LMFDB - Embedded newform 190.2.b.b.39.4

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.76156i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} +2.76156 q^{6} -0.761557i q^{7} -1.00000i q^{8} -4.62620 q^{9} +(0.432320 - 2.19388i) q^{10} -0.864641 q^{11} +2.76156i q^{12} -5.62620i q^{13} +0.761557 q^{14} +(-1.19388 + 6.05852i) q^{15} +1.00000 q^{16} -3.62620i q^{17} -4.62620i q^{18} -1.00000 q^{19} +(2.19388 + 0.432320i) q^{20} -2.10308 q^{21} -0.864641i q^{22} +8.01395i q^{23} -2.76156 q^{24} +(4.62620 + 1.89692i) q^{25} +5.62620 q^{26} +4.49084i q^{27} +0.761557i q^{28} +7.35548 q^{29} +(-6.05852 - 1.19388i) q^{30} +8.11704 q^{31} +1.00000i q^{32} +2.38776i q^{33} +3.62620 q^{34} +(-0.329237 + 1.67076i) q^{35} +4.62620 q^{36} +0.476886i q^{37} -1.00000i q^{38} -15.5371 q^{39} +(-0.432320 + 2.19388i) q^{40} -2.65847 q^{41} -2.10308i q^{42} -6.86464i q^{43} +0.864641 q^{44} +(10.1493 + 2.00000i) q^{45} -8.01395 q^{46} +1.25240i q^{47} -2.76156i q^{48} +6.42003 q^{49} +(-1.89692 + 4.62620i) q^{50} -10.0140 q^{51} +5.62620i q^{52} -2.37380i q^{53} -4.49084 q^{54} +(1.89692 + 0.373802i) q^{55} -0.761557 q^{56} +2.76156i q^{57} +7.35548i q^{58} -4.49084 q^{59} +(1.19388 - 6.05852i) q^{60} -10.8646 q^{61} +8.11704i q^{62} +3.52311i q^{63} -1.00000 q^{64} +(-2.43232 + 12.3432i) q^{65} -2.38776 q^{66} +1.03228i q^{67} +3.62620i q^{68} +22.1310 q^{69} +(-1.67076 - 0.329237i) q^{70} -10.1816 q^{71} +4.62620i q^{72} -16.4017i q^{73} -0.476886 q^{74} +(5.23844 - 12.7755i) q^{75} +1.00000 q^{76} +0.658473i q^{77} -15.5371i q^{78} +12.5693 q^{79} +(-2.19388 - 0.432320i) q^{80} -1.47689 q^{81} -2.65847i q^{82} +0.270718i q^{83} +2.10308 q^{84} +(-1.56768 + 7.95543i) q^{85} +6.86464 q^{86} -20.3126i q^{87} +0.864641i q^{88} -0.387755 q^{89} +(-2.00000 + 10.1493i) q^{90} -4.28467 q^{91} -8.01395i q^{92} -22.4157i q^{93} -1.25240 q^{94} +(2.19388 + 0.432320i) q^{95} +2.76156 q^{96} -8.50479i q^{97} +6.42003i q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.706317\pi$
$3$		−	2.76156i		−	1.59439i	0.603725	−	0.797193i	$-0.293683\pi$
$4$	−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	$-0.954029\pi$
$7$		−	0.761557i		−	0.287842i	0.989589	−	0.143921i	$-0.0459710\pi$
$8$		−	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	$-0.715111\pi$
$13$		−	5.62620i		−	1.56043i	0.625514	−	0.780213i	$-0.284889\pi$
$14$	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	$-0.855070\pi$
$17$		−	3.62620i		−	0.879482i	0.898125	−	0.439741i	$-0.144930\pi$
$18$		−	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	$0.314829\pi$
$23$			8.01395i			1.67102i	−0.549472	+	0.835512i	$0.685171\pi$
$24$	−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	$0.0124809\pi$
$37$			0.476886i			0.0783995i	−0.999231	+	0.0391998i	$0.987519\pi$
$38$		−	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	$-0.824654\pi$
$43$		−	6.86464i		−	1.04685i	0.852072	−	0.523424i	$-0.175346\pi$
$44$	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	$0.0291151\pi$
$47$			1.25240i			0.182681i	−0.995820	+	0.0913404i	$0.970885\pi$
$48$		−	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	$-0.947872\pi$
$53$		−	2.37380i		−	0.326067i	0.986621	−	0.163033i	$-0.0521278\pi$
$54$	−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	$0.0200848\pi$
$67$			1.03228i			0.126113i	−0.998010	+	0.0630563i	$0.979915\pi$
$68$			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	$-0.590519\pi$
$73$		−	16.4017i		−	1.91967i	0.280557	−	0.959837i	$-0.409481\pi$
$74$	−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	$0.00472949\pi$
$83$			0.270718i			0.0297152i	−0.999890	+	0.0148576i	$0.995271\pi$
$84$	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	$-0.857891\pi$
$97$		−	8.50479i		−	0.863531i	0.901986	−	0.431765i	$-0.142109\pi$
