LMFDB - Embedded newform 882.4.g.bj.667.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	882.667
Dual form			882.4.g.bj.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} -8.00000 q^{8} +(-10.4462 - 18.0934i) q^{10} +(30.5618 + 52.9346i) q^{11} +59.2311 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-10.2311 - 17.7208i) q^{17} +(-40.1693 + 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(-79.1236 + 137.046i) q^{23} +(7.93822 + 13.7494i) q^{25} +(59.2311 - 102.591i) q^{26} +85.1236 q^{29} +(121.747 + 210.872i) q^{31} +(16.0000 + 27.7128i) q^{32} -40.9244 q^{34} +(-145.185 + 251.468i) q^{37} +(80.3387 + 139.151i) q^{38} +(-41.7849 + 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(122.247 - 211.738i) q^{44} +(158.247 + 274.092i) q^{46} +(84.6453 - 146.610i) q^{47} +31.7529 q^{50} +(-118.462 - 205.183i) q^{52} +(-125.056 - 216.603i) q^{53} +638.510 q^{55} +(85.1236 - 147.438i) q^{58} +(402.610 + 697.341i) q^{59} +(16.5858 - 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(309.371 - 535.846i) q^{65} +(138.691 + 240.220i) q^{67} +(-40.9244 + 70.8832i) q^{68} +631.506 q^{71} +(-384.142 - 665.353i) q^{73} +(290.371 + 502.937i) q^{74} +321.355 q^{76} +(209.365 - 362.631i) q^{79} +(83.5698 + 144.747i) q^{80} +(-168.000 + 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(7.62934 - 13.2144i) q^{86} +(-244.494 - 423.476i) q^{88} +(786.048 - 1361.48i) q^{89} +632.988 q^{92} +(-169.291 - 293.220i) q^{94} +(419.618 + 726.799i) q^{95} -1045.16 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8} - 14 q^{10} + 25 q^{11} + 98 q^{13} - 32 q^{16} + 98 q^{17} - 119 q^{19} - 56 q^{20} + 100 q^{22} - 122 q^{23} + 129 q^{25} + 98 q^{26} + 146 q^{29} + 98 q^{31} + 64 q^{32} + 392 q^{34} - 289 q^{37} + 238 q^{38} - 56 q^{40} - 672 q^{41} + 614 q^{43} + 100 q^{44} + 244 q^{46} + 672 q^{47} + 516 q^{50} - 196 q^{52} + 375 q^{53} + 1526 q^{55} + 146 q^{58} + 763 q^{59} - 406 q^{61} + 392 q^{62} + 256 q^{64} + 654 q^{65} + 1041 q^{67} + 392 q^{68} + 3304 q^{71} - 189 q^{73} + 578 q^{74} + 952 q^{76} - 524 q^{79} + 112 q^{80} - 672 q^{82} - 574 q^{83} - 1244 q^{85} + 614 q^{86} - 200 q^{88} + 2394 q^{89} + 976 q^{92} - 1344 q^{94} + 706 q^{95} + 126 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8 - 14 * q^10 + 25 * q^11 + 98 * q^13 - 32 * q^16 + 98 * q^17 - 119 * q^19 - 56 * q^20 + 100 * q^22 - 122 * q^23 + 129 * q^25 + 98 * q^26 + 146 * q^29 + 98 * q^31 + 64 * q^32 + 392 * q^34 - 289 * q^37 + 238 * q^38 - 56 * q^40 - 672 * q^41 + 614 * q^43 + 100 * q^44 + 244 * q^46 + 672 * q^47 + 516 * q^50 - 196 * q^52 + 375 * q^53 + 1526 * q^55 + 146 * q^58 + 763 * q^59 - 406 * q^61 + 392 * q^62 + 256 * q^64 + 654 * q^65 + 1041 * q^67 + 392 * q^68 + 3304 * q^71 - 189 * q^73 + 578 * q^74 + 952 * q^76 - 524 * q^79 + 112 * q^80 - 672 * q^82 - 574 * q^83 - 1244 * q^85 + 614 * q^86 - 200 * q^88 + 2394 * q^89 + 976 * q^92 - 1344 * q^94 + 706 * q^95 + 126 * 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
$5$	5.22311	−	9.04669i	0.467169	−	0.809161i	−0.532127	−	0.846664i	$-0.678607\pi$
$5$	5.22311	−	9.04669i	0.467169	−	0.809161i	0.999296	+	0.0375035i	$0.0119405\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.4462	−	18.0934i	−0.330339	−	0.572163i
$11$	30.5618	+	52.9346i	0.837702	+	1.45094i	0.891811	+	0.452407i	$0.149435\pi$
$11$	30.5618	+	52.9346i	0.837702	+	1.45094i	−0.0541093	+	0.998535i	$0.517232\pi$
$12$		0			0
$13$	59.2311			1.26367			0.631837	−	0.775102i	$-0.282301\pi$
$13$	59.2311			1.26367			0.631837	+	0.775102i	$0.282301\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−10.2311	−	17.7208i	−0.145965	−	0.252819i	0.783767	−	0.621054i	$-0.213295\pi$
$17$	−10.2311	−	17.7208i	−0.145965	−	0.252819i	−0.929733	+	0.368235i	$0.879962\pi$
$18$		0			0
$19$	−40.1693	+	69.5753i	−0.485025	+	0.840088i	−0.999852	−	0.0172061i	$-0.994523\pi$
$19$	−40.1693	+	69.5753i	−0.485025	+	0.840088i	0.514827	+	0.857294i	$0.327856\pi$
$20$	−41.7849			−0.467169
$21$		0			0
$22$	122.247			1.18469
$23$	−79.1236	+	137.046i	−0.717322	+	1.24244i	0.244735	+	0.969590i	$0.421299\pi$
$23$	−79.1236	+	137.046i	−0.717322	+	1.24244i	−0.962057	+	0.272848i	$0.912034\pi$
$24$		0			0
$25$	7.93822	+	13.7494i	0.0635058	+	0.109995i
$26$	59.2311	−	102.591i	0.446776	−	0.773839i
$27$		0			0
$28$		0			0
$29$	85.1236			0.545071			0.272535	−	0.962146i	$-0.412138\pi$
$29$	85.1236			0.545071			0.272535	+	0.962146i	$0.412138\pi$
$30$		0			0
$31$	121.747	+	210.872i	0.705369	+	1.22173i	0.966558	+	0.256447i	$0.0825518\pi$
$31$	121.747	+	210.872i	0.705369	+	1.22173i	−0.261190	+	0.965287i	$0.584115\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	−40.9244			−0.206426
$35$		0			0
$36$		0			0
$37$	−145.185	+	251.468i	−0.645090	+	1.11733i	0.339191	+	0.940718i	$0.389847\pi$
$37$	−145.185	+	251.468i	−0.645090	+	1.11733i	−0.984281	+	0.176611i	$0.943487\pi$
$38$	80.3387	+	139.151i	0.342965	+	0.594032i
$39$		0			0
$40$	−41.7849	+	72.3735i	−0.165169	+	0.286082i
$41$	−168.000			−0.639932			−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000			−0.639932			−0.319966	+	0.947429i	$0.603671\pi$
$42$		0			0
$43$	7.62934			0.0270573			0.0135286	−	0.999908i	$-0.495694\pi$
$43$	7.62934			0.0270573			0.0135286	+	0.999908i	$0.495694\pi$
$44$	122.247	−	211.738i	0.418851	−	0.725471i
$45$		0			0
$46$	158.247	+	274.092i	0.507223	+	0.878536i
$47$	84.6453	−	146.610i	0.262698	−	0.455006i	−0.704260	−	0.709942i	$-0.748721\pi$
$47$	84.6453	−	146.610i	0.262698	−	0.455006i	0.966958	+	0.254936i	$0.0820545\pi$
$48$		0			0
$49$		0			0
$50$	31.7529			0.0898107
$51$		0			0
$52$	−118.462	−	205.183i	−0.315918	−	0.547187i
$53$	−125.056	−	216.603i	−0.324109	−	0.561373i	0.657223	−	0.753696i	$-0.271731\pi$
$53$	−125.056	−	216.603i	−0.324109	−	0.561373i	−0.981332	+	0.192324i	$0.938398\pi$
$54$		0			0
$55$	638.510			1.56539
$56$		0			0
$57$		0			0
$58$	85.1236	−	147.438i	0.192712	−	0.333786i
$59$	402.610	+	697.341i	0.888395	+	1.53875i	0.841772	+	0.539833i	$0.181513\pi$
$59$	402.610	+	697.341i	0.888395	+	1.53875i	0.0466235	+	0.998913i	$0.485154\pi$
$60$		0			0
$61$	16.5858	−	28.7274i	0.0348130	−	0.0602978i	−0.848094	−	0.529846i	$-0.822250\pi$
$61$	16.5858	−	28.7274i	0.0348130	−	0.0602978i	0.882907	+	0.469548i	$0.155583\pi$
$62$	486.988			0.997542
$63$		0			0
$64$	64.0000			0.125000
$65$	309.371	−	535.846i	0.590349	−	1.02252i
$66$		0			0
$67$	138.691	+	240.220i	0.252893	+	0.438023i	0.964321	−	0.264736i	$-0.0852847\pi$
$67$	138.691	+	240.220i	0.252893	+	0.438023i	−0.711428	+	0.702759i	$0.751951\pi$
$68$	−40.9244	+	70.8832i	−0.0729826	+	0.126410i
$69$		0			0
$70$		0			0
$71$	631.506			1.05558			0.527788	−	0.849376i	$-0.323021\pi$
$71$	631.506			1.05558			0.527788	+	0.849376i	$0.323021\pi$
$72$		0			0
$73$	−384.142	−	665.353i	−0.615896	−	1.06676i	−0.990227	−	0.139468i	$-0.955461\pi$
