LMFDB - Embedded newform 2240.2.bd.a.1681.3

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			1681.3
Character	$\chi$	$=$	2240.1681
Dual form			2240.2.bd.a.561.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92081 - 1.92081i) q^{3} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +4.37899i q^{9} +O(q^{10})$	\(q+(-1.92081 - 1.92081i) q^{3} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +4.37899i q^{9} +(-2.40494 + 2.40494i) q^{11} +(-0.230047 - 0.230047i) q^{13} -2.71643 q^{15} +3.07426 q^{17} +(-4.98381 - 4.98381i) q^{19} +(1.92081 - 1.92081i) q^{21} +2.85562i q^{23} -1.00000i q^{25} +(2.64876 - 2.64876i) q^{27} +(3.04810 + 3.04810i) q^{29} +5.50995 q^{31} +9.23884 q^{33} +(0.707107 + 0.707107i) q^{35} +(-5.74684 + 5.74684i) q^{37} +0.883751i q^{39} +2.73725i q^{41} +(1.65787 - 1.65787i) q^{43} +(3.09641 + 3.09641i) q^{45} +12.0114 q^{47} -1.00000 q^{49} +(-5.90505 - 5.90505i) q^{51} +(9.26864 - 9.26864i) q^{53} +3.40110i q^{55} +19.1459i q^{57} +(1.23554 - 1.23554i) q^{59} +(0.354752 + 0.354752i) q^{61} -4.37899 q^{63} -0.325336 q^{65} +(10.8475 + 10.8475i) q^{67} +(5.48509 - 5.48509i) q^{69} +1.43189i q^{71} +11.5526i q^{73} +(-1.92081 + 1.92081i) q^{75} +(-2.40494 - 2.40494i) q^{77} -8.10993 q^{79} +2.96144 q^{81} +(0.0148642 + 0.0148642i) q^{83} +(2.17383 - 2.17383i) q^{85} -11.7096i q^{87} -11.4609i q^{89} +(0.230047 - 0.230047i) q^{91} +(-10.5835 - 10.5835i) q^{93} -7.04817 q^{95} +7.61510 q^{97} +(-10.5312 - 10.5312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.92081	−	1.92081i	−1.10898	−	1.10898i	−0.993285	−	0.115692i	$-0.963091\pi$
$3$	−1.92081	−	1.92081i	−1.10898	−	1.10898i	−0.115692	−	0.993285i	$-0.536909\pi$
$4$		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
$9$			4.37899i			1.45966i
$10$		0			0
$11$	−2.40494	+	2.40494i	−0.725116	+	0.725116i	−0.969643	−	0.244526i	$-0.921368\pi$
$11$	−2.40494	+	2.40494i	−0.725116	+	0.725116i	0.244526	+	0.969643i	$0.421368\pi$
$12$		0			0
$13$	−0.230047	−	0.230047i	−0.0638036	−	0.0638036i	0.674485	−	0.738289i	$-0.264366\pi$
$13$	−0.230047	−	0.230047i	−0.0638036	−	0.0638036i	−0.738289	+	0.674485i	$0.764366\pi$
$14$		0			0
$15$	−2.71643			−0.701379
$16$		0			0
$17$	3.07426			0.745617			0.372809	−	0.927908i	$-0.378395\pi$
$17$	3.07426			0.745617			0.372809	+	0.927908i	$0.378395\pi$
$18$		0			0
$19$	−4.98381	−	4.98381i	−1.14336	−	1.14336i	−0.987831	−	0.155534i	$-0.950290\pi$
$19$	−4.98381	−	4.98381i	−1.14336	−	1.14336i	−0.155534	−	0.987831i	$-0.549710\pi$
$20$		0			0
$21$	1.92081	−	1.92081i	0.419154	−	0.419154i
$22$		0			0
$23$			2.85562i			0.595438i	0.954654	+	0.297719i	$0.0962258\pi$
$23$			2.85562i			0.595438i	−0.954654	+	0.297719i	$0.903774\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	2.64876	−	2.64876i	0.509755	−	0.509755i
$28$		0			0
$29$	3.04810	+	3.04810i	0.566018	+	0.566018i	0.931011	−	0.364992i	$-0.118928\pi$
$29$	3.04810	+	3.04810i	0.566018	+	0.566018i	−0.364992	+	0.931011i	$0.618928\pi$
$30$		0			0
$31$	5.50995			0.989616			0.494808	−	0.869002i	$-0.335238\pi$
$31$	5.50995			0.989616			0.494808	+	0.869002i	$0.335238\pi$
$32$		0			0
$33$	9.23884			1.60828
$34$		0			0
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$		0			0
$37$	−5.74684	+	5.74684i	−0.944774	+	0.944774i	−0.998553	−	0.0537789i	$-0.982873\pi$
$37$	−5.74684	+	5.74684i	−0.944774	+	0.944774i	0.0537789	+	0.998553i	$0.482873\pi$
$38$		0			0
$39$			0.883751i			0.141513i
$40$		0			0
$41$			2.73725i			0.427487i	0.976890	+	0.213744i	$0.0685657\pi$
$41$			2.73725i			0.427487i	−0.976890	+	0.213744i	$0.931434\pi$
$42$		0			0
$43$	1.65787	−	1.65787i	0.252822	−	0.252822i	−0.569304	−	0.822127i	$-0.692787\pi$
$43$	1.65787	−	1.65787i	0.252822	−	0.252822i	0.822127	+	0.569304i	$0.192787\pi$
$44$		0			0
$45$	3.09641	+	3.09641i	0.461586	+	0.461586i
$46$		0			0
$47$	12.0114			1.75204			0.876019	−	0.482276i	$-0.160190\pi$
$47$	12.0114			1.75204			0.876019	+	0.482276i	$0.160190\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−5.90505	−	5.90505i	−0.826873	−	0.826873i
$52$		0			0
$53$	9.26864	−	9.26864i	1.27315	−	1.27315i	0.328717	−	0.944428i	$-0.393384\pi$
$53$	9.26864	−	9.26864i	1.27315	−	1.27315i	0.944428	−	0.328717i	$-0.106616\pi$
$54$		0			0
$55$			3.40110i			0.458604i
$56$		0			0
$57$			19.1459i			2.53593i
$58$		0			0
$59$	1.23554	−	1.23554i	0.160854	−	0.160854i	−0.622091	−	0.782945i	$-0.713717\pi$
$59$	1.23554	−	1.23554i	0.160854	−	0.160854i	0.782945	+	0.622091i	$0.213717\pi$
$60$		0			0
$61$	0.354752	+	0.354752i	0.0454213	+	0.0454213i	0.729453	−	0.684031i	$-0.239775\pi$
$61$	0.354752	+	0.354752i	0.0454213	+	0.0454213i	−0.684031	+	0.729453i	$0.739775\pi$
$62$		0			0
$63$	−4.37899			−0.551700
$64$		0			0
$65$	−0.325336			−0.0403529
$66$		0			0
$67$	10.8475	+	10.8475i	1.32524	+	1.32524i	0.909474	+	0.415761i	$0.136485\pi$
$67$	10.8475	+	10.8475i	1.32524	+	1.32524i	0.415761	+	0.909474i	$0.363515\pi$
$68$		0			0
$69$	5.48509	−	5.48509i	0.660327	−	0.660327i
$70$		0			0
$71$			1.43189i			0.169934i	0.996384	+	0.0849671i	$0.0270785\pi$
$71$			1.43189i			0.169934i	−0.996384	+	0.0849671i	$0.972921\pi$
$72$		0			0
$73$			11.5526i			1.35213i	0.736844	+	0.676063i	$0.236315\pi$
$73$			11.5526i			1.35213i	−0.736844	+	0.676063i	$0.763685\pi$
$74$		0			0
$75$	−1.92081	+	1.92081i	−0.221795	+	0.221795i
$76$		0			0
$77$	−2.40494	−	2.40494i	−0.274068	−	0.274068i
$78$		0			0
$79$	−8.10993			−0.912439			−0.456219	−	0.889867i	$-0.650797\pi$
$79$	−8.10993			−0.912439			−0.456219	+	0.889867i	$0.650797\pi$
$80$		0			0
$81$	2.96144			0.329049
$82$		0			0
$83$	0.0148642	+	0.0148642i	0.00163155	+	0.00163155i	0.707922	−	0.706291i	$-0.249633\pi$
$83$	0.0148642	+	0.0148642i	0.00163155	+	0.00163155i	−0.706291	+	0.707922i	$0.749633\pi$
$84$		0			0
$85$	2.17383	−	2.17383i	0.235785	−	0.235785i
$86$		0			0
$87$		−	11.7096i		−	1.25540i
$88$		0			0
$89$		−	11.4609i		−	1.21486i	−0.794375	−	0.607428i	$-0.792201\pi$
