LMFDB - Embedded newform 882.2.h.t.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.t.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +(-0.448288 - 1.67303i) q^{6} -1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +(-0.258819 - 0.448288i) q^{10} -1.46410 q^{11} +(1.22474 - 1.22474i) q^{12} +(-1.22474 - 2.12132i) q^{13} +(0.866025 + 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.74238 - 3.01790i) q^{17} +3.00000i q^{18} +(0.258819 - 0.448288i) q^{19} +(0.258819 - 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} +7.92820 q^{23} +(1.67303 + 0.448288i) q^{24} -4.73205 q^{25} +(1.22474 - 2.12132i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(-1.36603 + 2.36603i) q^{29} +(0.232051 + 0.866025i) q^{30} +(3.67423 - 6.36396i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.44949 + 0.656339i) q^{33} +(1.74238 - 3.01790i) q^{34} +(-2.59808 + 1.50000i) q^{36} +(4.00000 - 6.92820i) q^{37} +0.517638 q^{38} +(1.09808 + 4.09808i) q^{39} +0.517638 q^{40} +(2.82843 + 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +(0.732051 - 1.26795i) q^{44} +(-1.34486 - 0.776457i) q^{45} +(3.96410 + 6.86603i) q^{46} +(-2.31079 - 4.00240i) q^{47} +(0.448288 + 1.67303i) q^{48} +(-2.36603 - 4.09808i) q^{50} +(1.56218 + 5.83013i) q^{51} +2.44949 q^{52} +(-3.36603 - 5.83013i) q^{53} +(1.34486 - 5.01910i) q^{54} +0.757875 q^{55} +(-0.633975 + 0.633975i) q^{57} -2.73205 q^{58} +(7.39924 - 12.8159i) q^{59} +(-0.633975 + 0.633975i) q^{60} +(2.19067 + 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(0.633975 + 1.09808i) q^{65} +(0.656339 + 2.44949i) q^{66} +(1.90192 - 3.29423i) q^{67} +3.48477 q^{68} +(-13.2641 - 3.55412i) q^{69} -0.803848 q^{71} +(-2.59808 - 1.50000i) q^{72} +(2.31079 + 4.00240i) q^{73} +8.00000 q^{74} +(7.91688 + 2.12132i) q^{75} +(0.258819 + 0.448288i) q^{76} +(-3.00000 + 3.00000i) q^{78} +(-7.06218 - 12.2321i) q^{79} +(0.258819 + 0.448288i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-2.82843 + 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} +12.1962 q^{86} +(3.34607 - 3.34607i) q^{87} +1.46410 q^{88} +(-8.05558 + 13.9527i) q^{89} -1.55291i q^{90} +(-3.96410 + 6.86603i) q^{92} +(-9.00000 + 9.00000i) q^{93} +(2.31079 - 4.00240i) q^{94} +(-0.133975 + 0.232051i) q^{95} +(-1.22474 + 1.22474i) q^{96} +(-0.517638 + 0.896575i) q^{97} +(-3.80385 - 2.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} + 8 q^{23} - 24 q^{25} - 4 q^{29} - 12 q^{30} + 4 q^{32} + 32 q^{37} - 12 q^{39} + 28 q^{43} - 8 q^{44} + 4 q^{46} - 12 q^{50} - 36 q^{51}+ \cdots - 72 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 + 8 * q^22 + 8 * q^23 - 24 * q^25 - 4 * q^29 - 12 * q^30 + 4 * q^32 + 32 * q^37 - 12 * q^39 + 28 * q^43 - 8 * q^44 + 4 * q^46 - 12 * q^50 - 36 * q^51 - 20 * q^53 - 12 * q^57 - 8 * q^58 - 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 + 64 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 + 28 * q^85 + 56 * q^86 - 16 * q^88 - 4 * q^92 - 72 * q^93 - 8 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.517638			−0.231495			−0.115747	−	0.993279i	$-0.536926\pi$
$5$	−0.517638			−0.231495			−0.115747	+	0.993279i	$0.536926\pi$
$6$	−0.448288	−	1.67303i	−0.183013	−	0.683013i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−0.258819	−	0.448288i	−0.0818458	−	0.141761i
$11$	−1.46410			−0.441443			−0.220722	−	0.975337i	$-0.570841\pi$
$11$	−1.46410			−0.441443			−0.220722	+	0.975337i	$0.570841\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	0.644690	−	0.764444i	$-0.276986\pi$
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	−0.984373	+	0.176096i	$0.943653\pi$
$14$		0			0
$15$	0.866025	+	0.232051i	0.223607	+	0.0599153i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.74238	−	3.01790i	−0.422590	−	0.731947i	0.573602	−	0.819134i	$-0.305546\pi$
$17$	−1.74238	−	3.01790i	−0.422590	−	0.731947i	−0.996192	+	0.0871869i	$0.972212\pi$
$18$			3.00000i			0.707107i
$19$	0.258819	−	0.448288i	0.0593772	−	0.102844i	−0.834809	−	0.550540i	$-0.814422\pi$
$19$	0.258819	−	0.448288i	0.0593772	−	0.102844i	0.894186	+	0.447696i	$0.147755\pi$
$20$	0.258819	−	0.448288i	0.0578737	−	0.100240i
$21$		0			0
$22$	−0.732051	−	1.26795i	−0.156074	−	0.270328i
$23$	7.92820			1.65314			0.826572	−	0.562831i	$-0.190288\pi$
$23$	7.92820			1.65314			0.826572	+	0.562831i	$0.190288\pi$
$24$	1.67303	+	0.448288i	0.341506	+	0.0915064i
$25$	−4.73205			−0.946410
$26$	1.22474	−	2.12132i	0.240192	−	0.416025i
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$		0			0
$29$	−1.36603	+	2.36603i	−0.253665	+	0.439360i	−0.964532	−	0.263966i	$-0.914969\pi$
$29$	−1.36603	+	2.36603i	−0.253665	+	0.439360i	0.710867	+	0.703326i	$0.248303\pi$
$30$	0.232051	+	0.866025i	0.0423665	+	0.158114i
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	−0.320726	−	0.947172i	$-0.603927\pi$
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	0.980638	−	0.195829i	$-0.0627398\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.44949	+	0.656339i	0.426401	+	0.114254i
$34$	1.74238	−	3.01790i	0.298816	−	0.517565i
$35$		0			0
$36$	−2.59808	+	1.50000i	−0.433013	+	0.250000i
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	0.517638			0.0839720
$39$	1.09808	+	4.09808i	0.175833	+	0.656217i
$40$	0.517638			0.0818458
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$44$	0.732051	−	1.26795i	0.110361	−	0.191151i
$45$	−1.34486	−	0.776457i	−0.200480	−	0.115747i
$46$	3.96410	+	6.86603i	0.584475	+	1.01234i
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	0.646816	−	0.762646i	$-0.276100\pi$
$47$	−2.31079	−	4.00240i	−0.337063	−	0.583811i	−0.983879	+	0.178836i	$0.942767\pi$
$48$	0.448288	+	1.67303i	0.0647048	+	0.241481i
$49$		0			0
$50$	−2.36603	−	4.09808i	−0.334607	−	0.579555i
$51$	1.56218	+	5.83013i	0.218749	+	0.816381i
$52$	2.44949			0.339683
$53$	−3.36603	−	5.83013i	−0.462359	−	0.800830i	0.536719	−	0.843761i	$-0.319664\pi$
$53$	−3.36603	−	5.83013i	−0.462359	−	0.800830i	−0.999078	+	0.0429316i	$0.986330\pi$
$54$	1.34486	−	5.01910i	0.183013	−	0.683013i
$55$	0.757875			0.102192
$56$		0			0
$57$	−0.633975	+	0.633975i	−0.0839720	+	0.0839720i
$58$	−2.73205			−0.358736
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.249180	−	0.968457i	$-0.419839\pi$
$59$	7.39924	−	12.8159i	0.963299	−	1.66848i	0.714118	−	0.700025i	$-0.246828\pi$
$60$	−0.633975	+	0.633975i	−0.0818458	+	0.0818458i
$61$	2.19067	+	3.79435i	0.280487	+	0.485817i	0.971505	−	0.237020i	$-0.0761708\pi$
$61$	2.19067	+	3.79435i	0.280487	+	0.485817i	−0.691018	+	0.722838i	$0.742837\pi$
$62$	7.34847			0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	0.633975	+	1.09808i	0.0786349	+	0.136200i
$66$	0.656339	+	2.44949i	0.0807897	+	0.301511i
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	−0.726144	−	0.687542i	$-0.758690\pi$
$67$	1.90192	−	3.29423i	0.232357	−	0.402454i	0.958501	+	0.285088i	$0.0920229\pi$
$68$	3.48477			0.422590
$69$	−13.2641	−	3.55412i	−1.59682	−	0.427865i
$70$		0			0
$71$	−0.803848			−0.0953992			−0.0476996	−	0.998862i	$-0.515189\pi$
$71$	−0.803848			−0.0953992			−0.0476996	+	0.998862i	$0.515189\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	2.31079	+	4.00240i	0.270457	+	0.468446i	0.968979	−	0.247143i	$-0.0794917\pi$
$73$	2.31079	+	4.00240i	0.270457	+	0.468446i	−0.698522	+	0.715589i	$0.746158\pi$
$74$	8.00000			0.929981
$75$	7.91688	+	2.12132i	0.914162	+	0.244949i
$76$	0.258819	+	0.448288i	0.0296886	+	0.0514221i
$77$		0			0
$78$	−3.00000	+	3.00000i	−0.339683	+	0.339683i
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	−0.923120	−	0.384512i	$-0.874370\pi$
$79$	−7.06218	−	12.2321i	−0.794557	−	1.37621i	0.128563	−	0.991701i	$-0.458964\pi$
$80$	0.258819	+	0.448288i	0.0289368	+	0.0501201i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−2.82843	+	4.89898i	−0.312348	+	0.541002i
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	0.455406	+	0.890284i	$0.349494\pi$
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	−0.998711	+	0.0507487i	$0.983839\pi$
$84$		0			0
$85$	0.901924	+	1.56218i	0.0978274	+	0.169442i
$86$	12.1962			1.31514
$87$	3.34607	−	3.34607i	0.358736	−	0.358736i
