LMFDB - Embedded newform 882.4.g.p.361.1

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 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.p.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} -8.00000 q^{8} +(12.0000 - 20.7846i) q^{10} +(24.0000 - 41.5692i) q^{11} +56.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-57.0000 + 98.7269i) q^{17} +(-1.00000 - 1.73205i) q^{19} +48.0000 q^{20} +96.0000 q^{22} +(-60.0000 - 103.923i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(56.0000 + 96.9948i) q^{26} +54.0000 q^{29} +(-118.000 + 204.382i) q^{31} +(16.0000 - 27.7128i) q^{32} -228.000 q^{34} +(-73.0000 - 126.440i) q^{37} +(2.00000 - 3.46410i) q^{38} +(48.0000 + 83.1384i) q^{40} -126.000 q^{41} -376.000 q^{43} +(96.0000 + 166.277i) q^{44} +(120.000 - 207.846i) q^{46} +(-6.00000 - 10.3923i) q^{47} -38.0000 q^{50} +(-112.000 + 193.990i) q^{52} +(87.0000 - 150.688i) q^{53} -576.000 q^{55} +(54.0000 + 93.5307i) q^{58} +(69.0000 - 119.512i) q^{59} +(-190.000 - 329.090i) q^{61} -472.000 q^{62} +64.0000 q^{64} +(-336.000 - 581.969i) q^{65} +(242.000 - 419.156i) q^{67} +(-228.000 - 394.908i) q^{68} -576.000 q^{71} +(575.000 - 995.929i) q^{73} +(146.000 - 252.879i) q^{74} +8.00000 q^{76} +(-388.000 - 672.036i) q^{79} +(-96.0000 + 166.277i) q^{80} +(-126.000 - 218.238i) q^{82} -378.000 q^{83} +1368.00 q^{85} +(-376.000 - 651.251i) q^{86} +(-192.000 + 332.554i) q^{88} +(-195.000 - 337.750i) q^{89} +480.000 q^{92} +(12.0000 - 20.7846i) q^{94} +(-12.0000 + 20.7846i) q^{95} -1330.00 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 12 q^{5} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 - 12 * q^5 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} - 12 q^{5} - 16 q^{8} + 24 q^{10} + 48 q^{11} + 112 q^{13} - 16 q^{16} - 114 q^{17} - 2 q^{19} + 96 q^{20} + 192 q^{22} - 120 q^{23} - 19 q^{25} + 112 q^{26} + 108 q^{29} - 236 q^{31} + 32 q^{32} - 456 q^{34} - 146 q^{37} + 4 q^{38} + 96 q^{40} - 252 q^{41} - 752 q^{43} + 192 q^{44} + 240 q^{46} - 12 q^{47} - 76 q^{50} - 224 q^{52} + 174 q^{53} - 1152 q^{55} + 108 q^{58} + 138 q^{59} - 380 q^{61} - 944 q^{62} + 128 q^{64} - 672 q^{65} + 484 q^{67} - 456 q^{68} - 1152 q^{71} + 1150 q^{73} + 292 q^{74} + 16 q^{76} - 776 q^{79} - 192 q^{80} - 252 q^{82} - 756 q^{83} + 2736 q^{85} - 752 q^{86} - 384 q^{88} - 390 q^{89} + 960 q^{92} + 24 q^{94} - 24 q^{95} - 2660 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 12 * q^5 - 16 * q^8 + 24 * q^10 + 48 * q^11 + 112 * q^13 - 16 * q^16 - 114 * q^17 - 2 * q^19 + 96 * q^20 + 192 * q^22 - 120 * q^23 - 19 * q^25 + 112 * q^26 + 108 * q^29 - 236 * q^31 + 32 * q^32 - 456 * q^34 - 146 * q^37 + 4 * q^38 + 96 * q^40 - 252 * q^41 - 752 * q^43 + 192 * q^44 + 240 * q^46 - 12 * q^47 - 76 * q^50 - 224 * q^52 + 174 * q^53 - 1152 * q^55 + 108 * q^58 + 138 * q^59 - 380 * q^61 - 944 * q^62 + 128 * q^64 - 672 * q^65 + 484 * q^67 - 456 * q^68 - 1152 * q^71 + 1150 * q^73 + 292 * q^74 + 16 * q^76 - 776 * q^79 - 192 * q^80 - 252 * q^82 - 756 * q^83 + 2736 * q^85 - 752 * q^86 - 384 * q^88 - 390 * q^89 + 960 * q^92 + 24 * q^94 - 24 * q^95 - 2660 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−6.00000	−	10.3923i	−0.536656	−	0.929516i	−0.999081	−	0.0428575i	$-0.986354\pi$
$5$	−6.00000	−	10.3923i	−0.536656	−	0.929516i	0.462425	−	0.886658i	$-0.346979\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	12.0000	−	20.7846i	0.379473	−	0.657267i
$11$	24.0000	−	41.5692i	0.657843	−	1.13942i	−0.323330	−	0.946286i	$-0.604802\pi$
$11$	24.0000	−	41.5692i	0.657843	−	1.13942i	0.981173	−	0.193131i	$-0.0618643\pi$
$12$		0			0
$13$	56.0000			1.19474			0.597369	−	0.801966i	$-0.296213\pi$
$13$	56.0000			1.19474			0.597369	+	0.801966i	$0.296213\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−57.0000	+	98.7269i	−0.813208	+	1.40852i	0.0974001	+	0.995245i	$0.468947\pi$
$17$	−57.0000	+	98.7269i	−0.813208	+	1.40852i	−0.910608	+	0.413272i	$0.864386\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.0120745	−	0.0209137i	0.859925	−	0.510420i	$-0.170510\pi$
$19$	−1.00000	−	1.73205i	−0.0120745	−	0.0209137i	−0.872000	+	0.489507i	$0.837177\pi$
$20$	48.0000			0.536656
$21$		0			0
$22$	96.0000			0.930330
$23$	−60.0000	−	103.923i	−0.543951	−	0.942150i	−0.998672	−	0.0515165i	$-0.983595\pi$
$23$	−60.0000	−	103.923i	−0.543951	−	0.942150i	0.454721	−	0.890634i	$-0.349739\pi$
$24$		0			0
$25$	−9.50000	+	16.4545i	−0.0760000	+	0.131636i
$26$	56.0000	+	96.9948i	0.422404	+	0.731625i
$27$		0			0
$28$		0			0
$29$	54.0000			0.345778			0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000			0.345778			0.172889	+	0.984941i	$0.444690\pi$
$30$		0			0
$31$	−118.000	+	204.382i	−0.683659	+	1.18413i	0.290197	+	0.956967i	$0.406279\pi$
$31$	−118.000	+	204.382i	−0.683659	+	1.18413i	−0.973856	+	0.227165i	$0.927054\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−228.000			−1.15005
$35$		0			0
$36$		0			0
$37$	−73.0000	−	126.440i	−0.324355	−	0.561799i	0.657027	−	0.753867i	$-0.271814\pi$
$37$	−73.0000	−	126.440i	−0.324355	−	0.561799i	−0.981382	+	0.192068i	$0.938480\pi$
$38$	2.00000	−	3.46410i	0.00853797	−	0.0147882i
$39$		0			0
$40$	48.0000	+	83.1384i	0.189737	+	0.328634i
$41$	−126.000			−0.479949			−0.239974	−	0.970779i	$-0.577139\pi$
$41$	−126.000			−0.479949			−0.239974	+	0.970779i	$0.577139\pi$
$42$		0			0
$43$	−376.000			−1.33348			−0.666738	−	0.745292i	$-0.732310\pi$
$43$	−376.000			−1.33348			−0.666738	+	0.745292i	$0.732310\pi$
$44$	96.0000	+	166.277i	0.328921	+	0.569709i
$45$		0			0
$46$	120.000	−	207.846i	0.384631	−	0.666201i
$47$	−6.00000	−	10.3923i	−0.0186211	−	0.0322526i	0.856565	−	0.516040i	$-0.172594\pi$
$47$	−6.00000	−	10.3923i	−0.0186211	−	0.0322526i	−0.875186	+	0.483787i	$0.839261\pi$
$48$		0			0
$49$		0			0
$50$	−38.0000			−0.107480
$51$		0			0
$52$	−112.000	+	193.990i	−0.298685	+	0.517337i
$53$	87.0000	−	150.688i	0.225479	−	0.390540i	−0.730984	−	0.682394i	$-0.760939\pi$
$53$	87.0000	−	150.688i	0.225479	−	0.390540i	0.956463	+	0.291854i	$0.0942721\pi$
$54$		0			0
$55$	−576.000			−1.41214
$56$		0			0
$57$		0			0
$58$	54.0000	+	93.5307i	0.122251	+	0.211745i
$59$	69.0000	−	119.512i	0.152255	−	0.263713i	−0.779801	−	0.626027i	$-0.784680\pi$
$59$	69.0000	−	119.512i	0.152255	−	0.263713i	0.932056	+	0.362314i	$0.118013\pi$
$60$		0			0
$61$	−190.000	−	329.090i	−0.398803	−	0.690748i	0.594775	−	0.803892i	$-0.297241\pi$
$61$	−190.000	−	329.090i	−0.398803	−	0.690748i	−0.993579	+	0.113144i	$0.963908\pi$
$62$	−472.000			−0.966840
$63$		0			0
$64$	64.0000			0.125000
$65$	−336.000	−	581.969i	−0.641164	−	1.11053i
$66$		0			0
$67$	242.000	−	419.156i	0.441269	−	0.764300i	−0.556515	−	0.830837i	$-0.687862\pi$
$67$	242.000	−	419.156i	0.441269	−	0.764300i	0.997784	+	0.0665376i	$0.0211952\pi$
$68$	−228.000	−	394.908i	−0.406604	−	0.704259i
$69$		0			0
$70$		0			0
$71$	−576.000			−0.962798			−0.481399	−	0.876502i	$-0.659871\pi$
