LMFDB - Embedded newform 2240.2.bd.a.561.9

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			561.9
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.659301 + 0.659301i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.13064i q^{9} +O(q^{10})$	\(q+(-0.659301 + 0.659301i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.13064i q^{9} +(-0.960793 - 0.960793i) q^{11} +(-4.69010 + 4.69010i) q^{13} -0.932392 q^{15} -6.14259 q^{17} +(3.50283 - 3.50283i) q^{19} +(0.659301 + 0.659301i) q^{21} -5.35566i q^{23} +1.00000i q^{25} +(-3.38264 - 3.38264i) q^{27} +(5.36906 - 5.36906i) q^{29} -5.04987 q^{31} +1.26690 q^{33} +(0.707107 - 0.707107i) q^{35} +(0.565470 + 0.565470i) q^{37} -6.18437i q^{39} -10.4927i q^{41} +(5.35789 + 5.35789i) q^{43} +(-1.50659 + 1.50659i) q^{45} -0.344543 q^{47} -1.00000 q^{49} +(4.04982 - 4.04982i) q^{51} +(5.16922 + 5.16922i) q^{53} -1.35877i q^{55} +4.61884i q^{57} +(-8.84373 - 8.84373i) q^{59} +(3.44525 - 3.44525i) q^{61} +2.13064 q^{63} -6.63280 q^{65} +(-5.29272 + 5.29272i) q^{67} +(3.53099 + 3.53099i) q^{69} +1.58226i q^{71} -12.7771i q^{73} +(-0.659301 - 0.659301i) q^{75} +(-0.960793 + 0.960793i) q^{77} -6.90790 q^{79} -1.93158 q^{81} +(0.0542596 - 0.0542596i) q^{83} +(-4.34347 - 4.34347i) q^{85} +7.07965i q^{87} +13.1595i q^{89} +(4.69010 + 4.69010i) q^{91} +(3.32938 - 3.32938i) q^{93} +4.95375 q^{95} -3.95386 q^{97} +(2.04711 - 2.04711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.659301	+	0.659301i	−0.380647	+	0.380647i	−0.871335	−	0.490688i	$-0.836746\pi$
$3$	−0.659301	+	0.659301i	−0.380647	+	0.380647i	0.490688	+	0.871335i	$0.336746\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			2.13064i			0.710215i
$10$		0			0
$11$	−0.960793	−	0.960793i	−0.289690	−	0.289690i	0.547268	−	0.836958i	$-0.315668\pi$
$11$	−0.960793	−	0.960793i	−0.289690	−	0.289690i	−0.836958	+	0.547268i	$0.815668\pi$
$12$		0			0
$13$	−4.69010	+	4.69010i	−1.30080	+	1.30080i	−0.372947	+	0.927853i	$0.621653\pi$
$13$	−4.69010	+	4.69010i	−1.30080	+	1.30080i	−0.927853	+	0.372947i	$0.878347\pi$
$14$		0			0
$15$	−0.932392			−0.240743
$16$		0			0
$17$	−6.14259			−1.48980			−0.744899	−	0.667177i	$-0.767502\pi$
$17$	−6.14259			−1.48980			−0.744899	+	0.667177i	$0.767502\pi$
$18$		0			0
$19$	3.50283	−	3.50283i	0.803605	−	0.803605i	−0.180052	−	0.983657i	$-0.557627\pi$
$19$	3.50283	−	3.50283i	0.803605	−	0.803605i	0.983657	+	0.180052i	$0.0576267\pi$
$20$		0			0
$21$	0.659301	+	0.659301i	0.143871	+	0.143871i
$22$		0			0
$23$		−	5.35566i		−	1.11673i	−0.829594	−	0.558366i	$-0.811428\pi$
$23$		−	5.35566i		−	1.11673i	0.829594	−	0.558366i	$-0.188572\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−3.38264	−	3.38264i	−0.650989	−	0.650989i
$28$		0			0
$29$	5.36906	−	5.36906i	0.997009	−	0.997009i	−0.00298654	−	0.999996i	$-0.500951\pi$
$29$	5.36906	−	5.36906i	0.997009	−	0.997009i	0.999996	+	0.00298654i	$0.000950646\pi$
$30$		0			0
$31$	−5.04987			−0.906983			−0.453492	−	0.891261i	$-0.649822\pi$
$31$	−5.04987			−0.906983			−0.453492	+	0.891261i	$0.649822\pi$
$32$		0			0
$33$	1.26690			0.220540
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	0.565470	+	0.565470i	0.0929626	+	0.0929626i	0.752059	−	0.659096i	$-0.229061\pi$
$37$	0.565470	+	0.565470i	0.0929626	+	0.0929626i	−0.659096	+	0.752059i	$0.729061\pi$
$38$		0			0
$39$		−	6.18437i		−	0.990292i
$40$		0			0
$41$		−	10.4927i		−	1.63869i	−0.573300	−	0.819346i	$-0.694337\pi$
$41$		−	10.4927i		−	1.63869i	0.573300	−	0.819346i	$-0.305663\pi$
$42$		0			0
$43$	5.35789	+	5.35789i	0.817071	+	0.817071i	0.985683	−	0.168612i	$-0.0539284\pi$
$43$	5.35789	+	5.35789i	0.817071	+	0.817071i	−0.168612	+	0.985683i	$0.553928\pi$
$44$		0			0
$45$	−1.50659	+	1.50659i	−0.224590	+	0.224590i
$46$		0			0
$47$	−0.344543			−0.0502567			−0.0251284	−	0.999684i	$-0.507999\pi$
$47$	−0.344543			−0.0502567			−0.0251284	+	0.999684i	$0.507999\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	4.04982	−	4.04982i	0.567088	−	0.567088i
$52$		0			0
$53$	5.16922	+	5.16922i	0.710047	+	0.710047i	0.966545	−	0.256498i	$-0.0825686\pi$
$53$	5.16922	+	5.16922i	0.710047	+	0.710047i	−0.256498	+	0.966545i	$0.582569\pi$
$54$		0			0
$55$		−	1.35877i		−	0.183216i
$56$		0			0
$57$			4.61884i			0.611780i
$58$		0			0
$59$	−8.84373	−	8.84373i	−1.15136	−	1.15136i	−0.986281	−	0.165074i	$-0.947214\pi$
$59$	−8.84373	−	8.84373i	−1.15136	−	1.15136i	−0.165074	−	0.986281i	$-0.552786\pi$
$60$		0			0
$61$	3.44525	−	3.44525i	0.441119	−	0.441119i	−0.451269	−	0.892388i	$-0.649028\pi$
$61$	3.44525	−	3.44525i	0.441119	−	0.441119i	0.892388	+	0.451269i	$0.149028\pi$
$62$		0			0
$63$	2.13064			0.268436
$64$		0			0
$65$	−6.63280			−0.822698
$66$		0			0
$67$	−5.29272	+	5.29272i	−0.646609	+	0.646609i	−0.952172	−	0.305563i	$-0.901155\pi$
$67$	−5.29272	+	5.29272i	−0.646609	+	0.646609i	0.305563	+	0.952172i	$0.401155\pi$
$68$		0			0
$69$	3.53099	+	3.53099i	0.425082	+	0.425082i
$70$		0			0
$71$			1.58226i			0.187779i	0.995583	+	0.0938896i	$0.0299301\pi$
$71$			1.58226i			0.187779i	−0.995583	+	0.0938896i	$0.970070\pi$
$72$		0			0
$73$		−	12.7771i		−	1.49544i	−0.664013	−	0.747721i	$-0.731148\pi$
$73$		−	12.7771i		−	1.49544i	0.664013	−	0.747721i	$-0.268852\pi$
$74$		0			0
$75$	−0.659301	−	0.659301i	−0.0761295	−	0.0761295i
$76$		0			0
$77$	−0.960793	+	0.960793i	−0.109493	+	0.109493i
$78$		0			0
$79$	−6.90790			−0.777200			−0.388600	−	0.921407i	$-0.627041\pi$
$79$	−6.90790			−0.777200			−0.388600	+	0.921407i	$0.627041\pi$
$80$		0			0
$81$	−1.93158			−0.214620
$82$		0			0
$83$	0.0542596	−	0.0542596i	0.00595576	−	0.00595576i	−0.704123	−	0.710078i	$-0.748659\pi$
$83$	0.0542596	−	0.0542596i	0.00595576	−	0.00595576i	0.710078	+	0.704123i	$0.248659\pi$
$84$		0			0
$85$	−4.34347	−	4.34347i	−0.471116	−	0.471116i
$86$		0			0
$87$			7.07965i			0.759018i
$88$		0			0
$89$			13.1595i			1.39490i	0.716633	+	0.697451i	$0.245682\pi$
$89$			13.1595i			1.39490i	−0.716633	+	0.697451i	$0.754318\pi$
