LMFDB - Embedded newform 280.2.b.d.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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([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("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (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:	$12$
Coefficient field:	12.0.8272021826830336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 $ x^12 + 3x^10 - 4x^9 + 4x^8 - 12x^7 + 10x^6 - 24x^5 + 16x^4 - 32x^3 + 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.2
Root			$-0.258252 + 1.39043i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39043 + 0.258252i) q^{2} -0.861041i q^{3} +(1.86661 - 0.718165i) q^{4} -1.00000i q^{5} +(0.222366 + 1.19722i) q^{6} +1.00000 q^{7} +(-2.40993 + 1.48062i) q^{8} +2.25861 q^{9} +O(q^{10})$	\(q+(-1.39043 + 0.258252i) q^{2} -0.861041i q^{3} +(1.86661 - 0.718165i) q^{4} -1.00000i q^{5} +(0.222366 + 1.19722i) q^{6} +1.00000 q^{7} +(-2.40993 + 1.48062i) q^{8} +2.25861 q^{9} +(0.258252 + 1.39043i) q^{10} +2.22560i q^{11} +(-0.618370 - 1.60723i) q^{12} -5.81986i q^{13} +(-1.39043 + 0.258252i) q^{14} -0.861041 q^{15} +(2.96848 - 2.68107i) q^{16} -3.57240 q^{17} +(-3.14045 + 0.583291i) q^{18} -1.87218i q^{19} +(-0.718165 - 1.86661i) q^{20} -0.861041i q^{21} +(-0.574766 - 3.09455i) q^{22} +6.40091 q^{23} +(1.27487 + 2.07505i) q^{24} -1.00000 q^{25} +(1.50299 + 8.09213i) q^{26} -4.52788i q^{27} +(1.86661 - 0.718165i) q^{28} -4.57288i q^{29} +(1.19722 - 0.222366i) q^{30} +2.83917 q^{31} +(-3.43508 + 4.49447i) q^{32} +1.91633 q^{33} +(4.96718 - 0.922579i) q^{34} -1.00000i q^{35} +(4.21594 - 1.62205i) q^{36} -10.4009i q^{37} +(0.483495 + 2.60314i) q^{38} -5.01114 q^{39} +(1.48062 + 2.40993i) q^{40} +6.46693 q^{41} +(0.222366 + 1.19722i) q^{42} +9.49994i q^{43} +(1.59835 + 4.15433i) q^{44} -2.25861i q^{45} +(-8.90004 + 1.65305i) q^{46} -10.4314 q^{47} +(-2.30851 - 2.55598i) q^{48} +1.00000 q^{49} +(1.39043 - 0.258252i) q^{50} +3.07598i q^{51} +(-4.17962 - 10.8634i) q^{52} +5.91764i q^{53} +(1.16933 + 6.29571i) q^{54} +2.22560 q^{55} +(-2.40993 + 1.48062i) q^{56} -1.61203 q^{57} +(1.18096 + 6.35828i) q^{58} +7.32290i q^{59} +(-1.60723 + 0.618370i) q^{60} +6.56125i q^{61} +(-3.94768 + 0.733223i) q^{62} +2.25861 q^{63} +(3.61554 - 7.13638i) q^{64} -5.81986 q^{65} +(-2.66453 + 0.494897i) q^{66} +11.7395i q^{67} +(-6.66827 + 2.56557i) q^{68} -5.51144i q^{69} +(0.258252 + 1.39043i) q^{70} -3.22811 q^{71} +(-5.44309 + 3.34414i) q^{72} -1.22811 q^{73} +(2.68606 + 14.4618i) q^{74} +0.861041i q^{75} +(-1.34454 - 3.49464i) q^{76} +2.22560i q^{77} +(6.96766 - 1.29414i) q^{78} -4.79924 q^{79} +(-2.68107 - 2.96848i) q^{80} +2.87714 q^{81} +(-8.99183 + 1.67010i) q^{82} +0.872662i q^{83} +(-0.618370 - 1.60723i) q^{84} +3.57240i q^{85} +(-2.45338 - 13.2090i) q^{86} -3.93743 q^{87} +(-3.29526 - 5.36354i) q^{88} -13.2611 q^{89} +(0.583291 + 3.14045i) q^{90} -5.81986i q^{91} +(11.9480 - 4.59691i) q^{92} -2.44464i q^{93} +(14.5042 - 2.69394i) q^{94} -1.87218 q^{95} +(3.86992 + 2.95774i) q^{96} +8.62317 q^{97} +(-1.39043 + 0.258252i) q^{98} +5.02676i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

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 $

$2$	−1.39043	+	0.258252i	−0.983185	+	0.182612i
$2$	−1.39043	+	0.258252i	−0.983185	+	0.182612i
$3$		−	0.861041i		−	0.497122i	−0.968616	−	0.248561i	$-0.920042\pi$
$3$		−	0.861041i		−	0.497122i	0.968616	−	0.248561i	$-0.0799577\pi$
$4$	1.86661	−	0.718165i	0.933306	−	0.359083i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.222366	+	1.19722i	0.0907805	+	0.488763i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.40993	+	1.48062i	−0.852039	+	0.523478i
$9$	2.25861			0.752869
$10$	0.258252	+	1.39043i	0.0816666	+	0.439694i
$11$			2.22560i			0.671043i	0.942032	+	0.335522i	$0.108913\pi$
$11$			2.22560i			0.671043i	−0.942032	+	0.335522i	$0.891087\pi$
$12$	−0.618370	−	1.60723i	−0.178508	−	0.463967i
$13$		−	5.81986i		−	1.61414i	−0.590456	−	0.807070i	$-0.701052\pi$
$13$		−	5.81986i		−	1.61414i	0.590456	−	0.807070i	$-0.298948\pi$
$14$	−1.39043	+	0.258252i	−0.371609	+	0.0690208i
$15$	−0.861041			−0.222320
$16$	2.96848	−	2.68107i	0.742119	−	0.670268i
$17$	−3.57240			−0.866433			−0.433217	−	0.901290i	$-0.642621\pi$
$17$	−3.57240			−0.866433			−0.433217	+	0.901290i	$0.642621\pi$
$18$	−3.14045	+	0.583291i	−0.740210	+	0.137483i
$19$		−	1.87218i		−	0.429508i	−0.976668	−	0.214754i	$-0.931105\pi$
$19$		−	1.87218i		−	0.429508i	0.976668	−	0.214754i	$-0.0688950\pi$
$20$	−0.718165	−	1.86661i	−0.160587	−	0.417387i
$21$		−	0.861041i		−	0.187895i
$22$	−0.574766	−	3.09455i	−0.122541	−	0.659760i
$23$	6.40091			1.33468			0.667341	−	0.744753i	$-0.267433\pi$
$23$	6.40091			1.33468			0.667341	+	0.744753i	$0.267433\pi$
$24$	1.27487	+	2.07505i	0.260232	+	0.423568i
$25$	−1.00000			−0.200000
$26$	1.50299	+	8.09213i	0.294761	+	1.58700i
$27$		−	4.52788i		−	0.871390i
$28$	1.86661	−	0.718165i	0.352756	−	0.135721i
$29$		−	4.57288i		−	0.849162i	−0.905390	−	0.424581i	$-0.860421\pi$
$29$		−	4.57288i		−	0.849162i	0.905390	−	0.424581i	$-0.139579\pi$
$30$	1.19722	−	0.222366i	0.218582	−	0.0405983i
$31$	2.83917			0.509930			0.254965	−	0.966950i	$-0.417936\pi$
$31$	2.83917			0.509930			0.254965	+	0.966950i	$0.417936\pi$
$32$	−3.43508	+	4.49447i	−0.607242	+	0.794517i
$33$	1.91633			0.333591
$34$	4.96718	−	0.922579i	0.851864	−	0.158221i
$35$		−	1.00000i		−	0.169031i
$36$	4.21594	−	1.62205i	0.702657	−	0.270342i
$37$		−	10.4009i		−	1.70990i	−0.518712	−	0.854949i	$-0.673588\pi$
$37$		−	10.4009i		−	1.70990i	0.518712	−	0.854949i	$-0.326412\pi$
$38$	0.483495	+	2.60314i	0.0784333	+	0.422286i
$39$	−5.01114			−0.802425
$40$	1.48062	+	2.40993i	0.234106	+	0.381044i
$41$	6.46693			1.00996			0.504982	−	0.863130i	$-0.331499\pi$
$41$	6.46693			1.00996			0.504982	+	0.863130i	$0.331499\pi$
$42$	0.222366	+	1.19722i	0.0343118	+	0.184735i
$43$			9.49994i			1.44873i	0.689418	+	0.724363i	$0.257866\pi$
$43$			9.49994i			1.44873i	−0.689418	+	0.724363i	$0.742134\pi$
$44$	1.59835	+	4.15433i	0.240960	+	0.626289i
$45$		−	2.25861i		−	0.336693i
$46$	−8.90004	+	1.65305i	−1.31224	+	0.243729i
$47$	−10.4314			−1.52158			−0.760789	−	0.649000i	$-0.775188\pi$
$47$	−10.4314			−1.52158			−0.760789	+	0.649000i	$0.775188\pi$
$48$	−2.30851	−	2.55598i	−0.333205	−	0.368924i
$49$	1.00000			0.142857
$50$	1.39043	−	0.258252i	0.196637	−	0.0365224i
$51$			3.07598i			0.430723i
$52$	−4.17962	−	10.8634i	−0.579610	−	1.50649i
$53$			5.91764i			0.812851i	0.913684	+	0.406425i	$0.133225\pi$
$53$			5.91764i			0.812851i	−0.913684	+	0.406425i	$0.866775\pi$
$54$	1.16933	+	6.29571i	0.159126	+	0.856738i
$55$	2.22560			0.300100
$56$	−2.40993	+	1.48062i	−0.322041	+	0.197856i
$57$	−1.61203			−0.213518
$58$	1.18096	+	6.35828i	0.155067	+	0.834883i
$59$			7.32290i			0.953360i	0.879077	+	0.476680i	$0.158160\pi$
$59$			7.32290i			0.953360i	−0.879077	+	0.476680i	$0.841840\pi$
$60$	−1.60723	+	0.618370i	−0.207492	+	0.0798312i
$61$			6.56125i			0.840083i	0.907505	+	0.420041i	$0.137984\pi$
$61$			6.56125i			0.840083i	−0.907505	+	0.420041i	$0.862016\pi$
$62$	−3.94768	+	0.733223i	−0.501356	+	0.0931194i
$63$	2.25861			0.284558
$64$	3.61554	−	7.13638i	0.451942	−	0.892047i
$65$	−5.81986			−0.721865
$66$	−2.66453	+	0.494897i	−0.327981	+	0.0609176i
$67$			11.7395i			1.43421i	0.696964	+	0.717106i	$0.254534\pi$
$67$			11.7395i			1.43421i	−0.696964	+	0.717106i	$0.745466\pi$
$68$	−6.66827	+	2.56557i	−0.808647	+	0.311121i
$69$		−	5.51144i		−	0.663500i
$70$	0.258252	+	1.39043i	0.0308671	+	0.166189i
$71$	−3.22811			−0.383106			−0.191553	−	0.981482i	$-0.561352\pi$
$71$	−3.22811			−0.383106			−0.191553	+	0.981482i	$0.561352\pi$
$72$	−5.44309	+	3.34414i	−0.641474	+	0.394110i
