LMFDB - Embedded newform 1890.2.d.b.1889.8

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:	$8$
Coefficient field:	8.0.77720518656.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 26x^{6} - 64x^{5} + 161x^{4} - 220x^{3} + 232x^{2} - 132x + 33 $ x^8 - 4x^7 + 26x^6 - 64x^5 + 161x^4 - 220x^3 + 232x^2 - 132*x + 33
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1889.8
Root			$0.500000 - 2.17595i$ of defining polynomial
Character	$\chi$	$=$	1890.1889
Dual form			1890.2.d.b.1889.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(2.34521 - 1.22474i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(2.34521 - 1.22474i) q^{7} -1.00000 q^{8} +(-1.73205 - 1.41421i) q^{10} -5.76611i q^{11} +6.42247 q^{13} +(-2.34521 + 1.22474i) q^{14} +1.00000 q^{16} +4.33035i q^{17} +4.24264i q^{19} +(1.73205 + 1.41421i) q^{20} +5.76611i q^{22} +3.00000 q^{23} +(1.00000 + 4.89898i) q^{25} -6.42247 q^{26} +(2.34521 - 1.22474i) q^{28} -3.31662i q^{29} -9.98720i q^{31} -1.00000 q^{32} -4.33035i q^{34} +(5.79407 + 1.19530i) q^{35} +4.89898i q^{37} -4.24264i q^{38} +(-1.73205 - 1.41421i) q^{40} -3.46410 q^{41} -9.94987i q^{43} -5.76611i q^{44} -3.00000 q^{46} -2.91614i q^{47} +(4.00000 - 5.74456i) q^{49} +(-1.00000 - 4.89898i) q^{50} +6.42247 q^{52} -14.1240 q^{53} +(8.15452 - 9.98720i) q^{55} +(-2.34521 + 1.22474i) q^{56} +3.31662i q^{58} -3.46410 q^{59} +4.24264i q^{61} +9.98720i q^{62} +1.00000 q^{64} +(11.1240 + 9.08274i) q^{65} +4.89898i q^{67} +4.33035i q^{68} +(-5.79407 - 1.19530i) q^{70} +6.63325i q^{71} +4.69042 q^{73} -4.89898i q^{74} +4.24264i q^{76} +(-7.06202 - 13.5227i) q^{77} +7.12404 q^{79} +(1.73205 + 1.41421i) q^{80} +3.46410 q^{82} +7.07107i q^{83} +(-6.12404 + 7.50038i) q^{85} +9.94987i q^{86} +5.76611i q^{88} -3.46410 q^{89} +(15.0620 - 7.86588i) q^{91} +3.00000 q^{92} +2.91614i q^{94} +(-6.00000 + 7.34847i) q^{95} -2.23779 q^{97} +(-4.00000 + 5.74456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 8 q^{16} + 24 q^{23} + 8 q^{25} - 8 q^{32} - 24 q^{46} + 32 q^{49} - 8 q^{50} - 48 q^{53} + 8 q^{64} + 24 q^{65} - 24 q^{77} - 8 q^{79} + 16 q^{85} + 88 q^{91} + 24 q^{92} - 48 q^{95} - 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 8 * q^16 + 24 * q^23 + 8 * q^25 - 8 * q^32 - 24 * q^46 + 32 * q^49 - 8 * q^50 - 48 * q^53 + 8 * q^64 + 24 * q^65 - 24 * q^77 - 8 * q^79 + 16 * q^85 + 88 * q^91 + 24 * q^92 - 48 * q^95 - 32 * 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
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$6$		0			0
$7$	2.34521	−	1.22474i	0.886405	−	0.462910i
$7$	2.34521	−	1.22474i	0.886405	−	0.462910i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.73205	−	1.41421i	−0.547723	−	0.447214i
$11$		−	5.76611i		−	1.73855i	−0.494330	−	0.869274i	$-0.664586\pi$
$11$		−	5.76611i		−	1.73855i	0.494330	−	0.869274i	$-0.335414\pi$
$12$		0			0
$13$	6.42247			1.78127			0.890636	−	0.454717i	$-0.150260\pi$
$13$	6.42247			1.78127			0.890636	+	0.454717i	$0.150260\pi$
$14$	−2.34521	+	1.22474i	−0.626783	+	0.327327i
$15$		0			0
$16$	1.00000			0.250000
$17$			4.33035i			1.05026i	0.851021	+	0.525132i	$0.175984\pi$
$17$			4.33035i			1.05026i	−0.851021	+	0.525132i	$0.824016\pi$
$18$		0			0
$19$			4.24264i			0.973329i	0.873589	+	0.486664i	$0.161786\pi$
$19$			4.24264i			0.973329i	−0.873589	+	0.486664i	$0.838214\pi$
$20$	1.73205	+	1.41421i	0.387298	+	0.316228i
$21$		0			0
$22$			5.76611i			1.22934i
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		0			0
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$	−6.42247			−1.25955
$27$		0			0
$28$	2.34521	−	1.22474i	0.443203	−	0.231455i
$29$		−	3.31662i		−	0.615882i	−0.951405	−	0.307941i	$-0.900360\pi$
$29$		−	3.31662i		−	0.615882i	0.951405	−	0.307941i	$-0.0996399\pi$
$30$		0			0
$31$		−	9.98720i		−	1.79375i	−0.442279	−	0.896877i	$-0.645830\pi$
$31$		−	9.98720i		−	1.79375i	0.442279	−	0.896877i	$-0.354170\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		−	4.33035i		−	0.742649i
$35$	5.79407	+	1.19530i	0.979377	+	0.202043i
$36$		0			0
$37$			4.89898i			0.805387i	0.915335	+	0.402694i	$0.131926\pi$
$37$			4.89898i			0.805387i	−0.915335	+	0.402694i	$0.868074\pi$
$38$		−	4.24264i		−	0.688247i
$39$		0			0
$40$	−1.73205	−	1.41421i	−0.273861	−	0.223607i
$41$	−3.46410			−0.541002			−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410			−0.541002			−0.270501	+	0.962720i	$0.587189\pi$
$42$		0			0
$43$		−	9.94987i		−	1.51734i	−0.651474	−	0.758671i	$-0.725849\pi$
$43$		−	9.94987i		−	1.51734i	0.651474	−	0.758671i	$-0.274151\pi$
$44$		−	5.76611i		−	0.869274i
$45$		0			0
$46$	−3.00000			−0.442326
$47$		−	2.91614i		−	0.425362i	−0.977122	−	0.212681i	$-0.931780\pi$
$47$		−	2.91614i		−	0.425362i	0.977122	−	0.212681i	$-0.0682195\pi$
$48$		0			0
$49$	4.00000	−	5.74456i	0.571429	−	0.820652i
$50$	−1.00000	−	4.89898i	−0.141421	−	0.692820i
$51$		0			0
$52$	6.42247			0.890636
$53$	−14.1240			−1.94009			−0.970043	−	0.242934i	$-0.921890\pi$
$53$	−14.1240			−1.94009			−0.970043	+	0.242934i	$0.921890\pi$
$54$		0			0
$55$	8.15452	−	9.98720i	1.09955	−	1.34667i
$56$	−2.34521	+	1.22474i	−0.313392	+	0.163663i
$57$		0			0
$58$			3.31662i			0.435494i
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$		0			0
$61$			4.24264i			0.543214i	0.962408	+	0.271607i	$0.0875552\pi$
$61$			4.24264i			0.543214i	−0.962408	+	0.271607i	$0.912445\pi$
$62$			9.98720i			1.26838i
$63$		0			0
$64$	1.00000			0.125000
$65$	11.1240	+	9.08274i	1.37977	+	1.12658i
$66$		0			0
$67$			4.89898i			0.598506i	0.954174	+	0.299253i	$0.0967374\pi$
$67$			4.89898i			0.598506i	−0.954174	+	0.299253i	$0.903263\pi$
$68$			4.33035i			0.525132i
$69$		0			0
$70$	−5.79407	−	1.19530i	−0.692524	−	0.142866i
$71$			6.63325i			0.787222i	0.919277	+	0.393611i	$0.128774\pi$
$71$			6.63325i			0.787222i	−0.919277	+	0.393611i	$0.871226\pi$
$72$		0			0
$73$	4.69042			0.548972			0.274486	−	0.961591i	$-0.411492\pi$
$73$	4.69042			0.548972			0.274486	+	0.961591i	$0.411492\pi$
$74$		−	4.89898i		−	0.569495i
$75$		0			0
$76$			4.24264i			0.486664i
$77$	−7.06202	−	13.5227i	−0.804792	−	1.54106i
$78$		0			0
