LMFDB - Embedded newform 2366.2.d.r.337.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2366,2,Mod(337,2366)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2366.337"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2366, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,4,-12,0,0,0,0,12,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.11
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.29079 q^{3} -1.00000 q^{4} -0.901839i q^{5} +2.29079i q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.24770 q^{9} +0.901839 q^{10} -4.33716i q^{11} -2.29079 q^{12} +1.00000 q^{14} -2.06592i q^{15} +1.00000 q^{16} -5.06592 q^{17} +2.24770i q^{18} -6.17238i q^{19} +0.901839i q^{20} -2.29079i q^{21} +4.33716 q^{22} -8.45117 q^{23} -2.29079i q^{24} +4.18669 q^{25} -1.72335 q^{27} +1.00000i q^{28} -2.19286 q^{29} +2.06592 q^{30} -0.873062i q^{31} +1.00000i q^{32} -9.93552i q^{33} -5.06592i q^{34} -0.901839 q^{35} -2.24770 q^{36} +0.144306i q^{37} +6.17238 q^{38} -0.901839 q^{40} -3.99654i q^{41} +2.29079 q^{42} -7.70851 q^{43} +4.33716i q^{44} -2.02707i q^{45} -8.45117i q^{46} +2.92115i q^{47} +2.29079 q^{48} -1.00000 q^{49} +4.18669i q^{50} -11.6049 q^{51} +1.69699 q^{53} -1.72335i q^{54} -3.91142 q^{55} -1.00000 q^{56} -14.1396i q^{57} -2.19286i q^{58} +8.54933i q^{59} +2.06592i q^{60} +8.33440 q^{61} +0.873062 q^{62} -2.24770i q^{63} -1.00000 q^{64} +9.93552 q^{66} -10.3828i q^{67} +5.06592 q^{68} -19.3598 q^{69} -0.901839i q^{70} +3.27856i q^{71} -2.24770i q^{72} -0.539023i q^{73} -0.144306 q^{74} +9.59081 q^{75} +6.17238i q^{76} -4.33716 q^{77} +6.53349 q^{79} -0.901839i q^{80} -10.6909 q^{81} +3.99654 q^{82} +13.2348i q^{83} +2.29079i q^{84} +4.56864i q^{85} -7.70851i q^{86} -5.02337 q^{87} -4.33716 q^{88} -7.79180i q^{89} +2.02707 q^{90} +8.45117 q^{92} -2.00000i q^{93} -2.92115 q^{94} -5.56649 q^{95} +2.29079i q^{96} -11.7061i q^{97} -1.00000i q^{98} -9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	2.29079	1.32259	0.661293	−	0.750128i	$-0.270008\pi$
$3$	2.29079	1.32259	0.661293	+	0.750128i	$0.270008\pi$
$4$	−1.00000	−0.500000
$5$	− 0.901839i	− 0.403315i	−0.979456	−	0.201657i	$-0.935367\pi$
$5$	− 0.901839i	− 0.403315i	0.979456	−	0.201657i	$-0.0646327\pi$
$6$	2.29079i	0.935210i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	2.24770	0.749235
$10$	0.901839	0.285186
$11$	− 4.33716i	− 1.30770i	−0.756622	−	0.653852i	$-0.773152\pi$
$11$	− 4.33716i	− 1.30770i	0.756622	−	0.653852i	$-0.226848\pi$
$12$	−2.29079	−0.661293
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	− 2.06592i	− 0.533418i
$16$	1.00000	0.250000
$17$	−5.06592	−1.22867	−0.614333	−	0.789047i	$-0.710575\pi$
$17$	−5.06592	−1.22867	−0.614333	+	0.789047i	$0.710575\pi$
$18$	2.24770i	0.529789i
$19$	− 6.17238i	− 1.41604i	−0.706192	−	0.708021i	$-0.749588\pi$
$19$	− 6.17238i	− 1.41604i	0.706192	−	0.708021i	$-0.250412\pi$
$20$	0.901839i	0.201657i
$21$	− 2.29079i	− 0.499891i
$22$	4.33716	0.924686
$23$	−8.45117	−1.76219	−0.881096	−	0.472938i	$-0.843193\pi$
$23$	−8.45117	−1.76219	−0.881096	+	0.472938i	$0.843193\pi$
$24$	− 2.29079i	− 0.467605i
$25$	4.18669	0.837337
$26$	0	0
$27$	−1.72335	−0.331659
$28$	1.00000i	0.188982i
$29$	−2.19286	−0.407203	−0.203602	−	0.979054i	$-0.565265\pi$
$29$	−2.19286	−0.407203	−0.203602	+	0.979054i	$0.565265\pi$
$30$	2.06592	0.377184
$31$	− 0.873062i	− 0.156807i	−0.996922	−	0.0784033i	$-0.975018\pi$
$31$	− 0.873062i	− 0.156807i	0.996922	−	0.0784033i	$-0.0249822\pi$
$32$	1.00000i	0.176777i
$33$	− 9.93552i	− 1.72955i
$34$	− 5.06592i	− 0.868798i
$35$	−0.901839	−0.152439
$36$	−2.24770	−0.374617
$37$	0.144306i	0.0237238i	0.999930	+	0.0118619i	$0.00377585\pi$
$37$	0.144306i	0.0237238i	−0.999930	+	0.0118619i	$0.996224\pi$
$38$	6.17238	1.00129
$39$	0	0
$40$	−0.901839	−0.142593
$41$	− 3.99654i	− 0.624154i	−0.950057	−	0.312077i	$-0.898975\pi$
$41$	− 3.99654i	− 0.624154i	0.950057	−	0.312077i	$-0.101025\pi$
$42$	2.29079	0.353476
$43$	−7.70851	−1.17554	−0.587768	−	0.809029i	$-0.699993\pi$
$43$	−7.70851	−1.17554	−0.587768	+	0.809029i	$0.699993\pi$
$44$	4.33716i	0.653852i
$45$	− 2.02707i	− 0.302177i
$46$	− 8.45117i	− 1.24606i
$47$	2.92115i	0.426093i	0.977042	+	0.213047i	$0.0683387\pi$
$47$	2.92115i	0.426093i	−0.977042	+	0.213047i	$0.931661\pi$
$48$	2.29079	0.330647
$49$	−1.00000	−0.142857
$50$	4.18669i	0.592087i
$51$	−11.6049	−1.62502
$52$	0	0
$53$	1.69699	0.233099	0.116549	−	0.993185i	$-0.462817\pi$
$53$	1.69699	0.233099	0.116549	+	0.993185i	$0.462817\pi$
$54$	− 1.72335i	− 0.234518i
$55$	−3.91142	−0.527416
$56$	−1.00000	−0.133631
$57$	− 14.1396i	− 1.87284i
$58$	− 2.19286i	− 0.287936i
$59$	8.54933i	1.11303i	0.830838	+	0.556514i	$0.187861\pi$
$59$	8.54933i	1.11303i	−0.830838	+	0.556514i	$0.812139\pi$
$60$	2.06592i	0.266709i
$61$	8.33440	1.06711	0.533555	−	0.845765i	$-0.320856\pi$
$61$	8.33440	1.06711	0.533555	+	0.845765i	$0.320856\pi$
$62$	0.873062	0.110879
$63$	− 2.24770i	− 0.283184i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	9.93552	1.22298
$67$	− 10.3828i	− 1.26847i	−0.773142	−	0.634233i	$-0.781316\pi$
$67$	− 10.3828i	− 1.26847i	0.773142	−	0.634233i	$-0.218684\pi$
$68$	5.06592	0.614333
$69$	−19.3598	−2.33065
$70$	− 0.901839i	− 0.107790i
$71$	3.27856i	0.389093i	0.980893	+	0.194547i	$0.0623236\pi$
$71$	3.27856i	0.389093i	−0.980893	+	0.194547i	$0.937676\pi$
$72$	− 2.24770i	− 0.264894i
$73$	− 0.539023i	− 0.0630879i	−0.999502	−	0.0315439i	$-0.989958\pi$
$73$	− 0.539023i	− 0.0630879i	0.999502	−	0.0315439i	$-0.0100424\pi$
$74$	−0.144306	−0.0167753
$75$	9.59081	1.10745
$76$	6.17238i	0.708021i
$77$	−4.33716	−0.494266
$78$	0	0
$79$	6.53349	0.735075	0.367537	−	0.930009i	$-0.380201\pi$
$79$	6.53349	0.735075	0.367537	+	0.930009i	$0.380201\pi$
$80$	− 0.901839i	− 0.100829i
$81$	−10.6909	−1.18788
