LMFDB - Embedded newform 165.2.c.b.34.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.5
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.2.c.b.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.48119i q^{2} +1.00000i q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} -1.48119 q^{6} -1.19394i q^{7} +2.67513i q^{8} -1.00000 q^{9} +(-2.48119 - 2.19394i) q^{10} +1.00000 q^{11} -0.193937i q^{12} +0.806063i q^{13} +1.76845 q^{14} +(-1.67513 - 1.48119i) q^{15} -4.35026 q^{16} -3.76845i q^{17} -1.48119i q^{18} +5.35026 q^{19} +(0.287258 - 0.324869i) q^{20} +1.19394 q^{21} +1.48119i q^{22} +4.00000i q^{23} -2.67513 q^{24} +(-0.612127 - 4.96239i) q^{25} -1.19394 q^{26} -1.00000i q^{27} +0.231548i q^{28} +4.31265 q^{29} +(2.19394 - 2.48119i) q^{30} +0.962389 q^{31} -1.09332i q^{32} +1.00000i q^{33} +5.58181 q^{34} +(2.00000 + 1.76845i) q^{35} +0.193937 q^{36} -1.61213i q^{37} +7.92478i q^{38} -0.806063 q^{39} +(-4.48119 - 3.96239i) q^{40} +9.08840 q^{41} +1.76845i q^{42} +4.41819i q^{43} -0.193937 q^{44} +(1.48119 - 1.67513i) q^{45} -5.92478 q^{46} -12.3127i q^{47} -4.35026i q^{48} +5.57452 q^{49} +(7.35026 - 0.906679i) q^{50} +3.76845 q^{51} -0.156325i q^{52} +1.42548i q^{53} +1.48119 q^{54} +(-1.48119 + 1.67513i) q^{55} +3.19394 q^{56} +5.35026i q^{57} +6.38787i q^{58} -13.2750 q^{59} +(0.324869 + 0.287258i) q^{60} -0.0752228 q^{61} +1.42548i q^{62} +1.19394i q^{63} -7.08110 q^{64} +(-1.35026 - 1.19394i) q^{65} -1.48119 q^{66} +2.70052i q^{67} +0.730841i q^{68} -4.00000 q^{69} +(-2.61942 + 2.96239i) q^{70} -14.0508 q^{71} -2.67513i q^{72} -10.7308i q^{73} +2.38787 q^{74} +(4.96239 - 0.612127i) q^{75} -1.03761 q^{76} -1.19394i q^{77} -1.19394i q^{78} -13.9756 q^{79} +(6.44358 - 7.28726i) q^{80} +1.00000 q^{81} +13.4617i q^{82} -9.89446i q^{83} -0.231548 q^{84} +(6.31265 + 5.58181i) q^{85} -6.54420 q^{86} +4.31265i q^{87} +2.67513i q^{88} -16.8872 q^{89} +(2.48119 + 2.19394i) q^{90} +0.962389 q^{91} -0.775746i q^{92} +0.962389i q^{93} +18.2374 q^{94} +(-7.92478 + 8.96239i) q^{95} +1.09332 q^{96} -11.4763i q^{97} +8.25694i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34}+ \cdots - 6 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.48119i			1.04736i	0.851914	+	0.523681i	$0.175442\pi$
$2$			1.48119i			1.04736i	−0.851914	+	0.523681i	$0.824558\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.193937			−0.0969683
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$6$	−1.48119			−0.604695
$7$		−	1.19394i		−	0.451266i	−0.974212	−	0.225633i	$-0.927555\pi$
$7$		−	1.19394i		−	0.451266i	0.974212	−	0.225633i	$-0.0724450\pi$
$8$			2.67513i			0.945802i
$9$	−1.00000			−0.333333
$10$	−2.48119	−	2.19394i	−0.784623	−	0.693784i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	0.193937i		−	0.0559847i
$13$			0.806063i			0.223562i	0.993733	+	0.111781i	$0.0356555\pi$
$13$			0.806063i			0.223562i	−0.993733	+	0.111781i	$0.964345\pi$
$14$	1.76845			0.472639
$15$	−1.67513	−	1.48119i	−0.432517	−	0.382443i
$16$	−4.35026			−1.08757
$17$		−	3.76845i		−	0.913984i	−0.889471	−	0.456992i	$-0.848927\pi$
$17$		−	3.76845i		−	0.913984i	0.889471	−	0.456992i	$-0.151073\pi$
$18$		−	1.48119i		−	0.349121i
$19$	5.35026			1.22743			0.613717	−	0.789526i	$-0.289674\pi$
$19$	5.35026			1.22743			0.613717	+	0.789526i	$0.289674\pi$
$20$	0.287258	−	0.324869i	0.0642328	−	0.0726429i
$21$	1.19394			0.260538
$22$			1.48119i			0.315792i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	−2.67513			−0.546059
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$	−1.19394			−0.234150
$27$		−	1.00000i		−	0.192450i
$28$			0.231548i			0.0437585i
$29$	4.31265			0.800839			0.400420	−	0.916332i	$-0.368864\pi$
$29$	4.31265			0.800839			0.400420	+	0.916332i	$0.368864\pi$
$30$	2.19394	−	2.48119i	0.400556	−	0.453002i
$31$	0.962389			0.172850			0.0864250	−	0.996258i	$-0.472456\pi$
$31$	0.962389			0.172850			0.0864250	+	0.996258i	$0.472456\pi$
$32$		−	1.09332i		−	0.193274i
$33$			1.00000i			0.174078i
$34$	5.58181			0.957272
$35$	2.00000	+	1.76845i	0.338062	+	0.298923i
$36$	0.193937			0.0323228
$37$		−	1.61213i		−	0.265032i	−0.991181	−	0.132516i	$-0.957694\pi$
$37$		−	1.61213i		−	0.265032i	0.991181	−	0.132516i	$-0.0423056\pi$
$38$			7.92478i			1.28557i
$39$	−0.806063			−0.129073
$40$	−4.48119	−	3.96239i	−0.708539	−	0.626509i
$41$	9.08840			1.41937			0.709685	−	0.704520i	$-0.248837\pi$
$41$	9.08840			1.41937			0.709685	+	0.704520i	$0.248837\pi$
$42$			1.76845i			0.272878i
$43$			4.41819i			0.673768i	0.941546	+	0.336884i	$0.109373\pi$
$43$			4.41819i			0.673768i	−0.941546	+	0.336884i	$0.890627\pi$
$44$	−0.193937			−0.0292370
$45$	1.48119	−	1.67513i	0.220803	−	0.249714i
$46$	−5.92478			−0.873561
$47$		−	12.3127i		−	1.79598i	−0.440011	−	0.897992i	$-0.645026\pi$
$47$		−	12.3127i		−	1.79598i	0.440011	−	0.897992i	$-0.354974\pi$
$48$		−	4.35026i		−	0.627906i
$49$	5.57452			0.796359
$50$	7.35026	−	0.906679i	1.03948	−	0.128224i
$51$	3.76845			0.527689
$52$		−	0.156325i		−	0.0216784i
$53$			1.42548i			0.195805i	0.995196	+	0.0979027i	$0.0312134\pi$
$53$			1.42548i			0.195805i	−0.995196	+	0.0979027i	$0.968787\pi$
$54$	1.48119			0.201565
$55$	−1.48119	+	1.67513i	−0.199724	+	0.225875i
$56$	3.19394			0.426808
$57$			5.35026i			0.708659i
$58$			6.38787i			0.838769i
$59$	−13.2750			−1.72826			−0.864131	−	0.503266i	$-0.832132\pi$
$59$	−13.2750			−1.72826			−0.864131	+	0.503266i	$0.832132\pi$
$60$	0.324869	+	0.287258i	0.0419404	+	0.0370848i
$61$	−0.0752228			−0.00963129			−0.00481565	−	0.999988i	$-0.501533\pi$
$61$	−0.0752228			−0.00963129			−0.00481565	+	0.999988i	$0.501533\pi$
$62$			1.42548i			0.181037i
$63$			1.19394i			0.150422i
$64$	−7.08110			−0.885138
$65$	−1.35026	−	1.19394i	−0.167479	−	0.148090i
$66$	−1.48119			−0.182322
$67$			2.70052i			0.329921i	0.986300	+	0.164961i	$0.0527497\pi$
$67$			2.70052i			0.329921i	−0.986300	+	0.164961i	$0.947250\pi$
$68$			0.730841i			0.0886274i
$69$	−4.00000			−0.481543
$70$	−2.61942	+	2.96239i	−0.313081	+	0.354073i
$71$	−14.0508			−1.66752			−0.833761	−	0.552126i	$-0.813817\pi$
$71$	−14.0508			−1.66752			−0.833761	+	0.552126i	$0.813817\pi$
$72$		−	2.67513i		−	0.315267i
$73$		−	10.7308i		−	1.25595i	−0.778234	−	0.627975i	$-0.783884\pi$
$73$		−	10.7308i		−	1.25595i	0.778234	−	0.627975i	$-0.216116\pi$
$74$	2.38787			0.277585
$75$	4.96239	−	0.612127i	0.573007	−	0.0706823i
$76$	−1.03761			−0.119022
$77$		−	1.19394i		−	0.136062i
$78$		−	1.19394i		−	0.135187i
$79$	−13.9756			−1.57237			−0.786187	−	0.617989i	$-0.787948\pi$
$79$	−13.9756			−1.57237			−0.786187	+	0.617989i	$0.787948\pi$
$80$	6.44358	−	7.28726i	0.720414	−	0.814740i
$81$	1.00000			0.111111
$82$			13.4617i			1.48659i
$83$		−	9.89446i		−	1.08606i	−0.839714	−	0.543029i	$-0.817277\pi$
$83$		−	9.89446i		−	1.08606i	0.839714	−	0.543029i	$-0.182723\pi$
$84$	−0.231548			−0.0252640
$85$	6.31265	+	5.58181i	0.684703	+	0.605432i
$86$	−6.54420			−0.705679
