LMFDB - Embedded newform 1386.2.bu.a.827.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.6
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.a.1205.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.411682 - 0.133764i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.411682 - 0.133764i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} -0.432868i q^{10} +(-0.137335 + 3.31378i) q^{11} +(-1.34433 - 0.436798i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.223592 - 0.688147i) q^{17} +(3.54176 + 4.87481i) q^{19} +(-0.411682 - 0.133764i) q^{20} +(3.10915 + 1.15463i) q^{22} -1.67094i q^{23} +(-3.89350 + 2.82879i) q^{25} +(-0.830839 + 1.14355i) q^{26} +(0.951057 - 0.309017i) q^{28} +(0.367221 + 0.266802i) q^{29} +(-1.99876 + 6.15157i) q^{31} +1.00000 q^{32} -0.723560 q^{34} +(-0.133764 + 0.411682i) q^{35} +(6.85544 + 4.98077i) q^{37} +(5.73068 - 1.86201i) q^{38} +(-0.254434 + 0.350198i) q^{40} +(1.35607 - 0.985240i) q^{41} +5.52992i q^{43} +(2.05890 - 2.60018i) q^{44} +(-1.58916 - 0.516349i) q^{46} +(2.88658 + 3.97304i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(1.48718 + 4.57708i) q^{50} +(0.830839 + 1.14355i) q^{52} +(0.253858 + 0.0824836i) q^{53} +(0.386725 + 1.38259i) q^{55} -1.00000i q^{56} +(0.367221 - 0.266802i) q^{58} +(3.56050 - 4.90061i) q^{59} +(0.756954 - 0.245949i) q^{61} +(5.23283 + 3.80188i) q^{62} +(0.309017 - 0.951057i) q^{64} -0.611863 q^{65} -0.680521 q^{67} +(-0.223592 + 0.688147i) q^{68} +(0.350198 + 0.254434i) q^{70} +(2.38456 - 0.774789i) q^{71} +(-3.78008 + 5.20283i) q^{73} +(6.85544 - 4.98077i) q^{74} -6.02559i q^{76} +(-2.60018 - 2.05890i) q^{77} +(-5.90957 - 1.92014i) q^{79} +(0.254434 + 0.350198i) q^{80} +(-0.517971 - 1.59415i) q^{82} +(1.83539 + 5.64875i) q^{83} +(-0.184098 - 0.253389i) q^{85} +(5.25926 + 1.70884i) q^{86} +(-1.83668 - 2.76163i) q^{88} -8.71973i q^{89} +(1.14355 - 0.830839i) q^{91} +(-0.982154 + 1.35182i) q^{92} +(4.67058 - 1.51756i) q^{94} +(2.11015 + 1.53311i) q^{95} +(-5.31870 + 16.3693i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.411682	−	0.133764i	0.184110	−	0.0598209i	−0.215511	−	0.976501i	$-0.569142\pi$
$5$	0.411682	−	0.133764i	0.184110	−	0.0598209i	0.399621	+	0.916680i	$0.369142\pi$
$6$		0			0
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$		−	0.432868i		−	0.136885i
$11$	−0.137335	+	3.31378i	−0.0414080	+	0.999142i
$11$	−0.137335	+	3.31378i	−0.0414080	+	0.999142i
$12$		0			0
$13$	−1.34433	−	0.436798i	−0.372849	−	0.121146i	0.116598	−	0.993179i	$-0.462801\pi$
$13$	−1.34433	−	0.436798i	−0.372849	−	0.121146i	−0.489447	+	0.872033i	$0.662801\pi$
$14$	0.587785	+	0.809017i	0.157092	+	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.223592	−	0.688147i	−0.0542291	−	0.166900i	0.920274	−	0.391275i	$-0.127966\pi$
$17$	−0.223592	−	0.688147i	−0.0542291	−	0.166900i	−0.974503	+	0.224375i	$0.927966\pi$
$18$		0			0
$19$	3.54176	+	4.87481i	0.812534	+	1.11836i	0.990927	+	0.134398i	$0.0429102\pi$
$19$	3.54176	+	4.87481i	0.812534	+	1.11836i	−0.178393	+	0.983959i	$0.557090\pi$
$20$	−0.411682	−	0.133764i	−0.0920549	−	0.0299105i
$21$		0			0
$22$	3.10915	+	1.15463i	0.662874	+	0.246167i
$23$		−	1.67094i		−	0.348415i	−0.984709	−	0.174207i	$-0.944264\pi$
$23$		−	1.67094i		−	0.348415i	0.984709	−	0.174207i	$-0.0557363\pi$
$24$		0			0
$25$	−3.89350	+	2.82879i	−0.778699	+	0.565758i
$26$	−0.830839	+	1.14355i	−0.162941	+	0.224269i
$27$		0			0
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	0.367221	+	0.266802i	0.0681913	+	0.0495439i	0.621359	−	0.783526i	$-0.286581\pi$
$29$	0.367221	+	0.266802i	0.0681913	+	0.0495439i	−0.553167	+	0.833070i	$0.686581\pi$
$30$		0			0
$31$	−1.99876	+	6.15157i	−0.358989	+	1.10485i	0.594672	+	0.803969i	$0.297282\pi$
$31$	−1.99876	+	6.15157i	−0.358989	+	1.10485i	−0.953660	+	0.300885i	$0.902718\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.723560			−0.124090
$35$	−0.133764	+	0.411682i	−0.0226102	+	0.0695870i
$36$		0			0
$37$	6.85544	+	4.98077i	1.12703	+	0.818833i	0.985259	−	0.171067i	$-0.0547214\pi$
$37$	6.85544	+	4.98077i	1.12703	+	0.818833i	0.141768	+	0.989900i	$0.454721\pi$
$38$	5.73068	−	1.86201i	0.929639	−	0.302058i
$39$		0			0
$40$	−0.254434	+	0.350198i	−0.0402295	+	0.0553711i
$41$	1.35607	−	0.985240i	0.211782	−	0.153869i	−0.476838	−	0.878991i	$-0.658217\pi$
$41$	1.35607	−	0.985240i	0.211782	−	0.153869i	0.688620	+	0.725123i	$0.258217\pi$
$42$		0			0
$43$			5.52992i			0.843304i	0.906758	+	0.421652i	$0.138550\pi$
$43$			5.52992i			0.843304i	−0.906758	+	0.421652i	$0.861450\pi$
$44$	2.05890	−	2.60018i	0.310390	−	0.391992i
$45$		0			0
$46$	−1.58916	−	0.516349i	−0.234309	−	0.0761315i
$47$	2.88658	+	3.97304i	0.421051	+	0.579527i	0.965870	−	0.259027i	$-0.0834018\pi$
$47$	2.88658	+	3.97304i	0.421051	+	0.579527i	−0.544819	+	0.838553i	$0.683402\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	1.48718	+	4.57708i	0.210319	+	0.647297i
$51$		0			0
$52$	0.830839	+	1.14355i	0.115217	+	0.158582i
$53$	0.253858	+	0.0824836i	0.0348701	+	0.0113300i	0.326400	−	0.945232i	$-0.394164\pi$
$53$	0.253858	+	0.0824836i	0.0348701	+	0.0113300i	−0.291530	+	0.956562i	$0.594164\pi$
$54$		0			0
$55$	0.386725	+	1.38259i	0.0521460	+	0.186429i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	0.367221	−	0.266802i	0.0482185	−	0.0350328i
$59$	3.56050	−	4.90061i	0.463538	−	0.638005i	−0.511700	−	0.859164i	$-0.670984\pi$
$59$	3.56050	−	4.90061i	0.463538	−	0.638005i	0.975238	+	0.221159i	$0.0709840\pi$
$60$		0			0
$61$	0.756954	−	0.245949i	0.0969180	−	0.0314906i	−0.260157	−	0.965566i	$-0.583774\pi$
$61$	0.756954	−	0.245949i	0.0969180	−	0.0314906i	0.357075	+	0.934076i	$0.383774\pi$
$62$	5.23283	+	3.80188i	0.664571	+	0.482839i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.611863			−0.0758922
$66$		0			0
$67$	−0.680521			−0.0831388			−0.0415694	−	0.999136i	$-0.513236\pi$
$67$	−0.680521			−0.0831388			−0.0415694	+	0.999136i	$0.513236\pi$
$68$	−0.223592	+	0.688147i	−0.0271146	+	0.0834501i
$69$		0			0
$70$	0.350198	+	0.254434i	0.0418566	+	0.0304106i
$71$	2.38456	−	0.774789i	0.282995	−	0.0919505i	−0.164080	−	0.986447i	$-0.552466\pi$
$71$	2.38456	−	0.774789i	0.282995	−	0.0919505i	0.447075	+	0.894496i	$0.352466\pi$
$72$		0			0
$73$	−3.78008	+	5.20283i	−0.442424	+	0.608945i	−0.970749	−	0.240098i	$-0.922821\pi$
$73$	−3.78008	+	5.20283i	−0.442424	+	0.608945i	0.528324	+	0.849043i	$0.322821\pi$
$74$	6.85544	−	4.98077i	0.796929	−	0.579003i
$75$		0			0
$76$		−	6.02559i		−	0.691183i
$77$	−2.60018	−	2.05890i	−0.296318	−	0.234633i
$78$		0			0
$79$	−5.90957	−	1.92014i	−0.664879	−	0.216032i	−0.0429156	−	0.999079i	$-0.513665\pi$
$79$	−5.90957	−	1.92014i	−0.664879	−	0.216032i	−0.621963	+	0.783046i	$0.713665\pi$
$80$	0.254434	+	0.350198i	0.0284465	+	0.0391533i
$81$		0			0
$82$	−0.517971	−	1.59415i	−0.0572004	−	0.176045i
$83$	1.83539	+	5.64875i	0.201460	+	0.620031i	0.999840	+	0.0178769i	$0.00569070\pi$
$83$	1.83539	+	5.64875i	0.201460	+	0.620031i	−0.798380	+	0.602154i	$0.794309\pi$
$84$		0			0
$85$	−0.184098	−	0.253389i	−0.0199682	−	0.0274839i
$86$	5.25926	+	1.70884i	0.567121	+	0.184269i
$87$		0			0
$88$	−1.83668	−	2.76163i	−0.195791	−	0.294391i
$89$		−	8.71973i		−	0.924290i	−0.886804	−	0.462145i	$-0.847080\pi$
