LMFDB - Embedded newform 2240.2.bd.b.561.7

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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.7
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51271 + 1.51271i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -1.57659i q^{9} +O(q^{10})$	\(q+(-1.51271 + 1.51271i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -1.57659i q^{9} +(-1.33628 - 1.33628i) q^{11} +(-1.57191 + 1.57191i) q^{13} -2.13930 q^{15} -1.88233 q^{17} +(-2.17857 + 2.17857i) q^{19} +(-1.51271 - 1.51271i) q^{21} -5.78214i q^{23} +1.00000i q^{25} +(-2.15321 - 2.15321i) q^{27} +(0.680065 - 0.680065i) q^{29} +5.89387 q^{31} +4.04281 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-3.16100 - 3.16100i) q^{37} -4.75570i q^{39} +0.297608i q^{41} +(-5.32432 - 5.32432i) q^{43} +(1.11481 - 1.11481i) q^{45} -7.55764 q^{47} -1.00000 q^{49} +(2.84743 - 2.84743i) q^{51} +(1.42960 + 1.42960i) q^{53} -1.88978i q^{55} -6.59109i q^{57} +(4.86492 + 4.86492i) q^{59} +(-9.53931 + 9.53931i) q^{61} +1.57659 q^{63} -2.22302 q^{65} +(-8.02272 + 8.02272i) q^{67} +(8.74670 + 8.74670i) q^{69} -2.77480i q^{71} -4.84780i q^{73} +(-1.51271 - 1.51271i) q^{75} +(1.33628 - 1.33628i) q^{77} +5.55737 q^{79} +11.2441 q^{81} +(6.81955 - 6.81955i) q^{83} +(-1.33101 - 1.33101i) q^{85} +2.05748i q^{87} -15.4223i q^{89} +(-1.57191 - 1.57191i) q^{91} +(-8.91572 + 8.91572i) q^{93} -3.08096 q^{95} +2.44035 q^{97} +(-2.10676 + 2.10676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) $ 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * 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
$3$	−1.51271	+	1.51271i	−0.873364	+	0.873364i	−0.992837	−	0.119474i	$-0.961879\pi$
$3$	−1.51271	+	1.51271i	−0.873364	+	0.873364i	0.119474	+	0.992837i	$0.461879\pi$
$4$		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
$9$		−	1.57659i		−	0.525528i
$10$		0			0
$11$	−1.33628	−	1.33628i	−0.402903	−	0.402903i	0.476352	−	0.879255i	$-0.341959\pi$
$11$	−1.33628	−	1.33628i	−0.402903	−	0.402903i	−0.879255	+	0.476352i	$0.841959\pi$
$12$		0			0
$13$	−1.57191	+	1.57191i	−0.435970	+	0.435970i	−0.890653	−	0.454683i	$-0.849752\pi$
$13$	−1.57191	+	1.57191i	−0.435970	+	0.435970i	0.454683	+	0.890653i	$0.349752\pi$
$14$		0			0
$15$	−2.13930			−0.552364
$16$		0			0
$17$	−1.88233			−0.456533			−0.228266	−	0.973599i	$-0.573306\pi$
$17$	−1.88233			−0.456533			−0.228266	+	0.973599i	$0.573306\pi$
$18$		0			0
$19$	−2.17857	+	2.17857i	−0.499798	+	0.499798i	−0.911375	−	0.411577i	$-0.864978\pi$
$19$	−2.17857	+	2.17857i	−0.499798	+	0.499798i	0.411577	+	0.911375i	$0.364978\pi$
$20$		0			0
$21$	−1.51271	−	1.51271i	−0.330100	−	0.330100i
$22$		0			0
$23$		−	5.78214i		−	1.20566i	−0.797870	−	0.602830i	$-0.794040\pi$
$23$		−	5.78214i		−	1.20566i	0.797870	−	0.602830i	$-0.205960\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−2.15321	−	2.15321i	−0.414386	−	0.414386i
$28$		0			0
$29$	0.680065	−	0.680065i	0.126285	−	0.126285i	−0.641140	−	0.767424i	$-0.721538\pi$
$29$	0.680065	−	0.680065i	0.126285	−	0.126285i	0.767424	+	0.641140i	$0.221538\pi$
$30$		0			0
$31$	5.89387			1.05857			0.529285	−	0.848444i	$-0.322460\pi$
$31$	5.89387			1.05857			0.529285	+	0.848444i	$0.322460\pi$
$32$		0			0
$33$	4.04281			0.703762
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	−3.16100	−	3.16100i	−0.519665	−	0.519665i	0.397805	−	0.917470i	$-0.369772\pi$
$37$	−3.16100	−	3.16100i	−0.519665	−	0.519665i	−0.917470	+	0.397805i	$0.869772\pi$
$38$		0			0
$39$		−	4.75570i		−	0.761521i
$40$		0			0
$41$			0.297608i			0.0464785i	0.999730	+	0.0232393i	$0.00739796\pi$
$41$			0.297608i			0.0464785i	−0.999730	+	0.0232393i	$0.992602\pi$
$42$		0			0
$43$	−5.32432	−	5.32432i	−0.811951	−	0.811951i	0.172975	−	0.984926i	$-0.444662\pi$
$43$	−5.32432	−	5.32432i	−0.811951	−	0.811951i	−0.984926	+	0.172975i	$0.944662\pi$
$44$		0			0
$45$	1.11481	−	1.11481i	0.166187	−	0.166187i
$46$		0			0
$47$	−7.55764			−1.10239			−0.551197	−	0.834375i	$-0.685829\pi$
$47$	−7.55764			−1.10239			−0.551197	+	0.834375i	$0.685829\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	2.84743	−	2.84743i	0.398719	−	0.398719i
$52$		0			0
$53$	1.42960	+	1.42960i	0.196370	+	0.196370i	0.798442	−	0.602072i	$-0.205658\pi$
$53$	1.42960	+	1.42960i	0.196370	+	0.196370i	−0.602072	+	0.798442i	$0.705658\pi$
$54$		0			0
$55$		−	1.88978i		−	0.254818i
$56$		0			0
$57$		−	6.59109i		−	0.873011i
$58$		0			0
$59$	4.86492	+	4.86492i	0.633359	+	0.633359i	0.948909	−	0.315550i	$-0.102189\pi$
$59$	4.86492	+	4.86492i	0.633359	+	0.633359i	−0.315550	+	0.948909i	$0.602189\pi$
$60$		0			0
$61$	−9.53931	+	9.53931i	−1.22138	+	1.22138i	−0.254243	+	0.967140i	$0.581826\pi$
$61$	−9.53931	+	9.53931i	−1.22138	+	1.22138i	−0.967140	+	0.254243i	$0.918174\pi$
$62$		0			0
$63$	1.57659			0.198631
$64$		0			0
$65$	−2.22302			−0.275732
$66$		0			0
$67$	−8.02272	+	8.02272i	−0.980131	+	0.980131i	−0.999806	−	0.0196755i	$-0.993737\pi$
$67$	−8.02272	+	8.02272i	−0.980131	+	0.980131i	0.0196755	+	0.999806i	$0.493737\pi$
$68$		0			0
$69$	8.74670	+	8.74670i	1.05298	+	1.05298i
$70$		0			0
$71$		−	2.77480i		−	0.329309i	−0.986351	−	0.164654i	$-0.947349\pi$
$71$		−	2.77480i		−	0.329309i	0.986351	−	0.164654i	$-0.0526509\pi$
$72$		0			0
$73$		−	4.84780i		−	0.567392i	−0.958914	−	0.283696i	$-0.908439\pi$
$73$		−	4.84780i		−	0.567392i	0.958914	−	0.283696i	$-0.0915606\pi$
$74$		0			0
$75$	−1.51271	−	1.51271i	−0.174673	−	0.174673i
$76$		0			0
$77$	1.33628	−	1.33628i	0.152283	−	0.152283i
$78$		0			0
$79$	5.55737			0.625253			0.312626	−	0.949876i	$-0.398791\pi$
$79$	5.55737			0.625253			0.312626	+	0.949876i	$0.398791\pi$
$80$		0			0
$81$	11.2441			1.24935
$82$		0			0
$83$	6.81955	−	6.81955i	0.748543	−	0.748543i	−0.225663	−	0.974205i	$-0.572455\pi$
$83$	6.81955	−	6.81955i	0.748543	−	0.748543i	0.974205	+	0.225663i	$0.0724547\pi$
$84$		0			0
$85$	−1.33101	−	1.33101i	−0.144368	−	0.144368i
$86$		0			0
