LMFDB - Embedded newform 256.2.i.a.81.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [256,2,Mod(17,256)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("256.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(256, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			81.4
Character	$\chi$	$=$	256.81
Dual form			256.2.i.a.177.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.123576 + 0.621259i) q^{3} +(0.660623 + 0.441414i) q^{5} +(0.860072 - 0.356253i) q^{7} +(2.40095 + 0.994505i) q^{9} +(0.0768198 - 0.0152804i) q^{11} +(-1.83807 + 1.22816i) q^{13} +(-0.355870 + 0.355870i) q^{15} +(3.15660 + 3.15660i) q^{17} +(3.67418 + 5.49880i) q^{19} +(0.115041 + 0.578352i) q^{21} +(2.85915 - 6.90260i) q^{23} +(-1.67184 - 4.03618i) q^{25} +(-1.97029 + 2.94875i) q^{27} +(-8.72686 - 1.73588i) q^{29} +4.18821i q^{31} +0.0496134i q^{33} +(0.725438 + 0.144299i) q^{35} +(2.71234 - 4.05931i) q^{37} +(-0.535863 - 1.29369i) q^{39} +(2.38360 - 5.75451i) q^{41} +(-0.476196 - 2.39400i) q^{43} +(1.14713 + 1.71680i) q^{45} +(-5.93827 - 5.93827i) q^{47} +(-4.33694 + 4.33694i) q^{49} +(-2.35115 + 1.57099i) q^{51} +(-1.38768 + 0.276027i) q^{53} +(0.0574939 + 0.0238148i) q^{55} +(-3.87022 + 1.60310i) q^{57} +(-10.1842 - 6.80486i) q^{59} +(0.575578 - 2.89363i) q^{61} +2.41928 q^{63} -1.75639 q^{65} +(1.81110 - 9.10504i) q^{67} +(3.93498 + 2.62927i) q^{69} +(-3.80374 + 1.57556i) q^{71} +(0.958083 + 0.396851i) q^{73} +(2.71412 - 0.539871i) q^{75} +(0.0606269 - 0.0405096i) q^{77} +(-7.08438 + 7.08438i) q^{79} +(3.92436 + 3.92436i) q^{81} +(3.50145 + 5.24029i) q^{83} +(0.691955 + 3.47869i) q^{85} +(2.15687 - 5.20713i) q^{87} +(-2.98468 - 7.20566i) q^{89} +(-1.14333 + 1.71112i) q^{91} +(-2.60196 - 0.517563i) q^{93} +5.25446i q^{95} -7.39898i q^{97} +(0.199637 + 0.0397102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.123576	+	0.621259i	−0.0713467	+	0.358684i	−0.999922	−	0.0124589i	$-0.996034\pi$
$3$	−0.123576	+	0.621259i	−0.0713467	+	0.358684i	0.928576	+	0.371143i	$0.121034\pi$
$4$		0			0
$5$	0.660623	+	0.441414i	0.295439	+	0.197406i	0.694452	−	0.719539i	$-0.255647\pi$
$5$	0.660623	+	0.441414i	0.295439	+	0.197406i	−0.399012	+	0.916946i	$0.630647\pi$
$6$		0			0
$7$	0.860072	−	0.356253i	0.325077	−	0.134651i	−0.214176	−	0.976795i	$-0.568707\pi$
$7$	0.860072	−	0.356253i	0.325077	−	0.134651i	0.539253	+	0.842144i	$0.318707\pi$
$8$		0			0
$9$	2.40095	+	0.994505i	0.800315	+	0.331502i
$10$		0			0
$11$	0.0768198	−	0.0152804i	0.0231621	−	0.00460722i	−0.183496	−	0.983021i	$-0.558741\pi$
$11$	0.0768198	−	0.0152804i	0.0231621	−	0.00460722i	0.206658	+	0.978413i	$0.433741\pi$
$12$		0			0
$13$	−1.83807	+	1.22816i	−0.509788	+	0.340629i	−0.783714	−	0.621121i	$-0.786677\pi$
$13$	−1.83807	+	1.22816i	−0.509788	+	0.340629i	0.273927	+	0.961751i	$0.411677\pi$
$14$		0			0
$15$	−0.355870	+	0.355870i	−0.0918852	+	0.0918852i
$16$		0			0
$17$	3.15660	+	3.15660i	0.765589	+	0.765589i	0.977326	−	0.211738i	$-0.0679123\pi$
$17$	3.15660	+	3.15660i	0.765589	+	0.765589i	−0.211738	+	0.977326i	$0.567912\pi$
$18$		0			0
$19$	3.67418	+	5.49880i	0.842914	+	1.26151i	0.963204	+	0.268771i	$0.0866176\pi$
$19$	3.67418	+	5.49880i	0.842914	+	1.26151i	−0.120290	+	0.992739i	$0.538382\pi$
$20$		0			0
$21$	0.115041	+	0.578352i	0.0251041	+	0.126207i
$22$		0			0
$23$	2.85915	−	6.90260i	0.596174	−	1.43929i	−0.281277	−	0.959627i	$-0.590758\pi$
$23$	2.85915	−	6.90260i	0.596174	−	1.43929i	0.877452	−	0.479665i	$-0.159242\pi$
$24$		0			0
$25$	−1.67184	−	4.03618i	−0.334368	−	0.807236i
$26$		0			0
$27$	−1.97029	+	2.94875i	−0.379183	+	0.567487i
$28$		0			0
$29$	−8.72686	−	1.73588i	−1.62054	−	0.322345i	−0.700343	−	0.713806i	$-0.746970\pi$
$29$	−8.72686	−	1.73588i	−1.62054	−	0.322345i	−0.920195	+	0.391461i	$0.871970\pi$
$30$		0			0
$31$			4.18821i			0.752225i	0.926574	+	0.376112i	$0.122739\pi$
$31$			4.18821i			0.752225i	−0.926574	+	0.376112i	$0.877261\pi$
$32$		0			0
$33$			0.0496134i			0.00863658i
$34$		0			0
$35$	0.725438	+	0.144299i	0.122621	+	0.0243909i
$36$		0			0
$37$	2.71234	−	4.05931i	0.445907	−	0.667346i	−0.538627	−	0.842545i	$-0.681057\pi$
$37$	2.71234	−	4.05931i	0.445907	−	0.667346i	0.984533	+	0.175198i	$0.0560566\pi$
$38$		0			0
$39$	−0.535863	−	1.29369i	−0.0858067	−	0.207156i
$40$		0			0
$41$	2.38360	−	5.75451i	0.372255	−	0.898703i	−0.621113	−	0.783721i	$-0.713319\pi$
$41$	2.38360	−	5.75451i	0.372255	−	0.898703i	0.993368	−	0.114982i	$-0.0366810\pi$
$42$		0			0
$43$	−0.476196	−	2.39400i	−0.0726192	−	0.365081i	0.927339	−	0.374222i	$-0.122090\pi$
$43$	−0.476196	−	2.39400i	−0.0726192	−	0.365081i	−0.999958	+	0.00914095i	$0.997090\pi$
$44$		0			0
$45$	1.14713	+	1.71680i	0.171004	+	0.255926i
$46$		0			0
$47$	−5.93827	−	5.93827i	−0.866186	−	0.866186i	0.125862	−	0.992048i	$-0.459830\pi$
$47$	−5.93827	−	5.93827i	−0.866186	−	0.866186i	−0.992048	+	0.125862i	$0.959830\pi$
$48$		0			0
$49$	−4.33694	+	4.33694i	−0.619563	+	0.619563i
$50$		0			0
$51$	−2.35115	+	1.57099i	−0.329227	+	0.219982i
$52$		0			0
$53$	−1.38768	+	0.276027i	−0.190613	+	0.0379152i	−0.289473	−	0.957186i	$-0.593480\pi$
$53$	−1.38768	+	0.276027i	−0.190613	+	0.0379152i	0.0988607	+	0.995101i	$0.468480\pi$
$54$		0			0
$55$	0.0574939	+	0.0238148i	0.00775248	+	0.00321118i
$56$		0			0
$57$	−3.87022	+	1.60310i	−0.512623	+	0.212335i
$58$		0			0
$59$	−10.1842	−	6.80486i	−1.32587	−	0.885918i	−0.327606	−	0.944815i	$-0.606242\pi$
$59$	−10.1842	−	6.80486i	−1.32587	−	0.885918i	−0.998264	+	0.0588967i	$0.981242\pi$
$60$		0			0
$61$	0.575578	−	2.89363i	0.0736952	−	0.370491i	−0.926285	−	0.376824i	$-0.877016\pi$
$61$	0.575578	−	2.89363i	0.0736952	−	0.370491i	0.999980	+	0.00633357i	$0.00201605\pi$
$62$		0			0
$63$	2.41928			0.304801
$64$		0			0
$65$	−1.75639			−0.217854
$66$		0			0
$67$	1.81110	−	9.10504i	0.221262	−	1.11236i	−0.697209	−	0.716868i	$-0.745575\pi$
$67$	1.81110	−	9.10504i	0.221262	−	1.11236i	0.918471	−	0.395489i	$-0.129425\pi$
$68$		0			0
$69$	3.93498	+	2.62927i	0.473716	+	0.316527i
$70$		0			0
$71$	−3.80374	+	1.57556i	−0.451421	+	0.186985i	−0.596798	−	0.802392i	$-0.703560\pi$
$71$	−3.80374	+	1.57556i	−0.451421	+	0.186985i	0.145377	+	0.989376i	$0.453560\pi$
$72$		0			0
$73$	0.958083	+	0.396851i	0.112135	+	0.0464479i	0.438046	−	0.898953i	$-0.355671\pi$
$73$	0.958083	+	0.396851i	0.112135	+	0.0464479i	−0.325910	+	0.945401i	$0.605671\pi$
$74$		0			0
$75$	2.71412	−	0.539871i	0.313399	−	0.0623390i
$76$		0			0
$77$	0.0606269	−	0.0405096i	0.00690908	−	0.00461650i
$78$		0			0
$79$	−7.08438	+	7.08438i	−0.797055	+	0.797055i	−0.982630	−	0.185575i	$-0.940585\pi$
$79$	−7.08438	+	7.08438i	−0.797055	+	0.797055i	0.185575	+	0.982630i	$0.440585\pi$
$80$		0			0
$81$	3.92436	+	3.92436i	0.436040	+	0.436040i
$82$		0			0
