LMFDB - Embedded newform 285.2.c.b.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(229,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("285.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.c (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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 25x^{12} + 242x^{10} + 1134x^{8} + 2605x^{6} + 2545x^{4} + 552x^{2} + 16 $ x^14 + 25x^12 + 242x^10 + 1134x^8 + 2605x^6 + 2545x^4 + 552x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.6
Root			$-0.498112i$ of defining polynomial
Character	$\chi$	$=$	285.229
Dual form			285.2.c.b.229.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.498112i q^{2} +1.00000i q^{3} +1.75188 q^{4} +(0.192457 + 2.22777i) q^{5} +0.498112 q^{6} -4.62756i q^{7} -1.86886i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.498112i q^{2} +1.00000i q^{3} +1.75188 q^{4} +(0.192457 + 2.22777i) q^{5} +0.498112 q^{6} -4.62756i q^{7} -1.86886i q^{8} -1.00000 q^{9} +(1.10968 - 0.0958652i) q^{10} +4.13949 q^{11} +1.75188i q^{12} +2.39138i q^{13} -2.30504 q^{14} +(-2.22777 + 0.192457i) q^{15} +2.57287 q^{16} +7.34369i q^{17} +0.498112i q^{18} -1.00000 q^{19} +(0.337163 + 3.90280i) q^{20} +4.62756 q^{21} -2.06193i q^{22} -2.69642i q^{23} +1.86886 q^{24} +(-4.92592 + 0.857501i) q^{25} +1.19117 q^{26} -1.00000i q^{27} -8.10695i q^{28} -0.979369 q^{29} +(0.0958652 + 1.10968i) q^{30} -5.10751 q^{31} -5.01929i q^{32} +4.13949i q^{33} +3.65798 q^{34} +(10.3091 - 0.890607i) q^{35} -1.75188 q^{36} -9.85293i q^{37} +0.498112i q^{38} -2.39138 q^{39} +(4.16339 - 0.359675i) q^{40} -4.52440 q^{41} -2.30504i q^{42} +3.43961i q^{43} +7.25190 q^{44} +(-0.192457 - 2.22777i) q^{45} -1.34312 q^{46} -5.09235i q^{47} +2.57287i q^{48} -14.4143 q^{49} +(0.427131 + 2.45366i) q^{50} -7.34369 q^{51} +4.18942i q^{52} +3.36319i q^{53} -0.498112 q^{54} +(0.796674 + 9.22182i) q^{55} -8.64825 q^{56} -1.00000i q^{57} +0.487835i q^{58} -13.4994 q^{59} +(-3.90280 + 0.337163i) q^{60} +6.64096 q^{61} +2.54411i q^{62} +4.62756i q^{63} +2.64557 q^{64} +(-5.32744 + 0.460238i) q^{65} +2.06193 q^{66} -7.28441i q^{67} +12.8653i q^{68} +2.69642 q^{69} +(-0.443622 - 5.13511i) q^{70} -7.28441 q^{71} +1.86886i q^{72} -3.82343i q^{73} -4.90786 q^{74} +(-0.857501 - 4.92592i) q^{75} -1.75188 q^{76} -19.1557i q^{77} +1.19117i q^{78} +16.1586 q^{79} +(0.495167 + 5.73176i) q^{80} +1.00000 q^{81} +2.25366i q^{82} +3.92122i q^{83} +8.10695 q^{84} +(-16.3601 + 1.41335i) q^{85} +1.71331 q^{86} -0.979369i q^{87} -7.73611i q^{88} -2.34446 q^{89} +(-1.10968 + 0.0958652i) q^{90} +11.0662 q^{91} -4.72382i q^{92} -5.10751i q^{93} -2.53656 q^{94} +(-0.192457 - 2.22777i) q^{95} +5.01929 q^{96} +2.34256i q^{97} +7.17994i q^{98} -4.13949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9	$ 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 38 q^{16} - 14 q^{19} + 12 q^{20} + 16 q^{21} - 18 q^{24} - 4 q^{25} - 40 q^{26} + 12 q^{29} + 4 q^{30} + 8 q^{31} - 4 q^{34} - 14 q^{35} + 22 q^{36} - 16 q^{39} + 18 q^{40} + 4 q^{41} + 64 q^{44} - 2 q^{45} - 8 q^{46} - 34 q^{49} + 4 q^{50} + 8 q^{51} - 6 q^{54} - 2 q^{55} - 44 q^{56} + 36 q^{59} - 18 q^{60} + 24 q^{61} - 22 q^{64} - 12 q^{65} + 24 q^{66} - 20 q^{69} - 60 q^{70} - 36 q^{71} - 12 q^{74} + 22 q^{76} + 8 q^{79} + 36 q^{80} + 14 q^{81} - 28 q^{84} - 18 q^{85} - 92 q^{86} + 16 q^{89} - 2 q^{90} + 24 q^{91} + 40 q^{94} - 2 q^{95} + 62 q^{96} + 8 q^{99}+O(q^{100}) $ 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^15 + 38 * q^16 - 14 * q^19 + 12 * q^20 + 16 * q^21 - 18 * q^24 - 4 * q^25 - 40 * q^26 + 12 * q^29 + 4 * q^30 + 8 * q^31 - 4 * q^34 - 14 * q^35 + 22 * q^36 - 16 * q^39 + 18 * q^40 + 4 * q^41 + 64 * q^44 - 2 * q^45 - 8 * q^46 - 34 * q^49 + 4 * q^50 + 8 * q^51 - 6 * q^54 - 2 * q^55 - 44 * q^56 + 36 * q^59 - 18 * q^60 + 24 * q^61 - 22 * q^64 - 12 * q^65 + 24 * q^66 - 20 * q^69 - 60 * q^70 - 36 * q^71 - 12 * q^74 + 22 * q^76 + 8 * q^79 + 36 * q^80 + 14 * q^81 - 28 * q^84 - 18 * q^85 - 92 * q^86 + 16 * q^89 - 2 * q^90 + 24 * q^91 + 40 * q^94 - 2 * q^95 + 62 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	0.498112i		−	0.352218i	−0.984371	−	0.176109i	$-0.943649\pi$
$2$		−	0.498112i		−	0.352218i	0.984371	−	0.176109i	$-0.0563512\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.75188			0.875942
$5$	0.192457	+	2.22777i	0.0860695	+	0.996289i
$5$	0.192457	+	2.22777i	0.0860695	+	0.996289i
$6$	0.498112			0.203353
$7$		−	4.62756i		−	1.74905i	−0.484977	−	0.874527i	$-0.661172\pi$
$7$		−	4.62756i		−	1.74905i	0.484977	−	0.874527i	$-0.338828\pi$
$8$		−	1.86886i		−	0.660741i
$9$	−1.00000			−0.333333
$10$	1.10968	−	0.0958652i	0.350911	−	0.0303152i
$11$	4.13949			1.24810			0.624051	−	0.781384i	$-0.285486\pi$
$11$	4.13949			1.24810			0.624051	+	0.781384i	$0.285486\pi$
$12$			1.75188i			0.505726i
$13$			2.39138i			0.663249i	0.943411	+	0.331624i	$0.107597\pi$
$13$			2.39138i			0.663249i	−0.943411	+	0.331624i	$0.892403\pi$
$14$	−2.30504			−0.616049
$15$	−2.22777	+	0.192457i	−0.575208	+	0.0496922i
$16$	2.57287			0.643217
$17$			7.34369i			1.78111i	0.454879	+	0.890553i	$0.349683\pi$
$17$			7.34369i			1.78111i	−0.454879	+	0.890553i	$0.650317\pi$
$18$			0.498112i			0.117406i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.337163	+	3.90280i	0.0753919	+	0.872692i
$21$	4.62756			1.00982
$22$		−	2.06193i		−	0.439604i
$23$		−	2.69642i		−	0.562243i	−0.959672	−	0.281121i	$-0.909294\pi$
$23$		−	2.69642i		−	0.562243i	0.959672	−	0.281121i	$-0.0907063\pi$
$24$	1.86886			0.381479
$25$	−4.92592	+	0.857501i	−0.985184	+	0.171500i
$26$	1.19117			0.233608
$27$		−	1.00000i		−	0.192450i
$28$		−	8.10695i		−	1.53207i
$29$	−0.979369			−0.181864			−0.0909321	−	0.995857i	$-0.528985\pi$
$29$	−0.979369			−0.181864			−0.0909321	+	0.995857i	$0.528985\pi$
$30$	0.0958652	+	1.10968i	0.0175025	+	0.202599i
$31$	−5.10751			−0.917336			−0.458668	−	0.888608i	$-0.651673\pi$
$31$	−5.10751			−0.917336			−0.458668	+	0.888608i	$0.651673\pi$
$32$		−	5.01929i		−	0.887294i
$33$			4.13949i			0.720592i
$34$	3.65798			0.627338
$35$	10.3091	−	0.890607i	1.74256	−	0.150540i
$36$	−1.75188			−0.291981
$37$		−	9.85293i		−	1.61981i	−0.586560	−	0.809906i	$-0.699518\pi$
$37$		−	9.85293i		−	1.61981i	0.586560	−	0.809906i	$-0.300482\pi$
$38$			0.498112i			0.0808044i
$39$	−2.39138			−0.382927
$40$	4.16339	−	0.359675i	0.658289	−	0.0568697i
$41$	−4.52440			−0.706593			−0.353296	−	0.935511i	$-0.614939\pi$
$41$	−4.52440			−0.706593			−0.353296	+	0.935511i	$0.614939\pi$
$42$		−	2.30504i		−	0.355676i
$43$			3.43961i			0.524535i	0.964995	+	0.262268i	$0.0844703\pi$
$43$			3.43961i			0.524535i	−0.964995	+	0.262268i	$0.915530\pi$
$44$	7.25190			1.09327
$45$	−0.192457	−	2.22777i	−0.0286898	−	0.332096i
$46$	−1.34312			−0.198032
$47$		−	5.09235i		−	0.742795i	−0.928474	−	0.371398i	$-0.878879\pi$
$47$		−	5.09235i		−	0.742795i	0.928474	−	0.371398i	$-0.121121\pi$
$48$			2.57287i			0.371362i
$49$	−14.4143			−2.05919
$50$	0.427131	+	2.45366i	0.0604055	+	0.347000i
$51$	−7.34369			−1.02832
$52$			4.18942i			0.580968i
$53$			3.36319i			0.461970i	0.972957	+	0.230985i	$0.0741949\pi$
$53$			3.36319i			0.461970i	−0.972957	+	0.230985i	$0.925805\pi$
$54$	−0.498112			−0.0677844
$55$	0.796674	+	9.22182i	0.107423	+	1.24347i