$82$	3.99654	0.441343
$83$	13.2348i	1.45271i	0.687319	+	0.726356i	$0.258788\pi$
$83$	13.2348i	1.45271i	−0.687319	+	0.726356i	$0.741212\pi$
$84$	2.29079i	0.249945i
$85$	4.56864i	0.495539i
$86$	− 7.70851i	− 0.831230i
$87$	−5.02337	−0.538562
$88$	−4.33716	−0.462343
$89$	− 7.79180i	− 0.825929i	−0.910747	−	0.412965i	$-0.864493\pi$
$89$	− 7.79180i	− 0.825929i	0.910747	−	0.412965i	$-0.135507\pi$
$90$	2.02707	0.213672
$91$	0	0
$92$	8.45117	0.881096
$93$	− 2.00000i	− 0.207390i
$94$	−2.92115	−0.301294
$95$	−5.56649	−0.571110
$96$	2.29079i	0.233802i
$97$	− 11.7061i	− 1.18857i	−0.804253	−	0.594287i	$-0.797434\pi$
$97$	− 11.7061i	− 1.18857i	0.804253	−	0.594287i	$-0.202566\pi$
$98$	− 1.00000i	− 0.101015i
$99$	− 9.74866i	− 0.979777i
$100$	−4.18669	−0.418669
$101$	10.7429	1.06896	0.534479	−	0.845182i	$-0.320508\pi$
$101$	10.7429	1.06896	0.534479	+	0.845182i	$0.320508\pi$
$102$	− 11.6049i	− 1.14906i
$103$	4.81099	0.474041	0.237021	−	0.971505i	$-0.423829\pi$
$103$	4.81099	0.474041	0.237021	+	0.971505i	$0.423829\pi$
$104$	0	0
$105$	−2.06592	−0.201613
$106$	1.69699i	0.164826i
$107$	13.6530	1.31989	0.659944	−	0.751315i	$-0.270580\pi$
$107$	13.6530	1.31989	0.659944	+	0.751315i	$0.270580\pi$
$108$	1.72335	0.165829
$109$	− 5.11747i	− 0.490165i	−0.969502	−	0.245082i	$-0.921185\pi$
$109$	− 5.11747i	− 0.490165i	0.969502	−	0.245082i	$-0.0788150\pi$
$110$	− 3.91142i	− 0.372940i
$111$	0.330575i	0.0313768i
$112$	− 1.00000i	− 0.0944911i
$113$	17.9321	1.68691	0.843453	−	0.537203i	$-0.180519\pi$
$113$	17.9321	1.68691	0.843453	+	0.537203i	$0.180519\pi$
$114$	14.1396	1.32430
$115$	7.62159i	0.710717i
$116$	2.19286	0.203602
$117$	0	0
$118$	−8.54933	−0.787030
$119$	5.06592i	0.464392i
$120$	−2.06592	−0.188592
$121$	−7.81099	−0.710090
$122$	8.33440i	0.754561i
$123$	− 9.15521i	− 0.825498i
$124$	0.873062i	0.0784033i
$125$	− 8.28491i	− 0.741025i
$126$	2.24770	0.200241
$127$	19.5136	1.73155	0.865777	−	0.500430i	$-0.166825\pi$
$127$	19.5136	1.73155	0.865777	+	0.500430i	$0.166825\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−17.6586	−1.55475
$130$	0	0
$131$	−20.6496	−1.80417	−0.902083	−	0.431562i	$-0.857963\pi$
$131$	−20.6496	−1.80417	−0.902083	+	0.431562i	$0.857963\pi$
$132$	9.93552i	0.864776i
$133$	−6.17238	−0.535213
$134$	10.3828	0.896941
$135$	1.55418i	0.133763i
$136$	5.06592i	0.434399i
$137$	− 3.18956i	− 0.272503i	−0.990674	−	0.136251i	$-0.956495\pi$
$137$	− 3.18956i	− 0.272503i	0.990674	−	0.136251i	$-0.0435055\pi$
$138$	− 19.3598i	− 1.64802i
$139$	−0.595710	−0.0505275	−0.0252637	−	0.999681i	$-0.508043\pi$
$139$	−0.595710	−0.0505275	−0.0252637	+	0.999681i	$0.508043\pi$
$140$	0.901839	0.0762193
$141$	6.69173i	0.563545i
$142$	−3.27856	−0.275131
$143$	0	0
$144$	2.24770	0.187309
$145$	1.97760i	0.164231i
$146$	0.539023	0.0446099
$147$	−2.29079	−0.188941
$148$	− 0.144306i	− 0.0118619i
$149$	− 11.2096i	− 0.918329i	−0.888351	−	0.459165i	$-0.848149\pi$
$149$	− 11.2096i	− 0.918329i	0.888351	−	0.459165i	$-0.151851\pi$
$150$	9.59081i	0.783086i
$151$	13.0731i	1.06387i	0.846785	+	0.531935i	$0.178535\pi$
$151$	13.0731i	1.06387i	−0.846785	+	0.531935i	$0.821465\pi$
$152$	−6.17238	−0.500646
$153$	−11.3867	−0.920559
$154$	− 4.33716i	− 0.349499i
$155$	−0.787362	−0.0632424
$156$	0	0
$157$	17.9245	1.43053	0.715266	−	0.698853i	$-0.246306\pi$
$157$	17.9245	1.43053	0.715266	+	0.698853i	$0.246306\pi$
$158$	6.53349i	0.519776i
$159$	3.88743	0.308293
$160$	0.901839	0.0712966
$161$	8.45117i	0.666046i
$162$	− 10.6909i	− 0.839959i
$163$	− 20.3179i	− 1.59142i	−0.605678	−	0.795710i	$-0.707098\pi$
$163$	− 20.3179i	− 1.59142i	0.605678	−	0.795710i	$-0.292902\pi$
$164$	3.99654i	0.312077i
$165$	−8.96024	−0.697553
$166$	−13.2348	−1.02722
$167$	− 3.23051i	− 0.249984i	−0.992158	−	0.124992i	$-0.960109\pi$
$167$	− 3.23051i	− 0.249984i	0.992158	−	0.124992i	$-0.0398905\pi$
$168$	−2.29079	−0.176738
$169$	0	0
$170$	−4.56864	−0.350399
$171$	− 13.8737i	− 1.06095i
$172$	7.70851	0.587768
$173$	9.17044	0.697216	0.348608	−	0.937269i	$-0.386655\pi$
$173$	9.17044	0.697216	0.348608	+	0.937269i	$0.386655\pi$
$174$	− 5.02337i	− 0.380821i
$175$	− 4.18669i	− 0.316484i
$176$	− 4.33716i	− 0.326926i
$177$	19.5847i	1.47208i
$178$	7.79180	0.584020
$179$	16.9549	1.26727	0.633636	−	0.773631i	$-0.281562\pi$
$179$	16.9549	1.26727	0.633636	+	0.773631i	$0.281562\pi$
$180$	2.02707i	0.151089i
$181$	−2.65743	−0.197525	−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743	−0.197525	−0.0987626	+	0.995111i	$0.531488\pi$
$182$	0	0
$183$	19.0923	1.41135
$184$	8.45117i	0.623029i
$185$	0.130141	0.00956816
$186$	2.00000	0.146647
$187$	21.9717i	1.60673i
$188$	− 2.92115i	− 0.213047i
$189$	1.72335i	0.125355i
$190$	− 5.56649i	− 0.403836i
$191$	−24.4861	−1.77175	−0.885875	−	0.463924i	$-0.846441\pi$
$191$	−24.4861	−1.77175	−0.885875	+	0.463924i	$0.846441\pi$
$192$	−2.29079	−0.165323
$193$	12.2409i	0.881120i	0.897723	+	0.440560i	$0.145220\pi$
$193$	12.2409i	0.881120i	−0.897723	+	0.440560i	$0.854780\pi$
$194$	11.7061	0.840449
$195$	0	0
$196$	1.00000	0.0714286
$197$	5.45751i	0.388832i	0.980919	+	0.194416i	$0.0622811\pi$
$197$	5.45751i	0.388832i	−0.980919	+	0.194416i	$0.937719\pi$
$198$	9.74866	0.692807
$199$	12.8166	0.908548	0.454274	−	0.890862i	$-0.349899\pi$
$199$	12.8166	0.908548	0.454274	+	0.890862i	$0.349899\pi$
$200$	− 4.18669i	− 0.296043i
$201$	− 23.7849i	− 1.67766i
$202$	10.7429i	0.755867i
$203$	2.19286i	0.153908i
$204$	11.6049	0.812509
$205$	−3.60423	−0.251730
$206$	4.81099i	0.335198i
$207$	−18.9957	−1.32029
$208$	0	0
$209$	−26.7706	−1.85176
$210$	− 2.06592i	− 0.142562i
$211$	−19.3110	−1.32943	−0.664713	−	0.747098i	$-0.731446\pi$
$211$	−19.3110	−1.32943	−0.664713	+	0.747098i	$0.731446\pi$
$212$	−1.69699	−0.116549
$213$	7.51048i	0.514610i
$214$	13.6530i	0.933302i
$215$	6.95183i	0.474111i