$73$	−384.142	−	665.353i	−0.615896	−	1.06676i	0.374331	−	0.927295i	$-0.377872\pi$
$74$	290.371	+	502.937i	0.456147	+	0.790070i
$75$		0			0
$76$	321.355			0.485025
$77$		0			0
$78$		0			0
$79$	209.365	−	362.631i	0.298169	−	0.516445i	−0.677548	−	0.735479i	$-0.736957\pi$
$79$	209.365	−	362.631i	0.298169	−	0.516445i	0.975717	+	0.219034i	$0.0702906\pi$
$80$	83.5698	+	144.747i	0.116792	+	0.202290i
$81$		0			0
$82$	−168.000	+	290.985i	−0.226250	+	0.391876i
$83$	−761.714			−1.00734			−0.503668	−	0.863897i	$-0.668017\pi$
$83$	−761.714			−1.00734			−0.503668	+	0.863897i	$0.668017\pi$
$84$		0			0
$85$	−213.753			−0.272762
$86$	7.62934	−	13.2144i	0.00956619	−	0.0165691i
$87$		0			0
$88$	−244.494	−	423.476i	−0.296172	−	0.512986i
$89$	786.048	−	1361.48i	0.936190	−	1.62153i	0.163692	−	0.986511i	$-0.447660\pi$
$89$	786.048	−	1361.48i	0.936190	−	1.62153i	0.772498	−	0.635017i	$-0.219007\pi$
$90$		0			0
$91$		0			0
$92$	632.988			0.717322
$93$		0			0
$94$	−169.291	−	293.220i	−0.185755	−	0.321738i
$95$	419.618	+	726.799i	0.453178	+	0.784927i
$96$		0			0
$97$	−1045.16			−1.09402			−0.547012	−	0.837125i	$-0.684235\pi$
$97$	−1045.16			−1.09402			−0.547012	+	0.837125i	$0.684235\pi$
$98$		0			0
$99$		0			0
$100$	31.7529	−	54.9976i	0.0317529	−	0.0549976i
$101$	−487.961	−	845.173i	−0.480732	−	0.832652i	0.519024	−	0.854760i	$-0.326296\pi$
$101$	−487.961	−	845.173i	−0.480732	−	0.832652i	−0.999756	+	0.0221078i	$0.992962\pi$
$102$		0			0
$103$	−321.572	+	556.979i	−0.307626	+	0.532823i	−0.977842	−	0.209342i	$-0.932868\pi$
$103$	−321.572	+	556.979i	−0.307626	+	0.532823i	0.670217	+	0.742165i	$0.266201\pi$
$104$	−473.849			−0.446776
$105$		0			0
$106$	−500.224			−0.458359
$107$	−155.797	+	269.849i	−0.140762	+	0.243806i	−0.927784	−	0.373119i	$-0.878288\pi$
$107$	−155.797	+	269.849i	−0.140762	+	0.243806i	0.787022	+	0.616925i	$0.211622\pi$
$108$		0			0
$109$	932.915	+	1615.86i	0.819790	+	1.41992i	0.905837	+	0.423626i	$0.139243\pi$
$109$	932.915	+	1615.86i	0.819790	+	1.41992i	−0.0860476	+	0.996291i	$0.527424\pi$
$110$	638.510	−	1105.93i	0.553451	−	0.958604i
$111$		0			0
$112$		0			0
$113$	1720.49			1.43231			0.716153	−	0.697944i	$-0.245901\pi$
$113$	1720.49			1.43231			0.716153	+	0.697944i	$0.245901\pi$
$114$		0			0
$115$	826.542	+	1431.61i	0.670221	+	1.16086i
$116$	−170.247	−	294.877i	−0.136268	−	0.236022i
$117$		0			0
$118$	1610.44			1.25638
$119$		0			0
$120$		0			0
$121$	−1202.54	+	2082.87i	−0.903489	+	1.56489i
$122$	−33.1715	−	57.4548i	−0.0246165	−	0.0426370i
$123$		0			0
$124$	486.988	−	843.489i	0.352684	−	0.610867i
$125$	1471.63			1.05301
$126$		0			0
$127$	142.236			0.0993808			0.0496904	−	0.998765i	$-0.484177\pi$
$127$	142.236			0.0993808			0.0496904	+	0.998765i	$0.484177\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−618.741	−	1071.69i	−0.417440	−	0.723027i
$131$	1243.26	−	2153.38i	0.829189	−	1.43620i	−0.0694870	−	0.997583i	$-0.522136\pi$
$131$	1243.26	−	2153.38i	0.829189	−	1.43620i	0.898676	−	0.438614i	$-0.144530\pi$
$132$		0			0
$133$		0			0
$134$	554.764			0.357644
$135$		0			0
$136$	81.8489	+	141.766i	0.0516065	+	0.0893851i
$137$	1298.61	+	2249.25i	0.809835	+	1.40268i	0.912978	+	0.408009i	$0.133777\pi$
$137$	1298.61	+	2249.25i	0.809835	+	1.40268i	−0.103143	+	0.994667i	$0.532890\pi$
$138$		0			0
$139$	−1600.52			−0.976651			−0.488325	−	0.872662i	$-0.662392\pi$
$139$	−1600.52			−0.976651			−0.488325	+	0.872662i	$0.662392\pi$
$140$		0			0
$141$		0			0
$142$	631.506	−	1093.80i	0.373203	−	0.646406i
$143$	1810.21	+	3135.37i	1.05858	+	1.83352i
$144$		0			0
$145$	444.610	−	770.087i	0.254640	−	0.441050i
$146$	−1536.57			−0.871008
$147$		0			0
$148$	1161.48			0.645090
$149$	1468.85	−	2544.13i	0.807605	−	1.39881i	−0.106913	−	0.994268i	$-0.534097\pi$
$149$	1468.85	−	2544.13i	0.807605	−	1.39881i	0.914518	−	0.404545i	$-0.132570\pi$
$150$		0			0
$151$	−911.662	−	1579.05i	−0.491325	−	0.850999i	0.508625	−	0.860988i	$-0.330154\pi$
$151$	−911.662	−	1579.05i	−0.491325	−	0.850999i	−0.999950	+	0.00998867i	$0.996820\pi$
$152$	321.355	−	556.603i	0.171482	−	0.297016i
$153$		0			0
$154$		0			0
$155$	2543.59			1.31811
$156$		0			0
$157$	316.824	+	548.755i	0.161053	+	0.278952i	0.935247	−	0.353997i	$-0.115178\pi$
$157$	316.824	+	548.755i	0.161053	+	0.278952i	−0.774194	+	0.632949i	$0.781844\pi$
$158$	−418.730	−	725.261i	−0.210838	−	0.365182i
$159$		0			0
$160$	334.279			0.165169
$161$		0			0
$162$		0			0
$163$	672.853	−	1165.42i	0.323325	−	0.560015i	−0.657847	−	0.753151i	$-0.728533\pi$
$163$	672.853	−	1165.42i	0.323325	−	0.560015i	0.981172	+	0.193137i	$0.0618660\pi$
$164$	336.000	+	581.969i	0.159983	+	0.277098i
$165$		0			0
$166$	−761.714	+	1319.33i	−0.356147	+	0.616865i
$167$	387.922			0.179750			0.0898751	−	0.995953i	$-0.471353\pi$
$167$	387.922			0.179750			0.0898751	+	0.995953i	$0.471353\pi$
$168$		0			0
$169$	1311.32			0.596870
$170$	−213.753	+	370.231i	−0.0964359	+	0.167032i
$171$		0			0
$172$	−15.2587	−	26.4288i	−0.00676432	−	0.0117161i
$173$	311.330	−	539.239i	0.136821	−	0.236980i	−0.789471	−	0.613788i	$-0.789645\pi$
$173$	311.330	−	539.239i	0.136821	−	0.236980i	0.926291	+	0.376808i	$0.122978\pi$
$174$		0			0
$175$		0			0
$176$	−977.977			−0.418851
$177$		0			0
$178$	−1572.10	−	2722.95i	−0.661986	−	1.14659i
$179$	−224.965	−	389.651i	−0.0939368	−	0.162703i	0.815228	−	0.579141i	$-0.196612\pi$
$179$	−224.965	−	389.651i	−0.0939368	−	0.162703i	−0.909164	+	0.416437i	$0.863279\pi$
$180$		0			0
$181$	−184.353			−0.0757063			−0.0378532	−	0.999283i	$-0.512052\pi$
$181$	−184.353			−0.0757063			−0.0378532	+	0.999283i	$0.512052\pi$
$182$		0			0
$183$		0			0
$184$	632.988	−	1096.37i	0.253612	−	0.439268i
$185$	1516.64	+	2626.89i	0.602732	+	1.04396i
$186$		0			0
$187$	625.362	−	1083.16i	0.244551	−	0.423574i
$188$	−677.163			−0.262698
$189$		0			0
$190$	1678.47			0.640890
$191$	175.483	−	303.945i	0.0664789	−	0.115145i	−0.830870	−	0.556466i	$-0.812157\pi$
$191$	175.483	−	303.945i	0.0664789	−	0.115145i	0.897349	+	0.441321i	$0.145490\pi$
$192$		0			0
$193$	−764.129	−	1323.51i	−0.284991	−	0.493619i	0.687616	−	0.726074i	$-0.258657\pi$
$193$	−764.129	−	1323.51i	−0.284991	−	0.493619i	−0.972607	+	0.232456i	$0.925324\pi$
$194$	−1045.16	+	1810.28i	−0.386796	+	0.669950i
$195$		0			0
$196$		0			0
$197$	−2874.65			−1.03965			−0.519823	−	0.854274i	$-0.674002\pi$
$197$	−2874.65			−1.03965			−0.519823	+	0.854274i	$0.674002\pi$
$198$		0			0
$199$	2474.35	+	4285.70i	0.881418	+	1.52666i	0.849765	+	0.527162i	$0.176744\pi$
$199$	2474.35	+	4285.70i	0.881418	+	1.52666i	0.0316529	+	0.999499i	$0.489923\pi$
$200$	−63.5058	−	109.995i	−0.0224527	−	0.0388892i
$201$		0			0
$202$	−1951.84			−0.679858
$203$		0			0
$204$		0			0
$205$	−877.483	+	1519.84i	−0.298956	+	0.517808i
$206$	643.144	+	1113.96i	0.217524	+	0.376763i
