LMFDB - Embedded newform 190.2.b.b.39.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(39,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("190.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.3
Root			$0.432320 - 0.432320i$ of defining polynomial
Character	$\chi$	$=$	190.39
Dual form			190.2.b.b.39.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.76156i q^{3} -1.00000 q^{4} +(-2.19388 + 0.432320i) q^{5} +2.76156 q^{6} +0.761557i q^{7} +1.00000i q^{8} -4.62620 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.76156i q^{3} -1.00000 q^{4} +(-2.19388 + 0.432320i) q^{5} +2.76156 q^{6} +0.761557i q^{7} +1.00000i q^{8} -4.62620 q^{9} +(0.432320 + 2.19388i) q^{10} -0.864641 q^{11} -2.76156i q^{12} +5.62620i q^{13} +0.761557 q^{14} +(-1.19388 - 6.05852i) q^{15} +1.00000 q^{16} +3.62620i q^{17} +4.62620i q^{18} -1.00000 q^{19} +(2.19388 - 0.432320i) q^{20} -2.10308 q^{21} +0.864641i q^{22} -8.01395i q^{23} -2.76156 q^{24} +(4.62620 - 1.89692i) q^{25} +5.62620 q^{26} -4.49084i q^{27} -0.761557i q^{28} +7.35548 q^{29} +(-6.05852 + 1.19388i) q^{30} +8.11704 q^{31} -1.00000i q^{32} -2.38776i q^{33} +3.62620 q^{34} +(-0.329237 - 1.67076i) q^{35} +4.62620 q^{36} -0.476886i q^{37} +1.00000i q^{38} -15.5371 q^{39} +(-0.432320 - 2.19388i) q^{40} -2.65847 q^{41} +2.10308i q^{42} +6.86464i q^{43} +0.864641 q^{44} +(10.1493 - 2.00000i) q^{45} -8.01395 q^{46} -1.25240i q^{47} +2.76156i q^{48} +6.42003 q^{49} +(-1.89692 - 4.62620i) q^{50} -10.0140 q^{51} -5.62620i q^{52} +2.37380i q^{53} -4.49084 q^{54} +(1.89692 - 0.373802i) q^{55} -0.761557 q^{56} -2.76156i q^{57} -7.35548i q^{58} -4.49084 q^{59} +(1.19388 + 6.05852i) q^{60} -10.8646 q^{61} -8.11704i q^{62} -3.52311i q^{63} -1.00000 q^{64} +(-2.43232 - 12.3432i) q^{65} -2.38776 q^{66} -1.03228i q^{67} -3.62620i q^{68} +22.1310 q^{69} +(-1.67076 + 0.329237i) q^{70} -10.1816 q^{71} -4.62620i q^{72} +16.4017i q^{73} -0.476886 q^{74} +(5.23844 + 12.7755i) q^{75} +1.00000 q^{76} -0.658473i q^{77} +15.5371i q^{78} +12.5693 q^{79} +(-2.19388 + 0.432320i) q^{80} -1.47689 q^{81} +2.65847i q^{82} -0.270718i q^{83} +2.10308 q^{84} +(-1.56768 - 7.95543i) q^{85} +6.86464 q^{86} +20.3126i q^{87} -0.864641i q^{88} -0.387755 q^{89} +(-2.00000 - 10.1493i) q^{90} -4.28467 q^{91} +8.01395i q^{92} +22.4157i q^{93} -1.25240 q^{94} +(2.19388 - 0.432320i) q^{95} +2.76156 q^{96} +8.50479i q^{97} -6.42003i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9} - 8 q^{14} + 8 q^{15} + 6 q^{16} - 6 q^{19} - 2 q^{20} - 20 q^{21} - 4 q^{24} + 10 q^{25} + 16 q^{26} + 16 q^{29} - 16 q^{30} + 8 q^{31} + 4 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{39} + 4 q^{41} + 18 q^{45} + 6 q^{49} - 4 q^{50} - 12 q^{51} - 4 q^{54} + 4 q^{55} + 8 q^{56} - 4 q^{59} - 8 q^{60} - 60 q^{61} - 6 q^{64} - 12 q^{65} + 16 q^{66} + 44 q^{69} - 20 q^{70} - 16 q^{71} - 28 q^{74} + 44 q^{75} + 6 q^{76} + 2 q^{80} - 34 q^{81} + 20 q^{84} - 12 q^{85} + 36 q^{86} + 28 q^{89} - 12 q^{90} + 12 q^{91} + 28 q^{94} - 2 q^{95} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9 - 8 * q^14 + 8 * q^15 + 6 * q^16 - 6 * q^19 - 2 * q^20 - 20 * q^21 - 4 * q^24 + 10 * q^25 + 16 * q^26 + 16 * q^29 - 16 * q^30 + 8 * q^31 + 4 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^39 + 4 * q^41 + 18 * q^45 + 6 * q^49 - 4 * q^50 - 12 * q^51 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 4 * q^59 - 8 * q^60 - 60 * q^61 - 6 * q^64 - 12 * q^65 + 16 * q^66 + 44 * q^69 - 20 * q^70 - 16 * q^71 - 28 * q^74 + 44 * q^75 + 6 * q^76 + 2 * q^80 - 34 * q^81 + 20 * q^84 - 12 * q^85 + 36 * q^86 + 28 * q^89 - 12 * q^90 + 12 * q^91 + 28 * q^94 - 2 * q^95 + 4 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			2.76156i			1.59439i	0.603725	+	0.797193i	$0.293683\pi$
$3$			2.76156i			1.59439i	−0.603725	+	0.797193i	$0.706317\pi$
$4$	−1.00000			−0.500000
$5$	−2.19388	+	0.432320i	−0.981132	+	0.193340i
$5$	−2.19388	+	0.432320i	−0.981132	+	0.193340i
$6$	2.76156			1.12740
$7$			0.761557i			0.287842i	0.989589	+	0.143921i	$0.0459710\pi$
$7$			0.761557i			0.287842i	−0.989589	+	0.143921i	$0.954029\pi$
$8$			1.00000i			0.353553i
$9$	−4.62620			−1.54207
$10$	0.432320	+	2.19388i	0.136712	+	0.693765i
$11$	−0.864641			−0.260699			−0.130350	−	0.991468i	$-0.541610\pi$
$11$	−0.864641			−0.260699			−0.130350	+	0.991468i	$0.541610\pi$
$12$		−	2.76156i		−	0.797193i
$13$			5.62620i			1.56043i	0.625514	+	0.780213i	$0.284889\pi$
$13$			5.62620i			1.56043i	−0.625514	+	0.780213i	$0.715111\pi$
$14$	0.761557			0.203535
$15$	−1.19388	−	6.05852i	−0.308258	−	1.56430i
$16$	1.00000			0.250000
$17$			3.62620i			0.879482i	0.898125	+	0.439741i	$0.144930\pi$
$17$			3.62620i			0.879482i	−0.898125	+	0.439741i	$0.855070\pi$
$18$			4.62620i			1.09041i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	2.19388	−	0.432320i	0.490566	−	0.0966698i
$21$	−2.10308			−0.458930
$22$			0.864641i			0.184342i
$23$		−	8.01395i		−	1.67102i	−0.549472	−	0.835512i	$-0.685171\pi$
$23$		−	8.01395i		−	1.67102i	0.549472	−	0.835512i	$-0.314829\pi$
$24$	−2.76156			−0.563700
$25$	4.62620	−	1.89692i	0.925240	−	0.379383i
$26$	5.62620			1.10339
$27$		−	4.49084i		−	0.864262i
$28$		−	0.761557i		−	0.143921i
$29$	7.35548			1.36588			0.682939	−	0.730475i	$-0.260701\pi$
$29$	7.35548			1.36588			0.682939	+	0.730475i	$0.260701\pi$
$30$	−6.05852	+	1.19388i	−1.10613	+	0.217971i
$31$	8.11704			1.45786			0.728931	−	0.684587i	$-0.240017\pi$
$31$	8.11704			1.45786			0.728931	+	0.684587i	$0.240017\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.38776i		−	0.415655i
$34$	3.62620			0.621888
$35$	−0.329237	−	1.67076i	−0.0556512	−	0.282411i
$36$	4.62620			0.771033
$37$		−	0.476886i		−	0.0783995i	−0.999231	−	0.0391998i	$-0.987519\pi$
$37$		−	0.476886i		−	0.0783995i	0.999231	−	0.0391998i	$-0.0124809\pi$
$38$			1.00000i			0.162221i
$39$	−15.5371			−2.48792
$40$	−0.432320	−	2.19388i	−0.0683559	−	0.346883i
$41$	−2.65847			−0.415184			−0.207592	−	0.978216i	$-0.566563\pi$
$41$	−2.65847			−0.415184			−0.207592	+	0.978216i	$0.566563\pi$
$42$			2.10308i			0.324513i
$43$			6.86464i			1.04685i	0.852072	+	0.523424i	$0.175346\pi$
$43$			6.86464i			1.04685i	−0.852072	+	0.523424i	$0.824654\pi$
$44$	0.864641			0.130350
$45$	10.1493	−	2.00000i	1.51297	−	0.298142i
$46$	−8.01395			−1.18159
$47$		−	1.25240i		−	0.182681i	−0.995820	−	0.0913404i	$-0.970885\pi$
$47$		−	1.25240i		−	0.182681i	0.995820	−	0.0913404i	$-0.0291151\pi$
$48$			2.76156i			0.398596i
$49$	6.42003			0.917147
$50$	−1.89692	−	4.62620i	−0.268264	−	0.654243i
$51$	−10.0140			−1.40223
$52$		−	5.62620i		−	0.780213i
$53$			2.37380i			0.326067i	0.986621	+	0.163033i	$0.0521278\pi$
$53$			2.37380i			0.326067i	−0.986621	+	0.163033i	$0.947872\pi$
$54$	−4.49084			−0.611126
$55$	1.89692	−	0.373802i	0.255780	−	0.0504034i
$56$	−0.761557			−0.101767
$57$		−	2.76156i		−	0.365777i
$58$		−	7.35548i		−	0.965822i
$59$	−4.49084			−0.584657			−0.292329	−	0.956318i	$-0.594430\pi$
$59$	−4.49084			−0.584657			−0.292329	+	0.956318i	$0.594430\pi$
$60$	1.19388	+	6.05852i	0.154129	+	0.782151i
$61$	−10.8646			−1.39107			−0.695537	−	0.718490i	$-0.744834\pi$
$61$	−10.8646			−1.39107			−0.695537	+	0.718490i	$0.744834\pi$
