LMFDB - Embedded newform 882.4.g.r.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.667
Dual form			882.4.g.r.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} -8.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(-4.00000 - 6.92820i) q^{11} +42.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-62.0000 + 107.387i) q^{19} +8.00000 q^{20} -16.0000 q^{22} +(38.0000 - 65.8179i) q^{23} +(60.5000 + 104.789i) q^{25} +(42.0000 - 72.7461i) q^{26} -254.000 q^{29} +(-36.0000 - 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +4.00000 q^{34} +(-199.000 + 344.678i) q^{37} +(124.000 + 214.774i) q^{38} +(8.00000 - 13.8564i) q^{40} +462.000 q^{41} +212.000 q^{43} +(-16.0000 + 27.7128i) q^{44} +(-76.0000 - 131.636i) q^{46} +(132.000 - 228.631i) q^{47} +242.000 q^{50} +(-84.0000 - 145.492i) q^{52} +(-81.0000 - 140.296i) q^{53} +16.0000 q^{55} +(-254.000 + 439.941i) q^{58} +(386.000 + 668.572i) q^{59} +(15.0000 - 25.9808i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-42.0000 + 72.7461i) q^{65} +(382.000 + 661.643i) q^{67} +(4.00000 - 6.92820i) q^{68} +236.000 q^{71} +(209.000 + 361.999i) q^{73} +(398.000 + 689.356i) q^{74} +496.000 q^{76} +(-276.000 + 478.046i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(462.000 - 800.207i) q^{82} +1036.00 q^{83} -4.00000 q^{85} +(212.000 - 367.195i) q^{86} +(32.0000 + 55.4256i) q^{88} +(-15.0000 + 25.9808i) q^{89} -304.000 q^{92} +(-264.000 - 457.261i) q^{94} +(-124.000 - 214.774i) q^{95} +1190.00 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{11} + 84 q^{13} - 16 q^{16} + 2 q^{17} - 124 q^{19} + 16 q^{20} - 32 q^{22} + 76 q^{23} + 121 q^{25} + 84 q^{26} - 508 q^{29} - 72 q^{31} + 32 q^{32} + 8 q^{34} - 398 q^{37} + 248 q^{38} + 16 q^{40} + 924 q^{41} + 424 q^{43} - 32 q^{44} - 152 q^{46} + 264 q^{47} + 484 q^{50} - 168 q^{52} - 162 q^{53} + 32 q^{55} - 508 q^{58} + 772 q^{59} + 30 q^{61} - 288 q^{62} + 128 q^{64} - 84 q^{65} + 764 q^{67} + 8 q^{68} + 472 q^{71} + 418 q^{73} + 796 q^{74} + 992 q^{76} - 552 q^{79} - 32 q^{80} + 924 q^{82} + 2072 q^{83} - 8 q^{85} + 424 q^{86} + 64 q^{88} - 30 q^{89} - 608 q^{92} - 528 q^{94} - 248 q^{95} + 2380 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^11 + 84 * q^13 - 16 * q^16 + 2 * q^17 - 124 * q^19 + 16 * q^20 - 32 * q^22 + 76 * q^23 + 121 * q^25 + 84 * q^26 - 508 * q^29 - 72 * q^31 + 32 * q^32 + 8 * q^34 - 398 * q^37 + 248 * q^38 + 16 * q^40 + 924 * q^41 + 424 * q^43 - 32 * q^44 - 152 * q^46 + 264 * q^47 + 484 * q^50 - 168 * q^52 - 162 * q^53 + 32 * q^55 - 508 * q^58 + 772 * q^59 + 30 * q^61 - 288 * q^62 + 128 * q^64 - 84 * q^65 + 764 * q^67 + 8 * q^68 + 472 * q^71 + 418 * q^73 + 796 * q^74 + 992 * q^76 - 552 * q^79 - 32 * q^80 + 924 * q^82 + 2072 * q^83 - 8 * q^85 + 424 * q^86 + 64 * q^88 - 30 * q^89 - 608 * q^92 - 528 * q^94 - 248 * q^95 + 2380 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.0894427	+	0.154919i	−0.907276	−	0.420536i	$-0.861842\pi$
$5$	−1.00000	+	1.73205i	−0.0894427	+	0.154919i	0.817833	+	0.575456i	$0.195175\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	2.00000	+	3.46410i	0.0632456	+	0.109545i
$11$	−4.00000	−	6.92820i	−0.109640	−	0.189903i	0.805984	−	0.591937i	$-0.201637\pi$
$11$	−4.00000	−	6.92820i	−0.109640	−	0.189903i	−0.915625	+	0.402034i	$0.868303\pi$
$12$		0			0
$13$	42.0000			0.896054			0.448027	−	0.894020i	$-0.352127\pi$
$13$	42.0000			0.896054			0.448027	+	0.894020i	$0.352127\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.0142668	+	0.0247108i	0.873071	−	0.487594i	$-0.162125\pi$
$17$	1.00000	+	1.73205i	0.0142668	+	0.0247108i	−0.858804	+	0.512305i	$0.828792\pi$
$18$		0			0
$19$	−62.0000	+	107.387i	−0.748620	+	1.29665i	0.199865	+	0.979824i	$0.435950\pi$
$19$	−62.0000	+	107.387i	−0.748620	+	1.29665i	−0.948484	+	0.316824i	$0.897384\pi$
$20$	8.00000			0.0894427
$21$		0			0
$22$	−16.0000			−0.155055
$23$	38.0000	−	65.8179i	0.344502	−	0.596695i	−0.640761	−	0.767740i	$-0.721381\pi$
$23$	38.0000	−	65.8179i	0.344502	−	0.596695i	0.985263	+	0.171045i	$0.0547144\pi$
$24$		0			0
$25$	60.5000	+	104.789i	0.484000	+	0.838313i
$26$	42.0000	−	72.7461i	0.316803	−	0.548719i
$27$		0			0
$28$		0			0
$29$	−254.000			−1.62644			−0.813218	−	0.581960i	$-0.802286\pi$
$29$	−254.000			−1.62644			−0.813218	+	0.581960i	$0.802286\pi$
$30$		0			0
$31$	−36.0000	−	62.3538i	−0.208574	−	0.361261i	0.742692	−	0.669634i	$-0.233549\pi$
$31$	−36.0000	−	62.3538i	−0.208574	−	0.361261i	−0.951266	+	0.308373i	$0.900216\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	4.00000			0.0201763
$35$		0			0
$36$		0			0
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.0375721	+	0.999294i	$0.511962\pi$
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.846628	+	0.532185i	$0.821371\pi$
$38$	124.000	+	214.774i	0.529354	+	0.916868i
$39$		0			0
$40$	8.00000	−	13.8564i	0.0316228	−	0.0547723i
$41$	462.000			1.75981			0.879906	−	0.475148i	$-0.157606\pi$
$41$	462.000			1.75981			0.879906	+	0.475148i	$0.157606\pi$
$42$		0			0
$43$	212.000			0.751853			0.375927	−	0.926649i	$-0.377324\pi$
$43$	212.000			0.751853			0.375927	+	0.926649i	$0.377324\pi$
$44$	−16.0000	+	27.7128i	−0.0548202	+	0.0949514i
$45$		0			0
$46$	−76.0000	−	131.636i	−0.243600	−	0.421927i
$47$	132.000	−	228.631i	0.409663	−	0.709558i	−0.585189	−	0.810897i	$-0.698979\pi$
$47$	132.000	−	228.631i	0.409663	−	0.709558i	0.994852	+	0.101339i	$0.0323128\pi$
$48$		0			0
$49$		0			0
$50$	242.000			0.684479
$51$		0			0
$52$	−84.0000	−	145.492i	−0.224014	−	0.388003i
$53$	−81.0000	−	140.296i	−0.209928	−	0.363607i	0.741763	−	0.670662i	$-0.233990\pi$
$53$	−81.0000	−	140.296i	−0.209928	−	0.363607i	−0.951692	+	0.307055i	$0.900656\pi$
$54$		0			0
$55$	16.0000			0.0392262
$56$		0			0
$57$		0			0
$58$	−254.000	+	439.941i	−0.575032	+	0.995984i
$59$	386.000	+	668.572i	0.851744	+	1.47526i	0.879633	+	0.475654i	$0.157788\pi$
$59$	386.000	+	668.572i	0.851744	+	1.47526i	−0.0278883	+	0.999611i	$0.508878\pi$
$60$		0			0
$61$	15.0000	−	25.9808i	0.0314845	−	0.0545327i	−0.849854	−	0.527018i	$-0.823310\pi$
$61$	15.0000	−	25.9808i	0.0314845	−	0.0545327i	0.881338	+	0.472486i	$0.156643\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	64.0000			0.125000
$65$	−42.0000	+	72.7461i	−0.0801455	+	0.138816i
$66$		0			0
$67$	382.000	+	661.643i	0.696548	+	1.20646i	0.969656	+	0.244473i	$0.0786151\pi$
$67$	382.000	+	661.643i	0.696548	+	1.20646i	−0.273108	+	0.961983i	$0.588052\pi$
$68$	4.00000	−	6.92820i	0.00713340	−	0.0123554i
$69$		0			0
$70$		0			0
$71$	236.000			0.394480			0.197240	−	0.980355i	$-0.436802\pi$
$71$	236.000			0.394480			0.197240	+	0.980355i	$0.436802\pi$
$72$		0			0
$73$	209.000	+	361.999i	0.335090	+	0.580394i	0.983502	−	0.180896i	$-0.0578998\pi$
$73$	209.000	+	361.999i	0.335090	+	0.580394i	−0.648412	+	0.761290i	$0.724566\pi$
$74$	398.000	+	689.356i	0.625224	+	1.08292i
$75$		0			0