$71$	−576.000			−0.962798			−0.481399	+	0.876502i	$0.659871\pi$
$72$		0			0
$73$	575.000	−	995.929i	0.921899	−	1.59678i	0.125426	−	0.992103i	$-0.459970\pi$
$73$	575.000	−	995.929i	0.921899	−	1.59678i	0.796473	−	0.604674i	$-0.206696\pi$
$74$	146.000	−	252.879i	0.229353	−	0.397252i
$75$		0			0
$76$	8.00000			0.0120745
$77$		0			0
$78$		0			0
$79$	−388.000	−	672.036i	−0.552575	−	0.957088i	−0.998088	−	0.0618122i	$-0.980312\pi$
$79$	−388.000	−	672.036i	−0.552575	−	0.957088i	0.445513	−	0.895275i	$-0.353021\pi$
$80$	−96.0000	+	166.277i	−0.134164	+	0.232379i
$81$		0			0
$82$	−126.000	−	218.238i	−0.169687	−	0.293907i
$83$	−378.000			−0.499890			−0.249945	−	0.968260i	$-0.580413\pi$
$83$	−378.000			−0.499890			−0.249945	+	0.968260i	$0.580413\pi$
$84$		0			0
$85$	1368.00			1.74565
$86$	−376.000	−	651.251i	−0.471455	−	0.816584i
$87$		0			0
$88$	−192.000	+	332.554i	−0.232583	+	0.402845i
$89$	−195.000	−	337.750i	−0.232247	−	0.402263i	0.726222	−	0.687460i	$-0.241274\pi$
$89$	−195.000	−	337.750i	−0.232247	−	0.402263i	−0.958469	+	0.285197i	$0.907941\pi$
$90$		0			0
$91$		0			0
$92$	480.000			0.543951
$93$		0			0
$94$	12.0000	−	20.7846i	0.0131671	−	0.0228061i
$95$	−12.0000	+	20.7846i	−0.0129597	+	0.0224469i
$96$		0			0
$97$	−1330.00			−1.39218			−0.696088	−	0.717957i	$-0.745078\pi$
$97$	−1330.00			−1.39218			−0.696088	+	0.717957i	$0.745078\pi$
$98$		0			0
$99$		0			0
$100$	−38.0000	−	65.8179i	−0.0380000	−	0.0658179i
$101$	−750.000	+	1299.04i	−0.738889	+	1.27979i	0.214107	+	0.976810i	$0.431316\pi$
$101$	−750.000	+	1299.04i	−0.738889	+	1.27979i	−0.952996	+	0.302983i	$0.902017\pi$
$102$		0			0
$103$	−190.000	−	329.090i	−0.181760	−	0.314817i	0.760720	−	0.649080i	$-0.224846\pi$
$103$	−190.000	−	329.090i	−0.181760	−	0.314817i	−0.942480	+	0.334263i	$0.891513\pi$
$104$	−448.000			−0.422404
$105$		0			0
$106$	348.000			0.318875
$107$	318.000	+	550.792i	0.287310	+	0.497636i	0.973167	−	0.230101i	$-0.0739055\pi$
$107$	318.000	+	550.792i	0.287310	+	0.497636i	−0.685856	+	0.727737i	$0.740572\pi$
$108$		0			0
$109$	−73.0000	+	126.440i	−0.0641480	+	0.111108i	−0.896316	−	0.443416i	$-0.853766\pi$
$109$	−73.0000	+	126.440i	−0.0641480	+	0.111108i	0.832168	+	0.554524i	$0.187100\pi$
$110$	−576.000	−	997.661i	−0.499268	−	0.864757i
$111$		0			0
$112$		0			0
$113$	−198.000			−0.164834			−0.0824171	−	0.996598i	$-0.526264\pi$
$113$	−198.000			−0.164834			−0.0824171	+	0.996598i	$0.526264\pi$
$114$		0			0
$115$	−720.000	+	1247.08i	−0.583829	+	1.01122i
$116$	−108.000	+	187.061i	−0.0864444	+	0.149726i
$117$		0			0
$118$	276.000			0.215321
$119$		0			0
$120$		0			0
$121$	−486.500	−	842.643i	−0.365515	−	0.633090i
$122$	380.000	−	658.179i	0.281997	−	0.488432i
$123$		0			0
$124$	−472.000	−	817.528i	−0.341829	−	0.592066i
$125$	−1272.00			−0.910169
$126$		0			0
$127$	−376.000			−0.262713			−0.131357	−	0.991335i	$-0.541933\pi$
$127$	−376.000			−0.262713			−0.131357	+	0.991335i	$0.541933\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	672.000	−	1163.94i	0.453372	−	0.785263i
$131$	1065.00	+	1844.63i	0.710301	+	1.23028i	0.964744	+	0.263190i	$0.0847747\pi$
$131$	1065.00	+	1844.63i	0.710301	+	1.23028i	−0.254443	+	0.967088i	$0.581892\pi$
$132$		0			0
$133$		0			0
$134$	968.000			0.624048
$135$		0			0
$136$	456.000	−	789.815i	0.287512	−	0.497986i
$137$	−39.0000	+	67.5500i	−0.0243211	+	0.0421254i	−0.877930	−	0.478789i	$-0.841076\pi$
$137$	−39.0000	+	67.5500i	−0.0243211	+	0.0421254i	0.853609	+	0.520915i	$0.174409\pi$
$138$		0			0
$139$	−2338.00			−1.42667			−0.713333	−	0.700825i	$-0.752815\pi$
$139$	−2338.00			−1.42667			−0.713333	+	0.700825i	$0.752815\pi$
$140$		0			0
$141$		0			0
$142$	−576.000	−	997.661i	−0.340400	−	0.589591i
$143$	1344.00	−	2327.88i	0.785951	−	1.36131i
$144$		0			0
$145$	−324.000	−	561.184i	−0.185564	−	0.321406i
$146$	2300.00			1.30376
$147$		0			0
$148$	584.000			0.324355
$149$	−501.000	−	867.757i	−0.275460	−	0.477110i	0.694791	−	0.719212i	$-0.255497\pi$
$149$	−501.000	−	867.757i	−0.275460	−	0.477110i	−0.970251	+	0.242101i	$0.922163\pi$
$150$		0			0
$151$	1376.00	−	2383.30i	0.741571	−	1.28444i	−0.210208	−	0.977657i	$-0.567414\pi$
$151$	1376.00	−	2383.30i	0.741571	−	1.28444i	0.951780	−	0.306783i	$-0.0992525\pi$
$152$	8.00000	+	13.8564i	0.00426898	+	0.00739410i
$153$		0			0
$154$		0			0
$155$	2832.00			1.46756
$156$		0			0
$157$	260.000	−	450.333i	0.132167	−	0.228920i	−0.792345	−	0.610074i	$-0.791140\pi$
$157$	260.000	−	450.333i	0.132167	−	0.228920i	0.924512	+	0.381154i	$0.124473\pi$
$158$	776.000	−	1344.07i	0.390729	−	0.676763i
$159$		0			0
$160$	−384.000			−0.189737
$161$		0			0
$162$		0			0
$163$	−640.000	−	1108.51i	−0.307538	−	0.532671i	0.670285	−	0.742104i	$-0.266172\pi$
$163$	−640.000	−	1108.51i	−0.307538	−	0.532671i	−0.977823	+	0.209432i	$0.932838\pi$
$164$	252.000	−	436.477i	0.119987	−	0.207824i
$165$		0			0
$166$	−378.000	−	654.715i	−0.176738	−	0.306119i
$167$	−1764.00			−0.817380			−0.408690	−	0.912673i	$-0.634014\pi$
$167$	−1764.00			−0.817380			−0.408690	+	0.912673i	$0.634014\pi$
$168$		0			0
$169$	939.000			0.427401
$170$	1368.00	+	2369.45i	0.617181	+	1.06899i
$171$		0			0
$172$	752.000	−	1302.50i	0.333369	−	0.577412i
$173$	−384.000	−	665.108i	−0.168757	−	0.292296i	0.769226	−	0.638977i	$-0.220642\pi$
$173$	−384.000	−	665.108i	−0.168757	−	0.292296i	−0.937983	+	0.346681i	$0.887309\pi$
$174$		0			0
$175$		0			0
$176$	−768.000			−0.328921
$177$		0			0
$178$	390.000	−	675.500i	0.164223	−	0.284443i
$179$	906.000	−	1569.24i	0.378311	−	0.655253i	−0.612506	−	0.790466i	$-0.709838\pi$
$179$	906.000	−	1569.24i	0.378311	−	0.655253i	0.990817	+	0.135213i	$0.0431718\pi$
$180$		0			0
$181$	−448.000			−0.183976			−0.0919878	−	0.995760i	$-0.529322\pi$
$181$	−448.000			−0.183976			−0.0919878	+	0.995760i	$0.529322\pi$
$182$		0			0
$183$		0			0
$184$	480.000	+	831.384i	0.192316	+	0.333100i
$185$	−876.000	+	1517.28i	−0.348134	+	0.602986i
$186$		0			0
$187$	2736.00	+	4738.89i	1.06993	+	1.85317i
$188$	48.0000			0.0186211
$189$		0			0
$190$	−48.0000			−0.0183278
$191$	−1068.00	−	1849.83i	−0.404596	−	0.700780i	0.589679	−	0.807638i	$-0.299254\pi$
$191$	−1068.00	−	1849.83i	−0.404596	−	0.700780i	−0.994274	+	0.106858i	$0.965921\pi$
$192$		0			0
$193$	−2215.00	+	3836.49i	−0.826110	+	1.43086i	0.0749584	+	0.997187i	$0.476118\pi$
$193$	−2215.00	+	3836.49i	−0.826110	+	1.43086i	−0.901068	+	0.433677i	$0.857216\pi$
$194$	−1330.00	−	2303.63i	−0.492208	−	0.852530i
$195$		0			0
$196$		0			0
$197$	−198.000			−0.0716087			−0.0358044	−	0.999359i	$-0.511399\pi$
$197$	−198.000			−0.0716087			−0.0358044	+	0.999359i	$0.511399\pi$
$198$		0			0
$199$	1142.00	−	1978.00i	0.406805	−	0.704607i	−0.587725	−	0.809061i	$-0.699976\pi$
$199$	1142.00	−	1978.00i	0.406805	−	0.704607i	0.994530	+	0.104454i	$0.0333094\pi$
$200$	76.0000	−	131.636i	0.0268701	−	0.0465403i
$201$		0			0
$202$	−3000.00			−1.04495
$203$		0			0
$204$		0			0
$205$	756.000	+	1309.43i	0.257567	+	0.446120i
$206$	380.000	−	658.179i	0.128524	−	0.222609i
