LMFDB - Embedded newform 154.2.c.a.153.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(153,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("154.153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			153.8
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	154.153
Dual form			154.2.c.a.153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +3.09557i q^{3} -1.00000 q^{4} +0.646084i q^{5} -3.09557 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} -6.58258 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +3.09557i q^{3} -1.00000 q^{4} +0.646084i q^{5} -3.09557 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} -6.58258 q^{9} -0.646084 q^{10} +(2.79129 - 1.79129i) q^{11} -3.09557i q^{12} -3.09557 q^{13} +(1.00000 + 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} +3.74166 q^{17} -6.58258i q^{18} -5.54506 q^{19} -0.646084i q^{20} +(3.09557 + 7.58258i) q^{21} +(1.79129 + 2.79129i) q^{22} +4.00000 q^{23} +3.09557 q^{24} +4.58258 q^{25} -3.09557i q^{26} -11.0901i q^{27} +(-2.44949 + 1.00000i) q^{28} +7.58258i q^{29} -2.00000i q^{30} +1.15732i q^{31} +1.00000i q^{32} +(5.54506 + 8.64064i) q^{33} +3.74166i q^{34} +(0.646084 + 1.58258i) q^{35} +6.58258 q^{36} -5.58258 q^{37} -5.54506i q^{38} -9.58258i q^{39} +0.646084 q^{40} +5.03383 q^{41} +(-7.58258 + 3.09557i) q^{42} -11.1652i q^{43} +(-2.79129 + 1.79129i) q^{44} -4.25290i q^{45} +4.00000i q^{46} -5.03383i q^{47} +3.09557i q^{48} +(5.00000 - 4.89898i) q^{49} +4.58258i q^{50} +11.5826i q^{51} +3.09557 q^{52} -2.41742 q^{53} +11.0901 q^{54} +(1.15732 + 1.80341i) q^{55} +(-1.00000 - 2.44949i) q^{56} -17.1652i q^{57} -7.58258 q^{58} -3.09557i q^{59} +2.00000 q^{60} -9.28672 q^{61} -1.15732 q^{62} +(-16.1240 + 6.58258i) q^{63} -1.00000 q^{64} -2.00000i q^{65} +(-8.64064 + 5.54506i) q^{66} +1.58258 q^{67} -3.74166 q^{68} +12.3823i q^{69} +(-1.58258 + 0.646084i) q^{70} +2.00000 q^{71} +6.58258i q^{72} -6.32599 q^{73} -5.58258i q^{74} +14.1857i q^{75} +5.54506 q^{76} +(5.04594 - 7.17903i) q^{77} +9.58258 q^{78} +4.00000i q^{79} +0.646084i q^{80} +14.5826 q^{81} +5.03383i q^{82} +9.15188 q^{83} +(-3.09557 - 7.58258i) q^{84} +2.41742i q^{85} +11.1652 q^{86} -23.4724 q^{87} +(-1.79129 - 2.79129i) q^{88} -9.79796i q^{89} +4.25290 q^{90} +(-7.58258 + 3.09557i) q^{91} -4.00000 q^{92} -3.58258 q^{93} +5.03383 q^{94} -3.58258i q^{95} -3.09557 q^{96} +15.9891i q^{97} +(4.89898 + 5.00000i) q^{98} +(-18.3739 + 11.7913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 16 * q^9	$ 8 q - 8 q^{4} - 16 q^{9} + 4 q^{11} + 8 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{22} + 32 q^{23} + 16 q^{36} - 8 q^{37} - 24 q^{42} - 4 q^{44} + 40 q^{49} - 56 q^{53} - 8 q^{56} - 24 q^{58} + 16 q^{60} - 8 q^{64} - 24 q^{67} + 24 q^{70} + 16 q^{71} + 4 q^{77} + 40 q^{78} + 80 q^{81} + 16 q^{86} + 4 q^{88} - 24 q^{91} - 32 q^{92} + 8 q^{93} - 92 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 16 * q^9 + 4 * q^11 + 8 * q^14 - 16 * q^15 + 8 * q^16 - 4 * q^22 + 32 * q^23 + 16 * q^36 - 8 * q^37 - 24 * q^42 - 4 * q^44 + 40 * q^49 - 56 * q^53 - 8 * q^56 - 24 * q^58 + 16 * q^60 - 8 * q^64 - 24 * q^67 + 24 * q^70 + 16 * q^71 + 4 * q^77 + 40 * q^78 + 80 * q^81 + 16 * q^86 + 4 * q^88 - 24 * q^91 - 32 * q^92 + 8 * q^93 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$-1$

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
$3$			3.09557i			1.78723i	0.448834	+	0.893615i	$0.351839\pi$
$3$			3.09557i			1.78723i	−0.448834	+	0.893615i	$0.648161\pi$
$4$	−1.00000			−0.500000
$5$			0.646084i			0.288937i	0.989509	+	0.144469i	$0.0461473\pi$
$5$			0.646084i			0.288937i	−0.989509	+	0.144469i	$0.953853\pi$
$6$	−3.09557			−1.26376
$7$	2.44949	−	1.00000i	0.925820	−	0.377964i
$7$	2.44949	−	1.00000i	0.925820	−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−6.58258			−2.19419
$10$	−0.646084			−0.204310
$11$	2.79129	−	1.79129i	0.841605	−	0.540094i
$11$	2.79129	−	1.79129i	0.841605	−	0.540094i
$12$		−	3.09557i		−	0.893615i
$13$	−3.09557			−0.858558			−0.429279	−	0.903172i	$-0.641232\pi$
$13$	−3.09557			−0.858558			−0.429279	+	0.903172i	$0.641232\pi$
$14$	1.00000	+	2.44949i	0.267261	+	0.654654i
$15$	−2.00000			−0.516398
$16$	1.00000			0.250000
$17$	3.74166			0.907485			0.453743	−	0.891133i	$-0.350089\pi$
$17$	3.74166			0.907485			0.453743	+	0.891133i	$0.350089\pi$
$18$		−	6.58258i		−	1.55153i
$19$	−5.54506			−1.27212			−0.636062	−	0.771638i	$-0.719438\pi$
$19$	−5.54506			−1.27212			−0.636062	+	0.771638i	$0.719438\pi$
$20$		−	0.646084i		−	0.144469i
$21$	3.09557	+	7.58258i	0.675510	+	1.65465i
$22$	1.79129	+	2.79129i	0.381904	+	0.595105i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$	3.09557			0.631881
$25$	4.58258			0.916515
$26$		−	3.09557i		−	0.607092i
$27$		−	11.0901i		−	2.13430i
$28$	−2.44949	+	1.00000i	−0.462910	+	0.188982i
$29$			7.58258i			1.40805i	0.710176	+	0.704024i	$0.248615\pi$
$29$			7.58258i			1.40805i	−0.710176	+	0.704024i	$0.751385\pi$
$30$		−	2.00000i		−	0.365148i
$31$			1.15732i			0.207861i	0.994585	+	0.103931i	$0.0331420\pi$
$31$			1.15732i			0.207861i	−0.994585	+	0.103931i	$0.966858\pi$
$32$			1.00000i			0.176777i
$33$	5.54506	+	8.64064i	0.965272	+	1.50414i
$34$			3.74166i			0.641689i
$35$	0.646084	+	1.58258i	0.109208	+	0.267504i
$36$	6.58258			1.09710
$37$	−5.58258			−0.917770			−0.458885	−	0.888496i	$-0.651751\pi$
$37$	−5.58258			−0.917770			−0.458885	+	0.888496i	$0.651751\pi$
$38$		−	5.54506i		−	0.899528i
$39$		−	9.58258i		−	1.53444i
$40$	0.646084			0.102155
$41$	5.03383			0.786151			0.393076	−	0.919506i	$-0.371411\pi$
$41$	5.03383			0.786151			0.393076	+	0.919506i	$0.371411\pi$
$42$	−7.58258	+	3.09557i	−1.17002	+	0.477657i
$43$		−	11.1652i		−	1.70267i	−0.524623	−	0.851335i	$-0.675794\pi$
$43$		−	11.1652i		−	1.70267i	0.524623	−	0.851335i	$-0.324206\pi$
$44$	−2.79129	+	1.79129i	−0.420802	+	0.270047i
$45$		−	4.25290i		−	0.633984i
$46$			4.00000i			0.589768i
$47$		−	5.03383i		−	0.734259i	−0.930170	−	0.367129i	$-0.880341\pi$
$47$		−	5.03383i		−	0.734259i	0.930170	−	0.367129i	$-0.119659\pi$
$48$			3.09557i			0.446808i
$49$	5.00000	−	4.89898i	0.714286	−	0.699854i
$50$			4.58258i			0.648074i
$51$			11.5826i			1.62189i
$52$	3.09557			0.429279
$53$	−2.41742			−0.332059			−0.166029	−	0.986121i	$-0.553095\pi$
$53$	−2.41742			−0.332059			−0.166029	+	0.986121i	$0.553095\pi$
$54$	11.0901			1.50918
$55$	1.15732	+	1.80341i	0.156053	+	0.243171i
$56$	−1.00000	−	2.44949i	−0.133631	−	0.327327i
$57$		−	17.1652i		−	2.27358i
$58$	−7.58258			−0.995641
$59$		−	3.09557i		−	0.403009i	−0.979488	−	0.201505i	$-0.935417\pi$
$59$		−	3.09557i		−	0.403009i	0.979488	−	0.201505i	$-0.0645831\pi$
$60$	2.00000			0.258199
$61$	−9.28672			−1.18904			−0.594521	−	0.804080i	$-0.702658\pi$
$61$	−9.28672			−1.18904			−0.594521	+	0.804080i	$0.702658\pi$
$62$	−1.15732			−0.146980
$63$	−16.1240	+	6.58258i	−2.03143	+	0.829327i
$64$	−1.00000			−0.125000
$65$		−	2.00000i		−	0.248069i
$66$	−8.64064	+	5.54506i	−1.06359	+	0.682550i
$67$	1.58258			0.193342			0.0966712	−	0.995316i	$-0.469180\pi$
$67$	1.58258			0.193342			0.0966712	+	0.995316i	$0.469180\pi$
