LMFDB - Embedded newform 512.2.i.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$4.08834058349$
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			97.4
Character	$\chi$	$=$	512.97
Dual form			512.2.i.b.417.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123576 - 0.621259i) q^{3} +(-0.660623 + 0.441414i) q^{5} +(-0.860072 - 0.356253i) q^{7} +(2.40095 - 0.994505i) q^{9} +O(q^{10})$	\(q+(-0.123576 - 0.621259i) q^{3} +(-0.660623 + 0.441414i) q^{5} +(-0.860072 - 0.356253i) q^{7} +(2.40095 - 0.994505i) q^{9} +(0.0768198 + 0.0152804i) q^{11} +(1.83807 + 1.22816i) q^{13} +(0.355870 + 0.355870i) q^{15} +(3.15660 - 3.15660i) q^{17} +(3.67418 - 5.49880i) q^{19} +(-0.115041 + 0.578352i) q^{21} +(-2.85915 - 6.90260i) q^{23} +(-1.67184 + 4.03618i) q^{25} +(-1.97029 - 2.94875i) q^{27} +(8.72686 - 1.73588i) q^{29} +4.18821i q^{31} -0.0496134i q^{33} +(0.725438 - 0.144299i) q^{35} +(-2.71234 - 4.05931i) q^{37} +(0.535863 - 1.29369i) q^{39} +(2.38360 + 5.75451i) q^{41} +(-0.476196 + 2.39400i) q^{43} +(-1.14713 + 1.71680i) q^{45} +(5.93827 - 5.93827i) q^{47} +(-4.33694 - 4.33694i) q^{49} +(-2.35115 - 1.57099i) q^{51} +(1.38768 + 0.276027i) q^{53} +(-0.0574939 + 0.0238148i) q^{55} +(-3.87022 - 1.60310i) q^{57} +(-10.1842 + 6.80486i) q^{59} +(-0.575578 - 2.89363i) q^{61} -2.41928 q^{63} -1.75639 q^{65} +(1.81110 + 9.10504i) q^{67} +(-3.93498 + 2.62927i) q^{69} +(3.80374 + 1.57556i) q^{71} +(0.958083 - 0.396851i) q^{73} +(2.71412 + 0.539871i) q^{75} +(-0.0606269 - 0.0405096i) q^{77} +(7.08438 + 7.08438i) q^{79} +(3.92436 - 3.92436i) q^{81} +(3.50145 - 5.24029i) q^{83} +(-0.691955 + 3.47869i) q^{85} +(-2.15687 - 5.20713i) q^{87} +(-2.98468 + 7.20566i) q^{89} +(-1.14333 - 1.71112i) q^{91} +(2.60196 - 0.517563i) q^{93} +5.25446i q^{95} +7.39898i q^{97} +(0.199637 - 0.0397102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

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	0.928576	−	0.371143i	$-0.121034\pi$
$3$	−0.123576	−	0.621259i	−0.0713467	−	0.358684i	−0.999922	+	0.0124589i	$0.996034\pi$
$4$		0			0
$5$	−0.660623	+	0.441414i	−0.295439	+	0.197406i	−0.694452	−	0.719539i	$-0.744353\pi$
$5$	−0.660623	+	0.441414i	−0.295439	+	0.197406i	0.399012	+	0.916946i	$0.369353\pi$
$6$		0			0
$7$	−0.860072	−	0.356253i	−0.325077	−	0.134651i	0.214176	−	0.976795i	$-0.431293\pi$
$7$	−0.860072	−	0.356253i	−0.325077	−	0.134651i	−0.539253	+	0.842144i	$0.681293\pi$
$8$		0			0
$9$	2.40095	−	0.994505i	0.800315	−	0.331502i
$10$		0			0
$11$	0.0768198	+	0.0152804i	0.0231621	+	0.00460722i	0.206658	−	0.978413i	$-0.433741\pi$
$11$	0.0768198	+	0.0152804i	0.0231621	+	0.00460722i	−0.183496	+	0.983021i	$0.558741\pi$
$12$		0			0
$13$	1.83807	+	1.22816i	0.509788	+	0.340629i	0.783714	−	0.621121i	$-0.213323\pi$
$13$	1.83807	+	1.22816i	0.509788	+	0.340629i	−0.273927	+	0.961751i	$0.588323\pi$
$14$		0			0
$15$	0.355870	+	0.355870i	0.0918852	+	0.0918852i
$16$		0			0
$17$	3.15660	−	3.15660i	0.765589	−	0.765589i	−0.211738	−	0.977326i	$-0.567912\pi$
$17$	3.15660	−	3.15660i	0.765589	−	0.765589i	0.977326	+	0.211738i	$0.0679123\pi$
$18$		0			0
$19$	3.67418	−	5.49880i	0.842914	−	1.26151i	−0.120290	−	0.992739i	$-0.538382\pi$
$19$	3.67418	−	5.49880i	0.842914	−	1.26151i	0.963204	−	0.268771i	$-0.0866176\pi$
$20$		0			0
$21$	−0.115041	+	0.578352i	−0.0251041	+	0.126207i
$22$		0			0
$23$	−2.85915	−	6.90260i	−0.596174	−	1.43929i	−0.877452	−	0.479665i	$-0.840758\pi$
$23$	−2.85915	−	6.90260i	−0.596174	−	1.43929i	0.281277	−	0.959627i	$-0.409242\pi$
$24$		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	$-0.253030\pi$
$29$	8.72686	−	1.73588i	1.62054	−	0.322345i	0.920195	+	0.391461i	$0.128030\pi$
$30$		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	$-0.318943\pi$
$37$	−2.71234	−	4.05931i	−0.445907	−	0.667346i	−0.984533	+	0.175198i	$0.943943\pi$
$38$		0			0
$39$	0.535863	−	1.29369i	0.0858067	−	0.207156i
$40$		0			0
$41$	2.38360	+	5.75451i	0.372255	+	0.898703i	0.993368	+	0.114982i	$0.0366810\pi$
$41$	2.38360	+	5.75451i	0.372255	+	0.898703i	−0.621113	+	0.783721i	$0.713319\pi$
$42$		0			0
$43$	−0.476196	+	2.39400i	−0.0726192	+	0.365081i	−0.999958	−	0.00914095i	$-0.997090\pi$