$56$	−8.64825			−1.15567
$57$		−	1.00000i		−	0.132453i
$58$			0.487835i			0.0640559i
$59$	−13.4994			−1.75748			−0.878738	−	0.477304i	$-0.841614\pi$
$59$	−13.4994			−1.75748			−0.878738	+	0.477304i	$0.841614\pi$
$60$	−3.90280	+	0.337163i	−0.503849	+	0.0435275i
$61$	6.64096			0.850287			0.425144	−	0.905126i	$-0.360224\pi$
$61$	6.64096			0.850287			0.425144	+	0.905126i	$0.360224\pi$
$62$			2.54411i			0.323102i
$63$			4.62756i			0.583018i
$64$	2.64557			0.330696
$65$	−5.32744	+	0.460238i	−0.660788	+	0.0570855i
$66$	2.06193			0.253806
$67$		−	7.28441i		−	0.889933i	−0.895547	−	0.444966i	$-0.853216\pi$
$67$		−	7.28441i		−	0.889933i	0.895547	−	0.444966i	$-0.146784\pi$
$68$			12.8653i			1.56015i
$69$	2.69642			0.324611
$70$	−0.443622	−	5.13511i	−0.0530230	−	0.613763i
$71$	−7.28441			−0.864501			−0.432250	−	0.901754i	$-0.642280\pi$
$71$	−7.28441			−0.864501			−0.432250	+	0.901754i	$0.642280\pi$
$72$			1.86886i			0.220247i
$73$		−	3.82343i		−	0.447499i	−0.974647	−	0.223749i	$-0.928170\pi$
$73$		−	3.82343i		−	0.447499i	0.974647	−	0.223749i	$-0.0718297\pi$
$74$	−4.90786			−0.570527
$75$	−0.857501	−	4.92592i	−0.0990157	−	0.568796i
$76$	−1.75188			−0.200955
$77$		−	19.1557i		−	2.18300i
$78$			1.19117i			0.134874i
$79$	16.1586			1.81799			0.908995	−	0.416807i	$-0.136851\pi$
$79$	16.1586			1.81799			0.908995	+	0.416807i	$0.136851\pi$
$80$	0.495167	+	5.73176i	0.0553614	+	0.640830i
$81$	1.00000			0.111111
$82$			2.25366i			0.248875i
$83$			3.92122i			0.430410i	0.976569	+	0.215205i	$0.0690419\pi$
$83$			3.92122i			0.430410i	−0.976569	+	0.215205i	$0.930958\pi$
$84$	8.10695			0.884541
$85$	−16.3601	+	1.41335i	−1.77450	+	0.153299i
$86$	1.71331			0.184751
$87$		−	0.979369i		−	0.104999i
$88$		−	7.73611i		−	0.824672i
$89$	−2.34446			−0.248513			−0.124256	−	0.992250i	$-0.539655\pi$
$89$	−2.34446			−0.248513			−0.124256	+	0.992250i	$0.539655\pi$
$90$	−1.10968	+	0.0958652i	−0.116970	+	0.0101051i
$91$	11.0662			1.16006
$92$		−	4.72382i		−	0.492492i
$93$		−	5.10751i		−	0.529624i
$94$	−2.53656			−0.261626
$95$	−0.192457	−	2.22777i	−0.0197457	−	0.228564i
$96$	5.01929			0.512279
$97$			2.34256i			0.237851i	0.992903	+	0.118926i	$0.0379450\pi$
$97$			2.34256i			0.237851i	−0.992903	+	0.118926i	$0.962055\pi$
$98$			7.17994i			0.725284i
$99$	−4.13949			−0.416034
$100$	−8.62964	+	1.50224i	−0.862964	+	0.150224i
$101$	−7.44953			−0.741256			−0.370628	−	0.928781i	$-0.620857\pi$
$101$	−7.44953			−0.741256			−0.370628	+	0.928781i	$0.620857\pi$
$102$			3.65798i			0.362194i
$103$			8.17714i			0.805718i	0.915262	+	0.402859i	$0.131983\pi$
$103$			8.17714i			0.805718i	−0.915262	+	0.402859i	$0.868017\pi$
$104$	4.46915			0.438236
$105$	0.890607	+	10.3091i	0.0869144	+	1.00607i
$106$	1.67525			0.162714
$107$			5.25512i			0.508032i	0.967200	+	0.254016i	$0.0817516\pi$
$107$			5.25512i			0.508032i	−0.967200	+	0.254016i	$0.918248\pi$
$108$		−	1.75188i		−	0.168575i
$109$	−7.50377			−0.718731			−0.359365	−	0.933197i	$-0.617007\pi$
$109$	−7.50377			−0.718731			−0.359365	+	0.933197i	$0.617007\pi$
$110$	4.59350	−	0.396833i	0.437973	−	0.0378365i
$111$	9.85293			0.935199
$112$		−	11.9061i		−	1.12502i
$113$			3.70723i			0.348747i	0.984680	+	0.174374i	$0.0557901\pi$
$113$			3.70723i			0.348747i	−0.984680	+	0.174374i	$0.944210\pi$
$114$	−0.498112			−0.0466525
$115$	6.00701	−	0.518946i	0.560156	−	0.0483919i
$116$	−1.71574			−0.159303
$117$		−	2.39138i		−	0.221083i
$118$			6.72423i			0.619015i
$119$	33.9834			3.11525
$120$	0.359675	+	4.16339i	0.0328337	+	0.380063i
$121$	6.13535			0.557759
$122$		−	3.30794i		−	0.299487i
$123$		−	4.52440i		−	0.407951i
$124$	−8.94777			−0.803533
$125$	−2.85834	−	10.8088i	−0.255658	−	0.966767i
$126$	2.30504			0.205350
$127$			18.4105i			1.63367i	0.576872	+	0.816834i	$0.304273\pi$
$127$			18.4105i			1.63367i	−0.576872	+	0.816834i	$0.695727\pi$
$128$		−	11.3564i		−	1.00377i
$129$	−3.43961			−0.302840
$130$	0.229250	+	2.65366i	0.0201066	+	0.232741i
$131$	−10.6541			−0.930850			−0.465425	−	0.885087i	$-0.654099\pi$
$131$	−10.6541			−0.930850			−0.465425	+	0.885087i	$0.654099\pi$
$132$			7.25190i			0.631197i
$133$			4.62756i			0.401260i
$134$	−3.62845			−0.313451
$135$	2.22777	−	0.192457i	0.191736	−	0.0165641i
$136$	13.7243			1.17685
$137$			2.31966i			0.198182i	0.995078	+	0.0990911i	$0.0315935\pi$
$137$			2.31966i			0.198182i	−0.995078	+	0.0990911i	$0.968406\pi$
$138$		−	1.34312i		−	0.114334i
$139$	15.8160			1.34149			0.670746	−	0.741687i	$-0.265974\pi$
$139$	15.8160			1.34149			0.670746	+	0.741687i	$0.265974\pi$
$140$	18.0604	−	1.56024i	1.52638	−	0.131864i
$141$	5.09235			0.428853
$142$			3.62845i			0.304493i
$143$			9.89908i			0.827802i
$144$	−2.57287			−0.214406
$145$	−0.188487	−	2.18181i	−0.0156530	−	0.181189i
$146$	−1.90450			−0.157617
$147$		−	14.4143i		−	1.18887i
$148$		−	17.2612i		−	1.41886i
$149$	7.70875			0.631525			0.315763	−	0.948838i	$-0.397740\pi$
$149$	7.70875			0.631525			0.315763	+	0.948838i	$0.397740\pi$
$150$	−2.45366	+	0.427131i	−0.200340	+	0.0348751i
$151$	−19.2214			−1.56421			−0.782106	−	0.623145i	$-0.785855\pi$
$151$	−19.2214			−1.56421			−0.782106	+	0.623145i	$0.785855\pi$
$152$			1.86886i			0.151584i
$153$		−	7.34369i		−	0.593702i
$154$	−9.54169			−0.768892
$155$	−0.982977	−	11.3784i	−0.0789546	−	0.913932i
$156$	−4.18942			−0.335422
$157$		−	13.6082i		−	1.08605i	−0.839716	−	0.543025i	$-0.817279\pi$
$157$		−	13.6082i		−	1.08605i	0.839716	−	0.543025i	$-0.182721\pi$
$158$		−	8.04882i		−	0.640329i
$159$	−3.36319			−0.266719
$160$	11.1818	−	0.965999i	0.884001	−	0.0763689i
$161$	−12.4779			−0.983392
$162$		−	0.498112i		−	0.0391354i
$163$		−	3.12532i		−	0.244794i	−0.992481	−	0.122397i	$-0.960942\pi$
$163$		−	3.12532i		−	0.244794i	0.992481	−	0.122397i	$-0.0390581\pi$
$164$	−7.92623			−0.618934
$165$	−9.22182	+	0.796674i	−0.717918	+	0.0620210i
$166$	1.95321			0.151598
$167$		−	2.86858i		−	0.221977i	−0.993822	−	0.110989i	$-0.964598\pi$
$167$		−	2.86858i		−	0.221977i	0.993822	−	0.110989i	$-0.0354017\pi$
$168$		−	8.64825i		−	0.667227i
$169$	7.28131			0.560101
$170$	0.704005	+	8.14914i	0.0539947	+	0.625010i
$171$	1.00000			0.0764719
$172$			6.02579i			0.459462i
$173$		−	4.85404i		−	0.369046i	−0.982828	−	0.184523i	$-0.940926\pi$
$173$		−	4.85404i		−	0.369046i	0.982828	−	0.184523i	$-0.0590739\pi$
$174$	−0.487835			−0.0369827
$175$	3.96814	+	22.7950i	0.299963	+	1.72314i
$176$	10.6504			0.802801
$177$		−	13.4994i		−	1.01468i
$178$			1.16781i			0.0875307i
$179$	16.7731			1.25368			0.626839	−	0.779149i	$-0.284348\pi$
$179$	16.7731			1.25368			0.626839	+	0.779149i	$0.284348\pi$
$180$	−0.337163	−	3.90280i	−0.0251306	−	0.290897i
$181$	17.0075			1.26416			0.632080	−	0.774903i	$-0.282201\pi$
$181$	17.0075			1.26416			0.632080	+	0.774903i	$0.282201\pi$
$182$		−	5.51223i		−	0.408594i
$183$			6.64096i			0.490914i
$184$	−5.03923			−0.371497
$185$	21.9501	−	1.89627i	1.61380	−	0.139416i
$186$	−2.54411			−0.186543
$187$			30.3991i			2.22300i
$188$		−	8.92120i		−	0.650646i
$189$	−4.62756			−0.336606
$190$	−1.10968	+	0.0958652i	−0.0805046	+	0.00695479i
$191$	2.57283			0.186163			0.0930816	−	0.995658i	$-0.470328\pi$
$191$	2.57283			0.186163			0.0930816	+	0.995658i	$0.470328\pi$
$192$			2.64557i			0.190927i
