LMFDB - Embedded newform 1617.2.c.a.538.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.6
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98162i q^{2} +1.00000i q^{3} -1.92681 q^{4} -0.364814i q^{5} +1.98162 q^{6} -0.145025i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.98162i q^{2} +1.00000i q^{3} -1.92681 q^{4} -0.364814i q^{5} +1.98162 q^{6} -0.145025i q^{8} -1.00000 q^{9} -0.722923 q^{10} +(3.27256 + 0.538824i) q^{11} -1.92681i q^{12} -5.43170 q^{13} +0.364814 q^{15} -4.14101 q^{16} -5.87420 q^{17} +1.98162i q^{18} -2.22448 q^{19} +0.702929i q^{20} +(1.06774 - 6.48497i) q^{22} +2.76990 q^{23} +0.145025 q^{24} +4.86691 q^{25} +10.7636i q^{26} -1.00000i q^{27} +2.01743i q^{29} -0.722923i q^{30} -5.77289i q^{31} +7.91586i q^{32} +(-0.538824 + 3.27256i) q^{33} +11.6404i q^{34} +1.92681 q^{36} -8.01109 q^{37} +4.40808i q^{38} -5.43170i q^{39} -0.0529073 q^{40} -8.88534 q^{41} -5.90706i q^{43} +(-6.30562 - 1.03821i) q^{44} +0.364814i q^{45} -5.48888i q^{46} -6.29502i q^{47} -4.14101i q^{48} -9.64436i q^{50} -5.87420i q^{51} +10.4659 q^{52} -12.9400 q^{53} -1.98162 q^{54} +(0.196570 - 1.19388i) q^{55} -2.22448i q^{57} +3.99777 q^{58} +8.54356i q^{59} -0.702929 q^{60} +2.70704 q^{61} -11.4397 q^{62} +7.40420 q^{64} +1.98156i q^{65} +(6.48497 + 1.06774i) q^{66} -14.6147 q^{67} +11.3185 q^{68} +2.76990i q^{69} +2.64558 q^{71} +0.145025i q^{72} +5.82364 q^{73} +15.8749i q^{74} +4.86691i q^{75} +4.28617 q^{76} -10.7636 q^{78} -1.83803i q^{79} +1.51070i q^{80} +1.00000 q^{81} +17.6074i q^{82} +5.21418 q^{83} +2.14299i q^{85} -11.7056 q^{86} -2.01743 q^{87} +(0.0781431 - 0.474605i) q^{88} +0.424694i q^{89} +0.722923 q^{90} -5.33708 q^{92} +5.77289 q^{93} -12.4743 q^{94} +0.811523i q^{95} -7.91586 q^{96} +10.0948i q^{97} +(-3.27256 - 0.538824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 24 * q^4 - 32 * q^9	$ 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.98162i		−	1.40122i	−0.713546	−	0.700608i	$-0.752912\pi$
$2$		−	1.98162i		−	1.40122i	0.713546	−	0.700608i	$-0.247088\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.92681			−0.963407
$5$		−	0.364814i		−	0.163150i	−0.996667	−	0.0815749i	$-0.974005\pi$
$5$		−	0.364814i		−	0.163150i	0.996667	−	0.0815749i	$-0.0259950\pi$
$6$	1.98162			0.808993
$7$		0			0
$7$		0			0
$8$		−	0.145025i		−	0.0512742i
$9$	−1.00000			−0.333333
$10$	−0.722923			−0.228608
$11$	3.27256	+	0.538824i	0.986715	+	0.162461i
$11$	3.27256	+	0.538824i	0.986715	+	0.162461i
$12$		−	1.92681i		−	0.556223i
$13$	−5.43170			−1.50648			−0.753242	−	0.657744i	$-0.771511\pi$
$13$	−5.43170			−1.50648			−0.753242	+	0.657744i	$0.771511\pi$
$14$		0			0
$15$	0.364814			0.0941946
$16$	−4.14101			−1.03525
$17$	−5.87420			−1.42470			−0.712351	−	0.701823i	$-0.752370\pi$
$17$	−5.87420			−1.42470			−0.712351	+	0.701823i	$0.752370\pi$
$18$			1.98162i			0.467072i
$19$	−2.22448			−0.510331			−0.255166	−	0.966897i	$-0.582130\pi$
$19$	−2.22448			−0.510331			−0.255166	+	0.966897i	$0.582130\pi$
$20$			0.702929i			0.157180i
$21$		0			0
$22$	1.06774	−	6.48497i	0.227644	−	1.38260i
$23$	2.76990			0.577564			0.288782	−	0.957395i	$-0.406750\pi$
$23$	2.76990			0.577564			0.288782	+	0.957395i	$0.406750\pi$
$24$	0.145025			0.0296032
$25$	4.86691			0.973382
$26$			10.7636i			2.11091i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			2.01743i			0.374627i	0.982300	+	0.187313i	$0.0599779\pi$
$29$			2.01743i			0.374627i	−0.982300	+	0.187313i	$0.940022\pi$
$30$		−	0.722923i		−	0.131987i
$31$		−	5.77289i		−	1.03684i	−0.855126	−	0.518421i	$-0.826520\pi$
$31$		−	5.77289i		−	1.03684i	0.855126	−	0.518421i	$-0.173480\pi$
$32$			7.91586i			1.39934i
$33$	−0.538824	+	3.27256i	−0.0937972	+	0.569680i
$34$			11.6404i			1.99632i
$35$		0			0
$36$	1.92681			0.321136
$37$	−8.01109			−1.31701			−0.658507	−	0.752574i	$-0.728812\pi$
$37$	−8.01109			−1.31701			−0.658507	+	0.752574i	$0.728812\pi$
$38$			4.40808i			0.715085i
$39$		−	5.43170i		−	0.869769i
$40$	−0.0529073			−0.00836538
$41$	−8.88534			−1.38766			−0.693829	−	0.720140i	$-0.744078\pi$
$41$	−8.88534			−1.38766			−0.693829	+	0.720140i	$0.744078\pi$
$42$		0			0
$43$		−	5.90706i		−	0.900819i	−0.892822	−	0.450409i	$-0.851278\pi$
$43$		−	5.90706i		−	0.900819i	0.892822	−	0.450409i	$-0.148722\pi$
$44$	−6.30562	−	1.03821i	−0.950608	−	0.156517i
$45$			0.364814i			0.0543833i
$46$		−	5.48888i		−	0.809292i
$47$		−	6.29502i		−	0.918224i	−0.888378	−	0.459112i	$-0.848168\pi$
$47$		−	6.29502i		−	0.918224i	0.888378	−	0.459112i	$-0.151832\pi$
$48$		−	4.14101i		−	0.597704i
$49$		0			0
$50$		−	9.64436i		−	1.36392i
$51$		−	5.87420i		−	0.822553i
$52$	10.4659			1.45136
$53$	−12.9400			−1.77745			−0.888725	−	0.458440i	$-0.848408\pi$
$53$	−12.9400			−1.77745			−0.888725	+	0.458440i	$0.848408\pi$
$54$	−1.98162			−0.269664
$55$	0.196570	−	1.19388i	0.0265056	−	0.160982i
$56$		0			0
$57$		−	2.22448i		−	0.294640i
$58$	3.99777			0.524933
$59$			8.54356i			1.11228i	0.831090	+	0.556139i	$0.187718\pi$
$59$			8.54356i			1.11228i	−0.831090	+	0.556139i	$0.812282\pi$
$60$	−0.702929			−0.0907478
$61$	2.70704			0.346601			0.173301	−	0.984869i	$-0.444557\pi$
$61$	2.70704			0.346601			0.173301	+	0.984869i	$0.444557\pi$
$62$	−11.4397			−1.45284
$63$		0			0
$64$	7.40420			0.925525
$65$			1.98156i			0.245783i
$66$	6.48497	+	1.06774i	0.798245	+	0.131430i
$67$	−14.6147			−1.78547			−0.892735	−	0.450582i	$-0.851216\pi$
$67$	−14.6147			−1.78547			−0.892735	+	0.450582i	$0.851216\pi$
$68$	11.3185			1.37257
$69$			2.76990i			0.333457i
$70$		0			0
$71$	2.64558			0.313973			0.156987	−	0.987601i	$-0.449822\pi$
$71$	2.64558			0.313973			0.156987	+	0.987601i	$0.449822\pi$
$72$			0.145025i			0.0170914i
$73$	5.82364			0.681605			0.340802	−	0.940135i	$-0.389301\pi$
$73$	5.82364			0.681605			0.340802	+	0.940135i	$0.389301\pi$
$74$			15.8749i			1.84542i
$75$			4.86691i			0.561982i
$76$	4.28617			0.491657
$77$		0			0
$78$	−10.7636			−1.21873
$79$		−	1.83803i		−	0.206795i	−0.994640	−	0.103397i	$-0.967029\pi$
$79$		−	1.83803i		−	0.206795i	0.994640	−	0.103397i	$-0.0329713\pi$
$80$			1.51070i			0.168901i
$81$	1.00000			0.111111
$82$			17.6074i			1.94441i
$83$	5.21418			0.572330			0.286165	−	0.958180i	$-0.407619\pi$
