LMFDB - Embedded newform 2240.2.bd.a.561.16

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			561.16
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16279 - 1.16279i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +0.295857i q^{9} +O(q^{10})$	\(q+(1.16279 - 1.16279i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +0.295857i q^{9} +(-3.97270 - 3.97270i) q^{11} +(-1.48922 + 1.48922i) q^{13} +1.64443 q^{15} -6.33574 q^{17} +(-4.80932 + 4.80932i) q^{19} +(-1.16279 - 1.16279i) q^{21} -4.65754i q^{23} +1.00000i q^{25} +(3.83238 + 3.83238i) q^{27} +(-4.24816 + 4.24816i) q^{29} +0.0294487 q^{31} -9.23880 q^{33} +(0.707107 - 0.707107i) q^{35} +(-5.73990 - 5.73990i) q^{37} +3.46329i q^{39} +0.919426i q^{41} +(3.37767 + 3.37767i) q^{43} +(-0.209203 + 0.209203i) q^{45} -12.5540 q^{47} -1.00000 q^{49} +(-7.36711 + 7.36711i) q^{51} +(0.0243993 + 0.0243993i) q^{53} -5.61825i q^{55} +11.1844i q^{57} +(5.91263 + 5.91263i) q^{59} +(1.34761 - 1.34761i) q^{61} +0.295857 q^{63} -2.10608 q^{65} +(9.68994 - 9.68994i) q^{67} +(-5.41572 - 5.41572i) q^{69} -11.0515i q^{71} +10.5102i q^{73} +(1.16279 + 1.16279i) q^{75} +(-3.97270 + 3.97270i) q^{77} +4.67417 q^{79} +8.02490 q^{81} +(-4.38372 + 4.38372i) q^{83} +(-4.48005 - 4.48005i) q^{85} +9.87940i q^{87} -10.3471i q^{89} +(1.48922 + 1.48922i) q^{91} +(0.0342425 - 0.0342425i) q^{93} -6.80141 q^{95} +0.578738 q^{97} +(1.17535 - 1.17535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.16279	−	1.16279i	0.671335	−	0.671335i	−0.286689	−	0.958024i	$-0.592555\pi$
$3$	1.16279	−	1.16279i	0.671335	−	0.671335i	0.958024	+	0.286689i	$0.0925546\pi$
$4$		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
$9$			0.295857i			0.0986191i
$10$		0			0
$11$	−3.97270	−	3.97270i	−1.19781	−	1.19781i	−0.974820	−	0.222995i	$-0.928417\pi$
$11$	−3.97270	−	3.97270i	−1.19781	−	1.19781i	−0.222995	−	0.974820i	$-0.571583\pi$
$12$		0			0
$13$	−1.48922	+	1.48922i	−0.413035	+	0.413035i	−0.882795	−	0.469759i	$-0.844341\pi$
$13$	−1.48922	+	1.48922i	−0.413035	+	0.413035i	0.469759	+	0.882795i	$0.344341\pi$
$14$		0			0
$15$	1.64443			0.424589
$16$		0			0
$17$	−6.33574			−1.53664			−0.768321	−	0.640064i	$-0.778908\pi$
$17$	−6.33574			−1.53664			−0.768321	+	0.640064i	$0.778908\pi$
$18$		0			0
$19$	−4.80932	+	4.80932i	−1.10333	+	1.10333i	−0.109329	+	0.994006i	$0.534870\pi$
$19$	−4.80932	+	4.80932i	−1.10333	+	1.10333i	−0.994006	+	0.109329i	$0.965130\pi$
$20$		0			0
$21$	−1.16279	−	1.16279i	−0.253741	−	0.253741i
$22$		0			0
$23$		−	4.65754i		−	0.971165i	−0.874191	−	0.485582i	$-0.838608\pi$
$23$		−	4.65754i		−	0.971165i	0.874191	−	0.485582i	$-0.161392\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	3.83238	+	3.83238i	0.737541	+	0.737541i
$28$		0			0
$29$	−4.24816	+	4.24816i	−0.788863	+	0.788863i	−0.981308	−	0.192444i	$-0.938358\pi$
$29$	−4.24816	+	4.24816i	−0.788863	+	0.788863i	0.192444	+	0.981308i	$0.438358\pi$
$30$		0			0
$31$	0.0294487			0.00528914			0.00264457	−	0.999997i	$-0.499158\pi$
$31$	0.0294487			0.00528914			0.00264457	+	0.999997i	$0.499158\pi$
$32$		0			0
$33$	−9.23880			−1.60827
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	−5.73990	−	5.73990i	−0.943634	−	0.943634i	0.0548603	−	0.998494i	$-0.482529\pi$
$37$	−5.73990	−	5.73990i	−0.943634	−	0.943634i	−0.998494	+	0.0548603i	$0.982529\pi$
$38$		0			0
$39$			3.46329i			0.554570i
$40$		0			0
$41$			0.919426i			0.143590i	0.997419	+	0.0717951i	$0.0228728\pi$
$41$			0.919426i			0.143590i	−0.997419	+	0.0717951i	$0.977127\pi$
$42$		0			0
$43$	3.37767	+	3.37767i	0.515090	+	0.515090i	0.916082	−	0.400992i	$-0.131334\pi$
$43$	3.37767	+	3.37767i	0.515090	+	0.515090i	−0.400992	+	0.916082i	$0.631334\pi$
$44$		0			0
$45$	−0.209203	+	0.209203i	−0.0311861	+	0.0311861i
$46$		0			0
$47$	−12.5540			−1.83119			−0.915594	−	0.402104i	$-0.868279\pi$
$47$	−12.5540			−1.83119			−0.915594	+	0.402104i	$0.868279\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−7.36711	+	7.36711i	−1.03160	+	1.03160i
$52$		0			0
$53$	0.0243993	+	0.0243993i	0.00335151	+	0.00335151i	0.708781	−	0.705429i	$-0.249246\pi$
$53$	0.0243993	+	0.0243993i	0.00335151	+	0.00335151i	−0.705429	+	0.708781i	$0.749246\pi$
$54$		0			0
$55$		−	5.61825i		−	0.757565i
$56$		0			0
$57$			11.1844i			1.48141i
$58$		0			0
$59$	5.91263	+	5.91263i	0.769759	+	0.769759i	0.978064	−	0.208305i	$-0.0667947\pi$
$59$	5.91263	+	5.91263i	0.769759	+	0.769759i	−0.208305	+	0.978064i	$0.566795\pi$
$60$		0			0
$61$	1.34761	−	1.34761i	0.172543	−	0.172543i	−0.615552	−	0.788096i	$-0.711067\pi$
$61$	1.34761	−	1.34761i	0.172543	−	0.172543i	0.788096	+	0.615552i	$0.211067\pi$
$62$		0			0
$63$	0.295857			0.0372745
$64$		0			0
$65$	−2.10608			−0.261226
$66$		0			0
$67$	9.68994	−	9.68994i	1.18381	−	1.18381i	0.205067	−	0.978748i	$-0.434259\pi$
$67$	9.68994	−	9.68994i	1.18381	−	1.18381i	0.978748	−	0.205067i	$-0.0657412\pi$
$68$		0			0
$69$	−5.41572	−	5.41572i	−0.651977	−	0.651977i
$70$		0			0
$71$		−	11.0515i		−	1.31157i	−0.754948	−	0.655784i	$-0.772338\pi$
$71$		−	11.0515i		−	1.31157i	0.754948	−	0.655784i	$-0.227662\pi$
$72$		0			0
$73$			10.5102i			1.23012i	0.788480	+	0.615060i	$0.210868\pi$
$73$			10.5102i			1.23012i	−0.788480	+	0.615060i	$0.789132\pi$
$74$		0			0
$75$	1.16279	+	1.16279i	0.134267	+	0.134267i
$76$		0			0
$77$	−3.97270	+	3.97270i	−0.452731	+	0.452731i
$78$		0			0
$79$	4.67417			0.525885			0.262943	−	0.964811i	$-0.415307\pi$
$79$	4.67417			0.525885			0.262943	+	0.964811i	$0.415307\pi$
$80$		0			0
$81$	8.02490			0.891655
$82$		0			0
$83$	−4.38372	+	4.38372i	−0.481175	+	0.481175i	−0.905507	−	0.424331i	$-0.860509\pi$
$83$	−4.38372	+	4.38372i	−0.481175	+	0.481175i	0.424331	+	0.905507i	$0.360509\pi$
$84$		0			0
$85$	−4.48005	−	4.48005i	−0.485929	−	0.485929i
$86$		0			0
$87$			9.87940i			1.05918i
$88$		0			0
$89$		−	10.3471i		−	1.09679i	−0.836220	−	0.548394i	$-0.815239\pi$
$89$		−	10.3471i		−	1.09679i	0.836220	−	0.548394i	$-0.184761\pi$
