LMFDB - Embedded newform 525.2.bc.a.493.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.493
Dual form			525.2.bc.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.189469 + 2.63896i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.189469 + 2.63896i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.517638 + 1.93185i) q^{12} +(1.41421 - 1.41421i) q^{13} +(2.00000 + 3.46410i) q^{16} +(5.79555 - 1.55291i) q^{17} +(1.73205 + 3.00000i) q^{19} +(2.50000 - 0.866025i) q^{21} +(0.707107 + 0.707107i) q^{27} +(2.31079 - 4.76028i) q^{28} +(-4.50000 - 2.59808i) q^{31} +(5.79555 + 1.55291i) q^{33} +2.00000 q^{36} +(8.36516 + 2.24144i) q^{37} +(-1.73205 - 1.00000i) q^{39} +10.3923i q^{41} +(3.67423 + 3.67423i) q^{43} +(10.3923 - 6.00000i) q^{44} +(-1.55291 + 5.79555i) q^{47} +(2.82843 - 2.82843i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-3.86370 + 1.03528i) q^{52} +(-10.0382 + 2.68973i) q^{53} +(2.44949 - 2.44949i) q^{57} +(-5.19615 + 9.00000i) q^{59} +(7.50000 - 4.33013i) q^{61} +(-1.48356 - 2.19067i) q^{63} -8.00000i q^{64} +(-0.896575 - 3.34607i) q^{67} +(-11.5911 - 3.10583i) q^{68} -6.00000 q^{71} +(0.258819 + 0.965926i) q^{73} -6.92820i q^{76} +(-14.2808 - 6.93237i) q^{77} +(4.33013 - 2.50000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(-5.19615 - 1.00000i) q^{84} +(5.19615 + 9.00000i) q^{89} +(4.00000 + 3.46410i) q^{91} +(-1.34486 + 5.01910i) q^{93} +(-9.19239 - 9.19239i) q^{97} -6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 24 q^{11} + 16 q^{16} + 20 q^{21} - 36 q^{31} + 16 q^{36} - 24 q^{51} + 60 q^{61} - 48 q^{71} + 4 q^{81} + 32 q^{91}+O(q^{100}) $ 8 * q - 24 * q^11 + 16 * q^16 + 20 * q^21 - 36 * q^31 + 16 * q^36 - 24 * q^51 + 60 * q^61 - 48 * q^71 + 4 * q^81 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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			0		0.258819	−	0.965926i	$-0.416667\pi$
$2$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$7$	0.189469	+	2.63896i	0.0716124	+	0.997433i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$	−0.517638	+	1.93185i	−0.149429	+	0.557678i
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	−0.483250	−	0.875482i	$-0.660544\pi$
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	0.875482	+	0.483250i	$0.160544\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	5.79555	−	1.55291i	1.40563	−	0.376637i	0.525266	−	0.850938i	$-0.323966\pi$
$17$	5.79555	−	1.55291i	1.40563	−	0.376637i	0.880363	+	0.474301i	$0.157299\pi$
$18$		0			0
$19$	1.73205	+	3.00000i	0.397360	+	0.688247i	0.993399	−	0.114708i	$-0.0365932\pi$
$19$	1.73205	+	3.00000i	0.397360	+	0.688247i	−0.596040	+	0.802955i	$0.703260\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.31079	−	4.76028i	0.436698	−	0.899608i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−4.50000	−	2.59808i	−0.808224	−	0.466628i	0.0381148	−	0.999273i	$-0.487865\pi$
$31$	−4.50000	−	2.59808i	−0.808224	−	0.466628i	−0.846339	+	0.532645i	$0.821198\pi$
$32$		0			0
$33$	5.79555	+	1.55291i	1.00888	+	0.270328i
$34$		0			0
$35$		0			0
$36$	2.00000			0.333333
$37$	8.36516	+	2.24144i	1.37522	+	0.368490i	0.869384	−	0.494137i	$-0.164516\pi$
$37$	8.36516	+	2.24144i	1.37522	+	0.368490i	0.505840	+	0.862627i	$0.331183\pi$
$38$		0			0
$39$	−1.73205	−	1.00000i	−0.277350	−	0.160128i
$40$		0			0
$41$			10.3923i			1.62301i	0.584349	+	0.811503i	$0.301350\pi$
$41$			10.3923i			1.62301i	−0.584349	+	0.811503i	$0.698650\pi$
$42$		0			0
$43$	3.67423	+	3.67423i	0.560316	+	0.560316i	0.929397	−	0.369082i	$-0.120328\pi$
$43$	3.67423	+	3.67423i	0.560316	+	0.560316i	−0.369082	+	0.929397i	$0.620328\pi$
$44$	10.3923	−	6.00000i	1.56670	−	0.904534i
$45$		0			0
$46$		0			0
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	0.755276	+	0.655407i	$0.227503\pi$
$47$	−1.55291	+	5.79555i	−0.226516	+	0.845369i	−0.981792	+	0.189961i	$0.939164\pi$
$48$	2.82843	−	2.82843i	0.408248	−	0.408248i
$49$	−6.92820	+	1.00000i	−0.989743	+	0.142857i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−3.86370	+	1.03528i	−0.535799	+	0.143567i
$53$	−10.0382	+	2.68973i	−1.37885	+	0.369462i	−0.870704	−	0.491807i	$-0.836336\pi$
$53$	−10.0382	+	2.68973i	−1.37885	+	0.369462i	−0.508148	+	0.861270i	$0.669670\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.44949	−	2.44949i	0.324443	−	0.324443i
$58$		0			0
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	0.299552	+	0.954080i	$0.403163\pi$
$59$	−5.19615	+	9.00000i	−0.676481	+	1.17170i	−0.976034	+	0.217620i	$0.930171\pi$
$60$		0			0
$61$	7.50000	−	4.33013i	0.960277	−	0.554416i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.50000	−	4.33013i	0.960277	−	0.554416i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$	−1.48356	−	2.19067i	−0.186911	−	0.275999i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$	−0.896575	−	3.34607i	−0.109534	−	0.408787i	0.889286	−	0.457352i	$-0.151202\pi$
$67$	−0.896575	−	3.34607i	−0.109534	−	0.408787i	−0.998820	+	0.0485648i	$0.984535\pi$
$68$	−11.5911	−	3.10583i	−1.40563	−	0.376637i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	0.258819	+	0.965926i	0.0302925	+	0.113053i	0.979417	−	0.201849i	$-0.0646950\pi$
$73$	0.258819	+	0.965926i	0.0302925	+	0.113053i	−0.949124	+	0.314902i	$0.898028\pi$
$74$		0			0
$75$		0			0
$76$		−	6.92820i		−	0.794719i
$77$	−14.2808	−	6.93237i	−1.62745	−	0.790017i
$78$		0			0
$79$	4.33013	−	2.50000i	0.487177	−	0.281272i	−0.236225	−	0.971698i	$-0.575910\pi$
$79$	4.33013	−	2.50000i	0.487177	−	0.281272i	0.723403	+	0.690426i	$0.242577\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$	−5.19615	−	1.00000i	−0.566947	−	0.109109i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		0			0
$91$	4.00000	+	3.46410i	0.419314	+	0.363137i
$92$		0			0
$93$	−1.34486	+	5.01910i	−0.139456	+	0.520456i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.19239	−	9.19239i	−0.933346	−	0.933346i	0.0645677	−	0.997913i	$-0.479433\pi$
$97$	−9.19239	−	9.19239i	−0.933346	−	0.933346i	−0.997913	+	0.0645677i	$0.979433\pi$
$98$		0			0