$43$	−0.476196	+	2.39400i	−0.0726192	+	0.365081i	0.927339	+	0.374222i	$0.122090\pi$
$44$		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	$-0.540170\pi$
$47$	5.93827	−	5.93827i	0.866186	−	0.866186i	0.992048	+	0.125862i	$0.0401697\pi$
$48$		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	$-0.406520\pi$
$53$	1.38768	+	0.276027i	0.190613	+	0.0379152i	−0.0988607	+	0.995101i	$0.531520\pi$
$54$		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	−0.998264	−	0.0588967i	$-0.981242\pi$
$59$	−10.1842	+	6.80486i	−1.32587	+	0.885918i	−0.327606	+	0.944815i	$0.606242\pi$
$60$		0			0
$61$	−0.575578	−	2.89363i	−0.0736952	−	0.370491i	0.926285	−	0.376824i	$-0.122984\pi$
$61$	−0.575578	−	2.89363i	−0.0736952	−	0.370491i	−0.999980	+	0.00633357i	$0.997984\pi$
$62$		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	0.918471	+	0.395489i	$0.129425\pi$
$67$	1.81110	+	9.10504i	0.221262	+	1.11236i	−0.697209	+	0.716868i	$0.745575\pi$
$68$		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	$-0.296440\pi$
$71$	3.80374	+	1.57556i	0.451421	+	0.186985i	−0.145377	+	0.989376i	$0.546440\pi$
$72$		0			0
$73$	0.958083	−	0.396851i	0.112135	−	0.0464479i	−0.325910	−	0.945401i	$-0.605671\pi$
$73$	0.958083	−	0.396851i	0.112135	−	0.0464479i	0.438046	+	0.898953i	$0.355671\pi$
$74$		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	$-0.0594147\pi$
$79$	7.08438	+	7.08438i	0.797055	+	0.797055i	−0.185575	+	0.982630i	$0.559415\pi$
$80$		0			0
$81$	3.92436	−	3.92436i	0.436040	−	0.436040i
$82$		0			0
$83$	3.50145	−	5.24029i	0.384334	−	0.575196i	−0.587980	−	0.808875i	$-0.700077\pi$
$83$	3.50145	−	5.24029i	0.384334	−	0.575196i	0.972314	+	0.233679i	$0.0750766\pi$
$84$		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	0.683065	+	0.730357i	$0.260646\pi$
$89$	−2.98468	+	7.20566i	−0.316375	+	0.763798i	−0.999441	+	0.0334406i	$0.989354\pi$
$90$		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	$0.122572\pi$
$97$			7.39898i			0.751252i	−0.926771	+	0.375626i	$0.877428\pi$
$98$		0			0
$99$	0.199637	−	0.0397102i	0.0200643	−	0.00399103i
$100$		0			0
$101$	−7.00497	−	10.4837i	−0.697020	−	1.04316i	−0.996039	−	0.0889173i	$-0.971659\pi$
$101$	−7.00497	−	10.4837i	−0.697020	−	1.04316i	0.299019	−	0.954247i	$-0.403341\pi$
$102$		0			0
$103$	−6.29127	+	15.1885i	−0.619897	+	1.49656i	0.231925	+	0.972734i	$0.425498\pi$
$103$	−6.29127	+	15.1885i	−0.619897	+	1.49656i	−0.851822	+	0.523831i	$0.824502\pi$
$104$		0			0
$105$	−0.179294	−	0.432854i	−0.0174973	−	0.0422422i
$106$		0			0
$107$	−1.51228	+	7.60273i	−0.146197	+	0.734983i	0.836236	+	0.548370i	$0.184751\pi$
$107$	−1.51228	+	7.60273i	−0.146197	+	0.734983i	−0.982433	+	0.186614i	$0.940249\pi$
$108$		0			0
$109$	−9.12348	+	13.6543i	−0.873871	+	1.30784i	0.0766107	+	0.997061i	$0.475590\pi$
$109$	−9.12348	+	13.6543i	−0.873871	+	1.30784i	−0.950482	+	0.310780i	$0.899410\pi$
$110$		0			0
$111$	−2.18670	+	2.18670i	−0.207553	+	0.207553i
$112$		0			0
$113$	−7.16639	−	7.16639i	−0.674158	−	0.674158i	0.284514	−	0.958672i	$-0.408168\pi$
$113$	−7.16639	−	7.16639i	−0.674158	−	0.674158i	−0.958672	+	0.284514i	$0.908168\pi$
$114$		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	$-0.689647\pi$
$127$	−12.6480			−1.12233			−0.561166	+	0.827704i	$0.689647\pi$
$128$		0			0
$129$	1.54614			0.136130
$130$		0			0
$131$	0.303754	+	1.52707i	0.0265391	+	0.133421i	0.991783	−	0.127928i	$-0.0408326\pi$
$131$	0.303754	+	1.52707i	0.0265391	+	0.133421i	−0.965244	+	0.261349i	$0.915833\pi$
$132$		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	−0.144378	−	0.989523i	$-0.546118\pi$
$137$	5.30492	−	2.19737i	0.453230	−	0.187734i	0.597608	+	0.801789i	$0.296118\pi$
$138$		0			0
$139$	18.9696	+	3.77329i	1.60898	+	0.320046i	0.916083	−	0.400988i	$-0.131333\pi$
$139$	18.9696	+	3.77329i	1.60898	+	0.320046i	0.692899	+	0.721035i	$0.256333\pi$
$140$		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	0.854098	+	0.520113i	$0.174110\pi$
$149$	−1.63597	+	8.22459i	−0.134024	+	0.673785i	−0.988122	+	0.153672i	$0.950890\pi$
$150$		0			0
$151$	2.47779	+	5.98190i	0.201639	+	0.486800i	0.992060	−	0.125764i	$-0.0401381\pi$
