LMFDB - Embedded newform 1155.2.i.c.76.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.3
Root			$-0.0566033 - 1.17421i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.c.76.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} -2.19849 q^{6} +(2.19849 + 1.47195i) q^{7} +1.83215i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} -2.19849 q^{6} +(2.19849 + 1.47195i) q^{7} +1.83215i q^{8} -1.00000 q^{9} +2.19849 q^{10} +(-1.23607 + 3.07768i) q^{11} +2.83337i q^{12} -6.52171 q^{13} +(3.23607 - 4.83337i) q^{14} +1.00000 q^{15} -1.63877 q^{16} -3.82309 q^{17} +2.19849i q^{18} -2.33228 q^{19} -2.83337i q^{20} +(1.47195 - 2.19849i) q^{21} +(6.76626 + 2.71749i) q^{22} +3.83337 q^{23} +1.83215 q^{24} -1.00000 q^{25} +14.3379i q^{26} +1.00000i q^{27} +(-6.22913 - 4.17057i) q^{28} +4.90983i q^{29} -2.19849i q^{30} +7.93290i q^{31} +7.26712i q^{32} +(3.07768 + 1.23607i) q^{33} +8.40503i q^{34} +(-1.47195 + 2.19849i) q^{35} +2.83337 q^{36} -7.93290 q^{37} +5.12749i q^{38} +6.52171i q^{39} -1.83215 q^{40} -10.1860 q^{41} +(-4.83337 - 3.23607i) q^{42} -6.37521i q^{43} +(3.50223 - 8.72020i) q^{44} -1.00000i q^{45} -8.42762i q^{46} -2.06710i q^{47} +1.63877i q^{48} +(2.66673 + 6.47214i) q^{49} +2.19849i q^{50} +3.82309i q^{51} +18.4784 q^{52} +10.0324 q^{53} +2.19849 q^{54} +(-3.07768 - 1.23607i) q^{55} +(-2.69683 + 4.02796i) q^{56} +2.33228i q^{57} +10.7942 q^{58} -3.76626i q^{59} -2.83337 q^{60} -9.22033 q^{61} +17.4404 q^{62} +(-2.19849 - 1.47195i) q^{63} +12.6992 q^{64} -6.52171i q^{65} +(2.71749 - 6.76626i) q^{66} -2.13887 q^{67} +10.8322 q^{68} -3.83337i q^{69} +(4.83337 + 3.23607i) q^{70} +8.40503 q^{71} -1.83215i q^{72} -8.34114 q^{73} +17.4404i q^{74} +1.00000i q^{75} +6.60819 q^{76} +(-7.24768 + 4.94683i) q^{77} +14.3379 q^{78} -13.1299i q^{79} -1.63877i q^{80} +1.00000 q^{81} +22.3939i q^{82} +15.3757 q^{83} +(-4.17057 + 6.22913i) q^{84} -3.82309i q^{85} -14.0158 q^{86} +4.90983 q^{87} +(-5.63877 - 2.26466i) q^{88} +0.705874i q^{89} -2.19849 q^{90} +(-14.3379 - 9.59963i) q^{91} -10.8613 q^{92} +7.93290 q^{93} -4.54451 q^{94} -2.33228i q^{95} +7.26712 q^{96} -10.0995i q^{97} +(14.2289 - 5.86279i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.19849i		−	1.55457i	−0.629150	−	0.777284i	$-0.716597\pi$
$2$		−	2.19849i		−	1.55457i	0.629150	−	0.777284i	$-0.283403\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−2.83337			−1.41668
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.19849			−0.897530
$7$	2.19849	+	1.47195i	0.830952	+	0.556344i
$7$	2.19849	+	1.47195i	0.830952	+	0.556344i
$8$			1.83215i			0.647762i
$9$	−1.00000			−0.333333
$10$	2.19849			0.695224
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$			2.83337i			0.817922i
$13$	−6.52171			−1.80880			−0.904399	−	0.426689i	$-0.859680\pi$
$13$	−6.52171			−1.80880			−0.904399	+	0.426689i	$0.859680\pi$
$14$	3.23607	−	4.83337i	0.864876	−	1.29177i
$15$	1.00000			0.258199
$16$	−1.63877			−0.409693
$17$	−3.82309			−0.927236			−0.463618	−	0.886035i	$-0.653449\pi$
$17$	−3.82309			−0.927236			−0.463618	+	0.886035i	$0.653449\pi$
$18$			2.19849i			0.518189i
$19$	−2.33228			−0.535061			−0.267531	−	0.963549i	$-0.586208\pi$
$19$	−2.33228			−0.535061			−0.267531	+	0.963549i	$0.586208\pi$
$20$		−	2.83337i		−	0.633560i
$21$	1.47195	−	2.19849i	0.321206	−	0.479750i
$22$	6.76626	+	2.71749i	1.44257	+	0.579370i
$23$	3.83337			0.799312			0.399656	−	0.916665i	$-0.369130\pi$
$23$	3.83337			0.799312			0.399656	+	0.916665i	$0.369130\pi$
$24$	1.83215			0.373986
$25$	−1.00000			−0.200000
$26$			14.3379i			2.81190i
$27$			1.00000i			0.192450i
$28$	−6.22913	−	4.17057i	−1.17720	−	0.788164i
$29$			4.90983i			0.911733i	0.890048	+	0.455866i	$0.150671\pi$
$29$			4.90983i			0.911733i	−0.890048	+	0.455866i	$0.849329\pi$
$30$		−	2.19849i		−	0.401388i
$31$			7.93290i			1.42479i	0.701779	+	0.712395i	$0.252390\pi$
$31$			7.93290i			1.42479i	−0.701779	+	0.712395i	$0.747610\pi$
$32$			7.26712i			1.28466i
$33$	3.07768	+	1.23607i	0.535756	+	0.215172i
$34$			8.40503i			1.44145i
$35$	−1.47195	+	2.19849i	−0.248805	+	0.371613i
$36$	2.83337			0.472228
$37$	−7.93290			−1.30416			−0.652080	−	0.758150i	$-0.726103\pi$
$37$	−7.93290			−1.30416			−0.652080	+	0.758150i	$0.726103\pi$
$38$			5.12749i			0.831789i
$39$			6.52171i			1.04431i
$40$	−1.83215			−0.289688
$41$	−10.1860			−1.59079			−0.795393	−	0.606093i	$-0.792736\pi$
$41$	−10.1860			−1.59079			−0.795393	+	0.606093i	$0.792736\pi$
$42$	−4.83337	−	3.23607i	−0.745805	−	0.499336i
$43$		−	6.37521i		−	0.972210i	−0.873900	−	0.486105i	$-0.838417\pi$
$43$		−	6.37521i		−	0.972210i	0.873900	−	0.486105i	$-0.161583\pi$
$44$	3.50223	−	8.72020i	0.527981	−	1.31462i
$45$		−	1.00000i		−	0.149071i
$46$		−	8.42762i		−	1.24259i
$47$		−	2.06710i		−	0.301518i	−0.988571	−	0.150759i	$-0.951828\pi$
$47$		−	2.06710i		−	0.301518i	0.988571	−	0.150759i	$-0.0481718\pi$
$48$			1.63877i			0.236536i
$49$	2.66673	+	6.47214i	0.380962	+	0.924591i
$50$			2.19849i			0.310914i
$51$			3.82309i			0.535340i
$52$	18.4784			2.56249
$53$	10.0324			1.37806			0.689030	−	0.724733i	$-0.258037\pi$
$53$	10.0324			1.37806			0.689030	+	0.724733i	$0.258037\pi$
$54$	2.19849			0.299177
$55$	−3.07768	−	1.23607i	−0.414995	−	0.166671i
$56$	−2.69683	+	4.02796i	−0.360379	+	0.538259i
$57$			2.33228i			0.308918i
$58$	10.7942			1.41735
$59$		−	3.76626i		−	0.490326i	−0.969482	−	0.245163i	$-0.921159\pi$
$59$		−	3.76626i		−	0.490326i	0.969482	−	0.245163i	$-0.0788414\pi$
$60$	−2.83337			−0.365786
$61$	−9.22033			−1.18054			−0.590271	−	0.807205i	$-0.700979\pi$
$61$	−9.22033			−1.18054			−0.590271	+	0.807205i	$0.700979\pi$
$62$	17.4404			2.21493
$63$	−2.19849	−	1.47195i	−0.276984	−	0.185448i
$64$	12.6992			1.58739
$65$		−	6.52171i		−	0.808919i
$66$	2.71749	−	6.76626i	0.334499	−	0.832869i
$67$	−2.13887			−0.261304			−0.130652	−	0.991428i	$-0.541707\pi$
$67$	−2.13887			−0.261304			−0.130652	+	0.991428i	$0.541707\pi$
$68$	10.8322			1.31360
$69$		−	3.83337i		−	0.461483i
$70$	4.83337	+	3.23607i	0.577698	+	0.386784i
$71$	8.40503			0.997494			0.498747	−	0.866748i	$-0.333794\pi$
$71$	8.40503			0.997494			0.498747	+	0.866748i	$0.333794\pi$
$72$		−	1.83215i		−	0.215921i
$73$	−8.34114			−0.976257			−0.488128	−	0.872772i	$-0.662320\pi$
$73$	−8.34114			−0.976257			−0.488128	+	0.872772i	$0.662320\pi$
$74$			17.4404i			2.02741i
$75$			1.00000i			0.115470i
$76$	6.60819			0.758012
$77$	−7.24768	+	4.94683i	−0.825950	+	0.563744i
$78$	14.3379			1.62345
$79$		−	13.1299i		−	1.47723i	−0.674128	−	0.738615i	$-0.735480\pi$
$79$		−	13.1299i		−	1.47723i	0.674128	−	0.738615i	$-0.264520\pi$
$80$		−	1.63877i		−	0.183220i
$81$	1.00000			0.111111
$82$			22.3939i			2.47299i
$83$	15.3757			1.68770			0.843851	−	0.536577i	$-0.180283\pi$
$83$	15.3757			1.68770			0.843851	+	0.536577i	$0.180283\pi$
