LMFDB - Embedded newform 1800.2.b.g.251.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(251,1800)]

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([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1800.251");

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.b (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.14
Root			$-0.744612 + 0.556573i$ of defining polynomial
Character	$\chi$	$=$	1800.251
Dual form			1800.2.b.g.251.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} +3.02045i q^{7} +(-1.53610 - 2.37495i) q^{8} +O(q^{10})$	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} +3.02045i q^{7} +(-1.53610 - 2.37495i) q^{8} +3.62258i q^{11} +1.69614i q^{13} +(2.80042 + 3.22550i) q^{14} +(-3.84233 - 1.11198i) q^{16} +6.60421i q^{17} -5.12311 q^{19} +(3.35869 + 3.86852i) q^{22} -6.67026 q^{23} +(1.57258 + 1.81129i) q^{26} +(5.98107 + 0.848071i) q^{28} -6.82867 q^{29} -1.73642i q^{31} +(-5.13416 + 2.37495i) q^{32} +(6.12311 + 7.05256i) q^{34} -0.371834i q^{37} +(-5.47091 + 4.74990i) q^{38} +5.83095i q^{41} -5.24477 q^{43} +(7.17341 + 1.01714i) q^{44} +(-7.12311 + 6.18435i) q^{46} +0.525853 q^{47} -2.12311 q^{49} +(3.35869 + 0.476236i) q^{52} +10.0054 q^{53} +(7.17341 - 4.63972i) q^{56} +(-7.29226 + 6.33122i) q^{58} -4.86270i q^{59} +(-1.60993 - 1.85431i) q^{62} +(-3.28078 + 7.29634i) q^{64} +13.4347 q^{67} +(13.0776 + 1.85431i) q^{68} -2.45567 q^{71} +14.5845 q^{73} +(-0.344747 - 0.397078i) q^{74} +(-1.43845 + 10.1447i) q^{76} -10.9418 q^{77} -14.1051i q^{79} +(5.40618 + 6.22681i) q^{82} +5.79119i q^{83} +(-5.60083 + 4.86270i) q^{86} +(8.60345 - 5.56466i) q^{88} +10.2477i q^{89} -5.12311 q^{91} +(-1.87285 + 13.2084i) q^{92} +(0.561553 - 0.487546i) q^{94} +9.33976 q^{97} +(-2.26724 + 1.96844i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4}+O(q^{10}) $ 16 * q - 12 * q^4	$ 16 q - 12 q^{4} - 12 q^{16} - 16 q^{19} + 32 q^{34} - 48 q^{46} + 32 q^{49} - 36 q^{64} - 56 q^{76} - 16 q^{91} - 24 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 - 12 * q^16 - 16 * q^19 + 32 * q^34 - 48 * q^46 + 32 * q^49 - 36 * q^64 - 56 * q^76 - 16 * q^91 - 24 * 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 $

$2$	1.06789	−	0.927153i	0.755112	−	0.655596i
$2$	1.06789	−	0.927153i	0.755112	−	0.655596i
$3$		0			0
$3$		0			0
$4$	0.280776	−	1.98019i	0.140388	−	0.990097i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.02045i			1.14162i	0.821081	+	0.570811i	$0.193371\pi$
$7$			3.02045i			1.14162i	−0.821081	+	0.570811i	$0.806629\pi$
$8$	−1.53610	−	2.37495i	−0.543094	−	0.839672i
$9$		0			0
$10$		0			0
$11$			3.62258i			1.09225i	0.837704	+	0.546125i	$0.183898\pi$
$11$			3.62258i			1.09225i	−0.837704	+	0.546125i	$0.816102\pi$
$12$		0			0
$13$			1.69614i			0.470425i	0.971944	+	0.235212i	$0.0755786\pi$
$13$			1.69614i			0.470425i	−0.971944	+	0.235212i	$0.924421\pi$
$14$	2.80042	+	3.22550i	0.748443	+	0.862052i
$15$		0			0
$16$	−3.84233	−	1.11198i	−0.960582	−	0.277996i
$17$			6.60421i			1.60176i	0.598828	+	0.800878i	$0.295633\pi$
$17$			6.60421i			1.60176i	−0.598828	+	0.800878i	$0.704367\pi$
$18$		0			0
$19$	−5.12311			−1.17532			−0.587661	−	0.809108i	$-0.699951\pi$
$19$	−5.12311			−1.17532			−0.587661	+	0.809108i	$0.699951\pi$
$20$		0			0
$21$		0			0
$22$	3.35869	+	3.86852i	0.716074	+	0.824771i
$23$	−6.67026			−1.39085			−0.695423	−	0.718601i	$-0.744783\pi$
$23$	−6.67026			−1.39085			−0.695423	+	0.718601i	$0.744783\pi$
$24$		0			0
$25$		0			0
$26$	1.57258	+	1.81129i	0.308409	+	0.355223i
$27$		0			0
$28$	5.98107	+	0.848071i	1.13032	+	0.160270i
$29$	−6.82867			−1.26805			−0.634026	−	0.773312i	$-0.718599\pi$
$29$	−6.82867			−1.26805			−0.634026	+	0.773312i	$0.718599\pi$
$30$		0			0
$31$		−	1.73642i		−	0.311870i	−0.987767	−	0.155935i	$-0.950161\pi$
$31$		−	1.73642i		−	0.311870i	0.987767	−	0.155935i	$-0.0498391\pi$
$32$	−5.13416	+	2.37495i	−0.907600	+	0.419836i
$33$		0			0
$34$	6.12311	+	7.05256i	1.05010	+	1.20950i
$35$		0			0
$36$		0			0
$37$		−	0.371834i		−	0.0611292i	−0.999533	−	0.0305646i	$-0.990269\pi$
$37$		−	0.371834i		−	0.0611292i	0.999533	−	0.0305646i	$-0.00973052\pi$
$38$	−5.47091	+	4.74990i	−0.887499	+	0.770536i
$39$		0			0
$40$		0			0
$41$			5.83095i			0.910642i	0.890327	+	0.455321i	$0.150475\pi$
$41$			5.83095i			0.910642i	−0.890327	+	0.455321i	$0.849525\pi$
$42$		0			0
$43$	−5.24477			−0.799819			−0.399910	−	0.916555i	$-0.630959\pi$
$43$	−5.24477			−0.799819			−0.399910	+	0.916555i	$0.630959\pi$
$44$	7.17341	+	1.01714i	1.08143	+	0.153339i
$45$		0			0
$46$	−7.12311	+	6.18435i	−1.05024	+	0.911833i
$47$	0.525853			0.0767035			0.0383518	−	0.999264i	$-0.487789\pi$
$47$	0.525853			0.0767035			0.0383518	+	0.999264i	$0.487789\pi$
$48$		0			0
$49$	−2.12311			−0.303301
$50$		0			0
$51$		0			0
$52$	3.35869	+	0.476236i	0.465766	+	0.0660421i
$53$	10.0054			1.37435			0.687173	−	0.726493i	$-0.258851\pi$
$53$	10.0054			1.37435			0.687173	+	0.726493i	$0.258851\pi$
$54$		0			0
$55$		0			0
$56$	7.17341	−	4.63972i	0.958588	−	0.620008i
$57$		0			0
$58$	−7.29226	+	6.33122i	−0.957521	+	0.831329i
$59$		−	4.86270i		−	0.633069i	−0.948581	−	0.316535i	$-0.897481\pi$
$59$		−	4.86270i		−	0.633069i	0.948581	−	0.316535i	$-0.102519\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−1.60993	−	1.85431i	−0.204461	−	0.235497i
$63$		0			0
$64$	−3.28078	+	7.29634i	−0.410097	+	0.912042i
$65$		0			0
$66$		0			0
$67$	13.4347			1.64132			0.820658	−	0.571420i	$-0.193607\pi$
$67$	13.4347			1.64132			0.820658	+	0.571420i	$0.193607\pi$
$68$	13.0776	+	1.85431i	1.58589	+	0.224868i
$69$		0			0
$70$		0			0
$71$	−2.45567			−0.291434			−0.145717	−	0.989326i	$-0.546549\pi$
$71$	−2.45567			−0.291434			−0.145717	+	0.989326i	$0.546549\pi$
$72$		0			0
$73$	14.5845			1.70699			0.853495	−	0.521102i	$-0.174479\pi$
$73$	14.5845			1.70699			0.853495	+	0.521102i	$0.174479\pi$
$74$	−0.344747	−	0.397078i	−0.0400760	−	0.0461594i
$75$		0			0
$76$	−1.43845	+	10.1447i	−0.165001	+	1.16368i
$77$	−10.9418			−1.24694
$78$		0			0
$79$		−	14.1051i		−	1.58695i	−0.608603	−	0.793475i	$-0.708270\pi$
$79$		−	14.1051i		−	1.58695i	0.608603	−	0.793475i	$-0.291730\pi$
