LMFDB - Embedded newform 315.2.g.a.314.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(314,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("315.314");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.g (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:	$2.51528766367$
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} + 32x^{14} + 324x^{12} + 1328x^{10} + 2314x^{8} + 1920x^{6} + 780x^{4} + 144x^{2} + 9 $ x^16 + 32x^14 + 324x^12 + 1328x^10 + 2314x^8 + 1920x^6 + 780x^4 + 144*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			314.14
Root			$2.73933i$ of defining polynomial
Character	$\chi$	$=$	315.314
Dual form			315.2.g.a.314.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.33441 q^{2} +3.44949 q^{4} +(-1.33239 + 1.79576i) q^{5} +(2.53958 - 0.741964i) q^{7} +3.38371 q^{8} +O(q^{10})$	\(q+2.33441 q^{2} +3.44949 q^{4} +(-1.33239 + 1.79576i) q^{5} +(2.53958 - 0.741964i) q^{7} +3.38371 q^{8} +(-3.11034 + 4.19204i) q^{10} +1.41421i q^{11} -1.14152 q^{13} +(5.92844 - 1.73205i) q^{14} +1.00000 q^{16} -5.20586i q^{17} -4.61552i q^{19} +(-4.59606 + 6.19445i) q^{20} +3.30136i q^{22} -3.61953 q^{23} +(-1.44949 - 4.78529i) q^{25} -2.66477 q^{26} +(8.76027 - 2.55940i) q^{28} +8.34242i q^{29} +8.38408i q^{31} -4.43300 q^{32} -12.1526i q^{34} +(-2.05132 + 5.54906i) q^{35} -8.08665i q^{37} -10.7745i q^{38} +(-4.50841 + 6.07632i) q^{40} -9.19211 q^{41} -5.11879i q^{43} +4.87832i q^{44} -8.44949 q^{46} +1.61435i q^{47} +(5.89898 - 3.76856i) q^{49} +(-3.38371 - 11.1708i) q^{50} -3.93765 q^{52} +3.14789 q^{53} +(-2.53958 - 1.88428i) q^{55} +(8.59322 - 2.51059i) q^{56} +19.4747i q^{58} +11.8569 q^{59} +7.53712i q^{61} +19.5719i q^{62} -12.3485 q^{64} +(1.52094 - 2.04989i) q^{65} +9.57058i q^{67} -17.9576i q^{68} +(-4.78864 + 12.9538i) q^{70} -5.51399i q^{71} +11.2999 q^{73} -18.8776i q^{74} -15.9212i q^{76} +(1.04930 + 3.59151i) q^{77} -4.00000 q^{79} +(-1.33239 + 1.79576i) q^{80} -21.4582 q^{82} +1.61435i q^{83} +(9.34847 + 6.93623i) q^{85} -11.9494i q^{86} +4.78529i q^{88} -7.99432 q^{89} +(-2.89898 + 0.846964i) q^{91} -12.4855 q^{92} +3.76856i q^{94} +(8.28836 + 6.14966i) q^{95} -1.14152 q^{97} +(13.7707 - 8.79738i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} + 16 q^{16} + 16 q^{25} - 96 q^{46} + 16 q^{49} - 80 q^{64} - 48 q^{70} - 64 q^{79} + 32 q^{85} + 32 q^{91}+O(q^{100}) $ 16 * q + 16 * q^4 + 16 * q^16 + 16 * q^25 - 96 * q^46 + 16 * q^49 - 80 * q^64 - 48 * q^70 - 64 * q^79 + 32 * q^85 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.33441			1.65068			0.825340	−	0.564636i	$-0.190983\pi$
$2$	2.33441			1.65068			0.825340	+	0.564636i	$0.190983\pi$
$3$		0			0
$3$		0			0
$4$	3.44949			1.72474
$5$	−1.33239	+	1.79576i	−0.595862	+	0.803087i
$5$	−1.33239	+	1.79576i	−0.595862	+	0.803087i
$6$		0			0
$7$	2.53958	−	0.741964i	0.959873	−	0.280436i
$7$	2.53958	−	0.741964i	0.959873	−	0.280436i
$8$	3.38371			1.19632
$9$		0			0
$10$	−3.11034	+	4.19204i	−0.983577	+	1.32564i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$		0			0
$13$	−1.14152			−0.316600			−0.158300	−	0.987391i	$-0.550601\pi$
$13$	−1.14152			−0.316600			−0.158300	+	0.987391i	$0.550601\pi$
$14$	5.92844	−	1.73205i	1.58444	−	0.462910i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.20586i		−	1.26261i	−0.775536	−	0.631304i	$-0.782520\pi$
$17$		−	5.20586i		−	1.26261i	0.775536	−	0.631304i	$-0.217480\pi$
$18$		0			0
$19$		−	4.61552i		−	1.05887i	−0.848349	−	0.529437i	$-0.822403\pi$
$19$		−	4.61552i		−	1.05887i	0.848349	−	0.529437i	$-0.177597\pi$
$20$	−4.59606	+	6.19445i	−1.02771	+	1.38512i
$21$		0			0
$22$			3.30136i			0.703852i
$23$	−3.61953			−0.754725			−0.377362	−	0.926066i	$-0.623169\pi$
$23$	−3.61953			−0.754725			−0.377362	+	0.926066i	$0.623169\pi$
$24$		0			0
$25$	−1.44949	−	4.78529i	−0.289898	−	0.957058i
$26$	−2.66477			−0.522605
$27$		0			0
$28$	8.76027	−	2.55940i	1.65554	−	0.483680i
$29$			8.34242i			1.54915i	0.632483	+	0.774574i	$0.282036\pi$
$29$			8.34242i			1.54915i	−0.632483	+	0.774574i	$0.717964\pi$
$30$		0			0
$31$			8.38408i			1.50583i	0.658120	+	0.752913i	$0.271352\pi$
$31$			8.38408i			1.50583i	−0.658120	+	0.752913i	$0.728648\pi$
$32$	−4.43300			−0.783652
$33$		0			0
$34$		−	12.1526i		−	2.08416i
$35$	−2.05132	+	5.54906i	−0.346737	+	0.937962i
$36$		0			0
$37$		−	8.08665i		−	1.32944i	−0.747094	−	0.664718i	$-0.768552\pi$
$37$		−	8.08665i		−	1.32944i	0.747094	−	0.664718i	$-0.231448\pi$
$38$		−	10.7745i		−	1.74786i
$39$		0			0
$40$	−4.50841	+	6.07632i	−0.712842	+	0.960751i
$41$	−9.19211			−1.43557			−0.717783	−	0.696267i	$-0.754843\pi$
$41$	−9.19211			−1.43557			−0.717783	+	0.696267i	$0.754843\pi$
$42$		0			0
$43$		−	5.11879i		−	0.780609i	−0.920686	−	0.390304i	$-0.872370\pi$
$43$		−	5.11879i		−	0.780609i	0.920686	−	0.390304i	$-0.127630\pi$
$44$			4.87832i			0.735434i
$45$		0			0
$46$	−8.44949			−1.24581
$47$			1.61435i			0.235477i	0.993045	+	0.117739i	$0.0375645\pi$
$47$			1.61435i			0.235477i	−0.993045	+	0.117739i	$0.962436\pi$
$48$		0			0
$49$	5.89898	−	3.76856i	0.842711	−	0.538366i
$50$	−3.38371	−	11.1708i	−0.478529	−	1.57980i
$51$		0			0
$52$	−3.93765			−0.546054
$53$	3.14789			0.432395			0.216198	−	0.976350i	$-0.430634\pi$
$53$	3.14789			0.432395			0.216198	+	0.976350i	$0.430634\pi$
$54$		0			0
$55$	−2.53958	−	1.88428i	−0.342438	−	0.254076i
$56$	8.59322	−	2.51059i	1.14832	−	0.335492i
$57$		0			0
$58$			19.4747i			2.55715i
$59$	11.8569			1.54363			0.771817	−	0.635844i	$-0.219348\pi$
$59$	11.8569			1.54363			0.771817	+	0.635844i	$0.219348\pi$
$60$		0			0
$61$			7.53712i			0.965029i	0.875888	+	0.482515i	$0.160276\pi$
$61$			7.53712i			0.965029i	−0.875888	+	0.482515i	$0.839724\pi$
$62$			19.5719i			2.48564i
$63$		0			0
$64$	−12.3485			−1.54356
$65$	1.52094	−	2.04989i	0.188650	−	0.254257i
$66$		0			0
$67$			9.57058i			1.16923i	0.811310	+	0.584616i	$0.198755\pi$
$67$			9.57058i			1.16923i	−0.811310	+	0.584616i	$0.801245\pi$
$68$		−	17.9576i		−	2.17768i
$69$		0			0
$70$	−4.78864	+	12.9538i	−0.572352	+	1.54828i
$71$		−	5.51399i		−	0.654390i	−0.944957	−	0.327195i	$-0.893897\pi$
$71$		−	5.51399i		−	0.654390i	0.944957	−	0.327195i	$-0.106103\pi$
$72$		0			0
$73$	11.2999			1.32255			0.661274	−	0.750144i	$-0.270016\pi$