$62$		−	8.11704i		−	1.03086i
$63$		−	3.52311i		−	0.443871i
$64$	−1.00000			−0.125000
$65$	−2.43232	−	12.3432i	−0.301692	−	1.53098i
$66$	−2.38776			−0.293912
$67$		−	1.03228i		−	0.126113i	−0.998010	−	0.0630563i	$-0.979915\pi$
$67$		−	1.03228i		−	0.126113i	0.998010	−	0.0630563i	$-0.0200848\pi$
$68$		−	3.62620i		−	0.439741i
$69$	22.1310			2.66426
$70$	−1.67076	+	0.329237i	−0.199694	+	0.0393513i
$71$	−10.1816			−1.20833			−0.604166	−	0.796858i	$-0.706494\pi$
$71$	−10.1816			−1.20833			−0.604166	+	0.796858i	$0.706494\pi$
$72$		−	4.62620i		−	0.545203i
$73$			16.4017i			1.91967i	0.280557	+	0.959837i	$0.409481\pi$
$73$			16.4017i			1.91967i	−0.280557	+	0.959837i	$0.590519\pi$
$74$	−0.476886			−0.0554368
$75$	5.23844	+	12.7755i	0.604883	+	1.47519i
$76$	1.00000			0.114708
$77$		−	0.658473i		−	0.0750400i
$78$			15.5371i			1.75923i
$79$	12.5693			1.41416			0.707081	−	0.707133i	$-0.250012\pi$
$79$	12.5693			1.41416			0.707081	+	0.707133i	$0.250012\pi$
$80$	−2.19388	+	0.432320i	−0.245283	+	0.0483349i
$81$	−1.47689			−0.164098
$82$			2.65847i			0.293579i
$83$		−	0.270718i		−	0.0297152i	−0.999890	−	0.0148576i	$-0.995271\pi$
$83$		−	0.270718i		−	0.0297152i	0.999890	−	0.0148576i	$-0.00472949\pi$
$84$	2.10308			0.229465
$85$	−1.56768	−	7.95543i	−0.170039	−	0.862888i
$86$	6.86464			0.740233
$87$			20.3126i			2.17774i
$88$		−	0.864641i		−	0.0921710i
$89$	−0.387755			−0.0411020			−0.0205510	−	0.999789i	$-0.506542\pi$
$89$	−0.387755			−0.0411020			−0.0205510	+	0.999789i	$0.506542\pi$
$90$	−2.00000	−	10.1493i	−0.210819	−	1.06983i
$91$	−4.28467			−0.449156
$92$			8.01395i			0.835512i
$93$			22.4157i			2.32440i
$94$	−1.25240			−0.129175
$95$	2.19388	−	0.432320i	0.225087	−	0.0443551i
$96$	2.76156			0.281850
$97$			8.50479i			0.863531i	0.901986	+	0.431765i	$0.142109\pi$
$97$			8.50479i			0.863531i	−0.901986	+	0.431765i	$0.857891\pi$
$98$		−	6.42003i		−	0.648521i
$99$	4.00000			0.402015
$100$	−4.62620	+	1.89692i	−0.462620	+	0.189692i
$101$	16.4157			1.63342			0.816710	−	0.577049i	$-0.195796\pi$
$101$	16.4157			1.63342			0.816710	+	0.577049i	$0.195796\pi$
$102$			10.0140i			0.991529i
$103$		−	9.64015i		−	0.949872i	−0.880020	−	0.474936i	$-0.842471\pi$
$103$		−	9.64015i		−	0.949872i	0.880020	−	0.474936i	$-0.157529\pi$
$104$	−5.62620			−0.551694
$105$	4.61391	−	0.909206i	0.450271	−	0.0887294i
$106$	2.37380			0.230564
$107$		−	4.28467i		−	0.414215i	−0.978318	−	0.207107i	$-0.933595\pi$
$107$		−	4.28467i		−	0.414215i	0.978318	−	0.207107i	$-0.0664050\pi$
$108$			4.49084i			0.432131i
$109$	13.4200			1.28541			0.642703	−	0.766116i	$-0.277813\pi$
$109$	13.4200			1.28541			0.642703	+	0.766116i	$0.277813\pi$
$110$	−0.373802	−	1.89692i	−0.0356406	−	0.180864i
$111$	1.31695			0.124999
$112$			0.761557i			0.0719604i
$113$		−	10.3232i		−	0.971125i	−0.874202	−	0.485563i	$-0.838615\pi$
$113$		−	10.3232i		−	0.971125i	0.874202	−	0.485563i	$-0.161385\pi$
$114$	−2.76156			−0.258644
$115$	3.46460	+	17.5816i	0.323075	+	1.63950i
$116$	−7.35548			−0.682939
$117$		−	26.0279i		−	2.40628i
$118$			4.49084i			0.413415i
$119$	−2.76156			−0.253152
$120$	6.05852	−	1.19388i	0.553065	−	0.108986i
$121$	−10.2524			−0.932036
$122$			10.8646i			0.983638i
$123$		−	7.34153i		−	0.661963i
$124$	−8.11704			−0.728931
$125$	−9.32924	+	6.16160i	−0.834432	+	0.551110i
$126$	−3.52311			−0.313864
$127$		−	16.9817i		−	1.50688i	−0.657517	−	0.753440i	$-0.728393\pi$
$127$		−	16.9817i		−	1.50688i	0.657517	−	0.753440i	$-0.271607\pi$
$128$			1.00000i			0.0883883i
$129$	−18.9571			−1.66908
$130$	−12.3432	+	2.43232i	−1.08257	+	0.213329i
$131$	0.541436			0.0473055			0.0236528	−	0.999720i	$-0.492470\pi$
$131$	0.541436			0.0473055			0.0236528	+	0.999720i	$0.492470\pi$
$132$			2.38776i			0.207827i
$133$		−	0.761557i		−	0.0660354i
$134$	−1.03228			−0.0891750
$135$	1.94148	+	9.85235i	0.167096	+	0.847955i
$136$	−3.62620			−0.310944
$137$		−	2.87859i		−	0.245935i	−0.992411	−	0.122967i	$-0.960759\pi$
$137$		−	2.87859i		−	0.245935i	0.992411	−	0.122967i	$-0.0392411\pi$
$138$		−	22.1310i		−	1.88392i
$139$	−3.58767			−0.304302			−0.152151	−	0.988357i	$-0.548620\pi$
$139$	−3.58767			−0.304302			−0.152151	+	0.988357i	$0.548620\pi$
$140$	0.329237	+	1.67076i	0.0278256	+	0.141205i
$141$	3.45856			0.291264
$142$			10.1816i			0.854420i
$143$		−	4.86464i		−	0.406802i
$144$	−4.62620			−0.385517
$145$	−16.1370	+	3.17992i	−1.34011	+	0.264078i
$146$	16.4017			1.35742
$147$			17.7293i			1.46229i
$148$			0.476886i			0.0391998i
$149$	16.8401			1.37959			0.689796	−	0.724004i	$-0.257700\pi$
$149$	16.8401			1.37959			0.689796	+	0.724004i	$0.257700\pi$
$150$	12.7755	−	5.23844i	1.04312	−	0.427717i
$151$	−16.9817			−1.38195			−0.690975	−	0.722879i	$-0.742818\pi$
$151$	−16.9817			−1.38195			−0.690975	+	0.722879i	$0.742818\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		−	16.7755i		−	1.35622i
$154$	−0.658473			−0.0530613
$155$	−17.8078	+	3.50916i	−1.43036	+	0.281863i
$156$	15.5371			1.24396
$157$		−	14.8401i		−	1.18437i	−0.805804	−	0.592183i	$-0.798266\pi$
$157$		−	14.8401i		−	1.18437i	0.805804	−	0.592183i	$-0.201734\pi$
$158$		−	12.5693i		−	0.999963i
$159$	−6.55539			−0.519876
$160$	0.432320	+	2.19388i	0.0341779	+	0.173441i
$161$	6.10308			0.480990
$162$			1.47689i			0.116035i
$163$			13.3694i			1.04717i	0.851972	+	0.523587i	$0.175407\pi$
$163$			13.3694i			1.04717i	−0.851972	+	0.523587i	$0.824593\pi$
$164$	2.65847			0.207592
$165$	1.03228	+	5.23844i	0.0803625	+	0.407812i
$166$	−0.270718			−0.0210118
$167$		−	9.84632i		−	0.761931i	−0.924589	−	0.380966i	$-0.875592\pi$
$167$		−	9.84632i		−	0.761931i	0.924589	−	0.380966i	$-0.124408\pi$
$168$		−	2.10308i		−	0.162256i
$169$	−18.6541			−1.43493
$170$	−7.95543	+	1.56768i	−0.610154	+	0.120236i
$171$	4.62620			0.353774
$172$		−	6.86464i		−	0.523424i
$173$			2.98168i			0.226693i	0.993556	+	0.113346i	$0.0361570\pi$
$173$			2.98168i			0.226693i	−0.993556	+	0.113346i	$0.963843\pi$
$174$	20.3126			1.53989
$175$	1.44461	+	3.52311i	0.109202	+	0.266322i
$176$	−0.864641			−0.0651748
$177$		−	12.4017i		−	0.932169i
$178$			0.387755i			0.0290635i
$179$	−11.7938			−0.881512			−0.440756	−	0.897627i	$-0.645290\pi$
$179$	−11.7938			−0.881512			−0.440756	+	0.897627i	$0.645290\pi$
$180$	−10.1493	+	2.00000i	−0.756485	+	0.149071i
$181$	14.5693			1.08293			0.541465	−	0.840723i	$-0.317870\pi$
$181$	14.5693			1.08293			0.541465	+	0.840723i	$0.317870\pi$
$182$			4.28467i			0.317601i
$183$		−	30.0033i		−	2.21791i
$184$	8.01395			0.590796
$185$	0.206167	+	1.04623i	0.0151577	+	0.0769203i
$186$	22.4157			1.64360
$187$		−	3.13536i		−	0.229280i
$188$			1.25240i			0.0913404i
$189$	3.42003			0.248771
$190$	−0.432320	−	2.19388i	−0.0313638	−	0.159161i
$191$	13.2384			0.957900			0.478950	−	0.877842i	$-0.341017\pi$
$191$	13.2384			0.957900			0.478950	+	0.877842i	$0.341017\pi$
$192$		−	2.76156i		−	0.199298i
$193$			2.54144i			0.182937i	0.995808	+	0.0914683i	$0.0291560\pi$
$193$			2.54144i			0.182937i	−0.995808	+	0.0914683i	$0.970844\pi$
$194$	8.50479			0.610609
$195$	34.0864	−	6.71699i	2.44098	−	0.481014i
$196$	−6.42003			−0.458574
$197$			19.9109i			1.41859i	0.704911	+	0.709295i	$0.250987\pi$
$197$			19.9109i			1.41859i	−0.704911	+	0.709295i	$0.749013\pi$
