LMFDB - Embedded newform 1890.2.d.f.1889.3

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			1889.3
Root			$1.98399 + 1.03140i$ of defining polynomial
Character	$\chi$	$=$	1890.1889
Dual form			1890.2.d.f.1889.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-1.88521 - 1.20249i) q^{5} +(2.61764 - 0.384656i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.88521 - 1.20249i) q^{5} +(2.61764 - 0.384656i) q^{7} +1.00000 q^{8} +(-1.88521 - 1.20249i) q^{10} -0.149444i q^{11} -5.72182 q^{13} +(2.61764 - 0.384656i) q^{14} +1.00000 q^{16} -6.33796i q^{17} -5.66504i q^{19} +(-1.88521 - 1.20249i) q^{20} -0.149444i q^{22} -4.59603 q^{23} +(2.10805 + 4.53389i) q^{25} -5.72182 q^{26} +(2.61764 - 0.384656i) q^{28} -5.06799i q^{29} +7.39709i q^{31} +1.00000 q^{32} -6.33796i q^{34} +(-5.39735 - 2.42252i) q^{35} +5.76125i q^{37} -5.66504i q^{38} +(-1.88521 - 1.20249i) q^{40} -4.02927 q^{41} -4.14923i q^{43} -0.149444i q^{44} -4.59603 q^{46} -12.0976i q^{47} +(6.70408 - 2.01378i) q^{49} +(2.10805 + 4.53389i) q^{50} -5.72182 q^{52} +9.38164 q^{53} +(-0.179704 + 0.281733i) q^{55} +(2.61764 - 0.384656i) q^{56} -5.06799i q^{58} -11.2159 q^{59} +7.39709i q^{62} +1.00000 q^{64} +(10.7868 + 6.88041i) q^{65} -15.6717i q^{67} -6.33796i q^{68} +(-5.39735 - 2.42252i) q^{70} +3.23047i q^{71} +8.74686 q^{73} +5.76125i q^{74} -5.66504i q^{76} +(-0.0574844 - 0.391190i) q^{77} -2.05057 q^{79} +(-1.88521 - 1.20249i) q^{80} -4.02927 q^{82} -8.07001i q^{83} +(-7.62131 + 11.9484i) q^{85} -4.14923i q^{86} -0.149444i q^{88} +2.31080 q^{89} +(-14.9777 + 2.20093i) q^{91} -4.59603 q^{92} -12.0976i q^{94} +(-6.81213 + 10.6798i) q^{95} -6.70014 q^{97} +(6.70408 - 2.01378i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.88521	−	1.20249i	−0.843093	−	0.537768i
$5$	−1.88521	−	1.20249i	−0.843093	−	0.537768i
$6$		0			0
$7$	2.61764	−	0.384656i	0.989375	−	0.145386i
$7$	2.61764	−	0.384656i	0.989375	−	0.145386i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.88521	−	1.20249i	−0.596157	−	0.380260i
$11$		−	0.149444i		−	0.0450589i	−0.999746	−	0.0225295i	$-0.992828\pi$
$11$		−	0.149444i		−	0.0450589i	0.999746	−	0.0225295i	$-0.00717196\pi$
$12$		0			0
$13$	−5.72182			−1.58695			−0.793474	−	0.608604i	$-0.791730\pi$
$13$	−5.72182			−1.58695			−0.793474	+	0.608604i	$0.791730\pi$
$14$	2.61764	−	0.384656i	0.699594	−	0.102804i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.33796i		−	1.53718i	−0.639741	−	0.768590i	$-0.720958\pi$
$17$		−	6.33796i		−	1.53718i	0.639741	−	0.768590i	$-0.279042\pi$
$18$		0			0
$19$		−	5.66504i		−	1.29965i	−0.760085	−	0.649824i	$-0.774842\pi$
$19$		−	5.66504i		−	1.29965i	0.760085	−	0.649824i	$-0.225158\pi$
$20$	−1.88521	−	1.20249i	−0.421546	−	0.268884i
$21$		0			0
$22$		−	0.149444i		−	0.0318615i
$23$	−4.59603			−0.958338			−0.479169	−	0.877723i	$-0.659062\pi$
$23$	−4.59603			−0.958338			−0.479169	+	0.877723i	$0.659062\pi$
$24$		0			0
$25$	2.10805	+	4.53389i	0.421610	+	0.906777i
$26$	−5.72182			−1.12214
$27$		0			0
$28$	2.61764	−	0.384656i	0.494687	−	0.0726932i
$29$		−	5.06799i		−	0.941101i	−0.882373	−	0.470551i	$-0.844055\pi$
$29$		−	5.06799i		−	0.941101i	0.882373	−	0.470551i	$-0.155945\pi$
$30$		0			0
$31$			7.39709i			1.32856i	0.747486	+	0.664278i	$0.231261\pi$
$31$			7.39709i			1.32856i	−0.747486	+	0.664278i	$0.768739\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$		−	6.33796i		−	1.08695i
$35$	−5.39735	−	2.42252i	−0.912319	−	0.409480i
$36$		0			0
$37$			5.76125i			0.947144i	0.880755	+	0.473572i	$0.157036\pi$
$37$			5.76125i			0.947144i	−0.880755	+	0.473572i	$0.842964\pi$
$38$		−	5.66504i		−	0.918990i
$39$		0			0
$40$	−1.88521	−	1.20249i	−0.298078	−	0.190130i
$41$	−4.02927			−0.629266			−0.314633	−	0.949213i	$-0.601881\pi$
$41$	−4.02927			−0.629266			−0.314633	+	0.949213i	$0.601881\pi$
$42$		0			0
$43$		−	4.14923i		−	0.632752i	−0.948634	−	0.316376i	$-0.897534\pi$
$43$		−	4.14923i		−	0.632752i	0.948634	−	0.316376i	$-0.102466\pi$
$44$		−	0.149444i		−	0.0225295i
$45$		0			0
$46$	−4.59603			−0.677647
$47$		−	12.0976i		−	1.76461i	−0.470675	−	0.882306i	$-0.655990\pi$
$47$		−	12.0976i		−	1.76461i	0.470675	−	0.882306i	$-0.344010\pi$
$48$		0			0
$49$	6.70408	−	2.01378i	0.957726	−	0.287683i
$50$	2.10805	+	4.53389i	0.298124	+	0.641188i
$51$		0			0
$52$	−5.72182			−0.793474
$53$	9.38164			1.28867			0.644334	−	0.764745i	$-0.277135\pi$
$53$	9.38164			1.28867			0.644334	+	0.764745i	$0.277135\pi$
$54$		0			0
$55$	−0.179704	+	0.281733i	−0.0242313	+	0.0379889i
$56$	2.61764	−	0.384656i	0.349797	−	0.0514019i
$57$		0			0
$58$		−	5.06799i		−	0.665459i
$59$	−11.2159			−1.46019			−0.730096	−	0.683345i	$-0.760525\pi$
$59$	−11.2159			−1.46019			−0.730096	+	0.683345i	$0.760525\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$			7.39709i			0.939431i
$63$		0			0
$64$	1.00000			0.125000
$65$	10.7868	+	6.88041i	1.33794	+	0.853410i
$66$		0			0
$67$		−	15.6717i		−	1.91461i	−0.289084	−	0.957304i	$-0.593351\pi$
$67$		−	15.6717i		−	1.91461i	0.289084	−	0.957304i	$-0.406649\pi$
$68$		−	6.33796i		−	0.768590i
$69$		0			0
$70$	−5.39735	−	2.42252i	−0.645107	−	0.289546i
$71$			3.23047i			0.383387i	0.981455	+	0.191693i	$0.0613979\pi$
$71$			3.23047i			0.383387i	−0.981455	+	0.191693i	$0.938602\pi$
$72$		0			0
$73$	8.74686			1.02374			0.511871	−	0.859062i	$-0.328952\pi$
$73$	8.74686			1.02374			0.511871	+	0.859062i	$0.328952\pi$
$74$			5.76125i			0.669732i
$75$		0			0
$76$		−	5.66504i		−	0.649824i
$77$	−0.0574844	−	0.391190i	−0.00655096	−	0.0445802i
$78$		0			0
$79$	−2.05057			−0.230707			−0.115353	−	0.993325i	$-0.536800\pi$
$79$	−2.05057			−0.230707			−0.115353	+	0.993325i	$0.536800\pi$
$80$	−1.88521	−	1.20249i	−0.210773	−	0.134442i
$81$		0			0
$82$	−4.02927			−0.444958
$83$		−	8.07001i		−	0.885799i	−0.896571	−	0.442899i	$-0.853950\pi$
$83$		−	8.07001i		−	0.885799i	0.896571	−	0.442899i	$-0.146050\pi$
$84$		0			0
$85$	−7.62131	+	11.9484i	−0.826647	+	1.29599i
$86$		−	4.14923i		−	0.447423i
$87$		0			0
$88$		−	0.149444i		−	0.0159307i