$83$	3.50145	+	5.24029i	0.384334	+	0.575196i	0.972314	−	0.233679i	$-0.0750766\pi$
$83$	3.50145	+	5.24029i	0.384334	+	0.575196i	−0.587980	+	0.808875i	$0.700077\pi$
$84$		0			0
$85$	0.691955	+	3.47869i	0.0750530	+	0.377317i
$86$		0			0
$87$	2.15687	−	5.20713i	0.231240	−	0.558263i
$88$		0			0
$89$	−2.98468	−	7.20566i	−0.316375	−	0.763798i	−0.999441	−	0.0334406i	$-0.989354\pi$
$89$	−2.98468	−	7.20566i	−0.316375	−	0.763798i	0.683065	−	0.730357i	$-0.260646\pi$
$90$		0			0
$91$	−1.14333	+	1.71112i	−0.119854	+	0.179374i
$92$		0			0
$93$	−2.60196	−	0.517563i	−0.269811	−	0.0536688i
$94$		0			0
$95$			5.25446i			0.539096i
$96$		0			0
$97$		−	7.39898i		−	0.751252i	−0.926771	−	0.375626i	$-0.877428\pi$
$97$		−	7.39898i		−	0.751252i	0.926771	−	0.375626i	$-0.122572\pi$
$98$		0			0
$99$	0.199637	+	0.0397102i	0.0200643	+	0.00399103i
$100$		0			0
$101$	7.00497	−	10.4837i	0.697020	−	1.04316i	−0.299019	−	0.954247i	$-0.596659\pi$
$101$	7.00497	−	10.4837i	0.697020	−	1.04316i	0.996039	−	0.0889173i	$-0.0283407\pi$
$102$		0			0
$103$	6.29127	+	15.1885i	0.619897	+	1.49656i	0.851822	+	0.523831i	$0.175498\pi$
$103$	6.29127	+	15.1885i	0.619897	+	1.49656i	−0.231925	+	0.972734i	$0.574502\pi$
$104$		0			0
$105$	−0.179294	+	0.432854i	−0.0174973	+	0.0422422i
$106$		0			0
$107$	−1.51228	−	7.60273i	−0.146197	−	0.734983i	−0.982433	−	0.186614i	$-0.940249\pi$
$107$	−1.51228	−	7.60273i	−0.146197	−	0.734983i	0.836236	−	0.548370i	$-0.184751\pi$
$108$		0			0
$109$	9.12348	+	13.6543i	0.873871	+	1.30784i	0.950482	+	0.310780i	$0.100590\pi$
$109$	9.12348	+	13.6543i	0.873871	+	1.30784i	−0.0766107	+	0.997061i	$0.524410\pi$
$110$		0			0
$111$	2.18670	+	2.18670i	0.207553	+	0.207553i
$112$		0			0
$113$	−7.16639	+	7.16639i	−0.674158	+	0.674158i	−0.958672	−	0.284514i	$-0.908168\pi$
$113$	−7.16639	+	7.16639i	−0.674158	+	0.674158i	0.284514	+	0.958672i	$0.408168\pi$
$114$		0			0
$115$	4.93572	−	3.29795i	0.460259	−	0.307535i
$116$		0			0
$117$	−5.63451	+	1.12077i	−0.520910	+	0.103615i
$118$		0			0
$119$	3.83946	+	1.59035i	0.351962	+	0.145788i
$120$		0			0
$121$	−10.1570	+	4.20717i	−0.923364	+	0.382470i
$122$		0			0
$123$	3.28049	+	2.19195i	0.295792	+	0.197642i
$124$		0			0
$125$	1.45219	−	7.30065i	0.129888	−	0.652990i
$126$		0			0
$127$	12.6480			1.12233			0.561166	−	0.827704i	$-0.310353\pi$
$127$	12.6480			1.12233			0.561166	+	0.827704i	$0.310353\pi$
$128$		0			0
$129$	1.54614			0.136130
$130$		0			0
$131$	0.303754	−	1.52707i	0.0265391	−	0.133421i	−0.965244	−	0.261349i	$-0.915833\pi$
$131$	0.303754	−	1.52707i	0.0265391	−	0.133421i	0.991783	+	0.127928i	$0.0408326\pi$
$132$		0			0
$133$	5.11902	+	3.42042i	0.443876	+	0.296588i
$134$		0			0
$135$	−2.60324	+	1.07830i	−0.224051	+	0.0928050i
$136$		0			0
$137$	5.30492	+	2.19737i	0.453230	+	0.187734i	0.597608	−	0.801789i	$-0.296118\pi$
$137$	5.30492	+	2.19737i	0.453230	+	0.187734i	−0.144378	+	0.989523i	$0.546118\pi$
$138$		0			0
$139$	18.9696	−	3.77329i	1.60898	−	0.320046i	0.692899	−	0.721035i	$-0.256333\pi$
$139$	18.9696	−	3.77329i	1.60898	−	0.320046i	0.916083	+	0.400988i	$0.131333\pi$
$140$		0			0
$141$	4.42303	−	2.95538i	0.372487	−	0.248888i
$142$		0			0
$143$	−0.122433	+	0.122433i	−0.0102384	+	0.0102384i
$144$		0			0
$145$	−4.99892	−	4.99892i	−0.415138	−	0.415138i
$146$		0			0
$147$	−2.15842	−	3.23031i	−0.178024	−	0.266431i
$148$		0			0
$149$	1.63597	+	8.22459i	0.134024	+	0.673785i	0.988122	+	0.153672i	$0.0491100\pi$
$149$	1.63597	+	8.22459i	0.134024	+	0.673785i	−0.854098	+	0.520113i	$0.825890\pi$
$150$		0			0
$151$	−2.47779	+	5.98190i	−0.201639	+	0.486800i	−0.992060	−	0.125764i	$-0.959862\pi$
$151$	−2.47779	+	5.98190i	−0.201639	+	0.486800i	0.790421	+	0.612564i	$0.209862\pi$
$152$		0			0
$153$	4.43958	+	10.7181i	0.358919	+	0.866506i
$154$		0			0
$155$	−1.84873	+	2.76683i	−0.148494	+	0.222237i
$156$		0			0
$157$	15.1994	+	3.02335i	1.21304	+	0.241289i	0.759836	−	0.650115i	$-0.225279\pi$
$157$	15.1994	+	3.02335i	1.21304	+	0.241289i	0.453208	+	0.891405i	$0.350279\pi$
$158$		0			0
$159$		−	0.896221i		−	0.0710749i
$160$		0			0
$161$		−	6.95532i		−	0.548156i
$162$		0			0
$163$	−13.1823	−	2.62213i	−1.03252	−	0.205381i	−0.350384	−	0.936606i	$-0.613949\pi$
$163$	−13.1823	−	2.62213i	−1.03252	−	0.205381i	−0.682136	+	0.731225i	$0.738949\pi$
$164$		0			0
$165$	−0.0219000	+	0.0327757i	−0.00170491	+	0.00255159i
$166$		0			0
$167$	−3.50753	−	8.46791i	−0.271420	−	0.655267i	0.728124	−	0.685445i	$-0.240392\pi$
$167$	−3.50753	−	8.46791i	−0.271420	−	0.655267i	−0.999545	+	0.0301784i	$0.990392\pi$
$168$		0			0
$169$	−3.10477	+	7.49557i	−0.238828	+	0.576582i
$170$		0			0
$171$	3.35293	+	16.8563i	0.256405	+	1.28903i
$172$		0			0
$173$	−4.17887	−	6.25411i	−0.317713	−	0.475491i	0.637898	−	0.770120i	$-0.279804\pi$
$173$	−4.17887	−	6.25411i	−0.317713	−	0.475491i	−0.955612	+	0.294629i	$0.904804\pi$
$174$		0			0
$175$	−2.87581	−	2.87581i	−0.217391	−	0.217391i
$176$		0			0
$177$	5.48611	−	5.48611i	0.412361	−	0.412361i
$178$		0			0
$179$	−4.20486	+	2.80960i	−0.314286	+	0.209999i	−0.702701	−	0.711485i	$-0.748023\pi$
$179$	−4.20486	+	2.80960i	−0.314286	+	0.209999i	0.388415	+	0.921485i	$0.373023\pi$
$180$		0			0
$181$	−5.52166	+	1.09833i	−0.410422	+	0.0816379i	−0.395983	−	0.918258i	$-0.629596\pi$
$181$	−5.52166	+	1.09833i	−0.410422	+	0.0816379i	−0.0144385	+	0.999896i	$0.504596\pi$
$182$		0			0
$183$	1.72656	+	0.715166i	0.127631	+	0.0528666i
$184$		0			0
$185$	3.58367	−	1.48441i	0.263477	−	0.109136i
$186$		0			0
$187$	0.290724	+	0.194256i	0.0212598	+	0.0142054i
$188$		0			0
$189$	−0.644090	+	3.23806i	−0.0468507	+	0.235534i
$190$		0			0
$191$	−1.29893			−0.0939871			−0.0469936	−	0.998895i	$-0.514964\pi$
$191$	−1.29893			−0.0939871			−0.0469936	+	0.998895i	$0.514964\pi$
$192$		0			0
$193$	−0.155182			−0.0111702			−0.00558511	−	0.999984i	$-0.501778\pi$
$193$	−0.155182			−0.0111702			−0.00558511	+	0.999984i	$0.501778\pi$
$194$		0			0
$195$	0.217048	−	1.09118i	0.0155432	−	0.0781407i
$196$		0			0
$197$	−10.0765	−	6.73293i	−0.717923	−	0.479701i	0.142167	−	0.989843i	$-0.454593\pi$
$197$	−10.0765	−	6.73293i	−0.717923	−	0.479701i	−0.860090	+	0.510142i	$0.829593\pi$
$198$		0			0
$199$	−22.3945	+	9.27612i	−1.58751	+	0.657566i	−0.989580	−	0.143985i	$-0.954008\pi$
$199$	−22.3945	+	9.27612i	−1.58751	+	0.657566i	−0.597926	+	0.801551i	$0.704008\pi$
$200$		0			0
$201$	5.43278	+	2.25033i	0.383199	+	0.158726i
$202$		0			0
$203$	−8.12414	+	1.61599i	−0.570203	+	0.113420i
$204$		0			0
$205$	4.11478	−	2.74941i	0.287388	−	0.192027i
$206$		0			0
$207$	13.7293	−	13.7293i	0.954255	−	0.954255i
$208$		0			0
$209$	0.366274	+	0.366274i	0.0253357	+	0.0253357i
$210$		0			0
$211$	−5.00786	−	7.49478i	−0.344755	−	0.515962i	0.618057	−	0.786133i	$-0.287920\pi$