$76$	496.000			0.748620
$77$		0			0
$78$		0			0
$79$	−276.000	+	478.046i	−0.393069	+	0.680815i	−0.992853	−	0.119347i	$-0.961920\pi$
$79$	−276.000	+	478.046i	−0.393069	+	0.680815i	0.599784	+	0.800162i	$0.295253\pi$
$80$	−16.0000	−	27.7128i	−0.0223607	−	0.0387298i
$81$		0			0
$82$	462.000	−	800.207i	0.622187	−	1.07766i
$83$	1036.00			1.37007			0.685035	−	0.728510i	$-0.259787\pi$
$83$	1036.00			1.37007			0.685035	+	0.728510i	$0.259787\pi$
$84$		0			0
$85$	−4.00000			−0.00510425
$86$	212.000	−	367.195i	0.265820	−	0.460414i
$87$		0			0
$88$	32.0000	+	55.4256i	0.0387638	+	0.0671408i
$89$	−15.0000	+	25.9808i	−0.0178651	+	0.0309433i	−0.874820	−	0.484449i	$-0.839020\pi$
$89$	−15.0000	+	25.9808i	−0.0178651	+	0.0309433i	0.856955	+	0.515392i	$0.172354\pi$
$90$		0			0
$91$		0			0
$92$	−304.000			−0.344502
$93$		0			0
$94$	−264.000	−	457.261i	−0.289676	−	0.501733i
$95$	−124.000	−	214.774i	−0.133917	−	0.231951i
$96$		0			0
$97$	1190.00			1.24563			0.622815	−	0.782369i	$-0.285989\pi$
$97$	1190.00			1.24563			0.622815	+	0.782369i	$0.285989\pi$
$98$		0			0
$99$		0			0
$100$	242.000	−	419.156i	0.242000	−	0.419156i
$101$	−685.000	−	1186.45i	−0.674852	−	1.16888i	−0.976512	−	0.215462i	$-0.930874\pi$
$101$	−685.000	−	1186.45i	−0.674852	−	1.16888i	0.301660	−	0.953416i	$-0.402459\pi$
$102$		0			0
$103$	232.000	−	401.836i	0.221938	−	0.384408i	−0.733458	−	0.679735i	$-0.762095\pi$
$103$	232.000	−	401.836i	0.221938	−	0.384408i	0.955396	+	0.295326i	$0.0954283\pi$
$104$	−336.000			−0.316803
$105$		0			0
$106$	−324.000			−0.296884
$107$	−1068.00	+	1849.83i	−0.964930	+	1.67131i	−0.255125	+	0.966908i	$0.582117\pi$
$107$	−1068.00	+	1849.83i	−0.964930	+	1.67131i	−0.709804	+	0.704399i	$0.751217\pi$
$108$		0			0
$109$	613.000	+	1061.75i	0.538667	+	0.932999i	0.998976	+	0.0452405i	$0.0144054\pi$
$109$	613.000	+	1061.75i	0.538667	+	0.932999i	−0.460309	+	0.887759i	$0.652261\pi$
$110$	16.0000	−	27.7128i	0.0138685	−	0.0240210i
$111$		0			0
$112$		0			0
$113$	−338.000			−0.281384			−0.140692	−	0.990053i	$-0.544933\pi$
$113$	−338.000			−0.281384			−0.140692	+	0.990053i	$0.544933\pi$
$114$		0			0
$115$	76.0000	+	131.636i	0.0616264	+	0.106740i
$116$	508.000	+	879.882i	0.406609	+	0.704267i
$117$		0			0
$118$	1544.00			1.20455
$119$		0			0
$120$		0			0
$121$	633.500	−	1097.25i	0.475958	−	0.824383i
$122$	−30.0000	−	51.9615i	−0.0222629	−	0.0385605i
$123$		0			0
$124$	−144.000	+	249.415i	−0.104287	+	0.180630i
$125$	−492.000			−0.352047
$126$		0			0
$127$	2088.00			1.45890			0.729449	−	0.684035i	$-0.239777\pi$
$127$	2088.00			1.45890			0.729449	+	0.684035i	$0.239777\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	84.0000	+	145.492i	0.0566714	+	0.0981578i
$131$	146.000	−	252.879i	0.0973747	−	0.168658i	−0.813223	−	0.581953i	$-0.802289\pi$
$131$	146.000	−	252.879i	0.0973747	−	0.168658i	0.910597	+	0.413295i	$0.135622\pi$
$132$		0			0
$133$		0			0
$134$	1528.00			0.985068
$135$		0			0
$136$	−8.00000	−	13.8564i	−0.00504408	−	0.00873660i
$137$	409.000	+	708.409i	0.255060	+	0.441777i	0.964912	−	0.262574i	$-0.0845714\pi$
$137$	409.000	+	708.409i	0.255060	+	0.441777i	−0.709852	+	0.704351i	$0.751238\pi$
$138$		0			0
$139$	2156.00			1.31561			0.657804	−	0.753189i	$-0.271485\pi$
$139$	2156.00			1.31561			0.657804	+	0.753189i	$0.271485\pi$
$140$		0			0
$141$		0			0
$142$	236.000	−	408.764i	0.139470	−	0.241568i
$143$	−168.000	−	290.985i	−0.0982438	−	0.170163i
$144$		0			0
$145$	254.000	−	439.941i	0.145473	−	0.251966i
$146$	836.000			0.473889
$147$		0			0
$148$	1592.00			0.884200
$149$	−1425.00	+	2468.17i	−0.783494	+	1.35705i	0.146401	+	0.989225i	$0.453231\pi$
$149$	−1425.00	+	2468.17i	−0.783494	+	1.35705i	−0.929895	+	0.367825i	$0.880102\pi$
$150$		0			0
$151$	−836.000	−	1447.99i	−0.450548	−	0.780372i	0.547872	−	0.836562i	$-0.315438\pi$
$151$	−836.000	−	1447.99i	−0.450548	−	0.780372i	−0.998420	+	0.0561903i	$0.982105\pi$
$152$	496.000	−	859.097i	0.264677	−	0.458434i
$153$		0			0
$154$		0			0
$155$	144.000			0.0746217
$156$		0			0
$157$	223.000	+	386.247i	0.113359	+	0.196343i	0.917123	−	0.398605i	$-0.130506\pi$
$157$	223.000	+	386.247i	0.113359	+	0.196343i	−0.803764	+	0.594949i	$0.797172\pi$
$158$	552.000	+	956.092i	0.277942	+	0.481409i
$159$		0			0
$160$	−64.0000			−0.0316228
$161$		0			0
$162$		0			0
$163$	−1354.00	+	2345.20i	−0.650635	+	1.12693i	0.332334	+	0.943162i	$0.392164\pi$
$163$	−1354.00	+	2345.20i	−0.650635	+	1.12693i	−0.982969	+	0.183771i	$0.941170\pi$
$164$	−924.000	−	1600.41i	−0.439953	−	0.762021i
$165$		0			0
$166$	1036.00	−	1794.40i	0.484393	−	0.838993i
$167$	896.000			0.415177			0.207589	−	0.978216i	$-0.433439\pi$
$167$	896.000			0.415177			0.207589	+	0.978216i	$0.433439\pi$
$168$		0			0
$169$	−433.000			−0.197087
$170$	−4.00000	+	6.92820i	−0.00180462	+	0.00312570i
$171$		0			0
$172$	−424.000	−	734.390i	−0.187963	−	0.325562i
$173$	−2017.00	+	3493.55i	−0.886414	+	1.53531i	−0.0423302	+	0.999104i	$0.513478\pi$
$173$	−2017.00	+	3493.55i	−0.886414	+	1.53531i	−0.844084	+	0.536211i	$0.819855\pi$
$174$		0			0
$175$		0			0
$176$	128.000			0.0548202
$177$		0			0
$178$	30.0000	+	51.9615i	0.0126326	+	0.0218802i
$179$	−1740.00	−	3013.77i	−0.726557	−	1.25843i	−0.958330	−	0.285664i	$-0.907786\pi$
$179$	−1740.00	−	3013.77i	−0.726557	−	1.25843i	0.231773	−	0.972770i	$-0.425547\pi$
$180$		0			0
$181$	2898.00			1.19009			0.595046	−	0.803692i	$-0.297134\pi$
$181$	2898.00			1.19009			0.595046	+	0.803692i	$0.297134\pi$
$182$		0			0
$183$		0			0
$184$	−304.000	+	526.543i	−0.121800	+	0.210964i
$185$	−398.000	−	689.356i	−0.158170	−	0.273959i
$186$		0			0
$187$	8.00000	−	13.8564i	0.00312844	−	0.00541861i
$188$	−1056.00			−0.409663
$189$		0			0
$190$	−496.000			−0.189387
$191$	1326.00	−	2296.70i	0.502335	−	0.870070i	−0.497661	−	0.867371i	$-0.665808\pi$
$191$	1326.00	−	2296.70i	0.502335	−	0.870070i	0.999996	−	0.00269837i	$-0.000858920\pi$
$192$		0			0
$193$	−73.0000	−	126.440i	−0.0272262	−	0.0471571i	0.852091	−	0.523393i	$-0.175334\pi$
$193$	−73.0000	−	126.440i	−0.0272262	−	0.0471571i	−0.879317	+	0.476236i	$0.842001\pi$
$194$	1190.00	−	2061.14i	0.440397	−	0.762790i
$195$		0			0
$196$		0			0
$197$	2546.00			0.920787			0.460393	−	0.887715i	$-0.347708\pi$
$197$	2546.00			0.920787			0.460393	+	0.887715i	$0.347708\pi$
$198$		0			0
$199$	−1268.00	−	2196.24i	−0.451689	−	0.782349i	0.546802	−	0.837262i	$-0.315845\pi$
$199$	−1268.00	−	2196.24i	−0.451689	−	0.782349i	−0.998491	+	0.0549134i	$0.982512\pi$
$200$	−484.000	−	838.313i	−0.171120	−	0.296388i
$201$		0			0
$202$	−2740.00			−0.954385
$203$		0			0
$204$		0			0
$205$	−462.000	+	800.207i	−0.157402	+	0.272629i
$206$	−464.000	−	803.672i	−0.156934	−	0.271818i
$207$		0			0
$208$	−336.000	+	581.969i	−0.112007	+	0.194001i
$209$	992.000			0.328316
$210$		0			0
$211$	−1300.00			−0.424150			−0.212075	−	0.977253i	$-0.568022\pi$
$211$	−1300.00			−0.424150			−0.212075	+	0.977253i	$0.568022\pi$
