LMFDB - Embedded newform 216.3.b.b.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(163,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.b (of order $2$, degree $1$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} - 56x^{10} + 400x^{8} - 896x^{6} - 512x^{4} - 8192x^{2} + 65536 $ x^16 - 2x^14 - 2x^12 - 56x^10 + 400x^8 - 896x^6 - 512x^4 - 8192*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.1
Root			$-1.98451 - 0.248465i$ of defining polynomial
Character	$\chi$	$=$	216.163
Dual form			216.3.b.b.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98451 - 0.248465i) q^{2} +(3.87653 + 0.986159i) q^{4} +8.47512i q^{5} +7.86423i q^{7} +(-7.44797 - 2.92022i) q^{8} +O(q^{10})$	\(q+(-1.98451 - 0.248465i) q^{2} +(3.87653 + 0.986159i) q^{4} +8.47512i q^{5} +7.86423i q^{7} +(-7.44797 - 2.92022i) q^{8} +(2.10577 - 16.8189i) q^{10} -12.3268 q^{11} -18.5728i q^{13} +(1.95398 - 15.6066i) q^{14} +(14.0550 + 7.64575i) q^{16} -2.63017 q^{17} -11.6192 q^{19} +(-8.35781 + 32.8541i) q^{20} +(24.4627 + 3.06278i) q^{22} +3.72601i q^{23} -46.8276 q^{25} +(-4.61467 + 36.8578i) q^{26} +(-7.75538 + 30.4859i) q^{28} -34.7892i q^{29} +30.1302i q^{31} +(-25.9925 - 18.6652i) q^{32} +(5.21958 + 0.653504i) q^{34} -66.6503 q^{35} +56.5421i q^{37} +(23.0584 + 2.88696i) q^{38} +(24.7492 - 63.1225i) q^{40} +47.2250 q^{41} -74.8399 q^{43} +(-47.7853 - 12.1562i) q^{44} +(0.925782 - 7.39429i) q^{46} +25.5404i q^{47} -12.8461 q^{49} +(92.9297 + 11.6350i) q^{50} +(18.3157 - 71.9979i) q^{52} +45.8348i q^{53} -104.471i q^{55} +(22.9653 - 58.5726i) q^{56} +(-8.64389 + 69.0394i) q^{58} +37.0444 q^{59} +28.6627i q^{61} +(7.48628 - 59.7935i) q^{62} +(46.9446 + 43.4994i) q^{64} +157.406 q^{65} +2.80385 q^{67} +(-10.1959 - 2.59376i) q^{68} +(132.268 + 16.5602i) q^{70} +1.77748i q^{71} +42.2399 q^{73} +(14.0487 - 112.208i) q^{74} +(-45.0423 - 11.4584i) q^{76} -96.9410i q^{77} +38.0946i q^{79} +(-64.7986 + 119.118i) q^{80} +(-93.7183 - 11.7337i) q^{82} -131.961 q^{83} -22.2910i q^{85} +(148.520 + 18.5951i) q^{86} +(91.8099 + 35.9970i) q^{88} +90.7241 q^{89} +146.061 q^{91} +(-3.67444 + 14.4440i) q^{92} +(6.34589 - 50.6851i) q^{94} -98.4742i q^{95} -22.8060 q^{97} +(25.4932 + 3.19181i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.98451	−	0.248465i	−0.992253	−	0.124232i
$2$	−1.98451	−	0.248465i	−0.992253	−	0.124232i
$3$		0			0
$3$		0			0
$4$	3.87653	+	0.986159i	0.969133	+	0.246540i
$5$			8.47512i			1.69502i	0.530777	+	0.847512i	$0.321900\pi$
$5$			8.47512i			1.69502i	−0.530777	+	0.847512i	$0.678100\pi$
$6$		0			0
$7$			7.86423i			1.12346i	0.827320	+	0.561731i	$0.189864\pi$
$7$			7.86423i			1.12346i	−0.827320	+	0.561731i	$0.810136\pi$
$8$	−7.44797	−	2.92022i	−0.930997	−	0.365027i
$9$		0			0
$10$	2.10577	−	16.8189i	0.210577	−	1.68189i
$11$	−12.3268			−1.12062			−0.560310	−	0.828283i	$-0.689318\pi$
$11$	−12.3268			−1.12062			−0.560310	+	0.828283i	$0.689318\pi$
$12$		0			0
$13$		−	18.5728i		−	1.42867i	−0.699802	−	0.714337i	$-0.746728\pi$
$13$		−	18.5728i		−	1.42867i	0.699802	−	0.714337i	$-0.253272\pi$
$14$	1.95398	−	15.6066i	0.139570	−	1.11476i
$15$		0			0
$16$	14.0550	+	7.64575i	0.878436	+	0.477860i
$17$	−2.63017			−0.154716			−0.0773579	−	0.997003i	$-0.524648\pi$
$17$	−2.63017			−0.154716			−0.0773579	+	0.997003i	$0.524648\pi$
$18$		0			0
$19$	−11.6192			−0.611538			−0.305769	−	0.952106i	$-0.598913\pi$
$19$	−11.6192			−0.611538			−0.305769	+	0.952106i	$0.598913\pi$