$88$	1.46410			0.156074
$89$	−8.05558	+	13.9527i	−0.853889	+	1.47898i	0.0237822	+	0.999717i	$0.492429\pi$
$89$	−8.05558	+	13.9527i	−0.853889	+	1.47898i	−0.877672	+	0.479263i	$0.840904\pi$
$90$		−	1.55291i		−	0.163692i
$91$		0			0
$92$	−3.96410	+	6.86603i	−0.413286	+	0.715833i
$93$	−9.00000	+	9.00000i	−0.933257	+	0.933257i
$94$	2.31079	−	4.00240i	0.238340	−	0.412816i
$95$	−0.133975	+	0.232051i	−0.0137455	+	0.0238079i
$96$	−1.22474	+	1.22474i	−0.125000	+	0.125000i
$97$	−0.517638	+	0.896575i	−0.0525582	+	0.0910334i	−0.891108	−	0.453792i	$-0.850071\pi$
$97$	−0.517638	+	0.896575i	−0.0525582	+	0.0910334i	0.838549	+	0.544826i	$0.183404\pi$
$98$		0			0
$99$	−3.80385	−	2.19615i	−0.382301	−	0.220722i
$100$	2.36603	−	4.09808i	0.236603	−	0.409808i
$101$	−5.79555			−0.576679			−0.288340	−	0.957528i	$-0.593103\pi$
$101$	−5.79555			−0.576679			−0.288340	+	0.957528i	$0.593103\pi$
$102$	−4.26795	+	4.26795i	−0.422590	+	0.422590i
$103$	11.2122			1.10477			0.552384	−	0.833590i	$-0.313718\pi$
$103$	11.2122			1.10477			0.552384	+	0.833590i	$0.313718\pi$
$104$	1.22474	+	2.12132i	0.120096	+	0.208013i
$105$		0			0
$106$	3.36603	−	5.83013i	0.326937	−	0.566272i
$107$	−1.53590	+	2.66025i	−0.148481	+	0.257176i	−0.930666	−	0.365869i	$-0.880772\pi$
$107$	−1.53590	+	2.66025i	−0.148481	+	0.257176i	0.782185	+	0.623046i	$0.214105\pi$
$108$	5.01910	−	1.34486i	0.482963	−	0.129410i
$109$	−5.29423	−	9.16987i	−0.507095	−	0.878315i	−0.999966	−	0.00821222i	$-0.997386\pi$
$109$	−5.29423	−	9.16987i	−0.507095	−	0.878315i	0.492871	−	0.870102i	$-0.335947\pi$
$110$	0.378937	+	0.656339i	0.0361303	+	0.0625794i
$111$	−9.79796	+	9.79796i	−0.929981	+	0.929981i
$112$		0			0
$113$	7.33013	+	12.6962i	0.689560	+	1.19435i	0.971980	+	0.235063i	$0.0755295\pi$
$113$	7.33013	+	12.6962i	0.689560	+	1.19435i	−0.282420	+	0.959291i	$0.591137\pi$
$114$	−0.866025	−	0.232051i	−0.0811107	−	0.0217335i
$115$	−4.10394			−0.382694
$116$	−1.36603	−	2.36603i	−0.126832	−	0.219680i
$117$		−	7.34847i		−	0.679366i
$118$	14.7985			1.36231
$119$		0			0
$120$	−0.866025	−	0.232051i	−0.0790569	−	0.0211832i
$121$	−8.85641			−0.805128
$122$	−2.19067	+	3.79435i	−0.198334	+	0.343525i
$123$	−2.53590	−	9.46410i	−0.228654	−	0.853349i
$124$	3.67423	+	6.36396i	0.329956	+	0.571501i
$125$	5.03768			0.450584
$126$		0			0
$127$	−5.92820			−0.526043			−0.263021	−	0.964790i	$-0.584719\pi$
$127$	−5.92820			−0.526043			−0.263021	+	0.964790i	$0.584719\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−14.9372	+	14.9372i	−1.31514	+	1.31514i
$130$	−0.633975	+	1.09808i	−0.0556033	+	0.0963077i
$131$	−12.4877			−1.09105			−0.545527	−	0.838093i	$-0.683670\pi$
$131$	−12.4877			−1.09105			−0.545527	+	0.838093i	$0.683670\pi$
$132$	−1.79315	+	1.79315i	−0.156074	+	0.156074i
$133$		0			0
$134$	3.80385			0.328602
$135$	1.90192	+	1.90192i	0.163692	+	0.163692i
$136$	1.74238	+	3.01790i	0.149408	+	0.258782i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−3.55412	−	13.2641i	−0.302546	−	1.12912i
$139$	−10.1075	−	17.5068i	−0.857311	−	1.48491i	−0.874485	−	0.485053i	$-0.838800\pi$
$139$	−10.1075	−	17.5068i	−0.857311	−	1.48491i	0.0171736	−	0.999853i	$-0.494533\pi$
$140$		0			0
$141$	2.07180	+	7.73205i	0.174477	+	0.651156i
$142$	−0.401924	−	0.696152i	−0.0337287	−	0.0584198i
$143$	1.79315	+	3.10583i	0.149951	+	0.259722i
$144$		−	3.00000i		−	0.250000i
$145$	0.707107	−	1.22474i	0.0587220	−	0.101710i
$146$	−2.31079	+	4.00240i	−0.191242	+	0.331241i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	−2.39230			−0.195985			−0.0979926	−	0.995187i	$-0.531242\pi$
$149$	−2.39230			−0.195985			−0.0979926	+	0.995187i	$0.531242\pi$
$150$	2.12132	+	7.91688i	0.173205	+	0.646410i
$151$	−17.3923			−1.41537			−0.707683	−	0.706530i	$-0.750259\pi$
$151$	−17.3923			−1.41537			−0.707683	+	0.706530i	$0.750259\pi$
$152$	−0.258819	+	0.448288i	−0.0209930	+	0.0363609i
$153$		−	10.4543i		−	0.845180i
$154$		0			0
$155$	−1.90192	+	3.29423i	−0.152766	+	0.264599i
$156$	−4.09808	−	1.09808i	−0.328109	−	0.0879165i
$157$	−8.64256	+	14.9694i	−0.689752	+	1.19469i	0.282166	+	0.959366i	$0.408947\pi$
$157$	−8.64256	+	14.9694i	−0.689752	+	1.19469i	−0.971918	+	0.235320i	$0.924386\pi$
$158$	7.06218	−	12.2321i	0.561837	−	0.973130i
$159$	3.01790	+	11.2629i	0.239335	+	0.893209i
$160$	−0.258819	+	0.448288i	−0.0204614	+	0.0354403i
$161$		0			0
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	3.53590	−	6.12436i	0.276953	−	0.479697i	−0.693673	−	0.720290i	$-0.744009\pi$
$163$	3.53590	−	6.12436i	0.276953	−	0.479697i	0.970626	+	0.240593i	$0.0773421\pi$
$164$	−5.65685			−0.441726
$165$	−1.26795	−	0.339746i	−0.0987097	−	0.0264492i
$166$	−9.89949			−0.768350
$167$	6.64136	+	11.5032i	0.513924	+	0.890143i	0.999870	+	0.0161534i	$0.00514202\pi$
$167$	6.64136	+	11.5032i	0.513924	+	0.890143i	−0.485945	+	0.873989i	$0.661525\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	−0.901924	+	1.56218i	−0.0691744	+	0.119814i
$171$	1.34486	−	0.776457i	0.102844	−	0.0593772i
$172$	6.09808	+	10.5622i	0.464974	+	0.805359i
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	−0.953287	−	0.302065i	$-0.902324\pi$
$173$	−9.71003	−	16.8183i	−0.738240	−	1.27867i	0.215048	−	0.976604i	$-0.431009\pi$
$174$	4.57081	+	1.22474i	0.346512	+	0.0928477i
$175$		0			0
$176$	0.732051	+	1.26795i	0.0551804	+	0.0955753i
$177$	−18.1244	+	18.1244i	−1.36231	+	1.36231i
$178$	−16.1112			−1.20758
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	0.977551	−	0.210699i	$-0.0675741\pi$
$179$	4.09808	+	7.09808i	0.306305	+	0.530535i	−0.671246	+	0.741234i	$0.734241\pi$
$180$	1.34486	−	0.776457i	0.100240	−	0.0578737i
$181$	20.9730			1.55891			0.779454	−	0.626459i	$-0.215497\pi$
$181$	20.9730			1.55891			0.779454	+	0.626459i	$0.215497\pi$
$182$		0			0
$183$	−1.96410	−	7.33013i	−0.145191	−	0.541859i
$184$	−7.92820			−0.584475
$185$	−2.07055	+	3.58630i	−0.152230	+	0.263670i
$186$	−12.2942	−	3.29423i	−0.901457	−	0.241545i
$187$	2.55103	+	4.41851i	0.186549	+	0.323113i
$188$	4.62158			0.337063
$189$		0			0
$190$	−0.267949			−0.0194391
$191$	3.59808	+	6.23205i	0.260348	+	0.450935i	0.966334	−	0.257290i	$-0.0828295\pi$
$191$	3.59808	+	6.23205i	0.260348	+	0.450935i	−0.705987	+	0.708225i	$0.749496\pi$
$192$	−1.67303	−	0.448288i	−0.120741	−	0.0323524i
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	−0.0233098	−	0.999728i	$-0.507420\pi$
$193$	11.8660	−	20.5526i	0.854135	−	1.47941i	0.877445	−	0.479677i	$-0.159246\pi$
$194$	−1.03528			−0.0743285
$195$	−0.568406	−	2.12132i	−0.0407044	−	0.151911i
$196$		0			0
$197$	9.66025			0.688265			0.344132	−	0.938921i	$-0.388173\pi$
$197$	9.66025			0.688265			0.344132	+	0.938921i	$0.388173\pi$
$198$		−	4.39230i		−	0.312148i
$199$	5.79555	+	10.0382i	0.410836	+	0.711589i	0.994981	−	0.100060i	$-0.0319035\pi$
$199$	5.79555	+	10.0382i	0.410836	+	0.711589i	−0.584145	+	0.811649i	$0.698570\pi$
$200$	4.73205			0.334607
$201$	−4.65874	+	4.65874i	−0.328602	+	0.328602i
$202$	−2.89778	−	5.01910i	−0.203887	−	0.353142i
$203$		0			0
$204$	−5.83013	−	1.56218i	−0.408191	−	0.109374i
$205$	−1.46410	−	2.53590i	−0.102257	−	0.177115i
$206$	5.60609	+	9.71003i	0.390595	+	0.676530i
$207$	20.5981	+	11.8923i	1.43167	+	0.826572i
$208$	−1.22474	+	2.12132i	−0.0849208	+	0.147087i
$209$	−0.378937	+	0.656339i	−0.0262116	+	0.0453999i
$210$		0			0
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	0.843378	−	0.537321i	$-0.180564\pi$
$211$	−0.633975	−	1.09808i	−0.0436446	−	0.0755947i	−0.887022	+	0.461726i	$0.847230\pi$
$212$	6.73205			0.462359
$213$	1.34486	+	0.360355i	0.0921485	+	0.0246911i
$214$	−3.07180			−0.209984
$215$	−3.15660	+	5.46739i	−0.215278	+	0.372873i
$216$	3.67423	+	3.67423i	0.250000	+	0.250000i
$217$		0			0
$218$	5.29423	−	9.16987i	0.358570	−	0.621062i
$219$	−2.07180	−	7.73205i	−0.139999	−	0.522484i
$220$	−0.378937	+	0.656339i	−0.0255480	+	0.0442504i
$221$	−4.26795	+	7.39230i	−0.287093	+	0.497260i
$222$	−13.3843	−	3.58630i	−0.898293	−	0.240697i
$223$	1.88108	−	3.25813i	0.125967	−	0.218181i	−0.796144	−	0.605108i	$-0.793130\pi$
$223$	1.88108	−	3.25813i	0.125967	−	0.218181i	0.922110	+	0.386927i	$0.126463\pi$
$224$		0			0
