LMFDB - Embedded newform 2240.2.bd.a.561.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.2
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18833 + 2.18833i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -6.57756i q^{9} +O(q^{10})$	\(q+(-2.18833 + 2.18833i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -6.57756i q^{9} +(-0.847972 - 0.847972i) q^{11} +(3.07718 - 3.07718i) q^{13} +3.09476 q^{15} -5.75841 q^{17} +(-3.49935 + 3.49935i) q^{19} +(2.18833 + 2.18833i) q^{21} -8.84350i q^{23} +1.00000i q^{25} +(7.82888 + 7.82888i) q^{27} +(-2.20718 + 2.20718i) q^{29} +5.44796 q^{31} +3.71128 q^{33} +(-0.707107 + 0.707107i) q^{35} +(4.16747 + 4.16747i) q^{37} +13.4677i q^{39} +4.94926i q^{41} +(7.34128 + 7.34128i) q^{43} +(-4.65104 + 4.65104i) q^{45} -5.42928 q^{47} -1.00000 q^{49} +(12.6013 - 12.6013i) q^{51} +(-2.14124 - 2.14124i) q^{53} +1.19921i q^{55} -15.3155i q^{57} +(3.49480 + 3.49480i) q^{59} +(-3.45415 + 3.45415i) q^{61} -6.57756 q^{63} -4.35179 q^{65} +(-3.12477 + 3.12477i) q^{67} +(19.3525 + 19.3525i) q^{69} -0.245356i q^{71} +0.160291i q^{73} +(-2.18833 - 2.18833i) q^{75} +(-0.847972 + 0.847972i) q^{77} +9.95271 q^{79} -14.5316 q^{81} +(-6.68896 + 6.68896i) q^{83} +(4.07181 + 4.07181i) q^{85} -9.66007i q^{87} +6.01478i q^{89} +(-3.07718 - 3.07718i) q^{91} +(-11.9219 + 11.9219i) q^{93} +4.94883 q^{95} -14.8733 q^{97} +(-5.57759 + 5.57759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.18833	+	2.18833i	−1.26343	+	1.26343i	−0.314013	+	0.949419i	$0.601674\pi$
$3$	−2.18833	+	2.18833i	−1.26343	+	1.26343i	−0.949419	+	0.314013i	$0.898326\pi$
$4$		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
$9$		−	6.57756i		−	2.19252i
$10$		0			0
$11$	−0.847972	−	0.847972i	−0.255673	−	0.255673i	0.567618	−	0.823292i	$-0.307865\pi$
$11$	−0.847972	−	0.847972i	−0.255673	−	0.255673i	−0.823292	+	0.567618i	$0.807865\pi$
$12$		0			0
$13$	3.07718	−	3.07718i	0.853455	−	0.853455i	−0.137102	−	0.990557i	$-0.543779\pi$
$13$	3.07718	−	3.07718i	0.853455	−	0.853455i	0.990557	+	0.137102i	$0.0437787\pi$
$14$		0			0
$15$	3.09476			0.799065
$16$		0			0
$17$	−5.75841			−1.39662			−0.698310	−	0.715796i	$-0.746064\pi$
$17$	−5.75841			−1.39662			−0.698310	+	0.715796i	$0.746064\pi$
$18$		0			0
$19$	−3.49935	+	3.49935i	−0.802806	+	0.802806i	−0.983533	−	0.180727i	$-0.942155\pi$
$19$	−3.49935	+	3.49935i	−0.802806	+	0.802806i	0.180727	+	0.983533i	$0.442155\pi$
$20$		0			0
$21$	2.18833	+	2.18833i	0.477532	+	0.477532i
$22$		0			0
$23$		−	8.84350i		−	1.84400i	−0.387193	−	0.921999i	$-0.626555\pi$
$23$		−	8.84350i		−	1.84400i	0.387193	−	0.921999i	$-0.373445\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	7.82888	+	7.82888i	1.50667	+	1.50667i
$28$		0			0
$29$	−2.20718	+	2.20718i	−0.409863	+	0.409863i	−0.881691	−	0.471828i	$-0.843594\pi$
$29$	−2.20718	+	2.20718i	−0.409863	+	0.409863i	0.471828	+	0.881691i	$0.343594\pi$
$30$		0			0
$31$	5.44796			0.978482			0.489241	−	0.872149i	$-0.337274\pi$
$31$	5.44796			0.978482			0.489241	+	0.872149i	$0.337274\pi$
$32$		0			0
$33$	3.71128			0.646051
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	4.16747	+	4.16747i	0.685128	+	0.685128i	0.961151	−	0.276023i	$-0.0890165\pi$
$37$	4.16747	+	4.16747i	0.685128	+	0.685128i	−0.276023	+	0.961151i	$0.589017\pi$
$38$		0			0
$39$			13.4677i			2.15657i
$40$		0			0
$41$			4.94926i			0.772944i	0.922301	+	0.386472i	$0.126306\pi$
$41$			4.94926i			0.772944i	−0.922301	+	0.386472i	$0.873694\pi$
$42$		0			0
$43$	7.34128	+	7.34128i	1.11954	+	1.11954i	0.991810	+	0.127726i	$0.0407677\pi$
$43$	7.34128	+	7.34128i	1.11954	+	1.11954i	0.127726	+	0.991810i	$0.459232\pi$
$44$		0			0
$45$	−4.65104	+	4.65104i	−0.693336	+	0.693336i
$46$		0			0
$47$	−5.42928			−0.791942			−0.395971	−	0.918263i	$-0.629592\pi$
$47$	−5.42928			−0.791942			−0.395971	+	0.918263i	$0.629592\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	12.6013	−	12.6013i	1.76453	−	1.76453i
$52$		0			0
$53$	−2.14124	−	2.14124i	−0.294122	−	0.294122i	0.544584	−	0.838706i	$-0.316688\pi$
$53$	−2.14124	−	2.14124i	−0.294122	−	0.294122i	−0.838706	+	0.544584i	$0.816688\pi$
$54$		0			0
$55$			1.19921i			0.161702i
$56$		0			0
$57$		−	15.3155i		−	2.02858i
$58$		0			0
$59$	3.49480	+	3.49480i	0.454984	+	0.454984i	0.897005	−	0.442021i	$-0.145738\pi$
$59$	3.49480	+	3.49480i	0.454984	+	0.454984i	−0.442021	+	0.897005i	$0.645738\pi$
$60$		0			0
$61$	−3.45415	+	3.45415i	−0.442258	+	0.442258i	−0.892770	−	0.450512i	$-0.851241\pi$
$61$	−3.45415	+	3.45415i	−0.442258	+	0.442258i	0.450512	+	0.892770i	$0.351241\pi$
$62$		0			0
$63$	−6.57756			−0.828695
$64$		0			0
$65$	−4.35179			−0.539773
$66$		0			0
$67$	−3.12477	+	3.12477i	−0.381751	+	0.381751i	−0.871733	−	0.489981i	$-0.837004\pi$
$67$	−3.12477	+	3.12477i	−0.381751	+	0.381751i	0.489981	+	0.871733i	$0.337004\pi$
$68$		0			0
$69$	19.3525	+	19.3525i	2.32977	+	2.32977i
$70$		0			0
$71$		−	0.245356i		−	0.0291184i	−0.999894	−	0.0145592i	$-0.995366\pi$
$71$		−	0.245356i		−	0.0291184i	0.999894	−	0.0145592i	$-0.00463449\pi$
$72$		0			0
$73$			0.160291i			0.0187606i	0.999956	+	0.00938030i	$0.00298589\pi$
$73$			0.160291i			0.0187606i	−0.999956	+	0.00938030i	$0.997014\pi$
$74$		0			0
$75$	−2.18833	−	2.18833i	−0.252686	−	0.252686i
$76$		0			0
$77$	−0.847972	+	0.847972i	−0.0966354	+	0.0966354i
$78$		0			0
$79$	9.95271			1.11977			0.559883	−	0.828571i	$-0.310846\pi$
$79$	9.95271			1.11977			0.559883	+	0.828571i	$0.310846\pi$
$80$		0			0
$81$	−14.5316			−1.61463
$82$		0			0
$83$	−6.68896	+	6.68896i	−0.734209	+	0.734209i	−0.971451	−	0.237242i	$-0.923757\pi$
$83$	−6.68896	+	6.68896i	−0.734209	+	0.734209i	0.237242	+	0.971451i	$0.423757\pi$
$84$		0			0
$85$	4.07181	+	4.07181i	0.441650	+	0.441650i
$86$		0			0
$87$		−	9.66007i		−	1.03567i
$88$		0			0
$89$			6.01478i			0.637565i	0.947828	+	0.318783i	$0.103274\pi$
$89$			6.01478i			0.637565i	−0.947828	+	0.318783i	$0.896726\pi$