$151$	2.47779	+	5.98190i	0.201639	+	0.486800i	−0.790421	+	0.612564i	$0.790138\pi$
$152$		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	$-0.774721\pi$
$157$	−15.1994	+	3.02335i	−1.21304	+	0.241289i	−0.453208	+	0.891405i	$0.649721\pi$
$158$		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	−0.682136	−	0.731225i	$-0.738949\pi$
$163$	−13.1823	+	2.62213i	−1.03252	+	0.205381i	−0.350384	+	0.936606i	$0.613949\pi$
$164$		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	$-0.759608\pi$
$167$	3.50753	−	8.46791i	0.271420	−	0.655267i	0.999545	+	0.0301784i	$0.00960755\pi$
$168$		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	$-0.720196\pi$
$173$	4.17887	−	6.25411i	0.317713	−	0.475491i	0.955612	+	0.294629i	$0.0951961\pi$
$174$		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	0.388415	−	0.921485i	$-0.373023\pi$
$179$	−4.20486	−	2.80960i	−0.314286	−	0.209999i	−0.702701	+	0.711485i	$0.748023\pi$
$180$		0			0
$181$	5.52166	+	1.09833i	0.410422	+	0.0816379i	0.395983	−	0.918258i	$-0.370404\pi$
$181$	5.52166	+	1.09833i	0.410422	+	0.0816379i	0.0144385	+	0.999896i	$0.495404\pi$
$182$		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	$-0.485036\pi$
$191$	1.29893			0.0939871			0.0469936	+	0.998895i	$0.485036\pi$
$192$		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	$-0.545407\pi$
$197$	10.0765	−	6.73293i	0.717923	−	0.479701i	0.860090	+	0.510142i	$0.170407\pi$
$198$		0			0
$199$	22.3945	+	9.27612i	1.58751	+	0.657566i	0.989580	−	0.143985i	$-0.0459917\pi$
$199$	22.3945	+	9.27612i	1.58751	+	0.657566i	0.597926	+	0.801551i	$0.295992\pi$
$200$		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	−0.962812	−	0.270171i	$-0.912920\pi$
$211$	−5.00786	+	7.49478i	−0.344755	+	0.515962i	0.618057	+	0.786133i	$0.287920\pi$
$212$		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	−0.245121	−	0.969492i	$-0.578828\pi$
$227$	−1.51532	+	0.301416i	−0.100575	+	0.0200057i	0.144546	+	0.989498i	$0.453828\pi$
$228$		0			0
$229$	10.8318	+	16.2109i	0.715784	+	1.07125i	0.993855	+	0.110686i	$0.0353049\pi$
$229$	10.8318	+	16.2109i	0.715784	+	1.07125i	−0.278071	+	0.960560i	$0.589695\pi$
$230$		0			0
$231$	−0.0176749	+	0.0426711i	−0.00116292	+	0.00280755i
$232$		0			0
$233$	0.955848	+	2.30762i	0.0626197	+	0.151177i	0.952092	−	0.305812i	$-0.0989278\pi$
$233$	0.955848	+	2.30762i	0.0626197	+	0.151177i	−0.889472	+	0.456989i	$0.848928\pi$
$234$		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	$-0.662454\pi$
$239$	5.93760	−	5.93760i	0.384072	−	0.384072i	0.872567	+	0.488495i	$0.162454\pi$
$240$		0			0
$241$	7.45454	+	7.45454i	0.480189	+	0.480189i	0.905192	−	0.425003i	$-0.139727\pi$
$241$	7.45454	+	7.45454i	0.480189	+	0.480189i	−0.425003	+	0.905192i	$0.639727\pi$
$242$		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	−0.0605253	−	0.998167i	$-0.519278\pi$
$251$	13.2843	−	8.87629i	0.838498	−	0.560267i	0.899024	+	0.437900i	$0.144278\pi$
$252$		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	$-0.713743\pi$
$263$	−26.2018	−	10.8532i	−1.61567	−	0.669234i	−0.993520	+	0.113660i	$0.963743\pi$
$264$		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	$-0.244718\pi$
$269$	5.76407	+	3.85143i	0.351442	+	0.234826i	−0.367301	+	0.930102i	$0.619718\pi$
$270$		0			0
$271$	−1.72051	−	1.72051i	−0.104513	−	0.104513i	0.652917	−	0.757430i	$-0.273545\pi$
$271$	−1.72051	−	1.72051i	−0.104513	−	0.104513i	−0.757430	+	0.652917i	$0.773545\pi$
$272$		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	−0.690473	−	0.723358i	$-0.742598\pi$
$277$	3.73240	−	18.7640i	0.224258	−	1.12742i	0.914731	−	0.404063i	$-0.132402\pi$
$278$		0			0
$279$	4.16519	+	10.0557i	0.249364	+	0.602017i
$280$		0			0
$281$	2.79945	−	6.75847i	0.167001	−	0.403177i	−0.818118	−	0.575051i	$-0.804982\pi$
$281$	2.79945	−	6.75847i	0.167001	−	0.403177i	0.985119	+	0.171874i	$0.0549823\pi$
$282$		0			0
$283$	−5.39086	−	8.06799i	−0.320453	−	0.479592i	0.635914	−	0.771760i	$-0.280623\pi$
$283$	−5.39086	−	8.06799i	−0.320453	−	0.479592i	−0.956367	+	0.292168i	$0.905623\pi$
$284$		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	$-0.102682\pi$