$87$			2.05748i			0.220585i
$88$		0			0
$89$		−	15.4223i		−	1.63476i	−0.576098	−	0.817381i	$-0.695425\pi$
$89$		−	15.4223i		−	1.63476i	0.576098	−	0.817381i	$-0.304575\pi$
$90$		0			0
$91$	−1.57191	−	1.57191i	−0.164781	−	0.164781i
$92$		0			0
$93$	−8.91572	+	8.91572i	−0.924517	+	0.924517i
$94$		0			0
$95$	−3.08096			−0.316100
$96$		0			0
$97$	2.44035			0.247780			0.123890	−	0.992296i	$-0.460463\pi$
$97$	2.44035			0.247780			0.123890	+	0.992296i	$0.460463\pi$
$98$		0			0
$99$	−2.10676	+	2.10676i	−0.211737	+	0.211737i
$100$		0			0
$101$	−3.30907	−	3.30907i	−0.329264	−	0.329264i	0.523042	−	0.852307i	$-0.324797\pi$
$101$	−3.30907	−	3.30907i	−0.329264	−	0.329264i	−0.852307	+	0.523042i	$0.824797\pi$
$102$		0			0
$103$		−	5.77538i		−	0.569066i	−0.958666	−	0.284533i	$-0.908162\pi$
$103$		−	5.77538i		−	0.569066i	0.958666	−	0.284533i	$-0.0918385\pi$
$104$		0			0
$105$		−	2.13930i		−	0.208774i
$106$		0			0
$107$	−10.4429	−	10.4429i	−1.00956	−	1.00956i	−0.999954	−	0.00960410i	$-0.996943\pi$
$107$	−10.4429	−	10.4429i	−1.00956	−	1.00956i	−0.00960410	−	0.999954i	$-0.503057\pi$
$108$		0			0
$109$	5.93518	−	5.93518i	0.568487	−	0.568487i	−0.363218	−	0.931704i	$-0.618322\pi$
$109$	5.93518	−	5.93518i	0.568487	−	0.568487i	0.931704	+	0.363218i	$0.118322\pi$
$110$		0			0
$111$	9.56335			0.907713
$112$		0			0
$113$	14.5215			1.36607			0.683034	−	0.730387i	$-0.260660\pi$
$113$	14.5215			1.36607			0.683034	+	0.730387i	$0.260660\pi$
$114$		0			0
$115$	4.08859	−	4.08859i	0.381263	−	0.381263i
$116$		0			0
$117$	2.47825	+	2.47825i	0.229115	+	0.229115i
$118$		0			0
$119$		−	1.88233i		−	0.172553i
$120$		0			0
$121$		−	7.42871i		−	0.675338i
$122$		0			0
$123$	−0.450195	−	0.450195i	−0.0405927	−	0.0405927i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−11.7490			−1.04256			−0.521278	−	0.853387i	$-0.674545\pi$
$127$	−11.7490			−1.04256			−0.521278	+	0.853387i	$0.674545\pi$
$128$		0			0
$129$	16.1083			1.41826
$130$		0			0
$131$	7.79323	−	7.79323i	0.680898	−	0.680898i	−0.279305	−	0.960203i	$-0.590104\pi$
$131$	7.79323	−	7.79323i	0.680898	−	0.680898i	0.960203	+	0.279305i	$0.0901040\pi$
$132$		0			0
$133$	−2.17857	−	2.17857i	−0.188906	−	0.188906i
$134$		0			0
$135$		−	3.04510i		−	0.262081i
$136$		0			0
$137$		−	10.5361i		−	0.900160i	−0.892988	−	0.450080i	$-0.851395\pi$
$137$		−	10.5361i		−	0.900160i	0.892988	−	0.450080i	$-0.148605\pi$
$138$		0			0
$139$	13.8949	+	13.8949i	1.17855	+	1.17855i	0.980115	+	0.198433i	$0.0635851\pi$
$139$	13.8949	+	13.8949i	1.17855	+	1.17855i	0.198433	+	0.980115i	$0.436415\pi$
$140$		0			0
$141$	11.4325	−	11.4325i	0.962792	−	0.962792i
$142$		0			0
$143$	4.20103			0.351308
$144$		0			0
$145$	0.961756			0.0798695
$146$		0			0
$147$	1.51271	−	1.51271i	0.124766	−	0.124766i
$148$		0			0
$149$	−4.52861	−	4.52861i	−0.370998	−	0.370998i	0.496843	−	0.867841i	$-0.334493\pi$
$149$	−4.52861	−	4.52861i	−0.370998	−	0.370998i	−0.867841	+	0.496843i	$0.834493\pi$
$150$		0			0
$151$		−	15.0956i		−	1.22847i	−0.789125	−	0.614233i	$-0.789466\pi$
$151$		−	15.0956i		−	1.22847i	0.789125	−	0.614233i	$-0.210534\pi$
$152$		0			0
$153$			2.96766i			0.239921i
$154$		0			0
$155$	4.16759	+	4.16759i	0.334749	+	0.334749i
$156$		0			0
$157$	−5.92770	+	5.92770i	−0.473082	+	0.473082i	−0.902910	−	0.429829i	$-0.858574\pi$
$157$	−5.92770	+	5.92770i	−0.473082	+	0.473082i	0.429829	+	0.902910i	$0.358574\pi$
$158$		0			0
$159$	−4.32513			−0.343005
$160$		0			0
$161$	5.78214			0.455696
$162$		0			0
$163$	14.1555	−	14.1555i	1.10875	−	1.10875i	0.115430	−	0.993316i	$-0.463175\pi$
$163$	14.1555	−	14.1555i	1.10875	−	1.10875i	0.993316	−	0.115430i	$-0.0368245\pi$
$164$		0			0
$165$	2.85870	+	2.85870i	0.222549	+	0.222549i
$166$		0			0
$167$			8.82758i			0.683099i	0.939864	+	0.341549i	$0.110952\pi$
$167$			8.82758i			0.683099i	−0.939864	+	0.341549i	$0.889048\pi$
$168$		0			0
$169$			8.05818i			0.619860i
$170$		0			0
$171$	3.43470	+	3.43470i	0.262658	+	0.262658i
$172$		0			0
$173$	−15.3054	+	15.3054i	−1.16365	+	1.16365i	−0.179974	+	0.983671i	$0.557601\pi$
$173$	−15.3054	+	15.3054i	−1.16365	+	1.16365i	−0.983671	+	0.179974i	$0.942399\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	−14.7184			−1.10631
$178$		0			0
$179$	−9.88606	+	9.88606i	−0.738919	+	0.738919i	−0.972369	−	0.233450i	$-0.924998\pi$
$179$	−9.88606	+	9.88606i	−0.738919	+	0.738919i	0.233450	+	0.972369i	$0.424998\pi$
$180$		0			0
$181$	−6.51302	−	6.51302i	−0.484109	−	0.484109i	0.422332	−	0.906441i	$-0.361212\pi$
$181$	−6.51302	−	6.51302i	−0.484109	−	0.484109i	−0.906441	+	0.422332i	$0.861212\pi$
$182$		0			0
$183$		−	28.8604i		−	2.13342i
$184$		0			0
$185$		−	4.47032i		−	0.328665i
$186$		0			0
$187$	2.51532	+	2.51532i	0.183939	+	0.183939i
$188$		0			0
$189$	2.15321	−	2.15321i	0.156623	−	0.156623i
$190$		0			0
$191$	8.43748			0.610515			0.305257	−	0.952270i	$-0.401258\pi$
$191$	8.43748			0.610515			0.305257	+	0.952270i	$0.401258\pi$
$192$		0			0
$193$	−4.10346			−0.295373			−0.147687	−	0.989034i	$-0.547183\pi$
$193$	−4.10346			−0.295373			−0.147687	+	0.989034i	$0.547183\pi$
$194$		0			0
$195$	3.36279	−	3.36279i	0.240814	−	0.240814i
$196$		0			0
$197$	−3.48848	−	3.48848i	−0.248544	−	0.248544i	0.571829	−	0.820373i	$-0.306234\pi$
$197$	−3.48848	−	3.48848i	−0.248544	−	0.248544i	−0.820373	+	0.571829i	$0.806234\pi$
$198$		0			0
$199$		−	20.4132i		−	1.44705i	−0.690296	−	0.723527i	$-0.742520\pi$
$199$		−	20.4132i		−	1.44705i	0.690296	−	0.723527i	$-0.257480\pi$
$200$		0			0
$201$		−	24.2721i		−	1.71202i
$202$		0			0
$203$	0.680065	+	0.680065i	0.0477312	+	0.0477312i
$204$		0			0
$205$	−0.210441	+	0.210441i	−0.0146978	+	0.0146978i
$206$		0			0
$207$	−9.11604			−0.633608
$208$		0			0
$209$	5.82235			0.402740
$210$		0			0
$211$	1.37987	−	1.37987i	0.0949939	−	0.0949939i	−0.658013	−	0.753007i	$-0.728603\pi$
$211$	1.37987	−	1.37987i	0.0949939	−	0.0949939i	0.753007	+	0.658013i	$0.228603\pi$
$212$		0			0
$213$	4.19747	+	4.19747i	0.287606	+	0.287606i