$73$	11.2999			1.32255			0.661274	+	0.750144i	$0.270016\pi$
$74$		−	18.8776i		−	2.19447i
$75$		0			0
$76$		−	15.9212i		−	1.82629i
$77$	1.04930	+	3.59151i	0.119578	+	0.409291i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.33239	+	1.79576i	−0.148965	+	0.200772i
$81$		0			0
$82$	−21.4582			−2.36966
$83$			1.61435i			0.177198i	0.996067	+	0.0885989i	$0.0282389\pi$
$83$			1.61435i			0.177198i	−0.996067	+	0.0885989i	$0.971761\pi$
$84$		0			0
$85$	9.34847	+	6.93623i	1.01398	+	0.752339i
$86$		−	11.9494i		−	1.28854i
$87$		0			0
$88$			4.78529i			0.510113i
$89$	−7.99432			−0.847396			−0.423698	−	0.905803i	$-0.639268\pi$
$89$	−7.99432			−0.847396			−0.423698	+	0.905803i	$0.639268\pi$
$90$		0			0
$91$	−2.89898	+	0.846964i	−0.303896	+	0.0887860i
$92$	−12.4855			−1.30171
$93$		0			0
$94$			3.76856i			0.388697i
$95$	8.28836	+	6.14966i	0.850368	+	0.630942i
$96$		0			0
$97$	−1.14152			−0.115904			−0.0579518	−	0.998319i	$-0.518457\pi$
$97$	−1.14152			−0.115904			−0.0579518	+	0.998319i	$0.518457\pi$
$98$	13.7707	−	8.79738i	1.39105	−	0.888669i
$99$		0			0
$100$	−5.00000	−	16.5068i	−0.500000	−	1.65068i
$101$	9.19211			0.914649			0.457325	−	0.889300i	$-0.348808\pi$
$101$	9.19211			0.914649			0.457325	+	0.889300i	$0.348808\pi$
$102$		0			0
$103$	−10.1583			−1.00093			−0.500465	−	0.865757i	$-0.666838\pi$
$103$	−10.1583			−1.00093			−0.500465	+	0.865757i	$0.666838\pi$
$104$	−3.86256			−0.378755
$105$		0			0
$106$	7.34847			0.713746
$107$	5.71812			0.552792			0.276396	−	0.961044i	$-0.410860\pi$
$107$	5.71812			0.552792			0.276396	+	0.961044i	$0.410860\pi$
$108$		0			0
$109$	12.8990			1.23550			0.617749	−	0.786375i	$-0.288045\pi$
$109$	12.8990			1.23550			0.617749	+	0.786375i	$0.288045\pi$
$110$	−5.92844	−	4.39869i	−0.565255	−	0.419399i
$111$		0			0
$112$	2.53958	−	0.741964i	0.239968	−	0.0701090i
$113$	10.3870			0.977122			0.488561	−	0.872530i	$-0.337522\pi$
$113$	10.3870			0.977122			0.488561	+	0.872530i	$0.337522\pi$
$114$		0			0
$115$	4.82262	−	6.49980i	0.449712	−	0.606110i
$116$			28.7771i			2.67188i
$117$		0			0
$118$	27.6789			2.54805
$119$	−3.86256	−	13.2207i	−0.354081	−	1.21194i
$120$		0			0
$121$	9.00000			0.818182
$122$			17.5948i			1.59295i
$123$		0			0
$124$			28.9208i			2.59717i
$125$	10.5245	+	3.77292i	0.941340	+	0.337461i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−19.9604			−1.76427
$129$		0			0
$130$	3.55051	−	4.78529i	0.311400	−	0.419698i
$131$	−17.1864			−1.50159			−0.750793	−	0.660538i	$-0.770328\pi$
$131$	−17.1864			−1.50159			−0.750793	+	0.660538i	$0.770328\pi$
$132$		0			0
$133$	−3.42455	−	11.7215i	−0.296946	−	1.01638i
$134$			22.3417i			1.93003i
$135$		0			0
$136$		−	17.6151i		−	1.51049i
$137$	1.04930			0.0896473			0.0448237	−	0.998995i	$-0.485727\pi$
$137$	1.04930			0.0896473			0.0448237	+	0.998995i	$0.485727\pi$
$138$		0			0
$139$			8.38408i			0.711129i	0.934652	+	0.355564i	$0.115711\pi$
$139$			8.38408i			0.711129i	−0.934652	+	0.355564i	$0.884289\pi$
$140$	−7.07602	+	19.1414i	−0.598032	+	1.61775i
$141$		0			0
$142$		−	12.8719i		−	1.08019i
$143$		−	1.61435i		−	0.134999i
$144$		0			0
$145$	−14.9810	−	11.1153i	−1.24410	−	0.923078i
$146$	26.3785			2.18310
$147$		0			0
$148$		−	27.8948i		−	2.29294i
$149$			9.89949i			0.810998i	0.914095	+	0.405499i	$0.132902\pi$
$149$			9.89949i			0.810998i	−0.914095	+	0.405499i	$0.867098\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		−	15.6176i		−	1.26675i
$153$		0			0
$154$	2.44949	+	8.38408i	0.197386	+	0.675609i
$155$	−15.0558	−	11.1708i	−1.20931	−	0.897264i
$156$		0			0
$157$	14.0960			1.12498			0.562491	−	0.826803i	$-0.309843\pi$
$157$	14.0960			1.12498			0.562491	+	0.826803i	$0.309843\pi$
$158$	−9.33766			−0.742864
$159$		0			0
$160$	5.90648	−	7.96060i	0.466948	−	0.629341i
$161$	−9.19211	+	2.68556i	−0.724440	+	0.211652i
$162$		0			0
$163$			23.4430i			1.83620i	0.396349	+	0.918100i	$0.370277\pi$
$163$			23.4430i			1.83620i	−0.396349	+	0.918100i	$0.629723\pi$
$164$	−31.7081			−2.47599
$165$		0			0
$166$			3.76856i			0.292497i
$167$		−	24.7778i		−	1.91736i	−0.284482	−	0.958681i	$-0.591822\pi$
$167$		−	24.7778i		−	1.91736i	0.284482	−	0.958681i	$-0.408178\pi$
$168$		0			0
$169$	−11.6969			−0.899764
$170$	21.8232	+	16.1920i	1.67376	+	1.24187i
$171$		0			0
$172$		−	17.6572i		−	1.34635i
$173$			3.59151i			0.273058i	0.990636	+	0.136529i	$0.0435947\pi$
$173$			3.59151i			0.273058i	−0.990636	+	0.136529i	$0.956405\pi$
$174$		0			0
$175$	−7.23161	−	11.0772i	−0.546658	−	0.837356i
$176$			1.41421i			0.106600i
$177$		0			0
$178$	−18.6621			−1.39878
$179$		−	13.9993i		−	1.04635i	−0.852224	−	0.523177i	$-0.824747\pi$
$179$		−	13.9993i		−	1.04635i	0.852224	−	0.523177i	$-0.175253\pi$
$180$		0			0
$181$			20.5367i			1.52648i	0.646113	+	0.763241i	$0.276393\pi$
$181$			20.5367i			1.52648i	−0.646113	+	0.763241i	$0.723607\pi$
$182$	−6.76742	+	1.97717i	−0.501634	+	0.146557i
$183$		0			0
$184$	−12.2474			−0.902894
$185$	14.5217	+	10.7745i	1.06765	+	0.792160i
$186$		0			0
$187$	7.36220			0.538378
$188$			5.56868i			0.406138i
$189$		0			0
$190$	19.3485	+	14.3559i	1.40369	+	1.04148i
$191$		−	8.62815i		−	0.624311i	−0.950031	−	0.312155i	$-0.898949\pi$
$191$		−	8.62815i		−	0.624311i	0.950031	−	0.312155i	$-0.101051\pi$
$192$		0			0
$193$			5.11879i			0.368459i	0.982883	+	0.184229i	$0.0589789\pi$
$193$			5.11879i			0.368459i	−0.982883	+	0.184229i	$0.941021\pi$
$194$	−2.66477			−0.191320
$195$		0			0
$196$	20.3485	−	12.9996i	1.45346	−	0.928543i
$197$	14.5841			1.03908			0.519538	−	0.854447i	$-0.326104\pi$
$197$	14.5841			1.03908			0.519538	+	0.854447i	$0.326104\pi$
$198$		0			0
$199$			4.61552i			0.327186i	0.986528	+	0.163593i	$0.0523084\pi$
$199$			4.61552i			0.327186i	−0.986528	+	0.163593i	$0.947692\pi$
$200$	−4.90465	−	16.1920i	−0.346811	−	1.14495i
$201$		0			0
$202$	21.4582			1.50979
$203$	6.18977	+	21.1863i	0.434437	+	1.48698i
$204$		0			0
$205$	12.2474	−	16.5068i	0.855399	−	1.15289i
$206$	−23.7138			−1.65222
$207$		0			0
$208$	−1.14152			−0.0791500
$209$	6.52734			0.451505
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	10.8586			0.745772
$213$		0			0
$214$	13.3485			0.912483
$215$	9.19211	+	6.82021i	0.626897	+	0.465135i
$216$		0			0
$217$	6.22069	+	21.2921i	0.422288	+	1.44540i
$218$	30.1116			2.03941