$79$	7.12404			0.801517			0.400758	−	0.916184i	$-0.368747\pi$
$79$	7.12404			0.801517			0.400758	+	0.916184i	$0.368747\pi$
$80$	1.73205	+	1.41421i	0.193649	+	0.158114i
$81$		0			0
$82$	3.46410			0.382546
$83$			7.07107i			0.776151i	0.921628	+	0.388075i	$0.126860\pi$
$83$			7.07107i			0.776151i	−0.921628	+	0.388075i	$0.873140\pi$
$84$		0			0
$85$	−6.12404	+	7.50038i	−0.664245	+	0.813531i
$86$			9.94987i			1.07292i
$87$		0			0
$88$			5.76611i			0.614670i
$89$	−3.46410			−0.367194			−0.183597	−	0.983002i	$-0.558774\pi$
$89$	−3.46410			−0.367194			−0.183597	+	0.983002i	$0.558774\pi$
$90$		0			0
$91$	15.0620	−	7.86588i	1.57893	−	0.824569i
$92$	3.00000			0.312772
$93$		0			0
$94$			2.91614i			0.300776i
$95$	−6.00000	+	7.34847i	−0.615587	+	0.753937i
$96$		0			0
$97$	−2.23779			−0.227213			−0.113606	−	0.993526i	$-0.536240\pi$
$97$	−2.23779			−0.227213			−0.113606	+	0.993526i	$0.536240\pi$
$98$	−4.00000	+	5.74456i	−0.404061	+	0.580288i
$99$		0			0
$100$	1.00000	+	4.89898i	0.100000	+	0.489898i
$101$	8.66025			0.861727			0.430864	−	0.902417i	$-0.358209\pi$
$101$	8.66025			0.861727			0.430864	+	0.902417i	$0.358209\pi$
$102$		0			0
$103$	−5.70189			−0.561824			−0.280912	−	0.959734i	$-0.590637\pi$
$103$	−5.70189			−0.561824			−0.280912	+	0.959734i	$0.590637\pi$
$104$	−6.42247			−0.629775
$105$		0			0
$106$	14.1240			1.37185
$107$	−2.12404			−0.205339			−0.102669	−	0.994716i	$-0.532738\pi$
$107$	−2.12404			−0.205339			−0.102669	+	0.994716i	$0.532738\pi$
$108$		0			0
$109$	4.12404			0.395011			0.197506	−	0.980302i	$-0.436716\pi$
$109$	4.12404			0.395011			0.197506	+	0.980302i	$0.436716\pi$
$110$	−8.15452	+	9.98720i	−0.777503	+	0.952242i
$111$		0			0
$112$	2.34521	−	1.22474i	0.221601	−	0.115728i
$113$	0.875962			0.0824035			0.0412018	−	0.999151i	$-0.486881\pi$
$113$	0.875962			0.0824035			0.0412018	+	0.999151i	$0.486881\pi$
$114$		0			0
$115$	5.19615	+	4.24264i	0.484544	+	0.395628i
$116$		−	3.31662i		−	0.307941i
$117$		0			0
$118$	3.46410			0.318896
$119$	5.30357	+	10.1556i	0.486178	+	0.930959i
$120$		0			0
$121$	−22.2481			−2.02255
$122$		−	4.24264i		−	0.384111i
$123$		0			0
$124$		−	9.98720i		−	0.896877i
$125$	−5.19615	+	9.89949i	−0.464758	+	0.885438i
$126$		0			0
$127$		−	4.89898i		−	0.434714i	−0.976092	−	0.217357i	$-0.930256\pi$
$127$		−	4.89898i		−	0.434714i	0.976092	−	0.217357i	$-0.0697436\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−11.1240	−	9.08274i	−0.975643	−	0.796609i
$131$	19.2674			1.68340			0.841700	−	0.539945i	$-0.181555\pi$
$131$	19.2674			1.68340			0.841700	+	0.539945i	$0.181555\pi$
$132$		0			0
$133$	5.19615	+	9.94987i	0.450564	+	0.862764i
$134$		−	4.89898i		−	0.423207i
$135$		0			0
$136$		−	4.33035i		−	0.371324i
$137$	16.2481			1.38817			0.694083	−	0.719895i	$-0.255810\pi$
$137$	16.2481			1.38817			0.694083	+	0.719895i	$0.255810\pi$
$138$		0			0
$139$		−	8.48528i		−	0.719712i	−0.933008	−	0.359856i	$-0.882826\pi$
$139$		−	8.48528i		−	0.719712i	0.933008	−	0.359856i	$-0.117174\pi$
$140$	5.79407	+	1.19530i	0.489688	+	0.101022i
$141$		0			0
$142$		−	6.63325i		−	0.556650i
$143$		−	37.0327i		−	3.09683i
$144$		0			0
$145$	4.69042	−	5.74456i	0.389518	−	0.477060i
$146$	−4.69042			−0.388182
$147$		0			0
$148$			4.89898i			0.402694i
$149$		−	18.0136i		−	1.47573i	−0.674949	−	0.737864i	$-0.735834\pi$
$149$		−	18.0136i		−	1.47573i	0.674949	−	0.737864i	$-0.264166\pi$
$150$		0			0
$151$	−15.1240			−1.23078			−0.615388	−	0.788224i	$-0.711001\pi$
$151$	−15.1240			−1.23078			−0.615388	+	0.788224i	$0.711001\pi$
$152$		−	4.24264i		−	0.344124i
$153$		0			0
$154$	7.06202	+	13.5227i	0.569074	+	1.08969i
$155$	14.1240	−	17.2983i	1.13447	−	1.38944i
$156$		0			0
$157$	−0.505737			−0.0403622			−0.0201811	−	0.999796i	$-0.506424\pi$
$157$	−0.505737			−0.0403622			−0.0201811	+	0.999796i	$0.506424\pi$
$158$	−7.12404			−0.566758
$159$		0			0
$160$	−1.73205	−	1.41421i	−0.136931	−	0.111803i
$161$	7.03562	−	3.67423i	0.554485	−	0.289570i
$162$		0			0
$163$			4.74706i			0.371819i	0.982567	+	0.185909i	$0.0595231\pi$
$163$			4.74706i			0.371819i	−0.982567	+	0.185909i	$0.940477\pi$
$164$	−3.46410			−0.270501
$165$		0			0
$166$		−	7.07107i		−	0.548821i
$167$		−	0.175417i		−	0.0135742i	−0.999977	−	0.00678708i	$-0.997840\pi$
$167$		−	0.175417i		−	0.0135742i	0.999977	−	0.00678708i	$-0.00216041\pi$
$168$		0			0
$169$	28.2481			2.17293
$170$	6.12404	−	7.50038i	0.469692	−	0.575253i
$171$		0			0
$172$		−	9.94987i		−	0.758671i
$173$		−	5.65685i		−	0.430083i	−0.976605	−	0.215041i	$-0.931011\pi$
$173$		−	5.65685i		−	0.430083i	0.976605	−	0.215041i	$-0.0689886\pi$
$174$		0			0
$175$	8.34521	+	10.2644i	0.630838	+	0.775914i
$176$		−	5.76611i		−	0.434637i
$177$		0			0
$178$	3.46410			0.259645
$179$			21.3302i			1.59429i	0.603786	+	0.797147i	$0.293658\pi$
$179$			21.3302i			1.59429i	−0.603786	+	0.797147i	$0.706342\pi$
$180$		0			0
$181$			11.4891i			0.853980i	0.904256	+	0.426990i	$0.140426\pi$
$181$			11.4891i			0.853980i	−0.904256	+	0.426990i	$0.859574\pi$
$182$	−15.0620	+	7.86588i	−1.11647	+	0.583058i
$183$		0			0
$184$	−3.00000			−0.221163
$185$	−6.92820	+	8.48528i	−0.509372	+	0.623850i
$186$		0			0
$187$	24.9693			1.82594
$188$		−	2.91614i		−	0.212681i
$189$		0			0
$190$	6.00000	−	7.34847i	0.435286	−	0.533114i
$191$		−	5.91803i		−	0.428214i	−0.976810	−	0.214107i	$-0.931316\pi$
$191$		−	5.91803i		−	0.428214i	0.976810	−	0.214107i	$-0.0686841\pi$
$192$		0			0
$193$			27.2482i			1.96137i	0.195595	+	0.980685i	$0.437336\pi$
$193$			27.2482i			1.96137i	−0.195595	+	0.980685i	$0.562664\pi$
$194$	2.23779			0.160664
$195$		0			0
$196$	4.00000	−	5.74456i	0.285714	−	0.410326i
$197$	20.1240			1.43378			0.716889	−	0.697187i	$-0.245565\pi$
$197$	20.1240			1.43378			0.716889	+	0.697187i	$0.245565\pi$
$198$		0			0
$199$			15.4686i			1.09654i	0.836300	+	0.548271i	$0.184714\pi$
$199$			15.4686i			1.09654i	−0.836300	+	0.548271i	$0.815286\pi$
$200$	−1.00000	−	4.89898i	−0.0707107	−	0.346410i
$201$		0			0
$202$	−8.66025			−0.609333
$203$	−4.06202	−	7.77817i	−0.285098	−	0.545921i
$204$		0			0
$205$	−6.00000	−	4.89898i	−0.419058	−	0.342160i
$206$	5.70189			0.397269
$207$		0			0
$208$	6.42247			0.445318
