.188908\pi$
$769$	−1.93609	−	3.35341i	−0.0698174	−	0.120927i	−0.898821	+	0.438316i	$0.855575\pi$
$770$		0			0
$771$	−26.4161	+	19.6258i	−0.951351	+	0.706806i
$772$		0			0
$773$	26.7361			0.961632			0.480816	−	0.876821i	$-0.340340\pi$
$773$	26.7361			0.961632			0.480816	+	0.876821i	$0.340340\pi$
$774$		0			0
$775$			4.69737i			0.168734i
$776$		0			0
$777$	31.2817	−	72.3242i	1.12223	−	2.59461i
$778$		0			0
$779$	−27.6396	+	15.9577i	−0.990290	+	0.571744i
$780$		0			0
$781$	3.48101	+	2.00976i	0.124560	+	0.0719150i
$782$		0			0
$783$	5.21437	−	29.0720i	0.186346	−	1.03895i
$784$		0			0
$785$	−0.339511	−	0.196017i	−0.0121177	−	0.00699614i
$786$		0			0
$787$	−4.82568	−	8.35833i	−0.172017	−	0.297942i	0.767108	−	0.641518i	$-0.221695\pi$
$787$	−4.82568	−	8.35833i	−0.172017	−	0.297942i	−0.939125	+	0.343576i	$0.888362\pi$
$788$		0			0
$789$	17.4355	−	40.3115i	0.620722	−	1.43513i
$790$		0			0
$791$	−1.64942			−0.0586466
$792$		0			0
$793$	15.6568			0.555988
$794$		0			0
$795$	−8.18123	−	11.0118i	−0.290158	−	0.390549i
$796$		0			0
$797$	−12.7189	−	22.0298i	−0.450528	−	0.780337i	0.547891	−	0.836550i	$-0.315431\pi$
$797$	−12.7189	−	22.0298i	−0.450528	−	0.780337i	−0.998419	+	0.0562130i	$0.982097\pi$
$798$		0			0
$799$	−2.26974	−	1.31044i	−0.0802978	−	0.0463600i
$800$		0			0
$801$	−8.87304	−	37.7681i	−0.313513	−	1.33447i
$802$		0			0
$803$	43.6512	+	25.2021i	1.54042	+	0.889361i
$804$		0			0
$805$	0.936072	−	0.540441i	0.0329922	−	0.0190481i
$806$		0			0
$807$	18.3042	−	2.12128i	0.644340	−	0.0746724i
$808$		0			0
$809$			10.7268i			0.377134i	0.982060	+	0.188567i	$0.0603843\pi$
$809$			10.7268i			0.377134i	−0.982060	+	0.188567i	$0.939616\pi$
$810$		0			0
$811$	−5.16201			−0.181263			−0.0906314	−	0.995885i	$-0.528889\pi$
$811$	−5.16201			−0.181263			−0.0906314	+	0.995885i	$0.528889\pi$
$812$		0			0
$813$	−4.56862	−	39.4221i	−0.160229	−	1.38259i
$814$		0			0
$815$	12.3153	+	21.3307i	0.431386	+	0.747183i
$816$		0			0
$817$	−11.4449	+	19.8231i	−0.400405	+	0.693521i
$818$		0			0
$819$	28.9399	−	6.79899i	1.01124	−	0.237576i
$820$		0			0
$821$	−9.71181	+	16.8213i	−0.338944	+	0.587069i	−0.984234	−	0.176869i	$-0.943403\pi$
$821$	−9.71181	+	16.8213i	−0.338944	+	0.587069i	0.645290	+	0.763938i	$0.276737\pi$
$822$		0			0
$823$	29.5617	−	17.0675i	1.03046	−	0.594935i	0.113342	−	0.993556i	$-0.463845\pi$
$823$	29.5617	−	17.0675i	1.03046	−	0.594935i	0.917116	+	0.398621i	$0.130511\pi$
$824$		0			0
$825$	6.56355	−	4.87639i	0.228513	−	0.169774i
$826$		0			0
$827$		−	21.1098i		−	0.734061i	−0.930209	−	0.367031i	$-0.880374\pi$
$827$		−	21.1098i		−	0.734061i	0.930209	−	0.367031i	$-0.119626\pi$
$828$		0			0
$829$		−	2.27907i		−	0.0791554i	−0.999216	−	0.0395777i	$-0.987399\pi$
