LMFDB - Embedded newform 1890.2.d.e.1889.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1889,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1890.1889");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.d (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 3 x^{14} + 5 x^{12} + 15 x^{11} - 12 x^{10} + 381 x^{9} - 1356 x^{8} + 1905 x^{7} + \cdots + 390625 $ x^16 - 3x^15 + 3x^14 + 5x^12 + 15x^11 - 12x^10 + 381x^9 - 1356x^8 + 1905x^7 - 300x^6 + 1875x^5 + 3125x^4 + 46875x^2 - 234375*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1889.7
Root			$1.83661 - 1.27549i$ of defining polynomial
Character	$\chi$	$=$	1890.1889
Dual form			1890.2.d.e.1889.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.186305 - 2.22829i) q^{5} +(-0.479366 - 2.60196i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.186305 - 2.22829i) q^{5} +(-0.479366 - 2.60196i) q^{7} -1.00000 q^{8} +(0.186305 + 2.22829i) q^{10} +4.09292i q^{11} -3.65475 q^{13} +(0.479366 + 2.60196i) q^{14} +1.00000 q^{16} +3.32090i q^{17} -6.04543i q^{19} +(-0.186305 - 2.22829i) q^{20} -4.09292i q^{22} -1.60984 q^{23} +(-4.93058 + 0.830286i) q^{25} +3.65475 q^{26} +(-0.479366 - 2.60196i) q^{28} +7.52516i q^{29} +4.31338i q^{31} -1.00000 q^{32} -3.32090i q^{34} +(-5.70863 + 1.55293i) q^{35} -4.55854i q^{37} +6.04543i q^{38} +(0.186305 + 2.22829i) q^{40} -7.46175 q^{41} +1.77168i q^{43} +4.09292i q^{44} +1.60984 q^{46} -3.40032i q^{47} +(-6.54042 + 2.49458i) q^{49} +(4.93058 - 0.830286i) q^{50} -3.65475 q^{52} +1.14213 q^{53} +(9.12022 - 0.762532i) q^{55} +(0.479366 + 2.60196i) q^{56} -7.52516i q^{58} -4.39312 q^{59} -4.31338i q^{62} +1.00000 q^{64} +(0.680900 + 8.14387i) q^{65} +10.8888i q^{67} +3.32090i q^{68} +(5.70863 - 1.55293i) q^{70} +11.0685i q^{71} +5.75780 q^{73} +4.55854i q^{74} -6.04543i q^{76} +(10.6496 - 1.96200i) q^{77} +15.5802 q^{79} +(-0.186305 - 2.22829i) q^{80} +7.46175 q^{82} +1.58885i q^{83} +(7.39993 - 0.618701i) q^{85} -1.77168i q^{86} -4.09292i q^{88} +14.2131 q^{89} +(1.75196 + 9.50954i) q^{91} -1.60984 q^{92} +3.40032i q^{94} +(-13.4710 + 1.12630i) q^{95} +1.54485 q^{97} +(6.54042 - 2.49458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.186305	−	2.22829i	−0.0833183	−	0.996523i
$5$	−0.186305	−	2.22829i	−0.0833183	−	0.996523i
$6$		0			0
$7$	−0.479366	−	2.60196i	−0.181183	−	0.983449i
$7$	−0.479366	−	2.60196i	−0.181183	−	0.983449i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.186305	+	2.22829i	0.0589149	+	0.704648i
$11$			4.09292i			1.23406i	0.786939	+	0.617030i	$0.211664\pi$
$11$			4.09292i			1.23406i	−0.786939	+	0.617030i	$0.788336\pi$
$12$		0			0
$13$	−3.65475			−1.01365			−0.506823	−	0.862050i	$-0.669180\pi$
$13$	−3.65475			−1.01365			−0.506823	+	0.862050i	$0.669180\pi$
$14$	0.479366	+	2.60196i	0.128116	+	0.695404i
$15$		0			0
$16$	1.00000			0.250000
$17$			3.32090i			0.805436i	0.915324	+	0.402718i	$0.131934\pi$
$17$			3.32090i			0.805436i	−0.915324	+	0.402718i	$0.868066\pi$
$18$		0			0
$19$		−	6.04543i		−	1.38692i	−0.720496	−	0.693459i	$-0.756086\pi$
$19$		−	6.04543i		−	1.38692i	0.720496	−	0.693459i	$-0.243914\pi$
$20$	−0.186305	−	2.22829i	−0.0416591	−	0.498261i
$21$		0			0
$22$		−	4.09292i		−	0.872613i
$23$	−1.60984			−0.335674			−0.167837	−	0.985815i	$-0.553678\pi$
$23$	−1.60984			−0.335674			−0.167837	+	0.985815i	$0.553678\pi$
$24$		0			0
$25$	−4.93058	+	0.830286i	−0.986116	+	0.166057i
$26$	3.65475			0.716756
$27$		0			0
$28$	−0.479366	−	2.60196i	−0.0905916	−	0.491725i
$29$			7.52516i			1.39739i	0.715421	+	0.698694i	$0.246235\pi$
$29$			7.52516i			1.39739i	−0.715421	+	0.698694i	$0.753765\pi$
$30$		0			0
$31$			4.31338i			0.774706i	0.921931	+	0.387353i	$0.126611\pi$
$31$			4.31338i			0.774706i	−0.921931	+	0.387353i	$0.873389\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	3.32090i		−	0.569529i
$35$	−5.70863	+	1.55293i	−0.964934	+	0.262493i
$36$		0			0
$37$		−	4.55854i		−	0.749420i	−0.927142	−	0.374710i	$-0.877742\pi$
$37$		−	4.55854i		−	0.749420i	0.927142	−	0.374710i	$-0.122258\pi$
$38$			6.04543i			0.980699i
$39$		0			0
$40$	0.186305	+	2.22829i	0.0294575	+	0.352324i
$41$	−7.46175			−1.16533			−0.582665	−	0.812713i	$-0.697990\pi$
$41$	−7.46175			−1.16533			−0.582665	+	0.812713i	$0.697990\pi$
$42$		0			0
$43$			1.77168i			0.270178i	0.990833	+	0.135089i	$0.0431321\pi$
$43$			1.77168i			0.270178i	−0.990833	+	0.135089i	$0.956868\pi$
$44$			4.09292i			0.617030i
$45$		0			0
$46$	1.60984			0.237357
$47$		−	3.40032i		−	0.495987i	−0.968762	−	0.247994i	$-0.920229\pi$
$47$		−	3.40032i		−	0.495987i	0.968762	−	0.247994i	$-0.0797712\pi$
$48$		0			0
$49$	−6.54042	+	2.49458i	−0.934345	+	0.356369i
$50$	4.93058	−	0.830286i	0.697289	−	0.117420i
$51$		0			0
$52$	−3.65475			−0.506823
$53$	1.14213			0.156883			0.0784416	−	0.996919i	$-0.475006\pi$
$53$	1.14213			0.156883			0.0784416	+	0.996919i	$0.475006\pi$
$54$		0			0
$55$	9.12022	−	0.762532i	1.22977	−	0.102820i
$56$	0.479366	+	2.60196i	0.0640579	+	0.347702i
$57$		0			0
$58$		−	7.52516i		−	0.988102i
$59$	−4.39312			−0.571935			−0.285967	−	0.958239i	$-0.592315\pi$
$59$	−4.39312			−0.571935			−0.285967	+	0.958239i	$0.592315\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		−	4.31338i		−	0.547800i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.680900	+	8.14387i	0.0844553	+	1.01012i
$66$		0			0
$67$			10.8888i			1.33027i	0.746721	+	0.665137i	$0.231627\pi$
$67$			10.8888i			1.33027i	−0.746721	+	0.665137i	$0.768373\pi$
$68$			3.32090i			0.402718i
$69$		0			0
$70$	5.70863	−	1.55293i	0.682311	−	0.185610i
$71$			11.0685i			1.31359i	0.754069	+	0.656796i	$0.228089\pi$
$71$			11.0685i			1.31359i	−0.754069	+	0.656796i	$0.771911\pi$
$72$		0			0
$73$	5.75780			0.673899			0.336950	−	0.941523i	$-0.390605\pi$
$73$	5.75780			0.673899			0.336950	+	0.941523i	$0.390605\pi$
$74$			4.55854i			0.529920i
$75$		0			0
$76$		−	6.04543i		−	0.693459i
$77$	10.6496	−	1.96200i	1.21364	−	0.223591i
$78$		0			0
$79$	15.5802			1.75291			0.876454	−	0.481485i	$-0.159902\pi$
$79$	15.5802			1.75291			0.876454	+	0.481485i	$0.159902\pi$
$80$	−0.186305	−	2.22829i	−0.0208296	−	0.249131i
$81$		0			0
$82$	7.46175			0.824012
