LMFDB - Embedded newform 804.2.i.d.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(37,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("804.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.i (of order $3$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 $ x^8 - x^7 + 11x^6 + 4x^5 + 91x^4 - 6x^3 + 129x^2 + 36x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-1.30177 - 2.25473i$ of defining polynomial
Character	$\chi$	$=$	804.37
Dual form			804.2.i.d.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -2.60354 q^{5} +(-1.30177 + 2.25473i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -2.60354 q^{5} +(-1.30177 + 2.25473i) q^{7} +1.00000 q^{9} +(1.00000 - 1.73205i) q^{11} +(2.19098 + 3.79488i) q^{13} +2.60354 q^{15} +(-1.69098 - 2.92886i) q^{17} +(-1.38921 - 2.40618i) q^{19} +(1.30177 - 2.25473i) q^{21} +(-0.798983 - 1.38388i) q^{23} +1.77841 q^{25} -1.00000 q^{27} +(2.10075 - 3.63861i) q^{29} +(4.90252 - 8.49142i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(3.38921 - 5.87028i) q^{35} +(-1.89199 - 3.27703i) q^{37} +(-2.19098 - 3.79488i) q^{39} +(4.48996 - 7.77684i) q^{41} -11.1870 q^{43} -2.60354 q^{45} +(4.48996 - 7.77684i) q^{47} +(0.110793 + 0.191900i) q^{49} +(1.69098 + 2.92886i) q^{51} +0.618048 q^{53} +(-2.60354 + 4.50946i) q^{55} +(1.38921 + 2.40618i) q^{57} +3.18045 q^{59} +(7.38474 + 12.7907i) q^{61} +(-1.30177 + 2.25473i) q^{63} +(-5.70429 - 9.88012i) q^{65} +(-4.38642 - 6.91081i) q^{67} +(0.798983 + 1.38388i) q^{69} +(-3.40809 + 5.90299i) q^{71} +(-0.613580 - 1.06275i) q^{73} -1.77841 q^{75} +(2.60354 + 4.50946i) q^{77} +(5.01610 - 8.68814i) q^{79} +1.00000 q^{81} +(-2.69098 - 4.66091i) q^{83} +(4.40252 + 7.62539i) q^{85} +(-2.10075 + 3.63861i) q^{87} -3.00557 q^{89} -11.4086 q^{91} +(-4.90252 + 8.49142i) q^{93} +(3.61685 + 6.26457i) q^{95} +(1.99721 + 3.45928i) q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	$ 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−2.60354			−1.16434			−0.582169	−	0.813068i	$-0.697796\pi$
$5$	−2.60354			−1.16434			−0.582169	+	0.813068i	$0.697796\pi$
$6$		0			0
$7$	−1.30177	+	2.25473i	−0.492023	+	0.852208i	−0.999958	−	0.00918719i	$-0.997076\pi$
$7$	−1.30177	+	2.25473i	−0.492023	+	0.852208i	0.507935	+	0.861395i	$0.330409\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	2.19098	+	3.79488i	0.607667	+	1.05251i	0.991624	+	0.129160i	$0.0412280\pi$
$13$	2.19098	+	3.79488i	0.607667	+	1.05251i	−0.383956	+	0.923351i	$0.625439\pi$
$14$		0			0
$15$	2.60354			0.672231
$16$		0			0
$17$	−1.69098	−	2.92886i	−0.410122	−	0.710352i	0.584781	−	0.811191i	$-0.301181\pi$
$17$	−1.69098	−	2.92886i	−0.410122	−	0.710352i	−0.994903	+	0.100839i	$0.967847\pi$
$18$		0			0
$19$	−1.38921	−	2.40618i	−0.318706	−	0.552015i	0.661512	−	0.749934i	$-0.269915\pi$
$19$	−1.38921	−	2.40618i	−0.318706	−	0.552015i	−0.980218	+	0.197919i	$0.936582\pi$
$20$		0			0
$21$	1.30177	−	2.25473i	0.284069	−	0.492023i
$22$		0			0
$23$	−0.798983	−	1.38388i	−0.166599	−	0.288559i	0.770623	−	0.637292i	$-0.219945\pi$
$23$	−0.798983	−	1.38388i	−0.166599	−	0.288559i	−0.937222	+	0.348733i	$0.886612\pi$
$24$		0			0
$25$	1.77841			0.355683
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.10075	−	3.63861i	0.390100	−	0.675673i	−0.602362	−	0.798223i	$-0.705774\pi$
$29$	2.10075	−	3.63861i	0.390100	−	0.675673i	0.992462	+	0.122550i	$0.0391071\pi$
$30$		0			0
$31$	4.90252	−	8.49142i	0.880519	−	1.52510i	0.0297538	−	0.999557i	$-0.490528\pi$
$31$	4.90252	−	8.49142i	0.880519	−	1.52510i	0.850765	−	0.525546i	$-0.176139\pi$
$32$		0			0
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$		0			0
$35$	3.38921	−	5.87028i	0.572880	−	0.992258i
$36$		0			0
$37$	−1.89199	−	3.27703i	−0.311042	−	0.538740i	0.667546	−	0.744568i	$-0.267345\pi$
$37$	−1.89199	−	3.27703i	−0.311042	−	0.538740i	−0.978588	+	0.205828i	$0.934011\pi$
$38$		0			0
$39$	−2.19098	−	3.79488i	−0.350837	−	0.607667i
$40$		0			0
$41$	4.48996	−	7.77684i	0.701214	−	1.21454i	−0.266827	−	0.963744i	$-0.585975\pi$
$41$	4.48996	−	7.77684i	0.701214	−	1.21454i	0.968041	−	0.250793i	$-0.0806915\pi$
$42$		0			0
$43$	−11.1870			−1.70600			−0.853000	−	0.521910i	$-0.825220\pi$
$43$	−11.1870			−1.70600			−0.853000	+	0.521910i	$0.825220\pi$
$44$		0			0
$45$	−2.60354			−0.388113
$46$		0			0
$47$	4.48996	−	7.77684i	0.654928	−	1.13437i	−0.326984	−	0.945030i	$-0.606032\pi$
$47$	4.48996	−	7.77684i	0.654928	−	1.13437i	0.981912	−	0.189338i	$-0.0606343\pi$
$48$		0			0
$49$	0.110793	+	0.191900i	0.0158276	+	0.0274142i
$50$		0			0
$51$	1.69098	+	2.92886i	0.236784	+	0.410122i
$52$		0			0
$53$	0.618048			0.0848954			0.0424477	−	0.999099i	$-0.486484\pi$
$53$	0.618048			0.0848954			0.0424477	+	0.999099i	$0.486484\pi$
$54$		0			0
$55$	−2.60354	+	4.50946i	−0.351061	+	0.608056i
$56$		0			0
$57$	1.38921	+	2.40618i	0.184005	+	0.318706i
$58$		0			0
$59$	3.18045			0.414059			0.207030	−	0.978335i	$-0.433620\pi$
$59$	3.18045			0.414059			0.207030	+	0.978335i	$0.433620\pi$
$60$		0			0
$61$	7.38474	+	12.7907i	0.945519	+	1.63769i	0.754709	+	0.656060i	$0.227778\pi$
$61$	7.38474	+	12.7907i	0.945519	+	1.63769i	0.190810	+	0.981627i	$0.438889\pi$
$62$		0			0
$63$	−1.30177	+	2.25473i	−0.164008	+	0.284069i
$64$		0			0
$65$	−5.70429	−	9.88012i	−0.707530	−	1.22548i
$66$		0			0
$67$	−4.38642	−	6.91081i	−0.535887	−	0.844290i
$67$	−4.38642	−	6.91081i	−0.535887	−	0.844290i
$68$		0			0
$69$	0.798983	+	1.38388i	0.0961862	+	0.166599i
$70$		0			0
$71$	−3.40809	+	5.90299i	−0.404466	+	0.700556i	−0.994259	−	0.106998i	$-0.965876\pi$
$71$	−3.40809	+	5.90299i	−0.404466	+	0.700556i	0.589793	+	0.807555i	$0.299209\pi$
$72$		0			0
$73$	−0.613580	−	1.06275i	−0.0718141	−	0.124386i	0.827882	−	0.560902i	$-0.189545\pi$
$73$	−0.613580	−	1.06275i	−0.0718141	−	0.124386i	−0.899696	+	0.436516i	$0.856212\pi$
$74$		0			0
$75$	−1.77841			−0.205353
$76$		0			0
$77$	2.60354	+	4.50946i	0.296701	+	0.513901i
$78$		0			0
$79$	5.01610	−	8.68814i	0.564355	−	0.977492i	−0.432754	−	0.901512i	$-0.642458\pi$
$79$	5.01610	−	8.68814i	0.564355	−	0.977492i	0.997109	−	0.0759802i	$-0.0242086\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−2.69098	−	4.66091i	−0.295373	−	0.511601i	0.679699	−	0.733492i	$-0.262111\pi$
$83$	−2.69098	−	4.66091i	−0.295373	−	0.511601i	−0.975072	+	0.221890i	$0.928777\pi$
$84$		0			0
$85$	4.40252	+	7.62539i	0.477521	+	0.827090i
