LMFDB - Embedded newform 483.2.h.c.160.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 $ x^12 + 17x^10 + 92x^8 + 180x^6 + 92x^4 + 17*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.8
Root			$-0.466018i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.c.160.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +1.97916 q^{10} +3.72389i q^{11} -0.611859i q^{12} +0.821806i q^{13} +(2.40830 + 1.97916i) q^{14} +1.67982i q^{15} -2.40191 q^{16} +1.97916 q^{17} -1.17819 q^{18} +3.72389 q^{19} -1.02781 q^{20} +(-1.67982 + 2.04406i) q^{21} +4.38746i q^{22} +(4.61186 - 1.31558i) q^{23} -3.07728i q^{24} -2.17819 q^{25} +0.968247i q^{26} -1.00000i q^{27} +(-1.25068 - 1.02781i) q^{28} -5.79005 q^{29} +1.97916i q^{30} -0.566335i q^{31} +3.32464 q^{32} -3.72389 q^{33} +2.33183 q^{34} +(3.43366 + 2.82181i) q^{35} +0.611859 q^{36} +1.25068i q^{37} +4.38746 q^{38} -0.821806 q^{39} -5.16928 q^{40} +5.00000i q^{41} +(-1.97916 + 2.40830i) q^{42} -7.01863i q^{43} -2.27849i q^{44} -1.67982 q^{45} +(5.43366 - 1.55001i) q^{46} -5.14644i q^{47} -2.40191i q^{48} +(1.35639 + 6.86733i) q^{49} -2.56634 q^{50} +1.97916i q^{51} -0.502829i q^{52} -0.0649054i q^{53} -1.17819i q^{54} +6.25547i q^{55} +(-6.29015 - 5.16928i) q^{56} +3.72389i q^{57} -6.82181 q^{58} -11.0455i q^{59} -1.02781i q^{60} +9.36202 q^{61} -0.667253i q^{62} +(-2.04406 - 1.67982i) q^{63} +8.72089 q^{64} +1.38049i q^{65} -4.38746 q^{66} -5.03947i q^{67} -1.21096 q^{68} +(1.31558 + 4.61186i) q^{69} +(4.04552 + 3.32464i) q^{70} -6.40191 q^{71} +3.07728 q^{72} -15.8811i q^{73} +1.47354i q^{74} -2.17819i q^{75} -2.27849 q^{76} +(-6.25547 + 7.61186i) q^{77} -0.968247 q^{78} -17.6032i q^{79} -4.03479 q^{80} +1.00000 q^{81} +5.89097i q^{82} -9.29712 q^{83} +(1.02781 - 1.25068i) q^{84} +3.32464 q^{85} -8.26931i q^{86} -5.79005i q^{87} -11.4594i q^{88} -11.8352 q^{89} -1.97916 q^{90} +(-1.38049 + 1.67982i) q^{91} +(-2.82181 + 0.804951i) q^{92} +0.566335 q^{93} -6.06351i q^{94} +6.25547 q^{95} +3.32464i q^{96} +14.9720 q^{97} +(1.59809 + 8.09105i) q^{98} -3.72389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9	$ 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.17819			0.833109			0.416555	−	0.909111i	$-0.363238\pi$
$2$	1.17819			0.833109			0.416555	+	0.909111i	$0.363238\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.611859			−0.305929
$5$	1.67982			0.751240			0.375620	−	0.926774i	$-0.377430\pi$
$5$	1.67982			0.751240			0.375620	+	0.926774i	$0.377430\pi$
$6$			1.17819i			0.480996i
$7$	2.04406	+	1.67982i	0.772583	+	0.634913i
$7$	2.04406	+	1.67982i	0.772583	+	0.634913i
$8$	−3.07728			−1.08798
$9$	−1.00000			−0.333333
$10$	1.97916			0.625865
$11$			3.72389i			1.12279i	0.827547	+	0.561397i	$0.189736\pi$
$11$			3.72389i			1.12279i	−0.827547	+	0.561397i	$0.810264\pi$
$12$		−	0.611859i		−	0.176628i
$13$			0.821806i			0.227928i	0.993485	+	0.113964i	$0.0363548\pi$
$13$			0.821806i			0.227928i	−0.993485	+	0.113964i	$0.963645\pi$
$14$	2.40830	+	1.97916i	0.643646	+	0.528952i
$15$			1.67982i			0.433728i
$16$	−2.40191			−0.600478
$17$	1.97916			0.480016			0.240008	−	0.970771i	$-0.422850\pi$
$17$	1.97916			0.480016			0.240008	+	0.970771i	$0.422850\pi$
$18$	−1.17819			−0.277703
$19$	3.72389			0.854318			0.427159	−	0.904176i	$-0.359514\pi$
$19$	3.72389			0.854318			0.427159	+	0.904176i	$0.359514\pi$
$20$	−1.02781			−0.229826
$21$	−1.67982	+	2.04406i	−0.366567	+	0.446051i
$22$			4.38746i			0.935410i
$23$	4.61186	−	1.31558i	0.961639	−	0.274318i
$23$	4.61186	−	1.31558i	0.961639	−	0.274318i
$24$		−	3.07728i		−	0.628146i
$25$	−2.17819			−0.435639
$26$			0.968247i			0.189889i
$27$		−	1.00000i		−	0.192450i
$28$	−1.25068	−	1.02781i	−0.236356	−	0.194239i
$29$	−5.79005			−1.07519			−0.537593	−	0.843205i	$-0.680666\pi$
$29$	−5.79005			−1.07519			−0.537593	+	0.843205i	$0.680666\pi$
$30$			1.97916i			0.361343i
$31$		−	0.566335i		−	0.101717i	−0.998706	−	0.0508584i	$-0.983804\pi$
$31$		−	0.566335i		−	0.101717i	0.998706	−	0.0508584i	$-0.0161957\pi$
$32$	3.32464			0.587718
$33$	−3.72389			−0.648245
$34$	2.33183			0.399906
$35$	3.43366	+	2.82181i	0.580395	+	0.476972i
$36$	0.611859			0.101976
$37$			1.25068i			0.205610i	0.994702	+	0.102805i	$0.0327818\pi$
$37$			1.25068i			0.205610i	−0.994702	+	0.102805i	$0.967218\pi$
$38$	4.38746			0.711740
$39$	−0.821806			−0.131594
$40$	−5.16928			−0.817335
$41$			5.00000i			0.780869i	0.920631	+	0.390434i	$0.127675\pi$
$41$			5.00000i			0.780869i	−0.920631	+	0.390434i	$0.872325\pi$
$42$	−1.97916	+	2.40830i	−0.305391	+	0.371609i
$43$		−	7.01863i		−	1.07033i	−0.844747	−	0.535165i	$-0.820249\pi$
$43$		−	7.01863i		−	1.07033i	0.844747	−	0.535165i	$-0.179751\pi$
$44$		−	2.27849i		−	0.343496i
$45$	−1.67982			−0.250413
$46$	5.43366	−	1.55001i	0.801150	−	0.228537i
$47$		−	5.14644i		−	0.750686i	−0.926886	−	0.375343i	$-0.877525\pi$
$47$		−	5.14644i		−	0.750686i	0.926886	−	0.375343i	$-0.122475\pi$
$48$		−	2.40191i		−	0.346686i
$49$	1.35639	+	6.86733i	0.193770	+	0.981047i
$50$	−2.56634			−0.362935
$51$			1.97916i			0.277138i
$52$		−	0.502829i		−	0.0697299i
$53$		−	0.0649054i		−	0.00891544i	−0.999990	−	0.00445772i	$-0.998581\pi$
$53$		−	0.0649054i		−	0.00891544i	0.999990	−	0.00445772i	$-0.00141894\pi$
$54$		−	1.17819i		−	0.160332i
$55$			6.25547i			0.843487i
$56$	−6.29015	−	5.16928i	−0.840556	−	0.690774i
$57$			3.72389i			0.493241i
$58$	−6.82181			−0.895747
$59$		−	11.0455i		−	1.43800i	−0.695008	−	0.719002i	$-0.744599\pi$
$59$		−	11.0455i		−	1.43800i	0.695008	−	0.719002i	$-0.255401\pi$
$60$		−	1.02781i		−	0.132690i
$61$	9.36202			1.19868			0.599342	−	0.800493i	$-0.295429\pi$
$61$	9.36202			1.19868			0.599342	+	0.800493i	$0.295429\pi$
$62$		−	0.667253i		−	0.0847412i
$63$	−2.04406	−	1.67982i	−0.257528	−	0.211638i
$64$	8.72089			1.09011
$65$			1.38049i			0.171229i
$66$	−4.38746			−0.540059
$67$		−	5.03947i		−	0.615669i	−0.951440	−	0.307835i	$-0.900396\pi$
$67$		−	5.03947i		−	0.615669i	0.951440	−	0.307835i	$-0.0996043\pi$
$68$	−1.21096			−0.146851
$69$	1.31558	+	4.61186i	0.158378	+	0.555203i
$70$	4.04552	+	3.32464i	0.483533	+	0.397370i
$71$	−6.40191			−0.759767			−0.379884	−	0.925034i	$-0.624036\pi$
$71$	−6.40191			−0.759767			−0.379884	+	0.925034i	$0.624036\pi$
$72$	3.07728			0.362661
$73$		−	15.8811i		−	1.85874i	−0.369147	−	0.929371i	$-0.620350\pi$
$73$		−	15.8811i		−	1.85874i	0.369147	−	0.929371i	$-0.379650\pi$
$74$			1.47354i			0.171296i
$75$		−	2.17819i		−	0.251516i
$76$	−2.27849			−0.261361
$77$	−6.25547	+	7.61186i	−0.712877	+	0.867452i
$78$	−0.968247			−0.109632
$79$		−	17.6032i		−	1.98051i	−0.139256	−	0.990256i	$-0.544471\pi$
$79$		−	17.6032i		−	1.98051i	0.139256	−	0.990256i	$-0.455529\pi$
$80$	−4.03479			−0.451103
$81$	1.00000			0.111111
$82$			5.89097i			0.650549i
$83$	−9.29712			−1.02049			−0.510246	−	0.860029i	$-0.670446\pi$
$83$	−9.29712			−1.02049			−0.510246	+	0.860029i	$0.670446\pi$
