LMFDB - Embedded newform 2240.2.bd.b.561.4

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			561.4
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.b.1681.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00539 + 2.00539i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -5.04319i q^{9} +O(q^{10})$	\(q+(-2.00539 + 2.00539i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -5.04319i q^{9} +(-4.24632 - 4.24632i) q^{11} +(3.19634 - 3.19634i) q^{13} -2.83605 q^{15} -1.88950 q^{17} +(1.39086 - 1.39086i) q^{19} +(-2.00539 - 2.00539i) q^{21} +7.29574i q^{23} +1.00000i q^{25} +(4.09739 + 4.09739i) q^{27} +(0.0710013 - 0.0710013i) q^{29} +9.55451 q^{31} +17.0311 q^{33} +(-0.707107 + 0.707107i) q^{35} +(8.01620 + 8.01620i) q^{37} +12.8198i q^{39} +1.80970i q^{41} +(2.23835 + 2.23835i) q^{43} +(3.56607 - 3.56607i) q^{45} +3.01597 q^{47} -1.00000 q^{49} +(3.78918 - 3.78918i) q^{51} +(-8.59501 - 8.59501i) q^{53} -6.00521i q^{55} +5.57844i q^{57} +(-6.44071 - 6.44071i) q^{59} +(-3.05212 + 3.05212i) q^{61} +5.04319 q^{63} +4.52031 q^{65} +(6.42396 - 6.42396i) q^{67} +(-14.6308 - 14.6308i) q^{69} +10.2817i q^{71} +14.0571i q^{73} +(-2.00539 - 2.00539i) q^{75} +(4.24632 - 4.24632i) q^{77} +1.35079 q^{79} -1.30417 q^{81} +(-3.34300 + 3.34300i) q^{83} +(-1.33608 - 1.33608i) q^{85} +0.284771i q^{87} +4.24285i q^{89} +(3.19634 + 3.19634i) q^{91} +(-19.1605 + 19.1605i) q^{93} +1.96697 q^{95} +2.54333 q^{97} +(-21.4150 + 21.4150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.00539	+	2.00539i	−1.15781	+	1.15781i	−0.172868	+	0.984945i	$0.555303\pi$
$3$	−2.00539	+	2.00539i	−1.15781	+	1.15781i	−0.984945	+	0.172868i	$0.944697\pi$
$4$		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
$9$		−	5.04319i		−	1.68106i
$10$		0			0
$11$	−4.24632	−	4.24632i	−1.28031	−	1.28031i	−0.940488	−	0.339826i	$-0.889632\pi$
$11$	−4.24632	−	4.24632i	−1.28031	−	1.28031i	−0.339826	−	0.940488i	$-0.610368\pi$
$12$		0			0
$13$	3.19634	−	3.19634i	0.886506	−	0.886506i	−0.107680	−	0.994186i	$-0.534342\pi$
$13$	3.19634	−	3.19634i	0.886506	−	0.886506i	0.994186	+	0.107680i	$0.0343421\pi$
$14$		0			0
$15$	−2.83605			−0.732265
$16$		0			0
$17$	−1.88950			−0.458271			−0.229135	−	0.973395i	$-0.573590\pi$
$17$	−1.88950			−0.458271			−0.229135	+	0.973395i	$0.573590\pi$
$18$		0			0
$19$	1.39086	−	1.39086i	0.319085	−	0.319085i	−0.529331	−	0.848416i	$-0.677557\pi$
$19$	1.39086	−	1.39086i	0.319085	−	0.319085i	0.848416	+	0.529331i	$0.177557\pi$
$20$		0			0
$21$	−2.00539	−	2.00539i	−0.437612	−	0.437612i
$22$		0			0
$23$			7.29574i			1.52127i	0.649182	+	0.760634i	$0.275112\pi$
$23$			7.29574i			1.52127i	−0.649182	+	0.760634i	$0.724888\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	4.09739	+	4.09739i	0.788543	+	0.788543i
$28$		0			0
$29$	0.0710013	−	0.0710013i	0.0131846	−	0.0131846i	−0.700484	−	0.713668i	$-0.747032\pi$
$29$	0.0710013	−	0.0710013i	0.0131846	−	0.0131846i	0.713668	+	0.700484i	$0.247032\pi$
$30$		0			0
$31$	9.55451			1.71604			0.858020	−	0.513616i	$-0.171694\pi$
$31$	9.55451			1.71604			0.858020	+	0.513616i	$0.171694\pi$
$32$		0			0
$33$	17.0311			2.96473
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	8.01620	+	8.01620i	1.31785	+	1.31785i	0.915471	+	0.402384i	$0.131818\pi$
$37$	8.01620	+	8.01620i	1.31785	+	1.31785i	0.402384	+	0.915471i	$0.368182\pi$
$38$		0			0
$39$			12.8198i			2.05282i
$40$		0			0
$41$			1.80970i			0.282628i	0.989965	+	0.141314i	$0.0451327\pi$
$41$			1.80970i			0.282628i	−0.989965	+	0.141314i	$0.954867\pi$
$42$		0			0
$43$	2.23835	+	2.23835i	0.341346	+	0.341346i	0.856873	−	0.515527i	$-0.172404\pi$
$43$	2.23835	+	2.23835i	0.341346	+	0.341346i	−0.515527	+	0.856873i	$0.672404\pi$
$44$		0			0
$45$	3.56607	−	3.56607i	0.531599	−	0.531599i
$46$		0			0
$47$	3.01597			0.439925			0.219962	−	0.975508i	$-0.429407\pi$
$47$	3.01597			0.439925			0.219962	+	0.975508i	$0.429407\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	3.78918	−	3.78918i	0.530592	−	0.530592i
$52$		0			0
$53$	−8.59501	−	8.59501i	−1.18062	−	1.18062i	−0.979585	−	0.201031i	$-0.935571\pi$
$53$	−8.59501	−	8.59501i	−1.18062	−	1.18062i	−0.201031	−	0.979585i	$-0.564429\pi$
$54$		0			0
$55$		−	6.00521i		−	0.809742i
$56$		0			0
$57$			5.57844i			0.738882i
$58$		0			0
$59$	−6.44071	−	6.44071i	−0.838510	−	0.838510i	0.150153	−	0.988663i	$-0.452023\pi$
$59$	−6.44071	−	6.44071i	−0.838510	−	0.838510i	−0.988663	+	0.150153i	$0.952023\pi$
$60$		0			0
$61$	−3.05212	+	3.05212i	−0.390784	+	0.390784i	−0.874967	−	0.484183i	$-0.839117\pi$
$61$	−3.05212	+	3.05212i	−0.390784	+	0.390784i	0.484183	+	0.874967i	$0.339117\pi$
$62$		0			0
$63$	5.04319			0.635382
$64$		0			0
$65$	4.52031			0.560676
$66$		0			0
$67$	6.42396	−	6.42396i	0.784812	−	0.784812i	−0.195826	−	0.980639i	$-0.562739\pi$
$67$	6.42396	−	6.42396i	0.784812	−	0.784812i	0.980639	+	0.195826i	$0.0627389\pi$
$68$		0			0
$69$	−14.6308	−	14.6308i	−1.76134	−	1.76134i
$70$		0			0
$71$			10.2817i			1.22021i	0.792321	+	0.610104i	$0.208873\pi$
$71$			10.2817i			1.22021i	−0.792321	+	0.610104i	$0.791127\pi$
$72$		0			0
$73$			14.0571i			1.64526i	0.568574	+	0.822632i	$0.307495\pi$
$73$			14.0571i			1.64526i	−0.568574	+	0.822632i	$0.692505\pi$
$74$		0			0
$75$	−2.00539	−	2.00539i	−0.231563	−	0.231563i
$76$		0			0
$77$	4.24632	−	4.24632i	0.483913	−	0.483913i
$78$		0			0
$79$	1.35079			0.151976			0.0759879	−	0.997109i	$-0.475789\pi$
$79$	1.35079			0.151976			0.0759879	+	0.997109i	$0.475789\pi$
$80$		0			0
$81$	−1.30417			−0.144908
$82$		0			0
$83$	−3.34300	+	3.34300i	−0.366941	+	0.366941i	−0.866361	−	0.499419i	$-0.833547\pi$
$83$	−3.34300	+	3.34300i	−0.366941	+	0.366941i	0.499419	+	0.866361i	$0.333547\pi$
$84$		0			0
$85$	−1.33608	−	1.33608i	−0.144918	−	0.144918i
$86$		0			0
$87$			0.284771i			0.0305306i
$88$		0			0
$89$			4.24285i			0.449741i	0.974389	+	0.224871i	$0.0721959\pi$
$89$			4.24285i			0.449741i	−0.974389	+	0.224871i	$0.927804\pi$