$90$		0			0
$91$	−3.07718	−	3.07718i	−0.322576	−	0.322576i
$92$		0			0
$93$	−11.9219	+	11.9219i	−1.23625	+	1.23625i
$94$		0			0
$95$	4.94883			0.507739
$96$		0			0
$97$	−14.8733			−1.51015			−0.755076	−	0.655637i	$-0.772400\pi$
$97$	−14.8733			−1.51015			−0.755076	+	0.655637i	$0.772400\pi$
$98$		0			0
$99$	−5.57759	+	5.57759i	−0.560569	+	0.560569i
$100$		0			0
$101$	13.6445	+	13.6445i	1.35768	+	1.35768i	0.876769	+	0.480913i	$0.159695\pi$
$101$	13.6445	+	13.6445i	1.35768	+	1.35768i	0.480913	+	0.876769i	$0.340305\pi$
$102$		0			0
$103$			1.46938i			0.144782i	0.997376	+	0.0723911i	$0.0230630\pi$
$103$			1.46938i			0.144782i	−0.997376	+	0.0723911i	$0.976937\pi$
$104$		0			0
$105$		−	3.09476i		−	0.302018i
$106$		0			0
$107$	−11.8430	−	11.8430i	−1.14490	−	1.14490i	−0.987541	−	0.157362i	$-0.949701\pi$
$107$	−11.8430	−	11.8430i	−1.14490	−	1.14490i	−0.157362	−	0.987541i	$-0.550299\pi$
$108$		0			0
$109$	−9.31425	+	9.31425i	−0.892144	+	0.892144i	−0.994725	−	0.102581i	$-0.967290\pi$
$109$	−9.31425	+	9.31425i	−0.892144	+	0.892144i	0.102581	+	0.994725i	$0.467290\pi$
$110$		0			0
$111$	−18.2396			−1.73123
$112$		0			0
$113$	5.90655			0.555641			0.277821	−	0.960633i	$-0.410388\pi$
$113$	5.90655			0.555641			0.277821	+	0.960633i	$0.410388\pi$
$114$		0			0
$115$	−6.25330	+	6.25330i	−0.583123	+	0.583123i
$116$		0			0
$117$	−20.2403	−	20.2403i	−1.87122	−	1.87122i
$118$		0			0
$119$			5.75841i			0.527873i
$120$		0			0
$121$		−	9.56189i		−	0.869262i
$122$		0			0
$123$	−10.8306	−	10.8306i	−0.976562	−	0.976562i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−20.4712			−1.81653			−0.908265	−	0.418396i	$-0.862592\pi$
$127$	−20.4712			−1.81653			−0.908265	+	0.418396i	$0.862592\pi$
$128$		0			0
$129$	−32.1303			−2.82891
$130$		0			0
$131$	0.656784	−	0.656784i	0.0573835	−	0.0573835i	−0.677833	−	0.735216i	$-0.737081\pi$
$131$	0.656784	−	0.656784i	0.0573835	−	0.0573835i	0.735216	+	0.677833i	$0.237081\pi$
$132$		0			0
$133$	3.49935	+	3.49935i	0.303432	+	0.303432i
$134$		0			0
$135$		−	11.0717i		−	0.952901i
$136$		0			0
$137$		−	16.6901i		−	1.42593i	−0.701201	−	0.712964i	$-0.747352\pi$
$137$		−	16.6901i		−	1.42593i	0.701201	−	0.712964i	$-0.252648\pi$
$138$		0			0
$139$	3.42603	+	3.42603i	0.290592	+	0.290592i	0.837314	−	0.546722i	$-0.184125\pi$
$139$	3.42603	+	3.42603i	0.290592	+	0.290592i	−0.546722	+	0.837314i	$0.684125\pi$
$140$		0			0
$141$	11.8810	−	11.8810i	1.00056	−	1.00056i
$142$		0			0
$143$	−5.21872			−0.436411
$144$		0			0
$145$	3.12142			0.259220
$146$		0			0
$147$	2.18833	−	2.18833i	0.180490	−	0.180490i
$148$		0			0
$149$	−5.45946	−	5.45946i	−0.447256	−	0.447256i	0.447185	−	0.894441i	$-0.352426\pi$
$149$	−5.45946	−	5.45946i	−0.447256	−	0.447256i	−0.894441	+	0.447185i	$0.852426\pi$
$150$		0			0
$151$			18.7152i			1.52302i	0.648154	+	0.761509i	$0.275541\pi$
$151$			18.7152i			1.52302i	−0.648154	+	0.761509i	$0.724459\pi$
$152$		0			0
$153$			37.8763i			3.06212i
$154$		0			0
$155$	−3.85229	−	3.85229i	−0.309423	−	0.309423i
$156$		0			0
$157$	−2.00348	+	2.00348i	−0.159895	+	0.159895i	−0.782520	−	0.622625i	$-0.786066\pi$
$157$	−2.00348	+	2.00348i	−0.159895	+	0.159895i	0.622625	+	0.782520i	$0.286066\pi$
$158$		0			0
$159$	9.37149			0.743207
$160$		0			0
$161$	−8.84350			−0.696965
$162$		0			0
$163$	6.13696	−	6.13696i	0.480684	−	0.480684i	−0.424666	−	0.905350i	$-0.639609\pi$
$163$	6.13696	−	6.13696i	0.480684	−	0.480684i	0.905350	+	0.424666i	$0.139609\pi$
$164$		0			0
$165$	−2.62427	−	2.62427i	−0.204299	−	0.204299i
$166$		0			0
$167$			6.50930i			0.503705i	0.967766	+	0.251852i	$0.0810398\pi$
$167$			6.50930i			0.503705i	−0.967766	+	0.251852i	$0.918960\pi$
$168$		0			0
$169$		−	5.93804i		−	0.456772i
$170$		0			0
$171$	23.0172	+	23.0172i	1.76017	+	1.76017i
$172$		0			0
$173$	6.01341	−	6.01341i	0.457191	−	0.457191i	−0.440541	−	0.897732i	$-0.645213\pi$
$173$	6.01341	−	6.01341i	0.457191	−	0.457191i	0.897732	+	0.440541i	$0.145213\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−15.2955			−1.14968
$178$		0			0
$179$	−4.11690	+	4.11690i	−0.307711	+	0.307711i	−0.844021	−	0.536310i	$-0.819818\pi$
$179$	−4.11690	+	4.11690i	−0.307711	+	0.307711i	0.536310	+	0.844021i	$0.319818\pi$
$180$		0			0
$181$	−11.5047	−	11.5047i	−0.855138	−	0.855138i	0.135623	−	0.990761i	$-0.456696\pi$
$181$	−11.5047	−	11.5047i	−0.855138	−	0.855138i	−0.990761	+	0.135623i	$0.956696\pi$
$182$		0			0
$183$		−	15.1176i		−	1.11753i
$184$		0			0
$185$		−	5.89370i		−	0.433313i
$186$		0			0
$187$	4.88297	+	4.88297i	0.357078	+	0.357078i
$188$		0			0
$189$	7.82888	−	7.82888i	0.569467	−	0.569467i
$190$		0			0
$191$	−3.24138			−0.234538			−0.117269	−	0.993100i	$-0.537414\pi$
$191$	−3.24138			−0.234538			−0.117269	+	0.993100i	$0.537414\pi$
$192$		0			0
$193$	23.1345			1.66526			0.832629	−	0.553831i	$-0.186835\pi$
$193$	23.1345			1.66526			0.832629	+	0.553831i	$0.186835\pi$
$194$		0			0
$195$	9.52314	−	9.52314i	0.681966	−	0.681966i
$196$		0			0
$197$	−5.22988	−	5.22988i	−0.372614	−	0.372614i	0.495815	−	0.868428i	$-0.334870\pi$
$197$	−5.22988	−	5.22988i	−0.372614	−	0.372614i	−0.868428	+	0.495815i	$0.834870\pi$
$198$		0			0
$199$			22.2685i			1.57857i	0.614027	+	0.789285i	$0.289549\pi$
$199$			22.2685i			1.57857i	−0.614027	+	0.789285i	$0.710451\pi$
$200$		0			0
$201$		−	13.6760i		−	0.964634i
$202$		0			0
$203$	2.20718	+	2.20718i	0.154914	+	0.154914i
$204$		0			0
$205$	3.49965	−	3.49965i	0.244426	−	0.244426i
$206$		0			0
$207$	−58.1687			−4.04300
$208$		0			0
$209$	5.93471			0.410512
$210$		0			0
$211$	−14.9441	+	14.9441i	−1.02879	+	1.02879i	−0.0292204	+	0.999573i	$0.509302\pi$
$211$	−14.9441	+	14.9441i	−1.02879	+	1.02879i	−0.999573	+	0.0292204i	$0.990698\pi$
$212$		0			0
$213$	0.536919	+	0.536919i	0.0367891	+	0.0367891i
$214$		0			0
$215$		−	10.3821i		−	0.708056i
$216$		0			0
$217$		−	5.44796i		−	0.369831i
$218$		0			0
$219$	−0.350768	−	0.350768i	−0.0237027	−	0.0237027i