$293$	5.00829	+	7.49544i	0.292587	+	0.437888i	−0.655832	+	0.754907i	$0.727682\pi$
$294$		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	0.859851	−	0.510546i	$-0.170557\pi$
$307$	12.5667	+	8.39679i	0.717218	+	0.479230i	−0.142632	+	0.989776i	$0.545557\pi$
$308$		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	$-0.666762\pi$
$311$	−4.26292	+	1.76576i	−0.241728	+	0.100127i	0.258531	+	0.966003i	$0.416762\pi$
$312$		0			0
$313$	19.1426	+	7.92911i	1.08200	+	0.448180i	0.851211	−	0.524824i	$-0.175869\pi$
$313$	19.1426	+	7.92911i	1.08200	+	0.448180i	0.230790	+	0.973004i	$0.425869\pi$
$314$		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	$-0.00903073\pi$
$317$	1.16146	+	5.83907i	0.0652342	+	0.327955i	−0.934363	+	0.356322i	$0.884031\pi$
$318$		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	−0.566372	−	0.824149i	$-0.691654\pi$
$331$	−25.5621	−	5.08462i	−1.40502	−	0.279476i	−0.838648	+	0.544674i	$0.816654\pi$
$332$		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	−0.984517	−	0.175292i	$-0.943913\pi$
$337$	−14.8554	+	14.8554i	−0.809225	+	0.809225i	0.175292	+	0.984517i	$0.443913\pi$
$338$		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	0.945374	+	0.325989i	$0.105697\pi$
$347$	16.4814	+	24.6662i	0.884769	+	1.32415i	−0.0606043	+	0.998162i	$0.519303\pi$
$348$		0			0
$349$	−31.9917	+	6.36355i	−1.71248	+	0.340633i	−0.951384	−	0.308009i	$-0.900337\pi$
$349$	−31.9917	+	6.36355i	−1.71248	+	0.340633i	−0.761094	+	0.648642i	$0.775337\pi$
$350$		0			0
$351$		−	7.83982i		−	0.418459i
$352$		0			0
$353$		−	33.6731i		−	1.79224i	−0.443814	−	0.896119i	$-0.646375\pi$
$353$		−	33.6731i		−	1.79224i	0.443814	−	0.896119i	$-0.353625\pi$
$354$		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	$-0.984145\pi$
$359$	−4.87560	+	11.7707i	−0.257324	+	0.621235i	0.741436	+	0.671024i	$0.234145\pi$
$360$		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	$-0.840513\pi$
$367$	−7.60045	+	7.60045i	−0.396740	+	0.396740i	0.480341	+	0.877082i	$0.340513\pi$
$368$		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	$-0.608945\pi$
$373$	−19.4325	−	3.86536i	−1.00618	−	0.200141i	−0.670558	+	0.741857i	$0.733945\pi$
$374$		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	0.211959	−	0.977279i	$-0.432016\pi$
$379$	23.2828	−	15.5571i	1.19596	−	0.799115i	0.984001	+	0.178164i	$0.0570158\pi$
$380$		0			0
$381$	1.56300	+	7.85771i	0.0800747	+	0.402563i
$382$		0			0
$383$	26.0613			1.33167			0.665835	−	0.746099i	$-0.268076\pi$
$383$	26.0613			1.33167			0.665835	+	0.746099i	$0.268076\pi$
$384$		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	$-0.862018\pi$
$389$	−17.0947	+	11.4223i	−0.866737	+	0.579135i	0.0407720	+	0.999168i	$0.487018\pi$
$390$		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	$-0.174968\pi$
$397$	13.8749	+	9.27088i	0.696359	+	0.465292i	−0.156334	+	0.987704i	$0.549968\pi$
$398$		0			0
$399$	2.75756	+	2.75756i	0.138051	+	0.138051i
$400$		0			0
$401$	13.1510	−	13.1510i	0.656731	−	0.656731i	−0.297874	−	0.954605i	$-0.596277\pi$
$401$	13.1510	−	13.1510i	0.656731	−	0.656731i	0.954605	+	0.297874i	$0.0962775\pi$
$402$		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	−0.994469	−	0.105030i	$-0.966506\pi$
$409$	−4.38868	+	10.5952i	−0.217006	+	0.523899i	0.777463	+	0.628929i	$0.216506\pi$
$410$		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	0.728174	−	0.685392i	$-0.240369\pi$
$419$	34.0450	−	6.77197i	1.66321	−	0.330832i	0.935033	+	0.354560i	$0.115369\pi$
$420$		0			0
$421$	4.93933	+	7.39223i	0.240728	+	0.360275i	0.932086	−	0.362238i	$-0.117987\pi$
$421$	4.93933	+	7.39223i	0.240728	+	0.360275i	−0.691358	+	0.722513i	$0.742987\pi$
$422$		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	−0.121745	+	0.992561i	$0.538849\pi$
$431$	−23.1336	+	23.1336i	−1.11431	+	1.11431i	−0.992561	+	0.121745i	$0.961151\pi$
$432$		0			0
$433$	−0.961924	−	0.961924i	−0.0462271	−	0.0462271i	0.683615	−	0.729842i	$-0.260407\pi$
$433$	−0.961924	−	0.961924i	−0.0462271	−	0.0462271i	−0.729842	+	0.683615i	$0.760407\pi$
$434$		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	$-0.444072\pi$