$99$		−	6.00000i		−	0.603023i
$100$		0			0
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	6.76148	+	1.81173i	0.666228	+	0.178515i	0.576055	−	0.817411i	$-0.304591\pi$
$103$	6.76148	+	1.81173i	0.666228	+	0.178515i	0.0901732	+	0.995926i	$0.471258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$107$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$108$	−0.517638	−	1.93185i	−0.0498097	−	0.185893i
$109$	−8.66025	−	5.00000i	−0.829502	−	0.478913i	0.0241802	−	0.999708i	$-0.492302\pi$
$109$	−8.66025	−	5.00000i	−0.829502	−	0.478913i	−0.853682	+	0.520794i	$0.825636\pi$
$110$		0			0
$111$		−	8.66025i		−	0.821995i
$112$	−8.76268	+	5.93426i	−0.827996	+	0.560734i
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	0.962515	−	0.271229i	$-0.0874301\pi$
$113$	7.34847	+	7.34847i	0.691286	+	0.691286i	−0.271229	+	0.962515i	$0.587430\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.517638	+	1.93185i	−0.0478557	+	0.178600i
$118$		0			0
$119$	5.19615	+	15.0000i	0.476331	+	1.37505i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		0			0
$123$	10.0382	−	2.68973i	0.905114	−	0.242524i
$124$	5.19615	+	9.00000i	0.466628	+	0.808224i
$125$		0			0
$126$		0			0
$127$	8.57321	−	8.57321i	0.760750	−	0.760750i	−0.215708	−	0.976458i	$-0.569206\pi$
$127$	8.57321	−	8.57321i	0.760750	−	0.760750i	0.976458	+	0.215708i	$0.0692060\pi$
$128$		0			0
$129$	2.59808	−	4.50000i	0.228748	−	0.396203i
$130$		0			0
$131$	9.00000	−	5.19615i	0.786334	−	0.453990i	−0.0523366	−	0.998630i	$-0.516667\pi$
$131$	9.00000	−	5.19615i	0.786334	−	0.453990i	0.838670	+	0.544640i	$0.183334\pi$
$132$	−8.48528	−	8.48528i	−0.738549	−	0.738549i
$133$	−7.58871	+	5.13922i	−0.658024	+	0.445627i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.37945	−	20.0764i	−0.459598	−	1.71524i	−0.674207	−	0.738542i	$-0.735515\pi$
$137$	−5.37945	−	20.0764i	−0.459598	−	1.71524i	0.214610	−	0.976700i	$-0.431152\pi$
$138$		0			0
$139$	1.73205			0.146911			0.0734553	−	0.997299i	$-0.476597\pi$
$139$	1.73205			0.146911			0.0734553	+	0.997299i	$0.476597\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	3.10583	+	11.5911i	0.259722	+	0.969297i
$144$	−3.46410	−	2.00000i	−0.288675	−	0.166667i
$145$		0			0
$146$		0			0
$147$	2.75908	+	6.43331i	0.227565	+	0.530611i
$148$	−12.2474	−	12.2474i	−1.00673	−	1.00673i
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	−0.00974235	−	0.999953i	$-0.503101\pi$
$149$	10.3923	−	6.00000i	0.851371	−	0.491539i	0.861113	+	0.508413i	$0.169768\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$		0			0
$153$	−4.24264	+	4.24264i	−0.342997	+	0.342997i
$154$		0			0
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	6.76148	−	1.81173i	0.539625	−	0.144592i	0.0212957	−	0.999773i	$-0.493221\pi$
$157$	6.76148	−	1.81173i	0.539625	−	0.144592i	0.518329	+	0.855181i	$0.326554\pi$
$158$		0			0
$159$	5.19615	+	9.00000i	0.412082	+	0.713746i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.24144	+	8.36516i	−0.175563	+	0.655210i	0.820892	+	0.571083i	$0.193477\pi$
$163$	−2.24144	+	8.36516i	−0.175563	+	0.655210i	−0.996455	+	0.0841267i	$0.973190\pi$
$164$	10.3923	−	18.0000i	0.811503	−	1.40556i
$165$		0			0
$166$		0			0
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$		0			0
$171$	−3.00000	−	1.73205i	−0.229416	−	0.132453i
$172$	−2.68973	−	10.0382i	−0.205090	−	0.765405i
$173$	−17.3867	−	4.65874i	−1.32188	−	0.354198i	−0.472200	−	0.881491i	$-0.656540\pi$
$173$	−17.3867	−	4.65874i	−1.32188	−	0.354198i	−0.849683	+	0.527294i	$0.823207\pi$
$174$		0			0
$175$		0			0
$176$	−24.0000			−1.80907
$177$	10.0382	+	2.68973i	0.754517	+	0.202172i
$178$		0			0
$179$	−20.7846	−	12.0000i	−1.55351	−	0.896922i	−0.997852	−	0.0655145i	$-0.979131\pi$
$179$	−20.7846	−	12.0000i	−1.55351	−	0.896922i	−0.555663	−	0.831408i	$-0.687536\pi$
$180$		0			0
$181$			5.19615i			0.386227i	0.981176	+	0.193113i	$0.0618586\pi$
$181$			5.19615i			0.386227i	−0.981176	+	0.193113i	$0.938141\pi$
$182$		0			0
$183$	−6.12372	−	6.12372i	−0.452679	−	0.452679i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.31749	+	34.7733i	−0.681362	+	2.54288i
$188$	8.48528	−	8.48528i	0.618853	−	0.618853i
$189$	−1.73205	+	2.00000i	−0.125988	+	0.145479i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−7.72741	+	2.07055i	−0.557678	+	0.149429i
$193$	15.0573	−	4.03459i	1.08385	−	0.290416i	0.327677	−	0.944790i	$-0.393734\pi$
$193$	15.0573	−	4.03459i	1.08385	−	0.290416i	0.756171	+	0.654374i	$0.227068\pi$
$194$		0			0
$195$		0			0
$196$	13.0000	+	5.19615i	0.928571	+	0.371154i
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	−0.918644	−	0.395087i	$-0.870714\pi$
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	0.395087	+	0.918644i	$0.370714\pi$
$198$		0			0
$199$	9.52628	−	16.5000i	0.675300	−	1.16965i	−0.301081	−	0.953599i	$-0.597347\pi$
$199$	9.52628	−	16.5000i	0.675300	−	1.16965i	0.976381	−	0.216055i	$-0.0693192\pi$
$200$		0			0
$201$	−3.00000	+	1.73205i	−0.211604	+	0.122169i
$202$		0			0
$203$		0			0
$204$			12.0000i			0.840168i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	7.72741	+	2.07055i	0.535799	+	0.143567i
$209$	−20.7846			−1.43770
$210$		0			0
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$	20.0764	+	5.37945i	1.37885	+	0.369462i
$213$	1.55291	+	5.79555i	0.106404	+	0.397105i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.00361	−	12.3676i	0.407551	−	0.839565i
$218$		0			0
$219$	0.866025	−	0.500000i	0.0585206	−	0.0337869i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	−0.815506	−	0.578749i	$-0.803541\pi$
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	0.578749	+	0.815506i	$0.303541\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.79555	−	1.55291i	0.384664	−	0.103071i	−0.0613041	−	0.998119i	$-0.519526\pi$
$227$	5.79555	−	1.55291i	0.384664	−	0.103071i	0.445969	+	0.895049i	$0.352859\pi$
$228$	−6.69213	+	1.79315i	−0.443197	+	0.118754i
$229$	3.46410	+	6.00000i	0.228914	+	0.396491i	0.957487	−	0.288478i	$-0.0931491\pi$
$229$	3.46410	+	6.00000i	0.228914	+	0.396491i	−0.728572	+	0.684969i	$0.759816\pi$
