LMFDB - Embedded newform 1176.2.p.a.979.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1176,2,Mod(979,1176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1176, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1176.979"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.25
Character	$\chi$	$=$	1176.979
Dual form			1176.2.p.a.979.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35356 - 0.409738i) q^{2} -1.00000i q^{3} +(1.66423 - 1.10921i) q^{4} +2.50301 q^{5} +(-0.409738 - 1.35356i) q^{6} +(1.79815 - 2.18327i) q^{8} -1.00000 q^{9} +(3.38796 - 1.02558i) q^{10} -5.67619 q^{11} +(-1.10921 - 1.66423i) q^{12} +5.31228 q^{13} -2.50301i q^{15} +(1.53933 - 3.69195i) q^{16} +0.454858i q^{17} +(-1.35356 + 0.409738i) q^{18} -3.69433i q^{19} +(4.16558 - 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} -5.12043i q^{23} +(-2.18327 - 1.79815i) q^{24} +1.26504 q^{25} +(7.19047 - 2.17664i) q^{26} +1.00000i q^{27} +2.57962i q^{29} +(-1.02558 - 3.38796i) q^{30} +6.00666 q^{31} +(0.570834 - 5.62798i) q^{32} +5.67619i q^{33} +(0.186372 + 0.615676i) q^{34} +(-1.66423 + 1.10921i) q^{36} +9.01565i q^{37} +(-1.51370 - 5.00048i) q^{38} -5.31228i q^{39} +(4.50077 - 5.46474i) q^{40} +4.65692i q^{41} +3.66703 q^{43} +(-9.44648 + 6.29606i) q^{44} -2.50301 q^{45} +(-2.09803 - 6.93080i) q^{46} -0.957682 q^{47} +(-3.69195 - 1.53933i) q^{48} +(1.71230 - 0.518335i) q^{50} +0.454858 q^{51} +(8.84086 - 5.89241i) q^{52} -6.24836i q^{53} +(0.409738 + 1.35356i) q^{54} -14.2075 q^{55} -3.69433 q^{57} +(1.05697 + 3.49166i) q^{58} +10.1222i q^{59} +(-2.77635 - 4.16558i) q^{60} -5.00367 q^{61} +(8.13036 - 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +13.2967 q^{65} +(2.32575 + 7.68304i) q^{66} -9.30266 q^{67} +(0.504531 + 0.756989i) q^{68} -5.12043 q^{69} +7.35240i q^{71} +(-1.79815 + 2.18327i) q^{72} -6.85362i q^{73} +(3.69405 + 12.2032i) q^{74} -1.26504i q^{75} +(-4.09777 - 6.14821i) q^{76} +(-2.17664 - 7.19047i) q^{78} +8.91293i q^{79} +(3.85294 - 9.24097i) q^{80} +1.00000 q^{81} +(1.90812 + 6.30341i) q^{82} +1.96259i q^{83} +1.13851i q^{85} +(4.96353 - 1.50252i) q^{86} +2.57962 q^{87} +(-10.2066 + 12.3927i) q^{88} +6.82845i q^{89} +(-3.38796 + 1.02558i) q^{90} +(-5.67961 - 8.52158i) q^{92} -6.00666i q^{93} +(-1.29628 + 0.392398i) q^{94} -9.24692i q^{95} +(-5.62798 - 0.570834i) q^{96} +3.71270i q^{97} +5.67619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	1.35356	−	0.409738i	0.957109	−	0.289728i
$2$	1.35356	−	0.409738i	0.957109	−	0.289728i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.66423	−	1.10921i	0.832115	−	0.554603i
$5$	2.50301			1.11938			0.559689	−	0.828703i	$-0.310920\pi$
$5$	2.50301			1.11938			0.559689	+	0.828703i	$0.310920\pi$
$6$	−0.409738	−	1.35356i	−0.167275	−	0.552587i
$7$		0			0
$7$		0			0
$8$	1.79815	−	2.18327i	0.635741	−	0.771903i
$9$	−1.00000			−0.333333
$10$	3.38796	−	1.02558i	1.07137	−	0.324315i
$11$	−5.67619			−1.71143			−0.855717	−	0.517443i	$-0.826884\pi$
$11$	−5.67619			−1.71143			−0.855717	+	0.517443i	$0.826884\pi$
$12$	−1.10921	−	1.66423i	−0.320200	−	0.480422i
$13$	5.31228			1.47336			0.736681	−	0.676241i	$-0.236392\pi$
$13$	5.31228			1.47336			0.736681	+	0.676241i	$0.236392\pi$
$14$		0			0
$15$		−	2.50301i		−	0.646273i
$16$	1.53933	−	3.69195i	0.384831	−	0.922987i
$17$			0.454858i			0.110319i	0.998478	+	0.0551596i	$0.0175668\pi$
$17$			0.454858i			0.110319i	−0.998478	+	0.0551596i	$0.982433\pi$
$18$	−1.35356	+	0.409738i	−0.319036	+	0.0965761i
$19$		−	3.69433i		−	0.847537i	−0.905771	−	0.423768i	$-0.860707\pi$
$19$		−	3.69433i		−	0.847537i	0.905771	−	0.423768i	$-0.139293\pi$
$20$	4.16558	−	2.77635i	0.931452	−	0.620811i
$21$		0			0
$22$	−7.68304	+	2.32575i	−1.63803	+	0.495851i
$23$		−	5.12043i		−	1.06768i	−0.845584	−	0.533842i	$-0.820748\pi$
$23$		−	5.12043i		−	1.06768i	0.845584	−	0.533842i	$-0.179252\pi$
$24$	−2.18327	−	1.79815i	−0.445658	−	0.367045i
$25$	1.26504			0.253008
$26$	7.19047	−	2.17664i	1.41017	−	0.426874i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			2.57962i			0.479024i	0.970893	+	0.239512i	$0.0769874\pi$
$29$			2.57962i			0.479024i	−0.970893	+	0.239512i	$0.923013\pi$
$30$	−1.02558	−	3.38796i	−0.187244	−	0.618554i
$31$	6.00666			1.07883			0.539414	−	0.842041i	$-0.318646\pi$
$31$	6.00666			1.07883			0.539414	+	0.842041i	$0.318646\pi$
$32$	0.570834	−	5.62798i	0.100910	−	0.994896i
$33$			5.67619i			0.988097i
$34$	0.186372	+	0.615676i	0.0319626	+	0.105588i
$35$		0			0
$36$	−1.66423	+	1.10921i	−0.277372	+	0.184868i
$37$			9.01565i			1.48216i	0.671415	+	0.741082i	$0.265687\pi$
$37$			9.01565i			1.48216i	−0.671415	+	0.741082i	$0.734313\pi$
$38$	−1.51370	−	5.00048i	−0.245555	−	0.811185i
$39$		−	5.31228i		−	0.850646i
$40$	4.50077	−	5.46474i	0.711635	−	0.864051i
$41$			4.65692i			0.727289i	0.931538	+	0.363644i	$0.118468\pi$
$41$			4.65692i			0.727289i	−0.931538	+	0.363644i	$0.881532\pi$
$42$		0			0
$43$	3.66703			0.559217			0.279608	−	0.960114i	$-0.409795\pi$
$43$	3.66703			0.559217			0.279608	+	0.960114i	$0.409795\pi$
$44$	−9.44648	+	6.29606i	−1.42411	+	0.949167i
$45$	−2.50301			−0.373126
$46$	−2.09803	−	6.93080i	−0.309338	−	1.02189i
$47$	−0.957682			−0.139692			−0.0698461	−	0.997558i	$-0.522251\pi$
$47$	−0.957682			−0.139692			−0.0698461	+	0.997558i	$0.522251\pi$
$48$	−3.69195	−	1.53933i	−0.532887	−	0.222182i
$49$		0			0
$50$	1.71230	−	0.518335i	0.242156	−	0.0733036i
$51$	0.454858			0.0636929
$52$	8.84086	−	5.89241i	1.22601	−	0.817131i
$53$		−	6.24836i		−	0.858278i	−0.903239	−	0.429139i	$-0.858817\pi$
$53$		−	6.24836i		−	0.858278i	0.903239	−	0.429139i	$-0.141183\pi$
$54$	0.409738	+	1.35356i	0.0557582	+	0.184196i
$55$	−14.2075			−1.91574
$56$		0			0
$57$	−3.69433			−0.489326
$58$	1.05697	+	3.49166i	0.138787	+	0.458478i
$59$			10.1222i			1.31779i	0.752234	+	0.658896i	$0.228976\pi$
$59$			10.1222i			1.31779i	−0.752234	+	0.658896i	$0.771024\pi$
$60$	−2.77635	−	4.16558i	−0.358425	−	0.537774i
$61$	−5.00367			−0.640654			−0.320327	−	0.947307i	$-0.603793\pi$
$61$	−5.00367			−0.640654			−0.320327	+	0.947307i	$0.603793\pi$
$62$	8.13036	−	2.46115i	1.03256	−	0.312567i
$63$		0			0
$64$	−1.53334	−	7.85168i	−0.191667	−	0.981460i
$65$	13.2967			1.64925
$66$	2.32575	+	7.68304i	0.286280	+	0.945717i
$67$	−9.30266			−1.13650			−0.568251	−	0.822856i	$-0.692380\pi$
$67$	−9.30266			−1.13650			−0.568251	+	0.822856i	$0.692380\pi$
$68$	0.504531	+	0.756989i	0.0611834	+	0.0917984i
$69$	−5.12043			−0.616428
$70$		0			0
$71$			7.35240i			0.872569i	0.899809	+	0.436285i	$0.143706\pi$
$71$			7.35240i			0.872569i	−0.899809	+	0.436285i	$0.856294\pi$
$72$	−1.79815	+	2.18327i	−0.211914	+	0.257301i
$73$		−	6.85362i		−	0.802155i	−0.916044	−	0.401078i	$-0.868636\pi$
$73$		−	6.85362i		−	0.802155i	0.916044	−	0.401078i	$-0.131364\pi$
$74$	3.69405	+	12.2032i	0.429424	+	1.41859i
$75$		−	1.26504i		−	0.146074i
$76$	−4.09777	−	6.14821i	−0.470046	−	0.705248i
$77$		0			0
$78$	−2.17664	−	7.19047i	−0.246456	−	0.814161i
$79$			8.91293i			1.00278i	0.865221	+	0.501391i	$0.167178\pi$
$79$			8.91293i			1.00278i	−0.865221	+	0.501391i	$0.832822\pi$
$80$	3.85294	−	9.24097i	0.430772	−	1.03317i
$81$	1.00000			0.111111
$82$	1.90812	+	6.30341i	0.210716	+	0.696095i
$83$			1.96259i			0.215423i	0.994182	+	0.107711i	$0.0343522\pi$
$83$			1.96259i			0.215423i	−0.994182	+	0.107711i	$0.965648\pi$
