LMFDB - Embedded newform 1120.2.bz.f.591.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.4
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.f.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90624 - 1.10057i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.584379 + 2.58041i) q^{7} +(0.922503 + 1.59782i) q^{9} +O(q^{10})$	\(q+(-1.90624 - 1.10057i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.584379 + 2.58041i) q^{7} +(0.922503 + 1.59782i) q^{9} +(2.90486 - 5.03137i) q^{11} -4.83332 q^{13} -2.20114i q^{15} +(3.78236 + 2.18375i) q^{17} +(-1.63783 + 0.945600i) q^{19} +(3.95388 - 4.27573i) q^{21} +(0.157820 - 0.0911173i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.54230i q^{27} +4.38898i q^{29} +(-2.03983 + 3.53308i) q^{31} +(-11.0747 + 6.39400i) q^{33} +(-2.52689 + 0.784117i) q^{35} +(-3.69132 + 2.13119i) q^{37} +(9.21347 + 5.31940i) q^{39} -3.44314i q^{41} +2.10796 q^{43} +(-0.922503 + 1.59782i) q^{45} +(0.946816 + 1.63993i) q^{47} +(-6.31700 - 3.01587i) q^{49} +(-4.80673 - 8.32550i) q^{51} +(8.54212 + 4.93180i) q^{53} +5.80972 q^{55} +4.16279 q^{57} +(6.35546 + 3.66932i) q^{59} +(4.89522 + 8.47877i) q^{61} +(-4.66212 + 1.44670i) q^{63} +(-2.41666 - 4.18577i) q^{65} +(-6.04954 + 10.4781i) q^{67} -0.401124 q^{69} +8.80669i q^{71} +(7.34998 + 4.24351i) q^{73} +(1.90624 - 1.10057i) q^{75} +(11.2854 + 10.4360i) q^{77} +(10.5541 - 6.09342i) q^{79} +(5.56549 - 9.63970i) q^{81} +16.9697i q^{83} +4.36749i q^{85} +(4.83037 - 8.36645i) q^{87} +(-5.11692 + 2.95425i) q^{89} +(2.82449 - 12.4719i) q^{91} +(7.77680 - 4.48994i) q^{93} +(-1.63783 - 0.945600i) q^{95} +13.2388i q^{97} +10.7190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−1.90624	−	1.10057i	−1.10057	−	0.635414i	−0.164198	−	0.986427i	$-0.552504\pi$
$3$	−1.90624	−	1.10057i	−1.10057	−	0.635414i	−0.936370	+	0.351014i	$0.885837\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.584379	+	2.58041i	−0.220874	+	0.975302i
$7$	−0.584379	+	2.58041i	−0.220874	+	0.975302i
$8$		0			0
$9$	0.922503	+	1.59782i	0.307501	+	0.532608i
$10$		0			0
$11$	2.90486	−	5.03137i	0.875849	−	1.51701i	0.0199929	−	0.999800i	$-0.493636\pi$
$11$	2.90486	−	5.03137i	0.875849	−	1.51701i	0.855856	−	0.517214i	$-0.173031\pi$
$12$		0			0
$13$	−4.83332			−1.34052			−0.670260	−	0.742126i	$-0.733818\pi$
$13$	−4.83332			−1.34052			−0.670260	+	0.742126i	$0.733818\pi$
$14$		0			0
$15$		−	2.20114i		−	0.568331i
$16$		0			0
$17$	3.78236	+	2.18375i	0.917357	+	0.529636i	0.882791	−	0.469766i	$-0.155662\pi$
$17$	3.78236	+	2.18375i	0.917357	+	0.529636i	0.0345662	+	0.999402i	$0.488995\pi$
$18$		0			0
$19$	−1.63783	+	0.945600i	−0.375743	+	0.216936i	−0.675965	−	0.736934i	$-0.736273\pi$
$19$	−1.63783	+	0.945600i	−0.375743	+	0.216936i	0.300221	+	0.953870i	$0.402939\pi$
$20$		0			0
$21$	3.95388	−	4.27573i	0.862808	−	0.933041i
$22$		0			0
$23$	0.157820	−	0.0911173i	0.0329077	−	0.0189993i	−0.483456	−	0.875369i	$-0.660619\pi$
$23$	0.157820	−	0.0911173i	0.0329077	−	0.0189993i	0.516364	+	0.856369i	$0.327285\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			2.54230i			0.489266i
$28$		0			0
$29$			4.38898i			0.815013i	0.913202	+	0.407506i	$0.133602\pi$
$29$			4.38898i			0.815013i	−0.913202	+	0.407506i	$0.866398\pi$
$30$		0			0
$31$	−2.03983	+	3.53308i	−0.366364	+	0.634560i	−0.988994	−	0.147956i	$-0.952731\pi$
$31$	−2.03983	+	3.53308i	−0.366364	+	0.634560i	0.622630	+	0.782516i	$0.286064\pi$
$32$		0			0
$33$	−11.0747	+	6.39400i	−1.92786	+	1.11305i
$34$		0			0
$35$	−2.52689	+	0.784117i	−0.427122	+	0.132540i
$36$		0			0
$37$	−3.69132	+	2.13119i	−0.606849	+	0.350365i	−0.771731	−	0.635949i	$-0.780609\pi$
$37$	−3.69132	+	2.13119i	−0.606849	+	0.350365i	0.164882	+	0.986313i	$0.447276\pi$
$38$		0			0
$39$	9.21347	+	5.31940i	1.47534	+	0.851785i
$40$		0			0
$41$		−	3.44314i		−	0.537729i	−0.963178	−	0.268864i	$-0.913352\pi$
$41$		−	3.44314i		−	0.537729i	0.963178	−	0.268864i	$-0.0866483\pi$
$42$		0			0
$43$	2.10796			0.321461			0.160731	−	0.986998i	$-0.448615\pi$
$43$	2.10796			0.321461			0.160731	+	0.986998i	$0.448615\pi$
$44$		0			0
$45$	−0.922503	+	1.59782i	−0.137519	+	0.238189i
$46$		0			0
$47$	0.946816	+	1.63993i	0.138107	+	0.239209i	0.926780	−	0.375604i	$-0.122565\pi$
$47$	0.946816	+	1.63993i	0.138107	+	0.239209i	−0.788673	+	0.614813i	$0.789231\pi$
$48$		0			0
$49$	−6.31700	−	3.01587i	−0.902429	−	0.430839i
$50$		0			0
$51$	−4.80673	−	8.32550i	−0.673076	−	1.16580i
$52$		0			0
$53$	8.54212	+	4.93180i	1.17335	+	0.677434i	0.954467	−	0.298317i	$-0.0964252\pi$
$53$	8.54212	+	4.93180i	1.17335	+	0.677434i	0.218884	+	0.975751i	$0.429758\pi$
$54$		0			0
$55$	5.80972			0.783383
$56$		0			0
$57$	4.16279			0.551375
$58$		0			0
$59$	6.35546	+	3.66932i	0.827410	+	0.477705i	0.852965	−	0.521968i	$-0.174802\pi$
$59$	6.35546	+	3.66932i	0.827410	+	0.477705i	−0.0255550	+	0.999673i	$0.508135\pi$
$60$		0			0
$61$	4.89522	+	8.47877i	0.626769	+	1.08560i	0.988196	+	0.153195i	$0.0489562\pi$
$61$	4.89522	+	8.47877i	0.626769	+	1.08560i	−0.361427	+	0.932400i	$0.617710\pi$
$62$		0			0
$63$	−4.66212	+	1.44670i	−0.587373	+	0.182267i
$64$		0			0
$65$	−2.41666	−	4.18577i	−0.299750	−	0.519181i
$66$		0			0
$67$	−6.04954	+	10.4781i	−0.739069	+	1.28011i	0.213845	+	0.976868i	$0.431401\pi$
$67$	−6.04954	+	10.4781i	−0.739069	+	1.28011i	−0.952915	+	0.303238i	$0.901932\pi$
$68$		0			0
$69$	−0.401124			−0.0482896
$70$		0			0
$71$			8.80669i			1.04516i	0.852590	+	0.522581i	$0.175031\pi$
$71$			8.80669i			1.04516i	−0.852590	+	0.522581i	$0.824969\pi$
$72$		0			0
$73$	7.34998	+	4.24351i	0.860250	+	0.496666i	0.864096	−	0.503327i	$-0.167891\pi$
$73$	7.34998	+	4.24351i	0.860250	+	0.496666i	−0.00384586	+	0.999993i	$0.501224\pi$
$74$		0			0
$75$	1.90624	−	1.10057i	0.220114	−	0.127083i
$76$		0			0
$77$	11.2854	+	10.4360i	1.28610	+	1.18929i
$78$		0			0
$79$	10.5541	−	6.09342i	1.18743	−	0.685563i	0.229708	−	0.973259i	$-0.426223\pi$
$79$	10.5541	−	6.09342i	1.18743	−	0.685563i	0.957722	+	0.287696i	$0.0928894\pi$
$80$		0			0
$81$	5.56549	−	9.63970i	0.618387	−	1.07108i
$82$		0			0
$83$			16.9697i			1.86267i	0.364163	+	0.931335i	$0.381355\pi$
$83$			16.9697i			1.86267i	−0.364163	+	0.931335i	$0.618645\pi$
$84$		0			0
$85$			4.36749i			0.473721i
$86$		0			0
$87$	4.83037	−	8.36645i	0.517870	−	0.896977i
$88$		0			0