$193$			17.2612i			1.24249i	0.783617	+	0.621244i	$0.213372\pi$
$193$			17.2612i			1.24249i	−0.783617	+	0.621244i	$0.786628\pi$
$194$	1.16686			0.0837755
$195$	−0.460238	−	5.32744i	−0.0329583	−	0.381506i
$196$	−25.2522			−1.80373
$197$			18.5625i			1.32252i	0.750156	+	0.661260i	$0.229978\pi$
$197$			18.5625i			1.32252i	−0.750156	+	0.661260i	$0.770022\pi$
$198$			2.06193i			0.146535i
$199$	4.24470			0.300899			0.150449	−	0.988618i	$-0.451928\pi$
$199$	4.24470			0.300899			0.150449	+	0.988618i	$0.451928\pi$
$200$	1.60255	+	9.20585i	0.113317	+	0.650952i
$201$	7.28441			0.513803
$202$			3.71070i			0.261084i
$203$			4.53209i			0.318090i
$204$	−12.8653			−0.900751
$205$	−0.870754	−	10.0793i	−0.0608161	−	0.703971i
$206$	4.07313			0.283788
$207$			2.69642i			0.187414i
$208$			6.15270i			0.426613i
$209$	−4.13949			−0.286334
$210$	5.13511	−	0.443622i	0.354356	−	0.0306128i
$211$	−1.20969			−0.0832786			−0.0416393	−	0.999133i	$-0.513258\pi$
$211$	−1.20969			−0.0832786			−0.0416393	+	0.999133i	$0.513258\pi$
$212$			5.89193i			0.404659i
$213$		−	7.28441i		−	0.499120i
$214$	2.61764			0.178938
$215$	−7.66265	+	0.661977i	−0.522589	+	0.0451465i
$216$	−1.86886			−0.127160
$217$			23.6353i			1.60447i
$218$			3.73772i			0.253150i
$219$	3.82343			0.258364
$220$	1.39568	+	16.1556i	0.0940968	+	1.08921i
$221$	−17.5615			−1.18132
$222$		−	4.90786i		−	0.329394i
$223$			6.22370i			0.416770i	0.978047	+	0.208385i	$0.0668206\pi$
$223$			6.22370i			0.416770i	−0.978047	+	0.208385i	$0.933179\pi$
$224$	−23.2271			−1.55192
$225$	4.92592	−	0.857501i	0.328395	−	0.0571667i
$226$	1.84662			0.122835
$227$		−	24.8143i		−	1.64698i	−0.567328	−	0.823492i	$-0.692023\pi$
$227$		−	24.8143i		−	1.64698i	0.567328	−	0.823492i	$-0.307977\pi$
$228$		−	1.75188i		−	0.116021i
$229$	−0.919180			−0.0607411			−0.0303706	−	0.999539i	$-0.509669\pi$
$229$	−0.919180			−0.0607411			−0.0303706	+	0.999539i	$0.509669\pi$
$230$	−0.258493	−	2.99216i	−0.0170445	−	0.197297i
$231$	19.1557			1.26035
$232$			1.83030i			0.120165i
$233$		−	13.9328i		−	0.912769i	−0.889783	−	0.456385i	$-0.849144\pi$
$233$		−	13.9328i		−	0.912769i	0.889783	−	0.456385i	$-0.150856\pi$
$234$	−1.19117			−0.0778695
$235$	11.3446	−	0.980059i	0.740039	−	0.0639320i
$236$	−23.6494			−1.53945
$237$			16.1586i			1.04962i
$238$		−	16.9275i		−	1.09725i
$239$	17.7987			1.15130			0.575650	−	0.817696i	$-0.304749\pi$
$239$	17.7987			1.15130			0.575650	+	0.817696i	$0.304749\pi$
$240$	−5.73176	+	0.495167i	−0.369984	+	0.0319629i
$241$	−10.5443			−0.679217			−0.339609	−	0.940567i	$-0.610295\pi$
$241$	−10.5443			−0.679217			−0.339609	+	0.940567i	$0.610295\pi$
$242$		−	3.05609i		−	0.196453i
$243$			1.00000i			0.0641500i
$244$	11.6342			0.744803
$245$	−2.77414	−	32.1118i	−0.177233	−	2.05155i
$246$	−2.25366			−0.143688
$247$		−	2.39138i		−	0.152160i
$248$			9.54521i			0.606121i
$249$	−3.92122			−0.248497
$250$	−5.38399	+	1.42378i	−0.340513	+	0.0900474i
$251$	−14.9840			−0.945784			−0.472892	−	0.881120i	$-0.656790\pi$
$251$	−14.9840			−0.945784			−0.472892	+	0.881120i	$0.656790\pi$
$252$			8.10695i			0.510690i
$253$		−	11.1618i		−	0.701736i
$254$	9.17049			0.575408
$255$	−1.41335	−	16.3601i	−0.0885072	−	1.02451i
$256$	−0.365609			−0.0228506
$257$			4.89838i			0.305553i	0.988261	+	0.152776i	$0.0488214\pi$
$257$			4.89838i			0.305553i	−0.988261	+	0.152776i	$0.951179\pi$
$258$			1.71331i			0.106666i
$259$	−45.5950			−2.83314
$260$	−9.33306	+	0.806284i	−0.578812	+	0.0500036i
$261$	0.979369			0.0606214
$262$			5.30692i			0.327863i
$263$		−	13.6398i		−	0.841063i	−0.907278	−	0.420532i	$-0.861844\pi$
$263$		−	13.6398i		−	0.841063i	0.907278	−	0.420532i	$-0.138156\pi$
$264$	7.73611			0.476125
$265$	−7.49242	+	0.647271i	−0.460256	+	0.0397615i
$266$	2.30504			0.141331
$267$		−	2.34446i		−	0.143479i
$268$		−	12.7614i		−	0.779530i
$269$	15.7729			0.961692			0.480846	−	0.876805i	$-0.340330\pi$
$269$	15.7729			0.961692			0.480846	+	0.876805i	$0.340330\pi$
$270$	−0.0958652	−	1.10968i	−0.00583417	−	0.0675329i
$271$	−5.12680			−0.311431			−0.155715	−	0.987802i	$-0.549768\pi$
$271$	−5.12680			−0.311431			−0.155715	+	0.987802i	$0.549768\pi$
$272$			18.8944i			1.14564i
$273$			11.0662i			0.669760i
$274$	1.15545			0.0698034
$275$	−20.3908	+	3.54961i	−1.22961	+	0.214050i
$276$	4.72382			0.284340
$277$		−	8.63811i		−	0.519013i	−0.965741	−	0.259507i	$-0.916440\pi$
$277$		−	8.63811i		−	0.519013i	0.965741	−	0.259507i	$-0.0835600\pi$
$278$		−	7.87811i		−	0.472498i
$279$	5.10751			0.305779
$280$	−1.66442	−	19.2663i	−0.0994681	−	1.15138i
$281$	18.5875			1.10884			0.554420	−	0.832237i	$-0.312940\pi$
$281$	18.5875			1.10884			0.554420	+	0.832237i	$0.312940\pi$
$282$		−	2.53656i		−	0.151050i
$283$			20.0035i			1.18908i	0.804065	+	0.594541i	$0.202666\pi$
$283$			20.0035i			1.18908i	−0.804065	+	0.594541i	$0.797334\pi$
$284$	−12.7614			−0.757253
$285$	2.22777	−	0.192457i	0.131962	−	0.0114002i
$286$	4.93085			0.291567
$287$			20.9369i			1.23587i
$288$			5.01929i			0.295765i
$289$	−36.9298			−2.17234
$290$	−1.08678	+	0.0938874i	−0.0638182	+	0.00551326i
$291$	−2.34256			−0.137323
$292$		−	6.69821i		−	0.391983i
$293$			11.0837i			0.647519i	0.946139	+	0.323760i	$0.104947\pi$
$293$			11.0837i			0.647519i	−0.946139	+	0.323760i	$0.895053\pi$
$294$	−7.17994			−0.418743
$295$	−2.59806	−	30.0736i	−0.151265	−	1.75095i
$296$	−18.4137			−1.07028
$297$		−	4.13949i		−	0.240197i
$298$		−	3.83982i		−	0.222435i
$299$	6.44816			0.372907
$300$	−1.50224	−	8.62964i	−0.0867320	−	0.498233i
$301$	15.9170			0.917440
$302$			9.57439i			0.550944i
$303$		−	7.44953i		−	0.427964i
$304$	−2.57287			−0.147564
$305$	1.27810	+	14.7945i	0.0731838	+	0.847132i
$306$	−3.65798			−0.209113
$307$		−	26.2854i		−	1.50019i	−0.661331	−	0.750094i	$-0.730008\pi$
$307$		−	26.2854i		−	1.50019i	0.661331	−	0.750094i	$-0.269992\pi$
$308$		−	33.5586i		−	1.91218i
$309$	−8.17714			−0.465181
$310$	−5.66769	+	0.489632i	−0.321903	+	0.0278093i
$311$	26.1287			1.48162			0.740811	−	0.671714i	$-0.234442\pi$
$311$	26.1287			1.48162			0.740811	+	0.671714i	$0.234442\pi$
$312$			4.46915i			0.253016i
$313$			3.78602i			0.213998i	0.994259	+	0.106999i	$0.0341242\pi$
$313$			3.78602i			0.213998i	−0.994259	+	0.106999i	$0.965876\pi$
$314$	−6.77840			−0.382527
$315$	−10.3091	+	0.890607i	−0.580854	+	0.0501800i
$316$	28.3081			1.59245
$317$			11.8420i			0.665113i	0.943083	+	0.332556i	$0.107911\pi$
$317$			11.8420i			0.665113i	−0.943083	+	0.332556i	$0.892089\pi$
$318$			1.67525i			0.0939432i
$319$	−4.05408			−0.226985
$320$	0.509159	+	5.89372i	0.0284628	+	0.329469i
$321$	−5.25512			−0.293312
$322$			6.21537i			0.346369i
$323$		−	7.34369i		−	0.408614i
$324$	1.75188			0.0973269
$325$	−2.05061	−	11.7797i	−0.113747	−	0.653422i
$326$	−1.55676			−0.0862209
$327$		−	7.50377i		−	0.414959i
$328$			8.45546i			0.466875i
$329$	−23.5651			−1.29919
$330$	0.396833	+	4.59350i	0.0218449	+	0.252864i
$331$	34.2726			1.88379			0.941897	−	0.335902i	$-0.109041\pi$
$331$	34.2726			1.88379			0.941897	+	0.335902i	$0.109041\pi$
$332$			6.86952i			0.377014i
$333$			9.85293i			0.539937i
$334$	−1.42887			−0.0781844
$335$	16.2280	−	1.40194i	0.886630	−	0.0765960i
$336$	11.9061			0.649531
$337$			10.4980i			0.571861i	0.958250	+	0.285930i	$0.0923026\pi$
