LMFDB - Embedded newform 1800.2.k.u.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1800.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.k (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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.180227832610816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 $ x^12 + x^10 - 8x^6 + 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.3
Root			$-0.806504 + 1.16170i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.u.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.806504 - 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} +0.746175 q^{7} +(2.74067 - 0.699104i) q^{8} +O(q^{10})$	\(q+(-0.806504 - 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} +0.746175 q^{7} +(2.74067 - 0.699104i) q^{8} -5.36068i q^{11} +2.92520i q^{13} +(-0.601793 - 0.866833i) q^{14} +(-3.02251 - 2.62001i) q^{16} -2.13466 q^{17} +1.73367i q^{19} +(-6.22751 + 4.32340i) q^{22} -7.49534 q^{23} +(3.39821 - 2.35918i) q^{26} +(-0.521653 + 1.39821i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-0.606006 + 5.62430i) q^{32} +(1.72161 + 2.47984i) q^{34} -1.07480i q^{37} +(2.01400 - 1.39821i) q^{38} +11.2936 q^{41} -7.44322i q^{43} +(10.0450 + 3.74767i) q^{44} +(6.04502 + 8.70735i) q^{46} -1.73367 q^{47} -6.44322 q^{49} +(-5.48133 - 2.04502i) q^{52} +7.72161i q^{53} +(2.04502 - 0.521653i) q^{56} +(-7.84052 + 5.44322i) q^{58} -6.85302i q^{59} -6.45203i q^{61} +(-2.13466 - 3.07480i) q^{62} +(7.02251 - 3.83202i) q^{64} -7.44322i q^{67} +(1.49235 - 4.00000i) q^{68} -13.2936 q^{71} -0.690358 q^{73} +(-1.24860 + 0.866833i) q^{74} +(-3.24860 - 1.21201i) q^{76} -4.00000i q^{77} +2.64681 q^{79} +(-9.10834 - 13.1198i) q^{82} -5.85039i q^{83} +(-8.64681 + 6.00299i) q^{86} +(-3.74767 - 14.6918i) q^{88} -7.59283 q^{89} +2.18271i q^{91} +(5.24002 - 14.0450i) q^{92} +(1.39821 + 2.01400i) q^{94} -14.1887 q^{97} +(5.19648 + 7.48511i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{4}+O(q^{10}) $ 12 * q - 2 * q^4	$ 12 q - 2 q^{4} - 20 q^{14} + 2 q^{16} + 28 q^{26} - 32 q^{31} - 24 q^{34} + 8 q^{41} + 44 q^{44} - 4 q^{46} + 12 q^{49} - 52 q^{56} + 46 q^{64} - 32 q^{71} + 36 q^{74} + 12 q^{76} - 32 q^{79} - 40 q^{86} - 40 q^{89} + 4 q^{94}+O(q^{100}) $ 12 * q - 2 * q^4 - 20 * q^14 + 2 * q^16 + 28 * q^26 - 32 * q^31 - 24 * q^34 + 8 * q^41 + 44 * q^44 - 4 * q^46 + 12 * q^49 - 52 * q^56 + 46 * q^64 - 32 * q^71 + 36 * q^74 + 12 * q^76 - 32 * q^79 - 40 * q^86 - 40 * q^89 + 4 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−0.806504	−	1.16170i	−0.570284	−	0.821447i
$2$	−0.806504	−	1.16170i	−0.570284	−	0.821447i
$3$		0			0
$3$		0			0
$4$	−0.699104	+	1.87383i	−0.349552	+	0.936917i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.746175			0.282028			0.141014	−	0.990008i	$-0.454964\pi$
$7$	0.746175			0.282028			0.141014	+	0.990008i	$0.454964\pi$
$8$	2.74067	−	0.699104i	0.968972	−	0.247170i
$9$		0			0
$10$		0			0
$11$		−	5.36068i		−	1.61630i	−0.588974	−	0.808152i	$-0.700468\pi$
$11$		−	5.36068i		−	1.61630i	0.588974	−	0.808152i	$-0.299532\pi$
$12$		0			0
$13$			2.92520i			0.811304i	0.914028	+	0.405652i	$0.132955\pi$
$13$			2.92520i			0.811304i	−0.914028	+	0.405652i	$0.867045\pi$
$14$	−0.601793	−	0.866833i	−0.160836	−	0.231671i
$15$		0			0
$16$	−3.02251	−	2.62001i	−0.755627	−	0.655002i
$17$	−2.13466			−0.517731			−0.258866	−	0.965913i	$-0.583349\pi$
$17$	−2.13466			−0.517731			−0.258866	+	0.965913i	$0.583349\pi$
$18$		0			0
$19$			1.73367i			0.397730i	0.980027	+	0.198865i	$0.0637255\pi$
$19$			1.73367i			0.397730i	−0.980027	+	0.198865i	$0.936274\pi$
$20$		0			0
$21$		0			0
$22$	−6.22751	+	4.32340i	−1.32771	+	0.921753i
$23$	−7.49534			−1.56289			−0.781443	−	0.623977i	$-0.785516\pi$
$23$	−7.49534			−1.56289			−0.781443	+	0.623977i	$0.785516\pi$
$24$		0			0
$25$		0			0
$26$	3.39821	−	2.35918i	0.666443	−	0.462674i
$27$		0			0
$28$	−0.521653	+	1.39821i	−0.0985832	+	0.264236i
$29$		−	6.74916i		−	1.25329i	−0.779306	−	0.626644i	$-0.784428\pi$
$29$		−	6.74916i		−	1.25329i	0.779306	−	0.626644i	$-0.215572\pi$
$30$		0			0
$31$	2.64681			0.475381			0.237690	−	0.971341i	$-0.423610\pi$
$31$	2.64681			0.475381			0.237690	+	0.971341i	$0.423610\pi$
$32$	−0.606006	+	5.62430i	−0.107128	+	0.994245i
$33$		0			0
$34$	1.72161	+	2.47984i	0.295254	+	0.425289i
$35$		0			0
$36$		0			0
$37$		−	1.07480i		−	0.176697i	−0.996090	−	0.0883483i	$-0.971841\pi$
$37$		−	1.07480i		−	0.176697i	0.996090	−	0.0883483i	$-0.0281588\pi$
$38$	2.01400	−	1.39821i	0.326714	−	0.226819i
$39$		0			0
$40$		0			0
$41$	11.2936			1.76377			0.881883	−	0.471468i	$-0.156276\pi$
$41$	11.2936			1.76377			0.881883	+	0.471468i	$0.156276\pi$
$42$		0			0
$43$		−	7.44322i		−	1.13508i	−0.823346	−	0.567540i	$-0.807895\pi$
$43$		−	7.44322i		−	1.13508i	0.823346	−	0.567540i	$-0.192105\pi$
$44$	10.0450	+	3.74767i	1.51434	+	0.564982i
$45$		0			0
$46$	6.04502	+	8.70735i	0.891289	+	1.28383i
$47$	−1.73367			−0.252881			−0.126441	−	0.991974i	$-0.540355\pi$
$47$	−1.73367			−0.252881			−0.126441	+	0.991974i	$0.540355\pi$
$48$		0			0
$49$	−6.44322			−0.920460
$50$		0			0
$51$		0			0
$52$	−5.48133	−	2.04502i	−0.760124	−	0.283593i
$53$			7.72161i			1.06064i	0.847796	+	0.530322i	$0.177929\pi$
$53$			7.72161i			1.06064i	−0.847796	+	0.530322i	$0.822071\pi$
$54$		0			0
$55$		0			0
$56$	2.04502	−	0.521653i	0.273277	−	0.0697089i
$57$		0			0
$58$	−7.84052	+	5.44322i	−1.02951	+	0.714730i
$59$		−	6.85302i		−	0.892188i	−0.894986	−	0.446094i	$-0.852815\pi$
$59$		−	6.85302i		−	0.892188i	0.894986	−	0.446094i	$-0.147185\pi$
$60$		0			0
$61$		−	6.45203i		−	0.826098i	−0.910709	−	0.413049i	$-0.864464\pi$
$61$		−	6.45203i		−	0.826098i	0.910709	−	0.413049i	$-0.135536\pi$
$62$	−2.13466	−	3.07480i	−0.271102	−	0.390500i
$63$		0			0
$64$	7.02251	−	3.83202i	0.877813	−	0.479003i
$65$		0			0
$66$		0			0
$67$		−	7.44322i		−	0.909334i	−0.890661	−	0.454667i	$-0.849758\pi$
$67$		−	7.44322i		−	0.909334i	0.890661	−	0.454667i	$-0.150242\pi$
$68$	1.49235	−	4.00000i	0.180974	−	0.485071i
$69$		0			0
$70$		0			0
$71$	−13.2936			−1.57766			−0.788831	−	0.614610i	$-0.789313\pi$
$71$	−13.2936			−1.57766			−0.788831	+	0.614610i	$0.789313\pi$
$72$		0			0
$73$	−0.690358			−0.0808003			−0.0404002	−	0.999184i	$-0.512863\pi$
$73$	−0.690358			−0.0808003			−0.0404002	+	0.999184i	$0.512863\pi$