$89$	−5.11692	+	2.95425i	−0.542392	+	0.313150i	−0.746048	−	0.665892i	$-0.768051\pi$
$89$	−5.11692	+	2.95425i	−0.542392	+	0.313150i	0.203656	+	0.979043i	$0.434718\pi$
$90$		0			0
$91$	2.82449	−	12.4719i	0.296087	−	1.30741i
$92$		0			0
$93$	7.77680	−	4.48994i	0.806417	−	0.465585i
$94$		0			0
$95$	−1.63783	−	0.945600i	−0.168038	−	0.0970165i
$96$		0			0
$97$			13.2388i			1.34420i	0.740461	+	0.672100i	$0.234607\pi$
$97$			13.2388i			1.34420i	−0.740461	+	0.672100i	$0.765393\pi$
$98$		0			0
$99$	10.7190			1.07730
$100$		0			0
$101$	1.23442	−	2.13807i	0.122829	−	0.212746i	−0.798053	−	0.602587i	$-0.794137\pi$
$101$	1.23442	−	2.13807i	0.122829	−	0.212746i	0.920882	+	0.389841i	$0.127470\pi$
$102$		0			0
$103$	0.920346	+	1.59409i	0.0906844	+	0.157070i	0.907799	−	0.419405i	$-0.137761\pi$
$103$	0.920346	+	1.59409i	0.0906844	+	0.157070i	−0.817115	+	0.576475i	$0.804428\pi$
$104$		0			0
$105$	5.67983	+	1.28630i	0.554295	+	0.125530i
$106$		0			0
$107$	−9.08674	−	15.7387i	−0.878448	−	1.52152i	−0.853044	−	0.521839i	$-0.825246\pi$
$107$	−9.08674	−	15.7387i	−0.878448	−	1.52152i	−0.0254044	−	0.999677i	$-0.508087\pi$
$108$		0			0
$109$	−3.40525	−	1.96602i	−0.326164	−	0.188311i	0.327973	−	0.944687i	$-0.393635\pi$
$109$	−3.40525	−	1.96602i	−0.326164	−	0.188311i	−0.654137	+	0.756376i	$0.726968\pi$
$110$		0			0
$111$	9.38206			0.890506
$112$		0			0
$113$	7.16641			0.674159			0.337079	−	0.941476i	$-0.390561\pi$
$113$	7.16641			0.674159			0.337079	+	0.941476i	$0.390561\pi$
$114$		0			0
$115$	0.157820	+	0.0911173i	0.0147168	+	0.00849673i
$116$		0			0
$117$	−4.45875	−	7.72278i	−0.412212	−	0.713972i
$118$		0			0
$119$	−7.84529	+	8.48390i	−0.719176	+	0.777717i
$120$		0			0
$121$	−11.3764	−	19.7046i	−1.03422	−	1.79133i
$122$		0			0
$123$	−3.78942	+	6.56346i	−0.341680	+	0.591808i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			2.88206i			0.255742i	0.991791	+	0.127871i	$0.0408143\pi$
$127$			2.88206i			0.255742i	−0.991791	+	0.127871i	$0.959186\pi$
$128$		0			0
$129$	−4.01829	−	2.31996i	−0.353790	−	0.204261i
$130$		0			0
$131$	−6.92953	+	4.00076i	−0.605436	+	0.349548i	−0.771177	−	0.636621i	$-0.780332\pi$
$131$	−6.92953	+	4.00076i	−0.605436	+	0.349548i	0.165741	+	0.986169i	$0.446998\pi$
$132$		0			0
$133$	−1.48292	−	4.77885i	−0.128586	−	0.414379i
$134$		0			0
$135$	−2.20170	+	1.27115i	−0.189492	+	0.109403i
$136$		0			0
$137$	5.09925	−	8.83216i	0.435658	−	0.754582i	−0.561691	−	0.827347i	$-0.689849\pi$
$137$	5.09925	−	8.83216i	0.435658	−	0.754582i	0.997349	+	0.0727651i	$0.0231823\pi$
$138$		0			0
$139$			9.93769i			0.842904i	0.906851	+	0.421452i	$0.138479\pi$
$139$			9.93769i			0.842904i	−0.906851	+	0.421452i	$0.861521\pi$
$140$		0			0
$141$		−	4.16814i		−	0.351021i
$142$		0			0
$143$	−14.0401	+	24.3182i	−1.17409	+	2.03359i
$144$		0			0
$145$	−3.80097	+	2.19449i	−0.315653	+	0.182242i
$146$		0			0
$147$	8.72256	+	12.7013i	0.719424	+	1.04758i
$148$		0			0
$149$	−13.6559	+	7.88422i	−1.11873	+	0.645900i	−0.941077	−	0.338192i	$-0.890185\pi$
$149$	−13.6559	+	7.88422i	−1.11873	+	0.645900i	−0.177655	+	0.984093i	$0.556851\pi$
$150$		0			0
$151$	−5.24155	−	3.02621i	−0.426552	−	0.246270i	0.271325	−	0.962488i	$-0.412538\pi$
$151$	−5.24155	−	3.02621i	−0.426552	−	0.246270i	−0.697877	+	0.716218i	$0.745872\pi$
$152$		0			0
$153$			8.05806i			0.651455i
$154$		0			0
$155$	−4.07965			−0.327686
$156$		0			0
$157$	10.2074	−	17.6798i	0.814641	−	1.41100i	−0.0949439	−	0.995483i	$-0.530267\pi$
$157$	10.2074	−	17.6798i	0.814641	−	1.41100i	0.909585	−	0.415518i	$-0.136400\pi$
$158$		0			0
$159$	−10.8556	−	18.8024i	−0.860902	−	1.49113i
$160$		0			0
$161$	0.142893	+	0.460486i	0.0112616	+	0.0362914i
$162$		0			0
$163$	−1.91267	−	3.31285i	−0.149812	−	0.259482i	0.781346	−	0.624098i	$-0.214534\pi$
$163$	−1.91267	−	3.31285i	−0.149812	−	0.259482i	−0.931158	+	0.364616i	$0.881200\pi$
$164$		0			0
$165$	−11.0747	−	6.39400i	−0.862167	−	0.497772i
$166$		0			0
$167$	−21.6531			−1.67556			−0.837782	−	0.546005i	$-0.816148\pi$
$167$	−21.6531			−1.67556			−0.837782	+	0.546005i	$0.816148\pi$
$168$		0			0
$169$	10.3609			0.796996
$170$		0			0
$171$	−3.02180	−	1.74464i	−0.231083	−	0.133416i
$172$		0			0
$173$	−5.20160	−	9.00944i	−0.395470	−	0.684975i	0.597691	−	0.801727i	$-0.296085\pi$
$173$	−5.20160	−	9.00944i	−0.395470	−	0.684975i	−0.993161	+	0.116752i	$0.962752\pi$
$174$		0			0
$175$	−1.94251	−	1.79629i	−0.146840	−	0.135787i
$176$		0			0
$177$	−8.07669	−	13.9892i	−0.607081	−	1.05150i
$178$		0			0
$179$	−3.80514	+	6.59069i	−0.284409	+	0.492611i	−0.972466	−	0.233046i	$-0.925131\pi$
$179$	−3.80514	+	6.59069i	−0.284409	+	0.492611i	0.688056	+	0.725657i	$0.258464\pi$
$180$		0			0
$181$	11.2225			0.834160			0.417080	−	0.908870i	$-0.363054\pi$
$181$	11.2225			0.834160			0.417080	+	0.908870i	$0.363054\pi$
$182$		0			0
$183$		−	21.5501i		−	1.59303i
$184$		0			0
$185$	−3.69132	−	2.13119i	−0.271391	−	0.156688i
$186$		0			0
$187$	21.9745	−	12.6870i	1.60693	−	0.927763i
$188$		0			0
$189$	−6.56017	−	1.48567i	−0.477182	−	0.108066i
$190$		0			0
$191$	6.68571	−	3.86000i	0.483761	−	0.279300i	−0.238222	−	0.971211i	$-0.576564\pi$
$191$	6.68571	−	3.86000i	0.483761	−	0.279300i	0.721983	+	0.691911i	$0.243231\pi$
$192$		0			0
$193$	−11.7011	+	20.2669i	−0.842265	+	1.45885i	0.0457097	+	0.998955i	$0.485445\pi$
$193$	−11.7011	+	20.2669i	−0.842265	+	1.45885i	−0.887975	+	0.459892i	$0.847888\pi$
$194$		0			0
$195$			10.6388i			0.761860i
$196$		0			0
$197$			20.4272i			1.45538i	0.685907	+	0.727689i	$0.259406\pi$
$197$			20.4272i			1.45538i	−0.685907	+	0.727689i	$0.740594\pi$
$198$		0			0
$199$	1.10091	−	1.90683i	0.0780413	−	0.135172i	−0.824363	−	0.566061i	$-0.808467\pi$
$199$	1.10091	−	1.90683i	0.0780413	−	0.135172i	0.902405	+	0.430889i	$0.141800\pi$
$200$		0			0
$201$	23.0638	−	13.3159i	1.62679	−	0.939230i
$202$		0			0
$203$	−11.3253	−	2.56482i	−0.794884	−	0.180015i
$204$		0			0
$205$	2.98185	−	1.72157i	0.208261	−	0.120240i
$206$		0			0
$207$	0.291179	+	0.168112i	0.0202383	+	0.0116846i
$208$		0			0
$209$			10.9874i			0.760011i
$210$		0			0
$211$	28.9363			1.99206			0.996028	−	0.0890425i	$-0.0283807\pi$
$211$	28.9363			1.99206			0.996028	+	0.0890425i	$0.0283807\pi$
$212$		0			0
$213$	9.69236	−	16.7877i	0.664110	−	1.15027i
$214$		0			0
$215$	1.05398	+	1.82555i	0.0718810	+	0.124501i
$216$		0			0
$217$	−7.92476	−	7.32824i	−0.537968	−	0.497473i
