LMFDB - Embedded newform 1170.2.o.c.287.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(53,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,4,0,-4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} - 4 x^{11} + 12 x^{10} - 16 x^{9} + 8 x^{8} - 8 x^{7} + 18 x^{6} + 32 x^{5} + 16 x^{4} + 36 x^{3} + \cdots + 2 $ x^12 - 4x^11 + 12x^10 - 16x^9 + 8x^8 - 8x^7 + 18x^6 + 32x^5 + 16x^4 + 36x^3 + 80x^2 - 24*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.5
Root			$-0.514363 - 1.24178i$ of defining polynomial
Character	$\chi$	$=$	1170.287
Dual form			1170.2.o.c.53.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.84387 + 1.26497i) q^{5} +(-3.59146 - 3.59146i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19828 - 0.409343i) q^{10} +1.71125i q^{11} +(-0.707107 + 0.707107i) q^{13} -5.07909 q^{14} -1.00000 q^{16} +(4.78487 - 4.78487i) q^{17} -7.31199i q^{19} +(1.26497 - 1.84387i) q^{20} +(1.21004 + 1.21004i) q^{22} +(-3.54508 - 3.54508i) q^{23} +(1.79970 + 4.66488i) q^{25} +1.00000i q^{26} +(-3.59146 + 3.59146i) q^{28} -5.62425 q^{29} -4.05036 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.76683i q^{34} +(-2.07909 - 11.1653i) q^{35} +(1.57389 + 1.57389i) q^{37} +(-5.17036 - 5.17036i) q^{38} +(-0.409343 - 2.19828i) q^{40} -5.00920i q^{41} +(4.54082 - 4.54082i) q^{43} +1.71125 q^{44} -5.01350 q^{46} +(8.44294 - 8.44294i) q^{47} +18.7972i q^{49} +(4.57115 + 2.02598i) q^{50} +(0.707107 + 0.707107i) q^{52} +(-0.817663 - 0.817663i) q^{53} +(-2.16468 + 3.15533i) q^{55} +5.07909i q^{56} +(-3.97695 + 3.97695i) q^{58} -5.36849 q^{59} -10.3407 q^{61} +(-2.86404 + 2.86404i) q^{62} +1.00000i q^{64} +(-2.19828 + 0.409343i) q^{65} +(10.8923 + 10.8923i) q^{67} +(-4.78487 - 4.78487i) q^{68} +(-9.36517 - 6.42490i) q^{70} +1.27407i q^{71} +(2.08637 - 2.08637i) q^{73} +2.22581 q^{74} -7.31199 q^{76} +(6.14590 - 6.14590i) q^{77} -9.68304i q^{79} +(-1.84387 - 1.26497i) q^{80} +(-3.54204 - 3.54204i) q^{82} +(3.21267 + 3.21267i) q^{83} +(14.8754 - 2.76995i) q^{85} -6.42168i q^{86} +(1.21004 - 1.21004i) q^{88} +7.44465 q^{89} +5.07909 q^{91} +(-3.54508 + 3.54508i) q^{92} -11.9401i q^{94} +(9.24945 - 13.4823i) q^{95} +(-3.37190 - 3.37190i) q^{97} +(13.2916 + 13.2916i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 4 q^{7} - 8 q^{14} - 12 q^{16} + 8 q^{17} + 4 q^{20} - 4 q^{22} + 12 q^{23} + 8 q^{25} - 4 q^{28} - 32 q^{29} - 16 q^{31} + 28 q^{35} + 16 q^{37} - 16 q^{38} - 4 q^{40} + 8 q^{43} + 64 q^{47}+ \cdots + 16 q^{98}+O(q^{100}) $ 12 * q + 4 * q^5 - 4 * q^7 - 8 * q^14 - 12 * q^16 + 8 * q^17 + 4 * q^20 - 4 * q^22 + 12 * q^23 + 8 * q^25 - 4 * q^28 - 32 * q^29 - 16 * q^31 + 28 * q^35 + 16 * q^37 - 16 * q^38 - 4 * q^40 + 8 * q^43 + 64 * q^47 + 16 * q^50 + 36 * q^53 - 36 * q^55 - 12 * q^58 - 48 * q^59 - 32 * q^61 - 4 * q^62 + 4 * q^67 - 8 * q^68 - 8 * q^70 + 16 * q^74 - 16 * q^76 + 40 * q^77 - 4 * q^80 - 8 * q^82 - 16 * q^83 + 36 * q^85 - 4 * q^88 - 64 * q^89 + 8 * q^91 + 12 * q^92 + 12 * q^95 - 32 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.84387	+	1.26497i	0.824603	+	0.565712i
$5$	1.84387	+	1.26497i	0.824603	+	0.565712i
$6$		0			0
$7$	−3.59146	−	3.59146i	−1.35744	−	1.35744i	−0.877056	−	0.480388i	$-0.840496\pi$
$7$	−3.59146	−	3.59146i	−1.35744	−	1.35744i	−0.480388	−	0.877056i	$-0.659504\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.19828	−	0.409343i	0.695157	−	0.129446i
$11$			1.71125i			0.515962i	0.966150	+	0.257981i	$0.0830573\pi$
$11$			1.71125i			0.515962i	−0.966150	+	0.257981i	$0.916943\pi$
$12$		0			0
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	−5.07909			−1.35744
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.78487	−	4.78487i	1.16050	−	1.16050i	0.176135	−	0.984366i	$-0.443640\pi$
$17$	4.78487	−	4.78487i	1.16050	−	1.16050i	0.984366	−	0.176135i	$-0.0563596\pi$
$18$		0			0
$19$		−	7.31199i		−	1.67749i	−0.544528	−	0.838743i	$-0.683291\pi$
$19$		−	7.31199i		−	1.67749i	0.544528	−	0.838743i	$-0.316709\pi$
$20$	1.26497	−	1.84387i	0.282856	−	0.412302i
$21$		0			0
$22$	1.21004	+	1.21004i	0.257981	+	0.257981i
$23$	−3.54508	−	3.54508i	−0.739201	−	0.739201i	0.233223	−	0.972423i	$-0.425073\pi$
$23$	−3.54508	−	3.54508i	−0.739201	−	0.739201i	−0.972423	+	0.233223i	$0.925073\pi$
$24$		0			0
$25$	1.79970	+	4.66488i	0.359940	+	0.932975i
$26$			1.00000i			0.196116i
$27$		0			0
$28$	−3.59146	+	3.59146i	−0.678722	+	0.678722i
$29$	−5.62425			−1.04440			−0.522199	−	0.852824i	$-0.674888\pi$
$29$	−5.62425			−1.04440			−0.522199	+	0.852824i	$0.674888\pi$
$30$		0			0
$31$	−4.05036			−0.727467			−0.363733	−	0.931503i	$-0.618498\pi$
$31$	−4.05036			−0.727467			−0.363733	+	0.931503i	$0.618498\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	6.76683i		−	1.16050i
$35$	−2.07909	−	11.1653i	−0.351430	−	1.88727i
$36$		0			0
$37$	1.57389	+	1.57389i	0.258746	+	0.258746i	0.824544	−	0.565798i	$-0.191432\pi$
$37$	1.57389	+	1.57389i	0.258746	+	0.258746i	−0.565798	+	0.824544i	$0.691432\pi$
$38$	−5.17036	−	5.17036i	−0.838743	−	0.838743i
$39$		0			0
$40$	−0.409343	−	2.19828i	−0.0647228	−	0.347579i
$41$		−	5.00920i		−	0.782305i	−0.920326	−	0.391152i	$-0.872077\pi$
$41$		−	5.00920i		−	0.782305i	0.920326	−	0.391152i	$-0.127923\pi$
$42$		0			0
$43$	4.54082	−	4.54082i	0.692468	−	0.692468i	−0.270306	−	0.962774i	$-0.587125\pi$
$43$	4.54082	−	4.54082i	0.692468	−	0.692468i	0.962774	+	0.270306i	$0.0871250\pi$
$44$	1.71125			0.257981
$45$		0			0
$46$	−5.01350			−0.739201
$47$	8.44294	−	8.44294i	1.23153	−	1.23153i	0.268153	−	0.963376i	$-0.413587\pi$
$47$	8.44294	−	8.44294i	1.23153	−	1.23153i	0.963376	−	0.268153i	$-0.0864132\pi$
$48$		0			0
$49$			18.7972i			2.68531i
$50$	4.57115	+	2.02598i	0.646458	+	0.286517i
$51$		0			0
$52$	0.707107	+	0.707107i	0.0980581	+	0.0980581i
$53$	−0.817663	−	0.817663i	−0.112315	−	0.112315i	0.648716	−	0.761031i	$-0.275306\pi$
$53$	−0.817663	−	0.817663i	−0.112315	−	0.112315i	−0.761031	+	0.648716i	$0.775306\pi$
$54$		0			0
$55$	−2.16468	+	3.15533i	−0.291886	+	0.425464i
$56$			5.07909i			0.678722i
$57$		0			0
$58$	−3.97695	+	3.97695i	−0.522199	+	0.522199i
$59$	−5.36849			−0.698918			−0.349459	−	0.936952i	$-0.613635\pi$
$59$	−5.36849			−0.698918			−0.349459	+	0.936952i	$0.613635\pi$
$60$		0			0
$61$	−10.3407			−1.32399			−0.661996	−	0.749507i	$-0.730291\pi$
$61$	−10.3407			−1.32399			−0.661996	+	0.749507i	$0.730291\pi$
$62$	−2.86404	+	2.86404i	−0.363733	+	0.363733i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−2.19828	+	0.409343i	−0.272663	+	0.0507728i
$66$		0			0
$67$	10.8923	+	10.8923i	1.33071	+	1.33071i	0.904739	+	0.425967i	$0.140066\pi$
$67$	10.8923	+	10.8923i	1.33071	+	1.33071i	0.425967	+	0.904739i	$0.359934\pi$
$68$	−4.78487	−	4.78487i	−0.580251	−	0.580251i
$69$		0			0
$70$	−9.36517	−	6.42490i	−1.11935	−	0.767922i
$71$			1.27407i			0.151204i	0.997138	+	0.0756021i	$0.0240879\pi$
$71$			1.27407i			0.151204i	−0.997138	+	0.0756021i	$0.975912\pi$
$72$		0			0