$74$	−1.24860	+	0.866833i	−0.145147	+	0.100767i
$75$		0			0
$76$	−3.24860	−	1.21201i	−0.372640	−	0.139027i
$77$		−	4.00000i		−	0.455842i
$78$		0			0
$79$	2.64681			0.297789			0.148895	−	0.988853i	$-0.452428\pi$
$79$	2.64681			0.297789			0.148895	+	0.988853i	$0.452428\pi$
$80$		0			0
$81$		0			0
$82$	−9.10834	−	13.1198i	−1.00585	−	1.44884i
$83$		−	5.85039i		−	0.642164i	−0.947051	−	0.321082i	$-0.895953\pi$
$83$		−	5.85039i		−	0.642164i	0.947051	−	0.321082i	$-0.104047\pi$
$84$		0			0
$85$		0			0
$86$	−8.64681	+	6.00299i	−0.932409	+	0.647319i
$87$		0			0
$88$	−3.74767	−	14.6918i	−0.399503	−	1.56615i
$89$	−7.59283			−0.804838			−0.402419	−	0.915456i	$-0.631831\pi$
$89$	−7.59283			−0.804838			−0.402419	+	0.915456i	$0.631831\pi$
$90$		0			0
$91$			2.18271i			0.228810i
$92$	5.24002	−	14.0450i	0.546310	−	1.46429i
$93$		0			0
$94$	1.39821	+	2.01400i	0.144214	+	0.207729i
$95$		0			0
$96$		0			0
$97$	−14.1887			−1.44064			−0.720321	−	0.693641i	$-0.756006\pi$
$97$	−14.1887			−1.44064			−0.720321	+	0.693641i	$0.756006\pi$
$98$	5.19648	+	7.48511i	0.524924	+	0.756110i
$99$		0			0
$100$		0			0
$101$			7.43952i			0.740260i	0.928980	+	0.370130i	$0.120687\pi$
$101$			7.43952i			0.740260i	−0.928980	+	0.370130i	$0.879313\pi$
$102$		0			0
$103$	7.19820			0.709260			0.354630	−	0.935007i	$-0.384607\pi$
$103$	7.19820			0.709260			0.354630	+	0.935007i	$0.384607\pi$
$104$	2.04502	+	8.01699i	0.200530	+	0.786131i
$105$		0			0
$106$	8.97021	−	6.22751i	0.871264	−	0.604869i
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$		−	19.9504i		−	1.91090i	−0.295158	−	0.955449i	$-0.595372\pi$
$109$		−	19.9504i		−	1.91090i	0.295158	−	0.955449i	$-0.404628\pi$
$110$		0			0
$111$		0			0
$112$	−2.25532	−	1.95498i	−0.213108	−	0.184729i
$113$	−12.0540			−1.13395			−0.566973	−	0.823736i	$-0.691886\pi$
$113$	−12.0540			−1.13395			−0.566973	+	0.823736i	$0.691886\pi$
$114$		0			0
$115$		0			0
$116$	12.6468	+	4.71836i	1.17423	+	0.438089i
$117$		0			0
$118$	−7.96117	+	5.52699i	−0.732885	+	0.508801i
$119$	−1.59283			−0.146014
$120$		0			0
$121$	−17.7368			−1.61244
$122$	−7.49534	+	5.20359i	−0.678596	+	0.471110i
$123$		0			0
$124$	−1.85039	+	4.95968i	−0.166170	+	0.445392i
$125$		0			0
$126$		0			0
$127$	−4.21351			−0.373888			−0.186944	−	0.982371i	$-0.559858\pi$
$127$	−4.21351			−0.373888			−0.186944	+	0.982371i	$0.559858\pi$
$128$	−10.1153	−	5.06752i	−0.894079	−	0.447910i
$129$		0			0
$130$		0			0
$131$		−	10.3204i		−	0.901694i	−0.892601	−	0.450847i	$-0.851122\pi$
$131$		−	10.3204i		−	0.901694i	0.892601	−	0.450847i	$-0.148878\pi$
$132$		0			0
$133$			1.29362i			0.112171i
$134$	−8.64681	+	6.00299i	−0.746970	+	0.518579i
$135$		0			0
$136$	−5.85039	+	1.49235i	−0.501667	+	0.127968i
$137$	−15.0387			−1.28484			−0.642422	−	0.766351i	$-0.722070\pi$
$137$	−15.0387			−1.28484			−0.642422	+	0.766351i	$0.722070\pi$
$138$		0			0
$139$		−	9.47032i		−	0.803262i	−0.915802	−	0.401631i	$-0.868443\pi$
$139$		−	9.47032i		−	0.803262i	0.915802	−	0.401631i	$-0.131557\pi$
$140$		0			0
$141$		0			0
$142$	10.7214	+	15.4432i	0.899716	+	1.29597i
$143$	15.6810			1.31131
$144$		0			0
$145$		0			0
$146$	0.556777	+	0.801991i	0.0460792	+	0.0663732i
$147$		0			0
$148$	2.01400	+	0.751399i	0.165550	+	0.0617646i
$149$		−	1.78948i		−	0.146600i	−0.997310	−	0.0733000i	$-0.976647\pi$
$149$		−	1.78948i		−	0.146600i	0.997310	−	0.0733000i	$-0.0233531\pi$
$150$		0			0
$151$	10.6468			0.866425			0.433212	−	0.901292i	$-0.357380\pi$
$151$	10.6468			0.866425			0.433212	+	0.901292i	$0.357380\pi$
$152$	1.21201	+	4.75140i	0.0983071	+	0.385389i
$153$		0			0
$154$	−4.64681	+	3.22601i	−0.374451	+	0.259960i
$155$		0			0
$156$		0			0
$157$			6.92520i			0.552691i	0.961058	+	0.276345i	$0.0891234\pi$
$157$			6.92520i			0.552691i	−0.961058	+	0.276345i	$0.910877\pi$
$158$	−2.13466	−	3.07480i	−0.169824	−	0.244618i
$159$		0			0
$160$		0			0
$161$	−5.59283			−0.440777
$162$		0			0
$163$		−	7.70079i		−	0.603172i	−0.953439	−	0.301586i	$-0.902484\pi$
$163$		−	7.70079i		−	0.603172i	0.953439	−	0.301586i	$-0.0975161\pi$
$164$	−7.89541	+	21.1624i	−0.616528	+	1.65250i
$165$		0			0
$166$	−6.79641	+	4.71836i	−0.527504	+	0.366216i
$167$	3.22601			0.249637			0.124818	−	0.992180i	$-0.460165\pi$
$167$	3.22601			0.249637			0.124818	+	0.992180i	$0.460165\pi$
$168$		0			0
$169$	4.44322			0.341786
$170$		0			0
$171$		0			0
$172$	13.9474	+	5.20359i	1.06348	+	0.396770i
$173$		−	6.42799i		−	0.488711i	−0.969686	−	0.244356i	$-0.921424\pi$
$173$		−	6.42799i		−	0.488711i	0.969686	−	0.244356i	$-0.0785764\pi$
$174$		0			0
$175$		0			0
$176$	−14.0450	+	16.2027i	−1.05868	+	1.22132i
$177$		0			0
$178$	6.12364	+	8.82061i	0.458987	+	0.661132i
$179$		−	8.13765i		−	0.608236i	−0.952634	−	0.304118i	$-0.901638\pi$
$179$		−	8.13765i		−	0.608236i	0.952634	−	0.304118i	$-0.0983618\pi$
$180$		0			0
$181$		−	1.49235i		−	0.110925i	−0.998461	−	0.0554627i	$-0.982337\pi$
$181$		−	1.49235i		−	0.110925i	0.998461	−	0.0554627i	$-0.0176634\pi$
$182$	2.53566	−	1.76036i	0.187955	−	0.130487i
$183$		0			0
$184$	−20.5422	+	5.24002i	−1.51439	+	0.386299i
$185$		0			0
$186$		0			0
$187$			11.4432i			0.836811i
$188$	1.21201	−	3.24860i	0.0883951	−	0.236929i
$189$		0			0
$190$		0			0
$191$	−6.88645			−0.498286			−0.249143	−	0.968467i	$-0.580149\pi$
$191$	−6.88645			−0.498286			−0.249143	+	0.968467i	$0.580149\pi$
$192$		0			0
$193$	−16.4830			−1.18647			−0.593237	−	0.805028i	$-0.702150\pi$
$193$	−16.4830			−1.18647			−0.593237	+	0.805028i	$0.702150\pi$
$194$	11.4432	+	16.4830i	0.821576	+	1.18341i
$195$		0			0
$196$	4.50448	−	12.0735i	0.321749	−	0.862395i
$197$			13.5720i			0.966965i	0.875354	+	0.483483i	$0.160628\pi$
$197$			13.5720i			0.966965i	−0.875354	+	0.483483i	$0.839372\pi$
$198$		0			0
$199$	9.05398			0.641820			0.320910	−	0.947110i	$-0.396011\pi$
$199$	9.05398			0.641820			0.320910	+	0.947110i	$0.396011\pi$
$200$		0			0
$201$		0			0
$202$	8.64251	−	6.00000i	0.608085	−	0.422159i
$203$		−	5.03605i		−	0.353462i
$204$		0			0
$205$		0			0
$206$	−5.80538	−	8.36217i	−0.404480	−	0.582620i
$207$		0			0
$208$	7.66404	−	8.84143i	0.531406	−	0.613043i
$209$	9.29362			0.642853
$210$		0			0
$211$			2.53566i			0.174562i	0.996184	+	0.0872809i	$0.0278178\pi$
$211$			2.53566i			0.174562i	−0.996184	+	0.0872809i	$0.972182\pi$
$212$	−14.4690	−	5.39821i	−0.993736	−	0.370750i
$213$		0			0
$214$	4.64681	−	3.22601i	0.317649	−	0.220526i
