LMFDB - Embedded newform 280.2.h.a.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(251,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.h (of order $2$, degree $1$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 $ x^16 - x^15 - 2x^12 + 6x^11 - 12x^9 + 8x^8 - 24x^7 + 48x^5 - 32x^4 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.3
Root			$-1.24098 + 0.678208i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.a.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24098 - 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} -1.00000 q^{5} +(-1.09238 + 1.99883i) q^{6} +(-2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +O(q^{10})$	\(q+(-1.24098 - 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} -1.00000 q^{5} +(-1.09238 + 1.99883i) q^{6} +(-2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +(1.24098 + 0.678208i) q^{10} -6.01679 q^{11} +(2.71124 - 1.73965i) q^{12} -4.25411 q^{13} +(3.70916 - 0.492075i) q^{14} +1.61069i q^{15} +(-1.66690 + 3.63613i) q^{16} -5.42124i q^{17} +(-0.503458 - 0.275145i) q^{18} +4.53588i q^{19} +(-1.08007 - 1.68329i) q^{20} +(2.51769 + 3.43822i) q^{21} +(7.46673 + 4.08064i) q^{22} +5.19890i q^{23} +(-4.54445 + 0.320086i) q^{24} +1.00000 q^{25} +(5.27927 + 2.88517i) q^{26} -5.48550i q^{27} +(-4.93673 - 1.90492i) q^{28} +0.376818i q^{29} +(1.09238 - 1.99883i) q^{30} -2.93636 q^{31} +(4.53465 - 3.38186i) q^{32} +9.69116i q^{33} +(-3.67672 + 6.72765i) q^{34} +(2.13463 - 1.56312i) q^{35} +(0.438177 + 0.682898i) q^{36} -0.372265i q^{37} +(3.07627 - 5.62894i) q^{38} +6.85203i q^{39} +(0.198727 + 2.82144i) q^{40} +5.75560i q^{41} +(-0.792578 - 5.97429i) q^{42} -4.96515 q^{43} +(-6.49855 - 10.1280i) q^{44} -0.405694 q^{45} +(3.52593 - 6.45173i) q^{46} -3.86303 q^{47} +(5.85666 + 2.68486i) q^{48} +(2.11332 - 6.67337i) q^{49} +(-1.24098 - 0.678208i) q^{50} -8.73190 q^{51} +(-4.59473 - 7.16089i) q^{52} -10.2224i q^{53} +(-3.72031 + 6.80740i) q^{54} +6.01679 q^{55} +(4.83445 + 5.71210i) q^{56} +7.30587 q^{57} +(0.255561 - 0.467624i) q^{58} -10.5835i q^{59} +(-2.71124 + 1.73965i) q^{60} +5.58001 q^{61} +(3.64396 + 1.99146i) q^{62} +(-0.866007 + 0.634147i) q^{63} +(-7.92102 + 1.12139i) q^{64} +4.25411 q^{65} +(6.57262 - 12.0265i) q^{66} -0.782596 q^{67} +(9.12549 - 5.85531i) q^{68} +8.37378 q^{69} +(-3.70916 + 0.492075i) q^{70} -15.3803i q^{71} +(-0.0806221 - 1.14464i) q^{72} +8.77164i q^{73} +(-0.252473 + 0.461974i) q^{74} -1.61069i q^{75} +(-7.63518 + 4.89906i) q^{76} +(12.8437 - 9.40496i) q^{77} +(4.64710 - 8.50324i) q^{78} -8.74609i q^{79} +(1.66690 - 3.63613i) q^{80} -7.61833 q^{81} +(3.90349 - 7.14259i) q^{82} +8.42742i q^{83} +(-3.06823 + 7.95151i) q^{84} +5.42124i q^{85} +(6.16165 + 3.36740i) q^{86} +0.606935 q^{87} +(1.19570 + 16.9760i) q^{88} +1.94765i q^{89} +(0.503458 + 0.275145i) q^{90} +(9.08097 - 6.64968i) q^{91} +(-8.75123 + 5.61516i) q^{92} +4.72954i q^{93} +(4.79395 + 2.61994i) q^{94} -4.53588i q^{95} +(-5.44711 - 7.30389i) q^{96} +3.14377i q^{97} +(-7.14852 + 6.84826i) q^{98} -2.44098 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9 - q^10 - 4 * q^11 - 14 * q^12 + 7 * q^14 + 9 * q^16 - 15 * q^18 - q^20 + 4 * q^21 + 6 * q^22 - 22 * q^24 + 16 * q^25 + 20 * q^26 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * q^42 - 4 * q^43 - 20 * q^44 + 16 * q^45 + 6 * q^46 + 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 + 38 * q^52 - 26 * q^54 + 4 * q^55 + q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 + 8 * q^61 - 28 * q^62 - 28 * q^63 - 23 * q^64 - 46 * q^66 + 20 * q^67 - 12 * q^68 + 40 * q^69 - 7 * q^70 - 13 * q^72 - 28 * q^74 - 34 * q^76 + 4 * q^77 - 6 * q^78 - 9 * q^80 + 24 * q^81 + 16 * q^82 + 10 * q^84 - 24 * q^86 - 72 * q^87 - 44 * q^88 + 15 * q^90 - 32 * q^91 - 30 * q^92 + 58 * q^94 + 30 * q^96 - 39 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−1.24098	−	0.678208i	−0.877506	−	0.479565i
$2$	−1.24098	−	0.678208i	−0.877506	−	0.479565i
$3$		−	1.61069i		−	0.929929i	−0.885329	−	0.464965i	$-0.846067\pi$
$3$		−	1.61069i		−	0.929929i	0.885329	−	0.464965i	$-0.153933\pi$
$4$	1.08007	+	1.68329i	0.540034	+	0.841643i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.09238	+	1.99883i	−0.445962	+	0.816019i
$7$	−2.13463	+	1.56312i	−0.806816	+	0.590803i
$7$	−2.13463	+	1.56312i	−0.806816	+	0.590803i
$8$	−0.198727	−	2.82144i	−0.0702605	−	0.997529i
$9$	0.405694			0.135231
$10$	1.24098	+	0.678208i	0.392433	+	0.214468i
$11$	−6.01679			−1.81413			−0.907066	−	0.420989i	$-0.861683\pi$
$11$	−6.01679			−1.81413			−0.907066	+	0.420989i	$0.861683\pi$
$12$	2.71124	−	1.73965i	0.782669	−	0.502194i
$13$	−4.25411			−1.17988			−0.589939	−	0.807448i	$-0.700848\pi$
$13$	−4.25411			−1.17988			−0.589939	+	0.807448i	$0.700848\pi$
$14$	3.70916	−	0.492075i	0.991314	−	0.131513i
$15$			1.61069i			0.415877i
$16$	−1.66690	+	3.63613i	−0.416726	+	0.909032i
$17$		−	5.42124i		−	1.31484i	−0.753523	−	0.657421i	$-0.771647\pi$
$17$		−	5.42124i		−	1.31484i	0.753523	−	0.657421i	$-0.228353\pi$
$18$	−0.503458	−	0.275145i	−0.118666	−	0.0648522i
$19$			4.53588i			1.04060i	0.853983	+	0.520301i	$0.174180\pi$
$19$			4.53588i			1.04060i	−0.853983	+	0.520301i	$0.825820\pi$
$20$	−1.08007	−	1.68329i	−0.241511	−	0.376394i
$21$	2.51769	+	3.43822i	0.549405	+	0.750282i
$22$	7.46673	+	4.08064i	1.59191	+	0.869995i
$23$			5.19890i			1.08404i	0.840364	+	0.542022i	$0.182341\pi$
$23$			5.19890i			1.08404i	−0.840364	+	0.542022i	$0.817659\pi$
$24$	−4.54445	+	0.320086i	−0.927631	+	0.0653373i
$25$	1.00000			0.200000
$26$	5.27927	+	2.88517i	1.03535	+	0.565829i
$27$		−	5.48550i		−	1.05568i
$28$	−4.93673	−	1.90492i	−0.932953	−	0.359997i
$29$			0.376818i			0.0699733i	0.999388	+	0.0349866i	$0.0111389\pi$
$29$			0.376818i			0.0699733i	−0.999388	+	0.0349866i	$0.988861\pi$
$30$	1.09238	−	1.99883i	0.199440	−	0.364935i
$31$	−2.93636			−0.527385			−0.263693	−	0.964607i	$-0.584940\pi$
$31$	−2.93636			−0.527385			−0.263693	+	0.964607i	$0.584940\pi$
$32$	4.53465	−	3.38186i	0.801620	−	0.597834i
$33$			9.69116i			1.68701i
$34$	−3.67672	+	6.72765i	−0.630553	+	1.15378i
$35$	2.13463	−	1.56312i	0.360819	−	0.264215i
$36$	0.438177	+	0.682898i	0.0730295	+	0.113816i
$37$		−	0.372265i		−	0.0612000i	−0.999532	−	0.0306000i	$-0.990258\pi$
$37$		−	0.372265i		−	0.0612000i	0.999532	−	0.0306000i	$-0.00974181\pi$
$38$	3.07627	−	5.62894i	0.499037	−	0.913135i
$39$			6.85203i			1.09720i
$40$	0.198727	+	2.82144i	0.0314214	+	0.446108i
$41$			5.75560i			0.898874i	0.893312	+	0.449437i	$0.148375\pi$
$41$			5.75560i			0.898874i	−0.893312	+	0.449437i	$0.851625\pi$
$42$	−0.792578	−	5.97429i	−0.122297	−	0.921853i
$43$	−4.96515			−0.757178			−0.378589	−	0.925565i	$-0.623591\pi$
$43$	−4.96515			−0.757178			−0.378589	+	0.925565i	$0.623591\pi$
$44$	−6.49855	−	10.1280i	−0.979693	−	1.52685i
$45$	−0.405694			−0.0604772
$46$	3.52593	−	6.45173i	0.519870	−	0.951256i
$47$	−3.86303			−0.563481			−0.281741	−	0.959491i	$-0.590912\pi$
$47$	−3.86303			−0.563481			−0.281741	+	0.959491i	$0.590912\pi$
$48$	5.85666	+	2.68486i	0.845336	+	0.387526i
$49$	2.11332	−	6.67337i	0.301903	−	0.953339i
$50$	−1.24098	−	0.678208i	−0.175501	−	0.0959131i
$51$	−8.73190			−1.22271
$52$	−4.59473	−	7.16089i	−0.637174	−	0.993036i
$53$		−	10.2224i		−	1.40416i	−0.712099	−	0.702079i	$-0.752255\pi$
$53$		−	10.2224i		−	1.40416i	0.712099	−	0.702079i	$-0.247745\pi$
$54$	−3.72031	+	6.80740i	−0.506270	+	0.926370i
$55$	6.01679			0.811304
$56$	4.83445	+	5.71210i	0.646030	+	0.763312i
$57$	7.30587			0.967686
$58$	0.255561	−	0.467624i	0.0335568	−	0.0614020i
$59$		−	10.5835i		−	1.37786i	−0.724828	−	0.688930i	$-0.758081\pi$
$59$		−	10.5835i		−	1.37786i	0.724828	−	0.688930i	$-0.241919\pi$
$60$	−2.71124	+	1.73965i	−0.350020	+	0.224588i
$61$	5.58001			0.714447			0.357223	−	0.934019i	$-0.383723\pi$
$61$	5.58001			0.714447			0.357223	+	0.934019i	$0.383723\pi$
$62$	3.64396	+	1.99146i	0.462784	+	0.252916i
$63$	−0.866007	+	0.634147i	−0.109107	+	0.0798950i
$64$	−7.92102	+	1.12139i	−0.990127	+	0.140174i
$65$	4.25411			0.527657
$66$	6.57262	−	12.0265i	0.809034	−	1.48037i
$67$	−0.782596			−0.0956093			−0.0478047	−	0.998857i	$-0.515223\pi$