$220$		0			0
$221$	−17.7196	+	17.7196i	−1.19195	+	1.19195i
$222$		0			0
$223$	−5.67149			−0.379791			−0.189896	−	0.981804i	$-0.560815\pi$
$223$	−5.67149			−0.379791			−0.189896	+	0.981804i	$0.560815\pi$
$224$		0			0
$225$	6.57756			0.438504
$226$		0			0
$227$	5.17740	−	5.17740i	0.343636	−	0.343636i	−0.514096	−	0.857732i	$-0.671873\pi$
$227$	5.17740	−	5.17740i	0.343636	−	0.343636i	0.857732	+	0.514096i	$0.171873\pi$
$228$		0			0
$229$	2.04579	+	2.04579i	0.135190	+	0.135190i	0.771463	−	0.636274i	$-0.219525\pi$
$229$	2.04579	+	2.04579i	0.135190	+	0.135190i	−0.636274	+	0.771463i	$0.719525\pi$
$230$		0			0
$231$		−	3.71128i		−	0.244184i
$232$		0			0
$233$			21.5432i			1.41135i	0.708538	+	0.705673i	$0.249355\pi$
$233$			21.5432i			1.41135i	−0.708538	+	0.705673i	$0.750645\pi$
$234$		0			0
$235$	3.83908	+	3.83908i	0.250434	+	0.250434i
$236$		0			0
$237$	−21.7798	+	21.7798i	−1.41475	+	1.41475i
$238$		0			0
$239$	23.1375			1.49664			0.748319	−	0.663339i	$-0.230861\pi$
$239$	23.1375			1.49664			0.748319	+	0.663339i	$0.230861\pi$
$240$		0			0
$241$	29.3260			1.88906			0.944528	−	0.328432i	$-0.106520\pi$
$241$	29.3260			1.88906			0.944528	+	0.328432i	$0.106520\pi$
$242$		0			0
$243$	8.31335	−	8.31335i	0.533301	−	0.533301i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$			21.5363i			1.37032i
$248$		0			0
$249$		−	29.2753i		−	1.85525i
$250$		0			0
$251$	10.8792	+	10.8792i	0.686691	+	0.686691i	0.961499	−	0.274808i	$-0.0886144\pi$
$251$	10.8792	+	10.8792i	0.686691	+	0.686691i	−0.274808	+	0.961499i	$0.588614\pi$
$252$		0			0
$253$	−7.49904	+	7.49904i	−0.471461	+	0.471461i
$254$		0			0
$255$	−17.8209			−1.11599
$256$		0			0
$257$	14.3719			0.896498			0.448249	−	0.893909i	$-0.352048\pi$
$257$	14.3719			0.896498			0.448249	+	0.893909i	$0.352048\pi$
$258$		0			0
$259$	4.16747	−	4.16747i	0.258954	−	0.258954i
$260$		0			0
$261$	14.5179	+	14.5179i	0.898633	+	0.898633i
$262$		0			0
$263$			19.7079i			1.21524i	0.794227	+	0.607621i	$0.207876\pi$
$263$			19.7079i			1.21524i	−0.794227	+	0.607621i	$0.792124\pi$
$264$		0			0
$265$			3.02818i			0.186019i
$266$		0			0
$267$	−13.1623	−	13.1623i	−0.805521	−	0.805521i
$268$		0			0
$269$	−8.14780	+	8.14780i	−0.496780	+	0.496780i	−0.910434	−	0.413654i	$-0.864252\pi$
$269$	−8.14780	+	8.14780i	−0.496780	+	0.496780i	0.413654	+	0.910434i	$0.364252\pi$
$270$		0			0
$271$	4.96255			0.301453			0.150727	−	0.988575i	$-0.451839\pi$
$271$	4.96255			0.301453			0.150727	+	0.988575i	$0.451839\pi$
$272$		0			0
$273$	13.4677			0.815105
$274$		0			0
$275$	0.847972	−	0.847972i	0.0511346	−	0.0511346i
$276$		0			0
$277$	6.05851	+	6.05851i	0.364021	+	0.364021i	0.865291	−	0.501270i	$-0.167134\pi$
$277$	6.05851	+	6.05851i	0.364021	+	0.364021i	−0.501270	+	0.865291i	$0.667134\pi$
$278$		0			0
$279$		−	35.8343i		−	2.14534i
$280$		0			0
$281$			5.84556i			0.348717i	0.984682	+	0.174358i	$0.0557851\pi$
$281$			5.84556i			0.348717i	−0.984682	+	0.174358i	$0.944215\pi$
$282$		0			0
$283$	−6.37132	−	6.37132i	−0.378735	−	0.378735i	0.491910	−	0.870646i	$-0.336299\pi$
$283$	−6.37132	−	6.37132i	−0.378735	−	0.378735i	−0.870646	+	0.491910i	$0.836299\pi$
$284$		0			0
$285$	−10.8297	+	10.8297i	−0.641494	+	0.641494i
$286$		0			0
$287$	4.94926			0.292145
$288$		0			0
$289$	16.1593			0.950546
$290$		0			0
$291$	32.5476	−	32.5476i	1.90797	−	1.90797i
$292$		0			0
$293$	8.51162	+	8.51162i	0.497254	+	0.497254i	0.910582	−	0.413328i	$-0.135634\pi$
$293$	8.51162	+	8.51162i	0.497254	+	0.497254i	−0.413328	+	0.910582i	$0.635634\pi$
$294$		0			0
$295$		−	4.94239i		−	0.287757i
$296$		0			0
$297$		−	13.2773i		−	0.770430i
$298$		0			0
$299$	−27.2130	−	27.2130i	−1.57377	−	1.57377i
$300$		0			0
$301$	7.34128	−	7.34128i	0.423145	−	0.423145i
$302$		0			0
$303$	−59.7174			−3.43068
$304$		0			0
$305$	4.88490			0.279709
$306$		0			0
$307$	−19.6732	+	19.6732i	−1.12281	+	1.12281i	−0.131494	+	0.991317i	$0.541978\pi$
$307$	−19.6732	+	19.6732i	−1.12281	+	1.12281i	−0.991317	+	0.131494i	$0.958022\pi$
$308$		0			0
$309$	−3.21548	−	3.21548i	−0.182923	−	0.182923i
$310$		0			0
$311$			11.3513i			0.643674i	0.946795	+	0.321837i	$0.104300\pi$
$311$			11.3513i			0.643674i	−0.946795	+	0.321837i	$0.895700\pi$
$312$		0			0
$313$			23.1011i			1.30575i	0.757466	+	0.652875i	$0.226437\pi$
$313$			23.1011i			1.30575i	−0.757466	+	0.652875i	$0.773563\pi$
$314$		0			0
$315$	4.65104	+	4.65104i	0.262056	+	0.262056i
$316$		0			0
$317$	−4.08023	+	4.08023i	−0.229169	+	0.229169i	−0.812345	−	0.583177i	$-0.801810\pi$
$317$	−4.08023	+	4.08023i	−0.229169	+	0.229169i	0.583177	+	0.812345i	$0.301810\pi$
$318$		0			0
$319$	3.74326			0.209582
$320$		0			0
$321$	51.8326			2.89301
$322$		0			0
$323$	20.1507	−	20.1507i	1.12122	−	1.12122i
$324$		0			0
$325$	3.07718	+	3.07718i	0.170691	+	0.170691i
$326$		0			0
$327$		−	40.7653i		−	2.25433i
$328$		0			0
$329$			5.42928i			0.299326i
$330$		0			0
$331$	−9.07863	−	9.07863i	−0.499007	−	0.499007i	0.412122	−	0.911129i	$-0.364788\pi$
$331$	−9.07863	−	9.07863i	−0.499007	−	0.499007i	−0.911129	+	0.412122i	$0.864788\pi$
$332$		0			0
$333$	27.4118	−	27.4118i	1.50216	−	1.50216i
$334$		0			0
$335$	4.41909			0.241441
$336$		0			0
$337$	15.6429			0.852123			0.426062	−	0.904694i	$-0.359901\pi$
$337$	15.6429			0.852123			0.426062	+	0.904694i	$0.359901\pi$
$338$		0			0
$339$	−12.9255	+	12.9255i	−0.702015	+	0.702015i
$340$		0			0
$341$	−4.61972	−	4.61972i	−0.250172	−	0.250172i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	27.3685i		−	1.47347i
$346$		0			0
$347$	7.96501	+	7.96501i	0.427584	+	0.427584i	0.887805	−	0.460220i	$-0.152230\pi$
$347$	7.96501	+	7.96501i	0.427584	+	0.427584i	−0.460220	+	0.887805i	$0.652230\pi$
$348$		0			0
$349$	−3.54063	+	3.54063i	−0.189525	+	0.189525i	−0.795491	−	0.605965i	$-0.792787\pi$
$349$	−3.54063	+	3.54063i	−0.189525	+	0.189525i	0.605965	+	0.795491i	$0.292787\pi$
$350$		0			0
$351$	48.1817			2.57175
