LMFDB - Embedded newform 700.2.t.e.299.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(199,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("700.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.14
Character	$\chi$	$=$	700.299
Dual form			700.2.t.e.199.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.183411 + 1.40227i) q^{2} +(2.33023 - 1.34536i) q^{3} +(-1.93272 - 0.514384i) q^{4} +(1.45917 + 3.51437i) q^{6} +(0.0832596 - 2.64444i) q^{7} +(1.07579 - 2.61585i) q^{8} +(2.11999 - 3.67193i) q^{9} +O(q^{10})$	\(q+(-0.183411 + 1.40227i) q^{2} +(2.33023 - 1.34536i) q^{3} +(-1.93272 - 0.514384i) q^{4} +(1.45917 + 3.51437i) q^{6} +(0.0832596 - 2.64444i) q^{7} +(1.07579 - 2.61585i) q^{8} +(2.11999 - 3.67193i) q^{9} +(-1.31689 + 0.760309i) q^{11} +(-5.19572 + 1.40157i) q^{12} -1.14083 q^{13} +(3.69295 + 0.601773i) q^{14} +(3.47082 + 1.98832i) q^{16} +(2.21516 + 3.83677i) q^{17} +(4.76020 + 3.64627i) q^{18} +(3.04859 - 5.28032i) q^{19} +(-3.36371 - 6.27418i) q^{21} +(-0.824625 - 1.98609i) q^{22} +(4.02522 - 6.97188i) q^{23} +(-1.01243 - 7.54287i) q^{24} +(0.209240 - 1.59975i) q^{26} -3.33644i q^{27} +(-1.52118 + 5.06814i) q^{28} +1.38419 q^{29} +(-4.92478 - 8.52996i) q^{31} +(-3.42475 + 4.50234i) q^{32} +(-2.04578 + 3.54340i) q^{33} +(-5.78647 + 2.40255i) q^{34} +(-5.98613 + 6.00632i) q^{36} +(8.48551 + 4.89911i) q^{37} +(6.84529 + 5.24342i) q^{38} +(-2.65839 + 1.53482i) q^{39} -1.36595i q^{41} +(9.41503 - 3.56608i) q^{42} -4.89552 q^{43} +(2.93628 - 0.792076i) q^{44} +(9.03818 + 6.92316i) q^{46} +(2.86528 + 1.65427i) q^{47} +(10.7628 - 0.0362457i) q^{48} +(-6.98614 - 0.440350i) q^{49} +(10.3237 + 5.96038i) q^{51} +(2.20490 + 0.586823i) q^{52} +(-8.36094 + 4.82719i) q^{53} +(4.67858 + 0.611940i) q^{54} +(-6.82789 - 3.06265i) q^{56} -16.4058i q^{57} +(-0.253876 + 1.94100i) q^{58} +(0.927258 + 1.60606i) q^{59} +(-3.93142 - 2.26981i) q^{61} +(12.8646 - 5.34137i) q^{62} +(-9.53369 - 5.91191i) q^{63} +(-5.68536 - 5.62821i) q^{64} +(-4.59358 - 3.51864i) q^{66} +(5.25787 + 9.10690i) q^{67} +(-2.30771 - 8.55485i) q^{68} -21.6615i q^{69} +6.04297i q^{71} +(-7.32456 - 9.49580i) q^{72} +(3.93073 + 6.80823i) q^{73} +(-8.42621 + 11.0004i) q^{74} +(-8.60820 + 8.63723i) q^{76} +(1.90095 + 3.54575i) q^{77} +(-1.66466 - 4.00928i) q^{78} +(-4.54388 - 2.62341i) q^{79} +(1.87126 + 3.24111i) q^{81} +(1.91544 + 0.250532i) q^{82} +8.98431i q^{83} +(3.27378 + 13.8565i) q^{84} +(0.897895 - 6.86484i) q^{86} +(3.22548 - 1.86223i) q^{87} +(0.572156 + 4.26273i) q^{88} +(12.9144 + 7.45614i) q^{89} +(-0.0949847 + 3.01685i) q^{91} +(-11.3658 + 11.4042i) q^{92} +(-22.9517 - 13.2512i) q^{93} +(-2.84526 + 3.71448i) q^{94} +(-1.92320 + 15.0990i) q^{96} -15.0890 q^{97} +(1.89883 - 9.71568i) q^{98} +6.44739i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) $ 64 * q - 2 * q^4 + 32 * q^9	$ 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) $ 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.183411	+	1.40227i	−0.129691	+	0.991554i
$2$	−0.183411	+	1.40227i	−0.129691	+	0.991554i
$3$	2.33023	−	1.34536i	1.34536	−	0.776744i	0.357772	−	0.933809i	$-0.383536\pi$
$3$	2.33023	−	1.34536i	1.34536	−	0.776744i	0.987588	+	0.157065i	$0.0502031\pi$
$4$	−1.93272	−	0.514384i	−0.966360	−	0.257192i
$5$		0			0
$5$		0			0
$6$	1.45917	+	3.51437i	0.595702	+	1.43474i
$7$	0.0832596	−	2.64444i	0.0314692	−	0.999505i
$7$	0.0832596	−	2.64444i	0.0314692	−	0.999505i
$8$	1.07579	−	2.61585i	0.380349	−	0.924843i
$9$	2.11999	−	3.67193i	0.706663	−	1.22398i
$10$		0			0
$11$	−1.31689	+	0.760309i	−0.397059	+	0.229242i	−0.685214	−	0.728342i	$-0.740291\pi$
$11$	−1.31689	+	0.760309i	−0.397059	+	0.229242i	0.288155	+	0.957584i	$0.406958\pi$
$12$	−5.19572	+	1.40157i	−1.49988	+	0.404598i
$13$	−1.14083			−0.316408			−0.158204	−	0.987406i	$-0.550570\pi$
$13$	−1.14083			−0.316408			−0.158204	+	0.987406i	$0.550570\pi$
$14$	3.69295	+	0.601773i	0.986982	+	0.160831i
$15$		0			0
$16$	3.47082	+	1.98832i	0.867704	+	0.497081i
$17$	2.21516	+	3.83677i	0.537255	+	0.930554i	0.999051	+	0.0435670i	$0.0138722\pi$
$17$	2.21516	+	3.83677i	0.537255	+	0.930554i	−0.461795	+	0.886987i	$0.652794\pi$
$18$	4.76020	+	3.64627i	1.12199	+	0.859434i
$19$	3.04859	−	5.28032i	0.699396	−	1.21139i	−0.269281	−	0.963062i	$-0.586786\pi$
$19$	3.04859	−	5.28032i	0.699396	−	1.21139i	0.968676	−	0.248327i	$-0.0798807\pi$
$20$		0			0
$21$	−3.36371	−	6.27418i	−0.734022	−	1.36914i
$22$	−0.824625	−	1.98609i	−0.175811	−	0.423436i
$23$	4.02522	−	6.97188i	0.839315	−	1.45374i	−0.0511526	−	0.998691i	$-0.516289\pi$
$23$	4.02522	−	6.97188i	0.839315	−	1.45374i	0.890468	−	0.455046i	$-0.150377\pi$
$24$	−1.01243	−	7.54287i	−0.206660	−	1.53968i
$25$		0			0
$26$	0.209240	−	1.59975i	0.0410354	−	0.313736i
$27$		−	3.33644i		−	0.642098i
$28$	−1.52118	+	5.06814i	−0.287475	+	0.957788i
$29$	1.38419			0.257037			0.128519	−	0.991707i	$-0.458978\pi$
$29$	1.38419			0.257037			0.128519	+	0.991707i	$0.458978\pi$
$30$		0			0
$31$	−4.92478	−	8.52996i	−0.884516	−	1.53203i	−0.846268	−	0.532758i	$-0.821156\pi$
$31$	−4.92478	−	8.52996i	−0.884516	−	1.53203i	−0.0382482	−	0.999268i	$-0.512178\pi$
$32$	−3.42475	+	4.50234i	−0.605416	+	0.795909i
$33$	−2.04578	+	3.54340i	−0.356125	+	0.616826i
$34$	−5.78647	+	2.40255i	−0.992372	+	0.412033i
$35$		0			0
$36$	−5.98613	+	6.00632i	−0.997688	+	1.00105i
$37$	8.48551	+	4.89911i	1.39501	+	0.805409i	0.993864	−	0.110606i	$-0.0352792\pi$
$37$	8.48551	+	4.89911i	1.39501	+	0.805409i	0.401144	+	0.916015i	$0.368613\pi$
$38$	6.84529	+	5.24342i	1.11045	+	0.850595i
$39$	−2.65839	+	1.53482i	−0.425683	+	0.245768i
$40$		0			0
$41$		−	1.36595i		−	0.213326i	−0.994295	−	0.106663i	$-0.965983\pi$
$41$		−	1.36595i		−	0.213326i	0.994295	−	0.106663i	$-0.0340166\pi$
$42$	9.41503	−	3.56608i	1.45277	−	0.550257i
$43$	−4.89552			−0.746560			−0.373280	−	0.927719i	$-0.621767\pi$
$43$	−4.89552			−0.746560			−0.373280	+	0.927719i	$0.621767\pi$
$44$	2.93628	−	0.792076i	0.442661	−	0.119410i
$45$		0			0
$46$	9.03818	+	6.92316i	1.33261	+	1.02076i
$47$	2.86528	+	1.65427i	0.417944	+	0.241300i	0.694197	−	0.719785i	$-0.255760\pi$
$47$	2.86528	+	1.65427i	0.417944	+	0.241300i	−0.276253	+	0.961085i	$0.589093\pi$
$48$	10.7628	−	0.0362457i	1.55348	−	0.00523162i
$49$	−6.98614	−	0.440350i	−0.998019	−	0.0629072i
$50$		0			0
$51$	10.3237	+	5.96038i	1.44560	+	0.834620i
$52$	2.20490	+	0.586823i	0.305764	+	0.0813777i
$53$	−8.36094	+	4.82719i	−1.14846	+	0.663065i	−0.948512	−	0.316740i	$-0.897412\pi$
$53$	−8.36094	+	4.82719i	−1.14846	+	0.663065i	−0.199951	+	0.979806i	$0.564078\pi$
$54$	4.67858	+	0.611940i	0.636675	+	0.0832746i
$55$		0			0
$56$	−6.82789	−	3.06265i	−0.912416	−	0.409264i
$57$		−	16.4058i		−	2.17301i
$58$	−0.253876	+	1.94100i	−0.0333355	+	0.254866i
$59$	0.927258	+	1.60606i	0.120719	+	0.209091i	0.920051	−	0.391798i	$-0.128147\pi$
$59$	0.927258	+	1.60606i	0.120719	+	0.209091i	−0.799333	+	0.600889i	$0.794813\pi$
$60$		0			0
$61$	−3.93142	−	2.26981i	−0.503367	−	0.290619i	0.226736	−	0.973956i	$-0.427195\pi$
$61$	−3.93142	−	2.26981i	−0.503367	−	0.290619i	−0.730103	+	0.683337i	$0.760528\pi$
$62$	12.8646	−	5.34137i	1.63380	−	0.678355i
$63$	−9.53369	−	5.91191i	−1.20113	−	0.744831i
$64$	−5.68536	−	5.62821i	−0.710670	−	0.703526i
$65$		0			0
$66$	−4.59358	−	3.51864i	−0.565430	−	0.433114i
$67$	5.25787	+	9.10690i	0.642351	+	1.11259i	0.984906	+	0.173088i	$0.0553743\pi$
$67$	5.25787	+	9.10690i	0.642351	+	1.11259i	−0.342555	+	0.939498i	$0.611292\pi$
$68$	−2.30771	−	8.55485i	−0.279851	−	1.03743i
$69$		−	21.6615i		−	2.60773i
$70$		0			0
$71$			6.04297i			0.717169i	0.933497	+	0.358584i	$0.116740\pi$
$71$			6.04297i			0.717169i	−0.933497	+	0.358584i	$0.883260\pi$
$72$	−7.32456	−	9.49580i	−0.863208	−	1.11909i
$73$	3.93073	+	6.80823i	0.460057	+	0.796843i	0.998963	−	0.0455231i	$-0.0144955\pi$
$73$	3.93073	+	6.80823i	0.460057	+	0.796843i	−0.538906	+	0.842366i	$0.681162\pi$
$74$	−8.42621	+	11.0004i	−0.979527	+	1.27877i
$75$		0			0
$76$	−8.60820	+	8.63723i	−0.987428	+	0.990759i
$77$	1.90095	+	3.54575i	0.216633	+	0.404076i
$78$	−1.66466	−	4.00928i	−0.188485	−	0.453962i
$79$	−4.54388	−	2.62341i	−0.511226	−	0.295157i	0.222111	−	0.975021i	$-0.428705\pi$