$209$	24.4636			1.69218
$210$		0			0
$211$	−8.24808			−0.567821			−0.283911	−	0.958851i	$-0.591632\pi$
$211$	−8.24808			−0.567821			−0.283911	+	0.958851i	$0.591632\pi$
$212$	−14.1240			−0.970043
$213$		0			0
$214$	2.12404			0.145196
$215$	14.0712	−	17.2337i	0.959651	−	1.17533i
$216$		0			0
$217$	−12.2318	−	23.4221i	−0.830347	−	1.58999i
$218$	−4.12404			−0.279315
$219$		0			0
$220$	8.15452	−	9.98720i	0.549777	−	0.673337i
$221$			27.8115i			1.87081i
$222$		0			0
$223$	−12.8449			−0.860160			−0.430080	−	0.902791i	$-0.641515\pi$
$223$	−12.8449			−0.860160			−0.430080	+	0.902791i	$0.641515\pi$
$224$	−2.34521	+	1.22474i	−0.156696	+	0.0818317i
$225$		0			0
$226$	−0.875962			−0.0582681
$227$		−	8.66070i		−	0.574831i	−0.957806	−	0.287415i	$-0.907204\pi$
$227$		−	8.66070i		−	0.574831i	0.957806	−	0.287415i	$-0.0927960\pi$
$228$		0			0
$229$		−	3.00384i		−	0.198500i	−0.995063	−	0.0992498i	$-0.968356\pi$
$229$		−	3.00384i		−	0.198500i	0.995063	−	0.0992498i	$-0.0316443\pi$
$230$	−5.19615	−	4.24264i	−0.342624	−	0.279751i
$231$		0			0
$232$			3.31662i			0.217747i
$233$	−10.2481			−0.671374			−0.335687	−	0.941974i	$-0.608968\pi$
$233$	−10.2481			−0.671374			−0.335687	+	0.941974i	$0.608968\pi$
$234$		0			0
$235$	4.12404	−	5.05089i	0.269023	−	0.329484i
$236$	−3.46410			−0.225494
$237$		0			0
$238$	−5.30357	−	10.1556i	−0.343780	−	0.658288i
$239$			13.9817i			0.904402i	0.891916	+	0.452201i	$0.149361\pi$
$239$			13.9817i			0.904402i	−0.891916	+	0.452201i	$0.850639\pi$
$240$		0			0
$241$		−	22.7151i		−	1.46321i	−0.681729	−	0.731605i	$-0.738772\pi$
$241$		−	22.7151i		−	1.46321i	0.681729	−	0.731605i	$-0.261228\pi$
$242$	22.2481			1.43016
$243$		0			0
$244$			4.24264i			0.271607i
$245$	15.0522	−	4.29302i	0.961652	−	0.274271i
$246$		0			0
$247$			27.2482i			1.73376i
$248$			9.98720i			0.634188i
$249$		0			0
$250$	5.19615	−	9.89949i	0.328634	−	0.626099i
$251$	15.8033			0.997495			0.498748	−	0.866747i	$-0.333793\pi$
$251$	15.8033			0.997495			0.498748	+	0.866747i	$0.333793\pi$
$252$		0			0
$253$		−	17.2983i		−	1.08754i
$254$			4.89898i			0.307389i
$255$		0			0
$256$	1.00000			0.0625000
$257$			24.3048i			1.51609i	0.652203	+	0.758045i	$0.273845\pi$
$257$			24.3048i			1.51609i	−0.652203	+	0.758045i	$0.726155\pi$
$258$		0			0
$259$	6.00000	+	11.4891i	0.372822	+	0.713900i
$260$	11.1240	+	9.08274i	0.689884	+	0.563288i
$261$		0			0
$262$	−19.2674			−1.19034
$263$	−22.2481			−1.37188			−0.685938	−	0.727660i	$-0.740608\pi$
$263$	−22.2481			−1.37188			−0.685938	+	0.727660i	$0.740608\pi$
$264$		0			0
$265$	−24.4636	−	19.9744i	−1.50278	−	1.22702i
$266$	−5.19615	−	9.94987i	−0.318597	−	0.610066i
$267$		0			0
$268$			4.89898i			0.299253i
$269$	1.73205			0.105605			0.0528025	−	0.998605i	$-0.483185\pi$
$269$	1.73205			0.105605			0.0528025	+	0.998605i	$0.483185\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$			4.33035i			0.262566i
$273$		0			0
$274$	−16.2481			−0.981582
$275$	28.2481	−	5.76611i	1.70342	−	0.347710i
$276$		0			0
$277$			14.6969i			0.883053i	0.897248	+	0.441527i	$0.145563\pi$
$277$			14.6969i			0.883053i	−0.897248	+	0.441527i	$0.854437\pi$
$278$			8.48528i			0.508913i
$279$		0			0
$280$	−5.79407	−	1.19530i	−0.346262	−	0.0714331i
$281$		−	10.5132i		−	0.627164i	−0.949561	−	0.313582i	$-0.898471\pi$
$281$		−	10.5132i		−	0.627164i	0.949561	−	0.313582i	$-0.101529\pi$
$282$		0			0
$283$	−16.3090			−0.969471			−0.484736	−	0.874661i	$-0.661084\pi$
$283$	−16.3090			−0.969471			−0.484736	+	0.874661i	$0.661084\pi$
$284$			6.63325i			0.393611i
$285$		0			0
$286$			37.0327i			2.18979i
$287$	−8.12404	+	4.24264i	−0.479547	+	0.250435i
$288$		0			0
$289$	−1.75192			−0.103054
$290$	−4.69042	+	5.74456i	−0.275431	+	0.337332i
$291$		0			0
$292$	4.69042			0.274486
$293$		−	18.3848i		−	1.07405i	−0.843566	−	0.537025i	$-0.819548\pi$
$293$		−	18.3848i		−	1.07405i	0.843566	−	0.537025i	$-0.180452\pi$
$294$		0			0
$295$	−6.00000	−	4.89898i	−0.349334	−	0.285230i
$296$		−	4.89898i		−	0.284747i
$297$		0			0
$298$			18.0136i			1.04350i
$299$	19.2674			1.11426
$300$		0			0
$301$	−12.1861	−	23.3345i	−0.702393	−	1.34498i
$302$	15.1240			0.870291
$303$		0			0
$304$			4.24264i			0.243332i
$305$	−6.00000	+	7.34847i	−0.343559	+	0.420772i
$306$		0			0
$307$	13.1358			0.749701			0.374851	−	0.927085i	$-0.377694\pi$
$307$	13.1358			0.749701			0.374851	+	0.927085i	$0.377694\pi$
$308$	−7.06202	−	13.5227i	−0.402396	−	0.770529i
$309$		0			0
$310$	−14.1240	+	17.2983i	−0.802191	+	0.982480i
$311$	14.0712			0.797907			0.398954	−	0.916971i	$-0.369373\pi$
$311$	14.0712			0.797907			0.398954	+	0.916971i	$0.369373\pi$
$312$		0			0
$313$	−19.7731			−1.11764			−0.558822	−	0.829288i	$-0.688746\pi$
$313$	−19.7731			−1.11764			−0.558822	+	0.829288i	$0.688746\pi$
$314$	0.505737			0.0285404
$315$		0			0
$316$	7.12404			0.400758
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$		0			0
$319$	−19.1240			−1.07074
$320$	1.73205	+	1.41421i	0.0968246	+	0.0790569i
$321$		0			0
$322$	−7.03562	+	3.67423i	−0.392080	+	0.204757i
$323$	−18.3721			−1.02225
$324$		0			0
$325$	6.42247	+	31.4635i	0.356254	+	1.74528i
$326$		−	4.74706i		−	0.262916i
$327$		0			0
$328$	3.46410			0.191273
$329$	−3.57152	−	6.83894i	−0.196904	−	0.377043i
$330$		0			0
$331$	−22.0000			−1.20923			−0.604615	−	0.796518i	$-0.706673\pi$
$331$	−22.0000			−1.20923			−0.604615	+	0.796518i	$0.706673\pi$
$332$			7.07107i			0.388075i
$333$		0			0
$334$			0.175417i			0.00959838i
$335$	−6.92820	+	8.48528i	−0.378528	+	0.463600i
$336$		0			0
$337$		−	24.4949i		−	1.33432i	−0.744914	−	0.667161i	$-0.767509\pi$
$337$		−	24.4949i		−	1.33432i	0.744914	−	0.667161i	$-0.232491\pi$
$338$	−28.2481			−1.53649
$339$		0			0
$340$	−6.12404	+	7.50038i	−0.332123	+	0.406765i
$341$	−57.5874			−3.11853
$342$		0			0
$343$	2.34521	−	18.3712i	0.126629	−	0.991950i
$344$			9.94987i			0.536461i
$345$		0			0
$346$			5.65685i			0.304114i
$347$	18.3721			0.986267			0.493133	−	0.869954i	$-0.335851\pi$
$347$	18.3721			0.986267			0.493133	+	0.869954i	$0.335851\pi$
$348$		0			0
$349$			25.4558i			1.36262i	0.731995	+	0.681310i	$0.238589\pi$