$212$	−324.000	+	561.184i	−0.104964	+	0.181803i
$213$		0			0
$214$	2136.00	+	3699.66i	0.682308	+	1.18179i
$215$	−212.000	+	367.195i	−0.0672478	+	0.116477i
$216$		0			0
$217$		0			0
$218$	2452.00			0.761791
$219$		0			0
$220$	−32.0000	−	55.4256i	−0.00980654	−	0.0169854i
$221$	42.0000	+	72.7461i	0.0127838	+	0.0221422i
$222$		0			0
$223$	−2576.00			−0.773550			−0.386775	−	0.922174i	$-0.626411\pi$
$223$	−2576.00			−0.773550			−0.386775	+	0.922174i	$0.626411\pi$
$224$		0			0
$225$		0			0
$226$	−338.000	+	585.433i	−0.0994842	+	0.172312i
$227$	918.000	+	1590.02i	0.268413	+	0.464905i	0.968452	−	0.249199i	$-0.0801674\pi$
$227$	918.000	+	1590.02i	0.268413	+	0.464905i	−0.700039	+	0.714105i	$0.746834\pi$
$228$		0			0
$229$	−937.000	+	1622.93i	−0.270387	+	0.468325i	−0.968961	−	0.247213i	$-0.920485\pi$
$229$	−937.000	+	1622.93i	−0.270387	+	0.468325i	0.698574	+	0.715538i	$0.253818\pi$
$230$	304.000			0.0871529
$231$		0			0
$232$	2032.00			0.575032
$233$	1865.00	−	3230.27i	0.524379	−	0.908250i	−0.475219	−	0.879868i	$-0.657631\pi$
$233$	1865.00	−	3230.27i	0.524379	−	0.908250i	0.999597	−	0.0283826i	$-0.00903567\pi$
$234$		0			0
$235$	264.000	+	457.261i	0.0732828	+	0.126930i
$236$	1544.00	−	2674.29i	0.425872	−	0.737632i
$237$		0			0
$238$		0			0
$239$	−2004.00			−0.542377			−0.271188	−	0.962526i	$-0.587417\pi$
$239$	−2004.00			−0.542377			−0.271188	+	0.962526i	$0.587417\pi$
$240$		0			0
$241$	−323.000	−	559.452i	−0.0863330	−	0.149533i	0.819625	−	0.572900i	$-0.194182\pi$
$241$	−323.000	−	559.452i	−0.0863330	−	0.149533i	−0.905958	+	0.423367i	$0.860848\pi$
$242$	−1267.00	−	2194.51i	−0.336553	−	0.582927i
$243$		0			0
$244$	−120.000			−0.0314845
$245$		0			0
$246$		0			0
$247$	−2604.00	+	4510.26i	−0.670804	+	1.16187i
$248$	288.000	+	498.831i	0.0737420	+	0.127725i
$249$		0			0
$250$	−492.000	+	852.169i	−0.124467	+	0.215584i
$251$	1260.00			0.316855			0.158427	−	0.987371i	$-0.449358\pi$
$251$	1260.00			0.316855			0.158427	+	0.987371i	$0.449358\pi$
$252$		0			0
$253$	−608.000			−0.151086
$254$	2088.00	−	3616.52i	0.515798	−	0.893389i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2955.00	+	5118.21i	−0.717229	+	1.24228i	0.244865	+	0.969557i	$0.421256\pi$
$257$	−2955.00	+	5118.21i	−0.717229	+	1.24228i	−0.962094	+	0.272720i	$0.912077\pi$
$258$		0			0
$259$		0			0
$260$	336.000			0.0801455
$261$		0			0
$262$	−292.000	−	505.759i	−0.0688543	−	0.119259i
$263$	1494.00	+	2587.68i	0.350281	+	0.606705i	0.986299	−	0.164970i	$-0.0527527\pi$
$263$	1494.00	+	2587.68i	0.350281	+	0.606705i	−0.636017	+	0.771675i	$0.719419\pi$
$264$		0			0
$265$	324.000			0.0751063
$266$		0			0
$267$		0			0
$268$	1528.00	−	2646.57i	0.348274	−	0.603228i
$269$	659.000	+	1141.42i	0.149368	+	0.258713i	0.930994	−	0.365035i	$-0.118943\pi$
$269$	659.000	+	1141.42i	0.149368	+	0.258713i	−0.781626	+	0.623747i	$0.785609\pi$
$270$		0			0
$271$	−2820.00	+	4884.38i	−0.632114	+	1.09485i	0.355005	+	0.934864i	$0.384479\pi$
$271$	−2820.00	+	4884.38i	−0.632114	+	1.09485i	−0.987119	+	0.159989i	$0.948854\pi$
$272$	−32.0000			−0.00713340
$273$		0			0
$274$	1636.00			0.360709
$275$	484.000	−	838.313i	0.106132	−	0.183826i
$276$		0			0
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	−0.968778	−	0.247929i	$-0.920250\pi$
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	0.269676	−	0.962951i	$-0.413083\pi$
$278$	2156.00	−	3734.30i	0.465138	−	0.805642i
$279$		0			0
$280$		0			0
$281$	−4930.00			−1.04662			−0.523308	−	0.852144i	$-0.675302\pi$
$281$	−4930.00			−1.04662			−0.523308	+	0.852144i	$0.675302\pi$
$282$		0			0
$283$	−3130.00	−	5421.32i	−0.657453	−	1.13874i	−0.981273	−	0.192623i	$-0.938301\pi$
$283$	−3130.00	−	5421.32i	−0.657453	−	1.13874i	0.323820	−	0.946119i	$-0.395033\pi$
$284$	−472.000	−	817.528i	−0.0986199	−	0.170815i
$285$		0			0
$286$	−672.000			−0.138938
$287$		0			0
$288$		0			0
$289$	2454.50	−	4251.32i	0.499593	−	0.865320i
$290$	−508.000	−	879.882i	−0.102865	−	0.178167i
$291$		0			0
$292$	836.000	−	1447.99i	0.167545	−	0.290197i
$293$	−2310.00			−0.460586			−0.230293	−	0.973121i	$-0.573968\pi$
$293$	−2310.00			−0.460586			−0.230293	+	0.973121i	$0.573968\pi$
$294$		0			0
$295$	−1544.00			−0.304729
$296$	1592.00	−	2757.42i	0.312612	−	0.541460i
$297$		0			0
$298$	2850.00	+	4936.34i	0.554014	+	0.959580i
$299$	1596.00	−	2764.35i	0.308693	−	0.534671i
$300$		0			0
$301$		0			0
$302$	−3344.00			−0.637171
$303$		0			0
$304$	−992.000	−	1718.19i	−0.187155	−	0.324162i
$305$	30.0000	+	51.9615i	0.00563211	+	0.00975511i
$306$		0			0
$307$	−196.000			−0.0364375			−0.0182187	−	0.999834i	$-0.505800\pi$
$307$	−196.000			−0.0364375			−0.0182187	+	0.999834i	$0.505800\pi$
$308$		0			0
$309$		0			0
$310$	144.000	−	249.415i	0.0263827	−	0.0456963i
$311$	3368.00	+	5833.55i	0.614089	+	1.06363i	0.990544	+	0.137199i	$0.0438099\pi$
$311$	3368.00	+	5833.55i	0.614089	+	1.06363i	−0.376454	+	0.926435i	$0.622857\pi$
$312$		0			0
$313$	197.000	−	341.214i	0.0355754	−	0.0616184i	−0.847690	−	0.530493i	$-0.822007\pi$
$313$	197.000	−	341.214i	0.0355754	−	0.0616184i	0.883265	+	0.468874i	$0.155340\pi$
$314$	892.000			0.160314
$315$		0			0
$316$	2208.00			0.393069
$317$	−3357.00	+	5814.49i	−0.594788	+	1.03020i	0.398788	+	0.917043i	$0.369431\pi$
$317$	−3357.00	+	5814.49i	−0.594788	+	1.03020i	−0.993577	+	0.113161i	$0.963903\pi$
$318$		0			0
$319$	1016.00	+	1759.76i	0.178323	+	0.308865i
$320$	−64.0000	+	110.851i	−0.0111803	+	0.0193649i
$321$		0			0
$322$		0			0
$323$	−248.000			−0.0427216
$324$		0			0
$325$	2541.00	+	4401.14i	0.433690	+	0.751173i
$326$	2708.00	+	4690.39i	0.460068	+	0.796862i
$327$		0			0
$328$	−3696.00			−0.622187
$329$		0			0
$330$		0			0
$331$	−346.000	+	599.290i	−0.0574558	+	0.0995164i	−0.893323	−	0.449416i	$-0.851632\pi$
$331$	−346.000	+	599.290i	−0.0574558	+	0.0995164i	0.835867	+	0.548932i	$0.184966\pi$
$332$	−2072.00	−	3588.81i	−0.342517	−	0.593258i
$333$		0			0
$334$	896.000	−	1551.92i	0.146787	−	0.254243i
$335$	−1528.00			−0.249205
$336$		0			0
$337$	−1566.00			−0.253132			−0.126566	−	0.991958i	$-0.540396\pi$
$337$	−1566.00			−0.253132			−0.126566	+	0.991958i	$0.540396\pi$
$338$	−433.000	+	749.978i	−0.0696808	+	0.120691i
$339$		0			0
$340$	8.00000	+	13.8564i	0.00127606	+	0.00221020i
$341$	−288.000	+	498.831i	−0.0457363	+	0.0792176i
$342$		0			0
$343$		0			0
$344$	−1696.00			−0.265820
$345$		0			0
$346$	4034.00	+	6987.09i	0.626790	+	1.08563i
$347$	−2664.00	−	4614.18i	−0.412135	−	0.713840i	0.582988	−	0.812481i	$-0.301884\pi$
$347$	−2664.00	−	4614.18i	−0.412135	−	0.713840i	−0.995123	+	0.0986415i	$0.968550\pi$
$348$		0			0
$349$	−11326.0			−1.73715			−0.868577	−	0.495554i	$-0.834965\pi$
$349$	−11326.0			−1.73715			−0.868577	+	0.495554i	$0.834965\pi$
$350$		0			0
$351$		0			0
$352$	128.000	−	221.703i	0.0193819	−	0.0335704i
$353$	1065.00	+	1844.63i	0.160579	+	0.278130i	0.935076	−	0.354446i	$-0.115331\pi$