$89$		−	8.71973i		−	0.924290i	0.886804	−	0.462145i	$-0.152920\pi$
$90$		0			0
$91$	1.14355	−	0.830839i	0.119877	−	0.0870956i
$92$	−0.982154	+	1.35182i	−0.102397	+	0.140937i
$93$		0			0
$94$	4.67058	−	1.51756i	0.481734	−	0.156525i
$95$	2.11015	+	1.53311i	0.216497	+	0.157294i
$96$		0			0
$97$	−5.31870	+	16.3693i	−0.540032	+	1.66205i	0.192485	+	0.981300i	$0.438345\pi$
$97$	−5.31870	+	16.3693i	−0.540032	+	1.66205i	−0.732517	+	0.680748i	$0.761655\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	4.81263			0.481263
$101$	4.14377	−	12.7532i	0.412321	−	1.26899i	−0.502305	−	0.864691i	$-0.667515\pi$
$101$	4.14377	−	12.7532i	0.412321	−	1.26899i	0.914626	−	0.404302i	$-0.132485\pi$
$102$		0			0
$103$	12.8354	+	9.32547i	1.26471	+	0.918866i	0.998979	−	0.0451806i	$-0.0143863\pi$
$103$	12.8354	+	9.32547i	1.26471	+	0.918866i	0.265732	+	0.964047i	$0.414386\pi$
$104$	1.34433	−	0.436798i	0.131822	−	0.0428316i
$105$		0			0
$106$	0.156893	−	0.215945i	0.0152388	−	0.0209744i
$107$	7.57351	−	5.50248i	0.732159	−	0.531945i	−0.158087	−	0.987425i	$-0.550533\pi$
$107$	7.57351	−	5.50248i	0.732159	−	0.531945i	0.890246	+	0.455481i	$0.150533\pi$
$108$		0			0
$109$			6.97485i			0.668070i	0.942561	+	0.334035i	$0.108410\pi$
$109$			6.97485i			0.668070i	−0.942561	+	0.334035i	$0.891590\pi$
$110$	1.43443	+	0.0594480i	0.136768	+	0.00566814i
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	2.72804	+	3.75483i	0.256633	+	0.353225i	0.917820	−	0.396996i	$-0.129947\pi$
$113$	2.72804	+	3.75483i	0.256633	+	0.353225i	−0.661188	+	0.750221i	$0.729947\pi$
$114$		0			0
$115$	−0.223511	−	0.687896i	−0.0208425	−	0.0641466i
$116$	−0.140266	−	0.431695i	−0.0130234	−	0.0400818i
$117$		0			0
$118$	−3.56050	−	4.90061i	−0.327771	−	0.451138i
$119$	0.688147	+	0.223592i	0.0630823	+	0.0204967i
$120$		0			0
$121$	−10.9623	−	0.910196i	−0.996571	−	0.0827451i
$122$		−	0.795908i		−	0.0720581i
$123$		0			0
$124$	5.23283	−	3.80188i	0.469922	−	0.341419i
$125$	−2.49666	+	3.43636i	−0.223308	+	0.307357i
$126$		0			0
$127$	7.68429	−	2.49678i	0.681870	−	0.221553i	0.0524563	−	0.998623i	$-0.483295\pi$
$127$	7.68429	−	2.49678i	0.681870	−	0.221553i	0.629414	+	0.777070i	$0.283295\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−0.189076	+	0.581916i	−0.0165831	+	0.0510374i
$131$	0.661431			0.0577895			0.0288947	−	0.999582i	$-0.490801\pi$
$131$	0.661431			0.0577895			0.0288947	+	0.999582i	$0.490801\pi$
$132$		0			0
$133$	−6.02559			−0.522485
$134$	−0.210292	+	0.647213i	−0.0181665	+	0.0559107i
$135$		0			0
$136$	0.585373	+	0.425298i	0.0501953	+	0.0364690i
$137$	−10.8993	+	3.54141i	−0.931194	+	0.302563i	−0.735051	−	0.678012i	$-0.762842\pi$
$137$	−10.8993	+	3.54141i	−0.931194	+	0.302563i	−0.196143	+	0.980575i	$0.562842\pi$
$138$		0			0
$139$	4.78786	−	6.58993i	0.406101	−	0.558950i	−0.556161	−	0.831075i	$-0.687726\pi$
$139$	4.78786	−	6.58993i	0.406101	−	0.558950i	0.962262	+	0.272124i	$0.0877262\pi$
$140$	0.350198	−	0.254434i	0.0295971	−	0.0215036i
$141$		0			0
$142$		−	2.50727i		−	0.210405i
$143$	1.63208	−	4.39481i	0.136481	−	0.367513i
$144$		0			0
$145$	0.186867	+	0.0607167i	0.0155184	+	0.00504225i
$146$	3.78008	+	5.20283i	0.312841	+	0.430589i
$147$		0			0
$148$	−2.61854	−	8.05905i	−0.215243	−	0.662450i
$149$	−0.933277	−	2.87233i	−0.0764570	−	0.235310i	0.905522	−	0.424298i	$-0.139479\pi$
$149$	−0.933277	−	2.87233i	−0.0764570	−	0.235310i	−0.981979	+	0.188988i	$0.939479\pi$
$150$		0			0
$151$	−11.7274	−	16.1414i	−0.954365	−	1.31357i	−0.949561	−	0.313582i	$-0.898471\pi$
$151$	−11.7274	−	16.1414i	−0.954365	−	1.31357i	−0.00480401	−	0.999988i	$-0.501529\pi$
$152$	−5.73068	−	1.86201i	−0.464820	−	0.151029i
$153$		0			0
$154$	−2.76163	+	1.83668i	−0.222538	+	0.148004i
$155$			2.79985i			0.224890i
$156$		0			0
$157$	4.07214	−	2.95858i	0.324992	−	0.236120i	−0.413311	−	0.910590i	$-0.635628\pi$
$157$	4.07214	−	2.95858i	0.324992	−	0.236120i	0.738303	+	0.674470i	$0.235628\pi$
$158$	−3.65232	+	5.02698i	−0.290563	+	0.399925i
$159$		0			0
$160$	0.411682	−	0.133764i	0.0325463	−	0.0105749i
$161$	1.35182	+	0.982154i	0.106538	+	0.0774045i
$162$		0			0
$163$	−0.630871	+	1.94162i	−0.0494136	+	0.152079i	−0.972719	−	0.231988i	$-0.925477\pi$
$163$	−0.630871	+	1.94162i	−0.0494136	+	0.152079i	0.923305	+	0.384067i	$0.125477\pi$
$164$	−1.67619			−0.130889
$165$		0			0
$166$	5.93945			0.460991
$167$	−7.44237	+	22.9052i	−0.575908	+	1.77246i	0.0571602	+	0.998365i	$0.481795\pi$
$167$	−7.44237	+	22.9052i	−0.575908	+	1.77246i	−0.633068	+	0.774096i	$0.718205\pi$
$168$		0			0
$169$	−8.90080	−	6.46681i	−0.684677	−	0.497447i
$170$	−0.297877	+	0.0967861i	−0.0228461	+	0.00742315i
$171$		0			0
$172$	3.25040	−	4.47380i	0.247841	−	0.341124i
$173$	4.45955	−	3.24005i	0.339053	−	0.246336i	−0.405209	−	0.914224i	$-0.632801\pi$
$173$	4.45955	−	3.24005i	0.339053	−	0.246336i	0.744262	+	0.667888i	$0.232801\pi$
$174$		0			0
$175$		−	4.81263i		−	0.363800i
$176$	−3.19403	+	0.893401i	−0.240759	+	0.0673426i
$177$		0			0
$178$	−8.29296	−	2.69455i	−0.621584	−	0.201965i
$179$	1.19340	+	1.64257i	0.0891988	+	0.122772i	0.851284	−	0.524705i	$-0.175824\pi$
$179$	1.19340	+	1.64257i	0.0891988	+	0.122772i	−0.762085	+	0.647477i	$0.775824\pi$
$180$		0			0
$181$	2.37496	+	7.30936i	0.176529	+	0.543300i	0.999700	−	0.0244931i	$-0.00779718\pi$
$181$	2.37496	+	7.30936i	0.176529	+	0.543300i	−0.823171	+	0.567794i	$0.807797\pi$
$182$	−0.436798	−	1.34433i	−0.0323776	−	0.0996481i
$183$		0			0
$184$	0.982154	+	1.35182i	0.0724053	+	0.0996574i
$185$	3.48851	+	1.13349i	0.256480	+	0.0833355i
$186$		0			0
$187$	2.31107	−	0.646430i	0.169002	−	0.0472716i
$188$		−	4.91094i		−	0.358167i
$189$		0			0
$190$	2.11015	−	1.53311i	0.153086	−	0.111224i
$191$	10.2920	−	14.1658i	0.744705	−	1.02500i	−0.253630	−	0.967301i	$-0.581624\pi$
$191$	10.2920	−	14.1658i	0.744705	−	1.02500i	0.998334	−	0.0576964i	$-0.0183756\pi$
$192$		0			0
$193$	−12.2410	+	3.97734i	−0.881125	+	0.286295i	−0.714425	−	0.699712i	$-0.753311\pi$
$193$	−12.2410	+	3.97734i	−0.881125	+	0.286295i	−0.166701	+	0.986008i	$0.553311\pi$
$194$	13.9245	+	10.1168i	0.999724	+	0.726342i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−25.5195			−1.81819			−0.909093	−	0.416593i	$-0.863224\pi$
$197$	−25.5195			−1.81819			−0.909093	+	0.416593i	$0.863224\pi$
$198$		0			0
$199$	23.8285			1.68916			0.844579	−	0.535431i	$-0.179851\pi$
$199$	23.8285			1.68916			0.844579	+	0.535431i	$0.179851\pi$
$200$	1.48718	−	4.57708i	0.105160	−	0.323648i
$201$		0			0
$202$	−10.8485	−	7.88192i	−0.763300	−	0.554570i
$203$	−0.431695	+	0.140266i	−0.0302990	+	0.00984475i
$204$		0			0
$205$	0.426479	−	0.586998i	0.0297866	−	0.0409977i
$206$	12.8354	−	9.32547i	0.894286	−	0.649737i
$207$		0			0
$208$		−	1.41351i		−	0.0980091i
$209$	−16.6404	+	11.0671i	−1.15104	+	0.765528i
$210$		0			0
$211$	−19.0322	−	6.18394i	−1.31023	−	0.425720i	−0.431102	−	0.902303i	$-0.641875\pi$
$211$	−19.0322	−	6.18394i	−1.31023	−	0.425720i	−0.879129	+	0.476583i	$0.841875\pi$
$212$	−0.156893	−	0.215945i	−0.0107755	−	0.0148312i
$213$		0			0
$214$	−2.89282	−	8.90319i	−0.197749	−	0.608610i
$215$	0.739702	+	2.27657i	0.0504473	+	0.155261i
$216$		0			0
$217$	−3.80188	−	5.23283i	−0.258088	−	0.355228i
$218$	6.63348	+	2.15535i	0.449276	+	0.145979i
$219$		0			0
$220$	0.499802	−	1.34585i	0.0336966	−	0.0907375i