$68$	−3.74166			−0.453743
$69$			12.3823i			1.49065i
$70$	−1.58258	+	0.646084i	−0.189154	+	0.0772218i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$			6.58258i			0.775764i
$73$	−6.32599			−0.740401			−0.370201	−	0.928952i	$-0.620711\pi$
$73$	−6.32599			−0.740401			−0.370201	+	0.928952i	$0.620711\pi$
$74$		−	5.58258i		−	0.648961i
$75$			14.1857i			1.63802i
$76$	5.54506			0.636062
$77$	5.04594	−	7.17903i	0.575039	−	0.818126i
$78$	9.58258			1.08501
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$			0.646084i			0.0722344i
$81$	14.5826			1.62029
$82$			5.03383i			0.555893i
$83$	9.15188			1.00455			0.502274	−	0.864708i	$-0.332497\pi$
$83$	9.15188			1.00455			0.502274	+	0.864708i	$0.332497\pi$
$84$	−3.09557	−	7.58258i	−0.337755	−	0.827327i
$85$			2.41742i			0.262206i
$86$	11.1652			1.20397
$87$	−23.4724			−2.51651
$88$	−1.79129	−	2.79129i	−0.190952	−	0.297552i
$89$		−	9.79796i		−	1.03858i	−0.854598	−	0.519291i	$-0.826196\pi$
$89$		−	9.79796i		−	1.03858i	0.854598	−	0.519291i	$-0.173804\pi$
$90$	4.25290			0.448295
$91$	−7.58258	+	3.09557i	−0.794870	+	0.324504i
$92$	−4.00000			−0.417029
$93$	−3.58258			−0.371496
$94$	5.03383			0.519199
$95$		−	3.58258i		−	0.367565i
$96$	−3.09557			−0.315941
$97$			15.9891i			1.62345i	0.584041	+	0.811724i	$0.301471\pi$
$97$			15.9891i			1.62345i	−0.584041	+	0.811724i	$0.698529\pi$
$98$	4.89898	+	5.00000i	0.494872	+	0.505076i
$99$	−18.3739	+	11.7913i	−1.84664	+	1.18507i
$100$	−4.58258			−0.458258
$101$	−0.511238			−0.0508701			−0.0254351	−	0.999676i	$-0.508097\pi$
$101$	−0.511238			−0.0508701			−0.0254351	+	0.999676i	$0.508097\pi$
$102$	−11.5826			−1.14685
$103$		−	13.5396i		−	1.33410i	−0.745014	−	0.667049i	$-0.767557\pi$
$103$		−	13.5396i		−	1.33410i	0.745014	−	0.667049i	$-0.232443\pi$
$104$			3.09557i			0.303546i
$105$	−4.89898	+	2.00000i	−0.478091	+	0.195180i
$106$		−	2.41742i		−	0.234801i
$107$		−	8.41742i		−	0.813743i	−0.913485	−	0.406872i	$-0.866620\pi$
$107$		−	8.41742i		−	0.813743i	0.913485	−	0.406872i	$-0.133380\pi$
$108$			11.0901i			1.06715i
$109$			1.16515i			0.111601i	0.998442	+	0.0558006i	$0.0177711\pi$
$109$			1.16515i			0.111601i	−0.998442	+	0.0558006i	$0.982229\pi$
$110$	−1.80341	+	1.15732i	−0.171948	+	0.110346i
$111$		−	17.2813i		−	1.64027i
$112$	2.44949	−	1.00000i	0.231455	−	0.0944911i
$113$	−16.7477			−1.57549			−0.787747	−	0.615999i	$-0.788752\pi$
$113$	−16.7477			−1.57549			−0.787747	+	0.615999i	$0.788752\pi$
$114$	17.1652			1.60766
$115$			2.58434i			0.240991i
$116$		−	7.58258i		−	0.704024i
$117$	20.3768			1.88384
$118$	3.09557			0.284971
$119$	9.16515	−	3.74166i	0.840168	−	0.342997i
$120$			2.00000i			0.182574i
$121$	4.58258	−	10.0000i	0.416598	−	0.909091i
$122$		−	9.28672i		−	0.840780i
$123$			15.5826i			1.40503i
$124$		−	1.15732i		−	0.103931i
$125$			6.19115i			0.553753i
$126$	−6.58258	−	16.1240i	−0.586422	−	1.43644i
$127$		−	5.58258i		−	0.495373i	−0.968840	−	0.247687i	$-0.920330\pi$
$127$		−	5.58258i		−	0.495373i	0.968840	−	0.247687i	$-0.0796704\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	34.5625			3.04306
$130$	2.00000			0.175412
$131$	9.42157			0.823166			0.411583	−	0.911372i	$-0.364976\pi$
$131$	9.42157			0.823166			0.411583	+	0.911372i	$0.364976\pi$
$132$	−5.54506	−	8.64064i	−0.482636	−	0.752071i
$133$	−13.5826	+	5.54506i	−1.17776	+	0.480818i
$134$			1.58258i			0.136714i
$135$	7.16515			0.616678
$136$		−	3.74166i		−	0.320844i
$137$	15.1652			1.29565			0.647823	−	0.761791i	$-0.275680\pi$
$137$	15.1652			1.29565			0.647823	+	0.761791i	$0.275680\pi$
$138$	−12.3823			−1.05405
$139$	3.23042			0.274001			0.137000	−	0.990571i	$-0.456254\pi$
$139$	3.23042			0.274001			0.137000	+	0.990571i	$0.456254\pi$
$140$	−0.646084	−	1.58258i	−0.0546040	−	0.133752i
$141$	15.5826			1.31229
$142$			2.00000i			0.167836i
$143$	−8.64064	+	5.54506i	−0.722566	+	0.463701i
$144$	−6.58258			−0.548548
$145$	−4.89898			−0.406838
$146$		−	6.32599i		−	0.523543i
$147$	15.1652	+	15.4779i	1.25080	+	1.27659i
$148$	5.58258			0.458885
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$	−14.1857			−1.15826
$151$			3.58258i			0.291546i	0.989318	+	0.145773i	$0.0465669\pi$
$151$			3.58258i			0.291546i	−0.989318	+	0.145773i	$0.953433\pi$
$152$			5.54506i			0.449764i
$153$	−24.6297			−1.99120
$154$	7.17903	+	5.04594i	0.578503	+	0.406614i
$155$	−0.747727			−0.0600589
$156$			9.58258i			0.767220i
$157$		−	20.5117i		−	1.63701i	−0.574498	−	0.818506i	$-0.694803\pi$
$157$		−	20.5117i		−	1.63701i	0.574498	−	0.818506i	$-0.305197\pi$
$158$	−4.00000			−0.318223
$159$		−	7.48331i		−	0.593465i
$160$	−0.646084			−0.0510774
$161$	9.79796	−	4.00000i	0.772187	−	0.315244i
$162$			14.5826i			1.14572i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−5.03383			−0.393076
$165$	−5.58258	+	3.58258i	−0.434603	+	0.278903i
$166$			9.15188i			0.710323i
$167$	−6.19115			−0.479085			−0.239543	−	0.970886i	$-0.576998\pi$
$167$	−6.19115			−0.479085			−0.239543	+	0.970886i	$0.576998\pi$
$168$	7.58258	−	3.09557i	0.585008	−	0.238829i
$169$	−3.41742			−0.262879
$170$	−2.41742			−0.185408
$171$	36.5008			2.79129
$172$			11.1652i			0.851335i
$173$	−22.9612			−1.74571			−0.872853	−	0.487983i	$-0.837733\pi$
$173$	−22.9612			−1.74571			−0.872853	+	0.487983i	$0.837733\pi$
$174$		−	23.4724i		−	1.77944i
$175$	11.2250	−	4.58258i	0.848528	−	0.346410i
$176$	2.79129	−	1.79129i	0.210401	−	0.135023i
$177$	9.58258			0.720270
$178$	9.79796			0.734388
$179$	−7.16515			−0.535549			−0.267774	−	0.963482i	$-0.586288\pi$
$179$	−7.16515			−0.535549			−0.267774	+	0.963482i	$0.586288\pi$
$180$			4.25290i			0.316992i
$181$		−	16.6352i		−	1.23648i	−0.785988	−	0.618242i	$-0.787845\pi$
$181$		−	16.6352i		−	1.23648i	0.785988	−	0.618242i	$-0.212155\pi$
$182$	−3.09557	−	7.58258i	−0.229459	−	0.562058i
$183$		−	28.7477i		−	2.12509i
$184$		−	4.00000i		−	0.294884i
$185$		−	3.60681i		−	0.265178i
$186$		−	3.58258i		−	0.262687i
$187$	10.4440	−	6.70239i	0.763744	−	0.490127i
$188$			5.03383i			0.367129i
$189$	−11.0901	−	27.1652i	−0.806688	−	1.97597i
$190$	3.58258			0.259907
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		−	3.09557i		−	0.223404i
$193$			20.3303i			1.46341i	0.681623	+	0.731704i	$0.261274\pi$
$193$			20.3303i			1.46341i	−0.681623	+	0.731704i	$0.738726\pi$
$194$	−15.9891			−1.14795
$195$	6.19115			0.443357
$196$	−5.00000	+	4.89898i	−0.357143	+	0.349927i
$197$			18.7477i			1.33572i	0.744287	+	0.667860i	$0.232790\pi$
$197$			18.7477i			1.33572i	−0.744287	+	0.667860i	$0.767210\pi$
$198$	−11.7913	−	18.3739i	−0.837970	−	1.30577i
$199$			24.6297i			1.74596i	0.487759	+	0.872978i	$0.337814\pi$
$199$			24.6297i			1.74596i	−0.487759	+	0.872978i	$0.662186\pi$
$200$		−	4.58258i		−	0.324037i
$201$			4.89898i			0.345547i
$202$		−	0.511238i		−	0.0359706i
$203$	7.58258	+	18.5734i	0.532192	+	1.30360i
$204$		−	11.5826i		−	0.810943i
$205$			3.25227i			0.227149i
$206$	13.5396			0.943350
$207$	−26.3303			−1.83008
$208$	−3.09557			−0.214639
$209$	−15.4779	+	9.93280i	−1.07063	+	0.687066i
$210$	−2.00000	−	4.89898i	−0.138013	−	0.338062i
$211$			10.7477i			0.739904i	0.929051	+	0.369952i	$0.120626\pi$
