LMFDB - Embedded newform 1155.2.k.b.769.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.15
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17317 q^{2} +1.00000 q^{3} -0.623669 q^{4} +(2.20931 - 0.344884i) q^{5} -1.17317 q^{6} +(-1.71739 + 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.17317 q^{2} +1.00000 q^{3} -0.623669 q^{4} +(2.20931 - 0.344884i) q^{5} -1.17317 q^{6} +(-1.71739 + 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +(-2.59190 + 0.404608i) q^{10} +(1.48217 - 2.96702i) q^{11} -0.623669 q^{12} -3.43348i q^{13} +(2.01480 - 2.36113i) q^{14} +(2.20931 - 0.344884i) q^{15} -2.36370 q^{16} -3.10231i q^{17} -1.17317 q^{18} -5.32112 q^{19} +(-1.37788 + 0.215094i) q^{20} +(-1.71739 + 2.01260i) q^{21} +(-1.73883 + 3.48082i) q^{22} -5.88666i q^{23} +3.07801 q^{24} +(4.76211 - 1.52391i) q^{25} +4.02806i q^{26} +1.00000 q^{27} +(1.07109 - 1.25520i) q^{28} +5.81504i q^{29} +(-2.59190 + 0.404608i) q^{30} -0.722644i q^{31} -3.38301 q^{32} +(1.48217 - 2.96702i) q^{33} +3.63954i q^{34} +(-3.10014 + 5.03876i) q^{35} -0.623669 q^{36} -1.11476i q^{37} +6.24259 q^{38} -3.43348i q^{39} +(6.80029 - 1.06156i) q^{40} +3.34512 q^{41} +(2.01480 - 2.36113i) q^{42} +7.30051 q^{43} +(-0.924381 + 1.85044i) q^{44} +(2.20931 - 0.344884i) q^{45} +6.90606i q^{46} +6.60481 q^{47} -2.36370 q^{48} +(-1.10113 - 6.91285i) q^{49} +(-5.58677 + 1.78781i) q^{50} -3.10231i q^{51} +2.14136i q^{52} -11.7433i q^{53} -1.17317 q^{54} +(2.25129 - 7.06624i) q^{55} +(-5.28616 + 6.19481i) q^{56} -5.32112 q^{57} -6.82204i q^{58} +14.7567i q^{59} +(-1.37788 + 0.215094i) q^{60} +5.25854 q^{61} +0.847785i q^{62} +(-1.71739 + 2.01260i) q^{63} +8.69624 q^{64} +(-1.18415 - 7.58563i) q^{65} +(-1.73883 + 3.48082i) q^{66} -1.98202i q^{67} +1.93481i q^{68} -5.88666i q^{69} +(3.63699 - 5.91133i) q^{70} -14.9478 q^{71} +3.07801 q^{72} -7.27698i q^{73} +1.30781i q^{74} +(4.76211 - 1.52391i) q^{75} +3.31862 q^{76} +(3.42596 + 8.07854i) q^{77} +4.02806i q^{78} -11.5312i q^{79} +(-5.22214 + 0.815202i) q^{80} +1.00000 q^{81} -3.92440 q^{82} -7.39391i q^{83} +(1.07109 - 1.25520i) q^{84} +(-1.06994 - 6.85396i) q^{85} -8.56475 q^{86} +5.81504i q^{87} +(4.56212 - 9.13252i) q^{88} -3.65152i q^{89} +(-2.59190 + 0.404608i) q^{90} +(6.91023 + 5.89663i) q^{91} +3.67133i q^{92} -0.722644i q^{93} -7.74857 q^{94} +(-11.7560 + 1.83517i) q^{95} -3.38301 q^{96} -3.77353 q^{97} +(1.29181 + 8.10996i) q^{98} +(1.48217 - 2.96702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	$ 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) $ 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.17317			−0.829557			−0.414779	−	0.909922i	$-0.636141\pi$
$2$	−1.17317			−0.829557			−0.414779	+	0.909922i	$0.636141\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.623669			−0.311835
$5$	2.20931	−	0.344884i	0.988034	−	0.154237i
$5$	2.20931	−	0.344884i	0.988034	−	0.154237i
$6$	−1.17317			−0.478945
$7$	−1.71739	+	2.01260i	−0.649113	+	0.760692i
$7$	−1.71739	+	2.01260i	−0.649113	+	0.760692i
$8$	3.07801			1.08824
$9$	1.00000			0.333333
$10$	−2.59190	+	0.404608i	−0.819631	+	0.127948i
$11$	1.48217	−	2.96702i	0.446890	−	0.894589i
$11$	1.48217	−	2.96702i	0.446890	−	0.894589i
$12$	−0.623669			−0.180038
$13$		−	3.43348i		−	0.952276i	−0.879371	−	0.476138i	$-0.842036\pi$
$13$		−	3.43348i		−	0.952276i	0.879371	−	0.476138i	$-0.157964\pi$
$14$	2.01480	−	2.36113i	0.538477	−	0.631037i
$15$	2.20931	−	0.344884i	0.570442	−	0.0890488i
$16$	−2.36370			−0.590924
$17$		−	3.10231i		−	0.752420i	−0.926534	−	0.376210i	$-0.877227\pi$
$17$		−	3.10231i		−	0.752420i	0.926534	−	0.376210i	$-0.122773\pi$
$18$	−1.17317			−0.276519
$19$	−5.32112			−1.22075			−0.610375	−	0.792113i	$-0.708981\pi$
$19$	−5.32112			−1.22075			−0.610375	+	0.792113i	$0.708981\pi$
$20$	−1.37788	+	0.215094i	−0.308103	+	0.0480965i
$21$	−1.71739	+	2.01260i	−0.374766	+	0.439186i
$22$	−1.73883	+	3.48082i	−0.370721	+	0.742113i
$23$		−	5.88666i		−	1.22745i	−0.789519	−	0.613726i	$-0.789670\pi$
$23$		−	5.88666i		−	1.22745i	0.789519	−	0.613726i	$-0.210330\pi$
$24$	3.07801			0.628297
$25$	4.76211	−	1.52391i	0.952422	−	0.304783i
$26$			4.02806i			0.789968i
$27$	1.00000			0.192450
$28$	1.07109	−	1.25520i	0.202416	−	0.237210i
$29$			5.81504i			1.07983i	0.841721	+	0.539913i	$0.181543\pi$
$29$			5.81504i			1.07983i	−0.841721	+	0.539913i	$0.818457\pi$
$30$	−2.59190	+	0.404608i	−0.473214	+	0.0738711i
$31$		−	0.722644i		−	0.129791i	−0.997892	−	0.0648954i	$-0.979329\pi$
$31$		−	0.722644i		−	0.129791i	0.997892	−	0.0648954i	$-0.0206714\pi$
$32$	−3.38301			−0.598036
$33$	1.48217	−	2.96702i	0.258012	−	0.516491i
$34$			3.63954i			0.624176i
$35$	−3.10014	+	5.03876i	−0.524019	+	0.851706i
$36$	−0.623669			−0.103945
$37$		−	1.11476i		−	0.183266i	−0.995793	−	0.0916331i	$-0.970791\pi$
$37$		−	1.11476i		−	0.183266i	0.995793	−	0.0916331i	$-0.0292087\pi$
$38$	6.24259			1.01268
$39$		−	3.43348i		−	0.549797i
$40$	6.80029	−	1.06156i	1.07522	−	0.167847i
$41$	3.34512			0.522420			0.261210	−	0.965282i	$-0.415878\pi$
$41$	3.34512			0.522420			0.261210	+	0.965282i	$0.415878\pi$
$42$	2.01480	−	2.36113i	0.310890	−	0.364330i
$43$	7.30051			1.11332			0.556659	−	0.830741i	$-0.312083\pi$
$43$	7.30051			1.11332			0.556659	+	0.830741i	$0.312083\pi$
$44$	−0.924381	+	1.85044i	−0.139356	+	0.278964i
$45$	2.20931	−	0.344884i	0.329345	−	0.0514123i
$46$			6.90606i			1.01824i
$47$	6.60481			0.963410			0.481705	−	0.876333i	$-0.340018\pi$
$47$	6.60481			0.963410			0.481705	+	0.876333i	$0.340018\pi$
$48$	−2.36370			−0.341170
$49$	−1.10113	−	6.91285i	−0.157304	−	0.987550i
$50$	−5.58677	+	1.78781i	−0.790089	+	0.252835i
$51$		−	3.10231i		−	0.434410i
$52$			2.14136i			0.296953i
$53$		−	11.7433i		−	1.61307i	−0.591186	−	0.806535i	$-0.701340\pi$
$53$		−	11.7433i		−	1.61307i	0.591186	−	0.806535i	$-0.298660\pi$
$54$	−1.17317			−0.159648
$55$	2.25129	−	7.06624i	0.303563	−	0.952811i
$56$	−5.28616	+	6.19481i	−0.706392	+	0.827817i
$57$	−5.32112			−0.704800
$58$		−	6.82204i		−	0.895777i
$59$			14.7567i			1.92116i	0.278003	+	0.960580i	$0.410328\pi$
$59$			14.7567i			1.92116i	−0.278003	+	0.960580i	$0.589672\pi$
$60$	−1.37788	+	0.215094i	−0.177884	+	0.0277685i
$61$	5.25854			0.673287			0.336643	−	0.941632i	$-0.390708\pi$
$61$	5.25854			0.673287			0.336643	+	0.941632i	$0.390708\pi$
$62$			0.847785i			0.107669i
$63$	−1.71739	+	2.01260i	−0.216371	+	0.253564i
$64$	8.69624			1.08703
$65$	−1.18415	−	7.58563i	−0.146876	−	0.940881i
$66$	−1.73883	+	3.48082i	−0.214036	+	0.428459i
$67$		−	1.98202i		−	0.242142i	−0.992644	−	0.121071i	$-0.961367\pi$
$67$		−	1.98202i		−	0.242142i	0.992644	−	0.121071i	$-0.0386329\pi$
$68$			1.93481i			0.234631i
$69$		−	5.88666i		−	0.708670i
$70$	3.63699	−	5.91133i	0.434704	−	0.706539i
$71$	−14.9478			−1.77398			−0.886990	−	0.461788i	$-0.847208\pi$
$71$	−14.9478			−1.77398			−0.886990	+	0.461788i	$0.847208\pi$
$72$	3.07801			0.362747
$73$		−	7.27698i		−	0.851706i	−0.904792	−	0.425853i	$-0.859974\pi$
$73$		−	7.27698i		−	0.851706i	0.904792	−	0.425853i	$-0.140026\pi$
$74$			1.30781i			0.152030i
$75$	4.76211	−	1.52391i	0.549881	−	0.175966i
$76$	3.31862			0.380672
$77$	3.42596	+	8.07854i	0.390424	+	0.920635i
$78$			4.02806i			0.456088i
$79$		−	11.5312i		−	1.29736i	−0.761061	−	0.648680i	$-0.775321\pi$
$79$		−	11.5312i		−	1.29736i	0.761061	−	0.648680i	$-0.224679\pi$
$80$	−5.22214	+	0.815202i	−0.583853	+	0.0911424i