$89$	2.31080			0.244945			0.122472	−	0.992472i	$-0.460918\pi$
$89$	2.31080			0.244945			0.122472	+	0.992472i	$0.460918\pi$
$90$		0			0
$91$	−14.9777	+	2.20093i	−1.57009	+	0.230721i
$92$	−4.59603			−0.479169
$93$		0			0
$94$		−	12.0976i		−	1.24777i
$95$	−6.81213	+	10.6798i	−0.698910	+	1.09572i
$96$		0			0
$97$	−6.70014			−0.680296			−0.340148	−	0.940372i	$-0.610477\pi$
$97$	−6.70014			−0.680296			−0.340148	+	0.940372i	$0.610477\pi$
$98$	6.70408	−	2.01378i	0.677214	−	0.203423i
$99$		0			0
$100$	2.10805	+	4.53389i	0.210805	+	0.453389i
$101$	−7.28201			−0.724587			−0.362293	−	0.932064i	$-0.618006\pi$
$101$	−7.28201			−0.724587			−0.362293	+	0.932064i	$0.618006\pi$
$102$		0			0
$103$	5.84830			0.576250			0.288125	−	0.957593i	$-0.406968\pi$
$103$	5.84830			0.576250			0.288125	+	0.957593i	$0.406968\pi$
$104$	−5.72182			−0.561071
$105$		0			0
$106$	9.38164			0.911225
$107$	4.16554			0.402698			0.201349	−	0.979520i	$-0.435468\pi$
$107$	4.16554			0.402698			0.201349	+	0.979520i	$0.435468\pi$
$108$		0			0
$109$	−16.1432			−1.54624			−0.773119	−	0.634261i	$-0.781305\pi$
$109$	−16.1432			−1.54624			−0.773119	+	0.634261i	$0.781305\pi$
$110$	−0.179704	+	0.281733i	−0.0171341	+	0.0268622i
$111$		0			0
$112$	2.61764	−	0.384656i	0.247344	−	0.0363466i
$113$	−12.1432			−1.14234			−0.571168	−	0.820833i	$-0.693510\pi$
$113$	−12.1432			−1.14234			−0.571168	+	0.820833i	$0.693510\pi$
$114$		0			0
$115$	8.66449	+	5.52666i	0.807968	+	0.515364i
$116$		−	5.06799i		−	0.470551i
$117$		0			0
$118$	−11.2159			−1.03251
$119$	−2.43794	−	16.5905i	−0.223485	−	1.52085i
$120$		0			0
$121$	10.9777			0.997970
$122$		0			0
$123$		0			0
$124$			7.39709i			0.664278i
$125$	1.47781	−	11.0822i	0.132180	−	0.991226i
$126$		0			0
$127$			7.74821i			0.687543i	0.939053	+	0.343771i	$0.111704\pi$
$127$			7.74821i			0.687543i	−0.939053	+	0.343771i	$0.888296\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	10.7868	+	6.88041i	0.946069	+	0.603452i
$131$	9.36577			0.818291			0.409145	−	0.912469i	$-0.365827\pi$
$131$	9.36577			0.818291			0.409145	+	0.912469i	$0.365827\pi$
$132$		0			0
$133$	−2.17909	−	14.8290i	−0.188951	−	1.28584i
$134$		−	15.6717i		−	1.35383i
$135$		0			0
$136$		−	6.33796i		−	0.543475i
$137$	2.56951			0.219528			0.109764	−	0.993958i	$-0.464991\pi$
$137$	2.56951			0.219528			0.109764	+	0.993958i	$0.464991\pi$
$138$		0			0
$139$			14.7066i			1.24740i	0.781665	+	0.623698i	$0.214371\pi$
$139$			14.7066i			1.24740i	−0.781665	+	0.623698i	$0.785629\pi$
$140$	−5.39735	−	2.42252i	−0.456159	−	0.204740i
$141$		0			0
$142$			3.23047i			0.271095i
$143$			0.855090i			0.0715062i
$144$		0			0
$145$	−6.09419	+	9.55423i	−0.506095	+	0.793436i
$146$	8.74686			0.723895
$147$		0			0
$148$			5.76125i			0.473572i
$149$		−	2.61325i		−	0.214086i	−0.994254	−	0.107043i	$-0.965862\pi$
$149$		−	2.61325i		−	0.214086i	0.994254	−	0.107043i	$-0.0341382\pi$
$150$		0			0
$151$	1.02652			0.0835369			0.0417685	−	0.999127i	$-0.486701\pi$
$151$	1.02652			0.0835369			0.0417685	+	0.999127i	$0.486701\pi$
$152$		−	5.66504i		−	0.459495i
$153$		0			0
$154$	−0.0574844	−	0.391190i	−0.00463223	−	0.0315230i
$155$	8.89490	−	13.9451i	0.714455	−	1.12010i
$156$		0			0
$157$	20.2216			1.61386			0.806932	−	0.590645i	$-0.201127\pi$
$157$	20.2216			1.61386			0.806932	+	0.590645i	$0.201127\pi$
$158$	−2.05057			−0.163134
$159$		0			0
$160$	−1.88521	−	1.20249i	−0.149039	−	0.0950649i
$161$	−12.0307	+	1.76789i	−0.948156	+	0.139329i
$162$		0			0
$163$		−	5.46879i		−	0.428349i	−0.976795	−	0.214174i	$-0.931294\pi$
$163$		−	5.46879i		−	0.428349i	0.976795	−	0.214174i	$-0.0687061\pi$
$164$	−4.02927			−0.314633
$165$		0			0
$166$		−	8.07001i		−	0.626354i
$167$		−	9.70748i		−	0.751187i	−0.926784	−	0.375594i	$-0.877439\pi$
$167$		−	9.70748i		−	0.751187i	0.926784	−	0.375594i	$-0.122561\pi$
$168$		0			0
$169$	19.7392			1.51840
$170$	−7.62131	+	11.9484i	−0.584528	+	0.916400i
$171$		0			0
$172$		−	4.14923i		−	0.316376i
$173$			19.3174i			1.46868i	0.678785	+	0.734338i	$0.262507\pi$
$173$			19.3174i			1.46868i	−0.678785	+	0.734338i	$0.737493\pi$
$174$		0			0
$175$	7.26211	+	11.0572i	0.548964	+	0.835846i
$176$		−	0.149444i		−	0.0112647i
$177$		0			0
$178$	2.31080			0.173202
$179$		−	10.9851i		−	0.821065i	−0.911846	−	0.410533i	$-0.865343\pi$
$179$		−	10.9851i		−	0.821065i	0.911846	−	0.410533i	$-0.134657\pi$
$180$		0			0
$181$		−	6.83362i		−	0.507939i	−0.967212	−	0.253970i	$-0.918264\pi$
$181$		−	6.83362i		−	0.507939i	0.967212	−	0.253970i	$-0.0817363\pi$
$182$	−14.9777	+	2.20093i	−1.11022	+	0.163144i
$183$		0			0
$184$	−4.59603			−0.338824
$185$	6.92783	−	10.8612i	0.509344	−	0.798530i
$186$		0			0
$187$	−0.947167			−0.0692637
$188$		−	12.0976i		−	0.882306i
$189$		0			0
$190$	−6.81213	+	10.6798i	−0.494204	+	0.774794i
$191$			16.2182i			1.17351i	0.809765	+	0.586754i	$0.199595\pi$
$191$			16.2182i			1.17351i	−0.809765	+	0.586754i	$0.800405\pi$
$192$		0			0
$193$		−	20.8379i		−	1.49994i	−0.661471	−	0.749971i	$-0.730067\pi$
$193$		−	20.8379i		−	1.49994i	0.661471	−	0.749971i	$-0.269933\pi$
$194$	−6.70014			−0.481042
$195$		0			0
$196$	6.70408	−	2.01378i	0.478863	−	0.143842i
$197$	5.64659			0.402303			0.201152	−	0.979560i	$-0.435532\pi$
$197$	5.64659			0.402303			0.201152	+	0.979560i	$0.435532\pi$
$198$		0			0
$199$			18.3142i			1.29826i	0.760679	+	0.649129i	$0.224866\pi$
$199$			18.3142i			1.29826i	−0.760679	+	0.649129i	$0.775134\pi$
$200$	2.10805	+	4.53389i	0.149062	+	0.320594i
$201$		0			0
$202$	−7.28201			−0.512360
$203$	−1.94943	−	13.2662i	−0.136823	−	0.931102i
$204$		0			0
$205$	7.59603	+	4.84514i	0.530530	+	0.338399i
$206$	5.84830			0.407470
$207$		0			0
$208$	−5.72182			−0.396737
$209$	−0.846603			−0.0585608
$210$		0			0
$211$	2.54546			0.175237			0.0876184	−	0.996154i	$-0.472074\pi$
$211$	2.54546			0.175237			0.0876184	+	0.996154i	$0.472074\pi$
$212$	9.38164			0.644334
$213$		0			0
$214$	4.16554			0.284750
$215$	−4.98939	+	7.82218i	−0.340274	+	0.533468i
$216$		0			0
$217$	2.84534	+	19.3629i	0.193154	+	1.31444i
$218$	−16.1432			−1.09336
$219$		0			0
