LMFDB - Embedded newform 1120.2.bz.f.591.1

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			591.1
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.f.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75363 - 1.58981i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.04250 + 2.43170i) q^{7} +(3.55500 + 6.15745i) q^{9} +O(q^{10})$	\(q+(-2.75363 - 1.58981i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.04250 + 2.43170i) q^{7} +(3.55500 + 6.15745i) q^{9} +(-1.21003 + 2.09584i) q^{11} +1.53832 q^{13} -3.17962i q^{15} +(-6.58087 - 3.79947i) q^{17} +(1.52991 - 0.883293i) q^{19} +(6.73663 - 5.03864i) q^{21} +(5.66247 - 3.26923i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.0683i q^{27} -2.34486i q^{29} +(-1.04132 + 1.80363i) q^{31} +(6.66397 - 3.84745i) q^{33} +(-2.62717 + 0.313017i) q^{35} +(-2.47037 + 1.42627i) q^{37} +(-4.23598 - 2.44564i) q^{39} +6.90356i q^{41} +1.39343 q^{43} +(-3.55500 + 6.15745i) q^{45} +(-5.65799 - 9.79993i) q^{47} +(-4.82637 - 5.07012i) q^{49} +(12.0809 + 20.9247i) q^{51} +(-6.82251 - 3.93898i) q^{53} -2.42006 q^{55} -5.61708 q^{57} +(-4.90087 - 2.82952i) q^{59} +(-4.93580 - 8.54905i) q^{61} +(-18.6792 + 2.22555i) q^{63} +(0.769162 + 1.33223i) q^{65} +(-3.13260 + 5.42583i) q^{67} -20.7898 q^{69} +3.98199i q^{71} +(-2.73292 - 1.57785i) q^{73} +(2.75363 - 1.58981i) q^{75} +(-3.83499 - 5.12736i) q^{77} +(-1.75753 + 1.01471i) q^{79} +(-10.1111 + 17.5129i) q^{81} +0.288923i q^{83} -7.59894i q^{85} +(-3.72789 + 6.45690i) q^{87} +(12.0399 - 6.95124i) q^{89} +(-1.60371 + 3.74075i) q^{91} +(5.73485 - 3.31102i) q^{93} +(1.52991 + 0.883293i) q^{95} +0.249149i q^{97} -17.2067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.75363	−	1.58981i	−1.58981	−	0.917878i	−0.993337	−	0.115247i	$-0.963234\pi$
$3$	−2.75363	−	1.58981i	−1.58981	−	0.917878i	−0.596475	−	0.802632i	$-0.703432\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.04250	+	2.43170i	−0.394030	+	0.919098i
$7$	−1.04250	+	2.43170i	−0.394030	+	0.919098i
$8$		0			0
$9$	3.55500	+	6.15745i	1.18500	+	2.05248i
$10$		0			0
$11$	−1.21003	+	2.09584i	−0.364838	+	0.631919i	−0.988750	−	0.149576i	$-0.952209\pi$
$11$	−1.21003	+	2.09584i	−0.364838	+	0.631919i	0.623912	+	0.781495i	$0.285542\pi$
$12$		0			0
$13$	1.53832			0.426654			0.213327	−	0.976981i	$-0.431570\pi$
$13$	1.53832			0.426654			0.213327	+	0.976981i	$0.431570\pi$
$14$		0			0
$15$		−	3.17962i		−	0.820975i
$16$		0			0
$17$	−6.58087	−	3.79947i	−1.59610	−	0.921506i	−0.992230	−	0.124421i	$-0.960293\pi$
$17$	−6.58087	−	3.79947i	−1.59610	−	0.921506i	−0.603866	−	0.797086i	$-0.706374\pi$
$18$		0			0
$19$	1.52991	−	0.883293i	0.350985	−	0.202641i	−0.314134	−	0.949379i	$-0.601714\pi$
$19$	1.52991	−	0.883293i	0.350985	−	0.202641i	0.665119	+	0.746737i	$0.268381\pi$
$20$		0			0
$21$	6.73663	−	5.03864i	1.47005	−	1.09952i
$22$		0			0
$23$	5.66247	−	3.26923i	1.18071	−	0.681681i	0.224528	−	0.974468i	$-0.427916\pi$
$23$	5.66247	−	3.26923i	1.18071	−	0.681681i	0.956178	+	0.292787i	$0.0945826\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	13.0683i		−	2.51499i
$28$		0			0
$29$		−	2.34486i		−	0.435430i	−0.976012	−	0.217715i	$-0.930140\pi$
$29$		−	2.34486i		−	0.435430i	0.976012	−	0.217715i	$-0.0698604\pi$
$30$		0			0
$31$	−1.04132	+	1.80363i	−0.187027	+	0.323941i	−0.944258	−	0.329207i	$-0.893219\pi$
$31$	−1.04132	+	1.80363i	−0.187027	+	0.323941i	0.757230	+	0.653148i	$0.226552\pi$
$32$		0			0
$33$	6.66397	−	3.84745i	1.16005	−	0.669754i
$34$		0			0
$35$	−2.62717	+	0.313017i	−0.444073	+	0.0529095i
$36$		0			0
$37$	−2.47037	+	1.42627i	−0.406126	+	0.234477i	−0.689124	−	0.724644i	$-0.742004\pi$
$37$	−2.47037	+	1.42627i	−0.406126	+	0.234477i	0.282998	+	0.959121i	$0.408671\pi$
$38$		0			0
$39$	−4.23598	−	2.44564i	−0.678300	−	0.391617i
$40$		0			0
$41$			6.90356i			1.07815i	0.842256	+	0.539077i	$0.181227\pi$
$41$			6.90356i			1.07815i	−0.842256	+	0.539077i	$0.818773\pi$
$42$		0			0
$43$	1.39343			0.212496			0.106248	−	0.994340i	$-0.466116\pi$
$43$	1.39343			0.212496			0.106248	+	0.994340i	$0.466116\pi$
$44$		0			0
$45$	−3.55500	+	6.15745i	−0.529949	+	0.917898i
$46$		0			0
$47$	−5.65799	−	9.79993i	−0.825303	−	1.42947i	−0.901688	−	0.432388i	$-0.857671\pi$
$47$	−5.65799	−	9.79993i	−0.825303	−	1.42947i	0.0763851	−	0.997078i	$-0.475662\pi$
$48$		0			0
$49$	−4.82637	−	5.07012i	−0.689481	−	0.724304i
$50$		0			0
$51$	12.0809	+	20.9247i	1.69166	+	2.93004i
$52$		0			0
$53$	−6.82251	−	3.93898i	−0.937144	−	0.541060i	−0.0480800	−	0.998843i	$-0.515310\pi$
$53$	−6.82251	−	3.93898i	−0.937144	−	0.541060i	−0.889064	+	0.457783i	$0.848644\pi$
$54$		0			0
$55$	−2.42006			−0.326321
$56$		0			0
$57$	−5.61708			−0.744000
$58$		0			0
$59$	−4.90087	−	2.82952i	−0.638038	−	0.368372i	0.145820	−	0.989311i	$-0.453418\pi$
$59$	−4.90087	−	2.82952i	−0.638038	−	0.368372i	−0.783859	+	0.620939i	$0.786751\pi$
$60$		0			0
$61$	−4.93580	−	8.54905i	−0.631964	−	1.09459i	−0.987150	−	0.159798i	$-0.948916\pi$
$61$	−4.93580	−	8.54905i	−0.631964	−	1.09459i	0.355186	−	0.934796i	$-0.384418\pi$
$62$		0			0
$63$	−18.6792	+	2.22555i	−2.35336	+	0.280393i
$64$		0			0
$65$	0.769162	+	1.33223i	0.0954027	+	0.165242i
$66$		0			0
$67$	−3.13260	+	5.42583i	−0.382708	+	0.662870i	−0.991448	−	0.130499i	$-0.958342\pi$
$67$	−3.13260	+	5.42583i	−0.382708	+	0.662870i	0.608740	+	0.793370i	$0.291675\pi$
$68$		0			0
$69$	−20.7898			−2.50280
$70$		0			0
$71$			3.98199i			0.472575i	0.971683	+	0.236287i	$0.0759307\pi$
$71$			3.98199i			0.472575i	−0.971683	+	0.236287i	$0.924069\pi$
$72$		0			0
$73$	−2.73292	−	1.57785i	−0.319865	−	0.184674i	0.331468	−	0.943467i	$-0.392456\pi$
$73$	−2.73292	−	1.57785i	−0.319865	−	0.184674i	−0.651332	+	0.758793i	$0.725790\pi$
$74$		0			0
$75$	2.75363	−	1.58981i	0.317962	−	0.183576i
$76$		0			0
$77$	−3.83499	−	5.12736i	−0.437038	−	0.584317i
$78$		0			0
$79$	−1.75753	+	1.01471i	−0.197738	+	0.114164i	−0.595600	−	0.803281i	$-0.703086\pi$
$79$	−1.75753	+	1.01471i	−0.197738	+	0.114164i	0.397862	+	0.917445i	$0.369752\pi$
$80$		0			0
$81$	−10.1111	+	17.5129i	−1.12345	+	1.94588i
$82$		0			0
$83$			0.288923i			0.0317134i	0.999874	+	0.0158567i	$0.00504756\pi$
$83$			0.288923i			0.0317134i	−0.999874	+	0.0158567i	$0.994952\pi$
$84$		0			0
$85$		−	7.59894i		−	0.824220i
$86$		0			0
$87$	−3.72789	+	6.45690i	−0.399672	+	0.692252i
$88$		0			0