$73$	2.08637	−	2.08637i	0.244191	−	0.244191i	−0.574390	−	0.818581i	$-0.694761\pi$
$73$	2.08637	−	2.08637i	0.244191	−	0.244191i	0.818581	+	0.574390i	$0.194761\pi$
$74$	2.22581			0.258746
$75$		0			0
$76$	−7.31199			−0.838743
$77$	6.14590	−	6.14590i	0.700390	−	0.700390i
$78$		0			0
$79$		−	9.68304i		−	1.08943i	−0.838622	−	0.544713i	$-0.816638\pi$
$79$		−	9.68304i		−	1.08943i	0.838622	−	0.544713i	$-0.183362\pi$
$80$	−1.84387	−	1.26497i	−0.206151	−	0.141428i
$81$		0			0
$82$	−3.54204	−	3.54204i	−0.391152	−	0.391152i
$83$	3.21267	+	3.21267i	0.352636	+	0.352636i	0.861089	−	0.508453i	$-0.169783\pi$
$83$	3.21267	+	3.21267i	0.352636	+	0.352636i	−0.508453	+	0.861089i	$0.669783\pi$
$84$		0			0
$85$	14.8754	−	2.76995i	1.61346	−	0.300444i
$86$		−	6.42168i		−	0.692468i
$87$		0			0
$88$	1.21004	−	1.21004i	0.128991	−	0.128991i
$89$	7.44465			0.789132			0.394566	−	0.918868i	$-0.370895\pi$
$89$	7.44465			0.789132			0.394566	+	0.918868i	$0.370895\pi$
$90$		0			0
$91$	5.07909			0.532433
$92$	−3.54508	+	3.54508i	−0.369600	+	0.369600i
$93$		0			0
$94$		−	11.9401i		−	1.23153i
$95$	9.24945	−	13.4823i	0.948973	−	1.38326i
$96$		0			0
$97$	−3.37190	−	3.37190i	−0.342365	−	0.342365i	0.514891	−	0.857256i	$-0.327832\pi$
$97$	−3.37190	−	3.37190i	−0.342365	−	0.342365i	−0.857256	+	0.514891i	$0.827832\pi$
$98$	13.2916	+	13.2916i	1.34265	+	1.34265i
$99$		0			0
$100$	4.66488	−	1.79970i	0.466488	−	0.179970i
$101$			4.76257i			0.473893i	0.971523	+	0.236947i	$0.0761466\pi$
$101$			4.76257i			0.473893i	−0.971523	+	0.236947i	$0.923853\pi$
$102$		0			0
$103$	−7.33383	+	7.33383i	−0.722623	+	0.722623i	−0.969139	−	0.246515i	$-0.920714\pi$
$103$	−7.33383	+	7.33383i	−0.722623	+	0.722623i	0.246515	+	0.969139i	$0.420714\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−1.15635			−0.112315
$107$	−1.88067	+	1.88067i	−0.181811	+	0.181811i	−0.792145	−	0.610333i	$-0.791035\pi$
$107$	−1.88067	+	1.88067i	−0.181811	+	0.181811i	0.610333	+	0.792145i	$0.291035\pi$
$108$		0			0
$109$		−	0.0981889i		−	0.00940479i	−0.999989	−	0.00470240i	$-0.998503\pi$
$109$		−	0.0981889i		−	0.00940479i	0.999989	−	0.00470240i	$-0.00149682\pi$
$110$	0.700490	+	3.76182i	0.0667891	+	0.358675i
$111$		0			0
$112$	3.59146	+	3.59146i	0.339361	+	0.339361i
$113$	7.46873	+	7.46873i	0.702599	+	0.702599i	0.964968	−	0.262369i	$-0.0845037\pi$
$113$	7.46873	+	7.46873i	0.702599	+	0.702599i	−0.262369	+	0.964968i	$0.584504\pi$
$114$		0			0
$115$	−2.05224	−	11.0211i	−0.191373	−	1.02772i
$116$			5.62425i			0.522199i
$117$		0			0
$118$	−3.79610	+	3.79610i	−0.349459	+	0.349459i
$119$	−34.3693			−3.15063
$120$		0			0
$121$	8.07161			0.733783
$122$	−7.31199	+	7.31199i	−0.661996	+	0.661996i
$123$		0			0
$124$			4.05036i			0.363733i
$125$	−2.58252	+	10.8780i	−0.230987	+	0.972957i
$126$		0			0
$127$	−4.02039	−	4.02039i	−0.356752	−	0.356752i	0.505862	−	0.862614i	$-0.331174\pi$
$127$	−4.02039	−	4.02039i	−0.356752	−	0.356752i	−0.862614	+	0.505862i	$0.831174\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−1.26497	+	1.84387i	−0.110945	+	0.161718i
$131$		−	4.58401i		−	0.400507i	−0.979744	−	0.200254i	$-0.935823\pi$
$131$		−	4.58401i		−	0.400507i	0.979744	−	0.200254i	$-0.0641766\pi$
$132$		0			0
$133$	−26.2607	+	26.2607i	−2.27709	+	2.27709i
$134$	15.4040			1.33071
$135$		0			0
$136$	−6.76683			−0.580251
$137$	12.1390	−	12.1390i	1.03710	−	1.03710i	0.0378175	−	0.999285i	$-0.487959\pi$
$137$	12.1390	−	12.1390i	1.03710	−	1.03710i	0.999285	−	0.0378175i	$-0.0120406\pi$
$138$		0			0
$139$			20.4519i			1.73470i	0.497695	+	0.867352i	$0.334180\pi$
$139$			20.4519i			1.73470i	−0.497695	+	0.867352i	$0.665820\pi$
$140$	−11.1653	+	2.07909i	−0.943637	+	0.175715i
$141$		0			0
$142$	0.900903	+	0.900903i	0.0756021	+	0.0756021i
$143$	−1.21004	−	1.21004i	−0.101189	−	0.101189i
$144$		0			0
$145$	−10.3704	−	7.11451i	−0.861213	−	0.590828i
$146$		−	2.95057i		−	0.244191i
$147$		0			0
$148$	1.57389	−	1.57389i	0.129373	−	0.129373i
$149$	11.1167			0.910718			0.455359	−	0.890308i	$-0.349511\pi$
$149$	11.1167			0.910718			0.455359	+	0.890308i	$0.349511\pi$
$150$		0			0
$151$	12.6297			1.02779			0.513897	−	0.857852i	$-0.328201\pi$
$151$	12.6297			1.02779			0.513897	+	0.857852i	$0.328201\pi$
$152$	−5.17036	+	5.17036i	−0.419371	+	0.419371i
$153$		0			0
$154$		−	8.69161i		−	0.700390i
$155$	−7.46834	−	5.12359i	−0.599871	−	0.411537i
$156$		0			0
$157$	0.138278	+	0.138278i	0.0110358	+	0.0110358i	0.712603	−	0.701567i	$-0.247516\pi$
$157$	0.138278	+	0.138278i	0.0110358	+	0.0110358i	−0.701567	+	0.712603i	$0.747516\pi$
$158$	−6.84694	−	6.84694i	−0.544713	−	0.544713i
$159$		0			0
$160$	−2.19828	+	0.409343i	−0.173789	+	0.0323614i
$161$			25.4640i			2.00685i
$162$		0			0
$163$	−13.9766	+	13.9766i	−1.09473	+	1.09473i	−0.0997147	+	0.995016i	$0.531793\pi$
$163$	−13.9766	+	13.9766i	−1.09473	+	1.09473i	−0.995016	+	0.0997147i	$0.968207\pi$
$164$	−5.00920			−0.391152
$165$		0			0
$166$	4.54340			0.352636
$167$	14.3179	−	14.3179i	1.10795	−	1.10795i	0.114529	−	0.993420i	$-0.463464\pi$
$167$	14.3179	−	14.3179i	1.10795	−	1.10795i	0.993420	−	0.114529i	$-0.0365359\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$	8.55983	−	12.4771i	0.656509	−	0.956953i
$171$		0			0
$172$	−4.54082	−	4.54082i	−0.346234	−	0.346234i
$173$	−0.153769	−	0.153769i	−0.0116908	−	0.0116908i	0.701237	−	0.712928i	$-0.252631\pi$
$173$	−0.153769	−	0.153769i	−0.0116908	−	0.0116908i	−0.712928	+	0.701237i	$0.752631\pi$
$174$		0			0
$175$	10.2902	−	23.2173i	0.777863	−	1.75506i
$176$		−	1.71125i		−	0.128991i
$177$		0			0
$178$	5.26417	−	5.26417i	0.394566	−	0.394566i
$179$	−5.18530			−0.387568			−0.193784	−	0.981044i	$-0.562076\pi$
$179$	−5.18530			−0.387568			−0.193784	+	0.981044i	$0.562076\pi$
$180$		0			0
$181$	−7.46337			−0.554748			−0.277374	−	0.960762i	$-0.589464\pi$
$181$	−7.46337			−0.554748			−0.277374	+	0.960762i	$0.589464\pi$
$182$	3.59146	−	3.59146i	0.266217	−	0.266217i
$183$		0			0
$184$			5.01350i			0.369600i
$185$	0.911121	+	4.89296i	0.0669870	+	0.359738i
$186$		0			0
$187$	8.18813	+	8.18813i	0.598775	+	0.598775i
$188$	−8.44294	−	8.44294i	−0.615765	−	0.615765i
$189$		0			0
$190$	−2.99311	−	16.0738i	−0.217143	−	1.16612i
$191$			14.7875i			1.06998i	0.844857	+	0.534992i	$0.179686\pi$
$191$			14.7875i			1.06998i	−0.844857	+	0.534992i	$0.820314\pi$
$192$		0			0
$193$	3.46825	−	3.46825i	0.249650	−	0.249650i	−0.571177	−	0.820827i	$-0.693513\pi$
$193$	3.46825	−	3.46825i	0.249650	−	0.249650i	0.820827	+	0.571177i	$0.193513\pi$
$194$	−4.76859			−0.342365
$195$		0			0
$196$	18.7972			1.34265
$197$	−11.1189	+	11.1189i	−0.792191	+	0.792191i	−0.981850	−	0.189659i	$-0.939262\pi$
$197$	−11.1189	+	11.1189i	−0.792191	+	0.792191i	0.189659	+	0.981850i	$0.439262\pi$
$198$		0			0
$199$			1.17646i			0.0833967i	0.999130	+	0.0416984i	$0.0132768\pi$
$199$			1.17646i			0.0833967i	−0.999130	+	0.0416984i	$0.986723\pi$
$200$	2.02598	−	4.57115i	0.143259	−	0.323229i
$201$		0			0