$219$		0			0
$220$	−8.76027	−	6.49980i	−0.590617	−	0.438217i
$221$			5.94258i			0.399741i
$222$		0			0
$223$	−12.9545			−0.867496			−0.433748	−	0.901034i	$-0.642809\pi$
$223$	−12.9545			−0.867496			−0.433748	+	0.901034i	$0.642809\pi$
$224$	−11.2580	+	3.28913i	−0.752206	+	0.219764i
$225$		0			0
$226$	24.2474			1.61292
$227$		−	19.9347i		−	1.32312i	−0.749894	−	0.661558i	$-0.769896\pi$
$227$		−	19.9347i		−	1.32312i	0.749894	−	0.661558i	$-0.230104\pi$
$228$		0			0
$229$			3.76856i			0.249033i	0.992218	+	0.124517i	$0.0397380\pi$
$229$			3.76856i			0.249033i	−0.992218	+	0.124517i	$0.960262\pi$
$230$	11.2580	−	15.1732i	0.742330	−	1.00049i
$231$		0			0
$232$			28.2283i			1.85328i
$233$	−19.7246			−1.29220			−0.646101	−	0.763252i	$-0.723602\pi$
$233$	−19.7246			−1.29220			−0.646101	+	0.763252i	$0.723602\pi$
$234$		0			0
$235$	−2.89898	−	2.15094i	−0.189109	−	0.140312i
$236$	40.9002			2.66238
$237$		0			0
$238$	−9.01682	−	30.8627i	−0.584474	−	2.00053i
$239$		−	0.142865i		−	0.00924114i	−0.999989	−	0.00462057i	$-0.998529\pi$
$239$		−	0.142865i		−	0.00924114i	0.999989	−	0.00462057i	$-0.00147078\pi$
$240$		0			0
$241$			5.46249i			0.351870i	0.984402	+	0.175935i	$0.0562948\pi$
$241$			5.46249i			0.351870i	−0.984402	+	0.175935i	$0.943705\pi$
$242$	21.0097			1.35056
$243$		0			0
$244$			25.9992i			1.66443i
$245$	−1.09230	+	15.6143i	−0.0697848	+	0.997562i
$246$		0			0
$247$			5.26870i			0.335239i
$248$			28.3693i			1.80145i
$249$		0			0
$250$	24.5685	+	8.80757i	1.55385	+	0.557039i
$251$	6.52734			0.412002			0.206001	−	0.978552i	$-0.433955\pi$
$251$	6.52734			0.412002			0.206001	+	0.978552i	$0.433955\pi$
$252$		0			0
$253$		−	5.11879i		−	0.321816i
$254$		0			0
$255$		0			0
$256$	−21.8990			−1.36869
$257$		−	9.16020i		−	0.571397i	−0.958320	−	0.285699i	$-0.907774\pi$
$257$		−	9.16020i		−	0.571397i	0.958320	−	0.285699i	$-0.0922256\pi$
$258$		0			0
$259$	−6.00000	−	20.5367i	−0.372822	−	1.27609i
$260$	5.24648	−	7.07107i	0.325373	−	0.438529i
$261$		0			0
$262$	−40.1203			−2.47864
$263$	−14.1125			−0.870213			−0.435107	−	0.900379i	$-0.643289\pi$
$263$	−14.1125			−0.870213			−0.435107	+	0.900379i	$0.643289\pi$
$264$		0			0
$265$	−4.19420	+	5.65284i	−0.257648	+	0.347251i
$266$	−7.99432	−	27.3629i	−0.490163	−	1.67773i
$267$		0			0
$268$			33.0136i			2.01663i
$269$	1.46699			0.0894437			0.0447218	−	0.998999i	$-0.485760\pi$
$269$	1.46699			0.0894437			0.0447218	+	0.998999i	$0.485760\pi$
$270$		0			0
$271$		−	15.9212i		−	0.967144i	−0.875305	−	0.483572i	$-0.839339\pi$
$271$		−	15.9212i		−	0.967144i	0.875305	−	0.483572i	$-0.160661\pi$
$272$		−	5.20586i		−	0.315652i
$273$		0			0
$274$	2.44949			0.147979
$275$	6.76742	−	2.04989i	0.408091	−	0.123613i
$276$		0			0
$277$		−	9.57058i		−	0.575040i	−0.957775	−	0.287520i	$-0.907169\pi$
$277$		−	9.57058i		−	0.575040i	0.957775	−	0.287520i	$-0.0928308\pi$
$278$			19.5719i			1.17385i
$279$		0			0
$280$	−6.94108	+	18.7764i	−0.414809	+	1.12211i
$281$			1.41421i			0.0843649i	0.999110	+	0.0421825i	$0.0134311\pi$
$281$			1.41421i			0.0843649i	−0.999110	+	0.0421825i	$0.986569\pi$
$282$		0			0
$283$	−12.9545			−0.770063			−0.385032	−	0.922903i	$-0.625810\pi$
$283$	−12.9545			−0.770063			−0.385032	+	0.922903i	$0.625810\pi$
$284$		−	19.0205i		−	1.12866i
$285$		0			0
$286$		−	3.76856i		−	0.222840i
$287$	−23.3441	+	6.82021i	−1.37796	+	0.402584i
$288$		0			0
$289$	−10.1010			−0.594178
$290$	−34.9718	−	25.9478i	−2.05361	−	1.52371i
$291$		0			0
$292$	38.9787			2.28106
$293$		−	22.8006i		−	1.33203i	−0.745940	−	0.666013i	$-0.767999\pi$
$293$		−	22.8006i		−	1.33203i	0.745940	−	0.666013i	$-0.232001\pi$
$294$		0			0
$295$	−15.7980	+	21.2921i	−0.919793	+	1.23967i
$296$		−	27.3629i		−	1.59043i
$297$		0			0
$298$			23.1095i			1.33870i
$299$	4.13176			0.238946
$300$		0			0
$301$	−3.79796	−	12.9996i	−0.218911	−	0.749285i
$302$	−23.3441			−1.34330
$303$		0			0
$304$		−	4.61552i		−	0.264718i
$305$	−13.5348	−	10.0424i	−0.775003	−	0.575024i
$306$		0			0
$307$	−0.513100			−0.0292842			−0.0146421	−	0.999893i	$-0.504661\pi$
$307$	−0.513100			−0.0292842			−0.0146421	+	0.999893i	$0.504661\pi$
$308$	3.61953	+	12.3889i	0.206242	+	0.705923i
$309$		0			0
$310$	−35.1464	−	26.0774i	−1.99618	−	1.48110i
$311$	−1.19779			−0.0679204			−0.0339602	−	0.999423i	$-0.510812\pi$
$311$	−1.19779			−0.0679204			−0.0339602	+	0.999423i	$0.510812\pi$
$312$		0			0
$313$	8.50372			0.480659			0.240329	−	0.970691i	$-0.422745\pi$
$313$	8.50372			0.480659			0.240329	+	0.970691i	$0.422745\pi$
$314$	32.9059			1.85699
$315$		0			0
$316$	−13.7980			−0.776196
$317$	1.04930			0.0589343			0.0294671	−	0.999566i	$-0.490619\pi$
$317$	1.04930			0.0589343			0.0294671	+	0.999566i	$0.490619\pi$
$318$		0			0
$319$	−11.7980			−0.660559
$320$	16.4529	−	22.1749i	0.919747	−	1.23961i
$321$		0			0
$322$	−21.4582	+	6.26922i	−1.19582	+	0.349370i
$323$	−24.0278			−1.33694
$324$		0			0
$325$	1.65462	+	5.46249i	0.0917817	+	0.303004i
$326$			54.7257i			3.03098i
$327$		0			0
$328$	−31.1034			−1.71740
$329$	1.19779	+	4.09978i	0.0660362	+	0.226028i
$330$		0			0
$331$	−27.3939			−1.50570			−0.752852	−	0.658190i	$-0.771322\pi$
$331$	−27.3939			−1.50570			−0.752852	+	0.658190i	$0.771322\pi$
$332$			5.56868i			0.305621i
$333$		0			0
$334$		−	57.8416i		−	3.16495i
$335$	−17.1864	−	12.7517i	−0.938995	−	0.696700i
$336$		0			0
$337$		−	21.9591i		−	1.19619i	−0.801426	−	0.598094i	$-0.795925\pi$
$337$		−	21.9591i		−	1.19619i	0.801426	−	0.598094i	$-0.204075\pi$
$338$	−27.3055			−1.48522
$339$		0			0
$340$	32.2474	+	23.9264i	1.74886	+	1.29759i
$341$	−11.8569			−0.642086
$342$		0			0
$343$	12.1848	−	13.9474i	0.657919	−	0.753089i
$344$		−	17.3205i		−	0.933859i
$345$		0			0
$346$			8.38408i			0.450731i
$347$	−13.9005			−0.746217			−0.373109	−	0.927788i	$-0.621708\pi$
$347$	−13.9005			−0.746217			−0.373109	+	0.927788i	$0.621708\pi$
$348$		0			0
$349$		−	1.69393i		−	0.0906739i	−0.998972	−	0.0453370i	$-0.985564\pi$
$349$		−	1.69393i		−	0.0906739i	0.998972	−	0.0453370i	$-0.0144362\pi$
$350$	−16.8816	−	25.8587i	−0.902358	−	1.38221i
$351$		0			0
$352$		−	6.26922i		−	0.334150i
$353$			3.59151i			0.191157i	0.995422	+	0.0955785i	$0.0304701\pi$
$353$			3.59151i			0.191157i	−0.995422	+	0.0955785i	$0.969530\pi$
$354$		0			0