$98$			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	$0.157529\pi$
$103$			9.64015i			0.949872i	−0.880020	+	0.474936i	$0.842471\pi$
$104$	−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	$0.0664050\pi$
$107$			4.28467i			0.414215i	−0.978318	+	0.207107i	$0.933595\pi$
$108$		−	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	$0.161385\pi$
$113$			10.3232i			0.971125i	−0.874202	+	0.485563i	$0.838615\pi$
$114$	−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	$0.271607\pi$
$127$			16.9817i			1.50688i	−0.657517	+	0.753440i	$0.728393\pi$
$128$		−	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	$0.0392411\pi$
$137$			2.87859i			0.245935i	−0.992411	+	0.122967i	$0.960759\pi$
$138$			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	$0.201734\pi$
$157$			14.8401i			1.18437i	−0.805804	+	0.592183i	$0.798266\pi$
$158$			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	$-0.824593\pi$
$163$		−	13.3694i		−	1.04717i	0.851972	−	0.523587i	$-0.175407\pi$
$164$	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	$0.124408\pi$
$167$			9.84632i			0.761931i	−0.924589	+	0.380966i	$0.875592\pi$
$168$			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	$-0.963843\pi$
$173$		−	2.98168i		−	0.226693i	0.993556	−	0.113346i	$-0.0361570\pi$
$174$	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	$-0.970844\pi$
$193$		−	2.54144i		−	0.182937i	0.995808	−	0.0914683i	$-0.0291560\pi$
$194$	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	$-0.749013\pi$
$197$		−	19.9109i		−	1.41859i	0.704911	−	0.709295i	$-0.250987\pi$
$198$			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	$0.149570\pi$
$223$			13.5231i			0.905575i	−0.891619	+	0.452787i	$0.850430\pi$
$224$	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	$0.149070\pi$
$227$			13.6016i			0.902771i	−0.892329	+	0.451386i	$0.850930\pi$
$228$		−	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	$-0.684336\pi$
$233$		−	25.5510i		−	1.67390i	0.547277	−	0.836952i	$-0.315664\pi$
$234$	−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	$-0.998474\pi$
$257$		−	0.153681i		−	0.00958637i	0.999989	−	0.00479319i	$-0.00152572\pi$
$258$		−	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	$-0.995046\pi$
$263$		−	0.504792i		−	0.0311268i	0.999879	−	0.0155634i	$-0.00495419\pi$
$264$	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	$0.127234\pi$
$277$			12.9538i			0.778317i	−0.921171	+	0.389158i	$0.872766\pi$
$278$		−	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	$0.182314\pi$
$283$			18.2341i			1.08390i	−0.840410	+	0.541952i	$0.817686\pi$
$284$	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	$-0.981035\pi$
$293$		−	2.03853i		−	0.119092i	0.998226	−	0.0595462i	$-0.0189654\pi$
$294$	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	$0.156480\pi$
$307$			16.5414i			0.944070i	−0.881580	+	0.472035i	$0.843520\pi$
$308$		−	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	$0.0100898\pi$
$313$			1.12141i			0.0633856i	−0.999498	+	0.0316928i	$0.989910\pi$
$314$	−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	$-0.682940\pi$
$317$		−	29.8882i		−	1.67869i	0.543601	−	0.839344i	$-0.317060\pi$
$318$		−	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	$0.254813\pi$
$337$			26.3511i			1.43544i	−0.696334	+	0.717718i	$0.745187\pi$
$338$		−	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	$-0.976264\pi$
$347$		−	2.77551i		−	0.148997i	0.997221	−	0.0744986i	$-0.0237356\pi$
$348$			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	$0.0717773\pi$
$353$			8.40171i			0.447178i	−0.974684	+	0.223589i	$0.928223\pi$
$354$	−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	$0.0338312\pi$
$367$			4.06455i			0.212168i	−0.994357	+	0.106084i	$0.966169\pi$