$218$		0			0
$219$	−9.34056	−	16.1783i	−0.631176	−	1.09323i
$220$		0			0
$221$	−18.2813	−	10.5547i	−1.22974	−	0.709989i
$222$		0			0
$223$	−11.0535			−0.740200			−0.370100	−	0.928992i	$-0.620677\pi$
$223$	−11.0535			−0.740200			−0.370100	+	0.928992i	$0.620677\pi$
$224$		0			0
$225$	−1.84501			−0.123000
$226$		0			0
$227$	−7.11916	−	4.11025i	−0.472515	−	0.272807i	0.244777	−	0.969579i	$-0.421285\pi$
$227$	−7.11916	−	4.11025i	−0.472515	−	0.272807i	−0.717292	+	0.696773i	$0.754619\pi$
$228$		0			0
$229$	−5.03725	−	8.72478i	−0.332871	−	0.576549i	0.650203	−	0.759761i	$-0.274684\pi$
$229$	−5.03725	−	8.72478i	−0.332871	−	0.576549i	−0.983074	+	0.183211i	$0.941351\pi$
$230$		0			0
$231$	−10.0273	−	32.3138i	−0.659747	−	2.12609i
$232$		0			0
$233$	3.68557	+	6.38359i	0.241450	+	0.418203i	0.961127	−	0.276105i	$-0.0890438\pi$
$233$	3.68557	+	6.38359i	0.241450	+	0.418203i	−0.719678	+	0.694308i	$0.755711\pi$
$234$		0			0
$235$	−0.946816	+	1.63993i	−0.0617634	+	0.106977i
$236$		0			0
$237$	−26.8249			−1.74246
$238$		0			0
$239$		−	20.9534i		−	1.35536i	−0.735355	−	0.677682i	$-0.762984\pi$
$239$		−	20.9534i		−	1.35536i	0.735355	−	0.677682i	$-0.237016\pi$
$240$		0			0
$241$	−2.42132	−	1.39795i	−0.155971	−	0.0900498i	0.419983	−	0.907532i	$-0.362036\pi$
$241$	−2.42132	−	1.39795i	−0.155971	−	0.0900498i	−0.575954	+	0.817482i	$0.695369\pi$
$242$		0			0
$243$	−14.6132	+	8.43695i	−0.937439	+	0.541231i
$244$		0			0
$245$	−0.546681	−	6.97862i	−0.0349262	−	0.445848i
$246$		0			0
$247$	7.91614	−	4.57039i	0.503692	−	0.290807i
$248$		0			0
$249$	18.6764	−	32.3484i	1.18357	−	2.05000i
$250$		0			0
$251$		−	18.7656i		−	1.18448i	−0.805763	−	0.592238i	$-0.798244\pi$
$251$		−	18.7656i		−	1.18448i	0.805763	−	0.592238i	$-0.201756\pi$
$252$		0			0
$253$		−	1.05873i		−	0.0665620i
$254$		0			0
$255$	4.80673	−	8.32550i	0.301009	−	0.521363i
$256$		0			0
$257$	−6.76564	+	3.90615i	−0.422029	+	0.243659i	−0.695945	−	0.718095i	$-0.745014\pi$
$257$	−6.76564	+	3.90615i	−0.422029	+	0.243659i	0.273916	+	0.961754i	$0.411681\pi$
$258$		0			0
$259$	−3.34220	−	10.7705i	−0.207674	−	0.669248i
$260$		0			0
$261$	−7.01281	+	4.04885i	−0.434082	+	0.250617i
$262$		0			0
$263$	5.03985	+	2.90976i	0.310770	+	0.179423i	0.647271	−	0.762260i	$-0.275910\pi$
$263$	5.03985	+	2.90976i	0.310770	+	0.179423i	−0.336501	+	0.941683i	$0.609243\pi$
$264$		0			0
$265$			9.86359i			0.605916i
$266$		0			0
$267$	13.0054			0.795920
$268$		0			0
$269$	−12.0950	+	20.9492i	−0.737445	+	1.27729i	0.216197	+	0.976350i	$0.430635\pi$
$269$	−12.0950	+	20.9492i	−0.737445	+	1.27729i	−0.953642	+	0.300943i	$0.902699\pi$
$270$		0			0
$271$	7.83742	+	13.5748i	0.476089	+	0.824611i	0.999625	−	0.0273932i	$-0.00872061\pi$
$271$	7.83742	+	13.5748i	0.476089	+	0.824611i	−0.523536	+	0.852004i	$0.675387\pi$
$272$		0			0
$273$	−19.1104	+	20.6660i	−1.15661	+	1.25076i
$274$		0			0
$275$	2.90486	+	5.03137i	0.175170	+	0.303403i
$276$		0			0
$277$	−12.6984	−	7.33142i	−0.762972	−	0.440502i	0.0673898	−	0.997727i	$-0.478533\pi$
$277$	−12.6984	−	7.33142i	−0.762972	−	0.440502i	−0.830362	+	0.557225i	$0.811866\pi$
$278$		0			0
$279$	−7.52699			−0.450629
$280$		0			0
$281$	15.0418			0.897320			0.448660	−	0.893703i	$-0.351901\pi$
$281$	15.0418			0.897320			0.448660	+	0.893703i	$0.351901\pi$
$282$		0			0
$283$	−4.29409	−	2.47919i	−0.255257	−	0.147373i	0.366912	−	0.930256i	$-0.380415\pi$
$283$	−4.29409	−	2.47919i	−0.255257	−	0.147373i	−0.622169	+	0.782883i	$0.713748\pi$
$284$		0			0
$285$	2.08140	+	3.60508i	0.123291	+	0.213547i
$286$		0			0
$287$	8.88471	+	2.01210i	0.524448	+	0.118771i
$288$		0			0
$289$	1.03750	+	1.79700i	0.0610294	+	0.105706i
$290$		0			0
$291$	14.5702	−	25.2364i	0.854123	−	1.47938i
$292$		0			0
$293$	−2.56812			−0.150031			−0.0750156	−	0.997182i	$-0.523901\pi$
$293$	−2.56812			−0.150031			−0.0750156	+	0.997182i	$0.523901\pi$
$294$		0			0
$295$			7.33865i			0.427273i
$296$		0			0
$297$	12.7912	+	7.38503i	0.742223	+	0.428523i
$298$		0			0
$299$	−0.762793	+	0.440399i	−0.0441135	+	0.0254689i
$300$		0			0
$301$	−1.23185	+	5.43941i	−0.0710026	+	0.313522i
$302$		0			0
$303$	−4.70619	+	2.71712i	−0.270363	+	0.156094i
$304$		0			0
$305$	−4.89522	+	8.47877i	−0.280299	+	0.485493i
$306$		0			0
$307$		−	14.4425i		−	0.824280i	−0.911121	−	0.412140i	$-0.864781\pi$
$307$		−	14.4425i		−	0.824280i	0.911121	−	0.412140i	$-0.135219\pi$
$308$		0			0
$309$		−	4.05162i		−	0.230488i
$310$		0			0
$311$	−8.26712	+	14.3191i	−0.468785	+	0.811960i	−0.999363	−	0.0356762i	$-0.988641\pi$
$311$	−8.26712	+	14.3191i	−0.468785	+	0.811960i	0.530578	+	0.847636i	$0.321975\pi$
$312$		0			0
$313$	2.19818	−	1.26912i	0.124248	−	0.0717348i	−0.436588	−	0.899662i	$-0.643813\pi$
$313$	2.19818	−	1.26912i	0.124248	−	0.0717348i	0.560836	+	0.827927i	$0.310480\pi$
$314$		0			0
$315$	−3.58394	−	3.31417i	−0.201932	−	0.186732i
$316$		0			0
$317$	14.8432	−	8.56971i	0.833676	−	0.481323i	−0.0214339	−	0.999770i	$-0.506823\pi$
$317$	14.8432	−	8.56971i	0.833676	−	0.481323i	0.855109	+	0.518447i	$0.173490\pi$
$318$		0			0
$319$	22.0826	+	12.7494i	1.23639	+	0.713828i
$320$		0			0
$321$			40.0023i			2.23271i
$322$		0			0
$323$	−8.25981			−0.459588
$324$		0			0
$325$	2.41666	−	4.18577i	0.134052	−	0.232185i
$326$		0			0
$327$	4.32749	+	7.49543i	0.239311	+	0.414498i
$328$		0			0
$329$	−4.78499	+	1.48483i	−0.263805	+	0.0818612i
$330$		0			0
$331$	11.9027	+	20.6161i	0.654233	+	1.13317i	0.982085	+	0.188436i	$0.0603418\pi$
$331$	11.9027	+	20.6161i	0.654233	+	1.13317i	−0.327852	+	0.944729i	$0.606325\pi$
$332$		0			0
$333$	−6.81051	−	3.93205i	−0.373214	−	0.215475i
$334$		0			0
$335$	−12.0991			−0.661044
$336$		0			0
$337$	1.22715			0.0668470			0.0334235	−	0.999441i	$-0.489359\pi$
$337$	1.22715			0.0668470			0.0334235	+	0.999441i	$0.489359\pi$
$338$		0			0
$339$	−13.6609	−	7.88712i	−0.741958	−	0.428370i
$340$		0			0
$341$	11.8508	+	20.5262i	0.641758	+	1.11156i
$342$		0			0
$343$	11.4737	−	14.5380i	0.619521	−	0.784980i
$344$		0			0
$345$	−0.200562	−	0.347383i	−0.0107979	−	0.0187025i
$346$		0			0
$347$	15.4834	−	26.8181i	0.831194	−	1.43967i	−0.0658983	−	0.997826i	$-0.520991\pi$
$347$	15.4834	−	26.8181i	0.831194	−	1.43967i	0.897092	−	0.441844i	$-0.145675\pi$
$348$		0			0
$349$	26.6776			1.42802			0.714010	−	0.700136i	$-0.246877\pi$
$349$	26.6776			1.42802			0.714010	+	0.700136i	$0.246877\pi$