$355$	9.90179	+	7.34677i	0.525532	+	0.389926i
$356$	−27.5763			−1.46154
$357$		0			0
$358$		−	32.6801i		−	1.72720i
$359$			9.89949i			0.522475i	0.965275	+	0.261238i	$0.0841306\pi$
$359$			9.89949i			0.522475i	−0.965275	+	0.261238i	$0.915869\pi$
$360$		0			0
$361$	−2.30306			−0.121214
$362$			47.9412i			2.51973i
$363$		0			0
$364$	−10.0000	+	2.92160i	−0.524142	+	0.153133i
$365$	−15.0558	+	20.2918i	−0.788056	+	1.06212i
$366$		0			0
$367$	17.5205			0.914565			0.457282	−	0.889322i	$-0.348823\pi$
$367$	17.5205			0.914565			0.457282	+	0.889322i	$0.348823\pi$
$368$	−3.61953			−0.188681
$369$		0			0
$370$	33.8996	+	25.1523i	1.76235	+	1.30760i
$371$	7.99432	−	2.33562i	0.415045	−	0.121259i
$372$		0			0
$373$			4.30188i			0.222743i	0.993779	+	0.111371i	$0.0355243\pi$
$373$			4.30188i			0.222743i	−0.993779	+	0.111371i	$0.964476\pi$
$374$	17.1864			0.888689
$375$		0			0
$376$			5.46249i			0.281706i
$377$		−	9.52301i		−	0.490460i
$378$		0			0
$379$	21.5959			1.10931			0.554654	−	0.832081i	$-0.312851\pi$
$379$	21.5959			1.10931			0.554654	+	0.832081i	$0.312851\pi$
$380$	28.5906	+	21.2132i	1.46667	+	1.08821i
$381$		0			0
$382$		−	20.1417i		−	1.03054i
$383$			18.3204i			0.936128i	0.883694	+	0.468064i	$0.155048\pi$
$383$			18.3204i			0.936128i	−0.883694	+	0.468064i	$0.844952\pi$
$384$		0			0
$385$	−7.84756	−	2.90101i	−0.399949	−	0.147849i
$386$			11.9494i			0.608208i
$387$		0			0
$388$	−3.93765			−0.199904
$389$			22.1988i			1.12553i	0.826619	+	0.562763i	$0.190261\pi$
$389$			22.1988i			1.12553i	−0.826619	+	0.562763i	$0.809739\pi$
$390$		0			0
$391$			18.8428i			0.952921i
$392$	19.9604	−	12.7517i	1.00815	−	0.644059i
$393$		0			0
$394$	34.0454			1.71518
$395$	5.32955	−	7.18303i	0.268159	−	0.361417i
$396$		0			0
$397$	−23.2281			−1.16579			−0.582893	−	0.812549i	$-0.698079\pi$
$397$	−23.2281			−1.16579			−0.582893	+	0.812549i	$0.698079\pi$
$398$			10.7745i			0.540079i
$399$		0			0
$400$	−1.44949	−	4.78529i	−0.0724745	−	0.239264i
$401$		−	8.62815i		−	0.430869i	−0.976518	−	0.215435i	$-0.930883\pi$
$401$		−	8.62815i		−	0.430869i	0.976518	−	0.215435i	$-0.0691168\pi$
$402$		0			0
$403$		−	9.57058i		−	0.476744i
$404$	31.7081			1.57754
$405$		0			0
$406$	14.4495	+	49.4575i	0.717116	+	2.45454i
$407$	11.4362			0.566874
$408$		0			0
$409$		−	28.0738i		−	1.38816i	−0.719897	−	0.694081i	$-0.755811\pi$
$409$		−	28.0738i		−	1.38816i	0.719897	−	0.694081i	$-0.244189\pi$
$410$	28.5906	−	38.5337i	1.41199	−	1.90304i
$411$		0			0
$412$	−35.0411			−1.72635
$413$	30.1116	−	8.79738i	1.48169	−	0.432891i
$414$		0			0
$415$	−2.89898	−	2.15094i	−0.142305	−	0.105585i
$416$	5.06035			0.248104
$417$		0			0
$418$	15.2375			0.745291
$419$	−10.6591			−0.520731			−0.260365	−	0.965510i	$-0.583843\pi$
$419$	−10.6591			−0.520731			−0.260365	+	0.965510i	$0.583843\pi$
$420$		0			0
$421$	16.6969			0.813759			0.406879	−	0.913482i	$-0.366617\pi$
$421$	16.6969			0.813759			0.406879	+	0.913482i	$0.366617\pi$
$422$	−23.3441			−1.13638
$423$		0			0
$424$	10.6515			0.517284
$425$	−24.9116	+	7.54585i	−1.20839	+	0.366027i
$426$		0			0
$427$	5.59227	+	19.1412i	0.270629	+	0.926305i
$428$	19.7246			0.953425
$429$		0			0
$430$	21.4582	+	15.9212i	1.03481	+	0.767789i
$431$		−	17.8133i		−	0.858037i	−0.903296	−	0.429019i	$-0.858859\pi$
$431$		−	17.8133i		−	0.858037i	0.903296	−	0.429019i	$-0.141141\pi$
$432$		0			0
$433$	−16.3790			−0.787126			−0.393563	−	0.919298i	$-0.628758\pi$
$433$	−16.3790			−0.787126			−0.393563	+	0.919298i	$0.628758\pi$
$434$	14.5217	+	49.7046i	0.697062	+	2.38590i
$435$		0			0
$436$	44.4949			2.13092
$437$			16.7060i			0.799158i
$438$		0			0
$439$		−	10.4587i		−	0.499167i	−0.968353	−	0.249584i	$-0.919706\pi$
$439$		−	10.4587i		−	0.499167i	0.968353	−	0.249584i	$-0.0802937\pi$
$440$	−8.59322	−	6.37586i	−0.409666	−	0.303957i
$441$		0			0
$442$			13.8725i			0.659845i
$443$	3.61953			0.171969			0.0859846	−	0.996296i	$-0.472596\pi$
$443$	3.61953			0.171969			0.0859846	+	0.996296i	$0.472596\pi$
$444$		0			0
$445$	10.6515	−	14.3559i	0.504931	−	0.680533i
$446$	−30.2411			−1.43196
$447$		0			0
$448$	−31.3600	+	9.16212i	−1.48162	+	0.432869i
$449$		−	36.3410i		−	1.71504i	−0.514454	−	0.857518i	$-0.672005\pi$
$449$		−	36.3410i		−	1.71504i	0.514454	−	0.857518i	$-0.327995\pi$
$450$		0			0
$451$		−	12.9996i		−	0.612128i
$452$	35.8297			1.68529
$453$		0			0
$454$		−	46.5359i		−	2.18404i
$455$	2.34162	−	6.33435i	0.109777	−	0.296959i
$456$		0			0
$457$		−	1.48393i		−	0.0694152i	−0.999398	−	0.0347076i	$-0.988950\pi$
$457$		−	1.48393i		−	0.0694152i	0.999398	−	0.0347076i	$-0.0110500\pi$
$458$			8.79738i			0.411075i
$459$		0			0
$460$	16.6356	−	22.4210i	0.775638	−	1.04538i
$461$	−0.269197			−0.0125377			−0.00626887	−	0.999980i	$-0.501995\pi$
$461$	−0.269197			−0.0125377			−0.00626887	+	0.999980i	$0.501995\pi$
$462$		0			0
$463$			4.30188i			0.199925i	0.994991	+	0.0999626i	$0.0318723\pi$
$463$			4.30188i			0.199925i	−0.994991	+	0.0999626i	$0.968128\pi$
$464$			8.34242i			0.387287i
$465$		0			0
$466$	−46.0454			−2.13301
$467$		−	15.9804i		−	0.739485i	−0.929134	−	0.369743i	$-0.879446\pi$
$467$		−	15.9804i		−	0.739485i	0.929134	−	0.369743i	$-0.120554\pi$
$468$		0			0
$469$	7.10102	+	24.3053i	0.327895	+	1.12231i
$470$	−6.76742	−	5.02118i	−0.312158	−	0.231610i
$471$		0			0
$472$	40.1203			1.84668
$473$	7.23907			0.332853
$474$		0			0
$475$	−22.0866	+	6.69015i	−1.01340	+	0.306965i
$476$	−13.3239	−	45.6048i	−0.610699	−	2.09029i
$477$		0			0
$478$		−	0.333505i		−	0.0152542i
$479$	14.2525			0.651212			0.325606	−	0.945506i	$-0.394432\pi$
$479$	14.2525			0.651212			0.325606	+	0.945506i	$0.394432\pi$
$480$		0			0
$481$			9.23105i			0.420900i
$482$			12.7517i			0.580825i
$483$		0			0
$484$	31.0454			1.41115
$485$	1.52094	−	2.04989i	0.0690625	−	0.0930806i
$486$		0			0
$487$			31.5297i			1.42875i	0.699765	+	0.714373i	$0.253288\pi$
$487$			31.5297i			1.42875i	−0.699765	+	0.714373i	$0.746712\pi$
$488$			25.5034i			1.15449i
$489$		0			0
$490$	−2.54989	+	36.4503i	−0.115192	+	1.64666i
$491$			26.8701i			1.21263i	0.795225	+	0.606314i	$0.207353\pi$
$491$			26.8701i			1.21263i	−0.795225	+	0.606314i	$0.792647\pi$
$492$		0			0
$493$	43.4295			1.95597
$494$			12.2993i			0.553373i
$495$		0			0
$496$			8.38408i			0.376456i