$83$	5.21418			0.572330			0.286165	+	0.958180i	$0.407619\pi$
$84$		0			0
$85$			2.14299i			0.232440i
$86$	−11.7056			−1.26224
$87$	−2.01743			−0.216291
$88$	0.0781431	−	0.474605i	0.00833008	−	0.0505930i
$89$			0.424694i			0.0450175i	0.999747	+	0.0225087i	$0.00716536\pi$
$89$			0.424694i			0.0450175i	−0.999747	+	0.0225087i	$0.992835\pi$
$90$	0.722923			0.0762027
$91$		0			0
$92$	−5.33708			−0.556429
$93$	5.77289			0.598621
$94$	−12.4743			−1.28663
$95$			0.811523i			0.0832605i
$96$	−7.91586			−0.807909
$97$			10.0948i			1.02497i	0.858695	+	0.512487i	$0.171276\pi$
$97$			10.0948i			1.02497i	−0.858695	+	0.512487i	$0.828724\pi$
$98$		0			0
$99$	−3.27256	−	0.538824i	−0.328905	−	0.0541538i
$100$	−9.37764			−0.937764
$101$	−15.2461			−1.51704			−0.758522	−	0.651648i	$-0.774078\pi$
$101$	−15.2461			−1.51704			−0.758522	+	0.651648i	$0.774078\pi$
$102$	−11.6404			−1.15257
$103$			5.28319i			0.520568i	0.965532	+	0.260284i	$0.0838163\pi$
$103$			5.28319i			0.520568i	−0.965532	+	0.260284i	$0.916184\pi$
$104$			0.787735i			0.0772438i
$105$		0			0
$106$			25.6422i			2.49059i
$107$			3.91130i			0.378119i	0.981966	+	0.189060i	$0.0605439\pi$
$107$			3.91130i			0.378119i	−0.981966	+	0.189060i	$0.939456\pi$
$108$			1.92681i			0.185408i
$109$		−	6.35799i		−	0.608985i	−0.952515	−	0.304492i	$-0.901513\pi$
$109$		−	6.35799i		−	0.608985i	0.952515	−	0.304492i	$-0.0984868\pi$
$110$	−2.36581	−	0.389528i	−0.225571	−	0.0371400i
$111$		−	8.01109i		−	0.760379i
$112$		0			0
$113$	4.20066			0.395165			0.197582	−	0.980286i	$-0.436691\pi$
$113$	4.20066			0.395165			0.197582	+	0.980286i	$0.436691\pi$
$114$	−4.40808			−0.412854
$115$		−	1.01050i		−	0.0942294i
$116$		−	3.88721i		−	0.360918i
$117$	5.43170			0.502161
$118$	16.9301			1.55854
$119$		0			0
$120$		−	0.0529073i		−	0.00482975i
$121$	10.4193	+	3.52667i	0.947213	+	0.320606i
$122$		−	5.36433i		−	0.485664i
$123$		−	8.88534i		−	0.801164i
$124$			11.1233i			0.998901i
$125$		−	3.59959i		−	0.321957i
$126$		0			0
$127$		−	14.3427i		−	1.27271i	−0.771396	−	0.636356i	$-0.780441\pi$
$127$		−	14.3427i		−	1.27271i	0.771396	−	0.636356i	$-0.219559\pi$
$128$			1.15943i			0.102480i
$129$	5.90706			0.520088
$130$	3.92670			0.344395
$131$	−5.10549			−0.446069			−0.223034	−	0.974811i	$-0.571596\pi$
$131$	−5.10549			−0.446069			−0.223034	+	0.974811i	$0.571596\pi$
$132$	1.03821	−	6.30562i	0.0903649	−	0.548834i
$133$		0			0
$134$			28.9608i			2.50183i
$135$	−0.364814			−0.0313982
$136$			0.851908i			0.0730505i
$137$	−2.39013			−0.204203			−0.102101	−	0.994774i	$-0.532557\pi$
$137$	−2.39013			−0.204203			−0.102101	+	0.994774i	$0.532557\pi$
$138$	5.48888			0.467245
$139$	16.1644			1.37104			0.685522	−	0.728052i	$-0.259574\pi$
$139$	16.1644			1.37104			0.685522	+	0.728052i	$0.259574\pi$
$140$		0			0
$141$	6.29502			0.530137
$142$		−	5.24254i		−	0.439944i
$143$	−17.7756	−	2.92673i	−1.48647	−	0.244746i
$144$	4.14101			0.345085
$145$	0.735985			0.0611203
$146$		−	11.5402i		−	0.955076i
$147$		0			0
$148$	15.4359			1.26882
$149$			18.4504i			1.51151i	0.654853	+	0.755756i	$0.272730\pi$
$149$			18.4504i			1.51151i	−0.654853	+	0.755756i	$0.727270\pi$
$150$	9.64436			0.787459
$151$			9.66091i			0.786194i	0.919497	+	0.393097i	$0.128596\pi$
$151$			9.66091i			0.786194i	−0.919497	+	0.393097i	$0.871404\pi$
$152$			0.322606i			0.0261668i
$153$	5.87420			0.474901
$154$		0			0
$155$	−2.10603			−0.169161
$156$			10.4659i			0.837942i
$157$		−	13.2694i		−	1.05902i	−0.848305	−	0.529508i	$-0.822377\pi$
$157$		−	13.2694i		−	1.05902i	0.848305	−	0.529508i	$-0.177623\pi$
$158$	−3.64228			−0.289764
$159$		−	12.9400i		−	1.02621i
$160$	2.88782			0.228302
$161$		0			0
$162$		−	1.98162i		−	0.155691i
$163$	−7.93302			−0.621362			−0.310681	−	0.950514i	$-0.600557\pi$
$163$	−7.93302			−0.621362			−0.310681	+	0.950514i	$0.600557\pi$
$164$	17.1204			1.33688
$165$	1.19388	+	0.196570i	0.0929432	+	0.0153030i
$166$		−	10.3325i		−	0.801959i
$167$	−0.682227			−0.0527923			−0.0263961	−	0.999652i	$-0.508403\pi$
$167$	−0.682227			−0.0527923			−0.0263961	+	0.999652i	$0.508403\pi$
$168$		0			0
$169$	16.5034			1.26949
$170$	4.24659			0.325699
$171$	2.22448			0.170110
$172$			11.3818i			0.867855i
$173$	−1.49877			−0.113949			−0.0569747	−	0.998376i	$-0.518145\pi$
$173$	−1.49877			−0.113949			−0.0569747	+	0.998376i	$0.518145\pi$
$174$			3.99777i			0.303070i
$175$		0			0
$176$	−13.5517	−	2.23128i	−1.02150	−	0.168189i
$177$	−8.54356			−0.642174
$178$	0.841582			0.0630793
$179$	−6.21242			−0.464338			−0.232169	−	0.972675i	$-0.574582\pi$
$179$	−6.21242			−0.464338			−0.232169	+	0.972675i	$0.574582\pi$
$180$		−	0.702929i		−	0.0523932i
$181$		−	9.87854i		−	0.734266i	−0.930168	−	0.367133i	$-0.880339\pi$
$181$		−	9.87854i		−	0.734266i	0.930168	−	0.367133i	$-0.119661\pi$
$182$		0			0
$183$			2.70704i			0.200110i
$184$		−	0.401706i		−	0.0296141i
$185$			2.92256i			0.214871i
$186$		−	11.4397i		−	0.838797i
$187$	−19.2237	−	3.16516i	−1.40578	−	0.231459i
$188$			12.1293i			0.884623i
$189$		0			0
$190$	1.60813			0.116666
$191$	0.879492			0.0636378			0.0318189	−	0.999494i	$-0.489870\pi$
$191$	0.879492			0.0636378			0.0318189	+	0.999494i	$0.489870\pi$
$192$			7.40420i			0.534352i
$193$		−	22.3397i		−	1.60804i	−0.594600	−	0.804022i	$-0.702690\pi$
$193$		−	22.3397i		−	1.60804i	0.594600	−	0.804022i	$-0.297310\pi$
$194$	20.0041			1.43621
$195$	−1.98156			−0.141903
$196$		0			0
$197$		−	1.93301i		−	0.137721i	−0.997626	−	0.0688607i	$-0.978064\pi$
$197$		−	1.93301i		−	0.137721i	0.997626	−	0.0688607i	$-0.0219364\pi$
$198$	−1.06774	+	6.48497i	−0.0758812	+	0.460867i
$199$		−	2.02755i		−	0.143730i	−0.997414	−	0.0718648i	$-0.977105\pi$
$199$		−	2.02755i		−	0.143730i	0.997414	−	0.0718648i	$-0.0228950\pi$
$200$		−	0.705825i		−	0.0499094i
$201$		−	14.6147i		−	1.03084i
$202$			30.2120i			2.12571i
$203$		0			0
$204$			11.3185i			0.792453i
$205$			3.24150i			0.226396i
$206$	10.4693			0.729429
$207$	−2.76990			−0.192521
$208$	22.4928			1.55959
$209$	−7.27976	−	1.19860i	−0.503551	−	0.0829092i
$210$		0			0
$211$		−	8.17186i		−	0.562574i	−0.959624	−	0.281287i	$-0.909239\pi$
$211$		−	8.17186i		−	0.562574i	0.959624	−	0.281287i	$-0.0907612\pi$
$212$	24.9330			1.71241
$213$			2.64558i			0.181272i
$214$	7.75070			0.529827