$216$	1.72335i	0.117259i
$217$	−0.873062	−0.0592673
$218$	5.11747	0.346599
$219$	− 1.23479i	− 0.0834391i
$220$	3.91142	0.263708
$221$	0	0
$222$	−0.330575	−0.0221867
$223$	− 10.6357i	− 0.712220i	−0.934444	−	0.356110i	$-0.884103\pi$
$223$	− 10.6357i	− 0.712220i	0.934444	−	0.356110i	$-0.115897\pi$
$224$	1.00000	0.0668153
$225$	9.41043	0.627362
$226$	17.9321i	1.19282i
$227$	− 22.7217i	− 1.50809i	−0.656821	−	0.754047i	$-0.728099\pi$
$227$	− 22.7217i	− 1.50809i	0.656821	−	0.754047i	$-0.271901\pi$
$228$	14.1396i	0.936418i
$229$	− 20.3094i	− 1.34208i	−0.741420	−	0.671042i	$-0.765847\pi$
$229$	− 20.3094i	− 1.34208i	0.741420	−	0.671042i	$-0.234153\pi$
$230$	−7.62159	−0.502553
$231$	−9.93552	−0.653709
$232$	2.19286i	0.143968i
$233$	10.6446	0.697352	0.348676	−	0.937243i	$-0.386631\pi$
$233$	10.6446	0.697352	0.348676	+	0.937243i	$0.386631\pi$
$234$	0	0
$235$	2.63441	0.171850
$236$	− 8.54933i	− 0.556514i
$237$	14.9668	0.972200
$238$	−5.06592	−0.328375
$239$	0.311564i	0.0201534i	0.999949	+	0.0100767i	$0.00320757\pi$
$239$	0.311564i	0.0201534i	−0.999949	+	0.0100767i	$0.996792\pi$
$240$	− 2.06592i	− 0.133355i
$241$	25.2995i	1.62969i	0.579682	+	0.814843i	$0.303177\pi$
$241$	25.2995i	1.62969i	−0.579682	+	0.814843i	$0.696823\pi$
$242$	− 7.81099i	− 0.502110i
$243$	−19.3206	−1.23942
$244$	−8.33440	−0.533555
$245$	0.901839i	0.0576164i
$246$	9.15521	0.583715
$247$	0	0
$248$	−0.873062	−0.0554395
$249$	30.3182i	1.92134i
$250$	8.28491	0.523984
$251$	−8.04030	−0.507499	−0.253750	−	0.967270i	$-0.581664\pi$
$251$	−8.04030	−0.507499	−0.253750	+	0.967270i	$0.581664\pi$
$252$	2.24770i	0.141592i
$253$	36.6541i	2.30442i
$254$	19.5136i	1.22439i
$255$	10.4658i	0.655393i
$256$	1.00000	0.0625000
$257$	16.9327	1.05623	0.528116	−	0.849172i	$-0.322899\pi$
$257$	16.9327	1.05623	0.528116	+	0.849172i	$0.322899\pi$
$258$	− 17.6586i	− 1.09937i
$259$	0.144306	0.00896676
$260$	0	0
$261$	−4.92890	−0.305091
$262$	− 20.6496i	− 1.27574i
$263$	10.3209	0.636414	0.318207	−	0.948021i	$-0.396919\pi$
$263$	10.3209	0.636414	0.318207	+	0.948021i	$0.396919\pi$
$264$	−9.93552	−0.611489
$265$	− 1.53041i	− 0.0940122i
$266$	− 6.17238i	− 0.378453i
$267$	− 17.8494i	− 1.09236i
$268$	10.3828i	0.634233i
$269$	−6.13999	−0.374362	−0.187181	−	0.982325i	$-0.559935\pi$
$269$	−6.13999	−0.374362	−0.187181	+	0.982325i	$0.559935\pi$
$270$	−1.55418	−0.0945846
$271$	10.6772i	0.648594i	0.945955	+	0.324297i	$0.105128\pi$
$271$	10.6772i	0.648594i	−0.945955	+	0.324297i	$0.894872\pi$
$272$	−5.06592	−0.307167
$273$	0	0
$274$	3.18956	0.192689
$275$	− 18.1583i	− 1.09499i
$276$	19.3598	1.16532
$277$	−21.9090	−1.31638	−0.658191	−	0.752851i	$-0.728678\pi$
$277$	−21.9090	−1.31638	−0.658191	+	0.752851i	$0.728678\pi$
$278$	− 0.595710i	− 0.0357283i
$279$	− 1.96239i	− 0.117485i
$280$	0.901839i	0.0538952i
$281$	25.7719i	1.53743i	0.639594	+	0.768713i	$0.279102\pi$
$281$	25.7719i	1.53743i	−0.639594	+	0.768713i	$0.720898\pi$
$282$	−6.69173	−0.398487
$283$	11.3269	0.673314	0.336657	−	0.941627i	$-0.390704\pi$
$283$	11.3269	0.673314	0.336657	+	0.941627i	$0.390704\pi$
$284$	− 3.27856i	− 0.194547i
$285$	−12.7516	−0.755342
$286$	0	0
$287$	−3.99654	−0.235908
$288$	2.24770i	0.132447i
$289$	8.66355	0.509621
$290$	−1.97760	−0.116129
$291$	− 26.8162i	− 1.57199i
$292$	0.539023i	0.0315439i
$293$	− 23.7459i	− 1.38725i	−0.720335	−	0.693626i	$-0.756012\pi$
$293$	− 23.7459i	− 1.38725i	0.720335	−	0.693626i	$-0.243988\pi$
$294$	− 2.29079i	− 0.133601i
$295$	7.71012	0.448901
$296$	0.144306	0.00838763
$297$	7.47445i	0.433712i
$298$	11.2096	0.649357
$299$	0	0
$300$	−9.59081	−0.553725
$301$	7.70851i	0.444311i
$302$	−13.0731	−0.752270
$303$	24.6097	1.41379
$304$	− 6.17238i	− 0.354010i
$305$	− 7.51629i	− 0.430381i
$306$	− 11.3867i	− 0.650934i
$307$	6.68810i	0.381710i	0.981618	+	0.190855i	$0.0611261\pi$
$307$	6.68810i	0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$308$	4.33716	0.247133
$309$	11.0210	0.626960
$310$	− 0.787362i	− 0.0447191i
$311$	9.18724	0.520961	0.260480	−	0.965479i	$-0.416119\pi$
$311$	9.18724	0.520961	0.260480	+	0.965479i	$0.416119\pi$
$312$	0	0
$313$	−17.1631	−0.970118	−0.485059	−	0.874481i	$-0.661202\pi$
$313$	−17.1631	−0.970118	−0.485059	+	0.874481i	$0.661202\pi$
$314$	17.9245i	1.01154i
$315$	−2.02707	−0.114212
$316$	−6.53349	−0.367537
$317$	3.76247i	0.211322i	0.994402	+	0.105661i	$0.0336958\pi$
$317$	3.76247i	0.211322i	−0.994402	+	0.105661i	$0.966304\pi$
$318$	3.88743i	0.217996i
$319$	9.51078i	0.532502i
$320$	0.901839i	0.0504143i
$321$	31.2762	1.74567
$322$	−8.45117	−0.470965
$323$	31.2688i	1.73984i
$324$	10.6909	0.593941
$325$	0	0
$326$	20.3179	1.12530
$327$	− 11.7230i	− 0.648285i
$328$	−3.99654	−0.220672
$329$	2.92115	0.161048
$330$	− 8.96024i	− 0.493245i
$331$	32.2257i	1.77129i	0.464367	+	0.885643i	$0.346282\pi$
$331$	32.2257i	1.77129i	−0.464367	+	0.885643i	$0.653718\pi$
$332$	− 13.2348i	− 0.726356i
$333$	0.324358i	0.0177747i
$334$	3.23051	0.176765
$335$	−9.36365	−0.511591
$336$	− 2.29079i	− 0.124973i
$337$	−3.01703	−0.164348	−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703	−0.164348	−0.0821740	+	0.996618i	$0.526186\pi$
$338$	0	0
$339$	41.0785	2.23108
$340$	− 4.56864i	− 0.247769i
$341$	−3.78662	−0.205057
$342$	13.8737	0.750203
$343$	1.00000i	0.0539949i
$344$	7.70851i	0.415615i
$345$	17.4594i	0.939985i
$346$	9.17044i	0.493006i
$347$	0.468540	0.0251526	0.0125763	−	0.999921i	$-0.495997\pi$
$347$	0.468540	0.0251526	0.0125763	+	0.999921i	$0.495997\pi$
$348$	5.02337	0.269281
$349$	− 32.2212i	− 1.72476i	−0.506262	−	0.862380i	$-0.668973\pi$
$349$	− 32.2212i	− 1.72476i	0.506262	−	0.862380i	$-0.331027\pi$
$350$	4.18669	0.223788
$351$	0	0
$352$	4.33716	0.231172
$353$	− 13.1154i	− 0.698063i	−0.937111	−	0.349031i	$-0.886511\pi$