$337$			10.4980i			0.571861i	−0.958250	+	0.285930i	$0.907697\pi$
$338$		−	3.62691i		−	0.197278i
$339$	−3.70723			−0.201349
$340$	−28.6609	+	2.47602i	−1.55436	+	0.134281i
$341$	−21.1425			−1.14493
$342$		−	0.498112i		−	0.0269348i
$343$			34.3102i			1.85258i
$344$	6.42814			0.346582
$345$	0.518946	+	6.00701i	0.0279391	+	0.323406i
$346$	−2.41785			−0.129985
$347$			18.8198i			1.01030i	0.863031	+	0.505151i	$0.168563\pi$
$347$			18.8198i			1.01030i	−0.863031	+	0.505151i	$0.831437\pi$
$348$		−	1.71574i		−	0.0919734i
$349$	14.4077			0.771227			0.385613	−	0.922660i	$-0.373990\pi$
$349$	14.4077			0.771227			0.385613	+	0.922660i	$0.373990\pi$
$350$	11.3545	−	1.97658i	0.606921	−	0.105652i
$351$	2.39138			0.127642
$352$		−	20.7773i		−	1.10743i
$353$			5.41582i			0.288255i	0.989559	+	0.144127i	$0.0460375\pi$
$353$			5.41582i			0.288255i	−0.989559	+	0.144127i	$0.953962\pi$
$354$	−6.72423			−0.357389
$355$	−1.40194	−	16.2280i	−0.0744071	−	0.861293i
$356$	−4.10723			−0.217683
$357$			33.9834i			1.79859i
$358$		−	8.35487i		−	0.441569i
$359$	20.7304			1.09411			0.547055	−	0.837097i	$-0.315749\pi$
$359$	20.7304			1.09411			0.547055	+	0.837097i	$0.315749\pi$
$360$	−4.16339	+	0.359675i	−0.219430	+	0.0189566i
$361$	1.00000			0.0526316
$362$		−	8.47166i		−	0.445260i
$363$			6.13535i			0.322022i
$364$	19.3868			1.01614
$365$	8.51773	−	0.735847i	0.445838	−	0.0385160i
$366$	3.30794			0.172909
$367$		−	2.60433i		−	0.135945i	−0.997687	−	0.0679725i	$-0.978347\pi$
$367$		−	2.60433i		−	0.135945i	0.997687	−	0.0679725i	$-0.0216530\pi$
$368$		−	6.93754i		−	0.361644i
$369$	4.52440			0.235531
$370$	−0.944553	−	10.9336i	−0.0491050	−	0.568410i
$371$	15.5634			0.808011
$372$		−	8.94777i		−	0.463920i
$373$			5.98299i			0.309787i	0.987931	+	0.154894i	$0.0495035\pi$
$373$			5.98299i			0.309787i	−0.987931	+	0.154894i	$0.950497\pi$
$374$	15.1422			0.782982
$375$	10.8088	−	2.85834i	0.558163	−	0.147604i
$376$	−9.51687			−0.490795
$377$		−	2.34204i		−	0.120621i
$378$			2.30504i			0.118559i
$379$	7.44400			0.382372			0.191186	−	0.981554i	$-0.438767\pi$
$379$	7.44400			0.382372			0.191186	+	0.981554i	$0.438767\pi$
$380$	−0.337163	−	3.90280i	−0.0172961	−	0.200209i
$381$	−18.4105			−0.943199
$382$		−	1.28156i		−	0.0655701i
$383$		−	15.5789i		−	0.796044i	−0.917376	−	0.398022i	$-0.869697\pi$
$383$		−	15.5789i		−	0.796044i	0.917376	−	0.398022i	$-0.130303\pi$
$384$	11.3564			0.579528
$385$	42.6745	−	3.68666i	2.17490	−	0.187889i
$386$	8.59801			0.437627
$387$		−	3.43961i		−	0.174845i
$388$			4.10390i			0.208344i
$389$	−16.7532			−0.849421			−0.424711	−	0.905329i	$-0.639624\pi$
$389$	−16.7532			−0.849421			−0.424711	+	0.905329i	$0.639624\pi$
$390$	−2.65366	+	0.229250i	−0.134373	+	0.0116085i
$391$	19.8017			1.00141
$392$			26.9383i			1.36059i
$393$		−	10.6541i		−	0.537427i
$394$	9.24618			0.465816
$395$	3.10985	+	35.9978i	0.156473	+	1.81124i
$396$	−7.25190			−0.364422
$397$			6.65505i			0.334008i	0.985956	+	0.167004i	$0.0534092\pi$
$397$			6.65505i			0.334008i	−0.985956	+	0.167004i	$0.946591\pi$
$398$		−	2.11433i		−	0.105982i
$399$	−4.62756			−0.231668
$400$	−12.6737	+	2.20624i	−0.633687	+	0.110312i
$401$	−30.8633			−1.54124			−0.770619	−	0.637296i	$-0.780053\pi$
$401$	−30.8633			−1.54124			−0.770619	+	0.637296i	$0.780053\pi$
$402$		−	3.62845i		−	0.180971i
$403$		−	12.2140i		−	0.608422i
$404$	−13.0507			−0.649297
$405$	0.192457	+	2.22777i	0.00956328	+	0.110699i
$406$	2.25749			0.112037
$407$		−	40.7861i		−	2.02169i
$408$			13.7243i			0.679455i
$409$	26.4257			1.30667			0.653334	−	0.757070i	$-0.273370\pi$
$409$	26.4257			1.30667			0.653334	+	0.757070i	$0.273370\pi$
$410$	−5.02063	+	0.433733i	−0.247951	+	0.0214205i
$411$	−2.31966			−0.114421
$412$			14.3254i			0.705762i
$413$			62.4694i			3.07392i
$414$	1.34312			0.0660107
$415$	−8.73557	+	0.754667i	−0.428812	+	0.0370451i
$416$	12.0030			0.588497
$417$			15.8160i			0.774511i
$418$			2.06193i			0.100852i
$419$	4.25514			0.207877			0.103939	−	0.994584i	$-0.466855\pi$
$419$	4.25514			0.207877			0.103939	+	0.994584i	$0.466855\pi$
$420$	1.56024	+	18.0604i	0.0761320	+	0.881259i
$421$	−13.3331			−0.649818			−0.324909	−	0.945745i	$-0.605334\pi$
$421$	−13.3331			−0.649818			−0.324909	+	0.945745i	$0.605334\pi$
$422$			0.602562i			0.0293323i
$423$			5.09235i			0.247598i
$424$	6.28533			0.305243
$425$	−6.29722	−	36.1744i	−0.305460	−	1.75472i
$426$	−3.62845			−0.175799
$427$		−	30.7314i		−	1.48720i
$428$			9.20637i			0.445006i
$429$	−9.89908			−0.477932
$430$	0.329739	+	3.81686i	0.0159014	+	0.184065i
$431$	−17.7752			−0.856199			−0.428100	−	0.903732i	$-0.640817\pi$
$431$	−17.7752			−0.856199			−0.428100	+	0.903732i	$0.640817\pi$
$432$		−	2.57287i		−	0.123787i
$433$		−	31.2503i		−	1.50179i	−0.660421	−	0.750896i	$-0.729622\pi$
$433$		−	31.2503i		−	1.50179i	0.660421	−	0.750896i	$-0.270378\pi$
$434$	11.7730			0.565123
$435$	2.18181	−	0.188487i	0.104610	−	0.00903724i
$436$	−13.1457			−0.629567
$437$			2.69642i			0.128987i
$438$		−	1.90450i		−	0.0910004i
$439$	11.8467			0.565412			0.282706	−	0.959207i	$-0.408768\pi$
$439$	11.8467			0.565412			0.282706	+	0.959207i	$0.408768\pi$
$440$	17.2343	−	1.48887i	0.821612	−	0.0709791i
$441$	14.4143			0.686396
$442$			8.74761i			0.416081i
$443$		−	31.3323i		−	1.48864i	−0.667820	−	0.744322i	$-0.732773\pi$
$443$		−	31.3323i		−	1.48864i	0.667820	−	0.744322i	$-0.267227\pi$
$444$	17.2612			0.819180
$445$	−0.451209	−	5.22293i	−0.0213894	−	0.247590i
$446$	3.10010			0.146794
$447$			7.70875i			0.364611i
$448$		−	12.2425i		−	0.578405i
$449$	8.67661			0.409475			0.204737	−	0.978817i	$-0.434366\pi$
$449$	8.67661			0.409475			0.204737	+	0.978817i	$0.434366\pi$
$450$	−0.427131	−	2.45366i	−0.0201352	−	0.115667i
$451$	−18.7287			−0.881900
$452$			6.49465i			0.305482i
$453$		−	19.2214i		−	0.903098i
$454$	−12.3603			−0.580098
$455$	2.12978	+	24.6531i	0.0998456	+	1.15575i
$456$	−1.86886			−0.0875173
$457$			25.3250i			1.18465i	0.805697	+	0.592327i	$0.201791\pi$
$457$			25.3250i			1.18465i	−0.805697	+	0.592327i	$0.798209\pi$
$458$			0.457854i			0.0213941i
$459$	7.34369			0.342774
$460$	10.5236	−	0.909133i	0.490664	−	0.0423885i
$461$	−24.3053			−1.13201			−0.566005	−	0.824402i	$-0.691512\pi$
$461$	−24.3053			−1.13201			−0.566005	+	0.824402i	$0.691512\pi$
$462$		−	9.54169i		−	0.443920i
$463$		−	15.8208i		−	0.735256i	−0.929973	−	0.367628i	$-0.880170\pi$
$463$		−	15.8208i		−	0.735256i	0.929973	−	0.367628i	$-0.119830\pi$
$464$	−2.51979			−0.116978
$465$	11.3784	−	0.982977i	0.527659	−	0.0455845i
$466$	−6.94010			−0.321494
$467$		−	1.84478i		−	0.0853661i	−0.999089	−	0.0426831i	$-0.986409\pi$
$467$		−	1.84478i		−	0.0853661i	0.999089	−	0.0426831i	$-0.0135906\pi$
$468$		−	4.18942i		−	0.193656i
$469$	−33.7091			−1.55654
$470$	−0.488179	−	5.65087i	−0.0225180	−	0.260655i
$471$	13.6082			0.627032
$472$			25.2285i			1.16124i
$473$			14.2382i			0.654673i
$474$	8.04882			0.369694
$475$	4.92592	−	0.857501i	0.226017	−	0.0393448i
$476$	59.5350			2.72878
$477$		−	3.36319i		−	0.153990i
$478$		−	8.86572i		−	0.405509i
$479$	10.9945			0.502350			0.251175	−	0.967942i	$-0.419183\pi$
$479$	10.9945			0.502350			0.251175	+	0.967942i	$0.419183\pi$
$480$	0.965999	+	11.1818i	0.0440916	+	0.510378i
$481$	23.5621			1.07434