$86$		0			0
$87$	−2.10075	+	3.63861i	−0.225224	+	0.390100i
$88$		0			0
$89$	−3.00557			−0.318590			−0.159295	−	0.987231i	$-0.550922\pi$
$89$	−3.00557			−0.318590			−0.159295	+	0.987231i	$0.550922\pi$
$90$		0			0
$91$	−11.4086			−1.19594
$92$		0			0
$93$	−4.90252	+	8.49142i	−0.508368	+	0.880519i
$94$		0			0
$95$	3.61685	+	6.26457i	0.371081	+	0.642732i
$96$		0			0
$97$	1.99721	+	3.45928i	0.202786	+	0.351236i	0.949425	−	0.313993i	$-0.101667\pi$
$97$	1.99721	+	3.45928i	0.202786	+	0.351236i	−0.746639	+	0.665230i	$0.768334\pi$
$98$		0			0
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$		0			0
$101$	7.07293	−	12.2507i	0.703783	−	1.21899i	−0.263346	−	0.964701i	$-0.584826\pi$
$101$	7.07293	−	12.2507i	0.703783	−	1.21899i	0.967129	−	0.254286i	$-0.0818404\pi$
$102$		0			0
$103$	1.99275	−	3.45154i	0.196351	−	0.340090i	−0.750992	−	0.660312i	$-0.770424\pi$
$103$	1.99275	−	3.45154i	0.196351	−	0.340090i	0.947343	+	0.320222i	$0.103757\pi$
$104$		0			0
$105$	−3.38921	+	5.87028i	−0.330753	+	0.572880i
$106$		0			0
$107$	−9.81062			−0.948428			−0.474214	−	0.880410i	$-0.657268\pi$
$107$	−9.81062			−0.948428			−0.474214	+	0.880410i	$0.657268\pi$
$108$		0			0
$109$	5.79053			0.554633			0.277316	−	0.960779i	$-0.410555\pi$
$109$	5.79053			0.554633			0.277316	+	0.960779i	$0.410555\pi$
$110$		0			0
$111$	1.89199	+	3.27703i	0.179580	+	0.311042i
$112$		0			0
$113$	1.52336	−	2.63853i	0.143305	−	0.248212i	−0.785434	−	0.618945i	$-0.787560\pi$
$113$	1.52336	−	2.63853i	0.143305	−	0.248212i	0.928739	+	0.370733i	$0.120894\pi$
$114$		0			0
$115$	2.08018	+	3.60298i	0.193978	+	0.335980i
$116$		0			0
$117$	2.19098	+	3.79488i	0.202556	+	0.350837i
$118$		0			0
$119$	8.80504			0.807157
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−4.48996	+	7.77684i	−0.404846	+	0.701214i
$124$		0			0
$125$	8.38753			0.750203
$126$		0			0
$127$	−3.08465	+	5.34277i	−0.273719	+	0.474094i	−0.969811	−	0.243858i	$-0.921587\pi$
$127$	−3.08465	+	5.34277i	−0.273719	+	0.474094i	0.696093	+	0.717952i	$0.254920\pi$
$128$		0			0
$129$	11.1870			0.984960
$130$		0			0
$131$	−18.1313			−1.58414			−0.792072	−	0.610428i	$-0.790997\pi$
$131$	−18.1313			−1.58414			−0.792072	+	0.610428i	$0.790997\pi$
$132$		0			0
$133$	7.23371			0.627242
$134$		0			0
$135$	2.60354			0.224077
$136$		0			0
$137$	10.9911			0.939030			0.469515	−	0.882925i	$-0.344429\pi$
$137$	10.9911			0.939030			0.469515	+	0.882925i	$0.344429\pi$
$138$		0			0
$139$	3.21265			0.272493			0.136247	−	0.990675i	$-0.456496\pi$
$139$	3.21265			0.272493			0.136247	+	0.990675i	$0.456496\pi$
$140$		0			0
$141$	−4.48996	+	7.77684i	−0.378123	+	0.654928i
$142$		0			0
$143$	8.76390			0.732874
$144$		0			0
$145$	−5.46939	+	9.47326i	−0.454208	+	0.786711i
$146$		0			0
$147$	−0.110793	−	0.191900i	−0.00913807	−	0.0158276i
$148$		0			0
$149$	−19.0588			−1.56136			−0.780680	−	0.624931i	$-0.785127\pi$
$149$	−19.0588			−1.56136			−0.780680	+	0.624931i	$0.785127\pi$
$150$		0			0
$151$	−6.87470	−	11.9073i	−0.559455	−	0.969004i	−0.997542	−	0.0700718i	$-0.977677\pi$
$151$	−6.87470	−	11.9073i	−0.559455	−	0.969004i	0.438087	−	0.898933i	$-0.355656\pi$
$152$		0			0
$153$	−1.69098	−	2.92886i	−0.136707	−	0.236784i
$154$		0			0
$155$	−12.7639	+	22.1077i	−1.02522	+	1.77574i
$156$		0			0
$157$	−4.00557	−	6.93786i	−0.319680	−	0.553701i	0.660742	−	0.750613i	$-0.270242\pi$
$157$	−4.00557	−	6.93786i	−0.319680	−	0.553701i	−0.980421	+	0.196912i	$0.936909\pi$
$158$		0			0
$159$	−0.618048			−0.0490144
$160$		0			0
$161$	4.16037			0.327883
$162$		0			0
$163$	−9.17815	+	15.8970i	−0.718888	+	1.24515i	0.242553	+	0.970138i	$0.422015\pi$
$163$	−9.17815	+	15.8970i	−0.718888	+	1.24515i	−0.961441	+	0.275012i	$0.911318\pi$
$164$		0			0
$165$	2.60354	−	4.50946i	0.202685	−	0.351061i
$166$		0			0
$167$	6.11964	−	10.5995i	0.473552	−	0.820216i	−0.525990	−	0.850491i	$-0.676305\pi$
$167$	6.11964	−	10.5995i	0.473552	−	0.820216i	0.999542	+	0.0302749i	$0.00963828\pi$
$168$		0			0
$169$	−3.10075	+	5.37066i	−0.238519	+	0.413128i
$170$		0			0
$171$	−1.38921	−	2.40618i	−0.106235	−	0.184005i
$172$		0			0
$173$	5.30177	+	9.18293i	0.403086	+	0.698166i	0.994097	−	0.108498i	$-0.0346042\pi$
$173$	5.30177	+	9.18293i	0.403086	+	0.698166i	−0.591011	+	0.806664i	$0.701271\pi$
$174$		0			0
$175$	−2.31508	+	4.00984i	−0.175004	+	0.303116i
$176$		0			0
$177$	−3.18045			−0.239057
$178$		0			0
$179$	−13.4086			−1.00220			−0.501102	−	0.865388i	$-0.667072\pi$
$179$	−13.4086			−1.00220			−0.501102	+	0.865388i	$0.667072\pi$
$180$		0			0
$181$	3.68651	−	6.38522i	0.274016	−	0.474610i	−0.695870	−	0.718167i	$-0.744981\pi$
$181$	3.68651	−	6.38522i	0.274016	−	0.474610i	0.969886	+	0.243558i	$0.0783145\pi$
$182$		0			0
$183$	−7.38474	−	12.7907i	−0.545896	−	0.945519i
$184$		0			0
$185$	4.92588	+	8.53187i	0.362158	+	0.627276i
$186$		0			0
$187$	−6.76390			−0.494626
$188$		0			0
$189$	1.30177	−	2.25473i	0.0946898	−	0.164008i
$190$		0			0
$191$	−12.5818	−	21.7923i	−0.910385	−	1.57683i	−0.813521	−	0.581536i	$-0.802452\pi$
$191$	−12.5818	−	21.7923i	−0.910385	−	1.57683i	−0.0968646	−	0.995298i	$-0.530881\pi$
$192$		0			0
$193$	11.5634			0.832350			0.416175	−	0.909285i	$-0.363370\pi$
$193$	11.5634			0.832350			0.416175	+	0.909285i	$0.363370\pi$
$194$		0			0
$195$	5.70429	+	9.88012i	0.408493	+	0.707530i
$196$		0			0
$197$	−12.7566	+	22.0952i	−0.908874	+	1.57422i	−0.0932423	+	0.995643i	$0.529723\pi$
$197$	−12.7566	+	22.0952i	−0.908874	+	1.57422i	−0.815631	+	0.578572i	$0.803610\pi$
$198$		0			0
$199$	6.18372	+	10.7105i	0.438352	+	0.759249i	0.997563	−	0.0697773i	$-0.0222289\pi$
$199$	6.18372	+	10.7105i	0.438352	+	0.759249i	−0.559210	+	0.829026i	$0.688896\pi$
$200$		0			0
$201$	4.38642	+	6.91081i	0.309394	+	0.487451i
$202$		0			0
$203$	5.46939	+	9.47326i	0.383876	+	0.664893i
$204$		0			0
$205$	−11.6898	+	20.2473i	−0.816450	+	1.41413i
$206$		0			0
$207$	−0.798983	−	1.38388i	−0.0555331	−	0.0961862i
$208$		0			0
$209$	−5.55683			−0.384374
$210$		0			0
$211$	−3.69544	−	6.40070i	−0.254405	−	0.440642i	0.710329	−	0.703870i	$-0.248546\pi$
$211$	−3.69544	−	6.40070i	−0.254405	−	0.440642i	−0.964734	+	0.263228i	$0.915213\pi$
$212$		0			0
$213$	3.40809	−	5.90299i	0.233519	−	0.404466i
$214$		0			0
$215$	29.1258			1.98636
$216$		0			0
$217$	12.7639	+	22.1077i	0.866470	+	1.50077i
$218$		0			0
$219$	0.613580	+	1.06275i	0.0414619	+	0.0718141i