$89$		−	11.4609i		−	1.21486i	0.794375	−	0.607428i	$-0.207799\pi$
$90$		0			0
$91$	0.230047	−	0.230047i	0.0241155	−	0.0241155i
$92$		0			0
$93$	−10.5835	−	10.5835i	−1.09746	−	1.09746i
$94$		0			0
$95$	−7.04817			−0.723127
$96$		0			0
$97$	7.61510			0.773197			0.386598	−	0.922248i	$-0.373650\pi$
$97$	7.61510			0.773197			0.386598	+	0.922248i	$0.373650\pi$
$98$		0			0
$99$	−10.5312	−	10.5312i	−1.05842	−	1.05842i
$100$		0			0
$101$	6.10829	−	6.10829i	0.607797	−	0.607797i	−0.334573	−	0.942370i	$-0.608592\pi$
$101$	6.10829	−	6.10829i	0.607797	−	0.607797i	0.942370	+	0.334573i	$0.108592\pi$
$102$		0			0
$103$		−	9.38744i		−	0.924972i	−0.886627	−	0.462486i	$-0.846958\pi$
$103$		−	9.38744i		−	0.924972i	0.886627	−	0.462486i	$-0.153042\pi$
$104$		0			0
$105$		−	2.71643i		−	0.265096i
$106$		0			0
$107$	4.06190	−	4.06190i	0.392679	−	0.392679i	−0.482962	−	0.875641i	$-0.660439\pi$
$107$	4.06190	−	4.06190i	0.392679	−	0.392679i	0.875641	+	0.482962i	$0.160439\pi$
$108$		0			0
$109$	−11.6383	−	11.6383i	−1.11475	−	1.11475i	−0.992499	−	0.122252i	$-0.960988\pi$
$109$	−11.6383	−	11.6383i	−1.11475	−	1.11475i	−0.122252	−	0.992499i	$-0.539012\pi$
$110$		0			0
$111$	22.0771			2.09547
$112$		0			0
$113$	−14.3735			−1.35215			−0.676074	−	0.736833i	$-0.736320\pi$
$113$	−14.3735			−1.35215			−0.676074	+	0.736833i	$0.736320\pi$
$114$		0			0
$115$	2.01923	+	2.01923i	0.188294	+	0.188294i
$116$		0			0
$117$	1.00737	−	1.00737i	0.0931316	−	0.0931316i
$118$		0			0
$119$			3.07426i			0.281817i
$120$		0			0
$121$		−	0.567460i		−	0.0515873i
$122$		0			0
$123$	5.25773	−	5.25773i	0.474074	−	0.474074i
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	16.3150			1.44772			0.723860	−	0.689947i	$-0.242366\pi$
$127$	16.3150			1.44772			0.723860	+	0.689947i	$0.242366\pi$
$128$		0			0
$129$	−6.36888			−0.560748
$130$		0			0
$131$	−1.51297	−	1.51297i	−0.132189	−	0.132189i	0.637917	−	0.770105i	$-0.279796\pi$
$131$	−1.51297	−	1.51297i	−0.132189	−	0.132189i	−0.770105	+	0.637917i	$0.779796\pi$
$132$		0			0
$133$	4.98381	−	4.98381i	0.432151	−	0.432151i
$134$		0			0
$135$		−	3.74592i		−	0.322397i
$136$		0			0
$137$		−	5.04227i		−	0.430790i	−0.976527	−	0.215395i	$-0.930896\pi$
$137$		−	5.04227i		−	0.430790i	0.976527	−	0.215395i	$-0.0691040\pi$
$138$		0			0
$139$	13.0200	−	13.0200i	1.10434	−	1.10434i	0.110465	−	0.993880i	$-0.464766\pi$
$139$	13.0200	−	13.0200i	1.10434	−	1.10434i	0.993880	−	0.110465i	$-0.0352339\pi$
$140$		0			0
$141$	−23.0715	−	23.0715i	−1.94297	−	1.94297i
$142$		0			0
$143$	1.10650			0.0925300
$144$		0			0
$145$	4.31067			0.357981
$146$		0			0
$147$	1.92081	+	1.92081i	0.158425	+	0.158425i
$148$		0			0
$149$	2.92851	−	2.92851i	0.239913	−	0.239913i	−0.576901	−	0.816814i	$-0.695738\pi$
$149$	2.92851	−	2.92851i	0.239913	−	0.239913i	0.816814	+	0.576901i	$0.195738\pi$
$150$		0			0
$151$		−	10.4902i		−	0.853682i	−0.904327	−	0.426841i	$-0.859626\pi$
$151$		−	10.4902i		−	0.853682i	0.904327	−	0.426841i	$-0.140374\pi$
$152$		0			0
$153$			13.4621i			1.08835i
$154$		0			0
$155$	3.89612	−	3.89612i	0.312944	−	0.312944i
$156$		0			0
$157$	11.3888	+	11.3888i	0.908924	+	0.908924i	0.996185	−	0.0872612i	$-0.0278115\pi$
$157$	11.3888	+	11.3888i	0.908924	+	0.908924i	−0.0872612	+	0.996185i	$0.527811\pi$
$158$		0			0
$159$	−35.6065			−2.82378
$160$		0			0
$161$	−2.85562			−0.225054
$162$		0			0
$163$	6.58819	+	6.58819i	0.516027	+	0.516027i	0.916367	−	0.400340i	$-0.131108\pi$
$163$	6.58819	+	6.58819i	0.516027	+	0.516027i	−0.400340	+	0.916367i	$0.631108\pi$
$164$		0			0
$165$	6.53284	−	6.53284i	0.508581	−	0.508581i
$166$		0			0
$167$			16.1238i			1.24770i	0.781544	+	0.623850i	$0.214432\pi$
$167$			16.1238i			1.24770i	−0.781544	+	0.623850i	$0.785568\pi$
$168$		0			0
$169$		−	12.8942i		−	0.991858i
$170$		0			0
$171$	21.8240	−	21.8240i	1.66893	−	1.66893i
$172$		0			0
$173$	−9.13304	−	9.13304i	−0.694372	−	0.694372i	0.268818	−	0.963191i	$-0.413367\pi$
$173$	−9.13304	−	9.13304i	−0.694372	−	0.694372i	−0.963191	+	0.268818i	$0.913367\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−4.74648			−0.356767
$178$		0			0
$179$	10.1552	+	10.1552i	0.759035	+	0.759035i	0.976147	−	0.217112i	$-0.0696637\pi$
$179$	10.1552	+	10.1552i	0.759035	+	0.759035i	−0.217112	+	0.976147i	$0.569664\pi$
$180$		0			0
$181$	9.05901	−	9.05901i	0.673351	−	0.673351i	−0.285136	−	0.958487i	$-0.592039\pi$
$181$	9.05901	−	9.05901i	0.673351	−	0.673351i	0.958487	+	0.285136i	$0.0920388\pi$
$182$		0			0
$183$		−	1.36282i		−	0.100742i
$184$		0			0
$185$			8.12725i			0.597528i
$186$		0			0
$187$	−7.39340	+	7.39340i	−0.540659	+	0.540659i
$188$		0			0
$189$	2.64876	+	2.64876i	0.192669	+	0.192669i
$190$		0			0
$191$	−22.0651			−1.59657			−0.798286	−	0.602279i	$-0.794259\pi$
$191$	−22.0651			−1.59657			−0.798286	+	0.602279i	$0.794259\pi$
$192$		0			0
$193$	23.6088			1.69940			0.849700	−	0.527267i	$-0.176783\pi$
$193$	23.6088			1.69940			0.849700	+	0.527267i	$0.176783\pi$
$194$		0			0
$195$	0.624906	+	0.624906i	0.0447505	+	0.0447505i
$196$		0			0
$197$	−1.33955	+	1.33955i	−0.0954387	+	0.0954387i	−0.753214	−	0.657775i	$-0.771498\pi$
$197$	−1.33955	+	1.33955i	−0.0954387	+	0.0954387i	0.657775	+	0.753214i	$0.271498\pi$
$198$		0			0
$199$			17.9500i			1.27244i	0.771508	+	0.636220i	$0.219503\pi$
$199$			17.9500i			1.27244i	−0.771508	+	0.636220i	$0.780497\pi$
$200$		0			0
$201$		−	41.6719i		−	2.93931i
$202$		0			0
$203$	−3.04810	+	3.04810i	−0.213935	+	0.213935i
$204$		0			0
$205$	1.93553	+	1.93553i	0.135183	+	0.135183i
$206$		0			0
$207$	−12.5047			−0.869138
$208$		0			0
$209$	23.9715			1.65814
$210$		0			0
$211$	10.8590	+	10.8590i	0.747567	+	0.747567i	0.974022	−	0.226455i	$-0.0727136\pi$
$211$	10.8590	+	10.8590i	0.747567	+	0.747567i	−0.226455	+	0.974022i	$0.572714\pi$
$212$		0			0
$213$	2.75038	−	2.75038i	0.188453	−	0.188453i
$214$		0			0
$215$		−	2.34458i		−	0.159899i
$216$		0			0
$217$			5.50995i			0.374040i
$218$		0			0