$89$	12.0399	−	6.95124i	1.27623	−	0.736830i	0.300074	−	0.953916i	$-0.402989\pi$
$89$	12.0399	−	6.95124i	1.27623	−	0.736830i	0.976152	+	0.217086i	$0.0696553\pi$
$90$		0			0
$91$	−1.60371	+	3.74075i	−0.168114	+	0.392137i
$92$		0			0
$93$	5.73485	−	3.31102i	0.594677	−	0.343337i
$94$		0			0
$95$	1.52991	+	0.883293i	0.156965	+	0.0906240i
$96$		0			0
$97$			0.249149i			0.0252972i	0.999920	+	0.0126486i	$0.00402629\pi$
$97$			0.249149i			0.0252972i	−0.999920	+	0.0126486i	$0.995974\pi$
$98$		0			0
$99$	−17.2067			−1.72934
$100$		0			0
$101$	4.87755	−	8.44817i	0.485335	−	0.840624i	−0.514523	−	0.857476i	$-0.672031\pi$
$101$	4.87755	−	8.44817i	0.485335	−	0.840624i	0.999858	+	0.0168520i	$0.00536443\pi$
$102$		0			0
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511902i	0.679565	−	0.733615i	$-0.262168\pi$
$103$	−2.99947	−	5.19523i	−0.295546	−	0.511902i	−0.975112	+	0.221713i	$0.928835\pi$
$104$		0			0
$105$	7.73190	+	3.31477i	0.754557	+	0.323489i
$106$		0			0
$107$	0.0626308	+	0.108480i	0.00605475	+	0.0104871i	0.869037	−	0.494747i	$-0.164739\pi$
$107$	0.0626308	+	0.108480i	0.00605475	+	0.0104871i	−0.862982	+	0.505234i	$0.831406\pi$
$108$		0			0
$109$	0.399788	+	0.230818i	0.0382928	+	0.0221083i	0.519024	−	0.854760i	$-0.326295\pi$
$109$	0.399788	+	0.230818i	0.0382928	+	0.0221083i	−0.480731	+	0.876868i	$0.659629\pi$
$110$		0			0
$111$	9.06999			0.860885
$112$		0			0
$113$	−9.65049			−0.907842			−0.453921	−	0.891042i	$-0.649975\pi$
$113$	−9.65049			−0.907842			−0.453921	+	0.891042i	$0.649975\pi$
$114$		0			0
$115$	5.66247	+	3.26923i	0.528028	+	0.304857i
$116$		0			0
$117$	5.46874	+	9.47214i	0.505586	+	0.875700i
$118$		0			0
$119$	16.0998	−	12.0418i	1.47586	−	1.10387i
$120$		0			0
$121$	2.57165	+	4.45422i	0.233786	+	0.404929i
$122$		0			0
$123$	10.9754	−	19.0099i	0.989615	−	1.71406i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	9.40385i		−	0.834457i	−0.908802	−	0.417229i	$-0.863001\pi$
$127$		−	9.40385i		−	0.834457i	0.908802	−	0.417229i	$-0.136999\pi$
$128$		0			0
$129$	−3.83699	−	2.21529i	−0.337828	−	0.195045i
$130$		0			0
$131$	−16.2949	+	9.40788i	−1.42369	+	0.821970i	−0.996612	−	0.0822423i	$-0.973792\pi$
$131$	−16.2949	+	9.40788i	−1.42369	+	0.821970i	−0.427082	+	0.904213i	$0.640459\pi$
$132$		0			0
$133$	0.552971	+	4.64112i	0.0479486	+	0.402436i
$134$		0			0
$135$	11.3175	−	6.53414i	0.974052	−	0.562369i
$136$		0			0
$137$	7.55473	−	13.0852i	0.645444	−	1.11794i	−0.338755	−	0.940875i	$-0.610006\pi$
$137$	7.55473	−	13.0852i	0.645444	−	1.11794i	0.984199	−	0.177067i	$-0.0566609\pi$
$138$		0			0
$139$		−	11.1193i		−	0.943129i	−0.881831	−	0.471565i	$-0.843689\pi$
$139$		−	11.1193i		−	0.943129i	0.881831	−	0.471565i	$-0.156311\pi$
$140$		0			0
$141$			35.9806i			3.03011i
$142$		0			0
$143$	−1.86142	+	3.22407i	−0.155660	+	0.269611i
$144$		0			0
$145$	2.03071	−	1.17243i	0.168641	−	0.0973652i
$146$		0			0
$147$	5.22951	+	21.6343i	0.431323	+	1.78437i
$148$		0			0
$149$	−9.67998	+	5.58874i	−0.793014	+	0.457847i	−0.841023	−	0.541000i	$-0.818046\pi$
$149$	−9.67998	+	5.58874i	−0.793014	+	0.457847i	0.0480082	+	0.998847i	$0.484713\pi$
$150$		0			0
$151$	−13.1832	−	7.61131i	−1.07283	−	0.619399i	−0.143878	−	0.989595i	$-0.545957\pi$
$151$	−13.1832	−	7.61131i	−1.07283	−	0.619399i	−0.928954	+	0.370196i	$0.879290\pi$
$152$		0			0
$153$		−	54.0285i		−	4.36794i
$154$		0			0
$155$	−2.08265			−0.167282
$156$		0			0
$157$	0.357836	−	0.619791i	0.0285584	−	0.0494647i	−0.851393	−	0.524528i	$-0.824242\pi$
$157$	0.357836	−	0.619791i	0.0285584	−	0.0494647i	0.879951	+	0.475064i	$0.157575\pi$
$158$		0			0
$159$	12.5245	+	21.6930i	0.993255	+	1.72037i
$160$		0			0
$161$	2.04664	+	17.1776i	0.161298	+	1.35379i
$162$		0			0
$163$	−0.890005	−	1.54153i	−0.0697105	−	0.120742i	0.829063	−	0.559155i	$-0.188874\pi$
$163$	−0.890005	−	1.54153i	−0.0697105	−	0.120742i	−0.898774	+	0.438413i	$0.855541\pi$
$164$		0			0
$165$	6.66397	+	3.84745i	0.518790	+	0.299523i
$166$		0			0
$167$	−5.69155			−0.440426			−0.220213	−	0.975452i	$-0.570675\pi$
$167$	−5.69155			−0.440426			−0.220213	+	0.975452i	$0.570675\pi$
$168$		0			0
$169$	−10.6336			−0.817966
$170$		0			0
$171$	10.8777	+	6.28022i	0.831835	+	0.480260i
$172$		0			0
$173$	−9.46941	−	16.4015i	−0.719946	−	1.24698i	−0.961021	−	0.276476i	$-0.910833\pi$
$173$	−9.46941	−	16.4015i	−0.719946	−	1.24698i	0.241075	−	0.970506i	$-0.422500\pi$
$174$		0			0
$175$	−1.58467	−	2.11869i	−0.119789	−	0.160158i
$176$		0			0
$177$	8.99680	+	15.5829i	0.676241	+	1.17128i
$178$		0			0
$179$	1.49172	−	2.58374i	0.111497	−	0.193118i	−0.804877	−	0.593441i	$-0.797769\pi$
$179$	1.49172	−	2.58374i	0.111497	−	0.193118i	0.916374	+	0.400323i	$0.131102\pi$
$180$		0			0
$181$	14.9790			1.11338			0.556691	−	0.830720i	$-0.312071\pi$
$181$	14.9790			1.11338			0.556691	+	0.830720i	$0.312071\pi$
$182$		0			0
$183$			31.3880i			2.32026i
$184$		0			0
$185$	−2.47037	−	1.42627i	−0.181625	−	0.104861i
$186$		0			0
$187$	15.9261	−	9.19496i	1.16463	−	0.672402i
$188$		0			0
$189$	31.7782	+	13.6237i	2.31152	+	0.990981i
$190$		0			0
$191$	22.4510	−	12.9621i	1.62450	−	0.937904i	0.638801	−	0.769372i	$-0.279431\pi$
$191$	22.4510	−	12.9621i	1.62450	−	0.937904i	0.985696	−	0.168532i	$-0.0539026\pi$
$192$		0			0
$193$	−3.55040	+	6.14947i	−0.255563	+	0.442648i	−0.965048	−	0.262072i	$-0.915594\pi$
$193$	−3.55040	+	6.14947i	−0.255563	+	0.442648i	0.709485	+	0.704720i	$0.248928\pi$
$194$		0			0
$195$		−	4.89129i		−	0.350272i
$196$		0			0
$197$		−	0.614082i		−	0.0437515i	−0.999761	−	0.0218758i	$-0.993036\pi$
$197$		−	0.614082i		−	0.0437515i	0.999761	−	0.0218758i	$-0.00696383\pi$
$198$		0			0
$199$	4.47143	−	7.74474i	0.316971	−	0.549010i	−0.662884	−	0.748723i	$-0.730668\pi$
$199$	4.47143	−	7.74474i	0.316971	−	0.549010i	0.979854	+	0.199713i	$0.0640009\pi$
$200$		0			0
$201$	17.2521	−	9.96050i	1.21687	−	0.702559i
$202$		0			0
$203$	5.70202	+	2.44453i	0.400203	+	0.171572i
$204$		0			0
$205$	−5.97866	+	3.45178i	−0.417568	+	0.241083i
$206$		0			0
$207$	40.2602	+	23.2442i	2.79828	+	1.61559i
$208$		0			0
$209$			4.27525i			0.295725i
$210$		0			0
$211$	−10.6756			−0.734942			−0.367471	−	0.930035i	$-0.619776\pi$
$211$	−10.6756			−0.734942			−0.367471	+	0.930035i	$0.619776\pi$
$212$		0			0
$213$	6.33061	−	10.9649i	0.433766	−	0.751305i
$214$		0			0
$215$	0.696713	+	1.20674i	0.0475154	+	0.0822992i
$216$		0			0