$220$		0			0
$221$	7.40978	−	12.8341i	0.498435	−	0.863316i
$222$		0			0
$223$	−2.83963			−0.190156			−0.0950780	−	0.995470i	$-0.530310\pi$
$223$	−2.83963			−0.190156			−0.0950780	+	0.995470i	$0.530310\pi$
$224$		0			0
$225$	1.77841			0.118561
$226$		0			0
$227$	12.0923	−	20.9445i	0.802594	−	1.39013i	−0.115309	−	0.993330i	$-0.536786\pi$
$227$	12.0923	−	20.9445i	0.802594	−	1.39013i	0.917903	−	0.396804i	$-0.129881\pi$
$228$		0			0
$229$	0.593010	+	1.02712i	0.0391872	+	0.0678743i	0.884954	−	0.465679i	$-0.154190\pi$
$229$	0.593010	+	1.02712i	0.0391872	+	0.0678743i	−0.845767	+	0.533553i	$0.820856\pi$
$230$		0			0
$231$	−2.60354	−	4.50946i	−0.171300	−	0.296701i
$232$		0			0
$233$	−7.49602	+	12.9835i	−0.491081	+	0.850576i	−0.999947	−	0.0102689i	$-0.996731\pi$
$233$	−7.49602	+	12.9835i	−0.491081	+	0.850576i	0.508867	+	0.860845i	$0.330065\pi$
$234$		0			0
$235$	−11.6898	+	20.2473i	−0.762557	+	1.32079i
$236$		0			0
$237$	−5.01610	+	8.68814i	−0.325831	+	0.564355i
$238$		0			0
$239$	−0.00725462	+	0.0125654i	−0.000469262	+	0.000812786i	−0.866260	−	0.499594i	$-0.833483\pi$
$239$	−0.00725462	+	0.0125654i	−0.000469262	+	0.000812786i	0.865791	+	0.500406i	$0.166816\pi$
$240$		0			0
$241$	1.36426			0.0878796			0.0439398	−	0.999034i	$-0.486009\pi$
$241$	1.36426			0.0878796			0.0439398	+	0.999034i	$0.486009\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−0.288455	−	0.499618i	−0.0184287	−	0.0319194i
$246$		0			0
$247$	6.08744	−	10.5438i	0.387334	−	0.670883i
$248$		0			0
$249$	2.69098	+	4.66091i	0.170534	+	0.295373i
$250$		0			0
$251$	0.817871	+	1.41659i	0.0516235	+	0.0894146i	0.890682	−	0.454626i	$-0.150227\pi$
$251$	0.817871	+	1.41659i	0.0516235	+	0.0894146i	−0.839059	+	0.544041i	$0.816894\pi$
$252$		0			0
$253$	−3.19593			−0.200926
$254$		0			0
$255$	−4.40252	−	7.62539i	−0.275697	−	0.477521i
$256$		0			0
$257$	0.946034	−	1.63858i	0.0590120	−	0.102212i	−0.835010	−	0.550234i	$-0.814538\pi$
$257$	0.946034	−	1.63858i	0.0590120	−	0.102212i	0.894022	+	0.448023i	$0.147872\pi$
$258$		0			0
$259$	9.85175			0.612158
$260$		0			0
$261$	2.10075	−	3.63861i	0.130033	−	0.225224i
$262$		0			0
$263$	−3.42309			−0.211077			−0.105538	−	0.994415i	$-0.533657\pi$
$263$	−3.42309			−0.211077			−0.105538	+	0.994415i	$0.533657\pi$
$264$		0			0
$265$	−1.60911			−0.0988469
$266$		0			0
$267$	3.00557			0.183938
$268$		0			0
$269$	2.48431			0.151471			0.0757356	−	0.997128i	$-0.475870\pi$
$269$	2.48431			0.151471			0.0757356	+	0.997128i	$0.475870\pi$
$270$		0			0
$271$	17.0533			1.03591			0.517956	−	0.855407i	$-0.326693\pi$
$271$	17.0533			1.03591			0.517956	+	0.855407i	$0.326693\pi$
$272$		0			0
$273$	11.4086			0.690479
$274$		0			0
$275$	1.77841	−	3.08030i	0.107242	−	0.185749i
$276$		0			0
$277$	−7.17487			−0.431096			−0.215548	−	0.976493i	$-0.569154\pi$
$277$	−7.17487			−0.431096			−0.215548	+	0.976493i	$0.569154\pi$
$278$		0			0
$279$	4.90252	−	8.49142i	0.293506	−	0.508368i
$280$		0			0
$281$	−16.1664	−	28.0011i	−0.964408	−	1.67040i	−0.711197	−	0.702993i	$-0.751847\pi$
$281$	−16.1664	−	28.0011i	−0.964408	−	1.67040i	−0.253211	−	0.967411i	$-0.581487\pi$
$282$		0			0
$283$	−0.737275			−0.0438264			−0.0219132	−	0.999760i	$-0.506976\pi$
$283$	−0.737275			−0.0438264			−0.0219132	+	0.999760i	$0.506976\pi$
$284$		0			0
$285$	−3.61685	−	6.26457i	−0.214244	−	0.371081i
$286$		0			0
$287$	11.6898	+	20.2473i	0.690026	+	1.19516i
$288$		0			0
$289$	2.78120	−	4.81718i	0.163600	−	0.283364i
$290$		0			0
$291$	−1.99721	−	3.45928i	−0.117079	−	0.202786i
$292$		0			0
$293$	−27.9444			−1.63253			−0.816263	−	0.577680i	$-0.803958\pi$
$293$	−27.9444			−1.63253			−0.816263	+	0.577680i	$0.803958\pi$
$294$		0			0
$295$	−8.28042			−0.482105
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	3.50110	−	6.06409i	0.202474	−	0.350695i
$300$		0			0
$301$	14.5629	−	25.2237i	0.839391	−	1.45387i
$302$		0			0
$303$	−7.07293	+	12.2507i	−0.406329	+	0.703783i
$304$		0			0
$305$	−19.2265	−	33.3012i	−1.10090	−	1.90682i
$306$		0			0
$307$	3.69376	+	6.39778i	0.210814	+	0.365141i	0.951970	−	0.306193i	$-0.0990552\pi$
$307$	3.69376	+	6.39778i	0.210814	+	0.365141i	−0.741155	+	0.671333i	$0.765722\pi$
$308$		0			0
$309$	−1.99275	+	3.45154i	−0.113363	+	0.196351i
$310$		0			0
$311$	6.94214			0.393653			0.196826	−	0.980438i	$-0.436936\pi$
$311$	6.94214			0.393653			0.196826	+	0.980438i	$0.436936\pi$
$312$		0			0
$313$	−23.2303			−1.31306			−0.656528	−	0.754301i	$-0.727976\pi$
$313$	−23.2303			−1.31306			−0.656528	+	0.754301i	$0.727976\pi$
$314$		0			0
$315$	3.38921	−	5.87028i	0.190960	−	0.330753i
$316$		0			0
$317$	0.972176	+	1.68386i	0.0546028	+	0.0945749i	0.892035	−	0.451967i	$-0.149277\pi$
$317$	0.972176	+	1.68386i	0.0546028	+	0.0945749i	−0.837432	+	0.546542i	$0.815944\pi$
$318$		0			0
$319$	−4.20150	−	7.27722i	−0.235239	−	0.407446i
$320$		0			0
$321$	9.81062			0.547575
$322$		0			0
$323$	−4.69823	+	8.13757i	−0.261417	+	0.452787i
$324$		0			0
$325$	3.89646	+	6.74887i	0.216137	+	0.374360i
$326$		0			0
$327$	−5.79053			−0.320217
$328$		0			0
$329$	11.6898	+	20.2473i	0.644479	+	1.11627i
$330$		0			0
$331$	−2.93592	+	5.08516i	−0.161373	+	0.279506i	−0.935361	−	0.353694i	$-0.884925\pi$
$331$	−2.93592	+	5.08516i	−0.161373	+	0.279506i	0.773989	+	0.633200i	$0.218259\pi$
$332$		0			0
$333$	−1.89199	−	3.27703i	−0.103681	−	0.179580i
$334$		0			0
$335$	11.4202	+	17.9926i	0.623953	+	0.983039i
$336$		0			0
$337$	−8.67974	−	15.0338i	−0.472816	−	0.818941i	0.526700	−	0.850051i	$-0.323429\pi$
$337$	−8.67974	−	15.0338i	−0.472816	−	0.818941i	−0.999516	+	0.0311104i	$0.990096\pi$
$338$		0			0
$339$	−1.52336	+	2.63853i	−0.0827373	+	0.143305i
$340$		0			0
$341$	−9.80504	−	16.9828i	−0.530973	−	0.919672i
$342$		0			0
$343$	−18.8017			−1.01520
$344$		0			0
$345$	−2.08018	−	3.60298i	−0.111993	−	0.193978i
$346$		0			0
$347$	10.0116	−	17.3407i	0.537453	−	0.930895i	−0.461588	−	0.887095i	$-0.652720\pi$
$347$	10.0116	−	17.3407i	0.537453	−	0.930895i	0.999040	−	0.0438007i	$-0.0139466\pi$
$348$		0			0
$349$	−3.36187			−0.179957			−0.0899784	−	0.995944i	$-0.528680\pi$
$349$	−3.36187			−0.179957			−0.0899784	+	0.995944i	$0.528680\pi$
$350$		0			0
$351$	−2.19098	−	3.79488i	−0.116946	−	0.202556i
$352$		0			0
$353$	12.4008	+	21.4789i	0.660030	+	1.14321i	0.980607	+	0.195983i	$0.0627898\pi$
$353$	12.4008	+	21.4789i	0.660030	+	1.14321i	−0.320577	+	0.947222i	$0.603877\pi$