$67$	−0.782596			−0.0956093			−0.0478047	+	0.998857i	$0.515223\pi$
$68$	9.12549	−	5.85531i	1.10663	−	0.710060i
$69$	8.37378			1.00809
$70$	−3.70916	+	0.492075i	−0.443329	+	0.0588142i
$71$		−	15.3803i		−	1.82531i	−0.408735	−	0.912653i	$-0.634030\pi$
$71$		−	15.3803i		−	1.82531i	0.408735	−	0.912653i	$-0.365970\pi$
$72$	−0.0806221	−	1.14464i	−0.00950141	−	0.134897i
$73$			8.77164i			1.02664i	0.858196	+	0.513321i	$0.171585\pi$
$73$			8.77164i			1.02664i	−0.858196	+	0.513321i	$0.828415\pi$
$74$	−0.252473	+	0.461974i	−0.0293494	+	0.0537034i
$75$		−	1.61069i		−	0.185986i
$76$	−7.63518	+	4.89906i	−0.875816	+	0.561961i
$77$	12.8437	−	9.40496i	1.46367	−	1.07179i
$78$	4.64710	−	8.50324i	0.526181	−	0.962803i
$79$		−	8.74609i		−	0.984012i	−0.870592	−	0.492006i	$-0.836264\pi$
$79$		−	8.74609i		−	0.984012i	0.870592	−	0.492006i	$-0.163736\pi$
$80$	1.66690	−	3.63613i	0.186366	−	0.406531i
$81$	−7.61833			−0.846481
$82$	3.90349	−	7.14259i	0.431069	−	0.788767i
$83$			8.42742i			0.925029i	0.886612	+	0.462515i	$0.153053\pi$
$83$			8.42742i			0.925029i	−0.886612	+	0.462515i	$0.846947\pi$
$84$	−3.06823	+	7.95151i	−0.334772	+	0.867581i
$85$			5.42124i			0.588016i
$86$	6.16165	+	3.36740i	0.664428	+	0.363116i
$87$	0.606935			0.0650702
$88$	1.19570	+	16.9760i	0.127462	+	1.80965i
$89$			1.94765i			0.206451i	0.994658	+	0.103225i	$0.0329163\pi$
$89$			1.94765i			0.206451i	−0.994658	+	0.103225i	$0.967084\pi$
$90$	0.503458	+	0.275145i	0.0530691	+	0.0290028i
$91$	9.08097	−	6.64968i	0.951944	−	0.697076i
$92$	−8.75123	+	5.61516i	−0.912379	+	0.585421i
$93$			4.72954i			0.490431i
$94$	4.79395	+	2.61994i	0.494458	+	0.270226i
$95$		−	4.53588i		−	0.465371i
$96$	−5.44711	−	7.30389i	−0.555943	−	0.745450i
$97$			3.14377i			0.319201i	0.987182	+	0.159601i	$0.0510206\pi$
$97$			3.14377i			0.319201i	−0.987182	+	0.159601i	$0.948979\pi$
$98$	−7.14852	+	6.84826i	−0.722110	+	0.691778i
$99$	−2.44098			−0.245327
$100$	1.08007	+	1.68329i	0.108007	+	0.168329i
$101$	−16.3016			−1.62207			−0.811037	−	0.584995i	$-0.801096\pi$
$101$	−16.3016			−1.62207			−0.811037	+	0.584995i	$0.801096\pi$
$102$	10.8361	+	5.92205i	1.07294	+	0.586370i
$103$	−11.8940			−1.17195			−0.585974	−	0.810330i	$-0.699288\pi$
$103$	−11.8940			−1.17195			−0.585974	+	0.810330i	$0.699288\pi$
$104$	0.845405	+	12.0027i	0.0828988	+	1.17696i
$105$	−2.51769	−	3.43822i	−0.245702	−	0.335536i
$106$	−6.93293	+	12.6858i	−0.673385	+	1.23216i
$107$	10.4794			1.01308			0.506542	−	0.862215i	$-0.330923\pi$
$107$	10.4794			1.01308			0.506542	+	0.862215i	$0.330923\pi$
$108$	9.23367	−	5.92471i	0.888510	−	0.570106i
$109$		−	0.676794i		−	0.0648251i	−0.999475	−	0.0324126i	$-0.989681\pi$
$109$		−	0.676794i		−	0.0648251i	0.999475	−	0.0324126i	$-0.0103190\pi$
$110$	−7.46673	−	4.08064i	−0.711925	−	0.389073i
$111$	−0.599602			−0.0569117
$112$	−2.12547	−	10.3674i	−0.200838	−	0.979624i
$113$	−9.10537			−0.856562			−0.428281	−	0.903646i	$-0.640881\pi$
$113$	−9.10537			−0.856562			−0.428281	+	0.903646i	$0.640881\pi$
$114$	−9.06645	−	4.95490i	−0.849151	−	0.464069i
$115$		−	5.19890i		−	0.484800i
$116$	−0.634292	+	0.406989i	−0.0588925	+	0.0377880i
$117$	−1.72587			−0.159556
$118$	−7.17784	+	13.1340i	−0.660774	+	1.20908i
$119$	8.47403	+	11.5724i	0.776813	+	1.06084i
$120$	4.54445	−	0.320086i	0.414849	−	0.0292197i
$121$	25.2018			2.29107
$122$	−6.92468	−	3.78440i	−0.626931	−	0.342624i
$123$	9.27046			0.835889
$124$	−3.17147	−	4.94273i	−0.284806	−	0.443870i
$125$	−1.00000			−0.0894427
$126$	1.50478	−	0.199632i	0.134057	−	0.0177846i
$127$			3.74123i			0.331980i	0.986127	+	0.165990i	$0.0530820\pi$
$127$			3.74123i			0.331980i	−0.986127	+	0.165990i	$0.946918\pi$
$128$	10.5904	+	3.98047i	0.936065	+	0.351827i
$129$			7.99729i			0.704122i
$130$	−5.27927	−	2.88517i	−0.463023	−	0.253046i
$131$			17.5774i			1.53575i	0.640601	+	0.767874i	$0.278685\pi$
$131$			17.5774i			1.53575i	−0.640601	+	0.767874i	$0.721315\pi$
$132$	−16.3130	+	10.4671i	−1.41986	+	0.911045i
$133$	−7.09012	−	9.68244i	−0.614791	−	0.839574i
$134$	0.971187	+	0.530763i	0.0838978	+	0.0458509i
$135$			5.48550i			0.472117i
$136$	−15.2957	+	1.07734i	−1.31159	+	0.0923815i
$137$	−0.767338			−0.0655581			−0.0327791	−	0.999463i	$-0.510436\pi$
$137$	−0.767338			−0.0655581			−0.0327791	+	0.999463i	$0.510436\pi$
$138$	−10.3917	−	5.67917i	−0.884601	−	0.483443i
$139$		−	2.01854i		−	0.171210i	−0.996329	−	0.0856052i	$-0.972718\pi$
$139$		−	2.01854i		−	0.171210i	0.996329	−	0.0856052i	$-0.0272824\pi$
$140$	4.93673	+	1.90492i	0.417229	+	0.160996i
$141$			6.22213i			0.523998i
$142$	−10.4310	+	19.0867i	−0.875354	+	1.60172i
$143$	25.5961			2.14045
$144$	−0.676253	+	1.47515i	−0.0563544	+	0.122930i
$145$		−	0.376818i		−	0.0312930i
$146$	5.94899	−	10.8854i	0.492342	−	0.900885i
$147$	−10.7487	−	3.40390i	−0.886538	−	0.280749i
$148$	0.626629	−	0.402072i	0.0515086	−	0.0330501i
$149$		−	4.23267i		−	0.346754i	−0.984856	−	0.173377i	$-0.944532\pi$
$149$		−	4.23267i		−	0.346754i	0.984856	−	0.173377i	$-0.0554679\pi$
$150$	−1.09238	+	1.99883i	−0.0891924	+	0.163204i
$151$			0.625768i			0.0509243i	0.999676	+	0.0254622i	$0.00810573\pi$
$151$			0.625768i			0.0509243i	−0.999676	+	0.0254622i	$0.991894\pi$
$152$	12.7977	−	0.901400i	1.03803	−	0.0731132i
$153$		−	2.19936i		−	0.177808i
$154$	−22.3172	+	2.96072i	−1.79838	+	0.238581i
$155$	2.93636			0.235854
$156$	−11.5339	+	7.40066i	−0.923454	+	0.592527i
$157$	2.91713			0.232812			0.116406	−	0.993202i	$-0.462863\pi$
$157$	2.91713			0.232812			0.116406	+	0.993202i	$0.462863\pi$
$158$	−5.93167	+	10.8537i	−0.471898	+	0.863477i
$159$	−16.4651			−1.30577
$160$	−4.53465	+	3.38186i	−0.358495	+	0.267359i
$161$	−8.12649	−	11.0977i	−0.640457	−	0.874624i
$162$	9.45421	+	5.16681i	0.742793	+	0.405943i
$163$	−7.14397			−0.559559			−0.279779	−	0.960064i	$-0.590261\pi$
$163$	−7.14397			−0.559559			−0.279779	+	0.960064i	$0.590261\pi$
$164$	−9.68833	+	6.21644i	−0.756531	+	0.485423i
$165$		−	9.69116i		−	0.754456i
$166$	5.71554	−	10.4583i	0.443612	−	0.811719i
$167$	−6.26796			−0.485029			−0.242515	−	0.970148i	$-0.577972\pi$
$167$	−6.26796			−0.485029			−0.242515	+	0.970148i	$0.577972\pi$
$168$	9.20040	−	7.78677i	0.709826	−	0.600763i
$169$	5.09746			0.392112
$170$	3.67672	−	6.72765i	0.281992	−	0.515987i
$171$			1.84018i			0.140722i
$172$	−5.36270	−	8.35776i	−0.408902	−	0.637274i
$173$	−9.11366			−0.692898			−0.346449	−	0.938069i	$-0.612613\pi$
$173$	−9.11366			−0.692898			−0.346449	+	0.938069i	$0.612613\pi$
$174$	−0.753195	−	0.411628i	−0.0570995	−	0.0312054i
$175$	−2.13463	+	1.56312i	−0.161363	+	0.118161i
$176$	10.0294	−	21.8778i	0.755996	−	1.64910i
$177$	−17.0468			−1.28131
$178$	1.32091	−	2.41700i	0.0990067	−	0.181162i
$179$	10.9518			0.818579			0.409290	−	0.912405i	$-0.365777\pi$
$179$	10.9518			0.818579			0.409290	+	0.912405i	$0.365777\pi$
$180$	−0.438177	−	0.682898i	−0.0326598	−	0.0509002i
$181$	18.7975			1.39721			0.698603	−	0.715509i	$-0.253805\pi$
$181$	18.7975			1.39721			0.698603	+	0.715509i	$0.253805\pi$
$182$	−15.7792	+	2.09334i	−1.16963	+	0.155169i
$183$		−	8.98763i		−	0.664385i
$184$	14.6684	−	1.03316i	1.08137	−	0.0761655i
$185$			0.372265i			0.0273695i
$186$	3.20761	−	5.86928i	0.235194	−	0.430356i
$187$			32.6185i			2.38530i
$188$	−4.17234	−	6.50259i	−0.304299	−	0.474250i
$189$	8.57449	+	11.7095i	0.623702	+	0.851743i
$190$	−3.07627	+	5.62894i	−0.223176	+	0.408366i
$191$			1.13019i			0.0817778i	0.999164	+	0.0408889i	$0.0130190\pi$
$191$			1.13019i			0.0817778i	−0.999164	+	0.0408889i	$0.986981\pi$
$192$	1.80621	+	12.7583i	0.130352	+	0.920748i
$193$	−3.27357			−0.235636			−0.117818	−	0.993035i	$-0.537590\pi$
$193$	−3.27357			−0.235636			−0.117818	+	0.993035i	$0.537590\pi$
$194$	2.13213	−	3.90136i	0.153078	−	0.280101i
$195$		−	6.85203i		−	0.490684i
$196$	13.5157	−	3.65037i	0.965409	−	0.260741i
$197$			21.2252i			1.51223i	0.654437	+	0.756116i	$0.272906\pi$
$197$			21.2252i			1.51223i	−0.654437	+	0.756116i	$0.727094\pi$
$198$	3.02920	+	1.65549i	0.215276	+	0.117650i
$199$	17.9614			1.27325			0.636626	−	0.771172i	$-0.280329\pi$
$199$	17.9614			1.27325			0.636626	+	0.771172i	$0.280329\pi$