$215$	−2.15498			−0.146968
$216$	−0.145025			−0.00986773
$217$		0			0
$218$	−12.5991			−0.853319
$219$			5.82364i			0.393525i
$220$	−0.378755	+	2.30038i	−0.0255356	+	0.155092i
$221$	31.9069			2.14629
$222$	−15.8749			−1.06546
$223$		−	24.2491i		−	1.62384i	−0.583767	−	0.811921i	$-0.698422\pi$
$223$		−	24.2491i		−	1.62384i	0.583767	−	0.811921i	$-0.301578\pi$
$224$		0			0
$225$	−4.86691			−0.324461
$226$		−	8.32411i		−	0.553711i
$227$	3.36031			0.223032			0.111516	−	0.993763i	$-0.464429\pi$
$227$	3.36031			0.223032			0.111516	+	0.993763i	$0.464429\pi$
$228$			4.28617i			0.283858i
$229$			21.8792i			1.44582i	0.690942	+	0.722910i	$0.257196\pi$
$229$			21.8792i			1.44582i	−0.690942	+	0.722910i	$0.742804\pi$
$230$	−2.00242			−0.132036
$231$		0			0
$232$	0.292578			0.0192087
$233$			7.94667i			0.520603i	0.965527	+	0.260302i	$0.0838220\pi$
$233$			7.94667i			0.520603i	−0.965527	+	0.260302i	$0.916178\pi$
$234$		−	10.7636i		−	0.703637i
$235$	−2.29651			−0.149808
$236$		−	16.4619i		−	1.07158i
$237$	1.83803			0.119393
$238$		0			0
$239$			18.3659i			1.18799i	0.804467	+	0.593997i	$0.202451\pi$
$239$			18.3659i			1.18799i	−0.804467	+	0.593997i	$0.797549\pi$
$240$	−1.51070			−0.0975153
$241$	9.17876			0.591256			0.295628	−	0.955303i	$-0.404471\pi$
$241$	9.17876			0.591256			0.295628	+	0.955303i	$0.404471\pi$
$242$	6.98851	−	20.6472i	0.449239	−	1.32725i
$243$			1.00000i			0.0641500i
$244$	−5.21597			−0.333918
$245$		0			0
$246$	−17.6074			−1.12260
$247$	12.0827			0.768806
$248$	−0.837216			−0.0531632
$249$			5.21418i			0.330435i
$250$	−7.13301			−0.451131
$251$		−	25.7949i		−	1.62816i	−0.580752	−	0.814080i	$-0.697242\pi$
$251$		−	25.7949i		−	1.62816i	0.580752	−	0.814080i	$-0.302758\pi$
$252$		0			0
$253$	9.06467	+	1.49249i	0.569891	+	0.0938318i
$254$	−28.4218			−1.78334
$255$	−2.14299			−0.134199
$256$	17.1059			1.06912
$257$			5.90959i			0.368630i	0.982867	+	0.184315i	$0.0590067\pi$
$257$			5.90959i			0.368630i	−0.982867	+	0.184315i	$0.940993\pi$
$258$		−	11.7056i		−	0.728756i
$259$		0			0
$260$		−	3.81810i		−	0.236789i
$261$		−	2.01743i		−	0.124876i
$262$			10.1171i			0.625039i
$263$			19.4137i			1.19710i	0.801085	+	0.598550i	$0.204256\pi$
$263$			19.4137i			1.19710i	−0.801085	+	0.598550i	$0.795744\pi$
$264$	0.474605	+	0.0781431i	0.0292099	+	0.00480937i
$265$			4.72071i			0.289991i
$266$		0			0
$267$	−0.424694			−0.0259909
$268$	28.1598			1.72013
$269$		−	28.4049i		−	1.73188i	−0.500148	−	0.865940i	$-0.666721\pi$
$269$		−	28.4049i		−	1.73188i	0.500148	−	0.865940i	$-0.333279\pi$
$270$			0.722923i			0.0439957i
$271$	15.7812			0.958639			0.479319	−	0.877641i	$-0.340884\pi$
$271$	15.7812			0.958639			0.479319	+	0.877641i	$0.340884\pi$
$272$	24.3251			1.47493
$273$		0			0
$274$			4.73633i			0.286132i
$275$	15.9273	+	2.62241i	0.960451	+	0.158137i
$276$		−	5.33708i		−	0.321255i
$277$		−	17.0585i		−	1.02494i	−0.858704	−	0.512472i	$-0.828730\pi$
$277$		−	17.0585i		−	1.02494i	0.858704	−	0.512472i	$-0.171270\pi$
$278$		−	32.0316i		−	1.92113i
$279$			5.77289i			0.345614i
$280$		0			0
$281$		−	26.5761i		−	1.58540i	−0.609612	−	0.792700i	$-0.708675\pi$
$281$		−	26.5761i		−	1.58540i	0.609612	−	0.792700i	$-0.291325\pi$
$282$		−	12.4743i		−	0.742836i
$283$	9.57418			0.569126			0.284563	−	0.958657i	$-0.408152\pi$
$283$	9.57418			0.569126			0.284563	+	0.958657i	$0.408152\pi$
$284$	−5.09755			−0.302484
$285$	−0.811523			−0.0480704
$286$	−5.79967	+	35.2245i	−0.342941	+	2.08287i
$287$		0			0
$288$		−	7.91586i		−	0.466447i
$289$	17.5062			1.02978
$290$		−	1.45844i		−	0.0856427i
$291$	−10.0948			−0.591769
$292$	−11.2211			−0.656663
$293$	16.8865			0.986518			0.493259	−	0.869883i	$-0.335806\pi$
$293$	16.8865			0.986518			0.493259	+	0.869883i	$0.335806\pi$
$294$		0			0
$295$	3.11681			0.181468
$296$			1.16181i			0.0675289i
$297$	0.538824	−	3.27256i	0.0312657	−	0.189893i
$298$	36.5616			2.11796
$299$	−15.0453			−0.870090
$300$		−	9.37764i		−	0.541418i
$301$		0			0
$302$	19.1443			1.10163
$303$		−	15.2461i		−	0.875865i
$304$	9.21161			0.528322
$305$		−	0.987568i		−	0.0565480i
$306$		−	11.6404i		−	0.665439i
$307$	1.57027			0.0896199			0.0448099	−	0.998996i	$-0.485732\pi$
$307$	1.57027			0.0896199			0.0448099	+	0.998996i	$0.485732\pi$
$308$		0			0
$309$	−5.28319			−0.300550
$310$			4.17335i			0.237031i
$311$			24.0720i			1.36500i	0.730886	+	0.682499i	$0.239107\pi$
$311$			24.0720i			1.36500i	−0.730886	+	0.682499i	$0.760893\pi$
$312$	−0.787735			−0.0445967
$313$		−	0.477550i		−	0.0269927i	−0.999909	−	0.0134964i	$-0.995704\pi$
$313$		−	0.477550i		−	0.0269927i	0.999909	−	0.0134964i	$-0.00429616\pi$
$314$	−26.2949			−1.48391
$315$		0			0
$316$			3.54154i			0.199227i
$317$	−9.41420			−0.528754			−0.264377	−	0.964419i	$-0.585166\pi$
$317$	−9.41420			−0.528754			−0.264377	+	0.964419i	$0.585166\pi$
$318$	−25.6422			−1.43794
$319$	−1.08704	+	6.60215i	−0.0608624	+	0.369650i
$320$		−	2.70116i		−	0.150999i
$321$	−3.91130			−0.218307
$322$		0			0
$323$	13.0671			0.727070
$324$	−1.92681			−0.107045
$325$	−26.4356			−1.46638
$326$			15.7202i			0.870663i
$327$	6.35799			0.351597
$328$			1.28860i			0.0711510i
$329$		0			0
$330$	0.389528	−	2.36581i	0.0214428	−	0.130234i
$331$	18.7986			1.03327			0.516633	−	0.856207i	$-0.327185\pi$
$331$	18.7986			1.03327			0.516633	+	0.856207i	$0.327185\pi$
$332$	−10.0468			−0.551387
$333$	8.01109			0.439005
$334$			1.35191i			0.0739734i
$335$			5.33165i			0.291299i
$336$		0			0
$337$		−	5.47186i		−	0.298071i	−0.988832	−	0.149036i	$-0.952383\pi$
$337$		−	5.47186i		−	0.298071i	0.988832	−	0.149036i	$-0.0476169\pi$
$338$		−	32.7035i		−	1.77883i
$339$			4.20066i			0.228148i
$340$		−	4.12915i		−	0.223934i
$341$	3.11057	−	18.8922i	0.168447	−	1.02307i
$342$		−	4.40808i		−	0.238362i
$343$		0			0
$344$	−0.856674			−0.0461888
$345$	1.01050			0.0544034
$346$			2.96999i			0.159668i
$347$		−	17.7670i		−	0.953782i	−0.878962	−	0.476891i	$-0.841764\pi$
$347$		−	17.7670i		−	0.953782i	0.878962	−	0.476891i	$-0.158236\pi$
$348$	3.88721			0.208376
$349$	−30.5643			−1.63607			−0.818035	−	0.575169i	$-0.804936\pi$
$349$	−30.5643			−1.63607			−0.818035	+	0.575169i	$0.804936\pi$
$350$		0			0
$351$			5.43170i			0.289923i
$352$	−4.26525	+	25.9052i	−0.227339	+	1.38075i