$90$		0			0
$91$	1.48922	+	1.48922i	0.156113	+	0.156113i
$92$		0			0
$93$	0.0342425	−	0.0342425i	0.00355078	−	0.00355078i
$94$		0			0
$95$	−6.80141			−0.697810
$96$		0			0
$97$	0.578738			0.0587619			0.0293810	−	0.999568i	$-0.490646\pi$
$97$	0.578738			0.0587619			0.0293810	+	0.999568i	$0.490646\pi$
$98$		0			0
$99$	1.17535	−	1.17535i	0.118127	−	0.118127i
$100$		0			0
$101$	−1.30170	−	1.30170i	−0.129524	−	0.129524i	0.639373	−	0.768897i	$-0.279194\pi$
$101$	−1.30170	−	1.30170i	−0.129524	−	0.129524i	−0.768897	+	0.639373i	$0.779194\pi$
$102$		0			0
$103$		−	12.6795i		−	1.24935i	−0.780885	−	0.624675i	$-0.785231\pi$
$103$		−	12.6795i		−	1.24935i	0.780885	−	0.624675i	$-0.214769\pi$
$104$		0			0
$105$		−	1.64443i		−	0.160480i
$106$		0			0
$107$	−7.36414	−	7.36414i	−0.711919	−	0.711919i	0.255018	−	0.966936i	$-0.417919\pi$
$107$	−7.36414	−	7.36414i	−0.711919	−	0.711919i	−0.966936	+	0.255018i	$0.917919\pi$
$108$		0			0
$109$	−4.86515	+	4.86515i	−0.465997	+	0.465997i	−0.900615	−	0.434618i	$-0.856883\pi$
$109$	−4.86515	+	4.86515i	−0.465997	+	0.465997i	0.434618	+	0.900615i	$0.356883\pi$
$110$		0			0
$111$	−13.3486			−1.26699
$112$		0			0
$113$	9.99365			0.940124			0.470062	−	0.882633i	$-0.344232\pi$
$113$	9.99365			0.940124			0.470062	+	0.882633i	$0.344232\pi$
$114$		0			0
$115$	3.29338	−	3.29338i	0.307109	−	0.307109i
$116$		0			0
$117$	−0.440597	−	0.440597i	−0.0407332	−	0.0407332i
$118$		0			0
$119$			6.33574i			0.580796i
$120$		0			0
$121$			20.5647i			1.86952i
$122$		0			0
$123$	1.06910	+	1.06910i	0.0963971	+	0.0963971i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−2.74622			−0.243687			−0.121844	−	0.992549i	$-0.538881\pi$
$127$	−2.74622			−0.243687			−0.121844	+	0.992549i	$0.538881\pi$
$128$		0			0
$129$	7.85502			0.691596
$130$		0			0
$131$	−5.19885	+	5.19885i	−0.454226	+	0.454226i	−0.896754	−	0.442529i	$-0.854081\pi$
$131$	−5.19885	+	5.19885i	−0.454226	+	0.454226i	0.442529	+	0.896754i	$0.354081\pi$
$132$		0			0
$133$	4.80932	+	4.80932i	0.417021	+	0.417021i
$134$		0			0
$135$			5.41980i			0.466462i
$136$		0			0
$137$		−	12.8527i		−	1.09808i	−0.835796	−	0.549041i	$-0.814993\pi$
$137$		−	12.8527i		−	1.09808i	0.835796	−	0.549041i	$-0.185007\pi$
$138$		0			0
$139$	−3.68042	−	3.68042i	−0.312169	−	0.312169i	0.533580	−	0.845749i	$-0.320846\pi$
$139$	−3.68042	−	3.68042i	−0.312169	−	0.312169i	−0.845749	+	0.533580i	$0.820846\pi$
$140$		0			0
$141$	−14.5976	+	14.5976i	−1.22934	+	1.22934i
$142$		0			0
$143$	11.8325			0.989480
$144$		0			0
$145$	−6.00781			−0.498921
$146$		0			0
$147$	−1.16279	+	1.16279i	−0.0959050	+	0.0959050i
$148$		0			0
$149$	5.25342	+	5.25342i	0.430377	+	0.430377i	0.888756	−	0.458380i	$-0.151570\pi$
$149$	5.25342	+	5.25342i	0.430377	+	0.430377i	−0.458380	+	0.888756i	$0.651570\pi$
$150$		0			0
$151$		−	17.1127i		−	1.39261i	−0.717745	−	0.696306i	$-0.754826\pi$
$151$		−	17.1127i		−	1.39261i	0.717745	−	0.696306i	$-0.245174\pi$
$152$		0			0
$153$		−	1.87448i		−	0.151542i
$154$		0			0
$155$	0.0208234	+	0.0208234i	0.00167257	+	0.00167257i
$156$		0			0
$157$	9.91207	−	9.91207i	0.791069	−	0.791069i	−0.190599	−	0.981668i	$-0.561043\pi$
$157$	9.91207	−	9.91207i	0.791069	−	0.791069i	0.981668	+	0.190599i	$0.0610430\pi$
$158$		0			0
$159$	0.0567424			0.00449997
$160$		0			0
$161$	−4.65754			−0.367066
$162$		0			0
$163$	−16.7175	+	16.7175i	−1.30942	+	1.30942i	−0.387580	+	0.921836i	$0.626689\pi$
$163$	−16.7175	+	16.7175i	−1.30942	+	1.30942i	−0.921836	+	0.387580i	$0.873311\pi$
$164$		0			0
$165$	−6.53282	−	6.53282i	−0.508579	−	0.508579i
$166$		0			0
$167$		−	20.9113i		−	1.61817i	−0.587695	−	0.809083i	$-0.699964\pi$
$167$		−	20.9113i		−	1.61817i	0.587695	−	0.809083i	$-0.300036\pi$
$168$		0			0
$169$			8.56445i			0.658804i
$170$		0			0
$171$	−1.42287	−	1.42287i	−0.108810	−	0.108810i
$172$		0			0
$173$	−2.68169	+	2.68169i	−0.203885	+	0.203885i	−0.801662	−	0.597777i	$-0.796051\pi$
$173$	−2.68169	+	2.68169i	−0.203885	+	0.203885i	0.597777	+	0.801662i	$0.296051\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	13.7502			1.03353
$178$		0			0
$179$	−8.19420	+	8.19420i	−0.612464	+	0.612464i	−0.943587	−	0.331124i	$-0.892572\pi$
$179$	−8.19420	+	8.19420i	−0.612464	+	0.612464i	0.331124	+	0.943587i	$0.392572\pi$
$180$		0			0
$181$	6.86243	+	6.86243i	0.510080	+	0.510080i	0.914551	−	0.404471i	$-0.132544\pi$
$181$	6.86243	+	6.86243i	0.510080	+	0.510080i	−0.404471	+	0.914551i	$0.632544\pi$
$182$		0			0
$183$		−	3.13396i		−	0.231669i
$184$		0			0
$185$		−	8.11744i		−	0.596806i
$186$		0			0
$187$	25.1700	+	25.1700i	1.84061	+	1.84061i
$188$		0			0
$189$	3.83238	−	3.83238i	0.278764	−	0.278764i
$190$		0			0
$191$	−13.7694			−0.996319			−0.498159	−	0.867085i	$-0.665991\pi$
$191$	−13.7694			−0.996319			−0.498159	+	0.867085i	$0.665991\pi$
$192$		0			0
$193$	−12.6996			−0.914140			−0.457070	−	0.889431i	$-0.651101\pi$
$193$	−12.6996			−0.914140			−0.457070	+	0.889431i	$0.651101\pi$
$194$		0			0
$195$	−2.44891	+	2.44891i	−0.175370	+	0.175370i
$196$		0			0
$197$	18.9643	+	18.9643i	1.35115	+	1.35115i	0.884380	+	0.466768i	$0.154582\pi$
$197$	18.9643	+	18.9643i	1.35115	+	1.35115i	0.466768	+	0.884380i	$0.345418\pi$
$198$		0			0
$199$			15.7513i			1.11658i	0.829645	+	0.558291i	$0.188543\pi$
$199$			15.7513i			1.11658i	−0.829645	+	0.558291i	$0.811457\pi$
$200$		0			0
$201$		−	22.5347i		−	1.58947i
$202$		0			0
$203$	4.24816	+	4.24816i	0.298162	+	0.298162i
$204$		0			0
$205$	−0.650132	+	0.650132i	−0.0454072	+	0.0454072i
$206$		0			0
$207$	1.37797			0.0957754
$208$		0			0
$209$	38.2120			2.64318
$210$		0			0
$211$	−17.8595	+	17.8595i	−1.22950	+	1.22950i	−0.265341	+	0.964155i	$0.585485\pi$
$211$	−17.8595	+	17.8595i	−1.22950	+	1.22950i	−0.964155	+	0.265341i	$0.914515\pi$
$212$		0			0
$213$	−12.8505	−	12.8505i	−0.880502	−	0.880502i
$214$		0			0
$215$			4.77675i			0.325772i
$216$		0			0
$217$		−	0.0294487i		−	0.00199911i
$218$		0			0
$219$	12.2211	+	12.2211i	0.825823	+	0.825823i