$221$			1.02276i			0.0687982i
$222$		0			0
$223$	12.0938	−	8.78667i	0.809862	−	0.588399i	−0.103929	−	0.994585i	$-0.533141\pi$
$223$	12.0938	−	8.78667i	0.809862	−	0.588399i	0.913790	+	0.406186i	$0.133141\pi$
$224$	−0.587785	+	0.809017i	−0.0392731	+	0.0540547i
$225$		0			0
$226$	4.41407	−	1.43422i	0.293619	−	0.0954027i
$227$	−9.53312	−	6.92622i	−0.632736	−	0.459709i	0.224611	−	0.974448i	$-0.427889\pi$
$227$	−9.53312	−	6.92622i	−0.632736	−	0.459709i	−0.857347	+	0.514739i	$0.827889\pi$
$228$		0			0
$229$	−2.70338	+	8.32013i	−0.178644	+	0.549810i	−0.999781	−	0.0209211i	$-0.993340\pi$
$229$	−2.70338	+	8.32013i	−0.178644	+	0.549810i	0.821137	+	0.570731i	$0.193340\pi$
$230$	−0.723297			−0.0476928
$231$		0			0
$232$	−0.453910			−0.0298007
$233$	6.44626	−	19.8396i	0.422309	−	1.29973i	−0.483239	−	0.875488i	$-0.660540\pi$
$233$	6.44626	−	19.8396i	0.422309	−	1.29973i	0.905548	−	0.424244i	$-0.139460\pi$
$234$		0			0
$235$	1.71980	+	1.24951i	0.112187	+	0.0815090i
$236$	−5.76102	+	1.87187i	−0.375010	+	0.121848i
$237$		0			0
$238$	0.425298	−	0.585373i	0.0275680	−	0.0379441i
$239$	−8.44787	+	6.13774i	−0.546447	+	0.397017i	−0.826474	−	0.562975i	$-0.809657\pi$
$239$	−8.44787	+	6.13774i	−0.546447	+	0.397017i	0.280027	+	0.959992i	$0.409657\pi$
$240$		0			0
$241$			9.99003i			0.643514i	0.946822	+	0.321757i	$0.104273\pi$
$241$			9.99003i			0.643514i	−0.946822	+	0.321757i	$0.895727\pi$
$242$	−4.25318	+	10.1445i	−0.273405	+	0.652112i
$243$		0			0
$244$	−0.756954	−	0.245949i	−0.0484590	−	0.0157453i
$245$	−0.254434	−	0.350198i	−0.0162552	−	0.0223733i
$246$		0			0
$247$	−2.63197	−	8.10036i	−0.167468	−	0.515414i
$248$	−1.99876	−	6.15157i	−0.126922	−	0.390625i
$249$		0			0
$250$	2.49666	+	3.43636i	0.157903	+	0.217334i
$251$	−17.3557	−	5.63922i	−1.09548	−	0.355944i	−0.295121	−	0.955460i	$-0.595360\pi$
$251$	−17.3557	−	5.63922i	−1.09548	−	0.355944i	−0.800363	+	0.599516i	$0.795360\pi$
$252$		0			0
$253$	5.53713	+	0.229478i	0.348116	+	0.0144272i
$254$		−	8.07974i		−	0.506968i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.7065	+	16.1126i	−0.730232	+	1.00508i	0.268890	+	0.963171i	$0.413343\pi$
$257$	−11.7065	+	16.1126i	−0.730232	+	1.00508i	−0.999122	+	0.0419068i	$0.986657\pi$
$258$		0			0
$259$	−8.05905	+	2.61854i	−0.500765	+	0.162708i
$260$	0.495007	+	0.359644i	0.0306991	+	0.0223042i
$261$		0			0
$262$	0.204393	−	0.629058i	0.0126275	−	0.0388633i
$263$	−26.0303			−1.60510			−0.802548	−	0.596587i	$-0.796523\pi$
$263$	−26.0303			−1.60510			−0.802548	+	0.596587i	$0.796523\pi$
$264$		0			0
$265$	0.115542			0.00709771
$266$	−1.86201	+	5.73068i	−0.114167	+	0.351371i
$267$		0			0
$268$	0.550553	+	0.400000i	0.0336304	+	0.0244339i
$269$	16.5020	−	5.36184i	1.00615	−	0.326917i	0.240828	−	0.970568i	$-0.422581\pi$
$269$	16.5020	−	5.36184i	1.00615	−	0.326917i	0.765319	+	0.643651i	$0.222581\pi$
$270$		0			0
$271$	8.59960	−	11.8363i	0.522388	−	0.719006i	−0.463558	−	0.886066i	$-0.653428\pi$
$271$	8.59960	−	11.8363i	0.522388	−	0.719006i	0.985947	+	0.167060i	$0.0534275\pi$
$272$	0.585373	−	0.425298i	0.0354934	−	0.0257875i
$273$		0			0
$274$			11.4603i			0.692339i
$275$	−8.83928	−	13.2907i	−0.533028	−	0.801458i
$276$		0			0
$277$	−16.8262	−	5.46716i	−1.01099	−	0.328490i	−0.243740	−	0.969841i	$-0.578374\pi$
$277$	−16.8262	−	5.46716i	−1.01099	−	0.328490i	−0.767248	+	0.641351i	$0.778374\pi$
$278$	−4.78786	−	6.58993i	−0.287157	−	0.395238i
$279$		0			0
$280$	−0.133764	−	0.411682i	−0.00799391	−	0.0246027i
$281$	5.75319	+	17.7065i	0.343206	+	1.05628i	0.962537	+	0.271150i	$0.0874040\pi$
$281$	5.75319	+	17.7065i	0.343206	+	1.05628i	−0.619331	+	0.785130i	$0.712596\pi$
$282$		0			0
$283$	4.85988	+	6.68905i	0.288890	+	0.397623i	0.928653	−	0.370949i	$-0.120968\pi$
$283$	4.85988	+	6.68905i	0.288890	+	0.397623i	−0.639763	+	0.768572i	$0.720968\pi$
$284$	−2.38456	−	0.774789i	−0.141497	−	0.0459753i
$285$		0			0
$286$	−3.67538	−	2.91027i	−0.217330	−	0.172088i
$287$			1.67619i			0.0989424i
$288$		0			0
$289$	13.3297	−	9.68462i	0.784102	−	0.569684i
$290$	0.115490	−	0.158958i	0.00678181	−	0.00933436i
$291$		0			0
$292$	6.11629	−	1.98730i	0.357929	−	0.116298i
$293$	−0.229381	−	0.166655i	−0.0134006	−	0.00973611i	0.581065	−	0.813857i	$-0.302636\pi$
$293$	−0.229381	−	0.166655i	−0.0134006	−	0.00973611i	−0.594465	+	0.804121i	$0.702636\pi$
$294$		0			0
$295$	0.810272	−	2.49376i	0.0471759	−	0.145192i
$296$	−8.47379			−0.492529
$297$		0			0
$298$	−3.02015			−0.174952
$299$	−0.729863	+	2.24629i	−0.0422091	+	0.129906i
$300$		0			0
$301$	−4.47380	−	3.25040i	−0.257865	−	0.187350i
$302$	−18.9754	+	6.16548i	−1.09191	+	0.354783i
$303$		0			0
$304$	−3.54176	+	4.87481i	−0.203134	+	0.279589i
$305$	0.278725	−	0.202506i	0.0159598	−	0.0115954i
$306$		0			0
$307$			0.411509i			0.0234861i	0.999931	+	0.0117430i	$0.00373801\pi$
$307$			0.411509i			0.0234861i	−0.999931	+	0.0117430i	$0.996262\pi$
$308$	0.893401	+	3.19403i	0.0509063	+	0.181997i
$309$		0			0
$310$	2.66282	+	0.865202i	0.151238	+	0.0491402i
$311$	1.85839	+	2.55785i	0.105379	+	0.145042i	0.858450	−	0.512898i	$-0.171428\pi$
$311$	1.85839	+	2.55785i	0.105379	+	0.145042i	−0.753070	+	0.657940i	$0.771428\pi$
$312$		0			0
$313$	−3.40476	−	10.4788i	−0.192449	−	0.592296i	−0.999997	−	0.00249427i	$-0.999206\pi$
$313$	−3.40476	−	10.4788i	−0.192449	−	0.592296i	0.807548	−	0.589801i	$-0.200794\pi$
$314$	−1.55542	−	4.78708i	−0.0877773	−	0.270151i
$315$		0			0
$316$	3.65232	+	5.02698i	0.205459	+	0.282790i
$317$	−17.3329	−	5.63180i	−0.973513	−	0.316314i	−0.221280	−	0.975210i	$-0.571023\pi$
$317$	−17.3329	−	5.63180i	−0.973513	−	0.316314i	−0.752233	+	0.658897i	$0.771023\pi$
$318$		0			0
$319$	−0.934555	+	1.18025i	−0.0523250	+	0.0660813i
$320$		−	0.432868i		−	0.0241981i
$321$		0			0
$322$	1.35182	−	0.982154i	0.0753339	−	0.0547333i
$323$	2.56267	−	3.52722i	0.142591	−	0.196260i
$324$		0			0
$325$	6.46974	−	2.10214i	0.358876	−	0.116606i
$326$	1.65164	+	1.19999i	0.0914759	+	0.0664612i
$327$		0			0
$328$	−0.517971	+	1.59415i	−0.0286002	+	0.0880223i
$329$	−4.91094			−0.270749
$330$		0			0
$331$	−2.59659			−0.142722			−0.0713609	−	0.997451i	$-0.522734\pi$
$331$	−2.59659			−0.142722			−0.0713609	+	0.997451i	$0.522734\pi$
$332$	1.83539	−	5.64875i	0.100730	−	0.310015i
$333$		0			0
$334$	19.4844	+	14.1562i	1.06614	+	0.774594i
$335$	−0.280158	+	0.0910289i	−0.0153067	+	0.00497344i
$336$		0			0
$337$	3.58518	−	4.93458i	0.195297	−	0.268804i	−0.700126	−	0.714019i	$-0.746873\pi$
$337$	3.58518	−	4.93458i	0.195297	−	0.268804i	0.895424	+	0.445215i	$0.146873\pi$
$338$	−8.90080	+	6.46681i	−0.484140	+	0.351748i
$339$		0			0
$340$			0.313206i			0.0169860i
$341$	−20.1104	−	7.46829i	−1.08904	−	0.404431i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$	−3.25040	−	4.47380i	−0.175250	−	0.241211i
$345$		0			0
$346$	−1.70340	−	5.24251i	−0.0915751	−	0.281839i
$347$	4.58888	+	14.1231i	0.246344	+	0.758170i	0.995412	+	0.0956767i	$0.0305015\pi$
$347$	4.58888	+	14.1231i	0.246344	+	0.758170i	−0.749068	+	0.662493i	$0.769498\pi$
$348$		0			0
$349$	1.87477	+	2.58040i	0.100354	+	0.138126i	0.856241	−	0.516577i	$-0.172794\pi$
$349$	1.87477	+	2.58040i	0.100354	+	0.138126i	−0.755887	+	0.654702i	$0.772794\pi$
$350$	−4.57708	−	1.48718i	−0.244655	−	0.0794933i
$351$		0			0