$87$			4.31265i			0.462365i
$88$			2.67513i			0.285170i
$89$	−16.8872			−1.79004			−0.895018	−	0.446030i	$-0.852837\pi$
$89$	−16.8872			−1.79004			−0.895018	+	0.446030i	$0.852837\pi$
$90$	2.48119	+	2.19394i	0.261541	+	0.231261i
$91$	0.962389			0.100886
$92$		−	0.775746i		−	0.0808771i
$93$			0.962389i			0.0997950i
$94$	18.2374			1.88105
$95$	−7.92478	+	8.96239i	−0.813065	+	0.919522i
$96$	1.09332			0.111587
$97$		−	11.4763i		−	1.16524i	−0.812745	−	0.582619i	$-0.802028\pi$
$97$		−	11.4763i		−	1.16524i	0.812745	−	0.582619i	$-0.197972\pi$
$98$			8.25694i			0.834077i
$99$	−1.00000			−0.100504
$100$	0.118714	+	0.962389i	0.0118714	+	0.0962389i
$101$	10.7612			1.07078			0.535388	−	0.844606i	$-0.320166\pi$
$101$	10.7612			1.07078			0.535388	+	0.844606i	$0.320166\pi$
$102$			5.58181i			0.552682i
$103$			16.9380i			1.66895i	0.551049	+	0.834473i	$0.314228\pi$
$103$			16.9380i			1.66895i	−0.551049	+	0.834473i	$0.685772\pi$
$104$	−2.15633			−0.211445
$105$	−1.76845	+	2.00000i	−0.172583	+	0.195180i
$106$	−2.11142			−0.205079
$107$		−	8.28233i		−	0.800683i	−0.916366	−	0.400342i	$-0.868891\pi$
$107$		−	8.28233i		−	0.800683i	0.916366	−	0.400342i	$-0.131109\pi$
$108$			0.193937i			0.0186616i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−2.48119	−	2.19394i	−0.236573	−	0.209184i
$111$	1.61213			0.153016
$112$			5.19394i			0.490781i
$113$			2.26187i			0.212778i	0.994325	+	0.106389i	$0.0339289\pi$
$113$			2.26187i			0.212778i	−0.994325	+	0.106389i	$0.966071\pi$
$114$	−7.92478			−0.742223
$115$	−6.70052	−	5.92478i	−0.624827	−	0.552488i
$116$	−0.836381			−0.0776560
$117$		−	0.806063i		−	0.0745206i
$118$		−	19.6629i		−	1.81012i
$119$	−4.49929			−0.412449
$120$	3.96239	−	4.48119i	0.361715	−	0.409075i
$121$	1.00000			0.0909091
$122$		−	0.111420i		−	0.0100875i
$123$			9.08840i			0.819473i
$124$	−0.186642			−0.0167610
$125$	9.21933	+	6.32487i	0.824602	+	0.565713i
$126$	−1.76845			−0.157546
$127$			13.8192i			1.22626i	0.789982	+	0.613130i	$0.210090\pi$
$127$			13.8192i			1.22626i	−0.789982	+	0.613130i	$0.789910\pi$
$128$		−	12.6751i		−	1.12033i
$129$	−4.41819			−0.389000
$130$	1.76845	−	2.00000i	0.155104	−	0.175412i
$131$	−5.92478			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$131$	−5.92478			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$132$		−	0.193937i		−	0.0168800i
$133$		−	6.38787i		−	0.553899i
$134$	−4.00000			−0.345547
$135$	1.67513	+	1.48119i	0.144172	+	0.127481i
$136$	10.0811			0.864447
$137$		−	3.35026i		−	0.286232i	−0.989706	−	0.143116i	$-0.954288\pi$
$137$		−	3.35026i		−	0.286232i	0.989706	−	0.143116i	$-0.0457122\pi$
$138$		−	5.92478i		−	0.504351i
$139$	21.1998			1.79814			0.899072	−	0.437800i	$-0.144242\pi$
$139$	21.1998			1.79814			0.899072	+	0.437800i	$0.144242\pi$
$140$	−0.387873	−	0.342968i	−0.0327813	−	0.0289860i
$141$	12.3127			1.03691
$142$		−	20.8119i		−	1.74650i
$143$			0.806063i			0.0674064i
$144$	4.35026			0.362522
$145$	−6.38787	+	7.22425i	−0.530484	+	0.599942i
$146$	15.8945			1.31543
$147$			5.57452i			0.459778i
$148$			0.312650i			0.0256997i
$149$	−6.38787			−0.523315			−0.261657	−	0.965161i	$-0.584269\pi$
$149$	−6.38787			−0.523315			−0.261657	+	0.965161i	$0.584269\pi$
$150$	0.906679	+	7.35026i	0.0740300	+	0.600146i
$151$	−2.64974			−0.215633			−0.107816	−	0.994171i	$-0.534386\pi$
$151$	−2.64974			−0.215633			−0.107816	+	0.994171i	$0.534386\pi$
$152$			14.3127i			1.16091i
$153$			3.76845i			0.304661i
$154$	1.76845			0.142506
$155$	−1.42548	+	1.61213i	−0.114498	+	0.129489i
$156$	0.156325			0.0125160
$157$		−	1.61213i		−	0.128662i	−0.997929	−	0.0643309i	$-0.979509\pi$
$157$		−	1.61213i		−	0.128662i	0.997929	−	0.0643309i	$-0.0204913\pi$
$158$		−	20.7005i		−	1.64685i
$159$	−1.42548			−0.113048
$160$	1.83146	+	1.61942i	0.144789	+	0.128026i
$161$	4.77575			0.376382
$162$			1.48119i			0.116374i
$163$		−	0.312650i		−	0.0244887i	−0.999925	−	0.0122443i	$-0.996102\pi$
$163$		−	0.312650i		−	0.0244887i	0.999925	−	0.0122443i	$-0.00389759\pi$
$164$	−1.76257			−0.137634
$165$	−1.67513	−	1.48119i	−0.130409	−	0.115311i
$166$	14.6556			1.13750
$167$		−	0.493413i		−	0.0381815i	−0.999818	−	0.0190907i	$-0.993923\pi$
$167$		−	0.493413i		−	0.0381815i	0.999818	−	0.0190907i	$-0.00607714\pi$
$168$			3.19394i			0.246418i
$169$	12.3503			0.950020
$170$	−8.26774	+	9.35026i	−0.634107	+	0.717132i
$171$	−5.35026			−0.409145
$172$		−	0.856849i		−	0.0653341i
$173$		−	23.3054i		−	1.77187i	−0.463806	−	0.885937i	$-0.653517\pi$
$173$		−	23.3054i		−	1.77187i	0.463806	−	0.885937i	$-0.346483\pi$
$174$	−6.38787			−0.484263
$175$	−5.92478	+	0.730841i	−0.447871	+	0.0552464i
$176$	−4.35026			−0.327913
$177$		−	13.2750i		−	0.997813i
$178$		−	25.0132i		−	1.87482i
$179$	10.7005			0.799795			0.399897	−	0.916560i	$-0.369046\pi$
$179$	10.7005			0.799795			0.399897	+	0.916560i	$0.369046\pi$
$180$	−0.287258	+	0.324869i	−0.0214109	+	0.0242143i
$181$	−7.79877			−0.579678			−0.289839	−	0.957075i	$-0.593602\pi$
$181$	−7.79877			−0.579678			−0.289839	+	0.957075i	$0.593602\pi$
$182$			1.42548i			0.105664i
$183$		−	0.0752228i		−	0.00556063i
$184$	−10.7005			−0.788853
$185$	2.70052	+	2.38787i	0.198546	+	0.175560i
$186$	−1.42548			−0.104522
$187$		−	3.76845i		−	0.275577i
$188$			2.38787i			0.174154i
$189$	−1.19394			−0.0868461
$190$	−13.2750	−	11.7381i	−0.963073	−	0.851574i
$191$	1.29948			0.0940268			0.0470134	−	0.998894i	$-0.485030\pi$
$191$	1.29948			0.0940268			0.0470134	+	0.998894i	$0.485030\pi$
$192$		−	7.08110i		−	0.511035i
$193$			8.59498i			0.618680i	0.950951	+	0.309340i	$0.100108\pi$
$193$			8.59498i			0.618680i	−0.950951	+	0.309340i	$0.899892\pi$
$194$	16.9986			1.22043
$195$	1.19394	−	1.35026i	0.0854996	−	0.0966943i
$196$	−1.08110			−0.0772216
$197$			20.7064i			1.47527i	0.675200	+	0.737635i	$0.264057\pi$
$197$			20.7064i			1.47527i	−0.675200	+	0.737635i	$0.735943\pi$
$198$		−	1.48119i		−	0.105264i
$199$	−5.55149			−0.393535			−0.196767	−	0.980450i	$-0.563044\pi$
$199$	−5.55149			−0.393535			−0.196767	+	0.980450i	$0.563044\pi$
$200$	13.2750	−	1.63752i	0.938687	−	0.115790i
$201$	−2.70052			−0.190480
$202$			15.9394i			1.12149i
$203$		−	5.14903i		−	0.361391i
$204$	−0.730841			−0.0511691
$205$	−13.4617	+	15.2243i	−0.940205	+	1.06331i
$206$	−25.0884			−1.74799
$207$		−	4.00000i		−	0.278019i
$208$		−	3.50659i		−	0.243138i
$209$	5.35026			0.370085
$210$	−2.96239	−	2.61942i	−0.204424	−	0.180757i
$211$	−18.4993			−1.27354			−0.636772	−	0.771052i	$-0.719731\pi$
$211$	−18.4993			−1.27354			−0.636772	+	0.771052i	$0.719731\pi$
$212$		−	0.276454i		−	0.0189869i
$213$		−	14.0508i		−	0.962744i
$214$	12.2677			0.838606
$215$	−7.40105	−	6.54420i	−0.504747	−	0.446311i
$216$	2.67513			0.182020
$217$		−	1.14903i		−	0.0780013i
$218$			14.8119i			1.00319i
$219$	10.7308			0.725123
$220$	0.287258	−	0.324869i	0.0193669	−	0.0219027i
$221$	3.03761			0.204332
$222$			2.38787i			0.160264i