$225$	−12.2942	−	7.09808i	−0.819615	−	0.473205i
$226$	−7.33013	+	12.6962i	−0.487593	+	0.844535i
$227$	−3.34607			−0.222086			−0.111043	−	0.993816i	$-0.535419\pi$
$227$	−3.34607			−0.222086			−0.111043	+	0.993816i	$0.535419\pi$
$228$	−0.232051	−	0.866025i	−0.0153679	−	0.0573539i
$229$	−13.8004			−0.911954			−0.455977	−	0.889992i	$-0.650710\pi$
$229$	−13.8004			−0.911954			−0.455977	+	0.889992i	$0.650710\pi$
$230$	−2.05197	−	3.55412i	−0.135303	−	0.234351i
$231$		0			0
$232$	1.36603	−	2.36603i	0.0896840	−	0.155337i
$233$	−0.696152	+	1.20577i	−0.0456065	+	0.0789927i	−0.887928	−	0.459983i	$-0.847855\pi$
$233$	−0.696152	+	1.20577i	−0.0456065	+	0.0789927i	0.842321	+	0.538976i	$0.181189\pi$
$234$	6.36396	−	3.67423i	0.416025	−	0.240192i
$235$	1.19615	+	2.07180i	0.0780284	+	0.135149i
$236$	7.39924	+	12.8159i	0.481649	+	0.834241i
$237$	6.33178	+	23.6305i	0.411293	+	1.53497i
$238$		0			0
$239$	6.23205	+	10.7942i	0.403118	+	0.698221i	0.994100	−	0.108464i	$-0.0345931\pi$
$239$	6.23205	+	10.7942i	0.403118	+	0.698221i	−0.590983	+	0.806684i	$0.701260\pi$
$240$	−0.232051	−	0.866025i	−0.0149788	−	0.0559017i
$241$	−12.7279			−0.819878			−0.409939	−	0.912113i	$-0.634450\pi$
$241$	−12.7279			−0.819878			−0.409939	+	0.912113i	$0.634450\pi$
$242$	−4.42820	−	7.66987i	−0.284656	−	0.493038i
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$	−4.38134			−0.280487
$245$		0			0
$246$	6.92820	−	6.92820i	0.441726	−	0.441726i
$247$	−1.26795			−0.0806777
$248$	−3.67423	+	6.36396i	−0.233314	+	0.404112i
$249$	12.1244	−	12.1244i	0.768350	−	0.768350i
$250$	2.51884	+	4.36276i	0.159305	+	0.275925i
$251$	0.517638			0.0326730			0.0163365	−	0.999867i	$-0.494800\pi$
$251$	0.517638			0.0326730			0.0163365	+	0.999867i	$0.494800\pi$
$252$		0			0
$253$	−11.6077			−0.729770
$254$	−2.96410	−	5.13397i	−0.185984	−	0.322134i
$255$	−0.808643	−	3.01790i	−0.0506392	−	0.188988i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.76217			−0.234678			−0.117339	−	0.993092i	$-0.537436\pi$
$257$	−3.76217			−0.234678			−0.117339	+	0.993092i	$0.537436\pi$
$258$	−20.4046	−	5.46739i	−1.27033	−	0.340385i
$259$		0			0
$260$	−1.26795			−0.0786349
$261$	−7.09808	+	4.09808i	−0.439360	+	0.253665i
$262$	−6.24384	−	10.8147i	−0.385746	−	0.668131i
$263$	2.66025			0.164038			0.0820191	−	0.996631i	$-0.473863\pi$
$263$	2.66025			0.164038			0.0820191	+	0.996631i	$0.473863\pi$
$264$	−2.44949	−	0.656339i	−0.150756	−	0.0403949i
$265$	1.74238	+	3.01790i	0.107034	+	0.185388i
$266$		0			0
$267$	19.7321	−	19.7321i	1.20758	−	1.20758i
$268$	1.90192	+	3.29423i	0.116178	+	0.201227i
$269$	13.4536	+	23.3023i	0.820281	+	1.42077i	0.905473	+	0.424404i	$0.139516\pi$
$269$	13.4536	+	23.3023i	0.820281	+	1.42077i	−0.0851918	+	0.996365i	$0.527150\pi$
$270$	−0.696152	+	2.59808i	−0.0423665	+	0.158114i
$271$	7.39924	−	12.8159i	0.449472	−	0.778508i	−0.548880	−	0.835901i	$-0.684946\pi$
$271$	7.39924	−	12.8159i	0.449472	−	0.778508i	0.998352	+	0.0573934i	$0.0182789\pi$
$272$	−1.74238	+	3.01790i	−0.105647	+	0.182987i
$273$		0			0
$274$		0			0
$275$	6.92820			0.417786
$276$	9.71003	−	9.71003i	0.584475	−	0.584475i
$277$	−16.1962			−0.973132			−0.486566	−	0.873644i	$-0.661751\pi$
$277$	−16.1962			−0.973132			−0.486566	+	0.873644i	$0.661751\pi$
$278$	10.1075	−	17.5068i	0.606210	−	1.04999i
$279$	19.0919	−	11.0227i	1.14300	−	0.659912i
$280$		0			0
$281$	8.69615	−	15.0622i	0.518769	−	0.898534i	−0.480993	−	0.876724i	$-0.659724\pi$
$281$	8.69615	−	15.0622i	0.518769	−	0.898534i	0.999762	−	0.0218099i	$-0.00694284\pi$
$282$	−5.66025	+	5.66025i	−0.337063	+	0.337063i
$283$	4.88040	−	8.45310i	0.290109	−	0.502484i	−0.683726	−	0.729739i	$-0.739642\pi$
$283$	4.88040	−	8.45310i	0.290109	−	0.502484i	0.973835	+	0.227255i	$0.0729749\pi$
$284$	0.401924	−	0.696152i	0.0238498	−	0.0413090i
$285$	0.328169	−	0.328169i	0.0194391	−	0.0194391i
$286$	−1.79315	+	3.10583i	−0.106031	+	0.183651i
$287$		0			0
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	2.42820	−	4.20577i	0.142835	−	0.247398i
$290$	1.41421			0.0830455
$291$	1.26795	−	1.26795i	0.0743285	−	0.0743285i
$292$	−4.62158			−0.270457
$293$	−1.48356	−	2.56961i	−0.0866707	−	0.150118i	0.819431	−	0.573178i	$-0.194289\pi$
$293$	−1.48356	−	2.56961i	−0.0866707	−	0.150118i	−0.906102	+	0.423059i	$0.860956\pi$
$294$		0			0
$295$	−3.83013	+	6.63397i	−0.222999	+	0.386245i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	5.37945	+	5.37945i	0.312148	+	0.312148i
$298$	−1.19615	−	2.07180i	−0.0692912	−	0.120016i
$299$	−9.71003	−	16.8183i	−0.561545	−	0.972625i
$300$	−5.79555	+	5.79555i	−0.334607	+	0.334607i
$301$		0			0
$302$	−8.69615	−	15.0622i	−0.500407	−	0.866731i
$303$	9.69615	+	2.59808i	0.557029	+	0.149256i
$304$	−0.517638			−0.0296886
$305$	−1.13397	−	1.96410i	−0.0649312	−	0.112464i
$306$	9.05369	−	5.22715i	0.517565	−	0.298816i
$307$	11.9329			0.681046			0.340523	−	0.940236i	$-0.389396\pi$
$307$	11.9329			0.681046			0.340523	+	0.940236i	$0.389396\pi$
$308$		0			0
$309$	−18.7583	−	5.02628i	−1.06712	−	0.285935i
$310$	−3.80385			−0.216044
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	−0.484343	−	0.874878i	$-0.660941\pi$
$311$	9.09085	−	15.7458i	0.515495	−	0.892863i	0.999838	−	0.0179854i	$-0.00572524\pi$
$312$	−1.09808	−	4.09808i	−0.0621663	−	0.232008i
$313$	−3.34607	−	5.79555i	−0.189131	−	0.327584i	0.755830	−	0.654768i	$-0.227234\pi$
$313$	−3.34607	−	5.79555i	−0.189131	−	0.327584i	−0.944961	+	0.327184i	$0.893900\pi$
$314$	−17.2851			−0.975456
$315$		0			0
$316$	14.1244			0.794557
$317$	−16.2942	−	28.2224i	−0.915175	−	1.58513i	−0.806645	−	0.591037i	$-0.798719\pi$
$317$	−16.2942	−	28.2224i	−0.915175	−	1.58513i	−0.108530	−	0.994093i	$-0.534614\pi$
$318$	−8.24504	+	8.24504i	−0.462359	+	0.462359i
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−0.517638			−0.0289368
$321$	3.76217	−	3.76217i	0.209984	−	0.209984i
$322$		0			0
$323$	−1.80385			−0.100369
$324$	−9.00000			−0.500000
$325$	5.79555	+	10.0382i	0.321480	+	0.556819i
$326$	7.07180			0.391671
$327$	4.74668	+	17.7148i	0.262492	+	0.979633i
$328$	−2.82843	−	4.89898i	−0.156174	−	0.270501i
$329$		0			0
$330$	−0.339746	−	1.26795i	−0.0187024	−	0.0697983i
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	0.982754	−	0.184917i	$-0.0592016\pi$
$331$	6.02628	+	10.4378i	0.331234	+	0.573715i	−0.651520	+	0.758632i	$0.725868\pi$
$332$	−4.94975	−	8.57321i	−0.271653	−	0.470516i
$333$	20.7846	−	12.0000i	1.13899	−	0.657596i
$334$	−6.64136	+	11.5032i	−0.363399	+	0.629426i
$335$	−0.984508	+	1.70522i	−0.0537894	+	0.0931660i
$336$		0			0
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	0.995396	+	0.0958434i	$0.0305548\pi$
$337$	10.6603	+	18.4641i	0.580701	+	1.00580i	−0.414695	+	0.909960i	$0.636112\pi$
$338$	7.00000			0.380750
$339$	−6.57201	−	24.5271i	−0.356943	−	1.33213i
$340$	−1.80385			−0.0978274
$341$	−5.37945	+	9.31749i	−0.291314	+	0.504570i
$342$	1.34486	+	0.776457i	0.0727219	+	0.0419860i
$343$		0			0
$344$	−6.09808	+	10.5622i	−0.328786	+	0.569474i
$345$	6.86603	+	1.83975i	0.369654	+	0.0990486i
$346$	9.71003	−	16.8183i	0.522014	−	0.904155i
$347$	−10.8564	+	18.8038i	−0.582802	+	1.00944i	0.412343	+	0.911029i	$0.364711\pi$
$347$	−10.8564	+	18.8038i	−0.582802	+	1.00944i	−0.995145	+	0.0984148i	$0.968623\pi$
$348$	1.22474	+	4.57081i	0.0656532	+	0.245021i
$349$	−17.2987	+	29.9623i	−0.925980	+	1.60384i	−0.136002	+	0.990709i	$0.543425\pi$
$349$	−17.2987	+	29.9623i	−0.925980	+	1.60384i	−0.789978	+	0.613136i	$0.789908\pi$
$350$		0			0
$351$	−3.29423	+	12.2942i	−0.175833	+	0.656217i
$352$	−0.732051	+	1.26795i	−0.0390184	+	0.0675819i
$353$	−0.101536			−0.00540421			−0.00270211	−	0.999996i	$-0.500860\pi$
$353$	−0.101536			−0.00540421			−0.00270211	+	0.999996i	$0.500860\pi$
$354$	−24.7583	−	6.63397i	−1.31589	−	0.352592i
$355$	0.416102			0.0220844
$356$	−8.05558	−	13.9527i	−0.426945	−	0.739490i
$357$		0			0
$358$	−4.09808	+	7.09808i	−0.216590	+	0.375145i
$359$	6.96410	−	12.0622i	0.367551	−	0.636617i	−0.621631	−	0.783310i	$-0.713530\pi$
$359$	6.96410	−	12.0622i	0.367551	−	0.636617i	0.989182	+	0.146693i	$0.0468629\pi$
$360$	1.34486	+	0.776457i	0.0708805	+	0.0409229i
$361$	9.36603	+	16.2224i	0.492949	+	0.853812i
