LMFDB - Embedded newform 115.2.b.b.24.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.b (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.527896576.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 7x^{4} - 10x^{3} + 8x^{2} + 4x + 1 $ x^8 - 2x^7 + 2x^6 + 2x^5 + 7x^4 - 10x^3 + 8x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.5
Root			$-1.07037 + 1.07037i$ of defining polynomial
Character	$\chi$	$=$	115.24
Dual form			115.2.b.b.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.291367i q^{2} -3.14073i q^{3} +1.91511 q^{4} +(-2.07037 + 0.844739i) q^{5} +0.915105 q^{6} -1.20647i q^{7} +1.14073i q^{8} -6.86420 q^{9} +O(q^{10})$	\(q+0.291367i q^{2} -3.14073i q^{3} +1.91511 q^{4} +(-2.07037 + 0.844739i) q^{5} +0.915105 q^{6} -1.20647i q^{7} +1.14073i q^{8} -6.86420 q^{9} +(-0.246129 - 0.603236i) q^{10} +3.65773 q^{11} -6.01483i q^{12} -0.859268i q^{13} +0.351526 q^{14} +(2.65310 + 6.50246i) q^{15} +3.49784 q^{16} +6.72347i q^{17} -2.00000i q^{18} +1.51699 q^{19} +(-3.96497 + 1.61776i) q^{20} -3.78921 q^{21} +1.06574i q^{22} +1.00000i q^{23} +3.58273 q^{24} +(3.57283 - 3.49784i) q^{25} +0.250362 q^{26} +12.1364i q^{27} -2.31052i q^{28} -0.548747 q^{29} +(-1.89460 + 0.773025i) q^{30} -5.99568 q^{31} +3.30062i q^{32} -11.4879i q^{33} -1.95900 q^{34} +(1.01915 + 2.49784i) q^{35} -13.1457 q^{36} +2.04100i q^{37} +0.442002i q^{38} -2.69873 q^{39} +(-0.963621 - 2.36173i) q^{40} -7.14998 q^{41} -1.10405i q^{42} +10.0799i q^{43} +7.00493 q^{44} +(14.2114 - 5.79846i) q^{45} -0.291367 q^{46} -9.17040i q^{47} -10.9858i q^{48} +5.54442 q^{49} +(1.01915 + 1.04100i) q^{50} +21.1166 q^{51} -1.64559i q^{52} -5.37896i q^{53} -3.53615 q^{54} +(-7.57283 + 3.08982i) q^{55} +1.37626 q^{56} -4.76447i q^{57} -0.159887i q^{58} +0.582734 q^{59} +(5.08097 + 12.4529i) q^{60} -8.83244 q^{61} -1.74694i q^{62} +8.28146i q^{63} +6.03399 q^{64} +(0.725857 + 1.77900i) q^{65} +3.34720 q^{66} -3.20647i q^{67} +12.8761i q^{68} +3.14073 q^{69} +(-0.727788 + 0.296948i) q^{70} -12.5784 q^{71} -7.83021i q^{72} -8.62597i q^{73} -0.594681 q^{74} +(-10.9858 - 11.2213i) q^{75} +2.90520 q^{76} -4.41294i q^{77} -0.786321i q^{78} -0.0700619 q^{79} +(-7.24181 + 2.95476i) q^{80} +17.5246 q^{81} -2.08327i q^{82} -6.74197i q^{83} -7.25673 q^{84} +(-5.67958 - 13.9200i) q^{85} -2.93696 q^{86} +1.72347i q^{87} +4.17248i q^{88} -4.96393 q^{89} +(1.68948 + 4.14073i) q^{90} -1.03668 q^{91} +1.91511i q^{92} +18.8308i q^{93} +2.67195 q^{94} +(-3.14073 + 1.28146i) q^{95} +10.3664 q^{96} +11.3380i q^{97} +1.61546i q^{98} -25.1074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9	$ 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + 6 q^{10} + 4 q^{11} + 8 q^{14} + 6 q^{15} + 4 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{21} + 24 q^{24} - 16 q^{25} + 12 q^{26} - 8 q^{29} - 2 q^{30} - 28 q^{34} + 28 q^{35} - 16 q^{36} + 16 q^{39} - 10 q^{40} - 16 q^{41} - 12 q^{44} + 24 q^{45} + 28 q^{50} + 20 q^{51} - 44 q^{54} - 16 q^{55} + 28 q^{56} - 16 q^{60} - 16 q^{61} + 40 q^{64} - 14 q^{65} - 16 q^{66} + 4 q^{69} - 28 q^{70} - 48 q^{71} + 72 q^{74} - 36 q^{76} - 48 q^{79} - 2 q^{80} + 16 q^{81} - 4 q^{84} + 12 q^{85} + 28 q^{86} + 16 q^{89} - 4 q^{90} + 52 q^{91} + 84 q^{94} - 4 q^{95} + 60 q^{96} - 72 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9 + 6 * q^10 + 4 * q^11 + 8 * q^14 + 6 * q^15 + 4 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^21 + 24 * q^24 - 16 * q^25 + 12 * q^26 - 8 * q^29 - 2 * q^30 - 28 * q^34 + 28 * q^35 - 16 * q^36 + 16 * q^39 - 10 * q^40 - 16 * q^41 - 12 * q^44 + 24 * q^45 + 28 * q^50 + 20 * q^51 - 44 * q^54 - 16 * q^55 + 28 * q^56 - 16 * q^60 - 16 * q^61 + 40 * q^64 - 14 * q^65 - 16 * q^66 + 4 * q^69 - 28 * q^70 - 48 * q^71 + 72 * q^74 - 36 * q^76 - 48 * q^79 - 2 * q^80 + 16 * q^81 - 4 * q^84 + 12 * q^85 + 28 * q^86 + 16 * q^89 - 4 * q^90 + 52 * q^91 + 84 * q^94 - 4 * q^95 + 60 * q^96 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.291367i			0.206028i	0.994680	+	0.103014i	$0.0328486\pi$
$2$			0.291367i			0.206028i	−0.994680	+	0.103014i	$0.967151\pi$
$3$		−	3.14073i		−	1.81330i	−0.421881	−	0.906651i	$-0.638630\pi$
$3$		−	3.14073i		−	1.81330i	0.421881	−	0.906651i	$-0.361370\pi$
$4$	1.91511			0.957553
$5$	−2.07037	+	0.844739i	−0.925896	+	0.377779i
$5$	−2.07037	+	0.844739i	−0.925896	+	0.377779i
$6$	0.915105			0.373590
$7$		−	1.20647i		−	0.456004i	−0.973661	−	0.228002i	$-0.926781\pi$
$7$		−	1.20647i		−	0.456004i	0.973661	−	0.228002i	$-0.0732192\pi$
$8$			1.14073i			0.403310i
$9$	−6.86420			−2.28807
$10$	−0.246129	−	0.603236i	−0.0778328	−	0.190760i
$11$	3.65773			1.10285			0.551423	−	0.834226i	$-0.314085\pi$
$11$	3.65773			1.10285			0.551423	+	0.834226i	$0.314085\pi$
$12$		−	6.01483i		−	1.73633i
$13$		−	0.859268i		−	0.238318i	−0.992875	−	0.119159i	$-0.961980\pi$
$13$		−	0.859268i		−	0.238318i	0.992875	−	0.119159i	$-0.0380198\pi$
$14$	0.351526			0.0939493
$15$	2.65310	+	6.50246i	0.685027	+	1.67893i
$16$	3.49784			0.874460
$17$			6.72347i			1.63068i	0.578982	+	0.815340i	$0.303450\pi$
$17$			6.72347i			1.63068i	−0.578982	+	0.815340i	$0.696550\pi$
$18$		−	2.00000i		−	0.471405i
$19$	1.51699			0.348022			0.174011	−	0.984744i	$-0.444327\pi$
$19$	1.51699			0.348022			0.174011	+	0.984744i	$0.444327\pi$
$20$	−3.96497	+	1.61776i	−0.886594	+	0.361743i
$21$	−3.78921			−0.826873
$22$			1.06574i			0.227217i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	3.58273			0.731322
$25$	3.57283	−	3.49784i	0.714566	−	0.699568i
$26$	0.250362			0.0491001
$27$			12.1364i			2.33565i
$28$		−	2.31052i		−	0.436648i
$29$	−0.548747			−0.101900			−0.0509498	−	0.998701i	$-0.516225\pi$
$29$	−0.548747			−0.101900			−0.0509498	+	0.998701i	$0.516225\pi$
$30$	−1.89460	+	0.773025i	−0.345906	+	0.141134i
$31$	−5.99568			−1.07686			−0.538428	−	0.842672i	$-0.680982\pi$
$31$	−5.99568			−1.07686			−0.538428	+	0.842672i	$0.680982\pi$
$32$			3.30062i			0.583472i
$33$		−	11.4879i		−	1.99979i
$34$	−1.95900			−0.335965
$35$	1.01915	+	2.49784i	0.172269	+	0.422212i
$36$	−13.1457			−2.19094
$37$			2.04100i			0.335539i	0.985826	+	0.167770i	$0.0536565\pi$
$37$			2.04100i			0.335539i	−0.985826	+	0.167770i	$0.946344\pi$
$38$			0.442002i			0.0717021i
$39$	−2.69873			−0.432143
$40$	−0.963621	−	2.36173i	−0.152362	−	0.373423i
$41$	−7.14998			−1.11664			−0.558320	−	0.829626i	$-0.688554\pi$
$41$	−7.14998			−1.11664			−0.558320	+	0.829626i	$0.688554\pi$
$42$		−	1.10405i		−	0.170358i
$43$			10.0799i			1.53717i	0.639745	+	0.768587i	$0.279040\pi$
$43$			10.0799i			1.53717i	−0.639745	+	0.768587i	$0.720960\pi$
$44$	7.00493			1.05603
$45$	14.2114	−	5.79846i	2.11851	−	0.864383i
$46$	−0.291367			−0.0429597
$47$		−	9.17040i		−	1.33764i	−0.743424	−	0.668820i	$-0.766800\pi$
$47$		−	9.17040i		−	1.33764i	0.743424	−	0.668820i	$-0.233200\pi$
$48$		−	10.9858i		−	1.58566i
$49$	5.54442			0.792061
$50$	1.01915	+	1.04100i	0.144130	+	0.147220i
$51$	21.1166			2.95692
$52$		−	1.64559i		−	0.228202i
$53$		−	5.37896i		−	0.738857i	−0.929259	−	0.369428i	$-0.879554\pi$
$53$		−	5.37896i		−	0.738857i	0.929259	−	0.369428i	$-0.120446\pi$
$54$	−3.53615			−0.481209
$55$	−7.57283	+	3.08982i	−1.02112	+	0.416632i
$56$	1.37626			0.183911
$57$		−	4.76447i		−	0.631070i
$58$		−	0.159887i		−	0.0209941i