$220$	−0.179704	+	0.281733i	−0.0121156	+	0.0189944i
$221$			36.2647i			2.43943i
$222$		0			0
$223$	29.7080			1.98940			0.994698	−	0.102843i	$-0.0327939\pi$
$223$	29.7080			1.98940			0.994698	+	0.102843i	$0.0327939\pi$
$224$	2.61764	−	0.384656i	0.174898	−	0.0257009i
$225$		0			0
$226$	−12.1432			−0.807754
$227$			20.7727i			1.37873i	0.724413	+	0.689366i	$0.242111\pi$
$227$			20.7727i			1.37873i	−0.724413	+	0.689366i	$0.757889\pi$
$228$		0			0
$229$			14.7942i			0.977627i	0.872388	+	0.488813i	$0.162570\pi$
$229$			14.7942i			0.977627i	−0.872388	+	0.488813i	$0.837430\pi$
$230$	8.66449	+	5.52666i	0.571319	+	0.364417i
$231$		0			0
$232$		−	5.06799i		−	0.332730i
$233$	13.7110			0.898237			0.449119	−	0.893472i	$-0.351738\pi$
$233$	13.7110			0.898237			0.449119	+	0.893472i	$0.351738\pi$
$234$		0			0
$235$	−14.5472	+	22.8065i	−0.948953	+	1.48773i
$236$	−11.2159			−0.730096
$237$		0			0
$238$	−2.43794	−	16.5905i	−0.158028	−	1.07540i
$239$		−	2.77836i		−	0.179717i	−0.995955	−	0.0898587i	$-0.971358\pi$
$239$		−	2.77836i		−	0.179717i	0.995955	−	0.0898587i	$-0.0286415\pi$
$240$		0			0
$241$			17.0438i			1.09789i	0.835860	+	0.548943i	$0.184969\pi$
$241$			17.0438i			1.09789i	−0.835860	+	0.548943i	$0.815031\pi$
$242$	10.9777			0.705671
$243$		0			0
$244$		0			0
$245$	−15.0602	−	4.26516i	−0.962158	−	0.272491i
$246$		0			0
$247$			32.4143i			2.06247i
$248$			7.39709i			0.469715i
$249$		0			0
$250$	1.47781	−	11.0822i	0.0934650	−	0.700902i
$251$	−17.5560			−1.10813			−0.554063	−	0.832475i	$-0.686923\pi$
$251$	−17.5560			−1.10813			−0.554063	+	0.832475i	$0.686923\pi$
$252$		0			0
$253$			0.686847i			0.0431817i
$254$			7.74821i			0.486166i
$255$		0			0
$256$	1.00000			0.0625000
$257$			5.74771i			0.358533i	0.983801	+	0.179266i	$0.0573724\pi$
$257$			5.74771i			0.358533i	−0.983801	+	0.179266i	$0.942628\pi$
$258$		0			0
$259$	2.21610	+	15.0809i	0.137702	+	0.937081i
$260$	10.7868	+	6.88041i	0.668972	+	0.426705i
$261$		0			0
$262$	9.36577			0.578619
$263$	26.5514			1.63723			0.818614	−	0.574345i	$-0.194743\pi$
$263$	26.5514			1.63723			0.818614	+	0.574345i	$0.194743\pi$
$264$		0			0
$265$	−17.6864	−	11.2813i	−1.08647	−	0.693005i
$266$	−2.17909	−	14.8290i	−0.133609	−	0.909226i
$267$		0			0
$268$		−	15.6717i		−	0.957304i
$269$	32.1200			1.95839			0.979196	−	0.202915i	$-0.0650415\pi$
$269$	32.1200			1.95839			0.979196	+	0.202915i	$0.0650415\pi$
$270$		0			0
$271$			10.4482i			0.634683i	0.948311	+	0.317342i	$0.102790\pi$
$271$			10.4482i			0.634683i	−0.948311	+	0.317342i	$0.897210\pi$
$272$		−	6.33796i		−	0.384295i
$273$		0			0
$274$	2.56951			0.155230
$275$	0.677560	−	0.315035i	0.0408584	−	0.0189973i
$276$		0			0
$277$		−	26.1223i		−	1.56954i	−0.619790	−	0.784768i	$-0.712782\pi$
$277$		−	26.1223i		−	1.56954i	0.619790	−	0.784768i	$-0.287218\pi$
$278$			14.7066i			0.882043i
$279$		0			0
$280$	−5.39735	−	2.42252i	−0.322553	−	0.144773i
$281$		−	8.68642i		−	0.518188i	−0.965852	−	0.259094i	$-0.916576\pi$
$281$		−	8.68642i		−	0.518188i	0.965852	−	0.259094i	$-0.0834240\pi$
$282$		0			0
$283$	−2.70267			−0.160657			−0.0803285	−	0.996768i	$-0.525597\pi$
$283$	−2.70267			−0.160657			−0.0803285	+	0.996768i	$0.525597\pi$
$284$			3.23047i			0.191693i
$285$		0			0
$286$			0.855090i			0.0505625i
$287$	−10.5472	+	1.54988i	−0.622580	+	0.0914867i
$288$		0			0
$289$	−23.1697			−1.36292
$290$	−6.09419	+	9.55423i	−0.357863	+	0.561044i
$291$		0			0
$292$	8.74686			0.511871
$293$			5.74771i			0.335785i	0.985805	+	0.167893i	$0.0536962\pi$
$293$			5.74771i			0.335785i	−0.985805	+	0.167893i	$0.946304\pi$
$294$		0			0
$295$	21.1444	+	13.4870i	1.23108	+	0.785245i
$296$			5.76125i			0.334866i
$297$		0			0
$298$		−	2.61325i		−	0.151381i
$299$	26.2976			1.52083
$300$		0			0
$301$	−1.59603	−	10.8612i	−0.0919935	−	0.626029i
$302$	1.02652			0.0590695
$303$		0			0
$304$		−	5.66504i		−	0.324912i
$305$		0			0
$306$		0			0
$307$	5.82304			0.332338			0.166169	−	0.986097i	$-0.446860\pi$
$307$	5.82304			0.332338			0.166169	+	0.986097i	$0.446860\pi$
$308$	−0.0574844	−	0.391190i	−0.00327548	−	0.0222901i
$309$		0			0
$310$	8.89490	−	13.9451i	0.505196	−	0.792027i
$311$	17.3290			0.982636			0.491318	−	0.870980i	$-0.336515\pi$
$311$	17.3290			0.982636			0.491318	+	0.870980i	$0.336515\pi$
$312$		0			0
$313$	1.43305			0.0810009			0.0405005	−	0.999180i	$-0.487105\pi$
$313$	1.43305			0.0810009			0.0405005	+	0.999180i	$0.487105\pi$
$314$	20.2216			1.14117
$315$		0			0
$316$	−2.05057			−0.115353
$317$	−3.31552			−0.186218			−0.0931091	−	0.995656i	$-0.529681\pi$
$317$	−3.31552			−0.186218			−0.0931091	+	0.995656i	$0.529681\pi$
$318$		0			0
$319$	−0.757378			−0.0424050
$320$	−1.88521	−	1.20249i	−0.105387	−	0.0672210i
$321$		0			0
$322$	−12.0307	+	1.76789i	−0.670447	+	0.0985207i
$323$	−35.9048			−1.99779
$324$		0			0
$325$	−12.0619	−	25.9421i	−0.669073	−	1.43901i
$326$		−	5.46879i		−	0.302888i
$327$		0			0
$328$	−4.02927			−0.222479
$329$	−4.65341	−	31.6671i	−0.256551	−	1.74586i
$330$		0			0
$331$	15.3087			0.841444			0.420722	−	0.907190i	$-0.361777\pi$
$331$	15.3087			0.841444			0.420722	+	0.907190i	$0.361777\pi$
$332$		−	8.07001i		−	0.442899i
$333$		0			0
$334$		−	9.70748i		−	0.531170i
$335$	−18.8451	+	29.5446i	−1.02962	+	1.61419i
$336$		0			0
$337$			11.7701i			0.641158i	0.947222	+	0.320579i	$0.103877\pi$
$337$			11.7701i			0.641158i	−0.947222	+	0.320579i	$0.896123\pi$
$338$	19.7392			1.07367
$339$		0			0
$340$	−7.62131	+	11.9484i	−0.413324	+	0.647993i
$341$	1.10545			0.0598633
$342$		0			0
$343$	16.7743	−	7.85013i	0.905724	−	0.423867i
$344$		−	4.14923i		−	0.223711i
$345$		0			0
$346$			19.3174i			1.03851i
$347$	−18.6483			−1.00109			−0.500547	−	0.865709i	$-0.666868\pi$
$347$	−18.6483			−1.00109			−0.500547	+	0.865709i	$0.666868\pi$
$348$		0			0
$349$		−	0.668016i		−	0.0357581i	−0.999840	−	0.0178790i	$-0.994309\pi$
$349$		−	0.668016i		−	0.0357581i	0.999840	−	0.0178790i	$-0.00569138\pi$
$350$	7.26211	+	11.0572i	0.388176	+	0.591032i
$351$		0			0
$352$		−	0.149444i		−	0.00796537i