$362$	10.4865	+	18.1631i	0.551157	+	0.954632i
$363$	14.8171	+	3.97022i	0.777694	+	0.208382i
$364$		0			0
$365$	−1.19615	−	2.07180i	−0.0626095	−	0.108443i
$366$	5.36603	−	5.36603i	0.280487	−	0.280487i
$367$	0.277401			0.0144802			0.00724012	−	0.999974i	$-0.497695\pi$
$367$	0.277401			0.0144802			0.00724012	+	0.999974i	$0.497695\pi$
$368$	−3.96410	−	6.86603i	−0.206643	−	0.357916i
$369$			16.9706i			0.883452i
$370$	−4.14110			−0.215286
$371$		0			0
$372$	−3.29423	−	12.2942i	−0.170798	−	0.637426i
$373$	19.1244			0.990222			0.495111	−	0.868830i	$-0.335127\pi$
$373$	19.1244			0.990222			0.495111	+	0.868830i	$0.335127\pi$
$374$	−2.55103	+	4.41851i	−0.131910	+	0.228476i
$375$	−8.42820	−	2.25833i	−0.435231	−	0.116620i
$376$	2.31079	+	4.00240i	0.119170	+	0.206408i
$377$	6.69213			0.344662
$378$		0			0
$379$	−27.5167			−1.41344			−0.706718	−	0.707495i	$-0.749825\pi$
$379$	−27.5167			−1.41344			−0.706718	+	0.707495i	$0.749825\pi$
$380$	−0.133975	−	0.232051i	−0.00687275	−	0.0119040i
$381$	9.91808	+	2.65754i	0.508118	+	0.136150i
$382$	−3.59808	+	6.23205i	−0.184094	+	0.318859i
$383$	34.2185			1.74849			0.874243	−	0.485489i	$-0.161359\pi$
$383$	34.2185			1.74849			0.874243	+	0.485489i	$0.161359\pi$
$384$	−0.448288	−	1.67303i	−0.0228766	−	0.0853766i
$385$		0			0
$386$	23.7321			1.20793
$387$	31.6865	−	18.2942i	1.61072	−	0.929948i
$388$	−0.517638	−	0.896575i	−0.0262791	−	0.0455167i
$389$	−4.87564			−0.247205			−0.123602	−	0.992332i	$-0.539445\pi$
$389$	−4.87564			−0.247205			−0.123602	+	0.992332i	$0.539445\pi$
$390$	1.55291	−	1.55291i	0.0786349	−	0.0786349i
$391$	−13.8140	−	23.9265i	−0.698602	−	1.21001i
$392$		0			0
$393$	20.8923	+	5.59808i	1.05388	+	0.282386i
$394$	4.83013	+	8.36603i	0.243338	+	0.421474i
$395$	3.65565	+	6.33178i	0.183936	+	0.318586i
$396$	3.80385	−	2.19615i	0.191151	−	0.110361i
$397$	13.1948	−	22.8541i	0.662228	−	1.14701i	−0.317801	−	0.948157i	$-0.602945\pi$
$397$	13.1948	−	22.8541i	0.662228	−	1.14701i	0.980029	−	0.198855i	$-0.0637222\pi$
$398$	−5.79555	+	10.0382i	−0.290505	+	0.503169i
$399$		0			0
$400$	2.36603	+	4.09808i	0.118301	+	0.204904i
$401$	−25.0526			−1.25107			−0.625533	−	0.780198i	$-0.715118\pi$
$401$	−25.0526			−1.25107			−0.625533	+	0.780198i	$0.715118\pi$
$402$	−6.36396	−	1.70522i	−0.317406	−	0.0850486i
$403$	−18.0000			−0.896644
$404$	2.89778	−	5.01910i	0.144170	−	0.249709i
$405$	−2.32937	−	4.03459i	−0.115747	−	0.200480i
$406$		0			0
$407$	−5.85641	+	10.1436i	−0.290291	+	0.502799i
$408$	−1.56218	−	5.83013i	−0.0773393	−	0.288634i
$409$	8.90138	−	15.4176i	0.440145	−	0.762354i	−0.557555	−	0.830140i	$-0.688260\pi$
$409$	8.90138	−	15.4176i	0.440145	−	0.762354i	0.997700	+	0.0677865i	$0.0215937\pi$
$410$	1.46410	−	2.53590i	0.0723068	−	0.125239i
$411$		0			0
$412$	−5.60609	+	9.71003i	−0.276192	+	0.478379i
$413$		0			0
$414$			23.7846i			1.16895i
$415$	2.56218	−	4.43782i	0.125772	−	0.217844i
$416$	−2.44949			−0.120096
$417$	9.06218	+	33.8205i	0.443777	+	1.65620i
$418$	−0.757875			−0.0370689
$419$	−11.3323	−	19.6281i	−0.553619	−	0.958896i	−0.998010	−	0.0630626i	$-0.979913\pi$
$419$	−11.3323	−	19.6281i	−0.553619	−	0.958896i	0.444391	−	0.895833i	$-0.353420\pi$
$420$		0			0
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	0.290276	+	0.956943i	$0.406253\pi$
$421$	−14.0263	+	24.2942i	−0.683599	+	1.18403i	−0.973875	+	0.227085i	$0.927080\pi$
$422$	0.633975	−	1.09808i	0.0308614	−	0.0534535i
$423$		−	13.8647i		−	0.674126i
$424$	3.36603	+	5.83013i	0.163469	+	0.283136i
$425$	8.24504	+	14.2808i	0.399943	+	0.692722i
$426$	0.360355	+	1.34486i	0.0174593	+	0.0651588i
$427$		0			0
$428$	−1.53590	−	2.66025i	−0.0742405	−	0.128588i
$429$	−1.60770	−	6.00000i	−0.0776203	−	0.289683i
$430$	−6.31319			−0.304449
$431$	13.3923	+	23.1962i	0.645085	+	1.11732i	0.984282	+	0.176604i	$0.0565112\pi$
$431$	13.3923	+	23.1962i	0.645085	+	1.11732i	−0.339197	+	0.940715i	$0.610155\pi$
$432$	−1.34486	+	5.01910i	−0.0647048	+	0.241481i
$433$	20.2523			0.973261			0.486631	−	0.873608i	$-0.338226\pi$
$433$	20.2523			0.973261			0.486631	+	0.873608i	$0.338226\pi$
$434$		0			0
$435$	−1.73205	+	1.73205i	−0.0830455	+	0.0830455i
$436$	10.5885			0.507095
$437$	2.05197	−	3.55412i	0.0981590	−	0.170016i
$438$	5.66025	−	5.66025i	0.270457	−	0.270457i
$439$	9.14162	+	15.8338i	0.436306	+	0.755704i	0.997401	−	0.0720474i	$-0.0229533\pi$
$439$	9.14162	+	15.8338i	0.436306	+	0.755704i	−0.561095	+	0.827751i	$0.689620\pi$
$440$	−0.757875			−0.0361303
$441$		0			0
$442$	−8.53590			−0.406011
$443$	18.4904	+	32.0263i	0.878505	+	1.52161i	0.852982	+	0.521940i	$0.174792\pi$
$443$	18.4904	+	32.0263i	0.878505	+	1.52161i	0.0255224	+	0.999674i	$0.491875\pi$
$444$	−3.58630	−	13.3843i	−0.170198	−	0.635189i
$445$	4.16987	−	7.22243i	0.197671	−	0.342376i
$446$	3.76217			0.178144
$447$	4.00240	+	1.07244i	0.189307	+	0.0507247i
$448$		0			0
$449$	−23.7846			−1.12247			−0.561233	−	0.827658i	$-0.689673\pi$
$449$	−23.7846			−1.12247			−0.561233	+	0.827658i	$0.689673\pi$
$450$		−	14.1962i		−	0.669213i
$451$	−4.14110	−	7.17260i	−0.194997	−	0.337745i
$452$	−14.6603			−0.689560
$453$	29.0979	+	7.79676i	1.36714	+	0.366324i
$454$	−1.67303	−	2.89778i	−0.0785193	−	0.135999i
$455$		0			0
$456$	0.633975	−	0.633975i	0.0296886	−	0.0296886i
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	0.999707	+	0.0242164i	$0.00770906\pi$
$457$	11.1340	+	19.2846i	0.520825	+	0.902096i	−0.478881	+	0.877880i	$0.658958\pi$
$458$	−6.90018	−	11.9515i	−0.322424	−	0.558455i
$459$	−4.68653	+	17.4904i	−0.218749	+	0.816381i
$460$	2.05197	−	3.55412i	0.0956736	−	0.165712i
$461$	19.4894	−	33.7566i	0.907712	−	1.57220i	0.0904771	−	0.995899i	$-0.471161\pi$
$461$	19.4894	−	33.7566i	0.907712	−	1.57220i	0.817235	−	0.576305i	$-0.195506\pi$
$462$		0			0
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	0.778209	−	0.628005i	$-0.216128\pi$
$463$	−3.33013	−	5.76795i	−0.154764	−	0.268059i	−0.932973	+	0.359946i	$0.882795\pi$
$464$	2.73205			0.126832
$465$	4.65874	−	4.65874i	0.216044	−	0.216044i
$466$	−1.39230			−0.0644973
$467$	12.2982	−	21.3011i	0.569094	−	0.985699i	−0.427562	−	0.903986i	$-0.640628\pi$
$467$	12.2982	−	21.3011i	0.569094	−	0.985699i	0.996656	−	0.0817131i	$-0.0260391\pi$
$468$	6.36396	+	3.67423i	0.294174	+	0.169842i
$469$		0			0
$470$	−1.19615	+	2.07180i	−0.0551744	+	0.0955649i
$471$	21.1699	−	21.1699i	0.975456	−	0.975456i
$472$	−7.39924	+	12.8159i	−0.340577	+	0.589898i
$473$	−8.92820	+	15.4641i	−0.410519	+	0.711040i
$474$	−17.2987	+	17.2987i	−0.794557	+	0.794557i
$475$	−1.22474	+	2.12132i	−0.0561951	+	0.0973329i
$476$		0			0
$477$		−	20.1962i		−	0.924718i
$478$	−6.23205	+	10.7942i	−0.285047	+	0.493717i
$479$	13.2827			0.606903			0.303452	−	0.952847i	$-0.401861\pi$
$479$	13.2827			0.606903			0.303452	+	0.952847i	$0.401861\pi$
$480$	0.633975	−	0.633975i	0.0289368	−	0.0289368i
$481$	−19.5959			−0.893497
$482$	−6.36396	−	11.0227i	−0.289870	−	0.502070i
$483$		0			0
$484$	4.42820	−	7.66987i	0.201282	−	0.348631i
$485$	0.267949	−	0.464102i	0.0121669	−	0.0210738i
$486$	11.0227	−	11.0227i	0.500000	−	0.500000i
$487$	16.1603	+	27.9904i	0.732291	+	1.26837i	0.955902	+	0.293687i	$0.0948822\pi$
$487$	16.1603	+	27.9904i	0.732291	+	1.26837i	−0.223611	+	0.974679i	$0.571784\pi$
$488$	−2.19067	−	3.79435i	−0.0991670	−	0.171762i
$489$	−8.66115	+	8.66115i	−0.391671	+	0.391671i
$490$		0			0
$491$	2.53590	+	4.39230i	0.114443	+	0.198222i	0.917557	−	0.397604i	$-0.130158\pi$
$491$	2.53590	+	4.39230i	0.114443	+	0.198222i	−0.803114	+	0.595826i	$0.796825\pi$
$492$	9.46410	+	2.53590i	0.426675	+	0.114327i
$493$	9.52056			0.428784
$494$	−0.633975	−	1.09808i	−0.0285239	−	0.0494048i
$495$	1.96902	+	1.13681i	0.0885007	+	0.0510959i
$496$	−7.34847			−0.329956
$497$		0			0
$498$	16.5622	+	4.43782i	0.742169	+	0.198864i
$499$	7.32051			0.327711			0.163855	−	0.986484i	$-0.447607\pi$
$499$	7.32051			0.327711			0.163855	+	0.986484i	$0.447607\pi$
$500$	−2.51884	+	4.36276i	−0.112646	+	0.195109i
$501$	−5.95448	−	22.2224i	−0.266027	−	0.992825i
$502$	0.258819	+	0.448288i	0.0115517	+	0.0200081i
$503$	−28.9406			−1.29040			−0.645199	−	0.764015i	$-0.723226\pi$