$80$		0			0
$81$		0			0
$82$	5.40618	+	6.22681i	0.597013	+	0.687636i
$83$			5.79119i			0.635666i	0.948147	+	0.317833i	$0.102955\pi$
$83$			5.79119i			0.635666i	−0.948147	+	0.317833i	$0.897045\pi$
$84$		0			0
$85$		0			0
$86$	−5.60083	+	4.86270i	−0.603953	+	0.524358i
$87$		0			0
$88$	8.60345	−	5.56466i	0.917131	−	0.593195i
$89$			10.2477i			1.08625i	0.839651	+	0.543126i	$0.182760\pi$
$89$			10.2477i			1.08625i	−0.839651	+	0.543126i	$0.817240\pi$
$90$		0			0
$91$	−5.12311			−0.537047
$92$	−1.87285	+	13.2084i	−0.195258	+	1.37707i
$93$		0			0
$94$	0.561553	−	0.487546i	0.0579198	−	0.0502865i
$95$		0			0
$96$		0			0
$97$	9.33976			0.948309			0.474154	−	0.880442i	$-0.342754\pi$
$97$	9.33976			0.948309			0.474154	+	0.880442i	$0.342754\pi$
$98$	−2.26724	+	1.96844i	−0.229026	+	0.198843i
$99$		0			0
$100$		0			0
$101$	−4.37300			−0.435129			−0.217565	−	0.976046i	$-0.569811\pi$
$101$	−4.37300			−0.435129			−0.217565	+	0.976046i	$0.569811\pi$
$102$		0			0
$103$			8.31768i			0.819565i	0.912183	+	0.409782i	$0.134395\pi$
$103$			8.31768i			0.819565i	−0.912183	+	0.409782i	$0.865605\pi$
$104$	4.02825	−	2.60545i	0.395002	−	0.255485i
$105$		0			0
$106$	10.6847	−	9.27653i	1.03779	−	0.901016i
$107$		−	7.41722i		−	0.717050i	−0.933520	−	0.358525i	$-0.883280\pi$
$107$		−	7.41722i		−	0.717050i	0.933520	−	0.358525i	$-0.116720\pi$
$108$		0			0
$109$		−	9.65719i		−	0.924991i	−0.886622	−	0.462496i	$-0.846954\pi$
$109$		−	9.65719i		−	0.924991i	0.886622	−	0.462496i	$-0.153046\pi$
$110$		0			0
$111$		0			0
$112$	3.35869	−	11.6056i	0.317366	−	1.09662i
$113$			0.813015i			0.0764820i	0.999269	+	0.0382410i	$0.0121755\pi$
$113$			0.813015i			0.0764820i	−0.999269	+	0.0382410i	$0.987825\pi$
$114$		0			0
$115$		0			0
$116$	−1.91733	+	13.5221i	−0.178019	+	1.25549i
$117$		0			0
$118$	−4.50846	−	5.19283i	−0.415038	−	0.478038i
$119$	−19.9477			−1.82860
$120$		0			0
$121$	−2.12311			−0.193010
$122$		0			0
$123$		0			0
$124$	−3.43845	−	0.487546i	−0.308782	−	0.0437829i
$125$		0			0
$126$		0			0
$127$			15.1022i			1.34011i	0.742313	+	0.670054i	$0.233729\pi$
$127$			15.1022i			1.34011i	−0.742313	+	0.670054i	$0.766271\pi$
$128$	3.26131	+	10.8335i	0.288262	+	0.957552i
$129$		0			0
$130$		0			0
$131$		−	6.45101i		−	0.563627i	−0.959469	−	0.281814i	$-0.909064\pi$
$131$		−	6.45101i		−	0.563627i	0.959469	−	0.281814i	$-0.0909360\pi$
$132$		0			0
$133$		−	15.4741i		−	1.34177i
$134$	14.3468	−	12.4561i	1.23938	−	1.07604i
$135$		0			0
$136$	15.6847	−	10.1447i	1.34495	−	0.869904i
$137$			6.60421i			0.564235i	0.959380	+	0.282118i	$0.0910369\pi$
$137$			6.60421i			0.564235i	−0.959380	+	0.282118i	$0.908963\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$		0			0
$142$	−2.62238	+	2.27678i	−0.220066	+	0.191063i
$143$	−6.14441			−0.513821
$144$		0			0
$145$		0			0
$146$	15.5747	−	13.5221i	1.28897	−	1.11910i
$147$		0			0
$148$	−0.736303	−	0.104402i	−0.0605238	−	0.00858181i
$149$	−15.5747			−1.27593			−0.637963	−	0.770067i	$-0.720223\pi$
$149$	−15.5747			−1.27593			−0.637963	+	0.770067i	$0.720223\pi$
$150$		0			0
$151$		−	10.6323i		−	0.865243i	−0.901576	−	0.432622i	$-0.857589\pi$
$151$		−	10.6323i		−	0.865243i	0.901576	−	0.432622i	$-0.142411\pi$
$152$	7.86962	+	12.1671i	0.638310	+	0.986884i
$153$		0			0
$154$	−11.6847	+	10.1447i	−0.941577	+	0.817486i
$155$		0			0
$156$		0			0
$157$		−	9.06134i		−	0.723174i	−0.932338	−	0.361587i	$-0.882235\pi$
$157$		−	9.06134i		−	0.723174i	0.932338	−	0.361587i	$-0.117765\pi$
$158$	−13.0776	−	15.0627i	−1.04040	−	1.19833i
$159$		0			0
$160$		0			0
$161$		−	20.1472i		−	1.58782i
$162$		0			0
$163$	−10.4895			−0.821604			−0.410802	−	0.911725i	$-0.634751\pi$
$163$	−10.4895			−0.821604			−0.410802	+	0.911725i	$0.634751\pi$
$164$	11.5464	+	1.63719i	0.901623	+	0.127843i
$165$		0			0
$166$	5.36932	+	6.18435i	0.416740	+	0.479999i
$167$	−4.79741			−0.371235			−0.185617	−	0.982622i	$-0.559429\pi$
$167$	−4.79741			−0.371235			−0.185617	+	0.982622i	$0.559429\pi$
$168$		0			0
$169$	10.1231			0.778700
$170$		0			0
$171$		0			0
$172$	−1.47261	+	10.3857i	−0.112285	+	0.791898i
$173$	−3.33513			−0.253565			−0.126783	−	0.991931i	$-0.540465\pi$
$173$	−3.33513			−0.253565			−0.126783	+	0.991931i	$0.540465\pi$
$174$		0			0
$175$		0			0
$176$	4.02825	−	13.9192i	0.303641	−	1.04920i
$177$		0			0
$178$	9.50117	+	10.9434i	0.712143	+	0.820243i
$179$			20.9413i			1.56523i	0.622506	+	0.782615i	$0.286114\pi$
$179$			20.9413i			1.56523i	−0.622506	+	0.782615i	$0.713886\pi$
$180$		0			0
$181$		−	6.18435i		−	0.459679i	−0.973229	−	0.229840i	$-0.926180\pi$
$181$		−	6.18435i		−	0.459679i	0.973229	−	0.229840i	$-0.0738202\pi$
$182$	−5.47091	+	4.74990i	−0.405531	+	0.352086i
$183$		0			0
$184$	10.2462	+	15.8415i	0.755361	+	1.16785i
$185$		0			0
$186$		0			0
$187$	−23.9243			−1.74952
$188$	0.147647	−	1.04129i	0.0107683	−	0.0759439i
$189$		0			0
$190$		0			0
$191$	−17.4920			−1.26568			−0.632838	−	0.774284i	$-0.718110\pi$
$191$	−17.4920			−1.26568			−0.632838	+	0.774284i	$0.718110\pi$
$192$		0			0
$193$	15.7343			1.13258			0.566290	−	0.824206i	$-0.308378\pi$
$193$	15.7343			1.13258			0.566290	+	0.824206i	$0.308378\pi$
$194$	9.97383	−	8.65938i	0.716079	−	0.621707i
$195$		0			0
$196$	−0.596118	+	4.20416i	−0.0425799	+	0.300297i
$197$	24.6929			1.75930			0.879649	−	0.475623i	$-0.157777\pi$
$197$	24.6929			1.75930			0.879649	+	0.475623i	$0.157777\pi$
$198$		0			0
$199$			10.6323i			0.753703i	0.926274	+	0.376851i	$0.122993\pi$
$199$			10.6323i			0.753703i	−0.926274	+	0.376851i	$0.877007\pi$
$200$		0			0
$201$		0			0
$202$	−4.66988	+	4.05444i	−0.328571	+	0.285269i
$203$		−	20.6256i		−	1.44764i
$204$		0			0
$205$		0			0
$206$	7.71175	+	8.88236i	0.537303	+	0.618863i
$207$		0			0
$208$	1.88608	−	6.51713i	0.130776	−	0.451882i
$209$		−	18.5589i		−	1.28374i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	2.80928	−	19.8126i	0.192942	−	1.36074i
$213$		0			0
$214$	−6.87689	−	7.92077i	−0.470095	−	0.541453i
$215$		0			0
$216$		0			0
$217$	5.24477			0.356038
$218$	−8.95369	−	10.3128i	−0.606420	−	0.698472i
$219$		0			0
$220$		0			0
$221$	−11.2017			−0.753505
$222$		0			0