$220$		0			0
$221$	9.43531	−	9.43531i	0.634688	−	0.634688i
$222$		0			0
$223$	13.5902			0.910070			0.455035	−	0.890473i	$-0.349627\pi$
$223$	13.5902			0.910070			0.455035	+	0.890473i	$0.349627\pi$
$224$		0			0
$225$	−0.295857			−0.0197238
$226$		0			0
$227$	−7.80140	+	7.80140i	−0.517797	+	0.517797i	−0.916904	−	0.399107i	$-0.869320\pi$
$227$	−7.80140	+	7.80140i	−0.517797	+	0.517797i	0.399107	+	0.916904i	$0.369320\pi$
$228$		0			0
$229$	−10.9217	−	10.9217i	−0.721728	−	0.721728i	0.247229	−	0.968957i	$-0.420480\pi$
$229$	−10.9217	−	10.9217i	−0.721728	−	0.721728i	−0.968957	+	0.247229i	$0.920480\pi$
$230$		0			0
$231$			9.23880i			0.607869i
$232$		0			0
$233$			3.44271i			0.225539i	0.993621	+	0.112770i	$0.0359722\pi$
$233$			3.44271i			0.225539i	−0.993621	+	0.112770i	$0.964028\pi$
$234$		0			0
$235$	−8.87701	−	8.87701i	−0.579072	−	0.579072i
$236$		0			0
$237$	5.43506	−	5.43506i	0.353045	−	0.353045i
$238$		0			0
$239$	5.82823			0.376997			0.188498	−	0.982073i	$-0.439638\pi$
$239$	5.82823			0.376997			0.188498	+	0.982073i	$0.439638\pi$
$240$		0			0
$241$	−9.14801			−0.589275			−0.294637	−	0.955609i	$-0.595199\pi$
$241$	−9.14801			−0.589275			−0.294637	+	0.955609i	$0.595199\pi$
$242$		0			0
$243$	−2.16589	+	2.16589i	−0.138942	+	0.138942i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	14.3243i		−	0.911432i
$248$		0			0
$249$			10.1946i			0.646060i
$250$		0			0
$251$	−2.71270	−	2.71270i	−0.171224	−	0.171224i	0.616293	−	0.787517i	$-0.288634\pi$
$251$	−2.71270	−	2.71270i	−0.171224	−	0.171224i	−0.787517	+	0.616293i	$0.788634\pi$
$252$		0			0
$253$	−18.5030	+	18.5030i	−1.16328	+	1.16328i
$254$		0			0
$255$	−10.4187			−0.652442
$256$		0			0
$257$	20.6688			1.28929			0.644643	−	0.764484i	$-0.277006\pi$
$257$	20.6688			1.28929			0.644643	+	0.764484i	$0.277006\pi$
$258$		0			0
$259$	−5.73990	+	5.73990i	−0.356660	+	0.356660i
$260$		0			0
$261$	−1.25685	−	1.25685i	−0.0777970	−	0.0777970i
$262$		0			0
$263$			0.726418i			0.0447929i	0.999749	+	0.0223964i	$0.00712960\pi$
$263$			0.726418i			0.0447929i	−0.999749	+	0.0223964i	$0.992870\pi$
$264$		0			0
$265$			0.0345059i			0.00211968i
$266$		0			0
$267$	−12.0314	−	12.0314i	−0.736312	−	0.736312i
$268$		0			0
$269$	−21.3362	+	21.3362i	−1.30089	+	1.30089i	−0.373098	+	0.927792i	$0.621704\pi$
$269$	−21.3362	+	21.3362i	−1.30089	+	1.30089i	−0.927792	+	0.373098i	$0.878296\pi$
$270$		0			0
$271$	−12.5537			−0.762580			−0.381290	−	0.924455i	$-0.624520\pi$
$271$	−12.5537			−0.762580			−0.381290	+	0.924455i	$0.624520\pi$
$272$		0			0
$273$	3.46329			0.209608
$274$		0			0
$275$	3.97270	−	3.97270i	0.239563	−	0.239563i
$276$		0			0
$277$	−12.8485	−	12.8485i	−0.771994	−	0.771994i	0.206461	−	0.978455i	$-0.433805\pi$
$277$	−12.8485	−	12.8485i	−0.771994	−	0.771994i	−0.978455	+	0.206461i	$0.933805\pi$
$278$		0			0
$279$			0.00871261i			0.000521610i
$280$		0			0
$281$		−	11.9678i		−	0.713941i	−0.934116	−	0.356970i	$-0.883810\pi$
$281$		−	11.9678i		−	0.713941i	0.934116	−	0.356970i	$-0.116190\pi$
$282$		0			0
$283$	9.50022	+	9.50022i	0.564730	+	0.564730i	0.930647	−	0.365918i	$-0.119245\pi$
$283$	9.50022	+	9.50022i	0.564730	+	0.564730i	−0.365918	+	0.930647i	$0.619245\pi$
$284$		0			0
$285$	−7.90858	+	7.90858i	−0.468464	+	0.468464i
$286$		0			0
$287$	0.919426			0.0542720
$288$		0			0
$289$	23.1416			1.36127
$290$		0			0
$291$	0.672948	−	0.672948i	0.0394489	−	0.0394489i
$292$		0			0
$293$	−8.77462	−	8.77462i	−0.512619	−	0.512619i	0.402709	−	0.915328i	$-0.368069\pi$
$293$	−8.77462	−	8.77462i	−0.512619	−	0.512619i	−0.915328	+	0.402709i	$0.868069\pi$
$294$		0			0
$295$			8.36172i			0.486838i
$296$		0			0
$297$		−	30.4498i		−	1.76688i
$298$		0			0
$299$	6.93610	+	6.93610i	0.401125	+	0.401125i
$300$		0			0
$301$	3.37767	−	3.37767i	0.194686	−	0.194686i
$302$		0			0
$303$	−3.02720			−0.173908
$304$		0			0
$305$	1.90580			0.109126
$306$		0			0
$307$	4.72956	−	4.72956i	0.269930	−	0.269930i	−0.559142	−	0.829072i	$-0.688869\pi$
$307$	4.72956	−	4.72956i	0.269930	−	0.269930i	0.829072	+	0.559142i	$0.188869\pi$
$308$		0			0
$309$	−14.7436	−	14.7436i	−0.838733	−	0.838733i
$310$		0			0
$311$		−	18.2568i		−	1.03525i	−0.855608	−	0.517625i	$-0.826816\pi$
$311$		−	18.2568i		−	1.03525i	0.855608	−	0.517625i	$-0.173184\pi$
$312$		0			0
$313$		−	1.15335i		−	0.0651914i	−0.999469	−	0.0325957i	$-0.989623\pi$
$313$		−	1.15335i		−	0.0651914i	0.999469	−	0.0325957i	$-0.0103774\pi$
$314$		0			0
$315$	0.209203	+	0.209203i	0.0117872	+	0.0117872i
$316$		0			0
$317$	8.28593	−	8.28593i	0.465384	−	0.465384i	−0.435031	−	0.900415i	$-0.643263\pi$
$317$	8.28593	−	8.28593i	0.465384	−	0.465384i	0.900415	+	0.435031i	$0.143263\pi$
$318$		0			0
$319$	33.7533			1.88982
$320$		0			0
$321$	−17.1258			−0.955872
$322$		0			0
$323$	30.4706	−	30.4706i	1.69543	−	1.69543i
$324$		0			0
$325$	−1.48922	−	1.48922i	−0.0826071	−	0.0826071i
$326$		0			0
$327$			11.3142i			0.625679i
$328$		0			0
$329$			12.5540i			0.692124i
$330$		0			0
$331$	−10.4064	−	10.4064i	−0.571989	−	0.571989i	0.360695	−	0.932684i	$-0.382540\pi$
$331$	−10.4064	−	10.4064i	−0.571989	−	0.571989i	−0.932684	+	0.360695i	$0.882540\pi$
$332$		0			0
$333$	1.69819	−	1.69819i	0.0930603	−	0.0930603i
$334$		0			0
$335$	13.7036			0.748710
$336$		0			0
$337$	12.3663			0.673637			0.336819	−	0.941570i	$-0.390649\pi$
$337$	12.3663			0.673637			0.336819	+	0.941570i	$0.390649\pi$
$338$		0			0
$339$	11.6205	−	11.6205i	0.631138	−	0.631138i
$340$		0			0
$341$	−0.116991	−	0.116991i	−0.00633541	−	0.00633541i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	7.65899i		−	0.412346i
$346$		0			0
$347$	−11.8205	−	11.8205i	−0.634556	−	0.634556i	0.314651	−	0.949207i	$-0.398113\pi$
$347$	−11.8205	−	11.8205i	−0.634556	−	0.634556i	−0.949207	+	0.314651i	$0.898113\pi$
$348$		0			0
$349$	6.12765	−	6.12765i	0.328006	−	0.328006i	−0.523822	−	0.851828i	$-0.675494\pi$
$349$	6.12765	−	6.12765i	0.328006	−	0.328006i	0.851828	+	0.523822i	$0.175494\pi$