$503$	−28.9406			−1.29040			−0.645199	+	0.764015i	$0.723226\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−5.80385	−	10.0526i	−0.258012	−	0.446891i
$507$	−8.57321	+	8.57321i	−0.380750	+	0.380750i
$508$	2.96410	−	5.13397i	0.131511	−	0.227783i
$509$	7.62587			0.338011			0.169005	−	0.985615i	$-0.445944\pi$
$509$	7.62587			0.338011			0.169005	+	0.985615i	$0.445944\pi$
$510$	2.20925	−	2.20925i	0.0978274	−	0.0978274i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−2.59808	+	0.696152i	−0.114708	+	0.0307359i
$514$	−1.88108	−	3.25813i	−0.0829710	−	0.143710i
$515$	−5.80385			−0.255748
$516$	−5.46739	−	20.4046i	−0.240688	−	0.898261i
$517$	3.38323	+	5.85993i	0.148794	+	0.257719i
$518$		0			0
$519$	8.70577	+	32.4904i	0.382141	+	1.42617i
$520$	−0.633975	−	1.09808i	−0.0278016	−	0.0481538i
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	−0.963910	−	0.266228i	$-0.914223\pi$
$521$	−16.2635	−	28.1691i	−0.712515	−	1.23411i	0.251395	−	0.967885i	$-0.419111\pi$
$522$	−7.09808	−	4.09808i	−0.310674	−	0.179368i
$523$	19.6281	−	33.9969i	0.858277	−	1.48658i	−0.0152941	−	0.999883i	$-0.504868\pi$
$523$	19.6281	−	33.9969i	0.858277	−	1.48658i	0.873571	−	0.486696i	$-0.161798\pi$
$524$	6.24384	−	10.8147i	0.272764	−	0.472440i
$525$		0			0
$526$	1.33013	+	2.30385i	0.0579963	+	0.100453i
$527$	−25.6077			−1.11549
$528$	−0.656339	−	2.44949i	−0.0285635	−	0.106600i
$529$	39.8564			1.73289
$530$	−1.74238	+	3.01790i	−0.0756843	+	0.131089i
$531$	38.4476	−	22.1977i	1.66848	−	0.963299i
$532$		0			0
$533$	6.92820	−	12.0000i	0.300094	−	0.519778i
$534$	26.9545	+	7.22243i	1.16643	+	0.312545i
$535$	0.795040	−	1.37705i	0.0343726	−	0.0595350i
$536$	−1.90192	+	3.29423i	−0.0821506	+	0.142289i
$537$	−3.67423	−	13.7124i	−0.158555	−	0.591735i
$538$	−13.4536	+	23.3023i	−0.580026	+	1.00464i
$539$		0			0
$540$	−2.59808	+	0.696152i	−0.111803	+	0.0299576i
$541$	−10.3660	+	17.9545i	−0.445670	+	0.771924i	−0.998099	−	0.0616369i	$-0.980368\pi$
$541$	−10.3660	+	17.9545i	−0.445670	+	0.771924i	0.552428	+	0.833560i	$0.313701\pi$
$542$	14.7985			0.635649
$543$	−35.0885	−	9.40192i	−1.50579	−	0.403475i
$544$	−3.48477			−0.149408
$545$	2.74049	+	4.74668i	0.117390	+	0.203325i
$546$		0			0
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	−0.717071	−	0.697000i	$-0.754518\pi$
$547$	5.73205	−	9.92820i	0.245085	−	0.424499i	0.962155	+	0.272501i	$0.0878509\pi$
$548$		0			0
$549$			13.1440i			0.560973i
$550$	3.46410	+	6.00000i	0.147710	+	0.255841i
$551$	0.707107	+	1.22474i	0.0301238	+	0.0521759i
$552$	13.2641	+	3.55412i	0.564559	+	0.151273i
$553$		0			0
$554$	−8.09808	−	14.0263i	−0.344054	−	0.595920i
$555$	5.07180	−	5.07180i	0.215286	−	0.215286i
$556$	20.2151			0.857311
$557$	−1.43782	−	2.49038i	−0.0609225	−	0.105521i	0.833956	−	0.551832i	$-0.186071\pi$
$557$	−1.43782	−	2.49038i	−0.0609225	−	0.105521i	−0.894878	+	0.446311i	$0.852738\pi$
$558$	19.0919	+	11.0227i	0.808224	+	0.466628i
$559$	−29.8744			−1.26355
$560$		0			0
$561$	−2.28719	−	8.53590i	−0.0965651	−	0.360386i
$562$	17.3923			0.733650
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	−0.879152	−	0.476542i	$-0.841890\pi$
$563$	−0.637756	+	1.10463i	−0.0268782	+	0.0465545i	0.852273	+	0.523097i	$0.175223\pi$
$564$	−7.73205	−	2.07180i	−0.325578	−	0.0872384i
$565$	−3.79435	−	6.57201i	−0.159630	−	0.276487i
$566$	9.76079			0.410277
$567$		0			0
$568$	0.803848			0.0337287
$569$	−13.4641	−	23.3205i	−0.564445	−	0.977647i	−0.997101	−	0.0760878i	$-0.975757\pi$
$569$	−13.4641	−	23.3205i	−0.564445	−	0.977647i	0.432657	−	0.901559i	$-0.357576\pi$
$570$	0.448288	+	0.120118i	0.0187767	+	0.00503120i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−3.58630			−0.149951
$573$	−3.22595	−	12.0394i	−0.134766	−	0.502953i
$574$		0			0
$575$	−37.5167			−1.56455
$576$	2.59808	+	1.50000i	0.108253	+	0.0625000i
$577$	13.1440	+	22.7661i	0.547193	+	0.947766i	0.998465	+	0.0553797i	$0.0176369\pi$
$577$	13.1440	+	22.7661i	0.547193	+	0.947766i	−0.451272	+	0.892386i	$0.649030\pi$
$578$	4.85641			0.202000
$579$	−29.0657	+	29.0657i	−1.20793	+	1.20793i
$580$	0.707107	+	1.22474i	0.0293610	+	0.0508548i
$581$		0			0
$582$	1.73205	+	0.464102i	0.0717958	+	0.0192376i
$583$	4.92820	+	8.53590i	0.204105	+	0.353521i
$584$	−2.31079	−	4.00240i	−0.0956211	−	0.165621i
$585$			3.80385i			0.157270i
$586$	1.48356	−	2.56961i	0.0612855	−	0.106150i
$587$	1.76097	−	3.05008i	0.0726828	−	0.125890i	−0.827393	−	0.561623i	$-0.810177\pi$
$587$	1.76097	−	3.05008i	0.0726828	−	0.125890i	0.900076	+	0.435732i	$0.143511\pi$
$588$		0			0
$589$	−1.90192	−	3.29423i	−0.0783674	−	0.135736i
$590$	−7.66025			−0.315368
$591$	−16.1619	−	4.33057i	−0.664813	−	0.178136i
$592$	−8.00000			−0.328798
$593$	−3.39683	+	5.88349i	−0.139491	+	0.241606i	−0.927304	−	0.374309i	$-0.877880\pi$
$593$	−3.39683	+	5.88349i	−0.139491	+	0.241606i	0.787813	+	0.615915i	$0.211213\pi$
$594$	−1.96902	+	7.34847i	−0.0807897	+	0.301511i
$595$		0			0
$596$	1.19615	−	2.07180i	0.0489963	−	0.0848641i
$597$	−5.19615	−	19.3923i	−0.212664	−	0.793674i
$598$	9.71003	−	16.8183i	0.397073	−	0.687750i
$599$	6.19615	−	10.7321i	0.253168	−	0.438500i	−0.711228	−	0.702961i	$-0.751861\pi$
$599$	6.19615	−	10.7321i	0.253168	−	0.438500i	0.964396	+	0.264461i	$0.0851941\pi$
$600$	−7.91688	−	2.12132i	−0.323205	−	0.0866025i
$601$	−20.9730	+	36.3262i	−0.855505	+	1.48178i	0.0206704	+	0.999786i	$0.493420\pi$
$601$	−20.9730	+	36.3262i	−0.855505	+	1.48178i	−0.876176	+	0.481992i	$0.839913\pi$
$602$		0			0
$603$	9.88269	−	5.70577i	0.402454	−	0.232357i
$604$	8.69615	−	15.0622i	0.353841	−	0.612871i
$605$	4.58441			0.186383
$606$	2.59808	+	9.69615i	0.105540	+	0.393879i
$607$	21.3891			0.868156			0.434078	−	0.900875i	$-0.357074\pi$
$607$	21.3891			0.868156			0.434078	+	0.900875i	$0.357074\pi$
$608$	−0.258819	−	0.448288i	−0.0104965	−	0.0181805i
$609$		0			0
$610$	1.13397	−	1.96410i	0.0459133	−	0.0795241i
$611$	−5.66025	+	9.80385i	−0.228989	+	0.396621i
$612$	9.05369	+	5.22715i	0.365974	+	0.211295i
$613$	−10.2224	−	17.7058i	−0.412880	−	0.715129i	0.582323	−	0.812957i	$-0.302144\pi$
$613$	−10.2224	−	17.7058i	−0.412880	−	0.715129i	−0.995203	+	0.0978280i	$0.968810\pi$
$614$	5.96644	+	10.3342i	0.240786	+	0.417054i
$615$	1.31268	+	4.89898i	0.0529323	+	0.197546i
$616$		0			0
$617$	−21.1962	−	36.7128i	−0.853325	−	1.47800i	−0.878190	−	0.478311i	$-0.841249\pi$
$617$	−21.1962	−	36.7128i	−0.853325	−	1.47800i	0.0248653	−	0.999691i	$-0.492084\pi$
$618$	−5.02628	−	18.7583i	−0.202187	−	0.754571i
$619$	7.48717			0.300935			0.150467	−	0.988615i	$-0.451922\pi$
$619$	7.48717			0.300935			0.150467	+	0.988615i	$0.451922\pi$
$620$	−1.90192	−	3.29423i	−0.0763831	−	0.132299i
$621$	−29.1301	−	29.1301i	−1.16895	−	1.16895i
$622$	18.1817			0.729020
$623$		0			0
$624$	3.00000	−	3.00000i	0.120096	−	0.120096i
$625$	21.0526			0.842102
$626$	3.34607	−	5.79555i	0.133736	−	0.231637i
$627$	0.928203	−	0.928203i	0.0370689	−	0.0370689i
$628$	−8.64256	−	14.9694i	−0.344876	−	0.597343i
$629$	−27.8781			−1.11157
$630$		0			0
$631$	−3.87564			−0.154287			−0.0771435	−	0.997020i	$-0.524580\pi$
$631$	−3.87564			−0.154287			−0.0771435	+	0.997020i	$0.524580\pi$
$632$	7.06218	+	12.2321i	0.280918	+	0.486565i
$633$	0.568406	+	2.12132i	0.0225921	+	0.0843149i
$634$	16.2942	−	28.2224i	0.647126	−	1.12086i
$635$	3.06866			0.121776
$636$	−11.2629	−	3.01790i	−0.446605	−	0.119667i
$637$		0			0
$638$	4.00000			0.158362
$639$	−2.08846	−	1.20577i	−0.0826181	−	0.0476996i
$640$	−0.258819	−	0.448288i	−0.0102307	−	0.0177201i
$641$	−3.05256			−0.120569			−0.0602844	−	0.998181i	$-0.519201\pi$
$641$	−3.05256			−0.120569			−0.0602844	+	0.998181i	$0.519201\pi$
$642$	5.13922	+	1.37705i	0.202829	+	0.0543478i
$643$	−0.845807	−	1.46498i	−0.0333554	−	0.0577732i	0.848866	−	0.528608i	$-0.177286\pi$
$643$	−0.845807	−	1.46498i	−0.0333554	−	0.0577732i	−0.882221	+	0.470835i	$0.843953\pi$
$644$		0			0
$645$	7.73205	−	7.73205i	0.304449	−	0.304449i
$646$	−0.901924	−	1.56218i	−0.0354857	−	0.0614631i
$647$	−7.91688	−	13.7124i	−0.311244	−	0.539091i	0.667388	−	0.744711i	$-0.267412\pi$
$647$	−7.91688	−	13.7124i	−0.311244	−	0.539091i	−0.978632	+	0.205619i	$0.934079\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−10.8332	+	18.7637i	−0.425242	+	0.736540i