$73$	−1.22811			−0.143739			−0.0718695	−	0.997414i	$-0.522897\pi$
$73$	−1.22811			−0.143739			−0.0718695	+	0.997414i	$0.522897\pi$
$74$	2.68606	+	14.4618i	0.312248	+	1.68115i
$75$			0.861041i			0.0994245i
$76$	−1.34454	−	3.49464i	−0.154229	−	0.400862i
$77$			2.22560i			0.253631i
$78$	6.96766	−	1.29414i	0.788932	−	0.146532i
$79$	−4.79924			−0.539957			−0.269978	−	0.962866i	$-0.587017\pi$
$79$	−4.79924			−0.539957			−0.269978	+	0.962866i	$0.587017\pi$
$80$	−2.68107	−	2.96848i	−0.299753	−	0.331886i
$81$	2.87714			0.319682
$82$	−8.99183	+	1.67010i	−0.992982	+	0.184432i
$83$			0.872662i			0.0957871i	0.998852	+	0.0478935i	$0.0152508\pi$
$83$			0.872662i			0.0957871i	−0.998852	+	0.0478935i	$0.984749\pi$
$84$	−0.618370	−	1.60723i	−0.0674697	−	0.175363i
$85$			3.57240i			0.387481i
$86$	−2.45338	−	13.2090i	−0.264555	−	1.42437i
$87$	−3.93743			−0.422137
$88$	−3.29526	−	5.36354i	−0.351276	−	0.571755i
$89$	−13.2611			−1.40567			−0.702837	−	0.711351i	$-0.748084\pi$
$89$	−13.2611			−1.40567			−0.702837	+	0.711351i	$0.748084\pi$
$90$	0.583291	+	3.14045i	0.0614843	+	0.331032i
$91$		−	5.81986i		−	0.610087i
$92$	11.9480	−	4.59691i	1.24567	−	0.479261i
$93$		−	2.44464i		−	0.253498i
$94$	14.5042	−	2.69394i	1.49599	−	0.277858i
$95$	−1.87218			−0.192082
$96$	3.86992	+	2.95774i	0.394972	+	0.301873i
$97$	8.62317			0.875550			0.437775	−	0.899085i	$-0.355767\pi$
$97$	8.62317			0.875550			0.437775	+	0.899085i	$0.355767\pi$
$98$	−1.39043	+	0.258252i	−0.140455	+	0.0260874i
$99$			5.02676i			0.505208i
$100$	−1.86661	+	0.718165i	−0.186661	+	0.0718165i
$101$			3.85538i			0.383625i	0.981432	+	0.191812i	$0.0614365\pi$
$101$			3.85538i			0.383625i	−0.981432	+	0.191812i	$0.938564\pi$
$102$	−0.794379	−	4.27694i	−0.0786552	−	0.423481i
$103$	18.5701			1.82977			0.914884	−	0.403716i	$-0.132282\pi$
$103$	18.5701			1.82977			0.914884	+	0.403716i	$0.132282\pi$
$104$	8.61699	+	14.0255i	0.844966	+	1.37531i
$105$	−0.861041			−0.0840290
$106$	−1.52825	−	8.22809i	−0.148436	−	0.799183i
$107$			6.27309i			0.606442i	0.952920	+	0.303221i	$0.0980621\pi$
$107$			6.27309i			0.606442i	−0.952920	+	0.303221i	$0.901938\pi$
$108$	−3.25177	−	8.45179i	−0.312901	−	0.813274i
$109$			13.0891i			1.25371i	0.779135	+	0.626856i	$0.215658\pi$
$109$			13.0891i			1.25371i	−0.779135	+	0.626856i	$0.784342\pi$
$110$	−3.09455	+	0.574766i	−0.295054	+	0.0548018i
$111$	−8.95561			−0.850029
$112$	2.96848	−	2.68107i	0.280495	−	0.253337i
$113$	7.07751			0.665796			0.332898	−	0.942963i	$-0.391973\pi$
$113$	7.07751			0.665796			0.332898	+	0.942963i	$0.391973\pi$
$114$	2.24141	−	0.416309i	0.209928	−	0.0389909i
$115$		−	6.40091i		−	0.596888i
$116$	−3.28408	−	8.53578i	−0.304919	−	0.792527i
$117$		−	13.1448i		−	1.21524i
$118$	−1.89116	−	10.1820i	−0.174095	−	0.937330i
$119$	−3.57240			−0.327481
$120$	2.07505	−	1.27487i	0.189425	−	0.116379i
$121$	6.04671			0.549701
$122$	−1.69446	−	9.12299i	−0.153409	−	0.825957i
$123$		−	5.56829i		−	0.502076i
$124$	5.29963	−	2.03900i	0.475921	−	0.183107i
$125$			1.00000i			0.0894427i
$126$	−3.14045	+	0.583291i	−0.279773	+	0.0519637i
$127$	−3.01621			−0.267645			−0.133823	−	0.991005i	$-0.542725\pi$
$127$	−3.01621			−0.267645			−0.133823	+	0.991005i	$0.542725\pi$
$128$	−3.18418	+	10.8564i	−0.281445	+	0.959577i
$129$	8.17983			0.720194
$130$	8.09213	−	1.50299i	0.709727	−	0.131821i
$131$		−	6.82237i		−	0.596073i	−0.954554	−	0.298037i	$-0.903668\pi$
$131$		−	6.82237i		−	0.596073i	0.954554	−	0.298037i	$-0.0963318\pi$
$132$	3.57705	−	1.37624i	0.311342	−	0.119787i
$133$		−	1.87218i		−	0.162339i
$134$	−3.03176	−	16.3230i	−0.261904	−	1.41010i
$135$	−4.52788			−0.389698
$136$	8.60923	−	5.28935i	0.738235	−	0.453558i
$137$	6.96872			0.595378			0.297689	−	0.954663i	$-0.403784\pi$
$137$	6.96872			0.595378			0.297689	+	0.954663i	$0.403784\pi$
$138$	1.42334	+	7.66330i	0.121163	+	0.652343i
$139$			0.178109i			0.0151070i	0.999971	+	0.00755350i	$0.00240438\pi$
$139$			0.178109i			0.0151070i	−0.999971	+	0.00755350i	$0.997596\pi$
$140$	−0.718165	−	1.86661i	−0.0606961	−	0.157757i
$141$			8.98187i			0.756410i
$142$	4.48847	−	0.833666i	0.376664	−	0.0699597i
$143$	12.9527			1.08316
$144$	6.70463	−	6.05549i	0.558719	−	0.504624i
$145$	−4.57288			−0.379757
$146$	1.70760	−	0.317162i	0.141322	−	0.0262485i
$147$		−	0.861041i		−	0.0710175i
$148$	−7.46957	−	19.4145i	−0.613995	−	1.59586i
$149$		−	8.79513i		−	0.720525i	−0.932851	−	0.360263i	$-0.882687\pi$
$149$		−	8.79513i		−	0.720525i	0.932851	−	0.360263i	$-0.117313\pi$
$150$	−0.222366	−	1.19722i	−0.0181561	−	0.0977526i
$151$	−12.5858			−1.02422			−0.512109	−	0.858920i	$-0.671136\pi$
$151$	−12.5858			−1.02422			−0.512109	+	0.858920i	$0.671136\pi$
$152$	2.77199	+	4.51183i	0.224838	+	0.365958i
$153$	−8.06864			−0.652311
$154$	−0.574766	−	3.09455i	−0.0463160	−	0.249366i
$155$		−	2.83917i		−	0.228048i
$156$	−9.35385	+	3.59883i	−0.748908	+	0.288137i
$157$			20.2047i			1.61251i	0.591566	+	0.806257i	$0.298510\pi$
$157$			20.2047i			1.61251i	−0.591566	+	0.806257i	$0.701490\pi$
$158$	6.67303	−	1.23942i	0.530878	−	0.0986026i
$159$	5.09533			0.404086
$160$	4.49447	+	3.43508i	0.355319	+	0.271567i
$161$	6.40091			0.504462
$162$	−4.00047	+	0.743027i	−0.314306	+	0.0583777i
$163$			19.3239i			1.51356i	0.653669	+	0.756781i	$0.273229\pi$
$163$			19.3239i			1.51356i	−0.653669	+	0.756781i	$0.726771\pi$
$164$	12.0712	−	4.64432i	0.942605	−	0.362661i
$165$		−	1.91633i		−	0.149186i
$166$	−0.225367	−	1.21338i	−0.0174919	−	0.0941764i
$167$	2.93040			0.226761			0.113381	−	0.993552i	$-0.463832\pi$
$167$	2.93040			0.226761			0.113381	+	0.993552i	$0.463832\pi$
$168$	1.27487	+	2.07505i	0.0983586	+	0.160094i
$169$	−20.8708			−1.60545
$170$	−0.922579	−	4.96718i	−0.0707586	−	0.380965i
$171$		−	4.22853i		−	0.323363i
$172$	6.82253	+	17.7327i	0.520213	+	1.35210i
$173$			10.9606i			0.833321i	0.909062	+	0.416661i	$0.136800\pi$
$173$			10.9606i			0.833321i	−0.909062	+	0.416661i	$0.863200\pi$
$174$	5.47474	−	1.01685i	0.415039	−	0.0770873i
$175$	−1.00000			−0.0755929
$176$	5.96699	+	6.60664i	0.449779	+	0.497994i
$177$	6.30532			0.473937
$178$	18.4387	−	3.42471i	1.38204	−	0.256693i
$179$		−	15.9301i		−	1.19067i	−0.803477	−	0.595336i	$-0.797019\pi$
$179$		−	15.9301i		−	1.19067i	0.803477	−	0.595336i	$-0.202981\pi$
$180$	−1.62205	−	4.21594i	−0.120901	−	0.314238i
$181$		−	24.3688i		−	1.81132i	−0.424003	−	0.905661i	$-0.639375\pi$
$181$		−	24.3688i		−	1.81132i	0.424003	−	0.905661i	$-0.360625\pi$
$182$	1.50299	+	8.09213i	0.111409	+	0.599829i
$183$	5.64951			0.417624
$184$	−15.4257	+	9.47730i	−1.13720	+	0.698676i
$185$	−10.4009			−0.764690
$186$	0.631335	+	3.39912i	0.0462917	+	0.249235i
$187$		−	7.95072i		−	0.581414i
$188$	−19.4714	+	7.49148i	−1.42010	+	0.546372i
$189$		−	4.52788i		−	0.329355i
$190$	2.60314	−	0.483495i	0.188852	−	0.0350764i
$191$	7.94403			0.574810			0.287405	−	0.957809i	$-0.407207\pi$
$191$	7.94403			0.574810			0.287405	+	0.957809i	$0.407207\pi$
$192$	−6.14471	−	3.11313i	−0.443456	−	0.224671i
$193$	−26.2242			−1.88766			−0.943830	−	0.330430i	$-0.892806\pi$
$193$	−26.2242			−1.88766			−0.943830	+	0.330430i	$0.892806\pi$
$194$	−11.9899	+	2.22695i	−0.860828	+	0.159886i
$195$			5.01114i			0.358855i
$196$	1.86661	−	0.718165i	0.133329	−	0.0512975i
$197$			17.5457i			1.25008i	0.780593	+	0.625040i	$0.214917\pi$
$197$			17.5457i			1.25008i	−0.780593	+	0.625040i	$0.785083\pi$
$198$	−1.29817	−	6.98937i	−0.0922570	−	0.496713i
$199$	−1.05077			−0.0744872			−0.0372436	−	0.999306i	$-0.511858\pi$
$199$	−1.05077			−0.0744872			−0.0372436	+	0.999306i	$0.511858\pi$
$200$	2.40993	−	1.48062i	0.170408	−	0.104696i
$201$	10.1082			0.712979
$202$	−0.995661	−	5.36065i	−0.0700545	−	0.377174i
$203$		−	4.57288i		−	0.320953i
$204$	2.20906	+	5.74166i	0.154665	+	0.401996i