$83$			1.58885i			0.174399i	0.996191	+	0.0871993i	$0.0277917\pi$
$83$			1.58885i			0.174399i	−0.996191	+	0.0871993i	$0.972208\pi$
$84$		0			0
$85$	7.39993	−	0.618701i	0.802636	−	0.0671075i
$86$		−	1.77168i		−	0.191045i
$87$		0			0
$88$		−	4.09292i		−	0.436306i
$89$	14.2131			1.50658			0.753291	−	0.657687i	$-0.228465\pi$
$89$	14.2131			1.50658			0.753291	+	0.657687i	$0.228465\pi$
$90$		0			0
$91$	1.75196	+	9.50954i	0.183656	+	0.996870i
$92$	−1.60984			−0.167837
$93$		0			0
$94$			3.40032i			0.350716i
$95$	−13.4710	+	1.12630i	−1.38210	+	0.115556i
$96$		0			0
$97$	1.54485			0.156856			0.0784280	−	0.996920i	$-0.475010\pi$
$97$	1.54485			0.156856			0.0784280	+	0.996920i	$0.475010\pi$
$98$	6.54042	−	2.49458i	0.660682	−	0.251991i
$99$		0			0
$100$	−4.93058	+	0.830286i	−0.493058	+	0.0830286i
$101$	6.34392			0.631243			0.315622	−	0.948885i	$-0.397787\pi$
$101$	6.34392			0.631243			0.315622	+	0.948885i	$0.397787\pi$
$102$		0			0
$103$	−11.8617			−1.16877			−0.584385	−	0.811476i	$-0.698664\pi$
$103$	−11.8617			−1.16877			−0.584385	+	0.811476i	$0.698664\pi$
$104$	3.65475			0.358378
$105$		0			0
$106$	−1.14213			−0.110933
$107$	−7.71903			−0.746227			−0.373114	−	0.927786i	$-0.621710\pi$
$107$	−7.71903			−0.746227			−0.373114	+	0.927786i	$0.621710\pi$
$108$		0			0
$109$	−2.96707			−0.284194			−0.142097	−	0.989853i	$-0.545384\pi$
$109$	−2.96707			−0.284194			−0.142097	+	0.989853i	$0.545384\pi$
$110$	−9.12022	+	0.762532i	−0.869579	+	0.0727046i
$111$		0			0
$112$	−0.479366	−	2.60196i	−0.0452958	−	0.245862i
$113$	−1.03293			−0.0971699			−0.0485849	−	0.998819i	$-0.515471\pi$
$113$	−1.03293			−0.0971699			−0.0485849	+	0.998819i	$0.515471\pi$
$114$		0			0
$115$	0.299921	+	3.58719i	0.0279678	+	0.334507i
$116$			7.52516i			0.698694i
$117$		0			0
$118$	4.39312			0.404419
$119$	8.64085	−	1.59192i	0.792106	−	0.145931i
$120$		0			0
$121$	−5.75196			−0.522906
$122$		0			0
$123$		0			0
$124$			4.31338i			0.387353i
$125$	2.76871	+	10.8321i	0.247641	+	0.968852i
$126$		0			0
$127$			18.1281i			1.60860i	0.594220	+	0.804302i	$0.297461\pi$
$127$			18.1281i			1.60860i	−0.594220	+	0.804302i	$0.702539\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−0.680900	−	8.14387i	−0.0597189	−	0.714264i
$131$	−18.7986			−1.64244			−0.821222	−	0.570609i	$-0.806707\pi$
$131$	−18.7986			−1.64244			−0.821222	+	0.570609i	$0.806707\pi$
$132$		0			0
$133$	−15.7300	+	2.89797i	−1.36396	+	0.251286i
$134$		−	10.8888i		−	0.940646i
$135$		0			0
$136$		−	3.32090i		−	0.284765i
$137$	−12.3289			−1.05333			−0.526663	−	0.850074i	$-0.676557\pi$
$137$	−12.3289			−1.05333			−0.526663	+	0.850074i	$0.676557\pi$
$138$		0			0
$139$		−	21.8230i		−	1.85100i	−0.378742	−	0.925502i	$-0.623643\pi$
$139$		−	21.8230i		−	1.85100i	0.378742	−	0.925502i	$-0.376357\pi$
$140$	−5.70863	+	1.55293i	−0.482467	+	0.131246i
$141$		0			0
$142$		−	11.0685i		−	0.928849i
$143$		−	14.9586i		−	1.25090i
$144$		0			0
$145$	16.7683	−	1.40198i	1.39253	−	0.116428i
$146$	−5.75780			−0.476519
$147$		0			0
$148$		−	4.55854i		−	0.374710i
$149$			18.3028i			1.49943i	0.661763	+	0.749713i	$0.269808\pi$
$149$			18.3028i			1.49943i	−0.661763	+	0.749713i	$0.730192\pi$
$150$		0			0
$151$	−14.9387			−1.21569			−0.607847	−	0.794054i	$-0.707967\pi$
$151$	−14.9387			−1.21569			−0.607847	+	0.794054i	$0.707967\pi$
$152$			6.04543i			0.490349i
$153$		0			0
$154$	−10.6496	+	1.96200i	−0.858170	+	0.158103i
$155$	9.61148	−	0.803606i	0.772013	−	0.0645472i
$156$		0			0
$157$	−5.72446			−0.456861			−0.228431	−	0.973560i	$-0.573359\pi$
$157$	−5.72446			−0.456861			−0.228431	+	0.973560i	$0.573359\pi$
$158$	−15.5802			−1.23949
$159$		0			0
$160$	0.186305	+	2.22829i	0.0147287	+	0.176162i
$161$	0.771700	+	4.18873i	0.0608185	+	0.330118i
$162$		0			0
$163$			18.2392i			1.42860i	0.699839	+	0.714301i	$0.253255\pi$
$163$			18.2392i			1.42860i	−0.699839	+	0.714301i	$0.746745\pi$
$164$	−7.46175			−0.582665
$165$		0			0
$166$		−	1.58885i		−	0.123318i
$167$			12.6234i			0.976832i	0.872611	+	0.488416i	$0.162425\pi$
$167$			12.6234i			0.976832i	−0.872611	+	0.488416i	$0.837575\pi$
$168$		0			0
$169$	0.357233			0.0274795
$170$	−7.39993	+	0.618701i	−0.567549	+	0.0474522i
$171$		0			0
$172$			1.77168i			0.135089i
$173$		−	6.15515i		−	0.467967i	−0.972241	−	0.233984i	$-0.924824\pi$
$173$		−	6.15515i		−	0.467967i	0.972241	−	0.233984i	$-0.0751762\pi$
$174$		0			0
$175$	4.52392	+	12.4312i	0.341976	+	0.939709i
$176$			4.09292i			0.308515i
$177$		0			0
$178$	−14.2131			−1.06531
$179$			1.56475i			0.116955i	0.998289	+	0.0584776i	$0.0186246\pi$
$179$			1.56475i			0.116955i	−0.998289	+	0.0584776i	$0.981375\pi$
$180$		0			0
$181$		−	5.83845i		−	0.433968i	−0.976175	−	0.216984i	$-0.930378\pi$
$181$		−	5.83845i		−	0.433968i	0.976175	−	0.216984i	$-0.0696220\pi$
$182$	−1.75196	−	9.50954i	−0.129864	−	0.704894i
$183$		0			0
$184$	1.60984			0.118679
$185$	−10.1578	+	0.849281i	−0.746814	+	0.0624404i
$186$		0			0
$187$	−13.5922			−0.993957
$188$		−	3.40032i		−	0.247994i
$189$		0			0
$190$	13.4710	−	1.12630i	0.977289	−	0.0817101i
$191$		−	3.41696i		−	0.247243i	−0.992329	−	0.123621i	$-0.960549\pi$
$191$		−	3.41696i		−	0.247243i	0.992329	−	0.123621i	$-0.0394508\pi$
$192$		0			0
$193$			1.33662i			0.0962123i	0.998842	+	0.0481062i	$0.0153186\pi$
$193$			1.33662i			0.0962123i	−0.998842	+	0.0481062i	$0.984681\pi$
$194$	−1.54485			−0.110914
$195$		0			0
$196$	−6.54042	+	2.49458i	−0.467173	+	0.178184i
$197$	18.1900			1.29599			0.647993	−	0.761646i	$-0.275609\pi$
$197$	18.1900			1.29599			0.647993	+	0.761646i	$0.275609\pi$
$198$		0			0
$199$			21.4113i			1.51780i	0.651205	+	0.758902i	$0.274264\pi$
$199$			21.4113i			1.51780i	−0.651205	+	0.758902i	$0.725736\pi$
$200$	4.93058	−	0.830286i	0.348645	−	0.0587101i
$201$		0			0
$202$	−6.34392			−0.446356
$203$	19.5802	−	3.60731i	1.37426	−	0.253183i
$204$		0			0
$205$	1.39016	+	16.6270i	0.0970932	+	1.16128i
$206$	11.8617			0.826446
$207$		0			0
$208$	−3.65475			−0.253412
$209$	24.7435			1.71154
$210$		0			0
$211$	13.9704			0.961759			0.480880	−	0.876787i	$-0.340317\pi$
$211$	13.9704			0.961759			0.480880	+	0.876787i	$0.340317\pi$
$212$	1.14213			0.0784416