$90$		0			0
$91$	3.19634	+	3.19634i	0.335068	+	0.335068i
$92$		0			0
$93$	−19.1605	+	19.1605i	−1.98685	+	1.98685i
$94$		0			0
$95$	1.96697			0.201807
$96$		0			0
$97$	2.54333			0.258236			0.129118	−	0.991629i	$-0.458785\pi$
$97$	2.54333			0.258236			0.129118	+	0.991629i	$0.458785\pi$
$98$		0			0
$99$	−21.4150	+	21.4150i	−2.15229	+	2.15229i
$100$		0			0
$101$	0.541054	+	0.541054i	0.0538369	+	0.0538369i	0.733513	−	0.679676i	$-0.237880\pi$
$101$	0.541054	+	0.541054i	0.0538369	+	0.0538369i	−0.679676	+	0.733513i	$0.737880\pi$
$102$		0			0
$103$		−	9.04153i		−	0.890889i	−0.895310	−	0.445444i	$-0.853046\pi$
$103$		−	9.04153i		−	0.890889i	0.895310	−	0.445444i	$-0.146954\pi$
$104$		0			0
$105$		−	2.83605i		−	0.276770i
$106$		0			0
$107$	12.9086	+	12.9086i	1.24792	+	1.24792i	0.956635	+	0.291290i	$0.0940844\pi$
$107$	12.9086	+	12.9086i	1.24792	+	1.24792i	0.291290	+	0.956635i	$0.405916\pi$
$108$		0			0
$109$	0.268159	−	0.268159i	0.0256850	−	0.0256850i	−0.694148	−	0.719833i	$-0.744219\pi$
$109$	0.268159	−	0.268159i	0.0256850	−	0.0256850i	0.719833	+	0.694148i	$0.244219\pi$
$110$		0			0
$111$	−32.1512			−3.05166
$112$		0			0
$113$	11.4241			1.07469			0.537346	−	0.843362i	$-0.319427\pi$
$113$	11.4241			1.07469			0.537346	+	0.843362i	$0.319427\pi$
$114$		0			0
$115$	−5.15887	+	5.15887i	−0.481067	+	0.481067i
$116$		0			0
$117$	−16.1198	−	16.1198i	−1.49027	−	1.49027i
$118$		0			0
$119$		−	1.88950i		−	0.173210i
$120$		0			0
$121$			25.0625i			2.27841i
$122$		0			0
$123$	−3.62916	−	3.62916i	−0.327230	−	0.327230i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	3.58897			0.318470			0.159235	−	0.987241i	$-0.449097\pi$
$127$	3.58897			0.318470			0.159235	+	0.987241i	$0.449097\pi$
$128$		0			0
$129$	−8.97754			−0.790429
$130$		0			0
$131$	2.35913	−	2.35913i	0.206118	−	0.206118i	−0.596497	−	0.802615i	$-0.703441\pi$
$131$	2.35913	−	2.35913i	0.206118	−	0.206118i	0.802615	+	0.596497i	$0.203441\pi$
$132$		0			0
$133$	1.39086	+	1.39086i	0.120603	+	0.120603i
$134$		0			0
$135$			5.79458i			0.498718i
$136$		0			0
$137$		−	7.69317i		−	0.657272i	−0.944457	−	0.328636i	$-0.893411\pi$
$137$		−	7.69317i		−	0.657272i	0.944457	−	0.328636i	$-0.106589\pi$
$138$		0			0
$139$	−6.50335	−	6.50335i	−0.551607	−	0.551607i	0.375297	−	0.926904i	$-0.377541\pi$
$139$	−6.50335	−	6.50335i	−0.551607	−	0.551607i	−0.926904	+	0.375297i	$0.877541\pi$
$140$		0			0
$141$	−6.04820	+	6.04820i	−0.509351	+	0.509351i
$142$		0			0
$143$	−27.1454			−2.27001
$144$		0			0
$145$	0.100411			0.00833868
$146$		0			0
$147$	2.00539	−	2.00539i	0.165402	−	0.165402i
$148$		0			0
$149$	12.9401	+	12.9401i	1.06010	+	1.06010i	0.998075	+	0.0620222i	$0.0197550\pi$
$149$	12.9401	+	12.9401i	1.06010	+	1.06010i	0.0620222	+	0.998075i	$0.480245\pi$
$150$		0			0
$151$		−	4.38451i		−	0.356807i	−0.983957	−	0.178403i	$-0.942907\pi$
$151$		−	4.38451i		−	0.356807i	0.983957	−	0.178403i	$-0.0570932\pi$
$152$		0			0
$153$			9.52910i			0.770382i
$154$		0			0
$155$	6.75606	+	6.75606i	0.542660	+	0.542660i
$156$		0			0
$157$	2.23654	−	2.23654i	0.178496	−	0.178496i	−0.612204	−	0.790700i	$-0.709717\pi$
$157$	2.23654	−	2.23654i	0.178496	−	0.178496i	0.790700	+	0.612204i	$0.209717\pi$
$158$		0			0
$159$	34.4727			2.73387
$160$		0			0
$161$	−7.29574			−0.574985
$162$		0			0
$163$	1.39407	−	1.39407i	0.109192	−	0.109192i	−0.650400	−	0.759592i	$-0.725399\pi$
$163$	1.39407	−	1.39407i	0.109192	−	0.109192i	0.759592	+	0.650400i	$0.225399\pi$
$164$		0			0
$165$	12.0428	+	12.0428i	0.937530	+	0.937530i
$166$		0			0
$167$		−	4.78833i		−	0.370532i	−0.982688	−	0.185266i	$-0.940685\pi$
$167$		−	4.78833i		−	0.370532i	0.982688	−	0.185266i	$-0.0593147\pi$
$168$		0			0
$169$		−	7.43321i		−	0.571786i
$170$		0			0
$171$	−7.01437	−	7.01437i	−0.536402	−	0.536402i
$172$		0			0
$173$	−8.95425	+	8.95425i	−0.680779	+	0.680779i	−0.960176	−	0.279397i	$-0.909865\pi$
$173$	−8.95425	+	8.95425i	−0.680779	+	0.680779i	0.279397	+	0.960176i	$0.409865\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	25.8323			1.94167
$178$		0			0
$179$	−11.6109	+	11.6109i	−0.867843	+	0.867843i	−0.992233	−	0.124390i	$-0.960303\pi$
$179$	−11.6109	+	11.6109i	−0.867843	+	0.867843i	0.124390	+	0.992233i	$0.460303\pi$
$180$		0			0
$181$	0.371916	+	0.371916i	0.0276443	+	0.0276443i	0.720794	−	0.693150i	$-0.243777\pi$
$181$	0.371916	+	0.371916i	0.0276443	+	0.0276443i	−0.693150	+	0.720794i	$0.743777\pi$
$182$		0			0
$183$		−	12.2414i		−	0.904908i
$184$		0			0
$185$			11.3366i			0.833485i
$186$		0			0
$187$	8.02342	+	8.02342i	0.586731	+	0.586731i
$188$		0			0
$189$	−4.09739	+	4.09739i	−0.298041	+	0.298041i
$190$		0			0
$191$	−7.10053			−0.513777			−0.256888	−	0.966441i	$-0.582697\pi$
$191$	−7.10053			−0.513777			−0.256888	+	0.966441i	$0.582697\pi$
$192$		0			0
$193$	0.488355			0.0351526			0.0175763	−	0.999846i	$-0.494405\pi$
$193$	0.488355			0.0351526			0.0175763	+	0.999846i	$0.494405\pi$
$194$		0			0
$195$	−9.06499	+	9.06499i	−0.649158	+	0.649158i
$196$		0			0
$197$	11.5915	+	11.5915i	0.825863	+	0.825863i	0.986942	−	0.161079i	$-0.0514973\pi$
$197$	11.5915	+	11.5915i	0.825863	+	0.825863i	−0.161079	+	0.986942i	$0.551497\pi$
$198$		0			0
$199$			4.86441i			0.344829i	0.985025	+	0.172414i	$0.0551568\pi$
$199$			4.86441i			0.344829i	−0.985025	+	0.172414i	$0.944843\pi$
$200$		0			0
$201$			25.7651i			1.81733i
$202$		0			0
$203$	0.0710013	+	0.0710013i	0.00498331	+	0.00498331i
$204$		0			0
$205$	−1.27965	+	1.27965i	−0.0893747	+	0.0893747i
$206$		0			0
$207$	36.7938			2.55734
$208$		0			0
$209$	−11.8121			−0.817059
$210$		0			0
$211$	−14.9976	+	14.9976i	−1.03248	+	1.03248i	−0.0330228	+	0.999455i	$0.510513\pi$
$211$	−14.9976	+	14.9976i	−1.03248	+	1.03248i	−0.999455	+	0.0330228i	$0.989487\pi$
$212$		0			0
$213$	−20.6188	−	20.6188i	−1.41277	−	1.41277i
$214$		0			0
$215$			3.16551i			0.215886i
$216$		0			0
$217$			9.55451i			0.648602i
$218$		0			0
