LMFDB - Embedded newform 1045.2.f.a.626.38

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			626.38
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.a.626.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52972 q^{2} +0.384887i q^{3} +4.39948 q^{4} -1.00000 q^{5} +0.973657i q^{6} +1.35297i q^{7} +6.07000 q^{8} +2.85186 q^{9} +O(q^{10})$	\(q+2.52972 q^{2} +0.384887i q^{3} +4.39948 q^{4} -1.00000 q^{5} +0.973657i q^{6} +1.35297i q^{7} +6.07000 q^{8} +2.85186 q^{9} -2.52972 q^{10} +(1.95002 + 2.68280i) q^{11} +1.69330i q^{12} -2.33668 q^{13} +3.42264i q^{14} -0.384887i q^{15} +6.55645 q^{16} -5.43006i q^{17} +7.21441 q^{18} +(-0.531936 + 4.32632i) q^{19} -4.39948 q^{20} -0.520743 q^{21} +(4.93299 + 6.78674i) q^{22} +0.981945 q^{23} +2.33627i q^{24} +1.00000 q^{25} -5.91114 q^{26} +2.25231i q^{27} +5.95238i q^{28} +3.04589 q^{29} -0.973657i q^{30} -8.09312i q^{31} +4.44597 q^{32} +(-1.03258 + 0.750537i) q^{33} -13.7365i q^{34} -1.35297i q^{35} +12.5467 q^{36} +1.40295i q^{37} +(-1.34565 + 10.9444i) q^{38} -0.899359i q^{39} -6.07000 q^{40} -1.12340 q^{41} -1.31733 q^{42} +2.01890i q^{43} +(8.57905 + 11.8029i) q^{44} -2.85186 q^{45} +2.48404 q^{46} -12.2984 q^{47} +2.52350i q^{48} +5.16946 q^{49} +2.52972 q^{50} +2.08996 q^{51} -10.2802 q^{52} -3.95467i q^{53} +5.69771i q^{54} +(-1.95002 - 2.68280i) q^{55} +8.21255i q^{56} +(-1.66515 - 0.204736i) q^{57} +7.70526 q^{58} +1.26044i q^{59} -1.69330i q^{60} -9.55786i q^{61} -20.4733i q^{62} +3.85849i q^{63} -1.86586 q^{64} +2.33668 q^{65} +(-2.61213 + 1.89865i) q^{66} -13.2712i q^{67} -23.8894i q^{68} +0.377938i q^{69} -3.42264i q^{70} +14.3607i q^{71} +17.3108 q^{72} -2.05840i q^{73} +3.54907i q^{74} +0.384887i q^{75} +(-2.34024 + 19.0335i) q^{76} +(-3.62976 + 2.63832i) q^{77} -2.27512i q^{78} -9.57041 q^{79} -6.55645 q^{80} +7.68870 q^{81} -2.84188 q^{82} +10.1838i q^{83} -2.29100 q^{84} +5.43006i q^{85} +5.10724i q^{86} +1.17233i q^{87} +(11.8366 + 16.2846i) q^{88} -12.3375i q^{89} -7.21441 q^{90} -3.16147i q^{91} +4.32004 q^{92} +3.11494 q^{93} -31.1114 q^{94} +(0.531936 - 4.32632i) q^{95} +1.71120i q^{96} -2.23673i q^{97} +13.0773 q^{98} +(5.56118 + 7.65098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.52972			1.78878			0.894391	−	0.447287i	$-0.147610\pi$
$2$	2.52972			1.78878			0.894391	+	0.447287i	$0.147610\pi$
$3$			0.384887i			0.222215i	0.993808	+	0.111107i	$0.0354398\pi$
$3$			0.384887i			0.222215i	−0.993808	+	0.111107i	$0.964560\pi$
$4$	4.39948			2.19974
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$			0.973657i			0.397494i
$7$			1.35297i			0.511376i	0.966759	+	0.255688i	$0.0823020\pi$
$7$			1.35297i			0.511376i	−0.966759	+	0.255688i	$0.917698\pi$
$8$	6.07000			2.14607
$9$	2.85186			0.950621
$10$	−2.52972			−0.799967
$11$	1.95002	+	2.68280i	0.587952	+	0.808896i
$11$	1.95002	+	2.68280i	0.587952	+	0.808896i
$12$			1.69330i			0.488815i
$13$	−2.33668			−0.648078			−0.324039	−	0.946044i	$-0.605041\pi$
$13$	−2.33668			−0.648078			−0.324039	+	0.946044i	$0.605041\pi$
$14$			3.42264i			0.914740i
$15$		−	0.384887i		−	0.0993775i
$16$	6.55645			1.63911
$17$		−	5.43006i		−	1.31698i	−0.752588	−	0.658492i	$-0.771195\pi$
$17$		−	5.43006i		−	1.31698i	0.752588	−	0.658492i	$-0.228805\pi$
$18$	7.21441			1.70045
$19$	−0.531936	+	4.32632i	−0.122035	+	0.992526i
$19$	−0.531936	+	4.32632i	−0.122035	+	0.992526i
$20$	−4.39948			−0.983753
$21$	−0.520743			−0.113635
$22$	4.93299	+	6.78674i	1.05172	+	1.44694i
$23$	0.981945			0.204750			0.102375	−	0.994746i	$-0.467356\pi$
$23$	0.981945			0.204750			0.102375	+	0.994746i	$0.467356\pi$
$24$			2.33627i			0.476889i
$25$	1.00000			0.200000
$26$	−5.91114			−1.15927
$27$			2.25231i			0.433457i
$28$			5.95238i			1.12489i
$29$	3.04589			0.565608			0.282804	−	0.959178i	$-0.408735\pi$
$29$	3.04589			0.565608			0.282804	+	0.959178i	$0.408735\pi$
$30$		−	0.973657i		−	0.177765i
$31$		−	8.09312i		−	1.45357i	−0.686866	−	0.726784i	$-0.741014\pi$
$31$		−	8.09312i		−	1.45357i	0.686866	−	0.726784i	$-0.258986\pi$
$32$	4.44597			0.785943
$33$	−1.03258	+	0.750537i	−0.179749	+	0.130652i
$34$		−	13.7365i		−	2.35580i
$35$		−	1.35297i		−	0.228694i
$36$	12.5467			2.09112
$37$			1.40295i			0.230644i	0.993328	+	0.115322i	$0.0367899\pi$
$37$			1.40295i			0.230644i	−0.993328	+	0.115322i	$0.963210\pi$
$38$	−1.34565	+	10.9444i	−0.218293	+	1.77541i
$39$		−	0.899359i		−	0.144013i
$40$	−6.07000			−0.959752
$41$	−1.12340			−0.175445			−0.0877226	−	0.996145i	$-0.527959\pi$
$41$	−1.12340			−0.175445			−0.0877226	+	0.996145i	$0.527959\pi$
$42$	−1.31733			−0.203269
$43$			2.01890i			0.307879i	0.988080	+	0.153939i	$0.0491960\pi$
$43$			2.01890i			0.307879i	−0.988080	+	0.153939i	$0.950804\pi$
$44$	8.57905	+	11.8029i	1.29334	+	1.77936i
$45$	−2.85186			−0.425130
$46$	2.48404			0.366252
$47$	−12.2984			−1.79390			−0.896950	−	0.442131i	$-0.854222\pi$
$47$	−12.2984			−1.79390			−0.896950	+	0.442131i	$0.854222\pi$
$48$			2.52350i			0.364235i
$49$	5.16946			0.738495
$50$	2.52972			0.357756
$51$	2.08996			0.292653
$52$	−10.2802			−1.42560
$53$		−	3.95467i		−	0.543216i	−0.962408	−	0.271608i	$-0.912445\pi$
$53$		−	3.95467i		−	0.543216i	0.962408	−	0.271608i	$-0.0875555\pi$
$54$			5.69771i			0.775360i
$55$	−1.95002	−	2.68280i	−0.262940	−	0.361749i
$56$			8.21255i			1.09745i
$57$	−1.66515	−	0.204736i	−0.220554	−	0.0271179i
$58$	7.70526			1.01175
$59$			1.26044i			0.164095i	0.996628	+	0.0820474i	$0.0261459\pi$
$59$			1.26044i			0.164095i	−0.996628	+	0.0820474i	$0.973854\pi$
$60$		−	1.69330i		−	0.218605i
$61$		−	9.55786i		−	1.22376i	−0.790951	−	0.611879i	$-0.790414\pi$
$61$		−	9.55786i		−	1.22376i	0.790951	−	0.611879i	$-0.209586\pi$
$62$		−	20.4733i		−	2.60011i
$63$			3.85849i			0.486124i
$64$	−1.86586			−0.233232
$65$	2.33668			0.289829
$66$	−2.61213	+	1.89865i	−0.321531	+	0.233707i
$67$		−	13.2712i		−	1.62134i	−0.585505	−	0.810669i	$-0.699104\pi$
$67$		−	13.2712i		−	1.62134i	0.585505	−	0.810669i	$-0.300896\pi$
$68$		−	23.8894i		−	2.89702i
$69$			0.377938i			0.0454984i
$70$		−	3.42264i		−	0.409084i
$71$			14.3607i			1.70431i	0.523292	+	0.852154i	$0.324704\pi$
$71$			14.3607i			1.70431i	−0.523292	+	0.852154i	$0.675296\pi$
$72$	17.3108			2.04010
$73$		−	2.05840i		−	0.240918i	−0.992718	−	0.120459i	$-0.961563\pi$
$73$		−	2.05840i		−	0.240918i	0.992718	−	0.120459i	$-0.0384366\pi$
$74$			3.54907i			0.412571i
$75$			0.384887i			0.0444430i
$76$	−2.34024	+	19.0335i	−0.268444	+	2.18330i
$77$	−3.62976	+	2.63832i	−0.413650	+	0.300665i
$78$		−	2.27512i		−	0.257607i
$79$	−9.57041			−1.07676			−0.538378	−	0.842704i	$-0.680963\pi$