$349$			25.4558i			1.36262i	−0.731995	+	0.681310i	$0.761411\pi$
$350$	−8.34521	−	10.2644i	−0.446070	−	0.548654i
$351$		0			0
$352$			5.76611i			0.307335i
$353$			15.8195i			0.841986i	0.907064	+	0.420993i	$0.138318\pi$
$353$			15.8195i			0.841986i	−0.907064	+	0.420993i	$0.861682\pi$
$354$		0			0
$355$	−9.38083	+	11.4891i	−0.497883	+	0.609779i
$356$	−3.46410			−0.183597
$357$		0			0
$358$		−	21.3302i		−	1.12734i
$359$			19.1845i			1.01252i	0.862381	+	0.506260i	$0.168973\pi$
$359$			19.1845i			1.01252i	−0.862381	+	0.506260i	$0.831027\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	11.4891i		−	0.603855i
$363$		0			0
$364$	15.0620	−	7.86588i	0.789464	−	0.412284i
$365$	8.12404	+	6.63325i	0.425232	+	0.347200i
$366$		0			0
$367$	−12.8449			−0.670500			−0.335250	−	0.942129i	$-0.608821\pi$
$367$	−12.8449			−0.670500			−0.335250	+	0.942129i	$0.608821\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	6.92820	−	8.48528i	0.360180	−	0.441129i
$371$	−33.1238	+	17.2983i	−1.71970	+	0.898085i
$372$		0			0
$373$		−	2.60141i		−	0.134696i	−0.997730	−	0.0673478i	$-0.978546\pi$
$373$		−	2.60141i		−	0.134696i	0.997730	−	0.0673478i	$-0.0214537\pi$
$374$	−24.9693			−1.29113
$375$		0			0
$376$			2.91614i			0.150388i
$377$		−	21.3009i		−	1.09705i
$378$		0			0
$379$	38.3721			1.97104			0.985522	−	0.169550i	$-0.0542314\pi$
$379$	38.3721			1.97104			0.985522	+	0.169550i	$0.0542314\pi$
$380$	−6.00000	+	7.34847i	−0.307794	+	0.376969i
$381$		0			0
$382$			5.91803i			0.302793i
$383$		−	31.3758i		−	1.60323i	−0.597841	−	0.801615i	$-0.703975\pi$
$383$		−	31.3758i		−	1.60323i	0.597841	−	0.801615i	$-0.296025\pi$
$384$		0			0
$385$	6.89226	−	33.4093i	0.351262	−	1.70269i
$386$		−	27.2482i		−	1.38690i
$387$		0			0
$388$	−2.23779			−0.113606
$389$			1.58235i			0.0802286i	0.999195	+	0.0401143i	$0.0127722\pi$
$389$			1.58235i			0.0802286i	−0.999195	+	0.0401143i	$0.987228\pi$
$390$		0			0
$391$			12.9910i			0.656985i
$392$	−4.00000	+	5.74456i	−0.202031	+	0.290144i
$393$		0			0
$394$	−20.1240			−1.01383
$395$	12.3392	+	10.0749i	0.620852	+	0.506924i
$396$		0			0
$397$	−18.2559			−0.916239			−0.458119	−	0.888891i	$-0.651477\pi$
$397$	−18.2559			−0.916239			−0.458119	+	0.888891i	$0.651477\pi$
$398$		−	15.4686i		−	0.775373i
$399$		0			0
$400$	1.00000	+	4.89898i	0.0500000	+	0.244949i
$401$		−	20.6150i		−	1.02946i	−0.857352	−	0.514731i	$-0.827892\pi$
$401$		−	20.6150i		−	1.02946i	0.857352	−	0.514731i	$-0.172108\pi$
$402$		0			0
$403$		−	64.1425i		−	3.19516i
$404$	8.66025			0.430864
$405$		0			0
$406$	4.06202	+	7.77817i	0.201595	+	0.386024i
$407$	28.2481			1.40021
$408$		0			0
$409$			20.2375i			1.00068i	0.865829	+	0.500341i	$0.166792\pi$
$409$			20.2375i			1.00068i	−0.865829	+	0.500341i	$0.833208\pi$
$410$	6.00000	+	4.89898i	0.296319	+	0.241943i
$411$		0			0
$412$	−5.70189			−0.280912
$413$	−8.12404	+	4.24264i	−0.399758	+	0.208767i
$414$		0			0
$415$	−10.0000	+	12.2474i	−0.490881	+	0.601204i
$416$	−6.42247			−0.314887
$417$		0			0
$418$	−24.4636			−1.19655
$419$	−1.94689			−0.0951119			−0.0475559	−	0.998869i	$-0.515143\pi$
$419$	−1.94689			−0.0951119			−0.0475559	+	0.998869i	$0.515143\pi$
$420$		0			0
$421$	−2.24808			−0.109565			−0.0547823	−	0.998498i	$-0.517446\pi$
$421$	−2.24808			−0.109565			−0.0547823	+	0.998498i	$0.517446\pi$
$422$	8.24808			0.401510
$423$		0			0
$424$	14.1240			0.685924
$425$	−21.2143	+	4.33035i	−1.02904	+	0.210053i
$426$		0			0
$427$	5.19615	+	9.94987i	0.251459	+	0.481508i
$428$	−2.12404			−0.102669
$429$		0			0
$430$	−14.0712	+	17.2337i	−0.678576	+	0.831082i
$431$			23.7797i			1.14543i	0.819756	+	0.572713i	$0.194109\pi$
$431$			23.7797i			1.14543i	−0.819756	+	0.572713i	$0.805891\pi$
$432$		0			0
$433$	21.7961			1.04745			0.523726	−	0.851886i	$-0.324541\pi$
$433$	21.7961			1.04745			0.523726	+	0.851886i	$0.324541\pi$
$434$	12.2318	+	23.4221i	0.587144	+	1.12430i
$435$		0			0
$436$	4.12404			0.197506
$437$			12.7279i			0.608859i
$438$		0			0
$439$			22.9783i			1.09669i	0.836252	+	0.548346i	$0.184742\pi$
$439$			22.9783i			1.09669i	−0.836252	+	0.548346i	$0.815258\pi$
$440$	−8.15452	+	9.98720i	−0.388751	+	0.476121i
$441$		0			0
$442$		−	27.8115i		−	1.32286i
$443$	1.75192			0.0832364			0.0416182	−	0.999134i	$-0.486749\pi$
$443$	1.75192			0.0832364			0.0416182	+	0.999134i	$0.486749\pi$
$444$		0			0
$445$	−6.00000	−	4.89898i	−0.284427	−	0.232234i
$446$	12.8449			0.608225
$447$		0			0
$448$	2.34521	−	1.22474i	0.110801	−	0.0578638i
$449$		−	35.3119i		−	1.66647i	−0.552918	−	0.833236i	$-0.686486\pi$
$449$		−	35.3119i		−	1.66647i	0.552918	−	0.833236i	$-0.313514\pi$
$450$		0			0
$451$			19.9744i			0.940558i
$452$	0.875962			0.0412018
$453$		0			0
$454$			8.66070i			0.406467i
$455$	37.2122	+	7.67680i	1.74454	+	0.359894i
$456$		0			0
$457$			2.14566i			0.100370i	0.998740	+	0.0501848i	$0.0159810\pi$
$457$			2.14566i			0.100370i	−0.998740	+	0.0501848i	$0.984019\pi$
$458$			3.00384i			0.140360i
$459$		0			0
$460$	5.19615	+	4.24264i	0.242272	+	0.197814i
$461$	−31.6066			−1.47207			−0.736033	−	0.676946i	$-0.763303\pi$
$461$	−31.6066			−1.47207			−0.736033	+	0.676946i	$0.763303\pi$
$462$		0			0
$463$			0.303831i			0.0141202i	0.999975	+	0.00706011i	$0.00224732\pi$
$463$			0.303831i			0.0141202i	−0.999975	+	0.00706011i	$0.997753\pi$
$464$		−	3.31662i		−	0.153970i
$465$		0			0
$466$	10.2481			0.474733
$467$			22.8028i			1.05519i	0.849496	+	0.527595i	$0.176906\pi$
$467$			22.8028i			1.05519i	−0.849496	+	0.527595i	$0.823094\pi$
$468$		0			0
$469$	6.00000	+	11.4891i	0.277054	+	0.530519i
$470$	−4.12404	+	5.05089i	−0.190228	+	0.232980i
$471$		0			0
$472$	3.46410			0.159448
$473$	−57.3721			−2.63797
$474$		0			0
$475$	−20.7846	+	4.24264i	−0.953663	+	0.194666i
$476$	5.30357	+	10.1556i	0.243089	+	0.465480i
$477$		0			0
$478$		−	13.9817i		−	0.639509i
$479$	17.7502			0.811027			0.405513	−	0.914089i	$-0.367093\pi$
$479$	17.7502			0.811027			0.405513	+	0.914089i	$0.367093\pi$
$480$		0			0
$481$			31.4635i			1.43461i
$482$			22.7151i			1.03465i
$483$		0			0
$484$	−22.2481			−1.01128
$485$	−3.87596	−	3.16471i	−0.175998	−	0.143702i
$486$		0			0
$487$		−	12.2474i		−	0.554985i	−0.960728	−	0.277492i	$-0.910497\pi$