$79$	−4.54388	−	2.62341i	−0.511226	−	0.295157i	−0.733338	+	0.679865i	$0.762038\pi$
$80$		0			0
$81$	1.87126	+	3.24111i	0.207918	+	0.360124i
$82$	1.91544	+	0.250532i	0.211525	+	0.0276666i
$83$			8.98431i			0.986156i	0.869985	+	0.493078i	$0.164128\pi$
$83$			8.98431i			0.986156i	−0.869985	+	0.493078i	$0.835872\pi$
$84$	3.27378	+	13.8565i	0.357198	+	1.51186i
$85$		0			0
$86$	0.897895	−	6.86484i	0.0968225	−	0.740255i
$87$	3.22548	−	1.86223i	0.345808	−	0.199652i
$88$	0.572156	+	4.26273i	0.0609921	+	0.454409i
$89$	12.9144	+	7.45614i	1.36893	+	0.790350i	0.990791	−	0.135401i	$-0.0432322\pi$
$89$	12.9144	+	7.45614i	1.36893	+	0.790350i	0.378135	+	0.925750i	$0.376566\pi$
$90$		0			0
$91$	−0.0949847	+	3.01685i	−0.00995710	+	0.316252i
$92$	−11.3658	+	11.4042i	−1.18497	+	1.18897i
$93$	−22.9517	−	13.2512i	−2.37999	−	1.37409i
$94$	−2.84526	+	3.71448i	−0.293466	+	0.383119i
$95$		0			0
$96$	−1.92320	+	15.0990i	−0.196286	+	1.54104i
$97$	−15.0890			−1.53206			−0.766028	−	0.642807i	$-0.777770\pi$
$97$	−15.0890			−1.53206			−0.766028	+	0.642807i	$0.777770\pi$
$98$	1.89883	−	9.71568i	0.191810	−	0.981432i
$99$			6.44739i			0.647987i
$100$		0			0
$101$	7.56651	−	4.36853i	0.752896	−	0.434685i	−0.0738431	−	0.997270i	$-0.523526\pi$
$101$	7.56651	−	4.36853i	0.752896	−	0.434685i	0.826739	+	0.562585i	$0.190193\pi$
$102$	−10.2515	+	13.3834i	−1.01505	+	1.32515i
$103$	10.6957	+	6.17515i	1.05388	+	0.608456i	0.923732	−	0.383039i	$-0.125123\pi$
$103$	10.6957	+	6.17515i	1.05388	+	0.608456i	0.130144	+	0.991495i	$0.458456\pi$
$104$	−1.22729	+	2.98423i	−0.120345	+	0.292628i
$105$		0			0
$106$	−5.23553	−	12.6097i	−0.508520	−	1.22476i
$107$	−6.53172	+	11.3133i	−0.631445	+	1.09370i	0.355811	+	0.934558i	$0.384205\pi$
$107$	−6.53172	+	11.3133i	−0.631445	+	1.09370i	−0.987256	+	0.159138i	$0.949129\pi$
$108$	−1.71621	+	6.44840i	−0.165142	+	0.620498i
$109$	1.09661	+	1.89938i	0.105036	+	0.181928i	0.913753	−	0.406270i	$-0.133171\pi$
$109$	1.09661	+	1.89938i	0.105036	+	0.181928i	−0.808717	+	0.588198i	$0.799838\pi$
$110$		0			0
$111$	26.3643			2.50239
$112$	5.54698	−	9.01282i	0.524140	−	0.851632i
$113$			0.438071i			0.0412102i	0.999788	+	0.0206051i	$0.00655927\pi$
$113$			0.438071i			0.0412102i	−0.999788	+	0.0206051i	$0.993441\pi$
$114$	23.0054	+	3.00902i	2.15465	+	0.281820i
$115$		0			0
$116$	−2.67525	−	0.712005i	−0.248391	−	0.0661080i
$117$	−2.41854	+	4.18903i	−0.223594	+	0.387276i
$118$	−2.42220	+	1.00570i	−0.222981	+	0.0925818i
$119$	10.3305	−	5.53841i	0.947000	−	0.507706i
$120$		0			0
$121$	−4.34386	+	7.52378i	−0.394896	+	0.683980i
$122$	3.90395	−	5.09661i	0.353447	−	0.461425i
$123$	−1.83770	−	3.18299i	−0.165700	−	0.287001i
$124$	5.13054	+	19.0193i	0.460736	+	1.70798i
$125$		0			0
$126$	10.0387	−	12.2845i	0.894317	−	1.09439i
$127$	−1.99716			−0.177219			−0.0886097	−	0.996066i	$-0.528242\pi$
$127$	−1.99716			−0.177219			−0.0886097	+	0.996066i	$0.528242\pi$
$128$	8.93502	−	6.94013i	0.789752	−	0.613426i
$129$	−11.4077	+	6.58624i	−1.00439	+	0.579886i
$130$		0			0
$131$	−2.97821	+	5.15841i	−0.260207	+	0.450693i	−0.966297	−	0.257430i	$-0.917124\pi$
$131$	−2.97821	+	5.15841i	−0.260207	+	0.450693i	0.706089	+	0.708123i	$0.250458\pi$
$132$	5.77659	−	5.79608i	0.502788	−	0.504484i
$133$	−13.7097	−	8.50147i	−1.18878	−	0.737171i
$134$	−13.7347	+	5.70265i	−1.18650	+	0.492634i
$135$		0			0
$136$	12.4195	−	1.66698i	1.06496	−	0.142942i
$137$	9.41669	−	5.43673i	0.804522	−	0.464491i	−0.0405280	−	0.999178i	$-0.512904\pi$
$137$	9.41669	−	5.43673i	0.804522	−	0.464491i	0.845050	+	0.534687i	$0.179571\pi$
$138$	30.3752	+	3.97296i	2.58571	+	0.338201i
$139$	3.31327			0.281028			0.140514	−	0.990079i	$-0.455124\pi$
$139$	3.31327			0.281028			0.140514	+	0.990079i	$0.455124\pi$
$140$		0			0
$141$	8.90235			0.749713
$142$	−8.47388	−	1.10835i	−0.711112	−	0.0930106i
$143$	1.50235	−	0.867381i	0.125633	−	0.0725340i
$144$	14.6591	−	8.52937i	1.22159	−	0.710781i
$145$		0			0
$146$	−10.2679	+	4.26324i	−0.849779	+	0.352828i
$147$	−16.8718	+	8.37275i	−1.39156	+	0.690573i
$148$	−13.8801	−	13.8334i	−1.14094	−	1.13710i
$149$	−3.19588	+	5.53542i	−0.261816	+	0.453479i	−0.966725	−	0.255819i	$-0.917655\pi$
$149$	−3.19588	+	5.53542i	−0.261816	+	0.453479i	0.704908	+	0.709299i	$0.250988\pi$
$150$		0			0
$151$	−8.15432	+	4.70790i	−0.663589	+	0.383123i	−0.793643	−	0.608384i	$-0.791818\pi$
$151$	−8.15432	+	4.70790i	−0.663589	+	0.383123i	0.130054	+	0.991507i	$0.458485\pi$
$152$	−10.5329	−	13.6552i	−0.854330	−	1.10758i
$153$	18.7845			1.51863
$154$	−5.32076	+	2.01531i	−0.428759	+	0.162398i
$155$		0			0
$156$	5.92741	−	1.59895i	0.474573	−	0.128018i
$157$	4.31144	+	7.46763i	0.344090	+	0.595981i	0.985188	−	0.171478i	$-0.0548541\pi$
$157$	4.31144	+	7.46763i	0.344090	+	0.595981i	−0.641098	+	0.767459i	$0.721521\pi$
$158$	4.51213	−	5.89058i	0.358965	−	0.468629i
$159$	−12.9886	+	22.4969i	−1.03006	+	1.78412i
$160$		0			0
$161$	−18.1016	−	11.2249i	−1.42660	−	0.884648i
$162$	−4.88813	+	2.02955i	−0.384047	+	0.159457i
$163$	−4.49487	+	7.78534i	−0.352065	+	0.609795i	−0.986611	−	0.163090i	$-0.947854\pi$
$163$	−4.49487	+	7.78534i	−0.352065	+	0.609795i	0.634546	+	0.772885i	$0.281187\pi$
$164$	−0.702626	+	2.64001i	−0.0548658	+	0.206150i
$165$		0			0
$166$	−12.5984	−	1.64783i	−0.977828	−	0.127896i
$167$		−	0.00367263i		−	0.000284197i	−1.00000		0.000142098i	$-0.999955\pi$
$167$		−	0.00367263i		−	0.000284197i	1.00000		0.000142098i	$-4.52313e-5\pi$
$168$	−20.0310	+	2.04928i	−1.54542	+	0.158106i
$169$	−11.6985			−0.899886
$170$		0			0
$171$	−12.9260	−	22.3884i	−0.988474	−	1.71209i
$172$	9.46168	+	2.51818i	0.721446	+	0.192010i
$173$	5.94042	−	10.2891i	0.451641	−	0.782266i	−0.546847	−	0.837233i	$-0.684172\pi$
$173$	5.94042	−	10.2891i	0.451641	−	0.782266i	0.998488	+	0.0549668i	$0.0175053\pi$
$174$	2.01976	+	4.86455i	0.153118	+	0.368780i
$175$		0			0
$176$	−6.08244	+	0.0204837i	−0.458481	+	0.00154402i
$177$	4.32145	+	2.49499i	0.324820	+	0.187535i
$178$	−12.8242	+	16.7420i	−0.961213	+	1.25486i
$179$	12.5385	−	7.23913i	0.937174	−	0.541078i	0.0481009	−	0.998842i	$-0.484683\pi$
$179$	12.5385	−	7.23913i	0.937174	−	0.541078i	0.889073	+	0.457765i	$0.151350\pi$
$180$		0			0
$181$		−	8.05013i		−	0.598361i	−0.954197	−	0.299181i	$-0.903287\pi$
$181$		−	8.05013i		−	0.598361i	0.954197	−	0.299181i	$-0.0967133\pi$
$182$	−4.21301	−	0.686518i	−0.312289	−	0.0508881i
$183$	−12.2148			−0.902947
$184$	−13.9071	−	18.0296i	−1.02525	−	1.32916i
$185$		0			0
$186$	22.7914	−	29.7541i	1.67114	−	2.18168i
$187$	−5.83427	−	3.36842i	−0.426644	−	0.246323i
$188$	−4.68685	−	4.67109i	−0.341824	−	0.340675i
$189$	−8.82301	−	0.277790i	−0.641780	−	0.0202063i
$190$		0			0
$191$	−13.3777	−	7.72364i	−0.967979	−	0.558863i	−0.0693596	−	0.997592i	$-0.522096\pi$
$191$	−13.3777	−	7.72364i	−0.967979	−	0.558863i	−0.898620	+	0.438729i	$0.855429\pi$
$192$	−20.8202	−	5.46618i	−1.50257	−	0.394487i
$193$	7.63645	−	4.40891i	0.549684	−	0.317360i	−0.199311	−	0.979936i	$-0.563870\pi$
$193$	7.63645	−	4.40891i	0.549684	−	0.317360i	0.748995	+	0.662576i	$0.230537\pi$
$194$	2.76750	−	21.1589i	0.198695	−	1.51912i
$195$		0			0
$196$	13.2757	+	4.44463i	0.948267	+	0.317474i
$197$		−	23.8599i		−	1.69995i	−0.526823	−	0.849975i	$-0.676617\pi$
$197$		−	23.8599i		−	1.69995i	0.526823	−	0.849975i	$-0.323383\pi$
$198$	−9.04098	−	1.18253i	−0.642515	−	0.0840384i
$199$	−4.11913	−	7.13455i	−0.291998	−	0.505755i	0.682284	−	0.731087i	$-0.260987\pi$
$199$	−4.11913	−	7.13455i	−0.291998	−	0.505755i	−0.974282	+	0.225332i	$0.927653\pi$
$200$		0			0
$201$	24.5041	+	14.1475i	1.72839	+	0.997885i
$202$	4.73807	+	11.4115i	0.333370	+	0.802913i
$203$	0.115247	−	3.66040i	0.00808875	−	0.256910i
$204$	−16.8869	−	16.8301i	−1.18232	−	1.17834i
$205$		0			0
$206$	−10.6209	+	13.8656i	−0.739996	+	0.966064i
$207$	−17.0668	−	29.5606i	−1.18623	−	2.05460i
$208$	−3.95960	−	2.26833i	−0.274549	−	0.157280i
$209$			9.27150i			0.641323i
$210$		0			0
$211$		−	17.1674i		−	1.18185i	−0.806726	−	0.590926i	$-0.798763\pi$
$211$		−	17.1674i		−	1.18185i	0.806726	−	0.590926i	$-0.201237\pi$
$212$	18.6424	−	5.02887i	1.28036	−	0.345384i
$213$	8.12997	+	14.0815i	0.557057	+	0.964851i
$214$	−14.6663	−	11.2342i	−1.00257	−	0.767955i
$215$		0			0
