LMFDB - Embedded newform 2240.2.bd.a.561.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (of order $4$, degree $2$, not 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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.14
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.605289 - 0.605289i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.26725i q^{9} +O(q^{10})$	\(q+(0.605289 - 0.605289i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.26725i q^{9} +(0.812056 + 0.812056i) q^{11} +(-2.79946 + 2.79946i) q^{13} -0.856008 q^{15} +4.69853 q^{17} +(1.00378 - 1.00378i) q^{19} +(-0.605289 - 0.605289i) q^{21} -8.15692i q^{23} +1.00000i q^{25} +(3.18821 + 3.18821i) q^{27} +(0.122932 - 0.122932i) q^{29} +2.46615 q^{31} +0.983058 q^{33} +(-0.707107 + 0.707107i) q^{35} +(3.53721 + 3.53721i) q^{37} +3.38897i q^{39} +4.84284i q^{41} +(2.21661 + 2.21661i) q^{43} +(1.60319 - 1.60319i) q^{45} +3.94282 q^{47} -1.00000 q^{49} +(2.84397 - 2.84397i) q^{51} +(7.19461 + 7.19461i) q^{53} -1.14842i q^{55} -1.21516i q^{57} +(6.54526 + 6.54526i) q^{59} +(-1.81508 + 1.81508i) q^{61} +2.26725 q^{63} +3.95904 q^{65} +(0.162648 - 0.162648i) q^{67} +(-4.93730 - 4.93730i) q^{69} -6.00458i q^{71} -7.09981i q^{73} +(0.605289 + 0.605289i) q^{75} +(0.812056 - 0.812056i) q^{77} +10.3006 q^{79} -2.94217 q^{81} +(7.83163 - 7.83163i) q^{83} +(-3.32236 - 3.32236i) q^{85} -0.148819i q^{87} -3.28176i q^{89} +(2.79946 + 2.79946i) q^{91} +(1.49274 - 1.49274i) q^{93} -1.41956 q^{95} +0.453882 q^{97} +(-1.84113 + 1.84113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.605289	−	0.605289i	0.349464	−	0.349464i	−0.510446	−	0.859910i	$-0.670520\pi$
$3$	0.605289	−	0.605289i	0.349464	−	0.349464i	0.859910	+	0.510446i	$0.170520\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			2.26725i			0.755750i
$10$		0			0
$11$	0.812056	+	0.812056i	0.244844	+	0.244844i	0.818851	−	0.574007i	$-0.194612\pi$
$11$	0.812056	+	0.812056i	0.244844	+	0.244844i	−0.574007	+	0.818851i	$0.694612\pi$
$12$		0			0
$13$	−2.79946	+	2.79946i	−0.776431	+	0.776431i	−0.979222	−	0.202791i	$-0.934999\pi$
$13$	−2.79946	+	2.79946i	−0.776431	+	0.776431i	0.202791	+	0.979222i	$0.434999\pi$
$14$		0			0
$15$	−0.856008			−0.221020
$16$		0			0
$17$	4.69853			1.13956			0.569780	−	0.821797i	$-0.307028\pi$
$17$	4.69853			1.13956			0.569780	+	0.821797i	$0.307028\pi$
$18$		0			0
$19$	1.00378	−	1.00378i	0.230283	−	0.230283i	−0.582528	−	0.812811i	$-0.697936\pi$
$19$	1.00378	−	1.00378i	0.230283	−	0.230283i	0.812811	+	0.582528i	$0.197936\pi$
$20$		0			0
$21$	−0.605289	−	0.605289i	−0.132085	−	0.132085i
$22$		0			0
$23$		−	8.15692i		−	1.70084i	−0.526107	−	0.850418i	$-0.676349\pi$
$23$		−	8.15692i		−	1.70084i	0.526107	−	0.850418i	$-0.323651\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	3.18821	+	3.18821i	0.613571	+	0.613571i
$28$		0			0
$29$	0.122932	−	0.122932i	0.0228279	−	0.0228279i	−0.695601	−	0.718429i	$-0.744862\pi$
$29$	0.122932	−	0.122932i	0.0228279	−	0.0228279i	0.718429	+	0.695601i	$0.244862\pi$
$30$		0			0
$31$	2.46615			0.442934			0.221467	−	0.975168i	$-0.428915\pi$
$31$	2.46615			0.442934			0.221467	+	0.975168i	$0.428915\pi$
$32$		0			0
$33$	0.983058			0.171128
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	3.53721	+	3.53721i	0.581513	+	0.581513i	0.935319	−	0.353806i	$-0.115113\pi$
$37$	3.53721	+	3.53721i	0.581513	+	0.581513i	−0.353806	+	0.935319i	$0.615113\pi$
$38$		0			0
$39$			3.38897i			0.542669i
$40$		0			0
$41$			4.84284i			0.756324i	0.925739	+	0.378162i	$0.123444\pi$
$41$			4.84284i			0.756324i	−0.925739	+	0.378162i	$0.876556\pi$
$42$		0			0
$43$	2.21661	+	2.21661i	0.338030	+	0.338030i	0.855625	−	0.517596i	$-0.173173\pi$
$43$	2.21661	+	2.21661i	0.338030	+	0.338030i	−0.517596	+	0.855625i	$0.673173\pi$
$44$		0			0
$45$	1.60319	−	1.60319i	0.238989	−	0.238989i
$46$		0			0
$47$	3.94282			0.575119			0.287560	−	0.957763i	$-0.407156\pi$
$47$	3.94282			0.575119			0.287560	+	0.957763i	$0.407156\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	2.84397	−	2.84397i	0.398235	−	0.398235i
$52$		0			0
$53$	7.19461	+	7.19461i	0.988255	+	0.988255i	0.999932	−	0.0116763i	$-0.00371678\pi$
$53$	7.19461	+	7.19461i	0.988255	+	0.988255i	−0.0116763	+	0.999932i	$0.503717\pi$
$54$		0			0
$55$		−	1.14842i		−	0.154853i
$56$		0			0
$57$		−	1.21516i		−	0.160951i
$58$		0			0
$59$	6.54526	+	6.54526i	0.852120	+	0.852120i	0.990394	−	0.138274i	$-0.0441555\pi$
$59$	6.54526	+	6.54526i	0.852120	+	0.852120i	−0.138274	+	0.990394i	$0.544155\pi$
$60$		0			0
$61$	−1.81508	+	1.81508i	−0.232398	+	0.232398i	−0.813693	−	0.581295i	$-0.802546\pi$
$61$	−1.81508	+	1.81508i	−0.232398	+	0.232398i	0.581295	+	0.813693i	$0.302546\pi$
$62$		0			0
$63$	2.26725			0.285647
$64$		0			0
$65$	3.95904			0.491058
$66$		0			0
$67$	0.162648	−	0.162648i	0.0198706	−	0.0198706i	−0.697102	−	0.716972i	$-0.745527\pi$
$67$	0.162648	−	0.162648i	0.0198706	−	0.0198706i	0.716972	+	0.697102i	$0.245527\pi$
$68$		0			0
$69$	−4.93730	−	4.93730i	−0.594381	−	0.594381i
$70$		0			0
$71$		−	6.00458i		−	0.712613i	−0.934369	−	0.356306i	$-0.884036\pi$
$71$		−	6.00458i		−	0.712613i	0.934369	−	0.356306i	$-0.115964\pi$
$72$		0			0
$73$		−	7.09981i		−	0.830970i	−0.909600	−	0.415485i	$-0.863612\pi$
$73$		−	7.09981i		−	0.830970i	0.909600	−	0.415485i	$-0.136388\pi$
$74$		0			0
$75$	0.605289	+	0.605289i	0.0698928	+	0.0698928i
$76$		0			0
$77$	0.812056	−	0.812056i	0.0925424	−	0.0925424i
$78$		0			0
$79$	10.3006			1.15890			0.579452	−	0.815006i	$-0.303267\pi$
$79$	10.3006			1.15890			0.579452	+	0.815006i	$0.303267\pi$
$80$		0			0
$81$	−2.94217			−0.326908
$82$		0			0
$83$	7.83163	−	7.83163i	0.859633	−	0.859633i	−0.131662	−	0.991295i	$-0.542031\pi$
$83$	7.83163	−	7.83163i	0.859633	−	0.859633i	0.991295	+	0.131662i	$0.0420314\pi$
$84$		0			0
$85$	−3.32236	−	3.32236i	−0.360361	−	0.360361i
$86$		0			0
$87$		−	0.148819i		−	0.0159551i
$88$		0			0