$829$		−	2.27907i		−	0.0791554i	0.999216	−	0.0395777i	$-0.0126013\pi$
$830$		0			0
$831$	24.3715	+	10.5412i	0.845439	+	0.365670i
$832$		0			0
$833$	15.0335	−	8.67959i	0.520880	−	0.300730i
$834$		0			0
$835$	1.50486	−	2.60649i	0.0520778	−	0.0902014i
$836$		0			0
$837$	−15.7442	+	18.6516i	−0.544200	+	0.644693i
$838$		0			0
$839$	−20.2338	+	35.0460i	−0.698548	+	1.20992i	0.270421	+	0.962742i	$0.412837\pi$
$839$	−20.2338	+	35.0460i	−0.698548	+	1.20992i	−0.968970	+	0.247179i	$0.920496\pi$
$840$		0			0
$841$	−1.65503	−	2.86660i	−0.0570700	−	0.0988481i
$842$		0			0
$843$	17.0794	+	7.38720i	0.588246	+	0.254429i
$844$		0			0
$845$	−8.33213			−0.286634
$846$		0			0
$847$		−	51.7654i		−	1.77868i
$848$		0			0
$849$	18.3617	+	24.7146i	0.630172	+	0.848202i
$850$		0			0
$851$	2.02444	−	1.16881i	0.0693971	−	0.0400664i
$852$		0			0
$853$	−14.2703	−	8.23893i	−0.488604	−	0.282096i	0.235391	−	0.971901i	$-0.424363\pi$
$853$	−14.2703	−	8.23893i	−0.488604	−	0.282096i	−0.723995	+	0.689805i	$0.757696\pi$
$854$		0			0
$855$	−8.95573	−	9.52987i	−0.306279	−	0.325915i
$856$		0			0
$857$	−41.2192	−	23.7979i	−1.40802	−	0.812921i	−0.412824	−	0.910811i	$-0.635457\pi$
$857$	−41.2192	−	23.7979i	−1.40802	−	0.812921i	−0.995197	+	0.0978896i	$0.968791\pi$
$858$		0			0
$859$	15.2357	+	26.3890i	0.519836	+	0.900382i	0.999734	+	0.0230580i	$0.00734025\pi$
$859$	15.2357	+	26.3890i	0.519836	+	0.900382i	−0.479898	+	0.877324i	$0.659326\pi$
$860$		0			0
$861$	57.7750	−	6.69554i	1.96897	−	0.228183i
$862$		0			0
$863$	30.4421			1.03626			0.518131	−	0.855301i	$-0.326628\pi$
$863$	30.4421			1.03626			0.518131	+	0.855301i	$0.326628\pi$
$864$		0			0
$865$	9.97631			0.339205
$866$		0			0
$867$	−26.6174	+	3.08469i	−0.903976	+	0.104762i
$868$		0			0
$869$	27.3045	+	47.2928i	0.926242	+	1.60430i
$870$		0			0
$871$	−28.1355	−	16.2440i	−0.953335	−	0.550408i
$872$		0			0
$873$	−1.41409	+	4.68991i	−0.0478597	+	0.158729i
$874$		0			0
$875$	3.97204	+	2.29326i	0.134279	+	0.0775262i
$876$		0			0
$877$	−22.1778	+	12.8044i	−0.748892	+	0.432373i	−0.825293	−	0.564704i	$-0.808990\pi$
$877$	−22.1778	+	12.8044i	−0.748892	+	0.432373i	0.0764015	+	0.997077i	$0.475657\pi$
$878$		0			0
$879$	−28.8957	−	38.8931i	−0.974626	−	1.31183i
$880$		0			0
$881$		−	43.3621i		−	1.46091i	−0.682963	−	0.730453i	$-0.739309\pi$
$881$		−	43.3621i		−	1.46091i	0.682963	−	0.730453i	$-0.260691\pi$
$882$		0			0
$883$	15.4645			0.520421			0.260210	−	0.965552i	$-0.416208\pi$
$883$	15.4645			0.520421			0.260210	+	0.965552i	$0.416208\pi$
$884$		0			0
$885$	−18.7199	−	8.09675i	−0.629263	−	0.272169i
$886$		0			0
$887$	−1.66974	−	2.89207i	−0.0560642	−	0.0971061i	0.836631	−	0.547767i	$-0.184522\pi$
$887$	−1.66974	−	2.89207i	−0.0560642	−	0.0971061i	−0.892695	+	0.450661i	$0.851188\pi$
$888$		0			0