$81$	1.00000			0.111111
$82$	−3.92440			−0.433378
$83$		−	7.39391i		−	0.811587i	−0.913965	−	0.405794i	$-0.866995\pi$
$83$		−	7.39391i		−	0.811587i	0.913965	−	0.405794i	$-0.133005\pi$
$84$	1.07109	−	1.25520i	0.116865	−	0.136953i
$85$	−1.06994	−	6.85396i	−0.116051	−	0.743417i
$86$	−8.56475			−0.923561
$87$			5.81504i			0.623438i
$88$	4.56212	−	9.13252i	0.486324	−	0.973529i
$89$		−	3.65152i		−	0.387060i	−0.981094	−	0.193530i	$-0.938006\pi$
$89$		−	3.65152i		−	0.387060i	0.981094	−	0.193530i	$-0.0619937\pi$
$90$	−2.59190	+	0.404608i	−0.273210	+	0.0426495i
$91$	6.91023	+	5.89663i	0.724389	+	0.618135i
$92$			3.67133i			0.382762i
$93$		−	0.722644i		−	0.0749347i
$94$	−7.74857			−0.799204
$95$	−11.7560	+	1.83517i	−1.20614	+	0.188285i
$96$	−3.38301			−0.345277
$97$	−3.77353			−0.383144			−0.191572	−	0.981479i	$-0.561359\pi$
$97$	−3.77353			−0.383144			−0.191572	+	0.981479i	$0.561359\pi$
$98$	1.29181	+	8.10996i	0.130492	+	0.819229i
$99$	1.48217	−	2.96702i	0.148963	−	0.298196i
$100$	−2.96998	+	0.950419i	−0.296998	+	0.0950419i
$101$	15.2917			1.52158			0.760791	−	0.648997i	$-0.224811\pi$
$101$	15.2917			1.52158			0.760791	+	0.648997i	$0.224811\pi$
$102$			3.63954i			0.360368i
$103$	1.35140			0.133158			0.0665789	−	0.997781i	$-0.478792\pi$
$103$	1.35140			0.133158			0.0665789	+	0.997781i	$0.478792\pi$
$104$		−	10.5683i		−	1.03631i
$105$	−3.10014	+	5.03876i	−0.302543	+	0.491733i
$106$			13.7769i			1.33813i
$107$	−1.77552			−0.171646			−0.0858228	−	0.996310i	$-0.527352\pi$
$107$	−1.77552			−0.171646			−0.0858228	+	0.996310i	$0.527352\pi$
$108$	−0.623669			−0.0600126
$109$			1.93909i			0.185731i	0.995679	+	0.0928656i	$0.0296027\pi$
$109$			1.93909i			0.185731i	−0.995679	+	0.0928656i	$0.970397\pi$
$110$	−2.64114	+	8.28991i	−0.251823	+	0.790411i
$111$		−	1.11476i		−	0.105809i
$112$	4.05940	−	4.75718i	0.383577	−	0.449511i
$113$			17.3740i			1.63441i	0.576350	+	0.817203i	$0.304477\pi$
$113$			17.3740i			1.63441i	−0.576350	+	0.817203i	$0.695523\pi$
$114$	6.24259			0.584672
$115$	−2.03022	−	13.0055i	−0.189319	−	1.21276i
$116$		−	3.62666i		−	0.336727i
$117$		−	3.43348i		−	0.317425i
$118$		−	17.3122i		−	1.59371i
$119$	6.24371	+	5.32788i	0.572360	+	0.488406i
$120$	6.80029	−	1.06156i	0.620779	−	0.0969066i
$121$	−6.60637	−	8.79522i	−0.600579	−	0.799565i
$122$	−6.16916			−0.558530
$123$	3.34512			0.301620
$124$			0.450691i			0.0404733i
$125$	9.99541	−	5.00918i	0.894016	−	0.448034i
$126$	2.01480	−	2.36113i	0.179492	−	0.210346i
$127$	6.23748			0.553487			0.276743	−	0.960944i	$-0.410745\pi$
$127$	6.23748			0.553487			0.276743	+	0.960944i	$0.410745\pi$
$128$	−3.43617			−0.303717
$129$	7.30051			0.642774
$130$	1.38922	+	8.89924i	0.121842	+	0.780515i
$131$	2.79723			0.244395			0.122198	−	0.992506i	$-0.461006\pi$
$131$	2.79723			0.244395			0.122198	+	0.992506i	$0.461006\pi$
$132$	−0.924381	+	1.85044i	−0.0804571	+	0.161060i
$133$	9.13845	−	10.7093i	0.792405	−	0.928614i
$134$			2.32525i			0.200871i
$135$	2.20931	−	0.344884i	0.190147	−	0.0296829i
$136$		−	9.54894i		−	0.818815i
$137$		−	18.1264i		−	1.54865i	−0.632791	−	0.774323i	$-0.718091\pi$
$137$		−	18.1264i		−	1.54865i	0.632791	−	0.774323i	$-0.281909\pi$
$138$			6.90606i			0.587882i
$139$	12.5540			1.06481			0.532407	−	0.846489i	$-0.321288\pi$
$139$	12.5540			1.06481			0.532407	+	0.846489i	$0.321288\pi$
$140$	1.93346	−	3.14252i	0.163407	−	0.265592i
$141$	6.60481			0.556225
$142$	17.5364			1.47162
$143$	−10.1872	−	5.08899i	−0.851896	−	0.425562i
$144$	−2.36370			−0.196975
$145$	2.00552	+	12.8472i	0.166549	+	1.06690i
$146$			8.53714i			0.706539i
$147$	−1.10113	−	6.91285i	−0.0908194	−	0.570162i
$148$			0.695245i			0.0571488i
$149$		−	3.14282i		−	0.257470i	−0.991679	−	0.128735i	$-0.958908\pi$
$149$		−	3.14282i		−	0.257470i	0.991679	−	0.128735i	$-0.0410916\pi$
$150$	−5.58677	+	1.78781i	−0.456158	+	0.145974i
$151$			0.939283i			0.0764378i	0.999269	+	0.0382189i	$0.0121684\pi$
$151$			0.939283i			0.0764378i	−0.999269	+	0.0382189i	$0.987832\pi$
$152$	−16.3785			−1.32847
$153$		−	3.10231i		−	0.250807i
$154$	−4.01924	−	9.47751i	−0.323879	−	0.763719i
$155$	−0.249229	−	1.59655i	−0.0200185	−	0.128238i
$156$			2.14136i			0.171446i
$157$	12.9739			1.03543			0.517715	−	0.855553i	$-0.326783\pi$
$157$	12.9739			1.03543			0.517715	+	0.855553i	$0.326783\pi$
$158$			13.5281i			1.07623i
$159$		−	11.7433i		−	0.931307i
$160$	−7.47411	+	1.16675i	−0.590880	+	0.0922393i
$161$	11.8475	+	10.1097i	0.933713	+	0.796756i
$162$	−1.17317			−0.0921730
$163$			9.34655i			0.732078i	0.930599	+	0.366039i	$0.119286\pi$
$163$			9.34655i			0.732078i	−0.930599	+	0.366039i	$0.880714\pi$
$164$	−2.08625			−0.162909
$165$	2.25129	−	7.06624i	0.175262	−	0.550106i
$166$			8.67432i			0.673258i
$167$			24.2687i			1.87797i	0.343964	+	0.938983i	$0.388230\pi$
$167$			24.2687i			1.87797i	−0.343964	+	0.938983i	$0.611770\pi$
$168$	−5.28616	+	6.19481i	−0.407836	+	0.477940i
$169$	1.21121			0.0931702
$170$	1.25522	+	8.04087i	0.0962710	+	0.616707i
$171$	−5.32112			−0.406916
$172$	−4.55311			−0.347171
$173$			0.0905291i			0.00688280i	0.999994	+	0.00344140i	$0.00109543\pi$
$173$			0.0905291i			0.00688280i	−0.999994	+	0.00344140i	$0.998905\pi$
$174$		−	6.82204i		−	0.517177i
$175$	−5.11138	+	12.2014i	−0.386384	+	0.922338i
$176$	−3.50339	+	7.01313i	−0.264078	+	0.528634i
$177$			14.7567i			1.10918i
$178$			4.28385i			0.321088i
$179$	−22.0633			−1.64909			−0.824543	−	0.565799i	$-0.808568\pi$
$179$	−22.0633			−1.64909			−0.824543	+	0.565799i	$0.808568\pi$
$180$	−1.37788	+	0.215094i	−0.102701	+	0.0160322i
$181$			5.43785i			0.404192i	0.979366	+	0.202096i	$0.0647753\pi$
$181$			5.43785i			0.404192i	−0.979366	+	0.202096i	$0.935225\pi$
$182$	−8.10688	−	6.91776i	−0.600922	−	0.512778i
$183$	5.25854			0.388722
$184$		−	18.1192i		−	1.33577i
$185$	−0.384465	−	2.46286i	−0.0282664	−	0.181073i
$186$			0.847785i			0.0621626i
$187$	−9.20460	−	4.59813i	−0.673107	−	0.336249i
$188$	−4.11922			−0.300425
$189$	−1.71739	+	2.01260i	−0.124922	+	0.146395i
$190$	13.7918	−	2.15297i	1.00056	−	0.156193i
$191$	−18.9758			−1.37304			−0.686521	−	0.727110i	$-0.740863\pi$
$191$	−18.9758			−1.37304			−0.686521	+	0.727110i	$0.740863\pi$
$192$	8.69624			0.627597
$193$	−16.3232			−1.17497			−0.587484	−	0.809235i	$-0.699882\pi$
$193$	−16.3232			−1.17497			−0.587484	+	0.809235i	$0.699882\pi$
$194$	4.42700			0.317840
$195$	−1.18415	−	7.58563i	−0.0847990	−	0.543218i
$196$	0.686739	+	4.31133i	0.0490528	+	0.307952i
$197$	16.1111			1.14787			0.573933	−	0.818902i	$-0.305417\pi$
$197$	16.1111			1.14787			0.573933	+	0.818902i	$0.305417\pi$
$198$	−1.73883	+	3.48082i	−0.123574	+	0.247371i
$199$		−	24.4971i		−	1.73656i	−0.496078	−	0.868278i	$-0.665227\pi$
$199$		−	24.4971i		−	1.73656i	0.496078	−	0.868278i	$-0.334773\pi$
$200$	14.6578	−	4.69063i	1.03647	−	0.331677i
$201$		−	1.98202i		−	0.139801i
$202$	−17.9398			−1.26224
$203$	−11.7034	−	9.98670i	−0.821414	−	0.700929i
$204$			1.93481i			0.135464i
$205$	7.39042	−	1.15368i	0.516169	−	0.0805765i
$206$	−1.58543			−0.110462
$207$		−	5.88666i		−	0.409151i
$208$			8.11571i			0.562723i
$209$	−7.88678	+	15.7879i	−0.545540	+	1.09207i
$210$	3.63699	−	5.91133i	0.250976	−	0.407921i
$211$			13.0894i			0.901112i	0.892748	+	0.450556i	$0.148774\pi$
$211$			13.0894i			0.901112i	−0.892748	+	0.450556i	$0.851226\pi$
$212$			7.32396i			0.503012i
$213$	−14.9478			−1.02421
$214$	2.08298			0.142390