$198$		−	4.00000i		−	0.284268i
$199$	20.3126			1.43992			0.719960	−	0.694015i	$-0.244160\pi$
$199$	20.3126			1.43992			0.719960	+	0.694015i	$0.244160\pi$
$200$	1.89692	+	4.62620i	0.134132	+	0.327122i
$201$	2.85069			0.201072
$202$		−	16.4157i		−	1.15500i
$203$			5.60162i			0.393157i
$204$	10.0140			0.701117
$205$	5.83237	−	1.14931i	0.407350	−	0.0802715i
$206$	−9.64015			−0.671661
$207$			37.0741i			2.57683i
$208$			5.62620i			0.390107i
$209$	0.864641			0.0598085
$210$	−0.909206	−	4.61391i	−0.0627412	−	0.318390i
$211$	18.0419			1.24205			0.621026	−	0.783790i	$-0.286716\pi$
$211$	18.0419			1.24205			0.621026	+	0.783790i	$0.286716\pi$
$212$		−	2.37380i		−	0.163033i
$213$		−	28.1170i		−	1.92655i
$214$	−4.28467			−0.292894
$215$	−2.96772	−	15.0602i	−0.202397	−	1.02710i
$216$	4.49084			0.305563
$217$			6.18159i			0.419634i
$218$		−	13.4200i		−	0.908919i
$219$	−45.2943			−3.06070
$220$	−1.89692	+	0.373802i	−0.127890	+	0.0252017i
$221$	−20.4017			−1.37237
$222$		−	1.31695i		−	0.0883877i
$223$		−	13.5231i		−	0.905575i	−0.891619	−	0.452787i	$-0.850430\pi$
$223$		−	13.5231i		−	0.905575i	0.891619	−	0.452787i	$-0.149570\pi$
$224$	0.761557			0.0508837
$225$	−21.4017	+	8.77551i	−1.42678	+	0.585034i
$226$	−10.3232			−0.686689
$227$		−	13.6016i		−	0.902771i	−0.892329	−	0.451386i	$-0.850930\pi$
$227$		−	13.6016i		−	0.902771i	0.892329	−	0.451386i	$-0.149070\pi$
$228$			2.76156i			0.182889i
$229$	−13.5877			−0.897898			−0.448949	−	0.893557i	$-0.648202\pi$
$229$	−13.5877			−0.897898			−0.448949	+	0.893557i	$0.648202\pi$
$230$	17.5816	−	3.46460i	1.15930	−	0.228449i
$231$	1.81841			0.119643
$232$			7.35548i			0.482911i
$233$			25.5510i			1.67390i	0.547277	+	0.836952i	$0.315664\pi$
$233$			25.5510i			1.67390i	−0.547277	+	0.836952i	$0.684336\pi$
$234$	−26.0279			−1.70150
$235$	0.541436	+	2.74760i	0.0353194	+	0.179234i
$236$	4.49084			0.292329
$237$			34.7110i			2.25472i
$238$			2.76156i			0.179005i
$239$	11.3309			0.732935			0.366468	−	0.930431i	$-0.380567\pi$
$239$	11.3309			0.732935			0.366468	+	0.930431i	$0.380567\pi$
$240$	−1.19388	−	6.05852i	−0.0770645	−	0.391076i
$241$	−1.25240			−0.0806739			−0.0403370	−	0.999186i	$-0.512843\pi$
$241$	−1.25240			−0.0806739			−0.0403370	+	0.999186i	$0.512843\pi$
$242$			10.2524i			0.659049i
$243$		−	17.5510i		−	1.12590i
$244$	10.8646			0.695537
$245$	−14.0848	+	2.77551i	−0.899842	+	0.177321i
$246$	−7.34153			−0.468079
$247$		−	5.62620i		−	0.357986i
$248$			8.11704i			0.515432i
$249$	0.747604			0.0473775
$250$	6.16160	+	9.32924i	0.389694	+	0.590033i
$251$	10.5939			0.668682			0.334341	−	0.942452i	$-0.391486\pi$
$251$	10.5939			0.668682			0.334341	+	0.942452i	$0.391486\pi$
$252$			3.52311i			0.221935i
$253$			6.92919i			0.435635i
$254$	−16.9817			−1.06553
$255$	21.9694	−	4.32924i	1.37578	−	0.271107i
$256$	1.00000			0.0625000
$257$			0.153681i			0.00958637i	0.999989	+	0.00479319i	$0.00152572\pi$
$257$			0.153681i			0.00958637i	−0.999989	+	0.00479319i	$0.998474\pi$
$258$			18.9571i			1.18022i
$259$	0.363176			0.0225666
$260$	2.43232	+	12.3432i	0.150846	+	0.765492i
$261$	−34.0279			−2.10627
$262$		−	0.541436i		−	0.0334501i
$263$			0.504792i			0.0311268i	0.999879	+	0.0155634i	$0.00495419\pi$
$263$			0.504792i			0.0311268i	−0.999879	+	0.0155634i	$0.995046\pi$
$264$	2.38776			0.146956
$265$	−1.02624	−	5.20783i	−0.0630416	−	0.319915i
$266$	−0.761557			−0.0466941
$267$		−	1.07081i		−	0.0655324i
$268$			1.03228i			0.0630563i
$269$	3.49521			0.213107			0.106553	−	0.994307i	$-0.466019\pi$
$269$	3.49521			0.213107			0.106553	+	0.994307i	$0.466019\pi$
$270$	9.85235	−	1.94148i	0.599595	−	0.118155i
$271$	5.47252			0.332432			0.166216	−	0.986089i	$-0.446845\pi$
$271$	5.47252			0.332432			0.166216	+	0.986089i	$0.446845\pi$
$272$			3.62620i			0.219871i
$273$		−	11.8324i		−	0.716127i
$274$	−2.87859			−0.173902
$275$	−4.00000	+	1.64015i	−0.241209	+	0.0989049i
$276$	−22.1310			−1.33213
$277$		−	12.9538i		−	0.778317i	−0.921171	−	0.389158i	$-0.872766\pi$
$277$		−	12.9538i		−	0.778317i	0.921171	−	0.389158i	$-0.127234\pi$
$278$			3.58767i			0.215174i
$279$	−37.5510			−2.24812
$280$	1.67076	−	0.329237i	0.0998472	−	0.0196757i
$281$	0.153681			0.00916785			0.00458393	−	0.999989i	$-0.498541\pi$
$281$	0.153681			0.00916785			0.00458393	+	0.999989i	$0.498541\pi$
$282$		−	3.45856i		−	0.205954i
$283$		−	18.2341i		−	1.08390i	−0.840410	−	0.541952i	$-0.817686\pi$
$283$		−	18.2341i		−	1.08390i	0.840410	−	0.541952i	$-0.182314\pi$
$284$	10.1816			0.604166
$285$	1.19388	+	6.05852i	0.0707192	+	0.358876i
$286$	−4.86464			−0.287652
$287$		−	2.02458i		−	0.119507i
$288$			4.62620i			0.272601i
$289$	3.85069			0.226511
$290$	3.17992	+	16.1370i	0.186732	+	0.947599i
$291$	−23.4865			−1.37680
$292$		−	16.4017i		−	0.959837i
$293$			2.03853i			0.119092i	0.998226	+	0.0595462i	$0.0189654\pi$
$293$			2.03853i			0.119092i	−0.998226	+	0.0595462i	$0.981035\pi$
$294$	17.7293			1.03399
$295$	9.85235	−	1.94148i	0.573626	−	0.113037i
$296$	0.476886			0.0277184
$297$			3.88296i			0.225312i
$298$		−	16.8401i		−	0.975519i
$299$	45.0881			2.60751
$300$	−5.23844	−	12.7755i	−0.302442	−	0.737594i
$301$	−5.22782			−0.301326
$302$			16.9817i			0.977186i
$303$			45.3328i			2.60430i
$304$	−1.00000			−0.0573539
$305$	23.8357	−	4.69701i	1.36483	−	0.268950i
$306$	−16.7755			−0.958992
$307$		−	16.5414i		−	0.944070i	−0.881580	−	0.472035i	$-0.843520\pi$
$307$		−	16.5414i		−	0.944070i	0.881580	−	0.472035i	$-0.156480\pi$
$308$			0.658473i			0.0375200i
$309$	26.6218			1.51446
$310$	3.50916	+	17.8078i	0.199307	+	1.01141i
$311$	−21.4725			−1.21759			−0.608797	−	0.793326i	$-0.708348\pi$
$311$	−21.4725			−1.21759			−0.608797	+	0.793326i	$0.708348\pi$
$312$		−	15.5371i		−	0.879613i
$313$		−	1.12141i		−	0.0633856i	−0.999498	−	0.0316928i	$-0.989910\pi$
$313$		−	1.12141i		−	0.0633856i	0.999498	−	0.0316928i	$-0.0100898\pi$
$314$	−14.8401			−0.837473
$315$	1.52311	+	7.72928i	0.0858178	+	0.435496i
$316$	−12.5693			−0.707081
$317$			29.8882i			1.67869i	0.543601	+	0.839344i	$0.317060\pi$
$317$			29.8882i			1.67869i	−0.543601	+	0.839344i	$0.682940\pi$
$318$			6.55539i			0.367608i
$319$	−6.35985			−0.356083
$320$	2.19388	−	0.432320i	0.122641	−	0.0241674i
$321$	11.8324			0.660418
$322$		−	6.10308i		−	0.340112i
$323$		−	3.62620i		−	0.201767i
$324$	1.47689			0.0820492
$325$	10.6724	+	26.0279i	0.592000	+	1.44377i
$326$	13.3694			0.740464
$327$			37.0602i			2.04943i
$328$		−	2.65847i		−	0.146790i
$329$	0.953771			0.0525831
$330$	5.23844	−	1.03228i	0.288367	−	0.0568249i
$331$	32.3126			1.77606			0.888030	−	0.459786i	$-0.152074\pi$
$331$	32.3126			1.77606			0.888030	+	0.459786i	$0.152074\pi$
$332$			0.270718i			0.0148576i
$333$			2.20617i			0.120897i
$334$	−9.84632			−0.538767
$335$	0.446274	+	2.26469i	0.0243825	+	0.123733i
$336$	−2.10308			−0.114733
$337$		−	26.3511i		−	1.43544i	−0.696334	−	0.717718i	$-0.745187\pi$
$337$		−	26.3511i		−	1.43544i	0.696334	−	0.717718i	$-0.254813\pi$
$338$			18.6541i			1.01465i
$339$	28.5081			1.54835
$340$	1.56768	+	7.95543i	0.0850194	+	0.431444i
$341$	−7.01832			−0.380063
$342$		−	4.62620i		−	0.250156i
$343$			10.2201i			0.551835i
$344$	−6.86464			−0.370117
$345$	−48.5527	+	9.56768i	−2.61399	+	0.515107i