$211$			10.7477i			0.739904i	−0.929051	+	0.369952i	$0.879374\pi$
$212$	2.41742			0.166029
$213$			6.19115i			0.424210i
$214$	8.41742			0.575403
$215$	7.21362			0.491965
$216$	−11.0901			−0.754588
$217$	1.15732	+	2.83485i	0.0785641	+	0.192442i
$218$	−1.16515			−0.0789140
$219$		−	19.5826i		−	1.32327i
$220$	−1.15732	−	1.80341i	−0.0780266	−	0.121586i
$221$	−11.5826			−0.779128
$222$	17.2813			1.15984
$223$			6.32599i			0.423620i	0.977311	+	0.211810i	$0.0679358\pi$
$223$			6.32599i			0.423620i	−0.977311	+	0.211810i	$0.932064\pi$
$224$	1.00000	+	2.44949i	0.0668153	+	0.163663i
$225$	−30.1652			−2.01101
$226$		−	16.7477i		−	1.11404i
$227$	−11.7362			−0.778960			−0.389480	−	0.921035i	$-0.627345\pi$
$227$	−11.7362			−0.778960			−0.389480	+	0.921035i	$0.627345\pi$
$228$			17.1652i			1.13679i
$229$		−	13.0284i		−	0.860939i	−0.902605	−	0.430470i	$-0.858348\pi$
$229$		−	13.0284i		−	0.860939i	0.902605	−	0.430470i	$-0.141652\pi$
$230$	−2.58434			−0.170406
$231$	22.2232	+	15.6201i	1.46218	+	1.02773i
$232$	7.58258			0.497820
$233$			8.83485i			0.578790i	0.957210	+	0.289395i	$0.0934541\pi$
$233$			8.83485i			0.578790i	−0.957210	+	0.289395i	$0.906546\pi$
$234$			20.3768i			1.33208i
$235$	3.25227			0.212155
$236$			3.09557i			0.201505i
$237$	−12.3823			−0.804316
$238$	3.74166	+	9.16515i	0.242536	+	0.594089i
$239$			17.5826i			1.13732i	0.822572	+	0.568661i	$0.192538\pi$
$239$			17.5826i			1.13732i	−0.822572	+	0.568661i	$0.807462\pi$
$240$	−2.00000			−0.129099
$241$	−25.9219			−1.66978			−0.834889	−	0.550419i	$-0.814468\pi$
$241$	−25.9219			−1.66978			−0.834889	+	0.550419i	$0.814468\pi$
$242$	10.0000	+	4.58258i	0.642824	+	0.294579i
$243$			11.8711i			0.761529i
$244$	9.28672			0.594521
$245$	3.16515	+	3.23042i	0.202214	+	0.206384i
$246$	−15.5826			−0.993509
$247$	17.1652			1.09219
$248$	1.15732			0.0734900
$249$			28.3303i			1.79536i
$250$	−6.19115			−0.391563
$251$			2.07310i			0.130853i	0.997857	+	0.0654264i	$0.0208407\pi$
$251$			2.07310i			0.130853i	−0.997857	+	0.0654264i	$0.979159\pi$
$252$	16.1240	−	6.58258i	1.01571	−	0.414663i
$253$	11.1652	−	7.16515i	0.701947	−	0.450469i
$254$	5.58258			0.350282
$255$	−7.48331			−0.468623
$256$	1.00000			0.0625000
$257$			4.89898i			0.305590i	0.988258	+	0.152795i	$0.0488274\pi$
$257$			4.89898i			0.305590i	−0.988258	+	0.152795i	$0.951173\pi$
$258$			34.5625i			2.15177i
$259$	−13.6745	+	5.58258i	−0.849690	+	0.346884i
$260$			2.00000i			0.124035i
$261$		−	49.9129i		−	3.08953i
$262$			9.42157i			0.582066i
$263$		−	28.3303i		−	1.74692i	−0.486895	−	0.873461i	$-0.661870\pi$
$263$		−	28.3303i		−	1.74692i	0.486895	−	0.873461i	$-0.338130\pi$
$264$	8.64064	−	5.54506i	0.531794	−	0.341275i
$265$		−	1.56186i		−	0.0959442i
$266$	−5.54506	−	13.5826i	−0.339990	−	0.832801i
$267$	30.3303			1.85618
$268$	−1.58258			−0.0966712
$269$			20.2420i			1.23418i	0.786894	+	0.617088i	$0.211688\pi$
$269$			20.2420i			1.23418i	−0.786894	+	0.617088i	$0.788312\pi$
$270$			7.16515i			0.436057i
$271$	−4.89898			−0.297592			−0.148796	−	0.988868i	$-0.547540\pi$
$271$	−4.89898			−0.297592			−0.148796	+	0.988868i	$0.547540\pi$
$272$	3.74166			0.226871
$273$	−9.58258	−	23.4724i	−0.579964	−	1.42062i
$274$			15.1652i			0.916160i
$275$	12.7913	−	8.20871i	0.771344	−	0.495004i
$276$		−	12.3823i		−	0.745327i
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$			3.23042i			0.193748i
$279$		−	7.61816i		−	0.456087i
$280$	1.58258	−	0.646084i	0.0945770	−	0.0386109i
$281$			7.16515i			0.427437i	0.976895	+	0.213719i	$0.0685575\pi$
$281$			7.16515i			0.427437i	−0.976895	+	0.213719i	$0.931442\pi$
$282$			15.5826i			0.927929i
$283$	15.6127			0.928079			0.464040	−	0.885814i	$-0.346399\pi$
$283$	15.6127			0.928079			0.464040	+	0.885814i	$0.346399\pi$
$284$	−2.00000			−0.118678
$285$	11.0901			0.656922
$286$	−5.54506	−	8.64064i	−0.327886	−	0.510932i
$287$	12.3303	−	5.03383i	0.727835	−	0.297137i
$288$		−	6.58258i		−	0.387882i
$289$	−3.00000			−0.176471
$290$		−	4.89898i		−	0.287678i
$291$	−49.4955			−2.90147
$292$	6.32599			0.370201
$293$	21.3993			1.25016			0.625081	−	0.780560i	$-0.285066\pi$
$293$	21.3993			1.25016			0.625081	+	0.780560i	$0.285066\pi$
$294$	−15.4779	+	15.1652i	−0.902688	+	0.884450i
$295$	2.00000			0.116445
$296$			5.58258i			0.324481i
$297$	−19.8656	−	30.9557i	−1.15272	−	1.79623i
$298$	−14.0000			−0.810998
$299$	−12.3823			−0.716087
$300$		−	14.1857i		−	0.819012i
$301$	−11.1652	−	27.3489i	−0.643549	−	1.57637i
$302$	−3.58258			−0.206154
$303$		−	1.58258i		−	0.0909166i
$304$	−5.54506			−0.318031
$305$		−	6.00000i		−	0.343559i
$306$		−	24.6297i		−	1.40799i
$307$	8.12940			0.463969			0.231985	−	0.972719i	$-0.425478\pi$
$307$	8.12940			0.463969			0.231985	+	0.972719i	$0.425478\pi$
$308$	−5.04594	+	7.17903i	−0.287519	+	0.409063i
$309$	41.9129			2.38434
$310$		−	0.747727i		−	0.0424680i
$311$			9.93280i			0.563238i	0.959526	+	0.281619i	$0.0908714\pi$
$311$			9.93280i			0.563238i	−0.959526	+	0.281619i	$0.909129\pi$
$312$	−9.58258			−0.542507
$313$			1.02248i			0.0577938i	0.999582	+	0.0288969i	$0.00919945\pi$
$313$			1.02248i			0.0577938i	−0.999582	+	0.0288969i	$0.990801\pi$
$314$	20.5117			1.15754
$315$	−4.25290	−	10.4174i	−0.239624	−	0.586955i
$316$		−	4.00000i		−	0.225018i
$317$	−9.16515			−0.514766			−0.257383	−	0.966309i	$-0.582860\pi$
$317$	−9.16515			−0.514766			−0.257383	+	0.966309i	$0.582860\pi$
$318$	7.48331			0.419643
$319$	13.5826	+	21.1652i	0.760478	+	1.18502i
$320$		−	0.646084i		−	0.0361172i
$321$	26.0568			1.45435
$322$	4.00000	+	9.79796i	0.222911	+	0.546019i
$323$	−20.7477			−1.15443
$324$	−14.5826			−0.810143
$325$	−14.1857			−0.786881
$326$			4.00000i			0.221540i
$327$	−3.60681			−0.199457
$328$		−	5.03383i		−	0.277946i
$329$	−5.03383	−	12.3303i	−0.277524	−	0.679792i
$330$	−3.58258	−	5.58258i	−0.197214	−	0.307311i
$331$	−14.4174			−0.792453			−0.396227	−	0.918153i	$-0.629681\pi$
$331$	−14.4174			−0.792453			−0.396227	+	0.918153i	$0.629681\pi$
$332$	−9.15188			−0.502274
$333$	36.7477			2.01376
$334$		−	6.19115i		−	0.338764i
$335$			1.02248i			0.0558639i
$336$	3.09557	+	7.58258i	0.168877	+	0.413663i
$337$		−	29.1652i		−	1.58873i	−0.607443	−	0.794364i	$-0.707805\pi$
$337$		−	29.1652i		−	1.58873i	0.607443	−	0.794364i	$-0.292195\pi$
$338$		−	3.41742i		−	0.185883i
$339$		−	51.8438i		−	2.81577i
$340$		−	2.41742i		−	0.131103i
$341$	2.07310	+	3.23042i	0.112264	+	0.174937i
$342$			36.5008i			1.97374i
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$	−11.1652			−0.601985
$345$	−8.00000			−0.430706
$346$		−	22.9612i		−	1.23440i
$347$			0.834849i			0.0448170i	0.999749	+	0.0224085i	$0.00713345\pi$
$347$			0.834849i			0.0448170i	−0.999749	+	0.0224085i	$0.992867\pi$
$348$	23.4724			1.25825
$349$	−2.07310			−0.110970			−0.0554852	−	0.998460i	$-0.517671\pi$
$349$	−2.07310			−0.110970			−0.0554852	+	0.998460i	$0.517671\pi$
$350$	4.58258	+	11.2250i	0.244949	+	0.600000i
$351$			34.3303i			1.83242i
$352$	1.79129	+	2.79129i	0.0954760	+	0.148776i
$353$			7.48331i			0.398297i	0.979969	+	0.199148i	$0.0638176\pi$
$353$			7.48331i			0.398297i	−0.979969	+	0.199148i	$0.936182\pi$
$354$			9.58258i			0.509308i
$355$			1.29217i			0.0685811i