$889$	−20.7064	+	35.8646i	−0.694471	+	1.20286i
$890$		0			0
$891$	42.4058	+	2.63671i	1.42065	+	0.0883332i
$892$		0			0
$893$	−4.61891	+	8.00019i	−0.154566	+	0.267716i
$894$		0			0
$895$	9.66482	−	5.57999i	0.323059	−	0.186518i
$896$		0			0
$897$	0.809426	+	0.350094i	0.0270259	+	0.0116893i
$898$		0			0
$899$			26.7007i			0.890519i
$900$		0			0
$901$		−	9.79544i		−	0.326333i
$902$		0			0
$903$	33.4838	−	24.8768i	1.11427	−	0.827847i
$904$		0			0
$905$	−4.16044	+	2.40203i	−0.138298	+	0.0798463i
$906$		0			0
$907$	−1.40422	+	2.43218i	−0.0466263	+	0.0807592i	−0.888397	−	0.459077i	$-0.848180\pi$
$907$	−1.40422	+	2.43218i	−0.0466263	+	0.0807592i	0.841770	+	0.539836i	$0.181514\pi$
$908$		0			0
$909$	−2.23215	+	7.40306i	−0.0740359	+	0.245544i
$910$		0			0
$911$	−15.6065	+	27.0312i	−0.517066	+	0.895585i	0.482738	+	0.875765i	$0.339642\pi$
$911$	−15.6065	+	27.0312i	−0.517066	+	0.895585i	−0.999804	+	0.0198195i	$0.993691\pi$
$912$		0			0
$913$	6.40609	+	11.0957i	0.212011	+	0.367213i
$914$		0			0
$915$	1.44495	+	12.4683i	0.0477684	+	0.412188i
$916$		0			0
$917$	−5.22242			−0.172460
$918$		0			0
$919$		−	41.3010i		−	1.36240i	−0.732100	−	0.681198i	$-0.761459\pi$
$919$		−	41.3010i		−	1.36240i	0.732100	−	0.681198i	$-0.238541\pi$
$920$		0			0
$921$	26.4815	−	3.06893i	0.872594	−	0.101125i
$922$		0			0
$923$	−1.59311	+	0.919780i	−0.0524377	+	0.0302749i
$924$		0			0
$925$	8.59033	+	4.95963i	0.282448	+	0.163072i
$926$		0			0
$927$	21.7742	−	20.4624i	0.715159	−	0.672073i
$928$		0			0
$929$	2.46762	+	1.42468i	0.0809599	+	0.0467422i	0.539933	−	0.841708i	$-0.318449\pi$
$929$	2.46762	+	1.42468i	0.0809599	+	0.0467422i	−0.458974	+	0.888450i	$0.651783\pi$
$930$		0			0
$931$	−30.5931	−	52.9887i	−1.00265	−	1.73664i
$932$		0			0
$933$	−20.4023	−	27.4612i	−0.667941	−	0.899039i
$934$		0			0
$935$	5.83853			0.190940
$936$		0			0
$937$	33.6983			1.10088			0.550438	−	0.834876i	$-0.314461\pi$
$937$	33.6983			1.10088			0.550438	+	0.834876i	$0.314461\pi$
$938$		0			0
$939$	12.1718	−	28.1414i	0.397211	−	0.918361i
$940$		0			0
$941$	−12.1325	−	21.0141i	−0.395507	−	0.685039i	0.597659	−	0.801751i	$-0.296098\pi$
$941$	−12.1325	−	21.0141i	−0.395507	−	0.685039i	−0.993166	+	0.116712i	$0.962765\pi$
$942$		0			0
$943$	1.49424	+	0.862700i	0.0486592	+	0.0280934i
$944$		0			0
$945$	8.08521	+	22.4188i	0.263012	+	0.729284i
$946$		0			0
$947$	31.5042	+	18.1890i	1.02375	+	0.591062i	0.915188	−	0.403028i	$-0.132042\pi$
$947$	31.5042	+	18.1890i	1.02375	+	0.591062i	0.108561	+	0.994090i	$0.465376\pi$
$948$		0			0
$949$	−19.9772	+	11.5339i	−0.648489	+	0.374405i
$950$		0			0
$951$	3.68423	−	8.51804i	0.119469	−	0.276217i
$952$		0			0
$953$		−	26.2586i		−	0.850598i	−0.905053	−	0.425299i	$-0.860169\pi$