$84$	−4.17057	+	6.22913i	−0.455047	+	0.679654i
$85$		−	3.82309i		−	0.414672i
$86$	−14.0158			−1.51137
$87$	4.90983			0.526389
$88$	−5.63877	−	2.26466i	−0.601095	−	0.241413i
$89$			0.705874i			0.0748225i	0.999300	+	0.0374113i	$0.0119112\pi$
$89$			0.705874i			0.0748225i	−0.999300	+	0.0374113i	$0.988089\pi$
$90$	−2.19849			−0.231741
$91$	−14.3379	−	9.59963i	−1.50302	−	1.00631i
$92$	−10.8613			−1.13237
$93$	7.93290			0.822603
$94$	−4.54451			−0.468731
$95$		−	2.33228i		−	0.239287i
$96$	7.26712			0.741697
$97$		−	10.0995i		−	1.02545i	−0.858552	−	0.512726i	$-0.828636\pi$
$97$		−	10.0995i		−	1.02545i	0.858552	−	0.512726i	$-0.171364\pi$
$98$	14.2289	−	5.86279i	1.43734	−	0.592231i
$99$	1.23607	−	3.07768i	0.124230	−	0.309319i
$100$	2.83337			0.283337
$101$	−1.45309			−0.144587			−0.0722937	−	0.997383i	$-0.523032\pi$
$101$	−1.45309			−0.144587			−0.0722937	+	0.997383i	$0.523032\pi$
$102$	8.40503			0.832222
$103$		−	8.96086i		−	0.882939i	−0.897276	−	0.441470i	$-0.854457\pi$
$103$		−	8.96086i		−	0.882939i	0.897276	−	0.441470i	$-0.145543\pi$
$104$		−	11.9487i		−	1.17167i
$105$	2.19849	+	1.47195i	0.214551	+	0.143648i
$106$		−	22.0562i		−	2.14229i
$107$			11.6514i			1.12638i	0.826327	+	0.563191i	$0.190426\pi$
$107$			11.6514i			1.12638i	−0.826327	+	0.563191i	$0.809574\pi$
$108$		−	2.83337i		−	0.272641i
$109$		−	8.73292i		−	0.836462i	−0.908341	−	0.418231i	$-0.862650\pi$
$109$		−	8.73292i		−	0.836462i	0.908341	−	0.418231i	$-0.137350\pi$
$110$	−2.71749	+	6.76626i	−0.259102	+	0.645138i
$111$			7.93290i			0.752957i
$112$	−3.60282	−	2.41219i	−0.340435	−	0.227930i
$113$	9.36589			0.881069			0.440534	−	0.897736i	$-0.354789\pi$
$113$	9.36589			0.881069			0.440534	+	0.897736i	$0.354789\pi$
$114$	5.12749			0.480234
$115$			3.83337i			0.357463i
$116$		−	13.9113i		−	1.29164i
$117$	6.52171			0.602932
$118$	−8.28009			−0.762245
$119$	−8.40503	−	5.62739i	−0.770488	−	0.515862i
$120$			1.83215i			0.167251i
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$			20.2708i			1.83523i
$123$			10.1860i			0.918441i
$124$		−	22.4768i		−	2.01848i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.23607	+	4.83337i	−0.288292	+	0.430590i
$127$			16.1949i			1.43706i	0.695495	+	0.718531i	$0.255185\pi$
$127$			16.1949i			1.43706i	−0.695495	+	0.718531i	$0.744815\pi$
$128$		−	13.3848i		−	1.18306i
$129$	−6.37521			−0.561306
$130$	−14.3379			−1.25752
$131$	−12.9824			−1.13428			−0.567138	−	0.823623i	$-0.691949\pi$
$131$	−12.9824			−1.13428			−0.567138	+	0.823623i	$0.691949\pi$
$132$	−8.72020	−	3.50223i	−0.758996	−	0.304830i
$133$	−5.12749	−	3.43299i	−0.444610	−	0.297678i
$134$			4.70228i			0.406215i
$135$	−1.00000			−0.0860663
$136$		−	7.00447i		−	0.600628i
$137$	−0.116115			−0.00992041			−0.00496021	−	0.999988i	$-0.501579\pi$
$137$	−0.116115			−0.00992041			−0.00496021	+	0.999988i	$0.501579\pi$
$138$	−8.42762			−0.717407
$139$	−2.18577			−0.185395			−0.0926974	−	0.995694i	$-0.529549\pi$
$139$	−2.18577			−0.185395			−0.0926974	+	0.995694i	$0.529549\pi$
$140$	4.17057	−	6.22913i	0.352478	−	0.526458i
$141$	−2.06710			−0.174082
$142$		−	18.4784i		−	1.55067i
$143$	8.06128	−	20.0718i	0.674118	−	1.67849i
$144$	1.63877			0.136564
$145$	−4.90983			−0.407739
$146$			18.3379i			1.51766i
$147$	6.47214	−	2.66673i	0.533813	−	0.219948i
$148$	22.4768			1.84758
$149$		−	5.43497i		−	0.445250i	−0.974904	−	0.222625i	$-0.928537\pi$
$149$		−	5.43497i		−	0.445250i	0.974904	−	0.222625i	$-0.0714626\pi$
$150$	2.19849			0.179506
$151$			22.7176i			1.84873i	0.381506	+	0.924366i	$0.375405\pi$
$151$			22.7176i			1.84873i	−0.381506	+	0.924366i	$0.624595\pi$
$152$		−	4.27308i		−	0.346592i
$153$	3.82309			0.309079
$154$	10.8756	+	15.9340i	0.876378	+	1.28400i
$155$	−7.93290			−0.637186
$156$		−	18.4784i		−	1.47946i
$157$		−	6.51147i		−	0.519672i	−0.965653	−	0.259836i	$-0.916331\pi$
$157$		−	6.51147i		−	0.519672i	0.965653	−	0.259836i	$-0.0836685\pi$
$158$	−28.8660			−2.29645
$159$		−	10.0324i		−	0.795623i
$160$	−7.26712			−0.574516
$161$	8.42762	+	5.64252i	0.664190	+	0.444693i
$162$		−	2.19849i		−	0.172730i
$163$	−10.7942			−0.845469			−0.422734	−	0.906254i	$-0.638930\pi$
$163$	−10.7942			−0.845469			−0.422734	+	0.906254i	$0.638930\pi$
$164$	28.8607			2.25364
$165$	−1.23607	+	3.07768i	−0.0962278	+	0.239597i
$166$		−	33.8033i		−	2.62365i
$167$	17.4027			1.34666			0.673330	−	0.739342i	$-0.264863\pi$
$167$	17.4027			1.34666			0.673330	+	0.739342i	$0.264863\pi$
$168$	4.02796	+	2.69683i	0.310764	+	0.208065i
$169$	29.5327			2.27175
$170$	−8.40503			−0.644637
$171$	2.33228			0.178354
$172$			18.0633i			1.37731i
$173$	−4.82437			−0.366790			−0.183395	−	0.983039i	$-0.558709\pi$
$173$	−4.82437			−0.366790			−0.183395	+	0.983039i	$0.558709\pi$
$174$		−	10.7942i		−	0.818308i
$175$	−2.19849	−	1.47195i	−0.166190	−	0.111269i
$176$	2.02563	−	5.04362i	0.152688	−	0.380177i
$177$	−3.76626			−0.283090
$178$	1.55186			0.116317
$179$	−22.3267			−1.66878			−0.834390	−	0.551175i	$-0.814180\pi$
$179$	−22.3267			−1.66878			−0.834390	+	0.551175i	$0.814180\pi$
$180$			2.83337i			0.211187i
$181$			13.2775i			0.986912i	0.869771	+	0.493456i	$0.164267\pi$
$181$			13.2775i			0.986912i	−0.869771	+	0.493456i	$0.835733\pi$
$182$	−21.1047	+	31.5218i	−1.56438	+	2.33655i
$183$			9.22033i			0.681587i
$184$			7.02329i			0.517764i
$185$		−	7.93290i		−	0.583238i
$186$		−	17.4404i		−	1.27879i
$187$	4.72560	−	11.7663i	0.345570	−	0.860434i
$188$			5.85686i			0.427156i
$189$	−1.47195	+	2.19849i	−0.107069	+	0.159917i
$190$	−5.12749			−0.371987
$191$	−4.52806			−0.327639			−0.163819	−	0.986490i	$-0.552381\pi$
$191$	−4.52806			−0.327639			−0.163819	+	0.986490i	$0.552381\pi$
$192$		−	12.6992i		−	0.916483i
$193$			4.39698i			0.316502i	0.987399	+	0.158251i	$0.0505855\pi$
$193$			4.39698i			0.316502i	−0.987399	+	0.158251i	$0.949415\pi$
$194$	−22.2037			−1.59414
$195$	−6.52171			−0.467029
$196$	−7.55583	−	18.3379i	−0.539702	−	1.30985i
$197$			22.8254i			1.62624i	0.582097	+	0.813120i	$0.302233\pi$
$197$			22.8254i			1.62624i	−0.582097	+	0.813120i	$0.697767\pi$
$198$	−6.76626	−	2.71749i	−0.480857	−	0.193123i
$199$			17.5325i			1.24285i	0.783475	+	0.621424i	$0.213445\pi$
$199$			17.5325i			1.24285i	−0.783475	+	0.621424i	$0.786555\pi$
$200$		−	1.83215i		−	0.129552i
$201$			2.13887i			0.150864i
$202$			3.19460i			0.224771i
$203$	−7.22702	+	10.7942i	−0.507237	+	0.757606i
$204$		−	10.8322i		−	0.758407i
$205$		−	10.1860i		−	0.711422i
$206$	−19.7004			−1.37259
$207$	−3.83337			−0.266437
$208$	10.6876			0.741051
$209$	2.88285	−	7.17801i	0.199411	−	0.496513i
$210$	3.23607	−	4.83337i	0.223310	−	0.333534i
$211$		−	12.9488i		−	0.891433i	−0.895174	−	0.445717i	$-0.852949\pi$
$211$		−	12.9488i		−	0.891433i	0.895174	−	0.445717i	$-0.147051\pi$
$212$	−28.4255			−1.95227
