LMFDB - Embedded newform 1176.2.p.a.979.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(979,1176)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.39040727770$
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			979.28
Character	$\chi$	$=$	1176.979
Dual form			1176.2.p.a.979.26

$q$-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	$-0.689080\pi$
$5$	−2.50301			−1.11938			−0.559689	+	0.828703i	$0.689080\pi$
$6$	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	$-0.763608\pi$
$13$	−5.31228			−1.47336			−0.736681	+	0.676241i	$0.763608\pi$
$14$		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	$0.179252\pi$
$23$			5.12043i			1.06768i	−0.845584	+	0.533842i	$0.820748\pi$
$24$	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	$-0.923013\pi$
$29$		−	2.57962i		−	0.479024i	0.970893	−	0.239512i	$-0.0769874\pi$
$30$	−1.02558	+	3.38796i	−0.187244	+	0.618554i
$31$	−6.00666			−1.07883			−0.539414	−	0.842041i	$-0.681354\pi$
$31$	−6.00666			−1.07883			−0.539414	+	0.842041i	$0.681354\pi$
$32$	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	$-0.734313\pi$
$37$		−	9.01565i		−	1.48216i	0.671415	−	0.741082i	$-0.265687\pi$
$38$	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	$-0.477749\pi$
$47$	0.957682			0.139692			0.0698461	+	0.997558i	$0.477749\pi$
$48$	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	$0.141183\pi$
$53$			6.24836i			0.858278i	−0.903239	+	0.429139i	$0.858817\pi$
$54$	−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	$-0.396207\pi$
$61$	5.00367			0.640654			0.320327	+	0.947307i	$0.396207\pi$
$62$	−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	$-0.856294\pi$
$71$		−	7.35240i		−	0.872569i	0.899809	−	0.436285i	$-0.143706\pi$
$72$	−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	$-0.832822\pi$
$79$		−	8.91293i		−	1.00278i	0.865221	−	0.501391i	$-0.167178\pi$
$80$	−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	$-0.591219\pi$
$101$	−5.68155			−0.565335			−0.282667	+	0.959218i	$0.591219\pi$
$102$	0.615676	+	0.186372i	0.0609610	+	0.0184536i
$103$	−5.90691			−0.582025			−0.291013	−	0.956719i	$-0.593992\pi$
$103$	−5.90691			−0.582025			−0.291013	+	0.956719i	$0.593992\pi$
$104$	−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	$-0.951348\pi$
$109$		−	3.17911i		−	0.304504i	0.988342	−	0.152252i	$-0.0486525\pi$
$110$	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	$0.0916096\pi$
$127$			6.39751i			0.567687i	−0.958871	+	0.283843i	$0.908390\pi$
$128$	−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	$-0.921557\pi$
$149$		−	5.95556i		−	0.487898i	0.969788	−	0.243949i	$-0.0784430\pi$
$150$	0.518335	−	1.71230i	0.0423219	−	0.139809i
$151$		−	3.59257i		−	0.292359i	−0.989258	−	0.146180i	$-0.953302\pi$
$151$		−	3.59257i		−	0.292359i	0.989258	−	0.146180i	$-0.0466977\pi$
$152$	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	$-0.487504\pi$
$157$	0.983524			0.0784937			0.0392469	+	0.999230i	$0.487504\pi$
$158$	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	$-0.565266\pi$
$167$	−5.26232			−0.407211			−0.203605	+	0.979053i	$0.565266\pi$
$168$		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	$-0.498262\pi$
$173$	0.143623			0.0109195			0.00545974	+	0.999985i	$0.498262\pi$
$174$	−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	$-0.190598\pi$
$181$	22.2260			1.65204			0.826022	+	0.563637i	$0.190598\pi$
$182$		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	$-0.859718\pi$
$191$		−	11.7909i		−	0.853162i	0.904449	−	0.426581i	$-0.140282\pi$
$192$	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	$0.201182\pi$
$197$			16.5842i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$198$	7.68304	+	2.32575i	0.546010	+	0.165284i
$199$	−11.4084			−0.808720			−0.404360	−	0.914600i	$-0.632506\pi$
$199$	−11.4084			−0.808720			−0.404360	+	0.914600i	$0.632506\pi$
$200$	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	$-0.707325\pi$
$223$	−18.1063			−1.21249			−0.606245	+	0.795278i	$0.707325\pi$
$224$		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	$-0.522692\pi$
$229$	−2.15573			−0.142455			−0.0712274	+	0.997460i	$0.522692\pi$
$230$	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	$-0.790759\pi$
$239$		−	18.8923i		−	1.22204i	0.791614	−	0.611021i	$-0.209241\pi$
$240$	−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	$-0.841301\pi$
$263$		−	15.5092i		−	0.956339i	0.878268	−	0.478169i	$-0.158699\pi$
$264$	−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	$-0.242521\pi$
$269$	23.7333			1.44705			0.723523	+	0.690300i	$0.242521\pi$