$213$		0			0
$214$	7.71903			0.527662
$215$	3.94782	−	0.330073i	0.269239	−	0.0225108i
$216$		0			0
$217$	11.2233	−	2.06769i	0.761885	−	0.140364i
$218$	2.96707			0.200955
$219$		0			0
$220$	9.12022	−	0.762532i	0.614885	−	0.0514099i
$221$		−	12.1371i		−	0.816428i
$222$		0			0
$223$	−26.3861			−1.76695			−0.883473	−	0.468482i	$-0.844801\pi$
$223$	−26.3861			−1.76695			−0.883473	+	0.468482i	$0.844801\pi$
$224$	0.479366	+	2.60196i	0.0320290	+	0.173851i
$225$		0			0
$226$	1.03293			0.0687095
$227$			0.493394i			0.0327477i	0.999866	+	0.0163739i	$0.00521219\pi$
$227$			0.493394i			0.0327477i	−0.999866	+	0.0163739i	$0.994788\pi$
$228$		0			0
$229$			8.62677i			0.570073i	0.958517	+	0.285036i	$0.0920057\pi$
$229$			8.62677i			0.570073i	−0.958517	+	0.285036i	$0.907994\pi$
$230$	−0.299921	−	3.58719i	−0.0197762	−	0.236532i
$231$		0			0
$232$		−	7.52516i		−	0.494051i
$233$	−28.6894			−1.87950			−0.939752	−	0.341856i	$-0.888944\pi$
$233$	−28.6894			−1.87950			−0.939752	+	0.341856i	$0.888944\pi$
$234$		0			0
$235$	−7.57691	+	0.633497i	−0.494263	+	0.0413248i
$236$	−4.39312			−0.285967
$237$		0			0
$238$	−8.64085	+	1.59192i	−0.560103	+	0.103189i
$239$			12.6299i			0.816958i	0.912768	+	0.408479i	$0.133941\pi$
$239$			12.6299i			0.816958i	−0.912768	+	0.408479i	$0.866059\pi$
$240$		0			0
$241$		−	22.2370i		−	1.43241i	−0.697889	−	0.716206i	$-0.745877\pi$
$241$		−	22.2370i		−	1.43241i	0.697889	−	0.716206i	$-0.254123\pi$
$242$	5.75196			0.369750
$243$		0			0
$244$		0			0
$245$	6.77718	+	14.1092i	0.432978	+	0.901405i
$246$		0			0
$247$			22.0946i			1.40584i
$248$		−	4.31338i		−	0.273900i
$249$		0			0
$250$	−2.76871	−	10.8321i	−0.175109	−	0.685082i
$251$	−26.0679			−1.64539			−0.822697	−	0.568481i	$-0.807531\pi$
$251$	−26.0679			−1.64539			−0.822697	+	0.568481i	$0.807531\pi$
$252$		0			0
$253$		−	6.58893i		−	0.414242i
$254$		−	18.1281i		−	1.13746i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	13.5700i		−	0.846473i	−0.906019	−	0.423237i	$-0.860894\pi$
$257$		−	13.5700i		−	0.846473i	0.906019	−	0.423237i	$-0.139106\pi$
$258$		0			0
$259$	−11.8612	+	2.18521i	−0.737017	+	0.135782i
$260$	0.680900	+	8.14387i	0.0422276	+	0.505061i
$261$		0			0
$262$	18.7986			1.16138
$263$	13.1138			0.808629			0.404315	−	0.914620i	$-0.367510\pi$
$263$	13.1138			0.808629			0.404315	+	0.914620i	$0.367510\pi$
$264$		0			0
$265$	−0.212784	−	2.54499i	−0.0130712	−	0.156338i
$266$	15.7300	−	2.89797i	0.964468	−	0.177686i
$267$		0			0
$268$			10.8888i			0.665137i
$269$	13.3801			0.815799			0.407900	−	0.913027i	$-0.366261\pi$
$269$	13.3801			0.815799			0.407900	+	0.913027i	$0.366261\pi$
$270$		0			0
$271$			5.85630i			0.355745i	0.984054	+	0.177872i	$0.0569214\pi$
$271$			5.85630i			0.355745i	−0.984054	+	0.177872i	$0.943079\pi$
$272$			3.32090i			0.201359i
$273$		0			0
$274$	12.3289			0.744814
$275$	−3.39829	−	20.1805i	−0.204925	−	1.21693i
$276$		0			0
$277$		−	2.58152i		−	0.155109i	−0.996988	−	0.0775543i	$-0.975289\pi$
$277$		−	2.58152i		−	0.155109i	0.996988	−	0.0775543i	$-0.0247111\pi$
$278$			21.8230i			1.30886i
$279$		0			0
$280$	5.70863	−	1.55293i	0.341156	−	0.0928051i
$281$		−	18.3181i		−	1.09277i	−0.837535	−	0.546383i	$-0.816004\pi$
$281$		−	18.3181i		−	1.09277i	0.837535	−	0.546383i	$-0.183996\pi$
$282$		0			0
$283$	−25.4955			−1.51555			−0.757776	−	0.652515i	$-0.773714\pi$
$283$	−25.4955			−1.51555			−0.757776	+	0.652515i	$0.773714\pi$
$284$			11.0685i			0.656796i
$285$		0			0
$286$			14.9586i			0.884521i
$287$	3.57691	+	19.4152i	0.211138	+	1.14604i
$288$		0			0
$289$	5.97164			0.351273
$290$	−16.7683	+	1.40198i	−0.984667	+	0.0823270i
$291$		0			0
$292$	5.75780			0.336950
$293$		−	13.5700i		−	0.792768i	−0.918085	−	0.396384i	$-0.870265\pi$
$293$		−	13.5700i		−	0.792768i	0.918085	−	0.396384i	$-0.129735\pi$
$294$		0			0
$295$	0.818461	+	9.78915i	0.0476526	+	0.569946i
$296$			4.55854i			0.264960i
$297$		0			0
$298$		−	18.3028i		−	1.06025i
$299$	5.88356			0.340255
$300$		0			0
$301$	4.60984	−	0.849281i	0.265707	−	0.0489517i
$302$	14.9387			0.859626
$303$		0			0
$304$		−	6.04543i		−	0.346729i
$305$		0			0
$306$		0			0
$307$	30.8739			1.76206			0.881032	−	0.473056i	$-0.156849\pi$
$307$	30.8739			1.76206			0.881032	+	0.473056i	$0.156849\pi$
$308$	10.6496	−	1.96200i	0.606818	−	0.111796i
$309$		0			0
$310$	−9.61148	+	0.803606i	−0.545895	+	0.0456418i
$311$	−0.599842			−0.0340139			−0.0170070	−	0.999855i	$-0.505414\pi$
$311$	−0.599842			−0.0340139			−0.0170070	+	0.999855i	$0.505414\pi$
$312$		0			0
$313$	−20.1648			−1.13978			−0.569890	−	0.821721i	$-0.693014\pi$
$313$	−20.1648			−1.13978			−0.569890	+	0.821721i	$0.693014\pi$
$314$	5.72446			0.323050
$315$		0			0
$316$	15.5802			0.876454
$317$	−27.6281			−1.55175			−0.775874	−	0.630887i	$-0.782691\pi$
$317$	−27.6281			−1.55175			−0.775874	+	0.630887i	$0.782691\pi$
$318$		0			0
$319$	−30.7999			−1.72446
$320$	−0.186305	−	2.22829i	−0.0104148	−	0.124565i
$321$		0			0
$322$	−0.771700	−	4.18873i	−0.0430052	−	0.233429i
$323$	20.0763			1.11707
$324$		0			0
$325$	18.0201	−	3.03449i	0.999573	−	0.168323i
$326$		−	18.2392i		−	1.01017i
$327$		0			0
$328$	7.46175			0.412006
$329$	−8.84750	+	1.63000i	−0.487779	+	0.0898646i
$330$		0			0
$331$	5.68610			0.312537			0.156268	−	0.987715i	$-0.450054\pi$
$331$	5.68610			0.312537			0.156268	+	0.987715i	$0.450054\pi$
$332$			1.58885i			0.0871993i
$333$		0			0
$334$		−	12.6234i		−	0.690724i
$335$	24.2634	−	2.02863i	1.32565	−	0.110836i
$336$		0			0
$337$		−	2.99720i		−	0.163268i	−0.996662	−	0.0816338i	$-0.973986\pi$
$337$		−	2.99720i		−	0.163268i	0.996662	−	0.0816338i	$-0.0260138\pi$
$338$	−0.357233			−0.0194309
$339$		0			0
$340$	7.39993	−	0.618701i	0.401318	−	0.0335538i
$341$	−17.6543			−0.956035
$342$		0			0
$343$	9.62606	+	15.8221i	0.519758	+	0.854313i
$344$		−	1.77168i		−	0.0955224i
$345$		0			0
$346$			6.15515i			0.330903i
$347$	−23.5835			−1.26603			−0.633014	−	0.774140i	$-0.718182\pi$
$347$	−23.5835			−1.26603			−0.633014	+	0.774140i	$0.718182\pi$
$348$		0			0
$349$			25.6498i			1.37300i	0.727130	+	0.686500i	$0.240854\pi$
$349$			25.6498i			1.37300i	−0.727130	+	0.686500i	$0.759146\pi$