$84$		0			0
$85$			1.13851i			0.123489i
$86$	4.96353	−	1.50252i	0.535231	−	0.162021i
$87$	2.57962			0.276565
$88$	−10.2066	+	12.3927i	−1.08803	+	1.32106i
$89$			6.82845i			0.723814i	0.932214	+	0.361907i	$0.117874\pi$
$89$			6.82845i			0.723814i	−0.932214	+	0.361907i	$0.882126\pi$
$90$	−3.38796	+	1.02558i	−0.357122	+	0.108105i
$91$		0			0
$92$	−5.67961	−	8.52158i	−0.592141	−	0.888436i
$93$		−	6.00666i		−	0.622862i
$94$	−1.29628	+	0.392398i	−0.133701	+	0.0404728i
$95$		−	9.24692i		−	0.948714i
$96$	−5.62798	−	0.570834i	−0.574403	−	0.0582605i
$97$			3.71270i			0.376967i	0.982076	+	0.188484i	$0.0603573\pi$
$97$			3.71270i			0.376967i	−0.982076	+	0.188484i	$0.939643\pi$
$98$		0			0
$99$	5.67619			0.570478
$100$	2.10532	−	1.40319i	0.210532	−	0.140319i
$101$	5.68155			0.565335			0.282667	−	0.959218i	$-0.408781\pi$
$101$	5.68155			0.565335			0.282667	+	0.959218i	$0.408781\pi$
$102$	0.615676	−	0.186372i	0.0609610	−	0.0184536i
$103$	5.90691			0.582025			0.291013	−	0.956719i	$-0.406008\pi$
$103$	5.90691			0.582025			0.291013	+	0.956719i	$0.406008\pi$
$104$	9.55226	−	11.5981i	0.936676	−	1.13729i
$105$		0			0
$106$	−2.56019	−	8.45750i	−0.248667	−	0.821465i
$107$	−10.6609			−1.03063			−0.515314	−	0.857002i	$-0.672325\pi$
$107$	−10.6609			−1.03063			−0.515314	+	0.857002i	$0.672325\pi$
$108$	1.10921	+	1.66423i	0.106733	+	0.160141i
$109$			3.17911i			0.304504i	0.988342	+	0.152252i	$0.0486525\pi$
$109$			3.17911i			0.304504i	−0.988342	+	0.152252i	$0.951348\pi$
$110$	−19.2307	+	5.82136i	−1.83358	+	0.555045i
$111$	9.01565			0.855727
$112$		0			0
$113$	−0.302446			−0.0284518			−0.0142259	−	0.999899i	$-0.504528\pi$
$113$	−0.302446			−0.0284518			−0.0142259	+	0.999899i	$0.504528\pi$
$114$	−5.00048	+	1.51370i	−0.468338	+	0.141771i
$115$		−	12.8165i		−	1.19514i
$116$	2.86133	+	4.29309i	0.265668	+	0.398603i
$117$	−5.31228			−0.491121
$118$	4.14742	+	13.7009i	0.381801	+	1.26127i
$119$		0			0
$120$	−5.46474	−	4.50077i	−0.498860	−	0.410862i
$121$	21.2191			1.92901
$122$	−6.77275	+	2.05019i	−0.613176	+	0.185616i
$123$	4.65692			0.419900
$124$	9.99647	−	6.66262i	0.897709	−	0.598321i
$125$	−9.34863			−0.836167
$126$		0			0
$127$		−	6.39751i		−	0.567687i	−0.958871	−	0.283843i	$-0.908390\pi$
$127$		−	6.39751i		−	0.567687i	0.958871	−	0.283843i	$-0.0916096\pi$
$128$	−5.29259	−	9.99943i	−0.467803	−	0.883833i
$129$		−	3.66703i		−	0.322864i
$130$	17.9978	−	5.44815i	1.57851	−	0.477834i
$131$		−	14.5026i		−	1.26710i	−0.773703	−	0.633549i	$-0.781598\pi$
$131$		−	14.5026i		−	1.26710i	0.773703	−	0.633549i	$-0.218402\pi$
$132$	6.29606	+	9.44648i	0.548002	+	0.822211i
$133$		0			0
$134$	−12.5917	+	3.81165i	−1.08776	+	0.329276i
$135$			2.50301i			0.215424i
$136$	0.993078	+	0.817902i	0.0851557	+	0.0701345i
$137$	1.23112			0.105182			0.0525908	−	0.998616i	$-0.483252\pi$
$137$	1.23112			0.105182			0.0525908	+	0.998616i	$0.483252\pi$
$138$	−6.93080	+	2.09803i	−0.589988	+	0.178596i
$139$			15.7788i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$139$			15.7788i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$140$		0			0
$141$			0.957682i			0.0806514i
$142$	3.01255	+	9.95188i	0.252808	+	0.835144i
$143$	−30.1535			−2.52156
$144$	−1.53933	+	3.69195i	−0.128277	+	0.307662i
$145$			6.45681i			0.536209i
$146$	−2.80819	−	9.27676i	−0.232407	−	0.767750i
$147$		0			0
$148$	10.0002	+	15.0041i	0.822012	+	1.23333i
$149$			5.95556i			0.487898i	0.969788	+	0.243949i	$0.0784430\pi$
$149$			5.95556i			0.487898i	−0.969788	+	0.243949i	$0.921557\pi$
$150$	−0.518335	−	1.71230i	−0.0423219	−	0.139809i
$151$			3.59257i			0.292359i	0.989258	+	0.146180i	$0.0466977\pi$
$151$			3.59257i			0.292359i	−0.989258	+	0.146180i	$0.953302\pi$
$152$	−8.06571	−	6.64294i	−0.654216	−	0.538814i
$153$		−	0.454858i		−	0.0367731i
$154$		0			0
$155$	15.0347			1.20762
$156$	−5.89241	−	8.84086i	−0.471771	−	0.707835i
$157$	−0.983524			−0.0784937			−0.0392469	−	0.999230i	$-0.512496\pi$
$157$	−0.983524			−0.0784937			−0.0392469	+	0.999230i	$0.512496\pi$
$158$	3.65196	+	12.0642i	0.290534	+	0.959772i
$159$	−6.24836			−0.495527
$160$	1.42880	−	14.0869i	0.112957	−	1.11366i
$161$		0			0
$162$	1.35356	−	0.409738i	0.106345	−	0.0321920i
$163$	2.52167			0.197512			0.0987562	−	0.995112i	$-0.468514\pi$
$163$	2.52167			0.197512			0.0987562	+	0.995112i	$0.468514\pi$
$164$	5.16548	+	7.75019i	0.403357	+	0.605188i
$165$			14.2075i			1.10606i
$166$	0.804149	+	2.65648i	0.0624140	+	0.206183i
$167$	5.26232			0.407211			0.203605	−	0.979053i	$-0.434734\pi$
$167$	5.26232			0.407211			0.203605	+	0.979053i	$0.434734\pi$
$168$		0			0
$169$	15.2203			1.17079
$170$	0.466491	+	1.54104i	0.0357783	+	0.118192i
$171$			3.69433i			0.282512i
$172$	6.10278	−	4.06749i	0.465333	−	0.310143i
$173$	−0.143623			−0.0109195			−0.00545974	−	0.999985i	$-0.501738\pi$
$173$	−0.143623			−0.0109195			−0.00545974	+	0.999985i	$0.501738\pi$
$174$	3.49166	−	1.05697i	0.264702	−	0.0801285i
$175$		0			0
$176$	−8.73750	+	20.9562i	−0.658614	+	1.57963i
$177$	10.1222			0.760827
$178$	2.79787	+	9.24270i	0.209709	+	0.692769i
$179$	−18.9248			−1.41450			−0.707252	−	0.706961i	$-0.750065\pi$
$179$	−18.9248			−1.41450			−0.707252	+	0.706961i	$0.750065\pi$
$180$	−4.16558	+	2.77635i	−0.310484	+	0.206937i
$181$	−22.2260			−1.65204			−0.826022	−	0.563637i	$-0.809402\pi$
$181$	−22.2260			−1.65204			−0.826022	+	0.563637i	$0.809402\pi$
$182$		0			0
$183$			5.00367i			0.369882i
$184$	−11.1793	−	9.20729i	−0.824148	−	0.678770i
$185$			22.5662i			1.65910i
$186$	−2.46115	−	8.13036i	−0.180461	−	0.596147i
$187$		−	2.58186i		−	0.188804i
$188$	−1.59380	+	1.06227i	−0.116240	+	0.0774737i
$189$		0			0
$190$	−3.78881	−	12.5162i	−0.274869	−	0.908023i
$191$			11.7909i			0.853162i	0.904449	+	0.426581i	$0.140282\pi$
$191$			11.7909i			0.853162i	−0.904449	+	0.426581i	$0.859718\pi$
$192$	−7.85168	+	1.53334i	−0.566646	+	0.110659i
$193$	26.8224			1.93072			0.965361	−	0.260918i	$-0.0840252\pi$
$193$	26.8224			1.93072			0.965361	+	0.260918i	$0.0840252\pi$
$194$	1.52123	+	5.02535i	0.109218	+	0.360799i
$195$		−	13.2967i		−	0.952195i
$196$		0			0
$197$		−	16.5842i		−	1.18157i	−0.806828	−	0.590786i	$-0.798818\pi$
$197$		−	16.5842i		−	1.18157i	0.806828	−	0.590786i	$-0.201182\pi$
$198$	7.68304	−	2.32575i	0.546010	−	0.165284i
$199$	11.4084			0.808720			0.404360	−	0.914600i	$-0.367494\pi$
$199$	11.4084			0.808720			0.404360	+	0.914600i	$0.367494\pi$
$200$	2.27473	−	2.76193i	0.160848	−	0.195298i
$201$			9.30266i			0.656159i
$202$	7.69029	−	2.32794i	0.541087	−	0.163793i
$203$		0			0
$204$	0.756989	−	0.504531i	0.0529998	−	0.0353242i
$205$			11.6563i			0.814112i
$206$	7.99534	−	2.42028i	0.557061	−	0.168629i
$207$			5.12043i			0.355895i
$208$	8.17733	−	19.6127i	0.566996	−	1.35989i
$209$			20.9697i			1.45050i
$210$		0			0
$211$	−4.13300			−0.284527			−0.142264	−	0.989829i	$-0.545438\pi$
$211$	−4.13300			−0.284527			−0.142264	+	0.989829i	$0.545438\pi$
$212$	−6.93071	−	10.3987i	−0.476003	−	0.714186i
$213$	7.35240			0.503778
$214$	−14.4301	+	4.36817i	−0.986423	+	0.298602i
$215$	9.17860			0.625975
$216$	2.18327	+	1.79815i	0.148553	+	0.122348i
$217$		0			0
$218$	1.30260	+	4.30311i	0.0882233	+	0.291443i
$219$	−6.85362			−0.463125
$220$	−23.6446	+	15.7591i	−1.59412	+	1.06248i
$221$			2.41633i			0.162540i
$222$	12.2032	−	3.69405i	0.819024	−	0.247928i