$270$	1.02558	−	3.38796i	0.0624145	−	0.206185i
$271$	−14.7137			−0.893793			−0.446896	−	0.894586i	$-0.647471\pi$
$271$	−14.7137			−0.893793			−0.446896	+	0.894586i	$0.647471\pi$
$272$	−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	$-0.931359\pi$
$277$		−	7.12245i		−	0.427947i	0.976840	−	0.213973i	$-0.0686406\pi$
$278$	−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	$-0.496894\pi$
$293$	0.334002			0.0195126			0.00975630	+	0.999952i	$0.496894\pi$
$294$		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	$-0.648610\pi$
$311$	−15.8750			−0.900189			−0.450095	+	0.892981i	$0.648610\pi$
$312$	−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	$0.141083\pi$
$317$			15.2712i			0.857714i	−0.903373	+	0.428857i	$0.858917\pi$
$318$	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	$-0.898488\pi$
$349$	−35.4792			−1.89916			−0.949578	+	0.313530i	$0.898488\pi$
$350$		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	$0.427453\pi$
$359$			36.9146i			1.94828i	−0.225947	+	0.974140i	$0.572547\pi$
$360$	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	$-0.504726\pi$
$367$	−0.568832			−0.0296928			−0.0148464	+	0.999890i	$0.504726\pi$
$368$	−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	$0.207482\pi$
$373$			23.4322i			1.21328i	−0.794979	+	0.606638i	$0.792518\pi$
$374$	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	$-0.459267\pi$
$383$	4.99508			0.255237			0.127618	+	0.991823i	$0.459267\pi$
$384$	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	$0.299566\pi$
$389$			31.8810i			1.61643i	−0.588887	+	0.808216i	$0.700434\pi$
$390$	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	$-0.809249\pi$
$397$	−32.9060			−1.65151			−0.825753	+	0.564032i	$0.809249\pi$
$398$	−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	$0.178205\pi$
$421$			21.7928i			1.06211i	−0.847336	+	0.531057i	$0.821795\pi$
$422$	−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	$0.130412\pi$
$431$			16.5393i			0.796669i	−0.917240	+	0.398335i	$0.869588\pi$
$432$	−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	$-0.234558\pi$
$439$	31.0331			1.48113			0.740564	+	0.671986i	$0.234558\pi$
$440$	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	$-0.467812\pi$
$461$	4.33499			0.201901			0.100950	+	0.994891i	$0.467812\pi$
$462$		0			0
$463$			35.3200i			1.64146i	0.571316	+	0.820730i	$0.306433\pi$
$463$			35.3200i			1.64146i	−0.571316	+	0.820730i	$0.693567\pi$
$464$	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	$-0.626392\pi$
$479$	−16.9275			−0.773437			−0.386719	+	0.922198i	$0.626392\pi$
$480$	−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	$-0.819336\pi$
$487$		−	23.7270i		−	1.07517i	0.843209	−	0.537586i	$-0.180664\pi$
$488$	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	$-0.449500\pi$
$503$	7.08646			0.315970			0.157985	+	0.987442i	$0.449500\pi$
$504$		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	$-0.817810\pi$
$509$	−37.9306			−1.68124			−0.840622	+	0.541623i	$0.817810\pi$
$510$	−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	$-0.948955\pi$
$541$		−	7.42798i		−	0.319354i	0.987169	−	0.159677i	$-0.0510452\pi$
$542$	−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	$-0.738414\pi$
$557$		−	34.5692i		−	1.46474i	0.680906	−	0.732371i	$-0.261586\pi$
$558$	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	$0.427138\pi$
$599$			47.6722i			1.94783i	−0.226908	+	0.973916i	$0.572862\pi$
$600$	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	$-0.216826\pi$
$607$	38.2781			1.55366			0.776831	+	0.629709i	$0.216826\pi$
$608$	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	$-0.870878\pi$
$613$		−	19.5404i		−	0.789230i	0.918847	−	0.394615i	$-0.129122\pi$
$614$	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	$0.0526024\pi$
$631$			8.26460i			0.329008i	−0.986376	+	0.164504i	$0.947398\pi$
$632$	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	$-0.577021\pi$
$647$	−12.1898			−0.479231			−0.239616	+	0.970868i	$0.577021\pi$
$648$	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	$0.0637259\pi$
$653$			10.1636i			0.397732i	−0.980027	+	0.198866i	$0.936274\pi$
$654$	−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	$-0.604752\pi$
$661$	−16.6178			−0.646358			−0.323179	+	0.946338i	$0.604752\pi$
$662$	−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	$-0.371510\pi$
$677$	20.4402			0.785580			0.392790	+	0.919628i	$0.371510\pi$
$678$	−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	$-0.734584\pi$
$701$		−	39.2121i		−	1.48102i	0.672045	−	0.740511i	$-0.265416\pi$