$205$		−	6.46693i		−	0.451670i
$206$	−25.8205	+	4.79578i	−1.79900	+	0.334138i
$207$	14.4571			1.00484
$208$	−15.6035	−	17.2761i	−1.08191	−	1.19788i
$209$	4.16673			0.288218
$210$	1.19722	−	0.222366i	0.0826161	−	0.0153447i
$211$			6.29734i			0.433527i	0.976224	+	0.216763i	$0.0695500\pi$
$211$			6.29734i			0.433527i	−0.976224	+	0.216763i	$0.930450\pi$
$212$	4.24985	+	11.0459i	0.291881	+	0.758638i
$213$			2.77953i			0.190450i
$214$	−1.62004	−	8.72231i	−0.110744	−	0.596245i
$215$	9.49994			0.647890
$216$	6.70406	+	10.9119i	0.456153	+	0.742459i
$217$	2.83917			0.192736
$218$	−3.38030	−	18.1996i	−0.228943	−	1.23263i
$219$			1.05745i			0.0714559i
$220$	4.15433	−	1.59835i	0.280085	−	0.107761i
$221$			20.7909i			1.39854i
$222$	12.4522	−	2.31281i	0.835736	−	0.155225i
$223$	4.94770			0.331322			0.165661	−	0.986183i	$-0.447024\pi$
$223$	4.94770			0.331322			0.165661	+	0.986183i	$0.447024\pi$
$224$	−3.43508	+	4.49447i	−0.229516	+	0.300299i
$225$	−2.25861			−0.150574
$226$	−9.84081	+	1.82778i	−0.654601	+	0.121582i
$227$		−	28.6190i		−	1.89951i	−0.312996	−	0.949754i	$-0.601333\pi$
$227$		−	28.6190i		−	1.89951i	0.312996	−	0.949754i	$-0.398667\pi$
$228$	−3.00903	+	1.15770i	−0.199278	+	0.0766706i
$229$			1.18979i			0.0786235i	0.999227	+	0.0393117i	$0.0125165\pi$
$229$			1.18979i			0.0786235i	−0.999227	+	0.0393117i	$0.987483\pi$
$230$	1.65305	+	8.90004i	0.108999	+	0.586851i
$231$	1.91633			0.126085
$232$	6.77068	+	11.0203i	0.444517	+	0.723519i
$233$	−10.1956			−0.667933			−0.333967	−	0.942585i	$-0.608387\pi$
$233$	−10.1956			−0.667933			−0.333967	+	0.942585i	$0.608387\pi$
$234$	3.39467	+	18.2770i	0.221917	+	1.19480i
$235$			10.4314i			0.680470i
$236$	5.25905	+	13.6690i	0.342335	+	0.889777i
$237$			4.13234i			0.268425i
$238$	4.96718	−	0.922579i	0.321974	−	0.0598019i
$239$	−24.2469			−1.56840			−0.784199	−	0.620509i	$-0.786926\pi$
$239$	−24.2469			−1.56840			−0.784199	+	0.620509i	$0.786926\pi$
$240$	−2.55598	+	2.30851i	−0.164988	+	0.149014i
$241$	−10.5107			−0.677051			−0.338526	−	0.940957i	$-0.609928\pi$
$241$	−10.5107			−0.677051			−0.338526	+	0.940957i	$0.609928\pi$
$242$	−8.40755	+	1.56158i	−0.540458	+	0.100382i
$243$		−	16.0610i		−	1.03031i
$244$	4.71207	+	12.2473i	0.301659	+	0.784054i
$245$		−	1.00000i		−	0.0638877i
$246$	1.43802	+	7.74234i	0.0916850	+	0.493633i
$247$	−10.8958			−0.693286
$248$	−6.84221	+	4.20373i	−0.434481	+	0.266937i
$249$	0.751398			0.0476179
$250$	−0.258252	−	1.39043i	−0.0163333	−	0.0879387i
$251$		−	9.68829i		−	0.611520i	−0.952109	−	0.305760i	$-0.901090\pi$
$251$		−	9.68829i		−	0.611520i	0.952109	−	0.305760i	$-0.0989104\pi$
$252$	4.21594	−	1.62205i	0.265580	−	0.102180i
$253$			14.2459i			0.895629i
$254$	4.19384	−	0.778943i	0.263145	−	0.0488752i
$255$	3.07598			0.192625
$256$	1.62371	−	15.9174i	0.101482	−	0.994837i
$257$	4.06448			0.253536			0.126768	−	0.991932i	$-0.459540\pi$
$257$	4.06448			0.253536			0.126768	+	0.991932i	$0.459540\pi$
$258$	−11.3735	+	2.11246i	−0.708084	+	0.131516i
$259$		−	10.4009i		−	0.646281i
$260$	−10.8634	+	4.17962i	−0.673721	+	0.259209i
$261$		−	10.3283i		−	0.639308i
$262$	1.76189	+	9.48605i	0.108850	+	0.586050i
$263$	2.34490			0.144593			0.0722963	−	0.997383i	$-0.476967\pi$
$263$	2.34490			0.144593			0.0722963	+	0.997383i	$0.476967\pi$
$264$	−4.61823	+	2.83736i	−0.284232	+	0.174627i
$265$	5.91764			0.363518
$266$	0.483495	+	2.60314i	0.0296450	+	0.159609i
$267$			11.4184i			0.698792i
$268$	8.43093	+	21.9132i	0.515001	+	1.33856i
$269$			21.6184i			1.31810i	0.752100	+	0.659049i	$0.229041\pi$
$269$			21.6184i			1.31810i	−0.752100	+	0.659049i	$0.770959\pi$
$270$	6.29571	−	1.16933i	0.383145	−	0.0711635i
$271$	−20.2455			−1.22983			−0.614915	−	0.788594i	$-0.710810\pi$
$271$	−20.2455			−1.22983			−0.614915	+	0.788594i	$0.710810\pi$
$272$	−10.6046	+	9.57785i	−0.642997	+	0.580742i
$273$	−5.01114			−0.303288
$274$	−9.68954	+	1.79969i	−0.585366	+	0.108723i
$275$		−	2.22560i		−	0.134209i
$276$	−3.95813	−	10.2877i	−0.238251	−	0.619248i
$277$			2.71683i			0.163239i	0.996664	+	0.0816194i	$0.0260092\pi$
$277$			2.71683i			0.163239i	−0.996664	+	0.0816194i	$0.973991\pi$
$278$	−0.0459971	−	0.247649i	−0.00275872	−	0.0148530i
$279$	6.41258			0.383911
$280$	1.48062	+	2.40993i	0.0884839	+	0.144021i
$281$	20.7895			1.24020			0.620100	−	0.784523i	$-0.287092\pi$
$281$	20.7895			1.24020			0.620100	+	0.784523i	$0.287092\pi$
$282$	−2.31959	−	12.4887i	−0.138130	−	0.743691i
$283$			4.37026i			0.259785i	0.991528	+	0.129893i	$0.0414633\pi$
$283$			4.37026i			0.259785i	−0.991528	+	0.129893i	$0.958537\pi$
$284$	−6.02562	+	2.31831i	−0.357555	+	0.137567i
$285$			1.61203i			0.0954881i
$286$	−18.0098	+	3.34506i	−1.06494	+	0.197798i
$287$	6.46693			0.381731
$288$	−7.75849	+	10.1512i	−0.457174	+	0.598168i
$289$	−4.23799			−0.249294
$290$	6.35828	−	1.18096i	0.373371	−	0.0693481i
$291$		−	7.42490i		−	0.435255i
$292$	−2.29240	+	0.881984i	−0.134152	+	0.0516142i
$293$		−	5.36199i		−	0.313251i	−0.987658	−	0.156625i	$-0.949939\pi$
$293$		−	5.36199i		−	0.313251i	0.987658	−	0.156625i	$-0.0500615\pi$
$294$	0.222366	+	1.19722i	0.0129686	+	0.0698233i
$295$	7.32290			0.426356
$296$	15.3998	+	25.0655i	0.895094	+	1.45690i
$297$	10.0772			0.584741
$298$	2.27136	+	12.2291i	0.131577	+	0.708410i
$299$		−	37.2524i		−	2.15436i
$300$	0.618370	+	1.60723i	0.0357016	+	0.0927934i
$301$			9.49994i			0.547567i
$302$	17.4997	−	3.25031i	1.00700	−	0.187035i
$303$	3.31964			0.190708
$304$	−5.01945	−	5.55753i	−0.287885	−	0.318746i
$305$	6.56125			0.375696
$306$	11.2189	−	2.08375i	0.641342	−	0.119120i
$307$			12.4357i			0.709743i	0.934915	+	0.354872i	$0.115475\pi$
$307$			12.4357i			0.709743i	−0.934915	+	0.354872i	$0.884525\pi$
$308$	1.59835	+	4.15433i	0.0910743	+	0.236715i
$309$		−	15.9896i		−	0.909619i
$310$	0.733223	+	3.94768i	0.0416443	+	0.224213i
$311$	16.1170			0.913909			0.456955	−	0.889490i	$-0.348940\pi$
$311$	16.1170			0.913909			0.456955	+	0.889490i	$0.348940\pi$
$312$	12.0765	−	7.41959i	0.683698	−	0.420051i
$313$	31.4727			1.77894			0.889472	−	0.456989i	$-0.151072\pi$
$313$	31.4727			1.77894			0.889472	+	0.456989i	$0.151072\pi$
$314$	−5.21792	−	28.0933i	−0.294464	−	1.58540i
$315$		−	2.25861i		−	0.127258i
$316$	−8.95832	+	3.44665i	−0.503945	+	0.193889i
$317$		−	12.2022i		−	0.685346i	−0.939455	−	0.342673i	$-0.888668\pi$
$317$		−	12.2022i		−	0.685346i	0.939455	−	0.342673i	$-0.111332\pi$
$318$	−7.08472	+	1.31588i	−0.397292	+	0.0737910i
$319$	10.1774			0.569824
$320$	−7.13638	−	3.61554i	−0.398936	−	0.202115i
$321$	5.40139			0.301476
$322$	−8.90004	+	1.65305i	−0.495980	+	0.0921208i
$323$			6.68817i			0.372140i
$324$	5.37050	−	2.06626i	0.298361	−	0.114792i
$325$			5.81986i			0.322828i
$326$	−4.99043	−	26.8685i	−0.276394	−	1.48811i
$327$	11.2703			0.623248
$328$	−15.5848	+	9.57505i	−0.860529	+	0.528694i
$329$	−10.4314			−0.575102
$330$	0.494897	+	2.66453i	0.0272432	+	0.146678i
$331$			2.01247i			0.110615i	0.998469	+	0.0553076i	$0.0176140\pi$
$331$			2.01247i			0.110615i	−0.998469	+	0.0553076i	$0.982386\pi$
$332$	0.626716	+	1.62892i	0.0343955	+	0.0893986i
$333$		−	23.4916i		−	1.28733i
$334$	−4.07453	+	0.756783i	−0.222948	+	0.0414093i
$335$	11.7395			0.641399
$336$	−2.30851	−	2.55598i	−0.125940	−	0.139440i
$337$	1.83852			0.100150			0.0500752	−	0.998745i	$-0.484054\pi$
$337$	1.83852			0.100150			0.0500752	+	0.998745i	$0.484054\pi$
$338$	29.0195	−	5.38993i	1.57845	−	0.293174i
$339$		−	6.09403i		−	0.330982i
$340$	2.56557	+	6.66827i	0.139138	+	0.361638i
$341$			6.31886i			0.342185i
$342$	1.09203	+	5.87948i	0.0590500	+	0.317926i
$343$	1.00000			0.0539949
$344$	−14.0658	−	22.8942i	−0.758376	−	1.23437i
$345$	−5.51144			−0.296726
$346$	−2.83061	−	15.2400i	−0.152174	−	0.819309i
$347$		−	34.9757i		−	1.87759i	−0.344472	−	0.938797i	$-0.611942\pi$