$217$	−3.30030	−	4.41248i	−0.224039	−	0.299539i
$218$		0			0
$219$	5.01698	+	8.68967i	0.339016	+	0.587194i
$220$		0			0
$221$	−10.1235	−	5.84481i	−0.680981	−	0.393164i
$222$		0			0
$223$	−1.40260			−0.0939252			−0.0469626	−	0.998897i	$-0.514954\pi$
$223$	−1.40260			−0.0939252			−0.0469626	+	0.998897i	$0.514954\pi$
$224$		0			0
$225$	−7.11001			−0.474000
$226$		0			0
$227$	−3.48428	−	2.01165i	−0.231260	−	0.133518i	0.379893	−	0.925030i	$-0.375961\pi$
$227$	−3.48428	−	2.01165i	−0.231260	−	0.133518i	−0.611153	+	0.791512i	$0.709294\pi$
$228$		0			0
$229$	10.8680	+	18.8239i	0.718178	+	1.24392i	0.961721	+	0.274031i	$0.0883571\pi$
$229$	10.8680	+	18.8239i	0.718178	+	1.24392i	−0.243542	+	0.969890i	$0.578310\pi$
$230$		0			0
$231$	2.40863	+	20.2158i	0.158476	+	1.33010i
$232$		0			0
$233$	5.69230	+	9.85935i	0.372915	+	0.645907i	0.990013	−	0.140979i	$-0.0450251\pi$
$233$	5.69230	+	9.85935i	0.372915	+	0.645907i	−0.617098	+	0.786886i	$0.711692\pi$
$234$		0			0
$235$	5.65799	−	9.79993i	0.369087	−	0.639277i
$236$		0			0
$237$	6.45281			0.419155
$238$		0			0
$239$		−	25.7524i		−	1.66578i	−0.553435	−	0.832892i	$-0.686683\pi$
$239$		−	25.7524i		−	1.66578i	0.553435	−	0.832892i	$-0.313317\pi$
$240$		0			0
$241$	−1.67062	−	0.964530i	−0.107614	−	0.0621309i	0.445227	−	0.895418i	$-0.353123\pi$
$241$	−1.67062	−	0.964530i	−0.107614	−	0.0621309i	−0.552841	+	0.833287i	$0.686456\pi$
$242$		0			0
$243$	21.7321	−	12.5470i	1.39412	−	0.804893i
$244$		0			0
$245$	1.97767	−	6.71482i	0.126349	−	0.428994i
$246$		0			0
$247$	2.35349	−	1.35879i	0.149749	−	0.0864577i
$248$		0			0
$249$	0.459334	−	0.795589i	0.0291091	−	0.0504184i
$250$		0			0
$251$		−	12.9948i		−	0.820222i	−0.912036	−	0.410111i	$-0.865490\pi$
$251$		−	12.9948i		−	0.820222i	0.912036	−	0.410111i	$-0.134510\pi$
$252$		0			0
$253$			15.8235i			0.994813i
$254$		0			0
$255$	−12.0809	+	20.9247i	−0.756534	+	1.31036i
$256$		0			0
$257$	−14.4110	+	8.32019i	−0.898933	+	0.518999i	−0.876854	−	0.480757i	$-0.840362\pi$
$257$	−14.4110	+	8.32019i	−0.898933	+	0.518999i	−0.0220792	+	0.999756i	$0.507029\pi$
$258$		0			0
$259$	−0.892891	−	7.49409i	−0.0554815	−	0.465660i
$260$		0			0
$261$	14.4384	−	8.33600i	0.893713	−	0.515985i
$262$		0			0
$263$	5.95477	+	3.43799i	0.367187	+	0.211995i	0.672229	−	0.740343i	$-0.265337\pi$
$263$	5.95477	+	3.43799i	0.367187	+	0.211995i	−0.305042	+	0.952339i	$0.598670\pi$
$264$		0			0
$265$		−	7.87796i		−	0.483939i
$266$		0			0
$267$	−44.2046			−2.70528
$268$		0			0
$269$	11.0639	−	19.1633i	0.674580	−	1.16841i	−0.302012	−	0.953304i	$-0.597658\pi$
$269$	11.0639	−	19.1633i	0.674580	−	1.16841i	0.976591	−	0.215102i	$-0.0690085\pi$
$270$		0			0
$271$	5.29547	+	9.17203i	0.321677	+	0.557161i	0.980834	−	0.194844i	$-0.0624201\pi$
$271$	5.29547	+	9.17203i	0.321677	+	0.557161i	−0.659157	+	0.752005i	$0.729087\pi$
$272$		0			0
$273$	10.3631	−	7.75105i	0.627204	−	0.469115i
$274$		0			0
$275$	−1.21003	−	2.09584i	−0.0729677	−	0.126384i
$276$		0			0
$277$	16.5032	+	9.52815i	0.991583	+	0.572491i	0.905747	−	0.423818i	$-0.139311\pi$
$277$	16.5032	+	9.52815i	0.991583	+	0.572491i	0.0858360	+	0.996309i	$0.472644\pi$
$278$		0			0
$279$	−14.8076			−0.886511
$280$		0			0
$281$	−17.6280			−1.05160			−0.525799	−	0.850609i	$-0.676234\pi$
$281$	−17.6280			−1.05160			−0.525799	+	0.850609i	$0.676234\pi$
$282$		0			0
$283$	−0.485654	−	0.280393i	−0.0288691	−	0.0166676i	0.485496	−	0.874239i	$-0.338639\pi$
$283$	−0.485654	−	0.280393i	−0.0288691	−	0.0166676i	−0.514365	+	0.857571i	$0.671972\pi$
$284$		0			0
$285$	−2.80854	−	4.86453i	−0.166364	−	0.288150i
$286$		0			0
$287$	−16.7874	−	7.19699i	−0.990930	−	0.424825i
$288$		0			0
$289$	20.3719	+	35.2852i	1.19835	+	2.07560i
$290$		0			0
$291$	0.396100	−	0.686065i	0.0232198	−	0.0402179i
$292$		0			0
$293$	23.8016			1.39051			0.695253	−	0.718765i	$-0.255292\pi$
$293$	23.8016			1.39051			0.695253	+	0.718765i	$0.255292\pi$
$294$		0			0
$295$		−	5.65903i		−	0.329482i
$296$		0			0
$297$	27.3890	+	15.8130i	1.58927	+	0.917565i
$298$		0			0
$299$	8.71070	−	5.02913i	0.503753	−	0.290842i
$300$		0			0
$301$	−1.45265	+	3.38840i	−0.0837295	+	0.195304i
$302$		0			0
$303$	−26.8620	+	15.5088i	−1.54318	+	0.890956i
$304$		0			0
$305$	4.93580	−	8.54905i	0.282623	−	0.489517i
$306$		0			0
$307$			9.32160i			0.532012i	0.963971	+	0.266006i	$0.0857041\pi$
$307$			9.32160i			0.532012i	−0.963971	+	0.266006i	$0.914296\pi$
$308$		0			0
$309$			19.0744i			1.08510i
$310$		0			0
$311$	−2.73260	+	4.73300i	−0.154951	+	0.268384i	−0.933041	−	0.359769i	$-0.882855\pi$
$311$	−2.73260	+	4.73300i	−0.154951	+	0.268384i	0.778090	+	0.628153i	$0.216189\pi$
$312$		0			0
$313$	−19.9919	+	11.5423i	−1.13001	+	0.652412i	−0.943937	−	0.330124i	$-0.892909\pi$
$313$	−19.9919	+	11.5423i	−1.13001	+	0.652412i	−0.186073	+	0.982536i	$0.559576\pi$
$314$		0			0
$315$	−11.2670	−	15.0639i	−0.634822	−	0.848754i
$316$		0			0
$317$	26.2154	−	15.1355i	1.47241	−	0.850094i	0.472887	−	0.881123i	$-0.343212\pi$
$317$	26.2154	−	15.1355i	1.47241	−	0.850094i	0.999518	+	0.0310291i	$0.00987845\pi$
$318$		0			0
$319$	4.91445	+	2.83736i	0.275157	+	0.158862i
$320$		0			0
$321$		−	0.398285i		−	0.0222301i
$322$		0			0
$323$	−13.4242			−0.746941
$324$		0			0
$325$	−0.769162	+	1.33223i	−0.0426654	+	0.0738987i
$326$		0			0
$327$	−0.733914	−	1.27118i	−0.0405855	−	0.0702962i
$328$		0			0
$329$	29.7290	−	3.54209i	1.63901	−	0.195282i
$330$		0			0
$331$	−0.262181	−	0.454110i	−0.0144108	−	0.0249602i	0.858730	−	0.512428i	$-0.171254\pi$
$331$	−0.262181	−	0.454110i	−0.0144108	−	0.0249602i	−0.873141	+	0.487468i	$0.837921\pi$
$332$		0			0
$333$	−17.5643	−	10.1408i	−0.962519	−	0.555711i
$334$		0			0
$335$	−6.26521			−0.342305
$336$		0			0
$337$	−3.41643			−0.186105			−0.0930524	−	0.995661i	$-0.529662\pi$
$337$	−3.41643			−0.186105			−0.0930524	+	0.995661i	$0.529662\pi$
$338$		0			0
$339$	26.5739	+	15.3425i	1.44330	+	0.833288i
$340$		0			0
$341$	−2.52007	−	4.36489i	−0.136470	−	0.236372i
$342$		0			0
$343$	17.3606	−	6.45067i	0.937382	−	0.348304i
$344$		0			0
$345$	−10.3949	−	18.0045i	−0.559643	−	0.969330i
$346$		0			0
$347$	−4.64349	+	8.04275i	−0.249275	+	0.431758i	−0.963325	−	0.268337i	$-0.913526\pi$
$347$	−4.64349	+	8.04275i	−0.249275	+	0.431758i	0.714050	+	0.700095i	$0.246859\pi$
$348$		0			0
$349$	−18.6699			−0.999374			−0.499687	−	0.866206i	$-0.666552\pi$