$90$		0			0
$91$	4.69010	+	4.69010i	0.491656	+	0.491656i
$92$		0			0
$93$	3.32938	−	3.32938i	0.345241	−	0.345241i
$94$		0			0
$95$	4.95375			0.508244
$96$		0			0
$97$	−3.95386			−0.401453			−0.200727	−	0.979647i	$-0.564330\pi$
$97$	−3.95386			−0.401453			−0.200727	+	0.979647i	$0.564330\pi$
$98$		0			0
$99$	2.04711	−	2.04711i	0.205742	−	0.205742i
$100$		0			0
$101$	3.29042	+	3.29042i	0.327409	+	0.327409i	0.851600	−	0.524191i	$-0.175632\pi$
$101$	3.29042	+	3.29042i	0.327409	+	0.327409i	−0.524191	+	0.851600i	$0.675632\pi$
$102$		0			0
$103$		−	10.7702i		−	1.06122i	−0.847615	−	0.530611i	$-0.821962\pi$
$103$		−	10.7702i		−	1.06122i	0.847615	−	0.530611i	$-0.178038\pi$
$104$		0			0
$105$			0.932392i			0.0909922i
$106$		0			0
$107$	−6.21743	−	6.21743i	−0.601061	−	0.601061i	0.339533	−	0.940594i	$-0.389731\pi$
$107$	−6.21743	−	6.21743i	−0.601061	−	0.601061i	−0.940594	+	0.339533i	$0.889731\pi$
$108$		0			0
$109$	−2.44960	+	2.44960i	−0.234629	+	0.234629i	−0.814622	−	0.579993i	$-0.803055\pi$
$109$	−2.44960	+	2.44960i	−0.234629	+	0.234629i	0.579993	+	0.814622i	$0.303055\pi$
$110$		0			0
$111$	−0.745629			−0.0707720
$112$		0			0
$113$	−1.35950			−0.127891			−0.0639453	−	0.997953i	$-0.520368\pi$
$113$	−1.35950			−0.127891			−0.0639453	+	0.997953i	$0.520368\pi$
$114$		0			0
$115$	3.78703	−	3.78703i	0.353142	−	0.353142i
$116$		0			0
$117$	−9.99294	−	9.99294i	−0.923847	−	0.923847i
$118$		0			0
$119$			6.14259i			0.563091i
$120$		0			0
$121$		−	9.15375i		−	0.832159i
$122$		0			0
$123$	6.91787	+	6.91787i	0.623764	+	0.623764i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−9.62545			−0.854121			−0.427061	−	0.904223i	$-0.640451\pi$
$127$	−9.62545			−0.854121			−0.427061	+	0.904223i	$0.640451\pi$
$128$		0			0
$129$	−7.06493			−0.622032
$130$		0			0
$131$	13.9965	−	13.9965i	1.22288	−	1.22288i	0.256271	−	0.966605i	$-0.417506\pi$
$131$	13.9965	−	13.9965i	1.22288	−	1.22288i	0.966605	−	0.256271i	$-0.0824939\pi$
$132$		0			0
$133$	−3.50283	−	3.50283i	−0.303734	−	0.303734i
$134$		0			0
$135$		−	4.78377i		−	0.411722i
$136$		0			0
$137$		−	16.1000i		−	1.37552i	−0.725938	−	0.687760i	$-0.758594\pi$
$137$		−	16.1000i		−	1.37552i	0.725938	−	0.687760i	$-0.241406\pi$
$138$		0			0
$139$	−2.38238	−	2.38238i	−0.202071	−	0.202071i	0.598816	−	0.800887i	$-0.295638\pi$
$139$	−2.38238	−	2.38238i	−0.202071	−	0.202071i	−0.800887	+	0.598816i	$0.795638\pi$
$140$		0			0
$141$	0.227157	−	0.227157i	0.0191301	−	0.0191301i
$142$		0			0
$143$	9.01243			0.753657
$144$		0			0
$145$	7.59299			0.630564
$146$		0			0
$147$	0.659301	−	0.659301i	0.0543782	−	0.0543782i
$148$		0			0
$149$	9.85068	+	9.85068i	0.806999	+	0.806999i	0.984179	−	0.177179i	$-0.0566973\pi$
$149$	9.85068	+	9.85068i	0.806999	+	0.806999i	−0.177179	+	0.984179i	$0.556697\pi$
$150$		0			0
$151$		−	6.55173i		−	0.533172i	−0.963811	−	0.266586i	$-0.914104\pi$
$151$		−	6.55173i		−	0.533172i	0.963811	−	0.266586i	$-0.0858957\pi$
$152$		0			0
$153$		−	13.0877i		−	1.05808i
$154$		0			0
$155$	−3.57080	−	3.57080i	−0.286813	−	0.286813i
$156$		0			0
$157$	−1.58242	+	1.58242i	−0.126291	+	0.126291i	−0.767427	−	0.641136i	$-0.778463\pi$
$157$	−1.58242	+	1.58242i	−0.126291	+	0.126291i	0.641136	+	0.767427i	$0.278463\pi$
$158$		0			0
$159$	−6.81614			−0.540555
$160$		0			0
$161$	−5.35566			−0.422085
$162$		0			0
$163$	11.5725	−	11.5725i	0.906430	−	0.906430i	−0.0895519	−	0.995982i	$-0.528544\pi$
$163$	11.5725	−	11.5725i	0.906430	−	0.906430i	0.995982	+	0.0895519i	$0.0285435\pi$
$164$		0			0
$165$	0.895836	+	0.895836i	0.0697407	+	0.0697407i
$166$		0			0
$167$			2.19781i			0.170071i	0.996378	+	0.0850357i	$0.0271004\pi$
$167$			2.19781i			0.170071i	−0.996378	+	0.0850357i	$0.972900\pi$
$168$		0			0
$169$		−	30.9941i		−	2.38416i
$170$		0			0
$171$	7.46329	+	7.46329i	0.570732	+	0.570732i
$172$		0			0
$173$	−4.15660	+	4.15660i	−0.316021	+	0.316021i	−0.847236	−	0.531216i	$-0.821735\pi$
$173$	−4.15660	+	4.15660i	−0.316021	+	0.316021i	0.531216	+	0.847236i	$0.321735\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	11.6614			0.876521
$178$		0			0
$179$	13.5812	−	13.5812i	1.01511	−	1.01511i	0.0152225	−	0.999884i	$-0.495154\pi$
$179$	13.5812	−	13.5812i	1.01511	−	1.01511i	0.999884	−	0.0152225i	$-0.00484567\pi$
$180$		0			0
$181$	−8.32103	−	8.32103i	−0.618497	−	0.618497i	0.326649	−	0.945146i	$-0.394081\pi$
$181$	−8.32103	−	8.32103i	−0.618497	−	0.618497i	−0.945146	+	0.326649i	$0.894081\pi$
$182$		0			0
$183$			4.54292i			0.335822i
$184$		0			0
$185$			0.799695i			0.0587947i
$186$		0			0
$187$	5.90176	+	5.90176i	0.431580	+	0.431580i
$188$		0			0
$189$	−3.38264	+	3.38264i	−0.246051	+	0.246051i
$190$		0			0
$191$	−22.5942			−1.63486			−0.817430	−	0.576028i	$-0.804602\pi$
$191$	−22.5942			−1.63486			−0.817430	+	0.576028i	$0.804602\pi$
$192$		0			0
$193$	−19.4036			−1.39670			−0.698351	−	0.715755i	$-0.746083\pi$
$193$	−19.4036			−1.39670			−0.698351	+	0.715755i	$0.746083\pi$
$194$		0			0
$195$	4.37301	−	4.37301i	0.313158	−	0.313158i
$196$		0			0
$197$	14.2195	+	14.2195i	1.01310	+	1.01310i	0.999913	+	0.0131820i	$0.00419608\pi$
$197$	14.2195	+	14.2195i	1.01310	+	1.01310i	0.0131820	+	0.999913i	$0.495804\pi$
$198$		0			0
$199$			17.0783i			1.21065i	0.795979	+	0.605324i	$0.206956\pi$
$199$			17.0783i			1.21065i	−0.795979	+	0.605324i	$0.793044\pi$
$200$		0			0
$201$		−	6.97899i		−	0.492260i
$202$		0			0
$203$	−5.36906	−	5.36906i	−0.376834	−	0.376834i
$204$		0			0
$205$	7.41949	−	7.41949i	0.518200	−	0.518200i
$206$		0			0
$207$	11.4110			0.793120
$208$		0			0
$209$	−6.73099			−0.465592
$210$		0			0
$211$	−13.7314	+	13.7314i	−0.945311	+	0.945311i	−0.998580	−	0.0532692i	$-0.983036\pi$
$211$	−13.7314	+	13.7314i	−0.945311	+	0.945311i	0.0532692	+	0.998580i	$0.483036\pi$
$212$		0			0
$213$	−1.04318	−	1.04318i	−0.0714777	−	0.0714777i
$214$		0			0
$215$			7.57720i			0.516761i
$216$		0			0
$217$			5.04987i			0.342807i
$218$		0			0