$223$			28.6714i			1.91998i	0.280040	+	0.959988i	$0.409652\pi$
$223$			28.6714i			1.91998i	−0.280040	+	0.959988i	$0.590348\pi$
$224$	−7.17341	−	15.5075i	−0.479294	−	1.03614i
$225$		0			0
$226$	0.753789	+	0.868210i	0.0501413	+	0.0577525i
$227$			13.2084i			0.876673i	0.898811	+	0.438337i	$0.144432\pi$
$227$			13.2084i			0.876673i	−0.898811	+	0.438337i	$0.855568\pi$
$228$		0			0
$229$		−	22.0259i		−	1.45551i	−0.685836	−	0.727756i	$-0.740563\pi$
$229$		−	22.0259i		−	1.45551i	0.685836	−	0.727756i	$-0.259437\pi$
$230$		0			0
$231$		0			0
$232$	10.4895	+	16.2177i	0.688672	+	1.06475i
$233$			21.4386i			1.40449i	0.711934	+	0.702246i	$0.247819\pi$
$233$			21.4386i			1.40449i	−0.711934	+	0.702246i	$0.752181\pi$
$234$		0			0
$235$		0			0
$236$	−9.62908	−	1.36533i	−0.626800	−	0.0888755i
$237$		0			0
$238$	−21.3019	+	18.4945i	−1.38080	+	1.19882i
$239$	−4.91134			−0.317688			−0.158844	−	0.987304i	$-0.550777\pi$
$239$	−4.91134			−0.317688			−0.158844	+	0.987304i	$0.550777\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$	−2.26724	+	1.96844i	−0.145744	+	0.126536i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	8.68951i		−	0.552900i
$248$	−4.12391	+	2.66732i	−0.261869	+	0.169375i
$249$		0			0
$250$		0			0
$251$		−	9.27944i		−	0.585713i	−0.956156	−	0.292856i	$-0.905394\pi$
$251$		−	9.27944i		−	0.585713i	0.956156	−	0.292856i	$-0.0946058\pi$
$252$		0			0
$253$		−	24.1636i		−	1.51915i
$254$	14.0021	+	16.1275i	0.878569	+	1.01193i
$255$		0			0
$256$	13.5270	+	8.54521i	0.845437	+	0.534076i
$257$		−	12.3954i		−	0.773204i	−0.922247	−	0.386602i	$-0.873649\pi$
$257$		−	12.3954i		−	0.773204i	0.922247	−	0.386602i	$-0.126351\pi$
$258$		0			0
$259$	1.12311			0.0697864
$260$		0			0
$261$		0			0
$262$	−5.98107	−	6.88897i	−0.369512	−	0.425602i
$263$	−12.2888			−0.757761			−0.378881	−	0.925446i	$-0.623691\pi$
$263$	−12.2888			−0.757761			−0.378881	+	0.925446i	$0.623691\pi$
$264$		0			0
$265$		0			0
$266$	−14.3468	−	16.5246i	−0.879660	−	1.01319i
$267$		0			0
$268$	3.77216	−	26.6034i	0.230421	−	1.62506i
$269$	−1.91733			−0.116902			−0.0584508	−	0.998290i	$-0.518616\pi$
$269$	−1.91733			−0.116902			−0.0584508	+	0.998290i	$0.518616\pi$
$270$		0			0
$271$			26.4738i			1.60817i	0.594514	+	0.804085i	$0.297344\pi$
$271$			26.4738i			1.60817i	−0.594514	+	0.804085i	$0.702656\pi$
$272$	7.34376	−	25.3755i	0.445281	−	1.53862i
$273$		0			0
$274$	6.12311	+	7.05256i	0.369910	+	0.426061i
$275$		0			0
$276$		0			0
$277$			11.8730i			0.713379i	0.934223	+	0.356689i	$0.116095\pi$
$277$			11.8730i			0.713379i	−0.934223	+	0.356689i	$0.883905\pi$
$278$	12.8147	−	11.1258i	0.768573	−	0.667283i
$279$		0			0
$280$		0			0
$281$			8.65938i			0.516575i	0.966068	+	0.258288i	$0.0831582\pi$
$281$			8.65938i			0.516575i	−0.966068	+	0.258288i	$0.916842\pi$
$282$		0			0
$283$	−15.7343			−0.935307			−0.467654	−	0.883912i	$-0.654900\pi$
$283$	−15.7343			−0.935307			−0.467654	+	0.883912i	$0.654900\pi$
$284$	−0.689494	+	4.86270i	−0.0409139	+	0.288548i
$285$		0			0
$286$	−6.56155	+	5.69681i	−0.387993	+	0.336859i
$287$	−17.6121			−1.03961
$288$		0			0
$289$	−26.6155			−1.56562
$290$		0			0
$291$		0			0
$292$	4.09499	−	28.8802i	0.239641	−	1.69008i
$293$	16.9710			0.991454			0.495727	−	0.868478i	$-0.334902\pi$
$293$	16.9710			0.991454			0.495727	+	0.868478i	$0.334902\pi$
$294$		0			0
$295$		0			0
$296$	−0.883088	+	0.571175i	−0.0513284	+	0.0331989i
$297$		0			0
$298$	−16.6320	+	14.4401i	−0.963467	+	0.836492i
$299$		−	11.3137i		−	0.654289i
$300$		0			0
$301$		−	15.8415i		−	0.913091i
$302$	−9.85775	−	11.3541i	−0.567250	−	0.653355i
$303$		0			0
$304$	19.6847	+	5.69681i	1.12899	+	0.326734i
$305$		0			0
$306$		0			0
$307$	−18.6795			−1.06610			−0.533048	−	0.846085i	$-0.678954\pi$
$307$	−18.6795			−1.06610			−0.533048	+	0.846085i	$0.678954\pi$
$308$	−3.07221	+	21.6669i	−0.175055	+	1.23459i
$309$		0			0
$310$		0			0
$311$	22.4033			1.27038			0.635188	−	0.772358i	$-0.280923\pi$
$311$	22.4033			1.27038			0.635188	+	0.772358i	$0.280923\pi$
$312$		0			0
$313$	−21.6247			−1.22230			−0.611151	−	0.791514i	$-0.709293\pi$
$313$	−21.6247			−1.22230			−0.611151	+	0.791514i	$0.709293\pi$
$314$	−8.40125	−	9.67651i	−0.474110	−	0.546077i
$315$		0			0
$316$	−27.9309	−	3.96039i	−1.57123	−	0.222789i
$317$	0.115279			0.00647473			0.00323737	−	0.999995i	$-0.498970\pi$
$317$	0.115279			0.00647473			0.00323737	+	0.999995i	$0.498970\pi$
$318$		0			0
$319$		−	24.7374i		−	1.38503i
$320$		0			0
$321$		0			0
$322$	−18.6795	−	21.5150i	−1.04097	−	1.19898i
$323$		−	33.8340i		−	1.88258i
$324$		0			0
$325$		0			0
$326$	−11.2017	+	9.72540i	−0.620403	+	0.538640i
$327$		0			0
$328$	13.8482	−	8.95694i	0.764640	−	0.494564i
$329$			1.58831i			0.0875664i
$330$		0			0
$331$	23.3693			1.28449			0.642247	−	0.766498i	$-0.278002\pi$
$331$	23.3693			1.28449			0.642247	+	0.766498i	$0.278002\pi$
$332$	11.4677	+	1.62603i	0.629370	+	0.0892400i
$333$		0			0
$334$	−5.12311	+	4.44793i	−0.280324	+	0.243380i
$335$		0			0
$336$		0			0
$337$	−12.2850			−0.669205			−0.334602	−	0.942359i	$-0.608602\pi$
$337$	−12.2850			−0.669205			−0.334602	+	0.942359i	$0.608602\pi$
$338$	10.8104	−	9.38566i	0.588006	−	0.510513i
$339$		0			0
$340$		0			0
$341$	6.29033			0.340640
$342$		0			0
$343$			14.7304i			0.795367i
$344$	8.05650	+	12.4561i	0.434377	+	0.671586i
$345$		0			0
$346$	−3.56155	+	3.09218i	−0.191470	+	0.166236i
$347$		−	5.79119i		−	0.310887i	−0.987845	−	0.155444i	$-0.950319\pi$
$347$		−	5.79119i		−	0.310887i	0.987845	−	0.155444i	$-0.0496807\pi$
$348$		0			0
$349$			6.94568i			0.371794i	0.982569	+	0.185897i	$0.0595190\pi$
$349$			6.94568i			0.371794i	−0.982569	+	0.185897i	$0.940481\pi$
$350$		0			0
$351$		0			0
$352$	−8.60345	−	18.5989i	−0.458566	−	0.991326i
$353$			33.0210i			1.75753i	0.477253	+	0.878766i	$0.341633\pi$
$353$			33.0210i			1.75753i	−0.477253	+	0.878766i	$0.658367\pi$
$354$		0			0
$355$		0			0
$356$	20.2924	+	2.87731i	1.07550	+	0.152497i
$357$		0			0
$358$	19.4158	+	22.3630i	1.02616	+	1.18192i
$359$	−19.9477			−1.05280			−0.526399	−	0.850238i	$-0.676458\pi$
$359$	−19.9477			−1.05280			−0.526399	+	0.850238i	$0.676458\pi$