$207$		0			0
$208$	−473.849	+	820.730i	−0.157959	+	0.273593i
$209$	−4910.58			−1.62523
$210$		0			0
$211$	−5280.90			−1.72299			−0.861497	−	0.507762i	$-0.830473\pi$
$211$	−5280.90			−1.72299			−0.861497	+	0.507762i	$0.830473\pi$
$212$	−500.224	+	866.413i	−0.162054	+	0.280686i
$213$		0			0
$214$	311.595	+	539.698i	0.0995335	+	0.172397i
$215$	39.8489	−	69.0203i	0.0126403	−	0.0218937i
$216$		0			0
$217$		0			0
$218$	3731.66			1.15936
$219$		0			0
$220$	−1277.02	−	2211.86i	−0.391349	−	0.677836i
$221$	−606.000	−	1049.62i	−0.184452	−	0.319481i
$222$		0			0
$223$	−3996.57			−1.20013			−0.600067	−	0.799950i	$-0.704859\pi$
$223$	−3996.57			−1.20013			−0.600067	+	0.799950i	$0.704859\pi$
$224$		0			0
$225$		0			0
$226$	1720.49	−	2979.98i	0.506396	−	0.877104i
$227$	−269.296	−	466.434i	−0.0787392	−	0.136380i	0.823967	−	0.566638i	$-0.191756\pi$
$227$	−269.296	−	466.434i	−0.0787392	−	0.136380i	−0.902706	+	0.430257i	$0.858423\pi$
$228$		0			0
$229$	2085.80	−	3612.72i	0.601895	−	1.04251i	−0.390639	−	0.920544i	$-0.627746\pi$
$229$	2085.80	−	3612.72i	0.601895	−	1.04251i	0.992534	−	0.121968i	$-0.0389206\pi$
$230$	3306.17			0.947836
$231$		0			0
$232$	−680.988			−0.192712
$233$	−769.865	+	1333.45i	−0.216461	+	0.374922i	−0.953724	−	0.300684i	$-0.902785\pi$
$233$	−769.865	+	1333.45i	−0.216461	+	0.374922i	0.737262	+	0.675607i	$0.236118\pi$
$234$		0			0
$235$	−884.224	−	1531.52i	−0.245449	−	0.425129i
$236$	1610.44	−	2789.36i	0.444198	−	0.769373i
$237$		0			0
$238$		0			0
$239$	3132.67			0.847848			0.423924	−	0.905698i	$-0.360652\pi$
$239$	3132.67			0.847848			0.423924	+	0.905698i	$0.360652\pi$
$240$		0			0
$241$	1303.35	+	2257.46i	0.348365	+	0.603386i	0.985959	−	0.166987i	$-0.0534037\pi$
$241$	1303.35	+	2257.46i	0.348365	+	0.603386i	−0.637594	+	0.770372i	$0.720070\pi$
$242$	2405.09	+	4165.74i	0.638863	+	1.10654i
$243$		0			0
$244$	−132.686			−0.0348130
$245$		0			0
$246$		0			0
$247$	−2379.27	+	4121.02i	−0.612913	+	1.06160i
$248$	−973.977	−	1686.98i	−0.249385	−	0.431948i
$249$		0			0
$250$	1471.63	−	2548.93i	0.372295	−	0.644834i
$251$	3426.24			0.861603			0.430801	−	0.902447i	$-0.358231\pi$
$251$	3426.24			0.861603			0.430801	+	0.902447i	$0.358231\pi$
$252$		0			0
$253$	−9672.63			−2.40361
$254$	142.236	−	246.359i	0.0351364	−	0.0608581i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2928.72	−	5072.69i	0.710850	−	1.23123i	−0.253688	−	0.967286i	$-0.581644\pi$
$257$	2928.72	−	5072.69i	0.710850	−	1.23123i	0.964538	−	0.263943i	$-0.0850230\pi$
$258$		0			0
$259$		0			0
$260$	−2474.97			−0.590349
$261$		0			0
$262$	−2486.51	−	4306.76i	−0.586325	−	1.01554i
$263$	542.965	+	940.443i	0.127303	+	0.220495i	0.922631	−	0.385684i	$-0.126035\pi$
$263$	542.965	+	940.443i	0.127303	+	0.220495i	−0.795328	+	0.606180i	$0.792701\pi$
$264$		0			0
$265$	−2612.73			−0.605654
$266$		0			0
$267$		0			0
$268$	554.764	−	960.880i	0.126446	−	0.219012i
$269$	−2789.73	−	4831.95i	−0.632315	−	1.09520i	−0.987077	−	0.160245i	$-0.948772\pi$
$269$	−2789.73	−	4831.95i	−0.632315	−	1.09520i	0.354763	−	0.934956i	$-0.384562\pi$
$270$		0			0
$271$	−280.164	+	485.258i	−0.0627997	+	0.108772i	−0.895716	−	0.444627i	$-0.853336\pi$
$271$	−280.164	+	485.258i	−0.0627997	+	0.108772i	0.832916	+	0.553399i	$0.186670\pi$
$272$	327.396			0.0729826
$273$		0			0
$274$	5194.42			1.14528
$275$	−485.212	+	840.413i	−0.106398	+	0.184286i
$276$		0			0
$277$	2254.04	+	3904.11i	0.488924	+	0.846842i	0.999919	−	0.0127421i	$-0.00405606\pi$
$277$	2254.04	+	3904.11i	0.488924	+	0.846842i	−0.510994	+	0.859584i	$0.670723\pi$
$278$	−1600.52	+	2772.19i	−0.345298	+	0.598074i
$279$		0			0
$280$		0			0
$281$	−4329.75			−0.919186			−0.459593	−	0.888130i	$-0.652005\pi$
$281$	−4329.75			−0.919186			−0.459593	+	0.888130i	$0.652005\pi$
$282$		0			0
$283$	−435.526	−	754.353i	−0.0914817	−	0.158451i	0.816653	−	0.577129i	$-0.195827\pi$
$283$	−435.526	−	754.353i	−0.0914817	−	0.158451i	−0.908135	+	0.418678i	$0.862494\pi$
$284$	−1263.01	−	2187.60i	−0.263894	−	0.457078i
$285$		0			0
$286$	7240.83			1.49706
$287$		0			0
$288$		0			0
$289$	2247.15	−	3892.18i	0.457388	−	0.792220i
$290$	−889.220	−	1540.17i	−0.180058	−	0.311869i
$291$		0			0
$292$	−1536.57	+	2661.41i	−0.307948	+	0.533381i
$293$	−1651.91			−0.329372			−0.164686	−	0.986346i	$-0.552661\pi$
$293$	−1651.91			−0.329372			−0.164686	+	0.986346i	$0.552661\pi$
$294$		0			0
$295$	8411.50			1.66012
$296$	1161.48	−	2011.75i	0.228074	−	0.395035i
$297$		0			0
$298$	−2937.71	−	5088.26i	−0.571063	−	0.989110i
$299$	−4686.58	+	8117.39i	−0.906460	+	1.57004i
$300$		0			0
$301$		0			0
$302$	−3646.65			−0.694838
$303$		0			0
$304$	−642.709	−	1113.21i	−0.121256	−	0.210022i
$305$	−173.259	−	300.093i	−0.0325271	−	0.0563386i
$306$		0			0
$307$	−1016.42			−0.188958			−0.0944791	−	0.995527i	$-0.530119\pi$
$307$	−1016.42			−0.188958			−0.0944791	+	0.995527i	$0.530119\pi$
$308$		0			0
$309$		0			0
$310$	2543.59	−	4405.64i	0.466021	−	0.807172i
$311$	−4596.53	−	7961.42i	−0.838087	−	1.45161i	−0.891492	−	0.453037i	$-0.850341\pi$
$311$	−4596.53	−	7961.42i	−0.838087	−	1.45161i	0.0534049	−	0.998573i	$-0.482993\pi$
$312$		0			0
$313$	−3346.30	+	5795.97i	−0.604295	+	1.04667i	0.387868	+	0.921715i	$0.373212\pi$
$313$	−3346.30	+	5795.97i	−0.604295	+	1.04667i	−0.992162	+	0.124954i	$0.960122\pi$
$314$	1267.30			0.227763
$315$		0			0
$316$	−1674.92			−0.298169
$317$	−3526.25	+	6107.64i	−0.624775	+	1.08214i	0.363809	+	0.931473i	$0.381476\pi$
$317$	−3526.25	+	6107.64i	−0.624775	+	1.08214i	−0.988584	+	0.150669i	$0.951857\pi$
$318$		0			0
$319$	2601.53	+	4505.98i	0.456607	+	0.790866i
$320$	334.279	−	578.988i	0.0583962	−	0.101145i
$321$		0			0
$322$		0			0
$323$	1643.91			0.283187
$324$		0			0
$325$	470.190	+	814.393i	0.0802506	+	0.138998i
$326$	−1345.71	−	2330.83i	−0.228625	−	0.395990i
$327$		0			0
$328$	1344.00			0.226250
$329$		0			0
$330$		0			0
$331$	−1570.19	+	2719.64i	−0.260741	+	0.451616i	−0.966439	−	0.256896i	$-0.917300\pi$
$331$	−1570.19	+	2719.64i	−0.260741	+	0.451616i	0.705698	+	0.708513i	$0.250633\pi$
$332$	1523.43	+	2638.65i	0.251834	+	0.436190i
$333$		0			0
$334$	387.922	−	671.900i	0.0635513	−	0.110074i
$335$	2897.60			0.472575
$336$		0			0
$337$	2743.87			0.443526			0.221763	−	0.975101i	$-0.428819\pi$
$337$	2743.87			0.443526			0.221763	+	0.975101i	$0.428819\pi$
$338$	1311.32	−	2271.28i	0.211026	−	0.365507i
$339$		0			0
$340$	427.506	+	740.462i	0.0681905	+	0.118109i
$341$	−7441.62	+	12889.3i	−1.18178	+	2.04690i
$342$		0			0
$343$		0			0
$344$	−61.0347			−0.00956619
$345$		0			0
$346$	−622.660	−	1078.48i	−0.0967468	−	0.167570i
$347$	−5218.45	−	9038.62i	−0.807323	−	1.39832i	−0.914712	−	0.404107i	$-0.867582\pi$
$347$	−5218.45	−	9038.62i	−0.807323	−	1.39832i	0.107389	−	0.994217i	$-0.465751\pi$
$348$		0			0
$349$	2257.01			0.346175			0.173087	−	0.984906i	$-0.444626\pi$