$350$	−4.52392	−	12.4312i	−0.241814	−	0.664474i
$351$		0			0
$352$		−	4.09292i		−	0.218153i
$353$			23.1322i			1.23120i	0.788057	+	0.615602i	$0.211087\pi$
$353$			23.1322i			1.23120i	−0.788057	+	0.615602i	$0.788913\pi$
$354$		0			0
$355$	24.6639	−	2.06212i	1.30902	−	0.109446i
$356$	14.2131			0.753291
$357$		0			0
$358$		−	1.56475i		−	0.0826998i
$359$		−	34.3699i		−	1.81398i	−0.421157	−	0.906988i	$-0.638376\pi$
$359$		−	34.3699i		−	1.81398i	0.421157	−	0.906988i	$-0.361624\pi$
$360$		0			0
$361$	−17.5473			−0.923540
$362$			5.83845i			0.306862i
$363$		0			0
$364$	1.75196	+	9.50954i	0.0918279	+	0.498435i
$365$	−1.07271	−	12.8301i	−0.0561481	−	0.671556i
$366$		0			0
$367$	10.5318			0.549757			0.274879	−	0.961479i	$-0.411362\pi$
$367$	10.5318			0.549757			0.274879	+	0.961479i	$0.411362\pi$
$368$	−1.60984			−0.0839185
$369$		0			0
$370$	10.1578	−	0.849281i	0.528077	−	0.0441520i
$371$	−0.547497	−	2.97177i	−0.0284246	−	0.154287i
$372$		0			0
$373$		−	30.1846i		−	1.56290i	−0.623969	−	0.781449i	$-0.714481\pi$
$373$		−	30.1846i		−	1.56290i	0.623969	−	0.781449i	$-0.285519\pi$
$374$	13.5922			0.702834
$375$		0			0
$376$			3.40032i			0.175358i
$377$		−	27.5026i		−	1.41646i
$378$		0			0
$379$	−0.780327			−0.0400827			−0.0200414	−	0.999799i	$-0.506380\pi$
$379$	−0.780327			−0.0400827			−0.0200414	+	0.999799i	$0.506380\pi$
$380$	−13.4710	+	1.12630i	−0.691048	+	0.0577778i
$381$		0			0
$382$			3.41696i			0.174827i
$383$			19.3055i			0.986464i	0.869898	+	0.493232i	$0.164185\pi$
$383$			19.3055i			0.986464i	−0.869898	+	0.493232i	$0.835815\pi$
$384$		0			0
$385$	−6.35600	−	23.3649i	−0.323932	−	1.19079i
$386$		−	1.33662i		−	0.0680324i
$387$		0			0
$388$	1.54485			0.0784280
$389$		−	29.5936i		−	1.50045i	−0.661181	−	0.750226i	$-0.729945\pi$
$389$		−	29.5936i		−	1.50045i	0.661181	−	0.750226i	$-0.270055\pi$
$390$		0			0
$391$		−	5.34610i		−	0.270364i
$392$	6.54042	−	2.49458i	0.330341	−	0.125995i
$393$		0			0
$394$	−18.1900			−0.916401
$395$	−2.90267	−	34.7172i	−0.146049	−	1.74681i
$396$		0			0
$397$	26.0817			1.30900			0.654500	−	0.756062i	$-0.272879\pi$
$397$	26.0817			1.30900			0.654500	+	0.756062i	$0.272879\pi$
$398$		−	21.4113i		−	1.07325i
$399$		0			0
$400$	−4.93058	+	0.830286i	−0.246529	+	0.0415143i
$401$		−	17.6319i		−	0.880493i	−0.897877	−	0.440246i	$-0.854891\pi$
$401$		−	17.6319i		−	0.880493i	0.897877	−	0.440246i	$-0.145109\pi$
$402$		0			0
$403$		−	15.7644i		−	0.785279i
$404$	6.34392			0.315622
$405$		0			0
$406$	−19.5802	+	3.60731i	−0.971749	+	0.179028i
$407$	18.6577			0.924830
$408$		0			0
$409$			20.0518i			0.991497i	0.868466	+	0.495749i	$0.165106\pi$
$409$			20.0518i			0.991497i	−0.868466	+	0.495749i	$0.834894\pi$
$410$	−1.39016	−	16.6270i	−0.0686553	−	0.821147i
$411$		0			0
$412$	−11.8617			−0.584385
$413$	2.10591	+	11.4307i	0.103625	+	0.562469i
$414$		0			0
$415$	3.54042	−	0.296011i	0.173792	−	0.0145306i
$416$	3.65475			0.179189
$417$		0			0
$418$	−24.7435			−1.21024
$419$	−0.614051			−0.0299984			−0.0149992	−	0.999888i	$-0.504775\pi$
$419$	−0.614051			−0.0299984			−0.0149992	+	0.999888i	$0.504775\pi$
$420$		0			0
$421$	38.4905			1.87591			0.937957	−	0.346751i	$-0.112715\pi$
$421$	38.4905			1.87591			0.937957	+	0.346751i	$0.112715\pi$
$422$	−13.9704			−0.680066
$423$		0			0
$424$	−1.14213			−0.0554666
$425$	−2.75729	−	16.3740i	−0.133748	−	0.794253i
$426$		0			0
$427$		0			0
$428$	−7.71903			−0.373114
$429$		0			0
$430$	−3.94782	+	0.330073i	−0.190381	+	0.0159175i
$431$		−	10.7021i		−	0.515503i	−0.966211	−	0.257751i	$-0.917018\pi$
$431$		−	10.7021i		−	0.515503i	0.966211	−	0.257751i	$-0.0829815\pi$
$432$		0			0
$433$	−28.0604			−1.34850			−0.674248	−	0.738505i	$-0.735532\pi$
$433$	−28.0604			−1.34850			−0.674248	+	0.738505i	$0.735532\pi$
$434$	−11.2233	+	2.06769i	−0.538734	+	0.0992522i
$435$		0			0
$436$	−2.96707			−0.142097
$437$			9.73216i			0.465552i
$438$		0			0
$439$		−	13.5767i		−	0.647983i	−0.946060	−	0.323991i	$-0.894975\pi$
$439$		−	13.5767i		−	0.647983i	0.946060	−	0.323991i	$-0.105025\pi$
$440$	−9.12022	+	0.762532i	−0.434789	+	0.0363523i
$441$		0			0
$442$			12.1371i			0.577301i
$443$	−38.4563			−1.82712			−0.913558	−	0.406709i	$-0.866676\pi$
$443$	−38.4563			−1.82712			−0.913558	+	0.406709i	$0.866676\pi$
$444$		0			0
$445$	−2.64797	−	31.6709i	−0.125526	−	1.50134i
$446$	26.3861			1.24942
$447$		0			0
$448$	−0.479366	−	2.60196i	−0.0226479	−	0.122931i
$449$		−	20.8463i		−	0.983797i	−0.870653	−	0.491898i	$-0.836303\pi$
$449$		−	20.8463i		−	0.983797i	0.870653	−	0.491898i	$-0.163697\pi$
$450$		0			0
$451$		−	30.5403i		−	1.43809i
$452$	−1.03293			−0.0485849
$453$		0			0
$454$		−	0.493394i		−	0.0231561i
$455$	20.8636	−	5.67557i	0.978102	−	0.266075i
$456$		0			0
$457$		−	32.5602i		−	1.52310i	−0.648106	−	0.761550i	$-0.724439\pi$
$457$		−	32.5602i		−	1.52310i	0.648106	−	0.761550i	$-0.275561\pi$
$458$		−	8.62677i		−	0.403102i
$459$		0			0
$460$	0.299921	+	3.58719i	0.0139839	+	0.167253i
$461$	−38.4037			−1.78864			−0.894320	−	0.447427i	$-0.852340\pi$
$461$	−38.4037			−1.78864			−0.894320	+	0.447427i	$0.852340\pi$
$462$		0			0
$463$			8.95761i			0.416295i	0.978097	+	0.208148i	$0.0667434\pi$
$463$			8.95761i			0.416295i	−0.978097	+	0.208148i	$0.933257\pi$
$464$			7.52516i			0.349347i
$465$		0			0
$466$	28.6894			1.32901
$467$		−	12.0449i		−	0.557373i	−0.960382	−	0.278687i	$-0.910101\pi$
$467$		−	12.0449i		−	0.557373i	0.960382	−	0.278687i	$-0.0898991\pi$
$468$		0			0
$469$	28.3322	−	5.21970i	1.30826	−	0.241023i
$470$	7.57691	−	0.633497i	0.349497	−	0.0292211i
$471$		0			0
$472$	4.39312			0.202210
$473$	−7.25132			−0.333416
$474$		0			0
$475$	5.01944	+	29.8075i	0.230308	+	1.36766i
$476$	8.64085	−	1.59192i	0.396053	−	0.0729657i
$477$		0			0
$478$		−	12.6299i		−	0.577677i
$479$	25.3227			1.15702			0.578512	−	0.815674i	$-0.303634\pi$
$479$	25.3227			1.15702			0.578512	+	0.815674i	$0.303634\pi$
$480$		0			0
$481$			16.6604i			0.759647i
$482$			22.2370i			1.01287i
$483$		0			0
$484$	−5.75196			−0.261453
$485$	−0.287814	−	3.44238i	−0.0130690	−	0.156311i
$486$		0			0
$487$			27.6150i			1.25135i	0.780083	+	0.625676i	$0.215177\pi$