$482$			5.25224i			0.239233i
$483$		−	12.4779i		−	0.567762i
$484$	10.7484			0.488564
$485$	−5.21869	+	0.450843i	−0.236969	+	0.0204717i
$486$	0.498112			0.0225948
$487$		−	32.2455i		−	1.46118i	−0.682816	−	0.730590i	$-0.739245\pi$
$487$		−	32.2455i		−	1.46118i	0.682816	−	0.730590i	$-0.260755\pi$
$488$		−	12.4110i		−	0.561820i
$489$	3.12532			0.141332
$490$	−15.9953	+	1.38183i	−0.722592	+	0.0624248i
$491$	−5.50201			−0.248302			−0.124151	−	0.992263i	$-0.539621\pi$
$491$	−5.50201			−0.248302			−0.124151	+	0.992263i	$0.539621\pi$
$492$		−	7.92623i		−	0.357342i
$493$		−	7.19218i		−	0.323920i
$494$	−1.19117			−0.0535934
$495$	−0.796674	−	9.22182i	−0.0358078	−	0.414490i
$496$	−13.1409			−0.590046
$497$			33.7091i			1.51206i
$498$			1.95321i			0.0875252i
$499$	16.5316			0.740054			0.370027	−	0.929021i	$-0.379348\pi$
$499$	16.5316			0.740054			0.370027	+	0.929021i	$0.379348\pi$
$500$	−5.00749	−	18.9357i	−0.223942	−	0.846832i
$501$	2.86858			0.128158
$502$			7.46373i			0.333122i
$503$			19.6030i			0.874056i	0.899448	+	0.437028i	$0.143969\pi$
$503$			19.6030i			0.874056i	−0.899448	+	0.437028i	$0.856031\pi$
$504$	8.64825			0.385224
$505$	−1.43372	−	16.5958i	−0.0637995	−	0.738505i
$506$	−5.55982			−0.247164
$507$			7.28131i			0.323374i
$508$			32.2531i			1.43100i
$509$	21.3635			0.946922			0.473461	−	0.880815i	$-0.343004\pi$
$509$	21.3635			0.946922			0.473461	+	0.880815i	$0.343004\pi$
$510$	−8.14914	+	0.704005i	−0.360850	+	0.0311738i
$511$	−17.6932			−0.782699
$512$		−	22.5306i		−	0.995723i
$513$			1.00000i			0.0441511i
$514$	2.43994			0.107621
$515$	−18.2168	+	1.57375i	−0.802728	+	0.0693477i
$516$	−6.02579			−0.265271
$517$		−	21.0797i		−	0.927084i
$518$			22.7114i			0.997883i
$519$	4.85404			0.213069
$520$	0.860119	+	9.95623i	0.0377187	+	0.436610i
$521$	25.7832			1.12958			0.564791	−	0.825234i	$-0.308957\pi$
$521$	25.7832			1.12958			0.564791	+	0.825234i	$0.308957\pi$
$522$		−	0.487835i		−	0.0213520i
$523$			24.4480i			1.06904i	0.845157	+	0.534518i	$0.179507\pi$
$523$			24.4480i			1.06904i	−0.845157	+	0.534518i	$0.820493\pi$
$524$	−18.6647			−0.815371
$525$	−22.7950	+	3.96814i	−0.994855	+	0.173184i
$526$	−6.79412			−0.296238
$527$		−	37.5080i		−	1.63387i
$528$			10.6504i			0.463497i
$529$	15.7293			0.683883
$530$	0.322413	+	3.73207i	0.0140047	+	0.162111i
$531$	13.4994			0.585825
$532$			8.10695i			0.351481i
$533$		−	10.8196i		−	0.468647i
$534$	−1.16781			−0.0505359
$535$	−11.7072	+	1.01139i	−0.506147	+	0.0437260i
$536$	−13.6135			−0.588015
$537$			16.7731i			0.723812i
$538$		−	7.85668i		−	0.338726i
$539$	−59.6679			−2.57008
$540$	3.90280	−	0.337163i	0.167950	−	0.0145092i
$541$	7.46518			0.320953			0.160477	−	0.987040i	$-0.448697\pi$
$541$	7.46518			0.320953			0.160477	+	0.987040i	$0.448697\pi$
$542$			2.55372i			0.109692i
$543$			17.0075i			0.729863i
$544$	36.8601			1.58037
$545$	−1.44415	−	16.7167i	−0.0618608	−	0.716064i
$546$	5.51223			0.235902
$547$			6.04764i			0.258578i	0.991607	+	0.129289i	$0.0412696\pi$
$547$			6.04764i			0.258578i	−0.991607	+	0.129289i	$0.958730\pi$
$548$			4.06378i			0.173596i
$549$	−6.64096			−0.283429
$550$	1.76810	+	10.1569i	0.0753922	+	0.433091i
$551$	0.979369			0.0417225
$552$		−	5.03923i		−	0.214484i
$553$		−	74.7751i		−	3.17976i
$554$	−4.30274			−0.182806
$555$	1.89627	+	21.9501i	0.0804921	+	0.931728i
$556$	27.7077			1.17507
$557$			28.3330i			1.20051i	0.799809	+	0.600255i	$0.204934\pi$
$557$			28.3330i			1.20051i	−0.799809	+	0.600255i	$0.795066\pi$
$558$		−	2.54411i		−	0.107701i
$559$	−8.22540			−0.347897
$560$	26.5241	−	2.29142i	1.12085	−	0.0968300i
$561$	−30.3991			−1.28345
$562$		−	9.25868i		−	0.390554i
$563$		−	39.5993i		−	1.66891i	−0.551074	−	0.834457i	$-0.685782\pi$
$563$		−	39.5993i		−	1.66891i	0.551074	−	0.834457i	$-0.314218\pi$
$564$	8.92120			0.375650
$565$	−8.25887	+	0.713484i	−0.347453	+	0.0300165i
$566$	9.96396			0.418816
$567$		−	4.62756i		−	0.194339i
$568$			13.6135i			0.571211i
$569$	−30.6989			−1.28697			−0.643483	−	0.765461i	$-0.722511\pi$
$569$	−30.6989			−1.28697			−0.643483	+	0.765461i	$0.722511\pi$
$570$	−0.0958652	−	1.10968i	−0.00401535	−	0.0464793i
$571$	−39.4360			−1.65035			−0.825173	−	0.564880i	$-0.808923\pi$
$571$	−39.4360			−1.65035			−0.825173	+	0.564880i	$0.808923\pi$
$572$			17.3420i			0.725107i
$573$			2.57283i			0.107481i
$574$	10.4289			0.435295
$575$	2.31218	+	13.2824i	0.0964247	+	0.553912i
$576$	−2.64557			−0.110232
$577$		−	8.15383i		−	0.339448i	−0.985492	−	0.169724i	$-0.945712\pi$
$577$		−	8.15383i		−	0.339448i	0.985492	−	0.169724i	$-0.0542877\pi$
$578$			18.3952i			0.765138i
$579$	−17.2612			−0.717351
$580$	−0.330207	−	3.82228i	−0.0137111	−	0.158711i
$581$	18.1457			0.752809
$582$			1.16686i			0.0483678i
$583$			13.9219i			0.576586i
$584$	−7.14545			−0.295681
$585$	5.32744	−	0.460238i	0.220263	−	0.0190285i
$586$	5.52094			0.228068
$587$		−	10.8871i		−	0.449360i	−0.974433	−	0.224680i	$-0.927866\pi$
$587$		−	10.8871i		−	0.449360i	0.974433	−	0.224680i	$-0.0721337\pi$
$588$		−	25.2522i		−	1.04138i
$589$	5.10751			0.210451
$590$	−14.9800	+	1.29413i	−0.616718	+	0.0532783i
$591$	−18.5625			−0.763558
$592$		−	25.3503i		−	1.04189i
$593$		−	3.13220i		−	0.128624i	−0.997930	−	0.0643120i	$-0.979515\pi$
$593$		−	3.13220i		−	0.128624i	0.997930	−	0.0643120i	$-0.0204853\pi$
$594$	−2.06193			−0.0846019
$595$	6.54035	+	75.7072i	0.268128	+	3.10369i
$596$	13.5048			0.553180
$597$			4.24470i			0.173724i
$598$		−	3.21191i		−	0.131345i
$599$	−24.2488			−0.990778			−0.495389	−	0.868671i	$-0.664975\pi$
$599$	−24.2488			−0.990778			−0.495389	+	0.868671i	$0.664975\pi$
$600$	−9.20585	+	1.60255i	−0.375827	+	0.0654237i
$601$	−9.24528			−0.377123			−0.188561	−	0.982061i	$-0.560382\pi$
$601$	−9.24528			−0.377123			−0.188561	+	0.982061i	$0.560382\pi$
$602$		−	7.92844i		−	0.323139i
$603$			7.28441i			0.296644i
$604$	−33.6736			−1.37016
$605$	1.18079	+	13.6681i	0.0480060	+	0.555689i
$606$	−3.71070			−0.150737
$607$			42.6285i			1.73024i	0.501569	+	0.865118i	$0.332756\pi$
$607$			42.6285i			1.73024i	−0.501569	+	0.865118i	$0.667244\pi$
$608$			5.01929i			0.203559i
$609$	−4.53209			−0.183649
$610$	7.36933	−	0.636637i	0.298375	−	0.0257767i
$611$	12.1777			0.492658
$612$		−	12.8653i		−	0.520049i
$613$		−	45.2670i		−	1.82832i	−0.405356	−	0.914159i	$-0.632852\pi$
$613$		−	45.2670i		−	1.82832i	0.405356	−	0.914159i	$-0.367148\pi$
$614$	−13.0931			−0.528394
$615$	10.0793	−	0.870754i	0.406438	−	0.0351122i
$616$	−35.7993			−1.44240
$617$		−	8.02773i		−	0.323184i	−0.986858	−	0.161592i	$-0.948337\pi$
$617$		−	8.02773i		−	0.323184i	0.986858	−	0.161592i	$-0.0516629\pi$
$618$			4.07313i			0.163845i
$619$	−15.1856			−0.610361			−0.305181	−	0.952294i	$-0.598717\pi$
$619$	−15.1856			−0.610361			−0.305181	+	0.952294i	$0.598717\pi$
$620$	−1.72206	−	19.9336i	−0.0691597	−	0.800551i
$621$	−2.69642			−0.108204
$622$		−	13.0150i		−	0.521854i
$623$			10.8491i			0.434662i
$624$	−6.15270			−0.246305
$625$	23.5294	−	8.44796i	0.941175	−	0.337918i
$626$	1.88586			0.0753741
$627$		−	4.13949i		−	0.165315i
$628$		−	23.8400i		−	0.951318i
$629$	72.3569			2.88506
$630$	0.443622	+	5.13511i	0.0176743	+	0.204588i
$631$	4.77803			0.190210			0.0951052	−	0.995467i	$-0.469681\pi$
