LMFDB - Embedded newform 980.2.g.a.391.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.20
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +O(q^{10})$	\(q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(-1.41080 + 0.0982654i) q^{10} -3.61296i q^{11} +(-1.31192 + 0.183648i) q^{12} -5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} -1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} -4.09577 q^{19} +(-0.277265 - 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(-0.388005 - 1.83280i) q^{24} -1.00000 q^{25} +(8.22532 - 0.572914i) q^{26} -3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} -8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} -2.39306i q^{33} +(1.93014 - 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(-0.402472 - 5.77829i) q^{38} -3.86171i q^{39} +(2.76710 - 0.585797i) q^{40} +0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} -2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} -6.89601 q^{47} +(2.54758 - 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(1.61653 + 11.5479i) q^{52} -7.41752 q^{53} +(-0.361965 - 5.19673i) q^{54} +3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} +7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} -1.48554i q^{61} +(-0.871427 - 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(3.37612 - 0.235155i) q^{66} -2.53761i q^{67} +(0.379333 + 2.70983i) q^{68} -2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} -5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} -0.662355 q^{75} +(8.11244 - 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(1.09835 + 3.84625i) q^{80} +5.24405 q^{81} +(-1.17481 + 0.0818286i) q^{82} -6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} +3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} -9.39121i q^{89} +(3.61345 - 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(-0.677640 - 9.72886i) q^{94} -4.09577i q^{95} +(1.27669 + 3.52263i) q^{96} +0.343189i q^{97} +9.25383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.0982654	+	1.41080i	0.0694842	+	0.997583i
$2$	0.0982654	+	1.41080i	0.0694842	+	0.997583i
$3$	0.662355			0.382411			0.191205	−	0.981550i	$-0.438760\pi$
$3$	0.662355			0.382411			0.191205	+	0.981550i	$0.438760\pi$
$4$	−1.98069	+	0.277265i	−0.990344	+	0.138632i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.0650866	+	0.934447i	0.0265715	+	0.381486i
$7$		0			0
$7$		0			0
$8$	−0.585797	−	2.76710i	−0.207111	−	0.978318i
$9$	−2.56129			−0.853762
$10$	−1.41080	+	0.0982654i	−0.446133	+	0.0310743i
$11$		−	3.61296i		−	1.08935i	−0.838648	−	0.544674i	$-0.816653\pi$
$11$		−	3.61296i		−	1.08935i	0.838648	−	0.544674i	$-0.183347\pi$
$12$	−1.31192	+	0.183648i	−0.378718	+	0.0530145i
$13$		−	5.83027i		−	1.61703i	−0.588478	−	0.808513i	$-0.700273\pi$
$13$		−	5.83027i		−	1.61703i	0.588478	−	0.808513i	$-0.299727\pi$
$14$		0			0
$15$			0.662355i			0.171019i
$16$	3.84625	−	1.09835i	0.961562	−	0.274588i
$17$		−	1.36813i		−	0.331819i	−0.986141	−	0.165910i	$-0.946944\pi$
$17$		−	1.36813i		−	0.331819i	0.986141	−	0.165910i	$-0.0530560\pi$
$18$	−0.251686	−	3.61345i	−0.0593229	−	0.851699i
$19$	−4.09577			−0.939634			−0.469817	−	0.882764i	$-0.655680\pi$
$19$	−4.09577			−0.939634			−0.469817	+	0.882764i	$0.655680\pi$
$20$	−0.277265	−	1.98069i	−0.0619983	−	0.442895i
$21$		0			0
$22$	5.09715	−	0.355029i	1.08672	−	0.0756925i
$23$		−	3.24519i		−	0.676669i	−0.941026	−	0.338334i	$-0.890136\pi$
$23$		−	3.24519i		−	0.676669i	0.941026	−	0.338334i	$-0.109864\pi$
$24$	−0.388005	−	1.83280i	−0.0792013	−	0.374119i
$25$	−1.00000			−0.200000
$26$	8.22532	−	0.572914i	1.61312	−	0.112358i
$27$	−3.68354			−0.708898
$28$		0			0
$29$	5.19327			0.964365			0.482183	−	0.876071i	$-0.339844\pi$
$29$	5.19327			0.964365			0.482183	+	0.876071i	$0.339844\pi$
$30$	−0.934447	+	0.0650866i	−0.170606	+	0.0118831i
$31$	−8.86809			−1.59276			−0.796378	−	0.604799i	$-0.793254\pi$
$31$	−8.86809			−1.59276			−0.796378	+	0.604799i	$0.793254\pi$
$32$	1.92750	+	5.31834i	0.340737	+	0.940159i
$33$		−	2.39306i		−	0.416579i
$34$	1.93014	−	0.134439i	0.331017	−	0.0230562i
$35$		0			0
$36$	5.07311	−	0.710155i	0.845518	−	0.118359i
$37$	10.7958			1.77482			0.887408	−	0.460985i	$-0.152504\pi$
$37$	10.7958			1.77482			0.887408	+	0.460985i	$0.152504\pi$
$38$	−0.402472	−	5.77829i	−0.0652897	−	0.937363i
$39$		−	3.86171i		−	0.618368i
$40$	2.76710	−	0.585797i	0.437517	−	0.0926227i
$41$			0.832730i			0.130051i	0.997884	+	0.0650253i	$0.0207128\pi$
$41$			0.832730i			0.130051i	−0.997884	+	0.0650253i	$0.979287\pi$
$42$		0			0
$43$			3.10642i			0.473725i	0.971543	+	0.236862i	$0.0761190\pi$
$43$			3.10642i			0.473725i	−0.971543	+	0.236862i	$0.923881\pi$
$44$	1.00175	+	7.15615i	0.151019	+	1.07883i
$45$		−	2.56129i		−	0.381814i
$46$	4.57830	−	0.318890i	0.675033	−	0.0470178i
$47$	−6.89601			−1.00589			−0.502943	−	0.864319i	$-0.667750\pi$
$47$	−6.89601			−1.00589			−0.502943	+	0.864319i	$0.667750\pi$
$48$	2.54758	−	0.727497i	0.367712	−	0.105005i
$49$		0			0
$50$	−0.0982654	−	1.41080i	−0.0138968	−	0.199517i
$51$		−	0.906184i		−	0.126891i
$52$	1.61653	+	11.5479i	0.224172	+	1.60141i
$53$	−7.41752			−1.01887			−0.509437	−	0.860508i	$-0.670146\pi$
$53$	−7.41752			−1.01887			−0.509437	+	0.860508i	$0.670146\pi$
$54$	−0.361965	−	5.19673i	−0.0492572	−	0.707185i
$55$	3.61296			0.487172
$56$		0			0
$57$	−2.71285			−0.359326
$58$	0.510319	+	7.32664i	0.0670081	+	0.962034i
$59$	7.47856			0.973626			0.486813	−	0.873506i	$-0.338159\pi$
$59$	7.47856			0.973626			0.486813	+	0.873506i	$0.338159\pi$
$60$	−0.183648	−	1.31192i	−0.0237088	−	0.169368i
$61$		−	1.48554i		−	0.190204i	−0.995468	−	0.0951022i	$-0.969682\pi$
$61$		−	1.48554i		−	0.190204i	0.995468	−	0.0951022i	$-0.0303178\pi$
$62$	−0.871427	−	12.5111i	−0.110671	−	1.58891i
$63$		0			0
$64$	−7.31368	+	3.24192i	−0.914210	+	0.405240i
$65$	5.83027			0.723156
$66$	3.37612	−	0.235155i	0.415572	−	0.0289456i
$67$		−	2.53761i		−	0.310018i	−0.987913	−	0.155009i	$-0.950459\pi$
$67$		−	2.53761i		−	0.310018i	0.987913	−	0.155009i	$-0.0495407\pi$
$68$	0.379333	+	2.70983i	0.0460009	+	0.328615i
$69$		−	2.14947i		−	0.258765i
$70$		0			0
$71$		−	3.52502i		−	0.418342i	−0.977879	−	0.209171i	$-0.932923\pi$
$71$		−	3.52502i		−	0.418342i	0.977879	−	0.209171i	$-0.0670766\pi$
$72$	1.50039	+	7.08734i	0.176823	+	0.835250i
$73$		−	5.16984i		−	0.605084i	−0.953136	−	0.302542i	$-0.902165\pi$
$73$		−	5.16984i		−	0.605084i	0.953136	−	0.302542i	$-0.0978353\pi$
$74$	1.06085	+	15.2306i	0.123322	+	1.77053i
$75$	−0.662355			−0.0764821
$76$	8.11244	−	1.13561i	0.930561	−	0.130264i
$77$		0			0
$78$	5.44808	−	0.379472i	0.616873	−	0.0429668i
$79$		−	11.3401i		−	1.27586i	−0.770094	−	0.637931i	$-0.779791\pi$
$79$		−	11.3401i		−	1.27586i	0.770094	−	0.637931i	$-0.220209\pi$
$80$	1.09835	+	3.84625i	0.122799	+	0.430024i
$81$	5.24405			0.582672
$82$	−1.17481	+	0.0818286i	−0.129736	+	0.00903646i
$83$	−6.49145			−0.712529			−0.356264	−	0.934385i	$-0.615950\pi$
$83$	−6.49145			−0.712529			−0.356264	+	0.934385i	$0.615950\pi$
$84$		0			0
$85$	1.36813			0.148394
$86$	−4.38252	+	0.305254i	−0.472580	+	0.0329164i
$87$	3.43978			0.368783
$88$	−9.99743	+	2.11646i	−1.06573	+	0.225616i
$89$		−	9.39121i		−	0.995466i	−0.867330	−	0.497733i	$-0.834166\pi$