$215$		0			0
$216$		0			0
$217$	1.97498			0.134070
$218$	−23.1764	+	16.0900i	−1.56970	+	1.08975i
$219$		0			0
$220$		0			0
$221$		−	6.24430i		−	0.420037i
$222$		0			0
$223$	12.1579			0.814152			0.407076	−	0.913394i	$-0.366548\pi$
$223$	12.1579			0.814152			0.407076	+	0.913394i	$0.366548\pi$
$224$	−0.452186	+	4.19671i	−0.0302130	+	0.280405i
$225$		0			0
$226$	9.72161	+	14.0032i	0.646672	+	0.931478i
$227$		−	20.7368i		−	1.37635i	−0.725544	−	0.688176i	$-0.758412\pi$
$227$		−	20.7368i		−	1.37635i	0.725544	−	0.688176i	$-0.241588\pi$
$228$		0			0
$229$			19.9504i			1.31836i	0.751987	+	0.659178i	$0.229096\pi$
$229$			19.9504i			1.31836i	−0.751987	+	0.659178i	$0.770904\pi$
$230$		0			0
$231$		0			0
$232$	−4.71836	−	18.4972i	−0.309776	−	1.21440i
$233$	13.3386			0.873844			0.436922	−	0.899499i	$-0.356069\pi$
$233$	13.3386			0.873844			0.436922	+	0.899499i	$0.356069\pi$
$234$		0			0
$235$		0			0
$236$	12.8414	+	4.79097i	0.835906	+	0.311866i
$237$		0			0
$238$	1.28462	+	1.85039i	0.0832697	+	0.119943i
$239$	−22.8864			−1.48040			−0.740201	−	0.672386i	$-0.765269\pi$
$239$	−22.8864			−1.48040			−0.740201	+	0.672386i	$0.765269\pi$
$240$		0			0
$241$	3.59283			0.231435			0.115717	−	0.993282i	$-0.463083\pi$
$241$	3.59283			0.231435			0.115717	+	0.993282i	$0.463083\pi$
$242$	14.3048	+	20.6049i	0.919549	+	1.32453i
$243$		0			0
$244$	12.0900	+	4.51064i	0.773985	+	0.288764i
$245$		0			0
$246$		0			0
$247$	−5.07131			−0.322680
$248$	7.25402	−	1.85039i	0.460631	−	0.117500i
$249$		0			0
$250$		0			0
$251$			8.82801i			0.557219i	0.960404	+	0.278609i	$0.0898735\pi$
$251$			8.82801i			0.557219i	−0.960404	+	0.278609i	$0.910127\pi$
$252$		0			0
$253$			40.1801i			2.52610i
$254$	3.39821	+	4.89484i	0.213222	+	0.307129i
$255$		0			0
$256$	2.27111	+	15.8380i	0.141944	+	0.989875i
$257$	22.2927			1.39058			0.695291	−	0.718728i	$-0.255275\pi$
$257$	22.2927			1.39058			0.695291	+	0.718728i	$0.255275\pi$
$258$		0			0
$259$		−	0.801991i		−	0.0498333i
$260$		0			0
$261$		0			0
$262$	−11.9892	+	8.32340i	−0.740694	+	0.514222i
$263$	21.2014			1.30733			0.653667	−	0.756783i	$-0.273230\pi$
$263$	21.2014			1.30733			0.653667	+	0.756783i	$0.273230\pi$
$264$		0			0
$265$		0			0
$266$	1.50280	−	1.04331i	0.0921424	−	0.0639693i
$267$		0			0
$268$	13.9474	+	5.20359i	0.851971	+	0.317860i
$269$		−	14.6935i		−	0.895881i	−0.894063	−	0.447940i	$-0.852158\pi$
$269$		−	14.6935i		−	0.895881i	0.894063	−	0.447940i	$-0.147842\pi$
$270$		0			0
$271$	−20.2396			−1.22947			−0.614735	−	0.788734i	$-0.710737\pi$
$271$	−20.2396			−1.22947			−0.614735	+	0.788734i	$0.710737\pi$
$272$	6.45203	+	5.59283i	0.391212	+	0.339115i
$273$		0			0
$274$	12.1288	+	17.4705i	0.732727	+	1.05543i
$275$		0			0
$276$		0			0
$277$			0.518027i			0.0311252i	0.999879	+	0.0155626i	$0.00495393\pi$
$277$			0.518027i			0.0311252i	−0.999879	+	0.0155626i	$0.995046\pi$
$278$	−11.0017	+	7.63785i	−0.659837	+	0.458088i
$279$		0			0
$280$		0			0
$281$	−13.7008			−0.817320			−0.408660	−	0.912687i	$-0.634004\pi$
$281$	−13.7008			−0.817320			−0.408660	+	0.912687i	$0.634004\pi$
$282$		0			0
$283$		−	18.0305i		−	1.07180i	−0.844282	−	0.535900i	$-0.819973\pi$
$283$		−	18.0305i		−	1.07180i	0.844282	−	0.535900i	$-0.180027\pi$
$284$	9.29362	−	24.9100i	0.551475	−	1.47814i
$285$		0			0
$286$	−12.6468	−	18.2167i	−0.747821	−	1.07718i
$287$	8.42701			0.497431
$288$		0			0
$289$	−12.4432			−0.731954
$290$		0			0
$291$		0			0
$292$	0.482632	−	1.29362i	0.0282439	−	0.0757032i
$293$			15.9792i			0.933513i	0.884386	+	0.466757i	$0.154578\pi$
$293$			15.9792i			0.933513i	−0.884386	+	0.466757i	$0.845422\pi$
$294$		0			0
$295$		0			0
$296$	−0.751399	−	2.94568i	−0.0436742	−	0.171214i
$297$		0			0
$298$	−2.07884	+	1.44322i	−0.120424	+	0.0836037i
$299$		−	21.9253i		−	1.26797i
$300$		0			0
$301$		−	5.55394i		−	0.320124i
$302$	−8.58669	−	12.3684i	−0.494108	−	0.711723i
$303$		0			0
$304$	4.54222	−	5.24002i	0.260514	−	0.300536i
$305$		0			0
$306$		0			0
$307$		−	22.5872i		−	1.28912i	−0.764553	−	0.644561i	$-0.777040\pi$
$307$		−	22.5872i		−	1.28912i	0.764553	−	0.644561i	$-0.222960\pi$
$308$	7.49534	+	2.79641i	0.427086	+	0.159341i
$309$		0			0
$310$		0			0
$311$	18.5872			1.05399			0.526993	−	0.849870i	$-0.323320\pi$
$311$	18.5872			1.05399			0.526993	+	0.849870i	$0.323320\pi$
$312$		0			0
$313$	−29.3871			−1.66106			−0.830528	−	0.556977i	$-0.811961\pi$
$313$	−29.3871			−1.66106			−0.830528	+	0.556977i	$0.811961\pi$
$314$	8.04502	−	5.58520i	0.454007	−	0.315191i
$315$		0			0
$316$	−1.85039	+	4.95968i	−0.104093	+	0.279004i
$317$			5.57201i			0.312955i	0.987682	+	0.156478i	$0.0500139\pi$
$317$			5.57201i			0.312955i	−0.987682	+	0.156478i	$0.949986\pi$
$318$		0			0
$319$	−36.1801			−2.02569
$320$		0			0
$321$		0			0
$322$	4.51064	+	6.49720i	0.251368	+	0.362075i
$323$		−	3.70079i		−	0.205917i
$324$		0			0
$325$		0			0
$326$	−8.94602	+	6.21071i	−0.495474	+	0.343980i
$327$		0			0
$328$	30.9520	−	7.89541i	1.70904	−	0.435951i
$329$	−1.29362			−0.0713194
$330$		0			0
$331$			13.7396i			0.755199i	0.925969	+	0.377599i	$0.123250\pi$
$331$			13.7396i			0.755199i	−0.925969	+	0.377599i	$0.876750\pi$
$332$	10.9627	+	4.09003i	0.601655	+	0.224470i
$333$		0			0
$334$	−2.60179	−	3.74767i	−0.142364	−	0.205063i
$335$		0			0
$336$		0			0
$337$	20.7523			1.13045			0.565226	−	0.824936i	$-0.308789\pi$
$337$	20.7523			1.13045			0.565226	+	0.824936i	$0.308789\pi$
$338$	−3.58348	−	5.16170i	−0.194915	−	0.280760i
$339$		0			0
$340$		0			0
$341$		−	14.1887i		−	0.768360i
$342$		0			0
$343$	−10.0310			−0.541623
$344$	−5.20359	−	20.3994i	−0.280559	−	1.09986i
$345$		0			0
$346$	−7.46742	+	5.18420i	−0.401451	+	0.278704i
$347$			4.73684i			0.254287i	0.991884	+	0.127143i	$0.0405809\pi$
$347$			4.73684i			0.254287i	−0.991884	+	0.127143i	$0.959419\pi$
$348$		0			0
$349$			0.482632i			0.0258347i	0.999917	+	0.0129174i	$0.00411184\pi$
$349$			0.482632i			0.0258347i	−0.999917	+	0.0129174i	$0.995888\pi$
$350$		0			0
$351$		0			0
$352$	30.1500	+	3.24860i	1.60700	+	0.173151i
$353$	2.13466			0.113617			0.0568083	−	0.998385i	$-0.481908\pi$
$353$	2.13466			0.113617			0.0568083	+	0.998385i	$0.481908\pi$
$354$		0			0
$355$		0			0
$356$	5.30818	−	14.2277i	0.281333	−	0.754067i
$357$		0			0
$358$	−9.45352	+	6.56304i	−0.499634	+	0.346868i
$359$	9.59283			0.506290			0.253145	−	0.967428i	$-0.418535\pi$