$79$	−9.57041			−1.07676			−0.538378	+	0.842704i	$0.680963\pi$
$80$	−6.55645			−0.733033
$81$	7.68870			0.854300
$82$	−2.84188			−0.313833
$83$			10.1838i			1.11782i	0.829230	+	0.558908i	$0.188779\pi$
$83$			10.1838i			1.11782i	−0.829230	+	0.558908i	$0.811221\pi$
$84$	−2.29100			−0.249968
$85$			5.43006i			0.588973i
$86$			5.10724i			0.550728i
$87$			1.17233i			0.125687i
$88$	11.8366	+	16.2846i	1.26179	+	1.73595i
$89$		−	12.3375i		−	1.30777i	−0.756594	−	0.653885i	$-0.773138\pi$
$89$		−	12.3375i		−	1.30777i	0.756594	−	0.653885i	$-0.226862\pi$
$90$	−7.21441			−0.760465
$91$		−	3.16147i		−	0.331412i
$92$	4.32004			0.450396
$93$	3.11494			0.323004
$94$	−31.1114			−3.20890
$95$	0.531936	−	4.32632i	0.0545755	−	0.443871i
$96$			1.71120i			0.174648i
$97$		−	2.23673i		−	0.227106i	−0.993532	−	0.113553i	$-0.963777\pi$
$97$		−	2.23673i		−	0.227106i	0.993532	−	0.113553i	$-0.0362231\pi$
$98$	13.0773			1.32101
$99$	5.56118	+	7.65098i	0.558919	+	0.768953i
$100$	4.39948			0.439948
$101$		−	5.08567i		−	0.506043i	−0.967461	−	0.253022i	$-0.918576\pi$
$101$		−	5.08567i		−	0.506043i	0.967461	−	0.253022i	$-0.0814244\pi$
$102$	5.28702			0.523493
$103$		−	6.81557i		−	0.671558i	−0.941941	−	0.335779i	$-0.891000\pi$
$103$		−	6.81557i		−	0.671558i	0.941941	−	0.335779i	$-0.109000\pi$
$104$	−14.1837			−1.39082
$105$	0.520743			0.0508193
$106$		−	10.0042i		−	0.971695i
$107$	−17.4233			−1.68438			−0.842188	−	0.539184i	$-0.818733\pi$
$107$	−17.4233			−1.68438			−0.842188	+	0.539184i	$0.818733\pi$
$108$			9.90898i			0.953492i
$109$	−16.9175			−1.62040			−0.810201	−	0.586152i	$-0.800642\pi$
$109$	−16.9175			−1.62040			−0.810201	+	0.586152i	$0.800642\pi$
$110$	−4.93299	−	6.78674i	−0.470342	−	0.647090i
$111$	−0.539978			−0.0512524
$112$			8.87070i			0.838203i
$113$		−	9.65154i		−	0.907940i	−0.891017	−	0.453970i	$-0.850007\pi$
$113$		−	9.65154i		−	0.907940i	0.891017	−	0.453970i	$-0.149993\pi$
$114$	−4.21235	−	0.517924i	−0.394523	−	0.0485080i
$115$	−0.981945			−0.0915668
$116$	13.4003			1.24419
$117$	−6.66389			−0.616077
$118$			3.18855i			0.293530i
$119$	7.34673			0.673474
$120$		−	2.33627i		−	0.213271i
$121$	−3.39487	+	10.4630i	−0.308625	+	0.951184i
$122$		−	24.1787i		−	2.18904i
$123$		−	0.432382i		−	0.0389865i
$124$		−	35.6055i		−	3.19747i
$125$	−1.00000			−0.0894427
$126$			9.76090i			0.869570i
$127$	−11.1944			−0.993347			−0.496673	−	0.867938i	$-0.665445\pi$
$127$	−11.1944			−0.993347			−0.496673	+	0.867938i	$0.665445\pi$
$128$	−13.6120			−1.20314
$129$	−0.777048			−0.0684152
$130$	5.91114			0.518442
$131$			11.7600i			1.02748i	0.857947	+	0.513738i	$0.171740\pi$
$131$			11.7600i			1.02748i	−0.857947	+	0.513738i	$0.828260\pi$
$132$	−4.54280	+	3.30197i	−0.395400	+	0.287400i
$133$	−5.85340	−	0.719696i	−0.507554	−	0.0624055i
$134$		−	33.5725i		−	2.90022i
$135$		−	2.25231i		−	0.193848i
$136$		−	32.9605i		−	2.82634i
$137$	5.82804			0.497923			0.248962	−	0.968513i	$-0.419911\pi$
$137$	5.82804			0.497923			0.248962	+	0.968513i	$0.419911\pi$
$138$			0.956078i			0.0813867i
$139$			1.94056i			0.164596i	0.996608	+	0.0822980i	$0.0262259\pi$
$139$			1.94056i			0.164596i	−0.996608	+	0.0822980i	$0.973774\pi$
$140$		−	5.95238i		−	0.503068i
$141$		−	4.73349i		−	0.398631i
$142$			36.3287i			3.04863i
$143$	−4.55656	−	6.26885i	−0.381039	−	0.524228i
$144$	18.6981			1.55817
$145$	−3.04589			−0.252948
$146$		−	5.20718i		−	0.430950i
$147$			1.98966i			0.164105i
$148$			6.17225i			0.507356i
$149$			9.35580i			0.766457i	0.923654	+	0.383228i	$0.125188\pi$
$149$			9.35580i			0.766457i	−0.923654	+	0.383228i	$0.874812\pi$
$150$			0.973657i			0.0794988i
$151$	9.35512			0.761309			0.380655	−	0.924717i	$-0.375699\pi$
$151$	9.35512			0.761309			0.380655	+	0.924717i	$0.375699\pi$
$152$	−3.22886	+	26.2608i	−0.261895	+	2.13003i
$153$		−	15.4858i		−	1.25195i
$154$	−9.18228	+	6.67421i	−0.739929	+	0.537823i
$155$			8.09312i			0.650055i
$156$		−	3.95671i		−	0.316790i
$157$	6.63790			0.529762			0.264881	−	0.964281i	$-0.414667\pi$
$157$	6.63790			0.529762			0.264881	+	0.964281i	$0.414667\pi$
$158$	−24.2104			−1.92608
$159$	1.52210			0.120711
$160$	−4.44597			−0.351484
$161$			1.32855i			0.104704i
$162$	19.4502			1.52816
$163$	14.1577			1.10892			0.554458	−	0.832212i	$-0.312926\pi$
$163$	14.1577			1.10892			0.554458	+	0.832212i	$0.312926\pi$
$164$	−4.94236			−0.385934
$165$	1.03258	−	0.750537i	0.0803861	−	0.0584292i
$166$			25.7621i			1.99953i
$167$	−2.40922			−0.186431			−0.0932155	−	0.995646i	$-0.529715\pi$
$167$	−2.40922			−0.186431			−0.0932155	+	0.995646i	$0.529715\pi$
$168$	−3.16091			−0.243869
$169$	−7.53993			−0.579994
$170$			13.7365i			1.05354i
$171$	−1.51701	+	12.3381i	−0.116009	+	0.943515i
$172$			8.88209i			0.677253i
$173$	10.2515			0.779410			0.389705	−	0.920940i	$-0.372577\pi$
$173$	10.2515			0.779410			0.389705	+	0.920940i	$0.372577\pi$
$174$			2.96566i			0.224826i
$175$			1.35297i			0.102275i
$176$	12.7852	+	17.5897i	0.963720	+	1.32587i
$177$	−0.485126			−0.0364643
$178$		−	31.2103i		−	2.33931i
$179$		−	16.5494i		−	1.23696i	−0.785799	−	0.618482i	$-0.787748\pi$
$179$		−	16.5494i		−	1.23696i	0.785799	−	0.618482i	$-0.212252\pi$
$180$	−12.5467			−0.935176
$181$			17.2195i			1.27992i	0.768410	+	0.639958i	$0.221048\pi$
$181$			17.2195i			1.27992i	−0.768410	+	0.639958i	$0.778952\pi$
$182$		−	7.99762i		−	0.592823i
$183$	3.67870			0.271937
$184$	5.96041			0.439407
$185$		−	1.40295i		−	0.103147i
$186$	7.87993			0.577784
$187$	14.5678	−	10.5887i	1.06530	−	0.774323i
$188$	−54.1064			−3.94611
$189$	−3.04731			−0.221659
$190$	1.34565	−	10.9444i	0.0976237	−	0.793988i
$191$	10.7378			0.776960			0.388480	−	0.921457i	$-0.373000\pi$
$191$	10.7378			0.776960			0.388480	+	0.921457i	$0.373000\pi$
$192$		−	0.718145i		−	0.0518276i
$193$	11.7328			0.844543			0.422272	−	0.906469i	$-0.361233\pi$
$193$	11.7328			0.844543			0.422272	+	0.906469i	$0.361233\pi$
$194$		−	5.65830i		−	0.406242i
$195$			0.899359i			0.0644044i
$196$	22.7429			1.62450
$197$			10.9577i			0.780704i	0.920666	+	0.390352i	$0.127647\pi$
$197$			10.9577i			0.780704i	−0.920666	+	0.390352i	$0.872353\pi$
$198$	14.0682	+	19.3548i	0.999785	+	1.37549i
$199$	15.9815			1.13290			0.566448	−	0.824098i	$-0.308317\pi$
$199$	15.9815			1.13290			0.566448	+	0.824098i	$0.308317\pi$
$200$	6.07000			0.429214
$201$	5.10793			0.360285
$202$		−	12.8653i		−	0.905201i
$203$			4.12101i			0.289238i
$204$	9.19475			0.643761
$205$	1.12340			0.0784615
$206$		−	17.2415i		−	1.20127i
$207$	2.80037			0.194639
$208$	−15.3203			−1.06227
$209$	−12.6440	+	7.00931i	−0.874600	+	0.484844i
$210$	1.31733			0.0909046