$350$		0			0
$351$	−11.4145			−0.609261
$352$		0			0
$353$	13.4244			0.714510			0.357255	−	0.934007i	$-0.383713\pi$
$353$	13.4244			0.714510			0.357255	+	0.934007i	$0.383713\pi$
$354$		0			0
$355$	7.81457	−	7.81457i	0.414754	−	0.414754i
$356$		0			0
$357$	7.36711	+	7.36711i	0.389909	+	0.389909i
$358$		0			0
$359$		−	10.4387i		−	0.550934i	−0.961310	−	0.275467i	$-0.911167\pi$
$359$		−	10.4387i		−	0.550934i	0.961310	−	0.275467i	$-0.0888325\pi$
$360$		0			0
$361$		−	27.2592i		−	1.43469i
$362$		0			0
$363$	23.9124	+	23.9124i	1.25507	+	1.25507i
$364$		0			0
$365$	−7.43180	+	7.43180i	−0.388998	+	0.388998i
$366$		0			0
$367$	9.04263			0.472022			0.236011	−	0.971750i	$-0.424160\pi$
$367$	9.04263			0.472022			0.236011	+	0.971750i	$0.424160\pi$
$368$		0			0
$369$	−0.272019			−0.0141607
$370$		0			0
$371$	0.0243993	−	0.0243993i	0.00126675	−	0.00126675i
$372$		0			0
$373$	23.2031	+	23.2031i	1.20141	+	1.20141i	0.973738	+	0.227673i	$0.0731119\pi$
$373$	23.2031	+	23.2031i	1.20141	+	1.20141i	0.227673	+	0.973738i	$0.426888\pi$
$374$		0			0
$375$			1.64443i			0.0849179i
$376$		0			0
$377$		−	12.6529i		−	0.651657i
$378$		0			0
$379$	−14.5814	−	14.5814i	−0.748998	−	0.748998i	0.225293	−	0.974291i	$-0.427666\pi$
$379$	−14.5814	−	14.5814i	−0.748998	−	0.748998i	−0.974291	+	0.225293i	$0.927666\pi$
$380$		0			0
$381$	−3.19326	+	3.19326i	−0.163596	+	0.163596i
$382$		0			0
$383$	11.5921			0.592331			0.296165	−	0.955137i	$-0.404292\pi$
$383$	11.5921			0.592331			0.296165	+	0.955137i	$0.404292\pi$
$384$		0			0
$385$	−5.61825			−0.286332
$386$		0			0
$387$	−0.999309	+	0.999309i	−0.0507977	+	0.0507977i
$388$		0			0
$389$	−12.4619	−	12.4619i	−0.631845	−	0.631845i	0.316686	−	0.948530i	$-0.397430\pi$
$389$	−12.4619	−	12.4619i	−0.631845	−	0.631845i	−0.948530	+	0.316686i	$0.897430\pi$
$390$		0			0
$391$			29.5090i			1.49233i
$392$		0			0
$393$			12.0903i			0.609875i
$394$		0			0
$395$	3.30514	+	3.30514i	0.166300	+	0.166300i
$396$		0			0
$397$	−21.1537	+	21.1537i	−1.06168	+	1.06168i	−0.0637068	+	0.997969i	$0.520292\pi$
$397$	−21.1537	+	21.1537i	−1.06168	+	1.06168i	−0.997969	+	0.0637068i	$0.979708\pi$
$398$		0			0
$399$	11.1844			0.559922
$400$		0			0
$401$	−17.7733			−0.887554			−0.443777	−	0.896137i	$-0.646362\pi$
$401$	−17.7733			−0.887554			−0.443777	+	0.896137i	$0.646362\pi$
$402$		0			0
$403$	−0.0438555	+	0.0438555i	−0.00218460	+	0.00218460i
$404$		0			0
$405$	5.67446	+	5.67446i	0.281966	+	0.281966i
$406$		0			0
$407$			45.6058i			2.26060i
$408$		0			0
$409$			28.5404i			1.41123i	0.708594	+	0.705616i	$0.249330\pi$
$409$			28.5404i			1.41123i	−0.708594	+	0.705616i	$0.750670\pi$
$410$		0			0
$411$	−14.9450	−	14.9450i	−0.737180	−	0.737180i
$412$		0			0
$413$	5.91263	−	5.91263i	0.290941	−	0.290941i
$414$		0			0
$415$	−6.19951			−0.304322
$416$		0			0
$417$	−8.55908			−0.419140
$418$		0			0
$419$	−4.72914	+	4.72914i	−0.231034	+	0.231034i	−0.813124	−	0.582090i	$-0.802235\pi$
$419$	−4.72914	+	4.72914i	−0.231034	+	0.231034i	0.582090	+	0.813124i	$0.302235\pi$
$420$		0			0
$421$	−17.0941	−	17.0941i	−0.833115	−	0.833115i	0.154827	−	0.987942i	$-0.450518\pi$
$421$	−17.0941	−	17.0941i	−0.833115	−	0.833115i	−0.987942	+	0.154827i	$0.950518\pi$
$422$		0			0
$423$		−	3.71419i		−	0.180590i
$424$		0			0
$425$		−	6.33574i		−	0.307329i
$426$		0			0
$427$	−1.34761	−	1.34761i	−0.0652153	−	0.0652153i
$428$		0			0
$429$	13.7586	−	13.7586i	0.664272	−	0.664272i
$430$		0			0
$431$	−2.55164			−0.122908			−0.0614541	−	0.998110i	$-0.519574\pi$
$431$	−2.55164			−0.122908			−0.0614541	+	0.998110i	$0.519574\pi$
$432$		0			0
$433$	7.58358			0.364444			0.182222	−	0.983257i	$-0.441671\pi$
$433$	7.58358			0.364444			0.182222	+	0.983257i	$0.441671\pi$
$434$		0			0
$435$	−6.98579	+	6.98579i	−0.334943	+	0.334943i
$436$		0			0
$437$	22.3996	+	22.3996i	1.07152	+	1.07152i
$438$		0			0
$439$		−	36.9647i		−	1.76423i	−0.471036	−	0.882114i	$-0.656120\pi$
$439$		−	36.9647i		−	1.76423i	0.471036	−	0.882114i	$-0.343880\pi$
$440$		0			0
$441$		−	0.295857i		−	0.0140884i
$442$		0			0
$443$	−19.2301	−	19.2301i	−0.913652	−	0.913652i	0.0829058	−	0.996557i	$-0.473580\pi$
$443$	−19.2301	−	19.2301i	−0.913652	−	0.913652i	−0.996557	+	0.0829058i	$0.973580\pi$
$444$		0			0
$445$	7.31649	−	7.31649i	0.346835	−	0.346835i
$446$		0			0
$447$	12.2172			0.577854
$448$		0			0
$449$	25.1219			1.18557			0.592787	−	0.805359i	$-0.298028\pi$
$449$	25.1219			1.18557			0.592787	+	0.805359i	$0.298028\pi$
$450$		0			0
$451$	3.65261	−	3.65261i	0.171994	−	0.171994i
$452$		0			0
$453$	−19.8984	−	19.8984i	−0.934909	−	0.934909i
$454$		0			0
$455$			2.10608i			0.0987343i
$456$		0			0
$457$			16.1744i			0.756605i	0.925682	+	0.378302i	$0.123492\pi$
$457$			16.1744i			0.756605i	−0.925682	+	0.378302i	$0.876508\pi$
$458$		0			0
$459$	−24.2809	−	24.2809i	−1.13334	−	1.13334i
$460$		0			0
$461$	6.33074	−	6.33074i	0.294852	−	0.294852i	−0.544142	−	0.838993i	$-0.683145\pi$
$461$	6.33074	−	6.33074i	0.294852	−	0.294852i	0.838993	+	0.544142i	$0.183145\pi$
$462$		0			0
$463$	−12.3492			−0.573917			−0.286959	−	0.957943i	$-0.592644\pi$
$463$	−12.3492			−0.573917			−0.286959	+	0.957943i	$0.592644\pi$
$464$		0			0
$465$	0.0484262			0.00224571
$466$		0			0
$467$	4.79813	−	4.79813i	0.222031	−	0.222031i	−0.587322	−	0.809353i	$-0.699818\pi$
$467$	4.79813	−	4.79813i	0.222031	−	0.222031i	0.809353	+	0.587322i	$0.199818\pi$
$468$		0			0
$469$	−9.68994	−	9.68994i	−0.447440	−	0.447440i
$470$		0			0
$471$		−	23.0512i		−	1.06214i
$472$		0			0
$473$		−	26.8370i		−	1.23396i
$474$		0			0
$475$	−4.80932	−	4.80932i	−0.220667	−	0.220667i
$476$		0			0
$477$	−0.00721872	+	0.00721872i	−0.000330523	+	0.000330523i
$478$		0			0
$479$	−23.0029			−1.05103			−0.525514	−	0.850785i	$-0.676127\pi$
$479$	−23.0029			−1.05103			−0.525514	+	0.850785i	$0.676127\pi$
$480$		0			0
$481$	17.0959			0.779508
$482$		0			0
$483$	−5.41572	+	5.41572i	−0.246424	+	0.246424i
