LMFDB - Embedded newform 1045.2.f.a.626.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.10
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.a.626.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55769 q^{2} -2.37450i q^{3} +0.426394 q^{4} -1.00000 q^{5} +3.69874i q^{6} +4.79166i q^{7} +2.45119 q^{8} -2.63826 q^{9} +O(q^{10})$	\(q-1.55769 q^{2} -2.37450i q^{3} +0.426394 q^{4} -1.00000 q^{5} +3.69874i q^{6} +4.79166i q^{7} +2.45119 q^{8} -2.63826 q^{9} +1.55769 q^{10} +(0.945954 - 3.17886i) q^{11} -1.01247i q^{12} +2.33007 q^{13} -7.46391i q^{14} +2.37450i q^{15} -4.67098 q^{16} -3.56362i q^{17} +4.10959 q^{18} +(-1.49848 + 4.09323i) q^{19} -0.426394 q^{20} +11.3778 q^{21} +(-1.47350 + 4.95168i) q^{22} -7.00987 q^{23} -5.82035i q^{24} +1.00000 q^{25} -3.62952 q^{26} -0.858944i q^{27} +2.04313i q^{28} -10.2556 q^{29} -3.69874i q^{30} +0.774958i q^{31} +2.37355 q^{32} +(-7.54822 - 2.24617i) q^{33} +5.55101i q^{34} -4.79166i q^{35} -1.12494 q^{36} -4.42896i q^{37} +(2.33416 - 6.37598i) q^{38} -5.53275i q^{39} -2.45119 q^{40} +5.97210 q^{41} -17.7231 q^{42} -5.30262i q^{43} +(0.403349 - 1.35545i) q^{44} +2.63826 q^{45} +10.9192 q^{46} -5.52361 q^{47} +11.0912i q^{48} -15.9600 q^{49} -1.55769 q^{50} -8.46183 q^{51} +0.993526 q^{52} -7.05543i q^{53} +1.33797i q^{54} +(-0.945954 + 3.17886i) q^{55} +11.7453i q^{56} +(9.71939 + 3.55814i) q^{57} +15.9751 q^{58} +4.96331i q^{59} +1.01247i q^{60} +13.0476i q^{61} -1.20714i q^{62} -12.6417i q^{63} +5.64470 q^{64} -2.33007 q^{65} +(11.7578 + 3.49883i) q^{66} -11.5913i q^{67} -1.51951i q^{68} +16.6449i q^{69} +7.46391i q^{70} +8.09779i q^{71} -6.46688 q^{72} +16.6572i q^{73} +6.89893i q^{74} -2.37450i q^{75} +(-0.638942 + 1.74533i) q^{76} +(15.2320 + 4.53269i) q^{77} +8.61830i q^{78} -14.9450 q^{79} +4.67098 q^{80} -9.95436 q^{81} -9.30267 q^{82} -3.17734i q^{83} +4.85142 q^{84} +3.56362i q^{85} +8.25984i q^{86} +24.3521i q^{87} +(2.31871 - 7.79199i) q^{88} -6.42461i q^{89} -4.10959 q^{90} +11.1649i q^{91} -2.98896 q^{92} +1.84014 q^{93} +8.60406 q^{94} +(1.49848 - 4.09323i) q^{95} -5.63600i q^{96} -13.4024i q^{97} +24.8607 q^{98} +(-2.49568 + 8.38668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) $ 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.55769			−1.10145			−0.550726	−	0.834686i	$-0.685649\pi$
$2$	−1.55769			−1.10145			−0.550726	+	0.834686i	$0.685649\pi$
$3$		−	2.37450i		−	1.37092i	−0.728110	−	0.685460i	$-0.759601\pi$
$3$		−	2.37450i		−	1.37092i	0.728110	−	0.685460i	$-0.240399\pi$
$4$	0.426394			0.213197
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$			3.69874i			1.51000i
$7$			4.79166i			1.81108i	0.424266	+	0.905538i	$0.360532\pi$
$7$			4.79166i			1.81108i	−0.424266	+	0.905538i	$0.639468\pi$
$8$	2.45119			0.866626
$9$	−2.63826			−0.879421
$10$	1.55769			0.492584
$11$	0.945954	−	3.17886i	0.285216	−	0.958463i
$11$	0.945954	−	3.17886i	0.285216	−	0.958463i
$12$		−	1.01247i		−	0.292276i
$13$	2.33007			0.646244			0.323122	−	0.946357i	$-0.395268\pi$
$13$	2.33007			0.646244			0.323122	+	0.946357i	$0.395268\pi$
$14$		−	7.46391i		−	1.99481i
$15$			2.37450i			0.613094i
$16$	−4.67098			−1.16774
$17$		−	3.56362i		−	0.864305i	−0.901801	−	0.432153i	$-0.857754\pi$
$17$		−	3.56362i		−	0.864305i	0.901801	−	0.432153i	$-0.142246\pi$
$18$	4.10959			0.968640
$19$	−1.49848	+	4.09323i	−0.343775	+	0.939052i
$19$	−1.49848	+	4.09323i	−0.343775	+	0.939052i
$20$	−0.426394			−0.0953445
$21$	11.3778			2.48284
$22$	−1.47350	+	4.95168i	−0.314152	+	1.05570i
$23$	−7.00987			−1.46166			−0.730829	−	0.682560i	$-0.760866\pi$
$23$	−7.00987			−1.46166			−0.730829	+	0.682560i	$0.760866\pi$
$24$		−	5.82035i		−	1.18807i
$25$	1.00000			0.200000
$26$	−3.62952			−0.711807
$27$		−	0.858944i		−	0.165304i
$28$			2.04313i			0.386116i
$29$	−10.2556			−1.90443			−0.952213	−	0.305435i	$-0.901198\pi$
$29$	−10.2556			−1.90443			−0.952213	+	0.305435i	$0.901198\pi$
$30$		−	3.69874i		−	0.675294i
$31$			0.774958i			0.139187i	0.997575	+	0.0695933i	$0.0221701\pi$
$31$			0.774958i			0.139187i	−0.997575	+	0.0695933i	$0.977830\pi$
$32$	2.37355			0.419588
$33$	−7.54822	−	2.24617i	−1.31398	−	0.391008i
$34$			5.55101i			0.951991i
$35$		−	4.79166i		−	0.809938i
$36$	−1.12494			−0.187490
$37$		−	4.42896i		−	0.728116i	−0.931376	−	0.364058i	$-0.881391\pi$
$37$		−	4.42896i		−	0.728116i	0.931376	−	0.364058i	$-0.118609\pi$
$38$	2.33416	−	6.37598i	0.378651	−	1.03432i
$39$		−	5.53275i		−	0.885949i
$40$	−2.45119			−0.387567
$41$	5.97210			0.932685			0.466343	−	0.884604i	$-0.345571\pi$
$41$	5.97210			0.932685			0.466343	+	0.884604i	$0.345571\pi$
$42$	−17.7231			−2.73473
$43$		−	5.30262i		−	0.808643i	−0.914617	−	0.404321i	$-0.867508\pi$
$43$		−	5.30262i		−	0.808643i	0.914617	−	0.404321i	$-0.132492\pi$
$44$	0.403349	−	1.35545i	0.0608071	−	0.204341i
$45$	2.63826			0.393289
$46$	10.9192			1.60995
$47$	−5.52361			−0.805701			−0.402850	−	0.915266i	$-0.631980\pi$
$47$	−5.52361			−0.805701			−0.402850	+	0.915266i	$0.631980\pi$
$48$			11.0912i			1.60088i
$49$	−15.9600			−2.27999
$50$	−1.55769			−0.220290
$51$	−8.46183			−1.18489
$52$	0.993526			0.137777
$53$		−	7.05543i		−	0.969137i	−0.874753	−	0.484569i	$-0.838977\pi$
$53$		−	7.05543i		−	0.969137i	0.874753	−	0.484569i	$-0.161023\pi$
$54$			1.33797i			0.182074i
$55$	−0.945954	+	3.17886i	−0.127552	+	0.428638i
$56$			11.7453i			1.56953i
$57$	9.71939	+	3.55814i	1.28737	+	0.471287i
$58$	15.9751			2.09763
$59$			4.96331i			0.646168i	0.946370	+	0.323084i	$0.104720\pi$
$59$			4.96331i			0.646168i	−0.946370	+	0.323084i	$0.895280\pi$
$60$			1.01247i			0.130710i
$61$			13.0476i			1.67058i	0.549811	+	0.835289i	$0.314700\pi$
$61$			13.0476i			1.67058i	−0.549811	+	0.835289i	$0.685300\pi$
$62$		−	1.20714i		−	0.153307i
$63$		−	12.6417i		−	1.59270i
$64$	5.64470			0.705588
$65$	−2.33007			−0.289009
$66$	11.7578	+	3.49883i	1.44728	+	0.430677i
$67$		−	11.5913i		−	1.41611i	−0.706159	−	0.708053i	$-0.749574\pi$
$67$		−	11.5913i		−	1.41611i	0.706159	−	0.708053i	$-0.250426\pi$
$68$		−	1.51951i		−	0.184267i
$69$			16.6449i			2.00382i
$70$			7.46391i			0.892108i
$71$			8.09779i			0.961031i	0.876986	+	0.480516i	$0.159550\pi$
$71$			8.09779i			0.961031i	−0.876986	+	0.480516i	$0.840450\pi$
$72$	−6.46688			−0.762129
$73$			16.6572i			1.94958i	0.223121	+	0.974791i	$0.428376\pi$
$73$			16.6572i			1.94958i	−0.223121	+	0.974791i	$0.571624\pi$
$74$			6.89893i			0.801985i
$75$		−	2.37450i		−	0.274184i
$76$	−0.638942	+	1.74533i	−0.0732917	+	0.200203i
$77$	15.2320	+	4.53269i	1.73585	+	0.516547i
$78$			8.61830i			0.975831i
$79$	−14.9450			−1.68144			−0.840720	−	0.541470i	$-0.817868\pi$
$79$	−14.9450			−1.68144			−0.840720	+	0.541470i	$0.817868\pi$