$487$			27.6150i			1.25135i	−0.780083	+	0.625676i	$0.784823\pi$
$488$		0			0
$489$		0			0
$490$	−6.77718	−	14.1092i	−0.306162	−	0.637389i
$491$		−	38.4884i		−	1.73696i	−0.495725	−	0.868479i	$-0.665098\pi$
$491$		−	38.4884i		−	1.73696i	0.495725	−	0.868479i	$-0.334902\pi$
$492$		0			0
$493$	−24.9903			−1.12551
$494$		−	22.0946i		−	0.994082i
$495$		0			0
$496$			4.31338i			0.193677i
$497$	28.7999	−	5.30587i	1.29185	−	0.238001i
$498$		0			0
$499$	20.2184			0.905100			0.452550	−	0.891739i	$-0.350514\pi$
$499$	20.2184			0.905100			0.452550	+	0.891739i	$0.350514\pi$
$500$	2.76871	+	10.8321i	0.123821	+	0.484426i
$501$		0			0
$502$	26.0679			1.16347
$503$			11.0805i			0.494056i	0.969008	+	0.247028i	$0.0794540\pi$
$503$			11.0805i			0.494056i	−0.969008	+	0.247028i	$0.920546\pi$
$504$		0			0
$505$	−1.18191	−	14.1361i	−0.0525941	−	0.629049i
$506$			6.58893i			0.292913i
$507$		0			0
$508$			18.1281i			0.804302i
$509$	11.1567			0.494512			0.247256	−	0.968950i	$-0.420471\pi$
$509$	11.1567			0.494512			0.247256	+	0.968950i	$0.420471\pi$
$510$		0			0
$511$	−2.76009	−	14.9816i	−0.122099	−	0.662746i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			13.5700i			0.598547i
$515$	2.20990	+	26.4314i	0.0973799	+	1.16471i
$516$		0			0
$517$	13.9172			0.612079
$518$	11.8612	−	2.18521i	0.521150	−	0.0960126i
$519$		0			0
$520$	−0.680900	−	8.14387i	−0.0298594	−	0.357132i
$521$	−24.6123			−1.07828			−0.539142	−	0.842215i	$-0.681251\pi$
$521$	−24.6123			−1.07828			−0.539142	+	0.842215i	$0.681251\pi$
$522$		0			0
$523$	−12.3304			−0.539171			−0.269585	−	0.962977i	$-0.586887\pi$
$523$	−12.3304			−0.539171			−0.269585	+	0.962977i	$0.586887\pi$
$524$	−18.7986			−0.821222
$525$		0			0
$526$	−13.1138			−0.571787
$527$	−14.3243			−0.623976
$528$		0			0
$529$	−20.4084			−0.887323
$530$	0.212784	+	2.54499i	0.00924276	+	0.110548i
$531$		0			0
$532$	−15.7300	+	2.89797i	−0.681982	+	0.125643i
$533$	27.2709			1.18123
$534$		0			0
$535$	1.43810	+	17.2003i	0.0621744	+	0.743633i
$536$		−	10.8888i		−	0.470323i
$537$		0			0
$538$	−13.3801			−0.576857
$539$	−10.2101	−	26.7694i	−0.439781	−	1.15304i
$540$		0			0
$541$	12.9671			0.557498			0.278749	−	0.960364i	$-0.410080\pi$
$541$	12.9671			0.557498			0.278749	+	0.960364i	$0.410080\pi$
$542$		−	5.85630i		−	0.251550i
$543$		0			0
$544$		−	3.32090i		−	0.142382i
$545$	0.552781	+	6.61150i	0.0236785	+	0.283206i
$546$		0			0
$547$		−	10.6301i		−	0.454509i	−0.973835	−	0.227254i	$-0.927025\pi$
$547$		−	10.6301i		−	0.454509i	0.973835	−	0.227254i	$-0.0729749\pi$
$548$	−12.3289			−0.526663
$549$		0			0
$550$	3.39829	+	20.1805i	0.144904	+	0.860497i
$551$	45.4929			1.93806
$552$		0			0
$553$	−7.46861	−	40.5391i	−0.317598	−	1.72390i
$554$			2.58152i			0.109678i
$555$		0			0
$556$		−	21.8230i		−	0.925502i
$557$	16.2513			0.688591			0.344295	−	0.938861i	$-0.388118\pi$
$557$	16.2513			0.688591			0.344295	+	0.938861i	$0.388118\pi$
$558$		0			0
$559$		−	6.47504i		−	0.273865i
$560$	−5.70863	+	1.55293i	−0.241234	+	0.0656231i
$561$		0			0
$562$			18.3181i			0.772703i
$563$			14.1093i			0.594637i	0.954778	+	0.297319i	$0.0960923\pi$
$563$			14.1093i			0.594637i	−0.954778	+	0.297319i	$0.903908\pi$
$564$		0			0
$565$	0.192440	+	2.30167i	0.00809603	+	0.0968320i
$566$	25.4955			1.07166
$567$		0			0
$568$		−	11.0685i		−	0.464425i
$569$		−	9.75216i		−	0.408832i	−0.978884	−	0.204416i	$-0.934470\pi$
$569$		−	9.75216i		−	0.408832i	0.978884	−	0.204416i	$-0.0655295\pi$
$570$		0			0
$571$	−22.1888			−0.928570			−0.464285	−	0.885686i	$-0.653689\pi$
$571$	−22.1888			−0.928570			−0.464285	+	0.885686i	$0.653689\pi$
$572$		−	14.9586i		−	0.625451i
$573$		0			0
$574$	−3.57691	−	19.4152i	−0.149297	−	0.810374i
$575$	7.93743	−	1.33662i	0.331014	−	0.0557411i
$576$		0			0
$577$	1.48358			0.0617623			0.0308812	−	0.999523i	$-0.490169\pi$
$577$	1.48358			0.0617623			0.0308812	+	0.999523i	$0.490169\pi$
$578$	−5.97164			−0.248387
$579$		0			0
$580$	16.7683	−	1.40198i	0.696265	−	0.0582140i
$581$	4.13412	−	0.761639i	0.171512	−	0.0315981i
$582$		0			0
$583$			4.67463i			0.193603i
$584$	−5.75780			−0.238259
$585$		0			0
$586$			13.5700i			0.560571i
$587$			37.1621i			1.53384i	0.641740	+	0.766922i	$0.278213\pi$
$587$			37.1621i			1.53384i	−0.641740	+	0.766922i	$0.721787\pi$
$588$		0			0
$589$	26.0763			1.07445
$590$	−0.818461	−	9.78915i	−0.0336955	−	0.403013i
$591$		0			0
$592$		−	4.55854i		−	0.187355i
$593$			35.2744i			1.44855i	0.689513	+	0.724273i	$0.257825\pi$
$593$			35.2744i			1.44855i	−0.689513	+	0.724273i	$0.742175\pi$
$594$		0			0
$595$	−5.15711	−	18.9578i	−0.211421	−	0.777193i
$596$			18.3028i			0.749713i
$597$		0			0
$598$	−5.88356			−0.240597
$599$			26.0468i			1.06424i	0.846668	+	0.532122i	$0.178605\pi$
$599$			26.0468i			1.06424i	−0.846668	+	0.532122i	$0.821395\pi$
$600$		0			0
$601$			42.9132i			1.75047i	0.483700	+	0.875234i	$0.339292\pi$
$601$			42.9132i			1.75047i	−0.483700	+	0.875234i	$0.660708\pi$
$602$	−4.60984	+	0.849281i	−0.187883	+	0.0346141i
$603$		0			0
$604$	−14.9387			−0.607847
$605$	1.07162	+	12.8171i	0.0435676	+	0.521088i
$606$		0			0
$607$	−19.1575			−0.777580			−0.388790	−	0.921327i	$-0.627107\pi$
$607$	−19.1575			−0.777580			−0.388790	+	0.921327i	$0.627107\pi$
$608$			6.04543i			0.245175i
$609$		0			0
$610$		0			0
$611$			12.4273i			0.502756i
$612$		0			0
$613$		−	17.7464i		−	0.716769i	−0.933574	−	0.358384i	$-0.883328\pi$
$613$		−	17.7464i		−	0.716769i	0.933574	−	0.358384i	$-0.116672\pi$
$614$	−30.8739			−1.24597
$615$		0			0
$616$	−10.6496	+	1.96200i	−0.429085	+	0.0790514i
$617$	30.4368			1.22534			0.612670	−	0.790339i	$-0.290096\pi$
$617$	30.4368			1.22534			0.612670	+	0.790339i	$0.290096\pi$
$618$		0			0
$619$		−	40.3063i		−	1.62005i	−0.586397	−	0.810024i	$-0.699454\pi$
$619$		−	40.3063i		−	1.62005i	0.586397	−	0.810024i	$-0.300546\pi$
$620$	9.61148	−	0.803606i	0.386006	−	0.0322736i
$621$		0			0
$622$	0.599842			0.0240515
$623$	−6.81326	−	36.9819i	−0.272967	−	1.48165i
$624$		0			0
$625$	23.6213	−	8.18758i	0.944850	−	0.327503i
$626$	20.1648			0.805946
$627$		0			0
$628$	−5.72446			−0.228431
$629$	15.1385			0.603610
$630$		0			0
$631$	−31.2992			−1.24600			−0.623001	−	0.782221i	$-0.714087\pi$