$211$	−5.00786	−	7.49478i	−0.344755	−	0.515962i	−0.962812	+	0.270171i	$0.912920\pi$
$212$		0			0
$213$	−0.508780	−	2.55781i	−0.0348610	−	0.175258i
$214$		0			0
$215$	0.742159	−	1.79173i	0.0506148	−	0.122195i
$216$		0			0
$217$	1.49206	+	3.60216i	0.101288	+	0.244531i
$218$		0			0
$219$	−0.364944	+	0.546177i	−0.0246606	+	0.0369072i
$220$		0			0
$221$	−9.67885	−	1.92524i	−0.651070	−	0.129506i
$222$		0			0
$223$		−	14.3604i		−	0.961644i	−0.876818	−	0.480822i	$-0.840338\pi$
$223$		−	14.3604i		−	0.961644i	0.876818	−	0.480822i	$-0.159662\pi$
$224$		0			0
$225$		−	11.3533i		−	0.756887i
$226$		0			0
$227$	−1.51532	−	0.301416i	−0.100575	−	0.0200057i	0.144546	−	0.989498i	$-0.453828\pi$
$227$	−1.51532	−	0.301416i	−0.100575	−	0.0200057i	−0.245121	+	0.969492i	$0.578828\pi$
$228$		0			0
$229$	−10.8318	+	16.2109i	−0.715784	+	1.07125i	0.278071	+	0.960560i	$0.410305\pi$
$229$	−10.8318	+	16.2109i	−0.715784	+	1.07125i	−0.993855	+	0.110686i	$0.964695\pi$
$230$		0			0
$231$	0.0176749	+	0.0426711i	0.00116292	+	0.00280755i
$232$		0			0
$233$	0.955848	−	2.30762i	0.0626197	−	0.151177i	−0.889472	−	0.456989i	$-0.848928\pi$
$233$	0.955848	−	2.30762i	0.0626197	−	0.151177i	0.952092	+	0.305812i	$0.0989278\pi$
$234$		0			0
$235$	−1.30172	−	6.54419i	−0.0849149	−	0.426896i
$236$		0			0
$237$	−3.52578	−	5.27670i	−0.229024	−	0.342759i
$238$		0			0
$239$	−5.93760	−	5.93760i	−0.384072	−	0.384072i	0.488495	−	0.872567i	$-0.337546\pi$
$239$	−5.93760	−	5.93760i	−0.384072	−	0.384072i	−0.872567	+	0.488495i	$0.837546\pi$
$240$		0			0
$241$	7.45454	−	7.45454i	0.480189	−	0.480189i	−0.425003	−	0.905192i	$-0.639727\pi$
$241$	7.45454	−	7.45454i	0.480189	−	0.480189i	0.905192	+	0.425003i	$0.139727\pi$
$242$		0			0
$243$	−11.7692	+	7.86396i	−0.754998	+	0.504473i
$244$		0			0
$245$	−4.77947	+	0.950695i	−0.305349	+	0.0607377i
$246$		0			0
$247$	−13.5068	−	5.59468i	−0.859415	−	0.355981i
$248$		0			0
$249$	−3.68827	+	1.52773i	−0.233735	+	0.0968161i
$250$		0			0
$251$	13.2843	+	8.87629i	0.838498	+	0.560267i	0.899024	−	0.437900i	$-0.144278\pi$
$251$	13.2843	+	8.87629i	0.838498	+	0.560267i	−0.0605253	+	0.998167i	$0.519278\pi$
$252$		0			0
$253$	0.114165	−	0.573946i	0.00717749	−	0.0360837i
$254$		0			0
$255$	−2.24668			−0.140693
$256$		0			0
$257$	0.502791			0.0313633			0.0156816	−	0.999877i	$-0.495008\pi$
$257$	0.502791			0.0313633			0.0156816	+	0.999877i	$0.495008\pi$
$258$		0			0
$259$	0.886668	−	4.45758i	0.0550949	−	0.276981i
$260$		0			0
$261$	−19.2264	−	12.8467i	−1.19008	−	0.795188i
$262$		0			0
$263$	26.2018	−	10.8532i	1.61567	−	0.669234i	0.622155	−	0.782894i	$-0.286257\pi$
$263$	26.2018	−	10.8532i	1.61567	−	0.669234i	0.993520	+	0.113660i	$0.0362574\pi$
$264$		0			0
$265$	−1.03858	−	0.430192i	−0.0637992	−	0.0264265i
$266$		0			0
$267$	4.84542	−	0.963813i	0.296535	−	0.0589844i
$268$		0			0
$269$	−5.76407	+	3.85143i	−0.351442	+	0.234826i	−0.718742	−	0.695276i	$-0.755282\pi$
$269$	−5.76407	+	3.85143i	−0.351442	+	0.234826i	0.367301	+	0.930102i	$0.380282\pi$
$270$		0			0
$271$	1.72051	−	1.72051i	0.104513	−	0.104513i	−0.652917	−	0.757430i	$-0.726455\pi$
$271$	1.72051	−	1.72051i	0.104513	−	0.104513i	0.757430	+	0.652917i	$0.226455\pi$
$272$		0			0
$273$	−0.921761	−	0.921761i	−0.0557875	−	0.0557875i
$274$		0			0
$275$	−0.190105	−	0.284512i	−0.0114638	−	0.0171567i
$276$		0			0
$277$	−3.73240	−	18.7640i	−0.224258	−	1.12742i	−0.914731	−	0.404063i	$-0.867598\pi$
$277$	−3.73240	−	18.7640i	−0.224258	−	1.12742i	0.690473	−	0.723358i	$-0.257402\pi$
$278$		0			0
$279$	−4.16519	+	10.0557i	−0.249364	+	0.602017i
$280$		0			0
$281$	2.79945	+	6.75847i	0.167001	+	0.403177i	0.985119	−	0.171874i	$-0.0549823\pi$
$281$	2.79945	+	6.75847i	0.167001	+	0.403177i	−0.818118	+	0.575051i	$0.804982\pi$
$282$		0			0
$283$	−5.39086	+	8.06799i	−0.320453	+	0.479592i	−0.956367	−	0.292168i	$-0.905623\pi$
$283$	−5.39086	+	8.06799i	−0.320453	+	0.479592i	0.635914	+	0.771760i	$0.280623\pi$
$284$		0			0
$285$	−3.26438	−	0.649326i	−0.193365	−	0.0384628i
$286$		0			0
$287$		−	5.79845i		−	0.342272i
$288$		0			0
$289$			2.92828i			0.172252i
$290$		0			0
$291$	4.59668	+	0.914337i	0.269462	+	0.0535994i
$292$		0			0
$293$	−5.00829	+	7.49544i	−0.292587	+	0.437888i	−0.948419	−	0.317019i	$-0.897318\pi$
$293$	−5.00829	+	7.49544i	−0.292587	+	0.437888i	0.655832	+	0.754907i	$0.272318\pi$
$294$		0			0
$295$	−3.72415	−	8.99089i	−0.216828	−	0.523470i
$296$		0			0
$297$	−0.106299	+	0.256629i	−0.00616811	+	0.0148911i
$298$		0			0
$299$	3.22217	+	16.1989i	0.186343	+	0.936808i
$300$		0			0
$301$	−1.26243	−	1.88936i	−0.0727654	−	0.108901i
$302$		0			0
$303$	5.64743	+	5.64743i	0.324437	+	0.324437i
$304$		0			0
$305$	1.65753	−	1.65753i	0.0949097	−	0.0949097i
$306$		0			0
$307$	12.5667	−	8.39679i	0.717218	−	0.479230i	−0.142632	−	0.989776i	$-0.545557\pi$
$307$	12.5667	−	8.39679i	0.717218	−	0.479230i	0.859851	+	0.510546i	$0.170557\pi$
$308$		0			0
$309$	−10.2134	+	2.03158i	−0.581022	+	0.115572i
$310$		0			0
$311$	4.26292	+	1.76576i	0.241728	+	0.100127i	0.500259	−	0.865876i	$-0.333238\pi$
$311$	4.26292	+	1.76576i	0.241728	+	0.100127i	−0.258531	+	0.966003i	$0.583238\pi$
$312$		0			0
$313$	19.1426	−	7.92911i	1.08200	−	0.448180i	0.230790	−	0.973004i	$-0.425869\pi$
$313$	19.1426	−	7.92911i	1.08200	−	0.448180i	0.851211	+	0.524824i	$0.175869\pi$
$314$		0			0
$315$	1.59823	+	1.06790i	0.0900502	+	0.0601696i
$316$		0			0
$317$	−1.16146	+	5.83907i	−0.0652342	+	0.327955i	−0.999598	−	0.0283671i	$-0.990969\pi$
$317$	−1.16146	+	5.83907i	−0.0652342	+	0.327955i	0.934363	+	0.356322i	$0.115969\pi$
$318$		0			0
$319$	−0.696921			−0.0390201
$320$		0			0
$321$	4.91015			0.274058
$322$		0			0
$323$	−5.75959	+	28.9554i	−0.320472	+	1.61112i
$324$		0			0
$325$	8.03002	+	5.36549i	0.445425	+	0.297624i
$326$		0			0
$327$	−9.61028	+	3.98071i	−0.531450	+	0.220134i
$328$		0			0
$329$	−7.22287	−	2.99181i	−0.398210	−	0.164944i
$330$		0			0
$331$	−25.5621	+	5.08462i	−1.40502	+	0.279476i	−0.838648	−	0.544674i	$-0.816654\pi$
$331$	−25.5621	+	5.08462i	−1.40502	+	0.279476i	−0.566372	+	0.824149i	$0.691654\pi$
$332$		0			0
$333$	10.5492	−	7.04875i	0.578092	−	0.386269i
$334$		0			0
$335$	5.21555	−	5.21555i	0.284956	−	0.284956i
$336$		0			0
$337$	−14.8554	−	14.8554i	−0.809225	−	0.809225i	0.175292	−	0.984517i	$-0.443913\pi$
$337$	−14.8554	−	14.8554i	−0.809225	−	0.809225i	−0.984517	+	0.175292i	$0.943913\pi$
$338$		0			0
$339$	−3.56659	−	5.33779i	−0.193711	−	0.289909i
$340$		0			0
$341$	0.0639976	+	0.321738i	0.00346566	+	0.0174231i
$342$		0			0
$343$	−4.67880	+	11.2956i	−0.252632	+	0.609907i
$344$		0			0
$345$	1.43894	+	3.47391i	0.0774700	+	0.187029i
$346$		0			0
$347$	16.4814	−	24.6662i	0.884769	−	1.32415i	−0.0606043	−	0.998162i	$-0.519303\pi$