$214$		0			0
$215$		−	7.52973i		−	0.513523i
$216$		0			0
$217$			5.89387i			0.400102i
$218$		0			0
$219$	7.33332	+	7.33332i	0.495540	+	0.495540i
$220$		0			0
$221$	2.95886	−	2.95886i	0.199035	−	0.199035i
$222$		0			0
$223$	12.4189			0.831630			0.415815	−	0.909449i	$-0.363496\pi$
$223$	12.4189			0.831630			0.415815	+	0.909449i	$0.363496\pi$
$224$		0			0
$225$	1.57659			0.105106
$226$		0			0
$227$	−5.00038	+	5.00038i	−0.331887	+	0.331887i	−0.853303	−	0.521416i	$-0.825404\pi$
$227$	−5.00038	+	5.00038i	−0.331887	+	0.331887i	0.521416	+	0.853303i	$0.325404\pi$
$228$		0			0
$229$	−20.7912	−	20.7912i	−1.37392	−	1.37392i	−0.854549	−	0.519371i	$-0.826166\pi$
$229$	−20.7912	−	20.7912i	−1.37392	−	1.37392i	−0.519371	−	0.854549i	$-0.673834\pi$
$230$		0			0
$231$			4.04281i			0.265997i
$232$		0			0
$233$			1.86435i			0.122138i	0.998134	+	0.0610689i	$0.0194509\pi$
$233$			1.86435i			0.122138i	−0.998134	+	0.0610689i	$0.980549\pi$
$234$		0			0
$235$	−5.34406	−	5.34406i	−0.348608	−	0.348608i
$236$		0			0
$237$	−8.40669	+	8.40669i	−0.546073	+	0.546073i
$238$		0			0
$239$	−28.8509			−1.86621			−0.933105	−	0.359603i	$-0.882912\pi$
$239$	−28.8509			−1.86621			−0.933105	+	0.359603i	$0.882912\pi$
$240$		0			0
$241$	0.109452			0.00705040			0.00352520	−	0.999994i	$-0.498878\pi$
$241$	0.109452			0.00705040			0.00352520	+	0.999994i	$0.498878\pi$
$242$		0			0
$243$	−10.5495	+	10.5495i	−0.676749	+	0.676749i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	6.84904i		−	0.435794i
$248$		0			0
$249$			20.6320i			1.30750i
$250$		0			0
$251$	21.5519	+	21.5519i	1.36034	+	1.36034i	0.873474	+	0.486871i	$0.161862\pi$
$251$	21.5519	+	21.5519i	1.36034	+	1.36034i	0.486871	+	0.873474i	$0.338138\pi$
$252$		0			0
$253$	−7.72656	+	7.72656i	−0.485764	+	0.485764i
$254$		0			0
$255$	4.02687			0.252172
$256$		0			0
$257$	−6.70385			−0.418175			−0.209087	−	0.977897i	$-0.567049\pi$
$257$	−6.70385			−0.418175			−0.209087	+	0.977897i	$0.567049\pi$
$258$		0			0
$259$	3.16100	−	3.16100i	0.196415	−	0.196415i
$260$		0			0
$261$	−1.07218	−	1.07218i	−0.0663663	−	0.0663663i
$262$		0			0
$263$			25.8270i			1.59256i	0.604929	+	0.796279i	$0.293201\pi$
$263$			25.8270i			1.59256i	−0.604929	+	0.796279i	$0.706799\pi$
$264$		0			0
$265$			2.02176i			0.124195i
$266$		0			0
$267$	23.3295	+	23.3295i	1.42774	+	1.42774i
$268$		0			0
$269$	18.9135	−	18.9135i	1.15318	−	1.15318i	0.167267	−	0.985912i	$-0.446506\pi$
$269$	18.9135	−	18.9135i	1.15318	−	1.15318i	0.985912	−	0.167267i	$-0.0534941\pi$
$270$		0			0
$271$	−11.1837			−0.679362			−0.339681	−	0.940541i	$-0.610319\pi$
$271$	−11.1837			−0.679362			−0.339681	+	0.940541i	$0.610319\pi$
$272$		0			0
$273$	4.75570			0.287828
$274$		0			0
$275$	1.33628	−	1.33628i	0.0805807	−	0.0805807i
$276$		0			0
$277$	−11.2171	−	11.2171i	−0.673968	−	0.673968i	0.284660	−	0.958628i	$-0.408119\pi$
$277$	−11.2171	−	11.2171i	−0.673968	−	0.673968i	−0.958628	+	0.284660i	$0.908119\pi$
$278$		0			0
$279$		−	9.29219i		−	0.556309i
$280$		0			0
$281$		−	19.3896i		−	1.15669i	−0.815793	−	0.578344i	$-0.803699\pi$
$281$		−	19.3896i		−	1.15669i	0.815793	−	0.578344i	$-0.196301\pi$
$282$		0			0
$283$	4.27702	+	4.27702i	0.254242	+	0.254242i	0.822707	−	0.568465i	$-0.192463\pi$
$283$	4.27702	+	4.27702i	0.254242	+	0.254242i	−0.568465	+	0.822707i	$0.692463\pi$
$284$		0			0
$285$	4.66060	−	4.66060i	0.276070	−	0.276070i
$286$		0			0
$287$	−0.297608			−0.0175672
$288$		0			0
$289$	−13.4568			−0.791578
$290$		0			0
$291$	−3.69155	+	3.69155i	−0.216402	+	0.216402i
$292$		0			0
$293$	7.99857	+	7.99857i	0.467281	+	0.467281i	0.901033	−	0.433751i	$-0.142810\pi$
$293$	7.99857	+	7.99857i	0.467281	+	0.467281i	−0.433751	+	0.901033i	$0.642810\pi$
$294$		0			0
$295$			6.88004i			0.400571i
$296$		0			0
$297$			5.75459i			0.333915i
$298$		0			0
$299$	9.08902	+	9.08902i	0.525631	+	0.525631i
$300$		0			0
$301$	5.32432	−	5.32432i	0.306889	−	0.306889i
$302$		0			0
$303$	10.0113			0.575135
$304$		0			0
$305$	−13.4906			−0.772471
$306$		0			0
$307$	5.24856	−	5.24856i	0.299551	−	0.299551i	−0.541287	−	0.840838i	$-0.682063\pi$
$307$	5.24856	−	5.24856i	0.299551	−	0.299551i	0.840838	+	0.541287i	$0.182063\pi$
$308$		0			0
$309$	8.73648	+	8.73648i	0.497001	+	0.497001i
$310$		0			0
$311$			23.9216i			1.35647i	0.734845	+	0.678235i	$0.237255\pi$
$311$			23.9216i			1.35647i	−0.734845	+	0.678235i	$0.762745\pi$
$312$		0			0
$313$		−	3.44088i		−	0.194490i	−0.995260	−	0.0972449i	$-0.968997\pi$
$313$		−	3.44088i		−	0.194490i	0.995260	−	0.0972449i	$-0.0310030\pi$
$314$		0			0
$315$	1.11481	+	1.11481i	0.0628127	+	0.0628127i
$316$		0			0
$317$	−7.57618	+	7.57618i	−0.425521	+	0.425521i	−0.887099	−	0.461579i	$-0.847283\pi$
$317$	−7.57618	+	7.57618i	−0.425521	+	0.425521i	0.461579	+	0.887099i	$0.347283\pi$
$318$		0			0
$319$	−1.81751			−0.101761
$320$		0			0
$321$	31.5943			1.76342
$322$		0			0
$323$	4.10079	−	4.10079i	0.228174	−	0.228174i
$324$		0			0
$325$	−1.57191	−	1.57191i	−0.0871940	−	0.0871940i
$326$		0			0
$327$			17.9564i			0.992991i
$328$		0			0
$329$		−	7.55764i		−	0.416666i
$330$		0			0
$331$	−15.9176	−	15.9176i	−0.874910	−	0.874910i	0.118092	−	0.993003i	$-0.462322\pi$
$331$	−15.9176	−	15.9176i	−0.874910	−	0.874910i	−0.993003	+	0.118092i	$0.962322\pi$
$332$		0			0
$333$	−4.98358	+	4.98358i	−0.273099	+	0.273099i
$334$		0			0
$335$	−11.3458			−0.619889
$336$		0			0
$337$	−31.6512			−1.72415			−0.862074	−	0.506782i	$-0.830835\pi$
$337$	−31.6512			−1.72415			−0.862074	+	0.506782i	$0.830835\pi$
$338$		0			0
$339$	−21.9668	+	21.9668i	−1.19307	+	1.19307i
$340$		0			0
$341$	−7.87586	−	7.87586i	−0.426501	−	0.426501i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			12.3697i			0.665963i
$346$		0			0
$347$	1.83783	+	1.83783i	0.0986600	+	0.0986600i	0.754714	−	0.656054i	$-0.227776\pi$
$347$	1.83783	+	1.83783i	0.0986600	+	0.0986600i	−0.656054	+	0.754714i	$0.727776\pi$
$348$		0			0
$349$	−19.9790	+	19.9790i	−1.06945	+	1.06945i	−0.0720530	+	0.997401i	$0.522955\pi$
