LMFDB - Embedded newform 1190.2.e.g.239.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(239,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.239"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,-2,-4,0,0,-14,4,-14,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 28x^{12} + 292x^{10} + 1457x^{8} + 3664x^{6} + 4360x^{4} + 1856x^{2} + 16 $ x^14 + 28x^12 + 292x^10 + 1457x^8 + 3664x^6 + 4360x^4 + 1856x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.12
Root			$1.58141i$ of defining polynomial
Character	$\chi$	$=$	1190.239
Dual form			1190.2.e.g.239.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.58141i q^{3} -1.00000 q^{4} +(-2.13915 - 0.651165i) q^{5} -1.58141 q^{6} -1.00000i q^{7} -1.00000i q^{8} +0.499141 q^{9} +(0.651165 - 2.13915i) q^{10} +2.47946 q^{11} -1.58141i q^{12} -1.48483i q^{13} +1.00000 q^{14} +(1.02976 - 3.38288i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +0.499141i q^{18} +4.85321 q^{19} +(2.13915 + 0.651165i) q^{20} +1.58141 q^{21} +2.47946i q^{22} -4.11626i q^{23} +1.58141 q^{24} +(4.15197 + 2.78589i) q^{25} +1.48483 q^{26} +5.53358i q^{27} +1.00000i q^{28} +3.24982 q^{29} +(3.38288 + 1.02976i) q^{30} -4.93212 q^{31} +1.00000i q^{32} +3.92105i q^{33} +1.00000 q^{34} +(-0.651165 + 2.13915i) q^{35} -0.499141 q^{36} -8.92252i q^{37} +4.85321i q^{38} +2.34812 q^{39} +(-0.651165 + 2.13915i) q^{40} +9.41904 q^{41} +1.58141i q^{42} +10.3912i q^{43} -2.47946 q^{44} +(-1.06774 - 0.325023i) q^{45} +4.11626 q^{46} +8.26867i q^{47} +1.58141i q^{48} -1.00000 q^{49} +(-2.78589 + 4.15197i) q^{50} +1.58141 q^{51} +1.48483i q^{52} +4.09224i q^{53} -5.53358 q^{54} +(-5.30396 - 1.61454i) q^{55} -1.00000 q^{56} +7.67492i q^{57} +3.24982i q^{58} -9.51108 q^{59} +(-1.02976 + 3.38288i) q^{60} +9.86895 q^{61} -4.93212i q^{62} -0.499141i q^{63} -1.00000 q^{64} +(-0.966869 + 3.17628i) q^{65} -3.92105 q^{66} -15.8048i q^{67} +1.00000i q^{68} +6.50950 q^{69} +(-2.13915 - 0.651165i) q^{70} +11.7828 q^{71} -0.499141i q^{72} +10.4393i q^{73} +8.92252 q^{74} +(-4.40563 + 6.56596i) q^{75} -4.85321 q^{76} -2.47946i q^{77} +2.34812i q^{78} +15.7552 q^{79} +(-2.13915 - 0.651165i) q^{80} -7.25344 q^{81} +9.41904i q^{82} +16.9990i q^{83} -1.58141 q^{84} +(-0.651165 + 2.13915i) q^{85} -10.3912 q^{86} +5.13930i q^{87} -2.47946i q^{88} -15.3955 q^{89} +(0.325023 - 1.06774i) q^{90} -1.48483 q^{91} +4.11626i q^{92} -7.79970i q^{93} -8.26867 q^{94} +(-10.3818 - 3.16024i) q^{95} -1.58141 q^{96} -14.0489i q^{97} -1.00000i q^{98} +1.23760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} + 4 q^{10} - 14 q^{11} + 14 q^{14} + 2 q^{15} + 14 q^{16} + 4 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{24} + 14 q^{25} + 2 q^{26} + 20 q^{29} - 2 q^{30} - 36 q^{31}+ \cdots + 88 q^{99}+O(q^{100}) $ 14 * q - 14 * q^4 - 2 * q^5 - 4 * q^6 - 14 * q^9 + 4 * q^10 - 14 * q^11 + 14 * q^14 + 2 * q^15 + 14 * q^16 + 4 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^24 + 14 * q^25 + 2 * q^26 + 20 * q^29 - 2 * q^30 - 36 * q^31 + 14 * q^34 - 4 * q^35 + 14 * q^36 + 50 * q^39 - 4 * q^40 + 34 * q^41 + 14 * q^44 + 8 * q^45 - 54 * q^46 - 14 * q^49 + 8 * q^50 + 4 * q^51 + 34 * q^54 - 16 * q^55 - 14 * q^56 - 2 * q^60 + 2 * q^61 - 14 * q^64 - 32 * q^65 - 16 * q^66 - 6 * q^69 - 2 * q^70 - 22 * q^71 + 24 * q^74 - 40 * q^75 - 4 * q^76 + 52 * q^79 - 2 * q^80 + 22 * q^81 - 4 * q^84 - 4 * q^85 - 14 * q^86 - 42 * q^89 - 38 * q^90 - 2 * q^91 + 16 * q^94 - 46 * q^95 - 4 * q^96 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1190\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			1.58141i			0.913028i	0.889716	+	0.456514i	$0.150902\pi$
$3$			1.58141i			0.913028i	−0.889716	+	0.456514i	$0.849098\pi$
$4$	−1.00000			−0.500000
$5$	−2.13915	−	0.651165i	−0.956659	−	0.291210i
$5$	−2.13915	−	0.651165i	−0.956659	−	0.291210i
$6$	−1.58141			−0.645608
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	0.499141			0.166380
$10$	0.651165	−	2.13915i	0.205917	−	0.676460i
$11$	2.47946			0.747587			0.373793	−	0.927512i	$-0.378057\pi$
$11$	2.47946			0.747587			0.373793	+	0.927512i	$0.378057\pi$
$12$		−	1.58141i		−	0.456514i
$13$		−	1.48483i		−	0.411817i	−0.978571	−	0.205909i	$-0.933985\pi$
$13$		−	1.48483i		−	0.411817i	0.978571	−	0.205909i	$-0.0660150\pi$
$14$	1.00000			0.267261
$15$	1.02976	−	3.38288i	0.265883	−	0.873456i
$16$	1.00000			0.250000
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$			0.499141i			0.117649i
$19$	4.85321			1.11340			0.556702	−	0.830713i	$-0.312067\pi$
$19$	4.85321			1.11340			0.556702	+	0.830713i	$0.312067\pi$
$20$	2.13915	+	0.651165i	0.478330	+	0.145605i
$21$	1.58141			0.345092
$22$			2.47946i			0.528624i
$23$		−	4.11626i		−	0.858299i	−0.903233	−	0.429150i	$-0.858813\pi$
$23$		−	4.11626i		−	0.858299i	0.903233	−	0.429150i	$-0.141187\pi$
$24$	1.58141			0.322804
$25$	4.15197	+	2.78589i	0.830393	+	0.557178i
$26$	1.48483			0.291199
$27$			5.53358i			1.06494i
$28$			1.00000i			0.188982i
$29$	3.24982			0.603477			0.301738	−	0.953391i	$-0.402433\pi$
$29$	3.24982			0.603477			0.301738	+	0.953391i	$0.402433\pi$
$30$	3.38288	+	1.02976i	0.617627	+	0.188008i
$31$	−4.93212			−0.885834			−0.442917	−	0.896563i	$-0.646056\pi$
$31$	−4.93212			−0.885834			−0.442917	+	0.896563i	$0.646056\pi$
$32$			1.00000i			0.176777i
$33$			3.92105i			0.682568i
$34$	1.00000			0.171499
$35$	−0.651165	+	2.13915i	−0.110067	+	0.361583i
$36$	−0.499141			−0.0831901
$37$		−	8.92252i		−	1.46685i	−0.679768	−	0.733427i	$-0.737920\pi$
$37$		−	8.92252i		−	1.46685i	0.679768	−	0.733427i	$-0.262080\pi$
$38$			4.85321i			0.787295i
$39$	2.34812			0.376001
$40$	−0.651165	+	2.13915i	−0.102958	+	0.338230i
$41$	9.41904			1.47101			0.735503	−	0.677521i	$-0.236946\pi$
$41$	9.41904			1.47101			0.735503	+	0.677521i	$0.236946\pi$
$42$			1.58141i			0.244017i
$43$			10.3912i			1.58465i	0.610099	+	0.792325i	$0.291130\pi$
$43$			10.3912i			1.58465i	−0.610099	+	0.792325i	$0.708870\pi$
$44$	−2.47946			−0.373793
$45$	−1.06774	−	0.325023i	−0.159169	−	0.0484516i
$46$	4.11626			0.606909
$47$			8.26867i			1.20611i	0.797700	+	0.603055i	$0.206050\pi$
$47$			8.26867i			1.20611i	−0.797700	+	0.603055i	$0.793950\pi$
$48$			1.58141i			0.228257i
$49$	−1.00000			−0.142857
$50$	−2.78589	+	4.15197i	−0.393984	+	0.587177i
$51$	1.58141			0.221442
$52$			1.48483i			0.205909i
$53$			4.09224i			0.562112i	0.959691	+	0.281056i	$0.0906847\pi$
$53$			4.09224i			0.562112i	−0.959691	+	0.281056i	$0.909315\pi$
$54$	−5.53358			−0.753025
$55$	−5.30396	−	1.61454i	−0.715186	−	0.217705i
$56$	−1.00000			−0.133631
$57$			7.67492i			1.01657i
$58$			3.24982i			0.426722i
$59$	−9.51108			−1.23824			−0.619119	−	0.785297i	$-0.712510\pi$
$59$	−9.51108			−1.23824			−0.619119	+	0.785297i	$0.712510\pi$
$60$	−1.02976	+	3.38288i	−0.132941	+	0.436728i
$61$	9.86895			1.26359			0.631795	−	0.775136i	$-0.282318\pi$
$61$	9.86895			1.26359			0.631795	+	0.775136i	$0.282318\pi$
$62$		−	4.93212i		−	0.626379i
$63$		−	0.499141i		−	0.0628858i
$64$	−1.00000			−0.125000
$65$	−0.966869	+	3.17628i	−0.119925	+	0.393969i