$349$	2257.01			0.346175			0.173087	+	0.984906i	$0.444626\pi$
$350$		0			0
$351$		0			0
$352$	−977.977	+	1693.91i	−0.148086	+	0.256493i
$353$	2808.22	+	4863.98i	0.423418	+	0.733381i	0.996271	−	0.0862770i	$-0.0274970\pi$
$353$	2808.22	+	4863.98i	0.423418	+	0.733381i	−0.572854	+	0.819658i	$0.694164\pi$
$354$		0			0
$355$	3298.42	−	5713.04i	0.493133	−	0.854131i
$356$	−6288.38			−0.936190
$357$		0			0
$358$	−899.861			−0.132847
$359$	397.795	−	689.002i	0.0584815	−	0.101293i	−0.835302	−	0.549791i	$-0.814707\pi$
$359$	397.795	−	689.002i	0.0584815	−	0.101293i	0.893784	+	0.448498i	$0.148041\pi$
$360$		0			0
$361$	202.349	+	350.479i	0.0295013	+	0.0510977i
$362$	−184.353	+	319.309i	−0.0267662	+	0.0463605i
$363$		0			0
$364$		0			0
$365$	−8025.66			−1.15091
$366$		0			0
$367$	4096.99	+	7096.19i	0.582727	+	1.00931i	0.995155	+	0.0983227i	$0.0313477\pi$
$367$	4096.99	+	7096.19i	0.582727	+	1.00931i	−0.412427	+	0.910990i	$0.635319\pi$
$368$	−1265.98	−	2192.74i	−0.179330	−	0.310609i
$369$		0			0
$370$	6066.55			0.852392
$371$		0			0
$372$		0			0
$373$	−7038.69	+	12191.4i	−0.977076	+	1.69235i	−0.304170	+	0.952618i	$0.598379\pi$
$373$	−7038.69	+	12191.4i	−0.977076	+	1.69235i	−0.672906	+	0.739728i	$0.734954\pi$
$374$	−1250.72	−	2166.32i	−0.172923	−	0.299512i
$375$		0			0
$376$	−677.163	+	1172.88i	−0.0928777	+	0.160869i
$377$	5041.96			0.688791
$378$		0			0
$379$	6221.22			0.843173			0.421587	−	0.906788i	$-0.361473\pi$
$379$	6221.22			0.843173			0.421587	+	0.906788i	$0.361473\pi$
$380$	1678.47	−	2907.20i	0.226589	−	0.392463i
$381$		0			0
$382$	−350.965	−	607.890i	−0.0470077	−	0.0814197i
$383$	−5350.71	+	9267.70i	−0.713860	+	1.23644i	0.249537	+	0.968365i	$0.419722\pi$
$383$	−5350.71	+	9267.70i	−0.713860	+	1.23644i	−0.963397	+	0.268077i	$0.913612\pi$
$384$		0			0
$385$		0			0
$386$	−3056.52			−0.403038
$387$		0			0
$388$	2090.33	+	3620.56i	0.273506	+	0.473726i
$389$	−2110.81	−	3656.03i	−0.275121	−	0.476524i	0.695044	−	0.718967i	$-0.255385\pi$
$389$	−2110.81	−	3656.03i	−0.275121	−	0.476524i	−0.970166	+	0.242443i	$0.922051\pi$
$390$		0			0
$391$	3238.09			0.418816
$392$		0			0
$393$		0			0
$394$	−2874.65	+	4979.04i	−0.367570	+	0.636651i
$395$	−2187.07	−	3788.12i	−0.278591	−	0.482534i
$396$		0			0
$397$	−6037.87	+	10457.9i	−0.763305	+	1.32208i	0.177833	+	0.984061i	$0.443091\pi$
$397$	−6037.87	+	10457.9i	−0.763305	+	1.32208i	−0.941138	+	0.338023i	$0.890242\pi$
$398$	9897.41			1.24651
$399$		0			0
$400$	−254.023			−0.0317529
$401$	2753.19	−	4768.66i	0.342862	−	0.593855i	−0.642101	−	0.766620i	$-0.721937\pi$
$401$	2753.19	−	4768.66i	0.342862	−	0.593855i	0.984963	+	0.172766i	$0.0552703\pi$
$402$		0			0
$403$	7211.22	+	12490.2i	0.891356	+	1.54387i
$404$	−1951.84	+	3380.69i	−0.240366	+	0.416326i
$405$		0			0
$406$		0			0
$407$	−17748.5			−2.16157
$408$		0			0
$409$	714.089	+	1236.84i	0.0863311	+	0.149530i	0.905958	−	0.423368i	$-0.139152\pi$
$409$	714.089	+	1236.84i	0.0863311	+	0.149530i	−0.819627	+	0.572898i	$0.805819\pi$
$410$	1754.97	+	3039.69i	0.211394	+	0.366145i
$411$		0			0
$412$	2572.58			0.307626
$413$		0			0
$414$		0			0
$415$	−3978.52	+	6890.99i	−0.470597	+	0.815097i
$416$	947.698	+	1641.46i	0.111694	+	0.193460i
$417$		0			0
$418$	−4910.58	+	8505.38i	−0.574604	+	0.995244i
$419$	−264.960			−0.0308929			−0.0154465	−	0.999881i	$-0.504917\pi$
$419$	−264.960			−0.0308929			−0.0154465	+	0.999881i	$0.504917\pi$
$420$		0			0
$421$	−281.066			−0.0325375			−0.0162688	−	0.999868i	$-0.505179\pi$
$421$	−281.066			−0.0325375			−0.0162688	+	0.999868i	$0.505179\pi$
$422$	−5280.90	+	9146.78i	−0.609171	+	1.05511i
$423$		0			0
$424$	1000.45	+	1732.83i	0.114590	+	0.198475i
$425$	162.434	−	281.343i	0.0185393	−	0.0321110i
$426$		0			0
$427$		0			0
$428$	1246.38			0.140762
$429$		0			0
$430$	−79.6978	−	138.041i	−0.00893806	−	0.0154812i
$431$	893.189	+	1547.05i	0.0998223	+	0.172897i	0.911611	−	0.411054i	$-0.134839\pi$
$431$	893.189	+	1547.05i	0.0998223	+	0.172897i	−0.811789	+	0.583951i	$0.801506\pi$
$432$		0			0
$433$	−184.621			−0.0204904			−0.0102452	−	0.999948i	$-0.503261\pi$
$433$	−184.621			−0.0204904			−0.0102452	+	0.999948i	$0.503261\pi$
$434$		0			0
$435$		0			0
$436$	3731.66	−	6463.43i	0.409895	−	0.709959i
$437$	−6356.68	−	11010.1i	−0.695838	−	1.20523i
$438$		0			0
$439$	5637.32	−	9764.12i	0.612881	−	1.06154i	−0.377872	−	0.925858i	$-0.623344\pi$
$439$	5637.32	−	9764.12i	0.612881	−	1.06154i	0.990752	−	0.135682i	$-0.0433227\pi$
$440$	−5108.08			−0.553451
$441$		0			0
$442$	−2424.00			−0.260855
$443$	−3984.92	+	6902.09i	−0.427380	+	0.740244i	−0.996639	−	0.0819142i	$-0.973897\pi$
$443$	−3984.92	+	6902.09i	−0.427380	+	0.740244i	0.569259	+	0.822158i	$0.307230\pi$
$444$		0			0
$445$	−8211.23	−	14222.3i	−0.874718	−	1.51506i
$446$	−3996.57	+	6922.25i	−0.424311	+	0.734929i
$447$		0			0
$448$		0			0
$449$	8850.37			0.930233			0.465117	−	0.885249i	$-0.346012\pi$
$449$	8850.37			0.930233			0.465117	+	0.885249i	$0.346012\pi$
$450$		0			0
$451$	−5134.38	−	8893.00i	−0.536072	−	0.928504i
$452$	−3440.99	−	5959.97i	−0.358076	−	0.620206i
$453$		0			0
$454$	−1077.18			−0.111354
$455$		0			0
$456$		0			0
$457$	6513.65	−	11282.0i	0.666730	−	1.15481i	−0.312083	−	0.950055i	$-0.601027\pi$
$457$	6513.65	−	11282.0i	0.666730	−	1.15481i	0.978813	−	0.204756i	$-0.0656400\pi$
$458$	−4171.61	−	7225.44i	−0.425604	−	0.737167i
$459$		0			0
$460$	3306.17	−	5726.45i	0.335111	−	0.580429i
$461$	−1261.05			−0.127403			−0.0637016	−	0.997969i	$-0.520291\pi$
$461$	−1261.05			−0.127403			−0.0637016	+	0.997969i	$0.520291\pi$
$462$		0			0
$463$	−4005.47			−0.402052			−0.201026	−	0.979586i	$-0.564427\pi$
$463$	−4005.47			−0.402052			−0.201026	+	0.979586i	$0.564427\pi$
$464$	−680.988	+	1179.51i	−0.0681338	+	0.118011i
$465$		0			0
$466$	1539.73	+	2666.89i	0.153061	+	0.265110i
$467$	8548.91	−	14807.1i	0.847101	−	1.46722i	−0.0366825	−	0.999327i	$-0.511679\pi$
$467$	8548.91	−	14807.1i	0.847101	−	1.46722i	0.883784	−	0.467895i	$-0.154988\pi$
$468$		0			0
$469$		0			0
$470$	−3536.90			−0.347117
$471$		0			0
$472$	−3220.88	−	5578.72i	−0.314095	−	0.544029i
$473$	233.166	+	403.856i	0.0226659	+	0.0392586i
$474$		0			0
$475$	−1275.49			−0.123208
$476$		0			0
$477$		0			0
$478$	3132.67	−	5425.95i	0.299760	−	0.519199i
$479$	5844.26	+	10122.6i	0.557477	+	0.965578i	0.997706	+	0.0676925i	$0.0215637\pi$
$479$	5844.26	+	10122.6i	0.557477	+	0.965578i	−0.440230	+	0.897885i	$0.645103\pi$
$480$		0			0
$481$	−8599.49	+	14894.8i	−0.815183	+	1.41194i
$482$	5213.39			0.492662
$483$		0			0
$484$	9620.36			0.903489
$485$	−5459.01	+	9455.28i	−0.511095	+	0.885242i
$486$		0			0
$487$	4812.40	+	8335.31i	0.447783	+	0.775583i	0.998241	−	0.0592793i	$-0.0188803\pi$
$487$	4812.40	+	8335.31i	0.447783	+	0.775583i	−0.550458	+	0.834863i	$0.685547\pi$