$215$	16.1291	−	2.51783i	1.10000	−	0.171715i
$216$	3.07801			0.209432
$217$	1.45439	+	1.24106i	0.0987307	+	0.0842489i
$218$		−	2.27489i		−	0.154075i
$219$		−	7.27698i		−	0.491733i
$220$	−1.40406	+	4.40700i	−0.0946616	+	0.297120i
$221$	−10.6517			−0.716512
$222$			1.30781i			0.0877744i
$223$	4.59749			0.307871			0.153935	−	0.988081i	$-0.450805\pi$
$223$	4.59749			0.307871			0.153935	+	0.988081i	$0.450805\pi$
$224$	5.80995	−	6.80864i	0.388193	−	0.454921i
$225$	4.76211	−	1.52391i	0.317474	−	0.101594i
$226$		−	20.3826i		−	1.35583i
$227$		−	18.9902i		−	1.26042i	−0.776424	−	0.630211i	$-0.782968\pi$
$227$		−	18.9902i		−	1.26042i	0.776424	−	0.630211i	$-0.217032\pi$
$228$	3.31862			0.219781
$229$			19.7583i			1.30566i	0.757503	+	0.652831i	$0.226419\pi$
$229$			19.7583i			1.30566i	−0.757503	+	0.652831i	$0.773581\pi$
$230$	2.38179	+	15.2576i	0.157051	+	1.00606i
$231$	3.42596	+	8.07854i	0.225412	+	0.531529i
$232$			17.8988i			1.17511i
$233$	19.0700			1.24932			0.624660	−	0.780897i	$-0.285238\pi$
$233$	19.0700			1.24932			0.624660	+	0.780897i	$0.285238\pi$
$234$			4.02806i			0.263323i
$235$	14.5921	−	2.27789i	0.951882	−	0.148593i
$236$		−	9.20331i		−	0.599085i
$237$		−	11.5312i		−	0.749031i
$238$	−7.32494	−	6.25051i	−0.474805	−	0.405161i
$239$			23.1560i			1.49784i	0.662661	+	0.748919i	$0.269427\pi$
$239$			23.1560i			1.49784i	−0.662661	+	0.748919i	$0.730573\pi$
$240$	−5.22214	+	0.815202i	−0.337088	+	0.0526211i
$241$	−15.7072			−1.01179			−0.505896	−	0.862595i	$-0.668838\pi$
$241$	−15.7072			−1.01179			−0.505896	+	0.862595i	$0.668838\pi$
$242$	7.75041	+	10.3183i	0.498215	+	0.663285i
$243$	1.00000			0.0641500
$244$	−3.27959			−0.209954
$245$	−4.81687	−	14.8929i	−0.307738	−	0.951471i
$246$	−3.92440			−0.250211
$247$			18.2700i			1.16249i
$248$		−	2.22431i		−	0.141244i
$249$		−	7.39391i		−	0.468570i
$250$	−11.7263	+	5.87662i	−0.741638	+	0.371670i
$251$			27.7124i			1.74919i	0.484854	+	0.874595i	$0.338873\pi$
$251$			27.7124i			1.74919i	−0.484854	+	0.874595i	$0.661127\pi$
$252$	1.07109	−	1.25520i	0.0674720	−	0.0790700i
$253$	−17.4658	−	8.72500i	−1.09807	−	0.548536i
$254$	−7.31763			−0.459149
$255$	−1.06994	−	6.85396i	−0.0670021	−	0.429212i
$256$	−13.3613			−0.835079
$257$	8.14674			0.508180			0.254090	−	0.967181i	$-0.418224\pi$
$257$	8.14674			0.508180			0.254090	+	0.967181i	$0.418224\pi$
$258$	−8.56475			−0.533218
$259$	2.24358	+	1.91449i	0.139409	+	0.118961i
$260$	0.738521	+	4.73092i	0.0458011	+	0.293399i
$261$			5.81504i			0.359942i
$262$	−3.28163			−0.202740
$263$	11.5514			0.712293			0.356146	−	0.934430i	$-0.384090\pi$
$263$	11.5514			0.712293			0.356146	+	0.934430i	$0.384090\pi$
$264$	4.56212	−	9.13252i	0.280779	−	0.562067i
$265$	−4.05009	−	25.9447i	−0.248795	−	1.59377i
$266$	−10.7210	+	12.5638i	−0.657345	+	0.770338i
$267$		−	3.65152i		−	0.223469i
$268$			1.23613i			0.0755084i
$269$			16.9804i			1.03531i	0.855589	+	0.517656i	$0.173195\pi$
$269$			16.9804i			1.03531i	−0.855589	+	0.517656i	$0.826805\pi$
$270$	−2.59190	+	0.404608i	−0.157738	+	0.0246237i
$271$	−18.3679			−1.11577			−0.557885	−	0.829918i	$-0.688387\pi$
$271$	−18.3679			−1.11577			−0.557885	+	0.829918i	$0.688387\pi$
$272$			7.33292i			0.444623i
$273$	6.91023	+	5.89663i	0.418226	+	0.356880i
$274$			21.2654i			1.28469i
$275$	2.53676	−	16.3879i	0.152972	−	0.988230i
$276$			3.67133i			0.220988i
$277$	−11.6755			−0.701514			−0.350757	−	0.936467i	$-0.614076\pi$
$277$	−11.6755			−0.701514			−0.350757	+	0.936467i	$0.614076\pi$
$278$	−14.7280			−0.883324
$279$		−	0.722644i		−	0.0432636i
$280$	−9.54227	+	15.5094i	−0.570260	+	0.926863i
$281$			7.54255i			0.449951i	0.974364	+	0.224975i	$0.0722302\pi$
$281$			7.54255i			0.449951i	−0.974364	+	0.224975i	$0.927770\pi$
$282$	−7.74857			−0.461421
$283$			4.89738i			0.291119i	0.989350	+	0.145559i	$0.0464982\pi$
$283$			4.89738i			0.291119i	−0.989350	+	0.145559i	$0.953502\pi$
$284$	9.32250			0.553189
$285$	−11.7560	+	1.83517i	−0.696366	+	0.108706i
$286$	11.9513	+	5.97025i	0.706696	+	0.353028i
$287$	−5.74489	+	6.73240i	−0.339110	+	0.397401i
$288$	−3.38301			−0.199345
$289$	7.37569			0.433864
$290$	−2.35281	−	15.0720i	−0.138162	−	0.885058i
$291$	−3.77353			−0.221208
$292$			4.53843i			0.265592i
$293$			7.63128i			0.445824i	0.974839	+	0.222912i	$0.0715563\pi$
$293$			7.63128i			0.445824i	−0.974839	+	0.222912i	$0.928444\pi$
$294$	1.29181	+	8.10996i	0.0753399	+	0.472982i
$295$	5.08936	+	32.6022i	0.296314	+	1.89817i
$296$		−	3.43126i		−	0.199438i
$297$	1.48217	−	2.96702i	0.0860040	−	0.172164i
$298$			3.68706i			0.213586i
$299$	−20.2117			−1.16887
$300$	−2.96998	+	0.950419i	−0.171472	+	0.0548724i
$301$	−12.5378	+	14.6930i	−0.722669	+	0.846891i
$302$		−	1.10194i		−	0.0634095i
$303$	15.2917			0.878486
$304$	12.5775			0.721370
$305$	11.6177	−	1.81359i	0.665230	−	0.103846i
$306$			3.63954i			0.208059i
$307$			29.9896i			1.71160i	0.517310	+	0.855798i	$0.326933\pi$
$307$			29.9896i			1.71160i	−0.517310	+	0.855798i	$0.673067\pi$
$308$	−2.13667	−	5.03834i	−0.121748	−	0.287086i
$309$	1.35140			0.0768787
$310$	0.292388	+	1.87302i	0.0166065	+	0.106380i
$311$			10.3684i			0.587939i	0.955815	+	0.293969i	$0.0949764\pi$
$311$			10.3684i			0.587939i	−0.955815	+	0.293969i	$0.905024\pi$
$312$		−	10.5683i		−	0.598312i
$313$	17.3488			0.980614			0.490307	−	0.871550i	$-0.336885\pi$
$313$	17.3488			0.980614			0.490307	+	0.871550i	$0.336885\pi$
$314$	−15.2206			−0.858948
$315$	−3.10014	+	5.03876i	−0.174673	+	0.283902i
$316$			7.19165i			0.404562i
$317$		−	20.0871i		−	1.12821i	−0.825704	−	0.564103i	$-0.809222\pi$
$317$		−	20.0871i		−	1.12821i	0.825704	−	0.564103i	$-0.190778\pi$
$318$			13.7769i			0.772572i
$319$	17.2533	+	8.61885i	0.966000	+	0.482563i
$320$	19.2127	−	2.99920i	1.07402	−	0.167660i
$321$	−1.77552			−0.0990996
$322$	−13.8991	−	11.8604i	−0.774568	−	0.660955i
$323$			16.5078i			0.918516i
$324$	−0.623669			−0.0346483
$325$	−5.23233	−	16.3506i	−0.290237	−	0.906969i
$326$		−	10.9651i		−	0.607301i
$327$			1.93909i			0.107232i
$328$	10.2963			0.568520
$329$	−11.3430	+	13.2928i	−0.625362	+	0.732858i
$330$	−2.64114	+	8.28991i	−0.145390	+	0.456344i
$331$	−17.1491			−0.942598			−0.471299	−	0.881973i	$-0.656215\pi$
$331$	−17.1491			−0.942598			−0.471299	+	0.881973i	$0.656215\pi$
$332$			4.61136i			0.253081i
$333$		−	1.11476i		−	0.0610887i
$334$		−	28.4713i		−	1.55788i
$335$	−0.683568	−	4.37890i	−0.0373473	−	0.239245i
$336$	4.05940	−	4.75718i	0.221458	−	0.259525i
$337$	−26.9388			−1.46745			−0.733724	−	0.679448i	$-0.762219\pi$
$337$	−26.9388			−1.46745			−0.733724	+	0.679448i	$0.762219\pi$
$338$	−1.42096			−0.0772900
$339$			17.3740i			0.943625i
$340$	0.667287	+	4.27461i	0.0361887	+	0.231823i
$341$	−2.14410	−	1.07108i	−0.116109	−	0.0580021i
$342$	6.24259			0.337560
$343$	15.8039	+	9.65595i	0.853329	+	0.521372i
$344$	22.4711			1.21156
$345$	−2.03022	−	13.0055i	−0.109303	−	0.700190i
$346$		−	0.106206i		−	0.00570968i
$347$	−27.4275			−1.47238			−0.736192	−	0.676773i	$-0.763378\pi$
$347$	−27.4275			−1.47238			−0.736192	+	0.676773i	$0.763378\pi$
$348$		−	3.62666i		−	0.194409i
$349$	−3.35671			−0.179681			−0.0898403	−	0.995956i	$-0.528636\pi$
$349$	−3.35671			−0.179681			−0.0898403	+	0.995956i	$0.528636\pi$
$350$	5.99652	−	14.3143i	0.320528	−	0.765132i
$351$		−	3.43348i		−	0.183266i
$352$	−5.01417	+	10.0374i	−0.267256	+	0.534997i
$353$	−17.3099			−0.921312			−0.460656	−	0.887579i	$-0.652386\pi$