$200$	−0.198727	−	2.82144i	−0.0140521	−	0.199506i
$201$			1.26052i			0.0889099i
$202$	20.2300	+	11.0559i	1.42338	+	0.777890i
$203$	−0.589011	−	0.804368i	−0.0413404	−	0.0564556i
$204$	−9.43105	−	14.6983i	−0.660306	−	1.02909i
$205$		−	5.75560i		−	0.401989i
$206$	14.7602	+	8.06659i	1.02839	+	0.562026i
$207$			2.10916i			0.146597i
$208$	7.09120	−	15.4685i	0.491686	−	1.07255i
$209$		−	27.2915i		−	1.88779i
$210$	0.792578	+	5.97429i	0.0546931	+	0.412265i
$211$	−7.43642			−0.511944			−0.255972	−	0.966684i	$-0.582396\pi$
$211$	−7.43642			−0.511944			−0.255972	+	0.966684i	$0.582396\pi$
$212$	17.2073	−	11.0409i	1.18180	−	0.758293i
$213$	−24.7728			−1.69741
$214$	−13.0048	−	7.10723i	−0.888988	−	0.485840i
$215$	4.96515			0.338620
$216$	−15.4770	+	1.09011i	−1.05308	+	0.0741729i
$217$	6.26804	−	4.58987i	0.425503	−	0.311581i
$218$	−0.459007	+	0.839889i	−0.0310879	+	0.0568845i
$219$	14.1283			0.954705
$220$	6.49855	+	10.1280i	0.438132	+	0.682829i
$221$			23.0625i			1.55135i
$222$	0.744095	+	0.406655i	0.0499404	+	0.0272929i
$223$	23.8641			1.59806			0.799029	−	0.601293i	$-0.205347\pi$
$223$	23.8641			1.59806			0.799029	+	0.601293i	$0.205347\pi$
$224$	−4.39357	+	14.3072i	−0.293558	+	0.955941i
$225$	0.405694			0.0270462
$226$	11.2996	+	6.17534i	0.751638	+	0.410777i
$227$			12.1282i			0.804974i	0.915426	+	0.402487i	$0.131854\pi$
$227$			12.1282i			0.804974i	−0.915426	+	0.402487i	$0.868146\pi$
$228$	7.89084	+	12.2979i	0.522584	+	0.814447i
$229$	16.4001			1.08375			0.541875	−	0.840459i	$-0.317715\pi$
$229$	16.4001			1.08375			0.541875	+	0.840459i	$0.317715\pi$
$230$	−3.52593	+	6.45173i	−0.232493	+	0.425415i
$231$	−15.1484	−	20.6871i	−0.996694	−	1.36111i
$232$	1.06317	−	0.0748837i	0.0698004	−	0.00491636i
$233$	−26.4108			−1.73023			−0.865114	−	0.501575i	$-0.832754\pi$
$233$	−26.4108			−1.73023			−0.865114	+	0.501575i	$0.832754\pi$
$234$	2.14177	+	1.17050i	0.140012	+	0.0765177i
$235$	3.86303			0.251997
$236$	17.8151	−	11.4310i	1.15967	−	0.744092i
$237$	−14.0872			−0.915062
$238$	−2.66766	−	20.1082i	−0.172918	−	1.30342i
$239$		−	1.68909i		−	0.109258i	−0.998507	−	0.0546292i	$-0.982602\pi$
$239$		−	1.68909i		−	0.109258i	0.998507	−	0.0546292i	$-0.0173977\pi$
$240$	−5.85666	−	2.68486i	−0.378046	−	0.173307i
$241$		−	5.25118i		−	0.338258i	−0.985594	−	0.169129i	$-0.945905\pi$
$241$		−	5.25118i		−	0.338258i	0.985594	−	0.169129i	$-0.0540955\pi$
$242$	−31.2750	−	17.0921i	−2.01043	−	1.09872i
$243$		−	4.18577i		−	0.268517i
$244$	6.02679	+	9.39275i	0.385826	+	0.601309i
$245$	−2.11332	+	6.67337i	−0.135015	+	0.426346i
$246$	−11.5045	−	6.28730i	−0.733498	−	0.400864i
$247$		−	19.2961i		−	1.22778i
$248$	0.583532	+	8.28474i	0.0370543	+	0.526082i
$249$	13.5739			0.860212
$250$	1.24098	+	0.678208i	0.0784865	+	0.0428936i
$251$			13.9692i			0.881730i	0.897574	+	0.440865i	$0.145328\pi$
$251$			13.9692i			0.881730i	−0.897574	+	0.440865i	$0.854672\pi$
$252$	−2.00280	−	0.772816i	−0.126164	−	0.0486828i
$253$		−	31.2807i		−	1.96660i
$254$	2.53733	−	4.64280i	0.159206	−	0.291315i
$255$	8.73190			0.546813
$256$	−10.4429	−	12.1222i	−0.652679	−	0.757635i
$257$		−	21.6938i		−	1.35322i	−0.736341	−	0.676610i	$-0.763448\pi$
$257$		−	21.6938i		−	1.35322i	0.736341	−	0.676610i	$-0.236552\pi$
$258$	5.42382	−	9.92448i	0.337672	−	0.617871i
$259$	0.581895	+	0.794650i	0.0361572	+	0.0493771i
$260$	4.59473	+	7.16089i	0.284953	+	0.444099i
$261$			0.152873i			0.00946257i
$262$	11.9212	−	21.8133i	0.736492	−	1.34763i
$263$			5.88968i			0.363173i	0.983375	+	0.181587i	$0.0581232\pi$
$263$			5.88968i			0.363173i	−0.983375	+	0.181587i	$0.941877\pi$
$264$	27.3430	−	1.92589i	1.68285	−	0.118530i
$265$			10.2224i			0.627958i
$266$	2.23199	+	16.8243i	0.136852	+	1.03156i
$267$	3.13706			0.191985
$268$	−0.845257	−	1.31733i	−0.0516323	−	0.0804689i
$269$	−13.3475			−0.813810			−0.406905	−	0.913470i	$-0.633392\pi$
$269$	−13.3475			−0.813810			−0.406905	+	0.913470i	$0.633392\pi$
$270$	3.72031	−	6.80740i	0.226411	−	0.414285i
$271$	−24.7908			−1.50593			−0.752966	−	0.658059i	$-0.771378\pi$
$271$	−24.7908			−1.50593			−0.752966	+	0.658059i	$0.771378\pi$
$272$	19.7123	+	9.03668i	1.19523	+	0.547929i
$273$	−10.7105	−	14.6266i	−0.648231	−	0.885241i
$274$	0.952252	+	0.520415i	0.0575277	+	0.0314394i
$275$	−6.01679			−0.362826
$276$	9.04426	+	14.0955i	0.544400	+	0.848448i
$277$		−	2.09066i		−	0.125616i	−0.998026	−	0.0628078i	$-0.979994\pi$
$277$		−	2.09066i		−	0.125616i	0.998026	−	0.0628078i	$-0.0200055\pi$
$278$	−1.36899	+	2.50497i	−0.0821065	+	0.150238i
$279$	−1.19126			−0.0713189
$280$	−4.83445	−	5.71210i	−0.288914	−	0.341363i
$281$	−4.09181			−0.244097			−0.122048	−	0.992524i	$-0.538946\pi$
$281$	−4.09181			−0.244097			−0.122048	+	0.992524i	$0.538946\pi$
$282$	4.21990	−	7.72155i	0.251291	−	0.459811i
$283$		−	5.92294i		−	0.352082i	−0.984383	−	0.176041i	$-0.943671\pi$
$283$		−	5.92294i		−	0.352082i	0.984383	−	0.176041i	$-0.0563291\pi$
$284$	25.8895	−	16.6118i	1.53626	−	0.985728i
$285$	−7.30587			−0.432763
$286$	−31.7643	−	17.3595i	−1.87826	−	1.02649i
$287$	−8.99669	−	12.2861i	−0.531058	−	0.725226i
$288$	1.83968	−	1.37200i	0.108404	−	0.0808458i
$289$	−12.3898			−0.728812
$290$	−0.255561	+	0.467624i	−0.0150070	+	0.0274598i
$291$	5.06362			0.296835
$292$	−14.7652	+	9.47397i	−0.864067	+	0.554422i
$293$	−9.44316			−0.551675			−0.275838	−	0.961204i	$-0.588955\pi$
$293$	−9.44316			−0.551675			−0.275838	+	0.961204i	$0.588955\pi$
$294$	11.0304	+	11.5140i	0.643305	+	0.671511i
$295$			10.5835i			0.616198i
$296$	−1.05032	+	0.0739790i	−0.0610488	+	0.00429994i
$297$			33.0051i			1.91515i
$298$	−2.87063	+	5.25267i	−0.166291	+	0.304279i
$299$		−	22.1167i		−	1.27904i
$300$	2.71124	−	1.73965i	0.156534	−	0.100439i
$301$	10.5988	−	7.76111i	0.610903	−	0.447343i
$302$	0.424401	−	0.776567i	0.0244215	−	0.0446864i
$303$			26.2568i			1.50841i
$304$	−16.4930	−	7.56088i	−0.945941	−	0.433646i
$305$	−5.58001			−0.319510
$306$	−1.49162	+	2.72937i	−0.0852704	+	0.156027i
$307$		−	24.1204i		−	1.37663i	−0.725414	−	0.688313i	$-0.758351\pi$
$307$		−	24.1204i		−	1.37663i	0.725414	−	0.688313i	$-0.241649\pi$
$308$	29.7033	+	11.4615i	1.69250	+	0.653082i
$309$			19.1574i			1.08983i
$310$	−3.64396	−	1.99146i	−0.206963	−	0.113107i
$311$	−16.5947			−0.941001			−0.470500	−	0.882400i	$-0.655927\pi$
$311$	−16.5947			−0.941001			−0.470500	+	0.882400i	$0.655927\pi$
$312$	19.3326	−	1.36168i	1.09449	−	0.0770900i
$313$			11.3871i			0.643637i	0.946801	+	0.321819i	$0.104294\pi$
$313$			11.3871i			0.643637i	−0.946801	+	0.321819i	$0.895706\pi$
$314$	−3.62010	−	1.97842i	−0.204294	−	0.111649i
$315$	0.866007	−	0.634147i	0.0487940	−	0.0357301i
$316$	14.7222	−	9.44638i	0.828187	−	0.531400i
$317$			26.7084i			1.50009i	0.661386	+	0.750046i	$0.269969\pi$
$317$			26.7084i			1.50009i	−0.661386	+	0.750046i	$0.730031\pi$
$318$	20.4329	+	11.1668i	1.14582	+	0.626201i
$319$		−	2.26723i		−	0.126941i
$320$	7.92102	−	1.12139i	0.442798	−	0.0626876i
$321$		−	16.8791i		−	0.942097i
$322$	2.55825	+	19.2835i	0.142566	+	1.07463i
$323$	24.5901			1.36823
$324$	−8.22832	−	12.8238i	−0.457129	−	0.712435i
$325$	−4.25411			−0.235976
$326$	8.86553	+	4.84510i	0.491016	+	0.268345i
$327$	−1.09010			−0.0602828
$328$	16.2391	−	1.14379i	0.896653	−	0.0631553i
$329$	8.24616	−	6.03838i	0.454626	−	0.332907i
$330$	−6.57262	+	12.0265i	−0.361811	+	0.662040i
$331$	−3.25364			−0.178836			−0.0894182	−	0.995994i	$-0.528501\pi$
$331$	−3.25364			−0.178836			−0.0894182	+	0.995994i	$0.528501\pi$
$332$	−14.1858	+	9.10219i	−0.778545	+	0.499547i
$333$		−	0.151026i		−	0.00827615i
$334$	7.77842	+	4.25098i	0.425616	+	0.232603i
$335$	0.782596			0.0427578
$336$	−16.6986	+	3.42346i	−0.910982	+	0.186765i
$337$	−12.0157			−0.654539			−0.327270	−	0.944931i	$-0.606129\pi$
$337$	−12.0157			−0.654539			−0.327270	+	0.944931i	$0.606129\pi$
$338$	−6.32585	−	3.45714i	−0.344081	−	0.188043i
$339$			14.6659i			0.796542i
$340$	−9.12549	+	5.85531i	−0.494899	+	0.317549i
$341$	17.6675			0.956746
$342$	1.24802	−	2.28363i	0.0674853	−	0.123484i
$343$	5.92010	+	17.5486i	0.319655	+	0.947534i
$344$	0.986707	+	14.0089i	0.0531997	+	0.755307i