$84$	1.02781	−	1.25068i	0.112144	−	0.136460i
$85$	3.32464			0.360607
$86$		−	8.26931i		−	0.891702i
$87$		−	5.79005i		−	0.620759i
$88$		−	11.4594i		−	1.22158i
$89$	−11.8352			−1.25453			−0.627266	−	0.778805i	$-0.715826\pi$
$89$	−11.8352			−1.25453			−0.627266	+	0.778805i	$0.715826\pi$
$90$	−1.97916			−0.208622
$91$	−1.38049	+	1.67982i	−0.144715	+	0.176093i
$92$	−2.82181	+	0.804951i	−0.294194	+	0.0839219i
$93$	0.566335			0.0587262
$94$		−	6.06351i		−	0.625403i
$95$	6.25547			0.641798
$96$			3.32464i			0.339319i
$97$	14.9720			1.52018			0.760089	−	0.649819i	$-0.225155\pi$
$97$	14.9720			1.52018			0.760089	+	0.649819i	$0.225155\pi$
$98$	1.59809	+	8.09105i	0.161431	+	0.817319i
$99$		−	3.72389i		−	0.374265i
$100$	1.33275			0.133275
$101$		−	12.2692i		−	1.22084i	−0.792080	−	0.610418i	$-0.791002\pi$
$101$		−	12.2692i		−	1.22084i	0.792080	−	0.610418i	$-0.208998\pi$
$102$			2.33183i			0.230886i
$103$	8.33421			0.821194			0.410597	−	0.911817i	$-0.365320\pi$
$103$	8.33421			0.821194			0.410597	+	0.911817i	$0.365320\pi$
$104$		−	2.52892i		−	0.247981i
$105$	−2.82181	+	3.43366i	−0.275380	+	0.335091i
$106$		−	0.0764712i		−	0.00742754i
$107$			15.1949i			1.46894i	0.678639	+	0.734472i	$0.262570\pi$
$107$			15.1949i			1.46894i	−0.678639	+	0.734472i	$0.737430\pi$
$108$			0.611859i			0.0588761i
$109$			7.22491i			0.692021i	0.938231	+	0.346010i	$0.112464\pi$
$109$			7.22491i			0.692021i	−0.938231	+	0.346010i	$0.887536\pi$
$110$			7.37016i			0.702717i
$111$	−1.25068			−0.118709
$112$	−4.90966	−	4.03479i	−0.463919	−	0.381251i
$113$		−	3.00697i		−	0.282872i	−0.989947	−	0.141436i	$-0.954828\pi$
$113$		−	3.00697i		−	0.282872i	0.989947	−	0.141436i	$-0.0451720\pi$
$114$			4.38746i			0.410923i
$115$	7.74711	−	2.20995i	0.722421	−	0.206079i
$116$	3.54269			0.328931
$117$		−	0.821806i		−	0.0759760i
$118$		−	13.0138i		−	1.19801i
$119$	4.04552	+	3.32464i	0.370853	+	0.304769i
$120$		−	5.16928i		−	0.471889i
$121$	−2.86733			−0.260666
$122$	11.0303			0.998635
$123$	−5.00000			−0.450835
$124$			0.346517i			0.0311182i
$125$	−12.0581			−1.07851
$126$	−2.40830	−	1.97916i	−0.214549	−	0.176317i
$127$	−2.32464			−0.206278			−0.103139	−	0.994667i	$-0.532889\pi$
$127$	−2.32464			−0.206278			−0.103139	+	0.994667i	$0.532889\pi$
$128$	3.62563			0.320463
$129$	7.01863			0.617956
$130$			1.62648i			0.142652i
$131$			6.13267i			0.535814i	0.963445	+	0.267907i	$0.0863320\pi$
$131$			6.13267i			0.535814i	−0.963445	+	0.267907i	$0.913668\pi$
$132$	2.27849			0.198317
$133$	7.61186	+	6.25547i	0.660032	+	0.542418i
$134$		−	5.93747i		−	0.512920i
$135$		−	1.67982i		−	0.144576i
$136$	−6.09042			−0.522249
$137$			17.7611i			1.51744i	0.651419	+	0.758718i	$0.274174\pi$
$137$			17.7611i			1.51744i	−0.651419	+	0.758718i	$0.725826\pi$
$138$	1.55001	+	5.43366i	0.131946	+	0.462544i
$139$			16.3465i			1.38649i	0.720700	+	0.693247i	$0.243820\pi$
$139$			16.3465i			1.38649i	−0.720700	+	0.693247i	$0.756180\pi$
$140$	−2.10092	−	1.72655i	−0.177560	−	0.145920i
$141$	5.14644			0.433409
$142$	−7.54269			−0.632969
$143$	−3.06031			−0.255916
$144$	2.40191			0.200159
$145$	−9.72626			−0.807722
$146$		−	18.7110i		−	1.54853i
$147$	−6.86733	+	1.35639i	−0.566408	+	0.111873i
$148$		−	0.765238i		−	0.0629022i
$149$			18.5661i			1.52099i	0.649342	+	0.760497i	$0.275045\pi$
$149$			18.5661i			1.52099i	−0.649342	+	0.760497i	$0.724955\pi$
$150$		−	2.56634i		−	0.209540i
$151$	−1.30099			−0.105873			−0.0529367	−	0.998598i	$-0.516858\pi$
$151$	−1.30099			−0.105873			−0.0529367	+	0.998598i	$0.516858\pi$
$152$	−11.4594			−0.929482
$153$	−1.97916			−0.160005
$154$	−7.37016	+	8.96825i	−0.593904	+	0.722682i
$155$		−	0.951343i		−	0.0764137i
$156$	0.502829			0.0402585
$157$	7.60573			0.607003			0.303502	−	0.952831i	$-0.401844\pi$
$157$	7.60573			0.607003			0.303502	+	0.952831i	$0.401844\pi$
$158$		−	20.7400i		−	1.64998i
$159$	0.0649054			0.00514733
$160$	5.58480			0.441517
$161$	11.6369	+	5.05797i	0.917114	+	0.398624i
$162$	1.17819			0.0925677
$163$	−6.68914			−0.523934			−0.261967	−	0.965077i	$-0.584371\pi$
$163$	−6.68914			−0.523934			−0.261967	+	0.965077i	$0.584371\pi$
$164$		−	3.05929i		−	0.238891i
$165$	−6.25547			−0.486988
$166$	−10.9538			−0.850181
$167$		−	2.79816i		−	0.216528i	−0.994122	−	0.108264i	$-0.965471\pi$
$167$		−	2.79816i		−	0.216528i	0.994122	−	0.108264i	$-0.0345293\pi$
$168$	5.16928	−	6.29015i	0.398819	−	0.485295i
$169$	12.3246			0.948049
$170$	3.91707			0.300425
$171$	−3.72389			−0.284773
$172$			4.29441i			0.327446i
$173$		−	5.88110i		−	0.447132i	−0.974689	−	0.223566i	$-0.928230\pi$
$173$		−	5.88110i		−	0.447132i	0.974689	−	0.223566i	$-0.0717698\pi$
$174$		−	6.82181i		−	0.517160i
$175$	−4.45237	−	3.65898i	−0.336567	−	0.276593i
$176$		−	8.94445i		−	0.674213i
$177$	11.0455			0.830232
$178$	−13.9442			−1.04516
$179$	−0.100918			−0.00754294			−0.00377147	−	0.999993i	$-0.501200\pi$
$179$	−0.100918			−0.00754294			−0.00377147	+	0.999993i	$0.501200\pi$
$180$	1.02781			0.0766088
$181$	−12.6568			−0.940770			−0.470385	−	0.882461i	$-0.655885\pi$
$181$	−12.6568			−0.940770			−0.470385	+	0.882461i	$0.655885\pi$
$182$	−1.62648	+	1.97916i	−0.120563	+	0.146705i
$183$			9.36202i			0.692061i
$184$	−14.1920	+	4.04841i	−1.04625	+	0.298453i
$185$			2.10092i			0.154463i
$186$	0.667253			0.0489254
$187$			7.37016i			0.538959i
$188$			3.14889i			0.229657i
$189$	1.67982	−	2.04406i	0.122189	−	0.148684i
$190$	7.37016			0.534687
$191$		−	7.16000i		−	0.518080i	−0.965867	−	0.259040i	$-0.916594\pi$
$191$		−	7.16000i		−	0.518080i	0.965867	−	0.259040i	$-0.0834061\pi$
$192$			8.72089i			0.629376i
$193$	−6.79005			−0.488759			−0.244379	−	0.969680i	$-0.578584\pi$
$193$	−6.79005			−0.488759			−0.244379	+	0.969680i	$0.578584\pi$
$194$	17.6399			1.26647
$195$	−1.38049			−0.0988588
$196$	−0.829918	−	4.20184i	−0.0592799	−	0.300131i
$197$	−14.4930			−1.03258			−0.516290	−	0.856414i	$-0.672687\pi$
$197$	−14.4930			−1.03258			−0.516290	+	0.856414i	$0.672687\pi$
$198$		−	4.38746i		−	0.311803i
$199$	11.3412			0.803955			0.401978	−	0.915650i	$-0.368323\pi$
$199$	11.3412			0.803955			0.401978	+	0.915650i	$0.368323\pi$
$200$	6.70291			0.473967
$201$	5.03947			0.355457
$202$		−	14.4555i		−	1.01709i
$203$	−11.8352	−	9.72626i	−0.830671	−	0.682650i
$204$		−	1.21096i		−	0.0847845i
$205$			8.39912i			0.586620i
$206$	9.81932			0.684144
$207$	−4.61186	+	1.31558i	−0.320546	+	0.0914394i
$208$		−	1.97391i		−	0.136866i
$209$			13.8673i			0.959223i
$210$	−3.32464	+	4.04552i	−0.229422	+	0.279168i
$211$	10.6436			0.732736			0.366368	−	0.930470i	$-0.380601\pi$
$211$	10.6436			0.732736			0.366368	+	0.930470i	$0.380601\pi$
$212$			0.0397129i			0.00272750i
$213$		−	6.40191i		−	0.438652i
$214$			17.9025i			1.22379i
$215$		−	11.7901i		−	0.804075i
$216$			3.07728i			0.209382i
$217$	0.951343	−	1.15763i	0.0645814	−	0.0785847i
$218$			8.51235i			0.576529i