$213$		−	8.40503i		−	0.575903i
$214$	25.6155			1.75104
$215$	6.37521			0.434786
$216$	−1.83215			−0.124662
$217$	−11.6768	+	17.4404i	−0.792674	+	1.18393i
$218$	−19.1993			−1.30034
$219$			8.34114i			0.563642i
$220$	8.72020	+	3.50223i	0.587916	+	0.236120i
$221$	24.9331			1.67718
$222$	17.4404			1.17052
$223$		−	1.62739i		−	0.108978i	−0.998514	−	0.0544892i	$-0.982647\pi$
$223$		−	1.62739i		−	0.108978i	0.998514	−	0.0544892i	$-0.0173530\pi$
$224$	−10.6968	+	15.9767i	−0.714712	+	1.06749i
$225$	1.00000			0.0666667
$226$		−	20.5908i		−	1.36968i
$227$	−15.1336			−1.00445			−0.502225	−	0.864737i	$-0.667485\pi$
$227$	−15.1336			−1.00445			−0.502225	+	0.864737i	$0.667485\pi$
$228$		−	6.60819i		−	0.437638i
$229$		−	4.85442i		−	0.320789i	−0.987053	−	0.160394i	$-0.948723\pi$
$229$		−	4.85442i		−	0.320789i	0.987053	−	0.160394i	$-0.0512766\pi$
$230$	8.42762			0.555701
$231$	4.94683	+	7.24768i	0.325478	+	0.476862i
$232$	−8.99553			−0.590586
$233$			18.9545i			1.24175i	0.783908	+	0.620876i	$0.213223\pi$
$233$			18.9545i			1.24175i	−0.783908	+	0.620876i	$0.786777\pi$
$234$		−	14.3379i		−	0.937300i
$235$	2.06710			0.134843
$236$			10.6712i			0.694636i
$237$	−13.1299			−0.852879
$238$	−12.3718	+	18.4784i	−0.801943	+	1.19778i
$239$		−	8.61185i		−	0.557055i	−0.960428	−	0.278527i	$-0.910154\pi$
$239$		−	8.61185i		−	0.557055i	0.960428	−	0.278527i	$-0.0898463\pi$
$240$	−1.63877			−0.105782
$241$	25.0234			1.61190			0.805950	−	0.591983i	$-0.201655\pi$
$241$	25.0234			1.61190			0.805950	+	0.591983i	$0.201655\pi$
$242$	−16.7271	+	17.4654i	−1.07526	+	1.12272i
$243$		−	1.00000i		−	0.0641500i
$244$	26.1246			1.67245
$245$	−6.47214	+	2.66673i	−0.413490	+	0.170371i
$246$	22.3939			1.42778
$247$	15.2104			0.967817
$248$	−14.5342			−0.922925
$249$		−	15.3757i		−	0.974395i
$250$	−2.19849			−0.139045
$251$		−	1.93981i		−	0.122440i	−0.998124	−	0.0612198i	$-0.980501\pi$
$251$		−	1.93981i		−	0.122440i	0.998124	−	0.0612198i	$-0.0194990\pi$
$252$	6.22913	+	4.17057i	0.392398	+	0.262721i
$253$	−4.73830	+	11.7979i	−0.297894	+	0.741727i
$254$	35.6043			2.23401
$255$	−3.82309			−0.239411
$256$	−4.02796			−0.251748
$257$			27.7987i			1.73403i	0.498278	+	0.867017i	$0.333966\pi$
$257$			27.7987i			1.73403i	−0.498278	+	0.867017i	$0.666034\pi$
$258$			14.0158i			0.872588i
$259$	−17.4404	−	11.6768i	−1.08369	−	0.725562i
$260$			18.4784i			1.14598i
$261$		−	4.90983i		−	0.303911i
$262$			28.5416i			1.76331i
$263$		−	2.96933i		−	0.183097i	−0.995801	−	0.0915485i	$-0.970818\pi$
$263$		−	2.96933i		−	0.183097i	0.995801	−	0.0915485i	$-0.0291817\pi$
$264$	−2.26466	+	5.63877i	−0.139380	+	0.347042i
$265$			10.0324i			0.616287i
$266$	−7.54741	+	11.2727i	−0.462761	+	0.691176i
$267$	0.705874			0.0431988
$268$	6.06019			0.370185
$269$		−	10.2943i		−	0.627656i	−0.949480	−	0.313828i	$-0.898389\pi$
$269$		−	10.2943i		−	0.627656i	0.949480	−	0.313828i	$-0.101611\pi$
$270$			2.19849i			0.133796i
$271$	−19.5051			−1.18485			−0.592426	−	0.805625i	$-0.701830\pi$
$271$	−19.5051			−1.18485			−0.592426	+	0.805625i	$0.701830\pi$
$272$	6.26517			0.379882
$273$	−9.59963	+	14.3379i	−0.580996	+	0.867771i
$274$			0.255279i			0.0154220i
$275$	1.23607	−	3.07768i	0.0745377	−	0.185591i
$276$			10.8613i			0.653775i
$277$		−	24.0609i		−	1.44568i	−0.691016	−	0.722839i	$-0.742837\pi$
$277$		−	24.0609i		−	1.44568i	0.691016	−	0.722839i	$-0.257163\pi$
$278$			4.80540i			0.288209i
$279$		−	7.93290i		−	0.474930i
$280$	−4.02796	−	2.69683i	−0.240717	−	0.161166i
$281$		−	2.65089i		−	0.158139i	−0.996869	−	0.0790695i	$-0.974805\pi$
$281$		−	2.65089i		−	0.158139i	0.996869	−	0.0790695i	$-0.0251949\pi$
$282$			4.54451i			0.270622i
$283$	−14.1047			−0.838439			−0.419219	−	0.907885i	$-0.637696\pi$
$283$	−14.1047			−0.838439			−0.419219	+	0.907885i	$0.637696\pi$
$284$	−23.8145			−1.41313
$285$	−2.33228			−0.138152
$286$	−44.1276	−	17.7227i	−2.60932	−	1.04796i
$287$	−22.3939	−	14.9933i	−1.32187	−	0.885026i
$288$		−	7.26712i		−	0.428219i
$289$	−2.38398			−0.140234
$290$			10.7942i			0.633859i
$291$	−10.0995			−0.592045
$292$	23.6335			1.38305
$293$	1.94262			0.113489			0.0567444	−	0.998389i	$-0.481928\pi$
$293$	1.94262			0.113489			0.0567444	+	0.998389i	$0.481928\pi$
$294$	−5.86279	−	14.2289i	−0.341925	−	0.829848i
$295$	3.76626			0.219280
$296$		−	14.5342i		−	0.844785i
$297$	−3.07768	−	1.23607i	−0.178585	−	0.0717239i
$298$	−11.9487			−0.692172
$299$	−25.0001			−1.44579
$300$		−	2.83337i		−	0.163584i
$301$	9.38398	−	14.0158i	0.540884	−	0.807860i
$302$	49.9445			2.87398
$303$			1.45309i			0.0834776i
$304$	3.82207			0.219211
$305$		−	9.22033i		−	0.527955i
$306$		−	8.40503i		−	0.480484i
$307$	8.03584			0.458630			0.229315	−	0.973352i	$-0.426351\pi$
$307$	8.03584			0.458630			0.229315	+	0.973352i	$0.426351\pi$
$308$	20.5353	−	14.0162i	1.17011	−	0.798646i
$309$	−8.96086			−0.509765
$310$			17.4404i			0.990548i
$311$			12.4949i			0.708520i	0.935147	+	0.354260i	$0.115267\pi$
$311$			12.4949i			0.708520i	−0.935147	+	0.354260i	$0.884733\pi$
$312$	−11.9487			−0.676464
$313$		−	4.68778i		−	0.264969i	−0.991185	−	0.132485i	$-0.957705\pi$
$313$		−	4.68778i		−	0.264969i	0.991185	−	0.132485i	$-0.0422955\pi$
$314$	−14.3154			−0.807866
$315$	1.47195	−	2.19849i	0.0829349	−	0.123871i
$316$			37.2018i			2.09277i
$317$	17.0604			0.958207			0.479103	−	0.877758i	$-0.340962\pi$
$317$	17.0604			0.958207			0.479103	+	0.877758i	$0.340962\pi$
$318$	−22.0562			−1.23685
$319$	−15.1109	−	6.06888i	−0.846048	−	0.339792i
$320$			12.6992i			0.709904i
$321$	11.6514			0.650317
$322$	12.4050	−	18.5281i	0.691305	−	1.03253i
$323$	8.91650			0.496128
$324$	−2.83337			−0.157409
$325$	6.52171			0.361759
$326$			23.7310i			1.31434i
$327$	−8.73292			−0.482932
$328$		−	18.6623i		−	1.03045i
$329$	3.04267	−	4.54451i	0.167748	−	0.250547i
$330$	6.76626	+	2.71749i	0.372470	+	0.149593i
$331$	17.0507			0.937192			0.468596	−	0.883413i	$-0.344760\pi$
$331$	17.0507			0.937192			0.468596	+	0.883413i	$0.344760\pi$
$332$	−43.5650			−2.39094
$333$	7.93290			0.434720
$334$		−	38.2596i		−	2.09347i
$335$		−	2.13887i		−	0.116859i
$336$	−2.41219	+	3.60282i	−0.131596	+	0.196550i
$337$			7.58616i			0.413244i	0.978421	+	0.206622i	$0.0662471\pi$
$337$			7.58616i			0.413244i	−0.978421	+	0.206622i	$0.933753\pi$
$338$		−	64.9274i		−	3.53159i
$339$		−	9.36589i		−	0.508685i
$340$			10.8322i			0.587459i
$341$	−24.4149	−	9.80560i	−1.32214	−	0.531003i
$342$		−	5.12749i		−	0.277263i
$343$	−3.66387	+	18.1542i	−0.197830	+	0.980236i
$344$	11.6803			0.629761
$345$	3.83337			0.206381
$346$			10.6063i			0.570201i
$347$		−	28.3235i		−	1.52048i	−0.649640	−	0.760242i	$-0.725080\pi$
$347$		−	28.3235i		−	1.52048i	0.649640	−	0.760242i	$-0.274920\pi$
$348$	−13.9113			−0.745726
$349$	19.9702			1.06898			0.534491	−	0.845174i	$-0.320503\pi$