$497$	−4.09118	−	14.0032i	−0.183515	−	0.628131i
$498$		0			0
$499$	−10.0000			−0.447661			−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000			−0.447661			−0.223831	+	0.974628i	$0.571856\pi$
$500$	36.3041	+	13.0147i	1.62357	+	0.582033i
$501$		0			0
$502$	15.2375			0.680083
$503$			28.0065i			1.24875i	0.781126	+	0.624374i	$0.214646\pi$
$503$			28.0065i			1.24875i	−0.781126	+	0.624374i	$0.785354\pi$
$504$		0			0
$505$	−12.2474	+	16.5068i	−0.545004	+	0.734543i
$506$		−	11.9494i		−	0.531215i
$507$		0			0
$508$		0			0
$509$	3.86256			0.171205			0.0856025	−	0.996329i	$-0.472718\pi$
$509$	3.86256			0.171205			0.0856025	+	0.996329i	$0.472718\pi$
$510$		0			0
$511$	28.6969	−	8.38408i	1.26948	−	0.370890i
$512$	−11.2004			−0.494993
$513$		0			0
$514$		−	21.3837i		−	0.943194i
$515$	13.5348	−	18.2419i	0.596416	−	0.803835i
$516$		0			0
$517$	−2.28303			−0.100408
$518$	−14.0065	−	47.9412i	−0.615410	−	2.10642i
$519$		0			0
$520$	5.14643	−	6.93623i	0.225686	−	0.304174i
$521$	30.5103			1.33668			0.668340	−	0.743856i	$-0.267005\pi$
$521$	30.5103			1.33668			0.668340	+	0.743856i	$0.267005\pi$
$522$		0			0
$523$	−29.4488			−1.28771			−0.643853	−	0.765149i	$-0.722665\pi$
$523$	−29.4488			−1.28771			−0.643853	+	0.765149i	$0.722665\pi$
$524$	−59.2844			−2.58985
$525$		0			0
$526$	−32.9444			−1.43644
$527$	43.6464			1.90127
$528$		0			0
$529$	−9.89898			−0.430390
$530$	−9.79100	+	13.1961i	−0.425294	+	0.573201i
$531$		0			0
$532$	−11.8130	−	40.4332i	−0.512157	−	1.75300i
$533$	10.4930			0.454500
$534$		0			0
$535$	−7.61875	+	10.2684i	−0.329387	+	0.443940i
$536$			32.3840i			1.39878i
$537$		0			0
$538$	3.42455			0.147643
$539$	5.32955	+	8.34242i	0.229560	+	0.359333i
$540$		0			0
$541$	30.8990			1.32845			0.664225	−	0.747532i	$-0.268761\pi$
$541$	30.8990			1.32845			0.664225	+	0.747532i	$0.268761\pi$
$542$		−	37.1667i		−	1.59645i
$543$		0			0
$544$			23.0776i			0.989445i
$545$	−17.1864	+	23.1634i	−0.736186	+	0.992213i
$546$		0			0
$547$		−	33.0136i		−	1.41156i	−0.708431	−	0.705780i	$-0.750597\pi$
$547$		−	33.0136i		−	1.41156i	0.708431	−	0.705780i	$-0.249403\pi$
$548$	3.61953			0.154619
$549$		0			0
$550$	15.7980	−	4.78529i	0.673627	−	0.204045i
$551$	38.5046			1.64035
$552$		0			0
$553$	−10.1583	+	2.96786i	−0.431976	+	0.126206i
$554$		−	22.3417i		−	0.949207i
$555$		0			0
$556$			28.9208i			1.22652i
$557$	−9.44366			−0.400141			−0.200070	−	0.979782i	$-0.564117\pi$
$557$	−9.44366			−0.400141			−0.200070	+	0.979782i	$0.564117\pi$
$558$		0			0
$559$			5.84319i			0.247141i
$560$	−2.05132	+	5.54906i	−0.0866842	+	0.234491i
$561$		0			0
$562$			3.30136i			0.139259i
$563$			18.3204i			0.772112i	0.922475	+	0.386056i	$0.126163\pi$
$563$			18.3204i			0.772112i	−0.922475	+	0.386056i	$0.873837\pi$
$564$		0			0
$565$	−13.8394	+	18.6524i	−0.582230	+	0.784714i
$566$	−30.2411			−1.27113
$567$		0			0
$568$		−	18.6577i		−	0.782861i
$569$		−	2.39983i		−	0.100606i	−0.998734	−	0.0503031i	$-0.983981\pi$
$569$		−	2.39983i		−	0.100606i	0.998734	−	0.0503031i	$-0.0160187\pi$
$570$		0			0
$571$	25.3939			1.06270			0.531350	−	0.847152i	$-0.321685\pi$
$571$	25.3939			1.06270			0.531350	+	0.847152i	$0.321685\pi$
$572$		−	5.56868i		−	0.232838i
$573$		0			0
$574$	−54.4949	+	15.9212i	−2.27457	+	0.664538i
$575$	5.24648	+	17.3205i	0.218793	+	0.722315i
$576$		0			0
$577$	33.3865			1.38990			0.694948	−	0.719060i	$-0.255427\pi$
$577$	33.3865			1.38990			0.694948	+	0.719060i	$0.255427\pi$
$578$	−23.5800			−0.980797
$579$		0			0
$580$	−51.6767	−	38.3422i	−2.14576	−	1.59207i
$581$	1.19779	+	4.09978i	0.0496926	+	0.170087i
$582$		0			0
$583$			4.45178i			0.184374i
$584$	38.2354			1.58219
$585$		0			0
$586$		−	53.2261i		−	2.19875i
$587$		−	7.18303i		−	0.296475i	−0.988952	−	0.148238i	$-0.952640\pi$
$587$		−	7.18303i		−	0.296475i	0.988952	−	0.148238i	$-0.0473601\pi$
$588$		0			0
$589$	38.6969			1.59448
$590$	−36.8790	+	49.7046i	−1.51828	+	2.04630i
$591$		0			0
$592$		−	8.08665i		−	0.332359i
$593$		−	25.8662i		−	1.06220i	−0.847309	−	0.531100i	$-0.821779\pi$
$593$		−	25.8662i		−	1.06220i	0.847309	−	0.531100i	$-0.178221\pi$
$594$		0			0
$595$	28.8877	+	10.6789i	1.18428	+	0.437792i
$596$			34.1482i			1.39877i
$597$		0			0
$598$	9.64524			0.394423
$599$			30.6841i			1.25372i	0.779133	+	0.626859i	$0.215660\pi$
$599$			30.6841i			1.25372i	−0.779133	+	0.626859i	$0.784340\pi$
$600$		0			0
$601$		−	42.7674i		−	1.74452i	−0.489044	−	0.872259i	$-0.662654\pi$
$601$		−	42.7674i		−	1.74452i	0.489044	−	0.872259i	$-0.337346\pi$
$602$	−8.86601	−	30.3465i	−0.361352	−	1.23683i
$603$		0			0
$604$	−34.4949			−1.40358
$605$	−11.9915	+	16.1618i	−0.487523	+	0.657071i
$606$		0			0
$607$	35.5542			1.44310			0.721550	−	0.692362i	$-0.243430\pi$
$607$	35.5542			1.44310			0.721550	+	0.692362i	$0.243430\pi$
$608$			20.4606i			0.829789i
$609$		0			0
$610$	−31.5959	−	23.4430i	−1.27928	−	0.949180i
$611$		−	1.84281i		−	0.0745520i
$612$		0			0
$613$		−	23.4430i		−	0.946855i	−0.880833	−	0.473427i	$-0.843017\pi$
$613$		−	23.4430i		−	0.946855i	0.880833	−	0.473427i	$-0.156983\pi$
$614$	−1.19779			−0.0483388
$615$		0			0
$616$	3.55051	+	12.1526i	0.143054	+	0.489644i
$617$	15.5274			0.625111			0.312555	−	0.949900i	$-0.398815\pi$
$617$	15.5274			0.625111			0.312555	+	0.949900i	$0.398815\pi$
$618$		0			0
$619$			41.9204i			1.68492i	0.538756	+	0.842462i	$0.318895\pi$
$619$			41.9204i			1.68492i	−0.538756	+	0.842462i	$0.681105\pi$
$620$	−51.9348	−	38.5337i	−2.08575	−	1.54755i
$621$		0			0
$622$	−2.79613			−0.112115
$623$	−20.3023	+	5.93150i	−0.813393	+	0.237640i
$624$		0			0
$625$	−20.7980	+	13.8725i	−0.831918	+	0.554898i
$626$	19.8512			0.793414
$627$		0			0
$628$	48.6240			1.94031
$629$	−42.0980			−1.67856
$630$		0			0
$631$	−13.7980			−0.549288			−0.274644	−	0.961546i	$-0.588560\pi$
$631$	−13.7980			−0.549288			−0.274644	+	0.961546i	$0.588560\pi$
$632$	−13.5348			−0.538387
$633$		0			0
$634$	2.44949			0.0972817
$635$		0			0
$636$		0			0
$637$	−6.73379	+	4.30188i	−0.266802	+	0.170447i
$638$	−27.5413			−1.09037
$639$		0			0
$640$	26.5950	−	35.8441i	1.05126	−	1.41686i
$641$			4.52837i			0.178860i	0.995993	+	0.0894299i	$0.0285045\pi$
$641$			4.52837i			0.178860i	−0.995993	+	0.0894299i	$0.971495\pi$
$642$		0			0
$643$	−12.9545			−0.510875			−0.255437	−	0.966826i	$-0.582219\pi$