$953$		−	26.2586i		−	0.850598i	0.905053	−	0.425299i	$-0.139831\pi$
$954$		0			0
$955$	0.287325			0.00929760
$956$		0			0
$957$	37.3085	−	27.7183i	1.20601	−	0.896007i
$958$		0			0
$959$	8.98369	+	15.5602i	0.290099	+	0.502466i
$960$		0			0
$961$	−4.46738	+	7.73773i	−0.144109	+	0.249604i
$962$		0			0
$963$	4.99775	+	21.2729i	0.161050	+	0.685509i
$964$		0			0
$965$	−1.19503	+	2.06986i	−0.0384695	+	0.0666311i
$966$		0			0
$967$	−42.3417	+	24.4460i	−1.36162	+	0.786130i	−0.989839	−	0.142192i	$-0.954585\pi$
$967$	−42.3417	+	24.4460i	−1.36162	+	0.786130i	−0.371777	+	0.928322i	$0.621251\pi$
$968$		0			0
$969$	−1.07498	−	9.27585i	−0.0345332	−	0.297983i
$970$		0			0
$971$			23.9838i			0.769678i	0.922984	+	0.384839i	$0.125743\pi$
$971$			23.9838i			0.769678i	−0.922984	+	0.384839i	$0.874257\pi$
$972$		0			0
$973$			52.3261i			1.67750i
$974$		0			0
$975$	0.430793	+	3.71726i	0.0137964	+	0.119048i
$976$		0			0
$977$	−23.1131	+	13.3444i	−0.739455	+	0.426924i	−0.821871	−	0.569674i	$-0.807070\pi$
$977$	−23.1131	+	13.3444i	−0.739455	+	0.426924i	0.0824164	+	0.996598i	$0.473736\pi$
$978$		0			0
$979$	30.5253	−	52.8714i	0.975593	−	1.68978i
$980$		0			0
$981$	−1.75994	−	7.49119i	−0.0561906	−	0.239175i
$982$		0			0
$983$	−21.9816	+	38.0733i	−0.701104	+	1.21435i	0.266975	+	0.963703i	$0.413976\pi$
$983$	−21.9816	+	38.0733i	−0.701104	+	1.21435i	−0.968079	+	0.250645i	$0.919357\pi$
$984$		0			0
$985$	5.40887	+	9.36843i	0.172341	+	0.298503i
$986$		0			0
$987$	13.5134	−	10.0398i	0.430135	−	0.319569i
$988$		0			0
$989$	1.23745			0.0393488
$990$		0			0
$991$		−	43.4855i		−	1.38136i	−0.723159	−	0.690682i	$-0.757311\pi$
$991$		−	43.4855i		−	1.38136i	0.723159	−	0.690682i	$-0.242689\pi$
$992$		0			0
$993$	17.7703	−	41.0853i	0.563922	−	1.30380i
$994$		0			0
$995$	4.42142	−	2.55271i	0.140168	−	0.0809262i
$996$		0			0
$997$	5.50039	+	3.17565i	0.174199	+	0.100574i	0.584564	−	0.811347i	$-0.301265\pi$
$997$	5.50039	+	3.17565i	0.174199	+	0.100574i	−0.410365	+	0.911921i	$0.634599\pi$
$998$		0			0
$999$	17.4859	+	48.4852i	0.553230	+	1.53401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.cc.b.911.1		48
3.2	odd	2		4320.2.cc.a.1871.2		48
4.3	odd	2		360.2.bm.b.11.5	yes	48
8.3	odd	2		1440.2.cc.a.911.1		48
8.5	even	2		360.2.bm.a.11.13	✓	48
9.4	even	3		4320.2.cc.b.3311.23		48
9.5	odd	6		1440.2.cc.a.1391.1		48
12.11	even	2		1080.2.bm.a.251.20		48
24.5	odd	2		1080.2.bm.b.251.12		48
24.11	even	2		4320.2.cc.b.1871.23		48
36.23	even	6		360.2.bm.a.131.13	yes	48
36.31	odd	6		1080.2.bm.b.611.12		48
72.5	odd	6		360.2.bm.b.131.5	yes	48
72.13	even	6		1080.2.bm.a.611.20		48
72.59	even	6	inner	1440.2.cc.b.1391.1		48
72.67	odd	6		4320.2.cc.a.3311.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.13	✓	48	8.5	even	2
360.2.bm.a.131.13	yes	48	36.23	even	6