$219$	−28.1901	−	28.1901i	−1.90491	−	1.90491i
$220$		0			0
$221$	−6.03949	+	6.03949i	−0.406260	+	0.406260i
$222$		0			0
$223$	5.37178			0.359721			0.179861	−	0.983692i	$-0.442435\pi$
$223$	5.37178			0.359721			0.179861	+	0.983692i	$0.442435\pi$
$224$		0			0
$225$	5.04319			0.336212
$226$		0			0
$227$	15.8055	−	15.8055i	1.04905	−	1.04905i	0.0503127	−	0.998734i	$-0.483978\pi$
$227$	15.8055	−	15.8055i	1.04905	−	1.04905i	0.998734	−	0.0503127i	$-0.0160218\pi$
$228$		0			0
$229$	0.0818183	+	0.0818183i	0.00540670	+	0.00540670i	0.709805	−	0.704398i	$-0.248783\pi$
$229$	0.0818183	+	0.0818183i	0.00540670	+	0.00540670i	−0.704398	+	0.709805i	$0.748783\pi$
$230$		0			0
$231$			17.0311i			1.12056i
$232$		0			0
$233$			17.1142i			1.12119i	0.828091	+	0.560594i	$0.189427\pi$
$233$			17.1142i			1.12119i	−0.828091	+	0.560594i	$0.810573\pi$
$234$		0			0
$235$	2.13261	+	2.13261i	0.139116	+	0.139116i
$236$		0			0
$237$	−2.70886	+	2.70886i	−0.175959	+	0.175959i
$238$		0			0
$239$	10.8283			0.700424			0.350212	−	0.936671i	$-0.386110\pi$
$239$	10.8283			0.700424			0.350212	+	0.936671i	$0.386110\pi$
$240$		0			0
$241$	−7.13877			−0.459849			−0.229924	−	0.973208i	$-0.573848\pi$
$241$	−7.13877			−0.459849			−0.229924	+	0.973208i	$0.573848\pi$
$242$		0			0
$243$	−9.67679	+	9.67679i	−0.620766	+	0.620766i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	8.89133i		−	0.565742i
$248$		0			0
$249$		−	13.4080i		−	0.849699i
$250$		0			0
$251$	18.0839	+	18.0839i	1.14145	+	1.14145i	0.988186	+	0.153261i	$0.0489774\pi$
$251$	18.0839	+	18.0839i	1.14145	+	1.14145i	0.153261	+	0.988186i	$0.451023\pi$
$252$		0			0
$253$	30.9801	−	30.9801i	1.94770	−	1.94770i
$254$		0			0
$255$	5.35872			0.335576
$256$		0			0
$257$	12.5522			0.782988			0.391494	−	0.920181i	$-0.371958\pi$
$257$	12.5522			0.782988			0.391494	+	0.920181i	$0.371958\pi$
$258$		0			0
$259$	−8.01620	+	8.01620i	−0.498102	+	0.498102i
$260$		0			0
$261$	−0.358073	−	0.358073i	−0.0221642	−	0.0221642i
$262$		0			0
$263$			7.57379i			0.467020i	0.972354	+	0.233510i	$0.0750212\pi$
$263$			7.57379i			0.467020i	−0.972354	+	0.233510i	$0.924979\pi$
$264$		0			0
$265$		−	12.1552i		−	0.746687i
$266$		0			0
$267$	−8.50857	−	8.50857i	−0.520716	−	0.520716i
$268$		0			0
$269$	0.543077	−	0.543077i	0.0331120	−	0.0331120i	−0.690357	−	0.723469i	$-0.742547\pi$
$269$	0.543077	−	0.543077i	0.0331120	−	0.0331120i	0.723469	+	0.690357i	$0.242547\pi$
$270$		0			0
$271$	27.1988			1.65221			0.826104	−	0.563517i	$-0.190552\pi$
$271$	27.1988			1.65221			0.826104	+	0.563517i	$0.190552\pi$
$272$		0			0
$273$	−12.8198			−0.775892
$274$		0			0
$275$	4.24632	−	4.24632i	0.256063	−	0.256063i
$276$		0			0
$277$	5.28670	+	5.28670i	0.317647	+	0.317647i	0.847863	−	0.530216i	$-0.177889\pi$
$277$	5.28670	+	5.28670i	0.317647	+	0.317647i	−0.530216	+	0.847863i	$0.677889\pi$
$278$		0			0
$279$		−	48.1852i		−	2.88477i
$280$		0			0
$281$		−	10.4777i		−	0.625045i	−0.949910	−	0.312523i	$-0.898826\pi$
$281$		−	10.4777i		−	0.625045i	0.949910	−	0.312523i	$-0.101174\pi$
$282$		0			0
$283$	2.56723	+	2.56723i	0.152606	+	0.152606i	0.779281	−	0.626675i	$-0.215585\pi$
$283$	2.56723	+	2.56723i	0.152606	+	0.152606i	−0.626675	+	0.779281i	$0.715585\pi$
$284$		0			0
$285$	−3.94455	+	3.94455i	−0.233655	+	0.233655i
$286$		0			0
$287$	−1.80970			−0.106823
$288$		0			0
$289$	−13.4298			−0.789988
$290$		0			0
$291$	−5.10036	+	5.10036i	−0.298988	+	0.298988i
$292$		0			0
$293$	−16.7521	−	16.7521i	−0.978666	−	0.978666i	0.0211107	−	0.999777i	$-0.493280\pi$
$293$	−16.7521	−	16.7521i	−0.978666	−	0.978666i	−0.999777	+	0.0211107i	$0.993280\pi$
$294$		0			0
$295$		−	9.10855i		−	0.530320i
$296$		0			0
$297$		−	34.7977i		−	2.01917i
$298$		0			0
$299$	23.3197	+	23.3197i	1.34861	+	1.34861i
$300$		0			0
$301$	−2.23835	+	2.23835i	−0.129016	+	0.129016i
$302$		0			0
$303$	−2.17005			−0.124666
$304$		0			0
$305$	−4.31634			−0.247153
$306$		0			0
$307$	6.45124	−	6.45124i	0.368192	−	0.368192i	−0.498626	−	0.866817i	$-0.666162\pi$
$307$	6.45124	−	6.45124i	0.368192	−	0.368192i	0.866817	+	0.498626i	$0.166162\pi$
$308$		0			0
$309$	18.1318	+	18.1318i	1.03148	+	1.03148i
$310$		0			0
$311$		−	5.52595i		−	0.313348i	−0.987650	−	0.156674i	$-0.949923\pi$
$311$		−	5.52595i		−	0.313348i	0.987650	−	0.156674i	$-0.0500772\pi$
$312$		0			0
$313$			8.81246i			0.498110i	0.968489	+	0.249055i	$0.0801200\pi$
$313$			8.81246i			0.498110i	−0.968489	+	0.249055i	$0.919880\pi$
$314$		0			0
$315$	3.56607	+	3.56607i	0.200925	+	0.200925i
$316$		0			0
$317$	18.1965	−	18.1965i	1.02202	−	1.02202i	0.0222677	−	0.999752i	$-0.492911\pi$
$317$	18.1965	−	18.1965i	1.02202	−	1.02202i	0.999752	−	0.0222677i	$-0.00708863\pi$
$318$		0			0
$319$	−0.602989			−0.0337609
$320$		0			0
$321$	−51.7737			−2.88973
$322$		0			0
$323$	−2.62803	+	2.62803i	−0.146227	+	0.146227i
$324$		0			0
$325$	3.19634	+	3.19634i	0.177301	+	0.177301i
$326$		0			0
$327$			1.07553i			0.0594768i
$328$		0			0
$329$			3.01597i			0.166276i
$330$		0			0
$331$	−4.71967	−	4.71967i	−0.259416	−	0.259416i	0.565400	−	0.824817i	$-0.308722\pi$
$331$	−4.71967	−	4.71967i	−0.259416	−	0.259416i	−0.824817	+	0.565400i	$0.808722\pi$
$332$		0			0
$333$	40.4272	−	40.4272i	2.21540	−	2.21540i
$334$		0			0
$335$	9.08486			0.496359
$336$		0			0
$337$	−19.2480			−1.04851			−0.524253	−	0.851563i	$-0.675655\pi$
$337$	−19.2480			−1.04851			−0.524253	+	0.851563i	$0.675655\pi$
$338$		0			0
$339$	−22.9099	+	22.9099i	−1.24429	+	1.24429i
$340$		0			0
$341$	−40.5715	−	40.5715i	−2.19707	−	2.19707i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	20.6911i		−	1.11397i
$346$		0			0
$347$	1.95859	+	1.95859i	0.105143	+	0.105143i	0.757721	−	0.652578i	$-0.226313\pi$
$347$	1.95859	+	1.95859i	0.105143	+	0.105143i	−0.652578	+	0.757721i	$0.726313\pi$
$348$		0			0
$349$	−16.8489	+	16.8489i	−0.901901	+	0.901901i	−0.995601	−	0.0936994i	$-0.970131\pi$
$349$	−16.8489	+	16.8489i	−0.901901	+	0.901901i	0.0936994	+	0.995601i	$0.470131\pi$