$216$	−8.72762	−	3.58930i	−0.593840	−	0.244221i
$217$	−22.9670	+	12.3131i	−1.55910	+	0.835866i
$218$	−2.86457	+	1.18937i	−0.194013	+	0.0805544i
$219$	18.3190	+	10.5765i	1.23789	+	0.714694i
$220$		0			0
$221$	−2.52711	−	4.37709i	−0.169992	−	0.294435i
$222$	−4.83551	+	36.9698i	−0.324538	+	2.48125i
$223$			6.43164i			0.430694i	0.976538	+	0.215347i	$0.0690883\pi$
$223$			6.43164i			0.430694i	−0.976538	+	0.215347i	$0.930912\pi$
$224$	11.6210	+	9.43142i	0.776463	+	0.630163i
$225$		0			0
$226$	−0.614293	−	0.0803471i	−0.0408622	−	0.00534461i
$227$	21.8972	−	12.6423i	1.45337	−	0.839101i	0.454694	−	0.890647i	$-0.349748\pi$
$227$	21.8972	−	12.6423i	1.45337	−	0.839101i	0.998671	+	0.0515468i	$0.0164151\pi$
$228$	−8.43891	+	31.7079i	−0.558880	+	2.09991i
$229$	0.643228	+	0.371368i	0.0425057	+	0.0245407i	0.521102	−	0.853494i	$-0.325521\pi$
$229$	0.643228	+	0.371368i	0.0425057	+	0.0245407i	−0.478597	+	0.878035i	$0.658854\pi$
$230$		0			0
$231$	9.19997	+	5.70497i	0.605314	+	0.375359i
$232$	1.48909	−	3.62083i	0.0977638	−	0.237719i
$233$	14.4250	+	8.32828i	0.945014	+	0.545604i	0.891528	−	0.452965i	$-0.149634\pi$
$233$	14.4250	+	8.32828i	0.945014	+	0.545604i	0.0534854	+	0.998569i	$0.482967\pi$
$234$	−5.43057	−	4.15976i	−0.355007	−	0.271932i
$235$		0			0
$236$	−0.965999	−	3.58103i	−0.0628812	−	0.233105i
$237$	−14.1177			−0.917045
$238$	5.87161	+	15.5020i	0.380600	+	1.00485i
$239$			0.321078i			0.0207688i	0.999946	+	0.0103844i	$0.00330552\pi$
$239$			0.321078i			0.0207688i	−0.999946	+	0.0103844i	$0.996694\pi$
$240$		0			0
$241$	−19.9495	+	11.5178i	−1.28506	+	0.741929i	−0.977768	−	0.209687i	$-0.932755\pi$
$241$	−19.9495	+	11.5178i	−1.28506	+	0.741929i	−0.307290	+	0.951616i	$0.599422\pi$
$242$	−9.75366	−	7.47121i	−0.626989	−	0.480268i
$243$	17.3893	+	10.0397i	1.11552	+	0.644046i
$244$	6.43079	+	6.40917i	0.411689	+	0.410305i
$245$		0			0
$246$	4.80047	−	1.99316i	0.306067	−	0.127079i
$247$	−3.47792	+	6.02393i	−0.221295	+	0.383293i
$248$	−27.6111	+	3.70605i	−1.75331	+	0.235334i
$249$	12.0871	+	20.9355i	0.765991	+	1.32674i
$250$		0			0
$251$	−24.0236			−1.51636			−0.758179	−	0.652047i	$-0.773910\pi$
$251$	−24.0236			−1.51636			−0.758179	+	0.652047i	$0.773910\pi$
$252$	15.3850	+	16.3301i	0.969162	+	1.02870i
$253$			12.2416i			0.769625i
$254$	0.366302	−	2.80056i	0.0229838	−	0.175723i
$255$		0			0
$256$	8.09315	+	13.8022i	0.505822	+	0.862638i
$257$	0.540249	−	0.935739i	0.0336998	−	0.0583698i	−0.848684	−	0.528901i	$-0.822604\pi$
$257$	0.540249	−	0.935739i	0.0336998	−	0.0583698i	0.882383	+	0.470531i	$0.155938\pi$
$258$	−7.14339	−	17.2047i	−0.444728	−	1.07112i
$259$	13.6619	−	22.0315i	0.848910	−	1.36897i
$260$		0			0
$261$	2.93446	−	5.08264i	0.181639	−	0.314608i
$262$	−6.68725	−	5.12237i	−0.413140	−	0.316461i
$263$	−11.8915	−	20.5968i	−0.733264	−	1.27005i	−0.955481	−	0.295053i	$-0.904663\pi$
$263$	−11.8915	−	20.5968i	−0.733264	−	1.27005i	0.222217	−	0.974997i	$-0.428671\pi$
$264$	7.06817	+	9.16340i	0.435016	+	0.563968i
$265$		0			0
$266$	14.4359	−	17.6654i	0.885119	−	1.08313i
$267$	40.1248			2.45560
$268$	−5.47755	−	20.3057i	−0.334595	−	1.24037i
$269$	1.16160	−	0.670652i	0.0708243	−	0.0408904i	−0.464170	−	0.885746i	$-0.653647\pi$
$269$	1.16160	−	0.670652i	0.0708243	−	0.0408904i	0.534994	+	0.844856i	$0.320314\pi$
$270$		0			0
$271$	0.200246	−	0.346836i	0.0121641	−	0.0210688i	−0.859879	−	0.510497i	$-0.829461\pi$
$271$	0.200246	−	0.346836i	0.0121641	−	0.0210688i	0.872043	+	0.489429i	$0.162795\pi$
$272$	0.0596792	+	17.7212i	0.00361858	+	1.07450i
$273$	3.83741	+	7.15774i	0.232251	+	0.433206i
$274$	5.89663	+	14.2019i	0.356228	+	0.857968i
$275$		0			0
$276$	−11.1423	+	41.8655i	−0.670689	+	2.52001i
$277$	2.48809	−	1.43650i	0.149495	−	0.0863109i	−0.423387	−	0.905949i	$-0.639159\pi$
$277$	2.48809	−	1.43650i	0.149495	−	0.0863109i	0.572882	+	0.819638i	$0.305826\pi$
$278$	−0.607692	+	4.64610i	−0.0364470	+	0.278655i
$279$	−41.7619			−2.50022
$280$		0			0
$281$	12.9931			0.775104			0.387552	−	0.921848i	$-0.373321\pi$
$281$	12.9931			0.775104			0.387552	+	0.921848i	$0.373321\pi$
$282$	−1.63279	+	12.4835i	−0.0972314	+	0.743382i
$283$	−2.91913	+	1.68536i	−0.173525	+	0.100184i	−0.584247	−	0.811576i	$-0.698610\pi$
$283$	−2.91913	+	1.68536i	−0.173525	+	0.100184i	0.410722	+	0.911761i	$0.365277\pi$
$284$	3.10841	−	11.6794i	0.184450	−	0.693043i
$285$		0			0
$286$	0.940754	+	2.26578i	0.0556280	+	0.133979i
$287$	−3.61219	−	0.113729i	−0.213221	−	0.00671320i
$288$	9.27184	+	22.1204i	0.546348	+	1.30345i
$289$	−1.31387	+	2.27570i	−0.0772867	+	0.133864i
$290$		0			0
$291$	−35.1609	+	20.3002i	−2.06117	+	1.19002i
$292$	−4.09496	−	15.1803i	−0.239639	−	0.888361i
$293$	7.10038			0.414809			0.207404	−	0.978255i	$-0.433498\pi$
$293$	7.10038			0.414809			0.207404	+	0.978255i	$0.433498\pi$
$294$	−8.64639	−	25.1944i	−0.504267	−	1.46937i
$295$		0			0
$296$	21.9440	−	16.9264i	1.27547	−	0.983828i
$297$	2.53672	+	4.39374i	0.147196	+	0.254950i
$298$	−7.17599	−	5.49674i	−0.415694	−	0.318418i
$299$	−4.59207	+	7.95370i	−0.265566	+	0.459974i
$300$		0			0
$301$	−0.407599	+	12.9459i	−0.0234936	+	0.746191i
$302$	−5.10615	−	12.2980i	−0.293826	−	0.707672i
$303$	11.7545	−	20.3594i	0.675278	−	1.16962i
$304$	21.0801	−	12.2654i	1.20903	−	0.703471i
$305$		0			0
$306$	−3.44529	+	26.3409i	−0.196954	+	1.50581i
$307$			7.14238i			0.407637i	0.979009	+	0.203818i	$0.0653352\pi$
$307$			7.14238i			0.407637i	−0.979009	+	0.203818i	$0.934665\pi$
$308$	−1.85012	−	7.83077i	−0.105421	−	0.446199i
$309$	33.2312			1.89046
$310$		0			0
$311$	1.77864	+	3.08069i	0.100857	+	0.174690i	0.912038	−	0.410106i	$-0.134508\pi$
$311$	1.77864	+	3.08069i	0.100857	+	0.174690i	−0.811181	+	0.584795i	$0.801175\pi$
$312$	1.15500	+	8.60510i	0.0653891	+	0.487168i
$313$	12.5484	−	21.7345i	0.709277	−	1.22850i	−0.255848	−	0.966717i	$-0.582355\pi$
$313$	12.5484	−	21.7345i	0.709277	−	1.22850i	0.965126	−	0.261788i	$-0.0843120\pi$
$314$	−11.2624	+	4.67615i	−0.635573	+	0.263890i
$315$		0			0
$316$	7.43260	+	7.40762i	0.418117	+	0.416711i
$317$	19.8275	+	11.4474i	1.11362	+	0.642949i	0.939765	−	0.341822i	$-0.111044\pi$
$317$	19.8275	+	11.4474i	1.11362	+	0.642949i	0.173856	+	0.984771i	$0.444377\pi$
$318$	−29.1645	−	22.3397i	−1.63547	−	1.25275i
$319$	−1.82283	+	1.05241i	−0.102059	+	0.0589237i
$320$		0			0
$321$			35.1501i			1.96189i
$322$	19.0604	−	23.3245i	1.06219	−	1.29982i
$323$	27.0125			1.50302
$324$	−1.94944	−	7.22671i	−0.108302	−	0.401484i
$325$		0			0
$326$	−10.0927	−	7.73094i	−0.558985	−	0.428177i
$327$	5.11070	+	2.95066i	0.282622	+	0.163172i
$328$	−3.57313	−	1.46948i	−0.197293	−	0.0811384i
$329$	4.61318	−	7.43933i	0.254333	−	0.410143i
$330$		0			0
$331$	18.7944	+	10.8509i	1.03303	+	0.596421i	0.917852	−	0.396923i	$-0.129922\pi$
$331$	18.7944	+	10.8509i	1.03303	+	0.596421i	0.115180	+	0.993345i	$0.463255\pi$
$332$	4.62139	−	17.3642i	0.253632	−	0.952982i
$333$	35.9784	−	20.7721i	1.97160	−	1.13831i
$334$	0.00515002		0.000673602i	0.000281797		3.68579e-5i
$335$		0			0
$336$	0.800258	−	28.4647i	0.0436577	−	1.55287i
$337$			29.6276i			1.61392i	0.590608	+	0.806959i	$0.298888\pi$
$337$			29.6276i			1.61392i	−0.590608	+	0.806959i	$0.701112\pi$
$338$	2.14564	−	16.4045i	0.116707	−	0.892286i
$339$	0.589363	+	1.02081i	0.0320098	+	0.0554426i
$340$		0			0
$341$	12.9708	+	7.48871i	0.702409	+	0.405536i
$342$	33.7654	−	14.0194i	1.82582	−	0.758083i
$343$	−1.74614	+	18.4378i	−0.0942828	+	0.995545i
$344$	−5.26655	+	12.8060i	−0.283953	+	0.690451i
$345$		0			0
$346$	13.3386	+	10.2172i	0.717085	+	0.549280i
$347$	−9.68969	−	16.7830i	−0.520170	−	0.900960i	−0.999725	−	0.0234488i	$-0.992535\pi$
$347$	−9.68969	−	16.7830i	−0.520170	−	0.900960i	0.479555	−	0.877512i	$-0.340798\pi$
$348$	−7.19185	+	1.94004i	−0.385524	+	0.103997i
$349$		−	0.0975379i		−	0.00522108i	−0.999997	−	0.00261054i	$-0.999169\pi$
$349$		−	0.0975379i		−	0.00522108i	0.999997	−	0.00261054i	$-0.000830962\pi$
$350$		0			0
$351$			3.80629i			0.203165i
$352$	1.08687	−	8.53298i	0.0579301	−	0.454809i
$353$	0.444916	+	0.770617i	0.0236805	+	0.0410158i	0.877623	−	0.479352i	$-0.159128\pi$
$353$	0.444916	+	0.770617i	0.0236805	+	0.0410158i	−0.853942	+	0.520368i	$0.825795\pi$