$354$		0			0
$355$	8.87311	−	15.3687i	0.470936	−	0.815684i
$356$		0			0
$357$	−8.80504			−0.466012
$358$		0			0
$359$	23.6769			1.24962			0.624809	−	0.780778i	$-0.285177\pi$
$359$	23.6769			1.24962			0.624809	+	0.780778i	$0.285177\pi$
$360$		0			0
$361$	5.64021	−	9.76913i	0.296853	−	0.514165i
$362$		0			0
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$		0			0
$365$	1.59748	+	2.76691i	0.0836158	+	0.144827i
$366$		0			0
$367$	12.0734	−	20.9118i	0.630227	−	1.09159i	−0.357278	−	0.933998i	$-0.616295\pi$
$367$	12.0734	−	20.9118i	0.630227	−	1.09159i	0.987505	−	0.157587i	$-0.0503716\pi$
$368$		0			0
$369$	4.48996	−	7.77684i	0.233738	−	0.404846i
$370$		0			0
$371$	−0.804556	+	1.39353i	−0.0417705	+	0.0723485i
$372$		0			0
$373$	7.11517	−	12.3238i	0.368410	−	0.638104i	−0.620907	−	0.783884i	$-0.713236\pi$
$373$	7.11517	−	12.3238i	0.368410	−	0.638104i	0.989317	+	0.145780i	$0.0465691\pi$
$374$		0			0
$375$	−8.38753			−0.433130
$376$		0			0
$377$	18.4108			0.948204
$378$		0			0
$379$	−0.607520	−	1.05225i	−0.0312062	−	0.0540507i	0.850001	−	0.526782i	$-0.176602\pi$
$379$	−0.607520	−	1.05225i	−0.0312062	−	0.0540507i	−0.881207	+	0.472731i	$0.843268\pi$
$380$		0			0
$381$	3.08465	−	5.34277i	0.158031	−	0.273719i
$382$		0			0
$383$	−0.320657	−	0.555394i	−0.0163848	−	0.0283793i	0.857717	−	0.514123i	$-0.171882\pi$
$383$	−0.320657	−	0.555394i	−0.0163848	−	0.0283793i	−0.874102	+	0.485743i	$0.838549\pi$
$384$		0			0
$385$	−6.77841	−	11.7406i	−0.345460	−	0.598354i
$386$		0			0
$387$	−11.1870			−0.568667
$388$		0			0
$389$	−3.98549	−	6.90307i	−0.202072	−	0.350000i	0.747124	−	0.664685i	$-0.231434\pi$
$389$	−3.98549	−	6.90307i	−0.202072	−	0.350000i	−0.949196	+	0.314685i	$0.898101\pi$
$390$		0			0
$391$	−2.70212	+	4.68021i	−0.136652	+	0.236689i
$392$		0			0
$393$	18.1313			0.914605
$394$		0			0
$395$	−13.0596	+	22.6199i	−0.657100	+	1.13813i
$396$		0			0
$397$	9.99106			0.501437			0.250719	−	0.968060i	$-0.419333\pi$
$397$	9.99106			0.501437			0.250719	+	0.968060i	$0.419333\pi$
$398$		0			0
$399$	−7.23371			−0.362138
$400$		0			0
$401$	15.4197			0.770024			0.385012	−	0.922911i	$-0.374197\pi$
$401$	15.4197			0.770024			0.385012	+	0.922911i	$0.374197\pi$
$402$		0			0
$403$	42.9652			2.14025
$404$		0			0
$405$	−2.60354			−0.129371
$406$		0			0
$407$	−7.56797			−0.375130
$408$		0			0
$409$	−4.11190	+	7.12202i	−0.203320	+	0.352161i	−0.949596	−	0.313476i	$-0.898507\pi$
$409$	−4.11190	+	7.12202i	−0.203320	+	0.352161i	0.746276	+	0.665637i	$0.231840\pi$
$410$		0			0
$411$	−10.9911			−0.542149
$412$		0			0
$413$	−4.14021	+	7.17105i	−0.203726	+	0.352864i
$414$		0			0
$415$	7.00606	+	12.1349i	0.343914	+	0.595676i
$416$		0			0
$417$	−3.21265			−0.157324
$418$		0			0
$419$	−4.32791	−	7.49616i	−0.211432	−	0.366212i	0.740731	−	0.671802i	$-0.234479\pi$
$419$	−4.32791	−	7.49616i	−0.211432	−	0.366212i	−0.952163	+	0.305591i	$0.901146\pi$
$420$		0			0
$421$	−18.9682	−	32.8539i	−0.924453	−	1.60120i	−0.792438	−	0.609952i	$-0.791189\pi$
$421$	−18.9682	−	32.8539i	−0.924453	−	1.60120i	−0.132015	−	0.991248i	$-0.542145\pi$
$422$		0			0
$423$	4.48996	−	7.77684i	0.218309	−	0.378123i
$424$		0			0
$425$	−3.00725	−	5.20872i	−0.145873	−	0.252660i
$426$		0			0
$427$	−38.4529			−1.86087
$428$		0			0
$429$	−8.76390			−0.423125
$430$		0			0
$431$	−7.75100	+	13.4251i	−0.373353	+	0.646666i	−0.990079	−	0.140512i	$-0.955125\pi$
$431$	−7.75100	+	13.4251i	−0.373353	+	0.646666i	0.616726	+	0.787178i	$0.288459\pi$
$432$		0			0
$433$	14.8222	−	25.6729i	0.712312	−	1.23376i	−0.251675	−	0.967812i	$-0.580982\pi$
$433$	14.8222	−	25.6729i	0.712312	−	1.23376i	0.963987	−	0.265949i	$-0.0856851\pi$
$434$		0			0
$435$	5.46939	−	9.47326i	0.262237	−	0.454208i
$436$		0			0
$437$	−2.21990	+	3.84499i	−0.106192	+	0.183931i
$438$		0			0
$439$	−14.9013	−	25.8099i	−0.711202	−	1.23184i	−0.964406	−	0.264425i	$-0.914818\pi$
$439$	−14.9013	−	25.8099i	−0.711202	−	1.23184i	0.253205	−	0.967413i	$-0.418515\pi$
$440$		0			0
$441$	0.110793	+	0.191900i	0.00527587	+	0.00913807i
$442$		0			0
$443$	−3.07461	+	5.32538i	−0.146079	+	0.253016i	−0.929775	−	0.368128i	$-0.879999\pi$
$443$	−3.07461	+	5.32538i	−0.146079	+	0.253016i	0.783696	+	0.621145i	$0.213332\pi$
$444$		0			0
$445$	7.82513			0.370947
$446$		0			0
$447$	19.0588			0.901452
$448$		0			0
$449$	−14.3941	+	24.9313i	−0.679298	+	1.17658i	0.295894	+	0.955221i	$0.404382\pi$
$449$	−14.3941	+	24.9313i	−0.679298	+	1.17658i	−0.975193	+	0.221358i	$0.928951\pi$
$450$		0			0
$451$	−8.97992	−	15.5537i	−0.422848	−	0.732394i
$452$		0			0
$453$	6.87470	+	11.9073i	0.323001	+	0.559455i
$454$		0			0
$455$	29.7027			1.39248
$456$		0			0
$457$	8.52057	−	14.7581i	0.398575	−	0.690353i	−0.594975	−	0.803744i	$-0.702838\pi$
$457$	8.52057	−	14.7581i	0.398575	−	0.690353i	0.993550	+	0.113391i	$0.0361714\pi$
$458$		0			0
$459$	1.69098	+	2.92886i	0.0789280	+	0.136707i
$460$		0			0
$461$	−23.1781			−1.07951			−0.539755	−	0.841822i	$-0.681483\pi$
$461$	−23.1781			−1.07951			−0.539755	+	0.841822i	$0.681483\pi$
$462$		0			0
$463$	8.26104	+	14.3085i	0.383923	+	0.664975i	0.991619	−	0.129195i	$-0.0412394\pi$
$463$	8.26104	+	14.3085i	0.383923	+	0.664975i	−0.607696	+	0.794170i	$0.707906\pi$
$464$		0			0
$465$	12.7639	−	22.1077i	0.591912	−	1.02522i
$466$		0			0
$467$	4.60403	+	7.97441i	0.213049	+	0.369012i	0.952667	−	0.304015i	$-0.0983273\pi$
$467$	4.60403	+	7.97441i	0.213049	+	0.369012i	−0.739618	+	0.673027i	$0.764994\pi$
$468$		0			0
$469$	21.2921	−	0.893914i	0.983179	−	0.0412771i
$470$		0			0
$471$	4.00557	+	6.93786i	0.184567	+	0.319680i
$472$		0			0
$473$	−11.1870	+	19.3764i	−0.514379	+	0.890930i
$474$		0			0
$475$	−2.47058	−	4.27918i	−0.113358	−	0.196342i
$476$		0			0
$477$	0.618048			0.0282985
$478$		0			0
$479$	11.9260	+	20.6564i	0.544911	+	0.943813i	0.998613	+	0.0526594i	$0.0167698\pi$
$479$	11.9260	+	20.6564i	0.544911	+	0.943813i	−0.453702	+	0.891154i	$0.649897\pi$
$480$		0			0
$481$	8.29062	−	14.3598i	0.378020	−	0.654750i
$482$		0			0
$483$	−4.16037			−0.189303
$484$		0			0
$485$	−5.19982	−	9.00636i	−0.236112	−	0.408958i
$486$		0			0
$487$	16.9081	+	29.2857i	0.766179	+	1.32706i	0.939621	+	0.342217i	$0.111178\pi$
$487$	16.9081	+	29.2857i	0.766179	+	1.32706i	−0.173442	+	0.984844i	$0.555489\pi$
$488$		0			0
$489$	9.17815	−	15.8970i	0.415050	−	0.718888i
$490$		0			0