$353$	1065.00	+	1844.63i	0.160579	+	0.278130i	−0.774498	+	0.632577i	$0.781997\pi$
$354$		0			0
$355$	−236.000	+	408.764i	−0.0352833	+	0.0611125i
$356$	120.000			0.0178651
$357$		0			0
$358$	−6960.00			−1.02751
$359$	1522.00	−	2636.18i	0.223755	−	0.387555i	−0.732190	−	0.681100i	$-0.761502\pi$
$359$	1522.00	−	2636.18i	0.223755	−	0.387555i	0.955945	+	0.293545i	$0.0948351\pi$
$360$		0			0
$361$	−4258.50	−	7375.94i	−0.620863	−	1.07537i
$362$	2898.00	−	5019.48i	0.420761	−	0.728780i
$363$		0			0
$364$		0			0
$365$	−836.000			−0.119886
$366$		0			0
$367$	6208.00	+	10752.6i	0.882984	+	1.52937i	0.848008	+	0.529984i	$0.177802\pi$
$367$	6208.00	+	10752.6i	0.882984	+	1.52937i	0.0349760	+	0.999388i	$0.488865\pi$
$368$	608.000	+	1053.09i	0.0861255	+	0.149174i
$369$		0			0
$370$	−1592.00			−0.223687
$371$		0			0
$372$		0			0
$373$	3721.00	−	6444.96i	0.516531	−	0.894658i	−0.483285	−	0.875463i	$-0.660556\pi$
$373$	3721.00	−	6444.96i	0.516531	−	0.894658i	0.999816	−	0.0191948i	$-0.00611026\pi$
$374$	−16.0000	−	27.7128i	−0.00221214	−	0.00383154i
$375$		0			0
$376$	−1056.00	+	1829.05i	−0.144838	+	0.250867i
$377$	−10668.0			−1.45737
$378$		0			0
$379$	100.000			0.0135532			0.00677659	−	0.999977i	$-0.497843\pi$
$379$	100.000			0.0135532			0.00677659	+	0.999977i	$0.497843\pi$
$380$	−496.000	+	859.097i	−0.0669586	+	0.115976i
$381$		0			0
$382$	−2652.00	−	4593.40i	−0.355205	−	0.615232i
$383$	−4040.00	+	6997.49i	−0.538993	+	0.933563i	0.459965	+	0.887937i	$0.347862\pi$
$383$	−4040.00	+	6997.49i	−0.538993	+	0.933563i	−0.998959	+	0.0456266i	$0.985472\pi$
$384$		0			0
$385$		0			0
$386$	−292.000			−0.0385036
$387$		0			0
$388$	−2380.00	−	4122.28i	−0.311408	−	0.539374i
$389$	−2741.00	−	4747.55i	−0.357260	−	0.618793i	0.630242	−	0.776399i	$-0.282956\pi$
$389$	−2741.00	−	4747.55i	−0.357260	−	0.618793i	−0.987502	+	0.157606i	$0.949622\pi$
$390$		0			0
$391$	152.000			0.0196598
$392$		0			0
$393$		0			0
$394$	2546.00	−	4409.80i	0.325547	−	0.563864i
$395$	−552.000	−	956.092i	−0.0703143	−	0.121788i
$396$		0			0
$397$	5223.00	−	9046.50i	0.660289	−	1.14365i	−0.320250	−	0.947333i	$-0.603767\pi$
$397$	5223.00	−	9046.50i	0.660289	−	1.14365i	0.980540	−	0.196322i	$-0.0628997\pi$
$398$	−5072.00			−0.638785
$399$		0			0
$400$	−1936.00			−0.242000
$401$	−5667.00	+	9815.53i	−0.705727	+	1.22235i	0.260702	+	0.965419i	$0.416046\pi$
$401$	−5667.00	+	9815.53i	−0.705727	+	1.22235i	−0.966429	+	0.256935i	$0.917287\pi$
$402$		0			0
$403$	−1512.00	−	2618.86i	−0.186894	−	0.323709i
$404$	−2740.00	+	4745.82i	−0.337426	+	0.584439i
$405$		0			0
$406$		0			0
$407$	3184.00			0.387776
$408$		0			0
$409$	4297.00	+	7442.62i	0.519494	+	0.899790i	0.999743	+	0.0226578i	$0.00721280\pi$
$409$	4297.00	+	7442.62i	0.519494	+	0.899790i	−0.480249	+	0.877132i	$0.659454\pi$
$410$	924.000	+	1600.41i	0.111300	+	0.192778i
$411$		0			0
$412$	−1856.00			−0.221938
$413$		0			0
$414$		0			0
$415$	−1036.00	+	1794.40i	−0.122543	+	0.212250i
$416$	672.000	+	1163.94i	0.0792007	+	0.137180i
$417$		0			0
$418$	992.000	−	1718.19i	0.116077	−	0.201052i
$419$	10500.0			1.22424			0.612122	−	0.790763i	$-0.290316\pi$
$419$	10500.0			1.22424			0.612122	+	0.790763i	$0.290316\pi$
$420$		0			0
$421$	−12066.0			−1.39682			−0.698410	−	0.715698i	$-0.746109\pi$
$421$	−12066.0			−1.39682			−0.698410	+	0.715698i	$0.746109\pi$
$422$	−1300.00	+	2251.67i	−0.149960	+	0.259738i
$423$		0			0
$424$	648.000	+	1122.37i	0.0742209	+	0.128554i
$425$	−121.000	+	209.578i	−0.0138103	+	0.0239201i
$426$		0			0
$427$		0			0
$428$	8544.00			0.964930
$429$		0			0
$430$	424.000	+	734.390i	0.0475514	+	0.0823614i
$431$	2166.00	+	3751.62i	0.242071	+	0.419279i	0.961304	−	0.275490i	$-0.0888400\pi$
$431$	2166.00	+	3751.62i	0.242071	+	0.419279i	−0.719233	+	0.694769i	$0.755507\pi$
$432$		0			0
$433$	1918.00			0.212871			0.106436	−	0.994320i	$-0.466056\pi$
$433$	1918.00			0.212871			0.106436	+	0.994320i	$0.466056\pi$
$434$		0			0
$435$		0			0
$436$	2452.00	−	4246.99i	0.269334	−	0.466500i
$437$	4712.00	+	8161.42i	0.515802	+	0.893395i
$438$		0			0
$439$	−3996.00	+	6921.28i	−0.434439	+	0.752470i	−0.997250	−	0.0741155i	$-0.976387\pi$
$439$	−3996.00	+	6921.28i	−0.434439	+	0.752470i	0.562811	+	0.826586i	$0.309720\pi$
$440$	−128.000			−0.0138685
$441$		0			0
$442$	168.000			0.0180791
$443$	1592.00	−	2757.42i	0.170741	−	0.295732i	−0.767938	−	0.640524i	$-0.778717\pi$
$443$	1592.00	−	2757.42i	0.170741	−	0.295732i	0.938679	+	0.344792i	$0.112051\pi$
$444$		0			0
$445$	−30.0000	−	51.9615i	−0.00319581	−	0.00553531i
$446$	−2576.00	+	4461.76i	−0.273491	+	0.473701i
$447$		0			0
$448$		0			0
$449$	−11426.0			−1.20095			−0.600475	−	0.799644i	$-0.705022\pi$
$449$	−11426.0			−1.20095			−0.600475	+	0.799644i	$0.705022\pi$
$450$		0			0
$451$	−1848.00	−	3200.83i	−0.192947	−	0.334193i
$452$	676.000	+	1170.87i	0.0703459	+	0.121843i
$453$		0			0
$454$	3672.00			0.379594
$455$		0			0
$456$		0			0
$457$	8467.00	−	14665.3i	0.866673	−	1.50112i	0.00129662	−	0.999999i	$-0.499587\pi$
$457$	8467.00	−	14665.3i	0.866673	−	1.50112i	0.865376	−	0.501122i	$-0.167079\pi$
$458$	1874.00	+	3245.86i	0.191193	+	0.331156i
$459$		0			0
$460$	304.000	−	526.543i	0.0308132	−	0.0533700i
$461$	−17038.0			−1.72134			−0.860671	−	0.509161i	$-0.829956\pi$
$461$	−17038.0			−1.72134			−0.860671	+	0.509161i	$0.829956\pi$
$462$		0			0
$463$	−13592.0			−1.36431			−0.682153	−	0.731209i	$-0.738956\pi$
$463$	−13592.0			−1.36431			−0.682153	+	0.731209i	$0.738956\pi$
$464$	2032.00	−	3519.53i	0.203304	−	0.352134i
$465$		0			0
$466$	−3730.00	−	6460.55i	−0.370792	−	0.642230i
$467$	−4306.00	+	7458.21i	−0.426676	+	0.739025i	−0.996575	−	0.0826895i	$-0.973649\pi$
$467$	−4306.00	+	7458.21i	−0.426676	+	0.739025i	0.569899	+	0.821715i	$0.306982\pi$
$468$		0			0
$469$		0			0
$470$	1056.00			0.103638
$471$		0			0
$472$	−3088.00	−	5348.57i	−0.301137	−	0.521585i
$473$	−848.000	−	1468.78i	−0.0824336	−	0.142779i
$474$		0			0
$475$	−15004.0			−1.44933
$476$		0			0
$477$		0			0
$478$	−2004.00	+	3471.03i	−0.191759	+	0.332136i
$479$	−3716.00	−	6436.30i	−0.354464	−	0.613950i	0.632562	−	0.774510i	$-0.282003\pi$
$479$	−3716.00	−	6436.30i	−0.354464	−	0.613950i	−0.987026	+	0.160560i	$0.948670\pi$
$480$		0			0
$481$	−8358.00	+	14476.5i	−0.792291	+	1.37229i
$482$	−1292.00			−0.122093
$483$		0			0
$484$	−5068.00			−0.475958
$485$	−1190.00	+	2061.14i	−0.111413	+	0.192972i
$486$		0			0
$487$	3308.00	+	5729.62i	0.307802	+	0.533129i	0.977881	−	0.209160i	$-0.0670731\pi$
$487$	3308.00	+	5729.62i	0.307802	+	0.533129i	−0.670079	+	0.742290i	$0.733740\pi$
$488$	−120.000	+	207.846i	−0.0111314	+	0.0192802i
$489$		0			0
$490$		0			0
$491$	−17040.0			−1.56620			−0.783100	−	0.621896i	$-0.786363\pi$
$491$	−17040.0			−1.56620			−0.783100	+	0.621896i	$0.786363\pi$
$492$		0			0
$493$	−254.000	−	439.941i	−0.0232040	−	0.0401906i
$494$	5208.00	+	9020.52i	0.474330	+	0.821564i