$349$	−19.9790	+	19.9790i	−1.06945	+	1.06945i	−0.997401	+	0.0720530i	$0.977045\pi$
$350$		0			0
$351$	6.76933			0.361320
$352$		0			0
$353$	26.4955			1.41021			0.705107	−	0.709101i	$-0.250899\pi$
$353$	26.4955			1.41021			0.705107	+	0.709101i	$0.250899\pi$
$354$		0			0
$355$	1.96208	−	1.96208i	0.104137	−	0.104137i
$356$		0			0
$357$	2.84743	+	2.84743i	0.150702	+	0.150702i
$358$		0			0
$359$			0.837266i			0.0441892i	0.999756	+	0.0220946i	$0.00703351\pi$
$359$			0.837266i			0.0441892i	−0.999756	+	0.0220946i	$0.992966\pi$
$360$		0			0
$361$			9.50768i			0.500404i
$362$		0			0
$363$	11.2375	+	11.2375i	0.589815	+	0.589815i
$364$		0			0
$365$	3.42791	−	3.42791i	0.179425	−	0.179425i
$366$		0			0
$367$	−16.8575			−0.879954			−0.439977	−	0.898009i	$-0.645013\pi$
$367$	−16.8575			−0.879954			−0.439977	+	0.898009i	$0.645013\pi$
$368$		0			0
$369$	0.469204			0.0244258
$370$		0			0
$371$	−1.42960	+	1.42960i	−0.0742210	+	0.0742210i
$372$		0			0
$373$	−23.6689	−	23.6689i	−1.22553	−	1.22553i	−0.965637	−	0.259893i	$-0.916313\pi$
$373$	−23.6689	−	23.6689i	−1.22553	−	1.22553i	−0.259893	−	0.965637i	$-0.583687\pi$
$374$		0			0
$375$		−	2.13930i		−	0.110473i
$376$		0			0
$377$			2.13800i			0.110113i
$378$		0			0
$379$	21.6983	+	21.6983i	1.11457	+	1.11457i	0.992525	+	0.122040i	$0.0389437\pi$
$379$	21.6983	+	21.6983i	1.11457	+	1.11457i	0.122040	+	0.992525i	$0.461056\pi$
$380$		0			0
$381$	17.7729	−	17.7729i	0.910531	−	0.910531i
$382$		0			0
$383$	−22.4881			−1.14909			−0.574543	−	0.818474i	$-0.694820\pi$
$383$	−22.4881			−1.14909			−0.574543	+	0.818474i	$0.694820\pi$
$384$		0			0
$385$	1.88978			0.0963123
$386$		0			0
$387$	−8.39425	+	8.39425i	−0.426704	+	0.426704i
$388$		0			0
$389$	−6.32500	−	6.32500i	−0.320690	−	0.320690i	0.528342	−	0.849032i	$-0.322814\pi$
$389$	−6.32500	−	6.32500i	−0.320690	−	0.320690i	−0.849032	+	0.528342i	$0.822814\pi$
$390$		0			0
$391$			10.8839i			0.550423i
$392$		0			0
$393$			23.5778i			1.18934i
$394$		0			0
$395$	3.92965	+	3.92965i	0.197722	+	0.197722i
$396$		0			0
$397$	−13.2621	+	13.2621i	−0.665607	+	0.665607i	−0.956696	−	0.291089i	$-0.905982\pi$
$397$	−13.2621	+	13.2621i	−0.665607	+	0.665607i	0.291089	+	0.956696i	$0.405982\pi$
$398$		0			0
$399$	6.59109			0.329967
$400$		0			0
$401$	3.98604			0.199054			0.0995268	−	0.995035i	$-0.468267\pi$
$401$	3.98604			0.199054			0.0995268	+	0.995035i	$0.468267\pi$
$402$		0			0
$403$	−9.26465	+	9.26465i	−0.461505	+	0.461505i
$404$		0			0
$405$	7.95080	+	7.95080i	0.395079	+	0.395079i
$406$		0			0
$407$			8.44795i			0.418749i
$408$		0			0
$409$			15.6386i			0.773280i	0.922231	+	0.386640i	$0.126364\pi$
$409$			15.6386i			0.773280i	−0.922231	+	0.386640i	$0.873636\pi$
$410$		0			0
$411$	15.9381	+	15.9381i	0.786167	+	0.786167i
$412$		0			0
$413$	−4.86492	+	4.86492i	−0.239387	+	0.239387i
$414$		0			0
$415$	9.64430			0.473420
$416$		0			0
$417$	−42.0378			−2.05860
$418$		0			0
$419$	7.69828	−	7.69828i	0.376085	−	0.376085i	−0.493602	−	0.869688i	$-0.664320\pi$
$419$	7.69828	−	7.69828i	0.376085	−	0.376085i	0.869688	+	0.493602i	$0.164320\pi$
$420$		0			0
$421$	14.9635	+	14.9635i	0.729276	+	0.729276i	0.970475	−	0.241200i	$-0.0775410\pi$
$421$	14.9635	+	14.9635i	0.729276	+	0.729276i	−0.241200	+	0.970475i	$0.577541\pi$
$422$		0			0
$423$			11.9153i			0.579340i
$424$		0			0
$425$		−	1.88233i		−	0.0913066i
$426$		0			0
$427$	−9.53931	−	9.53931i	−0.461640	−	0.461640i
$428$		0			0
$429$	−6.35494	+	6.35494i	−0.306819	+	0.306819i
$430$		0			0
$431$	−24.0186			−1.15694			−0.578468	−	0.815705i	$-0.696349\pi$
$431$	−24.0186			−1.15694			−0.578468	+	0.815705i	$0.696349\pi$
$432$		0			0
$433$	17.5563			0.843703			0.421851	−	0.906665i	$-0.361380\pi$
$433$	17.5563			0.843703			0.421851	+	0.906665i	$0.361380\pi$
$434$		0			0
$435$	−1.45486	+	1.45486i	−0.0697552	+	0.0697552i
$436$		0			0
$437$	12.5968	+	12.5968i	0.602586	+	0.602586i
$438$		0			0
$439$		−	0.0674791i		−	0.00322060i	−0.999999	−	0.00161030i	$-0.999487\pi$
$439$		−	0.0674791i		−	0.00322060i	0.999999	−	0.00161030i	$-0.000512575\pi$
$440$		0			0
$441$			1.57659i			0.0750755i
$442$		0			0
$443$	−22.7728	−	22.7728i	−1.08197	−	1.08197i	−0.996326	−	0.0856436i	$-0.972705\pi$
$443$	−22.7728	−	22.7728i	−1.08197	−	1.08197i	−0.0856436	−	0.996326i	$-0.527295\pi$
$444$		0			0
$445$	10.9052	−	10.9052i	0.516957	−	0.516957i
$446$		0			0
$447$	13.7009			0.648033
$448$		0			0
$449$	−7.08245			−0.334242			−0.167121	−	0.985936i	$-0.553447\pi$
$449$	−7.08245			−0.334242			−0.167121	+	0.985936i	$0.553447\pi$
$450$		0			0
$451$	0.397687	−	0.397687i	0.0187264	−	0.0187264i
$452$		0			0
$453$	22.8353	+	22.8353i	1.07290	+	1.07290i
$454$		0			0
$455$		−	2.22302i		−	0.104217i
$456$		0			0
$457$			29.3915i			1.37487i	0.726244	+	0.687437i	$0.241264\pi$
$457$			29.3915i			1.37487i	−0.726244	+	0.687437i	$0.758736\pi$
$458$		0			0
$459$	4.05307	+	4.05307i	0.189181	+	0.189181i
$460$		0			0
$461$	9.62033	−	9.62033i	0.448063	−	0.448063i	−0.446647	−	0.894710i	$-0.647382\pi$
$461$	9.62033	−	9.62033i	0.448063	−	0.448063i	0.894710	+	0.446647i	$0.147382\pi$
$462$		0			0
$463$	−35.3413			−1.64245			−0.821226	−	0.570604i	$-0.806709\pi$
$463$	−35.3413			−1.64245			−0.821226	+	0.570604i	$0.806709\pi$
$464$		0			0
$465$	−12.6087			−0.584716
$466$		0			0
$467$	5.80142	−	5.80142i	0.268458	−	0.268458i	−0.560021	−	0.828479i	$-0.689207\pi$
$467$	5.80142	−	5.80142i	0.268458	−	0.268458i	0.828479	+	0.560021i	$0.189207\pi$
$468$		0			0
$469$	−8.02272	−	8.02272i	−0.370455	−	0.370455i
$470$		0			0
$471$		−	17.9338i		−	0.826345i
$472$		0			0
$473$			14.2296i			0.654276i
$474$		0			0
$475$	−2.17857	−	2.17857i	−0.0999596	−	0.0999596i
$476$		0			0
$477$	2.25388	−	2.25388i	0.103198	−	0.103198i
$478$		0			0
$479$	2.99018			0.136625			0.0683125	−	0.997664i	$-0.478239\pi$
$479$	2.99018			0.136625			0.0683125	+	0.997664i	$0.478239\pi$
$480$		0			0
$481$	9.93762			0.453117
$482$		0			0