$488$	−132.686	+	229.819i	−0.0123082	+	0.0213185i
$489$		0			0
$490$		0			0
$491$	−6320.63			−0.580949			−0.290475	−	0.956883i	$-0.593813\pi$
$491$	−6320.63			−0.580949			−0.290475	+	0.956883i	$0.593813\pi$
$492$		0			0
$493$	−870.908	−	1508.46i	−0.0795613	−	0.137804i
$494$	4758.55	+	8242.05i	0.433395	+	0.750662i
$495$		0			0
$496$	−3895.91			−0.352684
$497$		0			0
$498$		0			0
$499$	7527.29	−	13037.6i	0.675286	−	1.16963i	−0.301100	−	0.953593i	$-0.597354\pi$
$499$	7527.29	−	13037.6i	0.675286	−	1.16963i	0.976385	−	0.216037i	$-0.0693130\pi$
$500$	−2943.25	−	5097.86i	−0.263253	−	0.455967i
$501$		0			0
$502$	3426.24	−	5934.42i	0.304623	−	0.527622i
$503$	−16559.1			−1.46786			−0.733930	−	0.679225i	$-0.762316\pi$
$503$	−16559.1			−1.46786			−0.733930	+	0.679225i	$0.762316\pi$
$504$		0			0
$505$	−10194.7			−0.898333
$506$	−9672.63	+	16753.5i	−0.849804	+	1.47190i
$507$		0			0
$508$	−284.471	−	492.718i	−0.0248452	−	0.0430332i
$509$	−6669.48	+	11551.9i	−0.580785	+	1.00595i	0.414601	+	0.910003i	$0.363921\pi$
$509$	−6669.48	+	11551.9i	−0.580785	+	1.00595i	−0.995387	+	0.0959462i	$0.969412\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−5857.44	−	10145.4i	−0.502647	−	0.870610i
$515$	3359.21	+	5818.33i	0.287426	+	0.497837i
$516$		0			0
$517$	10347.6			0.880250
$518$		0			0
$519$		0			0
$520$	−2474.97	+	4286.77i	−0.208720	+	0.361514i
$521$	−3591.35	−	6220.40i	−0.301996	−	0.523072i	0.674592	−	0.738191i	$-0.264320\pi$
$521$	−3591.35	−	6220.40i	−0.301996	−	0.523072i	−0.976588	+	0.215118i	$0.930986\pi$
$522$		0			0
$523$	4815.07	−	8339.94i	0.402578	−	0.697285i	−0.591459	−	0.806335i	$-0.701448\pi$
$523$	4815.07	−	8339.94i	0.402578	−	0.697285i	0.994036	+	0.109050i	$0.0347810\pi$
$524$	−9946.04			−0.829189
$525$		0			0
$526$	2171.86			0.180034
$527$	2491.22	−	4314.91i	0.205919	−	0.356661i
$528$		0			0
$529$	−6437.57	−	11150.2i	−0.529101	−	0.916430i
$530$	−2612.73	+	4525.37i	−0.214131	+	0.370886i
$531$		0			0
$532$		0			0
$533$	−9950.83			−0.808664
$534$		0			0
$535$	1627.49	+	2818.90i	0.131519	+	0.227798i
$536$	−1109.53	−	1921.76i	−0.0894111	−	0.154865i
$537$		0			0
$538$	−11158.9			−0.894228
$539$		0			0
$540$		0			0
$541$	−7774.74	+	13466.2i	−0.617860	+	1.07016i	0.372016	+	0.928227i	$0.378667\pi$
$541$	−7774.74	+	13466.2i	−0.617860	+	1.07016i	−0.989875	+	0.141938i	$0.954667\pi$
$542$	560.327	+	970.515i	0.0444061	+	0.0769136i
$543$		0			0
$544$	327.396	−	567.066i	0.0258032	−	0.0446925i
$545$	19490.9			1.53192
$546$		0			0
$547$	−5917.38			−0.462539			−0.231270	−	0.972890i	$-0.574288\pi$
$547$	−5917.38			−0.462539			−0.231270	+	0.972890i	$0.574288\pi$
$548$	5194.42	−	8997.01i	0.404918	−	0.701338i
$549$		0			0
$550$	970.425	+	1680.83i	0.0752346	+	0.130310i
$551$	−3419.36	+	5922.50i	−0.264373	+	0.457907i
$552$		0			0
$553$		0			0
$554$	9016.15			0.691444
$555$		0			0
$556$	3201.04	+	5544.37i	0.244163	+	0.422902i
$557$	−1065.93	−	1846.25i	−0.0810862	−	0.140445i	0.822631	−	0.568576i	$-0.192506\pi$
$557$	−1065.93	−	1846.25i	−0.0810862	−	0.140445i	−0.903717	+	0.428131i	$0.859172\pi$
$558$		0			0
$559$	451.894			0.0341916
$560$		0			0
$561$		0			0
$562$	−4329.75	+	7499.35i	−0.324981	+	0.562884i
$563$	−3687.95	−	6387.72i	−0.276072	−	0.478171i	0.694333	−	0.719654i	$-0.255700\pi$
$563$	−3687.95	−	6387.72i	−0.276072	−	0.478171i	−0.970405	+	0.241483i	$0.922366\pi$
$564$		0			0
$565$	8986.33	−	15564.8i	0.669129	−	1.15897i
$566$	−1742.10			−0.129375
$567$		0			0
$568$	−5052.05			−0.373203
$569$	6350.42	−	10999.3i	0.467880	−	0.810391i	−0.531447	−	0.847092i	$-0.678351\pi$
$569$	6350.42	−	10999.3i	0.467880	−	0.810391i	0.999326	+	0.0367005i	$0.0116847\pi$
$570$		0			0
$571$	3845.06	+	6659.84i	0.281805	+	0.488101i	0.971829	−	0.235686i	$-0.0757335\pi$
$571$	3845.06	+	6659.84i	0.281805	+	0.488101i	−0.690024	+	0.723786i	$0.742400\pi$
$572$	7240.83	−	12541.5i	0.529291	−	0.916759i
$573$		0			0
$574$		0			0
$575$	−2512.40			−0.182216
$576$		0			0
$577$	1547.43	+	2680.23i	0.111647	+	0.193379i	0.916435	−	0.400185i	$-0.131054\pi$
$577$	1547.43	+	2680.23i	0.111647	+	0.193379i	−0.804787	+	0.593563i	$0.797721\pi$
$578$	−4494.30	−	7784.35i	−0.323422	−	0.560184i
$579$		0			0
$580$	−3556.88			−0.254640
$581$		0			0
$582$		0			0
$583$	7643.87	−	13239.6i	0.543013	−	0.940526i
$584$	3073.13	+	5322.82i	0.217752	+	0.377158i
$585$		0			0
$586$	−1651.91	+	2861.20i	−0.116450	+	0.201698i
$587$	9967.83			0.700880			0.350440	−	0.936585i	$-0.386032\pi$
$587$	9967.83			0.700880			0.350440	+	0.936585i	$0.386032\pi$
$588$		0			0
$589$	−19562.0			−1.36849
$590$	8411.50	−	14569.1i	0.586942	−	1.01661i
$591$		0			0
$592$	−2322.97	−	4023.49i	−0.161272	−	0.279332i
$593$	884.864	−	1532.63i	0.0612766	−	0.106134i	−0.833760	−	0.552127i	$-0.813816\pi$
$593$	884.864	−	1532.63i	0.0612766	−	0.106134i	0.895036	+	0.445993i	$0.147149\pi$
$594$		0			0
$595$		0			0
$596$	−11750.8			−0.807605
$597$		0			0
$598$	9373.15	+	16234.8i	0.640964	+	1.11018i
$599$	3173.66	+	5496.95i	0.216481	+	0.374957i	0.953730	−	0.300665i	$-0.0972086\pi$
$599$	3173.66	+	5496.95i	0.216481	+	0.374957i	−0.737248	+	0.675622i	$0.763875\pi$
$600$		0			0
$601$	−22005.7			−1.49356			−0.746781	−	0.665070i	$-0.768401\pi$
$601$	−22005.7			−1.49356			−0.746781	+	0.665070i	$0.768401\pi$
$602$		0			0
$603$		0			0
$604$	−3646.65	+	6316.18i	−0.245662	+	0.425500i
$605$	12562.0	+	21758.1i	0.844165	+	1.46214i
$606$		0			0
$607$	8853.55	−	15334.8i	0.592017	−	1.02540i	−0.401943	−	0.915665i	$-0.631665\pi$
$607$	8853.55	−	15334.8i	0.592017	−	1.02540i	0.993960	−	0.109740i	$-0.0350017\pi$
$608$	−2570.84			−0.171482
$609$		0			0
$610$	−693.035			−0.0460003
$611$	5013.64	−	8683.87i	0.331964	−	0.574979i
$612$		0			0
$613$	−7923.32	−	13723.6i	−0.522055	−	0.904226i	−0.999671	−	0.0256570i	$-0.991832\pi$
$613$	−7923.32	−	13723.6i	−0.522055	−	0.904226i	0.477616	−	0.878569i	$-0.341501\pi$
$614$	−1016.42	+	1760.49i	−0.0668068	+	0.115713i
$615$		0			0
$616$		0			0
$617$	29473.4			1.92311			0.961553	−	0.274621i	$-0.0885524\pi$
$617$	29473.4			1.92311			0.961553	+	0.274621i	$0.0885524\pi$
$618$		0			0
$619$	5763.74	+	9983.08i	0.374255	+	0.648229i	0.990215	−	0.139548i	$-0.0445650\pi$
$619$	5763.74	+	9983.08i	0.374255	+	0.648229i	−0.615960	+	0.787778i	$0.711232\pi$
$620$	−5087.19	−	8811.27i	−0.329527	−	0.570757i
$621$		0			0
$622$	−18386.1			−1.18523
$623$		0			0
$624$		0			0
$625$	6694.19	−	11594.7i	0.428428	−	0.742059i
$626$	6692.61	+	11591.9i	0.427301	+	0.740107i
$627$		0			0
$628$	1267.30	−	2195.02i	0.0805265	−	0.139476i
$629$	5941.63			0.376643
$630$		0			0
$631$	25846.1			1.63062			0.815308	−	0.579027i	$-0.196568\pi$
$631$	25846.1			1.63062			0.815308	+	0.579027i	$0.196568\pi$
$632$	−1674.92	+	2901.04i	−0.105419	+	0.182591i
$633$		0			0
$634$	7052.49	+	12215.3i	0.441783	+	0.765190i