$211$	24.8040			1.70758			0.853790	−	0.520617i	$-0.174298\pi$
$211$	24.8040			1.70758			0.853790	+	0.520617i	$0.174298\pi$
$212$		−	17.3985i		−	1.19493i
$213$	−5.52727			−0.378722
$214$	−44.0761			−3.01298
$215$		−	2.01890i		−	0.137688i
$216$			13.6715i			0.930229i
$217$	10.9498			0.743319
$218$	−42.7965			−2.89855
$219$	0.792254			0.0535356
$220$	−8.57905	−	11.8029i	−0.578400	−	0.795754i
$221$			12.6883i			0.853509i
$222$	−1.36599			−0.0916794
$223$			26.5583i			1.77848i	0.457442	+	0.889239i	$0.348766\pi$
$223$			26.5583i			1.77848i	−0.457442	+	0.889239i	$0.651234\pi$
$224$			6.01527i			0.401912i
$225$	2.85186			0.190124
$226$		−	24.4157i		−	1.62411i
$227$	3.31971			0.220337			0.110168	−	0.993913i	$-0.464861\pi$
$227$	3.31971			0.220337			0.110168	+	0.993913i	$0.464861\pi$
$228$	−7.32577	−	0.900730i	−0.485161	−	0.0596523i
$229$	2.71143			0.179177			0.0895883	−	0.995979i	$-0.471445\pi$
$229$	2.71143			0.179177			0.0895883	+	0.995979i	$0.471445\pi$
$230$	−2.48404			−0.163793
$231$	−1.01546	−	1.39705i	−0.0668121	−	0.0919191i
$232$	18.4886			1.21384
$233$			2.91234i			0.190794i	0.995439	+	0.0953970i	$0.0304120\pi$
$233$			2.91234i			0.190794i	−0.995439	+	0.0953970i	$0.969588\pi$
$234$	−16.8578			−1.10203
$235$	12.2984			0.802257
$236$			5.54526i			0.360966i
$237$		−	3.68353i		−	0.239271i
$238$	18.5852			1.20470
$239$		−	20.7111i		−	1.33969i	−0.742502	−	0.669843i	$-0.766361\pi$
$239$		−	20.7111i		−	1.33969i	0.742502	−	0.669843i	$-0.233639\pi$
$240$		−	2.52350i		−	0.162891i
$241$	6.54934			0.421880			0.210940	−	0.977499i	$-0.432348\pi$
$241$	6.54934			0.421880			0.210940	+	0.977499i	$0.432348\pi$
$242$	−8.58807	+	26.4685i	−0.552062	+	1.70146i
$243$			9.71621i			0.623295i
$244$		−	42.0496i		−	2.69195i
$245$	−5.16946			−0.330265
$246$		−	1.09380i		−	0.0697384i
$247$	1.24296	−	10.1092i	0.0790879	−	0.643234i
$248$		−	49.1253i		−	3.11946i
$249$	−3.91961			−0.248395
$250$	−2.52972			−0.159993
$251$	−8.69353			−0.548731			−0.274365	−	0.961626i	$-0.588468\pi$
$251$	−8.69353			−0.548731			−0.274365	+	0.961626i	$0.588468\pi$
$252$			16.9754i			1.06935i
$253$	1.91481	+	2.63437i	0.120383	+	0.165621i
$254$	−28.3188			−1.77688
$255$	−2.08996			−0.130879
$256$	−30.7029			−1.91893
$257$		−	17.6353i		−	1.10006i	−0.835145	−	0.550030i	$-0.814616\pi$
$257$		−	17.6353i		−	1.10006i	0.835145	−	0.550030i	$-0.185384\pi$
$258$	−1.96571			−0.122380
$259$	−1.89815			−0.117946
$260$	10.2802			0.637549
$261$	8.68647			0.537679
$262$			29.7495i			1.83793i
$263$		−	24.9750i		−	1.54002i	−0.638030	−	0.770012i	$-0.720250\pi$
$263$		−	24.9750i		−	1.54002i	0.638030	−	0.770012i	$-0.279750\pi$
$264$	−6.26775	+	4.55576i	−0.385753	+	0.280388i
$265$			3.95467i			0.242934i
$266$	−14.8074	−	1.82063i	−0.907903	−	0.111630i
$267$	4.74854			0.290606
$268$		−	58.3864i		−	3.56652i
$269$			14.4347i			0.880096i	0.897974	+	0.440048i	$0.145039\pi$
$269$			14.4347i			0.880096i	−0.897974	+	0.440048i	$0.854961\pi$
$270$		−	5.69771i		−	0.346751i
$271$			3.81840i			0.231951i	0.993252	+	0.115976i	$0.0369994\pi$
$271$			3.81840i			0.231951i	−0.993252	+	0.115976i	$0.963001\pi$
$272$		−	35.6019i		−	2.15868i
$273$	1.21681			0.0736446
$274$	14.7433			0.890676
$275$	1.95002	+	2.68280i	0.117590	+	0.161779i
$276$			1.66273i			0.100085i
$277$			8.53684i			0.512929i	0.966554	+	0.256464i	$0.0825577\pi$
$277$			8.53684i			0.512929i	−0.966554	+	0.256464i	$0.917442\pi$
$278$			4.90907i			0.294426i
$279$		−	23.0805i		−	1.38179i
$280$		−	8.21255i		−	0.490794i
$281$	−11.5517			−0.689114			−0.344557	−	0.938765i	$-0.611971\pi$
$281$	−11.5517			−0.689114			−0.344557	+	0.938765i	$0.611971\pi$
$282$		−	11.9744i		−	0.713064i
$283$			23.1870i			1.37833i	0.724606	+	0.689163i	$0.242022\pi$
$283$			23.1870i			1.37833i	−0.724606	+	0.689163i	$0.757978\pi$
$284$			63.1798i			3.74903i
$285$	1.66515	+	0.204736i	0.0986348	+	0.0121275i
$286$	−11.5268	−	15.8584i	−0.681596	−	0.937729i
$287$		−	1.51993i		−	0.0897185i
$288$	12.6793			0.747134
$289$	−12.4856			−0.734446
$290$	−7.70526			−0.452468
$291$	0.860890			0.0504663
$292$		−	9.05590i		−	0.529957i
$293$	−24.5380			−1.43353			−0.716763	−	0.697317i	$-0.754377\pi$
$293$	−24.5380			−1.43353			−0.716763	+	0.697317i	$0.754377\pi$
$294$			5.03328i			0.293547i
$295$		−	1.26044i		−	0.0733854i
$296$			8.51591i			0.494977i
$297$	−6.04250	+	4.39204i	−0.350621	+	0.254852i
$298$			23.6675i			1.37102i
$299$	−2.29449			−0.132694
$300$			1.69330i			0.0977629i
$301$	−2.73151			−0.157442
$302$	23.6658			1.36182
$303$	1.95741			0.112450
$304$	−3.48761	+	28.3653i	−0.200028	+	1.62686i
$305$			9.55786i			0.547281i
$306$		−	39.1747i		−	2.23947i
$307$	21.7400			1.24077			0.620384	−	0.784298i	$-0.286977\pi$
$307$	21.7400			1.24077			0.620384	+	0.784298i	$0.286977\pi$
$308$	−15.9691	+	11.6072i	−0.909921	+	0.661383i
$309$	2.62323			0.149230
$310$			20.4733i			1.16281i
$311$	−1.75399			−0.0994594			−0.0497297	−	0.998763i	$-0.515836\pi$
$311$	−1.75399			−0.0994594			−0.0497297	+	0.998763i	$0.515836\pi$
$312$		−	5.45911i		−	0.309061i
$313$	9.69040			0.547734			0.273867	−	0.961768i	$-0.411697\pi$
$313$	9.69040			0.547734			0.273867	+	0.961768i	$0.411697\pi$
$314$	16.7920			0.947629
$315$		−	3.85849i		−	0.217401i
$316$	−42.1048			−2.36858
$317$		−	1.24283i		−	0.0698042i	−0.999391	−	0.0349021i	$-0.988888\pi$
$317$		−	1.24283i		−	0.0698042i	0.999391	−	0.0349021i	$-0.0111119\pi$
$318$	3.85050			0.215925
$319$	5.93954	+	8.17154i	0.332551	+	0.457518i
$320$	1.86586			0.104305
$321$		−	6.70602i		−	0.374293i
$322$			3.36085i			0.187293i
$323$	23.4922	+	2.88845i	1.30714	+	0.160718i
$324$	33.8263			1.87924
$325$	−2.33668			−0.129616
$326$	35.8150			1.98361
$327$		−	6.51133i		−	0.360078i
$328$	−6.81903			−0.376518
$329$		−	16.6394i		−	0.917357i
$330$	2.61213	−	1.89865i	0.143793	−	0.104517i
$331$			33.0877i			1.81866i	0.416073	+	0.909331i	$0.363406\pi$
$331$			33.0877i			1.81866i	−0.416073	+	0.909331i	$0.636594\pi$
$332$			44.8033i			2.45890i
$333$			4.00102i			0.219255i
$334$	−6.09465			−0.333484
$335$			13.2712i			0.725084i
$336$	−3.41422			−0.186261
$337$	0.317131			0.0172752			0.00863760	−	0.999963i	$-0.497251\pi$
$337$	0.317131			0.0172752			0.00863760	+	0.999963i	$0.497251\pi$
$338$	−19.0739			−1.03748
$339$	3.71476			0.201758
$340$			23.8894i			1.29559i
$341$	21.7123	−	15.7817i	1.17578	−	0.854628i
$342$	−3.83761	+	31.2118i	−0.207514	+	1.68774i
$343$			16.4650i			0.889024i
$344$			12.2547i			0.660729i
$345$		−	0.377938i		−	0.0203475i
$346$	25.9335			1.39419
$347$		−	10.3945i		−	0.558008i	−0.960290	−	0.279004i	$-0.909996\pi$
$347$		−	10.3945i		−	0.558008i	0.960290	−	0.279004i	$-0.0900043\pi$