$345$	−8.37378			−0.450829
$346$	11.3099	+	6.18095i	0.608023	+	0.332290i
$347$	−15.5740			−0.836057			−0.418028	−	0.908434i	$-0.637279\pi$
$347$	−15.5740			−0.836057			−0.418028	+	0.908434i	$0.637279\pi$
$348$	0.655531	+	1.02164i	0.0351401	+	0.0547659i
$349$	−34.7705			−1.86122			−0.930610	−	0.366012i	$-0.880723\pi$
$349$	−34.7705			−1.86122			−0.930610	+	0.366012i	$0.880723\pi$
$350$	3.70916	−	0.492075i	0.198263	−	0.0263025i
$351$			23.3359i			1.24558i
$352$	−27.2840	+	20.3479i	−1.45424	+	1.08455i
$353$			12.5154i			0.666126i	0.942905	+	0.333063i	$0.108082\pi$
$353$			12.5154i			0.666126i	−0.942905	+	0.333063i	$0.891918\pi$
$354$	21.1547	+	11.5612i	1.12436	+	0.614473i
$355$			15.3803i			0.816302i
$356$	−3.27846	+	2.10360i	−0.173758	+	0.111491i
$357$	18.6394	−	13.6490i	0.986502	−	0.722382i
$358$	−13.5910	−	7.42763i	−0.718308	−	0.392562i
$359$		−	31.0752i		−	1.64009i	−0.572301	−	0.820044i	$-0.693949\pi$
$359$		−	31.0752i		−	1.64009i	0.572301	−	0.820044i	$-0.306051\pi$
$360$	0.0806221	+	1.14464i	0.00424916	+	0.0603278i
$361$	−1.57420			−0.0828526
$362$	−23.3273	−	12.7486i	−1.22606	−	0.670052i
$363$		−	40.5922i		−	2.13054i
$364$	21.0014	+	8.10376i	1.10077	+	0.424752i
$365$		−	8.77164i		−	0.459129i
$366$	−6.09548	+	11.1535i	−0.318616	+	0.583002i
$367$	14.0542			0.733624			0.366812	−	0.930295i	$-0.380449\pi$
$367$	14.0542			0.733624			0.366812	+	0.930295i	$0.380449\pi$
$368$	−18.9039	−	8.66606i	−0.985431	−	0.451750i
$369$			2.33501i			0.121556i
$370$	0.252473	−	0.461974i	0.0131255	−	0.0240169i
$371$	15.9789	+	21.8211i	0.829581	+	1.13290i
$372$	−7.96118	+	5.10823i	−0.412768	+	0.264849i
$373$			19.7598i			1.02312i	0.859247	+	0.511561i	$0.170933\pi$
$373$			19.7598i			1.02312i	−0.859247	+	0.511561i	$0.829067\pi$
$374$	22.1221	−	40.4789i	1.14391	−	2.09311i
$375$			1.61069i			0.0831754i
$376$	0.767688	+	10.8993i	0.0395905	+	0.562089i
$377$		−	1.60302i		−	0.0825600i
$378$	−2.69928	−	20.3466i	−0.138836	−	1.04652i
$379$	−0.483016			−0.0248108			−0.0124054	−	0.999923i	$-0.503949\pi$
$379$	−0.483016			−0.0248108			−0.0124054	+	0.999923i	$0.503949\pi$
$380$	7.63518	−	4.89906i	0.391677	−	0.251316i
$381$	6.02594			0.308718
$382$	0.766505	−	1.40255i	0.0392178	−	0.0717605i
$383$	1.09585			0.0559953			0.0279977	−	0.999608i	$-0.491087\pi$
$383$	1.09585			0.0559953			0.0279977	+	0.999608i	$0.491087\pi$
$384$	6.41129	−	17.0577i	0.327175	−	0.870474i
$385$	−12.8437	+	9.40496i	−0.654573	+	0.479321i
$386$	4.06243	+	2.22016i	0.206772	+	0.113003i
$387$	−2.01433			−0.102394
$388$	−5.29186	+	3.39548i	−0.268654	+	0.172380i
$389$			18.3250i			0.929114i	0.885543	+	0.464557i	$0.153786\pi$
$389$			18.3250i			0.929114i	−0.885543	+	0.464557i	$0.846214\pi$
$390$	−4.64710	+	8.50324i	−0.235315	+	0.430578i
$391$	28.1844			1.42535
$392$	−19.2485	−	4.63643i	−0.972194	−	0.234175i
$393$	28.3117			1.42814
$394$	14.3951	−	26.3401i	0.725214	−	1.32699i
$395$			8.74609i			0.440064i
$396$	−2.63642	−	4.10886i	−0.132485	−	0.206478i
$397$	−0.717950			−0.0360329			−0.0180164	−	0.999838i	$-0.505735\pi$
$397$	−0.717950			−0.0360329			−0.0180164	+	0.999838i	$0.505735\pi$
$398$	−22.2898	−	12.1816i	−1.11729	−	0.610608i
$399$	−15.5954	+	11.4199i	−0.780745	+	0.571712i
$400$	−1.66690	+	3.63613i	−0.0833452	+	0.181806i
$401$	−21.1139			−1.05438			−0.527189	−	0.849748i	$-0.676754\pi$
$401$	−21.1139			−1.05438			−0.527189	+	0.849748i	$0.676754\pi$
$402$	0.854892	−	1.56428i	0.0426381	−	0.0780190i
$403$	12.4916			0.622250
$404$	−17.6069	−	27.4403i	−0.875975	−	1.36521i
$405$	7.61833			0.378558
$406$	0.185423	+	1.39768i	0.00920237	+	0.0693655i
$407$			2.23984i			0.111025i
$408$	1.73526	+	24.6365i	0.0859083	+	1.21969i
$409$		−	1.08609i		−	0.0537038i	−0.999639	−	0.0268519i	$-0.991452\pi$
$409$		−	1.08609i		−	0.0537038i	0.999639	−	0.0268519i	$-0.00854825\pi$
$410$	−3.90349	+	7.14259i	−0.192780	+	0.352748i
$411$			1.23594i			0.0609644i
$412$	−12.8463	−	20.0210i	−0.632892	−	0.986362i
$413$	16.5433	+	22.5920i	0.814044	+	1.11168i
$414$	1.43045	−	2.61743i	0.0703027	−	0.128639i
$415$		−	8.42742i		−	0.413686i
$416$	−19.2909	+	14.3868i	−0.945814	+	0.705371i
$417$	−3.25123			−0.159214
$418$	−18.5093	+	33.8682i	−0.905318	+	1.65655i
$419$			0.208107i			0.0101667i	0.999987	+	0.00508334i	$0.00161808\pi$
$419$			0.208107i			0.0101667i	−0.999987	+	0.00508334i	$0.998382\pi$
$420$	3.06823	−	7.95151i	0.149714	−	0.387994i
$421$		−	9.48511i		−	0.462276i	−0.972921	−	0.231138i	$-0.925755\pi$
$421$		−	9.48511i		−	0.462276i	0.972921	−	0.231138i	$-0.0742449\pi$
$422$	9.22846	+	5.04344i	0.449234	+	0.245511i
$423$	−1.56721			−0.0762003
$424$	−28.8419	+	2.03147i	−1.40069	+	0.0986568i
$425$		−	5.42124i		−	0.262969i
$426$	30.7426	+	16.8011i	1.48948	+	0.814017i
$427$	−11.9113	+	8.72221i	−0.576427	+	0.422097i
$428$	11.3185	+	17.6399i	0.547100	+	0.852656i
$429$		−	41.2273i		−	1.99047i
$430$	−6.16165	−	3.36740i	−0.297141	−	0.162391i
$431$			13.6900i			0.659423i	0.944082	+	0.329711i	$0.106951\pi$
$431$			13.6900i			0.659423i	−0.944082	+	0.329711i	$0.893049\pi$
$432$	19.9460	+	9.14381i	0.959651	+	0.439932i
$433$			6.48406i			0.311604i	0.987788	+	0.155802i	$0.0497962\pi$
$433$			6.48406i			0.311604i	−0.987788	+	0.155802i	$0.950204\pi$
$434$	−10.8914	+	1.44491i	−0.522805	+	0.0693578i
$435$	−0.606935			−0.0291003
$436$	1.13924	−	0.730984i	0.0545596	−	0.0350078i
$437$	−23.5816			−1.12806
$438$	−17.5330	−	9.58196i	−0.837760	−	0.457844i
$439$	−9.04411			−0.431652			−0.215826	−	0.976432i	$-0.569244\pi$
$439$	−9.04411			−0.431652			−0.215826	+	0.976432i	$0.569244\pi$
$440$	−1.19570	−	16.9760i	−0.0570026	−	0.809299i
$441$	0.857361	−	2.70734i	0.0408267	−	0.128921i
$442$	15.6412	−	28.6202i	0.743976	−	1.36132i
$443$	8.66264			0.411574			0.205787	−	0.978597i	$-0.434025\pi$
$443$	8.66264			0.411574			0.205787	+	0.978597i	$0.434025\pi$
$444$	−0.647611	−	1.00930i	−0.0307343	−	0.0478993i
$445$		−	1.94765i		−	0.0923277i
$446$	−29.6149	−	16.1848i	−1.40231	−	0.766373i
$447$	−6.81750			−0.322457
$448$	15.1556	−	14.7752i	0.716035	−	0.698064i
$449$	−26.5808			−1.25443			−0.627213	−	0.778848i	$-0.715804\pi$
$449$	−26.5808			−1.25443			−0.627213	+	0.778848i	$0.715804\pi$
$450$	−0.503458	−	0.275145i	−0.0237332	−	0.0129704i
$451$		−	34.6303i		−	1.63068i
$452$	−9.83443	−	15.3270i	−0.462573	−	0.720919i
$453$	1.00792			0.0473560
$454$	8.22541	−	15.0508i	0.386037	−	0.706369i
$455$	−9.08097	+	6.64968i	−0.425722	+	0.311742i
$456$	−1.45187	−	20.6131i	−0.0679901	−	0.965295i
$457$	33.4034			1.56254			0.781272	−	0.624191i	$-0.214571\pi$
$457$	33.4034			1.56254			0.781272	+	0.624191i	$0.214571\pi$
$458$	−20.3522	−	11.1227i	−0.950998	−	0.519729i
$459$	−29.7382			−1.38806
$460$	8.75123	−	5.61516i	0.408028	−	0.261808i
$461$	9.70385			0.451954			0.225977	−	0.974133i	$-0.427443\pi$
$461$	9.70385			0.451954			0.225977	+	0.974133i	$0.427443\pi$
$462$	4.76878	+	35.9461i	0.221864	+	1.67236i
$463$		−	28.6011i		−	1.32921i	−0.747196	−	0.664604i	$-0.768600\pi$
$463$		−	28.6011i		−	1.32921i	0.747196	−	0.664604i	$-0.231400\pi$
$464$	−1.37016	−	0.628119i	−0.0636080	−	0.0291597i
$465$		−	4.72954i		−	0.219327i
$466$	32.7753	+	17.9120i	1.51829	+	0.829758i
$467$		−	8.61107i		−	0.398473i	−0.979951	−	0.199236i	$-0.936154\pi$
$467$		−	8.61107i		−	0.398473i	0.979951	−	0.199236i	$-0.0638462\pi$
$468$	−1.86405	−	2.90513i	−0.0861659	−	0.134289i
$469$	1.67056	−	1.22329i	0.0771391	−	0.0564863i
$470$	−4.79395	−	2.61994i	−0.221129	−	0.120849i
$471$		−	4.69857i		−	0.216499i
$472$	−29.8608	+	2.10323i	−1.37445	+	0.0968091i
$473$	29.8743			1.37362
$474$	17.4819	+	9.55405i	0.802973	+	0.438832i
$475$			4.53588i			0.208120i
$476$	−10.3270	+	26.7632i	−0.473339	+	1.22669i
$477$		−	4.14717i		−	0.189886i
$478$	−1.14556	+	2.09613i	−0.0523965	+	0.0958749i
$479$	6.75741			0.308754			0.154377	−	0.988012i	$-0.450663\pi$
$479$	6.75741			0.308754			0.154377	+	0.988012i	$0.450663\pi$
$480$	5.44711	+	7.30389i	0.248625	+	0.333375i
$481$			1.58366i			0.0722086i
$482$	−3.56139	+	6.51661i	−0.162217	+	0.296824i
$483$	−17.8750	+	13.0892i	−0.813339	+	0.595580i
$484$	27.2197	+	42.4219i	1.23726	+	1.92827i
$485$		−	3.14377i		−	0.142751i