$350$		0			0
$351$	26.1933			1.39810
$352$		0			0
$353$	−20.0346			−1.06634			−0.533168	−	0.846009i	$-0.678999\pi$
$353$	−20.0346			−1.06634			−0.533168	+	0.846009i	$0.678999\pi$
$354$		0			0
$355$	−7.27023	+	7.27023i	−0.385864	+	0.385864i
$356$		0			0
$357$	3.78918	+	3.78918i	0.200545	+	0.200545i
$358$		0			0
$359$		−	11.1235i		−	0.587074i	−0.955948	−	0.293537i	$-0.905168\pi$
$359$		−	11.1235i		−	0.587074i	0.955948	−	0.293537i	$-0.0948325\pi$
$360$		0			0
$361$			15.1310i			0.796369i
$362$		0			0
$363$	−50.2602	−	50.2602i	−2.63797	−	2.63797i
$364$		0			0
$365$	−9.93991	+	9.93991i	−0.520278	+	0.520278i
$366$		0			0
$367$	12.7001			0.662942			0.331471	−	0.943465i	$-0.392455\pi$
$367$	12.7001			0.662942			0.331471	+	0.943465i	$0.392455\pi$
$368$		0			0
$369$	9.12666			0.475115
$370$		0			0
$371$	8.59501	−	8.59501i	0.446231	−	0.446231i
$372$		0			0
$373$	11.1021	+	11.1021i	0.574847	+	0.574847i	0.933479	−	0.358632i	$-0.116757\pi$
$373$	11.1021	+	11.1021i	0.574847	+	0.574847i	−0.358632	+	0.933479i	$0.616757\pi$
$374$		0			0
$375$		−	2.83605i		−	0.146453i
$376$		0			0
$377$		−	0.453889i		−	0.0233765i
$378$		0			0
$379$	18.2605	+	18.2605i	0.937981	+	0.937981i	0.998186	−	0.0602048i	$-0.0191754\pi$
$379$	18.2605	+	18.2605i	0.937981	+	0.937981i	−0.0602048	+	0.998186i	$0.519175\pi$
$380$		0			0
$381$	−7.19729	+	7.19729i	−0.368729	+	0.368729i
$382$		0			0
$383$	−10.5226			−0.537679			−0.268839	−	0.963185i	$-0.586640\pi$
$383$	−10.5226			−0.537679			−0.268839	+	0.963185i	$0.586640\pi$
$384$		0			0
$385$	6.00521			0.306054
$386$		0			0
$387$	11.2884	−	11.2884i	0.573823	−	0.573823i
$388$		0			0
$389$	0.113239	+	0.113239i	0.00574144	+	0.00574144i	0.709972	−	0.704230i	$-0.248708\pi$
$389$	0.113239	+	0.113239i	0.00574144	+	0.00574144i	−0.704230	+	0.709972i	$0.748708\pi$
$390$		0			0
$391$		−	13.7853i		−	0.697152i
$392$		0			0
$393$			9.46195i			0.477292i
$394$		0			0
$395$	0.955152	+	0.955152i	0.0480589	+	0.0480589i
$396$		0			0
$397$	5.28638	−	5.28638i	0.265316	−	0.265316i	−0.561894	−	0.827210i	$-0.689927\pi$
$397$	5.28638	−	5.28638i	0.265316	−	0.265316i	0.827210	+	0.561894i	$0.189927\pi$
$398$		0			0
$399$	−5.57844			−0.279271
$400$		0			0
$401$	5.29274			0.264307			0.132153	−	0.991229i	$-0.457811\pi$
$401$	5.29274			0.264307			0.132153	+	0.991229i	$0.457811\pi$
$402$		0			0
$403$	30.5395	−	30.5395i	1.52128	−	1.52128i
$404$		0			0
$405$	−0.922188	−	0.922188i	−0.0458239	−	0.0458239i
$406$		0			0
$407$		−	68.0787i		−	3.37454i
$408$		0			0
$409$			5.05352i			0.249881i	0.992164	+	0.124940i	$0.0398739\pi$
$409$			5.05352i			0.249881i	−0.992164	+	0.124940i	$0.960126\pi$
$410$		0			0
$411$	15.4278	+	15.4278i	0.760998	+	0.760998i
$412$		0			0
$413$	6.44071	−	6.44071i	0.316927	−	0.316927i
$414$		0			0
$415$	−4.72771			−0.232074
$416$		0			0
$417$	26.0835			1.27732
$418$		0			0
$419$	23.5218	−	23.5218i	1.14912	−	1.14912i	0.162389	−	0.986727i	$-0.448080\pi$
$419$	23.5218	−	23.5218i	1.14912	−	1.14912i	0.986727	−	0.162389i	$-0.0519198\pi$
$420$		0			0
$421$	−16.3920	−	16.3920i	−0.798896	−	0.798896i	0.184026	−	0.982921i	$-0.441087\pi$
$421$	−16.3920	−	16.3920i	−0.798896	−	0.798896i	−0.982921	+	0.184026i	$0.941087\pi$
$422$		0			0
$423$		−	15.2101i		−	0.739541i
$424$		0			0
$425$		−	1.88950i		−	0.0916542i
$426$		0			0
$427$	−3.05212	−	3.05212i	−0.147702	−	0.147702i
$428$		0			0
$429$	54.4372	−	54.4372i	2.62825	−	2.62825i
$430$		0			0
$431$	3.44838			0.166103			0.0830514	−	0.996545i	$-0.473533\pi$
$431$	3.44838			0.166103			0.0830514	+	0.996545i	$0.473533\pi$
$432$		0			0
$433$	27.5735			1.32510			0.662549	−	0.749018i	$-0.269474\pi$
$433$	27.5735			1.32510			0.662549	+	0.749018i	$0.269474\pi$
$434$		0			0
$435$	−0.201363	+	0.201363i	−0.00965463	+	0.00965463i
$436$		0			0
$437$	10.1474	+	10.1474i	0.485414	+	0.485414i
$438$		0			0
$439$		−	21.8348i		−	1.04212i	−0.853521	−	0.521059i	$-0.825537\pi$
$439$		−	21.8348i		−	1.04212i	0.853521	−	0.521059i	$-0.174463\pi$
$440$		0			0
$441$			5.04319i			0.240152i
$442$		0			0
$443$	13.5426	+	13.5426i	0.643429	+	0.643429i	0.951397	−	0.307968i	$-0.0996490\pi$
$443$	13.5426	+	13.5426i	0.643429	+	0.643429i	−0.307968	+	0.951397i	$0.599649\pi$
$444$		0			0
$445$	−3.00015	+	3.00015i	−0.142221	+	0.142221i
$446$		0			0
$447$	−51.9001			−2.45479
$448$		0			0
$449$	34.4484			1.62572			0.812859	−	0.582460i	$-0.197910\pi$
$449$	34.4484			1.62572			0.812859	+	0.582460i	$0.197910\pi$
$450$		0			0
$451$	7.68457	−	7.68457i	0.361852	−	0.361852i
$452$		0			0
$453$	8.79266	+	8.79266i	0.413115	+	0.413115i
$454$		0			0
$455$			4.52031i			0.211915i
$456$		0			0
$457$		−	13.3038i		−	0.622324i	−0.950357	−	0.311162i	$-0.899282\pi$
$457$		−	13.3038i		−	0.622324i	0.950357	−	0.311162i	$-0.100718\pi$
$458$		0			0
$459$	−7.74201	−	7.74201i	−0.361366	−	0.361366i
$460$		0			0
$461$	3.51980	−	3.51980i	0.163934	−	0.163934i	−0.620373	−	0.784307i	$-0.713019\pi$
$461$	3.51980	−	3.51980i	0.163934	−	0.163934i	0.784307	+	0.620373i	$0.213019\pi$
$462$		0			0
$463$	−10.0668			−0.467844			−0.233922	−	0.972255i	$-0.575156\pi$
$463$	−10.0668			−0.467844			−0.233922	+	0.972255i	$0.575156\pi$
$464$		0			0
$465$	−27.0971			−1.25660
$466$		0			0
$467$	−22.3554	+	22.3554i	−1.03448	+	1.03448i	−0.0350992	+	0.999384i	$0.511175\pi$
$467$	−22.3554	+	22.3554i	−1.03448	+	1.03448i	−0.999384	+	0.0350992i	$0.988825\pi$
$468$		0			0
$469$	6.42396	+	6.42396i	0.296631	+	0.296631i
$470$		0			0
$471$			8.97029i			0.413329i
$472$		0			0
$473$		−	19.0095i		−	0.874059i
$474$		0			0
$475$	1.39086	+	1.39086i	0.0638170	+	0.0638170i
$476$		0			0
$477$	−43.3463	+	43.3463i	−1.98469	+	1.98469i
$478$		0			0
$479$	34.6297			1.58227			0.791136	−	0.611640i	$-0.209490\pi$
$479$	34.6297			1.58227			0.791136	+	0.611640i	$0.209490\pi$
$480$		0			0
$481$	51.2450			2.33657
$482$		0			0
$483$	14.6308	−	14.6308i	0.665725	−	0.665725i
$484$		0			0