$230$		0			0
$231$	−3.00000	+	15.5885i	−0.197386	+	1.02565i
$232$		0			0
$233$	5.37945	−	20.0764i	0.352420	−	1.31525i	−0.531281	−	0.847196i	$-0.678289\pi$
$233$	5.37945	−	20.0764i	0.352420	−	1.31525i	0.883701	−	0.468052i	$-0.155044\pi$
$234$		0			0
$235$		0			0
$236$	18.0000	−	10.3923i	1.17170	−	0.676481i
$237$	−3.53553	−	3.53553i	−0.229658	−	0.229658i
$238$		0			0
$239$		−	18.0000i		−	1.16432i	−0.813073	−	0.582162i	$-0.802207\pi$
$239$		−	18.0000i		−	1.16432i	0.813073	−	0.582162i	$-0.197793\pi$
$240$		0			0
$241$	16.5000	+	9.52628i	1.06286	+	0.613642i	0.926222	−	0.376980i	$-0.123037\pi$
$241$	16.5000	+	9.52628i	1.06286	+	0.613642i	0.136637	+	0.990621i	$0.456371\pi$
$242$		0			0
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−17.3205			−1.10883
$245$		0			0
$246$		0			0
$247$	6.69213	+	1.79315i	0.425810	+	0.114095i
$248$		0			0
$249$	5.19615	+	3.00000i	0.329293	+	0.190117i
$250$		0			0
$251$			20.7846i			1.31191i	0.754799	+	0.655956i	$0.227735\pi$
$251$			20.7846i			1.31191i	−0.754799	+	0.655956i	$0.772265\pi$
$252$	0.378937	+	5.27792i	0.0238708	+	0.332478i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	1.55291	−	5.79555i	0.0968681	−	0.361517i	−0.900428	−	0.435005i	$-0.856747\pi$
$257$	1.55291	−	5.79555i	0.0968681	−	0.361517i	0.997296	+	0.0734884i	$0.0234132\pi$
$258$		0			0
$259$	−4.33013	+	22.5000i	−0.269061	+	1.39808i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	30.1146	−	8.06918i	1.85694	−	0.497567i	0.857100	−	0.515151i	$-0.172264\pi$
$263$	30.1146	−	8.06918i	1.85694	−	0.497567i	0.999845	+	0.0175838i	$0.00559740\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.34847	−	7.34847i	0.449719	−	0.449719i
$268$	−1.79315	+	6.69213i	−0.109534	+	0.408787i
$269$	−10.3923	+	18.0000i	−0.633630	+	1.09748i	0.353174	+	0.935558i	$0.385102\pi$
$269$	−10.3923	+	18.0000i	−0.633630	+	1.09748i	−0.986804	+	0.161922i	$0.948231\pi$
$270$		0			0
$271$	−27.0000	+	15.5885i	−1.64013	+	0.946931i	−0.659349	+	0.751837i	$0.729168\pi$
$271$	−27.0000	+	15.5885i	−1.64013	+	0.946931i	−0.980785	+	0.195094i	$0.937499\pi$
$272$	16.9706	+	16.9706i	1.02899	+	1.02899i
$273$	2.31079	−	4.76028i	0.139855	−	0.288105i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.58630	+	13.3843i	0.215480	+	0.804182i	0.985997	+	0.166763i	$0.0533314\pi$
$277$	3.58630	+	13.3843i	0.215480	+	0.804182i	−0.770517	+	0.637419i	$0.780002\pi$
$278$		0			0
$279$	5.19615			0.311086
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−4.14110	−	15.4548i	−0.246163	−	0.918693i	−0.972795	−	0.231667i	$-0.925582\pi$
$283$	−4.14110	−	15.4548i	−0.246163	−	0.918693i	0.726632	−	0.687027i	$-0.241084\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$		0			0
$286$		0			0
$287$	−27.4249	+	1.96902i	−1.61884	+	0.116227i
$288$		0			0
$289$	16.4545	−	9.50000i	0.967911	−	0.558824i
$290$		0			0
$291$	−6.50000	+	11.2583i	−0.381037	+	0.659975i
$292$	0.517638	−	1.93185i	0.0302925	−	0.113053i
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	−0.229691	−	0.973264i	$-0.573771\pi$
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	0.973264	+	0.229691i	$0.0737714\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.79555	+	1.55291i	−0.336292	+	0.0901092i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−9.00000	+	10.3923i	−0.518751	+	0.599002i
$302$		0			0
$303$		0			0
$304$	−6.92820	+	12.0000i	−0.397360	+	0.688247i
$305$		0			0
$306$		0			0
$307$	4.94975	+	4.94975i	0.282497	+	0.282497i	0.834104	−	0.551607i	$-0.185985\pi$
$307$	4.94975	+	4.94975i	0.282497	+	0.282497i	−0.551607	+	0.834104i	$0.685985\pi$
$308$	17.8028	+	26.2880i	1.01441	+	1.49790i
$309$		−	7.00000i		−	0.398216i
$310$		0			0
$311$	18.0000	+	10.3923i	1.02069	+	0.589294i	0.914303	−	0.405032i	$-0.132739\pi$
$311$	18.0000	+	10.3923i	1.02069	+	0.589294i	0.106384	+	0.994325i	$0.466073\pi$
$312$		0			0
$313$	−18.3526	−	4.91756i	−1.03735	−	0.277957i	−0.300335	−	0.953834i	$-0.597098\pi$
$313$	−18.3526	−	4.91756i	−1.03735	−	0.277957i	−0.737015	+	0.675877i	$0.763765\pi$
$314$		0			0
$315$		0			0
$316$	−10.0000			−0.562544
$317$	10.0382	+	2.68973i	0.563801	+	0.151070i	0.529452	−	0.848340i	$-0.322398\pi$
$317$	10.0382	+	2.68973i	0.563801	+	0.151070i	0.0343491	+	0.999410i	$0.489064\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	14.6969	+	14.6969i	0.817760	+	0.817760i
$324$	−1.73205	+	1.00000i	−0.0962250	+	0.0555556i
$325$		0			0
$326$		0			0
$327$	−2.58819	+	9.65926i	−0.143127	+	0.534158i
$328$		0			0
$329$	−15.5885	−	3.00000i	−0.859419	−	0.165395i
$330$		0			0
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	0.926516	−	0.376254i	$-0.122788\pi$
$331$	2.50000	+	4.33013i	0.137412	+	0.238005i	−0.789104	+	0.614260i	$0.789455\pi$
$332$	11.5911	−	3.10583i	0.636145	−	0.170454i
$333$	−8.36516	+	2.24144i	−0.458408	+	0.122830i
$334$		0			0
$335$		0			0
$336$	8.00000	+	6.92820i	0.436436	+	0.377964i
$337$	18.3712	−	18.3712i	1.00074	−	1.00074i	0.000741840	−	1.00000i	$-0.499764\pi$
$337$	18.3712	−	18.3712i	1.00074	−	1.00074i	1.00000		0.000741840i	$-0.000236135\pi$
$338$		0			0
$339$	5.19615	−	9.00000i	0.282216	−	0.488813i
$340$		0			0
$341$	27.0000	−	15.5885i	1.46213	−	0.844162i
$342$		0			0
$343$	−3.95164	−	18.0938i	−0.213368	−	0.976972i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.68973	+	10.0382i	0.144392	+	0.538879i	0.999782	+	0.0208935i	$0.00665108\pi$
$347$	2.68973	+	10.0382i	0.144392	+	0.538879i	−0.855390	+	0.517985i	$0.826682\pi$
$348$		0			0
$349$	20.7846			1.11257			0.556287	−	0.830990i	$-0.312225\pi$
$349$	20.7846			1.11257			0.556287	+	0.830990i	$0.312225\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−9.31749	−	34.7733i	−0.495920	−	1.85080i	−0.524817	−	0.851215i	$-0.675866\pi$
$353$	−9.31749	−	34.7733i	−0.495920	−	1.85080i	0.0288971	−	0.999582i	$-0.490800\pi$
$354$		0			0
$355$		0			0
$356$		−	20.7846i		−	1.10158i
$357$	13.1440	−	8.90138i	0.695656	−	0.471111i
$358$		0			0
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	−0.851356	−	0.524588i	$-0.824219\pi$