$356$			9.79796i			0.519291i
$357$	11.5826	+	28.3714i	0.613015	+	1.50157i
$358$		−	7.16515i		−	0.378690i
$359$			0.417424i			0.0220308i	0.999939	+	0.0110154i	$0.00350638\pi$
$359$			0.417424i			0.0220308i	−0.999939	+	0.0110154i	$0.996494\pi$
$360$	−4.25290			−0.224147
$361$	11.7477			0.618301
$362$	16.6352			0.874326
$363$	30.9557	+	14.1857i	1.62475	+	0.744556i
$364$	7.58258	−	3.09557i	0.397435	−	0.162252i
$365$		−	4.08712i		−	0.213930i
$366$	28.7477			1.50267
$367$			1.42701i			0.0744895i	0.999306	+	0.0372447i	$0.0118581\pi$
$367$			1.42701i			0.0744895i	−0.999306	+	0.0372447i	$0.988142\pi$
$368$	4.00000			0.208514
$369$	−33.1355			−1.72497
$370$	3.60681			0.187509
$371$	−5.92146	+	2.41742i	−0.307427	+	0.125506i
$372$	3.58258			0.185748
$373$		−	0.417424i		−	0.0216134i	−0.999942	−	0.0108067i	$-0.996560\pi$
$373$		−	0.417424i		−	0.0216134i	0.999942	−	0.0108067i	$-0.00343995\pi$
$374$	6.70239	+	10.4440i	0.346572	+	0.540049i
$375$	−19.1652			−0.989684
$376$	−5.03383			−0.259600
$377$		−	23.4724i		−	1.20889i
$378$	27.1652	−	11.0901i	1.39722	−	0.570415i
$379$	14.3303			0.736098			0.368049	−	0.929806i	$-0.380026\pi$
$379$	14.3303			0.736098			0.368049	+	0.929806i	$0.380026\pi$
$380$			3.58258i			0.183782i
$381$	17.2813			0.885346
$382$		−	18.0000i		−	0.920960i
$383$		−	4.76413i		−	0.243436i	−0.992565	−	0.121718i	$-0.961160\pi$
$383$		−	4.76413i		−	0.243436i	0.992565	−	0.121718i	$-0.0388403\pi$
$384$	3.09557			0.157970
$385$	4.63825	+	3.26010i	0.236387	+	0.166150i
$386$	−20.3303			−1.03479
$387$			73.4955i			3.73598i
$388$		−	15.9891i		−	0.811724i
$389$	10.0000			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$390$			6.19115i			0.313501i
$391$	14.9666			0.756895
$392$	−4.89898	−	5.00000i	−0.247436	−	0.252538i
$393$			29.1652i			1.47119i
$394$	−18.7477			−0.944497
$395$	−2.58434			−0.130032
$396$	18.3739	−	11.7913i	0.923321	−	0.592535i
$397$			23.8488i			1.19694i	0.801146	+	0.598469i	$0.204224\pi$
$397$			23.8488i			1.19694i	−0.801146	+	0.598469i	$0.795776\pi$
$398$	−24.6297			−1.23458
$399$	−17.1652	−	42.0459i	−0.859332	−	2.10493i
$400$	4.58258			0.229129
$401$	−1.58258			−0.0790301			−0.0395150	−	0.999219i	$-0.512581\pi$
$401$	−1.58258			−0.0790301			−0.0395150	+	0.999219i	$0.512581\pi$
$402$	−4.89898			−0.244339
$403$		−	3.58258i		−	0.178461i
$404$	0.511238			0.0254351
$405$			9.42157i			0.468161i
$406$	−18.5734	+	7.58258i	−0.921784	+	0.376317i
$407$	−15.5826	+	10.0000i	−0.772400	+	0.495682i
$408$	11.5826			0.573423
$409$	9.93280			0.491146			0.245573	−	0.969378i	$-0.421024\pi$
$409$	9.93280			0.491146			0.245573	+	0.969378i	$0.421024\pi$
$410$	−3.25227			−0.160618
$411$			46.9448i			2.31562i
$412$			13.5396i			0.667049i
$413$	−3.09557	−	7.58258i	−0.152323	−	0.373114i
$414$		−	26.3303i		−	1.29406i
$415$			5.91288i			0.290252i
$416$		−	3.09557i		−	0.151773i
$417$			10.0000i			0.489702i
$418$	−9.93280	−	15.4779i	−0.485829	−	0.757047i
$419$			5.67991i			0.277482i	0.990329	+	0.138741i	$0.0443055\pi$
$419$			5.67991i			0.277482i	−0.990329	+	0.138741i	$0.955694\pi$
$420$	4.89898	−	2.00000i	0.239046	−	0.0975900i
$421$	−1.58258			−0.0771300			−0.0385650	−	0.999256i	$-0.512279\pi$
$421$	−1.58258			−0.0771300			−0.0385650	+	0.999256i	$0.512279\pi$
$422$	−10.7477			−0.523191
$423$			33.1355i			1.61110i
$424$			2.41742i			0.117401i
$425$	17.1464			0.831724
$426$	−6.19115			−0.299962
$427$	−22.7477	+	9.28672i	−1.10084	+	0.449416i
$428$			8.41742i			0.406872i
$429$	−17.1652	−	26.7477i	−0.828741	−	1.29139i
$430$			7.21362i			0.347872i
$431$		−	17.9129i		−	0.862833i	−0.902153	−	0.431416i	$-0.858014\pi$
$431$		−	17.9129i		−	0.862833i	0.902153	−	0.431416i	$-0.141986\pi$
$432$		−	11.0901i		−	0.533574i
$433$		−	28.1017i		−	1.35048i	−0.737597	−	0.675241i	$-0.764040\pi$
$433$		−	28.1017i		−	1.35048i	0.737597	−	0.675241i	$-0.235960\pi$
$434$	−2.83485	+	1.15732i	−0.136077	+	0.0555532i
$435$		−	15.1652i		−	0.727113i
$436$		−	1.16515i		−	0.0558006i
$437$	−22.1803			−1.06103
$438$	19.5826			0.935692
$439$	2.31464			0.110472			0.0552360	−	0.998473i	$-0.482409\pi$
$439$	2.31464			0.110472			0.0552360	+	0.998473i	$0.482409\pi$
$440$	1.80341	−	1.15732i	0.0859740	−	0.0551732i
$441$	−32.9129	+	32.2479i	−1.56728	+	1.53561i
$442$		−	11.5826i		−	0.550927i
$443$	−3.16515			−0.150381			−0.0751904	−	0.997169i	$-0.523956\pi$
$443$	−3.16515			−0.150381			−0.0751904	+	0.997169i	$0.523956\pi$
$444$			17.2813i			0.820133i
$445$	6.33030			0.300085
$446$	−6.32599			−0.299544
$447$	−43.3380			−2.04982
$448$	−2.44949	+	1.00000i	−0.115728	+	0.0472456i
$449$	12.8348			0.605714			0.302857	−	0.953036i	$-0.402060\pi$
$449$	12.8348			0.605714			0.302857	+	0.953036i	$0.402060\pi$
$450$		−	30.1652i		−	1.42200i
$451$	14.0509	−	9.01703i	0.661629	−	0.424595i
$452$	16.7477			0.787747
$453$	−11.0901			−0.521060
$454$		−	11.7362i		−	0.550808i
$455$	−2.00000	−	4.89898i	−0.0937614	−	0.229668i
$456$	−17.1652			−0.803832
$457$		−	14.8348i		−	0.693945i	−0.937875	−	0.346972i	$-0.887210\pi$
$457$		−	14.8348i		−	0.693945i	0.937875	−	0.346972i	$-0.112790\pi$
$458$	13.0284			0.608776
$459$		−	41.4955i		−	1.93684i
$460$		−	2.58434i		−	0.120495i
$461$	26.2983			1.22483			0.612417	−	0.790535i	$-0.290197\pi$
$461$	26.2983			1.22483			0.612417	+	0.790535i	$0.290197\pi$
$462$	−15.6201	+	22.2232i	−0.726712	+	1.03392i
$463$	−13.1652			−0.611836			−0.305918	−	0.952058i	$-0.598963\pi$
$463$	−13.1652			−0.611836			−0.305918	+	0.952058i	$0.598963\pi$
$464$			7.58258i			0.352012i
$465$		−	2.31464i		−	0.107339i
$466$	−8.83485			−0.409266
$467$			0.511238i			0.0236573i	0.999930	+	0.0118286i	$0.00376526\pi$
$467$			0.511238i			0.0236573i	−0.999930	+	0.0118286i	$0.996235\pi$
$468$	−20.3768			−0.941920
$469$	3.87650	−	1.58258i	0.179000	−	0.0730766i
$470$			3.25227i			0.150016i
$471$	63.4955			2.92572
$472$	−3.09557			−0.142485
$473$	−20.0000	−	31.1652i	−0.919601	−	1.43298i
$474$		−	12.3823i		−	0.568738i
$475$	−25.4107			−1.16592
$476$	−9.16515	+	3.74166i	−0.420084	+	0.171499i
$477$	15.9129			0.728601
$478$	−17.5826			−0.804208
$479$	−6.46084			−0.295203			−0.147602	−	0.989047i	$-0.547155\pi$
$479$	−6.46084			−0.295203			−0.147602	+	0.989047i	$0.547155\pi$
$480$		−	2.00000i		−	0.0912871i
$481$	17.2813			0.787958
$482$		−	25.9219i		−	1.18071i
$483$	12.3823	+	30.3303i	0.563414	+	1.38008i
$484$	−4.58258	+	10.0000i	−0.208299	+	0.454545i
$485$	−10.3303			−0.469075
$486$	−11.8711			−0.538482
$487$	−33.4955			−1.51782			−0.758912	−	0.651193i	$-0.774269\pi$
$487$	−33.4955			−1.51782			−0.758912	+	0.651193i	$0.774269\pi$
$488$			9.28672i			0.420390i
$489$			12.3823i			0.559947i
$490$	−3.23042	+	3.16515i	−0.145935	+	0.142987i
$491$			21.4955i			0.970076i	0.874493	+	0.485038i	$0.161194\pi$
$491$			21.4955i			0.970076i	−0.874493	+	0.485038i	$0.838806\pi$
$492$		−	15.5826i		−	0.702517i
$493$			28.3714i			1.27778i
$494$			17.1652i			0.772297i
$495$	−7.61816	−	11.8711i	−0.342411	−	0.533564i
$496$			1.15732i			0.0519653i
$497$	4.89898	−	2.00000i	0.219749	−	0.0897123i
$498$	−28.3303			−1.26951
$499$	27.9129			1.24955			0.624776	−	0.780804i	$-0.285190\pi$