$354$	−4.29125	+	5.60223i	−0.228078	+	0.297755i
$355$		0			0
$356$	−21.1246	−	21.0536i	−1.11960	−	1.11584i
$357$	16.6214	−	26.8041i	0.879699	−	1.41862i
$358$	7.85150	+	18.9102i	0.414965	+	0.999432i
$359$	−10.0217	−	5.78602i	−0.528924	−	0.305375i	0.211654	−	0.977345i	$-0.432115\pi$
$359$	−10.0217	−	5.78602i	−0.528924	−	0.305375i	−0.740578	+	0.671970i	$0.765448\pi$
$360$		0			0
$361$	−9.08786	−	15.7406i	−0.478308	−	0.828454i
$362$	11.2884	+	1.47648i	0.593308	+	0.0776023i
$363$			23.3762i			1.22693i
$364$	1.73540	−	5.78186i	0.0909596	−	0.303052i
$365$		0			0
$366$	2.24034	−	17.1285i	0.117105	−	0.895321i
$367$	16.8200	−	9.71102i	0.877996	−	0.506911i	0.00799873	−	0.999968i	$-0.497454\pi$
$367$	16.8200	−	9.71102i	0.877996	−	0.506911i	0.869997	+	0.493057i	$0.164121\pi$
$368$	27.8331	−	16.1947i	1.45090	−	0.844206i
$369$	−5.01569	−	2.89581i	−0.261106	−	0.150750i
$370$		0			0
$371$	12.0691	+	22.5119i	0.626596	+	1.16876i
$372$	37.5431	+	37.4169i	1.94652	+	1.93997i
$373$	−5.91842	−	3.41700i	−0.306444	−	0.176926i	0.338890	−	0.940826i	$-0.389949\pi$
$373$	−5.91842	−	3.41700i	−0.306444	−	0.176926i	−0.645334	+	0.763900i	$0.723282\pi$
$374$	5.79350	−	7.56341i	0.299575	−	0.391095i
$375$		0			0
$376$	7.40976	−	5.71550i	0.382129	−	0.294754i
$377$	−1.57912			−0.0813287
$378$	2.00778	−	12.3213i	0.103269	−	0.633739i
$379$			4.36917i			0.224429i	0.993684	+	0.112214i	$0.0357944\pi$
$379$			4.36917i			0.224429i	−0.993684	+	0.112214i	$0.964206\pi$
$380$		0			0
$381$	−4.65385	+	2.68690i	−0.238424	+	0.137654i
$382$	13.2843	−	17.3426i	0.679682	−	0.887324i
$383$	−8.72942	−	5.03993i	−0.446052	−	0.257528i	0.260109	−	0.965579i	$-0.416241\pi$
$383$	−8.72942	−	5.03993i	−0.446052	−	0.257528i	−0.706162	+	0.708051i	$0.749575\pi$
$384$	11.4837	−	28.1929i	0.586026	−	1.43871i
$385$		0			0
$386$	4.78187	+	11.5170i	0.243391	+	0.586200i
$387$	−10.3785	+	17.9760i	−0.527567	+	0.913772i
$388$	29.1628	+	7.76155i	1.48052	+	0.394033i
$389$	4.61263	+	7.98931i	0.233870	+	0.405074i	0.958944	−	0.283597i	$-0.0915278\pi$
$389$	4.61263	+	7.98931i	0.233870	+	0.405074i	−0.725074	+	0.688671i	$0.758194\pi$
$390$		0			0
$391$	35.6660			1.80371
$392$	−8.66750	+	17.8010i	−0.437775	+	0.899085i
$393$			16.0271i			0.808459i
$394$	33.4581	+	4.37618i	1.68559	+	0.220469i
$395$		0			0
$396$	3.31644	−	12.4610i	0.166657	−	0.626189i
$397$	−16.5834	+	28.7233i	−0.832297	+	1.44158i	0.0639154	+	0.997955i	$0.479641\pi$
$397$	−16.5834	+	28.7233i	−0.832297	+	1.44158i	−0.896212	+	0.443625i	$0.853692\pi$
$398$	10.7601	−	4.46758i	0.539353	−	0.223939i
$399$	−43.3843	−	1.36594i	−2.17193	−	0.0683827i
$400$		0			0
$401$	5.90245	−	10.2234i	0.294754	−	0.510530i	−0.680173	−	0.733051i	$-0.738095\pi$
$401$	5.90245	−	10.2234i	0.294754	−	0.510530i	0.974928	+	0.222522i	$0.0714288\pi$
$402$	−24.3329	+	31.7666i	−1.21361	+	1.58437i
$403$	5.61831	+	9.73120i	0.279868	+	0.484746i
$404$	−16.8711	+	4.55105i	−0.839367	+	0.226423i
$405$		0			0
$406$	5.11174	+	0.832967i	0.253691	+	0.0413395i
$407$	−14.8994			−0.738534
$408$	26.6976	−	20.5931i	1.32173	−	1.01951i
$409$	0.0923266	−	0.0533048i	0.00456526	−	0.00263575i	−0.497716	−	0.867340i	$-0.665828\pi$
$409$	0.0923266	−	0.0533048i	0.00456526	−	0.00263575i	0.502281	+	0.864705i	$0.332494\pi$
$410$		0			0
$411$	14.6287	−	25.3377i	0.721581	−	1.24982i
$412$	−17.4954	−	17.4365i	−0.861934	−	0.859036i
$413$	4.32433	−	2.31836i	0.212786	−	0.114079i
$414$	44.5822	−	18.5105i	2.19110	−	0.909743i
$415$		0			0
$416$	3.90705	−	5.13639i	0.191559	−	0.251832i
$417$	7.72070	−	4.45755i	0.378084	−	0.218287i
$418$	−13.0011	−	1.70050i	−0.635907	−	0.0831741i
$419$	17.4417			0.852085			0.426042	−	0.904703i	$-0.359907\pi$
$419$	17.4417			0.852085			0.426042	+	0.904703i	$0.359907\pi$
$420$		0			0
$421$	−4.27682			−0.208440			−0.104220	−	0.994554i	$-0.533235\pi$
$421$	−4.27682			−0.208440			−0.104220	+	0.994554i	$0.533235\pi$
$422$	24.0733	+	3.14869i	1.17187	+	0.153276i
$423$	12.1487	−	7.01407i	0.590691	−	0.341036i
$424$	3.63261	+	27.0640i	0.176415	+	1.31434i
$425$		0			0
$426$	−21.2372	+	8.81770i	−1.02895	+	0.427219i
$427$	−6.32970	+	10.2074i	−0.306316	+	0.493972i
$428$	18.4434	−	18.5056i	0.891494	−	0.894501i
$429$	2.33388	−	4.04240i	0.112681	−	0.195169i
$430$		0			0
$431$	−24.8573	+	14.3514i	−1.19734	+	0.691282i	−0.959960	−	0.280136i	$-0.909621\pi$
$431$	−24.8573	+	14.3514i	−1.19734	+	0.691282i	−0.237376	+	0.971418i	$0.576287\pi$
$432$	6.63391	−	11.5802i	0.319174	−	0.557151i
$433$	−3.15057			−0.151407			−0.0757033	−	0.997130i	$-0.524120\pi$
$433$	−3.15057			−0.151407			−0.0757033	+	0.997130i	$0.524120\pi$
$434$	−13.0538	−	34.4643i	−0.626605	−	1.65434i
$435$		0			0
$436$	−1.14242	−	4.23505i	−0.0547122	−	0.202822i
$437$	−24.5425	−	42.5089i	−1.17403	−	2.03347i
$438$	−18.1910	+	23.7484i	−0.869201	+	1.13474i
$439$	0.748860	−	1.29706i	0.0357411	−	0.0619054i	−0.847602	−	0.530633i	$-0.821954\pi$
$439$	0.748860	−	1.29706i	0.0357411	−	0.0619054i	0.883343	+	0.468728i	$0.155287\pi$
$440$		0			0
$441$	−16.4275	+	24.7191i	−0.782260	+	1.17710i
$442$	6.60136	−	2.74089i	0.313995	−	0.130371i
$443$	−3.73555	+	6.47016i	−0.177481	+	0.307406i	−0.941017	−	0.338359i	$-0.890128\pi$
$443$	−3.73555	+	6.47016i	−0.177481	+	0.307406i	0.763536	+	0.645765i	$0.223462\pi$
$444$	−50.9548	−	13.5614i	−2.41821	−	0.643594i
$445$		0			0
$446$	−9.01889	−	1.17964i	−0.427057	−	0.0558574i
$447$			17.1984i			0.813458i
$448$	−15.3568	+	14.5660i	−0.725542	+	0.688178i
$449$	−6.36581			−0.300421			−0.150211	−	0.988654i	$-0.547995\pi$
$449$	−6.36581			−0.300421			−0.150211	+	0.988654i	$0.547995\pi$
$450$		0			0
$451$	1.03855	+	1.79882i	0.0489033	+	0.0847030i
$452$	0.225337	−	0.846668i	0.0105989	−	0.0398239i
$453$	−12.6676	+	21.9410i	−0.595178	+	1.03088i
$454$	13.7118	+	33.0245i	0.643525	+	1.54991i
$455$		0			0
$456$	−42.9152	−	17.6492i	−2.00969	−	0.826500i
$457$	−33.6768	−	19.4433i	−1.57533	−	0.909519i	−0.995498	−	0.0947843i	$-0.969784\pi$
$457$	−33.6768	−	19.4433i	−1.57533	−	0.909519i	−0.579835	−	0.814734i	$-0.696883\pi$
$458$	−0.638733	+	0.833865i	−0.0298460	+	0.0389640i
$459$	12.8011	−	7.39074i	0.597506	−	0.344970i
$460$		0			0
$461$			3.83079i			0.178418i	0.996013	+	0.0892088i	$0.0284338\pi$
$461$			3.83079i			0.178418i	−0.996013	+	0.0892088i	$0.971566\pi$
$462$	−9.68728	+	11.8545i	−0.450693	+	0.551520i
$463$	−6.41195			−0.297989			−0.148994	−	0.988838i	$-0.547604\pi$
$463$	−6.41195			−0.297989			−0.148994	+	0.988838i	$0.547604\pi$
$464$	4.80426	+	2.75221i	0.223032	+	0.127768i
$465$		0			0
$466$	−14.3242	+	18.7003i	−0.663556	+	0.866273i
$467$	22.1027	+	12.7610i	1.02279	+	0.590509i	0.914911	−	0.403655i	$-0.132260\pi$
$467$	22.1027	+	12.7610i	1.02279	+	0.590509i	0.107880	+	0.994164i	$0.465594\pi$
$468$	6.82913	−	6.85217i	0.315677	−	0.316742i
$469$	24.5204	−	13.1459i	1.13225	−	0.607021i
$470$		0			0
$471$	20.0933	+	11.6009i	0.925850	+	0.534540i
$472$	5.19874	−	0.697790i	0.239291	−	0.0321184i
$473$	6.44689	−	3.72211i	0.296428	−	0.171143i
$474$	2.58935	−	19.7969i	0.118933	−	0.909300i
$475$		0			0
$476$	−22.8149	+	5.39033i	−1.04572	+	0.247066i
$477$			40.9344i			1.87426i
$478$	−0.450238	−	0.0588894i	−0.0205934	−	0.00269354i
$479$	6.40721	+	11.0976i	0.292753	+	0.507063i	0.974460	−	0.224563i	$-0.0720954\pi$
$479$	6.40721	+	11.0976i	0.292753	+	0.507063i	−0.681707	+	0.731625i	$0.738762\pi$
$480$		0			0
$481$	−9.68049	−	5.58903i	−0.441392	−	0.254838i
$482$	−12.4921	−	30.0870i	−0.569002	−	1.37043i
$483$	−57.2825	−	1.80352i	−2.60644	−	0.0820632i
$484$	12.2656	−	12.3070i	0.557527	−	0.559407i
$485$		0			0
$486$	−17.2677	+	22.5430i	−0.783280	+	1.02257i
$487$	−8.51350	−	14.7458i	−0.385783	−	0.668196i	0.606094	−	0.795393i	$-0.292735\pi$
$487$	−8.51350	−	14.7458i	−0.385783	−	0.668196i	−0.991878	+	0.127197i	$0.959402\pi$
$488$	−10.1669	+	7.84219i	−0.460232	+	0.354999i
$489$			24.1889i			1.09386i
$490$		0			0
$491$		−	17.4067i		−	0.785553i	−0.919634	−	0.392777i	$-0.871515\pi$
$491$		−	17.4067i		−	0.785553i	0.919634	−	0.392777i	$-0.128485\pi$
$492$	1.91448	+	7.09712i	0.0863115	+	0.319963i
$493$	3.06620	+	5.31081i	0.138095	+	0.239187i
$494$	−7.80928	−	5.98183i	−0.351356	−	0.269135i
$495$		0			0
$496$	−0.132680	−	39.3980i	−0.00595749	−	1.76902i