$223$	18.1063			1.21249			0.606245	−	0.795278i	$-0.292675\pi$
$223$	18.1063			1.21249			0.606245	+	0.795278i	$0.292675\pi$
$224$		0			0
$225$	−1.26504			−0.0843361
$226$	−0.409378	+	0.123924i	−0.0272314	+	0.00824328i
$227$		−	7.92521i		−	0.526015i	−0.964794	−	0.263007i	$-0.915286\pi$
$227$		−	7.92521i		−	0.526015i	0.964794	−	0.263007i	$-0.0847143\pi$
$228$	−6.14821	+	4.09777i	−0.407175	+	0.271381i
$229$	2.15573			0.142455			0.0712274	−	0.997460i	$-0.477308\pi$
$229$	2.15573			0.142455			0.0712274	+	0.997460i	$0.477308\pi$
$230$	−5.25139	−	17.3478i	−0.346266	−	1.14388i
$231$		0			0
$232$	5.63201	+	4.63854i	0.369760	+	0.304535i
$233$	−20.0144			−1.31119			−0.655594	−	0.755114i	$-0.727582\pi$
$233$	−20.0144			−1.31119			−0.655594	+	0.755114i	$0.727582\pi$
$234$	−7.19047	+	2.17664i	−0.470056	+	0.142291i
$235$	−2.39708			−0.156369
$236$	11.2275	+	16.8456i	0.730851	+	1.09655i
$237$	8.91293			0.578957
$238$		0			0
$239$			18.8923i			1.22204i	0.791614	+	0.611021i	$0.209241\pi$
$239$			18.8923i			1.22204i	−0.791614	+	0.611021i	$0.790759\pi$
$240$	−9.24097	−	3.85294i	−0.596502	−	0.248706i
$241$			18.3083i			1.17934i	0.807643	+	0.589672i	$0.200743\pi$
$241$			18.3083i			1.17934i	−0.807643	+	0.589672i	$0.799257\pi$
$242$	28.7213	−	8.69426i	1.84627	−	0.558888i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.32726	+	5.55010i	−0.533098	+	0.355309i
$245$		0			0
$246$	6.30341	−	1.90812i	0.401890	−	0.121657i
$247$		−	19.6253i		−	1.24873i
$248$	10.8009	−	13.1142i	0.685855	−	0.832750i
$249$	1.96259			0.124374
$250$	−12.6539	+	3.83048i	−0.800302	+	0.242261i
$251$			3.43251i			0.216658i	0.994115	+	0.108329i	$0.0345500\pi$
$251$			3.43251i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$252$		0			0
$253$			29.0645i			1.82727i
$254$	−2.62130	−	8.65939i	−0.164475	−	0.543338i
$255$	1.13851			0.0712964
$256$	−11.2610	−	11.3662i	−0.703810	−	0.710389i
$257$			25.0690i			1.56376i	0.623426	+	0.781882i	$0.285740\pi$
$257$			25.0690i			1.56376i	−0.623426	+	0.781882i	$0.714260\pi$
$258$	−1.50252	−	4.96353i	−0.0935428	−	0.309016i
$259$		0			0
$260$	22.1287	−	14.7487i	1.37237	−	0.914678i
$261$		−	2.57962i		−	0.159675i
$262$	−5.94226	−	19.6301i	−0.367114	−	1.21275i
$263$			15.5092i			0.956339i	0.878268	+	0.478169i	$0.158699\pi$
$263$			15.5092i			0.956339i	−0.878268	+	0.478169i	$0.841301\pi$
$264$	12.3927	+	10.2066i	0.762715	+	0.628174i
$265$		−	15.6397i		−	0.960738i
$266$		0			0
$267$	6.82845			0.417894
$268$	−15.4818	+	10.3186i	−0.945700	+	0.630307i
$269$	−23.7333			−1.44705			−0.723523	−	0.690300i	$-0.757479\pi$
$269$	−23.7333			−1.44705			−0.723523	+	0.690300i	$0.757479\pi$
$270$	1.02558	+	3.38796i	0.0624145	+	0.206185i
$271$	14.7137			0.893793			0.446896	−	0.894586i	$-0.352529\pi$
$271$	14.7137			0.893793			0.446896	+	0.894586i	$0.352529\pi$
$272$	1.67931	+	0.700175i	0.101823	+	0.0424543i
$273$		0			0
$274$	1.66639	−	0.504436i	0.100670	−	0.0304741i
$275$	−7.18061			−0.433007
$276$	−8.52158	+	5.67961i	−0.512939	+	0.341873i
$277$			7.12245i			0.427947i	0.976840	+	0.213973i	$0.0686406\pi$
$277$			7.12245i			0.427947i	−0.976840	+	0.213973i	$0.931359\pi$
$278$	6.46518	+	21.3575i	0.387756	+	1.28094i
$279$	−6.00666			−0.359609
$280$		0			0
$281$	−13.0561			−0.778861			−0.389430	−	0.921056i	$-0.627328\pi$
$281$	−13.0561			−0.778861			−0.389430	+	0.921056i	$0.627328\pi$
$282$	0.392398	+	1.29628i	0.0233670	+	0.0771922i
$283$			2.11369i			0.125646i	0.998025	+	0.0628230i	$0.0200104\pi$
$283$			2.11369i			0.125646i	−0.998025	+	0.0628230i	$0.979990\pi$
$284$	8.15532	+	12.2361i	0.483929	+	0.726078i
$285$	−9.24692			−0.547740
$286$	−40.8145	+	12.3550i	−2.41341	+	0.730568i
$287$		0			0
$288$	−0.570834	+	5.62798i	−0.0336367	+	0.331632i
$289$	16.7931			0.987830
$290$	2.64560	+	8.73966i	0.155355	+	0.513210i
$291$	3.71270			0.217642
$292$	−7.60207	−	11.4060i	−0.444878	−	0.667486i
$293$	−0.334002			−0.0195126			−0.00975630	−	0.999952i	$-0.503106\pi$
$293$	−0.334002			−0.0195126			−0.00975630	+	0.999952i	$0.503106\pi$
$294$		0			0
$295$			25.3358i			1.47511i
$296$	19.6836	+	16.2115i	1.14409	+	0.942272i
$297$		−	5.67619i		−	0.329366i
$298$	2.44022	+	8.06119i	0.141358	+	0.466972i
$299$		−	27.2012i		−	1.57308i
$300$	−1.40319	−	2.10532i	−0.0810133	−	0.121551i
$301$		0			0
$302$	1.47201	+	4.86275i	0.0847047	+	0.279820i
$303$		−	5.68155i		−	0.326396i
$304$	−13.6393	−	5.68677i	−0.782265	−	0.326159i
$305$	−12.5242			−0.717135
$306$	−0.186372	−	0.615676i	−0.0106542	−	0.0351959i
$307$		−	9.39141i		−	0.535996i	−0.963419	−	0.267998i	$-0.913638\pi$
$307$		−	9.39141i		−	0.535996i	0.963419	−	0.267998i	$-0.0863621\pi$
$308$		0			0
$309$		−	5.90691i		−	0.336032i
$310$	20.3503	−	6.16029i	1.15582	−	0.349881i
$311$	15.8750			0.900189			0.450095	−	0.892981i	$-0.351390\pi$
$311$	15.8750			0.900189			0.450095	+	0.892981i	$0.351390\pi$
$312$	−11.5981	−	9.55226i	−0.656616	−	0.540790i
$313$		−	32.1656i		−	1.81811i	−0.416679	−	0.909054i	$-0.636806\pi$
$313$		−	32.1656i		−	1.81811i	0.416679	−	0.909054i	$-0.363194\pi$
$314$	−1.33125	+	0.402987i	−0.0751271	+	0.0227418i
$315$		0			0
$316$	9.88627	+	14.8332i	0.556146	+	0.834431i
$317$		−	15.2712i		−	0.857714i	−0.903373	−	0.428857i	$-0.858917\pi$
$317$		−	15.2712i		−	0.857714i	0.903373	−	0.428857i	$-0.141083\pi$
$318$	−8.45750	+	2.56019i	−0.474273	+	0.143568i
$319$		−	14.6424i		−	0.819818i
$320$	−3.83795	−	19.6528i	−0.214548	−	1.09863i
$321$			10.6609i			0.595033i
$322$		0			0
$323$	1.68039			0.0934996
$324$	1.66423	−	1.10921i	0.0924572	−	0.0616225i
$325$	6.72025			0.372773
$326$	3.41322	−	1.03322i	0.189041	−	0.0572249i
$327$	3.17911			0.175805
$328$	10.1673	+	8.37383i	0.561396	+	0.462367i
$329$		0			0
$330$	5.82136	+	19.2307i	0.320455	+	1.05862i
$331$	−21.0379			−1.15635			−0.578174	−	0.815914i	$-0.696234\pi$
$331$	−21.0379			−1.15635			−0.578174	+	0.815914i	$0.696234\pi$
$332$	2.17692	+	3.26621i	0.119474	+	0.179257i
$333$		−	9.01565i		−	0.494054i
$334$	7.12285	−	2.15617i	0.389745	−	0.117980i
$335$	−23.2846			−1.27217
$336$		0			0
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$	20.6016	−	6.23634i	1.12058	−	0.339212i
$339$			0.302446i			0.0164266i
$340$	1.26284	+	1.89475i	0.0684874	+	0.102757i
$341$	−34.0949			−1.84634
$342$	1.51370	+	5.00048i	0.0818517	+	0.270395i
$343$		0			0
$344$	6.59386	−	8.00612i	0.355517	−	0.431661i
$345$	−12.8165			−0.690016
$346$	−0.194402	+	0.0588479i	−0.0104511	+	0.00316368i
$347$	−4.81341			−0.258397			−0.129199	−	0.991619i	$-0.541241\pi$
$347$	−4.81341			−0.258397			−0.129199	+	0.991619i	$0.541241\pi$
$348$	4.29309	−	2.86133i	0.230134	−	0.153383i
$349$	35.4792			1.89916			0.949578	−	0.313530i	$-0.101512\pi$
$349$	35.4792			1.89916			0.949578	+	0.313530i	$0.101512\pi$
$350$		0			0
$351$			5.31228i			0.283549i
$352$	−3.24016	+	31.9455i	−0.172701	+	1.70270i
$353$			4.77713i			0.254261i	0.991886	+	0.127131i	$0.0405767\pi$
$353$			4.77713i			0.254261i	−0.991886	+	0.127131i	$0.959423\pi$
$354$	13.7009	−	4.14742i	0.728195	−	0.220433i
$355$			18.4031i			0.976735i
$356$	7.57416	+	11.3641i	0.401430	+	0.602297i
$357$		0			0
$358$	−25.6158	+	7.75419i	−1.35383	+	0.409822i
$359$		−	36.9146i		−	1.94828i	−0.225947	−	0.974140i	$-0.572547\pi$
$359$		−	36.9146i		−	1.94828i	0.225947	−	0.974140i	$-0.427453\pi$
$360$	−4.50077	+	5.46474i	−0.237212	+	0.288017i