$353$	− 13.1154i	− 0.698063i	0.937111	−	0.349031i	$-0.113489\pi$
$354$	−19.5847	−1.04091
$355$	2.95673	0.156927
$356$	7.79180i	0.412965i
$357$	11.6049i	0.614199i
$358$	16.9549i	0.896097i
$359$	− 4.37981i	− 0.231157i	−0.993298	−	0.115579i	$-0.963128\pi$
$359$	− 4.37981i	− 0.231157i	0.993298	−	0.115579i	$-0.0368722\pi$
$360$	−2.02707	−0.106836
$361$	−19.0983	−1.00517
$362$	− 2.65743i	− 0.139671i
$363$	−17.8933	−0.939156
$364$	0	0
$365$	−0.486112	−0.0254443
$366$	19.0923i	0.997972i
$367$	25.8188	1.34773	0.673865	−	0.738854i	$-0.264633\pi$
$367$	25.8188	1.34773	0.673865	+	0.738854i	$0.264633\pi$
$368$	−8.45117	−0.440548
$369$	− 8.98303i	− 0.467638i
$370$	0.130141i	0.00676571i
$371$	− 1.69699i	− 0.0881031i
$372$	2.00000i	0.103695i
$373$	30.6285	1.58588	0.792942	−	0.609297i	$-0.208548\pi$
$373$	30.6285	1.58588	0.792942	+	0.609297i	$0.208548\pi$
$374$	−21.9717	−1.13613
$375$	− 18.9790i	− 0.980069i
$376$	2.92115	0.150647
$377$	0	0
$378$	−1.72335	−0.0886395
$379$	− 38.1523i	− 1.95975i	−0.199604	−	0.979877i	$-0.563966\pi$
$379$	− 38.1523i	− 1.95975i	0.199604	−	0.979877i	$-0.436034\pi$
$380$	5.56649	0.285555
$381$	44.7016	2.29013
$382$	− 24.4861i	− 1.25282i
$383$	31.9602i	1.63309i	0.577283	+	0.816544i	$0.304113\pi$
$383$	31.9602i	1.63309i	−0.577283	+	0.816544i	$0.695887\pi$
$384$	− 2.29079i	− 0.116901i
$385$	3.91142i	0.199345i
$386$	−12.2409	−0.623046
$387$	−17.3265	−0.880753
$388$	11.7061i	0.594287i
$389$	5.24585	0.265975	0.132988	−	0.991118i	$-0.457543\pi$
$389$	5.24585	0.265975	0.132988	+	0.991118i	$0.457543\pi$
$390$	0	0
$391$	42.8130	2.16514
$392$	1.00000i	0.0505076i
$393$	−47.3039	−2.38617
$394$	−5.45751	−0.274946
$395$	− 5.89215i	− 0.296466i
$396$	9.74866i	0.489889i
$397$	− 24.5296i	− 1.23110i	−0.788096	−	0.615552i	$-0.788933\pi$
$397$	− 24.5296i	− 1.23110i	0.788096	−	0.615552i	$-0.211067\pi$
$398$	12.8166i	0.642440i
$399$	−14.1396	−0.707866
$400$	4.18669	0.209334
$401$	4.27143i	0.213305i	0.994296	+	0.106652i	$0.0340132\pi$
$401$	4.27143i	0.213305i	−0.994296	+	0.106652i	$0.965987\pi$
$402$	23.7849	1.18628
$403$	0	0
$404$	−10.7429	−0.534479
$405$	9.64150i	0.479090i
$406$	−2.19286	−0.108830
$407$	0.625880	0.0310237
$408$	11.6049i	0.574530i
$409$	1.61647i	0.0799293i	0.999201	+	0.0399646i	$0.0127245\pi$
$409$	1.61647i	0.0799293i	−0.999201	+	0.0399646i	$0.987275\pi$
$410$	− 3.60423i	− 0.178000i
$411$	− 7.30661i	− 0.360408i
$412$	−4.81099	−0.237021
$413$	8.54933	0.420685
$414$	− 18.9957i	− 0.933589i
$415$	11.9357	0.585900
$416$	0	0
$417$	−1.36464	−0.0668269
$418$	− 26.7706i	− 1.30939i
$419$	−26.0312	−1.27171	−0.635854	−	0.771810i	$-0.719352\pi$
$419$	−26.0312	−1.27171	−0.635854	+	0.771810i	$0.719352\pi$
$420$	2.06592	0.100807
$421$	− 37.5391i	− 1.82954i	−0.403971	−	0.914772i	$-0.632370\pi$
$421$	− 37.5391i	− 1.82954i	0.403971	−	0.914772i	$-0.367630\pi$
$422$	− 19.3110i	− 0.940047i
$423$	6.56588i	0.319244i
$424$	− 1.69699i	− 0.0824129i
$425$	−21.2094	−1.02881
$426$	−7.51048	−0.363884
$427$	− 8.33440i	− 0.403330i
$428$	−13.6530	−0.659944
$429$	0	0
$430$	−6.95183	−0.335247
$431$	21.5538i	1.03821i	0.854710	+	0.519106i	$0.173735\pi$
$431$	21.5538i	1.03821i	−0.854710	+	0.519106i	$0.826265\pi$
$432$	−1.72335	−0.0829147
$433$	−3.19917	−0.153742	−0.0768710	−	0.997041i	$-0.524493\pi$
$433$	−3.19917	−0.153742	−0.0768710	+	0.997041i	$0.524493\pi$
$434$	− 0.873062i	− 0.0419083i
$435$	4.53027i	0.217210i
$436$	5.11747i	0.245082i
$437$	52.1638i	2.49534i
$438$	1.23479	0.0590004
$439$	−26.6227	−1.27063	−0.635317	−	0.772252i	$-0.719130\pi$
$439$	−26.6227	−1.27063	−0.635317	+	0.772252i	$0.719130\pi$
$440$	3.91142i	0.186470i
$441$	−2.24770	−0.107034
$442$	0	0
$443$	9.09867	0.432291	0.216145	−	0.976361i	$-0.430652\pi$
$443$	9.09867	0.432291	0.216145	+	0.976361i	$0.430652\pi$
$444$	− 0.330575i	− 0.0156884i
$445$	−7.02695	−0.333109
$446$	10.6357	0.503615
$447$	− 25.6789i	− 1.21457i
$448$	1.00000i	0.0472456i
$449$	− 7.02693i	− 0.331621i	−0.986158	−	0.165811i	$-0.946976\pi$
$449$	− 7.02693i	− 0.331621i	0.986158	−	0.165811i	$-0.0530240\pi$
$450$	9.41043i	0.443612i
$451$	−17.3336	−0.816209
$452$	−17.9321	−0.843453
$453$	29.9476i	1.40706i
$454$	22.7217	1.06638
$455$	0	0
$456$	−14.1396	−0.662148
$457$	− 19.1511i	− 0.895851i	−0.894071	−	0.447926i	$-0.852163\pi$
$457$	− 19.1511i	− 0.895851i	0.894071	−	0.447926i	$-0.147837\pi$
$458$	20.3094	0.948996
$459$	8.73035	0.407498
$460$	− 7.62159i	− 0.355359i
$461$	3.25656i	0.151673i	0.997120	+	0.0758365i	$0.0241627\pi$
$461$	3.25656i	0.151673i	−0.997120	+	0.0758365i	$0.975837\pi$
$462$	− 9.93552i	− 0.462242i
$463$	− 21.2761i	− 0.988786i	−0.869238	−	0.494393i	$-0.835390\pi$
$463$	− 21.2761i	− 0.988786i	0.869238	−	0.494393i	$-0.164610\pi$
$464$	−2.19286	−0.101801
$465$	−1.80368	−0.0836435
$466$	10.6446i	0.493102i
$467$	−3.33171	−0.154173	−0.0770866	−	0.997024i	$-0.524562\pi$
$467$	−3.33171	−0.154173	−0.0770866	+	0.997024i	$0.524562\pi$
$468$	0	0
$469$	−10.3828	−0.479435
$470$	2.63441i	0.121516i
$471$	41.0612	1.89200
$472$	8.54933	0.393515
$473$	33.4331i	1.53725i
$474$	14.9668i	0.687449i
$475$	− 25.8418i	− 1.18570i
$476$	− 5.06592i	− 0.232196i
$477$	3.81432	0.174646
$478$	−0.311564	−0.0142506
$479$	− 0.185216i	− 0.00846273i	−0.999991	−	0.00423136i	$-0.998653\pi$
$479$	− 0.185216i	− 0.00846273i	0.999991	−	0.00423136i	$-0.00134689\pi$
$480$	2.06592	0.0942959
$481$	0	0
$482$	−25.2995	−1.15236
$483$	19.3598i	0.880903i
$484$	7.81099	0.355045
$485$	−10.5570	−0.479369
$486$	− 19.3206i	− 0.876401i
$487$	31.2308i	1.41520i	0.706613	+	0.707601i	$0.250222\pi$
$487$	31.2308i	1.41520i	−0.706613	+	0.707601i	$0.749778\pi$
$488$	− 8.33440i	− 0.377281i
$489$	− 46.5440i	− 2.10479i
$490$	−0.901839	−0.0407409
$491$	−26.8472	−1.21160	−0.605799	−	0.795618i	$-0.707146\pi$
$491$	−26.8472	−1.21160	−0.605799	+	0.795618i	$0.707146\pi$
