LMFDB - Embedded newform 2240.2.bd.b.561.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.11
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.363076 + 0.363076i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.73635i q^{9} +O(q^{10})$	\(q+(-0.363076 + 0.363076i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.73635i q^{9} +(3.76005 + 3.76005i) q^{11} +(-3.81880 + 3.81880i) q^{13} +0.513467 q^{15} -1.22933 q^{17} +(2.15074 - 2.15074i) q^{19} +(-0.363076 - 0.363076i) q^{21} -3.39953i q^{23} +1.00000i q^{25} +(-2.08273 - 2.08273i) q^{27} +(-3.86007 + 3.86007i) q^{29} +4.83612 q^{31} -2.73037 q^{33} +(0.707107 - 0.707107i) q^{35} +(-7.64574 - 7.64574i) q^{37} -2.77303i q^{39} -5.60526i q^{41} +(4.51884 + 4.51884i) q^{43} +(1.93489 - 1.93489i) q^{45} -11.1966 q^{47} -1.00000 q^{49} +(0.446342 - 0.446342i) q^{51} +(1.97411 + 1.97411i) q^{53} -5.31752i q^{55} +1.56176i q^{57} +(-4.83179 - 4.83179i) q^{59} +(-8.00261 + 8.00261i) q^{61} -2.73635 q^{63} +5.40060 q^{65} +(-4.32927 + 4.32927i) q^{67} +(1.23429 + 1.23429i) q^{69} +1.12005i q^{71} -10.0450i q^{73} +(-0.363076 - 0.363076i) q^{75} +(-3.76005 + 3.76005i) q^{77} +9.83517 q^{79} -6.69668 q^{81} +(-8.06188 + 8.06188i) q^{83} +(0.869271 + 0.869271i) q^{85} -2.80300i q^{87} +8.65099i q^{89} +(-3.81880 - 3.81880i) q^{91} +(-1.75588 + 1.75588i) q^{93} -3.04161 q^{95} -2.62430 q^{97} +(-10.2888 + 10.2888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) $ 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.363076	+	0.363076i	−0.209622	+	0.209622i	−0.804107	−	0.594485i	$-0.797356\pi$
$3$	−0.363076	+	0.363076i	−0.209622	+	0.209622i	0.594485	+	0.804107i	$0.297356\pi$
$4$		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
$9$			2.73635i			0.912117i
$10$		0			0
$11$	3.76005	+	3.76005i	1.13370	+	1.13370i	0.989557	+	0.144141i	$0.0460420\pi$
$11$	3.76005	+	3.76005i	1.13370	+	1.13370i	0.144141	+	0.989557i	$0.453958\pi$
$12$		0			0
$13$	−3.81880	+	3.81880i	−1.05915	+	1.05915i	−0.0610083	+	0.998137i	$0.519432\pi$
$13$	−3.81880	+	3.81880i	−1.05915	+	1.05915i	−0.998137	+	0.0610083i	$0.980568\pi$
$14$		0			0
$15$	0.513467			0.132577
$16$		0			0
$17$	−1.22933			−0.298157			−0.149079	−	0.988825i	$-0.547631\pi$
$17$	−1.22933			−0.298157			−0.149079	+	0.988825i	$0.547631\pi$
$18$		0			0
$19$	2.15074	−	2.15074i	0.493414	−	0.493414i	−0.415966	−	0.909380i	$-0.636557\pi$
$19$	2.15074	−	2.15074i	0.493414	−	0.493414i	0.909380	+	0.415966i	$0.136557\pi$
$20$		0			0
$21$	−0.363076	−	0.363076i	−0.0792296	−	0.0792296i
$22$		0			0
$23$		−	3.39953i		−	0.708851i	−0.935084	−	0.354425i	$-0.884677\pi$
$23$		−	3.39953i		−	0.708851i	0.935084	−	0.354425i	$-0.115323\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−2.08273	−	2.08273i	−0.400822	−	0.400822i
$28$		0			0
$29$	−3.86007	+	3.86007i	−0.716797	+	0.716797i	−0.967948	−	0.251151i	$-0.919191\pi$
$29$	−3.86007	+	3.86007i	−0.716797	+	0.716797i	0.251151	+	0.967948i	$0.419191\pi$
$30$		0			0
$31$	4.83612			0.868593			0.434296	−	0.900770i	$-0.356997\pi$
$31$	4.83612			0.868593			0.434296	+	0.900770i	$0.356997\pi$
$32$		0			0
$33$	−2.73037			−0.475296
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	−7.64574	−	7.64574i	−1.25695	−	1.25695i	−0.952541	−	0.304410i	$-0.901541\pi$
$37$	−7.64574	−	7.64574i	−1.25695	−	1.25695i	−0.304410	−	0.952541i	$-0.598459\pi$
$38$		0			0
$39$		−	2.77303i		−	0.444040i
$40$		0			0
$41$		−	5.60526i		−	0.875394i	−0.899122	−	0.437697i	$-0.855794\pi$
$41$		−	5.60526i		−	0.875394i	0.899122	−	0.437697i	$-0.144206\pi$
$42$		0			0
$43$	4.51884	+	4.51884i	0.689117	+	0.689117i	0.962037	−	0.272920i	$-0.0879895\pi$
$43$	4.51884	+	4.51884i	0.689117	+	0.689117i	−0.272920	+	0.962037i	$0.587989\pi$
$44$		0			0
$45$	1.93489	−	1.93489i	0.288437	−	0.288437i
$46$		0			0
$47$	−11.1966			−1.63319			−0.816593	−	0.577214i	$-0.804140\pi$
$47$	−11.1966			−1.63319			−0.816593	+	0.577214i	$0.804140\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	0.446342	−	0.446342i	0.0625003	−	0.0625003i
$52$		0			0
$53$	1.97411	+	1.97411i	0.271165	+	0.271165i	0.829569	−	0.558404i	$-0.188586\pi$
$53$	1.97411	+	1.97411i	0.271165	+	0.271165i	−0.558404	+	0.829569i	$0.688586\pi$
$54$		0			0
$55$		−	5.31752i		−	0.717014i
$56$		0			0
$57$			1.56176i			0.206861i
$58$		0			0
$59$	−4.83179	−	4.83179i	−0.629045	−	0.629045i	0.318783	−	0.947828i	$-0.396726\pi$
$59$	−4.83179	−	4.83179i	−0.629045	−	0.629045i	−0.947828	+	0.318783i	$0.896726\pi$
$60$		0			0
$61$	−8.00261	+	8.00261i	−1.02463	+	1.02463i	−0.0249402	+	0.999689i	$0.507940\pi$
$61$	−8.00261	+	8.00261i	−1.02463	+	1.02463i	−0.999689	+	0.0249402i	$0.992060\pi$
$62$		0			0
$63$	−2.73635			−0.344748
$64$		0			0
$65$	5.40060			0.669862
$66$		0			0
$67$	−4.32927	+	4.32927i	−0.528905	+	0.528905i	−0.920246	−	0.391341i	$-0.872011\pi$
$67$	−4.32927	+	4.32927i	−0.528905	+	0.528905i	0.391341	+	0.920246i	$0.372011\pi$
$68$		0			0
$69$	1.23429	+	1.23429i	0.148591	+	0.148591i
$70$		0			0
$71$			1.12005i			0.132925i	0.997789	+	0.0664627i	$0.0211713\pi$
$71$			1.12005i			0.132925i	−0.997789	+	0.0664627i	$0.978829\pi$
$72$		0			0
$73$		−	10.0450i		−	1.17567i	−0.808980	−	0.587836i	$-0.799980\pi$
$73$		−	10.0450i		−	1.17567i	0.808980	−	0.587836i	$-0.200020\pi$
$74$		0			0
$75$	−0.363076	−	0.363076i	−0.0419244	−	0.0419244i
$76$		0			0
$77$	−3.76005	+	3.76005i	−0.428498	+	0.428498i
$78$		0			0
$79$	9.83517			1.10654			0.553271	−	0.833001i	$-0.313379\pi$
$79$	9.83517			1.10654			0.553271	+	0.833001i	$0.313379\pi$
$80$		0			0
$81$	−6.69668			−0.744075
$82$		0			0
$83$	−8.06188	+	8.06188i	−0.884906	+	0.884906i	−0.994028	−	0.109123i	$-0.965196\pi$
$83$	−8.06188	+	8.06188i	−0.884906	+	0.884906i	0.109123	+	0.994028i	$0.465196\pi$
$84$		0			0
$85$	0.869271	+	0.869271i	0.0942857	+	0.0942857i
$86$		0			0
$87$		−	2.80300i		−	0.300513i
$88$		0			0
$89$			8.65099i			0.917004i	0.888693	+	0.458502i	$0.151614\pi$
$89$			8.65099i			0.917004i	−0.888693	+	0.458502i	$0.848386\pi$
$90$		0			0