$635$	742.912	−	1286.76i	0.0464277	−	0.0804151i
$636$		0			0
$637$		0			0
$638$	10406.1			0.645739
$639$		0			0
$640$	−668.558	−	1157.98i	−0.0412923	−	0.0715204i
$641$	−2767.39	−	4793.26i	−0.170523	−	0.295355i	0.768080	−	0.640354i	$-0.221212\pi$
$641$	−2767.39	−	4793.26i	−0.170523	−	0.295355i	−0.938603	+	0.344999i	$0.887879\pi$
$642$		0			0
$643$	−1634.56			−0.100250			−0.0501251	−	0.998743i	$-0.515962\pi$
$643$	−1634.56			−0.100250			−0.0501251	+	0.998743i	$0.515962\pi$
$644$		0			0
$645$		0			0
$646$	1643.91	−	2847.33i	0.100122	−	0.173416i
$647$	3769.00	+	6528.10i	0.229018	+	0.396671i	0.957517	−	0.288375i	$-0.0931151\pi$
$647$	3769.00	+	6528.10i	0.229018	+	0.396671i	−0.728499	+	0.685047i	$0.759782\pi$
$648$		0			0
$649$	−24608.9	+	42623.9i	−1.48842	+	2.57802i
$650$	1880.76			0.113491
$651$		0			0
$652$	−5382.83			−0.323325
$653$	6656.09	−	11528.7i	0.398887	−	0.690892i	−0.594702	−	0.803946i	$-0.702730\pi$
$653$	6656.09	−	11528.7i	0.398887	−	0.690892i	0.993589	+	0.113054i	$0.0360634\pi$
$654$		0			0
$655$	−12987.3	−	22494.7i	−0.774743	−	1.34189i
$656$	1344.00	−	2327.88i	0.0799914	−	0.138549i
$657$		0			0
$658$		0			0
$659$	10962.0			0.647981			0.323991	−	0.946060i	$-0.394975\pi$
$659$	10962.0			0.647981			0.323991	+	0.946060i	$0.394975\pi$
$660$		0			0
$661$	−11816.3	−	20466.4i	−0.695309	−	1.20431i	−0.970076	−	0.242800i	$-0.921934\pi$
$661$	−11816.3	−	20466.4i	−0.695309	−	1.20431i	0.274767	−	0.961511i	$-0.411399\pi$
$662$	3140.37	+	5439.28i	0.184372	+	0.319341i
$663$		0			0
$664$	6093.71			0.356147
$665$		0			0
$666$		0			0
$667$	−6735.28	+	11665.8i	−0.390991	+	0.677216i
$668$	−775.843	−	1343.80i	−0.0449376	−	0.0778341i
$669$		0			0
$670$	2897.60	−	5018.78i	0.167080	−	0.289392i
$671$	2027.56			0.116652
$672$		0			0
$673$	23483.0			1.34503			0.672513	−	0.740085i	$-0.265215\pi$
$673$	23483.0			1.34503			0.672513	+	0.740085i	$0.265215\pi$
$674$	2743.87	−	4752.53i	0.156810	−	0.271603i
$675$		0			0
$676$	−2622.65	−	4542.56i	−0.149218	−	0.258452i
$677$	12336.2	−	21367.0i	0.700325	−	1.21300i	−0.268028	−	0.963411i	$-0.586372\pi$
$677$	12336.2	−	21367.0i	0.700325	−	1.21300i	0.968352	−	0.249587i	$-0.0802948\pi$
$678$		0			0
$679$		0			0
$680$	1710.02			0.0964359
$681$		0			0
$682$	14883.2	+	25778.5i	0.835643	+	1.44738i
$683$	−4469.73	−	7741.80i	−0.250409	−	0.433721i	0.713229	−	0.700931i	$-0.247232\pi$
$683$	−4469.73	−	7741.80i	−0.250409	−	0.433721i	−0.963638	+	0.267209i	$0.913898\pi$
$684$		0			0
$685$	27131.1			1.51332
$686$		0			0
$687$		0			0
$688$	−61.0347	+	105.715i	−0.00338216	+	0.00585807i
$689$	−7407.21	−	12829.7i	−0.409568	−	0.709392i
$690$		0			0
$691$	7555.03	−	13085.7i	0.415929	−	0.720410i	−0.579597	−	0.814904i	$-0.696790\pi$
$691$	7555.03	−	13085.7i	0.415929	−	0.720410i	0.995525	+	0.0944937i	$0.0301232\pi$
$692$	−2490.64			−0.136821
$693$		0			0
$694$	−20873.8			−1.14173
$695$	−8359.70	+	14479.4i	−0.456261	+	0.790268i
$696$		0			0
$697$	1718.83	+	2977.09i	0.0934077	+	0.161787i
$698$	2257.01	−	3909.26i	0.122391	−	0.211988i
$699$		0			0
$700$		0			0
$701$	18353.3			0.988865			0.494432	−	0.869216i	$-0.335376\pi$
$701$	18353.3			0.988865			0.494432	+	0.869216i	$0.335376\pi$
$702$		0			0
$703$	−11664.0	−	20202.6i	−0.625769	−	1.08386i
$704$	1955.95	+	3387.81i	0.104713	+	0.181368i
$705$		0			0
$706$	11232.9			0.598803
$707$		0			0
$708$		0			0
$709$	5036.85	−	8724.07i	0.266802	−	0.462115i	−0.701232	−	0.712933i	$-0.747366\pi$
$709$	5036.85	−	8724.07i	0.266802	−	0.462115i	0.968034	+	0.250818i	$0.0806997\pi$
$710$	−6596.85	−	11426.1i	−0.348698	−	0.603962i
$711$		0			0
$712$	−6288.38	+	10891.8i	−0.330993	+	0.573297i
$713$	−38532.3			−2.02391
$714$		0			0
$715$	37819.7			1.97815
$716$	−899.861	+	1558.61i	−0.0469684	+	0.0813517i
$717$		0			0
$718$	−795.591	−	1378.00i	−0.0413526	−	0.0716249i
$719$	9944.63	−	17224.6i	0.515817	−	0.893420i	−0.484015	−	0.875060i	$-0.660822\pi$
$719$	9944.63	−	17224.6i	0.515817	−	0.893420i	0.999831	−	0.0183607i	$-0.00584472\pi$
$720$		0			0
$721$		0			0
$722$	809.397			0.0417211
$723$		0			0
$724$	368.706	+	638.617i	0.0189266	+	0.0327818i
$725$	675.730	+	1170.40i	0.0346151	+	0.0599552i
$726$		0			0
$727$	−13403.5			−0.683780			−0.341890	−	0.939740i	$-0.611067\pi$
$727$	−13403.5			−0.683780			−0.341890	+	0.939740i	$0.611067\pi$
$728$		0			0
$729$		0			0
$730$	−8025.66	+	13900.9i	−0.406908	+	0.704786i
$731$	−78.0566	−	135.198i	−0.00394942	−	0.00684060i
$732$		0			0
$733$	6627.50	−	11479.2i	0.333960	−	0.578435i	−0.649325	−	0.760511i	$-0.724948\pi$
$733$	6627.50	−	11479.2i	0.333960	−	0.578435i	0.983284	+	0.182076i	$0.0582817\pi$
$734$	16387.9			0.824101
$735$		0			0
$736$	−5063.91			−0.253612
$737$	−8477.29	+	14683.1i	−0.423698	+	0.733866i
$738$		0			0
$739$	−7710.19	−	13354.4i	−0.383794	−	0.664751i	0.607807	−	0.794085i	$-0.292049\pi$
$739$	−7710.19	−	13354.4i	−0.383794	−	0.664751i	−0.991601	+	0.129334i	$0.958716\pi$
$740$	6066.55	−	10507.6i	0.301366	−	0.521981i
$741$		0			0
$742$		0			0
$743$	943.019			0.0465626			0.0232813	−	0.999729i	$-0.492589\pi$
$743$	943.019			0.0465626			0.0232813	+	0.999729i	$0.492589\pi$
$744$		0			0
$745$	−15344.0	−	26576.5i	−0.754576	−	1.30696i
$746$	14077.4	+	24382.7i	0.690897	+	1.19667i
$747$		0			0
$748$	−5002.89			−0.244551
$749$		0			0
$750$		0			0
$751$	14297.9	−	24764.7i	0.694726	−	1.20330i	−0.275547	−	0.961287i	$-0.588859\pi$
$751$	14297.9	−	24764.7i	0.694726	−	1.20330i	0.970273	−	0.242013i	$-0.0778076\pi$
$752$	1354.33	+	2345.76i	0.0656744	+	0.113751i
$753$		0			0
$754$	5041.96	−	8732.94i	0.243524	−	0.421797i
$755$	−19046.9			−0.918127
$756$		0			0
$757$	−28984.4			−1.39162			−0.695810	−	0.718226i	$-0.744955\pi$
$757$	−28984.4			−1.39162			−0.695810	+	0.718226i	$0.744955\pi$
$758$	6221.22	−	10775.5i	0.298107	−	0.516336i
$759$		0			0
$760$	−3356.94	−	5814.39i	−0.160222	−	0.277513i
$761$	4465.05	−	7733.70i	0.212691	−	0.368392i	−0.739865	−	0.672756i	$-0.765110\pi$
$761$	4465.05	−	7733.70i	0.212691	−	0.368392i	0.952556	+	0.304364i	$0.0984438\pi$
$762$		0			0
$763$		0			0
$764$	−1403.86			−0.0664789
$765$		0			0
$766$	10701.4	+	18535.4i	0.504776	+	0.874297i
$767$	23847.0	+	41304.3i	1.12264	+	1.94447i
$768$		0			0
$769$	−2373.15			−0.111285			−0.0556424	−	0.998451i	$-0.517721\pi$
$769$	−2373.15			−0.111285			−0.0556424	+	0.998451i	$0.517721\pi$
$770$		0			0
$771$		0			0
$772$	−3056.52	+	5294.04i	−0.142495	+	0.246809i
$773$	13988.5	+	24228.8i	0.650881	+	1.12736i	0.982909	+	0.184089i	$0.0589336\pi$
$773$	13988.5	+	24228.8i	0.650881	+	1.12736i	−0.332029	+	0.943269i	$0.607733\pi$
$774$		0			0
$775$	−1932.91	+	3347.90i	−0.0895900	+	0.155174i
$776$	8361.32			0.386796
$777$		0			0
$778$	−8443.23			−0.389080
$779$	6748.45	−	11688.7i	0.310383	−	0.537599i
$780$		0			0
$781$	19299.9	+	33428.5i	0.884259	+	1.53158i
$782$	3238.09	−	5608.53i	0.148074	−	0.256471i