$349$	19.9702			1.06898			0.534491	+	0.845174i	$0.320503\pi$
$350$	−3.23607	+	4.83337i	−0.172975	+	0.258354i
$351$		−	6.52171i		−	0.348103i
$352$	−22.3659	−	8.98265i	−1.19211	−	0.478777i
$353$		−	15.5098i		−	0.825502i	−0.910844	−	0.412751i	$-0.864568\pi$
$353$		−	15.5098i		−	0.825502i	0.910844	−	0.412751i	$-0.135432\pi$
$354$			8.28009i			0.440082i
$355$			8.40503i			0.446093i
$356$		−	2.00000i		−	0.106000i
$357$	−5.62739	+	8.40503i	−0.297833	+	0.444841i
$358$			49.0852i			2.59423i
$359$			25.9068i			1.36731i	0.729806	+	0.683654i	$0.239610\pi$
$359$			25.9068i			1.36731i	−0.729806	+	0.683654i	$0.760390\pi$
$360$	1.83215			0.0965627
$361$	−13.5605			−0.713710
$362$	29.1906			1.53422
$363$	−7.60845	+	7.94427i	−0.399340	+	0.416966i
$364$	40.6246	+	27.1993i	2.12931	+	1.42563i
$365$		−	8.34114i		−	0.436595i
$366$	20.2708			1.05957
$367$			16.2943i			0.850557i	0.905063	+	0.425278i	$0.139824\pi$
$367$			16.2943i			0.850557i	−0.905063	+	0.425278i	$0.860176\pi$
$368$	−6.28201			−0.327472
$369$	10.1860			0.530262
$370$	−17.4404			−0.906684
$371$	22.0562	+	14.7672i	1.14510	+	0.766676i
$372$	−22.4768			−1.16537
$373$			10.6124i			0.549488i	0.961517	+	0.274744i	$0.0885931\pi$
$373$			10.6124i			0.549488i	−0.961517	+	0.274744i	$0.911407\pi$
$374$	−25.8680	−	10.3892i	−1.33760	−	0.537212i
$375$	−1.00000			−0.0516398
$376$	3.78724			0.195312
$377$		−	32.0205i		−	1.64914i
$378$	4.83337	+	3.23607i	0.248602	+	0.166445i
$379$	−26.9586			−1.38477			−0.692385	−	0.721528i	$-0.743440\pi$
$379$	−26.9586			−1.38477			−0.692385	+	0.721528i	$0.743440\pi$
$380$			6.60819i			0.338993i
$381$	16.1949			0.829688
$382$			9.95490i			0.509337i
$383$		−	10.2106i		−	0.521739i	−0.965374	−	0.260869i	$-0.915991\pi$
$383$		−	10.2106i		−	0.521739i	0.965374	−	0.260869i	$-0.0840092\pi$
$384$	−13.3848			−0.683038
$385$	−4.94683	−	7.24768i	−0.252114	−	0.369376i
$386$	9.66673			0.492024
$387$			6.37521i			0.324070i
$388$			28.6157i			1.45274i
$389$	9.57688			0.485567			0.242783	−	0.970081i	$-0.421940\pi$
$389$	9.57688			0.485567			0.242783	+	0.970081i	$0.421940\pi$
$390$			14.3379i			0.726029i
$391$	−14.6553			−0.741151
$392$	−11.8579	+	4.88585i	−0.598915	+	0.246772i
$393$			12.9824i			0.654874i
$394$	50.1814			2.52810
$395$	13.1299			0.660637
$396$	−3.50223	+	8.72020i	−0.175994	+	0.438207i
$397$			29.9264i			1.50196i	0.660324	+	0.750981i	$0.270419\pi$
$397$			29.9264i			1.50196i	−0.660324	+	0.750981i	$0.729581\pi$
$398$	38.5451			1.93209
$399$	−3.43299	+	5.12749i	−0.171865	+	0.256696i
$400$	1.63877			0.0819385
$401$	−27.5441			−1.37549			−0.687743	−	0.725954i	$-0.741398\pi$
$401$	−27.5441			−1.37549			−0.687743	+	0.725954i	$0.741398\pi$
$402$	4.70228			0.234529
$403$		−	51.7361i		−	2.57716i
$404$	4.11712			0.204834
$405$			1.00000i			0.0496904i
$406$	23.7310	+	15.8885i	1.17775	+	0.788535i
$407$	9.80560	−	24.4149i	0.486045	−	1.21020i
$408$	−7.00447			−0.346773
$409$	4.16714			0.206052			0.103026	−	0.994679i	$-0.467148\pi$
$409$	4.16714			0.206052			0.103026	+	0.994679i	$0.467148\pi$
$410$	−22.3939			−1.10595
$411$			0.116115i			0.00572755i
$412$			25.3894i			1.25085i
$413$	5.54375	−	8.28009i	0.272790	−	0.407437i
$414$			8.42762i			0.414195i
$415$			15.3757i			0.754763i
$416$		−	47.3940i		−	2.32368i
$417$			2.18577i			0.107038i
$418$	−15.7808	−	6.33793i	−0.771864	−	0.309998i
$419$			11.9005i			0.581376i	0.956818	+	0.290688i	$0.0938842\pi$
$419$			11.9005i			0.581376i	−0.956818	+	0.290688i	$0.906116\pi$
$420$	−6.22913	−	4.17057i	−0.303950	−	0.203503i
$421$	−25.9722			−1.26581			−0.632905	−	0.774230i	$-0.718137\pi$
$421$	−25.9722			−1.26581			−0.632905	+	0.774230i	$0.718137\pi$
$422$	−28.4679			−1.38579
$423$			2.06710i			0.100506i
$424$			18.3809i			0.892655i
$425$	3.82309			0.185447
$426$	−18.4784			−0.895281
$427$	−20.2708	−	13.5719i	−0.980974	−	0.656788i
$428$		−	33.0126i		−	1.59573i
$429$	−20.0718	−	8.06128i	−0.969074	−	0.389202i
$430$		−	14.0158i		−	0.675904i
$431$		−	19.3963i		−	0.934289i	−0.884181	−	0.467144i	$-0.845283\pi$
$431$		−	19.3963i		−	0.934289i	0.884181	−	0.467144i	$-0.154717\pi$
$432$		−	1.63877i		−	0.0788454i
$433$		−	3.16143i		−	0.151928i	−0.997111	−	0.0759642i	$-0.975797\pi$
$433$		−	3.16143i		−	0.151928i	0.997111	−	0.0759642i	$-0.0242035\pi$
$434$	38.3426	+	25.6714i	1.84050	+	1.23227i
$435$			4.90983i			0.235408i
$436$			24.7436i			1.18500i
$437$	−8.94047			−0.427681
$438$	18.3379			0.876220
$439$	−28.0569			−1.33908			−0.669542	−	0.742774i	$-0.733510\pi$
$439$	−28.0569			−1.33908			−0.669542	+	0.742774i	$0.733510\pi$
$440$	2.26466	−	5.63877i	0.107963	−	0.268818i
$441$	−2.66673	−	6.47214i	−0.126987	−	0.308197i
$442$		−	54.8152i		−	2.60729i
$443$	−32.9489			−1.56545			−0.782725	−	0.622367i	$-0.786171\pi$
$443$	−32.9489			−1.56545			−0.782725	+	0.622367i	$0.786171\pi$
$444$		−	22.4768i		−	1.06670i
$445$	−0.705874			−0.0334617
$446$	−3.57781			−0.169414
$447$	−5.43497			−0.257065
$448$	27.9190	+	18.6925i	1.31905	+	0.883138i
$449$	28.2106			1.33134			0.665671	−	0.746245i	$-0.268145\pi$
$449$	28.2106			1.33134			0.665671	+	0.746245i	$0.268145\pi$
$450$		−	2.19849i		−	0.103638i
$451$	12.5906	−	31.3493i	0.592868	−	1.47618i
$452$	−26.5370			−1.24819
$453$	22.7176			1.06737
$454$			33.2710i			1.56149i
$455$	9.59963	−	14.3379i	0.450037	−	0.672172i
$456$	−4.27308			−0.200105
$457$			4.26489i			0.199503i	0.995012	+	0.0997516i	$0.0318048\pi$
$457$			4.26489i			0.199503i	−0.995012	+	0.0997516i	$0.968195\pi$
$458$	−10.6724			−0.498688
$459$		−	3.82309i		−	0.178447i
$460$		−	10.8613i		−	0.506412i
$461$	−17.6002			−0.819724			−0.409862	−	0.912147i	$-0.634423\pi$
$461$	−17.6002			−0.819724			−0.409862	+	0.912147i	$0.634423\pi$
$462$	15.9340	−	10.8756i	0.741315	−	0.505977i
$463$	7.41641			0.344670			0.172335	−	0.985038i	$-0.444869\pi$
$463$	7.41641			0.344670			0.172335	+	0.985038i	$0.444869\pi$
$464$		−	8.04609i		−	0.373530i
$465$			7.93290i			0.367879i
$466$	41.6714			1.93039
$467$		−	2.27735i		−	0.105383i	−0.998611	−	0.0526915i	$-0.983220\pi$
$467$		−	2.27735i		−	0.105383i	0.998611	−	0.0526915i	$-0.0167800\pi$
$468$	−18.4784			−0.854164
$469$	−4.70228	−	3.14830i	−0.217131	−	0.145375i
$470$		−	4.54451i		−	0.209623i
$471$	−6.51147			−0.300033
$472$	6.90035			0.317614
$473$	19.6209	+	7.88019i	0.902169	+	0.362332i
$474$			28.8660i			1.32586i
$475$	2.33228			0.107012
$476$	23.8145	+	15.9445i	1.09154	+	0.730813i
$477$	−10.0324			−0.459353
$478$	−18.9331			−0.865979
$479$	−13.4221			−0.613269			−0.306635	−	0.951827i	$-0.599203\pi$
$479$	−13.4221			−0.613269			−0.306635	+	0.951827i	$0.599203\pi$
$480$			7.26712i			0.331697i
$481$	51.7361			2.35896
$482$		−	55.0138i		−	2.50581i
$483$	5.64252	−	8.42762i	0.256744	−	0.383470i
$484$	22.5090	+	21.5575i	1.02314	+	0.979888i
$485$	10.0995			0.458596
$486$	−2.19849			−0.0997256