$353$			16.4442i			0.875237i	0.899161	+	0.437619i	$0.144178\pi$
$353$			16.4442i			0.875237i	−0.899161	+	0.437619i	$0.855822\pi$
$354$			16.9301i			0.899824i
$355$		−	0.965146i		−	0.0512247i
$356$		−	0.818307i		−	0.0433702i
$357$		0			0
$358$			12.3107i			0.650639i
$359$		−	33.5681i		−	1.77166i	−0.464013	−	0.885828i	$-0.653591\pi$
$359$		−	33.5681i		−	1.77166i	0.464013	−	0.885828i	$-0.346409\pi$
$360$	0.0529073			0.00278846
$361$	−14.0517			−0.739562
$362$	−19.5755			−1.02887
$363$	−3.52667	+	10.4193i	−0.185102	+	0.546873i
$364$		0			0
$365$		−	2.12454i		−	0.111204i
$366$	5.36433			0.280398
$367$			6.07484i			0.317104i	0.987351	+	0.158552i	$0.0506825\pi$
$367$			6.07484i			0.317104i	−0.987351	+	0.158552i	$0.949317\pi$
$368$	−11.4702			−0.597925
$369$	8.88534			0.462552
$370$	5.79140			0.301080
$371$		0			0
$372$	−11.1233			−0.576716
$373$		−	34.9384i		−	1.80904i	−0.426427	−	0.904522i	$-0.640228\pi$
$373$		−	34.9384i		−	1.80904i	0.426427	−	0.904522i	$-0.359772\pi$
$374$	−6.27214	+	38.0940i	−0.324325	+	1.96980i
$375$	3.59959			0.185882
$376$	−0.912938			−0.0470812
$377$		−	10.9581i		−	0.564369i
$378$		0			0
$379$	−14.1967			−0.729235			−0.364617	−	0.931157i	$-0.618800\pi$
$379$	−14.1967			−0.729235			−0.364617	+	0.931157i	$0.618800\pi$
$380$		−	1.56365i		−	0.0802137i
$381$	14.3427			0.734800
$382$		−	1.74282i		−	0.0891704i
$383$		−	18.8790i		−	0.964674i	−0.875986	−	0.482337i	$-0.839788\pi$
$383$		−	18.8790i		−	0.964674i	0.875986	−	0.482337i	$-0.160212\pi$
$384$	−1.15943			−0.0591667
$385$		0			0
$386$	−44.2687			−2.25322
$387$			5.90706i			0.300273i
$388$		−	19.4508i		−	0.987467i
$389$	−3.64288			−0.184702			−0.0923508	−	0.995727i	$-0.529438\pi$
$389$	−3.64288			−0.184702			−0.0923508	+	0.995727i	$0.529438\pi$
$390$			3.92670i			0.198836i
$391$	−16.2709			−0.822857
$392$		0			0
$393$		−	5.10549i		−	0.257538i
$394$	−3.83049			−0.192978
$395$	−0.670539			−0.0337385
$396$	6.30562	+	1.03821i	0.316869	+	0.0521722i
$397$		−	18.7210i		−	0.939581i	−0.882778	−	0.469790i	$-0.844329\pi$
$397$		−	18.7210i		−	0.939581i	0.882778	−	0.469790i	$-0.155671\pi$
$398$	−4.01784			−0.201396
$399$		0			0
$400$	−20.1539			−1.00770
$401$	19.4518			0.971374			0.485687	−	0.874133i	$-0.338569\pi$
$401$	19.4518			0.971374			0.485687	+	0.874133i	$0.338569\pi$
$402$	−28.9608			−1.44443
$403$			31.3566i			1.56199i
$404$	29.3764			1.46153
$405$		−	0.364814i		−	0.0181278i
$406$		0			0
$407$	−26.2168	−	4.31656i	−1.29952	−	0.213964i
$408$	−0.851908			−0.0421757
$409$	4.01778			0.198666			0.0993331	−	0.995054i	$-0.468329\pi$
$409$	4.01778			0.198666			0.0993331	+	0.995054i	$0.468329\pi$
$410$	6.42342			0.317230
$411$		−	2.39013i		−	0.117896i
$412$		−	10.1797i		−	0.501519i
$413$		0			0
$414$			5.48888i			0.269764i
$415$		−	1.90221i		−	0.0933756i
$416$		−	42.9966i		−	2.10808i
$417$			16.1644i			0.791573i
$418$	−2.37518	+	14.4257i	−0.116174	+	0.705585i
$419$			18.7760i			0.917268i	0.888625	+	0.458634i	$0.151661\pi$
$419$			18.7760i			0.917268i	−0.888625	+	0.458634i	$0.848339\pi$
$420$		0			0
$421$	37.7836			1.84146			0.920730	−	0.390201i	$-0.127594\pi$
$421$	37.7836			1.84146			0.920730	+	0.390201i	$0.127594\pi$
$422$	−16.1935			−0.788287
$423$			6.29502i			0.306075i
$424$			1.87663i			0.0911374i
$425$	−28.5892			−1.38678
$426$	5.24254			0.254002
$427$		0			0
$428$		−	7.53634i		−	0.364283i
$429$	2.92673	−	17.7756i	0.141304	−	0.858214i
$430$			4.27035i			0.205935i
$431$		−	12.2285i		−	0.589025i	−0.955648	−	0.294512i	$-0.904843\pi$
$431$		−	12.2285i		−	0.589025i	0.955648	−	0.294512i	$-0.0951572\pi$
$432$			4.14101i			0.199235i
$433$		−	15.0598i		−	0.723726i	−0.932231	−	0.361863i	$-0.882141\pi$
$433$		−	15.0598i		−	0.723726i	0.932231	−	0.361863i	$-0.117859\pi$
$434$		0			0
$435$			0.735985i			0.0352878i
$436$			12.2507i			0.586700i
$437$	−6.16159			−0.294749
$438$	11.5402			0.551413
$439$	15.3359			0.731944			0.365972	−	0.930626i	$-0.380737\pi$
$439$	15.3359			0.731944			0.365972	+	0.930626i	$0.380737\pi$
$440$	−0.173142	−	0.0285077i	−0.00825424	−	0.00135905i
$441$		0			0
$442$		−	63.2274i		−	3.00742i
$443$	15.7375			0.747711			0.373855	−	0.927487i	$-0.378036\pi$
$443$	15.7375			0.747711			0.373855	+	0.927487i	$0.378036\pi$
$444$			15.4359i			0.732554i
$445$	0.154934			0.00734460
$446$	−48.0525			−2.27535
$447$	−18.4504			−0.872672
$448$		0			0
$449$	−14.0305			−0.662142			−0.331071	−	0.943606i	$-0.607410\pi$
$449$	−14.0305			−0.662142			−0.331071	+	0.943606i	$0.607410\pi$
$450$			9.64436i			0.454640i
$451$	−29.0778	−	4.78763i	−1.36922	−	0.225441i
$452$	−8.09389			−0.380705
$453$	−9.66091			−0.453909
$454$		−	6.65886i		−	0.312516i
$455$		0			0
$456$	−0.322606			−0.0151074
$457$			32.7246i			1.53079i	0.643560	+	0.765396i	$0.277457\pi$
$457$			32.7246i			1.53079i	−0.643560	+	0.765396i	$0.722543\pi$
$458$	43.3563			2.02591
$459$			5.87420i			0.274184i
$460$			1.94704i			0.0907813i
$461$	17.3441			0.807795			0.403897	−	0.914804i	$-0.367655\pi$
$461$	17.3441			0.807795			0.403897	+	0.914804i	$0.367655\pi$
$462$		0			0
$463$	−28.3707			−1.31850			−0.659250	−	0.751924i	$-0.729126\pi$
$463$	−28.3707			−1.31850			−0.659250	+	0.751924i	$0.729126\pi$
$464$		−	8.35419i		−	0.387833i
$465$		−	2.10603i		−	0.0976649i
$466$	15.7473			0.729478
$467$			35.6525i			1.64980i	0.565279	+	0.824899i	$0.308768\pi$
$467$			35.6525i			1.64980i	−0.565279	+	0.824899i	$0.691232\pi$
$468$	−10.4659			−0.483786
$469$		0			0
$470$			4.55082i			0.209913i
$471$	13.2694			0.611423
$472$	1.23903			0.0570311
$473$	3.18287	−	19.3312i	0.146348	−	0.888851i
$474$		−	3.64228i		−	0.167295i
$475$	−10.8264			−0.496747
$476$		0			0
$477$	12.9400			0.592483
$478$	36.3943			1.66464
$479$	26.2681			1.20022			0.600111	−	0.799917i	$-0.295123\pi$
$479$	26.2681			1.20022			0.600111	+	0.799917i	$0.295123\pi$
$480$			2.88782i			0.131810i
$481$	43.5139			1.98406
$482$		−	18.1888i		−	0.828478i
$483$		0			0
$484$	−20.0761	−	6.79524i	−0.912552	−	0.308874i
$485$	3.68273			0.167224
$486$	1.98162			0.0898881
$487$	−26.4237			−1.19737			−0.598687	−	0.800983i	$-0.704311\pi$
$487$	−26.4237			−1.19737			−0.598687	+	0.800983i	$0.704311\pi$
$488$		−	0.392590i		−	0.0177717i
$489$		−	7.93302i		−	0.358744i
$490$		0			0