$219$	8.42393	+	8.42393i	0.569236	+	0.569236i
$220$		0			0
$221$	28.8094	−	28.8094i	1.93793	−	1.93793i
$222$		0			0
$223$	−20.6804			−1.38486			−0.692430	−	0.721485i	$-0.743460\pi$
$223$	−20.6804			−1.38486			−0.692430	+	0.721485i	$0.743460\pi$
$224$		0			0
$225$	−2.13064			−0.142043
$226$		0			0
$227$	−4.61070	+	4.61070i	−0.306023	+	0.306023i	−0.843365	−	0.537342i	$-0.819428\pi$
$227$	−4.61070	+	4.61070i	−0.306023	+	0.306023i	0.537342	+	0.843365i	$0.319428\pi$
$228$		0			0
$229$	−2.36580	−	2.36580i	−0.156337	−	0.156337i	0.624605	−	0.780941i	$-0.285260\pi$
$229$	−2.36580	−	2.36580i	−0.156337	−	0.156337i	−0.780941	+	0.624605i	$0.785260\pi$
$230$		0			0
$231$		−	1.26690i		−	0.0833561i
$232$		0			0
$233$			19.8061i			1.29754i	0.760985	+	0.648770i	$0.224716\pi$
$233$			19.8061i			1.29754i	−0.760985	+	0.648770i	$0.775284\pi$
$234$		0			0
$235$	−0.243629	−	0.243629i	−0.0158926	−	0.0158926i
$236$		0			0
$237$	4.55439	−	4.55439i	0.295839	−	0.295839i
$238$		0			0
$239$	−14.9064			−0.964215			−0.482107	−	0.876112i	$-0.660128\pi$
$239$	−14.9064			−0.964215			−0.482107	+	0.876112i	$0.660128\pi$
$240$		0			0
$241$	2.65571			0.171069			0.0855346	−	0.996335i	$-0.472740\pi$
$241$	2.65571			0.171069			0.0855346	+	0.996335i	$0.472740\pi$
$242$		0			0
$243$	11.4214	−	11.4214i	0.732684	−	0.732684i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$			32.8572i			2.09066i
$248$		0			0
$249$			0.0715468i			0.00453409i
$250$		0			0
$251$	−19.1231	−	19.1231i	−1.20704	−	1.20704i	−0.971981	−	0.235059i	$-0.924472\pi$
$251$	−19.1231	−	19.1231i	−1.20704	−	1.20704i	−0.235059	−	0.971981i	$-0.575528\pi$
$252$		0			0
$253$	−5.14568	+	5.14568i	−0.323506	+	0.323506i
$254$		0			0
$255$	5.72731			0.358658
$256$		0			0
$257$	−14.7261			−0.918588			−0.459294	−	0.888284i	$-0.651898\pi$
$257$	−14.7261			−0.918588			−0.459294	+	0.888284i	$0.651898\pi$
$258$		0			0
$259$	0.565470	−	0.565470i	0.0351366	−	0.0351366i
$260$		0			0
$261$	11.4396	+	11.4396i	0.708091	+	0.708091i
$262$		0			0
$263$			25.9814i			1.60208i	0.598611	+	0.801040i	$0.295720\pi$
$263$			25.9814i			1.60208i	−0.598611	+	0.801040i	$0.704280\pi$
$264$		0			0
$265$			7.31038i			0.449073i
$266$		0			0
$267$	−8.67605	−	8.67605i	−0.530966	−	0.530966i
$268$		0			0
$269$	−9.91557	+	9.91557i	−0.604563	+	0.604563i	−0.941520	−	0.336957i	$-0.890602\pi$
$269$	−9.91557	+	9.91557i	−0.604563	+	0.604563i	0.336957	+	0.941520i	$0.390602\pi$
$270$		0			0
$271$	13.1335			0.797802			0.398901	−	0.916994i	$-0.369392\pi$
$271$	13.1335			0.797802			0.398901	+	0.916994i	$0.369392\pi$
$272$		0			0
$273$	−6.18437			−0.374295
$274$		0			0
$275$	0.960793	−	0.960793i	0.0579380	−	0.0579380i
$276$		0			0
$277$	15.6264	+	15.6264i	0.938901	+	0.938901i	0.998238	−	0.0593368i	$-0.0188986\pi$
$277$	15.6264	+	15.6264i	0.938901	+	0.938901i	−0.0593368	+	0.998238i	$0.518899\pi$
$278$		0			0
$279$		−	10.7595i		−	0.644153i
$280$		0			0
$281$		−	18.9892i		−	1.13280i	−0.824130	−	0.566400i	$-0.808336\pi$
$281$		−	18.9892i		−	1.13280i	0.824130	−	0.566400i	$-0.191664\pi$
$282$		0			0
$283$	−6.92426	−	6.92426i	−0.411604	−	0.411604i	0.470693	−	0.882297i	$-0.344004\pi$
$283$	−6.92426	−	6.92426i	−0.411604	−	0.411604i	−0.882297	+	0.470693i	$0.844004\pi$
$284$		0			0
$285$	−3.26601	+	3.26601i	−0.193462	+	0.193462i
$286$		0			0
$287$	−10.4927			−0.619367
$288$		0			0
$289$	20.7315			1.21950
$290$		0			0
$291$	2.60678	−	2.60678i	0.152812	−	0.152812i
$292$		0			0
$293$	−2.32304	−	2.32304i	−0.135714	−	0.135714i	0.635986	−	0.771700i	$-0.280593\pi$
$293$	−2.32304	−	2.32304i	−0.135714	−	0.135714i	−0.771700	+	0.635986i	$0.780593\pi$
$294$		0			0
$295$		−	12.5069i		−	0.728181i
$296$		0			0
$297$			6.50003i			0.377170i
$298$		0			0
$299$	25.1186	+	25.1186i	1.45265	+	1.45265i
$300$		0			0
$301$	5.35789	−	5.35789i	0.308824	−	0.308824i
$302$		0			0
$303$	−4.33875			−0.249255
$304$		0			0
$305$	4.87232			0.278988
$306$		0			0
$307$	−12.1706	+	12.1706i	−0.694610	+	0.694610i	−0.963243	−	0.268633i	$-0.913428\pi$
$307$	−12.1706	+	12.1706i	−0.694610	+	0.694610i	0.268633	+	0.963243i	$0.413428\pi$
$308$		0			0
$309$	7.10082	+	7.10082i	0.403952	+	0.403952i
$310$		0			0
$311$		−	6.14490i		−	0.348445i	−0.984706	−	0.174223i	$-0.944259\pi$
$311$		−	6.14490i		−	0.348445i	0.984706	−	0.174223i	$-0.0557412\pi$
$312$		0			0
$313$		−	14.8927i		−	0.841787i	−0.907110	−	0.420894i	$-0.861717\pi$
$313$		−	14.8927i		−	0.841787i	0.907110	−	0.420894i	$-0.138283\pi$
$314$		0			0
$315$	1.50659	+	1.50659i	0.0848869	+	0.0848869i
$316$		0			0
$317$	1.15952	−	1.15952i	0.0651254	−	0.0651254i	−0.673794	−	0.738919i	$-0.735336\pi$
$317$	1.15952	−	1.15952i	0.0651254	−	0.0651254i	0.738919	+	0.673794i	$0.235336\pi$
$318$		0			0
$319$	−10.3171			−0.577647
$320$		0			0
$321$	8.19831			0.457585
$322$		0			0
$323$	−21.5165	+	21.5165i	−1.19721	+	1.19721i
$324$		0			0
$325$	−4.69010	−	4.69010i	−0.260160	−	0.260160i
$326$		0			0
$327$		−	3.23004i		−	0.178622i
$328$		0			0
$329$			0.344543i			0.0189953i
$330$		0			0
$331$	−19.9934	−	19.9934i	−1.09893	−	1.09893i	−0.994535	−	0.104399i	$-0.966708\pi$
$331$	−19.9934	−	19.9934i	−1.09893	−	1.09893i	−0.104399	−	0.994535i	$-0.533292\pi$
$332$		0			0
$333$	−1.20481	+	1.20481i	−0.0660234	+	0.0660234i
$334$		0			0
$335$	−7.48504			−0.408951
$336$		0			0
$337$	−13.4465			−0.732479			−0.366239	−	0.930521i	$-0.619355\pi$
$337$	−13.4465			−0.732479			−0.366239	+	0.930521i	$0.619355\pi$
$338$		0			0
$339$	0.896317	−	0.896317i	0.0486813	−	0.0486813i
$340$		0			0
$341$	4.85188	+	4.85188i	0.262744	+	0.262744i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			4.99358i			0.268845i
$346$		0			0
$347$	−7.70011	−	7.70011i	−0.413364	−	0.413364i	0.469545	−	0.882909i	$-0.344418\pi$
$347$	−7.70011	−	7.70011i	−0.413364	−	0.413364i	−0.882909	+	0.469545i	$0.844418\pi$
$348$		0			0
$349$	−23.8684	+	23.8684i	−1.27764	+	1.27764i	−0.335661	+	0.941983i	$0.608960\pi$
$349$	−23.8684	+	23.8684i	−1.27764	+	1.27764i	−0.941983	+	0.335661i	$0.891040\pi$