$352$	−0.137335	+	3.31378i	−0.00731998	+	0.176625i
$353$		−	31.8777i		−	1.69668i	−0.529451	−	0.848340i	$-0.677602\pi$
$353$		−	31.8777i		−	1.69668i	0.529451	−	0.848340i	$-0.322398\pi$
$354$		0			0
$355$	0.878040	−	0.637934i	0.0466015	−	0.0338580i
$356$	−5.12533	+	7.05441i	−0.271642	+	0.373883i
$357$		0			0
$358$	1.93096	−	0.627407i	0.102054	−	0.0331595i
$359$	23.0617	+	16.7553i	1.21715	+	0.884310i	0.995860	−	0.0908985i	$-0.0289739\pi$
$359$	23.0617	+	16.7553i	1.21715	+	0.884310i	0.221288	+	0.975208i	$0.428974\pi$
$360$		0			0
$361$	−5.34840	+	16.4607i	−0.281495	+	0.866352i
$362$	7.68552			0.403942
$363$		0			0
$364$	−1.41351			−0.0740879
$365$	−0.860241	+	2.64755i	−0.0450271	+	0.138579i
$366$		0			0
$367$	21.5805	+	15.6791i	1.12649	+	0.818444i	0.985180	−	0.171522i	$-0.0548684\pi$
$367$	21.5805	+	15.6791i	1.12649	+	0.818444i	0.141311	+	0.989965i	$0.454868\pi$
$368$	1.58916	−	0.516349i	0.0828406	−	0.0269165i
$369$		0			0
$370$	2.15602	−	2.96750i	0.112086	−	0.154273i
$371$	−0.215945	+	0.156893i	−0.0112113	+	0.00814548i
$372$		0			0
$373$			1.51648i			0.0785203i	0.999229	+	0.0392601i	$0.0125001\pi$
$373$			1.51648i			0.0785203i	−0.999229	+	0.0392601i	$0.987500\pi$
$374$	0.0993701	−	2.39772i	0.00513831	−	0.123983i
$375$		0			0
$376$	−4.67058	−	1.51756i	−0.240867	−	0.0782624i
$377$	−0.377127	−	0.519070i	−0.0194230	−	0.0267335i
$378$		0			0
$379$	−8.55457	−	26.3283i	−0.439419	−	1.35239i	−0.888490	−	0.458896i	$-0.848245\pi$
$379$	−8.55457	−	26.3283i	−0.439419	−	1.35239i	0.449071	−	0.893496i	$-0.351755\pi$
$380$	−0.806006	−	2.48063i	−0.0413472	−	0.127254i
$381$		0			0
$382$	−10.2920	−	14.1658i	−0.526586	−	0.724783i
$383$	6.47940	+	2.10529i	0.331082	+	0.107575i	0.469841	−	0.882751i	$-0.344311\pi$
$383$	6.47940	+	2.10529i	0.331082	+	0.107575i	−0.138759	+	0.990326i	$0.544311\pi$
$384$		0			0
$385$	−1.34585	−	0.499802i	−0.0685911	−	0.0254723i
$386$			12.8709i			0.655113i
$387$		0			0
$388$	13.9245	−	10.1168i	0.706911	−	0.513601i
$389$	−2.47189	+	3.40227i	−0.125330	+	0.172502i	−0.867071	−	0.498184i	$-0.834000\pi$
$389$	−2.47189	+	3.40227i	−0.125330	+	0.172502i	0.741741	+	0.670686i	$0.234000\pi$
$390$		0			0
$391$	−1.14985	+	0.373609i	−0.0581505	+	0.0188942i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$		0			0
$394$	−7.88595	+	24.2704i	−0.397288	+	1.22273i
$395$	−2.68971			−0.135334
$396$		0			0
$397$	9.52539			0.478066			0.239033	−	0.971011i	$-0.423170\pi$
$397$	9.52539			0.478066			0.239033	+	0.971011i	$0.423170\pi$
$398$	7.36341	−	22.6623i	0.369095	−	1.13596i
$399$		0			0
$400$	−3.89350	−	2.82879i	−0.194675	−	0.141440i
$401$	3.19807	−	1.03912i	0.159704	−	0.0518910i	−0.228074	−	0.973644i	$-0.573243\pi$
$401$	3.19807	−	1.03912i	0.159704	−	0.0518910i	0.387778	+	0.921753i	$0.373243\pi$
$402$		0			0
$403$	5.37398	−	7.39665i	0.267697	−	0.368454i
$404$	−10.8485	+	7.88192i	−0.539735	+	0.392140i
$405$		0			0
$406$			0.453910i			0.0225272i
$407$	−17.4467	+	22.0334i	−0.864799	+	1.09215i
$408$		0			0
$409$	−4.23090	−	1.37470i	−0.209205	−	0.0679747i	0.202540	−	0.979274i	$-0.435080\pi$
$409$	−4.23090	−	1.37470i	−0.209205	−	0.0679747i	−0.411745	+	0.911299i	$0.635080\pi$
$410$	−0.426479	−	0.586998i	−0.0210623	−	0.0289898i
$411$		0			0
$412$	−4.90269	−	15.0889i	−0.241538	−	0.743378i
$413$	1.87187	+	5.76102i	0.0921086	+	0.283481i
$414$		0			0
$415$	1.51120	+	2.07998i	0.0741817	+	0.102102i
$416$	−1.34433	−	0.436798i	−0.0659110	−	0.0214158i
$417$		0			0
$418$	5.38327	+	19.2459i	0.263304	+	0.941349i
$419$		−	4.97536i		−	0.243062i	−0.992588	−	0.121531i	$-0.961220\pi$
$419$		−	4.97536i		−	0.243062i	0.992588	−	0.121531i	$-0.0387804\pi$
$420$		0			0
$421$	−18.6425	+	13.5445i	−0.908578	+	0.660120i	−0.940655	−	0.339365i	$-0.889788\pi$
$421$	−18.6425	+	13.5445i	−0.908578	+	0.660120i	0.0320770	+	0.999485i	$0.489788\pi$
$422$	−11.7626	+	16.1898i	−0.572592	+	0.788105i
$423$		0			0
$424$	−0.253858	+	0.0824836i	−0.0123285	+	0.00400576i
$425$	2.81718	+	2.04680i	0.136653	+	0.0992844i
$426$		0			0
$427$	−0.245949	+	0.756954i	−0.0119023	+	0.0366315i
$428$	−9.36137			−0.452499
$429$		0			0
$430$	2.39373			0.115436
$431$	−2.91841	+	8.98193i	−0.140575	+	0.432644i	−0.996415	−	0.0845951i	$-0.973040\pi$
$431$	−2.91841	+	8.98193i	−0.140575	+	0.432644i	0.855841	+	0.517239i	$0.173040\pi$
$432$		0			0
$433$	20.3932	+	14.8165i	0.980036	+	0.712038i	0.957717	−	0.287713i	$-0.0928949\pi$
$433$	20.3932	+	14.8165i	0.980036	+	0.712038i	0.0223195	+	0.999751i	$0.492895\pi$
$434$	−6.15157	+	1.99876i	−0.295285	+	0.0959438i
$435$		0			0
$436$	4.09972	−	5.64277i	0.196341	−	0.270240i
$437$	8.14551	−	5.91806i	0.389653	−	0.283099i
$438$		0			0
$439$		−	8.31162i		−	0.396692i	−0.980132	−	0.198346i	$-0.936443\pi$
$439$		−	8.31162i		−	0.396692i	0.980132	−	0.198346i	$-0.0635569\pi$
$440$	−1.12554	−	0.891231i	−0.0536578	−	0.0424878i
$441$		0			0
$442$	0.972701	+	0.316050i	0.0462667	+	0.0150330i
$443$	6.24221	+	8.59167i	0.296577	+	0.408203i	0.931136	−	0.364671i	$-0.118819\pi$
$443$	6.24221	+	8.59167i	0.296577	+	0.408203i	−0.634560	+	0.772874i	$0.718819\pi$
$444$		0			0
$445$	−1.16638	−	3.58976i	−0.0552919	−	0.170171i
$446$	−4.61943	−	14.2171i	−0.218736	−	0.673201i
$447$		0			0
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	−27.5740	−	8.95934i	−1.30130	−	0.422817i	−0.425265	−	0.905069i	$-0.639819\pi$
$449$	−27.5740	−	8.95934i	−1.30130	−	0.422817i	−0.876033	+	0.482251i	$0.839819\pi$
$450$		0			0
$451$	3.07863	+	4.62902i	0.144967	+	0.217972i
$452$		−	4.64122i		−	0.218305i
$453$		0			0
$454$	−9.53312	+	6.92622i	−0.447412	+	0.325064i
$455$	0.359644	−	0.495007i	0.0168604	−	0.0232063i
$456$		0			0
$457$	−21.0294	+	6.83285i	−0.983712	+	0.319627i	−0.756339	−	0.654180i	$-0.773014\pi$
$457$	−21.0294	+	6.83285i	−0.983712	+	0.319627i	−0.227373	+	0.973808i	$0.573014\pi$
$458$	7.07753	+	5.14213i	0.330711	+	0.240276i
$459$		0			0
$460$	−0.223511	+	0.687896i	−0.0104213	+	0.0320733i
$461$	−4.48889			−0.209069			−0.104534	−	0.994521i	$-0.533335\pi$
$461$	−4.48889			−0.209069			−0.104534	+	0.994521i	$0.533335\pi$
$462$		0			0
$463$	25.6417			1.19167			0.595836	−	0.803106i	$-0.296821\pi$
$463$	25.6417			1.19167			0.595836	+	0.803106i	$0.296821\pi$
$464$	−0.140266	+	0.431695i	−0.00651169	+	0.0200409i
$465$		0			0
$466$	−16.8765	−	12.2615i	−0.781790	−	0.568004i
$467$	15.9208	−	5.17297i	0.736725	−	0.239377i	0.0834657	−	0.996511i	$-0.473401\pi$
$467$	15.9208	−	5.17297i	0.736725	−	0.239377i	0.653259	+	0.757134i	$0.273401\pi$
$468$		0			0
$469$	0.400000	−	0.550553i	0.0184703	−	0.0254222i
$470$	1.71980	−	1.24951i	0.0793285	−	0.0576355i
$471$		0			0
$472$			6.05749i			0.278819i
$473$	−18.3249	−	0.759451i	−0.842581	−	0.0349196i
$474$		0			0
$475$	−27.5796	−	8.96116i	−1.26544	−	0.411166i
$476$	−0.425298	−	0.585373i	−0.0194935	−	0.0268305i
$477$		0			0
$478$	3.22680	+	9.93107i	0.147590	+	0.454237i
$479$	−0.397877	−	1.22454i	−0.0181795	−	0.0559506i	0.941555	−	0.336859i	$-0.109364\pi$
$479$	−0.397877	−	1.22454i	−0.0181795	−	0.0559506i	−0.959735	+	0.280908i	$0.909364\pi$
$480$		0			0
$481$	−7.04036	−	9.69022i	−0.321013	−	0.441836i
$482$	9.50108	+	3.08709i	0.432762	+	0.140613i
$483$		0			0
$484$	8.33367	+	7.17983i	0.378803	+	0.326356i
$485$			7.45039i			0.338305i
$486$		0			0