$361$	5.35195			0.281682
$362$	−30.0841	+	9.10682i	−1.58119	+	0.478644i
$363$		−	21.2191i		−	1.11371i
$364$		0			0
$365$		−	17.1547i		−	0.897916i
$366$	2.05019	+	6.77275i	0.107165	+	0.354017i
$367$	0.568832			0.0296928			0.0148464	−	0.999890i	$-0.495274\pi$
$367$	0.568832			0.0296928			0.0148464	+	0.999890i	$0.495274\pi$
$368$	−18.9044	−	7.88201i	−0.985458	−	0.410878i
$369$		−	4.65692i		−	0.242430i
$370$	9.24623	+	30.5447i	0.480689	+	1.58794i
$371$		0			0
$372$	−6.66262	−	9.99647i	−0.345441	−	0.518293i
$373$		−	23.4322i		−	1.21328i	−0.794979	−	0.606638i	$-0.792518\pi$
$373$		−	23.4322i		−	1.21328i	0.794979	−	0.606638i	$-0.207482\pi$
$374$	−1.05788	−	3.49469i	−0.0547019	−	0.180706i
$375$			9.34863i			0.482761i
$376$	−1.72205	+	2.09088i	−0.0888081	+	0.107829i
$377$			13.7037i			0.705775i
$378$		0			0
$379$	−14.7240			−0.756320			−0.378160	−	0.925740i	$-0.623443\pi$
$379$	−14.7240			−0.756320			−0.378160	+	0.925740i	$0.623443\pi$
$380$	−10.2567	−	15.3890i	−0.526160	−	0.789440i
$381$	−6.39751			−0.327754
$382$	4.83119	+	15.9597i	0.247185	+	0.816569i
$383$	−4.99508			−0.255237			−0.127618	−	0.991823i	$-0.540733\pi$
$383$	−4.99508			−0.255237			−0.127618	+	0.991823i	$0.540733\pi$
$384$	−9.99943	+	5.29259i	−0.510281	+	0.270086i
$385$		0			0
$386$	36.3057	−	10.9902i	1.84791	−	0.559385i
$387$	−3.66703			−0.186406
$388$	4.11815	+	6.17879i	0.209067	+	0.313680i
$389$		−	31.8810i		−	1.61643i	−0.588887	−	0.808216i	$-0.700434\pi$
$389$		−	31.8810i		−	1.61643i	0.588887	−	0.808216i	$-0.299566\pi$
$390$	−5.44815	−	17.9978i	−0.275878	−	0.911354i
$391$	2.32907			0.117786
$392$		0			0
$393$	−14.5026			−0.731559
$394$	−6.79515	−	22.4476i	−0.342335	−	1.13089i
$395$			22.3091i			1.12249i
$396$	9.44648	−	6.29606i	0.474704	−	0.316389i
$397$	32.9060			1.65151			0.825753	−	0.564032i	$-0.190751\pi$
$397$	32.9060			1.65151			0.825753	+	0.564032i	$0.190751\pi$
$398$	15.4419	−	4.67445i	0.774033	−	0.234309i
$399$		0			0
$400$	1.94731	−	4.67047i	0.0973655	−	0.233523i
$401$	0.212472			0.0106103			0.00530517	−	0.999986i	$-0.498311\pi$
$401$	0.212472			0.0106103			0.00530517	+	0.999986i	$0.498311\pi$
$402$	3.81165	+	12.5917i	0.190108	+	0.628016i
$403$	31.9091			1.58950
$404$	9.45540	−	6.30200i	0.470424	−	0.313536i
$405$	2.50301			0.124375
$406$		0			0
$407$		−	51.1745i		−	2.53663i
$408$	0.817902	−	0.993078i	0.0404922	−	0.0491647i
$409$		−	20.4715i		−	1.01225i	−0.862461	−	0.506124i	$-0.831078\pi$
$409$		−	20.4715i		−	1.01225i	0.862461	−	0.506124i	$-0.168922\pi$
$410$	4.77603	+	15.7775i	0.235871	+	0.779194i
$411$		−	1.23112i		−	0.0607266i
$412$	9.83046	−	6.55198i	0.484312	−	0.322793i
$413$		0			0
$414$	2.09803	+	6.93080i	0.103113	+	0.340630i
$415$			4.91239i			0.241140i
$416$	3.03243	−	29.8974i	0.148677	−	1.46584i
$417$	15.7788			0.772693
$418$	8.59207	+	28.3837i	0.420252	+	1.38829i
$419$		−	11.8439i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$419$		−	11.8439i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$420$		0			0
$421$		−	21.7928i		−	1.06211i	−0.847336	−	0.531057i	$-0.821795\pi$
$421$		−	21.7928i		−	1.06211i	0.847336	−	0.531057i	$-0.178205\pi$
$422$	−5.59425	+	1.69344i	−0.272324	+	0.0824356i
$423$	0.957682			0.0465641
$424$	−13.6419	−	11.2355i	−0.662507	−	0.545642i
$425$			0.575414i			0.0279117i
$426$	9.95188	−	3.01255i	0.482170	−	0.145959i
$427$		0			0
$428$	−17.7422	+	11.8251i	−0.857601	+	0.571589i
$429$			30.1535i			1.45582i
$430$	12.4238	−	3.76082i	0.599127	−	0.181363i
$431$		−	16.5393i		−	0.796669i	−0.917240	−	0.398335i	$-0.869588\pi$
$431$		−	16.5393i		−	0.796669i	0.917240	−	0.398335i	$-0.130412\pi$
$432$	3.69195	+	1.53933i	0.177629	+	0.0740608i
$433$		−	39.2724i		−	1.88731i	−0.330929	−	0.943656i	$-0.607362\pi$
$433$		−	39.2724i		−	1.88731i	0.330929	−	0.943656i	$-0.392638\pi$
$434$		0			0
$435$	6.45681			0.309580
$436$	3.52629	+	5.29078i	0.168879	+	0.253382i
$437$	−18.9166			−0.904901
$438$	−9.27676	+	2.80819i	−0.443261	+	0.134180i
$439$	−31.0331			−1.48113			−0.740564	−	0.671986i	$-0.765442\pi$
$439$	−31.0331			−1.48113			−0.740564	+	0.671986i	$0.765442\pi$
$440$	−25.5472	+	31.0189i	−1.21792	+	1.47877i
$441$		0			0
$442$	0.990063	+	3.27064i	0.0470925	+	0.155569i
$443$	−0.844928			−0.0401438			−0.0200719	−	0.999799i	$-0.506390\pi$
$443$	−0.844928			−0.0401438			−0.0200719	+	0.999799i	$0.506390\pi$
$444$	15.0041	−	10.0002i	0.712064	−	0.474589i
$445$			17.0917i			0.810222i
$446$	24.5079	−	7.41884i	1.16048	−	0.351292i
$447$	5.95556			0.281688
$448$		0			0
$449$	−41.7433			−1.96999			−0.984995	−	0.172585i	$-0.944788\pi$
$449$	−41.7433			−1.96999			−0.984995	+	0.172585i	$0.944788\pi$
$450$	−1.71230	+	0.518335i	−0.0807188	+	0.0244345i
$451$		−	26.4336i		−	1.24471i
$452$	−0.503341	+	0.335475i	−0.0236752	+	0.0157794i
$453$	3.59257			0.168794
$454$	−3.24726	−	10.7272i	−0.152401	−	0.503453i
$455$		0			0
$456$	−6.64294	+	8.06571i	−0.311084	+	0.377712i
$457$	−7.48572			−0.350167			−0.175083	−	0.984554i	$-0.556020\pi$
$457$	−7.48572			−0.350167			−0.175083	+	0.984554i	$0.556020\pi$
$458$	2.91791	−	0.883285i	0.136345	−	0.0412732i
$459$	−0.454858			−0.0212310
$460$	−14.2161	−	21.3296i	−0.662830	−	0.994496i
$461$	−4.33499			−0.201901			−0.100950	−	0.994891i	$-0.532188\pi$
$461$	−4.33499			−0.201901			−0.100950	+	0.994891i	$0.532188\pi$
$462$		0			0
$463$		−	35.3200i		−	1.64146i	−0.571316	−	0.820730i	$-0.693567\pi$
$463$		−	35.3200i		−	1.64146i	0.571316	−	0.820730i	$-0.306433\pi$
$464$	9.52383	+	3.97088i	0.442133	+	0.184343i
$465$		−	15.0347i		−	0.697218i
$466$	−27.0906	+	8.20065i	−1.25495	+	0.379888i
$467$			10.4987i			0.485821i	0.970049	+	0.242911i	$0.0781022\pi$
$467$			10.4987i			0.485821i	−0.970049	+	0.242911i	$0.921898\pi$
$468$	−8.84086	+	5.89241i	−0.408669	+	0.272377i
$469$		0			0
$470$	−3.24459	+	0.982175i	−0.149662	+	0.0453044i
$471$			0.983524i			0.0453184i
$472$	22.0994	+	18.2011i	1.01721	+	0.837774i
$473$	−20.8147			−0.957063
$474$	12.0642	−	3.65196i	0.554125	−	0.167740i
$475$		−	4.67348i		−	0.214434i
$476$		0			0
$477$			6.24836i			0.286093i
$478$	7.74089	+	25.5718i	0.354060	+	1.16963i
$479$	16.9275			0.773437			0.386719	−	0.922198i	$-0.373608\pi$
$479$	16.9275			0.773437			0.386719	+	0.922198i	$0.373608\pi$
$480$	−14.0869	−	1.42880i	−0.642975	−	0.0652156i
$481$			47.8937i			2.18376i
$482$	7.50161	+	24.7814i	0.341689	+	1.12876i
$483$		0			0
$484$	35.3135	−	23.5364i	1.60516	−	1.06983i
$485$			9.29291i			0.421969i
$486$	−0.409738	−	1.35356i	−0.0185861	−	0.0613986i
$487$			23.7270i			1.07517i	0.843209	+	0.537586i	$0.180664\pi$
$487$			23.7270i			1.07517i	−0.843209	+	0.537586i	$0.819336\pi$
$488$	−8.99733	+	10.9244i	−0.407290	+	0.494523i
$489$		−	2.52167i		−	0.114034i
$490$		0			0
$491$	−3.41198			−0.153980			−0.0769901	−	0.997032i	$-0.524531\pi$
$491$	−3.41198			−0.153980			−0.0769901	+	0.997032i	$0.524531\pi$
$492$	7.75019	−	5.16548i	0.349406	−	0.232878i
$493$	−1.17336			−0.0528456
$494$	−8.04122	−	26.5640i	−0.361792	−	1.19517i
$495$	14.2075			0.638581
$496$	9.24621	−	22.1763i	0.415167	−	0.995744i
$497$		0			0
$498$	2.65648	−	0.804149i	0.119040	−	0.0360348i
$499$	−17.4600			−0.781615			−0.390808	−	0.920472i	$-0.627804\pi$
$499$	−17.4600			−0.781615			−0.390808	+	0.920472i	$0.627804\pi$
$500$	−15.5583	+	10.3695i	−0.695787	+	0.463740i
$501$		−	5.26232i		−	0.235103i