$491$	−9.41195			−0.424755			−0.212378	−	0.977188i	$-0.568121\pi$
$491$	−9.41195			−0.424755			−0.212378	+	0.977188i	$0.568121\pi$
$492$		0			0
$493$	−14.2093			−0.639954
$494$		0			0
$495$	−2.60354	+	4.50946i	−0.117020	+	0.202685i
$496$		0			0
$497$	−8.87311	−	15.3687i	−0.398013	−	0.689379i
$498$		0			0
$499$	−6.40301	−	11.0903i	−0.286638	−	0.496472i	0.686367	−	0.727255i	$-0.259204\pi$
$499$	−6.40301	−	11.0903i	−0.286638	−	0.496472i	−0.973005	+	0.230784i	$0.925871\pi$
$500$		0			0
$501$	−6.11964	+	10.5995i	−0.273405	+	0.473552i
$502$		0			0
$503$	−0.0741226	+	0.128384i	−0.00330496	+	0.00572437i	−0.867673	−	0.497135i	$-0.834385\pi$
$503$	−0.0741226	+	0.128384i	−0.00330496	+	0.00572437i	0.864368	+	0.502859i	$0.167719\pi$
$504$		0			0
$505$	−18.4146	+	31.8951i	−0.819441	+	1.41931i
$506$		0			0
$507$	3.10075	−	5.37066i	0.137709	−	0.238519i
$508$		0			0
$509$	−2.84282			−0.126006			−0.0630029	−	0.998013i	$-0.520068\pi$
$509$	−2.84282			−0.126006			−0.0630029	+	0.998013i	$0.520068\pi$
$510$		0			0
$511$	3.19496			0.141337
$512$		0			0
$513$	1.38921	+	2.40618i	0.0613350	+	0.106235i
$514$		0			0
$515$	−5.18819	+	8.98621i	−0.228619	+	0.395980i
$516$		0			0
$517$	−8.97992	−	15.5537i	−0.394936	−	0.684050i
$518$		0			0
$519$	−5.30177	−	9.18293i	−0.232722	−	0.403086i
$520$		0			0
$521$	−7.78399			−0.341023			−0.170511	−	0.985356i	$-0.554542\pi$
$521$	−7.78399			−0.341023			−0.170511	+	0.985356i	$0.554542\pi$
$522$		0			0
$523$	9.38244	+	16.2509i	0.410265	+	0.710601i	0.994919	−	0.100683i	$-0.0321027\pi$
$523$	9.38244	+	16.2509i	0.410265	+	0.710601i	−0.584653	+	0.811283i	$0.698769\pi$
$524$		0			0
$525$	2.31508	−	4.00984i	0.101039	−	0.175004i
$526$		0			0
$527$	−33.1602			−1.44448
$528$		0			0
$529$	10.2233	−	17.7072i	0.444489	−	0.769878i
$530$		0			0
$531$	3.18045			0.138020
$532$		0			0
$533$	39.3496			1.70442
$534$		0			0
$535$	25.5423			1.10429
$536$		0			0
$537$	13.4086			0.578623
$538$		0			0
$539$	0.443173			0.0190888
$540$		0			0
$541$	−6.80186			−0.292435			−0.146217	−	0.989252i	$-0.546710\pi$
$541$	−6.80186			−0.292435			−0.146217	+	0.989252i	$0.546710\pi$
$542$		0			0
$543$	−3.68651	+	6.38522i	−0.158203	+	0.274016i
$544$		0			0
$545$	−15.0759			−0.645780
$546$		0			0
$547$	19.8863	−	34.4441i	0.850278	−	1.47272i	−0.0306793	−	0.999529i	$-0.509767\pi$
$547$	19.8863	−	34.4441i	0.850278	−	1.47272i	0.880957	−	0.473196i	$-0.156900\pi$
$548$		0			0
$549$	7.38474	+	12.7907i	0.315173	+	0.545896i
$550$		0			0
$551$	−11.6735			−0.497309
$552$		0			0
$553$	13.0596	+	22.6199i	0.555351	+	0.961897i
$554$		0			0
$555$	−4.92588	−	8.53187i	−0.209092	−	0.362158i
$556$		0			0
$557$	7.24055	−	12.5410i	0.306792	−	0.531379i	−0.670867	−	0.741578i	$-0.734078\pi$
$557$	7.24055	−	12.5410i	0.306792	−	0.531379i	0.977659	+	0.210199i	$0.0674111\pi$
$558$		0			0
$559$	−24.5104	−	42.4533i	−1.03668	−	1.79558i
$560$		0			0
$561$	6.76390			0.285572
$562$		0			0
$563$	−4.13374			−0.174216			−0.0871081	−	0.996199i	$-0.527763\pi$
$563$	−4.13374			−0.174216			−0.0871081	+	0.996199i	$0.527763\pi$
$564$		0			0
$565$	−3.96612	+	6.86951i	−0.166856	+	0.289003i
$566$		0			0
$567$	−1.30177	+	2.25473i	−0.0546692	+	0.0946898i
$568$		0			0
$569$	−18.0456	+	31.2559i	−0.756511	+	1.31031i	0.188109	+	0.982148i	$0.439764\pi$
$569$	−18.0456	+	31.2559i	−0.756511	+	1.31031i	−0.944620	+	0.328167i	$0.893569\pi$
$570$		0			0
$571$	22.9275	−	39.7115i	0.959485	−	1.66188i	0.235731	−	0.971818i	$-0.424252\pi$
$571$	22.9275	−	39.7115i	0.959485	−	1.66188i	0.723754	−	0.690058i	$-0.242415\pi$
$572$		0			0
$573$	12.5818	+	21.7923i	0.525611	+	0.910385i
$574$		0			0
$575$	−1.42092	−	2.46111i	−0.0592565	−	0.102635i
$576$		0			0
$577$	−14.1079	+	24.4356i	−0.587320	+	1.01727i	0.407262	+	0.913312i	$0.366484\pi$
$577$	−14.1079	+	24.4356i	−0.587320	+	1.01727i	−0.994582	+	0.103957i	$0.966850\pi$
$578$		0			0
$579$	−11.5634			−0.480557
$580$		0			0
$581$	14.0121			0.581321
$582$		0			0
$583$	0.618048	−	1.07049i	0.0255969	−	0.0443352i
$584$		0			0
$585$	−5.70429	−	9.88012i	−0.235843	−	0.408493i
$586$		0			0
$587$	14.3006	+	24.7693i	0.590248	+	1.02234i	0.994199	+	0.107559i	$0.0343033\pi$
$587$	14.3006	+	24.7693i	0.590248	+	1.02234i	−0.403951	+	0.914781i	$0.632363\pi$
$588$		0			0
$589$	−27.2425			−1.12251
$590$		0			0
$591$	12.7566	−	22.0952i	0.524738	−	0.908874i
$592$		0			0
$593$	−13.0177	−	22.5473i	−0.534573	−	0.925907i	−0.999184	−	0.0403922i	$-0.987139\pi$
$593$	−13.0177	−	22.5473i	−0.534573	−	0.925907i	0.464611	−	0.885515i	$-0.346194\pi$
$594$		0			0
$595$	−22.9243			−0.939803
$596$		0			0
$597$	−6.18372	−	10.7105i	−0.253083	−	0.438352i
$598$		0			0
$599$	−21.1063	+	36.5572i	−0.862381	+	1.49369i	0.00724324	+	0.999974i	$0.497694\pi$
$599$	−21.1063	+	36.5572i	−0.862381	+	1.49369i	−0.869624	+	0.493714i	$0.835639\pi$
$600$		0			0
$601$	−8.35860	−	14.4775i	−0.340954	−	0.590550i	0.643656	−	0.765315i	$-0.277417\pi$
$601$	−8.35860	−	14.4775i	−0.340954	−	0.590550i	−0.984610	+	0.174765i	$0.944083\pi$
$602$		0			0
$603$	−4.38642	−	6.91081i	−0.178629	−	0.281430i
$604$		0			0
$605$	−9.11239	−	15.7831i	−0.370471	−	0.641675i
$606$		0			0
$607$	5.15758	−	8.93319i	0.209340	−	0.362587i	−0.742167	−	0.670215i	$-0.766202\pi$
$607$	5.15758	−	8.93319i	0.209340	−	0.362587i	0.951507	+	0.307628i	$0.0995352\pi$
$608$		0			0
$609$	−5.46939	−	9.47326i	−0.221631	−	0.383876i
$610$		0			0
$611$	39.3496			1.59191
$612$		0			0
$613$	17.6129	+	30.5064i	0.711377	+	1.23214i	0.964340	+	0.264666i	$0.0852616\pi$
$613$	17.6129	+	30.5064i	0.711377	+	1.23214i	−0.252963	+	0.967476i	$0.581405\pi$
$614$		0			0
$615$	11.6898	−	20.2473i	0.471377	−	0.816450i
$616$		0			0
$617$	16.8685			0.679099			0.339550	−	0.940588i	$-0.389725\pi$
$617$	16.8685			0.679099			0.339550	+	0.940588i	$0.389725\pi$
$618$		0			0
$619$	8.02336	+	13.8969i	0.322486	+	0.558562i	0.981000	−	0.194006i	$-0.0621482\pi$
$619$	8.02336	+	13.8969i	0.322486	+	0.558562i	−0.658514	+	0.752568i	$0.728815\pi$
$620$		0			0
$621$	0.798983	+	1.38388i	0.0320621	+	0.0555331i
$622$		0			0
$623$	3.91256	−	6.77676i	0.156754	−	0.271505i
$624$		0			0
$625$	−30.7293			−1.22917
$626$		0			0
$627$	5.55683			0.221918
$628$		0			0
$629$	−6.39863	+	11.0828i	−0.255130	+	0.441898i
$630$		0			0
$631$	0.737762	+	1.27784i	0.0293698	+	0.0508701i	0.880337	−	0.474349i	$-0.157317\pi$
$631$	0.737762	+	1.27784i	0.0293698	+	0.0508701i	−0.850967	+	0.525219i	$0.823983\pi$