$483$	−8.74670	+	8.74670i	−0.397989	+	0.397989i
$484$		0			0
$485$	1.72559	+	1.72559i	0.0783550	+	0.0783550i
$486$		0			0
$487$			27.1217i			1.22900i	0.788917	+	0.614500i	$0.210642\pi$
$487$			27.1217i			1.22900i	−0.788917	+	0.614500i	$0.789358\pi$
$488$		0			0
$489$			42.8264i			1.93668i
$490$		0			0
$491$	0.963789	+	0.963789i	0.0434952	+	0.0434952i	0.728520	−	0.685025i	$-0.240209\pi$
$491$	0.963789	+	0.963789i	0.0434952	+	0.0434952i	−0.685025	+	0.728520i	$0.740209\pi$
$492$		0			0
$493$	−1.28011	+	1.28011i	−0.0576532	+	0.0576532i
$494$		0			0
$495$	−2.97941			−0.133914
$496$		0			0
$497$	2.77480			0.124467
$498$		0			0
$499$	−29.2555	+	29.2555i	−1.30966	+	1.30966i	−0.387995	+	0.921661i	$0.626832\pi$
$499$	−29.2555	+	29.2555i	−1.30966	+	1.30966i	−0.921661	+	0.387995i	$0.873168\pi$
$500$		0			0
$501$	−13.3536	−	13.3536i	−0.596594	−	0.596594i
$502$		0			0
$503$			16.9217i			0.754500i	0.926112	+	0.377250i	$0.123130\pi$
$503$			16.9217i			0.754500i	−0.926112	+	0.377250i	$0.876870\pi$
$504$		0			0
$505$		−	4.67973i		−	0.208245i
$506$		0			0
$507$	−12.1897	−	12.1897i	−0.541363	−	0.541363i
$508$		0			0
$509$	−7.56790	+	7.56790i	−0.335441	+	0.335441i	−0.854648	−	0.519207i	$-0.826227\pi$
$509$	−7.56790	+	7.56790i	−0.335441	+	0.335441i	0.519207	+	0.854648i	$0.326227\pi$
$510$		0			0
$511$	4.84780			0.214454
$512$		0			0
$513$	9.38185			0.414219
$514$		0			0
$515$	4.08381	−	4.08381i	0.179954	−	0.179954i
$516$		0			0
$517$	10.0991	+	10.0991i	0.444159	+	0.444159i
$518$		0			0
$519$		−	46.3052i		−	2.03257i
$520$		0			0
$521$			6.50111i			0.284819i	0.989808	+	0.142409i	$0.0454849\pi$
$521$			6.50111i			0.284819i	−0.989808	+	0.142409i	$0.954515\pi$
$522$		0			0
$523$	−21.7932	−	21.7932i	−0.952951	−	0.952951i	0.0459913	−	0.998942i	$-0.485355\pi$
$523$	−21.7932	−	21.7932i	−0.952951	−	0.952951i	−0.998942	+	0.0459913i	$0.985355\pi$
$524$		0			0
$525$	1.51271	−	1.51271i	0.0660201	−	0.0660201i
$526$		0			0
$527$	−11.0942			−0.483272
$528$		0			0
$529$	−10.4331			−0.453615
$530$		0			0
$531$	7.66997	−	7.66997i	0.332848	−	0.332848i
$532$		0			0
$533$	−0.467814	−	0.467814i	−0.0202633	−	0.0202633i
$534$		0			0
$535$		−	14.7686i		−	0.638501i
$536$		0			0
$537$		−	29.9095i		−	1.29069i
$538$		0			0
$539$	1.33628	+	1.33628i	0.0575576	+	0.0575576i
$540$		0			0
$541$	−24.7707	+	24.7707i	−1.06498	+	1.06498i	−0.0672404	+	0.997737i	$0.521419\pi$
$541$	−24.7707	+	24.7707i	−1.06498	+	1.06498i	−0.997737	+	0.0672404i	$0.978581\pi$
$542$		0			0
$543$	19.7046			0.845607
$544$		0			0
$545$	8.39361			0.359543
$546$		0			0
$547$	20.4488	−	20.4488i	0.874330	−	0.874330i	−0.118611	−	0.992941i	$-0.537844\pi$
$547$	20.4488	−	20.4488i	0.874330	−	0.874330i	0.992941	+	0.118611i	$0.0378442\pi$
$548$		0			0
$549$	15.0395	+	15.0395i	0.641872	+	0.641872i
$550$		0			0
$551$			2.96313i			0.126234i
$552$		0			0
$553$			5.55737i			0.236323i
$554$		0			0
$555$	6.76231	+	6.76231i	0.287044	+	0.287044i
$556$		0			0
$557$	−5.72748	+	5.72748i	−0.242681	+	0.242681i	−0.817958	−	0.575277i	$-0.804894\pi$
$557$	−5.72748	+	5.72748i	−0.242681	+	0.242681i	0.575277	+	0.817958i	$0.304894\pi$
$558$		0			0
$559$	16.7387			0.707973
$560$		0			0
$561$	−7.60991			−0.321291
$562$		0			0
$563$	−1.86202	+	1.86202i	−0.0784749	+	0.0784749i	−0.745255	−	0.666780i	$-0.767672\pi$
$563$	−1.86202	+	1.86202i	−0.0784749	+	0.0784749i	0.666780	+	0.745255i	$0.267672\pi$
$564$		0			0
$565$	10.2682	+	10.2682i	0.431988	+	0.431988i
$566$		0			0
$567$			11.2441i			0.472209i
$568$		0			0
$569$			38.5135i			1.61457i	0.590163	+	0.807284i	$0.299064\pi$
$569$			38.5135i			1.61457i	−0.590163	+	0.807284i	$0.700936\pi$
$570$		0			0
$571$	−3.43573	−	3.43573i	−0.143781	−	0.143781i	0.631552	−	0.775333i	$-0.282418\pi$
$571$	−3.43573	−	3.43573i	−0.143781	−	0.143781i	−0.775333	+	0.631552i	$0.782418\pi$
$572$		0			0
$573$	−12.7635	+	12.7635i	−0.533201	+	0.533201i
$574$		0			0
$575$	5.78214			0.241132
$576$		0			0
$577$	12.3672			0.514852			0.257426	−	0.966298i	$-0.417126\pi$
$577$	12.3672			0.514852			0.257426	+	0.966298i	$0.417126\pi$
$578$		0			0
$579$	6.20734	−	6.20734i	0.257968	−	0.257968i
$580$		0			0
$581$	6.81955	+	6.81955i	0.282923	+	0.282923i
$582$		0			0
$583$		−	3.82068i		−	0.158236i
$584$		0			0
$585$			3.50478i			0.144905i
$586$		0			0
$587$	−33.4150	−	33.4150i	−1.37919	−	1.37919i	−0.845995	−	0.533191i	$-0.820993\pi$
$587$	−33.4150	−	33.4150i	−1.37919	−	1.37919i	−0.533191	−	0.845995i	$-0.679007\pi$
$588$		0			0
$589$	−12.8402	+	12.8402i	−0.529071	+	0.529071i
$590$		0			0
$591$	10.5541			0.434139
$592$		0			0
$593$	11.2439			0.461732			0.230866	−	0.972986i	$-0.425844\pi$
$593$	11.2439			0.461732			0.230866	+	0.972986i	$0.425844\pi$
$594$		0			0
$595$	1.33101	−	1.33101i	0.0545661	−	0.0545661i
$596$		0			0
$597$	30.8793	+	30.8793i	1.26380	+	1.26380i
$598$		0			0
$599$		−	21.6830i		−	0.885945i	−0.896535	−	0.442973i	$-0.853924\pi$
$599$		−	21.6830i		−	0.885945i	0.896535	−	0.442973i	$-0.146076\pi$
$600$		0			0
$601$		−	27.8539i		−	1.13618i	−0.822965	−	0.568091i	$-0.807682\pi$
$601$		−	27.8539i		−	1.13618i	0.822965	−	0.568091i	$-0.192318\pi$
$602$		0			0
$603$	12.6485	+	12.6485i	0.515087	+	0.515087i
$604$		0			0
$605$	5.25289	−	5.25289i	0.213561	−	0.213561i
$606$		0			0
$607$	−32.2557			−1.30922			−0.654609	−	0.755968i	$-0.727167\pi$
$607$	−32.2557			−1.30922			−0.654609	+	0.755968i	$0.727167\pi$
$608$		0			0
$609$	−2.05748			−0.0833734
$610$		0			0
$611$	11.8799	−	11.8799i	0.480611	−	0.480611i
$612$		0			0
$613$	−29.6929	−	29.6929i	−1.19928	−	1.19928i	−0.974381	−	0.224903i	$-0.927793\pi$
$613$	−29.6929	−	29.6929i	−1.19928	−	1.19928i	−0.224903	−	0.974381i	$-0.572207\pi$
$614$		0			0
$615$		−	0.636671i		−	0.0256731i
$616$		0			0
$617$			14.1180i			0.568370i	0.958770	+	0.284185i	$0.0917229\pi$
$617$			14.1180i			0.568370i	−0.958770	+	0.284185i	$0.908277\pi$
$618$		0			0
$619$	−11.3361	−	11.3361i	−0.455635	−	0.455635i	0.441584	−	0.897220i	$-0.354417\pi$