$219$	15.8811			1.07315
$220$		−	3.82746i		−	0.258048i
$221$			1.62648i			0.109409i
$222$	−1.47354			−0.0988976
$223$		−	0.877200i		−	0.0587417i	−0.999569	−	0.0293708i	$-0.990650\pi$
$223$		−	0.877200i		−	0.0587417i	0.999569	−	0.0293708i	$-0.00935037\pi$
$224$	6.79576	+	5.58480i	0.454061	+	0.373150i
$225$	2.17819			0.145213
$226$		−	3.54280i		−	0.235663i
$227$	−7.95339			−0.527885			−0.263942	−	0.964538i	$-0.585023\pi$
$227$	−7.95339			−0.527885			−0.263942	+	0.964538i	$0.585023\pi$
$228$		−	2.27849i		−	0.150897i
$229$	12.3293			0.814742			0.407371	−	0.913263i	$-0.366446\pi$
$229$	12.3293			0.814742			0.407371	+	0.913263i	$0.366446\pi$
$230$	9.12760	−	2.60375i	0.601856	−	0.171686i
$231$	−7.61186	−	6.25547i	−0.500824	−	0.411580i
$232$	17.8176			1.16978
$233$	−3.38814			−0.221965			−0.110982	−	0.993822i	$-0.535400\pi$
$233$	−3.38814			−0.221965			−0.110982	+	0.993822i	$0.535400\pi$
$234$		−	0.968247i		−	0.0632963i
$235$		−	8.64511i		−	0.563945i
$236$			6.75830i			0.439928i
$237$	17.6032			1.14345
$238$	4.76641	+	3.91707i	0.308961	+	0.253906i
$239$	−13.7445			−0.889060			−0.444530	−	0.895764i	$-0.646629\pi$
$239$	−13.7445			−0.889060			−0.444530	+	0.895764i	$0.646629\pi$
$240$		−	4.03479i		−	0.260444i
$241$	19.0883			1.22958			0.614792	−	0.788689i	$-0.289240\pi$
$241$	19.0883			1.22958			0.614792	+	0.788689i	$0.289240\pi$
$242$	−3.37827			−0.217163
$243$			1.00000i			0.0641500i
$244$	−5.72824			−0.366713
$245$	2.27849	+	11.5359i	0.145568	+	0.737002i
$246$	−5.89097			−0.375595
$247$			3.06031i			0.194723i
$248$			1.74277i			0.110666i
$249$		−	9.29712i		−	0.589181i
$250$	−14.2068			−0.898516
$251$	7.57758			0.478293			0.239146	−	0.970984i	$-0.423132\pi$
$251$	7.57758			0.478293			0.239146	+	0.970984i	$0.423132\pi$
$252$	1.25068	+	1.02781i	0.0787853	+	0.0647462i
$253$	4.89908	+	17.1740i	0.308003	+	1.07972i
$254$	−2.73887			−0.171852
$255$			3.32464i			0.208197i
$256$	−13.1701			−0.823130
$257$			22.1048i			1.37886i	0.724352	+	0.689430i	$0.242139\pi$
$257$			22.1048i			1.37886i	−0.724352	+	0.689430i	$0.757861\pi$
$258$	8.26931			0.514824
$259$	−2.10092	+	2.55646i	−0.130545	+	0.158851i
$260$		−	0.844664i		−	0.0523838i
$261$	5.79005			0.358395
$262$			7.22548i			0.446391i
$263$		−	8.67030i		−	0.534634i	−0.963609	−	0.267317i	$-0.913863\pi$
$263$		−	8.67030i		−	0.534634i	0.963609	−	0.267317i	$-0.0861371\pi$
$264$	11.4594			0.705279
$265$		−	0.109030i		−	0.00669764i
$266$	8.96825	+	7.37016i	0.549878	+	0.451893i
$267$		−	11.8352i		−	0.724305i
$268$			3.08344i			0.188351i
$269$		−	19.6891i		−	1.20047i	−0.799825	−	0.600234i	$-0.795074\pi$
$269$		−	19.6891i		−	1.20047i	0.799825	−	0.600234i	$-0.204926\pi$
$270$		−	1.97916i		−	0.120448i
$271$			4.65738i			0.282916i	0.989944	+	0.141458i	$0.0451790\pi$
$271$			4.65738i			0.282916i	−0.989944	+	0.141458i	$0.954821\pi$
$272$	−4.75376			−0.288239
$273$	−1.67982	−	1.38049i	−0.101668	−	0.0835510i
$274$			20.9261i			1.26419i
$275$		−	8.11135i		−	0.489133i
$276$	−0.804951	−	2.82181i	−0.0484524	−	0.169853i
$277$	−23.5011			−1.41204			−0.706021	−	0.708191i	$-0.749512\pi$
$277$	−23.5011			−1.41204			−0.706021	+	0.708191i	$0.749512\pi$
$278$			19.2594i			1.15510i
$279$			0.566335i			0.0339056i
$280$	−10.5663	−	8.68348i	−0.631459	−	0.518937i
$281$		−	1.90269i		−	0.113505i	−0.998388	−	0.0567524i	$-0.981925\pi$
$281$		−	1.90269i		−	0.113505i	0.998388	−	0.0567524i	$-0.0180746\pi$
$282$	6.06351			0.361077
$283$	−12.3574			−0.734573			−0.367287	−	0.930108i	$-0.619713\pi$
$283$	−12.3574			−0.734573			−0.367287	+	0.930108i	$0.619713\pi$
$284$	3.91707			0.232435
$285$			6.25547i			0.370542i
$286$	−3.60564			−0.213206
$287$	−8.39912	+	10.2203i	−0.495784	+	0.603286i
$288$	−3.32464			−0.195906
$289$	−13.0829			−0.769584
$290$	−11.4594			−0.672921
$291$			14.9720i			0.877675i
$292$			9.71699i			0.568644i
$293$	28.4871			1.66423			0.832116	−	0.554601i	$-0.187129\pi$
$293$	28.4871			1.66423			0.832116	+	0.554601i	$0.187129\pi$
$294$	−8.09105	+	1.59809i	−0.471879	+	0.0932024i
$295$		−	18.5545i		−	1.08029i
$296$		−	3.84868i		−	0.223700i
$297$	3.72389			0.216082
$298$			21.8745i			1.26715i
$299$	1.08115	+	3.79005i	0.0625248	+	0.219184i
$300$			1.33275i			0.0769462i
$301$	11.7901	−	14.3465i	0.679567	−	0.826920i
$302$	−1.53282			−0.0882041
$303$	12.2692			0.704849
$304$	−8.94445			−0.512999
$305$	15.7265			0.900499
$306$	−2.33183			−0.133302
$307$		−	24.0357i		−	1.37179i	−0.727702	−	0.685894i	$-0.759412\pi$
$307$		−	24.0357i		−	1.37179i	0.727702	−	0.685894i	$-0.240588\pi$
$308$	3.82746	−	4.65738i	0.218090	−	0.265379i
$309$			8.33421i			0.474117i
$310$		−	1.12087i		−	0.0636610i
$311$			11.7029i			0.663611i	0.943348	+	0.331805i	$0.107658\pi$
$311$			11.7029i			0.663611i	−0.943348	+	0.331805i	$0.892342\pi$
$312$	2.52892			0.143172
$313$	−18.5661			−1.04942			−0.524709	−	0.851282i	$-0.675826\pi$
$313$	−18.5661			−1.04942			−0.524709	+	0.851282i	$0.675826\pi$
$314$	8.96103			0.505700
$315$	−3.43366	−	2.82181i	−0.193465	−	0.158991i
$316$			10.7707i			0.605897i
$317$	−19.1503			−1.07559			−0.537795	−	0.843076i	$-0.680743\pi$
$317$	−19.1503			−1.07559			−0.537795	+	0.843076i	$0.680743\pi$
$318$	0.0764712			0.00428829
$319$		−	21.5615i		−	1.20721i
$320$	14.6496			0.818935
$321$	−15.1949			−0.848095
$322$	13.7105	+	5.95927i	0.764056	+	0.332097i
$323$	7.37016			0.410087
$324$	−0.611859			−0.0339922
$325$		−	1.79005i		−	0.0992943i
$326$	−7.88110			−0.436494
$327$	−7.22491			−0.399538
$328$		−	15.3864i		−	0.849571i
$329$	8.64511	−	10.5197i	0.476620	−	0.579967i
$330$	−7.37016			−0.405714
$331$	16.8811			0.927869			0.463935	−	0.885869i	$-0.346437\pi$
$331$	16.8811			0.927869			0.463935	+	0.885869i	$0.346437\pi$
$332$	5.68852			0.312198
$333$		−	1.25068i		−	0.0685367i
$334$		−	3.29678i		−	0.180392i
$335$		−	8.46542i		−	0.462515i
$336$	4.03479	−	4.90966i	0.220116	−	0.267844i
$337$			32.7447i			1.78372i	0.452313	+	0.891859i	$0.350599\pi$
$337$			32.7447i			1.78372i	−0.452313	+	0.891859i	$0.649401\pi$
$338$	14.5208			0.789828
$339$	3.00697			0.163316
$340$	−2.03421			−0.110320
$341$	2.10897			0.114207
$342$	−4.38746			−0.237247
$343$	−8.76336	+	16.3157i	−0.473177	+	0.880968i
$344$			21.5983i			1.16450i
$345$	2.20995	+	7.74711i	0.118980	+	0.417090i
$346$		−	6.92908i		−	0.372509i
$347$	9.01377			0.483885			0.241942	−	0.970291i	$-0.422216\pi$
$347$	9.01377			0.483885			0.241942	+	0.970291i	$0.422216\pi$
$348$			3.54269i			0.189908i
$349$			23.6337i			1.26509i	0.774526	+	0.632543i	$0.217989\pi$
$349$			23.6337i			1.26509i	−0.774526	+	0.632543i	$0.782011\pi$
$350$	−5.24575	−	4.31099i	−0.280397	−	0.230432i
$351$	0.821806			0.0438648
$352$			12.3806i			0.659886i
$353$			20.0357i			1.06639i	0.845992	+	0.533195i	$0.179009\pi$
$353$			20.0357i			1.06639i	−0.845992	+	0.533195i	$0.820991\pi$
$354$	13.0138			0.691674
$355$	−10.7541			−0.570767