$219$	22.1902	−	22.1902i	1.49948	−	1.49948i
$220$		0			0
$221$	−0.707224	−	0.707224i	−0.0475731	−	0.0475731i
$222$		0			0
$223$	1.51828			0.101671			0.0508357	−	0.998707i	$-0.483812\pi$
$223$	1.51828			0.101671			0.0508357	+	0.998707i	$0.483812\pi$
$224$		0			0
$225$	4.37899			0.291932
$226$		0			0
$227$	6.58491	+	6.58491i	0.437056	+	0.437056i	0.891020	−	0.453964i	$-0.149991\pi$
$227$	6.58491	+	6.58491i	0.437056	+	0.437056i	−0.453964	+	0.891020i	$0.649991\pi$
$228$		0			0
$229$	−6.51956	+	6.51956i	−0.430825	+	0.430825i	−0.888909	−	0.458084i	$-0.848536\pi$
$229$	−6.51956	+	6.51956i	−0.430825	+	0.430825i	0.458084	+	0.888909i	$0.348536\pi$
$230$		0			0
$231$			9.23884i			0.607871i
$232$		0			0
$233$			18.0402i			1.18185i	0.806725	+	0.590927i	$0.201238\pi$
$233$			18.0402i			1.18185i	−0.806725	+	0.590927i	$0.798762\pi$
$234$		0			0
$235$	8.49332	−	8.49332i	0.554043	−	0.554043i
$236$		0			0
$237$	15.5776	+	15.5776i	1.01187	+	1.01187i
$238$		0			0
$239$	14.0959			0.911785			0.455892	−	0.890035i	$-0.349320\pi$
$239$	14.0959			0.911785			0.455892	+	0.890035i	$0.349320\pi$
$240$		0			0
$241$	11.0900			0.714370			0.357185	−	0.934034i	$-0.383737\pi$
$241$	11.0900			0.714370			0.357185	+	0.934034i	$0.383737\pi$
$242$		0			0
$243$	−13.6346	−	13.6346i	−0.874663	−	0.874663i
$244$		0			0
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$		0			0
$247$			2.29302i			0.145901i
$248$		0			0
$249$		−	0.0571023i		−	0.00361871i
$250$		0			0
$251$	6.24897	−	6.24897i	0.394432	−	0.394432i	−0.481832	−	0.876264i	$-0.660028\pi$
$251$	6.24897	−	6.24897i	0.394432	−	0.394432i	0.876264	+	0.481832i	$0.160028\pi$
$252$		0			0
$253$	−6.86759	−	6.86759i	−0.431762	−	0.431762i
$254$		0			0
$255$	−8.35101			−0.522960
$256$		0			0
$257$	−16.6585			−1.03913			−0.519564	−	0.854431i	$-0.673906\pi$
$257$	−16.6585			−1.03913			−0.519564	+	0.854431i	$0.673906\pi$
$258$		0			0
$259$	−5.74684	−	5.74684i	−0.357091	−	0.357091i
$260$		0			0
$261$	−13.3476	+	13.3476i	−0.826195	+	0.826195i
$262$		0			0
$263$		−	14.5446i		−	0.896860i	−0.893818	−	0.448430i	$-0.851983\pi$
$263$		−	14.5446i		−	0.896860i	0.893818	−	0.448430i	$-0.148017\pi$
$264$		0			0
$265$		−	13.1078i		−	0.805208i
$266$		0			0
$267$	−22.0142	+	22.0142i	−1.34725	+	1.34725i
$268$		0			0
$269$	−2.07516	−	2.07516i	−0.126525	−	0.126525i	0.641009	−	0.767534i	$-0.278516\pi$
$269$	−2.07516	−	2.07516i	−0.126525	−	0.126525i	−0.767534	+	0.641009i	$0.778516\pi$
$270$		0			0
$271$	7.78531			0.472924			0.236462	−	0.971641i	$-0.424012\pi$
$271$	7.78531			0.472924			0.236462	+	0.971641i	$0.424012\pi$
$272$		0			0
$273$	−0.883751			−0.0534871
$274$		0			0
$275$	2.40494	+	2.40494i	0.145023	+	0.145023i
$276$		0			0
$277$	−4.89400	+	4.89400i	−0.294052	+	0.294052i	−0.838679	−	0.544626i	$-0.816671\pi$
$277$	−4.89400	+	4.89400i	−0.294052	+	0.294052i	0.544626	+	0.838679i	$0.316671\pi$
$278$		0			0
$279$			24.1280i			1.44450i
$280$		0			0
$281$			8.10490i			0.483498i	0.970339	+	0.241749i	$0.0777210\pi$
$281$			8.10490i			0.483498i	−0.970339	+	0.241749i	$0.922279\pi$
$282$		0			0
$283$	−14.8117	+	14.8117i	−0.880467	+	0.880467i	−0.993582	−	0.113115i	$-0.963917\pi$
$283$	−14.8117	+	14.8117i	−0.880467	+	0.880467i	0.113115	+	0.993582i	$0.463917\pi$
$284$		0			0
$285$	13.5382	+	13.5382i	0.801932	+	0.801932i
$286$		0			0
$287$	−2.73725			−0.161575
$288$		0			0
$289$	−7.54893			−0.444055
$290$		0			0
$291$	−14.6271	−	14.6271i	−0.857458	−	0.857458i
$292$		0			0
$293$	−5.07959	+	5.07959i	−0.296753	+	0.296753i	−0.839741	−	0.542988i	$-0.817293\pi$
$293$	−5.07959	+	5.07959i	−0.296753	+	0.296753i	0.542988	+	0.839741i	$0.317293\pi$
$294$		0			0
$295$		−	1.74732i		−	0.101733i
$296$		0			0
$297$			12.7402i			0.739263i
$298$		0			0
$299$	0.656927	−	0.656927i	0.0379911	−	0.0379911i
$300$		0			0
$301$	1.65787	+	1.65787i	0.0955578	+	0.0955578i
$302$		0			0
$303$	−23.4657			−1.34807
$304$		0			0
$305$	0.501695			0.0287270
$306$		0			0
$307$	24.6662	+	24.6662i	1.40778	+	1.40778i	0.771275	+	0.636502i	$0.219619\pi$
$307$	24.6662	+	24.6662i	1.40778	+	1.40778i	0.636502	+	0.771275i	$0.280381\pi$
$308$		0			0
$309$	−18.0314	+	18.0314i	−1.02577	+	1.02577i
$310$		0			0
$311$		−	18.5460i		−	1.05165i	−0.850594	−	0.525823i	$-0.823757\pi$
$311$		−	18.5460i		−	1.05165i	0.850594	−	0.525823i	$-0.176243\pi$
$312$		0			0
$313$		−	10.3997i		−	0.587825i	−0.955832	−	0.293913i	$-0.905043\pi$
$313$		−	10.3997i		−	0.587825i	0.955832	−	0.293913i	$-0.0949575\pi$
$314$		0			0
$315$	−3.09641	+	3.09641i	−0.174463	+	0.174463i
$316$		0			0
$317$	−12.3716	−	12.3716i	−0.694857	−	0.694857i	0.268439	−	0.963297i	$-0.413492\pi$
$317$	−12.3716	−	12.3716i	−0.694857	−	0.694857i	−0.963297	+	0.268439i	$0.913492\pi$
$318$		0			0
$319$	−14.6610			−0.820858
$320$		0			0
$321$	−15.6042			−0.870944
$322$		0			0
$323$	−15.3215	−	15.3215i	−0.852512	−	0.852512i
$324$		0			0
$325$	−0.230047	+	0.230047i	−0.0127607	+	0.0127607i
$326$		0			0
$327$			44.7100i			2.47247i
$328$		0			0
$329$			12.0114i			0.662208i
$330$		0			0
$331$	17.6765	−	17.6765i	0.971590	−	0.971590i	−0.0280173	−	0.999607i	$-0.508919\pi$
$331$	17.6765	−	17.6765i	0.971590	−	0.971590i	0.999607	+	0.0280173i	$0.00891937\pi$
$332$		0			0
$333$	−25.1653	−	25.1653i	−1.37905	−	1.37905i
$334$		0			0
$335$	15.3407			0.838152
$336$		0			0
$337$	18.6279			1.01473			0.507364	−	0.861732i	$-0.330620\pi$
$337$	18.6279			1.01473			0.507364	+	0.861732i	$0.330620\pi$
$338$		0			0
$339$	27.6088	+	27.6088i	1.49950	+	1.49950i
$340$		0			0
$341$	−13.2511	+	13.2511i	−0.717587	+	0.717587i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	7.75709i		−	0.417628i
$346$		0			0
$347$	−7.00942	+	7.00942i	−0.376286	+	0.376286i	−0.869760	−	0.493475i	$-0.835727\pi$
$347$	−7.00942	+	7.00942i	−0.376286	+	0.376286i	0.493475	+	0.869760i	$0.335727\pi$
$348$		0			0
$349$	21.6394	+	21.6394i	1.15833	+	1.15833i	0.984835	+	0.173495i	$0.0555061\pi$