$352$		0			0
$353$	−22.2929			−1.18653			−0.593266	−	0.805007i	$-0.702162\pi$
$353$	−22.2929			−1.18653			−0.593266	+	0.805007i	$0.702162\pi$
$354$		0			0
$355$	−0.173493	+	0.173493i	−0.00920803	+	0.00920803i
$356$		0			0
$357$	−12.6013	−	12.6013i	−0.666931	−	0.666931i
$358$		0			0
$359$		−	12.8441i		−	0.677883i	−0.940807	−	0.338942i	$-0.889931\pi$
$359$		−	12.8441i		−	0.677883i	0.940807	−	0.338942i	$-0.110069\pi$
$360$		0			0
$361$		−	5.49093i		−	0.288996i
$362$		0			0
$363$	20.9245	+	20.9245i	1.09825	+	1.09825i
$364$		0			0
$365$	0.113343	−	0.113343i	0.00593262	−	0.00593262i
$366$		0			0
$367$	13.6296			0.711458			0.355729	−	0.934589i	$-0.384233\pi$
$367$	13.6296			0.711458			0.355729	+	0.934589i	$0.384233\pi$
$368$		0			0
$369$	32.5540			1.69470
$370$		0			0
$371$	−2.14124	+	2.14124i	−0.111168	+	0.111168i
$372$		0			0
$373$	6.73500	+	6.73500i	0.348725	+	0.348725i	0.859634	−	0.510910i	$-0.170691\pi$
$373$	6.73500	+	6.73500i	0.348725	+	0.348725i	−0.510910	+	0.859634i	$0.670691\pi$
$374$		0			0
$375$			3.09476i			0.159813i
$376$		0			0
$377$			13.5838i			0.699600i
$378$		0			0
$379$	13.0373	+	13.0373i	0.669679	+	0.669679i	0.957642	−	0.287963i	$-0.0929779\pi$
$379$	13.0373	+	13.0373i	0.669679	+	0.669679i	−0.287963	+	0.957642i	$0.592978\pi$
$380$		0			0
$381$	44.7978	−	44.7978i	2.29506	−	2.29506i
$382$		0			0
$383$	−9.00155			−0.459958			−0.229979	−	0.973196i	$-0.573866\pi$
$383$	−9.00155			−0.459958			−0.229979	+	0.973196i	$0.573866\pi$
$384$		0			0
$385$	1.19921			0.0611176
$386$		0			0
$387$	48.2877	−	48.2877i	2.45460	−	2.45460i
$388$		0			0
$389$	9.98081	+	9.98081i	0.506047	+	0.506047i	0.913311	−	0.407264i	$-0.133517\pi$
$389$	9.98081	+	9.98081i	0.506047	+	0.506047i	−0.407264	+	0.913311i	$0.633517\pi$
$390$		0			0
$391$			50.9245i			2.57536i
$392$		0			0
$393$			2.87452i			0.145000i
$394$		0			0
$395$	−7.03763	−	7.03763i	−0.354101	−	0.354101i
$396$		0			0
$397$	6.78250	−	6.78250i	0.340404	−	0.340404i	−0.516115	−	0.856519i	$-0.672622\pi$
$397$	6.78250	−	6.78250i	0.340404	−	0.340404i	0.856519	+	0.516115i	$0.172622\pi$
$398$		0			0
$399$	−15.3155			−0.766732
$400$		0			0
$401$	−12.1728			−0.607883			−0.303942	−	0.952691i	$-0.598303\pi$
$401$	−12.1728			−0.607883			−0.303942	+	0.952691i	$0.598303\pi$
$402$		0			0
$403$	16.7643	−	16.7643i	0.835091	−	0.835091i
$404$		0			0
$405$	10.2754	+	10.2754i	0.510590	+	0.510590i
$406$		0			0
$407$		−	7.06780i		−	0.350338i
$408$		0			0
$409$		−	13.9406i		−	0.689319i	−0.938728	−	0.344660i	$-0.887994\pi$
$409$		−	13.9406i		−	0.689319i	0.938728	−	0.344660i	$-0.112006\pi$
$410$		0			0
$411$	36.5233	+	36.5233i	1.80156	+	1.80156i
$412$		0			0
$413$	3.49480	−	3.49480i	0.171968	−	0.171968i
$414$		0			0
$415$	9.45962			0.464354
$416$		0			0
$417$	−14.9946			−0.734287
$418$		0			0
$419$	−0.656515	+	0.656515i	−0.0320729	+	0.0320729i	−0.722961	−	0.690888i	$-0.757220\pi$
$419$	−0.656515	+	0.656515i	−0.0320729	+	0.0320729i	0.690888	+	0.722961i	$0.257220\pi$
$420$		0			0
$421$	−20.5128	−	20.5128i	−0.999731	−	0.999731i	0.000268850	−	1.00000i	$-0.499914\pi$
$421$	−20.5128	−	20.5128i	−0.999731	−	0.999731i	−1.00000		0.000268850i	$0.999914\pi$
$422$		0			0
$423$			35.7114i			1.73635i
$424$		0			0
$425$		−	5.75841i		−	0.279324i
$426$		0			0
$427$	3.45415	+	3.45415i	0.167158	+	0.167158i
$428$		0			0
$429$	11.4203	−	11.4203i	0.551376	−	0.551376i
$430$		0			0
$431$	−24.0169			−1.15685			−0.578427	−	0.815734i	$-0.696333\pi$
$431$	−24.0169			−1.15685			−0.578427	+	0.815734i	$0.696333\pi$
$432$		0			0
$433$	−23.5582			−1.13213			−0.566067	−	0.824359i	$-0.691536\pi$
$433$	−23.5582			−1.13213			−0.566067	+	0.824359i	$0.691536\pi$
$434$		0			0
$435$	−6.83070	+	6.83070i	−0.327507	+	0.327507i
$436$		0			0
$437$	30.9465	+	30.9465i	1.48037	+	1.48037i
$438$		0			0
$439$			2.63689i			0.125852i	0.998018	+	0.0629259i	$0.0200432\pi$
$439$			2.63689i			0.125852i	−0.998018	+	0.0629259i	$0.979957\pi$
$440$		0			0
$441$			6.57756i			0.313217i
$442$		0			0
$443$	−5.38859	−	5.38859i	−0.256020	−	0.256020i	0.567413	−	0.823433i	$-0.307944\pi$
$443$	−5.38859	−	5.38859i	−0.256020	−	0.256020i	−0.823433	+	0.567413i	$0.807944\pi$
$444$		0			0
$445$	4.25309	−	4.25309i	0.201616	−	0.201616i
$446$		0			0
$447$	23.8942			1.13016
$448$		0			0
$449$	−20.9830			−0.990248			−0.495124	−	0.868822i	$-0.664877\pi$
$449$	−20.9830			−0.990248			−0.495124	+	0.868822i	$0.664877\pi$
$450$		0			0
$451$	4.19683	−	4.19683i	0.197621	−	0.197621i
$452$		0			0
$453$	−40.9549	−	40.9549i	−1.92423	−	1.92423i
$454$		0			0
$455$			4.35179i			0.204015i
$456$		0			0
$457$			19.5052i			0.912415i	0.889873	+	0.456208i	$0.150793\pi$
$457$			19.5052i			0.912415i	−0.889873	+	0.456208i	$0.849207\pi$
$458$		0			0
$459$	−45.0819	−	45.0819i	−2.10424	−	2.10424i
$460$		0			0
$461$	−14.8818	+	14.8818i	−0.693116	+	0.693116i	−0.962916	−	0.269800i	$-0.913042\pi$
$461$	−14.8818	+	14.8818i	−0.693116	+	0.693116i	0.269800	+	0.962916i	$0.413042\pi$
$462$		0			0
$463$	19.3913			0.901191			0.450595	−	0.892728i	$-0.351212\pi$
$463$	19.3913			0.901191			0.450595	+	0.892728i	$0.351212\pi$
$464$		0			0
$465$	16.8601			0.781870
$466$		0			0
$467$	−10.8576	+	10.8576i	−0.502430	+	0.502430i	−0.912192	−	0.409763i	$-0.865612\pi$
$467$	−10.8576	+	10.8576i	−0.502430	+	0.502430i	0.409763	+	0.912192i	$0.365612\pi$
$468$		0			0
$469$	3.12477	+	3.12477i	0.144288	+	0.144288i
$470$		0			0
$471$		−	8.76856i		−	0.404034i
$472$		0			0
$473$		−	12.4504i		−	0.572470i
$474$		0			0
$475$	−3.49935	−	3.49935i	−0.160561	−	0.160561i
$476$		0			0
$477$	−14.0842	+	14.0842i	−0.644869	+	0.644869i
$478$		0			0
$479$	28.6762			1.31025			0.655125	−	0.755520i	$-0.272616\pi$
$479$	28.6762			1.31025			0.655125	+	0.755520i	$0.272616\pi$
$480$		0			0
$481$	25.6481			1.16945
$482$		0			0
$483$	19.3525	−	19.3525i	0.880568	−	0.880568i
$484$		0			0
$485$	10.5170	+	10.5170i	0.477552	+	0.477552i