$491$			16.9030i			0.762823i	0.924405	+	0.381412i	$0.124562\pi$
$491$			16.9030i			0.762823i	−0.924405	+	0.381412i	$0.875438\pi$
$492$			17.1204i			0.771848i
$493$		−	11.8508i		−	0.533731i
$494$		−	23.9434i		−	1.07726i
$495$	−0.196570	+	1.19388i	−0.00883519	+	0.0536608i
$496$			23.9056i			1.07339i
$497$		0			0
$498$	10.3325			0.463011
$499$	−25.6181			−1.14682			−0.573411	−	0.819268i	$-0.694380\pi$
$499$	−25.6181			−1.14682			−0.573411	+	0.819268i	$0.694380\pi$
$500$			6.93574i			0.310176i
$501$		−	0.682227i		−	0.0304796i
$502$	−51.1157			−2.28141
$503$	−11.1759			−0.498307			−0.249153	−	0.968464i	$-0.580152\pi$
$503$	−11.1759			−0.498307			−0.249153	+	0.968464i	$0.580152\pi$
$504$		0			0
$505$			5.56199i			0.247505i
$506$	2.95754	−	17.9627i	0.131479	−	0.798540i
$507$			16.5034i			0.732942i
$508$			27.6358i			1.22614i
$509$			16.2623i			0.720814i	0.932795	+	0.360407i	$0.117362\pi$
$509$			16.2623i			0.720814i	−0.932795	+	0.360407i	$0.882638\pi$
$510$			4.24659i			0.188042i
$511$		0			0
$512$		−	31.5786i		−	1.39559i
$513$			2.22448i			0.0982133i
$514$	11.7106			0.516531
$515$	1.92738			0.0849307
$516$	−11.3818			−0.501057
$517$	3.39191	−	20.6009i	0.149176	−	0.906025i
$518$		0			0
$519$		−	1.49877i		−	0.0657887i
$520$	0.287377			0.0126023
$521$		−	39.4761i		−	1.72948i	−0.502222	−	0.864739i	$-0.667484\pi$
$521$		−	39.4761i		−	1.72948i	0.502222	−	0.864739i	$-0.332516\pi$
$522$	−3.99777			−0.174978
$523$	−5.41900			−0.236956			−0.118478	−	0.992957i	$-0.537802\pi$
$523$	−5.41900			−0.236956			−0.118478	+	0.992957i	$0.537802\pi$
$524$	9.83733			0.429746
$525$		0			0
$526$	38.4706			1.67740
$527$			33.9111i			1.47719i
$528$	2.23128	−	13.5517i	0.0971038	−	0.589763i
$529$	−15.3277			−0.666420
$530$	9.35464			0.406340
$531$		−	8.54356i		−	0.370759i
$532$		0			0
$533$	48.2626			2.09048
$534$			0.841582i			0.0364188i
$535$	1.42690			0.0616901
$536$			2.11950i			0.0915486i
$537$		−	6.21242i		−	0.268086i
$538$	−56.2878			−2.42674
$539$		0			0
$540$	0.702929			0.0302493
$541$		−	39.9434i		−	1.71730i	−0.512560	−	0.858651i	$-0.671303\pi$
$541$		−	39.9434i		−	1.71730i	0.512560	−	0.858651i	$-0.328697\pi$
$542$		−	31.2723i		−	1.34326i
$543$	9.87854			0.423929
$544$		−	46.4994i		−	1.99364i
$545$	−2.31948			−0.0993557
$546$		0			0
$547$			16.5342i			0.706952i	0.935444	+	0.353476i	$0.115000\pi$
$547$			16.5342i			0.706952i	−0.935444	+	0.353476i	$0.885000\pi$
$548$	4.60534			0.196730
$549$	−2.70704			−0.115534
$550$	5.19661	−	31.5618i	0.221584	−	1.34580i
$551$		−	4.48773i		−	0.191184i
$552$	0.401706			0.0170977
$553$		0			0
$554$	−33.8034			−1.43617
$555$	−2.92256			−0.124056
$556$	−31.1457			−1.32087
$557$			19.8094i			0.839352i	0.907674	+	0.419676i	$0.137856\pi$
$557$			19.8094i			0.839352i	−0.907674	+	0.419676i	$0.862144\pi$
$558$	11.4397			0.484280
$559$			32.0854i			1.35707i
$560$		0			0
$561$	3.16516	−	19.2237i	0.133633	−	0.811625i
$562$	−52.6638			−2.22149
$563$	4.26760			0.179858			0.0899289	−	0.995948i	$-0.471336\pi$
$563$	4.26760			0.179858			0.0899289	+	0.995948i	$0.471336\pi$
$564$	−12.1293			−0.510738
$565$		−	1.53246i		−	0.0644711i
$566$		−	18.9724i		−	0.797468i
$567$		0			0
$568$		−	0.383677i		−	0.0160987i
$569$		−	11.7556i		−	0.492818i	−0.969166	−	0.246409i	$-0.920749\pi$
$569$		−	11.7556i		−	0.492818i	0.969166	−	0.246409i	$-0.0792507\pi$
$570$			1.60813i			0.0673571i
$571$			19.8817i			0.832025i	0.909359	+	0.416012i	$0.136573\pi$
$571$			19.8817i			0.832025i	−0.909359	+	0.416012i	$0.863427\pi$
$572$	34.2503	+	5.63927i	1.43208	+	0.235790i
$573$			0.879492i			0.0367413i
$574$		0			0
$575$	13.4808			0.562190
$576$	−7.40420			−0.308508
$577$		−	0.281564i		−	0.0117217i	−0.999983	−	0.00586083i	$-0.998134\pi$
$577$		−	0.281564i		−	0.0117217i	0.999983	−	0.00586083i	$-0.00186557\pi$
$578$		−	34.6907i		−	1.44294i
$579$	22.3397			0.928404
$580$	−1.41811			−0.0588837
$581$		0			0
$582$			20.0041i			0.829196i
$583$	−42.3471	−	6.97240i	−1.75384	−	0.288767i
$584$		−	0.844575i		−	0.0349488i
$585$		−	1.98156i		−	0.0819275i
$586$		−	33.4625i		−	1.38233i
$587$			2.55977i			0.105653i	0.998604	+	0.0528265i	$0.0168230\pi$
$587$			2.55977i			0.105653i	−0.998604	+	0.0528265i	$0.983177\pi$
$588$		0			0
$589$			12.8417i			0.529133i
$590$		−	6.17634i		−	0.254276i
$591$	1.93301			0.0795135
$592$	33.1740			1.36344
$593$	−17.3493			−0.712448			−0.356224	−	0.934401i	$-0.615936\pi$
$593$	−17.3493			−0.712448			−0.356224	+	0.934401i	$0.615936\pi$
$594$	−6.48497	−	1.06774i	−0.266082	−	0.0438100i
$595$		0			0
$596$		−	35.5504i		−	1.45620i
$597$	2.02755			0.0829823
$598$			29.8140i			1.21918i
$599$	6.85842			0.280228			0.140114	−	0.990135i	$-0.455253\pi$
$599$	6.85842			0.280228			0.140114	+	0.990135i	$0.455253\pi$
$600$	0.705825			0.0288152
$601$	1.68577			0.0687641			0.0343821	−	0.999409i	$-0.489054\pi$
$601$	1.68577			0.0687641			0.0343821	+	0.999409i	$0.489054\pi$
$602$		0			0
$603$	14.6147			0.595157
$604$		−	18.6148i		−	0.757425i
$605$	1.28658	−	3.80112i	0.0523069	−	0.154538i
$606$	−30.2120			−1.22728
$607$	16.5150			0.670324			0.335162	−	0.942160i	$-0.391209\pi$
$607$	16.5150			0.670324			0.335162	+	0.942160i	$0.391209\pi$
$608$		−	17.6087i		−	0.714127i
$609$		0			0
$610$	−1.95698			−0.0792359
$611$			34.1927i			1.38329i
$612$	−11.3185			−0.457523
$613$			22.5205i			0.909596i	0.890595	+	0.454798i	$0.150289\pi$
$613$			22.5205i			0.909596i	−0.890595	+	0.454798i	$0.849711\pi$
$614$		−	3.11167i		−	0.125577i
$615$	−3.24150			−0.130710
$616$		0			0
$617$	28.3379			1.14084			0.570421	−	0.821353i	$-0.306780\pi$
$617$	28.3379			1.14084			0.570421	+	0.821353i	$0.306780\pi$
$618$			10.4693i			0.421136i
$619$		−	16.7815i		−	0.674507i	−0.941414	−	0.337253i	$-0.890502\pi$
$619$		−	16.7815i		−	0.674507i	0.941414	−	0.337253i	$-0.109498\pi$
$620$	4.05793			0.162971
$621$		−	2.76990i		−	0.111152i
$622$	47.7016			1.91266
$623$		0			0
$624$			22.4928i			0.900431i
$625$	23.0214			0.920855
$626$	−0.946322			−0.0378227
$627$	1.19860	−	7.27976i	0.0478676	−	0.290726i
$628$			25.5677i			1.02026i
$629$	47.0587			1.87635
$630$		0			0
$631$	−11.8060			−0.469991			−0.234995	−	0.971997i	$-0.575507\pi$
$631$	−11.8060			−0.469991			−0.234995	+	0.971997i	$0.575507\pi$