$66$	−3.92105			−0.482648
$67$		−	15.8048i		−	1.93086i	−0.260657	−	0.965431i	$-0.583939\pi$
$67$		−	15.8048i		−	1.93086i	0.260657	−	0.965431i	$-0.416061\pi$
$68$			1.00000i			0.121268i
$69$	6.50950			0.783651
$70$	−2.13915	−	0.651165i	−0.255678	−	0.0778292i
$71$	11.7828			1.39836			0.699181	−	0.714944i	$-0.253548\pi$
$71$	11.7828			1.39836			0.699181	+	0.714944i	$0.253548\pi$
$72$		−	0.499141i		−	0.0588243i
$73$			10.4393i			1.22183i	0.791697	+	0.610914i	$0.209198\pi$
$73$			10.4393i			1.22183i	−0.791697	+	0.610914i	$0.790802\pi$
$74$	8.92252			1.03722
$75$	−4.40563	+	6.56596i	−0.508719	+	0.758172i
$76$	−4.85321			−0.556702
$77$		−	2.47946i		−	0.282561i
$78$			2.34812i			0.265873i
$79$	15.7552			1.77260			0.886298	−	0.463115i	$-0.153268\pi$
$79$	15.7552			1.77260			0.886298	+	0.463115i	$0.153268\pi$
$80$	−2.13915	−	0.651165i	−0.239165	−	0.0728025i
$81$	−7.25344			−0.805937
$82$			9.41904i			1.04016i
$83$			16.9990i			1.86588i	0.360032	+	0.932940i	$0.382766\pi$
$83$			16.9990i			1.86588i	−0.360032	+	0.932940i	$0.617234\pi$
$84$	−1.58141			−0.172546
$85$	−0.651165	+	2.13915i	−0.0706288	+	0.232024i
$86$	−10.3912			−1.12052
$87$			5.13930i			0.550991i
$88$		−	2.47946i		−	0.264312i
$89$	−15.3955			−1.63192			−0.815961	−	0.578107i	$-0.803792\pi$
$89$	−15.3955			−1.63192			−0.815961	+	0.578107i	$0.803792\pi$
$90$	0.325023	−	1.06774i	0.0342604	−	0.112550i
$91$	−1.48483			−0.155652
$92$			4.11626i			0.429150i
$93$		−	7.79970i		−	0.808791i
$94$	−8.26867			−0.852849
$95$	−10.3818	−	3.16024i	−1.06515	−	0.324234i
$96$	−1.58141			−0.161402
$97$		−	14.0489i		−	1.42645i	−0.700933	−	0.713227i	$-0.747233\pi$
$97$		−	14.0489i		−	1.42645i	0.700933	−	0.713227i	$-0.252767\pi$
$98$		−	1.00000i		−	0.101015i
$99$	1.23760			0.124384
$100$	−4.15197	−	2.78589i	−0.415197	−	0.278589i
$101$	8.31807			0.827679			0.413840	−	0.910350i	$-0.364187\pi$
$101$	8.31807			0.827679			0.413840	+	0.910350i	$0.364187\pi$
$102$			1.58141i			0.156583i
$103$		−	16.1282i		−	1.58915i	−0.607163	−	0.794577i	$-0.707693\pi$
$103$		−	16.1282i		−	1.58915i	0.607163	−	0.794577i	$-0.292307\pi$
$104$	−1.48483			−0.145599
$105$	−3.38288	−	1.02976i	−0.330135	−	0.100494i
$106$	−4.09224			−0.397473
$107$			2.19983i			0.212665i	0.994331	+	0.106333i	$0.0339108\pi$
$107$			2.19983i			0.212665i	−0.994331	+	0.106333i	$0.966089\pi$
$108$		−	5.53358i		−	0.532469i
$109$	4.13495			0.396057			0.198028	−	0.980196i	$-0.436546\pi$
$109$	4.13495			0.396057			0.198028	+	0.980196i	$0.436546\pi$
$110$	1.61454	−	5.30396i	0.153941	−	0.505713i
$111$	14.1102			1.33928
$112$		−	1.00000i		−	0.0944911i
$113$		−	3.67558i		−	0.345769i	−0.984942	−	0.172885i	$-0.944691\pi$
$113$		−	3.67558i		−	0.345769i	0.984942	−	0.172885i	$-0.0553088\pi$
$114$	−7.67492			−0.718822
$115$	−2.68037	+	8.80532i	−0.249945	+	0.821100i
$116$	−3.24982			−0.301738
$117$		−	0.741138i		−	0.0685182i
$118$		−	9.51108i		−	0.875566i
$119$	−1.00000			−0.0916698
$120$	−3.38288	−	1.02976i	−0.308813	−	0.0940038i
$121$	−4.85225			−0.441114
$122$			9.86895i			0.893493i
$123$			14.8954i			1.34307i
$124$	4.93212			0.442917
$125$	−7.06763	−	8.66306i	−0.632148	−	0.774848i
$126$	0.499141			0.0444670
$127$			0.539711i			0.0478916i	0.999713	+	0.0239458i	$0.00762291\pi$
$127$			0.539711i			0.0478916i	−0.999713	+	0.0239458i	$0.992377\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−16.4328			−1.44683
$130$	−3.17628	−	0.966869i	−0.278578	−	0.0848000i
$131$	−8.07474			−0.705493			−0.352747	−	0.935719i	$-0.614752\pi$
$131$	−8.07474			−0.705493			−0.352747	+	0.935719i	$0.614752\pi$
$132$		−	3.92105i		−	0.341284i
$133$		−	4.85321i		−	0.420827i
$134$	15.8048			1.36533
$135$	3.60327	−	11.8372i	0.310121	−	1.01878i
$136$	−1.00000			−0.0857493
$137$		−	10.1767i		−	0.869451i	−0.900563	−	0.434725i	$-0.856845\pi$
$137$		−	10.1767i		−	0.869451i	0.900563	−	0.434725i	$-0.143155\pi$
$138$			6.50950i			0.554125i
$139$	17.9150			1.51953			0.759767	−	0.650196i	$-0.225313\pi$
$139$	17.9150			1.51953			0.759767	+	0.650196i	$0.225313\pi$
$140$	0.651165	−	2.13915i	0.0550335	−	0.180792i
$141$	−13.0762			−1.10121
$142$			11.7828i			0.988792i
$143$		−	3.68158i		−	0.307869i
$144$	0.499141			0.0415950
$145$	−6.95187	−	2.11617i	−0.577321	−	0.175738i
$146$	−10.4393			−0.863963
$147$		−	1.58141i		−	0.130433i
$148$			8.92252i			0.733427i
$149$	5.62465			0.460789			0.230395	−	0.973097i	$-0.425998\pi$
$149$	5.62465			0.460789			0.230395	+	0.973097i	$0.425998\pi$
$150$	−6.56596	−	4.40563i	−0.536109	−	0.359718i
$151$	17.0093			1.38419			0.692097	−	0.721805i	$-0.256687\pi$
$151$	17.0093			1.38419			0.692097	+	0.721805i	$0.256687\pi$
$152$		−	4.85321i		−	0.393647i
$153$		−	0.499141i		−	0.0403531i
$154$	2.47946			0.199801
$155$	10.5506	+	3.21162i	0.847441	+	0.257964i
$156$	−2.34812			−0.188000
$157$		−	8.76768i		−	0.699737i	−0.936799	−	0.349869i	$-0.886226\pi$
$157$		−	8.76768i		−	0.699737i	0.936799	−	0.349869i	$-0.113774\pi$
$158$			15.7552i			1.25341i
$159$	−6.47151			−0.513224
$160$	0.651165	−	2.13915i	0.0514792	−	0.169115i
$161$	−4.11626			−0.324407
$162$		−	7.25344i		−	0.569884i
$163$			15.9342i			1.24807i	0.781398	+	0.624033i	$0.214507\pi$
$163$			15.9342i			1.24807i	−0.781398	+	0.624033i	$0.785493\pi$
$164$	−9.41904			−0.735503
$165$	2.55325	−	8.38774i	0.198771	−	0.652984i
$166$	−16.9990			−1.31938
$167$		−	5.93877i		−	0.459555i	−0.973243	−	0.229778i	$-0.926200\pi$
$167$		−	5.93877i		−	0.459555i	0.973243	−	0.229778i	$-0.0737999\pi$
$168$		−	1.58141i		−	0.122008i
$169$	10.7953			0.830407
$170$	−2.13915	−	0.651165i	−0.164066	−	0.0499421i
$171$	2.42243			0.185248
$172$		−	10.3912i		−	0.792325i
$173$			19.9065i			1.51346i	0.653726	+	0.756731i	$0.273205\pi$
$173$			19.9065i			1.51346i	−0.653726	+	0.756731i	$0.726795\pi$
$174$	−5.13930			−0.389609
$175$	2.78589	−	4.15197i	0.210593	−	0.313859i
$176$	2.47946			0.186897
$177$		−	15.0409i		−	1.13055i
$178$		−	15.3955i		−	1.15394i
$179$	13.0850			0.978021			0.489011	−	0.872278i	$-0.337358\pi$
$179$	13.0850			0.978021			0.489011	+	0.872278i	$0.337358\pi$
$180$	1.06774	+	0.325023i	0.0795846	+	0.0242258i
$181$	5.13376			0.381589			0.190795	−	0.981630i	$-0.438894\pi$
$181$	5.13376			0.381589			0.190795	+	0.981630i	$0.438894\pi$
$182$		−	1.48483i		−	0.110063i
$183$			15.6069i			1.15369i
$184$	−4.11626			−0.303455
$185$	−5.81004	+	19.0867i	−0.427163	+	1.40328i
$186$	7.79970			0.571902
$187$		−	2.47946i		−	0.181316i
$188$		−	8.26867i		−	0.603055i
$189$	5.53358			0.402509
$190$	3.16024	−	10.3818i	0.229268	−	0.753173i
$191$	−19.5123			−1.41186			−0.705932	−	0.708280i	$-0.749471\pi$
$191$	−19.5123			−1.41186			−0.705932	+	0.708280i	$0.749471\pi$
$192$		−	1.58141i		−	0.114128i
$193$			2.08248i			0.149900i	0.997187	+	0.0749501i	$0.0238797\pi$
$193$			2.08248i			0.149900i	−0.997187	+	0.0749501i	$0.976120\pi$
$194$	14.0489			1.00865
$195$	−5.02300	−	1.52902i	−0.359704	−	0.109495i
$196$	1.00000			0.0714286
$197$			6.86555i			0.489150i	0.969630	+	0.244575i	$0.0786484\pi$