$202$	3.36764	+	3.36764i	0.236947	+	0.236947i
$203$	20.1993	+	20.1993i	1.41771	+	1.41771i
$204$		0			0
$205$	6.33648	−	9.23630i	0.442559	−	0.645091i
$206$			10.3716i			0.722623i
$207$		0			0
$208$	0.707107	−	0.707107i	0.0490290	−	0.0490290i
$209$	12.5127			0.865520
$210$		0			0
$211$	−2.39291			−0.164735			−0.0823674	−	0.996602i	$-0.526248\pi$
$211$	−2.39291			−0.164735			−0.0823674	+	0.996602i	$0.526248\pi$
$212$	−0.817663	+	0.817663i	−0.0561573	+	0.0561573i
$213$		0			0
$214$			2.65967i			0.181811i
$215$	14.1167	−	2.62867i	0.962748	−	0.179274i
$216$		0			0
$217$	14.5467	+	14.5467i	0.987496	+	0.987496i
$218$	−0.0694301	−	0.0694301i	−0.00470240	−	0.00470240i
$219$		0			0
$220$	3.15533	+	2.16468i	0.212732	+	0.145943i
$221$			6.76683i			0.455186i
$222$		0			0
$223$	6.52830	−	6.52830i	0.437167	−	0.437167i	−0.453890	−	0.891058i	$-0.649964\pi$
$223$	6.52830	−	6.52830i	0.437167	−	0.437167i	0.891058	+	0.453890i	$0.149964\pi$
$224$	5.07909			0.339361
$225$		0			0
$226$	10.5624			0.702599
$227$	−3.89911	+	3.89911i	−0.258793	+	0.258793i	−0.824563	−	0.565770i	$-0.808579\pi$
$227$	−3.89911	+	3.89911i	−0.258793	+	0.258793i	0.565770	+	0.824563i	$0.308579\pi$
$228$		0			0
$229$			8.58262i			0.567156i	0.958949	+	0.283578i	$0.0915214\pi$
$229$			8.58262i			0.567156i	−0.958949	+	0.283578i	$0.908479\pi$
$230$	−9.24424	−	6.34193i	−0.609547	−	0.418175i
$231$		0			0
$232$	3.97695	+	3.97695i	0.261099	+	0.261099i
$233$	−12.6344	−	12.6344i	−0.827709	−	0.827709i	0.159490	−	0.987200i	$-0.449015\pi$
$233$	−12.6344	−	12.6344i	−0.827709	−	0.827709i	−0.987200	+	0.159490i	$0.949015\pi$
$234$		0			0
$235$	26.2477	−	4.88760i	1.71221	−	0.318832i
$236$			5.36849i			0.349459i
$237$		0			0
$238$	−24.3028	+	24.3028i	−1.57532	+	1.57532i
$239$	1.24186			0.0803291			0.0401645	−	0.999193i	$-0.487212\pi$
$239$	1.24186			0.0803291			0.0401645	+	0.999193i	$0.487212\pi$
$240$		0			0
$241$	28.1888			1.81580			0.907899	−	0.419188i	$-0.137685\pi$
$241$	28.1888			1.81580			0.907899	+	0.419188i	$0.137685\pi$
$242$	5.70749	−	5.70749i	0.366891	−	0.366891i
$243$		0			0
$244$			10.3407i			0.661996i
$245$	−23.7778	+	34.6595i	−1.51911	+	2.21431i
$246$		0			0
$247$	5.17036	+	5.17036i	0.328982	+	0.328982i
$248$	2.86404	+	2.86404i	0.181867	+	0.181867i
$249$		0			0
$250$	5.86578	+	9.51801i	0.370985	+	0.601972i
$251$		−	15.9007i		−	1.00364i	−0.864971	−	0.501822i	$-0.832663\pi$
$251$		−	15.9007i		−	1.00364i	0.864971	−	0.501822i	$-0.167337\pi$
$252$		0			0
$253$	6.06654	−	6.06654i	0.381400	−	0.381400i
$254$	−5.68569			−0.356752
$255$		0			0
$256$	1.00000			0.0625000
$257$	18.7911	−	18.7911i	1.17216	−	1.17216i	0.190463	−	0.981694i	$-0.439001\pi$
$257$	18.7911	−	18.7911i	1.17216	−	1.17216i	0.981694	−	0.190463i	$-0.0609991\pi$
$258$		0			0
$259$		−	11.3051i		−	0.702465i
$260$	0.409343	+	2.19828i	0.0253864	+	0.136332i
$261$		0			0
$262$	−3.24139	−	3.24139i	−0.200254	−	0.200254i
$263$	18.5497	+	18.5497i	1.14383	+	1.14383i	0.987744	+	0.156081i	$0.0498860\pi$
$263$	18.5497	+	18.5497i	1.14383	+	1.14383i	0.156081	+	0.987744i	$0.450114\pi$
$264$		0			0
$265$	−0.473344	−	2.54198i	−0.0290773	−	0.156153i
$266$			37.1383i			2.27709i
$267$		0			0
$268$	10.8923	−	10.8923i	0.665353	−	0.665353i
$269$	17.4203			1.06214			0.531069	−	0.847329i	$-0.321791\pi$
$269$	17.4203			1.06214			0.531069	+	0.847329i	$0.321791\pi$
$270$		0			0
$271$	10.5944			0.643566			0.321783	−	0.946813i	$-0.395718\pi$
$271$	10.5944			0.643566			0.321783	+	0.946813i	$0.395718\pi$
$272$	−4.78487	+	4.78487i	−0.290125	+	0.290125i
$273$		0			0
$274$		−	17.1671i		−	1.03710i
$275$	−7.98279	+	3.07975i	−0.481380	+	0.185716i
$276$		0			0
$277$	12.9617	+	12.9617i	0.778792	+	0.778792i	0.979625	−	0.200833i	$-0.0643650\pi$
$277$	12.9617	+	12.9617i	0.778792	+	0.778792i	−0.200833	+	0.979625i	$0.564365\pi$
$278$	14.4616	+	14.4616i	0.867352	+	0.867352i
$279$		0			0
$280$	−6.42490	+	9.36517i	−0.383961	+	0.559676i
$281$		−	9.97862i		−	0.595275i	−0.954679	−	0.297637i	$-0.903801\pi$
$281$		−	9.97862i		−	0.595275i	0.954679	−	0.297637i	$-0.0961986\pi$
$282$		0			0
$283$	6.29606	−	6.29606i	0.374262	−	0.374262i	−0.494765	−	0.869027i	$-0.664746\pi$
$283$	6.29606	−	6.29606i	0.374262	−	0.374262i	0.869027	+	0.494765i	$0.164746\pi$
$284$	1.27407			0.0756021
$285$		0			0
$286$	−1.71125			−0.101189
$287$	−17.9903	+	17.9903i	−1.06194	+	1.06194i
$288$		0			0
$289$		−	28.7899i		−	1.69353i
$290$	−12.3637	+	2.30225i	−0.726021	+	0.135193i
$291$		0			0
$292$	−2.08637	−	2.08637i	−0.122095	−	0.122095i
$293$	17.0111	+	17.0111i	0.993798	+	0.993798i	0.999981	−	0.00618299i	$-0.00196812\pi$
$293$	17.0111	+	17.0111i	0.993798	+	0.993798i	−0.00618299	+	0.999981i	$0.501968\pi$
$294$		0			0
$295$	−9.89879	−	6.79098i	−0.576330	−	0.395386i
$296$		−	2.22581i		−	0.129373i
$297$		0			0
$298$	7.86072	−	7.86072i	0.455359	−	0.455359i
$299$	5.01350			0.289938
$300$		0			0
$301$	−32.6163			−1.87997
$302$	8.93058	−	8.93058i	0.513897	−	0.513897i
$303$		0			0
$304$			7.31199i			0.419371i
$305$	−19.0669	−	13.0807i	−1.09177	−	0.748998i
$306$		0			0
$307$	3.40431	+	3.40431i	0.194294	+	0.194294i	0.797549	−	0.603254i	$-0.206130\pi$
$307$	3.40431	+	3.40431i	0.194294	+	0.194294i	−0.603254	+	0.797549i	$0.706130\pi$
$308$	−6.14590	−	6.14590i	−0.350195	−	0.350195i
$309$		0			0
$310$	−8.90384	+	1.65799i	−0.505704	+	0.0941674i
$311$			3.82411i			0.216846i	0.994105	+	0.108423i	$0.0345800\pi$
$311$			3.82411i			0.216846i	−0.994105	+	0.108423i	$0.965420\pi$
$312$		0			0
$313$	8.63440	−	8.63440i	0.488045	−	0.488045i	−0.419644	−	0.907689i	$-0.637845\pi$
$313$	8.63440	−	8.63440i	0.488045	−	0.488045i	0.907689	+	0.419644i	$0.137845\pi$
$314$	0.195554			0.0110358
$315$		0			0
$316$	−9.68304			−0.544713
$317$	5.03283	−	5.03283i	0.282672	−	0.282672i	−0.551502	−	0.834174i	$-0.685945\pi$
$317$	5.03283	−	5.03283i	0.282672	−	0.282672i	0.834174	+	0.551502i	$0.185945\pi$
$318$		0			0
$319$		−	9.62452i		−	0.538870i
$320$	−1.26497	+	1.84387i	−0.0707140	+	0.103075i
$321$		0			0
$322$	18.0058	+	18.0058i	1.00342	+	1.00342i
$323$	−34.9869	−	34.9869i	−1.94672	−	1.94672i
$324$		0			0
$325$	−4.57115	−	2.02598i	−0.253562	−	0.112381i
$326$			19.7659i			1.09473i
$327$		0			0
$328$	−3.54204	+	3.54204i	−0.195576	+	0.195576i
$329$	−60.6449			−3.34346
$330$		0			0
$331$	−15.5941			−0.857131			−0.428566	−	0.903511i	$-0.640981\pi$
$331$	−15.5941			−0.857131			−0.428566	+	0.903511i	$0.640981\pi$
$332$	3.21267	−	3.21267i	0.176318	−	0.176318i
$333$		0			0
$334$		−	20.2485i		−	1.10795i
$335$	6.30553	+	33.8624i	0.344508	+	1.85010i
$336$		0			0
$337$	4.33551	+	4.33551i	0.236170	+	0.236170i	0.815262	−	0.579092i	$-0.196593\pi$
$337$	4.33551	+	4.33551i	0.236170	+	0.236170i	−0.579092	+	0.815262i	$0.696593\pi$
$338$	−0.707107	−	0.707107i	−0.0384615	−	0.0384615i
$339$		0			0
$340$	−2.76995	−	14.8754i	−0.150222	−	0.806731i
$341$		−	6.93120i		−	0.375346i
$342$		0			0
$343$	42.3690	−	42.3690i	2.28771	−	2.28771i