$486$	−2.83882	+	5.19446i	−0.128771	+	0.235625i
$487$		−	7.72534i		−	0.350069i	−0.984562	−	0.175034i	$-0.943996\pi$
$487$		−	7.72534i		−	0.350069i	0.984562	−	0.175034i	$-0.0560036\pi$
$488$	−1.10890	−	15.7436i	−0.0501974	−	0.712681i
$489$			11.5067i			0.520350i
$490$	7.14852	−	6.84826i	0.322937	−	0.309373i
$491$	−33.1648			−1.49671			−0.748354	−	0.663300i	$-0.769156\pi$
$491$	−33.1648			−1.49671			−0.748354	+	0.663300i	$0.769156\pi$
$492$	10.0127	+	15.6048i	0.451409	+	0.703521i
$493$	2.04282			0.0920039
$494$	−13.0868	+	23.9461i	−0.588802	+	1.07739i
$495$	2.44098			0.109714
$496$	4.89463	−	10.6770i	0.219775	−	0.479410i
$497$	24.0412	+	32.8313i	1.07840	+	1.47269i
$498$	−16.8450	−	9.20594i	−0.754841	−	0.412528i
$499$	−9.13507			−0.408942			−0.204471	−	0.978873i	$-0.565547\pi$
$499$	−9.13507			−0.408942			−0.204471	+	0.978873i	$0.565547\pi$
$500$	−1.08007	−	1.68329i	−0.0483021	−	0.0752788i
$501$			10.0957i			0.451043i
$502$	9.47404	−	17.3355i	0.422847	−	0.773723i
$503$	−13.9338			−0.621277			−0.310639	−	0.950528i	$-0.600543\pi$
$503$	−13.9338			−0.621277			−0.310639	+	0.950528i	$0.600543\pi$
$504$	1.96131	+	2.31736i	0.0873635	+	0.103224i
$505$	16.3016			0.725413
$506$	−21.2148	+	38.8187i	−0.943113	+	1.72570i
$507$		−	8.21040i		−	0.364637i
$508$	−6.29756	+	4.04078i	−0.279409	+	0.179281i
$509$	11.4366			0.506918			0.253459	−	0.967346i	$-0.418432\pi$
$509$	11.4366			0.506918			0.253459	+	0.967346i	$0.418432\pi$
$510$	−10.8361	−	5.92205i	−0.479832	−	0.262233i
$511$	−13.7111	−	18.7242i	−0.606544	−	0.828311i
$512$	4.73805	+	22.1258i	0.209394	+	0.977831i
$513$	24.8816			1.09855
$514$	−14.7129	+	26.9216i	−0.648958	+	1.18746i
$515$	11.8940			0.524111
$516$	−13.4617	+	8.63762i	−0.592619	+	0.380250i
$517$	23.2431			1.02223
$518$	−0.183182	−	1.38079i	−0.00804858	−	0.0606685i
$519$			14.6792i			0.644347i
$520$	−0.845405	−	12.0027i	−0.0370735	−	0.526353i
$521$			13.5526i			0.593751i	0.954916	+	0.296875i	$0.0959446\pi$
$521$			13.5526i			0.593751i	−0.954916	+	0.296875i	$0.904055\pi$
$522$	0.103679	−	0.189712i	0.00453792	−	0.00830347i
$523$			16.3634i			0.715522i	0.933813	+	0.357761i	$0.116460\pi$
$523$			16.3634i			0.715522i	−0.933813	+	0.357761i	$0.883540\pi$
$524$	−29.5879	+	18.9848i	−1.29255	+	0.829357i
$525$	2.51769	+	3.43822i	0.109881	+	0.150056i
$526$	3.99443	−	7.30898i	0.174165	−	0.318687i
$527$			15.9187i			0.693429i
$528$	−35.2383	−	16.1542i	−1.53355	−	0.703023i
$529$	−4.02852			−0.175153
$530$	6.93293	−	12.6858i	0.301147	−	0.551037i
$531$		−	4.29368i		−	0.186330i
$532$	8.64051	−	22.3924i	0.374614	−	0.970833i
$533$		−	24.4850i		−	1.06056i
$534$	−3.89303	−	2.12758i	−0.168468	−	0.0920693i
$535$	−10.4794			−0.453065
$536$	0.155523	+	2.20805i	0.00671756	+	0.0953731i
$537$		−	17.6400i		−	0.761221i
$538$	16.5640	+	9.05236i	0.714123	+	0.390275i
$539$	−12.7154	+	40.1523i	−0.547692	+	1.72948i
$540$	−9.23367	+	5.92471i	−0.397354	+	0.254959i
$541$		−	23.4050i		−	1.00626i	−0.864211	−	0.503129i	$-0.832182\pi$
$541$		−	23.4050i		−	1.00626i	0.864211	−	0.503129i	$-0.167818\pi$
$542$	30.7649	+	16.8133i	1.32146	+	0.722193i
$543$		−	30.2768i		−	1.29930i
$544$	−18.3339	−	24.5834i	−0.786058	−	1.05400i
$545$			0.676794i			0.0289907i
$546$	3.37172	+	25.4153i	0.144296	+	1.08767i
$547$	21.2928			0.910416			0.455208	−	0.890385i	$-0.349565\pi$
$547$	21.2928			0.910416			0.455208	+	0.890385i	$0.349565\pi$
$548$	−0.828778	−	1.29165i	−0.0354036	−	0.0551765i
$549$	2.26377			0.0966155
$550$	7.46673	+	4.08064i	0.318382	+	0.173999i
$551$	−1.70920			−0.0728144
$552$	−1.66409	−	23.6261i	−0.0708285	−	1.00559i
$553$	13.6712	+	18.6697i	0.581358	+	0.793917i
$554$	−1.41790	+	2.59447i	−0.0602409	+	0.110228i
$555$	0.599602			0.0254517
$556$	3.39778	−	2.18016i	0.144098	−	0.0924594i
$557$		−	2.06871i		−	0.0876541i	−0.999039	−	0.0438270i	$-0.986045\pi$
$557$		−	2.06871i		−	0.0876541i	0.999039	−	0.0438270i	$-0.0139551\pi$
$558$	1.47833	+	0.807922i	0.0625828	+	0.0342021i
$559$	21.1223			0.893378
$560$	2.12547	+	10.3674i	0.0898174	+	0.438101i
$561$	52.5381			2.21816
$562$	5.07785	+	2.77509i	0.214196	+	0.117060i
$563$		−	25.5312i		−	1.07601i	−0.842941	−	0.538006i	$-0.819178\pi$
$563$		−	25.5312i		−	1.07601i	0.842941	−	0.538006i	$-0.180822\pi$
$564$	−10.4736	+	6.72033i	−0.441019	+	0.282977i
$565$	9.10537			0.383066
$566$	−4.01698	+	7.35025i	−0.168846	+	0.308954i
$567$	16.2623	−	11.9084i	0.682954	−	0.500104i
$568$	−43.3946	+	3.05648i	−1.82080	+	0.128247i
$569$	26.3859			1.10616			0.553078	−	0.833130i	$-0.313453\pi$
$569$	26.3859			1.10616			0.553078	+	0.833130i	$0.313453\pi$
$570$	9.06645	+	4.95490i	0.379752	+	0.207538i
$571$	17.6202			0.737384			0.368692	−	0.929552i	$-0.379806\pi$
$571$	17.6202			0.737384			0.368692	+	0.929552i	$0.379806\pi$
$572$	27.6455	+	43.0856i	1.15592	+	1.80150i
$573$	1.82038			0.0760476
$574$	2.83219	+	21.3484i	0.118213	+	0.891067i
$575$			5.19890i			0.216809i
$576$	−3.21351	+	0.454941i	−0.133896	+	0.0189559i
$577$		−	29.5306i		−	1.22938i	−0.788770	−	0.614688i	$-0.789282\pi$
$577$		−	29.5306i		−	1.22938i	0.788770	−	0.614688i	$-0.210718\pi$
$578$	15.3755	+	8.40286i	0.639537	+	0.349513i
$579$			5.27268i			0.219125i
$580$	0.634292	−	0.406989i	0.0263375	−	0.0168993i
$581$	−13.1731	−	17.9895i	−0.546510	−	0.746328i
$582$	−6.28386	−	3.43419i	−0.260474	−	0.142352i
$583$			61.5062i			2.54733i
$584$	24.7486	−	1.74316i	1.02411	−	0.0721324i
$585$	1.72587			0.0713558
$586$	11.7188	+	6.40442i	0.484098	+	0.264564i
$587$		−	5.32153i		−	0.219643i	−0.993951	−	0.109822i	$-0.964972\pi$
$587$		−	5.32153i		−	0.219643i	0.993951	−	0.109822i	$-0.0350279\pi$
$588$	−5.87960	−	21.7696i	−0.242471	−	0.897762i
$589$		−	13.3190i		−	0.548798i
$590$	7.17784	−	13.1340i	0.295507	−	0.540717i
$591$	34.1871			1.40627
$592$	1.35360	+	0.620531i	0.0556328	+	0.0255037i
$593$		−	45.6864i		−	1.87611i	−0.346481	−	0.938057i	$-0.612623\pi$
$593$		−	45.6864i		−	1.87611i	0.346481	−	0.938057i	$-0.387377\pi$
$594$	22.3843	−	40.9587i	0.918440	−	1.68056i
$595$	−8.47403	−	11.5724i	−0.347401	−	0.474420i
$596$	7.12480	−	4.57158i	0.291843	−	0.187259i
$597$		−	28.9302i		−	1.18404i
$598$	−14.9997	+	27.4464i	−0.613384	+	1.12237i
$599$		−	22.5049i		−	0.919525i	−0.888042	−	0.459762i	$-0.847935\pi$
$599$		−	22.5049i		−	0.919525i	0.888042	−	0.459762i	$-0.152065\pi$
$600$	−4.54445	+	0.320086i	−0.185526	+	0.0130675i
$601$		−	4.49699i		−	0.183436i	−0.995785	−	0.0917181i	$-0.970764\pi$
$601$		−	4.49699i		−	0.183436i	0.995785	−	0.0917181i	$-0.0292359\pi$
$602$	−18.4165	+	2.44323i	−0.750601	+	0.0995784i
$603$	−0.317494			−0.0129294
$604$	−1.05335	+	0.675873i	−0.0428601	+	0.0275009i
$605$	−25.2018			−1.02460
$606$	17.8076	−	32.5842i	0.723383	−	1.32364i
$607$	−10.8910			−0.442051			−0.221025	−	0.975268i	$-0.570940\pi$
$607$	−10.8910			−0.442051			−0.221025	+	0.975268i	$0.570940\pi$
$608$	15.3397	+	20.5686i	0.622107	+	0.834167i
$609$	−1.29558	+	0.948711i	−0.0524997	+	0.0384437i
$610$	6.92468	+	3.78440i	0.280372	+	0.153226i
$611$	16.4338			0.664839
$612$	3.70215	−	2.37546i	0.149651	−	0.0960223i
$613$		−	30.5045i		−	1.23206i	−0.787721	−	0.616032i	$-0.788739\pi$
$613$		−	30.5045i		−	1.23206i	0.787721	−	0.616032i	$-0.211261\pi$
$614$	−16.3587	+	29.9330i	−0.660182	+	1.20800i
$615$	−9.27046			−0.373821
$616$	−29.0879	−	34.3685i	−1.17198	−	1.38475i
$617$	−39.6859			−1.59769			−0.798847	−	0.601534i	$-0.794557\pi$
$617$	−39.6859			−1.59769			−0.798847	+	0.601534i	$0.794557\pi$
$618$	12.9927	−	23.7740i	0.522644	−	0.956332i
$619$		−	13.7231i		−	0.551579i	−0.961218	−	0.275789i	$-0.911061\pi$
$619$		−	13.7231i		−	0.551579i	0.961218	−	0.275789i	$-0.0889392\pi$
$620$	3.17147	+	4.94273i	0.127369	+	0.198505i
$621$	28.5185			1.14441
$622$	20.5937	+	11.2547i	0.825734	+	0.451271i
$623$	−3.04441	−	4.15753i	−0.121972	−	0.166568i
$624$	−24.9149	−	11.4217i	−0.997393	−	0.457233i
$625$	1.00000			0.0400000
$626$	7.72283	−	14.1312i	0.308666	−	0.564796i
$627$	−43.9579			−1.75551
$628$	3.15070	+	4.91036i	0.125726	+	0.195945i
$629$	−2.01814			−0.0804684
$630$	−1.50478	+	0.199632i	−0.0599520	+	0.00795352i
$631$			36.7721i			1.46387i	0.681373	+	0.731936i	$0.261383\pi$