$347$		−	34.9757i		−	1.87759i	0.344472	−	0.938797i	$-0.388058\pi$
$348$	−7.34966	+	2.82773i	−0.393983	+	0.151582i
$349$			8.59987i			0.460341i	0.973150	+	0.230170i	$0.0739283\pi$
$349$			8.59987i			0.460341i	−0.973150	+	0.230170i	$0.926072\pi$
$350$	1.39043	−	0.258252i	0.0743218	−	0.0138042i
$351$	−26.3516			−1.40655
$352$	−10.0029	−	7.64510i	−0.533156	−	0.407485i
$353$	−30.4881			−1.62272			−0.811360	−	0.584547i	$-0.801272\pi$
$353$	−30.4881			−1.62272			−0.811360	+	0.584547i	$0.801272\pi$
$354$	−8.76713	+	1.62836i	−0.465967	+	0.0865465i
$355$			3.22811i			0.171330i
$356$	−24.7533	+	9.52366i	−1.31192	+	0.504753i
$357$			3.07598i			0.162798i
$358$	4.11399	+	22.1498i	0.217431	+	1.17065i
$359$	−16.0341			−0.846246			−0.423123	−	0.906072i	$-0.639066\pi$
$359$	−16.0341			−0.846246			−0.423123	+	0.906072i	$0.639066\pi$
$360$	3.34414	+	5.44309i	0.176251	+	0.286876i
$361$	15.4949			0.815523
$362$	6.29331	+	33.8833i	0.330769	+	1.78086i
$363$		−	5.20646i		−	0.273269i
$364$	−4.17962	−	10.8634i	−0.219072	−	0.569398i
$365$			1.22811i			0.0642821i
$366$	−7.85527	+	1.45900i	−0.410601	+	0.0762631i
$367$	−25.6011			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$367$	−25.6011			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$368$	19.0009	−	17.1613i	0.990493	−	0.894594i
$369$	14.6063			0.760371
$370$	14.4618	−	2.68606i	0.751832	−	0.139642i
$371$			5.91764i			0.307229i
$372$	−1.75566	−	4.56320i	−0.0910267	−	0.236591i
$373$		−	22.8185i		−	1.18150i	−0.806856	−	0.590749i	$-0.798832\pi$
$373$		−	22.8185i		−	1.18150i	0.806856	−	0.590749i	$-0.201168\pi$
$374$	2.05329	+	11.0549i	0.106173	+	0.571638i
$375$	0.861041			0.0444640
$376$	25.1390	−	15.4449i	1.29644	−	0.796512i
$377$	−26.6135			−1.37067
$378$	1.16933	+	6.29571i	0.0601441	+	0.323817i
$379$			16.9290i			0.869585i	0.900531	+	0.434793i	$0.143178\pi$
$379$			16.9290i			0.869585i	−0.900531	+	0.434793i	$0.856822\pi$
$380$	−3.49464	+	1.34454i	−0.179271	+	0.0689733i
$381$			2.59708i			0.133052i
$382$	−11.0457	+	2.05156i	−0.565145	+	0.104967i
$383$	14.3053			0.730968			0.365484	−	0.930818i	$-0.380904\pi$
$383$	14.3053			0.730968			0.365484	+	0.930818i	$0.380904\pi$
$384$	9.34779	+	2.74171i	0.477027	+	0.139912i
$385$	2.22560			0.113427
$386$	36.4630	−	6.77247i	1.85592	−	0.344709i
$387$			21.4566i			1.09070i
$388$	16.0961	−	6.19286i	0.817156	−	0.314395i
$389$		−	17.8010i		−	0.902544i	−0.892386	−	0.451272i	$-0.850970\pi$
$389$		−	17.8010i		−	0.902544i	0.892386	−	0.451272i	$-0.149030\pi$
$390$	−1.29414	−	6.96766i	−0.0655313	−	0.352821i
$391$	−22.8666			−1.15641
$392$	−2.40993	+	1.48062i	−0.121720	+	0.0747825i
$393$	−5.87434			−0.296321
$394$	−4.53122	−	24.3961i	−0.228279	−	1.22906i
$395$			4.79924i			0.241476i
$396$	3.61004	+	9.38300i	0.181411	+	0.471514i
$397$			7.04033i			0.353344i	0.984270	+	0.176672i	$0.0565332\pi$
$397$			7.04033i			0.353344i	−0.984270	+	0.176672i	$0.943467\pi$
$398$	1.46103	−	0.271364i	0.0732347	−	0.0136022i
$399$	−1.61203			−0.0807022
$400$	−2.96848	+	2.68107i	−0.148424	+	0.134054i
$401$	21.8698			1.09213			0.546064	−	0.837743i	$-0.316126\pi$
$401$	21.8698			1.09213			0.546064	+	0.837743i	$0.316126\pi$
$402$	−14.0548	+	2.61047i	−0.700990	+	0.130198i
$403$		−	16.5236i		−	0.823099i
$404$	2.76880	+	7.19650i	0.137753	+	0.358039i
$405$		−	2.87714i		−	0.142966i
$406$	1.18096	+	6.35828i	0.0586098	+	0.315556i
$407$	23.1482			1.14742
$408$	−4.55435	−	7.41290i	−0.225474	−	0.366993i
$409$	9.19521			0.454674			0.227337	−	0.973816i	$-0.426998\pi$
$409$	9.19521			0.454674			0.227337	+	0.973816i	$0.426998\pi$
$410$	1.67010	+	8.99183i	0.0824803	+	0.444075i
$411$		−	6.00035i		−	0.295975i
$412$	34.6632	−	13.3364i	1.70773	−	0.657038i
$413$			7.32290i			0.360336i
$414$	−20.1017	+	3.73359i	−0.987945	+	0.183496i
$415$	0.872662			0.0428373
$416$	26.1572	+	19.9917i	1.28246	+	0.980173i
$417$	0.153359			0.00751003
$418$	−5.79356	+	1.07607i	−0.283372	+	0.0526321i
$419$			23.1903i			1.13292i	0.824090	+	0.566459i	$0.191687\pi$
$419$			23.1903i			1.13292i	−0.824090	+	0.566459i	$0.808313\pi$
$420$	−1.60723	+	0.618370i	−0.0784247	+	0.0301734i
$421$		−	15.7572i		−	0.767961i	−0.923341	−	0.383981i	$-0.874553\pi$
$421$		−	15.7572i		−	0.767961i	0.923341	−	0.383981i	$-0.125447\pi$
$422$	−1.62630	−	8.75603i	−0.0791671	−	0.426237i
$423$	−23.5605			−1.14555
$424$	−8.76177	−	14.2611i	−0.425509	−	0.692581i
$425$	3.57240			0.173287
$426$	−0.717821	−	3.86476i	−0.0347785	−	0.187248i
$427$			6.56125i			0.317521i
$428$	4.50512	+	11.7094i	0.217763	+	0.565996i
$429$		−	11.1528i		−	0.538462i
$430$	−13.2090	+	2.45338i	−0.636996	+	0.118313i
$431$	8.66874			0.417558			0.208779	−	0.977963i	$-0.433051\pi$
$431$	8.66874			0.417558			0.208779	+	0.977963i	$0.433051\pi$
$432$	−12.1396	−	13.4409i	−0.584065	−	0.646676i
$433$	−22.7581			−1.09368			−0.546842	−	0.837236i	$-0.684170\pi$
$433$	−22.7581			−1.09368			−0.546842	+	0.837236i	$0.684170\pi$
$434$	−3.94768	+	0.733223i	−0.189495	+	0.0351958i
$435$			3.93743i			0.188785i
$436$	9.40016	+	24.4323i	0.450186	+	1.17010i
$437$		−	11.9837i		−	0.573256i
$438$	−0.273089	−	1.47031i	−0.0130487	−	0.0702544i
$439$	−15.7784			−0.753064			−0.376532	−	0.926404i	$-0.622884\pi$
$439$	−15.7784			−0.753064			−0.376532	+	0.926404i	$0.622884\pi$
$440$	−5.36354	+	3.29526i	−0.255697	+	0.157095i
$441$	2.25861			0.107553
$442$	−5.36929	−	28.9083i	−0.255391	−	1.37503i
$443$		−	10.2239i		−	0.485754i	−0.970057	−	0.242877i	$-0.921909\pi$
$443$		−	10.2239i		−	0.485754i	0.970057	−	0.242877i	$-0.0780911\pi$
$444$	−16.7166	+	6.43161i	−0.793337	+	0.305231i
$445$			13.2611i			0.628636i
$446$	−6.87944	+	1.27775i	−0.325751	+	0.0605034i
$447$	−7.57297			−0.358189
$448$	3.61554	−	7.13638i	0.170818	−	0.337162i
$449$	2.64641			0.124892			0.0624459	−	0.998048i	$-0.480110\pi$
$449$	2.64641			0.124892			0.0624459	+	0.998048i	$0.480110\pi$
$450$	3.14045	−	0.583291i	0.148042	−	0.0274966i
$451$			14.3928i			0.677730i
$452$	13.2110	−	5.08282i	0.621391	−	0.239076i
$453$			10.8369i			0.509162i
$454$	7.39092	+	39.7928i	0.346873	+	1.86757i
$455$	−5.81986			−0.272839
$456$	3.88487	−	2.38679i	0.181926	−	0.111772i
$457$	38.6186			1.80650			0.903250	−	0.429114i	$-0.141174\pi$
$457$	38.6186			1.80650			0.903250	+	0.429114i	$0.141174\pi$
$458$	−0.307266	−	1.65432i	−0.0143576	−	0.0773014i
$459$			16.1754i			0.755002i
$460$	−4.59691	−	11.9480i	−0.214332	−	0.557079i
$461$			6.64829i			0.309642i	0.987943	+	0.154821i	$0.0494801\pi$
$461$			6.64829i			0.309642i	−0.987943	+	0.154821i	$0.950520\pi$
$462$	−2.66453	+	0.494897i	−0.123965	+	0.0230247i
$463$	36.9639			1.71786			0.858928	−	0.512096i	$-0.171131\pi$
$463$	36.9639			1.71786			0.858928	+	0.512096i	$0.171131\pi$
$464$	−12.2602	−	13.5745i	−0.569166	−	0.630179i
$465$	−2.44464			−0.113368
$466$	14.1763	−	2.63303i	0.656702	−	0.121973i
$467$		−	8.46861i		−	0.391880i	−0.980616	−	0.195940i	$-0.937224\pi$
$467$		−	8.46861i		−	0.391880i	0.980616	−	0.195940i	$-0.0627759\pi$
$468$	−9.44013	−	24.5362i	−0.436370	−	1.13419i
$469$			11.7395i			0.542081i
$470$	−2.69394	−	14.5042i	−0.124262	−	0.669028i
$471$	17.3971			0.801616
$472$	−10.8424	−	17.6477i	−0.499063	−	0.812301i
$473$	−21.1430			−0.972158
$474$	−1.06719	−	5.74575i	−0.0490175	−	0.263911i
$475$			1.87218i			0.0859016i
$476$	−6.66827	+	2.56557i	−0.305640	+	0.117593i
$477$			13.3656i			0.611971i
$478$	33.7136	−	6.26181i	1.54203	−	0.286408i
$479$	−0.00126096			−5.76146e−5			−2.88073e−5	−	1.00000i	$-0.500009\pi$
$479$	−0.00126096			−5.76146e−5			−2.88073e−5		1.00000i	$0.500009\pi$
$480$	2.95774	−	3.86992i	0.135002	−	0.176637i
$481$	−60.5319			−2.76001
$482$	14.6144	−	2.71440i	0.665667	−	0.123638i
$483$		−	5.51144i		−	0.250779i
$484$	11.2869	−	4.34254i	0.513039	−	0.197388i