$350$		0			0
$351$	31.7298			1.69361
$352$		0			0
$353$	−5.56869			−0.296391			−0.148196	−	0.988958i	$-0.547347\pi$
$353$	−5.56869			−0.296391			−0.148196	+	0.988958i	$0.547347\pi$
$354$		0			0
$355$	−1.11882	+	1.11882i	−0.0593810	+	0.0593810i
$356$		0			0
$357$	−4.04982	−	4.04982i	−0.214339	−	0.214339i
$358$		0			0
$359$			12.9472i			0.683326i	0.939822	+	0.341663i	$0.110990\pi$
$359$			12.9472i			0.683326i	−0.939822	+	0.341663i	$0.889010\pi$
$360$		0			0
$361$		−	5.53965i		−	0.291561i
$362$		0			0
$363$	6.03508	+	6.03508i	0.316759	+	0.316759i
$364$		0			0
$365$	9.03475	−	9.03475i	0.472900	−	0.472900i
$366$		0			0
$367$	−7.19887			−0.375778			−0.187889	−	0.982190i	$-0.560165\pi$
$367$	−7.19887			−0.375778			−0.187889	+	0.982190i	$0.560165\pi$
$368$		0			0
$369$	22.3563			1.16382
$370$		0			0
$371$	5.16922	−	5.16922i	0.268373	−	0.268373i
$372$		0			0
$373$	7.65364	+	7.65364i	0.396290	+	0.396290i	0.876922	−	0.480632i	$-0.159593\pi$
$373$	7.65364	+	7.65364i	0.396290	+	0.396290i	−0.480632	+	0.876922i	$0.659593\pi$
$374$		0			0
$375$		−	0.932392i		−	0.0481485i
$376$		0			0
$377$			50.3628i			2.59382i
$378$		0			0
$379$	5.04908	+	5.04908i	0.259354	+	0.259354i	0.824791	−	0.565437i	$-0.191293\pi$
$379$	5.04908	+	5.04908i	0.259354	+	0.259354i	−0.565437	+	0.824791i	$0.691293\pi$
$380$		0			0
$381$	6.34607	−	6.34607i	0.325119	−	0.325119i
$382$		0			0
$383$	17.4527			0.891792			0.445896	−	0.895085i	$-0.352885\pi$
$383$	17.4527			0.891792			0.445896	+	0.895085i	$0.352885\pi$
$384$		0			0
$385$	−1.35877			−0.0692492
$386$		0			0
$387$	−11.4158	+	11.4158i	−0.580296	+	0.580296i
$388$		0			0
$389$	−7.95400	−	7.95400i	−0.403284	−	0.403284i	0.476105	−	0.879389i	$-0.342048\pi$
$389$	−7.95400	−	7.95400i	−0.403284	−	0.403284i	−0.879389	+	0.476105i	$0.842048\pi$
$390$		0			0
$391$			32.8977i			1.66371i
$392$		0			0
$393$			18.4557i			0.930969i
$394$		0			0
$395$	−4.88463	−	4.88463i	−0.245772	−	0.245772i
$396$		0			0
$397$	−5.08560	+	5.08560i	−0.255239	+	0.255239i	−0.823114	−	0.567875i	$-0.807766\pi$
$397$	−5.08560	+	5.08560i	−0.255239	+	0.255239i	0.567875	+	0.823114i	$0.307766\pi$
$398$		0			0
$399$	4.61884			0.231231
$400$		0			0
$401$	36.9616			1.84578			0.922888	−	0.385070i	$-0.125823\pi$
$401$	36.9616			1.84578			0.922888	+	0.385070i	$0.125823\pi$
$402$		0			0
$403$	23.6844	−	23.6844i	1.17980	−	1.17980i
$404$		0			0
$405$	−1.36584	−	1.36584i	−0.0678689	−	0.0678689i
$406$		0			0
$407$		−	1.08660i		−	0.0538607i
$408$		0			0
$409$		−	15.7549i		−	0.779030i	−0.921020	−	0.389515i	$-0.872643\pi$
$409$		−	15.7549i		−	0.779030i	0.921020	−	0.389515i	$-0.127357\pi$
$410$		0			0
$411$	10.6148	+	10.6148i	0.523588	+	0.523588i
$412$		0			0
$413$	−8.84373	+	8.84373i	−0.435171	+	0.435171i
$414$		0			0
$415$	0.0767346			0.00376675
$416$		0			0
$417$	3.14141			0.153836
$418$		0			0
$419$	4.05448	−	4.05448i	0.198074	−	0.198074i	−0.601100	−	0.799174i	$-0.705271\pi$
$419$	4.05448	−	4.05448i	0.198074	−	0.198074i	0.799174	+	0.601100i	$0.205271\pi$
$420$		0			0
$421$	2.53599	+	2.53599i	0.123597	+	0.123597i	0.766199	−	0.642603i	$-0.222145\pi$
$421$	2.53599	+	2.53599i	0.123597	+	0.123597i	−0.642603	+	0.766199i	$0.722145\pi$
$422$		0			0
$423$		−	0.734099i		−	0.0356931i
$424$		0			0
$425$		−	6.14259i		−	0.297960i
$426$		0			0
$427$	−3.44525	−	3.44525i	−0.166727	−	0.166727i
$428$		0			0
$429$	−5.94190	+	5.94190i	−0.286878	+	0.286878i
$430$		0			0
$431$	6.89121			0.331938			0.165969	−	0.986131i	$-0.446925\pi$
$431$	6.89121			0.331938			0.165969	+	0.986131i	$0.446925\pi$
$432$		0			0
$433$	−16.5564			−0.795648			−0.397824	−	0.917462i	$-0.630235\pi$
$433$	−16.5564			−0.795648			−0.397824	+	0.917462i	$0.630235\pi$
$434$		0			0
$435$	−5.00607	+	5.00607i	−0.240023	+	0.240023i
$436$		0			0
$437$	−18.7600	−	18.7600i	−0.897412	−	0.897412i
$438$		0			0
$439$			22.9506i			1.09537i	0.836683	+	0.547687i	$0.184492\pi$
$439$			22.9506i			1.09537i	−0.836683	+	0.547687i	$0.815508\pi$
$440$		0			0
$441$		−	2.13064i		−	0.101459i
$442$		0			0
$443$	21.6129	+	21.6129i	1.02686	+	1.02686i	0.999629	+	0.0272288i	$0.00866826\pi$
$443$	21.6129	+	21.6129i	1.02686	+	1.02686i	0.0272288	+	0.999629i	$0.491332\pi$
$444$		0			0
$445$	−9.30515	+	9.30515i	−0.441106	+	0.441106i
$446$		0			0
$447$	−12.9891			−0.614364
$448$		0			0
$449$	2.69974			0.127409			0.0637043	−	0.997969i	$-0.479709\pi$
$449$	2.69974			0.127409			0.0637043	+	0.997969i	$0.479709\pi$
$450$		0			0
$451$	−10.0814	+	10.0814i	−0.474713	+	0.474713i
$452$		0			0
$453$	4.31956	+	4.31956i	0.202951	+	0.202951i
$454$		0			0
$455$			6.63280i			0.310951i
$456$		0			0
$457$			6.12679i			0.286599i	0.989679	+	0.143300i	$0.0457713\pi$
$457$			6.12679i			0.286599i	−0.989679	+	0.143300i	$0.954229\pi$
$458$		0			0
$459$	20.7782	+	20.7782i	0.969842	+	0.969842i
$460$		0			0
$461$	−2.98053	+	2.98053i	−0.138817	+	0.138817i	−0.773101	−	0.634283i	$-0.781295\pi$
$461$	−2.98053	+	2.98053i	−0.138817	+	0.138817i	0.634283	+	0.773101i	$0.281295\pi$
$462$		0			0
$463$	12.3402			0.573498			0.286749	−	0.958006i	$-0.407425\pi$
$463$	12.3402			0.573498			0.286749	+	0.958006i	$0.407425\pi$
$464$		0			0
$465$	4.70846			0.218349
$466$		0			0
$467$	−21.7630	+	21.7630i	−1.00707	+	1.00707i	−0.00709576	+	0.999975i	$0.502259\pi$
$467$	−21.7630	+	21.7630i	−1.00707	+	1.00707i	−0.999975	+	0.00709576i	$0.997741\pi$
$468$		0			0
$469$	5.29272	+	5.29272i	0.244395	+	0.244395i
$470$		0			0
$471$		−	2.08659i		−	0.0961448i
$472$		0			0
$473$		−	10.2957i		−	0.473395i
$474$		0			0
$475$	3.50283	+	3.50283i	0.160721	+	0.160721i
$476$		0			0
$477$	−11.0138	+	11.0138i	−0.504286	+	0.504286i
$478$		0			0
$479$	−9.99891			−0.456862			−0.228431	−	0.973560i	$-0.573359\pi$
$479$	−9.99891			−0.456862			−0.228431	+	0.973560i	$0.573359\pi$
$480$		0			0
$481$	−5.30422			−0.241851
$482$		0			0
$483$	3.53099	−	3.53099i	0.160666	−	0.160666i
$484$		0			0