$91$	−3.81880	−	3.81880i	−0.400319	−	0.400319i
$92$		0			0
$93$	−1.75588	+	1.75588i	−0.182076	+	0.182076i
$94$		0			0
$95$	−3.04161			−0.312062
$96$		0			0
$97$	−2.62430			−0.266457			−0.133228	−	0.991085i	$-0.542534\pi$
$97$	−2.62430			−0.266457			−0.133228	+	0.991085i	$0.542534\pi$
$98$		0			0
$99$	−10.2888	+	10.2888i	−1.03407	+	1.03407i
$100$		0			0
$101$	8.20304	+	8.20304i	0.816233	+	0.816233i	0.985560	−	0.169327i	$-0.0541595\pi$
$101$	8.20304	+	8.20304i	0.816233	+	0.816233i	−0.169327	+	0.985560i	$0.554160\pi$
$102$		0			0
$103$			1.64842i			0.162424i	0.996697	+	0.0812119i	$0.0258791\pi$
$103$			1.64842i			0.162424i	−0.996697	+	0.0812119i	$0.974121\pi$
$104$		0			0
$105$			0.513467i			0.0501092i
$106$		0			0
$107$	8.65044	+	8.65044i	0.836270	+	0.836270i	0.988366	−	0.152096i	$-0.0486022\pi$
$107$	8.65044	+	8.65044i	0.836270	+	0.836270i	−0.152096	+	0.988366i	$0.548602\pi$
$108$		0			0
$109$	−10.0987	+	10.0987i	−0.967284	+	0.967284i	−0.999482	−	0.0321971i	$-0.989750\pi$
$109$	−10.0987	+	10.0987i	−0.967284	+	0.967284i	0.0321971	+	0.999482i	$0.489750\pi$
$110$		0			0
$111$	5.55196			0.526969
$112$		0			0
$113$	8.73583			0.821798			0.410899	−	0.911681i	$-0.365215\pi$
$113$	8.73583			0.821798			0.410899	+	0.911681i	$0.365215\pi$
$114$		0			0
$115$	−2.40383	+	2.40383i	−0.224158	+	0.224158i
$116$		0			0
$117$	−10.4496	−	10.4496i	−0.966065	−	0.966065i
$118$		0			0
$119$		−	1.22933i		−	0.112693i
$120$		0			0
$121$			17.2760i			1.57054i
$122$		0			0
$123$	2.03513	+	2.03513i	0.183502	+	0.183502i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	0.279431			0.0247955			0.0123977	−	0.999923i	$-0.496054\pi$
$127$	0.279431			0.0247955			0.0123977	+	0.999923i	$0.496054\pi$
$128$		0			0
$129$	−3.28136			−0.288908
$130$		0			0
$131$	−1.60664	+	1.60664i	−0.140372	+	0.140372i	−0.773801	−	0.633429i	$-0.781647\pi$
$131$	−1.60664	+	1.60664i	−0.140372	+	0.140372i	0.633429	+	0.773801i	$0.281647\pi$
$132$		0			0
$133$	2.15074	+	2.15074i	0.186493	+	0.186493i
$134$		0			0
$135$			2.94543i			0.253502i
$136$		0			0
$137$			14.1057i			1.20513i	0.798071	+	0.602564i	$0.205854\pi$
$137$			14.1057i			1.20513i	−0.798071	+	0.602564i	$0.794146\pi$
$138$		0			0
$139$	−11.5174	−	11.5174i	−0.976892	−	0.976892i	0.0228473	−	0.999739i	$-0.492727\pi$
$139$	−11.5174	−	11.5174i	−0.976892	−	0.976892i	−0.999739	+	0.0228473i	$0.992727\pi$
$140$		0			0
$141$	4.06520	−	4.06520i	0.342352	−	0.342352i
$142$		0			0
$143$	−28.7178			−2.40150
$144$		0			0
$145$	5.45896			0.453342
$146$		0			0
$147$	0.363076	−	0.363076i	0.0299460	−	0.0299460i
$148$		0			0
$149$	−11.5128	−	11.5128i	−0.943169	−	0.943169i	0.0553009	−	0.998470i	$-0.482388\pi$
$149$	−11.5128	−	11.5128i	−0.943169	−	0.943169i	−0.998470	+	0.0553009i	$0.982388\pi$
$150$		0			0
$151$			7.55056i			0.614456i	0.951636	+	0.307228i	$0.0994015\pi$
$151$			7.55056i			0.614456i	−0.951636	+	0.307228i	$0.900599\pi$
$152$		0			0
$153$		−	3.36389i		−	0.271955i
$154$		0			0
$155$	−3.41965	−	3.41965i	−0.274673	−	0.274673i
$156$		0			0
$157$	2.27451	−	2.27451i	0.181525	−	0.181525i	−0.610495	−	0.792020i	$-0.709029\pi$
$157$	2.27451	−	2.27451i	0.181525	−	0.181525i	0.792020	+	0.610495i	$0.209029\pi$
$158$		0			0
$159$	−1.43350			−0.113684
$160$		0			0
$161$	3.39953			0.267920
$162$		0			0
$163$	−6.61443	+	6.61443i	−0.518082	+	0.518082i	−0.916991	−	0.398909i	$-0.869389\pi$
$163$	−6.61443	+	6.61443i	−0.518082	+	0.518082i	0.398909	+	0.916991i	$0.369389\pi$
$164$		0			0
$165$	1.93066	+	1.93066i	0.150302	+	0.150302i
$166$		0			0
$167$		−	23.6910i		−	1.83326i	−0.399731	−	0.916632i	$-0.630897\pi$
$167$		−	23.6910i		−	1.83326i	0.399731	−	0.916632i	$-0.369103\pi$
$168$		0			0
$169$		−	16.1665i		−	1.24358i
$170$		0			0
$171$	5.88518	+	5.88518i	0.450051	+	0.450051i
$172$		0			0
$173$	−8.12855	+	8.12855i	−0.618002	+	0.618002i	−0.945019	−	0.327016i	$-0.893957\pi$
$173$	−8.12855	+	8.12855i	−0.618002	+	0.618002i	0.327016	+	0.945019i	$0.393957\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	3.50861			0.263723
$178$		0			0
$179$	4.12249	−	4.12249i	0.308129	−	0.308129i	−0.536054	−	0.844183i	$-0.680086\pi$
$179$	4.12249	−	4.12249i	0.308129	−	0.308129i	0.844183	+	0.536054i	$0.180086\pi$
$180$		0			0
$181$	−10.8448	−	10.8448i	−0.806085	−	0.806085i	0.177954	−	0.984039i	$-0.443052\pi$
$181$	−10.8448	−	10.8448i	−0.806085	−	0.806085i	−0.984039	+	0.177954i	$0.943052\pi$
$182$		0			0
$183$		−	5.81111i		−	0.429569i
$184$		0			0
$185$			10.8127i			0.794966i
$186$		0			0
$187$	−4.62236	−	4.62236i	−0.338021	−	0.338021i
$188$		0			0
$189$	2.08273	−	2.08273i	0.151496	−	0.151496i
$190$		0			0
$191$	3.95186			0.285946			0.142973	−	0.989727i	$-0.454334\pi$
$191$	3.95186			0.285946			0.142973	+	0.989727i	$0.454334\pi$
$192$		0			0
$193$	16.2261			1.16798			0.583991	−	0.811760i	$-0.301491\pi$
$193$	16.2261			1.16798			0.583991	+	0.811760i	$0.301491\pi$
$194$		0			0
$195$	−1.96083	+	1.96083i	−0.140418	+	0.140418i
$196$		0			0
$197$	−17.9538	−	17.9538i	−1.27916	−	1.27916i	−0.941141	−	0.338014i	$-0.890245\pi$
$197$	−17.9538	−	17.9538i	−1.27916	−	1.27916i	−0.338014	−	0.941141i	$-0.609755\pi$
$198$		0			0
$199$		−	5.76699i		−	0.408811i	−0.978886	−	0.204405i	$-0.934474\pi$
$199$		−	5.76699i		−	0.408811i	0.978886	−	0.204405i	$-0.0655261\pi$
$200$		0			0
$201$		−	3.14371i		−	0.221740i
$202$		0			0
$203$	−3.86007	−	3.86007i	−0.270924	−	0.270924i
$204$		0			0
$205$	−3.96352	+	3.96352i	−0.276824	+	0.276824i
$206$		0			0
$207$	9.30230			0.646555
$208$		0			0
$209$	16.1738			1.11876
$210$		0			0
$211$	−6.53326	+	6.53326i	−0.449768	+	0.449768i	−0.895277	−	0.445509i	$-0.853023\pi$
$211$	−6.53326	+	6.53326i	−0.449768	+	0.449768i	0.445509	+	0.895277i	$0.353023\pi$
$212$		0			0
$213$	−0.406663	−	0.406663i	−0.0278641	−	0.0278641i
$214$		0			0
$215$		−	6.39060i		−	0.435836i
$216$		0			0
$217$			4.83612i			0.328297i
$218$		0			0
$219$	3.64708	+	3.64708i	0.246447	+	0.246447i
$220$		0			0
$221$	4.69459	−	4.69459i	0.315792	−	0.315792i
$222$		0			0