$492$	9.15521i	0.412749i
$493$	11.1088	0.500317
$494$	0	0
$495$	−8.79172	−0.395158
$496$	− 0.873062i	− 0.0392017i
$497$	3.27856	0.147063
$498$	−30.3182	−1.35859
$499$	15.2869i	0.684337i	0.939639	+	0.342168i	$0.111161\pi$
$499$	15.2869i	0.684337i	−0.939639	+	0.342168i	$0.888839\pi$
$500$	8.28491i	0.370512i
$501$	− 7.40040i	− 0.330625i
$502$	− 8.04030i	− 0.358856i
$503$	−26.1102	−1.16419	−0.582097	−	0.813119i	$-0.697768\pi$
$503$	−26.1102	−1.16419	−0.582097	+	0.813119i	$0.697768\pi$
$504$	−2.24770	−0.100121
$505$	− 9.68836i	− 0.431126i
$506$	−36.6541	−1.62947
$507$	0	0
$508$	−19.5136	−0.865777
$509$	17.0271i	0.754715i	0.926068	+	0.377357i	$0.123167\pi$
$509$	17.0271i	0.754715i	−0.926068	+	0.377357i	$0.876833\pi$
$510$	−10.4658	−0.463433
$511$	−0.539023	−0.0238450
$512$	1.00000i	0.0441942i
$513$	10.6372i	0.469643i
$514$	16.9327i	0.746868i
$515$	− 4.33874i	− 0.191188i
$516$	17.6586	0.777375
$517$	12.6695	0.557204
$518$	0.144306i	0.00634045i
$519$	21.0075	0.922128
$520$	0	0
$521$	−18.7760	−0.822593	−0.411297	−	0.911502i	$-0.634924\pi$
$521$	−18.7760	−0.822593	−0.411297	+	0.911502i	$0.634924\pi$
$522$	− 4.92890i	− 0.215732i
$523$	−3.03247	−0.132601	−0.0663004	−	0.997800i	$-0.521120\pi$
$523$	−3.03247	−0.132601	−0.0663004	+	0.997800i	$0.521120\pi$
$524$	20.6496	0.902083
$525$	− 9.59081i	− 0.418577i
$526$	10.3209i	0.450013i
$527$	4.42286i	0.192663i
$528$	− 9.93552i	− 0.432388i
$529$	48.4223	2.10532
$530$	1.53041	0.0664766
$531$	19.2164i	0.833919i
$532$	6.17238	0.267607
$533$	0	0
$534$	17.8494	0.772417
$535$	− 12.3128i	− 0.532330i
$536$	−10.3828	−0.448470
$537$	38.8402	1.67608
$538$	− 6.13999i	− 0.264714i
$539$	4.33716i	0.186815i
$540$	− 1.55418i	− 0.0668814i
$541$	− 6.11845i	− 0.263053i	−0.991313	−	0.131526i	$-0.958012\pi$
$541$	− 6.11845i	− 0.263053i	0.991313	−	0.131526i	$-0.0419878\pi$
$542$	−10.6772	−0.458625
$543$	−6.08760	−0.261244
$544$	− 5.06592i	− 0.217200i
$545$	−4.61513	−0.197691
$546$	0	0
$547$	−37.4754	−1.60233	−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754	−1.60233	−0.801166	+	0.598442i	$0.795786\pi$
$548$	3.18956i	0.136251i
$549$	18.7333	0.799516
$550$	18.1583	0.774275
$551$	13.5352i	0.576617i
$552$	19.3598i	0.824009i
$553$	− 6.53349i	− 0.277832i
$554$	− 21.9090i	− 0.930823i
$555$	0.298125	0.0126547
$556$	0.595710	0.0252637
$557$	− 8.89051i	− 0.376703i	−0.982102	−	0.188352i	$-0.939686\pi$
$557$	− 8.89051i	− 0.376703i	0.982102	−	0.188352i	$-0.0603144\pi$
$558$	1.96239	0.0830744
$559$	0	0
$560$	−0.901839	−0.0381096
$561$	50.3325i	2.12504i
$562$	−25.7719	−1.08712
$563$	−17.7920	−0.749841	−0.374921	−	0.927057i	$-0.622330\pi$
$563$	−17.7920	−0.749841	−0.374921	+	0.927057i	$0.622330\pi$
$564$	− 6.69173i	− 0.281773i
$565$	− 16.1718i	− 0.680354i
$566$	11.3269i	0.476105i
$567$	10.6909i	0.448977i
$568$	3.27856	0.137565
$569$	−11.1737	−0.468425	−0.234212	−	0.972185i	$-0.575251\pi$
$569$	−11.1737	−0.468425	−0.234212	+	0.972185i	$0.575251\pi$
$570$	− 12.7516i	− 0.534108i
$571$	−16.7239	−0.699873	−0.349936	−	0.936773i	$-0.613797\pi$
$571$	−16.7239	−0.699873	−0.349936	+	0.936773i	$0.613797\pi$
$572$	0	0
$573$	−56.0924	−2.34329
$574$	− 3.99654i	− 0.166812i
$575$	−35.3824	−1.47555
$576$	−2.24770	−0.0936543
$577$	− 0.798887i	− 0.0332581i	−0.999862	−	0.0166291i	$-0.994707\pi$
$577$	− 0.798887i	− 0.0332581i	0.999862	−	0.0166291i	$-0.00529344\pi$
$578$	8.66355i	0.360356i
$579$	28.0413i	1.16536i
$580$	− 1.97760i	− 0.0821155i
$581$	13.2348	0.549074
$582$	26.8162	1.11157
$583$	− 7.36010i	− 0.304824i
$584$	−0.539023	−0.0223049
$585$	0	0
$586$	23.7459	0.980935
$587$	8.02425i	0.331196i	0.986193	+	0.165598i	$0.0529555\pi$
$587$	8.02425i	0.331196i	−0.986193	+	0.165598i	$0.947045\pi$
$588$	2.29079	0.0944705
$589$	−5.38887	−0.222045
$590$	7.71012i	0.317421i
$591$	12.5020i	0.514263i
$592$	0.144306i	0.00593095i
$593$	4.93120i	0.202500i	0.994861	+	0.101250i	$0.0322842\pi$
$593$	4.93120i	0.202500i	−0.994861	+	0.101250i	$0.967716\pi$
$594$	−7.47445	−0.306680
$595$	4.56864	0.187296
$596$	11.2096i	0.459165i
$597$	29.3602	1.20163
$598$	0	0
$599$	−17.8249	−0.728306	−0.364153	−	0.931339i	$-0.618642\pi$
$599$	−17.8249	−0.728306	−0.364153	+	0.931339i	$0.618642\pi$
$600$	− 9.59081i	− 0.391543i
$601$	−0.161833	−0.00660131	−0.00330065	−	0.999995i	$-0.501051\pi$
$601$	−0.161833	−0.00660131	−0.00330065	+	0.999995i	$0.501051\pi$
$602$	−7.70851	−0.314175
$603$	− 23.3375i	− 0.950378i
$604$	− 13.0731i	− 0.531935i
$605$	7.04426i	0.286390i
$606$	24.6097i	0.999700i
$607$	6.18846	0.251182	0.125591	−	0.992082i	$-0.459917\pi$
$607$	6.18846	0.251182	0.125591	+	0.992082i	$0.459917\pi$
$608$	6.17238	0.250323
$609$	5.02337i	0.203557i
$610$	7.51629	0.304326
$611$	0	0
$612$	11.3867	0.460280
$613$	37.2124i	1.50299i	0.659736	+	0.751497i	$0.270668\pi$
$613$	37.2124i	1.50299i	−0.659736	+	0.751497i	$0.729332\pi$
$614$	−6.68810	−0.269910
$615$	−8.25652	−0.332935
$616$	4.33716i	0.174749i
$617$	6.68036i	0.268941i	0.990918	+	0.134471i	$0.0429334\pi$
$617$	6.68036i	0.268941i	−0.990918	+	0.134471i	$0.957067\pi$
$618$	11.0210i	0.443328i
$619$	23.7344i	0.953965i	0.878913	+	0.476982i	$0.158269\pi$
$619$	23.7344i	0.953965i	−0.878913	+	0.476982i	$0.841731\pi$
$620$	0.787362	0.0316212
$621$	14.5643	0.584446
$622$	9.18724i	0.368375i
$623$	−7.79180	−0.312172
$624$	0	0
$625$	13.4618	0.538471
$626$	− 17.1631i	− 0.685977i
$627$	−61.3258	−2.44912
$628$	−17.9245	−0.715266
$629$	− 0.731044i	− 0.0291486i
$630$	− 2.02707i	− 0.0807603i
$631$	− 23.0187i	− 0.916359i	−0.888860	−	0.458180i	$-0.848502\pi$
$631$	− 23.0187i	− 0.916359i	0.888860	−	0.458180i	$-0.151498\pi$
$632$	− 6.53349i	− 0.259888i
$633$	−44.2375	−1.75828
$634$	−3.76247	−0.149427
$635$	− 17.5981i	− 0.698361i
$636$	−3.88743	−0.154147
$637$	0	0
$638$	−9.51078	−0.376536
$639$	7.36923i	0.291522i