$439$	20.8397	−	8.63209i	0.994625	−	0.411987i	0.819823	+	0.572616i	$0.194072\pi$
$440$		0			0
$441$	−14.7259	−	6.09965i	−0.701232	−	0.290460i
$442$		0			0
$443$	−30.4748	+	20.3626i	−1.44790	+	0.967458i	−0.450703	+	0.892674i	$0.648827\pi$
$443$	−30.4748	+	20.3626i	−1.44790	+	0.967458i	−0.997200	+	0.0747837i	$0.976173\pi$
$444$		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	−0.994220	−	0.107362i	$-0.965760\pi$
$457$	−34.6599	+	14.3566i	−1.62132	+	0.671574i	−0.627103	+	0.778936i	$0.715760\pi$
$458$		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	$-0.332008\pi$
$461$	−2.18684	−	1.46120i	−0.101851	−	0.0680548i	−0.605453	+	0.795881i	$0.707008\pi$
$462$		0			0
$463$	10.3078	+	10.3078i	0.479045	+	0.479045i	0.904826	−	0.425781i	$-0.140001\pi$
$463$	10.3078	+	10.3078i	0.479045	+	0.479045i	−0.425781	+	0.904826i	$0.640001\pi$
$464$		0			0
$465$	−1.49046	+	1.49046i	−0.0691183	+	0.0691183i
$466$		0			0
$467$	6.02523	−	9.01739i	0.278814	−	0.417275i	−0.665461	−	0.746433i	$-0.731765\pi$
$467$	6.02523	−	9.01739i	0.278814	−	0.417275i	0.944275	+	0.329158i	$0.106765\pi$
$468$		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	0.462520	+	0.886609i	$0.346945\pi$
$487$	−10.8455	+	26.1834i	−0.491458	+	1.18648i	−0.953978	+	0.299876i	$0.903055\pi$
$488$		0			0
$489$	3.25804	+	7.86562i	0.147334	+	0.355695i
$490$		0			0
$491$	−3.12805	+	15.7257i	−0.141167	+	0.709693i	0.843760	+	0.536721i	$0.180337\pi$
$491$	−3.12805	+	15.7257i	−0.141167	+	0.709693i	−0.984927	+	0.172972i	$0.944663\pi$
$492$		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	0.849525	−	0.527549i	$-0.176889\pi$
$499$	15.3516	+	10.2576i	0.687232	+	0.459194i	−0.162293	+	0.986743i	$0.551889\pi$
$500$		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	$-0.881694\pi$
$503$	−29.9129	+	12.3903i	−1.33375	+	0.552457i	−0.402027	+	0.915628i	$0.631694\pi$
$504$		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	0.818164	+	0.574985i	$0.194992\pi$
$509$	6.36934	+	32.0209i	0.282316	+	1.41930i	−0.535848	+	0.844315i	$0.680008\pi$
$510$		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	−0.751615	−	0.659602i	$-0.770725\pi$
$521$	−18.6410	+	7.72136i	−0.816677	+	0.338279i	−0.0650626	+	0.997881i	$0.520725\pi$
$522$		0			0
$523$	8.92581	+	1.77545i	0.390298	+	0.0776352i	0.386339	−	0.922357i	$-0.373740\pi$
$523$	8.92581	+	1.77545i	0.390298	+	0.0776352i	0.00395965	+	0.999992i	$0.498740\pi$
$524$		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	$-0.647178\pi$
$541$	−11.9947	+	2.38590i	−0.515694	+	0.102578i	−0.0696193	+	0.997574i	$0.522178\pi$
$542$		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	−0.572279	−	0.820059i	$-0.693941\pi$
$547$	−18.4104	+	3.66207i	−0.787174	+	0.156579i	−0.214894	+	0.976637i	$0.568941\pi$
$548$		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	$-0.645876\pi$
$557$	13.1089	−	19.6188i	0.555442	−	0.831277i	0.997850	+	0.0655364i	$0.0208759\pi$
$558$		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	0.395495	−	0.918468i	$-0.370573\pi$
$563$	−7.15885	−	4.78339i	−0.301710	−	0.201596i	−0.697205	+	0.716872i	$0.745573\pi$
$564$		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	0.353528	−	0.935424i	$-0.384982\pi$
$569$	−1.38195	−	0.572423i	−0.0579344	−	0.0239972i	−0.411462	+	0.911427i	$0.634982\pi$
$570$		0			0
$571$	−4.83659	+	3.23171i	−0.202405	+	0.135243i	−0.652642	−	0.757666i	$-0.726339\pi$
$571$	−4.83659	+	3.23171i	−0.202405	+	0.135243i	0.450237	+	0.892909i	$0.351339\pi$
$572$		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	−0.324191	−	0.945992i	$-0.605092\pi$
$587$	−23.8821	−	4.75045i	−0.985720	−	0.196072i	−0.661529	+	0.749920i	$0.730092\pi$
$588$		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	−0.350412	−	0.936596i	$-0.613958\pi$
$593$	14.2745	−	14.2745i	0.586184	−	0.586184i	0.936596	+	0.350412i	$0.113958\pi$
$594$		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	$-0.0528851\pi$
$599$	4.20762	+	10.1581i	0.171919	+	0.415048i	−0.814311	+	0.580428i	$0.802885\pi$
$600$		0			0
$601$	−3.87269	+	9.34950i	−0.157970	+	0.381374i	−0.982972	−	0.183756i	$-0.941174\pi$