$487$		−	12.2474i		−	0.554985i	0.960728	−	0.277492i	$-0.0895033\pi$
$488$		−	4.24264i		−	0.192055i
$489$		0			0
$490$	−15.0522	+	4.29302i	−0.679991	+	0.193939i
$491$		−	18.1655i		−	0.819797i	−0.912131	−	0.409898i	$-0.865564\pi$
$491$		−	18.1655i		−	0.819797i	0.912131	−	0.409898i	$-0.134436\pi$
$492$		0			0
$493$	14.3621			0.646838
$494$		−	27.2482i		−	1.22596i
$495$		0			0
$496$		−	9.98720i		−	0.448439i
$497$	8.12404	+	15.5563i	0.364413	+	0.697798i
$498$		0			0
$499$	−42.1240			−1.88573			−0.942865	−	0.333174i	$-0.891880\pi$
$499$	−42.1240			−1.88573			−0.942865	+	0.333174i	$0.891880\pi$
$500$	−5.19615	+	9.89949i	−0.232379	+	0.442719i
$501$		0			0
$502$	−15.8033			−0.705336
$503$		−	5.39373i		−	0.240494i	−0.992744	−	0.120247i	$-0.961631\pi$
$503$		−	5.39373i		−	0.240494i	0.992744	−	0.120247i	$-0.0383687\pi$
$504$		0			0
$505$	15.0000	+	12.2474i	0.667491	+	0.545004i
$506$			17.2983i			0.769005i
$507$		0			0
$508$		−	4.89898i		−	0.217357i
$509$	−12.5540			−0.556448			−0.278224	−	0.960516i	$-0.589746\pi$
$509$	−12.5540			−0.556448			−0.278224	+	0.960516i	$0.589746\pi$
$510$		0			0
$511$	11.0000	−	5.74456i	0.486611	−	0.254124i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	24.3048i		−	1.07204i
$515$	−9.87596	−	8.06369i	−0.435187	−	0.355329i
$516$		0			0
$517$	−16.8148			−0.739513
$518$	−6.00000	−	11.4891i	−0.263625	−	0.504803i
$519$		0			0
$520$	−11.1240	−	9.08274i	−0.487821	−	0.398304i
$521$	17.1057			0.749413			0.374706	−	0.927144i	$-0.377743\pi$
$521$	17.1057			0.749413			0.374706	+	0.927144i	$0.377743\pi$
$522$		0			0
$523$	−24.9693			−1.09183			−0.545915	−	0.837840i	$-0.683818\pi$
$523$	−24.9693			−1.09183			−0.545915	+	0.837840i	$0.683818\pi$
$524$	19.2674			0.841700
$525$		0			0
$526$	22.2481			0.970062
$527$	43.2481			1.88392
$528$		0			0
$529$	−14.0000			−0.608696
$530$	24.4636	+	19.9744i	1.06263	+	0.867633i
$531$		0			0
$532$	5.19615	+	9.94987i	0.225282	+	0.431382i
$533$	−22.2481			−0.963671
$534$		0			0
$535$	−3.67894	−	3.00384i	−0.159055	−	0.129867i
$536$		−	4.89898i		−	0.211604i
$537$		0			0
$538$	−1.73205			−0.0746740
$539$	−33.1238	−	23.0645i	−1.42674	−	0.993457i
$540$		0			0
$541$	−42.1240			−1.81105			−0.905527	−	0.424289i	$-0.860524\pi$
$541$	−42.1240			−1.81105			−0.905527	+	0.424289i	$0.860524\pi$
$542$		0			0
$543$		0			0
$544$		−	4.33035i		−	0.185662i
$545$	7.14304	+	5.83227i	0.305974	+	0.249827i
$546$		0			0
$547$			9.94987i			0.425426i	0.977115	+	0.212713i	$0.0682299\pi$
$547$			9.94987i			0.425426i	−0.977115	+	0.212713i	$0.931770\pi$
$548$	16.2481			0.694083
$549$		0			0
$550$	−28.2481	+	5.76611i	−1.20450	+	0.245868i
$551$	14.0712			0.599455
$552$		0			0
$553$	16.7074	−	8.72513i	0.710469	−	0.371030i
$554$		−	14.6969i		−	0.624413i
$555$		0			0
$556$		−	8.48528i		−	0.359856i
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$		0			0
$559$		−	63.9027i		−	2.70280i
$560$	5.79407	+	1.19530i	0.244844	+	0.0505108i
$561$		0			0
$562$			10.5132i			0.443472i
$563$			24.0416i			1.01323i	0.862171	+	0.506617i	$0.169104\pi$
$563$			24.0416i			1.01323i	−0.862171	+	0.506617i	$0.830896\pi$
$564$		0			0
$565$	1.51721	+	1.23880i	0.0638295	+	0.0521166i
$566$	16.3090			0.685520
$567$		0			0
$568$		−	6.63325i		−	0.278325i
$569$			8.77891i			0.368031i	0.982923	+	0.184015i	$0.0589097\pi$
$569$			8.77891i			0.368031i	−0.982923	+	0.184015i	$0.941090\pi$
$570$		0			0
$571$	−34.3721			−1.43843			−0.719214	−	0.694788i	$-0.755498\pi$
$571$	−34.3721			−1.43843			−0.719214	+	0.694788i	$0.755498\pi$
$572$		−	37.0327i		−	1.54841i
$573$		0			0
$574$	8.12404	−	4.24264i	0.339091	−	0.177084i
$575$	3.00000	+	14.6969i	0.125109	+	0.612905i
$576$		0			0
$577$	−37.0936			−1.54423			−0.772114	−	0.635484i	$-0.780801\pi$
$577$	−37.0936			−1.54423			−0.772114	+	0.635484i	$0.780801\pi$
$578$	1.75192			0.0728704
$579$		0			0
$580$	4.69042	−	5.74456i	0.194759	−	0.238530i
$581$	8.66025	+	16.5831i	0.359288	+	0.687984i
$582$		0			0
$583$			81.4408i			3.37293i
$584$	−4.69042			−0.194091
$585$		0			0
$586$			18.3848i			0.759468i
$587$		−	18.3848i		−	0.758821i	−0.925228	−	0.379410i	$-0.876127\pi$
$587$		−	18.3848i		−	0.758821i	0.925228	−	0.379410i	$-0.123873\pi$
$588$		0			0
$589$	42.3721			1.74591
$590$	6.00000	+	4.89898i	0.247016	+	0.201688i
$591$		0			0
$592$			4.89898i			0.201347i
$593$			7.33419i			0.301179i	0.988596	+	0.150590i	$0.0481172\pi$
$593$			7.33419i			0.301179i	−0.988596	+	0.150590i	$0.951883\pi$
$594$		0			0
$595$	−5.17609	+	25.0903i	−0.212199	+	1.02860i
$596$		−	18.0136i		−	0.737864i
$597$		0			0
$598$	−19.2674			−0.787903
$599$		−	23.3683i		−	0.954802i	−0.878685	−	0.477401i	$-0.841579\pi$
$599$		−	23.3683i		−	0.954802i	0.878685	−	0.477401i	$-0.158421\pi$
$600$		0			0
$601$			2.74072i			0.111796i	0.998436	+	0.0558981i	$0.0178022\pi$
$601$			2.74072i			0.111796i	−0.998436	+	0.0558981i	$0.982198\pi$
$602$	12.1861	+	23.3345i	0.496667	+	0.951044i
$603$		0			0
$604$	−15.1240			−0.615388
$605$	−38.5348	−	31.4635i	−1.56666	−	1.27917i
$606$		0			0
$607$	−19.7731			−0.802567			−0.401283	−	0.915954i	$-0.631436\pi$
$607$	−19.7731			−0.802567			−0.401283	+	0.915954i	$0.631436\pi$
$608$		−	4.24264i		−	0.172062i
$609$		0			0
$610$	6.00000	−	7.34847i	0.242933	−	0.297531i
$611$		−	18.7288i		−	0.757685i
$612$		0			0
$613$			12.3994i			0.500806i	0.968142	+	0.250403i	$0.0805631\pi$
$613$			12.3994i			0.500806i	−0.968142	+	0.250403i	$0.919437\pi$
$614$	−13.1358			−0.530119
$615$		0			0
$616$	7.06202	+	13.5227i	0.284537	+	0.544847i
$617$	−0.875962			−0.0352649			−0.0176324	−	0.999845i	$-0.505613\pi$
$617$	−0.875962			−0.0352649			−0.0176324	+	0.999845i	$0.505613\pi$
$618$		0			0
$619$		−	19.9744i		−	0.802839i	−0.915894	−	0.401420i	$-0.868517\pi$
$619$		−	19.9744i		−	0.802839i	0.915894	−	0.401420i	$-0.131483\pi$
$620$	14.1240	−	17.2983i	0.567235	−	0.694718i
$621$		0			0
$622$	−14.0712			−0.564206
$623$	−8.12404	+	4.24264i	−0.325483	+	0.169978i
$624$		0			0
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	19.7731			0.790293
$627$		0			0
$628$	−0.505737			−0.0201811
$629$	−21.2143			−0.845869