$353$	−17.3099			−0.921312			−0.460656	+	0.887579i	$0.652386\pi$
$354$		−	17.3122i		−	0.920130i
$355$	−33.0244	+	5.15527i	−1.75275	+	0.273613i
$356$			2.27734i			0.120699i
$357$	6.24371	+	5.32788i	0.330452	+	0.281981i
$358$	25.8840			1.36801
$359$		−	1.11316i		−	0.0587501i	−0.999568	−	0.0293751i	$-0.990648\pi$
$359$		−	1.11316i		−	0.0587501i	0.999568	−	0.0293751i	$-0.00935171\pi$
$360$	6.80029	−	1.06156i	0.358407	−	0.0559491i
$361$	9.31434			0.490228
$362$		−	6.37952i		−	0.335300i
$363$	−6.60637	−	8.79522i	−0.346745	−	0.461629i
$364$	−4.30970	−	3.67755i	−0.225890	−	0.192756i
$365$	−2.50972	−	16.0771i	−0.131365	−	0.841514i
$366$	−6.16916			−0.322467
$367$	−3.68482			−0.192346			−0.0961731	−	0.995365i	$-0.530660\pi$
$367$	−3.68482			−0.192346			−0.0961731	+	0.995365i	$0.530660\pi$
$368$			13.9143i			0.725332i
$369$	3.34512			0.174140
$370$	0.451043	+	2.88936i	0.0234486	+	0.150211i
$371$	23.6346	+	20.1679i	1.22705	+	1.04707i
$372$			0.450691i			0.0233672i
$373$	4.82270			0.249710			0.124855	−	0.992175i	$-0.460153\pi$
$373$	4.82270			0.249710			0.124855	+	0.992175i	$0.460153\pi$
$374$	10.7986	+	5.39440i	0.558381	+	0.278938i
$375$	9.99541	−	5.00918i	0.516161	−	0.258673i
$376$	20.3297			1.04842
$377$	19.9658			1.02829
$378$	2.01480	−	2.36113i	0.103630	−	0.121443i
$379$	−15.4604			−0.794148			−0.397074	−	0.917787i	$-0.629974\pi$
$379$	−15.4604			−0.794148			−0.397074	+	0.917787i	$0.629974\pi$
$380$	7.33187	−	1.14454i	0.376117	−	0.0587137i
$381$	6.23748			0.319556
$382$	22.2619			1.13902
$383$	−4.92470			−0.251640			−0.125820	−	0.992053i	$-0.540156\pi$
$383$	−4.92470			−0.251640			−0.125820	+	0.992053i	$0.540156\pi$
$384$	−3.43617			−0.175351
$385$	10.3552	+	16.6664i	0.527749	+	0.849401i
$386$	19.1499			0.974704
$387$	7.30051			0.371106
$388$	2.35344			0.119478
$389$	−8.29383			−0.420514			−0.210257	−	0.977646i	$-0.567430\pi$
$389$	−8.29383			−0.420514			−0.210257	+	0.977646i	$0.567430\pi$
$390$	1.38922	+	8.89924i	0.0703456	+	0.450630i
$391$	−18.2622			−0.923560
$392$	−3.38928	−	21.2778i	−0.171185	−	1.07469i
$393$	2.79723			0.141102
$394$	−18.9011			−0.952221
$395$	−3.97693	−	25.4760i	−0.200101	−	1.28184i
$396$	−0.924381	+	1.85044i	−0.0464519	+	0.0929880i
$397$	32.3860			1.62541			0.812704	−	0.582677i	$-0.197995\pi$
$397$	32.3860			1.62541			0.812704	+	0.582677i	$0.197995\pi$
$398$			28.7393i			1.44057i
$399$	9.13845	−	10.7093i	0.457495	−	0.536135i
$400$	−11.2562	+	3.60207i	−0.562809	+	0.180104i
$401$	−18.6858			−0.933124			−0.466562	−	0.884488i	$-0.654508\pi$
$401$	−18.6858			−0.933124			−0.466562	+	0.884488i	$0.654508\pi$
$402$			2.32525i			0.115973i
$403$	−2.48118			−0.123597
$404$	−9.53698			−0.474482
$405$	2.20931	−	0.344884i	0.109782	−	0.0171374i
$406$	13.7300	+	11.7161i	0.681410	+	0.581461i
$407$	−3.30753	−	1.65227i	−0.163948	−	0.0818998i
$408$		−	9.54894i		−	0.472743i
$409$	−7.69234			−0.380362			−0.190181	−	0.981749i	$-0.560907\pi$
$409$	−7.69234			−0.380362			−0.190181	+	0.981749i	$0.560907\pi$
$410$	−8.67022	+	1.35346i	−0.428192	+	0.0668429i
$411$		−	18.1264i		−	0.894111i
$412$	−0.842830			−0.0415232
$413$	−29.6994	−	25.3431i	−1.46141	−	1.24705i
$414$			6.90606i			0.339414i
$415$	−2.55004	−	16.3354i	−0.125177	−	0.801876i
$416$			11.6155i			0.569496i
$417$	12.5540			0.614771
$418$	9.25255	−	18.5219i	0.452557	−	0.905934i
$419$		−	7.32643i		−	0.357919i	−0.983856	−	0.178960i	$-0.942727\pi$
$419$		−	7.32643i		−	0.357919i	0.983856	−	0.178960i	$-0.0572732\pi$
$420$	1.93346	−	3.14252i	0.0943433	−	0.153339i
$421$	−1.91887			−0.0935201			−0.0467601	−	0.998906i	$-0.514890\pi$
$421$	−1.91887			−0.0935201			−0.0467601	+	0.998906i	$0.514890\pi$
$422$		−	15.3561i		−	0.747524i
$423$	6.60481			0.321137
$424$		−	36.1461i		−	1.75541i
$425$	−4.72765	−	14.7735i	−0.229325	−	0.716621i
$426$	17.5364			0.849639
$427$	−9.03097	+	10.5833i	−0.437039	+	0.512164i
$428$	1.10733			0.0535251
$429$	−10.1872	−	5.08899i	−0.491842	−	0.245699i
$430$	−18.9222	+	2.95385i	−0.912509	+	0.142447i
$431$			7.47238i			0.359932i	0.983673	+	0.179966i	$0.0575988\pi$
$431$			7.47238i			0.359932i	−0.983673	+	0.179966i	$0.942401\pi$
$432$	−2.36370			−0.113723
$433$	−13.5598			−0.651644			−0.325822	−	0.945431i	$-0.605641\pi$
$433$	−13.5598			−0.651644			−0.325822	+	0.945431i	$0.605641\pi$
$434$	−1.70625	−	1.45598i	−0.0819028	−	0.0698893i
$435$	2.00552	+	12.8472i	0.0961571	+	0.615977i
$436$		−	1.20935i		−	0.0579175i
$437$			31.3236i			1.49841i
$438$			8.53714i			0.407920i
$439$	30.6807			1.46431			0.732156	−	0.681137i	$-0.238514\pi$
$439$	30.6807			1.46431			0.732156	+	0.681137i	$0.238514\pi$
$440$	6.92949	−	21.7500i	0.330350	−	1.03689i
$441$	−1.10113	−	6.91285i	−0.0524346	−	0.329183i
$442$	12.4963			0.594387
$443$			29.3213i			1.39310i	0.717509	+	0.696549i	$0.245282\pi$
$443$			29.3213i			1.39310i	−0.717509	+	0.696549i	$0.754718\pi$
$444$			0.695245i			0.0329949i
$445$	−1.25935	−	8.06733i	−0.0596990	−	0.382428i
$446$	−5.39365			−0.255397
$447$		−	3.14282i		−	0.148650i
$448$	−14.9349	+	17.5021i	−0.705606	+	0.826895i
$449$	14.5550			0.686892			0.343446	−	0.939173i	$-0.388406\pi$
$449$	14.5550			0.686892			0.343446	+	0.939173i	$0.388406\pi$
$450$	−5.58677	+	1.78781i	−0.263363	+	0.0842783i
$451$	4.95802	−	9.92503i	0.233464	−	0.467352i
$452$		−	10.8356i		−	0.509665i
$453$			0.939283i			0.0441314i
$454$			22.2787i			1.04559i
$455$	17.3005	+	10.6443i	0.811060	+	0.499011i
$456$	−16.3785			−0.766993
$457$	−20.6452			−0.965741			−0.482870	−	0.875692i	$-0.660406\pi$
$457$	−20.6452			−0.965741			−0.482870	+	0.875692i	$0.660406\pi$
$458$		−	23.1798i		−	1.08312i
$459$		−	3.10231i		−	0.144803i
$460$	1.26618	+	8.11111i	0.0590361	+	0.378182i
$461$	7.59495			0.353732			0.176866	−	0.984235i	$-0.443404\pi$
$461$	7.59495			0.353732			0.176866	+	0.984235i	$0.443404\pi$
$462$	−4.01924	−	9.47751i	−0.186992	−	0.440934i
$463$		−	28.5815i		−	1.32829i	−0.747602	−	0.664147i	$-0.768795\pi$
$463$		−	28.5815i		−	1.32829i	0.747602	−	0.664147i	$-0.231205\pi$
$464$		−	13.7450i		−	0.638095i
$465$	−0.249229	−	1.59655i	−0.0115577	−	0.0740380i
$466$	−22.3724			−1.03638
$467$	−22.0580			−1.02072			−0.510360	−	0.859961i	$-0.670488\pi$
$467$	−22.0580			−1.02072			−0.510360	+	0.859961i	$0.670488\pi$
$468$			2.14136i			0.0989843i
$469$	3.98901	+	3.40391i	0.184196	+	0.157178i
$470$	−17.1190	+	2.67236i	−0.789640	+	0.123267i
$471$	12.9739			0.597806
$472$			45.4214i			2.09069i
$473$	10.8206	−	21.6607i	0.497530	−	0.995962i
$474$			13.5281i			0.621364i
$475$	−25.3398	+	8.10893i	−1.16267	+	0.372063i
$476$	−3.89401	−	3.32284i	−0.178482	−	0.152302i
$477$		−	11.7433i		−	0.537690i
$478$		−	27.1660i		−	1.24254i
$479$	30.3084			1.38483			0.692413	−	0.721501i	$-0.256548\pi$
$479$	30.3084			1.38483			0.692413	+	0.721501i	$0.256548\pi$
$480$	−7.47411	+	1.16675i	−0.341145	+	0.0532544i
$481$	−3.82752			−0.174520
$482$	18.4273			0.839339
$483$	11.8475	+	10.1097i	0.539080	+	0.460007i
$484$	4.12019	+	5.48531i	0.187281	+	0.249332i
$485$	−8.33691	+	1.30143i	−0.378559	+	0.0590950i
$486$	−1.17317			−0.0532161
$487$		−	10.1505i		−	0.459965i	−0.973195	−	0.229982i	$-0.926133\pi$
$487$		−	10.1505i		−	0.459965i	0.973195	−	0.229982i	$-0.0738668\pi$
$488$	16.1858			0.732699
$489$			9.34655i			0.422665i
$490$	5.65101	+	17.4719i	0.255286	+	0.789300i
$491$		−	34.2469i		−	1.54554i	−0.634685	−	0.772771i	$-0.718870\pi$