$89$		−	9.39121i		−	0.995466i	0.867330	−	0.497733i	$-0.165834\pi$
$90$	3.61345	−	0.251686i	0.380891	−	0.0265300i
$91$		0			0
$92$	0.899777	+	6.42771i	0.0938083	+	0.670135i
$93$	−5.87382			−0.609087
$94$	−0.677640	−	9.72886i	−0.0698932	−	1.00346i
$95$		−	4.09577i		−	0.420217i
$96$	1.27669	+	3.52263i	0.130302	+	0.359527i
$97$			0.343189i			0.0348455i	0.999848	+	0.0174228i	$0.00554612\pi$
$97$			0.343189i			0.0348455i	−0.999848	+	0.0174228i	$0.994454\pi$
$98$		0			0
$99$			9.25383i			0.930045i
$100$	1.98069	−	0.277265i	0.198069	−	0.0277265i
$101$			4.53635i			0.451384i	0.974199	+	0.225692i	$0.0724642\pi$
$101$			4.53635i			0.451384i	−0.974199	+	0.225692i	$0.927536\pi$
$102$	1.27844	−	0.0890466i	0.126584	−	0.00881693i
$103$	−6.13812			−0.604807			−0.302404	−	0.953180i	$-0.597789\pi$
$103$	−6.13812			−0.604807			−0.302404	+	0.953180i	$0.597789\pi$
$104$	−16.1329	+	3.41536i	−1.58196	+	0.334903i
$105$		0			0
$106$	−0.728886	−	10.4646i	−0.0707957	−	1.01641i
$107$		−	7.66797i		−	0.741291i	−0.928775	−	0.370645i	$-0.879137\pi$
$107$		−	7.66797i		−	0.741291i	0.928775	−	0.370645i	$-0.120863\pi$
$108$	7.29595	−	1.02132i	0.702053	−	0.0982763i
$109$	1.29523			0.124061			0.0620304	−	0.998074i	$-0.480242\pi$
$109$	1.29523			0.124061			0.0620304	+	0.998074i	$0.480242\pi$
$110$	0.355029	+	5.09715i	0.0338507	+	0.485994i
$111$	7.15064			0.678709
$112$		0			0
$113$	7.10591			0.668468			0.334234	−	0.942490i	$-0.391522\pi$
$113$	7.10591			0.668468			0.334234	+	0.942490i	$0.391522\pi$
$114$	−0.266580	−	3.82728i	−0.0249675	−	0.358457i
$115$	3.24519			0.302616
$116$	−10.2862	+	1.43991i	−0.955053	+	0.133692i
$117$			14.9330i			1.38056i
$118$	0.734884	+	10.5507i	0.0676516	+	0.971273i
$119$		0			0
$120$	1.83280	−	0.388005i	0.167311	−	0.0354199i
$121$	−2.05349			−0.186681
$122$	2.09580	−	0.145978i	0.189745	−	0.0132162i
$123$			0.551563i			0.0497327i
$124$	17.5649	−	2.45881i	1.57738	−	0.220808i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			17.0178i			1.51008i	0.655677	+	0.755041i	$0.272383\pi$
$127$			17.0178i			1.51008i	−0.655677	+	0.755041i	$0.727617\pi$
$128$	−5.29237	−	9.99954i	−0.467784	−	0.883843i
$129$			2.05755i			0.181157i
$130$	0.572914	+	8.22532i	0.0502479	+	0.721408i
$131$	−1.20613			−0.105380			−0.0526901	−	0.998611i	$-0.516780\pi$
$131$	−1.20613			−0.105380			−0.0526901	+	0.998611i	$0.516780\pi$
$132$	0.663512	+	4.73991i	0.0577513	+	0.412556i
$133$		0			0
$134$	3.58005	−	0.249359i	0.309269	−	0.0215414i
$135$		−	3.68354i		−	0.317029i
$136$	−3.78574	+	0.801444i	−0.324624	+	0.0687233i
$137$	2.14490			0.183252			0.0916258	−	0.995794i	$-0.470794\pi$
$137$	2.14490			0.183252			0.0916258	+	0.995794i	$0.470794\pi$
$138$	3.03246	−	0.211218i	0.258140	−	0.0179801i
$139$	3.39555			0.288007			0.144004	−	0.989577i	$-0.454002\pi$
$139$	3.39555			0.288007			0.144004	+	0.989577i	$0.454002\pi$
$140$		0			0
$141$	−4.56761			−0.384662
$142$	4.97308	−	0.346387i	0.417331	−	0.0290682i
$143$	−21.0645			−1.76151
$144$	−9.85134	+	2.81319i	−0.820945	+	0.234432i
$145$			5.19327i			0.431277i
$146$	7.29359	−	0.508017i	0.603622	−	0.0420438i
$147$		0			0
$148$	−21.3831	+	2.99329i	−1.75768	+	0.246047i
$149$	−19.0864			−1.56362			−0.781808	−	0.623519i	$-0.785703\pi$
$149$	−19.0864			−1.56362			−0.781808	+	0.623519i	$0.785703\pi$
$150$	−0.0650866	−	0.934447i	−0.00531430	−	0.0762973i
$151$			9.60595i			0.781721i	0.920450	+	0.390861i	$0.127823\pi$
$151$			9.60595i			0.781721i	−0.920450	+	0.390861i	$0.872177\pi$
$152$	2.39929	+	11.3334i	0.194608	+	0.919260i
$153$			3.50416i			0.283295i
$154$		0			0
$155$		−	8.86809i		−	0.712302i
$156$	1.07072	+	7.64883i	0.0857258	+	0.612397i
$157$			16.4624i			1.31384i	0.753961	+	0.656919i	$0.228141\pi$
$157$			16.4624i			1.31384i	−0.753961	+	0.656919i	$0.771859\pi$
$158$	15.9986	−	1.11434i	1.27278	−	0.0886522i
$159$	−4.91303			−0.389629
$160$	−5.31834	+	1.92750i	−0.420452	+	0.152382i
$161$		0			0
$162$	0.515309	+	7.39828i	0.0404865	+	0.581264i
$163$			7.15612i			0.560510i	0.959926	+	0.280255i	$0.0904191\pi$
$163$			7.15612i			0.560510i	−0.959926	+	0.280255i	$0.909581\pi$
$164$	−0.230887	−	1.64938i	−0.0180292	−	0.128795i
$165$	2.39306			0.186300
$166$	−0.637885	−	9.15810i	−0.0495095	−	0.710807i
$167$	−13.7127			−1.06112			−0.530562	−	0.847646i	$-0.678019\pi$
$167$	−13.7127			−1.06112			−0.530562	+	0.847646i	$0.678019\pi$
$168$		0			0
$169$	−20.9920			−1.61477
$170$	0.134439	+	1.93014i	0.0103110	+	0.148035i
$171$	10.4904			0.802224
$172$	−0.861301	−	6.15285i	−0.0656736	−	0.469150i
$173$		−	3.92439i		−	0.298366i	−0.988810	−	0.149183i	$-0.952336\pi$
$173$		−	3.92439i		−	0.298366i	0.988810	−	0.149183i	$-0.0476643\pi$
$174$	0.338012	+	4.85283i	0.0256246	+	0.367892i
$175$		0			0
$176$	−3.96830	−	13.8963i	−0.299122	−	1.04748i
$177$	4.95346			0.372325
$178$	13.2491	−	0.922831i	0.993060	−	0.0691691i
$179$		−	20.5539i		−	1.53627i	−0.640289	−	0.768134i	$-0.721185\pi$
$179$		−	20.5539i		−	1.53627i	0.640289	−	0.768134i	$-0.278815\pi$
$180$	0.710155	+	5.07311i	0.0529318	+	0.378127i
$181$			13.0603i			0.970762i	0.874303	+	0.485381i	$0.161319\pi$
$181$			13.0603i			0.970762i	−0.874303	+	0.485381i	$0.838681\pi$
$182$		0			0
$183$		−	0.983957i		−	0.0727362i
$184$	−8.97976	+	1.90102i	−0.661997	+	0.140145i
$185$			10.7958i			0.793722i
$186$	−0.577194	−	8.28676i	−0.0423219	−	0.607615i
$187$	−4.94298			−0.361467
$188$	13.6588	−	1.91202i	0.996174	−	0.139449i
$189$		0			0
$190$	5.77829	−	0.402472i	0.419201	−	0.0291984i
$191$		−	12.4751i		−	0.902667i	−0.892355	−	0.451334i	$-0.850948\pi$
$191$		−	12.4751i		−	0.902667i	0.892355	−	0.451334i	$-0.149052\pi$
$192$	−4.84425	+	2.14730i	−0.349604	+	0.154968i
$193$	19.0645			1.37229			0.686147	−	0.727463i	$-0.259301\pi$
$193$	19.0645			1.37229			0.686147	+	0.727463i	$0.259301\pi$
$194$	−0.484169	+	0.0337236i	−0.0347613	+	0.00242121i
$195$	3.86171			0.276543
$196$		0			0
$197$	1.93188			0.137641			0.0688203	−	0.997629i	$-0.478076\pi$
$197$	1.93188			0.137641			0.0688203	+	0.997629i	$0.478076\pi$
$198$	−13.0553	+	0.909332i	−0.927797	+	0.0646234i
$199$	20.5646			1.45778			0.728892	−	0.684629i	$-0.240036\pi$
$199$	20.5646			1.45778			0.728892	+	0.684629i	$0.240036\pi$
$200$	0.585797	+	2.76710i	0.0414221	+	0.195664i
$201$		−	1.68080i		−	0.118554i
$202$	−6.39986	+	0.445766i	−0.450293	+	0.0313640i
$203$		0			0
$204$	0.251253	+	1.79487i	0.0175912	+	0.125666i
$205$	−0.832730			−0.0581604
$206$	−0.603165	−	8.65963i	−0.0420245	−	0.603345i
$207$			8.31186i			0.577714i
$208$	−6.40368	−	22.4247i	−0.444015	−	1.55487i
$209$			14.7979i			1.02359i
$210$		0			0
$211$		−	9.98398i		−	0.687326i	−0.939093	−	0.343663i	$-0.888332\pi$
$211$		−	9.98398i		−	0.687326i	0.939093	−	0.343663i	$-0.111668\pi$
$212$	14.6918	−	2.05662i	1.00904	−	0.141249i
$213$		−	2.33481i		−	0.159979i
$214$	10.8179	−	0.753496i	0.739499	−	0.0515079i
$215$	−3.10642			−0.211856
$216$	2.15781	+	10.1927i	0.146820	+	0.693528i
$217$		0			0
$218$	0.127277	+	1.82731i	0.00862026	+	0.123761i
$219$		−	3.42427i		−	0.231391i
$220$	−7.15615	+	1.00175i	−0.482467	+	0.0675378i
$221$	−7.97654			−0.536560
$222$	0.702661	+	10.0881i	0.0471595	+	0.677068i
$223$	−16.8179			−1.12621			−0.563106	−	0.826384i	$-0.690394\pi$