$601$	−3.87269	+	9.34950i	−0.157970	+	0.381374i	0.825001	+	0.565131i	$0.191174\pi$
$602$		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	$-0.138323\pi$
$613$	4.23332	+	6.33562i	0.170982	+	0.255893i	−0.736075	+	0.676900i	$0.763323\pi$
$614$		0			0
$615$	−1.19961	+	2.89611i	−0.0483728	+	0.116782i
$616$		0			0
$617$	5.69105	+	13.7394i	0.229113	+	0.553128i	0.996070	−	0.0885706i	$-0.0282299\pi$
$617$	5.69105	+	13.7394i	0.229113	+	0.553128i	−0.766957	+	0.641699i	$0.778230\pi$
$618$		0			0
$619$	−6.79342	+	34.1528i	−0.273051	+	1.37272i	0.564083	+	0.825718i	$0.309230\pi$
$619$	−6.79342	+	34.1528i	−0.273051	+	1.37272i	−0.837133	+	0.546999i	$0.815770\pi$
$620$		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	$-0.462600\pi$
$631$	22.6667	−	9.38886i	0.902348	−	0.373765i	0.785122	+	0.619341i	$0.212600\pi$
$632$		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	−0.871835	−	0.489800i	$-0.837070\pi$
$643$	−6.43579	−	32.3549i	−0.253803	−	1.27595i	0.618032	−	0.786153i	$-0.287930\pi$
$644$		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	$-0.578924\pi$
$647$	−28.0926	−	11.6363i	−1.10443	−	0.457471i	−0.859017	+	0.511947i	$0.828924\pi$
$648$		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	$-0.314914\pi$
$653$	−0.322282	−	0.215342i	−0.0126119	−	0.00842699i	−0.561860	+	0.827232i	$0.689914\pi$
$654$		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	−0.603438	−	0.797410i	$-0.706203\pi$
$659$	9.34933	−	13.9923i	0.364198	−	0.545061i	0.967636	+	0.252349i	$0.0812030\pi$
$660$		0			0
$661$	4.92746	−	24.7720i	0.191656	−	0.963520i	−0.758483	−	0.651693i	$-0.774059\pi$
$661$	4.92746	−	24.7720i	0.191656	−	0.963520i	0.950139	−	0.311827i	$-0.100941\pi$
$662$		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	$-0.996744\pi$
$673$		−	0.530719i		−	0.0204577i	0.999948	−	0.0102289i	$-0.00325600\pi$
$674$		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	$-0.153641\pi$
$677$	3.06951	+	4.59384i	0.117971	+	0.176556i	−0.767785	+	0.640708i	$0.778641\pi$
$678$		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	−0.891119	−	0.453769i	$-0.850079\pi$
$683$	2.76547	−	13.9029i	0.105818	−	0.531981i	0.996937	−	0.0782118i	$-0.0249210\pi$
$684$		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	0.748844	−	0.662746i	$-0.230609\pi$
$691$	11.1224	+	7.43176i	0.423117	+	0.282717i	−0.325727	+	0.945464i	$0.605609\pi$
$692$		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	$-0.0817685\pi$
$701$	−0.624967	−	3.14192i	−0.0236047	−	0.118669i	−0.990791	+	0.135399i	$0.956768\pi$
$702$		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	$-0.667000\pi$
$709$	2.84972	−	1.90412i	0.107023	−	0.0715107i	0.607930	+	0.793991i	$0.292000\pi$
$710$		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	$-0.166969\pi$
$719$	9.77983	+	9.77983i	0.364726	+	0.364726i	−0.500823	+	0.865549i	$0.666969\pi$
$720$		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	−0.991149	−	0.132754i	$-0.957618\pi$
$727$	−10.3584	−	25.0074i	−0.384172	−	0.927474i	0.606977	−	0.794720i	$-0.292382\pi$
$728$		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	$-0.385470\pi$
$733$	28.0369	−	5.57688i	1.03557	−	0.205987i	0.683471	+	0.729978i	$0.260470\pi$
$734$		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	−0.498647	−	0.866805i	$-0.666169\pi$
$739$	−17.0617	+	3.39378i	−0.627624	+	0.124842i	−0.128977	+	0.991648i	$0.541169\pi$
$740$		0			0
$741$	−5.14487	−	7.69984i	−0.189001	−	0.282861i
$742$		0			0
$743$	−11.8271	+	28.5530i	−0.433893	+	1.04751i	0.544128	+	0.839002i	$0.316861\pi$
$743$	−11.8271	+	28.5530i	−0.433893	+	1.04751i	−0.978021	+	0.208507i	$0.933139\pi$
$744$		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	$-0.790579\pi$
$751$	−4.92726	+	4.92726i	−0.179798	+	0.179798i	0.611470	+	0.791268i	$0.290579\pi$
$752$		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	$-0.157355\pi$
$757$	41.6002	+	8.27479i	1.51198	+	0.300752i	0.631705	+	0.775209i	$0.282355\pi$
$758$		0			0
$759$	−0.342461	+	0.141852i	−0.0124306	+	0.00514890i
$760$		0			0
$761$	−29.3553	−	12.1594i	−1.06413	−	0.440777i	−0.219214	−	0.975677i	$-0.570349\pi$