$353$			1.16368i			0.0619363i	0.999520	+	0.0309682i	$0.00985905\pi$
$353$			1.16368i			0.0619363i	−0.999520	+	0.0309682i	$0.990141\pi$
$354$		0			0
$355$	3.88460	−	6.09013i	0.206173	−	0.323230i
$356$	2.31080			0.122472
$357$		0			0
$358$		−	10.9851i		−	0.580581i
$359$			27.8864i			1.47179i	0.677097	+	0.735893i	$0.263238\pi$
$359$			27.8864i			1.47179i	−0.677097	+	0.735893i	$0.736762\pi$
$360$		0			0
$361$	−13.0926			−0.689086
$362$		−	6.83362i		−	0.359167i
$363$		0			0
$364$	−14.9777	+	2.20093i	−0.785043	+	0.115360i
$365$	−16.4897	−	10.5180i	−0.863110	−	0.550536i
$366$		0			0
$367$	−27.6042			−1.44093			−0.720464	−	0.693492i	$-0.756071\pi$
$367$	−27.6042			−1.44093			−0.720464	+	0.693492i	$0.756071\pi$
$368$	−4.59603			−0.239584
$369$		0			0
$370$	6.92783	−	10.8612i	0.360161	−	0.564646i
$371$	24.5578	−	3.60871i	1.27498	−	0.187355i
$372$		0			0
$373$		−	34.6305i		−	1.79310i	−0.442941	−	0.896551i	$-0.646065\pi$
$373$		−	34.6305i		−	1.79310i	0.442941	−	0.896551i	$-0.353935\pi$
$374$	−0.947167			−0.0489769
$375$		0			0
$376$		−	12.0976i		−	0.623885i
$377$			28.9981i			1.49348i
$378$		0			0
$379$	−13.1921			−0.677630			−0.338815	−	0.940853i	$-0.610026\pi$
$379$	−13.1921			−0.677630			−0.338815	+	0.940853i	$0.610026\pi$
$380$	−6.81213	+	10.6798i	−0.349455	+	0.547862i
$381$		0			0
$382$			16.2182i			0.829796i
$383$			15.2023i			0.776799i	0.921491	+	0.388399i	$0.126972\pi$
$383$			15.2023i			0.776799i	−0.921491	+	0.388399i	$0.873028\pi$
$384$		0			0
$385$	−0.362030	+	0.806600i	−0.0184508	+	0.0411081i
$386$		−	20.8379i		−	1.06062i
$387$		0			0
$388$	−6.70014			−0.340148
$389$		−	27.0512i		−	1.37155i	−0.727813	−	0.685776i	$-0.759463\pi$
$389$		−	27.0512i		−	1.37155i	0.727813	−	0.685776i	$-0.240537\pi$
$390$		0			0
$391$			29.1294i			1.47314i
$392$	6.70408	−	2.01378i	0.338607	−	0.101711i
$393$		0			0
$394$	5.64659			0.284471
$395$	3.86575	+	2.46578i	0.194507	+	0.124067i
$396$		0			0
$397$	1.23781			0.0621241			0.0310621	−	0.999517i	$-0.490111\pi$
$397$	1.23781			0.0621241			0.0310621	+	0.999517i	$0.490111\pi$
$398$			18.3142i			0.918007i
$399$		0			0
$400$	2.10805	+	4.53389i	0.105403	+	0.226694i
$401$			36.2582i			1.81065i	0.424719	+	0.905325i	$0.360373\pi$
$401$			36.2582i			1.81065i	−0.424719	+	0.905325i	$0.639627\pi$
$402$		0			0
$403$		−	42.3248i		−	2.10835i
$404$	−7.28201			−0.362293
$405$		0			0
$406$	−1.94943	−	13.2662i	−0.0967487	−	0.658389i
$407$	0.860983			0.0426773
$408$		0			0
$409$		−	32.1246i		−	1.58846i	−0.607616	−	0.794231i	$-0.707874\pi$
$409$		−	32.1246i		−	1.58846i	0.607616	−	0.794231i	$-0.292126\pi$
$410$	7.59603	+	4.84514i	0.375141	+	0.239285i
$411$		0			0
$412$	5.84830			0.288125
$413$	−29.3593	+	4.31428i	−1.44468	+	0.212292i
$414$		0			0
$415$	−9.70408	+	15.2137i	−0.476355	+	0.746810i
$416$	−5.72182			−0.280535
$417$		0			0
$418$	−0.846603			−0.0414087
$419$	−12.6549			−0.618232			−0.309116	−	0.951024i	$-0.600033\pi$
$419$	−12.6549			−0.618232			−0.309116	+	0.951024i	$0.600033\pi$
$420$		0			0
$421$	−24.2468			−1.18172			−0.590859	−	0.806775i	$-0.701211\pi$
$421$	−24.2468			−1.18172			−0.590859	+	0.806775i	$0.701211\pi$
$422$	2.54546			0.123911
$423$		0			0
$424$	9.38164			0.455613
$425$	28.7356	−	13.3607i	1.39388	−	0.648091i
$426$		0			0
$427$		0			0
$428$	4.16554			0.201349
$429$		0			0
$430$	−4.98939	+	7.82218i	−0.240610	+	0.377219i
$431$			5.73916i			0.276446i	0.990401	+	0.138223i	$0.0441390\pi$
$431$			5.73916i			0.276446i	−0.990401	+	0.138223i	$0.955861\pi$
$432$		0			0
$433$	−8.54573			−0.410682			−0.205341	−	0.978691i	$-0.565830\pi$
$433$	−8.54573			−0.410682			−0.205341	+	0.978691i	$0.565830\pi$
$434$	2.84534	+	19.3629i	0.136581	+	0.929449i
$435$		0			0
$436$	−16.1432			−0.773119
$437$			26.0367i			1.24550i
$438$		0			0
$439$			8.38350i			0.400123i	0.979783	+	0.200061i	$0.0641142\pi$
$439$			8.38350i			0.400123i	−0.979783	+	0.200061i	$0.935886\pi$
$440$	−0.179704	+	0.281733i	−0.00856705	+	0.0134311i
$441$		0			0
$442$			36.2647i			1.72493i
$443$	6.61158			0.314126			0.157063	−	0.987589i	$-0.449798\pi$
$443$	6.61158			0.314126			0.157063	+	0.987589i	$0.449798\pi$
$444$		0			0
$445$	−4.35636	−	2.77871i	−0.206511	−	0.131724i
$446$	29.7080			1.40671
$447$		0			0
$448$	2.61764	−	0.384656i	0.123672	−	0.0181733i
$449$		−	19.5221i		−	0.921304i	−0.887581	−	0.460652i	$-0.847616\pi$
$449$		−	19.5221i		−	0.921304i	0.887581	−	0.460652i	$-0.152384\pi$
$450$		0			0
$451$			0.602148i			0.0283541i
$452$	−12.1432			−0.571168
$453$		0			0
$454$			20.7727i			0.974911i
$455$	30.8827	+	13.8612i	1.44780	+	0.649824i
$456$		0			0
$457$			16.2220i			0.758833i	0.925226	+	0.379416i	$0.123875\pi$
$457$			16.2220i			0.758833i	−0.925226	+	0.379416i	$0.876125\pi$
$458$			14.7942i			0.691286i
$459$		0			0
$460$	8.66449	+	5.52666i	0.403984	+	0.257682i
$461$	28.9692			1.34923			0.674614	−	0.738170i	$-0.264310\pi$
$461$	28.9692			1.34923			0.674614	+	0.738170i	$0.264310\pi$
$462$		0			0
$463$		−	17.6872i		−	0.821994i	−0.911637	−	0.410997i	$-0.865181\pi$
$463$		−	17.6872i		−	0.821994i	0.911637	−	0.410997i	$-0.134819\pi$
$464$		−	5.06799i		−	0.235275i
$465$		0			0
$466$	13.7110			0.635150
$467$			6.31118i			0.292047i	0.989281	+	0.146023i	$0.0466474\pi$
$467$			6.31118i			0.292047i	−0.989281	+	0.146023i	$0.953353\pi$
$468$		0			0
$469$	−6.02823	−	41.0230i	−0.278358	−	1.89426i
$470$	−14.5472	+	22.8065i	−0.671011	+	1.05199i
$471$		0			0
$472$	−11.2159			−0.516256
$473$	−0.620076			−0.0285111
$474$		0			0
$475$	25.6846	−	11.9422i	1.17849	−	0.547945i
$476$	−2.43794	−	16.5905i	−0.111743	−	0.760424i
$477$		0			0
$478$		−	2.77836i		−	0.127079i
$479$	10.0152			0.457605			0.228802	−	0.973473i	$-0.426519\pi$
$479$	10.0152			0.457605			0.228802	+	0.973473i	$0.426519\pi$
$480$		0			0
$481$		−	32.9649i		−	1.50307i
$482$			17.0438i			0.776322i
$483$		0			0
$484$	10.9777			0.498985
$485$	12.6312	+	8.05682i	0.573552	+	0.365842i
$486$		0			0
$487$		−	7.76766i		−	0.351986i	−0.984391	−	0.175993i	$-0.943686\pi$
$487$		−	7.76766i		−	0.351986i	0.984391	−	0.175993i	$-0.0563137\pi$