$348$			5.15763i			0.276478i
$349$			14.6428i			0.783812i	0.920005	+	0.391906i	$0.128184\pi$
$349$			14.6428i			0.783812i	−0.920005	+	0.391906i	$0.871816\pi$
$350$			3.42264i			0.182948i
$351$		−	5.26292i		−	0.280914i
$352$	8.66971	+	11.9277i	0.462097	+	0.635746i
$353$	10.5498			0.561507			0.280753	−	0.959780i	$-0.409416\pi$
$353$	10.5498			0.561507			0.280753	+	0.959780i	$0.409416\pi$
$354$	−1.22723			−0.0652267
$355$		−	14.3607i		−	0.762189i
$356$		−	54.2784i		−	2.87675i
$357$			2.82766i			0.149656i
$358$		−	41.8654i		−	2.21266i
$359$			20.9700i			1.10675i	0.832931	+	0.553376i	$0.186661\pi$
$359$			20.9700i			1.10675i	−0.832931	+	0.553376i	$0.813339\pi$
$360$	−17.3108			−0.912360
$361$	−18.4341	−	4.60265i	−0.970215	−	0.242245i
$362$			43.5605i			2.28949i
$363$	−4.02709	−	1.30664i	−0.211367	−	0.0685810i
$364$		−	13.9088i		−	0.729019i
$365$			2.05840i			0.107742i
$366$	9.30608			0.486437
$367$	−18.1151			−0.945599			−0.472799	−	0.881170i	$-0.656757\pi$
$367$	−18.1151			−0.945599			−0.472799	+	0.881170i	$0.656757\pi$
$368$	6.43807			0.335608
$369$	−3.20377			−0.166782
$370$		−	3.54907i		−	0.184507i
$371$	5.35057			0.277788
$372$	13.7041			0.710525
$373$	22.2513			1.15213			0.576064	−	0.817405i	$-0.304588\pi$
$373$	22.2513			1.15213			0.576064	+	0.817405i	$0.304588\pi$
$374$	36.8524	−	26.7865i	1.90559	−	1.38510i
$375$		−	0.384887i		−	0.0198755i
$376$	−74.6511			−3.84984
$377$	−7.11728			−0.366559
$378$	−7.70885			−0.396500
$379$			21.0036i			1.07888i	0.842024	+	0.539441i	$0.181364\pi$
$379$			21.0036i			1.07888i	−0.842024	+	0.539441i	$0.818636\pi$
$380$	2.34024	−	19.0335i	0.120052	−	0.976400i
$381$		−	4.30860i		−	0.220736i
$382$	27.1636			1.38981
$383$		−	17.6182i		−	0.900249i	−0.892966	−	0.450125i	$-0.851380\pi$
$383$		−	17.6182i		−	0.900249i	0.892966	−	0.450125i	$-0.148620\pi$
$384$		−	5.23910i		−	0.267357i
$385$	3.62976	−	2.63832i	0.184990	−	0.134461i
$386$	29.6806			1.51070
$387$			5.75761i			0.292676i
$388$		−	9.84045i		−	0.499573i
$389$	−12.7126			−0.644555			−0.322278	−	0.946645i	$-0.604448\pi$
$389$	−12.7126			−0.644555			−0.322278	+	0.946645i	$0.604448\pi$
$390$			2.27512i			0.115205i
$391$		−	5.33202i		−	0.269652i
$392$	31.3787			1.58486
$393$	−4.52628			−0.228321
$394$			27.7199i			1.39651i
$395$	9.57041			0.481540
$396$	24.4663	+	33.6603i	1.22948	+	1.69150i
$397$	−3.16750			−0.158972			−0.0794862	−	0.996836i	$-0.525328\pi$
$397$	−3.16750			−0.158972			−0.0794862	+	0.996836i	$0.525328\pi$
$398$	40.4286			2.02650
$399$	0.277002	−	2.25290i	0.0138674	−	0.112786i
$400$	6.55645			0.327822
$401$			10.7406i			0.536358i	0.963369	+	0.268179i	$0.0864219\pi$
$401$			10.7406i			0.536358i	−0.963369	+	0.268179i	$0.913578\pi$
$402$	12.9216			0.644472
$403$			18.9110i			0.942026i
$404$		−	22.3743i		−	1.11316i
$405$	−7.68870			−0.382055
$406$			10.4250i			0.517384i
$407$	−3.76384	+	2.73578i	−0.186567	+	0.135607i
$408$	12.6861			0.628055
$409$	16.5390			0.817801			0.408900	−	0.912579i	$-0.365912\pi$
$409$	16.5390			0.817801			0.408900	+	0.912579i	$0.365912\pi$
$410$	2.84188			0.140350
$411$			2.24314i			0.110646i
$412$		−	29.9849i		−	1.47725i
$413$	−1.70534			−0.0839141
$414$	7.08415			0.348167
$415$		−	10.1838i		−	0.499902i
$416$	−10.3888			−0.509353
$417$	−0.746897			−0.0365757
$418$	−31.9856	+	17.7316i	−1.56447	+	0.867281i
$419$	7.71720			0.377010			0.188505	−	0.982072i	$-0.439636\pi$
$419$	7.71720			0.377010			0.188505	+	0.982072i	$0.439636\pi$
$420$	2.29100			0.111789
$421$		−	25.5946i		−	1.24740i	−0.781662	−	0.623702i	$-0.785628\pi$
$421$		−	25.5946i		−	1.24740i	0.781662	−	0.623702i	$-0.214372\pi$
$422$	62.7473			3.05449
$423$	−35.0732			−1.70532
$424$		−	24.0049i		−	1.16578i
$425$		−	5.43006i		−	0.263397i
$426$	−13.9824			−0.677452
$427$	12.9315			0.625801
$428$	−76.6535			−3.70519
$429$	2.41280	−	1.75376i	0.116491	−	0.0846725i
$430$		−	5.10724i		−	0.246293i
$431$	33.3982			1.60873			0.804367	−	0.594133i	$-0.202505\pi$
$431$	33.3982			1.60873			0.804367	+	0.594133i	$0.202505\pi$
$432$			14.7671i			0.710485i
$433$			24.2308i			1.16446i	0.813025	+	0.582228i	$0.197819\pi$
$433$			24.2308i			1.16446i	−0.813025	+	0.582228i	$0.802181\pi$
$434$	27.6999			1.32964
$435$		−	1.17233i		−	0.0562088i
$436$	−74.4282			−3.56446
$437$	−0.522332	+	4.24821i	−0.0249865	+	0.203219i
$438$	2.00418			0.0957634
$439$	−30.2441			−1.44347			−0.721737	−	0.692167i	$-0.756656\pi$
$439$	−30.2441			−1.44347			−0.721737	+	0.692167i	$0.756656\pi$
$440$	−11.8366	−	16.2846i	−0.564288	−	0.776339i
$441$	14.7426			0.702028
$442$			32.0979i			1.52674i
$443$	−2.75876			−0.131073			−0.0655363	−	0.997850i	$-0.520876\pi$
$443$	−2.75876			−0.131073			−0.0655363	+	0.997850i	$0.520876\pi$
$444$	−2.37562			−0.112742
$445$			12.3375i			0.584852i
$446$			67.1852i			3.18131i
$447$	−3.60093			−0.170318
$448$		−	2.52445i		−	0.119269i
$449$			32.7641i			1.54623i	0.634265	+	0.773116i	$0.281303\pi$
$449$			32.7641i			1.54623i	−0.634265	+	0.773116i	$0.718697\pi$
$450$	7.21441			0.340090
$451$	−2.19064	−	3.01386i	−0.103153	−	0.141917i
$452$		−	42.4617i		−	1.99723i
$453$			3.60067i			0.169174i
$454$	8.39793			0.394134
$455$			3.16147i			0.148212i
$456$	−10.1074	−	1.24275i	−0.473325	−	0.0581969i
$457$		−	13.2581i		−	0.620186i	−0.950706	−	0.310093i	$-0.899640\pi$
$457$		−	13.2581i		−	0.620186i	0.950706	−	0.310093i	$-0.100360\pi$
$458$	6.85916			0.320508
$459$	12.2302			0.570856
$460$	−4.32004			−0.201423
$461$		−	23.8716i		−	1.11181i	−0.831246	−	0.555905i	$-0.812372\pi$
$461$		−	23.8716i		−	1.11181i	0.831246	−	0.555905i	$-0.187628\pi$
$462$	−2.56882	−	3.53414i	−0.119512	−	0.164423i
$463$	7.08380			0.329212			0.164606	−	0.986359i	$-0.447365\pi$
$463$	7.08380			0.329212			0.164606	+	0.986359i	$0.447365\pi$
$464$	19.9703			0.927096
$465$	−3.11494			−0.144452
$466$			7.36741i			0.341289i
$467$	0.535622			0.0247856			0.0123928	−	0.999923i	$-0.496055\pi$
$467$	0.535622			0.0247856			0.0123928	+	0.999923i	$0.496055\pi$
$468$	−29.3176			−1.35521
$469$	17.9556			0.829113
$470$	31.1114			1.43506
$471$			2.55485i			0.117721i
$472$			7.65085i			0.352159i
$473$	−5.41630	+	3.93688i	−0.249042	+	0.181018i
$474$		−	9.31830i		−	0.428004i
$475$	−0.531936	+	4.32632i	−0.0244069	+	0.198505i
$476$	32.3218			1.48147
$477$		−	11.2782i		−	0.516393i
$478$		−	52.3931i		−	2.39641i
$479$			19.4054i			0.886657i	0.896359	+	0.443329i	$0.146203\pi$
$479$			19.4054i			0.886657i	−0.896359	+	0.443329i	$0.853797\pi$
$480$		−	1.71120i		−	0.0781051i
$481$		−	3.27824i		−	0.149475i
$482$	16.5680			0.754651
$483$	−0.511340			−0.0232668