$89$		−	3.28176i		−	0.347866i	−0.984757	−	0.173933i	$-0.944352\pi$
$89$		−	3.28176i		−	0.347866i	0.984757	−	0.173933i	$-0.0556477\pi$
$90$		0			0
$91$	2.79946	+	2.79946i	0.293463	+	0.293463i
$92$		0			0
$93$	1.49274	−	1.49274i	0.154790	−	0.154790i
$94$		0			0
$95$	−1.41956			−0.145644
$96$		0			0
$97$	0.453882			0.0460847			0.0230424	−	0.999734i	$-0.492665\pi$
$97$	0.453882			0.0460847			0.0230424	+	0.999734i	$0.492665\pi$
$98$		0			0
$99$	−1.84113	+	1.84113i	−0.185041	+	0.185041i
$100$		0			0
$101$	−13.1056	−	13.1056i	−1.30405	−	1.30405i	−0.925635	−	0.378417i	$-0.876469\pi$
$101$	−13.1056	−	13.1056i	−1.30405	−	1.30405i	−0.378417	−	0.925635i	$-0.623531\pi$
$102$		0			0
$103$		−	7.66619i		−	0.755373i	−0.925934	−	0.377686i	$-0.876720\pi$
$103$		−	7.66619i		−	0.755373i	0.925934	−	0.377686i	$-0.123280\pi$
$104$		0			0
$105$			0.856008i			0.0835379i
$106$		0			0
$107$	0.120113	+	0.120113i	0.0116117	+	0.0116117i	0.712889	−	0.701277i	$-0.247386\pi$
$107$	0.120113	+	0.120113i	0.0116117	+	0.0116117i	−0.701277	+	0.712889i	$0.747386\pi$
$108$		0			0
$109$	3.37380	−	3.37380i	0.323152	−	0.323152i	−0.526823	−	0.849975i	$-0.676617\pi$
$109$	3.37380	−	3.37380i	0.323152	−	0.323152i	0.849975	+	0.526823i	$0.176617\pi$
$110$		0			0
$111$	4.28207			0.406436
$112$		0			0
$113$	19.2238			1.80843			0.904213	−	0.427081i	$-0.140458\pi$
$113$	19.2238			1.80843			0.904213	+	0.427081i	$0.140458\pi$
$114$		0			0
$115$	−5.76782	+	5.76782i	−0.537852	+	0.537852i
$116$		0			0
$117$	−6.34708	−	6.34708i	−0.586788	−	0.586788i
$118$		0			0
$119$		−	4.69853i		−	0.430714i
$120$		0			0
$121$		−	9.68113i		−	0.880103i
$122$		0			0
$123$	2.93132	+	2.93132i	0.264308	+	0.264308i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	4.68107			0.415377			0.207689	−	0.978195i	$-0.433406\pi$
$127$	4.68107			0.415377			0.207689	+	0.978195i	$0.433406\pi$
$128$		0			0
$129$	2.68338			0.236259
$130$		0			0
$131$	−3.72957	+	3.72957i	−0.325854	+	0.325854i	−0.851007	−	0.525154i	$-0.824008\pi$
$131$	−3.72957	+	3.72957i	−0.325854	+	0.325854i	0.525154	+	0.851007i	$0.324008\pi$
$132$		0			0
$133$	−1.00378	−	1.00378i	−0.0870389	−	0.0870389i
$134$		0			0
$135$		−	4.50881i		−	0.388057i
$136$		0			0
$137$			14.1902i			1.21235i	0.795331	+	0.606175i	$0.207297\pi$
$137$			14.1902i			1.21235i	−0.795331	+	0.606175i	$0.792703\pi$
$138$		0			0
$139$	7.05584	+	7.05584i	0.598468	+	0.598468i	0.939905	−	0.341437i	$-0.110913\pi$
$139$	7.05584	+	7.05584i	0.598468	+	0.598468i	−0.341437	+	0.939905i	$0.610913\pi$
$140$		0			0
$141$	2.38655	−	2.38655i	0.200983	−	0.200983i
$142$		0			0
$143$	−4.54664			−0.380209
$144$		0			0
$145$	−0.173852			−0.0144376
$146$		0			0
$147$	−0.605289	+	0.605289i	−0.0499234	+	0.0499234i
$148$		0			0
$149$	14.9614	+	14.9614i	1.22569	+	1.22569i	0.965580	+	0.260105i	$0.0837572\pi$
$149$	14.9614	+	14.9614i	1.22569	+	1.22569i	0.260105	+	0.965580i	$0.416243\pi$
$150$		0			0
$151$			1.18322i			0.0962888i	0.998840	+	0.0481444i	$0.0153308\pi$
$151$			1.18322i			0.0962888i	−0.998840	+	0.0481444i	$0.984669\pi$
$152$		0			0
$153$			10.6527i			0.861223i
$154$		0			0
$155$	−1.74383	−	1.74383i	−0.140068	−	0.140068i
$156$		0			0
$157$	4.99207	−	4.99207i	0.398411	−	0.398411i	−0.479262	−	0.877672i	$-0.659095\pi$
$157$	4.99207	−	4.99207i	0.398411	−	0.398411i	0.877672	+	0.479262i	$0.159095\pi$
$158$		0			0
$159$	8.70964			0.690719
$160$		0			0
$161$	−8.15692			−0.642856
$162$		0			0
$163$	−5.00263	+	5.00263i	−0.391836	+	0.391836i	−0.875341	−	0.483505i	$-0.839363\pi$
$163$	−5.00263	+	5.00263i	−0.391836	+	0.391836i	0.483505	+	0.875341i	$0.339363\pi$
$164$		0			0
$165$	−0.695127	−	0.695127i	−0.0541156	−	0.0541156i
$166$		0			0
$167$		−	24.8909i		−	1.92612i	−0.269293	−	0.963058i	$-0.586790\pi$
$167$		−	24.8909i		−	1.92612i	0.269293	−	0.963058i	$-0.413210\pi$
$168$		0			0
$169$		−	2.67398i		−	0.205691i
$170$		0			0
$171$	2.27582	+	2.27582i	0.174037	+	0.174037i
$172$		0			0
$173$	−10.3193	+	10.3193i	−0.784561	+	0.784561i	−0.980597	−	0.196036i	$-0.937193\pi$
$173$	−10.3193	+	10.3193i	−0.784561	+	0.784561i	0.196036	+	0.980597i	$0.437193\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	7.92355			0.595570
$178$		0			0
$179$	−16.6480	+	16.6480i	−1.24433	+	1.24433i	−0.286141	+	0.958188i	$0.592372\pi$
$179$	−16.6480	+	16.6480i	−1.24433	+	1.24433i	−0.958188	+	0.286141i	$0.907628\pi$
$180$		0			0
$181$	−9.09342	−	9.09342i	−0.675909	−	0.675909i	0.283163	−	0.959072i	$-0.408616\pi$
$181$	−9.09342	−	9.09342i	−0.675909	−	0.675909i	−0.959072	+	0.283163i	$0.908616\pi$
$182$		0			0
$183$			2.19730i			0.162429i
$184$		0			0
$185$		−	5.00237i		−	0.367781i
$186$		0			0
$187$	3.81547	+	3.81547i	0.279015	+	0.279015i
$188$		0			0
$189$	3.18821	−	3.18821i	0.231908	−	0.231908i
$190$		0			0
$191$	4.53246			0.327958			0.163979	−	0.986464i	$-0.447567\pi$
$191$	4.53246			0.327958			0.163979	+	0.986464i	$0.447567\pi$
$192$		0			0
$193$	21.9559			1.58042			0.790210	−	0.612836i	$-0.209971\pi$
$193$	21.9559			1.58042			0.790210	+	0.612836i	$0.209971\pi$
$194$		0			0
$195$	2.39636	−	2.39636i	0.171607	−	0.171607i
$196$		0			0
$197$	−2.00733	−	2.00733i	−0.143016	−	0.143016i	0.631974	−	0.774990i	$-0.282245\pi$
$197$	−2.00733	−	2.00733i	−0.143016	−	0.143016i	−0.774990	+	0.631974i	$0.782245\pi$
$198$		0			0
$199$			7.06629i			0.500916i	0.968127	+	0.250458i	$0.0805813\pi$
$199$			7.06629i			0.500916i	−0.968127	+	0.250458i	$0.919419\pi$
$200$		0			0
$201$		−	0.196898i		−	0.0138881i
$202$		0			0
$203$	−0.122932	−	0.122932i	−0.00862813	−	0.00862813i
$204$		0			0
$205$	3.42440	−	3.42440i	0.239171	−	0.239171i
$206$		0			0
$207$	18.4938			1.28541
$208$		0			0
$209$	1.63025			0.112767
$210$		0			0
$211$	5.92777	−	5.92777i	0.408084	−	0.408084i	−0.472986	−	0.881070i	$-0.656824\pi$
$211$	5.92777	−	5.92777i	0.408084	−	0.408084i	0.881070	+	0.472986i	$0.156824\pi$
$212$		0			0
$213$	−3.63451	−	3.63451i	−0.249033	−	0.249033i
$214$		0			0
$215$		−	3.13476i		−	0.213789i
$216$		0			0