$485$	−2.79580	−	2.79580i	−0.126951	−	0.126951i
$486$		0			0
$487$		−	2.44027i		−	0.110579i	−0.998470	−	0.0552896i	$-0.982392\pi$
$487$		−	2.44027i		−	0.110579i	0.998470	−	0.0552896i	$-0.0176082\pi$
$488$		0			0
$489$			15.2596i			0.690061i
$490$		0			0
$491$	7.90149	+	7.90149i	0.356589	+	0.356589i	0.862554	−	0.505965i	$-0.168864\pi$
$491$	7.90149	+	7.90149i	0.356589	+	0.356589i	−0.505965	+	0.862554i	$0.668864\pi$
$492$		0			0
$493$	−32.9799	+	32.9799i	−1.48534	+	1.48534i
$494$		0			0
$495$	2.89505			0.130123
$496$		0			0
$497$	1.58226			0.0709739
$498$		0			0
$499$	8.41551	−	8.41551i	0.376730	−	0.376730i	−0.493191	−	0.869921i	$-0.664170\pi$
$499$	8.41551	−	8.41551i	0.376730	−	0.376730i	0.869921	+	0.493191i	$0.164170\pi$
$500$		0			0
$501$	−1.44902	−	1.44902i	−0.0647373	−	0.0647373i
$502$		0			0
$503$		−	23.5472i		−	1.04992i	−0.851127	−	0.524959i	$-0.824081\pi$
$503$		−	23.5472i		−	1.04992i	0.851127	−	0.524959i	$-0.175919\pi$
$504$		0			0
$505$			4.65336i			0.207072i
$506$		0			0
$507$	20.4344	+	20.4344i	0.907524	+	0.907524i
$508$		0			0
$509$	7.12767	−	7.12767i	0.315929	−	0.315929i	−0.531272	−	0.847201i	$-0.678286\pi$
$509$	7.12767	−	7.12767i	0.315929	−	0.315929i	0.847201	+	0.531272i	$0.178286\pi$
$510$		0			0
$511$	−12.7771			−0.565224
$512$		0			0
$513$	−23.6976			−1.04628
$514$		0			0
$515$	7.61570	−	7.61570i	0.335588	−	0.335588i
$516$		0			0
$517$	0.331034	+	0.331034i	0.0145589	+	0.0145589i
$518$		0			0
$519$		−	5.48090i		−	0.240585i
$520$		0			0
$521$			15.8464i			0.694243i	0.937820	+	0.347122i	$0.112841\pi$
$521$			15.8464i			0.694243i	−0.937820	+	0.347122i	$0.887159\pi$
$522$		0			0
$523$	−23.7284	−	23.7284i	−1.03757	−	1.03757i	−0.999266	−	0.0383058i	$-0.987804\pi$
$523$	−23.7284	−	23.7284i	−1.03757	−	1.03757i	−0.0383058	−	0.999266i	$-0.512196\pi$
$524$		0			0
$525$	−0.659301	+	0.659301i	−0.0287742	+	0.0287742i
$526$		0			0
$527$	31.0193			1.35122
$528$		0			0
$529$	−5.68312			−0.247092
$530$		0			0
$531$	18.8428	−	18.8428i	0.817710	−	0.817710i
$532$		0			0
$533$	49.2120	+	49.2120i	2.13161	+	2.13161i
$534$		0			0
$535$		−	8.79277i		−	0.380145i
$536$		0			0
$537$			17.9082i			0.772796i
$538$		0			0
$539$	0.960793	+	0.960793i	0.0413843	+	0.0413843i
$540$		0			0
$541$	−1.85518	+	1.85518i	−0.0797604	+	0.0797604i	−0.745861	−	0.666101i	$-0.767962\pi$
$541$	−1.85518	+	1.85518i	−0.0797604	+	0.0797604i	0.666101	+	0.745861i	$0.267962\pi$
$542$		0			0
$543$	10.9721			0.470859
$544$		0			0
$545$	−3.46425			−0.148392
$546$		0			0
$547$	−6.18720	+	6.18720i	−0.264546	+	0.264546i	−0.826898	−	0.562352i	$-0.809897\pi$
$547$	−6.18720	+	6.18720i	−0.264546	+	0.264546i	0.562352	+	0.826898i	$0.309897\pi$
$548$		0			0
$549$	7.34061	+	7.34061i	0.313290	+	0.313290i
$550$		0			0
$551$		−	37.6138i		−	1.60240i
$552$		0			0
$553$			6.90790i			0.293754i
$554$		0			0
$555$	−0.527239	−	0.527239i	−0.0223801	−	0.0223801i
$556$		0			0
$557$	8.78974	−	8.78974i	0.372433	−	0.372433i	−0.495930	−	0.868363i	$-0.665173\pi$
$557$	8.78974	−	8.78974i	0.372433	−	0.372433i	0.868363	+	0.495930i	$0.165173\pi$
$558$		0			0
$559$	−50.2581			−2.12569
$560$		0			0
$561$	−7.78207			−0.328559
$562$		0			0
$563$	10.5175	−	10.5175i	0.443260	−	0.443260i	−0.449846	−	0.893106i	$-0.648521\pi$
$563$	10.5175	−	10.5175i	0.443260	−	0.443260i	0.893106	+	0.449846i	$0.148521\pi$
$564$		0			0
$565$	−0.961309	−	0.961309i	−0.0404426	−	0.0404426i
$566$		0			0
$567$			1.93158i			0.0811189i
$568$		0			0
$569$		−	20.8434i		−	0.873802i	−0.899510	−	0.436901i	$-0.856076\pi$
$569$		−	20.8434i		−	0.873802i	0.899510	−	0.436901i	$-0.143924\pi$
$570$		0			0
$571$	22.0991	+	22.0991i	0.924821	+	0.924821i	0.997365	−	0.0725446i	$-0.0231120\pi$
$571$	22.0991	+	22.0991i	0.924821	+	0.924821i	−0.0725446	+	0.997365i	$0.523112\pi$
$572$		0			0
$573$	14.8964	−	14.8964i	0.622306	−	0.622306i
$574$		0			0
$575$	5.35566			0.223347
$576$		0			0
$577$	−34.3697			−1.43083			−0.715415	−	0.698700i	$-0.753762\pi$
$577$	−34.3697			−1.43083			−0.715415	+	0.698700i	$0.753762\pi$
$578$		0			0
$579$	12.7928	−	12.7928i	0.531651	−	0.531651i
$580$		0			0
$581$	−0.0542596	−	0.0542596i	−0.00225107	−	0.00225107i
$582$		0			0
$583$		−	9.93311i		−	0.411387i
$584$		0			0
$585$		−	14.1321i		−	0.584292i
$586$		0			0
$587$	16.6890	+	16.6890i	0.688830	+	0.688830i	0.961973	−	0.273143i	$-0.0880633\pi$
$587$	16.6890	+	16.6890i	0.688830	+	0.688830i	−0.273143	+	0.961973i	$0.588063\pi$
$588$		0			0
$589$	−17.6888	+	17.6888i	−0.728856	+	0.728856i
$590$		0			0
$591$	−18.7498			−0.771264
$592$		0			0
$593$	44.7565			1.83793			0.918964	−	0.394342i	$-0.129027\pi$
$593$	44.7565			1.83793			0.918964	+	0.394342i	$0.129027\pi$
$594$		0			0
$595$	−4.34347	+	4.34347i	−0.178065	+	0.178065i
$596$		0			0
$597$	−11.2597	−	11.2597i	−0.460830	−	0.460830i
$598$		0			0
$599$			6.65832i			0.272052i	0.990705	+	0.136026i	$0.0434330\pi$
$599$			6.65832i			0.272052i	−0.990705	+	0.136026i	$0.956567\pi$
$600$		0			0
$601$		−	1.40008i		−	0.0571105i	−0.999592	−	0.0285553i	$-0.990909\pi$
$601$		−	1.40008i		−	0.0571105i	0.999592	−	0.0285553i	$-0.00909066\pi$
$602$		0			0
$603$	−11.2769	−	11.2769i	−0.459231	−	0.459231i
$604$		0			0
$605$	6.47268	−	6.47268i	0.263152	−	0.263152i
$606$		0			0
$607$	27.7699			1.12714			0.563572	−	0.826067i	$-0.309427\pi$
$607$	27.7699			1.12714			0.563572	+	0.826067i	$0.309427\pi$
$608$		0			0
$609$	7.07965			0.286882
$610$		0			0
$611$	1.61594	−	1.61594i	0.0653739	−	0.0653739i
$612$		0			0
$613$	2.31598	+	2.31598i	0.0935415	+	0.0935415i	0.752329	−	0.658788i	$-0.228930\pi$
$613$	2.31598	+	2.31598i	0.0935415	+	0.0935415i	−0.658788	+	0.752329i	$0.728930\pi$
$614$		0			0
$615$			9.78335i			0.394503i
$616$		0			0
$617$			16.1964i			0.652043i	0.945362	+	0.326021i	$0.105708\pi$
$617$			16.1964i			0.652043i	−0.945362	+	0.326021i	$0.894292\pi$
$618$		0			0
$619$	12.4869	+	12.4869i	0.501889	+	0.501889i	0.912025	−	0.410135i	$-0.134519\pi$