$344$	−6.42168			−0.346234
$345$		0			0
$346$	−0.217462			−0.0116908
$347$	7.91903	−	7.91903i	0.425116	−	0.425116i	−0.461845	−	0.886961i	$-0.652812\pi$
$347$	7.91903	−	7.91903i	0.425116	−	0.425116i	0.886961	+	0.461845i	$0.152812\pi$
$348$		0			0
$349$			4.26538i			0.228320i	0.993462	+	0.114160i	$0.0364177\pi$
$349$			4.26538i			0.228320i	−0.993462	+	0.114160i	$0.963582\pi$
$350$	−9.14085	−	23.6933i	−0.488599	−	1.26646i
$351$		0			0
$352$	−1.21004	−	1.21004i	−0.0644953	−	0.0644953i
$353$	−18.9673	−	18.9673i	−1.00953	−	1.00953i	−0.999954	−	0.00957293i	$-0.996953\pi$
$353$	−18.9673	−	18.9673i	−1.00953	−	1.00953i	−0.00957293	−	0.999954i	$-0.503047\pi$
$354$		0			0
$355$	−1.61166	+	2.34922i	−0.0855380	+	0.124683i
$356$		−	7.44465i		−	0.394566i
$357$		0			0
$358$	−3.66656	+	3.66656i	−0.193784	+	0.193784i
$359$	−2.11862			−0.111817			−0.0559083	−	0.998436i	$-0.517805\pi$
$359$	−2.11862			−0.111817			−0.0559083	+	0.998436i	$0.517805\pi$
$360$		0			0
$361$	−34.4652			−1.81396
$362$	−5.27740	+	5.27740i	−0.277374	+	0.277374i
$363$		0			0
$364$		−	5.07909i		−	0.266217i
$365$	6.48618	−	1.20780i	0.339502	−	0.0632189i
$366$		0			0
$367$	2.79585	+	2.79585i	0.145942	+	0.145942i	0.776303	−	0.630360i	$-0.217093\pi$
$367$	2.79585	+	2.79585i	0.145942	+	0.145942i	−0.630360	+	0.776303i	$0.717093\pi$
$368$	3.54508	+	3.54508i	0.184800	+	0.184800i
$369$		0			0
$370$	4.10411	+	2.81559i	0.213362	+	0.146375i
$371$			5.87321i			0.304922i
$372$		0			0
$373$	−12.8376	+	12.8376i	−0.664705	+	0.664705i	−0.956485	−	0.291780i	$-0.905752\pi$
$373$	−12.8376	+	12.8376i	−0.664705	+	0.664705i	0.291780	+	0.956485i	$0.405752\pi$
$374$	11.5798			0.598775
$375$		0			0
$376$	−11.9401			−0.615765
$377$	3.97695	−	3.97695i	0.204823	−	0.204823i
$378$		0			0
$379$			25.1235i			1.29051i	0.763969	+	0.645253i	$0.223248\pi$
$379$			25.1235i			1.29051i	−0.763969	+	0.645253i	$0.776752\pi$
$380$	−13.4823	−	9.24945i	−0.691630	−	0.474487i
$381$		0			0
$382$	10.4563	+	10.4563i	0.534992	+	0.534992i
$383$	5.60289	+	5.60289i	0.286294	+	0.286294i	0.835613	−	0.549319i	$-0.185113\pi$
$383$	5.60289	+	5.60289i	0.286294	+	0.286294i	−0.549319	+	0.835613i	$0.685113\pi$
$384$		0			0
$385$	19.1066	−	3.55785i	0.973763	−	0.181325i
$386$		−	4.90485i		−	0.249650i
$387$		0			0
$388$	−3.37190	+	3.37190i	−0.171183	+	0.171183i
$389$	−6.08318			−0.308430			−0.154215	−	0.988037i	$-0.549285\pi$
$389$	−6.08318			−0.308430			−0.154215	+	0.988037i	$0.549285\pi$
$390$		0			0
$391$	−33.9255			−1.71569
$392$	13.2916	−	13.2916i	0.671327	−	0.671327i
$393$		0			0
$394$			15.7245i			0.792191i
$395$	12.2487	−	17.8542i	0.616301	−	0.898345i
$396$		0			0
$397$	−23.4663	−	23.4663i	−1.17774	−	1.17774i	−0.980318	−	0.197424i	$-0.936743\pi$
$397$	−23.4663	−	23.4663i	−1.17774	−	1.17774i	−0.197424	−	0.980318i	$-0.563257\pi$
$398$	0.831879	+	0.831879i	0.0416984	+	0.0416984i
$399$		0			0
$400$	−1.79970	−	4.66488i	−0.0899851	−	0.233244i
$401$			18.8280i			0.940225i	0.882607	+	0.470112i	$0.155787\pi$
$401$			18.8280i			0.940225i	−0.882607	+	0.470112i	$0.844213\pi$
$402$		0			0
$403$	2.86404	−	2.86404i	0.142668	−	0.142668i
$404$	4.76257			0.236947
$405$		0			0
$406$	28.5661			1.41771
$407$	−2.69332	+	2.69332i	−0.133503	+	0.133503i
$408$		0			0
$409$			20.2581i			1.00170i	0.865535	+	0.500849i	$0.166979\pi$
$409$			20.2581i			1.00170i	−0.865535	+	0.500849i	$0.833021\pi$
$410$	−2.05048	−	11.0116i	−0.101266	−	0.543825i
$411$		0			0
$412$	7.33383	+	7.33383i	0.361312	+	0.361312i
$413$	19.2807	+	19.2807i	0.948742	+	0.948742i
$414$		0			0
$415$	1.85981	+	9.98766i	0.0912944	+	0.490275i
$416$		−	1.00000i		−	0.0490290i
$417$		0			0
$418$	8.84779	−	8.84779i	0.432760	−	0.432760i
$419$	−32.8195			−1.60334			−0.801668	−	0.597770i	$-0.796054\pi$
$419$	−32.8195			−1.60334			−0.801668	+	0.597770i	$0.796054\pi$
$420$		0			0
$421$	−36.7873			−1.79290			−0.896451	−	0.443142i	$-0.853864\pi$
$421$	−36.7873			−1.79290			−0.896451	+	0.443142i	$0.853864\pi$
$422$	−1.69204	+	1.69204i	−0.0823674	+	0.0823674i
$423$		0			0
$424$			1.15635i			0.0561573i
$425$	30.9322	+	13.7095i	1.50043	+	0.665008i
$426$		0			0
$427$	37.1383	+	37.1383i	1.79725	+	1.79725i
$428$	1.88067	+	1.88067i	0.0909056	+	0.0909056i
$429$		0			0
$430$	8.12324	−	11.8407i	0.391737	−	0.571011i
$431$		−	27.1329i		−	1.30695i	−0.756950	−	0.653473i	$-0.773311\pi$
$431$		−	27.1329i		−	1.30695i	0.756950	−	0.653473i	$-0.226689\pi$
$432$		0			0
$433$	−13.7048	+	13.7048i	−0.658612	+	0.658612i	−0.955052	−	0.296439i	$-0.904201\pi$
$433$	−13.7048	+	13.7048i	−0.658612	+	0.658612i	0.296439	+	0.955052i	$0.404201\pi$
$434$	20.5722			0.987496
$435$		0			0
$436$	−0.0981889			−0.00470240
$437$	−25.9216	+	25.9216i	−1.24000	+	1.24000i
$438$		0			0
$439$			7.76024i			0.370376i	0.982703	+	0.185188i	$0.0592894\pi$
$439$			7.76024i			0.370376i	−0.982703	+	0.185188i	$0.940711\pi$
$440$	3.76182	−	0.700490i	0.179338	−	0.0333945i
$441$		0			0
$442$	4.78487	+	4.78487i	0.227593	+	0.227593i
$443$	23.7075	+	23.7075i	1.12638	+	1.12638i	0.990762	+	0.135616i	$0.0433012\pi$
$443$	23.7075	+	23.7075i	1.12638	+	1.12638i	0.135616	+	0.990762i	$0.456699\pi$
$444$		0			0
$445$	13.7270	+	9.41726i	0.650720	+	0.446421i
$446$		−	9.23241i		−	0.437167i
$447$		0			0
$448$	3.59146	−	3.59146i	0.169680	−	0.169680i
$449$	2.75448			0.129992			0.0649960	−	0.997886i	$-0.479297\pi$
$449$	2.75448			0.129992			0.0649960	+	0.997886i	$0.479297\pi$
$450$		0			0
$451$	8.57201			0.403640
$452$	7.46873	−	7.46873i	0.351300	−	0.351300i
$453$		0			0
$454$			5.51417i			0.258793i
$455$	9.36517	+	6.42490i	0.439046	+	0.301204i
$456$		0			0
$457$	−21.6406	−	21.6406i	−1.01231	−	1.01231i	−0.999923	−	0.0123823i	$-0.996059\pi$
$457$	−21.6406	−	21.6406i	−1.01231	−	1.01231i	−0.0123823	−	0.999923i	$-0.503941\pi$
$458$	6.06883	+	6.06883i	0.283578	+	0.283578i
$459$		0			0
$460$	−11.0211	+	2.05224i	−0.513861	+	0.0956863i
$461$		−	32.5967i		−	1.51818i	−0.650986	−	0.759090i	$-0.725644\pi$
$461$		−	32.5967i		−	1.51818i	0.650986	−	0.759090i	$-0.274356\pi$
$462$		0			0
$463$	11.7158	−	11.7158i	0.544479	−	0.544479i	−0.380360	−	0.924839i	$-0.624200\pi$
$463$	11.7158	−	11.7158i	0.544479	−	0.544479i	0.924839	+	0.380360i	$0.124200\pi$
$464$	5.62425			0.261099
$465$		0			0
$466$	−17.8678			−0.827709
$467$	3.03350	−	3.03350i	0.140374	−	0.140374i	−0.633428	−	0.773802i	$-0.718353\pi$
$467$	3.03350	−	3.03350i	0.140374	−	0.140374i	0.773802	+	0.633428i	$0.218353\pi$
$468$		0			0
$469$		−	78.2385i		−	3.61272i
$470$	15.1039	−	22.0160i	0.696691	−	1.01552i
$471$		0			0
$472$	3.79610	+	3.79610i	0.174730	+	0.174730i
$473$	7.77049	+	7.77049i	0.357287	+	0.357287i
$474$		0			0
$475$	34.1095	−	13.1594i	1.56505	−	0.603795i
$476$			34.3693i			1.57532i
$477$		0			0
$478$	0.878126	−	0.878126i	0.0401645	−	0.0401645i
$479$	−6.20311			−0.283427			−0.141714	−	0.989908i	$-0.545261\pi$
$479$	−6.20311			−0.283427			−0.141714	+	0.989908i	$0.545261\pi$
$480$		0			0