$356$	7.24149			0.383798
$357$	−3.32464	+	4.04552i	−0.175958	+	0.214112i
$358$	−0.118901			−0.00628409
$359$			1.67982i			0.0886577i	0.999017	+	0.0443288i	$0.0141149\pi$
$359$			1.67982i			0.0886577i	−0.999017	+	0.0443288i	$0.985885\pi$
$360$	5.16928			0.272445
$361$	−5.13267			−0.270141
$362$	−14.9121			−0.783764
$363$		−	2.86733i		−	0.150496i
$364$	0.844664	−	1.02781i	0.0442724	−	0.0538721i
$365$		−	26.6774i		−	1.39636i
$366$			11.0303i			0.576562i
$367$	5.53352			0.288847			0.144424	−	0.989516i	$-0.453867\pi$
$367$	5.53352			0.288847			0.144424	+	0.989516i	$0.453867\pi$
$368$	−11.0773	+	3.15991i	−0.577443	+	0.164722i
$369$		−	5.00000i		−	0.260290i
$370$			2.47529i			0.128684i
$371$	0.109030	−	0.132671i	0.00566053	−	0.00688792i
$372$	−0.346517			−0.0179661
$373$		−	11.1998i		−	0.579904i	−0.957041	−	0.289952i	$-0.906361\pi$
$373$		−	11.1998i		−	0.579904i	0.957041	−	0.289952i	$-0.0936393\pi$
$374$			8.68348i			0.449012i
$375$		−	12.0581i		−	0.622677i
$376$			15.8370i			0.816732i
$377$		−	4.75830i		−	0.245065i
$378$	1.97916	−	2.40830i	0.101797	−	0.123870i
$379$		−	6.71929i		−	0.345147i	−0.984997	−	0.172573i	$-0.944792\pi$
$379$		−	6.71929i		−	0.345147i	0.984997	−	0.172573i	$-0.0552082\pi$
$380$	−3.82746			−0.196345
$381$		−	2.32464i		−	0.119095i
$382$		−	8.43587i		−	0.431617i
$383$	25.9655			1.32678			0.663389	−	0.748275i	$-0.269118\pi$
$383$	25.9655			1.32678			0.663389	+	0.748275i	$0.269118\pi$
$384$			3.62563i			0.185020i
$385$	−10.5081	+	12.7866i	−0.535542	+	0.651664i
$386$	−8.00000			−0.407189
$387$			7.01863i			0.356777i
$388$	−9.16076			−0.465067
$389$			9.29712i			0.471383i	0.971828	+	0.235691i	$0.0757354\pi$
$389$			9.29712i			0.471383i	−0.971828	+	0.235691i	$0.924265\pi$
$390$	−1.62648			−0.0823602
$391$	9.12760	−	2.60375i	0.461602	−	0.131677i
$392$	−4.17398	−	21.1327i	−0.210818	−	1.06736i
$393$	−6.13267			−0.309352
$394$	−17.0755			−0.860252
$395$		−	29.5702i		−	1.48784i
$396$			2.27849i			0.114499i
$397$		−	3.02188i		−	0.151664i	−0.997121	−	0.0758320i	$-0.975839\pi$
$397$		−	3.02188i		−	0.151664i	0.997121	−	0.0758320i	$-0.0241613\pi$
$398$	13.3621			0.669782
$399$	−6.25547	+	7.61186i	−0.313165	+	0.381070i
$400$	5.23183			0.261591
$401$		−	33.8540i		−	1.69059i	−0.534300	−	0.845295i	$-0.679425\pi$
$401$		−	33.8540i		−	1.69059i	0.534300	−	0.845295i	$-0.320575\pi$
$402$	5.93747			0.296134
$403$	0.465418			0.0231841
$404$			7.50704i			0.373489i
$405$	1.67982			0.0834711
$406$	−13.9442	−	11.4594i	−0.692039	−	0.568722i
$407$	−4.65738			−0.230858
$408$		−	6.09042i		−	0.301520i
$409$		−	18.8592i		−	0.932528i	−0.884646	−	0.466264i	$-0.845600\pi$
$409$		−	18.8592i		−	0.932528i	0.884646	−	0.466264i	$-0.154400\pi$
$410$			9.89579i			0.488718i
$411$	−17.7611			−0.876092
$412$	−5.09936			−0.251227
$413$	18.5545	−	22.5777i	0.913009	−	1.11098i
$414$	−5.43366	+	1.55001i	−0.267050	+	0.0761790i
$415$	−15.6175			−0.766634
$416$			2.73220i			0.133957i
$417$	−16.3465			−0.800492
$418$			16.3384i			0.799138i
$419$	−25.9490			−1.26769			−0.633845	−	0.773460i	$-0.718524\pi$
$419$	−25.9490			−1.26769			−0.633845	+	0.773460i	$0.718524\pi$
$420$	1.72655	−	2.10092i	0.0842468	−	0.102514i
$421$		−	1.15763i		−	0.0564192i	−0.999602	−	0.0282096i	$-0.991019\pi$
$421$		−	1.15763i		−	0.0564192i	0.999602	−	0.0282096i	$-0.00898059\pi$
$422$	12.5402			0.610449
$423$			5.14644i			0.250229i
$424$			0.199732i			0.00969984i
$425$	−4.31099			−0.209114
$426$		−	7.54269i		−	0.365445i
$427$	19.1366	+	15.7265i	0.926084	+	0.761061i
$428$		−	9.29712i		−	0.449393i
$429$		−	3.06031i		−	0.147753i
$430$		−	13.8910i		−	0.669882i
$431$		−	37.6962i		−	1.81576i	−0.419230	−	0.907880i	$-0.637700\pi$
$431$		−	37.6962i		−	1.81576i	0.419230	−	0.907880i	$-0.362300\pi$
$432$			2.40191i			0.115562i
$433$	−39.9213			−1.91850			−0.959248	−	0.282566i	$-0.908814\pi$
$433$	−39.9213			−1.91850			−0.959248	+	0.282566i	$0.908814\pi$
$434$	1.12087	−	1.36391i	0.0538033	−	0.0654696i
$435$		−	9.72626i		−	0.466339i
$436$		−	4.42062i		−	0.211709i
$437$	17.1740	−	4.89908i	0.821546	−	0.234355i
$438$	18.7110			0.894047
$439$		−	16.3483i		−	0.780261i	−0.920760	−	0.390130i	$-0.872430\pi$
$439$		−	16.3483i		−	0.780261i	0.920760	−	0.390130i	$-0.127570\pi$
$440$		−	19.2498i		−	0.917699i
$441$	−1.35639	−	6.86733i	−0.0645899	−	0.327016i
$442$			1.91631i			0.0911497i
$443$	12.1821			0.578789			0.289394	−	0.957210i	$-0.406546\pi$
$443$	12.1821			0.578789			0.289394	+	0.957210i	$0.406546\pi$
$444$	0.765238			0.0363166
$445$	−19.8811			−0.942455
$446$		−	1.03351i		−	0.0489382i
$447$	−18.5661			−0.878146
$448$	17.8260	+	14.6496i	0.842202	+	0.692126i
$449$	6.70291			0.316330			0.158165	−	0.987413i	$-0.449442\pi$
$449$	6.70291			0.316330			0.158165	+	0.987413i	$0.449442\pi$
$450$	2.56634			0.120978
$451$	−18.6194			−0.876755
$452$			1.83984i			0.0865389i
$453$		−	1.30099i		−	0.0611260i
$454$	−9.37064			−0.439786
$455$	−2.31898	+	2.82181i	−0.108715	+	0.132288i
$456$		−	11.4594i		−	0.536637i
$457$		−	27.3828i		−	1.28091i	−0.767995	−	0.640456i	$-0.778745\pi$
$457$		−	27.3828i		−	1.28091i	0.767995	−	0.640456i	$-0.221255\pi$
$458$	14.5263			0.678769
$459$		−	1.97916i		−	0.0923792i
$460$	−4.74013	+	1.35218i	−0.221010	+	0.0630455i
$461$			34.2357i			1.59452i	0.603638	+	0.797258i	$0.293717\pi$
$461$			34.2357i			1.59452i	−0.603638	+	0.797258i	$0.706283\pi$
$462$	−8.96825	−	7.37016i	−0.417241	−	0.342891i
$463$	22.8892			1.06375			0.531876	−	0.846822i	$-0.321487\pi$
$463$	22.8892			1.06375			0.531876	+	0.846822i	$0.321487\pi$
$464$	13.9072			0.645625
$465$	0.951343			0.0441175
$466$	−3.99189			−0.184921
$467$	6.19709			0.286767			0.143384	−	0.989667i	$-0.454202\pi$
$467$	6.19709			0.286767			0.143384	+	0.989667i	$0.454202\pi$
$468$			0.502829i			0.0232433i
$469$	8.46542	−	10.3010i	0.390897	−	0.475656i
$470$		−	10.1856i		−	0.469828i
$471$			7.60573i			0.350454i
$472$			33.9901i			1.56452i
$473$	26.1366			1.20176
$474$	20.7400			0.952618
$475$	−8.11135			−0.372174
$476$	−2.47529	−	2.03421i	−0.113455	−	0.0932377i
$477$			0.0649054i			0.00297181i
$478$	−16.1937			−0.740684
$479$	−34.1418			−1.55998			−0.779989	−	0.625793i	$-0.784775\pi$
$479$	−34.1418			−1.55998			−0.779989	+	0.625793i	$0.784775\pi$
$480$			5.58480i			0.254910i
$481$	−1.02781			−0.0468643
$482$	22.4897			1.02438
$483$	−5.05797	+	11.6369i	−0.230146	+	0.529496i
$484$	1.75440			0.0797455
$485$	25.1503			1.14202
$486$			1.17819i			0.0534440i
$487$	27.6793			1.25427			0.627134	−	0.778912i	$-0.284228\pi$
$487$	27.6793			1.25427			0.627134	+	0.778912i	$0.284228\pi$
$488$	−28.8095			−1.30415
$489$		−	6.68914i		−	0.302493i
$490$	2.68451	+	13.5915i	0.121274	+	0.614003i
$491$	5.62563			0.253881			0.126941	−	0.991910i	$-0.459484\pi$
$491$	5.62563			0.253881			0.126941	+	0.991910i	$0.459484\pi$
$492$	3.05929			0.137924
$493$	−11.4594			−0.516107
$494$			3.60564i			0.162225i