$485$		−	8.62317i		−	0.391558i
$486$	4.14778	+	22.3317i	0.188147	+	1.01299i
$487$	−2.34905			−0.106446			−0.0532229	−	0.998583i	$-0.516949\pi$
$487$	−2.34905			−0.106446			−0.0532229	+	0.998583i	$0.516949\pi$
$488$	−9.71471	−	15.8122i	−0.439764	−	0.715783i
$489$	16.6386			0.752425
$490$	0.258252	+	1.39043i	0.0116667	+	0.0628134i
$491$		−	12.6464i		−	0.570724i	−0.958420	−	0.285362i	$-0.907886\pi$
$491$		−	12.6464i		−	0.570724i	0.958420	−	0.285362i	$-0.0921138\pi$
$492$	−3.99895	−	10.3938i	−0.180287	−	0.468590i
$493$			16.3361i			0.735742i
$494$	15.1499	−	2.81388i	0.681628	−	0.126602i
$495$	5.02676			0.225936
$496$	8.42802	−	7.61203i	0.378429	−	0.341790i
$497$	−3.22811			−0.144800
$498$	−1.04477	+	0.194050i	−0.0468172	+	0.00869560i
$499$			11.1381i			0.498611i	0.968425	+	0.249306i	$0.0802023\pi$
$499$			11.1381i			0.498611i	−0.968425	+	0.249306i	$0.919798\pi$
$500$	0.718165	+	1.86661i	0.0321173	+	0.0834774i
$501$		−	2.52319i		−	0.112728i
$502$	2.50202	+	13.4709i	0.111671	+	0.601237i
$503$	−16.0086			−0.713787			−0.356893	−	0.934145i	$-0.616164\pi$
$503$	−16.0086			−0.713787			−0.356893	+	0.934145i	$0.616164\pi$
$504$	−5.44309	+	3.34414i	−0.242455	+	0.148960i
$505$	3.85538			0.171562
$506$	−3.67902	−	19.8079i	−0.163553	−	0.880569i
$507$			17.9706i			0.798103i
$508$	−5.63009	+	2.16614i	−0.249795	+	0.0961068i
$509$			14.4389i			0.639994i	0.947419	+	0.319997i	$0.103682\pi$
$509$			14.4389i			0.639994i	−0.947419	+	0.319997i	$0.896318\pi$
$510$	−4.27694	+	0.794379i	−0.189386	+	0.0351757i
$511$	−1.22811			−0.0543283
$512$	1.85305	+	22.5514i	0.0818939	+	0.996641i
$513$	−8.47701			−0.374269
$514$	−5.65140	+	1.04966i	−0.249272	+	0.0462986i
$515$		−	18.5701i		−	0.818298i
$516$	15.2686	−	5.87447i	0.672161	−	0.258609i
$517$		−	23.2161i		−	1.02104i
$518$	2.68606	+	14.4618i	0.118019	+	0.635414i
$519$	9.43755			0.414263
$520$	14.0255	−	8.61699i	0.615058	−	0.377880i
$521$	5.30292			0.232325			0.116163	−	0.993230i	$-0.462941\pi$
$521$	5.30292			0.232325			0.116163	+	0.993230i	$0.462941\pi$
$522$	2.66732	+	14.3609i	0.116745	+	0.628558i
$523$			41.2507i			1.80377i	0.431980	+	0.901883i	$0.357815\pi$
$523$			41.2507i			1.80377i	−0.431980	+	0.901883i	$0.642185\pi$
$524$	−4.89959	−	12.7347i	−0.214040	−	0.556319i
$525$			0.861041i			0.0375789i
$526$	−3.26042	+	0.605575i	−0.142161	+	0.0264043i
$527$	−10.1426			−0.441821
$528$	5.68859	−	5.13782i	0.247564	−	0.223595i
$529$	17.9716			0.781374
$530$	−8.22809	+	1.52825i	−0.357405	+	0.0663827i
$531$			16.5396i			0.717756i
$532$	−1.34454	−	3.49464i	−0.0582930	−	0.151512i
$533$		−	37.6366i		−	1.63022i
$534$	−2.94882	−	15.8765i	−0.127608	−	0.687042i
$535$	6.27309			0.271209
$536$	−17.3818	−	28.2915i	−0.750778	−	1.22201i
$537$	−13.7165			−0.591910
$538$	−5.58300	−	30.0590i	−0.240700	−	1.29593i
$539$			2.22560i			0.0958633i
$540$	−8.45179	+	3.25177i	−0.363707	+	0.139934i
$541$		−	13.1628i		−	0.565913i	−0.959133	−	0.282956i	$-0.908685\pi$
$541$		−	13.1628i		−	0.565913i	0.959133	−	0.282956i	$-0.0913151\pi$
$542$	28.1501	−	5.22846i	1.20915	−	0.224582i
$543$	−20.9826			−0.900448
$544$	12.2715	−	16.0560i	0.526134	−	0.688396i
$545$	13.0891			0.560677
$546$	6.96766	−	1.29414i	0.298188	−	0.0553840i
$547$		−	6.08377i		−	0.260123i	−0.991506	−	0.130062i	$-0.958482\pi$
$547$		−	6.08377i		−	0.260123i	0.991506	−	0.130062i	$-0.0415175\pi$
$548$	13.0079	−	5.00469i	0.555669	−	0.213790i
$549$			14.8193i			0.632473i
$550$	0.574766	+	3.09455i	0.0245081	+	0.131952i
$551$	−8.56125			−0.364722
$552$	8.16034	+	13.2822i	0.347327	+	0.565328i
$553$	−4.79924			−0.204085
$554$	−0.701629	−	3.77758i	−0.0298094	−	0.160494i
$555$			8.95561i			0.380144i
$556$	0.127912	+	0.332460i	0.00542466	+	0.0140995i
$557$			15.1910i			0.643665i	0.946797	+	0.321833i	$0.104299\pi$
$557$			15.1910i			0.643665i	−0.946797	+	0.321833i	$0.895701\pi$
$558$	−8.91627	+	1.65606i	−0.377456	+	0.0701068i
$559$	55.2883			2.33845
$560$	−2.68107	−	2.96848i	−0.113296	−	0.125441i
$561$	−6.84590			−0.289034
$562$	−28.9065	+	5.36895i	−1.21935	+	0.226475i
$563$		−	21.9276i		−	0.924138i	−0.886844	−	0.462069i	$-0.847107\pi$
$563$		−	21.9276i		−	0.924138i	0.886844	−	0.462069i	$-0.152893\pi$
$564$	6.45047	+	16.7657i	0.271614	+	0.705962i
$565$		−	7.07751i		−	0.297753i
$566$	−1.12863	−	6.07656i	−0.0474399	−	0.255417i
$567$	2.87714			0.120828
$568$	7.77952	−	4.77959i	0.326421	−	0.200547i
$569$	10.9610			0.459510			0.229755	−	0.973248i	$-0.426207\pi$
$569$	10.9610			0.459510			0.229755	+	0.973248i	$0.426207\pi$
$570$	−0.416309	−	2.24141i	−0.0174373	−	0.0938825i
$571$			36.7329i			1.53722i	0.639716	+	0.768611i	$0.279052\pi$
$571$			36.7329i			1.53722i	−0.639716	+	0.768611i	$0.720948\pi$
$572$	24.1776	−	9.30217i	1.01092	−	0.388943i
$573$		−	6.84014i		−	0.285751i
$574$	−8.99183	+	1.67010i	−0.375312	+	0.0697086i
$575$	−6.40091			−0.266936
$576$	8.16609	−	16.1183i	0.340254	−	0.671595i
$577$	20.8964			0.869930			0.434965	−	0.900447i	$-0.356761\pi$
$577$	20.8964			0.869930			0.434965	+	0.900447i	$0.356761\pi$
$578$	5.89264	−	1.09447i	0.245102	−	0.0455240i
$579$			22.5801i			0.938398i
$580$	−8.53578	+	3.28408i	−0.354429	+	0.136364i
$581$			0.872662i			0.0362041i
$582$	1.91750	+	10.3238i	0.0794828	+	0.427937i
$583$	−13.1703			−0.545458
$584$	2.95965	−	1.81836i	0.122471	−	0.0752442i
$585$	−13.1448			−0.543470
$586$	1.38475	+	7.45548i	0.0572033	+	0.307983i
$587$			39.3182i			1.62284i	0.584466	+	0.811418i	$0.301304\pi$
$587$			39.3182i			1.62284i	−0.584466	+	0.811418i	$0.698696\pi$
$588$	−0.618370	−	1.60723i	−0.0255011	−	0.0662810i
$589$		−	5.31545i		−	0.219019i
$590$	−10.1820	+	1.89116i	−0.419187	+	0.0778577i
$591$	15.1076			0.621442
$592$	−27.8856	−	30.8749i	−1.14609	−	1.26895i
$593$	4.63806			0.190462			0.0952311	−	0.995455i	$-0.469641\pi$
$593$	4.63806			0.190462			0.0952311	+	0.995455i	$0.469641\pi$
$594$	−14.0117	+	2.60247i	−0.574908	+	0.106781i
$595$			3.57240i			0.146454i
$596$	−6.31636	−	16.4171i	−0.258728	−	0.672471i
$597$			0.904757i			0.0370292i
$598$	9.62052	+	51.7970i	0.393412	+	2.11814i
$599$	40.2975			1.64651			0.823256	−	0.567671i	$-0.192155\pi$
$599$	40.2975			1.64651			0.823256	+	0.567671i	$0.192155\pi$
$600$	−1.27487	−	2.07505i	−0.0520465	−	0.0847136i
$601$	−19.7379			−0.805126			−0.402563	−	0.915392i	$-0.631881\pi$
$601$	−19.7379			−0.805126			−0.402563	+	0.915392i	$0.631881\pi$
$602$	−2.45338	−	13.2090i	−0.0999923	−	0.538360i
$603$			26.5150i			1.07977i
$604$	−23.4928	+	9.03869i	−0.955909	+	0.367779i
$605$		−	6.04671i		−	0.245834i
$606$	−4.61574	+	0.857305i	−0.187502	+	0.0348256i
$607$	−22.1777			−0.900165			−0.450082	−	0.892987i	$-0.648605\pi$
$607$	−22.1777			−0.900165			−0.450082	+	0.892987i	$0.648605\pi$
$608$	8.41446	+	6.43109i	0.341252	+	0.260815i
$609$	−3.93743			−0.159553
$610$	−9.12299	+	1.69446i	−0.369379	+	0.0686067i
$611$			60.7094i			2.45604i
$612$	−15.0610	+	5.79462i	−0.608806	+	0.234234i
$613$		−	15.6225i		−	0.630985i	−0.948928	−	0.315493i	$-0.897830\pi$
$613$		−	15.6225i		−	0.630985i	0.948928	−	0.315493i	$-0.102170\pi$
$614$	−3.21155	−	17.2910i	−0.129608	−	0.697809i
$615$	−5.56829			−0.224535
$616$	−3.29526	−	5.36354i	−0.132770	−	0.216103i
$617$	−29.5418			−1.18931			−0.594653	−	0.803982i	$-0.702711\pi$
$617$	−29.5418			−1.18931			−0.594653	+	0.803982i	$0.702711\pi$
$618$	4.12936	+	22.2325i	0.166107	+	0.894324i
$619$			0.465810i			0.0187225i	0.999956	+	0.00936125i	$0.00297982\pi$
$619$			0.465810i			0.0187225i	−0.999956	+	0.00936125i	$0.997020\pi$
$620$	−2.03900	−	5.29963i	−0.0818880	−	0.212838i
$621$		−	28.9825i		−	1.16303i
$622$	−22.4096	+	4.16224i	−0.898542	+	0.166891i
$623$	−13.2611			−0.531295
$624$	−14.8755	+	13.4352i	−0.595495	+	0.537840i
$625$	1.00000			0.0400000