$217$		−	2.46615i		−	0.167413i
$218$		0			0
$219$	−4.29744	−	4.29744i	−0.290394	−	0.290394i
$220$		0			0
$221$	−13.1534	+	13.1534i	−0.884791	+	0.884791i
$222$		0			0
$223$	−26.1813			−1.75323			−0.876615	−	0.481192i	$-0.840204\pi$
$223$	−26.1813			−1.75323			−0.876615	+	0.481192i	$0.840204\pi$
$224$		0			0
$225$	−2.26725			−0.151150
$226$		0			0
$227$	−2.25330	+	2.25330i	−0.149557	+	0.149557i	−0.777920	−	0.628363i	$-0.783725\pi$
$227$	−2.25330	+	2.25330i	−0.149557	+	0.149557i	0.628363	+	0.777920i	$0.283725\pi$
$228$		0			0
$229$	8.75526	+	8.75526i	0.578564	+	0.578564i	0.934507	−	0.355944i	$-0.115841\pi$
$229$	8.75526	+	8.75526i	0.578564	+	0.578564i	−0.355944	+	0.934507i	$0.615841\pi$
$230$		0			0
$231$		−	0.983058i		−	0.0646805i
$232$		0			0
$233$			24.0934i			1.57841i	0.614131	+	0.789204i	$0.289507\pi$
$233$			24.0934i			1.57841i	−0.614131	+	0.789204i	$0.710493\pi$
$234$		0			0
$235$	−2.78799	−	2.78799i	−0.181869	−	0.181869i
$236$		0			0
$237$	6.23482	−	6.23482i	0.404995	−	0.404995i
$238$		0			0
$239$	−21.4289			−1.38612			−0.693061	−	0.720879i	$-0.743738\pi$
$239$	−21.4289			−1.38612			−0.693061	+	0.720879i	$0.743738\pi$
$240$		0			0
$241$	7.30564			0.470598			0.235299	−	0.971923i	$-0.424393\pi$
$241$	7.30564			0.470598			0.235299	+	0.971923i	$0.424393\pi$
$242$		0			0
$243$	−11.3455	+	11.3455i	−0.727814	+	0.727814i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$			5.62010i			0.357598i
$248$		0			0
$249$		−	9.48080i		−	0.600821i
$250$		0			0
$251$	−14.2655	−	14.2655i	−0.900433	−	0.900433i	0.0950406	−	0.995473i	$-0.469702\pi$
$251$	−14.2655	−	14.2655i	−0.900433	−	0.900433i	−0.995473	+	0.0950406i	$0.969702\pi$
$252$		0			0
$253$	6.62388	−	6.62388i	0.416440	−	0.416440i
$254$		0			0
$255$	−4.02198			−0.251866
$256$		0			0
$257$	16.1267			1.00596			0.502979	−	0.864299i	$-0.332237\pi$
$257$	16.1267			1.00596			0.502979	+	0.864299i	$0.332237\pi$
$258$		0			0
$259$	3.53721	−	3.53721i	0.219791	−	0.219791i
$260$		0			0
$261$	0.278718	+	0.278718i	0.0172522	+	0.0172522i
$262$		0			0
$263$			16.7414i			1.03232i	0.856492	+	0.516160i	$0.172639\pi$
$263$			16.7414i			1.03232i	−0.856492	+	0.516160i	$0.827361\pi$
$264$		0			0
$265$		−	10.1747i		−	0.625028i
$266$		0			0
$267$	−1.98642	−	1.98642i	−0.121567	−	0.121567i
$268$		0			0
$269$	−7.19225	+	7.19225i	−0.438519	+	0.438519i	−0.891513	−	0.452994i	$-0.850356\pi$
$269$	−7.19225	+	7.19225i	−0.438519	+	0.438519i	0.452994	+	0.891513i	$0.350356\pi$
$270$		0			0
$271$	−18.4417			−1.12025			−0.560125	−	0.828408i	$-0.689247\pi$
$271$	−18.4417			−1.12025			−0.560125	+	0.828408i	$0.689247\pi$
$272$		0			0
$273$	3.38897			0.205110
$274$		0			0
$275$	−0.812056	+	0.812056i	−0.0489688	+	0.0489688i
$276$		0			0
$277$	−16.8558	−	16.8558i	−1.01277	−	1.01277i	−0.999917	−	0.0128486i	$-0.995910\pi$
$277$	−16.8558	−	16.8558i	−1.01277	−	1.01277i	−0.0128486	−	0.999917i	$-0.504090\pi$
$278$		0			0
$279$			5.59139i			0.334748i
$280$		0			0
$281$		−	17.9304i		−	1.06964i	−0.844967	−	0.534818i	$-0.820380\pi$
$281$		−	17.9304i		−	1.06964i	0.844967	−	0.534818i	$-0.179620\pi$
$282$		0			0
$283$	−19.6883	−	19.6883i	−1.17035	−	1.17035i	−0.982127	−	0.188222i	$-0.939728\pi$
$283$	−19.6883	−	19.6883i	−1.17035	−	1.17035i	−0.188222	−	0.982127i	$-0.560272\pi$
$284$		0			0
$285$	−0.859245	+	0.859245i	−0.0508973	+	0.0508973i
$286$		0			0
$287$	4.84284			0.285864
$288$		0			0
$289$	5.07618			0.298599
$290$		0			0
$291$	0.274730	−	0.274730i	0.0161049	−	0.0161049i
$292$		0			0
$293$	18.2273	+	18.2273i	1.06485	+	1.06485i	0.997746	+	0.0671045i	$0.0213761\pi$
$293$	18.2273	+	18.2273i	1.06485	+	1.06485i	0.0671045	+	0.997746i	$0.478624\pi$
$294$		0			0
$295$		−	9.25639i		−	0.538928i
$296$		0			0
$297$			5.17801i			0.300459i
$298$		0			0
$299$	22.8350	+	22.8350i	1.32058	+	1.32058i
$300$		0			0
$301$	2.21661	−	2.21661i	0.127763	−	0.127763i
$302$		0			0
$303$	−15.8653			−0.911438
$304$		0			0
$305$	2.56691			0.146981
$306$		0			0
$307$	−17.6406	+	17.6406i	−1.00680	+	1.00680i	−0.00682294	+	0.999977i	$0.502172\pi$
$307$	−17.6406	+	17.6406i	−1.00680	+	1.00680i	−0.999977	+	0.00682294i	$0.997828\pi$
$308$		0			0
$309$	−4.64027	−	4.64027i	−0.263975	−	0.263975i
$310$		0			0
$311$			18.4188i			1.04444i	0.852812	+	0.522218i	$0.174895\pi$
$311$			18.4188i			1.04444i	−0.852812	+	0.522218i	$0.825105\pi$
$312$		0			0
$313$		−	19.9601i		−	1.12821i	−0.825703	−	0.564105i	$-0.809221\pi$
$313$		−	19.9601i		−	1.12821i	0.825703	−	0.564105i	$-0.190779\pi$
$314$		0			0
$315$	−1.60319	−	1.60319i	−0.0903294	−	0.0903294i
$316$		0			0
$317$	−22.4232	+	22.4232i	−1.25941	+	1.25941i	−0.308035	+	0.951375i	$0.599671\pi$
$317$	−22.4232	+	22.4232i	−1.25941	+	1.25941i	−0.951375	+	0.308035i	$0.900329\pi$
$318$		0			0
$319$	0.199655			0.0111786
$320$		0			0
$321$	0.145406			0.00811576
$322$		0			0
$323$	4.71630	−	4.71630i	0.262422	−	0.262422i
$324$		0			0
$325$	−2.79946	−	2.79946i	−0.155286	−	0.155286i
$326$		0			0
$327$		−	4.08425i		−	0.225860i
$328$		0			0
$329$		−	3.94282i		−	0.217375i
$330$		0			0
$331$	−3.88438	−	3.88438i	−0.213505	−	0.213505i	0.592250	−	0.805754i	$-0.298240\pi$
$331$	−3.88438	−	3.88438i	−0.213505	−	0.213505i	−0.805754	+	0.592250i	$0.798240\pi$
$332$		0			0
$333$	−8.01973	+	8.01973i	−0.439479	+	0.439479i
$334$		0			0
$335$	−0.230019			−0.0125673
$336$		0			0
$337$	14.4218			0.785604			0.392802	−	0.919623i	$-0.371506\pi$
$337$	14.4218			0.785604			0.392802	+	0.919623i	$0.371506\pi$
$338$		0			0
$339$	11.6360	−	11.6360i	0.631980	−	0.631980i
$340$		0			0
$341$	2.00266	+	2.00266i	0.108450	+	0.108450i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			6.98240i			0.375920i
$346$		0			0
$347$	23.2708	+	23.2708i	1.24924	+	1.24924i	0.956056	+	0.293185i	$0.0947151\pi$
$347$	23.2708	+	23.2708i	1.24924	+	1.24924i	0.293185	+	0.956056i	$0.405285\pi$
$348$		0			0
$349$	3.49358	−	3.49358i	0.187007	−	0.187007i	−0.607394	−	0.794401i	$-0.707785\pi$