$360$		0			0
$361$	7.24621			0.381380
$362$	−5.73384	−	6.60421i	−0.301364	−	0.347109i
$363$		0			0
$364$	−1.43845	+	10.1447i	−0.0753951	+	0.531729i
$365$		0			0
$366$		0			0
$367$		−	19.9819i		−	1.04304i	−0.853238	−	0.521522i	$-0.825364\pi$
$367$		−	19.9819i		−	1.04304i	0.853238	−	0.521522i	$-0.174636\pi$
$368$	25.6294	+	7.41722i	1.33602	+	0.386649i
$369$		0			0
$370$		0			0
$371$			30.2208i			1.56898i
$372$		0			0
$373$		−	5.66906i		−	0.293533i	−0.989171	−	0.146766i	$-0.953113\pi$
$373$		−	5.66906i		−	0.293533i	0.989171	−	0.146766i	$-0.0468866\pi$
$374$	−25.5485	+	22.1815i	−1.32108	+	1.14698i
$375$		0			0
$376$	−0.807764	−	1.24887i	−0.0416573	−	0.0644058i
$377$		−	11.5824i		−	0.596523i
$378$		0			0
$379$	−16.4924			−0.847159			−0.423579	−	0.905859i	$-0.639227\pi$
$379$	−16.4924			−0.847159			−0.423579	+	0.905859i	$0.639227\pi$
$380$		0			0
$381$		0			0
$382$	−18.6795	+	16.2177i	−0.955727	+	0.829772i
$383$	14.6875			0.750498			0.375249	−	0.926924i	$-0.377557\pi$
$383$	14.6875			0.750498			0.375249	+	0.926924i	$0.377557\pi$
$384$		0			0
$385$		0			0
$386$	16.8025	−	14.5881i	0.855224	−	0.742515i
$387$		0			0
$388$	2.62238	−	18.4945i	0.133131	−	0.938917i
$389$	13.1190			0.665159			0.332580	−	0.943075i	$-0.392081\pi$
$389$	13.1190			0.665159			0.332580	+	0.943075i	$0.392081\pi$
$390$		0			0
$391$		−	44.0518i		−	2.22779i
$392$	3.26131	+	5.04227i	0.164721	+	0.254673i
$393$		0			0
$394$	26.3693	−	22.8941i	1.32847	−	1.15339i
$395$		0			0
$396$		0			0
$397$		−	33.2249i		−	1.66751i	−0.552134	−	0.833756i	$-0.686186\pi$
$397$		−	33.2249i		−	1.66751i	0.552134	−	0.833756i	$-0.313814\pi$
$398$	9.85775	+	11.3541i	0.494124	+	0.569130i
$399$		0			0
$400$		0			0
$401$			34.4634i			1.72102i	0.509433	+	0.860510i	$0.329855\pi$
$401$			34.4634i			1.72102i	−0.509433	+	0.860510i	$0.670145\pi$
$402$		0			0
$403$	2.94521			0.146712
$404$	−1.22783	+	8.65938i	−0.0610870	+	0.430820i
$405$		0			0
$406$	−19.1231	−	22.0259i	−0.949064	−	1.09313i
$407$	1.34700			0.0667683
$408$		0			0
$409$	5.12311			0.253321			0.126661	−	0.991946i	$-0.459574\pi$
$409$	5.12311			0.253321			0.126661	+	0.991946i	$0.459574\pi$
$410$		0			0
$411$		0			0
$412$	16.4706	+	2.33541i	0.811448	+	0.115057i
$413$	14.6875			0.722726
$414$		0			0
$415$		0			0
$416$	−4.02825	−	8.70826i	−0.197501	−	0.426958i
$417$		0			0
$418$	−17.2069	−	19.8188i	−0.841617	−	0.969371i
$419$		−	8.38752i		−	0.409757i	−0.978787	−	0.204878i	$-0.934320\pi$
$419$		−	8.38752i		−	0.409757i	0.978787	−	0.204878i	$-0.0656799\pi$
$420$		0			0
$421$			15.0802i			0.734965i	0.930030	+	0.367482i	$0.119780\pi$
$421$			15.0802i			0.734965i	−0.930030	+	0.367482i	$0.880220\pi$
$422$	4.27156	−	3.70861i	0.207936	−	0.180532i
$423$		0			0
$424$	−15.3693	−	23.7623i	−0.746400	−	1.15400i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−14.6875	−	2.08258i	−0.709948	−	0.100665i
$429$		0			0
$430$		0			0
$431$	−19.9477			−0.960845			−0.480422	−	0.877037i	$-0.659517\pi$
$431$	−19.9477			−0.960845			−0.480422	+	0.877037i	$0.659517\pi$
$432$		0			0
$433$	10.4895			0.504095			0.252047	−	0.967715i	$-0.418896\pi$
$433$	10.4895			0.504095			0.252047	+	0.967715i	$0.418896\pi$
$434$	5.60083	−	4.86270i	0.268849	−	0.233417i
$435$		0			0
$436$	−19.1231	−	2.71151i	−0.915831	−	0.129858i
$437$	34.1725			1.63469
$438$		0			0
$439$			23.0010i			1.09778i	0.835895	+	0.548889i	$0.184949\pi$
$439$			23.0010i			1.09778i	−0.835895	+	0.548889i	$0.815051\pi$
$440$		0			0
$441$		0			0
$442$	−11.9621	+	10.3857i	−0.568981	+	0.493995i
$443$		−	1.62603i		−	0.0772550i	−0.999254	−	0.0386275i	$-0.987701\pi$
$443$		−	1.62603i		−	0.0772550i	0.999254	−	0.0386275i	$-0.0122986\pi$
$444$		0			0
$445$		0			0
$446$	26.5827	+	30.6179i	1.25873	+	1.44980i
$447$		0			0
$448$	−22.0382	−	9.90941i	−1.04121	−	0.468176i
$449$			9.89949i			0.467186i	0.972334	+	0.233593i	$0.0750483\pi$
$449$			9.89949i			0.467186i	−0.972334	+	0.233593i	$0.924952\pi$
$450$		0			0
$451$	−21.1231			−0.994648
$452$	1.60993	+	0.228275i	0.0757246	+	0.0107372i
$453$		0			0
$454$	12.2462	+	14.1051i	0.574743	+	0.661986i
$455$		0			0
$456$		0			0
$457$	19.8293			0.927575			0.463788	−	0.885946i	$-0.346490\pi$
$457$	19.8293			0.927575			0.463788	+	0.885946i	$0.346490\pi$
$458$	−20.4214	−	23.5212i	−0.954228	−	1.09907i
$459$		0			0
$460$		0			0
$461$	15.5747			0.725384			0.362692	−	0.931909i	$-0.381858\pi$
$461$	15.5747			0.725384			0.362692	+	0.931909i	$0.381858\pi$
$462$		0			0
$463$		−	17.7509i		−	0.824952i	−0.910968	−	0.412476i	$-0.864664\pi$
$463$		−	17.7509i		−	0.824952i	0.910968	−	0.412476i	$-0.135336\pi$
$464$	26.2380	+	7.59336i	1.21807	+	0.352513i
$465$		0			0
$466$	19.8769	+	22.8941i	0.920779	+	1.06055i
$467$		−	28.0429i		−	1.29767i	−0.760930	−	0.648834i	$-0.775257\pi$
$467$		−	28.0429i		−	1.29767i	0.760930	−	0.648834i	$-0.224743\pi$
$468$		0			0
$469$			40.5790i			1.87376i
$470$		0			0
$471$		0			0
$472$	−11.5487	+	7.46960i	−0.531570	+	0.343816i
$473$		−	18.9996i		−	0.873603i
$474$		0			0
$475$		0			0
$476$	−5.60083	+	39.5002i	−0.256714	+	1.81049i
$477$		0			0
$478$	−5.24477	+	4.55356i	−0.239890	+	0.208275i
$479$	37.4396			1.71066			0.855331	−	0.518083i	$-0.173354\pi$
$479$	37.4396			1.71066			0.855331	+	0.518083i	$0.173354\pi$
$480$		0			0
$481$	0.630683			0.0287567
$482$	−4.27156	+	3.70861i	−0.194564	+	0.168923i
$483$		0			0
$484$	−0.596118	+	4.20416i	−0.0270963	+	0.191098i
$485$		0			0
$486$		0			0
$487$			4.50778i			0.204267i	0.994771	+	0.102134i	$0.0325669\pi$
$487$			4.50778i			0.204267i	−0.994771	+	0.102134i	$0.967433\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	10.5196i		−	0.474741i	−0.971419	−	0.237370i	$-0.923714\pi$
$491$		−	10.5196i		−	0.474741i	0.971419	−	0.237370i	$-0.0762855\pi$
$492$		0			0
$493$		−	45.0979i		−	2.03111i
$494$	−8.05650	−	9.27944i	−0.362479	−	0.417502i
$495$		0			0
$496$	−1.93087	+	6.67190i	−0.0866986	+	0.299577i
$497$		−	7.41722i		−	0.332708i
$498$		0			0
$499$	−25.1231			−1.12466			−0.562332	−	0.826911i	$-0.690096\pi$
$499$	−25.1231			−1.12466			−0.562332	+	0.826911i	$0.690096\pi$
$500$		0			0
$501$		0			0
$502$	−8.60345	−	9.90941i	−0.383991	−	0.442279i