$485$	1.79840	+	1.79840i	0.0816612	+	0.0816612i
$486$		0			0
$487$			26.0570i			1.18076i	0.807127	+	0.590378i	$0.201021\pi$
$487$			26.0570i			1.18076i	−0.807127	+	0.590378i	$0.798979\pi$
$488$		0			0
$489$			5.59131i			0.252848i
$490$		0			0
$491$	−0.607000	−	0.607000i	−0.0273935	−	0.0273935i	0.693277	−	0.720671i	$-0.256166\pi$
$491$	−0.607000	−	0.607000i	−0.0273935	−	0.0273935i	−0.720671	+	0.693277i	$0.756166\pi$
$492$		0			0
$493$	−0.134157	+	0.134157i	−0.00604212	+	0.00604212i
$494$		0			0
$495$	−30.2854			−1.36123
$496$		0			0
$497$	−10.2817			−0.461196
$498$		0			0
$499$	6.21783	−	6.21783i	0.278348	−	0.278348i	−0.554101	−	0.832449i	$-0.686938\pi$
$499$	6.21783	−	6.21783i	0.278348	−	0.278348i	0.832449	+	0.554101i	$0.186938\pi$
$500$		0			0
$501$	9.60248	+	9.60248i	0.429007	+	0.429007i
$502$		0			0
$503$			30.9804i			1.38135i	0.723166	+	0.690674i	$0.242686\pi$
$503$			30.9804i			1.38135i	−0.723166	+	0.690674i	$0.757314\pi$
$504$		0			0
$505$			0.765166i			0.0340494i
$506$		0			0
$507$	14.9065	+	14.9065i	0.662021	+	0.662021i
$508$		0			0
$509$	11.9538	−	11.9538i	0.529842	−	0.529842i	−0.390683	−	0.920525i	$-0.627761\pi$
$509$	11.9538	−	11.9538i	0.529842	−	0.529842i	0.920525	+	0.390683i	$0.127761\pi$
$510$		0			0
$511$	−14.0571			−0.621852
$512$		0			0
$513$	11.3978			0.503225
$514$		0			0
$515$	6.39333	−	6.39333i	0.281724	−	0.281724i
$516$		0			0
$517$	−12.8068	−	12.8068i	−0.563242	−	0.563242i
$518$		0			0
$519$		−	35.9135i		−	1.57643i
$520$		0			0
$521$		−	42.1163i		−	1.84515i	−0.385821	−	0.922574i	$-0.626082\pi$
$521$		−	42.1163i		−	1.84515i	0.385821	−	0.922574i	$-0.373918\pi$
$522$		0			0
$523$	20.3497	+	20.3497i	0.889832	+	0.889832i	0.994507	−	0.104674i	$-0.0333800\pi$
$523$	20.3497	+	20.3497i	0.889832	+	0.889832i	−0.104674	+	0.994507i	$0.533380\pi$
$524$		0			0
$525$	2.00539	−	2.00539i	0.0875224	−	0.0875224i
$526$		0			0
$527$	−18.0532			−0.786411
$528$		0			0
$529$	−30.2278			−1.31425
$530$		0			0
$531$	−32.4817	+	32.4817i	−1.40959	+	1.40959i
$532$		0			0
$533$	5.78442	+	5.78442i	0.250551	+	0.250551i
$534$		0			0
$535$			18.2556i			0.789257i
$536$		0			0
$537$		−	46.5690i		−	2.00960i
$538$		0			0
$539$	4.24632	+	4.24632i	0.182902	+	0.182902i
$540$		0			0
$541$	4.30506	−	4.30506i	0.185089	−	0.185089i	−0.608480	−	0.793569i	$-0.708221\pi$
$541$	4.30506	−	4.30506i	0.185089	−	0.185089i	0.793569	+	0.608480i	$0.208221\pi$
$542$		0			0
$543$	−1.49168			−0.0640139
$544$		0			0
$545$	0.379234			0.0162446
$546$		0			0
$547$	12.5707	−	12.5707i	0.537483	−	0.537483i	−0.385306	−	0.922789i	$-0.625904\pi$
$547$	12.5707	−	12.5707i	0.537483	−	0.537483i	0.922789	+	0.385306i	$0.125904\pi$
$548$		0			0
$549$	15.3924	+	15.3924i	0.656931	+	0.656931i
$550$		0			0
$551$		−	0.197506i		−	0.00841403i
$552$		0			0
$553$			1.35079i			0.0574414i
$554$		0			0
$555$	−22.7343	−	22.7343i	−0.965019	−	0.965019i
$556$		0			0
$557$	3.76491	−	3.76491i	0.159524	−	0.159524i	−0.622832	−	0.782356i	$-0.714018\pi$
$557$	3.76491	−	3.76491i	0.159524	−	0.159524i	0.782356	+	0.622832i	$0.214018\pi$
$558$		0			0
$559$	14.3091			0.605210
$560$		0			0
$561$	−32.1802			−1.35865
$562$		0			0
$563$	−19.3985	+	19.3985i	−0.817551	+	0.817551i	−0.985753	−	0.168202i	$-0.946204\pi$
$563$	−19.3985	+	19.3985i	−0.817551	+	0.817551i	0.168202	+	0.985753i	$0.446204\pi$
$564$		0			0
$565$	8.07809	+	8.07809i	0.339848	+	0.339848i
$566$		0			0
$567$		−	1.30417i		−	0.0547701i
$568$		0			0
$569$			5.30203i			0.222273i	0.993805	+	0.111136i	$0.0354490\pi$
$569$			5.30203i			0.222273i	−0.993805	+	0.111136i	$0.964551\pi$
$570$		0			0
$571$	0.750198	+	0.750198i	0.0313948	+	0.0313948i	0.722630	−	0.691235i	$-0.242933\pi$
$571$	0.750198	+	0.750198i	0.0313948	+	0.0313948i	−0.691235	+	0.722630i	$0.742933\pi$
$572$		0			0
$573$	14.2393	−	14.2393i	0.594857	−	0.594857i
$574$		0			0
$575$	−7.29574			−0.304253
$576$		0			0
$577$	23.5642			0.980993			0.490496	−	0.871443i	$-0.336816\pi$
$577$	23.5642			0.980993			0.490496	+	0.871443i	$0.336816\pi$
$578$		0			0
$579$	−0.979343	+	0.979343i	−0.0407001	+	0.0407001i
$580$		0			0
$581$	−3.34300	−	3.34300i	−0.138691	−	0.138691i
$582$		0			0
$583$			72.9944i			3.02312i
$584$		0			0
$585$		−	22.7968i		−	0.942531i
$586$		0			0
$587$	−19.0407	−	19.0407i	−0.785894	−	0.785894i	0.194924	−	0.980818i	$-0.437554\pi$
$587$	−19.0407	−	19.0407i	−0.785894	−	0.785894i	−0.980818	+	0.194924i	$0.937554\pi$
$588$		0			0
$589$	13.2890	−	13.2890i	0.547563	−	0.547563i
$590$		0			0
$591$	−46.4911			−1.91239
$592$		0			0
$593$	26.8156			1.10118			0.550591	−	0.834775i	$-0.314402\pi$
$593$	26.8156			1.10118			0.550591	+	0.834775i	$0.314402\pi$
$594$		0			0
$595$	1.33608	−	1.33608i	0.0547738	−	0.0547738i
$596$		0			0
$597$	−9.75504	−	9.75504i	−0.399247	−	0.399247i
$598$		0			0
$599$		−	31.7190i		−	1.29600i	−0.761638	−	0.648002i	$-0.775605\pi$
$599$		−	31.7190i		−	1.29600i	0.761638	−	0.648002i	$-0.224395\pi$
$600$		0			0
$601$		−	26.8408i		−	1.09486i	−0.836852	−	0.547429i	$-0.815607\pi$
$601$		−	26.8408i		−	1.09486i	0.836852	−	0.547429i	$-0.184393\pi$
$602$		0			0
$603$	−32.3972	−	32.3972i	−1.31932	−	1.31932i
$604$		0			0
$605$	−17.7219	+	17.7219i	−0.720497	+	0.720497i
$606$		0			0
$607$	−14.7538			−0.598839			−0.299419	−	0.954122i	$-0.596793\pi$
$607$	−14.7538			−0.598839			−0.299419	+	0.954122i	$0.596793\pi$
$608$		0			0
$609$	−0.284771			−0.0115395
$610$		0			0
$611$	9.64008	−	9.64008i	0.389996	−	0.389996i
$612$		0			0
$613$	32.8990	+	32.8990i	1.32878	+	1.32878i	0.906438	+	0.422340i	$0.138791\pi$
$613$	32.8990	+	32.8990i	1.32878	+	1.32878i	0.422340	+	0.906438i	$0.361209\pi$
$614$		0			0
$615$		−	5.13240i		−	0.206958i
$616$		0			0
$617$			3.32852i			0.134001i	0.997753	+	0.0670005i	$0.0213429\pi$
$617$			3.32852i			0.134001i	−0.997753	+	0.0670005i	$0.978657\pi$
$618$		0			0
$619$	−25.1347	−	25.1347i	−1.01025	−	1.01025i	−0.999947	−	0.0103008i	$-0.996721\pi$