$59$	0.582734			0.0758655			0.0379327	−	0.999280i	$-0.487923\pi$
$59$	0.582734			0.0758655			0.0379327	+	0.999280i	$0.487923\pi$
$60$	5.08097	+	12.4529i	0.655950	+	1.60766i
$61$	−8.83244			−1.13088			−0.565439	−	0.824790i	$-0.691293\pi$
$61$	−8.83244			−1.13088			−0.565439	+	0.824790i	$0.691293\pi$
$62$		−	1.74694i		−	0.221862i
$63$			8.28146i			1.04337i
$64$	6.03399			0.754248
$65$	0.725857	+	1.77900i	0.0900315	+	0.220658i
$66$	3.34720			0.412012
$67$		−	3.20647i		−	0.391733i	−0.980631	−	0.195866i	$-0.937248\pi$
$67$		−	3.20647i		−	0.391733i	0.980631	−	0.195866i	$-0.0627519\pi$
$68$			12.8761i			1.56146i
$69$	3.14073			0.378100
$70$	−0.727788	+	0.296948i	−0.0869873	+	0.0354921i
$71$	−12.5784			−1.49278			−0.746391	−	0.665507i	$-0.768215\pi$
$71$	−12.5784			−1.49278			−0.746391	+	0.665507i	$0.768215\pi$
$72$		−	7.83021i		−	0.922799i
$73$		−	8.62597i		−	1.00959i	−0.863238	−	0.504797i	$-0.831567\pi$
$73$		−	8.62597i		−	1.00959i	0.863238	−	0.504797i	$-0.168433\pi$
$74$	−0.594681			−0.0691303
$75$	−10.9858	−	11.2213i	−1.26853	−	1.29572i
$76$	2.90520			0.333250
$77$		−	4.41294i		−	0.502902i
$78$		−	0.786321i		−	0.0890333i
$79$	−0.0700619			−0.00788258			−0.00394129	−	0.999992i	$-0.501255\pi$
$79$	−0.0700619			−0.00788258			−0.00394129	+	0.999992i	$0.501255\pi$
$80$	−7.24181	+	2.95476i	−0.809659	+	0.330352i
$81$	17.5246			1.94718
$82$		−	2.08327i		−	0.230059i
$83$		−	6.74197i		−	0.740027i	−0.929026	−	0.370014i	$-0.879353\pi$
$83$		−	6.74197i		−	0.740027i	0.929026	−	0.370014i	$-0.120647\pi$
$84$	−7.25673			−0.791774
$85$	−5.67958	−	13.9200i	−0.616036	−	1.50984i
$86$	−2.93696			−0.316700
$87$			1.72347i			0.184775i
$88$			4.17248i			0.444788i
$89$	−4.96393			−0.526175			−0.263088	−	0.964772i	$-0.584741\pi$
$89$	−4.96393			−0.526175			−0.263088	+	0.964772i	$0.584741\pi$
$90$	1.68948	+	4.14073i	0.178087	+	0.436471i
$91$	−1.03668			−0.108674
$92$			1.91511i			0.199664i
$93$			18.8308i			1.95266i
$94$	2.67195			0.275591
$95$	−3.14073	+	1.28146i	−0.322232	+	0.131475i
$96$	10.3664			1.05801
$97$			11.3380i			1.15119i	0.817733	+	0.575597i	$0.195230\pi$
$97$			11.3380i			1.15119i	−0.817733	+	0.575597i	$0.804770\pi$
$98$			1.61546i			0.163186i
$99$	−25.1074			−2.52338
$100$	6.84235	−	6.69873i	0.684235	−	0.669873i
$101$	3.44693			0.342983			0.171491	−	0.985186i	$-0.445141\pi$
$101$	3.44693			0.342983			0.171491	+	0.985186i	$0.445141\pi$
$102$			6.15268i			0.609206i
$103$		−	9.13641i		−	0.900237i	−0.892969	−	0.450119i	$-0.851382\pi$
$103$		−	9.13641i		−	0.900237i	0.892969	−	0.450119i	$-0.148618\pi$
$104$	0.980194			0.0961160
$105$	7.84504	−	3.20089i	0.765598	−	0.312375i
$106$	1.56725			0.152225
$107$			9.24539i			0.893786i	0.894588	+	0.446893i	$0.147469\pi$
$107$			9.24539i			0.893786i	−0.894588	+	0.446893i	$0.852531\pi$
$108$			23.2425i			2.23651i
$109$	−1.64847			−0.157895			−0.0789476	−	0.996879i	$-0.525156\pi$
$109$	−1.64847			−0.157895			−0.0789476	+	0.996879i	$0.525156\pi$
$110$	−0.900273	−	2.20647i	−0.0858376	−	0.210379i
$111$	6.41025			0.608434
$112$		−	4.22005i		−	0.398757i
$113$		−	1.20647i		−	0.113495i	−0.998389	−	0.0567477i	$-0.981927\pi$
$113$		−	1.20647i		−	0.113495i	0.998389	−	0.0567477i	$-0.0180731\pi$
$114$	1.38821			0.130018
$115$	−0.844739	−	2.07037i	−0.0787723	−	0.193063i
$116$	−1.05091			−0.0975743
$117$			5.89819i			0.545287i
$118$			0.169789i			0.0156304i
$119$	8.11167			0.743596
$120$	−7.41757	+	3.02648i	−0.677128	+	0.276278i
$121$	2.37896			0.216269
$122$		−	2.57348i		−	0.232992i
$123$			22.4562i			2.02481i
$124$	−11.4824			−1.03115
$125$	−4.44231	+	10.2599i	−0.397332	+	0.917675i
$126$	−2.41294			−0.214962
$127$			15.3542i			1.36247i	0.732066	+	0.681233i	$0.238556\pi$
$127$			15.3542i			1.36247i	−0.732066	+	0.681233i	$0.761444\pi$
$128$			8.35934i			0.738868i
$129$	31.6583			2.78736
$130$	−0.518341	+	0.211491i	−0.0454616	+	0.0185490i
$131$	13.0734			1.14223			0.571113	−	0.820872i	$-0.306512\pi$
$131$	13.0734			1.14223			0.571113	+	0.820872i	$0.306512\pi$
$132$		−	22.0006i		−	1.91491i
$133$		−	1.83021i		−	0.158699i
$134$	0.934260			0.0807078
$135$	−10.2521	−	25.1268i	−0.882361	−	2.16257i
$136$	−7.66967			−0.657669
$137$		−	13.1840i		−	1.12638i	−0.826327	−	0.563191i	$-0.809573\pi$
$137$		−	13.1840i		−	1.12638i	0.826327	−	0.563191i	$-0.190427\pi$
$138$			0.915105i			0.0778989i
$139$	14.1160			1.19730			0.598652	−	0.801010i	$-0.295703\pi$
$139$	14.1160			1.19730			0.598652	+	0.801010i	$0.295703\pi$
$140$	1.95179	+	4.78363i	0.164956	+	0.404290i
$141$	−28.8018			−2.42555
$142$		−	3.66493i		−	0.307554i
$143$		−	3.14297i		−	0.262828i
$144$	−24.0099			−2.00082
$145$	1.13611	−	0.463548i	0.0943485	−	0.0384955i
$146$	2.51332			0.208004
$147$		−	17.4136i		−	1.43625i
$148$			3.90874i			0.321296i
$149$	6.54442			0.536140			0.268070	−	0.963399i	$-0.413614\pi$
$149$	6.54442			0.536140			0.268070	+	0.963399i	$0.413614\pi$
$150$	3.26952	−	3.20089i	0.266955	−	0.261352i
$151$	2.61672			0.212946			0.106473	−	0.994316i	$-0.466044\pi$
$151$	2.61672			0.212946			0.106473	+	0.994316i	$0.466044\pi$
$152$			1.73048i			0.140361i
$153$		−	46.1512i		−	3.73110i
$154$	1.28579			0.103612
$155$	12.4132	−	5.06479i	0.997056	−	0.406813i
$156$	−5.16835			−0.413799
$157$			8.81394i			0.703429i	0.936107	+	0.351715i	$0.114401\pi$
$157$			8.81394i			0.703429i	−0.936107	+	0.351715i	$0.885599\pi$
$158$		−	0.0204137i		−	0.00162403i
$159$	−16.8939			−1.33977
$160$	−2.78816	−	6.83349i	−0.220424	−	0.540235i
$161$	1.20647			0.0950833
$162$			5.10609i			0.401173i
$163$			10.1747i			0.796946i	0.917180	+	0.398473i	$0.130460\pi$
$163$			10.1747i			0.796946i	−0.917180	+	0.398473i	$0.869540\pi$
$164$	−13.6930			−1.06924
$165$	9.70431	+	23.7842i	0.755480	+	1.85160i
$166$	1.96439			0.152466
$167$		−	12.6647i		−	0.980027i	−0.871715	−	0.490014i	$-0.836992\pi$
$167$		−	12.6647i		−	0.980027i	0.871715	−	0.490014i	$-0.163008\pi$
$168$		−	4.32247i		−	0.333486i
$169$	12.2617			0.943205
$170$	4.05584	−	1.65484i	0.311069	−	0.126920i
$171$	−10.4129			−0.796298
$172$			19.3041i			1.47192i
$173$			15.6901i			1.19290i	0.802652	+	0.596448i	$0.203422\pi$
$173$			15.6901i			1.19290i	−0.802652	+	0.596448i	$0.796578\pi$
$174$	−0.502161			−0.0380687
$175$	−4.22005	−	4.31052i	−0.319005	−	0.325845i
$176$	12.7941			0.964394
$177$		−	1.83021i		−	0.137567i
$178$		−	1.44632i		−	0.108407i
$179$	2.39876			0.179292			0.0896460	−	0.995974i	$-0.471426\pi$
$179$	2.39876			0.179292			0.0896460	+	0.995974i	$0.471426\pi$
$180$	27.2163	−	11.1047i	2.02859	−	0.827692i
$181$	−9.87122			−0.733722			−0.366861	−	0.930276i	$-0.619567\pi$
$181$	−9.87122			−0.733722			−0.366861	+	0.930276i	$0.619567\pi$
$182$		−	0.302055i		−	0.0223898i
$183$			27.7403i			2.05063i
$184$	−1.14073			−0.0840959
$185$	−1.72412	−	4.22563i	−0.126760	−	0.310674i
$186$	−5.48668			−0.402303
$187$			24.5926i			1.79839i
$188$		−	17.5623i		−	1.28086i
$189$	14.6422			1.06507
$190$	−0.373376	−	0.915105i	−0.0270876	−	0.0663887i
$191$	−9.60617			−0.695078			−0.347539	−	0.937666i	$-0.612983\pi$
$191$	−9.60617			−0.695078			−0.347539	+	0.937666i	$0.612983\pi$
$192$		−	18.9511i		−	1.36768i
$193$		−	24.9709i		−	1.79745i	−0.438515	−	0.898724i	$-0.644495\pi$
$193$		−	24.9709i		−	1.79745i	0.438515	−	0.898724i	$-0.355505\pi$