$349$	3.49358	−	3.49358i	0.187007	−	0.187007i	0.794401	+	0.607394i	$0.207785\pi$
$350$		0			0
$351$	−17.8505			−0.952792
$352$		0			0
$353$	8.24329			0.438746			0.219373	−	0.975641i	$-0.429599\pi$
$353$	8.24329			0.438746			0.219373	+	0.975641i	$0.429599\pi$
$354$		0			0
$355$	−4.24588	+	4.24588i	−0.225348	+	0.225348i
$356$		0			0
$357$	−2.84397	−	2.84397i	−0.150519	−	0.150519i
$358$		0			0
$359$		−	20.9198i		−	1.10410i	−0.833810	−	0.552051i	$-0.813845\pi$
$359$		−	20.9198i		−	1.10410i	0.833810	−	0.552051i	$-0.186155\pi$
$360$		0			0
$361$			16.9848i			0.893939i
$362$		0			0
$363$	−5.85988	−	5.85988i	−0.307564	−	0.307564i
$364$		0			0
$365$	−5.02032	+	5.02032i	−0.262776	+	0.262776i
$366$		0			0
$367$	33.3855			1.74271			0.871355	−	0.490654i	$-0.163242\pi$
$367$	33.3855			1.74271			0.871355	+	0.490654i	$0.163242\pi$
$368$		0			0
$369$	−10.9799			−0.571592
$370$		0			0
$371$	7.19461	−	7.19461i	0.373525	−	0.373525i
$372$		0			0
$373$	−13.0059	−	13.0059i	−0.673421	−	0.673421i	0.285082	−	0.958503i	$-0.407979\pi$
$373$	−13.0059	−	13.0059i	−0.673421	−	0.673421i	−0.958503	+	0.285082i	$0.907979\pi$
$374$		0			0
$375$		−	0.856008i		−	0.0442041i
$376$		0			0
$377$			0.688287i			0.0354486i
$378$		0			0
$379$	−11.6155	−	11.6155i	−0.596649	−	0.596649i	0.342770	−	0.939419i	$-0.388635\pi$
$379$	−11.6155	−	11.6155i	−0.596649	−	0.596649i	−0.939419	+	0.342770i	$0.888635\pi$
$380$		0			0
$381$	2.83340	−	2.83340i	0.145159	−	0.145159i
$382$		0			0
$383$	29.1530			1.48965			0.744824	−	0.667261i	$-0.232533\pi$
$383$	29.1530			1.48965			0.744824	+	0.667261i	$0.232533\pi$
$384$		0			0
$385$	−1.14842			−0.0585289
$386$		0			0
$387$	−5.02561	+	5.02561i	−0.255466	+	0.255466i
$388$		0			0
$389$	15.9257	+	15.9257i	0.807466	+	0.807466i	0.984250	−	0.176784i	$-0.0565693\pi$
$389$	15.9257	+	15.9257i	0.807466	+	0.807466i	−0.176784	+	0.984250i	$0.556569\pi$
$390$		0			0
$391$		−	38.3255i		−	1.93821i
$392$		0			0
$393$			4.51494i			0.227748i
$394$		0			0
$395$	−7.28360	−	7.28360i	−0.366478	−	0.366478i
$396$		0			0
$397$	3.04529	−	3.04529i	0.152839	−	0.152839i	−0.626546	−	0.779385i	$-0.715532\pi$
$397$	3.04529	−	3.04529i	0.152839	−	0.152839i	0.779385	+	0.626546i	$0.215532\pi$
$398$		0			0
$399$	−1.21516			−0.0608339
$400$		0			0
$401$	−23.7861			−1.18782			−0.593909	−	0.804532i	$-0.702416\pi$
$401$	−23.7861			−1.18782			−0.593909	+	0.804532i	$0.702416\pi$
$402$		0			0
$403$	−6.90391	+	6.90391i	−0.343908	+	0.343908i
$404$		0			0
$405$	2.08043	+	2.08043i	0.103377	+	0.103377i
$406$		0			0
$407$			5.74482i			0.284760i
$408$		0			0
$409$		−	14.7195i		−	0.727831i	−0.931432	−	0.363916i	$-0.881440\pi$
$409$		−	14.7195i		−	0.727831i	0.931432	−	0.363916i	$-0.118560\pi$
$410$		0			0
$411$	8.58917	+	8.58917i	0.423673	+	0.423673i
$412$		0			0
$413$	6.54526	−	6.54526i	0.322071	−	0.322071i
$414$		0			0
$415$	−11.0756			−0.543679
$416$		0			0
$417$	8.54164			0.418286
$418$		0			0
$419$	−3.77105	+	3.77105i	−0.184228	+	0.184228i	−0.793195	−	0.608968i	$-0.791584\pi$
$419$	−3.77105	+	3.77105i	−0.184228	+	0.184228i	0.608968	+	0.793195i	$0.291584\pi$
$420$		0			0
$421$	−14.6768	−	14.6768i	−0.715305	−	0.715305i	0.252335	−	0.967640i	$-0.418801\pi$
$421$	−14.6768	−	14.6768i	−0.715305	−	0.715305i	−0.967640	+	0.252335i	$0.918801\pi$
$422$		0			0
$423$			8.93936i			0.434646i
$424$		0			0
$425$			4.69853i			0.227912i
$426$		0			0
$427$	1.81508	+	1.81508i	0.0878380	+	0.0878380i
$428$		0			0
$429$	−2.75203	+	2.75203i	−0.132869	+	0.132869i
$430$		0			0
$431$	1.85417			0.0893123			0.0446561	−	0.999002i	$-0.485781\pi$
$431$	1.85417			0.0893123			0.0446561	+	0.999002i	$0.485781\pi$
$432$		0			0
$433$	−31.1008			−1.49461			−0.747304	−	0.664482i	$-0.768652\pi$
$433$	−31.1008			−1.49461			−0.747304	+	0.664482i	$0.768652\pi$
$434$		0			0
$435$	−0.105231	+	0.105231i	−0.00504543	+	0.00504543i
$436$		0			0
$437$	−8.18777	−	8.18777i	−0.391674	−	0.391674i
$438$		0			0
$439$		−	8.31669i		−	0.396934i	−0.980108	−	0.198467i	$-0.936404\pi$
$439$		−	8.31669i		−	0.396934i	0.980108	−	0.198467i	$-0.0635963\pi$
$440$		0			0
$441$		−	2.26725i		−	0.107964i
$442$		0			0
$443$	−13.1234	−	13.1234i	−0.623512	−	0.623512i	0.322916	−	0.946428i	$-0.395337\pi$
$443$	−13.1234	−	13.1234i	−0.623512	−	0.623512i	−0.946428	+	0.322916i	$0.895337\pi$
$444$		0			0
$445$	−2.32056	+	2.32056i	−0.110005	+	0.110005i
$446$		0			0
$447$	18.1119			0.856666
$448$		0			0
$449$	23.1718			1.09355			0.546773	−	0.837281i	$-0.315856\pi$
$449$	23.1718			1.09355			0.546773	+	0.837281i	$0.315856\pi$
$450$		0			0
$451$	−3.93265	+	3.93265i	−0.185181	+	0.185181i
$452$		0			0
$453$	0.716188	+	0.716188i	0.0336495	+	0.0336495i
$454$		0			0
$455$		−	3.95904i		−	0.185603i
$456$		0			0
$457$			22.2382i			1.04026i	0.854088	+	0.520128i	$0.174116\pi$
$457$			22.2382i			1.04026i	−0.854088	+	0.520128i	$0.825884\pi$
$458$		0			0
$459$	14.9799	+	14.9799i	0.699202	+	0.699202i
$460$		0			0
$461$	−24.2390	+	24.2390i	−1.12892	+	1.12892i	−0.138567	+	0.990353i	$0.544250\pi$
$461$	−24.2390	+	24.2390i	−1.12892	+	1.12892i	−0.990353	+	0.138567i	$0.955750\pi$
$462$		0			0
$463$	2.31569			0.107619			0.0538097	−	0.998551i	$-0.482864\pi$
$463$	2.31569			0.107619			0.0538097	+	0.998551i	$0.482864\pi$
$464$		0			0
$465$	−2.11105			−0.0978975
$466$		0			0
$467$	−15.2836	+	15.2836i	−0.707242	+	0.707242i	−0.965954	−	0.258713i	$-0.916702\pi$
$467$	−15.2836	+	15.2836i	−0.707242	+	0.707242i	0.258713	+	0.965954i	$0.416702\pi$
$468$		0			0
$469$	−0.162648	−	0.162648i	−0.00751038	−	0.00751038i
$470$		0			0
$471$		−	6.04329i		−	0.278460i
$472$		0			0
$473$			3.60002i			0.165529i
$474$		0			0
$475$	1.00378	+	1.00378i	0.0460567	+	0.0460567i
$476$		0			0
$477$	−16.3120	+	16.3120i	−0.746874	+	0.746874i
$478$		0			0
$479$	−27.7338			−1.26719			−0.633594	−	0.773665i	$-0.718421\pi$
$479$	−27.7338			−1.26719			−0.633594	+	0.773665i	$0.718421\pi$
$480$		0			0
$481$	−19.8046			−0.903010
$482$		0			0
$483$	−4.93730	+	4.93730i	−0.224655	+	0.224655i