$631$			36.7721i			1.46387i	−0.681373	+	0.731936i	$0.738617\pi$
$632$	−24.6766	+	1.73808i	−0.981580	+	0.0691372i
$633$			11.9777i			0.476072i
$634$	18.1138	−	33.1446i	0.719392	−	1.31634i
$635$		−	3.74123i		−	0.148466i
$636$	−17.7834	−	27.7155i	−0.705159	−	1.09899i
$637$	−8.99031	+	28.3893i	−0.356209	+	1.12482i
$638$	−1.53766	+	2.81360i	−0.0608764	+	0.111391i
$639$		−	6.23969i		−	0.246838i
$640$	−10.5904	−	3.98047i	−0.418621	−	0.157342i
$641$	−40.2483			−1.58971			−0.794855	−	0.606799i	$-0.792453\pi$
$641$	−40.2483			−1.58971			−0.794855	+	0.606799i	$0.792453\pi$
$642$	−11.4475	+	20.9466i	−0.451797	+	0.826696i
$643$			12.3361i			0.486487i	0.969965	+	0.243243i	$0.0782114\pi$
$643$			12.3361i			0.486487i	−0.969965	+	0.243243i	$0.921789\pi$
$644$	9.90351	−	25.6655i	0.390253	−	1.01136i
$645$		−	7.99729i		−	0.314893i
$646$	−30.5158	−	16.6772i	−1.20063	−	0.656155i
$647$	47.9622			1.88559			0.942794	−	0.333376i	$-0.108188\pi$
$647$	47.9622			1.88559			0.942794	+	0.333376i	$0.108188\pi$
$648$	1.51397	+	21.4946i	0.0594742	+	0.844389i
$649$			63.6790i			2.49962i
$650$	5.27927	+	2.88517i	0.207070	+	0.113166i
$651$	−7.39284	−	10.0958i	−0.289748	−	0.395687i
$652$	−7.71598	−	12.0253i	−0.302181	−	0.470949i
$653$			36.7504i			1.43815i	0.694930	+	0.719077i	$0.255435\pi$
$653$			36.7504i			1.43815i	−0.694930	+	0.719077i	$0.744565\pi$
$654$	1.35280	+	0.739316i	0.0528985	+	0.0289095i
$655$		−	17.5774i		−	0.686808i
$656$	−20.9281	−	9.59404i	−0.817105	−	0.374584i
$657$			3.55860i			0.138834i
$658$	−14.3286	+	1.90090i	−0.558587	+	0.0741049i
$659$	15.4039			0.600050			0.300025	−	0.953931i	$-0.403005\pi$
$659$	15.4039			0.600050			0.300025	+	0.953931i	$0.403005\pi$
$660$	16.3130	−	10.4671i	0.634983	−	0.407432i
$661$	6.20639			0.241400			0.120700	−	0.992689i	$-0.461486\pi$
$661$	6.20639			0.241400			0.120700	+	0.992689i	$0.461486\pi$
$662$	4.03771	+	2.20665i	0.156930	+	0.0857638i
$663$	37.1465			1.44265
$664$	23.7774	−	1.67475i	0.922743	−	0.0649930i
$665$	7.09012	+	9.68244i	0.274943	+	0.375469i
$666$	−0.102427	+	0.187420i	−0.00396896	+	0.00726238i
$667$	−1.95904			−0.0758542
$668$	−6.76983	−	10.5508i	−0.261932	−	0.408222i
$669$		−	38.4375i		−	1.48608i
$670$	−0.971187	−	0.530763i	−0.0375202	−	0.0205052i
$671$	−33.5738			−1.29610
$672$	23.0444	+	7.07665i	0.888958	+	0.272988i
$673$	−46.2742			−1.78374			−0.891870	−	0.452291i	$-0.850607\pi$
$673$	−46.2742			−1.78374			−0.891870	+	0.452291i	$0.850607\pi$
$674$	14.9113	+	8.14917i	0.574362	+	0.313894i
$675$		−	5.48550i		−	0.211137i
$676$	5.50560	+	8.58048i	0.211754	+	0.330019i
$677$	0.112071			0.00430726			0.00215363	−	0.999998i	$-0.499314\pi$
$677$	0.112071			0.00430726			0.00215363	+	0.999998i	$0.499314\pi$
$678$	9.94652	−	18.2001i	0.381994	−	0.698970i
$679$	−4.91408	−	6.71079i	−0.188585	−	0.257537i
$680$	15.2957	−	1.07734i	0.586562	−	0.0413143i
$681$	19.5346			0.748569
$682$	−21.9250	−	11.9822i	−0.839551	−	0.458822i
$683$	0.561153			0.0214719			0.0107360	−	0.999942i	$-0.496583\pi$
$683$	0.561153			0.0214719			0.0107360	+	0.999942i	$0.496583\pi$
$684$	−3.09754	+	1.98752i	−0.118438	+	0.0759946i
$685$	0.767338			0.0293185
$686$	4.55485	−	25.7925i	0.173905	−	0.984762i
$687$		−	26.4154i		−	1.00781i
$688$	8.27643	−	18.0539i	0.315536	−	0.688299i
$689$			43.4873i			1.65673i
$690$	10.3917	+	5.67917i	0.395606	+	0.216202i
$691$		−	39.1762i		−	1.49033i	−0.666879	−	0.745166i	$-0.732370\pi$
$691$		−	39.1762i		−	1.49033i	0.666879	−	0.745166i	$-0.267630\pi$
$692$	−9.84337	−	15.3409i	−0.374189	−	0.583173i
$693$	5.21059	−	3.81553i	0.197934	−	0.144940i
$694$	19.3271	+	10.5624i	0.733645	+	0.400944i
$695$			2.01854i			0.0765676i
$696$	−0.120614	−	1.71243i	−0.00457187	−	0.0649094i
$697$	31.2025			1.18188
$698$	43.1495	+	23.5816i	1.63323	+	0.892577i
$699$			42.5395i			1.60899i
$700$	−4.93673	−	1.90492i	−0.186591	−	0.0719994i
$701$		−	49.6478i		−	1.87517i	−0.347753	−	0.937586i	$-0.613055\pi$
$701$		−	49.6478i		−	1.87517i	0.347753	−	0.937586i	$-0.386945\pi$
$702$	15.8266	−	28.9594i	0.597337	−	1.09300i
$703$	1.68855			0.0636849
$704$	47.6591	−	6.74717i	1.79622	−	0.254294i
$705$		−	6.22213i		−	0.234339i
$706$	8.48803	−	15.5313i	0.319451	−	0.584530i
$707$	34.7980	−	25.4814i	1.30871	−	0.958326i
$708$	−18.4117	−	28.6946i	−0.691953	−	1.07841i
$709$			13.0064i			0.488465i	0.969717	+	0.244233i	$0.0785360\pi$
$709$			13.0064i			0.488465i	−0.969717	+	0.244233i	$0.921464\pi$
$710$	10.4310	−	19.0867i	0.391470	−	0.716310i
$711$		−	3.54823i		−	0.133069i
$712$	5.49518	−	0.387051i	0.205941	−	0.0145053i
$713$		−	15.2658i		−	0.571709i
$714$	−32.3880	+	4.29675i	−1.21209	+	0.160802i
$715$	−25.5961			−0.957240
$716$	11.8287	+	18.4351i	0.442061	+	0.688952i
$717$	−2.72060			−0.101603
$718$	−21.0755	+	38.5638i	−0.786529	+	1.43919i
$719$	−12.4976			−0.466081			−0.233041	−	0.972467i	$-0.574868\pi$
$719$	−12.4976			−0.466081			−0.233041	+	0.972467i	$0.574868\pi$
$720$	0.676253	−	1.47515i	0.0252024	−	0.0549757i
$721$	25.3893	−	18.5917i	0.945546	−	0.692391i
$722$	1.95355	+	1.06763i	0.0727037	+	0.0397332i
$723$	−8.45800			−0.314556
$724$	20.3026	+	31.6415i	0.754539	+	1.17595i
$725$			0.376818i			0.0139947i
$726$	−27.5299	+	50.3741i	−1.02173	+	1.86956i
$727$	−49.8167			−1.84760			−0.923800	−	0.382875i	$-0.874934\pi$
$727$	−49.8167			−1.84760			−0.923800	+	0.382875i	$0.874934\pi$
$728$	−20.5663	−	24.2999i	−0.762237	−	0.900615i
$729$	−29.5969			−1.09618
$730$	−5.94899	+	10.8854i	−0.220182	+	0.402888i
$731$			26.9172i			0.995570i
$732$	15.1288	−	9.70726i	0.559175	−	0.358791i
$733$	48.8875			1.80570			0.902850	−	0.429955i	$-0.141471\pi$
$733$	48.8875			1.80570			0.902850	+	0.429955i	$0.141471\pi$
$734$	−17.4410	−	9.53168i	−0.643760	−	0.351821i
$735$	10.7487	+	3.40390i	0.396472	+	0.125555i
$736$	17.5819	+	23.5752i	0.648079	+	0.868992i
$737$	4.70872			0.173448
$738$	1.58362	−	2.89770i	0.0582940	−	0.106666i
$739$	−39.3743			−1.44841			−0.724204	−	0.689585i	$-0.757793\pi$
$739$	−39.3743			−1.44841			−0.724204	+	0.689585i	$0.757793\pi$
$740$	−0.626629	+	0.402072i	−0.0230353	+	0.0147805i
$741$	−31.0800			−1.14175
$742$	−5.03020	−	37.9166i	−0.184664	−	1.39196i
$743$			35.6179i			1.30669i	0.757059	+	0.653346i	$0.226635\pi$
$743$			35.6179i			1.30669i	−0.757059	+	0.653346i	$0.773365\pi$
$744$	13.3441	−	0.939887i	0.489219	−	0.0344579i
$745$			4.23267i			0.155073i
$746$	13.4012	−	24.5215i	0.490654	−	0.897797i
$747$			3.41895i			0.125093i
$748$	−54.9062	+	35.2302i	−2.00757	+	1.28814i
$749$	−22.3697	+	16.3806i	−0.817373	+	0.598534i
$750$	1.09238	−	1.99883i	0.0398880	−	0.0729869i
$751$		−	13.2839i		−	0.484738i	−0.970184	−	0.242369i	$-0.922076\pi$
$751$		−	13.2839i		−	0.484738i	0.970184	−	0.242369i	$-0.0779245\pi$
$752$	6.43931	−	14.0465i	0.234817	−	0.512223i
$753$	22.5000			0.819946
$754$	−1.08718	+	1.98932i	−0.0395929	+	0.0724469i
$755$		−	0.625768i		−	0.0227740i
$756$	−10.4495	+	27.0804i	−0.380043	+	0.984905i
$757$			20.0483i			0.728666i	0.931269	+	0.364333i	$0.118703\pi$
$757$			20.0483i			0.728666i	−0.931269	+	0.364333i	$0.881297\pi$
$758$	0.599413	+	0.327585i	0.0217717	+	0.0118984i
$759$	−50.3833			−1.82880
$760$	−12.7977	+	0.901400i	−0.464221	+	0.0326972i
$761$		−	28.5860i		−	1.03624i	−0.855307	−	0.518121i	$-0.826632\pi$
$761$		−	28.5860i		−	1.03624i	0.855307	−	0.518121i	$-0.173368\pi$
$762$	−7.47808	−	4.08684i	−0.270902	−	0.148051i
$763$	1.05791	+	1.44471i	0.0382989	+	0.0523019i
$764$	−1.90244	+	1.22068i	−0.0688277	+	0.0441628i
$765$			2.19936i			0.0795181i
$766$	−1.35993	−	0.743214i	−0.0491363	−	0.0268534i
$767$			45.0236i			1.62571i
$768$	−19.5250	+	16.8202i	−0.704547	+	0.606945i
$769$			26.3204i			0.949137i	0.880219	+	0.474569i	$0.157396\pi$
$769$			26.3204i			0.949137i	−0.880219	+	0.474569i	$0.842604\pi$
$770$	22.3172	−	2.96072i	0.804258	−	0.106697i
$771$	−34.9418			−1.25840
$772$	−3.53568	−	5.51035i	−0.127252	−	0.198322i
$773$	−0.586223			−0.0210850			−0.0105425	−	0.999944i	$-0.503356\pi$
$773$	−0.586223			−0.0210850			−0.0105425	+	0.999944i	$0.503356\pi$
$774$	2.49974	+	1.36613i	0.0898514	+	0.0491046i
$775$	−2.93636			−0.105477