$632$	−0.266561			−0.0106032
$633$	8.17186			0.324802
$634$			18.6554i			0.740899i
$635$	−5.23243			−0.207643
$636$			24.9330i			0.988660i
$637$		0			0
$638$	13.0830	+	2.15409i	0.517959	+	0.0852813i
$639$	−2.64558			−0.104658
$640$	0.422975			0.0167196
$641$	17.8022			0.703143			0.351572	−	0.936161i	$-0.385647\pi$
$641$	17.8022			0.703143			0.351572	+	0.936161i	$0.385647\pi$
$642$			7.75070i			0.305896i
$643$		−	35.8544i		−	1.41396i	−0.707233	−	0.706980i	$-0.750057\pi$
$643$		−	35.8544i		−	1.41396i	0.707233	−	0.706980i	$-0.249943\pi$
$644$		0			0
$645$		−	2.15498i		−	0.0848523i
$646$		−	25.8939i		−	1.01878i
$647$			40.1101i			1.57689i	0.615106	+	0.788444i	$0.289113\pi$
$647$			40.1101i			1.57689i	−0.615106	+	0.788444i	$0.710887\pi$
$648$		−	0.145025i		−	0.00569713i
$649$	−4.60347	+	27.9594i	−0.180702	+	1.09750i
$650$			52.3853i			2.05472i
$651$		0			0
$652$	15.2855			0.598625
$653$	8.61336			0.337067			0.168533	−	0.985696i	$-0.446097\pi$
$653$	8.61336			0.337067			0.168533	+	0.985696i	$0.446097\pi$
$654$		−	12.5991i		−	0.492664i
$655$			1.86255i			0.0727760i
$656$	36.7943			1.43658
$657$	−5.82364			−0.227202
$658$		0			0
$659$			16.0122i			0.623745i	0.950124	+	0.311873i	$0.100956\pi$
$659$			16.0122i			0.623745i	−0.950124	+	0.311873i	$0.899044\pi$
$660$	−2.30038	−	0.378755i	−0.0895422	−	0.0147430i
$661$		−	33.7807i		−	1.31392i	−0.753927	−	0.656958i	$-0.771843\pi$
$661$		−	33.7807i		−	1.31392i	0.753927	−	0.656958i	$-0.228157\pi$
$662$		−	37.2517i		−	1.44783i
$663$			31.9069i			1.23916i
$664$		−	0.756188i		−	0.0293458i
$665$		0			0
$666$		−	15.8749i		−	0.615141i
$667$			5.58806i			0.216371i
$668$	1.31452			0.0508605
$669$	24.2491			0.937525
$670$	10.5653			0.408173
$671$	8.85897	+	1.45862i	0.341997	+	0.0563094i
$672$		0			0
$673$			39.0078i			1.50364i	0.659368	+	0.751820i	$0.270824\pi$
$673$			39.0078i			1.50364i	−0.659368	+	0.751820i	$0.729176\pi$
$674$	−10.8431			−0.417662
$675$		−	4.86691i		−	0.187327i
$676$	−31.7990			−1.22304
$677$	22.9055			0.880329			0.440164	−	0.897917i	$-0.354920\pi$
$677$	22.9055			0.880329			0.440164	+	0.897917i	$0.354920\pi$
$678$	8.32411			0.319685
$679$		0			0
$680$	0.310788			0.0119182
$681$			3.36031i			0.128768i
$682$	−37.4370	−	6.16397i	−1.43354	−	0.236030i
$683$	−32.6741			−1.25024			−0.625120	−	0.780529i	$-0.714950\pi$
$683$	−32.6741			−1.25024			−0.625120	+	0.780529i	$0.714950\pi$
$684$	−4.28617			−0.163886
$685$			0.871953i			0.0333156i
$686$		0			0
$687$	−21.8792			−0.834745
$688$			24.4612i			0.932576i
$689$	70.2864			2.67770
$690$		−	2.00242i		−	0.0762309i
$691$		−	23.3420i		−	0.887973i	−0.896033	−	0.443986i	$-0.853564\pi$
$691$		−	23.3420i		−	0.887973i	0.896033	−	0.443986i	$-0.146436\pi$
$692$	2.88785			0.109780
$693$		0			0
$694$	−35.2074			−1.33646
$695$		−	5.89699i		−	0.223686i
$696$			0.292578i			0.0110901i
$697$	52.1943			1.97700
$698$			60.5668i			2.29249i
$699$	−7.94667			−0.300570
$700$		0			0
$701$			41.9176i			1.58321i	0.611036	+	0.791603i	$0.290753\pi$
$701$			41.9176i			1.58321i	−0.611036	+	0.791603i	$0.709247\pi$
$702$	10.7636			0.406245
$703$	17.8205			0.672114
$704$	24.2307	+	3.98956i	0.913229	+	0.150362i
$705$		−	2.29651i		−	0.0864917i
$706$	32.5862			1.22640
$707$		0			0
$708$	16.4619			0.618675
$709$	−31.3943			−1.17904			−0.589519	−	0.807754i	$-0.700683\pi$
$709$	−31.3943			−1.17904			−0.589519	+	0.807754i	$0.700683\pi$
$710$	−1.91255			−0.0717768
$711$			1.83803i			0.0689315i
$712$	0.0615914			0.00230824
$713$		−	15.9903i		−	0.598842i
$714$		0			0
$715$	−1.06771	+	6.48479i	−0.0399302	+	0.242517i
$716$	11.9702			0.447347
$717$	−18.3659			−0.685889
$718$	−66.5192			−2.48247
$719$		−	0.658961i		−	0.0245751i	−0.999925	−	0.0122876i	$-0.996089\pi$
$719$		−	0.658961i		−	0.0245751i	0.999925	−	0.0122876i	$-0.00391135\pi$
$720$		−	1.51070i		−	0.0563005i
$721$		0			0
$722$			27.8451i			1.03629i
$723$			9.17876i			0.341362i
$724$			19.0341i			0.707397i
$725$			9.81863i			0.364655i
$726$	20.6472	+	6.98851i	0.766288	+	0.259368i
$727$		−	3.90800i		−	0.144940i	−0.997371	−	0.0724698i	$-0.976912\pi$
$727$		−	3.90800i		−	0.144940i	0.997371	−	0.0724698i	$-0.0230881\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−4.21004			−0.155820
$731$			34.6993i			1.28340i
$732$		−	5.21597i		−	0.192788i
$733$	−32.1358			−1.18696			−0.593482	−	0.804848i	$-0.702247\pi$
$733$	−32.1358			−1.18696			−0.593482	+	0.804848i	$0.702247\pi$
$734$	12.0380			0.444331
$735$		0			0
$736$			21.9261i			0.808208i
$737$	−47.8275	−	7.87475i	−1.76175	−	0.290070i
$738$		−	17.6074i		−	0.648136i
$739$		−	10.0522i		−	0.369776i	−0.982760	−	0.184888i	$-0.940808\pi$
$739$		−	10.0522i		−	0.369776i	0.982760	−	0.184888i	$-0.0591922\pi$
$740$		−	5.63123i		−	0.207008i
$741$			12.0827i			0.443870i
$742$		0			0
$743$		−	1.22246i		−	0.0448476i	−0.999749	−	0.0224238i	$-0.992862\pi$
$743$		−	1.22246i		−	0.0448476i	0.999749	−	0.0224238i	$-0.00713831\pi$
$744$		−	0.837216i		−	0.0306938i
$745$	6.73095			0.246603
$746$	−69.2347			−2.53486
$747$	−5.21418			−0.190777
$748$	37.0405	+	6.09867i	1.35433	+	0.222990i
$749$		0			0
$750$		−	7.13301i		−	0.260461i
$751$	7.55892			0.275829			0.137914	−	0.990444i	$-0.455960\pi$
$751$	7.55892			0.275829			0.137914	+	0.990444i	$0.455960\pi$
$752$			26.0678i			0.950594i
$753$	25.7949			0.940019
$754$	−21.7147			−0.790803
$755$	3.52444			0.128267
$756$		0			0
$757$	−12.3734			−0.449721			−0.224860	−	0.974391i	$-0.572193\pi$
$757$	−12.3734			−0.449721			−0.224860	+	0.974391i	$0.572193\pi$
$758$			28.1324i			1.02182i
$759$	−1.49249	+	9.06467i	−0.0541738	+	0.329027i
$760$	0.117691			0.00426911
$761$	−53.8122			−1.95069			−0.975346	−	0.220683i	$-0.929171\pi$
$761$	−53.8122			−1.95069			−0.975346	+	0.220683i	$0.929171\pi$
$762$		−	28.4218i		−	1.02961i
$763$		0			0
$764$	−1.69462			−0.0613091
$765$		−	2.14299i		−	0.0774800i
$766$	−37.4111			−1.35172
$767$		−	46.4061i		−	1.67563i
$768$			17.1059i			0.617257i
$769$	22.8557			0.824199			0.412099	−	0.911139i	$-0.364796\pi$
$769$	22.8557			0.824199			0.412099	+	0.911139i	$0.364796\pi$
$770$		0			0
$771$	−5.90959			−0.212829
$772$			43.0444i			1.54920i
$773$			11.6753i			0.419932i	0.977709	+	0.209966i	$0.0673353\pi$