$359$	−15.5885	+	9.00000i	−0.822727	+	0.475002i	0.0286287	+	0.999590i	$0.490886\pi$
$360$		0			0
$361$	3.50000	−	6.06218i	0.184211	−	0.319062i
$362$		0			0
$363$	−17.6777	+	17.6777i	−0.927837	+	0.927837i
$364$	−3.46410	−	10.0000i	−0.181568	−	0.524142i
$365$		0			0
$366$		0			0
$367$	−16.4207	+	4.39992i	−0.857156	+	0.229674i	−0.660526	−	0.750804i	$-0.729666\pi$
$367$	−16.4207	+	4.39992i	−0.857156	+	0.229674i	−0.196630	+	0.980478i	$0.563000\pi$
$368$		0			0
$369$	−5.19615	−	9.00000i	−0.270501	−	0.468521i
$370$		0			0
$371$	−9.00000	−	25.9808i	−0.467257	−	1.34885i
$372$	7.34847	−	7.34847i	0.381000	−	0.381000i
$373$	−1.79315	+	6.69213i	−0.0928458	+	0.346505i	−0.996684	−	0.0813690i	$-0.974071\pi$
$373$	−1.79315	+	6.69213i	−0.0928458	+	0.346505i	0.903838	+	0.427874i	$0.140737\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$		0			0
$381$	−10.5000	−	6.06218i	−0.537931	−	0.310575i
$382$		0			0
$383$	23.1822	+	6.21166i	1.18456	+	0.317401i	0.796732	−	0.604333i	$-0.206560\pi$
$383$	23.1822	+	6.21166i	1.18456	+	0.317401i	0.387824	+	0.921733i	$0.373227\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.01910	−	1.34486i	−0.255135	−	0.0683632i
$388$	6.72930	+	25.1141i	0.341628	+	1.27497i
$389$	5.19615	+	3.00000i	0.263455	+	0.152106i	0.625910	−	0.779895i	$-0.284728\pi$
$389$	5.19615	+	3.00000i	0.263455	+	0.152106i	−0.362454	+	0.932002i	$0.618061\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−7.34847	−	7.34847i	−0.370681	−	0.370681i
$394$		0			0
$395$		0			0
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	1.81173	−	6.76148i	0.0909283	−	0.339349i	−0.905442	−	0.424469i	$-0.860461\pi$
$397$	1.81173	−	6.76148i	0.0909283	−	0.339349i	0.996371	+	0.0851201i	$0.0271274\pi$
$398$		0			0
$399$	6.92820	+	6.00000i	0.346844	+	0.300376i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	−10.0382	+	2.68973i	−0.500038	+	0.133985i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−36.7423	+	36.7423i	−1.82125	+	1.82125i
$408$		0			0
$409$	3.46410	−	6.00000i	0.171289	−	0.296681i	−0.767582	−	0.640951i	$-0.778540\pi$
$409$	3.46410	−	6.00000i	0.171289	−	0.296681i	0.938871	+	0.344270i	$0.111874\pi$
$410$		0			0
$411$	−18.0000	+	10.3923i	−0.887875	+	0.512615i
$412$	−9.89949	−	9.89949i	−0.487713	−	0.487713i
$413$	−24.7351	−	12.0072i	−1.21714	−	0.590836i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.448288	−	1.67303i	−0.0219527	−	0.0819288i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$		0			0
$423$	−1.55291	−	5.79555i	−0.0755053	−	0.281790i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.8480	+	18.9718i	0.621760	+	0.918108i
$428$		0			0
$429$	10.3923	−	6.00000i	0.501745	−	0.289683i
$430$		0			0
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	−1.03528	+	3.86370i	−0.0498097	+	0.185893i
$433$	−20.5061	+	20.5061i	−0.985460	+	0.985460i	−0.999896	−	0.0144357i	$-0.995405\pi$
$433$	−20.5061	+	20.5061i	−0.985460	+	0.985460i	0.0144357	+	0.999896i	$0.495405\pi$
$434$		0			0
$435$		0			0
$436$	10.0000	+	17.3205i	0.478913	+	0.829502i
$437$		0			0
$438$		0			0
$439$	−4.33013	−	7.50000i	−0.206666	−	0.357955i	0.743996	−	0.668184i	$-0.232928\pi$
$439$	−4.33013	−	7.50000i	−0.206666	−	0.357955i	−0.950662	+	0.310228i	$0.899595\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		0			0
$443$	−2.68973	+	10.0382i	−0.127793	+	0.476929i	−0.999924	−	0.0123433i	$-0.996071\pi$
$443$	−2.68973	+	10.0382i	−0.127793	+	0.476929i	0.872131	+	0.489272i	$0.162738\pi$
$444$	−8.66025	+	15.0000i	−0.410997	+	0.711868i
$445$		0			0
$446$		0			0
$447$	−8.48528	−	8.48528i	−0.401340	−	0.401340i
$448$	21.1117	−	1.51575i	0.997433	−	0.0716124i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$	−54.0000	−	31.1769i	−2.54276	−	1.46806i
$452$	−5.37945	−	20.0764i	−0.253028	−	0.944314i
$453$	4.82963	+	1.29410i	0.226916	+	0.0608019i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−18.4034	−	4.93117i	−0.860873	−	0.230670i	−0.198736	−	0.980053i	$-0.563684\pi$
$457$	−18.4034	−	4.93117i	−0.860873	−	0.230670i	−0.662137	+	0.749383i	$0.730350\pi$
$458$		0			0
$459$	5.19615	+	3.00000i	0.242536	+	0.140028i
$460$		0			0
$461$			31.1769i			1.45205i	0.687666	+	0.726027i	$0.258635\pi$
$461$			31.1769i			1.45205i	−0.687666	+	0.726027i	$0.741365\pi$
$462$		0			0
$463$	1.22474	+	1.22474i	0.0569187	+	0.0569187i	0.734993	−	0.678074i	$-0.237185\pi$
$463$	1.22474	+	1.22474i	0.0569187	+	0.0569187i	−0.678074	+	0.734993i	$0.737185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.76457	−	28.9778i	0.359302	−	1.34093i	−0.515683	−	0.856780i	$-0.672462\pi$
$467$	7.76457	−	28.9778i	0.359302	−	1.34093i	0.874984	−	0.484152i	$-0.160872\pi$
$468$	2.82843	−	2.82843i	0.130744	−	0.130744i
$469$	8.66025	−	3.00000i	0.399893	−	0.138527i
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$		0			0
$473$	−30.1146	+	8.06918i	−1.38467	+	0.371021i
$474$		0			0
$475$		0			0
$476$	6.00000	−	31.1769i	0.275010	−	1.42899i
$477$	7.34847	−	7.34847i	0.336463	−	0.336463i
$478$		0			0
$479$	10.3923	−	18.0000i	0.474837	−	0.822441i	−0.524748	−	0.851258i	$-0.675841\pi$
$479$	10.3923	−	18.0000i	0.474837	−	0.822441i	0.999585	+	0.0288165i	$0.00917385\pi$
$480$		0			0
$481$	15.0000	−	8.66025i	0.683941	−	0.394874i
$482$		0			0
$483$		0			0
$484$			50.0000i			2.27273i
$485$		0			0
$486$		0			0
$487$	−9.41404	−	35.1337i	−0.426591	−	1.59206i	−0.760424	−	0.649427i	$-0.775009\pi$
$487$	−9.41404	−	35.1337i	−0.426591	−	1.59206i	0.333833	−	0.942632i	$-0.391658\pi$
$488$		0			0
$489$	8.66025			0.391630
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	−20.0764	−	5.37945i	−0.905114	−	0.242524i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		−	20.7846i		−	0.933257i
$497$	−1.13681	−	15.8338i	−0.0509930	−	0.710241i
$498$		0			0
$499$	−17.3205	+	10.0000i	−0.775372	+	0.447661i	−0.834788	−	0.550572i	$-0.814410\pi$
$499$	−17.3205	+	10.0000i	−0.775372	+	0.447661i	0.0594153	+	0.998233i	$0.481076\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$		0			0