$350$		0			0
$351$		−	12.2877i		−	0.655871i
$352$		0			0
$353$	−12.1501	−	7.01487i	−0.646685	−	0.373364i	0.140500	−	0.990081i	$-0.455129\pi$
$353$	−12.1501	−	7.01487i	−0.646685	−	0.373364i	−0.787185	+	0.616717i	$0.788462\pi$
$354$		0			0
$355$	−7.62681	+	4.40334i	−0.404789	+	0.233705i
$356$		0			0
$357$	24.2921	−	7.53807i	1.28568	−	0.398957i
$358$		0			0
$359$	10.5164	−	6.07165i	0.555035	−	0.320450i	−0.196115	−	0.980581i	$-0.562833\pi$
$359$	10.5164	−	6.07165i	0.555035	−	0.320450i	0.751150	+	0.660131i	$0.229499\pi$
$360$		0			0
$361$	−7.71168	+	13.3570i	−0.405878	+	0.703001i
$362$		0			0
$363$			50.0822i			2.62864i
$364$		0			0
$365$			8.48703i			0.444231i
$366$		0			0
$367$	5.75583	−	9.96939i	0.300452	−	0.520398i	−0.675787	−	0.737097i	$-0.736196\pi$
$367$	5.75583	−	9.96939i	0.300452	−	0.520398i	0.976238	+	0.216700i	$0.0695292\pi$
$368$		0			0
$369$	5.50153	−	3.17631i	0.286398	−	0.165352i
$370$		0			0
$371$	−17.7179	+	19.1601i	−0.919866	+	0.994744i
$372$		0			0
$373$	−20.3241	+	11.7341i	−1.05234	+	0.607570i	−0.923304	−	0.384070i	$-0.874522\pi$
$373$	−20.3241	+	11.7341i	−1.05234	+	0.607570i	−0.129037	+	0.991640i	$0.541189\pi$
$374$		0			0
$375$	1.90624	+	1.10057i	0.0984379	+	0.0568331i
$376$		0			0
$377$		−	21.2133i		−	1.09254i
$378$		0			0
$379$	15.5653			0.799536			0.399768	−	0.916616i	$-0.369091\pi$
$379$	15.5653			0.799536			0.399768	+	0.916616i	$0.369091\pi$
$380$		0			0
$381$	3.17191	−	5.49391i	0.162502	−	0.281462i
$382$		0			0
$383$	−7.45943	−	12.9201i	−0.381159	−	0.660187i	0.610069	−	0.792348i	$-0.291142\pi$
$383$	−7.45943	−	12.9201i	−0.381159	−	0.660187i	−0.991228	+	0.132161i	$0.957808\pi$
$384$		0			0
$385$	−3.39508	+	14.9915i	−0.173029	+	0.764035i
$386$		0			0
$387$	1.94460	+	3.36815i	0.0988498	+	0.171213i
$388$		0			0
$389$	10.9524	+	6.32338i	0.555310	+	0.320608i	0.751261	−	0.660006i	$-0.229446\pi$
$389$	10.9524	+	6.32338i	0.555310	+	0.320608i	−0.195951	+	0.980614i	$0.562779\pi$
$390$		0			0
$391$	0.795909			0.0402508
$392$		0			0
$393$	17.6125			0.888431
$394$		0			0
$395$	10.5541	+	6.09342i	0.531035	+	0.306593i
$396$		0			0
$397$	−7.61650	−	13.1922i	−0.382261	−	0.662095i	0.609124	−	0.793075i	$-0.291521\pi$
$397$	−7.61650	−	13.1922i	−0.382261	−	0.662095i	−0.991385	+	0.130979i	$0.958188\pi$
$398$		0			0
$399$	−2.43265	+	10.7417i	−0.121785	+	0.537758i
$400$		0			0
$401$	−7.73594	−	13.3990i	−0.386315	−	0.669117i	0.605636	−	0.795742i	$-0.292919\pi$
$401$	−7.73594	−	13.3990i	−0.386315	−	0.669117i	−0.991951	+	0.126625i	$0.959585\pi$
$402$		0			0
$403$	9.85913	−	17.0765i	0.491118	−	0.850641i
$404$		0			0
$405$	11.1310			0.553102
$406$		0			0
$407$			24.7632i			1.22747i
$408$		0			0
$409$	−7.47055	−	4.31313i	−0.369395	−	0.213270i	0.303799	−	0.952736i	$-0.401745\pi$
$409$	−7.47055	−	4.31313i	−0.369395	−	0.213270i	−0.673194	+	0.739466i	$0.735078\pi$
$410$		0			0
$411$	−19.4408	+	11.2241i	−0.958944	+	0.553646i
$412$		0			0
$413$	−13.1823	+	14.2554i	−0.648661	+	0.701462i
$414$		0			0
$415$	−14.6962	+	8.48487i	−0.721409	+	0.416506i
$416$		0			0
$417$	10.9371	−	18.9436i	0.535592	−	0.927673i
$418$		0			0
$419$		−	10.6898i		−	0.522230i	−0.965308	−	0.261115i	$-0.915910\pi$
$419$		−	10.6898i		−	0.522230i	0.965308	−	0.261115i	$-0.0840902\pi$
$420$		0			0
$421$		−	20.4941i		−	0.998823i	−0.866365	−	0.499412i	$-0.833550\pi$
$421$		−	20.4941i		−	0.998823i	0.866365	−	0.499412i	$-0.166450\pi$
$422$		0			0
$423$	−1.74688	+	3.02569i	−0.0849363	+	0.147114i
$424$		0			0
$425$	−3.78236	+	2.18375i	−0.183471	+	0.105927i
$426$		0			0
$427$	−24.7393	+	7.67685i	−1.19722	+	0.371509i
$428$		0			0
$429$	53.5277	−	30.9042i	2.58434	−	1.49207i
$430$		0			0
$431$	20.9544	+	12.0980i	1.00934	+	0.582740i	0.910997	−	0.412412i	$-0.135314\pi$
$431$	20.9544	+	12.0980i	1.00934	+	0.582740i	0.0983389	+	0.995153i	$0.468647\pi$
$432$		0			0
$433$		−	20.2949i		−	0.975311i	−0.873036	−	0.487655i	$-0.837852\pi$
$433$		−	20.2949i		−	0.975311i	0.873036	−	0.487655i	$-0.162148\pi$
$434$		0			0
$435$	9.66074			0.463197
$436$		0			0
$437$	−0.172321	+	0.298469i	−0.00824324	+	0.0142777i
$438$		0			0
$439$	−2.52231	−	4.36878i	−0.120384	−	0.208510i	0.799535	−	0.600619i	$-0.205079\pi$
$439$	−2.52231	−	4.36878i	−0.120384	−	0.208510i	−0.919919	+	0.392109i	$0.871746\pi$
$440$		0			0
$441$	−1.00863	−	12.8756i	−0.0480300	−	0.613124i
$442$		0			0
$443$	4.04696	+	7.00955i	0.192277	+	0.333034i	0.946005	−	0.324153i	$-0.105079\pi$
$443$	4.04696	+	7.00955i	0.192277	+	0.333034i	−0.753727	+	0.657187i	$0.771746\pi$
$444$		0			0
$445$	−5.11692	−	2.95425i	−0.242565	−	0.140045i
$446$		0			0
$447$	34.7085			1.64166
$448$		0			0
$449$	−4.05786			−0.191502			−0.0957511	−	0.995405i	$-0.530525\pi$
$449$	−4.05786			−0.191502			−0.0957511	+	0.995405i	$0.530525\pi$
$450$		0			0
$451$	−17.3237	−	10.0019i	−0.815742	−	0.470969i
$452$		0			0
$453$	6.66111	+	11.5374i	0.312966	+	0.542074i
$454$		0			0
$455$	12.2132	−	3.78988i	0.572566	−	0.177673i
$456$		0			0
$457$	−2.70734	−	4.68925i	−0.126644	−	0.219354i	0.795730	−	0.605651i	$-0.207087\pi$
$457$	−2.70734	−	4.68925i	−0.126644	−	0.219354i	−0.922374	+	0.386297i	$0.873754\pi$
$458$		0			0
$459$	−5.55174	+	9.61589i	−0.259133	+	0.448831i
$460$		0			0
$461$	−18.9095			−0.880702			−0.440351	−	0.897826i	$-0.645146\pi$
$461$	−18.9095			−0.880702			−0.440351	+	0.897826i	$0.645146\pi$
$462$		0			0
$463$		−	0.304782i		−	0.0141644i	−0.999975	−	0.00708220i	$-0.997746\pi$
$463$		−	0.304782i		−	0.0141644i	0.999975	−	0.00708220i	$-0.00225435\pi$
$464$		0			0
$465$	7.77680	+	4.48994i	0.360641	+	0.208216i
$466$		0			0
$467$	3.35368	−	1.93625i	0.155190	−	0.0895989i	−0.420394	−	0.907342i	$-0.638108\pi$
$467$	3.35368	−	1.93625i	0.155190	−	0.0895989i	0.575584	+	0.817743i	$0.304775\pi$
$468$		0			0
$469$	−23.5026	−	21.7335i	−1.08525	−	1.00356i
$470$		0			0
$471$	−38.9156	+	22.4680i	−1.79314	+	1.03527i
$472$		0			0
$473$	6.12334	−	10.6059i	0.281552	−	0.487662i
$474$		0			0
$475$		−	1.89120i		−	0.0867742i
$476$		0			0
$477$			18.1984i			0.833247i
$478$		0			0
$479$	−16.4744	+	28.5344i	−0.752732	+	1.30377i	0.193761	+	0.981049i	$0.437931\pi$
$479$	−16.4744	+	28.5344i	−0.752732	+	1.30377i	−0.946494	+	0.322722i	$0.895402\pi$
$480$		0			0
$481$	17.8413	−	10.3007i	0.813494	−	0.469671i
$482$		0			0
$483$	0.234408	−	1.03506i	0.0106659	−	0.0470970i