$80$	4.67098			0.522231
$81$	−9.95436			−1.10604
$82$	−9.30267			−1.02731
$83$		−	3.17734i		−	0.348759i	−0.984679	−	0.174379i	$-0.944208\pi$
$83$		−	3.17734i		−	0.348759i	0.984679	−	0.174379i	$-0.0557919\pi$
$84$	4.85142			0.529334
$85$			3.56362i			0.386529i
$86$			8.25984i			0.890681i
$87$			24.3521i			2.61081i
$88$	2.31871	−	7.79199i	0.247175	−	0.830629i
$89$		−	6.42461i		−	0.681008i	−0.940243	−	0.340504i	$-0.889402\pi$
$89$		−	6.42461i		−	0.681008i	0.940243	−	0.340504i	$-0.110598\pi$
$90$	−4.10959			−0.433189
$91$			11.1649i			1.17040i
$92$	−2.98896			−0.311621
$93$	1.84014			0.190814
$94$	8.60406			0.887441
$95$	1.49848	−	4.09323i	0.153741	−	0.419957i
$96$		−	5.63600i		−	0.575222i
$97$		−	13.4024i		−	1.36080i	−0.732839	−	0.680402i	$-0.761805\pi$
$97$		−	13.4024i		−	1.36080i	0.732839	−	0.680402i	$-0.238195\pi$
$98$	24.8607			2.51130
$99$	−2.49568	+	8.38668i	−0.250825	+	0.842893i
$100$	0.426394			0.0426394
$101$			2.05517i			0.204497i	0.994759	+	0.102248i	$0.0326037\pi$
$101$			2.05517i			0.204497i	−0.994759	+	0.102248i	$0.967396\pi$
$102$	13.1809			1.30510
$103$			8.95612i			0.882473i	0.897391	+	0.441236i	$0.145460\pi$
$103$			8.95612i			0.882473i	−0.897391	+	0.441236i	$0.854540\pi$
$104$	5.71143			0.560052
$105$	−11.3778			−1.11036
$106$			10.9902i			1.06746i
$107$	4.35595			0.421106			0.210553	−	0.977582i	$-0.432474\pi$
$107$	4.35595			0.421106			0.210553	+	0.977582i	$0.432474\pi$
$108$		−	0.366248i		−	0.0352423i
$109$	−2.66103			−0.254881			−0.127440	−	0.991846i	$-0.540676\pi$
$109$	−2.66103			−0.254881			−0.127440	+	0.991846i	$0.540676\pi$
$110$	1.47350	−	4.95168i	0.140493	−	0.472124i
$111$	−10.5166			−0.998188
$112$		−	22.3817i		−	2.11487i
$113$		−	1.87733i		−	0.176605i	−0.996094	−	0.0883024i	$-0.971856\pi$
$113$		−	1.87733i		−	0.176605i	0.996094	−	0.0883024i	$-0.0281442\pi$
$114$	−15.1398	−	5.54248i	−1.41797	−	0.519101i
$115$	7.00987			0.653673
$116$	−4.37294			−0.406018
$117$	−6.14733			−0.568321
$118$		−	7.73129i		−	0.711723i
$119$	17.0756			1.56532
$120$			5.82035i			0.531323i
$121$	−9.21034	−	6.01412i	−0.837304	−	0.546738i
$122$		−	20.3241i		−	1.84006i
$123$		−	14.1808i		−	1.27864i
$124$			0.330437i			0.0296741i
$125$	−1.00000			−0.0894427
$126$			19.6918i			1.75428i
$127$	−15.0226			−1.33304			−0.666521	−	0.745487i	$-0.732217\pi$
$127$	−15.0226			−1.33304			−0.666521	+	0.745487i	$0.732217\pi$
$128$	−13.5398			−1.19676
$129$	−12.5911			−1.10858
$130$	3.62952			0.318330
$131$		−	4.44457i		−	0.388324i	−0.980969	−	0.194162i	$-0.937801\pi$
$131$		−	4.44457i		−	0.388324i	0.980969	−	0.194162i	$-0.0621987\pi$
$132$	−3.21851	−	0.957753i	−0.280136	−	0.0833617i
$133$	−19.6134	−	7.18019i	−1.70069	−	0.622602i
$134$			18.0557i			1.55977i
$135$			0.858944i			0.0739261i
$136$		−	8.73511i		−	0.749029i
$137$	−7.73021			−0.660437			−0.330218	−	0.943905i	$-0.607122\pi$
$137$	−7.73021			−0.660437			−0.330218	+	0.943905i	$0.607122\pi$
$138$		−	25.9276i		−	2.20711i
$139$			9.78752i			0.830166i	0.909783	+	0.415083i	$0.136248\pi$
$139$			9.78752i			0.830166i	−0.909783	+	0.415083i	$0.863752\pi$
$140$		−	2.04313i		−	0.172676i
$141$			13.1158i			1.10455i
$142$		−	12.6138i		−	1.05853i
$143$	2.20414	−	7.40696i	0.184319	−	0.619402i
$144$	12.3233			1.02694
$145$	10.2556			0.851685
$146$		−	25.9468i		−	2.14737i
$147$			37.8970i			3.12569i
$148$		−	1.88848i		−	0.155232i
$149$		−	0.678367i		−	0.0555740i	−0.999614	−	0.0277870i	$-0.991154\pi$
$149$		−	0.678367i		−	0.0555740i	0.999614	−	0.0277870i	$-0.00884601\pi$
$150$			3.69874i			0.302001i
$151$	−15.0308			−1.22319			−0.611597	−	0.791170i	$-0.709472\pi$
$151$	−15.0308			−1.22319			−0.611597	+	0.791170i	$0.709472\pi$
$152$	−3.67305	+	10.0333i	−0.297924	+	0.813807i
$153$			9.40177i			0.760088i
$154$	−23.7267	−	7.06051i	−1.91196	−	0.568952i
$155$		−	0.774958i		−	0.0622461i
$156$		−	2.35913i		−	0.188882i
$157$	−2.55743			−0.204105			−0.102053	−	0.994779i	$-0.532541\pi$
$157$	−2.55743			−0.204105			−0.102053	+	0.994779i	$0.532541\pi$
$158$	23.2796			1.85203
$159$	−16.7531			−1.32861
$160$	−2.37355			−0.187645
$161$		−	33.5889i		−	2.64717i
$162$	15.5058			1.21825
$163$	−3.00037			−0.235007			−0.117504	−	0.993072i	$-0.537489\pi$
$163$	−3.00037			−0.235007			−0.117504	+	0.993072i	$0.537489\pi$
$164$	2.54647			0.198846
$165$	7.54822	+	2.24617i	0.587628	+	0.174864i
$166$			4.94931i			0.384141i
$167$	−12.0559			−0.932912			−0.466456	−	0.884544i	$-0.654469\pi$
$167$	−12.0559			−0.932912			−0.466456	+	0.884544i	$0.654469\pi$
$168$	27.8891			2.15169
$169$	−7.57079			−0.582368
$170$		−	5.55101i		−	0.425743i
$171$	3.95338	−	10.7990i	0.302323	−	0.825822i
$172$		−	2.26101i		−	0.172400i
$173$	−18.5313			−1.40891			−0.704454	−	0.709749i	$-0.748808\pi$
$173$	−18.5313			−1.40891			−0.704454	+	0.709749i	$0.748808\pi$
$174$		−	37.9329i		−	2.87569i
$175$			4.79166i			0.362215i
$176$	−4.41853	+	14.8484i	−0.333059	+	1.11924i
$177$	11.7854			0.885845
$178$			10.0075i			0.750097i
$179$			21.2456i			1.58797i	0.607935	+	0.793987i	$0.291998\pi$
$179$			21.2456i			1.58797i	−0.607935	+	0.793987i	$0.708002\pi$
$180$	1.12494			0.0838480
$181$		−	10.9420i		−	0.813316i	−0.913580	−	0.406658i	$-0.866694\pi$
$181$		−	10.9420i		−	0.813316i	0.913580	−	0.406658i	$-0.133306\pi$
$182$		−	17.3914i		−	1.28914i
$183$	30.9816			2.29023
$184$	−17.1825			−1.26671
$185$			4.42896i			0.325623i
$186$	−2.86636			−0.210172
$187$	−11.3283	−	3.37102i	−0.828405	−	0.246514i
$188$	−2.35523			−0.171773
$189$	4.11576			0.299378
$190$	−2.33416	+	6.37598i	−0.169338	+	0.462562i
$191$	24.3369			1.76095			0.880477	−	0.474089i	$-0.157223\pi$
$191$	24.3369			1.76095			0.880477	+	0.474089i	$0.157223\pi$
$192$		−	13.4034i		−	0.967304i
$193$	5.75745			0.414430			0.207215	−	0.978295i	$-0.433560\pi$
$193$	5.75745			0.414430			0.207215	+	0.978295i	$0.433560\pi$
$194$			20.8767i			1.49886i
$195$			5.53275i			0.396209i
$196$	−6.80523			−0.486088
$197$		−	3.04673i		−	0.217071i	−0.994093	−	0.108535i	$-0.965384\pi$
$197$		−	3.04673i		−	0.217071i	0.994093	−	0.108535i	$-0.0346161\pi$
$198$	3.88749	−	13.0638i	0.276272	−	0.928406i
$199$	8.12114			0.575692			0.287846	−	0.957677i	$-0.407061\pi$
$199$	8.12114			0.575692			0.287846	+	0.957677i	$0.407061\pi$
$200$	2.45119			0.173325
$201$	−27.5237			−1.94137
$202$		−	3.20131i		−	0.225244i
$203$		−	49.1415i		−	3.44906i
$204$	−3.60807			−0.252615
$205$	−5.97210			−0.417110
$206$		−	13.9508i		−	0.972002i
$207$	18.4939			1.28541
$208$	−10.8837			−0.754648
$209$	11.5943	+	8.63547i	0.801997	+	0.597328i
$210$	17.7231			1.22301
$211$	1.49542			0.102949			0.0514744	−	0.998674i	$-0.483608\pi$