$761$	−29.3553	−	12.1594i	−1.06413	−	0.440777i	−0.844915	+	0.534900i	$0.820349\pi$
$762$		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	$-0.653066\pi$
$773$	4.99174	−	3.33537i	0.179540	−	0.119965i	0.642093	+	0.766627i	$0.278066\pi$
$774$		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	−0.223288	−	0.974752i	$-0.571679\pi$
$787$	21.3968	−	32.0226i	0.762714	−	1.14148i	0.986003	−	0.166730i	$-0.0533209\pi$
$788$		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	$-0.679548\pi$
$797$	−19.9075	+	3.95984i	−0.705159	+	0.140265i	−0.170531	+	0.985352i	$0.554548\pi$
$798$		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	0.975821	−	0.218571i	$-0.0701396\pi$
$809$	3.73336	+	9.01314i	0.131258	+	0.316885i	−0.844563	+	0.535456i	$0.820140\pi$
$810$		0			0
$811$	9.93194	−	49.9313i	0.348758	−	1.75332i	−0.265398	−	0.964139i	$-0.585504\pi$
$811$	9.93194	−	49.9313i	0.348758	−	1.75332i	0.614156	−	0.789185i	$-0.289496\pi$
$812$		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	$-0.172726\pi$
$821$	41.5441	+	8.26364i	1.44990	+	0.288403i	0.593549	+	0.804798i	$0.297726\pi$
$822$		0			0
$823$	−15.1760	+	6.28610i	−0.529001	+	0.219120i	−0.631166	−	0.775648i	$-0.717423\pi$
$823$	−15.1760	+	6.28610i	−0.529001	+	0.219120i	0.102164	+	0.994768i	$0.467423\pi$
$824$		0			0
$825$	0.200248	+	0.0829456i	0.00697176	+	0.00288780i
$826$		0			0
$827$	−9.22561	+	6.16435i	−0.320806	+	0.214356i	−0.705537	−	0.708673i	$-0.749294\pi$
$827$	−9.22561	+	6.16435i	−0.320806	+	0.214356i	0.384731	+	0.923029i	$0.374294\pi$
$828$		0			0
$829$	2.51090	+	12.6231i	0.0872070	+	0.438419i	0.999578	+	0.0290546i	$0.00924965\pi$
$829$	2.51090	+	12.6231i	0.0872070	+	0.438419i	−0.912371	+	0.409365i	$0.865750\pi$
$830$		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	$-0.0987805\pi$
$839$	40.8308	+	16.9127i	1.40963	+	0.583890i	0.457401	+	0.889261i	$0.348780\pi$
$840$		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	−0.744563	−	0.667553i	$-0.767342\pi$
$853$	5.80574	−	29.1874i	0.198785	−	0.999359i	0.943347	−	0.331806i	$-0.107658\pi$
$854$		0			0
$855$	5.22559	+	12.6157i	0.178711	+	0.431447i
$856$		0			0
$857$	3.96712	−	9.57747i	0.135514	−	0.327160i	−0.841526	−	0.540217i	$-0.818342\pi$
$857$	3.96712	−	9.57747i	0.135514	−	0.327160i	0.977040	+	0.213057i	$0.0683421\pi$
$858$		0			0
$859$	−10.3728	−	15.5239i	−0.353914	−	0.529670i	0.611208	−	0.791470i	$-0.290684\pi$
$859$	−10.3728	−	15.5239i	−0.353914	−	0.529670i	−0.965122	+	0.261800i	$0.915684\pi$
$860$		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	$-0.882132\pi$
$877$	−7.14103	+	10.6873i	−0.241136	+	0.360885i	0.691086	+	0.722772i	$0.257132\pi$
$878$		0			0
$879$	4.03771	−	4.03771i	0.136188	−	0.136188i
$880$		0			0
$881$	9.31796	+	9.31796i	0.313930	+	0.313930i	0.846430	−	0.532500i	$-0.178747\pi$
$881$	9.31796	+	9.31796i	0.313930	+	0.313930i	−0.532500	+	0.846430i	$0.678747\pi$
$882$		0			0
$883$	−21.6540	−	14.4687i	−0.728714	−	0.486911i	0.135031	−	0.990841i	$-0.456887\pi$
$883$	−21.6540	−	14.4687i	−0.728714	−	0.486911i	−0.863744	+	0.503931i	$0.831887\pi$
$884$		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	$-0.446683\pi$
$887$	29.2410	−	12.1120i	0.981816	−	0.406681i	0.815098	+	0.579323i	$0.196683\pi$
$888$		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	0.810289	−	0.586030i	$-0.199310\pi$
$907$	40.1944	+	7.99517i	1.33463	+	0.265475i	0.524346	+	0.851506i	$0.324310\pi$
$908$		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	$-0.483972\pi$
$911$	−28.6254	−	28.6254i	−0.948402	−	0.948402i	−0.998733	+	0.0503311i	$0.983972\pi$
$912$		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	−0.998450	−	0.0556618i	$-0.982273\pi$
$919$	−10.0585	−	24.2833i	−0.331798	−	0.801031i	0.666652	−	0.745369i	$-0.267727\pi$
$920$		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	$0.202966\pi$
$929$			36.2888i			1.19060i	−0.803505	+	0.595298i	$0.797034\pi$
$930$		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	−0.673449	−	0.739234i	$-0.735188\pi$
$937$	−22.0385	−	53.2056i	−0.719966	−	1.73815i	−0.0465174	−	0.998917i	$-0.514812\pi$
$938$		0			0
$939$	2.56047	−	12.8723i	0.0835577	−	0.420073i