$223$			17.6121i			1.17940i	0.807624	+	0.589698i	$0.200753\pi$
$223$			17.6121i			1.17940i	−0.807624	+	0.589698i	$0.799247\pi$
$224$	−1.30536			−0.0872178
$225$	0.612127	+	4.96239i	0.0408085	+	0.330826i
$226$	−3.35026			−0.222856
$227$			17.4314i			1.15696i	0.815696	+	0.578480i	$0.196354\pi$
$227$			17.4314i			1.15696i	−0.815696	+	0.578480i	$0.803646\pi$
$228$		−	1.03761i		−	0.0687175i
$229$	−13.0738			−0.863942			−0.431971	−	0.901888i	$-0.642182\pi$
$229$	−13.0738			−0.863942			−0.431971	+	0.901888i	$0.642182\pi$
$230$	8.77575	−	9.92478i	0.578656	−	0.654420i
$231$	1.19394			0.0785553
$232$			11.5369i			0.757435i
$233$		−	13.8437i		−	0.906929i	−0.891274	−	0.453465i	$-0.850188\pi$
$233$		−	13.8437i		−	0.906929i	0.891274	−	0.453465i	$-0.149812\pi$
$234$	1.19394			0.0780501
$235$	20.6253	+	18.2374i	1.34545	+	1.18968i
$236$	2.57452			0.167587
$237$		−	13.9756i		−	0.907810i
$238$		−	6.66433i		−	0.431984i
$239$	12.3733			0.800361			0.400181	−	0.916436i	$-0.368947\pi$
$239$	12.3733			0.800361			0.400181	+	0.916436i	$0.368947\pi$
$240$	7.28726	+	6.44358i	0.470390	+	0.415931i
$241$	−24.5501			−1.58141			−0.790705	−	0.612198i	$-0.790286\pi$
$241$	−24.5501			−1.58141			−0.790705	+	0.612198i	$0.790286\pi$
$242$			1.48119i			0.0952148i
$243$			1.00000i			0.0641500i
$244$	0.0145884			0.000933930
$245$	−8.25694	+	9.33804i	−0.527517	+	0.596586i
$246$	−13.4617			−0.858285
$247$			4.31265i			0.274407i
$248$			2.57452i			0.163482i
$249$	9.89446			0.627036
$250$	−9.36836	+	13.6556i	−0.592507	+	0.863657i
$251$	13.9003			0.877382			0.438691	−	0.898638i	$-0.355442\pi$
$251$	13.9003			0.877382			0.438691	+	0.898638i	$0.355442\pi$
$252$		−	0.231548i		−	0.0145862i
$253$			4.00000i			0.251478i
$254$	−20.4690			−1.28434
$255$	−5.58181	+	6.31265i	−0.349546	+	0.395313i
$256$	4.61213			0.288258
$257$			18.8872i			1.17815i	0.808079	+	0.589075i	$0.200508\pi$
$257$			18.8872i			1.17815i	−0.808079	+	0.589075i	$0.799492\pi$
$258$		−	6.54420i		−	0.407424i
$259$	−1.92478			−0.119600
$260$	0.261865	+	0.231548i	0.0162402	+	0.0143600i
$261$	−4.31265			−0.266946
$262$		−	8.77575i		−	0.542167i
$263$			20.8061i			1.28296i	0.767141	+	0.641478i	$0.221679\pi$
$263$			20.8061i			1.28296i	−0.767141	+	0.641478i	$0.778321\pi$
$264$	−2.67513			−0.164643
$265$	−2.38787	−	2.11142i	−0.146686	−	0.129703i
$266$	9.46168			0.580133
$267$		−	16.8872i		−	1.03348i
$268$		−	0.523730i		−	0.0319919i
$269$	32.3996			1.97544			0.987720	−	0.156233i	$-0.0499351\pi$
$269$	32.3996			1.97544			0.987720	+	0.156233i	$0.0499351\pi$
$270$	−2.19394	+	2.48119i	−0.133519	+	0.151001i
$271$	−16.8265			−1.02214			−0.511069	−	0.859539i	$-0.670751\pi$
$271$	−16.8265			−1.02214			−0.511069	+	0.859539i	$0.670751\pi$
$272$			16.3938i			0.994017i
$273$			0.962389i			0.0582464i
$274$	4.96239			0.299789
$275$	−0.612127	−	4.96239i	−0.0369126	−	0.299243i
$276$	0.775746			0.0466944
$277$		−	16.9076i		−	1.01588i	−0.861392	−	0.507941i	$-0.830407\pi$
$277$		−	16.9076i		−	1.01588i	0.861392	−	0.507941i	$-0.169593\pi$
$278$			31.4010i			1.88331i
$279$	−0.962389			−0.0576167
$280$	−4.73084	+	5.35026i	−0.282722	+	0.319739i
$281$	5.61213			0.334791			0.167396	−	0.985890i	$-0.446464\pi$
$281$	5.61213			0.334791			0.167396	+	0.985890i	$0.446464\pi$
$282$			18.2374i			1.08602i
$283$			5.81924i			0.345918i	0.984929	+	0.172959i	$0.0553328\pi$
$283$			5.81924i			0.345918i	−0.984929	+	0.172959i	$0.944667\pi$
$284$	2.72496			0.161697
$285$	−8.96239	−	7.92478i	−0.530886	−	0.469423i
$286$	−1.19394			−0.0705989
$287$		−	10.8510i		−	0.640512i
$288$			1.09332i			0.0644246i
$289$	2.79877			0.164633
$290$	−10.7005	−	9.46168i	−0.628356	−	0.555609i
$291$	11.4763			0.672751
$292$			2.08110i			0.121787i
$293$		−	8.29218i		−	0.484434i	−0.970222	−	0.242217i	$-0.922125\pi$
$293$		−	8.29218i		−	0.484434i	0.970222	−	0.242217i	$-0.0778747\pi$
$294$	−8.25694			−0.481555
$295$	19.6629	−	22.2374i	1.14482	−	1.29471i
$296$	4.31265			0.250668
$297$		−	1.00000i		−	0.0580259i
$298$		−	9.46168i		−	0.548100i
$299$	−3.22425			−0.186463
$300$	−0.962389	+	0.118714i	−0.0555635	+	0.00685394i
$301$	5.27504			0.304048
$302$		−	3.92478i		−	0.225846i
$303$			10.7612i			0.618212i
$304$	−23.2750			−1.33492
$305$	0.111420	−	0.126008i	0.00637987	−	0.00721520i
$306$	−5.58181			−0.319091
$307$		−	25.6688i		−	1.46500i	−0.680770	−	0.732498i	$-0.738354\pi$
$307$		−	25.6688i		−	1.46500i	0.680770	−	0.732498i	$-0.261646\pi$
$308$			0.231548i			0.0131937i
$309$	−16.9380			−0.963566
$310$	−2.38787	−	2.11142i	−0.135622	−	0.119921i
$311$	−15.7235			−0.891601			−0.445800	−	0.895132i	$-0.647081\pi$
$311$	−15.7235			−0.891601			−0.445800	+	0.895132i	$0.647081\pi$
$312$		−	2.15633i		−	0.122078i
$313$		−	26.8627i		−	1.51837i	−0.650874	−	0.759186i	$-0.725597\pi$
$313$		−	26.8627i		−	1.51837i	0.650874	−	0.759186i	$-0.274403\pi$
$314$	2.38787			0.134755
$315$	−2.00000	−	1.76845i	−0.112687	−	0.0996410i
$316$	2.71037			0.152470
$317$		−	0.710373i		−	0.0398985i	−0.999801	−	0.0199492i	$-0.993650\pi$
$317$		−	0.710373i		−	0.0398985i	0.999801	−	0.0199492i	$-0.00635046\pi$
$318$		−	2.11142i		−	0.118403i
$319$	4.31265			0.241462
$320$	10.4885	−	11.8618i	0.586324	−	0.663093i
$321$	8.28233			0.462275
$322$			7.07381i			0.394208i
$323$		−	20.1622i		−	1.12186i
$324$	−0.193937			−0.0107743
$325$	4.00000	−	0.493413i	0.221880	−	0.0273696i
$326$	0.463096			0.0256485
$327$			10.0000i			0.553001i
$328$			24.3127i			1.34244i
$329$	−14.7005			−0.810466
$330$	2.19394	−	2.48119i	0.120772	−	0.136585i
$331$	0.962389			0.0528977			0.0264488	−	0.999650i	$-0.491580\pi$
$331$	0.962389			0.0528977			0.0264488	+	0.999650i	$0.491580\pi$
$332$			1.91890i			0.105313i
$333$			1.61213i			0.0883440i
$334$	0.730841			0.0399898
$335$	−4.52373	−	4.00000i	−0.247158	−	0.218543i
$336$	−5.19394			−0.283352
$337$		−	19.8192i		−	1.07962i	−0.841786	−	0.539811i	$-0.818496\pi$
$337$		−	19.8192i		−	1.07962i	0.841786	−	0.539811i	$-0.181504\pi$
$338$			18.2931i			0.995015i
$339$	−2.26187			−0.122848
$340$	−1.22425	−	1.08252i	−0.0663945	−	0.0587077i
$341$	0.962389			0.0521163
$342$		−	7.92478i		−	0.428523i
$343$		−	15.0132i		−	0.810635i
$344$	−11.8192			−0.637251
$345$	5.92478	−	6.70052i	0.318979	−	0.360744i
$346$	34.5198			1.85579
$347$		−	6.20711i		−	0.333215i	−0.986023	−	0.166608i	$-0.946719\pi$
$347$		−	6.20711i		−	0.333215i	0.986023	−	0.166608i	$-0.0532813\pi$
$348$		−	0.836381i		−	0.0448347i
$349$	−4.44851			−0.238123			−0.119062	−	0.992887i	$-0.537989\pi$
$349$	−4.44851			−0.238123			−0.119062	+	0.992887i	$0.537989\pi$
$350$	−1.08252	−	8.77575i	−0.0578630	−	0.469083i
$351$	0.806063			0.0430245
$352$		−	1.09332i		−	0.0582742i
$353$			6.57452i			0.349926i	0.984575	+	0.174963i	$0.0559806\pi$
$353$			6.57452i			0.349926i	−0.984575	+	0.174963i	$0.944019\pi$
$354$	19.6629			1.04507
$355$	20.8119	−	23.5369i	1.10458	−	1.24921i
$356$	3.27504			0.173577
$357$		−	4.49929i		−	0.238128i
$358$			15.8496i			0.837675i