$487$	−21.0272			−0.952834			−0.476417	−	0.879219i	$-0.658065\pi$
$487$	−21.0272			−0.952834			−0.476417	+	0.879219i	$0.658065\pi$
$488$		−	16.8930i		−	0.764711i
$489$			10.7942i			0.488132i
$490$	5.86279	+	14.2289i	0.264854	+	0.642798i
$491$			29.1814i			1.31694i	0.752608	+	0.658469i	$0.228796\pi$
$491$			29.1814i			1.31694i	−0.752608	+	0.658469i	$0.771204\pi$
$492$		−	28.8607i		−	1.30114i
$493$		−	18.7707i		−	0.845391i
$494$		−	33.4400i		−	1.50454i
$495$	3.07768	+	1.23607i	0.138332	+	0.0555571i
$496$		−	13.0002i		−	0.583726i
$497$	18.4784	+	12.3718i	0.828869	+	0.554950i
$498$	−33.8033			−1.51476
$499$	−29.1156			−1.30339			−0.651696	−	0.758480i	$-0.725942\pi$
$499$	−29.1156			−1.30339			−0.651696	+	0.758480i	$0.725942\pi$
$500$			2.83337i			0.126712i
$501$		−	17.4027i		−	0.777494i
$502$	−4.26465			−0.190341
$503$	26.8337			1.19646			0.598228	−	0.801326i	$-0.295872\pi$
$503$	26.8337			1.19646			0.598228	+	0.801326i	$0.295872\pi$
$504$	2.69683	−	4.02796i	0.120126	−	0.179420i
$505$		−	1.45309i		−	0.0646614i
$506$	25.9376	+	10.4171i	1.15306	+	0.463097i
$507$		−	29.5327i		−	1.31159i
$508$		−	45.8860i		−	2.03586i
$509$		−	9.01678i		−	0.399662i	−0.979830	−	0.199831i	$-0.935961\pi$
$509$		−	9.01678i		−	0.399662i	0.979830	−	0.199831i	$-0.0640393\pi$
$510$			8.40503i			0.372181i
$511$	−18.3379	−	12.2777i	−0.811222	−	0.543135i
$512$		−	17.9141i		−	0.791698i
$513$		−	2.33228i		−	0.102973i
$514$	61.1152			2.69568
$515$	8.96086			0.394863
$516$	18.0633			0.795192
$517$	6.36189	+	2.55508i	0.279796	+	0.112372i
$518$	−25.6714	+	38.3426i	−1.12794	+	1.68468i
$519$			4.82437i			0.211766i
$520$	11.9487			0.523987
$521$			28.1829i			1.23471i	0.786683	+	0.617357i	$0.211797\pi$
$521$			28.1829i			1.23471i	−0.786683	+	0.617357i	$0.788203\pi$
$522$	−10.7942			−0.472450
$523$	32.3643			1.41519			0.707596	−	0.706617i	$-0.249780\pi$
$523$	32.3643			1.41519			0.707596	+	0.706617i	$0.249780\pi$
$524$	36.7838			1.60691
$525$	−1.47195	+	2.19849i	−0.0642411	+	0.0959500i
$526$	−6.52806			−0.284637
$527$		−	30.3282i		−	1.32112i
$528$	−5.04362	−	2.02563i	−0.219495	−	0.0881543i
$529$	−8.30531			−0.361100
$530$	22.0562			0.958060
$531$			3.76626i			0.163442i
$532$	14.5281	+	9.72692i	0.629871	+	0.421716i
$533$	66.4302			2.87741
$534$		−	1.55186i		−	0.0671555i
$535$	−11.6514			−0.503733
$536$		−	3.91872i		−	0.169263i
$537$			22.3267i			0.963470i
$538$	−22.6320			−0.975734
$539$	−23.2154	+	0.207355i	−0.999960	+	0.00893142i
$540$	2.83337			0.121929
$541$			4.01749i			0.172726i	0.996264	+	0.0863628i	$0.0275244\pi$
$541$			4.01749i			0.172726i	−0.996264	+	0.0863628i	$0.972476\pi$
$542$			42.8818i			1.84193i
$543$	13.2775			0.569794
$544$		−	27.7828i		−	1.19118i
$545$	8.73292			0.374077
$546$	31.5218	+	21.1047i	1.34901	+	0.903198i
$547$			4.86524i			0.208023i	0.994576	+	0.104011i	$0.0331679\pi$
$547$			4.86524i			0.208023i	−0.994576	+	0.104011i	$0.966832\pi$
$548$	0.328998			0.0140541
$549$	9.22033			0.393514
$550$	−6.76626	−	2.71749i	−0.288514	−	0.115874i
$551$		−	11.4511i		−	0.487833i
$552$	7.02329			0.298931
$553$	19.3266	−	28.8660i	0.821849	−	1.22751i
$554$	−52.8977			−2.24741
$555$	−7.93290			−0.336733
$556$	6.19310			0.262646
$557$		−	5.35951i		−	0.227090i	−0.993533	−	0.113545i	$-0.963779\pi$
$557$		−	5.35951i		−	0.227090i	0.993533	−	0.113545i	$-0.0362206\pi$
$558$	−17.4404			−0.738311
$559$			41.5773i			1.75853i
$560$	2.41219	−	3.60282i	0.101933	−	0.152247i
$561$	−11.7663	−	4.72560i	−0.496772	−	0.199515i
$562$	−5.82796			−0.245838
$563$	1.65063			0.0695659			0.0347829	−	0.999395i	$-0.488926\pi$
$563$	1.65063			0.0695659			0.0347829	+	0.999395i	$0.488926\pi$
$564$	5.85686			0.246618
$565$			9.36589i			0.394026i
$566$			31.0091i			1.30341i
$567$	2.19849	+	1.47195i	0.0923280	+	0.0618161i
$568$			15.3993i			0.646139i
$569$		−	39.4976i		−	1.65583i	−0.560856	−	0.827914i	$-0.689528\pi$
$569$		−	39.4976i		−	1.65583i	0.560856	−	0.827914i	$-0.310472\pi$
$570$			5.12749i			0.214767i
$571$			9.97531i			0.417454i	0.977974	+	0.208727i	$0.0669320\pi$
$571$			9.97531i			0.417454i	−0.977974	+	0.208727i	$0.933068\pi$
$572$	−22.8405	+	56.8706i	−0.955011	+	2.37788i
$573$			4.52806i			0.189162i
$574$	−32.9626	+	49.2327i	−1.37583	+	2.05493i
$575$	−3.83337			−0.159862
$576$	−12.6992			−0.529132
$577$			42.3245i			1.76199i	0.473124	+	0.880996i	$0.343126\pi$
$577$			42.3245i			1.76199i	−0.473124	+	0.880996i	$0.656874\pi$
$578$			5.24116i			0.218004i
$579$	4.39698			0.182732
$580$	13.9113			0.577637
$581$	33.8033	+	22.6322i	1.40240	+	0.938944i
$582$			22.2037i			0.920374i
$583$	−12.4008	+	30.8766i	−0.513587	+	1.27878i
$584$		−	15.2822i		−	0.632382i
$585$			6.52171i			0.269640i
$586$		−	4.27082i		−	0.176426i
$587$		−	0.386939i		−	0.0159707i	−0.999968	−	0.00798535i	$-0.997458\pi$
$587$		−	0.386939i		−	0.0159707i	0.999968	−	0.00798535i	$-0.00254184\pi$
$588$	−18.3379	+	7.55583i	−0.756243	+	0.311597i
$589$		−	18.5017i		−	0.762350i
$590$		−	8.28009i		−	0.340886i
$591$	22.8254			0.938910
$592$	13.0002			0.534305
$593$	7.48636			0.307428			0.153714	−	0.988115i	$-0.450877\pi$
$593$	7.48636			0.307428			0.153714	+	0.988115i	$0.450877\pi$
$594$	−2.71749	+	6.76626i	−0.111500	+	0.277623i
$595$	5.62739	−	8.40503i	0.230701	−	0.344573i
$596$			15.3993i			0.630778i
$597$	17.5325			0.717558
$598$			54.9625i			2.24758i
$599$	24.3939			0.996706			0.498353	−	0.866974i	$-0.333938\pi$
$599$	24.3939			0.996706			0.498353	+	0.866974i	$0.333938\pi$
$600$	−1.83215			−0.0747971
$601$	17.1086			0.697876			0.348938	−	0.937146i	$-0.386542\pi$
$601$	17.1086			0.697876			0.348938	+	0.937146i	$0.386542\pi$
$602$	−30.8137	−	20.6306i	−1.25587	−	0.840841i
$603$	2.13887			0.0871014
$604$		−	64.3673i		−	2.61907i
$605$	7.60845	−	7.94427i	0.309328	−	0.322981i
$606$	3.19460			0.129772
$607$	32.4398			1.31669			0.658345	−	0.752717i	$-0.271257\pi$
$607$	32.4398			1.31669			0.658345	+	0.752717i	$0.271257\pi$
$608$		−	16.9489i		−	0.687370i
$609$	10.7942	+	7.22702i	0.437404	+	0.292854i
$610$	−20.2708			−0.820742
$611$			13.4811i			0.545385i
$612$	−10.8322			−0.437866
$613$		−	12.1632i		−	0.491267i	−0.969363	−	0.245634i	$-0.921004\pi$
$613$		−	12.1632i		−	0.491267i	0.969363	−	0.245634i	$-0.0789960\pi$
$614$		−	17.6667i		−	0.712971i
$615$	−10.1860			−0.410739
$616$	−9.06333	−	13.2788i	−0.365172	−	0.535019i
$617$	−35.0831			−1.41239			−0.706197	−	0.708015i	$-0.749591\pi$
$617$	−35.0831			−1.41239			−0.706197	+	0.708015i	$0.749591\pi$
$618$			19.7004i			0.792465i
$619$			2.89877i			0.116511i	0.998302	+	0.0582557i	$0.0185539\pi$
$619$			2.89877i			0.116511i	−0.998302	+	0.0582557i	$0.981446\pi$
$620$	22.4768			0.902690
$621$			3.83337i			0.153828i
$622$	27.4699			1.10144
$623$	−1.03901	+	1.55186i	−0.0416271	+	0.0621739i
$624$		−	10.6876i		−	0.427846i