$486$		0			0
$487$		−	21.4381i		−	0.971453i	−0.874111	−	0.485726i	$-0.838555\pi$
$487$		−	21.4381i		−	0.971453i	0.874111	−	0.485726i	$-0.161445\pi$
$488$		0			0
$489$			26.8594i			1.21462i
$490$		0			0
$491$	−13.4057	−	13.4057i	−0.604991	−	0.604991i	0.336642	−	0.941633i	$-0.390709\pi$
$491$	−13.4057	−	13.4057i	−0.604991	−	0.604991i	−0.941633	+	0.336642i	$0.890709\pi$
$492$		0			0
$493$	12.7099	−	12.7099i	0.572423	−	0.572423i
$494$		0			0
$495$	7.88790			0.354535
$496$		0			0
$497$	−0.245356			−0.0110057
$498$		0			0
$499$	25.8696	−	25.8696i	1.15808	−	1.15808i	0.173196	−	0.984887i	$-0.444591\pi$
$499$	25.8696	−	25.8696i	1.15808	−	1.15808i	0.984887	−	0.173196i	$-0.0554094\pi$
$500$		0			0
$501$	−14.2445	−	14.2445i	−0.636397	−	0.636397i
$502$		0			0
$503$			21.5963i			0.962930i	0.876465	+	0.481465i	$0.159895\pi$
$503$			21.5963i			0.962930i	−0.876465	+	0.481465i	$0.840105\pi$
$504$		0			0
$505$		−	19.2963i		−	0.858673i
$506$		0			0
$507$	12.9944	+	12.9944i	0.577101	+	0.577101i
$508$		0			0
$509$	−2.49795	+	2.49795i	−0.110720	+	0.110720i	−0.760296	−	0.649577i	$-0.774946\pi$
$509$	−2.49795	+	2.49795i	−0.110720	+	0.110720i	0.649577	+	0.760296i	$0.274946\pi$
$510$		0			0
$511$	0.160291			0.00709084
$512$		0			0
$513$	−54.7920			−2.41913
$514$		0			0
$515$	1.03901	−	1.03901i	0.0457842	−	0.0457842i
$516$		0			0
$517$	4.60388	+	4.60388i	0.202478	+	0.202478i
$518$		0			0
$519$			26.3186i			1.15526i
$520$		0			0
$521$		−	3.85387i		−	0.168841i	−0.996430	−	0.0844206i	$-0.973096\pi$
$521$		−	3.85387i		−	0.168841i	0.996430	−	0.0844206i	$-0.0269039\pi$
$522$		0			0
$523$	−21.5930	−	21.5930i	−0.944197	−	0.944197i	0.0543258	−	0.998523i	$-0.482699\pi$
$523$	−21.5930	−	21.5930i	−0.944197	−	0.944197i	−0.998523	+	0.0543258i	$0.982699\pi$
$524$		0			0
$525$	−2.18833	+	2.18833i	−0.0955065	+	0.0955065i
$526$		0			0
$527$	−31.3716			−1.36657
$528$		0			0
$529$	−55.2075			−2.40033
$530$		0			0
$531$	22.9873	−	22.9873i	0.997562	−	0.997562i
$532$		0			0
$533$	15.2297	+	15.2297i	0.659673	+	0.659673i
$534$		0			0
$535$			16.7485i			0.724100i
$536$		0			0
$537$		−	18.0182i		−	0.777545i
$538$		0			0
$539$	0.847972	+	0.847972i	0.0365247	+	0.0365247i
$540$		0			0
$541$	−5.17070	+	5.17070i	−0.222306	+	0.222306i	−0.809469	−	0.587163i	$-0.800245\pi$
$541$	−5.17070	+	5.17070i	−0.222306	+	0.222306i	0.587163	+	0.809469i	$0.300245\pi$
$542$		0			0
$543$	50.3521			2.16082
$544$		0			0
$545$	13.1723			0.564241
$546$		0			0
$547$	−11.2461	+	11.2461i	−0.480847	+	0.480847i	−0.905402	−	0.424555i	$-0.860431\pi$
$547$	−11.2461	+	11.2461i	−0.480847	+	0.480847i	0.424555	+	0.905402i	$0.360431\pi$
$548$		0			0
$549$	22.7199	+	22.7199i	0.969660	+	0.969660i
$550$		0			0
$551$		−	15.4474i		−	0.658082i
$552$		0			0
$553$		−	9.95271i		−	0.423232i
$554$		0			0
$555$	12.8973	+	12.8973i	0.547462	+	0.547462i
$556$		0			0
$557$	−5.10566	+	5.10566i	−0.216334	+	0.216334i	−0.806951	−	0.590618i	$-0.798884\pi$
$557$	−5.10566	+	5.10566i	−0.216334	+	0.216334i	0.590618	+	0.806951i	$0.298884\pi$
$558$		0			0
$559$	45.1809			1.91095
$560$		0			0
$561$	−21.3711			−0.902288
$562$		0			0
$563$	29.5241	−	29.5241i	1.24429	−	1.24429i	0.286090	−	0.958203i	$-0.407644\pi$
$563$	29.5241	−	29.5241i	1.24429	−	1.24429i	0.958203	−	0.286090i	$-0.0923556\pi$
$564$		0			0
$565$	−4.17656	−	4.17656i	−0.175709	−	0.175709i
$566$		0			0
$567$			14.5316i			0.610271i
$568$		0			0
$569$		−	11.7289i		−	0.491702i	−0.969308	−	0.245851i	$-0.920933\pi$
$569$		−	11.7289i		−	0.491702i	0.969308	−	0.245851i	$-0.0790674\pi$
$570$		0			0
$571$	21.3982	+	21.3982i	0.895488	+	0.895488i	0.995033	−	0.0995448i	$-0.0317386\pi$
$571$	21.3982	+	21.3982i	0.895488	+	0.895488i	−0.0995448	+	0.995033i	$0.531739\pi$
$572$		0			0
$573$	7.09321	−	7.09321i	0.296323	−	0.296323i
$574$		0			0
$575$	8.84350			0.368799
$576$		0			0
$577$	39.3729			1.63912			0.819558	−	0.572997i	$-0.194219\pi$
$577$	39.3729			1.63912			0.819558	+	0.572997i	$0.194219\pi$
$578$		0			0
$579$	−50.6259	+	50.6259i	−2.10394	+	2.10394i
$580$		0			0
$581$	6.68896	+	6.68896i	0.277505	+	0.277505i
$582$		0			0
$583$			3.63143i			0.150398i
$584$		0			0
$585$			28.6241i			1.18346i
$586$		0			0
$587$	12.3201	+	12.3201i	0.508506	+	0.508506i	0.914068	−	0.405562i	$-0.132924\pi$
$587$	12.3201	+	12.3201i	0.508506	+	0.508506i	−0.405562	+	0.914068i	$0.632924\pi$
$588$		0			0
$589$	−19.0643	+	19.0643i	−0.785532	+	0.785532i
$590$		0			0
$591$	22.8894			0.941544
$592$		0			0
$593$	9.77506			0.401414			0.200707	−	0.979651i	$-0.435676\pi$
$593$	9.77506			0.401414			0.200707	+	0.979651i	$0.435676\pi$
$594$		0			0
$595$	4.07181	−	4.07181i	0.166928	−	0.166928i
$596$		0			0
$597$	−48.7307	−	48.7307i	−1.99442	−	1.99442i
$598$		0			0
$599$		−	23.5391i		−	0.961783i	−0.876780	−	0.480892i	$-0.840313\pi$
$599$		−	23.5391i		−	0.961783i	0.876780	−	0.480892i	$-0.159687\pi$
$600$		0			0
$601$			42.6943i			1.74154i	0.491692	+	0.870769i	$0.336379\pi$
$601$			42.6943i			1.74154i	−0.491692	+	0.870769i	$0.663621\pi$
$602$		0			0
$603$	20.5534	+	20.5534i	0.836998	+	0.836998i
$604$		0			0
$605$	−6.76127	+	6.76127i	−0.274885	+	0.274885i
$606$		0			0
$607$	−11.7930			−0.478663			−0.239331	−	0.970938i	$-0.576928\pi$
$607$	−11.7930			−0.478663			−0.239331	+	0.970938i	$0.576928\pi$
$608$		0			0
$609$	−9.66007			−0.391446
$610$		0			0
$611$	−16.7069	+	16.7069i	−0.675887	+	0.675887i
$612$		0			0
$613$	−3.78380	−	3.78380i	−0.152826	−	0.152826i	0.626553	−	0.779379i	$-0.284465\pi$
$613$	−3.78380	−	3.78380i	−0.152826	−	0.152826i	−0.779379	+	0.626553i	$0.784465\pi$
$614$		0			0
$615$			15.3168i			0.617632i
$616$		0			0
$617$			8.12770i			0.327209i	0.986526	+	0.163604i	$0.0523121\pi$
$617$			8.12770i			0.327209i	−0.986526	+	0.163604i	$0.947688\pi$
$618$		0			0
$619$	3.29631	+	3.29631i	0.132490	+	0.132490i	0.770242	−	0.637752i	$-0.220136\pi$
$619$	3.29631	+	3.29631i	0.132490	+	0.132490i	−0.637752	+	0.770242i	$0.720136\pi$