$495$		−	6.25547i		−	0.281162i
$496$			1.36029i			0.0610787i
$497$	−13.0859	−	10.7541i	−0.586983	−	0.482386i
$498$		−	10.9538i		−	0.490852i
$499$	−16.2555			−0.727695			−0.363847	−	0.931459i	$-0.618537\pi$
$499$	−16.2555			−0.727695			−0.363847	+	0.931459i	$0.618537\pi$
$500$	7.37785			0.329948
$501$	2.79816			0.125013
$502$	8.92786			0.398470
$503$	−16.5754			−0.739059			−0.369530	−	0.929219i	$-0.620481\pi$
$503$	−16.5754			−0.739059			−0.369530	+	0.929219i	$0.620481\pi$
$504$	6.29015	+	5.16928i	0.280185	+	0.230258i
$505$		−	20.6102i		−	0.917140i
$506$	5.77207	+	20.2343i	0.256600	+	0.899527i
$507$			12.3246i			0.547356i
$508$	1.42235			0.0631065
$509$		−	24.3067i		−	1.07737i	−0.842506	−	0.538687i	$-0.818921\pi$
$509$		−	24.3067i		−	1.07737i	0.842506	−	0.538687i	$-0.181079\pi$
$510$			3.91707i			0.173451i
$511$	26.6774	−	32.4620i	1.18014	−	1.43603i
$512$	−22.7682			−1.00622
$513$		−	3.72389i		−	0.164414i
$514$			26.0438i			1.14874i
$515$	14.0000			0.616914
$516$	−4.29441			−0.189051
$517$	19.1648			0.842865
$518$	−2.47529	+	3.01201i	−0.108758	+	0.132340i
$519$	5.88110			0.258152
$520$		−	4.24815i		−	0.186293i
$521$	−15.1783			−0.664973			−0.332487	−	0.943108i	$-0.607888\pi$
$521$	−15.1783			−0.664973			−0.332487	+	0.943108i	$0.607888\pi$
$522$	6.82181			0.298582
$523$	−21.4569			−0.938244			−0.469122	−	0.883133i	$-0.655430\pi$
$523$	−21.4569			−0.938244			−0.469122	+	0.883133i	$0.655430\pi$
$524$		−	3.75233i		−	0.163921i
$525$	3.65898	−	4.45237i	0.159691	−	0.194317i
$526$		−	10.2153i		−	0.445408i
$527$		−	1.12087i		−	0.0488257i
$528$	8.94445			0.389257
$529$	19.5385	−	12.1346i	0.849499	−	0.527590i
$530$		−	0.128458i		−	0.00557986i
$531$			11.0455i			0.479335i
$532$	−4.65738	−	3.82746i	−0.201923	−	0.165942i
$533$	−4.10903			−0.177982
$534$		−	13.9442i		−	0.603425i
$535$			25.5247i			1.10353i
$536$			15.5078i			0.669837i
$537$		−	0.100918i		−	0.00435492i
$538$		−	23.1976i		−	1.00012i
$539$	−25.5732	+	5.05104i	−1.10151	+	0.217563i
$540$			1.02781i			0.0442301i
$541$	−35.3920			−1.52162			−0.760811	−	0.648973i	$-0.775199\pi$
$541$	−35.3920			−1.52162			−0.760811	+	0.648973i	$0.775199\pi$
$542$			5.48730i			0.235700i
$543$		−	12.6568i		−	0.543154i
$544$	6.57998			0.282114
$545$			12.1366i			0.519874i
$546$	−1.97916	−	1.62648i	−0.0847001	−	0.0696071i
$547$	−13.4792			−0.576328			−0.288164	−	0.957581i	$-0.593045\pi$
$547$	−13.4792			−0.576328			−0.288164	+	0.957581i	$0.593045\pi$
$548$		−	10.8673i		−	0.464228i
$549$	−9.36202			−0.399561
$550$		−	9.55674i		−	0.407501i
$551$	−21.5615			−0.918551
$552$	−4.04841	−	14.1920i	−0.172312	−	0.604050i
$553$	29.5702	−	35.9820i	1.25745	−	1.53011i
$554$	−27.6888			−1.17639
$555$	−2.10092			−0.0891790
$556$		−	10.0018i		−	0.424169i
$557$			46.4826i			1.96953i	0.173883	+	0.984766i	$0.444369\pi$
$557$			46.4826i			1.96953i	−0.173883	+	0.984766i	$0.555631\pi$
$558$			0.667253i			0.0282471i
$559$	5.76795			0.243958
$560$	−8.24736	−	6.77773i	−0.348515	−	0.286411i
$561$	−7.37016			−0.311168
$562$		−	2.24173i		−	0.0945618i
$563$	4.98613			0.210140			0.105070	−	0.994465i	$-0.466493\pi$
$563$	4.98613			0.210140			0.105070	+	0.994465i	$0.466493\pi$
$564$	−3.14889			−0.132592
$565$		−	5.05118i		−	0.212505i
$566$	−14.5595			−0.611979
$567$	2.04406	+	1.67982i	0.0858426	+	0.0705459i
$568$	19.7005			0.826613
$569$		−	7.34611i		−	0.307965i	−0.988074	−	0.153982i	$-0.950790\pi$
$569$		−	7.34611i		−	0.307965i	0.988074	−	0.153982i	$-0.0492099\pi$
$570$			7.37016i			0.308702i
$571$		−	25.2039i		−	1.05475i	−0.849633	−	0.527375i	$-0.823176\pi$
$571$		−	25.2039i		−	1.05475i	0.849633	−	0.527375i	$-0.176824\pi$
$572$	1.87248			0.0782923
$573$	7.16000			0.299113
$574$	−9.89579	+	12.0415i	−0.413042	+	0.502603i
$575$	−10.0455	+	2.86560i	−0.418927	+	0.119504i
$576$	−8.72089			−0.363370
$577$			5.84545i			0.243349i	0.992570	+	0.121675i	$0.0388264\pi$
$577$			5.84545i			0.243349i	−0.992570	+	0.121675i	$0.961174\pi$
$578$	−15.4142			−0.641148
$579$		−	6.79005i		−	0.282185i
$580$	5.95110			0.247106
$581$	−19.0039	−	15.6175i	−0.788415	−	0.647924i
$582$			17.6399i			0.731199i
$583$	0.241700			0.0100102
$584$			48.8705i			2.02228i
$585$		−	1.38049i		−	0.0570762i
$586$	33.5633			1.38649
$587$		−	14.0318i		−	0.579152i	−0.957155	−	0.289576i	$-0.906486\pi$
$587$		−	14.0318i		−	0.579152i	0.957155	−	0.289576i	$-0.0935144\pi$
$588$	4.20184	−	0.829918i	0.173281	−	0.0342252i
$589$		−	2.10897i		−	0.0868985i
$590$		−	21.8608i		−	0.899996i
$591$		−	14.4930i		−	0.596161i
$592$		−	3.00402i		−	0.123464i
$593$		−	1.70712i		−	0.0701029i	−0.999386	−	0.0350515i	$-0.988840\pi$
$593$		−	1.70712i		−	0.0701029i	0.999386	−	0.0350515i	$-0.0111595\pi$
$594$	4.38746			0.180020
$595$	6.79576	+	5.58480i	0.278599	+	0.228954i
$596$		−	11.3598i		−	0.465317i
$597$			11.3412i			0.464164i
$598$	1.27381	+	4.46542i	0.0520899	+	0.182605i
$599$	2.97636			0.121611			0.0608054	−	0.998150i	$-0.480633\pi$
$599$	2.97636			0.121611			0.0608054	+	0.998150i	$0.480633\pi$
$600$			6.70291i			0.273645i
$601$			10.7502i			0.438509i	0.975668	+	0.219255i	$0.0703625\pi$
$601$			10.7502i			0.438509i	−0.975668	+	0.219255i	$0.929637\pi$
$602$	13.8910	−	16.9030i	0.566154	−	0.688914i
$603$			5.03947i			0.205223i
$604$	0.796024			0.0323898
$605$	−4.81661			−0.195823
$606$	14.4555			0.587216
$607$		−	26.4019i		−	1.07162i	−0.844338	−	0.535810i	$-0.820006\pi$
$607$		−	26.4019i		−	1.07162i	0.844338	−	0.535810i	$-0.179994\pi$
$608$	12.3806			0.502098
$609$	9.72626	−	11.8352i	0.394128	−	0.479588i
$610$	18.5289			0.750214
$611$	4.22938			0.171102
$612$	1.21096			0.0489504
$613$			36.7167i			1.48297i	0.670968	+	0.741486i	$0.265879\pi$
$613$			36.7167i			1.48297i	−0.670968	+	0.741486i	$0.734121\pi$
$614$		−	28.3187i		−	1.14285i
$615$	−8.39912			−0.338685
$616$	19.2498	−	23.4238i	0.775597	−	0.943772i
$617$		−	0.688767i		−	0.0277287i	−0.999904	−	0.0138644i	$-0.995587\pi$
$617$		−	0.688767i		−	0.0277287i	0.999904	−	0.0138644i	$-0.00441330\pi$
$618$			9.81932i			0.394991i
$619$	9.51998			0.382640			0.191320	−	0.981528i	$-0.438723\pi$
$619$	9.51998			0.382640			0.191320	+	0.981528i	$0.438723\pi$
$620$			0.582088i			0.0233772i
$621$	−1.31558	−	4.61186i	−0.0527925	−	0.185068i
$622$			13.7883i			0.552860i
$623$	−24.1920	−	19.8811i	−0.969231	−	0.796519i
$624$	1.97391			0.0790194
$625$	−9.36450			−0.374580
$626$	−21.8745			−0.874279
$627$	−13.8673			−0.553808
$628$	−4.65363			−0.185700
$629$			2.47529i			0.0986962i
$630$	−4.04552	−	3.32464i	−0.161178	−	0.132457i
$631$		−	23.8032i		−	0.947592i	−0.880635	−	0.473796i	$-0.842883\pi$
$631$		−	23.8032i		−	0.947592i	0.880635	−	0.473796i	$-0.157117\pi$
$632$			54.1699i			2.15476i
$633$			10.6436i			0.423046i
$634$	−22.5628			−0.896084
$635$	−3.90498			−0.154964
$636$	−0.0397129			−0.00157472
$637$	−5.64361	+	1.11469i	−0.223608	+	0.0441655i
$638$		−	25.4036i		−	1.00574i