$484$		0			0
$485$	−0.320943	−	0.320943i	−0.0145733	−	0.0145733i
$486$		0			0
$487$			37.6955i			1.70815i	0.520152	+	0.854074i	$0.325875\pi$
$487$			37.6955i			1.70815i	−0.520152	+	0.854074i	$0.674125\pi$
$488$		0			0
$489$			6.05608i			0.273865i
$490$		0			0
$491$	−13.0302	−	13.0302i	−0.588045	−	0.588045i	0.349056	−	0.937102i	$-0.386502\pi$
$491$	−13.0302	−	13.0302i	−0.588045	−	0.588045i	−0.937102	+	0.349056i	$0.886502\pi$
$492$		0			0
$493$	0.577600	−	0.577600i	0.0260138	−	0.0260138i
$494$		0			0
$495$	2.60376			0.117030
$496$		0			0
$497$	−6.00458			−0.269342
$498$		0			0
$499$	20.9927	−	20.9927i	0.939762	−	0.939762i	−0.0585244	−	0.998286i	$-0.518640\pi$
$499$	20.9927	−	20.9927i	0.939762	−	0.939762i	0.998286	+	0.0585244i	$0.0186395\pi$
$500$		0			0
$501$	−15.0662	−	15.0662i	−0.673108	−	0.673108i
$502$		0			0
$503$		−	7.53500i		−	0.335969i	−0.985790	−	0.167984i	$-0.946274\pi$
$503$		−	7.53500i		−	0.335969i	0.985790	−	0.167984i	$-0.0537258\pi$
$504$		0			0
$505$			18.5341i			0.824755i
$506$		0			0
$507$	−1.61853	−	1.61853i	−0.0718815	−	0.0718815i
$508$		0			0
$509$	−12.2119	+	12.2119i	−0.541281	+	0.541281i	−0.923905	−	0.382623i	$-0.875021\pi$
$509$	−12.2119	+	12.2119i	−0.541281	+	0.541281i	0.382623	+	0.923905i	$0.375021\pi$
$510$		0			0
$511$	−7.09981			−0.314077
$512$		0			0
$513$	6.40053			0.282590
$514$		0			0
$515$	−5.42082	+	5.42082i	−0.238870	+	0.238870i
$516$		0			0
$517$	3.20179	+	3.20179i	0.140815	+	0.140815i
$518$		0			0
$519$			12.4923i			0.548352i
$520$		0			0
$521$		−	20.0636i		−	0.879003i	−0.898242	−	0.439502i	$-0.855155\pi$
$521$		−	20.0636i		−	0.879003i	0.898242	−	0.439502i	$-0.144845\pi$
$522$		0			0
$523$	25.1733	+	25.1733i	1.10075	+	1.10075i	0.994320	+	0.106433i	$0.0339430\pi$
$523$	25.1733	+	25.1733i	1.10075	+	1.10075i	0.106433	+	0.994320i	$0.466057\pi$
$524$		0			0
$525$	0.605289	−	0.605289i	0.0264170	−	0.0264170i
$526$		0			0
$527$	11.5873			0.504751
$528$		0			0
$529$	−43.5354			−1.89284
$530$		0			0
$531$	−14.8397	+	14.8397i	−0.643990	+	0.643990i
$532$		0			0
$533$	−13.5573	−	13.5573i	−0.587233	−	0.587233i
$534$		0			0
$535$		−	0.169865i		−	0.00734391i
$536$		0			0
$537$			20.1537i			0.869696i
$538$		0			0
$539$	−0.812056	−	0.812056i	−0.0349777	−	0.0349777i
$540$		0			0
$541$	−2.43357	+	2.43357i	−0.104627	+	0.104627i	−0.757483	−	0.652855i	$-0.773571\pi$
$541$	−2.43357	+	2.43357i	−0.104627	+	0.104627i	0.652855	+	0.757483i	$0.273571\pi$
$542$		0			0
$543$	−11.0083			−0.472411
$544$		0			0
$545$	−4.77128			−0.204379
$546$		0			0
$547$	−2.34767	+	2.34767i	−0.100379	+	0.100379i	−0.755513	−	0.655134i	$-0.772612\pi$
$547$	−2.34767	+	2.34767i	−0.100379	+	0.100379i	0.655134	+	0.755513i	$0.272612\pi$
$548$		0			0
$549$	−4.11525	−	4.11525i	−0.175634	−	0.175634i
$550$		0			0
$551$		−	0.246794i		−	0.0105138i
$552$		0			0
$553$		−	10.3006i		−	0.438025i
$554$		0			0
$555$	−3.02788	−	3.02788i	−0.128526	−	0.128526i
$556$		0			0
$557$	14.3487	−	14.3487i	0.607973	−	0.607973i	−0.334443	−	0.942416i	$-0.608548\pi$
$557$	14.3487	−	14.3487i	0.607973	−	0.607973i	0.942416	+	0.334443i	$0.108548\pi$
$558$		0			0
$559$	−12.4106			−0.524914
$560$		0			0
$561$	4.61893			0.195011
$562$		0			0
$563$	18.2878	−	18.2878i	0.770739	−	0.770739i	−0.207497	−	0.978236i	$-0.566532\pi$
$563$	18.2878	−	18.2878i	0.770739	−	0.770739i	0.978236	+	0.207497i	$0.0665316\pi$
$564$		0			0
$565$	−13.5933	−	13.5933i	−0.571875	−	0.571875i
$566$		0			0
$567$			2.94217i			0.123560i
$568$		0			0
$569$			1.39010i			0.0582762i	0.999575	+	0.0291381i	$0.00927626\pi$
$569$			1.39010i			0.0582762i	−0.999575	+	0.0291381i	$0.990724\pi$
$570$		0			0
$571$	−10.6954	−	10.6954i	−0.447587	−	0.447587i	0.446965	−	0.894552i	$-0.352505\pi$
$571$	−10.6954	−	10.6954i	−0.447587	−	0.447587i	−0.894552	+	0.446965i	$0.852505\pi$
$572$		0			0
$573$	2.74345	−	2.74345i	0.114609	−	0.114609i
$574$		0			0
$575$	8.15692			0.340167
$576$		0			0
$577$	3.44573			0.143448			0.0717239	−	0.997425i	$-0.477150\pi$
$577$	3.44573			0.143448			0.0717239	+	0.997425i	$0.477150\pi$
$578$		0			0
$579$	13.2897	−	13.2897i	0.552300	−	0.552300i
$580$		0			0
$581$	−7.83163	−	7.83163i	−0.324911	−	0.324911i
$582$		0			0
$583$			11.6849i			0.483937i
$584$		0			0
$585$			8.97613i			0.371117i
$586$		0			0
$587$	−2.25967	−	2.25967i	−0.0932666	−	0.0932666i	0.658934	−	0.752201i	$-0.271008\pi$
$587$	−2.25967	−	2.25967i	−0.0932666	−	0.0932666i	−0.752201	+	0.658934i	$0.771008\pi$
$588$		0			0
$589$	2.47548	−	2.47548i	0.102000	−	0.102000i
$590$		0			0
$591$	−2.43003			−0.0999581
$592$		0			0
$593$	−26.4329			−1.08547			−0.542735	−	0.839904i	$-0.682611\pi$
$593$	−26.4329			−1.08547			−0.542735	+	0.839904i	$0.682611\pi$
$594$		0			0
$595$	−3.32236	+	3.32236i	−0.136204	+	0.136204i
$596$		0			0
$597$	4.27715	+	4.27715i	0.175052	+	0.175052i
$598$		0			0
$599$			41.6771i			1.70288i	0.524453	+	0.851439i	$0.324270\pi$
$599$			41.6771i			1.70288i	−0.524453	+	0.851439i	$0.675730\pi$
$600$		0			0
$601$		−	37.0190i		−	1.51004i	−0.655704	−	0.755018i	$-0.727628\pi$
$601$		−	37.0190i		−	1.51004i	0.655704	−	0.755018i	$-0.272372\pi$
$602$		0			0
$603$	0.368763	+	0.368763i	0.0150172	+	0.0150172i
$604$		0			0
$605$	−6.84559	+	6.84559i	−0.278313	+	0.278313i
$606$		0			0
$607$	−13.3712			−0.542720			−0.271360	−	0.962478i	$-0.587473\pi$
$607$	−13.3712			−0.542720			−0.271360	+	0.962478i	$0.587473\pi$
$608$		0			0
$609$	−0.148819			−0.00603044
$610$		0			0
$611$	−11.0378	+	11.0378i	−0.446541	+	0.446541i
$612$		0			0
$613$	22.7096	+	22.7096i	0.917233	+	0.917233i	0.996827	−	0.0795940i	$-0.0253624\pi$
$613$	22.7096	+	22.7096i	0.917233	+	0.917233i	−0.0795940	+	0.996827i	$0.525362\pi$
$614$		0			0
$615$		−	4.14551i		−	0.167163i
$616$		0			0
$617$			1.42378i			0.0573194i	0.999589	+	0.0286597i	$0.00912391\pi$
$617$			1.42378i			0.0573194i	−0.999589	+	0.0286597i	$0.990876\pi$
$618$		0			0
$619$	−19.8935	−	19.8935i	−0.799588	−	0.799588i	0.183442	−	0.983030i	$-0.441276\pi$