$194$	−3.30350			−0.237178
$195$	5.58736	−	2.27972i	0.400119	−	0.163254i
$196$	10.6182			0.758440
$197$		−	9.92292i		−	0.706979i	−0.935439	−	0.353489i	$-0.884995\pi$
$197$		−	9.92292i		−	0.706979i	0.935439	−	0.353489i	$-0.115005\pi$
$198$		−	7.31545i		−	0.519886i
$199$	−7.01818			−0.497506			−0.248753	−	0.968567i	$-0.580021\pi$
$199$	−7.01818			−0.497506			−0.248753	+	0.968567i	$0.580021\pi$
$200$	3.99010	+	4.07564i	0.282142	+	0.288191i
$201$	−10.0707			−0.710330
$202$			1.00432i			0.0706638i
$203$			0.662047i			0.0464666i
$204$	40.4405			2.83140
$205$	14.8031	−	6.03987i	1.03389	−	0.421843i
$206$	2.66205			0.185474
$207$		−	6.86420i		−	0.477095i
$208$		−	3.00558i		−	0.208400i
$209$	5.54875			0.383815
$210$	0.932634	+	2.28579i	0.0643578	+	0.157734i
$211$	7.44693			0.512668			0.256334	−	0.966588i	$-0.417485\pi$
$211$	7.44693			0.512668			0.256334	+	0.966588i	$0.417485\pi$
$212$		−	10.3013i		−	0.707494i
$213$			39.5054i			2.70687i
$214$	−2.69380			−0.184144
$215$	−8.51491	−	20.8691i	−0.580712	−	1.42326i
$216$	−13.8444			−0.941992
$217$			7.23362i			0.491050i
$218$		−	0.480311i		−	0.0325307i
$219$	−27.0919			−1.83070
$220$	−14.5028	+	5.91734i	−0.977776	+	0.398947i
$221$	5.77726			0.388620
$222$			1.86773i			0.125354i
$223$			10.2180i			0.684245i	0.939655	+	0.342123i	$0.111146\pi$
$223$			10.2180i			0.684245i	−0.939655	+	0.342123i	$0.888854\pi$
$224$	3.98210			0.266066
$225$	−24.5246	+	24.0099i	−1.63497	+	1.60066i
$226$	0.351526			0.0233832
$227$		−	5.83291i		−	0.387144i	−0.981086	−	0.193572i	$-0.937993\pi$
$227$		−	5.83291i		−	0.387144i	0.981086	−	0.193572i	$-0.0620072\pi$
$228$		−	9.12446i		−	0.604282i
$229$	−5.87061			−0.387941			−0.193970	−	0.981007i	$-0.562137\pi$
$229$	−5.87061			−0.387941			−0.193970	+	0.981007i	$0.562137\pi$
$230$	0.603236	−	0.246129i	0.0397762	−	0.0162293i
$231$	−13.8599			−0.911913
$232$		−	0.625973i		−	0.0410971i
$233$			0.839462i			0.0549950i	0.999622	+	0.0274975i	$0.00875383\pi$
$233$			0.839462i			0.0549950i	−0.999622	+	0.0274975i	$0.991246\pi$
$234$	−1.71854			−0.112344
$235$	7.74660	+	18.9861i	0.505332	+	1.23852i
$236$	1.11600			0.0726452
$237$			0.220046i			0.0142935i
$238$			2.36347i			0.153201i
$239$	21.3296			1.37970			0.689850	−	0.723953i	$-0.257677\pi$
$239$	21.3296			1.37970			0.689850	+	0.723953i	$0.257677\pi$
$240$	9.28012	+	22.7446i	0.599029	+	1.46816i
$241$	−20.7037			−1.33364			−0.666820	−	0.745219i	$-0.732345\pi$
$241$	−20.7037			−1.33364			−0.666820	+	0.745219i	$0.732345\pi$
$242$			0.693149i			0.0445573i
$243$		−	18.6309i		−	1.19517i
$244$	−16.9151			−1.08288
$245$	−11.4790	+	4.68359i	−0.733366	+	0.299224i
$246$	−6.54299			−0.417166
$247$		−	1.30350i		−	0.0829400i
$248$		−	6.83946i		−	0.434306i
$249$	−21.1747			−1.34189
$250$	−2.98940	−	1.29434i	−0.189066	−	0.0818613i
$251$	23.7290			1.49776			0.748881	−	0.662705i	$-0.230592\pi$
$251$	23.7290			1.49776			0.748881	+	0.662705i	$0.230592\pi$
$252$			15.8599i			0.999078i
$253$			3.65773i			0.229959i
$254$	−4.47371			−0.280706
$255$	−43.7191	+	17.8380i	−2.73780	+	1.11706i
$256$	9.63234			0.602021
$257$		−	18.2481i		−	1.13828i	−0.822239	−	0.569142i	$-0.807275\pi$
$257$		−	18.2481i		−	1.13828i	0.822239	−	0.569142i	$-0.192725\pi$
$258$			9.22419i			0.574273i
$259$	2.46242			0.153007
$260$	1.39009	+	3.40697i	0.0862099	+	0.211291i
$261$	3.76670			0.233153
$262$			3.80915i			0.235330i
$263$		−	25.8718i		−	1.59532i	−0.603104	−	0.797662i	$-0.706070\pi$
$263$		−	25.8718i		−	1.59532i	0.603104	−	0.797662i	$-0.293930\pi$
$264$	13.1047			0.806536
$265$	4.54382	+	11.1364i	0.279124	+	0.684104i
$266$	0.533263			0.0326964
$267$			15.5904i			0.954115i
$268$		−	6.14073i		−	0.375105i
$269$	−7.34497			−0.447831			−0.223915	−	0.974609i	$-0.571884\pi$
$269$	−7.34497			−0.447831			−0.223915	+	0.974609i	$0.571884\pi$
$270$	7.32112	−	2.98712i	0.445549	−	0.181791i
$271$	30.2278			1.83621			0.918105	−	0.396338i	$-0.129719\pi$
$271$	30.2278			1.83621			0.918105	+	0.396338i	$0.129719\pi$
$272$			23.5176i			1.42596i
$273$			3.25594i			0.197059i
$274$	3.84137			0.232066
$275$	13.0684	−	12.7941i	0.788056	−	0.771515i
$276$	6.01483			0.362050
$277$			2.50983i			0.150801i	0.997153	+	0.0754005i	$0.0240235\pi$
$277$			2.50983i			0.150801i	−0.997153	+	0.0754005i	$0.975976\pi$
$278$			4.11293i			0.246677i
$279$	41.1555			2.46392
$280$	−2.84937	+	1.16258i	−0.170282	+	0.0694776i
$281$	−10.4836			−0.625400			−0.312700	−	0.949852i	$-0.601233\pi$
$281$	−10.4836			−0.625400			−0.312700	+	0.949852i	$0.601233\pi$
$282$		−	8.39188i		−	0.499729i
$283$		−	3.83946i		−	0.228232i	−0.993467	−	0.114116i	$-0.963596\pi$
$283$		−	3.83946i		−	0.228232i	0.993467	−	0.114116i	$-0.0364036\pi$
$284$	−24.0890			−1.42942
$285$	4.02474	+	9.86420i	0.238405	+	0.584305i
$286$	0.915756			0.0541498
$287$			8.62626i			0.509192i
$288$		−	22.6561i		−	1.33502i
$289$	−28.2050			−1.65912
$290$	0.135062	+	0.331024i	0.00793114	+	0.0194384i
$291$	35.6095			2.08746
$292$		−	16.5196i		−	0.966739i
$293$		−	0.544425i		−	0.0318056i	−0.999874	−	0.0159028i	$-0.994938\pi$
$293$		−	0.544425i		−	0.0318056i	0.999874	−	0.0159028i	$-0.00506224\pi$
$294$	5.07373			0.295906
$295$	−1.20647	+	0.492258i	−0.0702435	+	0.0286604i
$296$	−2.32824			−0.135326
$297$			44.3917i			2.57587i
$298$			1.90683i			0.110460i
$299$	0.859268			0.0496927
$300$	−21.0389	−	21.4900i	−1.21468	−	1.24072i
$301$	12.1611			0.700957
$302$			0.762426i			0.0438727i
$303$		−	10.8259i		−	0.621931i
$304$	5.30620			0.304331
$305$	18.2864	−	7.46111i	1.04708	−	0.427222i
$306$	13.4469			0.768710
$307$			16.1850i			0.923729i	0.886950	+	0.461865i	$0.152819\pi$
$307$			16.1850i			0.923729i	−0.886950	+	0.461865i	$0.847181\pi$
$308$		−	8.45125i		−	0.481555i
$309$	−28.6950			−1.63240
$310$	1.47571	+	3.61681i	0.0838147	+	0.205421i
$311$	−7.51923			−0.426376			−0.213188	−	0.977011i	$-0.568385\pi$
$311$	−7.51923			−0.426376			−0.213188	+	0.977011i	$0.568385\pi$
$312$		−	3.07853i		−	0.174287i
$313$		−	25.2475i		−	1.42707i	−0.700619	−	0.713536i	$-0.747093\pi$
$313$		−	25.2475i		−	1.42707i	0.700619	−	0.713536i	$-0.252907\pi$
$314$	−2.56809			−0.144926
$315$	−6.99568	−	17.1457i	−0.394162	−	0.966049i
$316$	−0.134176			−0.00754799
$317$		−	13.4173i		−	0.753589i	−0.926297	−	0.376794i	$-0.877026\pi$
$317$		−	13.4173i		−	0.753589i	0.926297	−	0.376794i	$-0.122974\pi$
$318$		−	4.92231i		−	0.276030i
$319$	−2.00716			−0.112380
$320$	−12.4926	+	5.09715i	−0.698355	+	0.284939i
$321$	29.0373			1.62070
$322$			0.351526i			0.0195898i
$323$			10.1995i			0.567513i
$324$	33.5615			1.86453
$325$	−3.00558	−	3.07002i	−0.166720	−	0.170294i
$326$	−2.96458			−0.164193
$327$			5.17741i			0.286312i
$328$		−	8.15622i		−	0.450352i
$329$	−11.0638			−0.609969
$330$	−6.92994	+	2.82752i	−0.381481	+	0.155650i
$331$	−24.3748			−1.33976			−0.669880	−	0.742470i	$-0.733654\pi$
$331$	−24.3748			−1.33976			−0.669880	+	0.742470i	$0.733654\pi$
$332$		−	12.9116i		−	0.708615i
$333$		−	14.0099i		−	0.767736i
$334$	3.69009			0.201913
$335$	2.70863	+	6.63857i	0.147988	+	0.362704i
$336$	−13.2540			−0.723067
$337$			19.2454i			1.04836i	0.851607	+	0.524182i	$0.175629\pi$
$337$			19.2454i			1.04836i	−0.851607	+	0.524182i	$0.824371\pi$
$338$			3.57264i			0.194326i
$339$	−3.78921			−0.205801