$211$	1.49542			0.102949			0.0514744	+	0.998674i	$0.483608\pi$
$212$		−	3.00839i		−	0.206617i
$213$	19.2282			1.31750
$214$	−6.78521			−0.463828
$215$			5.30262i			0.361636i
$216$		−	2.10543i		−	0.143257i
$217$	−3.71333			−0.252077
$218$	4.14506			0.280739
$219$	39.5526			2.67272
$220$	−0.403349	+	1.35545i	−0.0271938	+	0.0913842i
$221$		−	8.30348i		−	0.558552i
$222$	16.3815			1.09946
$223$			10.0532i			0.673211i	0.941646	+	0.336606i	$0.109279\pi$
$223$			10.0532i			0.673211i	−0.941646	+	0.336606i	$0.890721\pi$
$224$			11.3732i			0.759906i
$225$	−2.63826			−0.175884
$226$			2.92430i			0.194522i
$227$	4.82225			0.320064			0.160032	−	0.987112i	$-0.448840\pi$
$227$	4.82225			0.320064			0.160032	+	0.987112i	$0.448840\pi$
$228$	4.14429	+	1.51717i	0.274462	+	0.100477i
$229$	2.79292			0.184561			0.0922805	−	0.995733i	$-0.470584\pi$
$229$	2.79292			0.184561			0.0922805	+	0.995733i	$0.470584\pi$
$230$	−10.9192			−0.719990
$231$	10.7629	−	36.1685i	0.708145	−	2.37971i
$232$	−25.1385			−1.65042
$233$			4.28122i			0.280472i	0.990118	+	0.140236i	$0.0447862\pi$
$233$			4.28122i			0.280472i	−0.990118	+	0.140236i	$0.955214\pi$
$234$	9.57563			0.625978
$235$	5.52361			0.360320
$236$			2.11632i			0.137761i
$237$			35.4869i			2.30512i
$238$	−26.5985			−1.72413
$239$		−	12.1857i		−	0.788228i	−0.919062	−	0.394114i	$-0.871051\pi$
$239$		−	12.1857i		−	0.788228i	0.919062	−	0.394114i	$-0.128949\pi$
$240$		−	11.0912i		−	0.715937i
$241$	−20.8561			−1.34346			−0.671729	−	0.740797i	$-0.734448\pi$
$241$	−20.8561			−1.34346			−0.671729	+	0.740797i	$0.734448\pi$
$242$	14.3468	+	9.36812i	0.922250	+	0.602206i
$243$			21.0598i			1.35099i
$244$			5.56343i			0.356162i
$245$	15.9600			1.01964
$246$			22.0892i			1.40836i
$247$	−3.49156	+	9.53751i	−0.222162	+	0.606857i
$248$			1.89957i			0.120623i
$249$	−7.54461			−0.478120
$250$	1.55769			0.0985169
$251$	−18.3727			−1.15967			−0.579836	−	0.814733i	$-0.696884\pi$
$251$	−18.3727			−1.15967			−0.579836	+	0.814733i	$0.696884\pi$
$252$		−	5.39032i		−	0.339558i
$253$	−6.63101	+	22.2834i	−0.416888	+	1.40095i
$254$	23.4005			1.46828
$255$	8.46183			0.529900
$256$	9.80136			0.612585
$257$		−	22.9270i		−	1.43015i	−0.699048	−	0.715074i	$-0.746393\pi$
$257$		−	22.9270i		−	1.43015i	0.699048	−	0.715074i	$-0.253607\pi$
$258$	19.6130			1.22105
$259$	21.2220			1.31867
$260$	−0.993526			−0.0616159
$261$	27.0571			1.67479
$262$			6.92326i			0.427720i
$263$			12.1950i			0.751976i	0.926624	+	0.375988i	$0.122697\pi$
$263$			12.1950i			0.751976i	−0.926624	+	0.375988i	$0.877303\pi$
$264$	−18.5021	−	5.50579i	−1.13873	−	0.338858i
$265$			7.05543i			0.433411i
$266$	30.5515	+	11.1845i	1.87323	+	0.685766i
$267$	−15.2553			−0.933607
$268$		−	4.94247i		−	0.301909i
$269$		−	12.1267i		−	0.739380i	−0.929155	−	0.369690i	$-0.879464\pi$
$269$		−	12.1267i		−	0.739380i	0.929155	−	0.369690i	$-0.120536\pi$
$270$		−	1.33797i		−	0.0814261i
$271$		−	5.37311i		−	0.326393i	−0.986594	−	0.163197i	$-0.947819\pi$
$271$		−	5.37311i		−	0.326393i	0.986594	−	0.163197i	$-0.0521805\pi$
$272$			16.6456i			1.00929i
$273$	26.5110			1.60452
$274$	12.0413			0.727439
$275$	0.945954	−	3.17886i	0.0570432	−	0.191693i
$276$			7.09730i			0.427207i
$277$		−	13.1535i		−	0.790317i	−0.918613	−	0.395158i	$-0.870690\pi$
$277$		−	13.1535i		−	0.790317i	0.918613	−	0.395158i	$-0.129310\pi$
$278$		−	15.2459i		−	0.914388i
$279$		−	2.04454i		−	0.122404i
$280$		−	11.7453i		−	0.701913i
$281$	−1.40018			−0.0835279			−0.0417640	−	0.999128i	$-0.513298\pi$
$281$	−1.40018			−0.0835279			−0.0417640	+	0.999128i	$0.513298\pi$
$282$		−	20.4304i		−	1.21661i
$283$		−	10.8385i		−	0.644283i	−0.946691	−	0.322142i	$-0.895597\pi$
$283$		−	10.8385i		−	0.644283i	0.946691	−	0.322142i	$-0.104403\pi$
$284$			3.45285i			0.204889i
$285$	−9.71939	−	3.55814i	−0.575727	−	0.210766i
$286$	−3.43336	+	11.5377i	−0.203019	+	0.682241i
$287$			28.6162i			1.68916i
$288$	−6.26205			−0.368995
$289$	4.30060			0.252977
$290$	−15.9751			−0.938090
$291$	−31.8239			−1.86555
$292$			7.10254i			0.415645i
$293$	12.0586			0.704470			0.352235	−	0.935912i	$-0.385422\pi$
$293$	12.0586			0.704470			0.352235	+	0.935912i	$0.385422\pi$
$294$		−	59.0317i		−	3.44280i
$295$		−	4.96331i		−	0.288975i
$296$		−	10.8562i		−	0.631004i
$297$	−2.73047	−	0.812522i	−0.158438	−	0.0471473i
$298$			1.05668i			0.0612121i
$299$	−16.3335			−0.944588
$300$		−	1.01247i		−	0.0584552i
$301$	25.4083			1.46451
$302$	23.4134			1.34729
$303$	4.88000			0.280349
$304$	6.99936	−	19.1194i	0.401441	−	1.09657i
$305$		−	13.0476i		−	0.747105i
$306$		−	14.6450i		−	0.837201i
$307$	24.9198			1.42225			0.711125	−	0.703065i	$-0.248186\pi$
$307$	24.9198			1.42225			0.711125	+	0.703065i	$0.248186\pi$
$308$	6.49484	+	1.93271i	0.370078	+	0.110126i
$309$	21.2663			1.20980
$310$			1.20714i			0.0685611i
$311$	−20.8950			−1.18484			−0.592422	−	0.805627i	$-0.701828\pi$
$311$	−20.8950			−1.18484			−0.592422	+	0.805627i	$0.701828\pi$
$312$		−	13.5618i		−	0.767787i
$313$	20.4238			1.15442			0.577210	−	0.816596i	$-0.304141\pi$
$313$	20.4238			1.15442			0.577210	+	0.816596i	$0.304141\pi$
$314$	3.98368			0.224812
$315$			12.6417i			0.712276i
$316$	−6.37244			−0.358478
$317$			16.8709i			0.947562i	0.880643	+	0.473781i	$0.157111\pi$
$317$			16.8709i			0.947562i	−0.880643	+	0.473781i	$0.842889\pi$
$318$	26.0962			1.46340
$319$	−9.70137	+	32.6013i	−0.543172	+	1.82532i
$320$	−5.64470			−0.315548
$321$		−	10.3432i		−	0.577302i
$322$			52.3210i			2.91573i
$323$	14.5867	+	5.34001i	0.811628	+	0.297126i
$324$	−4.24447			−0.235804
$325$	2.33007			0.129249
$326$	4.67364			0.258849
$327$			6.31863i			0.349421i
$328$	14.6387			0.808289
$329$		−	26.4672i		−	1.45918i
$330$	−11.7578	−	3.49883i	−0.647244	−	0.192604i
$331$		−	1.59178i		−	0.0874920i	−0.999043	−	0.0437460i	$-0.986071\pi$
$331$		−	1.59178i		−	0.0874920i	0.999043	−	0.0437460i	$-0.0139292\pi$
$332$		−	1.35480i		−	0.0743542i
$333$			11.6848i			0.640321i
$334$	18.7793			1.02756
$335$			11.5913i			0.633302i
$336$	−53.1454			−2.89932
$337$	−16.1059			−0.877343			−0.438672	−	0.898647i	$-0.644551\pi$
$337$	−16.1059			−0.877343			−0.438672	+	0.898647i	$0.644551\pi$
$338$	11.7929			0.641451
$339$	−4.45774			−0.242111
$340$			1.51951i			0.0824068i
$341$	2.46348	+	0.733074i	0.133405	+	0.0396982i
$342$	−6.15814	+	16.8215i	−0.332994	+	0.909604i
$343$		−	42.9331i		−	2.31817i
$344$		−	12.9977i		−	0.700791i
$345$		−	16.6449i		−	0.896134i
$346$	28.8660			1.55185
$347$		−	3.60273i		−	0.193405i	−0.995313	−	0.0967023i	$-0.969171\pi$
$347$		−	3.60273i		−	0.193405i	0.995313	−	0.0967023i	$-0.0308295\pi$
$348$			10.3836i			0.556617i
$349$		−	22.0968i		−	1.18282i	−0.806373	−	0.591408i	$-0.798572\pi$