$349$	21.6394	+	21.6394i	1.15833	+	1.15833i	0.173495	+	0.984835i	$0.444494\pi$
$350$		0			0
$351$	−1.21868			−0.0650483
$352$		0			0
$353$	29.6199			1.57651			0.788253	−	0.615351i	$-0.210986\pi$
$353$	29.6199			1.57651			0.788253	+	0.615351i	$0.210986\pi$
$354$		0			0
$355$	1.01250	+	1.01250i	0.0537379	+	0.0537379i
$356$		0			0
$357$	5.90505	−	5.90505i	0.312529	−	0.312529i
$358$		0			0
$359$		−	25.4894i		−	1.34528i	−0.739971	−	0.672638i	$-0.765161\pi$
$359$		−	25.4894i		−	1.34528i	0.739971	−	0.672638i	$-0.234839\pi$
$360$		0			0
$361$			30.6767i			1.61456i
$362$		0			0
$363$	−1.08998	+	1.08998i	−0.0572091	+	0.0572091i
$364$		0			0
$365$	8.16890	+	8.16890i	0.427580	+	0.427580i
$366$		0			0
$367$	−25.4780			−1.32994			−0.664970	−	0.746870i	$-0.731556\pi$
$367$	−25.4780			−1.32994			−0.664970	+	0.746870i	$0.731556\pi$
$368$		0			0
$369$	−11.9864			−0.623987
$370$		0			0
$371$	9.26864	+	9.26864i	0.481204	+	0.481204i
$372$		0			0
$373$	−9.10570	+	9.10570i	−0.471475	+	0.471475i	−0.902392	−	0.430917i	$-0.858190\pi$
$373$	−9.10570	+	9.10570i	−0.471475	+	0.471475i	0.430917	+	0.902392i	$0.358190\pi$
$374$		0			0
$375$			2.71643i			0.140276i
$376$		0			0
$377$		−	1.40241i		−	0.0722280i
$378$		0			0
$379$	9.54063	−	9.54063i	0.490069	−	0.490069i	−0.418259	−	0.908328i	$-0.637359\pi$
$379$	9.54063	−	9.54063i	0.490069	−	0.490069i	0.908328	+	0.418259i	$0.137359\pi$
$380$		0			0
$381$	−31.3379	−	31.3379i	−1.60549	−	1.60549i
$382$		0			0
$383$	2.95979			0.151238			0.0756191	−	0.997137i	$-0.475907\pi$
$383$	2.95979			0.151238			0.0756191	+	0.997137i	$0.475907\pi$
$384$		0			0
$385$	−3.40110			−0.173336
$386$		0			0
$387$	7.25977	+	7.25977i	0.369035	+	0.369035i
$388$		0			0
$389$	−17.7128	+	17.7128i	−0.898077	+	0.898077i	−0.995266	−	0.0971889i	$-0.969015\pi$
$389$	−17.7128	+	17.7128i	−0.898077	+	0.898077i	0.0971889	+	0.995266i	$0.469015\pi$
$390$		0			0
$391$			8.77891i			0.443969i
$392$		0			0
$393$			5.81224i			0.293189i
$394$		0			0
$395$	−5.73459	+	5.73459i	−0.288538	+	0.288538i
$396$		0			0
$397$	−3.14511	−	3.14511i	−0.157849	−	0.157849i	0.623764	−	0.781613i	$-0.285603\pi$
$397$	−3.14511	−	3.14511i	−0.157849	−	0.157849i	−0.781613	+	0.623764i	$0.785603\pi$
$398$		0			0
$399$	−19.1459			−0.958492
$400$		0			0
$401$	−23.9530			−1.19616			−0.598078	−	0.801438i	$-0.704069\pi$
$401$	−23.9530			−1.19616			−0.598078	+	0.801438i	$0.704069\pi$
$402$		0			0
$403$	−1.26755	−	1.26755i	−0.0631410	−	0.0631410i
$404$		0			0
$405$	2.09406	−	2.09406i	0.104054	−	0.104054i
$406$		0			0
$407$		−	27.6416i		−	1.37014i
$408$		0			0
$409$		−	5.26405i		−	0.260291i	−0.991495	−	0.130145i	$-0.958456\pi$
$409$		−	5.26405i		−	0.260291i	0.991495	−	0.130145i	$-0.0415444\pi$
$410$		0			0
$411$	−9.68522	+	9.68522i	−0.477737	+	0.477737i
$412$		0			0
$413$	1.23554	+	1.23554i	0.0607972	+	0.0607972i
$414$		0			0
$415$	0.0210211			0.00103188
$416$		0			0
$417$	−50.0179			−2.44939
$418$		0			0
$419$	5.40200	+	5.40200i	0.263905	+	0.263905i	0.826638	−	0.562733i	$-0.190250\pi$
$419$	5.40200	+	5.40200i	0.263905	+	0.263905i	−0.562733	+	0.826638i	$0.690250\pi$
$420$		0			0
$421$	−14.2595	+	14.2595i	−0.694963	+	0.694963i	−0.963320	−	0.268357i	$-0.913519\pi$
$421$	−14.2595	+	14.2595i	−0.694963	+	0.694963i	0.268357	+	0.963320i	$0.413519\pi$
$422$		0			0
$423$			52.5976i			2.55738i
$424$		0			0
$425$		−	3.07426i		−	0.149123i
$426$		0			0
$427$	−0.354752	+	0.354752i	−0.0171676	+	0.0171676i
$428$		0			0
$429$	−2.12537	−	2.12537i	−0.102614	−	0.102614i
$430$		0			0
$431$	5.88265			0.283357			0.141679	−	0.989913i	$-0.454750\pi$
$431$	5.88265			0.283357			0.141679	+	0.989913i	$0.454750\pi$
$432$		0			0
$433$	34.1231			1.63985			0.819925	−	0.572471i	$-0.194015\pi$
$433$	34.1231			1.63985			0.819925	+	0.572471i	$0.194015\pi$
$434$		0			0
$435$	−8.27995	−	8.27995i	−0.396993	−	0.396993i
$436$		0			0
$437$	14.2319	−	14.2319i	0.680802	−	0.680802i
$438$		0			0
$439$			30.0006i			1.43185i	0.698176	+	0.715926i	$0.253995\pi$
$439$			30.0006i			1.43185i	−0.698176	+	0.715926i	$0.746005\pi$
$440$		0			0
$441$		−	4.37899i		−	0.208523i
$442$		0			0
$443$	−21.0503	+	21.0503i	−1.00013	+	1.00013i	−0.000131473		1.00000i	$0.500042\pi$
$443$	−21.0503	+	21.0503i	−1.00013	+	1.00013i	−1.00000		0.000131473i	$0.999958\pi$
$444$		0			0
$445$	−8.10410	−	8.10410i	−0.384171	−	0.384171i
$446$		0			0
$447$	−11.2502			−0.532116
$448$		0			0
$449$	−13.0169			−0.614305			−0.307153	−	0.951660i	$-0.599376\pi$
$449$	−13.0169			−0.614305			−0.307153	+	0.951660i	$0.599376\pi$
$450$		0			0
$451$	−6.58293	−	6.58293i	−0.309978	−	0.309978i
$452$		0			0
$453$	−20.1497	+	20.1497i	−0.946715	+	0.946715i
$454$		0			0
$455$		−	0.325336i		−	0.0152520i
$456$		0			0
$457$			27.5356i			1.28806i	0.764999	+	0.644031i	$0.222739\pi$
$457$			27.5356i			1.28806i	−0.764999	+	0.644031i	$0.777261\pi$
$458$		0			0
$459$	8.14298	−	8.14298i	0.380082	−	0.380082i
$460$		0			0
$461$	−3.02388	−	3.02388i	−0.140836	−	0.140836i	0.633174	−	0.774010i	$-0.281752\pi$
$461$	−3.02388	−	3.02388i	−0.140836	−	0.140836i	−0.774010	+	0.633174i	$0.781752\pi$
$462$		0			0
$463$	29.8214			1.38592			0.692958	−	0.720978i	$-0.256307\pi$
$463$	29.8214			1.38592			0.692958	+	0.720978i	$0.256307\pi$
$464$		0			0
$465$	−14.9674			−0.694096
$466$		0			0
$467$	20.0298	+	20.0298i	0.926870	+	0.926870i	0.997502	−	0.0706323i	$-0.0225017\pi$
$467$	20.0298	+	20.0298i	0.926870	+	0.926870i	−0.0706323	+	0.997502i	$0.522502\pi$
$468$		0			0
$469$	−10.8475	+	10.8475i	−0.500892	+	0.500892i
$470$		0			0
$471$		−	43.7513i		−	2.01595i
$472$		0			0
$473$			7.97414i			0.366651i
$474$		0			0
$475$	−4.98381	+	4.98381i	−0.228673	+	0.228673i
$476$		0			0
$477$	40.5872	+	40.5872i	1.85836	+	1.85836i
$478$		0			0
$479$	−27.6154			−1.26178			−0.630889	−	0.775873i	$-0.717310\pi$
$479$	−27.6154			−1.26178			−0.630889	+	0.775873i	$0.717310\pi$
$480$		0			0
$481$	2.64409			0.120560
$482$		0			0
$483$	5.48509	+	5.48509i	0.249580	+	0.249580i