$632$		0			0
$633$	3.69544	+	6.40070i	0.146881	+	0.254405i
$634$		0			0
$635$	8.03101	−	13.9101i	0.318701	−	0.552006i
$636$		0			0
$637$	−0.485491	+	0.840895i	−0.0192358	+	0.0333175i
$638$		0			0
$639$	−3.40809	+	5.90299i	−0.134822	+	0.233519i
$640$		0			0
$641$	−16.0640	+	27.8237i	−0.634490	+	1.09897i	0.352134	+	0.935950i	$0.385456\pi$
$641$	−16.0640	+	27.8237i	−0.634490	+	1.09897i	−0.986623	+	0.163018i	$0.947877\pi$
$642$		0			0
$643$	−18.1202			−0.714591			−0.357295	−	0.933991i	$-0.616301\pi$
$643$	−18.1202			−0.714591			−0.357295	+	0.933991i	$0.616301\pi$
$644$		0			0
$645$	−29.1258			−1.14683
$646$		0			0
$647$	−21.7966	−	37.7528i	−0.856913	−	1.48422i	−0.874859	−	0.484377i	$-0.839046\pi$
$647$	−21.7966	−	37.7528i	−0.856913	−	1.48422i	0.0179468	−	0.999839i	$-0.494287\pi$
$648$		0			0
$649$	3.18045	−	5.50870i	0.124843	−	0.216235i
$650$		0			0
$651$	−12.7639	−	22.1077i	−0.500257	−	0.866470i
$652$		0			0
$653$	9.58783	+	16.6066i	0.375201	+	0.649867i	0.990357	−	0.138538i	$-0.0442404\pi$
$653$	9.58783	+	16.6066i	0.375201	+	0.649867i	−0.615156	+	0.788405i	$0.710907\pi$
$654$		0			0
$655$	47.2057			1.84448
$656$		0			0
$657$	−0.613580	−	1.06275i	−0.0239380	−	0.0414619i
$658$		0			0
$659$	−22.9932	+	39.8254i	−0.895689	+	1.55138i	−0.0627398	+	0.998030i	$0.519984\pi$
$659$	−22.9932	+	39.8254i	−0.895689	+	1.55138i	−0.832949	+	0.553349i	$0.813349\pi$
$660$		0			0
$661$	48.1113			1.87131			0.935656	−	0.352914i	$-0.114809\pi$
$661$	48.1113			1.87131			0.935656	+	0.352914i	$0.114809\pi$
$662$		0			0
$663$	−7.40978	+	12.8341i	−0.287772	+	0.498435i
$664$		0			0
$665$	−18.8332			−0.730322
$666$		0			0
$667$	−6.71386			−0.259962
$668$		0			0
$669$	2.83963			0.109787
$670$		0			0
$671$	29.5390			1.14034
$672$		0			0
$673$	19.6380			0.756987			0.378494	−	0.925604i	$-0.376442\pi$
$673$	19.6380			0.756987			0.378494	+	0.925604i	$0.376442\pi$
$674$		0			0
$675$	−1.77841			−0.0684512
$676$		0			0
$677$	16.5757	−	28.7100i	0.637056	−	1.10341i	−0.349019	−	0.937116i	$-0.613485\pi$
$677$	16.5757	−	28.7100i	0.637056	−	1.10341i	0.986075	−	0.166299i	$-0.0531815\pi$
$678$		0			0
$679$	−10.3996			−0.399102
$680$		0			0
$681$	−12.0923	+	20.9445i	−0.463378	+	0.802594i
$682$		0			0
$683$	−0.407607	−	0.705996i	−0.0155967	−	0.0270142i	0.858122	−	0.513446i	$-0.171631\pi$
$683$	−0.407607	−	0.705996i	−0.0155967	−	0.0270142i	−0.873718	+	0.486432i	$0.838298\pi$
$684$		0			0
$685$	−28.6157			−1.09335
$686$		0			0
$687$	−0.593010	−	1.02712i	−0.0226248	−	0.0391872i
$688$		0			0
$689$	1.35413	+	2.34542i	0.0515882	+	0.0893533i
$690$		0			0
$691$	−16.2928	+	28.2200i	−0.619809	+	1.07354i	0.369712	+	0.929146i	$0.379456\pi$
$691$	−16.2928	+	28.2200i	−0.619809	+	1.07354i	−0.989520	+	0.144393i	$0.953877\pi$
$692$		0			0
$693$	2.60354	+	4.50946i	0.0989003	+	0.171300i
$694$		0			0
$695$	−8.36426			−0.317274
$696$		0			0
$697$	−30.3697			−1.15033
$698$		0			0
$699$	7.49602	−	12.9835i	0.283525	−	0.491081i
$700$		0			0
$701$	23.1730	−	40.1368i	0.875231	−	1.51594i	0.0187148	−	0.999825i	$-0.494043\pi$
$701$	23.1730	−	40.1368i	0.875231	−	1.51594i	0.856516	−	0.516120i	$-0.172624\pi$
$702$		0			0
$703$	−5.25674	+	9.10494i	−0.198262	+	0.343399i
$704$		0			0
$705$	11.6898	−	20.2473i	0.440263	−	0.762557i
$706$		0			0
$707$	18.4146	+	31.8951i	0.692554	+	1.19954i
$708$		0			0
$709$	9.57452	+	16.5836i	0.359579	+	0.622808i	0.987890	−	0.155153i	$-0.0495871\pi$
$709$	9.57452	+	16.5836i	0.359579	+	0.622808i	−0.628312	+	0.777962i	$0.716254\pi$
$710$		0			0
$711$	5.01610	−	8.68814i	0.188118	−	0.325831i
$712$		0			0
$713$	−15.6681			−0.586776
$714$		0			0
$715$	−22.8172			−0.853314
$716$		0			0
$717$	0.00725462	−	0.0125654i	0.000270929	−	0.000469262i
$718$		0			0
$719$	18.4292	+	31.9204i	0.687294	+	1.19043i	0.972710	+	0.232025i	$0.0745350\pi$
$719$	18.4292	+	31.9204i	0.687294	+	1.19043i	−0.285416	+	0.958404i	$0.592132\pi$
$720$		0			0
$721$	5.18819	+	8.98621i	0.193218	+	0.334664i
$722$		0			0
$723$	−1.36426			−0.0507373
$724$		0			0
$725$	3.73601	−	6.47095i	0.138752	−	0.240325i
$726$		0			0
$727$	25.6592	+	44.4430i	0.951646	+	1.64830i	0.741863	+	0.670551i	$0.233942\pi$
$727$	25.6592	+	44.4430i	0.951646	+	1.64830i	0.209783	+	0.977748i	$0.432724\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	18.9169	+	32.7651i	0.699668	+	1.21186i
$732$		0			0
$733$	5.44157	−	9.42507i	0.200989	−	0.348123i	−0.747858	−	0.663858i	$-0.768918\pi$
$733$	5.44157	−	9.42507i	0.200989	−	0.348123i	0.948847	+	0.315735i	$0.102251\pi$
$734$		0			0
$735$	0.288455	+	0.499618i	0.0106398	+	0.0184287i
$736$		0			0
$737$	−16.3563	+	0.686691i	−0.602492	+	0.0252946i
$738$		0			0
$739$	22.1101	+	38.2958i	0.813333	+	1.40873i	0.910519	+	0.413467i	$0.135682\pi$
$739$	22.1101	+	38.2958i	0.813333	+	1.40873i	−0.0971863	+	0.995266i	$0.530984\pi$
$740$		0			0
$741$	−6.08744	+	10.5438i	−0.223628	+	0.387334i
$742$		0			0
$743$	−5.29403	−	9.16952i	−0.194219	−	0.336397i	0.752425	−	0.658678i	$-0.228884\pi$
$743$	−5.29403	−	9.16952i	−0.194219	−	0.336397i	−0.946644	+	0.322280i	$0.895551\pi$
$744$		0			0
$745$	49.6204			1.81795
$746$		0			0
$747$	−2.69098	−	4.66091i	−0.0984577	−	0.170534i
$748$		0			0
$749$	12.7712	−	22.1203i	0.466648	−	0.808258i
$750$		0			0
$751$	−32.7848			−1.19633			−0.598167	−	0.801372i	$-0.704104\pi$
$751$	−32.7848			−1.19633			−0.598167	+	0.801372i	$0.704104\pi$
$752$		0			0
$753$	−0.817871	−	1.41659i	−0.0298049	−	0.0516235i
$754$		0			0
$755$	17.8985	+	31.0012i	0.651395	+	1.12825i
$756$		0			0
$757$	−7.02949	+	12.1754i	−0.255491	+	0.442524i	−0.965029	−	0.262144i	$-0.915571\pi$
$757$	−7.02949	+	12.1754i	−0.255491	+	0.442524i	0.709538	+	0.704668i	$0.248904\pi$
$758$		0			0
$759$	3.19593			0.116005
$760$		0			0
$761$	9.07237			0.328873			0.164437	−	0.986388i	$-0.447419\pi$
$761$	9.07237			0.328873			0.164437	+	0.986388i	$0.447419\pi$
$762$		0			0
$763$	−7.53794	+	13.0561i	−0.272892	+	0.472662i
$764$		0			0
$765$	4.40252	+	7.62539i	0.159174	+	0.275697i
$766$		0			0
$767$	6.96828	+	12.0694i	0.251610	+	0.435802i
$768$		0			0
$769$	2.91654	−	5.05160i	0.105173	−	0.182165i	−0.808636	−	0.588310i	$-0.799794\pi$
$769$	2.91654	−	5.05160i	0.105173	−	0.182165i	0.913809	+	0.406144i	$0.133127\pi$
$770$		0			0
$771$	−0.946034	+	1.63858i	−0.0340706	+	0.0590120i
$772$		0			0