$340$	−10.8770	−	26.6583i	−0.589887	−	1.44575i
$341$	−21.9305			−1.18761
$342$		−	3.03399i		−	0.164059i
$343$		−	15.1345i		−	0.817186i
$344$	−11.4985			−0.619957
$345$	−6.50246	+	2.65310i	−0.350081	+	0.142838i
$346$	−4.57157			−0.245769
$347$		−	7.51044i		−	0.403181i	−0.979470	−	0.201591i	$-0.935389\pi$
$347$		−	7.51044i		−	0.403181i	0.979470	−	0.201591i	$-0.0646111\pi$
$348$			3.30062i			0.176932i
$349$	−12.3208			−0.659520			−0.329760	−	0.944065i	$-0.606968\pi$
$349$	−12.3208			−0.659520			−0.329760	+	0.944065i	$0.606968\pi$
$350$	1.25594	−	1.22958i	0.0671330	−	0.0657239i
$351$	10.4284			0.556628
$352$			12.0728i			0.643480i
$353$			11.7333i			0.624502i	0.950000	+	0.312251i	$0.101083\pi$
$353$			11.7333i			0.624502i	−0.950000	+	0.312251i	$0.898917\pi$
$354$	0.533263			0.0283426
$355$	26.0419	−	10.6255i	1.38216	−	0.563942i
$356$	−9.50644			−0.503840
$357$		−	25.4766i		−	1.34836i
$358$			0.698920i			0.0369391i
$359$	18.6879			0.986307			0.493154	−	0.869942i	$-0.335844\pi$
$359$	18.6879			0.986307			0.493154	+	0.869942i	$0.335844\pi$
$360$	6.61449	+	16.2114i	0.348614	+	0.854416i
$361$	−16.6987			−0.878881
$362$		−	2.87615i		−	0.151167i
$363$		−	7.47167i		−	0.392161i
$364$	−1.98536			−0.104061
$365$	7.28670	+	17.8589i	0.381403	+	0.934779i
$366$	−8.08262			−0.422485
$367$		−	23.0103i		−	1.20113i	−0.799576	−	0.600564i	$-0.794943\pi$
$367$		−	23.0103i		−	1.20113i	0.799576	−	0.600564i	$-0.205057\pi$
$368$			3.49784i			0.182337i
$369$	49.0789			2.55495
$370$	1.23121	−	0.502351i	0.0640074	−	0.0261160i
$371$	−6.48956			−0.336921
$372$			36.0630i			1.86978i
$373$		−	35.7402i		−	1.85056i	−0.379290	−	0.925278i	$-0.623832\pi$
$373$		−	35.7402i		−	1.85056i	0.379290	−	0.925278i	$-0.376168\pi$
$374$	−7.16547			−0.370518
$375$	32.2237	+	13.9521i	1.66402	+	0.720483i
$376$	10.4610			0.539483
$377$			0.471520i			0.0242845i
$378$			4.26626i			0.219433i
$379$	−9.65178			−0.495779			−0.247889	−	0.968788i	$-0.579737\pi$
$379$	−9.65178			−0.495779			−0.247889	+	0.968788i	$0.579737\pi$
$380$	−6.01483	+	2.45414i	−0.308554	+	0.125895i
$381$	48.2235			2.47056
$382$		−	2.79892i		−	0.143205i
$383$			25.0954i			1.28232i	0.767409	+	0.641158i	$0.221546\pi$
$383$			25.0954i			1.28232i	−0.767409	+	0.641158i	$0.778454\pi$
$384$	26.2545			1.33979
$385$	3.72779	+	9.13641i	0.189986	+	0.465635i
$386$	7.27571			0.370324
$387$		−	69.1906i		−	3.51715i
$388$			21.7134i			1.10233i
$389$	−16.8259			−0.853106			−0.426553	−	0.904462i	$-0.640272\pi$
$389$	−16.8259			−0.853106			−0.426553	+	0.904462i	$0.640272\pi$
$390$	0.664236	+	1.62797i	0.0336349	+	0.0824355i
$391$	−6.72347			−0.340020
$392$			6.32470i			0.319446i
$393$		−	41.0599i		−	2.07120i
$394$	2.89121			0.145657
$395$	0.145054	−	0.0591841i	0.00729845	−	0.00297787i
$396$	−48.0832			−2.41627
$397$			27.8080i			1.39564i	0.716272	+	0.697822i	$0.245847\pi$
$397$			27.8080i			1.39564i	−0.716272	+	0.697822i	$0.754153\pi$
$398$		−	2.04487i		−	0.102500i
$399$	−5.74820			−0.287770
$400$	12.4972	−	12.2349i	0.624859	−	0.611744i
$401$	1.46483			0.0731500			0.0365750	−	0.999331i	$-0.488355\pi$
$401$	1.46483			0.0731500			0.0365750	+	0.999331i	$0.488355\pi$
$402$		−	2.93426i		−	0.146348i
$403$			5.15189i			0.256634i
$404$	6.60124			0.328424
$405$	−36.2824	+	14.8037i	−1.80289	+	0.735603i
$406$	−0.192899			−0.00957340
$407$			7.46544i			0.370048i
$408$			24.0884i			1.19255i
$409$	−0.514906			−0.0254605			−0.0127302	−	0.999919i	$-0.504052\pi$
$409$	−0.514906			−0.0254605			−0.0127302	+	0.999919i	$0.504052\pi$
$410$	1.75982	+	4.31313i	0.0869113	+	0.213010i
$411$	−41.4073			−2.04247
$412$		−	17.4972i		−	0.862025i
$413$		−	0.703052i		−	0.0345949i
$414$	2.00000			0.0982946
$415$	5.69521	+	13.9583i	0.279567	+	0.685188i
$416$	2.83612			0.139052
$417$		−	44.3346i		−	2.17107i
$418$			1.61672i			0.0790764i
$419$	9.65387			0.471622			0.235811	−	0.971799i	$-0.424225\pi$
$419$	9.65387			0.471622			0.235811	+	0.971799i	$0.424225\pi$
$420$	15.0241	−	6.13004i	0.733100	−	0.299116i
$421$	14.2788			0.695905			0.347952	−	0.937512i	$-0.386877\pi$
$421$	14.2788			0.695905			0.347952	+	0.937512i	$0.386877\pi$
$422$			2.16979i			0.105624i
$423$			62.9474i			3.06061i
$424$	6.13595			0.297988
$425$	23.5176	+	24.0218i	1.14077	+	1.16523i
$426$	−11.5106			−0.557689
$427$			10.6561i			0.515685i
$428$			17.7059i			0.855847i
$429$	−9.87122			−0.476587
$430$	6.08057	−	2.48096i	0.293231	−	0.119643i
$431$	5.71198			0.275136			0.137568	−	0.990492i	$-0.456071\pi$
$431$	5.71198			0.275136			0.137568	+	0.990492i	$0.456071\pi$
$432$			42.4512i			2.04243i
$433$			30.3302i			1.45758i	0.684738	+	0.728789i	$0.259917\pi$
$433$			30.3302i			1.45758i	−0.684738	+	0.728789i	$0.740083\pi$
$434$	−2.10764			−0.101170
$435$	−1.45588	−	3.56821i	−0.0698041	−	0.171082i
$436$	−3.15700			−0.151193
$437$			1.51699i			0.0725676i
$438$		−	7.89367i		−	0.377174i
$439$	19.7579			0.942994			0.471497	−	0.881868i	$-0.343714\pi$
$439$	19.7579			0.942994			0.471497	+	0.881868i	$0.343714\pi$
$440$	−3.52466	−	8.63857i	−0.168032	−	0.411828i
$441$	−38.0580			−1.81229
$442$			1.68330i			0.0800665i
$443$		−	16.0643i		−	0.763236i	−0.924320	−	0.381618i	$-0.875367\pi$
$443$		−	16.0643i		−	0.763236i	0.924320	−	0.381618i	$-0.124633\pi$
$444$	12.2763			0.582607
$445$	10.2771	−	4.19322i	0.487183	−	0.198778i
$446$	−2.97717			−0.140973
$447$		−	20.5543i		−	0.972184i
$448$		−	7.27984i		−	0.343940i
$449$	−28.5881			−1.34916			−0.674579	−	0.738203i	$-0.735675\pi$
$449$	−28.5881			−1.34916			−0.674579	+	0.738203i	$0.735675\pi$
$450$	−6.99568	−	7.14566i	−0.329779	−	0.336850i
$451$	−26.1527			−1.23148
$452$		−	2.31052i		−	0.108678i
$453$		−	8.21842i		−	0.386135i
$454$	1.69952			0.0797622
$455$	2.14631	−	0.875727i	0.100621	−	0.0410547i
$456$	5.43498			0.254516
$457$			10.1209i			0.473437i	0.971578	+	0.236718i	$0.0760719\pi$
$457$			10.1209i			0.473437i	−0.971578	+	0.236718i	$0.923928\pi$
$458$		−	1.71050i		−	0.0799264i
$459$	−81.5987			−3.80870
$460$	−1.61776	−	3.96497i	−0.0754287	−	0.184868i
$461$	15.6931			0.730901			0.365450	−	0.930831i	$-0.380915\pi$
$461$	15.6931			0.730901			0.365450	+	0.930831i	$0.380915\pi$
$462$		−	4.03831i		−	0.187879i
$463$		−	12.9124i		−	0.600089i	−0.953925	−	0.300044i	$-0.902999\pi$
$463$		−	12.9124i		−	0.600089i	0.953925	−	0.300044i	$-0.0970015\pi$
$464$	−1.91943			−0.0891072
$465$	−15.9071	−	38.9867i	−0.737676	−	1.80796i
$466$	−0.244592			−0.0113305
$467$		−	7.10196i		−	0.328640i	−0.986407	−	0.164320i	$-0.947457\pi$
$467$		−	7.10196i		−	0.328640i	0.986407	−	0.164320i	$-0.0525429\pi$
$468$			11.2956i			0.522141i
$469$	−3.86852			−0.178632
$470$	−5.53191	+	2.25710i	−0.255168	+	0.104112i
$471$	27.6822			1.27553
$472$			0.664743i			0.0305973i
$473$			36.8696i			1.69527i
$474$	−0.0641140			−0.00294486
$475$	5.41996	−	5.30620i	0.248685	−	0.243465i
$476$	15.5347			0.712032
$477$			36.9222i			1.69055i
$478$			6.21475i			0.284256i
$479$	−16.7758			−0.766506			−0.383253	−	0.923643i	$-0.625196\pi$
$479$	−16.7758			−0.766506			−0.383253	+	0.923643i	$0.625196\pi$
$480$	−21.4622	+	8.75687i	−0.979609	+	0.399695i
$481$	1.75377			0.0799650
$482$		−	6.03236i		−	0.274767i
$483$		−	3.78921i		−	0.172415i
$484$	4.55595			0.207089
$485$	−9.57761	−	23.4737i	−0.434897	−	1.06589i