$484$		0			0
$485$	0.409229	+	0.409229i	0.0185822	+	0.0185822i
$486$		0			0
$487$		−	1.90977i		−	0.0865399i	−0.999063	−	0.0432700i	$-0.986222\pi$
$487$		−	1.90977i		−	0.0865399i	0.999063	−	0.0432700i	$-0.0137776\pi$
$488$		0			0
$489$			38.8778i			1.75811i
$490$		0			0
$491$	10.8069	+	10.8069i	0.487710	+	0.487710i	0.907583	−	0.419873i	$-0.137925\pi$
$491$	10.8069	+	10.8069i	0.487710	+	0.487710i	−0.419873	+	0.907583i	$0.637925\pi$
$492$		0			0
$493$	26.9152	−	26.9152i	1.21220	−	1.21220i
$494$		0			0
$495$	1.66220			0.0747104
$496$		0			0
$497$	−11.0515			−0.495726
$498$		0			0
$499$	17.2482	−	17.2482i	0.772136	−	0.772136i	−0.206344	−	0.978480i	$-0.566156\pi$
$499$	17.2482	−	17.2482i	0.772136	−	0.772136i	0.978480	+	0.206344i	$0.0661565\pi$
$500$		0			0
$501$	−24.3154	−	24.3154i	−1.08633	−	1.08633i
$502$		0			0
$503$		−	28.2064i		−	1.25766i	−0.777543	−	0.628830i	$-0.783534\pi$
$503$		−	28.2064i		−	1.25766i	0.777543	−	0.628830i	$-0.216466\pi$
$504$		0			0
$505$		−	1.84088i		−	0.0819183i
$506$		0			0
$507$	9.95862	+	9.95862i	0.442278	+	0.442278i
$508$		0			0
$509$	0.695650	−	0.695650i	0.0308341	−	0.0308341i	−0.691522	−	0.722356i	$-0.743059\pi$
$509$	0.695650	−	0.695650i	0.0308341	−	0.0308341i	0.722356	+	0.691522i	$0.243059\pi$
$510$		0			0
$511$	10.5102			0.464942
$512$		0			0
$513$	−36.8623			−1.62751
$514$		0			0
$515$	8.96578	−	8.96578i	0.395079	−	0.395079i
$516$		0			0
$517$	49.8733	+	49.8733i	2.19342	+	2.19342i
$518$		0			0
$519$			6.23645i			0.273750i
$520$		0			0
$521$			28.9638i			1.26893i	0.772952	+	0.634464i	$0.218779\pi$
$521$			28.9638i			1.26893i	−0.772952	+	0.634464i	$0.781221\pi$
$522$		0			0
$523$	24.6703	+	24.6703i	1.07876	+	1.07876i	0.996621	+	0.0821360i	$0.0261742\pi$
$523$	24.6703	+	24.6703i	1.07876	+	1.07876i	0.0821360	+	0.996621i	$0.473826\pi$
$524$		0			0
$525$	1.16279	−	1.16279i	0.0507481	−	0.0507481i
$526$		0			0
$527$	−0.186579			−0.00812751
$528$		0			0
$529$	1.30731			0.0568394
$530$		0			0
$531$	−1.74930	+	1.74930i	−0.0759130	+	0.0759130i
$532$		0			0
$533$	−1.36923	−	1.36923i	−0.0593078	−	0.0593078i
$534$		0			0
$535$		−	10.4145i		−	0.450257i
$536$		0			0
$537$			19.0562i			0.822336i
$538$		0			0
$539$	3.97270	+	3.97270i	0.171116	+	0.171116i
$540$		0			0
$541$	−1.88528	+	1.88528i	−0.0810547	+	0.0810547i	−0.746472	−	0.665417i	$-0.768254\pi$
$541$	−1.88528	+	1.88528i	−0.0810547	+	0.0810547i	0.665417	+	0.746472i	$0.268254\pi$
$542$		0			0
$543$	15.9591			0.684869
$544$		0			0
$545$	−6.88036			−0.294722
$546$		0			0
$547$	7.58192	−	7.58192i	0.324179	−	0.324179i	−0.526189	−	0.850368i	$-0.676379\pi$
$547$	7.58192	−	7.58192i	0.324179	−	0.324179i	0.850368	+	0.526189i	$0.176379\pi$
$548$		0			0
$549$	0.398700	+	0.398700i	0.0170161	+	0.0170161i
$550$		0			0
$551$		−	40.8615i		−	1.74076i
$552$		0			0
$553$		−	4.67417i		−	0.198766i
$554$		0			0
$555$	−9.43885	−	9.43885i	−0.400657	−	0.400657i
$556$		0			0
$557$	10.8760	−	10.8760i	0.460832	−	0.460832i	−0.438096	−	0.898928i	$-0.644347\pi$
$557$	10.8760	−	10.8760i	0.460832	−	0.460832i	0.898928	+	0.438096i	$0.144347\pi$
$558$		0			0
$559$	−10.0602			−0.425501
$560$		0			0
$561$	58.5347			2.47134
$562$		0			0
$563$	−17.4406	+	17.4406i	−0.735035	+	0.735035i	−0.971613	−	0.236578i	$-0.923974\pi$
$563$	−17.4406	+	17.4406i	−0.735035	+	0.735035i	0.236578	+	0.971613i	$0.423974\pi$
$564$		0			0
$565$	7.06658	+	7.06658i	0.297293	+	0.297293i
$566$		0			0
$567$		−	8.02490i		−	0.337014i
$568$		0			0
$569$		−	23.8027i		−	0.997861i	−0.866642	−	0.498931i	$-0.833726\pi$
$569$		−	23.8027i		−	0.997861i	0.866642	−	0.498931i	$-0.166274\pi$
$570$		0			0
$571$	11.8136	+	11.8136i	0.494385	+	0.494385i	0.909685	−	0.415300i	$-0.136323\pi$
$571$	11.8136	+	11.8136i	0.494385	+	0.494385i	−0.415300	+	0.909685i	$0.636323\pi$
$572$		0			0
$573$	−16.0109	+	16.0109i	−0.668864	+	0.668864i
$574$		0			0
$575$	4.65754			0.194233
$576$		0			0
$577$	13.0968			0.545226			0.272613	−	0.962124i	$-0.412112\pi$
$577$	13.0968			0.545226			0.272613	+	0.962124i	$0.412112\pi$
$578$		0			0
$579$	−14.7670	+	14.7670i	−0.613694	+	0.613694i
$580$		0			0
$581$	4.38372	+	4.38372i	0.181867	+	0.181867i
$582$		0			0
$583$		−	0.193863i		−	0.00802897i
$584$		0			0
$585$		−	0.623098i		−	0.0257619i
$586$		0			0
$587$	0.220405	+	0.220405i	0.00909709	+	0.00909709i	0.711641	−	0.702544i	$-0.247952\pi$
$587$	0.220405	+	0.220405i	0.00909709	+	0.00909709i	−0.702544	+	0.711641i	$0.747952\pi$
$588$		0			0
$589$	−0.141628	+	0.141628i	−0.00583569	+	0.00583569i
$590$		0			0
$591$	44.1028			1.81415
$592$		0			0
$593$	−14.8744			−0.610819			−0.305409	−	0.952221i	$-0.598793\pi$
$593$	−14.8744			−0.610819			−0.305409	+	0.952221i	$0.598793\pi$
$594$		0			0
$595$	−4.48005	+	4.48005i	−0.183664	+	0.183664i
$596$		0			0
$597$	18.3154	+	18.3154i	0.749600	+	0.749600i
$598$		0			0
$599$		−	21.1703i		−	0.864995i	−0.901635	−	0.432497i	$-0.857632\pi$
$599$		−	21.1703i		−	0.864995i	0.901635	−	0.432497i	$-0.142368\pi$
$600$		0			0
$601$		−	22.0011i		−	0.897444i	−0.893671	−	0.448722i	$-0.851879\pi$
$601$		−	22.0011i		−	0.897444i	0.893671	−	0.448722i	$-0.148121\pi$
$602$		0			0
$603$	2.86684	+	2.86684i	0.116747	+	0.116747i
$604$		0			0
$605$	−14.5415	+	14.5415i	−0.591194	+	0.591194i
$606$		0			0
$607$	23.0452			0.935377			0.467688	−	0.883893i	$-0.345087\pi$
$607$	23.0452			0.935377			0.467688	+	0.883893i	$0.345087\pi$
$608$		0			0
$609$	9.87940			0.400334
$610$		0			0
$611$	18.6957	−	18.6957i	0.756345	−	0.756345i
$612$		0			0
$613$	3.35701	+	3.35701i	0.135588	+	0.135588i	0.771644	−	0.636055i	$-0.219435\pi$
$613$	3.35701	+	3.35701i	0.135588	+	0.135588i	−0.636055	+	0.771644i	$0.719435\pi$
$614$		0			0
$615$			1.51193i			0.0609669i
$616$		0			0
$617$		−	38.4016i		−	1.54599i	−0.634411	−	0.772996i	$-0.718757\pi$
$617$		−	38.4016i		−	1.54599i	0.634411	−	0.772996i	$-0.281243\pi$
$618$		0			0
$619$	2.60221	+	2.60221i	0.104592	+	0.104592i	0.757466	−	0.652874i	$-0.226437\pi$