$349$		−	22.0968i		−	1.18282i	0.806373	−	0.591408i	$-0.201428\pi$
$350$		−	7.46391i		−	0.398963i
$351$		−	2.00140i		−	0.106827i
$352$	2.24527	−	7.54519i	0.119673	−	0.402160i
$353$	−4.56996			−0.243235			−0.121617	−	0.992577i	$-0.538808\pi$
$353$	−4.56996			−0.243235			−0.121617	+	0.992577i	$0.538808\pi$
$354$	−18.3580			−0.975715
$355$		−	8.09779i		−	0.429786i
$356$		−	2.73941i		−	0.145189i
$357$		−	40.5462i		−	2.14593i
$358$		−	33.0941i		−	1.74908i
$359$			31.7072i			1.67344i	0.547629	+	0.836721i	$0.315531\pi$
$359$			31.7072i			1.67344i	−0.547629	+	0.836721i	$0.684469\pi$
$360$	6.46688			0.340835
$361$	−14.5091	−	12.2672i	−0.763638	−	0.645645i
$362$			17.0443i			0.895829i
$363$	−14.2805	+	21.8700i	−0.749534	+	1.14788i
$364$			4.76063i			0.249525i
$365$		−	16.6572i		−	0.871879i
$366$	−48.2597			−2.52258
$367$	24.1129			1.25868			0.629342	−	0.777129i	$-0.283325\pi$
$367$	24.1129			1.25868			0.629342	+	0.777129i	$0.283325\pi$
$368$	32.7429			1.70684
$369$	−15.7560			−0.820223
$370$		−	6.89893i		−	0.358658i
$371$	33.8072			1.75518
$372$	0.784624			0.0406809
$373$	35.5048			1.83837			0.919183	−	0.393830i	$-0.128850\pi$
$373$	35.5048			1.83837			0.919183	+	0.393830i	$0.128850\pi$
$374$	17.6459	+	5.25100i	0.912448	+	0.271523i
$375$			2.37450i			0.122619i
$376$	−13.5394			−0.698241
$377$	−23.8963			−1.23072
$378$	−6.41108			−0.329750
$379$			5.82050i			0.298979i	0.988763	+	0.149490i	$0.0477630\pi$
$379$			5.82050i			0.298979i	−0.988763	+	0.149490i	$0.952237\pi$
$380$	0.638942	−	1.74533i	0.0327770	−	0.0895335i
$381$			35.6712i			1.82749i
$382$	−37.9092			−1.93961
$383$			11.8580i			0.605917i	0.953004	+	0.302959i	$0.0979744\pi$
$383$			11.8580i			0.605917i	−0.953004	+	0.302959i	$0.902026\pi$
$384$			32.1503i			1.64066i
$385$	−15.2320	−	4.53269i	−0.776295	−	0.231007i
$386$	−8.96831			−0.456475
$387$			13.9897i			0.711137i
$388$		−	5.71468i		−	0.290119i
$389$	−20.9613			−1.06278			−0.531389	−	0.847128i	$-0.678330\pi$
$389$	−20.9613			−1.06278			−0.531389	+	0.847128i	$0.678330\pi$
$390$		−	8.61830i		−	0.436405i
$391$			24.9805i			1.26332i
$392$	−39.1209			−1.97590
$393$	−10.5536			−0.532361
$394$			4.74586i			0.239093i
$395$	14.9450			0.751963
$396$	−1.06414	+	3.57603i	−0.0534751	+	0.179702i
$397$	27.0111			1.35565			0.677824	−	0.735225i	$-0.262923\pi$
$397$	27.0111			1.35565			0.677824	+	0.735225i	$0.262923\pi$
$398$	−12.6502			−0.634097
$399$	−17.0494	+	46.5720i	−0.853537	+	2.33152i
$400$	−4.67098			−0.233549
$401$		−	27.4962i		−	1.37310i	−0.727085	−	0.686548i	$-0.759125\pi$
$401$		−	27.4962i		−	1.37310i	0.727085	−	0.686548i	$-0.240875\pi$
$402$	42.8733			2.13832
$403$			1.80570i			0.0899485i
$404$			0.876311i			0.0435981i
$405$	9.95436			0.494636
$406$			76.5472i			3.79897i
$407$	−14.0790	−	4.18959i	−0.697872	−	0.207670i
$408$	−20.7415			−1.02686
$409$	19.5754			0.967942			0.483971	−	0.875084i	$-0.339194\pi$
$409$	19.5754			0.967942			0.483971	+	0.875084i	$0.339194\pi$
$410$	9.30267			0.459426
$411$			18.3554i			0.905406i
$412$			3.81883i			0.188140i
$413$	−23.7825			−1.17026
$414$	−28.8077			−1.41582
$415$			3.17734i			0.155970i
$416$	5.53053			0.271156
$417$	23.2405			1.13809
$418$	−18.0604	−	13.4514i	−0.883361	−	0.657928i
$419$	−10.9574			−0.535304			−0.267652	−	0.963516i	$-0.586248\pi$
$419$	−10.9574			−0.535304			−0.267652	+	0.963516i	$0.586248\pi$
$420$	−4.85142			−0.236725
$421$			29.4703i			1.43629i	0.695892	+	0.718146i	$0.255009\pi$
$421$			29.4703i			1.43629i	−0.695892	+	0.718146i	$0.744991\pi$
$422$	−2.32940			−0.113393
$423$	14.5727			0.708550
$424$		−	17.2942i		−	0.839880i
$425$		−	3.56362i		−	0.172861i
$426$	−29.9516			−1.45116
$427$	−62.5197			−3.02554
$428$	1.85735			0.0897784
$429$	−17.5879	−	5.23373i	−0.849150	−	0.252687i
$430$		−	8.25984i		−	0.398325i
$431$	19.2290			0.926227			0.463113	−	0.886299i	$-0.346732\pi$
$431$	19.2290			0.926227			0.463113	+	0.886299i	$0.346732\pi$
$432$			4.01211i			0.193033i
$433$		−	22.1886i		−	1.06631i	−0.846016	−	0.533157i	$-0.821005\pi$
$433$		−	22.1886i		−	1.06631i	0.846016	−	0.533157i	$-0.178995\pi$
$434$	5.78421			0.277651
$435$		−	24.3521i		−	1.16759i
$436$	−1.13465			−0.0543397
$437$	10.5041	−	28.6930i	0.502481	−	1.37257i
$438$	−61.6107			−2.94387
$439$	−12.1369			−0.579261			−0.289631	−	0.957138i	$-0.593532\pi$
$439$	−12.1369			−0.579261			−0.289631	+	0.957138i	$0.593532\pi$
$440$	−2.31871	+	7.79199i	−0.110540	+	0.371469i
$441$	42.1066			2.00508
$442$			12.9342i			0.615219i
$443$	8.12930			0.386235			0.193117	−	0.981176i	$-0.438140\pi$
$443$	8.12930			0.386235			0.193117	+	0.981176i	$0.438140\pi$
$444$	−4.48420			−0.212811
$445$			6.42461i			0.304556i
$446$		−	15.6597i		−	0.741510i
$447$	−1.61078			−0.0761875
$448$			27.0475i			1.27787i
$449$		−	3.60541i		−	0.170150i	−0.996375	−	0.0850749i	$-0.972887\pi$
$449$		−	3.60541i		−	0.170150i	0.996375	−	0.0850749i	$-0.0271130\pi$
$450$	4.10959			0.193728
$451$	5.64933	−	18.9845i	0.266017	−	0.893945i
$452$		−	0.800484i		−	0.0376516i
$453$			35.6908i			1.67690i
$454$	−7.51157			−0.352535
$455$		−	11.1649i		−	0.523418i
$456$	23.8241	+	8.72168i	1.11566	+	0.408430i
$457$		−	36.0371i		−	1.68575i	−0.538113	−	0.842873i	$-0.680863\pi$
$457$		−	36.0371i		−	1.68575i	0.538113	−	0.842873i	$-0.319137\pi$
$458$	−4.35049			−0.203285
$459$	−3.06095			−0.142873
$460$	2.98896			0.139361
$461$			4.38022i			0.204007i	0.994784	+	0.102004i	$0.0325253\pi$
$461$			4.38022i			0.204007i	−0.994784	+	0.102004i	$0.967475\pi$
$462$	−16.7652	+	56.3392i	−0.779988	+	2.62114i
$463$	−33.3438			−1.54962			−0.774809	−	0.632195i	$-0.782154\pi$
$463$	−33.3438			−1.54962			−0.774809	+	0.632195i	$0.782154\pi$
$464$	47.9039			2.22388
$465$	−1.84014			−0.0853344
$466$		−	6.66881i		−	0.308927i
$467$	23.1322			1.07043			0.535216	−	0.844715i	$-0.320230\pi$
$467$	23.1322			1.07043			0.535216	+	0.844715i	$0.320230\pi$
$468$	−2.62118			−0.121164
$469$	55.5417			2.56468
$470$	−8.60406			−0.396876
$471$			6.07263i			0.279812i
$472$			12.1660i			0.559986i
$473$	−16.8563	−	5.01604i	−0.775054	−	0.230638i
$474$		−	55.2775i		−	2.53898i
$475$	−1.49848	+	4.09323i	−0.0687549	+	0.187810i
$476$	7.28095			0.333722
$477$			18.6141i			0.852280i
$478$			18.9815i			0.868196i
$479$		−	3.68507i		−	0.168375i	−0.996450	−	0.0841876i	$-0.973171\pi$
$479$		−	3.68507i		−	0.168375i	0.996450	−	0.0841876i	$-0.0268295\pi$
$480$			5.63600i			0.257247i
$481$		−	10.3198i		−	0.470541i
$482$	32.4873			1.47975
$483$	−79.7569			−3.62906
$484$	−3.92723	−	2.56438i	−0.178511	−	0.116563i
$485$			13.4024i			0.608570i
$486$		−	32.8046i		−	1.48805i
$487$			17.7818i			0.805771i	0.915250	+	0.402885i	$0.131993\pi$