$346$	2.98168			0.160296
$347$			2.77551i			0.148997i	0.997221	+	0.0744986i	$0.0237356\pi$
$347$			2.77551i			0.148997i	−0.997221	+	0.0744986i	$0.976264\pi$
$348$		−	20.3126i		−	1.08887i
$349$	−11.5510			−0.618312			−0.309156	−	0.951011i	$-0.600047\pi$
$349$	−11.5510			−0.618312			−0.309156	+	0.951011i	$0.600047\pi$
$350$	3.52311	−	1.44461i	0.188318	−	0.0772177i
$351$	25.2663			1.34862
$352$			0.864641i			0.0460855i
$353$		−	8.40171i		−	0.447178i	−0.974684	−	0.223589i	$-0.928223\pi$
$353$		−	8.40171i		−	0.447178i	0.974684	−	0.223589i	$-0.0717773\pi$
$354$	−12.4017			−0.659143
$355$	22.3372	−	4.40171i	1.18553	−	0.233618i
$356$	0.387755			0.0205510
$357$		−	7.62620i		−	0.403621i
$358$			11.7938i			0.623323i
$359$	−22.7895			−1.20278			−0.601391	−	0.798955i	$-0.705387\pi$
$359$	−22.7895			−1.20278			−0.601391	+	0.798955i	$0.705387\pi$
$360$	2.00000	+	10.1493i	0.105409	+	0.534916i
$361$	1.00000			0.0526316
$362$		−	14.5693i		−	0.765748i
$363$		−	28.3126i		−	1.48602i
$364$	4.28467			0.224578
$365$	−7.09079	−	35.9833i	−0.371149	−	1.88345i
$366$	−30.0033			−1.56830
$367$		−	4.06455i		−	0.212168i	−0.994357	−	0.106084i	$-0.966169\pi$
$367$		−	4.06455i		−	0.212168i	0.994357	−	0.106084i	$-0.0338312\pi$
$368$		−	8.01395i		−	0.417756i
$369$	12.2986			0.640241
$370$	1.04623	−	0.206167i	0.0543908	−	0.0107181i
$371$	−1.80779			−0.0938556
$372$		−	22.4157i		−	1.16220i
$373$		−	18.4017i		−	0.952804i	−0.879227	−	0.476402i	$-0.841941\pi$
$373$		−	18.4017i		−	0.952804i	0.879227	−	0.476402i	$-0.158059\pi$
$374$	−3.13536			−0.162126
$375$	−17.0156	−	25.7632i	−0.878683	−	1.33041i
$376$	1.25240			0.0645874
$377$			41.3834i			2.13135i
$378$		−	3.42003i		−	0.175907i
$379$	−1.23844			−0.0636145			−0.0318073	−	0.999494i	$-0.510126\pi$
$379$	−1.23844			−0.0636145			−0.0318073	+	0.999494i	$0.510126\pi$
$380$	−2.19388	+	0.432320i	−0.112544	+	0.0221776i
$381$	46.8959			2.40255
$382$		−	13.2384i		−	0.677338i
$383$			16.8646i			0.861743i	0.902413	+	0.430871i	$0.141794\pi$
$383$			16.8646i			0.861743i	−0.902413	+	0.430871i	$0.858206\pi$
$384$	−2.76156			−0.140925
$385$	0.284672	+	1.44461i	0.0145082	+	0.0736242i
$386$	2.54144			0.129356
$387$		−	31.7572i		−	1.61431i
$388$		−	8.50479i		−	0.431765i
$389$	−8.59392			−0.435729			−0.217865	−	0.975979i	$-0.569909\pi$
$389$	−8.59392			−0.435729			−0.217865	+	0.975979i	$0.569909\pi$
$390$	−6.71699	−	34.0864i	−0.340128	−	1.72603i
$391$	29.0602			1.46964
$392$			6.42003i			0.324261i
$393$			1.49521i			0.0754233i
$394$	19.9109			1.00310
$395$	−27.5756	+	5.43398i	−1.38748	+	0.273413i
$396$	−4.00000			−0.201008
$397$		−	16.0558i		−	0.805818i	−0.915240	−	0.402909i	$-0.867999\pi$
$397$		−	16.0558i		−	0.805818i	0.915240	−	0.402909i	$-0.132001\pi$
$398$		−	20.3126i		−	1.01818i
$399$	2.10308			0.105286
$400$	4.62620	−	1.89692i	0.231310	−	0.0948458i
$401$	−14.8925			−0.743698			−0.371849	−	0.928293i	$-0.621276\pi$
$401$	−14.8925			−0.743698			−0.371849	+	0.928293i	$0.621276\pi$
$402$		−	2.85069i		−	0.142179i
$403$			45.6681i			2.27489i
$404$	−16.4157			−0.816710
$405$	3.24011	−	0.638488i	0.161002	−	0.0317267i
$406$	5.60162			0.278004
$407$			0.412335i			0.0204387i
$408$		−	10.0140i		−	0.495765i
$409$	18.3511			0.907404			0.453702	−	0.891153i	$-0.350103\pi$
$409$	18.3511			0.907404			0.453702	+	0.891153i	$0.350103\pi$
$410$	−1.14931	−	5.83237i	−0.0567605	−	0.288040i
$411$	7.94940			0.392115
$412$			9.64015i			0.474936i
$413$		−	3.42003i		−	0.168289i
$414$	37.0741			1.82209
$415$	0.117037	+	0.593923i	0.00574512	+	0.0291545i
$416$	5.62620			0.275847
$417$		−	9.90754i		−	0.485174i
$418$		−	0.864641i		−	0.0422910i
$419$	−34.7509			−1.69769			−0.848847	−	0.528639i	$-0.822703\pi$
$419$	−34.7509			−1.69769			−0.848847	+	0.528639i	$0.822703\pi$
$420$	−4.61391	+	0.909206i	−0.225136	+	0.0443647i
$421$	−40.1589			−1.95722			−0.978612	−	0.205713i	$-0.934049\pi$
$421$	−40.1589			−1.95722			−0.978612	+	0.205713i	$0.934049\pi$
$422$		−	18.0419i		−	0.878264i
$423$			5.79383i			0.281706i
$424$	−2.37380			−0.115282
$425$	6.87859	+	16.7755i	0.333661	+	0.813732i
$426$	−28.1170			−1.36227
$427$		−	8.27405i		−	0.400409i
$428$			4.28467i			0.207107i
$429$	13.4340			0.648599
$430$	−15.0602	+	2.96772i	−0.726266	+	0.143116i
$431$	34.9571			1.68382			0.841912	−	0.539615i	$-0.181430\pi$
$431$	34.9571			1.68382			0.841912	+	0.539615i	$0.181430\pi$
$432$		−	4.49084i		−	0.216066i
$433$			1.13536i			0.0545619i	0.999628	+	0.0272809i	$0.00868487\pi$
$433$			1.13536i			0.0545619i	−0.999628	+	0.0272809i	$0.991315\pi$
$434$	6.18159			0.296726
$435$	−8.78154	−	44.5633i	−0.421043	−	2.13665i
$436$	−13.4200			−0.642703
$437$			8.01395i			0.383359i
$438$			45.2943i			2.16424i
$439$	6.80009			0.324551			0.162275	−	0.986746i	$-0.448117\pi$
$439$	6.80009			0.324551			0.162275	+	0.986746i	$0.448117\pi$
$440$	0.373802	+	1.89692i	0.0178203	+	0.0904319i
$441$	−29.7003			−1.41430
$442$			20.4017i			0.970410i
$443$			38.0679i			1.80866i	0.426835	+	0.904330i	$0.359629\pi$
$443$			38.0679i			1.80866i	−0.426835	+	0.904330i	$0.640371\pi$
$444$	−1.31695			−0.0624995
$445$	0.850688	−	0.167635i	0.0403265	−	0.00794664i
$446$	−13.5231			−0.640338
$447$			46.5048i			2.19960i
$448$		−	0.761557i		−	0.0359802i
$449$	18.5414			0.875024			0.437512	−	0.899212i	$-0.355860\pi$
$449$	18.5414			0.875024			0.437512	+	0.899212i	$0.355860\pi$
$450$	8.77551	+	21.4017i	0.413682	+	1.00889i
$451$	2.29862			0.108238
$452$			10.3232i			0.485563i
$453$		−	46.8959i		−	2.20336i
$454$	−13.6016			−0.638356
$455$	9.40005	−	1.85235i	0.440681	−	0.0868396i
$456$	2.76156			0.129322
$457$		−	16.3738i		−	0.765934i	−0.923762	−	0.382967i	$-0.874902\pi$
$457$		−	16.3738i		−	0.765934i	0.923762	−	0.382967i	$-0.125098\pi$
$458$			13.5877i			0.634910i
$459$	16.2847			0.760103
$460$	−3.46460	−	17.5816i	−0.161538	−	0.819748i
$461$	1.70470			0.0793959			0.0396979	−	0.999212i	$-0.487360\pi$
$461$	1.70470			0.0793959			0.0396979	+	0.999212i	$0.487360\pi$
$462$		−	1.81841i		−	0.0846002i
$463$		−	10.0279i		−	0.466036i	−0.972472	−	0.233018i	$-0.925140\pi$
$463$		−	10.0279i		−	0.466036i	0.972472	−	0.233018i	$-0.0748602\pi$
$464$	7.35548			0.341470
$465$	−9.69075	−	49.1772i	−0.449398	−	2.28054i
$466$	25.5510			1.18363
$467$		−	32.7509i		−	1.51553i	−0.652526	−	0.757766i	$-0.726291\pi$
$467$		−	32.7509i		−	1.51553i	0.652526	−	0.757766i	$-0.273709\pi$
$468$			26.0279i			1.20314i
$469$	0.786137			0.0363004
$470$	2.74760	−	0.541436i	0.126738	−	0.0249746i
$471$	40.9817			1.88834
$472$		−	4.49084i		−	0.206708i
$473$		−	5.93545i		−	0.272912i
$474$	34.7110			1.59433
$475$	−4.62620	+	1.89692i	−0.212265	+	0.0870365i
$476$	2.76156			0.126576
$477$		−	10.9817i		−	0.502816i
$478$		−	11.3309i		−	0.518263i
$479$	−27.2803			−1.24647			−0.623234	−	0.782035i	$-0.714182\pi$
$479$	−27.2803			−1.24647			−0.623234	+	0.782035i	$0.714182\pi$
$480$	−6.05852	+	1.19388i	−0.276532	+	0.0544928i
$481$	2.68305			0.122337
$482$			1.25240i			0.0570451i
$483$			16.8540i			0.766884i
$484$	10.2524			0.466018
$485$	−3.67680	−	18.6585i	−0.166955	−	0.847238i
$486$	−17.5510			−0.796130
$487$			11.0741i			0.501817i	0.968011	+	0.250908i	$0.0807293\pi$