$776$	8.86994	−	0.624750i	0.318412	−	0.0224272i
$777$	1.27993	−	0.937249i	0.0459173	−	0.0336236i
$778$	12.4282	−	22.7410i	0.445571	−	0.815303i
$779$	−26.1067			−0.935370
$780$	11.5339	−	7.40066i	0.412981	−	0.264986i
$781$			92.5401i			3.31135i
$782$	−34.9764	−	19.1149i	−1.25075	−	0.683548i
$783$	2.06703			0.0738698
$784$	20.7425	+	18.8082i	0.740804	+	0.671721i
$785$	−2.91713			−0.104117
$786$	−35.1343	−	19.2012i	−1.25320	−	0.684885i
$787$		−	12.7886i		−	0.455864i	−0.973677	−	0.227932i	$-0.926804\pi$
$787$		−	12.7886i		−	0.455864i	0.973677	−	0.227932i	$-0.0731964\pi$
$788$	−35.7281	+	22.9247i	−1.27276	+	0.816657i
$789$	9.48642			0.337725
$790$	5.93167	−	10.8537i	0.211039	−	0.386159i
$791$	19.4366	−	14.2328i	0.691087	−	0.506059i
$792$	0.485087	+	6.88706i	0.0172368	+	0.244721i
$793$	−23.7380			−0.842960
$794$	0.890962	+	0.486919i	0.0316191	+	0.0172801i
$795$	16.4651			0.583957
$796$	19.3996	+	30.2342i	0.687600	+	1.07162i
$797$	27.5991			0.977609			0.488805	−	0.872393i	$-0.337433\pi$
$797$	27.5991			0.977609			0.488805	+	0.872393i	$0.337433\pi$
$798$	27.0986	−	3.59504i	0.959282	−	0.127263i
$799$			20.9424i			0.740890i
$800$	4.53465	−	3.38186i	0.160324	−	0.119567i
$801$			0.790151i			0.0279186i
$802$	26.2020	+	14.3196i	0.925223	+	0.505643i
$803$		−	52.7771i		−	1.86247i
$804$	−2.12181	+	1.36144i	−0.0748304	+	0.0480144i
$805$	8.12649	+	11.0977i	0.286421	+	0.391144i
$806$	−15.5018	−	8.47189i	−0.546028	−	0.298410i
$807$			21.4986i			0.756786i
$808$	3.23957	+	45.9940i	0.113968	+	1.61806i
$809$	−19.2283			−0.676030			−0.338015	−	0.941141i	$-0.609755\pi$
$809$	−19.2283			−0.676030			−0.338015	+	0.941141i	$0.609755\pi$
$810$	−9.45421	−	5.16681i	−0.332187	−	0.181543i
$811$		−	7.93942i		−	0.278791i	−0.990237	−	0.139395i	$-0.955484\pi$
$811$		−	7.93942i		−	0.278791i	0.990237	−	0.139395i	$-0.0445159\pi$
$812$	0.717809	−	1.86025i	0.0251902	−	0.0652818i
$813$			39.9301i			1.40041i
$814$	1.51908	−	2.77960i	0.0532437	−	0.0974250i
$815$	7.14397			0.250242
$816$	14.5553	−	31.7503i	0.509536	−	1.11148i
$817$		−	22.5213i		−	0.787921i
$818$	−0.736596	+	1.34782i	−0.0257545	+	0.0471254i
$819$	3.68409	−	2.69773i	0.128733	−	0.0942664i
$820$	9.68833	−	6.21644i	0.338331	−	0.217088i
$821$			26.3775i			0.920582i	0.887768	+	0.460291i	$0.152255\pi$
$821$			26.3775i			0.920582i	−0.887768	+	0.460291i	$0.847745\pi$
$822$	0.838224	−	1.53378i	0.0292364	−	0.0534967i
$823$		−	21.7419i		−	0.757875i	−0.925422	−	0.378938i	$-0.876289\pi$
$823$		−	21.7419i		−	0.757875i	0.925422	−	0.378938i	$-0.123711\pi$
$824$	2.36365	+	33.5581i	0.0823416	+	1.16905i
$825$			9.69116i			0.337403i
$826$	−5.20790	−	39.2560i	−0.181206	−	1.36589i
$827$	57.4711			1.99846			0.999232	−	0.0391762i	$-0.0124734\pi$
$827$	57.4711			1.99846			0.999232	+	0.0391762i	$0.0124734\pi$
$828$	−3.55032	+	2.27804i	−0.123382	+	0.0791672i
$829$	−7.16668			−0.248909			−0.124455	−	0.992225i	$-0.539718\pi$
$829$	−7.16668			−0.248909			−0.124455	+	0.992225i	$0.539718\pi$
$830$	−5.71554	+	10.4583i	−0.198389	+	0.363012i
$831$	−3.36740			−0.116814
$832$	33.6969	−	4.77051i	1.16823	−	0.165388i
$833$	−36.1779	−	11.4568i	−1.25349	−	0.396955i
$834$	4.03472	+	2.20501i	0.139711	+	0.0763533i
$835$	6.26796			0.216912
$836$	45.9393	−	29.4766i	1.58884	−	1.01947i
$837$			16.1074i			0.556753i
$838$	0.141140	−	0.258257i	0.00487559	−	0.00892133i
$839$	−12.0764			−0.416922			−0.208461	−	0.978031i	$-0.566845\pi$
$839$	−12.0764			−0.416922			−0.208461	+	0.978031i	$0.566845\pi$
$840$	−9.20040	+	7.78677i	−0.317444	+	0.268669i
$841$	28.8580			0.995104
$842$	−6.43288	+	11.7708i	−0.221692	+	0.405650i
$843$			6.59061i			0.226993i
$844$	−8.03184	−	12.5176i	−0.276467	−	0.430874i
$845$	−5.09746			−0.175358
$846$	1.94488	+	1.06289i	0.0668662	+	0.0365430i
$847$	−53.7966	+	39.3934i	−1.84847	+	1.35357i
$848$	37.1700	+	17.0398i	1.27642	+	0.585149i
$849$	−9.53998			−0.327411
$850$	−3.67672	+	6.72765i	−0.126111	+	0.230757i
$851$	1.93537			0.0663436
$852$	−26.7563	−	41.6998i	−0.916657	−	1.42861i
$853$	−40.3302			−1.38088			−0.690440	−	0.723390i	$-0.742583\pi$
$853$	−40.3302			−1.38088			−0.690440	+	0.723390i	$0.742583\pi$
$854$	20.6971	−	2.74578i	0.708241	−	0.0939588i
$855$		−	1.84018i		−	0.0629327i
$856$	−2.08254	−	29.5671i	−0.0711798	−	1.01058i
$857$		−	13.5485i		−	0.462810i	−0.972858	−	0.231405i	$-0.925668\pi$
$857$		−	13.5485i		−	0.462810i	0.972858	−	0.231405i	$-0.0743322\pi$
$858$	−27.9607	+	51.1623i	−0.954561	+	1.74665i
$859$		−	24.4181i		−	0.833136i	−0.909105	−	0.416568i	$-0.863233\pi$
$859$		−	24.4181i		−	0.833136i	0.909105	−	0.416568i	$-0.136767\pi$
$860$	5.36270	+	8.35776i	0.182866	+	0.284997i
$861$	−19.7890	+	14.4908i	−0.674409	+	0.493846i
$862$	9.28465	−	16.9890i	0.316236	−	0.578648i
$863$		−	33.4276i		−	1.13789i	−0.822376	−	0.568945i	$-0.807352\pi$
$863$		−	33.4276i		−	1.13789i	0.822376	−	0.568945i	$-0.192648\pi$
$864$	−18.5512	−	24.8748i	−0.631124	−	0.846258i
$865$	9.11366			0.309874
$866$	4.39754	−	8.04659i	0.149434	−	0.273434i
$867$			19.9561i			0.677743i
$868$	14.4960	+	5.59354i	0.492026	+	0.189857i
$869$			52.6234i			1.78513i
$870$	0.753195	+	0.411628i	0.0255357	+	0.0139555i
$871$	3.32925			0.112807
$872$	−1.90953	+	0.134497i	−0.0646649	+	0.00455464i
$873$			1.27541i			0.0431660i
$874$	29.2643	+	15.9932i	0.989879	+	0.540978i
$875$	2.13463	−	1.56312i	0.0721638	−	0.0528430i
$876$	15.2596	+	23.7821i	0.515573	+	0.803521i
$877$		−	33.1528i		−	1.11949i	−0.828664	−	0.559746i	$-0.810899\pi$
$877$		−	33.1528i		−	1.11949i	0.828664	−	0.559746i	$-0.189101\pi$
$878$	11.2236	+	6.13378i	0.378777	+	0.207005i
$879$			15.2100i			0.513019i
$880$	−10.0294	+	21.8778i	−0.338092	+	0.737502i
$881$			52.3710i			1.76442i	0.470853	+	0.882212i	$0.343946\pi$
$881$			52.3710i			1.76442i	−0.470853	+	0.882212i	$0.656054\pi$
$882$	−2.90011	+	2.77829i	−0.0976518	+	0.0935500i
$883$	3.17165			0.106735			0.0533673	−	0.998575i	$-0.483005\pi$
$883$	3.17165			0.106735			0.0533673	+	0.998575i	$0.483005\pi$
$884$	−38.8209	+	24.9091i	−1.30569	+	0.837784i
$885$	17.0468			0.573020
$886$	−10.7502	−	5.87507i	−0.361159	−	0.197377i
$887$	36.3723			1.22126			0.610632	−	0.791915i	$-0.290916\pi$
$887$	36.3723			1.22126			0.610632	+	0.791915i	$0.290916\pi$
$888$	0.119157	+	1.69174i	0.00399864	+	0.0567711i
$889$	−5.84798	−	7.98615i	−0.196135	−	0.267847i
$890$	−1.32091	+	2.41700i	−0.0442771	+	0.0810181i
$891$	45.8379			1.53563
$892$	25.7749	+	40.1701i	0.863006	+	1.34499i
$893$		−	17.5223i		−	0.586360i
$894$	8.46039	+	4.62368i	0.282958	+	0.154639i
$895$	−10.9518			−0.366080
$896$	−28.8285	+	8.05715i	−0.963093	+	0.269170i
$897$	−35.6230			−1.18942
$898$	32.9863	+	18.0273i	1.10077	+	0.601579i
$899$		−	1.10647i		−	0.0369029i
$900$	0.438177	+	0.682898i	0.0146059	+	0.0227633i
$901$	−55.4182			−1.84625
$902$	−23.4865	+	42.9755i	−0.782016	+	1.43093i
$903$	−12.5007	−	17.0713i	−0.415998	−	0.568097i
$904$	1.80948	+	25.6902i	0.0601824	+	0.854445i
$905$	−18.7975			−0.624850
$906$	−1.25080	−	0.683576i	−0.0415552	−	0.0227103i
$907$	−13.5038			−0.448388			−0.224194	−	0.974545i	$-0.571975\pi$
$907$	−13.5038			−0.448388			−0.224194	+	0.974545i	$0.571975\pi$
$908$	−20.4152	+	13.0992i	−0.677501	+	0.434713i
$909$	−6.61347			−0.219355
$910$	15.7792	−	2.09334i	0.523075	−	0.0693936i
$911$			6.93039i			0.229614i	0.993388	+	0.114807i	$0.0366250\pi$
$911$			6.93039i			0.229614i	−0.993388	+	0.114807i	$0.963375\pi$
$912$	−12.1782	+	26.5651i	−0.403260	+	0.879658i
$913$		−	50.7060i		−	1.67813i
$914$	−41.4529	−	22.6544i	−1.37114	−	0.749342i
$915$			8.98763i			0.297122i
$916$	17.7133	+	27.6061i	0.585262	+	0.912131i
$917$	−27.4756	−	37.5214i	−0.907325	−	1.23907i
$918$	36.9045	+	20.1687i	1.21803	+	0.665665i
$919$			18.9826i			0.626178i	0.949724	+	0.313089i	$0.101364\pi$
$919$			18.9826i			0.626178i	−0.949724	+	0.313089i	$0.898636\pi$
$920$	−14.6684	+	1.03316i	−0.483601	+	0.0340622i
$921$	−38.8504			−1.28017
$922$	−12.0423	−	6.58123i	−0.396592	−	0.216741i
$923$			65.4295i			2.15364i
$924$	18.4609	−	47.8426i	0.607320	−	1.57391i
$925$		−	0.372265i		−	0.0122400i
$926$	−19.3975	+	35.4935i	−0.637442	+	1.16639i
$927$	−4.82531			−0.158484