$491$		−	34.2469i		−	1.54554i	0.634685	−	0.772771i	$-0.281130\pi$
$492$	−2.08625			−0.0940554
$493$	18.0400			0.812482
$494$		−	21.4338i		−	0.964352i
$495$	2.25129	−	7.06624i	0.101188	−	0.317604i
$496$			1.70811i			0.0766965i
$497$	25.6713	−	30.0840i	1.15151	−	1.34945i
$498$			8.67432i			0.388706i
$499$	3.09687			0.138635			0.0693174	−	0.997595i	$-0.477918\pi$
$499$	3.09687			0.138635			0.0693174	+	0.997595i	$0.477918\pi$
$500$	−6.23383	+	3.12407i	−0.278785	+	0.139713i
$501$			24.2687i			1.08424i
$502$		−	32.5114i		−	1.45105i
$503$			19.8339i			0.884350i	0.896929	+	0.442175i	$0.145793\pi$
$503$			19.8339i			0.884350i	−0.896929	+	0.442175i	$0.854207\pi$
$504$	−5.28616	+	6.19481i	−0.235464	+	0.275939i
$505$	33.7842	−	5.27387i	1.50337	−	0.234684i
$506$	20.4904	+	10.2359i	0.910908	+	0.455042i
$507$	1.21121			0.0537918
$508$	−3.89013			−0.172596
$509$			1.89918i			0.0841798i	0.999114	+	0.0420899i	$0.0134016\pi$
$509$			1.89918i			0.0841798i	−0.999114	+	0.0420899i	$0.986598\pi$
$510$	1.25522	+	8.04087i	0.0555821	+	0.356056i
$511$	14.6457	+	12.4974i	0.647886	+	0.552854i
$512$	22.5474			0.996463
$513$	−5.32112			−0.234933
$514$	−9.55753			−0.421564
$515$	2.98567	−	0.466078i	0.131564	−	0.0205379i
$516$	−4.55311			−0.200439
$517$	9.78941	−	19.5966i	0.430538	−	0.861856i
$518$	−2.63210	−	2.24602i	−0.115648	−	0.0986846i
$519$			0.0905291i			0.00397379i
$520$	−3.64484	−	23.3487i	−0.159837	−	1.02391i
$521$		−	8.01305i		−	0.351058i	−0.984474	−	0.175529i	$-0.943836\pi$
$521$		−	8.01305i		−	0.351058i	0.984474	−	0.175529i	$-0.0561636\pi$
$522$		−	6.82204i		−	0.298592i
$523$			5.57803i			0.243910i	0.992536	+	0.121955i	$0.0389164\pi$
$523$			5.57803i			0.243910i	−0.992536	+	0.121955i	$0.961084\pi$
$524$	−1.74455			−0.0762109
$525$	−5.11138	+	12.2014i	−0.223079	+	0.532512i
$526$	−13.5518			−0.590888
$527$	−2.24186			−0.0976572
$528$	−3.50339	+	7.01313i	−0.152465	+	0.305207i
$529$	−11.6527			−0.506640
$530$	4.75145	+	30.4375i	0.206390	+	1.32212i
$531$			14.7567i			0.640387i
$532$	−5.69938	+	6.67906i	−0.247099	+	0.289574i
$533$		−	11.4854i		−	0.497488i
$534$			4.28385i			0.185380i
$535$	−3.92267	+	0.612348i	−0.169592	+	0.0264741i
$536$		−	6.10068i		−	0.263509i
$537$	−22.0633			−0.952100
$538$		−	19.9209i		−	0.858850i
$539$	−22.1426	−	6.97893i	−0.953749	−	0.300604i
$540$	−1.37788	+	0.215094i	−0.0592945	+	0.00925617i
$541$		−	12.9502i		−	0.556774i	−0.960469	−	0.278387i	$-0.910200\pi$
$541$		−	12.9502i		−	0.556774i	0.960469	−	0.278387i	$-0.0897997\pi$
$542$	21.5487			0.925595
$543$			5.43785i			0.233360i
$544$			10.4951i			0.449975i
$545$	0.668762	+	4.28406i	0.0286466	+	0.183509i
$546$	−8.10688	−	6.91776i	−0.346942	−	0.296053i
$547$	−9.04582			−0.386771			−0.193386	−	0.981123i	$-0.561947\pi$
$547$	−9.04582			−0.386771			−0.193386	+	0.981123i	$0.561947\pi$
$548$			11.3049i			0.482922i
$549$	5.25854			0.224429
$550$	−2.97605	+	19.2259i	−0.126899	+	0.819794i
$551$		−	30.9425i		−	1.31820i
$552$		−	18.1192i		−	0.771205i
$553$	23.2077	+	19.8036i	0.986891	+	0.842134i
$554$	13.6974			0.581946
$555$	−0.384465	−	2.46286i	−0.0163196	−	0.104543i
$556$	−7.82953			−0.332046
$557$	−35.0800			−1.48639			−0.743193	−	0.669077i	$-0.766690\pi$
$557$	−35.0800			−1.48639			−0.743193	+	0.669077i	$0.766690\pi$
$558$			0.847785i			0.0358896i
$559$		−	25.0662i		−	1.06019i
$560$	7.32779	−	11.9101i	0.309656	−	0.503294i
$561$	−9.20460	−	4.59813i	−0.388618	−	0.194133i
$562$		−	8.84870i		−	0.373260i
$563$		−	0.289494i		−	0.0122007i	−0.999981	−	0.00610035i	$-0.998058\pi$
$563$		−	0.289494i		−	0.0122007i	0.999981	−	0.00610035i	$-0.00194181\pi$
$564$	−4.11922			−0.173450
$565$	5.99201	+	38.3845i	0.252086	+	1.61485i
$566$		−	5.74546i		−	0.241500i
$567$	−1.71739	+	2.01260i	−0.0721237	+	0.0845213i
$568$	−46.0096			−1.93052
$569$			3.15902i			0.132433i	0.997805	+	0.0662165i	$0.0210928\pi$
$569$			3.15902i			0.132433i	−0.997805	+	0.0662165i	$0.978907\pi$
$570$	13.7918	−	2.15297i	0.577676	−	0.0901780i
$571$		−	13.2386i		−	0.554020i	−0.960867	−	0.277010i	$-0.910656\pi$
$571$		−	13.2386i		−	0.554020i	0.960867	−	0.277010i	$-0.0893435\pi$
$572$	6.35344	+	3.17384i	0.265651	+	0.132705i
$573$	−18.9758			−0.792726
$574$	6.73974	−	7.89825i	0.281311	−	0.329667i
$575$	−8.97076	−	28.0329i	−0.374106	−	1.16905i
$576$	8.69624			0.362343
$577$	30.8410			1.28393			0.641964	−	0.766734i	$-0.278120\pi$
$577$	30.8410			1.28393			0.641964	+	0.766734i	$0.278120\pi$
$578$	−8.65294			−0.359915
$579$	−16.3232			−0.678369
$580$	−1.25078	−	8.01242i	−0.0519358	−	0.332698i
$581$	14.8810	+	12.6982i	0.617368	+	0.526812i
$582$	4.42700			0.183505
$583$	−34.8427	−	17.4056i	−1.44304	−	0.720865i
$584$		−	22.3986i		−	0.926862i
$585$	−1.18415	−	7.58563i	−0.0489587	−	0.313627i
$586$		−	8.95280i		−	0.369837i
$587$	35.0865			1.44818			0.724088	−	0.689708i	$-0.242261\pi$
$587$	35.0865			1.44818			0.724088	+	0.689708i	$0.242261\pi$
$588$	0.686739	+	4.31133i	0.0283206	+	0.177796i
$589$			3.84528i			0.158442i
$590$	−5.97069	−	38.2479i	−0.245809	−	1.57464i
$591$	16.1111			0.662721
$592$			2.63497i			0.108296i
$593$			41.1114i			1.68824i	0.536151	+	0.844122i	$0.319878\pi$
$593$			41.1114i			1.68824i	−0.536151	+	0.844122i	$0.680122\pi$
$594$	−1.73883	+	3.48082i	−0.0713452	+	0.142820i
$595$	15.6318	+	9.61759i	0.640841	+	0.394283i
$596$			1.96008i			0.0802880i
$597$		−	24.4971i		−	1.00260i
$598$	23.7118			0.969648
$599$	11.6236			0.474927			0.237464	−	0.971396i	$-0.423684\pi$
$599$	11.6236			0.474927			0.237464	+	0.971396i	$0.423684\pi$
$600$	14.6578	−	4.69063i	0.598404	−	0.191494i
$601$	24.3506			0.993282			0.496641	−	0.867956i	$-0.334567\pi$
$601$	24.3506			0.993282			0.496641	+	0.867956i	$0.334567\pi$
$602$	14.7090	−	17.2374i	0.599495	−	0.702545i
$603$		−	1.98202i		−	0.0807141i
$604$		−	0.585802i		−	0.0238360i
$605$	−17.6289	−	17.1529i	−0.716715	−	0.697366i
$606$	−17.9398			−0.728754
$607$		−	14.1378i		−	0.573834i	−0.957955	−	0.286917i	$-0.907370\pi$
$607$		−	14.1378i		−	0.573834i	0.957955	−	0.286917i	$-0.0926305\pi$
$608$	18.0014			0.730052
$609$	−11.7034	−	9.98670i	−0.474244	−	0.404682i
$610$	−13.6296	+	2.12765i	−0.551846	+	0.0861460i
$611$		−	22.6775i		−	0.917432i
$612$			1.93481i			0.0782102i
$613$	3.49651			0.141223			0.0706114	−	0.997504i	$-0.477505\pi$
$613$	3.49651			0.141223			0.0706114	+	0.997504i	$0.477505\pi$
$614$		−	35.1829i		−	1.41987i
$615$	7.39042	−	1.15368i	0.298010	−	0.0465209i
$616$	10.5452	+	24.8659i	0.424876	+	1.00187i
$617$			3.42766i			0.137992i	0.997617	+	0.0689961i	$0.0219796\pi$
$617$			3.42766i			0.137992i	−0.997617	+	0.0689961i	$0.978020\pi$
$618$	−1.58543			−0.0637753
$619$		−	0.639680i		−	0.0257109i	−0.999917	−	0.0128555i	$-0.995908\pi$
$619$		−	0.639680i		−	0.0257109i	0.999917	−	0.0128555i	$-0.00409213\pi$
$620$	0.155436	+	0.995717i	0.00624247	+	0.0399889i
$621$		−	5.88666i		−	0.236223i
$622$		−	12.1639i		−	0.487729i
$623$	7.34905	+	6.27109i	0.294433	+	0.251246i
$624$			8.11571i			0.324888i
$625$	20.3554	−	14.5141i	0.814215	−	0.580564i
$626$	−20.3531			−0.813475
$627$	−7.88678	+	15.7879i	−0.314968	+	0.630506i
$628$	−8.09142			−0.322883
$629$	−3.45834			−0.137893
$630$	3.63699	−	5.91133i	0.144901	−	0.235513i
$631$	44.9853			1.79084			0.895418	−	0.445226i	$-0.146877\pi$
$631$	44.9853			1.79084			0.895418	+	0.445226i	$0.146877\pi$
$632$		−	35.4931i		−	1.41184i
$633$			13.0894i			0.520257i
$634$			23.5657i			0.935912i