$503$	−16.5604			−0.738391			−0.369195	−	0.929352i	$-0.620367\pi$
$503$	−16.5604			−0.738391			−0.369195	+	0.929352i	$0.620367\pi$
$504$		0			0
$505$		0			0
$506$	−22.4033	−	25.8040i	−0.995949	−	1.14713i
$507$		0			0
$508$	29.9054	+	4.24035i	1.32684	+	0.188135i
$509$	4.37300			0.193830			0.0969148	−	0.995293i	$-0.469103\pi$
$509$	4.37300			0.193830			0.0969148	+	0.995293i	$0.469103\pi$
$510$		0			0
$511$			44.0518i			1.94874i
$512$	22.3680	−	3.41624i	0.988537	−	0.150978i
$513$		0			0
$514$	−11.4924	−	13.2369i	−0.506909	−	0.583855i
$515$		0			0
$516$		0			0
$517$			1.90495i			0.0837794i
$518$	1.19935	−	1.04129i	0.0526965	−	0.0457517i
$519$		0			0
$520$		0			0
$521$		−	14.3162i		−	0.627206i	−0.949554	−	0.313603i	$-0.898464\pi$
$521$		−	14.3162i		−	0.627206i	0.949554	−	0.313603i	$-0.101536\pi$
$522$		0			0
$523$	−18.6795			−0.816798			−0.408399	−	0.912803i	$-0.633913\pi$
$523$	−18.6795			−0.816798			−0.408399	+	0.912803i	$0.633913\pi$
$524$	−12.7742	−	1.81129i	−0.558045	−	0.0791266i
$525$		0			0
$526$	−13.1231	+	11.3936i	−0.572195	+	0.496785i
$527$	11.4677			0.499540
$528$		0			0
$529$	21.4924			0.934453
$530$		0			0
$531$		0			0
$532$	−30.6417	−	4.34475i	−1.32848	−	0.188369i
$533$	−9.89012			−0.428389
$534$		0			0
$535$		0			0
$536$	−20.6372	−	31.9069i	−0.891389	−	1.37817i
$537$		0			0
$538$	−2.04750	+	1.77766i	−0.0882738	+	0.0766402i
$539$		−	7.69113i		−	0.331280i
$540$		0			0
$541$			37.8674i			1.62805i	0.580831	+	0.814024i	$0.302728\pi$
$541$			37.8674i			1.62805i	−0.580831	+	0.814024i	$0.697272\pi$
$542$	24.5453	+	28.2711i	1.05431	+	1.21435i
$543$		0			0
$544$	−15.6847	−	33.9071i	−0.672474	−	1.45375i
$545$		0			0
$546$		0			0
$547$	−32.1143			−1.37311			−0.686553	−	0.727079i	$-0.740877\pi$
$547$	−32.1143			−1.37311			−0.686553	+	0.727079i	$0.740877\pi$
$548$	13.0776	+	1.85431i	0.558647	+	0.0792120i
$549$		0			0
$550$		0			0
$551$	34.9840			1.49037
$552$		0			0
$553$	42.6038			1.81170
$554$	11.0081	+	12.6790i	0.467688	+	0.538681i
$555$		0			0
$556$	3.36932	−	23.7623i	0.142891	−	1.00775i
$557$	−9.18425			−0.389149			−0.194575	−	0.980888i	$-0.562333\pi$
$557$	−9.18425			−0.389149			−0.194575	+	0.980888i	$0.562333\pi$
$558$		0			0
$559$		−	8.89586i		−	0.376255i
$560$		0			0
$561$		0			0
$562$	8.02857	+	9.24726i	0.338665	+	0.390072i
$563$		−	5.79119i		−	0.244070i	−0.992526	−	0.122035i	$-0.961058\pi$
$563$		−	5.79119i		−	0.244070i	0.992526	−	0.122035i	$-0.0389419\pi$
$564$		0			0
$565$		0			0
$566$	−16.8025	+	14.5881i	−0.706262	+	0.613183i
$567$		0			0
$568$	3.77216	+	5.83209i	0.158276	+	0.244709i
$569$			6.72287i			0.281837i	0.990021	+	0.140919i	$0.0450056\pi$
$569$			6.72287i			0.281837i	−0.990021	+	0.140919i	$0.954994\pi$
$570$		0			0
$571$	−23.8617			−0.998583			−0.499291	−	0.866434i	$-0.666406\pi$
$571$	−23.8617			−0.998583			−0.499291	+	0.866434i	$0.666406\pi$
$572$	−1.72521	+	12.1671i	−0.0721345	+	0.508733i
$573$		0			0
$574$	−18.8078	+	16.3291i	−0.785021	+	0.681563i
$575$		0			0
$576$		0			0
$577$	−5.24477			−0.218342			−0.109171	−	0.994023i	$-0.534820\pi$
$577$	−5.24477			−0.218342			−0.109171	+	0.994023i	$0.534820\pi$
$578$	−28.4224	+	24.6767i	−1.18222	+	1.02641i
$579$		0			0
$580$		0			0
$581$	−17.4920			−0.725690
$582$		0			0
$583$			36.2454i			1.50113i
$584$	−22.4033	−	34.6375i	−0.927056	−	1.43331i
$585$		0			0
$586$	18.1231	−	15.7347i	0.748659	−	0.649993i
$587$			7.41722i			0.306141i	0.988215	+	0.153071i	$0.0489162\pi$
$587$			7.41722i			0.306141i	−0.988215	+	0.153071i	$0.951084\pi$
$588$		0			0
$589$			8.89586i			0.366548i
$590$		0			0
$591$		0			0
$592$	−0.413473	+	1.42871i	−0.0169936	+	0.0587196i
$593$		−	23.9778i		−	0.984649i	−0.870412	−	0.492325i	$-0.836147\pi$
$593$		−	23.9778i		−	0.984649i	0.870412	−	0.492325i	$-0.163853\pi$
$594$		0			0
$595$		0			0
$596$	−4.37300	+	30.8408i	−0.179125	+	1.26329i
$597$		0			0
$598$	−10.4895	−	12.0818i	−0.428949	−	0.494061i
$599$	29.7703			1.21638			0.608191	−	0.793790i	$-0.291895\pi$
$599$	29.7703			1.21638			0.608191	+	0.793790i	$0.291895\pi$
$600$		0			0
$601$	1.36932			0.0558556			0.0279278	−	0.999610i	$-0.491109\pi$
$601$	1.36932			0.0558556			0.0279278	+	0.999610i	$0.491109\pi$
$602$	−14.6875	−	16.9170i	−0.598619	−	0.689486i
$603$		0			0
$604$	−21.0540	−	2.98529i	−0.856674	−	0.121470i
$605$		0			0
$606$		0			0
$607$			43.4018i			1.76162i	0.473467	+	0.880812i	$0.343002\pi$
$607$			43.4018i			1.76162i	−0.473467	+	0.880812i	$0.656998\pi$
$608$	26.3029	−	12.1671i	1.06672	−	0.493442i
$609$		0			0
$610$		0			0
$611$			0.891921i			0.0360832i
$612$		0			0
$613$			22.6305i			0.914036i	0.889457	+	0.457018i	$0.151083\pi$
$613$			22.6305i			0.914036i	−0.889457	+	0.457018i	$0.848917\pi$
$614$	−19.9477	+	17.3188i	−0.805022	+	0.698928i
$615$		0			0
$616$	16.8078	+	25.9863i	0.677204	+	1.04702i
$617$			12.3954i			0.499020i	0.968372	+	0.249510i	$0.0802695\pi$
$617$			12.3954i			0.499020i	−0.968372	+	0.249510i	$0.919730\pi$
$618$		0			0
$619$	30.7386			1.23549			0.617745	−	0.786378i	$-0.288046\pi$
$619$	30.7386			1.23549			0.617745	+	0.786378i	$0.288046\pi$
$620$		0			0
$621$		0			0
$622$	23.9243	−	20.7713i	0.959276	−	0.832853i
$623$	−30.9526			−1.24009
$624$		0			0
$625$		0			0
$626$	−23.0928	+	20.0494i	−0.922975	+	0.801336i
$627$		0			0
$628$	−17.9432	−	2.54421i	−0.716012	−	0.101525i
$629$	2.45567			0.0979139
$630$		0			0
$631$		−	10.6323i		−	0.423265i	−0.977349	−	0.211632i	$-0.932122\pi$
$631$		−	10.6323i		−	0.423265i	0.977349	−	0.211632i	$-0.0678779\pi$
$632$	−33.4990	+	21.6669i	−1.33252	+	0.861864i
$633$		0			0
$634$	0.123106	−	0.106882i	0.00488915	−	0.00424481i
$635$		0			0
$636$		0			0
$637$		−	3.60109i		−	0.142680i
$638$	−22.9354	−	26.4168i	−0.908019	−	1.04585i
$639$		0			0
$640$		0			0
$641$		−	7.07107i		−	0.279290i	−0.990202	−	0.139645i	$-0.955404\pi$
$641$		−	7.07107i		−	0.279290i	0.990202	−	0.139645i	$-0.0445962\pi$
$642$		0			0
$643$	−37.3590			−1.47330			−0.736648	−	0.676276i	$-0.763593\pi$
$643$	−37.3590			−1.47330			−0.736648	+	0.676276i	$0.763593\pi$
$644$	−39.8953	−	5.65685i	−1.57210	−	0.222911i
$645$		0			0