$650$	−5.79555	+	10.0382i	−0.227320	+	0.393730i
$651$		0			0
$652$	3.53590	+	6.12436i	0.138476	+	0.239848i
$653$	−41.3205			−1.61700			−0.808498	−	0.588499i	$-0.799719\pi$
$653$	−41.3205			−1.61700			−0.808498	+	0.588499i	$0.799719\pi$
$654$	−12.9682	+	12.9682i	−0.507095	+	0.507095i
$655$	6.46410			0.252573
$656$	2.82843	−	4.89898i	0.110432	−	0.191273i
$657$			13.8647i			0.540915i
$658$		0			0
$659$	19.5622	−	33.8827i	0.762034	−	1.31988i	−0.179766	−	0.983709i	$-0.557534\pi$
$659$	19.5622	−	33.8827i	0.762034	−	1.31988i	0.941800	−	0.336173i	$-0.109133\pi$
$660$	0.928203	−	0.928203i	0.0361303	−	0.0361303i
$661$	10.7267	−	18.5792i	0.417221	−	0.722648i	−0.578438	−	0.815727i	$-0.696337\pi$
$661$	10.7267	−	18.5792i	0.417221	−	0.722648i	0.995659	+	0.0930785i	$0.0296708\pi$
$662$	−6.02628	+	10.4378i	−0.234218	+	0.405677i
$663$	10.4543	−	10.4543i	0.406011	−	0.406011i
$664$	4.94975	−	8.57321i	0.192087	−	0.332705i
$665$		0			0
$666$	20.7846	+	12.0000i	0.805387	+	0.464991i
$667$	−10.8301	+	18.7583i	−0.419344	+	0.726325i
$668$	−13.2827			−0.513924
$669$	−4.60770	+	4.60770i	−0.178144	+	0.178144i
$670$	−1.96902			−0.0760697
$671$	−3.20736	−	5.55532i	−0.123819	−	0.214461i
$672$		0			0
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	−0.160804	−	0.986986i	$-0.551409\pi$
$673$	20.0885	−	34.7942i	0.774353	−	1.34122i	0.935157	−	0.354233i	$-0.115258\pi$
$674$	−10.6603	+	18.4641i	−0.410618	+	0.711211i
$675$	17.3867	+	17.3867i	0.669213	+	0.669213i
$676$	3.50000	+	6.06218i	0.134615	+	0.233161i
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	0.876742	−	0.480962i	$-0.159712\pi$
$677$	0.568406	+	0.984508i	0.0218456	+	0.0378377i	−0.854896	+	0.518800i	$0.826379\pi$
$678$	17.9551	−	17.9551i	0.689560	−	0.689560i
$679$		0			0
$680$	−0.901924	−	1.56218i	−0.0345872	−	0.0599068i
$681$	5.59808	+	1.50000i	0.214519	+	0.0574801i
$682$	−10.7589			−0.411980
$683$	6.80385	+	11.7846i	0.260342	+	0.450926i	0.966333	−	0.257295i	$-0.0828314\pi$
$683$	6.80385	+	11.7846i	0.260342	+	0.450926i	−0.705991	+	0.708221i	$0.749498\pi$
$684$			1.55291i			0.0593772i
$685$		0			0
$686$		0			0
$687$	23.0885	+	6.18653i	0.880880	+	0.236031i
$688$	−12.1962			−0.464974
$689$	−8.24504	+	14.2808i	−0.314111	+	0.544057i
$690$	1.83975	+	6.86603i	0.0700379	+	0.261385i
$691$	−18.4913	−	32.0279i	−0.703442	−	1.21840i	−0.967251	−	0.253822i	$-0.918312\pi$
$691$	−18.4913	−	32.0279i	−0.703442	−	1.21840i	0.263809	−	0.964575i	$-0.415021\pi$
$692$	19.4201			0.738240
$693$		0			0
$694$	−21.7128			−0.824207
$695$	5.23205	+	9.06218i	0.198463	+	0.343748i
$696$	−3.34607	+	3.34607i	−0.126832	+	0.126832i
$697$	9.85641	−	17.0718i	0.373338	−	0.646640i
$698$	−34.5975			−1.30953
$699$	1.70522	−	1.70522i	0.0644973	−	0.0644973i
$700$		0			0
$701$	20.5359			0.775630			0.387815	−	0.921737i	$-0.373230\pi$
$701$	20.5359			0.775630			0.387815	+	0.921737i	$0.373230\pi$
$702$	−12.2942	+	3.29423i	−0.464016	+	0.124333i
$703$	−2.07055	−	3.58630i	−0.0780924	−	0.135260i
$704$	−1.46410			−0.0551804
$705$	−1.07244	−	4.00240i	−0.0403905	−	0.150739i
$706$	−0.0507680	−	0.0879327i	−0.00191068	−	0.00330939i
$707$		0			0
$708$	−6.63397	−	24.7583i	−0.249320	−	0.930475i
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	0.996248	−	0.0865418i	$-0.0275816\pi$
$709$	11.2679	+	19.5167i	0.423177	+	0.732964i	−0.573072	+	0.819505i	$0.694248\pi$
$710$	0.208051	+	0.360355i	0.00780802	+	0.0135239i
$711$		−	42.3731i		−	1.58911i
$712$	8.05558	−	13.9527i	0.301895	−	0.522898i
$713$	29.1301	−	50.4548i	1.09093	−	1.88955i
$714$		0			0
$715$	−0.928203	−	1.60770i	−0.0347128	−	0.0601244i
$716$	−8.19615			−0.306305
$717$	−5.58750	−	20.8528i	−0.208669	−	0.778764i
$718$	13.9282			0.519796
$719$	−17.0077	+	29.4582i	−0.634281	+	1.09861i	0.352386	+	0.935855i	$0.385371\pi$
$719$	−17.0077	+	29.4582i	−0.634281	+	1.09861i	−0.986667	+	0.162752i	$0.947963\pi$
$720$			1.55291i			0.0578737i
$721$		0			0
$722$	−9.36603	+	16.2224i	−0.348567	+	0.603736i
$723$	21.2942	+	5.70577i	0.791941	+	0.212200i
$724$	−10.4865	+	18.1631i	−0.389727	+	0.675027i
$725$	6.46410	−	11.1962i	0.240071	−	0.415815i
$726$	3.97022	+	14.8171i	0.147349	+	0.549913i
$727$	−14.8864	+	25.7840i	−0.552106	+	0.956276i	0.446016	+	0.895025i	$0.352842\pi$
$727$	−14.8864	+	25.7840i	−0.552106	+	0.956276i	−0.998122	+	0.0612512i	$0.980491\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	1.19615	−	2.07180i	0.0442716	−	0.0766806i
$731$	−42.5007			−1.57195
$732$	7.33013	+	1.96410i	0.270929	+	0.0725953i
$733$	−30.1146			−1.11231			−0.556154	−	0.831079i	$-0.687723\pi$
$733$	−30.1146			−1.11231			−0.556154	+	0.831079i	$0.687723\pi$
$734$	0.138701	+	0.240237i	0.00511954	+	0.00886730i
$735$		0			0
$736$	3.96410	−	6.86603i	0.146119	−	0.253085i
$737$	−2.78461	+	4.82309i	−0.102572	+	0.177661i
$738$	−14.6969	+	8.48528i	−0.541002	+	0.312348i
$739$	8.07180	+	13.9808i	0.296926	+	0.514291i	0.975431	−	0.220305i	$-0.0707052\pi$
$739$	8.07180	+	13.9808i	0.296926	+	0.514291i	−0.678505	+	0.734596i	$0.737372\pi$
$740$	−2.07055	−	3.58630i	−0.0761150	−	0.131835i
$741$	2.12132	+	0.568406i	0.0779287	+	0.0208809i
$742$		0			0
$743$	14.1244	+	24.4641i	0.518172	+	0.897501i	0.999777	+	0.0211123i	$0.00672076\pi$
$743$	14.1244	+	24.4641i	0.518172	+	0.897501i	−0.481605	+	0.876389i	$0.659946\pi$
$744$	9.00000	−	9.00000i	0.329956	−	0.329956i
$745$	1.23835			0.0453696
$746$	9.56218	+	16.5622i	0.350096	+	0.606384i
$747$	−25.7196	+	14.8492i	−0.941033	+	0.543305i
$748$	−5.10205			−0.186549
$749$		0			0
$750$	−2.25833	−	8.42820i	−0.0824626	−	0.307754i
$751$	−50.1769			−1.83098			−0.915491	−	0.402339i	$-0.868197\pi$
$751$	−50.1769			−1.83098			−0.915491	+	0.402339i	$0.868197\pi$
$752$	−2.31079	+	4.00240i	−0.0842658	+	0.145953i
$753$	−0.866025	−	0.232051i	−0.0315597	−	0.00845640i
$754$	3.34607	+	5.79555i	0.121857	+	0.211062i
$755$	9.00292			0.327650
$756$		0			0
$757$	20.2487			0.735952			0.367976	−	0.929835i	$-0.380051\pi$
$757$	20.2487			0.735952			0.367976	+	0.929835i	$0.380051\pi$
$758$	−13.7583	−	23.8301i	−0.499725	−	0.865549i
$759$	19.4201	+	5.20359i	0.704903	+	0.188878i
$760$	0.133975	−	0.232051i	0.00485977	−	0.00841737i
$761$	39.7738			1.44180			0.720900	−	0.693039i	$-0.243729\pi$
$761$	39.7738			1.44180			0.720900	+	0.693039i	$0.243729\pi$
$762$	2.65754	+	9.91808i	0.0962725	+	0.359294i
$763$		0			0
$764$	−7.19615			−0.260348
$765$			5.41154i			0.195655i
$766$	17.1093	+	29.6341i	0.618183	+	1.07072i
$767$	−36.2487			−1.30887
$768$	1.22474	−	1.22474i	0.0441942	−	0.0441942i
$769$	14.9372	+	25.8719i	0.538648	+	0.932966i	0.998977	+	0.0452178i	$0.0143982\pi$
$769$	14.9372	+	25.8719i	0.538648	+	0.932966i	−0.460329	+	0.887748i	$0.652268\pi$
$770$		0			0
$771$	6.29423	+	1.68653i	0.226681	+	0.0607390i
$772$	11.8660	+	20.5526i	0.427068	+	0.739703i
$773$	6.76148	+	11.7112i	0.243194	+	0.421224i	0.961622	−	0.274377i	$-0.0884716\pi$
$773$	6.76148	+	11.7112i	0.243194	+	0.421224i	−0.718429	+	0.695601i	$0.755138\pi$
$774$	31.6865	+	18.2942i	1.13895	+	0.657572i
$775$	−17.3867	+	30.1146i	−0.624547	+	1.08175i
$776$	0.517638	−	0.896575i	0.0185821	−	0.0321852i
$777$		0			0
$778$	−2.43782	−	4.22243i	−0.0874002	−	0.151382i
$779$	2.92820			0.104914
$780$	2.12132	+	0.568406i	0.0759555	+	0.0203522i
$781$	1.17691			0.0421133
$782$	13.8140	−	23.9265i	0.493986	−	0.855610i
$783$	13.7124	−	3.67423i	0.490042	−	0.131306i
$784$		0			0
$785$	4.47372	−	7.74871i	0.159674	−	0.276563i
$786$	5.59808	+	20.8923i	0.199677	+	0.745204i
$787$	−18.0938	+	31.3393i	−0.644973	+	1.11713i	0.339334	+	0.940666i	$0.389798\pi$
$787$	−18.0938	+	31.3393i	−0.644973	+	1.11713i	−0.984308	+	0.176461i	$0.943535\pi$
$788$	−4.83013	+	8.36603i	−0.172066	+	0.298027i
$789$	−4.45069	−	1.19256i	−0.158449	−	0.0424562i
$790$	−3.65565	+	6.33178i	−0.130062	+	0.225274i
$791$		0			0
$792$	3.80385	+	2.19615i	0.135164	+	0.0780369i
$793$	5.36603	−	9.29423i	0.190553	−	0.330048i
$794$	26.3896			0.936531
$795$	−1.56218	−	5.83013i	−0.0554047	−	0.206773i
$796$	−11.5911			−0.410836
$797$	12.2796	+	21.2690i	0.434967	+	0.753385i	0.997293	−	0.0735308i	$-0.0234267\pi$