$487$	21.1248	−	15.3481i	0.957258	−	0.695488i	0.00474544	−	0.999989i	$-0.498489\pi$
$487$	21.1248	−	15.3481i	0.957258	−	0.695488i	0.952512	+	0.304500i	$0.0984895\pi$
$488$	−0.467823	+	0.643903i	−0.0211774	+	0.0291481i
$489$		0			0
$490$	−0.411682	+	0.133764i	−0.0185979	+	0.00604283i
$491$	34.1694	+	24.8255i	1.54204	+	1.12036i	0.949037	+	0.315164i	$0.102059\pi$
$491$	34.1694	+	24.8255i	1.54204	+	1.12036i	0.593007	+	0.805197i	$0.297941\pi$
$492$		0			0
$493$	0.101491	−	0.312357i	0.00457092	−	0.0140679i
$494$	−8.51723			−0.383208
$495$		0			0
$496$	−6.46814			−0.290428
$497$	−0.774789	+	2.38456i	−0.0347540	+	0.106962i
$498$		0			0
$499$	13.0478	+	9.47979i	0.584100	+	0.424373i	0.840200	−	0.542277i	$-0.182438\pi$
$499$	13.0478	+	9.47979i	0.584100	+	0.424373i	−0.256100	+	0.966650i	$0.582438\pi$
$500$	4.03968	−	1.31257i	0.180660	−	0.0587000i
$501$		0			0
$502$	−10.7264	+	14.7637i	−0.478744	+	0.658934i
$503$	−4.09915	+	2.97821i	−0.182772	+	0.132792i	−0.675409	−	0.737443i	$-0.736033\pi$
$503$	−4.09915	+	2.97821i	−0.182772	+	0.132792i	0.492637	+	0.870235i	$0.336033\pi$
$504$		0			0
$505$		−	5.80456i		−	0.258299i
$506$	1.92931	−	5.19521i	0.0857684	−	0.230955i
$507$		0			0
$508$	−7.68429	−	2.49678i	−0.340935	−	0.110777i
$509$	3.81131	+	5.24582i	0.168933	+	0.232517i	0.885087	−	0.465426i	$-0.154099\pi$
$509$	3.81131	+	5.24582i	0.168933	+	0.232517i	−0.716153	+	0.697943i	$0.754099\pi$
$510$		0			0
$511$	−1.98730	−	6.11629i	−0.0879131	−	0.270569i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	11.7065	+	16.1126i	0.516352	+	0.710697i
$515$	6.53152	+	2.12222i	0.287813	+	0.0935162i
$516$		0			0
$517$	−13.5622	+	9.01985i	−0.596465	+	0.396693i
$518$			8.47379i			0.372317i
$519$		0			0
$520$	0.495007	−	0.359644i	0.0217075	−	0.0157714i
$521$	19.0136	−	26.1700i	0.833002	−	1.14653i	−0.154354	−	0.988016i	$-0.549330\pi$
$521$	19.0136	−	26.1700i	0.833002	−	1.14653i	0.987357	−	0.158514i	$-0.0506703\pi$
$522$		0			0
$523$	15.0501	−	4.89008i	0.658096	−	0.213828i	0.0391156	−	0.999235i	$-0.487546\pi$
$523$	15.0501	−	4.89008i	0.658096	−	0.213828i	0.618981	+	0.785406i	$0.287546\pi$
$524$	−0.535109	−	0.388779i	−0.0233763	−	0.0169839i
$525$		0			0
$526$	−8.04380	+	24.7563i	−0.350727	+	1.07943i
$527$	4.68009			0.203868
$528$		0			0
$529$	20.2080			0.878607
$530$	0.0357045	−	0.109887i	0.00155091	−	0.00477320i
$531$		0			0
$532$	4.87481	+	3.54176i	0.211350	+	0.153555i
$533$	−2.25335	+	0.732157i	−0.0976033	+	0.0317132i
$534$		0			0
$535$	2.38185	−	3.27833i	0.102976	−	0.141735i
$536$	0.550553	−	0.400000i	0.0237803	−	0.0172774i
$537$		0			0
$538$		−	17.3513i		−	0.748067i
$539$	3.19403	−	0.893401i	0.137577	−	0.0384815i
$540$		0			0
$541$	−15.1162	−	4.91155i	−0.649897	−	0.211164i	−0.0345281	−	0.999404i	$-0.510993\pi$
$541$	−15.1162	−	4.91155i	−0.649897	−	0.211164i	−0.615369	+	0.788240i	$0.710993\pi$
$542$	−8.59960	−	11.8363i	−0.369384	−	0.508414i
$543$		0			0
$544$	−0.223592	−	0.688147i	−0.00958645	−	0.0295041i
$545$	0.932982	+	2.87142i	0.0399646	+	0.122998i
$546$		0			0
$547$	−27.3534	−	37.6488i	−1.16955	−	1.60975i	−0.666556	−	0.745455i	$-0.732232\pi$
$547$	−27.3534	−	37.6488i	−1.16955	−	1.60975i	−0.502992	−	0.864291i	$-0.667768\pi$
$548$	10.8993	+	3.54141i	0.465597	+	0.151282i
$549$		0			0
$550$	−15.3717	+	4.29960i	−0.655450	+	0.183336i
$551$			2.73508i			0.116518i
$552$		0			0
$553$	5.02698	−	3.65232i	0.213769	−	0.155312i
$554$	−10.3992	+	14.3132i	−0.441818	+	0.608110i
$555$		0			0
$556$	−7.74693	+	2.51713i	−0.328543	+	0.106750i
$557$	−13.8514	−	10.0636i	−0.586903	−	0.426410i	0.254303	−	0.967124i	$-0.418154\pi$
$557$	−13.8514	−	10.0636i	−0.586903	−	0.426410i	−0.841206	+	0.540715i	$0.818154\pi$
$558$		0			0
$559$	2.41546	−	7.43401i	0.102163	−	0.314425i
$560$	−0.432868			−0.0182920
$561$		0			0
$562$	18.6177			0.785340
$563$	13.8929	−	42.7580i	0.585517	−	1.80204i	−0.0116659	−	0.999932i	$-0.503713\pi$
$563$	13.8929	−	42.7580i	0.585517	−	1.80204i	0.597183	−	0.802105i	$-0.296287\pi$
$564$		0			0
$565$	1.62535	+	1.18088i	0.0683788	+	0.0496801i
$566$	7.86345	−	2.55499i	0.330526	−	0.107394i
$567$		0			0
$568$	−1.47374	+	2.02842i	−0.0618366	+	0.0851108i
$569$	22.0315	−	16.0068i	0.923610	−	0.671042i	−0.0208100	−	0.999783i	$-0.506625\pi$
$569$	22.0315	−	16.0068i	0.923610	−	0.671042i	0.944420	+	0.328742i	$0.106625\pi$
$570$		0			0
$571$		−	14.0092i		−	0.586269i	−0.956071	−	0.293134i	$-0.905302\pi$
$571$		−	14.0092i		−	0.586269i	0.956071	−	0.293134i	$-0.0946983\pi$
$572$	−3.90358	+	2.59617i	−0.163217	+	0.108551i
$573$		0			0
$574$	1.59415	+	0.517971i	0.0665386	+	0.0216197i
$575$	4.72674	+	6.50580i	0.197119	+	0.271310i
$576$		0			0
$577$	−0.965705	−	2.97213i	−0.0402028	−	0.123732i	0.928941	−	0.370228i	$-0.120721\pi$
$577$	−0.965705	−	2.97213i	−0.0402028	−	0.123732i	−0.969144	+	0.246497i	$0.920721\pi$
$578$	−5.09151	−	15.6700i	−0.211779	−	0.651788i
$579$		0			0
$580$	−0.115490	−	0.158958i	−0.00479546	−	0.00660039i
$581$	−5.64875	−	1.83539i	−0.234350	−	0.0761448i
$582$		0			0
$583$	−0.308196	+	0.829903i	−0.0127642	+	0.0343711i
$584$		−	6.43105i		−	0.266119i
$585$		0			0
$586$	−0.229381	+	0.166655i	−0.00947566	+	0.00688447i
$587$	−17.4626	+	24.0352i	−0.720758	+	0.992038i	0.278741	+	0.960366i	$0.410083\pi$
$587$	−17.4626	+	24.0352i	−0.720758	+	0.992038i	−0.999498	+	0.0316714i	$0.989917\pi$
$588$		0			0
$589$	−37.0668	+	12.0437i	−1.52731	+	0.496254i
$590$	−2.12132	−	1.54123i	−0.0873334	−	0.0634514i
$591$		0			0
$592$	−2.61854	+	8.05905i	−0.107622	+	0.331225i
$593$	29.5395			1.21304			0.606520	−	0.795068i	$-0.292565\pi$
$593$	29.5395			1.21304			0.606520	+	0.795068i	$0.292565\pi$
$594$		0			0
$595$	0.313206			0.0128402
$596$	−0.933277	+	2.87233i	−0.0382285	+	0.117655i
$597$		0			0
$598$	1.91081	+	1.38828i	0.0781387	+	0.0567711i
$599$	22.7385	−	7.38820i	0.929071	−	0.301873i	0.194888	−	0.980825i	$-0.437566\pi$
$599$	22.7385	−	7.38820i	0.929071	−	0.301873i	0.734183	+	0.678952i	$0.237566\pi$
$600$		0			0
$601$	18.1447	−	24.9741i	0.740139	−	1.01871i	−0.258472	−	0.966019i	$-0.583219\pi$
$601$	18.1447	−	24.9741i	0.740139	−	1.01871i	0.998611	−	0.0526947i	$-0.0167810\pi$
$602$	−4.47380	+	3.25040i	−0.182338	+	0.132477i
$603$		0			0
$604$			19.9519i			0.811831i
$605$	−4.63473	+	1.09164i	−0.188428	+	0.0443816i
$606$		0			0
$607$	−22.5264	−	7.31929i	−0.914320	−	0.297081i	−0.186185	−	0.982515i	$-0.559613\pi$
$607$	−22.5264	−	7.31929i	−0.914320	−	0.297081i	−0.728135	+	0.685434i	$0.759613\pi$
$608$	3.54176	+	4.87481i	0.143637	+	0.197700i
$609$		0			0
$610$	−0.106464	−	0.327661i	−0.00431058	−	0.0132666i
$611$	−2.14509	−	6.60191i	−0.0867810	−	0.267085i
$612$		0			0
$613$	7.47583	+	10.2896i	0.301946	+	0.415593i	0.932848	−	0.360269i	$-0.117315\pi$
$613$	7.47583	+	10.2896i	0.301946	+	0.415593i	−0.630902	+	0.775862i	$0.717315\pi$
$614$	0.391369	+	0.127163i	0.0157943	+	0.00513190i
$615$		0			0
$616$	3.31378	+	0.137335i	0.133516	+	0.00553338i
$617$			1.34982i			0.0543416i	0.999631	+	0.0271708i	$0.00864980\pi$
$617$			1.34982i			0.0543416i	−0.999631	+	0.0271708i	$0.991350\pi$
$618$		0			0
$619$	27.5292	−	20.0011i	1.10649	−	0.803913i	0.124384	−	0.992234i	$-0.460304\pi$
$619$	27.5292	−	20.0011i	1.10649	−	0.803913i	0.982108	+	0.188321i	$0.0603045\pi$
$620$	1.64571	−	2.26513i	0.0660934	−	0.0909697i