$488$		0			0
$489$		0			0
$490$	−15.0602	−	4.26516i	−0.680349	−	0.192680i
$491$		−	12.1397i		−	0.547859i	−0.961750	−	0.273929i	$-0.911677\pi$
$491$		−	12.1397i		−	0.547859i	0.961750	−	0.273929i	$-0.0883234\pi$
$492$		0			0
$493$	−32.1207			−1.44664
$494$			32.4143i			1.45839i
$495$		0			0
$496$			7.39709i			0.332139i
$497$	1.24262	+	8.45622i	0.0557392	+	0.379313i
$498$		0			0
$499$	25.5231			1.14257			0.571286	−	0.820751i	$-0.306445\pi$
$499$	25.5231			1.14257			0.571286	+	0.820751i	$0.306445\pi$
$500$	1.47781	−	11.0822i	0.0660898	−	0.495613i
$501$		0			0
$502$	−17.5560			−0.783563
$503$		−	6.65636i		−	0.296792i	−0.988928	−	0.148396i	$-0.952589\pi$
$503$		−	6.65636i		−	0.296792i	0.988928	−	0.148396i	$-0.0474111\pi$
$504$		0			0
$505$	13.7281	+	8.75651i	0.610894	+	0.389660i
$506$			0.686847i			0.0305341i
$507$		0			0
$508$			7.74821i			0.343771i
$509$	−40.0580			−1.77554			−0.887769	−	0.460289i	$-0.847746\pi$
$509$	−40.0580			−1.77554			−0.887769	+	0.460289i	$0.847746\pi$
$510$		0			0
$511$	22.8961	−	3.36454i	1.01287	−	0.148838i
$512$	1.00000			0.0441942
$513$		0			0
$514$			5.74771i			0.253521i
$515$	−11.0253	−	7.03250i	−0.485832	−	0.309889i
$516$		0			0
$517$	−1.80791			−0.0795116
$518$	2.21610	+	15.0809i	0.0973700	+	0.662616i
$519$		0			0
$520$	10.7868	+	6.88041i	0.473035	+	0.301726i
$521$	−4.26743			−0.186960			−0.0934798	−	0.995621i	$-0.529799\pi$
$521$	−4.26743			−0.186960			−0.0934798	+	0.995621i	$0.529799\pi$
$522$		0			0
$523$	−6.36664			−0.278394			−0.139197	−	0.990265i	$-0.544452\pi$
$523$	−6.36664			−0.278394			−0.139197	+	0.990265i	$0.544452\pi$
$524$	9.36577			0.409145
$525$		0			0
$526$	26.5514			1.15769
$527$	46.8824			2.04223
$528$		0			0
$529$	−1.87653			−0.0815884
$530$	−17.6864	−	11.2813i	−0.768247	−	0.490028i
$531$		0			0
$532$	−2.17909	−	14.8290i	−0.0944756	−	0.642920i
$533$	23.0548			0.998612
$534$		0			0
$535$	−7.85292	−	5.00900i	−0.339511	−	0.216558i
$536$		−	15.6717i		−	0.676916i
$537$		0			0
$538$	32.1200			1.38479
$539$	−0.300947	−	1.00188i	−0.0129627	−	0.0431541i
$540$		0			0
$541$	26.1432			1.12398			0.561992	−	0.827143i	$-0.310035\pi$
$541$	26.1432			1.12398			0.561992	+	0.827143i	$0.310035\pi$
$542$			10.4482i			0.448789i
$543$		0			0
$544$		−	6.33796i		−	0.271738i
$545$	30.4334	+	19.4120i	1.30362	+	0.831518i
$546$		0			0
$547$			24.8954i			1.06445i	0.846603	+	0.532225i	$0.178644\pi$
$547$			24.8954i			1.06445i	−0.846603	+	0.532225i	$0.821356\pi$
$548$	2.56951			0.109764
$549$		0			0
$550$	0.677560	−	0.315035i	0.0288913	−	0.0134331i
$551$	−28.7103			−1.22310
$552$		0			0
$553$	−5.36765	+	0.788764i	−0.228256	+	0.0335416i
$554$		−	26.1223i		−	1.10983i
$555$		0			0
$556$			14.7066i			0.623698i
$557$	−8.37992			−0.355069			−0.177534	−	0.984115i	$-0.556812\pi$
$557$	−8.37992			−0.355069			−0.177534	+	0.984115i	$0.556812\pi$
$558$		0			0
$559$			23.7411i			1.00414i
$560$	−5.39735	−	2.42252i	−0.228080	−	0.102370i
$561$		0			0
$562$		−	8.68642i		−	0.366414i
$563$			10.0061i			0.421707i	0.977518	+	0.210853i	$0.0676243\pi$
$563$			10.0061i			0.421707i	−0.977518	+	0.210853i	$0.932376\pi$
$564$		0			0
$565$	22.8925	+	14.6020i	0.963095	+	0.614312i
$566$	−2.70267			−0.113602
$567$		0			0
$568$			3.23047i			0.135548i
$569$			23.8840i			1.00127i	0.865659	+	0.500634i	$0.166900\pi$
$569$			23.8840i			1.00127i	−0.865659	+	0.500634i	$0.833100\pi$
$570$		0			0
$571$	−16.0686			−0.672449			−0.336225	−	0.941782i	$-0.609150\pi$
$571$	−16.0686			−0.672449			−0.336225	+	0.941782i	$0.609150\pi$
$572$			0.855090i			0.0357531i
$573$		0			0
$574$	−10.5472	+	1.54988i	−0.440231	+	0.0646909i
$575$	−9.68866	−	20.8379i	−0.404045	−	0.868999i
$576$		0			0
$577$	−24.4786			−1.01906			−0.509529	−	0.860453i	$-0.670180\pi$
$577$	−24.4786			−1.01906			−0.509529	+	0.860453i	$0.670180\pi$
$578$	−23.1697			−0.963733
$579$		0			0
$580$	−6.09419	+	9.55423i	−0.253047	+	0.396718i
$581$	−3.10418	−	21.1244i	−0.128783	−	0.876387i
$582$		0			0
$583$		−	1.40203i		−	0.0580660i
$584$	8.74686			0.361948
$585$		0			0
$586$			5.74771i			0.237436i
$587$		−	7.26576i		−	0.299890i	−0.988694	−	0.149945i	$-0.952090\pi$
$587$		−	7.26576i		−	0.299890i	0.988694	−	0.149945i	$-0.0479097\pi$
$588$		0			0
$589$	41.9048			1.72666
$590$	21.1444	+	13.4870i	0.870503	+	0.555252i
$591$		0			0
$592$			5.76125i			0.236786i
$593$			9.67345i			0.397241i	0.980076	+	0.198621i	$0.0636461\pi$
$593$			9.67345i			0.397241i	−0.980076	+	0.198621i	$0.936354\pi$
$594$		0			0
$595$	−15.3538	+	34.2082i	−0.629445	+	1.40240i
$596$		−	2.61325i		−	0.107043i
$597$		0			0
$598$	26.2976			1.07539
$599$			23.7290i			0.969542i	0.874641	+	0.484771i	$0.161097\pi$
$599$			23.7290i			0.969542i	−0.874641	+	0.484771i	$0.838903\pi$
$600$		0			0
$601$		−	40.7532i		−	1.66236i	−0.556005	−	0.831179i	$-0.687666\pi$
$601$		−	40.7532i		−	1.66236i	0.556005	−	0.831179i	$-0.312334\pi$
$602$	−1.59603	−	10.8612i	−0.0650492	−	0.442669i
$603$		0			0
$604$	1.02652			0.0417685
$605$	−20.6952	−	13.2005i	−0.841381	−	0.536677i
$606$		0			0
$607$	13.1985			0.535710			0.267855	−	0.963459i	$-0.413685\pi$
$607$	13.1985			0.535710			0.267855	+	0.963459i	$0.413685\pi$
$608$		−	5.66504i		−	0.229748i
$609$		0			0
$610$		0			0
$611$			69.2202i			2.80035i
$612$		0			0
$613$		−	28.0175i		−	1.13162i	−0.824537	−	0.565808i	$-0.808564\pi$
$613$		−	28.0175i		−	1.13162i	0.824537	−	0.565808i	$-0.191436\pi$
$614$	5.82304			0.234999
$615$		0			0
$616$	−0.0574844	−	0.391190i	−0.00231611	−	0.0157615i
$617$	−41.0463			−1.65246			−0.826230	−	0.563333i	$-0.809519\pi$
$617$	−41.0463			−1.65246			−0.826230	+	0.563333i	$0.809519\pi$
$618$		0			0
$619$		−	46.8602i		−	1.88347i	−0.336355	−	0.941735i	$-0.609194\pi$
$619$		−	46.8602i		−	1.88347i	0.336355	−	0.941735i	$-0.390806\pi$
$620$	8.89490	−	13.9451i	0.357228	−	0.560048i
$621$		0			0
$622$	17.3290			0.694829
$623$	6.04885	−	0.888865i	0.242342	−	0.0356116i
$624$		0			0
$625$	−16.1122	+	19.1153i	−0.644489	+	0.764613i
$626$	1.43305			0.0572763
$627$		0			0
$628$	20.2216			0.806932
$629$	36.5146			1.45593