$499$	27.9129			1.24955			0.624776	+	0.780804i	$0.285190\pi$
$500$		−	6.19115i		−	0.276877i
$501$		−	19.1652i		−	0.856236i
$502$	−2.07310			−0.0925268
$503$	−31.9782			−1.42584			−0.712919	−	0.701246i	$-0.752627\pi$
$503$	−31.9782			−1.42584			−0.712919	+	0.701246i	$0.752627\pi$
$504$	6.58258	+	16.1240i	0.293211	+	0.718218i
$505$		−	0.330303i		−	0.0146983i
$506$	7.16515	+	11.1652i	0.318530	+	0.496352i
$507$		−	10.5789i		−	0.469825i
$508$			5.58258i			0.247687i
$509$			17.9274i			0.794616i	0.917685	+	0.397308i	$0.130056\pi$
$509$			17.9274i			0.794616i	−0.917685	+	0.397308i	$0.869944\pi$
$510$		−	7.48331i		−	0.331367i
$511$	−15.4955	+	6.32599i	−0.685479	+	0.279845i
$512$			1.00000i			0.0441942i
$513$			61.4955i			2.71509i
$514$	−4.89898			−0.216085
$515$	8.74773			0.385471
$516$	−34.5625			−1.52153
$517$	−9.01703	−	14.0509i	−0.396569	−	0.617956i
$518$	−5.58258	−	13.6745i	−0.245284	−	0.600821i
$519$		−	71.0780i		−	3.11998i
$520$	−2.00000			−0.0877058
$521$			35.5850i			1.55901i	0.626397	+	0.779504i	$0.284529\pi$
$521$			35.5850i			1.55901i	−0.626397	+	0.779504i	$0.715471\pi$
$522$	49.9129			2.18463
$523$	26.7028			1.16763			0.583817	−	0.811885i	$-0.301559\pi$
$523$	26.7028			1.16763			0.583817	+	0.811885i	$0.301559\pi$
$524$	−9.42157			−0.411583
$525$	14.1857	+	34.7477i	0.619115	+	1.51652i
$526$	28.3303			1.23526
$527$			4.33030i			0.188631i
$528$	5.54506	+	8.64064i	0.241318	+	0.376035i
$529$	−7.00000			−0.304348
$530$	1.56186			0.0678428
$531$			20.3768i			0.884280i
$532$	13.5826	−	5.54506i	0.588879	−	0.240409i
$533$	−15.5826			−0.674956
$534$			30.3303i			1.31252i
$535$	5.43836			0.235121
$536$		−	1.58258i		−	0.0683569i
$537$		−	22.1803i		−	0.957149i
$538$	−20.2420			−0.872695
$539$	5.18096	−	22.6309i	0.223160	−	0.974782i
$540$	−7.16515			−0.308339
$541$			9.25227i			0.397786i	0.980021	+	0.198893i	$0.0637347\pi$
$541$			9.25227i			0.397786i	−0.980021	+	0.198893i	$0.936265\pi$
$542$		−	4.89898i		−	0.210429i
$543$	51.4955			2.20988
$544$			3.74166i			0.160422i
$545$	−0.752785			−0.0322458
$546$	23.4724	−	9.58258i	1.00453	−	0.410096i
$547$		−	2.74773i		−	0.117484i	−0.998273	−	0.0587422i	$-0.981291\pi$
$547$		−	2.74773i		−	0.117484i	0.998273	−	0.0587422i	$-0.0187090\pi$
$548$	−15.1652			−0.647823
$549$	61.1305			2.60899
$550$	8.20871	+	12.7913i	0.350021	+	0.545422i
$551$		−	42.0459i		−	1.79121i
$552$	12.3823			0.527025
$553$	4.00000	+	9.79796i	0.170097	+	0.416652i
$554$	2.00000			0.0849719
$555$	11.1652			0.473934
$556$	−3.23042			−0.137000
$557$		−	9.91288i		−	0.420022i	−0.977699	−	0.210011i	$-0.932650\pi$
$557$		−	9.91288i		−	0.420022i	0.977699	−	0.210011i	$-0.0673500\pi$
$558$	7.61816			0.322502
$559$			34.5625i			1.46184i
$560$	0.646084	+	1.58258i	0.0273020	+	0.0668760i
$561$	20.7477	+	32.3303i	0.875970	+	1.36499i
$562$	−7.16515			−0.302244
$563$	42.4223			1.78788			0.893942	−	0.448182i	$-0.147928\pi$
$563$	42.4223			1.78788			0.893942	+	0.448182i	$0.147928\pi$
$564$	−15.5826			−0.656145
$565$		−	10.8204i		−	0.455219i
$566$			15.6127i			0.656251i
$567$	35.7199	−	14.5826i	1.50009	−	0.612411i
$568$		−	2.00000i		−	0.0839181i
$569$			15.4955i			0.649603i	0.945782	+	0.324802i	$0.105298\pi$
$569$			15.4955i			0.649603i	−0.945782	+	0.324802i	$0.894702\pi$
$570$			11.0901i			0.464514i
$571$		−	3.58258i		−	0.149926i	−0.997186	−	0.0749631i	$-0.976116\pi$
$571$		−	3.58258i		−	0.149926i	0.997186	−	0.0749631i	$-0.0238839\pi$
$572$	8.64064	−	5.54506i	0.361283	−	0.231851i
$573$		−	55.7203i		−	2.32775i
$574$	5.03383	+	12.3303i	0.210108	+	0.514657i
$575$	18.3303			0.764426
$576$	6.58258			0.274274
$577$			0.269691i			0.0112274i	0.999984	+	0.00561369i	$0.00178690\pi$
$577$			0.269691i			0.0112274i	−0.999984	+	0.00561369i	$0.998213\pi$
$578$		−	3.00000i		−	0.124784i
$579$	−62.9339			−2.61545
$580$	4.89898			0.203419
$581$	22.4174	−	9.15188i	0.930031	−	0.379684i
$582$		−	49.4955i		−	2.05165i
$583$	−6.74773	+	4.33030i	−0.279462	+	0.179343i
$584$			6.32599i			0.261771i
$585$			13.1652i			0.544312i
$586$			21.3993i			0.883998i
$587$		−	17.0397i		−	0.703305i	−0.936131	−	0.351652i	$-0.885620\pi$
$587$		−	17.0397i		−	0.703305i	0.936131	−	0.351652i	$-0.114380\pi$
$588$	−15.1652	−	15.4779i	−0.625400	−	0.638297i
$589$		−	6.41742i		−	0.264425i
$590$			2.00000i			0.0823387i
$591$	−58.0350			−2.38724
$592$	−5.58258			−0.229442
$593$	0.134846			0.00553744			0.00276872	−	0.999996i	$-0.499119\pi$
$593$	0.134846			0.00553744			0.00276872	+	0.999996i	$0.499119\pi$
$594$	30.9557	−	19.8656i	1.27013	−	0.815096i
$595$	2.41742	+	5.92146i	0.0991047	+	0.242756i
$596$		−	14.0000i		−	0.573462i
$597$	−76.2432			−3.12043
$598$		−	12.3823i		−	0.506350i
$599$	−2.83485			−0.115829			−0.0579144	−	0.998322i	$-0.518445\pi$
$599$	−2.83485			−0.115829			−0.0579144	+	0.998322i	$0.518445\pi$
$600$	14.1857			0.579129
$601$	−1.42701			−0.0582091			−0.0291045	−	0.999576i	$-0.509266\pi$
$601$	−1.42701			−0.0582091			−0.0291045	+	0.999576i	$0.509266\pi$
$602$	27.3489	−	11.1652i	1.11466	−	0.455058i
$603$	−10.4174			−0.424230
$604$		−	3.58258i		−	0.145773i
$605$	6.46084	+	2.96073i	0.262670	+	0.120371i
$606$	1.58258			0.0642877
$607$	46.9448			1.90543			0.952716	−	0.303862i	$-0.0982761\pi$
$607$	46.9448			1.90543			0.952716	+	0.303862i	$0.0982761\pi$
$608$		−	5.54506i		−	0.224882i
$609$	−57.4955	+	23.4724i	−2.32983	+	0.951150i
$610$	6.00000			0.242933
$611$			15.5826i			0.630404i
$612$	24.6297			0.995598
$613$			13.9129i			0.561936i	0.959717	+	0.280968i	$0.0906555\pi$
$613$			13.9129i			0.561936i	−0.959717	+	0.280968i	$0.909345\pi$
$614$			8.12940i			0.328076i
$615$	−10.0677			−0.405967
$616$	−7.17903	−	5.04594i	−0.289251	−	0.203307i
$617$	25.9129			1.04321			0.521607	−	0.853186i	$-0.325333\pi$
$617$	25.9129			1.04321			0.521607	+	0.853186i	$0.325333\pi$
$618$			41.9129i			1.68598i
$619$		−	0.780929i		−	0.0313882i	−0.999877	−	0.0156941i	$-0.995004\pi$
$619$		−	0.780929i		−	0.0313882i	0.999877	−	0.0156941i	$-0.00499579\pi$
$620$	0.747727			0.0300294
$621$		−	44.3605i		−	1.78013i
$622$	−9.93280			−0.398269
$623$	−9.79796	−	24.0000i	−0.392547	−	0.961540i
$624$		−	9.58258i		−	0.383610i
$625$	18.9129			0.756515
$626$	−1.02248			−0.0408664
$627$	−30.7477	−	47.9129i	−1.22795	−	1.91346i
$628$			20.5117i			0.818506i
$629$	−20.8881			−0.832863
$630$	10.4174	−	4.25290i	0.415040	−	0.169439i
$631$	−5.16515			−0.205621			−0.102811	−	0.994701i	$-0.532784\pi$
$631$	−5.16515			−0.205621			−0.102811	+	0.994701i	$0.532784\pi$
$632$	4.00000			0.159111
$633$	−33.2704			−1.32238
$634$		−	9.16515i		−	0.363995i
$635$	3.60681			0.143132
$636$			7.48331i			0.296733i
$637$	−15.4779	+	15.1652i	−0.613255	+	0.600865i
$638$	−21.1652	+	13.5826i	−0.837936	+	0.537739i
$639$	−13.1652			−0.520805
$640$	0.646084			0.0255387
$641$	29.9129			1.18149			0.590744	−	0.806859i	$-0.298834\pi$
$641$	29.9129			1.18149			0.590744	+	0.806859i	$0.298834\pi$
$642$			26.0568i			1.02838i
$643$		−	16.7700i		−	0.661346i	−0.943745	−	0.330673i	$-0.892724\pi$
$643$		−	16.7700i		−	0.661346i	0.943745	−	0.330673i	$-0.107276\pi$
$644$	−9.79796	+	4.00000i	−0.386094	+	0.157622i
$645$			22.3303i			0.879255i