$487$			11.0741i			0.501817i	−0.968011	+	0.250908i	$0.919271\pi$
$488$		−	10.8646i		−	0.491819i
$489$	−36.9205			−1.66960
$490$	2.77551	+	14.0848i	0.125385	+	0.636285i
$491$	8.11704			0.366317			0.183158	−	0.983083i	$-0.441368\pi$
$491$	8.11704			0.366317			0.183158	+	0.983083i	$0.441368\pi$
$492$			7.34153i			0.330982i
$493$			26.6724i			1.20127i
$494$	−5.62620			−0.253135
$495$	−8.77551	+	1.72928i	−0.394430	+	0.0777254i
$496$	8.11704			0.364466
$497$		−	7.75386i		−	0.347808i
$498$		−	0.747604i		−	0.0335009i
$499$	−0.295298			−0.0132193			−0.00660967	−	0.999978i	$-0.502104\pi$
$499$	−0.295298			−0.0132193			−0.00660967	+	0.999978i	$0.502104\pi$
$500$	9.32924	−	6.16160i	0.417216	−	0.275555i
$501$	27.1912			1.21481
$502$		−	10.5939i		−	0.472830i
$503$			19.6016i			0.873993i	0.899463	+	0.436996i	$0.143958\pi$
$503$			19.6016i			0.873993i	−0.899463	+	0.436996i	$0.856042\pi$
$504$	3.52311			0.156932
$505$	−36.0140	+	7.09683i	−1.60260	+	0.315805i
$506$	6.92919			0.308040
$507$		−	51.5144i		−	2.28783i
$508$			16.9817i			0.753440i
$509$	1.79383			0.0795102			0.0397551	−	0.999209i	$-0.487342\pi$
$509$	1.79383			0.0795102			0.0397551	+	0.999209i	$0.487342\pi$
$510$	−4.32924	−	21.9694i	−0.191702	−	0.972821i
$511$	−12.4908			−0.552562
$512$		−	1.00000i		−	0.0441942i
$513$			4.49084i			0.198275i
$514$	0.153681			0.00677859
$515$	4.16763	+	21.1493i	0.183648	+	0.931950i
$516$	18.9571			0.834540
$517$			1.08287i			0.0476247i
$518$		−	0.363176i		−	0.0159570i
$519$	−8.23407			−0.361436
$520$	12.3432	−	2.43232i	0.541285	−	0.106664i
$521$	−2.61850			−0.114719			−0.0573593	−	0.998354i	$-0.518268\pi$
$521$	−2.61850			−0.114719			−0.0573593	+	0.998354i	$0.518268\pi$
$522$			34.0279i			1.48936i
$523$			14.9956i			0.655713i	0.944728	+	0.327857i	$0.106326\pi$
$523$			14.9956i			0.655713i	−0.944728	+	0.327857i	$0.893674\pi$
$524$	−0.541436			−0.0236528
$525$	−9.72928	+	3.98937i	−0.424621	+	0.174111i
$526$	0.504792			0.0220100
$527$			29.4340i			1.28216i
$528$		−	2.38776i		−	0.103914i
$529$	−41.2234			−1.79232
$530$	−5.20783	+	1.02624i	−0.226214	+	0.0445772i
$531$	20.7755			0.901580
$532$			0.761557i			0.0330177i
$533$		−	14.9571i		−	0.647864i
$534$	−1.07081			−0.0463384
$535$	1.85235	+	9.40005i	0.0800841	+	0.406399i
$536$	1.03228			0.0445875
$537$		−	32.5693i		−	1.40547i
$538$		−	3.49521i		−	0.150689i
$539$	−5.55102			−0.239099
$540$	−1.94148	−	9.85235i	−0.0835481	−	0.423978i
$541$	3.40608			0.146439			0.0732194	−	0.997316i	$-0.476673\pi$
$541$	3.40608			0.146439			0.0732194	+	0.997316i	$0.476673\pi$
$542$		−	5.47252i		−	0.235065i
$543$			40.2341i			1.72661i
$544$	3.62620			0.155472
$545$	−29.4419	+	5.80175i	−1.26115	+	0.248520i
$546$	−11.8324			−0.506378
$547$		−	4.74760i		−	0.202993i	−0.994836	−	0.101496i	$-0.967637\pi$
$547$		−	4.74760i		−	0.202993i	0.994836	−	0.101496i	$-0.0323630\pi$
$548$			2.87859i			0.122967i
$549$	50.2620			2.14513
$550$	1.64015	+	4.00000i	0.0699363	+	0.170561i
$551$	−7.35548			−0.313354
$552$			22.1310i			0.941958i
$553$			9.57227i			0.407054i
$554$	−12.9538			−0.550353
$555$	−2.88922	+	0.569343i	−0.122641	+	0.0241673i
$556$	3.58767			0.152151
$557$		−	43.0462i		−	1.82393i	−0.410271	−	0.911964i	$-0.634566\pi$
$557$		−	43.0462i		−	1.82393i	0.410271	−	0.911964i	$-0.365434\pi$
$558$			37.5510i			1.58966i
$559$	−38.6218			−1.63353
$560$	−0.329237	−	1.67076i	−0.0139128	−	0.0706026i
$561$	8.65847			0.365561
$562$		−	0.153681i		−	0.00648265i
$563$			17.0096i			0.716869i	0.933555	+	0.358434i	$0.116689\pi$
$563$			17.0096i			0.716869i	−0.933555	+	0.358434i	$0.883311\pi$
$564$	−3.45856			−0.145632
$565$	4.46293	+	22.6478i	0.187757	+	0.952802i
$566$	−18.2341			−0.766435
$567$		−	1.12473i		−	0.0472343i
$568$		−	10.1816i		−	0.427210i
$569$	19.7572			0.828264			0.414132	−	0.910217i	$-0.364085\pi$
$569$	19.7572			0.828264			0.414132	+	0.910217i	$0.364085\pi$
$570$	6.05852	−	1.19388i	0.253763	−	0.0500060i
$571$	−11.3973			−0.476964			−0.238482	−	0.971147i	$-0.576650\pi$
$571$	−11.3973			−0.476964			−0.238482	+	0.971147i	$0.576650\pi$
$572$			4.86464i			0.203401i
$573$			36.5587i			1.52726i
$574$	−2.02458			−0.0845043
$575$	−15.2018	−	37.0741i	−0.633959	−	1.54610i
$576$	4.62620			0.192758
$577$			18.3372i			0.763386i	0.924289	+	0.381693i	$0.124659\pi$
$577$			18.3372i			0.763386i	−0.924289	+	0.381693i	$0.875341\pi$
$578$		−	3.85069i		−	0.160167i
$579$	−7.01832			−0.291672
$580$	16.1370	−	3.17992i	0.670053	−	0.132039i
$581$	0.206167			0.00855327
$582$			23.4865i			0.973546i
$583$		−	2.05249i		−	0.0850053i
$584$	−16.4017			−0.678708
$585$	11.2524	+	57.1020i	0.465229	+	2.36088i
$586$	2.03853			0.0842110
$587$			11.9475i			0.493127i	0.969127	+	0.246563i	$0.0793013\pi$
$587$			11.9475i			0.493127i	−0.969127	+	0.246563i	$0.920699\pi$
$588$		−	17.7293i		−	0.731143i
$589$	−8.11704			−0.334457
$590$	−1.94148	−	9.85235i	−0.0799295	−	0.405615i
$591$	−54.9850			−2.26178
$592$		−	0.476886i		−	0.0195999i
$593$		−	24.3911i		−	1.00162i	−0.865557	−	0.500811i	$-0.833035\pi$
$593$		−	24.3911i		−	1.00162i	0.865557	−	0.500811i	$-0.166965\pi$
$594$	3.88296			0.159320
$595$	6.05852	−	1.19388i	0.248375	−	0.0489442i
$596$	−16.8401			−0.689796
$597$			56.0943i			2.29579i
$598$		−	45.0881i		−	1.84379i
$599$	21.0708			0.860930			0.430465	−	0.902607i	$-0.358350\pi$
$599$	21.0708			0.860930			0.430465	+	0.902607i	$0.358350\pi$
$600$	−12.7755	+	5.23844i	−0.521558	+	0.213859i
$601$	32.3878			1.32112			0.660562	−	0.750771i	$-0.270318\pi$
$601$	32.3878			1.32112			0.660562	+	0.750771i	$0.270318\pi$
$602$			5.22782i			0.213070i
$603$			4.77551i			0.194474i
$604$	16.9817			0.690975
$605$	22.4925	−	4.43232i	0.914450	−	0.180199i
$606$	45.3328			1.84152
$607$		−	19.0183i		−	0.771930i	−0.922513	−	0.385965i	$-0.873869\pi$
$607$		−	19.0183i		−	0.771930i	0.922513	−	0.385965i	$-0.126131\pi$
$608$			1.00000i			0.0405554i
$609$	−15.4692			−0.626843
$610$	−4.69701	−	23.8357i	−0.190176	−	0.965079i
$611$	7.04623			0.285060
$612$			16.7755i			0.678110i
$613$		−	23.5756i		−	0.952210i	−0.879389	−	0.476105i	$-0.842048\pi$
$613$		−	23.5756i		−	0.952210i	0.879389	−	0.476105i	$-0.157952\pi$
$614$	−16.5414			−0.667558
$615$	3.17389	+	16.1064i	0.127984	+	0.649473i
$616$	0.658473			0.0265307
$617$			26.2707i			1.05762i	0.848740	+	0.528810i	$0.177361\pi$
$617$			26.2707i			1.05762i	−0.848740	+	0.528810i	$0.822639\pi$
$618$		−	26.6218i		−	1.07089i
$619$	−11.4985			−0.462165			−0.231083	−	0.972934i	$-0.574227\pi$
$619$	−11.4985			−0.462165			−0.231083	+	0.972934i	$0.574227\pi$
$620$	17.8078	−	3.50916i	0.715178	−	0.140931i
$621$	−35.9894			−1.44420
$622$			21.4725i			0.860969i
$623$		−	0.295298i		−	0.0118309i
$624$	−15.5371			−0.621980
$625$	17.8034	−	17.5510i	0.712137	−	0.702041i
$626$	−1.12141			−0.0448204
$627$			2.38776i			0.0953578i
$628$			14.8401i			0.592183i
$629$	1.72928			0.0689510
$630$	7.72928	−	1.52311i	0.307942	−	0.0606823i
$631$	−45.8130			−1.82379			−0.911893	−	0.410427i	$-0.865380\pi$
$631$	−45.8130			−1.82379			−0.911893	+	0.410427i	$0.865380\pi$
$632$			12.5693i			0.499982i
$633$			49.8236i			1.98031i
$634$	29.8882			1.18701
$635$	7.34153	+	37.2557i	0.291340	+	1.47845i
$636$	6.55539			0.259938
$637$			36.1204i			1.43114i