$619$	−19.8935	−	19.8935i	−0.799588	−	0.799588i	−0.983030	+	0.183442i	$0.941276\pi$
$620$		0			0
$621$	26.0060	−	26.0060i	1.04358	−	1.04358i
$622$		0			0
$623$	−3.28176			−0.131481
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	0.986775	−	0.986775i	0.0394080	−	0.0394080i
$628$		0			0
$629$	16.6197	+	16.6197i	0.662670	+	0.662670i
$630$		0			0
$631$		−	9.15758i		−	0.364558i	−0.983247	−	0.182279i	$-0.941653\pi$
$631$		−	9.15758i		−	0.364558i	0.983247	−	0.182279i	$-0.0583473\pi$
$632$		0			0
$633$		−	7.17603i		−	0.285221i
$634$		0			0
$635$	−3.31001	−	3.31001i	−0.131354	−	0.131354i
$636$		0			0
$637$	2.79946	−	2.79946i	0.110919	−	0.110919i
$638$		0			0
$639$	13.6139			0.538557
$640$		0			0
$641$	−22.5024			−0.888793			−0.444396	−	0.895830i	$-0.646582\pi$
$641$	−22.5024			−0.888793			−0.444396	+	0.895830i	$0.646582\pi$
$642$		0			0
$643$	5.57036	−	5.57036i	0.219673	−	0.219673i	−0.588687	−	0.808361i	$-0.700355\pi$
$643$	5.57036	−	5.57036i	0.219673	−	0.219673i	0.808361	+	0.588687i	$0.200355\pi$
$644$		0			0
$645$	−1.89744	−	1.89744i	−0.0747115	−	0.0747115i
$646$		0			0
$647$		−	34.4395i		−	1.35396i	−0.736003	−	0.676979i	$-0.763289\pi$
$647$		−	34.4395i		−	1.35396i	0.736003	−	0.676979i	$-0.236711\pi$
$648$		0			0
$649$			10.6302i			0.417273i
$650$		0			0
$651$	−1.49274	−	1.49274i	−0.0585050	−	0.0585050i
$652$		0			0
$653$	21.9881	−	21.9881i	0.860459	−	0.860459i	−0.130932	−	0.991391i	$-0.541797\pi$
$653$	21.9881	−	21.9881i	0.860459	−	0.860459i	0.991391	+	0.130932i	$0.0417970\pi$
$654$		0			0
$655$	5.27441			0.206088
$656$		0			0
$657$	16.0970			0.628005
$658$		0			0
$659$	32.2167	−	32.2167i	1.25498	−	1.25498i	0.301527	−	0.953458i	$-0.402504\pi$
$659$	32.2167	−	32.2167i	1.25498	−	1.25498i	0.953458	−	0.301527i	$-0.0974965\pi$
$660$		0			0
$661$	−19.7402	−	19.7402i	−0.767803	−	0.767803i	0.209916	−	0.977719i	$-0.432681\pi$
$661$	−19.7402	−	19.7402i	−0.767803	−	0.767803i	−0.977719	+	0.209916i	$0.932681\pi$
$662$		0			0
$663$			15.9232i			0.618405i
$664$		0			0
$665$			1.41956i			0.0550482i
$666$		0			0
$667$	−1.00275	−	1.00275i	−0.0388265	−	0.0388265i
$668$		0			0
$669$	−15.8473	+	15.8473i	−0.612691	+	0.612691i
$670$		0			0
$671$	−2.94790			−0.113802
$672$		0			0
$673$	−14.0802			−0.542752			−0.271376	−	0.962473i	$-0.587479\pi$
$673$	−14.0802			−0.542752			−0.271376	+	0.962473i	$0.587479\pi$
$674$		0			0
$675$	−3.18821	+	3.18821i	−0.122714	+	0.122714i
$676$		0			0
$677$	22.3722	+	22.3722i	0.859834	+	0.859834i	0.991318	−	0.131485i	$-0.0419744\pi$
$677$	22.3722	+	22.3722i	0.859834	+	0.859834i	−0.131485	+	0.991318i	$0.541974\pi$
$678$		0			0
$679$		−	0.453882i		−	0.0174184i
$680$		0			0
$681$			2.72780i			0.104529i
$682$		0			0
$683$	−0.229997	−	0.229997i	−0.00880059	−	0.00880059i	0.702693	−	0.711493i	$-0.251981\pi$
$683$	−0.229997	−	0.229997i	−0.00880059	−	0.00880059i	−0.711493	+	0.702693i	$0.751981\pi$
$684$		0			0
$685$	10.0340	−	10.0340i	0.383379	−	0.383379i
$686$		0			0
$687$	10.5989			0.404374
$688$		0			0
$689$	−40.2821			−1.53462
$690$		0			0
$691$	−14.0479	+	14.0479i	−0.534407	+	0.534407i	−0.921881	−	0.387474i	$-0.873348\pi$
$691$	−14.0479	+	14.0479i	−0.534407	+	0.534407i	0.387474	+	0.921881i	$0.373348\pi$
$692$		0			0
$693$	1.84113	+	1.84113i	0.0699389	+	0.0699389i
$694$		0			0
$695$		−	9.97846i		−	0.378504i
$696$		0			0
$697$			22.7542i			0.861877i
$698$		0			0
$699$	14.5835	+	14.5835i	0.551597	+	0.551597i
$700$		0			0
$701$	−28.2923	+	28.2923i	−1.06859	+	1.06859i	−0.0711175	+	0.997468i	$0.522657\pi$
$701$	−28.2923	+	28.2923i	−1.06859	+	1.06859i	−0.997468	+	0.0711175i	$0.977343\pi$
$702$		0			0
$703$	7.10117			0.267826
$704$		0			0
$705$	−3.37509			−0.127113
$706$		0			0
$707$	−13.1056	+	13.1056i	−0.492885	+	0.492885i
$708$		0			0
$709$	24.0847	+	24.0847i	0.904521	+	0.904521i	0.995823	−	0.0913019i	$-0.0291028\pi$
$709$	24.0847	+	24.0847i	0.904521	+	0.904521i	−0.0913019	+	0.995823i	$0.529103\pi$
$710$		0			0
$711$			23.3539i			0.875842i
$712$		0			0
$713$		−	20.1162i		−	0.753359i
$714$		0			0
$715$	3.21496	+	3.21496i	0.120233	+	0.120233i
$716$		0			0
$717$	−12.9707	+	12.9707i	−0.484399	+	0.484399i
$718$		0			0
$719$	−41.4094			−1.54431			−0.772154	−	0.635435i	$-0.780821\pi$
$719$	−41.4094			−1.54431			−0.772154	+	0.635435i	$0.780821\pi$
$720$		0			0
$721$	−7.66619			−0.285504
$722$		0			0
$723$	4.42203	−	4.42203i	0.164457	−	0.164457i
$724$		0			0
$725$	0.122932	+	0.122932i	0.00456558	+	0.00456558i
$726$		0			0
$727$		−	35.4737i		−	1.31565i	−0.753172	−	0.657824i	$-0.771477\pi$
$727$		−	35.4737i		−	1.31565i	0.753172	−	0.657824i	$-0.228523\pi$
$728$		0			0
$729$			4.90810i			0.181782i
$730$		0			0
$731$	10.4148	+	10.4148i	0.385206	+	0.385206i
$732$		0			0
$733$	−3.87401	+	3.87401i	−0.143090	+	0.143090i	−0.775023	−	0.631933i	$-0.782262\pi$
$733$	−3.87401	+	3.87401i	−0.143090	+	0.143090i	0.631933	+	0.775023i	$0.282262\pi$
$734$		0			0
$735$	0.856008			0.0315743
$736$		0			0
$737$	0.264158			0.00973039
$738$		0			0
$739$	6.10697	−	6.10697i	0.224649	−	0.224649i	−0.585804	−	0.810453i	$-0.699221\pi$
$739$	6.10697	−	6.10697i	0.224649	−	0.224649i	0.810453	+	0.585804i	$0.199221\pi$
$740$		0			0
$741$	3.40179	+	3.40179i	0.124968	+	0.124968i
$742$		0			0
$743$			30.6238i			1.12348i	0.827314	+	0.561739i	$0.189868\pi$
$743$			30.6238i			1.12348i	−0.827314	+	0.561739i	$0.810132\pi$
$744$		0			0
$745$		−	21.1586i		−	0.775191i
$746$		0			0
$747$	17.7562	+	17.7562i	0.649667	+	0.649667i
$748$		0			0
$749$	0.120113	−	0.120113i	0.00438882	−	0.00438882i
$750$		0			0
$751$	−8.12562			−0.296508			−0.148254	−	0.988949i	$-0.547365\pi$
$751$	−8.12562			−0.296508			−0.148254	+	0.988949i	$0.547365\pi$
$752$		0			0
$753$	−17.2696			−0.629338
$754$		0			0
$755$	0.836660	−	0.836660i	0.0304492	−	0.0304492i
$756$		0			0
$757$	−25.0324	−	25.0324i	−0.909816	−	0.909816i	0.0864406	−	0.996257i	$-0.472451\pi$