$223$	13.5801			0.909388			0.454694	−	0.890648i	$-0.349749\pi$
$223$	13.5801			0.909388			0.454694	+	0.890648i	$0.349749\pi$
$224$		0			0
$225$	−2.73635			−0.182423
$226$		0			0
$227$	−13.3137	+	13.3137i	−0.883663	+	0.883663i	−0.993905	−	0.110241i	$-0.964838\pi$
$227$	−13.3137	+	13.3137i	−0.883663	+	0.883663i	0.110241	+	0.993905i	$0.464838\pi$
$228$		0			0
$229$	14.3302	+	14.3302i	0.946969	+	0.946969i	0.998663	−	0.0516939i	$-0.0164620\pi$
$229$	14.3302	+	14.3302i	0.946969	+	0.946969i	−0.0516939	+	0.998663i	$0.516462\pi$
$230$		0			0
$231$		−	2.73037i		−	0.179645i
$232$		0			0
$233$		−	19.4016i		−	1.27104i	−0.772083	−	0.635522i	$-0.780785\pi$
$233$		−	19.4016i		−	1.27104i	0.772083	−	0.635522i	$-0.219215\pi$
$234$		0			0
$235$	7.91716	+	7.91716i	0.516459	+	0.516459i
$236$		0			0
$237$	−3.57091	+	3.57091i	−0.231956	+	0.231956i
$238$		0			0
$239$	−26.0171			−1.68290			−0.841452	−	0.540332i	$-0.818298\pi$
$239$	−26.0171			−1.68290			−0.841452	+	0.540332i	$0.818298\pi$
$240$		0			0
$241$	2.47780			0.159609			0.0798045	−	0.996811i	$-0.474570\pi$
$241$	2.47780			0.159609			0.0798045	+	0.996811i	$0.474570\pi$
$242$		0			0
$243$	8.67959	−	8.67959i	0.556796	−	0.556796i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$			16.4265i			1.04519i
$248$		0			0
$249$		−	5.85414i		−	0.370991i
$250$		0			0
$251$	17.7772	+	17.7772i	1.12209	+	1.12209i	0.991427	+	0.130663i	$0.0417105\pi$
$251$	17.7772	+	17.7772i	1.12209	+	1.12209i	0.130663	+	0.991427i	$0.458289\pi$
$252$		0			0
$253$	12.7824	−	12.7824i	0.803623	−	0.803623i
$254$		0			0
$255$	−0.631223			−0.0395287
$256$		0			0
$257$	7.36578			0.459465			0.229732	−	0.973254i	$-0.426215\pi$
$257$	7.36578			0.459465			0.229732	+	0.973254i	$0.426215\pi$
$258$		0			0
$259$	7.64574	−	7.64574i	0.475083	−	0.475083i
$260$		0			0
$261$	−10.5625	−	10.5625i	−0.653803	−	0.653803i
$262$		0			0
$263$			6.29121i			0.387933i	0.981008	+	0.193966i	$0.0621352\pi$
$263$			6.29121i			0.387933i	−0.981008	+	0.193966i	$0.937865\pi$
$264$		0			0
$265$		−	2.79181i		−	0.171500i
$266$		0			0
$267$	−3.14097	−	3.14097i	−0.192224	−	0.192224i
$268$		0			0
$269$	5.13348	−	5.13348i	0.312994	−	0.312994i	−0.533075	−	0.846068i	$-0.678964\pi$
$269$	5.13348	−	5.13348i	0.312994	−	0.312994i	0.846068	+	0.533075i	$0.178964\pi$
$270$		0			0
$271$	7.86495			0.477762			0.238881	−	0.971049i	$-0.423219\pi$
$271$	7.86495			0.477762			0.238881	+	0.971049i	$0.423219\pi$
$272$		0			0
$273$	2.77303			0.167831
$274$		0			0
$275$	−3.76005	+	3.76005i	−0.226740	+	0.226740i
$276$		0			0
$277$	5.15437	+	5.15437i	0.309696	+	0.309696i	0.844792	−	0.535096i	$-0.179724\pi$
$277$	5.15437	+	5.15437i	0.309696	+	0.309696i	−0.535096	+	0.844792i	$0.679724\pi$
$278$		0			0
$279$			13.2333i			0.792258i
$280$		0			0
$281$		−	13.0340i		−	0.777543i	−0.921334	−	0.388771i	$-0.872900\pi$
$281$		−	13.0340i		−	0.777543i	0.921334	−	0.388771i	$-0.127100\pi$
$282$		0			0
$283$	1.81621	+	1.81621i	0.107963	+	0.107963i	0.759025	−	0.651062i	$-0.225676\pi$
$283$	1.81621	+	1.81621i	0.107963	+	0.107963i	−0.651062	+	0.759025i	$0.725676\pi$
$284$		0			0
$285$	1.10433	−	1.10433i	0.0654151	−	0.0654151i
$286$		0			0
$287$	5.60526			0.330868
$288$		0			0
$289$	−15.4887			−0.911102
$290$		0			0
$291$	0.952819	−	0.952819i	0.0558552	−	0.0558552i
$292$		0			0
$293$	−15.3437	−	15.3437i	−0.896390	−	0.896390i	0.0987249	−	0.995115i	$-0.468524\pi$
$293$	−15.3437	−	15.3437i	−0.896390	−	0.896390i	−0.995115	+	0.0987249i	$0.968524\pi$
$294$		0			0
$295$			6.83318i			0.397843i
$296$		0			0
$297$		−	15.6624i		−	0.908822i
$298$		0			0
$299$	12.9821	+	12.9821i	0.750776	+	0.750776i
$300$		0			0
$301$	−4.51884	+	4.51884i	−0.260462	+	0.260462i
$302$		0			0
$303$	−5.95665			−0.342200
$304$		0			0
$305$	11.3174			0.648032
$306$		0			0
$307$	7.35015	−	7.35015i	0.419495	−	0.419495i	−0.465535	−	0.885030i	$-0.654138\pi$
$307$	7.35015	−	7.35015i	0.419495	−	0.419495i	0.885030	+	0.465535i	$0.154138\pi$
$308$		0			0
$309$	−0.598502	−	0.598502i	−0.0340476	−	0.0340476i
$310$		0			0
$311$		−	22.3350i		−	1.26650i	−0.773947	−	0.633250i	$-0.781720\pi$
$311$		−	22.3350i		−	1.26650i	0.773947	−	0.633250i	$-0.218280\pi$
$312$		0			0
$313$			28.6748i			1.62080i	0.585879	+	0.810399i	$0.300749\pi$
$313$			28.6748i			1.62080i	−0.585879	+	0.810399i	$0.699251\pi$
$314$		0			0
$315$	1.93489	+	1.93489i	0.109019	+	0.109019i
$316$		0			0
$317$	−4.09720	+	4.09720i	−0.230122	+	0.230122i	−0.812744	−	0.582622i	$-0.802027\pi$
$317$	−4.09720	+	4.09720i	−0.230122	+	0.230122i	0.582622	+	0.812744i	$0.302027\pi$
$318$		0			0
$319$	−29.0281			−1.62526
$320$		0			0
$321$	−6.28153			−0.350601
$322$		0			0
$323$	−2.64398	+	2.64398i	−0.147115	+	0.147115i
$324$		0			0
$325$	−3.81880	−	3.81880i	−0.211829	−	0.211829i
$326$		0			0
$327$		−	7.33322i		−	0.405528i
$328$		0			0
$329$		−	11.1966i		−	0.617286i
$330$		0			0
$331$	23.0608	+	23.0608i	1.26753	+	1.26753i	0.947358	+	0.320175i	$0.103742\pi$
$331$	23.0608	+	23.0608i	1.26753	+	1.26753i	0.320175	+	0.947358i	$0.396258\pi$
$332$		0			0
$333$	20.9214	−	20.9214i	1.14649	−	1.14649i
$334$		0			0
$335$	6.12252			0.334509
$336$		0			0
$337$	−14.8774			−0.810423			−0.405211	−	0.914223i	$-0.632802\pi$
$337$	−14.8774			−0.810423			−0.405211	+	0.914223i	$0.632802\pi$
$338$		0			0
$339$	−3.17177	+	3.17177i	−0.172267	+	0.172267i
$340$		0			0
$341$	18.1841	+	18.1841i	0.984722	+	0.984722i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	1.74554i		−	0.0939770i
$346$		0			0
$347$	−7.52134	−	7.52134i	−0.403766	−	0.403766i	0.475792	−	0.879558i	$-0.342162\pi$
$347$	−7.52134	−	7.52134i	−0.403766	−	0.403766i	−0.879558	+	0.475792i	$0.842162\pi$
$348$		0			0
$349$	−15.2493	+	15.2493i	−0.816278	+	0.816278i	−0.985567	−	0.169289i	$-0.945853\pi$
$349$	−15.2493	+	15.2493i	−0.816278	+	0.816278i	0.169289	+	0.985567i	$0.445853\pi$
$350$		0			0
$351$	15.9071			0.849057
$352$		0			0
$353$	−1.42888			−0.0760514			−0.0380257	−	0.999277i	$-0.512107\pi$
$353$	−1.42888			−0.0760514			−0.0380257	+	0.999277i	$0.512107\pi$