$635$	13.7805	−	2.15121i	0.546864	−	0.0853682i
$636$			7.32396i			0.290414i
$637$	−23.7351	+	3.78070i	−0.940421	+	0.149797i
$638$	−20.2411	−	10.1114i	−0.801352	−	0.400314i
$639$	−14.9478			−0.591327
$640$	−7.59156	+	1.18508i	−0.300083	+	0.0468444i
$641$	26.6120			1.05111			0.525556	−	0.850759i	$-0.323857\pi$
$641$	26.6120			1.05111			0.525556	+	0.850759i	$0.323857\pi$
$642$	2.08298			0.0822088
$643$	32.0498			1.26392			0.631960	−	0.775001i	$-0.282251\pi$
$643$	32.0498			1.26392			0.631960	+	0.775001i	$0.282251\pi$
$644$	−7.38892	−	6.30511i	−0.291164	−	0.248456i
$645$	16.1291	−	2.51783i	0.635083	−	0.0991396i
$646$		−	19.3664i		−	0.761962i
$647$	2.30057			0.0904447			0.0452223	−	0.998977i	$-0.485600\pi$
$647$	2.30057			0.0904447			0.0452223	+	0.998977i	$0.485600\pi$
$648$	3.07801			0.120916
$649$	43.7834	+	21.8719i	1.71865	+	0.858547i
$650$	6.13842	+	19.1821i	0.240768	+	0.752382i
$651$	1.45439	+	1.24106i	0.0570022	+	0.0486411i
$652$		−	5.82916i		−	0.228287i
$653$			30.8146i			1.20587i	0.797791	+	0.602934i	$0.206002\pi$
$653$			30.8146i			1.20587i	−0.797791	+	0.602934i	$0.793998\pi$
$654$		−	2.27489i		−	0.0889551i
$655$	6.17995	−	0.964721i	0.241471	−	0.0376948i
$656$	−7.90686			−0.308711
$657$		−	7.27698i		−	0.283902i
$658$	13.3073	−	15.5948i	0.518774	−	0.607948i
$659$			42.0492i			1.63801i	0.573789	+	0.819003i	$0.305473\pi$
$659$			42.0492i			1.63801i	−0.573789	+	0.819003i	$0.694527\pi$
$660$	−1.40406	+	4.40700i	−0.0546529	+	0.171542i
$661$			10.9191i			0.424704i	0.977193	+	0.212352i	$0.0681124\pi$
$661$			10.9191i			0.424704i	−0.977193	+	0.212352i	$0.931888\pi$
$662$	20.1188			0.781939
$663$	−10.6517			−0.413678
$664$		−	22.7586i		−	0.883203i
$665$	16.4962	−	26.8119i	0.639696	−	1.03972i
$666$			1.30781i			0.0506766i
$667$	34.2311			1.32543
$668$		−	15.1356i		−	0.585615i
$669$	4.59749			0.177749
$670$	0.801942	+	5.13720i	0.0309817	+	0.198467i
$671$	7.79402	−	15.6022i	0.300885	−	0.602315i
$672$	5.80995	−	6.80864i	0.224124	−	0.262649i
$673$	−16.5791			−0.639078			−0.319539	−	0.947573i	$-0.603528\pi$
$673$	−16.5791			−0.639078			−0.319539	+	0.947573i	$0.603528\pi$
$674$	31.6038			1.21733
$675$	4.76211	−	1.52391i	0.183294	−	0.0586555i
$676$	−0.755396			−0.0290537
$677$		−	38.2674i		−	1.47074i	−0.677667	−	0.735369i	$-0.737009\pi$
$677$		−	38.2674i		−	1.47074i	0.677667	−	0.735369i	$-0.262991\pi$
$678$		−	20.3826i		−	0.782791i
$679$	6.48064	−	7.59461i	0.248704	−	0.291455i
$680$	−3.29328	−	21.0966i	−0.126292	−	0.809017i
$681$		−	18.9902i		−	0.727705i
$682$	2.51539	+	1.25656i	0.0963194	+	0.0481161i
$683$		−	2.74520i		−	0.105042i	−0.998620	−	0.0525211i	$-0.983274\pi$
$683$		−	2.74520i		−	0.105042i	0.998620	−	0.0525211i	$-0.0167257\pi$
$684$	3.31862			0.126891
$685$	−6.25152	−	40.0469i	−0.238858	−	1.53011i
$686$	−18.5407	−	11.3281i	−0.707886	−	0.432508i
$687$			19.7583i			0.753825i
$688$	−17.2562			−0.657886
$689$	−40.3205			−1.53609
$690$	2.38179	+	15.2576i	0.0906732	+	0.580848i
$691$		−	18.2714i		−	0.695079i	−0.937665	−	0.347539i	$-0.887017\pi$
$691$		−	18.2714i		−	0.695079i	0.937665	−	0.347539i	$-0.112983\pi$
$692$		−	0.0564602i		−	0.00214630i
$693$	3.42596	+	8.07854i	0.130141	+	0.306878i
$694$	32.1771			1.22143
$695$	27.7356	−	4.32967i	1.05207	−	0.164234i
$696$			17.8988i			0.678451i
$697$		−	10.3776i		−	0.393080i
$698$	3.93799			0.149055
$699$	19.0700			0.721295
$700$	3.18781	−	7.60963i	0.120488	−	0.287617i
$701$			8.67328i			0.327585i	0.986495	+	0.163793i	$0.0523728\pi$
$701$			8.67328i			0.327585i	−0.986495	+	0.163793i	$0.947627\pi$
$702$			4.02806i			0.152029i
$703$			5.93180i			0.223722i
$704$	12.8893	−	25.8019i	0.485782	−	0.972445i
$705$	14.5921	−	2.27789i	0.549569	−	0.0857905i
$706$	20.3075			0.764281
$707$	−26.2619	+	30.7761i	−0.987679	+	1.15746i
$708$		−	9.20331i		−	0.345882i
$709$	−26.4116			−0.991907			−0.495954	−	0.868349i	$-0.665181\pi$
$709$	−26.4116			−0.991907			−0.495954	+	0.868349i	$0.665181\pi$
$710$	38.7433	−	6.04802i	1.45401	−	0.226978i
$711$		−	11.5312i		−	0.432453i
$712$		−	11.2394i		−	0.421215i
$713$	−4.25396			−0.159312
$714$	−7.32494	−	6.25051i	−0.274129	−	0.233920i
$715$	−24.2618	−	7.72975i	−0.907339	−	0.289076i
$716$	13.7602			0.514242
$717$			23.1560i			0.864777i
$718$			1.30592i			0.0487366i
$719$			52.5438i			1.95955i	0.200091	+	0.979777i	$0.435876\pi$
$719$			52.5438i			1.95955i	−0.200091	+	0.979777i	$0.564124\pi$
$720$	−5.22214	+	0.815202i	−0.194618	+	0.0303808i
$721$	−2.32089	+	2.71984i	−0.0864345	+	0.101292i
$722$	−10.9273			−0.406673
$723$	−15.7072			−0.584158
$724$		−	3.39142i		−	0.126041i
$725$	8.86162	+	27.6918i	0.329112	+	1.02845i
$726$	7.75041	+	10.3183i	0.287645	+	0.382948i
$727$	−30.1240			−1.11724			−0.558619	−	0.829424i	$-0.688669\pi$
$727$	−30.1240			−1.11724			−0.558619	+	0.829424i	$0.688669\pi$
$728$	21.2698	+	18.1499i	0.788310	+	0.672681i
$729$	1.00000			0.0370370
$730$	2.94433	+	18.8612i	0.108974	+	0.698084i
$731$		−	22.6484i		−	0.837682i
$732$	−3.27959			−0.121217
$733$		−	12.6817i		−	0.468408i	−0.972187	−	0.234204i	$-0.924752\pi$
$733$		−	12.6817i		−	0.468408i	0.972187	−	0.234204i	$-0.0752484\pi$
$734$	4.32293			0.159562
$735$	−4.81687	−	14.8929i	−0.177673	−	0.549332i
$736$			19.9146i			0.734061i
$737$	−5.88068	−	2.93768i	−0.216618	−	0.108211i
$738$	−3.92440			−0.144459
$739$		−	16.2962i		−	0.599464i	−0.954023	−	0.299732i	$-0.903103\pi$
$739$		−	16.2962i		−	0.599464i	0.954023	−	0.299732i	$-0.0968973\pi$
$740$	0.239779	+	1.53601i	0.00881445	+	0.0564649i
$741$			18.2700i			0.671164i
$742$	−27.7275	−	23.6604i	−1.01791	−	0.868601i
$743$	−3.73982			−0.137201			−0.0686003	−	0.997644i	$-0.521853\pi$
$743$	−3.73982			−0.137201			−0.0686003	+	0.997644i	$0.521853\pi$
$744$		−	2.22431i		−	0.0815471i
$745$	−1.08391	−	6.94346i	−0.0397114	−	0.254389i
$746$	−5.65786			−0.207149
$747$		−	7.39391i		−	0.270529i
$748$	5.74063	+	2.86772i	0.209898	+	0.104854i
$749$	3.04926	−	3.57340i	0.111417	−	0.130569i
$750$	−11.7263	+	5.87662i	−0.428185	+	0.214584i
$751$	−21.8888			−0.798735			−0.399367	−	0.916791i	$-0.630770\pi$
$751$	−21.8888			−0.798735			−0.399367	+	0.916791i	$0.630770\pi$
$752$	−15.6118			−0.569302
$753$			27.7124i			1.00990i
$754$	−23.4233			−0.853027
$755$	0.323944	+	2.07517i	0.0117895	+	0.0755231i
$756$	1.07109	−	1.25520i	0.0389550	−	0.0456511i
$757$		−	49.3842i		−	1.79490i	−0.441118	−	0.897449i	$-0.645418\pi$
$757$		−	49.3842i		−	1.79490i	0.441118	−	0.897449i	$-0.354582\pi$
$758$	18.1377			0.658791
$759$	−17.4658	−	8.72500i	−0.633969	−	0.316697i
$760$	−36.1852	+	5.64868i	−1.31257	+	0.204899i
$761$	−26.4800			−0.959898			−0.479949	−	0.877296i	$-0.659345\pi$
$761$	−26.4800			−0.959898			−0.479949	+	0.877296i	$0.659345\pi$
$762$	−7.31763			−0.265090
$763$	−3.90262	−	3.33018i	−0.141284	−	0.120561i
$764$	11.8346			0.428162
$765$	−1.06994	−	6.85396i	−0.0386837	−	0.247806i
$766$	5.77751			0.208750
$767$	50.6669			1.82948
$768$	−13.3613			−0.482133
$769$	2.91216			0.105015			0.0525075	−	0.998621i	$-0.483279\pi$
$769$	2.91216			0.105015			0.0525075	+	0.998621i	$0.483279\pi$
$770$	−12.1484	−	19.5526i	−0.437798	−	0.704626i
$771$	8.14674			0.293398
$772$	10.1803			0.366396
$773$	46.6347			1.67733			0.838666	−	0.544646i	$-0.183336\pi$
$773$	46.6347			1.67733			0.838666	+	0.544646i	$0.183336\pi$
$774$	−8.56475			−0.307854
$775$	−1.10125	−	3.44131i	−0.0395580	−	0.123616i
$776$	−11.6150			−0.416954