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.145690	−	0.989330i	$-0.453460\pi$
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.989330	−	0.145690i	$-0.0465401\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.69333	−	2.32937i	0.386084	−	0.103451i
$508$	−23.4225	+	6.27603i	−1.03920	+	0.278454i
$509$	5.19615	+	9.00000i	0.230315	+	0.398918i	0.957901	−	0.287099i	$-0.0926909\pi$
$509$	5.19615	+	9.00000i	0.230315	+	0.398918i	−0.727586	+	0.686017i	$0.759358\pi$
$510$		0			0
$511$	−2.50000	+	0.866025i	−0.110593	+	0.0383107i
$512$		0			0
$513$	−0.896575	+	3.34607i	−0.0395848	+	0.147732i
$514$		0			0
$515$		0			0
$516$	−9.00000	+	5.19615i	−0.396203	+	0.228748i
$517$	−25.4558	−	25.4558i	−1.11955	−	1.11955i
$518$		0			0
$519$			18.0000i			0.790112i
$520$		0			0
$521$	−9.00000	−	5.19615i	−0.394297	−	0.227648i	0.289723	−	0.957110i	$-0.406437\pi$
$521$	−9.00000	−	5.19615i	−0.394297	−	0.227648i	−0.684020	+	0.729463i	$0.739770\pi$
$522$		0			0
$523$	6.76148	+	1.81173i	0.295659	+	0.0792216i	0.403599	−	0.914936i	$-0.367759\pi$
$523$	6.76148	+	1.81173i	0.295659	+	0.0792216i	−0.107941	+	0.994157i	$0.534426\pi$
$524$	−20.7846			−0.907980
$525$		0			0
$526$		0			0
$527$	−30.1146	−	8.06918i	−1.31181	−	0.351499i
$528$	6.21166	+	23.1822i	0.270328	+	1.00888i
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$		0			0
$531$		−	10.3923i		−	0.450988i
$532$	18.2832	−	1.31268i	0.792679	−	0.0569118i
$533$	14.6969	+	14.6969i	0.636595	+	0.636595i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.21166	+	23.1822i	−0.268053	+	1.00039i
$538$		0			0
$539$	15.5885	−	39.0000i	0.671442	−	1.67985i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$		0			0
$543$	5.01910	−	1.34486i	0.215390	−	0.0577136i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−22.0454	+	22.0454i	−0.942594	+	0.942594i	−0.998439	−	0.0558458i	$-0.982214\pi$
$547$	−22.0454	+	22.0454i	−0.942594	+	0.942594i	0.0558458	+	0.998439i	$0.482214\pi$
$548$	−10.7589	+	40.1528i	−0.459598	+	1.71524i
$549$	−4.33013	+	7.50000i	−0.184805	+	0.320092i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	7.41782	+	10.9534i	0.315438	+	0.465784i
$554$		0			0
$555$		0			0
$556$	−3.00000	−	1.73205i	−0.127228	−	0.0734553i
$557$	2.68973	+	10.0382i	0.113967	+	0.425332i	0.999208	−	0.0398021i	$-0.0126728\pi$
$557$	2.68973	+	10.0382i	0.113967	+	0.425332i	−0.885240	+	0.465134i	$0.846006\pi$
$558$		0			0
$559$	10.3923			0.439548
$560$		0			0
$561$	36.0000			1.51992
$562$		0			0
$563$	−1.55291	−	5.79555i	−0.0654475	−	0.244254i	0.925450	−	0.378869i	$-0.123687\pi$
$563$	−1.55291	−	5.79555i	−0.0654475	−	0.244254i	−0.990898	+	0.134615i	$0.957020\pi$
$564$	−10.3923	−	6.00000i	−0.437595	−	0.252646i
$565$		0			0
$566$		0			0
$567$	2.38014	+	1.15539i	0.0999565	+	0.0485220i
$568$		0			0
$569$	−20.7846	+	12.0000i	−0.871336	+	0.503066i	−0.867792	−	0.496928i	$-0.834461\pi$
$569$	−20.7846	+	12.0000i	−0.871336	+	0.503066i	−0.00354413	+	0.999994i	$0.501128\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	6.21166	−	23.1822i	0.259722	−	0.969297i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	−6.76148	+	1.81173i	−0.281484	+	0.0754234i	−0.396799	−	0.917906i	$-0.629879\pi$
$577$	−6.76148	+	1.81173i	−0.281484	+	0.0754234i	0.115315	+	0.993329i	$0.463212\pi$
$578$		0			0
$579$	−7.79423	−	13.5000i	−0.323917	−	0.561041i
$580$		0			0
$581$	−12.0000	−	10.3923i	−0.497844	−	0.431145i
$582$		0			0
$583$	16.1384	−	60.2292i	0.668383	−	2.49444i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.7279	+	12.7279i	0.525338	+	0.525338i	0.919179	−	0.393841i	$-0.128854\pi$
$587$	12.7279	+	12.7279i	0.525338	+	0.525338i	−0.393841	+	0.919179i	$0.628854\pi$
$588$	1.65445	−	13.9019i	0.0682284	−	0.573305i
$589$		−	18.0000i		−	0.741677i
$590$		0			0
$591$	9.00000	+	5.19615i	0.370211	+	0.213741i
$592$	8.96575	+	33.4607i	0.368490	+	1.37522i
$593$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$593$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$594$		0			0
$595$		0			0
$596$	−24.0000			−0.983078
$597$	−18.4034	−	4.93117i	−0.753199	−	0.201819i
$598$		0			0
$599$	−10.3923	−	6.00000i	−0.424618	−	0.245153i	0.272433	−	0.962175i	$-0.412172\pi$
$599$	−10.3923	−	6.00000i	−0.424618	−	0.245153i	−0.697051	+	0.717021i	$0.745505\pi$
$600$		0			0
$601$		−	34.6410i		−	1.41304i	−0.707695	−	0.706518i	$-0.750265\pi$
$601$		−	34.6410i		−	1.41304i	0.707695	−	0.706518i	$-0.249735\pi$
$602$		0			0
$603$	2.44949	+	2.44949i	0.0997509	+	0.0997509i
$604$	8.66025	−	5.00000i	0.352381	−	0.203447i
$605$		0			0
$606$		0			0
$607$	6.47048	−	24.1481i	0.262629	−	0.980143i	−0.701057	−	0.713105i	$-0.747288\pi$
$607$	6.47048	−	24.1481i	0.262629	−	0.980143i	0.963686	−	0.267038i	$-0.0860450\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	11.5911	−	3.10583i	0.468543	−	0.125546i
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.34847	+	7.34847i	−0.295838	+	0.295838i	−0.839381	−	0.543543i	$-0.817082\pi$
$617$	−7.34847	+	7.34847i	−0.295838	+	0.295838i	0.543543	+	0.839381i	$0.317082\pi$
$618$		0			0
$619$	−23.3827	+	40.5000i	−0.939829	+	1.62783i	−0.174042	+	0.984738i	$0.555683\pi$
$619$	−23.3827	+	40.5000i	−0.939829	+	1.62783i	−0.765787	+	0.643094i	$0.777650\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.7661	+	15.4176i	−0.912105	+	0.617695i
$624$		−	8.00000i		−	0.320256i
$625$		0			0
$626$		0			0
$627$	5.37945	+	20.0764i	0.214835	+	0.801774i
$628$	−13.5230	−	3.62347i	−0.539625	−	0.144592i
$629$	51.9615			2.07184
$630$		0			0
$631$	−1.00000			−0.0398094			−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	−1.00000			−0.0398094			−0.0199047	+	0.999802i	$0.506336\pi$
$632$		0			0
$633$	−1.81173	−	6.76148i	−0.0720099	−	0.268745i
$634$		0			0
$635$		0			0
$636$		−	20.7846i		−	0.824163i
$637$	−8.38375	+	11.2122i	−0.332176	+	0.444242i
$638$		0			0
$639$	5.19615	−	3.00000i	0.205557	−	0.118678i
$640$		0			0
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$		0			0
$643$	−20.5061	+	20.5061i	−0.808682	+	0.808682i	−0.984434	−	0.175753i	$-0.943764\pi$