$783$		0			0
$784$		0			0
$785$	6619.23			0.300956
$786$		0			0
$787$	17180.5	+	29757.4i	0.778167	+	1.34782i	0.932997	+	0.359883i	$0.117183\pi$
$787$	17180.5	+	29757.4i	0.778167	+	1.34782i	−0.154831	+	0.987941i	$0.549483\pi$
$788$	5749.30	+	9958.08i	0.259911	+	0.450180i
$789$		0			0
$790$	−8748.29			−0.393987
$791$		0			0
$792$		0			0
$793$	982.394	−	1701.56i	0.0439922	−	0.0761968i
$794$	12075.7	+	20915.8i	0.539738	+	0.934854i
$795$		0			0
$796$	9897.41	−	17142.8i	0.440709	−	0.763330i
$797$	10399.5			0.462196			0.231098	−	0.972930i	$-0.425768\pi$
$797$	10399.5			0.462196			0.231098	+	0.972930i	$0.425768\pi$
$798$		0			0
$799$	−3464.06			−0.153379
$800$	−254.023	+	439.981i	−0.0112263	+	0.0194446i
$801$		0			0
$802$	−5506.38	−	9537.33i	−0.242440	−	0.419919i
$803$	23480.1	−	40668.7i	1.03187	−	1.78726i
$804$		0			0
$805$		0			0
$806$	28844.9			1.26057
$807$		0			0
$808$	3903.69	+	6761.38i	0.169964	+	0.294387i
$809$	8971.53	+	15539.1i	0.389891	+	0.675312i	0.992435	−	0.122775i	$-0.0391792\pi$
$809$	8971.53	+	15539.1i	0.389891	+	0.675312i	−0.602543	+	0.798086i	$0.705846\pi$
$810$		0			0
$811$	571.663			0.0247519			0.0123760	−	0.999923i	$-0.496061\pi$
$811$	571.663			0.0247519			0.0123760	+	0.999923i	$0.496061\pi$
$812$		0			0
$813$		0			0
$814$	−17748.5	+	30741.3i	−0.764231	+	1.32369i
$815$	−7028.78	−	12174.2i	−0.302095	−	0.523244i
$816$		0			0
$817$	−306.465	+	530.814i	−0.0131235	+	0.0227305i
$818$	2856.36			0.122091
$819$		0			0
$820$	7019.86			0.298956
$821$	−6947.84	+	12034.0i	−0.295349	+	0.511559i	−0.975066	−	0.221915i	$-0.928769\pi$
$821$	−6947.84	+	12034.0i	−0.295349	+	0.511559i	0.679717	+	0.733474i	$0.262103\pi$
$822$		0			0
$823$	10814.6	+	18731.5i	0.458049	+	0.793364i	0.998858	−	0.0477816i	$-0.0152152\pi$
$823$	10814.6	+	18731.5i	0.458049	+	0.793364i	−0.540809	+	0.841145i	$0.681882\pi$
$824$	2572.58	−	4455.83i	0.108762	−	0.188381i
$825$		0			0
$826$		0			0
$827$	4700.10			0.197628			0.0988140	−	0.995106i	$-0.468495\pi$
$827$	4700.10			0.197628			0.0988140	+	0.995106i	$0.468495\pi$
$828$		0			0
$829$	−19055.4	−	33004.9i	−0.798337	−	1.38276i	−0.920698	−	0.390275i	$-0.872380\pi$
$829$	−19055.4	−	33004.9i	−0.798337	−	1.38276i	0.122361	−	0.992486i	$-0.460953\pi$
$830$	7957.03	+	13782.0i	0.332762	+	0.576361i
$831$		0			0
$832$	3790.79			0.157959
$833$		0			0
$834$		0			0
$835$	2026.16	−	3509.41i	0.0839738	−	0.145447i
$836$	9821.17	+	17010.8i	0.406307	+	0.703744i
$837$		0			0
$838$	−264.960	+	458.924i	−0.0109223	+	0.0189180i
$839$	−20080.2			−0.826277			−0.413138	−	0.910668i	$-0.635567\pi$
$839$	−20080.2			−0.826277			−0.413138	+	0.910668i	$0.635567\pi$
$840$		0			0
$841$	−17143.0			−0.702898
$842$	−281.066	+	486.820i	−0.0115038	+	0.0199251i
$843$		0			0
$844$	10561.8	+	18293.6i	0.430749	+	0.746079i
$845$	6849.19	−	11863.1i	0.278840	−	0.482964i
$846$		0			0
$847$		0			0
$848$	4001.79			0.162054
$849$		0			0
$850$	−324.867	−	562.687i	−0.0131092	−	0.0227059i
$851$	−22975.2	−	39794.1i	−0.925474	−	1.60297i
$852$		0			0
$853$	34906.8			1.40116			0.700578	−	0.713576i	$-0.252926\pi$
$853$	34906.8			1.40116			0.700578	+	0.713576i	$0.252926\pi$
$854$		0			0
$855$		0			0
$856$	1246.38	−	2158.79i	0.0497668	−	0.0861985i
$857$	24023.4	+	41609.7i	0.957553	+	1.65853i	0.728414	+	0.685137i	$0.240258\pi$
$857$	24023.4	+	41609.7i	0.957553	+	1.65853i	0.229139	+	0.973394i	$0.426409\pi$
$858$		0			0
$859$	−17603.1	+	30489.5i	−0.699198	+	1.21105i	0.269547	+	0.962987i	$0.413126\pi$
$859$	−17603.1	+	30489.5i	−0.699198	+	1.21105i	−0.968745	+	0.248059i	$0.920207\pi$
$860$	−318.791			−0.0126403
$861$		0			0
$862$	3572.76			0.141170
$863$	17928.8	−	31053.7i	0.707190	−	1.22489i	−0.258705	−	0.965956i	$-0.583296\pi$
$863$	17928.8	−	31053.7i	0.707190	−	1.22489i	0.965895	−	0.258933i	$-0.0833708\pi$
$864$		0			0
$865$	−3252.22	−	5633.01i	−0.127837	−	0.221420i
$866$	−184.621	+	319.773i	−0.00724444	+	0.0125477i
$867$		0			0
$868$		0			0
$869$	25594.3			0.999109
$870$		0			0
$871$	8214.83	+	14228.5i	0.319574	+	0.553518i
$872$	−7463.32	−	12926.9i	−0.289839	−	0.502017i
$873$		0			0
$874$	−25426.7			−0.984064
$875$		0			0
$876$		0			0
$877$	−3683.09	+	6379.30i	−0.141812	+	0.245625i	−0.928179	−	0.372134i	$-0.878626\pi$
$877$	−3683.09	+	6379.30i	−0.141812	+	0.245625i	0.786367	+	0.617760i	$0.211959\pi$
$878$	−11274.6	−	19528.2i	−0.433372	−	0.750622i
$879$		0			0
$880$	−5108.08	+	8847.46i	−0.195674	+	0.338918i
$881$	−3628.00			−0.138741			−0.0693703	−	0.997591i	$-0.522099\pi$
$881$	−3628.00			−0.138741			−0.0693703	+	0.997591i	$0.522099\pi$
$882$		0			0
$883$	25123.0			0.957483			0.478741	−	0.877956i	$-0.341093\pi$
$883$	25123.0			0.957483			0.478741	+	0.877956i	$0.341093\pi$
$884$	−2424.00	+	4198.49i	−0.0922262	+	0.159740i
$885$		0			0
$886$	7969.84	+	13804.2i	0.302203	+	0.523431i
$887$	−7887.38	+	13661.3i	−0.298571	+	0.517140i	−0.975809	−	0.218624i	$-0.929843\pi$
$887$	−7887.38	+	13661.3i	−0.298571	+	0.517140i	0.677238	+	0.735764i	$0.263177\pi$
$888$		0			0
$889$		0			0
$890$	−32844.9			−1.23704
$891$		0			0
$892$	7993.13	+	13844.5i	0.300033	+	0.519673i
$893$	6800.29	+	11778.5i	0.254830	+	0.441378i
$894$		0			0
$895$	−4700.07			−0.175538
$896$		0			0
$897$		0			0
$898$	8850.37	−	15329.3i	0.328887	−	0.569649i
$899$	10363.5	+	17950.2i	0.384476	+	0.665931i
$900$		0			0
$901$	−2558.92	+	4432.19i	−0.0946172	+	0.163882i
$902$	−20537.5			−0.758120
$903$		0			0
$904$	−13764.0			−0.506396
$905$	−962.896	+	1667.78i	−0.0353677	+	0.0612586i
$906$		0			0
$907$	2556.99	+	4428.84i	0.0936092	+	0.162136i	0.909027	−	0.416737i	$-0.136826\pi$
$907$	2556.99	+	4428.84i	0.0936092	+	0.162136i	−0.815418	+	0.578872i	$0.803493\pi$
$908$	−1077.18	+	1865.74i	−0.0393696	+	0.0681902i
$909$		0			0
$910$		0			0
$911$	10279.1			0.373834			0.186917	−	0.982376i	$-0.440150\pi$
$911$	10279.1			0.373834			0.186917	+	0.982376i	$0.440150\pi$
$912$		0			0
$913$	−23279.3	−	40321.0i	−0.843848	−	1.46159i
$914$	−13027.3	−	22563.9i	−0.471449	−	0.816574i
$915$		0			0
$916$	−16686.4			−0.601895
$917$		0			0
$918$		0			0
$919$	19461.0	−	33707.4i	0.698540	−	1.20991i	−0.270433	−	0.962739i	$-0.587167\pi$
$919$	19461.0	−	33707.4i	0.698540	−	1.20991i	0.968973	−	0.247168i	$-0.0794999\pi$
$920$	−6612.34	−	11452.9i	−0.236959	−	0.410425i
$921$		0			0
$922$	−1261.05	+	2184.20i	−0.0450439	+	0.0780182i
$923$	37404.8			1.33390
$924$		0			0
$925$	−4610.05			−0.163868
$926$	−4005.47	+	6937.67i	−0.142147	+	0.246205i
$927$		0			0
$928$	1361.98	+	2359.01i	0.0481779	+	0.0834466i
$929$	−7483.82	+	12962.4i	−0.264302	+	0.457784i	−0.967380	−	0.253328i	$-0.918475\pi$
$929$	−7483.82	+	12962.4i	−0.264302	+	0.457784i	0.703079	+	0.711112i	$0.251808\pi$
$930$		0			0
$931$		0			0
$932$	6158.92			0.216461
$933$		0			0
$934$	−17097.8	−	29614.3i	−0.598991	−	1.03748i