$495$		0			0
$496$	1152.00			0.104287
$497$		0			0
$498$		0			0
$499$	1474.00	−	2553.04i	0.132235	−	0.229038i	−0.792303	−	0.610128i	$-0.791118\pi$
$499$	1474.00	−	2553.04i	0.132235	−	0.229038i	0.924538	+	0.381090i	$0.124451\pi$
$500$	984.000	+	1704.34i	0.0880116	+	0.152441i
$501$		0			0
$502$	1260.00	−	2182.38i	0.112025	−	0.194033i
$503$	17304.0			1.53389			0.766946	−	0.641712i	$-0.221776\pi$
$503$	17304.0			1.53389			0.766946	+	0.641712i	$0.221776\pi$
$504$		0			0
$505$	2740.00			0.241442
$506$	−608.000	+	1053.09i	−0.0534168	+	0.0925206i
$507$		0			0
$508$	−4176.00	−	7233.04i	−0.364724	−	0.631721i
$509$	−2325.00	+	4027.02i	−0.202463	+	0.350677i	−0.949322	−	0.314307i	$-0.898228\pi$
$509$	−2325.00	+	4027.02i	−0.202463	+	0.350677i	0.746858	+	0.664983i	$0.231561\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	5910.00	+	10236.4i	0.507157	+	0.878422i
$515$	464.000	+	803.672i	0.0397015	+	0.0687651i
$516$		0			0
$517$	−2112.00			−0.179663
$518$		0			0
$519$		0			0
$520$	336.000	−	581.969i	0.0283357	−	0.0490789i
$521$	−8427.00	−	14596.0i	−0.708625	−	1.22737i	−0.965367	−	0.260894i	$-0.915983\pi$
$521$	−8427.00	−	14596.0i	−0.708625	−	1.22737i	0.256742	−	0.966480i	$-0.417351\pi$
$522$		0			0
$523$	−62.0000	+	107.387i	−0.00518369	+	0.00897842i	−0.868606	−	0.495504i	$-0.834983\pi$
$523$	−62.0000	+	107.387i	−0.00518369	+	0.00897842i	0.863422	+	0.504482i	$0.168317\pi$
$524$	−1168.00			−0.0973747
$525$		0			0
$526$	5976.00			0.495373
$527$	72.0000	−	124.708i	0.00595136	−	0.0103081i
$528$		0			0
$529$	3195.50	+	5534.77i	0.262637	+	0.454900i
$530$	324.000	−	561.184i	0.0265541	−	0.0459930i
$531$		0			0
$532$		0			0
$533$	19404.0			1.57689
$534$		0			0
$535$	−2136.00	−	3699.66i	−0.172612	−	0.298972i
$536$	−3056.00	−	5293.15i	−0.246267	−	0.426547i
$537$		0			0
$538$	2636.00			0.211238
$539$		0			0
$540$		0			0
$541$	−2691.00	+	4660.95i	−0.213854	+	0.370406i	−0.952918	−	0.303230i	$-0.901935\pi$
$541$	−2691.00	+	4660.95i	−0.213854	+	0.370406i	0.739063	+	0.673636i	$0.235268\pi$
$542$	5640.00	+	9768.77i	0.446972	+	0.774178i
$543$		0			0
$544$	−32.0000	+	55.4256i	−0.00252204	+	0.00436830i
$545$	−2452.00			−0.192720
$546$		0			0
$547$	17460.0			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$547$	17460.0			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$548$	1636.00	−	2833.64i	0.127530	−	0.220888i
$549$		0			0
$550$	−968.000	−	1676.63i	−0.0750467	−	0.129985i
$551$	15748.0	−	27276.3i	1.21758	−	2.10891i
$552$		0			0
$553$		0			0
$554$	−12892.0			−0.988680
$555$		0			0
$556$	−4312.00	−	7468.60i	−0.328902	−	0.569675i
$557$	−4757.00	−	8239.37i	−0.361868	−	0.626774i	0.626400	−	0.779502i	$-0.284528\pi$
$557$	−4757.00	−	8239.37i	−0.361868	−	0.626774i	−0.988268	+	0.152728i	$0.951194\pi$
$558$		0			0
$559$	8904.00			0.673701
$560$		0			0
$561$		0			0
$562$	−4930.00	+	8539.01i	−0.370035	+	0.640919i
$563$	−1994.00	−	3453.71i	−0.149267	−	0.258537i	0.781690	−	0.623667i	$-0.214358\pi$
$563$	−1994.00	−	3453.71i	−0.149267	−	0.258537i	−0.930957	+	0.365130i	$0.881025\pi$
$564$		0			0
$565$	338.000	−	585.433i	0.0251677	−	0.0435918i
$566$	−12520.0			−0.929779
$567$		0			0
$568$	−1888.00			−0.139470
$569$	5673.00	−	9825.92i	0.417969	−	0.723944i	−0.577766	−	0.816203i	$-0.696075\pi$
$569$	5673.00	−	9825.92i	0.417969	−	0.723944i	0.995735	+	0.0922585i	$0.0294086\pi$
$570$		0			0
$571$	4218.00	+	7305.79i	0.309138	+	0.535443i	0.978174	−	0.207787i	$-0.0666262\pi$
$571$	4218.00	+	7305.79i	0.309138	+	0.535443i	−0.669036	+	0.743230i	$0.733293\pi$
$572$	−672.000	+	1163.94i	−0.0491219	+	0.0850816i
$573$		0			0
$574$		0			0
$575$	9196.00			0.666956
$576$		0			0
$577$	1049.00	+	1816.92i	0.0756853	+	0.131091i	0.901384	−	0.433020i	$-0.142552\pi$
$577$	1049.00	+	1816.92i	0.0756853	+	0.131091i	−0.825699	+	0.564111i	$0.809219\pi$
$578$	−4909.00	−	8502.64i	−0.353266	−	0.611874i
$579$		0			0
$580$	−2032.00			−0.145473
$581$		0			0
$582$		0			0
$583$	−648.000	+	1122.37i	−0.0460333	+	0.0797320i
$584$	−1672.00	−	2895.99i	−0.118472	−	0.205200i
$585$		0			0
$586$	−2310.00	+	4001.04i	−0.162842	+	0.282050i
$587$	9436.00			0.663484			0.331742	−	0.943370i	$-0.392364\pi$
$587$	9436.00			0.663484			0.331742	+	0.943370i	$0.392364\pi$
$588$		0			0
$589$	8928.00			0.624570
$590$	−1544.00	+	2674.29i	−0.107738	+	0.186608i
$591$		0			0
$592$	−3184.00	−	5514.85i	−0.221050	−	0.382870i
$593$	657.000	−	1137.96i	0.0454971	−	0.0788032i	−0.842380	−	0.538884i	$-0.818846\pi$
$593$	657.000	−	1137.96i	0.0454971	−	0.0788032i	0.887877	+	0.460081i	$0.152180\pi$
$594$		0			0
$595$		0			0
$596$	11400.0			0.783494
$597$		0			0
$598$	−3192.00	−	5528.71i	−0.218279	−	0.378070i
$599$	−4470.00	−	7742.27i	−0.304907	−	0.528114i	0.672334	−	0.740248i	$-0.265292\pi$
$599$	−4470.00	−	7742.27i	−0.304907	−	0.528114i	−0.977241	+	0.212134i	$0.931959\pi$
$600$		0			0
$601$	−16058.0			−1.08988			−0.544941	−	0.838474i	$-0.683448\pi$
$601$	−16058.0			−1.08988			−0.544941	+	0.838474i	$0.683448\pi$
$602$		0			0
$603$		0			0
$604$	−3344.00	+	5791.98i	−0.225274	+	0.390186i
$605$	1267.00	+	2194.51i	0.0851419	+	0.147470i
$606$		0			0
$607$	1968.00	−	3408.68i	0.131596	−	0.227931i	−0.792696	−	0.609617i	$-0.791323\pi$
$607$	1968.00	−	3408.68i	0.131596	−	0.227931i	0.924292	+	0.381686i	$0.124657\pi$
$608$	−3968.00			−0.264677
$609$		0			0
$610$	120.000			0.00796501
$611$	5544.00	−	9602.49i	0.367081	−	0.635802i
$612$		0			0
$613$	−87.0000	−	150.688i	−0.00573230	−	0.00992863i	0.863145	−	0.504956i	$-0.168491\pi$
$613$	−87.0000	−	150.688i	−0.00573230	−	0.00992863i	−0.868877	+	0.495027i	$0.835158\pi$
$614$	−196.000	+	339.482i	−0.0128826	+	0.0223133i
$615$		0			0
$616$		0			0
$617$	−16018.0			−1.04515			−0.522577	−	0.852592i	$-0.675029\pi$
$617$	−16018.0			−1.04515			−0.522577	+	0.852592i	$0.675029\pi$
$618$		0			0
$619$	−1534.00	−	2656.97i	−0.0996069	−	0.172524i	0.811915	−	0.583776i	$-0.198425\pi$
$619$	−1534.00	−	2656.97i	−0.0996069	−	0.172524i	−0.911522	+	0.411251i	$0.865092\pi$
$620$	−288.000	−	498.831i	−0.0186554	−	0.0323121i
$621$		0			0
$622$	13472.0			0.868453
$623$		0			0
$624$		0			0
$625$	−7070.50	+	12246.5i	−0.452512	+	0.783774i
$626$	−394.000	−	682.428i	−0.0251556	−	0.0435708i
$627$		0			0
$628$	892.000	−	1544.99i	0.0566794	−	0.0981716i
$629$	−796.000			−0.0504588
$630$		0			0
$631$	24656.0			1.55553			0.777765	−	0.628555i	$-0.216353\pi$
$631$	24656.0			1.55553			0.777765	+	0.628555i	$0.216353\pi$
$632$	2208.00	−	3824.37i	0.138971	−	0.240704i
$633$		0			0
$634$	6714.00	+	11629.0i	0.420579	+	0.728464i
$635$	−2088.00	+	3616.52i	−0.130488	+	0.226011i
$636$		0			0
$637$		0			0
$638$	4064.00			0.252187
$639$		0			0
$640$	128.000	+	221.703i	0.00790569	+	0.0136931i
$641$	3797.00	+	6576.60i	0.233966	+	0.405242i	0.958972	−	0.283501i	$-0.0914961\pi$
$641$	3797.00	+	6576.60i	0.233966	+	0.405242i	−0.725005	+	0.688743i	$0.758163\pi$
$642$		0			0