$621$		0			0
$622$	3.00693	−	0.977011i	0.120567	−	0.0391746i
$623$	7.05441	+	5.12533i	0.282629	+	0.205342i
$624$		0			0
$625$	6.86774	−	21.1367i	0.274710	−	0.845470i
$626$	−11.0180			−0.440369
$627$		0			0
$628$	−5.03344			−0.200856
$629$	1.89468	−	5.83121i	0.0755457	−	0.232506i
$630$		0			0
$631$	6.72906	+	4.88895i	0.267880	+	0.194626i	0.713614	−	0.700540i	$-0.247057\pi$
$631$	6.72906	+	4.88895i	0.267880	+	0.194626i	−0.445734	+	0.895165i	$0.647057\pi$
$632$	5.90957	−	1.92014i	0.235070	−	0.0763789i
$633$		0			0
$634$	−10.7123	+	14.7443i	−0.425441	+	0.585569i
$635$	2.82951	−	2.05576i	0.112286	−	0.0815802i
$636$		0			0
$637$			1.41351i			0.0560052i
$638$	0.833690	+	1.25353i	0.0330061	+	0.0496278i
$639$		0			0
$640$	−0.411682	−	0.133764i	−0.0162732	−	0.00528747i
$641$	24.8703	+	34.2311i	0.982319	+	1.35205i	0.935570	+	0.353140i	$0.114886\pi$
$641$	24.8703	+	34.2311i	0.982319	+	1.35205i	0.0467490	+	0.998907i	$0.485114\pi$
$642$		0			0
$643$	5.24494	+	16.1423i	0.206840	+	0.636589i	0.999633	+	0.0270972i	$0.00862637\pi$
$643$	5.24494	+	16.1423i	0.206840	+	0.636589i	−0.792793	+	0.609492i	$0.791374\pi$
$644$	−0.516349	−	1.58916i	−0.0203470	−	0.0626216i
$645$		0			0
$646$	−2.56267	−	3.52722i	−0.100827	−	0.138777i
$647$	31.9166	+	10.3703i	1.25477	+	0.407700i	0.859629	−	0.510919i	$-0.170695\pi$
$647$	31.9166	+	10.3703i	1.25477	+	0.407700i	0.395144	+	0.918619i	$0.370695\pi$
$648$		0			0
$649$	15.7506	+	12.4718i	0.618264	+	0.489559i
$650$		−	6.80268i		−	0.266823i
$651$		0			0
$652$	1.65164	−	1.19999i	0.0646833	−	0.0469951i
$653$	27.6582	−	38.0683i	1.08235	−	1.48973i	0.225444	−	0.974256i	$-0.427617\pi$
$653$	27.6582	−	38.0683i	1.08235	−	1.48973i	0.856906	−	0.515472i	$-0.172383\pi$
$654$		0			0
$655$	0.272299	−	0.0884754i	0.0106396	−	0.00345702i
$656$	1.35607	+	0.985240i	0.0529455	+	0.0384672i
$657$		0			0
$658$	−1.51756	+	4.67058i	−0.0591608	+	0.182078i
$659$	45.5121			1.77290			0.886449	−	0.462826i	$-0.153164\pi$
$659$	45.5121			1.77290			0.886449	+	0.462826i	$0.153164\pi$
$660$		0			0
$661$	5.59604			0.217661			0.108830	−	0.994060i	$-0.465289\pi$
$661$	5.59604			0.217661			0.108830	+	0.994060i	$0.465289\pi$
$662$	−0.802392	+	2.46951i	−0.0311858	+	0.0959801i
$663$		0			0
$664$	−4.80511	−	3.49112i	−0.186475	−	0.135482i
$665$	−2.48063	+	0.806006i	−0.0961947	+	0.0312556i
$666$		0			0
$667$	0.445810	−	0.613605i	0.0172618	−	0.0237589i
$668$	19.4844	−	14.1562i	0.753873	−	0.547721i
$669$		0			0
$670$			0.294576i			0.0113805i
$671$	0.711065	+	2.54216i	0.0274504	+	0.0981388i
$672$		0			0
$673$	−20.4493	−	6.64438i	−0.788262	−	0.256122i	−0.112898	−	0.993607i	$-0.536013\pi$
$673$	−20.4493	−	6.64438i	−0.788262	−	0.256122i	−0.675364	+	0.737485i	$0.736013\pi$
$674$	−3.58518	−	4.93458i	−0.138096	−	0.190073i
$675$		0			0
$676$	3.39980	+	10.4635i	0.130762	+	0.402443i
$677$	3.38945	+	10.4317i	0.130267	+	0.400922i	0.994824	−	0.101614i	$-0.0324006\pi$
$677$	3.38945	+	10.4317i	0.130267	+	0.400922i	−0.864557	+	0.502535i	$0.832401\pi$
$678$		0			0
$679$	−10.1168	−	13.9245i	−0.388246	−	0.534375i
$680$	0.297877	+	0.0967861i	0.0114231	+	0.00371158i
$681$		0			0
$682$	−13.3172	+	16.8183i	−0.509943	+	0.644007i
$683$			27.7384i			1.06138i	0.847566	+	0.530690i	$0.178067\pi$
$683$			27.7384i			1.06138i	−0.847566	+	0.530690i	$0.821933\pi$
$684$		0			0
$685$	−4.01336	+	2.91587i	−0.153342	+	0.111410i
$686$	0.587785	−	0.809017i	0.0224417	−	0.0308884i
$687$		0			0
$688$	−5.25926	+	1.70884i	−0.200508	+	0.0651488i
$689$	−0.305240	−	0.221770i	−0.0116287	−	0.00844875i
$690$		0			0
$691$	−4.49473	+	13.8333i	−0.170987	+	0.526245i	−0.999428	−	0.0338325i	$-0.989229\pi$
$691$	−4.49473	+	13.8333i	−0.170987	+	0.526245i	0.828440	+	0.560078i	$0.189229\pi$
$692$	−5.51230			−0.209546
$693$		0			0
$694$	14.8499			0.563696
$695$	1.08959	−	3.35340i	0.0413303	−	0.127202i
$696$		0			0
$697$	−0.981196	−	0.712881i	−0.0371655	−	0.0270023i
$698$	3.03344	−	0.985625i	0.114817	−	0.0373065i
$699$		0			0
$700$	−2.82879	+	3.89350i	−0.106918	+	0.147160i
$701$	8.97681	−	6.52203i	0.339049	−	0.246334i	−0.405211	−	0.914223i	$-0.632802\pi$
$701$	8.97681	−	6.52203i	0.339049	−	0.246334i	0.744261	+	0.667889i	$0.232802\pi$
$702$		0			0
$703$			51.0596i			1.92575i
$704$	3.10915	+	1.15463i	0.117181	+	0.0435167i
$705$		0			0
$706$	−30.3175	−	9.85076i	−1.14102	−	0.370738i
$707$	7.88192	+	10.8485i	0.296430	+	0.408001i
$708$		0			0
$709$	2.32213	+	7.14677i	0.0872093	+	0.268403i	0.985145	−	0.171724i	$-0.0549337\pi$
$709$	2.32213	+	7.14677i	0.0872093	+	0.268403i	−0.897936	+	0.440126i	$0.854934\pi$
$710$	−0.335382	−	1.03220i	−0.0125866	−	0.0387377i
$711$		0			0
$712$	5.12533	+	7.05441i	0.192080	+	0.264375i
$713$	10.2789	+	3.33982i	0.384948	+	0.125077i
$714$		0			0
$715$	0.0840302	−	2.02758i	0.00314255	−	0.0758272i
$716$		−	2.03033i		−	0.0758771i
$717$		0			0
$718$	23.0617	−	16.7553i	0.860654	−	0.625302i
$719$	20.6497	−	28.4218i	0.770103	−	1.05996i	−0.226203	−	0.974080i	$-0.572631\pi$
$719$	20.6497	−	28.4218i	0.770103	−	1.05996i	0.996306	−	0.0858754i	$-0.0273687\pi$
$720$		0			0
$721$	−15.0889	+	4.90269i	−0.561941	+	0.182586i
$722$	14.0023	+	10.1733i	0.521111	+	0.378610i
$723$		0			0
$724$	2.37496	−	7.30936i	0.0882645	−	0.271650i
$725$	−2.18450			−0.0811303
$726$		0			0
$727$	38.3016			1.42053			0.710264	−	0.703936i	$-0.248576\pi$
$727$	38.3016			1.42053			0.710264	+	0.703936i	$0.248576\pi$
$728$	−0.436798	+	1.34433i	−0.0161888	+	0.0498240i
$729$		0			0
$730$	2.25214	+	1.63628i	0.0833554	+	0.0605613i
$731$	3.80539	−	1.23645i	0.140748	−	0.0457317i
$732$		0			0
$733$	−2.65944	+	3.66041i	−0.0982287	+	0.135200i	−0.855302	−	0.518130i	$-0.826628\pi$
$733$	−2.65944	+	3.66041i	−0.0982287	+	0.135200i	0.757073	+	0.653330i	$0.226628\pi$
$734$	21.5805	−	15.6791i	0.796549	−	0.578727i
$735$		0			0
$736$		−	1.67094i		−	0.0615916i
$737$	0.0934593	−	2.25510i	0.00344262	−	0.0830675i
$738$		0			0
$739$	−4.40476	−	1.43119i	−0.162032	−	0.0526473i	0.226878	−	0.973923i	$-0.427148\pi$
$739$	−4.40476	−	1.43119i	−0.162032	−	0.0526473i	−0.388910	+	0.921276i	$0.627148\pi$
$740$	−2.15602	−	2.96750i	−0.0792568	−	0.109088i
$741$		0			0
$742$	0.0824836	+	0.253858i	0.00302807	+	0.00931943i
$743$	1.84992	+	5.69348i	0.0678671	+	0.208873i	0.979239	−	0.202712i	$-0.0649754\pi$
$743$	1.84992	+	5.69348i	0.0678671	+	0.208873i	−0.911371	+	0.411585i	$0.864975\pi$
$744$		0			0
$745$	−0.768427	−	1.05765i	−0.0281530	−	0.0387493i
$746$	1.44226	+	0.468618i	0.0528048	+	0.0171573i
$747$		0			0
$748$	−2.24966	−	0.835443i	−0.0822557	−	0.0305468i
$749$			9.36137i			0.342057i
$750$		0			0
$751$	24.1411	−	17.5395i	0.880920	−	0.640026i	−0.0525747	−	0.998617i	$-0.516743\pi$
$751$	24.1411	−	17.5395i	0.880920	−	0.640026i	0.933495	+	0.358591i	$0.116743\pi$
$752$	−2.88658	+	3.97304i	−0.105263	+	0.144882i
$753$		0			0
$754$	−0.610204	+	0.198267i	−0.0222223	+	0.00722046i
$755$	−6.98711	−	5.07643i	−0.254287	−	0.184750i
$756$		0			0
$757$	−2.05610	+	6.32803i	−0.0747303	+	0.229996i	−0.981443	−	0.191752i	$-0.938583\pi$
$757$	−2.05610	+	6.32803i	−0.0747303	+	0.229996i	0.906713	+	0.421748i	$0.138583\pi$
$758$	−27.6832			−1.00550
$759$		0			0
$760$	−2.60829			−0.0946126
$761$	15.8365	−	48.7399i	0.574074	−	1.76682i	−0.0652354	−	0.997870i	$-0.520780\pi$