$359$	−8.62530			−0.455226			−0.227613	−	0.973752i	$-0.573092\pi$
$359$	−8.62530			−0.455226			−0.227613	+	0.973752i	$0.573092\pi$
$360$	4.48119	+	3.96239i	0.236180	+	0.208836i
$361$	9.62530			0.506595
$362$		−	11.5515i		−	0.607133i
$363$			1.00000i			0.0524864i
$364$	−0.186642			−0.00978272
$365$	17.9756	+	15.8945i	0.940884	+	0.831954i
$366$	0.111420			0.00582399
$367$		−	23.0132i		−	1.20128i	−0.799520	−	0.600639i	$-0.794913\pi$
$367$		−	23.0132i		−	1.20128i	0.799520	−	0.600639i	$-0.205087\pi$
$368$		−	17.4010i		−	0.907092i
$369$	−9.08840			−0.473123
$370$	−3.53690	+	4.00000i	−0.183875	+	0.207950i
$371$	1.70194			0.0883602
$372$		−	0.186642i		−	0.00967695i
$373$			28.1925i			1.45975i	0.683579	+	0.729877i	$0.260423\pi$
$373$			28.1925i			1.45975i	−0.683579	+	0.729877i	$0.739577\pi$
$374$	5.58181			0.288629
$375$	−6.32487	+	9.21933i	−0.326615	+	0.476084i
$376$	32.9380			1.69865
$377$			3.47627i			0.179037i
$378$		−	1.76845i		−	0.0909594i
$379$	−3.74798			−0.192521			−0.0962605	−	0.995356i	$-0.530688\pi$
$379$	−3.74798			−0.192521			−0.0962605	+	0.995356i	$0.530688\pi$
$380$	1.53690	−	1.73813i	0.0788415	−	0.0891644i
$381$	−13.8192			−0.707981
$382$			1.92478i			0.0984802i
$383$			1.76257i			0.0900632i	0.998986	+	0.0450316i	$0.0143389\pi$
$383$			1.76257i			0.0900632i	−0.998986	+	0.0450316i	$0.985661\pi$
$384$	12.6751			0.646825
$385$	2.00000	+	1.76845i	0.101929	+	0.0901287i
$386$	−12.7308			−0.647983
$387$		−	4.41819i		−	0.224589i
$388$			2.22567i			0.112991i
$389$	−6.52373			−0.330766			−0.165383	−	0.986229i	$-0.552886\pi$
$389$	−6.52373			−0.330766			−0.165383	+	0.986229i	$0.552886\pi$
$390$	2.00000	+	1.76845i	0.101274	+	0.0895491i
$391$	15.0738			0.762315
$392$			14.9126i			0.753198i
$393$		−	5.92478i		−	0.298865i
$394$	−30.6702			−1.54514
$395$	20.7005	−	23.4109i	1.04156	−	1.17793i
$396$	0.193937			0.00974568
$397$			23.6991i			1.18942i	0.803939	+	0.594712i	$0.202734\pi$
$397$			23.6991i			1.18942i	−0.803939	+	0.594712i	$0.797266\pi$
$398$		−	8.22284i		−	0.412174i
$399$	6.38787			0.319794
$400$	2.66291	+	21.5877i	0.133146	+	1.07938i
$401$	8.88717			0.443804			0.221902	−	0.975069i	$-0.428774\pi$
$401$	8.88717			0.443804			0.221902	+	0.975069i	$0.428774\pi$
$402$		−	4.00000i		−	0.199502i
$403$			0.775746i			0.0386427i
$404$	−2.08698			−0.103831
$405$	−1.48119	+	1.67513i	−0.0736011	+	0.0832379i
$406$	7.62672			0.378508
$407$		−	1.61213i		−	0.0799102i
$408$			10.0811i			0.499089i
$409$	4.85097			0.239865			0.119932	−	0.992782i	$-0.461732\pi$
$409$	4.85097			0.239865			0.119932	+	0.992782i	$0.461732\pi$
$410$	−22.5501	−	19.9394i	−1.11367	−	0.984735i
$411$	3.35026			0.165256
$412$		−	3.28489i		−	0.161835i
$413$			15.8496i			0.779906i
$414$	5.92478			0.291187
$415$	16.5745	+	14.6556i	0.813611	+	0.719416i
$416$	0.881286			0.0432086
$417$			21.1998i			1.03816i
$418$			7.92478i			0.387614i
$419$	10.7005			0.522755			0.261377	−	0.965237i	$-0.415823\pi$
$419$	10.7005			0.522755			0.261377	+	0.965237i	$0.415823\pi$
$420$	0.342968	−	0.387873i	0.0167351	−	0.0189263i
$421$	−30.6009			−1.49139			−0.745697	−	0.666285i	$-0.767884\pi$
$421$	−30.6009			−1.49139			−0.745697	+	0.666285i	$0.767884\pi$
$422$		−	27.4010i		−	1.33386i
$423$			12.3127i			0.598662i
$424$	−3.81336			−0.185193
$425$	−18.7005	+	2.30677i	−0.907109	+	0.111895i
$426$	20.8119			1.00834
$427$			0.0898112i			0.00434627i
$428$			1.60625i			0.0776409i
$429$	−0.806063			−0.0389171
$430$	9.69323	−	10.9624i	0.467449	−	0.528653i
$431$	−5.92478			−0.285386			−0.142693	−	0.989767i	$-0.545576\pi$
$431$	−5.92478			−0.285386			−0.142693	+	0.989767i	$0.545576\pi$
$432$			4.35026i			0.209302i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	1.70194			0.0816956
$435$	−7.22425	−	6.38787i	−0.346376	−	0.306275i
$436$	−1.93937			−0.0928788
$437$			21.4010i			1.02375i
$438$			15.8945i			0.759467i
$439$	−5.35026			−0.255354			−0.127677	−	0.991816i	$-0.540752\pi$
$439$	−5.35026			−0.255354			−0.127677	+	0.991816i	$0.540752\pi$
$440$	−4.48119	−	3.96239i	−0.213633	−	0.188899i
$441$	−5.57452			−0.265453
$442$			4.49929i			0.214010i
$443$			19.6873i			0.935374i	0.883894	+	0.467687i	$0.154913\pi$
$443$			19.6873i			0.935374i	−0.883894	+	0.467687i	$0.845087\pi$
$444$	−0.312650			−0.0148377
$445$	25.0132	−	28.2882i	1.18574	−	1.34099i
$446$	−26.0870			−1.23525
$447$		−	6.38787i		−	0.302136i
$448$			8.45439i			0.399432i
$449$	31.3357			1.47882			0.739411	−	0.673254i	$-0.235104\pi$
$449$	31.3357			1.47882			0.739411	+	0.673254i	$0.235104\pi$
$450$	−7.35026	+	0.906679i	−0.346495	+	0.0427412i
$451$	9.08840			0.427956
$452$		−	0.438658i		−	0.0206328i
$453$		−	2.64974i		−	0.124496i
$454$	−25.8192			−1.21176
$455$	−1.42548	+	1.61213i	−0.0668277	+	0.0755777i
$456$	−14.3127			−0.670251
$457$			37.5936i			1.75855i	0.476312	+	0.879276i	$0.341973\pi$
$457$			37.5936i			1.75855i	−0.476312	+	0.879276i	$0.658027\pi$
$458$		−	19.3649i		−	0.904860i
$459$	−3.76845			−0.175896
$460$	1.29948	+	1.14903i	0.0605884	+	0.0535738i
$461$	17.9854			0.837664			0.418832	−	0.908064i	$-0.362440\pi$
$461$	17.9854			0.837664			0.418832	+	0.908064i	$0.362440\pi$
$462$			1.76845i			0.0822758i
$463$			39.0132i			1.81310i	0.422103	+	0.906548i	$0.361292\pi$
$463$			39.0132i			1.81310i	−0.422103	+	0.906548i	$0.638708\pi$
$464$	−18.7612			−0.870965
$465$	−1.61213	−	1.42548i	−0.0747606	−	0.0661053i
$466$	20.5052			0.949884
$467$		−	14.5501i		−	0.673297i	−0.941630	−	0.336649i	$-0.890707\pi$
$467$		−	14.5501i		−	0.673297i	0.941630	−	0.336649i	$-0.109293\pi$
$468$			0.156325i			0.00722613i
$469$	3.22425			0.148882
$470$	−27.0132	+	30.5501i	−1.24602	+	1.40917i
$471$	1.61213			0.0742829
$472$		−	35.5125i		−	1.63459i
$473$			4.41819i			0.203149i
$474$	20.7005			0.950807
$475$	−3.27504	−	26.5501i	−0.150269	−	1.21820i
$476$	0.872577			0.0399945
$477$		−	1.42548i		−	0.0652685i
$478$			18.3272i			0.838268i
$479$	−28.6253			−1.30792			−0.653962	−	0.756528i	$-0.726894\pi$
$479$	−28.6253			−1.30792			−0.653962	+	0.756528i	$0.726894\pi$
$480$	−1.61942	+	1.83146i	−0.0739161	+	0.0835941i
$481$	1.29948			0.0592510
$482$		−	36.3634i		−	1.65631i
$483$			4.77575i			0.217304i
$484$	−0.193937			−0.00881530
$485$	19.2243	+	16.9986i	0.872928	+	0.771866i
$486$	−1.48119			−0.0671883
$487$		−	1.44992i		−	0.0657022i	−0.999460	−	0.0328511i	$-0.989541\pi$
$487$		−	1.44992i		−	0.0657022i	0.999460	−	0.0328511i	$-0.0104587\pi$
$488$		−	0.201231i		−	0.00910929i
$489$	0.312650			0.0141385
$490$	−13.8315	−	12.2301i	−0.624841	−	0.552501i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$		−	1.76257i		−	0.0794629i
$493$		−	16.2520i		−	0.731954i
$494$	−6.38787			−0.287404
$495$	1.48119	−	1.67513i	0.0665747	−	0.0752915i
$496$	−4.18664			−0.187986
$497$			16.7757i			0.752495i
$498$			14.6556i			0.656734i
$499$	−30.7005			−1.37434			−0.687172	−	0.726495i	$-0.741148\pi$
$499$	−30.7005			−1.37434			−0.687172	+	0.726495i	$0.741148\pi$