$773$			11.6753i			0.419932i	−0.977709	+	0.209966i	$0.932665\pi$
$774$	11.7056			0.420747
$775$		−	28.0961i		−	1.00924i
$776$	1.46400			0.0525547
$777$		0			0
$778$			7.21881i			0.258807i
$779$	19.7653			0.708165
$780$	3.81810			0.136710
$781$	8.65784	+	1.42550i	0.309802	+	0.0510085i
$782$			32.2428i			1.15300i
$783$	2.01743			0.0720969
$784$		0			0
$785$	−4.84087			−0.172778
$786$	−10.1171			−0.360866
$787$	−12.1319			−0.432456			−0.216228	−	0.976343i	$-0.569375\pi$
$787$	−12.1319			−0.432456			−0.216228	+	0.976343i	$0.569375\pi$
$788$			3.72456i			0.132682i
$789$	−19.4137			−0.691146
$790$			1.32875i			0.0472749i
$791$		0			0
$792$	−0.0781431	+	0.474605i	−0.00277669	+	0.0168643i
$793$	−14.7039			−0.522149
$794$	−37.0979			−1.31656
$795$	−4.72071			−0.167426
$796$			3.90672i			0.138470i
$797$		−	1.57399i		−	0.0557537i	−0.999611	−	0.0278769i	$-0.991125\pi$
$797$		−	1.57399i		−	0.0557537i	0.999611	−	0.0278769i	$-0.00887463\pi$
$798$		0			0
$799$			36.9782i			1.30820i
$800$			38.5258i			1.36209i
$801$		−	0.424694i		−	0.0150058i
$802$		−	38.5460i		−	1.36111i
$803$	19.0582	+	3.13791i	0.672550	+	0.110735i
$804$			28.1598i			0.993120i
$805$		0			0
$806$	62.1369			2.18868
$807$	28.4049			0.999901
$808$			2.21107i			0.0777852i
$809$			48.8998i			1.71922i	0.510947	+	0.859612i	$0.329295\pi$
$809$			48.8998i			1.71922i	−0.510947	+	0.859612i	$0.670705\pi$
$810$	−0.722923			−0.0254009
$811$	46.4357			1.63058			0.815290	−	0.579053i	$-0.196578\pi$
$811$	46.4357			1.63058			0.815290	+	0.579053i	$0.196578\pi$
$812$		0			0
$813$			15.7812i			0.553470i
$814$	−8.55378	+	51.9517i	−0.299810	+	1.82091i
$815$			2.89408i			0.101375i
$816$			24.3251i			0.851551i
$817$			13.1402i			0.459716i
$818$		−	7.96170i		−	0.278374i
$819$		0			0
$820$		−	6.24577i		−	0.218112i
$821$			19.8601i			0.693121i	0.938028	+	0.346560i	$0.112650\pi$
$821$			19.8601i			0.693121i	−0.938028	+	0.346560i	$0.887350\pi$
$822$	−4.73633			−0.165198
$823$	−19.0601			−0.664393			−0.332197	−	0.943210i	$-0.607790\pi$
$823$	−19.0601			−0.664393			−0.332197	+	0.943210i	$0.607790\pi$
$824$	0.766197			0.0266917
$825$	−2.62241	+	15.9273i	−0.0913005	+	0.554516i
$826$		0			0
$827$		−	37.0755i		−	1.28924i	−0.764502	−	0.644621i	$-0.777015\pi$
$827$		−	37.0755i		−	1.28924i	0.764502	−	0.644621i	$-0.222985\pi$
$828$	5.33708			0.185476
$829$		−	5.80581i		−	0.201644i	−0.994904	−	0.100822i	$-0.967853\pi$
$829$		−	5.80581i		−	0.201644i	0.994904	−	0.100822i	$-0.0321473\pi$
$830$	−3.76945			−0.130839
$831$	17.0585			0.591752
$832$	−40.2174			−1.39429
$833$		0			0
$834$	32.0316			1.10916
$835$			0.248886i			0.00861305i
$836$	14.0267	+	2.30949i	0.485125	+	0.0798753i
$837$	−5.77289			−0.199540
$838$	37.2069			1.28529
$839$			11.3409i			0.391530i	0.980651	+	0.195765i	$0.0627190\pi$
$839$			11.3409i			0.391530i	−0.980651	+	0.195765i	$0.937281\pi$
$840$		0			0
$841$	24.9300			0.859655
$842$		−	74.8727i		−	2.58028i
$843$	26.5761			0.915331
$844$			15.7457i			0.541988i
$845$		−	6.02068i		−	0.207118i
$846$	12.4743			0.428877
$847$		0			0
$848$	53.5849			1.84011
$849$			9.57418i			0.328585i
$850$			56.6529i			1.94318i
$851$	−22.1899			−0.760660
$852$		−	5.09755i		−	0.174639i
$853$	−13.7963			−0.472377			−0.236189	−	0.971707i	$-0.575898\pi$
$853$	−13.7963			−0.472377			−0.236189	+	0.971707i	$0.575898\pi$
$854$		0			0
$855$		−	0.811523i		−	0.0277535i
$856$	0.567237			0.0193878
$857$	−30.5730			−1.04435			−0.522177	−	0.852837i	$-0.674880\pi$
$857$	−30.5730			−1.04435			−0.522177	+	0.852837i	$0.674880\pi$
$858$	−35.2245	−	5.79967i	−1.20254	−	0.197997i
$859$			40.5872i			1.38482i	0.721505	+	0.692410i	$0.243451\pi$
$859$			40.5872i			1.38482i	−0.721505	+	0.692410i	$0.756549\pi$
$860$	4.15225			0.141590
$861$		0			0
$862$	−24.2322			−0.825351
$863$	29.2067			0.994206			0.497103	−	0.867691i	$-0.334397\pi$
$863$	29.2067			0.994206			0.497103	+	0.867691i	$0.334397\pi$
$864$	7.91586			0.269303
$865$			0.546772i			0.0185908i
$866$	−29.8427			−1.01410
$867$			17.5062i			0.594543i
$868$		0			0
$869$	0.990374	−	6.01507i	0.0335961	−	0.204047i
$870$	1.45844			0.0494458
$871$	79.3827			2.68978
$872$	−0.922069			−0.0312252
$873$		−	10.0948i		−	0.341658i
$874$			12.2099i			0.413007i
$875$		0			0
$876$		−	11.2211i		−	0.379125i
$877$		−	13.4625i		−	0.454596i	−0.973825	−	0.227298i	$-0.927011\pi$
$877$		−	13.4625i		−	0.454596i	0.973825	−	0.227298i	$-0.0729892\pi$
$878$		−	30.3900i		−	1.02561i
$879$			16.8865i			0.569566i
$880$	−0.814001	+	4.94386i	−0.0274400	+	0.166658i
$881$			47.1355i			1.58803i	0.607896	+	0.794017i	$0.292014\pi$
$881$			47.1355i			1.58803i	−0.607896	+	0.794017i	$0.707986\pi$
$882$		0			0
$883$	6.67601			0.224666			0.112333	−	0.993671i	$-0.464168\pi$
$883$	6.67601			0.224666			0.112333	+	0.993671i	$0.464168\pi$
$884$	−61.4787			−2.06775
$885$			3.11681i			0.104771i
$886$		−	31.1857i		−	1.04770i
$887$	6.43271			0.215989			0.107995	−	0.994151i	$-0.465557\pi$
$887$	6.43271			0.215989			0.107995	+	0.994151i	$0.465557\pi$
$888$	−1.16181			−0.0389878
$889$		0			0
$890$		−	0.307021i		−	0.0102914i
$891$	3.27256	+	0.538824i	0.109635	+	0.0180513i
$892$			46.7236i			1.56442i
$893$			14.0032i			0.468598i
$894$			36.5616i			1.22280i
$895$			2.26638i			0.0757567i
$896$		0			0
$897$		−	15.0453i		−	0.502347i
$898$			27.8032i			0.927805i
$899$	11.6464			0.388428
$900$	9.37764			0.312588
$901$	76.0124			2.53234
$902$	−9.48727	+	57.6212i	−0.315891	+	1.91858i
$903$		0			0
$904$		−	0.609202i		−	0.0202618i
$905$	−3.60383			−0.119795
$906$			19.1443i			0.636025i
$907$	−41.3676			−1.37359			−0.686795	−	0.726851i	$-0.740983\pi$
$907$	−41.3676			−1.37359			−0.686795	+	0.726851i	$0.740983\pi$
$908$	−6.47470			−0.214871
$909$	15.2461			0.505681
$910$		0			0
$911$	−42.9021			−1.42141			−0.710705	−	0.703490i	$-0.751624\pi$
$911$	−42.9021			−1.42141			−0.710705	+	0.703490i	$0.751624\pi$
$912$			9.21161i			0.305027i
$913$	17.0637	+	2.80952i	0.564727	+	0.0929816i
$914$	64.8476			2.14497
$915$	0.987568			0.0326480
$916$		−	42.1572i		−	1.39291i
$917$		0			0
$918$	11.6404			0.384191
$919$			24.3322i			0.802647i	0.915936	+	0.401323i	$0.131450\pi$
$919$			24.3322i			0.802647i	−0.915936	+	0.401323i	$0.868550\pi$
$920$	−0.146548			−0.00483154
$921$			1.57027i			0.0517421i