$197$			6.86555i			0.489150i	−0.969630	+	0.244575i	$0.921352\pi$
$198$			1.23760i			0.0879525i
$199$	7.97203			0.565122			0.282561	−	0.959249i	$-0.408816\pi$
$199$	7.97203			0.565122			0.282561	+	0.959249i	$0.408816\pi$
$200$	2.78589	−	4.15197i	0.196992	−	0.293588i
$201$	24.9939			1.76293
$202$			8.31807i			0.585258i
$203$		−	3.24982i		−	0.228093i
$204$	−1.58141			−0.110721
$205$	−20.1488	−	6.13335i	−1.40725	−	0.428372i
$206$	16.1282			1.12370
$207$		−	2.05459i		−	0.142804i
$208$		−	1.48483i		−	0.102954i
$209$	12.0334			0.832365
$210$	1.02976	−	3.38288i	0.0710602	−	0.233441i
$211$	9.87489			0.679815			0.339908	−	0.940459i	$-0.389604\pi$
$211$	9.87489			0.679815			0.339908	+	0.940459i	$0.389604\pi$
$212$		−	4.09224i		−	0.281056i
$213$			18.6335i			1.27674i
$214$	−2.19983			−0.150377
$215$	6.76642	−	22.2285i	0.461466	−	1.51597i
$216$	5.53358			0.376512
$217$			4.93212i			0.334814i
$218$			4.13495i			0.280054i
$219$	−16.5088			−1.11556
$220$	5.30396	+	1.61454i	0.357593	+	0.108852i
$221$	−1.48483			−0.0998803
$222$			14.1102i			0.947013i
$223$			0.615959i			0.0412477i	0.999787	+	0.0206238i	$0.00656524\pi$
$223$			0.615959i			0.0412477i	−0.999787	+	0.0206238i	$0.993435\pi$
$224$	1.00000			0.0668153
$225$	2.07242	+	1.39055i	0.138161	+	0.0927033i
$226$	3.67558			0.244496
$227$		−	13.0080i		−	0.863370i	−0.902025	−	0.431685i	$-0.857919\pi$
$227$		−	13.0080i		−	0.863370i	0.902025	−	0.431685i	$-0.142081\pi$
$228$		−	7.67492i		−	0.508284i
$229$	−16.7881			−1.10939			−0.554695	−	0.832054i	$-0.687165\pi$
$229$	−16.7881			−1.10939			−0.554695	+	0.832054i	$0.687165\pi$
$230$	−8.80532	−	2.68037i	−0.580605	−	0.176738i
$231$	3.92105			0.257986
$232$		−	3.24982i		−	0.213361i
$233$		−	7.50071i		−	0.491388i	−0.969347	−	0.245694i	$-0.920984\pi$
$233$		−	7.50071i		−	0.491388i	0.969347	−	0.245694i	$-0.0790158\pi$
$234$	0.741138			0.0484497
$235$	5.38428	−	17.6880i	0.351231	−	1.15384i
$236$	9.51108			0.619119
$237$			24.9154i			1.61843i
$238$		−	1.00000i		−	0.0648204i
$239$	7.82561			0.506196			0.253098	−	0.967441i	$-0.418550\pi$
$239$	7.82561			0.506196			0.253098	+	0.967441i	$0.418550\pi$
$240$	1.02976	−	3.38288i	0.0664707	−	0.218364i
$241$	−22.5508			−1.45263			−0.726313	−	0.687364i	$-0.758768\pi$
$241$	−22.5508			−1.45263			−0.726313	+	0.687364i	$0.758768\pi$
$242$		−	4.85225i		−	0.311915i
$243$			5.13007i			0.329094i
$244$	−9.86895			−0.631795
$245$	2.13915	+	0.651165i	0.136666	+	0.0416014i
$246$	−14.8954			−0.949694
$247$		−	7.20618i		−	0.458519i
$248$			4.93212i			0.313190i
$249$	−26.8824			−1.70360
$250$	8.66306	−	7.06763i	0.547900	−	0.446996i
$251$	28.6256			1.80683			0.903417	−	0.428764i	$-0.141051\pi$
$251$	28.6256			1.80683			0.903417	+	0.428764i	$0.141051\pi$
$252$			0.499141i			0.0314429i
$253$		−	10.2061i		−	0.641653i
$254$	−0.539711			−0.0338645
$255$	−3.38288	−	1.02976i	−0.211844	−	0.0644861i
$256$	1.00000			0.0625000
$257$			9.67057i			0.603233i	0.953429	+	0.301617i	$0.0975263\pi$
$257$			9.67057i			0.603233i	−0.953429	+	0.301617i	$0.902474\pi$
$258$		−	16.4328i		−	1.02306i
$259$	−8.92252			−0.554419
$260$	0.966869	−	3.17628i	0.0599626	−	0.196984i
$261$	1.62212			0.100407
$262$		−	8.07474i		−	0.498859i
$263$			10.5324i			0.649457i	0.945807	+	0.324728i	$0.105273\pi$
$263$			10.5324i			0.649457i	−0.945807	+	0.324728i	$0.894727\pi$
$264$	3.92105			0.241324
$265$	2.66472	−	8.75393i	0.163693	−	0.537750i
$266$	4.85321			0.297569
$267$		−	24.3466i		−	1.48999i
$268$			15.8048i			0.965431i
$269$	9.77949			0.596266			0.298133	−	0.954524i	$-0.403636\pi$
$269$	9.77949			0.596266			0.298133	+	0.954524i	$0.403636\pi$
$270$	11.8372	+	3.60327i	0.720388	+	0.219288i
$271$	−18.7381			−1.13826			−0.569130	−	0.822247i	$-0.692720\pi$
$271$	−18.7381			−1.13826			−0.569130	+	0.822247i	$0.692720\pi$
$272$		−	1.00000i		−	0.0606339i
$273$		−	2.34812i		−	0.142115i
$274$	10.1767			0.614795
$275$	10.2947	+	6.90751i	0.620791	+	0.416539i
$276$	−6.50950			−0.391826
$277$		−	18.3954i		−	1.10527i	−0.833422	−	0.552637i	$-0.813622\pi$
$277$		−	18.3954i		−	1.10527i	0.833422	−	0.552637i	$-0.186378\pi$
$278$			17.9150i			1.07447i
$279$	−2.46182			−0.147385
$280$	2.13915	+	0.651165i	0.127839	+	0.0389146i
$281$	−15.4172			−0.919711			−0.459855	−	0.887994i	$-0.652099\pi$
$281$	−15.4172			−0.919711			−0.459855	+	0.887994i	$0.652099\pi$
$282$		−	13.0762i		−	0.778675i
$283$		−	3.20689i		−	0.190630i	−0.995447	−	0.0953150i	$-0.969614\pi$
$283$		−	3.20689i		−	0.190630i	0.995447	−	0.0953150i	$-0.0303858\pi$
$284$	−11.7828			−0.699181
$285$	4.99764	−	16.4178i	0.296035	−	0.972509i
$286$	3.68158			0.217696
$287$		−	9.41904i		−	0.555988i
$288$			0.499141i			0.0294121i
$289$	−1.00000			−0.0588235
$290$	2.11617	−	6.95187i	0.124266	−	0.408228i
$291$	22.2171			1.30239
$292$		−	10.4393i		−	0.610914i
$293$		−	0.379629i		−	0.0221782i	−0.999939	−	0.0110891i	$-0.996470\pi$
$293$		−	0.379629i		−	0.0221782i	0.999939	−	0.0110891i	$-0.00352983\pi$
$294$	1.58141			0.0922297
$295$	20.3457	+	6.19329i	1.18457	+	0.360587i
$296$	−8.92252			−0.518611
$297$			13.7203i			0.796133i
$298$			5.62465i			0.325827i
$299$	−6.11194			−0.353462
$300$	4.40563	−	6.56596i	0.254359	−	0.379086i
$301$	10.3912			0.598942
$302$			17.0093i			0.978773i
$303$			13.1543i			0.755694i
$304$	4.85321			0.278351
$305$	−21.1112	−	6.42632i	−1.20882	−	0.367970i
$306$	0.499141			0.0285340
$307$		−	5.97695i		−	0.341123i	−0.985347	−	0.170561i	$-0.945442\pi$
$307$		−	5.97695i		−	0.341123i	0.985347	−	0.170561i	$-0.0545581\pi$
$308$			2.47946i			0.141281i
$309$	25.5052			1.45094
$310$	−3.21162	+	10.5506i	−0.182408	+	0.599232i
$311$	−30.5004			−1.72952			−0.864759	−	0.502188i	$-0.832529\pi$
$311$	−30.5004			−1.72952			−0.864759	+	0.502188i	$0.832529\pi$
$312$		−	2.34812i		−	0.132936i
$313$		−	20.5359i		−	1.16076i	−0.814347	−	0.580378i	$-0.802905\pi$
$313$		−	20.5359i		−	1.16076i	0.814347	−	0.580378i	$-0.197095\pi$
$314$	8.76768			0.494789
$315$	−0.325023	+	1.06774i	−0.0183130	+	0.0601603i
$316$	−15.7552			−0.886298
$317$		−	9.79660i		−	0.550232i	−0.961411	−	0.275116i	$-0.911284\pi$
$317$		−	9.79660i		−	0.550232i	0.961411	−	0.275116i	$-0.0887162\pi$
$318$		−	6.47151i		−	0.362904i
$319$	8.05782			0.451151
$320$	2.13915	+	0.651165i	0.119582	+	0.0364013i
$321$	−3.47883			−0.194169
$322$		−	4.11626i		−	0.229390i
$323$		−	4.85321i		−	0.270040i
$324$	7.25344			0.402969
$325$	4.13656	−	6.16496i	0.229455	−	0.341970i
$326$	−15.9342			−0.882516
$327$			6.53906i			0.361611i
$328$		−	9.41904i		−	0.520079i
$329$	8.26867			0.455867
$330$	8.38774	+	2.55325i	0.461730	+	0.140552i
$331$	−9.38887			−0.516059			−0.258030	−	0.966137i	$-0.583073\pi$
$331$	−9.38887			−0.516059			−0.258030	+	0.966137i	$0.583073\pi$
$332$		−	16.9990i		−	0.932940i
$333$		−	4.45359i		−	0.244055i
$334$	5.93877			0.324955
$335$	−10.2915	+	33.8089i	−0.562287	+	1.84718i
$336$	1.58141			0.0862730
$337$			3.89003i			0.211904i	0.994371	+	0.105952i	$0.0337889\pi$
$337$			3.89003i			0.211904i	−0.994371	+	0.105952i	$0.966211\pi$
$338$			10.7953i			0.587186i
$339$	5.81260			0.315697