$797$	12.2796	+	21.2690i	0.434967	+	0.753385i	−0.562326	+	0.826916i	$0.690093\pi$
$798$		0			0
$799$	−8.05256	+	13.9474i	−0.284879	+	0.493425i
$800$	−2.36603	+	4.09808i	−0.0836516	+	0.144889i
$801$	−41.8580	+	24.1667i	−1.47898	+	0.853889i
$802$	−12.5263	−	21.6962i	−0.442318	−	0.766118i
$803$	−3.38323	−	5.85993i	−0.119392	−	0.206792i
$804$	−1.70522	−	6.36396i	−0.0601384	−	0.224440i
$805$		0			0
$806$	−9.00000	−	15.5885i	−0.317011	−	0.549080i
$807$	−12.0622	−	45.0167i	−0.424609	−	1.58466i
$808$	5.79555			0.203887
$809$	−16.6603	−	28.8564i	−0.585743	−	1.01454i	−0.994782	−	0.102020i	$-0.967469\pi$
$809$	−16.6603	−	28.8564i	−0.585743	−	1.01454i	0.409039	−	0.912517i	$-0.365864\pi$
$810$	2.32937	−	4.03459i	0.0818458	−	0.141761i
$811$	−7.82894			−0.274911			−0.137456	−	0.990508i	$-0.543892\pi$
$811$	−7.82894			−0.274911			−0.137456	+	0.990508i	$0.543892\pi$
$812$		0			0
$813$	−18.1244	+	18.1244i	−0.635649	+	0.635649i
$814$	−11.7128			−0.410534
$815$	−1.83032	+	3.17020i	−0.0641132	+	0.111047i
$816$	4.26795	−	4.26795i	0.149408	−	0.149408i
$817$	−3.15660	−	5.46739i	−0.110435	−	0.191280i
$818$	17.8028			0.622459
$819$		0			0
$820$	2.92820			0.102257
$821$	3.33975	+	5.78461i	0.116558	+	0.201884i	0.918401	−	0.395650i	$-0.129481\pi$
$821$	3.33975	+	5.78461i	0.116558	+	0.201884i	−0.801844	+	0.597534i	$0.796147\pi$
$822$		0			0
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	−0.795153	−	0.606408i	$-0.792610\pi$
$823$	3.66025	−	6.33975i	0.127588	−	0.220990i	0.922742	+	0.385419i	$0.125943\pi$
$824$	−11.2122			−0.390595
$825$	−11.5911	−	3.10583i	−0.403551	−	0.108131i
$826$		0			0
$827$	−52.7321			−1.83367			−0.916837	−	0.399263i	$-0.869266\pi$
$827$	−52.7321			−1.83367			−0.916837	+	0.399263i	$0.869266\pi$
$828$	−20.5981	+	11.8923i	−0.715833	+	0.413286i
$829$	−0.947343	−	1.64085i	−0.0329026	−	0.0569890i	0.849105	−	0.528224i	$-0.177142\pi$
$829$	−0.947343	−	1.64085i	−0.0329026	−	0.0569890i	−0.882008	+	0.471235i	$0.843808\pi$
$830$	5.12436			0.177869
$831$	27.0967	+	7.26054i	0.939974	+	0.251865i
$832$	−1.22474	−	2.12132i	−0.0424604	−	0.0735436i
$833$		0			0
$834$	−24.7583	+	24.7583i	−0.857311	+	0.857311i
$835$	−3.43782	−	5.95448i	−0.118971	−	0.206063i
$836$	−0.378937	−	0.656339i	−0.0131058	−	0.0227000i
$837$	−36.8827	+	9.88269i	−1.27485	+	0.341596i
$838$	11.3323	−	19.6281i	0.391467	−	0.678042i
$839$	−22.4751	+	38.9280i	−0.775927	+	1.34395i	0.158345	+	0.987384i	$0.449384\pi$
$839$	−22.4751	+	38.9280i	−0.775927	+	1.34395i	−0.934272	+	0.356561i	$0.883949\pi$
$840$		0			0
$841$	10.7679	+	18.6506i	0.371309	+	0.643125i
$842$	−28.0526			−0.966755
$843$	−21.3011	+	21.3011i	−0.733650	+	0.733650i
$844$	1.26795			0.0436446
$845$	−1.81173	+	3.13801i	−0.0623255	+	0.107951i
$846$	12.0072	−	6.93237i	0.412816	−	0.238340i
$847$		0			0
$848$	−3.36603	+	5.83013i	−0.115590	+	0.200207i
$849$	−11.9545	+	11.9545i	−0.410277	+	0.410277i
$850$	−8.24504	+	14.2808i	−0.282803	+	0.489829i
$851$	31.7128	−	54.9282i	1.08710	−	1.88291i
$852$	−0.984508	+	0.984508i	−0.0337287	+	0.0337287i
$853$	11.7992	−	20.4367i	0.403996	−	0.699741i	−0.590208	−	0.807251i	$-0.700954\pi$
$853$	11.7992	−	20.4367i	0.403996	−	0.699741i	0.994204	+	0.107510i	$0.0342878\pi$
$854$		0			0
$855$	−0.696152	+	0.401924i	−0.0238079	+	0.0137455i
$856$	1.53590	−	2.66025i	0.0524959	−	0.0909256i
$857$	−5.45378			−0.186298			−0.0931488	−	0.995652i	$-0.529693\pi$
$857$	−5.45378			−0.186298			−0.0931488	+	0.995652i	$0.529693\pi$
$858$	4.39230	−	4.39230i	0.149951	−	0.149951i
$859$	−9.69642			−0.330838			−0.165419	−	0.986223i	$-0.552898\pi$
$859$	−9.69642			−0.330838			−0.165419	+	0.986223i	$0.552898\pi$
$860$	−3.15660	−	5.46739i	−0.107639	−	0.186436i
$861$		0			0
$862$	−13.3923	+	23.1962i	−0.456144	+	0.790064i
$863$	−10.5981	+	18.3564i	−0.360763	+	0.624859i	−0.988087	−	0.153899i	$-0.950817\pi$
$863$	−10.5981	+	18.3564i	−0.360763	+	0.624859i	0.627324	+	0.778758i	$0.284150\pi$
$864$	−5.01910	+	1.34486i	−0.170753	+	0.0457532i
$865$	5.02628	+	8.70577i	0.170899	+	0.296005i
$866$	10.1261	+	17.5390i	0.344100	+	0.595998i
$867$	−5.94786	+	5.94786i	−0.202000	+	0.202000i
$868$		0			0
$869$	10.3397	+	17.9090i	0.350752	+	0.607520i
$870$	−2.36603	−	0.633975i	−0.0802158	−	0.0214938i
$871$	−9.31749			−0.315711
$872$	5.29423	+	9.16987i	0.179285	+	0.310531i
$873$	−2.68973	+	1.55291i	−0.0910334	+	0.0525582i
$874$	4.10394			0.138818
$875$		0			0
$876$	7.73205	+	2.07180i	0.261242	+	0.0699995i
$877$	24.0526			0.812197			0.406099	−	0.913829i	$-0.366889\pi$
$877$	24.0526			0.812197			0.406099	+	0.913829i	$0.366889\pi$
$878$	−9.14162	+	15.8338i	−0.308515	+	0.534363i
$879$	1.33013	+	4.96410i	0.0448641	+	0.167435i
$880$	−0.378937	−	0.656339i	−0.0127740	−	0.0221252i
$881$	−0.480473			−0.0161876			−0.00809378	−	0.999967i	$-0.502576\pi$
$881$	−0.480473			−0.0161876			−0.00809378	+	0.999967i	$0.502576\pi$
$882$		0			0
$883$	38.2487			1.28717			0.643586	−	0.765374i	$-0.277446\pi$
$883$	38.2487			1.28717			0.643586	+	0.765374i	$0.277446\pi$
$884$	−4.26795	−	7.39230i	−0.143547	−	0.248630i
$885$	9.38186	−	9.38186i	0.315368	−	0.315368i
$886$	−18.4904	+	32.0263i	−0.621197	+	1.07594i
$887$	−26.9716			−0.905617			−0.452809	−	0.891608i	$-0.649578\pi$
$887$	−26.9716			−0.905617			−0.452809	+	0.891608i	$0.649578\pi$
$888$	9.79796	−	9.79796i	0.328798	−	0.328798i
$889$		0			0
$890$	8.33975			0.279549
$891$	−6.58846	−	11.4115i	−0.220722	−	0.382301i
$892$	1.88108	+	3.25813i	0.0629833	+	0.109090i
$893$	−2.39230			−0.0800554
$894$	1.07244	+	4.00240i	0.0358678	+	0.133860i
$895$	−2.12132	−	3.67423i	−0.0709079	−	0.122816i
$896$		0			0
$897$	8.70577	+	32.4904i	0.290677	+	1.08482i
$898$	−11.8923	−	20.5981i	−0.396851	−	0.687367i
$899$	10.0382	+	17.3867i	0.334793	+	0.579878i
$900$	12.2942	−	7.09808i	0.409808	−	0.236603i
$901$	−11.7298	+	20.3166i	−0.390777	+	0.676845i
$902$	4.14110	−	7.17260i	0.137884	−	0.238822i
$903$		0			0
$904$	−7.33013	−	12.6962i	−0.243796	−	0.422268i
$905$	−10.8564			−0.360879
$906$	7.79676	+	29.0979i	0.259030	+	0.966713i
$907$	−5.12436			−0.170151			−0.0850757	−	0.996374i	$-0.527113\pi$
$907$	−5.12436			−0.170151			−0.0850757	+	0.996374i	$0.527113\pi$
$908$	1.67303	−	2.89778i	0.0555215	−	0.0961661i
$909$	−15.0573	−	8.69333i	−0.499419	−	0.288340i
$910$		0			0
$911$	−13.8923	+	24.0622i	−0.460273	+	0.797216i	−0.998974	−	0.0452811i	$-0.985582\pi$
$911$	−13.8923	+	24.0622i	−0.460273	+	0.797216i	0.538702	+	0.842497i	$0.318915\pi$
$912$	0.866025	+	0.232051i	0.0286770	+	0.00768397i
$913$	7.24693	−	12.5521i	0.239838	−	0.415412i
$914$	−11.1340	+	19.2846i	−0.368279	+	0.637878i
$915$	1.01669	+	3.79435i	0.0336109	+	0.125437i
$916$	6.90018	−	11.9515i	0.227988	−	0.394888i
$917$		0			0
$918$	−17.4904	+	4.68653i	−0.577269	+	0.154679i
$919$	−8.18653	+	14.1795i	−0.270049	+	0.467738i	−0.968874	−	0.247554i	$-0.920373\pi$
$919$	−8.18653	+	14.1795i	−0.270049	+	0.467738i	0.698825	+	0.715292i	$0.253707\pi$
$920$	4.10394			0.135303
$921$	−19.9641	−	5.34936i	−0.657840	−	0.176268i
$922$	38.9788			1.28370
$923$	0.984508	+	1.70522i	0.0324055	+	0.0561279i
$924$		0			0
$925$	−18.9282	+	32.7846i	−0.622355	+	1.07795i
$926$	3.33013	−	5.76795i	0.109435	−	0.189547i
$927$	29.1301	+	16.8183i	0.956757	+	0.552384i
$928$	1.36603	+	2.36603i	0.0448420	+	0.0776686i
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	0.897255	−	0.441512i	$-0.145558\pi$
$929$	2.01978	+	3.49837i	0.0662670	+	0.114778i	−0.830988	+	0.556290i	$0.812224\pi$
$930$	6.36396	+	1.70522i	0.208683	+	0.0559163i
$931$		0			0
$932$	−0.696152	−	1.20577i	−0.0228032	−	0.0394964i
$933$	−22.2679	+	22.2679i	−0.729020	+	0.729020i
$934$	24.5964			0.804820
$935$	−1.32051	−	2.28719i	−0.0431852	−	0.0747990i
$936$			7.34847i			0.240192i
$937$	−31.7690			−1.03785			−0.518925	−	0.854820i	$-0.673667\pi$
$937$	−31.7690			−1.03785			−0.518925	+	0.854820i	$0.673667\pi$
$938$		0			0
$939$	3.00000	+	11.1962i	0.0979013	+	0.365373i
$940$	−2.39230			−0.0780284
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.210510	+	0.977592i	$0.567512\pi$
$941$	−29.1994	+	50.5749i	−0.951874	+	1.64869i	−0.741364	+	0.671103i	$0.765821\pi$