$481$	−2.22581			−0.101488
$482$	19.9325	−	19.9325i	0.907899	−	0.907899i
$483$		0			0
$484$		−	8.07161i		−	0.366891i
$485$	−1.95199	−	10.4827i	−0.0886353	−	0.475995i
$486$		0			0
$487$	−18.9805	−	18.9805i	−0.860091	−	0.860091i	0.131258	−	0.991348i	$-0.458098\pi$
$487$	−18.9805	−	18.9805i	−0.860091	−	0.860091i	−0.991348	+	0.131258i	$0.958098\pi$
$488$	7.31199	+	7.31199i	0.330998	+	0.330998i
$489$		0			0
$490$	7.69448	+	41.3214i	0.347601	+	1.86671i
$491$			0.808273i			0.0364768i	0.999834	+	0.0182384i	$0.00580579\pi$
$491$			0.808273i			0.0364768i	−0.999834	+	0.0182384i	$0.994194\pi$
$492$		0			0
$493$	−26.9113	+	26.9113i	−1.21202	+	1.21202i
$494$	7.31199			0.328982
$495$		0			0
$496$	4.05036			0.181867
$497$	4.57577	−	4.57577i	0.205251	−	0.205251i
$498$		0			0
$499$		−	7.50350i		−	0.335903i	−0.985795	−	0.167951i	$-0.946285\pi$
$499$		−	7.50350i		−	0.335903i	0.985795	−	0.167951i	$-0.0537152\pi$
$500$	10.8780	+	2.58252i	0.486478	+	0.115494i
$501$		0			0
$502$	−11.2435	−	11.2435i	−0.501822	−	0.501822i
$503$	−10.2038	−	10.2038i	−0.454963	−	0.454963i	0.442035	−	0.896998i	$-0.354257\pi$
$503$	−10.2038	−	10.2038i	−0.454963	−	0.454963i	−0.896998	+	0.442035i	$0.854257\pi$
$504$		0			0
$505$	−6.02451	+	8.78155i	−0.268087	+	0.390774i
$506$		−	8.57938i		−	0.381400i
$507$		0			0
$508$	−4.02039	+	4.02039i	−0.178376	+	0.178376i
$509$	28.4806			1.26238			0.631190	−	0.775628i	$-0.282567\pi$
$509$	28.4806			1.26238			0.631190	+	0.775628i	$0.282567\pi$
$510$		0			0
$511$	−14.9862			−0.662951
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	26.5747i		−	1.17216i
$515$	−22.7997	+	4.24554i	−1.00467	+	0.187081i
$516$		0			0
$517$	14.4480	+	14.4480i	0.635423	+	0.635423i
$518$	−7.99392	−	7.99392i	−0.351233	−	0.351233i
$519$		0			0
$520$	1.84387	+	1.26497i	0.0808590	+	0.0554726i
$521$			10.4221i			0.456602i	0.973591	+	0.228301i	$0.0733170\pi$
$521$			10.4221i			0.456602i	−0.973591	+	0.228301i	$0.926683\pi$
$522$		0			0
$523$	−5.42102	+	5.42102i	−0.237045	+	0.237045i	−0.815625	−	0.578581i	$-0.803607\pi$
$523$	−5.42102	+	5.42102i	−0.237045	+	0.237045i	0.578581	+	0.815625i	$0.303607\pi$
$524$	−4.58401			−0.200254
$525$		0			0
$526$	26.2333			1.14383
$527$	−19.3805	+	19.3805i	−0.844226	+	0.844226i
$528$		0			0
$529$			2.13521i			0.0928352i
$530$	−2.13216	−	1.46275i	−0.0926150	−	0.0635377i
$531$		0			0
$532$	26.2607	+	26.2607i	1.13855	+	1.13855i
$533$	3.54204	+	3.54204i	0.153423	+	0.153423i
$534$		0			0
$535$	−5.84670	+	1.08872i	−0.252775	+	0.0470693i
$536$		−	15.4040i		−	0.665353i
$537$		0			0
$538$	12.3180	−	12.3180i	0.531069	−	0.531069i
$539$	−32.1667			−1.38552
$540$		0			0
$541$	−42.8418			−1.84191			−0.920955	−	0.389668i	$-0.872590\pi$
$541$	−42.8418			−1.84191			−0.920955	+	0.389668i	$0.872590\pi$
$542$	7.49140	−	7.49140i	0.321783	−	0.321783i
$543$		0			0
$544$			6.76683i			0.290125i
$545$	0.124206	−	0.181047i	0.00532040	−	0.00775522i
$546$		0			0
$547$	−23.8615	−	23.8615i	−1.02025	−	1.02025i	−0.999791	−	0.0204542i	$-0.993489\pi$
$547$	−23.8615	−	23.8615i	−1.02025	−	1.02025i	−0.0204542	−	0.999791i	$-0.506511\pi$
$548$	−12.1390	−	12.1390i	−0.518551	−	0.518551i
$549$		0			0
$550$	−3.46697	+	7.82239i	−0.147832	+	0.333548i
$551$			41.1245i			1.75196i
$552$		0			0
$553$	−34.7762	+	34.7762i	−1.47884	+	1.47884i
$554$	18.3306			0.778792
$555$		0			0
$556$	20.4519			0.867352
$557$	14.8257	−	14.8257i	0.628185	−	0.628185i	−0.319426	−	0.947611i	$-0.603490\pi$
$557$	14.8257	−	14.8257i	0.628185	−	0.628185i	0.947611	+	0.319426i	$0.103490\pi$
$558$		0			0
$559$			6.42168i			0.271608i
$560$	2.07909	+	11.1653i	0.0878576	+	0.471819i
$561$		0			0
$562$	−7.05595	−	7.05595i	−0.297637	−	0.297637i
$563$	−24.7799	−	24.7799i	−1.04435	−	1.04435i	−0.998970	−	0.0453802i	$-0.985550\pi$
$563$	−24.7799	−	24.7799i	−1.04435	−	1.04435i	−0.0453802	−	0.998970i	$-0.514450\pi$
$564$		0			0
$565$	4.32364	+	23.2191i	0.181897	+	0.976834i
$566$		−	8.90398i		−	0.374262i
$567$		0			0
$568$	0.900903	−	0.900903i	0.0378010	−	0.0378010i
$569$	37.8539			1.58692			0.793460	−	0.608623i	$-0.208278\pi$
$569$	37.8539			1.58692			0.793460	+	0.608623i	$0.208278\pi$
$570$		0			0
$571$	−20.4324			−0.855068			−0.427534	−	0.903999i	$-0.640618\pi$
$571$	−20.4324			−0.855068			−0.427534	+	0.903999i	$0.640618\pi$
$572$	−1.21004	+	1.21004i	−0.0505943	+	0.0505943i
$573$		0			0
$574$			25.4422i			1.06194i
$575$	10.1573	−	22.9175i	0.423588	−	0.955724i
$576$		0			0
$577$	25.6648	+	25.6648i	1.06844	+	1.06844i	0.997479	+	0.0709599i	$0.0226062\pi$
$577$	25.6648	+	25.6648i	1.06844	+	1.06844i	0.0709599	+	0.997479i	$0.477394\pi$
$578$	−20.3576	−	20.3576i	−0.846763	−	0.846763i
$579$		0			0
$580$	−7.11451	+	10.3704i	−0.295414	+	0.430607i
$581$		−	23.0763i		−	0.957367i
$582$		0			0
$583$	1.39923	−	1.39923i	0.0579501	−	0.0579501i
$584$	−2.95057			−0.122095
$585$		0			0
$586$	24.0573			0.993798
$587$	23.4279	−	23.4279i	0.966973	−	0.966973i	−0.0324987	−	0.999472i	$-0.510346\pi$
$587$	23.4279	−	23.4279i	0.966973	−	0.966973i	0.999472	+	0.0324987i	$0.0103465\pi$
$588$		0			0
$589$			29.6162i			1.22032i
$590$	−11.8015	+	2.19756i	−0.485858	+	0.0904719i
$591$		0			0
$592$	−1.57389	−	1.57389i	−0.0646864	−	0.0646864i
$593$	−1.99530	−	1.99530i	−0.0819371	−	0.0819371i	0.664950	−	0.746888i	$-0.268453\pi$
$593$	−1.99530	−	1.99530i	−0.0819371	−	0.0819371i	−0.746888	+	0.664950i	$0.768453\pi$
$594$		0			0
$595$	−63.3725	−	43.4762i	−2.59802	−	1.78235i
$596$		−	11.1167i		−	0.455359i
$597$		0			0
$598$	3.54508	−	3.54508i	0.144969	−	0.144969i
$599$	−10.8720			−0.444218			−0.222109	−	0.975022i	$-0.571294\pi$
$599$	−10.8720			−0.444218			−0.222109	+	0.975022i	$0.571294\pi$
$600$		0			0
$601$	−12.4043			−0.505983			−0.252991	−	0.967469i	$-0.581414\pi$
$601$	−12.4043			−0.505983			−0.252991	+	0.967469i	$0.581414\pi$
$602$	−23.0632	+	23.0632i	−0.939986	+	0.939986i
$603$		0			0
$604$		−	12.6297i		−	0.513897i
$605$	14.8830	+	10.2103i	0.605079	+	0.415110i
$606$		0			0
$607$	−29.1414	−	29.1414i	−1.18281	−	1.18281i	−0.979012	−	0.203802i	$-0.934670\pi$
$607$	−29.1414	−	29.1414i	−1.18281	−	1.18281i	−0.203802	−	0.979012i	$-0.565330\pi$
$608$	5.17036	+	5.17036i	0.209686	+	0.209686i
$609$		0			0
$610$	−22.7318	+	4.23290i	−0.920383	+	0.171385i
$611$			11.9401i			0.483045i
$612$		0			0
$613$	−22.8508	+	22.8508i	−0.922935	+	0.922935i	−0.997236	−	0.0743005i	$-0.976328\pi$
$613$	−22.8508	+	22.8508i	−0.922935	+	0.922935i	0.0743005	+	0.997236i	$0.476328\pi$
$614$	4.81443			0.194294
$615$		0			0
$616$	−8.69161			−0.350195
$617$	24.7096	−	24.7096i	0.994771	−	0.994771i	−0.00521527	−	0.999986i	$-0.501660\pi$
$617$	24.7096	−	24.7096i	0.994771	−	0.994771i	0.999986	+	0.00521527i	$0.00166008\pi$
$618$		0			0
$619$			5.50448i			0.221244i	0.993863	+	0.110622i	$0.0352842\pi$
$619$			5.50448i			0.221244i	−0.993863	+	0.110622i	$0.964716\pi$
$620$	−5.12359	+	7.46834i	−0.205768	+	0.299936i
$621$		0			0
$622$	2.70406	+	2.70406i	0.108423	+	0.108423i