$646$		−	20.7477i		−	0.816308i
$647$		−	44.7650i		−	1.75990i	−0.475071	−	0.879948i	$-0.657577\pi$
$647$		−	44.7650i		−	1.75990i	0.475071	−	0.879948i	$-0.342423\pi$
$648$		−	14.5826i		−	0.572858i
$649$	−5.54506	−	8.64064i	−0.217663	−	0.339175i
$650$		−	14.1857i		−	0.556409i
$651$	−8.77548	+	3.58258i	−0.343938	+	0.140412i
$652$	−4.00000			−0.156652
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		−	3.60681i		−	0.141038i
$655$			6.08712i			0.237844i
$656$	5.03383			0.196538
$657$	41.6413			1.62458
$658$	12.3303	−	5.03383i	0.480685	−	0.196239i
$659$		−	30.3303i		−	1.18150i	−0.806854	−	0.590750i	$-0.798832\pi$
$659$		−	30.3303i		−	1.18150i	0.806854	−	0.590750i	$-0.201168\pi$
$660$	5.58258	−	3.58258i	0.217301	−	0.139452i
$661$			25.4107i			0.988361i	0.869359	+	0.494180i	$0.164532\pi$
$661$			25.4107i			0.988361i	−0.869359	+	0.494180i	$0.835468\pi$
$662$		−	14.4174i		−	0.560349i
$663$		−	35.8547i		−	1.39248i
$664$		−	9.15188i		−	0.355162i
$665$	−3.58258	−	8.77548i	−0.138926	−	0.340299i
$666$			36.7477i			1.42395i
$667$			30.3303i			1.17439i
$668$	6.19115			0.239543
$669$	−19.5826			−0.757106
$670$	−1.02248			−0.0395017
$671$	−25.9219	+	16.6352i	−1.00070	+	0.642194i
$672$	−7.58258	+	3.09557i	−0.292504	+	0.119414i
$673$		−	18.3303i		−	0.706581i	−0.935514	−	0.353291i	$-0.885063\pi$
$673$		−	18.3303i		−	0.706581i	0.935514	−	0.353291i	$-0.114937\pi$
$674$	29.1652			1.12340
$675$		−	50.8213i		−	1.95611i
$676$	3.41742			0.131439
$677$	31.4670			1.20937			0.604687	−	0.796463i	$-0.293298\pi$
$677$	31.4670			1.20937			0.604687	+	0.796463i	$0.293298\pi$
$678$	51.8438			1.99105
$679$	15.9891	+	39.1652i	0.613606	+	1.50302i
$680$	2.41742			0.0927040
$681$		−	36.3303i		−	1.39218i
$682$	−3.23042	+	2.07310i	−0.123699	+	0.0793830i
$683$	45.4955			1.74084			0.870418	−	0.492314i	$-0.163849\pi$
$683$	45.4955			1.74084			0.870418	+	0.492314i	$0.163849\pi$
$684$	−36.5008			−1.39564
$685$			9.79796i			0.374361i
$686$	17.0000	+	7.34847i	0.649063	+	0.280566i
$687$	40.3303			1.53870
$688$		−	11.1652i		−	0.425667i
$689$	7.48331			0.285092
$690$		−	8.00000i		−	0.304555i
$691$			37.6581i			1.43258i	0.697801	+	0.716291i	$0.254162\pi$
$691$			37.6581i			1.43258i	−0.697801	+	0.716291i	$0.745838\pi$
$692$	22.9612			0.872853
$693$	−33.2153	+	47.2565i	−1.26175	+	1.79513i
$694$	−0.834849			−0.0316904
$695$			2.08712i			0.0791690i
$696$			23.4724i			0.889720i
$697$	18.8348			0.713421
$698$		−	2.07310i		−	0.0784679i
$699$	−27.3489			−1.03443
$700$	−11.2250	+	4.58258i	−0.424264	+	0.173205i
$701$			24.3303i			0.918943i	0.888193	+	0.459471i	$0.151961\pi$
$701$			24.3303i			0.918943i	−0.888193	+	0.459471i	$0.848039\pi$
$702$	−34.3303			−1.29571
$703$	30.9557			1.16752
$704$	−2.79129	+	1.79129i	−0.105201	+	0.0675117i
$705$			10.0677i			0.379170i
$706$	−7.48331			−0.281638
$707$	−1.25227	+	0.511238i	−0.0470966	+	0.0192271i
$708$	−9.58258			−0.360135
$709$	15.6697			0.588488			0.294244	−	0.955730i	$-0.404932\pi$
$709$	15.6697			0.588488			0.294244	+	0.955730i	$0.404932\pi$
$710$	−1.29217			−0.0484942
$711$		−	26.3303i		−	0.987464i
$712$	−9.79796			−0.367194
$713$			4.62929i			0.173368i
$714$	−28.3714	+	11.5826i	−1.06177	+	0.433467i
$715$	−3.58258	−	5.58258i	−0.133981	−	0.208776i
$716$	7.16515			0.267774
$717$	−54.4282			−2.03266
$718$	−0.417424			−0.0155781
$719$			15.8543i			0.591264i	0.955302	+	0.295632i	$0.0955302\pi$
$719$			15.8543i			0.591264i	−0.955302	+	0.295632i	$0.904470\pi$
$720$		−	4.25290i		−	0.158496i
$721$	−13.5396	−	33.1652i	−0.504242	−	1.23513i
$722$			11.7477i			0.437205i
$723$		−	80.2432i		−	2.98428i
$724$			16.6352i			0.618242i
$725$			34.7477i			1.29050i
$726$	−14.1857	+	30.9557i	−0.526481	+	1.14888i
$727$			52.2484i			1.93778i	0.247483	+	0.968892i	$0.420396\pi$
$727$			52.2484i			1.93778i	−0.247483	+	0.968892i	$0.579604\pi$
$728$	3.09557	+	7.58258i	0.114730	+	0.281029i
$729$	7.00000			0.259259
$730$	4.08712			0.151271
$731$		−	41.7762i		−	1.54515i
$732$			28.7477i			1.06255i
$733$	−22.9612			−0.848091			−0.424045	−	0.905641i	$-0.639390\pi$
$733$	−22.9612			−0.848091			−0.424045	+	0.905641i	$0.639390\pi$
$734$	−1.42701			−0.0526720
$735$	−10.0000	+	9.79796i	−0.368856	+	0.361403i
$736$			4.00000i			0.147442i
$737$	4.41742	−	2.83485i	0.162718	−	0.104423i
$738$		−	33.1355i		−	1.21974i
$739$			7.58258i			0.278930i	0.990227	+	0.139465i	$0.0445382\pi$
$739$			7.58258i			0.278930i	−0.990227	+	0.139465i	$0.955462\pi$
$740$			3.60681i			0.132589i
$741$			53.1360i			1.95200i
$742$	−2.41742	−	5.92146i	−0.0887464	−	0.217383i
$743$			43.9129i			1.61101i	0.592591	+	0.805504i	$0.298105\pi$
$743$			43.9129i			1.61101i	−0.592591	+	0.805504i	$0.701895\pi$
$744$			3.58258i			0.131344i
$745$	−9.04517			−0.331390
$746$	0.417424			0.0152830
$747$	−60.2429			−2.20417
$748$	−10.4440	+	6.70239i	−0.381872	+	0.245063i
$749$	−8.41742	−	20.6184i	−0.307566	−	0.753380i
$750$		−	19.1652i		−	0.699812i
$751$	13.4955			0.492456			0.246228	−	0.969212i	$-0.420809\pi$
$751$	13.4955			0.492456			0.246228	+	0.969212i	$0.420809\pi$
$752$		−	5.03383i		−	0.183565i
$753$	−6.41742			−0.233864
$754$	23.4724			0.854815
$755$	−2.31464			−0.0842385
$756$	11.0901	+	27.1652i	0.403344	+	0.987987i
$757$	−49.1652			−1.78694			−0.893469	−	0.449125i	$-0.851736\pi$
$757$	−49.1652			−1.78694			−0.893469	+	0.449125i	$0.851736\pi$
$758$			14.3303i			0.520500i
$759$	22.1803	+	34.5625i	0.805092	+	1.25454i
$760$	−3.58258			−0.129954
$761$	20.7532			0.752304			0.376152	−	0.926558i	$-0.377247\pi$
$761$	20.7532			0.752304			0.376152	+	0.926558i	$0.377247\pi$
$762$			17.2813i			0.626034i
$763$	1.16515	+	2.85403i	0.0421813	+	0.103323i
$764$	18.0000			0.651217
$765$		−	15.9129i		−	0.575331i
$766$	4.76413			0.172135
$767$			9.58258i			0.346007i
$768$			3.09557i			0.111702i
$769$	29.7984			1.07456			0.537279	−	0.843404i	$-0.319452\pi$
$769$	29.7984			1.07456			0.537279	+	0.843404i	$0.319452\pi$
$770$	−3.26010	+	4.63825i	−0.117486	+	0.167151i
$771$	−15.1652			−0.546160
$772$		−	20.3303i		−	0.731704i
$773$		−	51.1977i		−	1.84145i	−0.390207	−	0.920727i	$-0.627596\pi$
$773$		−	51.1977i		−	1.84145i	0.390207	−	0.920727i	$-0.372404\pi$
$774$	−73.4955			−2.64174
$775$			5.30352i			0.190508i
$776$	15.9891			0.573975
$777$	−17.2813	−	42.3303i	−0.619962	−	1.51859i
$778$			10.0000i			0.358517i
$779$	−27.9129			−1.00008
$780$	−6.19115			−0.221679
$781$	5.58258	−	3.58258i	0.199760	−	0.128195i
$782$			14.9666i			0.535206i
$783$	84.0917			3.00519
$784$	5.00000	−	4.89898i	0.178571	−	0.174964i
$785$	13.2523			0.472994
$786$	−29.1652			−1.04029
$787$	−40.3773			−1.43930			−0.719648	−	0.694339i	$-0.755697\pi$
$787$	−40.3773			−1.43930			−0.719648	+	0.694339i	$0.755697\pi$
$788$		−	18.7477i		−	0.667860i
$789$	87.6985			3.12215
$790$		−	2.58434i		−	0.0919465i
$791$	−41.0234	+	16.7477i	−1.45862	+	0.595481i
$792$	11.7913	+	18.3739i	0.418985	+	0.652887i
$793$	28.7477			1.02086
$794$	−23.8488			−0.846363
$795$	4.83485			0.171474
$796$		−	24.6297i		−	0.872978i
$797$		−	36.2311i		−	1.28337i	−0.766968	−	0.641686i	$-0.778235\pi$
$797$		−	36.2311i		−	1.28337i	0.766968	−	0.641686i	$-0.221765\pi$