$631$	4.77803			0.190210			0.0951052	+	0.995467i	$0.469681\pi$
$632$		−	30.1982i		−	1.20122i
$633$		−	1.20969i		−	0.0480809i
$634$	5.89864			0.234265
$635$	−41.0144	+	3.54324i	−1.62761	+	0.140609i
$636$	−5.89193			−0.233630
$637$		−	34.4701i		−	1.36575i
$638$			2.01939i			0.0799483i
$639$	7.28441			0.288167
$640$	25.2994	−	2.18562i	1.00005	−	0.0863941i
$641$	−28.6332			−1.13094			−0.565472	−	0.824767i	$-0.691306\pi$
$641$	−28.6332			−1.13094			−0.565472	+	0.824767i	$0.691306\pi$
$642$			2.61764i			0.103310i
$643$			33.5682i			1.32380i	0.749593	+	0.661899i	$0.230249\pi$
$643$			33.5682i			1.32380i	−0.749593	+	0.661899i	$0.769751\pi$
$644$	−21.8598			−0.861395
$645$	−0.661977	−	7.66265i	−0.0260653	−	0.301717i
$646$	−3.65798			−0.143921
$647$		−	29.3005i		−	1.15192i	−0.817478	−	0.575960i	$-0.804628\pi$
$647$		−	29.3005i		−	1.15192i	0.817478	−	0.575960i	$-0.195372\pi$
$648$		−	1.86886i		−	0.0734157i
$649$	−55.8807			−2.19351
$650$	−5.86763	+	1.02143i	−0.230147	+	0.0400639i
$651$	−23.6353			−0.926341
$652$		−	5.47520i		−	0.214425i
$653$			47.8047i			1.87074i	0.353666	+	0.935372i	$0.384935\pi$
$653$			47.8047i			1.87074i	−0.353666	+	0.935372i	$0.615065\pi$
$654$	−3.73772			−0.146156
$655$	−2.05045	−	23.7348i	−0.0801178	−	0.927396i
$656$	−11.6407			−0.454493
$657$			3.82343i			0.149166i
$658$			11.7381i			0.457598i
$659$	−17.6309			−0.686801			−0.343401	−	0.939189i	$-0.611579\pi$
$659$	−17.6309			−0.686801			−0.343401	+	0.939189i	$0.611579\pi$
$660$	−16.1556	+	1.39568i	−0.628855	+	0.0543268i
$661$	−14.5024			−0.564079			−0.282039	−	0.959403i	$-0.591011\pi$
$661$	−14.5024			−0.564079			−0.282039	+	0.959403i	$0.591011\pi$
$662$		−	17.0716i		−	0.663507i
$663$		−	17.5615i		−	0.682034i
$664$	7.32820			0.284389
$665$	−10.3091	+	0.890607i	−0.399771	+	0.0345363i
$666$	4.90786			0.190176
$667$			2.64079i			0.102252i
$668$		−	5.02541i		−	0.194439i
$669$	−6.22370			−0.240622
$670$	−0.698322	−	8.08336i	−0.0269785	−	0.312287i
$671$	27.4901			1.06125
$672$		−	23.2271i		−	0.896004i
$673$			34.8772i			1.34442i	0.740361	+	0.672209i	$0.234654\pi$
$673$			34.8772i			1.34442i	−0.740361	+	0.672209i	$0.765346\pi$
$674$	5.22916			0.201420
$675$	0.857501	+	4.92592i	0.0330052	+	0.189599i
$676$	12.7560			0.490616
$677$		−	15.0784i		−	0.579512i	−0.957101	−	0.289756i	$-0.906426\pi$
$677$		−	15.0784i		−	0.579512i	0.957101	−	0.289756i	$-0.0935741\pi$
$678$			1.84662i			0.0709189i
$679$	10.8403			0.416014
$680$	2.64134	+	30.5746i	0.101291	+	1.17248i
$681$	24.8143			0.950887
$682$			10.5313i			0.403265i
$683$			28.5584i			1.09276i	0.837539	+	0.546378i	$0.183994\pi$
$683$			28.5584i			1.09276i	−0.837539	+	0.546378i	$0.816006\pi$
$684$	1.75188			0.0669850
$685$	−5.16768	+	0.446436i	−0.197447	+	0.0170574i
$686$	17.0903			0.652511
$687$		−	0.919180i		−	0.0350689i
$688$			8.84966i			0.337390i
$689$	−8.04267			−0.306401
$690$	2.99216	−	0.258493i	0.113910	−	0.00984066i
$691$	−45.5752			−1.73376			−0.866882	−	0.498514i	$-0.833879\pi$
$691$	−45.5752			−1.73376			−0.866882	+	0.498514i	$0.833879\pi$
$692$		−	8.50371i		−	0.323263i
$693$			19.1557i			0.727666i
$694$	9.37438			0.355847
$695$	3.04389	+	35.2343i	0.115461	+	1.33651i
$696$	−1.83030			−0.0693774
$697$		−	33.2258i		−	1.25852i
$698$		−	7.17665i		−	0.271640i
$699$	13.9328			0.526987
$700$	6.95172	+	39.9342i	0.262750	+	1.50937i
$701$	47.2207			1.78350			0.891750	−	0.452528i	$-0.149478\pi$
$701$	47.2207			1.78350			0.891750	+	0.452528i	$0.149478\pi$
$702$		−	1.19117i		−	0.0449580i
$703$			9.85293i			0.371610i
$704$	10.9513			0.412742
$705$	0.980059	+	11.3446i	0.0369112	+	0.427262i
$706$	2.69768			0.101529
$707$			34.4731i			1.29650i
$708$		−	23.6494i		−	0.888800i
$709$	−21.4475			−0.805479			−0.402739	−	0.915315i	$-0.631942\pi$
$709$	−21.4475			−0.805479			−0.402739	+	0.915315i	$0.631942\pi$
$710$	−8.08336	+	0.698322i	−0.303363	+	0.0262075i
$711$	−16.1586			−0.605997
$712$			4.38147i			0.164203i
$713$			13.7720i			0.515765i
$714$	16.9275			0.633497
$715$	−22.0529	+	1.90515i	−0.824730	+	0.0712485i
$716$	29.3845			1.09815
$717$			17.7987i			0.664703i
$718$		−	10.3261i		−	0.385365i
$719$	−30.7936			−1.14841			−0.574203	−	0.818713i	$-0.694688\pi$
$719$	−30.7936			−1.14841			−0.574203	+	0.818713i	$0.694688\pi$
$720$	−0.495167	−	5.73176i	−0.0184538	−	0.213610i
$721$	37.8402			1.40924
$722$		−	0.498112i		−	0.0185378i
$723$		−	10.5443i		−	0.392146i
$724$	29.7952			1.10733
$725$	4.82429	−	0.839809i	0.179170	−	0.0311897i
$726$	3.05609			0.113422
$727$		−	35.1442i		−	1.30343i	−0.758465	−	0.651714i	$-0.774050\pi$
$727$		−	35.1442i		−	1.30343i	0.758465	−	0.651714i	$-0.225950\pi$
$728$		−	20.6812i		−	0.766498i
$729$	−1.00000			−0.0370370
$730$	−0.366534	−	4.24278i	−0.0135660	−	0.157032i
$731$	−25.2594			−0.934253
$732$			11.6342i			0.430012i
$733$			13.1160i			0.484449i	0.970220	+	0.242225i	$0.0778771\pi$
$733$			13.1160i			0.484449i	−0.970220	+	0.242225i	$0.922123\pi$
$734$	−1.29725			−0.0478823
$735$	32.1118	−	2.77414i	1.18446	−	0.102326i
$736$	−13.5341			−0.498874
$737$		−	30.1537i		−	1.11073i
$738$		−	2.25366i		−	0.0829583i
$739$	−15.7315			−0.578691			−0.289346	−	0.957225i	$-0.593438\pi$
$739$	−15.7315			−0.578691			−0.289346	+	0.957225i	$0.593438\pi$
$740$	38.4540	−	3.32204i	1.41360	−	0.122121i
$741$	2.39138			0.0878495
$742$		−	7.75231i		−	0.284596i
$743$			5.59959i			0.205429i	0.994711	+	0.102715i	$0.0327528\pi$
$743$			5.59959i			0.205429i	−0.994711	+	0.102715i	$0.967247\pi$
$744$	−9.54521			−0.349944
$745$	1.48360	+	17.1733i	0.0543550	+	0.629182i
$746$	2.98020			0.109113
$747$		−	3.92122i		−	0.143470i
$748$			53.2557i			1.94722i
$749$	24.3184			0.888575
$750$	−1.42378	−	5.38399i	−0.0519889	−	0.196595i
$751$	−1.87281			−0.0683397			−0.0341698	−	0.999416i	$-0.510879\pi$
$751$	−1.87281			−0.0683397			−0.0341698	+	0.999416i	$0.510879\pi$
$752$		−	13.1019i		−	0.477779i
$753$		−	14.9840i		−	0.546049i
$754$	−1.16660			−0.0424850
$755$	−3.69929	−	42.8208i	−0.134631	−	1.55841i
$756$	−8.10695			−0.294847
$757$			30.2362i			1.09895i	0.835509	+	0.549476i	$0.185173\pi$
$757$			30.2362i			1.09895i	−0.835509	+	0.549476i	$0.814827\pi$
$758$		−	3.70794i		−	0.134679i
$759$	11.1618			0.405148
$760$	−4.16339	+	0.359675i	−0.151022	+	0.0130468i
$761$	−17.5630			−0.636659			−0.318330	−	0.947980i	$-0.603122\pi$
$761$	−17.5630			−0.636659			−0.318330	+	0.947980i	$0.603122\pi$
$762$			9.17049i			0.332212i
$763$			34.7241i			1.25710i
$764$	4.50730			0.163068
$765$	16.3601	−	1.41335i	0.591499	−	0.0510996i
$766$	−7.76003			−0.280381
$767$		−	32.2822i		−	1.16564i
$768$		−	0.365609i		−	0.0131928i
$769$	−18.2587			−0.658426			−0.329213	−	0.944256i	$-0.606783\pi$
$769$	−18.2587			−0.658426			−0.329213	+	0.944256i	$0.606783\pi$
$770$	−1.83637	−	21.2567i	−0.0661781	−	0.766038i
$771$	−4.89838			−0.176411
$772$			30.2396i			1.08835i
$773$		−	7.79018i		−	0.280193i	−0.990138	−	0.140097i	$-0.955259\pi$
$773$		−	7.79018i		−	0.280193i	0.990138	−	0.140097i	$-0.0447413\pi$
$774$	−1.71331			−0.0615836
$775$	25.1592	−	4.37969i	0.903745	−	0.157323i
$776$	4.37792			0.157158
$777$		−	45.5950i		−	1.63571i
$778$			8.34497i			0.299182i
$779$	4.52440			0.162103
$780$	−0.806284	−	9.33306i	−0.0288696	−	0.334177i
$781$	−30.1537			−1.07898
$782$		−	9.86345i		−	0.352716i