$942$	28.9186	+	7.74871i	0.942218	+	0.252467i
$943$	22.4243	+	38.8401i	0.730237	+	1.26481i
$944$	−14.7985			−0.481649
$945$		0			0
$946$	−17.8564			−0.580562
$947$	17.8301	+	30.8827i	0.579401	+	1.00355i	0.995548	+	0.0942550i	$0.0300469\pi$
$947$	17.8301	+	30.8827i	0.579401	+	1.00355i	−0.416147	+	0.909297i	$0.636620\pi$
$948$	−23.6305	−	6.33178i	−0.767483	−	0.205647i
$949$	5.66025	−	9.80385i	0.183740	−	0.318246i
$950$	−2.44949			−0.0794719
$951$	14.6090	+	54.5216i	0.473729	+	1.76798i
$952$		0			0
$953$	23.7128			0.768133			0.384067	−	0.923305i	$-0.374523\pi$
$953$	23.7128			0.768133			0.384067	+	0.923305i	$0.374523\pi$
$954$	17.4904	−	10.0981i	0.566272	−	0.326937i
$955$	−1.86250	−	3.22595i	−0.0602691	−	0.104389i
$956$	−12.4641			−0.403118
$957$	−4.89898	+	4.89898i	−0.158362	+	0.158362i
$958$	6.64136	+	11.5032i	0.214573	+	0.371651i
$959$		0			0
$960$	0.866025	+	0.232051i	0.0279508	+	0.00748941i
$961$	−11.5000	−	19.9186i	−0.370968	−	0.642535i
$962$	−9.79796	−	16.9706i	−0.315899	−	0.547153i
$963$	−7.98076	+	4.60770i	−0.257176	+	0.148481i
$964$	6.36396	−	11.0227i	0.204969	−	0.355017i
$965$	−6.14231	+	10.6388i	−0.197728	+	0.342475i
$966$		0			0
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	0.869732	−	0.493524i	$-0.164291\pi$
$967$	0.232051	+	0.401924i	0.00746225	+	0.0129250i	−0.862270	+	0.506449i	$0.830958\pi$
$968$	8.85641			0.284656
$969$	3.01790	+	0.808643i	0.0969488	+	0.0259773i
$970$	0.535898			0.0172067
$971$	14.2994	−	24.7673i	0.458890	−	0.794821i	−0.540012	−	0.841657i	$-0.681580\pi$
$971$	14.2994	−	24.7673i	0.458890	−	0.794821i	0.998903	+	0.0468359i	$0.0149138\pi$
$972$	15.0573	+	4.03459i	0.482963	+	0.129410i
$973$		0			0
$974$	−16.1603	+	27.9904i	−0.517808	+	0.896870i
$975$	−5.19615	−	19.3923i	−0.166410	−	0.621051i
$976$	2.19067	−	3.79435i	0.0701217	−	0.121454i
$977$	8.07180	−	13.9808i	0.258240	−	0.447284i	−0.707531	−	0.706683i	$-0.750191\pi$
$977$	8.07180	−	13.9808i	0.258240	−	0.447284i	0.965770	+	0.259398i	$0.0835242\pi$
$978$	−11.8313	−	3.17020i	−0.378325	−	0.101372i
$979$	11.7942	−	20.4281i	0.376944	−	0.652886i
$980$		0			0
$981$		−	31.7654i		−	1.01419i
$982$	−2.53590	+	4.39230i	−0.0809238	+	0.140164i
$983$	23.6355			0.753855			0.376927	−	0.926243i	$-0.376981\pi$
$983$	23.6355			0.753855			0.376927	+	0.926243i	$0.376981\pi$
$984$	2.53590	+	9.46410i	0.0808415	+	0.301705i
$985$	−5.00052			−0.159330
$986$	4.76028	+	8.24504i	0.151598	+	0.262576i
$987$		0			0
$988$	0.633975	−	1.09808i	0.0201694	−	0.0349345i
$989$	48.3468	−	83.7391i	1.53734	−	2.66275i
$990$			2.27362i			0.0722605i
$991$	−7.33975	−	12.7128i	−0.233155	−	0.403836i	0.725580	−	0.688138i	$-0.241572\pi$
$991$	−7.33975	−	12.7128i	−0.233155	−	0.403836i	−0.958735	+	0.284302i	$0.908238\pi$
$992$	−3.67423	−	6.36396i	−0.116657	−	0.202056i
$993$	−5.40301	−	20.1643i	−0.171459	−	0.639895i
$994$		0			0
$995$	−3.00000	−	5.19615i	−0.0951064	−	0.164729i
$996$	4.43782	+	16.5622i	0.140618	+	0.524793i
$997$	−43.8778			−1.38962			−0.694812	−	0.719192i	$-0.744512\pi$
$997$	−43.8778			−1.38962			−0.694812	+	0.719192i	$0.744512\pi$
$998$	3.66025	+	6.33975i	0.115863	+	0.200681i
$999$	−40.1528	+	10.7589i	−1.27038	+	0.340397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.t.79.1		8
3.2	odd	2		2646.2.h.q.667.3		8
7.2	even	3		882.2.f.s.295.3	yes	8
7.3	odd	6		882.2.e.q.655.2		8
7.4	even	3		882.2.e.q.655.3		8
7.5	odd	6		882.2.f.s.295.2	✓	8
7.6	odd	2	inner	882.2.h.t.79.4		8
9.4	even	3		882.2.e.q.373.3		8
9.5	odd	6		2646.2.e.t.1549.2		8
21.2	odd	6		2646.2.f.q.883.2		8
21.5	even	6		2646.2.f.q.883.3		8
21.11	odd	6		2646.2.e.t.2125.2		8
21.17	even	6		2646.2.e.t.2125.3		8
21.20	even	2		2646.2.h.q.667.2		8
63.2	odd	6		7938.2.a.co.1.3		4
63.4	even	3	inner	882.2.h.t.67.1		8
63.5	even	6		2646.2.f.q.1765.3		8
63.13	odd	6		882.2.e.q.373.2		8
63.16	even	3		7938.2.a.cj.1.2		4
63.23	odd	6		2646.2.f.q.1765.2		8
63.31	odd	6	inner	882.2.h.t.67.4		8
63.32	odd	6		2646.2.h.q.361.3		8
63.40	odd	6		882.2.f.s.589.1	yes	8
63.41	even	6		2646.2.e.t.1549.3		8
63.47	even	6		7938.2.a.co.1.2		4
63.58	even	3		882.2.f.s.589.4	yes	8
63.59	even	6		2646.2.h.q.361.2		8
63.61	odd	6		7938.2.a.cj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.2		8	63.13	odd	6
882.2.e.q.373.3		8	9.4	even	3
882.2.e.q.655.2		8	7.3	odd	6
882.2.e.q.655.3		8	7.4	even	3
882.2.f.s.295.2	✓	8	7.5	odd	6
882.2.f.s.295.3	yes	8	7.2	even	3
882.2.f.s.589.1	yes	8	63.40	odd	6
882.2.f.s.589.4	yes	8	63.58	even	3
882.2.h.t.67.1		8	63.4	even	3	inner
882.2.h.t.67.4		8	63.31	odd	6	inner
882.2.h.t.79.1		8	1.1	even	1	trivial
882.2.h.t.79.4		8	7.6	odd	2	inner
2646.2.e.t.1549.2		8	9.5	odd	6
2646.2.e.t.1549.3		8	63.41	even	6
2646.2.e.t.2125.2		8	21.11	odd	6
2646.2.e.t.2125.3		8	21.17	even	6
2646.2.f.q.883.2		8	21.2	odd	6
2646.2.f.q.883.3		8	21.5	even	6
2646.2.f.q.1765.2		8	63.23	odd	6
2646.2.f.q.1765.3		8	63.5	even	6
2646.2.h.q.361.2		8	63.59	even	6
2646.2.h.q.361.3		8	63.32	odd	6
2646.2.h.q.667.2		8	21.20	even	2
2646.2.h.q.667.3		8	3.2	odd	2
7938.2.a.cj.1.2		4	63.16	even	3
7938.2.a.cj.1.3		4	63.61	odd	6
7938.2.a.co.1.2		4	63.47	even	6
7938.2.a.co.1.3		4	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(-0.500000 + 0.866025i) q^{4} -0.517638 q^{5} +(-0.448288 - 1.67303i) q^{6} -1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +(-0.258819 - 0.448288i) q^{10} -1.46410 q^{11} +(1.22474 - 1.22474i) q^{12} +(-1.22474 - 2.12132i) q^{13} +(0.866025 + 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.74238 - 3.01790i) q^{17} +3.00000i q^{18} +(0.258819 - 0.448288i) q^{19} +(0.258819 - 0.448288i) q^{20} +(-0.732051 - 1.26795i) q^{22} +7.92820 q^{23} +(1.67303 + 0.448288i) q^{24} -4.73205 q^{25} +(1.22474 - 2.12132i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(-1.36603 + 2.36603i) q^{29} +(0.232051 + 0.866025i) q^{30} +(3.67423 - 6.36396i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.44949 + 0.656339i) q^{33} +(1.74238 - 3.01790i) q^{34} +(-2.59808 + 1.50000i) q^{36} +(4.00000 - 6.92820i) q^{37} +0.517638 q^{38} +(1.09808 + 4.09808i) q^{39} +0.517638 q^{40} +(2.82843 + 4.89898i) q^{41} +(6.09808 - 10.5622i) q^{43} +(0.732051 - 1.26795i) q^{44} +(-1.34486 - 0.776457i) q^{45} +(3.96410 + 6.86603i) q^{46} +(-2.31079 - 4.00240i) q^{47} +(0.448288 + 1.67303i) q^{48} +(-2.36603 - 4.09808i) q^{50} +(1.56218 + 5.83013i) q^{51} +2.44949 q^{52} +(-3.36603 - 5.83013i) q^{53} +(1.34486 - 5.01910i) q^{54} +0.757875 q^{55} +(-0.633975 + 0.633975i) q^{57} -2.73205 q^{58} +(7.39924 - 12.8159i) q^{59} +(-0.633975 + 0.633975i) q^{60} +(2.19067 + 3.79435i) q^{61} +7.34847 q^{62} +1.00000 q^{64} +(0.633975 + 1.09808i) q^{65} +(0.656339 + 2.44949i) q^{66} +(1.90192 - 3.29423i) q^{67} +3.48477 q^{68} +(-13.2641 - 3.55412i) q^{69} -0.803848 q^{71} +(-2.59808 - 1.50000i) q^{72} +(2.31079 + 4.00240i) q^{73} +8.00000 q^{74} +(7.91688 + 2.12132i) q^{75} +(0.258819 + 0.448288i) q^{76} +(-3.00000 + 3.00000i) q^{78} +(-7.06218 - 12.2321i) q^{79} +(0.258819 + 0.448288i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-2.82843 + 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(0.901924 + 1.56218i) q^{85} +12.1962 q^{86} +(3.34607 - 3.34607i) q^{87} +1.46410 q^{88} +(-8.05558 + 13.9527i) q^{89} -1.55291i q^{90} +(-3.96410 + 6.86603i) q^{92} +(-9.00000 + 9.00000i) q^{93} +(2.31079 - 4.00240i) q^{94} +(-0.133975 + 0.232051i) q^{95} +(-1.22474 + 1.22474i) q^{96} +(-0.517638 + 0.896575i) q^{97} +(-3.80385 - 2.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} + 8 q^{23} - 24 q^{25} - 4 q^{29} - 12 q^{30} + 4 q^{32} + 32 q^{37} - 12 q^{39} + 28 q^{43} - 8 q^{44} + 4 q^{46} - 12 q^{50} - 36 q^{51}+ \cdots - 72 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 + 8 * q^22 + 8 * q^23 - 24 * q^25 - 4 * q^29 - 12 * q^30 + 4 * q^32 + 32 * q^37 - 12 * q^39 + 28 * q^43 - 8 * q^44 + 4 * q^46 - 12 * q^50 - 36 * q^51 - 20 * q^53 - 12 * q^57 - 8 * q^58 - 12 * q^60 + 8 * q^64 + 12 * q^65 + 36 * q^67 - 48 * q^71 + 64 * q^74 - 24 * q^78 - 8 * q^79 + 36 * q^81 + 28 * q^85 + 56 * q^86 - 16 * q^88 - 4 * q^92 - 72 * q^93 - 8 * q^95 - 72 * q^99

Introduction

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