$626$	−43.7608	+	8.12791i	−1.74903	+	0.324857i
$627$		−	3.58772i		−	0.143280i
$628$	14.5103	+	37.7144i	0.579026	+	1.50497i
$629$			37.1562i			1.48151i
$630$	0.583291	+	3.14045i	0.0232389	+	0.125118i
$631$	−47.8907			−1.90650			−0.953250	−	0.302182i	$-0.902285\pi$
$631$	−47.8907			−1.90650			−0.953250	+	0.302182i	$0.902285\pi$
$632$	11.5658	−	7.10584i	0.460065	−	0.282655i
$633$	5.42227			0.215516
$634$	3.15126	+	16.9664i	0.125152	+	0.673822i
$635$			3.01621i			0.119695i
$636$	9.51101	−	3.65929i	0.377136	−	0.145100i
$637$		−	5.81986i		−	0.230591i
$638$	−14.1510	+	2.62833i	−0.560243	+	0.104057i
$639$	−7.29103			−0.288429
$640$	10.8564	+	3.18418i	0.429136	+	0.125866i
$641$	37.4537			1.47933			0.739666	−	0.672974i	$-0.234984\pi$
$641$	37.4537			1.47933			0.739666	+	0.672974i	$0.234984\pi$
$642$	−7.51027	+	1.39492i	−0.296407	+	0.0550531i
$643$		−	7.45000i		−	0.293799i	−0.989151	−	0.146900i	$-0.953071\pi$
$643$		−	7.45000i		−	0.293799i	0.989151	−	0.146900i	$-0.0469294\pi$
$644$	11.9480	−	4.59691i	0.470817	−	0.181144i
$645$		−	8.17983i		−	0.322081i
$646$	−1.72724	−	9.29946i	−0.0679572	−	0.365882i
$647$	−36.3684			−1.42979			−0.714894	−	0.699233i	$-0.753525\pi$
$647$	−36.3684			−1.42979			−0.714894	+	0.699233i	$0.753525\pi$
$648$	−6.93370	+	4.25994i	−0.272382	+	0.167346i
$649$	−16.2978			−0.639746
$650$	−1.50299	−	8.09213i	−0.0589522	−	0.317400i
$651$		−	2.44464i		−	0.0958132i
$652$	13.8777	+	36.0701i	0.543494	+	1.41262i
$653$			16.1170i			0.630707i	0.948974	+	0.315354i	$0.102123\pi$
$653$			16.1170i			0.630707i	−0.948974	+	0.315354i	$0.897877\pi$
$654$	−15.6706	+	2.91058i	−0.612768	+	0.113813i
$655$	−6.82237			−0.266572
$656$	19.1969	−	17.3383i	0.749514	−	0.676947i
$657$	−2.77381			−0.108217
$658$	14.5042	−	2.69394i	0.565432	−	0.105021i
$659$		−	16.7915i		−	0.654105i	−0.945006	−	0.327053i	$-0.893945\pi$
$659$		−	16.7915i		−	0.654105i	0.945006	−	0.327053i	$-0.106055\pi$
$660$	−1.37624	−	3.57705i	−0.0535702	−	0.139236i
$661$			0.951853i			0.0370228i	0.999829	+	0.0185114i	$0.00589270\pi$
$661$			0.951853i			0.0370228i	−0.999829	+	0.0185114i	$0.994107\pi$
$662$	−0.519725	−	2.79820i	−0.0201997	−	0.108755i
$663$	17.9018			0.695247
$664$	−1.29208	−	2.10306i	−0.0501424	−	0.0816144i
$665$	−1.87218			−0.0726001
$666$	6.06675	+	32.6635i	0.235082	+	1.26568i
$667$		−	29.2706i		−	1.13336i
$668$	5.46992	−	2.10451i	0.211637	−	0.0814260i
$669$		−	4.26017i		−	0.164708i
$670$	−16.3230	+	3.03176i	−0.630614	+	0.117127i
$671$	−14.6027			−0.563732
$672$	3.86992	+	2.95774i	0.149285	+	0.114097i
$673$	10.2242			0.394115			0.197057	−	0.980392i	$-0.436861\pi$
$673$	10.2242			0.394115			0.197057	+	0.980392i	$0.436861\pi$
$674$	−2.55634	+	0.474801i	−0.0984664	+	0.0182887i
$675$			4.52788i			0.174278i
$676$	−38.9577	+	14.9887i	−1.49837	+	0.576488i
$677$			19.0538i			0.732297i	0.930556	+	0.366148i	$0.119324\pi$
$677$			19.0538i			0.732297i	−0.930556	+	0.366148i	$0.880676\pi$
$678$	1.57380	+	8.47334i	0.0604413	+	0.325417i
$679$	8.62317			0.330927
$680$	−5.28935	−	8.60923i	−0.202837	−	0.330149i
$681$	−24.6421			−0.944288
$682$	−1.63186	−	8.78596i	−0.0624872	−	0.336432i
$683$		−	1.60649i		−	0.0614707i	−0.999528	−	0.0307354i	$-0.990215\pi$
$683$		−	1.60649i		−	0.0614707i	0.999528	−	0.0307354i	$-0.00978491\pi$
$684$	−3.03678	−	7.89301i	−0.116114	−	0.301797i
$685$		−	6.96872i		−	0.266261i
$686$	−1.39043	+	0.258252i	−0.0530870	+	0.00986012i
$687$	1.02446			0.0390855
$688$	25.4700	+	28.2003i	0.971035	+	1.07513i
$689$	34.4399			1.31205
$690$	7.66330	−	1.42334i	0.291737	−	0.0541857i
$691$		−	37.1550i		−	1.41344i	−0.707492	−	0.706721i	$-0.750174\pi$
$691$		−	37.1550i		−	1.41344i	0.707492	−	0.706721i	$-0.249826\pi$
$692$	7.87155	+	20.4592i	0.299231	+	0.777743i
$693$			5.02676i			0.190951i
$694$	9.03255	+	48.6314i	0.342871	+	1.84602i
$695$	0.178109			0.00675606
$696$	9.48894	−	5.82984i	0.359678	−	0.220979i
$697$	−23.1024			−0.875066
$698$	−2.22094	−	11.9576i	−0.0840637	−	0.452600i
$699$			8.77880i			0.332045i
$700$	−1.86661	+	0.718165i	−0.0705513	+	0.0271441i
$701$		−	22.7570i		−	0.859520i	−0.902943	−	0.429760i	$-0.858598\pi$
$701$		−	22.7570i		−	0.859520i	0.902943	−	0.429760i	$-0.141402\pi$
$702$	36.6402	−	6.80537i	1.38289	−	0.256852i
$703$	−19.4724			−0.734415
$704$	15.8827	+	8.04674i	0.598602	+	0.303273i
$705$	8.98187			0.338277
$706$	42.3917	−	7.87363i	1.59543	−	0.296328i
$707$			3.85538i			0.144997i
$708$	11.7696	−	4.52826i	0.442328	−	0.170182i
$709$		−	29.9997i		−	1.12666i	−0.826231	−	0.563332i	$-0.809519\pi$
$709$		−	29.9997i		−	1.12666i	0.826231	−	0.563332i	$-0.190481\pi$
$710$	−0.833666	−	4.48847i	−0.0312869	−	0.168449i
$711$	−10.8396			−0.406517
$712$	31.9583	−	19.6346i	1.19769	−	0.735839i
$713$	18.1733			0.680595
$714$	−0.794379	−	4.27694i	−0.0297289	−	0.160061i
$715$		−	12.9527i		−	0.484403i
$716$	−11.4405	−	29.7353i	−0.427550	−	1.11126i
$717$			20.8775i			0.779686i
$718$	22.2943	−	4.14084i	0.832017	−	0.154535i
$719$	3.59889			0.134216			0.0671079	−	0.997746i	$-0.478623\pi$
$719$	3.59889			0.134216			0.0671079	+	0.997746i	$0.478623\pi$
$720$	−6.05549	−	6.70463i	−0.225675	−	0.249867i
$721$	18.5701			0.691588
$722$	−21.5447	+	4.00160i	−0.801810	+	0.148924i
$723$			9.05011i			0.336577i
$724$	−17.5009	−	45.4872i	−0.650414	−	1.69052i
$725$			4.57288i			0.169832i
$726$	1.34458	+	7.23924i	0.0499021	+	0.268674i
$727$	−7.87212			−0.291961			−0.145980	−	0.989287i	$-0.546634\pi$
$727$	−7.87212			−0.291961			−0.145980	+	0.989287i	$0.546634\pi$
$728$	8.61699	+	14.0255i	0.319367	+	0.519819i
$729$	−5.19774			−0.192509
$730$	−0.317162	−	1.70760i	−0.0117387	−	0.0632012i
$731$		−	33.9375i		−	1.25522i
$732$	10.5454	−	4.05728i	0.389771	−	0.149961i
$733$			23.4101i			0.864673i	0.901712	+	0.432336i	$0.142311\pi$
$733$			23.4101i			0.864673i	−0.901712	+	0.432336i	$0.857689\pi$
$734$	35.5967	−	6.61155i	1.31390	−	0.244037i
$735$	−0.861041			−0.0317600
$736$	−21.9876	+	28.7687i	−0.810474	+	1.06043i
$737$	−26.1275			−0.962419
$738$	−20.3090	+	3.77210i	−0.747586	+	0.138853i
$739$			37.1844i			1.36785i	0.729553	+	0.683924i	$0.239728\pi$
$739$			37.1844i			1.36785i	−0.729553	+	0.683924i	$0.760272\pi$
$740$	−19.4145	+	7.46957i	−0.713689	+	0.274587i
$741$			9.38177i			0.344648i
$742$	−1.52825	−	8.22809i	−0.0561037	−	0.302063i
$743$	5.99428			0.219909			0.109954	−	0.993937i	$-0.464930\pi$
$743$	5.99428			0.219909			0.109954	+	0.993937i	$0.464930\pi$
$744$	3.61958	+	5.89142i	0.132700	+	0.215990i
$745$	−8.79513			−0.322229
$746$	5.89293	+	31.7276i	0.215756	+	1.16163i
$747$			1.97100i			0.0721152i
$748$	−5.70993	−	14.8409i	−0.208776	−	0.542637i
$749$			6.27309i			0.229214i
$750$	−1.19722	+	0.222366i	−0.0437163	+	0.00811965i
$751$	18.5868			0.678241			0.339120	−	0.940743i	$-0.389871\pi$
$751$	18.5868			0.678241			0.339120	+	0.940743i	$0.389871\pi$
$752$	−30.9654	+	27.9674i	−1.12919	+	1.01986i
$753$	−8.34202			−0.304000
$754$	37.0043	−	6.87300i	1.34762	−	0.250300i
$755$			12.5858i			0.458044i
$756$	−3.25177	−	8.45179i	−0.118266	−	0.307389i
$757$		−	42.5555i		−	1.54670i	−0.633977	−	0.773352i	$-0.718579\pi$
$757$		−	42.5555i		−	1.54670i	0.633977	−	0.773352i	$-0.281421\pi$
$758$	−4.37196	−	23.5387i	−0.158797	−	0.854963i
$759$	12.2663			0.445237
$760$	4.51183	−	2.77199i	0.163661	−	0.100551i
$761$	−9.78893			−0.354849			−0.177424	−	0.984134i	$-0.556776\pi$
$761$	−9.78893			−0.354849			−0.177424	+	0.984134i	$0.556776\pi$
$762$	−0.670702	−	3.61107i	−0.0242970	−	0.130815i
$763$			13.0891i			0.473858i
$764$	14.8284	−	5.70513i	0.536473	−	0.206404i
$765$			8.06864i			0.291722i
$766$	−19.8906	+	3.69438i	−0.718676	+	0.133483i
$767$	42.6183			1.53886
$768$	−13.7055	−	1.39808i	−0.494556	−	0.0504488i
$769$	34.2947			1.23670			0.618349	−	0.785903i	$-0.287802\pi$