$340$	0.651165	−	2.13915i	0.0353144	−	0.116012i
$341$	−12.2290			−0.662238
$342$			2.42243i			0.130990i
$343$			1.00000i			0.0539949i
$344$	10.3912			0.560259
$345$	−13.9248	−	4.23876i	−0.749687	−	0.228207i
$346$	−19.9065			−1.07018
$347$			5.56440i			0.298713i	0.988783	+	0.149356i	$0.0477202\pi$
$347$			5.56440i			0.298713i	−0.988783	+	0.149356i	$0.952280\pi$
$348$		−	5.13930i		−	0.275495i
$349$	−16.9111			−0.905231			−0.452615	−	0.891706i	$-0.649509\pi$
$349$	−16.9111			−0.905231			−0.452615	+	0.891706i	$0.649509\pi$
$350$	4.15197	+	2.78589i	0.221932	+	0.148912i
$351$	8.21641			0.438560
$352$			2.47946i			0.132156i
$353$		−	1.79189i		−	0.0953729i	−0.998862	−	0.0476865i	$-0.984815\pi$
$353$		−	1.79189i		−	0.0953729i	0.998862	−	0.0476865i	$-0.0151848\pi$
$354$	15.0409			0.799416
$355$	−25.2053	−	7.67256i	−1.33776	−	0.407217i
$356$	15.3955			0.815961
$357$		−	1.58141i		−	0.0836971i
$358$			13.0850i			0.691565i
$359$	−6.81835			−0.359859			−0.179929	−	0.983680i	$-0.557587\pi$
$359$	−6.81835			−0.359859			−0.179929	+	0.983680i	$0.557587\pi$
$360$	−0.325023	+	1.06774i	−0.0171302	+	0.0562748i
$361$	4.55366			0.239667
$362$			5.13376i			0.269824i
$363$		−	7.67341i		−	0.402749i
$364$	1.48483			0.0778261
$365$	6.79771	−	22.3313i	0.355808	−	1.16887i
$366$	−15.6069			−0.815784
$367$		−	25.1760i		−	1.31418i	−0.753813	−	0.657089i	$-0.771788\pi$
$367$		−	25.1760i		−	1.31418i	0.753813	−	0.657089i	$-0.228212\pi$
$368$		−	4.11626i		−	0.214575i
$369$	4.70142			0.244746
$370$	−19.0867	−	5.81004i	−0.992268	−	0.302050i
$371$	4.09224			0.212458
$372$			7.79970i			0.404396i
$373$		−	30.7407i		−	1.59169i	−0.605499	−	0.795846i	$-0.707026\pi$
$373$		−	30.7407i		−	1.59169i	0.605499	−	0.795846i	$-0.292974\pi$
$374$	2.47946			0.128210
$375$	13.6999	−	11.1768i	0.707458	−	0.577168i
$376$	8.26867			0.426424
$377$		−	4.82542i		−	0.248522i
$378$			5.53358i			0.284617i
$379$	13.1580			0.675881			0.337940	−	0.941168i	$-0.390270\pi$
$379$	13.1580			0.675881			0.337940	+	0.941168i	$0.390270\pi$
$380$	10.3818	+	3.16024i	0.532574	+	0.162117i
$381$	−0.853504			−0.0437264
$382$		−	19.5123i		−	0.998338i
$383$			25.8537i			1.32106i	0.750798	+	0.660532i	$0.229669\pi$
$383$			25.8537i			1.32106i	−0.750798	+	0.660532i	$0.770331\pi$
$384$	1.58141			0.0807010
$385$	−1.61454	+	5.30396i	−0.0822847	+	0.270315i
$386$	−2.08248			−0.105995
$387$			5.18669i			0.263654i
$388$			14.0489i			0.713227i
$389$	−28.0199			−1.42067			−0.710334	−	0.703865i	$-0.751456\pi$
$389$	−28.0199			−1.42067			−0.710334	+	0.703865i	$0.751456\pi$
$390$	1.52902	−	5.02300i	0.0774248	−	0.254349i
$391$	−4.11626			−0.208168
$392$			1.00000i			0.0505076i
$393$		−	12.7695i		−	0.644135i
$394$	−6.86555			−0.345881
$395$	−33.7028	−	10.2592i	−1.69577	−	0.516198i
$396$	−1.23760			−0.0621918
$397$			22.4810i			1.12829i	0.825677	+	0.564144i	$0.190794\pi$
$397$			22.4810i			1.12829i	−0.825677	+	0.564144i	$0.809206\pi$
$398$			7.97203i			0.399602i
$399$	7.67492			0.384227
$400$	4.15197	+	2.78589i	0.207598	+	0.139294i
$401$	−24.3231			−1.21464			−0.607318	−	0.794459i	$-0.707754\pi$
$401$	−24.3231			−1.21464			−0.607318	+	0.794459i	$0.707754\pi$
$402$			24.9939i			1.24658i
$403$			7.32334i			0.364802i
$404$	−8.31807			−0.413840
$405$	15.5162	+	4.72319i	0.771007	+	0.234697i
$406$	3.24982			0.161286
$407$		−	22.1231i		−	1.09660i
$408$		−	1.58141i		−	0.0782915i
$409$	−28.8624			−1.42716			−0.713578	−	0.700576i	$-0.752927\pi$
$409$	−28.8624			−1.42716			−0.713578	+	0.700576i	$0.752927\pi$
$410$	6.13335	−	20.1488i	0.302905	−	0.995077i
$411$	16.0935			0.793833
$412$			16.1282i			0.794577i
$413$			9.51108i			0.468010i
$414$	2.05459			0.100978
$415$	11.0691	−	36.3634i	0.543363	−	1.78501i
$416$	1.48483			0.0727997
$417$			28.3310i			1.38738i
$418$			12.0334i			0.588571i
$419$	−16.3304			−0.797790			−0.398895	−	0.916997i	$-0.630606\pi$
$419$	−16.3304			−0.797790			−0.398895	+	0.916997i	$0.630606\pi$
$420$	3.38288	+	1.02976i	0.165068	+	0.0502471i
$421$	−26.6939			−1.30098			−0.650491	−	0.759514i	$-0.725437\pi$
$421$	−26.6939			−1.30098			−0.650491	+	0.759514i	$0.725437\pi$
$422$			9.87489i			0.480702i
$423$			4.12723i			0.200673i
$424$	4.09224			0.198737
$425$	2.78589	−	4.15197i	0.135135	−	0.201400i
$426$	−18.6335			−0.902794
$427$		−	9.86895i		−	0.477592i
$428$		−	2.19983i		−	0.106333i
$429$	5.82209			0.281093
$430$	22.2285	+	6.76642i	1.07195	+	0.326306i
$431$	−6.02989			−0.290450			−0.145225	−	0.989399i	$-0.546391\pi$
$431$	−6.02989			−0.290450			−0.145225	+	0.989399i	$0.546391\pi$
$432$			5.53358i			0.266234i
$433$			16.9902i			0.816497i	0.912871	+	0.408248i	$0.133860\pi$
$433$			16.9902i			0.816497i	−0.912871	+	0.408248i	$0.866140\pi$
$434$	−4.93212			−0.236749
$435$	3.34654	−	10.9938i	0.160454	−	0.527111i
$436$	−4.13495			−0.198028
$437$		−	19.9771i		−	0.955633i
$438$		−	16.5088i		−	0.788822i
$439$	20.3664			0.972035			0.486018	−	0.873949i	$-0.338449\pi$
$439$	20.3664			0.972035			0.486018	+	0.873949i	$0.338449\pi$
$440$	−1.61454	+	5.30396i	−0.0769703	+	0.252856i
$441$	−0.499141			−0.0237686
$442$		−	1.48483i		−	0.0706261i
$443$			12.5581i			0.596654i	0.954464	+	0.298327i	$0.0964285\pi$
$443$			12.5581i			0.596654i	−0.954464	+	0.298327i	$0.903571\pi$
$444$	−14.1102			−0.669639
$445$	32.9334	+	10.0250i	1.56119	+	0.475232i
$446$	−0.615959			−0.0291665
$447$			8.89488i			0.420714i
$448$			1.00000i			0.0472456i
$449$	−25.7519			−1.21531			−0.607654	−	0.794202i	$-0.707889\pi$
$449$	−25.7519			−1.21531			−0.607654	+	0.794202i	$0.707889\pi$
$450$	−1.39055	+	2.07242i	−0.0655511	+	0.0976946i
$451$	23.3542			1.09971
$452$			3.67558i			0.172885i
$453$			26.8986i			1.26381i
$454$	13.0080			0.610495
$455$	3.17628	+	0.966869i	0.148906	+	0.0453275i
$456$	7.67492			0.359411
$457$			28.4616i			1.33138i	0.746229	+	0.665689i	$0.231862\pi$
$457$			28.4616i			1.33138i	−0.746229	+	0.665689i	$0.768138\pi$
$458$		−	16.7881i		−	0.784457i
$459$	5.53358			0.258285
$460$	2.68037	−	8.80532i	0.124973	−	0.410550i
$461$	−3.91476			−0.182329			−0.0911643	−	0.995836i	$-0.529059\pi$
$461$	−3.91476			−0.182329			−0.0911643	+	0.995836i	$0.529059\pi$
$462$			3.92105i			0.182424i
$463$		−	24.4445i		−	1.13603i	−0.823017	−	0.568016i	$-0.807711\pi$
$463$		−	24.4445i		−	1.13603i	0.823017	−	0.568016i	$-0.192289\pi$
$464$	3.24982			0.150869
$465$	−5.07890	+	16.6848i	−0.235528	+	0.773738i
$466$	7.50071			0.347464
$467$		−	15.8270i		−	0.732385i	−0.930539	−	0.366192i	$-0.880661\pi$
$467$		−	15.8270i		−	0.732385i	0.930539	−	0.366192i	$-0.119339\pi$
$468$			0.741138i			0.0342591i
$469$	−15.8048			−0.729798
$470$	17.6880	+	5.38428i	0.815885	+	0.248358i
$471$	13.8653			0.638879
$472$			9.51108i			0.437783i
$473$			25.7647i			1.18466i
$474$	−24.9154			−1.14440
$475$	20.1504	+	13.5205i	0.924563	+	0.620363i
$476$	1.00000			0.0458349
$477$			2.04260i			0.0935243i
$478$			7.82561i			0.357935i
$479$	−34.7707			−1.58871			−0.794357	−	0.607452i	$-0.792192\pi$
$479$	−34.7707			−1.58871			−0.794357	+	0.607452i	$0.792192\pi$