$347$	16.4814	−	24.6662i	0.884769	−	1.32415i	0.945374	−	0.325989i	$-0.105697\pi$
$348$		0			0
$349$	31.9917	+	6.36355i	1.71248	+	0.340633i	0.951384	−	0.308009i	$-0.0996626\pi$
$349$	31.9917	+	6.36355i	1.71248	+	0.340633i	0.761094	+	0.648642i	$0.224663\pi$
$350$		0			0
$351$		−	7.83982i		−	0.418459i
$352$		0			0
$353$			33.6731i			1.79224i	0.443814	+	0.896119i	$0.353625\pi$
$353$			33.6731i			1.79224i	−0.443814	+	0.896119i	$0.646375\pi$
$354$		0			0
$355$	−3.20831	−	0.638172i	−0.170279	−	0.0338707i
$356$		0			0
$357$	−1.46249	+	2.18877i	−0.0774031	+	0.115842i
$358$		0			0
$359$	4.87560	+	11.7707i	0.257324	+	0.621235i	0.998760	−	0.0497885i	$-0.0158547\pi$
$359$	4.87560	+	11.7707i	0.257324	+	0.621235i	−0.741436	+	0.671024i	$0.765855\pi$
$360$		0			0
$361$	−9.46619	+	22.8534i	−0.498220	+	1.20281i
$362$		0			0
$363$	−1.35858	−	6.83004i	−0.0713070	−	0.358484i
$364$		0			0
$365$	0.457756	+	0.685080i	0.0239600	+	0.0358587i
$366$		0			0
$367$	7.60045	+	7.60045i	0.396740	+	0.396740i	0.877082	−	0.480341i	$-0.159487\pi$
$367$	7.60045	+	7.60045i	0.396740	+	0.396740i	−0.480341	+	0.877082i	$0.659487\pi$
$368$		0			0
$369$	11.4458	−	11.4458i	0.595843	−	0.595843i
$370$		0			0
$371$	−1.09517	+	0.731770i	−0.0568584	+	0.0379916i
$372$		0			0
$373$	19.4325	−	3.86536i	1.00618	−	0.200141i	0.335618	−	0.941998i	$-0.391055\pi$
$373$	19.4325	−	3.86536i	1.00618	−	0.200141i	0.670558	+	0.741857i	$0.266055\pi$
$374$		0			0
$375$	4.35614	+	1.80437i	0.224950	+	0.0931775i
$376$		0			0
$377$	18.1725	−	7.52729i	0.935931	−	0.387675i
$378$		0			0
$379$	23.2828	+	15.5571i	1.19596	+	0.799115i	0.984001	−	0.178164i	$-0.0570158\pi$
$379$	23.2828	+	15.5571i	1.19596	+	0.799115i	0.211959	+	0.977279i	$0.432016\pi$
$380$		0			0
$381$	−1.56300	+	7.85771i	−0.0800747	+	0.402563i
$382$		0			0
$383$	−26.0613			−1.33167			−0.665835	−	0.746099i	$-0.731924\pi$
$383$	−26.0613			−1.33167			−0.665835	+	0.746099i	$0.731924\pi$
$384$		0			0
$385$	0.0579330			0.00295254
$386$		0			0
$387$	1.23752	−	6.22144i	0.0629068	−	0.316254i
$388$		0			0
$389$	17.0947	+	11.4223i	0.866737	+	0.579135i	0.907509	−	0.420034i	$-0.137982\pi$
$389$	17.0947	+	11.4223i	0.866737	+	0.579135i	−0.0407720	+	0.999168i	$0.512982\pi$
$390$		0			0
$391$	30.8140	−	12.7636i	1.55833	−	0.645481i
$392$		0			0
$393$	0.911172	+	0.377420i	0.0459626	+	0.0190383i
$394$		0			0
$395$	−7.80725	+	1.55296i	−0.392825	+	0.0781378i
$396$		0			0
$397$	−13.8749	+	9.27088i	−0.696359	+	0.465292i	−0.852693	−	0.522412i	$-0.825032\pi$
$397$	−13.8749	+	9.27088i	−0.696359	+	0.465292i	0.156334	+	0.987704i	$0.450032\pi$
$398$		0			0
$399$	−2.75756	+	2.75756i	−0.138051	+	0.138051i
$400$		0			0
$401$	13.1510	+	13.1510i	0.656731	+	0.656731i	0.954605	−	0.297874i	$-0.0962775\pi$
$401$	13.1510	+	13.1510i	0.656731	+	0.656731i	−0.297874	+	0.954605i	$0.596277\pi$
$402$		0			0
$403$	−5.14378	−	7.69820i	−0.256230	−	0.383475i
$404$		0			0
$405$	0.860253	+	4.32479i	0.0427463	+	0.214900i
$406$		0			0
$407$	0.146334	−	0.353281i	0.00725350	−	0.0175115i
$408$		0			0
$409$	−4.38868	−	10.5952i	−0.217006	−	0.523899i	0.777463	−	0.628929i	$-0.216506\pi$
$409$	−4.38868	−	10.5952i	−0.217006	−	0.523899i	−0.994469	+	0.105030i	$0.966506\pi$
$410$		0			0
$411$	−2.02070	+	3.02419i	−0.0996737	+	0.149172i
$412$		0			0
$413$	−11.1834	−	2.22452i	−0.550299	−	0.109461i
$414$		0			0
$415$			5.00744i			0.245806i
$416$		0			0
$417$			12.2513i			0.599951i
$418$		0			0
$419$	34.0450	+	6.77197i	1.66321	+	0.330832i	0.935033	−	0.354560i	$-0.115369\pi$
$419$	34.0450	+	6.77197i	1.66321	+	0.330832i	0.728174	+	0.685392i	$0.240369\pi$
$420$		0			0
$421$	−4.93933	+	7.39223i	−0.240728	+	0.360275i	−0.932086	−	0.362238i	$-0.882013\pi$
$421$	−4.93933	+	7.39223i	−0.240728	+	0.360275i	0.691358	+	0.722513i	$0.257013\pi$
$422$		0			0
$423$	−8.35183	−	20.1631i	−0.406080	−	0.980364i
$424$		0			0
$425$	7.46328	−	18.0180i	0.362022	−	0.873999i
$426$		0			0
$427$	−0.535826	−	2.69378i	−0.0259304	−	0.130361i
$428$		0			0
$429$	−0.0609330	−	0.0911926i	−0.00294187	−	0.00440282i
$430$		0			0
$431$	23.1336	+	23.1336i	1.11431	+	1.11431i	0.992561	+	0.121745i	$0.0388490\pi$
$431$	23.1336	+	23.1336i	1.11431	+	1.11431i	0.121745	+	0.992561i	$0.461151\pi$
$432$		0			0
$433$	−0.961924	+	0.961924i	−0.0462271	+	0.0462271i	−0.729842	−	0.683615i	$-0.760407\pi$
$433$	−0.961924	+	0.961924i	−0.0462271	+	0.0462271i	0.683615	+	0.729842i	$0.260407\pi$
$434$		0			0
$435$	3.72338	−	2.48788i	0.178522	−	0.119285i
$436$		0			0
$437$	48.4610	−	9.63950i	2.31820	−	0.461120i
$438$		0			0
$439$	−20.8397	−	8.63209i	−0.994625	−	0.411987i	−0.174802	−	0.984604i	$-0.555928\pi$
$439$	−20.8397	−	8.63209i	−0.994625	−	0.411987i	−0.819823	+	0.572616i	$0.805928\pi$
$440$		0			0
$441$	−14.7259	+	6.09965i	−0.701232	+	0.290460i
$442$		0			0
$443$	−30.4748	−	20.3626i	−1.44790	−	0.967458i	−0.997200	−	0.0747837i	$-0.976173\pi$
$443$	−30.4748	−	20.3626i	−1.44790	−	0.967458i	−0.450703	−	0.892674i	$-0.648827\pi$
$444$		0			0
$445$	1.20893	−	6.07770i	0.0573088	−	0.288111i
$446$		0			0
$447$	−5.31177			−0.251238
$448$		0			0
$449$	−15.6259			−0.737431			−0.368715	−	0.929542i	$-0.620202\pi$
$449$	−15.6259			−0.737431			−0.368715	+	0.929542i	$0.620202\pi$
$450$		0			0
$451$	0.0951761	−	0.478483i	0.00448167	−	0.0225309i
$452$		0			0
$453$	−3.41012	−	2.27857i	−0.160221	−	0.107057i
$454$		0			0
$455$	−1.51062	+	0.625721i	−0.0708192	+	0.0293343i
$456$		0			0
$457$	−34.6599	−	14.3566i	−1.62132	−	0.671574i	−0.627103	−	0.778936i	$-0.715760\pi$
$457$	−34.6599	−	14.3566i	−1.62132	−	0.671574i	−0.994220	+	0.107362i	$0.965760\pi$
$458$		0			0
$459$	−15.5275	+	3.08860i	−0.724759	+	0.144164i
$460$		0			0
$461$	2.18684	−	1.46120i	0.101851	−	0.0680548i	−0.503602	−	0.863936i	$-0.667992\pi$
$461$	2.18684	−	1.46120i	0.101851	−	0.0680548i	0.605453	+	0.795881i	$0.292992\pi$
$462$		0			0
$463$	−10.3078	+	10.3078i	−0.479045	+	0.479045i	−0.904826	−	0.425781i	$-0.859999\pi$
$463$	−10.3078	+	10.3078i	−0.479045	+	0.479045i	0.425781	+	0.904826i	$0.359999\pi$
$464$		0			0
$465$	−1.49046	−	1.49046i	−0.0691183	−	0.0691183i
$466$		0			0
$467$	6.02523	+	9.01739i	0.278814	+	0.417275i	0.944275	−	0.329158i	$-0.106765\pi$
$467$	6.02523	+	9.01739i	0.278814	+	0.417275i	−0.665461	+	0.746433i	$0.731765\pi$
$468$		0			0
$469$	−1.68602	−	8.47620i	−0.0778532	−	0.391394i
$470$		0			0
$471$	−3.75657	+	9.06916i	−0.173094	+	0.417885i
$472$		0			0
$473$	−0.0731626	−	0.176630i	−0.00336402	−	0.00812146i
$474$		0			0
$475$	16.0515	−	24.0228i	0.736493	−	1.10224i
$476$		0			0
$477$	−3.60626	−	0.717330i	−0.165119	−	0.0328443i
$478$		0			0
$479$			31.1948i			1.42533i	0.701506	+	0.712663i	$0.252511\pi$
$479$			31.1948i			1.42533i	−0.701506	+	0.712663i	$0.747489\pi$