$486$	5.42843			0.246239
$487$			7.02488i			0.318328i	0.987252	+	0.159164i	$0.0508798\pi$
$487$			7.02488i			0.318328i	−0.987252	+	0.159164i	$0.949120\pi$
$488$		−	10.0755i		−	0.456094i
$489$	31.9561			1.44510
$490$	−1.36464	−	3.34460i	−0.0616483	−	0.151094i
$491$	11.1500			0.503192			0.251596	−	0.967832i	$-0.419045\pi$
$491$	11.1500			0.503192			0.251596	+	0.967832i	$0.419045\pi$
$492$			43.0060i			1.93886i
$493$		−	3.68948i		−	0.166166i
$494$	0.379798			0.0170879
$495$	51.9814	−	21.2092i	2.33639	−	0.953281i
$496$	−20.9719			−0.941667
$497$			15.1755i			0.680714i
$498$		−	6.16961i		−	0.276467i
$499$	−14.8347			−0.664091			−0.332046	−	0.943263i	$-0.607739\pi$
$499$	−14.8347			−0.664091			−0.332046	+	0.943263i	$0.607739\pi$
$500$	−8.50748	+	19.6488i	−0.380466	+	0.878722i
$501$	−39.7766			−1.77709
$502$			6.91385i			0.308580i
$503$			3.10196i			0.138310i	0.997606	+	0.0691548i	$0.0220302\pi$
$503$			3.10196i			0.138310i	−0.997606	+	0.0691548i	$0.977970\pi$
$504$	−9.44693			−0.420800
$505$	−7.13641	+	2.91176i	−0.317566	+	0.129572i
$506$	−1.06574			−0.0473779
$507$		−	38.5106i		−	1.71032i
$508$			29.4050i			1.30463i
$509$	22.3353			0.989993			0.494996	−	0.868895i	$-0.335169\pi$
$509$	22.3353			0.989993			0.494996	+	0.868895i	$0.335169\pi$
$510$	−5.19741	−	12.7383i	−0.230145	−	0.564061i
$511$	−10.4070			−0.460378
$512$			19.5252i			0.862901i
$513$			18.4109i			0.812859i
$514$	5.31689			0.234518
$515$	7.71788	+	18.9157i	0.340091	+	0.833526i
$516$	60.6290			2.66904
$517$		−	33.5428i		−	1.47521i
$518$			0.717466i			0.0315237i
$519$	49.2784			2.16308
$520$	−2.02936	+	0.828009i	−0.0889934	+	0.0363106i
$521$	−14.2147			−0.622758			−0.311379	−	0.950286i	$-0.600791\pi$
$521$	−14.2147			−0.622758			−0.311379	+	0.950286i	$0.600791\pi$
$522$			1.09749i			0.0480360i
$523$		−	4.09494i		−	0.179059i	−0.995984	−	0.0895297i	$-0.971464\pi$
$523$		−	4.09494i		−	0.179059i	0.995984	−	0.0895297i	$-0.0285364\pi$
$524$	25.0369			1.09374
$525$	−13.5382	+	13.2540i	−0.590855	+	0.578453i
$526$	7.53819			0.328681
$527$		−	40.3117i		−	1.75601i
$528$		−	40.1830i		−	1.74874i
$529$	−1.00000			−0.0434783
$530$	−3.24478	+	1.32392i	−0.140944	+	0.0575073i
$531$	−4.00000			−0.173585
$532$		−	3.50505i		−	0.151963i
$533$			6.14375i			0.266115i
$534$	−4.54251			−0.196574
$535$	−7.80994	−	19.1413i	−0.337653	−	0.827552i
$536$	3.65773			0.157990
$537$		−	7.53387i		−	0.325111i
$538$		−	2.14008i		−	0.0922654i
$539$	20.2800			0.873521
$540$	−19.6339	−	48.1205i	−0.844907	−	2.07078i
$541$	33.6902			1.44846			0.724228	−	0.689560i	$-0.242196\pi$
$541$	33.6902			1.44846			0.724228	+	0.689560i	$0.242196\pi$
$542$			8.80739i			0.378310i
$543$			31.0028i			1.33046i
$544$	−22.1916			−0.951457
$545$	3.41294	−	1.39253i	0.146194	−	0.0596495i
$546$	−0.948674			−0.0405995
$547$		−	32.9358i		−	1.40823i	−0.710084	−	0.704117i	$-0.751343\pi$
$547$		−	32.9358i		−	1.40823i	0.710084	−	0.704117i	$-0.248657\pi$
$548$		−	25.2487i		−	1.07857i
$549$	60.6277			2.58753
$550$	3.72779	+	3.80771i	0.158953	+	0.162361i
$551$	−0.832445			−0.0354633
$552$			3.58273i			0.152491i
$553$			0.0845278i			0.00359449i
$554$	−0.731281			−0.0310692
$555$	−13.2716	+	5.41499i	−0.563346	+	0.229853i
$556$	27.0336			1.14648
$557$			20.8337i			0.882751i	0.897323	+	0.441375i	$0.145509\pi$
$557$			20.8337i			0.882751i	−0.897323	+	0.441375i	$0.854491\pi$
$558$			11.9914i			0.507635i
$559$	8.66135			0.366336
$560$	3.56484	+	8.73704i	0.150642	+	0.369207i
$561$	77.2387			3.26102
$562$		−	3.05458i		−	0.128850i
$563$			30.4368i			1.28276i	0.767223	+	0.641380i	$0.221638\pi$
$563$			30.4368i			1.28276i	−0.767223	+	0.641380i	$0.778362\pi$
$564$	−55.1584			−2.32259
$565$	1.01915	+	2.49784i	0.0428762	+	0.105085i
$566$	1.11869			0.0470221
$567$		−	21.1430i		−	0.887921i
$568$		−	14.3486i		−	0.602054i
$569$	−39.4801			−1.65509			−0.827545	−	0.561399i	$-0.810263\pi$
$569$	−39.4801			−1.65509			−0.827545	+	0.561399i	$0.810263\pi$
$570$	−2.87410	+	1.17267i	−0.120383	+	0.0491179i
$571$	27.0301			1.13118			0.565588	−	0.824688i	$-0.308649\pi$
$571$	27.0301			1.13118			0.565588	+	0.824688i	$0.308649\pi$
$572$		−	6.01911i		−	0.251672i
$573$			30.1704i			1.26039i
$574$	−2.51341			−0.104908
$575$	3.49784	+	3.57283i	0.145870	+	0.148997i
$576$	−41.4185			−1.72577
$577$		−	4.68818i		−	0.195171i	−0.995227	−	0.0975857i	$-0.968888\pi$
$577$		−	4.68818i		−	0.195171i	0.995227	−	0.0975857i	$-0.0311120\pi$
$578$		−	8.21800i		−	0.341824i
$579$	−78.4270			−3.25932
$580$	2.17576	−	0.887743i	0.0903436	−	0.0368615i
$581$	−8.13400			−0.337455
$582$			10.3754i			0.430075i
$583$		−	19.6747i		−	0.814845i
$584$	9.83992			0.407179
$585$	−4.98243	−	12.2114i	−0.205998	−	0.504879i
$586$	0.158627			0.00655284
$587$		−	9.61718i		−	0.396944i	−0.980107	−	0.198472i	$-0.936402\pi$
$587$		−	9.61718i		−	0.396944i	0.980107	−	0.198472i	$-0.0635978\pi$
$588$		−	33.3488i		−	1.37528i
$589$	−9.09541			−0.374770
$590$	−0.143428	−	0.351526i	−0.00590483	−	0.0144721i
$591$	−31.1652			−1.28197
$592$			7.13911i			0.293415i
$593$			8.68902i			0.356815i	0.983957	+	0.178408i	$0.0570946\pi$
$593$			8.68902i			0.356815i	−0.983957	+	0.178408i	$0.942905\pi$
$594$	−12.9343			−0.530699
$595$	−16.7941	+	6.85225i	−0.688492	+	0.280915i
$596$	12.5333			0.513382
$597$			22.0422i			0.902128i
$598$			0.250362i			0.0102381i
$599$	−11.7581			−0.480421			−0.240211	−	0.970721i	$-0.577217\pi$
$599$	−11.7581			−0.480421			−0.240211	+	0.970721i	$0.577217\pi$
$600$	12.8005	−	12.5318i	0.522578	−	0.511610i
$601$	37.9388			1.54756			0.773778	−	0.633457i	$-0.218365\pi$
$601$	37.9388			1.54756			0.773778	+	0.633457i	$0.218365\pi$
$602$			3.54336i			0.144416i
$603$			22.0099i			0.896311i
$604$	5.01130			0.203907
$605$	−4.92531	+	2.00960i	−0.200242	+	0.0817018i
$606$	3.15431			0.128135
$607$		−	9.01418i		−	0.365874i	−0.983125	−	0.182937i	$-0.941440\pi$
$607$		−	9.01418i		−	0.365874i	0.983125	−	0.182937i	$-0.0585605\pi$
$608$			5.00702i			0.203061i
$609$	2.07931			0.0842580
$610$	2.17392	+	5.32805i	0.0880195	+	0.215726i
$611$	−7.87983			−0.318784
$612$		−	88.3844i		−	3.57273i
$613$			42.5846i			1.71997i	0.510316	+	0.859987i	$0.329528\pi$
$613$			42.5846i			1.71997i	−0.510316	+	0.859987i	$0.670472\pi$
$614$	−4.71578			−0.190314
$615$	−18.9696	−	46.4925i	−0.764929	−	1.87476i
$616$	5.03399			0.202825
$617$			12.6190i			0.508020i	0.967202	+	0.254010i	$0.0817496\pi$
$617$			12.6190i			0.508020i	−0.967202	+	0.254010i	$0.918250\pi$
$618$		−	8.36078i		−	0.336320i
$619$	26.0638			1.04759			0.523796	−	0.851844i	$-0.324515\pi$
$619$	26.0638			1.04759			0.523796	+	0.851844i	$0.324515\pi$
$620$	23.7727	−	9.69960i	0.954734	−	0.389545i
$621$	−12.1364			−0.487017
$622$		−	2.19085i		−	0.0878452i
$623$			5.98884i			0.239938i
$624$	−9.43972			−0.377891
$625$	0.530243	−	24.9944i	0.0212097	−	0.999775i
$626$	7.35628			0.294016
$627$		−	17.4271i		−	0.695972i
$628$			16.8796i			0.673570i
$629$	−13.7226			−0.547157
$630$	4.99568	−	2.03831i	0.199033	−	0.0812082i
$631$	−46.1083			−1.83554			−0.917771	−	0.397110i	$-0.870013\pi$
$631$	−46.1083			−1.83554			−0.917771	+	0.397110i	$0.870013\pi$
$632$		−	0.0799219i		−	0.00317912i
$633$		−	23.3888i		−	0.929622i
$634$	3.90935			0.155260
$635$	−12.9703	−	31.7889i	−0.514711	−	1.26150i