$484$		0			0
$485$	5.38469	−	5.38469i	0.244506	−	0.244506i
$486$		0			0
$487$		−	26.5614i		−	1.20361i	−0.798642	−	0.601807i	$-0.794448\pi$
$487$		−	26.5614i		−	1.20361i	0.798642	−	0.601807i	$-0.205552\pi$
$488$		0			0
$489$		−	25.3092i		−	1.14452i
$490$		0			0
$491$	1.69651	−	1.69651i	0.0765626	−	0.0765626i	−0.667789	−	0.744351i	$-0.732759\pi$
$491$	1.69651	−	1.69651i	0.0765626	−	0.0765626i	0.744351	+	0.667789i	$0.232759\pi$
$492$		0			0
$493$	9.37066	+	9.37066i	0.422033	+	0.422033i
$494$		0			0
$495$	−14.8934			−0.669406
$496$		0			0
$497$	−1.43189			−0.0642291
$498$		0			0
$499$	18.0448	+	18.0448i	0.807795	+	0.807795i	0.984300	−	0.176505i	$-0.0564791\pi$
$499$	18.0448	+	18.0448i	0.807795	+	0.807795i	−0.176505	+	0.984300i	$0.556479\pi$
$500$		0			0
$501$	30.9707	−	30.9707i	1.38367	−	1.38367i
$502$		0			0
$503$		−	28.8592i		−	1.28677i	−0.765544	−	0.643383i	$-0.777530\pi$
$503$		−	28.8592i		−	1.28677i	0.765544	−	0.643383i	$-0.222470\pi$
$504$		0			0
$505$		−	8.63842i		−	0.384405i
$506$		0			0
$507$	−24.7672	+	24.7672i	−1.09995	+	1.09995i
$508$		0			0
$509$	12.7993	+	12.7993i	0.567318	+	0.567318i	0.931376	−	0.364058i	$-0.118609\pi$
$509$	12.7993	+	12.7993i	0.567318	+	0.567318i	−0.364058	+	0.931376i	$0.618609\pi$
$510$		0			0
$511$	−11.5526			−0.511056
$512$		0			0
$513$	−26.4019			−1.16567
$514$		0			0
$515$	−6.63792	−	6.63792i	−0.292502	−	0.292502i
$516$		0			0
$517$	−28.8866	+	28.8866i	−1.27043	+	1.27043i
$518$		0			0
$519$			35.0856i			1.54009i
$520$		0			0
$521$			35.5497i			1.55746i	0.627358	+	0.778731i	$0.284136\pi$
$521$			35.5497i			1.55746i	−0.627358	+	0.778731i	$0.715864\pi$
$522$		0			0
$523$	−2.94875	+	2.94875i	−0.128940	+	0.128940i	−0.768632	−	0.639692i	$-0.779062\pi$
$523$	−2.94875	+	2.94875i	−0.128940	+	0.128940i	0.639692	+	0.768632i	$0.279062\pi$
$524$		0			0
$525$	−1.92081	−	1.92081i	−0.0838308	−	0.0838308i
$526$		0			0
$527$	16.9390			0.737875
$528$		0			0
$529$	14.8454			0.645454
$530$		0			0
$531$	5.41043	+	5.41043i	0.234793	+	0.234793i
$532$		0			0
$533$	0.629697	−	0.629697i	0.0272752	−	0.0272752i
$534$		0			0
$535$		−	5.74439i		−	0.248352i
$536$		0			0
$537$		−	39.0123i		−	1.68350i
$538$		0			0
$539$	2.40494	−	2.40494i	0.103588	−	0.103588i
$540$		0			0
$541$	−0.870655	−	0.870655i	−0.0374324	−	0.0374324i	0.688143	−	0.725575i	$-0.258426\pi$
$541$	−0.870655	−	0.870655i	−0.0374324	−	0.0374324i	−0.725575	+	0.688143i	$0.758426\pi$
$542$		0			0
$543$	−34.8012			−1.49346
$544$		0			0
$545$	−16.4591			−0.705030
$546$		0			0
$547$	−27.4186	−	27.4186i	−1.17233	−	1.17233i	−0.981652	−	0.190681i	$-0.938930\pi$
$547$	−27.4186	−	27.4186i	−1.17233	−	1.17233i	−0.190681	−	0.981652i	$-0.561070\pi$
$548$		0			0
$549$	−1.55345	+	1.55345i	−0.0662998	+	0.0662998i
$550$		0			0
$551$		−	30.3823i		−	1.29433i
$552$		0			0
$553$		−	8.10993i		−	0.344869i
$554$		0			0
$555$	15.6109	−	15.6109i	0.662645	−	0.662645i
$556$		0			0
$557$	9.50051	+	9.50051i	0.402550	+	0.402550i	0.879131	−	0.476581i	$-0.158124\pi$
$557$	9.50051	+	9.50051i	0.402550	+	0.402550i	−0.476581	+	0.879131i	$0.658124\pi$
$558$		0			0
$559$	−0.762775			−0.0322619
$560$		0			0
$561$	28.4026			1.19916
$562$		0			0
$563$	23.3659	+	23.3659i	0.984754	+	0.984754i	0.999886	−	0.0151319i	$-0.00481681\pi$
$563$	23.3659	+	23.3659i	0.984754	+	0.984754i	−0.0151319	+	0.999886i	$0.504817\pi$
$564$		0			0
$565$	−10.1636	+	10.1636i	−0.427587	+	0.427587i
$566$		0			0
$567$			2.96144i			0.124369i
$568$		0			0
$569$			3.93387i			0.164917i	0.996595	+	0.0824583i	$0.0262771\pi$
$569$			3.93387i			0.164917i	−0.996595	+	0.0824583i	$0.973723\pi$
$570$		0			0
$571$	−13.0268	+	13.0268i	−0.545157	+	0.545157i	−0.925036	−	0.379879i	$-0.875965\pi$
$571$	−13.0268	+	13.0268i	−0.545157	+	0.545157i	0.379879	+	0.925036i	$0.375965\pi$
$572$		0			0
$573$	42.3827	+	42.3827i	1.77056	+	1.77056i
$574$		0			0
$575$	2.85562			0.119088
$576$		0			0
$577$	18.7292			0.779709			0.389854	−	0.920877i	$-0.372525\pi$
$577$	18.7292			0.779709			0.389854	+	0.920877i	$0.372525\pi$
$578$		0			0
$579$	−45.3479	−	45.3479i	−1.88460	−	1.88460i
$580$		0			0
$581$	−0.0148642	+	0.0148642i	−0.000616669	+	0.000616669i
$582$		0			0
$583$			44.5810i			1.84636i
$584$		0			0
$585$		−	1.42464i		−	0.0589016i
$586$		0			0
$587$	2.58925	−	2.58925i	0.106870	−	0.106870i	−0.651650	−	0.758520i	$-0.725923\pi$
$587$	2.58925	−	2.58925i	0.106870	−	0.106870i	0.758520	+	0.651650i	$0.225923\pi$
$588$		0			0
$589$	−27.4605	−	27.4605i	−1.13149	−	1.13149i
$590$		0			0
$591$	5.14601			0.211679
$592$		0			0
$593$	35.5707			1.46072			0.730358	−	0.683065i	$-0.239353\pi$
$593$	35.5707			1.46072			0.730358	+	0.683065i	$0.239353\pi$
$594$		0			0
$595$	2.17383	+	2.17383i	0.0891183	+	0.0891183i
$596$		0			0
$597$	34.4784	−	34.4784i	1.41111	−	1.41111i
$598$		0			0
$599$			16.7637i			0.684945i	0.939528	+	0.342473i	$0.111264\pi$
$599$			16.7637i			0.684945i	−0.939528	+	0.342473i	$0.888736\pi$
$600$		0			0
$601$			31.5684i			1.28770i	0.765151	+	0.643850i	$0.222664\pi$
$601$			31.5684i			1.28770i	−0.765151	+	0.643850i	$0.777336\pi$
$602$		0			0
$603$	−47.5011	+	47.5011i	−1.93440	+	1.93440i
$604$		0			0
$605$	−0.401255	−	0.401255i	−0.0163133	−	0.0163133i
$606$		0			0
$607$	5.46877			0.221970			0.110985	−	0.993822i	$-0.464599\pi$
$607$	5.46877			0.221970			0.110985	+	0.993822i	$0.464599\pi$
$608$		0			0
$609$	11.7096			0.474498
$610$		0			0
$611$	−2.76318	−	2.76318i	−0.111786	−	0.111786i
$612$		0			0
$613$	26.1963	−	26.1963i	1.05806	−	1.05806i	0.0598509	−	0.998207i	$-0.480937\pi$
$613$	26.1963	−	26.1963i	1.05806	−	1.05806i	0.998207	−	0.0598509i	$-0.0190625\pi$
$614$		0			0
$615$		−	7.43555i		−	0.299830i
$616$		0			0
$617$			26.9821i			1.08626i	0.839649	+	0.543129i	$0.182761\pi$
$617$			26.9821i			1.08626i	−0.839649	+	0.543129i	$0.817239\pi$
$618$		0			0
$619$	−27.0870	+	27.0870i	−1.08872	+	1.08872i	−0.0930566	+	0.995661i	$0.529664\pi$