$620$		0			0
$621$	69.2347	−	69.2347i	2.77829	−	2.77829i
$622$		0			0
$623$	6.01478			0.240977
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−12.9871	+	12.9871i	−0.518654	+	0.518654i
$628$		0			0
$629$	−23.9980	−	23.9980i	−0.956863	−	0.956863i
$630$		0			0
$631$		−	43.1144i		−	1.71636i	−0.513353	−	0.858178i	$-0.671597\pi$
$631$		−	43.1144i		−	1.71636i	0.513353	−	0.858178i	$-0.328403\pi$
$632$		0			0
$633$		−	65.4051i		−	2.59962i
$634$		0			0
$635$	14.4754	+	14.4754i	0.574437	+	0.574437i
$636$		0			0
$637$	−3.07718	+	3.07718i	−0.121922	+	0.121922i
$638$		0			0
$639$	−1.61384			−0.0638426
$640$		0			0
$641$	−22.9054			−0.904707			−0.452354	−	0.891839i	$-0.649415\pi$
$641$	−22.9054			−0.904707			−0.452354	+	0.891839i	$0.649415\pi$
$642$		0			0
$643$	16.6642	−	16.6642i	0.657172	−	0.657172i	−0.297538	−	0.954710i	$-0.596166\pi$
$643$	16.6642	−	16.6642i	0.657172	−	0.657172i	0.954710	+	0.297538i	$0.0961656\pi$
$644$		0			0
$645$	22.7195	+	22.7195i	0.894581	+	0.894581i
$646$		0			0
$647$			1.66057i			0.0652837i	0.999467	+	0.0326419i	$0.0103921\pi$
$647$			1.66057i			0.0652837i	−0.999467	+	0.0326419i	$0.989608\pi$
$648$		0			0
$649$		−	5.92698i		−	0.232654i
$650$		0			0
$651$	11.9219	+	11.9219i	0.467257	+	0.467257i
$652$		0			0
$653$	17.3717	−	17.3717i	0.679807	−	0.679807i	−0.280150	−	0.959956i	$-0.590384\pi$
$653$	17.3717	−	17.3717i	0.679807	−	0.679807i	0.959956	+	0.280150i	$0.0903841\pi$
$654$		0			0
$655$	−0.928833			−0.0362925
$656$		0			0
$657$	1.05432			0.0411330
$658$		0			0
$659$	−0.126108	+	0.126108i	−0.00491247	+	0.00491247i	−0.709559	−	0.704646i	$-0.751106\pi$
$659$	−0.126108	+	0.126108i	−0.00491247	+	0.00491247i	0.704646	+	0.709559i	$0.251106\pi$
$660$		0			0
$661$	−9.17026	−	9.17026i	−0.356682	−	0.356682i	0.505906	−	0.862588i	$-0.331158\pi$
$661$	−9.17026	−	9.17026i	−0.356682	−	0.356682i	−0.862588	+	0.505906i	$0.831158\pi$
$662$		0			0
$663$		−	77.5528i		−	3.01190i
$664$		0			0
$665$		−	4.94883i		−	0.191907i
$666$		0			0
$667$	19.5192	+	19.5192i	0.755787	+	0.755787i
$668$		0			0
$669$	12.4111	−	12.4111i	0.479840	−	0.479840i
$670$		0			0
$671$	5.85804			0.226147
$672$		0			0
$673$	12.9697			0.499943			0.249972	−	0.968253i	$-0.419579\pi$
$673$	12.9697			0.499943			0.249972	+	0.968253i	$0.419579\pi$
$674$		0			0
$675$	−7.82888	+	7.82888i	−0.301334	+	0.301334i
$676$		0			0
$677$	−36.0230	−	36.0230i	−1.38448	−	1.38448i	−0.836479	−	0.547998i	$-0.815390\pi$
$677$	−36.0230	−	36.0230i	−1.38448	−	1.38448i	−0.547998	−	0.836479i	$-0.684610\pi$
$678$		0			0
$679$			14.8733i			0.570784i
$680$		0			0
$681$			22.6597i			0.868322i
$682$		0			0
$683$	−27.7472	−	27.7472i	−1.06172	−	1.06172i	−0.997966	−	0.0637518i	$-0.979693\pi$
$683$	−27.7472	−	27.7472i	−1.06172	−	1.06172i	−0.0637518	−	0.997966i	$-0.520307\pi$
$684$		0			0
$685$	−11.8016	+	11.8016i	−0.450918	+	0.450918i
$686$		0			0
$687$	−8.95372			−0.341606
$688$		0			0
$689$	−13.1780			−0.502041
$690$		0			0
$691$	−28.3182	+	28.3182i	−1.07728	+	1.07728i	−0.0805238	+	0.996753i	$0.525659\pi$
$691$	−28.3182	+	28.3182i	−1.07728	+	1.07728i	−0.996753	+	0.0805238i	$0.974341\pi$
$692$		0			0
$693$	5.57759	+	5.57759i	0.211875	+	0.211875i
$694$		0			0
$695$		−	4.84514i		−	0.183787i
$696$		0			0
$697$		−	28.4999i		−	1.07951i
$698$		0			0
$699$	−47.1437	−	47.1437i	−1.78314	−	1.78314i
$700$		0			0
$701$	−22.2724	+	22.2724i	−0.841215	+	0.841215i	−0.989017	−	0.147802i	$-0.952780\pi$
$701$	−22.2724	+	22.2724i	−0.841215	+	0.841215i	0.147802	+	0.989017i	$0.452780\pi$
$702$		0			0
$703$	−29.1669			−1.10005
$704$		0			0
$705$	−16.8023			−0.632813
$706$		0			0
$707$	13.6445	−	13.6445i	0.513155	−	0.513155i
$708$		0			0
$709$	24.1894	+	24.1894i	0.908452	+	0.908452i	0.996147	−	0.0876953i	$-0.0279502\pi$
$709$	24.1894	+	24.1894i	0.908452	+	0.908452i	−0.0876953	+	0.996147i	$0.527950\pi$
$710$		0			0
$711$		−	65.4645i		−	2.45511i
$712$		0			0
$713$		−	48.1790i		−	1.80432i
$714$		0			0
$715$	3.69019	+	3.69019i	0.138005	+	0.138005i
$716$		0			0
$717$	−50.6323	+	50.6323i	−1.89090	+	1.89090i
$718$		0			0
$719$	−35.6643			−1.33006			−0.665028	−	0.746819i	$-0.731580\pi$
$719$	−35.6643			−1.33006			−0.665028	+	0.746819i	$0.731580\pi$
$720$		0			0
$721$	1.46938			0.0547225
$722$		0			0
$723$	−64.1750	+	64.1750i	−2.38669	+	2.38669i
$724$		0			0
$725$	−2.20718	−	2.20718i	−0.0819726	−	0.0819726i
$726$		0			0
$727$		−	16.4452i		−	0.609918i	−0.952366	−	0.304959i	$-0.901357\pi$
$727$		−	16.4452i		−	0.609918i	0.952366	−	0.304959i	$-0.0986427\pi$
$728$		0			0
$729$		−	7.21024i		−	0.267046i
$730$		0			0
$731$	−42.2741	−	42.2741i	−1.56356	−	1.56356i
$732$		0			0
$733$	−10.2414	+	10.2414i	−0.378273	+	0.378273i	−0.870479	−	0.492206i	$-0.836191\pi$
$733$	−10.2414	+	10.2414i	−0.378273	+	0.378273i	0.492206	+	0.870479i	$0.336191\pi$
$734$		0			0
$735$	−3.09476			−0.114152
$736$		0			0
$737$	5.29944			0.195207
$738$		0			0
$739$	−26.3254	+	26.3254i	−0.968394	+	0.968394i	−0.999516	−	0.0311219i	$-0.990092\pi$
$739$	−26.3254	+	26.3254i	−0.968394	+	0.968394i	0.0311219	+	0.999516i	$0.490092\pi$
$740$		0			0
$741$	−47.1284	−	47.1284i	−1.73130	−	1.73130i
$742$		0			0
$743$			3.64694i			0.133793i	0.997760	+	0.0668966i	$0.0213098\pi$
$743$			3.64694i			0.133793i	−0.997760	+	0.0668966i	$0.978690\pi$
$744$		0			0
$745$			7.72084i			0.282870i
$746$		0			0
$747$	43.9970	+	43.9970i	1.60977	+	1.60977i
$748$		0			0
$749$	−11.8430	+	11.8430i	−0.432733	+	0.432733i
$750$		0			0
$751$	48.6372			1.77480			0.887398	−	0.461004i	$-0.152511\pi$
$751$	48.6372			1.77480			0.887398	+	0.461004i	$0.152511\pi$
$752$		0			0
$753$	−47.6146			−1.73517
$754$		0			0
$755$	13.2336	−	13.2336i	0.481621	−	0.481621i
$756$		0			0
$757$	27.3450	+	27.3450i	0.993870	+	0.993870i	0.999981	−	0.00611134i	$-0.00194531\pi$
$757$	27.3450	+	27.3450i	0.993870	+	0.993870i	−0.00611134	+	0.999981i	$0.501945\pi$