$640$	−0.901839	−0.0356483
$641$	−12.6508	−0.499676	−0.249838	−	0.968288i	$-0.580377\pi$
$641$	−12.6508	−0.499676	−0.249838	+	0.968288i	$0.580377\pi$
$642$	31.2762i	1.23437i
$643$	15.2388i	0.600958i	0.953788	+	0.300479i	$0.0971465\pi$
$643$	15.2388i	0.600958i	−0.953788	+	0.300479i	$0.902854\pi$
$644$	− 8.45117i	− 0.333023i
$645$	15.9252i	0.627053i
$646$	−31.2688	−1.23025
$647$	29.3642	1.15443	0.577213	−	0.816594i	$-0.304140\pi$
$647$	29.3642	1.15443	0.577213	+	0.816594i	$0.304140\pi$
$648$	10.6909i	0.419980i
$649$	37.0799	1.45551
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	20.3179i	0.795710i
$653$	−29.0211	−1.13568	−0.567842	−	0.823137i	$-0.692222\pi$
$653$	−29.0211	−1.13568	−0.567842	+	0.823137i	$0.692222\pi$
$654$	11.7230	0.458407
$655$	18.6226i	0.727647i
$656$	− 3.99654i	− 0.156038i
$657$	− 1.21156i	− 0.0472676i
$658$	2.92115i	0.113878i
$659$	7.97303	0.310585	0.155293	−	0.987869i	$-0.450368\pi$
$659$	7.97303	0.310585	0.155293	+	0.987869i	$0.450368\pi$
$660$	8.96024	0.348777
$661$	3.93370i	0.153003i	0.997069	+	0.0765015i	$0.0243750\pi$
$661$	3.93370i	0.153003i	−0.997069	+	0.0765015i	$0.975625\pi$
$662$	−32.2257	−1.25249
$663$	0	0
$664$	13.2348	0.513611
$665$	5.56649i	0.215859i
$666$	−0.324358	−0.0125686
$667$	18.5322	0.717570
$668$	3.23051i	0.124992i
$669$	− 24.3641i	− 0.941972i
$670$	− 9.36365i	− 0.361749i
$671$	− 36.1477i	− 1.39547i
$672$	2.29079	0.0883690
$673$	−36.3199	−1.40003	−0.700014	−	0.714129i	$-0.746823\pi$
$673$	−36.3199	−1.40003	−0.700014	+	0.714129i	$0.746823\pi$
$674$	− 3.01703i	− 0.116212i
$675$	−7.21513	−0.277710
$676$	0	0
$677$	−21.1068	−0.811201	−0.405600	−	0.914051i	$-0.632938\pi$
$677$	−21.1068	−0.811201	−0.405600	+	0.914051i	$0.632938\pi$
$678$	41.0785i	1.57761i
$679$	−11.7061	−0.449239
$680$	4.56864	0.175199
$681$	− 52.0506i	− 1.99458i
$682$	− 3.78662i	− 0.144997i
$683$	26.4258i	1.01115i	0.862782	+	0.505577i	$0.168720\pi$
$683$	26.4258i	1.01115i	−0.862782	+	0.505577i	$0.831280\pi$
$684$	13.8737i	0.530474i
$685$	−2.87647	−0.109904
$686$	−1.00000	−0.0381802
$687$	− 46.5245i	− 1.77502i
$688$	−7.70851	−0.293884
$689$	0	0
$690$	−17.4594	−0.664670
$691$	0.779759i	0.0296634i	0.999890	+	0.0148317i	$0.00472125\pi$
$691$	0.779759i	0.0296634i	−0.999890	+	0.0148317i	$0.995279\pi$
$692$	−9.17044	−0.348608
$693$	−9.74866	−0.370321
$694$	0.468540i	0.0177855i
$695$	0.537234i	0.0203785i
$696$	5.02337i	0.190410i
$697$	20.2461i	0.766877i
$698$	32.2212	1.21959
$699$	24.3845	0.922308
$700$	4.18669i	0.158242i
$701$	21.5491	0.813899	0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491	0.813899	0.406950	+	0.913451i	$0.366592\pi$
$702$	0	0
$703$	0.890713	0.0335939
$704$	4.33716i	0.163463i
$705$	6.03486	0.227286
$706$	13.1154	0.493605
$707$	− 10.7429i	− 0.404028i
$708$	− 19.5847i	− 0.736038i
$709$	4.53742i	0.170406i	0.996364	+	0.0852031i	$0.0271539\pi$
$709$	4.53742i	0.170406i	−0.996364	+	0.0852031i	$0.972846\pi$
$710$	2.95673i	0.110964i
$711$	14.6853	0.550743
$712$	−7.79180	−0.292010
$713$	7.37840i	0.276323i
$714$	−11.6049	−0.434304
$715$	0	0
$716$	−16.9549	−0.633636
$717$	0.713727i	0.0266546i
$718$	4.37981	0.163453
$719$	14.6007	0.544515	0.272258	−	0.962224i	$-0.412230\pi$
$719$	14.6007	0.544515	0.272258	+	0.962224i	$0.412230\pi$
$720$	− 2.02707i	− 0.0755443i
$721$	− 4.81099i	− 0.179171i
$722$	− 19.0983i	− 0.710764i
$723$	57.9558i	2.15540i
$724$	2.65743	0.0987626
$725$	−9.18081	−0.340967
$726$	− 17.8933i	− 0.664083i
$727$	30.6315	1.13606	0.568030	−	0.823008i	$-0.307706\pi$
$727$	30.6315	1.13606	0.568030	+	0.823008i	$0.307706\pi$
$728$	0	0
$729$	−12.1866	−0.451355
$730$	− 0.486112i	− 0.0179918i
$731$	39.0507	1.44434
$732$	−19.0923	−0.705673
$733$	− 17.7195i	− 0.654484i	−0.944941	−	0.327242i	$-0.893881\pi$
$733$	− 17.7195i	− 0.654484i	0.944941	−	0.327242i	$-0.106119\pi$
$734$	25.8188i	0.952989i
$735$	2.06592i	0.0762026i
$736$	− 8.45117i	− 0.311514i
$737$	−45.0321	−1.65878
$738$	8.98303	0.330670
$739$	− 10.4502i	− 0.384417i	−0.981354	−	0.192208i	$-0.938435\pi$
$739$	− 10.4502i	− 0.384417i	0.981354	−	0.192208i	$-0.0615649\pi$
$740$	−0.130141	−0.00478408
$741$	0	0
$742$	1.69699	0.0622983
$743$	48.5094i	1.77964i	0.456316	+	0.889818i	$0.349169\pi$
$743$	48.5094i	1.77964i	−0.456316	+	0.889818i	$0.650831\pi$
$744$	−2.00000	−0.0733236
$745$	−10.1093	−0.370376
$746$	30.6285i	1.12139i
$747$	29.7480i	1.08842i
$748$	− 21.9717i	− 0.803366i
$749$	− 13.6530i	− 0.498871i
$750$	18.9790	0.693014
$751$	−31.4555	−1.14783	−0.573914	−	0.818915i	$-0.694576\pi$
$751$	−31.4555	−1.14783	−0.573914	+	0.818915i	$0.694576\pi$
$752$	2.92115i	0.106523i
$753$	−18.4186	−0.671212
$754$	0	0
$755$	11.7898	0.429075
$756$	− 1.72335i	− 0.0626776i
$757$	48.6884	1.76961	0.884805	−	0.465962i	$-0.154292\pi$
$757$	48.6884	1.76961	0.884805	+	0.465962i	$0.154292\pi$
$758$	38.1523	1.38575
$759$	83.9668i	3.04780i
$760$	5.56649i	0.201918i
$761$	46.5749i	1.68834i	0.536077	+	0.844169i	$0.319906\pi$
$761$	46.5749i	1.68834i	−0.536077	+	0.844169i	$0.680094\pi$
$762$	44.7016i	1.61937i
$763$	−5.11747	−0.185265
$764$	24.4861	0.885875
$765$	10.2690i	0.371275i
$766$	−31.9602	−1.15477
$767$	0	0
$768$	2.29079	0.0826616
$769$	− 27.8362i	− 1.00380i	−0.864926	−	0.501899i	$-0.832635\pi$
$769$	− 27.8362i	− 1.00380i	0.864926	−	0.501899i	$-0.167365\pi$
$770$	−3.91142	−0.140958
$771$	38.7891	1.39696
$772$	− 12.2409i	− 0.440560i
$773$	− 28.4724i	− 1.02408i	−0.858961	−	0.512040i	$-0.828890\pi$
$773$	− 28.4724i	− 1.02408i	0.858961	−	0.512040i	$-0.171110\pi$
$774$	− 17.3265i	− 0.622786i
$775$	− 3.65524i	− 0.131300i
$776$	−11.7061	−0.420224
$777$	0.330575	0.0118593
$778$	5.24585i	0.188073i
$779$	−24.6681	−0.883828
$780$	0	0
$781$	14.2196	0.508819
$782$	42.8130i	1.53099i
$783$	3.77906	0.135053
$784$	−1.00000	−0.0357143