$619$	−27.0870	+	27.0870i	−1.08872	+	1.08872i	−0.995661	+	0.0930566i	$0.970336\pi$
$620$		0			0
$621$	7.56386	+	7.56386i	0.303527	+	0.303527i
$622$		0			0
$623$	11.4609			0.459172
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−46.0446	−	46.0446i	−1.83884	−	1.83884i
$628$		0			0
$629$	−17.6673	+	17.6673i	−0.704440	+	0.704440i
$630$		0			0
$631$			30.8360i			1.22756i	0.789476	+	0.613781i	$0.210352\pi$
$631$			30.8360i			1.22756i	−0.789476	+	0.613781i	$0.789648\pi$
$632$		0			0
$633$		−	41.7162i		−	1.65807i
$634$		0			0
$635$	11.5364	−	11.5364i	0.457809	−	0.457809i
$636$		0			0
$637$	0.230047	+	0.230047i	0.00911480	+	0.00911480i
$638$		0			0
$639$	−6.27023			−0.248046
$640$		0			0
$641$	−21.0782			−0.832540			−0.416270	−	0.909241i	$-0.636663\pi$
$641$	−21.0782			−0.832540			−0.416270	+	0.909241i	$0.636663\pi$
$642$		0			0
$643$	−25.6837	−	25.6837i	−1.01286	−	1.01286i	−0.999916	−	0.0129487i	$-0.995878\pi$
$643$	−25.6837	−	25.6837i	−1.01286	−	1.01286i	−0.0129487	−	0.999916i	$-0.504122\pi$
$644$		0			0
$645$	−4.50348	+	4.50348i	−0.177324	+	0.177324i
$646$		0			0
$647$			4.30694i			0.169323i	0.996410	+	0.0846616i	$0.0269809\pi$
$647$			4.30694i			0.169323i	−0.996410	+	0.0846616i	$0.973019\pi$
$648$		0			0
$649$			5.94282i			0.233276i
$650$		0			0
$651$	10.5835	−	10.5835i	0.414802	−	0.414802i
$652$		0			0
$653$	7.40886	+	7.40886i	0.289931	+	0.289931i	0.837053	−	0.547122i	$-0.184277\pi$
$653$	7.40886	+	7.40886i	0.289931	+	0.289931i	−0.547122	+	0.837053i	$0.684277\pi$
$654$		0			0
$655$	−2.13966			−0.0836035
$656$		0			0
$657$	−50.5885			−1.97365
$658$		0			0
$659$	−5.83069	−	5.83069i	−0.227132	−	0.227132i	0.584362	−	0.811493i	$-0.301345\pi$
$659$	−5.83069	−	5.83069i	−0.227132	−	0.227132i	−0.811493	+	0.584362i	$0.801345\pi$
$660$		0			0
$661$	21.9055	−	21.9055i	0.852026	−	0.852026i	−0.138357	−	0.990382i	$-0.544182\pi$
$661$	21.9055	−	21.9055i	0.852026	−	0.852026i	0.990382	+	0.138357i	$0.0441821\pi$
$662$		0			0
$663$			2.71688i			0.105515i
$664$		0			0
$665$		−	7.04817i		−	0.273316i
$666$		0			0
$667$	−8.70422	+	8.70422i	−0.337029	+	0.337029i
$668$		0			0
$669$	−2.91631	−	2.91631i	−0.112751	−	0.112751i
$670$		0			0
$671$	−1.70631			−0.0658715
$672$		0			0
$673$	22.3632			0.862038			0.431019	−	0.902343i	$-0.358154\pi$
$673$	22.3632			0.862038			0.431019	+	0.902343i	$0.358154\pi$
$674$		0			0
$675$	−2.64876	−	2.64876i	−0.101951	−	0.101951i
$676$		0			0
$677$	8.00808	−	8.00808i	0.307775	−	0.307775i	−0.536271	−	0.844046i	$-0.680167\pi$
$677$	8.00808	−	8.00808i	0.307775	−	0.307775i	0.844046	+	0.536271i	$0.180167\pi$
$678$		0			0
$679$			7.61510i			0.292241i
$680$		0			0
$681$		−	25.2966i		−	0.969369i
$682$		0			0
$683$	31.7140	−	31.7140i	1.21350	−	1.21350i	0.243636	−	0.969867i	$-0.421660\pi$
$683$	31.7140	−	31.7140i	1.21350	−	1.21350i	0.969867	−	0.243636i	$-0.0783401\pi$
$684$		0			0
$685$	−3.56542	−	3.56542i	−0.136228	−	0.136228i
$686$		0			0
$687$	25.0456			0.955550
$688$		0			0
$689$	−4.26445			−0.162462
$690$		0			0
$691$	−33.6095	−	33.6095i	−1.27857	−	1.27857i	−0.941471	−	0.337095i	$-0.890556\pi$
$691$	−33.6095	−	33.6095i	−1.27857	−	1.27857i	−0.337095	−	0.941471i	$-0.609444\pi$
$692$		0			0
$693$	10.5312	−	10.5312i	0.400047	−	0.400047i
$694$		0			0
$695$		−	18.4131i		−	0.698449i
$696$		0			0
$697$			8.41502i			0.318742i
$698$		0			0
$699$	34.6518	−	34.6518i	1.31065	−	1.31065i
$700$		0			0
$701$	−12.7954	−	12.7954i	−0.483277	−	0.483277i	0.422900	−	0.906176i	$-0.361012\pi$
$701$	−12.7954	−	12.7954i	−0.483277	−	0.483277i	−0.906176	+	0.422900i	$0.861012\pi$
$702$		0			0
$703$	57.2823			2.16044
$704$		0			0
$705$	−32.6280			−1.22884
$706$		0			0
$707$	6.10829	+	6.10829i	0.229726	+	0.229726i
$708$		0			0
$709$	16.8053	−	16.8053i	0.631135	−	0.631135i	−0.317218	−	0.948353i	$-0.602749\pi$
$709$	16.8053	−	16.8053i	0.631135	−	0.631135i	0.948353	+	0.317218i	$0.102749\pi$
$710$		0			0
$711$		−	35.5133i		−	1.33185i
$712$		0			0
$713$			15.7343i			0.589255i
$714$		0			0
$715$	0.782412	−	0.782412i	0.0292606	−	0.0292606i
$716$		0			0
$717$	−27.0754	−	27.0754i	−1.01115	−	1.01115i
$718$		0			0
$719$	33.0315			1.23187			0.615934	−	0.787798i	$-0.288779\pi$
$719$	33.0315			1.23187			0.615934	+	0.787798i	$0.288779\pi$
$720$		0			0
$721$	9.38744			0.349606
$722$		0			0
$723$	−21.3017	−	21.3017i	−0.792220	−	0.792220i
$724$		0			0
$725$	3.04810	−	3.04810i	0.113204	−	0.113204i
$726$		0			0
$727$		−	41.3991i		−	1.53541i	−0.640805	−	0.767704i	$-0.721399\pi$
$727$		−	41.3991i		−	1.53541i	0.640805	−	0.767704i	$-0.278601\pi$
$728$		0			0
$729$			43.4947i			1.61091i
$730$		0			0
$731$	5.09671	−	5.09671i	0.188509	−	0.188509i
$732$		0			0
$733$	19.7963	+	19.7963i	0.731195	+	0.731195i	0.970856	−	0.239662i	$-0.0770366\pi$
$733$	19.7963	+	19.7963i	0.731195	+	0.731195i	−0.239662	+	0.970856i	$0.577037\pi$
$734$		0			0
$735$	2.71643			0.100197
$736$		0			0
$737$	−52.1752			−1.92190
$738$		0			0
$739$	−0.304171	−	0.304171i	−0.0111891	−	0.0111891i	0.701490	−	0.712679i	$-0.252518\pi$
$739$	−0.304171	−	0.304171i	−0.0111891	−	0.0111891i	−0.712679	+	0.701490i	$0.752518\pi$
$740$		0			0
$741$	4.40445	−	4.40445i	0.161801	−	0.161801i
$742$		0			0
$743$		−	47.0701i		−	1.72684i	−0.504490	−	0.863418i	$-0.668319\pi$
$743$		−	47.0701i		−	1.72684i	0.504490	−	0.863418i	$-0.331681\pi$
$744$		0			0
$745$		−	4.14154i		−	0.151734i
$746$		0			0
$747$	−0.0650899	+	0.0650899i	−0.00238152	+	0.00238152i
$748$		0			0
$749$	4.06190	+	4.06190i	0.148419	+	0.148419i
$750$		0			0
$751$	17.5637			0.640910			0.320455	−	0.947264i	$-0.396164\pi$
$751$	17.5637			0.640910			0.320455	+	0.947264i	$0.396164\pi$
$752$		0			0
$753$	−24.0061			−0.874831
$754$		0			0
$755$	−7.41771	−	7.41771i	−0.269958	−	0.269958i
$756$		0			0
$757$	−7.56441	+	7.56441i	−0.274933	+	0.274933i	−0.831082	−	0.556149i	$-0.812278\pi$
$757$	−7.56441	+	7.56441i	−0.274933	+	0.274933i	0.556149	+	0.831082i	$0.312278\pi$
$758$		0			0