$630$		0			0
$631$	−10.1150			−0.402671			−0.201335	−	0.979522i	$-0.564528\pi$
$631$	−10.1150			−0.402671			−0.201335	+	0.979522i	$0.564528\pi$
$632$	−2.05057			−0.0815672
$633$		0			0
$634$	−3.31552			−0.131676
$635$	9.31712	−	14.6070i	0.369739	−	0.579662i
$636$		0			0
$637$	−38.3595	+	11.5225i	−1.51986	+	0.456538i
$638$	−0.757378			−0.0299849
$639$		0			0
$640$	−1.88521	−	1.20249i	−0.0745196	−	0.0475325i
$641$			21.7604i			0.859484i	0.902952	+	0.429742i	$0.141395\pi$
$641$			21.7604i			0.859484i	−0.902952	+	0.429742i	$0.858605\pi$
$642$		0			0
$643$	−17.9750			−0.708866			−0.354433	−	0.935081i	$-0.615326\pi$
$643$	−17.9750			−0.708866			−0.354433	+	0.935081i	$0.615326\pi$
$644$	−12.0307	+	1.76789i	−0.474078	+	0.0696647i
$645$		0			0
$646$	−35.9048			−1.41265
$647$		−	26.3383i		−	1.03546i	−0.855543	−	0.517732i	$-0.826777\pi$
$647$		−	26.3383i		−	1.03546i	0.855543	−	0.517732i	$-0.173223\pi$
$648$		0			0
$649$			1.67615i			0.0657947i
$650$	−12.0619	−	25.9421i	−0.473106	−	1.01753i
$651$		0			0
$652$		−	5.46879i		−	0.214174i
$653$	8.28222			0.324108			0.162054	−	0.986782i	$-0.448188\pi$
$653$	8.28222			0.324108			0.162054	+	0.986782i	$0.448188\pi$
$654$		0			0
$655$	−17.6565	−	11.2622i	−0.689895	−	0.440051i
$656$	−4.02927			−0.157317
$657$		0			0
$658$	−4.65341	−	31.6671i	−0.181409	−	1.23451i
$659$		−	0.515309i		−	0.0200736i	−0.999950	−	0.0100368i	$-0.996805\pi$
$659$		−	0.515309i		−	0.0200736i	0.999950	−	0.0100368i	$-0.00319486\pi$
$660$		0			0
$661$		−	9.37717i		−	0.364730i	−0.983231	−	0.182365i	$-0.941625\pi$
$661$		−	9.37717i		−	0.364730i	0.983231	−	0.182365i	$-0.0583752\pi$
$662$	15.3087			0.594991
$663$		0			0
$664$		−	8.07001i		−	0.313177i
$665$	−13.7237	+	30.5762i	−0.532180	+	1.18569i
$666$		0			0
$667$			23.2926i			0.901893i
$668$		−	9.70748i		−	0.375594i
$669$		0			0
$670$	−18.8451	+	29.5446i	−0.728048	+	1.14141i
$671$		0			0
$672$		0			0
$673$		−	11.8974i		−	0.458613i	−0.973354	−	0.229306i	$-0.926354\pi$
$673$		−	11.8974i		−	0.458613i	0.973354	−	0.229306i	$-0.0736457\pi$
$674$			11.7701i			0.453367i
$675$		0			0
$676$	19.7392			0.759201
$677$		−	7.55519i		−	0.290370i	−0.989405	−	0.145185i	$-0.953622\pi$
$677$		−	7.55519i		−	0.290370i	0.989405	−	0.145185i	$-0.0463777\pi$
$678$		0			0
$679$	−17.5385	+	2.57725i	−0.673068	+	0.0989058i
$680$	−7.62131	+	11.9484i	−0.292264	+	0.458200i
$681$		0			0
$682$	1.10545			0.0423298
$683$	−2.71271			−0.103799			−0.0518995	−	0.998652i	$-0.516528\pi$
$683$	−2.71271			−0.103799			−0.0518995	+	0.998652i	$0.516528\pi$
$684$		0			0
$685$	−4.84407	−	3.08980i	−0.185082	−	0.118055i
$686$	16.7743	−	7.85013i	0.640444	−	0.299719i
$687$		0			0
$688$		−	4.14923i		−	0.158188i
$689$	−53.6801			−2.04505
$690$		0			0
$691$		−	21.7710i		−	0.828209i	−0.910229	−	0.414104i	$-0.864095\pi$
$691$		−	21.7710i		−	0.828209i	0.910229	−	0.414104i	$-0.135905\pi$
$692$			19.3174i			0.734338i
$693$		0			0
$694$	−18.6483			−0.707880
$695$	17.6845	−	27.7250i	0.670810	−	1.05167i
$696$		0			0
$697$			25.5373i			0.967296i
$698$		−	0.668016i		−	0.0252848i
$699$		0			0
$700$	7.26211	+	11.0572i	0.274482	+	0.417923i
$701$		−	17.6523i		−	0.666717i	−0.942800	−	0.333359i	$-0.891818\pi$
$701$		−	17.6523i		−	0.666717i	0.942800	−	0.333359i	$-0.108182\pi$
$702$		0			0
$703$	32.6377			1.23095
$704$		−	0.149444i		−	0.00563237i
$705$		0			0
$706$			1.16368i			0.0437956i
$707$	−19.0617	+	2.80107i	−0.716888	+	0.105345i
$708$		0			0
$709$	22.2443			0.835404			0.417702	−	0.908584i	$-0.362836\pi$
$709$	22.2443			0.835404			0.417702	+	0.908584i	$0.362836\pi$
$710$	3.88460	−	6.09013i	0.145786	−	0.228558i
$711$		0			0
$712$	2.31080			0.0866010
$713$		−	33.9972i		−	1.27321i
$714$		0			0
$715$	1.02823	−	1.61203i	0.0384538	−	0.0602863i
$716$		−	10.9851i		−	0.410533i
$717$		0			0
$718$			27.8864i			1.04071i
$719$	13.6286			0.508262			0.254131	−	0.967170i	$-0.418211\pi$
$719$	13.6286			0.508262			0.254131	+	0.967170i	$0.418211\pi$
$720$		0			0
$721$	15.3087	−	2.24958i	0.570127	−	0.0837789i
$722$	−13.0926			−0.487257
$723$		0			0
$724$		−	6.83362i		−	0.253970i
$725$	22.9777	−	10.6836i	0.853369	−	0.396778i
$726$		0			0
$727$	34.1615			1.26698			0.633490	−	0.773751i	$-0.281622\pi$
$727$	34.1615			1.26698			0.633490	+	0.773751i	$0.281622\pi$
$728$	−14.9777	+	2.20093i	−0.555109	+	0.0815721i
$729$		0			0
$730$	−16.4897	−	10.5180i	−0.610311	−	0.389288i
$731$	−26.2976			−0.972653
$732$		0			0
$733$	0.783653			0.0289449			0.0144724	−	0.999895i	$-0.495393\pi$
$733$	0.783653			0.0289449			0.0144724	+	0.999895i	$0.495393\pi$
$734$	−27.6042			−1.01889
$735$		0			0
$736$	−4.59603			−0.169412
$737$	−2.34204			−0.0862702
$738$		0			0
$739$	17.1921			0.632420			0.316210	−	0.948689i	$-0.397590\pi$
$739$	17.1921			0.632420			0.316210	+	0.948689i	$0.397590\pi$
$740$	6.92783	−	10.8612i	0.254672	−	0.399265i
$741$		0			0
$742$	24.5578	−	3.60871i	0.901544	−	0.132480i
$743$	39.4123			1.44590			0.722949	−	0.690901i	$-0.242786\pi$
$743$	39.4123			1.44590			0.722949	+	0.690901i	$0.242786\pi$
$744$		0			0
$745$	−3.14240	+	4.92653i	−0.115128	+	0.180494i
$746$		−	34.6305i		−	1.26791i
$747$		0			0
$748$	−0.947167			−0.0346319
$749$	10.9039	−	1.60230i	0.398419	−	0.0585468i
$750$		0			0
$751$	−7.93560			−0.289574			−0.144787	−	0.989463i	$-0.546250\pi$
$751$	−7.93560			−0.289574			−0.144787	+	0.989463i	$0.546250\pi$
$752$		−	12.0976i		−	0.441153i
$753$		0			0
$754$			28.9981i			1.05605i
$755$	−1.93521	−	1.23438i	−0.0704294	−	0.0449235i
$756$		0			0
$757$		−	23.7949i		−	0.864840i	−0.901672	−	0.432420i	$-0.857660\pi$
$757$		−	23.7949i		−	0.864840i	0.901672	−	0.432420i	$-0.142340\pi$
$758$	−13.1921			−0.479157
$759$		0			0
$760$	−6.81213	+	10.6798i	−0.247102	+	0.387397i
$761$	36.7800			1.33327			0.666637	−	0.745383i	$-0.267733\pi$
$761$	36.7800			1.33327			0.666637	+	0.745383i	$0.267733\pi$
$762$		0			0
$763$	−42.2571	+	6.20959i	−1.52981	+	0.224802i
$764$			16.2182i			0.586754i
$765$		0			0
$766$			15.2023i			0.549280i
$767$	64.1756			2.31725
$768$		0			0