$497$	15.9803	+	0.503135i	0.716814	+	0.0225687i
$498$	−31.5742	+	13.1096i	−1.41487	+	0.587456i
$499$	−13.6168	−	7.86167i	−0.609572	−	0.351937i	0.163226	−	0.986589i	$-0.447810\pi$
$499$	−13.6168	−	7.86167i	−0.609572	−	0.351937i	−0.772798	+	0.634652i	$0.781143\pi$
$500$		0			0
$501$	−0.00494101	−	0.00855809i	−0.000220748	−	0.000382347i
$502$	4.40620	−	33.6876i	0.196659	−	1.50355i
$503$			25.7928i			1.15004i	0.818138	+	0.575022i	$0.195006\pi$
$503$			25.7928i			1.15004i	−0.818138	+	0.575022i	$0.804994\pi$
$504$	−25.7209	+	18.5788i	−1.14570	+	0.827563i
$505$		0			0
$506$	−17.1661	−	2.24526i	−0.763125	−	0.0998138i
$507$	−27.2603	+	15.7387i	−1.21067	+	0.698981i
$508$	3.85995	+	1.02731i	0.171258	+	0.0455795i
$509$	−6.90728	−	3.98792i	−0.306160	−	0.176761i	0.339047	−	0.940769i	$-0.389895\pi$
$509$	−6.90728	−	3.98792i	−0.306160	−	0.176761i	−0.645207	+	0.764008i	$0.723229\pi$
$510$		0			0
$511$	18.3312	−	9.82774i	0.810926	−	0.434754i
$512$	−20.8388	+	8.81729i	−0.920953	+	0.389673i
$513$	−17.6175	−	10.1714i	−0.777830	−	0.449080i
$514$	1.21307	+	0.929200i	0.0535062	+	0.0409853i
$515$		0			0
$516$	25.4358	−	6.86142i	1.11975	−	0.302057i
$517$	−5.03103			−0.221264
$518$	28.3884	+	23.1985i	1.24731	+	1.01928i
$519$		−	31.9680i		−	1.40324i
$520$		0			0
$521$	22.0559	−	12.7340i	0.966286	−	0.557885i	0.0681838	−	0.997673i	$-0.478280\pi$
$521$	22.0559	−	12.7340i	0.966286	−	0.557885i	0.898102	+	0.439787i	$0.144946\pi$
$522$	6.58902	+	5.04712i	0.288394	+	0.220907i
$523$	21.0312	+	12.1424i	0.919629	+	0.530948i	0.883517	−	0.468400i	$-0.155169\pi$
$523$	21.0312	+	12.1424i	0.919629	+	0.530948i	0.0361122	+	0.999348i	$0.488503\pi$
$524$	8.40946	−	8.43782i	0.367369	−	0.368608i
$525$		0			0
$526$	31.0633	−	12.8975i	1.35442	−	0.562357i
$527$	21.8183	−	37.7905i	0.950422	−	1.64618i
$528$	−14.1459	+	8.23081i	−0.615623	+	0.358200i
$529$	−20.9047	−	36.2080i	−0.908901	−	1.57426i
$530$		0			0
$531$	7.86311			0.341230
$532$	22.1239	+	23.4830i	0.959195	+	1.01812i
$533$			1.55832i			0.0674982i
$534$	−7.35935	+	56.2658i	−0.318470	+	2.43486i
$535$		0			0
$536$	29.4787	−	3.95671i	1.27328	−	0.170904i
$537$	19.4785	−	33.7377i	0.840558	−	1.45589i
$538$	0.727384	+	1.75189i	0.0313598	+	0.0755292i
$539$	9.53481	−	4.73173i	0.410693	−	0.203810i
$540$		0			0
$541$	−12.1108	+	20.9765i	−0.520684	+	0.901852i	0.479026	+	0.877800i	$0.340990\pi$
$541$	−12.1108	+	20.9765i	−0.520684	+	0.901852i	−0.999711	+	0.0240512i	$0.992344\pi$
$542$	0.449631	+	0.344413i	0.0193133	+	0.0147938i
$543$	−10.8303	−	18.7587i	−0.464774	−	0.805011i
$544$	−24.8608	−	3.16658i	−1.06590	−	0.135766i
$545$		0			0
$546$	−10.7409	+	4.06827i	−0.459669	+	0.174106i
$547$	−33.9283			−1.45067			−0.725335	−	0.688396i	$-0.758315\pi$
$547$	−33.9283			−1.45067			−0.725335	+	0.688396i	$0.758315\pi$
$548$	−20.9964	+	5.66388i	−0.896921	+	0.241949i
$549$	−16.6692	+	9.62394i	−0.711422	+	0.410740i
$550$		0			0
$551$	4.21983	−	7.30896i	0.179771	−	0.311372i
$552$	−56.6632	−	23.3032i	−2.41174	−	0.991848i
$553$	−7.31577	+	11.7976i	−0.311098	+	0.501685i
$554$	1.55802	+	3.75244i	0.0661937	+	0.159426i
$555$		0			0
$556$	−6.40363	−	1.70430i	−0.271574	−	0.0722783i
$557$	−2.04438	+	1.18032i	−0.0866232	+	0.0500119i	−0.542686	−	0.839936i	$-0.682593\pi$
$557$	−2.04438	+	1.18032i	−0.0866232	+	0.0500119i	0.456063	+	0.889948i	$0.349259\pi$
$558$	7.65961	−	58.5614i	0.324257	−	2.47910i
$559$	5.58494			0.236218
$560$		0			0
$561$	−18.1269			−0.765320
$562$	−2.38309	+	18.2199i	−0.100524	+	0.768558i
$563$	−21.1249	+	12.1965i	−0.890310	+	0.514021i	−0.874044	−	0.485847i	$-0.838511\pi$
$563$	−21.1249	+	12.1965i	−0.890310	+	0.514021i	−0.0162660	+	0.999868i	$0.505178\pi$
$564$	−17.2058	−	4.57923i	−0.724493	−	0.192820i
$565$		0			0
$566$	−1.82793	−	4.40253i	−0.0768337	−	0.185052i
$567$	8.72674	−	4.67858i	0.366488	−	0.196482i
$568$	15.8075	+	6.50096i	0.663269	+	0.272774i
$569$	14.1181	−	24.4533i	0.591864	−	1.02514i	−0.402118	−	0.915588i	$-0.631726\pi$
$569$	14.1181	−	24.4533i	0.591864	−	1.02514i	0.993981	−	0.109550i	$-0.0349409\pi$
$570$		0			0
$571$	−3.36494	+	1.94275i	−0.140819	+	0.0813016i	−0.568754	−	0.822508i	$-0.692574\pi$
$571$	−3.36494	+	1.94275i	−0.140819	+	0.0813016i	0.427936	+	0.903809i	$0.359241\pi$
$572$	−3.34979	+	0.903620i	−0.140062	+	0.0377823i
$573$	−41.5643			−1.73637
$574$	0.821994	−	5.04440i	0.0343094	−	0.210549i
$575$		0			0
$576$	−32.7193	+	8.94449i	−1.36330	+	0.372687i
$577$	20.6475	+	35.7624i	0.859565	+	1.48881i	0.872345	+	0.488891i	$0.162599\pi$
$577$	20.6475	+	35.7624i	0.859565	+	1.48881i	−0.0127799	+	0.999918i	$0.504068\pi$
$578$	−2.95016	−	2.25979i	−0.122710	−	0.0939950i
$579$	11.8631	−	20.5476i	0.493015	−	0.853928i
$580$		0			0
$581$	23.7585	+	0.748030i	0.985668	+	0.0310335i
$582$	−22.0174	−	53.0283i	−0.912650	−	2.19810i
$583$	7.34032	−	12.7138i	0.304005	−	0.526552i
$584$	22.0380	−	2.95800i	0.911937	−	0.122403i
$585$		0			0
$586$	−1.30229	+	9.95665i	−0.0537971	+	0.411305i
$587$			27.1349i			1.11998i	0.828500	+	0.559989i	$0.189195\pi$
$587$			27.1349i			1.11998i	−0.828500	+	0.559989i	$0.810805\pi$
$588$	36.9152	−	7.50362i	1.52236	−	0.309444i
$589$	−60.0546			−2.47451
$590$		0			0
$591$	−32.1002	−	55.5992i	−1.32043	−	2.28705i
$592$	19.7106	+	33.8758i	0.810102	+	1.39229i
$593$	−3.16125	+	5.47544i	−0.129817	+	0.224849i	−0.923605	−	0.383344i	$-0.874772\pi$
$593$	−3.16125	+	5.47544i	−0.129817	+	0.224849i	0.793789	+	0.608194i	$0.208106\pi$
$594$	−6.62647	+	2.75131i	−0.271887	+	0.112888i
$595$		0			0
$596$	9.02407	−	9.05451i	0.369640	−	0.370887i
$597$	−19.1971	−	11.0834i	−0.785684	−	0.453615i
$598$	−10.3110	−	7.89812i	−0.421648	−	0.322978i
$599$	−8.63935	+	4.98793i	−0.352994	+	0.203801i	−0.666003	−	0.745949i	$-0.731996\pi$
$599$	−8.63935	+	4.98793i	−0.352994	+	0.203801i	0.313009	+	0.949750i	$0.398663\pi$
$600$		0			0
$601$		−	14.6833i		−	0.598943i	−0.954105	−	0.299471i	$-0.903190\pi$
$601$		−	14.6833i		−	0.598943i	0.954105	−	0.299471i	$-0.0968103\pi$
$602$	−18.0789	−	2.94599i	−0.736842	−	0.120070i
$603$	44.5865			1.81570
$604$	18.1817	−	4.90460i	0.739802	−	0.199565i
$605$		0			0
$606$	26.3934	+	20.2171i	1.07216	+	0.821264i
$607$	−24.7343	−	14.2804i	−1.00394	−	0.579622i	−0.0945251	−	0.995522i	$-0.530133\pi$
$607$	−24.7343	−	14.2804i	−1.00394	−	0.579622i	−0.909410	+	0.415900i	$0.863467\pi$
$608$	13.3331	+	31.8096i	0.540730	+	1.29005i
$609$	−4.65601	−	8.68464i	−0.188671	−	0.351919i
$610$		0			0
$611$	−3.26878	−	1.88723i	−0.132241	−	0.0763493i
$612$	−36.3051	−	9.66244i	−1.46755	−	0.390581i
$613$	−6.76648	+	3.90663i	−0.273296	+	0.157787i	−0.630384	−	0.776283i	$-0.717103\pi$
$613$	−6.76648	+	3.90663i	−0.273296	+	0.157787i	0.357089	+	0.934070i	$0.383769\pi$
$614$	−10.0155	−	1.30999i	−0.404194	−	0.0528670i
$615$		0			0
$616$	11.3202	−	1.15812i	0.456103	−	0.0466620i
$617$			14.1859i			0.571103i	0.958363	+	0.285551i	$0.0921767\pi$
$617$			14.1859i			0.571103i	−0.958363	+	0.285551i	$0.907823\pi$
$618$	−6.09498	+	46.5991i	−0.245176	+	1.87449i
$619$	14.3856	+	24.9166i	0.578207	+	1.00148i	0.995685	+	0.0927974i	$0.0295809\pi$
$619$	14.3856	+	24.9166i	0.578207	+	1.00148i	−0.417478	+	0.908687i	$0.637086\pi$
$620$		0			0
$621$	−23.2612	−	13.4299i	−0.933441	−	0.538922i
$622$	−4.64618	+	1.92909i	−0.186295	+	0.0773496i
$623$	20.7926	−	33.5306i	0.833037	−	1.34338i
$624$	−12.2785	+	0.0413500i	−0.491534	+	0.00165533i
$625$		0			0
$626$	28.1761	+	21.5826i	1.12614	+	0.862614i
$627$	12.4735	+	21.6048i	0.498144	+	0.862811i
$628$	−4.49157	−	16.6506i	−0.179233	−	0.664430i
$629$			43.4093i			1.73084i
$630$		0			0
$631$		−	6.74409i		−	0.268478i	−0.990949	−	0.134239i	$-0.957141\pi$
$631$		−	6.74409i		−	0.268478i	0.990949	−	0.134239i	$-0.0428590\pi$
$632$	−11.7507	+	9.06387i	−0.467418	+	0.360542i
$633$	−23.0963	−	40.0040i	−0.917997	−	1.59002i
$634$	−19.6889	+	25.7039i	−0.781946	+	1.02083i
$635$		0			0
$636$	36.6755	−	36.7992i	1.45428	−	1.45918i
$637$	7.96997	+	0.502363i	0.315782	+	0.0199043i
$638$	−1.14144	−	2.74912i	−0.0451899	−	0.108839i
$639$	22.1894	+	12.8110i	0.877798	+	0.506797i
$640$		0			0
$641$	−18.5938	−	32.2054i	−0.734410	−	1.27204i	−0.954982	−	0.296665i	$-0.904126\pi$
$641$	−18.5938	−	32.2054i	−0.734410	−	1.27204i	0.220571	−	0.975371i	$-0.429208\pi$