$207$		0			0
$208$	−448.000	−	775.959i	−0.149342	−	0.258669i
$209$	−96.0000			−0.0317725
$210$		0			0
$211$	4412.00			1.43950			0.719750	−	0.694233i	$-0.244256\pi$
$211$	4412.00			1.43950			0.719750	+	0.694233i	$0.244256\pi$
$212$	348.000	+	602.754i	0.112739	+	0.195270i
$213$		0			0
$214$	−636.000	+	1101.58i	−0.203159	+	0.351882i
$215$	2256.00	+	3907.51i	0.715618	+	1.23949i
$216$		0			0
$217$		0			0
$218$	−292.000			−0.0907190
$219$		0			0
$220$	1152.00	−	1995.32i	0.353036	−	0.611476i
$221$	−3192.00	+	5528.71i	−0.971571	+	1.68281i
$222$		0			0
$223$	2072.00			0.622204			0.311102	−	0.950377i	$-0.399302\pi$
$223$	2072.00			0.622204			0.311102	+	0.950377i	$0.399302\pi$
$224$		0			0
$225$		0			0
$226$	−198.000	−	342.946i	−0.0582777	−	0.100940i
$227$	−183.000	+	316.965i	−0.0535072	+	0.0926772i	−0.891538	−	0.452945i	$-0.850373\pi$
$227$	−183.000	+	316.965i	−0.0535072	+	0.0926772i	0.838031	+	0.545622i	$0.183707\pi$
$228$		0			0
$229$	188.000	+	325.626i	0.0542506	+	0.0939648i	0.891875	−	0.452281i	$-0.149390\pi$
$229$	188.000	+	325.626i	0.0542506	+	0.0939648i	−0.837625	+	0.546246i	$0.816056\pi$
$230$	−2880.00			−0.825659
$231$		0			0
$232$	−432.000			−0.122251
$233$	−1131.00	−	1958.95i	−0.318001	−	0.550794i	0.662070	−	0.749442i	$-0.269678\pi$
$233$	−1131.00	−	1958.95i	−0.318001	−	0.550794i	−0.980071	+	0.198648i	$0.936345\pi$
$234$		0			0
$235$	−72.0000	+	124.708i	−0.0199862	+	0.0346172i
$236$	276.000	+	478.046i	0.0761274	+	0.131857i
$237$		0			0
$238$		0			0
$239$	−2592.00			−0.701517			−0.350758	−	0.936466i	$-0.614076\pi$
$239$	−2592.00			−0.701517			−0.350758	+	0.936466i	$0.614076\pi$
$240$		0			0
$241$	−55.0000	+	95.2628i	−0.0147007	+	0.0254623i	−0.873282	−	0.487215i	$-0.838013\pi$
$241$	−55.0000	+	95.2628i	−0.0147007	+	0.0254623i	0.858581	+	0.512677i	$0.171346\pi$
$242$	973.000	−	1685.29i	0.258458	−	0.447662i
$243$		0			0
$244$	1520.00			0.398803
$245$		0			0
$246$		0			0
$247$	−56.0000	−	96.9948i	−0.0144259	−	0.0249864i
$248$	944.000	−	1635.06i	0.241710	−	0.418654i
$249$		0			0
$250$	−1272.00	−	2203.17i	−0.321793	−	0.557362i
$251$	1890.00			0.475282			0.237641	−	0.971353i	$-0.423626\pi$
$251$	1890.00			0.475282			0.237641	+	0.971353i	$0.423626\pi$
$252$		0			0
$253$	−5760.00			−1.43134
$254$	−376.000	−	651.251i	−0.0928832	−	0.160878i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1065.00	+	1844.63i	0.258494	+	0.447724i	0.965839	−	0.259144i	$-0.0834406\pi$
$257$	1065.00	+	1844.63i	0.258494	+	0.447724i	−0.707345	+	0.706869i	$0.750107\pi$
$258$		0			0
$259$		0			0
$260$	2688.00			0.641164
$261$		0			0
$262$	−2130.00	+	3689.27i	−0.502259	+	0.869938i
$263$	−2496.00	+	4323.20i	−0.585209	+	1.01361i	0.409640	+	0.912247i	$0.365654\pi$
$263$	−2496.00	+	4323.20i	−0.585209	+	1.01361i	−0.994849	+	0.101365i	$0.967679\pi$
$264$		0			0
$265$	−2088.00			−0.484018
$266$		0			0
$267$		0			0
$268$	968.000	+	1676.63i	0.220634	+	0.382150i
$269$	3408.00	−	5902.83i	0.772451	−	1.33793i	−0.163764	−	0.986499i	$-0.552364\pi$
$269$	3408.00	−	5902.83i	0.772451	−	1.33793i	0.936216	−	0.351426i	$-0.114303\pi$
$270$		0			0
$271$	−4096.00	−	7094.48i	−0.918134	−	1.59025i	−0.802247	−	0.596992i	$-0.796362\pi$
$271$	−4096.00	−	7094.48i	−0.918134	−	1.59025i	−0.115887	−	0.993262i	$-0.536971\pi$
$272$	1824.00			0.406604
$273$		0			0
$274$	−156.000			−0.0343953
$275$	456.000	+	789.815i	0.0999921	+	0.173191i
$276$		0			0
$277$	−1207.00	+	2090.59i	−0.261811	+	0.453470i	−0.966723	−	0.255825i	$-0.917653\pi$
$277$	−1207.00	+	2090.59i	−0.261811	+	0.453470i	0.704912	+	0.709294i	$0.250986\pi$
$278$	−2338.00	−	4049.53i	−0.504403	−	0.873651i
$279$		0			0
$280$		0			0
$281$	−1962.00			−0.416524			−0.208262	−	0.978073i	$-0.566781\pi$
$281$	−1962.00			−0.416524			−0.208262	+	0.978073i	$0.566781\pi$
$282$		0			0
$283$	−2701.00	+	4678.27i	−0.567342	+	0.982665i	0.429486	+	0.903074i	$0.358695\pi$
$283$	−2701.00	+	4678.27i	−0.567342	+	0.982665i	−0.996828	+	0.0795914i	$0.974638\pi$
$284$	1152.00	−	1995.32i	0.240699	−	0.416904i
$285$		0			0
$286$	5376.00			1.11150
$287$		0			0
$288$		0			0
$289$	−4041.50	−	7000.08i	−0.822613	−	1.42481i
$290$	648.000	−	1122.37i	0.131213	−	0.227268i
$291$		0			0
$292$	2300.00	+	3983.72i	0.460950	+	0.798388i
$293$	4788.00			0.954669			0.477334	−	0.878722i	$-0.341603\pi$
$293$	4788.00			0.954669			0.477334	+	0.878722i	$0.341603\pi$
$294$		0			0
$295$	−1656.00			−0.326834
$296$	584.000	+	1011.52i	0.114677	+	0.198626i
$297$		0			0
$298$	1002.00	−	1735.51i	0.194780	−	0.337368i
$299$	−3360.00	−	5819.69i	−0.649879	−	1.12562i
$300$		0			0
$301$		0			0
$302$	5504.00			1.04874
$303$		0			0
$304$	−16.0000	+	27.7128i	−0.00301863	+	0.00522842i
$305$	−2280.00	+	3949.08i	−0.428041	+	0.741388i
$306$		0			0
$307$	−574.000			−0.106710			−0.0533549	−	0.998576i	$-0.516991\pi$
$307$	−574.000			−0.106710			−0.0533549	+	0.998576i	$0.516991\pi$
$308$		0			0
$309$		0			0
$310$	2832.00	+	4905.17i	0.518861	+	0.898693i
$311$	−4404.00	+	7627.95i	−0.802984	+	1.39081i	0.114660	+	0.993405i	$0.463422\pi$
$311$	−4404.00	+	7627.95i	−0.802984	+	1.39081i	−0.917644	+	0.397404i	$0.869911\pi$
$312$		0			0
$313$	1385.00	+	2398.89i	0.250111	+	0.433205i	0.963556	−	0.267506i	$-0.0861995\pi$
$313$	1385.00	+	2398.89i	0.250111	+	0.433205i	−0.713445	+	0.700711i	$0.752866\pi$
$314$	1040.00			0.186913
$315$		0			0
$316$	3104.00			0.552575
$317$	3783.00	+	6552.35i	0.670266	+	1.16094i	0.977828	+	0.209407i	$0.0671535\pi$
$317$	3783.00	+	6552.35i	0.670266	+	1.16094i	−0.307562	+	0.951528i	$0.599513\pi$
$318$		0			0
$319$	1296.00	−	2244.74i	0.227467	−	0.393985i
$320$	−384.000	−	665.108i	−0.0670820	−	0.116190i
$321$		0			0
$322$		0			0
$323$	228.000			0.0392763
$324$		0			0
$325$	−532.000	+	921.451i	−0.0908002	+	0.157270i
$326$	1280.00	−	2217.03i	0.217462	−	0.376655i
$327$		0			0
$328$	1008.00			0.169687
$329$		0			0
$330$		0			0
$331$	5660.00	+	9803.41i	0.939884	+	1.62793i	0.765684	+	0.643217i	$0.222401\pi$
$331$	5660.00	+	9803.41i	0.939884	+	1.62793i	0.174201	+	0.984710i	$0.444266\pi$
$332$	756.000	−	1309.43i	0.124973	−	0.216459i
$333$		0			0
$334$	−1764.00	−	3055.34i	−0.288987	−	0.500541i
$335$	−5808.00			−0.947239
$336$		0			0
$337$	−4786.00			−0.773620			−0.386810	−	0.922159i	$-0.626423\pi$
$337$	−4786.00			−0.773620			−0.386810	+	0.922159i	$0.626423\pi$
$338$	939.000	+	1626.40i	0.151109	+	0.261729i
$339$		0			0
$340$	−2736.00	+	4738.89i	−0.436413	+	0.755890i
$341$	5664.00	+	9810.34i	0.899480	+	1.55795i
$342$		0			0
$343$		0			0
$344$	3008.00			0.471455
$345$		0			0
$346$	768.000	−	1330.22i	0.119329	−	0.206684i
$347$	6324.00	−	10953.5i	0.978358	−	1.69457i	0.309980	−	0.950743i	$-0.399678\pi$
$347$	6324.00	−	10953.5i	0.978358	−	1.69457i	0.668378	−	0.743822i	$-0.266989\pi$
$348$		0			0
$349$	9632.00			1.47733			0.738666	−	0.674071i	$-0.235456\pi$
$349$	9632.00			1.47733			0.738666	+	0.674071i	$0.235456\pi$
$350$		0			0
$351$		0			0