$643$	−20.5061	+	20.5061i	−0.808682	+	0.808682i	0.175753	+	0.984434i	$0.443764\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.3867	−	4.65874i	0.683540	−	0.183154i	0.0996938	−	0.995018i	$-0.468214\pi$
$647$	17.3867	−	4.65874i	0.683540	−	0.183154i	0.583846	+	0.811864i	$0.301547\pi$
$648$		0			0
$649$	−31.1769	−	54.0000i	−1.22380	−	2.11969i
$650$		0			0
$651$	−13.5000	−	2.59808i	−0.529107	−	0.101827i
$652$	12.2474	−	12.2474i	0.479647	−	0.479647i
$653$	2.68973	−	10.0382i	0.105257	−	0.392825i	−0.893117	−	0.449824i	$-0.851487\pi$
$653$	2.68973	−	10.0382i	0.105257	−	0.392825i	0.998374	+	0.0569993i	$0.0181533\pi$
$654$		0			0
$655$		0			0
$656$	−36.0000	+	20.7846i	−1.40556	+	0.811503i
$657$	−0.707107	−	0.707107i	−0.0275869	−	0.0275869i
$658$		0			0
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.998942	−	0.0459936i	$-0.0146454\pi$
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.459639	+	0.888106i	$0.347979\pi$
$662$		0			0
$663$	−11.5911	−	3.10583i	−0.450161	−	0.120620i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−6.21166	−	23.1822i	−0.240336	−	0.896947i
$669$	4.33013	+	2.50000i	0.167412	+	0.0966556i
$670$		0			0
$671$			51.9615i			2.00595i
$672$		0			0
$673$	−8.57321	−	8.57321i	−0.330473	−	0.330473i	0.522293	−	0.852766i	$-0.325077\pi$
$673$	−8.57321	−	8.57321i	−0.330473	−	0.330473i	−0.852766	+	0.522293i	$0.825077\pi$
$674$		0			0
$675$		0			0
$676$	9.00000	−	15.5885i	0.346154	−	0.599556i
$677$	12.4233	−	46.3644i	0.477467	−	1.78193i	−0.134354	−	0.990933i	$-0.542896\pi$
$677$	12.4233	−	46.3644i	0.477467	−	1.78193i	0.611820	−	0.790997i	$-0.290438\pi$
$678$		0			0
$679$	22.5167	−	26.0000i	0.864110	−	0.997788i
$680$		0			0
$681$	−3.00000	−	5.19615i	−0.114960	−	0.199117i
$682$		0			0
$683$	−30.1146	+	8.06918i	−1.15230	+	0.308759i	−0.783888	−	0.620903i	$-0.786766\pi$
$683$	−30.1146	+	8.06918i	−1.15230	+	0.308759i	−0.368415	+	0.929661i	$0.620099\pi$
$684$	3.46410	+	6.00000i	0.132453	+	0.229416i
$685$		0			0
$686$		0			0
$687$	4.89898	−	4.89898i	0.186908	−	0.186908i
$688$	−5.37945	+	20.0764i	−0.205090	+	0.765405i
$689$	−10.3923	+	18.0000i	−0.395915	+	0.685745i
$690$		0			0
$691$	10.5000	−	6.06218i	0.399439	−	0.230616i	−0.286803	−	0.957990i	$-0.592593\pi$
$691$	10.5000	−	6.06218i	0.399439	−	0.230616i	0.686242	+	0.727373i	$0.259259\pi$
$692$	25.4558	+	25.4558i	0.967686	+	0.967686i
$693$	15.8338	−	1.13681i	0.601474	−	0.0431839i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	16.1384	+	60.2292i	0.611284	+	2.28134i
$698$		0			0
$699$	−20.7846			−0.786146
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	7.76457	+	28.9778i	0.292846	+	1.09292i
$704$	41.5692	+	24.0000i	1.56670	+	0.904534i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−14.6969	−	14.6969i	−0.552345	−	0.552345i
$709$	−26.8468	+	15.5000i	−1.00825	+	0.582115i	−0.910679	−	0.413114i	$-0.864441\pi$
$709$	−26.8468	+	15.5000i	−1.00825	+	0.582115i	−0.0975728	+	0.995228i	$0.531108\pi$
$710$		0			0
$711$	−2.50000	+	4.33013i	−0.0937573	+	0.162392i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	24.0000	+	41.5692i	0.896922	+	1.55351i
$717$	−17.3867	+	4.65874i	−0.649317	+	0.173984i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−3.50000	+	18.1865i	−0.130347	+	0.677302i
$722$		0			0
$723$	4.93117	−	18.4034i	0.183392	−	0.684428i
$724$	5.19615	−	9.00000i	0.193113	−	0.334482i
$725$		0			0
$726$		0			0
$727$	28.2843	+	28.2843i	1.04901	+	1.04901i	0.998736	+	0.0502699i	$0.0160081\pi$
$727$	28.2843	+	28.2843i	1.04901	+	1.04901i	0.0502699	+	0.998736i	$0.483992\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	27.0000	+	15.5885i	0.998631	+	0.576560i
$732$	4.48288	+	16.7303i	0.165692	+	0.618371i
$733$	45.3985	+	12.1645i	1.67683	+	0.449306i	0.966940	−	0.255004i	$-0.0820769\pi$
$733$	45.3985	+	12.1645i	1.67683	+	0.449306i	0.709892	+	0.704310i	$0.248744\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.0764	+	5.37945i	0.739523	+	0.198155i
$738$		0			0
$739$	−0.866025	−	0.500000i	−0.0318573	−	0.0183928i	0.483987	−	0.875075i	$-0.339188\pi$
$739$	−0.866025	−	0.500000i	−0.0318573	−	0.0183928i	−0.515844	+	0.856683i	$0.672522\pi$
$740$		0			0
$741$		−	6.92820i		−	0.254514i
$742$		0			0
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.55291	−	5.79555i	0.0568182	−	0.212048i
$748$	50.9117	−	50.9117i	1.86152	−	1.86152i
$749$		0			0
$750$		0			0
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	0.748056	−	0.663636i	$-0.230988\pi$
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	−23.1822	+	6.21166i	−0.845369	+	0.226516i
$753$	20.0764	−	5.37945i	0.731624	−	0.196038i
$754$		0			0
$755$		0			0
$756$	5.00000	−	1.73205i	0.181848	−	0.0629941i
$757$	20.8207	−	20.8207i	0.756740	−	0.756740i	−0.218988	−	0.975728i	$-0.570275\pi$
$757$	20.8207	−	20.8207i	0.756740	−	0.756740i	0.975728	+	0.218988i	$0.0702755\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.0000	+	10.3923i	−0.652499	+	0.376721i	−0.789413	−	0.613862i	$-0.789615\pi$
$761$	−18.0000	+	10.3923i	−0.652499	+	0.376721i	0.136914	+	0.990583i	$0.456282\pi$
$762$		0			0
$763$	11.5539	−	23.8014i	0.418281	−	0.861668i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.37945	+	20.0764i	0.194241	+	0.724916i
$768$	15.4548	+	4.14110i	0.557678	+	0.149429i
$769$	5.19615			0.187378			0.0936890	−	0.995602i	$-0.470134\pi$
$769$	5.19615			0.187378			0.0936890	+	0.995602i	$0.470134\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	−30.1146	−	8.06918i	−1.08385	−	0.290416i
$773$	6.21166	+	23.1822i	0.223418	+	0.833806i	0.983032	+	0.183433i	$0.0587210\pi$
$773$	6.21166	+	23.1822i	0.223418	+	0.833806i	−0.759614	+	0.650374i	$0.774612\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	22.8541	−	1.64085i	0.819884	−	0.0588651i
$778$		0			0
$779$	−31.1769	+	18.0000i	−1.11703	+	0.644917i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$		0			0
$784$	−17.3205	−	22.0000i	−0.618590	−	0.785714i
$785$		0			0
$786$		0			0
$787$	10.6252	−	2.84701i	0.378747	−	0.101485i	−0.0644227	−	0.997923i	$-0.520521\pi$