$500$	−1.78797	−	1.22662i	−0.0799602	−	0.0548563i
$501$	0.493413			0.0220441
$502$			20.5891i			0.918937i
$503$		−	19.7586i		−	0.880993i	−0.897754	−	0.440496i	$-0.854802\pi$
$503$		−	19.7586i		−	0.880993i	0.897754	−	0.440496i	$-0.145198\pi$
$504$	−3.19394			−0.142269
$505$	−15.9394	+	18.0263i	−0.709292	+	0.802162i
$506$	−5.92478			−0.263388
$507$			12.3503i			0.548494i
$508$		−	2.68006i		−	0.118908i
$509$	−22.1016			−0.979635			−0.489817	−	0.871825i	$-0.662937\pi$
$509$	−22.1016			−0.979635			−0.489817	+	0.871825i	$0.662937\pi$
$510$	−9.35026	−	8.26774i	−0.414037	−	0.366102i
$511$	−12.8119			−0.566767
$512$		−	18.5188i		−	0.818423i
$513$		−	5.35026i		−	0.236220i
$514$	−27.9756			−1.23395
$515$	−28.3733	−	25.0884i	−1.25028	−	1.10553i
$516$	0.856849			0.0377207
$517$		−	12.3127i		−	0.541510i
$518$		−	2.85097i		−	0.125264i
$519$	23.3054			1.02299
$520$	3.19394	−	3.61213i	0.140063	−	0.158402i
$521$	−22.8119			−0.999409			−0.499705	−	0.866196i	$-0.666558\pi$
$521$	−22.8119			−0.999409			−0.499705	+	0.866196i	$0.666558\pi$
$522$		−	6.38787i		−	0.279590i
$523$		−	12.2677i		−	0.536431i	−0.963359	−	0.268216i	$-0.913566\pi$
$523$		−	12.2677i		−	0.536431i	0.963359	−	0.268216i	$-0.0864339\pi$
$524$	1.14903			0.0501957
$525$	−0.730841	−	5.92478i	−0.0318965	−	0.258578i
$526$	−30.8178			−1.34372
$527$		−	3.62672i		−	0.157982i
$528$		−	4.35026i		−	0.189321i
$529$	7.00000			0.304348
$530$	3.12742	−	3.53690i	0.135847	−	0.153633i
$531$	13.2750			0.576088
$532$			1.23884i			0.0537106i
$533$			7.32582i			0.317317i
$534$	25.0132			1.08243
$535$	13.8740	+	12.2677i	0.599825	+	0.530381i
$536$	−7.22425			−0.312040
$537$			10.7005i			0.461762i
$538$			47.9902i			2.06900i
$539$	5.57452			0.240111
$540$	−0.324869	−	0.287258i	−0.0139801	−	0.0123616i
$541$	−5.22425			−0.224608			−0.112304	−	0.993674i	$-0.535823\pi$
$541$	−5.22425			−0.224608			−0.112304	+	0.993674i	$0.535823\pi$
$542$		−	24.9234i		−	1.07055i
$543$		−	7.79877i		−	0.334677i
$544$	−4.12013			−0.176649
$545$	−14.8119	+	16.7513i	−0.634474	+	0.717547i
$546$	−1.42548			−0.0610051
$547$			17.9697i			0.768328i	0.923265	+	0.384164i	$0.125510\pi$
$547$			17.9697i			0.768328i	−0.923265	+	0.384164i	$0.874490\pi$
$548$			0.649738i			0.0277554i
$549$	0.0752228			0.00321043
$550$	7.35026	−	0.906679i	0.313416	−	0.0386609i
$551$	23.0738			0.982977
$552$		−	10.7005i		−	0.455445i
$553$			16.6859i			0.709558i
$554$	25.0435			1.06400
$555$	−2.38787	+	2.70052i	−0.101360	+	0.114631i
$556$	−4.11142			−0.174363
$557$		−	15.8700i		−	0.672434i	−0.941784	−	0.336217i	$-0.890852\pi$
$557$		−	15.8700i		−	0.672434i	0.941784	−	0.336217i	$-0.109148\pi$
$558$		−	1.42548i		−	0.0603456i
$559$	−3.56134			−0.150629
$560$	−8.70052	−	7.69323i	−0.367664	−	0.325098i
$561$	3.76845			0.159104
$562$			8.31265i			0.350648i
$563$			31.6688i			1.33468i	0.744753	+	0.667340i	$0.232567\pi$
$563$			31.6688i			1.33468i	−0.744753	+	0.667340i	$0.767433\pi$
$564$	−2.38787			−0.100548
$565$	−3.78892	−	3.35026i	−0.159401	−	0.140947i
$566$	−8.61942			−0.362301
$567$		−	1.19394i		−	0.0501406i
$568$		−	37.5877i		−	1.57714i
$569$	24.3127			1.01924			0.509620	−	0.860400i	$-0.329786\pi$
$569$	24.3127			1.01924			0.509620	+	0.860400i	$0.329786\pi$
$570$	11.7381	−	13.2750i	0.491656	−	0.556030i
$571$	8.05079			0.336915			0.168457	−	0.985709i	$-0.446121\pi$
$571$	8.05079			0.336915			0.168457	+	0.985709i	$0.446121\pi$
$572$		−	0.156325i		−	0.00653628i
$573$			1.29948i			0.0542864i
$574$	16.0724			0.670849
$575$	19.8496	−	2.44851i	0.827784	−	0.102110i
$576$	7.08110			0.295046
$577$			44.5355i			1.85404i	0.375016	+	0.927018i	$0.377637\pi$
$577$			44.5355i			1.85404i	−0.375016	+	0.927018i	$0.622363\pi$
$578$			4.14552i			0.172431i
$579$	−8.59498			−0.357195
$580$	1.23884	−	1.40105i	0.0514401	−	0.0581753i
$581$	−11.8134			−0.490101
$582$			16.9986i			0.704614i
$583$			1.42548i			0.0590375i
$584$	28.7064			1.18788
$585$	1.35026	+	1.19394i	0.0558265	+	0.0493632i
$586$	12.2823			0.507379
$587$			15.4763i			0.638774i	0.947624	+	0.319387i	$0.103477\pi$
$587$			15.4763i			0.638774i	−0.947624	+	0.319387i	$0.896523\pi$
$588$		−	1.08110i		−	0.0445839i
$589$	5.14903			0.212162
$590$	32.9380	+	29.1246i	1.35603	+	1.19904i
$591$	−20.7064			−0.851748
$592$			7.01317i			0.288240i
$593$		−	9.53102i		−	0.391392i	−0.980665	−	0.195696i	$-0.937303\pi$
$593$		−	9.53102i		−	0.391392i	0.980665	−	0.195696i	$-0.0626966\pi$
$594$	1.48119			0.0607741
$595$	6.66433	−	7.53690i	0.273211	−	0.308983i
$596$	1.23884			0.0507450
$597$		−	5.55149i		−	0.227207i
$598$		−	4.77575i		−	0.195295i
$599$	25.5515			1.04401			0.522003	−	0.852944i	$-0.325185\pi$
$599$	25.5515			1.04401			0.522003	+	0.852944i	$0.325185\pi$
$600$	1.63752	+	13.2750i	0.0668515	+	0.541951i
$601$	12.0263			0.490565			0.245282	−	0.969452i	$-0.421119\pi$
$601$	12.0263			0.490565			0.245282	+	0.969452i	$0.421119\pi$
$602$			7.81336i			0.318449i
$603$		−	2.70052i		−	0.109974i
$604$	0.513881			0.0209095
$605$	−1.48119	+	1.67513i	−0.0602191	+	0.0681038i
$606$	−15.9394			−0.647492
$607$			6.86670i			0.278711i	0.990242	+	0.139355i	$0.0445030\pi$
$607$			6.86670i			0.278711i	−0.990242	+	0.139355i	$0.955497\pi$
$608$		−	5.84955i		−	0.237231i
$609$	5.14903			0.208649
$610$	0.186642	+	0.165034i	0.00755693	+	0.00668203i
$611$	9.92478			0.401514
$612$		−	0.730841i		−	0.0295425i
$613$		−	7.25457i		−	0.293009i	−0.989210	−	0.146505i	$-0.953198\pi$
$613$		−	7.25457i		−	0.293009i	0.989210	−	0.146505i	$-0.0468023\pi$
$614$	38.0205			1.53438
$615$	−15.2243	−	13.4617i	−0.613901	−	0.542827i
$616$	3.19394			0.128687
$617$		−	38.3634i		−	1.54445i	−0.635347	−	0.772227i	$-0.719143\pi$
$617$		−	38.3634i		−	1.54445i	0.635347	−	0.772227i	$-0.280857\pi$
$618$		−	25.0884i		−	1.00920i
$619$	29.6893			1.19331			0.596656	−	0.802497i	$-0.296496\pi$
$619$	29.6893			1.19331			0.596656	+	0.802497i	$0.296496\pi$
$620$	0.276454	−	0.312650i	0.0111026	−	0.0125563i
$621$	4.00000			0.160514
$622$		−	23.2896i		−	0.933829i
$623$			20.1622i			0.807782i
$624$	3.50659			0.140376
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	39.7889			1.59029
$627$			5.35026i			0.213669i
$628$			0.312650i			0.0124761i
$629$	−6.07522			−0.242235
$630$	2.61942	−	2.96239i	0.104360	−	0.118024i
$631$	−19.6991			−0.784209			−0.392105	−	0.919921i	$-0.628253\pi$
$631$	−19.6991			−0.784209			−0.392105	+	0.919921i	$0.628253\pi$
$632$		−	37.3865i		−	1.48715i
$633$		−	18.4993i		−	0.735281i
$634$	1.05220			0.0417882
$635$	−23.1490	−	20.4690i	−0.918641	−	0.812287i
$636$	0.276454			0.0109621
$637$			4.49341i			0.178036i
$638$			6.38787i			0.252898i
$639$	14.0508			0.555840
$640$	21.2325	+	18.7743i	0.839288	+	0.742121i
$641$	−31.4372			−1.24170			−0.620848	−	0.783931i	$-0.713212\pi$
$641$	−31.4372			−1.24170			−0.620848	+	0.783931i	$0.713212\pi$
$642$			12.2677i			0.484169i
$643$		−	34.4894i		−	1.36013i	−0.733151	−	0.680065i	$-0.761951\pi$