$646$	−31.3693	−	36.1310i	−1.23421	−	1.42156i
$647$	4.27156			0.167932			0.0839661	−	0.996469i	$-0.473241\pi$
$647$	4.27156			0.167932			0.0839661	+	0.996469i	$0.473241\pi$
$648$		0			0
$649$	17.6155			0.691470
$650$		0			0
$651$		0			0
$652$	−2.94521	+	20.7713i	−0.115343	+	0.813467i
$653$	10.5312			0.412120			0.206060	−	0.978539i	$-0.433936\pi$
$653$	10.5312			0.412120			0.206060	+	0.978539i	$0.433936\pi$
$654$		0			0
$655$		0			0
$656$	6.48392	−	22.4044i	0.253155	−	0.874746i
$657$		0			0
$658$	1.47261	+	1.69614i	0.0574082	+	0.0661225i
$659$			27.4901i			1.07086i	0.844579	+	0.535431i	$0.179851\pi$
$659$			27.4901i			1.07086i	−0.844579	+	0.535431i	$0.820149\pi$
$660$		0			0
$661$		−	33.6333i		−	1.30818i	−0.756416	−	0.654091i	$-0.773051\pi$
$661$		−	33.6333i		−	1.30818i	0.756416	−	0.654091i	$-0.226949\pi$
$662$	24.9559	−	21.6669i	0.969937	−	0.842109i
$663$		0			0
$664$	13.7538	−	8.89586i	0.533751	−	0.345226i
$665$		0			0
$666$		0			0
$667$	45.5490			1.76366
$668$	−1.34700	+	9.49980i	−0.0521170	+	0.367558i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$	−13.1190	+	11.3900i	−0.505325	+	0.438728i
$675$		0			0
$676$	2.84233	−	20.0457i	0.109320	−	0.770989i
$677$	−44.7037			−1.71810			−0.859052	−	0.511889i	$-0.828946\pi$
$677$	−44.7037			−1.71810			−0.859052	+	0.511889i	$0.828946\pi$
$678$		0			0
$679$			28.2102i			1.08261i
$680$		0			0
$681$		0			0
$682$	6.71737	−	5.83209i	0.257222	−	0.223322i
$683$			32.2080i			1.23241i	0.787588	+	0.616203i	$0.211330\pi$
$683$			32.2080i			1.23241i	−0.787588	+	0.616203i	$0.788670\pi$
$684$		0			0
$685$		0			0
$686$	13.6573	+	15.7304i	0.521439	+	0.600591i
$687$		0			0
$688$	20.1521	+	5.83209i	0.768292	+	0.222346i
$689$			16.9706i			0.646527i
$690$		0			0
$691$	−14.8769			−0.565944			−0.282972	−	0.959128i	$-0.591320\pi$
$691$	−14.8769			−0.565944			−0.282972	+	0.959128i	$0.591320\pi$
$692$	−0.936426	+	6.60421i	−0.0355976	+	0.251054i
$693$		0			0
$694$	−5.36932	−	6.18435i	−0.203816	−	0.234755i
$695$		0			0
$696$		0			0
$697$	−38.5088			−1.45862
$698$	6.43971	+	7.41722i	0.243746	+	0.280746i
$699$		0			0
$700$		0			0
$701$	9.28434			0.350665			0.175332	−	0.984509i	$-0.443900\pi$
$701$	9.28434			0.350665			0.175332	+	0.984509i	$0.443900\pi$
$702$		0			0
$703$			1.90495i			0.0718464i
$704$	−26.4316	−	11.8849i	−0.996178	−	0.447928i
$705$		0			0
$706$	30.6155	+	35.2628i	1.15223	+	1.32713i
$707$		−	13.2084i		−	0.496753i
$708$		0			0
$709$		−	15.0802i		−	0.566349i	−0.959068	−	0.283175i	$-0.908612\pi$
$709$		−	15.0802i		−	0.566349i	0.959068	−	0.283175i	$-0.0913876\pi$
$710$		0			0
$711$		0			0
$712$	24.3378	−	15.7415i	0.912096	−	0.589938i
$713$			11.5824i			0.433764i
$714$		0			0
$715$		0			0
$716$	41.4679	+	5.87983i	1.54973	+	0.219740i
$717$		0			0
$718$	−21.3019	+	18.4945i	−0.794980	+	0.690209i
$719$	47.2623			1.76259			0.881294	−	0.472569i	$-0.156673\pi$
$719$	47.2623			1.76259			0.881294	+	0.472569i	$0.156673\pi$
$720$		0			0
$721$	−25.1231			−0.935633
$722$	7.73815	−	6.71834i	0.287984	−	0.250031i
$723$		0			0
$724$	−12.2462	−	1.73642i	−0.455127	−	0.0645335i
$725$		0			0
$726$		0			0
$727$		−	5.66906i		−	0.210254i	−0.994459	−	0.105127i	$-0.966475\pi$
$727$		−	5.66906i		−	0.210254i	0.994459	−	0.105127i	$-0.0335249\pi$
$728$	7.86962	+	12.1671i	0.291667	+	0.450943i
$729$		0			0
$730$		0			0
$731$		−	34.6375i		−	1.28111i
$732$		0			0
$733$			23.9548i			0.884790i	0.896820	+	0.442395i	$0.145871\pi$
$733$			23.9548i			0.884790i	−0.896820	+	0.442395i	$0.854129\pi$
$734$	−18.5262	−	21.3384i	−0.683816	−	0.787615i
$735$		0			0
$736$	34.2462	−	15.8415i	1.26233	−	0.583927i
$737$			48.6685i			1.79273i
$738$		0			0
$739$	5.61553			0.206571			0.103285	−	0.994652i	$-0.467065\pi$
$739$	5.61553			0.206571			0.103285	+	0.994652i	$0.467065\pi$
$740$		0			0
$741$		0			0
$742$	28.0193	+	32.2725i	1.02862	+	1.18476i
$743$	14.6875			0.538833			0.269417	−	0.963024i	$-0.413169\pi$
$743$	14.6875			0.538833			0.269417	+	0.963024i	$0.413169\pi$
$744$		0			0
$745$		0			0
$746$	−5.25608	−	6.05393i	−0.192439	−	0.221650i
$747$		0			0
$748$	−6.71737	+	47.3747i	−0.245611	+	1.73219i
$749$	22.4033			0.818600
$750$		0			0
$751$		−	8.68210i		−	0.316814i	−0.987374	−	0.158407i	$-0.949364\pi$
$751$		−	8.68210i		−	0.316814i	0.987374	−	0.158407i	$-0.0506359\pi$
$752$	−2.02050	−	0.584739i	−0.0736800	−	0.0213233i
$753$		0			0
$754$	−10.7386	−	12.3687i	−0.391078	−	0.450442i
$755$		0			0
$756$		0			0
$757$		−	1.69614i		−	0.0616473i	−0.999525	−	0.0308236i	$-0.990187\pi$
$757$		−	1.69614i		−	0.0616473i	0.999525	−	0.0308236i	$-0.00981303\pi$
$758$	−17.6121	+	15.2910i	−0.639700	+	0.555394i
$759$		0			0
$760$		0			0
$761$		−	32.3314i		−	1.17201i	−0.810307	−	0.586006i	$-0.800700\pi$
$761$		−	32.3314i		−	1.17201i	0.810307	−	0.586006i	$-0.199300\pi$
$762$		0			0
$763$	29.1690			1.05599
$764$	−4.91134	+	34.6375i	−0.177686	+	1.25314i
$765$		0			0
$766$	15.6847	−	13.6176i	0.566710	−	0.492023i
$767$	8.24782			0.297812
$768$		0			0
$769$	15.6155			0.563110			0.281555	−	0.959545i	$-0.409150\pi$
$769$	15.6155			0.563110			0.281555	+	0.959545i	$0.409150\pi$
$770$		0			0
$771$		0			0
$772$	4.41782	−	31.1570i	0.159001	−	1.12136i
$773$	16.1498			0.580868			0.290434	−	0.956895i	$-0.406200\pi$
$773$	16.1498			0.580868			0.290434	+	0.956895i	$0.406200\pi$
$774$		0			0
$775$		0			0
$776$	−14.3468	−	22.1815i	−0.515021	−	0.796268i
$777$		0			0
$778$	14.0096	−	12.1633i	0.502270	−	0.436076i
$779$		−	29.8726i		−	1.07030i
$780$		0			0
$781$		−	8.89586i		−	0.318319i
$782$	−40.8427	−	47.0425i	−1.46053	−	1.68223i
$783$		0			0
$784$	8.15767	+	2.36086i	0.291345	+	0.0843163i
$785$		0			0
$786$		0			0
$787$	8.18998			0.291941			0.145971	−	0.989289i	$-0.453369\pi$
$787$	8.18998			0.291941			0.145971	+	0.989289i	$0.453369\pi$
$788$	6.93319	−	48.8968i	0.246985	−	1.74187i
$789$		0			0
$790$		0			0
$791$	−2.45567			−0.0873135
$792$		0			0
$793$		0			0
$794$	−30.8046	−	35.4806i	−1.09321	−	1.25916i
$795$		0			0
$796$	21.0540	+	2.98529i	0.746238	+	0.105811i
$797$	−24.1671			−0.856042			−0.428021	−	0.903769i	$-0.640789\pi$
$797$	−24.1671			−0.856042			−0.428021	+	0.903769i	$0.640789\pi$