$630$		0			0
$631$	−8.24808			−0.328351			−0.164175	−	0.986431i	$-0.552496\pi$
$631$	−8.24808			−0.328351			−0.164175	+	0.986431i	$0.552496\pi$
$632$	−7.12404			−0.283379
$633$		0			0
$634$	12.0000			0.476581
$635$	6.92820	−	8.48528i	0.274937	−	0.336728i
$636$		0			0
$637$	25.6899	−	36.8943i	1.01787	−	1.46180i
$638$	19.1240			0.757128
$639$		0			0
$640$	−1.73205	−	1.41421i	−0.0684653	−	0.0559017i
$641$		−	27.9634i		−	1.10449i	−0.833682	−	0.552245i	$-0.813771\pi$
$641$		−	27.9634i		−	1.10449i	0.833682	−	0.552245i	$-0.186229\pi$
$642$		0			0
$643$	27.4219			1.08141			0.540707	−	0.841211i	$-0.318157\pi$
$643$	27.4219			1.08141			0.540707	+	0.841211i	$0.318157\pi$
$644$	7.03562	−	3.67423i	0.277242	−	0.144785i
$645$		0			0
$646$	18.3721			0.722841
$647$			11.3137i			0.444788i	0.974957	+	0.222394i	$0.0713871\pi$
$647$			11.3137i			0.444788i	−0.974957	+	0.222394i	$0.928613\pi$
$648$		0			0
$649$			19.9744i			0.784064i
$650$	−6.42247	−	31.4635i	−0.251910	−	1.23410i
$651$		0			0
$652$			4.74706i			0.185909i
$653$	−20.1240			−0.787514			−0.393757	−	0.919214i	$-0.628825\pi$
$653$	−20.1240			−0.787514			−0.393757	+	0.919214i	$0.628825\pi$
$654$		0			0
$655$	33.3721	+	27.2482i	1.30396	+	1.06468i
$656$	−3.46410			−0.135250
$657$		0			0
$658$	3.57152	+	6.83894i	0.139232	+	0.266610i
$659$			16.4312i			0.640069i	0.947406	+	0.320035i	$0.103695\pi$
$659$			16.4312i			0.640069i	−0.947406	+	0.320035i	$0.896305\pi$
$660$		0			0
$661$		−	39.9488i		−	1.55383i	−0.629606	−	0.776914i	$-0.716784\pi$
$661$		−	39.9488i		−	1.55383i	0.629606	−	0.776914i	$-0.283216\pi$
$662$	22.0000			0.855054
$663$		0			0
$664$		−	7.07107i		−	0.274411i
$665$	−5.07125	+	24.5822i	−0.196655	+	0.953255i
$666$		0			0
$667$		−	9.94987i		−	0.385261i
$668$		−	0.175417i		−	0.00678708i
$669$		0			0
$670$	6.92820	−	8.48528i	0.267660	−	0.327815i
$671$	24.4636			0.944405
$672$		0			0
$673$			2.75332i			0.106133i	0.998591	+	0.0530664i	$0.0168995\pi$
$673$			2.75332i			0.106133i	−0.998591	+	0.0530664i	$0.983101\pi$
$674$			24.4949i			0.943508i
$675$		0			0
$676$	28.2481			1.08646
$677$			34.2920i			1.31795i	0.752166	+	0.658974i	$0.229009\pi$
$677$			34.2920i			1.31795i	−0.752166	+	0.658974i	$0.770991\pi$
$678$		0			0
$679$	−5.24808	+	2.74072i	−0.201403	+	0.105179i
$680$	6.12404	−	7.50038i	0.234846	−	0.287627i
$681$		0			0
$682$	57.5874			2.20513
$683$	−24.3721			−0.932573			−0.466287	−	0.884634i	$-0.654408\pi$
$683$	−24.3721			−0.932573			−0.466287	+	0.884634i	$0.654408\pi$
$684$		0			0
$685$	28.1425	+	22.9783i	1.07527	+	0.877954i
$686$	−2.34521	+	18.3712i	−0.0895405	+	0.701415i
$687$		0			0
$688$		−	9.94987i		−	0.379335i
$689$	−90.7112			−3.45582
$690$		0			0
$691$		−	28.4597i		−	1.08266i	−0.840811	−	0.541329i	$-0.817921\pi$
$691$		−	28.4597i		−	1.08266i	0.840811	−	0.541329i	$-0.182079\pi$
$692$		−	5.65685i		−	0.215041i
$693$		0			0
$694$	−18.3721			−0.697396
$695$	12.0000	−	14.6969i	0.455186	−	0.557487i
$696$		0			0
$697$		−	15.0008i		−	0.568195i
$698$		−	25.4558i		−	0.963518i
$699$		0			0
$700$	8.34521	+	10.2644i	0.315419	+	0.387957i
$701$			26.3811i			0.996400i	0.867062	+	0.498200i	$0.166005\pi$
$701$			26.3811i			0.996400i	−0.867062	+	0.498200i	$0.833995\pi$
$702$		0			0
$703$	−20.7846			−0.783906
$704$		−	5.76611i		−	0.217319i
$705$		0			0
$706$		−	15.8195i		−	0.595374i
$707$	20.3101	−	10.6066i	0.763840	−	0.398902i
$708$		0			0
$709$	−16.0000			−0.600893			−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000			−0.600893			−0.300446	+	0.953799i	$0.597136\pi$
$710$	9.38083	−	11.4891i	0.352056	−	0.431179i
$711$		0			0
$712$	3.46410			0.129823
$713$		−	29.9616i		−	1.12207i
$714$		0			0
$715$	52.3721	−	64.1425i	1.95861	−	2.39879i
$716$			21.3302i			0.797147i
$717$		0			0
$718$		−	19.1845i		−	0.715960i
$719$	17.5353			0.653958			0.326979	−	0.945032i	$-0.393969\pi$
$719$	17.5353			0.653958			0.326979	+	0.945032i	$0.393969\pi$
$720$		0			0
$721$	−13.3721	+	6.98336i	−0.498004	+	0.260074i
$722$	−1.00000			−0.0372161
$723$		0			0
$724$			11.4891i			0.426990i
$725$	16.2481	−	3.31662i	0.603438	−	0.123176i
$726$		0			0
$727$	−16.0942			−0.596901			−0.298450	−	0.954425i	$-0.596470\pi$
$727$	−16.0942			−0.596901			−0.298450	+	0.954425i	$0.596470\pi$
$728$	−15.0620	+	7.86588i	−0.558236	+	0.291529i
$729$		0			0
$730$	−8.12404	−	6.63325i	−0.300684	−	0.245508i
$731$	43.0864			1.59361
$732$		0			0
$733$	−2.02295			−0.0747192			−0.0373596	−	0.999302i	$-0.511895\pi$
$733$	−2.02295			−0.0747192			−0.0373596	+	0.999302i	$0.511895\pi$
$734$	12.8449			0.474115
$735$		0			0
$736$	−3.00000			−0.110581
$737$	28.2481			1.04053
$738$		0			0
$739$	−16.3721			−0.602258			−0.301129	−	0.953583i	$-0.597363\pi$
$739$	−16.3721			−0.602258			−0.301129	+	0.953583i	$0.597363\pi$
$740$	−6.92820	+	8.48528i	−0.254686	+	0.311925i
$741$		0			0
$742$	33.1238	−	17.2983i	1.21601	−	0.635042i
$743$	3.00000			0.110059			0.0550297	−	0.998485i	$-0.482475\pi$
$743$	3.00000			0.110059			0.0550297	+	0.998485i	$0.482475\pi$
$744$		0			0
$745$	25.4750	−	31.2004i	0.933333	−	1.14309i
$746$			2.60141i			0.0952442i
$747$		0			0
$748$	24.9693			0.912968
$749$	−4.98131	+	2.60141i	−0.182013	+	0.0950533i
$750$		0			0
$751$	29.3721			1.07180			0.535902	−	0.844280i	$-0.319972\pi$
$751$	29.3721			1.07180			0.535902	+	0.844280i	$0.319972\pi$
$752$		−	2.91614i		−	0.106341i
$753$		0			0
$754$			21.3009i			0.775733i
$755$	−26.1956	−	21.3886i	−0.953356	−	0.778412i
$756$		0			0
$757$		−	7.50038i		−	0.272606i	−0.990667	−	0.136303i	$-0.956478\pi$
$757$		−	7.50038i		−	0.272606i	0.990667	−	0.136303i	$-0.0435221\pi$
$758$	−38.3721			−1.39374
$759$		0			0
$760$	6.00000	−	7.34847i	0.217643	−	0.266557i
$761$	−20.7846			−0.753442			−0.376721	−	0.926327i	$-0.622948\pi$
$761$	−20.7846			−0.753442			−0.376721	+	0.926327i	$0.622948\pi$
$762$		0			0
$763$	9.67173	−	5.05089i	0.350140	−	0.182855i
$764$		−	5.91803i		−	0.214107i
$765$		0			0
$766$			31.3758i			1.13365i
$767$	−22.2481			−0.803331
$768$		0			0
$769$			28.1966i			1.01679i	0.861123	+	0.508397i	$0.169762\pi$
$769$			28.1966i			1.01679i	−0.861123	+	0.508397i	$0.830238\pi$