$769$	34.2947			1.23670			0.618349	+	0.785903i	$0.287802\pi$
$770$	−3.09455	+	0.574766i	−0.111520	+	0.0207131i
$771$		−	3.49969i		−	0.126038i
$772$	−48.9504	+	18.8333i	−1.76176	+	0.677826i
$773$		−	34.1445i		−	1.22809i	−0.789270	−	0.614046i	$-0.789541\pi$
$773$		−	34.1445i		−	1.22809i	0.789270	−	0.614046i	$-0.210459\pi$
$774$	−5.54123	−	29.8340i	−0.199175	−	1.07236i
$775$	−2.83917			−0.101986
$776$	−20.7812	+	12.7676i	−0.746003	+	0.458331i
$777$	−8.95561			−0.321281
$778$	4.59714	+	24.7510i	0.164815	+	0.887368i
$779$		−	12.1073i		−	0.433788i
$780$	3.59883	+	9.35385i	0.128859	+	0.334922i
$781$		−	7.18447i		−	0.257081i
$782$	31.7945	−	5.90535i	1.13697	−	0.211175i
$783$	−20.7054			−0.739951
$784$	2.96848	−	2.68107i	0.106017	−	0.0957526i
$785$	20.2047			0.721138
$786$	8.16788	−	1.51706i	0.291339	−	0.0541118i
$787$		−	18.9204i		−	0.674439i	−0.941426	−	0.337219i	$-0.890514\pi$
$787$		−	18.9204i		−	0.674439i	0.941426	−	0.337219i	$-0.109486\pi$
$788$	12.6007	+	32.7510i	0.448882	+	1.16671i
$789$		−	2.01905i		−	0.0718802i
$790$	−1.23942	−	6.67303i	−0.0440964	−	0.237416i
$791$	7.07751			0.251647
$792$	−7.44271	−	12.1141i	−0.264465	−	0.430457i
$793$	38.1856			1.35601
$794$	−1.81818	−	9.78911i	−0.0645249	−	0.347403i
$795$		−	5.09533i		−	0.180713i
$796$	−1.96138	+	0.754627i	−0.0695193	+	0.0267471i
$797$		−	46.0941i		−	1.63274i	−0.577532	−	0.816368i	$-0.695984\pi$
$797$		−	46.0941i		−	1.63274i	0.577532	−	0.816368i	$-0.304016\pi$
$798$	2.24141	−	0.416309i	0.0793452	−	0.0147372i
$799$	37.2651			1.31835
$800$	3.43508	−	4.49447i	0.121448	−	0.158903i
$801$	−29.9516			−1.05829
$802$	−30.4086	+	5.64794i	−1.07376	+	0.199436i
$803$		−	2.73327i		−	0.0964551i
$804$	18.8681	−	7.25938i	0.665427	−	0.256018i
$805$		−	6.40091i		−	0.225602i
$806$	4.26726	+	22.9750i	0.150308	+	0.809259i
$807$	18.6143			0.655256
$808$	−5.70835	−	9.29120i	−0.200819	−	0.326863i
$809$	−8.28447			−0.291267			−0.145633	−	0.989339i	$-0.546522\pi$
$809$	−8.28447			−0.291267			−0.145633	+	0.989339i	$0.546522\pi$
$810$	0.743027	+	4.00047i	0.0261073	+	0.140562i
$811$		−	51.0687i		−	1.79326i	−0.442777	−	0.896632i	$-0.646007\pi$
$811$		−	51.0687i		−	1.79326i	0.442777	−	0.896632i	$-0.353993\pi$
$812$	−3.28408	−	8.53578i	−0.115249	−	0.299547i
$813$			17.4322i			0.611375i
$814$	−32.1861	+	5.97809i	−1.12812	+	0.209532i
$815$	19.3239			0.676885
$816$	8.24692	+	9.13097i	0.288700	+	0.319648i
$817$	17.7856			0.622240
$818$	−12.7853	+	2.37468i	−0.447028	+	0.0830289i
$819$		−	13.1448i		−	0.459316i
$820$	−4.64432	−	12.0712i	−0.162187	−	0.421546i
$821$			39.6347i			1.38326i	0.722251	+	0.691631i	$0.243107\pi$
$821$			39.6347i			1.38326i	−0.722251	+	0.691631i	$0.756893\pi$
$822$	1.54960	+	8.34309i	0.0540487	+	0.290999i
$823$	−29.0114			−1.01127			−0.505637	−	0.862746i	$-0.668743\pi$
$823$	−29.0114			−1.01127			−0.505637	+	0.862746i	$0.668743\pi$
$824$	−44.7527	+	27.4953i	−1.55904	+	0.957843i
$825$	−1.91633			−0.0667181
$826$	−1.89116	−	10.1820i	−0.0658017	−	0.354277i
$827$		−	42.6709i		−	1.48381i	−0.670504	−	0.741906i	$-0.733922\pi$
$827$		−	42.6709i		−	1.48381i	0.670504	−	0.741906i	$-0.266078\pi$
$828$	26.9859	−	10.3826i	0.937824	−	0.360821i
$829$		−	32.0586i		−	1.11344i	−0.830700	−	0.556720i	$-0.812060\pi$
$829$		−	32.0586i		−	1.11344i	0.830700	−	0.556720i	$-0.187940\pi$
$830$	−1.21338	+	0.225367i	−0.0421170	+	0.00782260i
$831$	2.33931			0.0811496
$832$	−41.5327	−	21.0419i	−1.43989	−	0.729498i
$833$	−3.57240			−0.123776
$834$	−0.213236	+	0.0396053i	−0.00738375	+	0.00137142i
$835$		−	2.93040i		−	0.101411i
$836$	7.77766	−	2.99240i	0.268996	−	0.103494i
$837$		−	12.8554i		−	0.444349i
$838$	−5.98894	−	32.2445i	−0.206884	−	1.11387i
$839$	−20.3563			−0.702776			−0.351388	−	0.936230i	$-0.614290\pi$
$839$	−20.3563			−0.702776			−0.351388	+	0.936230i	$0.614290\pi$
$840$	2.07505	−	1.27487i	0.0715960	−	0.0439873i
$841$	8.08881			0.278924
$842$	4.06935	+	21.9094i	0.140239	+	0.755048i
$843$		−	17.9006i		−	0.616531i
$844$	4.52253	+	11.7547i	0.155672	+	0.404613i
$845$			20.8708i			0.717978i
$846$	32.7593	−	6.08455i	1.12629	−	0.209191i
$847$	6.04671			0.207767
$848$	15.8656	+	17.5664i	0.544828	+	0.603232i
$849$	3.76298			0.129145
$850$	−4.96718	+	0.922579i	−0.170373	+	0.0316442i
$851$		−	66.5752i		−	2.28217i
$852$	1.99616	+	5.18831i	0.0683875	+	0.177748i
$853$		−	5.29815i		−	0.181405i	−0.995878	−	0.0907026i	$-0.971089\pi$
$853$		−	5.29815i		−	0.181405i	0.995878	−	0.0907026i	$-0.0289113\pi$
$854$	−1.69446	−	9.12299i	−0.0579832	−	0.312182i
$855$	−4.22853			−0.144613
$856$	−9.28805	−	15.1177i	−0.317459	−	0.516713i
$857$	56.2615			1.92185			0.960927	−	0.276801i	$-0.0892743\pi$
$857$	56.2615			1.92185			0.960927	+	0.276801i	$0.0892743\pi$
$858$	2.88023	+	15.5072i	0.0983296	+	0.529408i
$859$			23.5706i			0.804220i	0.915591	+	0.402110i	$0.131723\pi$
$859$			23.5706i			0.804220i	−0.915591	+	0.402110i	$0.868277\pi$
$860$	17.7327	−	6.82253i	0.604680	−	0.232646i
$861$		−	5.56829i		−	0.189767i
$862$	−12.0533	+	2.23872i	−0.410537	+	0.0762512i
$863$	−53.0398			−1.80550			−0.902748	−	0.430170i	$-0.858454\pi$
$863$	−53.0398			−1.80550			−0.902748	+	0.430170i	$0.858454\pi$
$864$	20.3504	+	15.5536i	0.692335	+	0.529144i
$865$	10.9606			0.372673
$866$	31.6436	−	5.87733i	1.07529	−	0.199720i
$867$			3.64908i			0.123929i
$868$	5.29963	−	2.03900i	0.179881	−	0.0692080i
$869$		−	10.6812i		−	0.362334i
$870$	−1.01685	−	5.47474i	−0.0344745	−	0.185611i
$871$	68.3225			2.31502
$872$	−19.3800	−	31.5439i	−0.656290	−	1.06821i
$873$	19.4764			0.659175
$874$	3.09481	+	16.6625i	0.104683	+	0.563617i
$875$			1.00000i			0.0338062i
$876$	0.759424	+	1.97385i	0.0256586	+	0.0666902i
$877$			2.32917i			0.0786504i	0.999226	+	0.0393252i	$0.0125208\pi$
$877$			2.32917i			0.0786504i	−0.999226	+	0.0393252i	$0.987479\pi$
$878$	21.9389	−	4.07482i	0.740401	−	0.137519i
$879$	−4.61689			−0.155724
$880$	6.60664	−	5.96699i	0.222710	−	0.201147i
$881$	−21.3636			−0.719758			−0.359879	−	0.932999i	$-0.617182\pi$
$881$	−21.3636			−0.719758			−0.359879	+	0.932999i	$0.617182\pi$
$882$	−3.14045	+	0.583291i	−0.105744	+	0.0196404i
$883$		−	34.0046i		−	1.14435i	−0.820133	−	0.572173i	$-0.806101\pi$
$883$		−	34.0046i		−	1.14435i	0.820133	−	0.572173i	$-0.193899\pi$
$884$	14.9313	+	38.8084i	0.502193	+	1.30527i
$885$		−	6.30532i		−	0.211951i
$886$	2.64035	+	14.2157i	0.0887044	+	0.477586i
$887$	−36.6557			−1.23078			−0.615389	−	0.788224i	$-0.711001\pi$
$887$	−36.6557			−1.23078			−0.615389	+	0.788224i	$0.711001\pi$
$888$	21.5824	−	13.2598i	0.724258	−	0.444971i
$889$	−3.01621			−0.101160
$890$	−3.42471	−	18.4387i	−0.114797	−	0.618066i
$891$			6.40335i			0.214520i
$892$	9.23543	−	3.55327i	0.309225	−	0.118972i
$893$			19.5295i			0.653530i
$894$	10.5297	−	1.95574i	0.352166	−	0.0654097i
$895$	−15.9301			−0.532485
$896$	−3.18418	+	10.8564i	−0.106376	+	0.362686i
$897$	−32.0758			−1.07098
$898$	−3.67966	+	0.683442i	−0.122792	+	0.0228068i
$899$		−	12.9832i		−	0.433013i
$900$	−4.21594	+	1.62205i	−0.140531	+	0.0540685i
$901$		−	21.1402i		−	0.704281i
$902$	−3.71697	−	20.0122i	−0.123762	−	0.666334i
$903$	8.17983			0.272208
$904$	−17.0563	+	10.4791i	−0.567285	+	0.348529i
$905$	−24.3688			−0.810048
$906$	−2.79865	−	15.0680i	−0.0929791	−	0.500600i
$907$		−	6.63971i		−	0.220468i	−0.993906	−	0.110234i	$-0.964840\pi$
$907$		−	6.63971i		−	0.220468i	0.993906	−	0.110234i	$-0.0351600\pi$
$908$	−20.5532	−	53.4205i	−0.682081	−	1.77282i
$909$			8.70779i			0.288819i
$910$	8.09213	−	1.50299i	0.268252	−	0.0498237i
$911$	38.1305			1.26332			0.631659	−	0.775246i	$-0.282374\pi$
$911$	38.1305			1.26332			0.631659	+	0.775246i	$0.282374\pi$
$912$	−4.78526	+	4.32196i	−0.158456	+	0.143114i
$913$	−1.94220			−0.0642773
$914$	−53.6966	+	9.97334i	−1.77612	+	0.329889i
$915$		−	5.64951i		−	0.186767i