$636$	−32.3535			−1.28290
$637$		−	4.76415i		−	0.188762i
$638$		−	0.584821i		−	0.0231533i
$639$	86.3407			3.41559
$640$	−7.06146	−	17.3069i	−0.279129	−	0.684115i
$641$	19.3319			0.763563			0.381781	−	0.924253i	$-0.375311\pi$
$641$	19.3319			0.763563			0.381781	+	0.924253i	$0.375311\pi$
$642$			8.46051i			0.333910i
$643$		−	2.27891i		−	0.0898713i	−0.998990	−	0.0449356i	$-0.985692\pi$
$643$		−	2.27891i		−	0.0898713i	0.998990	−	0.0449356i	$-0.0143083\pi$
$644$	2.31052			0.0910473
$645$	−65.5443	+	26.7430i	−2.58081	+	1.05301i
$646$	−2.97178			−0.116923
$647$			47.5054i			1.86763i	0.357755	+	0.933815i	$0.383542\pi$
$647$			47.5054i			1.86763i	−0.357755	+	0.933815i	$0.616458\pi$
$648$			19.9909i			0.785317i
$649$	2.13148			0.0836679
$650$	0.894502	−	0.875727i	0.0350853	−	0.0343488i
$651$	22.7189			0.890422
$652$			19.4857i			0.763117i
$653$		−	2.73226i		−	0.106921i	−0.998570	−	0.0534607i	$-0.982975\pi$
$653$		−	2.73226i		−	0.106921i	0.998570	−	0.0534607i	$-0.0170252\pi$
$654$	−1.50853			−0.0589881
$655$	−27.0667	+	11.0436i	−1.05758	+	0.431509i
$656$	−25.0095			−0.976457
$657$			59.2104i			2.31002i
$658$		−	3.22363i		−	0.125670i
$659$	12.1375			0.472809			0.236405	−	0.971655i	$-0.424031\pi$
$659$	12.1375			0.472809			0.236405	+	0.971655i	$0.424031\pi$
$660$	18.5848	+	45.5493i	0.723412	+	1.77300i
$661$	41.1992			1.60246			0.801232	−	0.598354i	$-0.204178\pi$
$661$	41.1992			1.60246			0.801232	+	0.598354i	$0.204178\pi$
$662$		−	7.10200i		−	0.276027i
$663$		−	18.1448i		−	0.704686i
$664$	7.69078			0.298460
$665$	1.54605	+	3.78921i	0.0599533	+	0.146939i
$666$	4.08201			0.158175
$667$		−	0.548747i		−	0.0212476i
$668$		−	24.2543i		−	0.938428i
$669$	32.0919			1.24074
$670$	−1.93426	+	0.789206i	−0.0747270	+	0.0304897i
$671$	−32.3067			−1.24718
$672$		−	12.5067i		−	0.482457i
$673$		−	24.2175i		−	0.933516i	−0.884385	−	0.466758i	$-0.845422\pi$
$673$		−	24.2175i		−	0.933516i	0.884385	−	0.466758i	$-0.154578\pi$
$674$	−5.60747			−0.215992
$675$	42.4512	+	43.3613i	1.63395	+	1.66898i
$676$	23.4824			0.903168
$677$			48.1512i			1.85060i	0.379235	+	0.925300i	$0.376187\pi$
$677$			48.1512i			1.85060i	−0.379235	+	0.925300i	$0.623813\pi$
$678$		−	1.10405i		−	0.0424008i
$679$	13.6789			0.524949
$680$	15.8790	−	6.47887i	0.608933	−	0.248453i
$681$	−18.3196			−0.702008
$682$		−	6.38984i		−	0.244679i
$683$		−	12.1351i		−	0.464337i	−0.972676	−	0.232169i	$-0.925418\pi$
$683$		−	12.1351i		−	0.464337i	0.972676	−	0.232169i	$-0.0745821\pi$
$684$	−19.9419			−0.762497
$685$	11.1370	+	27.2956i	0.425524	+	1.04291i
$686$	4.40969			0.168363
$687$			18.4380i			0.703454i
$688$			35.2579i			1.34420i
$689$	−4.62197			−0.176083
$690$	−0.773025	−	1.89460i	−0.0294286	−	0.0721263i
$691$	−13.8289			−0.526076			−0.263038	−	0.964785i	$-0.584725\pi$
$691$	−13.8289			−0.526076			−0.263038	+	0.964785i	$0.584725\pi$
$692$			30.0482i			1.14226i
$693$			30.2913i			1.15067i
$694$	2.18829			0.0830665
$695$	−29.2253	+	11.9243i	−1.10858	+	0.452316i
$696$	−1.96601			−0.0745215
$697$		−	48.0727i		−	1.82088i
$698$		−	3.58989i		−	0.135879i
$699$	2.63653			0.0997226
$700$	−8.08183	−	8.25510i	−0.305465	−	0.312014i
$701$	−15.2263			−0.575089			−0.287544	−	0.957767i	$-0.592839\pi$
$701$	−15.2263			−0.575089			−0.287544	+	0.957767i	$0.592839\pi$
$702$			3.03850i			0.114681i
$703$			3.09619i			0.116775i
$704$	22.0707			0.831820
$705$	59.6302	−	24.3300i	2.24580	−	0.916320i
$706$	−3.41870			−0.128665
$707$		−	4.15863i		−	0.156401i
$708$		−	3.50505i		−	0.131728i
$709$	−15.2317			−0.572037			−0.286019	−	0.958224i	$-0.592332\pi$
$709$	−15.2317			−0.572037			−0.286019	+	0.958224i	$0.592332\pi$
$710$	3.09591	+	7.58775i	0.116188	+	0.284763i
$711$	0.480919			0.0180359
$712$		−	5.66251i		−	0.212211i
$713$		−	5.99568i		−	0.224540i
$714$	7.42304			0.277800
$715$	2.65499	+	6.50709i	0.0992909	+	0.243351i
$716$	4.59388			0.171681
$717$		−	66.9907i		−	2.50181i
$718$			5.44502i			0.203206i
$719$	−4.58943			−0.171157			−0.0855784	−	0.996331i	$-0.527274\pi$
$719$	−4.58943			−0.171157			−0.0855784	+	0.996331i	$0.527274\pi$
$720$	49.7092	−	20.2821i	1.85255	−	0.755868i
$721$	−11.0228			−0.410511
$722$		−	4.86546i		−	0.181074i
$723$			65.0246i			2.41829i
$724$	−18.9044			−0.702577
$725$	−1.96058	+	1.91943i	−0.0728141	+	0.0712857i
$726$	2.17700			0.0807959
$727$			21.2414i			0.787800i	0.919153	+	0.393900i	$0.128874\pi$
$727$			21.2414i			0.787800i	−0.919153	+	0.393900i	$0.871126\pi$
$728$		−	1.18258i		−	0.0438292i
$729$	−5.94082			−0.220030
$730$	−5.20350	+	2.12310i	−0.192590	+	0.0785796i
$731$	−67.7720			−2.50664
$732$			53.1257i			1.96358i
$733$		−	40.5297i		−	1.49700i	−0.663136	−	0.748499i	$-0.730775\pi$
$733$		−	40.5297i		−	1.49700i	0.663136	−	0.748499i	$-0.269225\pi$
$734$	6.70445			0.247466
$735$	14.7099	+	36.0524i	0.542583	+	1.32981i
$736$	−3.30062			−0.121662
$737$		−	11.7284i		−	0.432021i
$738$			14.3000i			0.526389i
$739$	−30.6476			−1.12739			−0.563695	−	0.825983i	$-0.690621\pi$
$739$	−30.6476			−1.12739			−0.563695	+	0.825983i	$0.690621\pi$
$740$	−3.30187	−	8.09252i	−0.121379	−	0.297487i
$741$	−4.09396			−0.150395
$742$		−	1.89084i		−	0.0694151i
$743$		−	1.01357i		−	0.0371844i	−0.999827	−	0.0185922i	$-0.994082\pi$
$743$		−	1.01357i		−	0.0371844i	0.999827	−	0.0185922i	$-0.00591842\pi$
$744$	−21.4809			−0.787529
$745$	−13.5494	+	5.52833i	−0.496410	+	0.202542i
$746$	10.4135			0.381265
$747$			46.2782i			1.69323i
$748$			47.0974i			1.72205i
$749$	11.1543			0.407569
$750$	−4.06518	+	9.38891i	−0.148439	+	0.342834i
$751$	−21.0644			−0.768652			−0.384326	−	0.923197i	$-0.625566\pi$
$751$	−21.0644			−0.768652			−0.384326	+	0.923197i	$0.625566\pi$
$752$		−	32.0766i		−	1.16971i
$753$		−	74.5264i		−	2.71589i
$754$	−0.137385			−0.00500328
$755$	−5.41757	+	2.21045i	−0.197166	+	0.0804464i
$756$	28.0414			1.01986
$757$		−	13.2109i		−	0.480160i	−0.970753	−	0.240080i	$-0.922826\pi$
$757$		−	13.2109i		−	0.480160i	0.970753	−	0.240080i	$-0.0771736\pi$
$758$		−	2.81221i		−	0.102144i
$759$	11.4879			0.416986
$760$	−1.46181	−	3.58273i	−0.0530253	−	0.129959i
$761$	−11.9759			−0.434125			−0.217063	−	0.976158i	$-0.569648\pi$
$761$	−11.9759			−0.434125			−0.217063	+	0.976158i	$0.569648\pi$
$762$			14.0507i			0.509004i
$763$			1.98884i			0.0720008i
$764$	−18.3968			−0.665574
$765$	38.9857	+	95.5499i	1.40953	+	3.45461i
$766$	−7.31197			−0.264192
$767$		−	0.500724i		−	0.0180801i
$768$		−	30.2526i		−	1.09165i
$769$	−39.6569			−1.43006			−0.715031	−	0.699092i	$-0.753588\pi$
$769$	−39.6569			−1.43006			−0.715031	+	0.699092i	$0.753588\pi$
$770$	−2.66205	+	1.08615i	−0.0959335	+	0.0391423i
$771$	−57.3123			−2.06405
$772$		−	47.8220i		−	1.72115i
$773$		−	16.0305i		−	0.576575i	−0.957544	−	0.288288i	$-0.906914\pi$
$773$		−	16.0305i		−	0.576575i	0.957544	−	0.288288i	$-0.0930859\pi$
$774$	20.1598			0.724631
$775$	−21.4215	+	20.9719i	−0.769485	+	0.753334i
$776$	−12.9336			−0.464288
$777$		−	7.73379i		−	0.277448i
$778$		−	4.90251i		−	0.175763i
$779$	−10.8465			−0.388615
$780$	10.7004	−	4.36591i	0.383135	−	0.156325i
$781$	−46.0084			−1.64631
$782$		−	1.95900i		−	0.0700535i
$783$		−	6.65981i		−	0.238002i
$784$	19.3935			0.692625
$785$	−7.44548	−	18.2481i	−0.265741	−	0.651302i
$786$	11.9635			0.426724