$759$			26.3826i			0.957628i
$760$		0			0
$761$		−	48.4501i		−	1.75631i	−0.478372	−	0.878157i	$-0.658773\pi$
$761$		−	48.4501i		−	1.75631i	0.478372	−	0.878157i	$-0.341227\pi$
$762$		0			0
$763$	11.6383	−	11.6383i	0.421336	−	0.421336i
$764$		0			0
$765$	9.51917	+	9.51917i	0.344166	+	0.344166i
$766$		0			0
$767$	−0.568467			−0.0205262
$768$		0			0
$769$	1.55437			0.0560519			0.0280259	−	0.999607i	$-0.491078\pi$
$769$	1.55437			0.0560519			0.0280259	+	0.999607i	$0.491078\pi$
$770$		0			0
$771$	31.9977	+	31.9977i	1.15237	+	1.15237i
$772$		0			0
$773$	−8.53373	+	8.53373i	−0.306937	+	0.306937i	−0.843720	−	0.536783i	$-0.819639\pi$
$773$	−8.53373	+	8.53373i	−0.306937	+	0.306937i	0.536783	+	0.843720i	$0.319639\pi$
$774$		0			0
$775$		−	5.50995i		−	0.197923i
$776$		0			0
$777$			22.0771i			0.792012i
$778$		0			0
$779$	13.6419	−	13.6419i	0.488774	−	0.488774i
$780$		0			0
$781$	−3.44361	−	3.44361i	−0.123222	−	0.123222i
$782$		0			0
$783$	16.1474			0.577061
$784$		0			0
$785$	16.1062			0.574854
$786$		0			0
$787$	−0.786007	−	0.786007i	−0.0280181	−	0.0280181i	0.692959	−	0.720977i	$-0.256307\pi$
$787$	−0.786007	−	0.786007i	−0.0280181	−	0.0280181i	−0.720977	+	0.692959i	$0.756307\pi$
$788$		0			0
$789$	−27.9374	+	27.9374i	−0.994598	+	0.994598i
$790$		0			0
$791$		−	14.3735i		−	0.511064i
$792$		0			0
$793$		−	0.163219i		−	0.00579609i
$794$		0			0
$795$	−25.1776	+	25.1776i	−0.892957	+	0.892957i
$796$		0			0
$797$	−22.3948	−	22.3948i	−0.793264	−	0.793264i	0.188759	−	0.982023i	$-0.439554\pi$
$797$	−22.3948	−	22.3948i	−0.793264	−	0.793264i	−0.982023	+	0.188759i	$0.939554\pi$
$798$		0			0
$799$	36.9261			1.30635
$800$		0			0
$801$	50.1872			1.77328
$802$		0			0
$803$	−27.7832	−	27.7832i	−0.980449	−	0.980449i
$804$		0			0
$805$	−2.01923	+	2.01923i	−0.0711684	+	0.0711684i
$806$		0			0
$807$			7.97196i			0.280626i
$808$		0			0
$809$			4.46309i			0.156914i	0.996918	+	0.0784569i	$0.0249993\pi$
$809$			4.46309i			0.156914i	−0.996918	+	0.0784569i	$0.975001\pi$
$810$		0			0
$811$	−38.5046	+	38.5046i	−1.35208	+	1.35208i	−0.468750	+	0.883331i	$0.655296\pi$
$811$	−38.5046	+	38.5046i	−1.35208	+	1.35208i	−0.883331	+	0.468750i	$0.844704\pi$
$812$		0			0
$813$	−14.9541	−	14.9541i	−0.524462	−	0.524462i
$814$		0			0
$815$	9.31710			0.326364
$816$		0			0
$817$	−16.5250			−0.578136
$818$		0			0
$819$	1.00737	+	1.00737i	0.0352005	+	0.0352005i
$820$		0			0
$821$	−9.18132	+	9.18132i	−0.320430	+	0.320430i	−0.848932	−	0.528502i	$-0.822754\pi$
$821$	−9.18132	+	9.18132i	−0.320430	+	0.320430i	0.528502	+	0.848932i	$0.322754\pi$
$822$		0			0
$823$			42.0956i			1.46736i	0.679495	+	0.733680i	$0.262199\pi$
$823$			42.0956i			1.46736i	−0.679495	+	0.733680i	$0.737801\pi$
$824$		0			0
$825$		−	9.23884i		−	0.321655i
$826$		0			0
$827$	−34.6267	+	34.6267i	−1.20409	+	1.20409i	−0.231178	+	0.972912i	$0.574258\pi$
$827$	−34.6267	+	34.6267i	−1.20409	+	1.20409i	−0.972912	+	0.231178i	$0.925742\pi$
$828$		0			0
$829$	−4.45262	−	4.45262i	−0.154646	−	0.154646i	0.625543	−	0.780189i	$-0.284877\pi$
$829$	−4.45262	−	4.45262i	−0.154646	−	0.154646i	−0.780189	+	0.625543i	$0.784877\pi$
$830$		0			0
$831$	18.8009			0.652195
$832$		0			0
$833$	−3.07426			−0.106517
$834$		0			0
$835$	11.4013	+	11.4013i	0.394557	+	0.394557i
$836$		0			0
$837$	14.5945	−	14.5945i	0.504461	−	0.504461i
$838$		0			0
$839$			7.15578i			0.247045i	0.992342	+	0.123523i	$0.0394191\pi$
$839$			7.15578i			0.247045i	−0.992342	+	0.123523i	$0.960581\pi$
$840$		0			0
$841$		−	10.4181i		−	0.359247i
$842$		0			0
$843$	15.5679	−	15.5679i	0.536188	−	0.536188i
$844$		0			0
$845$	−9.11755	−	9.11755i	−0.313653	−	0.313653i
$846$		0			0
$847$	0.567460			0.0194982
$848$		0			0
$849$	56.9010			1.95284
$850$		0			0
$851$	−16.4108	−	16.4108i	−0.562554	−	0.562554i
$852$		0			0
$853$	−17.4128	+	17.4128i	−0.596205	+	0.596205i	−0.939300	−	0.343096i	$-0.888524\pi$
$853$	−17.4128	+	17.4128i	−0.596205	+	0.596205i	0.343096	+	0.939300i	$0.388524\pi$
$854$		0			0
$855$		−	30.8638i		−	1.05552i
$856$		0			0
$857$		−	33.3568i		−	1.13945i	−0.821837	−	0.569723i	$-0.807050\pi$
$857$		−	33.3568i		−	1.13945i	0.821837	−	0.569723i	$-0.192950\pi$
$858$		0			0
$859$	−2.96984	+	2.96984i	−0.101330	+	0.101330i	−0.755954	−	0.654624i	$-0.772827\pi$
$859$	−2.96984	+	2.96984i	−0.101330	+	0.101330i	0.654624	+	0.755954i	$0.272827\pi$
$860$		0			0
$861$	5.25773	+	5.25773i	0.179183	+	0.179183i
$862$		0			0
$863$	−30.1859			−1.02754			−0.513770	−	0.857928i	$-0.671751\pi$
$863$	−30.1859			−1.02754			−0.513770	+	0.857928i	$0.671751\pi$
$864$		0			0
$865$	−12.9161			−0.439160
$866$		0			0
$867$	14.5000	+	14.5000i	0.492447	+	0.492447i
$868$		0			0
$869$	19.5039	−	19.5039i	0.661624	−	0.661624i
$870$		0			0
$871$		−	4.99088i		−	0.169109i
$872$		0			0
$873$			33.3464i			1.12861i
$874$		0			0
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$		0			0
$877$	17.5002	+	17.5002i	0.590941	+	0.590941i	0.937886	−	0.346945i	$-0.112781\pi$
$877$	17.5002	+	17.5002i	0.590941	+	0.590941i	−0.346945	+	0.937886i	$0.612781\pi$
$878$		0			0
$879$	19.5138			0.658184
$880$		0			0
$881$	27.1194			0.913677			0.456839	−	0.889550i	$-0.348982\pi$
$881$	27.1194			0.913677			0.456839	+	0.889550i	$0.348982\pi$
$882$		0			0
$883$	26.3544	+	26.3544i	0.886897	+	0.886897i	0.994224	−	0.107326i	$-0.0342290\pi$
$883$	26.3544	+	26.3544i	0.886897	+	0.886897i	−0.107326	+	0.994224i	$0.534229\pi$
$884$		0			0
$885$	−3.35627	+	3.35627i	−0.112820	+	0.112820i
$886$		0			0
$887$		−	34.8464i		−	1.17003i	−0.811024	−	0.585013i	$-0.801089\pi$
$887$		−	34.8464i		−	1.17003i	0.811024	−	0.585013i	$-0.198911\pi$
$888$		0			0
$889$			16.3150i			0.547187i
$890$		0			0
$891$	−7.12209	+	7.12209i	−0.238599	+	0.238599i
$892$		0			0
$893$	−59.8624	−	59.8624i	−2.00322	−	2.00322i
$894$		0			0
$895$	14.3616			0.480056
$896$		0			0
$897$	−2.52366			−0.0842625
$898$		0			0
$899$	16.7949	+	16.7949i	0.560141	+	0.560141i
$900$		0			0