$484$	−14.9357	+	46.0318i	−0.678894	+	2.09236i
$485$			2.23673i			0.101565i
$486$			24.5793i			1.11494i
$487$			7.55916i			0.342538i	0.985224	+	0.171269i	$0.0547867\pi$
$487$			7.55916i			0.342538i	−0.985224	+	0.171269i	$0.945213\pi$
$488$		−	58.0163i		−	2.62627i
$489$			5.44912i			0.246418i
$490$	−13.0773			−0.590772
$491$			30.9535i			1.39691i	0.715654	+	0.698455i	$0.246129\pi$
$491$			30.9535i			1.39691i	−0.715654	+	0.698455i	$0.753871\pi$
$492$		−	1.90225i		−	0.0857602i
$493$		−	16.5394i		−	0.744897i
$494$	3.14435	−	25.5735i	0.141471	−	1.15061i
$495$	−5.56118	−	7.65098i	−0.249956	−	0.343886i
$496$		−	53.0621i		−	2.38256i
$497$	−19.4297			−0.871542
$498$	−9.91551			−0.444325
$499$	40.9890			1.83492			0.917459	−	0.397831i	$-0.130237\pi$
$499$	40.9890			1.83492			0.917459	+	0.397831i	$0.130237\pi$
$500$	−4.39948			−0.196751
$501$		−	0.927278i		−	0.0414277i
$502$	−21.9922			−0.981559
$503$		−	17.7033i		−	0.789350i	−0.918821	−	0.394675i	$-0.870857\pi$
$503$		−	17.7033i		−	0.789350i	0.918821	−	0.394675i	$-0.129143\pi$
$504$			23.4211i			1.04326i
$505$			5.08567i			0.226310i
$506$	4.84393	+	6.66420i	0.215339	+	0.296260i
$507$		−	2.90202i		−	0.128883i
$508$	−49.2497			−2.18510
$509$		−	40.5717i		−	1.79831i	−0.437630	−	0.899155i	$-0.644182\pi$
$509$		−	40.5717i		−	1.79831i	0.437630	−	0.899155i	$-0.355818\pi$
$510$	−5.28702			−0.234113
$511$	2.78497			0.123200
$512$	−50.4456			−2.22940
$513$	−9.74421	−	1.19808i	−0.430217	−	0.0528967i
$514$		−	44.6124i		−	1.96777i
$515$			6.81557i			0.300330i
$516$	−3.41860			−0.150496
$517$	−23.9820	−	32.9941i	−1.05473	−	1.45108i
$518$	−4.80180			−0.210979
$519$			3.94569i			0.173196i
$520$	14.1837			0.621994
$521$			28.1322i			1.23249i	0.787553	+	0.616247i	$0.211348\pi$
$521$			28.1322i			1.23249i	−0.787553	+	0.616247i	$0.788652\pi$
$522$	21.9743			0.961790
$523$	13.7730			0.602252			0.301126	−	0.953584i	$-0.402638\pi$
$523$	13.7730			0.602252			0.301126	+	0.953584i	$0.402638\pi$
$524$			51.7379i			2.26018i
$525$	−0.520743			−0.0227271
$526$		−	63.1797i		−	2.75477i
$527$	−43.9462			−1.91432
$528$	−6.77004	+	4.92086i	−0.294628	+	0.214153i
$529$	−22.0358			−0.958078
$530$			10.0042i			0.434555i
$531$			3.59459i			0.155992i
$532$	−25.7519	−	3.16628i	−1.11649	−	0.137276i
$533$	2.62502			0.113702
$534$	12.0125			0.519830
$535$	17.4233			0.753276
$536$		−	80.5564i		−	3.47951i
$537$	6.36967			0.274872
$538$			36.5156i			1.57430i
$539$	10.0805	+	13.8687i	0.434200	+	0.597365i
$540$		−	9.90898i		−	0.426415i
$541$		−	19.7937i		−	0.850996i	−0.904959	−	0.425498i	$-0.860099\pi$
$541$		−	19.7937i		−	0.850996i	0.904959	−	0.425498i	$-0.139901\pi$
$542$			9.65947i			0.414910i
$543$	−6.62757			−0.284416
$544$		−	24.1419i		−	1.03507i
$545$	16.9175			0.724666
$546$	3.07818			0.131734
$547$	−38.3756			−1.64082			−0.820411	−	0.571774i	$-0.806256\pi$
$547$	−38.3756			−1.64082			−0.820411	+	0.571774i	$0.806256\pi$
$548$	25.6403			1.09530
$549$		−	27.2577i		−	1.16333i
$550$	4.93299	+	6.78674i	0.210344	+	0.289388i
$551$	−1.62022	+	13.1775i	−0.0690238	+	0.561381i
$552$			2.29409i			0.0976428i
$553$		−	12.9485i		−	0.550627i
$554$			21.5958i			0.917518i
$555$	0.539978			0.0229208
$556$			8.53744i			0.362068i
$557$		−	17.2554i		−	0.731136i	−0.930785	−	0.365568i	$-0.880875\pi$
$557$		−	17.2554i		−	0.731136i	0.930785	−	0.365568i	$-0.119125\pi$
$558$		−	58.3871i		−	2.47172i
$559$		−	4.71751i		−	0.199529i
$560$		−	8.87070i		−	0.374856i
$561$	4.07546	+	5.60696i	0.172066	+	0.236726i
$562$	−29.2224			−1.23267
$563$	−27.2632			−1.14901			−0.574503	−	0.818502i	$-0.694805\pi$
$563$	−27.2632			−1.14901			−0.574503	+	0.818502i	$0.694805\pi$
$564$		−	20.8249i		−	0.876885i
$565$			9.65154i			0.406043i
$566$			58.6567i			2.46553i
$567$			10.4026i			0.436868i
$568$			87.1698i			3.65756i
$569$	−28.1885			−1.18172			−0.590862	−	0.806772i	$-0.701212\pi$
$569$	−28.1885			−1.18172			−0.590862	+	0.806772i	$0.701212\pi$
$570$	4.21235	+	0.517924i	0.176436	+	0.0216934i
$571$		−	20.8031i		−	0.870581i	−0.900290	−	0.435290i	$-0.856646\pi$
$571$		−	20.8031i		−	0.870581i	0.900290	−	0.435290i	$-0.143354\pi$
$572$	−20.0465	−	27.5797i	−0.838186	−	1.15316i
$573$			4.13284i			0.172652i
$574$		−	3.84499i		−	0.160487i
$575$	0.981945			0.0409499
$576$	−5.32116			−0.221715
$577$	−43.6723			−1.81810			−0.909051	−	0.416685i	$-0.863192\pi$
$577$	−43.6723			−1.81810			−0.909051	+	0.416685i	$0.863192\pi$
$578$	−31.5850			−1.31376
$579$			4.51580i			0.187670i
$580$	−13.4003			−0.556419
$581$	−13.7784			−0.571624
$582$	2.17781			0.0902731
$583$	10.6096	−	7.71168i	0.439405	−	0.319385i
$584$		−	12.4945i		−	0.517027i
$585$	6.66389			0.275518
$586$	−62.0743			−2.56426
$587$	−27.5563			−1.13737			−0.568685	−	0.822555i	$-0.692548\pi$
$587$	−27.5563			−1.13737			−0.568685	+	0.822555i	$0.692548\pi$
$588$			8.75347i			0.360987i
$589$	35.0134	+	4.30502i	1.44270	+	0.177385i
$590$		−	3.18855i		−	0.131270i
$591$	−4.21748			−0.173484
$592$			9.19837i			0.378051i
$593$			17.1694i			0.705063i	0.935800	+	0.352531i	$0.114679\pi$
$593$			17.1694i			0.705063i	−0.935800	+	0.352531i	$0.885321\pi$
$594$	−15.2858	+	11.1106i	−0.627185	+	0.455874i
$595$	−7.34673			−0.301187
$596$			41.1606i			1.68600i
$597$			6.15106i			0.251746i
$598$	−5.80442			−0.237360
$599$			6.49020i			0.265182i	0.991171	+	0.132591i	$0.0423297\pi$
$599$			6.49020i			0.265182i	−0.991171	+	0.132591i	$0.957670\pi$
$600$			2.33627i			0.0953778i
$601$	44.8595			1.82986			0.914928	−	0.403618i	$-0.132247\pi$
$601$	44.8595			1.82986			0.914928	+	0.403618i	$0.132247\pi$
$602$	−6.90996			−0.281629
$603$		−	37.8477i		−	1.54128i
$604$	41.1577			1.67468
$605$	3.39487	−	10.4630i	0.138021	−	0.425382i
$606$	4.95170			0.201149
$607$	30.0795			1.22089			0.610446	−	0.792058i	$-0.290990\pi$
$607$	30.0795			1.22089			0.610446	+	0.792058i	$0.290990\pi$
$608$	−2.36497	+	19.2347i	−0.0959122	+	0.780069i
$609$	−1.58613			−0.0642731
$610$			24.1787i			0.978967i
$611$	28.7373			1.16259
$612$		−	68.1294i		−	2.75397i
$613$		−	13.4630i		−	0.543764i	−0.962331	−	0.271882i	$-0.912354\pi$
$613$		−	13.4630i		−	0.543764i	0.962331	−	0.271882i	$-0.0876460\pi$
$614$	54.9962			2.21946
$615$			0.432382i			0.0174353i
$616$	−22.0327	+	16.0146i	−0.887722	+	0.645247i
$617$	9.32634			0.375464			0.187732	−	0.982220i	$-0.439886\pi$
$617$	9.32634			0.375464			0.187732	+	0.982220i	$0.439886\pi$
$618$	6.63603			0.266940
$619$	17.9855			0.722899			0.361449	−	0.932392i	$-0.382282\pi$
$619$	17.9855			0.722899			0.361449	+	0.932392i	$0.382282\pi$
$620$			35.6055i			1.42995i
$621$			2.21164i			0.0887502i
$622$	−4.43709			−0.177911