$643$		−	34.4894i		−	1.36013i	0.733151	−	0.680065i	$-0.238049\pi$
$644$	−0.926192			−0.0364971
$645$	6.54420	−	7.40105i	0.257678	−	0.291416i
$646$	29.8641			1.17499
$647$			5.61213i			0.220635i	0.993896	+	0.110318i	$0.0351868\pi$
$647$			5.61213i			0.220635i	−0.993896	+	0.110318i	$0.964813\pi$
$648$			2.67513i			0.105089i
$649$	−13.2750			−0.521091
$650$	0.730841	+	5.92478i	0.0286659	+	0.232389i
$651$	1.14903			0.0450341
$652$			0.0606343i			0.00237462i
$653$			4.06537i			0.159090i	0.996831	+	0.0795452i	$0.0253468\pi$
$653$			4.06537i			0.159090i	−0.996831	+	0.0795452i	$0.974653\pi$
$654$	−14.8119			−0.579193
$655$	8.77575	−	9.92478i	0.342897	−	0.387793i
$656$	−39.5369			−1.54366
$657$			10.7308i			0.418650i
$658$		−	21.7743i		−	0.848852i
$659$	−11.3747			−0.443095			−0.221548	−	0.975150i	$-0.571111\pi$
$659$	−11.3747			−0.443095			−0.221548	+	0.975150i	$0.571111\pi$
$660$	0.324869	+	0.287258i	0.0126455	+	0.0111815i
$661$	−42.4749			−1.65208			−0.826040	−	0.563611i	$-0.809412\pi$
$661$	−42.4749			−1.65208			−0.826040	+	0.563611i	$0.809412\pi$
$662$			1.42548i			0.0554030i
$663$			3.03761i			0.117971i
$664$	26.4690			1.02720
$665$	10.7005	+	9.46168i	0.414949	+	0.366908i
$666$	−2.38787			−0.0925282
$667$			17.2506i			0.667946i
$668$			0.0956908i			0.00370239i
$669$	−17.6121			−0.680924
$670$	5.92478	−	6.70052i	0.228894	−	0.258864i
$671$	−0.0752228			−0.00290394
$672$		−	1.30536i		−	0.0503552i
$673$		−	14.8813i		−	0.573631i	−0.957986	−	0.286816i	$-0.907403\pi$
$673$		−	14.8813i		−	0.573631i	0.957986	−	0.286816i	$-0.0925967\pi$
$674$	29.3561			1.13076
$675$	−4.96239	+	0.612127i	−0.191002	+	0.0235608i
$676$	−2.39517			−0.0921218
$677$			27.7685i			1.06723i	0.845728	+	0.533614i	$0.179167\pi$
$677$			27.7685i			1.06723i	−0.845728	+	0.533614i	$0.820833\pi$
$678$		−	3.35026i		−	0.128666i
$679$	−13.7019			−0.525832
$680$	−14.9321	+	16.8872i	−0.572619	+	0.647593i
$681$	−17.4314			−0.667971
$682$			1.42548i			0.0545846i
$683$		−	25.4617i		−	0.974264i	−0.873328	−	0.487132i	$-0.838043\pi$
$683$		−	25.4617i		−	0.974264i	0.873328	−	0.487132i	$-0.161957\pi$
$684$	1.03761			0.0396741
$685$	5.61213	+	4.96239i	0.214428	+	0.189603i
$686$	22.2374			0.849029
$687$		−	13.0738i		−	0.498797i
$688$		−	19.2203i		−	0.732766i
$689$	−1.14903			−0.0437746
$690$	9.92478	+	8.77575i	0.377830	+	0.334087i
$691$	43.6991			1.66239			0.831196	−	0.555979i	$-0.187657\pi$
$691$	43.6991			1.66239			0.831196	+	0.555979i	$0.187657\pi$
$692$			4.51976i			0.171816i
$693$			1.19394i			0.0453539i
$694$	9.19394			0.348997
$695$	−31.4010	+	35.5125i	−1.19111	+	1.34706i
$696$	−11.5369			−0.437305
$697$		−	34.2492i		−	1.29728i
$698$		−	6.58910i		−	0.249401i
$699$	13.8437			0.523616
$700$	1.14903	−	0.141737i	0.0434293	−	0.00535714i
$701$	7.01317			0.264884			0.132442	−	0.991191i	$-0.457718\pi$
$701$	7.01317			0.264884			0.132442	+	0.991191i	$0.457718\pi$
$702$			1.19394i			0.0450622i
$703$		−	8.62530i		−	0.325309i
$704$	−7.08110			−0.266879
$705$	−18.2374	+	20.6253i	−0.686861	+	0.776794i
$706$	−9.73813			−0.366500
$707$		−	12.8481i		−	0.483204i
$708$			2.57452i			0.0967562i
$709$	−45.6747			−1.71535			−0.857674	−	0.514194i	$-0.828091\pi$
$709$	−45.6747			−1.71535			−0.857674	+	0.514194i	$0.828091\pi$
$710$	34.8627	+	30.8265i	1.30837	+	1.15690i
$711$	13.9756			0.524125
$712$		−	45.1754i		−	1.69302i
$713$			3.84955i			0.144167i
$714$	6.66433			0.249406
$715$	−1.35026	−	1.19394i	−0.0504969	−	0.0446507i
$716$	−2.07522			−0.0775547
$717$			12.3733i			0.462089i
$718$		−	12.7757i		−	0.476787i
$719$	−16.2520			−0.606098			−0.303049	−	0.952975i	$-0.598005\pi$
$719$	−16.2520			−0.606098			−0.303049	+	0.952975i	$0.598005\pi$
$720$	−6.44358	+	7.28726i	−0.240138	+	0.271580i
$721$	20.2228			0.753138
$722$			14.2569i			0.530588i
$723$		−	24.5501i		−	0.913027i
$724$	1.51247			0.0562104
$725$	−2.63989	−	21.4010i	−0.0980430	−	0.794815i
$726$	−1.48119			−0.0549723
$727$		−	15.2243i		−	0.564636i	−0.959321	−	0.282318i	$-0.908897\pi$
$727$		−	15.2243i		−	0.564636i	0.959321	−	0.282318i	$-0.0911034\pi$
$728$			2.57452i			0.0954179i
$729$	−1.00000			−0.0370370
$730$	−23.5428	+	26.6253i	−0.871358	+	0.985447i
$731$	16.6497			0.615813
$732$			0.0145884i			0.000539205i
$733$		−	43.5066i		−	1.60695i	−0.595337	−	0.803476i	$-0.702981\pi$
$733$		−	43.5066i		−	1.60695i	0.595337	−	0.803476i	$-0.297019\pi$
$734$	34.0870			1.25817
$735$	−9.33804	−	8.25694i	−0.344439	−	0.304562i
$736$	4.37328			0.161201
$737$			2.70052i			0.0994751i
$738$		−	13.4617i		−	0.495531i
$739$	7.02302			0.258346			0.129173	−	0.991622i	$-0.458768\pi$
$739$	7.02302			0.258346			0.129173	+	0.991622i	$0.458768\pi$
$740$	−0.523730	−	0.463096i	−0.0192527	−	0.0170237i
$741$	−4.31265			−0.158429
$742$			2.52090i			0.0925452i
$743$		−	2.94192i		−	0.107929i	−0.998543	−	0.0539643i	$-0.982814\pi$
$743$		−	2.94192i		−	0.107929i	0.998543	−	0.0539643i	$-0.0171857\pi$
$744$	−2.57452			−0.0943863
$745$	9.46168	−	10.7005i	0.346649	−	0.392037i
$746$	−41.7586			−1.52889
$747$			9.89446i			0.362019i
$748$			0.730841i			0.0267222i
$749$	−9.88858			−0.361321
$750$	−13.6556	−	9.36836i	−0.498633	−	0.342084i
$751$	24.1016			0.879479			0.439739	−	0.898125i	$-0.355071\pi$
$751$	24.1016			0.879479			0.439739	+	0.898125i	$0.355071\pi$
$752$			53.5633i			1.95325i
$753$			13.9003i			0.506557i
$754$	−5.14903			−0.187517
$755$	3.92478	−	4.43866i	0.142837	−	0.161539i
$756$	0.231548			0.00842132
$757$			16.3127i			0.592893i	0.955049	+	0.296447i	$0.0958017\pi$
$757$			16.3127i			0.592893i	−0.955049	+	0.296447i	$0.904198\pi$
$758$		−	5.55149i		−	0.201639i
$759$	−4.00000			−0.145191
$760$	−23.9756	−	21.1998i	−0.869685	−	0.768998i
$761$	−5.08840			−0.184454			−0.0922271	−	0.995738i	$-0.529399\pi$
$761$	−5.08840			−0.184454			−0.0922271	+	0.995738i	$0.529399\pi$
$762$		−	20.4690i		−	0.741513i
$763$		−	11.9394i		−	0.432234i
$764$	−0.252016			−0.00911762
$765$	−6.31265	−	5.58181i	−0.228234	−	0.201811i
$766$	−2.61071			−0.0943289
$767$		−	10.7005i		−	0.386374i
$768$			4.61213i			0.166426i
$769$	−2.10157			−0.0757846			−0.0378923	−	0.999282i	$-0.512064\pi$
$769$	−2.10157			−0.0757846			−0.0378923	+	0.999282i	$0.512064\pi$
$770$	−2.61942	+	2.96239i	−0.0943974	+	0.106757i
$771$	−18.8872			−0.680205
$772$		−	1.66688i		−	0.0599924i
$773$			46.0625i			1.65675i	0.560171	+	0.828377i	$0.310736\pi$
$773$			46.0625i			1.65675i	−0.560171	+	0.828377i	$0.689264\pi$
$774$	6.54420			0.235226
$775$	−0.589104	−	4.77575i	−0.0211612	−	0.171550i
$776$	30.7005			1.10208
$777$		−	1.92478i		−	0.0690510i
$778$		−	9.66291i		−	0.346432i
$779$	48.6253			1.74218
$780$	−0.231548	+	0.261865i	−0.00829075	+	0.00937628i
$781$	−14.0508			−0.502777
$782$			22.3272i			0.798420i
$783$		−	4.31265i		−	0.154122i
$784$	−24.2506			−0.866093
$785$	2.70052	+	2.38787i	0.0963858	+	0.0852268i
$786$	8.77575			0.313021
$787$			26.0303i			0.927881i	0.885866	+	0.463940i	$0.153565\pi$