$798$		0			0
$799$			3.47284i			0.122860i
$800$		0			0
$801$		0			0
$802$	31.9528	+	36.8031i	1.12829	+	1.29956i
$803$			52.8336i			1.86446i
$804$		0			0
$805$		0			0
$806$	3.14516	−	2.73066i	0.110784	−	0.0961835i
$807$		0			0
$808$	6.71737	+	10.3857i	0.236316	+	0.365366i
$809$		−	37.6400i		−	1.32335i	−0.749789	−	0.661677i	$-0.769845\pi$
$809$		−	37.6400i		−	1.32335i	0.749789	−	0.661677i	$-0.230155\pi$
$810$		0			0
$811$	49.4773			1.73738			0.868691	−	0.495354i	$-0.164962\pi$
$811$	49.4773			1.73738			0.868691	+	0.495354i	$0.164962\pi$
$812$	−40.8427	−	5.79119i	−1.43330	−	0.203231i
$813$		0			0
$814$	1.43845	−	1.24887i	0.0504175	−	0.0437730i
$815$		0			0
$816$		0			0
$817$	26.8695			0.940045
$818$	5.47091	−	4.74990i	0.191286	−	0.166076i
$819$		0			0
$820$		0			0
$821$	37.9780			1.32544			0.662720	−	0.748867i	$-0.269402\pi$
$821$	37.9780			1.32544			0.662720	+	0.748867i	$0.269402\pi$
$822$		0			0
$823$		−	32.0636i		−	1.11767i	−0.829279	−	0.558834i	$-0.811249\pi$
$823$		−	32.0636i		−	1.11767i	0.829279	−	0.558834i	$-0.188751\pi$
$824$	19.7541	−	12.7768i	0.688165	−	0.445101i
$825$		0			0
$826$	15.6847	−	13.6176i	0.545739	−	0.473816i
$827$			4.16516i			0.144837i	0.997374	+	0.0724184i	$0.0230717\pi$
$827$			4.16516i			0.144837i	−0.997374	+	0.0724184i	$0.976928\pi$
$828$		0			0
$829$			6.18435i			0.214791i	0.994216	+	0.107396i	$0.0342512\pi$
$829$			6.18435i			0.214791i	−0.994216	+	0.107396i	$0.965749\pi$
$830$		0			0
$831$		0			0
$832$	−12.3756	−	5.56466i	−0.429047	−	0.192920i
$833$		−	14.0214i		−	0.485814i
$834$		0			0
$835$		0			0
$836$	−36.7502	−	5.21089i	−1.27103	−	0.180223i
$837$		0			0
$838$	−7.77651	−	8.95694i	−0.268635	−	0.309412i
$839$	−15.0363			−0.519111			−0.259556	−	0.965728i	$-0.583576\pi$
$839$	−15.0363			−0.519111			−0.259556	+	0.965728i	$0.583576\pi$
$840$		0			0
$841$	17.6307			0.607955
$842$	13.9817	+	16.1040i	0.481840	+	0.554981i
$843$		0			0
$844$	1.12311	−	7.92077i	0.0386589	−	0.272644i
$845$		0			0
$846$		0			0
$847$		−	6.41273i		−	0.220344i
$848$	−38.4440	−	11.1258i	−1.32017	−	0.382063i
$849$		0			0
$850$		0			0
$851$			2.48023i			0.0850213i
$852$		0			0
$853$			22.3044i			0.763689i	0.924227	+	0.381844i	$0.124711\pi$
$853$			22.3044i			0.763689i	−0.924227	+	0.381844i	$0.875289\pi$
$854$		0			0
$855$		0			0
$856$	−17.6155	+	11.3936i	−0.602086	+	0.389426i
$857$			10.7694i			0.367875i	0.982938	+	0.183937i	$0.0588843\pi$
$857$			10.7694i			0.367875i	−0.982938	+	0.183937i	$0.941116\pi$
$858$		0			0
$859$	50.2462			1.71438			0.857189	−	0.515001i	$-0.172209\pi$
$859$	50.2462			1.71438			0.857189	+	0.515001i	$0.172209\pi$
$860$		0			0
$861$		0			0
$862$	−21.3019	+	18.4945i	−0.725545	+	0.629926i
$863$	6.43971			0.219210			0.109605	−	0.993975i	$-0.465041\pi$
$863$	6.43971			0.219210			0.109605	+	0.993975i	$0.465041\pi$
$864$		0			0
$865$		0			0
$866$	11.2017	−	9.72540i	0.380648	−	0.330482i
$867$		0			0
$868$	1.47261	−	10.3857i	0.0499835	−	0.352512i
$869$	51.0970			1.73335
$870$		0			0
$871$			22.7872i			0.772116i
$872$	−22.9354	+	14.8344i	−0.776689	+	0.502358i
$873$		0			0
$874$	36.4924	−	31.6831i	1.23437	−	1.07170i
$875$		0			0
$876$		0			0
$877$			0.789443i			0.0266576i	0.999911	+	0.0133288i	$0.00424281\pi$
$877$			0.789443i			0.0266576i	−0.999911	+	0.0133288i	$0.995757\pi$
$878$	21.3254	+	24.5625i	0.719698	+	0.828945i
$879$		0			0
$880$		0			0
$881$		−	5.83095i		−	0.196450i	−0.995164	−	0.0982249i	$-0.968684\pi$
$881$		−	5.83095i		−	0.196450i	0.995164	−	0.0982249i	$-0.0313164\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	−3.14516	+	22.1815i	−0.105783	+	0.746043i
$885$		0			0
$886$	−1.50758	−	1.73642i	−0.0506481	−	0.0583362i
$887$	18.1379			0.609012			0.304506	−	0.952510i	$-0.401509\pi$
$887$	18.1379			0.609012			0.304506	+	0.952510i	$0.401509\pi$
$888$		0			0
$889$	−45.6155			−1.52990
$890$		0			0
$891$		0			0
$892$	56.7748	+	8.05024i	1.90096	+	0.269542i
$893$	−2.69400			−0.0901513
$894$		0			0
$895$		0			0
$896$	−32.7219	+	9.85061i	−1.09316	+	0.329086i
$897$		0			0
$898$	9.17834	+	10.5716i	0.306285	+	0.352778i
$899$			11.8574i			0.395468i
$900$		0			0
$901$			66.0777i			2.20137i
$902$	−22.5571	+	19.5843i	−0.751071	+	0.652087i
$903$		0			0
$904$	1.93087	−	1.24887i	0.0642198	−	0.0415369i
$905$		0			0
$906$		0			0
$907$	32.1143			1.06634			0.533168	−	0.846009i	$-0.321001\pi$
$907$	32.1143			1.06634			0.533168	+	0.846009i	$0.321001\pi$
$908$	26.1552	+	3.70861i	0.867991	+	0.123075i
$909$		0			0
$910$		0			0
$911$	−12.5807			−0.416816			−0.208408	−	0.978042i	$-0.566828\pi$
$911$	−12.5807			−0.416816			−0.208408	+	0.978042i	$0.566828\pi$
$912$		0			0
$913$	−20.9791			−0.694306
$914$	21.1755	−	18.3848i	0.700423	−	0.608114i
$915$		0			0
$916$	−43.6155	−	6.18435i	−1.44110	−	0.204337i
$917$	19.4849			0.643449
$918$		0			0
$919$			49.2611i			1.62497i	0.582981	+	0.812486i	$0.301886\pi$
$919$			49.2611i			1.62497i	−0.582981	+	0.812486i	$0.698114\pi$
$920$		0			0
$921$		0			0
$922$	16.6320	−	14.4401i	0.547746	−	0.475559i
$923$		−	4.16516i		−	0.137098i
$924$		0			0
$925$		0			0
$926$	−16.4577	−	18.9560i	−0.540835	−	0.622931i
$927$		0			0
$928$	35.0595	−	16.2177i	1.15088	−	0.532373i
$929$			8.65938i			0.284105i	0.989859	+	0.142053i	$0.0453702\pi$
$929$			8.65938i			0.284105i	−0.989859	+	0.142053i	$0.954630\pi$
$930$		0			0
$931$	10.8769			0.356476
$932$	42.4527	+	6.01947i	1.39058	+	0.197174i
$933$		0			0
$934$	−26.0000	−	29.9467i	−0.850746	−	0.979885i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	37.6229	+	43.3338i	1.22843	+	1.41490i
$939$		0			0
$940$		0			0
$941$	4.37300			0.142556			0.0712778	−	0.997457i	$-0.477292\pi$
$941$	4.37300			0.142556			0.0712778	+	0.997457i	$0.477292\pi$
$942$		0			0
$943$		−	38.8940i		−	1.26656i
$944$	−5.40724	+	18.6841i	−0.175991	+	0.608115i
$945$		0			0
$946$	−17.6155	−	20.2895i	−0.572730	−	0.659668i
$947$			22.2517i			0.723082i	0.932356	+	0.361541i	$0.117749\pi$
$947$			22.2517i			0.723082i	−0.932356	+	0.361541i	$0.882251\pi$
$948$		0			0
$949$			24.7374i			0.803010i
$950$		0			0
$951$		0			0
$952$	30.6417	+	47.3747i	0.993102	+	1.53542i