$368$			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	$0.158059\pi$
$373$			18.4017i			0.952804i	−0.879227	+	0.476402i	$0.841941\pi$
$374$	−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	$-0.858206\pi$
$383$		−	16.8646i		−	0.861743i	0.902413	−	0.430871i	$-0.141794\pi$
$384$	−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	$0.132001\pi$
$397$			16.0558i			0.805818i	−0.915240	+	0.402909i	$0.867999\pi$
$398$			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	$-0.991315\pi$
$433$		−	1.13536i		−	0.0545619i	0.999628	−	0.0272809i	$-0.00868487\pi$
$434$	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	$-0.640371\pi$
$443$		−	38.0679i		−	1.80866i	0.426835	−	0.904330i	$-0.359629\pi$
$444$	−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	$0.125098\pi$
$457$			16.3738i			0.765934i	−0.923762	+	0.382967i	$0.874902\pi$
$458$		−	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	$0.0748602\pi$
$463$			10.0279i			0.466036i	−0.972472	+	0.233018i	$0.925140\pi$
$464$	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	$0.273709\pi$
$467$			32.7509i			1.51553i	−0.652526	+	0.757766i	$0.726291\pi$
$468$		−	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	$-0.919271\pi$
$487$		−	11.0741i		−	0.501817i	0.968011	−	0.250908i	$-0.0807293\pi$
$488$			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	$-0.856042\pi$
$503$		−	19.6016i		−	0.873993i	0.899463	−	0.436996i	$-0.143958\pi$
$504$	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	$-0.893674\pi$
$523$		−	14.9956i		−	0.655713i	0.944728	−	0.327857i	$-0.106326\pi$
$524$	−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	$0.0323630\pi$
$547$			4.74760i			0.202993i	−0.994836	+	0.101496i	$0.967637\pi$
$548$		−	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	$0.365434\pi$
$557$			43.0462i			1.82393i	−0.410271	+	0.911964i	$0.634566\pi$
$558$		−	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	$-0.883311\pi$
$563$		−	17.0096i		−	0.716869i	0.933555	−	0.358434i	$-0.116689\pi$
$564$	−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	$-0.875341\pi$
$577$		−	18.3372i		−	0.763386i	0.924289	−	0.381693i	$-0.124659\pi$
$578$			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	$-0.920699\pi$
$587$		−	11.9475i		−	0.493127i	0.969127	−	0.246563i	$-0.0793013\pi$
$588$			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	$0.166965\pi$
$593$			24.3911i			1.00162i	−0.865557	+	0.500811i	$0.833035\pi$
$594$	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	$0.126131\pi$
$607$			19.0183i			0.771930i	−0.922513	+	0.385965i	$0.873869\pi$
$608$		−	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	$0.157952\pi$
$613$			23.5756i			0.952210i	−0.879389	+	0.476105i	$0.842048\pi$
$614$	−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	$-0.822639\pi$
$617$		−	26.2707i		−	1.05762i	0.848740	−	0.528810i	$-0.177361\pi$
$618$			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	$0.162201\pi$
$643$			24.7389i			0.975606i	−0.872954	+	0.487803i	$0.837799\pi$
$644$	−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	$-0.957160\pi$
$647$		−	6.82611i		−	0.268362i	0.990957	−	0.134181i	$-0.0428404\pi$
$648$			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	$-0.956786\pi$
$653$		−	6.91713i		−	0.270688i	0.990799	−	0.135344i	$-0.0432140\pi$
$654$	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	$-0.923823\pi$
$673$		−	12.2986i		−	0.474077i	0.971500	−	0.237039i	$-0.0761768\pi$
$674$	−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	$-0.757220\pi$
$677$		−	35.9527i		−	1.38178i	0.722962	−	0.690888i	$-0.242780\pi$
$678$			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	$0.0551428\pi$
$683$			9.00958i			0.344742i	−0.985032	+	0.172371i	$0.944857\pi$
$684$	−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	$-0.803688\pi$