$487$			17.7818i			0.805771i	−0.915250	+	0.402885i	$0.868007\pi$
$488$			31.9822i			1.44777i
$489$			7.12438i			0.322176i
$490$	−24.8607			−1.12309
$491$			32.9589i			1.48742i	0.668505	+	0.743708i	$0.266935\pi$
$491$			32.9589i			1.48742i	−0.668505	+	0.743708i	$0.733065\pi$
$492$		−	6.04659i		−	0.272601i
$493$			36.5472i			1.64600i
$494$	5.43876	−	14.8565i	0.244701	−	0.668424i
$495$	2.49568	−	8.38668i	0.112172	−	0.376953i
$496$		−	3.61981i		−	0.162534i
$497$	−38.8018			−1.74050
$498$	11.7521			0.526626
$499$	15.4731			0.692673			0.346336	−	0.938110i	$-0.387426\pi$
$499$	15.4731			0.692673			0.346336	+	0.938110i	$0.387426\pi$
$500$	−0.426394			−0.0190689
$501$			28.6267i			1.27895i
$502$	28.6189			1.27732
$503$		−	18.3367i		−	0.817593i	−0.912626	−	0.408796i	$-0.865949\pi$
$503$		−	18.3367i		−	0.817593i	0.912626	−	0.408796i	$-0.134051\pi$
$504$		−	30.9871i		−	1.38027i
$505$		−	2.05517i		−	0.0914538i
$506$	10.3291	−	34.7106i	0.459182	−	1.54307i
$507$			17.9769i			0.798380i
$508$	−6.40555			−0.284200
$509$		−	2.58425i		−	0.114545i	−0.998359	−	0.0572725i	$-0.981760\pi$
$509$		−	2.58425i		−	0.114545i	0.998359	−	0.0572725i	$-0.0182404\pi$
$510$	−13.1809			−0.583660
$511$	−79.8157			−3.53084
$512$	11.8121			0.522026
$513$	3.51586	+	1.28711i	0.155229	+	0.0568273i
$514$			35.7132i			1.57524i
$515$		−	8.95612i		−	0.394654i
$516$	−5.36876			−0.236347
$517$	−5.22508	+	17.5588i	−0.229799	+	0.772235i
$518$	−33.0573			−1.45245
$519$			44.0026i			1.93150i
$520$	−5.71143			−0.250463
$521$		−	9.40216i		−	0.411916i	−0.978561	−	0.205958i	$-0.933969\pi$
$521$		−	9.40216i		−	0.411916i	0.978561	−	0.205958i	$-0.0660311\pi$
$522$	−42.1465			−1.84470
$523$	−42.3010			−1.84969			−0.924846	−	0.380341i	$-0.875807\pi$
$523$	−42.3010			−1.84969			−0.924846	+	0.380341i	$0.875807\pi$
$524$		−	1.89514i		−	0.0827894i
$525$	11.3778			0.496568
$526$		−	18.9960i		−	0.828266i
$527$	2.76166			0.120300
$528$	35.2576	+	10.4918i	1.53439	+	0.456597i
$529$	26.1382			1.13644
$530$		−	10.9902i		−	0.477382i
$531$		−	13.0945i		−	0.568254i
$532$	−8.36302	−	3.06159i	−0.362583	−	0.132737i
$533$	13.9154			0.602743
$534$	23.7630			1.02832
$535$	−4.35595			−0.188324
$536$		−	28.4125i		−	1.22723i
$537$	50.4478			2.17698
$538$			18.8897i			0.814391i
$539$	−15.0974	+	50.7345i	−0.650291	+	2.18529i
$540$			0.366248i			0.0157608i
$541$			16.8647i			0.725071i	0.931970	+	0.362536i	$0.118089\pi$
$541$			16.8647i			0.725071i	−0.931970	+	0.362536i	$0.881911\pi$
$542$			8.36964i			0.359507i
$543$	−25.9819			−1.11499
$544$		−	8.45843i		−	0.362652i
$545$	2.66103			0.113986
$546$	−41.2959			−1.76730
$547$	−22.4549			−0.960103			−0.480052	−	0.877240i	$-0.659382\pi$
$547$	−22.4549			−0.960103			−0.480052	+	0.877240i	$0.659382\pi$
$548$	−3.29611			−0.140803
$549$		−	34.4231i		−	1.46914i
$550$	−1.47350	+	4.95168i	−0.0628303	+	0.211140i
$551$	15.3679	−	41.9788i	0.654693	−	1.78836i
$552$			40.7999i			1.73656i
$553$		−	71.6111i		−	3.04522i
$554$			20.4890i			0.870496i
$555$	10.5166			0.446403
$556$			4.17333i			0.176989i
$557$		−	7.23585i		−	0.306593i	−0.988180	−	0.153296i	$-0.951011\pi$
$557$		−	7.23585i		−	0.306593i	0.988180	−	0.153296i	$-0.0489889\pi$
$558$			3.18476i			0.134822i
$559$		−	12.3555i		−	0.522581i
$560$			22.3817i			0.945800i
$561$	−8.00450	+	26.8990i	−0.337950	+	1.13568i
$562$	2.18105			0.0920020
$563$	−10.7575			−0.453376			−0.226688	−	0.973967i	$-0.572790\pi$
$563$	−10.7575			−0.453376			−0.226688	+	0.973967i	$0.572790\pi$
$564$			5.59250i			0.235487i
$565$			1.87733i			0.0789801i
$566$			16.8830i			0.709647i
$567$		−	47.6978i		−	2.00312i
$568$			19.8492i			0.832855i
$569$	−8.63805			−0.362126			−0.181063	−	0.983472i	$-0.557954\pi$
$569$	−8.63805			−0.362126			−0.181063	+	0.983472i	$0.557954\pi$
$570$	15.1398	+	5.54248i	0.634136	+	0.232149i
$571$		−	6.75592i		−	0.282726i	−0.989958	−	0.141363i	$-0.954851\pi$
$571$		−	6.75592i		−	0.282726i	0.989958	−	0.141363i	$-0.0451485\pi$
$572$	0.939830	−	3.15828i	0.0392963	−	0.132054i
$573$		−	57.7879i		−	2.41413i
$574$		−	44.5752i		−	1.86053i
$575$	−7.00987			−0.292332
$576$	−14.8922			−0.620509
$577$	8.40911			0.350076			0.175038	−	0.984562i	$-0.443995\pi$
$577$	8.40911			0.350076			0.175038	+	0.984562i	$0.443995\pi$
$578$	−6.69900			−0.278642
$579$		−	13.6711i		−	0.568150i
$580$	4.37294			0.181577
$581$	15.2247			0.631628
$582$	49.5718			2.05482
$583$	−22.4282	−	6.67411i	−0.928883	−	0.276413i
$584$			40.8300i			1.68956i
$585$	6.14733			0.254161
$586$	−18.7835			−0.775940
$587$	29.7963			1.22982			0.614911	−	0.788596i	$-0.289192\pi$
$587$	29.7963			1.22982			0.614911	+	0.788596i	$0.289192\pi$
$588$			16.1590i			0.666387i
$589$	−3.17208	−	1.16126i	−0.130703	−	0.0478488i
$590$			7.73129i			0.318292i
$591$	−7.23448			−0.297587
$592$			20.6875i			0.850253i
$593$		−	6.04800i		−	0.248362i	−0.992260	−	0.124181i	$-0.960370\pi$
$593$		−	6.04800i		−	0.248362i	0.992260	−	0.124181i	$-0.0396303\pi$
$594$	4.25321	+	1.26566i	0.174512	+	0.0519305i
$595$	−17.0756			−0.700033
$596$		−	0.289251i		−	0.0118482i
$597$		−	19.2837i		−	0.789228i
$598$	25.4424			1.04042
$599$		−	26.7559i		−	1.09322i	−0.837388	−	0.546609i	$-0.815919\pi$
$599$		−	26.7559i		−	1.09322i	0.837388	−	0.546609i	$-0.184081\pi$
$600$		−	5.82035i		−	0.237615i
$601$	17.1651			0.700177			0.350089	−	0.936717i	$-0.386151\pi$
$601$	17.1651			0.700177			0.350089	+	0.936717i	$0.386151\pi$
$602$	−39.5783			−1.61309
$603$			30.5810i			1.24535i
$604$	−6.40906			−0.260781
$605$	9.21034	+	6.01412i	0.374454	+	0.244509i
$606$	−7.60152			−0.308791
$607$	−19.3790			−0.786569			−0.393285	−	0.919417i	$-0.628661\pi$
$607$	−19.3790			−0.786569			−0.393285	+	0.919417i	$0.628661\pi$
$608$	−3.55671	+	9.71549i	−0.144244	+	0.394015i
$609$	−116.687			−4.72838
$610$			20.3241i			0.822900i
$611$	−12.8704			−0.520680
$612$			4.00886i			0.162048i
$613$		−	37.8266i		−	1.52780i	−0.645334	−	0.763900i	$-0.723282\pi$
$613$		−	37.8266i		−	1.52780i	0.645334	−	0.763900i	$-0.276718\pi$
$614$	−38.8174			−1.56654
$615$			14.1808i			0.571824i
$616$	37.3365	+	11.1105i	1.50433	+	0.447653i
$617$	3.95293			0.159139			0.0795694	−	0.996829i	$-0.474645\pi$
$617$	3.95293			0.159139			0.0795694	+	0.996829i	$0.474645\pi$
$618$	−33.1263			−1.33254
$619$	−2.22273			−0.0893392			−0.0446696	−	0.999002i	$-0.514224\pi$
$619$	−2.22273			−0.0893392			−0.0446696	+	0.999002i	$0.514224\pi$
$620$		−	0.330437i		−	0.0132707i
$621$			6.02108i			0.241618i
$622$	32.5479			1.30505
$623$	30.7845			1.23336
$624$			25.8433i			1.03456i
$625$	1.00000			0.0400000
$626$	−31.8139			−1.27154
$627$	20.5049	−	27.5308i	0.818889	−	1.09947i
$628$	−1.09047			−0.0435146