$352$	−768.000	−	1330.22i	−0.116291	−	0.201422i
$353$	−1695.00	+	2935.83i	−0.255569	+	0.442658i	−0.965050	−	0.262066i	$-0.915596\pi$
$353$	−1695.00	+	2935.83i	−0.255569	+	0.442658i	0.709481	+	0.704724i	$0.248929\pi$
$354$		0			0
$355$	3456.00	+	5985.97i	0.516691	+	0.894936i
$356$	1560.00			0.232247
$357$		0			0
$358$	3624.00			0.535012
$359$	−5352.00	−	9269.94i	−0.786818	−	1.36281i	−0.927907	−	0.372812i	$-0.878394\pi$
$359$	−5352.00	−	9269.94i	−0.786818	−	1.36281i	0.141089	−	0.989997i	$-0.454940\pi$
$360$		0			0
$361$	3427.50	−	5936.60i	0.499708	−	0.865520i
$362$	−448.000	−	775.959i	−0.0650452	−	0.112662i
$363$		0			0
$364$		0			0
$365$	−13800.0			−1.97897
$366$		0			0
$367$	4292.00	−	7433.96i	0.610465	−	1.05736i	−0.380697	−	0.924700i	$-0.624316\pi$
$367$	4292.00	−	7433.96i	0.610465	−	1.05736i	0.991162	−	0.132656i	$-0.0423507\pi$
$368$	−960.000	+	1662.77i	−0.135988	+	0.235538i
$369$		0			0
$370$	−3504.00			−0.492336
$371$		0			0
$372$		0			0
$373$	1061.00	+	1837.71i	0.147283	+	0.255101i	0.930222	−	0.366997i	$-0.119614\pi$
$373$	1061.00	+	1837.71i	0.147283	+	0.255101i	−0.782939	+	0.622098i	$0.786281\pi$
$374$	−5472.00	+	9477.78i	−0.756552	+	1.31039i
$375$		0			0
$376$	48.0000	+	83.1384i	0.00658354	+	0.0114030i
$377$	3024.00			0.413114
$378$		0			0
$379$	−4912.00			−0.665732			−0.332866	−	0.942974i	$-0.608016\pi$
$379$	−4912.00			−0.665732			−0.332866	+	0.942974i	$0.608016\pi$
$380$	−48.0000	−	83.1384i	−0.00647986	−	0.0112235i
$381$		0			0
$382$	2136.00	−	3699.66i	0.286092	−	0.495526i
$383$	4530.00	+	7846.19i	0.604366	+	1.04679i	0.992151	+	0.125043i	$0.0399069\pi$
$383$	4530.00	+	7846.19i	0.604366	+	1.04679i	−0.387785	+	0.921750i	$0.626760\pi$
$384$		0			0
$385$		0			0
$386$	−8860.00			−1.16830
$387$		0			0
$388$	2660.00	−	4607.26i	0.348044	−	0.602830i
$389$	4497.00	−	7789.03i	0.586136	−	1.01522i	−0.408597	−	0.912715i	$-0.633982\pi$
$389$	4497.00	−	7789.03i	0.586136	−	1.01522i	0.994733	−	0.102502i	$-0.0326850\pi$
$390$		0			0
$391$	13680.0			1.76938
$392$		0			0
$393$		0			0
$394$	−198.000	−	342.946i	−0.0253175	−	0.0438512i
$395$	−4656.00	+	8064.43i	−0.593086	+	1.02725i
$396$		0			0
$397$	6488.00	+	11237.5i	0.820210	+	1.42065i	0.905526	+	0.424291i	$0.139477\pi$
$397$	6488.00	+	11237.5i	0.820210	+	1.42065i	−0.0853156	+	0.996354i	$0.527190\pi$
$398$	4568.00			0.575309
$399$		0			0
$400$	304.000			0.0380000
$401$	−1761.00	−	3050.14i	−0.219302	−	0.379842i	0.735293	−	0.677750i	$-0.237045\pi$
$401$	−1761.00	−	3050.14i	−0.219302	−	0.379842i	−0.954595	+	0.297907i	$0.903711\pi$
$402$		0			0
$403$	−6608.00	+	11445.4i	−0.816794	+	1.41473i
$404$	−3000.00	−	5196.15i	−0.369445	−	0.639897i
$405$		0			0
$406$		0			0
$407$	−7008.00			−0.853498
$408$		0			0
$409$	−6355.00	+	11007.2i	−0.768300	+	1.33073i	0.170185	+	0.985412i	$0.445564\pi$
$409$	−6355.00	+	11007.2i	−0.768300	+	1.33073i	−0.938484	+	0.345322i	$0.887770\pi$
$410$	−1512.00	+	2618.86i	−0.182128	+	0.315454i
$411$		0			0
$412$	1520.00			0.181760
$413$		0			0
$414$		0			0
$415$	2268.00	+	3928.29i	0.268269	+	0.464656i
$416$	896.000	−	1551.92i	0.105601	−	0.182906i
$417$		0			0
$418$	−96.0000	−	166.277i	−0.0112333	−	0.0194566i
$419$	−1638.00			−0.190982			−0.0954911	−	0.995430i	$-0.530442\pi$
$419$	−1638.00			−0.190982			−0.0954911	+	0.995430i	$0.530442\pi$
$420$		0			0
$421$	−12850.0			−1.48758			−0.743789	−	0.668414i	$-0.766973\pi$
$421$	−12850.0			−1.48758			−0.743789	+	0.668414i	$0.766973\pi$
$422$	4412.00	+	7641.81i	0.508940	+	0.881510i
$423$		0			0
$424$	−696.000	+	1205.51i	−0.0797187	+	0.138077i
$425$	−1083.00	−	1875.81i	−0.123608	−	0.214095i
$426$		0			0
$427$		0			0
$428$	−2544.00			−0.287310
$429$		0			0
$430$	−4512.00	+	7815.01i	−0.506019	+	0.876450i
$431$	−4008.00	+	6942.06i	−0.447932	+	0.775840i	−0.998251	−	0.0591136i	$-0.981173\pi$
$431$	−4008.00	+	6942.06i	−0.447932	+	0.775840i	0.550320	+	0.834954i	$0.314506\pi$
$432$		0			0
$433$	2198.00			0.243947			0.121974	−	0.992533i	$-0.461078\pi$
$433$	2198.00			0.243947			0.121974	+	0.992533i	$0.461078\pi$
$434$		0			0
$435$		0			0
$436$	−292.000	−	505.759i	−0.0320740	−	0.0555538i
$437$	−120.000	+	207.846i	−0.0131359	+	0.0227520i
$438$		0			0
$439$	188.000	+	325.626i	0.0204391	+	0.0354015i	0.876064	−	0.482195i	$-0.160160\pi$
$439$	188.000	+	325.626i	0.0204391	+	0.0354015i	−0.855625	+	0.517596i	$0.826827\pi$
$440$	4608.00			0.499268
$441$		0			0
$442$	−12768.0			−1.37401
$443$	3594.00	+	6224.99i	0.385454	+	0.667626i	0.991832	−	0.127551i	$-0.0407115\pi$
$443$	3594.00	+	6224.99i	0.385454	+	0.667626i	−0.606378	+	0.795176i	$0.707378\pi$
$444$		0			0
$445$	−2340.00	+	4053.00i	−0.249273	+	0.431754i
$446$	2072.00	+	3588.81i	0.219982	+	0.381020i
$447$		0			0
$448$		0			0
$449$	14670.0			1.54192			0.770958	−	0.636886i	$-0.219778\pi$
$449$	14670.0			1.54192			0.770958	+	0.636886i	$0.219778\pi$
$450$		0			0
$451$	−3024.00	+	5237.72i	−0.315731	+	0.546862i
$452$	396.000	−	685.892i	0.0412086	−	0.0713753i
$453$		0			0
$454$	−732.000			−0.0756706
$455$		0			0
$456$		0			0
$457$	2573.00	+	4456.57i	0.263370	+	0.456169i	0.967135	−	0.254263i	$-0.0818328\pi$
$457$	2573.00	+	4456.57i	0.263370	+	0.456169i	−0.703766	+	0.710432i	$0.748499\pi$
$458$	−376.000	+	651.251i	−0.0383610	+	0.0664432i
$459$		0			0
$460$	−2880.00	−	4988.31i	−0.291915	−	0.505611i
$461$	1512.00			0.152757			0.0763784	−	0.997079i	$-0.475664\pi$
$461$	1512.00			0.152757			0.0763784	+	0.997079i	$0.475664\pi$
$462$		0			0
$463$	7184.00			0.721099			0.360549	−	0.932740i	$-0.382589\pi$
$463$	7184.00			0.721099			0.360549	+	0.932740i	$0.382589\pi$
$464$	−432.000	−	748.246i	−0.0432222	−	0.0748630i
$465$		0			0
$466$	2262.00	−	3917.90i	0.224861	−	0.389470i
$467$	−8259.00	−	14305.0i	−0.818375	−	1.41747i	−0.906879	−	0.421391i	$-0.861542\pi$
$467$	−8259.00	−	14305.0i	−0.818375	−	1.41747i	0.0885046	−	0.996076i	$-0.471791\pi$
$468$		0			0
$469$		0			0
$470$	−288.000			−0.0282648
$471$		0			0
$472$	−552.000	+	956.092i	−0.0538302	+	0.0932367i
$473$	−9024.00	+	15630.0i	−0.877218	+	1.51939i
$474$		0			0
$475$	38.0000			0.00367065
$476$		0			0
$477$		0			0
$478$	−2592.00	−	4489.48i	−0.248024	−	0.429590i
$479$	5046.00	−	8739.93i	0.481331	−	0.833690i	−0.518439	−	0.855114i	$-0.673487\pi$
$479$	5046.00	−	8739.93i	0.481331	−	0.833690i	0.999770	+	0.0214244i	$0.00682012\pi$
$480$		0			0
$481$	−4088.00	−	7080.62i	−0.387519	−	0.671203i
$482$	−220.000			−0.0207899
$483$		0			0
$484$	3892.00			0.365515
$485$	7980.00	+	13821.8i	0.747120	+	1.29405i
$486$		0			0
$487$	−3916.00	+	6782.71i	−0.364376	+	0.631117i	−0.988676	−	0.150068i	$-0.952051\pi$
$487$	−3916.00	+	6782.71i	−0.364376	+	0.631117i	0.624300	+	0.781185i	$0.285384\pi$
$488$	1520.00	+	2632.72i	0.140998	+	0.244216i
$489$		0			0
$490$		0			0
$491$	6732.00			0.618759			0.309380	−	0.950939i	$-0.399879\pi$
$491$	6732.00			0.618759			0.309380	+	0.950939i	$0.399879\pi$
$492$		0			0
$493$	−3078.00	+	5331.25i	−0.281189	+	0.487034i
$494$	112.000	−	193.990i	0.0102006	−	0.0176680i