$480$	3.38288	+	1.02976i	0.154407	+	0.0470019i
$481$	−13.2484			−0.604076
$482$		−	22.5508i		−	1.02716i
$483$		−	6.50950i		−	0.296192i
$484$	4.85225			0.220557
$485$	−9.14818	+	30.0529i	−0.415398	+	1.36463i
$486$	−5.13007			−0.232705
$487$		−	30.7487i		−	1.39336i	−0.717383	−	0.696679i	$-0.754660\pi$
$487$		−	30.7487i		−	1.39336i	0.717383	−	0.696679i	$-0.245340\pi$
$488$		−	9.86895i		−	0.446747i
$489$	−25.1986			−1.13952
$490$	−0.651165	+	2.13915i	−0.0294167	+	0.0966372i
$491$	33.6199			1.51724			0.758621	−	0.651532i	$-0.225873\pi$
$491$	33.6199			1.51724			0.758621	+	0.651532i	$0.225873\pi$
$492$		−	14.8954i		−	0.671535i
$493$		−	3.24982i		−	0.146365i
$494$	7.20618			0.324222
$495$	−2.64742	−	0.805883i	−0.118993	−	0.0362218i
$496$	−4.93212			−0.221459
$497$		−	11.7828i		−	0.528531i
$498$		−	26.8824i		−	1.20463i
$499$	31.2932			1.40087			0.700437	−	0.713714i	$-0.252988\pi$
$499$	31.2932			1.40087			0.700437	+	0.713714i	$0.252988\pi$
$500$	7.06763	+	8.66306i	0.316074	+	0.387424i
$501$	9.39163			0.419587
$502$			28.6256i			1.27762i
$503$			18.5131i			0.825459i	0.910854	+	0.412730i	$0.135425\pi$
$503$			18.5131i			0.825459i	−0.910854	+	0.412730i	$0.864575\pi$
$504$	−0.499141			−0.0222335
$505$	−17.7936	−	5.41644i	−0.791807	−	0.241028i
$506$	10.2061			0.453717
$507$			17.0718i			0.758184i
$508$		−	0.539711i		−	0.0239458i
$509$	16.4622			0.729674			0.364837	−	0.931071i	$-0.381125\pi$
$509$	16.4622			0.729674			0.364837	+	0.931071i	$0.381125\pi$
$510$	1.02976	−	3.38288i	0.0455985	−	0.149797i
$511$	10.4393			0.461807
$512$			1.00000i			0.0441942i
$513$			26.8556i			1.18570i
$514$	−9.67057			−0.426550
$515$	−10.5021	+	34.5006i	−0.462778	+	1.52028i
$516$	16.4328			0.723415
$517$			20.5019i			0.901672i
$518$		−	8.92252i		−	0.392033i
$519$	−31.4803			−1.38183
$520$	3.17628	+	0.966869i	0.139289	+	0.0424000i
$521$	−30.6959			−1.34481			−0.672406	−	0.740183i	$-0.734739\pi$
$521$	−30.6959			−1.34481			−0.672406	+	0.740183i	$0.734739\pi$
$522$			1.62212i			0.0709982i
$523$		−	18.5329i		−	0.810389i	−0.914231	−	0.405194i	$-0.867204\pi$
$523$		−	18.5329i		−	0.810389i	0.914231	−	0.405194i	$-0.132796\pi$
$524$	8.07474			0.352747
$525$	6.56596	+	4.40563i	0.286562	+	0.192278i
$526$	−10.5324			−0.459235
$527$			4.93212i			0.214846i
$528$			3.92105i			0.170642i
$529$	6.05641			0.263322
$530$	8.75393	+	2.66472i	0.380246	+	0.115748i
$531$	−4.74737			−0.206018
$532$			4.85321i			0.210413i
$533$		−	13.9857i		−	0.605786i
$534$	24.3466			1.05358
$535$	1.43245	−	4.70577i	0.0619302	−	0.203448i
$536$	−15.8048			−0.682663
$537$			20.6928i			0.892961i
$538$			9.77949i			0.421624i
$539$	−2.47946			−0.106798
$540$	−3.60327	+	11.8372i	−0.155060	+	0.509391i
$541$	25.0160			1.07552			0.537761	−	0.843097i	$-0.319270\pi$
$541$	25.0160			1.07552			0.537761	+	0.843097i	$0.319270\pi$
$542$		−	18.7381i		−	0.804872i
$543$			8.11858i			0.348402i
$544$	1.00000			0.0428746
$545$	−8.84531	−	2.69254i	−0.378891	−	0.115336i
$546$	2.34812			0.100490
$547$			12.0619i			0.515730i	0.966181	+	0.257865i	$0.0830190\pi$
$547$			12.0619i			0.515730i	−0.966181	+	0.257865i	$0.916981\pi$
$548$			10.1767i			0.434725i
$549$	4.92599			0.210236
$550$	−6.90751	+	10.2947i	−0.294537	+	0.438966i
$551$	15.7721			0.671913
$552$		−	6.50950i		−	0.277063i
$553$		−	15.7552i		−	0.669978i
$554$	18.3954			0.781547
$555$	−30.1838	−	9.18806i	−1.28123	−	0.390011i
$556$	−17.9150			−0.759767
$557$			17.5136i			0.742073i	0.928618	+	0.371037i	$0.120998\pi$
$557$			17.5136i			0.742073i	−0.928618	+	0.371037i	$0.879002\pi$
$558$		−	2.46182i		−	0.104217i
$559$	15.4292			0.652586
$560$	−0.651165	+	2.13915i	−0.0275168	+	0.0903958i
$561$	3.92105			0.165547
$562$		−	15.4172i		−	0.650334i
$563$			17.5043i			0.737720i	0.929485	+	0.368860i	$0.120252\pi$
$563$			17.5043i			0.737720i	−0.929485	+	0.368860i	$0.879748\pi$
$564$	13.0762			0.550606
$565$	−2.39341	+	7.86263i	−0.100691	+	0.330783i
$566$	3.20689			0.134796
$567$			7.25344i			0.304616i
$568$		−	11.7828i		−	0.494396i
$569$	−35.7406			−1.49832			−0.749162	−	0.662387i	$-0.769543\pi$
$569$	−35.7406			−1.49832			−0.749162	+	0.662387i	$0.769543\pi$
$570$	16.4178	+	4.99764i	0.687668	+	0.209328i
$571$	−27.4858			−1.15024			−0.575122	−	0.818067i	$-0.695046\pi$
$571$	−27.4858			−1.15024			−0.575122	+	0.818067i	$0.695046\pi$
$572$			3.68158i			0.153935i
$573$		−	30.8570i		−	1.28907i
$574$	9.41904			0.393143
$575$	11.4674	−	17.0906i	0.478225	−	0.712726i
$576$	−0.499141			−0.0207975
$577$			18.4175i			0.766730i	0.923597	+	0.383365i	$0.125235\pi$
$577$			18.4175i			0.766730i	−0.923597	+	0.383365i	$0.874765\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	−3.29326			−0.136863
$580$	6.95187	+	2.11617i	0.288661	+	0.0878692i
$581$	16.9990			0.705236
$582$			22.2171i			0.920930i
$583$			10.1466i			0.420228i
$584$	10.4393			0.431981
$585$	−0.482603	+	1.58541i	−0.0199532	+	0.0655486i
$586$	0.379629			0.0156823
$587$			39.8719i			1.64569i	0.568265	+	0.822845i	$0.307615\pi$
$587$			39.8719i			1.64569i	−0.568265	+	0.822845i	$0.692385\pi$
$588$			1.58141i			0.0652163i
$589$	−23.9366			−0.986291
$590$	−6.19329	+	20.3457i	−0.254974	+	0.837618i
$591$	−10.8572			−0.446608
$592$		−	8.92252i		−	0.366713i
$593$		−	15.8586i		−	0.651234i	−0.945502	−	0.325617i	$-0.894428\pi$
$593$		−	15.8586i		−	0.651234i	0.945502	−	0.325617i	$-0.105572\pi$
$594$	−13.7203			−0.562951
$595$	2.13915	+	0.651165i	0.0876968	+	0.0266952i
$596$	−5.62465			−0.230395
$597$			12.6071i			0.515972i
$598$		−	6.11194i		−	0.249936i
$599$	−6.37001			−0.260272			−0.130136	−	0.991496i	$-0.541541\pi$
$599$	−6.37001			−0.260272			−0.130136	+	0.991496i	$0.541541\pi$
$600$	6.56596	+	4.40563i	0.268054	+	0.179859i
$601$	4.47924			0.182712			0.0913559	−	0.995818i	$-0.470880\pi$
$601$	4.47924			0.182712			0.0913559	+	0.995818i	$0.470880\pi$
$602$			10.3912i			0.423516i
$603$		−	7.88881i		−	0.321257i
$604$	−17.0093			−0.692097
$605$	10.3797	+	3.15962i	0.421996	+	0.128457i
$606$	−13.1543			−0.534356
$607$		−	5.46432i		−	0.221790i	−0.993832	−	0.110895i	$-0.964628\pi$
$607$		−	5.46432i		−	0.221790i	0.993832	−	0.110895i	$-0.0353717\pi$
$608$			4.85321i			0.196824i
$609$	5.13930			0.208255
$610$	6.42632	−	21.1112i	0.260194	−	0.854768i
$611$	12.2776			0.496697
$612$			0.499141i			0.0201766i
$613$		−	29.5706i		−	1.19435i	−0.802112	−	0.597173i	$-0.796290\pi$
$613$		−	29.5706i		−	1.19435i	0.802112	−	0.597173i	$-0.203710\pi$
$614$	5.97695			0.241210
$615$	9.69935	−	31.8635i	0.391115	−	1.28486i
$616$	−2.47946			−0.0999005
$617$			3.08987i			0.124394i	0.998064	+	0.0621968i	$0.0198106\pi$
$617$			3.08987i			0.124394i	−0.998064	+	0.0621968i	$0.980189\pi$
$618$			25.5052i			1.02597i
$619$	33.1577			1.33272			0.666361	−	0.745629i	$-0.267851\pi$
$619$	33.1577			1.33272			0.666361	+	0.745629i	$0.267851\pi$
$620$	−10.5506	−	3.21162i	−0.423721	−	0.128982i
$621$	22.7776			0.914035
$622$		−	30.5004i		−	1.22295i
$623$			15.3955i			0.616808i
$624$	2.34812			0.0940001
$625$	9.47766	+	23.1338i	0.379106	+	0.925353i