$785$	− 16.1650i	− 0.576954i
$786$	− 47.3039i	− 1.68727i
$787$	− 15.1319i	− 0.539393i	−0.962945	−	0.269697i	$-0.913077\pi$
$787$	− 15.1319i	− 0.539393i	0.962945	−	0.269697i	$-0.0869234\pi$
$788$	− 5.45751i	− 0.194416i
$789$	23.6430	0.841713
$790$	5.89215	0.209633
$791$	− 17.9321i	− 0.637590i
$792$	−9.74866	−0.346404
$793$	0	0
$794$	24.5296	0.870522
$795$	− 3.50584i	− 0.124339i
$796$	−12.8166	−0.454274
$797$	−13.9447	−0.493946	−0.246973	−	0.969022i	$-0.579436\pi$
$797$	−13.9447	−0.493946	−0.246973	+	0.969022i	$0.579436\pi$
$798$	− 14.1396i	− 0.500537i
$799$	− 14.7983i	− 0.523527i
$800$	4.18669i	0.148022i
$801$	− 17.5137i	− 0.618815i
$802$	−4.27143	−0.150829
$803$	−2.33783	−0.0825003
$804$	23.7849i	0.838828i
$805$	7.62159	0.268626
$806$	0	0
$807$	−14.0654	−0.495125
$808$	− 10.7429i	− 0.377934i
$809$	−21.7429	−0.764440	−0.382220	−	0.924071i	$-0.624840\pi$
$809$	−21.7429	−0.764440	−0.382220	+	0.924071i	$0.624840\pi$
$810$	−9.64150	−0.338768
$811$	− 21.1256i	− 0.741819i	−0.928669	−	0.370910i	$-0.879046\pi$
$811$	− 21.1256i	− 0.741819i	0.928669	−	0.370910i	$-0.120954\pi$
$812$	− 2.19286i	− 0.0769542i
$813$	24.4592i	0.857822i
$814$	0.625880i	0.0219371i
$815$	−18.3235	−0.641843
$816$	−11.6049	−0.406254
$817$	47.5799i	1.66461i
$818$	−1.61647	−0.0565185
$819$	0	0
$820$	3.60423	0.125865
$821$	− 16.2736i	− 0.567951i	−0.958831	−	0.283976i	$-0.908347\pi$
$821$	− 16.2736i	− 0.567951i	0.958831	−	0.283976i	$-0.0916535\pi$
$822$	7.30661	0.254847
$823$	−18.6543	−0.650246	−0.325123	−	0.945672i	$-0.605406\pi$
$823$	−18.6543	−0.650246	−0.325123	+	0.945672i	$0.605406\pi$
$824$	− 4.81099i	− 0.167599i
$825$	− 41.5969i	− 1.44822i
$826$	8.54933i	0.297469i
$827$	− 47.3361i	− 1.64604i	−0.568015	−	0.823018i	$-0.692288\pi$
$827$	− 47.3361i	− 1.64604i	0.568015	−	0.823018i	$-0.307712\pi$
$828$	18.9957	0.660147
$829$	−0.921975	−0.0320215	−0.0160108	−	0.999872i	$-0.505097\pi$
$829$	−0.921975	−0.0320215	−0.0160108	+	0.999872i	$0.505097\pi$
$830$	11.9357i	0.414294i
$831$	−50.1888	−1.74103
$832$	0	0
$833$	5.06592	0.175524
$834$	− 1.36464i	− 0.0472538i
$835$	−2.91339	−0.100822
$836$	26.7706	0.925881
$837$	1.50459i	0.0520063i
$838$	− 26.0312i	− 0.899233i
$839$	16.6155i	0.573631i	0.957986	+	0.286815i	$0.0925966\pi$
$839$	16.6155i	0.573631i	−0.957986	+	0.286815i	$0.907403\pi$
$840$	2.06592i	0.0712810i
$841$	−24.1914	−0.834185
$842$	37.5391	1.29368
$843$	59.0380i	2.03338i
$844$	19.3110	0.664713
$845$	0	0
$846$	−6.56588	−0.225740
$847$	7.81099i	0.268389i
$848$	1.69699	0.0582747
$849$	25.9475	0.890515
$850$	− 21.2094i	− 0.727477i
$851$	− 1.21956i	− 0.0418059i
$852$	− 7.51048i	− 0.257305i
$853$	26.3277i	0.901445i	0.892664	+	0.450722i	$0.148834\pi$
$853$	26.3277i	0.901445i	−0.892664	+	0.450722i	$0.851166\pi$
$854$	8.33440	0.285197
$855$	−12.5118	−0.427895
$856$	− 13.6530i	− 0.466651i
$857$	14.1058	0.481845	0.240923	−	0.970544i	$-0.422550\pi$
$857$	14.1058	0.481845	0.240923	+	0.970544i	$0.422550\pi$
$858$	0	0
$859$	23.4719	0.800850	0.400425	−	0.916329i	$-0.368862\pi$
$859$	23.4719	0.800850	0.400425	+	0.916329i	$0.368862\pi$
$860$	− 6.95183i	− 0.237056i
$861$	−9.15521	−0.312009
$862$	−21.5538	−0.734127
$863$	− 11.9484i	− 0.406727i	−0.979103	−	0.203364i	$-0.934813\pi$
$863$	− 11.9484i	− 0.406727i	0.979103	−	0.203364i	$-0.0651874\pi$
$864$	− 1.72335i	− 0.0586295i
$865$	− 8.27026i	− 0.281197i
$866$	− 3.19917i	− 0.108712i
$867$	19.8463	0.674017
$868$	0.873062	0.0296337
$869$	− 28.3368i	− 0.961260i
$870$	−4.53027	−0.153591
$871$	0	0
$872$	−5.11747	−0.173299
$873$	− 26.3118i	− 0.890521i
$874$	−52.1638	−1.76447
$875$	−8.28491	−0.280081
$876$	1.23479i	0.0417196i
$877$	32.7341i	1.10535i	0.833396	+	0.552677i	$0.186394\pi$
$877$	32.7341i	1.10535i	−0.833396	+	0.552677i	$0.813606\pi$
$878$	− 26.6227i	− 0.898474i
$879$	− 54.3969i	− 1.83476i
$880$	−3.91142	−0.131854
$881$	10.5908	0.356813	0.178407	−	0.983957i	$-0.442906\pi$
$881$	10.5908	0.356813	0.178407	+	0.983957i	$0.442906\pi$
$882$	− 2.24770i	− 0.0756841i
$883$	−38.6713	−1.30139	−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713	−1.30139	−0.650696	+	0.759338i	$0.725523\pi$
$884$	0	0
$885$	17.6622	0.593710
$886$	9.09867i	0.305676i
$887$	4.72164	0.158537	0.0792685	−	0.996853i	$-0.474742\pi$
$887$	4.72164	0.158537	0.0792685	+	0.996853i	$0.474742\pi$
$888$	0.330575	0.0110934
$889$	− 19.5136i	− 0.654466i
$890$	− 7.02695i	− 0.235544i
$891$	46.3684i	1.55340i
$892$	10.6357i	0.356110i
$893$	18.0304	0.603366
$894$	25.6789	0.858831
$895$	− 15.2906i	− 0.511109i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	7.02693	0.234492
$899$	1.91450i	0.0638522i
$900$	−9.41043	−0.313681
$901$	−8.59679	−0.286401
$902$	− 17.3336i	− 0.577147i
$903$	17.6586i	0.587640i
$904$	− 17.9321i	− 0.596411i
$905$	2.39657i	0.0796648i
$906$	−29.9476	−0.994943
$907$	41.9309	1.39229	0.696146	−	0.717900i	$-0.254896\pi$
$907$	41.9309	1.39229	0.696146	+	0.717900i	$0.254896\pi$
$908$	22.7217i	0.754047i
$909$	24.1468	0.800900
$910$	0	0
$911$	−54.1425	−1.79382	−0.896910	−	0.442213i	$-0.854194\pi$
$911$	−54.1425	−1.79382	−0.896910	+	0.442213i	$0.854194\pi$
$912$	− 14.1396i	− 0.468209i
$913$	57.4017	1.89972
$914$	19.1511	0.633462
$915$	− 17.2182i	− 0.569216i
$916$	20.3094i	0.671042i
$917$	20.6496i	0.681911i
$918$	8.73035i	0.288145i
$919$	−25.8233	−0.851832	−0.425916	−	0.904763i	$-0.640048\pi$
$919$	−25.8233	−0.851832	−0.425916	+	0.904763i	$0.640048\pi$
$920$	7.62159	0.251277
$921$	15.3210i	0.504845i
$922$	−3.25656	−0.107249
$923$	0	0
$924$	9.93552	0.326855
$925$	0.604165i	0.0198648i
$926$	21.2761	0.699178
$927$	10.8137	0.355168
$928$	− 2.19286i	− 0.0719841i
$929$	− 16.0322i	− 0.525999i	−0.964796	−	0.263000i	$-0.915288\pi$
$929$	− 16.0322i	− 0.525999i	0.964796	−	0.263000i	$-0.0847118\pi$
$930$	− 1.80368i	− 0.0591449i