$916$	0.854465	+	2.22087i	0.0282323	+	0.0733797i
$917$		−	6.82237i		−	0.225295i
$918$	−4.17733	−	22.4908i	−0.137872	−	0.742306i
$919$	20.3296			0.670611			0.335305	−	0.942110i	$-0.391161\pi$
$919$	20.3296			0.670611			0.335305	+	0.942110i	$0.391161\pi$
$920$	9.47730	+	15.4257i	0.312457	+	0.508572i
$921$	10.7077			0.352829
$922$	−1.71694	−	9.24401i	−0.0565443	−	0.304435i
$923$			18.7871i			0.618386i
$924$	3.57705	−	1.37624i	0.117676	−	0.0452751i
$925$			10.4009i			0.341980i
$926$	−51.3958	+	9.54600i	−1.68897	+	0.313701i
$927$	41.9426			1.37758
$928$	20.5526	+	15.7082i	0.674674	+	0.515646i
$929$	14.7472			0.483841			0.241921	−	0.970296i	$-0.422223\pi$
$929$	14.7472			0.483841			0.241921	+	0.970296i	$0.422223\pi$
$930$	3.39912	−	0.631335i	0.111461	−	0.0207023i
$931$		−	1.87218i		−	0.0613583i
$932$	−19.0312	+	7.32210i	−0.623386	+	0.239843i
$933$		−	13.8774i		−	0.454325i
$934$	2.18704	+	11.7750i	0.0715621	+	0.385291i
$935$	−7.95072			−0.260016
$936$	19.4624	+	31.6780i	0.636149	+	1.03543i
$937$	1.94684			0.0636005			0.0318002	−	0.999494i	$-0.489876\pi$
$937$	1.94684			0.0636005			0.0318002	+	0.999494i	$0.489876\pi$
$938$	−3.03176	−	16.3230i	−0.0989905	−	0.532966i
$939$		−	27.0993i		−	0.884353i
$940$	7.49148	+	19.4714i	0.244345	+	0.635087i
$941$		−	17.9023i		−	0.583599i	−0.956480	−	0.291799i	$-0.905746\pi$
$941$		−	17.9023i		−	0.583599i	0.956480	−	0.291799i	$-0.0942540\pi$
$942$	−24.1895	+	4.49284i	−0.788137	+	0.146385i
$943$	41.3942			1.34798
$944$	19.6332	+	21.7379i	0.639007	+	0.707507i
$945$	−4.52788			−0.147292
$946$	29.3980	−	5.46024i	0.955812	−	0.177528i
$947$			36.4781i			1.18538i	0.805431	+	0.592689i	$0.201934\pi$
$947$			36.4781i			1.18538i	−0.805431	+	0.592689i	$0.798066\pi$
$948$	2.96771	+	7.71348i	0.0963866	+	0.250522i
$949$			7.14741i			0.232015i
$950$	−0.483495	−	2.60314i	−0.0156867	−	0.0844572i
$951$	−10.5066			−0.340701
$952$	8.60923	−	5.28935i	0.279027	−	0.171429i
$953$	42.1319			1.36479			0.682393	−	0.730986i	$-0.260940\pi$
$953$	42.1319			1.36479			0.682393	+	0.730986i	$0.260940\pi$
$954$	−3.45171	−	18.5840i	−0.111753	−	0.601680i
$955$		−	7.94403i		−	0.257063i
$956$	−45.2595	+	17.4133i	−1.46380	+	0.563185i
$957$		−	8.76315i		−	0.283272i
$958$	0.00175328		0.000325645i	5.66458e−5		1.05211e-5i
$959$	6.96872			0.225032
$960$	−3.11313	+	6.14471i	−0.100476	+	0.198320i
$961$	−22.9391			−0.739971
$962$	84.1655	−	15.6325i	2.71361	−	0.504012i
$963$			14.1685i			0.456572i
$964$	−19.6193	+	7.54839i	−0.631896	+	0.243117i
$965$			26.2242i			0.844188i
$966$	1.42334	+	7.66330i	0.0457953	+	0.246563i
$967$	−3.82231			−0.122917			−0.0614585	−	0.998110i	$-0.519575\pi$
$967$	−3.82231			−0.122917			−0.0614585	+	0.998110i	$0.519575\pi$
$968$	−14.5722	+	8.95287i	−0.468367	+	0.287756i
$969$	5.75879			0.184999
$970$	2.22695	+	11.9899i	0.0715031	+	0.384974i
$971$			57.1336i			1.83350i	0.399456	+	0.916752i	$0.369199\pi$
$971$			57.1336i			1.83350i	−0.399456	+	0.916752i	$0.630801\pi$
$972$	−11.5344	−	29.9796i	−0.369967	−	0.961596i
$973$			0.178109i			0.00570991i
$974$	3.26620	−	0.606649i	0.104656	−	0.0194383i
$975$	5.01114			0.160485
$976$	17.5912	+	19.4769i	0.563080	+	0.623441i
$977$	−50.1437			−1.60424			−0.802119	−	0.597165i	$-0.796294\pi$
$977$	−50.1437			−1.60424			−0.802119	+	0.597165i	$0.796294\pi$
$978$	−23.1349	+	4.29697i	−0.739773	+	0.137402i
$979$		−	29.5139i		−	0.943268i
$980$	−0.718165	−	1.86661i	−0.0229410	−	0.0596267i
$981$			29.5632i			0.943881i
$982$	3.26596	+	17.5840i	0.104221	+	0.561127i
$983$	−38.5456			−1.22941			−0.614706	−	0.788756i	$-0.710726\pi$
$983$	−38.5456			−1.22941			−0.614706	+	0.788756i	$0.710726\pi$
$984$	8.24451	+	13.4192i	0.262825	+	0.427788i
$985$	17.5457			0.559052
$986$	−4.21884	−	22.7143i	−0.134355	−	0.723370i
$987$			8.98187i			0.285896i
$988$	−20.3383	+	7.82502i	−0.647048	+	0.248947i
$989$			60.8082i			1.93359i
$990$	−6.98937	+	1.29817i	−0.222137	+	0.0412586i
$991$	−1.79872			−0.0571382			−0.0285691	−	0.999592i	$-0.509095\pi$
$991$	−1.79872			−0.0571382			−0.0285691	+	0.999592i	$0.509095\pi$
$992$	−9.75278	+	12.7606i	−0.309651	+	0.405149i
$993$	1.73282			0.0549893
$994$	4.48847	−	0.833666i	0.142366	−	0.0264423i
$995$			1.05077i			0.0333117i
$996$	1.40257	−	0.539628i	0.0444421	−	0.0170988i
$997$			9.44578i			0.299151i	0.988750	+	0.149575i	$0.0477907\pi$
$997$			9.44578i			0.299151i	−0.988750	+	0.149575i	$0.952209\pi$
$998$	−2.87645	−	15.4868i	−0.0910524	−	0.490227i
$999$	−47.0940			−1.48999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.2	yes	12
4.3	odd	2		1120.2.b.d.561.7		12
8.3	odd	2		1120.2.b.d.561.6		12
8.5	even	2	inner	280.2.b.d.141.1	✓	12
16.3	odd	4		8960.2.a.cd.1.3		6
16.5	even	4		8960.2.a.cf.1.3		6
16.11	odd	4		8960.2.a.cg.1.4		6
16.13	even	4		8960.2.a.ca.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.1	✓	12	8.5	even	2	inner
280.2.b.d.141.2	yes	12	1.1	even	1	trivial
1120.2.b.d.561.6		12	8.3	odd	2
1120.2.b.d.561.7		12	4.3	odd	2
8960.2.a.ca.1.4		6	16.13	even	4
8960.2.a.cd.1.3		6	16.3	odd	4
8960.2.a.cf.1.3		6	16.5	even	4
8960.2.a.cg.1.4		6	16.11	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39043 + 0.258252i) q^{2} -0.861041i q^{3} +(1.86661 - 0.718165i) q^{4} -1.00000i q^{5} +(0.222366 + 1.19722i) q^{6} +1.00000 q^{7} +(-2.40993 + 1.48062i) q^{8} +2.25861 q^{9} +O(q^{10})\)	\(q+(-1.39043 + 0.258252i) q^{2} -0.861041i q^{3} +(1.86661 - 0.718165i) q^{4} -1.00000i q^{5} +(0.222366 + 1.19722i) q^{6} +1.00000 q^{7} +(-2.40993 + 1.48062i) q^{8} +2.25861 q^{9} +(0.258252 + 1.39043i) q^{10} +2.22560i q^{11} +(-0.618370 - 1.60723i) q^{12} -5.81986i q^{13} +(-1.39043 + 0.258252i) q^{14} -0.861041 q^{15} +(2.96848 - 2.68107i) q^{16} -3.57240 q^{17} +(-3.14045 + 0.583291i) q^{18} -1.87218i q^{19} +(-0.718165 - 1.86661i) q^{20} -0.861041i q^{21} +(-0.574766 - 3.09455i) q^{22} +6.40091 q^{23} +(1.27487 + 2.07505i) q^{24} -1.00000 q^{25} +(1.50299 + 8.09213i) q^{26} -4.52788i q^{27} +(1.86661 - 0.718165i) q^{28} -4.57288i q^{29} +(1.19722 - 0.222366i) q^{30} +2.83917 q^{31} +(-3.43508 + 4.49447i) q^{32} +1.91633 q^{33} +(4.96718 - 0.922579i) q^{34} -1.00000i q^{35} +(4.21594 - 1.62205i) q^{36} -10.4009i q^{37} +(0.483495 + 2.60314i) q^{38} -5.01114 q^{39} +(1.48062 + 2.40993i) q^{40} +6.46693 q^{41} +(0.222366 + 1.19722i) q^{42} +9.49994i q^{43} +(1.59835 + 4.15433i) q^{44} -2.25861i q^{45} +(-8.90004 + 1.65305i) q^{46} -10.4314 q^{47} +(-2.30851 - 2.55598i) q^{48} +1.00000 q^{49} +(1.39043 - 0.258252i) q^{50} +3.07598i q^{51} +(-4.17962 - 10.8634i) q^{52} +5.91764i q^{53} +(1.16933 + 6.29571i) q^{54} +2.22560 q^{55} +(-2.40993 + 1.48062i) q^{56} -1.61203 q^{57} +(1.18096 + 6.35828i) q^{58} +7.32290i q^{59} +(-1.60723 + 0.618370i) q^{60} +6.56125i q^{61} +(-3.94768 + 0.733223i) q^{62} +2.25861 q^{63} +(3.61554 - 7.13638i) q^{64} -5.81986 q^{65} +(-2.66453 + 0.494897i) q^{66} +11.7395i q^{67} +(-6.66827 + 2.56557i) q^{68} -5.51144i q^{69} +(0.258252 + 1.39043i) q^{70} -3.22811 q^{71} +(-5.44309 + 3.34414i) q^{72} -1.22811 q^{73} +(2.68606 + 14.4618i) q^{74} +0.861041i q^{75} +(-1.34454 - 3.49464i) q^{76} +2.22560i q^{77} +(6.96766 - 1.29414i) q^{78} -4.79924 q^{79} +(-2.68107 - 2.96848i) q^{80} +2.87714 q^{81} +(-8.99183 + 1.67010i) q^{82} +0.872662i q^{83} +(-0.618370 - 1.60723i) q^{84} +3.57240i q^{85} +(-2.45338 - 13.2090i) q^{86} -3.93743 q^{87} +(-3.29526 - 5.36354i) q^{88} -13.2611 q^{89} +(0.583291 + 3.14045i) q^{90} -5.81986i q^{91} +(11.9480 - 4.59691i) q^{92} -2.44464i q^{93} +(14.5042 - 2.69394i) q^{94} -1.87218 q^{95} +(3.86992 + 2.95774i) q^{96} +8.62317 q^{97} +(-1.39043 + 0.258252i) q^{98} +5.02676i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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