$619$	12.4869	+	12.4869i	0.501889	+	0.501889i	−0.410135	+	0.912025i	$0.634519\pi$
$620$		0			0
$621$	−18.1163	+	18.1163i	−0.726981	+	0.726981i
$622$		0			0
$623$	13.1595			0.527223
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	4.43775	−	4.43775i	0.177227	−	0.177227i
$628$		0			0
$629$	−3.47345	−	3.47345i	−0.138496	−	0.138496i
$630$		0			0
$631$		−	32.9143i		−	1.31030i	−0.755500	−	0.655149i	$-0.772606\pi$
$631$		−	32.9143i		−	1.31030i	0.755500	−	0.655149i	$-0.227394\pi$
$632$		0			0
$633$		−	18.1063i		−	0.719660i
$634$		0			0
$635$	−6.80622	−	6.80622i	−0.270097	−	0.270097i
$636$		0			0
$637$	4.69010	−	4.69010i	0.185828	−	0.185828i
$638$		0			0
$639$	−3.37123			−0.133364
$640$		0			0
$641$	47.9639			1.89446			0.947230	−	0.320555i	$-0.103869\pi$
$641$	47.9639			1.89446			0.947230	+	0.320555i	$0.103869\pi$
$642$		0			0
$643$	−24.9790	+	24.9790i	−0.985075	+	0.985075i	−0.999890	−	0.0148149i	$-0.995284\pi$
$643$	−24.9790	+	24.9790i	−0.985075	+	0.985075i	0.0148149	+	0.999890i	$0.495284\pi$
$644$		0			0
$645$	−4.99566	−	4.99566i	−0.196704	−	0.196704i
$646$		0			0
$647$			15.0737i			0.592609i	0.955094	+	0.296304i	$0.0957543\pi$
$647$			15.0737i			0.592609i	−0.955094	+	0.296304i	$0.904246\pi$
$648$		0			0
$649$			16.9940i			0.667072i
$650$		0			0
$651$	−3.32938	−	3.32938i	−0.130489	−	0.130489i
$652$		0			0
$653$	17.3955	−	17.3955i	0.680740	−	0.680740i	−0.279427	−	0.960167i	$-0.590145\pi$
$653$	17.3955	−	17.3955i	0.680740	−	0.680740i	0.960167	+	0.279427i	$0.0901445\pi$
$654$		0			0
$655$	19.7940			0.773415
$656$		0			0
$657$	27.2234			1.06209
$658$		0			0
$659$	−28.0617	+	28.0617i	−1.09313	+	1.09313i	−0.0979348	+	0.995193i	$0.531224\pi$
$659$	−28.0617	+	28.0617i	−1.09313	+	1.09313i	−0.995193	+	0.0979348i	$0.968776\pi$
$660$		0			0
$661$	14.2661	+	14.2661i	0.554888	+	0.554888i	0.927848	−	0.372959i	$-0.121657\pi$
$661$	14.2661	+	14.2661i	0.554888	+	0.554888i	−0.372959	+	0.927848i	$0.621657\pi$
$662$		0			0
$663$			37.9881i			1.47534i
$664$		0			0
$665$		−	4.95375i		−	0.192098i
$666$		0			0
$667$	−28.7549	−	28.7549i	−1.11339	−	1.11339i
$668$		0			0
$669$	13.6346	−	13.6346i	0.527143	−	0.527143i
$670$		0			0
$671$	−6.62035			−0.255576
$672$		0			0
$673$	−20.0237			−0.771859			−0.385929	−	0.922528i	$-0.626119\pi$
$673$	−20.0237			−0.771859			−0.385929	+	0.922528i	$0.626119\pi$
$674$		0			0
$675$	3.38264	−	3.38264i	0.130198	−	0.130198i
$676$		0			0
$677$	−23.2930	−	23.2930i	−0.895224	−	0.895224i	0.0997846	−	0.995009i	$-0.468185\pi$
$677$	−23.2930	−	23.2930i	−0.895224	−	0.895224i	−0.995009	+	0.0997846i	$0.968185\pi$
$678$		0			0
$679$			3.95386i			0.151735i
$680$		0			0
$681$		−	6.07967i		−	0.232973i
$682$		0			0
$683$	−0.0776228	−	0.0776228i	−0.00297016	−	0.00297016i	0.705620	−	0.708590i	$-0.250669\pi$
$683$	−0.0776228	−	0.0776228i	−0.00297016	−	0.00297016i	−0.708590	+	0.705620i	$0.750669\pi$
$684$		0			0
$685$	11.3845	−	11.3845i	0.434978	−	0.434978i
$686$		0			0
$687$	3.11955			0.119018
$688$		0			0
$689$	−48.4883			−1.84726
$690$		0			0
$691$	5.35886	−	5.35886i	0.203861	−	0.203861i	−0.597791	−	0.801652i	$-0.703955\pi$
$691$	5.35886	−	5.35886i	0.203861	−	0.203861i	0.801652	+	0.597791i	$0.203955\pi$
$692$		0			0
$693$	−2.04711	−	2.04711i	−0.0777633	−	0.0777633i
$694$		0			0
$695$		−	3.36920i		−	0.127801i
$696$		0			0
$697$			64.4527i			2.44132i
$698$		0			0
$699$	−13.0582	−	13.0582i	−0.493905	−	0.493905i
$700$		0			0
$701$	−10.9411	+	10.9411i	−0.413240	+	0.413240i	−0.882866	−	0.469626i	$-0.844389\pi$
$701$	−10.9411	+	10.9411i	−0.413240	+	0.413240i	0.469626	+	0.882866i	$0.344389\pi$
$702$		0			0
$703$	3.96149			0.149410
$704$		0			0
$705$	0.321249			0.0120989
$706$		0			0
$707$	3.29042	−	3.29042i	0.123749	−	0.123749i
$708$		0			0
$709$	−25.2552	−	25.2552i	−0.948477	−	0.948477i	0.0502589	−	0.998736i	$-0.483995\pi$
$709$	−25.2552	−	25.2552i	−0.948477	−	0.948477i	−0.998736	+	0.0502589i	$0.983995\pi$
$710$		0			0
$711$		−	14.7183i		−	0.551979i
$712$		0			0
$713$			27.0454i			1.01286i
$714$		0			0
$715$	6.37275	+	6.37275i	0.238327	+	0.238327i
$716$		0			0
$717$	9.82780	−	9.82780i	0.367026	−	0.367026i
$718$		0			0
$719$	−6.19189			−0.230919			−0.115459	−	0.993312i	$-0.536834\pi$
$719$	−6.19189			−0.230919			−0.115459	+	0.993312i	$0.536834\pi$
$720$		0			0
$721$	−10.7702			−0.401104
$722$		0			0
$723$	−1.75091	+	1.75091i	−0.0651171	+	0.0651171i
$724$		0			0
$725$	5.36906	+	5.36906i	0.199402	+	0.199402i
$726$		0			0
$727$			15.1530i			0.561992i	0.959709	+	0.280996i	$0.0906648\pi$
$727$			15.1530i			0.561992i	−0.959709	+	0.280996i	$0.909335\pi$
$728$		0			0
$729$			9.26554i			0.343168i
$730$		0			0
$731$	−32.9114	−	32.9114i	−1.21727	−	1.21727i
$732$		0			0
$733$	0.627547	−	0.627547i	0.0231790	−	0.0231790i	−0.695422	−	0.718601i	$-0.744783\pi$
$733$	0.627547	−	0.627547i	0.0231790	−	0.0231790i	0.718601	+	0.695422i	$0.244783\pi$
$734$		0			0
$735$	0.932392			0.0343918
$736$		0			0
$737$	10.1704			0.374632
$738$		0			0
$739$	−17.5942	+	17.5942i	−0.647214	+	0.647214i	−0.952319	−	0.305105i	$-0.901308\pi$
$739$	−17.5942	+	17.5942i	−0.647214	+	0.647214i	0.305105	+	0.952319i	$0.401308\pi$
$740$		0			0
$741$	−21.6628	−	21.6628i	−0.795803	−	0.795803i
$742$		0			0
$743$		−	30.4930i		−	1.11868i	−0.828938	−	0.559340i	$-0.811054\pi$
$743$		−	30.4930i		−	1.11868i	0.828938	−	0.559340i	$-0.188946\pi$
$744$		0			0
$745$			13.9310i			0.510391i
$746$		0			0
$747$	0.115608	+	0.115608i	0.00422987	+	0.00422987i
$748$		0			0
$749$	−6.21743	+	6.21743i	−0.227180	+	0.227180i
$750$		0			0
$751$	34.8167			1.27048			0.635240	−	0.772315i	$-0.280901\pi$
$751$	34.8167			1.27048			0.635240	+	0.772315i	$0.280901\pi$
$752$		0			0
$753$	25.2158			0.918913
$754$		0			0
$755$	4.63277	−	4.63277i	0.168604	−	0.168604i
$756$		0			0
$757$	−12.8210	−	12.8210i	−0.465985	−	0.465985i	0.434626	−	0.900611i	$-0.356881\pi$
$757$	−12.8210	−	12.8210i	−0.465985	−	0.465985i	−0.900611	+	0.434626i	$0.856881\pi$
$758$		0			0