$495$		0			0
$496$	3776.00			0.341829
$497$		0			0
$498$		0			0
$499$	−9334.00	−	16167.0i	−0.837369	−	1.45037i	−0.892087	−	0.451864i	$-0.850759\pi$
$499$	−9334.00	−	16167.0i	−0.837369	−	1.45037i	0.0547176	−	0.998502i	$-0.482574\pi$
$500$	2544.00	−	4406.34i	0.227542	−	0.394115i
$501$		0			0
$502$	1890.00	+	3273.58i	0.168038	+	0.291049i
$503$	6048.00			0.536117			0.268059	−	0.963403i	$-0.413618\pi$
$503$	6048.00			0.536117			0.268059	+	0.963403i	$0.413618\pi$
$504$		0			0
$505$	18000.0			1.58612
$506$	−5760.00	−	9976.61i	−0.506054	−	0.876511i
$507$		0			0
$508$	752.000	−	1302.50i	0.0656784	−	0.113758i
$509$	5664.00	+	9810.34i	0.493227	+	0.854294i	0.999970	−	0.00780356i	$-0.00248398\pi$
$509$	5664.00	+	9810.34i	0.493227	+	0.854294i	−0.506743	+	0.862097i	$0.669151\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−2130.00	+	3689.27i	−0.182783	+	0.316589i
$515$	−2280.00	+	3949.08i	−0.195085	+	0.337897i
$516$		0			0
$517$	−576.000			−0.0489989
$518$		0			0
$519$		0			0
$520$	2688.00	+	4655.75i	0.226686	+	0.392631i
$521$	−2073.00	+	3590.54i	−0.174318	+	0.301928i	−0.939925	−	0.341381i	$-0.889105\pi$
$521$	−2073.00	+	3590.54i	−0.174318	+	0.301928i	0.765607	+	0.643309i	$0.222439\pi$
$522$		0			0
$523$	503.000	+	871.222i	0.0420548	+	0.0728410i	0.886287	−	0.463137i	$-0.153276\pi$
$523$	503.000	+	871.222i	0.0420548	+	0.0728410i	−0.844232	+	0.535978i	$0.819943\pi$
$524$	−8520.00			−0.710301
$525$		0			0
$526$	−9984.00			−0.827610
$527$	−13452.0	−	23299.5i	−1.11191	−	1.92589i
$528$		0			0
$529$	−1116.50	+	1933.83i	−0.0917646	+	0.158941i
$530$	−2088.00	−	3616.52i	−0.171126	−	0.296399i
$531$		0			0
$532$		0			0
$533$	−7056.00			−0.573413
$534$		0			0
$535$	3816.00	−	6609.51i	0.308374	−	0.534119i
$536$	−1936.00	+	3353.25i	−0.156012	+	0.270221i
$537$		0			0
$538$	13632.0			1.09241
$539$		0			0
$540$		0			0
$541$	7361.00	+	12749.6i	0.584980	+	1.01321i	0.994878	+	0.101084i	$0.0322309\pi$
$541$	7361.00	+	12749.6i	0.584980	+	1.01321i	−0.409898	+	0.912131i	$0.634436\pi$
$542$	8192.00	−	14189.0i	0.649219	−	1.12448i
$543$		0			0
$544$	1824.00	+	3159.26i	0.143756	+	0.248993i
$545$	1752.00			0.137702
$546$		0			0
$547$	−13480.0			−1.05368			−0.526840	−	0.849964i	$-0.676623\pi$
$547$	−13480.0			−1.05368			−0.526840	+	0.849964i	$0.676623\pi$
$548$	−156.000	−	270.200i	−0.0121606	−	0.0210627i
$549$		0			0
$550$	−912.000	+	1579.63i	−0.0707051	+	0.122465i
$551$	−54.0000	−	93.5307i	−0.00417509	−	0.00723148i
$552$		0			0
$553$		0			0
$554$	−4828.00			−0.370256
$555$		0			0
$556$	4676.00	−	8099.07i	0.356666	−	0.617764i
$557$	3111.00	−	5388.41i	0.236656	−	0.409900i	−0.723097	−	0.690747i	$-0.757282\pi$
$557$	3111.00	−	5388.41i	0.236656	−	0.409900i	0.959753	+	0.280847i	$0.0906153\pi$
$558$		0			0
$559$	−21056.0			−1.59316
$560$		0			0
$561$		0			0
$562$	−1962.00	−	3398.28i	−0.147263	−	0.255068i
$563$	2463.00	−	4266.04i	0.184375	−	0.319347i	−0.758991	−	0.651101i	$-0.774307\pi$
$563$	2463.00	−	4266.04i	0.184375	−	0.319347i	0.943366	+	0.331755i	$0.107641\pi$
$564$		0			0
$565$	1188.00	+	2057.68i	0.0884594	+	0.153216i
$566$	−10804.0			−0.802343
$567$		0			0
$568$	4608.00			0.340400
$569$	11091.0	+	19210.2i	0.817151	+	1.41535i	0.907773	+	0.419462i	$0.137781\pi$
$569$	11091.0	+	19210.2i	0.817151	+	1.41535i	−0.0906221	+	0.995885i	$0.528886\pi$
$570$		0			0
$571$	−1648.00	+	2854.42i	−0.120782	+	0.209201i	−0.920076	−	0.391739i	$-0.871874\pi$
$571$	−1648.00	+	2854.42i	−0.120782	+	0.209201i	0.799294	+	0.600940i	$0.205207\pi$
$572$	5376.00	+	9311.51i	0.392975	+	0.680653i
$573$		0			0
$574$		0			0
$575$	2280.00			0.165361
$576$		0			0
$577$	12167.0	−	21073.9i	0.877849	−	1.52048i	0.0241523	−	0.999708i	$-0.492311\pi$
$577$	12167.0	−	21073.9i	0.877849	−	1.52048i	0.853697	−	0.520771i	$-0.174355\pi$
$578$	8083.00	−	14000.2i	0.581676	−	1.00749i
$579$		0			0
$580$	2592.00			0.185564
$581$		0			0
$582$		0			0
$583$	−4176.00	−	7233.04i	−0.296659	−	0.513829i
$584$	−4600.00	+	7967.43i	−0.325941	+	0.564546i
$585$		0			0
$586$	4788.00	+	8293.06i	0.337526	+	0.584613i
$587$	−1638.00			−0.115175			−0.0575873	−	0.998340i	$-0.518341\pi$
$587$	−1638.00			−0.115175			−0.0575873	+	0.998340i	$0.518341\pi$
$588$		0			0
$589$	472.000			0.0330194
$590$	−1656.00	−	2868.28i	−0.115553	−	0.200144i
$591$		0			0
$592$	−1168.00	+	2023.04i	−0.0810887	+	0.140450i
$593$	−3723.00	−	6448.43i	−0.257817	−	0.446552i	0.707840	−	0.706373i	$-0.249670\pi$
$593$	−3723.00	−	6448.43i	−0.257817	−	0.446552i	−0.965657	+	0.259821i	$0.916336\pi$
$594$		0			0
$595$		0			0
$596$	4008.00			0.275460
$597$		0			0
$598$	6720.00	−	11639.4i	0.459534	−	0.795936i
$599$	−3252.00	+	5632.63i	−0.221825	+	0.384212i	−0.955362	−	0.295437i	$-0.904535\pi$
$599$	−3252.00	+	5632.63i	−0.221825	+	0.384212i	0.733537	+	0.679649i	$0.237868\pi$
$600$		0			0
$601$	16058.0			1.08988			0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0			1.08988			0.544941	+	0.838474i	$0.316552\pi$
$602$		0			0
$603$		0			0
$604$	5504.00	+	9533.21i	0.370786	+	0.642220i
$605$	−5838.00	+	10111.7i	−0.392311	+	0.679503i
$606$		0			0
$607$	−5104.00	−	8840.39i	−0.341293	−	0.591137i	0.643380	−	0.765547i	$-0.277532\pi$
$607$	−5104.00	−	8840.39i	−0.341293	−	0.591137i	−0.984673	+	0.174410i	$0.944198\pi$
$608$	−64.0000			−0.00426898
$609$		0			0
$610$	−9120.00			−0.605341
$611$	−336.000	−	581.969i	−0.0222473	−	0.0385335i
$612$		0			0
$613$	7487.00	−	12967.9i	0.493307	−	0.854432i	−0.506663	−	0.862144i	$-0.669121\pi$
$613$	7487.00	−	12967.9i	0.493307	−	0.854432i	0.999970	+	0.00771145i	$0.00245465\pi$
$614$	−574.000	−	994.197i	−0.0377276	−	0.0653461i
$615$		0			0
$616$		0			0
$617$	−7254.00			−0.473314			−0.236657	−	0.971593i	$-0.576052\pi$
$617$	−7254.00			−0.473314			−0.236657	+	0.971593i	$0.576052\pi$
$618$		0			0
$619$	−6229.00	+	10788.9i	−0.404466	+	0.700556i	−0.994259	−	0.106998i	$-0.965876\pi$
$619$	−6229.00	+	10788.9i	−0.404466	+	0.700556i	0.589793	+	0.807555i	$0.299209\pi$
$620$	−5664.00	+	9810.34i	−0.366890	+	0.635472i
$621$		0			0
$622$	−17616.0			−1.13559
$623$		0			0
$624$		0			0
$625$	8819.50	+	15275.8i	0.564448	+	0.977653i
$626$	−2770.00	+	4797.78i	−0.176855	+	0.306322i
$627$		0			0
$628$	1040.00	+	1801.33i	0.0660836	+	0.114460i
$629$	16644.0			1.05507
$630$		0			0
$631$	28352.0			1.78871			0.894354	−	0.447359i	$-0.147635\pi$
$631$	28352.0			1.78871			0.894354	+	0.447359i	$0.147635\pi$
$632$	3104.00	+	5376.29i	0.195365	+	0.338382i
$633$		0			0
$634$	−7566.00	+	13104.7i	−0.473950	+	0.820905i
$635$	2256.00	+	3907.51i	0.140987	+	0.244196i
$636$		0			0
$637$		0			0
$638$	5184.00			0.321687
$639$		0			0
$640$	768.000	−	1330.22i	0.0474342	−	0.0821584i
$641$	13695.0	−	23720.4i	0.843869	−	1.46162i	−0.0427309	−	0.999087i	$-0.513606\pi$
$641$	13695.0	−	23720.4i	0.843869	−	1.46162i	0.886600	−	0.462537i	$-0.153061\pi$
$642$		0			0
$643$	−21490.0			−1.31801			−0.659007	−	0.752137i	$-0.729023\pi$