$758$		0			0
$759$		−	32.8207i		−	1.19132i
$760$		0			0
$761$			6.63482i			0.240512i	0.992743	+	0.120256i	$0.0383715\pi$
$761$			6.63482i			0.240512i	−0.992743	+	0.120256i	$0.961628\pi$
$762$		0			0
$763$	9.31425	+	9.31425i	0.337199	+	0.337199i
$764$		0			0
$765$	26.7826	−	26.7826i	0.968326	−	0.968326i
$766$		0			0
$767$	21.5082			0.776617
$768$		0			0
$769$	9.61482			0.346719			0.173360	−	0.984859i	$-0.444538\pi$
$769$	9.61482			0.346719			0.173360	+	0.984859i	$0.444538\pi$
$770$		0			0
$771$	−31.4505	+	31.4505i	−1.13266	+	1.13266i
$772$		0			0
$773$	−7.09164	−	7.09164i	−0.255069	−	0.255069i	0.567976	−	0.823045i	$-0.307727\pi$
$773$	−7.09164	−	7.09164i	−0.255069	−	0.255069i	−0.823045	+	0.567976i	$0.807727\pi$
$774$		0			0
$775$			5.44796i			0.195696i
$776$		0			0
$777$			18.2396i			0.654342i
$778$		0			0
$779$	−17.3192	−	17.3192i	−0.620525	−	0.620525i
$780$		0			0
$781$	−0.208055	+	0.208055i	−0.00744478	+	0.00744478i
$782$		0			0
$783$	−34.5595			−1.23506
$784$		0			0
$785$	2.83335			0.101127
$786$		0			0
$787$	−32.5040	+	32.5040i	−1.15864	+	1.15864i	−0.173873	+	0.984768i	$0.555628\pi$
$787$	−32.5040	+	32.5040i	−1.15864	+	1.15864i	−0.984768	+	0.173873i	$0.944372\pi$
$788$		0			0
$789$	−43.1274	−	43.1274i	−1.53538	−	1.53538i
$790$		0			0
$791$		−	5.90655i		−	0.210013i
$792$		0			0
$793$			21.2580i			0.754895i
$794$		0			0
$795$	−6.62664	−	6.62664i	−0.235023	−	0.235023i
$796$		0			0
$797$	−5.69973	+	5.69973i	−0.201895	+	0.201895i	−0.800811	−	0.598917i	$-0.795598\pi$
$797$	−5.69973	+	5.69973i	−0.201895	+	0.201895i	0.598917	+	0.800811i	$0.295598\pi$
$798$		0			0
$799$	31.2640			1.10604
$800$		0			0
$801$	39.5626			1.39788
$802$		0			0
$803$	0.135922	−	0.135922i	0.00479658	−	0.00479658i
$804$		0			0
$805$	6.25330	+	6.25330i	0.220400	+	0.220400i
$806$		0			0
$807$		−	35.6601i		−	1.25530i
$808$		0			0
$809$			16.5904i			0.583288i	0.956527	+	0.291644i	$0.0942022\pi$
$809$			16.5904i			0.583288i	−0.956527	+	0.291644i	$0.905798\pi$
$810$		0			0
$811$	−2.28734	−	2.28734i	−0.0803195	−	0.0803195i	0.665806	−	0.746125i	$-0.268088\pi$
$811$	−2.28734	−	2.28734i	−0.0803195	−	0.0803195i	−0.746125	+	0.665806i	$0.768088\pi$
$812$		0			0
$813$	−10.8597	+	10.8597i	−0.380866	+	0.380866i
$814$		0			0
$815$	−8.67897			−0.304011
$816$		0			0
$817$	−51.3795			−1.79754
$818$		0			0
$819$	−20.2403	+	20.2403i	−0.707254	+	0.707254i
$820$		0			0
$821$	37.2996	+	37.2996i	1.30176	+	1.30176i	0.927201	+	0.374563i	$0.122207\pi$
$821$	37.2996	+	37.2996i	1.30176	+	1.30176i	0.374563	+	0.927201i	$0.377793\pi$
$822$		0			0
$823$		−	3.52918i		−	0.123020i	−0.998106	−	0.0615098i	$-0.980408\pi$
$823$		−	3.52918i		−	0.123020i	0.998106	−	0.0615098i	$-0.0195915\pi$
$824$		0			0
$825$			3.71128i			0.129210i
$826$		0			0
$827$	−32.9003	−	32.9003i	−1.14406	−	1.14406i	−0.987701	−	0.156355i	$-0.950026\pi$
$827$	−32.9003	−	32.9003i	−1.14406	−	1.14406i	−0.156355	−	0.987701i	$-0.549974\pi$
$828$		0			0
$829$	−6.40321	+	6.40321i	−0.222393	+	0.222393i	−0.809505	−	0.587113i	$-0.800265\pi$
$829$	−6.40321	+	6.40321i	−0.222393	+	0.222393i	0.587113	+	0.809505i	$0.300265\pi$
$830$		0			0
$831$	−26.5160			−0.919831
$832$		0			0
$833$	5.75841			0.199517
$834$		0			0
$835$	4.60277	−	4.60277i	0.159285	−	0.159285i
$836$		0			0
$837$	42.6514	+	42.6514i	1.47425	+	1.47425i
$838$		0			0
$839$			0.558194i			0.0192710i	0.999954	+	0.00963550i	$0.00306712\pi$
$839$			0.558194i			0.0192710i	−0.999954	+	0.00963550i	$0.996933\pi$
$840$		0			0
$841$			19.2567i			0.664024i
$842$		0			0
$843$	−12.7920	−	12.7920i	−0.440580	−	0.440580i
$844$		0			0
$845$	−4.19883	+	4.19883i	−0.144444	+	0.144444i
$846$		0			0
$847$	−9.56189			−0.328550
$848$		0			0
$849$	27.8851			0.957013
$850$		0			0
$851$	36.8550	−	36.8550i	1.26337	−	1.26337i
$852$		0			0
$853$	−0.0903143	−	0.0903143i	−0.00309230	−	0.00309230i	0.705559	−	0.708651i	$-0.250696\pi$
$853$	−0.0903143	−	0.0903143i	−0.00309230	−	0.00309230i	−0.708651	+	0.705559i	$0.750696\pi$
$854$		0			0
$855$		−	32.5512i		−	1.11323i
$856$		0			0
$857$		−	1.11983i		−	0.0382526i	−0.999817	−	0.0191263i	$-0.993912\pi$
$857$		−	1.11983i		−	0.0382526i	0.999817	−	0.0191263i	$-0.00608846\pi$
$858$		0			0
$859$	1.38287	+	1.38287i	0.0471828	+	0.0471828i	0.730305	−	0.683122i	$-0.239378\pi$
$859$	1.38287	+	1.38287i	0.0471828	+	0.0471828i	−0.683122	+	0.730305i	$0.739378\pi$
$860$		0			0
$861$	−10.8306	+	10.8306i	−0.369106	+	0.369106i
$862$		0			0
$863$	31.4276			1.06981			0.534904	−	0.844913i	$-0.320348\pi$
$863$	31.4276			1.06981			0.534904	+	0.844913i	$0.320348\pi$
$864$		0			0
$865$	−8.50425			−0.289153
$866$		0			0
$867$	−35.3618	+	35.3618i	−1.20095	+	1.20095i
$868$		0			0
$869$	−8.43962	−	8.43962i	−0.286294	−	0.286294i
$870$		0			0
$871$			19.2309i			0.651616i
$872$		0			0
$873$			97.8299i			3.31104i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	−25.6685	+	25.6685i	−0.866764	+	0.866764i	−0.992113	−	0.125349i	$-0.959995\pi$
$877$	−25.6685	+	25.6685i	−0.866764	+	0.866764i	0.125349	+	0.992113i	$0.459995\pi$
$878$		0			0
$879$	−37.2524			−1.25649
$880$		0			0
$881$	1.58788			0.0534972			0.0267486	−	0.999642i	$-0.491485\pi$
$881$	1.58788			0.0534972			0.0267486	+	0.999642i	$0.491485\pi$
$882$		0			0
$883$	−23.4314	+	23.4314i	−0.788529	+	0.788529i	−0.981253	−	0.192724i	$-0.938268\pi$
$883$	−23.4314	+	23.4314i	−0.788529	+	0.788529i	0.192724	+	0.981253i	$0.438268\pi$
$884$		0			0
$885$	10.8156	+	10.8156i	0.363562	+	0.363562i
$886$		0			0
$887$			57.9216i			1.94482i	0.233284	+	0.972409i	$0.425053\pi$
$887$			57.9216i			1.94482i	−0.233284	+	0.972409i	$0.574947\pi$
$888$		0			0
$889$			20.4712i			0.686584i
$890$		0			0
$891$	12.3224	+	12.3224i	0.412817	+	0.412817i
$892$		0			0
$893$	18.9990	−	18.9990i	0.635776	−	0.635776i
$894$		0			0
$895$	5.82217			0.194614
$896$		0			0
$897$	119.102			3.97670
$898$		0			0
$899$	−12.0246	+	12.0246i	−0.401044	+	0.401044i