$623$	−26.7372	−	26.7372i	−1.07120	−	1.07120i
$624$		0			0
$625$	−18.5221	+	16.7908i	−0.740886	+	0.671631i
$626$		−	12.2109i		−	0.488045i
$627$		0			0
$628$	0.138278	−	0.138278i	0.00551788	−	0.00551788i
$629$	15.0617			0.600549
$630$		0			0
$631$	19.3796			0.771491			0.385746	−	0.922605i	$-0.373944\pi$
$631$	19.3796			0.771491			0.385746	+	0.922605i	$0.373944\pi$
$632$	−6.84694	+	6.84694i	−0.272357	+	0.272357i
$633$		0			0
$634$		−	7.11750i		−	0.282672i
$635$	−2.32740	−	12.4987i	−0.0923600	−	0.495998i
$636$		0			0
$637$	−13.2916	−	13.2916i	−0.526632	−	0.526632i
$638$	−6.80557	−	6.80557i	−0.269435	−	0.269435i
$639$		0			0
$640$	0.409343	+	2.19828i	0.0161807	+	0.0868947i
$641$		−	17.1209i		−	0.676237i	−0.941104	−	0.338118i	$-0.890210\pi$
$641$		−	17.1209i		−	0.676237i	0.941104	−	0.338118i	$-0.109790\pi$
$642$		0			0
$643$	13.0974	−	13.0974i	0.516509	−	0.516509i	−0.400004	−	0.916513i	$-0.630991\pi$
$643$	13.0974	−	13.0974i	0.516509	−	0.516509i	0.916513	+	0.400004i	$0.130991\pi$
$644$	25.4640			1.00342
$645$		0			0
$646$	−49.4790			−1.94672
$647$	8.42447	−	8.42447i	0.331200	−	0.331200i	−0.521842	−	0.853042i	$-0.674755\pi$
$647$	8.42447	−	8.42447i	0.331200	−	0.331200i	0.853042	+	0.521842i	$0.174755\pi$
$648$		0			0
$649$		−	9.18685i		−	0.360616i
$650$	−4.66488	+	1.79970i	−0.182972	+	0.0705901i
$651$		0			0
$652$	13.9766	+	13.9766i	0.547365	+	0.547365i
$653$	4.26386	+	4.26386i	0.166858	+	0.166858i	0.785597	−	0.618739i	$-0.212356\pi$
$653$	4.26386	+	4.26386i	0.166858	+	0.166858i	−0.618739	+	0.785597i	$0.712356\pi$
$654$		0			0
$655$	5.79864	−	8.45232i	0.226572	−	0.330259i
$656$			5.00920i			0.195576i
$657$		0			0
$658$	−42.8824	+	42.8824i	−1.67173	+	1.67173i
$659$	−12.4071			−0.483313			−0.241656	−	0.970362i	$-0.577691\pi$
$659$	−12.4071			−0.483313			−0.241656	+	0.970362i	$0.577691\pi$
$660$		0			0
$661$	5.88278			0.228814			0.114407	−	0.993434i	$-0.463503\pi$
$661$	5.88278			0.228814			0.114407	+	0.993434i	$0.463503\pi$
$662$	−11.0267	+	11.0267i	−0.428566	+	0.428566i
$663$		0			0
$664$		−	4.54340i		−	0.176318i
$665$	−81.6403	+	15.2023i	−3.16588	+	0.589519i
$666$		0			0
$667$	19.9384	+	19.9384i	0.772019	+	0.772019i
$668$	−14.3179	−	14.3179i	−0.553974	−	0.553974i
$669$		0			0
$670$	28.4030	+	19.4856i	1.09730	+	0.752796i
$671$		−	17.6956i		−	0.683131i
$672$		0			0
$673$	10.5670	−	10.5670i	0.407329	−	0.407329i	−0.473477	−	0.880806i	$-0.657001\pi$
$673$	10.5670	−	10.5670i	0.407329	−	0.407329i	0.880806	+	0.473477i	$0.157001\pi$
$674$	6.13133			0.236170
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	−19.4286	+	19.4286i	−0.746701	+	0.746701i	−0.973858	−	0.227157i	$-0.927057\pi$
$677$	−19.4286	+	19.4286i	−0.746701	+	0.746701i	0.227157	+	0.973858i	$0.427057\pi$
$678$		0			0
$679$			24.2201i			0.929483i
$680$	−12.4771	−	8.55983i	−0.478476	−	0.328255i
$681$		0			0
$682$	−4.90110	−	4.90110i	−0.187673	−	0.187673i
$683$	12.7030	+	12.7030i	0.486065	+	0.486065i	0.907062	−	0.420997i	$-0.138320\pi$
$683$	12.7030	+	12.7030i	0.486065	+	0.486065i	−0.420997	+	0.907062i	$0.638320\pi$
$684$		0			0
$685$	37.7381	−	7.02723i	1.44190	−	0.268497i
$686$		−	59.9188i		−	2.28771i
$687$		0			0
$688$	−4.54082	+	4.54082i	−0.173117	+	0.173117i
$689$	1.15635			0.0440534
$690$		0			0
$691$	−9.55542			−0.363505			−0.181753	−	0.983344i	$-0.558177\pi$
$691$	−9.55542			−0.363505			−0.181753	+	0.983344i	$0.558177\pi$
$692$	−0.153769	+	0.153769i	−0.00584542	+	0.00584542i
$693$		0			0
$694$		−	11.1992i		−	0.425116i
$695$	−25.8710	+	37.7105i	−0.981343	+	1.43044i
$696$		0			0
$697$	−23.9683	−	23.9683i	−0.907866	−	0.907866i
$698$	3.01608	+	3.01608i	0.114160	+	0.114160i
$699$		0			0
$700$	−23.2173	−	10.2902i	−0.877530	−	0.388931i
$701$		−	36.7288i		−	1.38723i	−0.720348	−	0.693613i	$-0.756018\pi$
$701$		−	36.7288i		−	1.38723i	0.720348	−	0.693613i	$-0.243982\pi$
$702$		0			0
$703$	11.5083	−	11.5083i	0.434042	−	0.434042i
$704$	−1.71125			−0.0644953
$705$		0			0
$706$	−26.8238			−1.00953
$707$	17.1046	−	17.1046i	0.643283	−	0.643283i
$708$		0			0
$709$			13.0331i			0.489470i	0.969590	+	0.244735i	$0.0787010\pi$
$709$			13.0331i			0.489470i	−0.969590	+	0.244735i	$0.921299\pi$
$710$	0.521531	+	2.80076i	0.0195727	+	0.105111i
$711$		0			0
$712$	−5.26417	−	5.26417i	−0.197283	−	0.197283i
$713$	14.3589	+	14.3589i	0.537744	+	0.537744i
$714$		0			0
$715$	−0.700490	−	3.76182i	−0.0261968	−	0.140684i
$716$			5.18530i			0.193784i
$717$		0			0
$718$	−1.49809	+	1.49809i	−0.0559083	+	0.0559083i
$719$	−7.86257			−0.293224			−0.146612	−	0.989194i	$-0.546837\pi$
$719$	−7.86257			−0.293224			−0.146612	+	0.989194i	$0.546837\pi$
$720$		0			0
$721$	52.6783			1.96184
$722$	−24.3706	+	24.3706i	−0.906979	+	0.906979i
$723$		0			0
$724$			7.46337i			0.277374i
$725$	−10.1220	−	26.2364i	−0.375921	−	0.974397i
$726$		0			0
$727$	−24.7849	−	24.7849i	−0.919223	−	0.919223i	0.0777502	−	0.996973i	$-0.475226\pi$
$727$	−24.7849	−	24.7849i	−0.919223	−	0.919223i	−0.996973	+	0.0777502i	$0.975226\pi$
$728$	−3.59146	−	3.59146i	−0.133108	−	0.133108i
$729$		0			0
$730$	3.73238	−	5.44046i	0.138142	−	0.201361i
$731$		−	43.4544i		−	1.60722i
$732$		0			0
$733$	25.0621	−	25.0621i	0.925690	−	0.925690i	−0.0717338	−	0.997424i	$-0.522853\pi$
$733$	25.0621	−	25.0621i	0.925690	−	0.925690i	0.997424	+	0.0717338i	$0.0228532\pi$
$734$	3.95393			0.145942
$735$		0			0
$736$	5.01350			0.184800
$737$	−18.6395	+	18.6395i	−0.686594	+	0.686594i
$738$		0			0
$739$		−	9.68127i		−	0.356131i	−0.984019	−	0.178066i	$-0.943016\pi$
$739$		−	9.68127i		−	0.356131i	0.984019	−	0.178066i	$-0.0569839\pi$
$740$	4.89296	−	0.911121i	0.179869	−	0.0334935i
$741$		0			0
$742$	4.15298	+	4.15298i	0.152461	+	0.152461i
$743$	−6.68940	−	6.68940i	−0.245410	−	0.245410i	0.573674	−	0.819084i	$-0.305518\pi$
$743$	−6.68940	−	6.68940i	−0.245410	−	0.245410i	−0.819084	+	0.573674i	$0.805518\pi$
$744$		0			0
$745$	20.4978	+	14.0623i	0.750981	+	0.515204i
$746$			18.1551i			0.664705i
$747$		0			0
$748$	8.18813	−	8.18813i	0.299388	−	0.299388i
$749$	13.5087			0.493597
$750$		0			0
$751$	15.0058			0.547569			0.273785	−	0.961791i	$-0.411724\pi$
$751$	15.0058			0.547569			0.273785	+	0.961791i	$0.411724\pi$
$752$	−8.44294	+	8.44294i	−0.307882	+	0.307882i
$753$		0			0
$754$		−	5.62425i		−	0.204823i
$755$	23.2876	+	15.9762i	0.847522	+	0.581435i
$756$		0			0
$757$	−0.776511	−	0.776511i	−0.0282228	−	0.0282228i	0.692855	−	0.721077i	$-0.256353\pi$
$757$	−0.776511	−	0.776511i	−0.0282228	−	0.0282228i	−0.721077	+	0.692855i	$0.756353\pi$
$758$	17.7650	+	17.7650i	0.645253	+	0.645253i
$759$		0			0
$760$	−16.0738	+	2.99311i	−0.583058	+	0.108572i
$761$			7.91919i			0.287070i	0.989645	+	0.143535i	$0.0458470\pi$
$761$			7.91919i			0.287070i	−0.989645	+	0.143535i	$0.954153\pi$
$762$		0			0
$763$	−0.352642	+	0.352642i	−0.0127665	+	0.0127665i
$764$	14.7875			0.534992
$765$		0			0
$766$	7.92368			0.286294
$767$	3.79610	−	3.79610i	0.137069	−	0.137069i