$223$	−16.8179			−1.12621			−0.563106	+	0.826384i	$0.690394\pi$
$224$		0			0
$225$	2.56129			0.170752
$226$	0.698266	+	10.0250i	0.0464479	+	0.666852i
$227$	−19.8338			−1.31642			−0.658209	−	0.752835i	$-0.728686\pi$
$227$	−19.8338			−1.31642			−0.658209	+	0.752835i	$0.728686\pi$
$228$	5.37331	−	0.752178i	0.355856	−	0.0498142i
$229$		−	13.9331i		−	0.920725i	−0.887731	−	0.460363i	$-0.847719\pi$
$229$		−	13.9331i		−	0.920725i	0.887731	−	0.460363i	$-0.152281\pi$
$230$	0.318890	+	4.57830i	0.0210270	+	0.301884i
$231$		0			0
$232$	−3.04220	−	14.3703i	−0.199730	−	0.943455i
$233$	10.2257			0.669905			0.334953	−	0.942235i	$-0.391280\pi$
$233$	10.2257			0.669905			0.334953	+	0.942235i	$0.391280\pi$
$234$	−21.0674	+	1.46740i	−1.37722	+	0.0959267i
$235$		−	6.89601i		−	0.449846i
$236$	−14.8127	+	2.07354i	−0.964225	+	0.134976i
$237$		−	7.51117i		−	0.487903i
$238$		0			0
$239$		−	17.0835i		−	1.10504i	−0.833501	−	0.552518i	$-0.813667\pi$
$239$		−	17.0835i		−	1.10504i	0.833501	−	0.552518i	$-0.186333\pi$
$240$	0.727497	+	2.54758i	0.0469598	+	0.164446i
$241$		−	18.4837i		−	1.19064i	−0.803489	−	0.595320i	$-0.797025\pi$
$241$		−	18.4837i		−	1.19064i	0.803489	−	0.595320i	$-0.202975\pi$
$242$	−0.201787	−	2.89705i	−0.0129714	−	0.186230i
$243$	14.5241			0.931718
$244$	0.411889	+	2.94240i	0.0263685	+	0.188368i
$245$		0			0
$246$	−0.778142	+	0.0541995i	−0.0496125	+	0.00345564i
$247$			23.8794i			1.51941i
$248$	5.19490	+	24.5389i	0.329877	+	1.55822i
$249$	−4.29964			−0.272479
$250$	1.41080	−	0.0982654i	0.0892265	−	0.00621485i
$251$	−16.5313			−1.04344			−0.521722	−	0.853116i	$-0.674710\pi$
$251$	−16.5313			−1.04344			−0.521722	+	0.853116i	$0.674710\pi$
$252$		0			0
$253$	−11.7247			−0.737128
$254$	−24.0086	+	1.67226i	−1.50643	+	0.104927i
$255$	0.906184			0.0567475
$256$	13.5873	−	8.44906i	0.849203	−	0.528066i
$257$			6.19499i			0.386433i	0.981156	+	0.193216i	$0.0618919\pi$
$257$			6.19499i			0.386433i	−0.981156	+	0.193216i	$0.938108\pi$
$258$	−2.90279	+	0.202186i	−0.180720	+	0.0125876i
$259$		0			0
$260$	−11.5479	+	1.61653i	−0.716173	+	0.100253i
$261$	−13.3014			−0.823338
$262$	−0.118521	−	1.70161i	−0.00732226	−	0.105126i
$263$			21.1536i			1.30439i	0.758053	+	0.652194i	$0.226151\pi$
$263$			21.1536i			1.30439i	−0.758053	+	0.652194i	$0.773849\pi$
$264$	−6.62184	+	1.40185i	−0.407546	+	0.0862778i
$265$		−	7.41752i		−	0.455655i
$266$		0			0
$267$		−	6.22031i		−	0.380677i
$268$	0.703590	+	5.02621i	0.0429786	+	0.307025i
$269$		−	30.9866i		−	1.88928i	−0.328102	−	0.944642i	$-0.606409\pi$
$269$		−	30.9866i		−	1.88928i	0.328102	−	0.944642i	$-0.393591\pi$
$270$	5.19673	−	0.361965i	0.316263	−	0.0220285i
$271$	23.0381			1.39946			0.699732	−	0.714405i	$-0.253303\pi$
$271$	23.0381			1.39946			0.699732	+	0.714405i	$0.253303\pi$
$272$	−1.50268	−	5.26215i	−0.0911134	−	0.319065i
$273$		0			0
$274$	0.210770	+	3.02602i	0.0127331	+	0.182809i
$275$			3.61296i			0.217870i
$276$	0.595972	+	4.25742i	0.0358733	+	0.256267i
$277$	6.94562			0.417322			0.208661	−	0.977988i	$-0.433089\pi$
$277$	6.94562			0.417322			0.208661	+	0.977988i	$0.433089\pi$
$278$	0.333665	+	4.79043i	0.0200119	+	0.287311i
$279$	22.7137			1.35984
$280$		0			0
$281$	−4.24391			−0.253170			−0.126585	−	0.991956i	$-0.540402\pi$
$281$	−4.24391			−0.253170			−0.126585	+	0.991956i	$0.540402\pi$
$282$	−0.448838	−	6.44396i	−0.0267279	−	0.383732i
$283$	−8.53198			−0.507174			−0.253587	−	0.967313i	$-0.581610\pi$
$283$	−8.53198			−0.507174			−0.253587	+	0.967313i	$0.581610\pi$
$284$	0.977363	+	6.98195i	0.0579958	+	0.414303i
$285$		−	2.71285i		−	0.160695i
$286$	−2.06992	−	29.7178i	−0.122397	−	1.75725i
$287$		0			0
$288$	−4.93688	−	13.6218i	−0.290909	−	0.802672i
$289$	15.1282			0.889896
$290$	−7.32664	+	0.510319i	−0.430235	+	0.0299669i
$291$			0.227313i			0.0133253i
$292$	1.43342	+	10.2398i	0.0838843	+	0.599241i
$293$			25.2319i			1.47406i	0.675857	+	0.737032i	$0.263773\pi$
$293$			25.2319i			1.47406i	−0.675857	+	0.737032i	$0.736227\pi$
$294$		0			0
$295$			7.47856i			0.435419i
$296$	−6.32414	−	29.8730i	−0.367583	−	1.73633i
$297$			13.3085i			0.772238i
$298$	−1.87553	−	26.9270i	−0.108647	−	1.55984i
$299$	−18.9203			−1.09419
$300$	1.31192	−	0.183648i	0.0757436	−	0.0106029i
$301$		0			0
$302$	−13.5520	+	0.943933i	−0.779832	+	0.0543172i
$303$			3.00467i			0.172614i
$304$	−15.7533	+	4.49859i	−0.903516	+	0.258012i
$305$	1.48554			0.0850620
$306$	−4.94365	+	0.344338i	−0.282610	+	0.0196845i
$307$	29.2635			1.67016			0.835078	−	0.550132i	$-0.185423\pi$
$307$	29.2635			1.67016			0.835078	+	0.550132i	$0.185423\pi$
$308$		0			0
$309$	−4.06561			−0.231285
$310$	12.5111	−	0.871427i	0.710581	−	0.0494937i
$311$	−22.7461			−1.28981			−0.644906	−	0.764262i	$-0.723104\pi$
$311$	−22.7461			−1.28981			−0.644906	+	0.764262i	$0.723104\pi$
$312$	−10.6857	+	2.26218i	−0.604960	+	0.128071i
$313$		−	6.58481i		−	0.372195i	−0.982531	−	0.186098i	$-0.940416\pi$
$313$		−	6.58481i		−	0.372195i	0.982531	−	0.186098i	$-0.0595841\pi$
$314$	−23.2250	+	1.61768i	−1.31066	+	0.0912910i
$315$		0			0
$316$	3.14421	+	22.4612i	0.176876	+	1.26354i
$317$	−14.1217			−0.793154			−0.396577	−	0.918001i	$-0.629802\pi$
$317$	−14.1217			−0.793154			−0.396577	+	0.918001i	$0.629802\pi$
$318$	−0.482781	−	6.93128i	−0.0270730	−	0.388687i
$319$		−	18.7631i		−	1.05053i
$320$	−3.24192	−	7.31368i	−0.181229	−	0.408847i
$321$		−	5.07891i		−	0.283477i
$322$		0			0
$323$			5.60352i			0.311788i
$324$	−10.3868	+	1.45399i	−0.577046	+	0.0807772i
$325$			5.83027i			0.323405i
$326$	−10.0958	+	0.703199i	−0.559155	+	0.0389466i
$327$	0.857903			0.0474422
$328$	2.30425	−	0.487811i	0.127231	−	0.0269349i
$329$		0			0
$330$	0.235155	+	3.37612i	0.0129449	+	0.185849i
$331$			20.3224i			1.11702i	0.829498	+	0.558510i	$0.188627\pi$
$331$			20.3224i			1.11702i	−0.829498	+	0.558510i	$0.811373\pi$
$332$	12.8575	−	1.79985i	0.705649	−	0.0987796i
$333$	−27.6511			−1.51527
$334$	−1.34749	−	19.3459i	−0.0737313	−	1.05856i
$335$	2.53761			0.138644
$336$		0			0
$337$	15.7704			0.859067			0.429533	−	0.903051i	$-0.358678\pi$
$337$	15.7704			0.859067			0.429533	+	0.903051i	$0.358678\pi$
$338$	−2.06279	−	29.6155i	−0.112201	−	1.61087i
$339$	4.70663			0.255629
$340$	−2.70983	+	0.379333i	−0.146961	+	0.0205722i
$341$			32.0401i			1.73507i
$342$	1.03085	+	14.7999i	0.0557418	+	0.800285i
$343$		0			0
$344$	8.59578	−	1.81973i	0.463453	−	0.0981134i
$345$	2.14947			0.115723
$346$	5.53651	−	0.385632i	0.297644	−	0.0207317i
$347$			3.04784i			0.163616i	0.996648	+	0.0818082i	$0.0260695\pi$
$347$			3.04784i			0.163616i	−0.996648	+	0.0818082i	$0.973930\pi$
$348$	−6.81314	+	0.953731i	−0.365222	+	0.0511254i
$349$			8.40462i			0.449889i	0.974372	+	0.224944i	$0.0722201\pi$
$349$			8.40462i			0.449889i	−0.974372	+	0.224944i	$0.927780\pi$
$350$		0			0
$351$			21.4761i			1.14631i
$352$	19.2150	−	6.96399i	1.02416	−	0.371182i
$353$			0.432821i			0.0230367i	0.999934	+	0.0115184i	$0.00366649\pi$
$353$			0.432821i			0.0230367i	−0.999934	+	0.0115184i	$0.996334\pi$
$354$	0.486754	+	6.98832i	0.0258707	+	0.371425i
$355$	3.52502			0.187088
$356$	2.60385	+	18.6011i	0.138004	+	0.985854i
$357$		0			0
$358$	28.9973	−	2.01973i	1.53255	−	0.106746i
$359$			26.9810i			1.42400i	0.702178	+	0.712002i	$0.252211\pi$