$626$	20.5359			0.820778
$627$			19.0297i			0.759973i
$628$			8.76768i			0.349869i
$629$	−8.92252			−0.355764
$630$	−1.06774	−	0.325023i	−0.0425397	−	0.0129492i
$631$	−9.39738			−0.374104			−0.187052	−	0.982350i	$-0.559893\pi$
$631$	−9.39738			−0.374104			−0.187052	+	0.982350i	$0.559893\pi$
$632$		−	15.7552i		−	0.626707i
$633$			15.6162i			0.620690i
$634$	9.79660			0.389073
$635$	0.351441	−	1.15453i	0.0139465	−	0.0458159i
$636$	6.47151			0.256612
$637$			1.48483i			0.0588310i
$638$			8.05782i			0.319012i
$639$	5.88128			0.232660
$640$	−0.651165	+	2.13915i	−0.0257396	+	0.0845575i
$641$	41.7840			1.65037			0.825185	−	0.564862i	$-0.191071\pi$
$641$	41.7840			1.65037			0.825185	+	0.564862i	$0.191071\pi$
$642$		−	3.47883i		−	0.137298i
$643$			0.121038i			0.00477329i	0.999997	+	0.00238664i	$0.000759693\pi$
$643$			0.121038i			0.00477329i	−0.999997	+	0.00238664i	$0.999240\pi$
$644$	4.11626			0.162203
$645$	35.1524	+	10.7005i	1.38412	+	0.421331i
$646$	4.85321			0.190947
$647$			15.0998i			0.593633i	0.954934	+	0.296817i	$0.0959250\pi$
$647$			15.0998i			0.593633i	−0.954934	+	0.296817i	$0.904075\pi$
$648$			7.25344i			0.284942i
$649$	−23.5824			−0.925690
$650$	6.16496	+	4.13656i	0.241809	+	0.162249i
$651$	−7.79970			−0.305694
$652$		−	15.9342i		−	0.624033i
$653$			30.3759i			1.18870i	0.804206	+	0.594350i	$0.202591\pi$
$653$			30.3759i			1.18870i	−0.804206	+	0.594350i	$0.797409\pi$
$654$	−6.53906			−0.255698
$655$	17.2731	+	5.25799i	0.674917	+	0.205447i
$656$	9.41904			0.367752
$657$			5.21068i			0.203288i
$658$			8.26867i			0.322346i
$659$	26.6257			1.03719			0.518596	−	0.855020i	$-0.326455\pi$
$659$	26.6257			1.03719			0.518596	+	0.855020i	$0.326455\pi$
$660$	−2.55325	+	8.38774i	−0.0993853	+	0.326492i
$661$	−37.2936			−1.45055			−0.725276	−	0.688458i	$-0.758288\pi$
$661$	−37.2936			−1.45055			−0.725276	+	0.688458i	$0.758288\pi$
$662$		−	9.38887i		−	0.364909i
$663$		−	2.34812i		−	0.0911935i
$664$	16.9990			0.659688
$665$	−3.16024	+	10.3818i	−0.122549	+	0.402588i
$666$	4.45359			0.172573
$667$		−	13.3771i		−	0.517964i
$668$			5.93877i			0.229778i
$669$	−0.974084			−0.0376603
$670$	−33.8089	−	10.2915i	−1.30615	−	0.397597i
$671$	24.4697			0.944643
$672$			1.58141i			0.0610042i
$673$			20.4641i			0.788835i	0.918931	+	0.394417i	$0.129054\pi$
$673$			20.4641i			0.788835i	−0.918931	+	0.394417i	$0.870946\pi$
$674$	−3.89003			−0.149838
$675$	−15.4159	+	22.9752i	−0.593359	+	0.884317i
$676$	−10.7953			−0.415203
$677$		−	35.0668i		−	1.34773i	−0.738856	−	0.673864i	$-0.764634\pi$
$677$		−	35.0668i		−	1.34773i	0.738856	−	0.673864i	$-0.235366\pi$
$678$			5.81260i			0.223231i
$679$	−14.0489			−0.539149
$680$	2.13915	+	0.651165i	0.0820328	+	0.0249711i
$681$	20.5709			0.788280
$682$		−	12.2290i		−	0.468273i
$683$			9.05059i			0.346311i	0.984894	+	0.173156i	$0.0553964\pi$
$683$			9.05059i			0.346311i	−0.984894	+	0.173156i	$0.944604\pi$
$684$	−2.42243			−0.0926241
$685$	−6.62669	+	21.7695i	−0.253193	+	0.831768i
$686$	−1.00000			−0.0381802
$687$		−	26.5489i		−	1.01290i
$688$			10.3912i			0.396163i
$689$	6.07627			0.231487
$690$	4.23876	−	13.9248i	0.161367	−	0.530109i
$691$	−38.3558			−1.45912			−0.729562	−	0.683914i	$-0.760276\pi$
$691$	−38.3558			−1.45912			−0.729562	+	0.683914i	$0.760276\pi$
$692$		−	19.9065i		−	0.756731i
$693$		−	1.23760i		−	0.0470126i
$694$	−5.56440			−0.211222
$695$	−38.3230	−	11.6657i	−1.45368	−	0.442503i
$696$	5.13930			0.194805
$697$		−	9.41904i		−	0.356772i
$698$		−	16.9111i		−	0.640095i
$699$	11.8617			0.448651
$700$	−2.78589	+	4.15197i	−0.105297	+	0.156930i
$701$	−38.0045			−1.43541			−0.717706	−	0.696347i	$-0.754808\pi$
$701$	−38.0045			−1.43541			−0.717706	+	0.696347i	$0.754808\pi$
$702$			8.21641i			0.310108i
$703$		−	43.3029i		−	1.63320i
$704$	−2.47946			−0.0934483
$705$	27.9720	+	8.51475i	1.05348	+	0.320684i
$706$	1.79189			0.0674389
$707$		−	8.31807i		−	0.312833i
$708$			15.0409i			0.565273i
$709$	−31.3781			−1.17843			−0.589214	−	0.807977i	$-0.700562\pi$
$709$	−31.3781			−1.17843			−0.589214	+	0.807977i	$0.700562\pi$
$710$	7.67256	−	25.2053i	0.287946	−	0.945937i
$711$	7.86405			0.294925
$712$			15.3955i			0.576971i
$713$			20.3019i			0.760311i
$714$	1.58141			0.0591828
$715$	−2.39732	+	7.87547i	−0.0896546	+	0.294526i
$716$	−13.0850			−0.489011
$717$			12.3755i			0.462171i
$718$		−	6.81835i		−	0.254459i
$719$	−41.6679			−1.55395			−0.776975	−	0.629531i	$-0.783247\pi$
$719$	−41.6679			−1.55395			−0.776975	+	0.629531i	$0.783247\pi$
$720$	−1.06774	−	0.325023i	−0.0397923	−	0.0121129i
$721$	−16.1282			−0.600644
$722$			4.55366i			0.169470i
$723$		−	35.6621i		−	1.32629i
$724$	−5.13376			−0.190795
$725$	13.4931	+	9.05364i	0.501123	+	0.336244i
$726$	7.67341			0.284787
$727$			29.0321i			1.07674i	0.842708	+	0.538371i	$0.180960\pi$
$727$			29.0321i			1.07674i	−0.842708	+	0.538371i	$0.819040\pi$
$728$			1.48483i			0.0550314i
$729$	−29.8731			−1.10641
$730$	22.3313	+	6.79771i	0.826518	+	0.251595i
$731$	10.3912			0.384334
$732$		−	15.6069i		−	0.576846i
$733$			14.3941i			0.531659i	0.964020	+	0.265829i	$0.0856457\pi$
$733$			14.3941i			0.531659i	−0.964020	+	0.265829i	$0.914354\pi$
$734$	25.1760			0.929264
$735$	−1.02976	+	3.38288i	−0.0379833	+	0.124779i
$736$	4.11626			0.151727
$737$		−	39.1874i		−	1.44349i
$738$			4.70142i			0.173062i
$739$	23.5565			0.866539			0.433270	−	0.901264i	$-0.357360\pi$
$739$	23.5565			0.866539			0.433270	+	0.901264i	$0.357360\pi$
$740$	5.81004	−	19.0867i	0.213581	−	0.701640i
$741$	11.3959			0.418640
$742$			4.09224i			0.150231i
$743$		−	10.5929i		−	0.388614i	−0.980941	−	0.194307i	$-0.937754\pi$
$743$		−	10.5929i		−	0.388614i	0.980941	−	0.194307i	$-0.0622458\pi$
$744$	−7.79970			−0.285951
$745$	−12.0320	−	3.66258i	−0.440818	−	0.134187i
$746$	30.7407			1.12550
$747$			8.48488i			0.310446i
$748$			2.47946i			0.0906582i
$749$	2.19983			0.0803799
$750$	11.1768	+	13.6999i	0.408120	+	0.500248i
$751$	−11.2811			−0.411653			−0.205827	−	0.978588i	$-0.565988\pi$
$751$	−11.2811			−0.411653			−0.205827	+	0.978588i	$0.565988\pi$
$752$			8.26867i			0.301528i
$753$			45.2689i			1.64969i
$754$	4.82542			0.175732
$755$	−36.3854	−	11.0758i	−1.32420	−	0.403091i
$756$	−5.53358			−0.201254
$757$		−	13.9885i		−	0.508420i	−0.967149	−	0.254210i	$-0.918185\pi$
$757$		−	13.9885i		−	0.508420i	0.967149	−	0.254210i	$-0.0818154\pi$
$758$			13.1580i			0.477920i
$759$	16.1401			0.585847
$760$	−3.16024	+	10.3818i	−0.114634	+	0.376586i
$761$	23.9575			0.868460			0.434230	−	0.900802i	$-0.357021\pi$
$761$	23.9575			0.868460			0.434230	+	0.900802i	$0.357021\pi$
$762$		−	0.853504i		−	0.0309192i
$763$		−	4.13495i		−	0.149695i
$764$	19.5123			0.705932
$765$	−0.325023	+	1.06774i	−0.0117512	+	0.0386042i
$766$	−25.8537			−0.934133
$767$			14.1223i			0.509927i
$768$			1.58141i			0.0570642i
$769$	−14.8024			−0.533789			−0.266895	−	0.963726i	$-0.585998\pi$
$769$	−14.8024			−0.533789			−0.266895	+	0.963726i	$0.585998\pi$
$770$	−5.30396	−	1.61454i	−0.191141	−	0.0581841i
$771$	−15.2931			−0.550769
$772$		−	2.08248i		−	0.0749501i