$623$	16.6923			0.668762
$624$		−	5.89660i		−	0.236053i
$625$	1.00000			0.0400000
$626$	24.5140			0.979776
$627$	−2.69780	−	4.86650i	−0.107740	−	0.194349i
$628$	29.2033			1.16534
$629$	7.61811			0.303754
$630$		−	9.76090i		−	0.388884i
$631$	10.4925			0.417701			0.208850	−	0.977948i	$-0.433028\pi$
$631$	10.4925			0.417701			0.208850	+	0.977948i	$0.433028\pi$
$632$	−58.0924			−2.31079
$633$			9.54677i			0.379450i
$634$		−	3.14401i		−	0.124864i
$635$	11.1944			0.444238
$636$	6.69647			0.265532
$637$	−12.0794			−0.478602
$638$	15.0254	+	20.6717i	0.594860	+	0.818400i
$639$			40.9549i			1.62015i
$640$	13.6120			0.538062
$641$			6.59173i			0.260358i	0.991491	+	0.130179i	$0.0415551\pi$
$641$			6.59173i			0.260358i	−0.991491	+	0.130179i	$0.958445\pi$
$642$		−	16.9643i		−	0.669529i
$643$	42.3494			1.67010			0.835049	−	0.550176i	$-0.185439\pi$
$643$	42.3494			1.67010			0.835049	+	0.550176i	$0.185439\pi$
$644$			5.84491i			0.230322i
$645$	0.777048			0.0305962
$646$	59.4286	+	7.30696i	2.33819	+	0.287488i
$647$	−37.6226			−1.47910			−0.739549	−	0.673103i	$-0.764961\pi$
$647$	−37.6226			−1.47910			−0.739549	+	0.673103i	$0.764961\pi$
$648$	46.6704			1.83339
$649$	−3.38150	+	2.45787i	−0.132736	+	0.0964798i
$650$	−5.91114			−0.231854
$651$			4.21443i			0.165177i
$652$	62.2864			2.43932
$653$	2.79930			0.109545			0.0547726	−	0.998499i	$-0.482557\pi$
$653$	2.79930			0.109545			0.0547726	+	0.998499i	$0.482557\pi$
$654$		−	16.4718i		−	0.644100i
$655$		−	11.7600i		−	0.459501i
$656$	−7.36550			−0.287574
$657$		−	5.87028i		−	0.229022i
$658$		−	42.0929i		−	1.64095i
$659$	28.1649			1.09715			0.548574	−	0.836102i	$-0.315171\pi$
$659$	28.1649			1.09715			0.548574	+	0.836102i	$0.315171\pi$
$660$	4.54280	−	3.30197i	0.176828	−	0.128529i
$661$			23.2863i			0.905731i	0.891579	+	0.452865i	$0.149598\pi$
$661$			23.2863i			0.905731i	−0.891579	+	0.452865i	$0.850402\pi$
$662$			83.7025i			3.25319i
$663$	−4.88357			−0.189662
$664$			61.8156i			2.39891i
$665$	5.85340	+	0.719696i	0.226985	+	0.0279086i
$666$			10.1215i			0.392198i
$667$	2.99090			0.115808
$668$	−10.5993			−0.410099
$669$	−10.2220			−0.395204
$670$			33.5725i			1.29702i
$671$	25.6419	−	18.6380i	0.989893	−	0.719511i
$672$	−2.31520			−0.0893109
$673$	−21.5800			−0.831847			−0.415924	−	0.909400i	$-0.636542\pi$
$673$	−21.5800			−0.831847			−0.415924	+	0.909400i	$0.636542\pi$
$674$	0.802251			0.0309016
$675$			2.25231i			0.0866914i
$676$	−33.1717			−1.27584
$677$	−40.3794			−1.55190			−0.775952	−	0.630791i	$-0.782730\pi$
$677$	−40.3794			−1.55190			−0.775952	+	0.630791i	$0.782730\pi$
$678$	9.39729			0.360901
$679$	3.02624			0.116136
$680$			32.9605i			1.26398i
$681$			1.27771i			0.0489621i
$682$	54.9259	−	39.9233i	2.10322	−	1.52874i
$683$		−	36.7147i		−	1.40485i	−0.711758	−	0.702424i	$-0.752101\pi$
$683$		−	36.7147i		−	1.40485i	0.711758	−	0.702424i	$-0.247899\pi$
$684$	−6.67405	+	54.2810i	−0.255189	+	2.07549i
$685$	−5.82804			−0.222678
$686$			41.6517i			1.59027i
$687$			1.04360i			0.0398157i
$688$			13.2368i			0.504648i
$689$			9.24081i			0.352047i
$690$		−	0.956078i		−	0.0363973i
$691$	13.6882			0.520724			0.260362	−	0.965511i	$-0.416158\pi$
$691$	13.6882			0.520724			0.260362	+	0.965511i	$0.416158\pi$
$692$	45.1014			1.71450
$693$	−10.3516	+	7.52412i	−0.393224	+	0.285818i
$694$		−	26.2953i		−	0.998155i
$695$		−	1.94056i		−	0.0736096i
$696$			7.11603i			0.269732i
$697$			6.10012i			0.231059i
$698$			37.0422i			1.40207i
$699$	−1.12092			−0.0423972
$700$			5.95238i			0.224979i
$701$		−	28.9116i		−	1.09197i	−0.837793	−	0.545987i	$-0.816155\pi$
$701$		−	28.9116i		−	1.09197i	0.837793	−	0.545987i	$-0.183845\pi$
$702$		−	13.3137i		−	0.502494i
$703$	−6.06961	−	0.746280i	−0.228920	−	0.0281465i
$704$	−3.63845	−	5.00573i	−0.137129	−	0.188660i
$705$			4.73349i			0.178273i
$706$	26.6879			1.00441
$707$	6.88078			0.258778
$708$	−2.13430			−0.0802119
$709$	16.2679			0.610954			0.305477	−	0.952199i	$-0.401184\pi$
$709$	16.2679			0.610954			0.305477	+	0.952199i	$0.401184\pi$
$710$		−	36.3287i		−	1.36339i
$711$	−27.2935			−1.02359
$712$		−	74.8885i		−	2.80657i
$713$		−	7.94700i		−	0.297617i
$714$			7.15320i			0.267702i
$715$	4.55656	+	6.26885i	0.170406	+	0.234442i
$716$		−	72.8089i		−	2.72100i
$717$	7.97143			0.297698
$718$			53.0481i			1.97974i
$719$	−9.82583			−0.366442			−0.183221	−	0.983072i	$-0.558652\pi$
$719$	−9.82583			−0.366442			−0.183221	+	0.983072i	$0.558652\pi$
$720$	−18.6981			−0.696837
$721$	9.22128			0.343418
$722$	−46.6331	−	11.6434i	−1.73550	−	0.433323i
$723$			2.52076i			0.0937480i
$724$			75.7568i			2.81548i
$725$	3.04589			0.113122
$726$	−10.1874	−	3.30544i	−0.378090	−	0.122676i
$727$	−29.2149			−1.08352			−0.541760	−	0.840533i	$-0.682242\pi$
$727$	−29.2149			−1.08352			−0.541760	+	0.840533i	$0.682242\pi$
$728$		−	19.1901i		−	0.711233i
$729$	19.3265			0.715795
$730$			5.20718i			0.192727i
$731$	10.9627			0.405471
$732$	16.1844			0.598191
$733$			27.2427i			1.00623i	0.864219	+	0.503116i	$0.167813\pi$
$733$			27.2427i			1.00623i	−0.864219	+	0.503116i	$0.832187\pi$
$734$	−45.8260			−1.69147
$735$		−	1.98966i		−	0.0733898i
$736$	4.36569			0.160922
$737$	35.6041	−	25.8791i	1.31149	−	0.953269i
$738$	−8.10465			−0.298336
$739$		−	12.3404i		−	0.453950i	−0.973901	−	0.226975i	$-0.927116\pi$
$739$		−	12.3404i		−	0.453950i	0.973901	−	0.226975i	$-0.0728835\pi$
$740$		−	6.17225i		−	0.226896i
$741$	3.89091	+	0.478402i	0.142936	+	0.0175745i
$742$	13.5354			0.496901
$743$	16.2242			0.595207			0.297603	−	0.954690i	$-0.403813\pi$
$743$	16.2242			0.595207			0.297603	+	0.954690i	$0.403813\pi$
$744$	18.9077			0.693190
$745$		−	9.35580i		−	0.342770i
$746$	56.2895			2.06090
$747$			29.0427i			1.06262i
$748$	64.0907	−	46.5848i	2.34339	−	1.70331i
$749$		−	23.5733i		−	0.861349i
$750$		−	0.973657i		−	0.0355529i
$751$		−	5.85396i		−	0.213614i	−0.994280	−	0.106807i	$-0.965937\pi$
$751$		−	5.85396i		−	0.213614i	0.994280	−	0.106807i	$-0.0340627\pi$
$752$	−80.6336			−2.94040
$753$		−	3.34603i		−	0.121936i
$754$	−18.0047			−0.655693
$755$	−9.35512			−0.340468
$756$	−13.4066			−0.487593
$757$	−40.7510			−1.48112			−0.740561	−	0.671989i	$-0.765440\pi$
$757$	−40.7510			−1.48112			−0.740561	+	0.671989i	$0.765440\pi$
$758$			53.1331i			1.92988i
$759$	−1.01393	+	0.736986i	−0.0368035	+	0.0267509i
$760$	3.22886	−	26.2608i	0.117123	−	0.952579i
$761$			12.3774i			0.448681i	0.974511	+	0.224340i	$0.0720227\pi$
$761$			12.3774i			0.448681i	−0.974511	+	0.224340i	$0.927977\pi$
$762$		−	10.8996i		−	0.394849i
$763$		−	22.8889i		−	0.828635i
$764$	47.2407			1.70911
$765$			15.4858i			0.559890i