$502$	1.40643	+	4.64610i	0.0627720	+	0.207366i
$503$	−7.08646			−0.315970			−0.157985	−	0.987442i	$-0.550500\pi$
$503$	−7.08646			−0.315970			−0.157985	+	0.987442i	$0.550500\pi$
$504$		0			0
$505$	14.2209			0.632824
$506$	11.9088	+	39.3405i	0.529412	+	1.74890i
$507$		−	15.2203i		−	0.675959i
$508$	−7.09615	−	10.6469i	−0.314841	−	0.472381i
$509$	37.9306			1.68124			0.840622	−	0.541623i	$-0.182190\pi$
$509$	37.9306			1.68124			0.840622	+	0.541623i	$0.182190\pi$
$510$	1.54104	−	0.466491i	0.0682385	−	0.0206566i
$511$		0			0
$512$	−19.8995	−	10.7708i	−0.879442	−	0.476006i
$513$	3.69433			0.163109
$514$	10.2717	+	33.9324i	0.453067	+	1.49669i
$515$	14.7850			0.651506
$516$	−4.06749	−	6.10278i	−0.179061	−	0.268660i
$517$	5.43598			0.239074
$518$		0			0
$519$			0.143623i			0.00630436i
$520$	23.9094	−	29.0302i	1.04850	−	1.27306i
$521$		−	7.98089i		−	0.349649i	−0.984600	−	0.174825i	$-0.944064\pi$
$521$		−	7.98089i		−	0.349649i	0.984600	−	0.174825i	$-0.0559358\pi$
$522$	−1.05697	−	3.49166i	−0.0462622	−	0.152826i
$523$			14.2336i			0.622393i	0.950346	+	0.311196i	$0.100730\pi$
$523$			14.2336i			0.622393i	−0.950346	+	0.311196i	$0.899270\pi$
$524$	−16.0864	−	24.1357i	−0.702736	−	1.05437i
$525$		0			0
$526$	6.35470	+	20.9926i	0.277078	+	0.915320i
$527$			2.73218i			0.119016i
$528$	20.9562	+	8.73750i	0.912001	+	0.380251i
$529$	−3.21883			−0.139949
$530$	−6.40816	−	21.1692i	−0.278353	−	0.919531i
$531$		−	10.1222i		−	0.439264i
$532$		0			0
$533$			24.7389i			1.07156i
$534$	9.24270	−	2.79787i	0.399971	−	0.121076i
$535$	−26.6843			−1.15366
$536$	−16.7275	+	20.3102i	−0.722520	+	0.877268i
$537$			18.9248i			0.816664i
$538$	−32.1244	+	9.72444i	−1.38498	+	0.419250i
$539$		0			0
$540$	2.77635	+	4.16558i	0.119475	+	0.179258i
$541$			7.42798i			0.319354i	0.987169	+	0.159677i	$0.0510452\pi$
$541$			7.42798i			0.319354i	−0.987169	+	0.159677i	$0.948955\pi$
$542$	19.9158	−	6.02875i	0.855457	−	0.258957i
$543$			22.2260i			0.953809i
$544$	2.55993	+	0.259649i	0.109756	+	0.0111323i
$545$			7.95734i			0.340855i
$546$		0			0
$547$	−28.2287			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$547$	−28.2287			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$548$	2.04887	−	1.36556i	0.0875232	−	0.0583340i
$549$	5.00367			0.213551
$550$	−9.71936	+	2.94217i	−0.414435	+	0.125454i
$551$	9.52997			0.405990
$552$	−9.20729	+	11.1793i	−0.391888	+	0.475822i
$553$		0			0
$554$	2.91834	+	9.64064i	0.123988	+	0.409592i
$555$	22.5662			0.957883
$556$	17.5020	+	26.2596i	0.742249	+	1.11366i
$557$			34.5692i			1.46474i	0.680906	+	0.732371i	$0.261586\pi$
$557$			34.5692i			1.46474i	−0.680906	+	0.732371i	$0.738414\pi$
$558$	−8.13036	+	2.46115i	−0.344185	+	0.104189i
$559$	19.4803			0.823929
$560$		0			0
$561$	−2.58186			−0.109006
$562$	−17.6722	+	5.34957i	−0.745455	+	0.225658i
$563$			11.7207i			0.493967i	0.969020	+	0.246983i	$0.0794393\pi$
$563$			11.7207i			0.493967i	−0.969020	+	0.246983i	$0.920561\pi$
$564$	1.06227	+	1.59380i	0.0447295	+	0.0671112i
$565$	−0.757026			−0.0318483
$566$	0.866059	+	2.86100i	0.0364032	+	0.120257i
$567$		0			0
$568$	16.0523	+	13.2207i	0.673538	+	0.554728i
$569$	−11.1065			−0.465608			−0.232804	−	0.972524i	$-0.574790\pi$
$569$	−11.1065			−0.465608			−0.232804	+	0.972524i	$0.574790\pi$
$570$	−12.5162	+	3.78881i	−0.524247	+	0.158696i
$571$	−35.5114			−1.48610			−0.743052	−	0.669234i	$-0.766622\pi$
$571$	−35.5114			−1.48610			−0.743052	+	0.669234i	$0.766622\pi$
$572$	−50.1824	+	33.4464i	−2.09823	+	1.39847i
$573$	11.7909			0.492573
$574$		0			0
$575$		−	6.47756i		−	0.270133i
$576$	1.53334	+	7.85168i	0.0638891	+	0.327153i
$577$			27.0551i			1.12632i	0.826348	+	0.563159i	$0.190414\pi$
$577$			27.0551i			1.12632i	−0.826348	+	0.563159i	$0.809586\pi$
$578$	22.7304	−	6.88076i	0.945461	−	0.286202i
$579$		−	26.8224i		−	1.11470i
$580$	7.16193	+	10.7456i	0.297383	+	0.446188i
$581$		0			0
$582$	5.02535	−	1.52123i	0.208307	−	0.0630571i
$583$			35.4668i			1.46889i
$584$	−14.9633	−	12.3238i	−0.619186	−	0.509963i
$585$	−13.2967			−0.549750
$586$	−0.452090	+	0.136853i	−0.0186757	+	0.00565335i
$587$		−	35.3797i		−	1.46027i	−0.683300	−	0.730137i	$-0.739456\pi$
$587$		−	35.3797i		−	1.46027i	0.683300	−	0.730137i	$-0.260544\pi$
$588$		0			0
$589$		−	22.1906i		−	0.914347i
$590$	10.3810	+	34.2934i	0.427380	+	1.41184i
$591$	−16.5842			−0.682181
$592$	33.2853	+	13.8780i	1.36802	+	0.570383i
$593$		−	39.2204i		−	1.61059i	−0.592875	−	0.805294i	$-0.702007\pi$
$593$		−	39.2204i		−	1.61059i	0.592875	−	0.805294i	$-0.297993\pi$
$594$	−2.32575	−	7.68304i	−0.0954266	−	0.315239i
$595$		0			0
$596$	6.60594	+	9.91142i	0.270590	+	0.405988i
$597$		−	11.4084i		−	0.466915i
$598$	−11.1453	−	36.8183i	−0.455767	−	1.50561i
$599$		−	47.6722i		−	1.94783i	−0.226908	−	0.973916i	$-0.572862\pi$
$599$		−	47.6722i		−	1.94783i	0.226908	−	0.973916i	$-0.427138\pi$
$600$	−2.76193	−	2.27473i	−0.112755	−	0.0928654i
$601$		−	13.4207i		−	0.547442i	−0.961809	−	0.273721i	$-0.911746\pi$
$601$		−	13.4207i		−	0.547442i	0.961809	−	0.273721i	$-0.0882544\pi$
$602$		0			0
$603$	9.30266			0.378834
$604$	3.98490	+	5.97886i	0.162143	+	0.243277i
$605$	53.1116			2.15929
$606$	−2.32794	−	7.69029i	−0.0945662	−	0.312397i
$607$	−38.2781			−1.55366			−0.776831	−	0.629709i	$-0.783174\pi$
$607$	−38.2781			−1.55366			−0.776831	+	0.629709i	$0.783174\pi$
$608$	−20.7916	−	2.10885i	−0.843210	−	0.0855251i
$609$		0			0
$610$	−16.9522	+	5.13164i	−0.686376	+	0.207774i
$611$	−5.08748			−0.205817
$612$	−0.504531	−	0.756989i	−0.0203945	−	0.0305995i
$613$			19.5404i			0.789230i	0.918847	+	0.394615i	$0.129122\pi$
$613$			19.5404i			0.789230i	−0.918847	+	0.394615i	$0.870878\pi$
$614$	−3.84801	−	12.7118i	−0.155293	−	0.513007i
$615$	11.6563			0.470028
$616$		0			0
$617$	−1.16195			−0.0467785			−0.0233892	−	0.999726i	$-0.507446\pi$
$617$	−1.16195			−0.0467785			−0.0233892	+	0.999726i	$0.507446\pi$
$618$	−2.42028	−	7.99534i	−0.0973580	−	0.321620i
$619$		−	35.8930i		−	1.44266i	−0.692592	−	0.721330i	$-0.743531\pi$
$619$		−	35.8930i		−	1.44266i	0.692592	−	0.721330i	$-0.256469\pi$
$620$	25.0212	−	16.6766i	1.00488	−	0.669748i
$621$	5.12043			0.205476
$622$	21.4877	−	6.50459i	0.861579	−	0.260810i
$623$		0			0
$624$	−19.6127	−	8.17733i	−0.785135	−	0.327355i
$625$	−29.7249			−1.18900
$626$	−13.1795	−	43.5380i	−0.526757	−	1.74013i
$627$	20.9697			0.837449
$628$	−1.63681	+	1.09093i	−0.0653158	+	0.0435329i
$629$	−4.10084			−0.163511
$630$		0			0
$631$		−	8.26460i		−	0.329008i	−0.986376	−	0.164504i	$-0.947398\pi$
$631$		−	8.26460i		−	0.329008i	0.986376	−	0.164504i	$-0.0526024\pi$
$632$	19.4593	+	16.0268i	0.774051	+	0.637510i
$633$			4.13300i			0.164272i
$634$	−6.25716	−	20.6704i	−0.248504	−	0.820925i
$635$		−	16.0130i		−	0.635457i
$636$	−10.3987	+	6.93071i	−0.412335	+	0.274821i
$637$		0			0
$638$	−5.99955	−	19.8193i	−0.237524	−	0.784655i
$639$		−	7.35240i		−	0.290856i
$640$	−13.2474	−	25.0286i	−0.523649	−	0.989343i
$641$	28.9910			1.14508			0.572539	−	0.819878i	$-0.305959\pi$
$641$	28.9910			1.14508			0.572539	+	0.819878i	$0.305959\pi$
$642$	4.36817	+	14.4301i	0.172398	+	0.569512i
$643$			39.1239i			1.54289i	0.636293	+	0.771447i	$0.280467\pi$
$643$			39.1239i			1.54289i	−0.636293	+	0.771447i	$0.719533\pi$
$644$		0			0
$645$		−	9.17860i		−	0.361407i
$646$	2.27451	−	0.688521i	0.0894893	−	0.0270895i