$484$		0			0
$485$	−11.4652	+	6.61941i	−0.520606	+	0.300572i
$486$		0			0
$487$	−35.8923	−	20.7224i	−1.62643	−	0.939022i	−0.985145	−	0.171722i	$-0.945067\pi$
$487$	−35.8923	−	20.7224i	−1.62643	−	0.939022i	−0.641289	−	0.767300i	$-0.721600\pi$
$488$		0			0
$489$			8.42012i			0.380771i
$490$		0			0
$491$	25.4339			1.14782			0.573908	−	0.818920i	$-0.305427\pi$
$491$	25.4339			1.14782			0.573908	+	0.818920i	$0.305427\pi$
$492$		0			0
$493$	−9.58441	+	16.6007i	−0.431660	+	0.747658i
$494$		0			0
$495$	5.35949	+	9.28291i	0.240891	+	0.417236i
$496$		0			0
$497$	−22.7248	−	5.14644i	−1.01935	−	0.230849i
$498$		0			0
$499$	−3.25059	−	5.63019i	−0.145516	−	0.252042i	0.784049	−	0.620699i	$-0.213151\pi$
$499$	−3.25059	−	5.63019i	−0.145516	−	0.252042i	−0.929565	+	0.368657i	$0.879818\pi$
$500$		0			0
$501$	41.2759	+	23.8307i	1.84407	+	1.06468i
$502$		0			0
$503$	23.4094			1.04378			0.521888	−	0.853014i	$-0.325228\pi$
$503$	23.4094			1.04378			0.521888	+	0.853014i	$0.325228\pi$
$504$		0			0
$505$	2.46883			0.109862
$506$		0			0
$507$	−19.7505	−	11.4029i	−0.877149	−	0.506422i
$508$		0			0
$509$	8.44031	+	14.6190i	0.374110	+	0.647978i	0.990193	−	0.139703i	$-0.0446148\pi$
$509$	8.44031	+	14.6190i	0.374110	+	0.647978i	−0.616083	+	0.787681i	$0.711281\pi$
$510$		0			0
$511$	−15.2452	+	16.4861i	−0.674406	+	0.729303i
$512$		0			0
$513$	−2.40400	−	4.16385i	−0.106139	−	0.183838i
$514$		0			0
$515$	−0.920346	+	1.59409i	−0.0405553	+	0.0702438i
$516$		0			0
$517$	11.0015			0.483844
$518$		0			0
$519$			22.8989i			1.00515i
$520$		0			0
$521$	21.2245	+	12.2540i	0.929864	+	0.536857i	0.886769	−	0.462214i	$-0.152945\pi$
$521$	21.2245	+	12.2540i	0.929864	+	0.536857i	0.0430955	+	0.999071i	$0.486278\pi$
$522$		0			0
$523$	25.2087	−	14.5543i	1.10230	−	0.636414i	0.165476	−	0.986214i	$-0.447084\pi$
$523$	25.2087	−	14.5543i	1.10230	−	0.636414i	0.936824	+	0.349800i	$0.113751\pi$
$524$		0			0
$525$	1.72595	+	5.56203i	0.0753266	+	0.242747i
$526$		0			0
$527$	−15.4307	+	8.90893i	−0.672173	+	0.388079i
$528$		0			0
$529$	−11.4834	+	19.8898i	−0.499278	+	0.864775i
$530$		0			0
$531$			13.5399i			0.587580i
$532$		0			0
$533$			16.6418i			0.720837i
$534$		0			0
$535$	9.08674	−	15.7387i	0.392854	−	0.680443i
$536$		0			0
$537$	14.5070	−	8.37563i	0.626024	−	0.361435i
$538$		0			0
$539$	−33.5240	+	23.0225i	−1.44398	+	0.991649i
$540$		0			0
$541$	−3.98939	+	2.30327i	−0.171517	+	0.0990254i	−0.583301	−	0.812256i	$-0.698239\pi$
$541$	−3.98939	+	2.30327i	−0.171517	+	0.0990254i	0.411784	+	0.911282i	$0.364906\pi$
$542$		0			0
$543$	−21.3927	−	12.3511i	−0.918050	−	0.530036i
$544$		0			0
$545$		−	3.93204i		−	0.168430i
$546$		0			0
$547$	−4.27444			−0.182762			−0.0913808	−	0.995816i	$-0.529128\pi$
$547$	−4.27444			−0.182762			−0.0913808	+	0.995816i	$0.529128\pi$
$548$		0			0
$549$	−9.03171	+	15.6434i	−0.385464	+	0.667644i
$550$		0			0
$551$	−4.15022	−	7.18839i	−0.176805	−	0.306236i
$552$		0			0
$553$	9.55590	+	30.7948i	0.406358	+	1.30953i
$554$		0			0
$555$	4.69103	+	8.12511i	0.199123	+	0.344892i
$556$		0			0
$557$	−16.1482	−	9.32317i	−0.684221	−	0.395035i	0.117222	−	0.993106i	$-0.462601\pi$
$557$	−16.1482	−	9.32317i	−0.684221	−	0.395035i	−0.801443	+	0.598070i	$0.795934\pi$
$558$		0			0
$559$	−10.1885			−0.430926
$560$		0			0
$561$	−55.8515			−2.35805
$562$		0			0
$563$	19.1853	+	11.0766i	0.808565	+	0.466825i	0.846457	−	0.532457i	$-0.178731\pi$
$563$	19.1853	+	11.0766i	0.808565	+	0.466825i	−0.0378926	+	0.999282i	$0.512064\pi$
$564$		0			0
$565$	3.58320	+	6.20629i	0.150746	+	0.261101i
$566$		0			0
$567$	21.6220	+	19.9945i	0.908039	+	0.839688i
$568$		0			0
$569$	−0.619323	−	1.07270i	−0.0259634	−	0.0449699i	0.852752	−	0.522316i	$-0.174932\pi$
$569$	−0.619323	−	1.07270i	−0.0259634	−	0.0449699i	−0.878715	+	0.477346i	$0.841599\pi$
$570$		0			0
$571$	−10.3953	+	18.0051i	−0.435028	+	0.753490i	−0.997298	−	0.0734633i	$-0.976595\pi$
$571$	−10.3953	+	18.0051i	−0.435028	+	0.753490i	0.562270	+	0.826954i	$0.309928\pi$
$572$		0			0
$573$	−16.9928			−0.709883
$574$		0			0
$575$			0.182235i			0.00759971i
$576$		0			0
$577$	−29.9908	−	17.3152i	−1.24853	−	0.720842i	−0.277717	−	0.960663i	$-0.589578\pi$
$577$	−29.9908	−	17.3152i	−1.24853	−	0.720842i	−0.970817	+	0.239821i	$0.922911\pi$
$578$		0			0
$579$	44.6103	−	25.7558i	1.85394	−	1.07037i
$580$		0			0
$581$	−43.7888	−	9.91675i	−1.81667	−	0.411416i
$582$		0			0
$583$	49.6274	−	28.6524i	2.05536	−	1.18666i
$584$		0			0
$585$	4.45875	−	7.72278i	0.184347	−	0.319298i
$586$		0			0
$587$			22.4911i			0.928306i	0.885755	+	0.464153i	$0.153641\pi$
$587$			22.4911i			0.928306i	−0.885755	+	0.464153i	$0.846359\pi$
$588$		0			0
$589$		−	7.71544i		−	0.317909i
$590$		0			0
$591$	22.4815	−	38.9392i	0.924767	−	1.60174i
$592$		0			0
$593$	−3.70525	+	2.13923i	−0.152156	+	0.0878474i	−0.574145	−	0.818754i	$-0.694665\pi$
$593$	−3.70525	+	2.13923i	−0.152156	+	0.0878474i	0.421989	+	0.906601i	$0.361332\pi$
$594$		0			0
$595$	−11.2699	−	2.55227i	−0.462021	−	0.104633i
$596$		0			0
$597$	−4.19719	+	2.42325i	−0.171780	+	0.0991771i
$598$		0			0
$599$	5.50041	+	3.17566i	0.224741	+	0.129754i	0.608143	−	0.793827i	$-0.291915\pi$
$599$	5.50041	+	3.17566i	0.224741	+	0.129754i	−0.383403	+	0.923581i	$0.625248\pi$
$600$		0			0
$601$			3.72971i			0.152138i	0.997103	+	0.0760691i	$0.0242369\pi$
$601$			3.72971i			0.152138i	−0.997103	+	0.0760691i	$0.975763\pi$
$602$		0			0
$603$	−22.3229			−0.909059
$604$		0			0
$605$	11.3764	−	19.7046i	0.462518	−	0.801105i
$606$		0			0
$607$	−9.66175	−	16.7346i	−0.392158	−	0.679238i	0.600576	−	0.799568i	$-0.294938\pi$
$607$	−9.66175	−	16.7346i	−0.392158	−	0.679238i	−0.992734	+	0.120330i	$0.961605\pi$
$608$		0			0
$609$	18.7661	+	17.3535i	0.760440	+	0.703199i
$610$		0			0
$611$	−4.57626	−	7.92631i	−0.185136	−	0.320664i
$612$		0			0
$613$	26.3430	+	15.2092i	1.06399	+	0.614292i	0.926532	−	0.376216i	$-0.122775\pi$
$613$	26.3430	+	15.2092i	1.06399	+	0.614292i	0.137453	+	0.990508i	$0.456108\pi$
$614$		0			0
$615$	−7.57883			−0.305608
$616$		0			0
$617$	9.32522			0.375419			0.187710	−	0.982225i	$-0.439894\pi$
$617$	9.32522			0.375419			0.187710	+	0.982225i	$0.439894\pi$
$618$		0			0
$619$	9.29185	+	5.36465i	0.373471	+	0.215624i	0.674974	−	0.737842i	$-0.264155\pi$
$619$	9.29185	+	5.36465i	0.373471	+	0.215624i	−0.301503	+	0.953465i	$0.597488\pi$
$620$		0			0