$629$	−15.7831			−0.629314
$630$		−	19.6918i		−	0.784538i
$631$	40.2236			1.60128			0.800638	−	0.599149i	$-0.204494\pi$
$631$	40.2236			1.60128			0.800638	+	0.599149i	$0.204494\pi$
$632$	−36.6329			−1.45718
$633$		−	3.55087i		−	0.141135i
$634$		−	26.2796i		−	1.04369i
$635$	15.0226			0.596154
$636$	−7.14343			−0.283255
$637$	−37.1878			−1.47343
$638$	15.1117	−	50.7827i	0.598278	−	2.01050i
$639$		−	21.3641i		−	0.845151i
$640$	13.5398			0.535207
$641$		−	2.21257i		−	0.0873913i	−0.999045	−	0.0436956i	$-0.986087\pi$
$641$		−	2.21257i		−	0.0873913i	0.999045	−	0.0436956i	$-0.0139132\pi$
$642$			16.1115i			0.635871i
$643$	−14.5219			−0.572688			−0.286344	−	0.958127i	$-0.592440\pi$
$643$	−14.5219			−0.572688			−0.286344	+	0.958127i	$0.592440\pi$
$644$		−	14.3221i		−	0.564369i
$645$	12.5911			0.495774
$646$	−22.7216	−	8.31807i	−0.893969	−	0.327270i
$647$	36.4241			1.43198			0.715989	−	0.698112i	$-0.245976\pi$
$647$	36.4241			1.43198			0.715989	+	0.698112i	$0.245976\pi$
$648$	−24.4000			−0.958523
$649$	15.7777	+	4.69506i	0.619328	+	0.184297i
$650$	−3.62952			−0.142361
$651$			8.81731i			0.345578i
$652$	−1.27934			−0.0501028
$653$	1.67268			0.0654571			0.0327285	−	0.999464i	$-0.489580\pi$
$653$	1.67268			0.0654571			0.0327285	+	0.999464i	$0.489580\pi$
$654$		−	9.84245i		−	0.384870i
$655$			4.44457i			0.173664i
$656$	−27.8955			−1.08914
$657$		−	43.9462i		−	1.71450i
$658$			41.2277i			1.60722i
$659$	−24.5033			−0.954513			−0.477256	−	0.878764i	$-0.658369\pi$
$659$	−24.5033			−0.954513			−0.477256	+	0.878764i	$0.658369\pi$
$660$	3.21851	+	0.957753i	0.125280	+	0.0372805i
$661$			21.0244i			0.817754i	0.912589	+	0.408877i	$0.134080\pi$
$661$			21.0244i			0.817754i	−0.912589	+	0.408877i	$0.865920\pi$
$662$			2.47949i			0.0963682i
$663$	−19.7166			−0.765730
$664$		−	7.78826i		−	0.302243i
$665$	19.6134	+	7.18019i	0.760574	+	0.278436i
$666$		−	18.2012i		−	0.705282i
$667$	71.8907			2.78362
$668$	−5.14055			−0.198894
$669$	23.8713			0.922919
$670$		−	18.0557i		−	0.697552i
$671$	41.4766	+	12.3425i	1.60119	+	0.476475i
$672$	27.0058			1.04177
$673$	31.0885			1.19837			0.599187	−	0.800609i	$-0.295491\pi$
$673$	31.0885			1.19837			0.599187	+	0.800609i	$0.295491\pi$
$674$	25.0879			0.966352
$675$		−	0.858944i		−	0.0330608i
$676$	−3.22814			−0.124159
$677$	−6.99489			−0.268835			−0.134418	−	0.990925i	$-0.542916\pi$
$677$	−6.99489			−0.268835			−0.134418	+	0.990925i	$0.542916\pi$
$678$	6.94376			0.266674
$679$	64.2195			2.46452
$680$			8.73511i			0.334976i
$681$		−	11.4505i		−	0.438782i
$682$	−3.83734	−	1.14190i	−0.146939	−	0.0437257i
$683$			20.3498i			0.778663i	0.921098	+	0.389332i	$0.127294\pi$
$683$			20.3498i			0.778663i	−0.921098	+	0.389332i	$0.872706\pi$
$684$	1.68570	−	4.60464i	0.0644542	−	0.176063i
$685$	7.73021			0.295356
$686$			66.8763i			2.55335i
$687$		−	6.63179i		−	0.253018i
$688$			24.7684i			0.944287i
$689$		−	16.4396i		−	0.626300i
$690$			25.9276i			0.987049i
$691$	−32.6827			−1.24331			−0.621655	−	0.783291i	$-0.713539\pi$
$691$	−32.6827			−1.24331			−0.621655	+	0.783291i	$0.713539\pi$
$692$	−7.90163			−0.300375
$693$	−40.1861	−	11.9584i	−1.52654	−	0.454263i
$694$			5.61193i			0.213026i
$695$		−	9.78752i		−	0.371262i
$696$			59.6915i			2.26260i
$697$		−	21.2823i		−	0.806125i
$698$			34.4200i			1.30281i
$699$	10.1658			0.384505
$700$			2.04313i			0.0772231i
$701$		−	39.3557i		−	1.48645i	−0.669044	−	0.743223i	$-0.733296\pi$
$701$		−	39.3557i		−	1.48645i	0.669044	−	0.743223i	$-0.266704\pi$
$702$			3.11755i			0.117664i
$703$	18.1288	+	6.63670i	0.683739	+	0.250308i
$704$	5.33963	−	17.9437i	0.201245	−	0.676280i
$705$		−	13.1158i		−	0.493970i
$706$	7.11858			0.267911
$707$	−9.84766			−0.370359
$708$	5.02522			0.188859
$709$	15.2727			0.573577			0.286788	−	0.957994i	$-0.407412\pi$
$709$	15.2727			0.573577			0.286788	+	0.957994i	$0.407412\pi$
$710$			12.6138i			0.473389i
$711$	39.4288			1.47869
$712$		−	15.7479i		−	0.590179i
$713$		−	5.43235i		−	0.203443i
$714$			63.1583i			2.36364i
$715$	−2.20414	+	7.40696i	−0.0824300	+	0.277005i
$716$			9.05900i			0.338551i
$717$	−28.9350			−1.08060
$718$		−	49.3900i		−	1.84322i
$719$	20.6047			0.768424			0.384212	−	0.923245i	$-0.374473\pi$
$719$	20.6047			0.768424			0.384212	+	0.923245i	$0.374473\pi$
$720$	−12.3233			−0.459261
$721$	−42.9146			−1.59823
$722$	22.6007	+	19.1085i	0.841111	+	0.711147i
$723$			49.5228i			1.84177i
$724$		−	4.66562i		−	0.173396i
$725$	−10.2556			−0.380885
$726$	22.2446	−	34.0666i	0.825576	−	1.26433i
$727$	−42.9642			−1.59345			−0.796727	−	0.604340i	$-0.793437\pi$
$727$	−42.9642			−1.59345			−0.796727	+	0.604340i	$0.793437\pi$
$728$			27.3672i			1.01430i
$729$	20.1435			0.746056
$730$			25.9468i			0.960333i
$731$	−18.8965			−0.698914
$732$	13.2104			0.488269
$733$			49.8996i			1.84308i	0.388279	+	0.921542i	$0.373070\pi$
$733$			49.8996i			1.84308i	−0.388279	+	0.921542i	$0.626930\pi$
$734$	−37.5604			−1.38638
$735$		−	37.8970i		−	1.39785i
$736$	−16.6383			−0.613294
$737$	−36.8473	−	10.9649i	−1.35729	−	0.403896i
$738$	24.5429			0.903437
$739$			11.1553i			0.410356i	0.978725	+	0.205178i	$0.0657773\pi$
$739$			11.1553i			0.410356i	−0.978725	+	0.205178i	$0.934223\pi$
$740$			1.88848i			0.0694219i
$741$	22.6468	+	8.29071i	0.831953	+	0.304567i
$742$	−52.6610			−1.93325
$743$	36.8663			1.35249			0.676247	−	0.736675i	$-0.263605\pi$
$743$	36.8663			1.35249			0.676247	+	0.736675i	$0.263605\pi$
$744$	4.51053			0.165364
$745$			0.678367i			0.0248534i
$746$	−55.3053			−2.02487
$747$			8.38267i			0.306706i
$748$	−4.83030	−	1.43738i	−0.176613	−	0.0525559i
$749$			20.8722i			0.762654i
$750$		−	3.69874i		−	0.135059i
$751$		−	12.2375i		−	0.446553i	−0.974755	−	0.223276i	$-0.928325\pi$
$751$		−	12.2375i		−	0.446553i	0.974755	−	0.223276i	$-0.0716752\pi$
$752$	25.8006			0.940852
$753$			43.6260i			1.58982i
$754$	37.2231			1.35558
$755$	15.0308			0.547029
$756$	1.75494			0.0638264
$757$	−38.0304			−1.38224			−0.691119	−	0.722741i	$-0.742882\pi$
$757$	−38.0304			−1.38224			−0.691119	+	0.722741i	$0.742882\pi$
$758$		−	9.06653i		−	0.329311i
$759$	52.9120	+	15.7454i	1.92058	+	0.571520i
$760$	3.67305	−	10.0333i	0.133236	−	0.363946i
$761$		−	7.95315i		−	0.288301i	−0.989556	−	0.144151i	$-0.953955\pi$
$761$		−	7.95315i		−	0.288301i	0.989556	−	0.144151i	$-0.0460450\pi$
$762$		−	55.5647i		−	2.01290i
$763$		−	12.7507i		−	0.461608i
$764$	10.3771			0.375430
$765$		−	9.40177i		−	0.339922i
$766$		−	18.4711i		−	0.667389i
$767$			11.5648i			0.417582i
$768$		−	23.2734i		−	0.839805i
$769$			20.0588i			0.723337i	0.932307	+	0.361669i	$0.117793\pi$
$769$			20.0588i			0.723337i	−0.932307	+	0.361669i	$0.882207\pi$