$647$	12.1898			0.479231			0.239616	−	0.970868i	$-0.422979\pi$
$647$	12.1898			0.479231			0.239616	+	0.970868i	$0.422979\pi$
$648$	1.79815	−	2.18327i	0.0706379	−	0.0857670i
$649$		−	57.4552i		−	2.25531i
$650$	9.09624	−	2.75354i	0.356784	−	0.108003i
$651$		0			0
$652$	4.19664	−	2.79705i	0.164353	−	0.109541i
$653$		−	10.1636i		−	0.397732i	−0.980027	−	0.198866i	$-0.936274\pi$
$653$		−	10.1636i		−	0.397732i	0.980027	−	0.198866i	$-0.0637259\pi$
$654$	4.30311	−	1.30260i	0.168265	−	0.0509358i
$655$		−	36.3001i		−	1.41836i
$656$	17.1931	+	7.16852i	0.671278	+	0.279884i
$657$			6.85362i			0.267385i
$658$		0			0
$659$	−8.28558			−0.322760			−0.161380	−	0.986892i	$-0.551595\pi$
$659$	−8.28558			−0.322760			−0.161380	+	0.986892i	$0.551595\pi$
$660$	15.7591	+	23.6446i	0.613421	+	0.920365i
$661$	16.6178			0.646358			0.323179	−	0.946338i	$-0.395248\pi$
$661$	16.6178			0.646358			0.323179	+	0.946338i	$0.395248\pi$
$662$	−28.4760	+	8.62001i	−1.10675	+	0.335026i
$663$	2.41633			0.0938426
$664$	4.28487	+	3.52903i	0.166285	+	0.136953i
$665$		0			0
$666$	−3.69405	−	12.2032i	−0.143141	−	0.472864i
$667$	13.2088			0.511446
$668$	8.75771	−	5.83700i	0.338846	−	0.225840i
$669$		−	18.1063i		−	0.700031i
$670$	−31.5171	+	9.54058i	−1.21761	+	0.368585i
$671$	28.4018			1.09644
$672$		0			0
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$	1.60194	−	0.484927i	0.0617045	−	0.0186787i
$675$			1.26504i			0.0486915i
$676$	25.3301	−	16.8825i	0.974236	−	0.649326i
$677$	−20.4402			−0.785580			−0.392790	−	0.919628i	$-0.628490\pi$
$677$	−20.4402			−0.785580			−0.392790	+	0.919628i	$0.628490\pi$
$678$	0.123924	+	0.409378i	0.00475926	+	0.0157221i
$679$		0			0
$680$	2.48568	+	2.04721i	0.0953215	+	0.0785070i
$681$	−7.92521			−0.303695
$682$	−46.1494	+	13.9700i	−1.76715	+	0.534938i
$683$	−15.7455			−0.602484			−0.301242	−	0.953548i	$-0.597401\pi$
$683$	−15.7455			−0.602484			−0.301242	+	0.953548i	$0.597401\pi$
$684$	4.09777	+	6.14821i	0.156682	+	0.235083i
$685$	3.08150			0.117738
$686$		0			0
$687$		−	2.15573i		−	0.0822464i
$688$	5.64475	−	13.5385i	0.215204	−	0.516150i
$689$		−	33.1930i		−	1.26455i
$690$	−17.3478	+	5.25139i	−0.660420	+	0.199917i
$691$			3.19097i			0.121390i	0.998156	+	0.0606952i	$0.0193318\pi$
$691$			3.19097i			0.121390i	−0.998156	+	0.0606952i	$0.980668\pi$
$692$	−0.239022	+	0.159308i	−0.00908626	+	0.00605597i
$693$		0			0
$694$	−6.51522	+	1.97223i	−0.247314	+	0.0748650i
$695$			39.4945i			1.49811i
$696$	4.63854	−	5.63201i	0.175823	−	0.213481i
$697$	−2.11824			−0.0802340
$698$	48.0231	−	14.5371i	1.81770	−	0.550239i
$699$			20.0144i			0.757015i
$700$		0			0
$701$			39.2121i			1.48102i	0.672045	+	0.740511i	$0.265416\pi$
$701$			39.2121i			1.48102i	−0.672045	+	0.740511i	$0.734584\pi$
$702$	2.17664	+	7.19047i	0.0821520	+	0.271387i
$703$	33.3067			1.25619
$704$	8.70351	+	44.5676i	0.328026	+	1.67970i
$705$			2.39708i			0.0902794i
$706$	1.95737	+	6.46612i	0.0736666	+	0.243356i
$707$		0			0
$708$	16.8456	−	11.2275i	0.633096	−	0.421957i
$709$		−	38.5269i		−	1.44691i	−0.690372	−	0.723454i	$-0.742553\pi$
$709$		−	38.5269i		−	1.44691i	0.690372	−	0.723454i	$-0.257447\pi$
$710$	7.54044	+	24.9096i	0.282988	+	0.934842i
$711$		−	8.91293i		−	0.334261i
$712$	14.9084	+	12.2786i	0.558714	+	0.460158i
$713$		−	30.7567i		−	1.15185i
$714$		0			0
$715$	−75.4744			−2.82258
$716$	−31.4952	+	20.9915i	−1.17703	+	0.784488i
$717$	18.8923			0.705547
$718$	−15.1253	−	49.9660i	−0.564471	−	1.86472i
$719$	23.0018			0.857824			0.428912	−	0.903346i	$-0.358897\pi$
$719$	23.0018			0.857824			0.428912	+	0.903346i	$0.358897\pi$
$720$	−3.85294	+	9.24097i	−0.143591	+	0.344391i
$721$		0			0
$722$	7.24417	−	2.19289i	0.269600	−	0.0816111i
$723$	18.3083			0.680894
$724$	−36.9892	+	24.6532i	−1.37469	+	0.916229i
$725$			3.26333i			0.121197i
$726$	−8.69426	−	28.7213i	−0.322674	−	1.06595i
$727$	−21.8433			−0.810125			−0.405062	−	0.914289i	$-0.632750\pi$
$727$	−21.8433			−0.810125			−0.405062	+	0.914289i	$0.632750\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−7.02891	−	23.2198i	−0.260151	−	0.859403i
$731$			1.66798i			0.0616924i
$732$	5.55010	+	8.32726i	0.205138	+	0.307784i
$733$	−48.1361			−1.77795			−0.888974	−	0.457957i	$-0.848581\pi$
$733$	−48.1361			−1.77795			−0.888974	+	0.457957i	$0.848581\pi$
$734$	0.769946	−	0.233072i	0.0284192	−	0.00860283i
$735$		0			0
$736$	−28.8177	−	2.92292i	−1.06223	−	0.107740i
$737$	52.8037			1.94505
$738$	−1.90812	−	6.30341i	−0.0702387	−	0.232032i
$739$	−6.46911			−0.237970			−0.118985	−	0.992896i	$-0.537964\pi$
$739$	−6.46911			−0.237970			−0.118985	+	0.992896i	$0.537964\pi$
$740$	25.0306	+	37.5554i	0.920143	+	1.38056i
$741$	−19.6253			−0.720953
$742$		0			0
$743$			16.6709i			0.611597i	0.952096	+	0.305798i	$0.0989234\pi$
$743$			16.6709i			0.611597i	−0.952096	+	0.305798i	$0.901077\pi$
$744$	−13.1142	−	10.8009i	−0.480789	−	0.395979i
$745$			14.9068i			0.546143i
$746$	−9.60107	−	31.7169i	−0.351520	−	1.16124i
$747$		−	1.96259i		−	0.0718076i
$748$	−2.86381	−	4.29681i	−0.104711	−	0.157107i
$749$		0			0
$750$	3.83048	+	12.6539i	0.139869	+	0.462055i
$751$		−	24.5602i		−	0.896215i	−0.893980	−	0.448108i	$-0.852098\pi$
$751$		−	24.5602i		−	0.896215i	0.893980	−	0.448108i	$-0.147902\pi$
$752$	−1.47418	+	3.53571i	−0.0537580	+	0.128934i
$753$	3.43251			0.125088
$754$	5.61491	+	18.5487i	0.204483	+	0.675504i
$755$			8.99223i			0.327261i
$756$		0			0
$757$		−	2.80888i		−	0.102091i	−0.998696	−	0.0510453i	$-0.983745\pi$
$757$		−	2.80888i		−	0.102091i	0.998696	−	0.0510453i	$-0.0162553\pi$
$758$	−19.9297	+	6.03296i	−0.723880	+	0.219127i
$759$	29.0645			1.05498
$760$	−20.1885	−	16.6273i	−0.732315	−	0.603136i
$761$		−	20.1736i		−	0.731292i	−0.930754	−	0.365646i	$-0.880848\pi$
$761$		−	20.1736i		−	0.731292i	0.930754	−	0.365646i	$-0.119152\pi$
$762$	−8.65939	+	2.62130i	−0.313697	+	0.0949596i
$763$		0			0
$764$	13.0786	+	19.6228i	0.473166	+	0.709929i
$765$		−	1.13851i		−	0.0411630i
$766$	−6.76113	+	2.04667i	−0.244289	+	0.0739493i
$767$			53.7717i			1.94158i
$768$	−11.3662	+	11.2610i	−0.410143	+	0.406345i
$769$		−	32.1388i		−	1.15895i	−0.814988	−	0.579477i	$-0.803257\pi$
$769$		−	32.1388i		−	1.15895i	0.814988	−	0.579477i	$-0.196743\pi$
$770$		0			0
$771$	25.0690			0.902840
$772$	44.6387	−	29.7516i	1.60658	−	1.07078i
$773$	−22.5863			−0.812371			−0.406186	−	0.913791i	$-0.633141\pi$
$773$	−22.5863			−0.812371			−0.406186	+	0.913791i	$0.633141\pi$
$774$	−4.96353	+	1.50252i	−0.178410	+	0.0540070i
$775$	7.59867			0.272952
$776$	8.10583	+	6.67598i	0.290982	+	0.239654i
$777$		0			0
$778$	−13.0628	−	43.1528i	−0.468326	−	1.54710i
$779$	17.2042			0.616404
$780$	−14.7487	−	22.1287i	−0.528090	−	0.792336i
$781$		−	41.7336i		−	1.49335i
$782$	3.15253	−	0.954308i	0.112734	−	0.0341260i
$783$	−2.57962			−0.0921882
$784$		0			0
$785$	−2.46177			−0.0878642
$786$	−19.6301	+	5.94226i	−0.700182	+	0.211953i
$787$			33.7858i			1.20433i	0.798371	+	0.602166i	$0.205696\pi$
$787$			33.7858i			1.20433i	−0.798371	+	0.602166i	$0.794304\pi$
$788$	−18.3952	−	27.5999i	−0.655303	−	0.983204i
$789$	15.5092			0.552142
$790$	9.14088	+	30.1967i	0.325218	+	1.07435i
$791$		0			0
$792$	10.2066	−	12.3927i	0.362676	−	0.440354i
$793$	−26.5809			−0.943916
$794$	44.5402	−	13.4828i	1.58067	−	0.478488i
$795$	−15.6397			−0.554682
$796$	18.9862	−	12.6543i	0.672948	−	0.448518i