$642$	−49.2899	−	6.44692i	−1.94532	−	0.254440i
$643$		−	33.2862i		−	1.31268i	−0.754465	−	0.656340i	$-0.772104\pi$
$643$		−	33.2862i		−	1.31268i	0.754465	−	0.656340i	$-0.227896\pi$
$644$	29.2114	+	31.0058i	1.15109	+	1.22180i
$645$		0			0
$646$	−4.95440	+	37.8788i	−0.194928	+	1.49032i
$647$	13.5027	−	7.79580i	0.530847	−	0.306484i	−0.210515	−	0.977591i	$-0.567514\pi$
$647$	13.5027	−	7.79580i	0.530847	−	0.306484i	0.741361	+	0.671106i	$0.234181\pi$
$648$	10.4914	−	1.40818i	0.412139	−	0.0553185i
$649$	−2.44220	−	1.41001i	−0.0958648	−	0.0553476i
$650$		0			0
$651$	−36.9530	+	59.5912i	−1.44830	+	2.33557i
$652$	12.6920	−	12.7348i	0.497057	−	0.498733i
$653$	26.2113	+	15.1331i	1.02573	+	0.592204i	0.915758	−	0.401731i	$-0.131591\pi$
$653$	26.2113	+	15.1331i	1.02573	+	0.592204i	0.109970	+	0.993935i	$0.464925\pi$
$654$	−5.07499	+	6.62540i	−0.198448	+	0.259073i
$655$		0			0
$656$	2.71596	−	4.74098i	0.106040	−	0.185104i
$657$	33.3324			1.30042
$658$	9.58583	+	7.83338i	0.373695	+	0.305377i
$659$			22.5477i			0.878334i	0.898406	+	0.439167i	$0.144726\pi$
$659$			22.5477i			0.878334i	−0.898406	+	0.439167i	$0.855274\pi$
$660$		0			0
$661$	36.8945	−	21.3010i	1.43503	−	0.828515i	0.437531	−	0.899203i	$-0.355853\pi$
$661$	36.8945	−	21.3010i	1.43503	−	0.828515i	0.997498	+	0.0706888i	$0.0225197\pi$
$662$	−18.6630	+	24.3646i	−0.725360	+	0.946957i
$663$	−11.7775	−	6.79976i	−0.457401	−	0.264081i
$664$	23.5016	+	9.66522i	0.912040	+	0.375083i
$665$		0			0
$666$	22.5293	+	54.2612i	0.872992	+	2.10258i
$667$	5.57165	−	9.65039i	0.215735	−	0.373665i
$668$	−0.00188914	+	0.00709817i	−7.30932e−5	+	0.000274636i
$669$	8.65287	+	14.9872i	0.334539	+	0.579439i
$670$		0			0
$671$	6.90303			0.266488
$672$	39.7684	+	6.34292i	1.53410	+	0.244684i
$673$		−	38.7450i		−	1.49351i	−0.665100	−	0.746755i	$-0.731611\pi$
$673$		−	38.7450i		−	1.49351i	0.665100	−	0.746755i	$-0.268389\pi$
$674$	−41.5459	−	5.43404i	−1.60029	−	0.209311i
$675$		0			0
$676$	22.6100	+	6.01753i	0.869614	+	0.231444i
$677$	7.73124	−	13.3909i	0.297136	−	0.514654i	−0.678344	−	0.734745i	$-0.737302\pi$
$677$	7.73124	−	13.3909i	0.297136	−	0.514654i	0.975479	+	0.220091i	$0.0706353\pi$
$678$	−1.53954	+	0.639218i	−0.0591257	+	0.0245490i
$679$	−1.25630	+	39.9020i	−0.0482125	+	1.53130i
$680$		0			0
$681$	34.0170	−	58.9191i	1.30353	−	2.25779i
$682$	−12.8802	+	16.8151i	−0.493208	+	0.643882i
$683$	−6.99092	−	12.1086i	−0.267500	−	0.463324i	0.700715	−	0.713441i	$-0.252864\pi$
$683$	−6.99092	−	12.1086i	−0.267500	−	0.463324i	−0.968216	+	0.250117i	$0.919531\pi$
$684$	13.4660	+	49.9195i	0.514887	+	1.90872i
$685$		0			0
$686$	−25.5344	−	5.83026i	−0.974910	−	0.222600i
$687$	1.99849			0.0762473
$688$	−16.9915	−	9.73388i	−0.647794	−	0.371101i
$689$	9.53838	−	5.50698i	0.363383	−	0.209799i
$690$		0			0
$691$	−2.89835	+	5.02008i	−0.110258	+	0.190973i	−0.915874	−	0.401465i	$-0.868501\pi$
$691$	−2.89835	+	5.02008i	−0.110258	+	0.190973i	0.805616	+	0.592438i	$0.201834\pi$
$692$	−16.7737	+	16.8303i	−0.637641	+	0.639792i
$693$	17.0497	+	0.536807i	0.647666	+	0.0203916i
$694$	25.3115	−	10.5094i	0.960813	−	0.398930i
$695$		0			0
$696$	−1.40139	−	10.4407i	−0.0531194	−	0.395755i
$697$	5.24085	−	3.02581i	0.198511	−	0.114611i
$698$	0.136774	+	0.0178896i	0.00517699	+	0.000677130i
$699$	44.8182			1.69518
$700$		0			0
$701$	−35.6505			−1.34650			−0.673251	−	0.739414i	$-0.735103\pi$
$701$	−35.6505			−1.34650			−0.673251	+	0.739414i	$0.735103\pi$
$702$	−5.33745	−	0.698118i	−0.201449	−	0.0263488i
$703$	51.7377	−	29.8708i	1.95133	−	1.12660i
$704$	11.7662	+	3.08912i	0.443455	+	0.116426i
$705$		0			0
$706$	−1.16222	+	0.482552i	−0.0437406	+	0.0181611i
$707$	−10.9223	−	20.3729i	−0.410777	−	0.766203i
$708$	−7.06877	−	7.04501i	−0.265661	−	0.264768i
$709$	7.87301	−	13.6365i	0.295677	−	0.512128i	−0.679465	−	0.733708i	$-0.737788\pi$
$709$	7.87301	−	13.6365i	0.295677	−	0.512128i	0.975142	+	0.221580i	$0.0711214\pi$
$710$		0			0
$711$	−19.2659	+	11.1232i	−0.722529	+	0.417152i
$712$	33.3974	−	25.7610i	1.25162	−	0.965433i
$713$	−79.2931			−2.96955
$714$	34.5380	+	28.2239i	1.29255	+	1.05625i
$715$		0			0
$716$	−27.9572	+	7.54158i	−1.04481	+	0.281842i
$717$	0.431966	+	0.748187i	0.0161321	+	0.0279416i
$718$	9.95165	−	12.9919i	0.371392	−	0.484853i
$719$	−5.36307	+	9.28912i	−0.200009	+	0.346426i	−0.948531	−	0.316684i	$-0.897430\pi$
$719$	−5.36307	+	9.28912i	−0.200009	+	0.346426i	0.748522	+	0.663110i	$0.230764\pi$
$720$		0			0
$721$	17.2203	−	27.7699i	0.641319	−	1.03421i
$722$	23.7394	−	9.85662i	0.883490	−	0.366825i
$723$	−30.9913	+	53.6784i	−1.15258	+	1.99632i
$724$	−4.14086	+	15.5586i	−0.153894	+	0.578232i
$725$		0			0
$726$	−32.7798	−	4.28747i	−1.21657	−	0.159123i
$727$			10.2152i			0.378861i	0.981894	+	0.189431i	$0.0606642\pi$
$727$			10.2152i			0.378861i	−0.981894	+	0.189431i	$0.939336\pi$
$728$	7.78944	+	3.49396i	0.288696	+	0.129495i
$729$	42.8004			1.58520
$730$		0			0
$731$	−10.8444	−	18.7830i	−0.401094	−	0.694714i
$732$	23.6079	+	6.28313i	0.872572	+	0.232231i
$733$	16.2546	−	28.1538i	0.600378	−	1.03989i	−0.392385	−	0.919801i	$-0.628350\pi$
$733$	16.2546	−	28.1538i	0.600378	−	1.03989i	0.992764	−	0.120085i	$-0.0383167\pi$
$734$	10.5325	+	25.3673i	0.388761	+	0.936323i
$735$		0			0
$736$	17.6044	+	41.9998i	0.648907	+	1.54813i
$737$	−13.8481	−	7.99522i	−0.510102	−	0.294508i
$738$	4.98064	−	6.50222i	0.183340	−	0.239350i
$739$	21.0789	−	12.1699i	0.775399	−	0.447677i	−0.0593981	−	0.998234i	$-0.518918\pi$
$739$	21.0789	−	12.1699i	0.775399	−	0.447677i	0.834797	+	0.550557i	$0.185585\pi$
$740$		0			0
$741$			18.7162i			0.687557i
$742$	−33.7814	+	12.7952i	−1.24015	+	0.469726i
$743$	−50.8575			−1.86578			−0.932891	−	0.360158i	$-0.882723\pi$
$743$	−50.8575			−1.86578			−0.932891	+	0.360158i	$0.882723\pi$
$744$	−59.3544	+	45.7829i	−2.17604	+	1.67848i
$745$		0			0
$746$	5.87706	−	7.67250i	0.215175	−	0.280910i
$747$	32.9898	+	19.0466i	1.20703	+	0.696880i
$748$	9.54335	+	9.51126i	0.348939	+	0.347766i
$749$	29.3735	+	18.2147i	1.07328	+	0.665550i
$750$		0			0
$751$	−5.75684	−	3.32371i	−0.210070	−	0.121284i	0.391274	−	0.920274i	$-0.372035\pi$
$751$	−5.75684	−	3.32371i	−0.210070	−	0.121284i	−0.601344	+	0.798990i	$0.705368\pi$
$752$	6.65564	+	11.4388i	0.242706	+	0.417129i
$753$	−55.9806	+	32.3204i	−2.04005	+	1.17782i
$754$	0.289628	−	2.21435i	0.0105476	−	0.0806418i
$755$		0			0
$756$	16.9095	+	5.07531i	0.614993	+	0.184587i
$757$			0.655421i			0.0238217i	0.999929	+	0.0119108i	$0.00379143\pi$
$757$			0.655421i			0.0238217i	−0.999929	+	0.0119108i	$0.996209\pi$
$758$	−6.12675	−	0.801355i	−0.222534	−	0.0291065i
$759$	16.4694	+	28.5259i	0.597802	+	1.03542i
$760$		0			0
$761$	29.3115	+	16.9230i	1.06254	+	0.613459i	0.926135	−	0.377193i	$-0.123111\pi$
$761$	29.3115	+	16.9230i	1.06254	+	0.613459i	0.136408	+	0.990653i	$0.456444\pi$
$762$	−2.91419	−	7.01876i	−0.105570	−	0.254263i
$763$	5.11410	−	2.74177i	0.185143	−	0.0992588i
$764$	21.8825	+	21.8089i	0.791681	+	0.789020i
$765$		0			0
$766$	8.66842	−	11.3166i	0.313203	−	0.408886i
$767$	−1.05784	−	1.83223i	−0.0381964	−	0.0661581i
$768$	37.4279	+	21.2742i	1.35056	+	0.767665i
$769$		−	7.84764i		−	0.282993i	−0.989939	−	0.141497i	$-0.954809\pi$
$769$		−	7.84764i		−	0.282993i	0.989939	−	0.141497i	$-0.0451914\pi$
$770$		0			0
$771$		−	2.90732i		−	0.104705i
$772$	−17.0270	+	4.59311i	−0.612815	+	0.165310i
$773$	25.9303	+	44.9126i	0.932647	+	1.61539i	0.778777	+	0.627301i	$0.215841\pi$
$773$	25.9303	+	44.9126i	0.932647	+	1.61539i	0.153871	+	0.988091i	$0.450826\pi$
$774$	−23.3037	−	17.8504i	−0.837634	−	0.641619i
$775$		0			0
$776$	−16.2326	+	39.4706i	−0.582716	+	1.41691i
$777$	2.19508	−	69.7188i	0.0787480	−	2.50115i
$778$	−12.0492	+	5.00282i	−0.431984	+	0.179360i
$779$	−7.21268	−	4.16424i	−0.258421	−	0.149199i
$780$		0			0
$781$	−4.59453	−	7.95796i	−0.164405	−	0.284758i
$782$	−6.54155	+	50.0133i	−0.233925	+	1.78847i
$783$		−	4.61826i		−	0.165043i
$784$	−23.3720	−	15.4191i	−0.834716	−	0.550681i
$785$		0			0
$786$	−22.4743	−	2.93955i	−0.801631	−	0.104850i
$787$	−9.37791	+	5.41434i	−0.334286	+	0.193000i	−0.657742	−	0.753243i	$-0.728488\pi$