$639$	6.40191			0.253256
$640$	6.09042			0.240745
$641$		−	14.4383i		−	0.570277i	−0.958486	−	0.285138i	$-0.907960\pi$
$641$		−	14.4383i		−	0.570277i	0.958486	−	0.285138i	$-0.0920395\pi$
$642$	−17.9025			−0.706556
$643$	−3.08846			−0.121797			−0.0608985	−	0.998144i	$-0.519397\pi$
$643$	−3.08846			−0.121797			−0.0608985	+	0.998144i	$0.519397\pi$
$644$	−7.12012	−	3.09476i	−0.280572	−	0.121951i
$645$	11.7901			0.464233
$646$	8.68348			0.341647
$647$			49.1503i			1.93230i	0.257982	+	0.966150i	$0.416942\pi$
$647$			49.1503i			1.93230i	−0.257982	+	0.966150i	$0.583058\pi$
$648$	−3.07728			−0.120887
$649$	41.1323			1.61458
$650$		−	2.10903i		−	0.0827229i
$651$	1.15763	+	0.951343i	0.0453709	+	0.0372861i
$652$	4.09281			0.160287
$653$	−21.3684			−0.836210			−0.418105	−	0.908399i	$-0.637306\pi$
$653$	−21.3684			−0.836210			−0.418105	+	0.908399i	$0.637306\pi$
$654$	−8.51235			−0.332859
$655$			10.3018i			0.402525i
$656$		−	12.0096i		−	0.468894i
$657$			15.8811i			0.619581i
$658$	10.1856	−	12.3942i	0.397077	−	0.483176i
$659$			19.0601i			0.742478i	0.928537	+	0.371239i	$0.121067\pi$
$659$			19.0601i			0.742478i	−0.928537	+	0.371239i	$0.878933\pi$
$660$	3.82746			0.148984
$661$	−26.3500			−1.02489			−0.512447	−	0.858719i	$-0.671261\pi$
$661$	−26.3500			−1.02489			−0.512447	+	0.858719i	$0.671261\pi$
$662$	19.8892			0.773016
$663$	−1.62648			−0.0631674
$664$	28.6098			1.11028
$665$	12.7866	+	10.5081i	0.495842	+	0.407486i
$666$		−	1.47354i		−	0.0570986i
$667$	−26.7029	+	7.61730i	−1.03394	+	0.294943i
$668$			1.71208i			0.0662424i
$669$	0.877200			0.0339145
$670$		−	9.97391i		−	0.385326i
$671$			34.8631i			1.34588i
$672$	−5.58480	+	6.79576i	−0.215438	+	0.262152i
$673$	−31.4474			−1.21221			−0.606105	−	0.795385i	$-0.707269\pi$
$673$	−31.4474			−1.21221			−0.606105	+	0.795385i	$0.707269\pi$
$674$			38.5796i			1.48603i
$675$			2.17819i			0.0838387i
$676$	−7.54094			−0.290036
$677$	22.9586			0.882369			0.441185	−	0.897416i	$-0.354558\pi$
$677$	22.9586			0.882369			0.441185	+	0.897416i	$0.354558\pi$
$678$	3.54280			0.136060
$679$	30.6037	+	25.1503i	1.17446	+	0.965181i
$680$	−10.2308			−0.392334
$681$		−	7.95339i		−	0.304775i
$682$	2.48477			0.0951469
$683$	−26.0829			−0.998036			−0.499018	−	0.866592i	$-0.666306\pi$
$683$	−26.0829			−0.998036			−0.499018	+	0.866592i	$0.666306\pi$
$684$	2.27849			0.0871203
$685$			29.8356i			1.13996i
$686$	−10.3249	+	19.2231i	−0.394208	+	0.733942i
$687$			12.3293i			0.470392i
$688$			16.8581i			0.642710i
$689$	0.0533396			0.00203208
$690$	2.60375	+	9.12760i	0.0991229	+	0.347482i
$691$		−	22.9404i		−	0.872694i	−0.899779	−	0.436347i	$-0.856272\pi$
$691$		−	22.9404i		−	0.872694i	0.899779	−	0.436347i	$-0.143728\pi$
$692$			3.59840i			0.136791i
$693$	6.25547	−	7.61186i	0.237626	−	0.289151i
$694$	10.6200			0.403129
$695$			27.4593i			1.04159i
$696$			17.8176i			0.675374i
$697$			9.89579i			0.374830i
$698$			27.8451i			1.05395i
$699$		−	3.38814i		−	0.128151i
$700$	2.72422	+	2.23878i	0.102966	+	0.0846179i
$701$			42.0469i			1.58809i	0.607860	+	0.794044i	$0.292028\pi$
$701$			42.0469i			1.58809i	−0.607860	+	0.794044i	$0.707972\pi$
$702$	0.968247			0.0365441
$703$			4.65738i			0.175656i
$704$			32.4756i			1.22397i
$705$	8.64511			0.325594
$706$			23.6059i			0.888419i
$707$	20.6102	−	25.0791i	0.775125	−	0.943197i
$708$	−6.75830			−0.253992
$709$			25.1440i			0.944303i	0.881517	+	0.472152i	$0.156522\pi$
$709$			25.1440i			0.944303i	−0.881517	+	0.472152i	$0.843478\pi$
$710$	−12.6704			−0.475511
$711$			17.6032i			0.660171i
$712$	36.4203			1.36491
$713$	−0.745061	−	2.61186i	−0.0279028	−	0.0978149i
$714$	−3.91707	+	4.76641i	−0.146592	+	0.178378i
$715$	−5.14078			−0.192254
$716$	0.0617473			0.00230761
$717$		−	13.7445i		−	0.513299i
$718$			1.97916i			0.0738615i
$719$		−	40.4831i		−	1.50976i	−0.655860	−	0.754882i	$-0.727694\pi$
$719$		−	40.4831i		−	1.50976i	0.655860	−	0.754882i	$-0.272306\pi$
$720$	4.03479			0.150368
$721$	17.0357	+	14.0000i	0.634441	+	0.521387i
$722$	−6.04728			−0.225057
$723$			19.0883i			0.709901i
$724$	7.74415			0.287809
$725$	12.6119			0.468393
$726$		−	3.37827i		−	0.125379i
$727$	46.9536			1.74141			0.870706	−	0.491805i	$-0.163663\pi$
$727$	46.9536			1.74141			0.870706	+	0.491805i	$0.163663\pi$
$728$	4.24815	−	5.16928i	0.157447	−	0.191586i
$729$	−1.00000			−0.0370370
$730$		−	31.4312i		−	1.16332i
$731$		−	13.8910i		−	0.513776i
$732$		−	5.72824i		−	0.211722i
$733$	30.7288			1.13499			0.567497	−	0.823375i	$-0.307912\pi$
$733$	30.7288			1.13499			0.567497	+	0.823375i	$0.307912\pi$
$734$	6.51956			0.240641
$735$	−11.5359	+	2.27849i	−0.425508	+	0.0840435i
$736$	15.3327	−	4.37383i	0.565173	−	0.161222i
$737$	18.7664			0.691270
$738$		−	5.89097i		−	0.216850i
$739$	45.8338			1.68602			0.843012	−	0.537895i	$-0.180780\pi$
$739$	45.8338			1.68602			0.843012	+	0.537895i	$0.180780\pi$
$740$		−	1.28546i		−	0.0472546i
$741$	−3.06031			−0.112423
$742$	0.128458	−	0.156312i	0.00471584	−	0.00573839i
$743$			23.6056i			0.866004i	0.901393	+	0.433002i	$0.142546\pi$
$743$			23.6056i			0.866004i	−0.901393	+	0.433002i	$0.857454\pi$
$744$	−1.74277			−0.0638931
$745$			31.1878i			1.14263i
$746$		−	13.1955i		−	0.483123i
$747$	9.29712			0.340164
$748$		−	4.50950i		−	0.164883i
$749$	−25.5247	+	31.0593i	−0.932653	+	1.13488i
$750$		−	14.2068i		−	0.518758i
$751$			1.36391i			0.0497697i	0.999690	+	0.0248848i	$0.00792191\pi$
$751$			1.36391i			0.0497697i	−0.999690	+	0.0248848i	$0.992078\pi$
$752$			12.3613i			0.450770i
$753$			7.57758i			0.276142i
$754$		−	5.60620i		−	0.204166i
$755$	−2.18544			−0.0795363
$756$	−1.02781	+	1.25068i	−0.0373812	+	0.0454867i
$757$			49.5797i			1.80201i	0.433814	+	0.901003i	$0.357168\pi$
$757$			49.5797i			1.80201i	−0.433814	+	0.901003i	$0.642832\pi$
$758$		−	7.91663i		−	0.287545i
$759$	−17.1740	+	4.89908i	−0.623378	+	0.177825i
$760$	−19.2498			−0.698264
$761$		−	31.9227i		−	1.15720i	−0.815612	−	0.578599i	$-0.803600\pi$
$761$		−	31.9227i		−	1.15720i	0.815612	−	0.578599i	$-0.196400\pi$
$762$		−	2.73887i		−	0.0992188i
$763$	−12.1366	+	14.7682i	−0.439373	+	0.534644i
$764$			4.38091i			0.158496i
$765$	−3.32464			−0.120202
$766$	30.5924			1.10535
$767$	9.07728			0.327761
$768$		−	13.1701i		−	0.475234i
$769$	−18.7009			−0.674372			−0.337186	−	0.941438i	$-0.609475\pi$
$769$	−18.7009			−0.674372			−0.337186	+	0.941438i	$0.609475\pi$
$770$	−12.3806	+	15.0651i	−0.446165	+	0.542907i
$771$	−22.1048			−0.796086
$772$	4.15455			0.149526
$773$	−6.40633			−0.230420			−0.115210	−	0.993341i	$-0.536754\pi$
$773$	−6.40633			−0.230420			−0.115210	+	0.993341i	$0.536754\pi$
$774$			8.26931i			0.297234i
$775$			1.23359i			0.0443118i
$776$	−46.0730			−1.65393
$777$	−2.55646	−	2.10092i	−0.0917127	−	0.0753700i
$778$			10.9538i			0.392713i
$779$			18.6194i			0.667110i
$780$	0.844664			0.0302438
$781$		−	23.8400i		−	0.853062i