$770$	23.7267	+	7.06051i	0.855052	+	0.254443i
$771$	−54.4403			−1.96062
$772$	2.45494			0.0883552
$773$		−	26.8403i		−	0.965379i	−0.875791	−	0.482690i	$-0.839660\pi$
$773$		−	26.8403i		−	0.965379i	0.875791	−	0.482690i	$-0.160340\pi$
$774$		−	21.7916i		−	0.783284i
$775$			0.774958i			0.0278373i
$776$		−	32.8517i		−	1.17931i
$777$		−	50.3918i		−	1.80779i
$778$	32.6511			1.17060
$779$	−8.94907	+	24.4452i	−0.320634	+	0.875840i
$780$			2.35913i			0.0844704i
$781$	25.7418	+	7.66014i	0.921113	+	0.274101i
$782$		−	38.9119i		−	1.39149i
$783$			8.80903i			0.314809i
$784$	74.5486			2.66245
$785$	2.55743			0.0912786
$786$	16.4393			0.586370
$787$	41.2630			1.47087			0.735433	−	0.677597i	$-0.236979\pi$
$787$	41.2630			1.47087			0.735433	+	0.677597i	$0.236979\pi$
$788$		−	1.29911i		−	0.0462788i
$789$	28.9571			1.03090
$790$	−23.2796			−0.828251
$791$	8.99554			0.319845
$792$	−6.11737	+	20.5573i	−0.217371	+	0.730473i
$793$			30.4019i			1.07960i
$794$	−42.0748			−1.49318
$795$	16.7531			0.594172
$796$	3.46280			0.122736
$797$		−	5.30720i		−	0.187991i	−0.995573	−	0.0939954i	$-0.970036\pi$
$797$		−	5.30720i		−	0.187991i	0.995573	−	0.0939954i	$-0.0299639\pi$
$798$	26.5576	−	72.5447i	0.940130	−	2.56805i
$799$			19.6840i			0.696371i
$800$	2.37355			0.0839176
$801$			16.9498i			0.598893i
$802$			42.8305i			1.51240i
$803$	52.9511	+	15.7570i	1.86860	+	0.556052i
$804$	−11.7359			−0.413894
$805$			33.5889i			1.18385i
$806$		−	2.81272i		−	0.0990740i
$807$	−28.7950			−1.01363
$808$			5.03761i			0.177222i
$809$		−	11.0851i		−	0.389731i	−0.980830	−	0.194865i	$-0.937573\pi$
$809$		−	11.0851i		−	0.389731i	0.980830	−	0.194865i	$-0.0624270\pi$
$810$	−15.5058			−0.544818
$811$	3.46284			0.121597			0.0607984	−	0.998150i	$-0.480635\pi$
$811$	3.46284			0.121597			0.0607984	+	0.998150i	$0.480635\pi$
$812$		−	20.9536i		−	0.735328i
$813$	−12.7585			−0.447459
$814$	21.9308	+	6.52607i	0.768673	+	0.228739i
$815$	3.00037			0.105098
$816$	39.5250			1.38365
$817$	21.7049	+	7.94587i	0.759358	+	0.277991i
$818$	−30.4924			−1.06614
$819$		−	29.4559i		−	1.02927i
$820$	−2.54647			−0.0889265
$821$			24.0378i			0.838925i	0.907773	+	0.419463i	$0.137781\pi$
$821$			24.0378i			0.838925i	−0.907773	+	0.419463i	$0.862219\pi$
$822$		−	28.5920i		−	0.997261i
$823$	11.1714			0.389409			0.194704	−	0.980862i	$-0.437625\pi$
$823$	11.1714			0.389409			0.194704	+	0.980862i	$0.437625\pi$
$824$			21.9531i			0.764774i
$825$	−7.54822	−	2.24617i	−0.262795	−	0.0782016i
$826$	37.0457			1.28898
$827$	−24.8728			−0.864911			−0.432456	−	0.901655i	$-0.642353\pi$
$827$	−24.8728			−0.864911			−0.432456	+	0.901655i	$0.642353\pi$
$828$	7.88567			0.274046
$829$		−	26.8601i		−	0.932891i	−0.884550	−	0.466446i	$-0.845534\pi$
$829$		−	26.8601i		−	0.932891i	0.884550	−	0.466446i	$-0.154466\pi$
$830$		−	4.94931i		−	0.171793i
$831$	−31.2330			−1.08346
$832$	13.1525			0.455982
$833$			56.8753i			1.97061i
$834$	−36.2014			−1.25355
$835$	12.0559			0.417211
$836$	4.94375	+	3.68211i	0.170983	+	0.127348i
$837$	0.665645			0.0230081
$838$	17.0682			0.589611
$839$		−	6.64212i		−	0.229311i	−0.993405	−	0.114656i	$-0.963424\pi$
$839$		−	6.64212i		−	0.229311i	0.993405	−	0.114656i	$-0.0365765\pi$
$840$	−27.8891			−0.962266
$841$	76.1783			2.62684
$842$		−	45.9055i		−	1.58201i
$843$			3.32474i			0.114510i
$844$	0.637637			0.0219484
$845$	7.57079			0.260443
$846$	−22.6998			−0.780434
$847$	28.8176	−	44.1328i	0.990184	−	1.51642i
$848$			32.9557i			1.13170i
$849$	−25.7361			−0.883261
$850$			5.55101i			0.190398i
$851$			31.0464i			1.06426i
$852$	8.19880			0.280886
$853$		−	18.1521i		−	0.621517i	−0.950489	−	0.310759i	$-0.899417\pi$
$853$		−	18.1521i		−	0.621517i	0.950489	−	0.310759i	$-0.100583\pi$
$854$	97.3863			3.33249
$855$	−3.95338	+	10.7990i	−0.135203	+	0.369319i
$856$	10.6773			0.364941
$857$	−34.8509			−1.19048			−0.595241	−	0.803547i	$-0.702944\pi$
$857$	−34.8509			−1.19048			−0.595241	+	0.803547i	$0.702944\pi$
$858$	27.3964	+	8.15252i	0.935298	+	0.278322i
$859$	38.7887			1.32345			0.661727	−	0.749745i	$-0.269824\pi$
$859$	38.7887			1.32345			0.661727	+	0.749745i	$0.269824\pi$
$860$			2.26101i			0.0770996i
$861$	67.9494			2.31571
$862$	−29.9527			−1.02019
$863$		−	43.2025i		−	1.47063i	−0.677725	−	0.735315i	$-0.737034\pi$
$863$		−	43.2025i		−	1.47063i	0.677725	−	0.735315i	$-0.262966\pi$
$864$		−	2.03875i		−	0.0693595i
$865$	18.5313			0.630083
$866$			34.5629i			1.17449i
$867$		−	10.2118i		−	0.346811i
$868$	−1.58334			−0.0537421
$869$	−14.1373	+	47.5080i	−0.479574	+	1.61160i
$870$			37.9329i			1.28605i
$871$		−	27.0086i		−	0.915151i
$872$	−6.52269			−0.220886
$873$			35.3590i			1.19672i
$874$	−16.3622	+	44.6948i	−0.553459	+	1.51182i
$875$		−	4.79166i		−	0.161988i
$876$	16.8650			0.569815
$877$	17.3676			0.586463			0.293231	−	0.956042i	$-0.405269\pi$
$877$	17.3676			0.586463			0.293231	+	0.956042i	$0.405269\pi$
$878$	18.9055			0.638029
$879$		−	28.6332i		−	0.965772i
$880$	4.41853	−	14.8484i	0.148949	−	0.500539i
$881$	6.33610			0.213469			0.106734	−	0.994288i	$-0.465961\pi$
$881$	6.33610			0.213469			0.106734	+	0.994288i	$0.465961\pi$
$882$	−65.5889			−2.20849
$883$	8.95444			0.301341			0.150670	−	0.988584i	$-0.451857\pi$
$883$	8.95444			0.301341			0.150670	+	0.988584i	$0.451857\pi$
$884$		−	3.54055i		−	0.119082i
$885$	−11.7854			−0.396162
$886$	−12.6629			−0.425419
$887$	−40.1138			−1.34689			−0.673445	−	0.739238i	$-0.735186\pi$
$887$	−40.1138			−1.34689			−0.673445	+	0.739238i	$0.735186\pi$
$888$	−25.7781			−0.865056
$889$		−	71.9832i		−	2.41424i
$890$		−	10.0075i		−	0.335454i
$891$	−9.41636	+	31.6435i	−0.315460	+	1.06010i
$892$			4.28662i			0.143527i
$893$	8.27700	−	22.6094i	0.276979	−	0.756595i
$894$	2.50910			0.0839169
$895$		−	21.2456i		−	0.710163i
$896$		−	64.8780i		−	2.16742i
$897$			38.7838i			1.29495i
$898$			5.61610i			0.187412i
$899$		−	7.94769i		−	0.265070i
$900$	−1.12494			−0.0374980
$901$	−25.1429			−0.837630
$902$	−8.79990	+	29.5719i	−0.293005	+	0.984637i
$903$		−	60.3322i		−	2.00773i
$904$		−	4.60170i		−	0.153050i
$905$			10.9420i			0.363726i
$906$		−	55.5951i		−	1.84702i
$907$			38.5122i			1.27878i	0.768884	+	0.639388i	$0.220812\pi$
$907$			38.5122i			1.27878i	−0.768884	+	0.639388i	$0.779188\pi$
$908$	2.05618			0.0682367
$909$		−	5.42208i		−	0.179839i
$910$			17.3914i			0.576519i
$911$			9.56321i			0.316843i	0.987372	+	0.158422i	$0.0506405\pi$
$911$			9.56321i			0.316843i	−0.987372	+	0.158422i	$0.949359\pi$
$912$	−45.3991	−	16.6200i	−1.50331	−	0.550343i
$913$	−10.1003	−	3.00562i	−0.334272	−	0.0994715i
$914$			56.1346i			1.85677i
$915$	−30.9816			−1.02422
$916$	1.19088			0.0393478
$917$	21.2968			0.703284
$918$	4.76801			0.157368