$787$	−9.37791	+	5.41434i	−0.334286	+	0.193000i	0.323456	+	0.946243i	$0.395155\pi$
$788$	−12.2732	+	46.1146i	−0.437214	+	1.64276i
$789$	−55.4201	−	31.9968i	−1.97301	−	1.13912i
$790$		0			0
$791$	1.15845	+	0.0364736i	0.0411898	+	0.00129685i
$792$	16.8654	+	6.93603i	0.599287	+	0.246461i
$793$	4.48507	+	2.58946i	0.159270	+	0.0919543i
$794$	−37.2362	−	28.5226i	−1.32146	−	1.01223i
$795$		0			0
$796$	4.29123	+	15.9079i	0.152099	+	0.563841i
$797$	46.9913			1.66452			0.832258	−	0.554388i	$-0.187048\pi$
$797$	46.9913			1.66452			0.832258	+	0.554388i	$0.187048\pi$
$798$	9.87259	−	60.5859i	0.349486	−	2.14472i
$799$			14.6579i			0.518559i
$800$		0			0
$801$	54.7569	−	31.6139i	1.93474	−	1.11702i
$802$	13.2533	+	10.1519i	0.467991	+	0.358476i
$803$	−10.3527	−	5.97715i	−0.365340	−	0.210929i
$804$	−40.0824	−	39.9476i	−1.41360	−	1.40884i
$805$		0			0
$806$	−14.6762	+	6.09358i	−0.516948	+	0.214637i
$807$	1.80454	−	3.12555i	0.0635228	−	0.110025i
$808$	−3.28745	−	24.4925i	−0.115652	−	0.861643i
$809$	−24.8361	−	43.0174i	−0.873191	−	1.51241i	−0.858677	−	0.512517i	$-0.828713\pi$
$809$	−24.8361	−	43.0174i	−0.873191	−	1.51241i	−0.0145146	−	0.999895i	$-0.504620\pi$
$810$		0			0
$811$	−17.4823			−0.613885			−0.306943	−	0.951728i	$-0.599306\pi$
$811$	−17.4823			−0.613885			−0.306943	+	0.951728i	$0.599306\pi$
$812$	−2.10559	+	7.01526i	−0.0738919	+	0.246187i
$813$		−	1.07761i		−	0.0377935i
$814$	2.73271	−	20.8929i	0.0957815	−	0.732296i
$815$		0			0
$816$	23.9804	+	41.2142i	0.839484	+	1.44279i
$817$	−14.9245	+	25.8499i	−0.522141	+	0.904375i
$818$	0.0578140	+	0.139244i	0.00202142	+	0.00486854i
$819$	10.8763	+	6.74446i	0.380048	+	0.235671i
$820$		0			0
$821$	−14.2765	+	24.7277i	−0.498254	+	0.863002i	−0.999998	−	0.00201446i	$-0.999359\pi$
$821$	−14.2765	+	24.7277i	−0.498254	+	0.863002i	0.501744	+	0.865016i	$0.332692\pi$
$822$	32.8472	+	25.1606i	1.14568	+	0.877577i
$823$	−27.4979	−	47.6278i	−0.958517	−	1.66020i	−0.726107	−	0.687581i	$-0.758673\pi$
$823$	−27.4979	−	47.6278i	−0.958517	−	1.66020i	−0.232409	−	0.972618i	$-0.574661\pi$
$824$	27.6596	−	21.3351i	0.963567	−	0.743245i
$825$		0			0
$826$	2.45783	+	6.48909i	0.0855189	+	0.225784i
$827$	26.3044			0.914692			0.457346	−	0.889289i	$-0.348800\pi$
$827$	26.3044			0.914692			0.457346	+	0.889289i	$0.348800\pi$
$828$	17.7799	+	65.9113i	0.617894	+	2.29058i
$829$	−25.0705	+	14.4744i	−0.870733	+	0.502718i	−0.867592	−	0.497277i	$-0.834333\pi$
$829$	−25.0705	+	14.4744i	−0.870733	+	0.502718i	−0.00314107	+	0.999995i	$0.501000\pi$
$830$		0			0
$831$	3.86522	−	6.69475i	0.134083	−	0.232238i
$832$	6.48600	+	6.42080i	0.224862	+	0.222601i
$833$	−13.7859	−	27.7796i	−0.477653	−	0.962508i
$834$	4.83462	+	11.6441i	0.167409	+	0.403201i
$835$		0			0
$836$	4.76912	−	17.9192i	0.164943	−	0.619749i
$837$	−28.4597	+	16.4312i	−0.983710	+	0.567945i
$838$	−3.19901	+	24.4580i	−0.110508	+	0.844888i
$839$	−57.7409			−1.99344			−0.996718	−	0.0809484i	$-0.974205\pi$
$839$	−57.7409			−1.99344			−0.996718	+	0.0809484i	$0.974205\pi$
$840$		0			0
$841$	−27.0840			−0.933932
$842$	0.784418	−	5.99726i	0.0270328	−	0.206679i
$843$	30.2770	−	17.4804i	1.04279	−	0.602058i
$844$	−8.83064	+	33.1798i	−0.303963	+	1.14209i
$845$		0			0
$846$	7.60740	+	18.3222i	0.261548	+	0.629932i
$847$	19.5345	+	12.1135i	0.671215	+	0.416225i
$848$	−38.6173	+	0.130051i	−1.32612	+	0.00446595i
$849$	−4.53484	+	7.85457i	−0.155635	+	0.269568i
$850$		0			0
$851$	68.3120	−	39.4399i	2.34170	−	1.35198i
$852$	−8.46965	−	31.3976i	−0.290165	−	1.07566i
$853$	−2.09064			−0.0715821			−0.0357910	−	0.999359i	$-0.511395\pi$
$853$	−2.09064			−0.0715821			−0.0357910	+	0.999359i	$0.511395\pi$
$854$	−13.1526	−	10.7481i	−0.450074	−	0.367793i
$855$		0			0
$856$	22.5671	+	29.2567i	0.771327	+	0.999974i
$857$	−9.16045	−	15.8664i	−0.312915	−	0.541985i	0.666077	−	0.745883i	$-0.267972\pi$
$857$	−9.16045	−	15.8664i	−0.312915	−	0.541985i	−0.978992	+	0.203898i	$0.934639\pi$
$858$	5.24047	+	4.01415i	0.178907	+	0.137041i
$859$	2.34970	−	4.06979i	0.0801706	−	0.138860i	−0.823152	−	0.567820i	$-0.807787\pi$
$859$	2.34970	−	4.06979i	0.0801706	−	0.138860i	0.903323	+	0.428961i	$0.141120\pi$
$860$		0			0
$861$	−8.57024	+	4.59468i	−0.292073	+	0.156586i
$862$	−15.5654	−	37.4889i	−0.530160	−	1.27688i
$863$	−12.1954	+	21.1231i	−0.415138	+	0.719039i	−0.995443	−	0.0953597i	$-0.969600\pi$
$863$	−12.1954	+	21.1231i	−0.415138	+	0.719039i	0.580305	+	0.814399i	$0.302933\pi$
$864$	15.0218	+	11.4265i	0.511051	+	0.388736i
$865$		0			0
$866$	0.577850	−	4.41795i	0.0196361	−	0.150128i
$867$			7.07053i			0.240128i
$868$	50.7225	−	11.9839i	1.72163	−	0.406759i
$869$	7.97841			0.270649
$870$		0			0
$871$	−5.99832	−	10.3894i	−0.203245	−	0.352031i
$872$	6.14821	−	0.825231i	0.208205	−	0.0279458i
$873$	−31.9885	+	55.4058i	−1.08265	+	1.87520i
$874$	64.1102	−	26.6186i	2.16856	−	0.900387i
$875$		0			0
$876$	−29.9652	−	29.8645i	−1.01243	−	1.00903i
$877$	−16.7613	−	9.67714i	−0.565989	−	0.326774i	0.189557	−	0.981870i	$-0.439295\pi$
$877$	−16.7613	−	9.67714i	−0.565989	−	0.326774i	−0.755546	+	0.655096i	$0.772628\pi$
$878$	1.68148	+	1.28800i	0.0567473	+	0.0434679i
$879$	16.5455	−	9.55257i	0.558067	−	0.322200i
$880$		0			0
$881$			13.4062i			0.451667i	0.974166	+	0.225833i	$0.0725105\pi$
$881$			13.4062i			0.451667i	−0.974166	+	0.225833i	$0.927490\pi$
$882$	−31.6498	−	27.5695i	−1.06570	−	0.928313i
$883$	−22.7466			−0.765485			−0.382742	−	0.923855i	$-0.625020\pi$
$883$	−22.7466			−0.765485			−0.382742	+	0.923855i	$0.625020\pi$
$884$	2.63270	+	9.75960i	0.0885472	+	0.328251i
$885$		0			0
$886$	−8.38776	−	6.42494i	−0.281792	−	0.215850i
$887$	−43.3249	−	25.0136i	−1.45471	−	0.839875i	−0.455963	−	0.889999i	$-0.650705\pi$
$887$	−43.3249	−	25.0136i	−1.45471	−	0.839875i	−0.998743	+	0.0501233i	$0.984039\pi$
$888$	28.3624	−	68.9650i	0.951779	−	2.31431i
$889$	−0.166283	+	5.28138i	−0.00557695	+	0.177132i
$890$		0			0
$891$	−4.92850	−	2.84547i	−0.165111	−	0.0953269i
$892$	3.30833	−	12.4306i	0.110771	−	0.416206i
$893$	17.4701	−	10.0864i	0.584616	−	0.337528i
$894$	−24.1168	−	3.15439i	−0.806587	−	0.105498i
$895$		0			0
$896$	−17.6088	−	24.2060i	−0.588270	−	0.808665i
$897$			24.7120i			0.825108i
$898$	1.16756	−	8.92659i	0.0389621	−	0.297884i
$899$	−6.81682	−	11.8071i	−0.227354	−	0.393788i
$900$		0			0
$901$	−37.0416	−	21.3860i	−1.23404	−	0.712471i
$902$	−2.71291	+	1.12640i	−0.0903300	+	0.0375050i
$903$	16.4671	+	30.7154i	0.547992	+	1.02214i
$904$	1.14593	+	0.471271i	0.0381130	+	0.0156743i
$905$		0			0
$906$	−28.4438	−	21.7877i	−0.944982	−	0.723847i
$907$	−0.527523	−	0.913696i	−0.0175161	−	0.0303388i	0.857134	−	0.515093i	$-0.172243\pi$
$907$	−0.527523	−	0.913696i	−0.0175161	−	0.0303388i	−0.874651	+	0.484754i	$0.838909\pi$
$908$	−48.8241	+	13.1705i	−1.62028	+	0.437079i
$909$		−	37.0449i		−	1.22870i
$910$		0			0
$911$			49.6924i			1.64638i	0.567765	+	0.823191i	$0.307808\pi$
$911$			49.6924i			1.64638i	−0.567765	+	0.823191i	$0.692192\pi$
$912$	32.6201	−	56.9417i	1.08016	−	1.88553i
$913$	−6.83086	−	11.8314i	−0.226068	−	0.391562i
$914$	33.4414	−	43.6578i	1.10614	−	1.44407i
$915$		0			0
$916$	−1.05215	−	1.04862i	−0.0347641	−	0.0346473i
$917$	13.3932	+	8.30519i	0.442281	+	0.274262i
$918$	8.01594	+	19.3062i	0.264565	+	0.637200i
$919$	−21.9492	−	12.6724i	−0.724036	−	0.418022i	0.0922005	−	0.995740i	$-0.470610\pi$
$919$	−21.9492	−	12.6724i	−0.724036	−	0.418022i	−0.816236	+	0.577718i	$0.803943\pi$
$920$		0			0
$921$	9.60907	+	16.6434i	0.316630	+	0.548419i
$922$	−5.37180	−	0.702610i	−0.176911	−	0.0231392i
$923$		−	6.89398i		−	0.226918i
$924$	−14.8464	−	15.7584i	−0.488412	−	0.518414i
$925$		0			0
$926$	1.17603	−	8.99129i	0.0386466	−	0.295472i
$927$	45.3494	−	26.1825i	1.48947	−	0.859946i
$928$	−4.74050	+	6.23209i	−0.155615	+	0.204578i
$929$	0.978904	+	0.565171i	0.0321168	+	0.0185426i	0.515972	−	0.856605i	$-0.327431\pi$
$929$	0.978904	+	0.565171i	0.0321168	+	0.0185426i	−0.483856	+	0.875148i	$0.660764\pi$
$930$		0			0
$931$	−23.6231	+	35.5466i	−0.774215	+	1.16499i
$932$	−23.5956	−	23.5162i	−0.772899	−	0.770300i
$933$	8.28927	+	4.78581i	0.271379	+	0.156681i
$934$	−21.9483	+	28.6534i	−0.718169	+	0.937569i
$935$		0			0
$936$	8.35605	+	10.8331i	0.273126	+	0.354089i