$777$	2.24358	+	1.91449i	0.0804879	+	0.0686819i
$778$	9.73008			0.348840
$779$	−17.7998			−0.637744
$780$	0.738521	+	4.73092i	0.0264433	+	0.169394i
$781$	−22.1552	+	44.3505i	−0.792774	+	1.58698i
$782$	21.4247			0.766146
$783$			5.81504i			0.207813i
$784$	2.60273	+	16.3399i	0.0929546	+	0.583567i
$785$	28.6634	−	4.47450i	1.02304	−	0.159702i
$786$	−3.28163			−0.117052
$787$			23.3539i			0.832478i	0.909255	+	0.416239i	$0.136652\pi$
$787$			23.3539i			0.832478i	−0.909255	+	0.416239i	$0.863348\pi$
$788$	−10.0480			−0.357945
$789$	11.5514			0.411242
$790$	4.66562	+	29.8877i	0.165995	+	1.06336i
$791$	−34.9669	−	29.8379i	−1.24328	−	1.06091i
$792$	4.56212	−	9.13252i	0.162108	−	0.324510i
$793$		−	18.0551i		−	0.641155i
$794$	−37.9943			−1.34837
$795$	−4.05009	−	25.9447i	−0.143642	−	0.920163i
$796$			15.2781i			0.541518i
$797$	−31.0609			−1.10023			−0.550117	−	0.835087i	$-0.685417\pi$
$797$	−31.0609			−1.10023			−0.550117	+	0.835087i	$0.685417\pi$
$798$	−10.7210	+	12.5638i	−0.379518	+	0.444755i
$799$		−	20.4901i		−	0.724889i
$800$	−16.1102	+	5.15541i	−0.569583	+	0.182271i
$801$		−	3.65152i		−	0.129020i
$802$	21.9216			0.774080
$803$	−21.5909	−	10.7857i	−0.761927	−	0.380619i
$804$			1.23613i			0.0435948i
$805$	29.6615	+	18.2495i	1.04543	+	0.643209i
$806$	2.91085			0.102530
$807$			16.9804i			0.597737i
$808$	47.0681			1.65585
$809$			34.0603i			1.19750i	0.800938	+	0.598748i	$0.204335\pi$
$809$			34.0603i			1.19750i	−0.800938	+	0.598748i	$0.795665\pi$
$810$	−2.59190	+	0.404608i	−0.0910701	+	0.0142165i
$811$	−52.8198			−1.85475			−0.927377	−	0.374129i	$-0.877942\pi$
$811$	−52.8198			−1.85475			−0.927377	+	0.374129i	$0.877942\pi$
$812$	7.29902	+	6.22840i	0.256146	+	0.218574i
$813$	−18.3679			−0.644190
$814$	3.88029	+	1.93839i	0.136004	+	0.0679405i
$815$	3.22348	+	20.6494i	0.112914	+	0.723318i
$816$			7.33292i			0.256703i
$817$	−38.8469			−1.35908
$818$	9.02443			0.315532
$819$	6.91023	+	5.89663i	0.241463	+	0.206045i
$820$	−4.60918	+	0.719515i	−0.160959	+	0.0251266i
$821$		−	7.76941i		−	0.271154i	−0.990767	−	0.135577i	$-0.956711\pi$
$821$		−	7.76941i		−	0.271154i	0.990767	−	0.135577i	$-0.0432888\pi$
$822$			21.2654i			0.741716i
$823$			1.80568i			0.0629422i	0.999505	+	0.0314711i	$0.0100192\pi$
$823$			1.80568i			0.0629422i	−0.999505	+	0.0314711i	$0.989981\pi$
$824$	4.15964			0.144908
$825$	2.53676	−	16.3879i	0.0883185	−	0.570555i
$826$	34.8425	+	29.7318i	1.21232	+	1.03450i
$827$	−52.6701			−1.83152			−0.915760	−	0.401726i	$-0.868411\pi$
$827$	−52.6701			−1.83152			−0.915760	+	0.401726i	$0.868411\pi$
$828$			3.67133i			0.127587i
$829$		−	7.36227i		−	0.255702i	−0.991793	−	0.127851i	$-0.959192\pi$
$829$		−	7.36227i		−	0.255702i	0.991793	−	0.127851i	$-0.0408079\pi$
$830$	2.99164	+	19.1643i	0.103841	+	0.665202i
$831$	−11.6755			−0.405019
$832$		−	29.8584i		−	1.03515i
$833$	−21.4458	+	3.41603i	−0.743053	+	0.118359i
$834$	−14.7280			−0.509987
$835$	8.36988	+	53.6170i	0.289652	+	1.85549i
$836$	4.91875	−	9.84640i	0.170118	−	0.340545i
$837$		−	0.722644i		−	0.0249782i
$838$			8.59516i			0.296915i
$839$			17.7190i			0.611728i	0.952075	+	0.305864i	$0.0989454\pi$
$839$			17.7190i			0.611728i	−0.952075	+	0.305864i	$0.901055\pi$
$840$	−9.54227	+	15.5094i	−0.329240	+	0.535124i
$841$	−4.81467			−0.166023
$842$	2.25117			0.0775803
$843$			7.54255i			0.259779i
$844$		−	8.16346i		−	0.280998i
$845$	2.67594	−	0.417728i	0.0920553	−	0.0143703i
$846$	−7.74857			−0.266401
$847$	29.0470	+	1.80885i	0.998067	+	0.0621527i
$848$			27.7577i			0.953203i
$849$			4.89738i			0.168078i
$850$	5.54634	+	17.3319i	0.190238	+	0.594478i
$851$	−6.56224			−0.224951
$852$	9.32250			0.319384
$853$		−	40.5291i		−	1.38769i	−0.720125	−	0.693844i	$-0.755916\pi$
$853$		−	40.5291i		−	1.38769i	0.720125	−	0.693844i	$-0.244084\pi$
$854$	10.5949	−	12.4161i	0.362549	−	0.424869i
$855$	−11.7560	+	1.83517i	−0.402047	+	0.0627616i
$856$	−5.46506			−0.186792
$857$			33.2959i			1.13737i	0.822556	+	0.568683i	$0.192547\pi$
$857$			33.2959i			1.13737i	−0.822556	+	0.568683i	$0.807453\pi$
$858$	11.9513	+	5.97025i	0.408011	+	0.203821i
$859$			49.0304i			1.67289i	0.548048	+	0.836447i	$0.315371\pi$
$859$			49.0304i			1.67289i	−0.548048	+	0.836447i	$0.684629\pi$
$860$	−10.0592	+	1.57030i	−0.343017	+	0.0535466i
$861$	−5.74489	+	6.73240i	−0.195785	+	0.229439i
$862$		−	8.76638i		−	0.298584i
$863$			10.0731i			0.342891i	0.985194	+	0.171446i	$0.0548438\pi$
$863$			10.0731i			0.342891i	−0.985194	+	0.171446i	$0.945156\pi$
$864$	−3.38301			−0.115092
$865$	0.0312221	+	0.200007i	0.00106158	+	0.00680044i
$866$	15.9080			0.540576
$867$	7.37569			0.250491
$868$	−0.907061	−	0.774014i	−0.0307877	−	0.0262717i
$869$	−34.2132	−	17.0911i	−1.16060	−	0.579777i
$870$	−2.35281	−	15.0720i	−0.0797679	−	0.510989i
$871$	−6.80522			−0.230586
$872$			5.96855i			0.202121i
$873$	−3.77353			−0.127715
$874$		−	36.7480i		−	1.24302i
$875$	−7.08456	+	28.7195i	−0.239502	+	0.970896i
$876$			4.53843i			0.153339i
$877$	15.1073			0.510136			0.255068	−	0.966923i	$-0.417902\pi$
$877$	15.1073			0.510136			0.255068	+	0.966923i	$0.417902\pi$
$878$	−35.9937			−1.21473
$879$			7.63128i			0.257397i
$880$	−5.32136	+	16.7024i	−0.179383	+	0.563039i
$881$			28.6024i			0.963639i	0.876271	+	0.481819i	$0.160024\pi$
$881$			28.6024i			0.963639i	−0.876271	+	0.481819i	$0.839976\pi$
$882$	1.29181	+	8.10996i	0.0434975	+	0.273076i
$883$			12.6564i			0.425921i	0.977061	+	0.212960i	$0.0683106\pi$
$883$			12.6564i			0.425921i	−0.977061	+	0.212960i	$0.931689\pi$
$884$	6.64315			0.223433
$885$	5.08936	+	32.6022i	0.171077	+	1.09591i
$886$		−	34.3989i		−	1.15565i
$887$		−	11.2443i		−	0.377547i	−0.982021	−	0.188774i	$-0.939549\pi$
$887$		−	11.2443i		−	0.377547i	0.982021	−	0.188774i	$-0.0604512\pi$
$888$		−	3.43126i		−	0.115146i
$889$	−10.7122	+	12.5536i	−0.359276	+	0.421033i
$890$	1.47743	+	9.46436i	0.0495237	+	0.317246i
$891$	1.48217	−	2.96702i	0.0496544	−	0.0993988i
$892$	−2.86732			−0.0960048
$893$	−35.1450			−1.17608
$894$			3.68706i			0.123314i
$895$	−48.7446	+	7.60928i	−1.62935	+	0.254350i
$896$	5.90125	−	6.91563i	0.197147	−	0.231035i
$897$	−20.2117			−0.674850
$898$	−17.0755			−0.569816
$899$	4.20220			0.140151
$900$	−2.96998	+	0.950419i	−0.0989994	+	0.0316806i
$901$	−36.4314			−1.21371
$902$	−5.81661	+	11.6438i	−0.193672	+	0.387695i
$903$	−12.5378	+	14.6930i	−0.417233	+	0.488953i
$904$			53.4773i			1.77863i
$905$	1.87543	+	12.0139i	0.0623413	+	0.399355i
$906$		−	1.10194i		−	0.0366095i
$907$			46.9653i			1.55946i	0.626117	+	0.779729i	$0.284643\pi$
$907$			46.9653i			1.55946i	−0.626117	+	0.779729i	$0.715357\pi$
$908$			11.8436i			0.393043i
$909$	15.2917			0.507194
$910$	−20.2964	−	12.4875i	−0.672821	−	0.413958i
$911$	7.80180			0.258485			0.129243	−	0.991613i	$-0.458745\pi$
$911$	7.80180			0.258485			0.129243	+	0.991613i	$0.458745\pi$
$912$	12.5775			0.416483
$913$	−21.9379	−	10.9590i	−0.726037	−	0.362690i
$914$	24.2203			0.801137
$915$	11.6177	−	1.81359i	0.384071	−	0.0599553i
$916$		−	12.3226i		−	0.407151i
$917$	−4.80394	+	5.62971i	−0.158640	+	0.185909i
$918$			3.63954i			0.120123i
$919$			28.8139i			0.950484i	0.879855	+	0.475242i	$0.157639\pi$
$919$			28.8139i			0.950484i	−0.879855	+	0.475242i	$0.842361\pi$
$920$	−6.24903	−	40.0310i	−0.206024	−	1.31978i
$921$			29.9896i			0.988190i
$922$	−8.91017			−0.293441
$923$			51.3231i			1.68932i
$924$	−2.13667	−	5.03834i	−0.0702912	−	0.165749i