$359$			26.9810i			1.42400i	−0.702178	+	0.712002i	$0.747789\pi$
$360$	−7.08734	+	1.50039i	−0.373535	+	0.0790777i
$361$	−2.22468			−0.117088
$362$	−18.4254	+	1.28337i	−0.968415	+	0.0674526i
$363$	−1.36014			−0.0713888
$364$		0			0
$365$	5.16984			0.270602
$366$	1.38816	−	0.0966889i	0.0725604	−	0.00505401i
$367$	20.8212			1.08686			0.543430	−	0.839455i	$-0.317125\pi$
$367$	20.8212			1.08686			0.543430	+	0.839455i	$0.317125\pi$
$368$	−3.56436	−	12.4818i	−0.185805	−	0.650659i
$369$		−	2.13286i		−	0.111032i
$370$	−15.2306	+	1.06085i	−0.791804	+	0.0551511i
$371$		0			0
$372$	11.6342	−	1.62860i	0.603206	−	0.0844392i
$373$	−17.6614			−0.914475			−0.457237	−	0.889345i	$-0.651161\pi$
$373$	−17.6614			−0.914475			−0.457237	+	0.889345i	$0.651161\pi$
$374$	−0.485724	−	6.97354i	−0.0251162	−	0.360593i
$375$		−	0.662355i		−	0.0342038i
$376$	4.03966	+	19.0820i	0.208330	+	0.984077i
$377$		−	30.2781i		−	1.55940i
$378$		0			0
$379$		−	15.0551i		−	0.773331i	−0.922220	−	0.386665i	$-0.873627\pi$
$379$		−	15.0551i		−	0.773331i	0.922220	−	0.386665i	$-0.126373\pi$
$380$	1.13561	+	8.11244i	0.0582557	+	0.416159i
$381$			11.2718i			0.577472i
$382$	17.5998	−	1.22587i	0.900486	−	0.0627211i
$383$	30.3505			1.55084			0.775420	−	0.631446i	$-0.217538\pi$
$383$	30.3505			1.55084			0.775420	+	0.631446i	$0.217538\pi$
$384$	−3.50542	−	6.62324i	−0.178885	−	0.337991i
$385$		0			0
$386$	1.87338	+	26.8961i	0.0953527	+	1.36898i
$387$		−	7.95643i		−	0.404448i
$388$	−0.0951542	−	0.679750i	−0.00483072	−	0.0345091i
$389$	−6.27818			−0.318316			−0.159158	−	0.987253i	$-0.550878\pi$
$389$	−6.27818			−0.318316			−0.159158	+	0.987253i	$0.550878\pi$
$390$	0.379472	+	5.44808i	0.0192153	+	0.275874i
$391$	−4.43983			−0.224532
$392$		0			0
$393$	−0.798887			−0.0402985
$394$	0.189837	+	2.72549i	0.00956384	+	0.137308i
$395$	11.3401			0.570583
$396$	−2.56576	−	18.3289i	−0.128934	−	0.921064i
$397$			9.72207i			0.487937i	0.969783	+	0.243968i	$0.0784493\pi$
$397$			9.72207i			0.487937i	−0.969783	+	0.243968i	$0.921551\pi$
$398$	2.02079	+	29.0124i	0.101293	+	1.45426i
$399$		0			0
$400$	−3.84625	+	1.09835i	−0.192312	+	0.0549175i
$401$	6.98744			0.348936			0.174468	−	0.984663i	$-0.444179\pi$
$401$	6.98744			0.348936			0.174468	+	0.984663i	$0.444179\pi$
$402$	2.37126	−	0.165164i	0.118268	−	0.00823764i
$403$			51.7034i			2.57553i
$404$	−1.25777	−	8.98509i	−0.0625764	−	0.447025i
$405$			5.24405i			0.260579i
$406$		0			0
$407$		−	39.0048i		−	1.93339i
$408$	−2.50750	+	0.530840i	−0.124140	+	0.0262805i
$409$			2.24559i			0.111037i	0.998458	+	0.0555186i	$0.0176812\pi$
$409$			2.24559i			0.111037i	−0.998458	+	0.0555186i	$0.982319\pi$
$410$	−0.0818286	−	1.17481i	−0.00404123	−	0.0580198i
$411$	1.42069			0.0700773
$412$	12.1577	−	1.70189i	0.598967	−	0.0838459i
$413$		0			0
$414$	−11.7263	+	0.816769i	−0.576318	+	0.0401420i
$415$		−	6.49145i		−	0.318653i
$416$	31.0074	−	11.2379i	1.52026	−	0.550981i
$417$	2.24906			0.110137
$418$	−20.8767	+	1.45412i	−1.02111	+	0.0711232i
$419$	18.3565			0.896775			0.448388	−	0.893839i	$-0.351998\pi$
$419$	18.3565			0.896775			0.448388	+	0.893839i	$0.351998\pi$
$420$		0			0
$421$	2.27310			0.110784			0.0553921	−	0.998465i	$-0.482359\pi$
$421$	2.27310			0.110784			0.0553921	+	0.998465i	$0.482359\pi$
$422$	14.0854	−	0.981080i	0.685664	−	0.0477582i
$423$	17.6627			0.858788
$424$	4.34516	+	20.5250i	0.211020	+	0.996783i
$425$			1.36813i			0.0663638i
$426$	3.29394	−	0.229431i	0.159592	−	0.0111160i
$427$		0			0
$428$	2.12606	+	15.1879i	0.102767	+	0.734133i
$429$	−13.9522			−0.673618
$430$	−0.305254	−	4.38252i	−0.0147206	−	0.211344i
$431$			12.8610i			0.619490i	0.950820	+	0.309745i	$0.100244\pi$
$431$			12.8610i			0.619490i	−0.950820	+	0.309745i	$0.899756\pi$
$432$	−14.1678	+	4.04582i	−0.681650	+	0.194655i
$433$		−	33.6307i		−	1.61619i	−0.589054	−	0.808094i	$-0.700499\pi$
$433$		−	33.6307i		−	1.61619i	0.589054	−	0.808094i	$-0.299501\pi$
$434$		0			0
$435$			3.43978i			0.164925i
$436$	−2.56545	+	0.359122i	−0.122863	+	0.0171988i
$437$			13.2915i			0.635821i
$438$	4.83094	−	0.336487i	0.230831	−	0.0160780i
$439$	24.8870			1.18779			0.593896	−	0.804542i	$-0.297589\pi$
$439$	24.8870			1.18779			0.593896	+	0.804542i	$0.297589\pi$
$440$	−2.11646	−	9.99743i	−0.100898	−	0.476609i
$441$		0			0
$442$	−0.783818	−	11.2533i	−0.0372824	−	0.535263i
$443$			7.94772i			0.377608i	0.982015	+	0.188804i	$0.0604610\pi$
$443$			7.94772i			0.377608i	−0.982015	+	0.188804i	$0.939539\pi$
$444$	−14.1632	+	1.98262i	−0.672155	+	0.0940910i
$445$	9.39121			0.445186
$446$	−1.65262	−	23.7267i	−0.0782540	−	1.12349i
$447$	−12.6420			−0.597944
$448$		0			0
$449$	14.3027			0.674988			0.337494	−	0.941328i	$-0.390421\pi$
$449$	14.3027			0.674988			0.337494	+	0.941328i	$0.390421\pi$
$450$	0.251686	+	3.61345i	0.0118646	+	0.170340i
$451$	3.00862			0.141670
$452$	−14.0746	+	1.97022i	−0.662013	+	0.0926714i
$453$			6.36255i			0.298939i
$454$	−1.94898	−	27.9815i	−0.0914702	−	1.31324i
$455$		0			0
$456$	1.58918	+	7.50673i	0.0744202	+	0.351535i
$457$	22.1786			1.03747			0.518737	−	0.854934i	$-0.326403\pi$
$457$	22.1786			1.03747			0.518737	+	0.854934i	$0.326403\pi$
$458$	19.6568	−	1.36914i	0.918500	−	0.0639758i
$459$			5.03955i			0.235226i
$460$	−6.42771	+	0.899777i	−0.299693	+	0.0419523i
$461$		−	32.8587i		−	1.53038i	−0.643803	−	0.765192i	$-0.722644\pi$
$461$		−	32.8587i		−	1.53038i	0.643803	−	0.765192i	$-0.277356\pi$
$462$		0			0
$463$			3.31392i			0.154011i	0.997031	+	0.0770055i	$0.0245359\pi$
$463$			3.31392i			0.154011i	−0.997031	+	0.0770055i	$0.975464\pi$
$464$	19.9746	−	5.70402i	0.927297	−	0.264803i
$465$		−	5.87382i		−	0.272392i
$466$	1.00483	+	14.4263i	0.0465478	+	0.668286i
$467$	35.1334			1.62578			0.812890	−	0.582417i	$-0.197893\pi$
$467$	35.1334			1.62578			0.812890	+	0.582417i	$0.197893\pi$
$468$	−4.14039	−	29.5776i	−0.191390	−	1.36722i
$469$		0			0
$470$	9.72886	−	0.677640i	0.448759	−	0.0312572i
$471$			10.9039i			0.502426i
$472$	−4.38092	−	20.6939i	−0.201648	−	0.952516i
$473$	11.2234			0.516051
$474$	10.5967	−	0.738088i	0.486724	−	0.0339015i
$475$	4.09577			0.187927
$476$		0			0
$477$	18.9984			0.869877
$478$	24.1013	−	1.67871i	1.10237	−	0.0767825i
$479$	22.3266			1.02013			0.510065	−	0.860136i	$-0.329621\pi$
$479$	22.3266			1.02013			0.510065	+	0.860136i	$0.329621\pi$
$480$	−3.52263	+	1.27669i	−0.160785	+	0.0582726i
$481$		−	62.9423i		−	2.86992i
$482$	26.0767	−	1.81631i	1.18776	−	0.0827306i
$483$		0			0
$484$	4.06732	−	0.569361i	0.184878	−	0.0258800i
$485$	−0.343189			−0.0155834
$486$	1.42721	+	20.4905i	0.0647397	+	0.929466i
$487$			7.18519i			0.325592i	0.986660	+	0.162796i	$0.0520512\pi$
$487$			7.18519i			0.325592i	−0.986660	+	0.162796i	$0.947949\pi$
$488$	−4.11065	+	0.870227i	−0.186080	+	0.0393933i
$489$			4.73989i			0.214345i
$490$		0			0
$491$			5.80059i			0.261777i	0.991397	+	0.130889i	$0.0417830\pi$
$491$			5.80059i			0.261777i	−0.991397	+	0.130889i	$0.958217\pi$
$492$	−0.152929	−	1.09247i	−0.00689457	−	0.0492525i
$493$		−	7.10504i		−	0.319995i
$494$	−33.6890	+	2.34652i	−1.51574	+	0.105575i
$495$	−9.25383			−0.415929
$496$	−34.1089	+	9.74027i	−1.53153	+	0.437351i
$497$		0			0
$498$	−0.422506	−	6.06591i	−0.0189329	−	0.271820i
$499$		−	39.6601i		−	1.77543i	−0.460394	−	0.887715i	$-0.652292\pi$