$935$	−6532.67	−	11314.9i	−0.228493	−	0.395762i
$936$		0			0
$937$	22353.0			0.779339			0.389669	−	0.920955i	$-0.372589\pi$
$937$	22353.0			0.779339			0.389669	+	0.920955i	$0.372589\pi$
$938$		0			0
$939$		0			0
$940$	−3536.90	+	6126.08i	−0.122724	+	0.212565i
$941$	−6690.77	−	11588.7i	−0.231788	−	0.401469i	0.726546	−	0.687118i	$-0.241124\pi$
$941$	−6690.77	−	11588.7i	−0.231788	−	0.401469i	−0.958334	+	0.285649i	$0.907791\pi$
$942$		0			0
$943$	13292.8	−	23023.7i	0.459037	−	0.795075i
$944$	−12883.5			−0.444198
$945$		0			0
$946$	932.665			0.0320545
$947$	316.888	−	548.867i	0.0108738	−	0.0188340i	−0.860537	−	0.509387i	$-0.829872\pi$
$947$	316.888	−	548.867i	0.0108738	−	0.0188340i	0.871411	+	0.490553i	$0.163205\pi$
$948$		0			0
$949$	−22753.1	−	39409.6i	−0.778291	−	1.34804i
$950$	−1275.49	+	2209.22i	−0.0435605	+	0.0754489i
$951$		0			0
$952$		0			0
$953$	−49340.0			−1.67710			−0.838551	−	0.544823i	$-0.816597\pi$
$953$	−49340.0			−1.67710			−0.838551	+	0.544823i	$0.816597\pi$
$954$		0			0
$955$	−1833.13	−	3175.08i	−0.0621138	−	0.107584i
$956$	−6265.34	−	10851.9i	−0.211962	−	0.367129i
$957$		0			0
$958$	23377.1			0.788391
$959$		0			0
$960$		0			0
$961$	−14749.2	+	25546.4i	−0.495090	+	0.857520i
$962$	17199.0	+	29789.5i	0.576421	+	0.998391i
$963$		0			0
$964$	5213.39	−	9029.85i	0.174182	−	0.301693i
$965$	−15964.5			−0.532556
$966$		0			0
$967$	−3340.71			−0.111096			−0.0555480	−	0.998456i	$-0.517691\pi$
$967$	−3340.71			−0.111096			−0.0555480	+	0.998456i	$0.517691\pi$
$968$	9620.36	−	16662.9i	0.319432	−	0.553272i
$969$		0			0
$970$	10918.0	+	18910.6i	0.361398	+	0.625960i
$971$	−2435.20	+	4217.89i	−0.0804833	+	0.139401i	−0.903458	−	0.428677i	$-0.858980\pi$
$971$	−2435.20	+	4217.89i	−0.0804833	+	0.139401i	0.822974	+	0.568079i	$0.192313\pi$
$972$		0			0
$973$		0			0
$974$	19249.6			0.633261
$975$		0			0
$976$	265.372	+	459.638i	0.00870324	+	0.0150745i
$977$	3420.67	+	5924.78i	0.112013	+	0.194013i	0.916582	−	0.399847i	$-0.130937\pi$
$977$	3420.67	+	5924.78i	0.112013	+	0.194013i	−0.804569	+	0.593860i	$0.797603\pi$
$978$		0			0
$979$	96092.1			3.13699
$980$		0			0
$981$		0			0
$982$	−6320.63	+	10947.7i	−0.205397	+	0.355757i
$983$	5344.94	+	9257.71i	0.173425	+	0.300382i	0.939615	−	0.342233i	$-0.111183\pi$
$983$	5344.94	+	9257.71i	0.173425	+	0.300382i	−0.766190	+	0.642614i	$0.777850\pi$
$984$		0			0
$985$	−15014.6	+	26006.1i	−0.485691	+	0.841241i
$986$	−3483.63			−0.112517
$987$		0			0
$988$	19034.2			0.612913
$989$	−603.660	+	1045.57i	−0.0194088	+	0.0336170i
$990$		0			0
$991$	−3732.84	−	6465.48i	−0.119655	−	0.207248i	0.799976	−	0.600032i	$-0.204845\pi$
$991$	−3732.84	−	6465.48i	−0.119655	−	0.207248i	−0.919631	+	0.392784i	$0.871512\pi$
$992$	−3895.91	+	6747.91i	−0.124693	+	0.215974i
$993$		0			0
$994$		0			0
$995$	51695.3			1.64709
$996$		0			0
$997$	−8677.41	−	15029.7i	−0.275643	−	0.477428i	0.694654	−	0.719344i	$-0.255557\pi$
$997$	−8677.41	−	15029.7i	−0.275643	−	0.477428i	−0.970297	+	0.241916i	$0.922224\pi$
$998$	−15054.6	−	26075.3i	−0.477499	−	0.827053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bj.667.2		4
3.2	odd	2		882.4.g.z.667.1		4
7.2	even	3		882.4.a.u.1.1		2
7.3	odd	6		126.4.g.f.109.1	yes	4
7.4	even	3	inner	882.4.g.bj.361.2		4
7.5	odd	6		882.4.a.ba.1.2		2
7.6	odd	2		126.4.g.f.37.1	yes	4
21.2	odd	6		882.4.a.bh.1.2		2
21.5	even	6		882.4.a.bd.1.1		2
21.11	odd	6		882.4.g.z.361.1		4
21.17	even	6		126.4.g.e.109.2	yes	4
21.20	even	2		126.4.g.e.37.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.g.e.37.2	✓	4	21.20	even	2
126.4.g.e.109.2	yes	4	21.17	even	6
126.4.g.f.37.1	yes	4	7.6	odd	2
126.4.g.f.109.1	yes	4	7.3	odd	6
882.4.a.u.1.1		2	7.2	even	3
882.4.a.ba.1.2		2	7.5	odd	6
882.4.a.bd.1.1		2	21.5	even	6
882.4.a.bh.1.2		2	21.2	odd	6
882.4.g.z.361.1		4	21.11	odd	6
882.4.g.z.667.1		4	3.2	odd	2
882.4.g.bj.361.2		4	7.4	even	3	inner
882.4.g.bj.667.2		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(5.22311 - 9.04669i) q^{5} -8.00000 q^{8} +(-10.4462 - 18.0934i) q^{10} +(30.5618 + 52.9346i) q^{11} +59.2311 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-10.2311 - 17.7208i) q^{17} +(-40.1693 + 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(-79.1236 + 137.046i) q^{23} +(7.93822 + 13.7494i) q^{25} +(59.2311 - 102.591i) q^{26} +85.1236 q^{29} +(121.747 + 210.872i) q^{31} +(16.0000 + 27.7128i) q^{32} -40.9244 q^{34} +(-145.185 + 251.468i) q^{37} +(80.3387 + 139.151i) q^{38} +(-41.7849 + 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(122.247 - 211.738i) q^{44} +(158.247 + 274.092i) q^{46} +(84.6453 - 146.610i) q^{47} +31.7529 q^{50} +(-118.462 - 205.183i) q^{52} +(-125.056 - 216.603i) q^{53} +638.510 q^{55} +(85.1236 - 147.438i) q^{58} +(402.610 + 697.341i) q^{59} +(16.5858 - 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(309.371 - 535.846i) q^{65} +(138.691 + 240.220i) q^{67} +(-40.9244 + 70.8832i) q^{68} +631.506 q^{71} +(-384.142 - 665.353i) q^{73} +(290.371 + 502.937i) q^{74} +321.355 q^{76} +(209.365 - 362.631i) q^{79} +(83.5698 + 144.747i) q^{80} +(-168.000 + 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(7.62934 - 13.2144i) q^{86} +(-244.494 - 423.476i) q^{88} +(786.048 - 1361.48i) q^{89} +632.988 q^{92} +(-169.291 - 293.220i) q^{94} +(419.618 + 726.799i) q^{95} -1045.16 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8} - 14 q^{10} + 25 q^{11} + 98 q^{13} - 32 q^{16} + 98 q^{17} - 119 q^{19} - 56 q^{20} + 100 q^{22} - 122 q^{23} + 129 q^{25} + 98 q^{26} + 146 q^{29} + 98 q^{31} + 64 q^{32} + 392 q^{34} - 289 q^{37} + 238 q^{38} - 56 q^{40} - 672 q^{41} + 614 q^{43} + 100 q^{44} + 244 q^{46} + 672 q^{47} + 516 q^{50} - 196 q^{52} + 375 q^{53} + 1526 q^{55} + 146 q^{58} + 763 q^{59} - 406 q^{61} + 392 q^{62} + 256 q^{64} + 654 q^{65} + 1041 q^{67} + 392 q^{68} + 3304 q^{71} - 189 q^{73} + 578 q^{74} + 952 q^{76} - 524 q^{79} + 112 q^{80} - 672 q^{82} - 574 q^{83} - 1244 q^{85} + 614 q^{86} - 200 q^{88} + 2394 q^{89} + 976 q^{92} - 1344 q^{94} + 706 q^{95} + 126 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8 - 14 * q^10 + 25 * q^11 + 98 * q^13 - 32 * q^16 + 98 * q^17 - 119 * q^19 - 56 * q^20 + 100 * q^22 - 122 * q^23 + 129 * q^25 + 98 * q^26 + 146 * q^29 + 98 * q^31 + 64 * q^32 + 392 * q^34 - 289 * q^37 + 238 * q^38 - 56 * q^40 - 672 * q^41 + 614 * q^43 + 100 * q^44 + 244 * q^46 + 672 * q^47 + 516 * q^50 - 196 * q^52 + 375 * q^53 + 1526 * q^55 + 146 * q^58 + 763 * q^59 - 406 * q^61 + 392 * q^62 + 256 * q^64 + 654 * q^65 + 1041 * q^67 + 392 * q^68 + 3304 * q^71 - 189 * q^73 + 578 * q^74 + 952 * q^76 - 524 * q^79 + 112 * q^80 - 672 * q^82 - 574 * q^83 - 1244 * q^85 + 614 * q^86 - 200 * q^88 + 2394 * q^89 + 976 * q^92 - 1344 * q^94 + 706 * q^95 + 126 * q^97

Introduction

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