$625$	1.00000			0.0400000
$626$	−10.3060			−0.411913
$627$	−7.17801	−	2.88285i	−0.286662	−	0.115130i
$628$			18.4494i			0.736211i
$629$	30.3282			1.20926
$630$	−4.83337	−	3.23607i	−0.192566	−	0.128928i
$631$	34.8050			1.38557			0.692784	−	0.721146i	$-0.256384\pi$
$631$	34.8050			1.38557			0.692784	+	0.721146i	$0.256384\pi$
$632$	24.0559			0.956893
$633$	−12.9488			−0.514669
$634$		−	37.5071i		−	1.48960i
$635$	−16.1949			−0.642674
$636$			28.4255i			1.12715i
$637$	−17.3917	−	42.2094i	−0.689082	−	1.67240i
$638$	−13.3424	+	33.2212i	−0.528230	+	1.31524i
$639$	−8.40503			−0.332498
$640$	13.3848			0.529079
$641$	20.5976			0.813555			0.406778	−	0.913527i	$-0.366652\pi$
$641$	20.5976			0.813555			0.406778	+	0.913527i	$0.366652\pi$
$642$		−	25.6155i		−	1.01096i
$643$			20.1269i			0.793729i	0.917877	+	0.396865i	$0.129902\pi$
$643$			20.1269i			0.793729i	−0.917877	+	0.396865i	$0.870098\pi$
$644$	−23.8785	−	15.9873i	−0.940946	−	0.629989i
$645$		−	6.37521i		−	0.251024i
$646$		−	19.6029i		−	0.771264i
$647$		−	5.14333i		−	0.202205i	−0.994876	−	0.101103i	$-0.967763\pi$
$647$		−	5.14333i		−	0.202205i	0.994876	−	0.101103i	$-0.0322370\pi$
$648$			1.83215i			0.0719736i
$649$	11.5914	+	4.65536i	0.455001	+	0.182739i
$650$		−	14.3379i		−	0.562380i
$651$	17.4404	+	11.6768i	0.683543	+	0.457651i
$652$	30.5840			1.19776
$653$	−30.9118			−1.20967			−0.604837	−	0.796349i	$-0.706762\pi$
$653$	−30.9118			−1.20967			−0.604837	+	0.796349i	$0.706762\pi$
$654$			19.1993i			0.750750i
$655$		−	12.9824i		−	0.507263i
$656$	16.6925			0.651734
$657$	8.34114			0.325419
$658$	−9.99107	−	6.68929i	−0.389492	−	0.260776i
$659$		−	2.92161i		−	0.113810i	−0.998380	−	0.0569048i	$-0.981877\pi$
$659$		−	2.92161i		−	0.113810i	0.998380	−	0.0569048i	$-0.0181231\pi$
$660$	3.50223	−	8.72020i	0.136324	−	0.339433i
$661$			15.7991i			0.614513i	0.951627	+	0.307256i	$0.0994109\pi$
$661$			15.7991i			0.614513i	−0.951627	+	0.307256i	$0.900589\pi$
$662$		−	37.4859i		−	1.45693i
$663$		−	24.9331i		−	0.968321i
$664$			28.1705i			1.09323i
$665$	3.43299	−	5.12749i	0.133126	−	0.198836i
$666$		−	17.4404i		−	0.675802i
$667$			18.8212i			0.728759i
$668$	−49.3081			−1.90779
$669$	−1.62739			−0.0629187
$670$	−4.70228			−0.181665
$671$	11.3970	−	28.3773i	0.439975	−	1.09549i
$672$	15.9767	+	10.6968i	0.616315	+	0.412639i
$673$		−	13.1809i		−	0.508088i	−0.967193	−	0.254044i	$-0.918239\pi$
$673$		−	13.1809i		−	0.508088i	0.967193	−	0.254044i	$-0.0817608\pi$
$674$	16.6781			0.642417
$675$		−	1.00000i		−	0.0384900i
$676$	−83.6770			−3.21835
$677$	24.6857			0.948747			0.474373	−	0.880324i	$-0.342675\pi$
$677$	24.6857			0.948747			0.474373	+	0.880324i	$0.342675\pi$
$678$	−20.5908			−0.790786
$679$	14.8660	−	22.2037i	0.570505	−	0.852101i
$680$	7.00447			0.268609
$681$			15.1336i			0.579919i
$682$	−21.5575	+	53.6760i	−0.825480	+	2.05536i
$683$	36.4028			1.39291			0.696457	−	0.717599i	$-0.254759\pi$
$683$	36.4028			1.39291			0.696457	+	0.717599i	$0.254759\pi$
$684$	−6.60819			−0.252671
$685$		−	0.116115i		−	0.00443654i
$686$	39.9119	+	8.05498i	1.52384	+	0.307541i
$687$	−4.85442			−0.185208
$688$			10.4475i			0.398307i
$689$	−65.4286			−2.49263
$690$		−	8.42762i		−	0.320834i
$691$			35.8885i			1.36526i	0.730762	+	0.682632i	$0.239165\pi$
$691$			35.8885i			1.36526i	−0.730762	+	0.682632i	$0.760835\pi$
$692$	13.6692			0.519626
$693$	7.24768	−	4.94683i	0.275317	−	0.187915i
$694$	−62.2690			−2.36370
$695$		−	2.18577i		−	0.0829111i
$696$			8.99553i			0.340975i
$697$	38.9420			1.47503
$698$		−	43.9044i		−	1.66181i
$699$	18.9545			0.716926
$700$	6.22913	+	4.17057i	0.235439	+	0.157633i
$701$			10.3071i			0.389293i	0.980873	+	0.194646i	$0.0623559\pi$
$701$			10.3071i			0.389293i	−0.980873	+	0.194646i	$0.937644\pi$
$702$	−14.3379			−0.541150
$703$	18.5017			0.697805
$704$	−15.6970	+	39.0840i	−0.591604	+	1.47303i
$705$		−	2.06710i		−	0.0778516i
$706$	−34.0981			−1.28330
$707$	−3.19460	−	2.13887i	−0.120145	−	0.0804404i
$708$	10.6712			0.401048
$709$	−20.5273			−0.770919			−0.385460	−	0.922725i	$-0.625957\pi$
$709$	−20.5273			−0.770919			−0.385460	+	0.922725i	$0.625957\pi$
$710$	18.4784			0.693482
$711$			13.1299i			0.492410i
$712$	−1.29327			−0.0484672
$713$			30.4097i			1.13885i
$714$	18.4784	+	12.3718i	0.691536	+	0.463002i
$715$	20.0718	+	8.06128i	0.750641	+	0.301475i
$716$	63.2598			2.36413
$717$	−8.61185			−0.321616
$718$	56.9558			2.12557
$719$		−	0.665030i		−	0.0248014i	−0.999923	−	0.0124007i	$-0.996053\pi$
$719$		−	0.665030i		−	0.0248014i	0.999923	−	0.0124007i	$-0.00394737\pi$
$720$			1.63877i			0.0610734i
$721$	13.1899	−	19.7004i	0.491219	−	0.733680i
$722$			29.8126i			1.10951i
$723$		−	25.0234i		−	0.930631i
$724$		−	37.6201i		−	1.39814i
$725$		−	4.90983i		−	0.182347i
$726$	17.4654	+	16.7271i	0.648202	+	0.620802i
$727$		−	32.3592i		−	1.20014i	−0.799949	−	0.600068i	$-0.795140\pi$
$727$		−	32.3592i		−	1.20014i	0.799949	−	0.600068i	$-0.204860\pi$
$728$	17.5879	−	26.2692i	0.651852	−	0.973601i
$729$	−1.00000			−0.0370370
$730$	−18.3379			−0.678717
$731$			24.3730i			0.901468i
$732$		−	26.1246i		−	0.965592i
$733$	−37.9468			−1.40160			−0.700799	−	0.713359i	$-0.747173\pi$
$733$	−37.9468			−1.40160			−0.700799	+	0.713359i	$0.747173\pi$
$734$	35.8229			1.32225
$735$	2.66673	+	6.47214i	0.0983639	+	0.238728i
$736$			27.8575i			1.02684i
$737$	2.64379	−	6.58276i	0.0973851	−	0.242479i
$738$		−	22.3939i		−	0.824329i
$739$		−	17.3895i		−	0.639684i	−0.947471	−	0.319842i	$-0.896370\pi$
$739$		−	17.3895i		−	0.639684i	0.947471	−	0.319842i	$-0.103630\pi$
$740$			22.4768i			0.826263i
$741$		−	15.2104i		−	0.558769i
$742$	32.4656	−	48.4904i	1.19185	−	1.78014i
$743$			11.3236i			0.415423i	0.978190	+	0.207712i	$0.0666016\pi$
$743$			11.3236i			0.415423i	−0.978190	+	0.207712i	$0.933398\pi$
$744$			14.5342i			0.532851i
$745$	5.43497			0.199122
$746$	23.3312			0.854216
$747$	−15.3757			−0.562567
$748$	−13.3894	+	33.3381i	−0.489563	+	1.21896i
$749$	−17.1502	+	25.6155i	−0.626656	+	0.935969i
$750$			2.19849i			0.0802776i
$751$	−43.7038			−1.59477			−0.797387	−	0.603468i	$-0.793785\pi$
$751$	−43.7038			−1.59477			−0.797387	+	0.603468i	$0.793785\pi$
$752$			3.38751i			0.123530i
$753$	−1.93981			−0.0706905
$754$	−70.3968			−2.56370
$755$	−22.7176			−0.826778
$756$	4.17057	−	6.22913i	0.151682	−	0.226551i
$757$	−51.0654			−1.85600			−0.928002	−	0.372574i	$-0.878475\pi$
$757$	−51.0654			−1.85600			−0.928002	+	0.372574i	$0.878475\pi$
$758$			59.2683i			2.15272i
$759$	11.7979	+	4.73830i	0.428236	+	0.171989i
$760$	4.27308			0.155001
$761$	43.3228			1.57045			0.785226	−	0.619209i	$-0.212547\pi$
$761$	43.3228			1.57045			0.785226	+	0.619209i	$0.212547\pi$
$762$		−	35.6043i		−	1.28981i
$763$	12.8544	−	19.1993i	0.465361	−	0.695060i
$764$	12.8296			0.464160
$765$			3.82309i			0.138224i