$621$	0.231647	+	0.401225i	0.00929569	+	0.0161006i
$622$		0			0
$623$	−4.63296	−	14.9301i	−0.185616	−	0.598163i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	12.0923	−	20.9445i	0.482921	−	0.836444i
$628$		0			0
$629$	−18.6159			−0.742264
$630$		0			0
$631$			7.84644i			0.312362i	0.987728	+	0.156181i	$0.0499183\pi$
$631$			7.84644i			0.312362i	−0.987728	+	0.156181i	$0.950082\pi$
$632$		0			0
$633$	−55.1595	−	31.8464i	−2.19239	−	1.26578i
$634$		0			0
$635$	−2.49594	+	1.44103i	−0.0990484	+	0.0571856i
$636$		0			0
$637$	30.5321	+	14.5767i	1.20972	+	0.577548i
$638$		0			0
$639$	−14.0715	+	8.12420i	−0.556661	+	0.321388i
$640$		0			0
$641$	6.79977	−	11.7775i	0.268575	−	0.465185i	−0.699919	−	0.714222i	$-0.746781\pi$
$641$	6.79977	−	11.7775i	0.268575	−	0.465185i	0.968494	+	0.249037i	$0.0801141\pi$
$642$		0			0
$643$			5.68857i			0.224335i	0.993689	+	0.112168i	$0.0357794\pi$
$643$			5.68857i			0.224335i	−0.993689	+	0.112168i	$0.964221\pi$
$644$		0			0
$645$		−	4.63992i		−	0.182697i
$646$		0			0
$647$	−0.225415	+	0.390431i	−0.00886200	+	0.0153494i	−0.870422	−	0.492306i	$-0.836154\pi$
$647$	−0.225415	+	0.390431i	−0.00886200	+	0.0153494i	0.861560	+	0.507655i	$0.169488\pi$
$648$		0			0
$649$	36.9234	−	21.3178i	1.44937	−	0.836795i
$650$		0			0
$651$	7.04127	+	22.6911i	0.275969	+	0.889336i
$652$		0			0
$653$	3.69894	−	2.13559i	0.144751	−	0.0835720i	−0.425875	−	0.904782i	$-0.640034\pi$
$653$	3.69894	−	2.13559i	0.144751	−	0.0835720i	0.570626	+	0.821210i	$0.306700\pi$
$654$		0			0
$655$	−6.92953	−	4.00076i	−0.270759	−	0.156323i
$656$		0			0
$657$			15.6586i			0.610901i
$658$		0			0
$659$	−15.5436			−0.605493			−0.302746	−	0.953071i	$-0.597903\pi$
$659$	−15.5436			−0.605493			−0.302746	+	0.953071i	$0.597903\pi$
$660$		0			0
$661$	14.4897	−	25.0969i	0.563583	−	0.976155i	−0.433597	−	0.901107i	$-0.642756\pi$
$661$	14.4897	−	25.0969i	0.563583	−	0.976155i	0.997180	−	0.0750479i	$-0.0239110\pi$
$662$		0			0
$663$	23.2324	+	40.2398i	0.902273	+	1.56278i
$664$		0			0
$665$	3.39715	−	3.67367i	0.131736	−	0.142459i
$666$		0			0
$667$	0.399912	+	0.692668i	0.0154846	+	0.0268202i
$668$		0			0
$669$	21.0707	+	12.1652i	0.814641	+	0.470333i
$670$		0			0
$671$	56.8797			2.19582
$672$		0			0
$673$	32.3539			1.24715			0.623576	−	0.781763i	$-0.285679\pi$
$673$	32.3539			1.24715			0.623576	+	0.781763i	$0.285679\pi$
$674$		0			0
$675$	−2.20170	−	1.27115i	−0.0847433	−	0.0489266i
$676$		0			0
$677$	22.4527	+	38.8892i	0.862927	+	1.49463i	0.869091	+	0.494652i	$0.164705\pi$
$677$	22.4527	+	38.8892i	0.862927	+	1.49463i	−0.00616405	+	0.999981i	$0.501962\pi$
$678$		0			0
$679$	−34.1616	−	7.73649i	−1.31100	−	0.296899i
$680$		0			0
$681$	9.04722	+	15.6703i	0.346690	+	0.600485i
$682$		0			0
$683$	−5.62256	+	9.73856i	−0.215141	+	0.372636i	−0.953316	−	0.301974i	$-0.902355\pi$
$683$	−5.62256	+	9.73856i	−0.215141	+	0.372636i	0.738175	+	0.674609i	$0.235688\pi$
$684$		0			0
$685$	10.1985			0.389665
$686$		0			0
$687$			22.1754i			0.846043i
$688$		0			0
$689$	−41.2868	−	23.8369i	−1.57290	−	0.908115i
$690$		0			0
$691$	8.53812	−	4.92949i	0.324805	−	0.187527i	−0.328727	−	0.944425i	$-0.606620\pi$
$691$	8.53812	−	4.92949i	0.324805	−	0.187527i	0.653533	+	0.756898i	$0.273286\pi$
$692$		0			0
$693$	−6.26394	+	27.6593i	−0.237948	+	1.05069i
$694$		0			0
$695$	−8.60629	+	4.96884i	−0.326455	+	0.188479i
$696$		0			0
$697$	7.51896	−	13.0232i	0.284801	−	0.493289i
$698$		0			0
$699$		−	16.2249i		−	0.613681i
$700$		0			0
$701$			6.00307i			0.226733i	0.993553	+	0.113366i	$0.0361634\pi$
$701$			6.00307i			0.226733i	−0.993553	+	0.113366i	$0.963837\pi$
$702$		0			0
$703$	4.03050	−	6.98103i	0.152013	−	0.263294i
$704$		0			0
$705$	3.60972	−	2.08407i	0.135950	−	0.0784907i
$706$		0			0
$707$	4.79573	+	4.43474i	0.180362	+	0.166785i
$708$		0			0
$709$	10.2323	−	5.90764i	0.384283	−	0.221866i	−0.295397	−	0.955375i	$-0.595452\pi$
$709$	10.2323	−	5.90764i	0.384283	−	0.221866i	0.679680	+	0.733508i	$0.262119\pi$
$710$		0			0
$711$	19.4724	+	11.2424i	0.730272	+	0.421623i
$712$		0			0
$713$			0.743454i			0.0278426i
$714$		0			0
$715$	−28.0802			−1.05014
$716$		0			0
$717$	−23.0607	+	39.9423i	−0.861217	+	1.49167i
$718$		0			0
$719$	3.06796	+	5.31386i	0.114415	+	0.198173i	0.917546	−	0.397630i	$-0.130167\pi$
$719$	3.06796	+	5.31386i	0.114415	+	0.198173i	−0.803130	+	0.595803i	$0.796834\pi$
$720$		0			0
$721$	−4.65122	+	1.44332i	−0.173221	+	0.0537520i
$722$		0			0
$723$	3.07708	+	5.32966i	0.114438	+	0.198212i
$724$		0			0
$725$	−3.80097	−	2.19449i	−0.141164	−	0.0815013i
$726$		0			0
$727$	−14.8986			−0.552558			−0.276279	−	0.961077i	$-0.589101\pi$
$727$	−14.8986			−0.552558			−0.276279	+	0.961077i	$0.589101\pi$
$728$		0			0
$729$	3.74887			0.138847
$730$		0			0
$731$	7.97308	+	4.60326i	0.294895	+	0.170258i
$732$		0			0
$733$	−23.7602	−	41.1539i	−0.877604	−	1.52006i	−0.853962	−	0.520335i	$-0.825807\pi$
$733$	−23.7602	−	41.1539i	−0.877604	−	1.52006i	−0.0236421	−	0.999720i	$-0.507526\pi$
$734$		0			0
$735$	−6.63835	+	13.9046i	−0.244859	+	0.512879i
$736$		0			0
$737$	35.1462	+	60.8750i	1.29463	+	2.24236i
$738$		0			0
$739$	−1.95274	+	3.38225i	−0.0718328	+	0.124418i	−0.899705	−	0.436499i	$-0.856218\pi$
$739$	−1.95274	+	3.38225i	−0.0718328	+	0.124418i	0.827872	+	0.560917i	$0.189551\pi$
$740$		0			0
$741$	−20.1201			−0.739130
$742$		0			0
$743$			48.0392i			1.76239i	0.472755	+	0.881194i	$0.343259\pi$
$743$			48.0392i			1.76239i	−0.472755	+	0.881194i	$0.656741\pi$
$744$		0			0
$745$	−13.6559	−	7.88422i	−0.500312	−	0.288855i
$746$		0			0
$747$	−27.1146	+	15.6546i	−0.992073	+	0.572773i
$748$		0			0
$749$	45.9223	−	14.2501i	1.67797	−	0.520688i
$750$		0			0
$751$	−0.139857	+	0.0807464i	−0.00510345	+	0.00294648i	−0.502550	−	0.864548i	$-0.667605\pi$
$751$	−0.139857	+	0.0807464i	−0.00510345	+	0.00294648i	0.497446	+	0.867495i	$0.334271\pi$
$752$		0			0
$753$	−20.6529	+	35.7718i	−0.752633	+	1.30360i
$754$		0			0
$755$		−	6.05243i		−	0.220270i
$756$		0			0
$757$		−	17.0175i		−	0.618513i	−0.950979	−	0.309257i	$-0.899920\pi$
$757$		−	17.0175i		−	0.618513i	0.950979	−	0.309257i	$-0.100080\pi$
$758$		0			0
$759$	−1.16521	+	2.01820i	−0.0422944	+	0.0732560i
$760$		0			0
$761$	23.5345	−	13.5876i	0.853125	−	0.492552i	−0.00857924	−	0.999963i	$-0.502731\pi$
$761$	23.5345	−	13.5876i	0.853125	−	0.492552i	0.861704	+	0.507411i	$0.169398\pi$