$354$		0			0
$355$	0.791994	−	0.791994i	0.0420347	−	0.0420347i
$356$		0			0
$357$	0.446342	+	0.446342i	0.0236229	+	0.0236229i
$358$		0			0
$359$			7.84741i			0.414170i	0.978323	+	0.207085i	$0.0663977\pi$
$359$			7.84741i			0.414170i	−0.978323	+	0.207085i	$0.933602\pi$
$360$		0			0
$361$			9.74863i			0.513086i
$362$		0			0
$363$	−6.27249	−	6.27249i	−0.329221	−	0.329221i
$364$		0			0
$365$	−7.10285	+	7.10285i	−0.371780	+	0.371780i
$366$		0			0
$367$	15.4075			0.804267			0.402134	−	0.915581i	$-0.368269\pi$
$367$	15.4075			0.804267			0.402134	+	0.915581i	$0.368269\pi$
$368$		0			0
$369$	15.3380			0.798462
$370$		0			0
$371$	−1.97411	+	1.97411i	−0.102491	+	0.102491i
$372$		0			0
$373$	21.2830	+	21.2830i	1.10199	+	1.10199i	0.994171	+	0.107819i	$0.0343868\pi$
$373$	21.2830	+	21.2830i	1.10199	+	1.10199i	0.107819	+	0.994171i	$0.465613\pi$
$374$		0			0
$375$			0.513467i			0.0265153i
$376$		0			0
$377$		−	29.4817i		−	1.51838i
$378$		0			0
$379$	18.9535	+	18.9535i	0.973577	+	0.973577i	0.999660	−	0.0260831i	$-0.00830344\pi$
$379$	18.9535	+	18.9535i	0.973577	+	0.973577i	−0.0260831	+	0.999660i	$0.508303\pi$
$380$		0			0
$381$	−0.101454	+	0.101454i	−0.00519767	+	0.00519767i
$382$		0			0
$383$	−21.3722			−1.09207			−0.546035	−	0.837762i	$-0.683863\pi$
$383$	−21.3722			−1.09207			−0.546035	+	0.837762i	$0.683863\pi$
$384$		0			0
$385$	5.31752			0.271006
$386$		0			0
$387$	−12.3651	+	12.3651i	−0.628555	+	0.628555i
$388$		0			0
$389$	15.0496	+	15.0496i	0.763043	+	0.763043i	0.976871	−	0.213828i	$-0.0685932\pi$
$389$	15.0496	+	15.0496i	0.763043	+	0.763043i	−0.213828	+	0.976871i	$0.568593\pi$
$390$		0			0
$391$			4.17916i			0.211349i
$392$		0			0
$393$		−	1.16666i		−	0.0588503i
$394$		0			0
$395$	−6.95451	−	6.95451i	−0.349919	−	0.349919i
$396$		0			0
$397$	0.208010	−	0.208010i	0.0104397	−	0.0104397i	−0.701868	−	0.712307i	$-0.747650\pi$
$397$	0.208010	−	0.208010i	0.0104397	−	0.0104397i	0.712307	+	0.701868i	$0.247650\pi$
$398$		0			0
$399$	−1.56176			−0.0781860
$400$		0			0
$401$	11.7484			0.586687			0.293344	−	0.956007i	$-0.405232\pi$
$401$	11.7484			0.586687			0.293344	+	0.956007i	$0.405232\pi$
$402$		0			0
$403$	−18.4682	+	18.4682i	−0.919966	+	0.919966i
$404$		0			0
$405$	4.73527	+	4.73527i	0.235297	+	0.235297i
$406$		0			0
$407$		−	57.4967i		−	2.85001i
$408$		0			0
$409$			17.4569i			0.863186i	0.902068	+	0.431593i	$0.142048\pi$
$409$			17.4569i			0.863186i	−0.902068	+	0.431593i	$0.857952\pi$
$410$		0			0
$411$	−5.12142	−	5.12142i	−0.252621	−	0.252621i
$412$		0			0
$413$	4.83179	−	4.83179i	0.237757	−	0.237757i
$414$		0			0
$415$	11.4012			0.559664
$416$		0			0
$417$	8.36337			0.409556
$418$		0			0
$419$	24.9444	−	24.9444i	1.21861	−	1.21861i	0.250495	−	0.968118i	$-0.419407\pi$
$419$	24.9444	−	24.9444i	1.21861	−	1.21861i	0.968118	−	0.250495i	$-0.0805935\pi$
$420$		0			0
$421$	9.66427	+	9.66427i	0.471007	+	0.471007i	0.902241	−	0.431233i	$-0.141921\pi$
$421$	9.66427	+	9.66427i	0.471007	+	0.471007i	−0.431233	+	0.902241i	$0.641921\pi$
$422$		0			0
$423$		−	30.6377i		−	1.48966i
$424$		0			0
$425$		−	1.22933i		−	0.0596315i
$426$		0			0
$427$	−8.00261	−	8.00261i	−0.387273	−	0.387273i
$428$		0			0
$429$	10.4267	−	10.4267i	0.503408	−	0.503408i
$430$		0			0
$431$	33.4546			1.61145			0.805726	−	0.592288i	$-0.201775\pi$
$431$	33.4546			1.61145			0.805726	+	0.592288i	$0.201775\pi$
$432$		0			0
$433$	−0.505752			−0.0243049			−0.0121525	−	0.999926i	$-0.503868\pi$
$433$	−0.505752			−0.0243049			−0.0121525	+	0.999926i	$0.503868\pi$
$434$		0			0
$435$	−1.98202	+	1.98202i	−0.0950305	+	0.0950305i
$436$		0			0
$437$	−7.31150	−	7.31150i	−0.349757	−	0.349757i
$438$		0			0
$439$			8.60667i			0.410774i	0.978681	+	0.205387i	$0.0658453\pi$
$439$			8.60667i			0.410774i	−0.978681	+	0.205387i	$0.934155\pi$
$440$		0			0
$441$		−	2.73635i		−	0.130302i
$442$		0			0
$443$	−18.0162	−	18.0162i	−0.855977	−	0.855977i	0.134885	−	0.990861i	$-0.456934\pi$
$443$	−18.0162	−	18.0162i	−0.855977	−	0.855977i	−0.990861	+	0.134885i	$0.956934\pi$
$444$		0			0
$445$	6.11718	−	6.11718i	0.289982	−	0.289982i
$446$		0			0
$447$	8.36007			0.395418
$448$		0			0
$449$	−35.9343			−1.69585			−0.847923	−	0.530120i	$-0.822147\pi$
$449$	−35.9343			−1.69585			−0.847923	+	0.530120i	$0.822147\pi$
$450$		0			0
$451$	21.0761	−	21.0761i	0.992433	−	0.992433i
$452$		0			0
$453$	−2.74143	−	2.74143i	−0.128804	−	0.128804i
$454$		0			0
$455$			5.40060i			0.253184i
$456$		0			0
$457$			21.2833i			0.995591i	0.867295	+	0.497795i	$0.165857\pi$
$457$			21.2833i			0.995591i	−0.867295	+	0.497795i	$0.834143\pi$
$458$		0			0
$459$	2.56037	+	2.56037i	0.119508	+	0.119508i
$460$		0			0
$461$	13.8686	−	13.8686i	0.645927	−	0.645927i	−0.306079	−	0.952006i	$-0.599017\pi$
$461$	13.8686	−	13.8686i	0.645927	−	0.645927i	0.952006	+	0.306079i	$0.0990172\pi$
$462$		0			0
$463$	30.0488			1.39649			0.698243	−	0.715861i	$-0.253965\pi$
$463$	30.0488			1.39649			0.698243	+	0.715861i	$0.253965\pi$
$464$		0			0
$465$	2.48319			0.115155
$466$		0			0
$467$	−8.45956	+	8.45956i	−0.391462	+	0.391462i	−0.875208	−	0.483746i	$-0.839276\pi$
$467$	−8.45956	+	8.45956i	−0.391462	+	0.391462i	0.483746	+	0.875208i	$0.339276\pi$
$468$		0			0
$469$	−4.32927	−	4.32927i	−0.199907	−	0.199907i
$470$		0			0
$471$			1.65164i			0.0761034i
$472$		0			0
$473$			33.9821i			1.56250i
$474$		0			0
$475$	2.15074	+	2.15074i	0.0986827	+	0.0986827i
$476$		0			0
$477$	−5.40186	+	5.40186i	−0.247334	+	0.247334i
$478$		0			0
$479$	4.59025			0.209734			0.104867	−	0.994486i	$-0.466558\pi$
$479$	4.59025			0.209734			0.104867	+	0.994486i	$0.466558\pi$
$480$		0			0
$481$	58.3951			2.66259
$482$		0			0
$483$	−1.23429	+	1.23429i	−0.0561620	+	0.0561620i
$484$		0			0
$485$	1.85566	+	1.85566i	0.0842611	+	0.0842611i
$486$		0			0
$487$		−	9.51381i		−	0.431112i	−0.976491	−	0.215556i	$-0.930844\pi$
$487$		−	9.51381i		−	0.431112i	0.976491	−	0.215556i	$-0.0691564\pi$
$488$		0			0
$489$		−	4.80308i		−	0.217203i
$490$		0			0