$638$			6.35985i			0.251789i
$639$	47.1020			1.86333
$640$	−0.432320	−	2.19388i	−0.0170890	−	0.0867206i
$641$	1.36943			0.0540894			0.0270447	−	0.999634i	$-0.491390\pi$
$641$	1.36943			0.0540894			0.0270447	+	0.999634i	$0.491390\pi$
$642$		−	11.8324i		−	0.466986i
$643$		−	24.7389i		−	0.975606i	−0.872954	−	0.487803i	$-0.837799\pi$
$643$		−	24.7389i		−	0.975606i	0.872954	−	0.487803i	$-0.162201\pi$
$644$	−6.10308			−0.240495
$645$	41.5896	−	8.19554i	1.63759	−	0.322699i
$646$	−3.62620			−0.142671
$647$			6.82611i			0.268362i	0.990957	+	0.134181i	$0.0428404\pi$
$647$			6.82611i			0.268362i	−0.990957	+	0.134181i	$0.957160\pi$
$648$		−	1.47689i		−	0.0580175i
$649$	3.88296			0.152420
$650$	26.0279	−	10.6724i	1.02090	−	0.418607i
$651$	−17.0708			−0.669058
$652$		−	13.3694i		−	0.523587i
$653$			6.91713i			0.270688i	0.990799	+	0.135344i	$0.0432140\pi$
$653$			6.91713i			0.270688i	−0.990799	+	0.135344i	$0.956786\pi$
$654$	37.0602			1.44917
$655$	−1.18785	+	0.234074i	−0.0464130	+	0.00914603i
$656$	−2.65847			−0.103796
$657$		−	75.8776i		−	2.96027i
$658$		−	0.953771i		−	0.0371819i
$659$	−9.44461			−0.367910			−0.183955	−	0.982935i	$-0.558890\pi$
$659$	−9.44461			−0.367910			−0.183955	+	0.982935i	$0.558890\pi$
$660$	−1.03228	−	5.23844i	−0.0401813	−	0.203906i
$661$	−22.1955			−0.863306			−0.431653	−	0.902040i	$-0.642070\pi$
$661$	−22.1955			−0.863306			−0.431653	+	0.902040i	$0.642070\pi$
$662$		−	32.3126i		−	1.25586i
$663$		−	56.3405i		−	2.18808i
$664$	0.270718			0.0105059
$665$	0.329237	+	1.67076i	0.0127673	+	0.0647894i
$666$	2.20617			0.0854873
$667$		−	58.9465i		−	2.28242i
$668$			9.84632i			0.380966i
$669$	37.3449			1.44384
$670$	2.26469	−	0.446274i	0.0874925	−	0.0172411i
$671$	9.39401			0.362652
$672$			2.10308i			0.0811282i
$673$			12.2986i			0.474077i	0.971500	+	0.237039i	$0.0761768\pi$
$673$			12.2986i			0.474077i	−0.971500	+	0.237039i	$0.923823\pi$
$674$	−26.3511			−1.01501
$675$	−8.51875	−	20.7755i	−0.327887	−	0.799650i
$676$	18.6541			0.717466
$677$			35.9527i			1.38178i	0.722962	+	0.690888i	$0.242780\pi$
$677$			35.9527i			1.38178i	−0.722962	+	0.690888i	$0.757220\pi$
$678$		−	28.5081i		−	1.09485i
$679$	−6.47689			−0.248560
$680$	7.95543	−	1.56768i	0.305077	−	0.0601178i
$681$	37.5616			1.43937
$682$			7.01832i			0.268745i
$683$		−	9.00958i		−	0.344742i	−0.985032	−	0.172371i	$-0.944857\pi$
$683$		−	9.00958i		−	0.344742i	0.985032	−	0.172371i	$-0.0551428\pi$
$684$	−4.62620			−0.176887
$685$	1.24448	+	6.31528i	0.0475490	+	0.241295i
$686$	10.2201			0.390206
$687$		−	37.5231i		−	1.43160i
$688$			6.86464i			0.261712i
$689$	−13.3555			−0.508803
$690$	9.56768	+	48.5527i	0.364235	+	1.84837i
$691$	−9.11078			−0.346590			−0.173295	−	0.984870i	$-0.555441\pi$
$691$	−9.11078			−0.346590			−0.173295	+	0.984870i	$0.555441\pi$
$692$		−	2.98168i		−	0.113346i
$693$			3.04623i			0.115717i
$694$	2.77551			0.105357
$695$	7.87090	−	1.55102i	0.298560	−	0.0588336i
$696$	−20.3126			−0.769946
$697$		−	9.64015i		−	0.365147i
$698$			11.5510i			0.437213i
$699$	−70.5606			−2.66885
$700$	−1.44461	−	3.52311i	−0.0546011	−	0.133161i
$701$	−14.7476			−0.557009			−0.278505	−	0.960435i	$-0.589839\pi$
$701$	−14.7476			−0.557009			−0.278505	+	0.960435i	$0.589839\pi$
$702$		−	25.2663i		−	0.953617i
$703$			0.476886i			0.0179861i
$704$	0.864641			0.0325874
$705$	−7.58767	+	1.49521i	−0.285768	+	0.0563128i
$706$	−8.40171			−0.316202
$707$			12.5015i			0.470166i
$708$			12.4017i			0.466085i
$709$	8.63389			0.324253			0.162126	−	0.986770i	$-0.448165\pi$
$709$	8.63389			0.324253			0.162126	+	0.986770i	$0.448165\pi$
$710$	−4.40171	−	22.3372i	−0.165193	−	0.838299i
$711$	−58.1483			−2.18073
$712$		−	0.387755i		−	0.0145317i
$713$		−	65.0496i		−	2.43613i
$714$	−7.62620			−0.285403
$715$	2.10308	+	10.6724i	0.0786509	+	0.399126i
$716$	11.7938			0.440756
$717$			31.2909i			1.16858i
$718$			22.7895i			0.850495i
$719$	38.2759			1.42745			0.713726	−	0.700425i	$-0.247006\pi$
$719$	38.2759			1.42745			0.713726	+	0.700425i	$0.247006\pi$
$720$	10.1493	−	2.00000i	0.378243	−	0.0745356i
$721$	7.34153			0.273413
$722$		−	1.00000i		−	0.0372161i
$723$		−	3.45856i		−	0.128625i
$724$	−14.5693			−0.541465
$725$	34.0279	−	13.9527i	1.26376	−	0.518191i
$726$	−28.3126			−1.05078
$727$			31.1893i			1.15675i	0.815772	+	0.578373i	$0.196312\pi$
$727$			31.1893i			1.15675i	−0.815772	+	0.578373i	$0.803688\pi$
$728$		−	4.28467i		−	0.158800i
$729$	44.0375			1.63102
$730$	−35.9833	+	7.09079i	−1.33180	+	0.262442i
$731$	−24.8925			−0.920684
$732$			30.0033i			1.10895i
$733$		−	13.9634i		−	0.515748i	−0.966179	−	0.257874i	$-0.916978\pi$
$733$		−	13.9634i		−	0.515748i	0.966179	−	0.257874i	$-0.0830220\pi$
$734$	−4.06455			−0.150025
$735$	−7.66473	−	38.8959i	−0.282718	−	1.43470i
$736$	−8.01395			−0.295398
$737$			0.892548i			0.0328774i
$738$		−	12.2986i		−	0.452719i
$739$	−9.02165			−0.331867			−0.165933	−	0.986137i	$-0.553064\pi$
$739$	−9.02165			−0.331867			−0.165933	+	0.986137i	$0.553064\pi$
$740$	−0.206167	−	1.04623i	−0.00757886	−	0.0384601i
$741$	15.5371			0.570768
$742$			1.80779i			0.0663659i
$743$		−	15.0342i		−	0.551550i	−0.961222	−	0.275775i	$-0.911066\pi$
$743$		−	15.0342i		−	0.551550i	0.961222	−	0.275775i	$-0.0889345\pi$
$744$	−22.4157			−0.821798
$745$	−36.9450	+	7.28030i	−1.35356	+	0.266730i
$746$	−18.4017			−0.673734
$747$			1.25240i			0.0458228i
$748$			3.13536i			0.114640i
$749$	3.26302			0.119228
$750$	−25.7632	+	17.0156i	−0.940740	+	0.621322i
$751$	29.6681			1.08260			0.541301	−	0.840829i	$-0.317932\pi$
$751$	29.6681			1.08260			0.541301	+	0.840829i	$0.317932\pi$
$752$		−	1.25240i		−	0.0456702i
$753$			29.2557i			1.06614i
$754$	41.3834			1.50709
$755$	37.2557	−	7.34153i	1.35587	−	0.267186i
$756$	−3.42003			−0.124385
$757$		−	10.5819i		−	0.384604i	−0.981336	−	0.192302i	$-0.938405\pi$
$757$		−	10.5819i		−	0.384604i	0.981336	−	0.192302i	$-0.0615953\pi$
$758$			1.23844i			0.0449823i
$759$	−19.1354			−0.694570
$760$	0.432320	+	2.19388i	0.0156819	+	0.0795803i
$761$	−0.979789			−0.0355173			−0.0177587	−	0.999842i	$-0.505653\pi$
$761$	−0.979789			−0.0355173			−0.0177587	+	0.999842i	$0.505653\pi$
$762$		−	46.8959i		−	1.69886i
$763$			10.2201i			0.369993i
$764$	−13.2384			−0.478950
$765$	7.25240	+	36.8034i	0.262211	+	1.33063i
$766$	16.8646			0.609344
$767$		−	25.2663i		−	0.912315i
$768$			2.76156i			0.0996491i
$769$	−43.1772			−1.55701			−0.778505	−	0.627638i	$-0.784022\pi$
$769$	−43.1772			−1.55701			−0.778505	+	0.627638i	$0.784022\pi$
$770$	1.44461	−	0.284672i	0.0520601	−	0.0102589i
$771$	−0.424399			−0.0152844
$772$		−	2.54144i		−	0.0914683i
$773$			37.5250i			1.34968i	0.737964	+	0.674840i	$0.235787\pi$
$773$			37.5250i			1.34968i	−0.737964	+	0.674840i	$0.764213\pi$
$774$	−31.7572			−1.14149
$775$	37.5510	−	15.3973i	1.34887	−	0.553089i
$776$	−8.50479			−0.305304
$777$			1.00293i			0.0359799i
$778$			8.59392i			0.308107i
$779$	2.65847			0.0952497
$780$	−34.0864	+	6.71699i	−1.22049	+	0.240507i
$781$	8.80342			0.315011
$782$		−	29.0602i		−	1.03919i
$783$		−	33.0323i		−	1.18048i
$784$	6.42003			0.229287
$785$	6.41566	+	32.5573i	0.228985	+	1.16202i
$786$	1.49521			0.0533323
$787$		−	22.5833i		−	0.805008i	−0.915418	−	0.402504i	$-0.868140\pi$