$762$		0			0
$763$	7.06309	−	7.63803i	0.255701	−	0.276515i
$764$		0			0
$765$	−6.97848	+	4.02903i	−0.252308	+	0.145670i
$766$		0			0
$767$	−30.7179	−	17.7350i	−1.10916	−	0.640374i
$768$		0			0
$769$			16.2516i			0.586049i	0.956105	+	0.293025i	$0.0946618\pi$
$769$			16.2516i			0.586049i	−0.956105	+	0.293025i	$0.905338\pi$
$770$		0			0
$771$	17.1959			0.619296
$772$		0			0
$773$	2.07903	−	3.60098i	0.0747774	−	0.129518i	−0.826212	−	0.563359i	$-0.809509\pi$
$773$	2.07903	−	3.60098i	0.0747774	−	0.129518i	0.900989	+	0.433841i	$0.142842\pi$
$774$		0			0
$775$	−2.03983	−	3.53308i	−0.0732727	−	0.126912i
$776$		0			0
$777$	−5.48268	+	24.2095i	−0.196690	+	0.868513i
$778$		0			0
$779$	3.25584	+	5.63928i	0.116652	+	0.202048i
$780$		0			0
$781$	44.3097	+	25.5822i	1.58552	+	0.915403i
$782$		0			0
$783$	−11.1581			−0.398758
$784$		0			0
$785$	20.4149			0.728637
$786$		0			0
$787$	−0.346588	−	0.200103i	−0.0123545	−	0.00713289i	0.493810	−	0.869570i	$-0.335604\pi$
$787$	−0.346588	−	0.200103i	−0.0123545	−	0.00713289i	−0.506165	+	0.862437i	$0.668937\pi$
$788$		0			0
$789$	−6.40478	−	11.0934i	−0.228016	−	0.394936i
$790$		0			0
$791$	−4.18790	+	18.4922i	−0.148904	+	0.657509i
$792$		0			0
$793$	−23.6601	−	40.9806i	−0.840196	−	1.45526i
$794$		0			0
$795$	10.8556	−	18.8024i	0.385007	−	0.666852i
$796$		0			0
$797$	−4.32443			−0.153179			−0.0765895	−	0.997063i	$-0.524403\pi$
$797$	−4.32443			−0.153179			−0.0765895	+	0.997063i	$0.524403\pi$
$798$		0			0
$799$			8.27042i			0.292586i
$800$		0			0
$801$	−9.44075	−	5.45062i	−0.333572	−	0.192588i
$802$		0			0
$803$	42.7014	−	24.6536i	1.50690	−	0.870008i
$804$		0			0
$805$	−0.327346	+	0.353992i	−0.0115374	+	0.0124766i
$806$		0			0
$807$	46.1120	−	26.6228i	1.62322	−	0.937165i
$808$		0			0
$809$	−18.2699	+	31.6444i	−0.642335	+	1.11256i	0.342576	+	0.939490i	$0.388701\pi$
$809$	−18.2699	+	31.6444i	−0.642335	+	1.11256i	−0.984910	+	0.173066i	$0.944633\pi$
$810$		0			0
$811$		−	17.6473i		−	0.619680i	−0.950789	−	0.309840i	$-0.899725\pi$
$811$		−	17.6473i		−	0.619680i	0.950789	−	0.309840i	$-0.100275\pi$
$812$		0			0
$813$		−	34.5025i		−	1.21005i
$814$		0			0
$815$	1.91267	−	3.31285i	0.0669981	−	0.116044i
$816$		0			0
$817$	−3.45248	+	1.99329i	−0.120787	+	0.0697364i
$818$		0			0
$819$	22.5335	−	6.99236i	0.787385	−	0.244333i
$820$		0			0
$821$	−37.1429	+	21.4445i	−1.29630	+	0.748418i	−0.979763	−	0.200163i	$-0.935853\pi$
$821$	−37.1429	+	21.4445i	−1.29630	+	0.748418i	−0.316535	+	0.948581i	$0.602520\pi$
$822$		0			0
$823$	31.2832	+	18.0614i	1.09046	+	0.629580i	0.933700	−	0.358056i	$-0.116560\pi$
$823$	31.2832	+	18.0614i	1.09046	+	0.629580i	0.156764	+	0.987636i	$0.449894\pi$
$824$		0			0
$825$		−	12.7880i		−	0.445221i
$826$		0			0
$827$	7.53954			0.262176			0.131088	−	0.991371i	$-0.458153\pi$
$827$	7.53954			0.262176			0.131088	+	0.991371i	$0.458153\pi$
$828$		0			0
$829$	−28.0133	+	48.5204i	−0.972941	+	1.68518i	−0.286370	+	0.958119i	$0.592449\pi$
$829$	−28.0133	+	48.5204i	−0.972941	+	1.68518i	−0.686570	+	0.727063i	$0.740885\pi$
$830$		0			0
$831$	16.1375	+	27.9509i	0.559802	+	0.969606i
$832$		0			0
$833$	−17.3073	−	25.2018i	−0.599662	−	0.873192i
$834$		0			0
$835$	−10.8265	−	18.7521i	−0.374667	−	0.648943i
$836$		0			0
$837$	−8.98215	−	5.18585i	−0.310469	−	0.179249i
$838$		0			0
$839$	−33.7497			−1.16517			−0.582584	−	0.812770i	$-0.697958\pi$
$839$	−33.7497			−1.16517			−0.582584	+	0.812770i	$0.697958\pi$
$840$		0			0
$841$	9.73688			0.335755
$842$		0			0
$843$	−28.6733	−	16.5546i	−0.987562	−	0.570169i
$844$		0			0
$845$	5.18047	+	8.97285i	0.178214	+	0.308675i
$846$		0			0
$847$	57.4940	−	17.8409i	1.97552	−	0.613021i
$848$		0			0
$849$	5.45705	+	9.45188i	0.187285	+	0.324388i
$850$		0			0
$851$	−0.388376	+	0.672687i	−0.0133133	+	0.0230594i
$852$		0			0
$853$	53.4433			1.82987			0.914933	−	0.403607i	$-0.132244\pi$
$853$	53.4433			1.82987			0.914933	+	0.403607i	$0.132244\pi$
$854$		0			0
$855$		−	3.48928i		−	0.119331i
$856$		0			0
$857$	30.9412	+	17.8639i	1.05693	+	0.610220i	0.924582	−	0.380983i	$-0.124414\pi$
$857$	30.9412	+	17.8639i	1.05693	+	0.610220i	0.132350	+	0.991203i	$0.457748\pi$
$858$		0			0
$859$	−4.24262	+	2.44948i	−0.144756	+	0.0835751i	−0.570629	−	0.821208i	$-0.693300\pi$
$859$	−4.24262	+	2.44948i	−0.144756	+	0.0835751i	0.425873	+	0.904783i	$0.359967\pi$
$860$		0			0
$861$	−14.7220	−	13.6138i	−0.501723	−	0.463957i
$862$		0			0
$863$	−27.0242	+	15.6024i	−0.919914	+	0.531113i	−0.883608	−	0.468228i	$-0.844893\pi$
$863$	−27.0242	+	15.6024i	−0.919914	+	0.531113i	−0.0363065	+	0.999341i	$0.511559\pi$
$864$		0			0
$865$	5.20160	−	9.00944i	0.176860	−	0.306330i
$866$		0			0
$867$		−	4.56736i		−	0.155116i
$868$		0			0
$869$		−	70.8021i		−	2.40180i
$870$		0			0
$871$	29.2394	−	50.6441i	0.990738	−	1.71601i
$872$		0			0
$873$	−21.1533	+	12.2129i	−0.715931	+	0.413343i
$874$		0			0
$875$	0.584379	−	2.58041i	0.0197556	−	0.0872337i
$876$		0			0
$877$	−4.65217	+	2.68593i	−0.157092	+	0.0906974i	−0.576485	−	0.817107i	$-0.695576\pi$
$877$	−4.65217	+	2.68593i	−0.157092	+	0.0906974i	0.419393	+	0.907805i	$0.362243\pi$
$878$		0			0
$879$	4.89545	+	2.82639i	0.165120	+	0.0953318i
$880$		0			0
$881$		−	12.9255i		−	0.435471i	−0.976008	−	0.217736i	$-0.930133\pi$
$881$		−	12.9255i		−	0.435471i	0.976008	−	0.217736i	$-0.0698670\pi$
$882$		0			0
$883$	−42.5290			−1.43122			−0.715608	−	0.698502i	$-0.753850\pi$
$883$	−42.5290			−1.43122			−0.715608	+	0.698502i	$0.753850\pi$
$884$		0			0
$885$	8.07669	−	13.9892i	0.271495	−	0.470243i
$886$		0			0
$887$	−19.2391	−	33.3231i	−0.645987	−	1.11888i	−0.984073	−	0.177766i	$-0.943113\pi$
$887$	−19.2391	−	33.3231i	−0.645987	−	1.11888i	0.338086	−	0.941115i	$-0.390220\pi$
$888$		0			0
$889$	−7.43690	−	1.68422i	−0.249426	−	0.0564868i
$890$		0			0
$891$	−32.3339	−	56.0040i	−1.08323	−	1.87620i
$892$		0			0
$893$	−3.10144	−	1.79062i	−0.103786	−	0.0599207i
$894$		0			0
$895$	−7.61028			−0.254383
$896$		0			0
$897$	1.93876			0.0647332
$898$		0			0
$899$	−15.5066	−	8.95275i	−0.517175	−	0.298591i
$900$		0			0
$901$	21.5396	+	37.3077i	0.717588	+	1.24290i
$902$		0			0
$903$	8.33464	−	9.01308i	0.277359	−	0.299937i
$904$		0			0
$905$	5.61124	+	9.71894i	0.186524	+	0.323069i
$906$		0			0
$907$	−29.8056	+	51.6248i	−0.989679	+	1.71417i	−0.370738	+	0.928737i	$0.620895\pi$