$619$	−25.1347	−	25.1347i	−1.01025	−	1.01025i	−0.0103008	−	0.999947i	$-0.503279\pi$
$620$		0			0
$621$	−29.8935	+	29.8935i	−1.19958	+	1.19958i
$622$		0			0
$623$	−4.24285			−0.169986
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	23.6878	−	23.6878i	0.946002	−	0.946002i
$628$		0			0
$629$	−15.1466	−	15.1466i	−0.603934	−	0.603934i
$630$		0			0
$631$			33.5859i			1.33703i	0.743698	+	0.668516i	$0.233070\pi$
$631$			33.5859i			1.33703i	−0.743698	+	0.668516i	$0.766930\pi$
$632$		0			0
$633$		−	60.1521i		−	2.39083i
$634$		0			0
$635$	2.53779	+	2.53779i	0.100709	+	0.100709i
$636$		0			0
$637$	−3.19634	+	3.19634i	−0.126644	+	0.126644i
$638$		0			0
$639$	51.8523			2.05125
$640$		0			0
$641$	5.72496			0.226122			0.113061	−	0.993588i	$-0.463934\pi$
$641$	5.72496			0.226122			0.113061	+	0.993588i	$0.463934\pi$
$642$		0			0
$643$	−20.2653	+	20.2653i	−0.799186	+	0.799186i	−0.982967	−	0.183781i	$-0.941166\pi$
$643$	−20.2653	+	20.2653i	−0.799186	+	0.799186i	0.183781	+	0.982967i	$0.441166\pi$
$644$		0			0
$645$	−6.34808	−	6.34808i	−0.249956	−	0.249956i
$646$		0			0
$647$			19.6615i			0.772972i	0.922295	+	0.386486i	$0.126311\pi$
$647$			19.6615i			0.772972i	−0.922295	+	0.386486i	$0.873689\pi$
$648$		0			0
$649$			54.6987i			2.14711i
$650$		0			0
$651$	−19.1605	−	19.1605i	−0.750960	−	0.750960i
$652$		0			0
$653$	−3.24961	+	3.24961i	−0.127167	+	0.127167i	−0.767826	−	0.640659i	$-0.778661\pi$
$653$	−3.24961	+	3.24961i	−0.127167	+	0.127167i	0.640659	+	0.767826i	$0.278661\pi$
$654$		0			0
$655$	3.33631			0.130361
$656$		0			0
$657$	70.8928			2.76579
$658$		0			0
$659$	−30.5441	+	30.5441i	−1.18983	+	1.18983i	−0.212717	+	0.977114i	$0.568231\pi$
$659$	−30.5441	+	30.5441i	−1.18983	+	1.18983i	−0.977114	+	0.212717i	$0.931769\pi$
$660$		0			0
$661$	−6.92446	−	6.92446i	−0.269330	−	0.269330i	0.559500	−	0.828830i	$-0.310993\pi$
$661$	−6.92446	−	6.92446i	−0.269330	−	0.269330i	−0.828830	+	0.559500i	$0.810993\pi$
$662$		0			0
$663$		−	24.2231i		−	0.940746i
$664$		0			0
$665$			1.96697i			0.0762760i
$666$		0			0
$667$	0.518007	+	0.518007i	0.0200573	+	0.0200573i
$668$		0			0
$669$	−10.7725	+	10.7725i	−0.416490	+	0.416490i
$670$		0			0
$671$	25.9205			1.00065
$672$		0			0
$673$	8.16111			0.314588			0.157294	−	0.987552i	$-0.449723\pi$
$673$	8.16111			0.314588			0.157294	+	0.987552i	$0.449723\pi$
$674$		0			0
$675$	−4.09739	+	4.09739i	−0.157709	+	0.157709i
$676$		0			0
$677$	−17.4422	−	17.4422i	−0.670360	−	0.670360i	0.287439	−	0.957799i	$-0.407196\pi$
$677$	−17.4422	−	17.4422i	−0.670360	−	0.670360i	−0.957799	+	0.287439i	$0.907196\pi$
$678$		0			0
$679$			2.54333i			0.0976039i
$680$		0			0
$681$			63.3923i			2.42920i
$682$		0			0
$683$	30.5930	+	30.5930i	1.17061	+	1.17061i	0.982065	+	0.188542i	$0.0603763\pi$
$683$	30.5930	+	30.5930i	1.17061	+	1.17061i	0.188542	+	0.982065i	$0.439624\pi$
$684$		0			0
$685$	5.43990	−	5.43990i	0.207848	−	0.207848i
$686$		0			0
$687$	−0.328155			−0.0125199
$688$		0			0
$689$	−54.9452			−2.09325
$690$		0			0
$691$	19.1138	−	19.1138i	0.727124	−	0.727124i	−0.242922	−	0.970046i	$-0.578106\pi$
$691$	19.1138	−	19.1138i	0.727124	−	0.727124i	0.970046	+	0.242922i	$0.0781059\pi$
$692$		0			0
$693$	−21.4150	−	21.4150i	−0.813489	−	0.813489i
$694$		0			0
$695$		−	9.19713i		−	0.348867i
$696$		0			0
$697$		−	3.41943i		−	0.129520i
$698$		0			0
$699$	−34.3206	−	34.3206i	−1.29813	−	1.29813i
$700$		0			0
$701$	−15.1156	+	15.1156i	−0.570907	+	0.570907i	−0.932382	−	0.361475i	$-0.882273\pi$
$701$	−15.1156	+	15.1156i	−0.570907	+	0.570907i	0.361475	+	0.932382i	$0.382273\pi$
$702$		0			0
$703$	22.2988			0.841016
$704$		0			0
$705$	−8.55345			−0.322142
$706$		0			0
$707$	−0.541054	+	0.541054i	−0.0203484	+	0.0203484i
$708$		0			0
$709$	−29.3194	−	29.3194i	−1.10111	−	1.10111i	−0.994277	−	0.106836i	$-0.965928\pi$
$709$	−29.3194	−	29.3194i	−1.10111	−	1.10111i	−0.106836	−	0.994277i	$-0.534072\pi$
$710$		0			0
$711$		−	6.81228i		−	0.255481i
$712$		0			0
$713$			69.7072i			2.61056i
$714$		0			0
$715$	−19.1947	−	19.1947i	−0.717841	−	0.717841i
$716$		0			0
$717$	−21.7149	+	21.7149i	−0.810960	+	0.810960i
$718$		0			0
$719$	−23.3687			−0.871505			−0.435752	−	0.900067i	$-0.643518\pi$
$719$	−23.3687			−0.871505			−0.435752	+	0.900067i	$0.643518\pi$
$720$		0			0
$721$	9.04153			0.336724
$722$		0			0
$723$	14.3160	−	14.3160i	0.532419	−	0.532419i
$724$		0			0
$725$	0.0710013	+	0.0710013i	0.00263692	+	0.00263692i
$726$		0			0
$727$			45.4372i			1.68517i	0.538561	+	0.842587i	$0.318968\pi$
$727$			45.4372i			1.68517i	−0.538561	+	0.842587i	$0.681032\pi$
$728$		0			0
$729$		−	42.7240i		−	1.58237i
$730$		0			0
$731$	−4.22936	−	4.22936i	−0.156429	−	0.156429i
$732$		0			0
$733$	25.6921	−	25.6921i	0.948959	−	0.948959i	−0.0497999	−	0.998759i	$-0.515858\pi$
$733$	25.6921	−	25.6921i	0.948959	−	0.948959i	0.998759	+	0.0497999i	$0.0158584\pi$
$734$		0			0
$735$	2.83605			0.104609
$736$		0			0
$737$	−54.5565			−2.00961
$738$		0			0
$739$	32.1797	−	32.1797i	1.18375	−	1.18375i	0.204983	−	0.978765i	$-0.434286\pi$
$739$	32.1797	−	32.1797i	1.18375	−	1.18375i	0.978765	−	0.204983i	$-0.0657141\pi$
$740$		0			0
$741$	17.8306	+	17.8306i	0.655023	+	0.655023i
$742$		0			0
$743$			30.3884i			1.11484i	0.830230	+	0.557421i	$0.188209\pi$
$743$			30.3884i			1.11484i	−0.830230	+	0.557421i	$0.811791\pi$
$744$		0			0
$745$			18.3001i			0.670464i
$746$		0			0
$747$	16.8593	+	16.8593i	0.616851	+	0.616851i
$748$		0			0
$749$	−12.9086	+	12.9086i	−0.471671	+	0.471671i
$750$		0			0
$751$	−25.2391			−0.920987			−0.460493	−	0.887663i	$-0.652327\pi$
$751$	−25.2391			−0.920987			−0.460493	+	0.887663i	$0.652327\pi$
$752$		0			0
$753$	−72.5306			−2.64316
$754$		0			0
$755$	3.10032	−	3.10032i	0.112832	−	0.112832i
$756$		0			0
$757$	5.04085	+	5.04085i	0.183213	+	0.183213i	0.792754	−	0.609541i	$-0.208646\pi$
$757$	5.04085	+	5.04085i	0.183213	+	0.183213i	−0.609541	+	0.792754i	$0.708646\pi$
$758$		0			0