$349$	−18.6699			−0.999374			−0.499687	+	0.866206i	$0.666552\pi$
$350$		0			0
$351$		−	20.1032i		−	1.07303i
$352$		0			0
$353$	−11.7057	−	6.75828i	−0.623030	−	0.359707i	0.155018	−	0.987912i	$-0.450457\pi$
$353$	−11.7057	−	6.75828i	−0.623030	−	0.359707i	−0.778048	+	0.628205i	$0.783790\pi$
$354$		0			0
$355$	−3.44850	+	1.99099i	−0.183027	+	0.105671i
$356$		0			0
$357$	−63.4770	+	7.56303i	−3.35956	+	0.400278i
$358$		0			0
$359$	−22.8266	+	13.1789i	−1.20474	+	0.695558i	−0.961606	−	0.274435i	$-0.911509\pi$
$359$	−22.8266	+	13.1789i	−1.20474	+	0.695558i	−0.243135	+	0.969992i	$0.578176\pi$
$360$		0			0
$361$	−7.93959	+	13.7518i	−0.417873	+	0.723777i
$362$		0			0
$363$		−	16.3537i		−	0.858348i
$364$		0			0
$365$		−	3.15571i		−	0.165177i
$366$		0			0
$367$	−17.7819	+	30.7992i	−0.928208	+	1.60770i	−0.141889	+	0.989883i	$0.545318\pi$
$367$	−17.7819	+	30.7992i	−0.928208	+	1.60770i	−0.786319	+	0.617821i	$0.788016\pi$
$368$		0			0
$369$	−42.5083	+	24.5422i	−2.21289	+	1.27761i
$370$		0			0
$371$	16.6909	−	12.4839i	0.866550	−	0.648133i
$372$		0			0
$373$	−20.6623	+	11.9294i	−1.06985	+	0.617680i	−0.928141	−	0.372228i	$-0.878594\pi$
$373$	−20.6623	+	11.9294i	−1.06985	+	0.617680i	−0.141712	+	0.989908i	$0.545261\pi$
$374$		0			0
$375$	2.75363	+	1.58981i	0.142197	+	0.0820975i
$376$		0			0
$377$		−	3.60716i		−	0.185778i
$378$		0			0
$379$	25.9215			1.33150			0.665748	−	0.746177i	$-0.268113\pi$
$379$	25.9215			1.33150			0.665748	+	0.746177i	$0.268113\pi$
$380$		0			0
$381$	−14.9504	+	25.8948i	−0.765930	+	1.32663i
$382$		0			0
$383$	−16.8541	−	29.1922i	−0.861205	−	1.49165i	−0.870766	−	0.491697i	$-0.836377\pi$
$383$	−16.8541	−	29.1922i	−0.861205	−	1.49165i	0.00956071	−	0.999954i	$-0.496957\pi$
$384$		0			0
$385$	2.52293	−	5.88488i	0.128580	−	0.299921i
$386$		0			0
$387$	4.95364	+	8.57995i	0.251807	+	0.436143i
$388$		0			0
$389$	−29.0131	−	16.7507i	−1.47102	−	0.849294i	−0.471550	−	0.881839i	$-0.656305\pi$
$389$	−29.0131	−	16.7507i	−1.47102	−	0.849294i	−0.999470	+	0.0325451i	$0.989639\pi$
$390$		0			0
$391$	−49.6853			−2.51269
$392$		0			0
$393$	59.8271			3.01788
$394$		0			0
$395$	−1.75753	−	1.01471i	−0.0884311	−	0.0510557i
$396$		0			0
$397$	2.24042	+	3.88052i	0.112443	+	0.194757i	0.916755	−	0.399450i	$-0.130799\pi$
$397$	2.24042	+	3.88052i	0.112443	+	0.194757i	−0.804312	+	0.594208i	$0.797466\pi$
$398$		0			0
$399$	5.85583	−	13.6591i	0.293158	−	0.683809i
$400$		0			0
$401$	−15.5291	−	26.8973i	−0.775488	−	1.34318i	−0.934520	−	0.355911i	$-0.884171\pi$
$401$	−15.5291	−	26.8973i	−0.775488	−	1.34318i	0.159032	−	0.987273i	$-0.449163\pi$
$402$		0			0
$403$	−1.60189	+	2.77456i	−0.0797960	+	0.138211i
$404$		0			0
$405$	−20.2222			−1.00485
$406$		0			0
$407$		−	6.90332i		−	0.342185i
$408$		0			0
$409$	−22.6647	−	13.0855i	−1.12070	−	0.647034i	−0.179117	−	0.983828i	$-0.557324\pi$
$409$	−22.6647	−	13.0855i	−1.12070	−	0.647034i	−0.941579	+	0.336794i	$0.890658\pi$
$410$		0			0
$411$	−41.6059	+	24.0212i	−2.05227	+	1.18488i
$412$		0			0
$413$	11.9897	−	8.96767i	0.589976	−	0.441270i
$414$		0			0
$415$	−0.250215	+	0.144462i	−0.0122826	+	0.00709134i
$416$		0			0
$417$	−17.6776	+	30.6186i	−0.865678	+	1.49940i
$418$		0			0
$419$			3.71538i			0.181508i	0.995873	+	0.0907540i	$0.0289277\pi$
$419$			3.71538i			0.181508i	−0.995873	+	0.0907540i	$0.971072\pi$
$420$		0			0
$421$		−	9.89335i		−	0.482172i	−0.970504	−	0.241086i	$-0.922496\pi$
$421$		−	9.89335i		−	0.482172i	0.970504	−	0.241086i	$-0.0775037\pi$
$422$		0			0
$423$	40.2283	−	69.6775i	1.95597	−	3.38784i
$424$		0			0
$425$	6.58087	−	3.79947i	0.319219	−	0.184301i
$426$		0			0
$427$	25.9344	−	3.08997i	1.25505	−	0.149534i
$428$		0			0
$429$	10.2513	−	5.91862i	0.494940	−	0.285753i
$430$		0			0
$431$	21.9155	+	12.6529i	1.05563	+	0.609471i	0.924222	−	0.381857i	$-0.124715\pi$
$431$	21.9155	+	12.6529i	1.05563	+	0.609471i	0.131413	+	0.991328i	$0.458049\pi$
$432$		0			0
$433$			3.51643i			0.168989i	0.996424	+	0.0844944i	$0.0269275\pi$
$433$			3.51643i			0.168989i	−0.996424	+	0.0844944i	$0.973073\pi$
$434$		0			0
$435$	−7.45579			−0.357478
$436$		0			0
$437$	5.77537	−	10.0032i	0.276273	−	0.478520i
$438$		0			0
$439$	4.56047	+	7.89896i	0.217659	+	0.376997i	0.954092	−	0.299514i	$-0.0968245\pi$
$439$	4.56047	+	7.89896i	0.217659	+	0.376997i	−0.736433	+	0.676511i	$0.763491\pi$
$440$		0			0
$441$	14.0613	−	47.7424i	0.669584	−	2.27345i
$442$		0			0
$443$	1.72708	+	2.99140i	0.0820563	+	0.142126i	0.904133	−	0.427251i	$-0.140518\pi$
$443$	1.72708	+	2.99140i	0.0820563	+	0.142126i	−0.822077	+	0.569377i	$0.807185\pi$
$444$		0			0
$445$	12.0399	+	6.95124i	0.570746	+	0.329520i
$446$		0			0
$447$	35.5402			1.68099
$448$		0			0
$449$	10.3646			0.489133			0.244567	−	0.969632i	$-0.421354\pi$
$449$	10.3646			0.489133			0.244567	+	0.969632i	$0.421354\pi$
$450$		0			0
$451$	−14.4687	−	8.35353i	−0.681306	−	0.393352i
$452$		0			0
$453$	24.2011	+	41.9175i	1.13707	+	1.96946i
$454$		0			0
$455$	−4.04144	+	0.481521i	−0.189465	+	0.0225740i
$456$		0			0
$457$	13.4566	+	23.3076i	0.629475	+	1.09028i	0.987657	+	0.156630i	$0.0500632\pi$
$457$	13.4566	+	23.3076i	0.629475	+	1.09028i	−0.358183	+	0.933652i	$0.616603\pi$
$458$		0			0
$459$	−49.6525	+	86.0006i	−2.31758	+	4.01417i
$460$		0			0
$461$	−9.19023			−0.428032			−0.214016	−	0.976830i	$-0.568654\pi$
$461$	−9.19023			−0.428032			−0.214016	+	0.976830i	$0.568654\pi$
$462$		0			0
$463$			10.8548i			0.504464i	0.967667	+	0.252232i	$0.0811645\pi$
$463$			10.8548i			0.504464i	−0.967667	+	0.252232i	$0.918835\pi$
$464$		0			0
$465$	5.73485	+	3.31102i	0.265947	+	0.153545i
$466$		0			0
$467$	−25.9792	+	14.9991i	−1.20218	+	0.694077i	−0.961039	−	0.276414i	$-0.910854\pi$
$467$	−25.9792	+	14.9991i	−1.20218	+	0.694077i	−0.241137	+	0.970491i	$0.577520\pi$
$468$		0			0
$469$	−9.92825	−	13.2740i	−0.458444	−	0.612937i
$470$		0			0
$471$	−1.97070	+	1.13778i	−0.0908051	+	0.0524263i
$472$		0			0
$473$	−1.68609	+	2.92039i	−0.0775265	+	0.134280i
$474$		0			0
$475$			1.76659i			0.0810565i
$476$		0			0
$477$		−	56.0123i		−	2.56463i
$478$		0			0
$479$	4.67977	−	8.10560i	0.213824	−	0.370355i	−0.739084	−	0.673613i	$-0.764741\pi$
$479$	4.67977	−	8.10560i	0.213824	−	0.370355i	0.952908	+	0.303259i	$0.0980747\pi$
$480$		0			0
$481$	−3.80022	+	2.19406i	−0.173275	+	0.100041i
$482$		0			0
$483$	21.6735	−	50.5547i	0.986177	−	2.30032i
$484$		0			0