$761$	15.8365	−	48.7399i	0.574074	−	1.76682i	0.639310	−	0.768949i	$-0.279220\pi$
$762$		0			0
$763$	−5.64277	−	4.09972i	−0.204282	−	0.148420i
$764$	−16.6528	+	5.41084i	−0.602479	+	0.195757i
$765$		0			0
$766$	4.00449	−	5.51171i	0.144688	−	0.199146i
$767$	−6.92705	+	5.03280i	−0.250121	+	0.181724i
$768$		0			0
$769$			40.5398i			1.46190i	0.682430	+	0.730951i	$0.260923\pi$
$769$			40.5398i			1.46190i	−0.682430	+	0.730951i	$0.739077\pi$
$770$	−0.891231	+	1.12554i	−0.0321178	+	0.0405615i
$771$		0			0
$772$	12.2410	+	3.97734i	0.440563	+	0.143148i
$773$	29.1039	+	40.0581i	1.04680	+	1.44079i	0.891554	+	0.452914i	$0.149616\pi$
$773$	29.1039	+	40.0581i	1.04680	+	1.44079i	0.155242	+	0.987876i	$0.450384\pi$
$774$		0			0
$775$	−9.61931	−	29.6052i	−0.345536	−	1.06345i
$776$	−5.31870	−	16.3693i	−0.190930	−	0.587623i
$777$		0			0
$778$	2.47189	+	3.40227i	0.0886216	+	0.121977i
$779$	9.60571	+	3.12109i	0.344160	+	0.111825i
$780$		0			0
$781$	2.24000	+	8.00830i	0.0801534	+	0.286559i
$782$			1.20903i			0.0432347i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	1.28068	−	1.76270i	0.0457093	−	0.0629134i
$786$		0			0
$787$	−9.02926	+	2.93379i	−0.321858	+	0.104578i	−0.465490	−	0.885053i	$-0.654122\pi$
$787$	−9.02926	+	2.93379i	−0.321858	+	0.104578i	0.143632	+	0.989631i	$0.454122\pi$
$788$	20.6457	+	15.0000i	0.735472	+	0.534351i
$789$		0			0
$790$	−0.831166	+	2.55807i	−0.0295716	+	0.0910119i
$791$	−4.64122			−0.165023
$792$		0			0
$793$	−1.12502			−0.0399507
$794$	2.94351	−	9.05918i	0.104461	−	0.321498i
$795$		0			0
$796$	−19.2777	−	14.0060i	−0.683279	−	0.496431i
$797$	−2.65463	+	0.862542i	−0.0940318	+	0.0305528i	−0.355655	−	0.934617i	$-0.615742\pi$
$797$	−2.65463	+	0.862542i	−0.0940318	+	0.0305528i	0.261623	+	0.965170i	$0.415742\pi$
$798$		0			0
$799$	2.08861	−	2.87473i	0.0738899	−	0.101701i
$800$	−3.89350	+	2.82879i	−0.137656	+	0.100013i
$801$		0			0
$802$		−	3.36265i		−	0.118739i
$803$	−16.7219	−	13.2409i	−0.590103	−	0.467260i
$804$		0			0
$805$	0.687896	+	0.223511i	0.0242452	+	0.00787773i
$806$	−5.37398	−	7.39665i	−0.189290	−	0.260536i
$807$		0			0
$808$	4.14377	+	12.7532i	0.145777	+	0.448657i
$809$	−1.84794	−	5.68738i	−0.0649702	−	0.199958i	0.913302	−	0.407284i	$-0.133524\pi$
$809$	−1.84794	−	5.68738i	−0.0649702	−	0.199958i	−0.978272	+	0.207326i	$0.933524\pi$
$810$		0			0
$811$	20.1810	+	27.7767i	0.708650	+	0.975374i	0.999825	+	0.0187036i	$0.00595390\pi$
$811$	20.1810	+	27.7767i	0.708650	+	0.975374i	−0.291175	+	0.956670i	$0.594046\pi$
$812$	0.431695	+	0.140266i	0.0151495	+	0.00492237i
$813$		0			0
$814$	15.5637	+	23.4015i	0.545507	+	0.820221i
$815$			0.883718i			0.0309553i
$816$		0			0
$817$	−26.9573	+	19.5856i	−0.943116	+	0.685214i
$818$	−2.61484	+	3.59902i	−0.0914258	+	0.125837i
$819$		0			0
$820$	−0.690058	+	0.224213i	−0.0240979	+	0.00782987i
$821$	9.41267	+	6.83870i	0.328504	+	0.238672i	0.739796	−	0.672832i	$-0.234922\pi$
$821$	9.41267	+	6.83870i	0.328504	+	0.238672i	−0.411291	+	0.911504i	$0.634922\pi$
$822$		0			0
$823$	−4.67004	+	14.3729i	−0.162787	+	0.501008i	−0.998866	−	0.0476011i	$-0.984842\pi$
$823$	−4.67004	+	14.3729i	−0.162787	+	0.501008i	0.836079	+	0.548609i	$0.184842\pi$
$824$	−15.8654			−0.552699
$825$		0			0
$826$	6.05749			0.210767
$827$	6.34576	−	19.5302i	0.220664	−	0.679133i	−0.778039	−	0.628216i	$-0.783786\pi$
$827$	6.34576	−	19.5302i	0.220664	−	0.679133i	0.998703	−	0.0509172i	$-0.0162144\pi$
$828$		0			0
$829$	32.4123	+	23.5489i	1.12573	+	0.817888i	0.985067	−	0.172171i	$-0.0550780\pi$
$829$	32.4123	+	23.5489i	1.12573	+	0.817888i	0.140658	+	0.990058i	$0.455078\pi$
$830$	2.44517	−	0.794482i	0.0848729	−	0.0275769i
$831$		0			0
$832$	−0.830839	+	1.14355i	−0.0288042	+	0.0396455i
$833$	−0.585373	+	0.425298i	−0.0202820	+	0.0147357i
$834$		0			0
$835$			10.4252i			0.360779i
$836$	19.9675	+	0.827525i	0.690590	+	0.0286205i
$837$		0			0
$838$	−4.73184	−	1.53747i	−0.163459	−	0.0531110i
$839$	19.4282	+	26.7407i	0.670737	+	0.923191i	0.999777	−	0.0211255i	$-0.00672495\pi$
$839$	19.4282	+	26.7407i	0.670737	+	0.923191i	−0.329040	+	0.944316i	$0.606725\pi$
$840$		0			0
$841$	−8.89782	−	27.3847i	−0.306822	−	0.944300i
$842$	7.12078	+	21.9155i	0.245398	+	0.755259i
$843$		0			0
$844$	11.7626	+	16.1898i	0.404884	+	0.557275i
$845$	−4.52933	−	1.47167i	−0.155814	−	0.0506269i
$846$		0			0
$847$	7.17983	−	8.33367i	0.246702	−	0.286348i
$848$			0.266922i			0.00916616i
$849$		0			0
$850$	2.81718	−	2.04680i	0.0966284	−	0.0702047i
$851$	8.32256	−	11.4550i	0.285294	−	0.392673i
$852$		0			0
$853$	9.03686	−	2.93625i	0.309416	−	0.100535i	−0.150193	−	0.988657i	$-0.547990\pi$
$853$	9.03686	−	2.93625i	0.309416	−	0.100535i	0.459609	+	0.888121i	$0.347990\pi$
$854$	0.643903	+	0.467823i	0.0220339	+	0.0160086i
$855$		0			0
$856$	−2.89282	+	8.90319i	−0.0988747	+	0.304305i
$857$	−15.4592			−0.528078			−0.264039	−	0.964512i	$-0.585055\pi$
$857$	−15.4592			−0.528078			−0.264039	+	0.964512i	$0.585055\pi$
$858$		0			0
$859$	−30.4109			−1.03761			−0.518803	−	0.854894i	$-0.673622\pi$
$859$	−30.4109			−1.03761			−0.518803	+	0.854894i	$0.673622\pi$
$860$	0.739702	−	2.27657i	0.0252236	−	0.0776303i
$861$		0			0
$862$	7.64049	+	5.55114i	0.260236	+	0.189073i
$863$	−1.37014	+	0.445185i	−0.0466400	+	0.0151543i	−0.332244	−	0.943193i	$-0.607806\pi$
$863$	−1.37014	+	0.445185i	−0.0466400	+	0.0151543i	0.285604	+	0.958348i	$0.407806\pi$
$864$		0			0
$865$	1.40251	−	1.93040i	0.0476869	−	0.0656354i
$866$	20.3932	−	14.8165i	0.692990	−	0.503487i
$867$		0			0
$868$			6.46814i			0.219543i
$869$	7.17450	−	19.3193i	0.243378	−	0.655363i
$870$		0			0
$871$	0.914841	+	0.297250i	0.0309982	+	0.0100719i
$872$	−4.09972	−	5.64277i	−0.138834	−	0.191088i
$873$		0			0
$874$	−3.11131	−	9.57562i	−0.105242	−	0.323900i
$875$	−1.31257	−	4.03968i	−0.0443731	−	0.136566i
$876$		0			0
$877$	−19.4712	−	26.7998i	−0.657495	−	0.904964i	0.341901	−	0.939736i	$-0.388929\pi$
$877$	−19.4712	−	26.7998i	−0.657495	−	0.904964i	−0.999395	+	0.0347724i	$0.988929\pi$
$878$	−7.90482	−	2.56843i	−0.266775	−	0.0866803i
$879$		0			0
$880$	−1.19542	+	0.795043i	−0.0402976	+	0.0268009i
$881$			7.35470i			0.247786i	0.992296	+	0.123893i	$0.0395380\pi$
$881$			7.35470i			0.247786i	−0.992296	+	0.123893i	$0.960462\pi$
$882$		0			0
$883$	15.3730	−	11.1691i	0.517342	−	0.375871i	−0.298259	−	0.954485i	$-0.596406\pi$
$883$	15.3730	−	11.1691i	0.517342	−	0.375871i	0.815602	+	0.578614i	$0.196406\pi$
$884$	0.601162	−	0.827429i	0.0202193	−	0.0278294i
$885$		0			0
$886$	10.1001	−	3.28173i	0.339320	−	0.110252i
$887$	28.5496	+	20.7425i	0.958603	+	0.696466i	0.952826	−	0.303517i	$-0.0981610\pi$
$887$	28.5496	+	20.7425i	0.958603	+	0.696466i	0.00577729	+	0.999983i	$0.498161\pi$
$888$		0			0
$889$	−2.49678	+	7.68429i	−0.0837392	+	0.257723i
$890$	−3.77450			−0.126521
$891$		0			0
$892$	−14.9488			−0.500522
$893$	−9.14423	+	28.1430i	−0.306000	+	0.941771i
$894$		0			0
$895$	0.711018	+	0.516585i	0.0237667	+	0.0172675i
$896$	0.951057	−	0.309017i	0.0317726	−	0.0103235i
$897$		0			0
$898$	−17.0417	+	23.4559i	−0.568688	+	0.782732i
$899$	−2.37524	+	1.72571i	−0.0792186	+	0.0575557i
$900$		0			0
$901$		−	0.193135i		−	0.00643424i
$902$	5.35381	−	1.49751i	0.178262	−	0.0498617i
$903$		0			0
$904$	−4.41407	−	1.43422i	−0.146810	−	0.0477013i