$773$			13.8809i			0.499262i	0.968341	+	0.249631i	$0.0803093\pi$
$773$			13.8809i			0.499262i	−0.968341	+	0.249631i	$0.919691\pi$
$774$	−5.18669			−0.186432
$775$	−20.4780	−	13.7403i	−0.735591	−	0.493567i
$776$	−14.0489			−0.504327
$777$		−	14.1102i		−	0.506200i
$778$		−	28.0199i		−	1.00456i
$779$	45.7126			1.63782
$780$	5.02300	+	1.52902i	0.179852	+	0.0547476i
$781$	29.2151			1.04540
$782$		−	4.11626i		−	0.147197i
$783$			17.9831i			0.642665i
$784$	−1.00000			−0.0357143
$785$	−5.70921	+	18.7554i	−0.203770	+	0.669410i
$786$	12.7695			0.455472
$787$		−	12.2264i		−	0.435823i	−0.975968	−	0.217912i	$-0.930076\pi$
$787$		−	12.2264i		−	0.435823i	0.975968	−	0.217912i	$-0.0699245\pi$
$788$		−	6.86555i		−	0.244575i
$789$	−16.6561			−0.592972
$790$	10.2592	−	33.7028i	0.365007	−	1.19909i
$791$	−3.67558			−0.130688
$792$		−	1.23760i		−	0.0439763i
$793$		−	14.6537i		−	0.520368i
$794$	−22.4810			−0.797820
$795$	13.8436	+	4.21402i	0.490980	+	0.149456i
$796$	−7.97203			−0.282561
$797$			32.2049i			1.14076i	0.821382	+	0.570378i	$0.193203\pi$
$797$			32.2049i			1.14076i	−0.821382	+	0.570378i	$0.806797\pi$
$798$			7.67492i			0.271689i
$799$	8.26867			0.292525
$800$	−2.78589	+	4.15197i	−0.0984960	+	0.146794i
$801$	−7.68453			−0.271519
$802$		−	24.3231i		−	0.858877i
$803$			25.8839i			0.913422i
$804$	−24.9939			−0.881466
$805$	8.80532	+	2.68037i	0.310347	+	0.0944705i
$806$	−7.32334			−0.257954
$807$			15.4654i			0.544408i
$808$		−	8.31807i		−	0.292629i
$809$	−5.71907			−0.201072			−0.100536	−	0.994933i	$-0.532056\pi$
$809$	−5.71907			−0.201072			−0.100536	+	0.994933i	$0.532056\pi$
$810$	−4.72319	+	15.5162i	−0.165956	+	0.545185i
$811$	53.4561			1.87710			0.938549	−	0.345146i	$-0.112171\pi$
$811$	53.4561			1.87710			0.938549	+	0.345146i	$0.112171\pi$
$812$			3.24982i			0.114046i
$813$		−	29.6327i		−	1.03926i
$814$	22.1231			0.775414
$815$	10.3758	−	34.0858i	0.363449	−	1.19397i
$816$	1.58141			0.0553604
$817$			50.4309i			1.76435i
$818$		−	28.8624i		−	1.00915i
$819$	−0.741138			−0.0258975
$820$	20.1488	+	6.13335i	0.703626	+	0.214186i
$821$	46.8617			1.63548			0.817742	−	0.575585i	$-0.195226\pi$
$821$	46.8617			1.63548			0.817742	+	0.575585i	$0.195226\pi$
$822$			16.0935i			0.561325i
$823$			42.3243i			1.47533i	0.675166	+	0.737666i	$0.264072\pi$
$823$			42.3243i			1.47533i	−0.675166	+	0.737666i	$0.735928\pi$
$824$	−16.1282			−0.561851
$825$	−10.9236	+	16.2801i	−0.380311	+	0.566800i
$826$	−9.51108			−0.330933
$827$			50.2887i			1.74871i	0.485289	+	0.874354i	$0.338715\pi$
$827$			50.2887i			1.74871i	−0.485289	+	0.874354i	$0.661285\pi$
$828$			2.05459i			0.0714020i
$829$	−27.5620			−0.957269			−0.478634	−	0.878014i	$-0.658868\pi$
$829$	−27.5620			−0.957269			−0.478634	+	0.878014i	$0.658868\pi$
$830$	36.3634	+	11.0691i	1.26219	+	0.384216i
$831$	29.0907			1.00915
$832$			1.48483i			0.0514771i
$833$			1.00000i			0.0346479i
$834$	−28.3310			−0.981023
$835$	−3.86712	+	12.7039i	−0.133827	+	0.439638i
$836$	−12.0334			−0.416183
$837$		−	27.2922i		−	0.943358i
$838$		−	16.3304i		−	0.564123i
$839$	−14.6191			−0.504707			−0.252353	−	0.967635i	$-0.581205\pi$
$839$	−14.6191			−0.504707			−0.252353	+	0.967635i	$0.581205\pi$
$840$	−1.02976	+	3.38288i	−0.0355301	+	0.116721i
$841$	−18.4387			−0.635816
$842$		−	26.6939i		−	0.919934i
$843$		−	24.3809i		−	0.839722i
$844$	−9.87489			−0.339908
$845$	−23.0928	−	7.02952i	−0.794416	−	0.241823i
$846$	−4.12723			−0.141897
$847$			4.85225i			0.166725i
$848$			4.09224i			0.140528i
$849$	5.07142			0.174051
$850$	4.15197	+	2.78589i	0.142411	+	0.0955552i
$851$	−36.7274			−1.25900
$852$		−	18.6335i		−	0.638372i
$853$		−	26.4546i		−	0.905788i	−0.891564	−	0.452894i	$-0.850392\pi$
$853$		−	26.4546i		−	0.905788i	0.891564	−	0.452894i	$-0.149608\pi$
$854$	9.86895			0.337709
$855$	−5.18196	−	1.57741i	−0.177219	−	0.0539461i
$856$	2.19983			0.0751885
$857$		−	0.294081i		−	0.0100456i	−0.999987	−	0.00502280i	$-0.998401\pi$
$857$		−	0.294081i		−	0.0100456i	0.999987	−	0.00502280i	$-0.00159881\pi$
$858$			5.82209i			0.198763i
$859$	−16.6946			−0.569612			−0.284806	−	0.958585i	$-0.591929\pi$
$859$	−16.6946			−0.569612			−0.284806	+	0.958585i	$0.591929\pi$
$860$	−6.76642	+	22.2285i	−0.230733	+	0.757985i
$861$	14.8954			0.507633
$862$		−	6.02989i		−	0.205379i
$863$			7.15399i			0.243525i	0.992559	+	0.121762i	$0.0388545\pi$
$863$			7.15399i			0.243525i	−0.992559	+	0.121762i	$0.961145\pi$
$864$	−5.53358			−0.188256
$865$	12.9624	−	42.5831i	0.440736	−	1.44787i
$866$	−16.9902			−0.577350
$867$		−	1.58141i		−	0.0537075i
$868$		−	4.93212i		−	0.167407i
$869$	39.0644			1.32517
$870$	10.9938	+	3.34654i	0.372723	+	0.113458i
$871$	−23.4674			−0.795163
$872$		−	4.13495i		−	0.140027i
$873$		−	7.01239i		−	0.237334i
$874$	19.9771			0.675735
$875$	−8.66306	+	7.06763i	−0.292865	+	0.238929i
$876$	16.5088			0.557781
$877$			19.9502i			0.673670i	0.941564	+	0.336835i	$0.109356\pi$
$877$			19.9502i			0.673670i	−0.941564	+	0.336835i	$0.890644\pi$
$878$			20.3664i			0.687333i
$879$	0.600349			0.0202493
$880$	−5.30396	−	1.61454i	−0.178796	−	0.0544262i
$881$	57.6910			1.94366			0.971829	−	0.235685i	$-0.0757334\pi$
$881$	57.6910			1.94366			0.971829	+	0.235685i	$0.0757334\pi$
$882$		−	0.499141i		−	0.0168069i
$883$			1.74844i			0.0588396i	0.999567	+	0.0294198i	$0.00936596\pi$
$883$			1.74844i			0.0588396i	−0.999567	+	0.0294198i	$0.990634\pi$
$884$	1.48483			0.0499402
$885$	−9.79413	+	32.1749i	−0.329226	+	1.08155i
$886$	−12.5581			−0.421898
$887$			5.63604i			0.189240i	0.995513	+	0.0946199i	$0.0301636\pi$
$887$			5.63604i			0.189240i	−0.995513	+	0.0946199i	$0.969836\pi$
$888$		−	14.1102i		−	0.473506i
$889$	0.539711			0.0181013
$890$	−10.0250	+	32.9334i	−0.336040	+	1.10393i
$891$	−17.9846			−0.602508
$892$		−	0.615959i		−	0.0206238i
$893$			40.1296i			1.34289i
$894$	−8.89488			−0.297489
$895$	−27.9909	−	8.52052i	−0.935633	−	0.284810i
$896$	−1.00000			−0.0334077
$897$		−	9.66548i		−	0.322721i
$898$		−	25.7519i		−	0.859353i
$899$	−16.0285			−0.534580
$900$	−2.07242	−	1.39055i	−0.0690805	−	0.0463517i
$901$	4.09224			0.136332
$902$			23.3542i			0.777609i
$903$			16.4328i			0.546850i
$904$	−3.67558			−0.122248
$905$	−10.9819	−	3.34293i	−0.365051	−	0.111123i
$906$	−26.8986			−0.893647
$907$		−	38.5509i		−	1.28006i	−0.768349	−	0.640031i	$-0.778921\pi$
$907$		−	38.5509i		−	1.28006i	0.768349	−	0.640031i	$-0.221079\pi$
$908$			13.0080i			0.431685i
$909$	4.15189			0.137709
$910$	−0.966869	+	3.17628i	−0.0320514	+	0.105293i
$911$	2.35799			0.0781237			0.0390618	−	0.999237i	$-0.487563\pi$
$911$	2.35799			0.0781237			0.0390618	+	0.999237i	$0.487563\pi$
$912$			7.67492i			0.254142i
$913$			42.1484i			1.39491i
$914$	−28.4616			−0.941426
$915$	10.1627	−	33.3855i	0.335967	−	1.10369i
$916$	16.7881			0.554695
$917$			8.07474i			0.266651i
$918$			5.53358i			0.182635i
$919$	−47.1055			−1.55387			−0.776934	−	0.629582i	$-0.783226\pi$
$919$	−47.1055			−1.55387			−0.776934	+	0.629582i	$0.783226\pi$
$920$	8.80532	+	2.68037i	0.290303	+	0.0883691i