$480$		0			0
$481$			10.7925i			0.492094i
$482$		0			0
$483$	4.32106	+	0.859511i	0.196615	+	0.0391091i
$484$		0			0
$485$	3.26601	−	4.88793i	0.148302	−	0.221950i
$486$		0			0
$487$	10.8455	+	26.1834i	0.491458	+	1.18648i	0.953978	+	0.299876i	$0.0969453\pi$
$487$	10.8455	+	26.1834i	0.491458	+	1.18648i	−0.462520	+	0.886609i	$0.653055\pi$
$488$		0			0
$489$	3.25804	−	7.86562i	0.147334	−	0.355695i
$490$		0			0
$491$	−3.12805	−	15.7257i	−0.141167	−	0.709693i	−0.984927	−	0.172972i	$-0.944663\pi$
$491$	−3.12805	−	15.7257i	−0.141167	−	0.709693i	0.843760	−	0.536721i	$-0.180337\pi$
$492$		0			0
$493$	−22.0678	−	33.0267i	−0.993882	−	1.48745i
$494$		0			0
$495$	0.114356	+	0.114356i	0.00513992	+	0.00513992i
$496$		0			0
$497$	−2.71019	+	2.71019i	−0.121569	+	0.121569i
$498$		0			0
$499$	15.3516	−	10.2576i	0.687232	−	0.459194i	−0.162293	−	0.986743i	$-0.551889\pi$
$499$	15.3516	−	10.2576i	0.687232	−	0.459194i	0.849525	+	0.527549i	$0.176889\pi$
$500$		0			0
$501$	5.69422	−	1.13265i	0.254399	−	0.0506031i
$502$		0			0
$503$	29.9129	+	12.3903i	1.33375	+	0.552457i	0.931723	−	0.363171i	$-0.118306\pi$
$503$	29.9129	+	12.3903i	1.33375	+	0.552457i	0.402027	+	0.915628i	$0.368306\pi$
$504$		0			0
$505$	9.25528	−	3.83366i	0.411855	−	0.170596i
$506$		0			0
$507$	−4.27302	−	2.85514i	−0.189771	−	0.126801i
$508$		0			0
$509$	−6.36934	+	32.0209i	−0.282316	+	1.41930i	0.535848	+	0.844315i	$0.319992\pi$
$509$	−6.36934	+	32.0209i	−0.282316	+	1.41930i	−0.818164	+	0.574985i	$0.805008\pi$
$510$		0			0
$511$	0.965400			0.0427068
$512$		0			0
$513$	−23.4538			−1.03551
$514$		0			0
$515$	−2.54825	+	12.8109i	−0.112289	+	0.564516i
$516$		0			0
$517$	−0.546916	−	0.365438i	−0.0240533	−	0.0160719i
$518$		0			0
$519$	4.40184	−	1.82330i	0.193219	−	0.0800340i
$520$		0			0
$521$	−18.6410	−	7.72136i	−0.816677	−	0.338279i	−0.0650626	−	0.997881i	$-0.520725\pi$
$521$	−18.6410	−	7.72136i	−0.816677	−	0.338279i	−0.751615	+	0.659602i	$0.770725\pi$
$522$		0			0
$523$	8.92581	−	1.77545i	0.390298	−	0.0776352i	0.00395965	−	0.999992i	$-0.498740\pi$
$523$	8.92581	−	1.77545i	0.390298	−	0.0776352i	0.386339	+	0.922357i	$0.373740\pi$
$524$		0			0
$525$	2.14200	−	1.43124i	0.0934847	−	0.0624645i
$526$		0			0
$527$	−13.2205	+	13.2205i	−0.575895	+	0.575895i
$528$		0			0
$529$	−23.2077	−	23.2077i	−1.00903	−	1.00903i
$530$		0			0
$531$	−17.6842	−	26.4663i	−0.767431	−	1.14854i
$532$		0			0
$533$	2.68623	+	13.5046i	0.116354	+	0.584949i
$534$		0			0
$535$	2.35691	−	5.69007i	0.101898	−	0.246003i
$536$		0			0
$537$	−1.22587	−	2.95951i	−0.0529001	−	0.127712i
$538$		0			0
$539$	−0.266893	+	0.399433i	−0.0114959	+	0.0172048i
$540$		0			0
$541$	11.9947	+	2.38590i	0.515694	+	0.102578i	0.446075	−	0.894996i	$-0.352822\pi$
$541$	11.9947	+	2.38590i	0.515694	+	0.102578i	0.0696193	+	0.997574i	$0.477822\pi$
$542$		0			0
$543$		−	3.56611i		−	0.153036i
$544$		0			0
$545$			13.0475i			0.558895i
$546$		0			0
$547$	−18.4104	−	3.66207i	−0.787174	−	0.156579i	−0.214894	−	0.976637i	$-0.568941\pi$
$547$	−18.4104	−	3.66207i	−0.787174	−	0.156579i	−0.572279	+	0.820059i	$0.693941\pi$
$548$		0			0
$549$	4.25965	−	6.37502i	0.181798	−	0.272079i
$550$		0			0
$551$	−22.5188	−	54.3652i	−0.959333	−	2.31603i
$552$		0			0
$553$	−3.56924	+	8.61691i	−0.151780	+	0.366428i
$554$		0			0
$555$	0.479344	+	2.40983i	0.0203470	+	0.102291i
$556$		0			0
$557$	−13.1089	−	19.6188i	−0.555442	−	0.831277i	0.442409	−	0.896814i	$-0.354124\pi$
$557$	−13.1089	−	19.6188i	−0.555442	−	0.831277i	−0.997850	+	0.0655364i	$0.979124\pi$
$558$		0			0
$559$	3.81548	+	3.81548i	0.161378	+	0.161378i
$560$		0			0
$561$	−0.156610	+	0.156610i	−0.00661206	+	0.00661206i
$562$		0			0
$563$	−7.15885	+	4.78339i	−0.301710	+	0.201596i	−0.697205	−	0.716872i	$-0.745573\pi$
$563$	−7.15885	+	4.78339i	−0.301710	+	0.201596i	0.395495	+	0.918468i	$0.370573\pi$
$564$		0			0
$565$	−7.89763	+	1.57094i	−0.332256	+	0.0660898i
$566$		0			0
$567$	4.77330	+	1.97716i	0.200460	+	0.0830331i
$568$		0			0
$569$	−1.38195	+	0.572423i	−0.0579344	+	0.0239972i	−0.411462	−	0.911427i	$-0.634982\pi$
$569$	−1.38195	+	0.572423i	−0.0579344	+	0.0239972i	0.353528	+	0.935424i	$0.384982\pi$
$570$		0			0
$571$	−4.83659	−	3.23171i	−0.202405	−	0.135243i	0.450237	−	0.892909i	$-0.351339\pi$
$571$	−4.83659	−	3.23171i	−0.202405	−	0.135243i	−0.652642	+	0.757666i	$0.726339\pi$
$572$		0			0
$573$	0.160517	−	0.806971i	0.00670567	−	0.0337117i
$574$		0			0
$575$	−32.6402			−1.36119
$576$		0			0
$577$	29.0642			1.20996			0.604980	−	0.796241i	$-0.293181\pi$
$577$	29.0642			1.20996			0.604980	+	0.796241i	$0.293181\pi$
$578$		0			0
$579$	0.0191768	−	0.0964081i	0.000796959	−	0.00400658i
$580$		0			0
$581$	4.87837	+	3.25962i	0.202389	+	0.135232i
$582$		0			0
$583$	−0.102384	+	0.0424087i	−0.00424030	+	0.00175639i
$584$		0			0
$585$	−4.21701	−	1.74674i	−0.174352	−	0.0722189i
$586$		0			0
$587$	−23.8821	+	4.75045i	−0.985720	+	0.196072i	−0.661529	−	0.749920i	$-0.730092\pi$
$587$	−23.8821	+	4.75045i	−0.985720	+	0.196072i	−0.324191	+	0.945992i	$0.605092\pi$
$588$		0			0
$589$	−23.0301	+	15.3882i	−0.948939	+	0.634061i
$590$		0			0
$591$	5.42811	−	5.42811i	0.223283	−	0.223283i
$592$		0			0
$593$	14.2745	+	14.2745i	0.586184	+	0.586184i	0.936596	−	0.350412i	$-0.113958\pi$
$593$	14.2745	+	14.2745i	0.586184	+	0.586184i	−0.350412	+	0.936596i	$0.613958\pi$
$594$		0			0
$595$	1.83443	+	2.74541i	0.0752042	+	0.112551i
$596$		0			0
$597$	−2.99544	−	15.0591i	−0.122595	−	0.616329i
$598$		0			0
$599$	−4.20762	+	10.1581i	−0.171919	+	0.415048i	−0.986230	−	0.165380i	$-0.947115\pi$
$599$	−4.20762	+	10.1581i	−0.171919	+	0.415048i	0.814311	+	0.580428i	$0.197115\pi$
$600$		0			0
$601$	−3.87269	−	9.34950i	−0.157970	−	0.381374i	0.825001	−	0.565131i	$-0.191174\pi$
$601$	−3.87269	−	9.34950i	−0.157970	−	0.381374i	−0.982972	+	0.183756i	$0.941174\pi$
$602$		0			0
$603$	13.4034	−	20.0595i	0.545827	−	0.816888i
$604$		0			0
$605$	−8.56705	−	1.70409i	−0.348300	−	0.0692812i
$606$		0			0
$607$		−	11.7468i		−	0.476790i	−0.971168	−	0.238395i	$-0.923379\pi$
$607$		−	11.7468i		−	0.476790i	0.971168	−	0.238395i	$-0.0766212\pi$
$608$		0			0
$609$		−	5.24690i		−	0.212615i
$610$		0			0
$611$	18.2081	+	3.62181i	0.736619	+	0.146523i
$612$		0			0
$613$	−4.23332	+	6.33562i	−0.170982	+	0.255893i	−0.907058	−	0.421007i	$-0.861677\pi$
$613$	−4.23332	+	6.33562i	−0.170982	+	0.255893i	0.736075	+	0.676900i	$0.236677\pi$
$614$		0			0
$615$	1.19961	+	2.89611i	0.0483728	+	0.116782i
$616$		0			0
$617$	5.69105	−	13.7394i	0.229113	−	0.553128i	−0.766957	−	0.641699i	$-0.778230\pi$
$617$	5.69105	−	13.7394i	0.229113	−	0.553128i	0.996070	+	0.0885706i	$0.0282299\pi$
$618$		0			0
$619$	−6.79342	−	34.1528i	−0.273051	−	1.37272i	−0.837133	−	0.546999i	$-0.815770\pi$