$905$	1.95545	+	2.69145i	0.0650015	+	0.0894669i
$906$		0			0
$907$	7.29705	+	22.4580i	0.242295	+	0.745706i	0.996070	+	0.0885736i	$0.0282309\pi$
$907$	7.29705	+	22.4580i	0.242295	+	0.745706i	−0.753775	+	0.657133i	$0.771769\pi$
$908$	3.64133	+	11.2069i	0.120842	+	0.371913i
$909$		0			0
$910$	−0.359644	−	0.495007i	−0.0119221	−	0.0164093i
$911$	−33.6865	−	10.9454i	−1.11608	−	0.362638i	−0.307813	−	0.951447i	$-0.599597\pi$
$911$	−33.6865	−	10.9454i	−1.11608	−	0.362638i	−0.808272	+	0.588809i	$0.799597\pi$
$912$		0			0
$913$	−18.9708	+	5.30631i	−0.627841	+	0.175613i
$914$			22.1116i			0.731386i
$915$		0			0
$916$	7.07753	−	5.14213i	0.233848	−	0.169901i
$917$	−0.388779	+	0.535109i	−0.0128386	+	0.0176709i
$918$		0			0
$919$	26.0766	−	8.47279i	0.860187	−	0.279492i	0.154480	−	0.987996i	$-0.450630\pi$
$919$	26.0766	−	8.47279i	0.860187	−	0.279492i	0.705707	+	0.708504i	$0.250630\pi$
$920$	0.585159	+	0.425143i	0.0192921	+	0.0140166i
$921$		0			0
$922$	−1.38714	+	4.26919i	−0.0456832	+	0.140598i
$923$	−3.54405			−0.116654
$924$		0			0
$925$	−40.7812			−1.34088
$926$	7.92373	−	24.3867i	0.260390	−	0.801398i
$927$		0			0
$928$	0.367221	+	0.266802i	0.0120546	+	0.00875820i
$929$	27.4184	−	8.90878i	0.899569	−	0.292288i	0.177510	−	0.984119i	$-0.443196\pi$
$929$	27.4184	−	8.90878i	0.899569	−	0.292288i	0.722059	+	0.691831i	$0.243196\pi$
$930$		0			0
$931$	3.54176	−	4.87481i	0.116076	−	0.159765i
$932$	−16.8765	+	12.2615i	−0.552809	+	0.401639i
$933$		0			0
$934$		−	16.7401i		−	0.547752i
$935$	0.864959	−	0.575261i	0.0282872	−	0.0188131i
$936$		0			0
$937$	−16.3128	−	5.30036i	−0.532917	−	0.173155i	0.0301823	−	0.999544i	$-0.490391\pi$
$937$	−16.3128	−	5.30036i	−0.532917	−	0.173155i	−0.563099	+	0.826389i	$0.690391\pi$
$938$	−0.400000	−	0.550553i	−0.0130605	−	0.0179762i
$939$		0			0
$940$	−0.656906	−	2.02175i	−0.0214259	−	0.0659421i
$941$	−3.59334	−	11.0592i	−0.117140	−	0.360519i	0.875248	−	0.483675i	$-0.160698\pi$
$941$	−3.59334	−	11.0592i	−0.117140	−	0.360519i	−0.992387	+	0.123156i	$0.960698\pi$
$942$		0			0
$943$	−1.64628	−	2.26591i	−0.0536102	−	0.0737880i
$944$	5.76102	+	1.87187i	0.187505	+	0.0609241i
$945$		0			0
$946$	−6.38499	+	17.1934i	−0.207594	+	0.559004i
$947$			25.2047i			0.819044i	0.912300	+	0.409522i	$0.134305\pi$
$947$			25.2047i			0.819044i	−0.912300	+	0.409522i	$0.865695\pi$
$948$		0			0
$949$	7.35424	−	5.34317i	0.238729	−	0.173447i
$950$	−17.0451	+	23.4606i	−0.553017	+	0.761163i
$951$		0			0
$952$	−0.688147	+	0.223592i	−0.0223030	+	0.00724667i
$953$	−14.2361	−	10.3432i	−0.461154	−	0.335048i	0.332830	−	0.942987i	$-0.391997\pi$
$953$	−14.2361	−	10.3432i	−0.461154	−	0.335048i	−0.793984	+	0.607939i	$0.791997\pi$
$954$		0			0
$955$	2.34218	−	7.20849i	0.0757911	−	0.233261i
$956$	10.4421			0.337723
$957$		0			0
$958$	−1.28756			−0.0415991
$959$	3.54141	−	10.8993i	0.114358	−	0.351958i
$960$		0			0
$961$	−8.76717	−	6.36973i	−0.282812	−	0.205475i
$962$	−11.3915	+	3.70133i	−0.367278	+	0.119336i
$963$		0			0
$964$	5.87199	−	8.08210i	0.189124	−	0.260307i
$965$	−4.50737	+	3.27480i	−0.145097	+	0.105419i
$966$		0			0
$967$		−	39.0261i		−	1.25499i	−0.778619	−	0.627497i	$-0.784080\pi$
$967$		−	39.0261i		−	1.25499i	0.778619	−	0.627497i	$-0.215920\pi$
$968$	9.40367	−	5.70710i	0.302245	−	0.183433i
$969$		0			0
$970$	7.08574	+	2.30230i	0.227509	+	0.0739223i
$971$	−18.2949	−	25.1808i	−0.587111	−	0.808089i	0.407342	−	0.913276i	$-0.366456\pi$
$971$	−18.2949	−	25.1808i	−0.587111	−	0.808089i	−0.994452	+	0.105187i	$0.966456\pi$
$972$		0			0
$973$	2.51713	+	7.74693i	0.0806954	+	0.248355i
$974$	−8.06897	−	24.8337i	−0.258546	−	0.795724i
$975$		0			0
$976$	0.467823	+	0.643903i	0.0149746	+	0.0206108i
$977$	−49.1490	−	15.9695i	−1.57241	−	0.510909i	−0.612326	−	0.790605i	$-0.709766\pi$
$977$	−49.1490	−	15.9695i	−1.57241	−	0.510909i	−0.960088	+	0.279697i	$0.909766\pi$
$978$		0			0
$979$	28.8953	+	1.19752i	0.923497	+	0.0382730i
$980$			0.432868i			0.0138275i
$981$		0			0
$982$	34.1694	−	24.8255i	1.09039	−	0.792215i
$983$	−26.3359	+	36.2483i	−0.839985	+	1.15614i	0.145997	+	0.989285i	$0.453361\pi$
$983$	−26.3359	+	36.2483i	−0.839985	+	1.15614i	−0.985981	+	0.166855i	$0.946639\pi$
$984$		0			0
$985$	−10.5059	+	3.41358i	−0.334746	+	0.108766i
$986$	−0.265707	−	0.193047i	−0.00846183	−	0.00614788i
$987$		0			0
$988$	−2.63197	+	8.10036i	−0.0837340	+	0.257707i
$989$	9.24016			0.293820
$990$		0			0
$991$	26.8969			0.854409			0.427204	−	0.904155i	$-0.359498\pi$
$991$	26.8969			0.854409			0.427204	+	0.904155i	$0.359498\pi$
$992$	−1.99876	+	6.15157i	−0.0634608	+	0.195312i
$993$		0			0
$994$	2.02842	+	1.47374i	0.0643377	+	0.0467441i
$995$	9.80977	−	3.18739i	0.310991	−	0.101047i
$996$		0			0
$997$	32.3277	−	44.4953i	1.02383	−	1.40918i	0.114346	−	0.993441i	$-0.463523\pi$
$997$	32.3277	−	44.4953i	1.02383	−	1.40918i	0.909483	−	0.415740i	$-0.136477\pi$
$998$	13.0478	−	9.47979i	0.413021	−	0.300077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.827.6	✓	48
3.2	odd	2		1386.2.bu.b.827.7	yes	48
11.6	odd	10		1386.2.bu.b.1205.7	yes	48
33.17	even	10	inner	1386.2.bu.a.1205.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.6	✓	48	1.1	even	1	trivial
1386.2.bu.a.1205.6	yes	48	33.17	even	10	inner
1386.2.bu.b.827.7	yes	48	3.2	odd	2
1386.2.bu.b.1205.7	yes	48	11.6	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.411682 - 0.133764i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.411682 - 0.133764i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(-0.809017 + 0.587785i) q^{8} -0.432868i q^{10} +(-0.137335 + 3.31378i) q^{11} +(-1.34433 - 0.436798i) q^{13} +(0.587785 + 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.223592 - 0.688147i) q^{17} +(3.54176 + 4.87481i) q^{19} +(-0.411682 - 0.133764i) q^{20} +(3.10915 + 1.15463i) q^{22} -1.67094i q^{23} +(-3.89350 + 2.82879i) q^{25} +(-0.830839 + 1.14355i) q^{26} +(0.951057 - 0.309017i) q^{28} +(0.367221 + 0.266802i) q^{29} +(-1.99876 + 6.15157i) q^{31} +1.00000 q^{32} -0.723560 q^{34} +(-0.133764 + 0.411682i) q^{35} +(6.85544 + 4.98077i) q^{37} +(5.73068 - 1.86201i) q^{38} +(-0.254434 + 0.350198i) q^{40} +(1.35607 - 0.985240i) q^{41} +5.52992i q^{43} +(2.05890 - 2.60018i) q^{44} +(-1.58916 - 0.516349i) q^{46} +(2.88658 + 3.97304i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(1.48718 + 4.57708i) q^{50} +(0.830839 + 1.14355i) q^{52} +(0.253858 + 0.0824836i) q^{53} +(0.386725 + 1.38259i) q^{55} -1.00000i q^{56} +(0.367221 - 0.266802i) q^{58} +(3.56050 - 4.90061i) q^{59} +(0.756954 - 0.245949i) q^{61} +(5.23283 + 3.80188i) q^{62} +(0.309017 - 0.951057i) q^{64} -0.611863 q^{65} -0.680521 q^{67} +(-0.223592 + 0.688147i) q^{68} +(0.350198 + 0.254434i) q^{70} +(2.38456 - 0.774789i) q^{71} +(-3.78008 + 5.20283i) q^{73} +(6.85544 - 4.98077i) q^{74} -6.02559i q^{76} +(-2.60018 - 2.05890i) q^{77} +(-5.90957 - 1.92014i) q^{79} +(0.254434 + 0.350198i) q^{80} +(-0.517971 - 1.59415i) q^{82} +(1.83539 + 5.64875i) q^{83} +(-0.184098 - 0.253389i) q^{85} +(5.25926 + 1.70884i) q^{86} +(-1.83668 - 2.76163i) q^{88} -8.71973i q^{89} +(1.14355 - 0.830839i) q^{91} +(-0.982154 + 1.35182i) q^{92} +(4.67058 - 1.51756i) q^{94} +(2.11015 + 1.53311i) q^{95} +(-5.31870 + 16.3693i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more