$757$	−25.0324	−	25.0324i	−0.909816	−	0.909816i	−0.996257	+	0.0864406i	$0.972451\pi$
$758$		0			0
$759$		−	8.01873i		−	0.291061i
$760$		0			0
$761$		−	25.7347i		−	0.932884i	−0.884552	−	0.466442i	$-0.845536\pi$
$761$		−	25.7347i		−	0.932884i	0.884552	−	0.466442i	$-0.154464\pi$
$762$		0			0
$763$	−3.37380	−	3.37380i	−0.122140	−	0.122140i
$764$		0			0
$765$	7.53262	−	7.53262i	0.272343	−	0.272343i
$766$		0			0
$767$	−36.6464			−1.32322
$768$		0			0
$769$	−36.8962			−1.33051			−0.665256	−	0.746616i	$-0.731677\pi$
$769$	−36.8962			−1.33051			−0.665256	+	0.746616i	$0.731677\pi$
$770$		0			0
$771$	9.76133	−	9.76133i	0.351546	−	0.351546i
$772$		0			0
$773$	8.52408	+	8.52408i	0.306590	+	0.306590i	0.843585	−	0.536995i	$-0.180441\pi$
$773$	8.52408	+	8.52408i	0.306590	+	0.306590i	−0.536995	+	0.843585i	$0.680441\pi$
$774$		0			0
$775$			2.46615i			0.0885869i
$776$		0			0
$777$		−	4.28207i		−	0.153618i
$778$		0			0
$779$	4.86115	+	4.86115i	0.174169	+	0.174169i
$780$		0			0
$781$	4.87606	−	4.87606i	0.174479	−	0.174479i
$782$		0			0
$783$	0.783866			0.0280131
$784$		0			0
$785$	−7.05985			−0.251977
$786$		0			0
$787$	27.9778	−	27.9778i	0.997302	−	0.997302i	−0.00269473	−	0.999996i	$-0.500858\pi$
$787$	27.9778	−	27.9778i	0.997302	−	0.997302i	0.999996	+	0.00269473i	$0.000857761\pi$
$788$		0			0
$789$	10.1334	+	10.1334i	0.360759	+	0.360759i
$790$		0			0
$791$		−	19.2238i		−	0.683521i
$792$		0			0
$793$		−	10.1625i		−	0.360881i
$794$		0			0
$795$	−6.15865	−	6.15865i	−0.218425	−	0.218425i
$796$		0			0
$797$	38.7907	−	38.7907i	1.37404	−	1.37404i	0.519675	−	0.854364i	$-0.326053\pi$
$797$	38.7907	−	38.7907i	1.37404	−	1.37404i	0.854364	−	0.519675i	$-0.173947\pi$
$798$		0			0
$799$	18.5255			0.655383
$800$		0			0
$801$	7.44058			0.262900
$802$		0			0
$803$	5.76544	−	5.76544i	0.203458	−	0.203458i
$804$		0			0
$805$	5.76782	+	5.76782i	0.203289	+	0.203289i
$806$		0			0
$807$			8.70679i			0.306493i
$808$		0			0
$809$			17.4239i			0.612592i	0.951936	+	0.306296i	$0.0990898\pi$
$809$			17.4239i			0.612592i	−0.951936	+	0.306296i	$0.900910\pi$
$810$		0			0
$811$	−28.3952	−	28.3952i	−0.997089	−	0.997089i	0.00290663	−	0.999996i	$-0.499075\pi$
$811$	−28.3952	−	28.3952i	−0.997089	−	0.997089i	−0.999996	+	0.00290663i	$0.999075\pi$
$812$		0			0
$813$	−11.1625	+	11.1625i	−0.391487	+	0.391487i
$814$		0			0
$815$	7.07479			0.247819
$816$		0			0
$817$	4.44999			0.155685
$818$		0			0
$819$	−6.34708	+	6.34708i	−0.221785	+	0.221785i
$820$		0			0
$821$	15.5070	+	15.5070i	0.541198	+	0.541198i	0.923880	−	0.382682i	$-0.124999\pi$
$821$	15.5070	+	15.5070i	0.541198	+	0.541198i	−0.382682	+	0.923880i	$0.624999\pi$
$822$		0			0
$823$		−	4.43237i		−	0.154503i	−0.997012	−	0.0772513i	$-0.975386\pi$
$823$		−	4.43237i		−	0.154503i	0.997012	−	0.0772513i	$-0.0246144\pi$
$824$		0			0
$825$			0.983058i			0.0342257i
$826$		0			0
$827$	−12.0984	−	12.0984i	−0.420704	−	0.420704i	0.464742	−	0.885446i	$-0.346147\pi$
$827$	−12.0984	−	12.0984i	−0.420704	−	0.420704i	−0.885446	+	0.464742i	$0.846147\pi$
$828$		0			0
$829$	−7.49482	+	7.49482i	−0.260306	+	0.260306i	−0.825178	−	0.564873i	$-0.808925\pi$
$829$	−7.49482	+	7.49482i	−0.260306	+	0.260306i	0.564873	+	0.825178i	$0.308925\pi$
$830$		0			0
$831$	−20.4053			−0.707850
$832$		0			0
$833$	−4.69853			−0.162794
$834$		0			0
$835$	−17.6005	+	17.6005i	−0.609092	+	0.609092i
$836$		0			0
$837$	7.86262	+	7.86262i	0.271772	+	0.271772i
$838$		0			0
$839$		−	6.63304i		−	0.228998i	−0.993423	−	0.114499i	$-0.963474\pi$
$839$		−	6.63304i		−	0.228998i	0.993423	−	0.114499i	$-0.0365263\pi$
$840$		0			0
$841$			28.9698i			0.998958i
$842$		0			0
$843$	−10.8531	−	10.8531i	−0.373799	−	0.373799i
$844$		0			0
$845$	−1.89079	+	1.89079i	−0.0650451	+	0.0650451i
$846$		0			0
$847$	−9.68113			−0.332648
$848$		0			0
$849$	−23.8342			−0.817989
$850$		0			0
$851$	28.8527	−	28.8527i	0.989059	−	0.989059i
$852$		0			0
$853$	−14.2806	−	14.2806i	−0.488958	−	0.488958i	0.419019	−	0.907977i	$-0.362374\pi$
$853$	−14.2806	−	14.2806i	−0.488958	−	0.488958i	−0.907977	+	0.419019i	$0.862374\pi$
$854$		0			0
$855$		−	3.21850i		−	0.110070i
$856$		0			0
$857$			49.1654i			1.67946i	0.543005	+	0.839729i	$0.317286\pi$
$857$			49.1654i			1.67946i	−0.543005	+	0.839729i	$0.682714\pi$
$858$		0			0
$859$	−26.6661	−	26.6661i	−0.909836	−	0.909836i	0.0864230	−	0.996259i	$-0.472456\pi$
$859$	−26.6661	−	26.6661i	−0.909836	−	0.909836i	−0.996259	+	0.0864230i	$0.972456\pi$
$860$		0			0
$861$	2.93132	−	2.93132i	0.0998990	−	0.0998990i
$862$		0			0
$863$	−42.6788			−1.45280			−0.726402	−	0.687270i	$-0.758809\pi$
$863$	−42.6788			−1.45280			−0.726402	+	0.687270i	$0.758809\pi$
$864$		0			0
$865$	14.5937			0.496200
$866$		0			0
$867$	3.07256	−	3.07256i	0.104350	−	0.104350i
$868$		0			0
$869$	8.36464	+	8.36464i	0.283751	+	0.283751i
$870$		0			0
$871$			0.910653i			0.0308563i
$872$		0			0
$873$			1.02906i			0.0348285i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	17.9270	−	17.9270i	0.605350	−	0.605350i	−0.336377	−	0.941727i	$-0.609202\pi$
$877$	17.9270	−	17.9270i	0.605350	−	0.605350i	0.941727	+	0.336377i	$0.109202\pi$
$878$		0			0
$879$	22.0656			0.744254
$880$		0			0
$881$	−6.43903			−0.216937			−0.108468	−	0.994100i	$-0.534595\pi$
$881$	−6.43903			−0.216937			−0.108468	+	0.994100i	$0.534595\pi$
$882$		0			0
$883$	39.6889	−	39.6889i	1.33564	−	1.33564i	0.435401	−	0.900236i	$-0.356606\pi$
$883$	39.6889	−	39.6889i	1.33564	−	1.33564i	0.900236	−	0.435401i	$-0.143394\pi$
$884$		0			0
$885$	−5.60279	−	5.60279i	−0.188336	−	0.188336i
$886$		0			0
$887$			26.0147i			0.873490i	0.899585	+	0.436745i	$0.143869\pi$
$887$			26.0147i			0.873490i	−0.899585	+	0.436745i	$0.856131\pi$
$888$		0			0
$889$		−	4.68107i		−	0.156998i
$890$		0			0
$891$	−2.38921	−	2.38921i	−0.0800415	−	0.0800415i
$892$		0			0
$893$	3.95773	−	3.95773i	0.132440	−	0.132440i
$894$		0			0
$895$	23.5438			0.786982
$896$		0			0
$897$	27.6436			0.922992
$898$		0			0