$485$	−0.215769	+	0.124575i	−0.00979758	+	0.00565664i
$486$		0			0
$487$	14.9682	+	8.64189i	0.678273	+	0.391601i	0.799204	−	0.601060i	$-0.205255\pi$
$487$	14.9682	+	8.64189i	0.678273	+	0.391601i	−0.120931	+	0.992661i	$0.538588\pi$
$488$		0			0
$489$			5.65976i			0.255943i
$490$		0			0
$491$	28.4313			1.28309			0.641543	−	0.767087i	$-0.278295\pi$
$491$	28.4313			1.28309			0.641543	+	0.767087i	$0.278295\pi$
$492$		0			0
$493$	−8.90924	+	15.4313i	−0.401252	+	0.694989i
$494$		0			0
$495$	−8.60334	−	14.9014i	−0.386691	−	0.669769i
$496$		0			0
$497$	−9.68301	−	4.15124i	−0.434343	−	0.186209i
$498$		0			0
$499$	−12.1835	−	21.1025i	−0.545409	−	0.944676i	−0.998581	−	0.0532527i	$-0.983041\pi$
$499$	−12.1835	−	21.1025i	−0.545409	−	0.944676i	0.453172	−	0.891423i	$-0.350292\pi$
$500$		0			0
$501$	15.6725	+	9.04850i	0.700194	+	0.404257i
$502$		0			0
$503$	22.0798			0.984489			0.492245	−	0.870457i	$-0.336177\pi$
$503$	22.0798			0.984489			0.492245	+	0.870457i	$0.336177\pi$
$504$		0			0
$505$	9.75511			0.434097
$506$		0			0
$507$	29.2809	+	16.9054i	1.30041	+	0.750794i
$508$		0			0
$509$	7.47946	+	12.9548i	0.331521	+	0.574212i	0.982810	−	0.184618i	$-0.0591048\pi$
$509$	7.47946	+	12.9548i	0.331521	+	0.574212i	−0.651289	+	0.758830i	$0.725771\pi$
$510$		0			0
$511$	6.68596	−	5.00074i	0.295770	−	0.221220i
$512$		0			0
$513$	−11.5431	−	19.9933i	−0.509641	−	0.882724i
$514$		0			0
$515$	2.99947	−	5.19523i	0.132172	−	0.228929i
$516$		0			0
$517$	27.3854			1.20441
$518$		0			0
$519$			60.2183i			2.64329i
$520$		0			0
$521$	13.6812	+	7.89884i	0.599384	+	0.346055i	0.768799	−	0.639490i	$-0.220855\pi$
$521$	13.6812	+	7.89884i	0.599384	+	0.346055i	−0.169415	+	0.985545i	$0.554188\pi$
$522$		0			0
$523$	−17.4282	+	10.0622i	−0.762083	+	0.439989i	−0.830043	−	0.557699i	$-0.811684\pi$
$523$	−17.4282	+	10.0622i	−0.762083	+	0.439989i	0.0679602	+	0.997688i	$0.478351\pi$
$524$		0			0
$525$	0.995275	+	8.35341i	0.0434374	+	0.364573i
$526$		0			0
$527$	13.7056	−	7.91296i	0.597027	−	0.344694i
$528$		0			0
$529$	9.87568	−	17.1052i	0.429377	−	0.743703i
$530$		0			0
$531$		−	40.2358i		−	1.74608i
$532$		0			0
$533$			10.6199i			0.459999i
$534$		0			0
$535$	−0.0626308	+	0.108480i	−0.00270776	+	0.00468999i
$536$		0			0
$537$	−8.21532	+	4.74312i	−0.354517	+	0.204681i
$538$		0			0
$539$	16.4662	−	3.98027i	0.709250	−	0.171442i
$540$		0			0
$541$	14.0280	−	8.09904i	0.603109	−	0.348205i	−0.167155	−	0.985931i	$-0.553458\pi$
$541$	14.0280	−	8.09904i	0.603109	−	0.348205i	0.770264	+	0.637726i	$0.220125\pi$
$542$		0			0
$543$	−41.2467	−	23.8138i	−1.77007	−	1.02195i
$544$		0			0
$545$			0.461636i			0.0197743i
$546$		0			0
$547$	29.9614			1.28106			0.640529	−	0.767934i	$-0.278715\pi$
$547$	29.9614			1.28106			0.640529	+	0.767934i	$0.278715\pi$
$548$		0			0
$549$	35.0936	−	60.7838i	1.49776	−	2.59419i
$550$		0			0
$551$	−2.07120	−	3.58743i	−0.0882362	−	0.152830i
$552$		0			0
$553$	−0.635244	−	5.33165i	−0.0270133	−	0.226725i
$554$		0			0
$555$	4.53499	+	7.85484i	0.192500	+	0.333419i
$556$		0			0
$557$	36.5898	+	21.1251i	1.55036	+	0.895100i	0.998112	+	0.0614182i	$0.0195623\pi$
$557$	36.5898	+	21.1251i	1.55036	+	0.895100i	0.552246	+	0.833681i	$0.313771\pi$
$558$		0			0
$559$	2.14354			0.0906621
$560$		0			0
$561$	−58.4730			−2.46873
$562$		0			0
$563$	−19.4740	−	11.2433i	−0.820731	−	0.473849i	0.0299372	−	0.999552i	$-0.490469\pi$
$563$	−19.4740	−	11.2433i	−0.820731	−	0.473849i	−0.850669	+	0.525702i	$0.823803\pi$
$564$		0			0
$565$	−4.82525	−	8.35757i	−0.203000	−	0.351606i
$566$		0			0
$567$	−32.0454	−	42.8445i	−1.34578	−	1.79930i
$568$		0			0
$569$	−15.7198	−	27.2275i	−0.659008	−	1.14144i	−0.980873	−	0.194650i	$-0.937643\pi$
$569$	−15.7198	−	27.2275i	−0.659008	−	1.14144i	0.321864	−	0.946786i	$-0.395690\pi$
$570$		0			0
$571$	4.27788	−	7.40950i	0.179024	−	0.310078i	−0.762523	−	0.646961i	$-0.776039\pi$
$571$	4.27788	−	7.40950i	0.179024	−	0.310078i	0.941546	+	0.336883i	$0.109373\pi$
$572$		0			0
$573$	−82.4291			−3.44353
$574$		0			0
$575$			6.53845i			0.272672i
$576$		0			0
$577$	35.0221	+	20.2200i	1.45799	+	0.841771i	0.998912	−	0.0466251i	$-0.0148466\pi$
$577$	35.0221	+	20.2200i	1.45799	+	0.841771i	0.459078	+	0.888396i	$0.348180\pi$
$578$		0			0
$579$	19.5530	−	11.2889i	0.812595	−	0.469152i
$580$		0			0
$581$	−0.702576	−	0.301204i	−0.0291478	−	0.0124960i
$582$		0			0
$583$	16.5109	−	9.53258i	0.683812	−	0.394799i
$584$		0			0
$585$	−5.46874	+	9.47214i	−0.226105	+	0.391625i
$586$		0			0
$587$			46.5032i			1.91939i	0.281038	+	0.959697i	$0.409321\pi$
$587$			46.5032i			1.91939i	−0.281038	+	0.959697i	$0.590679\pi$
$588$		0			0
$589$			3.67918i			0.151598i
$590$		0			0
$591$	−0.976274	+	1.69096i	−0.0401586	+	0.0695567i
$592$		0			0
$593$	5.42655	−	3.13302i	0.222842	−	0.128658i	−0.384424	−	0.923157i	$-0.625600\pi$
$593$	5.42655	−	3.13302i	0.222842	−	0.128658i	0.607265	+	0.794499i	$0.292267\pi$
$594$		0			0
$595$	18.4784	+	7.92193i	0.757539	+	0.324767i
$596$		0			0
$597$	−24.6253	+	14.2175i	−1.00785	+	0.581882i
$598$		0			0
$599$	−35.7470	−	20.6385i	−1.46058	−	0.843268i	−0.461544	−	0.887117i	$-0.652705\pi$
$599$	−35.7470	−	20.6385i	−1.46058	−	0.843268i	−0.999038	+	0.0438493i	$0.986038\pi$
$600$		0			0
$601$			18.4478i			0.752502i	0.926518	+	0.376251i	$0.122787\pi$
$601$			18.4478i			0.752502i	−0.926518	+	0.376251i	$0.877213\pi$
$602$		0			0
$603$	−44.5457			−1.81404
$604$		0			0
$605$	−2.57165	+	4.45422i	−0.104552	+	0.181090i
$606$		0			0
$607$	3.76477	+	6.52077i	0.152807	+	0.264670i	0.932258	−	0.361793i	$-0.117835\pi$
$607$	3.76477	+	6.52077i	0.152807	+	0.264670i	−0.779451	+	0.626463i	$0.784502\pi$
$608$		0			0
$609$	−11.8149	−	15.7965i	−0.478765	−	0.640106i
$610$		0			0
$611$	−8.70382	−	15.0755i	−0.352119	−	0.609888i
$612$		0			0
$613$	−15.3991	−	8.89067i	−0.621963	−	0.359091i	0.155670	−	0.987809i	$-0.450246\pi$
$613$	−15.3991	−	8.89067i	−0.621963	−	0.359091i	−0.777633	+	0.628719i	$0.783580\pi$
$614$		0			0
$615$	21.9507			0.885138
$616$		0			0
$617$	−25.4606			−1.02500			−0.512502	−	0.858686i	$-0.671281\pi$
$617$	−25.4606			−1.02500			−0.512502	+	0.858686i	$0.671281\pi$
$618$		0			0
$619$	−1.54568	−	0.892398i	−0.0621261	−	0.0358685i	0.468615	−	0.883402i	$-0.344753\pi$
$619$	−1.54568	−	0.892398i	−0.0621261	−	0.0358685i	−0.530741	+	0.847534i	$0.678086\pi$
$620$		0			0
$621$	−42.7231	−	73.9987i	−1.71442	−	2.96946i