$643$	−21490.0			−1.31801			−0.659007	+	0.752137i	$0.729023\pi$
$644$		0			0
$645$		0			0
$646$	228.000	+	394.908i	0.0138863	+	0.0240518i
$647$	8826.00	−	15287.1i	0.536300	−	0.928898i	−0.462800	−	0.886463i	$-0.653155\pi$
$647$	8826.00	−	15287.1i	0.536300	−	0.928898i	0.999099	−	0.0424353i	$-0.0135116\pi$
$648$		0			0
$649$	−3312.00	−	5736.55i	−0.200320	−	0.346964i
$650$	−2128.00			−0.128411
$651$		0			0
$652$	5120.00			0.307538
$653$	−2391.00	−	4141.33i	−0.143288	−	0.248182i	0.785445	−	0.618932i	$-0.212434\pi$
$653$	−2391.00	−	4141.33i	−0.143288	−	0.248182i	−0.928733	+	0.370749i	$0.879101\pi$
$654$		0			0
$655$	12780.0	−	22135.6i	0.762375	−	1.32047i
$656$	1008.00	+	1745.91i	0.0599936	+	0.103912i
$657$		0			0
$658$		0			0
$659$	27144.0			1.60452			0.802261	−	0.596973i	$-0.203630\pi$
$659$	27144.0			1.60452			0.802261	+	0.596973i	$0.203630\pi$
$660$		0			0
$661$	5930.00	−	10271.1i	0.348941	−	0.604384i	−0.637120	−	0.770764i	$-0.719875\pi$
$661$	5930.00	−	10271.1i	0.348941	−	0.604384i	0.986062	+	0.166380i	$0.0532079\pi$
$662$	−11320.0	+	19606.8i	−0.664599	+	1.15112i
$663$		0			0
$664$	3024.00			0.176738
$665$		0			0
$666$		0			0
$667$	−3240.00	−	5611.84i	−0.188086	−	0.325774i
$668$	3528.00	−	6110.68i	0.204345	−	0.353936i
$669$		0			0
$670$	−5808.00	−	10059.8i	−0.334899	−	0.580063i
$671$	−18240.0			−1.04940
$672$		0			0
$673$	5546.00			0.317656			0.158828	−	0.987306i	$-0.449228\pi$
$673$	5546.00			0.317656			0.158828	+	0.987306i	$0.449228\pi$
$674$	−4786.00	−	8289.60i	−0.273516	−	0.473744i
$675$		0			0
$676$	−1878.00	+	3252.79i	−0.106850	+	0.185070i
$677$	−7440.00	−	12886.5i	−0.422367	−	0.731561i	0.573804	−	0.818993i	$-0.305467\pi$
$677$	−7440.00	−	12886.5i	−0.422367	−	0.731561i	−0.996170	+	0.0874320i	$0.972134\pi$
$678$		0			0
$679$		0			0
$680$	−10944.0			−0.617181
$681$		0			0
$682$	−11328.0	+	19620.7i	−0.636029	+	1.10163i
$683$	10482.0	−	18155.4i	0.587237	−	1.01712i	−0.407356	−	0.913269i	$-0.633549\pi$
$683$	10482.0	−	18155.4i	0.587237	−	1.01712i	0.994593	−	0.103854i	$-0.0331175\pi$
$684$		0			0
$685$	936.000			0.0522084
$686$		0			0
$687$		0			0
$688$	3008.00	+	5210.01i	0.166684	+	0.288706i
$689$	4872.00	−	8438.55i	0.269388	−	0.466594i
$690$		0			0
$691$	−6553.00	−	11350.1i	−0.360764	−	0.624861i	0.627323	−	0.778759i	$-0.284151\pi$
$691$	−6553.00	−	11350.1i	−0.360764	−	0.624861i	−0.988087	+	0.153898i	$0.950817\pi$
$692$	3072.00			0.168757
$693$		0			0
$694$	25296.0			1.38361
$695$	14028.0	+	24297.2i	0.765629	+	1.32611i
$696$		0			0
$697$	7182.00	−	12439.6i	0.390298	−	0.676016i
$698$	9632.00	+	16683.1i	0.522316	+	0.904678i
$699$		0			0
$700$		0			0
$701$	4590.00			0.247307			0.123653	−	0.992325i	$-0.460539\pi$
$701$	4590.00			0.247307			0.123653	+	0.992325i	$0.460539\pi$
$702$		0			0
$703$	−146.000	+	252.879i	−0.00783285	+	0.0135669i
$704$	1536.00	−	2660.43i	0.0822304	−	0.142427i
$705$		0			0
$706$	−6780.00			−0.361429
$707$		0			0
$708$		0			0
$709$	431.000	+	746.514i	0.0228301	+	0.0395429i	0.877215	−	0.480098i	$-0.159399\pi$
$709$	431.000	+	746.514i	0.0228301	+	0.0395429i	−0.854385	+	0.519641i	$0.826066\pi$
$710$	−6912.00	+	11971.9i	−0.365356	+	0.632815i
$711$		0			0
$712$	1560.00	+	2702.00i	0.0821116	+	0.142221i
$713$	28320.0			1.48751
$714$		0			0
$715$	−32256.0			−1.68714
$716$	3624.00	+	6276.95i	0.189155	+	0.327627i
$717$		0			0
$718$	10704.0	−	18539.9i	0.556365	−	0.963652i
$719$	−1770.00	−	3065.73i	−0.0918079	−	0.159016i	0.816464	−	0.577396i	$-0.195931\pi$
$719$	−1770.00	−	3065.73i	−0.0918079	−	0.159016i	−0.908272	+	0.418380i	$0.862598\pi$
$720$		0			0
$721$		0			0
$722$	13710.0			0.706694
$723$		0			0
$724$	896.000	−	1551.92i	0.0459939	−	0.0796638i
$725$	−513.000	+	888.542i	−0.0262791	+	0.0455167i
$726$		0			0
$727$	−4228.00			−0.215692			−0.107846	−	0.994168i	$-0.534395\pi$
$727$	−4228.00			−0.215692			−0.107846	+	0.994168i	$0.534395\pi$
$728$		0			0
$729$		0			0
$730$	−13800.0	−	23902.3i	−0.699672	−	1.21187i
$731$	21432.0	−	37121.3i	1.08439	−	1.87822i
$732$		0			0
$733$	−2710.00	−	4693.86i	−0.136557	−	0.236523i	0.789634	−	0.613578i	$-0.210270\pi$
$733$	−2710.00	−	4693.86i	−0.136557	−	0.236523i	−0.926191	+	0.377054i	$0.876937\pi$
$734$	17168.0			0.863328
$735$		0			0
$736$	−3840.00			−0.192316
$737$	−11616.0	−	20119.5i	−0.580571	−	1.00558i
$738$		0			0
$739$	−640.000	+	1108.51i	−0.0318576	+	0.0551790i	−0.881515	−	0.472157i	$-0.843476\pi$
$739$	−640.000	+	1108.51i	−0.0318576	+	0.0551790i	0.849657	+	0.527336i	$0.176809\pi$
$740$	−3504.00	−	6069.11i	−0.174067	−	0.301493i
$741$		0			0
$742$		0			0
$743$	35712.0			1.76332			0.881660	−	0.471886i	$-0.156427\pi$
$743$	35712.0			1.76332			0.881660	+	0.471886i	$0.156427\pi$
$744$		0			0
$745$	−6012.00	+	10413.1i	−0.295655	+	0.512089i
$746$	−2122.00	+	3675.41i	−0.104145	+	0.180384i
$747$		0			0
$748$	−21888.0			−1.06993
$749$		0			0
$750$		0			0
$751$	−12232.0	−	21186.4i	−0.594344	−	1.02943i	−0.993639	−	0.112611i	$-0.964079\pi$
$751$	−12232.0	−	21186.4i	−0.594344	−	1.02943i	0.399296	−	0.916822i	$-0.369255\pi$
$752$	−96.0000	+	166.277i	−0.00465527	+	0.00806316i
$753$		0			0
$754$	3024.00	+	5237.72i	0.146058	+	0.252980i
$755$	−33024.0			−1.59188
$756$		0			0
$757$	30242.0			1.45200			0.726000	−	0.687695i	$-0.241377\pi$
$757$	30242.0			1.45200			0.726000	+	0.687695i	$0.241377\pi$
$758$	−4912.00	−	8507.83i	−0.235372	−	0.407676i
$759$		0			0
$760$	96.0000	−	166.277i	0.00458196	−	0.00793618i
$761$	−1077.00	−	1865.42i	−0.0513025	−	0.0888586i	0.839234	−	0.543771i	$-0.183004\pi$
$761$	−1077.00	−	1865.42i	−0.0513025	−	0.0888586i	−0.890536	+	0.454912i	$0.849671\pi$
$762$		0			0
$763$		0			0
$764$	8544.00			0.404596
$765$		0			0
$766$	−9060.00	+	15692.4i	−0.427351	+	0.740194i
$767$	3864.00	−	6692.64i	0.181905	−	0.315068i
$768$		0			0
$769$	10262.0			0.481219			0.240609	−	0.970622i	$-0.422653\pi$
$769$	10262.0			0.481219			0.240609	+	0.970622i	$0.422653\pi$
$770$		0			0
$771$		0			0
$772$	−8860.00	−	15346.0i	−0.413055	−	0.715432i
$773$	4542.00	−	7866.97i	0.211338	−	0.366048i	−0.740795	−	0.671731i	$-0.765551\pi$
$773$	4542.00	−	7866.97i	0.211338	−	0.366048i	0.952134	+	0.305682i	$0.0988845\pi$
$774$		0			0
$775$	−2242.00	−	3883.26i	−0.103916	−	0.179988i
$776$	10640.0			0.492208
$777$		0			0
$778$	17988.0			0.828922
$779$	126.000	+	218.238i	0.00579515	+	0.0100375i
$780$		0			0
$781$	−13824.0	+	23943.9i	−0.633370	+	1.09703i
$782$	13680.0	+	23694.5i	0.625570	+	1.08352i
$783$		0			0
$784$		0			0
$785$	−6240.00			−0.283714
$786$		0			0
$787$	9899.00	−	17145.6i	0.448362	−	0.776587i	−0.549917	−	0.835219i	$-0.685341\pi$
$787$	9899.00	−	17145.6i	0.448362	−	0.776587i	0.998280	+	0.0586327i	$0.0186741\pi$
$788$	396.000	−	685.892i	0.0179022	−	0.0310075i
$789$		0			0
$790$	−18624.0			−0.838750
$791$		0			0
$792$		0			0
$793$	−10640.0	−	18429.0i	−0.476466	−	0.825263i
$794$	−12976.0	+	22475.1i	−0.579976	+	1.00455i
$795$		0			0
$796$	4568.00	+	7912.01i	0.203403	+	0.352304i