$491$	5.84959	+	5.84959i	0.263988	+	0.263988i	0.826672	−	0.562684i	$-0.190231\pi$
$491$	5.84959	+	5.84959i	0.263988	+	0.263988i	−0.562684	+	0.826672i	$0.690231\pi$
$492$		0			0
$493$	4.74532	−	4.74532i	0.213718	−	0.213718i
$494$		0			0
$495$	14.5506			0.654001
$496$		0			0
$497$	−1.12005			−0.0502411
$498$		0			0
$499$	14.4037	−	14.4037i	0.644799	−	0.644799i	−0.306932	−	0.951731i	$-0.599303\pi$
$499$	14.4037	−	14.4037i	0.644799	−	0.644799i	0.951731	+	0.306932i	$0.0993026\pi$
$500$		0			0
$501$	8.60163	+	8.60163i	0.384292	+	0.384292i
$502$		0			0
$503$			21.2968i			0.949575i	0.880100	+	0.474788i	$0.157475\pi$
$503$			21.2968i			0.949575i	−0.880100	+	0.474788i	$0.842525\pi$
$504$		0			0
$505$		−	11.6008i		−	0.516231i
$506$		0			0
$507$	5.86967	+	5.86967i	0.260681	+	0.260681i
$508$		0			0
$509$	0.516988	−	0.516988i	0.0229151	−	0.0229151i	−0.695556	−	0.718471i	$-0.744842\pi$
$509$	0.516988	−	0.516988i	0.0229151	−	0.0229151i	0.718471	+	0.695556i	$0.244842\pi$
$510$		0			0
$511$	10.0450			0.444362
$512$		0			0
$513$	−8.95883			−0.395542
$514$		0			0
$515$	1.16561	−	1.16561i	0.0513629	−	0.0513629i
$516$		0			0
$517$	−42.0996	−	42.0996i	−1.85154	−	1.85154i
$518$		0			0
$519$		−	5.90256i		−	0.259094i
$520$		0			0
$521$		−	1.89674i		−	0.0830978i	−0.999136	−	0.0415489i	$-0.986771\pi$
$521$		−	1.89674i		−	0.0830978i	0.999136	−	0.0415489i	$-0.0132292\pi$
$522$		0			0
$523$	17.2225	+	17.2225i	0.753089	+	0.753089i	0.975055	−	0.221965i	$-0.0712471\pi$
$523$	17.2225	+	17.2225i	0.753089	+	0.753089i	−0.221965	+	0.975055i	$0.571247\pi$
$524$		0			0
$525$	0.363076	−	0.363076i	0.0158459	−	0.0158459i
$526$		0			0
$527$	−5.94521			−0.258977
$528$		0			0
$529$	11.4432			0.497531
$530$		0			0
$531$	13.2215	−	13.2215i	0.573763	−	0.573763i
$532$		0			0
$533$	21.4054	+	21.4054i	0.927170	+	0.927170i
$534$		0			0
$535$		−	12.2336i		−	0.528904i
$536$		0			0
$537$			2.99355i			0.129181i
$538$		0			0
$539$	−3.76005	−	3.76005i	−0.161957	−	0.161957i
$540$		0			0
$541$	−10.0372	+	10.0372i	−0.431535	+	0.431535i	−0.889150	−	0.457615i	$-0.848704\pi$
$541$	−10.0372	+	10.0372i	−0.431535	+	0.431535i	0.457615	+	0.889150i	$0.348704\pi$
$542$		0			0
$543$	7.87495			0.337946
$544$		0			0
$545$	14.2818			0.611764
$546$		0			0
$547$	−23.4562	+	23.4562i	−1.00292	+	1.00292i	−0.00292062	+	0.999996i	$0.500930\pi$
$547$	−23.4562	+	23.4562i	−1.00292	+	1.00292i	−0.999996	+	0.00292062i	$0.999070\pi$
$548$		0			0
$549$	−21.8980	−	21.8980i	−0.934582	−	0.934582i
$550$		0			0
$551$			16.6040i			0.707355i
$552$		0			0
$553$			9.83517i			0.418234i
$554$		0			0
$555$	−3.92583	−	3.92583i	−0.166642	−	0.166642i
$556$		0			0
$557$	−30.9681	+	30.9681i	−1.31216	+	1.31216i	−0.392340	+	0.919820i	$0.628334\pi$
$557$	−30.9681	+	30.9681i	−1.31216	+	1.31216i	−0.919820	+	0.392340i	$0.871666\pi$
$558$		0			0
$559$	−34.5131			−1.45975
$560$		0			0
$561$	3.35654			0.141713
$562$		0			0
$563$	18.0062	−	18.0062i	0.758869	−	0.758869i	−0.217247	−	0.976117i	$-0.569708\pi$
$563$	18.0062	−	18.0062i	0.758869	−	0.758869i	0.976117	+	0.217247i	$0.0697078\pi$
$564$		0			0
$565$	−6.17716	−	6.17716i	−0.259875	−	0.259875i
$566$		0			0
$567$		−	6.69668i		−	0.281234i
$568$		0			0
$569$		−	27.5520i		−	1.15504i	−0.816376	−	0.577521i	$-0.804020\pi$
$569$		−	27.5520i		−	1.15504i	0.816376	−	0.577521i	$-0.195980\pi$
$570$		0			0
$571$	14.9312	+	14.9312i	0.624850	+	0.624850i	0.946768	−	0.321918i	$-0.104328\pi$
$571$	14.9312	+	14.9312i	0.624850	+	0.624850i	−0.321918	+	0.946768i	$0.604328\pi$
$572$		0			0
$573$	−1.43482	+	1.43482i	−0.0599406	+	0.0599406i
$574$		0			0
$575$	3.39953			0.141770
$576$		0			0
$577$	8.57685			0.357059			0.178530	−	0.983935i	$-0.442866\pi$
$577$	8.57685			0.357059			0.178530	+	0.983935i	$0.442866\pi$
$578$		0			0
$579$	−5.89131	+	5.89131i	−0.244834	+	0.244834i
$580$		0			0
$581$	−8.06188	−	8.06188i	−0.334463	−	0.334463i
$582$		0			0
$583$			14.8455i			0.614838i
$584$		0			0
$585$			14.7780i			0.610993i
$586$		0			0
$587$	−29.6584	−	29.6584i	−1.22413	−	1.22413i	−0.966149	−	0.257984i	$-0.916942\pi$
$587$	−29.6584	−	29.6584i	−1.22413	−	1.22413i	−0.257984	−	0.966149i	$-0.583058\pi$
$588$		0			0
$589$	10.4012	−	10.4012i	0.428576	−	0.428576i
$590$		0			0
$591$	13.0372			0.536278
$592$		0			0
$593$	−4.12537			−0.169409			−0.0847044	−	0.996406i	$-0.526995\pi$
$593$	−4.12537			−0.169409			−0.0847044	+	0.996406i	$0.526995\pi$
$594$		0			0
$595$	−0.869271	+	0.869271i	−0.0356366	+	0.0356366i
$596$		0			0
$597$	2.09385	+	2.09385i	0.0856957	+	0.0856957i
$598$		0			0
$599$			23.0861i			0.943274i	0.881793	+	0.471637i	$0.156337\pi$
$599$			23.0861i			0.943274i	−0.881793	+	0.471637i	$0.843663\pi$
$600$		0			0
$601$			24.5699i			1.00223i	0.865382	+	0.501113i	$0.167076\pi$
$601$			24.5699i			1.00223i	−0.865382	+	0.501113i	$0.832924\pi$
$602$		0			0
$603$	−11.8464	−	11.8464i	−0.482423	−	0.482423i
$604$		0			0
$605$	12.2160	−	12.2160i	0.496650	−	0.496650i
$606$		0			0
$607$	6.18418			0.251008			0.125504	−	0.992093i	$-0.459945\pi$
$607$	6.18418			0.251008			0.125504	+	0.992093i	$0.459945\pi$
$608$		0			0
$609$	2.80300			0.113583
$610$		0			0
$611$	42.7575	−	42.7575i	1.72978	−	1.72978i
$612$		0			0
$613$	15.2829	+	15.2829i	0.617271	+	0.617271i	0.944831	−	0.327559i	$-0.106226\pi$
$613$	15.2829	+	15.2829i	0.617271	+	0.617271i	−0.327559	+	0.944831i	$0.606226\pi$
$614$		0			0
$615$		−	2.87811i		−	0.116057i
$616$		0			0
$617$			16.5972i			0.668180i	0.942541	+	0.334090i	$0.108429\pi$
$617$			16.5972i			0.668180i	−0.942541	+	0.334090i	$0.891571\pi$
$618$		0			0
$619$	−20.3800	−	20.3800i	−0.819143	−	0.819143i	0.166841	−	0.985984i	$-0.446643\pi$
$619$	−20.3800	−	20.3800i	−0.819143	−	0.819143i	−0.985984	+	0.166841i	$0.946643\pi$
$620$		0			0
$621$	−7.08030	+	7.08030i	−0.284123	+	0.284123i
$622$		0			0
$623$	−8.65099			−0.346595
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−5.87231	+	5.87231i	−0.234518	+	0.234518i
$628$		0			0
$629$	9.39917	+	9.39917i	0.374769	+	0.374769i
$630$		0			0