$769$		−	24.4381i		−	0.881261i	−0.897688	−	0.440631i	$-0.854755\pi$
$769$		−	24.4381i		−	0.881261i	0.897688	−	0.440631i	$-0.145245\pi$
$770$	−0.362030	+	0.806600i	−0.0130467	+	0.0290678i
$771$		0			0
$772$		−	20.8379i		−	0.749971i
$773$		−	31.9157i		−	1.14793i	−0.818880	−	0.573964i	$-0.805405\pi$
$773$		−	31.9157i		−	1.14793i	0.818880	−	0.573964i	$-0.194595\pi$
$774$		0			0
$775$	−33.5375	+	15.5934i	−1.20470	+	0.560133i
$776$	−6.70014			−0.240521
$777$		0			0
$778$		−	27.0512i		−	0.969833i
$779$			22.8260i			0.817825i
$780$		0			0
$781$	0.482774			0.0172750
$782$			29.1294i			1.04167i
$783$		0			0
$784$	6.70408	−	2.01378i	0.239431	−	0.0719208i
$785$	−38.1221	−	24.3163i	−1.36064	−	0.867885i
$786$		0			0
$787$	38.4244			1.36968			0.684841	−	0.728693i	$-0.259872\pi$
$787$	38.4244			1.36968			0.684841	+	0.728693i	$0.259872\pi$
$788$	5.64659			0.201152
$789$		0			0
$790$	3.86575	+	2.46578i	0.137537	+	0.0877285i
$791$	−31.7865	+	4.67096i	−1.13020	+	0.166080i
$792$		0			0
$793$		0			0
$794$	1.23781			0.0439284
$795$		0			0
$796$			18.3142i			0.649129i
$797$		−	36.4968i		−	1.29278i	−0.763006	−	0.646391i	$-0.776278\pi$
$797$		−	36.4968i		−	1.29278i	0.763006	−	0.646391i	$-0.223722\pi$
$798$		0			0
$799$	−76.6739			−2.71253
$800$	2.10805	+	4.53389i	0.0745309	+	0.160297i
$801$		0			0
$802$			36.2582i			1.28032i
$803$		−	1.30716i		−	0.0461288i
$804$		0			0
$805$	24.8064	+	11.1340i	0.874310	+	0.392421i
$806$		−	42.3248i		−	1.49083i
$807$		0			0
$808$	−7.28201			−0.256180
$809$		−	27.1786i		−	0.955548i	−0.878483	−	0.477774i	$-0.841444\pi$
$809$		−	27.1786i		−	0.955548i	0.878483	−	0.477774i	$-0.158556\pi$
$810$		0			0
$811$			11.1896i			0.392919i	0.980512	+	0.196459i	$0.0629443\pi$
$811$			11.1896i			0.392919i	−0.980512	+	0.196459i	$0.937056\pi$
$812$	−1.94943	−	13.2662i	−0.0684117	−	0.465551i
$813$		0			0
$814$	0.860983			0.0301774
$815$	−6.57615	+	10.3098i	−0.230352	+	0.361138i
$816$		0			0
$817$	−23.5055			−0.822355
$818$		−	32.1246i		−	1.12321i
$819$		0			0
$820$	7.59603	+	4.84514i	0.265265	+	0.169200i
$821$			26.1287i			0.911898i	0.890006	+	0.455949i	$0.150700\pi$
$821$			26.1287i			0.911898i	−0.890006	+	0.455949i	$0.849300\pi$
$822$		0			0
$823$		−	21.5532i		−	0.751298i	−0.926762	−	0.375649i	$-0.877420\pi$
$823$		−	21.5532i		−	0.751298i	0.926762	−	0.375649i	$-0.122580\pi$
$824$	5.84830			0.203735
$825$		0			0
$826$	−29.3593	+	4.31428i	−1.02154	+	0.150113i
$827$	−43.9107			−1.52692			−0.763462	−	0.645853i	$-0.776502\pi$
$827$	−43.9107			−1.52692			−0.763462	+	0.645853i	$0.776502\pi$
$828$		0			0
$829$		−	28.8397i		−	1.00165i	−0.865550	−	0.500823i	$-0.833031\pi$
$829$		−	28.8397i		−	1.00165i	0.865550	−	0.500823i	$-0.166969\pi$
$830$	−9.70408	+	15.2137i	−0.336833	+	0.528075i
$831$		0			0
$832$	−5.72182			−0.198368
$833$	−12.7633	−	42.4902i	−0.442221	−	1.47220i
$834$		0			0
$835$	−11.6731	+	18.3007i	−0.403965	+	0.633320i
$836$	−0.846603			−0.0292804
$837$		0			0
$838$	−12.6549			−0.437156
$839$	−27.7255			−0.957189			−0.478595	−	0.878036i	$-0.658854\pi$
$839$	−27.7255			−0.957189			−0.478595	+	0.878036i	$0.658854\pi$
$840$		0			0
$841$	3.31552			0.114328
$842$	−24.2468			−0.835600
$843$		0			0
$844$	2.54546			0.0876184
$845$	−37.2126	−	23.7362i	−1.28015	−	0.816549i
$846$		0			0
$847$	28.7356	−	4.22263i	0.987366	−	0.145091i
$848$	9.38164			0.322167
$849$		0			0
$850$	28.7356	−	13.3607i	0.985622	−	0.458270i
$851$		−	26.4789i		−	0.907684i
$852$		0			0
$853$	24.2528			0.830400			0.415200	−	0.909730i	$-0.363712\pi$
$853$	24.2528			0.830400			0.415200	+	0.909730i	$0.363712\pi$
$854$		0			0
$855$		0			0
$856$	4.16554			0.142375
$857$			0.779409i			0.0266241i	0.999911	+	0.0133120i	$0.00423748\pi$
$857$			0.779409i			0.0266241i	−0.999911	+	0.0133120i	$0.995763\pi$
$858$		0			0
$859$			16.0573i			0.547869i	0.961748	+	0.273935i	$0.0883252\pi$
$859$			16.0573i			0.547869i	−0.961748	+	0.273935i	$0.911675\pi$
$860$	−4.98939	+	7.82218i	−0.170137	+	0.266734i
$861$		0			0
$862$			5.73916i			0.195477i
$863$	18.5430			0.631211			0.315605	−	0.948891i	$-0.397792\pi$
$863$	18.5430			0.631211			0.315605	+	0.948891i	$0.397792\pi$
$864$		0			0
$865$	23.2289	−	36.4174i	0.789807	−	1.23823i
$866$	−8.54573			−0.290396
$867$		0			0
$868$	2.84534	+	19.3629i	0.0965770	+	0.657220i
$869$			0.306444i			0.0103954i
$870$		0			0
$871$			89.6709i			3.03838i
$872$	−16.1432			−0.546678
$873$		0			0
$874$			26.0367i			0.880703i
$875$	−0.394475	−	29.5778i	−0.0133357	−	0.999911i
$876$		0			0
$877$		−	26.5808i		−	0.897570i	−0.893640	−	0.448785i	$-0.851857\pi$
$877$		−	26.5808i		−	0.897570i	0.893640	−	0.448785i	$-0.148143\pi$
$878$			8.38350i			0.282930i
$879$		0			0
$880$	−0.179704	+	0.281733i	−0.00605782	+	0.00949722i
$881$	−15.7648			−0.531129			−0.265565	−	0.964093i	$-0.585558\pi$
$881$	−15.7648			−0.531129			−0.265565	+	0.964093i	$0.585558\pi$
$882$		0			0
$883$		−	52.3087i		−	1.76033i	−0.474670	−	0.880164i	$-0.657433\pi$
$883$		−	52.3087i		−	1.76033i	0.474670	−	0.880164i	$-0.342567\pi$
$884$			36.2647i			1.21971i
$885$		0			0
$886$	6.61158			0.222120
$887$		−	33.6308i		−	1.12921i	−0.825361	−	0.564606i	$-0.809028\pi$
$887$		−	33.6308i		−	1.12921i	0.825361	−	0.564606i	$-0.190972\pi$
$888$		0			0
$889$	2.98040	+	20.2820i	0.0999594	+	0.680237i
$890$	−4.35636	−	2.77871i	−0.146025	−	0.0931426i
$891$		0			0
$892$	29.7080			0.994698
$893$	−68.5332			−2.29338
$894$		0			0
$895$	−13.2094	+	20.7093i	−0.441543	+	0.692234i
$896$	2.61764	−	0.384656i	0.0874492	−	0.0128505i
$897$		0			0
$898$		−	19.5221i		−	0.651460i
$899$	37.4883			1.25031
$900$		0			0
$901$		−	59.4604i		−	1.98091i
$902$			0.602148i			0.0200494i
$903$		0			0
$904$	−12.1432			−0.403877
$905$	−8.21734	+	12.8828i	−0.273154	+	0.428240i
$906$		0			0
$907$			35.2451i			1.17030i	0.810927	+	0.585148i	$0.198963\pi$
$907$			35.2451i			1.17030i	−0.810927	+	0.585148i	$0.801037\pi$
$908$			20.7727i			0.689366i
$909$		0			0
$910$	30.8827	+	13.8612i	1.02375	+	0.459495i
$911$		−	31.1169i		−	1.03095i	−0.856905	−	0.515474i	$-0.827616\pi$