$768$		0			0
$769$			14.7029i			0.530199i	0.964221	+	0.265099i	$0.0854048\pi$
$769$			14.7029i			0.530199i	−0.964221	+	0.265099i	$0.914595\pi$
$770$	10.9946	−	16.0262i	0.396219	−	0.577544i
$771$		0			0
$772$	−3.46825	−	3.46825i	−0.124825	−	0.124825i
$773$	23.3264	+	23.3264i	0.838992	+	0.838992i	0.988726	−	0.149735i	$-0.0478420\pi$
$773$	23.3264	+	23.3264i	0.838992	+	0.838992i	−0.149735	+	0.988726i	$0.547842\pi$
$774$		0			0
$775$	−7.28945	−	18.8945i	−0.261845	−	0.678709i
$776$			4.76859i			0.171183i
$777$		0			0
$778$	−4.30146	+	4.30146i	−0.154215	+	0.154215i
$779$	−36.6272			−1.31231
$780$		0			0
$781$	−2.18026			−0.0780157
$782$	−23.9890	+	23.9890i	−0.857843	+	0.857843i
$783$		0			0
$784$		−	18.7972i		−	0.671327i
$785$	0.0800487	+	0.429883i	0.00285706	+	0.0153432i
$786$		0			0
$787$	−2.70024	−	2.70024i	−0.0962531	−	0.0962531i	0.657341	−	0.753594i	$-0.271681\pi$
$787$	−2.70024	−	2.70024i	−0.0962531	−	0.0962531i	−0.753594	+	0.657341i	$0.771681\pi$
$788$	11.1189	+	11.1189i	0.396096	+	0.396096i
$789$		0			0
$790$	−3.96368	−	21.2860i	−0.141022	−	0.757323i
$791$		−	53.6473i		−	1.90748i
$792$		0			0
$793$	7.31199	−	7.31199i	0.259656	−	0.259656i
$794$	−33.1864			−1.17774
$795$		0			0
$796$	1.17646			0.0416984
$797$	−1.92662	+	1.92662i	−0.0682442	+	0.0682442i	−0.740405	−	0.672161i	$-0.765366\pi$
$797$	−1.92662	+	1.92662i	−0.0682442	+	0.0682442i	0.672161	+	0.740405i	$0.265366\pi$
$798$		0			0
$799$		−	80.7967i		−	2.85838i
$800$	−4.57115	−	2.02598i	−0.161614	−	0.0716294i
$801$		0			0
$802$	13.3134	+	13.3134i	0.470112	+	0.470112i
$803$	3.57031	+	3.57031i	0.125993	+	0.125993i
$804$		0			0
$805$	−32.2112	+	46.9523i	−1.13530	+	1.65485i
$806$		−	4.05036i		−	0.142668i
$807$		0			0
$808$	3.36764	−	3.36764i	0.118473	−	0.118473i
$809$	−26.1622			−0.919813			−0.459906	−	0.887967i	$-0.652117\pi$
$809$	−26.1622			−0.919813			−0.459906	+	0.887967i	$0.652117\pi$
$810$		0			0
$811$	22.3254			0.783951			0.391975	−	0.919976i	$-0.371792\pi$
$811$	22.3254			0.783951			0.391975	+	0.919976i	$0.371792\pi$
$812$	20.1993	−	20.1993i	0.708856	−	0.708856i
$813$		0			0
$814$			3.80893i			0.133503i
$815$	−43.4509	+	8.09102i	−1.52202	+	0.283416i
$816$		0			0
$817$	−33.2024	−	33.2024i	−1.16160	−	1.16160i
$818$	14.3246	+	14.3246i	0.500849	+	0.500849i
$819$		0			0
$820$	−9.23630	−	6.33648i	−0.322546	−	0.221280i
$821$			15.5053i			0.541137i	0.962701	+	0.270569i	$0.0872117\pi$
$821$			15.5053i			0.541137i	−0.962701	+	0.270569i	$0.912788\pi$
$822$		0			0
$823$	−8.72280	+	8.72280i	−0.304058	+	0.304058i	−0.842599	−	0.538541i	$-0.818976\pi$
$823$	−8.72280	+	8.72280i	−0.304058	+	0.304058i	0.538541	+	0.842599i	$0.318976\pi$
$824$	10.3716			0.361312
$825$		0			0
$826$	27.2671			0.948742
$827$	28.0679	−	28.0679i	0.976018	−	0.976018i	−0.0237013	−	0.999719i	$-0.507545\pi$
$827$	28.0679	−	28.0679i	0.976018	−	0.976018i	0.999719	+	0.0237013i	$0.00754506\pi$
$828$		0			0
$829$			27.9728i			0.971536i	0.874088	+	0.485768i	$0.161460\pi$
$829$			27.9728i			0.971536i	−0.874088	+	0.485768i	$0.838540\pi$
$830$	8.37743	+	5.74726i	0.290785	+	0.199490i
$831$		0			0
$832$	−0.707107	−	0.707107i	−0.0245145	−	0.0245145i
$833$	89.9419	+	89.9419i	3.11630	+	3.11630i
$834$		0			0
$835$	44.5119	−	8.28858i	1.54040	−	0.286838i
$836$		−	12.5127i		−	0.432760i
$837$		0			0
$838$	−23.2069	+	23.2069i	−0.801668	+	0.801668i
$839$	52.1327			1.79982			0.899911	−	0.436074i	$-0.143631\pi$
$839$	52.1327			1.79982			0.899911	+	0.436074i	$0.143631\pi$
$840$		0			0
$841$	2.63222			0.0907662
$842$	−26.0125	+	26.0125i	−0.896451	+	0.896451i
$843$		0			0
$844$			2.39291i			0.0823674i
$845$	1.26497	−	1.84387i	0.0435163	−	0.0634310i
$846$		0			0
$847$	−28.9889	−	28.9889i	−0.996069	−	0.996069i
$848$	0.817663	+	0.817663i	0.0280787	+	0.0280787i
$849$		0			0
$850$	31.5664	−	12.1783i	1.08272	−	0.417711i
$851$		−	11.1591i		−	0.382530i
$852$		0			0
$853$	31.5359	−	31.5359i	1.07977	−	1.07977i	0.0832382	−	0.996530i	$-0.473474\pi$
$853$	31.5359	−	31.5359i	1.07977	−	1.07977i	0.996530	−	0.0832382i	$-0.0265262\pi$
$854$	52.5214			1.79725
$855$		0			0
$856$	2.65967			0.0909056
$857$	16.3191	−	16.3191i	0.557451	−	0.557451i	−0.371130	−	0.928581i	$-0.621030\pi$
$857$	16.3191	−	16.3191i	0.557451	−	0.557451i	0.928581	+	0.371130i	$0.121030\pi$
$858$		0			0
$859$			30.6059i			1.04426i	0.852865	+	0.522131i	$0.174863\pi$
$859$			30.6059i			1.04426i	−0.852865	+	0.522131i	$0.825137\pi$
$860$	−2.62867	−	14.1167i	−0.0896369	−	0.481374i
$861$		0			0
$862$	−19.1859	−	19.1859i	−0.653473	−	0.653473i
$863$	17.0492	+	17.0492i	0.580361	+	0.580361i	0.935002	−	0.354641i	$-0.115397\pi$
$863$	17.0492	+	17.0492i	0.580361	+	0.580361i	−0.354641	+	0.935002i	$0.615397\pi$
$864$		0			0
$865$	−0.0890167	−	0.478043i	−0.00302666	−	0.0162540i
$866$			19.3816i			0.658612i
$867$		0			0
$868$	14.5467	−	14.5467i	0.493748	−	0.493748i
$869$	16.5701			0.562103
$870$		0			0
$871$	−15.4040			−0.521946
$872$	−0.0694301	+	0.0694301i	−0.00235120	+	0.00235120i
$873$		0			0
$874$			36.6587i			1.24000i
$875$	48.3428	−	29.7928i	1.63429	−	1.00718i
$876$		0			0
$877$	35.5379	+	35.5379i	1.20003	+	1.20003i	0.974157	+	0.225872i	$0.0725230\pi$
$877$	35.5379	+	35.5379i	1.20003	+	1.20003i	0.225872	+	0.974157i	$0.427477\pi$
$878$	5.48732	+	5.48732i	0.185188	+	0.185188i
$879$		0			0
$880$	2.16468	−	3.15533i	0.0729715	−	0.106366i
$881$		−	0.540239i		−	0.0182011i	−0.999959	−	0.00910055i	$-0.997103\pi$
$881$		−	0.540239i		−	0.0182011i	0.999959	−	0.00910055i	$-0.00289684\pi$
$882$		0			0
$883$	3.42941	−	3.42941i	0.115409	−	0.115409i	−0.647044	−	0.762453i	$-0.723995\pi$
$883$	3.42941	−	3.42941i	0.115409	−	0.115409i	0.762453	+	0.647044i	$0.223995\pi$
$884$	6.76683			0.227593
$885$		0			0
$886$	33.5275			1.12638
$887$	−32.3524	+	32.3524i	−1.08629	+	1.08629i	−0.0903810	+	0.995907i	$0.528808\pi$
$887$	−32.3524	+	32.3524i	−1.08629	+	1.08629i	−0.995907	+	0.0903810i	$0.971192\pi$
$888$		0			0
$889$			28.8781i			0.968542i
$890$	16.3654	−	3.04742i	0.548571	−	0.102150i
$891$		0			0
$892$	−6.52830	−	6.52830i	−0.218584	−	0.218584i
$893$	−61.7347	−	61.7347i	−2.06587	−	2.06587i
$894$		0			0
$895$	−9.56101	−	6.55925i	−0.319589	−	0.219252i
$896$		−	5.07909i		−	0.169680i
$897$		0			0
$898$	1.94771	−	1.94771i	0.0649960	−	0.0649960i
$899$	22.7803			0.759765
$900$		0			0
$901$	−7.82482			−0.260683
$902$	6.06132	−	6.06132i	0.201820	−	0.201820i
$903$		0			0
$904$		−	10.5624i		−	0.351300i
$905$	−13.7615	−	9.44094i	−0.457447	−	0.313827i
$906$		0			0
$907$	1.12583	+	1.12583i	0.0373826	+	0.0373826i	0.725551	−	0.688168i	$-0.241585\pi$
$907$	1.12583	+	1.12583i	0.0373826	+	0.0373826i	−0.688168	+	0.725551i	$0.741585\pi$
$908$	3.89911	+	3.89911i	0.129396	+	0.129396i
$909$		0			0
$910$	11.1653	−	2.07909i	0.370125	−	0.0689212i
$911$		−	13.3271i		−	0.441548i	−0.975325	−	0.220774i	$-0.929142\pi$
$911$		−	13.3271i		−	0.441548i	0.975325	−	0.220774i	$-0.0708583\pi$
$912$		0			0