$619$	2.60221	+	2.60221i	0.104592	+	0.104592i	−0.652874	+	0.757466i	$0.726437\pi$
$620$		0			0
$621$	17.8495	−	17.8495i	0.716274	−	0.716274i
$622$		0			0
$623$	−10.3471			−0.414547
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	44.4324	−	44.4324i	1.77446	−	1.77446i
$628$		0			0
$629$	36.3665	+	36.3665i	1.45003	+	1.45003i
$630$		0			0
$631$			45.6979i			1.81920i	0.415481	+	0.909602i	$0.363613\pi$
$631$			45.6979i			1.81920i	−0.415481	+	0.909602i	$0.636387\pi$
$632$		0			0
$633$			41.5335i			1.65081i
$634$		0			0
$635$	−1.94187	−	1.94187i	−0.0770607	−	0.0770607i
$636$		0			0
$637$	1.48922	−	1.48922i	0.0590050	−	0.0590050i
$638$		0			0
$639$	3.26966			0.129346
$640$		0			0
$641$	−40.0534			−1.58201			−0.791007	−	0.611807i	$-0.790443\pi$
$641$	−40.0534			−1.58201			−0.791007	+	0.611807i	$0.790443\pi$
$642$		0			0
$643$	−18.6888	+	18.6888i	−0.737014	+	0.737014i	−0.971999	−	0.234985i	$-0.924496\pi$
$643$	−18.6888	+	18.6888i	−0.737014	+	0.737014i	0.234985	+	0.971999i	$0.424496\pi$
$644$		0			0
$645$	5.55434	+	5.55434i	0.218702	+	0.218702i
$646$		0			0
$647$			33.7799i			1.32802i	0.747722	+	0.664012i	$0.231148\pi$
$647$			33.7799i			1.32802i	−0.747722	+	0.664012i	$0.768852\pi$
$648$		0			0
$649$		−	46.9782i		−	1.84406i
$650$		0			0
$651$	−0.0342425	−	0.0342425i	−0.00134207	−	0.00134207i
$652$		0			0
$653$	12.5543	−	12.5543i	0.491289	−	0.491289i	−0.417423	−	0.908712i	$-0.637067\pi$
$653$	12.5543	−	12.5543i	0.491289	−	0.491289i	0.908712	+	0.417423i	$0.137067\pi$
$654$		0			0
$655$	−7.35228			−0.287277
$656$		0			0
$657$	−3.10951			−0.121313
$658$		0			0
$659$	19.8807	−	19.8807i	0.774443	−	0.774443i	−0.204437	−	0.978880i	$-0.565536\pi$
$659$	19.8807	−	19.8807i	0.774443	−	0.774443i	0.978880	+	0.204437i	$0.0655363\pi$
$660$		0			0
$661$	−10.1929	−	10.1929i	−0.396460	−	0.396460i	0.480523	−	0.876982i	$-0.340447\pi$
$661$	−10.1929	−	10.1929i	−0.396460	−	0.396460i	−0.876982	+	0.480523i	$0.840447\pi$
$662$		0			0
$663$		−	21.9425i		−	0.852176i
$664$		0			0
$665$			6.80141i			0.263747i
$666$		0			0
$667$	19.7860	+	19.7860i	0.766116	+	0.766116i
$668$		0			0
$669$	15.8026	−	15.8026i	0.610962	−	0.610962i
$670$		0			0
$671$	−10.7073			−0.413350
$672$		0			0
$673$	8.14797			0.314081			0.157041	−	0.987592i	$-0.449805\pi$
$673$	8.14797			0.314081			0.157041	+	0.987592i	$0.449805\pi$
$674$		0			0
$675$	−3.83238	+	3.83238i	−0.147508	+	0.147508i
$676$		0			0
$677$	13.7512	+	13.7512i	0.528503	+	0.528503i	0.920126	−	0.391623i	$-0.128086\pi$
$677$	13.7512	+	13.7512i	0.528503	+	0.528503i	−0.391623	+	0.920126i	$0.628086\pi$
$678$		0			0
$679$		−	0.578738i		−	0.0222099i
$680$		0			0
$681$			18.1427i			0.695230i
$682$		0			0
$683$	−10.9048	−	10.9048i	−0.417262	−	0.417262i	0.466997	−	0.884259i	$-0.345336\pi$
$683$	−10.9048	−	10.9048i	−0.417262	−	0.417262i	−0.884259	+	0.466997i	$0.845336\pi$
$684$		0			0
$685$	9.08824	−	9.08824i	0.347244	−	0.347244i
$686$		0			0
$687$	−25.3993			−0.969043
$688$		0			0
$689$	−0.0726719			−0.00276858
$690$		0			0
$691$	−17.5590	+	17.5590i	−0.667977	+	0.667977i	−0.957247	−	0.289271i	$-0.906587\pi$
$691$	−17.5590	+	17.5590i	−0.667977	+	0.667977i	0.289271	+	0.957247i	$0.406587\pi$
$692$		0			0
$693$	−1.17535	−	1.17535i	−0.0446480	−	0.0446480i
$694$		0			0
$695$		−	5.20490i		−	0.197433i
$696$		0			0
$697$		−	5.82524i		−	0.220647i
$698$		0			0
$699$	4.00314	+	4.00314i	0.151412	+	0.151412i
$700$		0			0
$701$	14.7247	−	14.7247i	0.556146	−	0.556146i	−0.372062	−	0.928208i	$-0.621349\pi$
$701$	14.7247	−	14.7247i	0.556146	−	0.556146i	0.928208	+	0.372062i	$0.121349\pi$
$702$		0			0
$703$	55.2101			2.08229
$704$		0			0
$705$	−20.6441			−0.777503
$706$		0			0
$707$	−1.30170	+	1.30170i	−0.0489555	+	0.0489555i
$708$		0			0
$709$	−4.15445	−	4.15445i	−0.156023	−	0.156023i	0.624779	−	0.780802i	$-0.285189\pi$
$709$	−4.15445	−	4.15445i	−0.156023	−	0.156023i	−0.780802	+	0.624779i	$0.785189\pi$
$710$		0			0
$711$			1.38289i			0.0518624i
$712$		0			0
$713$		−	0.137158i		−	0.00513662i
$714$		0			0
$715$	8.36681	+	8.36681i	0.312901	+	0.312901i
$716$		0			0
$717$	6.77699	−	6.77699i	0.253091	−	0.253091i
$718$		0			0
$719$	−14.2575			−0.531717			−0.265858	−	0.964012i	$-0.585655\pi$
$719$	−14.2575			−0.531717			−0.265858	+	0.964012i	$0.585655\pi$
$720$		0			0
$721$	−12.6795			−0.472210
$722$		0			0
$723$	−10.6372	+	10.6372i	−0.395601	+	0.395601i
$724$		0			0
$725$	−4.24816	−	4.24816i	−0.157773	−	0.157773i
$726$		0			0
$727$			12.2178i			0.453135i	0.973995	+	0.226567i	$0.0727504\pi$
$727$			12.2178i			0.453135i	−0.973995	+	0.226567i	$0.927250\pi$
$728$		0			0
$729$			29.1116i			1.07821i
$730$		0			0
$731$	−21.4001	−	21.4001i	−0.791509	−	0.791509i
$732$		0			0
$733$	22.9048	−	22.9048i	0.846009	−	0.846009i	−0.143624	−	0.989632i	$-0.545876\pi$
$733$	22.9048	−	22.9048i	0.846009	−	0.846009i	0.989632	+	0.143624i	$0.0458755\pi$
$734$		0			0
$735$	−1.64443			−0.0606556
$736$		0			0
$737$	−76.9905			−2.83598
$738$		0			0
$739$	−13.3203	+	13.3203i	−0.489997	+	0.489997i	−0.908305	−	0.418308i	$-0.862623\pi$
$739$	−13.3203	+	13.3203i	−0.489997	+	0.489997i	0.418308	+	0.908305i	$0.362623\pi$
$740$		0			0
$741$	−16.6561	−	16.6561i	−0.611876	−	0.611876i
$742$		0			0
$743$			1.88792i			0.0692610i	0.999400	+	0.0346305i	$0.0110254\pi$
$743$			1.88792i			0.0692610i	−0.999400	+	0.0346305i	$0.988975\pi$
$744$		0			0
$745$			7.42945i			0.272194i
$746$		0			0
$747$	−1.29696	−	1.29696i	−0.0474531	−	0.0474531i
$748$		0			0
$749$	−7.36414	+	7.36414i	−0.269080	+	0.269080i
$750$		0			0
$751$	−5.29005			−0.193037			−0.0965183	−	0.995331i	$-0.530771\pi$
$751$	−5.29005			−0.193037			−0.0965183	+	0.995331i	$0.530771\pi$
$752$		0			0
$753$	−6.30859			−0.229898
$754$		0			0
$755$	12.1005	−	12.1005i	0.440383	−	0.440383i
$756$		0			0
$757$	26.4798	+	26.4798i	0.962423	+	0.962423i	0.999319	−	0.0368961i	$-0.0117471\pi$
$757$	26.4798	+	26.4798i	0.962423	+	0.962423i	−0.0368961	+	0.999319i	$0.511747\pi$