$900$		0			0
$901$	12.3302	+	12.3302i	0.410777	+	0.410777i
$902$		0			0
$903$			32.1303i			1.06923i
$904$		0			0
$905$			16.2701i			0.540837i
$906$		0			0
$907$	16.8139	+	16.8139i	0.558297	+	0.558297i	0.928822	−	0.370525i	$-0.120822\pi$
$907$	16.8139	+	16.8139i	0.558297	+	0.558297i	−0.370525	+	0.928822i	$0.620822\pi$
$908$		0			0
$909$	89.7477	−	89.7477i	2.97674	−	2.97674i
$910$		0			0
$911$	44.6449			1.47915			0.739576	−	0.673073i	$-0.235026\pi$
$911$	44.6449			1.47915			0.739576	+	0.673073i	$0.235026\pi$
$912$		0			0
$913$	11.3441			0.375435
$914$		0			0
$915$	−10.6898	+	10.6898i	−0.353393	+	0.353393i
$916$		0			0
$917$	−0.656784	−	0.656784i	−0.0216889	−	0.0216889i
$918$		0			0
$919$		−	10.1210i		−	0.333862i	−0.985969	−	0.166931i	$-0.946614\pi$
$919$		−	10.1210i		−	0.333862i	0.985969	−	0.166931i	$-0.0533858\pi$
$920$		0			0
$921$		−	86.1030i		−	2.83719i
$922$		0			0
$923$	−0.755003	−	0.755003i	−0.0248512	−	0.0248512i
$924$		0			0
$925$	−4.16747	+	4.16747i	−0.137026	+	0.137026i
$926$		0			0
$927$	9.66493			0.317438
$928$		0			0
$929$	−36.1823			−1.18710			−0.593551	−	0.804796i	$-0.702274\pi$
$929$	−36.1823			−1.18710			−0.593551	+	0.804796i	$0.702274\pi$
$930$		0			0
$931$	3.49935	−	3.49935i	0.114687	−	0.114687i
$932$		0			0
$933$	−24.8404	−	24.8404i	−0.813239	−	0.813239i
$934$		0			0
$935$		−	6.90556i		−	0.225836i
$936$		0			0
$937$		−	51.9642i		−	1.69760i	−0.528718	−	0.848798i	$-0.677327\pi$
$937$		−	51.9642i		−	1.69760i	0.528718	−	0.848798i	$-0.322673\pi$
$938$		0			0
$939$	−50.5527	−	50.5527i	−1.64973	−	1.64973i
$940$		0			0
$941$	11.7290	−	11.7290i	0.382356	−	0.382356i	−0.489594	−	0.871950i	$-0.662855\pi$
$941$	11.7290	−	11.7290i	0.382356	−	0.382356i	0.871950	+	0.489594i	$0.162855\pi$
$942$		0			0
$943$	43.7688			1.42531
$944$		0			0
$945$	−11.0717			−0.360163
$946$		0			0
$947$	8.81428	−	8.81428i	0.286426	−	0.286426i	−0.549239	−	0.835665i	$-0.685082\pi$
$947$	8.81428	−	8.81428i	0.286426	−	0.286426i	0.835665	+	0.549239i	$0.185082\pi$
$948$		0			0
$949$	0.493243	+	0.493243i	0.0160113	+	0.0160113i
$950$		0			0
$951$		−	17.8578i		−	0.579078i
$952$		0			0
$953$			32.4726i			1.05189i	0.850519	+	0.525945i	$0.176288\pi$
$953$			32.4726i			1.05189i	−0.850519	+	0.525945i	$0.823712\pi$
$954$		0			0
$955$	2.29200	+	2.29200i	0.0741675	+	0.0741675i
$956$		0			0
$957$	−8.19147	+	8.19147i	−0.264793	+	0.264793i
$958$		0			0
$959$	−16.6901			−0.538950
$960$		0			0
$961$	−1.31977			−0.0425734
$962$		0			0
$963$	−77.8979	+	77.8979i	−2.51022	+	2.51022i
$964$		0			0
$965$	−16.3586	−	16.3586i	−0.526601	−	0.526601i
$966$		0			0
$967$			5.87401i			0.188895i	0.995530	+	0.0944477i	$0.0301085\pi$
$967$			5.87401i			0.188895i	−0.995530	+	0.0944477i	$0.969891\pi$
$968$		0			0
$969$			88.1927i			2.83316i
$970$		0			0
$971$	−26.6323	−	26.6323i	−0.854670	−	0.854670i	0.136034	−	0.990704i	$-0.456564\pi$
$971$	−26.6323	−	26.6323i	−0.854670	−	0.854670i	−0.990704	+	0.136034i	$0.956564\pi$
$972$		0			0
$973$	3.42603	−	3.42603i	0.109834	−	0.109834i
$974$		0			0
$975$	−13.4677			−0.431313
$976$		0			0
$977$	−37.4838			−1.19921			−0.599607	−	0.800294i	$-0.704677\pi$
$977$	−37.4838			−1.19921			−0.599607	+	0.800294i	$0.704677\pi$
$978$		0			0
$979$	5.10037	−	5.10037i	0.163008	−	0.163008i
$980$		0			0
$981$	61.2651	+	61.2651i	1.95604	+	1.95604i
$982$		0			0
$983$		−	6.16848i		−	0.196744i	−0.995150	−	0.0983719i	$-0.968637\pi$
$983$		−	6.16848i		−	0.196744i	0.995150	−	0.0983719i	$-0.0313635\pi$
$984$		0			0
$985$			7.39617i			0.235662i
$986$		0			0
$987$	−11.8810	−	11.8810i	−0.378178	−	0.378178i
$988$		0			0
$989$	64.9226	−	64.9226i	2.06442	−	2.06442i
$990$		0			0
$991$	−8.10013			−0.257309			−0.128655	−	0.991689i	$-0.541066\pi$
$991$	−8.10013			−0.257309			−0.128655	+	0.991689i	$0.541066\pi$
$992$		0			0
$993$	39.7341			1.26092
$994$		0			0
$995$	15.7462	−	15.7462i	0.499188	−	0.499188i
$996$		0			0
$997$	9.76260	+	9.76260i	0.309185	+	0.309185i	0.844593	−	0.535409i	$-0.179842\pi$
$997$	9.76260	+	9.76260i	0.309185	+	0.309185i	−0.535409	+	0.844593i	$0.679842\pi$
$998$		0			0
$999$			65.2533i			2.06452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.2		44
4.3	odd	2		560.2.bd.a.421.19	yes	44
16.3	odd	4		560.2.bd.a.141.19	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.19	✓	44	16.3	odd	4
560.2.bd.a.421.19	yes	44	4.3	odd	2
2240.2.bd.a.561.2		44	1.1	even	1	trivial
2240.2.bd.a.1681.2		44	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.18833 + 2.18833i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -6.57756i q^{9} +O(q^{10})\)	\(q+(-2.18833 + 2.18833i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -6.57756i q^{9} +(-0.847972 - 0.847972i) q^{11} +(3.07718 - 3.07718i) q^{13} +3.09476 q^{15} -5.75841 q^{17} +(-3.49935 + 3.49935i) q^{19} +(2.18833 + 2.18833i) q^{21} -8.84350i q^{23} +1.00000i q^{25} +(7.82888 + 7.82888i) q^{27} +(-2.20718 + 2.20718i) q^{29} +5.44796 q^{31} +3.71128 q^{33} +(-0.707107 + 0.707107i) q^{35} +(4.16747 + 4.16747i) q^{37} +13.4677i q^{39} +4.94926i q^{41} +(7.34128 + 7.34128i) q^{43} +(-4.65104 + 4.65104i) q^{45} -5.42928 q^{47} -1.00000 q^{49} +(12.6013 - 12.6013i) q^{51} +(-2.14124 - 2.14124i) q^{53} +1.19921i q^{55} -15.3155i q^{57} +(3.49480 + 3.49480i) q^{59} +(-3.45415 + 3.45415i) q^{61} -6.57756 q^{63} -4.35179 q^{65} +(-3.12477 + 3.12477i) q^{67} +(19.3525 + 19.3525i) q^{69} -0.245356i q^{71} +0.160291i q^{73} +(-2.18833 - 2.18833i) q^{75} +(-0.847972 + 0.847972i) q^{77} +9.95271 q^{79} -14.5316 q^{81} +(-6.68896 + 6.68896i) q^{83} +(4.07181 + 4.07181i) q^{85} -9.66007i q^{87} +6.01478i q^{89} +(-3.07718 - 3.07718i) q^{91} +(-11.9219 + 11.9219i) q^{93} +4.94883 q^{95} -14.8733 q^{97} +(-5.57759 + 5.57759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 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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