$797$	−27.0472			−0.958061			−0.479030	−	0.877798i	$-0.659012\pi$
$797$	−27.0472			−0.958061			−0.479030	+	0.877798i	$0.659012\pi$
$798$		0			0
$799$		−	0.435609i		−	0.0154108i
$800$	0.722129	−	7.11963i	0.0255311	−	0.251717i
$801$		−	6.82845i		−	0.241271i
$802$	0.287593	−	0.0870577i	0.0101553	−	0.00307411i
$803$			38.9024i			1.37284i
$804$	10.3186	+	15.4818i	0.363908	+	0.546000i
$805$		0			0
$806$	43.1907	−	13.0743i	1.52133	−	0.460524i
$807$			23.7333i			0.835453i
$808$	10.2163	−	12.4044i	0.359407	−	0.436384i
$809$	−49.8449			−1.75245			−0.876226	−	0.481900i	$-0.839947\pi$
$809$	−49.8449			−1.75245			−0.876226	+	0.481900i	$0.839947\pi$
$810$	3.38796	−	1.02558i	0.119041	−	0.0360351i
$811$			36.5330i			1.28285i	0.767188	+	0.641423i	$0.221655\pi$
$811$			36.5330i			1.28285i	−0.767188	+	0.641423i	$0.778345\pi$
$812$		0			0
$813$		−	14.7137i		−	0.516031i
$814$	−20.9681	−	69.2676i	−0.734932	−	2.42783i
$815$	6.31175			0.221091
$816$	0.700175	−	1.67931i	0.0245110	−	0.0587877i
$817$		−	13.5472i		−	0.473957i
$818$	−8.38793	−	27.7093i	−0.293277	−	0.968832i
$819$		0			0
$820$	12.9292	+	19.3988i	0.451509	+	0.677435i
$821$			3.00119i			0.104742i	0.998628	+	0.0523711i	$0.0166779\pi$
$821$			3.00119i			0.104742i	−0.998628	+	0.0523711i	$0.983322\pi$
$822$	−0.504436	−	1.66639i	−0.0175942	−	0.0581220i
$823$			15.9975i			0.557639i	0.960343	+	0.278820i	$0.0899432\pi$
$823$			15.9975i			0.557639i	−0.960343	+	0.278820i	$0.910057\pi$
$824$	10.6215	−	12.8964i	0.370017	−	0.449267i
$825$			7.18061i			0.249997i
$826$		0			0
$827$	4.57856			0.159212			0.0796060	−	0.996826i	$-0.474634\pi$
$827$	4.57856			0.159212			0.0796060	+	0.996826i	$0.474634\pi$
$828$	5.67961	+	8.52158i	0.197380	+	0.296145i
$829$	−3.06153			−0.106331			−0.0531657	−	0.998586i	$-0.516931\pi$
$829$	−3.06153			−0.106331			−0.0531657	+	0.998586i	$0.516931\pi$
$830$	2.01279	+	6.64919i	0.0698649	+	0.230797i
$831$	7.12245			0.247075
$832$	−8.14552	−	41.7103i	−0.282395	−	1.44605i
$833$		0			0
$834$	21.3575	−	6.46518i	0.739551	−	0.223871i
$835$	13.1716			0.455823
$836$	23.2597	+	34.8984i	0.804454	+	1.20699i
$837$			6.00666i			0.207621i
$838$	−4.85290	−	16.0314i	−0.167641	−	0.553796i
$839$	39.0864			1.34941			0.674706	−	0.738087i	$-0.264270\pi$
$839$	39.0864			1.34941			0.674706	+	0.738087i	$0.264270\pi$
$840$		0			0
$841$	22.3456			0.770536
$842$	−8.92932	−	29.4977i	−0.307725	−	1.01656i
$843$			13.0561i			0.449676i
$844$	−6.87826	+	4.58435i	−0.236760	+	0.157800i
$845$	38.0966			1.31056
$846$	1.29628	−	0.392398i	0.0445669	−	0.0134909i
$847$		0			0
$848$	−23.0686	−	9.61825i	−0.792179	−	0.330292i
$849$	2.11369			0.0725418
$850$	0.235769	+	0.778856i	0.00808680	+	0.0267145i
$851$	46.1640			1.58248
$852$	12.2361	−	8.15532i	0.419201	−	0.279397i
$853$	26.4897			0.906989			0.453495	−	0.891259i	$-0.350177\pi$
$853$	26.4897			0.906989			0.453495	+	0.891259i	$0.350177\pi$
$854$		0			0
$855$			9.24692i			0.316238i
$856$	−19.1699	+	23.2756i	−0.655212	+	0.795544i
$857$		−	44.9255i		−	1.53462i	−0.641273	−	0.767312i	$-0.721594\pi$
$857$		−	44.9255i		−	1.53462i	0.641273	−	0.767312i	$-0.278406\pi$
$858$	12.3550	+	40.8145i	0.421794	+	1.39338i
$859$			35.4056i			1.20802i	0.796976	+	0.604011i	$0.206432\pi$
$859$			35.4056i			1.20802i	−0.796976	+	0.604011i	$0.793568\pi$
$860$	15.2753	−	10.1810i	0.520883	−	0.347168i
$861$		0			0
$862$	−6.77677	−	22.3869i	−0.230818	−	0.762499i
$863$		−	2.77632i		−	0.0945072i	−0.998883	−	0.0472536i	$-0.984953\pi$
$863$		−	2.77632i		−	0.0945072i	0.998883	−	0.0472536i	$-0.0150469\pi$
$864$	5.62798	+	0.570834i	0.191468	+	0.0194202i
$865$	−0.359490			−0.0122230
$866$	−16.0914	−	53.1574i	−0.546807	−	1.80636i
$867$		−	16.7931i		−	0.570324i
$868$		0			0
$869$		−	50.5915i		−	1.71620i
$870$	8.73966	−	2.64560i	0.296302	−	0.0896942i
$871$	−49.4184			−1.67448
$872$	6.94086	+	5.71651i	0.235047	+	0.193585i
$873$		−	3.71270i		−	0.125656i
$874$	−25.6046	+	7.75082i	−0.866089	+	0.262175i
$875$		0			0
$876$	−11.4060	+	7.60207i	−0.385373	+	0.256850i
$877$			16.5427i			0.558608i	0.960203	+	0.279304i	$0.0901036\pi$
$877$			16.5427i			0.558608i	−0.960203	+	0.279304i	$0.909896\pi$
$878$	−42.0050	+	12.7154i	−1.41760	+	0.429125i
$879$			0.334002i			0.0112656i
$880$	−21.8700	+	52.4535i	−0.737238	+	1.76821i
$881$			24.6158i			0.829327i	0.909975	+	0.414664i	$0.136101\pi$
$881$			24.6158i			0.829327i	−0.909975	+	0.414664i	$0.863899\pi$
$882$		0			0
$883$	40.4623			1.36167			0.680833	−	0.732439i	$-0.261618\pi$
$883$	40.4623			1.36167			0.680833	+	0.732439i	$0.261618\pi$
$884$	2.68021	+	4.02134i	0.0901453	+	0.135252i
$885$	25.3358			0.851654
$886$	−1.14366	+	0.346199i	−0.0384219	+	0.0116308i
$887$	9.28462			0.311747			0.155873	−	0.987777i	$-0.450181\pi$
$887$	9.28462			0.311747			0.155873	+	0.987777i	$0.450181\pi$
$888$	16.2115	−	19.6836i	0.544021	−	0.660538i
$889$		0			0
$890$	7.00309	+	23.1345i	0.234744	+	0.775471i
$891$	−5.67619			−0.190159
$892$	30.1331	−	20.0836i	1.00893	−	0.672450i
$893$			3.53799i			0.118394i
$894$	8.06119	−	2.44022i	0.269606	−	0.0816130i
$895$	−47.3688			−1.58337
$896$		0			0
$897$	−27.2012			−0.908221
$898$	−56.5019	+	17.1038i	−1.88549	+	0.570761i
$899$			15.4949i			0.516784i
$900$	−2.10532	+	1.40319i	−0.0701773	+	0.0467730i
$901$	2.84212			0.0946846
$902$	−10.8308	−	35.7793i	−0.360627	−	1.19132i
$903$		0			0
$904$	−0.543843	+	0.660322i	−0.0180880	+	0.0219620i
$905$	−55.6318			−1.84926
$906$	4.86275	−	1.47201i	0.161554	−	0.0489043i
$907$	5.10654			0.169560			0.0847800	−	0.996400i	$-0.472981\pi$
$907$	5.10654			0.169560			0.0847800	+	0.996400i	$0.472981\pi$
$908$	−8.79069	−	13.1894i	−0.291729	−	0.437705i
$909$	−5.68155			−0.188445
$910$		0			0
$911$			36.3702i			1.20500i	0.798119	+	0.602500i	$0.205829\pi$
$911$			36.3702i			1.20500i	−0.798119	+	0.602500i	$0.794171\pi$
$912$	−5.68677	+	13.6393i	−0.188308	+	0.451641i
$913$		−	11.1401i		−	0.368682i
$914$	−10.1323	+	3.06718i	−0.335148	+	0.101453i
$915$			12.5242i			0.414038i
$916$	3.58764	−	2.39115i	0.118539	−	0.0790059i
$917$		0			0
$918$	−0.615676	+	0.186372i	−0.0203203	+	0.00615121i
$919$		−	46.6786i		−	1.53978i	−0.638174	−	0.769892i	$-0.720310\pi$
$919$		−	46.6786i		−	1.53978i	0.638174	−	0.769892i	$-0.279690\pi$
$920$	−27.9818	−	23.0459i	−0.922534	−	0.759801i
$921$	−9.39141			−0.309458
$922$	−5.86765	+	1.77621i	−0.193241	+	0.0584963i
$923$			39.0580i			1.28561i
$924$		0			0
$925$			11.4052i			0.375000i
$926$	−14.4719	−	47.8076i	−0.475577	−	1.57106i
$927$	−5.90691			−0.194008
$928$	14.5181	+	1.47254i	0.476579	+	0.0483384i
$929$			39.1063i			1.28304i	0.767108	+	0.641518i	$0.221695\pi$
$929$			39.1063i			1.28304i	−0.767108	+	0.641518i	$0.778305\pi$
$930$	−6.16029	−	20.3503i	−0.202004	−	0.667314i
$931$		0			0
$932$	−33.3086	+	22.2001i	−1.09106	+	0.727188i
$933$		−	15.8750i		−	0.519724i
$934$	4.30170	+	14.2106i	0.140756	+	0.464984i
$935$		−	6.46241i		−	0.211343i
$936$	−9.55226	+	11.5981i	−0.312225	+	0.379097i
$937$		−	14.4038i		−	0.470551i	−0.971929	−	0.235275i	$-0.924401\pi$
$937$		−	14.4038i		−	0.470551i	0.971929	−	0.235275i	$-0.0755992\pi$
$938$		0			0
$939$	−32.1656			−1.04969
$940$	−3.98930	+	2.65886i	−0.130117	+	0.0867224i
$941$	−26.2537			−0.855848			−0.427924	−	0.903815i	$-0.640755\pi$
$941$	−26.2537			−0.855848			−0.427924	+	0.903815i	$0.640755\pi$