$919$			44.8729i			1.48022i	0.672486	+	0.740110i	$0.265227\pi$
$919$			44.8729i			1.48022i	−0.672486	+	0.740110i	$0.734773\pi$
$920$	17.1825			0.566490
$921$		−	59.1722i		−	1.94979i
$922$		−	6.82302i		−	0.224704i
$923$			18.8684i			0.621061i
$924$	4.58922	−	15.4220i	0.150974	−	0.507347i
$925$		−	4.42896i		−	0.145623i
$926$	51.9393			1.70683
$927$		−	23.6286i		−	0.776065i
$928$	−24.3423			−0.799074
$929$	−39.9930			−1.31213			−0.656063	−	0.754706i	$-0.727780\pi$
$929$	−39.9930			−1.31213			−0.656063	+	0.754706i	$0.727780\pi$
$930$	2.86636			0.0939918
$931$	23.9157	−	65.3279i	0.783804	−	2.14103i
$932$			1.82549i			0.0597958i
$933$			49.6152i			1.62433i
$934$	−36.0328			−1.17903
$935$	11.3283	+	3.37102i	0.370474	+	0.110244i
$936$	−15.0683			−0.492522
$937$			20.7335i			0.677335i	0.940906	+	0.338668i	$0.109976\pi$
$937$			20.7335i			0.677335i	−0.940906	+	0.338668i	$0.890024\pi$
$938$	−86.5166			−2.82487
$939$		−	48.4963i		−	1.58262i
$940$	2.35523			0.0768191
$941$	19.0915			0.622366			0.311183	−	0.950350i	$-0.399275\pi$
$941$	19.0915			0.622366			0.311183	+	0.950350i	$0.399275\pi$
$942$		−	9.45926i		−	0.308199i
$943$	−41.8636			−1.36327
$944$		−	23.1835i		−	0.754559i
$945$	−4.11576			−0.133886
$946$	26.2569	+	7.81342i	0.853685	+	0.254036i
$947$	8.36390			0.271790			0.135895	−	0.990723i	$-0.456609\pi$
$947$	8.36390			0.271790			0.135895	+	0.990723i	$0.456609\pi$
$948$			15.1314i			0.491444i
$949$			38.8125i			1.25991i
$950$	2.33416	−	6.37598i	0.0757302	−	0.206864i
$951$	40.0599			1.29903
$952$	41.8556			1.35655
$953$	14.8372			0.480625			0.240312	−	0.970696i	$-0.422750\pi$
$953$	14.8372			0.480625			0.240312	+	0.970696i	$0.422750\pi$
$954$		−	28.9949i		−	0.938746i
$955$	−24.3369			−0.787522
$956$		−	5.19591i		−	0.168048i
$957$	77.4119	+	23.0359i	2.50237	+	0.744646i
$958$			5.74019i			0.185457i
$959$		−	37.0405i		−	1.19610i
$960$			13.4034i			0.432592i
$961$	30.3994			0.980627
$962$			16.0750i			0.518278i
$963$	−11.4921			−0.370329
$964$	−8.89290			−0.286421
$965$	−5.75745			−0.185339
$966$	124.236			3.99724
$967$		−	28.1772i		−	0.906116i	−0.891481	−	0.453058i	$-0.850333\pi$
$967$		−	28.1772i		−	0.906116i	0.891481	−	0.453058i	$-0.149667\pi$
$968$	−22.5763	−	14.7417i	−0.725629	−	0.473817i
$969$	12.6799	−	34.6362i	0.407336	−	1.11268i
$970$		−	20.8767i		−	0.670311i
$971$		−	21.5049i		−	0.690126i	−0.938579	−	0.345063i	$-0.887857\pi$
$971$		−	21.5049i		−	0.690126i	0.938579	−	0.345063i	$-0.112143\pi$
$972$			8.97977i			0.288026i
$973$	−46.8984			−1.50349
$974$		−	27.6985i		−	0.887518i
$975$		−	5.53275i		−	0.177190i
$976$		−	60.9452i		−	1.95081i
$977$		−	26.2004i		−	0.838225i	−0.907934	−	0.419112i	$-0.862341\pi$
$977$		−	26.2004i		−	0.838225i	0.907934	−	0.419112i	$-0.137659\pi$
$978$		−	11.0976i		−	0.354861i
$979$	−20.4230	−	6.07739i	−0.652721	−	0.194234i
$980$	6.80523			0.217385
$981$	7.02050			0.224147
$982$		−	51.3397i		−	1.63832i
$983$			2.40421i			0.0766825i	0.999265	+	0.0383412i	$0.0122074\pi$
$983$			2.40421i			0.0766825i	−0.999265	+	0.0383412i	$0.987793\pi$
$984$		−	34.7597i		−	1.10810i
$985$			3.04673i			0.0970770i
$986$		−	56.9292i		−	1.81300i
$987$	−62.8465			−2.00043
$988$	−1.48878	+	4.06673i	−0.0473643	+	0.129380i
$989$			37.1707i			1.18196i
$990$	−3.88749	+	13.0638i	−0.123552	+	0.415196i
$991$			14.3995i			0.457416i	0.973495	+	0.228708i	$0.0734502\pi$
$991$			14.3995i			0.457416i	−0.973495	+	0.228708i	$0.926550\pi$
$992$			1.83940i			0.0584010i
$993$	−3.77968			−0.119944
$994$	60.4412			1.91708
$995$	−8.12114			−0.257457
$996$	−3.21697			−0.101934
$997$		−	11.9989i		−	0.380009i	−0.981783	−	0.190005i	$-0.939150\pi$
$997$		−	11.9989i		−	0.380009i	0.981783	−	0.190005i	$-0.0608503\pi$
$998$	−24.1023			−0.762946
$999$	−3.80423			−0.120360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.a.626.10	yes	40
11.10	odd	2	inner	1045.2.f.a.626.32	yes	40
19.18	odd	2	inner	1045.2.f.a.626.31	yes	40
209.208	even	2	inner	1045.2.f.a.626.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.a.626.9	✓	40	209.208	even	2	inner
1045.2.f.a.626.10	yes	40	1.1	even	1	trivial
1045.2.f.a.626.31	yes	40	19.18	odd	2	inner
1045.2.f.a.626.32	yes	40	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.55769 q^{2} -2.37450i q^{3} +0.426394 q^{4} -1.00000 q^{5} +3.69874i q^{6} +4.79166i q^{7} +2.45119 q^{8} -2.63826 q^{9} +O(q^{10})\)	\(q-1.55769 q^{2} -2.37450i q^{3} +0.426394 q^{4} -1.00000 q^{5} +3.69874i q^{6} +4.79166i q^{7} +2.45119 q^{8} -2.63826 q^{9} +1.55769 q^{10} +(0.945954 - 3.17886i) q^{11} -1.01247i q^{12} +2.33007 q^{13} -7.46391i q^{14} +2.37450i q^{15} -4.67098 q^{16} -3.56362i q^{17} +4.10959 q^{18} +(-1.49848 + 4.09323i) q^{19} -0.426394 q^{20} +11.3778 q^{21} +(-1.47350 + 4.95168i) q^{22} -7.00987 q^{23} -5.82035i q^{24} +1.00000 q^{25} -3.62952 q^{26} -0.858944i q^{27} +2.04313i q^{28} -10.2556 q^{29} -3.69874i q^{30} +0.774958i q^{31} +2.37355 q^{32} +(-7.54822 - 2.24617i) q^{33} +5.55101i q^{34} -4.79166i q^{35} -1.12494 q^{36} -4.42896i q^{37} +(2.33416 - 6.37598i) q^{38} -5.53275i q^{39} -2.45119 q^{40} +5.97210 q^{41} -17.7231 q^{42} -5.30262i q^{43} +(0.403349 - 1.35545i) q^{44} +2.63826 q^{45} +10.9192 q^{46} -5.52361 q^{47} +11.0912i q^{48} -15.9600 q^{49} -1.55769 q^{50} -8.46183 q^{51} +0.993526 q^{52} -7.05543i q^{53} +1.33797i q^{54} +(-0.945954 + 3.17886i) q^{55} +11.7453i q^{56} +(9.71939 + 3.55814i) q^{57} +15.9751 q^{58} +4.96331i q^{59} +1.01247i q^{60} +13.0476i q^{61} -1.20714i q^{62} -12.6417i q^{63} +5.64470 q^{64} -2.33007 q^{65} +(11.7578 + 3.49883i) q^{66} -11.5913i q^{67} -1.51951i q^{68} +16.6449i q^{69} +7.46391i q^{70} +8.09779i q^{71} -6.46688 q^{72} +16.6572i q^{73} +6.89893i q^{74} -2.37450i q^{75} +(-0.638942 + 1.74533i) q^{76} +(15.2320 + 4.53269i) q^{77} +8.61830i q^{78} -14.9450 q^{79} +4.67098 q^{80} -9.95436 q^{81} -9.30267 q^{82} -3.17734i q^{83} +4.85142 q^{84} +3.56362i q^{85} +8.25984i q^{86} +24.3521i q^{87} +(2.31871 - 7.79199i) q^{88} -6.42461i q^{89} -4.10959 q^{90} +11.1649i q^{91} -2.98896 q^{92} +1.84014 q^{93} +8.60406 q^{94} +(1.49848 - 4.09323i) q^{95} -5.63600i q^{96} -13.4024i q^{97} +24.8607 q^{98} +(-2.49568 + 8.38668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) \) 40 * q + 40 * q^4 - 40 * q^5 - 28 * q^9 - 4 * q^11 + 32 * q^16 - 40 * q^20 - 16 * q^23 + 40 * q^25 + 8 * q^26 + 8 * q^36 + 28 * q^38 - 84 * q^42 - 48 * q^44 + 28 * q^45 + 32 * q^47 - 20 * q^49 + 4 * q^55 - 20 * q^58 + 72 * q^64 + 36 * q^66 + 16 * q^77 - 32 * q^80 + 16 * q^81 + 16 * q^82 - 20 * q^92 - 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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