$499$		−	39.6601i		−	1.77543i	0.460394	−	0.887715i	$-0.347708\pi$
$500$	0.277265	+	1.98069i	0.0123997	+	0.0885791i
$501$	−9.08270			−0.405785
$502$	−1.62445	−	23.3222i	−0.0725028	−	1.04092i
$503$	−8.22384			−0.366683			−0.183341	−	0.983049i	$-0.558691\pi$
$503$	−8.22384			−0.366683			−0.183341	+	0.983049i	$0.558691\pi$
$504$		0			0
$505$	−4.53635			−0.201865
$506$	−1.15214	−	16.5412i	−0.0512187	−	0.735347i
$507$	−13.9042			−0.617506
$508$	−4.71843	−	33.7069i	−0.209346	−	1.49550i
$509$			32.5719i			1.44373i	0.692036	+	0.721863i	$0.256714\pi$
$509$			32.5719i			1.44373i	−0.692036	+	0.721863i	$0.743286\pi$
$510$	0.0890466	+	1.27844i	0.00394305	+	0.0566103i
$511$		0			0
$512$	13.2550	+	18.3386i	0.585796	+	0.810459i
$513$	15.0869			0.666105
$514$	−8.73986	+	0.608753i	−0.385499	+	0.0268509i
$515$		−	6.13812i		−	0.270478i
$516$	−0.570487	−	4.07537i	−0.0251143	−	0.179408i
$517$			24.9150i			1.09576i
$518$		0			0
$519$		−	2.59934i		−	0.114098i
$520$	−3.41536	−	16.1329i	−0.149773	−	0.707476i
$521$		−	5.64398i		−	0.247267i	−0.992328	−	0.123634i	$-0.960545\pi$
$521$		−	5.64398i		−	0.247267i	0.992328	−	0.123634i	$-0.0394547\pi$
$522$	−1.30707	−	18.7656i	−0.0572090	−	0.821348i
$523$	2.73410			0.119554			0.0597770	−	0.998212i	$-0.480961\pi$
$523$	2.73410			0.119554			0.0597770	+	0.998212i	$0.480961\pi$
$524$	2.38897	−	0.334418i	0.104363	−	0.0146091i
$525$		0			0
$526$	−29.8434	+	2.07867i	−1.30123	+	0.0906342i
$527$			12.1327i			0.528507i
$528$	−2.62842	−	9.20431i	−0.114387	−	0.400566i
$529$	12.4687			0.542119
$530$	10.4646	−	0.728886i	0.454553	−	0.0316608i
$531$	−19.1547			−0.831245
$532$		0			0
$533$	4.85504			0.210295
$534$	8.77559	−	0.611242i	0.379757	−	0.0264510i
$535$	7.66797			0.331515
$536$	−7.02182	+	1.48652i	−0.303296	+	0.0642081i
$537$		−	13.6139i		−	0.587485i
$538$	43.7157	−	3.04491i	1.88472	−	0.131275i
$539$		0			0
$540$	1.02132	+	7.29595i	0.0439505	+	0.313968i
$541$	28.2999			1.21671			0.608355	−	0.793665i	$-0.291830\pi$
$541$	28.2999			1.21671			0.608355	+	0.793665i	$0.291830\pi$
$542$	2.26385	+	32.5020i	0.0972406	+	1.39608i
$543$			8.65052i			0.371230i
$544$	7.27616	−	2.63706i	0.311963	−	0.113063i
$545$			1.29523i			0.0554817i
$546$		0			0
$547$			20.7596i			0.887616i	0.896122	+	0.443808i	$0.146373\pi$
$547$			20.7596i			0.887616i	−0.896122	+	0.443808i	$0.853627\pi$
$548$	−4.24839	+	0.594707i	−0.181482	+	0.0254046i
$549$			3.80490i			0.162389i
$550$	−5.09715	+	0.355029i	−0.217343	+	0.0151385i
$551$	−21.2704			−0.906150
$552$	−5.94779	+	1.25915i	−0.253155	+	0.0535930i
$553$		0			0
$554$	0.682514	+	9.79885i	0.0289973	+	0.416313i
$555$			7.15064i			0.303528i
$556$	−6.72553	+	0.941468i	−0.285226	+	0.0399271i
$557$	−18.7575			−0.794781			−0.397391	−	0.917650i	$-0.630084\pi$
$557$	−18.7575			−0.794781			−0.397391	+	0.917650i	$0.630084\pi$
$558$	2.23197	+	32.0444i	0.0944870	+	1.35655i
$559$	18.1113			0.766025
$560$		0			0
$561$	−3.27401			−0.138229
$562$	−0.417029	−	5.98728i	−0.0175913	−	0.252558i
$563$	−33.3740			−1.40655			−0.703274	−	0.710919i	$-0.748279\pi$
$563$	−33.3740			−1.40655			−0.703274	+	0.710919i	$0.748279\pi$
$564$	9.04700	−	1.26644i	0.380947	−	0.0533266i
$565$			7.10591i			0.298948i
$566$	−0.838399	−	12.0369i	−0.0352405	−	0.505948i
$567$		0			0
$568$	−9.75407	+	2.06494i	−0.409272	+	0.0866431i
$569$	13.0300			0.546247			0.273124	−	0.961979i	$-0.411943\pi$
$569$	13.0300			0.546247			0.273124	+	0.961979i	$0.411943\pi$
$570$	3.82728	−	0.266580i	0.160307	−	0.0111658i
$571$			32.9558i			1.37916i	0.724211	+	0.689579i	$0.242204\pi$
$571$			32.9558i			1.37916i	−0.724211	+	0.689579i	$0.757796\pi$
$572$	41.7223	−	5.84046i	1.74450	−	0.244202i
$573$		−	8.26295i		−	0.345190i
$574$		0			0
$575$			3.24519i			0.135334i
$576$	18.7324	−	8.30348i	0.780518	−	0.345978i
$577$		−	36.3874i		−	1.51483i	−0.652935	−	0.757414i	$-0.726462\pi$
$577$		−	36.3874i		−	1.51483i	0.652935	−	0.757414i	$-0.273538\pi$
$578$	1.48658	+	21.3428i	0.0618337	+	0.887745i
$579$	12.6275			0.524780
$580$	−1.43991	−	10.2862i	−0.0597890	−	0.427113i
$581$		0			0
$582$	−0.320692	+	0.0223370i	−0.0132931	+	0.000925898i
$583$			26.7992i			1.10991i
$584$	−14.3055	+	3.02848i	−0.591964	+	0.125319i
$585$	−14.9330			−0.617403
$586$	−35.5971	+	2.47943i	−1.47050	+	0.102424i
$587$	28.4245			1.17321			0.586603	−	0.809875i	$-0.300465\pi$
$587$	28.4245			1.17321			0.586603	+	0.809875i	$0.300465\pi$
$588$		0			0
$589$	36.3217			1.49661
$590$	−10.5507	+	0.734884i	−0.434366	+	0.0302547i
$591$	1.27959			0.0526352
$592$	41.5233	−	11.8576i	1.70660	−	0.487342i
$593$		−	7.57149i		−	0.310924i	−0.987842	−	0.155462i	$-0.950313\pi$
$593$		−	7.57149i		−	0.310924i	0.987842	−	0.155462i	$-0.0496866\pi$
$594$	−18.7756	+	1.30777i	−0.770371	+	0.0536583i
$595$		0			0
$596$	37.8042	−	5.29198i	1.54852	−	0.216768i
$597$	13.6210			0.557472
$598$	−1.85921	−	26.6927i	−0.0760289	−	1.09155i
$599$		−	47.4510i		−	1.93879i	−0.245499	−	0.969397i	$-0.578952\pi$
$599$		−	47.4510i		−	1.93879i	0.245499	−	0.969397i	$-0.421048\pi$
$600$	0.388005	+	1.83280i	0.0158403	+	0.0748238i
$601$			13.3242i			0.543506i	0.962367	+	0.271753i	$0.0876034\pi$
$601$			13.3242i			0.543506i	−0.962367	+	0.271753i	$0.912397\pi$
$602$		0			0
$603$			6.49954i			0.264682i
$604$	−2.66339	−	19.0264i	−0.108372	−	0.774173i
$605$		−	2.05349i		−	0.0834862i
$606$	−4.23898	+	0.295255i	−0.172197	+	0.0119939i
$607$	15.0816			0.612143			0.306072	−	0.952008i	$-0.400985\pi$
$607$	15.0816			0.612143			0.306072	+	0.952008i	$0.400985\pi$
$608$	−7.89460	−	21.7827i	−0.320168	−	0.883405i
$609$		0			0
$610$	0.145978	+	2.09580i	0.00591046	+	0.0848564i
$611$			40.2056i			1.62654i
$612$	−0.971581	−	6.94065i	−0.0392738	−	0.280559i
$613$	−5.20469			−0.210215			−0.105108	−	0.994461i	$-0.533519\pi$
$613$	−5.20469			−0.210215			−0.105108	+	0.994461i	$0.533519\pi$
$614$	2.87559	+	41.2848i	0.116049	+	1.66612i
$615$	−0.551563			−0.0222412
$616$		0			0
$617$	−35.7404			−1.43885			−0.719426	−	0.694569i	$-0.755595\pi$
$617$	−35.7404			−1.43885			−0.719426	+	0.694569i	$0.755595\pi$
$618$	−0.399509	−	5.73575i	−0.0160706	−	0.230726i
$619$	38.2437			1.53715			0.768573	−	0.639762i	$-0.220967\pi$
$619$	38.2437			1.53715			0.768573	+	0.639762i	$0.220967\pi$
$620$	2.45881	+	17.5649i	0.0987482	+	0.705424i
$621$			11.9538i			0.479689i
$622$	−2.23515	−	32.0901i	−0.0896215	−	1.28670i
$623$		0			0
$624$	−4.24151	−	14.8531i	−0.169796	−	0.594599i
$625$	1.00000			0.0400000
$626$	9.28981	−	0.647059i	0.371296	−	0.0258617i
$627$			9.80143i			0.391431i
$628$	−4.56443	−	32.6068i	−0.182141	−	1.30115i
$629$		−	14.7700i		−	0.588918i
$630$		0			0
$631$			12.0334i			0.479042i	0.970891	+	0.239521i	$0.0769904\pi$
$631$			12.0334i			0.479042i	−0.970891	+	0.239521i	$0.923010\pi$
$632$	−31.3792	+	6.64300i	−1.24820	+	0.264244i
$633$		−	6.61294i		−	0.262841i
$634$	−1.38768	−	19.9229i	−0.0551117	−	0.791237i
$635$	−17.0178			−0.675329
$636$	9.73118	−	1.36221i	0.385866	−	0.0540152i
$637$		0			0
$638$	26.4709	−	1.84376i	1.04799	−	0.0729952i
$639$			9.02857i			0.357165i
$640$	9.99954	−	5.29237i	0.395267	−	0.209199i
$641$	22.9352			0.905888			0.452944	−	0.891539i	$-0.350374\pi$
$641$	22.9352			0.905888			0.452944	+	0.891539i	$0.350374\pi$
$642$	7.16531	−	0.499082i	0.282792	−	0.0196972i