$758$		0			0
$759$			43.0301i			1.56189i
$760$		0			0
$761$			26.0367i			0.943828i	0.881645	+	0.471914i	$0.156437\pi$
$761$			26.0367i			0.943828i	−0.881645	+	0.471914i	$0.843563\pi$
$762$		0			0
$763$	4.86515	+	4.86515i	0.176130	+	0.176130i
$764$		0			0
$765$	1.32545	−	1.32545i	0.0479219	−	0.0479219i
$766$		0			0
$767$	−17.6104			−0.635875
$768$		0			0
$769$	−17.7514			−0.640132			−0.320066	−	0.947395i	$-0.603705\pi$
$769$	−17.7514			−0.640132			−0.320066	+	0.947395i	$0.603705\pi$
$770$		0			0
$771$	24.0334	−	24.0334i	0.865542	−	0.865542i
$772$		0			0
$773$	−11.6700	−	11.6700i	−0.419740	−	0.419740i	0.465374	−	0.885114i	$-0.345920\pi$
$773$	−11.6700	−	11.6700i	−0.419740	−	0.419740i	−0.885114	+	0.465374i	$0.845920\pi$
$774$		0			0
$775$			0.0294487i			0.00105783i
$776$		0			0
$777$			13.3486i			0.478877i
$778$		0			0
$779$	−4.42182	−	4.42182i	−0.158428	−	0.158428i
$780$		0			0
$781$	−43.9042	+	43.9042i	−1.57102	+	1.57102i
$782$		0			0
$783$	−32.5611			−1.16364
$784$		0			0
$785$	14.0178			0.500316
$786$		0			0
$787$	18.4037	−	18.4037i	0.656020	−	0.656020i	−0.298416	−	0.954436i	$-0.596458\pi$
$787$	18.4037	−	18.4037i	0.656020	−	0.656020i	0.954436	+	0.298416i	$0.0964584\pi$
$788$		0			0
$789$	0.844669	+	0.844669i	0.0300710	+	0.0300710i
$790$		0			0
$791$		−	9.99365i		−	0.355333i
$792$		0			0
$793$			4.01377i			0.142533i
$794$		0			0
$795$	0.0401229	+	0.0401229i	0.00142301	+	0.00142301i
$796$		0			0
$797$	−6.85581	+	6.85581i	−0.242845	+	0.242845i	−0.818026	−	0.575181i	$-0.804932\pi$
$797$	−6.85581	+	6.85581i	−0.242845	+	0.242845i	0.575181	+	0.818026i	$0.304932\pi$
$798$		0			0
$799$	79.5388			2.81388
$800$		0			0
$801$	3.06126			0.108164
$802$		0			0
$803$	41.7537	−	41.7537i	1.47346	−	1.47346i
$804$		0			0
$805$	−3.29338	−	3.29338i	−0.116076	−	0.116076i
$806$		0			0
$807$			49.6188i			1.74667i
$808$		0			0
$809$			37.5597i			1.32053i	0.751033	+	0.660264i	$0.229556\pi$
$809$			37.5597i			1.32053i	−0.751033	+	0.660264i	$0.770444\pi$
$810$		0			0
$811$	23.4281	+	23.4281i	0.822670	+	0.822670i	0.986490	−	0.163820i	$-0.0523816\pi$
$811$	23.4281	+	23.4281i	0.822670	+	0.822670i	−0.163820	+	0.986490i	$0.552382\pi$
$812$		0			0
$813$	−14.5972	+	14.5972i	−0.511947	+	0.511947i
$814$		0			0
$815$	−23.6421			−0.828148
$816$		0			0
$817$	−32.4886			−1.13663
$818$		0			0
$819$	−0.440597	+	0.440597i	−0.0153957	+	0.0153957i
$820$		0			0
$821$	7.51385	+	7.51385i	0.262235	+	0.262235i	0.825962	−	0.563727i	$-0.190633\pi$
$821$	7.51385	+	7.51385i	0.262235	+	0.262235i	−0.563727	+	0.825962i	$0.690633\pi$
$822$		0			0
$823$			16.8403i			0.587015i	0.955957	+	0.293507i	$0.0948225\pi$
$823$			16.8403i			0.587015i	−0.955957	+	0.293507i	$0.905177\pi$
$824$		0			0
$825$		−	9.23880i		−	0.321654i
$826$		0			0
$827$	37.1528	+	37.1528i	1.29193	+	1.29193i	0.933593	+	0.358336i	$0.116656\pi$
$827$	37.1528	+	37.1528i	1.29193	+	1.29193i	0.358336	+	0.933593i	$0.383344\pi$
$828$		0			0
$829$	−4.41271	+	4.41271i	−0.153260	+	0.153260i	−0.779572	−	0.626312i	$-0.784563\pi$
$829$	−4.41271	+	4.41271i	−0.153260	+	0.153260i	0.626312	+	0.779572i	$0.284563\pi$
$830$		0			0
$831$	−29.8802			−1.03653
$832$		0			0
$833$	6.33574			0.219520
$834$		0			0
$835$	14.7865	−	14.7865i	0.511709	−	0.511709i
$836$		0			0
$837$	0.112858	+	0.112858i	0.00390096	+	0.00390096i
$838$		0			0
$839$		−	16.3798i		−	0.565493i	−0.959195	−	0.282747i	$-0.908754\pi$
$839$		−	16.3798i		−	0.565493i	0.959195	−	0.282747i	$-0.0912456\pi$
$840$		0			0
$841$		−	7.09372i		−	0.244611i
$842$		0			0
$843$	−13.9160	−	13.9160i	−0.479293	−	0.479293i
$844$		0			0
$845$	−6.05598	+	6.05598i	−0.208332	+	0.208332i
$846$		0			0
$847$	20.5647			0.706612
$848$		0			0
$849$	22.0935			0.758245
$850$		0			0
$851$	−26.7338	+	26.7338i	−0.916424	+	0.916424i
$852$		0			0
$853$	11.3173	+	11.3173i	0.387496	+	0.387496i	0.873793	−	0.486298i	$-0.161653\pi$
$853$	11.3173	+	11.3173i	0.387496	+	0.387496i	−0.486298	+	0.873793i	$0.661653\pi$
$854$		0			0
$855$		−	2.01225i		−	0.0688174i
$856$		0			0
$857$		−	0.712110i		−	0.0243252i	−0.999926	−	0.0121626i	$-0.996128\pi$
$857$		−	0.712110i		−	0.0243252i	0.999926	−	0.0121626i	$-0.00387158\pi$
$858$		0			0
$859$	16.0220	+	16.0220i	0.546662	+	0.546662i	0.925474	−	0.378812i	$-0.123667\pi$
$859$	16.0220	+	16.0220i	0.546662	+	0.546662i	−0.378812	+	0.925474i	$0.623667\pi$
$860$		0			0
$861$	1.06910	−	1.06910i	0.0364347	−	0.0364347i
$862$		0			0
$863$	−7.70788			−0.262379			−0.131190	−	0.991357i	$-0.541880\pi$
$863$	−7.70788			−0.262379			−0.131190	+	0.991357i	$0.541880\pi$
$864$		0			0
$865$	−3.79248			−0.128948
$866$		0			0
$867$	26.9087	−	26.9087i	0.913869	−	0.913869i
$868$		0			0
$869$	−18.5691	−	18.5691i	−0.629913	−	0.629913i
$870$		0			0
$871$			28.8609i			0.977915i
$872$		0			0
$873$			0.171224i			0.00579505i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	−11.2828	+	11.2828i	−0.380994	+	0.380994i	−0.871460	−	0.490466i	$-0.836827\pi$
$877$	−11.2828	+	11.2828i	−0.380994	+	0.380994i	0.490466	+	0.871460i	$0.336827\pi$
$878$		0			0
$879$	−20.4060			−0.688277
$880$		0			0
$881$	−53.4988			−1.80242			−0.901210	−	0.433383i	$-0.857320\pi$
$881$	−53.4988			−1.80242			−0.901210	+	0.433383i	$0.857320\pi$
$882$		0			0
$883$	−24.6980	+	24.6980i	−0.831154	+	0.831154i	−0.987675	−	0.156521i	$-0.949972\pi$
$883$	−24.6980	+	24.6980i	−0.831154	+	0.831154i	0.156521	+	0.987675i	$0.449972\pi$
$884$		0			0
$885$	9.72289	+	9.72289i	0.326831	+	0.326831i
$886$		0			0
$887$		−	18.4063i		−	0.618022i	−0.951059	−	0.309011i	$-0.900002\pi$
$887$		−	18.4063i		−	0.618022i	0.951059	−	0.309011i	$-0.0999979\pi$
$888$		0			0
$889$			2.74622i			0.0921052i
$890$		0			0
$891$	−31.8805	−	31.8805i	−1.06804	−	1.06804i
$892$		0			0
$893$	60.3762	−	60.3762i	2.02041	−	2.02041i
$894$		0			0
$895$	−11.5884			−0.387356
$896$		0			0
$897$	16.1304			0.538579
$898$		0			0
$899$	−0.125103	+	0.125103i	−0.00417241	+	0.00417241i