$622$		0			0
$623$	4.35170	+	36.5242i	0.174347	+	1.46331i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	6.79685	−	11.7725i	0.271440	−	0.470148i
$628$		0			0
$629$	21.6762			0.864288
$630$		0			0
$631$			25.2033i			1.00333i	0.865063	+	0.501663i	$0.167278\pi$
$631$			25.2033i			1.00333i	−0.865063	+	0.501663i	$0.832722\pi$
$632$		0			0
$633$	29.3968	+	16.9723i	1.16842	+	0.674587i
$634$		0			0
$635$	8.14398	−	4.70193i	0.323184	−	0.186590i
$636$		0			0
$637$	−7.42451	−	7.79949i	−0.294170	−	0.309027i
$638$		0			0
$639$	−24.5189	+	14.1560i	−0.969952	+	0.560002i
$640$		0			0
$641$	1.24626	−	2.15858i	0.0492242	−	0.0852587i	−0.840363	−	0.542023i	$-0.817658\pi$
$641$	1.24626	−	2.15858i	0.0492242	−	0.0852587i	0.889588	+	0.456765i	$0.150992\pi$
$642$		0			0
$643$			39.1121i			1.54243i	0.636575	+	0.771215i	$0.280350\pi$
$643$			39.1121i			1.54243i	−0.636575	+	0.771215i	$0.719650\pi$
$644$		0			0
$645$		−	4.43057i		−	0.174454i
$646$		0			0
$647$	−7.69474	+	13.3277i	−0.302512	+	0.523965i	−0.976704	−	0.214590i	$-0.931158\pi$
$647$	−7.69474	+	13.3277i	−0.302512	+	0.523965i	0.674193	+	0.738556i	$0.264492\pi$
$648$		0			0
$649$	11.8604	−	6.84761i	0.465562	−	0.268792i
$650$		0			0
$651$	2.07281	+	17.3972i	0.0812398	+	0.681851i
$652$		0			0
$653$	1.33623	−	0.771475i	0.0522909	−	0.0301902i	−0.473627	−	0.880726i	$-0.657055\pi$
$653$	1.33623	−	0.771475i	0.0522909	−	0.0301902i	0.525918	+	0.850536i	$0.323722\pi$
$654$		0			0
$655$	−16.2949	−	9.40788i	−0.636696	−	0.367596i
$656$		0			0
$657$		−	22.4371i		−	0.875355i
$658$		0			0
$659$	−23.4292			−0.912670			−0.456335	−	0.889808i	$-0.650838\pi$
$659$	−23.4292			−0.912670			−0.456335	+	0.889808i	$0.650838\pi$
$660$		0			0
$661$	−10.1419	+	17.5663i	−0.394474	+	0.683249i	−0.993034	−	0.117829i	$-0.962407\pi$
$661$	−10.1419	+	17.5663i	−0.394474	+	0.683249i	0.598560	+	0.801078i	$0.295740\pi$
$662$		0			0
$663$	18.5843	+	32.1889i	0.721754	+	1.25011i
$664$		0			0
$665$	−3.74284	+	2.79945i	−0.145141	+	0.108558i
$666$		0			0
$667$	−7.66589	−	13.2777i	−0.296825	−	0.514115i
$668$		0			0
$669$	3.86225	+	2.22987i	0.149323	+	0.0862119i
$670$		0			0
$671$	23.8899			0.922259
$672$		0			0
$673$	−14.3296			−0.552364			−0.276182	−	0.961105i	$-0.589069\pi$
$673$	−14.3296			−0.552364			−0.276182	+	0.961105i	$0.589069\pi$
$674$		0			0
$675$	11.3175	+	6.53414i	0.435609	+	0.251499i
$676$		0			0
$677$	9.11144	+	15.7815i	0.350181	+	0.606531i	0.986281	−	0.165075i	$-0.0527868\pi$
$677$	9.11144	+	15.7815i	0.350181	+	0.606531i	−0.636100	+	0.771607i	$0.719453\pi$
$678$		0			0
$679$	−0.605857	−	0.259739i	−0.0232506	−	0.00996787i
$680$		0			0
$681$	6.39628	+	11.0787i	0.245106	+	0.424536i
$682$		0			0
$683$	−11.4579	+	19.8456i	−0.438422	+	0.759370i	−0.997568	−	0.0696995i	$-0.977796\pi$
$683$	−11.4579	+	19.8456i	−0.438422	+	0.759370i	0.559146	+	0.829069i	$0.311129\pi$
$684$		0			0
$685$	15.1095			0.577302
$686$		0			0
$687$		−	69.1124i		−	2.63680i
$688$		0			0
$689$	−10.4952	−	6.05942i	−0.399836	−	0.230846i
$690$		0			0
$691$	−14.4278	+	8.32990i	−0.548860	+	0.316884i	−0.748662	−	0.662952i	$-0.769303\pi$
$691$	−14.4278	+	8.32990i	−0.548860	+	0.316884i	0.199802	+	0.979836i	$0.435970\pi$
$692$		0			0
$693$	17.9380	−	41.8415i	0.681410	−	1.58943i
$694$		0			0
$695$	9.62962	−	5.55967i	0.365272	−	0.210890i
$696$		0			0
$697$	26.2299	−	45.4314i	0.993526	−	1.72084i
$698$		0			0
$699$		−	36.1987i		−	1.36916i
$700$		0			0
$701$			3.87396i			0.146317i	0.997320	+	0.0731587i	$0.0233080\pi$
$701$			3.87396i			0.146317i	−0.997320	+	0.0731587i	$0.976692\pi$
$702$		0			0
$703$	−2.51962	+	4.36412i	−0.0950294	+	0.164596i
$704$		0			0
$705$	−31.1601	+	17.9903i	−1.17356	+	0.677553i
$706$		0			0
$707$	15.4586	+	20.6680i	0.581380	+	0.777301i
$708$		0			0
$709$	−24.1848	+	13.9631i	−0.908281	+	0.524396i	−0.879878	−	0.475200i	$-0.842376\pi$
$709$	−24.1848	+	13.9631i	−0.908281	+	0.524396i	−0.0284031	+	0.999597i	$0.509042\pi$
$710$		0			0
$711$	−12.4961	−	7.21462i	−0.468640	−	0.270569i
$712$		0			0
$713$			13.6173i			0.509972i
$714$		0			0
$715$	−3.72284			−0.139226
$716$		0			0
$717$	−40.9415	+	70.9127i	−1.52899	+	2.64828i
$718$		0			0
$719$	−8.27114	−	14.3260i	−0.308461	−	0.534271i	0.669565	−	0.742754i	$-0.266481\pi$
$719$	−8.27114	−	14.3260i	−0.308461	−	0.534271i	−0.978026	+	0.208483i	$0.933147\pi$
$720$		0			0
$721$	15.7602	−	1.87777i	0.586942	−	0.0699317i
$722$		0			0
$723$	3.06684	+	5.31193i	0.114057	+	0.197553i
$724$		0			0
$725$	2.03071	+	1.17243i	0.0754188	+	0.0435430i
$726$		0			0
$727$	−6.76375			−0.250854			−0.125427	−	0.992103i	$-0.540030\pi$
$727$	−6.76375			−0.250854			−0.125427	+	0.992103i	$0.540030\pi$
$728$		0			0
$729$	−19.1232			−0.708268
$730$		0			0
$731$	−9.16996	−	5.29428i	−0.339163	−	0.195816i
$732$		0			0
$733$	17.1394	+	29.6863i	0.633059	+	1.09649i	0.986923	+	0.161193i	$0.0515341\pi$
$733$	17.1394	+	29.6863i	0.633059	+	1.09649i	−0.353864	+	0.935297i	$0.615133\pi$
$734$		0			0
$735$	−16.1211	+	15.3460i	−0.594635	+	0.566047i
$736$		0			0
$737$	−7.58110	−	13.1309i	−0.279253	−	0.483681i
$738$		0			0
$739$	19.2212	−	33.2921i	0.707063	−	1.22467i	−0.258879	−	0.965910i	$-0.583353\pi$
$739$	19.2212	−	33.2921i	0.707063	−	1.22467i	0.965942	−	0.258759i	$-0.0833135\pi$
$740$		0			0
$741$	−8.64088			−0.317431
$742$		0			0
$743$		−	30.1845i		−	1.10736i	−0.832729	−	0.553681i	$-0.813223\pi$
$743$		−	30.1845i		−	1.10736i	0.832729	−	0.553681i	$-0.186777\pi$
$744$		0			0
$745$	−9.67998	−	5.58874i	−0.354647	−	0.204755i
$746$		0			0
$747$	−1.77903	+	1.02712i	−0.0650913	+	0.0375805i
$748$		0			0
$749$	−0.329083	+	0.0392089i	−0.0120244	+	0.00143266i
$750$		0			0
$751$	26.8007	−	15.4734i	0.977972	−	0.564632i	0.0763147	−	0.997084i	$-0.475685\pi$
$751$	26.8007	−	15.4734i	0.977972	−	0.564632i	0.901657	+	0.432451i	$0.142351\pi$
$752$		0			0
$753$	−20.6592	+	35.7828i	−0.752864	+	1.30400i
$754$		0			0
$755$		−	15.2226i		−	0.554008i
$756$		0			0
$757$		−	32.7932i		−	1.19189i	−0.803025	−	0.595945i	$-0.796777\pi$
$757$		−	32.7932i		−	1.19189i	0.803025	−	0.595945i	$-0.203223\pi$
$758$		0			0
$759$	25.1563	−	43.5721i	0.913117	−	1.58157i
$760$		0			0
$761$	−11.1966	+	6.46436i	−0.405876	+	0.234333i	−0.689016	−	0.724746i	$-0.741957\pi$
$761$	−11.1966	+	6.46436i	−0.405876	+	0.234333i	0.283140	+	0.959079i	$0.408624\pi$
$762$		0			0
$763$	−0.978062	+	0.731538i	−0.0354082	+	0.0264835i