$783$			0.979369i			0.0349998i
$784$	−37.0861			−1.32451
$785$	30.3159	−	2.61899i	1.08202	−	0.0934758i
$786$	−5.30692			−0.189292
$787$			1.66566i			0.0593744i	0.999559	+	0.0296872i	$0.00945111\pi$
$787$			1.66566i			0.0593744i	−0.999559	+	0.0296872i	$0.990549\pi$
$788$			32.5193i			1.15845i
$789$	13.6398			0.485588
$790$	17.9309	−	1.54905i	0.637953	−	0.0551128i
$791$	17.1555			0.609978
$792$			7.73611i			0.274891i
$793$			15.8810i			0.563952i
$794$	3.31496			0.117644
$795$	−0.647271	−	7.49242i	−0.0229563	−	0.265729i
$796$	7.43622			0.263570
$797$		−	26.1199i		−	0.925215i	−0.886563	−	0.462607i	$-0.846914\pi$
$797$		−	26.1199i		−	0.925215i	0.886563	−	0.462607i	$-0.153086\pi$
$798$			2.30504i			0.0815976i
$799$	37.3966			1.32300
$800$	4.30405	+	24.7246i	0.152171	+	0.874148i
$801$	2.34446			0.0828375
$802$			15.3734i			0.542852i
$803$		−	15.8270i		−	0.558524i
$804$	12.7614			0.450062
$805$	−2.40145	−	27.7978i	−0.0846401	−	0.979743i
$806$	−6.08393			−0.214297
$807$			15.7729i			0.555233i
$808$			13.9221i			0.489778i
$809$	−10.7020			−0.376261			−0.188130	−	0.982144i	$-0.560243\pi$
$809$	−10.7020			−0.376261			−0.188130	+	0.982144i	$0.560243\pi$
$810$	1.10968	−	0.0958652i	0.0389901	−	0.00336836i
$811$	41.3040			1.45038			0.725190	−	0.688549i	$-0.241752\pi$
$811$	41.3040			1.45038			0.725190	+	0.688549i	$0.241752\pi$
$812$			7.93969i			0.278629i
$813$		−	5.12680i		−	0.179805i
$814$	−20.3160			−0.712076
$815$	6.96249	−	0.601490i	0.243885	−	0.0210693i
$816$	−18.8944			−0.661435
$817$		−	3.43961i		−	0.120337i
$818$		−	13.1630i		−	0.460232i
$819$	−11.0662			−0.386686
$820$	−1.52546	−	17.6578i	−0.0532714	−	0.616638i
$821$	31.6822			1.10572			0.552858	−	0.833276i	$-0.313537\pi$
$821$	31.6822			1.10572			0.552858	+	0.833276i	$0.313537\pi$
$822$			1.15545i			0.0403010i
$823$			20.7292i			0.722575i	0.932454	+	0.361288i	$0.117663\pi$
$823$			20.7292i			0.722575i	−0.932454	+	0.361288i	$0.882337\pi$
$824$	15.2819			0.532371
$825$	−3.54961	−	20.3908i	−0.123582	−	0.709916i
$826$	31.1168			1.08269
$827$			24.6668i			0.857750i	0.903364	+	0.428875i	$0.141090\pi$
$827$			24.6668i			0.857750i	−0.903364	+	0.428875i	$0.858910\pi$
$828$			4.72382i			0.164164i
$829$	52.3442			1.81799			0.908995	−	0.416808i	$-0.136851\pi$
$829$	52.3442			1.81799			0.908995	+	0.416808i	$0.136851\pi$
$830$	0.375908	+	4.35129i	0.0130480	+	0.151036i
$831$	8.63811			0.299653
$832$			6.32655i			0.219334i
$833$		−	105.854i		−	3.66763i
$834$	7.87811			0.272797
$835$	6.39053	−	0.552078i	0.221153	−	0.0191054i
$836$	−7.25190			−0.250812
$837$			5.10751i			0.176541i
$838$		−	2.11954i		−	0.0732182i
$839$	1.72696			0.0596214			0.0298107	−	0.999556i	$-0.490510\pi$
$839$	1.72696			0.0596214			0.0298107	+	0.999556i	$0.490510\pi$
$840$	19.2663	−	1.66442i	0.664751	−	0.0574279i
$841$	−28.0408			−0.966925
$842$			6.64140i			0.228878i
$843$			18.5875i			0.640189i
$844$	−2.11924			−0.0729473
$845$	1.40134	+	16.2211i	0.0482076	+	0.558022i
$846$	2.53656			0.0872087
$847$		−	28.3917i		−	0.975550i
$848$			8.65306i			0.297147i
$849$	−20.0035			−0.686517
$850$	−18.0189	+	3.13672i	−0.618044	+	0.107589i
$851$	−26.5676			−0.910727
$852$		−	12.7614i		−	0.437200i
$853$			5.71206i			0.195577i	0.995207	+	0.0977886i	$0.0311769\pi$
$853$			5.71206i			0.195577i	−0.995207	+	0.0977886i	$0.968823\pi$
$854$	−15.3077			−0.523818
$855$	0.192457	+	2.22777i	0.00658190	+	0.0761881i
$856$	9.82108			0.335677
$857$			8.45967i			0.288977i	0.989507	+	0.144488i	$0.0461536\pi$
$857$			8.45967i			0.288977i	−0.989507	+	0.144488i	$0.953846\pi$
$858$			4.93085i			0.168336i
$859$	9.60383			0.327678			0.163839	−	0.986487i	$-0.447612\pi$
$859$	9.60383			0.327678			0.163839	+	0.986487i	$0.447612\pi$
$860$	−13.4241	+	1.15971i	−0.457757	+	0.0395457i
$861$	−20.9369			−0.713529
$862$			8.85402i			0.301569i
$863$			7.21724i			0.245678i	0.992427	+	0.122839i	$0.0391999\pi$
$863$			7.21724i			0.245678i	−0.992427	+	0.122839i	$0.960800\pi$
$864$	−5.01929			−0.170760
$865$	10.8137	−	0.934194i	0.367676	−	0.0317636i
$866$	−15.5661			−0.528958
$867$		−	36.9298i		−	1.25420i
$868$			41.4063i			1.40542i
$869$	66.8885			2.26904
$870$	−0.0938874	−	1.08678i	−0.00318308	−	0.0368454i
$871$	17.4198			0.590247
$872$			14.0235i			0.474895i
$873$		−	2.34256i		−	0.0792837i
$874$	1.34312			0.0454317
$875$	−50.0183	+	13.2272i	−1.69093	+	0.447160i
$876$	6.69821			0.226312
$877$			12.7856i			0.431740i	0.976422	+	0.215870i	$0.0692588\pi$
$877$			12.7856i			0.431740i	−0.976422	+	0.215870i	$0.930741\pi$
$878$		−	5.90098i		−	0.199148i
$879$	−11.0837			−0.373845
$880$	2.04974	+	23.7265i	0.0690966	+	0.799822i
$881$	−52.4525			−1.76717			−0.883586	−	0.468270i	$-0.844878\pi$
$881$	−52.4525			−1.76717			−0.883586	+	0.468270i	$0.844878\pi$
$882$		−	7.17994i		−	0.241761i
$883$		−	13.2387i		−	0.445517i	−0.974874	−	0.222758i	$-0.928494\pi$
$883$		−	13.2387i		−	0.445517i	0.974874	−	0.222758i	$-0.0715061\pi$
$884$	−30.7658			−1.03477
$885$	30.0736	−	2.59806i	1.01091	−	0.0873329i
$886$	−15.6070			−0.524328
$887$		−	33.9046i		−	1.13840i	−0.822198	−	0.569202i	$-0.807252\pi$
$887$		−	33.9046i		−	1.13840i	0.822198	−	0.569202i	$-0.192748\pi$
$888$		−	18.4137i		−	0.617924i
$889$	85.1958			2.85737
$890$	−2.60160	+	0.224753i	−0.0872059	+	0.00753372i
$891$	4.13949			0.138678
$892$			10.9032i			0.365066i
$893$			5.09235i			0.170409i
$894$	3.83982			0.128423
$895$	3.22810	+	37.3666i	0.107903	+	1.24903i
$896$	−52.5523			−1.75565
$897$			6.44816i			0.215298i
$898$		−	4.32192i		−	0.144224i
$899$	5.00213			0.166830
$900$	8.62964	−	1.50224i	0.287655	−	0.0500748i
$901$	−24.6983			−0.822818
$902$			9.32898i			0.310621i
$903$			15.9170i			0.529684i
$904$	6.92830			0.230432
$905$	3.27322	+	37.8889i	0.108806	+	1.25947i
$906$	−9.57439			−0.318088
$907$		−	26.0357i		−	0.864502i	−0.901753	−	0.432251i	$-0.857719\pi$
$907$		−	26.0357i		−	0.864502i	0.901753	−	0.432251i	$-0.142281\pi$
$908$		−	43.4718i		−	1.44266i
$909$	7.44953			0.247085
$910$	12.2800	−	1.06087i	0.407077	−	0.0351674i
$911$	53.0788			1.75858			0.879289	−	0.476289i	$-0.158018\pi$
$911$	53.0788			1.75858			0.879289	+	0.476289i	$0.158018\pi$
$912$		−	2.57287i		−	0.0851962i
$913$			16.2318i			0.537195i
$914$	12.6147			0.417257
$915$	−14.7945	+	1.27810i	−0.489092	+	0.0422527i
$916$	−1.61030			−0.0532057
$917$			49.3023i			1.62811i
$918$		−	3.65798i		−	0.120731i
$919$	−28.1784			−0.929521			−0.464760	−	0.885436i	$-0.653860\pi$
$919$	−28.1784			−0.929521			−0.464760	+	0.885436i	$0.653860\pi$
$920$	−0.969836	−	11.2262i	−0.0319745	−	0.370118i
$921$	26.2854			0.866134
$922$			12.1067i			0.398714i
$923$		−	17.4198i		−	0.573379i
$924$	33.5586			1.10400
$925$	8.44890	+	48.5347i	0.277798	+	1.59581i
$926$	−7.88054			−0.258971
$927$		−	8.17714i		−	0.268573i
$928$			4.91574i			0.161367i
$929$	−2.33284			−0.0765381			−0.0382690	−	0.999267i	$-0.512184\pi$
$929$	−2.33284			−0.0765381			−0.0382690	+	0.999267i	$0.512184\pi$
$930$	−0.489632	−	5.66769i	−0.0160557	−	0.185851i
$931$	14.4143			0.472410
$932$		−	24.4087i		−	0.799533i
$933$			26.1287i			0.855415i
$934$	−0.918906			−0.0300675
$935$	−67.7222	+	5.85053i	−2.21475	+	0.191333i
$936$	−4.46915			−0.146079
$937$		−	1.92340i		−	0.0628349i	−0.999506	−	0.0314174i	$-0.989998\pi$