$359$	9.59283			0.506290			0.253145	+	0.967428i	$0.418535\pi$
$360$		0			0
$361$	15.9944			0.841811
$362$	−1.73367	+	1.20359i	−0.0911194	+	0.0632590i
$363$		0			0
$364$	−4.09003	−	1.52594i	−0.214376	−	0.0799809i
$365$		0			0
$366$		0			0
$367$	34.0832			1.77913			0.889565	−	0.456809i	$-0.151008\pi$
$367$	34.0832			1.77913			0.889565	+	0.456809i	$0.151008\pi$
$368$	22.6547	+	19.6378i	1.18096	+	1.02369i
$369$		0			0
$370$		0			0
$371$			5.76167i			0.299131i
$372$		0			0
$373$		−	4.33796i		−	0.224611i	−0.993674	−	0.112306i	$-0.964176\pi$
$373$		−	4.33796i		−	0.224611i	0.993674	−	0.112306i	$-0.0358236\pi$
$374$	13.2936	−	9.22900i	0.687397	−	0.477220i
$375$		0			0
$376$	−4.75140	+	1.21201i	−0.245035	+	0.0625047i
$377$	19.7426			1.01680
$378$		0			0
$379$		−	6.90107i		−	0.354484i	−0.984167	−	0.177242i	$-0.943282\pi$
$379$		−	6.90107i		−	0.354484i	0.984167	−	0.177242i	$-0.0567176\pi$
$380$		0			0
$381$		0			0
$382$	5.55394	+	8.00000i	0.284165	+	0.409316i
$383$	−22.3744			−1.14328			−0.571639	−	0.820506i	$-0.693692\pi$
$383$	−22.3744			−1.14328			−0.571639	+	0.820506i	$0.693692\pi$
$384$		0			0
$385$		0			0
$386$	13.2936	+	19.1484i	0.676627	+	0.974626i
$387$		0			0
$388$	9.91936	−	26.5872i	0.503579	−	1.34976i
$389$			11.0185i			0.558659i	0.960195	+	0.279330i	$0.0901122\pi$
$389$			11.0185i			0.558659i	−0.960195	+	0.279330i	$0.909888\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−17.6587	+	4.50448i	−0.891900	+	0.227511i
$393$		0			0
$394$	15.7666	−	10.9459i	0.794311	−	0.551445i
$395$		0			0
$396$		0			0
$397$			25.2549i			1.26751i	0.773536	+	0.633753i	$0.218486\pi$
$397$			25.2549i			1.26751i	−0.773536	+	0.633753i	$0.781514\pi$
$398$	−7.30207	−	10.5180i	−0.366020	−	0.527221i
$399$		0			0
$400$		0			0
$401$	−7.29362			−0.364226			−0.182113	−	0.983278i	$-0.558294\pi$
$401$	−7.29362			−0.364226			−0.182113	+	0.983278i	$0.558294\pi$
$402$		0			0
$403$			7.74244i			0.385678i
$404$	−13.9404	−	5.20100i	−0.693562	−	0.258759i
$405$		0			0
$406$	−5.85039	+	4.06160i	−0.290350	+	0.201574i
$407$	−5.76167			−0.285595
$408$		0			0
$409$	15.8504			0.783752			0.391876	−	0.920018i	$-0.371826\pi$
$409$	15.8504			0.783752			0.391876	+	0.920018i	$0.371826\pi$
$410$		0			0
$411$		0			0
$412$	−5.03229	+	13.4882i	−0.247923	+	0.664518i
$413$		−	5.11355i		−	0.251622i
$414$		0			0
$415$		0			0
$416$	−16.4522	−	1.77269i	−0.806635	−	0.0869131i
$417$		0			0
$418$	−7.49534	−	10.7964i	−0.366609	−	0.528070i
$419$			8.02602i			0.392097i	0.980594	+	0.196048i	$0.0628109\pi$
$419$			8.02602i			0.392097i	−0.980594	+	0.196048i	$0.937189\pi$
$420$		0			0
$421$			22.9351i			1.11779i	0.829240	+	0.558893i	$0.188774\pi$
$421$			22.9351i			1.11779i	−0.829240	+	0.558893i	$0.811226\pi$
$422$	2.94568	−	2.04502i	0.143393	−	0.0995498i
$423$		0			0
$424$	5.39821	+	21.1624i	0.262160	+	1.02774i
$425$		0			0
$426$		0			0
$427$		−	4.81434i		−	0.232982i
$428$	−7.49534	−	2.79641i	−0.362301	−	0.135170i
$429$		0			0
$430$		0			0
$431$	35.0665			1.68909			0.844547	−	0.535481i	$-0.179870\pi$
$431$	35.0665			1.68909			0.844547	+	0.535481i	$0.179870\pi$
$432$		0			0
$433$	17.0773			0.820682			0.410341	−	0.911932i	$-0.365410\pi$
$433$	17.0773			0.820682			0.410341	+	0.911932i	$0.365410\pi$
$434$	−1.59283	−	2.29434i	−0.0764583	−	0.110132i
$435$		0			0
$436$	37.3836	+	13.9474i	1.79035	+	0.667958i
$437$		−	12.9944i		−	0.621607i
$438$		0			0
$439$	8.53885			0.407537			0.203769	−	0.979019i	$-0.434681\pi$
$439$	8.53885			0.407537			0.203769	+	0.979019i	$0.434681\pi$
$440$		0			0
$441$		0			0
$442$	−7.25402	+	5.03605i	−0.345039	+	0.239541i
$443$		−	20.7368i		−	0.985237i	−0.870245	−	0.492619i	$-0.836040\pi$
$443$		−	20.7368i		−	0.985237i	0.870245	−	0.492619i	$-0.163960\pi$
$444$		0			0
$445$		0			0
$446$	−9.80538	−	14.1238i	−0.464298	−	0.668783i
$447$		0			0
$448$	5.24002	−	2.85936i	0.247568	−	0.135092i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$		−	60.5414i		−	2.85078i
$452$	8.42701	−	22.5872i	0.396373	−	1.06241i
$453$		0			0
$454$	−24.0900	+	16.7243i	−1.13060	+	0.784912i
$455$		0			0
$456$		0			0
$457$	1.28462			0.0600921			0.0300461	−	0.999549i	$-0.490435\pi$
$457$	1.28462			0.0600921			0.0300461	+	0.999549i	$0.490435\pi$
$458$	23.1764	−	16.0900i	1.08296	−	0.751838i
$459$		0			0
$460$		0			0
$461$		−	15.7033i		−	0.731374i	−0.930738	−	0.365687i	$-0.880834\pi$
$461$		−	15.7033i		−	0.731374i	0.930738	−	0.365687i	$-0.119166\pi$
$462$		0			0
$463$	18.7215			0.870064			0.435032	−	0.900415i	$-0.356737\pi$
$463$	18.7215			0.870064			0.435032	+	0.900415i	$0.356737\pi$
$464$	−17.6829	+	20.3994i	−0.820906	+	0.947018i
$465$		0			0
$466$	−10.7577	−	15.4955i	−0.498339	−	0.717817i
$467$			2.14961i			0.0994719i	0.998762	+	0.0497360i	$0.0158380\pi$
$467$			2.14961i			0.0994719i	−0.998762	+	0.0497360i	$0.984162\pi$
$468$		0			0
$469$		−	5.55394i		−	0.256457i
$470$		0			0
$471$		0			0
$472$	−4.79097	−	18.7819i	−0.220522	−	0.864505i
$473$	−39.9007			−1.83464
$474$		0			0
$475$		0			0
$476$	1.11355	−	2.98470i	0.0510396	−	0.136803i
$477$		0			0
$478$	18.4580	+	26.5872i	0.844249	+	1.21607i
$479$	12.1801			0.556521			0.278261	−	0.960506i	$-0.410242\pi$
$479$	12.1801			0.556521			0.278261	+	0.960506i	$0.410242\pi$
$480$		0			0
$481$	3.14401			0.143355
$482$	−2.89763	−	4.17380i	−0.131983	−	0.190111i
$483$		0			0
$484$	12.3999	−	33.2359i	0.563631	−	1.51072i
$485$		0			0
$486$		0			0
$487$	25.7678			1.16765			0.583826	−	0.811879i	$-0.301555\pi$
$487$	25.7678			1.16765			0.583826	+	0.811879i	$0.301555\pi$
$488$	−4.51064	−	17.6829i	−0.204187	−	0.800466i
$489$		0			0
$490$		0			0
$491$			16.7724i			0.756927i	0.925616	+	0.378464i	$0.123547\pi$
$491$			16.7724i			0.756927i	−0.925616	+	0.378464i	$0.876453\pi$
$492$		0			0
$493$			14.4072i			0.648866i
$494$	4.09003	+	5.89135i	0.184019	+	0.265065i
$495$		0			0
$496$	−8.00000	−	6.93466i	−0.359211	−	0.311375i
$497$	−9.91936			−0.444944
$498$		0			0
$499$			17.6224i			0.788888i	0.918920	+	0.394444i	$0.129063\pi$
$499$			17.6224i			0.788888i	−0.918920	+	0.394444i	$0.870937\pi$
$500$		0			0
$501$		0			0
$502$	10.2555	−	7.11982i	0.457726	−	0.317773i
$503$	27.1263			1.20950			0.604752	−	0.796414i	$-0.293272\pi$
$503$	27.1263			1.20950			0.604752	+	0.796414i	$0.293272\pi$
$504$		0			0
$505$		0			0
$506$	46.6773	−	32.4054i	2.07506	−	1.44059i