$619$	−11.3361	−	11.3361i	−0.455635	−	0.455635i	−0.897220	+	0.441584i	$0.854417\pi$
$620$		0			0
$621$	−12.4502	+	12.4502i	−0.499609	+	0.499609i
$622$		0			0
$623$	15.4223			0.617882
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−8.80753	+	8.80753i	−0.351739	+	0.351739i
$628$		0			0
$629$	5.95005	+	5.95005i	0.237244	+	0.237244i
$630$		0			0
$631$		−	7.35809i		−	0.292921i	−0.989217	−	0.146461i	$-0.953212\pi$
$631$		−	7.35809i		−	0.292921i	0.989217	−	0.146461i	$-0.0467881\pi$
$632$		0			0
$633$			4.17468i			0.165928i
$634$		0			0
$635$	−8.30781	−	8.30781i	−0.329685	−	0.329685i
$636$		0			0
$637$	1.57191	−	1.57191i	0.0622814	−	0.0622814i
$638$		0			0
$639$	−4.37472			−0.173061
$640$		0			0
$641$	34.1532			1.34897			0.674486	−	0.738288i	$-0.264365\pi$
$641$	34.1532			1.34897			0.674486	+	0.738288i	$0.264365\pi$
$642$		0			0
$643$	−8.19913	+	8.19913i	−0.323342	+	0.323342i	−0.850048	−	0.526706i	$-0.823427\pi$
$643$	−8.19913	+	8.19913i	−0.323342	+	0.323342i	0.526706	+	0.850048i	$0.323427\pi$
$644$		0			0
$645$	11.3903	+	11.3903i	0.448493	+	0.448493i
$646$		0			0
$647$			39.5781i			1.55598i	0.628279	+	0.777988i	$0.283760\pi$
$647$			39.5781i			1.55598i	−0.628279	+	0.777988i	$0.716240\pi$
$648$		0			0
$649$		−	13.0018i		−	0.510365i
$650$		0			0
$651$	−8.91572	−	8.91572i	−0.349434	−	0.349434i
$652$		0			0
$653$	17.8814	−	17.8814i	0.699755	−	0.699755i	−0.264603	−	0.964358i	$-0.585241\pi$
$653$	17.8814	−	17.8814i	0.699755	−	0.699755i	0.964358	+	0.264603i	$0.0852408\pi$
$654$		0			0
$655$	11.0213			0.430638
$656$		0			0
$657$	−7.64297			−0.298181
$658$		0			0
$659$	−0.344708	+	0.344708i	−0.0134279	+	0.0134279i	−0.713789	−	0.700361i	$-0.753022\pi$
$659$	−0.344708	+	0.344708i	−0.0134279	+	0.0134279i	0.700361	+	0.713789i	$0.253022\pi$
$660$		0			0
$661$	6.86346	+	6.86346i	0.266958	+	0.266958i	0.827873	−	0.560915i	$-0.189551\pi$
$661$	6.86346	+	6.86346i	0.266958	+	0.266958i	−0.560915	+	0.827873i	$0.689551\pi$
$662$		0			0
$663$			8.95181i			0.347659i
$664$		0			0
$665$		−	3.08096i		−	0.119475i
$666$		0			0
$667$	−3.93223	−	3.93223i	−0.152256	−	0.152256i
$668$		0			0
$669$	−18.7862	+	18.7862i	−0.726315	+	0.726315i
$670$		0			0
$671$	25.4944			0.984199
$672$		0			0
$673$	−5.89766			−0.227338			−0.113669	−	0.993519i	$-0.536260\pi$
$673$	−5.89766			−0.227338			−0.113669	+	0.993519i	$0.536260\pi$
$674$		0			0
$675$	2.15321	−	2.15321i	0.0828772	−	0.0828772i
$676$		0			0
$677$	32.0539	+	32.0539i	1.23193	+	1.23193i	0.963221	+	0.268709i	$0.0865970\pi$
$677$	32.0539	+	32.0539i	1.23193	+	1.23193i	0.268709	+	0.963221i	$0.413403\pi$
$678$		0			0
$679$			2.44035i			0.0936521i
$680$		0			0
$681$		−	15.1283i		−	0.579716i
$682$		0			0
$683$	−25.7603	−	25.7603i	−0.985691	−	0.985691i	0.0142076	−	0.999899i	$-0.495477\pi$
$683$	−25.7603	−	25.7603i	−0.985691	−	0.985691i	−0.999899	+	0.0142076i	$0.995477\pi$
$684$		0			0
$685$	7.45015	−	7.45015i	0.284656	−	0.284656i
$686$		0			0
$687$	62.9021			2.39986
$688$		0			0
$689$	−4.49440			−0.171223
$690$		0			0
$691$	−15.7698	+	15.7698i	−0.599910	+	0.599910i	−0.940289	−	0.340378i	$-0.889445\pi$
$691$	−15.7698	+	15.7698i	−0.599910	+	0.599910i	0.340378	+	0.940289i	$0.389445\pi$
$692$		0			0
$693$	−2.10676	−	2.10676i	−0.0800291	−	0.0800291i
$694$		0			0
$695$			19.6503i			0.745379i
$696$		0			0
$697$		−	0.560197i		−	0.0212190i
$698$		0			0
$699$	−2.82022	−	2.82022i	−0.106671	−	0.106671i
$700$		0			0
$701$	28.7984	−	28.7984i	1.08770	−	1.08770i	0.0919372	−	0.995765i	$-0.470694\pi$
$701$	28.7984	−	28.7984i	1.08770	−	1.08770i	0.995765	−	0.0919372i	$-0.0293059\pi$
$702$		0			0
$703$	13.7729			0.519455
$704$		0			0
$705$	16.1680			0.608923
$706$		0			0
$707$	3.30907	−	3.30907i	0.124450	−	0.124450i
$708$		0			0
$709$	−13.0274	−	13.0274i	−0.489253	−	0.489253i	0.418817	−	0.908071i	$-0.362445\pi$
$709$	−13.0274	−	13.0274i	−0.489253	−	0.489253i	−0.908071	+	0.418817i	$0.862445\pi$
$710$		0			0
$711$		−	8.76167i		−	0.328588i
$712$		0			0
$713$		−	34.0792i		−	1.27628i
$714$		0			0
$715$	2.97058	+	2.97058i	0.111093	+	0.111093i
$716$		0			0
$717$	43.6431	−	43.6431i	1.62988	−	1.62988i
$718$		0			0
$719$	−31.9118			−1.19011			−0.595055	−	0.803685i	$-0.702870\pi$
$719$	−31.9118			−1.19011			−0.595055	+	0.803685i	$0.702870\pi$
$720$		0			0
$721$	5.77538			0.215087
$722$		0			0
$723$	−0.165569	+	0.165569i	−0.00615756	+	0.00615756i
$724$		0			0
$725$	0.680065	+	0.680065i	0.0252570	+	0.0252570i
$726$		0			0
$727$		−	2.75661i		−	0.102237i	−0.998693	−	0.0511185i	$-0.983721\pi$
$727$		−	2.75661i		−	0.102237i	0.998693	−	0.0511185i	$-0.0162786\pi$
$728$		0			0
$729$			1.81580i			0.0672517i
$730$		0			0
$731$	10.0221	+	10.0221i	0.370683	+	0.370683i
$732$		0			0
$733$	1.45739	−	1.45739i	0.0538300	−	0.0538300i	−0.679679	−	0.733509i	$-0.737881\pi$
$733$	1.45739	−	1.45739i	0.0538300	−	0.0538300i	0.733509	+	0.679679i	$0.237881\pi$
$734$		0			0
$735$	2.13930			0.0789091
$736$		0			0
$737$	21.4412			0.789796
$738$		0			0
$739$	4.14667	−	4.14667i	0.152538	−	0.152538i	−0.626713	−	0.779250i	$-0.715600\pi$
$739$	4.14667	−	4.14667i	0.152538	−	0.152538i	0.779250	+	0.626713i	$0.215600\pi$
$740$		0			0
$741$	10.3606	+	10.3606i	0.380606	+	0.380606i
$742$		0			0
$743$		−	36.1056i		−	1.32459i	−0.749245	−	0.662293i	$-0.769584\pi$
$743$		−	36.1056i		−	1.32459i	0.749245	−	0.662293i	$-0.230416\pi$
$744$		0			0
$745$		−	6.40442i		−	0.234640i
$746$		0			0
$747$	−10.7516	−	10.7516i	−0.393381	−	0.393381i
$748$		0			0
$749$	10.4429	−	10.4429i	0.381577	−	0.381577i
$750$		0			0
$751$	38.6767			1.41133			0.705667	−	0.708544i	$-0.250648\pi$
$751$	38.6767			1.41133			0.705667	+	0.708544i	$0.250648\pi$
$752$		0			0
$753$	−65.2036			−2.37615
$754$		0			0
$755$	10.6742	−	10.6742i	0.388475	−	0.388475i
$756$		0			0
$757$	8.96400	+	8.96400i	0.325802	+	0.325802i	0.850988	−	0.525185i	$-0.176004\pi$
$757$	8.96400	+	8.96400i	0.325802	+	0.325802i	−0.525185	+	0.850988i	$0.676004\pi$