$766$		−	44.5691i		−	1.61035i
$767$		−	2.94523i		−	0.106346i
$768$		−	11.8172i		−	0.426415i
$769$		−	27.3673i		−	0.986889i	−0.869777	−	0.493444i	$-0.835738\pi$
$769$		−	27.3673i		−	0.986889i	0.869777	−	0.493444i	$-0.164262\pi$
$770$	9.18228	−	6.67421i	0.330906	−	0.240522i
$771$	6.78761			0.244450
$772$	51.6181			1.85778
$773$			44.5435i			1.60212i	0.598586	+	0.801059i	$0.295729\pi$
$773$			44.5435i			1.60212i	−0.598586	+	0.801059i	$0.704271\pi$
$774$			14.5651i			0.523533i
$775$		−	8.09312i		−	0.290714i
$776$		−	13.5770i		−	0.487385i
$777$		−	0.730576i		−	0.0262093i
$778$	−32.1593			−1.15297
$779$	0.597576	−	4.86018i	0.0214104	−	0.174134i
$780$			3.95671i			0.141673i
$781$	−38.5271	+	28.0037i	−1.37861	+	1.00205i
$782$		−	13.4885i		−	0.482348i
$783$			6.86029i			0.245167i
$784$	33.8933			1.21048
$785$	−6.63790			−0.236917
$786$	−11.4502			−0.408416
$787$	14.5204			0.517596			0.258798	−	0.965932i	$-0.416674\pi$
$787$	14.5204			0.517596			0.258798	+	0.965932i	$0.416674\pi$
$788$			48.2082i			1.71734i
$789$	9.61256			0.342216
$790$	24.2104			0.861369
$791$	13.0583			0.464299
$792$	33.7564	+	46.4415i	1.19948	+	1.65023i
$793$			22.3337i			0.793091i
$794$	−8.01289			−0.284367
$795$	−1.52210			−0.0539835
$796$	70.3101			2.49207
$797$			4.45183i			0.157692i	0.996887	+	0.0788459i	$0.0251235\pi$
$797$			4.45183i			0.157692i	−0.996887	+	0.0788459i	$0.974876\pi$
$798$	0.700737	−	5.69920i	0.0248058	−	0.201750i
$799$			66.7809i			2.36254i
$800$	4.44597			0.157189
$801$		−	35.1848i		−	1.24319i
$802$			27.1706i			0.959428i
$803$	5.52229	−	4.01392i	0.194878	−	0.141648i
$804$	22.4722			0.792534
$805$		−	1.32855i		−	0.0468251i
$806$			47.8396i			1.68508i
$807$	−5.55572			−0.195571
$808$		−	30.8701i		−	1.08600i
$809$			44.2999i			1.55750i	0.627334	+	0.778750i	$0.284146\pi$
$809$			44.2999i			1.55750i	−0.627334	+	0.778750i	$0.715854\pi$
$810$	−19.4502			−0.683412
$811$	−23.0013			−0.807683			−0.403842	−	0.914829i	$-0.632325\pi$
$811$	−23.0013			−0.807683			−0.403842	+	0.914829i	$0.632325\pi$
$812$			18.1303i			0.636249i
$813$	−1.46965			−0.0515430
$814$	−9.52146	+	6.92074i	−0.333727	+	0.242572i
$815$	−14.1577			−0.495922
$816$	13.7027			0.479692
$817$	−8.73439	−	1.07392i	−0.305578	−	0.0375718i
$818$	41.8390			1.46287
$819$		−	9.01606i		−	0.315047i
$820$	4.94236			0.172595
$821$		−	27.6565i		−	0.965218i	−0.875836	−	0.482609i	$-0.839689\pi$
$821$		−	27.6565i		−	0.965218i	0.875836	−	0.482609i	$-0.160311\pi$
$822$			5.67451i			0.197921i
$823$	11.9083			0.415098			0.207549	−	0.978225i	$-0.433451\pi$
$823$	11.9083			0.415098			0.207549	+	0.978225i	$0.433451\pi$
$824$		−	41.3705i		−	1.44121i
$825$	−1.03258	+	0.750537i	−0.0359497	+	0.0261303i
$826$	−4.31402			−0.150104
$827$	−11.4708			−0.398879			−0.199440	−	0.979910i	$-0.563912\pi$
$827$	−11.4708			−0.398879			−0.199440	+	0.979910i	$0.563912\pi$
$828$	12.3202			0.428156
$829$			39.9028i			1.38588i	0.720995	+	0.692941i	$0.243685\pi$
$829$			39.9028i			1.38588i	−0.720995	+	0.692941i	$0.756315\pi$
$830$		−	25.7621i		−	0.894216i
$831$	−3.28572			−0.113980
$832$	4.35991			0.151153
$833$		−	28.0705i		−	0.972586i
$834$	−1.88944			−0.0654259
$835$	2.40922			0.0833745
$836$	−55.6268	+	30.8373i	−1.92389	+	1.06653i
$837$	18.2282			0.630059
$838$	19.5223			0.674388
$839$		−	31.4430i		−	1.08553i	−0.839884	−	0.542766i	$-0.817377\pi$
$839$		−	31.4430i		−	1.08553i	0.839884	−	0.542766i	$-0.182623\pi$
$840$	3.16091			0.109062
$841$	−19.7225			−0.680087
$842$		−	64.7471i		−	2.23133i
$843$		−	4.44609i		−	0.153131i
$844$	109.125			3.75623
$845$	7.53993			0.259381
$846$	−88.7254			−3.05044
$847$	−14.1562	−	4.59317i	−0.486412	−	0.157823i
$848$		−	25.9286i		−	0.890393i
$849$	−8.92440			−0.306285
$850$		−	13.7365i		−	0.471159i
$851$			1.37762i			0.0472242i
$852$	−24.3171			−0.833090
$853$			29.2514i			1.00155i	0.865578	+	0.500775i	$0.166951\pi$
$853$			29.2514i			1.00155i	−0.865578	+	0.500775i	$0.833049\pi$
$854$	32.7131			1.11942
$855$	1.51701	−	12.3381i	0.0518806	−	0.421953i
$856$	−105.760			−3.61479
$857$	3.26967			0.111690			0.0558449	−	0.998439i	$-0.482215\pi$
$857$	3.26967			0.111690			0.0558449	+	0.998439i	$0.482215\pi$
$858$	6.10371	−	4.43653i	0.208377	−	0.151461i
$859$	44.4634			1.51707			0.758536	−	0.651631i	$-0.225915\pi$
$859$	44.4634			1.51707			0.758536	+	0.651631i	$0.225915\pi$
$860$		−	8.88209i		−	0.302877i
$861$	0.585001			0.0199368
$862$	84.4880			2.87767
$863$			24.8514i			0.845951i	0.906141	+	0.422975i	$0.139014\pi$
$863$			24.8514i			0.845951i	−0.906141	+	0.422975i	$0.860986\pi$
$864$			10.0137i			0.340672i
$865$	−10.2515			−0.348563
$866$			61.2971i			2.08296i
$867$		−	4.80555i		−	0.163205i
$868$	48.1733			1.63511
$869$	−18.6625	−	25.6755i	−0.633081	−	0.870983i
$870$		−	2.96566i		−	0.100545i
$871$			31.0106i			1.05075i
$872$	−102.689			−3.47750
$873$		−	6.37885i		−	0.215891i
$874$	−1.32135	+	10.7468i	−0.0446954	+	0.363515i
$875$		−	1.35297i		−	0.0457388i
$876$	3.48550			0.117764
$877$	−1.81191			−0.0611839			−0.0305919	−	0.999532i	$-0.509739\pi$
$877$	−1.81191			−0.0611839			−0.0305919	+	0.999532i	$0.509739\pi$
$878$	−76.5092			−2.58206
$879$		−	9.44437i		−	0.318551i
$880$	−12.7852	−	17.5897i	−0.430989	−	0.592948i
$881$	−45.3998			−1.52956			−0.764779	−	0.644293i	$-0.777152\pi$
$881$	−45.3998			−1.52956			−0.764779	+	0.644293i	$0.777152\pi$
$882$	37.2946			1.25578
$883$	31.4299			1.05770			0.528851	−	0.848715i	$-0.322623\pi$
$883$	31.4299			1.05770			0.528851	+	0.848715i	$0.322623\pi$
$884$			55.8220i			1.87750i
$885$	0.485126			0.0163073
$886$	−6.97889			−0.234460
$887$	−12.8799			−0.432464			−0.216232	−	0.976342i	$-0.569377\pi$
$887$	−12.8799			−0.432464			−0.216232	+	0.976342i	$0.569377\pi$
$888$	−3.27767			−0.109991
$889$		−	15.1458i		−	0.507974i
$890$			31.2103i			1.04617i
$891$	14.9931	+	20.6273i	0.502287	+	0.691040i
$892$			116.843i			3.91219i
$893$	6.54195	−	53.2067i	0.218918	−	1.78049i
$894$	−9.10934			−0.304662
$895$			16.5494i			0.553187i
$896$		−	18.4167i		−	0.615259i
$897$		−	0.883121i		−	0.0294865i
$898$			82.8839i			2.76587i
$899$		−	24.6508i		−	0.822150i
$900$	12.5467			0.418223
$901$	−21.4741			−0.715407
$902$	−5.54171	−	7.62421i	−0.184519	−	0.253858i
$903$		−	1.05132i		−	0.0349859i
$904$		−	58.5849i		−	1.94850i
$905$		−	17.2195i		−	0.572395i
$906$			9.10868i			0.302616i
$907$			45.1329i			1.49861i	0.662222	+	0.749307i	$0.269613\pi$
$907$			45.1329i			1.49861i	−0.662222	+	0.749307i	$0.730387\pi$
$908$	14.6050			0.484683
$909$		−	14.5036i		−	0.481055i
$910$			7.99762i			0.265118i
$911$		−	45.2270i		−	1.49844i	−0.662323	−	0.749219i	$-0.730429\pi$