$631$			2.79654i			0.111329i	0.998450	+	0.0556643i	$0.0177277\pi$
$631$			2.79654i			0.111329i	−0.998450	+	0.0556643i	$0.982272\pi$
$632$		0			0
$633$		−	4.74414i		−	0.188563i
$634$		0			0
$635$	−0.197587	−	0.197587i	−0.00784101	−	0.00784101i
$636$		0			0
$637$	3.81880	−	3.81880i	0.151307	−	0.151307i
$638$		0			0
$639$	−3.06485			−0.121244
$640$		0			0
$641$	−15.7177			−0.620811			−0.310406	−	0.950604i	$-0.600465\pi$
$641$	−15.7177			−0.620811			−0.310406	+	0.950604i	$0.600465\pi$
$642$		0			0
$643$	26.6705	−	26.6705i	1.05178	−	1.05178i	0.0531974	−	0.998584i	$-0.483059\pi$
$643$	26.6705	−	26.6705i	1.05178	−	1.05178i	0.998584	−	0.0531974i	$-0.0169412\pi$
$644$		0			0
$645$	2.32027	+	2.32027i	0.0913607	+	0.0913607i
$646$		0			0
$647$		−	21.3249i		−	0.838370i	−0.907901	−	0.419185i	$-0.862316\pi$
$647$		−	21.3249i		−	0.838370i	0.907901	−	0.419185i	$-0.137684\pi$
$648$		0			0
$649$		−	36.3355i		−	1.42629i
$650$		0			0
$651$	−1.75588	−	1.75588i	−0.0688183	−	0.0688183i
$652$		0			0
$653$	−2.92010	+	2.92010i	−0.114272	+	0.114272i	−0.761931	−	0.647658i	$-0.775748\pi$
$653$	−2.92010	+	2.92010i	−0.114272	+	0.114272i	0.647658	+	0.761931i	$0.275748\pi$
$654$		0			0
$655$	2.27213			0.0887793
$656$		0			0
$657$	27.4865			1.07235
$658$		0			0
$659$	28.3196	−	28.3196i	1.10317	−	1.10317i	0.109149	−	0.994025i	$-0.465187\pi$
$659$	28.3196	−	28.3196i	1.10317	−	1.10317i	0.994025	−	0.109149i	$-0.0348127\pi$
$660$		0			0
$661$	30.5397	+	30.5397i	1.18786	+	1.18786i	0.977659	+	0.210198i	$0.0674108\pi$
$661$	30.5397	+	30.5397i	1.18786	+	1.18786i	0.210198	+	0.977659i	$0.432589\pi$
$662$		0			0
$663$			3.40898i			0.132394i
$664$		0			0
$665$		−	3.04161i		−	0.117948i
$666$		0			0
$667$	13.1224	+	13.1224i	0.508102	+	0.508102i
$668$		0			0
$669$	−4.93059	+	4.93059i	−0.190628	+	0.190628i
$670$		0			0
$671$	−60.1805			−2.32324
$672$		0			0
$673$	−39.2018			−1.51112			−0.755559	−	0.655080i	$-0.772635\pi$
$673$	−39.2018			−1.51112			−0.755559	+	0.655080i	$0.772635\pi$
$674$		0			0
$675$	2.08273	−	2.08273i	0.0801643	−	0.0801643i
$676$		0			0
$677$	−2.76100	−	2.76100i	−0.106114	−	0.106114i	0.652057	−	0.758170i	$-0.273906\pi$
$677$	−2.76100	−	2.76100i	−0.106114	−	0.106114i	−0.758170	+	0.652057i	$0.773906\pi$
$678$		0			0
$679$		−	2.62430i		−	0.100711i
$680$		0			0
$681$		−	9.66779i		−	0.370470i
$682$		0			0
$683$	−1.56733	−	1.56733i	−0.0599721	−	0.0599721i	0.676485	−	0.736457i	$-0.263503\pi$
$683$	−1.56733	−	1.56733i	−0.0599721	−	0.0599721i	−0.736457	+	0.676485i	$0.763503\pi$
$684$		0			0
$685$	9.97421	−	9.97421i	0.381095	−	0.381095i
$686$		0			0
$687$	−10.4059			−0.397011
$688$		0			0
$689$	−15.0775			−0.574406
$690$		0			0
$691$	−11.0725	+	11.0725i	−0.421218	+	0.421218i	−0.885623	−	0.464405i	$-0.846268\pi$
$691$	−11.0725	+	11.0725i	−0.421218	+	0.421218i	0.464405	+	0.885623i	$0.346268\pi$
$692$		0			0
$693$	−10.2888	−	10.2888i	−0.390840	−	0.390840i
$694$		0			0
$695$			16.2880i			0.617841i
$696$		0			0
$697$			6.89074i			0.261005i
$698$		0			0
$699$	7.04427	+	7.04427i	0.266439	+	0.266439i
$700$		0			0
$701$	31.4299	−	31.4299i	1.18709	−	1.18709i	0.209225	−	0.977867i	$-0.432906\pi$
$701$	31.4299	−	31.4299i	1.18709	−	1.18709i	0.977867	−	0.209225i	$-0.0670942\pi$
$702$		0			0
$703$	−32.8880			−1.24039
$704$		0			0
$705$	−5.74906			−0.216522
$706$		0			0
$707$	−8.20304	+	8.20304i	−0.308507	+	0.308507i
$708$		0			0
$709$	−21.0383	−	21.0383i	−0.790111	−	0.790111i	0.191401	−	0.981512i	$-0.438697\pi$
$709$	−21.0383	−	21.0383i	−0.790111	−	0.790111i	−0.981512	+	0.191401i	$0.938697\pi$
$710$		0			0
$711$			26.9125i			1.00930i
$712$		0			0
$713$		−	16.4405i		−	0.615702i
$714$		0			0
$715$	20.3066	+	20.3066i	0.759422	+	0.759422i
$716$		0			0
$717$	9.44616	−	9.44616i	0.352773	−	0.352773i
$718$		0			0
$719$	37.4693			1.39737			0.698685	−	0.715429i	$-0.253769\pi$
$719$	37.4693			1.39737			0.698685	+	0.715429i	$0.253769\pi$
$720$		0			0
$721$	−1.64842			−0.0613904
$722$		0			0
$723$	−0.899628	+	0.899628i	−0.0334575	+	0.0334575i
$724$		0			0
$725$	−3.86007	−	3.86007i	−0.143359	−	0.143359i
$726$		0			0
$727$			47.8511i			1.77470i	0.461096	+	0.887350i	$0.347456\pi$
$727$			47.8511i			1.77470i	−0.461096	+	0.887350i	$0.652544\pi$
$728$		0			0
$729$		−	13.7873i		−	0.510642i
$730$		0			0
$731$	−5.55517	−	5.55517i	−0.205465	−	0.205465i
$732$		0			0
$733$	−19.6508	+	19.6508i	−0.725818	+	0.725818i	−0.969784	−	0.243966i	$-0.921551\pi$
$733$	−19.6508	+	19.6508i	−0.725818	+	0.725818i	0.243966	+	0.969784i	$0.421551\pi$
$734$		0			0
$735$	−0.513467			−0.0189395
$736$		0			0
$737$	−32.5566			−1.19924
$738$		0			0
$739$	10.0150	−	10.0150i	0.368409	−	0.368409i	−0.498488	−	0.866897i	$-0.666111\pi$
$739$	10.0150	−	10.0150i	0.368409	−	0.368409i	0.866897	+	0.498488i	$0.166111\pi$
$740$		0			0
$741$	−5.96407	−	5.96407i	−0.219096	−	0.219096i
$742$		0			0
$743$		−	20.3800i		−	0.747671i	−0.927495	−	0.373836i	$-0.878042\pi$
$743$		−	20.3800i		−	0.747671i	0.927495	−	0.373836i	$-0.121958\pi$
$744$		0			0
$745$			16.2816i			0.596512i
$746$		0			0
$747$	−22.0601	−	22.0601i	−0.807138	−	0.807138i
$748$		0			0
$749$	−8.65044	+	8.65044i	−0.316080	+	0.316080i
$750$		0			0
$751$	17.2955			0.631122			0.315561	−	0.948905i	$-0.397807\pi$
$751$	17.2955			0.631122			0.315561	+	0.948905i	$0.397807\pi$
$752$		0			0
$753$	−12.9090			−0.470429
$754$		0			0
$755$	5.33906	−	5.33906i	0.194308	−	0.194308i
$756$		0			0
$757$	28.4693	+	28.4693i	1.03473	+	1.03473i	0.999375	+	0.0353583i	$0.0112573\pi$
$757$	28.4693	+	28.4693i	1.03473	+	1.03473i	0.0353583	+	0.999375i	$0.488743\pi$
$758$		0			0
$759$			9.28196i			0.336914i
$760$		0			0
$761$			14.1940i			0.514534i	0.966340	+	0.257267i	$0.0828219\pi$
$761$			14.1940i			0.514534i	−0.966340	+	0.257267i	$0.917178\pi$
$762$		0			0
$763$	−10.0987	−	10.0987i	−0.365599	−	0.365599i
$764$		0			0
$765$	−2.37863	+	2.37863i	−0.0859996	+	0.0859996i
$766$		0			0
$767$	36.9033			1.33250
$768$		0			0
$769$	−53.7786			−1.93931			−0.969654	−	0.244483i	$-0.921382\pi$