$507$		0			0
$508$	2.94568	−	7.89541i	0.130693	−	0.350302i
$509$			15.9782i			0.708220i	0.935204	+	0.354110i	$0.115216\pi$
$509$			15.9782i			0.708220i	−0.935204	+	0.354110i	$0.884784\pi$
$510$		0			0
$511$	−0.515128			−0.0227879
$512$	16.5674	−	15.4118i	0.732181	−	0.681110i
$513$		0			0
$514$	−17.9792	−	25.8975i	−0.793027	−	1.14229i
$515$		0			0
$516$		0			0
$517$			9.29362i			0.408733i
$518$	−0.931674	+	0.646809i	−0.0409354	+	0.0284191i
$519$		0			0
$520$		0			0
$521$	−0.886447			−0.0388359			−0.0194180	−	0.999811i	$-0.506181\pi$
$521$	−0.886447			−0.0388359			−0.0194180	+	0.999811i	$0.506181\pi$
$522$		0			0
$523$		−	41.7729i		−	1.82660i	−0.407286	−	0.913301i	$-0.633525\pi$
$523$		−	41.7729i		−	1.82660i	0.407286	−	0.913301i	$-0.366475\pi$
$524$	19.3386	+	7.21500i	0.844812	+	0.315189i
$525$		0			0
$526$	−17.0990	−	24.6297i	−0.745552	−	1.07391i
$527$	−5.65004			−0.246120
$528$		0			0
$529$	33.1801			1.44261
$530$		0			0
$531$		0			0
$532$	−2.42402	−	0.904373i	−0.105095	−	0.0392095i
$533$			33.0361i			1.43095i
$534$		0			0
$535$		0			0
$536$	−5.20359	−	20.3994i	−0.224761	−	0.881120i
$537$		0			0
$538$	−17.0695	+	11.8504i	−0.735919	+	0.510907i
$539$			34.5400i			1.48774i
$540$		0			0
$541$		−	4.47705i		−	0.192483i	−0.995358	−	0.0962417i	$-0.969318\pi$
$541$		−	4.47705i		−	0.192483i	0.995358	−	0.0962417i	$-0.0306822\pi$
$542$	16.3233	+	23.5124i	0.701148	+	1.00995i
$543$		0			0
$544$	1.29362	−	12.0060i	0.0554634	−	0.514752i
$545$		0			0
$546$		0			0
$547$		−	14.3297i		−	0.612692i	−0.951920	−	0.306346i	$-0.900893\pi$
$547$		−	14.3297i		−	0.612692i	0.951920	−	0.306346i	$-0.0991065\pi$
$548$	10.5136	−	28.1801i	0.449120	−	1.20379i
$549$		0			0
$550$		0			0
$551$	11.7008			0.498470
$552$		0			0
$553$	1.97498			0.0839848
$554$	0.601793	−	0.417790i	0.0255677	−	0.0177502i
$555$		0			0
$556$	17.7458	+	6.62073i	0.752590	+	0.280782i
$557$		−	2.68556i		−	0.113791i	−0.998380	−	0.0568954i	$-0.981880\pi$
$557$		−	2.68556i		−	0.113791i	0.998380	−	0.0568954i	$-0.0181201\pi$
$558$		0			0
$559$	21.7729			0.920895
$560$		0			0
$561$		0			0
$562$	11.0497	+	15.9162i	0.466105	+	0.671386i
$563$			20.7368i			0.873954i	0.899473	+	0.436977i	$0.143951\pi$
$563$			20.7368i			0.873954i	−0.899473	+	0.436977i	$0.856049\pi$
$564$		0			0
$565$		0			0
$566$	−20.9460	+	14.5416i	−0.880427	+	0.611230i
$567$		0			0
$568$	−36.4334	+	9.29362i	−1.52871	+	0.389952i
$569$	−4.40717			−0.184758			−0.0923791	−	0.995724i	$-0.529447\pi$
$569$	−4.40717			−0.184758			−0.0923791	+	0.995724i	$0.529447\pi$
$570$		0			0
$571$			23.6590i			0.990098i	0.868865	+	0.495049i	$0.164850\pi$
$571$			23.6590i			0.990098i	−0.868865	+	0.495049i	$0.835150\pi$
$572$	−10.9627	+	29.3836i	−0.458372	+	1.22859i
$573$		0			0
$574$	−6.79641	−	9.78968i	−0.283677	−	0.408613i
$575$		0			0
$576$		0			0
$577$	−6.56366			−0.273249			−0.136624	−	0.990623i	$-0.543625\pi$
$577$	−6.56366			−0.273249			−0.136624	+	0.990623i	$0.543625\pi$
$578$	10.0355	+	14.4553i	0.417422	+	0.601262i
$579$		0			0
$580$		0			0
$581$		−	4.36542i		−	0.181108i
$582$		0			0
$583$	41.3931			1.71433
$584$	−1.89204	+	0.482632i	−0.0782933	+	0.0199715i
$585$		0			0
$586$	18.5630	−	12.8873i	0.766832	−	0.532368i
$587$			16.2992i			0.672741i	0.941730	+	0.336370i	$0.109199\pi$
$587$			16.2992i			0.672741i	−0.941730	+	0.336370i	$0.890801\pi$
$588$		0			0
$589$			4.58868i			0.189073i
$590$		0			0
$591$		0			0
$592$	−2.81599	+	3.24860i	−0.115737	+	0.133517i
$593$	16.3233			0.670319			0.335160	−	0.942161i	$-0.391210\pi$
$593$	16.3233			0.670319			0.335160	+	0.942161i	$0.391210\pi$
$594$		0			0
$595$		0			0
$596$	3.35319	+	1.25103i	0.137352	+	0.0512443i
$597$		0			0
$598$	−25.4707	+	17.6829i	−1.04157	+	0.723106i
$599$	25.5928			1.04569			0.522847	−	0.852426i	$-0.324870\pi$
$599$	25.5928			1.04569			0.522847	+	0.852426i	$0.324870\pi$
$600$		0			0
$601$	29.9225			1.22056			0.610282	−	0.792184i	$-0.291056\pi$
$601$	29.9225			1.22056			0.610282	+	0.792184i	$0.291056\pi$
$602$	−6.45203	+	4.47928i	−0.262965	+	0.182562i
$603$		0			0
$604$	−7.44322	+	19.9504i	−0.302860	+	0.811768i
$605$		0			0
$606$		0			0
$607$	−20.6965			−0.840046			−0.420023	−	0.907513i	$-0.637978\pi$
$607$	−20.6965			−0.840046			−0.420023	+	0.907513i	$0.637978\pi$
$608$	−9.75065	−	1.05061i	−0.395441	−	0.0426079i
$609$		0			0
$610$		0			0
$611$		−	5.07131i		−	0.205163i
$612$		0			0
$613$		−	22.6676i		−	0.915537i	−0.889071	−	0.457769i	$-0.848649\pi$
$613$		−	22.6676i		−	0.915537i	0.889071	−	0.457769i	$-0.151351\pi$
$614$	−26.2396	+	18.2167i	−1.05895	+	0.735166i
$615$		0			0
$616$	−2.79641	−	10.9627i	−0.112671	−	0.441698i
$617$	−22.1966			−0.893603			−0.446802	−	0.894633i	$-0.647437\pi$
$617$	−22.1966			−0.893603			−0.446802	+	0.894633i	$0.647437\pi$
$618$		0			0
$619$		−	16.8204i		−	0.676070i	−0.941133	−	0.338035i	$-0.890238\pi$
$619$		−	16.8204i		−	0.676070i	0.941133	−	0.338035i	$-0.109762\pi$
$620$		0			0
$621$		0			0
$622$	−14.9907	−	21.5928i	−0.601071	−	0.865794i
$623$	−5.66558			−0.226987
$624$		0			0
$625$		0			0
$626$	23.7008	+	34.1390i	0.947274	+	1.36447i
$627$		0			0
$628$	−12.9767	−	4.84143i	−0.517825	−	0.193194i
$629$			2.29434i			0.0914813i
$630$		0			0
$631$	−44.1205			−1.75641			−0.878204	−	0.478285i	$-0.841258\pi$
$631$	−44.1205			−1.75641			−0.878204	+	0.478285i	$0.841258\pi$
$632$	7.25402	−	1.85039i	0.288549	−	0.0736047i
$633$		0			0
$634$	6.47301	−	4.49384i	0.257076	−	0.178473i
$635$		0			0
$636$		0			0
$637$		−	18.8477i		−	0.746773i
$638$	29.1794	+	42.0305i	1.15522	+	1.66400i
$639$		0			0
$640$		0			0
$641$	1.18566			0.0468307			0.0234154	−	0.999726i	$-0.492546\pi$
$641$	1.18566			0.0468307			0.0234154	+	0.999726i	$0.492546\pi$
$642$		0			0
$643$			22.5872i			0.890754i	0.895343	+	0.445377i	$0.146930\pi$
$643$			22.5872i			0.890754i	−0.895343	+	0.445377i	$0.853070\pi$
$644$	3.90997	−	10.4800i	0.154074	−	0.412971i
$645$		0			0
$646$	−4.29921	+	2.98470i	−0.169150	+	0.117431i
$647$	19.7090			0.774842			0.387421	−	0.921903i	$-0.373366\pi$
$647$	19.7090			0.774842			0.387421	+	0.921903i	$0.373366\pi$
$648$		0			0
$649$	−36.7368			−1.44205
$650$		0			0
$651$		0			0
$652$	14.4300	+	5.38365i	0.565122	+	0.210840i
$653$		−	44.4585i		−	1.73979i	−0.493234	−	0.869897i	$-0.664185\pi$
$653$		−	44.4585i		−	1.73979i	0.493234	−	0.869897i	$-0.335815\pi$
$654$		0			0
$655$		0			0