$797$	−30240.0			−1.34398			−0.671992	−	0.740558i	$-0.734561\pi$
$797$	−30240.0			−1.34398			−0.671992	+	0.740558i	$0.734561\pi$
$798$		0			0
$799$	1368.00			0.0605712
$800$	304.000	+	526.543i	0.0134350	+	0.0232702i
$801$		0			0
$802$	3522.00	−	6100.28i	0.155070	−	0.268589i
$803$	−27600.0	−	47804.6i	−1.21293	−	2.10086i
$804$		0			0
$805$		0			0
$806$	−26432.0			−1.15512
$807$		0			0
$808$	6000.00	−	10392.3i	0.261237	−	0.452475i
$809$	−1173.00	+	2031.70i	−0.0509771	+	0.0882949i	−0.890388	−	0.455202i	$-0.849567\pi$
$809$	−1173.00	+	2031.70i	−0.0509771	+	0.0882949i	0.839411	+	0.543497i	$0.182900\pi$
$810$		0			0
$811$	−29806.0			−1.29054			−0.645271	−	0.763953i	$-0.723256\pi$
$811$	−29806.0			−1.29054			−0.645271	+	0.763953i	$0.723256\pi$
$812$		0			0
$813$		0			0
$814$	−7008.00	−	12138.2i	−0.301757	−	0.522659i
$815$	−7680.00	+	13302.2i	−0.330084	+	0.571723i
$816$		0			0
$817$	376.000	+	651.251i	0.0161011	+	0.0278879i
$818$	−25420.0			−1.08654
$819$		0			0
$820$	−6048.00			−0.257567
$821$	−753.000	−	1304.23i	−0.0320096	−	0.0554423i	0.849577	−	0.527465i	$-0.176857\pi$
$821$	−753.000	−	1304.23i	−0.0320096	−	0.0554423i	−0.881586	+	0.472023i	$0.843524\pi$
$822$		0			0
$823$	10196.0	−	17660.0i	0.431847	−	0.747981i	−0.565185	−	0.824964i	$-0.691195\pi$
$823$	10196.0	−	17660.0i	0.431847	−	0.747981i	0.997032	+	0.0769828i	$0.0245286\pi$
$824$	1520.00	+	2632.72i	0.0642618	+	0.111305i
$825$		0			0
$826$		0			0
$827$	−36108.0			−1.51826			−0.759128	−	0.650941i	$-0.774374\pi$
$827$	−36108.0			−1.51826			−0.759128	+	0.650941i	$0.774374\pi$
$828$		0			0
$829$	6938.00	−	12017.0i	0.290672	−	0.503458i	−0.683297	−	0.730140i	$-0.739455\pi$
$829$	6938.00	−	12017.0i	0.290672	−	0.503458i	0.973969	+	0.226683i	$0.0727880\pi$
$830$	−4536.00	+	7856.58i	−0.189695	+	0.328561i
$831$		0			0
$832$	3584.00			0.149342
$833$		0			0
$834$		0			0
$835$	10584.0	+	18332.0i	0.438652	+	0.759768i
$836$	192.000	−	332.554i	0.00794313	−	0.0137579i
$837$		0			0
$838$	−1638.00	−	2837.10i	−0.0675224	−	0.116952i
$839$	−23436.0			−0.964363			−0.482182	−	0.876071i	$-0.660155\pi$
$839$	−23436.0			−0.964363			−0.482182	+	0.876071i	$0.660155\pi$
$840$		0			0
$841$	−21473.0			−0.880438
$842$	−12850.0	−	22256.9i	−0.525939	−	0.910952i
$843$		0			0
$844$	−8824.00	+	15283.6i	−0.359875	+	0.623322i
$845$	−5634.00	−	9758.37i	−0.229367	−	0.397276i
$846$		0			0
$847$		0			0
$848$	−2784.00			−0.112739
$849$		0			0
$850$	2166.00	−	3751.62i	0.0874037	−	0.151388i
$851$	−8760.00	+	15172.8i	−0.352866	+	0.611182i
$852$		0			0
$853$	8120.00			0.325936			0.162968	−	0.986631i	$-0.447893\pi$
$853$	8120.00			0.325936			0.162968	+	0.986631i	$0.447893\pi$
$854$		0			0
$855$		0			0
$856$	−2544.00	−	4406.34i	−0.101580	−	0.175941i
$857$	−25005.0	+	43309.9i	−0.996680	+	1.72630i	−0.427826	+	0.903861i	$0.640721\pi$
$857$	−25005.0	+	43309.9i	−0.996680	+	1.72630i	−0.568853	+	0.822439i	$0.692613\pi$
$858$		0			0
$859$	−17263.0	−	29900.4i	−0.685688	−	1.18765i	−0.973220	−	0.229875i	$-0.926168\pi$
$859$	−17263.0	−	29900.4i	−0.685688	−	1.18765i	0.287532	−	0.957771i	$-0.407165\pi$
$860$	−18048.0			−0.715618
$861$		0			0
$862$	−16032.0			−0.633471
$863$	−8628.00	−	14944.1i	−0.340325	−	0.589460i	0.644168	−	0.764884i	$-0.277204\pi$
$863$	−8628.00	−	14944.1i	−0.340325	−	0.589460i	−0.984493	+	0.175424i	$0.943870\pi$
$864$		0			0
$865$	−4608.00	+	7981.29i	−0.181129	+	0.313725i
$866$	2198.00	+	3807.05i	0.0862484	+	0.149387i
$867$		0			0
$868$		0			0
$869$	−37248.0			−1.45403
$870$		0			0
$871$	13552.0	−	23472.8i	0.527201	−	0.913139i
$872$	584.000	−	1011.52i	0.0226797	−	0.0392825i
$873$		0			0
$874$	−480.000			−0.0185769
$875$		0			0
$876$		0			0
$877$	−4357.00	−	7546.55i	−0.167760	−	0.290569i	0.769872	−	0.638198i	$-0.220320\pi$
$877$	−4357.00	−	7546.55i	−0.167760	−	0.290569i	−0.937632	+	0.347630i	$0.886987\pi$
$878$	−376.000	+	651.251i	−0.0144526	+	0.0250326i
$879$		0			0
$880$	4608.00	+	7981.29i	0.176518	+	0.305738i
$881$	22806.0			0.872138			0.436069	−	0.899913i	$-0.356370\pi$
$881$	22806.0			0.872138			0.436069	+	0.899913i	$0.356370\pi$
$882$		0			0
$883$	40196.0			1.53194			0.765970	−	0.642876i	$-0.222259\pi$
$883$	40196.0			1.53194			0.765970	+	0.642876i	$0.222259\pi$
$884$	−12768.0	−	22114.8i	−0.485785	−	0.841405i
$885$		0			0
$886$	−7188.00	+	12450.0i	−0.272557	+	0.472083i
$887$	20406.0	+	35344.2i	0.772454	+	1.33793i	0.936215	+	0.351429i	$0.114304\pi$
$887$	20406.0	+	35344.2i	0.772454	+	1.33793i	−0.163761	+	0.986500i	$0.552363\pi$
$888$		0			0
$889$		0			0
$890$	−9360.00			−0.352526
$891$		0			0
$892$	−4144.00	+	7177.62i	−0.155551	+	0.269422i
$893$	−12.0000	+	20.7846i	−0.000449681	+	0.000778869i
$894$		0			0
$895$	−21744.0			−0.812091
$896$		0			0
$897$		0			0
$898$	14670.0	+	25409.2i	0.545149	+	0.944227i
$899$	−6372.00	+	11036.6i	−0.236394	+	0.409446i
$900$		0			0
$901$	9918.00	+	17178.5i	0.366722	+	0.635181i
$902$	−12096.0			−0.446511
$903$		0			0
$904$	1584.00			0.0582777
$905$	2688.00	+	4655.75i	0.0987317	+	0.171008i
$906$		0			0
$907$	6794.00	−	11767.6i	0.248722	−	0.430800i	−0.714449	−	0.699687i	$-0.753323\pi$
$907$	6794.00	−	11767.6i	0.248722	−	0.430800i	0.963172	+	0.268888i	$0.0866560\pi$
$908$	−732.000	−	1267.86i	−0.0267536	−	0.0463386i
$909$		0			0
$910$		0			0
$911$	47304.0			1.72036			0.860182	−	0.509987i	$-0.170350\pi$
$911$	47304.0			1.72036			0.860182	+	0.509987i	$0.170350\pi$
$912$		0			0
$913$	−9072.00	+	15713.2i	−0.328849	+	0.569584i
$914$	−5146.00	+	8913.13i	−0.186230	+	0.322560i
$915$		0			0
$916$	−1504.00			−0.0542506
$917$		0			0
$918$		0			0
$919$	−892.000	−	1544.99i	−0.0320178	−	0.0554565i	0.849572	−	0.527472i	$-0.176860\pi$
$919$	−892.000	−	1544.99i	−0.0320178	−	0.0554565i	−0.881590	+	0.472015i	$0.843527\pi$
$920$	5760.00	−	9976.61i	0.206415	−	0.357521i
$921$		0			0
$922$	1512.00	+	2618.86i	0.0540077	+	0.0935440i
$923$	−32256.0			−1.15029
$924$		0			0
$925$	2774.00			0.0986038
$926$	7184.00	+	12443.1i	0.254947	+	0.441581i
$927$		0			0
$928$	864.000	−	1496.49i	0.0305627	−	0.0529362i
$929$	−17961.0	−	31109.4i	−0.634318	−	1.09867i	−0.986659	−	0.162799i	$-0.947948\pi$
$929$	−17961.0	−	31109.4i	−0.634318	−	1.09867i	0.352341	−	0.935872i	$-0.385386\pi$
$930$		0			0
$931$		0			0
$932$	9048.00			0.318001
$933$		0			0
$934$	16518.0	−	28610.0i	0.578678	−	1.00230i
$935$	32832.0	−	56866.7i	1.14836	−	1.98903i
$936$		0			0
$937$	−26782.0			−0.933756			−0.466878	−	0.884322i	$-0.654621\pi$
$937$	−26782.0			−0.933756			−0.466878	+	0.884322i	$0.654621\pi$
$938$		0			0
$939$		0			0
$940$	−288.000	−	498.831i	−0.00999311	−	0.0173086i
$941$	2022.00	−	3502.21i	0.0700482	−	0.121327i	−0.828874	−	0.559435i	$-0.811018\pi$
$941$	2022.00	−	3502.21i	0.0700482	−	0.121327i	0.898922	+	0.438108i	$0.144351\pi$
$942$		0			0
$943$	7560.00	+	13094.3i	0.261068	+	0.452184i
$944$	−2208.00			−0.0761274
$945$		0			0
$946$	−36096.0			−1.24057
$947$	−1068.00	−	1849.83i	−0.0366477	−	0.0634756i	0.847120	−	0.531402i	$-0.178335\pi$