$643$	1.23955			0.0488833			0.0244416	−	0.999701i	$-0.492219\pi$
$643$	1.23955			0.0488833			0.0244416	+	0.999701i	$0.492219\pi$
$644$		0			0
$645$	−2.05755			−0.0810160
$646$	−7.90543	+	0.550633i	−0.311035	+	0.0216644i
$647$	−14.1415			−0.555962			−0.277981	−	0.960587i	$-0.589665\pi$
$647$	−14.1415			−0.555962			−0.277981	+	0.960587i	$0.589665\pi$
$648$	−3.07195	−	14.5108i	−0.120678	−	0.570038i
$649$		−	27.0198i		−	1.06062i
$650$	−8.22532	+	0.572914i	−0.322624	+	0.0224715i
$651$		0			0
$652$	−1.98414	−	14.1740i	−0.0777049	−	0.555098i
$653$	−17.0916			−0.668845			−0.334423	−	0.942423i	$-0.608541\pi$
$653$	−17.0916			−0.668845			−0.334423	+	0.942423i	$0.608541\pi$
$654$	0.0843022	+	1.21033i	0.00329648	+	0.0473275i
$655$		−	1.20613i		−	0.0471275i
$656$	0.914629	+	3.20289i	0.0357103	+	0.125052i
$657$			13.2414i			0.516598i
$658$		0			0
$659$		−	3.45765i		−	0.134691i	−0.997730	−	0.0673455i	$-0.978547\pi$
$659$		−	3.45765i		−	0.134691i	0.997730	−	0.0673455i	$-0.0214530\pi$
$660$	−4.73991	+	0.663512i	−0.184501	+	0.0258272i
$661$			15.1632i			0.589780i	0.955531	+	0.294890i	$0.0952830\pi$
$661$			15.1632i			0.589780i	−0.955531	+	0.294890i	$0.904717\pi$
$662$	−28.6707	+	1.99699i	−1.11432	+	0.0776152i
$663$	−5.28330			−0.205186
$664$	3.80267	+	17.9625i	0.147572	+	0.697079i
$665$		0			0
$666$	−2.71715	−	39.0100i	−0.105287	−	1.51161i
$667$		−	16.8531i		−	0.652556i
$668$	27.1607	−	3.80206i	1.05088	−	0.147106i
$669$	−11.1394			−0.430676
$670$	0.249359	+	3.58005i	0.00963359	+	0.138309i
$671$	−5.36721			−0.207199
$672$		0			0
$673$	−11.2116			−0.432175			−0.216087	−	0.976374i	$-0.569330\pi$
$673$	−11.2116			−0.432175			−0.216087	+	0.976374i	$0.569330\pi$
$674$	1.54968	+	22.2488i	0.0596915	+	0.856991i
$675$	3.68354			0.141780
$676$	41.5787	−	5.82036i	1.59918	−	0.223860i
$677$		−	3.67637i		−	0.141294i	−0.997501	−	0.0706471i	$-0.977494\pi$
$677$		−	3.67637i		−	0.141294i	0.997501	−	0.0706471i	$-0.0225064\pi$
$678$	0.462500	+	6.64010i	0.0177622	+	0.255011i
$679$		0			0
$680$	−0.801444	−	3.78574i	−0.0307340	−	0.145176i
$681$	−13.1370			−0.503412
$682$	−45.2020	+	3.14843i	−1.73087	+	0.120560i
$683$		−	42.1877i		−	1.61427i	−0.590369	−	0.807133i	$-0.701018\pi$
$683$		−	42.1877i		−	1.61427i	0.590369	−	0.807133i	$-0.298982\pi$
$684$	−20.7783	+	2.90863i	−0.794477	+	0.111214i
$685$			2.14490i			0.0819526i
$686$		0			0
$687$		−	9.22865i		−	0.352095i
$688$	3.41194	+	11.9481i	0.130079	+	0.455516i
$689$			43.2461i			1.64755i
$690$	0.211218	+	3.03246i	0.00804094	+	0.115444i
$691$	−23.1230			−0.879640			−0.439820	−	0.898086i	$-0.644958\pi$
$691$	−23.1230			−0.879640			−0.439820	+	0.898086i	$0.644958\pi$
$692$	1.08809	+	7.77298i	0.0413631	+	0.295485i
$693$		0			0
$694$	−4.29987	+	0.299497i	−0.163221	+	0.0113688i
$695$			3.39555i			0.128801i
$696$	−2.01502	−	9.51822i	−0.0763790	−	0.360787i
$697$	1.13928			0.0431533
$698$	−11.8572	+	0.825884i	−0.448802	+	0.0312602i
$699$	6.77301			0.256179
$700$		0			0
$701$	29.3192			1.10737			0.553686	−	0.832725i	$-0.313221\pi$
$701$	29.3192			1.10737			0.553686	+	0.832725i	$0.313221\pi$
$702$	−30.2983	+	2.11035i	−1.14354	+	0.0796502i
$703$	−44.2170			−1.66768
$704$	11.7129	+	26.4241i	0.441448	+	0.995894i
$705$		−	4.56761i		−	0.172026i
$706$	−0.610622	+	0.0425314i	−0.0229811	+	0.00160069i
$707$		0			0
$708$	−9.81126	+	1.37342i	−0.368730	+	0.0516163i
$709$	3.35439			0.125977			0.0629884	−	0.998014i	$-0.479937\pi$
$709$	3.35439			0.125977			0.0629884	+	0.998014i	$0.479937\pi$
$710$	0.346387	+	4.97308i	0.0129997	+	0.186636i
$711$			29.0453i			1.08928i
$712$	−25.9864	+	5.50134i	−0.973882	+	0.206172i
$713$			28.7786i			1.07777i
$714$		0			0
$715$		−	21.0645i		−	0.787769i
$716$	5.69886	+	40.7108i	0.212977	+	1.52143i
$717$		−	11.3153i		−	0.422578i
$718$	−38.0647	+	2.65130i	−1.42056	+	0.0989457i
$719$	−31.0284			−1.15717			−0.578583	−	0.815624i	$-0.696394\pi$
$719$	−31.0284			−1.15717			−0.578583	+	0.815624i	$0.696394\pi$
$720$	−2.81319	−	9.85134i	−0.104841	−	0.367138i
$721$		0			0
$722$	−0.218609	−	3.13857i	−0.00813579	−	0.116805i
$723$		−	12.2428i		−	0.455313i
$724$	−3.62115	−	25.8683i	−0.134579	−	0.961388i
$725$	−5.19327			−0.192873
$726$	−0.133655	−	1.91888i	−0.00496039	−	0.0712162i
$727$	−37.9906			−1.40899			−0.704497	−	0.709707i	$-0.748827\pi$
$727$	−37.9906			−1.40899			−0.704497	+	0.709707i	$0.748827\pi$
$728$		0			0
$729$	−6.11207			−0.226373
$730$	0.508017	+	7.29359i	0.0188025	+	0.269948i
$731$	4.24997			0.157191
$732$	0.272817	+	1.94891i	0.0100836	+	0.0720338i
$733$			30.9751i			1.14409i	0.820222	+	0.572046i	$0.193850\pi$
$733$			30.9751i			1.14409i	−0.820222	+	0.572046i	$0.806150\pi$
$734$	2.04601	+	29.3745i	0.0755195	+	1.08423i
$735$		0			0
$736$	17.2590	−	6.25511i	0.636176	−	0.230566i
$737$	−9.16828			−0.337718
$738$	3.00903	−	0.209586i	0.110764	−	0.00771498i
$739$		−	2.92228i		−	0.107498i	−0.998554	−	0.0537488i	$-0.982883\pi$
$739$		−	2.92228i		−	0.107498i	0.998554	−	0.0537488i	$-0.0171170\pi$
$740$	−2.99329	−	21.3831i	−0.110036	−	0.786058i
$741$			15.8167i			0.581039i
$742$		0			0
$743$		−	36.6505i		−	1.34457i	−0.740290	−	0.672287i	$-0.765312\pi$
$743$		−	36.6505i		−	1.34457i	0.740290	−	0.672287i	$-0.234688\pi$
$744$	3.44087	+	16.2535i	0.126148	+	0.595881i
$745$		−	19.0864i		−	0.699271i
$746$	−1.73551	−	24.9167i	−0.0635415	−	0.912265i
$747$	16.6265			0.608330
$748$	9.79051	−	1.37052i	0.357976	−	0.0501110i
$749$		0			0
$750$	0.934447	−	0.0650866i	0.0341212	−	0.00237663i
$751$		−	36.1831i		−	1.32034i	−0.751116	−	0.660170i	$-0.770484\pi$
$751$		−	36.1831i		−	1.32034i	0.751116	−	0.660170i	$-0.229516\pi$
$752$	−26.5238	+	7.57424i	−0.967223	+	0.276204i
$753$	−10.9496			−0.399024
$754$	42.7163	−	2.97529i	1.55563	−	0.108354i
$755$	−9.60595			−0.349596
$756$		0			0
$757$	−1.44394			−0.0524807			−0.0262404	−	0.999656i	$-0.508354\pi$
$757$	−1.44394			−0.0524807			−0.0262404	+	0.999656i	$0.508354\pi$
$758$	21.2397	−	1.47940i	0.771462	−	0.0537342i
$759$	−7.76594			−0.281886
$760$	−11.3334	+	2.39929i	−0.411106	+	0.0870314i
$761$			28.2334i			1.02346i	0.859146	+	0.511730i	$0.170995\pi$
$761$			28.2334i			1.02346i	−0.859146	+	0.511730i	$0.829005\pi$
$762$	−15.9022	+	1.10763i	−0.576076	+	0.0401251i
$763$		0			0
$764$	3.45891	+	24.7093i	0.125139	+	0.893951i
$765$	−3.50416			−0.126693
$766$	2.98241	+	42.8184i	0.107759	+	1.54709i
$767$		−	43.6020i		−	1.57438i
$768$	8.99958	−	5.59627i	0.324744	−	0.201938i
$769$		−	38.3866i		−	1.38426i	−0.721774	−	0.692129i	$-0.756673\pi$
$769$		−	38.3866i		−	1.38426i	0.721774	−	0.692129i	$-0.243327\pi$
$770$		0			0
$771$			4.10328i			0.147776i
$772$	−37.7608	+	5.28592i	−1.35904	+	0.190244i
$773$			19.0817i			0.686322i	0.939277	+	0.343161i	$0.111498\pi$
$773$			19.0817i			0.686322i	−0.939277	+	0.343161i	$0.888502\pi$
$774$	11.2249	−	0.781842i	0.403471	−	0.0281027i
$775$	8.86809			0.318551
$776$	0.949638	−	0.201039i	0.0340900	−	0.00721688i
$777$		0			0
$778$	−0.616928	−	8.85722i	−0.0221179	−	0.317547i
$779$		−	3.41067i		−	0.122200i
$780$	−7.64883	+	1.07072i	−0.273872	+	0.0383378i
$781$	−12.7357			−0.455721
$782$	−0.436281	−	6.26369i	−0.0156014	−	0.223989i
$783$	−19.1296			−0.683637
$784$		0			0
$785$	−16.4624			−0.587567