$787$			26.0303i			0.927881i	−0.885866	+	0.463940i	$0.846435\pi$
$788$		−	4.01573i		−	0.143054i
$789$	−20.8061			−0.740715
$790$	34.6761	+	30.6615i	1.23372	+	1.09089i
$791$	2.70052			0.0960196
$792$		−	2.67513i		−	0.0950566i
$793$		−	0.0606343i		−	0.00215319i
$794$	−35.1030			−1.24576
$795$	2.11142	−	2.38787i	0.0748843	−	0.0846891i
$796$	1.07664			0.0381604
$797$			29.9902i			1.06231i	0.847276	+	0.531153i	$0.178241\pi$
$797$			29.9902i			1.06231i	−0.847276	+	0.531153i	$0.821759\pi$
$798$			9.46168i			0.334940i
$799$	−46.3996			−1.64150
$800$	−5.42548	+	0.669251i	−0.191820	+	0.0236616i
$801$	16.8872			0.596679
$802$			13.1636i			0.464824i
$803$		−	10.7308i		−	0.378683i
$804$	0.523730			0.0184705
$805$	−7.07381	+	8.00000i	−0.249319	+	0.281963i
$806$	−1.14903			−0.0404729
$807$			32.3996i			1.14052i
$808$			28.7875i			1.01274i
$809$	−39.7597			−1.39788			−0.698939	−	0.715181i	$-0.746344\pi$
$809$	−39.7597			−1.39788			−0.698939	+	0.715181i	$0.746344\pi$
$810$	−2.48119	−	2.19394i	−0.0871803	−	0.0770871i
$811$	−10.2765			−0.360855			−0.180428	−	0.983588i	$-0.557748\pi$
$811$	−10.2765			−0.360855			−0.180428	+	0.983588i	$0.557748\pi$
$812$			0.998585i			0.0350435i
$813$		−	16.8265i		−	0.590132i
$814$	2.38787			0.0836949
$815$	0.523730	+	0.463096i	0.0183455	+	0.0162215i
$816$	−16.3938			−0.573896
$817$			23.6385i			0.827006i
$818$			7.18523i			0.251226i
$819$	−0.962389			−0.0336286
$820$	2.61071	−	2.95254i	0.0911700	−	0.103107i
$821$	50.0870			1.74805			0.874024	−	0.485883i	$-0.161502\pi$
$821$	50.0870			1.74805			0.874024	+	0.485883i	$0.161502\pi$
$822$			4.96239i			0.173083i
$823$			29.7137i			1.03575i	0.855455	+	0.517877i	$0.173278\pi$
$823$			29.7137i			1.03575i	−0.855455	+	0.517877i	$0.826722\pi$
$824$	−45.3112			−1.57849
$825$	4.96239	−	0.612127i	0.172768	−	0.0213115i
$826$	−23.4763			−0.816844
$827$			2.41819i			0.0840887i	0.999116	+	0.0420444i	$0.0133871\pi$
$827$			2.41819i			0.0840887i	−0.999116	+	0.0420444i	$0.986613\pi$
$828$			0.775746i			0.0269590i
$829$	23.2750			0.808376			0.404188	−	0.914676i	$-0.367554\pi$
$829$	23.2750			0.808376			0.404188	+	0.914676i	$0.367554\pi$
$830$	−21.7078	+	24.5501i	−0.753489	+	0.852146i
$831$	16.9076			0.586519
$832$		−	5.70782i		−	0.197883i
$833$		−	21.0073i		−	0.727860i
$834$	−31.4010			−1.08733
$835$	0.826531	+	0.730841i	0.0286033	+	0.0252918i
$836$	−1.03761			−0.0358865
$837$		−	0.962389i		−	0.0332650i
$838$			15.8496i			0.547514i
$839$	18.8265			0.649964			0.324982	−	0.945720i	$-0.394642\pi$
$839$	18.8265			0.649964			0.324982	+	0.945720i	$0.394642\pi$
$840$	−5.35026	−	4.73084i	−0.184602	−	0.163230i
$841$	−10.4010			−0.358657
$842$		−	45.3258i		−	1.56203i
$843$			5.61213i			0.193292i
$844$	3.58769			0.123493
$845$	−18.2931	+	20.6883i	−0.629303	+	0.711699i
$846$	−18.2374			−0.627016
$847$		−	1.19394i		−	0.0410241i
$848$		−	6.20123i		−	0.212951i
$849$	−5.81924			−0.199716
$850$	−3.41678	−	27.6991i	−0.117194	−	0.950072i
$851$	6.44851			0.221052
$852$			2.72496i			0.0933556i
$853$		−	24.9076i		−	0.852821i	−0.904530	−	0.426411i	$-0.859778\pi$
$853$		−	24.9076i		−	0.852821i	0.904530	−	0.426411i	$-0.140222\pi$
$854$	−0.133028			−0.00455212
$855$	7.92478	−	8.96239i	0.271022	−	0.306507i
$856$	22.1563			0.757288
$857$			7.60625i			0.259824i	0.991525	+	0.129912i	$0.0414696\pi$
$857$			7.60625i			0.259824i	−0.991525	+	0.129912i	$0.958530\pi$
$858$		−	1.19394i		−	0.0407603i
$859$	2.14060			0.0730362			0.0365181	−	0.999333i	$-0.488373\pi$
$859$	2.14060			0.0730362			0.0365181	+	0.999333i	$0.488373\pi$
$860$	1.43533	+	1.26916i	0.0489445	+	0.0432780i
$861$	10.8510			0.369800
$862$		−	8.77575i		−	0.298903i
$863$			29.3112i			0.997766i	0.866669	+	0.498883i	$0.166256\pi$
$863$			29.3112i			0.997766i	−0.866669	+	0.498883i	$0.833744\pi$
$864$	−1.09332			−0.0371955
$865$	39.0395	+	34.5198i	1.32738	+	1.17371i
$866$	23.6991			0.805329
$867$			2.79877i			0.0950512i
$868$			0.222839i			0.00756365i
$869$	−13.9756			−0.474088
$870$	9.46168	−	10.7005i	0.320781	−	0.362782i
$871$	−2.17679			−0.0737578
$872$			26.7513i			0.905914i
$873$			11.4763i			0.388413i
$874$	−31.6991			−1.07224
$875$	7.55149	−	11.0073i	0.255287	−	0.372114i
$876$	−2.08110			−0.0703139
$877$		−	31.5183i		−	1.06430i	−0.846650	−	0.532149i	$-0.821384\pi$
$877$		−	31.5183i		−	1.06430i	0.846650	−	0.532149i	$-0.178616\pi$
$878$		−	7.92478i		−	0.267448i
$879$	8.29218			0.279688
$880$	6.44358	−	7.28726i	0.217213	−	0.245653i
$881$	10.6253			0.357975			0.178988	−	0.983851i	$-0.442718\pi$
$881$	10.6253			0.357975			0.178988	+	0.983851i	$0.442718\pi$
$882$		−	8.25694i		−	0.278026i
$883$		−	6.29806i		−	0.211947i	−0.994369	−	0.105973i	$-0.966204\pi$
$883$		−	6.29806i		−	0.211947i	0.994369	−	0.105973i	$-0.0337958\pi$
$884$	−0.589104			−0.0198137
$885$	22.2374	+	19.6629i	0.747503	+	0.660962i
$886$	−29.1608			−0.979676
$887$		−	29.1187i		−	0.977711i	−0.872365	−	0.488855i	$-0.837415\pi$
$887$		−	29.1187i		−	0.977711i	0.872365	−	0.488855i	$-0.162585\pi$
$888$			4.31265i			0.144723i
$889$	16.4993			0.553369
$890$	41.9003	+	37.0494i	1.40450	+	1.24190i
$891$	1.00000			0.0335013
$892$		−	3.41564i		−	0.114364i
$893$		−	65.8759i		−	2.20445i
$894$	9.46168			0.316446
$895$	−15.8496	+	17.9248i	−0.529792	+	0.599159i
$896$	−15.1333			−0.505568
$897$		−	3.22425i		−	0.107655i
$898$			46.4142i			1.54886i
$899$	4.15045			0.138425
$900$	−0.118714	−	0.962389i	−0.00395713	−	0.0320796i
$901$	5.37187			0.178963
$902$			13.4617i			0.448225i
$903$			5.27504i			0.175542i
$904$	−6.05079			−0.201246
$905$	11.5515	−	13.0640i	0.383985	−	0.434261i
$906$	3.92478			0.130392
$907$			57.3112i			1.90299i	0.307667	+	0.951494i	$0.400452\pi$
$907$			57.3112i			1.90299i	−0.307667	+	0.951494i	$0.599548\pi$
$908$		−	3.38058i		−	0.112188i
$909$	−10.7612			−0.356925
$910$	−2.38787	−	2.11142i	−0.0791572	−	0.0699929i
$911$	−5.52232			−0.182962			−0.0914812	−	0.995807i	$-0.529160\pi$
$911$	−5.52232			−0.182962			−0.0914812	+	0.995807i	$0.529160\pi$
$912$		−	23.2750i		−	0.770714i
$913$		−	9.89446i		−	0.327459i
$914$	−55.6834			−1.84184
$915$	0.126008	+	0.111420i	0.00416570	+	0.00368342i
$916$	2.53549			0.0837749
$917$			7.07381i			0.233598i
$918$		−	5.58181i		−	0.184227i
$919$	5.75272			0.189765			0.0948824	−	0.995488i	$-0.469752\pi$
$919$	5.75272			0.189765			0.0948824	+	0.995488i	$0.469752\pi$
$920$	15.8496	−	17.9248i	0.522544	−	0.590962i
$921$	25.6688			0.845815
$922$			26.6399i			0.877338i
$923$		−	11.3258i		−	0.372794i
$924$	−0.231548			−0.00761737
$925$	−8.00000	+	0.986826i	−0.263038	+	0.0324466i
$926$	−57.7861			−1.89897
$927$		−	16.9380i		−	0.556315i
$928$		−	4.71511i		−	0.154781i
$929$	−41.4274			−1.35919			−0.679594	−	0.733588i	$-0.737844\pi$
$929$	−41.4274			−1.35919			−0.679594	+	0.733588i	$0.737844\pi$
$930$	2.11142	−	2.38787i	0.0692362	−	0.0783014i
$931$	29.8251			0.977479
$932$			2.68479i			0.0879434i
$933$		−	15.7235i		−	0.514766i