$643$	−12.9545			−0.510875			−0.255437	+	0.966826i	$0.582219\pi$
$644$	−31.7081	+	9.26382i	−1.24947	+	0.365046i
$645$		0			0
$646$	−56.0908			−2.20686
$647$			6.45740i			0.253866i	0.991911	+	0.126933i	$0.0405134\pi$
$647$			6.45740i			0.253866i	−0.991911	+	0.126933i	$0.959487\pi$
$648$		0			0
$649$			16.7682i			0.658208i
$650$	3.86256	+	12.7517i	0.151502	+	0.500163i
$651$		0			0
$652$			80.8665i			3.16698i
$653$	0.106000			0.00414811			0.00207406	−	0.999998i	$-0.499340\pi$
$653$	0.106000			0.00414811			0.00207406	+	0.999998i	$0.499340\pi$
$654$		0			0
$655$	22.8990	−	30.8627i	0.894737	−	1.20590i
$656$	−9.19211			−0.358892
$657$		0			0
$658$	2.79613	+	9.57058i	0.109005	+	0.373100i
$659$		−	44.8262i		−	1.74618i	−0.487557	−	0.873091i	$-0.662112\pi$
$659$		−	44.8262i		−	1.74618i	0.487557	−	0.873091i	$-0.337888\pi$
$660$		0			0
$661$		−	48.6106i		−	1.89073i	−0.326011	−	0.945366i	$-0.605705\pi$
$661$		−	48.6106i		−	1.89073i	0.326011	−	0.945366i	$-0.394295\pi$
$662$	−63.9487			−2.48544
$663$		0			0
$664$			5.46249i			0.211986i
$665$	25.6118	+	9.46793i	0.993184	+	0.367150i
$666$		0			0
$667$		−	30.1957i		−	1.16918i
$668$		−	85.4707i		−	3.30696i
$669$		0			0
$670$	−40.1203	−	29.7678i	−1.54998	−	1.15003i
$671$	−10.6591			−0.411490
$672$		0			0
$673$			43.4011i			1.67299i	0.547975	+	0.836495i	$0.315399\pi$
$673$			43.4011i			1.67299i	−0.547975	+	0.836495i	$0.684601\pi$
$674$		−	51.2616i		−	1.97452i
$675$		0			0
$676$	−40.3485			−1.55186
$677$			2.70280i			0.103877i	0.998650	+	0.0519385i	$0.0165400\pi$
$677$			2.70280i			0.103877i	−0.998650	+	0.0519385i	$0.983460\pi$
$678$		0			0
$679$	−2.89898	+	0.846964i	−0.111253	+	0.0325035i
$680$	31.6325	+	23.4702i	1.21305	+	0.900040i
$681$		0			0
$682$	−27.6789			−1.05988
$683$	23.4501			0.897295			0.448647	−	0.893709i	$-0.351906\pi$
$683$	23.4501			0.897295			0.448647	+	0.893709i	$0.351906\pi$
$684$		0			0
$685$	−1.39807	+	1.88428i	−0.0534174	+	0.0719946i
$686$	28.4444	−	32.5590i	1.08601	−	1.24311i
$687$		0			0
$688$		−	5.11879i		−	0.195152i
$689$	−3.59337			−0.136896
$690$		0			0
$691$			0.846964i			0.0322200i	0.999870	+	0.0161100i	$0.00512820\pi$
$691$			0.846964i			0.0322200i	−0.999870	+	0.0161100i	$0.994872\pi$
$692$			12.3889i			0.470955i
$693$		0			0
$694$	−32.4495			−1.23177
$695$	−15.0558	−	11.1708i	−0.571098	−	0.423734i
$696$		0			0
$697$			47.8529i			1.81256i
$698$		−	3.95433i		−	0.149674i
$699$		0			0
$700$	−24.9454	−	38.2106i	−0.942846	−	1.44422i
$701$			6.78534i			0.256279i	0.991756	+	0.128139i	$0.0409005\pi$
$701$			6.78534i			0.256279i	−0.991756	+	0.128139i	$0.959100\pi$
$702$		0			0
$703$	−37.3241			−1.40771
$704$		−	17.4634i		−	0.658176i
$705$		0			0
$706$			8.38408i			0.315539i
$707$	23.3441	−	6.82021i	0.877947	−	0.256501i
$708$		0			0
$709$	5.79796			0.217747			0.108873	−	0.994056i	$-0.465276\pi$
$709$	5.79796			0.217747			0.108873	+	0.994056i	$0.465276\pi$
$710$	23.1149	+	17.1504i	0.867486	+	0.643643i
$711$		0			0
$712$	−27.0505			−1.01376
$713$		−	30.3465i		−	1.13648i
$714$		0			0
$715$	2.89898	+	2.15094i	0.108416	+	0.0804405i
$716$		−	48.2903i		−	1.80469i
$717$		0			0
$718$			23.1095i			0.862440i
$719$	−35.5707			−1.32656			−0.663281	−	0.748371i	$-0.730836\pi$
$719$	−35.5707			−1.32656			−0.663281	+	0.748371i	$0.730836\pi$
$720$		0			0
$721$	−25.7980	+	7.53712i	−0.960766	+	0.280697i
$722$	−5.37630			−0.200085
$723$		0			0
$724$			70.8412i			2.63279i
$725$	39.9209	−	12.0922i	1.48262	−	0.449095i
$726$		0			0
$727$	−35.0411			−1.29960			−0.649801	−	0.760104i	$-0.725148\pi$
$727$	−35.0411			−1.29960			−0.649801	+	0.760104i	$0.725148\pi$
$728$	−9.80930	+	2.86588i	−0.363557	+	0.106217i
$729$		0			0
$730$	−35.1464	+	47.3695i	−1.30083	+	1.75322i
$731$	−26.6477			−0.985602
$732$		0			0
$733$	23.7412			0.876902			0.438451	−	0.898755i	$-0.355527\pi$
$733$	23.7412			0.876902			0.438451	+	0.898755i	$0.355527\pi$
$734$	40.9002			1.50965
$735$		0			0
$736$	16.0454			0.591442
$737$	−13.5348			−0.498562
$738$		0			0
$739$	−21.3939			−0.786986			−0.393493	−	0.919328i	$-0.628734\pi$
$739$	−21.3939			−0.786986			−0.393493	+	0.919328i	$0.628734\pi$
$740$	50.0923	+	37.1667i	1.84143	+	1.36627i
$741$		0			0
$742$	18.6621	−	5.45230i	0.685106	−	0.200160i
$743$	14.1125			0.517737			0.258868	−	0.965913i	$-0.416650\pi$
$743$	14.1125			0.517737			0.258868	+	0.965913i	$0.416650\pi$
$744$		0			0
$745$	−17.7771	−	13.1900i	−0.651302	−	0.483243i
$746$			10.0424i			0.367677i
$747$		0			0
$748$	25.3958			0.928564
$749$	14.5217	−	4.24264i	0.530610	−	0.155023i
$750$		0			0
$751$	53.1918			1.94100			0.970499	−	0.241106i	$-0.0775101\pi$
$751$	53.1918			1.94100			0.970499	+	0.241106i	$0.0775101\pi$
$752$			1.61435i			0.0588693i
$753$		0			0
$754$		−	22.2307i		−	0.809593i
$755$	13.3239	−	17.9576i	0.484905	−	0.653543i
$756$		0			0
$757$		−	36.7984i		−	1.33746i	−0.743505	−	0.668730i	$-0.766838\pi$
$757$		−	36.7984i		−	1.33746i	0.743505	−	0.668730i	$-0.233162\pi$
$758$	50.4138			1.83111
$759$		0			0
$760$	28.0454	+	20.8087i	1.01731	+	0.754810i
$761$	23.4446			0.849865			0.424933	−	0.905225i	$-0.360298\pi$
$761$	23.4446			0.849865			0.424933	+	0.905225i	$0.360298\pi$
$762$		0			0
$763$	32.7580	−	9.57058i	1.18592	−	0.346478i
$764$		−	29.7627i		−	1.07678i
$765$		0			0
$766$			42.7674i			1.54525i
$767$	−13.5348			−0.488715
$768$		0			0
$769$			42.7674i			1.54223i	0.636695	+	0.771116i	$0.280301\pi$
$769$			42.7674i			1.54223i	−0.636695	+	0.771116i	$0.719699\pi$
$770$	−18.3194	−	6.77215i	−0.660187	−	0.244052i
$771$		0			0
$772$			17.6572i			0.635497i
$773$		−	0.362817i		−	0.0130496i	−0.999979	−	0.00652480i	$-0.997923\pi$
$773$		−	0.362817i		−	0.0130496i	0.999979	−	0.00652480i	$-0.00207692\pi$
$774$		0			0
$775$	40.1203	−	12.1526i	1.44116	−	0.436536i
$776$	−3.86256			−0.138658
$777$		0			0
$778$			51.8212i			1.85788i
$779$			42.4264i			1.52008i
$780$		0			0
$781$	7.79796			0.279033
$782$			43.9869i			1.57297i
$783$		0			0
$784$	5.89898	−	3.76856i	0.210678	−	0.134591i
$785$	−18.7813	+	25.3130i	−0.670334	+	0.903459i
$786$		0			0
$787$	−41.8902			−1.49322			−0.746612	−	0.665260i	$-0.768321\pi$
$787$	−41.8902			−1.49322			−0.746612	+	0.665260i	$0.768321\pi$
$788$	50.3078			1.79214
$789$		0			0