$764$		0			0
$765$	46.7900	−	27.0142i	1.69170	−	0.976702i
$766$		0			0
$767$	−7.53912	−	4.35271i	−0.272222	−	0.157167i
$768$		0			0
$769$		−	1.25520i		−	0.0452635i	−0.999744	−	0.0226318i	$-0.992795\pi$
$769$		−	1.25520i		−	0.0452635i	0.999744	−	0.0226318i	$-0.00720453\pi$
$770$		0			0
$771$	52.9102			1.90551
$772$		0			0
$773$	11.0046	−	19.0605i	0.395808	−	0.685559i	−0.597396	−	0.801946i	$-0.703798\pi$
$773$	11.0046	−	19.0605i	0.395808	−	0.685559i	0.993204	+	0.116387i	$0.0371313\pi$
$774$		0			0
$775$	−1.04132	−	1.80363i	−0.0374055	−	0.0647882i
$776$		0			0
$777$	−9.45550	+	22.0555i	−0.339214	+	0.791238i
$778$		0			0
$779$	6.09787	+	10.5618i	0.218479	+	0.378416i
$780$		0			0
$781$	−8.34560	−	4.81833i	−0.298629	−	0.172413i
$782$		0			0
$783$	−30.6433			−1.09510
$784$		0			0
$785$	0.715672			0.0255434
$786$		0			0
$787$	−29.8525	−	17.2354i	−1.06413	−	0.614375i	−0.137557	−	0.990494i	$-0.543925\pi$
$787$	−29.8525	−	17.2354i	−1.06413	−	0.614375i	−0.926571	+	0.376119i	$0.877258\pi$
$788$		0			0
$789$	−10.9315	−	18.9339i	−0.389172	−	0.674066i
$790$		0			0
$791$	10.0607	−	23.4671i	0.357717	−	0.834395i
$792$		0			0
$793$	−7.59285	−	13.1512i	−0.269630	−	0.467013i
$794$		0			0
$795$	−12.5245	+	21.6930i	−0.444197	+	0.769372i
$796$		0			0
$797$	−21.2444			−0.752515			−0.376258	−	0.926515i	$-0.622789\pi$
$797$	−21.2444			−0.752515			−0.376258	+	0.926515i	$0.622789\pi$
$798$		0			0
$799$			85.9894i			3.04209i
$800$		0			0
$801$	85.6037	+	49.4233i	3.02466	+	1.74629i
$802$		0			0
$803$	6.61385	−	3.81851i	0.233398	−	0.134752i
$804$		0			0
$805$	−13.8529	+	10.3613i	−0.488252	+	0.365186i
$806$		0			0
$807$	−60.9321	+	35.1791i	−2.14491	+	1.23836i
$808$		0			0
$809$	−1.39597	+	2.41789i	−0.0490796	+	0.0850084i	−0.889522	−	0.456893i	$-0.848962\pi$
$809$	−1.39597	+	2.41789i	−0.0490796	+	0.0850084i	0.840442	+	0.541902i	$0.182295\pi$
$810$		0			0
$811$			46.1196i			1.61948i	0.586790	+	0.809739i	$0.300391\pi$
$811$			46.1196i			1.61948i	−0.586790	+	0.809739i	$0.699609\pi$
$812$		0			0
$813$		−	33.6752i		−	1.18104i
$814$		0			0
$815$	0.890005	−	1.54153i	0.0311755	−	0.0539975i
$816$		0			0
$817$	2.13181	−	1.23080i	0.0745828	−	0.0430604i
$818$		0			0
$819$	−28.7346	+	3.42362i	−1.00407	+	0.119631i
$820$		0			0
$821$	−47.1623	+	27.2292i	−1.64598	+	0.950305i	−0.667327	+	0.744765i	$0.732562\pi$
$821$	−47.1623	+	27.2292i	−1.64598	+	0.950305i	−0.978649	+	0.205540i	$0.934105\pi$
$822$		0			0
$823$	11.9130	+	6.87795i	0.415259	+	0.239750i	0.693047	−	0.720892i	$-0.256268\pi$
$823$	11.9130	+	6.87795i	0.415259	+	0.239750i	−0.277788	+	0.960643i	$0.589601\pi$
$824$		0			0
$825$			7.69489i			0.267902i
$826$		0			0
$827$	−19.8375			−0.689816			−0.344908	−	0.938636i	$-0.612090\pi$
$827$	−19.8375			−0.689816			−0.344908	+	0.938636i	$0.612090\pi$
$828$		0			0
$829$	−1.25335	+	2.17087i	−0.0435308	+	0.0753975i	−0.886970	−	0.461827i	$-0.847194\pi$
$829$	−1.25335	+	2.17087i	−0.0435308	+	0.0753975i	0.843439	+	0.537225i	$0.180527\pi$
$830$		0			0
$831$	−30.2959	−	52.4741i	−1.05095	−	1.82031i
$832$		0			0
$833$	12.4979	+	51.7035i	0.433028	+	1.79142i
$834$		0			0
$835$	−2.84578	−	4.92903i	−0.0984822	−	0.170576i
$836$		0			0
$837$	23.5703	+	13.6083i	0.814708	+	0.470372i
$838$		0			0
$839$	27.1009			0.935628			0.467814	−	0.883827i	$-0.345042\pi$
$839$	27.1009			0.935628			0.467814	+	0.883827i	$0.345042\pi$
$840$		0			0
$841$	23.5016			0.810400
$842$		0			0
$843$	48.5411	+	28.0252i	1.67184	+	0.965240i
$844$		0			0
$845$	−5.31678	−	9.20893i	−0.182903	−	0.316797i
$846$		0			0
$847$	−13.5123	+	1.60994i	−0.464288	+	0.0553180i
$848$		0			0
$849$	0.891543	+	1.54420i	0.0305977	+	0.0529967i
$850$		0			0
$851$	−9.32558	+	16.1524i	−0.319677	+	0.553697i
$852$		0			0
$853$	−8.16785			−0.279662			−0.139831	−	0.990175i	$-0.544656\pi$
$853$	−8.16785			−0.279662			−0.139831	+	0.990175i	$0.544656\pi$
$854$		0			0
$855$			12.5604i			0.429558i
$856$		0			0
$857$	−13.4380	−	7.75845i	−0.459035	−	0.265024i	0.252604	−	0.967570i	$-0.418713\pi$
$857$	−13.4380	−	7.75845i	−0.459035	−	0.265024i	−0.711638	+	0.702546i	$0.752046\pi$
$858$		0			0
$859$	−46.6347	+	26.9246i	−1.59116	+	0.918654i	−0.598046	+	0.801462i	$0.704056\pi$
$859$	−46.6347	+	26.9246i	−1.59116	+	0.918654i	−0.993109	+	0.117192i	$0.962611\pi$
$860$		0			0
$861$	34.7845	+	46.5067i	1.18545	+	1.58494i
$862$		0			0
$863$	−33.2448	+	19.1939i	−1.13167	+	0.653368i	−0.944353	−	0.328932i	$-0.893311\pi$
$863$	−33.2448	+	19.1939i	−1.13167	+	0.653368i	−0.187313	+	0.982300i	$0.559978\pi$
$864$		0			0
$865$	9.46941	−	16.4015i	0.321969	−	0.557667i
$866$		0			0
$867$		−	129.550i		−	4.39975i
$868$		0			0
$869$		−	4.91134i		−	0.166606i
$870$		0			0
$871$	−4.81896	+	8.34668i	−0.163284	+	0.282816i
$872$		0			0
$873$	−1.53412	+	0.885726i	−0.0519222	+	0.0299773i
$874$		0			0
$875$	1.04250	−	2.43170i	0.0352431	−	0.0822066i
$876$		0			0
$877$	−15.9417	+	9.20394i	−0.538313	+	0.310795i	−0.744395	−	0.667740i	$-0.767262\pi$
$877$	−15.9417	+	9.20394i	−0.538313	+	0.310795i	0.206082	+	0.978535i	$0.433929\pi$
$878$		0			0
$879$	−65.5410	−	37.8401i	−2.21064	−	1.27632i
$880$		0			0
$881$			21.5756i			0.726902i	0.931613	+	0.363451i	$0.118402\pi$
$881$			21.5756i			0.726902i	−0.931613	+	0.363451i	$0.881598\pi$
$882$		0			0
$883$	−23.5384			−0.792131			−0.396065	−	0.918222i	$-0.629625\pi$
$883$	−23.5384			−0.792131			−0.396065	+	0.918222i	$0.629625\pi$
$884$		0			0
$885$	−8.99680	+	15.5829i	−0.302424	+	0.523814i
$886$		0			0
$887$	16.6515	+	28.8413i	0.559104	+	0.968397i	0.997572	+	0.0696497i	$0.0221881\pi$
$887$	16.6515	+	28.8413i	0.559104	+	0.968397i	−0.438467	+	0.898747i	$0.644479\pi$
$888$		0			0
$889$	22.8674	+	9.80356i	0.766948	+	0.328801i
$890$		0			0
$891$	−24.4695	−	42.3824i	−0.819759	−	1.41986i
$892$		0			0
$893$	−17.3124	−	9.99533i	−0.579338	−	0.334481i
$894$		0			0
$895$	2.98345			0.0997256
$896$		0			0
$897$	−31.9815			−1.06783
$898$		0			0
$899$	4.22926	+	2.44176i	0.141054	+	0.0814374i
$900$		0			0
$901$	29.9320	+	51.8438i	0.997181	+	1.72717i
$902$		0			0
$903$	9.38700	−	7.02097i	0.312380	−	0.233643i
$904$		0			0
$905$	7.48951	+	12.9722i	0.248960	+	0.431211i
$906$		0			0
$907$	25.9103	−	44.8780i	0.860338	−	1.49015i	−0.0112647	−	0.999937i	$-0.503586\pi$
$907$	25.9103	−	44.8780i	0.860338	−	1.49015i	0.871603	−	0.490213i	$-0.163081\pi$
$908$		0			0