$786$	−0.0785030	−	1.12707i	−0.00280011	−	0.0402011i
$787$	5.10214			0.181872			0.0909358	−	0.995857i	$-0.471014\pi$
$787$	5.10214			0.181872			0.0909358	+	0.995857i	$0.471014\pi$
$788$	−3.82645	+	0.535642i	−0.136312	+	0.0190815i
$789$			14.0112i			0.498811i
$790$	1.11434	+	15.9986i	0.0396464	+	0.569203i
$791$		0			0
$792$	25.6063	−	5.42087i	0.909879	−	0.192622i
$793$	−8.66112			−0.307565
$794$	−13.7159	+	0.955344i	−0.486758	+	0.0339039i
$795$		−	4.91303i		−	0.174247i
$796$	−40.7320	+	5.70183i	−1.44371	+	0.202096i
$797$			25.6101i			0.907155i	0.891217	+	0.453578i	$0.149852\pi$
$797$			25.6101i			0.907155i	−0.891217	+	0.453578i	$0.850148\pi$
$798$		0			0
$799$			9.43461i			0.333772i
$800$	−1.92750	−	5.31834i	−0.0681475	−	0.188032i
$801$			24.0536i			0.849891i
$802$	0.686624	+	9.85785i	0.0242455	+	0.348093i
$803$	−18.6784			−0.659148
$804$	0.466026	+	3.32913i	0.0164355	+	0.117409i
$805$		0			0
$806$	−72.9429	+	5.08065i	−2.56930	+	0.178958i
$807$		−	20.5241i		−	0.722483i
$808$	12.5525	−	2.65738i	0.441597	−	0.0934863i
$809$	50.4761			1.77465			0.887323	−	0.461148i	$-0.152562\pi$
$809$	50.4761			1.77465			0.887323	+	0.461148i	$0.152562\pi$
$810$	−7.39828	+	0.515309i	−0.259949	+	0.0181061i
$811$	3.15050			0.110629			0.0553145	−	0.998469i	$-0.482384\pi$
$811$	3.15050			0.110629			0.0553145	+	0.998469i	$0.482384\pi$
$812$		0			0
$813$	15.2594			0.535170
$814$	55.0277	−	3.83282i	1.92872	−	0.134340i
$815$	−7.15612			−0.250668
$816$	−0.995308	−	3.48541i	−0.0348427	−	0.122014i
$817$		−	12.7232i		−	0.445128i
$818$	−3.16807	+	0.220664i	−0.110769	+	0.00771533i
$819$		0			0
$820$	1.64938	−	0.230887i	0.0575988	−	0.00806292i
$821$	−35.4832			−1.23837			−0.619187	−	0.785244i	$-0.712538\pi$
$821$	−35.4832			−1.23837			−0.619187	+	0.785244i	$0.712538\pi$
$822$	0.139604	+	2.00430i	0.00486927	+	0.0699080i
$823$		−	8.41130i		−	0.293199i	−0.989196	−	0.146600i	$-0.953167\pi$
$823$		−	8.41130i		−	0.293199i	0.989196	−	0.146600i	$-0.0468329\pi$
$824$	3.59569	+	16.9848i	0.125262	+	0.591693i
$825$			2.39306i			0.0833157i
$826$		0			0
$827$			4.33435i			0.150720i	0.997156	+	0.0753601i	$0.0240106\pi$
$827$			4.33435i			0.150720i	−0.997156	+	0.0753601i	$0.975989\pi$
$828$	−2.30459	−	16.4632i	−0.0800899	−	0.572136i
$829$			24.1798i			0.839801i	0.907570	+	0.419900i	$0.137935\pi$
$829$			24.1798i			0.839801i	−0.907570	+	0.419900i	$0.862065\pi$
$830$	9.15810	−	0.637885i	0.317882	−	0.0221413i
$831$	4.60046			0.159588
$832$	18.9013	+	42.6407i	0.655283	+	1.47830i
$833$		0			0
$834$	0.221005	+	3.17296i	0.00765277	+	0.109871i
$835$		−	13.7127i		−	0.474549i
$836$	−4.10293	−	29.3099i	−0.141903	−	1.01371i
$837$	32.6660			1.12910
$838$	1.80381	+	25.8973i	0.0623117	+	0.894608i
$839$	18.3056			0.631979			0.315989	−	0.948763i	$-0.397664\pi$
$839$	18.3056			0.631979			0.315989	+	0.948763i	$0.397664\pi$
$840$		0			0
$841$	−2.02999			−0.0699998
$842$	0.223367	+	3.20688i	0.00769774	+	0.110516i
$843$	−2.81097			−0.0968150
$844$	2.76821	+	19.7752i	0.0952856	+	0.680689i
$845$		−	20.9920i		−	0.722148i
$846$	1.73563	+	24.9184i	0.0596722	+	0.856712i
$847$		0			0
$848$	−28.5296	+	8.14704i	−0.979711	+	0.279770i
$849$	−5.65120			−0.193949
$850$	−1.93014	+	0.134439i	−0.0662034	+	0.00461123i
$851$		−	35.0344i		−	1.20096i
$852$	0.647361	+	4.62453i	0.0221782	+	0.158434i
$853$		−	16.9533i		−	0.580469i	−0.956956	−	0.290234i	$-0.906267\pi$
$853$		−	16.9533i		−	0.580469i	0.956956	−	0.290234i	$-0.0937332\pi$
$854$		0			0
$855$			10.4904i			0.358765i
$856$	−21.2180	+	4.49187i	−0.725218	+	0.153529i
$857$		−	50.5745i		−	1.72759i	−0.503843	−	0.863795i	$-0.668081\pi$
$857$		−	50.5745i		−	1.72759i	0.503843	−	0.863795i	$-0.331919\pi$
$858$	−1.37102	−	19.6837i	−0.0468058	−	0.671990i
$859$	−5.03849			−0.171911			−0.0859555	−	0.996299i	$-0.527394\pi$
$859$	−5.03849			−0.171911			−0.0859555	+	0.996299i	$0.527394\pi$
$860$	6.15285	−	0.861301i	0.209810	−	0.0293701i
$861$		0			0
$862$	−18.1442	+	1.26379i	−0.617993	+	0.0430448i
$863$		−	11.7417i		−	0.399691i	−0.979827	−	0.199846i	$-0.935956\pi$
$863$		−	11.7417i		−	0.399691i	0.979827	−	0.199846i	$-0.0640441\pi$
$864$	−7.10003	−	19.5903i	−0.241548	−	0.666477i
$865$	3.92439			0.133433
$866$	47.4460	−	3.30473i	1.61228	−	0.112299i
$867$	10.0203			0.340306
$868$		0			0
$869$	−40.9714			−1.38986
$870$	−4.85283	+	0.338012i	−0.164526	+	0.0114597i
$871$	−14.7949			−0.501307
$872$	−0.758743	−	3.58404i	−0.0256943	−	0.121371i
$873$		−	0.879005i		−	0.0297498i
$874$	−18.7517	+	1.30610i	−0.634284	+	0.0441795i
$875$		0			0
$876$	0.949429	+	6.78241i	0.0320782	+	0.229156i
$877$	−24.1824			−0.816581			−0.408290	−	0.912852i	$-0.633875\pi$
$877$	−24.1824			−0.816581			−0.408290	+	0.912852i	$0.633875\pi$
$878$	2.44553	+	35.1105i	0.0825327	+	1.18492i
$879$			16.7125i			0.563698i
$880$	13.8963	−	3.96830i	0.468446	−	0.133771i
$881$		−	19.6285i		−	0.661301i	−0.943753	−	0.330651i	$-0.892732\pi$
$881$		−	19.6285i		−	0.661301i	0.943753	−	0.330651i	$-0.107268\pi$
$882$		0			0
$883$			11.2418i			0.378315i	0.981947	+	0.189158i	$0.0605757\pi$
$883$			11.2418i			0.378315i	−0.981947	+	0.189158i	$0.939424\pi$
$884$	15.7990	−	2.21161i	0.531379	−	0.0743846i
$885$			4.95346i			0.166509i
$886$	−11.2126	+	0.780987i	−0.376695	+	0.0262378i
$887$	−41.8099			−1.40384			−0.701920	−	0.712256i	$-0.747674\pi$
$887$	−41.8099			−1.40384			−0.701920	+	0.712256i	$0.747674\pi$
$888$	−4.18882	−	19.7865i	−0.140568	−	0.663993i
$889$		0			0
$890$	0.922831	+	13.2491i	0.0309334	+	0.444110i
$891$		−	18.9465i		−	0.634733i
$892$	33.3111	−	4.66303i	1.11534	−	0.156130i
$893$	28.2445			0.945165
$894$	−1.24227	−	17.8352i	−0.0415476	−	0.596499i
$895$	20.5539			0.687040
$896$		0			0
$897$	−12.5320			−0.418430
$898$	1.40546	+	20.1782i	0.0469009	+	0.673356i
$899$	−46.0544			−1.53600
$900$	−5.07311	+	0.710155i	−0.169104	+	0.0236718i
$901$			10.1481i			0.338082i
$902$	0.295644	+	4.24455i	0.00984385	+	0.141328i
$903$		0			0
$904$	−4.16262	−	19.6628i	−0.138447	−	0.653974i
$905$	−13.0603			−0.434138
$906$	−8.97625	+	0.625218i	−0.298216	+	0.0207715i
$907$			21.8089i			0.724151i	0.932149	+	0.362076i	$0.117932\pi$
$907$			21.8089i			0.724151i	−0.932149	+	0.362076i	$0.882068\pi$
$908$	39.2846	−	5.49923i	1.30371	−	0.182498i
$909$		−	11.6189i		−	0.385374i
$910$		0			0
$911$		−	2.40991i		−	0.0798440i	−0.999203	−	0.0399220i	$-0.987289\pi$
$911$		−	2.40991i		−	0.0798440i	0.999203	−	0.0399220i	$-0.0127109\pi$
$912$	−10.4343	+	2.97966i	−0.345514	+	0.0986664i
$913$			23.4533i			0.776192i
$914$	2.17939	+	31.2895i	0.0720879	+	1.03497i
$915$	0.983957			0.0325286
$916$	3.86316	+	27.5971i	0.127642	+	0.911835i
$917$		0			0
$918$	−7.10977	+	0.495214i	−0.234657	+	0.0163445i
$919$		−	15.2029i		−	0.501498i	−0.968052	−	0.250749i	$-0.919323\pi$
$919$		−	15.2029i		−	0.501498i	0.968052	−	0.250749i	$-0.0806768\pi$
$920$	−1.90102	−	8.97976i	−0.0626749	−	0.296054i
$921$	19.3828			0.638685
$922$	46.3569	−	3.22888i	1.52668	−	0.106337i
$923$	−20.5518			−0.676470
$924$		0			0
$925$	−10.7958			−0.354963
$926$	−4.67526	+	0.325644i	−0.153639	+	0.0107013i
$927$	15.7215			0.516361
$928$	10.0100	+	27.6196i	0.328595	+	0.906656i
$929$		−	20.8695i		−	0.684704i	−0.939572	−	0.342352i	$-0.888776\pi$
$929$		−	20.8695i		−	0.684704i	0.939572	−	0.342352i	$-0.111224\pi$