$787$		−	39.0352i		−	1.39145i	−0.718306	−	0.695727i	$-0.755082\pi$
$787$		−	39.0352i		−	1.39145i	0.718306	−	0.695727i	$-0.244918\pi$
$788$		−	19.0034i		−	0.676969i
$789$	−81.2565			−2.89281
$790$	0.0172443	+	0.0422639i	0.000613524	+	0.00150368i
$791$	−1.45558			−0.0517543
$792$		−	28.6408i		−	1.01771i
$793$			7.58944i			0.269509i
$794$	−8.10233			−0.287541
$795$	34.9765	−	14.2709i	1.24049	−	0.506137i
$796$	−13.4406			−0.476388
$797$		−	3.37687i		−	0.119615i	−0.998210	−	0.0598074i	$-0.980951\pi$
$797$		−	3.37687i		−	0.119615i	0.998210	−	0.0598074i	$-0.0190487\pi$
$798$		−	1.67484i		−	0.0592885i
$799$	61.6569			2.18126
$800$	11.5450	+	11.7926i	0.408179	+	0.416930i
$801$	34.0734			1.20392
$802$			0.426802i			0.0150709i
$803$		−	31.5514i		−	1.11343i
$804$	−19.2864			−0.680179
$805$	−2.49784	+	1.01915i	−0.0880373	+	0.0359205i
$806$	−1.50109			−0.0528737
$807$			23.0686i			0.812053i
$808$			3.93203i			0.138328i
$809$	49.3406			1.73472			0.867361	−	0.497680i	$-0.165814\pi$
$809$	49.3406			1.73472			0.867361	+	0.497680i	$0.165814\pi$
$810$	−4.31332	−	10.5715i	−0.151555	−	0.371444i
$811$	18.3582			0.644645			0.322322	−	0.946630i	$-0.395537\pi$
$811$	18.3582			0.644645			0.322322	+	0.946630i	$0.395537\pi$
$812$			1.26789i			0.0444942i
$813$		−	94.9375i		−	3.32960i
$814$	−2.17518			−0.0762400
$815$	−8.59499	−	21.0654i	−0.301069	−	0.737889i
$816$	73.8625			2.58570
$817$			15.2912i			0.534971i
$818$		−	0.150027i		−	0.00524556i
$819$	7.11600			0.248653
$820$	28.3495	−	11.5670i	0.990006	−	0.403937i
$821$	19.4610			0.679192			0.339596	−	0.940571i	$-0.389710\pi$
$821$	19.4610			0.679192			0.339596	+	0.940571i	$0.389710\pi$
$822$		−	12.0647i		−	0.420806i
$823$			47.2973i			1.64868i	0.566094	+	0.824341i	$0.308454\pi$
$823$			47.2973i			1.64868i	−0.566094	+	0.824341i	$0.691546\pi$
$824$	10.4222			0.363074
$825$	−40.1830	−	41.0445i	−1.39899	−	1.42898i
$826$	0.204846			0.00712751
$827$			26.2901i			0.914197i	0.889416	+	0.457098i	$0.151111\pi$
$827$			26.2901i			0.914197i	−0.889416	+	0.457098i	$0.848889\pi$
$828$		−	13.1457i		−	0.456843i
$829$	20.0140			0.695116			0.347558	−	0.937658i	$-0.387011\pi$
$829$	20.0140			0.695116			0.347558	+	0.937658i	$0.387011\pi$
$830$	−4.06700	+	1.65939i	−0.141168	+	0.0575984i
$831$	7.88270			0.273448
$832$		−	5.18481i		−	0.179751i
$833$			37.2778i			1.29160i
$834$	12.9176			0.447301
$835$	10.6984	+	26.2207i	0.370234	+	0.907403i
$836$	10.6264			0.367523
$837$		−	72.7660i		−	2.51516i
$838$			2.81282i			0.0971671i
$839$	40.7210			1.40585			0.702923	−	0.711266i	$-0.251878\pi$
$839$	40.7210			1.40585			0.702923	+	0.711266i	$0.251878\pi$
$840$	3.65136	+	8.94909i	0.125984	+	0.308773i
$841$	−28.6989			−0.989616
$842$			4.16036i			0.143375i
$843$			32.9262i			1.13404i
$844$	14.2617			0.490907
$845$	−25.3861	+	10.3579i	−0.873309	+	0.356323i
$846$	−18.3408			−0.630570
$847$		−	2.87015i		−	0.0986194i
$848$		−	18.8147i		−	0.646100i
$849$	−12.0587			−0.413854
$850$	−6.99916	+	6.85225i	−0.240069	+	0.235030i
$851$	−2.04100			−0.0699647
$852$			75.6570i			2.59197i
$853$		−	5.34390i		−	0.182972i	−0.995806	−	0.0914858i	$-0.970838\pi$
$853$		−	5.34390i		−	0.182972i	0.995806	−	0.0914858i	$-0.0291616\pi$
$854$	−3.10483			−0.106245
$855$	21.5586	−	8.79622i	0.737289	−	0.300824i
$856$	−10.5465			−0.360472
$857$			48.4603i			1.65537i	0.561192	+	0.827686i	$0.310343\pi$
$857$			48.4603i			1.65537i	−0.561192	+	0.827686i	$0.689657\pi$
$858$		−	2.87615i		−	0.0981900i
$859$	51.3123			1.75075			0.875377	−	0.483440i	$-0.160613\pi$
$859$	51.3123			1.75075			0.875377	+	0.483440i	$0.160613\pi$
$860$	−16.3069	−	39.9666i	−0.556062	−	1.36285i
$861$	27.0928			0.923319
$862$			1.66428i			0.0566857i
$863$		−	24.5507i		−	0.835714i	−0.908513	−	0.417857i	$-0.862781\pi$
$863$		−	24.5507i		−	0.835714i	0.908513	−	0.417857i	$-0.137219\pi$
$864$	−40.0577			−1.36279
$865$	−13.2540	−	32.4842i	−0.450651	−	1.10450i
$866$	−8.83723			−0.300301
$867$			88.5843i			3.00848i
$868$			13.8531i			0.470206i
$869$	−0.256267			−0.00869327
$870$	1.03966	−	0.424195i	0.0352477	−	0.0143816i
$871$	−2.75522			−0.0933570
$872$		−	1.88047i		−	0.0636807i
$873$		−	77.8260i		−	2.63401i
$874$	−0.442002			−0.0149509
$875$	12.3783	+	5.35952i	0.418463	+	0.181185i
$876$	−51.8838			−1.75299
$877$			30.1400i			1.01776i	0.860838	+	0.508878i	$0.169940\pi$
$877$			30.1400i			1.01776i	−0.860838	+	0.508878i	$0.830060\pi$
$878$			5.75680i			0.194283i
$879$	−1.70989			−0.0576732
$880$	−26.4885	+	10.8077i	−0.892929	+	0.364328i
$881$	36.4729			1.22880			0.614401	−	0.788994i	$-0.289398\pi$
$881$	36.4729			1.22880			0.614401	+	0.788994i	$0.289398\pi$
$882$		−	11.0888i		−	0.373381i
$883$			2.17426i			0.0731696i	0.999331	+	0.0365848i	$0.0116479\pi$
$883$			2.17426i			0.0731696i	−0.999331	+	0.0365848i	$0.988352\pi$
$884$	11.0641			0.372125
$885$	1.54605	+	3.78921i	0.0519699	+	0.127373i
$886$	4.68059			0.157248
$887$		−	16.1463i		−	0.542139i	−0.962560	−	0.271069i	$-0.912623\pi$
$887$		−	16.1463i		−	0.542139i	0.962560	−	0.271069i	$-0.0873773\pi$
$888$			7.31238i			0.245387i
$889$	18.5244			0.621290
$890$	1.22177	+	2.99442i	0.0409537	+	0.100373i
$891$	64.1003			2.14744
$892$			19.5685i			0.655201i
$893$		−	13.9114i		−	0.465528i
$894$	5.98884			0.200297
$895$	−4.96632	+	2.02633i	−0.166006	+	0.0677327i
$896$	10.0853			0.336927
$897$		−	2.69873i		−	0.0901080i
$898$		−	8.32963i		−	0.277963i
$899$	3.29011			0.109731
$900$	−46.9672	+	45.9814i	−1.56557	+	1.53271i
$901$	36.1652			1.20484
$902$		−	7.62002i		−	0.253719i
$903$		−	38.1949i		−	1.27105i
$904$	1.37626			0.0457738
$905$	20.4370	−	8.33860i	0.679350	−	0.277185i
$906$	2.39458			0.0795544
$907$		−	4.74475i		−	0.157547i	−0.996893	−	0.0787734i	$-0.974900\pi$
$907$		−	4.74475i		−	0.157547i	0.996893	−	0.0787734i	$-0.0251004\pi$
$908$		−	11.1706i		−	0.370710i
$909$	−23.6604			−0.784767
$910$	0.255158	+	0.625365i	0.00845840	+	0.0207306i
$911$	38.8650			1.28765			0.643827	−	0.765171i	$-0.277346\pi$
$911$	38.8650			1.28765			0.643827	+	0.765171i	$0.277346\pi$
$912$		−	16.6654i		−	0.551845i
$913$		−	24.6603i		−	0.816136i
$914$	−2.94890			−0.0975410
$915$	−23.4334	−	57.4327i	−0.774683	−	1.89867i
$916$	−11.2428			−0.371474
$917$		−	15.7727i		−	0.520859i
$918$		−	23.7752i		−	0.784698i
$919$	−40.5516			−1.33767			−0.668837	−	0.743409i	$-0.733207\pi$
$919$	−40.5516			−1.33767			−0.668837	+	0.743409i	$0.733207\pi$
$920$	2.36173	−	0.963621i	0.0778640	−	0.0317697i
$921$	50.8329			1.67500
$922$			4.57245i			0.150586i
$923$			10.8082i			0.355757i
$924$	−26.5431			−0.873205
$925$	7.13911	+	7.29216i	0.234732	+	0.239765i
$926$	3.76224			0.123635
$927$			62.7141i			2.05980i
$928$		−	1.81120i		−	0.0594557i
$929$	−19.4994			−0.639755			−0.319878	−	0.947459i	$-0.603642\pi$
$929$	−19.4994			−0.639755			−0.319878	+	0.947459i	$0.603642\pi$
$930$	11.3594	−	4.63481i	0.372490	−	0.151981i
$931$	8.41086			0.275655
$932$			1.60766i			0.0526606i
$933$			23.6159i			0.773149i
$934$	2.06928			0.0677088
$935$	−20.7743	−	50.9157i	−0.679393	−	1.66512i
$936$	−6.72825			−0.219920
$937$		−	24.9361i		−	0.814626i	−0.913289	−	0.407313i	$-0.866466\pi$
$937$		−	24.9361i		−	0.814626i	0.913289	−	0.407313i	$-0.133534\pi$
$938$		−	1.12716i		−	0.0368030i
$939$	−79.2956			−2.58771