$947$	−1068.00	−	1849.83i	−0.0366477	−	0.0634756i	−0.883767	+	0.467926i	$0.845001\pi$
$948$		0			0
$949$	32200.0	−	55772.0i	1.10143	−	1.90773i
$950$	38.0000	+	65.8179i	0.00129777	+	0.00224781i
$951$		0			0
$952$		0			0
$953$	15174.0			0.515776			0.257888	−	0.966175i	$-0.416974\pi$
$953$	15174.0			0.515776			0.257888	+	0.966175i	$0.416974\pi$
$954$		0			0
$955$	−12816.0	+	22198.0i	−0.434258	+	0.752156i
$956$	5184.00	−	8978.95i	0.175379	−	0.303766i
$957$		0			0
$958$	20184.0			0.680705
$959$		0			0
$960$		0			0
$961$	−12952.5	−	22434.4i	−0.434779	−	0.753059i
$962$	8176.00	−	14161.2i	0.274017	−	0.474612i
$963$		0			0
$964$	−220.000	−	381.051i	−0.00735033	−	0.0127312i
$965$	53160.0			1.77335
$966$		0			0
$967$	25832.0			0.859050			0.429525	−	0.903055i	$-0.358681\pi$
$967$	25832.0			0.859050			0.429525	+	0.903055i	$0.358681\pi$
$968$	3892.00	+	6741.14i	0.129229	+	0.223831i
$969$		0			0
$970$	−15960.0	+	27643.5i	−0.528294	+	0.915031i
$971$	−18843.0	−	32637.0i	−0.622761	−	1.07865i	−0.988969	−	0.148120i	$-0.952678\pi$
$971$	−18843.0	−	32637.0i	−0.622761	−	1.07865i	0.366209	−	0.930533i	$-0.380656\pi$
$972$		0			0
$973$		0			0
$974$	−15664.0			−0.515305
$975$		0			0
$976$	−3040.00	+	5265.43i	−0.0997008	+	0.172687i
$977$	−27003.0	+	46770.6i	−0.884240	+	1.53155i	−0.0376578	+	0.999291i	$0.511990\pi$
$977$	−27003.0	+	46770.6i	−0.884240	+	1.53155i	−0.846582	+	0.532258i	$0.821344\pi$
$978$		0			0
$979$	−18720.0			−0.611127
$980$		0			0
$981$		0			0
$982$	6732.00	+	11660.2i	0.218765	+	0.378911i
$983$	16638.0	−	28817.9i	0.539847	−	0.935043i	−0.459065	−	0.888403i	$-0.651815\pi$
$983$	16638.0	−	28817.9i	0.539847	−	0.935043i	0.998912	−	0.0466399i	$-0.0148513\pi$
$984$		0			0
$985$	1188.00	+	2057.68i	0.0384293	+	0.0665614i
$986$	−12312.0			−0.397661
$987$		0			0
$988$	448.000			0.0144259
$989$	22560.0	+	39075.1i	0.725345	+	1.25633i
$990$		0			0
$991$	1880.00	−	3256.26i	0.0602625	−	0.104378i	−0.834320	−	0.551280i	$-0.814140\pi$
$991$	1880.00	−	3256.26i	0.0602625	−	0.104378i	0.894583	+	0.446902i	$0.147473\pi$
$992$	3776.00	+	6540.22i	0.120855	+	0.209327i
$993$		0			0
$994$		0			0
$995$	−27408.0			−0.873258
$996$		0			0
$997$	−18262.0	+	31630.7i	−0.580104	+	1.00477i	0.415363	+	0.909656i	$0.363655\pi$
$997$	−18262.0	+	31630.7i	−0.580104	+	1.00477i	−0.995466	+	0.0951132i	$0.969679\pi$
$998$	18668.0	−	32333.9i	0.592109	−	1.02556i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.p.361.1		2
3.2	odd	2		98.4.c.c.67.1		2
7.2	even	3	inner	882.4.g.p.667.1		2
7.3	odd	6		882.4.a.b.1.1		1
7.4	even	3		126.4.a.d.1.1		1
7.5	odd	6		882.4.g.v.667.1		2
7.6	odd	2		882.4.g.v.361.1		2
21.2	odd	6		98.4.c.c.79.1		2
21.5	even	6		98.4.c.b.79.1		2
21.11	odd	6		14.4.a.b.1.1	✓	1
21.17	even	6		98.4.a.e.1.1		1
21.20	even	2		98.4.c.b.67.1		2
28.11	odd	6		1008.4.a.r.1.1		1
84.11	even	6		112.4.a.e.1.1		1
84.59	odd	6		784.4.a.h.1.1		1
105.32	even	12		350.4.c.g.99.2		2
105.53	even	12		350.4.c.g.99.1		2
105.59	even	6		2450.4.a.i.1.1		1
105.74	odd	6		350.4.a.f.1.1		1
168.11	even	6		448.4.a.g.1.1		1
168.53	odd	6		448.4.a.k.1.1		1
231.32	even	6		1694.4.a.b.1.1		1
273.116	odd	6		2366.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.b.1.1	✓	1	21.11	odd	6
98.4.a.e.1.1		1	21.17	even	6
98.4.c.b.67.1		2	21.20	even	2
98.4.c.b.79.1		2	21.5	even	6
98.4.c.c.67.1		2	3.2	odd	2
98.4.c.c.79.1		2	21.2	odd	6
112.4.a.e.1.1		1	84.11	even	6
126.4.a.d.1.1		1	7.4	even	3
350.4.a.f.1.1		1	105.74	odd	6
350.4.c.g.99.1		2	105.53	even	12
350.4.c.g.99.2		2	105.32	even	12
448.4.a.g.1.1		1	168.11	even	6
448.4.a.k.1.1		1	168.53	odd	6
784.4.a.h.1.1		1	84.59	odd	6
882.4.a.b.1.1		1	7.3	odd	6
882.4.g.p.361.1		2	1.1	even	1	trivial
882.4.g.p.667.1		2	7.2	even	3	inner
882.4.g.v.361.1		2	7.6	odd	2
882.4.g.v.667.1		2	7.5	odd	6
1008.4.a.r.1.1		1	28.11	odd	6
1694.4.a.b.1.1		1	231.32	even	6
2366.4.a.c.1.1		1	273.116	odd	6
2450.4.a.i.1.1		1	105.59	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-6.00000 - 10.3923i) q^{5} -8.00000 q^{8} +(12.0000 - 20.7846i) q^{10} +(24.0000 - 41.5692i) q^{11} +56.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-57.0000 + 98.7269i) q^{17} +(-1.00000 - 1.73205i) q^{19} +48.0000 q^{20} +96.0000 q^{22} +(-60.0000 - 103.923i) q^{23} +(-9.50000 + 16.4545i) q^{25} +(56.0000 + 96.9948i) q^{26} +54.0000 q^{29} +(-118.000 + 204.382i) q^{31} +(16.0000 - 27.7128i) q^{32} -228.000 q^{34} +(-73.0000 - 126.440i) q^{37} +(2.00000 - 3.46410i) q^{38} +(48.0000 + 83.1384i) q^{40} -126.000 q^{41} -376.000 q^{43} +(96.0000 + 166.277i) q^{44} +(120.000 - 207.846i) q^{46} +(-6.00000 - 10.3923i) q^{47} -38.0000 q^{50} +(-112.000 + 193.990i) q^{52} +(87.0000 - 150.688i) q^{53} -576.000 q^{55} +(54.0000 + 93.5307i) q^{58} +(69.0000 - 119.512i) q^{59} +(-190.000 - 329.090i) q^{61} -472.000 q^{62} +64.0000 q^{64} +(-336.000 - 581.969i) q^{65} +(242.000 - 419.156i) q^{67} +(-228.000 - 394.908i) q^{68} -576.000 q^{71} +(575.000 - 995.929i) q^{73} +(146.000 - 252.879i) q^{74} +8.00000 q^{76} +(-388.000 - 672.036i) q^{79} +(-96.0000 + 166.277i) q^{80} +(-126.000 - 218.238i) q^{82} -378.000 q^{83} +1368.00 q^{85} +(-376.000 - 651.251i) q^{86} +(-192.000 + 332.554i) q^{88} +(-195.000 - 337.750i) q^{89} +480.000 q^{92} +(12.0000 - 20.7846i) q^{94} +(-12.0000 + 20.7846i) q^{95} -1330.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 12 q^{5} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 12 * q^5 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 12 q^{5} - 16 q^{8} + 24 q^{10} + 48 q^{11} + 112 q^{13} - 16 q^{16} - 114 q^{17} - 2 q^{19} + 96 q^{20} + 192 q^{22} - 120 q^{23} - 19 q^{25} + 112 q^{26} + 108 q^{29} - 236 q^{31} + 32 q^{32} - 456 q^{34} - 146 q^{37} + 4 q^{38} + 96 q^{40} - 252 q^{41} - 752 q^{43} + 192 q^{44} + 240 q^{46} - 12 q^{47} - 76 q^{50} - 224 q^{52} + 174 q^{53} - 1152 q^{55} + 108 q^{58} + 138 q^{59} - 380 q^{61} - 944 q^{62} + 128 q^{64} - 672 q^{65} + 484 q^{67} - 456 q^{68} - 1152 q^{71} + 1150 q^{73} + 292 q^{74} + 16 q^{76} - 776 q^{79} - 192 q^{80} - 252 q^{82} - 756 q^{83} + 2736 q^{85} - 752 q^{86} - 384 q^{88} - 390 q^{89} + 960 q^{92} + 24 q^{94} - 24 q^{95} - 2660 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 12 * q^5 - 16 * q^8 + 24 * q^10 + 48 * q^11 + 112 * q^13 - 16 * q^16 - 114 * q^17 - 2 * q^19 + 96 * q^20 + 192 * q^22 - 120 * q^23 - 19 * q^25 + 112 * q^26 + 108 * q^29 - 236 * q^31 + 32 * q^32 - 456 * q^34 - 146 * q^37 + 4 * q^38 + 96 * q^40 - 252 * q^41 - 752 * q^43 + 192 * q^44 + 240 * q^46 - 12 * q^47 - 76 * q^50 - 224 * q^52 + 174 * q^53 - 1152 * q^55 + 108 * q^58 + 138 * q^59 - 380 * q^61 - 944 * q^62 + 128 * q^64 - 672 * q^65 + 484 * q^67 - 456 * q^68 - 1152 * q^71 + 1150 * q^73 + 292 * q^74 + 16 * q^76 - 776 * q^79 - 192 * q^80 - 252 * q^82 - 756 * q^83 + 2736 * q^85 - 752 * q^86 - 384 * q^88 - 390 * q^89 + 960 * q^92 + 24 * q^94 - 24 * q^95 - 2660 * q^97

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