$770$	−6.89226	+	33.4093i	−0.248380	+	1.20399i
$771$		0			0
$772$			27.2482i			0.980685i
$773$			14.3176i			0.514967i	0.966283	+	0.257483i	$0.0828932\pi$
$773$			14.3176i			0.514967i	−0.966283	+	0.257483i	$0.917107\pi$
$774$		0			0
$775$	48.9271	−	9.98720i	1.75751	−	0.358751i
$776$	2.23779			0.0803319
$777$		0			0
$778$		−	1.58235i		−	0.0567302i
$779$		−	14.6969i		−	0.526572i
$780$		0			0
$781$	38.2481			1.36862
$782$		−	12.9910i		−	0.464559i
$783$		0			0
$784$	4.00000	−	5.74456i	0.142857	−	0.205163i
$785$	−0.875962	−	0.715220i	−0.0312644	−	0.0255273i
$786$		0			0
$787$	30.8860			1.10097			0.550484	−	0.834846i	$-0.314443\pi$
$787$	30.8860			1.10097			0.550484	+	0.834846i	$0.314443\pi$
$788$	20.1240			0.716889
$789$		0			0
$790$	−12.3392	−	10.0749i	−0.439009	−	0.358449i
$791$	2.05431	−	1.07283i	0.0730429	−	0.0381454i
$792$		0			0
$793$			27.2482i			0.967613i
$794$	18.2559			0.647879
$795$		0			0
$796$			15.4686i			0.548271i
$797$			30.0493i			1.06440i	0.846618	+	0.532201i	$0.178635\pi$
$797$			30.0493i			1.06440i	−0.846618	+	0.532201i	$0.821365\pi$
$798$		0			0
$799$	12.6279			0.446742
$800$	−1.00000	−	4.89898i	−0.0353553	−	0.173205i
$801$		0			0
$802$			20.6150i			0.727940i
$803$		−	27.0455i		−	0.954414i
$804$		0			0
$805$	17.3822	+	3.58591i	0.612642	+	0.126387i
$806$			64.1425i			2.25932i
$807$		0			0
$808$	−8.66025			−0.304667
$809$			21.6340i			0.760612i	0.924861	+	0.380306i	$0.124181\pi$
$809$			21.6340i			0.760612i	−0.924861	+	0.380306i	$0.875819\pi$
$810$		0			0
$811$		−	38.1838i		−	1.34081i	−0.741994	−	0.670407i	$-0.766120\pi$
$811$		−	38.1838i		−	1.34081i	0.741994	−	0.670407i	$-0.233880\pi$
$812$	−4.06202	−	7.77817i	−0.142549	−	0.272960i
$813$		0			0
$814$	−28.2481			−0.990095
$815$	−6.71336	+	8.22216i	−0.235159	+	0.288010i
$816$		0			0
$817$	42.2137			1.47687
$818$		−	20.2375i		−	0.707589i
$819$		0			0
$820$	−6.00000	−	4.89898i	−0.209529	−	0.171080i
$821$			6.93708i			0.242106i	0.992646	+	0.121053i	$0.0386271\pi$
$821$			6.93708i			0.242106i	−0.992646	+	0.121053i	$0.961373\pi$
$822$		0			0
$823$			46.5403i			1.62229i	0.584843	+	0.811147i	$0.301156\pi$
$823$			46.5403i			1.62229i	−0.584843	+	0.811147i	$0.698844\pi$
$824$	5.70189			0.198635
$825$		0			0
$826$	8.12404	−	4.24264i	0.282671	−	0.147620i
$827$	−46.2481			−1.60820			−0.804102	−	0.594492i	$-0.797353\pi$
$827$	−46.2481			−1.60820			−0.804102	+	0.594492i	$0.797353\pi$
$828$		0			0
$829$		−	14.4930i		−	0.503362i	−0.967810	−	0.251681i	$-0.919017\pi$
$829$		−	14.4930i		−	0.503362i	0.967810	−	0.251681i	$-0.0809833\pi$
$830$	10.0000	−	12.2474i	0.347105	−	0.425115i
$831$		0			0
$832$	6.42247			0.222659
$833$	24.8760	+	17.3214i	0.861901	+	0.600151i
$834$		0			0
$835$	0.248077	−	0.303831i	0.00858505	−	0.0105145i
$836$	24.4636			0.846090
$837$		0			0
$838$	1.94689			0.0672543
$839$	35.2855			1.21819			0.609096	−	0.793096i	$-0.291532\pi$
$839$	35.2855			1.21819			0.609096	+	0.793096i	$0.291532\pi$
$840$		0			0
$841$	18.0000			0.620690
$842$	2.24808			0.0774738
$843$		0			0
$844$	−8.24808			−0.283911
$845$	48.9271	+	39.9488i	1.68314	+	1.37428i
$846$		0			0
$847$	−52.1764	+	27.2482i	−1.79280	+	0.936260i
$848$	−14.1240			−0.485021
$849$		0			0
$850$	21.2143	−	4.33035i	0.727644	−	0.148530i
$851$			14.6969i			0.503805i
$852$		0			0
$853$	−21.2903			−0.728968			−0.364484	−	0.931210i	$-0.618755\pi$
$853$	−21.2903			−0.728968			−0.364484	+	0.931210i	$0.618755\pi$
$854$	−5.19615	−	9.94987i	−0.177809	−	0.340478i
$855$		0			0
$856$	2.12404			0.0725981
$857$			37.2958i			1.27400i	0.770864	+	0.637000i	$0.219825\pi$
$857$			37.2958i			1.27400i	−0.770864	+	0.637000i	$0.780175\pi$
$858$		0			0
$859$		−	42.9527i		−	1.46553i	−0.680484	−	0.732763i	$-0.738230\pi$
$859$		−	42.9527i		−	1.46553i	0.680484	−	0.732763i	$-0.261770\pi$
$860$	14.0712	−	17.2337i	0.479826	−	0.587664i
$861$		0			0
$862$		−	23.7797i		−	0.809939i
$863$	10.7519			0.366000			0.183000	−	0.983113i	$-0.441419\pi$
$863$	10.7519			0.366000			0.183000	+	0.983113i	$0.441419\pi$
$864$		0			0
$865$	8.00000	−	9.79796i	0.272008	−	0.333141i
$866$	−21.7961			−0.740661
$867$		0			0
$868$	−12.2318	−	23.4221i	−0.415174	−	0.794997i
$869$		−	41.0780i		−	1.39348i
$870$		0			0
$871$			31.4635i			1.06610i
$872$	−4.12404			−0.139658
$873$		0			0
$874$		−	12.7279i		−	0.430528i
$875$	−0.0617020	+	29.5803i	−0.00208591	+	0.999998i
$876$		0			0
$877$			21.8935i			0.739291i	0.929173	+	0.369645i	$0.120521\pi$
$877$			21.8935i			0.739291i	−0.929173	+	0.369645i	$0.879479\pi$
$878$		−	22.9783i		−	0.775478i
$879$		0			0
$880$	8.15452	−	9.98720i	0.274889	−	0.336669i
$881$	38.3200			1.29103			0.645516	−	0.763747i	$-0.276642\pi$
$881$	38.3200			1.29103			0.645516	+	0.763747i	$0.276642\pi$
$882$		0			0
$883$			44.6985i			1.50422i	0.659036	+	0.752112i	$0.270965\pi$
$883$			44.6985i			1.50422i	−0.659036	+	0.752112i	$0.729035\pi$
$884$			27.8115i			0.935403i
$885$		0			0
$886$	−1.75192			−0.0588570
$887$		−	14.4053i		−	0.483681i	−0.970316	−	0.241841i	$-0.922249\pi$
$887$		−	14.4053i		−	0.483681i	0.970316	−	0.241841i	$-0.0777511\pi$
$888$		0			0
$889$	−6.00000	−	11.4891i	−0.201234	−	0.385333i
$890$	6.00000	+	4.89898i	0.201120	+	0.164214i
$891$		0			0
$892$	−12.8449			−0.430080
$893$	12.3721			0.414017
$894$		0			0
$895$	−30.1654	+	36.9450i	−1.00832	+	1.23493i
$896$	−2.34521	+	1.22474i	−0.0783479	+	0.0409159i
$897$		0			0
$898$			35.3119i			1.17837i
$899$	−33.1238			−1.10474
$900$		0			0
$901$		−	61.1620i		−	2.03760i
$902$		−	19.9744i		−	0.665075i
$903$		0			0
$904$	−0.875962			−0.0291340
$905$	−16.2481	+	19.8997i	−0.540104	+	0.661490i
$906$		0			0
$907$			24.9506i			0.828473i	0.910169	+	0.414236i	$0.135951\pi$
$907$			24.9506i			0.828473i	−0.910169	+	0.414236i	$0.864049\pi$
$908$		−	8.66070i		−	0.287415i
$909$		0			0
$910$	−37.2122	−	7.67680i	−1.23357	−	0.254484i
$911$			16.1274i			0.534324i	0.963652	+	0.267162i	$0.0860859\pi$
$911$			16.1274i			0.534324i	−0.963652	+	0.267162i	$0.913914\pi$
$912$		0			0
$913$	40.7726			1.34938
$914$		−	2.14566i		−	0.0709721i
$915$		0			0
$916$		−	3.00384i		−	0.0992498i
$917$	45.1861	−	23.5976i	1.49218	−	0.779263i
$918$		0			0