$769$	−53.7786			−1.93931			−0.969654	+	0.244483i	$0.921382\pi$
$770$		0			0
$771$	−2.67434	+	2.67434i	−0.0963138	+	0.0963138i
$772$		0			0
$773$	11.8696	+	11.8696i	0.426919	+	0.426919i	0.887578	−	0.460658i	$-0.152387\pi$
$773$	11.8696	+	11.8696i	0.426919	+	0.426919i	−0.460658	+	0.887578i	$0.652387\pi$
$774$		0			0
$775$			4.83612i			0.173719i
$776$		0			0
$777$			5.55196i			0.199176i
$778$		0			0
$779$	−12.0555	−	12.0555i	−0.431932	−	0.431932i
$780$		0			0
$781$	−4.21144	+	4.21144i	−0.150697	+	0.150697i
$782$		0			0
$783$	16.0790			0.574616
$784$		0			0
$785$	−3.21664			−0.114807
$786$		0			0
$787$	−14.3371	+	14.3371i	−0.511062	+	0.511062i	−0.914852	−	0.403789i	$-0.867693\pi$
$787$	−14.3371	+	14.3371i	−0.511062	+	0.511062i	0.403789	+	0.914852i	$0.367693\pi$
$788$		0			0
$789$	−2.28419	−	2.28419i	−0.0813192	−	0.0813192i
$790$		0			0
$791$			8.73583i			0.310610i
$792$		0			0
$793$		−	61.1208i		−	2.17046i
$794$		0			0
$795$	1.01364	+	1.01364i	0.0359501	+	0.0359501i
$796$		0			0
$797$	17.5732	−	17.5732i	0.622474	−	0.622474i	−0.323689	−	0.946163i	$-0.604923\pi$
$797$	17.5732	−	17.5732i	0.622474	−	0.622474i	0.946163	+	0.323689i	$0.104923\pi$
$798$		0			0
$799$	13.7643			0.486947
$800$		0			0
$801$	−23.6722			−0.836415
$802$		0			0
$803$	37.7695	−	37.7695i	1.33286	−	1.33286i
$804$		0			0
$805$	−2.40383	−	2.40383i	−0.0847238	−	0.0847238i
$806$		0			0
$807$			3.72768i			0.131221i
$808$		0			0
$809$		−	2.44819i		−	0.0860736i	−0.999073	−	0.0430368i	$-0.986297\pi$
$809$		−	2.44819i		−	0.0860736i	0.999073	−	0.0430368i	$-0.0137033\pi$
$810$		0			0
$811$	−3.38354	−	3.38354i	−0.118812	−	0.118812i	0.645201	−	0.764013i	$-0.276774\pi$
$811$	−3.38354	−	3.38354i	−0.118812	−	0.118812i	−0.764013	+	0.645201i	$0.776774\pi$
$812$		0			0
$813$	−2.85557	+	2.85557i	−0.100149	+	0.100149i
$814$		0			0
$815$	9.35421			0.327664
$816$		0			0
$817$	19.4377			0.680039
$818$		0			0
$819$	10.4496	−	10.4496i	0.365138	−	0.365138i
$820$		0			0
$821$	33.1335	+	33.1335i	1.15637	+	1.15637i	0.985251	+	0.171117i	$0.0547375\pi$
$821$	33.1335	+	33.1335i	1.15637	+	1.15637i	0.171117	+	0.985251i	$0.445263\pi$
$822$		0			0
$823$			1.60587i			0.0559772i	0.999608	+	0.0279886i	$0.00891021\pi$
$823$			1.60587i			0.0559772i	−0.999608	+	0.0279886i	$0.991090\pi$
$824$		0			0
$825$		−	2.73037i		−	0.0950592i
$826$		0			0
$827$	23.7249	+	23.7249i	0.824996	+	0.824996i	0.986820	−	0.161823i	$-0.0517375\pi$
$827$	23.7249	+	23.7249i	0.824996	+	0.824996i	−0.161823	+	0.986820i	$0.551737\pi$
$828$		0			0
$829$	38.2323	−	38.2323i	1.32786	−	1.32786i	0.420630	−	0.907232i	$-0.361809\pi$
$829$	38.2323	−	38.2323i	1.32786	−	1.32786i	0.907232	−	0.420630i	$-0.138191\pi$
$830$		0			0
$831$	−3.74285			−0.129838
$832$		0			0
$833$	1.22933			0.0425939
$834$		0			0
$835$	−16.7521	+	16.7521i	−0.579729	+	0.579729i
$836$		0			0
$837$	−10.0723	−	10.0723i	−0.348151	−	0.348151i
$838$		0			0
$839$		−	6.78963i		−	0.234404i	−0.993108	−	0.117202i	$-0.962607\pi$
$839$		−	6.78963i		−	0.234404i	0.993108	−	0.117202i	$-0.0373925\pi$
$840$		0			0
$841$		−	0.800274i		−	0.0275956i
$842$		0			0
$843$	4.73233	+	4.73233i	0.162990	+	0.162990i
$844$		0			0
$845$	−11.4315	+	11.4315i	−0.393254	+	0.393254i
$846$		0			0
$847$	−17.2760			−0.593610
$848$		0			0
$849$	−1.31885			−0.0452627
$850$		0			0
$851$	−25.9919	+	25.9919i	−0.890991	+	0.890991i
$852$		0			0
$853$	8.25362	+	8.25362i	0.282599	+	0.282599i	0.834145	−	0.551546i	$-0.185962\pi$
$853$	8.25362	+	8.25362i	0.282599	+	0.282599i	−0.551546	+	0.834145i	$0.685962\pi$
$854$		0			0
$855$		−	8.32291i		−	0.284637i
$856$		0			0
$857$			0.789262i			0.0269607i	0.999909	+	0.0134803i	$0.00429106\pi$
$857$			0.789262i			0.0269607i	−0.999909	+	0.0134803i	$0.995709\pi$
$858$		0			0
$859$	−27.4114	−	27.4114i	−0.935265	−	0.935265i	0.0627635	−	0.998028i	$-0.480009\pi$
$859$	−27.4114	−	27.4114i	−0.935265	−	0.935265i	−0.998028	+	0.0627635i	$0.980009\pi$
$860$		0			0
$861$	−2.03513	+	2.03513i	−0.0693572	+	0.0693572i
$862$		0			0
$863$	19.6198			0.667866			0.333933	−	0.942597i	$-0.391624\pi$
$863$	19.6198			0.667866			0.333933	+	0.942597i	$0.391624\pi$
$864$		0			0
$865$	11.4955			0.390859
$866$		0			0
$867$	5.62359	−	5.62359i	0.190987	−	0.190987i
$868$		0			0
$869$	36.9807	+	36.9807i	1.25449	+	1.25449i
$870$		0			0
$871$		−	33.0653i		−	1.12037i
$872$		0			0
$873$		−	7.18100i		−	0.243040i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	13.5030	−	13.5030i	0.455965	−	0.455965i	−0.441363	−	0.897328i	$-0.645505\pi$
$877$	13.5030	−	13.5030i	0.455965	−	0.455965i	0.897328	+	0.441363i	$0.145505\pi$
$878$		0			0
$879$	11.1419			0.375806
$880$		0			0
$881$	31.4352			1.05908			0.529539	−	0.848286i	$-0.322365\pi$
$881$	31.4352			1.05908			0.529539	+	0.848286i	$0.322365\pi$
$882$		0			0
$883$	24.9084	−	24.9084i	0.838236	−	0.838236i	−0.150391	−	0.988627i	$-0.548053\pi$
$883$	24.9084	−	24.9084i	0.838236	−	0.838236i	0.988627	+	0.150391i	$0.0480532\pi$
$884$		0			0
$885$	−2.48096	−	2.48096i	−0.0833966	−	0.0833966i
$886$		0			0
$887$			27.1740i			0.912415i	0.889873	+	0.456208i	$0.150793\pi$
$887$			27.1740i			0.912415i	−0.889873	+	0.456208i	$0.849207\pi$
$888$		0			0
$889$			0.279431i			0.00937180i
$890$		0			0
$891$	−25.1799	−	25.1799i	−0.843557	−	0.843557i
$892$		0			0
$893$	−24.0809	+	24.0809i	−0.805836	+	0.805836i
$894$		0			0
$895$	−5.83007			−0.194878
$896$		0			0
$897$	−9.42699			−0.314758
$898$		0			0
$899$	−18.6678	+	18.6678i	−0.622605	+	0.622605i
$900$		0			0
$901$	−2.42684	−	2.42684i	−0.0808498	−	0.0808498i
$902$		0			0
$903$		−	3.28136i		−	0.109197i
$904$		0			0
$905$			15.3368i			0.509813i
$906$		0			0
$907$	7.24783	+	7.24783i	0.240660	+	0.240660i	0.817123	−	0.576463i	$-0.195568\pi$
$907$	7.24783	+	7.24783i	0.240660	+	0.240660i	−0.576463	+	0.817123i	$0.695568\pi$
$908$		0			0
$909$	−22.4464	+	22.4464i	−0.744500	+	0.744500i
$910$		0			0
$911$	−29.8463			−0.988852			−0.494426	−	0.869220i	$-0.664622\pi$
$911$	−29.8463			−0.988852			−0.494426	+	0.869220i	$0.664622\pi$