$759$		−	6.78511i		−	0.246284i
$760$		0			0
$761$			3.04532i			0.110393i	0.998476	+	0.0551964i	$0.0175785\pi$
$761$			3.04532i			0.110393i	−0.998476	+	0.0551964i	$0.982421\pi$
$762$		0			0
$763$	2.44960	+	2.44960i	0.0886814	+	0.0886814i
$764$		0			0
$765$	9.25439	−	9.25439i	0.334593	−	0.334593i
$766$		0			0
$767$	82.9559			2.99536
$768$		0			0
$769$	−7.95026			−0.286694			−0.143347	−	0.989673i	$-0.545786\pi$
$769$	−7.95026			−0.286694			−0.143347	+	0.989673i	$0.545786\pi$
$770$		0			0
$771$	9.70892	−	9.70892i	0.349658	−	0.349658i
$772$		0			0
$773$	−13.7659	−	13.7659i	−0.495125	−	0.495125i	0.414791	−	0.909917i	$-0.363855\pi$
$773$	−13.7659	−	13.7659i	−0.495125	−	0.495125i	−0.909917	+	0.414791i	$0.863855\pi$
$774$		0			0
$775$		−	5.04987i		−	0.181397i
$776$		0			0
$777$			0.745629i			0.0267493i
$778$		0			0
$779$	−36.7543	−	36.7543i	−1.31686	−	1.31686i
$780$		0			0
$781$	1.52022	−	1.52022i	0.0543978	−	0.0543978i
$782$		0			0
$783$	−36.3232			−1.29808
$784$		0			0
$785$	−2.23788			−0.0798735
$786$		0			0
$787$	−21.7742	+	21.7742i	−0.776168	+	0.776168i	−0.979177	−	0.203009i	$-0.934928\pi$
$787$	−21.7742	+	21.7742i	−0.776168	+	0.776168i	0.203009	+	0.979177i	$0.434928\pi$
$788$		0			0
$789$	−17.1295	−	17.1295i	−0.609828	−	0.609828i
$790$		0			0
$791$			1.35950i			0.0483381i
$792$		0			0
$793$			32.3172i			1.14762i
$794$		0			0
$795$	−4.81974	−	4.81974i	−0.170939	−	0.170939i
$796$		0			0
$797$	29.1965	−	29.1965i	1.03419	−	1.03419i	0.0348005	−	0.999394i	$-0.488920\pi$
$797$	29.1965	−	29.1965i	1.03419	−	1.03419i	0.999394	−	0.0348005i	$-0.0110796\pi$
$798$		0			0
$799$	2.11639			0.0748724
$800$		0			0
$801$	−28.0382			−0.990680
$802$		0			0
$803$	−12.2761	+	12.2761i	−0.433215	+	0.433215i
$804$		0			0
$805$	−3.78703	−	3.78703i	−0.133475	−	0.133475i
$806$		0			0
$807$		−	13.0747i		−	0.460251i
$808$		0			0
$809$		−	9.53368i		−	0.335186i	−0.985856	−	0.167593i	$-0.946400\pi$
$809$		−	9.53368i		−	0.335186i	0.985856	−	0.167593i	$-0.0535995\pi$
$810$		0			0
$811$	21.2501	+	21.2501i	0.746192	+	0.746192i	0.973762	−	0.227570i	$-0.0730780\pi$
$811$	21.2501	+	21.2501i	0.746192	+	0.746192i	−0.227570	+	0.973762i	$0.573078\pi$
$812$		0			0
$813$	−8.65891	+	8.65891i	−0.303681	+	0.303681i
$814$		0			0
$815$	16.3660			0.573277
$816$		0			0
$817$	37.5356			1.31320
$818$		0			0
$819$	−9.99294	+	9.99294i	−0.349181	+	0.349181i
$820$		0			0
$821$	23.8253	+	23.8253i	0.831510	+	0.831510i	0.987723	−	0.156213i	$-0.0499287\pi$
$821$	23.8253	+	23.8253i	0.831510	+	0.831510i	−0.156213	+	0.987723i	$0.549929\pi$
$822$		0			0
$823$		−	46.4651i		−	1.61967i	−0.586657	−	0.809836i	$-0.699556\pi$
$823$		−	46.4651i		−	1.61967i	0.586657	−	0.809836i	$-0.300444\pi$
$824$		0			0
$825$			1.26690i			0.0441079i
$826$		0			0
$827$	−26.0985	−	26.0985i	−0.907533	−	0.907533i	0.0885400	−	0.996073i	$-0.471780\pi$
$827$	−26.0985	−	26.0985i	−0.907533	−	0.907533i	−0.996073	+	0.0885400i	$0.971780\pi$
$828$		0			0
$829$	−1.55555	+	1.55555i	−0.0540266	+	0.0540266i	−0.733604	−	0.679577i	$-0.762163\pi$
$829$	−1.55555	+	1.55555i	−0.0540266	+	0.0540266i	0.679577	+	0.733604i	$0.262163\pi$
$830$		0			0
$831$	−20.6050			−0.714781
$832$		0			0
$833$	6.14259			0.212828
$834$		0			0
$835$	−1.55408	+	1.55408i	−0.0537813	+	0.0537813i
$836$		0			0
$837$	17.0819	+	17.0819i	0.590436	+	0.590436i
$838$		0			0
$839$		−	19.4089i		−	0.670069i	−0.942206	−	0.335035i	$-0.891252\pi$
$839$		−	19.4089i		−	0.670069i	0.942206	−	0.335035i	$-0.108748\pi$
$840$		0			0
$841$		−	28.6536i		−	0.988054i
$842$		0			0
$843$	12.5196	+	12.5196i	0.431198	+	0.431198i
$844$		0			0
$845$	21.9161	−	21.9161i	0.753937	−	0.753937i
$846$		0			0
$847$	−9.15375			−0.314527
$848$		0			0
$849$	9.13033			0.313352
$850$		0			0
$851$	3.02846	−	3.02846i	0.103814	−	0.103814i
$852$		0			0
$853$	−7.66028	−	7.66028i	−0.262283	−	0.262283i	0.563698	−	0.825981i	$-0.309378\pi$
$853$	−7.66028	−	7.66028i	−0.262283	−	0.262283i	−0.825981	+	0.563698i	$0.809378\pi$
$854$		0			0
$855$			10.5547i			0.360963i
$856$		0			0
$857$			19.5707i			0.668521i	0.942481	+	0.334261i	$0.108487\pi$
$857$			19.5707i			0.668521i	−0.942481	+	0.334261i	$0.891513\pi$
$858$		0			0
$859$	21.4084	+	21.4084i	0.730444	+	0.730444i	0.970708	−	0.240264i	$-0.0772340\pi$
$859$	21.4084	+	21.4084i	0.730444	+	0.730444i	−0.240264	+	0.970708i	$0.577234\pi$
$860$		0			0
$861$	6.91787	−	6.91787i	0.235761	−	0.235761i
$862$		0			0
$863$	−39.7438			−1.35290			−0.676448	−	0.736491i	$-0.736482\pi$
$863$	−39.7438			−1.35290			−0.676448	+	0.736491i	$0.736482\pi$
$864$		0			0
$865$	−5.87832			−0.199869
$866$		0			0
$867$	−13.6683	+	13.6683i	−0.464199	+	0.464199i
$868$		0			0
$869$	6.63707	+	6.63707i	0.225147	+	0.225147i
$870$		0			0
$871$		−	49.6468i		−	1.68222i
$872$		0			0
$873$		−	8.42427i		−	0.285118i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	−5.77601	+	5.77601i	−0.195042	+	0.195042i	−0.797871	−	0.602829i	$-0.794040\pi$
$877$	−5.77601	+	5.77601i	−0.195042	+	0.195042i	0.602829	+	0.797871i	$0.294040\pi$
$878$		0			0
$879$	3.06317			0.103318
$880$		0			0
$881$	8.78386			0.295936			0.147968	−	0.988992i	$-0.452727\pi$
$881$	8.78386			0.295936			0.147968	+	0.988992i	$0.452727\pi$
$882$		0			0
$883$	−21.6861	+	21.6861i	−0.729795	+	0.729795i	−0.970579	−	0.240784i	$-0.922596\pi$
$883$	−21.6861	+	21.6861i	−0.729795	+	0.729795i	0.240784	+	0.970579i	$0.422596\pi$
$884$		0			0
$885$	8.24582	+	8.24582i	0.277180	+	0.277180i
$886$		0			0
$887$			20.9414i			0.703142i	0.936161	+	0.351571i	$0.114352\pi$
$887$			20.9414i			0.703142i	−0.936161	+	0.351571i	$0.885648\pi$
$888$		0			0
$889$			9.62545i			0.322827i
$890$		0			0
$891$	1.85585	+	1.85585i	0.0621734	+	0.0621734i
$892$		0			0
$893$	−1.20688	+	1.20688i	−0.0403865	+	0.0403865i
$894$		0			0
$895$	19.2067			0.642010
$896$		0			0
$897$	−33.1214			−1.10589
$898$		0			0
$899$	−27.1130	+	27.1130i	−0.904270	+	0.904270i
$900$		0			0
$901$	−31.7524	−	31.7524i	−1.05783	−	1.05783i