$773$	−11.2594	+	19.5019i	−0.404974	+	0.701435i	−0.994318	−	0.106447i	$-0.966053\pi$
$773$	−11.2594	+	19.5019i	−0.404974	+	0.701435i	0.589345	+	0.807882i	$0.299386\pi$
$774$		0			0
$775$	8.71871	−	15.1012i	0.313185	−	0.542453i
$776$		0			0
$777$	−9.85175			−0.353430
$778$		0			0
$779$	−24.9499			−0.893924
$780$		0			0
$781$	6.81619	+	11.8060i	0.243902	+	0.422451i
$782$		0			0
$783$	−2.10075	+	3.63861i	−0.0750748	+	0.130033i
$784$		0			0
$785$	10.4287	+	18.0630i	0.372215	+	0.644695i
$786$		0			0
$787$	−17.4815	−	30.2789i	−0.623149	−	1.07932i	−0.988896	−	0.148611i	$-0.952520\pi$
$787$	−17.4815	−	30.2789i	−0.623149	−	1.07932i	0.365747	−	0.930714i	$-0.380813\pi$
$788$		0			0
$789$	3.42309			0.121865
$790$		0			0
$791$	3.96612	+	6.86951i	0.141019	+	0.244252i
$792$		0			0
$793$	−32.3596	+	56.0484i	−1.14912	+	1.99034i
$794$		0			0
$795$	1.60911			0.0570693
$796$		0			0
$797$	−15.1129	+	26.1763i	−0.535325	+	0.927211i	0.463822	+	0.885928i	$0.346478\pi$
$797$	−15.1129	+	26.1763i	−0.535325	+	0.927211i	−0.999148	+	0.0412825i	$0.986856\pi$
$798$		0			0
$799$	−30.3697			−1.07440
$800$		0			0
$801$	−3.00557			−0.106197
$802$		0			0
$803$	−2.45432			−0.0866110
$804$		0			0
$805$	−10.8317			−0.381766
$806$		0			0
$807$	−2.48431			−0.0874519
$808$		0			0
$809$	−16.3652			−0.575371			−0.287685	−	0.957725i	$-0.592886\pi$
$809$	−16.3652			−0.575371			−0.287685	+	0.957725i	$0.592886\pi$
$810$		0			0
$811$	−18.7209	+	32.4255i	−0.657379	+	1.13861i	0.323913	+	0.946087i	$0.395002\pi$
$811$	−18.7209	+	32.4255i	−0.657379	+	1.13861i	−0.981292	+	0.192527i	$0.938332\pi$
$812$		0			0
$813$	−17.0533			−0.598084
$814$		0			0
$815$	23.8957	−	41.3885i	0.837029	−	1.44978i
$816$		0			0
$817$	15.5410	+	26.9179i	0.543712	+	0.941738i
$818$		0			0
$819$	−11.4086			−0.398648
$820$		0			0
$821$	20.2933	+	35.1491i	0.708242	+	1.22671i	0.965509	+	0.260370i	$0.0838447\pi$
$821$	20.2933	+	35.1491i	0.708242	+	1.22671i	−0.257267	+	0.966340i	$0.582822\pi$
$822$		0			0
$823$	17.1813	+	29.7589i	0.598904	+	1.03733i	0.992983	+	0.118255i	$0.0377301\pi$
$823$	17.1813	+	29.7589i	0.598904	+	1.03733i	−0.394080	+	0.919076i	$0.628937\pi$
$824$		0			0
$825$	−1.77841	+	3.08030i	−0.0619164	+	0.107242i
$826$		0			0
$827$	9.77771	+	16.9355i	0.340004	+	0.588904i	0.984433	−	0.175760i	$-0.0562382\pi$
$827$	9.77771	+	16.9355i	0.340004	+	0.588904i	−0.644429	+	0.764664i	$0.722905\pi$
$828$		0			0
$829$	−44.4833			−1.54497			−0.772485	−	0.635034i	$-0.780986\pi$
$829$	−44.4833			−1.54497			−0.772485	+	0.635034i	$0.780986\pi$
$830$		0			0
$831$	7.17487			0.248894
$832$		0			0
$833$	0.374698	−	0.648995i	0.0129825	−	0.0224863i
$834$		0			0
$835$	−15.9327	+	27.5963i	−0.551374	+	0.955009i
$836$		0			0
$837$	−4.90252	+	8.49142i	−0.169456	+	0.293506i
$838$		0			0
$839$	−1.32840	+	2.30085i	−0.0458614	+	0.0794343i	−0.888045	−	0.459757i	$-0.847937\pi$
$839$	−1.32840	+	2.30085i	−0.0458614	+	0.0794343i	0.842183	+	0.539191i	$0.181270\pi$
$840$		0			0
$841$	5.67368	+	9.82710i	0.195644	+	0.338866i
$842$		0			0
$843$	16.1664	+	28.0011i	0.556801	+	0.964408i
$844$		0			0
$845$	8.07293	−	13.9827i	0.277717	−	0.481020i
$846$		0			0
$847$	−18.2248			−0.626211
$848$		0			0
$849$	0.737275			0.0253032
$850$		0			0
$851$	−3.02334	+	5.23658i	−0.103639	+	0.179508i
$852$		0			0
$853$	25.2615	+	43.7542i	0.864938	+	1.49812i	0.867109	+	0.498119i	$0.165976\pi$
$853$	25.2615	+	43.7542i	0.864938	+	1.49812i	−0.00217110	+	0.999998i	$0.500691\pi$
$854$		0			0
$855$	3.61685	+	6.26457i	0.123694	+	0.214244i
$856$		0			0
$857$	−33.8460			−1.15616			−0.578079	−	0.815981i	$-0.696197\pi$
$857$	−33.8460			−1.15616			−0.578079	+	0.815981i	$0.696197\pi$
$858$		0			0
$859$	0.754570	−	1.30695i	0.0257456	−	0.0445927i	−0.852866	−	0.522131i	$-0.825137\pi$
$859$	0.754570	−	1.30695i	0.0257456	−	0.0445927i	0.878611	+	0.477538i	$0.158471\pi$
$860$		0			0
$861$	−11.6898	−	20.2473i	−0.398387	−	0.690026i
$862$		0			0
$863$	6.85830			0.233459			0.116730	−	0.993164i	$-0.462759\pi$
$863$	6.85830			0.233459			0.116730	+	0.993164i	$0.462759\pi$
$864$		0			0
$865$	−13.8034	−	23.9081i	−0.469328	−	0.812901i
$866$		0			0
$867$	−2.78120	+	4.81718i	−0.0944545	+	0.163600i
$868$		0			0
$869$	−10.0322	−	17.3763i	−0.340319	−	0.589450i
$870$		0			0
$871$	16.6152	−	31.7874i	0.562984	−	1.07707i
$872$		0			0
$873$	1.99721	+	3.45928i	0.0675954	+	0.117079i
$874$		0			0
$875$	−10.9186	+	18.9116i	−0.369117	+	0.639329i
$876$		0			0
$877$	−26.4114	−	45.7458i	−0.891849	−	1.54473i	−0.837657	−	0.546196i	$-0.816075\pi$
$877$	−26.4114	−	45.7458i	−0.891849	−	1.54473i	−0.0541914	−	0.998531i	$-0.517258\pi$
$878$		0			0
$879$	27.9444			0.942540
$880$		0			0
$881$	−26.1657	−	45.3204i	−0.881545	−	1.52688i	−0.849623	−	0.527391i	$-0.823170\pi$
$881$	−26.1657	−	45.3204i	−0.881545	−	1.52688i	−0.0319229	−	0.999490i	$-0.510163\pi$
$882$		0			0
$883$	−0.0617824	+	0.107010i	−0.00207914	+	0.00360118i	−0.867063	−	0.498198i	$-0.833995\pi$
$883$	−0.0617824	+	0.107010i	−0.00207914	+	0.00360118i	0.864984	+	0.501800i	$0.167328\pi$
$884$		0			0
$885$	8.28042			0.278343
$886$		0			0
$887$	8.51730	+	14.7524i	0.285983	+	0.495337i	0.972847	−	0.231449i	$-0.0743466\pi$
$887$	8.51730	+	14.7524i	0.285983	+	0.495337i	−0.686864	+	0.726786i	$0.741013\pi$
$888$		0			0
$889$	−8.03101	−	13.9101i	−0.269351	−	0.466530i
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$		0			0
$893$	−24.9499			−0.834917
$894$		0			0
$895$	34.9098			1.16690
$896$		0			0
$897$	−3.50110	+	6.06409i	−0.116898	+	0.202474i
$898$		0			0
$899$	−20.5980	−	35.6767i	−0.686981	−	1.18989i
$900$		0			0
$901$	−1.04510	−	1.81017i	−0.0348175	−	0.0603056i
$902$		0			0
$903$	−14.5629	+	25.2237i	−0.484623	+	0.839391i
$904$		0			0
$905$	−9.59797	+	16.6242i	−0.319047	+	0.552606i
$906$		0			0
$907$	15.7498	−	27.2795i	0.522964	−	0.905800i	−0.476679	−	0.879077i	$-0.658160\pi$
$907$	15.7498	−	27.2795i	0.522964	−	0.905800i	0.999643	−	0.0267225i	$-0.00850704\pi$
$908$		0			0
$909$	7.07293	−	12.2507i	0.234594	−	0.406329i
$910$		0			0
$911$	35.3408			1.17089			0.585447	−	0.810711i	$-0.300919\pi$
$911$	35.3408			1.17089			0.585447	+	0.810711i	$0.300919\pi$
$912$		0			0
$913$	−10.7639			−0.356233
$914$		0			0
$915$	19.2265	+	33.3012i	0.635607	+	1.10090i
$916$		0			0
$917$	23.6028	−	40.8813i	0.779434	−	1.35002i
$918$		0			0
$919$	2.35622	+	4.08110i	0.0777246	+	0.134623i	0.902268	−	0.431176i	$-0.141901\pi$