$643$	3724.00			0.228398			0.114199	−	0.993458i	$-0.463570\pi$
$643$	3724.00			0.228398			0.114199	+	0.993458i	$0.463570\pi$
$644$		0			0
$645$		0			0
$646$	−248.000	+	429.549i	−0.0151044	+	0.0261616i
$647$	−1896.00	−	3283.97i	−0.115208	−	0.199546i	0.802655	−	0.596444i	$-0.203420\pi$
$647$	−1896.00	−	3283.97i	−0.115208	−	0.199546i	−0.917863	+	0.396898i	$0.870087\pi$
$648$		0			0
$649$	3088.00	−	5348.57i	0.186771	−	0.323497i
$650$	10164.0			0.613331
$651$		0			0
$652$	10832.0			0.650635
$653$	12351.0	−	21392.6i	0.740171	−	1.28201i	−0.212245	−	0.977216i	$-0.568078\pi$
$653$	12351.0	−	21392.6i	0.740171	−	1.28201i	0.952417	−	0.304798i	$-0.0985890\pi$
$654$		0			0
$655$	292.000	+	505.759i	0.0174189	+	0.0301704i
$656$	−3696.00	+	6401.66i	−0.219976	+	0.381010i
$657$		0			0
$658$		0			0
$659$	20144.0			1.19074			0.595371	−	0.803451i	$-0.297005\pi$
$659$	20144.0			1.19074			0.595371	+	0.803451i	$0.297005\pi$
$660$		0			0
$661$	−1261.00	−	2184.12i	−0.0742015	−	0.128521i	0.826537	−	0.562882i	$-0.190307\pi$
$661$	−1261.00	−	2184.12i	−0.0742015	−	0.128521i	−0.900739	+	0.434361i	$0.856974\pi$
$662$	692.000	+	1198.58i	0.0406274	+	0.0703687i
$663$		0			0
$664$	−8288.00			−0.484393
$665$		0			0
$666$		0			0
$667$	−9652.00	+	16717.8i	−0.560310	+	0.970486i
$668$	−1792.00	−	3103.84i	−0.103794	−	0.179777i
$669$		0			0
$670$	−1528.00	+	2646.57i	−0.0881071	+	0.152606i
$671$	−240.000			−0.0138079
$672$		0			0
$673$	−10414.0			−0.596479			−0.298239	−	0.954491i	$-0.596399\pi$
$673$	−10414.0			−0.596479			−0.298239	+	0.954491i	$0.596399\pi$
$674$	−1566.00	+	2712.39i	−0.0894956	+	0.155011i
$675$		0			0
$676$	866.000	+	1499.96i	0.0492717	+	0.0853411i
$677$	11115.0	−	19251.7i	0.630996	−	1.09292i	−0.356353	−	0.934352i	$-0.615980\pi$
$677$	11115.0	−	19251.7i	0.630996	−	1.09292i	0.987348	−	0.158565i	$-0.0506868\pi$
$678$		0			0
$679$		0			0
$680$	32.0000			0.00180462
$681$		0			0
$682$	576.000	+	997.661i	0.0323404	+	0.0560153i
$683$	9096.00	+	15754.7i	0.509588	+	0.882633i	0.999938	+	0.0111072i	$0.00353559\pi$
$683$	9096.00	+	15754.7i	0.509588	+	0.882633i	−0.490350	+	0.871526i	$0.663131\pi$
$684$		0			0
$685$	−1636.00			−0.0912531
$686$		0			0
$687$		0			0
$688$	−1696.00	+	2937.56i	−0.0939817	+	0.162781i
$689$	−3402.00	−	5892.44i	−0.188107	−	0.325811i
$690$		0			0
$691$	4054.00	−	7021.73i	0.223186	−	0.386569i	−0.732588	−	0.680673i	$-0.761688\pi$
$691$	4054.00	−	7021.73i	0.223186	−	0.386569i	0.955774	+	0.294103i	$0.0950210\pi$
$692$	16136.0			0.886414
$693$		0			0
$694$	−10656.0			−0.582848
$695$	−2156.00	+	3734.30i	−0.117672	+	0.203813i
$696$		0			0
$697$	462.000	+	800.207i	0.0251069	+	0.0434864i
$698$	−11326.0	+	19617.2i	−0.614177	+	1.06379i
$699$		0			0
$700$		0			0
$701$	5794.00			0.312177			0.156089	−	0.987743i	$-0.450111\pi$
$701$	5794.00			0.312177			0.156089	+	0.987743i	$0.450111\pi$
$702$		0			0
$703$	−24676.0	−	42740.1i	−1.32386	−	2.29299i
$704$	−256.000	−	443.405i	−0.0137051	−	0.0237379i
$705$		0			0
$706$	4260.00			0.227092
$707$		0			0
$708$		0			0
$709$	977.000	−	1692.21i	0.0517518	−	0.0896367i	−0.838989	−	0.544148i	$-0.816853\pi$
$709$	977.000	−	1692.21i	0.0517518	−	0.0896367i	0.890741	+	0.454512i	$0.150186\pi$
$710$	472.000	+	817.528i	0.0249491	+	0.0432131i
$711$		0			0
$712$	120.000	−	207.846i	0.00631628	−	0.0109401i
$713$	−5472.00			−0.287417
$714$		0			0
$715$	672.000			0.0351488
$716$	−6960.00	+	12055.1i	−0.363279	+	0.629217i
$717$		0			0
$718$	−3044.00	−	5272.36i	−0.158219	−	0.274043i
$719$	16008.0	−	27726.7i	0.830317	−	1.43815i	−0.0674706	−	0.997721i	$-0.521493\pi$
$719$	16008.0	−	27726.7i	0.830317	−	1.43815i	0.897787	−	0.440429i	$-0.145174\pi$
$720$		0			0
$721$		0			0
$722$	−17034.0			−0.878033
$723$		0			0
$724$	−5796.00	−	10039.0i	−0.297523	−	0.515325i
$725$	−15367.0	−	26616.4i	−0.787195	−	1.36346i
$726$		0			0
$727$	23072.0			1.17702			0.588510	−	0.808490i	$-0.299715\pi$
$727$	23072.0			1.17702			0.588510	+	0.808490i	$0.299715\pi$
$728$		0			0
$729$		0			0
$730$	−836.000	+	1447.99i	−0.0423860	+	0.0734146i
$731$	212.000	+	367.195i	0.0107265	+	0.0185789i
$732$		0			0
$733$	15891.0	−	27524.0i	0.800747	−	1.38693i	−0.118378	−	0.992969i	$-0.537770\pi$
$733$	15891.0	−	27524.0i	0.800747	−	1.38693i	0.919125	−	0.393966i	$-0.128897\pi$
$734$	24832.0			1.24873
$735$		0			0
$736$	2432.00			0.121800
$737$	3056.00	−	5293.15i	0.152740	−	0.264553i
$738$		0			0
$739$	12198.0	+	21127.6i	0.607186	+	1.05168i	0.991702	+	0.128559i	$0.0410352\pi$
$739$	12198.0	+	21127.6i	0.607186	+	1.05168i	−0.384516	+	0.923119i	$0.625631\pi$
$740$	−1592.00	+	2757.42i	−0.0790852	+	0.136980i
$741$		0			0
$742$		0			0
$743$	32604.0			1.60986			0.804929	−	0.593371i	$-0.202203\pi$
$743$	32604.0			1.60986			0.804929	+	0.593371i	$0.202203\pi$
$744$		0			0
$745$	−2850.00	−	4936.34i	−0.140156	−	0.242757i
$746$	−7442.00	−	12889.9i	−0.365243	−	0.632619i
$747$		0			0
$748$	−64.0000			−0.00312844
$749$		0			0
$750$		0			0
$751$	3840.00	−	6651.08i	0.186583	−	0.323171i	−0.757526	−	0.652805i	$-0.773592\pi$
$751$	3840.00	−	6651.08i	0.186583	−	0.323171i	0.944109	+	0.329634i	$0.106925\pi$
$752$	2112.00	+	3658.09i	0.102416	+	0.177389i
$753$		0			0
$754$	−10668.0	+	18477.5i	−0.515259	+	0.892456i
$755$	3344.00			0.161193
$756$		0			0
$757$	366.000			0.0175727			0.00878633	−	0.999961i	$-0.497203\pi$
$757$	366.000			0.0175727			0.00878633	+	0.999961i	$0.497203\pi$
$758$	100.000	−	173.205i	0.00479177	−	0.00829959i
$759$		0			0
$760$	992.000	+	1718.19i	0.0473469	+	0.0820072i
$761$	−14687.0	+	25438.6i	−0.699610	+	1.21176i	0.268992	+	0.963143i	$0.413310\pi$
$761$	−14687.0	+	25438.6i	−0.699610	+	1.21176i	−0.968602	+	0.248618i	$0.920024\pi$
$762$		0			0
$763$		0			0
$764$	−10608.0			−0.502335
$765$		0			0
$766$	8080.00	+	13995.0i	0.381126	+	0.660129i
$767$	16212.0	+	28080.0i	0.763209	+	1.32192i
$768$		0			0
$769$	38990.0			1.82837			0.914184	−	0.405299i	$-0.132833\pi$
$769$	38990.0			1.82837			0.914184	+	0.405299i	$0.132833\pi$
$770$		0			0
$771$		0			0
$772$	−292.000	+	505.759i	−0.0136131	+	0.0235786i
$773$	10235.0	+	17727.5i	0.476232	+	0.824858i	0.999629	−	0.0272308i	$-0.00866890\pi$
$773$	10235.0	+	17727.5i	0.476232	+	0.824858i	−0.523397	+	0.852089i	$0.675336\pi$
$774$		0			0
$775$	4356.00	−	7544.81i	0.201900	−	0.349700i
$776$	−9520.00			−0.440397
$777$		0			0
$778$	−10964.0			−0.505242
$779$	−28644.0	+	49612.9i	−1.31743	+	2.28186i
$780$		0			0
$781$	−944.000	−	1635.06i	−0.0432509	−	0.0749128i
$782$	152.000	−	263.272i	0.00695078	−	0.0120391i
$783$		0			0
$784$		0			0
$785$	−892.000			−0.0405565
$786$		0			0
$787$	14958.0	+	25908.0i	0.677503	+	1.17347i	0.975730	+	0.218975i	$0.0702714\pi$
$787$	14958.0	+	25908.0i	0.677503	+	1.17347i	−0.298227	+	0.954495i	$0.596395\pi$
$788$	−5092.00	−	8819.60i	−0.230197	−	0.398712i
$789$		0			0
$790$	−2208.00			−0.0994394
$791$		0			0
$792$		0			0