$911$		−	45.2270i		−	1.49844i	0.662323	−	0.749219i	$-0.269571\pi$
$912$	−10.9174	−	1.34234i	−0.361513	−	0.0444493i
$913$	−27.3211	+	19.8585i	−0.904196	+	0.657222i
$914$		−	33.5392i		−	1.10938i
$915$	−3.67870			−0.121614
$916$	11.9289			0.394142
$917$	−15.9110			−0.525427
$918$	30.9389			1.02114
$919$		−	50.4139i		−	1.66300i	−0.555525	−	0.831500i	$-0.687483\pi$
$919$		−	50.4139i		−	1.66300i	0.555525	−	0.831500i	$-0.312517\pi$
$920$	−5.96041			−0.196509
$921$			8.36746i			0.275717i
$922$		−	60.3884i		−	1.98879i
$923$		−	33.5565i		−	1.10452i
$924$	−4.46748	−	6.14629i	−0.146969	−	0.202198i
$925$			1.40295i			0.0461287i
$926$	17.9200			0.588889
$927$		−	19.4371i		−	0.638397i
$928$	13.5419			0.444536
$929$	−18.1263			−0.594704			−0.297352	−	0.954768i	$-0.596103\pi$
$929$	−18.1263			−0.594704			−0.297352	+	0.954768i	$0.596103\pi$
$930$	−7.87993			−0.258393
$931$	−2.74982	+	22.3648i	−0.0901219	+	0.732975i
$932$			12.8128i			0.419697i
$933$		−	0.675087i		−	0.0221014i
$934$	1.35497			0.0443361
$935$	−14.5678	+	10.5887i	−0.476418	+	0.346288i
$936$	−40.4498			−1.32214
$937$		−	39.2538i		−	1.28237i	−0.767388	−	0.641183i	$-0.778444\pi$
$937$		−	39.2538i		−	1.28237i	0.767388	−	0.641183i	$-0.221556\pi$
$938$	45.4226			1.48310
$939$			3.72971i			0.121715i
$940$	54.1064			1.76476
$941$	19.7778			0.644739			0.322370	−	0.946614i	$-0.395521\pi$
$941$	19.7778			0.644739			0.322370	+	0.946614i	$0.395521\pi$
$942$			6.46304i			0.210577i
$943$	−1.10311			−0.0359224
$944$			8.26398i			0.268970i
$945$	3.04731			0.0991291
$946$	−13.7017	+	9.95920i	−0.445481	+	0.323801i
$947$	14.7874			0.480527			0.240263	−	0.970708i	$-0.422766\pi$
$947$	14.7874			0.480527			0.240263	+	0.970708i	$0.422766\pi$
$948$		−	16.2056i		−	0.526334i
$949$			4.80983i			0.156134i
$950$	−1.34565	+	10.9444i	−0.0436586	+	0.355082i
$951$	0.478349			0.0155115
$952$	44.5947			1.44532
$953$	−24.2111			−0.784274			−0.392137	−	0.919907i	$-0.628264\pi$
$953$	−24.2111			−0.784274			−0.392137	+	0.919907i	$0.628264\pi$
$954$		−	28.5306i		−	0.923713i
$955$	−10.7378			−0.347467
$956$		−	91.1178i		−	2.94696i
$957$	−3.14512	+	2.28606i	−0.101667	+	0.0738977i
$958$			49.0903i			1.58604i
$959$			7.88518i			0.254626i
$960$			0.718145i			0.0231780i
$961$	−34.4986			−1.11286
$962$		−	8.29304i		−	0.267378i
$963$	−49.6889			−1.60120
$964$	28.8137			0.928026
$965$	−11.7328			−0.377691
$966$	−1.29355			−0.0416192
$967$		−	0.150839i		−	0.00485064i	−0.999997	−	0.00242532i	$-0.999228\pi$
$967$		−	0.150839i		−	0.00485064i	0.999997	−	0.00242532i	$-0.000772005\pi$
$968$	−20.6069	+	63.5106i	−0.662330	+	2.04131i
$969$	−1.11173	+	9.04185i	−0.0357138	+	0.290466i
$970$			5.65830i			0.181677i
$971$		−	1.13243i		−	0.0363415i	−0.999835	−	0.0181708i	$-0.994216\pi$
$971$		−	1.13243i		−	0.0363415i	0.999835	−	0.0181708i	$-0.00578425\pi$
$972$			42.7462i			1.37109i
$973$	−2.62552			−0.0841704
$974$			19.1225i			0.612726i
$975$		−	0.899359i		−	0.0288025i
$976$		−	62.6656i		−	2.00588i
$977$		−	14.0511i		−	0.449534i	−0.974413	−	0.224767i	$-0.927838\pi$
$977$		−	14.0511i		−	0.449534i	0.974413	−	0.224767i	$-0.0721621\pi$
$978$			13.7847i			0.440787i
$979$	33.0990	−	24.0583i	1.05785	−	0.768906i
$980$	−22.7429			−0.726497
$981$	−48.2464			−1.54039
$982$			78.3035i			2.49877i
$983$			29.6116i			0.944464i	0.881474	+	0.472232i	$0.156551\pi$
$983$			29.6116i			0.944464i	−0.881474	+	0.472232i	$0.843449\pi$
$984$		−	2.62456i		−	0.0836679i
$985$		−	10.9577i		−	0.349141i
$986$		−	41.8400i		−	1.33246i
$987$	6.40428			0.203850
$988$	5.46840	−	44.4753i	0.173973	−	1.41495i
$989$			1.98244i			0.0630381i
$990$	−14.0682	−	19.3548i	−0.447117	−	0.615137i
$991$			1.64752i			0.0523351i	0.999658	+	0.0261675i	$0.00833034\pi$
$991$			1.64752i			0.0523351i	−0.999658	+	0.0261675i	$0.991670\pi$
$992$		−	35.9817i		−	1.14242i
$993$	−12.7350			−0.404134
$994$	−49.1517			−1.55900
$995$	−15.9815			−0.506646
$996$	−17.2442			−0.546405
$997$		−	23.4405i		−	0.742369i	−0.928559	−	0.371185i	$-0.878952\pi$
$997$		−	23.4405i		−	0.742369i	0.928559	−	0.371185i	$-0.121048\pi$
$998$	103.691			3.28227
$999$	−3.15988			−0.0999741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.a.626.38	yes	40
11.10	odd	2	inner	1045.2.f.a.626.4	yes	40
19.18	odd	2	inner	1045.2.f.a.626.3	✓	40
209.208	even	2	inner	1045.2.f.a.626.37	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.a.626.3	✓	40	19.18	odd	2	inner
1045.2.f.a.626.4	yes	40	11.10	odd	2	inner
1045.2.f.a.626.37	yes	40	209.208	even	2	inner
1045.2.f.a.626.38	yes	40	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.52972 q^{2} +0.384887i q^{3} +4.39948 q^{4} -1.00000 q^{5} +0.973657i q^{6} +1.35297i q^{7} +6.07000 q^{8} +2.85186 q^{9} +O(q^{10})\)	\(q+2.52972 q^{2} +0.384887i q^{3} +4.39948 q^{4} -1.00000 q^{5} +0.973657i q^{6} +1.35297i q^{7} +6.07000 q^{8} +2.85186 q^{9} -2.52972 q^{10} +(1.95002 + 2.68280i) q^{11} +1.69330i q^{12} -2.33668 q^{13} +3.42264i q^{14} -0.384887i q^{15} +6.55645 q^{16} -5.43006i q^{17} +7.21441 q^{18} +(-0.531936 + 4.32632i) q^{19} -4.39948 q^{20} -0.520743 q^{21} +(4.93299 + 6.78674i) q^{22} +0.981945 q^{23} +2.33627i q^{24} +1.00000 q^{25} -5.91114 q^{26} +2.25231i q^{27} +5.95238i q^{28} +3.04589 q^{29} -0.973657i q^{30} -8.09312i q^{31} +4.44597 q^{32} +(-1.03258 + 0.750537i) q^{33} -13.7365i q^{34} -1.35297i q^{35} +12.5467 q^{36} +1.40295i q^{37} +(-1.34565 + 10.9444i) q^{38} -0.899359i q^{39} -6.07000 q^{40} -1.12340 q^{41} -1.31733 q^{42} +2.01890i q^{43} +(8.57905 + 11.8029i) q^{44} -2.85186 q^{45} +2.48404 q^{46} -12.2984 q^{47} +2.52350i q^{48} +5.16946 q^{49} +2.52972 q^{50} +2.08996 q^{51} -10.2802 q^{52} -3.95467i q^{53} +5.69771i q^{54} +(-1.95002 - 2.68280i) q^{55} +8.21255i q^{56} +(-1.66515 - 0.204736i) q^{57} +7.70526 q^{58} +1.26044i q^{59} -1.69330i q^{60} -9.55786i q^{61} -20.4733i q^{62} +3.85849i q^{63} -1.86586 q^{64} +2.33668 q^{65} +(-2.61213 + 1.89865i) q^{66} -13.2712i q^{67} -23.8894i q^{68} +0.377938i q^{69} -3.42264i q^{70} +14.3607i q^{71} +17.3108 q^{72} -2.05840i q^{73} +3.54907i q^{74} +0.384887i q^{75} +(-2.34024 + 19.0335i) q^{76} +(-3.62976 + 2.63832i) q^{77} -2.27512i q^{78} -9.57041 q^{79} -6.55645 q^{80} +7.68870 q^{81} -2.84188 q^{82} +10.1838i q^{83} -2.29100 q^{84} +5.43006i q^{85} +5.10724i q^{86} +1.17233i q^{87} +(11.8366 + 16.2846i) q^{88} -12.3375i q^{89} -7.21441 q^{90} -3.16147i q^{91} +4.32004 q^{92} +3.11494 q^{93} -31.1114 q^{94} +(0.531936 - 4.32632i) q^{95} +1.71120i q^{96} -2.23673i q^{97} +13.0773 q^{98} +(5.56118 + 7.65098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more