$759$			124.254i			4.51015i
$760$		0			0
$761$		−	24.7274i		−	0.896366i	−0.893942	−	0.448183i	$-0.852071\pi$
$761$		−	24.7274i		−	0.896366i	0.893942	−	0.448183i	$-0.147929\pi$
$762$		0			0
$763$	0.268159	+	0.268159i	0.00970801	+	0.00970801i
$764$		0			0
$765$	−6.73809	+	6.73809i	−0.243616	+	0.243616i
$766$		0			0
$767$	−41.1735			−1.48669
$768$		0			0
$769$	33.4831			1.20743			0.603715	−	0.797200i	$-0.293686\pi$
$769$	33.4831			1.20743			0.603715	+	0.797200i	$0.293686\pi$
$770$		0			0
$771$	−25.1722	+	25.1722i	−0.906553	+	0.906553i
$772$		0			0
$773$	−27.1079	−	27.1079i	−0.975005	−	0.975005i	0.0246905	−	0.999695i	$-0.492140\pi$
$773$	−27.1079	−	27.1079i	−0.975005	−	0.975005i	−0.999695	+	0.0246905i	$0.992140\pi$
$774$		0			0
$775$			9.55451i			0.343208i
$776$		0			0
$777$		−	32.1512i		−	1.15342i
$778$		0			0
$779$	2.51704	+	2.51704i	0.0901823	+	0.0901823i
$780$		0			0
$781$	43.6593	−	43.6593i	1.56225	−	1.56225i
$782$		0			0
$783$	0.581840			0.0207933
$784$		0			0
$785$	3.16295			0.112891
$786$		0			0
$787$	30.7982	−	30.7982i	1.09784	−	1.09784i	0.103174	−	0.994663i	$-0.467100\pi$
$787$	30.7982	−	30.7982i	1.09784	−	1.09784i	0.994663	−	0.103174i	$-0.0328999\pi$
$788$		0			0
$789$	−15.1884	−	15.1884i	−0.540722	−	0.540722i
$790$		0			0
$791$			11.4241i			0.406196i
$792$		0			0
$793$			19.5112i			0.692864i
$794$		0			0
$795$	24.3759	+	24.3759i	0.864524	+	0.864524i
$796$		0			0
$797$	−37.5197	+	37.5197i	−1.32902	+	1.32902i	−0.422786	+	0.906229i	$0.638948\pi$
$797$	−37.5197	+	37.5197i	−1.32902	+	1.32902i	−0.906229	+	0.422786i	$0.861052\pi$
$798$		0			0
$799$	−5.69868			−0.201605
$800$		0			0
$801$	21.3975			0.756043
$802$		0			0
$803$	59.6912	−	59.6912i	2.10646	−	2.10646i
$804$		0			0
$805$	−5.15887	−	5.15887i	−0.181826	−	0.181826i
$806$		0			0
$807$			2.17816i			0.0766750i
$808$		0			0
$809$			3.57657i			0.125746i	0.998022	+	0.0628728i	$0.0200263\pi$
$809$			3.57657i			0.125746i	−0.998022	+	0.0628728i	$0.979974\pi$
$810$		0			0
$811$	1.41315	+	1.41315i	0.0496224	+	0.0496224i	0.731483	−	0.681860i	$-0.238829\pi$
$811$	1.41315	+	1.41315i	0.0496224	+	0.0496224i	−0.681860	+	0.731483i	$0.738829\pi$
$812$		0			0
$813$	−54.5442	+	54.5442i	−1.91295	+	1.91295i
$814$		0			0
$815$	1.97151			0.0690591
$816$		0			0
$817$	6.22647			0.217837
$818$		0			0
$819$	16.1198	−	16.1198i	0.563270	−	0.563270i
$820$		0			0
$821$	20.6442	+	20.6442i	0.720488	+	0.720488i	0.968705	−	0.248217i	$-0.0798444\pi$
$821$	20.6442	+	20.6442i	0.720488	+	0.720488i	−0.248217	+	0.968705i	$0.579844\pi$
$822$		0			0
$823$			30.4917i			1.06287i	0.847098	+	0.531436i	$0.178348\pi$
$823$			30.4917i			1.06287i	−0.847098	+	0.531436i	$0.821652\pi$
$824$		0			0
$825$			17.0311i			0.592946i
$826$		0			0
$827$	12.9323	+	12.9323i	0.449700	+	0.449700i	0.895255	−	0.445554i	$-0.146993\pi$
$827$	12.9323	+	12.9323i	0.449700	+	0.449700i	−0.445554	+	0.895255i	$0.646993\pi$
$828$		0			0
$829$	24.8019	−	24.8019i	0.861407	−	0.861407i	−0.130095	−	0.991502i	$-0.541528\pi$
$829$	24.8019	−	24.8019i	0.861407	−	0.861407i	0.991502	+	0.130095i	$0.0415282\pi$
$830$		0			0
$831$	−21.2038			−0.735552
$832$		0			0
$833$	1.88950			0.0654673
$834$		0			0
$835$	3.38586	−	3.38586i	0.117173	−	0.117173i
$836$		0			0
$837$	39.1485	+	39.1485i	1.35317	+	1.35317i
$838$		0			0
$839$			7.59932i			0.262358i	0.991359	+	0.131179i	$0.0418762\pi$
$839$			7.59932i			0.262358i	−0.991359	+	0.131179i	$0.958124\pi$
$840$		0			0
$841$			28.9899i			0.999652i
$842$		0			0
$843$	21.0118	+	21.0118i	0.723686	+	0.723686i
$844$		0			0
$845$	5.25607	−	5.25607i	0.180814	−	0.180814i
$846$		0			0
$847$	−25.0625			−0.861158
$848$		0			0
$849$	−10.2966			−0.353379
$850$		0			0
$851$	−58.4841	+	58.4841i	−2.00481	+	2.00481i
$852$		0			0
$853$	−13.6647	−	13.6647i	−0.467870	−	0.467870i	0.433354	−	0.901224i	$-0.357330\pi$
$853$	−13.6647	−	13.6647i	−0.467870	−	0.467870i	−0.901224	+	0.433354i	$0.857330\pi$
$854$		0			0
$855$		−	9.91981i		−	0.339250i
$856$		0			0
$857$		−	7.08036i		−	0.241860i	−0.992661	−	0.120930i	$-0.961412\pi$
$857$		−	7.08036i		−	0.241860i	0.992661	−	0.120930i	$-0.0385877\pi$
$858$		0			0
$859$	−0.0841770	−	0.0841770i	−0.00287208	−	0.00287208i	0.705669	−	0.708541i	$-0.250646\pi$
$859$	−0.0841770	−	0.0841770i	−0.00287208	−	0.00287208i	−0.708541	+	0.705669i	$0.750646\pi$
$860$		0			0
$861$	3.62916	−	3.62916i	0.123681	−	0.123681i
$862$		0			0
$863$	−27.4876			−0.935688			−0.467844	−	0.883811i	$-0.654969\pi$
$863$	−27.4876			−0.935688			−0.467844	+	0.883811i	$0.654969\pi$
$864$		0			0
$865$	−12.6632			−0.430562
$866$		0			0
$867$	26.9320	−	26.9320i	0.914658	−	0.914658i
$868$		0			0
$869$	−5.73589	−	5.73589i	−0.194577	−	0.194577i
$870$		0			0
$871$		−	41.0664i		−	1.39148i
$872$		0			0
$873$		−	12.8265i		−	0.434110i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	33.1562	−	33.1562i	1.11961	−	1.11961i	0.127806	−	0.991799i	$-0.459206\pi$
$877$	33.1562	−	33.1562i	1.11961	−	1.11961i	0.991799	−	0.127806i	$-0.0407936\pi$
$878$		0			0
$879$	67.1889			2.26623
$880$		0			0
$881$	−16.0170			−0.539625			−0.269812	−	0.962913i	$-0.586962\pi$
$881$	−16.0170			−0.539625			−0.269812	+	0.962913i	$0.586962\pi$
$882$		0			0
$883$	−32.3591	+	32.3591i	−1.08897	+	1.08897i	−0.0933341	+	0.995635i	$0.529752\pi$
$883$	−32.3591	+	32.3591i	−1.08897	+	1.08897i	−0.995635	+	0.0933341i	$0.970248\pi$
$884$		0			0
$885$	18.2662	+	18.2662i	0.614011	+	0.614011i
$886$		0			0
$887$		−	35.2386i		−	1.18320i	−0.806233	−	0.591598i	$-0.798497\pi$
$887$		−	35.2386i		−	1.18320i	0.806233	−	0.591598i	$-0.201503\pi$
$888$		0			0
$889$			3.58897i			0.120370i
$890$		0			0
$891$	5.53793	+	5.53793i	0.185528	+	0.185528i
$892$		0			0
$893$	4.19480	−	4.19480i	0.140373	−	0.140373i
$894$		0			0
$895$	−16.4204			−0.548872
$896$		0			0
$897$	−93.5302			−3.12288
$898$		0			0
$899$	0.678383	−	0.678383i	0.0226253	−	0.0226253i
$900$		0			0
$901$	16.2403	+	16.2403i	0.541042	+	0.541042i