$928$	1.27434	+	1.70874i	0.0418324	+	0.0560920i
$929$		−	55.6476i		−	1.82574i	−0.408250	−	0.912870i	$-0.633861\pi$
$929$		−	55.6476i		−	1.82574i	0.408250	−	0.912870i	$-0.366139\pi$
$930$	−3.20761	+	5.86928i	−0.105182	+	0.192461i
$931$	30.2696	+	9.58577i	0.992046	+	0.314161i
$932$	−28.5255	−	44.4569i	−0.934383	−	1.45624i
$933$			26.7289i			0.875064i
$934$	−5.84009	+	10.6862i	−0.191094	+	0.349662i
$935$		−	32.6185i		−	1.06674i
$936$	0.342975	+	4.86942i	0.0112105	+	0.159162i
$937$			30.8690i			1.00845i	0.863574	+	0.504223i	$0.168221\pi$
$937$			30.8690i			1.00845i	−0.863574	+	0.504223i	$0.831779\pi$
$938$	−2.90277	+	0.385096i	−0.0947789	+	0.0125738i
$939$	18.3410			0.598537
$940$	4.17234	+	6.50259i	0.136087	+	0.212091i
$941$	−14.1430			−0.461048			−0.230524	−	0.973067i	$-0.574044\pi$
$941$	−14.1430			−0.461048			−0.230524	+	0.973067i	$0.574044\pi$
$942$	−3.18661	+	5.83084i	−0.103825	+	0.189979i
$943$	−29.9228			−0.974420
$944$	38.4831	+	17.6418i	1.25252	+	0.574190i
$945$	−8.57449	−	11.7095i	−0.278928	−	0.380911i
$946$	−37.0734	−	20.2610i	−1.20536	−	0.658741i
$947$	10.5002			0.341212			0.170606	−	0.985339i	$-0.445428\pi$
$947$	10.5002			0.341212			0.170606	+	0.985339i	$0.445428\pi$
$948$	−15.2151	−	23.7128i	−0.494165	−	0.770156i
$949$		−	37.3155i		−	1.21131i
$950$	3.07627	−	5.62894i	0.0998073	−	0.182627i
$951$	43.0188			1.39498
$952$	30.9666	−	26.2087i	1.00363	−	0.849428i
$953$	36.8415			1.19341			0.596706	−	0.802460i	$-0.296476\pi$
$953$	36.8415			1.19341			0.596706	+	0.802460i	$0.296476\pi$
$954$	−2.81264	+	5.14656i	−0.0910627	+	0.166626i
$955$		−	1.13019i		−	0.0365721i
$956$	2.84323	−	1.82434i	0.0919566	−	0.0590033i
$957$	−3.65180			−0.118046
$958$	−8.38581	−	4.58293i	−0.270933	−	0.148068i
$959$	1.63799	−	1.19944i	0.0528933	−	0.0387319i
$960$	−1.80621	−	12.7583i	−0.0582950	−	0.411771i
$961$	−22.3778			−0.721865
$962$	1.07405	−	1.96529i	0.0346287	−	0.0633635i
$963$	4.25144			0.137001
$964$	8.83924	−	5.67163i	0.284693	−	0.182671i
$965$	3.27357			0.105380
$966$	31.0597	−	4.12053i	0.999329	−	0.132576i
$967$		−	48.0941i		−	1.54660i	−0.634040	−	0.773301i	$-0.718604\pi$
$967$		−	48.0941i		−	1.54660i	0.634040	−	0.773301i	$-0.281396\pi$
$968$	−5.00827	−	71.1053i	−0.160972	−	2.28541i
$969$		−	39.6069i		−	1.27236i
$970$	−2.13213	+	3.90136i	−0.0684585	+	0.125265i
$971$		−	13.7904i		−	0.442555i	−0.975211	−	0.221277i	$-0.928977\pi$
$971$		−	13.7904i		−	0.442555i	0.975211	−	0.221277i	$-0.0710226\pi$
$972$	7.04584	−	4.52091i	0.225996	−	0.145008i
$973$	3.15522	+	4.30884i	0.101152	+	0.138135i
$974$	−5.23939	+	9.58700i	−0.167881	+	0.307187i
$975$			6.85203i			0.219441i
$976$	−9.30134	+	20.2896i	−0.297729	+	0.649455i
$977$	19.9730			0.638992			0.319496	−	0.947588i	$-0.396486\pi$
$977$	19.9730			0.638992			0.319496	+	0.947588i	$0.396486\pi$
$978$	7.80393	−	14.2796i	0.249542	−	0.456611i
$979$		−	11.7186i		−	0.374529i
$980$	−13.5157	+	3.65037i	−0.431744	+	0.116607i
$981$		−	0.274571i		−	0.00876638i
$982$	41.1569	+	22.4926i	1.31337	+	0.717769i
$983$	−50.8845			−1.62296			−0.811482	−	0.584377i	$-0.801339\pi$
$983$	−50.8845			−1.62296			−0.811482	+	0.584377i	$0.801339\pi$
$984$	−1.84229	−	26.1560i	−0.0587300	−	0.833824i
$985$		−	21.2252i		−	0.676291i
$986$	−2.53510	−	1.38546i	−0.0807340	−	0.0441219i
$987$	−9.72593	−	13.2820i	−0.309580	−	0.422770i
$988$	32.4809	−	20.8411i	1.03336	−	0.663045i
$989$		−	25.8133i		−	0.820815i
$990$	−3.02920	−	1.65549i	−0.0962744	−	0.0526149i
$991$			41.0233i			1.30315i	0.758585	+	0.651574i	$0.225891\pi$
$991$			41.0233i			1.30315i	−0.758585	+	0.651574i	$0.774109\pi$
$992$	−13.3153	+	9.93034i	−0.422763	+	0.315289i
$993$			5.24060i			0.166305i
$994$	−7.56827	−	57.0480i	−0.240051	−	1.80945i
$995$	−17.9614			−0.569416
$996$	14.6608	+	22.8488i	0.464544	+	0.723992i
$997$	29.5605			0.936189			0.468095	−	0.883678i	$-0.344941\pi$
$997$	29.5605			0.936189			0.468095	+	0.883678i	$0.344941\pi$
$998$	11.3365	+	6.19548i	0.358849	+	0.196114i
$999$	−2.04206			−0.0646079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.a.251.3	✓	16
4.3	odd	2		1120.2.h.a.111.12		16
7.6	odd	2		280.2.h.b.251.3	yes	16
8.3	odd	2		280.2.h.b.251.4	yes	16
8.5	even	2		1120.2.h.b.111.12		16
28.27	even	2		1120.2.h.b.111.5		16
56.13	odd	2		1120.2.h.a.111.5		16
56.27	even	2	inner	280.2.h.a.251.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.3	✓	16	1.1	even	1	trivial
280.2.h.a.251.4	yes	16	56.27	even	2	inner
280.2.h.b.251.3	yes	16	7.6	odd	2
280.2.h.b.251.4	yes	16	8.3	odd	2
1120.2.h.a.111.5		16	56.13	odd	2
1120.2.h.a.111.12		16	4.3	odd	2
1120.2.h.b.111.5		16	28.27	even	2
1120.2.h.b.111.12		16	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24098 - 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} -1.00000 q^{5} +(-1.09238 + 1.99883i) q^{6} +(-2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +O(q^{10})\)	\(q+(-1.24098 - 0.678208i) q^{2} -1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} -1.00000 q^{5} +(-1.09238 + 1.99883i) q^{6} +(-2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +(1.24098 + 0.678208i) q^{10} -6.01679 q^{11} +(2.71124 - 1.73965i) q^{12} -4.25411 q^{13} +(3.70916 - 0.492075i) q^{14} +1.61069i q^{15} +(-1.66690 + 3.63613i) q^{16} -5.42124i q^{17} +(-0.503458 - 0.275145i) q^{18} +4.53588i q^{19} +(-1.08007 - 1.68329i) q^{20} +(2.51769 + 3.43822i) q^{21} +(7.46673 + 4.08064i) q^{22} +5.19890i q^{23} +(-4.54445 + 0.320086i) q^{24} +1.00000 q^{25} +(5.27927 + 2.88517i) q^{26} -5.48550i q^{27} +(-4.93673 - 1.90492i) q^{28} +0.376818i q^{29} +(1.09238 - 1.99883i) q^{30} -2.93636 q^{31} +(4.53465 - 3.38186i) q^{32} +9.69116i q^{33} +(-3.67672 + 6.72765i) q^{34} +(2.13463 - 1.56312i) q^{35} +(0.438177 + 0.682898i) q^{36} -0.372265i q^{37} +(3.07627 - 5.62894i) q^{38} +6.85203i q^{39} +(0.198727 + 2.82144i) q^{40} +5.75560i q^{41} +(-0.792578 - 5.97429i) q^{42} -4.96515 q^{43} +(-6.49855 - 10.1280i) q^{44} -0.405694 q^{45} +(3.52593 - 6.45173i) q^{46} -3.86303 q^{47} +(5.85666 + 2.68486i) q^{48} +(2.11332 - 6.67337i) q^{49} +(-1.24098 - 0.678208i) q^{50} -8.73190 q^{51} +(-4.59473 - 7.16089i) q^{52} -10.2224i q^{53} +(-3.72031 + 6.80740i) q^{54} +6.01679 q^{55} +(4.83445 + 5.71210i) q^{56} +7.30587 q^{57} +(0.255561 - 0.467624i) q^{58} -10.5835i q^{59} +(-2.71124 + 1.73965i) q^{60} +5.58001 q^{61} +(3.64396 + 1.99146i) q^{62} +(-0.866007 + 0.634147i) q^{63} +(-7.92102 + 1.12139i) q^{64} +4.25411 q^{65} +(6.57262 - 12.0265i) q^{66} -0.782596 q^{67} +(9.12549 - 5.85531i) q^{68} +8.37378 q^{69} +(-3.70916 + 0.492075i) q^{70} -15.3803i q^{71} +(-0.0806221 - 1.14464i) q^{72} +8.77164i q^{73} +(-0.252473 + 0.461974i) q^{74} -1.61069i q^{75} +(-7.63518 + 4.89906i) q^{76} +(12.8437 - 9.40496i) q^{77} +(4.64710 - 8.50324i) q^{78} -8.74609i q^{79} +(1.66690 - 3.63613i) q^{80} -7.61833 q^{81} +(3.90349 - 7.14259i) q^{82} +8.42742i q^{83} +(-3.06823 + 7.95151i) q^{84} +5.42124i q^{85} +(6.16165 + 3.36740i) q^{86} +0.606935 q^{87} +(1.19570 + 16.9760i) q^{88} +1.94765i q^{89} +(0.503458 + 0.275145i) q^{90} +(9.08097 - 6.64968i) q^{91} +(-8.75123 + 5.61516i) q^{92} +4.72954i q^{93} +(4.79395 + 2.61994i) q^{94} -4.53588i q^{95} +(-5.44711 - 7.30389i) q^{96} +3.14377i q^{97} +(-7.14852 + 6.84826i) q^{98} -2.44098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9 - q^10 - 4 * q^11 - 14 * q^12 + 7 * q^14 + 9 * q^16 - 15 * q^18 - q^20 + 4 * q^21 + 6 * q^22 - 22 * q^24 + 16 * q^25 + 20 * q^26 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * q^42 - 4 * q^43 - 20 * q^44 + 16 * q^45 + 6 * q^46 + 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 + 38 * q^52 - 26 * q^54 + 4 * q^55 + q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 + 8 * q^61 - 28 * q^62 - 28 * q^63 - 23 * q^64 - 46 * q^66 + 20 * q^67 - 12 * q^68 + 40 * q^69 - 7 * q^70 - 13 * q^72 - 28 * q^74 - 34 * q^76 + 4 * q^77 - 6 * q^78 - 9 * q^80 + 24 * q^81 + 16 * q^82 + 10 * q^84 - 24 * q^86 - 72 * q^87 - 44 * q^88 + 15 * q^90 - 32 * q^91 - 30 * q^92 + 58 * q^94 + 30 * q^96 - 39 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

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