$758$		0			0
$759$		−	23.3761i		−	0.848498i
$760$		0			0
$761$		−	20.3668i		−	0.738296i	−0.929371	−	0.369148i	$-0.879650\pi$
$761$		−	20.3668i		−	0.738296i	0.929371	−	0.369148i	$-0.120350\pi$
$762$		0			0
$763$	5.93518	+	5.93518i	0.214868	+	0.214868i
$764$		0			0
$765$	−2.09845	+	2.09845i	−0.0758697	+	0.0758697i
$766$		0			0
$767$	−15.2945			−0.552251
$768$		0			0
$769$	9.92004			0.357726			0.178863	−	0.983874i	$-0.442758\pi$
$769$	9.92004			0.357726			0.178863	+	0.983874i	$0.442758\pi$
$770$		0			0
$771$	10.1410	−	10.1410i	0.365218	−	0.365218i
$772$		0			0
$773$	19.7984	+	19.7984i	0.712098	+	0.712098i	0.966974	−	0.254876i	$-0.0820346\pi$
$773$	19.7984	+	19.7984i	0.712098	+	0.712098i	−0.254876	+	0.966974i	$0.582035\pi$
$774$		0			0
$775$			5.89387i			0.211714i
$776$		0			0
$777$			9.56335i			0.343083i
$778$		0			0
$779$	−0.648359	−	0.648359i	−0.0232299	−	0.0232299i
$780$		0			0
$781$	−3.70791	+	3.70791i	−0.132680	+	0.132680i
$782$		0			0
$783$	−2.92865			−0.104661
$784$		0			0
$785$	−8.38303			−0.299203
$786$		0			0
$787$	−1.14523	+	1.14523i	−0.0408231	+	0.0408231i	−0.727224	−	0.686401i	$-0.759190\pi$
$787$	−1.14523	+	1.14523i	−0.0408231	+	0.0408231i	0.686401	+	0.727224i	$0.259190\pi$
$788$		0			0
$789$	−39.0687	−	39.0687i	−1.39088	−	1.39088i
$790$		0			0
$791$			14.5215i			0.516325i
$792$		0			0
$793$		−	29.9899i		−	1.06497i
$794$		0			0
$795$	−3.05833	−	3.05833i	−0.108468	−	0.108468i
$796$		0			0
$797$	−2.26921	+	2.26921i	−0.0803795	+	0.0803795i	−0.746153	−	0.665774i	$-0.768101\pi$
$797$	−2.26921	+	2.26921i	−0.0803795	+	0.0803795i	0.665774	+	0.746153i	$0.268101\pi$
$798$		0			0
$799$	14.2260			0.503279
$800$		0			0
$801$	−24.3146			−0.859114
$802$		0			0
$803$	−6.47801	+	6.47801i	−0.228604	+	0.228604i
$804$		0			0
$805$	4.08859	+	4.08859i	0.144104	+	0.144104i
$806$		0			0
$807$			57.2214i			2.01429i
$808$		0			0
$809$		−	27.2170i		−	0.956899i	−0.878115	−	0.478450i	$-0.841199\pi$
$809$		−	27.2170i		−	0.956899i	0.878115	−	0.478450i	$-0.158801\pi$
$810$		0			0
$811$	−33.1400	−	33.1400i	−1.16370	−	1.16370i	−0.983659	−	0.180043i	$-0.942376\pi$
$811$	−33.1400	−	33.1400i	−1.16370	−	1.16370i	−0.180043	−	0.983659i	$-0.557624\pi$
$812$		0			0
$813$	16.9177	−	16.9177i	0.593330	−	0.593330i
$814$		0			0
$815$	20.0189			0.701232
$816$		0			0
$817$	23.1988			0.811623
$818$		0			0
$819$	−2.47825	+	2.47825i	−0.0865972	+	0.0865972i
$820$		0			0
$821$	4.26974	+	4.26974i	0.149015	+	0.149015i	0.777678	−	0.628663i	$-0.216397\pi$
$821$	4.26974	+	4.26974i	0.149015	+	0.149015i	−0.628663	+	0.777678i	$0.716397\pi$
$822$		0			0
$823$			30.2895i			1.05583i	0.849299	+	0.527913i	$0.177025\pi$
$823$			30.2895i			1.05583i	−0.849299	+	0.527913i	$0.822975\pi$
$824$		0			0
$825$			4.04281i			0.140752i
$826$		0			0
$827$	32.8285	+	32.8285i	1.14156	+	1.14156i	0.988165	+	0.153394i	$0.0490204\pi$
$827$	32.8285	+	32.8285i	1.14156	+	1.14156i	0.153394	+	0.988165i	$0.450980\pi$
$828$		0			0
$829$	−5.01641	+	5.01641i	−0.174227	+	0.174227i	−0.788834	−	0.614607i	$-0.789315\pi$
$829$	−5.01641	+	5.01641i	−0.174227	+	0.174227i	0.614607	+	0.788834i	$0.289315\pi$
$830$		0			0
$831$	33.9363			1.17724
$832$		0			0
$833$	1.88233			0.0652190
$834$		0			0
$835$	−6.24204	+	6.24204i	−0.216015	+	0.216015i
$836$		0			0
$837$	−12.6908	−	12.6908i	−0.438657	−	0.438657i
$838$		0			0
$839$			48.2228i			1.66483i	0.554149	+	0.832417i	$0.313044\pi$
$839$			48.2228i			1.66483i	−0.554149	+	0.832417i	$0.686956\pi$
$840$		0			0
$841$			28.0750i			0.968104i
$842$		0			0
$843$	29.3309	+	29.3309i	1.01021	+	1.01021i
$844$		0			0
$845$	−5.69800	+	5.69800i	−0.196017	+	0.196017i
$846$		0			0
$847$	7.42871			0.255254
$848$		0			0
$849$	−12.9398			−0.444092
$850$		0			0
$851$	−18.2773	+	18.2773i	−0.626539	+	0.626539i
$852$		0			0
$853$	−34.5910	−	34.5910i	−1.18437	−	1.18437i	−0.978600	−	0.205773i	$-0.934029\pi$
$853$	−34.5910	−	34.5910i	−1.18437	−	1.18437i	−0.205773	−	0.978600i	$-0.565971\pi$
$854$		0			0
$855$			4.85740i			0.166119i
$856$		0			0
$857$		−	13.1805i		−	0.450239i	−0.974331	−	0.225120i	$-0.927723\pi$
$857$		−	13.1805i		−	0.450239i	0.974331	−	0.225120i	$-0.0722773\pi$
$858$		0			0
$859$	−30.5253	−	30.5253i	−1.04151	−	1.04151i	−0.999100	−	0.0424095i	$-0.986497\pi$
$859$	−30.5253	−	30.5253i	−1.04151	−	1.04151i	−0.0424095	−	0.999100i	$-0.513503\pi$
$860$		0			0
$861$	0.450195	−	0.450195i	0.0153426	−	0.0153426i
$862$		0			0
$863$	6.76454			0.230268			0.115134	−	0.993350i	$-0.463270\pi$
$863$	6.76454			0.230268			0.115134	+	0.993350i	$0.463270\pi$
$864$		0			0
$865$	−21.6451			−0.735954
$866$		0			0
$867$	20.3563	−	20.3563i	0.691335	−	0.691335i
$868$		0			0
$869$	−7.42620	−	7.42620i	−0.251916	−	0.251916i
$870$		0			0
$871$		−	25.2220i		−	0.854615i
$872$		0			0
$873$		−	3.84742i		−	0.130216i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	23.8177	−	23.8177i	0.804267	−	0.804267i	−0.179492	−	0.983759i	$-0.557446\pi$
$877$	23.8177	−	23.8177i	0.804267	−	0.804267i	0.983759	+	0.179492i	$0.0574455\pi$
$878$		0			0
$879$	−24.1990			−0.816213
$880$		0			0
$881$	−25.5291			−0.860097			−0.430048	−	0.902806i	$-0.641504\pi$
$881$	−25.5291			−0.860097			−0.430048	+	0.902806i	$0.641504\pi$
$882$		0			0
$883$	−23.3128	+	23.3128i	−0.784538	+	0.784538i	−0.980593	−	0.196055i	$-0.937187\pi$
$883$	−23.3128	+	23.3128i	−0.784538	+	0.784538i	0.196055	+	0.980593i	$0.437187\pi$
$884$		0			0
$885$	−10.4075	−	10.4075i	−0.349845	−	0.349845i
$886$		0			0
$887$			29.8396i			1.00191i	0.865472	+	0.500957i	$0.167019\pi$
$887$			29.8396i			1.00191i	−0.865472	+	0.500957i	$0.832981\pi$
$888$		0			0
$889$		−	11.7490i		−	0.394049i
$890$		0			0
$891$	−15.0253	−	15.0253i	−0.503367	−	0.503367i
$892$		0			0
$893$	16.4648	−	16.4648i	0.550974	−	0.550974i
$894$		0			0
$895$	−13.9810			−0.467333
$896$		0			0
$897$	−27.4981			−0.918135
$898$		0			0
$899$	4.00821	−	4.00821i	0.133681	−	0.133681i
$900$		0			0