$909$	69.3589			2.30049
$910$		0			0
$911$		−	3.37980i		−	0.111978i	−0.998431	−	0.0559889i	$-0.982169\pi$
$911$		−	3.37980i		−	0.111978i	0.998431	−	0.0559889i	$-0.0178312\pi$
$912$		0			0
$913$	−0.605536	−	0.349606i	−0.0200403	−	0.0115703i
$914$		0			0
$915$	−27.1828	+	15.6940i	−0.898635	+	0.518827i
$916$		0			0
$917$	−5.88965	−	49.4322i	−0.194493	−	1.63240i
$918$		0			0
$919$	16.6978	−	9.64048i	0.550810	−	0.318010i	−0.198639	−	0.980073i	$-0.563652\pi$
$919$	16.6978	−	9.64048i	0.550810	−	0.318010i	0.749448	+	0.662063i	$0.230319\pi$
$920$		0			0
$921$	14.8196	−	25.6683i	0.488322	−	0.845799i
$922$		0			0
$923$			6.12558i			0.201626i
$924$		0			0
$925$		−	2.85253i		−	0.0937908i
$926$		0			0
$927$	21.3262	−	36.9381i	0.700446	−	1.21321i
$928$		0			0
$929$	29.0690	−	16.7830i	0.953724	−	0.550633i	0.0594882	−	0.998229i	$-0.481053\pi$
$929$	29.0690	−	16.7830i	0.953724	−	0.550633i	0.894236	+	0.447596i	$0.147720\pi$
$930$		0			0
$931$	−11.8623	−	3.49373i	−0.388771	−	0.114502i
$932$		0			0
$933$	15.0492	−	8.68863i	0.492687	−	0.284453i
$934$		0			0
$935$	15.9261	+	9.19496i	0.520840	+	0.300707i
$936$		0			0
$937$		−	21.4342i		−	0.700224i	−0.936708	−	0.350112i	$-0.886144\pi$
$937$		−	21.4342i		−	0.700224i	0.936708	−	0.350112i	$-0.113856\pi$
$938$		0			0
$939$	73.4006			2.39534
$940$		0			0
$941$	7.43223	−	12.8730i	0.242284	−	0.419648i	−0.719081	−	0.694927i	$-0.755437\pi$
$941$	7.43223	−	12.8730i	0.242284	−	0.419648i	0.961364	+	0.275279i	$0.0887702\pi$
$942$		0			0
$943$	22.5693	+	39.0912i	0.734957	+	1.27298i
$944$		0			0
$945$	4.09059	+	34.3326i	0.133067	+	1.11684i
$946$		0			0
$947$	−21.9761	−	38.0637i	−0.714127	−	1.23690i	−0.963295	−	0.268444i	$-0.913490\pi$
$947$	−21.9761	−	38.0637i	−0.714127	−	1.23690i	0.249168	−	0.968460i	$-0.419843\pi$
$948$		0			0
$949$	−4.20412	−	2.42725i	−0.136472	−	0.0787919i
$950$		0			0
$951$	−96.2503			−3.12113
$952$		0			0
$953$	−24.5807			−0.796246			−0.398123	−	0.917332i	$-0.630338\pi$
$953$	−24.5807			−0.796246			−0.398123	+	0.917332i	$0.630338\pi$
$954$		0			0
$955$	22.4510	+	12.9621i	0.726497	+	0.419443i
$956$		0			0
$957$	−9.02174	−	15.6261i	−0.291631	−	0.505120i
$958$		0			0
$959$	23.9434	+	32.0122i	0.773173	+	1.03373i
$960$		0			0
$961$	13.3313	+	23.0905i	0.430042	+	0.744854i
$962$		0			0
$963$	−0.445305	+	0.771291i	−0.0143498	+	0.0248545i
$964$		0			0
$965$	−7.10080			−0.228583
$966$		0			0
$967$			9.58755i			0.308315i	0.988046	+	0.154157i	$0.0492663\pi$
$967$			9.58755i			0.308315i	−0.988046	+	0.154157i	$0.950734\pi$
$968$		0			0
$969$	36.9653	+	21.3419i	1.18750	+	0.685601i
$970$		0			0
$971$	19.5510	−	11.2878i	0.627421	−	0.362242i	−0.152332	−	0.988329i	$-0.548678\pi$
$971$	19.5510	−	11.2878i	0.627421	−	0.362242i	0.779753	+	0.626088i	$0.215345\pi$
$972$		0			0
$973$	27.0389	+	11.5920i	0.866828	+	0.371621i
$974$		0			0
$975$	4.23598	−	2.44564i	0.135660	−	0.0783233i
$976$		0			0
$977$	9.57609	−	16.5863i	0.306366	−	0.530642i	−0.671198	−	0.741278i	$-0.734220\pi$
$977$	9.57609	−	16.5863i	0.306366	−	0.530642i	0.977565	+	0.210636i	$0.0675535\pi$
$978$		0			0
$979$			33.6449i			1.07529i
$980$		0			0
$981$			3.28223i			0.104794i
$982$		0			0
$983$	−14.3326	+	24.8248i	−0.457139	+	0.791787i	−0.998808	−	0.0488042i	$-0.984459\pi$
$983$	−14.3326	+	24.8248i	−0.457139	+	0.791787i	0.541670	+	0.840591i	$0.317792\pi$
$984$		0			0
$985$	0.531810	−	0.307041i	0.0169449	−	0.00978314i
$986$		0			0
$987$	−87.4941	−	37.5099i	−2.78497	−	1.19395i
$988$		0			0
$989$	7.89023	−	4.55543i	0.250895	−	0.144854i
$990$		0			0
$991$	17.8817	+	10.3240i	0.568030	+	0.327952i	0.756362	−	0.654153i	$-0.226975\pi$
$991$	17.8817	+	10.3240i	0.568030	+	0.327952i	−0.188332	+	0.982105i	$0.560308\pi$
$992$		0			0
$993$			1.66727i			0.0529093i
$994$		0			0
$995$	8.94285			0.283507
$996$		0			0
$997$	−9.92952	+	17.1984i	−0.314471	+	0.544680i	−0.979325	−	0.202294i	$-0.935160\pi$
$997$	−9.92952	+	17.1984i	−0.314471	+	0.544680i	0.664854	+	0.746973i	$0.268494\pi$
$998$		0			0
$999$	18.6389	+	32.2834i	0.589707	+	1.02140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.f.591.1		24
4.3	odd	2		280.2.bj.e.171.2	yes	24
7.5	odd	6		1120.2.bz.e.271.1		24
8.3	odd	2		1120.2.bz.e.591.1		24
8.5	even	2		280.2.bj.f.171.9	yes	24
28.19	even	6		280.2.bj.f.131.9	yes	24
56.5	odd	6		280.2.bj.e.131.2	✓	24
56.19	even	6	inner	1120.2.bz.f.271.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.2	✓	24	56.5	odd	6
280.2.bj.e.171.2	yes	24	4.3	odd	2
280.2.bj.f.131.9	yes	24	28.19	even	6
280.2.bj.f.171.9	yes	24	8.5	even	2
1120.2.bz.e.271.1		24	7.5	odd	6
1120.2.bz.e.591.1		24	8.3	odd	2
1120.2.bz.f.271.1		24	56.19	even	6	inner
1120.2.bz.f.591.1		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)

\(f(q)\)	\(=\)	\(q+(-2.75363 - 1.58981i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.04250 + 2.43170i) q^{7} +(3.55500 + 6.15745i) q^{9} +O(q^{10})\)	\(q+(-2.75363 - 1.58981i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.04250 + 2.43170i) q^{7} +(3.55500 + 6.15745i) q^{9} +(-1.21003 + 2.09584i) q^{11} +1.53832 q^{13} -3.17962i q^{15} +(-6.58087 - 3.79947i) q^{17} +(1.52991 - 0.883293i) q^{19} +(6.73663 - 5.03864i) q^{21} +(5.66247 - 3.26923i) q^{23} +(-0.500000 + 0.866025i) q^{25} -13.0683i q^{27} -2.34486i q^{29} +(-1.04132 + 1.80363i) q^{31} +(6.66397 - 3.84745i) q^{33} +(-2.62717 + 0.313017i) q^{35} +(-2.47037 + 1.42627i) q^{37} +(-4.23598 - 2.44564i) q^{39} +6.90356i q^{41} +1.39343 q^{43} +(-3.55500 + 6.15745i) q^{45} +(-5.65799 - 9.79993i) q^{47} +(-4.82637 - 5.07012i) q^{49} +(12.0809 + 20.9247i) q^{51} +(-6.82251 - 3.93898i) q^{53} -2.42006 q^{55} -5.61708 q^{57} +(-4.90087 - 2.82952i) q^{59} +(-4.93580 - 8.54905i) q^{61} +(-18.6792 + 2.22555i) q^{63} +(0.769162 + 1.33223i) q^{65} +(-3.13260 + 5.42583i) q^{67} -20.7898 q^{69} +3.98199i q^{71} +(-2.73292 - 1.57785i) q^{73} +(2.75363 - 1.58981i) q^{75} +(-3.83499 - 5.12736i) q^{77} +(-1.75753 + 1.01471i) q^{79} +(-10.1111 + 17.5129i) q^{81} +0.288923i q^{83} -7.59894i q^{85} +(-3.72789 + 6.45690i) q^{87} +(12.0399 - 6.95124i) q^{89} +(-1.60371 + 3.74075i) q^{91} +(5.73485 - 3.31102i) q^{93} +(1.52991 + 0.883293i) q^{95} +0.249149i q^{97} -17.2067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) \) 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

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