$940$	14.8355	+	36.3603i	0.483882	+	1.18594i
$941$	−41.9160			−1.36642			−0.683211	−	0.730221i	$-0.739417\pi$
$941$	−41.9160			−1.36642			−0.683211	+	0.730221i	$0.739417\pi$
$942$			8.06568i			0.262794i
$943$		−	7.14998i		−	0.232836i
$944$	2.03831			0.0663413
$945$	−30.3148	+	12.3689i	−0.986141	+	0.402360i
$946$	−10.7426			−0.349271
$947$		−	29.3006i		−	0.952141i	−0.879407	−	0.476070i	$-0.842061\pi$
$947$		−	29.3006i		−	0.952141i	0.879407	−	0.476070i	$-0.157939\pi$
$948$			0.421411i			0.0136868i
$949$	−7.41202			−0.240604
$950$	1.54605	+	1.57920i	0.0501605	+	0.0512359i
$951$	−42.1400			−1.36648
$952$			9.25325i			0.299899i
$953$			24.9759i			0.809048i	0.914527	+	0.404524i	$0.132563\pi$
$953$			24.9759i			0.809048i	−0.914527	+	0.404524i	$0.867437\pi$
$954$	−10.7579			−0.348300
$955$	19.8883	−	8.11471i	0.643570	−	0.262586i
$956$	40.8485			1.32113
$957$			6.30397i			0.203778i
$958$		−	4.88792i		−	0.157921i
$959$	−15.9061			−0.513635
$960$	16.0088	+	39.2358i	0.516681	+	1.26633i
$961$	4.94816			0.159618
$962$			0.510990i			0.0164750i
$963$		−	63.4622i		−	2.04504i
$964$	−39.6497			−1.27703
$965$	21.0939	+	51.6990i	0.679038	+	1.66425i
$966$	1.10405			0.0355222
$967$			0.405142i			0.0130285i	0.999979	+	0.00651424i	$0.00207356\pi$
$967$			0.405142i			0.0130285i	−0.999979	+	0.00651424i	$0.997926\pi$
$968$			2.71375i			0.0872233i
$969$	32.0338			1.02907
$970$	6.83946	−	2.79060i	0.219602	−	0.0896008i
$971$	38.8032			1.24525			0.622627	−	0.782519i	$-0.286065\pi$
$971$	38.8032			1.24525			0.622627	+	0.782519i	$0.286065\pi$
$972$		−	35.6801i		−	1.14444i
$973$		−	17.0306i		−	0.545975i
$974$	−2.04682			−0.0655843
$975$	−9.64211	+	9.43972i	−0.308795	+	0.302313i
$976$	−30.8945			−0.988908
$977$		−	39.9940i		−	1.27952i	−0.768575	−	0.639760i	$-0.779034\pi$
$977$		−	39.9940i		−	1.27952i	0.768575	−	0.639760i	$-0.220966\pi$
$978$			9.31094i			0.297731i
$979$	−18.1567			−0.580290
$980$	−21.9835	+	8.96957i	−0.702236	+	0.286523i
$981$	11.3155			0.361275
$982$			3.24874i			0.103671i
$983$		−	21.3563i		−	0.681160i	−0.940216	−	0.340580i	$-0.889377\pi$
$983$		−	21.3563i		−	0.681160i	0.940216	−	0.340580i	$-0.110623\pi$
$984$	−25.6165			−0.816624
$985$	8.38228	+	20.5441i	0.267082	+	0.654589i
$986$	1.07499			0.0342347
$987$			34.7485i			1.10606i
$988$		−	2.49635i		−	0.0794194i
$989$	−10.0799			−0.320523
$990$	6.17965	+	15.1457i	0.196402	+	0.481361i
$991$	4.39444			0.139594			0.0697970	−	0.997561i	$-0.477765\pi$
$991$	4.39444			0.139594			0.0697970	+	0.997561i	$0.477765\pi$
$992$		−	19.7894i		−	0.628316i
$993$			76.5547i			2.42939i
$994$	−4.42164			−0.140246
$995$	14.5302	−	5.92853i	0.460638	−	0.187947i
$996$	−40.5518			−1.28493
$997$			28.9420i			0.916603i	0.888797	+	0.458302i	$0.151542\pi$
$997$			28.9420i			0.916603i	−0.888797	+	0.458302i	$0.848458\pi$
$998$		−	4.32233i		−	0.136821i
$999$	−24.7705			−0.783703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.b.b.24.5	yes	8
3.2	odd	2		1035.2.b.e.829.4		8
4.3	odd	2		1840.2.e.d.369.8		8
5.2	odd	4		575.2.a.i.1.2		4
5.3	odd	4		575.2.a.j.1.3		4
5.4	even	2	inner	115.2.b.b.24.4	✓	8
15.2	even	4		5175.2.a.bv.1.3		4
15.8	even	4		5175.2.a.bw.1.2		4
15.14	odd	2		1035.2.b.e.829.5		8
20.3	even	4		9200.2.a.ck.1.1		4
20.7	even	4		9200.2.a.cq.1.4		4
20.19	odd	2		1840.2.e.d.369.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.b.b.24.4	✓	8	5.4	even	2	inner
115.2.b.b.24.5	yes	8	1.1	even	1	trivial
575.2.a.i.1.2		4	5.2	odd	4
575.2.a.j.1.3		4	5.3	odd	4
1035.2.b.e.829.4		8	3.2	odd	2
1035.2.b.e.829.5		8	15.14	odd	2
1840.2.e.d.369.1		8	20.19	odd	2
1840.2.e.d.369.8		8	4.3	odd	2
5175.2.a.bv.1.3		4	15.2	even	4
5175.2.a.bw.1.2		4	15.8	even	4
9200.2.a.ck.1.1		4	20.3	even	4
9200.2.a.cq.1.4		4	20.7	even	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.291367i q^{2} -3.14073i q^{3} +1.91511 q^{4} +(-2.07037 + 0.844739i) q^{5} +0.915105 q^{6} -1.20647i q^{7} +1.14073i q^{8} -6.86420 q^{9} +O(q^{10})\)	\(q+0.291367i q^{2} -3.14073i q^{3} +1.91511 q^{4} +(-2.07037 + 0.844739i) q^{5} +0.915105 q^{6} -1.20647i q^{7} +1.14073i q^{8} -6.86420 q^{9} +(-0.246129 - 0.603236i) q^{10} +3.65773 q^{11} -6.01483i q^{12} -0.859268i q^{13} +0.351526 q^{14} +(2.65310 + 6.50246i) q^{15} +3.49784 q^{16} +6.72347i q^{17} -2.00000i q^{18} +1.51699 q^{19} +(-3.96497 + 1.61776i) q^{20} -3.78921 q^{21} +1.06574i q^{22} +1.00000i q^{23} +3.58273 q^{24} +(3.57283 - 3.49784i) q^{25} +0.250362 q^{26} +12.1364i q^{27} -2.31052i q^{28} -0.548747 q^{29} +(-1.89460 + 0.773025i) q^{30} -5.99568 q^{31} +3.30062i q^{32} -11.4879i q^{33} -1.95900 q^{34} +(1.01915 + 2.49784i) q^{35} -13.1457 q^{36} +2.04100i q^{37} +0.442002i q^{38} -2.69873 q^{39} +(-0.963621 - 2.36173i) q^{40} -7.14998 q^{41} -1.10405i q^{42} +10.0799i q^{43} +7.00493 q^{44} +(14.2114 - 5.79846i) q^{45} -0.291367 q^{46} -9.17040i q^{47} -10.9858i q^{48} +5.54442 q^{49} +(1.01915 + 1.04100i) q^{50} +21.1166 q^{51} -1.64559i q^{52} -5.37896i q^{53} -3.53615 q^{54} +(-7.57283 + 3.08982i) q^{55} +1.37626 q^{56} -4.76447i q^{57} -0.159887i q^{58} +0.582734 q^{59} +(5.08097 + 12.4529i) q^{60} -8.83244 q^{61} -1.74694i q^{62} +8.28146i q^{63} +6.03399 q^{64} +(0.725857 + 1.77900i) q^{65} +3.34720 q^{66} -3.20647i q^{67} +12.8761i q^{68} +3.14073 q^{69} +(-0.727788 + 0.296948i) q^{70} -12.5784 q^{71} -7.83021i q^{72} -8.62597i q^{73} -0.594681 q^{74} +(-10.9858 - 11.2213i) q^{75} +2.90520 q^{76} -4.41294i q^{77} -0.786321i q^{78} -0.0700619 q^{79} +(-7.24181 + 2.95476i) q^{80} +17.5246 q^{81} -2.08327i q^{82} -6.74197i q^{83} -7.25673 q^{84} +(-5.67958 - 13.9200i) q^{85} -2.93696 q^{86} +1.72347i q^{87} +4.17248i q^{88} -4.96393 q^{89} +(1.68948 + 4.14073i) q^{90} -1.03668 q^{91} +1.91511i q^{92} +18.8308i q^{93} +2.67195 q^{94} +(-3.14073 + 1.28146i) q^{95} +10.3664 q^{96} +11.3380i q^{97} +1.61546i q^{98} -25.1074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9	\( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + 6 q^{10} + 4 q^{11} + 8 q^{14} + 6 q^{15} + 4 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{21} + 24 q^{24} - 16 q^{25} + 12 q^{26} - 8 q^{29} - 2 q^{30} - 28 q^{34} + 28 q^{35} - 16 q^{36} + 16 q^{39} - 10 q^{40} - 16 q^{41} - 12 q^{44} + 24 q^{45} + 28 q^{50} + 20 q^{51} - 44 q^{54} - 16 q^{55} + 28 q^{56} - 16 q^{60} - 16 q^{61} + 40 q^{64} - 14 q^{65} - 16 q^{66} + 4 q^{69} - 28 q^{70} - 48 q^{71} + 72 q^{74} - 36 q^{76} - 48 q^{79} - 2 q^{80} + 16 q^{81} - 4 q^{84} + 12 q^{85} + 28 q^{86} + 16 q^{89} - 4 q^{90} + 52 q^{91} + 84 q^{94} - 4 q^{95} + 60 q^{96} - 72 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9 + 6 * q^10 + 4 * q^11 + 8 * q^14 + 6 * q^15 + 4 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^21 + 24 * q^24 - 16 * q^25 + 12 * q^26 - 8 * q^29 - 2 * q^30 - 28 * q^34 + 28 * q^35 - 16 * q^36 + 16 * q^39 - 10 * q^40 - 16 * q^41 - 12 * q^44 + 24 * q^45 + 28 * q^50 + 20 * q^51 - 44 * q^54 - 16 * q^55 + 28 * q^56 - 16 * q^60 - 16 * q^61 + 40 * q^64 - 14 * q^65 - 16 * q^66 + 4 * q^69 - 28 * q^70 - 48 * q^71 + 72 * q^74 - 36 * q^76 - 48 * q^79 - 2 * q^80 + 16 * q^81 - 4 * q^84 + 12 * q^85 + 28 * q^86 + 16 * q^89 - 4 * q^90 + 52 * q^91 + 84 * q^94 - 4 * q^95 + 60 * q^96 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more