$798$	42.0459	−	17.1652i	1.48841	−	0.607640i
$799$		−	18.8348i		−	0.666329i
$800$			4.58258i			0.162019i
$801$			64.4958i			2.27885i
$802$		−	1.58258i		−	0.0558827i
$803$	−17.6577	+	11.3317i	−0.623126	+	0.399886i
$804$		−	4.89898i		−	0.172774i
$805$	2.58434	+	6.33030i	0.0910859	+	0.223114i
$806$	3.58258			0.126191
$807$	−62.6606			−2.20576
$808$			0.511238i			0.0179853i
$809$		−	33.1652i		−	1.16602i	−0.812463	−	0.583012i	$-0.801874\pi$
$809$		−	33.1652i		−	1.16602i	0.812463	−	0.583012i	$-0.198126\pi$
$810$	−9.42157			−0.331040
$811$	−30.3097			−1.06432			−0.532158	−	0.846645i	$-0.678619\pi$
$811$	−30.3097			−1.06432			−0.532158	+	0.846645i	$0.678619\pi$
$812$	−7.58258	−	18.5734i	−0.266096	−	0.651800i
$813$		−	15.1652i		−	0.531865i
$814$	−10.0000	−	15.5826i	−0.350500	−	0.546169i
$815$			2.58434i			0.0905253i
$816$			11.5826i			0.405471i
$817$			61.9115i			2.16601i
$818$			9.93280i			0.347292i
$819$	49.9129	−	20.3768i	1.74410	−	0.712025i
$820$		−	3.25227i		−	0.113574i
$821$		−	11.4955i		−	0.401194i	−0.979674	−	0.200597i	$-0.935712\pi$
$821$		−	11.4955i		−	0.401194i	0.979674	−	0.200597i	$-0.0642882\pi$
$822$	−46.9448			−1.63739
$823$	−40.3303			−1.40583			−0.702913	−	0.711276i	$-0.748118\pi$
$823$	−40.3303			−1.40583			−0.702913	+	0.711276i	$0.748118\pi$
$824$	−13.5396			−0.471675
$825$	25.4107	+	39.5964i	0.884686	+	1.37857i
$826$	7.58258	−	3.09557i	0.263832	−	0.107709i
$827$			15.1652i			0.527344i	0.964612	+	0.263672i	$0.0849337\pi$
$827$			15.1652i			0.527344i	−0.964612	+	0.263672i	$0.915066\pi$
$828$	26.3303			0.915041
$829$		−	4.25290i		−	0.147709i	−0.997269	−	0.0738546i	$-0.976470\pi$
$829$		−	4.25290i		−	0.147709i	0.997269	−	0.0738546i	$-0.0235301\pi$
$830$	−5.91288			−0.205239
$831$	6.19115			0.214769
$832$	3.09557			0.107320
$833$	18.7083	−	18.3303i	0.648204	−	0.635107i
$834$	−10.0000			−0.346272
$835$		−	4.00000i		−	0.138426i
$836$	15.4779	−	9.93280i	0.535313	−	0.343533i
$837$	12.8348			0.443637
$838$	−5.67991			−0.196209
$839$			24.6297i			0.850313i	0.905120	+	0.425157i	$0.139781\pi$
$839$			24.6297i			0.850313i	−0.905120	+	0.425157i	$0.860219\pi$
$840$	2.00000	+	4.89898i	0.0690066	+	0.169031i
$841$	−28.4955			−0.982602
$842$		−	1.58258i		−	0.0545392i
$843$	−22.1803			−0.763929
$844$		−	10.7477i		−	0.369952i
$845$		−	2.20794i		−	0.0759555i
$846$	−33.1355			−1.13922
$847$	1.22497	−	29.0775i	0.0420905	−	0.999114i
$848$	−2.41742			−0.0830147
$849$			48.3303i			1.65869i
$850$			17.1464i			0.588118i
$851$	−22.3303			−0.765473
$852$		−	6.19115i		−	0.212105i
$853$	30.1748			1.03317			0.516583	−	0.856237i	$-0.327204\pi$
$853$	30.1748			1.03317			0.516583	+	0.856237i	$0.327204\pi$
$854$	−9.28672	−	22.7477i	−0.317785	−	0.778411i
$855$			23.5826i			0.806507i
$856$	−8.41742			−0.287702
$857$	21.2926			0.727342			0.363671	−	0.931527i	$-0.381523\pi$
$857$	21.2926			0.727342			0.363671	+	0.931527i	$0.381523\pi$
$858$	26.7477	−	17.1652i	0.913152	−	0.586009i
$859$		−	31.7367i		−	1.08284i	−0.840752	−	0.541421i	$-0.817887\pi$
$859$		−	31.7367i		−	1.08284i	0.840752	−	0.541421i	$-0.182113\pi$
$860$	−7.21362			−0.245983
$861$	15.5826	+	38.1694i	0.531053	+	1.30081i
$862$	17.9129			0.610115
$863$	−33.1652			−1.12895			−0.564477	−	0.825448i	$-0.690922\pi$
$863$	−33.1652			−1.12895			−0.564477	+	0.825448i	$0.690922\pi$
$864$	11.0901			0.377294
$865$		−	14.8348i		−	0.504400i
$866$	28.1017			0.954935
$867$		−	9.28672i		−	0.315394i
$868$	−1.15732	−	2.83485i	−0.0392821	−	0.0962210i
$869$	7.16515	+	11.1652i	0.243061	+	0.378752i
$870$	15.1652			0.514147
$871$	−4.89898			−0.165996
$872$	1.16515			0.0394570
$873$		−	105.250i		−	3.56216i
$874$		−	22.1803i		−	0.750258i
$875$	6.19115	+	15.1652i	0.209299	+	0.512676i
$876$			19.5826i			0.661634i
$877$			25.1652i			0.849767i	0.905248	+	0.424883i	$0.139685\pi$
$877$			25.1652i			0.849767i	−0.905248	+	0.424883i	$0.860315\pi$
$878$			2.31464i			0.0781155i
$879$			66.2432i			2.23433i
$880$	1.15732	+	1.80341i	0.0390133	+	0.0607928i
$881$		−	22.1803i		−	0.747272i	−0.927575	−	0.373636i	$-0.878111\pi$
$881$		−	22.1803i		−	0.747272i	0.927575	−	0.373636i	$-0.121889\pi$
$882$	−32.2479	−	32.9129i	−1.08584	−	1.10823i
$883$	31.1652			1.04879			0.524395	−	0.851475i	$-0.324291\pi$
$883$	31.1652			1.04879			0.524395	+	0.851475i	$0.324291\pi$
$884$	11.5826			0.389564
$885$			6.19115i			0.208113i
$886$		−	3.16515i		−	0.106335i
$887$	28.9108			0.970729			0.485365	−	0.874312i	$-0.338687\pi$
$887$	28.9108			0.970729			0.485365	+	0.874312i	$0.338687\pi$
$888$	−17.2813			−0.579922
$889$	−5.58258	−	13.6745i	−0.187234	−	0.458627i
$890$			6.33030i			0.212192i
$891$	40.7042	−	26.1216i	1.36364	−	0.875106i
$892$		−	6.32599i		−	0.211810i
$893$			27.9129i			0.934069i
$894$		−	43.3380i		−	1.44944i
$895$		−	4.62929i		−	0.154740i
$896$	−1.00000	−	2.44949i	−0.0334077	−	0.0818317i
$897$		−	38.3303i		−	1.27981i
$898$			12.8348i			0.428304i
$899$	−8.77548			−0.292679
$900$	30.1652			1.00551
$901$	−9.04517			−0.301338
$902$	9.01703	+	14.0509i	0.300234	+	0.467842i
$903$	84.6606	−	34.5625i	2.81733	−	1.15017i
$904$			16.7477i			0.557021i
$905$	10.7477			0.357267
$906$		−	11.0901i		−	0.368445i
$907$	−39.9129			−1.32529			−0.662643	−	0.748936i	$-0.730565\pi$
$907$	−39.9129			−1.32529			−0.662643	+	0.748936i	$0.730565\pi$
$908$	11.7362			0.389480
$909$	3.36526			0.111619
$910$	4.89898	−	2.00000i	0.162400	−	0.0662994i
$911$	−15.1652			−0.502444			−0.251222	−	0.967930i	$-0.580832\pi$
$911$	−15.1652			−0.502444			−0.251222	+	0.967930i	$0.580832\pi$
$912$		−	17.1652i		−	0.568395i
$913$	25.5455	−	16.3936i	0.845433	−	0.542550i
$914$	14.8348			0.490693
$915$	18.5734			0.614019
$916$			13.0284i			0.430470i
$917$	23.0780	−	9.42157i	0.762104	−	0.311128i
$918$	41.4955			1.36955
$919$			35.4955i			1.17089i	0.810713	+	0.585443i	$0.199080\pi$
$919$			35.4955i			1.17089i	−0.810713	+	0.585443i	$0.800920\pi$
$920$	2.58434			0.0852030
$921$			25.1652i			0.829220i
$922$			26.2983i			0.866088i
$923$	−6.19115			−0.203784
$924$	−22.2232	−	15.6201i	−0.731090	−	0.513863i
$925$	−25.5826			−0.841150
$926$		−	13.1652i		−	0.432634i
$927$			89.1255i			2.92727i
$928$	−7.58258			−0.248910
$929$			38.7087i			1.26999i	0.772515	+	0.634996i	$0.218998\pi$
$929$			38.7087i			1.26999i	−0.772515	+	0.634996i	$0.781002\pi$
$930$	2.31464			0.0759002
$931$	−27.7253	+	27.1652i	−0.908661	+	0.890302i
$932$		−	8.83485i		−	0.289395i
$933$	−30.7477			−1.00664
$934$	−0.511238			−0.0167282
$935$	4.33030	+	6.74773i	0.141616	+	0.220674i
$936$		−	20.3768i		−	0.666038i
$937$	−44.7650			−1.46241			−0.731205	−	0.682158i	$-0.761042\pi$
$937$	−44.7650			−1.46241			−0.731205	+	0.682158i	$0.761042\pi$
$938$	1.58258	+	3.87650i	0.0516729	+	0.126572i
$939$	−3.16515			−0.103291
$940$	−3.25227			−0.106077
$941$	−31.4670			−1.02579			−0.512897	−	0.858450i	$-0.671428\pi$
$941$	−31.4670			−1.02579			−0.512897	+	0.858450i	$0.671428\pi$
$942$			63.4955i			2.06879i
$943$	20.1353			0.655696
$944$		−	3.09557i		−	0.100752i
$945$	17.5510	−	7.16515i	0.570933	−	0.233082i
$946$	31.1652	−	20.0000i	1.01327	−	0.650256i
$947$	−5.58258			−0.181409			−0.0907047	−	0.995878i	$-0.528912\pi$