$619$	−6.79342	−	34.1528i	−0.273051	−	1.37272i	0.564083	−	0.825718i	$-0.309230\pi$
$620$		0			0
$621$	14.7207	+	22.0310i	0.590720	+	0.884076i
$622$		0			0
$623$	−5.13408	−	5.13408i	−0.205693	−	0.205693i
$624$		0			0
$625$	−11.2638	+	11.2638i	−0.450553	+	0.450553i
$626$		0			0
$627$	−0.272814	+	0.182288i	−0.0108951	+	0.00727989i
$628$		0			0
$629$	21.3754	−	4.25184i	0.852294	−	0.169532i
$630$		0			0
$631$	−22.6667	−	9.38886i	−0.902348	−	0.373765i	−0.117225	−	0.993105i	$-0.537400\pi$
$631$	−22.6667	−	9.38886i	−0.902348	−	0.373765i	−0.785122	+	0.619341i	$0.787400\pi$
$632$		0			0
$633$	5.27506	−	2.18500i	0.209665	−	0.0868460i
$634$		0			0
$635$	8.35558	+	5.58302i	0.331581	+	0.221555i
$636$		0			0
$637$	2.64514	−	13.2980i	0.104804	−	0.526887i
$638$		0			0
$639$	−10.6995			−0.423265
$640$		0			0
$641$	8.35272			0.329913			0.164956	−	0.986301i	$-0.447252\pi$
$641$	8.35272			0.329913			0.164956	+	0.986301i	$0.447252\pi$
$642$		0			0
$643$	−6.43579	+	32.3549i	−0.253803	+	1.27595i	0.618032	+	0.786153i	$0.287930\pi$
$643$	−6.43579	+	32.3549i	−0.253803	+	1.27595i	−0.871835	+	0.489800i	$0.837070\pi$
$644$		0			0
$645$	1.02142	+	0.682488i	0.0402182	+	0.0268729i
$646$		0			0
$647$	28.0926	−	11.6363i	1.10443	−	0.457471i	0.245416	−	0.969418i	$-0.421076\pi$
$647$	28.0926	−	11.6363i	1.10443	−	0.457471i	0.859017	+	0.511947i	$0.171076\pi$
$648$		0			0
$649$	−0.886330	−	0.367130i	−0.0347915	−	0.0144111i
$650$		0			0
$651$	−2.42226	+	0.481818i	−0.0949359	+	0.0188839i
$652$		0			0
$653$	0.322282	−	0.215342i	0.0126119	−	0.00842699i	−0.549248	−	0.835659i	$-0.685086\pi$
$653$	0.322282	−	0.215342i	0.0126119	−	0.00842699i	0.561860	+	0.827232i	$0.310086\pi$
$654$		0			0
$655$	0.874738	−	0.874738i	0.0341789	−	0.0341789i
$656$		0			0
$657$	1.90564	+	1.90564i	0.0743460	+	0.0743460i
$658$		0			0
$659$	9.34933	+	13.9923i	0.364198	+	0.545061i	0.967636	−	0.252349i	$-0.0812030\pi$
$659$	9.34933	+	13.9923i	0.364198	+	0.545061i	−0.603438	+	0.797410i	$0.706203\pi$
$660$		0			0
$661$	−4.92746	−	24.7720i	−0.191656	−	0.963520i	−0.950139	−	0.311827i	$-0.899059\pi$
$661$	−4.92746	−	24.7720i	−0.191656	−	0.963520i	0.758483	−	0.651693i	$-0.225941\pi$
$662$		0			0
$663$	2.39215	−	5.77516i	0.0929034	−	0.224289i
$664$		0			0
$665$	1.87192	+	4.51922i	0.0725900	+	0.175248i
$666$		0			0
$667$	−36.9335	+	55.2749i	−1.43007	+	2.14025i
$668$		0			0
$669$	8.92154	+	1.77461i	0.344927	+	0.0686102i
$670$		0			0
$671$		−	0.231083i		−	0.00892086i
$672$		0			0
$673$			0.530719i			0.0204577i	0.999948	+	0.0102289i	$0.00325600\pi$
$673$			0.530719i			0.0204577i	−0.999948	+	0.0102289i	$0.996744\pi$
$674$		0			0
$675$	15.1957	+	3.02261i	0.584883	+	0.116340i
$676$		0			0
$677$	−3.06951	+	4.59384i	−0.117971	+	0.176556i	−0.885755	−	0.464152i	$-0.846359\pi$
$677$	−3.06951	+	4.59384i	−0.117971	+	0.176556i	0.767785	+	0.640708i	$0.221359\pi$
$678$		0			0
$679$	−2.63591	−	6.36365i	−0.101157	−	0.244215i
$680$		0			0
$681$	0.374516	−	0.904160i	0.0143515	−	0.0346475i
$682$		0			0
$683$	2.76547	+	13.9029i	0.105818	+	0.531981i	0.996937	+	0.0782118i	$0.0249210\pi$
$683$	2.76547	+	13.9029i	0.105818	+	0.531981i	−0.891119	+	0.453769i	$0.850079\pi$
$684$		0			0
$685$	2.53460	+	3.79330i	0.0968421	+	0.144934i
$686$		0			0
$687$	−8.73263	−	8.73263i	−0.333171	−	0.333171i
$688$		0			0
$689$	2.21165	−	2.21165i	0.0842570	−	0.0842570i
$690$		0			0
$691$	11.1224	−	7.43176i	0.423117	−	0.282717i	−0.325727	−	0.945464i	$-0.605609\pi$
$691$	11.1224	−	7.43176i	0.423117	−	0.282717i	0.748844	+	0.662746i	$0.230609\pi$
$692$		0			0
$693$	0.185849	−	0.0369676i	0.00705982	−	0.00140428i
$694$		0			0
$695$	14.1973	+	5.88073i	0.538536	+	0.223069i
$696$		0			0
$697$	25.6888	−	10.6406i	0.973031	−	0.403043i
$698$		0			0
$699$	1.31551	+	0.878997i	0.0497572	+	0.0332467i
$700$		0			0
$701$	0.624967	−	3.14192i	0.0236047	−	0.118669i	−0.967187	−	0.254067i	$-0.918232\pi$
$701$	0.624967	−	3.14192i	0.0236047	−	0.118669i	0.990791	+	0.135399i	$0.0432315\pi$
$702$		0			0
$703$	32.2869			1.21773
$704$		0			0
$705$	4.22650			0.159179
$706$		0			0
$707$	2.28993	−	11.5123i	0.0861217	−	0.432963i
$708$		0			0
$709$	−2.84972	−	1.90412i	−0.107023	−	0.0715107i	0.500907	−	0.865501i	$-0.333000\pi$
$709$	−2.84972	−	1.90412i	−0.107023	−	0.0715107i	−0.607930	+	0.793991i	$0.708000\pi$
$710$		0			0
$711$	−24.0547	+	9.96377i	−0.902121	+	0.373671i
$712$		0			0
$713$	28.9095	+	11.9747i	1.08267	+	0.448457i
$714$		0			0
$715$	−0.134926	+	0.0268384i	−0.00504594	+	0.00100370i
$716$		0			0
$717$	4.42254	−	2.95505i	0.165163	−	0.110358i
$718$		0			0
$719$	−9.77983	+	9.77983i	−0.364726	+	0.364726i	−0.865549	−	0.500823i	$-0.833031\pi$
$719$	−9.77983	+	9.77983i	−0.364726	+	0.364726i	0.500823	+	0.865549i	$0.333031\pi$
$720$		0			0
$721$	10.8219	+	10.8219i	0.403028	+	0.403028i
$722$		0			0
$723$	3.71000	+	5.55240i	0.137976	+	0.206496i
$724$		0			0
$725$	7.58360	+	38.1253i	0.281648	+	1.41594i
$726$		0			0
$727$	10.3584	−	25.0074i	0.384172	−	0.927474i	−0.606977	−	0.794720i	$-0.707618\pi$
$727$	10.3584	−	25.0074i	0.384172	−	0.927474i	0.991149	−	0.132754i	$-0.0423821\pi$
$728$		0			0
$729$	2.94038	+	7.09871i	0.108903	+	0.262915i
$730$		0			0
$731$	6.05374	−	9.06006i	0.223906	−	0.335099i
$732$		0			0
$733$	−28.0369	−	5.57688i	−1.03557	−	0.205987i	−0.352094	−	0.935964i	$-0.614530\pi$
$733$	−28.0369	−	5.57688i	−1.03557	−	0.205987i	−0.683471	+	0.729978i	$0.739530\pi$
$734$		0			0
$735$		−	3.08677i		−	0.113857i
$736$		0			0
$737$		−	0.727122i		−	0.0267839i
$738$		0			0
$739$	−17.0617	−	3.39378i	−0.627624	−	0.124842i	−0.128977	−	0.991648i	$-0.541169\pi$
$739$	−17.0617	−	3.39378i	−0.627624	−	0.124842i	−0.498647	+	0.866805i	$0.666169\pi$
$740$		0			0
$741$	5.14487	−	7.69984i	0.189001	−	0.282861i
$742$		0			0
$743$	11.8271	+	28.5530i	0.433893	+	1.04751i	0.978021	+	0.208507i	$0.0668605\pi$
$743$	11.8271	+	28.5530i	0.433893	+	1.04751i	−0.544128	+	0.839002i	$0.683139\pi$
$744$		0			0
$745$	−2.54969	+	6.15549i	−0.0934134	+	0.225520i
$746$		0			0
$747$	3.19530	+	16.0638i	0.116910	+	0.587746i
$748$		0			0
$749$	−4.00916	−	6.00014i	−0.146492	−	0.219240i
$750$		0			0
$751$	4.92726	+	4.92726i	0.179798	+	0.179798i	0.791268	−	0.611470i	$-0.209421\pi$
$751$	4.92726	+	4.92726i	0.179798	+	0.179798i	−0.611470	+	0.791268i	$0.709421\pi$
$752$		0			0
$753$	−7.15611	+	7.15611i	−0.260783	+	0.260783i
$754$		0			0
$755$	−4.27738	+	2.85805i	−0.155670	+	0.104015i
$756$		0			0
$757$	−41.6002	+	8.27479i	−1.51198	+	0.300752i	−0.880279	−	0.474456i	$-0.842645\pi$
$757$	−41.6002	+	8.27479i	−1.51198	+	0.300752i	−0.631705	+	0.775209i	$0.717645\pi$
$758$		0			0
$759$	0.342461	+	0.141852i	0.0124306	+	0.00514890i
$760$		0			0
$761$	−29.3553	+	12.1594i	−1.06413	+	0.440777i	−0.844915	−	0.534900i	$-0.820349\pi$