$631$	−31.2992			−1.24600			−0.623001	+	0.782221i	$0.714087\pi$
$632$	−15.5802			−0.619747
$633$		0			0
$634$	27.6281			1.09725
$635$	40.3946	−	3.37735i	1.60301	−	0.134026i
$636$		0			0
$637$	23.9036	−	9.11709i	0.947096	−	0.361232i
$638$	30.7999			1.21938
$639$		0			0
$640$	0.186305	+	2.22829i	0.00736436	+	0.0880810i
$641$			28.0169i			1.10660i	0.832981	+	0.553301i	$0.186632\pi$
$641$			28.0169i			1.10660i	−0.832981	+	0.553301i	$0.813368\pi$
$642$		0			0
$643$	−30.5557			−1.20500			−0.602499	−	0.798120i	$-0.705828\pi$
$643$	−30.5557			−1.20500			−0.602499	+	0.798120i	$0.705828\pi$
$644$	0.771700	+	4.18873i	0.0304093	+	0.165059i
$645$		0			0
$646$	−20.0763			−0.789890
$647$		−	4.60654i		−	0.181102i	−0.995892	−	0.0905508i	$-0.971137\pi$
$647$		−	4.60654i		−	0.181102i	0.995892	−	0.0905508i	$-0.0288628\pi$
$648$		0			0
$649$		−	17.9807i		−	0.705802i
$650$	−18.0201	+	3.03449i	−0.706805	+	0.119023i
$651$		0			0
$652$			18.2392i			0.714301i
$653$	−14.6248			−0.572313			−0.286157	−	0.958183i	$-0.592378\pi$
$653$	−14.6248			−0.572313			−0.286157	+	0.958183i	$0.592378\pi$
$654$		0			0
$655$	3.50228	+	41.8888i	0.136846	+	1.63673i
$656$	−7.46175			−0.291332
$657$		0			0
$658$	8.84750	−	1.63000i	0.344912	−	0.0635439i
$659$			4.57881i			0.178365i	0.996015	+	0.0891826i	$0.0284255\pi$
$659$			4.57881i			0.178365i	−0.996015	+	0.0891826i	$0.971575\pi$
$660$		0			0
$661$		−	25.1550i		−	0.978417i	−0.872167	−	0.489209i	$-0.837286\pi$
$661$		−	25.1550i		−	0.978417i	0.872167	−	0.489209i	$-0.162714\pi$
$662$	−5.68610			−0.220997
$663$		0			0
$664$		−	1.58885i		−	0.0616592i
$665$	9.38811	+	34.5111i	0.364055	+	1.33828i
$666$		0			0
$667$		−	12.1143i		−	0.469067i
$668$			12.6234i			0.488416i
$669$		0			0
$670$	−24.2634	+	2.02863i	−0.937375	+	0.0783730i
$671$		0			0
$672$		0			0
$673$		−	16.3564i		−	0.630492i	−0.949010	−	0.315246i	$-0.897913\pi$
$673$		−	16.3564i		−	0.630492i	0.949010	−	0.315246i	$-0.102087\pi$
$674$			2.99720i			0.115448i
$675$		0			0
$676$	0.357233			0.0137397
$677$		−	37.2594i		−	1.43199i	−0.698103	−	0.715997i	$-0.745972\pi$
$677$		−	37.2594i		−	1.43199i	0.698103	−	0.715997i	$-0.254028\pi$
$678$		0			0
$679$	−0.740549	−	4.01965i	−0.0284197	−	0.154260i
$680$	−7.39993	+	0.618701i	−0.283775	+	0.0237261i
$681$		0			0
$682$	17.6543			0.676019
$683$	−0.704060			−0.0269401			−0.0134700	−	0.999909i	$-0.504288\pi$
$683$	−0.704060			−0.0269401			−0.0134700	+	0.999909i	$0.504288\pi$
$684$		0			0
$685$	2.29693	+	27.4723i	0.0877613	+	1.04966i
$686$	−9.62606	−	15.8221i	−0.367525	−	0.604091i
$687$		0			0
$688$			1.77168i			0.0675445i
$689$	−4.17420			−0.159024
$690$		0			0
$691$			38.6747i			1.47126i	0.677386	+	0.735628i	$0.263113\pi$
$691$			38.6747i			1.47126i	−0.677386	+	0.735628i	$0.736887\pi$
$692$		−	6.15515i		−	0.233984i
$693$		0			0
$694$	23.5835			0.895217
$695$	−48.6281	+	4.06575i	−1.84457	+	0.154223i
$696$		0			0
$697$		−	24.7797i		−	0.938598i
$698$		−	25.6498i		−	0.970858i
$699$		0			0
$700$	4.52392	+	12.4312i	0.170988	+	0.469854i
$701$			17.2926i			0.653133i	0.945174	+	0.326567i	$0.105892\pi$
$701$			17.2926i			0.653133i	−0.945174	+	0.326567i	$0.894108\pi$
$702$		0			0
$703$	−27.5584			−1.03938
$704$			4.09292i			0.154258i
$705$		0			0
$706$		−	23.1322i		−	0.870592i
$707$	−3.04106	−	16.5066i	−0.114371	−	0.620796i
$708$		0			0
$709$	−26.1933			−0.983711			−0.491855	−	0.870677i	$-0.663681\pi$
$709$	−26.1933			−0.983711			−0.491855	+	0.870677i	$0.663681\pi$
$710$	−24.6639	+	2.06212i	−0.925620	+	0.0773901i
$711$		0			0
$712$	−14.2131			−0.532657
$713$		−	6.94384i		−	0.260049i
$714$		0			0
$715$	−33.3322	+	2.78687i	−1.24655	+	0.104223i
$716$			1.56475i			0.0584776i
$717$		0			0
$718$			34.3699i			1.28267i
$719$	−46.9833			−1.75218			−0.876091	−	0.482146i	$-0.839858\pi$
$719$	−46.9833			−1.75218			−0.876091	+	0.482146i	$0.839858\pi$
$720$		0			0
$721$	5.68610	+	30.8638i	0.211762	+	1.14943i
$722$	17.5473			0.653042
$723$		0			0
$724$		−	5.83845i		−	0.216984i
$725$	−6.24804	−	37.1034i	−0.232046	−	1.37799i
$726$		0			0
$727$	8.34913			0.309652			0.154826	−	0.987942i	$-0.450518\pi$
$727$	8.34913			0.309652			0.154826	+	0.987942i	$0.450518\pi$
$728$	−1.75196	−	9.50954i	−0.0649321	−	0.352447i
$729$		0			0
$730$	1.07271	+	12.8301i	0.0397027	+	0.474862i
$731$	−5.88356			−0.217611
$732$		0			0
$733$	23.9566			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$733$	23.9566			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$734$	−10.5318			−0.388737
$735$		0			0
$736$	1.60984			0.0593394
$737$	−44.5668			−1.64164
$738$		0			0
$739$	4.78033			0.175847			0.0879236	−	0.996127i	$-0.471977\pi$
$739$	4.78033			0.175847			0.0879236	+	0.996127i	$0.471977\pi$
$740$	−10.1578	+	0.849281i	−0.373407	+	0.0312202i
$741$		0			0
$742$	0.547497	+	2.97177i	0.0200992	+	0.109097i
$743$	19.7715			0.725346			0.362673	−	0.931916i	$-0.381864\pi$
$743$	19.7715			0.725346			0.362673	+	0.931916i	$0.381864\pi$
$744$		0			0
$745$	40.7841	−	3.40991i	1.49421	−	0.124930i
$746$			30.1846i			1.10514i
$747$		0			0
$748$	−13.5922			−0.496978
$749$	3.70024	+	20.0846i	0.135204	+	0.733877i
$750$		0			0
$751$	30.8794			1.12681			0.563403	−	0.826182i	$-0.309492\pi$
$751$	30.8794			1.12681			0.563403	+	0.826182i	$0.309492\pi$
$752$		−	3.40032i		−	0.123997i
$753$		0			0
$754$			27.5026i			1.00159i
$755$	2.78316	+	33.2878i	0.101290	+	1.21147i
$756$		0			0
$757$		−	32.7128i		−	1.18897i	−0.804108	−	0.594483i	$-0.797357\pi$
$757$		−	32.7128i		−	1.18897i	0.804108	−	0.594483i	$-0.202643\pi$
$758$	0.780327			0.0283428
$759$		0			0
$760$	13.4710	−	1.12630i	0.488644	−	0.0408551i
$761$	−40.0866			−1.45314			−0.726569	−	0.687093i	$-0.758886\pi$
$761$	−40.0866			−1.45314			−0.726569	+	0.687093i	$0.758886\pi$
$762$		0			0
$763$	1.42231	+	7.72020i	0.0514911	+	0.279490i
$764$		−	3.41696i		−	0.123621i
$765$		0			0
$766$		−	19.3055i		−	0.697535i
$767$	16.0558			0.579740
$768$		0			0
$769$		−	50.0563i		−	1.80508i	−0.430609	−	0.902539i	$-0.641701\pi$
$769$		−	50.0563i		−	1.80508i	0.430609	−	0.902539i	$-0.358299\pi$
$770$	6.35600	+	23.3649i	0.229054	+	0.842014i
$771$		0			0
$772$			1.33662i			0.0481062i