$911$		−	31.1169i		−	1.03095i	0.856905	−	0.515474i	$-0.172384\pi$
$912$		0			0
$913$	−1.20601			−0.0399132
$914$			16.2220i			0.536576i
$915$		0			0
$916$			14.7942i			0.488813i
$917$	24.5162	−	3.60260i	0.809597	−	0.118968i
$918$		0			0
$919$	55.2177			1.82146			0.910732	−	0.412998i	$-0.135518\pi$
$919$	55.2177			1.82146			0.910732	+	0.412998i	$0.135518\pi$
$920$	8.66449	+	5.52666i	0.285660	+	0.182209i
$921$		0			0
$922$	28.9692			0.954049
$923$		−	18.4842i		−	0.608414i
$924$		0			0
$925$	−26.1209	+	12.1450i	−0.858849	+	0.399326i
$926$		−	17.6872i		−	0.581238i
$927$		0			0
$928$		−	5.06799i		−	0.166365i
$929$	37.5882			1.23323			0.616615	−	0.787265i	$-0.288504\pi$
$929$	37.5882			1.23323			0.616615	+	0.787265i	$0.288504\pi$
$930$		0			0
$931$	−11.4082	−	37.9789i	−0.373887	−	1.24471i
$932$	13.7110			0.449119
$933$		0			0
$934$			6.31118i			0.206508i
$935$	1.78561	+	1.13896i	0.0583958	+	0.0372479i
$936$		0			0
$937$	−35.0452			−1.14488			−0.572438	−	0.819948i	$-0.694002\pi$
$937$	−35.0452			−1.14488			−0.572438	+	0.819948i	$0.694002\pi$
$938$	−6.02823	−	41.0230i	−0.196829	−	1.33945i
$939$		0			0
$940$	−14.5472	+	22.8065i	−0.474477	+	0.743866i
$941$	−13.4203			−0.437489			−0.218745	−	0.975782i	$-0.570196\pi$
$941$	−13.4203			−0.437489			−0.218745	+	0.975782i	$0.570196\pi$
$942$		0			0
$943$	18.5186			0.603050
$944$	−11.2159			−0.365048
$945$		0			0
$946$	−0.620076			−0.0201604
$947$	51.7451			1.68149			0.840745	−	0.541431i	$-0.182117\pi$
$947$	51.7451			1.68149			0.840745	+	0.541431i	$0.182117\pi$
$948$		0			0
$949$	−50.0480			−1.62463
$950$	25.6846	−	11.9422i	0.833319	−	0.387456i
$951$		0			0
$952$	−2.43794	−	16.5905i	−0.0790140	−	0.537701i
$953$	29.5796			0.958177			0.479089	−	0.877767i	$-0.340967\pi$
$953$	29.5796			0.958177			0.479089	+	0.877767i	$0.340967\pi$
$954$		0			0
$955$	19.5022	−	30.5748i	0.631076	−	0.989376i
$956$		−	2.77836i		−	0.0898587i
$957$		0			0
$958$	10.0152			0.323575
$959$	6.72605	−	0.988378i	0.217195	−	0.0319164i
$960$		0			0
$961$	−23.7169			−0.765061
$962$		−	32.9649i		−	1.06283i
$963$		0			0
$964$			17.0438i			0.548943i
$965$	−25.0573	+	39.2838i	−0.806621	+	1.26459i
$966$		0			0
$967$		−	29.8966i		−	0.961409i	−0.876883	−	0.480704i	$-0.840381\pi$
$967$		−	29.8966i		−	0.961409i	0.876883	−	0.480704i	$-0.159619\pi$
$968$	10.9777			0.352836
$969$		0			0
$970$	12.6312	+	8.05682i	0.405563	+	0.258689i
$971$	−24.7109			−0.793010			−0.396505	−	0.918033i	$-0.629777\pi$
$971$	−24.7109			−0.793010			−0.396505	+	0.918033i	$0.629777\pi$
$972$		0			0
$973$	5.65698	+	38.4966i	0.181355	+	1.23414i
$974$		−	7.76766i		−	0.248892i
$975$		0			0
$976$		0			0
$977$	−1.32936			−0.0425299			−0.0212649	−	0.999774i	$-0.506769\pi$
$977$	−1.32936			−0.0425299			−0.0212649	+	0.999774i	$0.506769\pi$
$978$		0			0
$979$		−	0.345335i		−	0.0110369i
$980$	−15.0602	−	4.26516i	−0.481079	−	0.136245i
$981$		0			0
$982$		−	12.1397i		−	0.387395i
$983$			36.7355i			1.17168i	0.810427	+	0.585840i	$0.199235\pi$
$983$			36.7355i			1.17168i	−0.810427	+	0.585840i	$0.800765\pi$
$984$		0			0
$985$	−10.6450	−	6.78995i	−0.339179	−	0.216346i
$986$	−32.1207			−1.02293
$987$		0			0
$988$			32.4143i			1.03124i
$989$			19.0700i			0.606390i
$990$		0			0
$991$	−27.0805			−0.860241			−0.430120	−	0.902772i	$-0.641529\pi$
$991$	−27.0805			−0.860241			−0.430120	+	0.902772i	$0.641529\pi$
$992$			7.39709i			0.234858i
$993$		0			0
$994$	1.24262	+	8.45622i	0.0394136	+	0.268215i
$995$	22.0226	−	34.5261i	0.698162	−	1.09455i
$996$		0			0
$997$	−52.3312			−1.65735			−0.828673	−	0.559733i	$-0.810904\pi$
$997$	−52.3312			−1.65735			−0.828673	+	0.559733i	$0.810904\pi$
$998$	25.5231			0.807920
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.d.f.1889.3	yes	16
3.2	odd	2		1890.2.d.e.1889.14	yes	16
5.4	even	2		1890.2.d.e.1889.4	yes	16
7.6	odd	2	inner	1890.2.d.f.1889.14	yes	16
15.14	odd	2	inner	1890.2.d.f.1889.13	yes	16
21.20	even	2		1890.2.d.e.1889.3	✓	16
35.34	odd	2		1890.2.d.e.1889.13	yes	16
105.104	even	2	inner	1890.2.d.f.1889.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.d.e.1889.3	✓	16	21.20	even	2
1890.2.d.e.1889.4	yes	16	5.4	even	2
1890.2.d.e.1889.13	yes	16	35.34	odd	2
1890.2.d.e.1889.14	yes	16	3.2	odd	2
1890.2.d.f.1889.3	yes	16	1.1	even	1	trivial
1890.2.d.f.1889.4	yes	16	105.104	even	2	inner
1890.2.d.f.1889.13	yes	16	15.14	odd	2	inner
1890.2.d.f.1889.14	yes	16	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.88521 - 1.20249i) q^{5} +(2.61764 - 0.384656i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.88521 - 1.20249i) q^{5} +(2.61764 - 0.384656i) q^{7} +1.00000 q^{8} +(-1.88521 - 1.20249i) q^{10} -0.149444i q^{11} -5.72182 q^{13} +(2.61764 - 0.384656i) q^{14} +1.00000 q^{16} -6.33796i q^{17} -5.66504i q^{19} +(-1.88521 - 1.20249i) q^{20} -0.149444i q^{22} -4.59603 q^{23} +(2.10805 + 4.53389i) q^{25} -5.72182 q^{26} +(2.61764 - 0.384656i) q^{28} -5.06799i q^{29} +7.39709i q^{31} +1.00000 q^{32} -6.33796i q^{34} +(-5.39735 - 2.42252i) q^{35} +5.76125i q^{37} -5.66504i q^{38} +(-1.88521 - 1.20249i) q^{40} -4.02927 q^{41} -4.14923i q^{43} -0.149444i q^{44} -4.59603 q^{46} -12.0976i q^{47} +(6.70408 - 2.01378i) q^{49} +(2.10805 + 4.53389i) q^{50} -5.72182 q^{52} +9.38164 q^{53} +(-0.179704 + 0.281733i) q^{55} +(2.61764 - 0.384656i) q^{56} -5.06799i q^{58} -11.2159 q^{59} +7.39709i q^{62} +1.00000 q^{64} +(10.7868 + 6.88041i) q^{65} -15.6717i q^{67} -6.33796i q^{68} +(-5.39735 - 2.42252i) q^{70} +3.23047i q^{71} +8.74686 q^{73} +5.76125i q^{74} -5.66504i q^{76} +(-0.0574844 - 0.391190i) q^{77} -2.05057 q^{79} +(-1.88521 - 1.20249i) q^{80} -4.02927 q^{82} -8.07001i q^{83} +(-7.62131 + 11.9484i) q^{85} -4.14923i q^{86} -0.149444i q^{88} +2.31080 q^{89} +(-14.9777 + 2.20093i) q^{91} -4.59603 q^{92} -12.0976i q^{94} +(-6.81213 + 10.6798i) q^{95} -6.70014 q^{97} +(6.70408 - 2.01378i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8}+O(q^{10}) \) 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

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