$919$	2.35622	+	4.08110i	0.0777246	+	0.134623i	−0.824543	+	0.565799i	$0.808568\pi$
$920$		0			0
$921$	−3.69376	−	6.39778i	−0.121714	−	0.210814i
$922$		0			0
$923$	−29.8682			−0.983124
$924$		0			0
$925$	−3.36475	−	5.82791i	−0.110632	−	0.191621i
$926$		0			0
$927$	1.99275	−	3.45154i	0.0654503	−	0.113363i
$928$		0			0
$929$	−10.5344			−0.345621			−0.172811	−	0.984955i	$-0.555285\pi$
$929$	−10.5344			−0.345621			−0.172811	+	0.984955i	$0.555285\pi$
$930$		0			0
$931$	0.307829	−	0.533176i	0.0100887	−	0.0174741i
$932$		0			0
$933$	−6.94214			−0.227276
$934$		0			0
$935$	17.6101			0.575911
$936$		0			0
$937$	13.6936			0.447350			0.223675	−	0.974664i	$-0.428195\pi$
$937$	13.6936			0.447350			0.223675	+	0.974664i	$0.428195\pi$
$938$		0			0
$939$	23.2303			0.758094
$940$		0			0
$941$	39.5055			1.28784			0.643922	−	0.765092i	$-0.277306\pi$
$941$	39.5055			1.28784			0.643922	+	0.765092i	$0.277306\pi$
$942$		0			0
$943$	−14.3496			−0.467287
$944$		0			0
$945$	−3.38921	+	5.87028i	−0.110251	+	0.190960i
$946$		0			0
$947$	−15.2860			−0.496728			−0.248364	−	0.968667i	$-0.579893\pi$
$947$	−15.2860			−0.496728			−0.248364	+	0.968667i	$0.579893\pi$
$948$		0			0
$949$	2.68868	−	4.65692i	0.0872781	−	0.151170i
$950$		0			0
$951$	−0.972176	−	1.68386i	−0.0315250	−	0.0546028i
$952$		0			0
$953$	−32.3875			−1.04913			−0.524567	−	0.851369i	$-0.675773\pi$
$953$	−32.3875			−1.04913			−0.524567	+	0.851369i	$0.675773\pi$
$954$		0			0
$955$	32.7571	+	56.7370i	1.06000	+	1.83597i
$956$		0			0
$957$	4.20150	+	7.27722i	0.135815	+	0.235239i
$958$		0			0
$959$	−14.3078	+	24.7819i	−0.462024	+	0.800249i
$960$		0			0
$961$	−32.5694	−	56.4119i	−1.05063	−	1.81974i
$962$		0			0
$963$	−9.81062			−0.316143
$964$		0			0
$965$	−30.1057			−0.969137
$966$		0			0
$967$	2.41305	−	4.17952i	0.0775985	−	0.134404i	−0.824615	−	0.565695i	$-0.808608\pi$
$967$	2.41305	−	4.17952i	0.0775985	−	0.134404i	0.902213	+	0.431290i	$0.141941\pi$
$968$		0			0
$969$	4.69823	−	8.13757i	0.150929	−	0.261417i
$970$		0			0
$971$	6.12181	−	10.6033i	0.196458	−	0.340276i	−0.750919	−	0.660394i	$-0.770389\pi$
$971$	6.12181	−	10.6033i	0.196458	−	0.340276i	0.947378	+	0.320118i	$0.103723\pi$
$972$		0			0
$973$	−4.18213	+	7.24366i	−0.134073	+	0.232221i
$974$		0			0
$975$	−3.89646	−	6.74887i	−0.124787	−	0.216137i
$976$		0			0
$977$	−20.3490	−	35.2456i	−0.651024	−	1.12761i	−0.982875	−	0.184274i	$-0.941007\pi$
$977$	−20.3490	−	35.2456i	−0.651024	−	1.12761i	0.331851	−	0.943332i	$-0.392327\pi$
$978$		0			0
$979$	−3.00557	+	5.20580i	−0.0960585	+	0.166378i
$980$		0			0
$981$	5.79053			0.184878
$982$		0			0
$983$	38.0387			1.21325			0.606624	−	0.794989i	$-0.292523\pi$
$983$	38.0387			1.21325			0.606624	+	0.794989i	$0.292523\pi$
$984$		0			0
$985$	33.2124	−	57.5256i	1.05824	−	1.83292i
$986$		0			0
$987$	−11.6898	−	20.2473i	−0.372090	−	0.644479i
$988$		0			0
$989$	8.93822	+	15.4814i	0.284219	+	0.492281i
$990$		0			0
$991$	44.9074			1.42653			0.713265	−	0.700895i	$-0.247216\pi$
$991$	44.9074			1.42653			0.713265	+	0.700895i	$0.247216\pi$
$992$		0			0
$993$	2.93592	−	5.08516i	0.0931686	−	0.161373i
$994$		0			0
$995$	−16.0996	−	27.8853i	−0.510390	−	0.884022i
$996$		0			0
$997$	4.11825			0.130426			0.0652132	−	0.997871i	$-0.479227\pi$
$997$	4.11825			0.130426			0.0652132	+	0.997871i	$0.479227\pi$
$998$		0			0
$999$	1.89199	+	3.27703i	0.0598600	+	0.103681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.i.d.37.1	✓	8
3.2	odd	2		2412.2.l.e.37.4		8
67.29	even	3	inner	804.2.i.d.565.1	yes	8
201.29	odd	6		2412.2.l.e.1369.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.d.37.1	✓	8	1.1	even	1	trivial
804.2.i.d.565.1	yes	8	67.29	even	3	inner
2412.2.l.e.37.4		8	3.2	odd	2
2412.2.l.e.1369.4		8	201.29	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -2.60354 q^{5} +(-1.30177 + 2.25473i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -2.60354 q^{5} +(-1.30177 + 2.25473i) q^{7} +1.00000 q^{9} +(1.00000 - 1.73205i) q^{11} +(2.19098 + 3.79488i) q^{13} +2.60354 q^{15} +(-1.69098 - 2.92886i) q^{17} +(-1.38921 - 2.40618i) q^{19} +(1.30177 - 2.25473i) q^{21} +(-0.798983 - 1.38388i) q^{23} +1.77841 q^{25} -1.00000 q^{27} +(2.10075 - 3.63861i) q^{29} +(4.90252 - 8.49142i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(3.38921 - 5.87028i) q^{35} +(-1.89199 - 3.27703i) q^{37} +(-2.19098 - 3.79488i) q^{39} +(4.48996 - 7.77684i) q^{41} -11.1870 q^{43} -2.60354 q^{45} +(4.48996 - 7.77684i) q^{47} +(0.110793 + 0.191900i) q^{49} +(1.69098 + 2.92886i) q^{51} +0.618048 q^{53} +(-2.60354 + 4.50946i) q^{55} +(1.38921 + 2.40618i) q^{57} +3.18045 q^{59} +(7.38474 + 12.7907i) q^{61} +(-1.30177 + 2.25473i) q^{63} +(-5.70429 - 9.88012i) q^{65} +(-4.38642 - 6.91081i) q^{67} +(0.798983 + 1.38388i) q^{69} +(-3.40809 + 5.90299i) q^{71} +(-0.613580 - 1.06275i) q^{73} -1.77841 q^{75} +(2.60354 + 4.50946i) q^{77} +(5.01610 - 8.68814i) q^{79} +1.00000 q^{81} +(-2.69098 - 4.66091i) q^{83} +(4.40252 + 7.62539i) q^{85} +(-2.10075 + 3.63861i) q^{87} -3.00557 q^{89} -11.4086 q^{91} +(-4.90252 + 8.49142i) q^{93} +(3.61685 + 6.26457i) q^{95} +(1.99721 + 3.45928i) q^{97} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9	\( 8 q - 8 q^{3} + 2 q^{5} + q^{7} + 8 q^{9} + 8 q^{11} - 2 q^{15} + 4 q^{17} - 5 q^{19} - q^{21} + q^{23} + 2 q^{25} - 8 q^{27} - 2 q^{29} + 9 q^{31} - 8 q^{33} + 21 q^{35} - 5 q^{37} + 11 q^{41} + 6 q^{43} + 2 q^{45} + 11 q^{47} + 7 q^{49} - 4 q^{51} + 40 q^{53} + 2 q^{55} + 5 q^{57} + 28 q^{59} + 20 q^{61} + q^{63} - 4 q^{65} - 33 q^{67} - q^{69} + 11 q^{71} - 7 q^{73} - 2 q^{75} - 2 q^{77} + 12 q^{79} + 8 q^{81} - 4 q^{83} + 5 q^{85} + 2 q^{87} - 16 q^{89} - 8 q^{91} - 9 q^{93} - 18 q^{95} + 20 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^3 + 2 * q^5 + q^7 + 8 * q^9 + 8 * q^11 - 2 * q^15 + 4 * q^17 - 5 * q^19 - q^21 + q^23 + 2 * q^25 - 8 * q^27 - 2 * q^29 + 9 * q^31 - 8 * q^33 + 21 * q^35 - 5 * q^37 + 11 * q^41 + 6 * q^43 + 2 * q^45 + 11 * q^47 + 7 * q^49 - 4 * q^51 + 40 * q^53 + 2 * q^55 + 5 * q^57 + 28 * q^59 + 20 * q^61 + q^63 - 4 * q^65 - 33 * q^67 - q^69 + 11 * q^71 - 7 * q^73 - 2 * q^75 - 2 * q^77 + 12 * q^79 + 8 * q^81 - 4 * q^83 + 5 * q^85 + 2 * q^87 - 16 * q^89 - 8 * q^91 - 9 * q^93 - 18 * q^95 + 20 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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