$702$	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	$0.257447\pi$
$709$			38.5269i			1.44691i	−0.690372	+	0.723454i	$0.742553\pi$
$710$	−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	$-0.641103\pi$
$719$	−23.0018			−0.857824			−0.428912	+	0.903346i	$0.641103\pi$
$720$	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	$-0.367250\pi$
$727$	21.8433			0.810125			0.405062	+	0.914289i	$0.367250\pi$
$728$		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	$-0.151419\pi$
$733$	48.1361			1.77795			0.888974	+	0.457957i	$0.151419\pi$
$734$	−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	$-0.901077\pi$
$743$		−	16.6709i		−	0.611597i	0.952096	−	0.305798i	$-0.0989234\pi$
$744$	−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	$0.147902\pi$
$751$			24.5602i			0.896215i	−0.893980	+	0.448108i	$0.852098\pi$
$752$	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	$0.0162553\pi$
$757$			2.80888i			0.102091i	−0.998696	+	0.0510453i	$0.983745\pi$
$758$	−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	$-0.366859\pi$
$773$	22.5863			0.812371			0.406186	+	0.913791i	$0.366859\pi$
$774$	−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	$-0.340988\pi$
$797$	27.0472			0.958061			0.479030	+	0.877798i	$0.340988\pi$
$798$		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	$-0.983322\pi$
$821$		−	3.00119i		−	0.104742i	0.998628	−	0.0523711i	$-0.0166779\pi$
$822$	0.504436	−	1.66639i	0.0175942	−	0.0581220i
$823$		−	15.9975i		−	0.557639i	−0.960343	−	0.278820i	$-0.910057\pi$
$823$		−	15.9975i		−	0.557639i	0.960343	−	0.278820i	$-0.0899432\pi$
$824$	−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	$-0.483069\pi$
$829$	3.06153			0.106331			0.0531657	+	0.998586i	$0.483069\pi$
$830$	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	$-0.735730\pi$
$839$	−39.0864			−1.34941			−0.674706	+	0.738087i	$0.735730\pi$
$840$		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	$-0.649823\pi$
$853$	−26.4897			−0.906989			−0.453495	+	0.891259i	$0.649823\pi$
$854$		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	$0.0150469\pi$
$863$			2.77632i			0.0945072i	−0.998883	+	0.0472536i	$0.984953\pi$
$864$	−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	$-0.909896\pi$
$877$		−	16.5427i		−	0.558608i	0.960203	−	0.279304i	$-0.0901036\pi$
$878$	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	$-0.549819\pi$
$887$	−9.28462			−0.311747			−0.155873	+	0.987777i	$0.549819\pi$
$888$	−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	$-0.794171\pi$
$911$		−	36.3702i		−	1.20500i	0.798119	−	0.602500i	$-0.205829\pi$
$912$	−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	$0.279690\pi$
$919$			46.6786i			1.53978i	−0.638174	+	0.769892i	$0.720310\pi$
$920$	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	$-0.359245\pi$
$941$	26.2537			0.855848			0.427924	+	0.903815i	$0.359245\pi$
$942$	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	$-0.996560\pi$
$967$		−	0.672082i		−	0.0216127i	0.999942	−	0.0108063i	$-0.00343983\pi$
$968$	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	$-0.261340\pi$
$983$	42.7322			1.36294			0.681472	+	0.731844i	$0.261340\pi$
$984$	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	$-0.743475\pi$
$991$		−	45.4228i		−	1.44290i	0.692465	−	0.721451i	$-0.256525\pi$
$992$	−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	$-0.256427\pi$
$997$	43.7436			1.38537			0.692687	+	0.721239i	$0.256427\pi$
$998$	−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.979.28		32
4.3	odd	2		4704.2.p.a.3919.16		32
7.2	even	3		168.2.t.a.115.8	yes	32
7.3	odd	6		168.2.t.a.19.4	✓	32
7.6	odd	2	inner	1176.2.p.a.979.27		32
8.3	odd	2	inner	1176.2.p.a.979.25		32
8.5	even	2		4704.2.p.a.3919.2		32
21.2	odd	6		504.2.bk.c.451.9		32
21.17	even	6		504.2.bk.c.19.13		32
28.3	even	6		672.2.bb.a.271.2		32
28.23	odd	6		672.2.bb.a.367.7		32
28.27	even	2		4704.2.p.a.3919.1		32
56.3	even	6		168.2.t.a.19.8	yes	32
56.13	odd	2		4704.2.p.a.3919.15		32
56.27	even	2	inner	1176.2.p.a.979.26		32
56.37	even	6		672.2.bb.a.367.2		32
56.45	odd	6		672.2.bb.a.271.7		32
56.51	odd	6		168.2.t.a.115.4	yes	32
84.23	even	6		2016.2.bs.c.1711.4		32
84.59	odd	6		2016.2.bs.c.271.13		32
168.59	odd	6		504.2.bk.c.19.9		32
168.101	even	6		2016.2.bs.c.271.4		32
168.107	even	6		504.2.bk.c.451.13		32
168.149	odd	6		2016.2.bs.c.1711.13		32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
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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