$937$	36.3080			1.18613			0.593065	−	0.805155i	$-0.297918\pi$
$937$	36.3080			1.18613			0.593065	+	0.805155i	$0.297918\pi$
$938$	13.9368	+	36.7954i	0.455052	+	1.20141i
$939$		−	67.5285i		−	2.20371i
$940$		0			0
$941$	−48.6016	+	28.0601i	−1.58437	+	0.914734i	−0.590155	+	0.807290i	$0.700933\pi$
$941$	−48.6016	+	28.0601i	−1.58437	+	0.914734i	−0.994211	+	0.107444i	$0.965733\pi$
$942$	−19.9529	+	26.0485i	−0.650100	+	0.848706i
$943$	−9.52327	−	5.49826i	−0.310120	−	0.179048i
$944$	0.0249815	+	7.41802i	0.000813078	+	0.241436i
$945$		0			0
$946$	4.03697	+	9.72295i	0.131253	+	0.316121i
$947$	−25.2454	+	43.7264i	−0.820367	+	1.42092i	0.0850430	+	0.996377i	$0.472897\pi$
$947$	−25.2454	+	43.7264i	−0.820367	+	1.42092i	−0.905410	+	0.424539i	$0.860436\pi$
$948$	27.2856	+	7.26194i	0.886195	+	0.235857i
$949$	−4.48428	−	7.76700i	−0.145566	−	0.252128i
$950$		0			0
$951$	61.6034			1.99763
$952$	−3.37418	−	32.9813i	−0.109358	−	1.06893i
$953$			3.90743i			0.126574i	0.997995	+	0.0632870i	$0.0201583\pi$
$953$			3.90743i			0.126574i	−0.997995	+	0.0632870i	$0.979842\pi$
$954$	−57.4010	−	7.50783i	−1.85843	−	0.243075i
$955$		0			0
$956$	0.165158	−	0.620554i	0.00534158	−	0.0200702i
$957$	−2.83174	+	4.90473i	−0.0915373	+	0.158547i
$958$	−16.7370	+	6.94920i	−0.540748	+	0.224519i
$959$	−13.5931	−	25.3545i	−0.438943	−	0.818741i
$960$		0			0
$961$	−33.0068	+	57.1695i	−1.06474	+	1.84418i
$962$	9.61284	−	12.5496i	0.309930	−	0.404614i
$963$	27.6944	+	47.9680i	0.892438	+	1.54575i
$964$	44.4813	−	11.9991i	1.43265	−	0.386463i
$965$		0			0
$966$	13.0353	−	79.9947i	0.419403	−	2.57379i
$967$	−47.3377			−1.52228			−0.761139	−	0.648589i	$-0.775360\pi$
$967$	−47.3377			−1.52228			−0.761139	+	0.648589i	$0.775360\pi$
$968$	15.0080	+	19.4569i	0.482376	+	0.625368i
$969$	62.9454	−	36.3416i	2.02210	−	1.16746i
$970$		0			0
$971$	12.8186	−	22.2024i	0.411367	−	0.712509i	−0.583672	−	0.811989i	$-0.698385\pi$
$971$	12.8186	−	22.2024i	0.411367	−	0.712509i	0.995040	+	0.0994804i	$0.0317181\pi$
$972$	−28.4443	−	28.3487i	−0.912351	−	0.909284i
$973$	0.275862	−	8.76176i	0.00884372	−	0.280889i
$974$	22.2391	−	9.23367i	0.712586	−	0.295866i
$975$		0			0
$976$	−9.13214	−	15.6950i	−0.292313	−	0.502386i
$977$	−18.7083	+	10.8012i	−0.598530	+	0.345562i	−0.768463	−	0.639894i	$-0.778978\pi$
$977$	−18.7083	+	10.8012i	−0.598530	+	0.345562i	0.169933	+	0.985456i	$0.445645\pi$
$978$	−33.9193	−	4.43652i	−1.08462	−	0.141864i
$979$	−22.6759			−0.724725
$980$		0			0
$981$	9.29919			0.296900
$982$	24.4089	+	3.19259i	0.778919	+	0.101879i
$983$	0.0672839	−	0.0388464i	0.00214602	−	0.00123901i	−0.498927	−	0.866644i	$-0.666272\pi$
$983$	0.0672839	−	0.0388464i	0.00214602	−	0.00123901i	0.501073	+	0.865405i	$0.332939\pi$
$984$	−10.3032	+	1.38293i	−0.328454	+	0.0440861i
$985$		0			0
$986$	−8.00957	+	3.32557i	−0.255077	+	0.105908i
$987$	0.741206	−	23.5417i	0.0235929	−	0.749342i
$988$	9.82045	−	9.85358i	0.312430	−	0.313484i
$989$	−19.7055	+	34.1310i	−0.626600	+	1.08530i
$990$		0			0
$991$	8.06088	−	4.65395i	0.256062	−	0.147838i	−0.366475	−	0.930428i	$-0.619435\pi$
$991$	8.06088	−	4.65395i	0.256062	−	0.147838i	0.622537	+	0.782590i	$0.286102\pi$
$992$	55.2709	+	7.03999i	1.75485	+	0.223520i
$993$	58.3937			1.85307
$994$	−3.63650	+	22.3164i	−0.115343	+	0.707833i
$995$		0			0
$996$	−12.5921	−	46.6800i	−0.398997	−	1.47911i
$997$	20.7119	+	35.8741i	0.655954	+	1.13615i	0.981654	+	0.190672i	$0.0610667\pi$
$997$	20.7119	+	35.8741i	0.655954	+	1.13615i	−0.325700	+	0.945473i	$0.605600\pi$
$998$	13.5217	−	17.6525i	0.428021	−	0.558781i
$999$	16.3456	−	28.3114i	0.517151	−	0.895732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.t.e.299.14		64
4.3	odd	2	inner	700.2.t.e.299.25		64
5.2	odd	4		700.2.p.d.551.2	yes	32
5.3	odd	4		700.2.p.f.551.15	yes	32
5.4	even	2	inner	700.2.t.e.299.19		64
7.3	odd	6	inner	700.2.t.e.199.8		64
20.3	even	4		700.2.p.f.551.4	yes	32
20.7	even	4		700.2.p.d.551.13	yes	32
20.19	odd	2	inner	700.2.t.e.299.8		64
28.3	even	6	inner	700.2.t.e.199.19		64
35.3	even	12		700.2.p.f.451.4	yes	32
35.17	even	12		700.2.p.d.451.13	yes	32
35.24	odd	6	inner	700.2.t.e.199.25		64
140.3	odd	12		700.2.p.f.451.15	yes	32
140.59	even	6	inner	700.2.t.e.199.14		64
140.87	odd	12		700.2.p.d.451.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.p.d.451.2	✓	32	140.87	odd	12
700.2.p.d.451.13	yes	32	35.17	even	12
700.2.p.d.551.2	yes	32	5.2	odd	4
700.2.p.d.551.13	yes	32	20.7	even	4
700.2.p.f.451.4	yes	32	35.3	even	12
700.2.p.f.451.15	yes	32	140.3	odd	12
700.2.p.f.551.4	yes	32	20.3	even	4
700.2.p.f.551.15	yes	32	5.3	odd	4
700.2.t.e.199.8		64	7.3	odd	6	inner
700.2.t.e.199.14		64	140.59	even	6	inner
700.2.t.e.199.19		64	28.3	even	6	inner
700.2.t.e.199.25		64	35.24	odd	6	inner
700.2.t.e.299.8		64	20.19	odd	2	inner
700.2.t.e.299.14		64	1.1	even	1	trivial
700.2.t.e.299.19		64	5.4	even	2	inner
700.2.t.e.299.25		64	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.183411 + 1.40227i) q^{2} +(2.33023 - 1.34536i) q^{3} +(-1.93272 - 0.514384i) q^{4} +(1.45917 + 3.51437i) q^{6} +(0.0832596 - 2.64444i) q^{7} +(1.07579 - 2.61585i) q^{8} +(2.11999 - 3.67193i) q^{9} +O(q^{10})\)	\(q+(-0.183411 + 1.40227i) q^{2} +(2.33023 - 1.34536i) q^{3} +(-1.93272 - 0.514384i) q^{4} +(1.45917 + 3.51437i) q^{6} +(0.0832596 - 2.64444i) q^{7} +(1.07579 - 2.61585i) q^{8} +(2.11999 - 3.67193i) q^{9} +(-1.31689 + 0.760309i) q^{11} +(-5.19572 + 1.40157i) q^{12} -1.14083 q^{13} +(3.69295 + 0.601773i) q^{14} +(3.47082 + 1.98832i) q^{16} +(2.21516 + 3.83677i) q^{17} +(4.76020 + 3.64627i) q^{18} +(3.04859 - 5.28032i) q^{19} +(-3.36371 - 6.27418i) q^{21} +(-0.824625 - 1.98609i) q^{22} +(4.02522 - 6.97188i) q^{23} +(-1.01243 - 7.54287i) q^{24} +(0.209240 - 1.59975i) q^{26} -3.33644i q^{27} +(-1.52118 + 5.06814i) q^{28} +1.38419 q^{29} +(-4.92478 - 8.52996i) q^{31} +(-3.42475 + 4.50234i) q^{32} +(-2.04578 + 3.54340i) q^{33} +(-5.78647 + 2.40255i) q^{34} +(-5.98613 + 6.00632i) q^{36} +(8.48551 + 4.89911i) q^{37} +(6.84529 + 5.24342i) q^{38} +(-2.65839 + 1.53482i) q^{39} -1.36595i q^{41} +(9.41503 - 3.56608i) q^{42} -4.89552 q^{43} +(2.93628 - 0.792076i) q^{44} +(9.03818 + 6.92316i) q^{46} +(2.86528 + 1.65427i) q^{47} +(10.7628 - 0.0362457i) q^{48} +(-6.98614 - 0.440350i) q^{49} +(10.3237 + 5.96038i) q^{51} +(2.20490 + 0.586823i) q^{52} +(-8.36094 + 4.82719i) q^{53} +(4.67858 + 0.611940i) q^{54} +(-6.82789 - 3.06265i) q^{56} -16.4058i q^{57} +(-0.253876 + 1.94100i) q^{58} +(0.927258 + 1.60606i) q^{59} +(-3.93142 - 2.26981i) q^{61} +(12.8646 - 5.34137i) q^{62} +(-9.53369 - 5.91191i) q^{63} +(-5.68536 - 5.62821i) q^{64} +(-4.59358 - 3.51864i) q^{66} +(5.25787 + 9.10690i) q^{67} +(-2.30771 - 8.55485i) q^{68} -21.6615i q^{69} +6.04297i q^{71} +(-7.32456 - 9.49580i) q^{72} +(3.93073 + 6.80823i) q^{73} +(-8.42621 + 11.0004i) q^{74} +(-8.60820 + 8.63723i) q^{76} +(1.90095 + 3.54575i) q^{77} +(-1.66466 - 4.00928i) q^{78} +(-4.54388 - 2.62341i) q^{79} +(1.87126 + 3.24111i) q^{81} +(1.91544 + 0.250532i) q^{82} +8.98431i q^{83} +(3.27378 + 13.8565i) q^{84} +(0.897895 - 6.86484i) q^{86} +(3.22548 - 1.86223i) q^{87} +(0.572156 + 4.26273i) q^{88} +(12.9144 + 7.45614i) q^{89} +(-0.0949847 + 3.01685i) q^{91} +(-11.3658 + 11.4042i) q^{92} +(-22.9517 - 13.2512i) q^{93} +(-2.84526 + 3.71448i) q^{94} +(-1.92320 + 15.0990i) q^{96} -15.0890 q^{97} +(1.89883 - 9.71568i) q^{98} +6.44739i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 2 q^{4} + 32 q^{9}+O(q^{10}) \) 64 * q - 2 * q^4 + 32 * q^9	\( 64 q - 2 q^{4} + 32 q^{9} + 26 q^{14} + 2 q^{16} + 24 q^{21} + 36 q^{24} - 30 q^{26} - 16 q^{29} - 60 q^{36} - 24 q^{44} + 4 q^{46} - 40 q^{49} - 114 q^{54} - 62 q^{56} - 24 q^{61} - 80 q^{64} - 132 q^{66} + 2 q^{74} - 72 q^{81} - 134 q^{84} + 8 q^{86} + 120 q^{89} - 90 q^{94} + 186 q^{96}+O(q^{100}) \) 64 * q - 2 * q^4 + 32 * q^9 + 26 * q^14 + 2 * q^16 + 24 * q^21 + 36 * q^24 - 30 * q^26 - 16 * q^29 - 60 * q^36 - 24 * q^44 + 4 * q^46 - 40 * q^49 - 114 * q^54 - 62 * q^56 - 24 * q^61 - 80 * q^64 - 132 * q^66 + 2 * q^74 - 72 * q^81 - 134 * q^84 + 8 * q^86 + 120 * q^89 - 90 * q^94 + 186 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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