$787$	10.6252	−	2.84701i	0.378747	−	0.101485i	0.443170	+	0.896438i	$0.353854\pi$
$788$	20.0764	−	5.37945i	0.715192	−	0.191635i
$789$	−15.5885	−	27.0000i	−0.554964	−	0.961225i
$790$		0			0
$791$	−18.0000	+	20.7846i	−0.640006	+	0.739016i
$792$		0			0
$793$	4.48288	−	16.7303i	0.159192	−	0.594111i
$794$		0			0
$795$		0			0
$796$	−33.0000	+	19.0526i	−1.16965	+	0.675300i
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	0.841235	−	0.540670i	$-0.181829\pi$
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	−0.540670	+	0.841235i	$0.681829\pi$
$798$		0			0
$799$			36.0000i			1.27359i
$800$		0			0
$801$	−9.00000	−	5.19615i	−0.317999	−	0.183597i
$802$		0			0
$803$	−5.79555	−	1.55291i	−0.204521	−	0.0548012i
$804$	6.92820			0.244339
$805$		0			0
$806$		0			0
$807$	20.0764	+	5.37945i	0.706722	+	0.189366i
$808$		0			0
$809$	20.7846	+	12.0000i	0.730748	+	0.421898i	0.818696	−	0.574228i	$-0.194698\pi$
$809$	20.7846	+	12.0000i	0.730748	+	0.421898i	−0.0879478	+	0.996125i	$0.528031\pi$
$810$		0			0
$811$			39.8372i			1.39887i	0.714695	+	0.699436i	$0.246565\pi$
$811$			39.8372i			1.39887i	−0.714695	+	0.699436i	$0.753435\pi$
$812$		0			0
$813$	22.0454	+	22.0454i	0.773166	+	0.773166i
$814$		0			0
$815$		0			0
$816$	12.0000	−	20.7846i	0.420084	−	0.727607i
$817$	−4.65874	+	17.3867i	−0.162989	+	0.608282i
$818$		0			0
$819$	−5.19615	−	1.00000i	−0.181568	−	0.0349428i
$820$		0			0
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	0.995819	−	0.0913446i	$-0.0291165\pi$
$821$	12.0000	+	20.7846i	0.418803	+	0.725388i	−0.577016	+	0.816733i	$0.695783\pi$
$822$		0			0
$823$	38.4797	−	10.3106i	1.34132	−	0.359406i	0.484396	−	0.874849i	$-0.339039\pi$
$823$	38.4797	−	10.3106i	1.34132	−	0.359406i	0.856924	+	0.515443i	$0.172373\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.0454	+	22.0454i	−0.766594	+	0.766594i	−0.977505	−	0.210911i	$-0.932357\pi$
$827$	−22.0454	+	22.0454i	−0.766594	+	0.766594i	0.210911	+	0.977505i	$0.432357\pi$
$828$		0			0
$829$	4.33013	−	7.50000i	0.150392	−	0.260486i	−0.780980	−	0.624556i	$-0.785280\pi$
$829$	4.33013	−	7.50000i	0.150392	−	0.260486i	0.931371	+	0.364070i	$0.118613\pi$
$830$		0			0
$831$	12.0000	−	6.92820i	0.416275	−	0.240337i
$832$	−11.3137	−	11.3137i	−0.392232	−	0.392232i
$833$	−38.5999	+	16.5545i	−1.33741	+	0.573578i
$834$		0			0
$835$		0			0
$836$	36.0000	+	20.7846i	1.24509	+	0.718851i
$837$	−1.34486	−	5.01910i	−0.0464853	−	0.173485i
$838$		0			0
$839$	31.1769			1.07635			0.538173	−	0.842834i	$-0.319115\pi$
$839$	31.1769			1.07635			0.538173	+	0.842834i	$0.319115\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	1.55291	+	5.79555i	0.0534852	+	0.199610i
$844$	−12.1244	−	7.00000i	−0.417338	−	0.240950i
$845$		0			0
$846$		0			0
$847$	54.7668	−	37.0891i	1.88181	−	1.27440i
$848$	−29.3939	−	29.3939i	−1.00939	−	1.00939i
$849$	−13.8564	+	8.00000i	−0.475551	+	0.274559i
$850$		0			0
$851$		0			0
$852$	3.10583	−	11.5911i	0.106404	−	0.397105i
$853$	−13.4350	+	13.4350i	−0.460007	+	0.460007i	−0.898658	−	0.438651i	$-0.855456\pi$
$853$	−13.4350	+	13.4350i	−0.460007	+	0.460007i	0.438651	+	0.898658i	$0.355456\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.1822	+	6.21166i	−0.791890	+	0.212186i	−0.632020	−	0.774952i	$-0.717774\pi$
$857$	−23.1822	+	6.21166i	−0.791890	+	0.212186i	−0.159869	+	0.987138i	$0.551107\pi$
$858$		0			0
$859$	5.19615	+	9.00000i	0.177290	+	0.307076i	0.940952	−	0.338541i	$-0.109933\pi$
$859$	5.19615	+	9.00000i	0.177290	+	0.307076i	−0.763661	+	0.645617i	$0.776600\pi$
$860$		0			0
$861$	9.00000	+	25.9808i	0.306719	+	0.885422i
$862$		0			0
$863$	8.06918	−	30.1146i	0.274678	−	1.02511i	−0.681379	−	0.731931i	$-0.738619\pi$
$863$	8.06918	−	30.1146i	0.274678	−	1.02511i	0.956057	−	0.293181i	$-0.0947140\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.4350	−	13.4350i	−0.456278	−	0.456278i
$868$	−22.7661	+	15.4176i	−0.772732	+	0.523309i
$869$			30.0000i			1.01768i
$870$		0			0
$871$	−6.00000	−	3.46410i	−0.203302	−	0.117377i
$872$		0			0
$873$	12.5570	+	3.36465i	0.424991	+	0.113876i
$874$		0			0
$875$		0			0
$876$	−2.00000			−0.0675737
$877$	−21.7494	−	5.82774i	−0.734426	−	0.196789i	−0.127827	−	0.991797i	$-0.540800\pi$
$877$	−21.7494	−	5.82774i	−0.734426	−	0.196789i	−0.606599	+	0.795008i	$0.707467\pi$
$878$		0			0
$879$	−15.5885	−	9.00000i	−0.525786	−	0.303562i
$880$		0			0
$881$			10.3923i			0.350126i	0.984557	+	0.175063i	$0.0560129\pi$
$881$			10.3923i			0.350126i	−0.984557	+	0.175063i	$0.943987\pi$
$882$		0			0
$883$	−2.44949	−	2.44949i	−0.0824319	−	0.0824319i	0.664689	−	0.747121i	$-0.268564\pi$
$883$	−2.44949	−	2.44949i	−0.0824319	−	0.0824319i	−0.747121	+	0.664689i	$0.768564\pi$
$884$	−20.7846	+	12.0000i	−0.699062	+	0.403604i
$885$		0			0
$886$		0			0
$887$	4.65874	−	17.3867i	0.156425	−	0.583787i	−0.842554	−	0.538612i	$-0.818949\pi$
$887$	4.65874	−	17.3867i	0.156425	−	0.583787i	0.998979	−	0.0451749i	$-0.0143845\pi$
$888$		0			0
$889$	24.2487	+	21.0000i	0.813276	+	0.704317i
$890$		0			0
$891$	3.00000	+	5.19615i	0.100504	+	0.174078i
$892$	9.65926	−	2.58819i	0.323416	−	0.0866590i
$893$	−20.0764	+	5.37945i	−0.671831	+	0.180017i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−54.0000	+	31.1769i	−1.79900	+	1.03865i
$902$		0			0
$903$	12.3676	+	6.00361i	0.411567	+	0.199787i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.448288	+	1.67303i	0.0148851	+	0.0555521i	0.972969	−	0.230936i	$-0.0741788\pi$
$907$	0.448288	+	1.67303i	0.0148851	+	0.0555521i	−0.958084	+	0.286488i	$0.907512\pi$
$908$	−11.5911	−	3.10583i	−0.384664	−	0.103071i
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	13.3843	+	3.58630i	0.443197	+	0.118754i
$913$	−9.31749	−	34.7733i	−0.308364	−	1.15083i
$914$		0			0
$915$		0			0
$916$		−	13.8564i		−	0.457829i
$917$	15.4176	+	22.7661i	0.509136	+	0.751803i
$918$		0			0
$919$	−21.6506	+	12.5000i	−0.714189	+	0.412337i	−0.812610	−	0.582808i	$-0.801954\pi$
$919$	−21.6506	+	12.5000i	−0.714189	+	0.412337i	0.0984214	+	0.995145i	$0.468621\pi$
$920$		0			0