$953$		−	0.813015i		−	0.0263361i	−0.999913	−	0.0131681i	$-0.995808\pi$
$953$		−	0.813015i		−	0.0263361i	0.999913	−	0.0131681i	$-0.00419165\pi$
$954$		0			0
$955$		0			0
$956$	−1.37899	+	9.72540i	−0.0445997	+	0.314542i
$957$		0			0
$958$	39.9814	−	34.7123i	1.29174	−	1.12150i
$959$	−19.9477			−0.644143
$960$		0			0
$961$	27.9848			0.902737
$962$	0.673500	−	0.584739i	0.0217145	−	0.0188528i
$963$		0			0
$964$	−1.12311	+	7.92077i	−0.0361728	+	0.255111i
$965$		0			0
$966$		0			0
$967$			23.7917i			0.765091i	0.923937	+	0.382546i	$0.124952\pi$
$967$			23.7917i			0.765091i	−0.923937	+	0.382546i	$0.875048\pi$
$968$	3.26131	+	5.04227i	0.104822	+	0.162065i
$969$		0			0
$970$		0			0
$971$			32.6032i			1.04629i	0.852244	+	0.523144i	$0.175241\pi$
$971$			32.6032i			1.04629i	−0.852244	+	0.523144i	$0.824759\pi$
$972$		0			0
$973$			36.2454i			1.16197i
$974$	4.17940	+	4.81382i	0.133917	+	0.154245i
$975$		0			0
$976$		0			0
$977$		−	2.43904i		−	0.0780319i	−0.999239	−	0.0390160i	$-0.987578\pi$
$977$		−	2.43904i		−	0.0780319i	0.999239	−	0.0390160i	$-0.0124223\pi$
$978$		0			0
$979$	−37.1231			−1.18646
$980$		0			0
$981$		0			0
$982$	−9.75323	−	11.2337i	−0.311238	−	0.358482i
$983$	−12.5841			−0.401371			−0.200685	−	0.979656i	$-0.564317\pi$
$983$	−12.5841			−0.401371			−0.200685	+	0.979656i	$0.564317\pi$
$984$		0			0
$985$		0			0
$986$	−41.8126	−	48.1596i	−1.33159	−	1.53371i
$987$		0			0
$988$	−17.2069	−	2.43981i	−0.547425	−	0.0776207i
$989$	34.9840			1.11243
$990$		0			0
$991$			10.6323i			0.337746i	0.985638	+	0.168873i	$0.0540127\pi$
$991$			10.6323i			0.337746i	−0.985638	+	0.168873i	$0.945987\pi$
$992$	4.12391	+	8.91506i	0.130934	+	0.283053i
$993$		0			0
$994$	−6.87689	−	7.92077i	−0.218122	−	0.251232i
$995$		0			0
$996$		0			0
$997$			32.4813i			1.02869i	0.857583	+	0.514346i	$0.171965\pi$
$997$			32.4813i			1.02869i	−0.857583	+	0.514346i	$0.828035\pi$
$998$	−26.8287	+	23.2930i	−0.849248	+	0.737325i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.b.g.251.14		16
3.2	odd	2	inner	1800.2.b.g.251.4		16
4.3	odd	2		7200.2.b.i.4751.2		16
5.2	odd	4		360.2.m.c.179.11	yes	16
5.3	odd	4		360.2.m.c.179.5	✓	16
5.4	even	2	inner	1800.2.b.g.251.3		16
8.3	odd	2	inner	1800.2.b.g.251.1		16
8.5	even	2		7200.2.b.i.4751.14		16
12.11	even	2		7200.2.b.i.4751.3		16
15.2	even	4		360.2.m.c.179.6	yes	16
15.8	even	4		360.2.m.c.179.12	yes	16
15.14	odd	2	inner	1800.2.b.g.251.13		16
20.3	even	4		1440.2.m.c.719.1		16
20.7	even	4		1440.2.m.c.719.4		16
20.19	odd	2		7200.2.b.i.4751.13		16
24.5	odd	2		7200.2.b.i.4751.15		16
24.11	even	2	inner	1800.2.b.g.251.15		16
40.3	even	4		360.2.m.c.179.8	yes	16
40.13	odd	4		1440.2.m.c.719.16		16
40.19	odd	2	inner	1800.2.b.g.251.16		16
40.27	even	4		360.2.m.c.179.10	yes	16
40.29	even	2		7200.2.b.i.4751.1		16
40.37	odd	4		1440.2.m.c.719.13		16
60.23	odd	4		1440.2.m.c.719.15		16
60.47	odd	4		1440.2.m.c.719.14		16
60.59	even	2		7200.2.b.i.4751.16		16
120.29	odd	2		7200.2.b.i.4751.4		16
120.53	even	4		1440.2.m.c.719.2		16
120.59	even	2	inner	1800.2.b.g.251.2		16
120.77	even	4		1440.2.m.c.719.3		16
120.83	odd	4		360.2.m.c.179.9	yes	16
120.107	odd	4		360.2.m.c.179.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.m.c.179.5	✓	16	5.3	odd	4
360.2.m.c.179.6	yes	16	15.2	even	4
360.2.m.c.179.7	yes	16	120.107	odd	4
360.2.m.c.179.8	yes	16	40.3	even	4
360.2.m.c.179.9	yes	16	120.83	odd	4
360.2.m.c.179.10	yes	16	40.27	even	4
360.2.m.c.179.11	yes	16	5.2	odd	4
360.2.m.c.179.12	yes	16	15.8	even	4
1440.2.m.c.719.1		16	20.3	even	4
1440.2.m.c.719.2		16	120.53	even	4
1440.2.m.c.719.3		16	120.77	even	4
1440.2.m.c.719.4		16	20.7	even	4
1440.2.m.c.719.13		16	40.37	odd	4
1440.2.m.c.719.14		16	60.47	odd	4
1440.2.m.c.719.15		16	60.23	odd	4
1440.2.m.c.719.16		16	40.13	odd	4
1800.2.b.g.251.1		16	8.3	odd	2	inner
1800.2.b.g.251.2		16	120.59	even	2	inner
1800.2.b.g.251.3		16	5.4	even	2	inner
1800.2.b.g.251.4		16	3.2	odd	2	inner
1800.2.b.g.251.13		16	15.14	odd	2	inner
1800.2.b.g.251.14		16	1.1	even	1	trivial
1800.2.b.g.251.15		16	24.11	even	2	inner
1800.2.b.g.251.16		16	40.19	odd	2	inner
7200.2.b.i.4751.1		16	40.29	even	2
7200.2.b.i.4751.2		16	4.3	odd	2
7200.2.b.i.4751.3		16	12.11	even	2
7200.2.b.i.4751.4		16	120.29	odd	2
7200.2.b.i.4751.13		16	20.19	odd	2
7200.2.b.i.4751.14		16	8.5	even	2
7200.2.b.i.4751.15		16	24.5	odd	2
7200.2.b.i.4751.16		16	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} +3.02045i q^{7} +(-1.53610 - 2.37495i) q^{8} +O(q^{10})\)	\(q+(1.06789 - 0.927153i) q^{2} +(0.280776 - 1.98019i) q^{4} +3.02045i q^{7} +(-1.53610 - 2.37495i) q^{8} +3.62258i q^{11} +1.69614i q^{13} +(2.80042 + 3.22550i) q^{14} +(-3.84233 - 1.11198i) q^{16} +6.60421i q^{17} -5.12311 q^{19} +(3.35869 + 3.86852i) q^{22} -6.67026 q^{23} +(1.57258 + 1.81129i) q^{26} +(5.98107 + 0.848071i) q^{28} -6.82867 q^{29} -1.73642i q^{31} +(-5.13416 + 2.37495i) q^{32} +(6.12311 + 7.05256i) q^{34} -0.371834i q^{37} +(-5.47091 + 4.74990i) q^{38} +5.83095i q^{41} -5.24477 q^{43} +(7.17341 + 1.01714i) q^{44} +(-7.12311 + 6.18435i) q^{46} +0.525853 q^{47} -2.12311 q^{49} +(3.35869 + 0.476236i) q^{52} +10.0054 q^{53} +(7.17341 - 4.63972i) q^{56} +(-7.29226 + 6.33122i) q^{58} -4.86270i q^{59} +(-1.60993 - 1.85431i) q^{62} +(-3.28078 + 7.29634i) q^{64} +13.4347 q^{67} +(13.0776 + 1.85431i) q^{68} -2.45567 q^{71} +14.5845 q^{73} +(-0.344747 - 0.397078i) q^{74} +(-1.43845 + 10.1447i) q^{76} -10.9418 q^{77} -14.1051i q^{79} +(5.40618 + 6.22681i) q^{82} +5.79119i q^{83} +(-5.60083 + 4.86270i) q^{86} +(8.60345 - 5.56466i) q^{88} +10.2477i q^{89} -5.12311 q^{91} +(-1.87285 + 13.2084i) q^{92} +(0.561553 - 0.487546i) q^{94} +9.33976 q^{97} +(-2.26724 + 1.96844i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4}+O(q^{10}) \) 16 * q - 12 * q^4	\( 16 q - 12 q^{4} - 12 q^{16} - 16 q^{19} + 32 q^{34} - 48 q^{46} + 32 q^{49} - 36 q^{64} - 56 q^{76} - 16 q^{91} - 24 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 - 12 * q^16 - 16 * q^19 + 32 * q^34 - 48 * q^46 + 32 * q^49 - 36 * q^64 - 56 * q^76 - 16 * q^91 - 24 * q^94

Introduction

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