$901$	−2.69098	−	2.69098i	−0.0896495	−	0.0896495i
$902$		0			0
$903$			16.1083i			0.536051i
$904$		0			0
$905$		−	9.21080i		−	0.306177i
$906$		0			0
$907$	−16.5731	−	16.5731i	−0.550300	−	0.550300i	0.376228	−	0.926527i	$-0.377221\pi$
$907$	−16.5731	−	16.5731i	−0.550300	−	0.550300i	−0.926527	+	0.376228i	$0.877221\pi$
$908$		0			0
$909$	−5.21703	+	5.21703i	−0.173038	+	0.173038i
$910$		0			0
$911$	2.96000			0.0980692			0.0490346	−	0.998797i	$-0.484386\pi$
$911$	2.96000			0.0980692			0.0490346	+	0.998797i	$0.484386\pi$
$912$		0			0
$913$	−18.2256			−0.603181
$914$		0			0
$915$	20.4074	−	20.4074i	0.674648	−	0.674648i
$916$		0			0
$917$	7.79323	+	7.79323i	0.257355	+	0.257355i
$918$		0			0
$919$			24.8359i			0.819262i	0.912251	+	0.409631i	$0.134342\pi$
$919$			24.8359i			0.819262i	−0.912251	+	0.409631i	$0.865658\pi$
$920$		0			0
$921$			15.8791i			0.523234i
$922$		0			0
$923$	4.36175	+	4.36175i	0.143569	+	0.143569i
$924$		0			0
$925$	3.16100	−	3.16100i	0.103933	−	0.103933i
$926$		0			0
$927$	−9.10539			−0.299060
$928$		0			0
$929$	34.2428			1.12347			0.561735	−	0.827317i	$-0.310134\pi$
$929$	34.2428			1.12347			0.561735	+	0.827317i	$0.310134\pi$
$930$		0			0
$931$	2.17857	−	2.17857i	0.0713997	−	0.0713997i
$932$		0			0
$933$	−36.1865	−	36.1865i	−1.18469	−	1.18469i
$934$		0			0
$935$			3.55720i			0.116333i
$936$		0			0
$937$		−	32.7889i		−	1.07117i	−0.844482	−	0.535584i	$-0.820092\pi$
$937$		−	32.7889i		−	1.07117i	0.844482	−	0.535584i	$-0.179908\pi$
$938$		0			0
$939$	5.20505	+	5.20505i	0.169860	+	0.169860i
$940$		0			0
$941$	−7.23752	+	7.23752i	−0.235936	+	0.235936i	−0.815165	−	0.579229i	$-0.803354\pi$
$941$	−7.23752	+	7.23752i	−0.235936	+	0.235936i	0.579229	+	0.815165i	$0.303354\pi$
$942$		0			0
$943$	1.72081			0.0560373
$944$		0			0
$945$	3.04510			0.0990573
$946$		0			0
$947$	24.0905	−	24.0905i	0.782836	−	0.782836i	−0.197473	−	0.980308i	$-0.563273\pi$
$947$	24.0905	−	24.0905i	0.782836	−	0.782836i	0.980308	+	0.197473i	$0.0632734\pi$
$948$		0			0
$949$	7.62032	+	7.62032i	0.247366	+	0.247366i
$950$		0			0
$951$		−	22.9211i		−	0.743269i
$952$		0			0
$953$		−	30.7508i		−	0.996117i	−0.867143	−	0.498059i	$-0.834046\pi$
$953$		−	30.7508i		−	0.996117i	0.867143	−	0.498059i	$-0.165954\pi$
$954$		0			0
$955$	5.96620	+	5.96620i	0.193062	+	0.193062i
$956$		0			0
$957$	2.74937	−	2.74937i	0.0888745	−	0.0888745i
$958$		0			0
$959$	10.5361			0.340229
$960$		0			0
$961$	3.73768			0.120570
$962$		0			0
$963$	−16.4642	+	16.4642i	−0.530551	+	0.530551i
$964$		0			0
$965$	−2.90158	−	2.90158i	−0.0934052	−	0.0934052i
$966$		0			0
$967$			41.8010i			1.34423i	0.740448	+	0.672114i	$0.234614\pi$
$967$			41.8010i			1.34423i	−0.740448	+	0.672114i	$0.765386\pi$
$968$		0			0
$969$			12.4066i			0.398558i
$970$		0			0
$971$	13.3840	+	13.3840i	0.429512	+	0.429512i	0.888462	−	0.458950i	$-0.151774\pi$
$971$	13.3840	+	13.3840i	0.429512	+	0.429512i	−0.458950	+	0.888462i	$0.651774\pi$
$972$		0			0
$973$	−13.8949	+	13.8949i	−0.445449	+	0.445449i
$974$		0			0
$975$	4.75570			0.152304
$976$		0			0
$977$	−23.4162			−0.749151			−0.374576	−	0.927196i	$-0.622212\pi$
$977$	−23.4162			−0.749151			−0.374576	+	0.927196i	$0.622212\pi$
$978$		0			0
$979$	−20.6085	+	20.6085i	−0.658651	+	0.658651i
$980$		0			0
$981$	−9.35731	−	9.35731i	−0.298756	−	0.298756i
$982$		0			0
$983$		−	14.6282i		−	0.466567i	−0.972409	−	0.233284i	$-0.925053\pi$
$983$		−	14.6282i		−	0.466567i	0.972409	−	0.233284i	$-0.0749470\pi$
$984$		0			0
$985$		−	4.93346i		−	0.157193i
$986$		0			0
$987$	11.4325	+	11.4325i	0.363901	+	0.363901i
$988$		0			0
$989$	−30.7860	+	30.7860i	−0.978937	+	0.978937i
$990$		0			0
$991$	−49.6832			−1.57824			−0.789120	−	0.614239i	$-0.789463\pi$
$991$	−49.6832			−1.57824			−0.789120	+	0.614239i	$0.789463\pi$
$992$		0			0
$993$	48.1574			1.52823
$994$		0			0
$995$	14.4343	−	14.4343i	0.457599	−	0.457599i
$996$		0			0
$997$	5.62375	+	5.62375i	0.178106	+	0.178106i	0.790530	−	0.612424i	$-0.209805\pi$
$997$	5.62375	+	5.62375i	0.178106	+	0.178106i	−0.612424	+	0.790530i	$0.709805\pi$
$998$		0			0
$999$			13.6126i			0.430684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.7		52
4.3	odd	2		560.2.bd.b.421.22	yes	52
16.3	odd	4		560.2.bd.b.141.22	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.7		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.22	✓	52	16.3	odd	4
560.2.bd.b.421.22	yes	52	4.3	odd	2
2240.2.bd.b.561.7		52	1.1	even	1	trivial
2240.2.bd.b.1681.7		52	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)

\(f(q)\)	\(=\)	\(q+(-1.51271 + 1.51271i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -1.57659i q^{9} +O(q^{10})\)	\(q+(-1.51271 + 1.51271i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -1.57659i q^{9} +(-1.33628 - 1.33628i) q^{11} +(-1.57191 + 1.57191i) q^{13} -2.13930 q^{15} -1.88233 q^{17} +(-2.17857 + 2.17857i) q^{19} +(-1.51271 - 1.51271i) q^{21} -5.78214i q^{23} +1.00000i q^{25} +(-2.15321 - 2.15321i) q^{27} +(0.680065 - 0.680065i) q^{29} +5.89387 q^{31} +4.04281 q^{33} +(-0.707107 + 0.707107i) q^{35} +(-3.16100 - 3.16100i) q^{37} -4.75570i q^{39} +0.297608i q^{41} +(-5.32432 - 5.32432i) q^{43} +(1.11481 - 1.11481i) q^{45} -7.55764 q^{47} -1.00000 q^{49} +(2.84743 - 2.84743i) q^{51} +(1.42960 + 1.42960i) q^{53} -1.88978i q^{55} -6.59109i q^{57} +(4.86492 + 4.86492i) q^{59} +(-9.53931 + 9.53931i) q^{61} +1.57659 q^{63} -2.22302 q^{65} +(-8.02272 + 8.02272i) q^{67} +(8.74670 + 8.74670i) q^{69} -2.77480i q^{71} -4.84780i q^{73} +(-1.51271 - 1.51271i) q^{75} +(1.33628 - 1.33628i) q^{77} +5.55737 q^{79} +11.2441 q^{81} +(6.81955 - 6.81955i) q^{83} +(-1.33101 - 1.33101i) q^{85} +2.05748i q^{87} -15.4223i q^{89} +(-1.57191 - 1.57191i) q^{91} +(-8.91572 + 8.91572i) q^{93} -3.08096 q^{95} +2.44035 q^{97} +(-2.10676 + 2.10676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) \) 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * q^99

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