$919$	−25.3721			−0.836949			−0.418474	−	0.908229i	$-0.637435\pi$
$919$	−25.3721			−0.836949			−0.418474	+	0.908229i	$0.637435\pi$
$920$	−5.19615	−	4.24264i	−0.171312	−	0.139876i
$921$		0			0
$922$	31.6066			1.04091
$923$			42.6018i			1.40226i
$924$		0			0
$925$	−24.0000	+	4.89898i	−0.789115	+	0.161077i
$926$		−	0.303831i		−	0.00998450i
$927$		0			0
$928$			3.31662i			0.108874i
$929$	45.2482			1.48454			0.742272	−	0.670099i	$-0.233748\pi$
$929$	45.2482			1.48454			0.742272	+	0.670099i	$0.233748\pi$
$930$		0			0
$931$	24.3721	+	16.9706i	0.798764	+	0.556188i
$932$	−10.2481			−0.335687
$933$		0			0
$934$		−	22.8028i		−	0.746132i
$935$	43.2481	+	35.3119i	1.41436	+	1.15482i
$936$		0			0
$937$	42.7955			1.39807			0.699035	−	0.715088i	$-0.253613\pi$
$937$	42.7955			1.39807			0.699035	+	0.715088i	$0.253613\pi$
$938$	−6.00000	−	11.4891i	−0.195907	−	0.375133i
$939$		0			0
$940$	4.12404	−	5.05089i	0.134511	−	0.164742i
$941$	5.19615			0.169390			0.0846949	−	0.996407i	$-0.473008\pi$
$941$	5.19615			0.169390			0.0846949	+	0.996407i	$0.473008\pi$
$942$		0			0
$943$	−10.3923			−0.338420
$944$	−3.46410			−0.112747
$945$		0			0
$946$	57.3721			1.86533
$947$	36.3721			1.18193			0.590967	−	0.806695i	$-0.298746\pi$
$947$	36.3721			1.18193			0.590967	+	0.806695i	$0.298746\pi$
$948$		0			0
$949$	30.1240			0.977868
$950$	20.7846	−	4.24264i	0.674342	−	0.137649i
$951$		0			0
$952$	−5.30357	−	10.1556i	−0.171890	−	0.329144i
$953$	−24.8760			−0.805811			−0.402906	−	0.915241i	$-0.632000\pi$
$953$	−24.8760			−0.805811			−0.402906	+	0.915241i	$0.632000\pi$
$954$		0			0
$955$	8.36936	−	10.2503i	0.270826	−	0.331693i
$956$			13.9817i			0.452201i
$957$		0			0
$958$	−17.7502			−0.573483
$959$	38.1051	−	19.8997i	1.23048	−	0.642596i
$960$		0			0
$961$	−68.7442			−2.21756
$962$		−	31.4635i		−	1.01442i
$963$		0			0
$964$		−	22.7151i		−	0.731605i
$965$	−38.5348	+	47.1953i	−1.24048	+	1.51927i
$966$		0			0
$967$		−	19.8997i		−	0.639933i	−0.947429	−	0.319966i	$-0.896328\pi$
$967$		−	19.8997i		−	0.639933i	0.947429	−	0.319966i	$-0.103672\pi$
$968$	22.2481			0.715080
$969$		0			0
$970$	3.87596	+	3.16471i	0.124450	+	0.101613i
$971$	−60.8366			−1.95234			−0.976170	−	0.217007i	$-0.930370\pi$
$971$	−60.8366			−1.95234			−0.976170	+	0.217007i	$0.930370\pi$
$972$		0			0
$973$	−10.3923	−	19.8997i	−0.333162	−	0.637957i
$974$			12.2474i			0.392434i
$975$		0			0
$976$			4.24264i			0.135804i
$977$	−43.6202			−1.39553			−0.697767	−	0.716325i	$-0.745823\pi$
$977$	−43.6202			−1.39553			−0.697767	+	0.716325i	$0.745823\pi$
$978$		0			0
$979$			19.9744i			0.638385i
$980$	15.0522	−	4.29302i	0.480826	−	0.137135i
$981$		0			0
$982$			18.1655i			0.579684i
$983$		−	45.3425i		−	1.44620i	−0.690742	−	0.723101i	$-0.742716\pi$
$983$		−	45.3425i		−	1.44620i	0.690742	−	0.723101i	$-0.257284\pi$
$984$		0			0
$985$	34.8559	+	28.4597i	1.11060	+	0.906801i
$986$	−14.3621			−0.457384
$987$		0			0
$988$			27.2482i			0.866881i
$989$		−	29.8496i		−	0.949163i
$990$		0			0
$991$	−43.3721			−1.37776			−0.688880	−	0.724875i	$-0.741897\pi$
$991$	−43.3721			−1.37776			−0.688880	+	0.724875i	$0.741897\pi$
$992$			9.98720i			0.317094i
$993$		0			0
$994$	−8.12404	−	15.5563i	−0.257679	−	0.493417i
$995$	−21.8760	+	26.7925i	−0.693515	+	0.849378i
$996$		0			0
$997$	9.88657			0.313111			0.156555	−	0.987669i	$-0.449961\pi$
$997$	9.88657			0.313111			0.156555	+	0.987669i	$0.449961\pi$
$998$	42.1240			1.33341
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.d.b.1889.8	yes	8
3.2	odd	2		1890.2.d.c.1889.2	yes	8
5.4	even	2		1890.2.d.c.1889.5	yes	8
7.6	odd	2	inner	1890.2.d.b.1889.1	✓	8
15.14	odd	2	inner	1890.2.d.b.1889.3	yes	8
21.20	even	2		1890.2.d.c.1889.7	yes	8
35.34	odd	2		1890.2.d.c.1889.4	yes	8
105.104	even	2	inner	1890.2.d.b.1889.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.d.b.1889.1	✓	8	7.6	odd	2	inner
1890.2.d.b.1889.3	yes	8	15.14	odd	2	inner
1890.2.d.b.1889.6	yes	8	105.104	even	2	inner
1890.2.d.b.1889.8	yes	8	1.1	even	1	trivial
1890.2.d.c.1889.2	yes	8	3.2	odd	2
1890.2.d.c.1889.4	yes	8	35.34	odd	2
1890.2.d.c.1889.5	yes	8	5.4	even	2
1890.2.d.c.1889.7	yes	8	21.20	even	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(2.34521 - 1.22474i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.73205 + 1.41421i) q^{5} +(2.34521 - 1.22474i) q^{7} -1.00000 q^{8} +(-1.73205 - 1.41421i) q^{10} -5.76611i q^{11} +6.42247 q^{13} +(-2.34521 + 1.22474i) q^{14} +1.00000 q^{16} +4.33035i q^{17} +4.24264i q^{19} +(1.73205 + 1.41421i) q^{20} +5.76611i q^{22} +3.00000 q^{23} +(1.00000 + 4.89898i) q^{25} -6.42247 q^{26} +(2.34521 - 1.22474i) q^{28} -3.31662i q^{29} -9.98720i q^{31} -1.00000 q^{32} -4.33035i q^{34} +(5.79407 + 1.19530i) q^{35} +4.89898i q^{37} -4.24264i q^{38} +(-1.73205 - 1.41421i) q^{40} -3.46410 q^{41} -9.94987i q^{43} -5.76611i q^{44} -3.00000 q^{46} -2.91614i q^{47} +(4.00000 - 5.74456i) q^{49} +(-1.00000 - 4.89898i) q^{50} +6.42247 q^{52} -14.1240 q^{53} +(8.15452 - 9.98720i) q^{55} +(-2.34521 + 1.22474i) q^{56} +3.31662i q^{58} -3.46410 q^{59} +4.24264i q^{61} +9.98720i q^{62} +1.00000 q^{64} +(11.1240 + 9.08274i) q^{65} +4.89898i q^{67} +4.33035i q^{68} +(-5.79407 - 1.19530i) q^{70} +6.63325i q^{71} +4.69042 q^{73} -4.89898i q^{74} +4.24264i q^{76} +(-7.06202 - 13.5227i) q^{77} +7.12404 q^{79} +(1.73205 + 1.41421i) q^{80} +3.46410 q^{82} +7.07107i q^{83} +(-6.12404 + 7.50038i) q^{85} +9.94987i q^{86} +5.76611i q^{88} -3.46410 q^{89} +(15.0620 - 7.86588i) q^{91} +3.00000 q^{92} +2.91614i q^{94} +(-6.00000 + 7.34847i) q^{95} -2.23779 q^{97} +(-4.00000 + 5.74456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 8 q^{16} + 24 q^{23} + 8 q^{25} - 8 q^{32} - 24 q^{46} + 32 q^{49} - 8 q^{50} - 48 q^{53} + 8 q^{64} + 24 q^{65} - 24 q^{77} - 8 q^{79} + 16 q^{85} + 88 q^{91} + 24 q^{92} - 48 q^{95} - 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^8 + 8 * q^16 + 24 * q^23 + 8 * q^25 - 8 * q^32 - 24 * q^46 + 32 * q^49 - 8 * q^50 - 48 * q^53 + 8 * q^64 + 24 * q^65 - 24 * q^77 - 8 * q^79 + 16 * q^85 + 88 * q^91 + 24 * q^92 - 48 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more