$902$		0			0
$903$		−	8.97754i		−	0.298754i
$904$		0			0
$905$			0.525969i			0.0174838i
$906$		0			0
$907$	10.2565	+	10.2565i	0.340560	+	0.340560i	0.856578	−	0.516018i	$-0.172586\pi$
$907$	10.2565	+	10.2565i	0.340560	+	0.340560i	−0.516018	+	0.856578i	$0.672586\pi$
$908$		0			0
$909$	2.72864	−	2.72864i	0.0905032	−	0.0905032i
$910$		0			0
$911$	−54.6781			−1.81157			−0.905783	−	0.423742i	$-0.860716\pi$
$911$	−54.6781			−1.81157			−0.905783	+	0.423742i	$0.860716\pi$
$912$		0			0
$913$	28.3909			0.939601
$914$		0			0
$915$	8.65596	−	8.65596i	0.286157	−	0.286157i
$916$		0			0
$917$	2.35913	+	2.35913i	0.0779053	+	0.0779053i
$918$		0			0
$919$		−	17.6469i		−	0.582119i	−0.956705	−	0.291060i	$-0.905992\pi$
$919$		−	17.6469i		−	0.582119i	0.956705	−	0.291060i	$-0.0940078\pi$
$920$		0			0
$921$			25.8745i			0.852594i
$922$		0			0
$923$	32.8637	+	32.8637i	1.08172	+	1.08172i
$924$		0			0
$925$	−8.01620	+	8.01620i	−0.263571	+	0.263571i
$926$		0			0
$927$	−45.5981			−1.49764
$928$		0			0
$929$	28.7903			0.944580			0.472290	−	0.881443i	$-0.343427\pi$
$929$	28.7903			0.944580			0.472290	+	0.881443i	$0.343427\pi$
$930$		0			0
$931$	−1.39086	+	1.39086i	−0.0455836	+	0.0455836i
$932$		0			0
$933$	11.0817	+	11.0817i	0.362798	+	0.362798i
$934$		0			0
$935$			11.3468i			0.371081i
$936$		0			0
$937$			21.3212i			0.696534i	0.937395	+	0.348267i	$0.113230\pi$
$937$			21.3212i			0.696534i	−0.937395	+	0.348267i	$0.886770\pi$
$938$		0			0
$939$	−17.6724	−	17.6724i	−0.576718	−	0.576718i
$940$		0			0
$941$	−24.5808	+	24.5808i	−0.801312	+	0.801312i	−0.983301	−	0.181989i	$-0.941747\pi$
$941$	−24.5808	+	24.5808i	−0.801312	+	0.801312i	0.181989	+	0.983301i	$0.441747\pi$
$942$		0			0
$943$	−13.2031			−0.429952
$944$		0			0
$945$	−5.79458			−0.188498
$946$		0			0
$947$	−32.4717	+	32.4717i	−1.05519	+	1.05519i	−0.0568019	+	0.998385i	$0.518090\pi$
$947$	−32.4717	+	32.4717i	−1.05519	+	1.05519i	−0.998385	+	0.0568019i	$0.981910\pi$
$948$		0			0
$949$	44.9315	+	44.9315i	1.45854	+	1.45854i
$950$		0			0
$951$			72.9824i			2.36662i
$952$		0			0
$953$		−	11.7786i		−	0.381547i	−0.981634	−	0.190774i	$-0.938900\pi$
$953$		−	11.7786i		−	0.381547i	0.981634	−	0.190774i	$-0.0610997\pi$
$954$		0			0
$955$	−5.02084	−	5.02084i	−0.162470	−	0.162470i
$956$		0			0
$957$	1.20923	−	1.20923i	0.0390888	−	0.0390888i
$958$		0			0
$959$	7.69317			0.248426
$960$		0			0
$961$	60.2887			1.94480
$962$		0			0
$963$	65.1006	−	65.1006i	2.09784	−	2.09784i
$964$		0			0
$965$	0.345319	+	0.345319i	0.0111162	+	0.0111162i
$966$		0			0
$967$		−	37.3484i		−	1.20104i	−0.799609	−	0.600522i	$-0.794960\pi$
$967$		−	37.3484i		−	1.20104i	0.799609	−	0.600522i	$-0.205040\pi$
$968$		0			0
$969$		−	10.5405i		−	0.338608i
$970$		0			0
$971$	−19.4658	−	19.4658i	−0.624686	−	0.624686i	0.322040	−	0.946726i	$-0.395631\pi$
$971$	−19.4658	−	19.4658i	−0.624686	−	0.624686i	−0.946726	+	0.322040i	$0.895631\pi$
$972$		0			0
$973$	6.50335	−	6.50335i	0.208488	−	0.208488i
$974$		0			0
$975$	−12.8198			−0.410563
$976$		0			0
$977$	42.2447			1.35153			0.675763	−	0.737119i	$-0.263814\pi$
$977$	42.2447			1.35153			0.675763	+	0.737119i	$0.263814\pi$
$978$		0			0
$979$	18.0165	−	18.0165i	0.575810	−	0.575810i
$980$		0			0
$981$	−1.35238	−	1.35238i	−0.0431781	−	0.0431781i
$982$		0			0
$983$		−	48.9667i		−	1.56180i	−0.624659	−	0.780898i	$-0.714762\pi$
$983$		−	48.9667i		−	1.56180i	0.624659	−	0.780898i	$-0.285238\pi$
$984$		0			0
$985$			16.3929i			0.522321i
$986$		0			0
$987$	−6.04820	−	6.04820i	−0.192516	−	0.192516i
$988$		0			0
$989$	−16.3304	+	16.3304i	−0.519278	+	0.519278i
$990$		0			0
$991$	53.7618			1.70780			0.853901	−	0.520436i	$-0.174231\pi$
$991$	53.7618			1.70780			0.853901	+	0.520436i	$0.174231\pi$
$992$		0			0
$993$	18.9296			0.600711
$994$		0			0
$995$	−3.43966	+	3.43966i	−0.109044	+	0.109044i
$996$		0			0
$997$	−25.5795	−	25.5795i	−0.810112	−	0.810112i	0.174538	−	0.984650i	$-0.444157\pi$
$997$	−25.5795	−	25.5795i	−0.810112	−	0.810112i	−0.984650	+	0.174538i	$0.944157\pi$
$998$		0			0
$999$			65.6910i			2.07837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.b.561.4		52
4.3	odd	2		560.2.bd.b.421.8	yes	52
16.3	odd	4		560.2.bd.b.141.8	✓	52
16.13	even	4	inner	2240.2.bd.b.1681.4		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.8	✓	52	16.3	odd	4
560.2.bd.b.421.8	yes	52	4.3	odd	2
2240.2.bd.b.561.4		52	1.1	even	1	trivial
2240.2.bd.b.1681.4		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)

\(f(q)\)	\(=\)	\(q+(-2.00539 + 2.00539i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -5.04319i q^{9} +O(q^{10})\)	\(q+(-2.00539 + 2.00539i) q^{3} +(0.707107 + 0.707107i) q^{5} +1.00000i q^{7} -5.04319i q^{9} +(-4.24632 - 4.24632i) q^{11} +(3.19634 - 3.19634i) q^{13} -2.83605 q^{15} -1.88950 q^{17} +(1.39086 - 1.39086i) q^{19} +(-2.00539 - 2.00539i) q^{21} +7.29574i q^{23} +1.00000i q^{25} +(4.09739 + 4.09739i) q^{27} +(0.0710013 - 0.0710013i) q^{29} +9.55451 q^{31} +17.0311 q^{33} +(-0.707107 + 0.707107i) q^{35} +(8.01620 + 8.01620i) q^{37} +12.8198i q^{39} +1.80970i q^{41} +(2.23835 + 2.23835i) q^{43} +(3.56607 - 3.56607i) q^{45} +3.01597 q^{47} -1.00000 q^{49} +(3.78918 - 3.78918i) q^{51} +(-8.59501 - 8.59501i) q^{53} -6.00521i q^{55} +5.57844i q^{57} +(-6.44071 - 6.44071i) q^{59} +(-3.05212 + 3.05212i) q^{61} +5.04319 q^{63} +4.52031 q^{65} +(6.42396 - 6.42396i) q^{67} +(-14.6308 - 14.6308i) q^{69} +10.2817i q^{71} +14.0571i q^{73} +(-2.00539 - 2.00539i) q^{75} +(4.24632 - 4.24632i) q^{77} +1.35079 q^{79} -1.30417 q^{81} +(-3.34300 + 3.34300i) q^{83} +(-1.33608 - 1.33608i) q^{85} +0.284771i q^{87} +4.24285i q^{89} +(3.19634 + 3.19634i) q^{91} +(-19.1605 + 19.1605i) q^{93} +1.96697 q^{95} +2.54333 q^{97} +(-21.4150 + 21.4150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 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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