$656$	−34.1350	−	29.5894i	−1.33275	−	1.15527i
$657$		0			0
$658$	1.04331	+	1.50280i	0.0406723	+	0.0585852i
$659$			41.5863i			1.61997i	0.586448	+	0.809987i	$0.300526\pi$
$659$			41.5863i			1.61997i	−0.586448	+	0.809987i	$0.699474\pi$
$660$		0			0
$661$		−	12.0060i		−	0.466978i	−0.972359	−	0.233489i	$-0.924986\pi$
$661$		−	12.0060i		−	0.466978i	0.972359	−	0.233489i	$-0.0750143\pi$
$662$	15.9614	−	11.0811i	0.620356	−	0.430678i
$663$		0			0
$664$	−4.09003	−	16.0340i	−0.158724	−	0.622239i
$665$		0			0
$666$		0			0
$667$			50.5872i			1.95875i
$668$	−2.25532	+	6.04502i	−0.0872609	+	0.233889i
$669$		0			0
$670$		0			0
$671$	−34.5872			−1.33523
$672$		0			0
$673$	14.5080			0.559244			0.279622	−	0.960110i	$-0.409791\pi$
$673$	14.5080			0.559244			0.279622	+	0.960110i	$0.409791\pi$
$674$	−16.7368	−	24.1080i	−0.644679	−	0.928607i
$675$		0			0
$676$	−3.10627	+	8.32586i	−0.119472	+	0.320226i
$677$			43.8600i			1.68568i	0.538166	+	0.842839i	$0.319117\pi$
$677$			43.8600i			1.68568i	−0.538166	+	0.842839i	$0.680883\pi$
$678$		0			0
$679$	−10.5872			−0.406301
$680$		0			0
$681$		0			0
$682$	−16.4830	+	11.4432i	−0.631168	+	0.438184i
$683$			5.33527i			0.204148i	0.994777	+	0.102074i	$0.0325479\pi$
$683$			5.33527i			0.204148i	−0.994777	+	0.102074i	$0.967452\pi$
$684$		0			0
$685$		0			0
$686$	8.09003	+	11.6530i	0.308879	+	0.444915i
$687$		0			0
$688$	−19.5013	+	22.4972i	−0.743480	+	0.857698i
$689$	−22.5872			−0.860505
$690$		0			0
$691$			39.7710i			1.51296i	0.654016	+	0.756480i	$0.273083\pi$
$691$			39.7710i			1.51296i	−0.654016	+	0.756480i	$0.726917\pi$
$692$	12.0450	+	4.49383i	0.457882	+	0.170830i
$693$		0			0
$694$	5.50280	−	3.82028i	0.208883	−	0.145016i
$695$		0			0
$696$		0			0
$697$	−24.1080			−0.913157
$698$	0.560675	−	0.389245i	0.0212219	−	0.0147331i
$699$		0			0
$700$		0			0
$701$			27.5015i			1.03872i	0.854556	+	0.519359i	$0.173829\pi$
$701$			27.5015i			1.03872i	−0.854556	+	0.519359i	$0.826171\pi$
$702$		0			0
$703$	1.86335			0.0702775
$704$	−20.5422	−	37.6454i	−0.774214	−	1.41881i
$705$		0			0
$706$	−1.72161	−	2.47984i	−0.0647937	−	0.0933300i
$707$			5.55118i			0.208774i
$708$		0			0
$709$			0.111632i			0.00419244i	0.999998	+	0.00209622i	$0.000667249\pi$
$709$			0.111632i			0.00419244i	−0.999998	+	0.00209622i	$0.999333\pi$
$710$		0			0
$711$		0			0
$712$	−20.8094	+	5.30818i	−0.779866	+	0.198932i
$713$	−19.8387			−0.742966
$714$		0			0
$715$		0			0
$716$	15.2486	+	5.68906i	0.569867	+	0.212610i
$717$		0			0
$718$	−7.73665	−	11.1440i	−0.288729	−	0.415891i
$719$	−10.7064			−0.399281			−0.199640	−	0.979869i	$-0.563977\pi$
$719$	−10.7064			−0.399281			−0.199640	+	0.979869i	$0.563977\pi$
$720$		0			0
$721$	5.37112			0.200031
$722$	−12.8995	−	18.5807i	−0.480071	−	0.691503i
$723$		0			0
$724$	2.79641	+	1.04331i	0.103928	+	0.0387742i
$725$		0			0
$726$		0			0
$727$	−25.6562			−0.951536			−0.475768	−	0.879571i	$-0.657830\pi$
$727$	−25.6562			−0.951536			−0.475768	+	0.879571i	$0.657830\pi$
$728$	1.52594	+	5.98207i	0.0565551	+	0.221710i
$729$		0			0
$730$		0			0
$731$			15.8888i			0.587667i
$732$		0			0
$733$			30.3684i			1.12168i	0.827923	+	0.560842i	$0.189522\pi$
$733$			30.3684i			1.12168i	−0.827923	+	0.560842i	$0.810478\pi$
$734$	−27.4882	−	39.5945i	−1.01461	−	1.46146i
$735$		0			0
$736$	4.54222	−	42.1560i	0.167428	−	1.55389i
$737$	−39.9007			−1.46976
$738$		0			0
$739$			20.1917i			0.742763i	0.928480	+	0.371381i	$0.121116\pi$
$739$			20.1917i			0.742763i	−0.928480	+	0.371381i	$0.878884\pi$
$740$		0			0
$741$		0			0
$742$	6.69335	−	4.64681i	0.245720	−	0.170590i
$743$	−46.3863			−1.70175			−0.850875	−	0.525369i	$-0.823927\pi$
$743$	−46.3863			−1.70175			−0.850875	+	0.525369i	$0.823927\pi$
$744$		0			0
$745$		0			0
$746$	−5.03942	+	3.49858i	−0.184506	+	0.128092i
$747$		0			0
$748$	−21.4427	−	8.00000i	−0.784023	−	0.292509i
$749$			2.98470i			0.109059i
$750$		0			0
$751$	−27.1261			−0.989845			−0.494922	−	0.868937i	$-0.664804\pi$
$751$	−27.1261			−0.989845			−0.494922	+	0.868937i	$0.664804\pi$
$752$	5.24002	+	4.54222i	0.191084	+	0.165638i
$753$		0			0
$754$	−15.9225	−	22.9351i	−0.579863	−	0.835245i
$755$		0			0
$756$		0			0
$757$		−	45.2549i		−	1.64482i	−0.568898	−	0.822408i	$-0.692630\pi$
$757$		−	45.2549i		−	1.64482i	0.568898	−	0.822408i	$-0.307370\pi$
$758$	−8.01699	+	5.56574i	−0.291190	+	0.202157i
$759$		0			0
$760$		0			0
$761$	−16.8864			−0.612133			−0.306067	−	0.952010i	$-0.599013\pi$
$761$	−16.8864			−0.612133			−0.306067	+	0.952010i	$0.599013\pi$
$762$		0			0
$763$		−	14.8864i		−	0.538926i
$764$	4.81434	−	12.9041i	0.174177	−	0.466852i
$765$		0			0
$766$	18.0450	+	25.9924i	0.651993	+	0.939142i
$767$	20.0464			0.723835
$768$		0			0
$769$	16.3297			0.588863			0.294431	−	0.955673i	$-0.404870\pi$
$769$	16.3297			0.588863			0.294431	+	0.955673i	$0.404870\pi$
$770$		0			0
$771$		0			0
$772$	11.5233	−	30.8864i	0.414734	−	1.11163i
$773$			41.3144i			1.48598i	0.669304	+	0.742989i	$0.266592\pi$
$773$			41.3144i			1.48598i	−0.669304	+	0.742989i	$0.733408\pi$
$774$		0			0
$775$		0			0
$776$	−38.8864	+	9.91936i	−1.39594	+	0.356084i
$777$		0			0
$778$	12.8002	−	8.88645i	0.458909	−	0.318595i
$779$			19.5794i			0.701503i
$780$		0			0
$781$			71.2628i			2.54998i
$782$	−12.9041	−	18.5872i	−0.461448	−	0.664678i
$783$		0			0
$784$	19.4747	+	16.8813i	0.695525	+	0.602904i
$785$		0			0
$786$		0			0
$787$		−	11.4849i		−	0.409391i	−0.978826	−	0.204696i	$-0.934380\pi$
$787$		−	11.4849i		−	0.409391i	0.978826	−	0.204696i	$-0.0656205\pi$
$788$	−25.4317	−	9.48824i	−0.905966	−	0.338005i
$789$		0			0
$790$		0			0
$791$	−8.99440			−0.319804
$792$		0			0
$793$	18.8735			0.670216
$794$	29.3386	−	20.3681i	1.04119	−	0.722838i
$795$		0			0
$796$	−6.32967	+	16.9657i	−0.224349	+	0.601332i
$797$		−	45.4945i		−	1.61150i	−0.592257	−	0.805749i	$-0.701763\pi$
$797$		−	45.4945i		−	1.61150i	0.592257	−	0.805749i	$-0.298237\pi$
$798$		0			0
$799$	3.70079			0.130924
$800$		0			0
$801$		0			0
$802$	5.88233	+	8.47301i	0.207712	+	0.299192i
$803$			3.70079i			0.130598i
$804$		0			0
$805$		0			0
$806$	8.99440	−	6.24430i	0.316814	−	0.219946i
$807$		0			0
$808$	5.20100	+	20.3892i	0.182970	+	0.717291i
$809$	36.0721			1.26823			0.634114	−	0.773240i	$-0.281365\pi$
$809$	36.0721			1.26823			0.634114	+	0.773240i	$0.281365\pi$
$810$		0			0
$811$		−	44.5230i		−	1.56341i	−0.623646	−	0.781707i	$-0.714349\pi$