$787$		−	22.5833i		−	0.805008i	0.915418	−	0.402504i	$-0.131860\pi$
$788$		−	19.9109i		−	0.709295i
$789$	−1.39401			−0.0496282
$790$	5.43398	+	27.5756i	0.193332	+	0.981096i
$791$	7.86171			0.279530
$792$			4.00000i			0.142134i
$793$		−	61.1266i		−	2.17067i
$794$	−16.0558			−0.569799
$795$	14.3817	−	2.83403i	0.510067	−	0.100513i
$796$	−20.3126			−0.719960
$797$		−	35.9806i		−	1.27450i	−0.770657	−	0.637250i	$-0.780072\pi$
$797$		−	35.9806i		−	1.27450i	0.770657	−	0.637250i	$-0.219928\pi$
$798$		−	2.10308i		−	0.0744484i
$799$	4.54144			0.160664
$800$	−1.89692	−	4.62620i	−0.0670661	−	0.163561i
$801$	1.79383			0.0633820
$802$			14.8925i			0.525874i
$803$		−	14.1816i		−	0.500457i
$804$	−2.85069			−0.100536
$805$	−13.3894	+	2.63849i	−0.471915	+	0.0929945i
$806$	45.6681			1.60859
$807$			9.65222i			0.339774i
$808$			16.4157i			0.577501i
$809$	0.955660			0.0335992			0.0167996	−	0.999859i	$-0.494652\pi$
$809$	0.955660			0.0335992			0.0167996	+	0.999859i	$0.494652\pi$
$810$	−0.638488	−	3.24011i	−0.0224342	−	0.113846i
$811$	−7.53707			−0.264662			−0.132331	−	0.991206i	$-0.542246\pi$
$811$	−7.53707			−0.264662			−0.132331	+	0.991206i	$0.542246\pi$
$812$		−	5.60162i		−	0.196578i
$813$			15.1127i			0.530024i
$814$	0.412335			0.0144523
$815$	−5.77988	−	29.3309i	−0.202460	−	1.02742i
$816$	−10.0140			−0.350558
$817$		−	6.86464i		−	0.240163i
$818$		−	18.3511i		−	0.641632i
$819$	19.8217			0.692628
$820$	−5.83237	+	1.14931i	−0.203675	+	0.0401357i
$821$	13.3082			0.464460			0.232230	−	0.972661i	$-0.425398\pi$
$821$	13.3082			0.464460			0.232230	+	0.972661i	$0.425398\pi$
$822$		−	7.94940i		−	0.277267i
$823$			24.4050i			0.850706i	0.905028	+	0.425353i	$0.139850\pi$
$823$			24.4050i			0.850706i	−0.905028	+	0.425353i	$0.860150\pi$
$824$	9.64015			0.335831
$825$	−4.52937	−	11.0462i	−0.157692	−	0.384580i
$826$	−3.42003			−0.118998
$827$			11.6874i			0.406411i	0.979136	+	0.203206i	$0.0651360\pi$
$827$			11.6874i			0.406411i	−0.979136	+	0.203206i	$0.934864\pi$
$828$		−	37.0741i		−	1.28842i
$829$	−25.6541			−0.891004			−0.445502	−	0.895281i	$-0.646975\pi$
$829$	−25.6541			−0.891004			−0.445502	+	0.895281i	$0.646975\pi$
$830$	0.593923	−	0.117037i	0.0206154	−	0.00406241i
$831$	35.7726			1.24094
$832$		−	5.62620i		−	0.195053i
$833$			23.2803i			0.806615i
$834$	−9.90754			−0.343070
$835$	4.25676	+	21.6016i	0.147311	+	0.747555i
$836$	−0.864641			−0.0299042
$837$		−	36.4523i		−	1.25998i
$838$			34.7509i			1.20045i
$839$	2.91713			0.100710			0.0503552	−	0.998731i	$-0.483965\pi$
$839$	2.91713			0.100710			0.0503552	+	0.998731i	$0.483965\pi$
$840$	0.909206	+	4.61391i	0.0313706	+	0.159195i
$841$	25.1031			0.865624
$842$			40.1589i			1.38397i
$843$			0.424399i			0.0146171i
$844$	−18.0419			−0.621026
$845$	40.9248	−	8.06455i	1.40786	−	0.277429i
$846$	5.79383			0.199196
$847$		−	7.80779i		−	0.268279i
$848$			2.37380i			0.0815167i
$849$	50.3544			1.72816
$850$	16.7755	−	6.87859i	0.575395	−	0.235934i
$851$	−3.82174			−0.131008
$852$			28.1170i			0.963274i
$853$		−	6.24281i		−	0.213750i	−0.994272	−	0.106875i	$-0.965916\pi$
$853$		−	6.24281i		−	0.213750i	0.994272	−	0.106875i	$-0.0340844\pi$
$854$	−8.27405			−0.283132
$855$	−10.1493	+	2.00000i	−0.347099	+	0.0683986i
$856$	4.28467			0.146447
$857$			23.2158i			0.793035i	0.918027	+	0.396517i	$0.129781\pi$
$857$			23.2158i			0.793035i	−0.918027	+	0.396517i	$0.870219\pi$
$858$		−	13.4340i		−	0.458629i
$859$	7.13536			0.243455			0.121728	−	0.992564i	$-0.461157\pi$
$859$	7.13536			0.243455			0.121728	+	0.992564i	$0.461157\pi$
$860$	2.96772	+	15.0602i	0.101199	+	0.513548i
$861$	5.59099			0.190541
$862$		−	34.9571i		−	1.19064i
$863$		−	7.31362i		−	0.248959i	−0.992222	−	0.124479i	$-0.960274\pi$
$863$		−	7.31362i		−	0.248959i	0.992222	−	0.124479i	$-0.0397260\pi$
$864$	−4.49084			−0.152781
$865$	−1.28904	−	6.54144i	−0.0438287	−	0.222416i
$866$	1.13536			0.0385811
$867$			10.6339i			0.361146i
$868$		−	6.18159i		−	0.209817i
$869$	−10.8680			−0.368671
$870$	−44.5633	+	8.78154i	−1.51084	+	0.297722i
$871$	5.80779			0.196789
$872$			13.4200i			0.454460i
$873$		−	39.3449i		−	1.33162i
$874$	8.01395			0.271076
$875$	−4.69241	−	7.10475i	−0.158632	−	0.240184i
$876$	45.2943			1.53035
$877$			22.0173i			0.743471i	0.928339	+	0.371735i	$0.121237\pi$
$877$			22.0173i			0.743471i	−0.928339	+	0.371735i	$0.878763\pi$
$878$		−	6.80009i		−	0.229492i
$879$	−5.62953			−0.189879
$880$	1.89692	−	0.373802i	0.0639450	−	0.0126009i
$881$	11.7572			0.396110			0.198055	−	0.980191i	$-0.436538\pi$
$881$	11.7572			0.396110			0.198055	+	0.980191i	$0.436538\pi$
$882$			29.7003i			1.00006i
$883$			55.6560i			1.87297i	0.350703	+	0.936487i	$0.385943\pi$
$883$			55.6560i			1.87297i	−0.350703	+	0.936487i	$0.614057\pi$
$884$	20.4017			0.686184
$885$	5.36151	+	27.2078i	0.180225	+	0.914581i
$886$	38.0679			1.27892
$887$			6.41566i			0.215417i	0.994183	+	0.107708i	$0.0343513\pi$
$887$			6.41566i			0.215417i	−0.994183	+	0.107708i	$0.965649\pi$
$888$			1.31695i			0.0441938i
$889$	12.9325			0.433743
$890$	−0.167635	−	0.850688i	−0.00561912	−	0.0285151i
$891$	1.27698			0.0427803
$892$			13.5231i			0.452787i
$893$			1.25240i			0.0419098i
$894$	46.5048			1.55535
$895$	25.8742	−	5.09871i	0.864880	−	0.170431i
$896$	−0.761557			−0.0254418
$897$			124.513i			4.15738i
$898$		−	18.5414i		−	0.618736i
$899$	59.7047			1.99126
$900$	21.4017	−	8.77551i	0.713390	−	0.292517i
$901$	−8.60788			−0.286770
$902$		−	2.29862i		−	0.0765358i
$903$		−	14.4369i		−	0.480430i
$904$	10.3232			0.343345
$905$	−31.9634	+	6.29862i	−1.06250	+	0.209373i
$906$	−46.8959			−1.55801
$907$			57.1160i			1.89651i	0.317516	+	0.948253i	$0.397151\pi$
$907$			57.1160i			1.89651i	−0.317516	+	0.948253i	$0.602849\pi$
$908$			13.6016i			0.451386i
$909$	−75.9421			−2.51884
$910$	−1.85235	−	9.40005i	−0.0614048	−	0.311608i
$911$	−26.6339			−0.882420			−0.441210	−	0.897404i	$-0.645451\pi$
$911$	−26.6339			−0.882420			−0.441210	+	0.897404i	$0.645451\pi$
$912$		−	2.76156i		−	0.0914443i
$913$			0.234074i			0.00774672i
$914$	−16.3738			−0.541597
$915$	12.9711	+	65.8236i	0.428810	+	2.17606i
$916$	13.5877			0.448949
$917$			0.412335i			0.0136165i
$918$		−	16.2847i		−	0.537474i
$919$	−6.63246			−0.218785			−0.109392	−	0.993999i	$-0.534890\pi$
$919$	−6.63246			−0.218785			−0.109392	+	0.993999i	$0.534890\pi$
$920$	−17.5816	+	3.46460i	−0.579649	+	0.114224i
$921$	45.6801			1.50521
$922$		−	1.70470i		−	0.0561414i
$923$		−	57.2836i		−	1.88551i
$924$	−1.81841			−0.0598214
$925$	−0.904612	−	2.20617i	−0.0297435	−	0.0725383i
$926$	−10.0279			−0.329537
$927$			44.5972i			1.46477i
$928$		−	7.35548i		−	0.241455i
$929$	50.0173			1.64101			0.820507	−	0.571637i	$-0.193691\pi$
$929$	50.0173			1.64101			0.820507	+	0.571637i	$0.193691\pi$
$930$	−49.1772	+	9.69075i	−1.61258	+	0.317772i
$931$	−6.42003			−0.210408
$932$		−	25.5510i		−	0.836952i
$933$		−	59.2976i		−	1.94132i
$934$	−32.7509			−1.07164
$935$	1.35548	+	6.87859i	0.0443289	+	0.224954i
$936$	26.0279			0.850749
$937$			39.8882i			1.30309i	0.758610	+	0.651545i	$0.225879\pi$
$937$			39.8882i			1.30309i	−0.758610	+	0.651545i	$0.774121\pi$
$938$		−	0.786137i		−	0.0256683i
$939$	3.09683			0.101061