$793$	630.000	−	1091.19i	0.0282118	−	0.0488643i
$794$	−10446.0	−	18093.0i	−0.466895	−	0.808686i
$795$		0			0
$796$	−5072.00	+	8784.96i	−0.225845	+	0.391174i
$797$	4914.00			0.218398			0.109199	−	0.994020i	$-0.465172\pi$
$797$	4914.00			0.218398			0.109199	+	0.994020i	$0.465172\pi$
$798$		0			0
$799$	528.000			0.0233783
$800$	−1936.00	+	3353.25i	−0.0855599	+	0.148194i
$801$		0			0
$802$	11334.0	+	19631.1i	0.499024	+	0.864335i
$803$	1672.00	−	2895.99i	0.0734790	−	0.127269i
$804$		0			0
$805$		0			0
$806$	−6048.00			−0.264307
$807$		0			0
$808$	5480.00	+	9491.64i	0.238596	+	0.413261i
$809$	17125.0	+	29661.4i	0.744231	+	1.28905i	0.950553	+	0.310562i	$0.100517\pi$
$809$	17125.0	+	29661.4i	0.744231	+	1.28905i	−0.206322	+	0.978484i	$0.566149\pi$
$810$		0			0
$811$	41804.0			1.81003			0.905017	−	0.425376i	$-0.139858\pi$
$811$	41804.0			1.81003			0.905017	+	0.425376i	$0.139858\pi$
$812$		0			0
$813$		0			0
$814$	3184.00	−	5514.85i	0.137100	−	0.237464i
$815$	−2708.00	−	4690.39i	−0.116389	−	0.201592i
$816$		0			0
$817$	−13144.0	+	22766.1i	−0.562852	+	0.974889i
$818$	17188.0			0.734675
$819$		0			0
$820$	3696.00			0.157402
$821$	15431.0	−	26727.3i	0.655963	−	1.13616i	−0.325688	−	0.945477i	$-0.605596\pi$
$821$	15431.0	−	26727.3i	0.655963	−	1.13616i	0.981651	−	0.190684i	$-0.0610706\pi$
$822$		0			0
$823$	−5288.00	−	9159.08i	−0.223971	−	0.387929i	0.732039	−	0.681262i	$-0.238569\pi$
$823$	−5288.00	−	9159.08i	−0.223971	−	0.387929i	−0.956010	+	0.293333i	$0.905235\pi$
$824$	−1856.00	+	3214.69i	−0.0784670	+	0.135909i
$825$		0			0
$826$		0			0
$827$	10680.0			0.449069			0.224534	−	0.974466i	$-0.427914\pi$
$827$	10680.0			0.449069			0.224534	+	0.974466i	$0.427914\pi$
$828$		0			0
$829$	−589.000	−	1020.18i	−0.0246765	−	0.0427409i	0.853423	−	0.521218i	$-0.174522\pi$
$829$	−589.000	−	1020.18i	−0.0246765	−	0.0427409i	−0.878100	+	0.478477i	$0.841189\pi$
$830$	2072.00	+	3588.81i	0.0866508	+	0.150084i
$831$		0			0
$832$	2688.00			0.112007
$833$		0			0
$834$		0			0
$835$	−896.000	+	1551.92i	−0.0371346	+	0.0643189i
$836$	−1984.00	−	3436.39i	−0.0820790	−	0.142165i
$837$		0			0
$838$	10500.0	−	18186.5i	0.432836	−	0.749694i
$839$	−5600.00			−0.230433			−0.115217	−	0.993340i	$-0.536756\pi$
$839$	−5600.00			−0.230433			−0.115217	+	0.993340i	$0.536756\pi$
$840$		0			0
$841$	40127.0			1.64529
$842$	−12066.0	+	20898.9i	−0.493850	+	0.855374i
$843$		0			0
$844$	2600.00	+	4503.33i	0.106038	+	0.183662i
$845$	433.000	−	749.978i	0.0176280	−	0.0305326i
$846$		0			0
$847$		0			0
$848$	2592.00			0.104964
$849$		0			0
$850$	242.000	+	419.156i	0.00976533	+	0.0169140i
$851$	15124.0	+	26195.5i	0.609217	+	1.05520i
$852$		0			0
$853$	826.000			0.0331556			0.0165778	−	0.999863i	$-0.494723\pi$
$853$	826.000			0.0331556			0.0165778	+	0.999863i	$0.494723\pi$
$854$		0			0
$855$		0			0
$856$	8544.00	−	14798.6i	0.341154	−	0.590896i
$857$	−22959.0	−	39766.2i	−0.915128	−	1.58505i	−0.806714	−	0.590942i	$-0.798756\pi$
$857$	−22959.0	−	39766.2i	−0.915128	−	1.58505i	−0.108414	−	0.994106i	$-0.534577\pi$
$858$		0			0
$859$	21190.0	−	36702.2i	0.841669	−	1.45781i	−0.0468143	−	0.998904i	$-0.514907\pi$
$859$	21190.0	−	36702.2i	0.841669	−	1.45781i	0.888483	−	0.458909i	$-0.151760\pi$
$860$	1696.00			0.0672478
$861$		0			0
$862$	8664.00			0.342340
$863$	−13262.0	+	22970.5i	−0.523110	+	0.906053i	0.476529	+	0.879159i	$0.341895\pi$
$863$	−13262.0	+	22970.5i	−0.523110	+	0.906053i	−0.999638	+	0.0268937i	$0.991438\pi$
$864$		0			0
$865$	−4034.00	−	6987.09i	−0.158567	−	0.274645i
$866$	1918.00	−	3322.07i	0.0752613	−	0.130356i
$867$		0			0
$868$		0			0
$869$	4416.00			0.172385
$870$		0			0
$871$	16044.0	+	27789.0i	0.624145	+	1.08105i
$872$	−4904.00	−	8493.98i	−0.190448	−	0.329865i
$873$		0			0
$874$	18848.0			0.729454
$875$		0			0
$876$		0			0
$877$	−10307.0	+	17852.2i	−0.396856	+	0.687375i	−0.993336	−	0.115253i	$-0.963232\pi$
$877$	−10307.0	+	17852.2i	−0.396856	+	0.687375i	0.596480	+	0.802628i	$0.296565\pi$
$878$	7992.00	+	13842.6i	0.307195	+	0.532077i
$879$		0			0
$880$	−128.000	+	221.703i	−0.00490327	+	0.00849272i
$881$	−23730.0			−0.907473			−0.453737	−	0.891136i	$-0.649909\pi$
$881$	−23730.0			−0.907473			−0.453737	+	0.891136i	$0.649909\pi$
$882$		0			0
$883$	−9028.00			−0.344073			−0.172036	−	0.985091i	$-0.555035\pi$
$883$	−9028.00			−0.344073			−0.172036	+	0.985091i	$0.555035\pi$
$884$	168.000	−	290.985i	0.00639191	−	0.0110711i
$885$		0			0
$886$	−3184.00	−	5514.85i	−0.120732	−	0.209114i
$887$	−18600.0	+	32216.1i	−0.704089	+	1.21952i	0.262930	+	0.964815i	$0.415311\pi$
$887$	−18600.0	+	32216.1i	−0.704089	+	1.21952i	−0.967019	+	0.254703i	$0.918022\pi$
$888$		0			0
$889$		0			0
$890$	−120.000			−0.00451956
$891$		0			0
$892$	5152.00	+	8923.53i	0.193388	+	0.334957i
$893$	16368.0	+	28350.2i	0.613364	+	1.06238i
$894$		0			0
$895$	6960.00			0.259941
$896$		0			0
$897$		0			0
$898$	−11426.0	+	19790.4i	−0.424600	+	0.735428i
$899$	9144.00	+	15837.9i	0.339232	+	0.587567i
$900$		0			0
$901$	162.000	−	280.592i	0.00599001	−	0.0103750i
$902$	−7392.00			−0.272868
$903$		0			0
$904$	2704.00			0.0994842
$905$	−2898.00	+	5019.48i	−0.106445	+	0.184368i
$906$		0			0
$907$	−11994.0	−	20774.2i	−0.439090	−	0.760525i	0.558530	−	0.829484i	$-0.311366\pi$
$907$	−11994.0	−	20774.2i	−0.439090	−	0.760525i	−0.997619	+	0.0689589i	$0.978032\pi$
$908$	3672.00	−	6360.09i	0.134207	−	0.232453i
$909$		0			0
$910$		0			0
$911$	−15276.0			−0.555561			−0.277781	−	0.960645i	$-0.589599\pi$
$911$	−15276.0			−0.555561			−0.277781	+	0.960645i	$0.589599\pi$
$912$		0			0
$913$	−4144.00	−	7177.62i	−0.150215	−	0.260180i
$914$	−16934.0	−	29330.5i	−0.612830	−	1.06145i
$915$		0			0
$916$	7496.00			0.270387
$917$		0			0
$918$		0			0
$919$	5380.00	−	9318.43i	0.193112	−	0.334480i	−0.753168	−	0.657828i	$-0.771475\pi$
$919$	5380.00	−	9318.43i	0.193112	−	0.334480i	0.946280	+	0.323349i	$0.104809\pi$
$920$	−608.000	−	1053.09i	−0.0217882	−	0.0377383i
$921$		0			0
$922$	−17038.0	+	29510.7i	−0.608586	+	1.05410i
$923$	9912.00			0.353475
$924$		0			0
$925$	−48158.0			−1.71181
$926$	−13592.0	+	23542.0i	−0.482355	+	0.835464i
$927$		0			0
$928$	−4064.00	−	7039.05i	−0.143758	−	0.248996i
$929$	26445.0	−	45804.1i	0.933942	−	1.61764i	0.157433	−	0.987530i	$-0.449678\pi$
$929$	26445.0	−	45804.1i	0.933942	−	1.61764i	0.776509	−	0.630106i	$-0.216988\pi$
$930$		0			0
$931$		0			0
$932$	−14920.0			−0.524379
$933$		0			0
$934$	8612.00	+	14916.4i	0.301706	+	0.522570i
$935$	16.0000	+	27.7128i	0.000559632	+	0.000969311i
$936$		0			0
$937$	6118.00			0.213305			0.106652	−	0.994296i	$-0.465987\pi$
$937$	6118.00			0.213305			0.106652	+	0.994296i	$0.465987\pi$
$938$		0			0
$939$		0			0
$940$	1056.00	−	1829.05i	0.0366414	−	0.0634648i
$941$	16115.0	+	27912.0i	0.558272	+	0.966956i	0.997641	+	0.0686488i	$0.0218688\pi$
$941$	16115.0	+	27912.0i	0.558272	+	0.966956i	−0.439369	+	0.898307i	$0.644798\pi$
$942$		0			0