$931$	6.17238i	0.202292i
$932$	−10.6446	−0.348676
$933$	21.0460	0.689016
$934$	− 3.33171i	− 0.109017i
$935$	19.8150	0.648018
$936$	0	0
$937$	47.0232	1.53618	0.768091	−	0.640340i	$-0.221207\pi$
$937$	47.0232	1.53618	0.768091	+	0.640340i	$0.221207\pi$
$938$	− 10.3828i	− 0.339012i
$939$	−39.3171	−1.28307
$940$	−2.63441	−0.0859248
$941$	52.8569i	1.72308i	0.507686	+	0.861542i	$0.330501\pi$
$941$	52.8569i	1.72308i	−0.507686	+	0.861542i	$0.669499\pi$
$942$	41.0612i	1.33785i
$943$	33.7754i	1.09988i
$944$	8.54933i	0.278257i
$945$	1.55418	0.0505576
$946$	−33.4331	−1.08700
$947$	− 38.5704i	− 1.25337i	−0.779273	−	0.626684i	$-0.784412\pi$
$947$	− 38.5704i	− 1.25337i	0.779273	−	0.626684i	$-0.215588\pi$
$948$	−14.9668	−0.486100
$949$	0	0
$950$	25.8418	0.838419
$951$	8.61903i	0.279491i
$952$	5.06592	0.164187
$953$	−27.3009	−0.884364	−0.442182	−	0.896925i	$-0.645796\pi$
$953$	−27.3009	−0.884364	−0.442182	+	0.896925i	$0.645796\pi$
$954$	3.81432i	0.123493i
$955$	22.0825i	0.714572i
$956$	− 0.311564i	− 0.0100767i
$957$	21.7872i	0.704279i
$958$	0.185216	0.00598405
$959$	−3.18956	−0.102996
$960$	2.06592i	0.0666773i
$961$	30.2378	0.975412
$962$	0	0
$963$	30.6880	0.988906
$964$	− 25.2995i	− 0.814843i
$965$	11.0393	0.355369
$966$	−19.3598	−0.622892
$967$	25.2494i	0.811966i	0.913881	+	0.405983i	$0.133071\pi$
$967$	25.2494i	0.811966i	−0.913881	+	0.405983i	$0.866929\pi$
$968$	7.81099i	0.251055i
$969$	71.6301i	2.30109i
$970$	− 10.5570i	− 0.338965i
$971$	−6.57364	−0.210958	−0.105479	−	0.994422i	$-0.533638\pi$
$971$	−6.57364	−0.210958	−0.105479	+	0.994422i	$0.533638\pi$
$972$	19.3206	0.619709
$973$	0.595710i	0.0190976i
$974$	−31.2308	−1.00070
$975$	0	0
$976$	8.33440	0.266778
$977$	13.9457i	0.446163i	0.974800	+	0.223081i	$0.0716116\pi$
$977$	13.9457i	0.446163i	−0.974800	+	0.223081i	$0.928388\pi$
$978$	46.5440	1.48831
$979$	−33.7943	−1.08007
$980$	− 0.901839i	− 0.0288082i
$981$	− 11.5026i	− 0.367249i
$982$	− 26.8472i	− 0.856729i
$983$	− 47.1390i	− 1.50350i	−0.659449	−	0.751750i	$-0.729210\pi$
$983$	− 47.1390i	− 1.50350i	0.659449	−	0.751750i	$-0.270790\pi$
$984$	−9.15521	−0.291857
$985$	4.92180	0.156821
$986$	11.1088i	0.353778i
$987$	6.69173	0.213000
$988$	0	0
$989$	65.1459	2.07152
$990$	− 8.79172i	− 0.279419i
$991$	9.41609	0.299112	0.149556	−	0.988753i	$-0.452216\pi$
$991$	9.41609	0.299112	0.149556	+	0.988753i	$0.452216\pi$
$992$	0.873062	0.0277198
$993$	73.8223i	2.34268i
$994$	3.27856i	0.103990i
$995$	− 11.5585i	− 0.366430i
$996$	− 30.3182i	− 0.960669i
$997$	40.5215	1.28333	0.641664	−	0.766986i	$-0.278245\pi$
$997$	40.5215	1.28333	0.641664	+	0.766986i	$0.278245\pi$
$998$	−15.2869	−0.483899
$999$	− 0.248690i	− 0.00786821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.11		12
13.5	odd	4		2366.2.a.bh.1.5		6
13.8	odd	4		2366.2.a.bf.1.5		6
13.9	even	3		182.2.m.b.127.4	yes	12
13.10	even	6		182.2.m.b.43.4	✓	12
13.12	even	2	inner	2366.2.d.r.337.5		12
39.23	odd	6		1638.2.bj.g.1135.2		12
39.35	odd	6		1638.2.bj.g.127.2		12
52.23	odd	6		1456.2.cc.d.225.5		12
52.35	odd	6		1456.2.cc.d.673.5		12
91.9	even	3		1274.2.v.e.361.3		12
91.10	odd	6		1274.2.v.d.667.1		12
91.23	even	6		1274.2.o.d.459.1		12
91.48	odd	6		1274.2.m.c.491.6		12
91.61	odd	6		1274.2.v.d.361.1		12
91.62	odd	6		1274.2.m.c.589.6		12
91.74	even	3		1274.2.o.d.569.4		12
91.75	odd	6		1274.2.o.e.459.3		12
91.87	odd	6		1274.2.o.e.569.6		12
91.88	even	6		1274.2.v.e.667.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	13.10	even	6
182.2.m.b.127.4	yes	12	13.9	even	3
1274.2.m.c.491.6		12	91.48	odd	6
1274.2.m.c.589.6		12	91.62	odd	6
1274.2.o.d.459.1		12	91.23	even	6
1274.2.o.d.569.4		12	91.74	even	3
1274.2.o.e.459.3		12	91.75	odd	6
1274.2.o.e.569.6		12	91.87	odd	6
1274.2.v.d.361.1		12	91.61	odd	6
1274.2.v.d.667.1		12	91.10	odd	6
1274.2.v.e.361.3		12	91.9	even	3
1274.2.v.e.667.3		12	91.88	even	6
1456.2.cc.d.225.5		12	52.23	odd	6
1456.2.cc.d.673.5		12	52.35	odd	6
1638.2.bj.g.127.2		12	39.35	odd	6
1638.2.bj.g.1135.2		12	39.23	odd	6
2366.2.a.bf.1.5		6	13.8	odd	4
2366.2.a.bh.1.5		6	13.5	odd	4
2366.2.d.r.337.5		12	13.12	even	2	inner
2366.2.d.r.337.11		12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.29079 q^{3} -1.00000 q^{4} -0.901839i q^{5} +2.29079i q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.24770 q^{9} +0.901839 q^{10} -4.33716i q^{11} -2.29079 q^{12} +1.00000 q^{14} -2.06592i q^{15} +1.00000 q^{16} -5.06592 q^{17} +2.24770i q^{18} -6.17238i q^{19} +0.901839i q^{20} -2.29079i q^{21} +4.33716 q^{22} -8.45117 q^{23} -2.29079i q^{24} +4.18669 q^{25} -1.72335 q^{27} +1.00000i q^{28} -2.19286 q^{29} +2.06592 q^{30} -0.873062i q^{31} +1.00000i q^{32} -9.93552i q^{33} -5.06592i q^{34} -0.901839 q^{35} -2.24770 q^{36} +0.144306i q^{37} +6.17238 q^{38} -0.901839 q^{40} -3.99654i q^{41} +2.29079 q^{42} -7.70851 q^{43} +4.33716i q^{44} -2.02707i q^{45} -8.45117i q^{46} +2.92115i q^{47} +2.29079 q^{48} -1.00000 q^{49} +4.18669i q^{50} -11.6049 q^{51} +1.69699 q^{53} -1.72335i q^{54} -3.91142 q^{55} -1.00000 q^{56} -14.1396i q^{57} -2.19286i q^{58} +8.54933i q^{59} +2.06592i q^{60} +8.33440 q^{61} +0.873062 q^{62} -2.24770i q^{63} -1.00000 q^{64} +9.93552 q^{66} -10.3828i q^{67} +5.06592 q^{68} -19.3598 q^{69} -0.901839i q^{70} +3.27856i q^{71} -2.24770i q^{72} -0.539023i q^{73} -0.144306 q^{74} +9.59081 q^{75} +6.17238i q^{76} -4.33716 q^{77} +6.53349 q^{79} -0.901839i q^{80} -10.6909 q^{81} +3.99654 q^{82} +13.2348i q^{83} +2.29079i q^{84} +4.56864i q^{85} -7.70851i q^{86} -5.02337 q^{87} -4.33716 q^{88} -7.79180i q^{89} +2.02707 q^{90} +8.45117 q^{92} -2.00000i q^{93} -2.92115 q^{94} -5.56649 q^{95} +2.29079i q^{96} -11.7061i q^{97} -1.00000i q^{98} -9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

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