$811$		−	44.5230i		−	1.56341i	0.623646	−	0.781707i	$-0.285651\pi$
$812$	9.43673	+	3.52072i	0.331164	+	0.123553i
$813$		0			0
$814$	4.64681	+	6.69335i	0.162871	+	0.234602i
$815$		0			0
$816$		0			0
$817$	12.9041			0.451456
$818$	−12.7834	−	18.4134i	−0.446961	−	0.643811i
$819$		0			0
$820$		0			0
$821$			34.1613i			1.19224i	0.802897	+	0.596118i	$0.203291\pi$
$821$			34.1613i			1.19224i	−0.802897	+	0.596118i	$0.796709\pi$
$822$		0			0
$823$	−2.12689			−0.0741388			−0.0370694	−	0.999313i	$-0.511802\pi$
$823$	−2.12689			−0.0741388			−0.0370694	+	0.999313i	$0.511802\pi$
$824$	19.7279	−	5.03229i	0.687253	−	0.175308i
$825$		0			0
$826$	−5.94043	+	4.12410i	−0.206694	+	0.143496i
$827$		−	38.5872i		−	1.34181i	−0.741543	−	0.670905i	$-0.765906\pi$
$827$		−	38.5872i		−	1.34181i	0.741543	−	0.670905i	$-0.234094\pi$
$828$		0			0
$829$			34.2351i			1.18904i	0.804083	+	0.594518i	$0.202657\pi$
$829$			34.2351i			1.18904i	−0.804083	+	0.594518i	$0.797343\pi$
$830$		0			0
$831$		0			0
$832$	11.2094	+	20.5422i	0.388617	+	0.712173i
$833$	13.7541			0.476551
$834$		0			0
$835$		0			0
$836$	−6.49720	+	17.4147i	−0.224710	+	0.602300i
$837$		0			0
$838$	9.32384	−	6.47301i	0.322087	−	0.223606i
$839$	41.5928			1.43594			0.717972	−	0.696072i	$-0.245071\pi$
$839$	41.5928			1.43594			0.717972	+	0.696072i	$0.245071\pi$
$840$		0			0
$841$	−16.5512			−0.570730
$842$	26.6437	−	18.4972i	0.918202	−	0.637456i
$843$		0			0
$844$	−4.75140	−	1.77269i	−0.163550	−	0.0610184i
$845$		0			0
$846$		0			0
$847$	−13.2348			−0.454752
$848$	20.2307	−	23.3386i	0.694725	−	0.801452i
$849$		0			0
$850$		0			0
$851$			8.05601i			0.276156i
$852$		0			0
$853$		−	23.1828i		−	0.793763i	−0.917870	−	0.396881i	$-0.870092\pi$
$853$		−	23.1828i		−	0.793763i	0.917870	−	0.396881i	$-0.129908\pi$
$854$	−5.59283	+	3.88278i	−0.191383	+	0.132866i
$855$		0			0
$856$	2.79641	+	10.9627i	0.0955795	+	0.374696i
$857$	−9.38868			−0.320711			−0.160356	−	0.987059i	$-0.551264\pi$
$857$	−9.38868			−0.320711			−0.160356	+	0.987059i	$0.551264\pi$
$858$		0			0
$859$			8.98769i			0.306656i	0.988175	+	0.153328i	$0.0489991\pi$
$859$			8.98769i			0.306656i	−0.988175	+	0.153328i	$0.951001\pi$
$860$		0			0
$861$		0			0
$862$	−28.2813	−	40.7368i	−0.963264	−	1.38750i
$863$	12.2473			0.416903			0.208451	−	0.978033i	$-0.433158\pi$
$863$	12.2473			0.416903			0.208451	+	0.978033i	$0.433158\pi$
$864$		0			0
$865$		0			0
$866$	−13.7729	−	19.8387i	−0.468022	−	0.674147i
$867$		0			0
$868$	−1.38072	+	3.70079i	−0.0468646	+	0.125613i
$869$		−	14.1887i		−	0.481318i
$870$		0			0
$871$	21.7729			0.737746
$872$	−13.9474	−	54.6773i	−0.472317	−	1.85161i
$873$		0			0
$874$	−15.0956	+	10.4800i	−0.510617	+	0.354492i
$875$		0			0
$876$		0			0
$877$			26.1109i			0.881701i	0.897581	+	0.440850i	$0.145323\pi$
$877$			26.1109i			0.881701i	−0.897581	+	0.440850i	$0.854677\pi$
$878$	−6.88661	−	9.91960i	−0.232412	−	0.334770i
$879$		0			0
$880$		0			0
$881$	38.4793			1.29640			0.648200	−	0.761470i	$-0.275522\pi$
$881$	38.4793			1.29640			0.648200	+	0.761470i	$0.275522\pi$
$882$		0			0
$883$			6.58723i			0.221678i	0.993838	+	0.110839i	$0.0353538\pi$
$883$			6.58723i			0.221678i	−0.993838	+	0.110839i	$0.964646\pi$
$884$	11.7008	+	4.36542i	0.393540	+	0.146825i
$885$		0			0
$886$	−24.0900	+	16.7243i	−0.809320	+	0.561865i
$887$	−50.9595			−1.71105			−0.855526	−	0.517760i	$-0.826766\pi$
$887$	−50.9595			−1.71105			−0.855526	+	0.517760i	$0.826766\pi$
$888$		0			0
$889$	−3.14401			−0.105447
$890$		0			0
$891$		0			0
$892$	−8.49962	+	22.7819i	−0.284588	+	0.762793i
$893$		−	3.00560i		−	0.100578i
$894$		0			0
$895$		0			0
$896$	−7.54781	−	3.78126i	−0.252155	−	0.126323i
$897$		0			0
$898$	−1.61301	−	2.32340i	−0.0538268	−	0.0775330i
$899$		−	17.8637i		−	0.595789i
$900$		0			0
$901$		−	16.4830i		−	0.549129i
$902$	−70.3311	+	48.8269i	−2.34177	+	1.62576i
$903$		0			0
$904$	−33.0361	+	8.42701i	−1.09876	+	0.280278i
$905$		0			0
$906$		0			0
$907$		−	24.5568i		−	0.815394i	−0.913117	−	0.407697i	$-0.866332\pi$
$907$		−	24.5568i		−	0.815394i	0.913117	−	0.407697i	$-0.133668\pi$
$908$	38.8574	+	14.4972i	1.28953	+	0.481107i
$909$		0			0
$910$		0			0
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$	−31.3621			−1.03793
$914$	−1.03605	−	1.49235i	−0.0342696	−	0.0493625i
$915$		0			0
$916$	−37.3836	−	13.9474i	−1.23519	−	0.460834i
$917$		−	7.70079i		−	0.254302i
$918$		0			0
$919$	28.7548			0.948532			0.474266	−	0.880382i	$-0.342713\pi$
$919$	28.7548			0.948532			0.474266	+	0.880382i	$0.342713\pi$
$920$		0			0
$921$		0			0
$922$	−18.2425	+	12.6647i	−0.600785	+	0.417091i
$923$		−	38.8864i		−	1.27996i
$924$		0			0
$925$		0			0
$926$	−15.0990	−	21.7489i	−0.496184	−	0.714712i
$927$		0			0
$928$	37.9593	+	4.09003i	1.24608	+	0.134262i
$929$	−28.2880			−0.928100			−0.464050	−	0.885809i	$-0.653604\pi$
$929$	−28.2880			−0.928100			−0.464050	+	0.885809i	$0.653604\pi$
$930$		0			0
$931$		−	11.1704i		−	0.366095i
$932$	−9.32510	+	24.9944i	−0.305454	+	0.818719i
$933$		0			0
$934$	2.49720	−	1.73367i	0.0817110	−	0.0567273i
$935$		0			0
$936$		0			0
$937$	−33.9313			−1.10849			−0.554244	−	0.832354i	$-0.686992\pi$
$937$	−33.9313			−1.10849			−0.554244	+	0.832354i	$0.686992\pi$
$938$	−6.45203	+	4.47928i	−0.210666	+	0.146254i
$939$		0			0
$940$		0			0
$941$			38.8016i			1.26490i	0.774603	+	0.632448i	$0.217950\pi$
$941$			38.8016i			1.26490i	−0.774603	+	0.632448i	$0.782050\pi$
$942$		0			0
$943$	−84.6495			−2.75657
$944$	−17.9550	+	20.7133i	−0.584385	+	0.674161i
$945$		0			0
$946$	32.1801	+	46.3527i	1.04626	+	1.50706i
$947$		−	17.7729i		−	0.577541i	−0.957398	−	0.288771i	$-0.906753\pi$
$947$		−	17.7729i		−	0.577541i	0.957398	−	0.288771i	$-0.0932465\pi$
$948$		0			0
$949$		−	2.01943i		−	0.0655536i
$950$		0			0
$951$		0			0
$952$	−4.36542	+	1.11355i	−0.141484	+	0.0360905i
$953$	46.3047			1.49996			0.749978	−	0.661463i	$-0.230064\pi$
$953$	46.3047			1.49996			0.749978	+	0.661463i	$0.230064\pi$
$954$		0			0
$955$		0			0
$956$	16.0000	−	42.8854i	0.517477	−	1.38701i
$957$		0			0
$958$	−9.82327	−	14.1496i	−0.317375	−	0.457153i
$959$	−11.2215			−0.362361
$960$		0			0
$961$	−23.9944			−0.774013
$962$	−2.53566	−	3.65240i	−0.0817528	−	0.117758i
$963$		0			0
$964$	−2.51176	+	6.73237i	−0.0808984	+	0.216835i
$965$		0			0
$966$		0			0
$967$	9.28482			0.298580			0.149290	−	0.988793i	$-0.452301\pi$