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$		0			0
$923$	−8.48528	+	8.48528i	−0.279296	+	0.279296i
$924$	20.7846	−	24.0000i	0.683763	−	0.789542i
$925$		0			0
$926$		0			0
$927$	−6.76148	+	1.81173i	−0.222076	+	0.0595051i
$928$		0			0
$929$	−5.19615	−	9.00000i	−0.170480	−	0.295280i	0.768108	−	0.640321i	$-0.221199\pi$
$929$	−5.19615	−	9.00000i	−0.170480	−	0.295280i	−0.938588	+	0.345040i	$0.887865\pi$
$930$		0			0
$931$	−15.0000	−	19.0526i	−0.491605	−	0.624422i
$932$	−29.3939	+	29.3939i	−0.962828	+	0.962828i
$933$	5.37945	−	20.0764i	0.176115	−	0.657272i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	20.5061	+	20.5061i	0.669905	+	0.669905i	0.957694	−	0.287789i	$-0.0929201\pi$
$937$	20.5061	+	20.5061i	0.669905	+	0.669905i	−0.287789	+	0.957694i	$0.592920\pi$
$938$		0			0
$939$			19.0000i			0.620042i
$940$		0			0
$941$	−27.0000	−	15.5885i	−0.880175	−	0.508169i	−0.00945879	−	0.999955i	$-0.503011\pi$
$941$	−27.0000	−	15.5885i	−0.880175	−	0.508169i	−0.870716	+	0.491786i	$0.836344\pi$
$942$		0			0
$943$		0			0
$944$	−41.5692			−1.35296
$945$		0			0
$946$		0			0
$947$	−10.0382	−	2.68973i	−0.326198	−	0.0874044i	0.0920040	−	0.995759i	$-0.470673\pi$
$947$	−10.0382	−	2.68973i	−0.326198	−	0.0874044i	−0.418202	+	0.908354i	$0.637339\pi$
$948$	2.58819	+	9.65926i	0.0840605	+	0.313718i
$949$	1.73205	+	1.00000i	0.0562247	+	0.0324614i
$950$		0			0
$951$		−	10.3923i		−	0.336994i
$952$		0			0
$953$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$953$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$954$		0			0
$955$		0			0
$956$	−18.0000	+	31.1769i	−0.582162	+	1.00833i
$957$		0			0
$958$		0			0
$959$	51.9615	−	18.0000i	1.67793	−	0.581250i
$960$		0			0
$961$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i
$962$		0			0
$963$		0			0
$964$	−19.0526	−	33.0000i	−0.613642	−	1.06286i
$965$		0			0
$966$		0			0
$967$	−30.6186	+	30.6186i	−0.984628	+	0.984628i	−0.999884	−	0.0152551i	$-0.995144\pi$
$967$	−30.6186	+	30.6186i	−0.984628	+	0.984628i	0.0152551	+	0.999884i	$0.495144\pi$
$968$		0			0
$969$	10.3923	−	18.0000i	0.333849	−	0.578243i
$970$		0			0
$971$	18.0000	−	10.3923i	0.577647	−	0.333505i	−0.182550	−	0.983196i	$-0.558435\pi$
$971$	18.0000	−	10.3923i	0.577647	−	0.333505i	0.760198	+	0.649692i	$0.225102\pi$
$972$	1.41421	+	1.41421i	0.0453609	+	0.0453609i
$973$	0.328169	+	4.57081i	0.0105206	+	0.146533i
$974$		0			0
$975$		0			0
$976$	30.0000	+	17.3205i	0.960277	+	0.554416i
$977$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$977$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$978$		0			0
$979$	−62.3538			−1.99284
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	10.8704	+	40.5689i	0.346712	+	1.29395i	0.890600	+	0.454788i	$0.150285\pi$
$983$	10.8704	+	40.5689i	0.346712	+	1.29395i	−0.543888	+	0.839158i	$0.683048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.13681	+	15.8338i	0.0361851	+	0.503994i
$988$	−9.79796	−	9.79796i	−0.311715	−	0.311715i
$989$		0			0
$990$		0			0
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	−0.538384	−	0.842700i	$-0.680965\pi$
$991$	14.5000	−	25.1147i	0.460608	−	0.797796i	0.998991	+	0.0449040i	$0.0142982\pi$
$992$		0			0
$993$	3.53553	−	3.53553i	0.112197	−	0.112197i
$994$		0			0
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−4.82963	+	1.29410i	−0.152956	+	0.0409844i	−0.334484	−	0.942401i	$-0.608562\pi$
$997$	−4.82963	+	1.29410i	−0.152956	+	0.0409844i	0.181529	+	0.983386i	$0.441896\pi$
$998$		0			0
$999$	4.33013	+	7.50000i	0.136999	+	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.a.493.1	yes	8
5.2	odd	4	inner	525.2.bc.a.157.1	yes	8
5.3	odd	4	inner	525.2.bc.a.157.2	yes	8
5.4	even	2	inner	525.2.bc.a.493.2	yes	8
7.5	odd	6	inner	525.2.bc.a.418.1	yes	8
35.12	even	12	inner	525.2.bc.a.82.1	✓	8
35.19	odd	6	inner	525.2.bc.a.418.2	yes	8
35.33	even	12	inner	525.2.bc.a.82.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.a.82.1	✓	8	35.12	even	12	inner
525.2.bc.a.82.2	yes	8	35.33	even	12	inner
525.2.bc.a.157.1	yes	8	5.2	odd	4	inner
525.2.bc.a.157.2	yes	8	5.3	odd	4	inner
525.2.bc.a.418.1	yes	8	7.5	odd	6	inner
525.2.bc.a.418.2	yes	8	35.19	odd	6	inner
525.2.bc.a.493.1	yes	8	1.1	even	1	trivial
525.2.bc.a.493.2	yes	8	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.189469 + 2.63896i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(0.189469 + 2.63896i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-3.00000 + 5.19615i) q^{11} +(-0.517638 + 1.93185i) q^{12} +(1.41421 - 1.41421i) q^{13} +(2.00000 + 3.46410i) q^{16} +(5.79555 - 1.55291i) q^{17} +(1.73205 + 3.00000i) q^{19} +(2.50000 - 0.866025i) q^{21} +(0.707107 + 0.707107i) q^{27} +(2.31079 - 4.76028i) q^{28} +(-4.50000 - 2.59808i) q^{31} +(5.79555 + 1.55291i) q^{33} +2.00000 q^{36} +(8.36516 + 2.24144i) q^{37} +(-1.73205 - 1.00000i) q^{39} +10.3923i q^{41} +(3.67423 + 3.67423i) q^{43} +(10.3923 - 6.00000i) q^{44} +(-1.55291 + 5.79555i) q^{47} +(2.82843 - 2.82843i) q^{48} +(-6.92820 + 1.00000i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-3.86370 + 1.03528i) q^{52} +(-10.0382 + 2.68973i) q^{53} +(2.44949 - 2.44949i) q^{57} +(-5.19615 + 9.00000i) q^{59} +(7.50000 - 4.33013i) q^{61} +(-1.48356 - 2.19067i) q^{63} -8.00000i q^{64} +(-0.896575 - 3.34607i) q^{67} +(-11.5911 - 3.10583i) q^{68} -6.00000 q^{71} +(0.258819 + 0.965926i) q^{73} -6.92820i q^{76} +(-14.2808 - 6.93237i) q^{77} +(4.33013 - 2.50000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(-5.19615 - 1.00000i) q^{84} +(5.19615 + 9.00000i) q^{89} +(4.00000 + 3.46410i) q^{91} +(-1.34486 + 5.01910i) q^{93} +(-9.19239 - 9.19239i) q^{97} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 24 q^{11} + 16 q^{16} + 20 q^{21} - 36 q^{31} + 16 q^{36} - 24 q^{51} + 60 q^{61} - 48 q^{71} + 4 q^{81} + 32 q^{91}+O(q^{100}) \) 8 * q - 24 * q^11 + 16 * q^16 + 20 * q^21 - 36 * q^31 + 16 * q^36 - 24 * q^51 + 60 * q^61 - 48 * q^71 + 4 * q^81 + 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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