$940$		0			0
$941$	−32.5815	+	48.7616i	−1.06213	+	1.58958i	−0.286832	+	0.957981i	$0.592602\pi$
$941$	−32.5815	+	48.7616i	−1.06213	+	1.58958i	−0.775293	+	0.631602i	$0.782398\pi$
$942$		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	0.114050	−	0.993475i	$-0.463618\pi$
$947$	−23.3926	−	15.6304i	−0.760156	−	0.507920i	−0.874206	+	0.485555i	$0.838618\pi$
$948$		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	−0.0385243	−	0.999258i	$-0.512266\pi$
$953$	−23.8429	−	9.87605i	−0.772347	−	0.319917i	−0.733823	+	0.679341i	$0.762266\pi$
$954$		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	$-0.0858479\pi$
$967$	45.3076	+	18.7670i	1.45699	+	0.603507i	0.493143	+	0.869948i	$0.335848\pi$
$968$		0			0
$969$	−17.2771	+	7.15640i	−0.555020	+	0.229897i
$970$		0			0
$971$	−14.9013	−	2.96405i	−0.478205	−	0.0951208i	−0.0498981	−	0.998754i	$-0.515890\pi$
$971$	−14.9013	−	2.96405i	−0.478205	−	0.0951208i	−0.428307	+	0.903634i	$0.640890\pi$
$972$		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	−0.959487	−	0.281753i	$-0.909084\pi$
$977$	−21.1839	+	21.1839i	−0.677734	+	0.677734i	0.281753	+	0.959487i	$0.409084\pi$
$978$		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	−0.998422	−	0.0561482i	$-0.982118\pi$
$983$	−10.4133	−	25.1400i	−0.332134	−	0.801842i	0.666289	−	0.745694i	$-0.267882\pi$
$984$		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	$-0.161975\pi$
$997$	2.81043	+	4.20611i	0.0890073	+	0.133209i	−0.784294	+	0.620389i	$0.786975\pi$
$998$		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	512.2.i.b.97.4		56
4.3	odd	2		512.2.i.a.97.4		56
8.3	odd	2		256.2.i.a.177.4		56
8.5	even	2		64.2.i.a.21.5	✓	56
24.5	odd	2		576.2.bd.a.469.3		56
64.3	odd	16		512.2.i.a.417.4		56
64.29	even	16		64.2.i.a.61.5	yes	56
64.35	odd	16		256.2.i.a.81.4		56
64.61	even	16	inner	512.2.i.b.417.4		56
192.29	odd	16		576.2.bd.a.253.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.5	✓	56	8.5	even	2
64.2.i.a.61.5	yes	56	64.29	even	16
256.2.i.a.81.4		56	64.35	odd	16
256.2.i.a.177.4		56	8.3	odd	2
512.2.i.a.97.4		56	4.3	odd	2
512.2.i.a.417.4		56	64.3	odd	16
512.2.i.b.97.4		56	1.1	even	1	trivial
512.2.i.b.417.4		56	64.61	even	16	inner
576.2.bd.a.253.3		56	192.29	odd	16
576.2.bd.a.469.3		56	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.123576 - 0.621259i) q^{3} +(-0.660623 + 0.441414i) q^{5} +(-0.860072 - 0.356253i) q^{7} +(2.40095 - 0.994505i) q^{9} +O(q^{10})\)	\(q+(-0.123576 - 0.621259i) q^{3} +(-0.660623 + 0.441414i) q^{5} +(-0.860072 - 0.356253i) q^{7} +(2.40095 - 0.994505i) q^{9} +(0.0768198 + 0.0152804i) q^{11} +(1.83807 + 1.22816i) q^{13} +(0.355870 + 0.355870i) q^{15} +(3.15660 - 3.15660i) q^{17} +(3.67418 - 5.49880i) q^{19} +(-0.115041 + 0.578352i) q^{21} +(-2.85915 - 6.90260i) q^{23} +(-1.67184 + 4.03618i) q^{25} +(-1.97029 - 2.94875i) q^{27} +(8.72686 - 1.73588i) q^{29} +4.18821i q^{31} -0.0496134i q^{33} +(0.725438 - 0.144299i) q^{35} +(-2.71234 - 4.05931i) q^{37} +(0.535863 - 1.29369i) q^{39} +(2.38360 + 5.75451i) q^{41} +(-0.476196 + 2.39400i) q^{43} +(-1.14713 + 1.71680i) q^{45} +(5.93827 - 5.93827i) q^{47} +(-4.33694 - 4.33694i) q^{49} +(-2.35115 - 1.57099i) q^{51} +(1.38768 + 0.276027i) q^{53} +(-0.0574939 + 0.0238148i) q^{55} +(-3.87022 - 1.60310i) q^{57} +(-10.1842 + 6.80486i) q^{59} +(-0.575578 - 2.89363i) q^{61} -2.41928 q^{63} -1.75639 q^{65} +(1.81110 + 9.10504i) q^{67} +(-3.93498 + 2.62927i) q^{69} +(3.80374 + 1.57556i) q^{71} +(0.958083 - 0.396851i) q^{73} +(2.71412 + 0.539871i) q^{75} +(-0.0606269 - 0.0405096i) q^{77} +(7.08438 + 7.08438i) q^{79} +(3.92436 - 3.92436i) q^{81} +(3.50145 - 5.24029i) q^{83} +(-0.691955 + 3.47869i) q^{85} +(-2.15687 - 5.20713i) q^{87} +(-2.98468 + 7.20566i) q^{89} +(-1.14333 - 1.71112i) q^{91} +(2.60196 - 0.517563i) q^{93} +5.25446i q^{95} +7.39898i q^{97} +(0.199637 - 0.0397102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 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

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Representations

Groups

Database

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