$902$		0			0
$903$			7.06493i			0.235106i
$904$		0			0
$905$		−	11.7677i		−	0.391172i
$906$		0			0
$907$	−7.51323	−	7.51323i	−0.249473	−	0.249473i	0.571281	−	0.820754i	$-0.306446\pi$
$907$	−7.51323	−	7.51323i	−0.249473	−	0.249473i	−0.820754	+	0.571281i	$0.806446\pi$
$908$		0			0
$909$	−7.01072	+	7.01072i	−0.232531	+	0.232531i
$910$		0			0
$911$	30.1478			0.998843			0.499421	−	0.866359i	$-0.333546\pi$
$911$	30.1478			0.998843			0.499421	+	0.866359i	$0.333546\pi$
$912$		0			0
$913$	−0.104264			−0.00345065
$914$		0			0
$915$	−3.21233	+	3.21233i	−0.106196	+	0.106196i
$916$		0			0
$917$	−13.9965	−	13.9965i	−0.462204	−	0.462204i
$918$		0			0
$919$			28.8350i			0.951179i	0.879667	+	0.475589i	$0.157765\pi$
$919$			28.8350i			0.951179i	−0.879667	+	0.475589i	$0.842235\pi$
$920$		0			0
$921$		−	16.0481i		−	0.528803i
$922$		0			0
$923$	−7.42094	−	7.42094i	−0.244263	−	0.244263i
$924$		0			0
$925$	−0.565470	+	0.565470i	−0.0185925	+	0.0185925i
$926$		0			0
$927$	22.9475			0.753696
$928$		0			0
$929$	−3.82157			−0.125382			−0.0626908	−	0.998033i	$-0.519968\pi$
$929$	−3.82157			−0.125382			−0.0626908	+	0.998033i	$0.519968\pi$
$930$		0			0
$931$	−3.50283	+	3.50283i	−0.114801	+	0.114801i
$932$		0			0
$933$	4.05133	+	4.05133i	0.132635	+	0.132635i
$934$		0			0
$935$			8.34635i			0.272955i
$936$		0			0
$937$		−	6.92274i		−	0.226156i	−0.993586	−	0.113078i	$-0.963929\pi$
$937$		−	6.92274i		−	0.226156i	0.993586	−	0.113078i	$-0.0360710\pi$
$938$		0			0
$939$	9.81879	+	9.81879i	0.320424	+	0.320424i
$940$		0			0
$941$	2.23266	−	2.23266i	0.0727825	−	0.0727825i	−0.669778	−	0.742561i	$-0.733611\pi$
$941$	2.23266	−	2.23266i	0.0727825	−	0.0727825i	0.742561	+	0.669778i	$0.233611\pi$
$942$		0			0
$943$	−56.1956			−1.82998
$944$		0			0
$945$	−4.78377			−0.155616
$946$		0			0
$947$	1.96805	−	1.96805i	0.0639531	−	0.0639531i	−0.674407	−	0.738360i	$-0.735601\pi$
$947$	1.96805	−	1.96805i	0.0639531	−	0.0639531i	0.738360	+	0.674407i	$0.235601\pi$
$948$		0			0
$949$	59.9257	+	59.9257i	1.94527	+	1.94527i
$950$		0			0
$951$			1.52895i			0.0495796i
$952$		0			0
$953$		−	34.3506i		−	1.11273i	−0.830939	−	0.556363i	$-0.812196\pi$
$953$		−	34.3506i		−	1.11273i	0.830939	−	0.556363i	$-0.187804\pi$
$954$		0			0
$955$	−15.9765	−	15.9765i	−0.516988	−	0.516988i
$956$		0			0
$957$	6.80208	−	6.80208i	0.219880	−	0.219880i
$958$		0			0
$959$	−16.1000			−0.519898
$960$		0			0
$961$	−5.49882			−0.177381
$962$		0			0
$963$	13.2471	−	13.2471i	0.426883	−	0.426883i
$964$		0			0
$965$	−13.7204	−	13.7204i	−0.441676	−	0.441676i
$966$		0			0
$967$		−	55.3801i		−	1.78090i	−0.455076	−	0.890452i	$-0.650388\pi$
$967$		−	55.3801i		−	1.78090i	0.455076	−	0.890452i	$-0.349612\pi$
$968$		0			0
$969$		−	28.3717i		−	0.911429i
$970$		0			0
$971$	21.6248	+	21.6248i	0.693974	+	0.693974i	0.963104	−	0.269130i	$-0.0867360\pi$
$971$	21.6248	+	21.6248i	0.693974	+	0.693974i	−0.269130	+	0.963104i	$0.586736\pi$
$972$		0			0
$973$	−2.38238	+	2.38238i	−0.0763757	+	0.0763757i
$974$		0			0
$975$	6.18437			0.198058
$976$		0			0
$977$	26.7790			0.856737			0.428369	−	0.903604i	$-0.359088\pi$
$977$	26.7790			0.856737			0.428369	+	0.903604i	$0.359088\pi$
$978$		0			0
$979$	12.6435	−	12.6435i	0.404089	−	0.404089i
$980$		0			0
$981$	−5.21922	−	5.21922i	−0.166637	−	0.166637i
$982$		0			0
$983$			8.96003i			0.285781i	0.989739	+	0.142890i	$0.0456396\pi$
$983$			8.96003i			0.285781i	−0.989739	+	0.142890i	$0.954360\pi$
$984$		0			0
$985$			20.1094i			0.640738i
$986$		0			0
$987$	−0.227157	−	0.227157i	−0.00723050	−	0.00723050i
$988$		0			0
$989$	28.6951	−	28.6951i	0.912450	−	0.912450i
$990$		0			0
$991$	36.1487			1.14830			0.574151	−	0.818750i	$-0.305332\pi$
$991$	36.1487			1.14830			0.574151	+	0.818750i	$0.305332\pi$
$992$		0			0
$993$	26.3633			0.836613
$994$		0			0
$995$	−12.0762	+	12.0762i	−0.382841	+	0.382841i
$996$		0			0
$997$	31.6707	+	31.6707i	1.00302	+	1.00302i	0.999995	+	0.00302495i	$0.000962875\pi$
$997$	31.6707	+	31.6707i	1.00302	+	1.00302i	0.00302495	+	0.999995i	$0.499037\pi$
$998$		0			0
$999$		−	3.82556i		−	0.121035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.9		44
4.3	odd	2		560.2.bd.a.421.8	yes	44
16.3	odd	4		560.2.bd.a.141.8	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.9		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.8	✓	44	16.3	odd	4
560.2.bd.a.421.8	yes	44	4.3	odd	2
2240.2.bd.a.561.9		44	1.1	even	1	trivial
2240.2.bd.a.1681.9		44	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.659301 + 0.659301i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.13064i q^{9} +O(q^{10})\)	\(q+(-0.659301 + 0.659301i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.13064i q^{9} +(-0.960793 - 0.960793i) q^{11} +(-4.69010 + 4.69010i) q^{13} -0.932392 q^{15} -6.14259 q^{17} +(3.50283 - 3.50283i) q^{19} +(0.659301 + 0.659301i) q^{21} -5.35566i q^{23} +1.00000i q^{25} +(-3.38264 - 3.38264i) q^{27} +(5.36906 - 5.36906i) q^{29} -5.04987 q^{31} +1.26690 q^{33} +(0.707107 - 0.707107i) q^{35} +(0.565470 + 0.565470i) q^{37} -6.18437i q^{39} -10.4927i q^{41} +(5.35789 + 5.35789i) q^{43} +(-1.50659 + 1.50659i) q^{45} -0.344543 q^{47} -1.00000 q^{49} +(4.04982 - 4.04982i) q^{51} +(5.16922 + 5.16922i) q^{53} -1.35877i q^{55} +4.61884i q^{57} +(-8.84373 - 8.84373i) q^{59} +(3.44525 - 3.44525i) q^{61} +2.13064 q^{63} -6.63280 q^{65} +(-5.29272 + 5.29272i) q^{67} +(3.53099 + 3.53099i) q^{69} +1.58226i q^{71} -12.7771i q^{73} +(-0.659301 - 0.659301i) q^{75} +(-0.960793 + 0.960793i) q^{77} -6.90790 q^{79} -1.93158 q^{81} +(0.0542596 - 0.0542596i) q^{83} +(-4.34347 - 4.34347i) q^{85} +7.07965i q^{87} +13.1595i q^{89} +(4.69010 + 4.69010i) q^{91} +(3.32938 - 3.32938i) q^{93} +4.95375 q^{95} -3.95386 q^{97} +(2.04711 - 2.04711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 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

L-functions

Modular forms

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