360.2.bm.b.11.5	yes	48	4.3	odd	2
360.2.bm.b.131.5	yes	48	72.5	odd	6
1080.2.bm.a.251.20		48	12.11	even	2
1080.2.bm.a.611.20		48	72.13	even	6
1080.2.bm.b.251.12		48	24.5	odd	2
1080.2.bm.b.611.12		48	36.31	odd	6
1440.2.cc.a.911.1		48	8.3	odd	2
1440.2.cc.a.1391.1		48	9.5	odd	6
1440.2.cc.b.911.1		48	1.1	even	1	trivial
1440.2.cc.b.1391.1		48	72.59	even	6	inner
4320.2.cc.a.1871.2		48	3.2	odd	2
4320.2.cc.a.3311.2		48	72.67	odd	6
4320.2.cc.b.1871.23		48	24.11	even	2
4320.2.cc.b.3311.23		48	9.4	even	3

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72054 + 0.199393i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(2.92049 - 0.686124i) q^{9} +O(q^{10})\)	\(q+(-1.72054 + 0.199393i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-3.97204 - 2.29326i) q^{7} +(2.92049 - 0.686124i) q^{9} +(4.08838 + 2.36043i) q^{11} +(-1.87107 + 1.08026i) q^{13} +(-1.03295 - 1.39033i) q^{15} -1.23675i q^{17} -4.35920 q^{19} +(7.29129 + 3.15363i) q^{21} +(0.117833 + 0.204092i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-4.88799 + 1.76282i) q^{27} +(-2.84210 + 4.92266i) q^{29} +(4.06804 - 2.34868i) q^{31} +(-7.50485 - 3.24600i) q^{33} -4.58651i q^{35} -9.91926i q^{37} +(3.00385 - 2.23171i) q^{39} +(6.34052 - 3.66070i) q^{41} +(2.62545 - 4.54741i) q^{43} +(2.05444 + 2.18615i) q^{45} +(1.05958 - 1.83524i) q^{47} +(7.01804 + 12.1556i) q^{49} +(0.246600 + 2.12788i) q^{51} +7.92028 q^{53} +4.72085i q^{55} +(7.50016 - 0.869192i) q^{57} +(10.1979 - 5.88778i) q^{59} +(-6.27586 - 3.62337i) q^{61} +(-13.1737 - 3.97211i) q^{63} +(-1.87107 - 1.08026i) q^{65} +(7.51856 + 13.0225i) q^{67} +(-0.243430 - 0.327653i) q^{69} +0.851441 q^{71} +10.6769 q^{73} +(0.687589 - 1.58972i) q^{75} +(-10.8261 - 18.7514i) q^{77} +(10.0179 + 5.78381i) q^{79} +(8.05847 - 4.00763i) q^{81} +(2.35035 + 1.35698i) q^{83} +(1.07106 - 0.618377i) q^{85} +(3.90839 - 9.03630i) q^{87} -12.9321i q^{89} +9.90928 q^{91} +(-6.53089 + 4.85213i) q^{93} +(-2.17960 - 3.77518i) q^{95} +(-0.816409 + 1.41406i) q^{97} +(13.5596 + 4.08846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5}+O(q^{10}) \) 48 * q + 24 * q^5	\( 48 q + 24 q^{5} + 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} + 16 q^{39} + 12 q^{41} + 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} - 12 q^{61} + 56 q^{63} + 40 q^{69} - 8 q^{81} + 60 q^{83} + 36 q^{87} + 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 + 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 + 16 * q^39 + 12 * q^41 + 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 - 12 * q^61 + 56 * q^63 + 40 * q^69 - 8 * q^81 + 60 * q^83 + 36 * q^87 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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