$930$	8.28676	−	0.577194i	0.271734	−	0.0189269i
$931$		0			0
$932$	−20.2538	+	2.83522i	−0.663437	+	0.0928706i
$933$	−15.0660			−0.493238
$934$	3.45240	+	49.5661i	0.112966	+	1.62185i
$935$		−	4.94298i		−	0.161653i
$936$	41.3211	−	8.74770i	1.35062	−	0.285928i
$937$			10.9083i			0.356358i	0.983998	+	0.178179i	$0.0570206\pi$
$937$			10.9083i			0.356358i	−0.983998	+	0.178179i	$0.942979\pi$
$938$		0			0
$939$		−	4.36148i		−	0.142331i
$940$	1.91202	+	13.6588i	0.0623633	+	0.445502i
$941$		−	49.3714i		−	1.60946i	−0.593641	−	0.804730i	$-0.702310\pi$
$941$		−	49.3714i		−	1.60946i	0.593641	−	0.804730i	$-0.297690\pi$
$942$	−15.3832	+	1.07148i	−0.501212	+	0.0349106i
$943$	2.70237			0.0880012
$944$	28.7644	−	8.21408i	0.936202	−	0.267346i
$945$		0			0
$946$	1.10287	+	15.8339i	0.0358574	+	0.514804i
$947$			14.5586i			0.473091i	0.971620	+	0.236545i	$0.0760152\pi$
$947$			14.5586i			0.473091i	−0.971620	+	0.236545i	$0.923985\pi$
$948$	2.08258	+	14.8773i	0.0676392	+	0.483192i
$949$	−30.1416			−0.978437
$950$	0.402472	+	5.77829i	0.0130579	+	0.187473i
$951$	−9.35358			−0.303311
$952$		0			0
$953$	−9.87954			−0.320030			−0.160015	−	0.987115i	$-0.551154\pi$
$953$	−9.87954			−0.320030			−0.160015	+	0.987115i	$0.551154\pi$
$954$	1.86689	+	26.8028i	0.0604426	+	0.867774i
$955$	12.4751			0.403685
$956$	4.73664	+	33.8370i	0.153194	+	1.09437i
$957$		−	12.4278i		−	0.401734i
$958$	2.19394	+	31.4983i	0.0708829	+	1.01766i
$959$		0			0
$960$	−2.14730	−	4.84425i	−0.0693038	−	0.156348i
$961$	47.6431			1.53687
$962$	88.7988	−	6.18506i	2.86299	−	0.199414i
$963$			19.6399i			0.632886i
$964$	5.12488	+	36.6104i	0.165061	+	1.17914i
$965$			19.0645i			0.613708i
$966$		0			0
$967$			15.5047i			0.498597i	0.968427	+	0.249298i	$0.0802000\pi$
$967$			15.5047i			0.498597i	−0.968427	+	0.249298i	$0.919800\pi$
$968$	1.20293	+	5.68221i	0.0386636	+	0.182633i
$969$			3.71152i			0.119231i
$970$	−0.0337236	−	0.484169i	−0.00108280	−	0.0155457i
$971$	33.0347			1.06013			0.530067	−	0.847956i	$-0.322167\pi$
$971$	33.0347			1.06013			0.530067	+	0.847956i	$0.322167\pi$
$972$	−28.7676	+	4.02701i	−0.922721	+	0.129166i
$973$		0			0
$974$	−10.1368	+	0.706056i	−0.324805	+	0.0226235i
$975$			3.86171i			0.123674i
$976$	−1.63165	−	5.71377i	−0.0522278	−	0.182893i
$977$	−50.9720			−1.63074			−0.815369	−	0.578941i	$-0.803466\pi$
$977$	−50.9720			−1.63074			−0.815369	+	0.578941i	$0.803466\pi$
$978$	−6.68701	+	0.465767i	−0.213827	+	0.0148936i
$979$	−33.9301			−1.08441
$980$		0			0
$981$	−3.31746			−0.105918
$982$	−8.18345	+	0.569998i	−0.261144	+	0.0181894i
$983$	24.5284			0.782336			0.391168	−	0.920319i	$-0.372071\pi$
$983$	24.5284			0.782336			0.391168	+	0.920319i	$0.372071\pi$
$984$	1.52623	−	0.323104i	0.0486544	−	0.0103002i
$985$			1.93188i			0.0615548i
$986$	10.0238	−	0.698180i	0.319221	−	0.0222346i
$987$		0			0
$988$	−6.62093	−	47.2977i	−0.210640	−	1.50474i
$989$	10.0809			0.320555
$990$	−0.909332	−	13.0553i	−0.0289005	−	0.414923i
$991$		−	52.9169i		−	1.68096i	−0.541841	−	0.840481i	$-0.682273\pi$
$991$		−	52.9169i		−	1.68096i	0.541841	−	0.840481i	$-0.317727\pi$
$992$	−17.0933	−	47.1635i	−0.542712	−	1.49744i
$993$			13.4606i			0.427160i
$994$		0			0
$995$			20.5646i			0.651941i
$996$	8.51624	−	1.19214i	0.269847	−	0.0377744i
$997$			17.0230i			0.539123i	0.962983	+	0.269561i	$0.0868787\pi$
$997$			17.0230i			0.539123i	−0.962983	+	0.269561i	$0.913121\pi$
$998$	55.9523	−	3.89722i	1.77114	−	0.123364i
$999$	−39.7667			−1.25816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.g.a.391.20		32
4.3	odd	2	inner	980.2.g.a.391.17		32
7.2	even	3		980.2.o.f.31.14		32
7.3	odd	6		980.2.o.f.411.2		32
7.4	even	3		140.2.o.a.131.2	yes	32
7.5	odd	6		140.2.o.a.31.14	yes	32
7.6	odd	2	inner	980.2.g.a.391.19		32
28.3	even	6		980.2.o.f.411.14		32
28.11	odd	6		140.2.o.a.131.14	yes	32
28.19	even	6		140.2.o.a.31.2	✓	32
28.23	odd	6		980.2.o.f.31.2		32
28.27	even	2	inner	980.2.g.a.391.18		32
35.4	even	6		700.2.p.c.551.15		32
35.12	even	12		700.2.t.c.199.12		32
35.18	odd	12		700.2.t.c.299.7		32
35.19	odd	6		700.2.p.c.451.3		32
35.32	odd	12		700.2.t.d.299.10		32
35.33	even	12		700.2.t.d.199.5		32
140.19	even	6		700.2.p.c.451.15		32
140.39	odd	6		700.2.p.c.551.3		32
140.47	odd	12		700.2.t.c.199.7		32
140.67	even	12		700.2.t.d.299.5		32
140.103	odd	12		700.2.t.d.199.10		32
140.123	even	12		700.2.t.c.299.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.2	✓	32	28.19	even	6
140.2.o.a.31.14	yes	32	7.5	odd	6
140.2.o.a.131.2	yes	32	7.4	even	3
140.2.o.a.131.14	yes	32	28.11	odd	6
700.2.p.c.451.3		32	35.19	odd	6
700.2.p.c.451.15		32	140.19	even	6
700.2.p.c.551.3		32	140.39	odd	6
700.2.p.c.551.15		32	35.4	even	6
700.2.t.c.199.7		32	140.47	odd	12
700.2.t.c.199.12		32	35.12	even	12
700.2.t.c.299.7		32	35.18	odd	12
700.2.t.c.299.12		32	140.123	even	12
700.2.t.d.199.5		32	35.33	even	12
700.2.t.d.199.10		32	140.103	odd	12
700.2.t.d.299.5		32	140.67	even	12
700.2.t.d.299.10		32	35.32	odd	12
980.2.g.a.391.17		32	4.3	odd	2	inner
980.2.g.a.391.18		32	28.27	even	2	inner
980.2.g.a.391.19		32	7.6	odd	2	inner
980.2.g.a.391.20		32	1.1	even	1	trivial
980.2.o.f.31.2		32	28.23	odd	6
980.2.o.f.31.14		32	7.2	even	3
980.2.o.f.411.2		32	7.3	odd	6
980.2.o.f.411.14		32	28.3	even	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +O(q^{10})\)	\(q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(-1.41080 + 0.0982654i) q^{10} -3.61296i q^{11} +(-1.31192 + 0.183648i) q^{12} -5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} -1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} -4.09577 q^{19} +(-0.277265 - 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(-0.388005 - 1.83280i) q^{24} -1.00000 q^{25} +(8.22532 - 0.572914i) q^{26} -3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} -8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} -2.39306i q^{33} +(1.93014 - 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(-0.402472 - 5.77829i) q^{38} -3.86171i q^{39} +(2.76710 - 0.585797i) q^{40} +0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} -2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} -6.89601 q^{47} +(2.54758 - 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(1.61653 + 11.5479i) q^{52} -7.41752 q^{53} +(-0.361965 - 5.19673i) q^{54} +3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} +7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} -1.48554i q^{61} +(-0.871427 - 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(3.37612 - 0.235155i) q^{66} -2.53761i q^{67} +(0.379333 + 2.70983i) q^{68} -2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} -5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} -0.662355 q^{75} +(8.11244 - 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(1.09835 + 3.84625i) q^{80} +5.24405 q^{81} +(-1.17481 + 0.0818286i) q^{82} -6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} +3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} -9.39121i q^{89} +(3.61345 - 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(-0.677640 - 9.72886i) q^{94} -4.09577i q^{95} +(1.27669 + 3.52263i) q^{96} +0.343189i q^{97} +9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

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