$773$		−	29.0109i		−	1.04345i	−0.853114	−	0.521725i	$-0.825289\pi$
$773$		−	29.0109i		−	1.04345i	0.853114	−	0.521725i	$-0.174711\pi$
$774$		0			0
$775$	−3.58134	−	21.2675i	−0.128646	−	0.763950i
$776$	−1.54485			−0.0554570
$777$		0			0
$778$			29.5936i			1.06098i
$779$			45.1095i			1.61622i
$780$		0			0
$781$	−45.3025			−1.62105
$782$			5.34610i			0.191176i
$783$		0			0
$784$	−6.54042	+	2.49458i	−0.233586	+	0.0890922i
$785$	1.06650	+	12.7558i	0.0380649	+	0.455273i
$786$		0			0
$787$	36.5338			1.30229			0.651145	−	0.758953i	$-0.274289\pi$
$787$	36.5338			1.30229			0.651145	+	0.758953i	$0.274289\pi$
$788$	18.1900			0.647993
$789$		0			0
$790$	2.90267	+	34.7172i	0.103272	+	1.23518i
$791$	0.495151	+	2.68765i	0.0176055	+	0.0955617i
$792$		0			0
$793$		0			0
$794$	−26.0817			−0.925603
$795$		0			0
$796$			21.4113i			0.758902i
$797$		−	24.1671i		−	0.856042i	−0.903769	−	0.428021i	$-0.859211\pi$
$797$		−	24.1671i		−	0.856042i	0.903769	−	0.428021i	$-0.140789\pi$
$798$		0			0
$799$	11.2921			0.399486
$800$	4.93058	−	0.830286i	0.174322	−	0.0293550i
$801$		0			0
$802$			17.6319i			0.622602i
$803$			23.5662i			0.831632i
$804$		0			0
$805$	9.18996	−	2.49996i	0.323903	−	0.0881119i
$806$			15.7644i			0.555276i
$807$		0			0
$808$	−6.34392			−0.223178
$809$		−	10.2400i		−	0.360019i	−0.983665	−	0.180009i	$-0.942387\pi$
$809$		−	10.2400i		−	0.360019i	0.983665	−	0.180009i	$-0.0576128\pi$
$810$		0			0
$811$		−	2.74913i		−	0.0965351i	−0.998834	−	0.0482676i	$-0.984630\pi$
$811$		−	2.74913i		−	0.0965351i	0.998834	−	0.0482676i	$-0.0153700\pi$
$812$	19.5802	−	3.60731i	0.687130	−	0.126592i
$813$		0			0
$814$	−18.6577			−0.653953
$815$	40.6422	−	3.39805i	1.42363	−	0.119029i
$816$		0			0
$817$	10.7106			0.374715
$818$		−	20.0518i		−	0.701094i
$819$		0			0
$820$	1.39016	+	16.6270i	0.0485466	+	0.580639i
$821$			2.91326i			0.101674i	0.998707	+	0.0508368i	$0.0161888\pi$
$821$			2.91326i			0.101674i	−0.998707	+	0.0508368i	$0.983811\pi$
$822$		0			0
$823$			28.6810i			0.999756i	0.866096	+	0.499878i	$0.166622\pi$
$823$			28.6810i			0.999756i	−0.866096	+	0.499878i	$0.833378\pi$
$824$	11.8617			0.413223
$825$		0			0
$826$	−2.10591	−	11.4307i	−0.0732739	−	0.397726i
$827$	−23.0079			−0.800062			−0.400031	−	0.916502i	$-0.631001\pi$
$827$	−23.0079			−0.800062			−0.400031	+	0.916502i	$0.631001\pi$
$828$		0			0
$829$			30.7629i			1.06844i	0.845345	+	0.534221i	$0.179395\pi$
$829$			30.7629i			1.06844i	−0.845345	+	0.534221i	$0.820605\pi$
$830$	−3.54042	+	0.296011i	−0.122890	+	0.0102747i
$831$		0			0
$832$	−3.65475			−0.126706
$833$	−8.28425	−	21.7201i	−0.287032	−	0.752555i
$834$		0			0
$835$	28.1287	−	2.35181i	0.973435	−	0.0813879i
$836$	24.7435			0.855770
$837$		0			0
$838$	0.614051			0.0212120
$839$	−11.6217			−0.401227			−0.200613	−	0.979670i	$-0.564294\pi$
$839$	−11.6217			−0.401227			−0.200613	+	0.979670i	$0.564294\pi$
$840$		0			0
$841$	−27.6281			−0.952693
$842$	−38.4905			−1.32647
$843$		0			0
$844$	13.9704			0.480880
$845$	−0.0665545	−	0.796021i	−0.00228954	−	0.0273839i
$846$		0			0
$847$	2.75729	+	14.9664i	0.0947417	+	0.514251i
$848$	1.14213			0.0392208
$849$		0			0
$850$	2.75729	+	16.3740i	0.0945744	+	0.561622i
$851$			7.33851i			0.251561i
$852$		0			0
$853$	46.4644			1.59091			0.795455	−	0.606013i	$-0.207232\pi$
$853$	46.4644			1.59091			0.795455	+	0.606013i	$0.207232\pi$
$854$		0			0
$855$		0			0
$856$	7.71903			0.263831
$857$			35.7824i			1.22230i	0.791513	+	0.611152i	$0.209293\pi$
$857$			35.7824i			1.22230i	−0.791513	+	0.611152i	$0.790707\pi$
$858$		0			0
$859$		−	4.34687i		−	0.148313i	−0.997247	−	0.0741567i	$-0.976374\pi$
$859$		−	4.34687i		−	0.148313i	0.997247	−	0.0741567i	$-0.0236265\pi$
$860$	3.94782	−	0.330073i	0.134619	−	0.0112554i
$861$		0			0
$862$			10.7021i			0.364515i
$863$	−44.2676			−1.50689			−0.753443	−	0.657513i	$-0.771608\pi$
$863$	−44.2676			−1.50689			−0.753443	+	0.657513i	$0.771608\pi$
$864$		0			0
$865$	−13.7155	+	1.14674i	−0.466340	+	0.0389902i
$866$	28.0604			0.953531
$867$		0			0
$868$	11.2233	−	2.06769i	0.380942	−	0.0701819i
$869$			63.7684i			2.16320i
$870$		0			0
$871$		−	39.7958i		−	1.34843i
$872$	2.96707			0.100478
$873$		0			0
$874$		−	9.73216i		−	0.329195i
$875$	26.8575	−	12.3966i	0.907948	−	0.419082i
$876$		0			0
$877$			26.6116i			0.898611i	0.893378	+	0.449306i	$0.148329\pi$
$877$			26.6116i			0.898611i	−0.893378	+	0.449306i	$0.851671\pi$
$878$			13.5767i			0.458193i
$879$		0			0
$880$	9.12022	−	0.762532i	0.307442	−	0.0257049i
$881$	33.6174			1.13260			0.566300	−	0.824199i	$-0.308374\pi$
$881$	33.6174			1.13260			0.566300	+	0.824199i	$0.308374\pi$
$882$		0			0
$883$			3.76058i			0.126554i	0.997996	+	0.0632768i	$0.0201551\pi$
$883$			3.76058i			0.126554i	−0.997996	+	0.0632768i	$0.979845\pi$
$884$		−	12.1371i		−	0.408214i
$885$		0			0
$886$	38.4563			1.29197
$887$			23.8315i			0.800185i	0.916475	+	0.400092i	$0.131022\pi$
$887$			23.8315i			0.800185i	−0.916475	+	0.400092i	$0.868978\pi$
$888$		0			0
$889$	47.1685	−	8.68997i	1.58198	−	0.291452i
$890$	2.64797	+	31.6709i	0.0887602	+	1.06161i
$891$		0			0
$892$	−26.3861			−0.883473
$893$	−20.5564			−0.687894
$894$		0			0
$895$	3.48673	−	0.291522i	0.116549	−	0.00974450i
$896$	0.479366	+	2.60196i	0.0160145	+	0.0869255i
$897$		0			0
$898$			20.8463i			0.695649i
$899$	−32.4589			−1.08257
$900$		0			0
$901$			3.79289i			0.126359i
$902$			30.5403i			1.01688i
$903$		0			0
$904$	1.03293			0.0343547
$905$	−13.0098	+	1.08773i	−0.432459	+	0.0361575i
$906$		0			0
$907$		−	29.6691i		−	0.985146i	−0.870271	−	0.492573i	$-0.836056\pi$
$907$		−	29.6691i		−	0.985146i	0.870271	−	0.492573i	$-0.163944\pi$
$908$			0.493394i			0.0163739i
$909$		0			0
$910$	−20.8636	+	5.67557i	−0.691623	+	0.188143i
$911$			23.3014i			0.772010i	0.922497	+	0.386005i	$0.126145\pi$
$911$			23.3014i			0.772010i	−0.922497	+	0.386005i	$0.873855\pi$
$912$		0			0
$913$	−6.50302			−0.215218
$914$			32.5602i			1.07699i
$915$		0			0
$916$			8.62677i			0.285036i
$917$	9.01141	+	48.9133i	0.297583	+	1.61526i
$918$		0			0
$919$	−2.92830			−0.0965957			−0.0482978	−	0.998833i	$-0.515380\pi$
$919$	−2.92830			−0.0965957			−0.0482978	+	0.998833i	$0.515380\pi$