$761$	−29.3553	+	12.1594i	−1.06413	+	0.440777i	−0.219214	+	0.975677i	$0.570349\pi$
$762$		0			0
$763$	12.7112	+	8.49337i	0.460177	+	0.307481i
$764$		0			0
$765$	−1.79823	+	9.04030i	−0.0650151	+	0.326853i
$766$		0			0
$767$	27.0767			0.977682
$768$		0			0
$769$	27.7099			0.999245			0.499623	−	0.866243i	$-0.333472\pi$
$769$	27.7099			0.999245			0.499623	+	0.866243i	$0.333472\pi$
$770$		0			0
$771$	−0.0621330	+	0.312364i	−0.00223767	+	0.0112495i
$772$		0			0
$773$	−4.99174	−	3.33537i	−0.179540	−	0.119965i	0.462553	−	0.886592i	$-0.346934\pi$
$773$	−4.99174	−	3.33537i	−0.179540	−	0.119965i	−0.642093	+	0.766627i	$0.721934\pi$
$774$		0			0
$775$	16.9044	−	7.00202i	0.607223	−	0.251520i
$776$		0			0
$777$	2.65974	+	1.10170i	0.0954177	+	0.0395233i
$778$		0			0
$779$	40.4006	−	8.03618i	1.44750	−	0.287926i
$780$		0			0
$781$	−0.268127	+	0.179157i	−0.00959435	+	0.00641074i
$782$		0			0
$783$	22.3131	−	22.3131i	0.797406	−	0.797406i
$784$		0			0
$785$	8.70652	+	8.70652i	0.310749	+	0.310749i
$786$		0			0
$787$	21.3968	+	32.0226i	0.762714	+	1.14148i	0.986003	+	0.166730i	$0.0533209\pi$
$787$	21.3968	+	32.0226i	0.762714	+	1.14148i	−0.223288	+	0.974752i	$0.571679\pi$
$788$		0			0
$789$	3.50470	+	17.6193i	0.124771	+	0.627265i
$790$		0			0
$791$	−3.61056	+	8.71667i	−0.128377	+	0.309929i
$792$		0			0
$793$	2.49587	+	6.02557i	0.0886311	+	0.213974i
$794$		0			0
$795$	0.395604	−	0.592064i	0.0140306	−	0.0209983i
$796$		0			0
$797$	19.9075	+	3.95984i	0.705159	+	0.140265i	0.534628	−	0.845088i	$-0.320452\pi$
$797$	19.9075	+	3.95984i	0.705159	+	0.140265i	0.170531	+	0.985352i	$0.445452\pi$
$798$		0			0
$799$		−	37.4895i		−	1.32628i
$800$		0			0
$801$		−	20.2687i		−	0.716158i
$802$		0			0
$803$	0.0796639	+	0.0158461i	0.00281128	+	0.000559198i
$804$		0			0
$805$	3.07017	−	4.59484i	0.108209	−	0.161947i
$806$		0			0
$807$	−1.68043	−	4.05693i	−0.0591541	−	0.142811i
$808$		0			0
$809$	3.73336	−	9.01314i	0.131258	−	0.316885i	−0.844563	−	0.535456i	$-0.820140\pi$
$809$	3.73336	−	9.01314i	0.131258	−	0.316885i	0.975821	+	0.218571i	$0.0701396\pi$
$810$		0			0
$811$	9.93194	+	49.9313i	0.348758	+	1.75332i	0.614156	+	0.789185i	$0.289496\pi$
$811$	9.93194	+	49.9313i	0.348758	+	1.75332i	−0.265398	+	0.964139i	$0.585504\pi$
$812$		0			0
$813$	0.856267	+	1.28149i	0.0300306	+	0.0449440i
$814$		0			0
$815$	−7.55110	−	7.55110i	−0.264504	−	0.264504i
$816$		0			0
$817$	11.4145	−	11.4145i	0.399342	−	0.399342i
$818$		0			0
$819$	−4.44680	+	2.97126i	−0.155384	+	0.103824i
$820$		0			0
$821$	−41.5441	+	8.26364i	−1.44990	+	0.288403i	−0.856350	−	0.516395i	$-0.827274\pi$
$821$	−41.5441	+	8.26364i	−1.44990	+	0.288403i	−0.593549	+	0.804798i	$0.702274\pi$
$822$		0			0
$823$	15.1760	+	6.28610i	0.529001	+	0.219120i	0.631166	−	0.775648i	$-0.282577\pi$
$823$	15.1760	+	6.28610i	0.529001	+	0.219120i	−0.102164	+	0.994768i	$0.532577\pi$
$824$		0			0
$825$	0.200248	−	0.0829456i	0.00697176	−	0.00288780i
$826$		0			0
$827$	−9.22561	−	6.16435i	−0.320806	−	0.214356i	0.384731	−	0.923029i	$-0.374294\pi$
$827$	−9.22561	−	6.16435i	−0.320806	−	0.214356i	−0.705537	+	0.708673i	$0.749294\pi$
$828$		0			0
$829$	−2.51090	+	12.6231i	−0.0872070	+	0.438419i	0.912371	+	0.409365i	$0.134250\pi$
$829$	−2.51090	+	12.6231i	−0.0872070	+	0.438419i	−0.999578	+	0.0290546i	$0.990750\pi$
$830$		0			0
$831$	12.1186			0.420388
$832$		0			0
$833$	−27.3800			−0.948661
$834$		0			0
$835$	1.42071	−	7.14237i	0.0491655	−	0.247172i
$836$		0			0
$837$	−12.3500	−	8.25199i	−0.426878	−	0.285230i
$838$		0			0
$839$	−40.8308	+	16.9127i	−1.40963	+	0.583890i	−0.952233	−	0.305371i	$-0.901220\pi$
$839$	−40.8308	+	16.9127i	−1.40963	+	0.583890i	−0.457401	+	0.889261i	$0.651220\pi$
$840$		0			0
$841$	46.3524	+	19.1998i	1.59836	+	0.662061i
$842$		0			0
$843$	−4.54471	+	0.903999i	−0.156528	+	0.0311354i
$844$		0			0
$845$	−5.35973	+	3.58126i	−0.184380	+	0.123199i
$846$		0			0
$847$	−7.23694	+	7.23694i	−0.248664	+	0.248664i
$848$		0			0
$849$	−4.34613	−	4.34613i	−0.149159	−	0.149159i
$850$		0			0
$851$	−20.2648	−	30.3284i	−0.694668	−	1.03964i
$852$		0			0
$853$	−5.80574	−	29.1874i	−0.198785	−	0.999359i	−0.943347	−	0.331806i	$-0.892342\pi$
$853$	−5.80574	−	29.1874i	−0.198785	−	0.999359i	0.744563	−	0.667553i	$-0.232658\pi$
$854$		0			0
$855$	−5.22559	+	12.6157i	−0.178711	+	0.431447i
$856$		0			0
$857$	3.96712	+	9.57747i	0.135514	+	0.327160i	0.977040	−	0.213057i	$-0.0683421\pi$
$857$	3.96712	+	9.57747i	0.135514	+	0.327160i	−0.841526	+	0.540217i	$0.818342\pi$
$858$		0			0
$859$	−10.3728	+	15.5239i	−0.353914	+	0.529670i	−0.965122	−	0.261800i	$-0.915684\pi$
$859$	−10.3728	+	15.5239i	−0.353914	+	0.529670i	0.611208	+	0.791470i	$0.290684\pi$
$860$		0			0
$861$	3.60234	+	0.716551i	0.122768	+	0.0244200i
$862$		0			0
$863$			6.37504i			0.217009i	0.994096	+	0.108504i	$0.0346062\pi$
$863$			6.37504i			0.217009i	−0.994096	+	0.108504i	$0.965394\pi$
$864$		0			0
$865$		−	5.97622i		−	0.203198i
$866$		0			0
$867$	−1.81922	−	0.361866i	−0.0617841	−	0.0122896i
$868$		0			0
$869$	−0.435969	+	0.652473i	−0.0147892	+	0.0221336i
$870$		0			0
$871$	7.85348	+	18.9600i	0.266105	+	0.642434i
$872$		0			0
$873$	7.35831	−	17.7645i	0.249041	−	0.601239i
$874$		0			0
$875$	−1.35190	−	6.79644i	−0.0457024	−	0.229761i
$876$		0			0
$877$	7.14103	+	10.6873i	0.241136	+	0.360885i	0.932222	−	0.361887i	$-0.117868\pi$
$877$	7.14103	+	10.6873i	0.241136	+	0.360885i	−0.691086	+	0.722772i	$0.742868\pi$
$878$		0			0
$879$	−4.03771	−	4.03771i	−0.136188	−	0.136188i
$880$		0			0
$881$	9.31796	−	9.31796i	0.313930	−	0.313930i	−0.532500	−	0.846430i	$-0.678747\pi$
$881$	9.31796	−	9.31796i	0.313930	−	0.313930i	0.846430	+	0.532500i	$0.178747\pi$
$882$		0			0
$883$	−21.6540	+	14.4687i	−0.728714	+	0.486911i	−0.863744	−	0.503931i	$-0.831887\pi$
$883$	−21.6540	+	14.4687i	−0.728714	+	0.486911i	0.135031	+	0.990841i	$0.456887\pi$
$884$		0			0
$885$	6.04589	−	1.20260i	0.203231	−	0.0404251i
$886$		0			0
$887$	−29.2410	−	12.1120i	−0.981816	−	0.406681i	−0.166718	−	0.986005i	$-0.553317\pi$
$887$	−29.2410	−	12.1120i	−0.981816	−	0.406681i	−0.815098	+	0.579323i	$0.803317\pi$
$888$		0			0
$889$	10.8782	−	4.50590i	0.364844	−	0.151123i
$890$		0			0
$891$	0.361434	+	0.241503i	0.0121085	+	0.00809065i
$892$		0			0
$893$	10.8351	−	54.4716i	0.362582	−	1.82282i
$894$		0			0
$895$	−4.01802			−0.134308
$896$		0			0
$897$	−10.4619			−0.349313
$898$		0			0
$899$	7.27023	−	36.5499i	0.242476	−	1.21901i
$900$		0			0
$901$	−5.25167	−	3.50905i	−0.174958	−	0.116903i
$902$		0			0
$903$	1.32979	−	0.550818i	0.0442527	−	0.0183301i
$904$		0			0
$905$	−4.13255	−	1.71176i	−0.137371	−	0.0569007i
$906$		0			0
$907$	40.1944	−	7.99517i	1.33463	−	0.265475i	0.524346	−	0.851506i	$-0.324310\pi$