$899$	0.303169	−	0.303169i	0.0101113	−	0.0101113i
$900$		0			0
$901$	33.8041	+	33.8041i	1.12618	+	1.12618i
$902$		0			0
$903$		−	2.68338i		−	0.0892973i
$904$		0			0
$905$			12.8600i			0.427482i
$906$		0			0
$907$	−8.98598	−	8.98598i	−0.298375	−	0.298375i	0.542002	−	0.840377i	$-0.317666\pi$
$907$	−8.98598	−	8.98598i	−0.298375	−	0.298375i	−0.840377	+	0.542002i	$0.817666\pi$
$908$		0			0
$909$	29.7136	−	29.7136i	0.985537	−	0.985537i
$910$		0			0
$911$	−10.7782			−0.357096			−0.178548	−	0.983931i	$-0.557140\pi$
$911$	−10.7782			−0.357096			−0.178548	+	0.983931i	$0.557140\pi$
$912$		0			0
$913$	12.7194			0.420952
$914$		0			0
$915$	1.55373	−	1.55373i	0.0513646	−	0.0513646i
$916$		0			0
$917$	3.72957	+	3.72957i	0.123161	+	0.123161i
$918$		0			0
$919$		−	9.09715i		−	0.300087i	−0.988679	−	0.150044i	$-0.952059\pi$
$919$		−	9.09715i		−	0.300087i	0.988679	−	0.150044i	$-0.0479414\pi$
$920$		0			0
$921$			21.3553i			0.703680i
$922$		0			0
$923$	16.8096	+	16.8096i	0.553295	+	0.553295i
$924$		0			0
$925$	−3.53721	+	3.53721i	−0.116303	+	0.116303i
$926$		0			0
$927$	17.3812			0.570873
$928$		0			0
$929$	22.8390			0.749323			0.374662	−	0.927162i	$-0.377759\pi$
$929$	22.8390			0.749323			0.374662	+	0.927162i	$0.377759\pi$
$930$		0			0
$931$	−1.00378	+	1.00378i	−0.0328976	+	0.0328976i
$932$		0			0
$933$	11.1487	+	11.1487i	0.364993	+	0.364993i
$934$		0			0
$935$		−	5.39589i		−	0.176464i
$936$		0			0
$937$		−	33.3961i		−	1.09100i	−0.838110	−	0.545501i	$-0.816339\pi$
$937$		−	33.3961i		−	1.09100i	0.838110	−	0.545501i	$-0.183661\pi$
$938$		0			0
$939$	−12.0816	−	12.0816i	−0.394268	−	0.394268i
$940$		0			0
$941$	29.0501	−	29.0501i	0.947005	−	0.947005i	−0.0516599	−	0.998665i	$-0.516451\pi$
$941$	29.0501	−	29.0501i	0.947005	−	0.947005i	0.998665	+	0.0516599i	$0.0164512\pi$
$942$		0			0
$943$	39.5026			1.28638
$944$		0			0
$945$	−4.50881			−0.146672
$946$		0			0
$947$	−25.7211	+	25.7211i	−0.835822	+	0.835822i	−0.988306	−	0.152484i	$-0.951273\pi$
$947$	−25.7211	+	25.7211i	−0.835822	+	0.835822i	0.152484	+	0.988306i	$0.451273\pi$
$948$		0			0
$949$	19.8757	+	19.8757i	0.645191	+	0.645191i
$950$		0			0
$951$			27.1450i			0.880237i
$952$		0			0
$953$		−	54.2832i		−	1.75841i	−0.476447	−	0.879203i	$-0.658076\pi$
$953$		−	54.2832i		−	1.75841i	0.476447	−	0.879203i	$-0.341924\pi$
$954$		0			0
$955$	−3.20494	−	3.20494i	−0.103709	−	0.103709i
$956$		0			0
$957$	0.120849	−	0.120849i	0.00390650	−	0.00390650i
$958$		0			0
$959$	14.1902			0.458225
$960$		0			0
$961$	−24.9181			−0.803809
$962$		0			0
$963$	−0.272326	+	0.272326i	−0.00877557	+	0.00877557i
$964$		0			0
$965$	−15.5252	−	15.5252i	−0.499773	−	0.499773i
$966$		0			0
$967$			45.1018i			1.45038i	0.688550	+	0.725188i	$0.258247\pi$
$967$			45.1018i			1.45038i	−0.688550	+	0.725188i	$0.741753\pi$
$968$		0			0
$969$		−	5.70945i		−	0.183414i
$970$		0			0
$971$	5.81628	+	5.81628i	0.186653	+	0.186653i	0.794248	−	0.607594i	$-0.207865\pi$
$971$	5.81628	+	5.81628i	0.186653	+	0.186653i	−0.607594	+	0.794248i	$0.707865\pi$
$972$		0			0
$973$	7.05584	−	7.05584i	0.226200	−	0.226200i
$974$		0			0
$975$	−3.38897			−0.108534
$976$		0			0
$977$	34.1397			1.09223			0.546113	−	0.837712i	$-0.316107\pi$
$977$	34.1397			1.09223			0.546113	+	0.837712i	$0.316107\pi$
$978$		0			0
$979$	2.66498	−	2.66498i	0.0851730	−	0.0851730i
$980$		0			0
$981$	7.64925	+	7.64925i	0.244222	+	0.244222i
$982$		0			0
$983$			36.7941i			1.17355i	0.809750	+	0.586775i	$0.199603\pi$
$983$			36.7941i			1.17355i	−0.809750	+	0.586775i	$0.800397\pi$
$984$		0			0
$985$			2.83879i			0.0904515i
$986$		0			0
$987$	−2.38655	−	2.38655i	−0.0759646	−	0.0759646i
$988$		0			0
$989$	18.0807	−	18.0807i	0.574933	−	0.574933i
$990$		0			0
$991$	10.4310			0.331350			0.165675	−	0.986180i	$-0.447020\pi$
$991$	10.4310			0.331350			0.165675	+	0.986180i	$0.447020\pi$
$992$		0			0
$993$	−4.70235			−0.149224
$994$		0			0
$995$	4.99663	−	4.99663i	0.158404	−	0.158404i
$996$		0			0
$997$	−6.70639	−	6.70639i	−0.212393	−	0.212393i	0.592890	−	0.805283i	$-0.297987\pi$
$997$	−6.70639	−	6.70639i	−0.212393	−	0.212393i	−0.805283	+	0.592890i	$0.797987\pi$
$998$		0			0
$999$			22.5547i			0.713600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.14		44
4.3	odd	2		560.2.bd.a.421.12	yes	44
16.3	odd	4		560.2.bd.a.141.12	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.12	✓	44	16.3	odd	4
560.2.bd.a.421.12	yes	44	4.3	odd	2
2240.2.bd.a.561.14		44	1.1	even	1	trivial
2240.2.bd.a.1681.14		44	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.605289 - 0.605289i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.26725i q^{9} +O(q^{10})\)	\(q+(0.605289 - 0.605289i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} +2.26725i q^{9} +(0.812056 + 0.812056i) q^{11} +(-2.79946 + 2.79946i) q^{13} -0.856008 q^{15} +4.69853 q^{17} +(1.00378 - 1.00378i) q^{19} +(-0.605289 - 0.605289i) q^{21} -8.15692i q^{23} +1.00000i q^{25} +(3.18821 + 3.18821i) q^{27} +(0.122932 - 0.122932i) q^{29} +2.46615 q^{31} +0.983058 q^{33} +(-0.707107 + 0.707107i) q^{35} +(3.53721 + 3.53721i) q^{37} +3.38897i q^{39} +4.84284i q^{41} +(2.21661 + 2.21661i) q^{43} +(1.60319 - 1.60319i) q^{45} +3.94282 q^{47} -1.00000 q^{49} +(2.84397 - 2.84397i) q^{51} +(7.19461 + 7.19461i) q^{53} -1.14842i q^{55} -1.21516i q^{57} +(6.54526 + 6.54526i) q^{59} +(-1.81508 + 1.81508i) q^{61} +2.26725 q^{63} +3.95904 q^{65} +(0.162648 - 0.162648i) q^{67} +(-4.93730 - 4.93730i) q^{69} -6.00458i q^{71} -7.09981i q^{73} +(0.605289 + 0.605289i) q^{75} +(0.812056 - 0.812056i) q^{77} +10.3006 q^{79} -2.94217 q^{81} +(7.83163 - 7.83163i) q^{83} +(-3.32236 - 3.32236i) q^{85} -0.148819i q^{87} -3.28176i q^{89} +(2.79946 + 2.79946i) q^{91} +(1.49274 - 1.49274i) q^{93} -1.41956 q^{95} +0.453882 q^{97} +(-1.84113 + 1.84113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

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Modular forms

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