$942$	0.402987	+	1.33125i	0.0131300	+	0.0433746i
$943$	23.8455			0.776515
$944$	37.3704	+	15.5813i	1.21630	+	0.507128i
$945$		0			0
$946$	−28.1739	+	8.52858i	−0.916014	+	0.277288i
$947$	15.7071			0.510412			0.255206	−	0.966887i	$-0.417857\pi$
$947$	15.7071			0.510412			0.255206	+	0.966887i	$0.417857\pi$
$948$	14.8332	−	9.88627i	0.481759	−	0.321091i
$949$		−	36.4084i		−	1.18187i
$950$	−1.91490	−	6.32581i	−0.0621275	−	0.205236i
$951$	−15.2712			−0.495201
$952$		0			0
$953$	42.8466			1.38794			0.693968	−	0.720006i	$-0.255861\pi$
$953$	42.8466			1.38794			0.693968	+	0.720006i	$0.255861\pi$
$954$	2.56019	+	8.45750i	0.0828891	+	0.273822i
$955$			29.5128i			0.955011i
$956$	20.9555	+	31.4412i	0.677748	+	1.01688i
$957$	−14.6424			−0.473322
$958$	22.9123	−	6.93583i	0.740264	−	0.224087i
$959$		0			0
$960$	−19.6528	+	3.83795i	−0.634292	+	0.123869i
$961$	5.07998			0.163870
$962$	19.6238	+	64.8268i	0.632698	+	2.09010i
$963$	10.6609			0.343543
$964$	20.3077	+	30.4693i	0.654067	+	0.981350i
$965$	67.1368			2.16121
$966$		0			0
$967$			0.672082i			0.0216127i	0.999942	+	0.0108063i	$0.00343983\pi$
$967$			0.672082i			0.0216127i	−0.999942	+	0.0108063i	$0.996560\pi$
$968$	38.1551	−	46.3270i	1.22635	−	1.48901i
$969$		−	1.68039i		−	0.0539820i
$970$	3.80765	+	12.5785i	0.122256	+	0.403871i
$971$		−	7.45749i		−	0.239322i	−0.992815	−	0.119661i	$-0.961819\pi$
$971$		−	7.45749i		−	0.239322i	0.992815	−	0.119661i	$-0.0381808\pi$
$972$	−1.10921	−	1.66423i	−0.0355778	−	0.0533802i
$973$		0			0
$974$	9.72184	+	32.1158i	0.311508	+	1.02906i
$975$		−	6.72025i		−	0.215220i
$976$	−7.70228	+	18.4733i	−0.246544	+	0.591316i
$977$	17.5740			0.562243			0.281121	−	0.959672i	$-0.409294\pi$
$977$	17.5740			0.562243			0.281121	+	0.959672i	$0.409294\pi$
$978$	−1.03322	−	3.41322i	−0.0330388	−	0.109143i
$979$		−	38.7596i		−	1.23876i
$980$		0			0
$981$		−	3.17911i		−	0.101501i
$982$	−4.61830	+	1.39801i	−0.147376	+	0.0446124i
$983$	−42.7322			−1.36294			−0.681472	−	0.731844i	$-0.738660\pi$
$983$	−42.7322			−1.36294			−0.681472	+	0.731844i	$0.738660\pi$
$984$	8.37383	−	10.1673i	0.266948	−	0.324122i
$985$		−	41.5103i		−	1.32263i
$986$	−1.58821	+	0.480770i	−0.0505790	+	0.0153108i
$987$		0			0
$988$	−21.7685	−	32.6610i	−0.692548	−	1.03909i
$989$		−	18.7768i		−	0.597067i
$990$	19.2307	−	5.82136i	0.611192	−	0.185015i
$991$			45.4228i			1.44290i	0.692465	+	0.721451i	$0.256525\pi$
$991$			45.4228i			1.44290i	−0.692465	+	0.721451i	$0.743475\pi$
$992$	3.42881	−	33.8054i	0.108865	−	1.07332i
$993$			21.0379i			0.667617i
$994$		0			0
$995$	28.5553			0.905264
$996$	3.26621	−	2.17692i	0.103494	−	0.0689784i
$997$	−43.7436			−1.38537			−0.692687	−	0.721239i	$-0.743573\pi$
$997$	−43.7436			−1.38537			−0.692687	+	0.721239i	$0.743573\pi$
$998$	−23.6330	+	7.15400i	−0.748091	+	0.226456i
$999$	−9.01565			−0.285242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.p.a.979.25		32
4.3	odd	2		4704.2.p.a.3919.2		32
7.2	even	3		168.2.t.a.115.4	yes	32
7.3	odd	6		168.2.t.a.19.8	yes	32
7.6	odd	2	inner	1176.2.p.a.979.26		32
8.3	odd	2	inner	1176.2.p.a.979.28		32
8.5	even	2		4704.2.p.a.3919.16		32
21.2	odd	6		504.2.bk.c.451.13		32
21.17	even	6		504.2.bk.c.19.9		32
28.3	even	6		672.2.bb.a.271.7		32
28.23	odd	6		672.2.bb.a.367.2		32
28.27	even	2		4704.2.p.a.3919.15		32
56.3	even	6		168.2.t.a.19.4	✓	32
56.13	odd	2		4704.2.p.a.3919.1		32
56.27	even	2	inner	1176.2.p.a.979.27		32
56.37	even	6		672.2.bb.a.367.7		32
56.45	odd	6		672.2.bb.a.271.2		32
56.51	odd	6		168.2.t.a.115.8	yes	32
84.23	even	6		2016.2.bs.c.1711.13		32
84.59	odd	6		2016.2.bs.c.271.4		32
168.59	odd	6		504.2.bk.c.19.13		32
168.101	even	6		2016.2.bs.c.271.13		32
168.107	even	6		504.2.bk.c.451.9		32
168.149	odd	6		2016.2.bs.c.1711.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	56.3	even	6
168.2.t.a.19.8	yes	32	7.3	odd	6
168.2.t.a.115.4	yes	32	7.2	even	3
168.2.t.a.115.8	yes	32	56.51	odd	6
504.2.bk.c.19.9		32	21.17	even	6
504.2.bk.c.19.13		32	168.59	odd	6
504.2.bk.c.451.9		32	168.107	even	6
504.2.bk.c.451.13		32	21.2	odd	6
672.2.bb.a.271.2		32	56.45	odd	6
672.2.bb.a.271.7		32	28.3	even	6
672.2.bb.a.367.2		32	28.23	odd	6
672.2.bb.a.367.7		32	56.37	even	6
1176.2.p.a.979.25		32	1.1	even	1	trivial
1176.2.p.a.979.26		32	7.6	odd	2	inner
1176.2.p.a.979.27		32	56.27	even	2	inner
1176.2.p.a.979.28		32	8.3	odd	2	inner
2016.2.bs.c.271.4		32	84.59	odd	6
2016.2.bs.c.271.13		32	168.101	even	6
2016.2.bs.c.1711.4		32	168.149	odd	6
2016.2.bs.c.1711.13		32	84.23	even	6
4704.2.p.a.3919.1		32	56.13	odd	2
4704.2.p.a.3919.2		32	4.3	odd	2
4704.2.p.a.3919.15		32	28.27	even	2
4704.2.p.a.3919.16		32	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35356 - 0.409738i) q^{2} -1.00000i q^{3} +(1.66423 - 1.10921i) q^{4} +2.50301 q^{5} +(-0.409738 - 1.35356i) q^{6} +(1.79815 - 2.18327i) q^{8} -1.00000 q^{9} +(3.38796 - 1.02558i) q^{10} -5.67619 q^{11} +(-1.10921 - 1.66423i) q^{12} +5.31228 q^{13} -2.50301i q^{15} +(1.53933 - 3.69195i) q^{16} +0.454858i q^{17} +(-1.35356 + 0.409738i) q^{18} -3.69433i q^{19} +(4.16558 - 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} -5.12043i q^{23} +(-2.18327 - 1.79815i) q^{24} +1.26504 q^{25} +(7.19047 - 2.17664i) q^{26} +1.00000i q^{27} +2.57962i q^{29} +(-1.02558 - 3.38796i) q^{30} +6.00666 q^{31} +(0.570834 - 5.62798i) q^{32} +5.67619i q^{33} +(0.186372 + 0.615676i) q^{34} +(-1.66423 + 1.10921i) q^{36} +9.01565i q^{37} +(-1.51370 - 5.00048i) q^{38} -5.31228i q^{39} +(4.50077 - 5.46474i) q^{40} +4.65692i q^{41} +3.66703 q^{43} +(-9.44648 + 6.29606i) q^{44} -2.50301 q^{45} +(-2.09803 - 6.93080i) q^{46} -0.957682 q^{47} +(-3.69195 - 1.53933i) q^{48} +(1.71230 - 0.518335i) q^{50} +0.454858 q^{51} +(8.84086 - 5.89241i) q^{52} -6.24836i q^{53} +(0.409738 + 1.35356i) q^{54} -14.2075 q^{55} -3.69433 q^{57} +(1.05697 + 3.49166i) q^{58} +10.1222i q^{59} +(-2.77635 - 4.16558i) q^{60} -5.00367 q^{61} +(8.13036 - 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +13.2967 q^{65} +(2.32575 + 7.68304i) q^{66} -9.30266 q^{67} +(0.504531 + 0.756989i) q^{68} -5.12043 q^{69} +7.35240i q^{71} +(-1.79815 + 2.18327i) q^{72} -6.85362i q^{73} +(3.69405 + 12.2032i) q^{74} -1.26504i q^{75} +(-4.09777 - 6.14821i) q^{76} +(-2.17664 - 7.19047i) q^{78} +8.91293i q^{79} +(3.85294 - 9.24097i) q^{80} +1.00000 q^{81} +(1.90812 + 6.30341i) q^{82} +1.96259i q^{83} +1.13851i q^{85} +(4.96353 - 1.50252i) q^{86} +2.57962 q^{87} +(-10.2066 + 12.3927i) q^{88} +6.82845i q^{89} +(-3.38796 + 1.02558i) q^{90} +(-5.67961 - 8.52158i) q^{92} -6.00666i q^{93} +(-1.29628 + 0.392398i) q^{94} -9.24692i q^{95} +(-5.62798 - 0.570834i) q^{96} +3.71270i q^{97} +5.67619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{4} + 16 q^{8} - 32 q^{9} - 16 q^{11} - 12 q^{16} - 4 q^{18} - 20 q^{22} + 32 q^{25} + 16 q^{30} + 24 q^{32} - 4 q^{36} - 16 q^{43} - 48 q^{44} - 16 q^{46} + 76 q^{50} + 16 q^{57} + 12 q^{58}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^4 + 16 * q^8 - 32 * q^9 - 16 * q^11 - 12 * q^16 - 4 * q^18 - 20 * q^22 + 32 * q^25 + 16 * q^30 + 24 * q^32 - 4 * q^36 - 16 * q^43 - 48 * q^44 - 16 * q^46 + 76 * q^50 + 16 * q^57 + 12 * q^58 + 4 * q^60 + 76 * q^64 + 64 * q^67 - 16 * q^72 + 68 * q^74 - 12 * q^78 + 32 * q^81 - 100 * q^86 + 28 * q^88 - 128 * q^92 + 16 * q^99

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