$921$	9.45202			0.311455
$922$		−	3.91476i		−	0.128926i
$923$		−	17.4955i		−	0.575870i
$924$	−3.92105			−0.128993
$925$	24.8572	−	37.0460i	0.817298	−	1.21807i
$926$	24.4445			0.803296
$927$		−	8.05022i		−	0.264404i
$928$			3.24982i			0.106681i
$929$	1.58032			0.0518487			0.0259243	−	0.999664i	$-0.491747\pi$
$929$	1.58032			0.0518487			0.0259243	+	0.999664i	$0.491747\pi$
$930$	−16.6848	−	5.07890i	−0.547115	−	0.166544i
$931$	−4.85321			−0.159058
$932$			7.50071i			0.245694i
$933$		−	48.2336i		−	1.57910i
$934$	15.8270			0.517874
$935$	−1.61454	+	5.30396i	−0.0528012	+	0.173458i
$936$	−0.741138			−0.0242248
$937$		−	32.8668i		−	1.07371i	−0.843674	−	0.536856i	$-0.819612\pi$
$937$		−	32.8668i		−	1.07371i	0.843674	−	0.536856i	$-0.180388\pi$
$938$		−	15.8048i		−	0.516045i
$939$	32.4756			1.05980
$940$	−5.38428	+	17.6880i	−0.175616	+	0.576918i
$941$	7.67130			0.250077			0.125039	−	0.992152i	$-0.460095\pi$
$941$	7.67130			0.250077			0.125039	+	0.992152i	$0.460095\pi$
$942$			13.8653i			0.451756i
$943$		−	38.7712i		−	1.26256i
$944$	−9.51108			−0.309559
$945$	−11.8372	−	3.60327i	−0.385063	−	0.117215i
$946$	−25.7647			−0.837684
$947$		−	43.5425i		−	1.41494i	−0.706744	−	0.707470i	$-0.749837\pi$
$947$		−	43.5425i		−	1.41494i	0.706744	−	0.707470i	$-0.250163\pi$
$948$		−	24.9154i		−	0.809215i
$949$	15.5006			0.503170
$950$	−13.5205	+	20.1504i	−0.438663	+	0.653764i
$951$	15.4924			0.502377
$952$			1.00000i			0.0324102i
$953$		−	40.6687i		−	1.31739i	−0.752411	−	0.658694i	$-0.771109\pi$
$953$		−	40.6687i		−	1.31739i	0.752411	−	0.658694i	$-0.228891\pi$
$954$	−2.04260			−0.0661317
$955$	41.7399	+	12.7058i	1.35067	+	0.411149i
$956$	−7.82561			−0.253098
$957$			12.7427i			0.411914i
$958$		−	34.7707i		−	1.12339i
$959$	−10.1767			−0.328622
$960$	−1.02976	+	3.38288i	−0.0332354	+	0.109182i
$961$	−6.67423			−0.215298
$962$		−	13.2484i		−	0.427146i
$963$			1.09802i			0.0353833i
$964$	22.5508			0.726313
$965$	1.35604	−	4.45475i	0.0436524	−	0.143403i
$966$	6.50950			0.209440
$967$		−	29.1570i		−	0.937625i	−0.883298	−	0.468813i	$-0.844682\pi$
$967$		−	29.1570i		−	0.937625i	0.883298	−	0.468813i	$-0.155318\pi$
$968$			4.85225i			0.155957i
$969$	7.67492			0.246554
$970$	−30.0529	−	9.14818i	−0.964939	−	0.293730i
$971$	36.8404			1.18227			0.591133	−	0.806574i	$-0.298681\pi$
$971$	36.8404			1.18227			0.591133	+	0.806574i	$0.298681\pi$
$972$		−	5.13007i		−	0.164547i
$973$		−	17.9150i		−	0.574330i
$974$	30.7487			0.985252
$975$	9.74933	+	6.54161i	0.312228	+	0.209499i
$976$	9.86895			0.315897
$977$		−	11.2487i		−	0.359876i	−0.983678	−	0.179938i	$-0.942410\pi$
$977$		−	11.2487i		−	0.359876i	0.983678	−	0.179938i	$-0.0575898\pi$
$978$		−	25.1986i		−	0.805762i
$979$	−38.1726			−1.22000
$980$	−2.13915	−	0.651165i	−0.0683328	−	0.0208007i
$981$	2.06392			0.0658960
$982$			33.6199i			1.07285i
$983$		−	34.7209i		−	1.10743i	−0.832708	−	0.553713i	$-0.813211\pi$
$983$		−	34.7209i		−	1.10743i	0.832708	−	0.553713i	$-0.186789\pi$
$984$	14.8954			0.474847
$985$	4.47061	−	14.6865i	0.142445	−	0.467950i
$986$	3.24982			0.103495
$987$			13.0762i			0.416219i
$988$			7.20618i			0.229259i
$989$	42.7731			1.36010
$990$	0.805883	−	2.64742i	0.0256127	−	0.0841406i
$991$	9.11416			0.289521			0.144760	−	0.989467i	$-0.453759\pi$
$991$	9.11416			0.289521			0.144760	+	0.989467i	$0.453759\pi$
$992$		−	4.93212i		−	0.156595i
$993$		−	14.8477i		−	0.471176i
$994$	11.7828			0.373728
$995$	−17.0534	−	5.19111i	−0.540629	−	0.164569i
$996$	26.8824			0.851800
$997$			23.6110i			0.747768i	0.927476	+	0.373884i	$0.121974\pi$
$997$			23.6110i			0.747768i	−0.927476	+	0.373884i	$0.878026\pi$
$998$			31.2932i			0.990568i
$999$	49.3735			1.56211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.e.g.239.12	yes	14
5.2	odd	4		5950.2.a.cb.1.5		7
5.3	odd	4		5950.2.a.cc.1.3		7
5.4	even	2	inner	1190.2.e.g.239.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.e.g.239.3	✓	14	5.4	even	2	inner
1190.2.e.g.239.12	yes	14	1.1	even	1	trivial
5950.2.a.cb.1.5		7	5.2	odd	4
5950.2.a.cc.1.3		7	5.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.58141i q^{3} -1.00000 q^{4} +(-2.13915 - 0.651165i) q^{5} -1.58141 q^{6} -1.00000i q^{7} -1.00000i q^{8} +0.499141 q^{9} +(0.651165 - 2.13915i) q^{10} +2.47946 q^{11} -1.58141i q^{12} -1.48483i q^{13} +1.00000 q^{14} +(1.02976 - 3.38288i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +0.499141i q^{18} +4.85321 q^{19} +(2.13915 + 0.651165i) q^{20} +1.58141 q^{21} +2.47946i q^{22} -4.11626i q^{23} +1.58141 q^{24} +(4.15197 + 2.78589i) q^{25} +1.48483 q^{26} +5.53358i q^{27} +1.00000i q^{28} +3.24982 q^{29} +(3.38288 + 1.02976i) q^{30} -4.93212 q^{31} +1.00000i q^{32} +3.92105i q^{33} +1.00000 q^{34} +(-0.651165 + 2.13915i) q^{35} -0.499141 q^{36} -8.92252i q^{37} +4.85321i q^{38} +2.34812 q^{39} +(-0.651165 + 2.13915i) q^{40} +9.41904 q^{41} +1.58141i q^{42} +10.3912i q^{43} -2.47946 q^{44} +(-1.06774 - 0.325023i) q^{45} +4.11626 q^{46} +8.26867i q^{47} +1.58141i q^{48} -1.00000 q^{49} +(-2.78589 + 4.15197i) q^{50} +1.58141 q^{51} +1.48483i q^{52} +4.09224i q^{53} -5.53358 q^{54} +(-5.30396 - 1.61454i) q^{55} -1.00000 q^{56} +7.67492i q^{57} +3.24982i q^{58} -9.51108 q^{59} +(-1.02976 + 3.38288i) q^{60} +9.86895 q^{61} -4.93212i q^{62} -0.499141i q^{63} -1.00000 q^{64} +(-0.966869 + 3.17628i) q^{65} -3.92105 q^{66} -15.8048i q^{67} +1.00000i q^{68} +6.50950 q^{69} +(-2.13915 - 0.651165i) q^{70} +11.7828 q^{71} -0.499141i q^{72} +10.4393i q^{73} +8.92252 q^{74} +(-4.40563 + 6.56596i) q^{75} -4.85321 q^{76} -2.47946i q^{77} +2.34812i q^{78} +15.7552 q^{79} +(-2.13915 - 0.651165i) q^{80} -7.25344 q^{81} +9.41904i q^{82} +16.9990i q^{83} -1.58141 q^{84} +(-0.651165 + 2.13915i) q^{85} -10.3912 q^{86} +5.13930i q^{87} -2.47946i q^{88} -15.3955 q^{89} +(0.325023 - 1.06774i) q^{90} -1.48483 q^{91} +4.11626i q^{92} -7.79970i q^{93} -8.26867 q^{94} +(-10.3818 - 3.16024i) q^{95} -1.58141 q^{96} -14.0489i q^{97} -1.00000i q^{98} +1.23760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} + 4 q^{10} - 14 q^{11} + 14 q^{14} + 2 q^{15} + 14 q^{16} + 4 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{24} + 14 q^{25} + 2 q^{26} + 20 q^{29} - 2 q^{30} - 36 q^{31}+ \cdots + 88 q^{99}+O(q^{100}) \) 14 * q - 14 * q^4 - 2 * q^5 - 4 * q^6 - 14 * q^9 + 4 * q^10 - 14 * q^11 + 14 * q^14 + 2 * q^15 + 14 * q^16 + 4 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^24 + 14 * q^25 + 2 * q^26 + 20 * q^29 - 2 * q^30 - 36 * q^31 + 14 * q^34 - 4 * q^35 + 14 * q^36 + 50 * q^39 - 4 * q^40 + 34 * q^41 + 14 * q^44 + 8 * q^45 - 54 * q^46 - 14 * q^49 + 8 * q^50 + 4 * q^51 + 34 * q^54 - 16 * q^55 - 14 * q^56 - 2 * q^60 + 2 * q^61 - 14 * q^64 - 32 * q^65 - 16 * q^66 - 6 * q^69 - 2 * q^70 - 22 * q^71 + 24 * q^74 - 40 * q^75 - 4 * q^76 + 52 * q^79 - 2 * q^80 + 22 * q^81 - 4 * q^84 - 4 * q^85 - 14 * q^86 - 42 * q^89 - 38 * q^90 - 2 * q^91 + 16 * q^94 - 46 * q^95 - 4 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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