$912$		0			0
$913$	−60.6261			−2.00643
$914$		0			0
$915$	−4.10907	+	4.10907i	−0.135842	+	0.135842i
$916$		0			0
$917$	−1.60664	−	1.60664i	−0.0530558	−	0.0530558i
$918$		0			0
$919$			44.1212i			1.45542i	0.685883	+	0.727712i	$0.259416\pi$
$919$			44.1212i			1.45542i	−0.685883	+	0.727712i	$0.740584\pi$
$920$		0			0
$921$			5.33732i			0.175871i
$922$		0			0
$923$	−4.27725	−	4.27725i	−0.140787	−	0.140787i
$924$		0			0
$925$	7.64574	−	7.64574i	0.251390	−	0.251390i
$926$		0			0
$927$	−4.51066			−0.148150
$928$		0			0
$929$	−29.6604			−0.973127			−0.486563	−	0.873645i	$-0.661750\pi$
$929$	−29.6604			−0.973127			−0.486563	+	0.873645i	$0.661750\pi$
$930$		0			0
$931$	−2.15074	+	2.15074i	−0.0704877	+	0.0704877i
$932$		0			0
$933$	8.10929	+	8.10929i	0.265486	+	0.265486i
$934$		0			0
$935$			6.53701i			0.213783i
$936$		0			0
$937$			0.565528i			0.0184750i	0.999957	+	0.00923749i	$0.00294043\pi$
$937$			0.565528i			0.0184750i	−0.999957	+	0.00923749i	$0.997060\pi$
$938$		0			0
$939$	−10.4111	−	10.4111i	−0.339755	−	0.339755i
$940$		0			0
$941$	−40.3902	+	40.3902i	−1.31668	+	1.31668i	−0.400299	+	0.916385i	$0.631094\pi$
$941$	−40.3902	+	40.3902i	−1.31668	+	1.31668i	−0.916385	+	0.400299i	$0.868906\pi$
$942$		0			0
$943$	−19.0552			−0.620524
$944$		0			0
$945$	−2.94543			−0.0958147
$946$		0			0
$947$	1.27770	−	1.27770i	0.0415197	−	0.0415197i	−0.686042	−	0.727562i	$-0.740653\pi$
$947$	1.27770	−	1.27770i	0.0415197	−	0.0415197i	0.727562	+	0.686042i	$0.240653\pi$
$948$		0			0
$949$	38.3597	+	38.3597i	1.24521	+	1.24521i
$950$		0			0
$951$		−	2.97519i		−	0.0964772i
$952$		0			0
$953$			20.9161i			0.677539i	0.940869	+	0.338770i	$0.110011\pi$
$953$			20.9161i			0.677539i	−0.940869	+	0.338770i	$0.889989\pi$
$954$		0			0
$955$	−2.79438	−	2.79438i	−0.0904241	−	0.0904241i
$956$		0			0
$957$	10.5394	−	10.5394i	0.340691	−	0.340691i
$958$		0			0
$959$	−14.1057			−0.455495
$960$		0			0
$961$	−7.61195			−0.245547
$962$		0			0
$963$	−23.6707	+	23.6707i	−0.762776	+	0.762776i
$964$		0			0
$965$	−11.4736	−	11.4736i	−0.369348	−	0.369348i
$966$		0			0
$967$		−	10.9368i		−	0.351705i	−0.984417	−	0.175852i	$-0.943732\pi$
$967$		−	10.9368i		−	0.351705i	0.984417	−	0.175852i	$-0.0562682\pi$
$968$		0			0
$969$		−	1.91993i		−	0.0616771i
$970$		0			0
$971$	−6.96534	−	6.96534i	−0.223529	−	0.223529i	0.586454	−	0.809983i	$-0.300523\pi$
$971$	−6.96534	−	6.96534i	−0.223529	−	0.223529i	−0.809983	+	0.586454i	$0.800523\pi$
$972$		0			0
$973$	11.5174	−	11.5174i	0.369230	−	0.369230i
$974$		0			0
$975$	2.77303			0.0888081
$976$		0			0
$977$	−3.21921			−0.102992			−0.0514958	−	0.998673i	$-0.516399\pi$
$977$	−3.21921			−0.102992			−0.0514958	+	0.998673i	$0.516399\pi$
$978$		0			0
$979$	−32.5282	+	32.5282i	−1.03961	+	1.03961i
$980$		0			0
$981$	−27.6337	−	27.6337i	−0.882277	−	0.882277i
$982$		0			0
$983$			47.2080i			1.50570i	0.658192	+	0.752850i	$0.271321\pi$
$983$			47.2080i			1.50570i	−0.658192	+	0.752850i	$0.728679\pi$
$984$		0			0
$985$			25.3905i			0.809009i
$986$		0			0
$987$	4.06520	+	4.06520i	0.129397	+	0.129397i
$988$		0			0
$989$	15.3619	−	15.3619i	0.488481	−	0.488481i
$990$		0			0
$991$	−15.5300			−0.493326			−0.246663	−	0.969101i	$-0.579334\pi$
$991$	−15.5300			−0.493326			−0.246663	+	0.969101i	$0.579334\pi$
$992$		0			0
$993$	−16.7456			−0.531406
$994$		0			0
$995$	−4.07788	+	4.07788i	−0.129277	+	0.129277i
$996$		0			0
$997$	−32.4493	−	32.4493i	−1.02768	−	1.02768i	−0.999606	−	0.0280743i	$-0.991062\pi$
$997$	−32.4493	−	32.4493i	−1.02768	−	1.02768i	−0.0280743	−	0.999606i	$-0.508938\pi$
$998$		0			0
$999$			31.8480i			1.00763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.11		52
4.3	odd	2		560.2.bd.b.421.10	yes	52
16.3	odd	4		560.2.bd.b.141.10	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.11		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.10	✓	52	16.3	odd	4
560.2.bd.b.421.10	yes	52	4.3	odd	2
2240.2.bd.b.561.11		52	1.1	even	1	trivial
2240.2.bd.b.1681.11		52	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.363076 + 0.363076i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.73635i q^{9} +O(q^{10})\)	\(q+(-0.363076 + 0.363076i) q^{3} +(-0.707107 - 0.707107i) q^{5} +1.00000i q^{7} +2.73635i q^{9} +(3.76005 + 3.76005i) q^{11} +(-3.81880 + 3.81880i) q^{13} +0.513467 q^{15} -1.22933 q^{17} +(2.15074 - 2.15074i) q^{19} +(-0.363076 - 0.363076i) q^{21} -3.39953i q^{23} +1.00000i q^{25} +(-2.08273 - 2.08273i) q^{27} +(-3.86007 + 3.86007i) q^{29} +4.83612 q^{31} -2.73037 q^{33} +(0.707107 - 0.707107i) q^{35} +(-7.64574 - 7.64574i) q^{37} -2.77303i q^{39} -5.60526i q^{41} +(4.51884 + 4.51884i) q^{43} +(1.93489 - 1.93489i) q^{45} -11.1966 q^{47} -1.00000 q^{49} +(0.446342 - 0.446342i) q^{51} +(1.97411 + 1.97411i) q^{53} -5.31752i q^{55} +1.56176i q^{57} +(-4.83179 - 4.83179i) q^{59} +(-8.00261 + 8.00261i) q^{61} -2.73635 q^{63} +5.40060 q^{65} +(-4.32927 + 4.32927i) q^{67} +(1.23429 + 1.23429i) q^{69} +1.12005i q^{71} -10.0450i q^{73} +(-0.363076 - 0.363076i) q^{75} +(-3.76005 + 3.76005i) q^{77} +9.83517 q^{79} -6.69668 q^{81} +(-8.06188 + 8.06188i) q^{83} +(0.869271 + 0.869271i) q^{85} -2.80300i q^{87} +8.65099i q^{89} +(-3.81880 - 3.81880i) q^{91} +(-1.75588 + 1.75588i) q^{93} -3.04161 q^{95} -2.62430 q^{97} +(-10.2888 + 10.2888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 4 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 4 q^{29} - 12 q^{37} - 36 q^{43} - 52 q^{49} + 8 q^{51} - 4 q^{53} - 24 q^{59} - 16 q^{61} + 68 q^{63} + 40 q^{65} + 12 q^{67} - 72 q^{69} - 4 q^{77} + 16 q^{79} - 116 q^{81} + 16 q^{85} + 8 q^{93} + 32 q^{95} + 52 q^{99}+O(q^{100}) \) 52 * q + 4 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 4 * q^29 - 12 * q^37 - 36 * q^43 - 52 * q^49 + 8 * q^51 - 4 * q^53 - 24 * q^59 - 16 * q^61 + 68 * q^63 + 40 * q^65 + 12 * q^67 - 72 * q^69 - 4 * q^77 + 16 * q^79 - 116 * q^81 + 16 * q^85 + 8 * q^93 + 32 * q^95 + 52 * q^99

Introduction

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