$900$		0			0
$901$	−0.154588	−	0.154588i	−0.00515007	−	0.00515007i
$902$		0			0
$903$		−	7.85502i		−	0.261399i
$904$		0			0
$905$			9.70494i			0.322603i
$906$		0			0
$907$	−8.25702	−	8.25702i	−0.274170	−	0.274170i	0.556607	−	0.830776i	$-0.312103\pi$
$907$	−8.25702	−	8.25702i	−0.274170	−	0.274170i	−0.830776	+	0.556607i	$0.812103\pi$
$908$		0			0
$909$	0.385118	−	0.385118i	0.0127736	−	0.0127736i
$910$		0			0
$911$	−37.4980			−1.24236			−0.621182	−	0.783666i	$-0.713347\pi$
$911$	−37.4980			−1.24236			−0.621182	+	0.783666i	$0.713347\pi$
$912$		0			0
$913$	34.8304			1.15272
$914$		0			0
$915$	2.21604	−	2.21604i	0.0732601	−	0.0732601i
$916$		0			0
$917$	5.19885	+	5.19885i	0.171681	+	0.171681i
$918$		0			0
$919$		−	1.19070i		−	0.0392775i	−0.999807	−	0.0196388i	$-0.993748\pi$
$919$		−	1.19070i		−	0.0392775i	0.999807	−	0.0196388i	$-0.00625162\pi$
$920$		0			0
$921$		−	10.9989i		−	0.362427i
$922$		0			0
$923$	16.4581	+	16.4581i	0.541724	+	0.541724i
$924$		0			0
$925$	5.73990	−	5.73990i	0.188727	−	0.188727i
$926$		0			0
$927$	3.75133			0.123210
$928$		0			0
$929$	−20.5448			−0.674052			−0.337026	−	0.941495i	$-0.609421\pi$
$929$	−20.5448			−0.674052			−0.337026	+	0.941495i	$0.609421\pi$
$930$		0			0
$931$	4.80932	−	4.80932i	0.157619	−	0.157619i
$932$		0			0
$933$	−21.2288	−	21.2288i	−0.694999	−	0.694999i
$934$		0			0
$935$			35.5958i			1.16411i
$936$		0			0
$937$			20.6843i			0.675727i	0.941195	+	0.337863i	$0.109704\pi$
$937$			20.6843i			0.675727i	−0.941195	+	0.337863i	$0.890296\pi$
$938$		0			0
$939$	−1.34110	−	1.34110i	−0.0437653	−	0.0437653i
$940$		0			0
$941$	−18.7569	+	18.7569i	−0.611459	+	0.611459i	−0.943326	−	0.331867i	$-0.892321\pi$
$941$	−18.7569	+	18.7569i	−0.611459	+	0.611459i	0.331867	+	0.943326i	$0.392321\pi$
$942$		0			0
$943$	4.28226			0.139450
$944$		0			0
$945$	5.41980			0.176306
$946$		0			0
$947$	19.7221	−	19.7221i	0.640881	−	0.640881i	−0.309891	−	0.950772i	$-0.600293\pi$
$947$	19.7221	−	19.7221i	0.640881	−	0.640881i	0.950772	+	0.309891i	$0.100293\pi$
$948$		0			0
$949$	−15.6519	−	15.6519i	−0.508083	−	0.508083i
$950$		0			0
$951$		−	19.2695i		−	0.624857i
$952$		0			0
$953$		−	42.2504i		−	1.36862i	−0.729190	−	0.684312i	$-0.760103\pi$
$953$		−	42.2504i		−	1.36862i	0.729190	−	0.684312i	$-0.239897\pi$
$954$		0			0
$955$	−9.73644	−	9.73644i	−0.315064	−	0.315064i
$956$		0			0
$957$	39.2479	−	39.2479i	1.26870	−	1.26870i
$958$		0			0
$959$	−12.8527			−0.415036
$960$		0			0
$961$	−30.9991			−0.999972
$962$		0			0
$963$	2.17874	−	2.17874i	0.0702088	−	0.0702088i
$964$		0			0
$965$	−8.98000	−	8.98000i	−0.289077	−	0.289077i
$966$		0			0
$967$			37.1348i			1.19418i	0.802176	+	0.597088i	$0.203676\pi$
$967$			37.1348i			1.19418i	−0.802176	+	0.597088i	$0.796324\pi$
$968$		0			0
$969$		−	70.8616i		−	2.27640i
$970$		0			0
$971$	6.58118	+	6.58118i	0.211200	+	0.211200i	0.804777	−	0.593577i	$-0.202285\pi$
$971$	6.58118	+	6.58118i	0.211200	+	0.211200i	−0.593577	+	0.804777i	$0.702285\pi$
$972$		0			0
$973$	−3.68042	+	3.68042i	−0.117989	+	0.117989i
$974$		0			0
$975$	−3.46329			−0.110914
$976$		0			0
$977$	33.6155			1.07546			0.537728	−	0.843118i	$-0.319283\pi$
$977$	33.6155			1.07546			0.537728	+	0.843118i	$0.319283\pi$
$978$		0			0
$979$	−41.1058	+	41.1058i	−1.31375	+	1.31375i
$980$		0			0
$981$	−1.43939	−	1.43939i	−0.0459562	−	0.0459562i
$982$		0			0
$983$			34.8765i			1.11239i	0.831053	+	0.556193i	$0.187738\pi$
$983$			34.8765i			1.11239i	−0.831053	+	0.556193i	$0.812262\pi$
$984$		0			0
$985$			26.8195i			0.854541i
$986$		0			0
$987$	14.5976	+	14.5976i	0.464647	+	0.464647i
$988$		0			0
$989$	15.7316	−	15.7316i	0.500237	−	0.500237i
$990$		0			0
$991$	−22.2085			−0.705477			−0.352738	−	0.935722i	$-0.614749\pi$
$991$	−22.2085			−0.705477			−0.352738	+	0.935722i	$0.614749\pi$
$992$		0			0
$993$	−24.2009			−0.767993
$994$		0			0
$995$	−11.1379	+	11.1379i	−0.353094	+	0.353094i
$996$		0			0
$997$	−23.5079	−	23.5079i	−0.744503	−	0.744503i	0.228938	−	0.973441i	$-0.426475\pi$
$997$	−23.5079	−	23.5079i	−0.744503	−	0.744503i	−0.973441	+	0.228938i	$0.926475\pi$
$998$		0			0
$999$		−	43.9949i		−	1.39194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.16		44
4.3	odd	2		560.2.bd.a.421.11	yes	44
16.3	odd	4		560.2.bd.a.141.11	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.11	✓	44	16.3	odd	4
560.2.bd.a.421.11	yes	44	4.3	odd	2
2240.2.bd.a.561.16		44	1.1	even	1	trivial
2240.2.bd.a.1681.16		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)

\(f(q)\)	\(=\)	\(q+(1.16279 - 1.16279i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +0.295857i q^{9} +O(q^{10})\)	\(q+(1.16279 - 1.16279i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +0.295857i q^{9} +(-3.97270 - 3.97270i) q^{11} +(-1.48922 + 1.48922i) q^{13} +1.64443 q^{15} -6.33574 q^{17} +(-4.80932 + 4.80932i) q^{19} +(-1.16279 - 1.16279i) q^{21} -4.65754i q^{23} +1.00000i q^{25} +(3.83238 + 3.83238i) q^{27} +(-4.24816 + 4.24816i) q^{29} +0.0294487 q^{31} -9.23880 q^{33} +(0.707107 - 0.707107i) q^{35} +(-5.73990 - 5.73990i) q^{37} +3.46329i q^{39} +0.919426i q^{41} +(3.37767 + 3.37767i) q^{43} +(-0.209203 + 0.209203i) q^{45} -12.5540 q^{47} -1.00000 q^{49} +(-7.36711 + 7.36711i) q^{51} +(0.0243993 + 0.0243993i) q^{53} -5.61825i q^{55} +11.1844i q^{57} +(5.91263 + 5.91263i) q^{59} +(1.34761 - 1.34761i) q^{61} +0.295857 q^{63} -2.10608 q^{65} +(9.68994 - 9.68994i) q^{67} +(-5.41572 - 5.41572i) q^{69} -11.0515i q^{71} +10.5102i q^{73} +(1.16279 + 1.16279i) q^{75} +(-3.97270 + 3.97270i) q^{77} +4.67417 q^{79} +8.02490 q^{81} +(-4.38372 + 4.38372i) q^{83} +(-4.48005 - 4.48005i) q^{85} +9.87940i q^{87} -10.3471i q^{89} +(1.48922 + 1.48922i) q^{91} +(0.0342425 - 0.0342425i) q^{93} -6.80141 q^{95} +0.578738 q^{97} +(1.17535 - 1.17535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 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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