$782$	10.7541	−	3.06772i	0.384565	−	0.109701i
$783$			5.79005i			0.206920i
$784$	−3.25792	−	16.4947i	−0.116354	−	0.589097i
$785$	12.7763			0.456005
$786$	−7.22548			−0.257724
$787$	46.2085			1.64716			0.823578	−	0.567204i	$-0.191975\pi$
$787$	46.2085			1.64716			0.823578	+	0.567204i	$0.191975\pi$
$788$	8.86764			0.315897
$789$	8.67030			0.308671
$790$		−	34.8395i		−	1.23953i
$791$	5.05118	−	6.14644i	0.179599	−	0.218542i
$792$			11.4594i			0.407193i
$793$			7.69377i			0.273214i
$794$		−	3.56036i		−	0.126353i
$795$	0.109030			0.00386688
$796$	−6.93920			−0.245953
$797$	47.2111			1.67230			0.836152	−	0.548498i	$-0.184800\pi$
$797$	47.2111			1.67230			0.836152	+	0.548498i	$0.184800\pi$
$798$	−7.37016	+	8.96825i	−0.260901	+	0.317472i
$799$		−	10.1856i		−	0.360341i
$800$	−7.24170			−0.256033
$801$	11.8352			0.418177
$802$		−	39.8866i		−	1.40845i
$803$	59.1394			2.08698
$804$	−3.08344			−0.108745
$805$	19.5479	+	8.49650i	0.688973	+	0.299462i
$806$	0.548352			0.0193149
$807$	19.6891			0.693090
$808$			37.7558i			1.32825i
$809$	−45.4513			−1.59798			−0.798992	−	0.601342i	$-0.794633\pi$
$809$	−45.4513			−1.59798			−0.798992	+	0.601342i	$0.794633\pi$
$810$	1.97916			0.0695405
$811$			26.2375i			0.921323i	0.887576	+	0.460661i	$0.152388\pi$
$811$			26.2375i			0.921323i	−0.887576	+	0.460661i	$0.847612\pi$
$812$	7.24149	+	5.95110i	0.254127	+	0.208843i
$813$	−4.65738			−0.163342
$814$	−5.48730			−0.192330
$815$	−11.2366			−0.393600
$816$		−	4.75376i		−	0.166415i
$817$		−	26.1366i		−	0.914403i
$818$		−	22.2198i		−	0.776898i
$819$	1.38049	−	1.67982i	0.0482382	−	0.0586978i
$820$		−	5.13907i		−	0.179464i
$821$	31.0692			1.08432			0.542161	−	0.840275i	$-0.317606\pi$
$821$	31.0692			1.08432			0.542161	+	0.840275i	$0.317606\pi$
$822$	−20.9261			−0.729881
$823$	−44.6694			−1.55708			−0.778539	−	0.627597i	$-0.784039\pi$
$823$	−44.6694			−1.55708			−0.778539	+	0.627597i	$0.784039\pi$
$824$	−25.6467			−0.893444
$825$	8.11135			0.282401
$826$	21.8608	−	26.6010i	0.760636	−	0.925566i
$827$		−	18.7327i		−	0.651398i	−0.945473	−	0.325699i	$-0.894400\pi$
$827$		−	18.7327i		−	0.651398i	0.945473	−	0.325699i	$-0.105600\pi$
$828$	2.82181	−	0.804951i	0.0980645	−	0.0279740i
$829$			35.6355i			1.23767i	0.785520	+	0.618836i	$0.212395\pi$
$829$			35.6355i			1.23767i	−0.785520	+	0.618836i	$0.787605\pi$
$830$	−18.4005			−0.638689
$831$		−	23.5011i		−	0.815243i
$832$			7.16688i			0.248467i
$833$	2.68451	+	13.5915i	0.0930126	+	0.470919i
$834$	−19.2594			−0.666897
$835$		−	4.70042i		−	0.162665i
$836$		−	8.48485i		−	0.293455i
$837$	−0.566335			−0.0195754
$838$	−30.5729			−1.05612
$839$	−27.3063			−0.942719			−0.471359	−	0.881941i	$-0.656237\pi$
$839$	−27.3063			−0.942719			−0.471359	+	0.881941i	$0.656237\pi$
$840$	8.68348	−	10.5663i	0.299608	−	0.364573i
$841$	4.52471			0.156025
$842$		−	1.36391i		−	0.0470033i
$843$	1.90269			0.0655320
$844$	−6.51239			−0.224166
$845$	20.7032			0.712212
$846$			6.06351i			0.208468i
$847$	−5.86100	−	4.81661i	−0.201386	−	0.165501i
$848$			0.155897i			0.00535353i
$849$		−	12.3574i		−	0.424106i
$850$	−5.07918			−0.174215
$851$	1.64537	+	5.76795i	0.0564026	+	0.197723i
$852$			3.91707i			0.134196i
$853$			49.8730i			1.70762i	0.520586	+	0.853809i	$0.325714\pi$
$853$			49.8730i			1.70762i	−0.520586	+	0.853809i	$0.674286\pi$
$854$	22.5466	+	18.5289i	0.771529	+	0.634047i
$855$	−6.25547			−0.213933
$856$		−	46.7588i		−	1.59818i
$857$		−	1.05539i		−	0.0360516i	−0.999838	−	0.0180258i	$-0.994262\pi$
$857$		−	1.05539i		−	0.0360516i	0.999838	−	0.0180258i	$-0.00573810\pi$
$858$		−	3.60564i		−	0.123095i
$859$		−	58.0910i		−	1.98204i	−0.133710	−	0.991020i	$-0.542689\pi$
$859$		−	58.0910i		−	1.98204i	0.133710	−	0.991020i	$-0.457311\pi$
$860$			7.21385i			0.245990i
$861$	−10.2203	−	8.39912i	−0.348307	−	0.286241i
$862$		−	44.4134i		−	1.51273i
$863$	14.2018			0.483436			0.241718	−	0.970347i	$-0.422289\pi$
$863$	14.2018			0.483436			0.241718	+	0.970347i	$0.422289\pi$
$864$		−	3.32464i		−	0.113106i
$865$		−	9.87921i		−	0.335903i
$866$	−47.0350			−1.59832
$867$		−	13.0829i		−	0.444320i
$868$	−0.582088	+	0.708303i	−0.0197573	+	0.0240414i
$869$	65.5523			2.22371
$870$		−	11.4594i		−	0.388511i
$871$	4.14147			0.140328
$872$		−	22.2330i		−	0.752906i
$873$	−14.9720			−0.506726
$874$	20.2343	−	5.77207i	0.684437	−	0.195243i
$875$	−24.6475	−	20.2555i	−0.833238	−	0.684760i
$876$	−9.71699			−0.328307
$877$	−14.8973			−0.503047			−0.251523	−	0.967851i	$-0.580932\pi$
$877$	−14.8973			−0.503047			−0.251523	+	0.967851i	$0.580932\pi$
$878$		−	19.2614i		−	0.650042i
$879$			28.4871i			0.960845i
$880$		−	15.0251i		−	0.506496i
$881$	−30.5759			−1.03013			−0.515064	−	0.857152i	$-0.672232\pi$
$881$	−30.5759			−1.03013			−0.515064	+	0.857152i	$0.672232\pi$
$882$	−1.59809	−	8.09105i	−0.0538104	−	0.272440i
$883$	−41.6532			−1.40174			−0.700870	−	0.713289i	$-0.747205\pi$
$883$	−41.6532			−1.40174			−0.700870	+	0.713289i	$0.747205\pi$
$884$		−	0.995178i		−	0.0334715i
$885$	18.5545			0.623704
$886$	14.3529			0.482194
$887$		−	10.2911i		−	0.345542i	−0.984962	−	0.172771i	$-0.944728\pi$
$887$		−	10.2911i		−	0.345542i	0.984962	−	0.172771i	$-0.0552721\pi$
$888$	3.84868			0.129153
$889$	−4.75170	−	3.90498i	−0.159367	−	0.130969i
$890$	−23.4238			−0.785167
$891$			3.72389i			0.124755i
$892$			0.536723i			0.0179708i
$893$		−	19.1648i		−	0.641324i
$894$	−21.8745			−0.731591
$895$	−0.169524			−0.00566655
$896$	7.41101	+	6.09042i	0.247585	+	0.203467i
$897$	−3.79005	+	1.08115i	−0.126546	+	0.0360987i
$898$	7.89732			0.263537
$899$			3.27911i			0.109364i
$900$	−1.33275			−0.0444249
$901$		−	0.128458i		−	0.00427956i
$902$	−21.9373			−0.730432
$903$	14.3465	+	11.7901i	0.477422	+	0.392348i
$904$			9.25328i			0.307760i
$905$	−21.2611			−0.706744
$906$		−	1.53282i		−	0.0509246i
$907$			48.4221i			1.60783i	0.594745	+	0.803915i	$0.297253\pi$
$907$			48.4221i			1.60783i	−0.594745	+	0.803915i	$0.702747\pi$
$908$	4.86635			0.161496
$909$			12.2692i			0.406945i
$910$	−2.73220	+	3.32464i	−0.0905717	+	0.110211i
$911$			12.0048i			0.397735i	0.980026	+	0.198868i	$0.0637264\pi$
$911$			12.0048i			0.397735i	−0.980026	+	0.198868i	$0.936274\pi$
$912$		−	8.94445i		−	0.296180i
$913$		−	34.6214i		−	1.14580i
$914$		−	32.2622i		−	1.06714i
$915$			15.7265i			0.519904i
$916$	−7.54378			−0.249254
$917$	−10.3018	+	12.5356i	−0.340195	+	0.413961i
$918$		−	2.33183i		−	0.0769619i
$919$		−	51.3757i		−	1.69473i	−0.531012	−	0.847364i	$-0.678188\pi$
$919$		−	51.3757i		−	1.69473i	0.531012	−	0.847364i	$-0.321812\pi$
$920$	−23.8400	+	6.80062i	−0.785981	+	0.224210i
$921$	24.0357			0.792002
$922$			40.3363i			1.32841i
$923$		−	5.26113i		−	0.173172i
$924$	4.65738	+	3.82746i	0.153217	+	0.125914i
$925$		−	2.72422i		−	0.0895718i
$926$	26.9679			0.886221
$927$	−8.33421			−0.273731
$928$	−19.2498			−0.631906
$929$		−	33.4157i		−	1.09633i	−0.836369	−	0.548166i	$-0.815326\pi$