$766$	−22.4480			−0.811079
$767$			24.5625i			0.886899i
$768$			4.02796i			0.145347i
$769$	−27.7894			−1.00211			−0.501055	−	0.865415i	$-0.667055\pi$
$769$	−27.7894			−1.00211			−0.501055	+	0.865415i	$0.667055\pi$
$770$	−15.9340	+	10.8756i	−0.574220	+	0.391928i
$771$	27.7987			1.00115
$772$		−	12.4583i		−	0.448383i
$773$		−	30.3758i		−	1.09254i	−0.837609	−	0.546270i	$-0.816047\pi$
$773$		−	30.3758i		−	1.09254i	0.837609	−	0.546270i	$-0.183953\pi$
$774$	14.0158			0.503789
$775$		−	7.93290i		−	0.284958i
$776$	18.5038			0.664249
$777$	−11.6768	+	17.4404i	−0.418904	+	0.625671i
$778$		−	21.0547i		−	0.754847i
$779$	23.7566			0.851168
$780$	18.4784			0.661633
$781$	−10.3892	+	25.8680i	−0.371754	+	0.925631i
$782$			32.2196i			1.15217i
$783$	−4.90983			−0.175463
$784$	−4.37016	−	10.6063i	−0.156077	−	0.378798i
$785$	6.51147			0.232404
$786$	28.5416			1.01805
$787$	−11.5972			−0.413395			−0.206698	−	0.978405i	$-0.566272\pi$
$787$	−11.5972			−0.413395			−0.206698	+	0.978405i	$0.566272\pi$
$788$		−	64.6726i		−	2.30387i
$789$	−2.96933			−0.105711
$790$		−	28.8660i		−	1.02701i
$791$	20.5908	+	13.7861i	0.732126	+	0.490178i
$792$	5.63877	+	2.26466i	0.200365	+	0.0804711i
$793$	60.1323			2.13536
$794$	65.7929			2.33490
$795$	10.0324			0.355813
$796$		−	49.6760i		−	1.76072i
$797$		−	17.6112i		−	0.623821i	−0.950112	−	0.311910i	$-0.899031\pi$
$797$		−	17.6112i		−	0.623821i	0.950112	−	0.311910i	$-0.100969\pi$
$798$	11.2727	+	7.54741i	0.399051	+	0.267175i
$799$			7.90273i			0.279578i
$800$		−	7.26712i		−	0.256931i
$801$		−	0.705874i		−	0.0249408i
$802$			60.5555i			2.13829i
$803$	10.3102	−	25.6714i	0.363840	−	0.905924i
$804$		−	6.06019i		−	0.213727i
$805$	−5.64252	+	8.42762i	−0.198873	+	0.297035i
$806$	−113.741			−4.00637
$807$	−10.2943			−0.362377
$808$		−	2.66227i		−	0.0936582i
$809$		−	14.3510i		−	0.504555i	−0.967655	−	0.252278i	$-0.918820\pi$
$809$		−	14.3510i		−	0.504555i	0.967655	−	0.252278i	$-0.0811796\pi$
$810$	2.19849			0.0772471
$811$	−6.31314			−0.221684			−0.110842	−	0.993838i	$-0.535355\pi$
$811$	−6.31314			−0.221684			−0.110842	+	0.993838i	$0.535355\pi$
$812$	20.4768	−	30.5840i	0.718595	−	1.07329i
$813$			19.5051i			0.684074i
$814$	−53.6760	−	21.5575i	−1.88134	−	0.755591i
$815$		−	10.7942i		−	0.378105i
$816$		−	6.26517i		−	0.219325i
$817$			14.8687i			0.520192i
$818$		−	9.16143i		−	0.320322i
$819$	14.3379	+	9.59963i	0.501008	+	0.335438i
$820$			28.8607i			1.00786i
$821$			51.0311i			1.78100i	0.454986	+	0.890499i	$0.349644\pi$
$821$			51.0311i			1.78100i	−0.454986	+	0.890499i	$0.650356\pi$
$822$	0.255279			0.00890387
$823$	47.7810			1.66554			0.832770	−	0.553619i	$-0.186754\pi$
$823$	47.7810			1.66554			0.832770	+	0.553619i	$0.186754\pi$
$824$	16.4176			0.571935
$825$	−3.07768	−	1.23607i	−0.107151	−	0.0430344i
$826$	−18.2037	−	12.1879i	−0.633388	−	0.424071i
$827$			3.94416i			0.137152i	0.997646	+	0.0685759i	$0.0218455\pi$
$827$			3.94416i			0.137152i	−0.997646	+	0.0685759i	$0.978154\pi$
$828$	10.8613			0.377457
$829$			23.9638i			0.832298i	0.909297	+	0.416149i	$0.136620\pi$
$829$			23.9638i			0.832298i	−0.909297	+	0.416149i	$0.863380\pi$
$830$	33.8033			1.17333
$831$	−24.0609			−0.834663
$832$	−82.8202			−2.87128
$833$	−10.1952	−	24.7436i	−0.353241	−	0.857314i
$834$	4.80540			0.166398
$835$			17.4027i			0.602244i
$836$	−8.16818	+	20.3379i	−0.282502	+	0.703402i
$837$	−7.93290			−0.274201
$838$	26.1631			0.903789
$839$		−	23.2339i		−	0.802124i	−0.916051	−	0.401062i	$-0.868641\pi$
$839$		−	23.2339i		−	0.802124i	0.916051	−	0.401062i	$-0.131359\pi$
$840$	−2.69683	+	4.02796i	−0.0930494	+	0.138978i
$841$	4.89356			0.168743
$842$			57.0997i			1.96779i
$843$	−2.65089			−0.0913015
$844$			36.6887i			1.26288i
$845$			29.5327i			1.01596i
$846$	4.54451			0.156244
$847$	−6.26616	−	28.4207i	−0.215308	−	0.976546i
$848$	−16.4408			−0.564581
$849$			14.1047i			0.484073i
$850$		−	8.40503i		−	0.288290i
$851$	−30.4097			−1.04243
$852$			23.8145i			0.815872i
$853$	27.8240			0.952674			0.476337	−	0.879263i	$-0.341964\pi$
$853$	27.8240			0.952674			0.476337	+	0.879263i	$0.341964\pi$
$854$	−29.8376	+	44.5652i	−1.02102	+	1.52499i
$855$			2.33228i			0.0797622i
$856$	−21.3471			−0.729627
$857$	3.63200			0.124067			0.0620334	−	0.998074i	$-0.480241\pi$
$857$	3.63200			0.124067			0.0620334	+	0.998074i	$0.480241\pi$
$858$	−17.7227	+	44.1276i	−0.605041	+	1.50649i
$859$		−	23.3644i		−	0.797182i	−0.917129	−	0.398591i	$-0.869499\pi$
$859$		−	23.3644i		−	0.797182i	0.917129	−	0.398591i	$-0.130501\pi$
$860$	−18.0633			−0.615953
$861$	−14.9933	+	22.3939i	−0.510970	+	0.763180i
$862$	−42.6427			−1.45242
$863$	7.16683			0.243962			0.121981	−	0.992532i	$-0.461075\pi$
$863$	7.16683			0.243962			0.121981	+	0.992532i	$0.461075\pi$
$864$	−7.26712			−0.247232
$865$		−	4.82437i		−	0.164034i
$866$	−6.95037			−0.236183
$867$			2.38398i			0.0809643i
$868$	33.0847	−	49.4150i	1.12297	−	1.67726i
$869$	40.4097	+	16.2295i	1.37080	+	0.550547i
$870$	10.7942			0.365958
$871$	13.9491			0.472646
$872$	16.0000			0.541828
$873$			10.0995i			0.341817i
$874$			19.6555i			0.664859i
$875$	1.47195	−	2.19849i	0.0497610	−	0.0743226i
$876$		−	23.6335i		−	0.798502i
$877$		−	20.0190i		−	0.675993i	−0.941147	−	0.337997i	$-0.890251\pi$
$877$		−	20.0190i		−	0.675993i	0.941147	−	0.337997i	$-0.109749\pi$
$878$			61.6830i			2.08170i
$879$		−	1.94262i		−	0.0655228i
$880$	5.04362	+	2.02563i	0.170020	+	0.0682840i
$881$			14.0814i			0.474416i	0.971459	+	0.237208i	$0.0762322\pi$
$881$			14.0814i			0.474416i	−0.971459	+	0.237208i	$0.923768\pi$
$882$	−14.2289	+	5.86279i	−0.479113	+	0.197410i
$883$	−12.1161			−0.407740			−0.203870	−	0.978998i	$-0.565352\pi$
$883$	−12.1161			−0.407740			−0.203870	+	0.978998i	$0.565352\pi$
$884$	−70.6446			−2.37603
$885$		−	3.76626i		−	0.126602i
$886$			72.4380i			2.43360i
$887$	−1.96381			−0.0659384			−0.0329692	−	0.999456i	$-0.510496\pi$
$887$	−1.96381			−0.0659384			−0.0329692	+	0.999456i	$0.510496\pi$
$888$	−14.5342			−0.487737
$889$	−23.8380	+	35.6043i	−0.799502	+	1.19413i
$890$			1.55186i			0.0520184i
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$			4.61100i			0.154388i
$893$			4.82106i			0.161331i
$894$			11.9487i			0.399626i
$895$		−	22.3267i		−	0.746301i
$896$	19.7017	−	29.4263i	0.658187	−	0.983063i
$897$			25.0001i			0.834729i
$898$		−	62.0208i		−	2.06966i
$899$	−38.9492			−1.29903
$900$	−2.83337			−0.0944455
$901$	−38.3549			−1.27779
$902$	−68.9212	−	27.6803i	−2.29482	−	0.921654i
$903$	−14.0158	−	9.38398i	−0.466418	−	0.312279i
$904$			17.1597i			0.570723i
$905$	−13.2775			−0.441360
$906$		−	49.9445i		−	1.65929i
$907$	35.5032			1.17887			0.589433	−	0.807817i	$-0.299351\pi$
$907$	35.5032			1.17887			0.589433	+	0.807817i	$0.299351\pi$
$908$	42.8789			1.42299
$909$	1.45309			0.0481958
$910$	−31.5218	−	21.1047i	−1.04494	−	0.699614i