$922$		−	34.3694i		−	1.13190i
$923$	−14.3700			−0.472995
$924$		0			0
$925$	−38.9892			−1.28196
$926$			56.2200i			1.84750i
$927$		−	5.28319i		−	0.173523i
$928$	−15.9697			−0.524230
$929$		−	37.9911i		−	1.24645i	−0.782044	−	0.623224i	$-0.785823\pi$
$929$		−	37.9911i		−	1.24645i	0.782044	−	0.623224i	$-0.214177\pi$
$930$	−4.17335			−0.136850
$931$		0			0
$932$		−	15.3118i		−	0.501553i
$933$	−24.0720			−0.788082
$934$	70.6496			2.31173
$935$	−1.15469	+	7.01307i	−0.0377625	+	0.229352i
$936$		−	0.787735i		−	0.0257479i
$937$	−31.8024			−1.03894			−0.519469	−	0.854489i	$-0.673870\pi$
$937$	−31.8024			−1.03894			−0.519469	+	0.854489i	$0.673870\pi$
$938$		0			0
$939$	0.477550			0.0155843
$940$	4.42496			0.144326
$941$	−5.07658			−0.165492			−0.0827460	−	0.996571i	$-0.526369\pi$
$941$	−5.07658			−0.165492			−0.0827460	+	0.996571i	$0.526369\pi$
$942$		−	26.2949i		−	0.856736i
$943$	−24.6115			−0.801461
$944$		−	35.3790i		−	1.15149i
$945$		0			0
$946$	−38.3072	−	6.30723i	−1.24547	−	0.205066i
$947$	−41.0883			−1.33519			−0.667595	−	0.744525i	$-0.732676\pi$
$947$	−41.0883			−1.33519			−0.667595	+	0.744525i	$0.732676\pi$
$948$	−3.54154			−0.115024
$949$	−31.6323			−1.02683
$950$			21.4537i			0.696050i
$951$		−	9.41420i		−	0.305276i
$952$		0			0
$953$		−	1.56947i		−	0.0508402i	−0.999677	−	0.0254201i	$-0.991908\pi$
$953$		−	1.56947i		−	0.0508402i	0.999677	−	0.0254201i	$-0.00809234\pi$
$954$		−	25.6422i		−	0.830198i
$955$		−	0.320851i		−	0.0103825i
$956$		−	35.3878i		−	1.14452i
$957$	−6.60215	−	1.08704i	−0.213417	−	0.0351389i
$958$		−	52.0535i		−	1.68177i
$959$		0			0
$960$	2.70116			0.0871794
$961$	−2.32627			−0.0750410
$962$		−	86.2279i		−	2.78010i
$963$		−	3.91130i		−	0.126040i
$964$	−17.6858			−0.569621
$965$	−8.14982			−0.262352
$966$		0			0
$967$		−	45.6739i		−	1.46877i	−0.678732	−	0.734386i	$-0.737470\pi$
$967$		−	45.6739i		−	1.46877i	0.678732	−	0.734386i	$-0.262530\pi$
$968$	0.511456	−	1.51107i	0.0164388	−	0.0485676i
$969$			13.0671i			0.419774i
$970$		−	7.29777i		−	0.234317i
$971$			5.62141i			0.180400i	0.995924	+	0.0901998i	$0.0287506\pi$
$971$			5.62141i			0.180400i	−0.995924	+	0.0901998i	$0.971249\pi$
$972$		−	1.92681i		−	0.0618026i
$973$		0			0
$974$			52.3618i			1.67778i
$975$		−	26.4356i		−	0.846617i
$976$	−11.2099			−0.358820
$977$	3.97230			0.127085			0.0635426	−	0.997979i	$-0.479760\pi$
$977$	3.97230			0.127085			0.0635426	+	0.997979i	$0.479760\pi$
$978$	−15.7202			−0.502677
$979$	−0.228835	+	1.38984i	−0.00731361	+	0.0444194i
$980$		0			0
$981$			6.35799i			0.202995i
$982$	33.4954			1.06888
$983$		−	35.8780i		−	1.14433i	−0.820139	−	0.572165i	$-0.806104\pi$
$983$		−	35.8780i		−	1.14433i	0.820139	−	0.572165i	$-0.193896\pi$
$984$	−1.28860			−0.0410791
$985$	−0.705190			−0.0224692
$986$	−23.4837			−0.747873
$987$		0			0
$988$	−23.2812			−0.740673
$989$		−	16.3620i		−	0.520280i
$990$	2.36581	+	0.389528i	0.0751904	+	0.0123800i
$991$	−17.6565			−0.560879			−0.280439	−	0.959872i	$-0.590480\pi$
$991$	−17.6565			−0.560879			−0.280439	+	0.959872i	$0.590480\pi$
$992$	45.6974			1.45089
$993$			18.7986i			0.596557i
$994$		0			0
$995$	−0.739680			−0.0234494
$996$		−	10.0468i		−	0.318344i
$997$	−39.3038			−1.24476			−0.622382	−	0.782713i	$-0.713835\pi$
$997$	−39.3038			−1.24476			−0.622382	+	0.782713i	$0.713835\pi$
$998$			50.7653i			1.60695i
$999$			8.01109i			0.253460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.6		32
7.4	even	3		231.2.p.a.208.14	yes	32
7.5	odd	6		231.2.p.a.10.3	✓	32
7.6	odd	2	inner	1617.2.c.a.538.5		32
11.10	odd	2	inner	1617.2.c.a.538.28		32
21.5	even	6		693.2.bg.b.10.14		32
21.11	odd	6		693.2.bg.b.208.3		32
77.32	odd	6		231.2.p.a.208.3	yes	32
77.54	even	6		231.2.p.a.10.14	yes	32
77.76	even	2	inner	1617.2.c.a.538.27		32
231.32	even	6		693.2.bg.b.208.14		32
231.131	odd	6		693.2.bg.b.10.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.3	✓	32	7.5	odd	6
231.2.p.a.10.14	yes	32	77.54	even	6
231.2.p.a.208.3	yes	32	77.32	odd	6
231.2.p.a.208.14	yes	32	7.4	even	3
693.2.bg.b.10.3		32	231.131	odd	6
693.2.bg.b.10.14		32	21.5	even	6
693.2.bg.b.208.3		32	21.11	odd	6
693.2.bg.b.208.14		32	231.32	even	6
1617.2.c.a.538.5		32	7.6	odd	2	inner
1617.2.c.a.538.6		32	1.1	even	1	trivial
1617.2.c.a.538.27		32	77.76	even	2	inner
1617.2.c.a.538.28		32	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.98162i q^{2} +1.00000i q^{3} -1.92681 q^{4} -0.364814i q^{5} +1.98162 q^{6} -0.145025i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.98162i q^{2} +1.00000i q^{3} -1.92681 q^{4} -0.364814i q^{5} +1.98162 q^{6} -0.145025i q^{8} -1.00000 q^{9} -0.722923 q^{10} +(3.27256 + 0.538824i) q^{11} -1.92681i q^{12} -5.43170 q^{13} +0.364814 q^{15} -4.14101 q^{16} -5.87420 q^{17} +1.98162i q^{18} -2.22448 q^{19} +0.702929i q^{20} +(1.06774 - 6.48497i) q^{22} +2.76990 q^{23} +0.145025 q^{24} +4.86691 q^{25} +10.7636i q^{26} -1.00000i q^{27} +2.01743i q^{29} -0.722923i q^{30} -5.77289i q^{31} +7.91586i q^{32} +(-0.538824 + 3.27256i) q^{33} +11.6404i q^{34} +1.92681 q^{36} -8.01109 q^{37} +4.40808i q^{38} -5.43170i q^{39} -0.0529073 q^{40} -8.88534 q^{41} -5.90706i q^{43} +(-6.30562 - 1.03821i) q^{44} +0.364814i q^{45} -5.48888i q^{46} -6.29502i q^{47} -4.14101i q^{48} -9.64436i q^{50} -5.87420i q^{51} +10.4659 q^{52} -12.9400 q^{53} -1.98162 q^{54} +(0.196570 - 1.19388i) q^{55} -2.22448i q^{57} +3.99777 q^{58} +8.54356i q^{59} -0.702929 q^{60} +2.70704 q^{61} -11.4397 q^{62} +7.40420 q^{64} +1.98156i q^{65} +(6.48497 + 1.06774i) q^{66} -14.6147 q^{67} +11.3185 q^{68} +2.76990i q^{69} +2.64558 q^{71} +0.145025i q^{72} +5.82364 q^{73} +15.8749i q^{74} +4.86691i q^{75} +4.28617 q^{76} -10.7636 q^{78} -1.83803i q^{79} +1.51070i q^{80} +1.00000 q^{81} +17.6074i q^{82} +5.21418 q^{83} +2.14299i q^{85} -11.7056 q^{86} -2.01743 q^{87} +(0.0781431 - 0.474605i) q^{88} +0.424694i q^{89} +0.722923 q^{90} -5.33708 q^{92} +5.77289 q^{93} -12.4743 q^{94} +0.811523i q^{95} -7.91586 q^{96} +10.0948i q^{97} +(-3.27256 - 0.538824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 24 * q^4 - 32 * q^9	\( 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Introduction

L-functions

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