$934$	21.5515			0.705186
$935$	6.31265	+	5.58181i	0.206446	+	0.182545i
$936$	2.15633			0.0704817
$937$			14.9222i			0.487488i	0.969840	+	0.243744i	$0.0783756\pi$
$937$			14.9222i			0.487488i	−0.969840	+	0.243744i	$0.921624\pi$
$938$			4.77575i			0.155934i
$939$	26.8627			0.876632
$940$	−4.00000	−	3.53690i	−0.130466	−	0.115361i
$941$	57.0395			1.85944			0.929718	−	0.368273i	$-0.120051\pi$
$941$	57.0395			1.85944			0.929718	+	0.368273i	$0.120051\pi$
$942$			2.38787i			0.0778011i
$943$			36.3536i			1.18384i
$944$	57.7499			1.87960
$945$	1.76845	−	2.00000i	0.0575277	−	0.0650600i
$946$	−6.54420			−0.212770
$947$		−	30.2374i		−	0.982584i	−0.870995	−	0.491292i	$-0.836525\pi$
$947$		−	30.2374i		−	0.982584i	0.870995	−	0.491292i	$-0.163475\pi$
$948$			2.71037i			0.0880288i
$949$	8.64974			0.280782
$950$	39.3258	−	4.85097i	1.27590	−	0.157386i
$951$	0.710373			0.0230354
$952$		−	12.0362i		−	0.390095i
$953$		−	46.2697i		−	1.49882i	−0.662106	−	0.749411i	$-0.730337\pi$
$953$		−	46.2697i		−	1.49882i	0.662106	−	0.749411i	$-0.269663\pi$
$954$	2.11142			0.0683597
$955$	−1.92478	+	2.17679i	−0.0622843	+	0.0704394i
$956$	−2.39963			−0.0776097
$957$			4.31265i			0.139408i
$958$		−	42.3996i		−	1.36987i
$959$	−4.00000			−0.129167
$960$	11.8618	+	10.4885i	0.382837	+	0.338515i
$961$	−30.0738			−0.970123
$962$			1.92478i			0.0620573i
$963$			8.28233i			0.266894i
$964$	4.76116			0.153347
$965$	−14.3977	−	12.7308i	−0.463479	−	0.409820i
$966$	−7.07381			−0.227596
$967$		−	49.5790i		−	1.59435i	−0.603747	−	0.797176i	$-0.706326\pi$
$967$		−	49.5790i		−	1.59435i	0.603747	−	0.797176i	$-0.293674\pi$
$968$			2.67513i			0.0859820i
$969$	20.1622			0.647703
$970$	−25.1782	+	28.4749i	−0.808424	+	0.914272i
$971$	−3.12268			−0.100212			−0.0501058	−	0.998744i	$-0.515956\pi$
$971$	−3.12268			−0.100212			−0.0501058	+	0.998744i	$0.515956\pi$
$972$		−	0.193937i		−	0.00622052i
$973$		−	25.3112i		−	0.811441i
$974$	2.14762			0.0688141
$975$	0.493413	+	4.00000i	0.0158019	+	0.128103i
$976$	0.327239			0.0104747
$977$		−	5.15377i		−	0.164884i	−0.996596	−	0.0824419i	$-0.973728\pi$
$977$		−	5.15377i		−	0.164884i	0.996596	−	0.0824419i	$-0.0262719\pi$
$978$			0.463096i			0.0148082i
$979$	−16.8872			−0.539716
$980$	1.60132	−	1.81099i	0.0511524	−	0.0578499i
$981$	−10.0000			−0.319275
$982$		−	11.8496i		−	0.378134i
$983$			14.8627i			0.474047i	0.971504	+	0.237024i	$0.0761719\pi$
$983$			14.8627i			0.474047i	−0.971504	+	0.237024i	$0.923828\pi$
$984$	−24.3127			−0.775059
$985$	−34.6859	−	30.6702i	−1.10519	−	0.977234i
$986$	24.0724			0.766621
$987$		−	14.7005i		−	0.467923i
$988$		−	0.836381i		−	0.0266088i
$989$	−17.6728			−0.561961
$990$	2.48119	+	2.19394i	0.0788575	+	0.0697279i
$991$	4.43866			0.140999			0.0704993	−	0.997512i	$-0.477541\pi$
$991$	4.43866			0.140999			0.0704993	+	0.997512i	$0.477541\pi$
$992$		−	1.05220i		−	0.0334074i
$993$			0.962389i			0.0305405i
$994$	−24.8481			−0.788135
$995$	8.22284	−	9.29948i	0.260682	−	0.294813i
$996$	−1.91890			−0.0608026
$997$			38.8324i			1.22983i	0.788592	+	0.614917i	$0.210811\pi$
$997$			38.8324i			1.22983i	−0.788592	+	0.614917i	$0.789189\pi$
$998$		−	45.4734i		−	1.43944i
$999$	−1.61213			−0.0510054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.c.b.34.5	yes	6
3.2	odd	2		495.2.c.e.199.2		6
4.3	odd	2		2640.2.d.h.529.1		6
5.2	odd	4		825.2.a.l.1.1		3
5.3	odd	4		825.2.a.j.1.3		3
5.4	even	2	inner	165.2.c.b.34.2	✓	6
11.10	odd	2		1815.2.c.e.364.2		6
15.2	even	4		2475.2.a.ba.1.3		3
15.8	even	4		2475.2.a.bc.1.1		3
15.14	odd	2		495.2.c.e.199.5		6
20.19	odd	2		2640.2.d.h.529.4		6
55.32	even	4		9075.2.a.cg.1.3		3
55.43	even	4		9075.2.a.ch.1.1		3
55.54	odd	2		1815.2.c.e.364.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.c.b.34.2	✓	6	5.4	even	2	inner
165.2.c.b.34.5	yes	6	1.1	even	1	trivial
495.2.c.e.199.2		6	3.2	odd	2
495.2.c.e.199.5		6	15.14	odd	2
825.2.a.j.1.3		3	5.3	odd	4
825.2.a.l.1.1		3	5.2	odd	4
1815.2.c.e.364.2		6	11.10	odd	2
1815.2.c.e.364.5		6	55.54	odd	2
2475.2.a.ba.1.3		3	15.2	even	4
2475.2.a.bc.1.1		3	15.8	even	4
2640.2.d.h.529.1		6	4.3	odd	2
2640.2.d.h.529.4		6	20.19	odd	2
9075.2.a.cg.1.3		3	55.32	even	4
9075.2.a.ch.1.1		3	55.43	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.48119i q^{2} +1.00000i q^{3} -0.193937 q^{4} +(-1.48119 + 1.67513i) q^{5} -1.48119 q^{6} -1.19394i q^{7} +2.67513i q^{8} -1.00000 q^{9} +(-2.48119 - 2.19394i) q^{10} +1.00000 q^{11} -0.193937i q^{12} +0.806063i q^{13} +1.76845 q^{14} +(-1.67513 - 1.48119i) q^{15} -4.35026 q^{16} -3.76845i q^{17} -1.48119i q^{18} +5.35026 q^{19} +(0.287258 - 0.324869i) q^{20} +1.19394 q^{21} +1.48119i q^{22} +4.00000i q^{23} -2.67513 q^{24} +(-0.612127 - 4.96239i) q^{25} -1.19394 q^{26} -1.00000i q^{27} +0.231548i q^{28} +4.31265 q^{29} +(2.19394 - 2.48119i) q^{30} +0.962389 q^{31} -1.09332i q^{32} +1.00000i q^{33} +5.58181 q^{34} +(2.00000 + 1.76845i) q^{35} +0.193937 q^{36} -1.61213i q^{37} +7.92478i q^{38} -0.806063 q^{39} +(-4.48119 - 3.96239i) q^{40} +9.08840 q^{41} +1.76845i q^{42} +4.41819i q^{43} -0.193937 q^{44} +(1.48119 - 1.67513i) q^{45} -5.92478 q^{46} -12.3127i q^{47} -4.35026i q^{48} +5.57452 q^{49} +(7.35026 - 0.906679i) q^{50} +3.76845 q^{51} -0.156325i q^{52} +1.42548i q^{53} +1.48119 q^{54} +(-1.48119 + 1.67513i) q^{55} +3.19394 q^{56} +5.35026i q^{57} +6.38787i q^{58} -13.2750 q^{59} +(0.324869 + 0.287258i) q^{60} -0.0752228 q^{61} +1.42548i q^{62} +1.19394i q^{63} -7.08110 q^{64} +(-1.35026 - 1.19394i) q^{65} -1.48119 q^{66} +2.70052i q^{67} +0.730841i q^{68} -4.00000 q^{69} +(-2.61942 + 2.96239i) q^{70} -14.0508 q^{71} -2.67513i q^{72} -10.7308i q^{73} +2.38787 q^{74} +(4.96239 - 0.612127i) q^{75} -1.03761 q^{76} -1.19394i q^{77} -1.19394i q^{78} -13.9756 q^{79} +(6.44358 - 7.28726i) q^{80} +1.00000 q^{81} +13.4617i q^{82} -9.89446i q^{83} -0.231548 q^{84} +(6.31265 + 5.58181i) q^{85} -6.54420 q^{86} +4.31265i q^{87} +2.67513i q^{88} -16.8872 q^{89} +(2.48119 + 2.19394i) q^{90} +0.962389 q^{91} -0.775746i q^{92} +0.962389i q^{93} +18.2374 q^{94} +(-7.92478 + 8.96239i) q^{95} +1.09332 q^{96} -11.4763i q^{97} +8.25694i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34}+ \cdots - 6 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^9 - 4 * q^10 + 6 * q^11 - 12 * q^14 - 6 * q^16 + 12 * q^19 - 10 * q^20 + 8 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 14 * q^30 - 16 * q^31 + 36 * q^34 + 12 * q^35 + 2 * q^36 - 4 * q^39 - 16 * q^40 + 16 * q^41 - 2 * q^44 - 2 * q^45 + 8 * q^46 + 10 * q^49 + 24 * q^50 - 2 * q^54 + 2 * q^55 + 20 * q^56 - 16 * q^59 + 12 * q^60 - 44 * q^61 + 22 * q^64 + 12 * q^65 + 2 * q^66 - 24 * q^69 - 40 * q^70 - 24 * q^71 + 16 * q^74 + 8 * q^75 - 28 * q^76 + 20 * q^79 + 6 * q^80 + 6 * q^81 - 24 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 + 4 * q^90 - 16 * q^91 + 24 * q^94 - 4 * q^95 - 6 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more