$790$	12.4414	−	16.7682i	0.442644	−	0.596585i
$791$	26.3785	−	7.70674i	0.937913	−	0.274020i
$792$		0			0
$793$		−	8.60375i		−	0.305528i
$794$	−54.2241			−1.92434
$795$		0			0
$796$			15.9212i			0.564312i
$797$			38.7810i			1.37369i	0.726802	+	0.686847i	$0.241006\pi$
$797$			38.7810i			1.37369i	−0.726802	+	0.686847i	$0.758994\pi$
$798$		0			0
$799$	8.40408			0.297315
$800$	6.42559	+	21.2132i	0.227179	+	0.750000i
$801$		0			0
$802$		−	20.1417i		−	0.711227i
$803$			15.9804i			0.563936i
$804$		0			0
$805$	7.42483	−	20.0850i	0.261691	−	0.707904i
$806$		−	22.3417i		−	0.786952i
$807$		0			0
$808$	31.1034			1.09421
$809$		−	22.4846i		−	0.790515i	−0.918570	−	0.395257i	$-0.870655\pi$
$809$		−	22.4846i		−	0.790515i	0.918570	−	0.395257i	$-0.129345\pi$
$810$		0			0
$811$		−	15.9212i		−	0.559069i	−0.960136	−	0.279535i	$-0.909820\pi$
$811$		−	15.9212i		−	0.559069i	0.960136	−	0.279535i	$-0.0901801\pi$
$812$	21.3516	+	73.0818i	0.749293	+	2.56467i
$813$		0			0
$814$	26.6969			0.935727
$815$	−42.0980	−	31.2352i	−1.47463	−	1.09412i
$816$		0			0
$817$	−23.6259			−0.826566
$818$		−	65.5360i		−	2.29141i
$819$		0			0
$820$	42.2474	−	56.9400i	1.47534	−	1.98843i
$821$			13.7135i			0.478606i	0.970945	+	0.239303i	$0.0769189\pi$
$821$			13.7135i			0.478606i	−0.970945	+	0.239303i	$0.923081\pi$
$822$		0			0
$823$		−	19.1412i		−	0.667219i	−0.942711	−	0.333609i	$-0.891733\pi$
$823$		−	19.1412i		−	0.667219i	0.942711	−	0.333609i	$-0.108267\pi$
$824$	−34.3729			−1.19744
$825$		0			0
$826$	70.2929	−	20.5367i	2.44580	−	0.714564i
$827$	22.2948			0.775268			0.387634	−	0.921813i	$-0.373292\pi$
$827$	22.2948			0.775268			0.387634	+	0.921813i	$0.373292\pi$
$828$		0			0
$829$		−	11.3057i		−	0.392662i	−0.980538	−	0.196331i	$-0.937097\pi$
$829$		−	11.3057i		−	0.392662i	0.980538	−	0.196331i	$-0.0629028\pi$
$830$	−6.76742	−	5.02118i	−0.234901	−	0.174288i
$831$		0			0
$832$	14.0960			0.488691
$833$	−19.6186	−	30.7093i	−0.679745	−	1.06401i
$834$		0			0
$835$	44.4949	+	33.0136i	1.53981	+	1.14248i
$836$	22.5160			0.778731
$837$		0			0
$838$	−24.8827			−0.859560
$839$	7.72513			0.266701			0.133350	−	0.991069i	$-0.457426\pi$
$839$	7.72513			0.266701			0.133350	+	0.991069i	$0.457426\pi$
$840$		0			0
$841$	−40.5959			−1.39986
$842$	38.9776			1.34326
$843$		0			0
$844$	−34.4949			−1.18736
$845$	15.5848	−	21.0049i	0.536135	−	0.722589i
$846$		0			0
$847$	22.8563	−	6.67767i	0.785350	−	0.229448i
$848$	3.14789			0.108099
$849$		0			0
$850$	−58.1539	+	17.6151i	−1.99466	+	0.604194i
$851$			29.2699i			1.00336i
$852$		0			0
$853$	32.1296			1.10010			0.550049	−	0.835132i	$-0.314609\pi$
$853$	32.1296			1.10010			0.550049	+	0.835132i	$0.314609\pi$
$854$	13.0547	+	44.6834i	0.446722	+	1.52903i
$855$		0			0
$856$	19.3485			0.661317
$857$			38.7810i			1.32473i	0.749179	+	0.662367i	$0.230448\pi$
$857$			38.7810i			1.32473i	−0.749179	+	0.662367i	$0.769552\pi$
$858$		0			0
$859$			10.4587i			0.356847i	0.983954	+	0.178423i	$0.0570997\pi$
$859$			10.4587i			0.356847i	−0.983954	+	0.178423i	$0.942900\pi$
$860$	31.7081	+	23.5263i	1.08124	+	0.802239i
$861$		0			0
$862$		−	41.5837i		−	1.41635i
$863$	−6.87342			−0.233974			−0.116987	−	0.993133i	$-0.537324\pi$
$863$	−6.87342			−0.233974			−0.116987	+	0.993133i	$0.537324\pi$
$864$		0			0
$865$	−6.44949	−	4.78529i	−0.219289	−	0.162705i
$866$	−38.2354			−1.29929
$867$		0			0
$868$	21.4582	+	73.4468i	0.728339	+	2.49295i
$869$		−	5.65685i		−	0.191896i
$870$		0			0
$871$		−	10.9250i		−	0.370179i
$872$	43.6464			1.47805
$873$		0			0
$874$			38.9988i			1.31915i
$875$	29.5272	+	1.77286i	0.998202	+	0.0599337i
$876$		0			0
$877$		−	19.1412i		−	0.646351i	−0.946339	−	0.323175i	$-0.895250\pi$
$877$		−	19.1412i		−	0.646351i	0.946339	−	0.323175i	$-0.104750\pi$
$878$		−	24.4150i		−	0.823965i
$879$		0			0
$880$	−2.53958	−	1.88428i	−0.0856094	−	0.0635191i
$881$	23.9830			0.808007			0.404003	−	0.914758i	$-0.367618\pi$
$881$	23.9830			0.808007			0.404003	+	0.914758i	$0.367618\pi$
$882$		0			0
$883$		−	4.45178i		−	0.149814i	−0.997191	−	0.0749072i	$-0.976134\pi$
$883$		−	4.45178i		−	0.149814i	0.997191	−	0.0749072i	$-0.0238661\pi$
$884$			20.4989i			0.689452i
$885$		0			0
$886$	8.44949			0.283866
$887$			9.52301i			0.319751i	0.987137	+	0.159876i	$0.0511094\pi$
$887$			9.52301i			0.319751i	−0.987137	+	0.159876i	$0.948891\pi$
$888$		0			0
$889$		0			0
$890$	24.8651	−	33.5125i	0.833480	−	1.12334i
$891$		0			0
$892$	−44.6863			−1.49621
$893$	7.45107			0.249340
$894$		0			0
$895$	25.1393	+	18.6524i	0.840314	+	0.623483i
$896$	−50.6912	+	14.8099i	−1.69347	+	0.494765i
$897$		0			0
$898$		−	84.8349i		−	2.83098i
$899$	−69.9435			−2.33275
$900$		0			0
$901$		−	16.3875i		−	0.545946i
$902$		−	30.3465i		−	1.01043i
$903$		0			0
$904$	35.1464			1.16895
$905$	−36.8790	−	27.3629i	−1.22590	−	0.909572i
$906$		0			0
$907$			21.9591i			0.729140i	0.931176	+	0.364570i	$0.118784\pi$
$907$			21.9591i			0.729140i	−0.931176	+	0.364570i	$0.881216\pi$
$908$		−	68.7647i		−	2.28204i
$909$		0			0
$910$	5.46631	−	14.7870i	0.181206	−	0.490184i
$911$			26.8701i			0.890245i	0.895470	+	0.445122i	$0.146840\pi$
$911$			26.8701i			0.890245i	−0.895470	+	0.445122i	$0.853160\pi$
$912$		0			0
$913$	−2.28303			−0.0755574
$914$		−	3.46410i		−	0.114582i
$915$		0			0
$916$			12.9996i			0.429519i
$917$	−43.6464	+	12.7517i	−1.44133	+	0.421099i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	16.3183	−	21.9934i	0.538000	−	0.725102i
$921$		0			0
$922$	−0.628417			−0.0206958
$923$			6.29431i			0.207180i
$924$		0			0
$925$	−38.6969	+	11.7215i	−1.27235	+	0.385401i
$926$			10.0424i			0.330012i
$927$		0			0
$928$		−	36.9820i		−	1.21399i
$929$	31.7081			1.04031			0.520154	−	0.854072i	$-0.325874\pi$
$929$	31.7081			1.04031			0.520154	+	0.854072i	$0.325874\pi$
$930$		0			0
$931$	−17.3939	−	27.2269i	−0.570061	−	0.892325i
$932$	−68.0398			−2.22872
$933$		0			0
$934$		−	37.3049i		−	1.22065i
$935$	−9.80930	+	13.2207i	−0.320799	+	0.432364i
$936$		0			0
$937$	−3.93765			−0.128637			−0.0643187	−	0.997929i	$-0.520487\pi$
$937$	−3.93765			−0.128637			−0.0643187	+	0.997929i	$0.520487\pi$
$938$	16.5767	+	56.7386i	0.541249	+	1.85258i
$939$		0			0
$940$	−10.0000	−	7.41964i	−0.326164	−	0.242002i
$941$	−28.7741			−0.938010			−0.469005	−	0.883196i	$-0.655387\pi$