$907$	40.1944	−	7.99517i	1.33463	−	0.265475i	0.810289	+	0.586030i	$0.199310\pi$
$908$		0			0
$909$	27.2446	−	18.2043i	0.903647	−	0.603797i
$910$		0			0
$911$	28.6254	−	28.6254i	0.948402	−	0.948402i	−0.0503311	−	0.998733i	$-0.516028\pi$
$911$	28.6254	−	28.6254i	0.948402	−	0.948402i	0.998733	+	0.0503311i	$0.0160276\pi$
$912$		0			0
$913$	0.349054	+	0.349054i	0.0115520	+	0.0115520i
$914$		0			0
$915$	0.824923	+	1.23458i	0.0272711	+	0.0408141i
$916$		0			0
$917$	−0.282775	−	1.42161i	−0.00933806	−	0.0469456i
$918$		0			0
$919$	10.0585	−	24.2833i	0.331798	−	0.801031i	−0.666652	−	0.745369i	$-0.732273\pi$
$919$	10.0585	−	24.2833i	0.331798	−	0.801031i	0.998450	−	0.0556618i	$-0.0177269\pi$
$920$		0			0
$921$	3.66364	+	8.84481i	0.120721	+	0.291446i
$922$		0			0
$923$	5.05649	−	7.56757i	0.166436	−	0.249090i
$924$		0			0
$925$	−20.9187	−	4.16099i	−0.687803	−	0.136813i
$926$		0			0
$927$			42.7234i			1.40322i
$928$		0			0
$929$		−	36.2888i		−	1.19060i	−0.803505	−	0.595298i	$-0.797034\pi$
$929$		−	36.2888i		−	1.19060i	0.803505	−	0.595298i	$-0.202966\pi$
$930$		0			0
$931$	−39.7826	−	7.91326i	−1.30382	−	0.259347i
$932$		0			0
$933$	−1.62379	+	2.43017i	−0.0531605	+	0.0795603i
$934$		0			0
$935$	0.106312	+	0.256659i	0.00347677	+	0.00839365i
$936$		0			0
$937$	−22.0385	+	53.2056i	−0.719966	+	1.73815i	−0.0465174	+	0.998917i	$0.514812\pi$
$937$	−22.0385	+	53.2056i	−0.719966	+	1.73815i	−0.673449	+	0.739234i	$0.735188\pi$
$938$		0			0
$939$	2.56047	+	12.8723i	0.0835577	+	0.420073i
$940$		0			0
$941$	32.5815	+	48.7616i	1.06213	+	1.58958i	0.775293	+	0.631602i	$0.217602\pi$
$941$	32.5815	+	48.7616i	1.06213	+	1.58958i	0.286832	+	0.957981i	$0.407398\pi$
$942$		0			0
$943$	−32.9060	−	32.9060i	−1.07157	−	1.07157i
$944$		0			0
$945$	−1.85482	+	1.85482i	−0.0603375	+	0.0603375i
$946$		0			0
$947$	−23.3926	+	15.6304i	−0.760156	+	0.507920i	−0.874206	−	0.485555i	$-0.838618\pi$
$947$	−23.3926	+	15.6304i	−0.760156	+	0.507920i	0.114050	+	0.993475i	$0.463618\pi$
$948$		0			0
$949$	−2.24842	+	0.447238i	−0.0729867	+	0.0145180i
$950$		0			0
$951$	−3.48405	−	1.44314i	−0.112978	−	0.0467970i
$952$		0			0
$953$	−23.8429	+	9.87605i	−0.772347	+	0.319917i	−0.733823	−	0.679341i	$-0.762266\pi$
$953$	−23.8429	+	9.87605i	−0.772347	+	0.319917i	−0.0385243	+	0.999258i	$0.512266\pi$
$954$		0			0
$955$	−0.858101	−	0.573365i	−0.0277675	−	0.0185536i
$956$		0			0
$957$	0.0861229	−	0.432969i	0.00278396	−	0.0139959i
$958$		0			0
$959$	5.34543			0.172613
$960$		0			0
$961$	13.4589			0.434158
$962$		0			0
$963$	3.93005	−	19.7577i	0.126644	−	0.636683i
$964$		0			0
$965$	−0.102517	−	0.0684994i	−0.00330012	−	0.00220507i
$966$		0			0
$967$	−45.3076	+	18.7670i	−1.45699	+	0.603507i	−0.963851	−	0.266441i	$-0.914152\pi$
$967$	−45.3076	+	18.7670i	−1.45699	+	0.603507i	−0.493143	+	0.869948i	$0.664152\pi$
$968$		0			0
$969$	−17.2771	−	7.15640i	−0.555020	−	0.229897i
$970$		0			0
$971$	−14.9013	+	2.96405i	−0.478205	+	0.0951208i	−0.428307	−	0.903634i	$-0.640890\pi$
$971$	−14.9013	+	2.96405i	−0.478205	+	0.0951208i	−0.0498981	+	0.998754i	$0.515890\pi$
$972$		0			0
$973$	14.9710	−	10.0033i	0.479948	−	0.320691i
$974$		0			0
$975$	−4.32568	+	4.32568i	−0.138533	+	0.138533i
$976$		0			0
$977$	−21.1839	−	21.1839i	−0.677734	−	0.677734i	0.281753	−	0.959487i	$-0.409084\pi$
$977$	−21.1839	−	21.1839i	−0.677734	−	0.677734i	−0.959487	+	0.281753i	$0.909084\pi$
$978$		0			0
$979$	−0.339388	−	0.507930i	−0.0108469	−	0.0162335i
$980$		0			0
$981$	8.32577	+	41.8565i	0.265821	+	1.33637i
$982$		0			0
$983$	10.4133	−	25.1400i	0.332134	−	0.801842i	−0.666289	−	0.745694i	$-0.732118\pi$
$983$	10.4133	−	25.1400i	0.332134	−	0.801842i	0.998422	−	0.0561482i	$-0.0178819\pi$
$984$		0			0
$985$	−3.68478	−	8.89585i	−0.117407	−	0.283445i
$986$		0			0
$987$	2.75126	−	4.11756i	0.0875737	−	0.131063i
$988$		0			0
$989$	−17.8863	−	3.55781i	−0.568752	−	0.113132i
$990$		0			0
$991$		−	11.9640i		−	0.380050i	−0.981779	−	0.190025i	$-0.939143\pi$
$991$		−	11.9640i		−	0.380050i	0.981779	−	0.190025i	$-0.0608569\pi$
$992$		0			0
$993$		−	16.5090i		−	0.523899i
$994$		0			0
$995$	−18.8889	−	3.75724i	−0.598820	−	0.119113i
$996$		0			0
$997$	−2.81043	+	4.20611i	−0.0890073	+	0.133209i	−0.873301	−	0.487180i	$-0.838025\pi$
$997$	−2.81043	+	4.20611i	−0.0890073	+	0.133209i	0.784294	+	0.620389i	$0.213025\pi$
$998$		0			0
$999$	6.62578	+	15.9960i	0.209630	+	0.506092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.81.4		56
4.3	odd	2		64.2.i.a.61.5	yes	56
8.3	odd	2		512.2.i.b.417.4		56
8.5	even	2		512.2.i.a.417.4		56
12.11	even	2		576.2.bd.a.253.3		56
64.11	odd	16		512.2.i.b.97.4		56
64.21	even	16	inner	256.2.i.a.177.4		56
64.43	odd	16		64.2.i.a.21.5	✓	56
64.53	even	16		512.2.i.a.97.4		56
192.107	even	16		576.2.bd.a.469.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.5	✓	56	64.43	odd	16
64.2.i.a.61.5	yes	56	4.3	odd	2
256.2.i.a.81.4		56	1.1	even	1	trivial
256.2.i.a.177.4		56	64.21	even	16	inner
512.2.i.a.97.4		56	64.53	even	16
512.2.i.a.417.4		56	8.5	even	2
512.2.i.b.97.4		56	64.11	odd	16
512.2.i.b.417.4		56	8.3	odd	2
576.2.bd.a.253.3		56	12.11	even	2
576.2.bd.a.469.3		56	192.107	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.123576 + 0.621259i) q^{3} +(0.660623 + 0.441414i) q^{5} +(0.860072 - 0.356253i) q^{7} +(2.40095 + 0.994505i) q^{9} +(0.0768198 - 0.0152804i) q^{11} +(-1.83807 + 1.22816i) q^{13} +(-0.355870 + 0.355870i) q^{15} +(3.15660 + 3.15660i) q^{17} +(3.67418 + 5.49880i) q^{19} +(0.115041 + 0.578352i) q^{21} +(2.85915 - 6.90260i) q^{23} +(-1.67184 - 4.03618i) q^{25} +(-1.97029 + 2.94875i) q^{27} +(-8.72686 - 1.73588i) q^{29} +4.18821i q^{31} +0.0496134i q^{33} +(0.725438 + 0.144299i) q^{35} +(2.71234 - 4.05931i) q^{37} +(-0.535863 - 1.29369i) q^{39} +(2.38360 - 5.75451i) q^{41} +(-0.476196 - 2.39400i) q^{43} +(1.14713 + 1.71680i) q^{45} +(-5.93827 - 5.93827i) q^{47} +(-4.33694 + 4.33694i) q^{49} +(-2.35115 + 1.57099i) q^{51} +(-1.38768 + 0.276027i) q^{53} +(0.0574939 + 0.0238148i) q^{55} +(-3.87022 + 1.60310i) q^{57} +(-10.1842 - 6.80486i) q^{59} +(0.575578 - 2.89363i) q^{61} +2.41928 q^{63} -1.75639 q^{65} +(1.81110 - 9.10504i) q^{67} +(3.93498 + 2.62927i) q^{69} +(-3.80374 + 1.57556i) q^{71} +(0.958083 + 0.396851i) q^{73} +(2.71412 - 0.539871i) q^{75} +(0.0606269 - 0.0405096i) q^{77} +(-7.08438 + 7.08438i) q^{79} +(3.92436 + 3.92436i) q^{81} +(3.50145 + 5.24029i) q^{83} +(0.691955 + 3.47869i) q^{85} +(2.15687 - 5.20713i) q^{87} +(-2.98468 - 7.20566i) q^{89} +(-1.14333 + 1.71112i) q^{91} +(-2.60196 - 0.517563i) q^{93} +5.25446i q^{95} -7.39898i q^{97} +(0.199637 + 0.0397102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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