$943$	17556.0	−	30407.9i	0.606259	−	1.05007i
$944$	−12352.0			−0.425872
$945$		0			0
$946$	−3392.00			−0.116579
$947$	−9272.00	+	16059.6i	−0.318162	+	0.551073i	−0.980105	−	0.198482i	$-0.936399\pi$
$947$	−9272.00	+	16059.6i	−0.318162	+	0.551073i	0.661942	+	0.749555i	$0.269732\pi$
$948$		0			0
$949$	8778.00	+	15203.9i	0.300259	+	0.520064i
$950$	−15004.0	+	25987.7i	−0.512415	+	0.887528i
$951$		0			0
$952$		0			0
$953$	−25930.0			−0.881380			−0.440690	−	0.897659i	$-0.645266\pi$
$953$	−25930.0			−0.881380			−0.440690	+	0.897659i	$0.645266\pi$
$954$		0			0
$955$	2652.00	+	4593.40i	0.0898604	+	0.155643i
$956$	4008.00	+	6942.06i	0.135594	+	0.234856i
$957$		0			0
$958$	−14864.0			−0.501288
$959$		0			0
$960$		0			0
$961$	12303.5	−	21310.3i	0.412994	−	0.715326i
$962$	16716.0	+	28953.0i	0.560234	+	0.970354i
$963$		0			0
$964$	−1292.00	+	2237.81i	−0.0431665	+	0.0747666i
$965$	292.000			0.00974074
$966$		0			0
$967$	8192.00			0.272427			0.136214	−	0.990680i	$-0.456507\pi$
$967$	8192.00			0.272427			0.136214	+	0.990680i	$0.456507\pi$
$968$	−5068.00	+	8778.03i	−0.168277	+	0.291464i
$969$		0			0
$970$	2380.00	+	4122.28i	0.0787806	+	0.136452i
$971$	27222.0	−	47149.9i	0.899686	−	1.55830i	0.0717914	−	0.997420i	$-0.477128\pi$
$971$	27222.0	−	47149.9i	0.899686	−	1.55830i	0.827895	−	0.560883i	$-0.189538\pi$
$972$		0			0
$973$		0			0
$974$	13232.0			0.435298
$975$		0			0
$976$	240.000	+	415.692i	0.00787112	+	0.0136332i
$977$	−12723.0	−	22036.9i	−0.416627	−	0.721620i	0.578970	−	0.815348i	$-0.303455\pi$
$977$	−12723.0	−	22036.9i	−0.416627	−	0.721620i	−0.995598	+	0.0937289i	$0.970121\pi$
$978$		0			0
$979$	240.000			0.00783497
$980$		0			0
$981$		0			0
$982$	−17040.0	+	29514.1i	−0.553735	+	0.959098i
$983$	−16596.0	−	28745.1i	−0.538484	−	0.932682i	−0.998986	−	0.0450235i	$-0.985664\pi$
$983$	−16596.0	−	28745.1i	−0.538484	−	0.932682i	0.460502	−	0.887659i	$-0.347670\pi$
$984$		0			0
$985$	−2546.00	+	4409.80i	−0.0823577	+	0.142648i
$986$	−1016.00			−0.0328154
$987$		0			0
$988$	20832.0			0.670804
$989$	8056.00	−	13953.4i	0.259015	−	0.448627i
$990$		0			0
$991$	−5512.00	−	9547.06i	−0.176685	−	0.306027i	0.764058	−	0.645147i	$-0.223204\pi$
$991$	−5512.00	−	9547.06i	−0.176685	−	0.306027i	−0.940743	+	0.339120i	$0.889871\pi$
$992$	1152.00	−	1995.32i	0.0368710	−	0.0638625i
$993$		0			0
$994$		0			0
$995$	5072.00			0.161601
$996$		0			0
$997$	−20357.0	−	35259.4i	−0.646653	−	1.12004i	−0.983917	−	0.178625i	$-0.942835\pi$
$997$	−20357.0	−	35259.4i	−0.646653	−	1.12004i	0.337265	−	0.941410i	$-0.390498\pi$
$998$	−2948.00	−	5106.09i	−0.0935043	−	0.161954i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.r.667.1		2
3.2	odd	2		294.4.e.d.79.1		2
7.2	even	3		882.4.a.d.1.1		1
7.3	odd	6		882.4.g.s.361.1		2
7.4	even	3	inner	882.4.g.r.361.1		2
7.5	odd	6		126.4.a.c.1.1		1
7.6	odd	2		882.4.g.s.667.1		2
21.2	odd	6		294.4.a.h.1.1		1
21.5	even	6		42.4.a.b.1.1	✓	1
21.11	odd	6		294.4.e.d.67.1		2
21.17	even	6		294.4.e.a.67.1		2
21.20	even	2		294.4.e.a.79.1		2
28.19	even	6		1008.4.a.j.1.1		1
84.23	even	6		2352.4.a.ba.1.1		1
84.47	odd	6		336.4.a.d.1.1		1
105.47	odd	12		1050.4.g.n.799.2		2
105.68	odd	12		1050.4.g.n.799.1		2
105.89	even	6		1050.4.a.d.1.1		1
168.5	even	6		1344.4.a.f.1.1		1
168.131	odd	6		1344.4.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.b.1.1	✓	1	21.5	even	6
126.4.a.c.1.1		1	7.5	odd	6
294.4.a.h.1.1		1	21.2	odd	6
294.4.e.a.67.1		2	21.17	even	6
294.4.e.a.79.1		2	21.20	even	2
294.4.e.d.67.1		2	21.11	odd	6
294.4.e.d.79.1		2	3.2	odd	2
336.4.a.d.1.1		1	84.47	odd	6
882.4.a.d.1.1		1	7.2	even	3
882.4.g.r.361.1		2	7.4	even	3	inner
882.4.g.r.667.1		2	1.1	even	1	trivial
882.4.g.s.361.1		2	7.3	odd	6
882.4.g.s.667.1		2	7.6	odd	2
1008.4.a.j.1.1		1	28.19	even	6
1050.4.a.d.1.1		1	105.89	even	6
1050.4.g.n.799.1		2	105.68	odd	12
1050.4.g.n.799.2		2	105.47	odd	12
1344.4.a.f.1.1		1	168.5	even	6
1344.4.a.t.1.1		1	168.131	odd	6
2352.4.a.ba.1.1		1	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} -8.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(-4.00000 - 6.92820i) q^{11} +42.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-62.0000 + 107.387i) q^{19} +8.00000 q^{20} -16.0000 q^{22} +(38.0000 - 65.8179i) q^{23} +(60.5000 + 104.789i) q^{25} +(42.0000 - 72.7461i) q^{26} -254.000 q^{29} +(-36.0000 - 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} +4.00000 q^{34} +(-199.000 + 344.678i) q^{37} +(124.000 + 214.774i) q^{38} +(8.00000 - 13.8564i) q^{40} +462.000 q^{41} +212.000 q^{43} +(-16.0000 + 27.7128i) q^{44} +(-76.0000 - 131.636i) q^{46} +(132.000 - 228.631i) q^{47} +242.000 q^{50} +(-84.0000 - 145.492i) q^{52} +(-81.0000 - 140.296i) q^{53} +16.0000 q^{55} +(-254.000 + 439.941i) q^{58} +(386.000 + 668.572i) q^{59} +(15.0000 - 25.9808i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(-42.0000 + 72.7461i) q^{65} +(382.000 + 661.643i) q^{67} +(4.00000 - 6.92820i) q^{68} +236.000 q^{71} +(209.000 + 361.999i) q^{73} +(398.000 + 689.356i) q^{74} +496.000 q^{76} +(-276.000 + 478.046i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(462.000 - 800.207i) q^{82} +1036.00 q^{83} -4.00000 q^{85} +(212.000 - 367.195i) q^{86} +(32.0000 + 55.4256i) q^{88} +(-15.0000 + 25.9808i) q^{89} -304.000 q^{92} +(-264.000 - 457.261i) q^{94} +(-124.000 - 214.774i) q^{95} +1190.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 2 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{11} + 84 q^{13} - 16 q^{16} + 2 q^{17} - 124 q^{19} + 16 q^{20} - 32 q^{22} + 76 q^{23} + 121 q^{25} + 84 q^{26} - 508 q^{29} - 72 q^{31} + 32 q^{32} + 8 q^{34} - 398 q^{37} + 248 q^{38} + 16 q^{40} + 924 q^{41} + 424 q^{43} - 32 q^{44} - 152 q^{46} + 264 q^{47} + 484 q^{50} - 168 q^{52} - 162 q^{53} + 32 q^{55} - 508 q^{58} + 772 q^{59} + 30 q^{61} - 288 q^{62} + 128 q^{64} - 84 q^{65} + 764 q^{67} + 8 q^{68} + 472 q^{71} + 418 q^{73} + 796 q^{74} + 992 q^{76} - 552 q^{79} - 32 q^{80} + 924 q^{82} + 2072 q^{83} - 8 q^{85} + 424 q^{86} + 64 q^{88} - 30 q^{89} - 608 q^{92} - 528 q^{94} - 248 q^{95} + 2380 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^11 + 84 * q^13 - 16 * q^16 + 2 * q^17 - 124 * q^19 + 16 * q^20 - 32 * q^22 + 76 * q^23 + 121 * q^25 + 84 * q^26 - 508 * q^29 - 72 * q^31 + 32 * q^32 + 8 * q^34 - 398 * q^37 + 248 * q^38 + 16 * q^40 + 924 * q^41 + 424 * q^43 - 32 * q^44 - 152 * q^46 + 264 * q^47 + 484 * q^50 - 168 * q^52 - 162 * q^53 + 32 * q^55 - 508 * q^58 + 772 * q^59 + 30 * q^61 - 288 * q^62 + 128 * q^64 - 84 * q^65 + 764 * q^67 + 8 * q^68 + 472 * q^71 + 418 * q^73 + 796 * q^74 + 992 * q^76 - 552 * q^79 - 32 * q^80 + 924 * q^82 + 2072 * q^83 - 8 * q^85 + 424 * q^86 + 64 * q^88 - 30 * q^89 - 608 * q^92 - 528 * q^94 - 248 * q^95 + 2380 * q^97

Introduction

L-functions

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Database

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