$947$	−5.58258			−0.181409			−0.0907047	+	0.995878i	$0.528912\pi$
$948$	12.3823			0.402158
$949$	19.5826			0.635677
$950$		−	25.4107i		−	0.824431i
$951$		−	28.3714i		−	0.920006i
$952$	−3.74166	−	9.16515i	−0.121268	−	0.297044i
$953$		−	18.3303i		−	0.593777i	−0.954912	−	0.296888i	$-0.904051\pi$
$953$		−	18.3303i		−	0.593777i	0.954912	−	0.296888i	$-0.0959489\pi$
$954$			15.9129i			0.515198i
$955$		−	11.6295i		−	0.376322i
$956$		−	17.5826i		−	0.568661i
$957$	−65.5183	+	42.0459i	−2.11791	+	1.35915i
$958$		−	6.46084i		−	0.208740i
$959$	37.1469	−	15.1652i	1.19954	−	0.489708i
$960$	2.00000			0.0645497
$961$	29.6606			0.956794
$962$			17.2813i			0.557171i
$963$			55.4083i			1.78551i
$964$	25.9219			0.834889
$965$	−13.1351			−0.422833
$966$	−30.3303	+	12.3823i	−0.975861	+	0.398394i
$967$			31.5826i			1.01563i	0.861467	+	0.507814i	$0.169546\pi$
$967$			31.5826i			1.01563i	−0.861467	+	0.507814i	$0.830454\pi$
$968$	−10.0000	−	4.58258i	−0.321412	−	0.147290i
$969$		−	64.2261i		−	2.06324i
$970$		−	10.3303i		−	0.331686i
$971$		−	17.7925i		−	0.570989i	−0.958380	−	0.285494i	$-0.907842\pi$
$971$		−	17.7925i		−	0.570989i	0.958380	−	0.285494i	$-0.0921578\pi$
$972$		−	11.8711i		−	0.380764i
$973$	7.91288	−	3.23042i	0.253675	−	0.103562i
$974$		−	33.4955i		−	1.07326i
$975$		−	43.9129i		−	1.40634i
$976$	−9.28672			−0.297261
$977$	−9.16515			−0.293219			−0.146610	−	0.989194i	$-0.546836\pi$
$977$	−9.16515			−0.293219			−0.146610	+	0.989194i	$0.546836\pi$
$978$	−12.3823			−0.395942
$979$	−17.5510	−	27.3489i	−0.560931	−	0.874075i
$980$	−3.16515	−	3.23042i	−0.101107	−	0.103192i
$981$		−	7.66970i		−	0.244875i
$982$	−21.4955			−0.685948
$983$			1.69670i			0.0541165i	0.999634	+	0.0270582i	$0.00861395\pi$
$983$			1.69670i			0.0541165i	−0.999634	+	0.0270582i	$0.991386\pi$
$984$	15.5826			0.496754
$985$	−12.1126			−0.385940
$986$	−28.3714			−0.903529
$987$	38.1694	−	15.5826i	1.21494	−	0.495999i
$988$	−17.1652			−0.546096
$989$		−	44.6606i		−	1.42012i
$990$	11.8711	−	7.61816i	0.377287	−	0.242121i
$991$	−26.6606			−0.846902			−0.423451	−	0.905919i	$-0.639181\pi$
$991$	−26.6606			−0.846902			−0.423451	+	0.905919i	$0.639181\pi$
$992$	−1.15732			−0.0367450
$993$		−	44.6302i		−	1.41630i
$994$	2.00000	+	4.89898i	0.0634361	+	0.155386i
$995$	−15.9129			−0.504472
$996$		−	28.3303i		−	0.897680i
$997$	33.7816			1.06987			0.534937	−	0.844892i	$-0.320335\pi$
$997$	33.7816			1.06987			0.534937	+	0.844892i	$0.320335\pi$
$998$			27.9129i			0.883567i
$999$			61.9115i			1.95879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.c.a.153.8	yes	8
3.2	odd	2		1386.2.e.b.307.2		8
4.3	odd	2		1232.2.e.e.769.1		8
7.2	even	3		1078.2.i.b.1011.5		16
7.3	odd	6		1078.2.i.b.901.1		16
7.4	even	3		1078.2.i.b.901.4		16
7.5	odd	6		1078.2.i.b.1011.8		16
7.6	odd	2	inner	154.2.c.a.153.5	yes	8
11.10	odd	2	inner	154.2.c.a.153.4	yes	8
21.20	even	2		1386.2.e.b.307.3		8
28.27	even	2		1232.2.e.e.769.8		8
33.32	even	2		1386.2.e.b.307.6		8
44.43	even	2		1232.2.e.e.769.2		8
77.10	even	6		1078.2.i.b.901.5		16
77.32	odd	6		1078.2.i.b.901.8		16
77.54	even	6		1078.2.i.b.1011.4		16
77.65	odd	6		1078.2.i.b.1011.1		16
77.76	even	2	inner	154.2.c.a.153.1	✓	8
231.230	odd	2		1386.2.e.b.307.7		8
308.307	odd	2		1232.2.e.e.769.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.c.a.153.1	✓	8	77.76	even	2	inner
154.2.c.a.153.4	yes	8	11.10	odd	2	inner
154.2.c.a.153.5	yes	8	7.6	odd	2	inner
154.2.c.a.153.8	yes	8	1.1	even	1	trivial
1078.2.i.b.901.1		16	7.3	odd	6
1078.2.i.b.901.4		16	7.4	even	3
1078.2.i.b.901.5		16	77.10	even	6
1078.2.i.b.901.8		16	77.32	odd	6
1078.2.i.b.1011.1		16	77.65	odd	6
1078.2.i.b.1011.4		16	77.54	even	6
1078.2.i.b.1011.5		16	7.2	even	3
1078.2.i.b.1011.8		16	7.5	odd	6
1232.2.e.e.769.1		8	4.3	odd	2
1232.2.e.e.769.2		8	44.43	even	2
1232.2.e.e.769.7		8	308.307	odd	2
1232.2.e.e.769.8		8	28.27	even	2
1386.2.e.b.307.2		8	3.2	odd	2
1386.2.e.b.307.3		8	21.20	even	2
1386.2.e.b.307.6		8	33.32	even	2
1386.2.e.b.307.7		8	231.230	odd	2

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +3.09557i q^{3} -1.00000 q^{4} +0.646084i q^{5} -3.09557 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} -6.58258 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +3.09557i q^{3} -1.00000 q^{4} +0.646084i q^{5} -3.09557 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} -6.58258 q^{9} -0.646084 q^{10} +(2.79129 - 1.79129i) q^{11} -3.09557i q^{12} -3.09557 q^{13} +(1.00000 + 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} +3.74166 q^{17} -6.58258i q^{18} -5.54506 q^{19} -0.646084i q^{20} +(3.09557 + 7.58258i) q^{21} +(1.79129 + 2.79129i) q^{22} +4.00000 q^{23} +3.09557 q^{24} +4.58258 q^{25} -3.09557i q^{26} -11.0901i q^{27} +(-2.44949 + 1.00000i) q^{28} +7.58258i q^{29} -2.00000i q^{30} +1.15732i q^{31} +1.00000i q^{32} +(5.54506 + 8.64064i) q^{33} +3.74166i q^{34} +(0.646084 + 1.58258i) q^{35} +6.58258 q^{36} -5.58258 q^{37} -5.54506i q^{38} -9.58258i q^{39} +0.646084 q^{40} +5.03383 q^{41} +(-7.58258 + 3.09557i) q^{42} -11.1652i q^{43} +(-2.79129 + 1.79129i) q^{44} -4.25290i q^{45} +4.00000i q^{46} -5.03383i q^{47} +3.09557i q^{48} +(5.00000 - 4.89898i) q^{49} +4.58258i q^{50} +11.5826i q^{51} +3.09557 q^{52} -2.41742 q^{53} +11.0901 q^{54} +(1.15732 + 1.80341i) q^{55} +(-1.00000 - 2.44949i) q^{56} -17.1652i q^{57} -7.58258 q^{58} -3.09557i q^{59} +2.00000 q^{60} -9.28672 q^{61} -1.15732 q^{62} +(-16.1240 + 6.58258i) q^{63} -1.00000 q^{64} -2.00000i q^{65} +(-8.64064 + 5.54506i) q^{66} +1.58258 q^{67} -3.74166 q^{68} +12.3823i q^{69} +(-1.58258 + 0.646084i) q^{70} +2.00000 q^{71} +6.58258i q^{72} -6.32599 q^{73} -5.58258i q^{74} +14.1857i q^{75} +5.54506 q^{76} +(5.04594 - 7.17903i) q^{77} +9.58258 q^{78} +4.00000i q^{79} +0.646084i q^{80} +14.5826 q^{81} +5.03383i q^{82} +9.15188 q^{83} +(-3.09557 - 7.58258i) q^{84} +2.41742i q^{85} +11.1652 q^{86} -23.4724 q^{87} +(-1.79129 - 2.79129i) q^{88} -9.79796i q^{89} +4.25290 q^{90} +(-7.58258 + 3.09557i) q^{91} -4.00000 q^{92} -3.58258 q^{93} +5.03383 q^{94} -3.58258i q^{95} -3.09557 q^{96} +15.9891i q^{97} +(4.89898 + 5.00000i) q^{98} +(-18.3739 + 11.7913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 16 * q^9	\( 8 q - 8 q^{4} - 16 q^{9} + 4 q^{11} + 8 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{22} + 32 q^{23} + 16 q^{36} - 8 q^{37} - 24 q^{42} - 4 q^{44} + 40 q^{49} - 56 q^{53} - 8 q^{56} - 24 q^{58} + 16 q^{60} - 8 q^{64} - 24 q^{67} + 24 q^{70} + 16 q^{71} + 4 q^{77} + 40 q^{78} + 80 q^{81} + 16 q^{86} + 4 q^{88} - 24 q^{91} - 32 q^{92} + 8 q^{93} - 92 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 16 * q^9 + 4 * q^11 + 8 * q^14 - 16 * q^15 + 8 * q^16 - 4 * q^22 + 32 * q^23 + 16 * q^36 - 8 * q^37 - 24 * q^42 - 4 * q^44 + 40 * q^49 - 56 * q^53 - 8 * q^56 - 24 * q^58 + 16 * q^60 - 8 * q^64 - 24 * q^67 + 24 * q^70 + 16 * q^71 + 4 * q^77 + 40 * q^78 + 80 * q^81 + 16 * q^86 + 4 * q^88 - 24 * q^91 - 32 * q^92 + 8 * q^93 - 92 * q^99

Introduction

L-functions

Modular forms

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Database

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