$940$	−0.541436	−	2.74760i	−0.0176597	−	0.0896170i
$941$	−5.59829			−0.182499			−0.0912495	−	0.995828i	$-0.529086\pi$
$941$	−5.59829			−0.182499			−0.0912495	+	0.995828i	$0.529086\pi$
$942$		−	40.9817i		−	1.33526i
$943$			21.3049i			0.693782i
$944$	−4.49084			−0.146164
$945$	−7.50313	+	1.47855i	−0.244077	+	0.0480972i
$946$	−5.93545			−0.192978
$947$		−	12.7110i		−	0.413051i	−0.978441	−	0.206525i	$-0.933784\pi$
$947$		−	12.7110i		−	0.413051i	0.978441	−	0.206525i	$-0.0662156\pi$
$948$		−	34.7110i		−	1.12736i
$949$	−92.2793			−2.99551
$950$	1.89692	+	4.62620i	0.0615441	+	0.150094i
$951$	−82.5379			−2.67648
$952$		−	2.76156i		−	0.0895026i
$953$		−	57.0129i		−	1.84683i	−0.383804	−	0.923415i	$-0.625386\pi$
$953$		−	57.0129i		−	1.84683i	0.383804	−	0.923415i	$-0.374614\pi$
$954$	−10.9817			−0.355545
$955$	−29.0435	+	5.72325i	−0.939826	+	0.185200i
$956$	−11.3309			−0.366468
$957$		−	17.5631i		−	0.567734i
$958$			27.2803i			0.881387i
$959$	2.19221			0.0707903
$960$	1.19388	+	6.05852i	0.0385322	+	0.195538i
$961$	34.8863			1.12536
$962$		−	2.68305i		−	0.0865051i
$963$			19.8217i			0.638747i
$964$	1.25240			0.0403370
$965$	−1.09871	−	5.57560i	−0.0353689	−	0.179485i
$966$	16.8540			0.542269
$967$			33.0183i			1.06180i	0.847435	+	0.530899i	$0.178146\pi$
$967$			33.0183i			1.06180i	−0.847435	+	0.530899i	$0.821854\pi$
$968$		−	10.2524i		−	0.329524i
$969$	10.0140			0.321695
$970$	−18.6585	+	3.67680i	−0.599087	+	0.118055i
$971$	−3.04623			−0.0977581			−0.0488791	−	0.998805i	$-0.515565\pi$
$971$	−3.04623			−0.0977581			−0.0488791	+	0.998805i	$0.515565\pi$
$972$			17.5510i			0.562949i
$973$		−	2.73221i		−	0.0875907i
$974$	11.0741			0.354838
$975$	−71.8776	+	29.4725i	−2.30192	+	0.943876i
$976$	−10.8646			−0.347769
$977$		−	13.4465i		−	0.430192i	−0.976593	−	0.215096i	$-0.930994\pi$
$977$		−	13.4465i		−	0.430192i	0.976593	−	0.215096i	$-0.0690064\pi$
$978$			36.9205i			1.18059i
$979$	0.335269			0.0107152
$980$	14.0848	−	2.77551i	0.449921	−	0.0886604i
$981$	−62.0837			−1.98218
$982$		−	8.11704i		−	0.259025i
$983$		−	22.0646i		−	0.703750i	−0.936047	−	0.351875i	$-0.885544\pi$
$983$		−	22.0646i		−	0.703750i	0.936047	−	0.351875i	$-0.114456\pi$
$984$	7.34153			0.234039
$985$	−8.60788	−	43.6820i	−0.274270	−	1.39182i
$986$	26.6724			0.849423
$987$			2.63389i			0.0838378i
$988$			5.62620i			0.178993i
$989$	55.0129			1.74931
$990$	1.72928	+	8.77551i	0.0549602	+	0.278904i
$991$	51.9946			1.65166			0.825831	−	0.563917i	$-0.190706\pi$
$991$	51.9946			1.65166			0.825831	+	0.563917i	$0.190706\pi$
$992$		−	8.11704i		−	0.257716i
$993$			89.2330i			2.83172i
$994$	−7.75386			−0.245938
$995$	−44.5633	+	8.78154i	−1.41275	+	0.278394i
$996$	−0.747604			−0.0236887
$997$			37.7693i			1.19616i	0.801435	+	0.598082i	$0.204070\pi$
$997$			37.7693i			1.19616i	−0.801435	+	0.598082i	$0.795930\pi$
$998$			0.295298i			0.00934749i
$999$	−2.14162			−0.0677578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.b.b.39.3	✓	6
3.2	odd	2		1710.2.d.d.1369.6		6
4.3	odd	2		1520.2.d.j.609.1		6
5.2	odd	4		950.2.a.n.1.3		3
5.3	odd	4		950.2.a.i.1.1		3
5.4	even	2	inner	190.2.b.b.39.4	yes	6
15.2	even	4		8550.2.a.ck.1.1		3
15.8	even	4		8550.2.a.cl.1.3		3
15.14	odd	2		1710.2.d.d.1369.3		6
20.3	even	4		7600.2.a.cd.1.3		3
20.7	even	4		7600.2.a.bi.1.1		3
20.19	odd	2		1520.2.d.j.609.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.3	✓	6	1.1	even	1	trivial
190.2.b.b.39.4	yes	6	5.4	even	2	inner
950.2.a.i.1.1		3	5.3	odd	4
950.2.a.n.1.3		3	5.2	odd	4
1520.2.d.j.609.1		6	4.3	odd	2
1520.2.d.j.609.6		6	20.19	odd	2
1710.2.d.d.1369.3		6	15.14	odd	2
1710.2.d.d.1369.6		6	3.2	odd	2
7600.2.a.bi.1.1		3	20.7	even	4
7600.2.a.cd.1.3		3	20.3	even	4
8550.2.a.ck.1.1		3	15.2	even	4
8550.2.a.cl.1.3		3	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.76156i q^{3} -1.00000 q^{4} +(-2.19388 + 0.432320i) q^{5} +2.76156 q^{6} +0.761557i q^{7} +1.00000i q^{8} -4.62620 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.76156i q^{3} -1.00000 q^{4} +(-2.19388 + 0.432320i) q^{5} +2.76156 q^{6} +0.761557i q^{7} +1.00000i q^{8} -4.62620 q^{9} +(0.432320 + 2.19388i) q^{10} -0.864641 q^{11} -2.76156i q^{12} +5.62620i q^{13} +0.761557 q^{14} +(-1.19388 - 6.05852i) q^{15} +1.00000 q^{16} +3.62620i q^{17} +4.62620i q^{18} -1.00000 q^{19} +(2.19388 - 0.432320i) q^{20} -2.10308 q^{21} +0.864641i q^{22} -8.01395i q^{23} -2.76156 q^{24} +(4.62620 - 1.89692i) q^{25} +5.62620 q^{26} -4.49084i q^{27} -0.761557i q^{28} +7.35548 q^{29} +(-6.05852 + 1.19388i) q^{30} +8.11704 q^{31} -1.00000i q^{32} -2.38776i q^{33} +3.62620 q^{34} +(-0.329237 - 1.67076i) q^{35} +4.62620 q^{36} -0.476886i q^{37} +1.00000i q^{38} -15.5371 q^{39} +(-0.432320 - 2.19388i) q^{40} -2.65847 q^{41} +2.10308i q^{42} +6.86464i q^{43} +0.864641 q^{44} +(10.1493 - 2.00000i) q^{45} -8.01395 q^{46} -1.25240i q^{47} +2.76156i q^{48} +6.42003 q^{49} +(-1.89692 - 4.62620i) q^{50} -10.0140 q^{51} -5.62620i q^{52} +2.37380i q^{53} -4.49084 q^{54} +(1.89692 - 0.373802i) q^{55} -0.761557 q^{56} -2.76156i q^{57} -7.35548i q^{58} -4.49084 q^{59} +(1.19388 + 6.05852i) q^{60} -10.8646 q^{61} -8.11704i q^{62} -3.52311i q^{63} -1.00000 q^{64} +(-2.43232 - 12.3432i) q^{65} -2.38776 q^{66} -1.03228i q^{67} -3.62620i q^{68} +22.1310 q^{69} +(-1.67076 + 0.329237i) q^{70} -10.1816 q^{71} -4.62620i q^{72} +16.4017i q^{73} -0.476886 q^{74} +(5.23844 + 12.7755i) q^{75} +1.00000 q^{76} -0.658473i q^{77} +15.5371i q^{78} +12.5693 q^{79} +(-2.19388 + 0.432320i) q^{80} -1.47689 q^{81} +2.65847i q^{82} -0.270718i q^{83} +2.10308 q^{84} +(-1.56768 - 7.95543i) q^{85} +6.86464 q^{86} +20.3126i q^{87} -0.864641i q^{88} -0.387755 q^{89} +(-2.00000 - 10.1493i) q^{90} -4.28467 q^{91} +8.01395i q^{92} +22.4157i q^{93} -1.25240 q^{94} +(2.19388 - 0.432320i) q^{95} +2.76156 q^{96} +8.50479i q^{97} -6.42003i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} + 4 q^{6} - 10 q^{9} - 8 q^{14} + 8 q^{15} + 6 q^{16} - 6 q^{19} - 2 q^{20} - 20 q^{21} - 4 q^{24} + 10 q^{25} + 16 q^{26} + 16 q^{29} - 16 q^{30} + 8 q^{31} + 4 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{39} + 4 q^{41} + 18 q^{45} + 6 q^{49} - 4 q^{50} - 12 q^{51} - 4 q^{54} + 4 q^{55} + 8 q^{56} - 4 q^{59} - 8 q^{60} - 60 q^{61} - 6 q^{64} - 12 q^{65} + 16 q^{66} + 44 q^{69} - 20 q^{70} - 16 q^{71} - 28 q^{74} + 44 q^{75} + 6 q^{76} + 2 q^{80} - 34 q^{81} + 20 q^{84} - 12 q^{85} + 36 q^{86} + 28 q^{89} - 12 q^{90} + 12 q^{91} + 28 q^{94} - 2 q^{95} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 + 4 * q^6 - 10 * q^9 - 8 * q^14 + 8 * q^15 + 6 * q^16 - 6 * q^19 - 2 * q^20 - 20 * q^21 - 4 * q^24 + 10 * q^25 + 16 * q^26 + 16 * q^29 - 16 * q^30 + 8 * q^31 + 4 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^39 + 4 * q^41 + 18 * q^45 + 6 * q^49 - 4 * q^50 - 12 * q^51 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 4 * q^59 - 8 * q^60 - 60 * q^61 - 6 * q^64 - 12 * q^65 + 16 * q^66 + 44 * q^69 - 20 * q^70 - 16 * q^71 - 28 * q^74 + 44 * q^75 + 6 * q^76 + 2 * q^80 - 34 * q^81 + 20 * q^84 - 12 * q^85 + 36 * q^86 + 28 * q^89 - 12 * q^90 + 12 * q^91 + 28 * q^94 - 2 * q^95 + 4 * q^96 + 24 * q^99

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