$913$	−5.49769	+	5.49769i	−0.181947	+	0.181947i
$914$	−30.6045			−1.01231
$915$		0			0
$916$	8.58262			0.283578
$917$	−16.4633	+	16.4633i	−0.543666	+	0.543666i
$918$		0			0
$919$			15.9159i			0.525018i	0.964930	+	0.262509i	$0.0845499\pi$
$919$			15.9159i			0.525018i	−0.964930	+	0.262509i	$0.915450\pi$
$920$	−6.34193	+	9.24424i	−0.209087	+	0.304774i
$921$		0			0
$922$	−23.0493	−	23.0493i	−0.759090	−	0.759090i
$923$	−0.900903	−	0.900903i	−0.0296536	−	0.0296536i
$924$		0			0
$925$	−4.50946	+	10.1745i	−0.148270	+	0.334536i
$926$		−	16.5686i		−	0.544479i
$927$		0			0
$928$	3.97695	−	3.97695i	0.130550	−	0.130550i
$929$	44.3230			1.45419			0.727096	−	0.686536i	$-0.240870\pi$
$929$	44.3230			1.45419			0.727096	+	0.686536i	$0.240870\pi$
$930$		0			0
$931$	137.445			4.50457
$932$	−12.6344	+	12.6344i	−0.413855	+	0.413855i
$933$		0			0
$934$		−	4.29002i		−	0.140374i
$935$	4.74009	+	25.4556i	0.155018	+	0.832486i
$936$		0			0
$937$	30.0986	+	30.0986i	0.983279	+	0.983279i	0.999862	−	0.0165833i	$-0.00527886\pi$
$937$	30.0986	+	30.0986i	0.983279	+	0.983279i	−0.0165833	+	0.999862i	$0.505279\pi$
$938$	−55.3229	−	55.3229i	−1.80636	−	1.80636i
$939$		0			0
$940$	−4.88760	−	26.2477i	−0.159416	−	0.856107i
$941$		−	35.0136i		−	1.14141i	−0.821154	−	0.570706i	$-0.806670\pi$
$941$		−	35.0136i		−	1.14141i	0.821154	−	0.570706i	$-0.193330\pi$
$942$		0			0
$943$	−17.7580	+	17.7580i	−0.578280	+	0.578280i
$944$	5.36849			0.174730
$945$		0			0
$946$	10.9891			0.357287
$947$	−9.31018	+	9.31018i	−0.302540	+	0.302540i	−0.842007	−	0.539467i	$-0.818626\pi$
$947$	−9.31018	+	9.31018i	−0.302540	+	0.302540i	0.539467	+	0.842007i	$0.318626\pi$
$948$		0			0
$949$			2.95057i			0.0957796i
$950$	14.8140	−	33.4242i	0.480629	−	1.08442i
$951$		0			0
$952$	24.3028	+	24.3028i	0.787658	+	0.787658i
$953$	23.5750	+	23.5750i	0.763669	+	0.763669i	0.976984	−	0.213315i	$-0.0684260\pi$
$953$	23.5750	+	23.5750i	0.763669	+	0.763669i	−0.213315	+	0.976984i	$0.568426\pi$
$954$		0			0
$955$	−18.7057	+	27.2662i	−0.605303	+	0.882313i
$956$		−	1.24186i		−	0.0401645i
$957$		0			0
$958$	−4.38626	+	4.38626i	−0.141714	+	0.141714i
$959$	−87.1932			−2.81562
$960$		0			0
$961$	−14.5945			−0.470792
$962$	−1.57389	+	1.57389i	−0.0507442	+	0.0507442i
$963$		0			0
$964$		−	28.1888i		−	0.907899i
$965$	10.7822	−	2.00777i	0.347092	−	0.0646323i
$966$		0			0
$967$	−27.5665	−	27.5665i	−0.886479	−	0.886479i	0.107704	−	0.994183i	$-0.465650\pi$
$967$	−27.5665	−	27.5665i	−0.886479	−	0.886479i	−0.994183	+	0.107704i	$0.965650\pi$
$968$	−5.70749	−	5.70749i	−0.183446	−	0.183446i
$969$		0			0
$970$	−8.79266	−	6.03213i	−0.282315	−	0.193680i
$971$			50.8374i			1.63145i	0.578440	+	0.815725i	$0.303662\pi$
$971$			50.8374i			1.63145i	−0.578440	+	0.815725i	$0.696338\pi$
$972$		0			0
$973$	73.4520	−	73.4520i	2.35476	−	2.35476i
$974$	−26.8425			−0.860091
$975$		0			0
$976$	10.3407			0.330998
$977$	−25.0969	+	25.0969i	−0.802919	+	0.802919i	−0.983551	−	0.180631i	$-0.942186\pi$
$977$	−25.0969	+	25.0969i	−0.802919	+	0.802919i	0.180631	+	0.983551i	$0.442186\pi$
$978$		0			0
$979$			12.7397i			0.407162i
$980$	34.6595	+	23.7778i	1.10716	+	0.759555i
$981$		0			0
$982$	0.571535	+	0.571535i	0.0182384	+	0.0182384i
$983$	9.41214	+	9.41214i	0.300201	+	0.300201i	0.841092	−	0.540892i	$-0.181913\pi$
$983$	9.41214	+	9.41214i	0.300201	+	0.300201i	−0.540892	+	0.841092i	$0.681913\pi$
$984$		0			0
$985$	−34.5670	+	6.43673i	−1.10140	+	0.205091i
$986$			38.0583i			1.21202i
$987$		0			0
$988$	5.17036	−	5.17036i	0.164491	−	0.164491i
$989$	−32.1951			−1.02375
$990$		0			0
$991$	5.13968			0.163267			0.0816337	−	0.996662i	$-0.473986\pi$
$991$	5.13968			0.163267			0.0816337	+	0.996662i	$0.473986\pi$
$992$	2.86404	−	2.86404i	0.0909334	−	0.0909334i
$993$		0			0
$994$		−	6.47111i		−	0.205251i
$995$	−1.48818	+	2.16923i	−0.0471785	+	0.0687692i
$996$		0			0
$997$	−17.9263	−	17.9263i	−0.567732	−	0.567732i	0.363760	−	0.931493i	$-0.381493\pi$
$997$	−17.9263	−	17.9263i	−0.567732	−	0.567732i	−0.931493	+	0.363760i	$0.881493\pi$
$998$	−5.30578	−	5.30578i	−0.167951	−	0.167951i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.o.c.287.5	yes	12
3.2	odd	2		1170.2.o.a.287.2	yes	12
5.3	odd	4		1170.2.o.a.53.2	✓	12
15.8	even	4	inner	1170.2.o.c.53.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.o.a.53.2	✓	12	5.3	odd	4
1170.2.o.a.287.2	yes	12	3.2	odd	2
1170.2.o.c.53.5	yes	12	15.8	even	4	inner
1170.2.o.c.287.5	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.84387 + 1.26497i) q^{5} +(-3.59146 - 3.59146i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19828 - 0.409343i) q^{10} +1.71125i q^{11} +(-0.707107 + 0.707107i) q^{13} -5.07909 q^{14} -1.00000 q^{16} +(4.78487 - 4.78487i) q^{17} -7.31199i q^{19} +(1.26497 - 1.84387i) q^{20} +(1.21004 + 1.21004i) q^{22} +(-3.54508 - 3.54508i) q^{23} +(1.79970 + 4.66488i) q^{25} +1.00000i q^{26} +(-3.59146 + 3.59146i) q^{28} -5.62425 q^{29} -4.05036 q^{31} +(-0.707107 + 0.707107i) q^{32} -6.76683i q^{34} +(-2.07909 - 11.1653i) q^{35} +(1.57389 + 1.57389i) q^{37} +(-5.17036 - 5.17036i) q^{38} +(-0.409343 - 2.19828i) q^{40} -5.00920i q^{41} +(4.54082 - 4.54082i) q^{43} +1.71125 q^{44} -5.01350 q^{46} +(8.44294 - 8.44294i) q^{47} +18.7972i q^{49} +(4.57115 + 2.02598i) q^{50} +(0.707107 + 0.707107i) q^{52} +(-0.817663 - 0.817663i) q^{53} +(-2.16468 + 3.15533i) q^{55} +5.07909i q^{56} +(-3.97695 + 3.97695i) q^{58} -5.36849 q^{59} -10.3407 q^{61} +(-2.86404 + 2.86404i) q^{62} +1.00000i q^{64} +(-2.19828 + 0.409343i) q^{65} +(10.8923 + 10.8923i) q^{67} +(-4.78487 - 4.78487i) q^{68} +(-9.36517 - 6.42490i) q^{70} +1.27407i q^{71} +(2.08637 - 2.08637i) q^{73} +2.22581 q^{74} -7.31199 q^{76} +(6.14590 - 6.14590i) q^{77} -9.68304i q^{79} +(-1.84387 - 1.26497i) q^{80} +(-3.54204 - 3.54204i) q^{82} +(3.21267 + 3.21267i) q^{83} +(14.8754 - 2.76995i) q^{85} -6.42168i q^{86} +(1.21004 - 1.21004i) q^{88} +7.44465 q^{89} +5.07909 q^{91} +(-3.54508 + 3.54508i) q^{92} -11.9401i q^{94} +(9.24945 - 13.4823i) q^{95} +(-3.37190 - 3.37190i) q^{97} +(13.2916 + 13.2916i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 4 q^{7} - 8 q^{14} - 12 q^{16} + 8 q^{17} + 4 q^{20} - 4 q^{22} + 12 q^{23} + 8 q^{25} - 4 q^{28} - 32 q^{29} - 16 q^{31} + 28 q^{35} + 16 q^{37} - 16 q^{38} - 4 q^{40} + 8 q^{43} + 64 q^{47}+ \cdots + 16 q^{98}+O(q^{100}) \) 12 * q + 4 * q^5 - 4 * q^7 - 8 * q^14 - 12 * q^16 + 8 * q^17 + 4 * q^20 - 4 * q^22 + 12 * q^23 + 8 * q^25 - 4 * q^28 - 32 * q^29 - 16 * q^31 + 28 * q^35 + 16 * q^37 - 16 * q^38 - 4 * q^40 + 8 * q^43 + 64 * q^47 + 16 * q^50 + 36 * q^53 - 36 * q^55 - 12 * q^58 - 48 * q^59 - 32 * q^61 - 4 * q^62 + 4 * q^67 - 8 * q^68 - 8 * q^70 + 16 * q^74 - 16 * q^76 + 40 * q^77 - 4 * q^80 - 8 * q^82 - 16 * q^83 + 36 * q^85 - 4 * q^88 - 64 * q^89 + 8 * q^91 + 12 * q^92 + 12 * q^95 - 32 * q^97 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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