$727$		−	31.1893i		−	1.15675i	0.815772	−	0.578373i	$-0.196312\pi$
$728$			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	$0.0830220\pi$
$733$			13.9634i			0.515748i	−0.966179	+	0.257874i	$0.916978\pi$
$734$	−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	$0.0889345\pi$
$743$			15.0342i			0.551550i	−0.961222	+	0.275775i	$0.911066\pi$
$744$	−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	$0.0615953\pi$
$757$			10.5819i			0.384604i	−0.981336	+	0.192302i	$0.938405\pi$
$758$		−	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	$-0.764213\pi$
$773$		−	37.5250i		−	1.34968i	0.737964	−	0.674840i	$-0.235787\pi$
$774$	−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	$0.131860\pi$
$787$			22.5833i			0.805008i	−0.915418	+	0.402504i	$0.868140\pi$
$788$			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	$0.219928\pi$
$797$			35.9806i			1.27450i	−0.770657	+	0.637250i	$0.780072\pi$
$798$			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	$-0.860150\pi$
$823$		−	24.4050i		−	0.850706i	0.905028	−	0.425353i	$-0.139850\pi$
$824$	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	$-0.934864\pi$
$827$		−	11.6874i		−	0.406411i	0.979136	−	0.203206i	$-0.0651360\pi$
$828$			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	$0.0340844\pi$
$853$			6.24281i			0.213750i	−0.994272	+	0.106875i	$0.965916\pi$
$854$	−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	$-0.870219\pi$
$857$		−	23.2158i		−	0.793035i	0.918027	−	0.396517i	$-0.129781\pi$
$858$			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	$0.0397260\pi$
$863$			7.31362i			0.248959i	−0.992222	+	0.124479i	$0.960274\pi$
$864$	−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	$-0.878763\pi$
$877$		−	22.0173i		−	0.743471i	0.928339	−	0.371735i	$-0.121237\pi$
$878$			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	$-0.614057\pi$
$883$		−	55.6560i		−	1.87297i	0.350703	−	0.936487i	$-0.385943\pi$
$884$	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	$-0.965649\pi$
$887$		−	6.41566i		−	0.215417i	0.994183	−	0.107708i	$-0.0343513\pi$
$888$		−	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	$-0.602849\pi$
$907$		−	57.1160i		−	1.89651i	0.317516	−	0.948253i	$-0.397151\pi$
$908$		−	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	$-0.774121\pi$
$937$		−	39.8882i		−	1.30309i	0.758610	−	0.651545i	$-0.225879\pi$
$938$			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	$0.0662156\pi$
$947$			12.7110i			0.413051i	−0.978441	+	0.206525i	$0.933784\pi$
$948$			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	$0.374614\pi$
$953$			57.0129i			1.84683i	−0.383804	+	0.923415i	$0.625386\pi$
$954$	−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	$-0.821854\pi$
$967$		−	33.0183i		−	1.06180i	0.847435	−	0.530899i	$-0.178146\pi$
$968$			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	$0.0690064\pi$
$977$			13.4465i			0.430192i	−0.976593	+	0.215096i	$0.930994\pi$
$978$		−	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	$0.114456\pi$
$983$			22.0646i			0.703750i	−0.936047	+	0.351875i	$0.885544\pi$
$984$	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	$-0.795930\pi$
$997$		−	37.7693i		−	1.19616i	0.801435	−	0.598082i	$-0.204070\pi$
$998$		−	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.39.4	yes	6
3.2	odd	2		1710.2.d.d.1369.3		6
4.3	odd	2		1520.2.d.j.609.6		6
5.2	odd	4		950.2.a.i.1.1		3
5.3	odd	4		950.2.a.n.1.3		3
5.4	even	2	inner	190.2.b.b.39.3	✓	6
15.2	even	4		8550.2.a.cl.1.3		3
15.8	even	4		8550.2.a.ck.1.1		3
15.14	odd	2		1710.2.d.d.1369.6		6
20.3	even	4		7600.2.a.bi.1.1		3
20.7	even	4		7600.2.a.cd.1.3		3
20.19	odd	2		1520.2.d.j.609.1		6

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

Introduction

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