$925$	−1.69881	−	5.30863i	−0.0558564	−	0.174547i
$926$			33.5310i			1.10190i
$927$	1.35140			0.0443859
$928$		−	19.6723i		−	0.645775i
$929$		−	0.852646i		−	0.0279744i	−0.999902	−	0.0139872i	$-0.995548\pi$
$929$		−	0.852646i		−	0.0279744i	0.999902	−	0.0139872i	$-0.00445241\pi$
$930$	0.292388	+	1.87302i	0.00958778	+	0.0614188i
$931$	5.85923	+	36.7841i	0.192028	+	1.20555i
$932$	−11.8934			−0.389581
$933$			10.3684i			0.339447i
$934$	25.8778			0.846746
$935$	−21.9216	−	6.98418i	−0.716914	−	0.228407i
$936$		−	10.5683i		−	0.345436i
$937$		−	16.0248i		−	0.523507i	−0.965135	−	0.261754i	$-0.915699\pi$
$937$		−	16.0248i		−	0.523507i	0.965135	−	0.261754i	$-0.0843008\pi$
$938$	−4.67980	−	3.99336i	−0.152801	−	0.130388i
$939$	17.3488			0.566157
$940$	−9.10063	+	1.42065i	−0.296830	+	0.0463366i
$941$	29.0243			0.946164			0.473082	−	0.881018i	$-0.343141\pi$
$941$	29.0243			0.946164			0.473082	+	0.881018i	$0.343141\pi$
$942$	−15.2206			−0.495914
$943$		−	19.6916i		−	0.641246i
$944$		−	34.8804i		−	1.13526i
$945$	−3.10014	+	5.03876i	−0.100848	+	0.163911i
$946$	−12.6944	+	25.4117i	−0.412730	+	0.826207i
$947$			11.9719i			0.389035i	0.980899	+	0.194518i	$0.0623142\pi$
$947$			11.9719i			0.389035i	−0.980899	+	0.194518i	$0.937686\pi$
$948$			7.19165i			0.233574i
$949$	−24.9854			−0.811059
$950$	29.7279	−	9.51316i	0.964500	−	0.308648i
$951$		−	20.0871i		−	0.651370i
$952$	19.2182	+	16.3993i	0.622866	+	0.531504i
$953$	27.7753			0.899730			0.449865	−	0.893096i	$-0.351472\pi$
$953$	27.7753			0.899730			0.449865	+	0.893096i	$0.351472\pi$
$954$			13.7769i			0.446045i
$955$	−41.9235	+	6.54446i	−1.35661	+	0.211774i
$956$		−	14.4417i		−	0.467078i
$957$	17.2533	+	8.61885i	0.557720	+	0.278608i
$958$	−35.5570			−1.14879
$959$	36.4813	+	31.1302i	1.17804	+	1.00525i
$960$	19.2127	−	2.99920i	0.620087	−	0.0967987i
$961$	30.4778			0.983154
$962$	4.49034			0.144774
$963$	−1.77552			−0.0572152
$964$	9.79612			0.315512
$965$	−36.0630	+	5.62961i	−1.16091	+	0.181224i
$966$	−13.8991	−	11.8604i	−0.447197	−	0.381602i
$967$	50.2899			1.61722			0.808608	−	0.588348i	$-0.200222\pi$
$967$	50.2899			1.61722			0.808608	+	0.588348i	$0.200222\pi$
$968$	−20.3345	−	27.0718i	−0.653576	−	0.870120i
$969$			16.5078i			0.530306i
$970$	9.78062	−	1.52680i	0.314037	−	0.0490227i
$971$		−	43.1696i		−	1.38538i	−0.721237	−	0.692688i	$-0.756426\pi$
$971$		−	43.1696i		−	1.38538i	0.721237	−	0.692688i	$-0.243574\pi$
$972$	−0.623669			−0.0200042
$973$	−21.5601	+	25.2661i	−0.691185	+	0.809995i
$974$			11.9083i			0.381567i
$975$	−5.23233	−	16.3506i	−0.167569	−	0.523639i
$976$	−12.4296			−0.397861
$977$			34.3037i			1.09747i	0.835996	+	0.548736i	$0.184891\pi$
$977$			34.3037i			1.09747i	−0.835996	+	0.548736i	$0.815109\pi$
$978$		−	10.9651i		−	0.350625i
$979$	−10.8341	−	5.41215i	−0.346260	−	0.172973i
$980$	3.00413	+	9.28823i	0.0959635	+	0.296702i
$981$			1.93909i			0.0619104i
$982$			40.1775i			1.28212i
$983$	−50.9060			−1.62365			−0.811825	−	0.583901i	$-0.801526\pi$
$983$	−50.9060			−1.62365			−0.811825	+	0.583901i	$0.801526\pi$
$984$	10.2963			0.328235
$985$	35.5944	−	5.55646i	1.13413	−	0.177044i
$986$	−21.1641			−0.674001
$987$	−11.3430	+	13.2928i	−0.361053	+	0.423116i
$988$		−	11.3944i		−	0.362505i
$989$		−	42.9756i		−	1.36654i
$990$	−2.64114	+	8.28991i	−0.0839411	+	0.263470i
$991$	39.1588			1.24392			0.621960	−	0.783049i	$-0.286336\pi$
$991$	39.1588			1.24392			0.621960	+	0.783049i	$0.286336\pi$
$992$			2.44471i			0.0776196i
$993$	−17.1491			−0.544209
$994$	−30.1168	+	35.2937i	−0.955247	+	1.11945i
$995$	−8.44868	−	54.1218i	−0.267841	−	1.71578i
$996$			4.61136i			0.146116i
$997$			27.4294i			0.868698i	0.900745	+	0.434349i	$0.143022\pi$
$997$			27.4294i			0.868698i	−0.900745	+	0.434349i	$0.856978\pi$
$998$	−3.63316			−0.115006
$999$		−	1.11476i		−	0.0352696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.b.769.15	yes	48
5.4	even	2		1155.2.k.a.769.34	yes	48
7.6	odd	2		1155.2.k.a.769.16	yes	48
11.10	odd	2	inner	1155.2.k.b.769.34	yes	48
35.34	odd	2	inner	1155.2.k.b.769.33	yes	48
55.54	odd	2		1155.2.k.a.769.15	✓	48
77.76	even	2		1155.2.k.a.769.33	yes	48
385.384	even	2	inner	1155.2.k.b.769.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.15	✓	48	55.54	odd	2
1155.2.k.a.769.16	yes	48	7.6	odd	2
1155.2.k.a.769.33	yes	48	77.76	even	2
1155.2.k.a.769.34	yes	48	5.4	even	2
1155.2.k.b.769.15	yes	48	1.1	even	1	trivial
1155.2.k.b.769.16	yes	48	385.384	even	2	inner
1155.2.k.b.769.33	yes	48	35.34	odd	2	inner
1155.2.k.b.769.34	yes	48	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.17317 q^{2} +1.00000 q^{3} -0.623669 q^{4} +(2.20931 - 0.344884i) q^{5} -1.17317 q^{6} +(-1.71739 + 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.17317 q^{2} +1.00000 q^{3} -0.623669 q^{4} +(2.20931 - 0.344884i) q^{5} -1.17317 q^{6} +(-1.71739 + 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +(-2.59190 + 0.404608i) q^{10} +(1.48217 - 2.96702i) q^{11} -0.623669 q^{12} -3.43348i q^{13} +(2.01480 - 2.36113i) q^{14} +(2.20931 - 0.344884i) q^{15} -2.36370 q^{16} -3.10231i q^{17} -1.17317 q^{18} -5.32112 q^{19} +(-1.37788 + 0.215094i) q^{20} +(-1.71739 + 2.01260i) q^{21} +(-1.73883 + 3.48082i) q^{22} -5.88666i q^{23} +3.07801 q^{24} +(4.76211 - 1.52391i) q^{25} +4.02806i q^{26} +1.00000 q^{27} +(1.07109 - 1.25520i) q^{28} +5.81504i q^{29} +(-2.59190 + 0.404608i) q^{30} -0.722644i q^{31} -3.38301 q^{32} +(1.48217 - 2.96702i) q^{33} +3.63954i q^{34} +(-3.10014 + 5.03876i) q^{35} -0.623669 q^{36} -1.11476i q^{37} +6.24259 q^{38} -3.43348i q^{39} +(6.80029 - 1.06156i) q^{40} +3.34512 q^{41} +(2.01480 - 2.36113i) q^{42} +7.30051 q^{43} +(-0.924381 + 1.85044i) q^{44} +(2.20931 - 0.344884i) q^{45} +6.90606i q^{46} +6.60481 q^{47} -2.36370 q^{48} +(-1.10113 - 6.91285i) q^{49} +(-5.58677 + 1.78781i) q^{50} -3.10231i q^{51} +2.14136i q^{52} -11.7433i q^{53} -1.17317 q^{54} +(2.25129 - 7.06624i) q^{55} +(-5.28616 + 6.19481i) q^{56} -5.32112 q^{57} -6.82204i q^{58} +14.7567i q^{59} +(-1.37788 + 0.215094i) q^{60} +5.25854 q^{61} +0.847785i q^{62} +(-1.71739 + 2.01260i) q^{63} +8.69624 q^{64} +(-1.18415 - 7.58563i) q^{65} +(-1.73883 + 3.48082i) q^{66} -1.98202i q^{67} +1.93481i q^{68} -5.88666i q^{69} +(3.63699 - 5.91133i) q^{70} -14.9478 q^{71} +3.07801 q^{72} -7.27698i q^{73} +1.30781i q^{74} +(4.76211 - 1.52391i) q^{75} +3.31862 q^{76} +(3.42596 + 8.07854i) q^{77} +4.02806i q^{78} -11.5312i q^{79} +(-5.22214 + 0.815202i) q^{80} +1.00000 q^{81} -3.92440 q^{82} -7.39391i q^{83} +(1.07109 - 1.25520i) q^{84} +(-1.06994 - 6.85396i) q^{85} -8.56475 q^{86} +5.81504i q^{87} +(4.56212 - 9.13252i) q^{88} -3.65152i q^{89} +(-2.59190 + 0.404608i) q^{90} +(6.91023 + 5.89663i) q^{91} +3.67133i q^{92} -0.722644i q^{93} -7.74857 q^{94} +(-11.7560 + 1.83517i) q^{95} -3.38301 q^{96} -3.77353 q^{97} +(1.29181 + 8.10996i) q^{98} +(1.48217 - 2.96702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9	\( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) 48 * q + 48 * q^3 + 48 * q^4 - 4 * q^5 + 48 * q^9 + 48 * q^12 - 4 * q^15 + 40 * q^16 - 18 * q^20 + 20 * q^25 + 48 * q^27 + 48 * q^36 - 20 * q^38 - 16 * q^44 - 4 * q^45 + 8 * q^47 + 40 * q^48 + 24 * q^49 - 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 + 20 * q^75 - 32 * q^77 - 46 * q^80 + 48 * q^81 - 32 * q^82 - 16 * q^86 + 68 * q^97

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