$911$	−36.4032			−1.20609			−0.603045	−	0.797707i	$-0.706046\pi$
$911$	−36.4032			−1.20609			−0.603045	+	0.797707i	$0.706046\pi$
$912$		−	3.82207i		−	0.126561i
$913$	−19.0054	+	47.3215i	−0.628987	+	1.56611i
$914$	9.37633			0.310141
$915$	−9.22033			−0.304815
$916$			13.7543i			0.454456i
$917$	−28.5416	−	19.1094i	−0.942528	−	0.631048i
$918$	−8.40503			−0.277407
$919$		−	43.9423i		−	1.44952i	−0.688999	−	0.724762i	$-0.741950\pi$
$919$		−	43.9423i		−	1.44952i	0.688999	−	0.724762i	$-0.258050\pi$
$920$	−7.02329			−0.231551
$921$		−	8.03584i		−	0.264790i
$922$			38.6939i			1.27432i
$923$	−54.8152			−1.80426
$924$	−14.0162	−	20.5353i	−0.461099	−	0.675563i
$925$	7.93290			0.260832
$926$		−	16.3049i		−	0.535813i
$927$			8.96086i			0.294313i
$928$	−35.6803			−1.17126
$929$		−	20.4209i		−	0.669987i	−0.942220	−	0.334994i	$-0.891266\pi$
$929$		−	20.4209i		−	0.669987i	0.942220	−	0.334994i	$-0.108734\pi$
$930$	17.4404			0.571893
$931$	−6.21956	−	15.0948i	−0.203838	−	0.494713i
$932$		−	53.7051i		−	1.75917i
$933$	12.4949			0.409064
$934$	−5.00673			−0.163825
$935$	11.7663	+	4.72560i	0.384798	+	0.154544i
$936$			11.9487i			0.390557i
$937$	−24.1831			−0.790026			−0.395013	−	0.918676i	$-0.629260\pi$
$937$	−24.1831			−0.790026			−0.395013	+	0.918676i	$0.629260\pi$
$938$	−6.92152	+	10.3379i	−0.225996	+	0.337545i
$939$	−4.68778			−0.152980
$940$	−5.85686			−0.191030
$941$	−10.6236			−0.346321			−0.173160	−	0.984894i	$-0.555398\pi$
$941$	−10.6236			−0.346321			−0.173160	+	0.984894i	$0.555398\pi$
$942$			14.3154i			0.466422i
$943$	−39.0467			−1.27154
$944$			6.17204i			0.200883i
$945$	−2.19849	−	1.47195i	−0.0715169	−	0.0478825i
$946$	17.3245	−	43.1363i	0.563269	−	1.40248i
$947$	−14.1439			−0.459614			−0.229807	−	0.973236i	$-0.573810\pi$
$947$	−14.1439			−0.459614			−0.229807	+	0.973236i	$0.573810\pi$
$948$	37.2018			1.20826
$949$	54.3985			1.76585
$950$		−	5.12749i		−	0.166358i
$951$		−	17.0604i		−	0.553221i
$952$	10.3102	−	15.3993i	0.334156	−	0.499093i
$953$		−	27.8095i		−	0.900840i	−0.892817	−	0.450420i	$-0.851274\pi$
$953$		−	27.8095i		−	0.900840i	0.892817	−	0.450420i	$-0.148726\pi$
$954$			22.0562i			0.714096i
$955$		−	4.52806i		−	0.146525i
$956$			24.4005i			0.789170i
$957$	−6.06888	+	15.1109i	−0.196179	+	0.488466i
$958$			29.5083i			0.953369i
$959$	−0.255279	−	0.170916i	−0.00824338	−	0.00551917i
$960$	12.6992			0.409864
$961$	−31.9308			−1.03003
$962$		−	113.741i		−	3.66717i
$963$		−	11.6514i		−	0.375461i
$964$	−70.9005			−2.28355
$965$	−4.39698			−0.141544
$966$	−18.5281	−	12.4050i	−0.596130	−	0.399125i
$967$		−	11.4103i		−	0.366930i	−0.983026	−	0.183465i	$-0.941269\pi$
$967$		−	11.4103i		−	0.366930i	0.983026	−	0.183465i	$-0.0587313\pi$
$968$	13.9398	−	14.5551i	0.448042	−	0.467818i
$969$		−	8.91650i		−	0.286439i
$970$		−	22.2037i		−	0.712919i
$971$			45.1873i			1.45013i	0.688680	+	0.725065i	$0.258190\pi$
$971$			45.1873i			1.45013i	−0.688680	+	0.725065i	$0.741810\pi$
$972$			2.83337i			0.0908802i
$973$	−4.80540	−	3.21735i	−0.154054	−	0.103143i
$974$			46.2282i			1.48125i
$975$		−	6.52171i		−	0.208862i
$976$	15.1100			0.483660
$977$	49.5094			1.58395			0.791973	−	0.610556i	$-0.209054\pi$
$977$	49.5094			1.58395			0.791973	+	0.610556i	$0.209054\pi$
$978$	23.7310			0.758834
$979$	−2.17246	−	0.872509i	−0.0694320	−	0.0278855i
$980$	18.3379	−	7.55583i	0.585784	−	0.241362i
$981$			8.73292i			0.278821i
$982$	64.1551			2.04727
$983$			1.65631i			0.0528282i	0.999651	+	0.0264141i	$0.00840884\pi$
$983$			1.65631i			0.0528282i	−0.999651	+	0.0264141i	$0.991591\pi$
$984$	−18.6623			−0.594931
$985$	−22.8254			−0.727276
$986$	−41.2673			−1.31422
$987$	−4.54451	−	3.04267i	−0.144653	−	0.0968493i
$988$	−43.0967			−1.37109
$989$		−	24.4385i		−	0.777099i
$990$	2.71749	−	6.76626i	0.0863673	−	0.215046i
$991$	57.7821			1.83551			0.917754	−	0.397148i	$-0.130000\pi$
$991$	57.7821			1.83551			0.917754	+	0.397148i	$0.130000\pi$
$992$	−57.6493			−1.83037
$993$		−	17.0507i		−	0.541088i
$994$	27.1993	−	40.6246i	0.862708	−	1.28853i
$995$	−17.5325			−0.555818
$996$			43.5650i			1.38041i
$997$	49.4028			1.56460			0.782300	−	0.622901i	$-0.214046\pi$
$997$	49.4028			1.56460			0.782300	+	0.622901i	$0.214046\pi$
$998$			64.0103i			2.02621i
$999$		−	7.93290i		−	0.250986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.c.76.3	✓	16
7.6	odd	2	inner	1155.2.i.c.76.4	yes	16
11.10	odd	2	inner	1155.2.i.c.76.13	yes	16
77.76	even	2	inner	1155.2.i.c.76.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.c.76.3	✓	16	1.1	even	1	trivial
1155.2.i.c.76.4	yes	16	7.6	odd	2	inner
1155.2.i.c.76.13	yes	16	11.10	odd	2	inner
1155.2.i.c.76.14	yes	16	77.76	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} -2.19849 q^{6} +(2.19849 + 1.47195i) q^{7} +1.83215i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} -2.19849 q^{6} +(2.19849 + 1.47195i) q^{7} +1.83215i q^{8} -1.00000 q^{9} +2.19849 q^{10} +(-1.23607 + 3.07768i) q^{11} +2.83337i q^{12} -6.52171 q^{13} +(3.23607 - 4.83337i) q^{14} +1.00000 q^{15} -1.63877 q^{16} -3.82309 q^{17} +2.19849i q^{18} -2.33228 q^{19} -2.83337i q^{20} +(1.47195 - 2.19849i) q^{21} +(6.76626 + 2.71749i) q^{22} +3.83337 q^{23} +1.83215 q^{24} -1.00000 q^{25} +14.3379i q^{26} +1.00000i q^{27} +(-6.22913 - 4.17057i) q^{28} +4.90983i q^{29} -2.19849i q^{30} +7.93290i q^{31} +7.26712i q^{32} +(3.07768 + 1.23607i) q^{33} +8.40503i q^{34} +(-1.47195 + 2.19849i) q^{35} +2.83337 q^{36} -7.93290 q^{37} +5.12749i q^{38} +6.52171i q^{39} -1.83215 q^{40} -10.1860 q^{41} +(-4.83337 - 3.23607i) q^{42} -6.37521i q^{43} +(3.50223 - 8.72020i) q^{44} -1.00000i q^{45} -8.42762i q^{46} -2.06710i q^{47} +1.63877i q^{48} +(2.66673 + 6.47214i) q^{49} +2.19849i q^{50} +3.82309i q^{51} +18.4784 q^{52} +10.0324 q^{53} +2.19849 q^{54} +(-3.07768 - 1.23607i) q^{55} +(-2.69683 + 4.02796i) q^{56} +2.33228i q^{57} +10.7942 q^{58} -3.76626i q^{59} -2.83337 q^{60} -9.22033 q^{61} +17.4404 q^{62} +(-2.19849 - 1.47195i) q^{63} +12.6992 q^{64} -6.52171i q^{65} +(2.71749 - 6.76626i) q^{66} -2.13887 q^{67} +10.8322 q^{68} -3.83337i q^{69} +(4.83337 + 3.23607i) q^{70} +8.40503 q^{71} -1.83215i q^{72} -8.34114 q^{73} +17.4404i q^{74} +1.00000i q^{75} +6.60819 q^{76} +(-7.24768 + 4.94683i) q^{77} +14.3379 q^{78} -13.1299i q^{79} -1.63877i q^{80} +1.00000 q^{81} +22.3939i q^{82} +15.3757 q^{83} +(-4.17057 + 6.22913i) q^{84} -3.82309i q^{85} -14.0158 q^{86} +4.90983 q^{87} +(-5.63877 - 2.26466i) q^{88} +0.705874i q^{89} -2.19849 q^{90} +(-14.3379 - 9.59963i) q^{91} -10.8613 q^{92} +7.93290 q^{93} -4.54451 q^{94} -2.33228i q^{95} +7.26712 q^{96} -10.0995i q^{97} +(14.2289 - 5.86279i) q^{98} +(1.23607 - 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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