$967$	9.28482			0.298580			0.149290	+	0.988793i	$0.452301\pi$
$968$	−48.6108	+	12.3999i	−1.56241	+	0.398548i
$969$		0			0
$970$		0			0
$971$		−	20.9301i		−	0.671678i	−0.941919	−	0.335839i	$-0.890980\pi$
$971$		−	20.9301i		−	0.671678i	0.941919	−	0.335839i	$-0.109020\pi$
$972$		0			0
$973$		−	7.06651i		−	0.226542i
$974$	−20.7819	−	29.9346i	−0.665894	−	0.959165i
$975$		0			0
$976$	−16.9044	+	19.5013i	−0.541096	+	0.624222i
$977$	30.8314			0.986383			0.493192	−	0.869921i	$-0.335830\pi$
$977$	30.8314			0.986383			0.493192	+	0.869921i	$0.335830\pi$
$978$		0			0
$979$			40.7027i			1.30086i
$980$		0			0
$981$		0			0
$982$	19.4845	−	13.5270i	0.621776	−	0.431664i
$983$	−31.3285			−0.999223			−0.499612	−	0.866250i	$-0.666524\pi$
$983$	−31.3285			−0.999223			−0.499612	+	0.866250i	$0.666524\pi$
$984$		0			0
$985$		0			0
$986$	16.7368	−	11.6194i	0.533010	−	0.370038i
$987$		0			0
$988$	3.54537	−	9.50280i	0.112793	−	0.302324i
$989$			55.7895i			1.77400i
$990$		0			0
$991$	31.3420			0.995611			0.497806	−	0.867289i	$-0.334139\pi$
$991$	31.3420			0.995611			0.497806	+	0.867289i	$0.334139\pi$
$992$	−1.60398	+	14.8864i	−0.0509265	+	0.472645i
$993$		0			0
$994$	8.00000	+	11.5233i	0.253745	+	0.365498i
$995$		0			0
$996$		0			0
$997$			20.9557i			0.663672i	0.943337	+	0.331836i	$0.107668\pi$
$997$			20.9557i			0.663672i	−0.943337	+	0.331836i	$0.892332\pi$
$998$	20.4720	−	14.2125i	0.648030	−	0.449890i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.u.901.3		12
3.2	odd	2		600.2.k.f.301.10		12
4.3	odd	2		7200.2.k.u.3601.6		12
5.2	odd	4		360.2.d.e.109.5		6
5.3	odd	4		360.2.d.f.109.2		6
5.4	even	2	inner	1800.2.k.u.901.10		12
8.3	odd	2		7200.2.k.u.3601.5		12
8.5	even	2	inner	1800.2.k.u.901.4		12
12.11	even	2		2400.2.k.f.1201.9		12
15.2	even	4		120.2.d.b.109.2	yes	6
15.8	even	4		120.2.d.a.109.5	✓	6
15.14	odd	2		600.2.k.f.301.3		12
20.3	even	4		1440.2.d.e.1009.5		6
20.7	even	4		1440.2.d.f.1009.1		6
20.19	odd	2		7200.2.k.u.3601.8		12
24.5	odd	2		600.2.k.f.301.9		12
24.11	even	2		2400.2.k.f.1201.3		12
40.3	even	4		1440.2.d.f.1009.2		6
40.13	odd	4		360.2.d.e.109.6		6
40.19	odd	2		7200.2.k.u.3601.7		12
40.27	even	4		1440.2.d.e.1009.6		6
40.29	even	2	inner	1800.2.k.u.901.9		12
40.37	odd	4		360.2.d.f.109.1		6
60.23	odd	4		480.2.d.a.49.2		6
60.47	odd	4		480.2.d.b.49.6		6
60.59	even	2		2400.2.k.f.1201.4		12
120.29	odd	2		600.2.k.f.301.4		12
120.53	even	4		120.2.d.b.109.1	yes	6
120.59	even	2		2400.2.k.f.1201.10		12
120.77	even	4		120.2.d.a.109.6	yes	6
120.83	odd	4		480.2.d.b.49.5		6
120.107	odd	4		480.2.d.a.49.1		6
240.53	even	4		3840.2.f.l.769.2		12
240.77	even	4		3840.2.f.l.769.5		12
240.83	odd	4		3840.2.f.m.769.5		12
240.107	odd	4		3840.2.f.m.769.2		12
240.173	even	4		3840.2.f.l.769.11		12
240.197	even	4		3840.2.f.l.769.8		12
240.203	odd	4		3840.2.f.m.769.8		12
240.227	odd	4		3840.2.f.m.769.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.5	✓	6	15.8	even	4
120.2.d.a.109.6	yes	6	120.77	even	4
120.2.d.b.109.1	yes	6	120.53	even	4
120.2.d.b.109.2	yes	6	15.2	even	4
360.2.d.e.109.5		6	5.2	odd	4
360.2.d.e.109.6		6	40.13	odd	4
360.2.d.f.109.1		6	40.37	odd	4
360.2.d.f.109.2		6	5.3	odd	4
480.2.d.a.49.1		6	120.107	odd	4
480.2.d.a.49.2		6	60.23	odd	4
480.2.d.b.49.5		6	120.83	odd	4
480.2.d.b.49.6		6	60.47	odd	4
600.2.k.f.301.3		12	15.14	odd	2
600.2.k.f.301.4		12	120.29	odd	2
600.2.k.f.301.9		12	24.5	odd	2
600.2.k.f.301.10		12	3.2	odd	2
1440.2.d.e.1009.5		6	20.3	even	4
1440.2.d.e.1009.6		6	40.27	even	4
1440.2.d.f.1009.1		6	20.7	even	4
1440.2.d.f.1009.2		6	40.3	even	4
1800.2.k.u.901.3		12	1.1	even	1	trivial
1800.2.k.u.901.4		12	8.5	even	2	inner
1800.2.k.u.901.9		12	40.29	even	2	inner
1800.2.k.u.901.10		12	5.4	even	2	inner
2400.2.k.f.1201.3		12	24.11	even	2
2400.2.k.f.1201.4		12	60.59	even	2
2400.2.k.f.1201.9		12	12.11	even	2
2400.2.k.f.1201.10		12	120.59	even	2
3840.2.f.l.769.2		12	240.53	even	4
3840.2.f.l.769.5		12	240.77	even	4
3840.2.f.l.769.8		12	240.197	even	4
3840.2.f.l.769.11		12	240.173	even	4
3840.2.f.m.769.2		12	240.107	odd	4
3840.2.f.m.769.5		12	240.83	odd	4
3840.2.f.m.769.8		12	240.203	odd	4
3840.2.f.m.769.11		12	240.227	odd	4
7200.2.k.u.3601.5		12	8.3	odd	2
7200.2.k.u.3601.6		12	4.3	odd	2
7200.2.k.u.3601.7		12	40.19	odd	2
7200.2.k.u.3601.8		12	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.806504 - 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} +0.746175 q^{7} +(2.74067 - 0.699104i) q^{8} +O(q^{10})\)	\(q+(-0.806504 - 1.16170i) q^{2} +(-0.699104 + 1.87383i) q^{4} +0.746175 q^{7} +(2.74067 - 0.699104i) q^{8} -5.36068i q^{11} +2.92520i q^{13} +(-0.601793 - 0.866833i) q^{14} +(-3.02251 - 2.62001i) q^{16} -2.13466 q^{17} +1.73367i q^{19} +(-6.22751 + 4.32340i) q^{22} -7.49534 q^{23} +(3.39821 - 2.35918i) q^{26} +(-0.521653 + 1.39821i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-0.606006 + 5.62430i) q^{32} +(1.72161 + 2.47984i) q^{34} -1.07480i q^{37} +(2.01400 - 1.39821i) q^{38} +11.2936 q^{41} -7.44322i q^{43} +(10.0450 + 3.74767i) q^{44} +(6.04502 + 8.70735i) q^{46} -1.73367 q^{47} -6.44322 q^{49} +(-5.48133 - 2.04502i) q^{52} +7.72161i q^{53} +(2.04502 - 0.521653i) q^{56} +(-7.84052 + 5.44322i) q^{58} -6.85302i q^{59} -6.45203i q^{61} +(-2.13466 - 3.07480i) q^{62} +(7.02251 - 3.83202i) q^{64} -7.44322i q^{67} +(1.49235 - 4.00000i) q^{68} -13.2936 q^{71} -0.690358 q^{73} +(-1.24860 + 0.866833i) q^{74} +(-3.24860 - 1.21201i) q^{76} -4.00000i q^{77} +2.64681 q^{79} +(-9.10834 - 13.1198i) q^{82} -5.85039i q^{83} +(-8.64681 + 6.00299i) q^{86} +(-3.74767 - 14.6918i) q^{88} -7.59283 q^{89} +2.18271i q^{91} +(5.24002 - 14.0450i) q^{92} +(1.39821 + 2.01400i) q^{94} -14.1887 q^{97} +(5.19648 + 7.48511i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{4}+O(q^{10}) \) 12 * q - 2 * q^4	\( 12 q - 2 q^{4} - 20 q^{14} + 2 q^{16} + 28 q^{26} - 32 q^{31} - 24 q^{34} + 8 q^{41} + 44 q^{44} - 4 q^{46} + 12 q^{49} - 52 q^{56} + 46 q^{64} - 32 q^{71} + 36 q^{74} + 12 q^{76} - 32 q^{79} - 40 q^{86} - 40 q^{89} + 4 q^{94}+O(q^{100}) \) 12 * q - 2 * q^4 - 20 * q^14 + 2 * q^16 + 28 * q^26 - 32 * q^31 - 24 * q^34 + 8 * q^41 + 44 * q^44 - 4 * q^46 + 12 * q^49 - 52 * q^56 + 46 * q^64 - 32 * q^71 + 36 * q^74 + 12 * q^76 - 32 * q^79 - 40 * q^86 - 40 * q^89 + 4 * q^94

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