$941$	−28.7741			−0.938010			−0.469005	+	0.883196i	$0.655387\pi$
$942$		0			0
$943$	33.2711			1.08346
$944$	11.8569			0.385909
$945$		0			0
$946$	16.8990			0.549433
$947$	−52.4064			−1.70298			−0.851490	−	0.524371i	$-0.824300\pi$
$947$	−52.4064			−1.70298			−0.851490	+	0.524371i	$0.824300\pi$
$948$		0			0
$949$	−12.8990			−0.418719
$950$	−51.5593	+	15.6176i	−1.67280	+	0.506702i
$951$		0			0
$952$	−13.0698	−	44.7351i	−0.423594	−	1.44987i
$953$	−52.8781			−1.71289			−0.856444	−	0.516240i	$-0.827331\pi$
$953$	−52.8781			−1.71289			−0.856444	+	0.516240i	$0.827331\pi$
$954$		0			0
$955$	15.4941	+	11.4960i	0.501376	+	0.372003i
$956$		−	0.492810i		−	0.0159386i
$957$		0			0
$958$	33.2711			1.07494
$959$	2.66477	−	0.778539i	0.0860500	−	0.0251403i
$960$		0			0
$961$	−39.2929			−1.26751
$962$			21.5491i			0.694771i
$963$		0			0
$964$			18.8428i			0.606886i
$965$	−9.19211	−	6.82021i	−0.295905	−	0.219550i
$966$		0			0
$967$		−	37.3155i		−	1.19998i	−0.800006	−	0.599992i	$-0.795170\pi$
$967$		−	37.3155i		−	1.19998i	0.800006	−	0.599992i	$-0.204830\pi$
$968$	30.4534			0.978809
$969$		0			0
$970$	3.55051	−	4.78529i	0.114000	−	0.153646i
$971$	26.1093			0.837889			0.418944	−	0.908012i	$-0.362400\pi$
$971$	26.1093			0.837889			0.418944	+	0.908012i	$0.362400\pi$
$972$		0			0
$973$	6.22069	+	21.2921i	0.199426	+	0.682593i
$974$			73.6033i			2.35840i
$975$		0			0
$976$			7.53712i			0.241257i
$977$	−50.7795			−1.62458			−0.812290	−	0.583254i	$-0.801779\pi$
$977$	−50.7795			−1.62458			−0.812290	+	0.583254i	$0.801779\pi$
$978$		0			0
$979$		−	11.3057i		−	0.361331i
$980$	−3.76789	+	53.8614i	−0.120361	+	1.72054i
$981$		0			0
$982$			62.7258i			2.00166i
$983$			11.3004i			0.360428i	0.983627	+	0.180214i	$0.0576791\pi$
$983$			11.3004i			0.360428i	−0.983627	+	0.180214i	$0.942321\pi$
$984$		0			0
$985$	−19.4317	+	26.1896i	−0.619146	+	0.834469i
$986$	101.382			3.22867
$987$		0			0
$988$			18.1743i			0.578202i
$989$			18.5276i			0.589145i
$990$		0			0
$991$	4.20204			0.133482			0.0667411	−	0.997770i	$-0.478740\pi$
$991$	4.20204			0.133482			0.0667411	+	0.997770i	$0.478740\pi$
$992$		−	37.1667i		−	1.18004i
$993$		0			0
$994$	−9.55051	−	32.6894i	−0.302924	−	1.03684i
$995$	−8.28836	−	6.14966i	−0.262759	−	0.194957i
$996$		0			0
$997$	−28.8204			−0.912751			−0.456376	−	0.889787i	$-0.650853\pi$
$997$	−28.8204			−0.912751			−0.456376	+	0.889787i	$0.650853\pi$
$998$	−23.3441			−0.738946
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.g.a.314.14	yes	16
3.2	odd	2	inner	315.2.g.a.314.3	yes	16
4.3	odd	2		5040.2.k.g.1889.7		16
5.2	odd	4		1575.2.b.h.251.16		16
5.3	odd	4		1575.2.b.h.251.1		16
5.4	even	2	inner	315.2.g.a.314.1	✓	16
7.6	odd	2	inner	315.2.g.a.314.15	yes	16
12.11	even	2		5040.2.k.g.1889.9		16
15.2	even	4		1575.2.b.h.251.4		16
15.8	even	4		1575.2.b.h.251.13		16
15.14	odd	2	inner	315.2.g.a.314.16	yes	16
20.19	odd	2		5040.2.k.g.1889.6		16
21.20	even	2	inner	315.2.g.a.314.2	yes	16
28.27	even	2		5040.2.k.g.1889.10		16
35.13	even	4		1575.2.b.h.251.2		16
35.27	even	4		1575.2.b.h.251.15		16
35.34	odd	2	inner	315.2.g.a.314.4	yes	16
60.59	even	2		5040.2.k.g.1889.12		16
84.83	odd	2		5040.2.k.g.1889.8		16
105.62	odd	4		1575.2.b.h.251.3		16
105.83	odd	4		1575.2.b.h.251.14		16
105.104	even	2	inner	315.2.g.a.314.13	yes	16
140.139	even	2		5040.2.k.g.1889.11		16
420.419	odd	2		5040.2.k.g.1889.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.g.a.314.1	✓	16	5.4	even	2	inner
315.2.g.a.314.2	yes	16	21.20	even	2	inner
315.2.g.a.314.3	yes	16	3.2	odd	2	inner
315.2.g.a.314.4	yes	16	35.34	odd	2	inner
315.2.g.a.314.13	yes	16	105.104	even	2	inner
315.2.g.a.314.14	yes	16	1.1	even	1	trivial
315.2.g.a.314.15	yes	16	7.6	odd	2	inner
315.2.g.a.314.16	yes	16	15.14	odd	2	inner
1575.2.b.h.251.1		16	5.3	odd	4
1575.2.b.h.251.2		16	35.13	even	4
1575.2.b.h.251.3		16	105.62	odd	4
1575.2.b.h.251.4		16	15.2	even	4
1575.2.b.h.251.13		16	15.8	even	4
1575.2.b.h.251.14		16	105.83	odd	4
1575.2.b.h.251.15		16	35.27	even	4
1575.2.b.h.251.16		16	5.2	odd	4
5040.2.k.g.1889.5		16	420.419	odd	2
5040.2.k.g.1889.6		16	20.19	odd	2
5040.2.k.g.1889.7		16	4.3	odd	2
5040.2.k.g.1889.8		16	84.83	odd	2
5040.2.k.g.1889.9		16	12.11	even	2
5040.2.k.g.1889.10		16	28.27	even	2
5040.2.k.g.1889.11		16	140.139	even	2
5040.2.k.g.1889.12		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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.33441 q^{2} +3.44949 q^{4} +(-1.33239 + 1.79576i) q^{5} +(2.53958 - 0.741964i) q^{7} +3.38371 q^{8} +O(q^{10})\)	\(q+2.33441 q^{2} +3.44949 q^{4} +(-1.33239 + 1.79576i) q^{5} +(2.53958 - 0.741964i) q^{7} +3.38371 q^{8} +(-3.11034 + 4.19204i) q^{10} +1.41421i q^{11} -1.14152 q^{13} +(5.92844 - 1.73205i) q^{14} +1.00000 q^{16} -5.20586i q^{17} -4.61552i q^{19} +(-4.59606 + 6.19445i) q^{20} +3.30136i q^{22} -3.61953 q^{23} +(-1.44949 - 4.78529i) q^{25} -2.66477 q^{26} +(8.76027 - 2.55940i) q^{28} +8.34242i q^{29} +8.38408i q^{31} -4.43300 q^{32} -12.1526i q^{34} +(-2.05132 + 5.54906i) q^{35} -8.08665i q^{37} -10.7745i q^{38} +(-4.50841 + 6.07632i) q^{40} -9.19211 q^{41} -5.11879i q^{43} +4.87832i q^{44} -8.44949 q^{46} +1.61435i q^{47} +(5.89898 - 3.76856i) q^{49} +(-3.38371 - 11.1708i) q^{50} -3.93765 q^{52} +3.14789 q^{53} +(-2.53958 - 1.88428i) q^{55} +(8.59322 - 2.51059i) q^{56} +19.4747i q^{58} +11.8569 q^{59} +7.53712i q^{61} +19.5719i q^{62} -12.3485 q^{64} +(1.52094 - 2.04989i) q^{65} +9.57058i q^{67} -17.9576i q^{68} +(-4.78864 + 12.9538i) q^{70} -5.51399i q^{71} +11.2999 q^{73} -18.8776i q^{74} -15.9212i q^{76} +(1.04930 + 3.59151i) q^{77} -4.00000 q^{79} +(-1.33239 + 1.79576i) q^{80} -21.4582 q^{82} +1.61435i q^{83} +(9.34847 + 6.93623i) q^{85} -11.9494i q^{86} +4.78529i q^{88} -7.99432 q^{89} +(-2.89898 + 0.846964i) q^{91} -12.4855 q^{92} +3.76856i q^{94} +(8.28836 + 6.14966i) q^{95} -1.14152 q^{97} +(13.7707 - 8.79738i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} + 16 q^{16} + 16 q^{25} - 96 q^{46} + 16 q^{49} - 80 q^{64} - 48 q^{70} - 64 q^{79} + 32 q^{85} + 32 q^{91}+O(q^{100}) \) 16 * q + 16 * q^4 + 16 * q^16 + 16 * q^25 - 96 * q^46 + 16 * q^49 - 80 * q^64 - 48 * q^70 - 64 * q^79 + 32 * q^85 + 32 * q^91

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