$929$		−	33.4157i		−	1.09633i	0.836369	−	0.548166i	$-0.184674\pi$
$930$	1.12087			0.0367547
$931$	5.05104	+	25.5732i	0.165541	+	0.838126i
$932$	2.07306			0.0679055
$933$	−11.7029			−0.383136
$934$	7.30138			0.238908
$935$			12.3806i			0.404888i
$936$			2.52892i			0.0826605i
$937$	−36.8746			−1.20464			−0.602321	−	0.798254i	$-0.705757\pi$
$937$	−36.8746			−1.20464			−0.602321	+	0.798254i	$0.705757\pi$
$938$	9.97391	−	12.1366i	0.325660	−	0.396273i
$939$		−	18.5661i		−	0.605882i
$940$			5.28959i			0.172527i
$941$	43.8283			1.42876			0.714382	−	0.699756i	$-0.246708\pi$
$941$	43.8283			1.42876			0.714382	+	0.699756i	$0.246708\pi$
$942$			8.96103i			0.291966i
$943$	6.57792	+	23.0593i	0.214206	+	0.750914i
$944$			26.5304i			0.863490i
$945$	2.82181	−	3.43366i	0.0917934	−	0.111697i
$946$	30.7940			1.00120
$947$	0.0635063			0.00206368			0.00103184	−	0.999999i	$-0.499672\pi$
$947$	0.0635063			0.00206368			0.00103184	+	0.999999i	$0.499672\pi$
$948$	−10.7707			−0.349815
$949$	13.0512			0.423659
$950$	−9.55674			−0.310062
$951$		−	19.1503i		−	0.620992i
$952$	−12.4492	−	10.2308i	−0.403481	−	0.331583i
$953$			6.83754i			0.221490i	0.993849	+	0.110745i	$0.0353236\pi$
$953$			6.83754i			0.221490i	−0.993849	+	0.110745i	$0.964676\pi$
$954$			0.0764712i			0.00247585i
$955$		−	12.0275i		−	0.389202i
$956$	8.40971			0.271989
$957$	21.5615			0.696984
$958$	−40.2257			−1.29963
$959$	−29.8356	+	36.3049i	−0.963441	+	1.17235i
$960$			14.6496i			0.472812i
$961$	30.6793			0.989654
$962$	−1.21096			−0.0390431
$963$		−	15.1949i		−	0.489648i
$964$	−11.6793			−0.376166
$965$	−11.4061			−0.367175
$966$	−5.95927	+	13.7105i	−0.191736	+	0.441128i
$967$	19.7819			0.636144			0.318072	−	0.948067i	$-0.396965\pi$
$967$	19.7819			0.636144			0.318072	+	0.948067i	$0.396965\pi$
$968$	8.82356			0.283600
$969$			7.37016i			0.236764i
$970$	29.6320			0.951426
$971$	−36.9395			−1.18545			−0.592723	−	0.805406i	$-0.701947\pi$
$971$	−36.9395			−1.18545			−0.592723	+	0.805406i	$0.701947\pi$
$972$		−	0.611859i		−	0.0196254i
$973$	−27.4593	+	33.4133i	−0.880303	+	1.07118i
$974$	32.6115			1.04494
$975$	1.79005			0.0573276
$976$	−22.4868			−0.719783
$977$		−	30.1186i		−	0.963578i	−0.876287	−	0.481789i	$-0.839987\pi$
$977$		−	30.1186i		−	0.963578i	0.876287	−	0.481789i	$-0.160013\pi$
$978$		−	7.88110i		−	0.252010i
$979$		−	44.0731i		−	1.40858i
$980$	−1.39412	−	7.05834i	−0.0445334	−	0.225470i
$981$		−	7.22491i		−	0.230674i
$982$	6.62808			0.211511
$983$	22.5727			0.719958			0.359979	−	0.932960i	$-0.382784\pi$
$983$	22.5727			0.719958			0.359979	+	0.932960i	$0.382784\pi$
$984$	15.3864			0.490500
$985$	−24.3456			−0.775716
$986$	−13.5014			−0.429973
$987$	10.5197	+	8.64511i	0.334844	+	0.275177i
$988$		−	1.87248i		−	0.0595715i
$989$	−9.23359	−	32.3689i	−0.293611	−	1.02927i
$990$		−	7.37016i		−	0.234239i
$991$	6.45165			0.204943			0.102472	−	0.994736i	$-0.467325\pi$
$991$	6.45165			0.204943			0.102472	+	0.994736i	$0.467325\pi$
$992$		−	1.88286i		−	0.0597808i
$993$			16.8811i			0.535705i
$994$	−15.4177	−	12.6704i	−0.489021	−	0.401880i
$995$	19.0512			0.603963
$996$			5.68852i			0.180248i
$997$			18.9227i			0.599289i	0.954051	+	0.299644i	$0.0968680\pi$
$997$			18.9227i			0.599289i	−0.954051	+	0.299644i	$0.903132\pi$
$998$	−19.1521			−0.606249
$999$	1.25068			0.0395697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.c.160.8	yes	12
3.2	odd	2		1449.2.h.e.1126.6		12
7.6	odd	2	inner	483.2.h.c.160.5	✓	12
21.20	even	2		1449.2.h.e.1126.8		12
23.22	odd	2	inner	483.2.h.c.160.7	yes	12
69.68	even	2		1449.2.h.e.1126.7		12
161.160	even	2	inner	483.2.h.c.160.6	yes	12
483.482	odd	2		1449.2.h.e.1126.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.c.160.5	✓	12	7.6	odd	2	inner
483.2.h.c.160.6	yes	12	161.160	even	2	inner
483.2.h.c.160.7	yes	12	23.22	odd	2	inner
483.2.h.c.160.8	yes	12	1.1	even	1	trivial
1449.2.h.e.1126.5		12	483.482	odd	2
1449.2.h.e.1126.6		12	3.2	odd	2
1449.2.h.e.1126.7		12	69.68	even	2
1449.2.h.e.1126.8		12	21.20	even	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.17819 q^{2} +1.00000i q^{3} -0.611859 q^{4} +1.67982 q^{5} +1.17819i q^{6} +(2.04406 + 1.67982i) q^{7} -3.07728 q^{8} -1.00000 q^{9} +1.97916 q^{10} +3.72389i q^{11} -0.611859i q^{12} +0.821806i q^{13} +(2.40830 + 1.97916i) q^{14} +1.67982i q^{15} -2.40191 q^{16} +1.97916 q^{17} -1.17819 q^{18} +3.72389 q^{19} -1.02781 q^{20} +(-1.67982 + 2.04406i) q^{21} +4.38746i q^{22} +(4.61186 - 1.31558i) q^{23} -3.07728i q^{24} -2.17819 q^{25} +0.968247i q^{26} -1.00000i q^{27} +(-1.25068 - 1.02781i) q^{28} -5.79005 q^{29} +1.97916i q^{30} -0.566335i q^{31} +3.32464 q^{32} -3.72389 q^{33} +2.33183 q^{34} +(3.43366 + 2.82181i) q^{35} +0.611859 q^{36} +1.25068i q^{37} +4.38746 q^{38} -0.821806 q^{39} -5.16928 q^{40} +5.00000i q^{41} +(-1.97916 + 2.40830i) q^{42} -7.01863i q^{43} -2.27849i q^{44} -1.67982 q^{45} +(5.43366 - 1.55001i) q^{46} -5.14644i q^{47} -2.40191i q^{48} +(1.35639 + 6.86733i) q^{49} -2.56634 q^{50} +1.97916i q^{51} -0.502829i q^{52} -0.0649054i q^{53} -1.17819i q^{54} +6.25547i q^{55} +(-6.29015 - 5.16928i) q^{56} +3.72389i q^{57} -6.82181 q^{58} -11.0455i q^{59} -1.02781i q^{60} +9.36202 q^{61} -0.667253i q^{62} +(-2.04406 - 1.67982i) q^{63} +8.72089 q^{64} +1.38049i q^{65} -4.38746 q^{66} -5.03947i q^{67} -1.21096 q^{68} +(1.31558 + 4.61186i) q^{69} +(4.04552 + 3.32464i) q^{70} -6.40191 q^{71} +3.07728 q^{72} -15.8811i q^{73} +1.47354i q^{74} -2.17819i q^{75} -2.27849 q^{76} +(-6.25547 + 7.61186i) q^{77} -0.968247 q^{78} -17.6032i q^{79} -4.03479 q^{80} +1.00000 q^{81} +5.89097i q^{82} -9.29712 q^{83} +(1.02781 - 1.25068i) q^{84} +3.32464 q^{85} -8.26931i q^{86} -5.79005i q^{87} -11.4594i q^{88} -11.8352 q^{89} -1.97916 q^{90} +(-1.38049 + 1.67982i) q^{91} +(-2.82181 + 0.804951i) q^{92} +0.566335 q^{93} -6.06351i q^{94} +6.25547 q^{95} +3.32464i q^{96} +14.9720 q^{97} +(1.59809 + 8.09105i) q^{98} -3.72389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9	\( 12 q + 4 q^{2} + 36 q^{4} - 24 q^{8} - 12 q^{9} + 68 q^{16} - 4 q^{18} + 12 q^{23} - 16 q^{25} - 16 q^{29} - 44 q^{32} + 8 q^{35} - 36 q^{36} - 20 q^{39} + 32 q^{46} - 4 q^{49} - 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} + 20 q^{71} + 24 q^{72} - 52 q^{77} + 52 q^{78} + 12 q^{81} - 44 q^{85} - 44 q^{92} + 40 q^{93} + 52 q^{95} + 116 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 36 * q^4 - 24 * q^8 - 12 * q^9 + 68 * q^16 - 4 * q^18 + 12 * q^23 - 16 * q^25 - 16 * q^29 - 44 * q^32 + 8 * q^35 - 36 * q^36 - 20 * q^39 + 32 * q^46 - 4 * q^49 - 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 + 20 * q^71 + 24 * q^72 - 52 * q^77 + 52 * q^78 + 12 * q^81 - 44 * q^85 - 44 * q^92 + 40 * q^93 + 52 * q^95 + 116 * q^98

Introduction

L-functions

Modular forms

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