$920$	−0.299921	−	3.58719i	−0.00988810	−	0.118266i
$921$		0			0
$922$	38.4037			1.26476
$923$		−	40.4527i		−	1.33152i
$924$		0			0
$925$	3.78489	+	22.4763i	0.124447	+	0.739015i
$926$		−	8.95761i		−	0.294365i
$927$		0			0
$928$		−	7.52516i		−	0.247026i
$929$	17.0628			0.559812			0.279906	−	0.960027i	$-0.409697\pi$
$929$	17.0628			0.559812			0.279906	+	0.960027i	$0.409697\pi$
$930$		0			0
$931$	15.0808	+	39.5397i	0.494254	+	1.29586i
$932$	−28.6894			−0.939752
$933$		0			0
$934$			12.0449i			0.394122i
$935$	2.53229	+	30.2873i	0.0828148	+	0.990501i
$936$		0			0
$937$	−38.2446			−1.24940			−0.624699	−	0.780866i	$-0.714778\pi$
$937$	−38.2446			−1.24940			−0.624699	+	0.780866i	$0.714778\pi$
$938$	−28.3322	+	5.21970i	−0.925078	+	0.170429i
$939$		0			0
$940$	−7.57691	+	0.633497i	−0.247131	+	0.0206624i
$941$	−31.3987			−1.02357			−0.511784	−	0.859114i	$-0.671015\pi$
$941$	−31.3987			−1.02357			−0.511784	+	0.859114i	$0.671015\pi$
$942$		0			0
$943$	12.0122			0.391171
$944$	−4.39312			−0.142984
$945$		0			0
$946$	7.25132			0.235761
$947$	18.7269			0.608542			0.304271	−	0.952585i	$-0.401587\pi$
$947$	18.7269			0.608542			0.304271	+	0.952585i	$0.401587\pi$
$948$		0			0
$949$	−21.0433			−0.683096
$950$	−5.01944	−	29.8075i	−0.162852	−	0.967083i
$951$		0			0
$952$	−8.64085	+	1.59192i	−0.280052	+	0.0515946i
$953$	44.4459			1.43974			0.719872	−	0.694106i	$-0.244200\pi$
$953$	44.4459			1.43974			0.719872	+	0.694106i	$0.244200\pi$
$954$		0			0
$955$	−7.61399	+	0.636598i	−0.246383	+	0.0205998i
$956$			12.6299i			0.408479i
$957$		0			0
$958$	−25.3227			−0.818140
$959$	5.91004	+	32.0793i	0.190845	+	1.03589i
$960$		0			0
$961$	12.3947			0.399830
$962$		−	16.6604i		−	0.537152i
$963$		0			0
$964$		−	22.2370i		−	0.716206i
$965$	2.97839	−	0.249020i	0.0958778	−	0.00801624i
$966$		0			0
$967$			24.6636i			0.793129i	0.918007	+	0.396564i	$0.129798\pi$
$967$			24.6636i			0.793129i	−0.918007	+	0.396564i	$0.870202\pi$
$968$	5.75196			0.184875
$969$		0			0
$970$	0.287814	+	3.44238i	0.00924115	+	0.110528i
$971$	−42.5779			−1.36639			−0.683196	−	0.730236i	$-0.739410\pi$
$971$	−42.5779			−1.36639			−0.683196	+	0.730236i	$0.739410\pi$
$972$		0			0
$973$	−56.7827	+	10.4612i	−1.82037	+	0.335371i
$974$		−	27.6150i		−	0.884840i
$975$		0			0
$976$		0			0
$977$	26.8315			0.858416			0.429208	−	0.903206i	$-0.358793\pi$
$977$	26.8315			0.858416			0.429208	+	0.903206i	$0.358793\pi$
$978$		0			0
$979$			58.1729i			1.85921i
$980$	6.77718	+	14.1092i	0.216489	+	0.450702i
$981$		0			0
$982$			38.4884i			1.22822i
$983$		−	7.92638i		−	0.252812i	−0.991979	−	0.126406i	$-0.959656\pi$
$983$		−	7.92638i		−	0.252812i	0.991979	−	0.126406i	$-0.0403443\pi$
$984$		0			0
$985$	−3.38890	−	40.5327i	−0.107979	−	1.29148i
$986$	24.9903			0.795853
$987$		0			0
$988$			22.0946i			0.702922i
$989$		−	2.85211i		−	0.0906918i
$990$		0			0
$991$	43.3058			1.37565			0.687827	−	0.725875i	$-0.258565\pi$
$991$	43.3058			1.37565			0.687827	+	0.725875i	$0.258565\pi$
$992$		−	4.31338i		−	0.136950i
$993$		0			0
$994$	−28.7999	+	5.30587i	−0.913476	+	0.168292i
$995$	47.7106	−	3.98903i	1.51253	−	0.126461i
$996$		0			0
$997$	−9.74860			−0.308741			−0.154371	−	0.988013i	$-0.549335\pi$
$997$	−9.74860			−0.308741			−0.154371	+	0.988013i	$0.549335\pi$
$998$	−20.2184			−0.640002
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.d.e.1889.7	✓	16
3.2	odd	2		1890.2.d.f.1889.10	yes	16
5.4	even	2		1890.2.d.f.1889.8	yes	16
7.6	odd	2	inner	1890.2.d.e.1889.10	yes	16
15.14	odd	2	inner	1890.2.d.e.1889.9	yes	16
21.20	even	2		1890.2.d.f.1889.7	yes	16
35.34	odd	2		1890.2.d.f.1889.9	yes	16
105.104	even	2	inner	1890.2.d.e.1889.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.d.e.1889.7	✓	16	1.1	even	1	trivial
1890.2.d.e.1889.8	yes	16	105.104	even	2	inner
1890.2.d.e.1889.9	yes	16	15.14	odd	2	inner
1890.2.d.e.1889.10	yes	16	7.6	odd	2	inner
1890.2.d.f.1889.7	yes	16	21.20	even	2
1890.2.d.f.1889.8	yes	16	5.4	even	2
1890.2.d.f.1889.9	yes	16	35.34	odd	2
1890.2.d.f.1889.10	yes	16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.186305 - 2.22829i) q^{5} +(-0.479366 - 2.60196i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.186305 - 2.22829i) q^{5} +(-0.479366 - 2.60196i) q^{7} -1.00000 q^{8} +(0.186305 + 2.22829i) q^{10} +4.09292i q^{11} -3.65475 q^{13} +(0.479366 + 2.60196i) q^{14} +1.00000 q^{16} +3.32090i q^{17} -6.04543i q^{19} +(-0.186305 - 2.22829i) q^{20} -4.09292i q^{22} -1.60984 q^{23} +(-4.93058 + 0.830286i) q^{25} +3.65475 q^{26} +(-0.479366 - 2.60196i) q^{28} +7.52516i q^{29} +4.31338i q^{31} -1.00000 q^{32} -3.32090i q^{34} +(-5.70863 + 1.55293i) q^{35} -4.55854i q^{37} +6.04543i q^{38} +(0.186305 + 2.22829i) q^{40} -7.46175 q^{41} +1.77168i q^{43} +4.09292i q^{44} +1.60984 q^{46} -3.40032i q^{47} +(-6.54042 + 2.49458i) q^{49} +(4.93058 - 0.830286i) q^{50} -3.65475 q^{52} +1.14213 q^{53} +(9.12022 - 0.762532i) q^{55} +(0.479366 + 2.60196i) q^{56} -7.52516i q^{58} -4.39312 q^{59} -4.31338i q^{62} +1.00000 q^{64} +(0.680900 + 8.14387i) q^{65} +10.8888i q^{67} +3.32090i q^{68} +(5.70863 - 1.55293i) q^{70} +11.0685i q^{71} +5.75780 q^{73} +4.55854i q^{74} -6.04543i q^{76} +(10.6496 - 1.96200i) q^{77} +15.5802 q^{79} +(-0.186305 - 2.22829i) q^{80} +7.46175 q^{82} +1.58885i q^{83} +(7.39993 - 0.618701i) q^{85} -1.77168i q^{86} -4.09292i q^{88} +14.2131 q^{89} +(1.75196 + 9.50954i) q^{91} -1.60984 q^{92} +3.40032i q^{94} +(-13.4710 + 1.12630i) q^{95} +1.54485 q^{97} +(6.54042 - 2.49458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} + 16 q^{16} + 8 q^{23} - 6 q^{25} - 16 q^{32} - q^{35} - 8 q^{46} + 2 q^{49} + 6 q^{50} - 16 q^{53} + 16 q^{64} - 40 q^{65} + q^{70} - 14 q^{77} - 8 q^{79} - 44 q^{85} - 40 q^{91} + 8 q^{92} - 36 q^{95} - 2 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 + 16 * q^16 + 8 * q^23 - 6 * q^25 - 16 * q^32 - q^35 - 8 * q^46 + 2 * q^49 + 6 * q^50 - 16 * q^53 + 16 * q^64 - 40 * q^65 + q^70 - 14 * q^77 - 8 * q^79 - 44 * q^85 - 40 * q^91 + 8 * q^92 - 36 * q^95 - 2 * q^98

Introduction

L-functions

Modular forms

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