$907$	−29.8056	+	51.6248i	−0.989679	+	1.71417i	−0.618941	+	0.785438i	$0.712438\pi$
$908$		0			0
$909$	4.55501			0.151080
$910$		0			0
$911$		−	40.9457i		−	1.35659i	−0.734790	−	0.678295i	$-0.762719\pi$
$911$		−	40.9457i		−	1.35659i	0.734790	−	0.678295i	$-0.237281\pi$
$912$		0			0
$913$	85.3810	+	49.2947i	2.82570	+	1.63142i
$914$		0			0
$915$	18.6629	−	10.7751i	0.616978	−	0.356212i
$916$		0			0
$917$	−6.27413	−	20.2190i	−0.207190	−	0.667689i
$918$		0			0
$919$	22.8509	−	13.1930i	0.753781	−	0.435196i	−0.0732776	−	0.997312i	$-0.523346\pi$
$919$	22.8509	−	13.1930i	0.753781	−	0.435196i	0.827058	+	0.562116i	$0.190013\pi$
$920$		0			0
$921$	−15.8950	+	27.5310i	−0.523759	+	0.907177i
$922$		0			0
$923$		−	42.5655i		−	1.40106i
$924$		0			0
$925$		−	4.26237i		−	0.140146i
$926$		0			0
$927$	−1.69805	+	2.94110i	−0.0557711	+	0.0965984i
$928$		0			0
$929$	−38.7083	+	22.3482i	−1.26998	+	0.733222i	−0.974984	−	0.222277i	$-0.928651\pi$
$929$	−38.7083	+	22.3482i	−1.26998	+	0.733222i	−0.294994	+	0.955499i	$0.595318\pi$
$930$		0			0
$931$	13.1980	−	1.03388i	0.432546	−	0.0338842i
$932$		0			0
$933$	31.5182	−	18.1971i	1.03186	−	0.595745i
$934$		0			0
$935$	21.9745	+	12.6870i	0.718642	+	0.414908i
$936$		0			0
$937$			14.4033i			0.470535i	0.971931	+	0.235268i	$0.0755967\pi$
$937$			14.4033i			0.470535i	−0.971931	+	0.235268i	$0.924403\pi$
$938$		0			0
$939$	−5.58701			−0.182325
$940$		0			0
$941$	5.58349	−	9.67088i	0.182016	−	0.315262i	−0.760551	−	0.649279i	$-0.775071\pi$
$941$	5.58349	−	9.67088i	0.182016	−	0.315262i	0.942567	+	0.334017i	$0.108404\pi$
$942$		0			0
$943$	−0.313730	−	0.543396i	−0.0102165	−	0.0176954i
$944$		0			0
$945$	−1.99346	−	6.42410i	−0.0648472	−	0.208976i
$946$		0			0
$947$	10.3303	+	17.8927i	0.335691	+	0.581434i	0.983617	−	0.180269i	$-0.0576968\pi$
$947$	10.3303	+	17.8927i	0.335691	+	0.581434i	−0.647926	+	0.761703i	$0.724364\pi$
$948$		0			0
$949$	−35.5248	−	20.5102i	−1.15318	−	0.665791i
$950$		0			0
$951$	−37.7262			−1.22336
$952$		0			0
$953$	29.6708			0.961132			0.480566	−	0.876959i	$-0.340431\pi$
$953$	29.6708			0.961132			0.480566	+	0.876959i	$0.340431\pi$
$954$		0			0
$955$	6.68571	+	3.86000i	0.216344	+	0.124907i
$956$		0			0
$957$	−28.0631	−	48.6067i	−0.907152	−	1.57123i
$958$		0			0
$959$	19.8107	+	18.3195i	0.639720	+	0.591566i
$960$		0			0
$961$	7.17822	+	12.4330i	0.231555	+	0.401066i
$962$		0			0
$963$	16.7651	−	29.0380i	0.540248	−	0.935736i
$964$		0			0
$965$	−23.4022			−0.753345
$966$		0			0
$967$			50.5419i			1.62532i	0.582740	+	0.812658i	$0.301980\pi$
$967$			50.5419i			1.62532i	−0.582740	+	0.812658i	$0.698020\pi$
$968$		0			0
$969$	15.7452	+	9.09048i	0.505808	+	0.292028i
$970$		0			0
$971$	−30.5599	+	17.6438i	−0.980715	+	0.566216i	−0.902486	−	0.430719i	$-0.858260\pi$
$971$	−30.5599	+	17.6438i	−0.980715	+	0.566216i	−0.0782293	+	0.996935i	$0.524927\pi$
$972$		0			0
$973$	−25.6433	−	5.80737i	−0.822086	−	0.186176i
$974$		0			0
$975$	−9.21347	+	5.31940i	−0.295067	+	0.170357i
$976$		0			0
$977$	−13.3142	+	23.0609i	−0.425960	+	0.737784i	−0.996510	−	0.0834788i	$-0.973397\pi$
$977$	−13.3142	+	23.0609i	−0.425960	+	0.737784i	0.570550	+	0.821263i	$0.306730\pi$
$978$		0			0
$979$			34.3268i			1.09709i
$980$		0			0
$981$		−	7.25465i		−	0.231623i
$982$		0			0
$983$	9.60664	−	16.6392i	0.306404	−	0.530708i	−0.671169	−	0.741305i	$-0.734207\pi$
$983$	9.60664	−	16.6392i	0.306404	−	0.530708i	0.977573	+	0.210597i	$0.0675408\pi$
$984$		0			0
$985$	−17.6905	+	10.2136i	−0.563666	+	0.325432i
$986$		0			0
$987$	10.7555	+	2.43577i	0.342351	+	0.0775315i
$988$		0			0
$989$	0.332678	−	0.192072i	0.0105786	−	0.00610753i
$990$		0			0
$991$	−52.2605	−	30.1726i	−1.66011	−	0.958465i	−0.972660	−	0.232233i	$-0.925397\pi$
$991$	−52.2605	−	30.1726i	−1.66011	−	0.958465i	−0.687450	−	0.726232i	$-0.741270\pi$
$992$		0			0
$993$		−	52.3991i		−	1.66283i
$994$		0			0
$995$	2.20182			0.0698023
$996$		0			0
$997$	8.59147	−	14.8809i	0.272095	−	0.471282i	−0.697303	−	0.716776i	$-0.745617\pi$
$997$	8.59147	−	14.8809i	0.272095	−	0.471282i	0.969398	+	0.245495i	$0.0789503\pi$
$998$		0			0
$999$	−5.41811	−	9.38444i	−0.171421	−	0.296911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.f.591.4		24
4.3	odd	2		280.2.bj.e.171.11	yes	24
7.5	odd	6		1120.2.bz.e.271.4		24
8.3	odd	2		1120.2.bz.e.591.4		24
8.5	even	2		280.2.bj.f.171.2	yes	24
28.19	even	6		280.2.bj.f.131.2	yes	24
56.5	odd	6		280.2.bj.e.131.11	✓	24
56.19	even	6	inner	1120.2.bz.f.271.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.11	✓	24	56.5	odd	6
280.2.bj.e.171.11	yes	24	4.3	odd	2
280.2.bj.f.131.2	yes	24	28.19	even	6
280.2.bj.f.171.2	yes	24	8.5	even	2
1120.2.bz.e.271.4		24	7.5	odd	6
1120.2.bz.e.591.4		24	8.3	odd	2
1120.2.bz.f.271.4		24	56.19	even	6	inner
1120.2.bz.f.591.4		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.90624 - 1.10057i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.584379 + 2.58041i) q^{7} +(0.922503 + 1.59782i) q^{9} +O(q^{10})\)	\(q+(-1.90624 - 1.10057i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.584379 + 2.58041i) q^{7} +(0.922503 + 1.59782i) q^{9} +(2.90486 - 5.03137i) q^{11} -4.83332 q^{13} -2.20114i q^{15} +(3.78236 + 2.18375i) q^{17} +(-1.63783 + 0.945600i) q^{19} +(3.95388 - 4.27573i) q^{21} +(0.157820 - 0.0911173i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.54230i q^{27} +4.38898i q^{29} +(-2.03983 + 3.53308i) q^{31} +(-11.0747 + 6.39400i) q^{33} +(-2.52689 + 0.784117i) q^{35} +(-3.69132 + 2.13119i) q^{37} +(9.21347 + 5.31940i) q^{39} -3.44314i q^{41} +2.10796 q^{43} +(-0.922503 + 1.59782i) q^{45} +(0.946816 + 1.63993i) q^{47} +(-6.31700 - 3.01587i) q^{49} +(-4.80673 - 8.32550i) q^{51} +(8.54212 + 4.93180i) q^{53} +5.80972 q^{55} +4.16279 q^{57} +(6.35546 + 3.66932i) q^{59} +(4.89522 + 8.47877i) q^{61} +(-4.66212 + 1.44670i) q^{63} +(-2.41666 - 4.18577i) q^{65} +(-6.04954 + 10.4781i) q^{67} -0.401124 q^{69} +8.80669i q^{71} +(7.34998 + 4.24351i) q^{73} +(1.90624 - 1.10057i) q^{75} +(11.2854 + 10.4360i) q^{77} +(10.5541 - 6.09342i) q^{79} +(5.56549 - 9.63970i) q^{81} +16.9697i q^{83} +4.36749i q^{85} +(4.83037 - 8.36645i) q^{87} +(-5.11692 + 2.95425i) q^{89} +(2.82449 - 12.4719i) q^{91} +(7.77680 - 4.48994i) q^{93} +(-1.63783 - 0.945600i) q^{95} +13.2388i q^{97} +10.7190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more