$937$		−	1.92340i		−	0.0628349i	0.999506	−	0.0314174i	$-0.0100021\pi$
$938$			16.7909i			0.548242i
$939$	−3.78602			−0.123552
$940$	19.8744	−	1.71695i	0.648231	−	0.0560007i
$941$	55.5001			1.80925			0.904626	−	0.426205i	$-0.140150\pi$
$941$	55.5001			1.80925			0.904626	+	0.426205i	$0.140150\pi$
$942$		−	6.77840i		−	0.220852i
$943$			12.1997i			0.397276i
$944$	−34.7323			−1.13044
$945$	−0.890607	−	10.3091i	−0.0289715	−	0.335356i
$946$	7.09222			0.230588
$947$			37.1931i			1.20861i	0.796752	+	0.604307i	$0.206550\pi$
$947$			37.1931i			1.20861i	−0.796752	+	0.604307i	$0.793450\pi$
$948$			28.3081i			0.919404i
$949$	9.14327			0.296803
$950$	−0.427131	−	2.45366i	−0.0138580	−	0.0796072i
$951$	−11.8420			−0.384003
$952$		−	63.5101i		−	2.05837i
$953$			54.4958i			1.76529i	0.470039	+	0.882646i	$0.344240\pi$
$953$			54.4958i			1.76529i	−0.470039	+	0.882646i	$0.655760\pi$
$954$	−1.67525			−0.0542381
$955$	0.495159	+	5.73167i	0.0160230	+	0.185472i
$956$	31.1812			1.00847
$957$		−	4.05408i		−	0.131050i
$958$		−	5.47648i		−	0.176937i
$959$	10.7344			0.346631
$960$	−5.89372	+	0.509159i	−0.190219	+	0.0164330i
$961$	−4.91335			−0.158495
$962$		−	11.7366i		−	0.378402i
$963$		−	5.25512i		−	0.169344i
$964$	−18.4724			−0.594955
$965$	−38.4540	+	3.32204i	−1.23788	+	0.106940i
$966$	−6.21537			−0.199976
$967$			28.6863i			0.922490i	0.887273	+	0.461245i	$0.152597\pi$
$967$			28.6863i			0.922490i	−0.887273	+	0.461245i	$0.847403\pi$
$968$		−	11.4661i		−	0.368534i
$969$	7.34369			0.235913
$970$	0.224570	+	2.59949i	0.00721052	+	0.0834647i
$971$	35.0585			1.12508			0.562540	−	0.826770i	$-0.309824\pi$
$971$	35.0585			1.12508			0.562540	+	0.826770i	$0.309824\pi$
$972$			1.75188i			0.0561917i
$973$		−	73.1893i		−	2.34634i
$974$	−16.0618			−0.514655
$975$	11.7797	−	2.05061i	0.377254	−	0.0656720i
$976$	17.0863			0.546919
$977$		−	49.1831i		−	1.57351i	−0.617267	−	0.786754i	$-0.711760\pi$
$977$		−	49.1831i		−	1.57351i	0.617267	−	0.786754i	$-0.288240\pi$
$978$		−	1.55676i		−	0.0497796i
$979$	−9.70487			−0.310169
$980$	−4.85997	−	56.2561i	−0.155246	−	1.79704i
$981$	7.50377			0.239577
$982$			2.74062i			0.0874567i
$983$			7.88117i			0.251370i	0.992070	+	0.125685i	$0.0401129\pi$
$983$			7.88117i			0.251370i	−0.992070	+	0.125685i	$0.959887\pi$
$984$	−8.45546			−0.269550
$985$	−41.3529	+	3.57248i	−1.31761	+	0.113829i
$986$	−3.58251			−0.114090
$987$		−	23.5651i		−	0.750087i
$988$		−	4.18942i		−	0.133283i
$989$	9.27463			0.294916
$990$	−4.59350	+	0.396833i	−0.145991	+	0.0126122i
$991$	24.6229			0.782174			0.391087	−	0.920354i	$-0.372099\pi$
$991$	24.6229			0.782174			0.391087	+	0.920354i	$0.372099\pi$
$992$			25.6361i			0.813946i
$993$			34.2726i			1.08761i
$994$	16.7909			0.532574
$995$	0.816922	+	9.45621i	0.0258982	+	0.299782i
$996$	−6.86952			−0.217669
$997$		−	47.6543i		−	1.50923i	−0.656169	−	0.754614i	$-0.727824\pi$
$997$		−	47.6543i		−	1.50923i	0.656169	−	0.754614i	$-0.272176\pi$
$998$		−	8.23456i		−	0.260661i
$999$	−9.85293			−0.311733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.c.b.229.6	✓	14
3.2	odd	2		855.2.c.g.514.9		14
5.2	odd	4		1425.2.a.z.1.4		7
5.3	odd	4		1425.2.a.y.1.4		7
5.4	even	2	inner	285.2.c.b.229.9	yes	14
15.2	even	4		4275.2.a.bv.1.4		7
15.8	even	4		4275.2.a.bw.1.4		7
15.14	odd	2		855.2.c.g.514.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.6	✓	14	1.1	even	1	trivial
285.2.c.b.229.9	yes	14	5.4	even	2	inner
855.2.c.g.514.6		14	15.14	odd	2
855.2.c.g.514.9		14	3.2	odd	2
1425.2.a.y.1.4		7	5.3	odd	4
1425.2.a.z.1.4		7	5.2	odd	4
4275.2.a.bv.1.4		7	15.2	even	4
4275.2.a.bw.1.4		7	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.498112i q^{2} +1.00000i q^{3} +1.75188 q^{4} +(0.192457 + 2.22777i) q^{5} +0.498112 q^{6} -4.62756i q^{7} -1.86886i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.498112i q^{2} +1.00000i q^{3} +1.75188 q^{4} +(0.192457 + 2.22777i) q^{5} +0.498112 q^{6} -4.62756i q^{7} -1.86886i q^{8} -1.00000 q^{9} +(1.10968 - 0.0958652i) q^{10} +4.13949 q^{11} +1.75188i q^{12} +2.39138i q^{13} -2.30504 q^{14} +(-2.22777 + 0.192457i) q^{15} +2.57287 q^{16} +7.34369i q^{17} +0.498112i q^{18} -1.00000 q^{19} +(0.337163 + 3.90280i) q^{20} +4.62756 q^{21} -2.06193i q^{22} -2.69642i q^{23} +1.86886 q^{24} +(-4.92592 + 0.857501i) q^{25} +1.19117 q^{26} -1.00000i q^{27} -8.10695i q^{28} -0.979369 q^{29} +(0.0958652 + 1.10968i) q^{30} -5.10751 q^{31} -5.01929i q^{32} +4.13949i q^{33} +3.65798 q^{34} +(10.3091 - 0.890607i) q^{35} -1.75188 q^{36} -9.85293i q^{37} +0.498112i q^{38} -2.39138 q^{39} +(4.16339 - 0.359675i) q^{40} -4.52440 q^{41} -2.30504i q^{42} +3.43961i q^{43} +7.25190 q^{44} +(-0.192457 - 2.22777i) q^{45} -1.34312 q^{46} -5.09235i q^{47} +2.57287i q^{48} -14.4143 q^{49} +(0.427131 + 2.45366i) q^{50} -7.34369 q^{51} +4.18942i q^{52} +3.36319i q^{53} -0.498112 q^{54} +(0.796674 + 9.22182i) q^{55} -8.64825 q^{56} -1.00000i q^{57} +0.487835i q^{58} -13.4994 q^{59} +(-3.90280 + 0.337163i) q^{60} +6.64096 q^{61} +2.54411i q^{62} +4.62756i q^{63} +2.64557 q^{64} +(-5.32744 + 0.460238i) q^{65} +2.06193 q^{66} -7.28441i q^{67} +12.8653i q^{68} +2.69642 q^{69} +(-0.443622 - 5.13511i) q^{70} -7.28441 q^{71} +1.86886i q^{72} -3.82343i q^{73} -4.90786 q^{74} +(-0.857501 - 4.92592i) q^{75} -1.75188 q^{76} -19.1557i q^{77} +1.19117i q^{78} +16.1586 q^{79} +(0.495167 + 5.73176i) q^{80} +1.00000 q^{81} +2.25366i q^{82} +3.92122i q^{83} +8.10695 q^{84} +(-16.3601 + 1.41335i) q^{85} +1.71331 q^{86} -0.979369i q^{87} -7.73611i q^{88} -2.34446 q^{89} +(-1.10968 + 0.0958652i) q^{90} +11.0662 q^{91} -4.72382i q^{92} -5.10751i q^{93} -2.53656 q^{94} +(-0.192457 - 2.22777i) q^{95} +5.01929 q^{96} +2.34256i q^{97} +7.17994i q^{98} -4.13949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9	\( 14 q - 22 q^{4} + 2 q^{5} + 6 q^{6} - 14 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 38 q^{16} - 14 q^{19} + 12 q^{20} + 16 q^{21} - 18 q^{24} - 4 q^{25} - 40 q^{26} + 12 q^{29} + 4 q^{30} + 8 q^{31} - 4 q^{34} - 14 q^{35} + 22 q^{36} - 16 q^{39} + 18 q^{40} + 4 q^{41} + 64 q^{44} - 2 q^{45} - 8 q^{46} - 34 q^{49} + 4 q^{50} + 8 q^{51} - 6 q^{54} - 2 q^{55} - 44 q^{56} + 36 q^{59} - 18 q^{60} + 24 q^{61} - 22 q^{64} - 12 q^{65} + 24 q^{66} - 20 q^{69} - 60 q^{70} - 36 q^{71} - 12 q^{74} + 22 q^{76} + 8 q^{79} + 36 q^{80} + 14 q^{81} - 28 q^{84} - 18 q^{85} - 92 q^{86} + 16 q^{89} - 2 q^{90} + 24 q^{91} + 40 q^{94} - 2 q^{95} + 62 q^{96} + 8 q^{99}+O(q^{100}) \) 14 * q - 22 * q^4 + 2 * q^5 + 6 * q^6 - 14 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^15 + 38 * q^16 - 14 * q^19 + 12 * q^20 + 16 * q^21 - 18 * q^24 - 4 * q^25 - 40 * q^26 + 12 * q^29 + 4 * q^30 + 8 * q^31 - 4 * q^34 - 14 * q^35 + 22 * q^36 - 16 * q^39 + 18 * q^40 + 4 * q^41 + 64 * q^44 - 2 * q^45 - 8 * q^46 - 34 * q^49 + 4 * q^50 + 8 * q^51 - 6 * q^54 - 2 * q^55 - 44 * q^56 + 36 * q^59 - 18 * q^60 + 24 * q^61 - 22 * q^64 - 12 * q^65 + 24 * q^66 - 20 * q^69 - 60 * q^70 - 36 * q^71 - 12 * q^74 + 22 * q^76 + 8 * q^79 + 36 * q^80 + 14 * q^81 - 28 * q^84 - 18 * q^85 - 92 * q^86 + 16 * q^89 - 2 * q^90 + 24 * q^91 + 40 * q^94 - 2 * q^95 + 62 * q^96 + 8 * q^99

Introduction

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