$901$	28.4942	−	28.4942i	0.949279	−	0.949279i
$902$		0			0
$903$		−	6.36888i		−	0.211943i
$904$		0			0
$905$		−	12.8114i		−	0.425865i
$906$		0			0
$907$	−5.34624	+	5.34624i	−0.177519	+	0.177519i	−0.790273	−	0.612754i	$-0.790062\pi$
$907$	−5.34624	+	5.34624i	−0.177519	+	0.177519i	0.612754	+	0.790273i	$0.290062\pi$
$908$		0			0
$909$	26.7481	+	26.7481i	0.887178	+	0.887178i
$910$		0			0
$911$	−14.0817			−0.466546			−0.233273	−	0.972411i	$-0.574944\pi$
$911$	−14.0817			−0.466546			−0.233273	+	0.972411i	$0.574944\pi$
$912$		0			0
$913$	−0.0714948			−0.00236613
$914$		0			0
$915$	−0.963658	−	0.963658i	−0.0318576	−	0.0318576i
$916$		0			0
$917$	1.51297	−	1.51297i	0.0499626	−	0.0499626i
$918$		0			0
$919$		−	12.1569i		−	0.401020i	−0.979692	−	0.200510i	$-0.935740\pi$
$919$		−	12.1569i		−	0.401020i	0.979692	−	0.200510i	$-0.0642599\pi$
$920$		0			0
$921$		−	94.7581i		−	3.12239i
$922$		0			0
$923$	0.329402	−	0.329402i	0.0108424	−	0.0108424i
$924$		0			0
$925$	5.74684	+	5.74684i	0.188955	+	0.188955i
$926$		0			0
$927$	41.1075			1.35015
$928$		0			0
$929$	−38.5694			−1.26542			−0.632711	−	0.774388i	$-0.718058\pi$
$929$	−38.5694			−1.26542			−0.632711	+	0.774388i	$0.718058\pi$
$930$		0			0
$931$	4.98381	+	4.98381i	0.163338	+	0.163338i
$932$		0			0
$933$	−35.6232	+	35.6232i	−1.16625	+	1.16625i
$934$		0			0
$935$			10.4559i			0.341943i
$936$		0			0
$937$		−	0.399807i		−	0.0130611i	−0.999979	−	0.00653056i	$-0.997921\pi$
$937$		−	0.399807i		−	0.0130611i	0.999979	−	0.00653056i	$-0.00207876\pi$
$938$		0			0
$939$	−19.9758	+	19.9758i	−0.651885	+	0.651885i
$940$		0			0
$941$	35.2038	+	35.2038i	1.14761	+	1.14761i	0.987021	+	0.160589i	$0.0513394\pi$
$941$	35.2038	+	35.2038i	1.14761	+	1.14761i	0.160589	+	0.987021i	$0.448661\pi$
$942$		0			0
$943$	−7.81655			−0.254542
$944$		0			0
$945$	3.74592			0.121855
$946$		0			0
$947$	16.0232	+	16.0232i	0.520685	+	0.520685i	0.917778	−	0.397093i	$-0.129981\pi$
$947$	16.0232	+	16.0232i	0.520685	+	0.520685i	−0.397093	+	0.917778i	$0.629981\pi$
$948$		0			0
$949$	2.65764	−	2.65764i	0.0862705	−	0.0862705i
$950$		0			0
$951$			47.5268i			1.54116i
$952$		0			0
$953$			29.2213i			0.946572i	0.880909	+	0.473286i	$0.156932\pi$
$953$			29.2213i			0.946572i	−0.880909	+	0.473286i	$0.843068\pi$
$954$		0			0
$955$	−15.6023	+	15.6023i	−0.504880	+	0.504880i
$956$		0			0
$957$	28.1609	+	28.1609i	0.910313	+	0.910313i
$958$		0			0
$959$	5.04227			0.162823
$960$		0			0
$961$	−0.640466			−0.0206602
$962$		0			0
$963$	17.7870	+	17.7870i	0.573178	+	0.573178i
$964$		0			0
$965$	16.6940	−	16.6940i	0.537397	−	0.537397i
$966$		0			0
$967$		−	10.4230i		−	0.335183i	−0.985857	−	0.167591i	$-0.946401\pi$
$967$		−	10.4230i		−	0.335183i	0.985857	−	0.167591i	$-0.0535989\pi$
$968$		0			0
$969$			58.8593i			1.89083i
$970$		0			0
$971$	2.97442	−	2.97442i	0.0954537	−	0.0954537i	−0.657767	−	0.753221i	$-0.728499\pi$
$971$	2.97442	−	2.97442i	0.0954537	−	0.0954537i	0.753221	+	0.657767i	$0.228499\pi$
$972$		0			0
$973$	13.0200	+	13.0200i	0.417403	+	0.417403i
$974$		0			0
$975$	0.883751			0.0283027
$976$		0			0
$977$	−12.4194			−0.397331			−0.198666	−	0.980067i	$-0.563661\pi$
$977$	−12.4194			−0.397331			−0.198666	+	0.980067i	$0.563661\pi$
$978$		0			0
$979$	27.5628	+	27.5628i	0.880911	+	0.880911i
$980$		0			0
$981$	50.9641	−	50.9641i	1.62716	−	1.62716i
$982$		0			0
$983$		−	44.7477i		−	1.42723i	−0.700538	−	0.713615i	$-0.747057\pi$
$983$		−	44.7477i		−	1.42723i	0.700538	−	0.713615i	$-0.252943\pi$
$984$		0			0
$985$			1.89440i			0.0603607i
$986$		0			0
$987$	23.0715	−	23.0715i	0.734374	−	0.734374i
$988$		0			0
$989$	4.73424	+	4.73424i	0.150540	+	0.150540i
$990$		0			0
$991$	16.8014			0.533714			0.266857	−	0.963736i	$-0.414015\pi$
$991$	16.8014			0.533714			0.266857	+	0.963736i	$0.414015\pi$
$992$		0			0
$993$	−67.9064			−2.15494
$994$		0			0
$995$	12.6925	+	12.6925i	0.402381	+	0.402381i
$996$		0			0
$997$	−8.71750	+	8.71750i	−0.276086	+	0.276086i	−0.831544	−	0.555458i	$-0.812543\pi$
$997$	−8.71750	+	8.71750i	−0.276086	+	0.276086i	0.555458	+	0.831544i	$0.312543\pi$
$998$		0			0
$999$			30.4440i			0.963206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.1681.3		44
4.3	odd	2		560.2.bd.a.141.2	✓	44
16.5	even	4	inner	2240.2.bd.a.561.3		44
16.11	odd	4		560.2.bd.a.421.2	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.2	✓	44	4.3	odd	2
560.2.bd.a.421.2	yes	44	16.11	odd	4
2240.2.bd.a.561.3		44	16.5	even	4	inner
2240.2.bd.a.1681.3		44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.92081 - 1.92081i) q^{3} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +4.37899i q^{9} +O(q^{10})\)	\(q+(-1.92081 - 1.92081i) q^{3} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +4.37899i q^{9} +(-2.40494 + 2.40494i) q^{11} +(-0.230047 - 0.230047i) q^{13} -2.71643 q^{15} +3.07426 q^{17} +(-4.98381 - 4.98381i) q^{19} +(1.92081 - 1.92081i) q^{21} +2.85562i q^{23} -1.00000i q^{25} +(2.64876 - 2.64876i) q^{27} +(3.04810 + 3.04810i) q^{29} +5.50995 q^{31} +9.23884 q^{33} +(0.707107 + 0.707107i) q^{35} +(-5.74684 + 5.74684i) q^{37} +0.883751i q^{39} +2.73725i q^{41} +(1.65787 - 1.65787i) q^{43} +(3.09641 + 3.09641i) q^{45} +12.0114 q^{47} -1.00000 q^{49} +(-5.90505 - 5.90505i) q^{51} +(9.26864 - 9.26864i) q^{53} +3.40110i q^{55} +19.1459i q^{57} +(1.23554 - 1.23554i) q^{59} +(0.354752 + 0.354752i) q^{61} -4.37899 q^{63} -0.325336 q^{65} +(10.8475 + 10.8475i) q^{67} +(5.48509 - 5.48509i) q^{69} +1.43189i q^{71} +11.5526i q^{73} +(-1.92081 + 1.92081i) q^{75} +(-2.40494 - 2.40494i) q^{77} -8.10993 q^{79} +2.96144 q^{81} +(0.0148642 + 0.0148642i) q^{83} +(2.17383 - 2.17383i) q^{85} -11.7096i q^{87} -11.4609i q^{89} +(0.230047 - 0.230047i) q^{91} +(-10.5835 - 10.5835i) q^{93} -7.04817 q^{95} +7.61510 q^{97} +(-10.5312 - 10.5312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 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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