$20$	−8.35781	+	32.8541i	−0.417891	+	1.64270i
$21$		0			0
$22$	24.4627	+	3.06278i	1.11194	+	0.139217i
$23$			3.72601i			0.162000i	0.996714	+	0.0810002i	$0.0258115\pi$
$23$			3.72601i			0.162000i	−0.996714	+	0.0810002i	$0.974189\pi$
$24$		0			0
$25$	−46.8276			−1.87310
$26$	−4.61467	+	36.8578i	−0.177487	+	1.41761i
$27$		0			0
$28$	−7.75538	+	30.4859i	−0.276978	+	1.08878i
$29$		−	34.7892i		−	1.19963i	−0.800139	−	0.599814i	$-0.795241\pi$
$29$		−	34.7892i		−	1.19963i	0.800139	−	0.599814i	$-0.204759\pi$
$30$		0			0
$31$			30.1302i			0.971941i	0.873975	+	0.485970i	$0.161534\pi$
$31$			30.1302i			0.971941i	−0.873975	+	0.485970i	$0.838466\pi$
$32$	−25.9925	−	18.6652i	−0.812266	−	0.583288i
$33$		0			0
$34$	5.21958	+	0.653504i	0.153517	+	0.0192207i
$35$	−66.6503			−1.90429
$36$		0			0
$37$			56.5421i			1.52817i	0.645118	+	0.764083i	$0.276808\pi$
$37$			56.5421i			1.52817i	−0.645118	+	0.764083i	$0.723192\pi$
$38$	23.0584	+	2.88696i	0.606800	+	0.0759727i
$39$		0			0
$40$	24.7492	−	63.1225i	0.618730	−	1.57806i
$41$	47.2250			1.15183			0.575915	−	0.817510i	$-0.304646\pi$
$41$	47.2250			1.15183			0.575915	+	0.817510i	$0.304646\pi$
$42$		0			0
$43$	−74.8399			−1.74046			−0.870231	−	0.492644i	$-0.836030\pi$
$43$	−74.8399			−1.74046			−0.870231	+	0.492644i	$0.836030\pi$
$44$	−47.7853	−	12.1562i	−1.08603	−	0.276278i
$45$		0			0
$46$	0.925782	−	7.39429i	0.0201257	−	0.160745i
$47$			25.5404i			0.543413i	0.962380	+	0.271707i	$0.0875880\pi$
$47$			25.5404i			0.543413i	−0.962380	+	0.271707i	$0.912412\pi$
$48$		0			0
$49$	−12.8461			−0.262166
$50$	92.9297	+	11.6350i	1.85859	+	0.232700i
$51$		0			0
$52$	18.3157	−	71.9979i	0.352225	−	1.38457i
$53$			45.8348i			0.864807i	0.901680	+	0.432404i	$0.142334\pi$
$53$			45.8348i			0.864807i	−0.901680	+	0.432404i	$0.857666\pi$
$54$		0			0
$55$		−	104.471i		−	1.89948i
$56$	22.9653	−	58.5726i	0.410094	−	1.04594i
$57$		0			0
$58$	−8.64389	+	69.0394i	−0.149033	+	1.19033i
$59$	37.0444			0.627871			0.313936	−	0.949444i	$-0.398352\pi$
$59$	37.0444			0.627871			0.313936	+	0.949444i	$0.398352\pi$
$60$		0			0
$61$			28.6627i			0.469880i	0.972010	+	0.234940i	$0.0754894\pi$
$61$			28.6627i			0.469880i	−0.972010	+	0.234940i	$0.924511\pi$
$62$	7.48628	−	59.7935i	0.120746	−	0.964412i
$63$		0			0
$64$	46.9446	+	43.4994i	0.733510	+	0.679679i
$65$	157.406			2.42164
$66$		0			0
$67$	2.80385			0.0418485			0.0209242	−	0.999781i	$-0.493339\pi$
$67$	2.80385			0.0418485			0.0209242	+	0.999781i	$0.493339\pi$
$68$	−10.1959	−	2.59376i	−0.149940	−	0.0381436i
$69$		0			0
$70$	132.268	+	16.5602i	1.88954	+	0.236575i
$71$			1.77748i			0.0250350i	0.999922	+	0.0125175i	$0.00398454\pi$
$71$			1.77748i			0.0250350i	−0.999922	+	0.0125175i	$0.996015\pi$
$72$		0			0
$73$	42.2399			0.578629			0.289314	−	0.957234i	$-0.406573\pi$
$73$	42.2399			0.578629			0.289314	+	0.957234i	$0.406573\pi$
$74$	14.0487	−	112.208i	0.189848	−	1.51633i
$75$		0			0
$76$	−45.0423	−	11.4584i	−0.592661	−	0.150768i
$77$		−	96.9410i		−	1.25897i
$78$		0			0
$79$			38.0946i			0.482210i	0.970499	+	0.241105i	$0.0775098\pi$
$79$			38.0946i			0.482210i	−0.970499	+	0.241105i	$0.922490\pi$
$80$	−64.7986	+	119.118i	−0.809983	+	1.48897i
$81$		0			0
$82$	−93.7183	−	11.7337i	−1.14291	−	0.143094i
$83$	−131.961			−1.58989			−0.794944	−	0.606683i	$-0.792500\pi$
$83$	−131.961			−1.58989			−0.794944	+	0.606683i	$0.792500\pi$
$84$		0			0
$85$		−	22.2910i		−	0.262247i
$86$	148.520	+	18.5951i	1.72698	+	0.216222i
$87$		0			0
$88$	91.8099	+	35.9970i	1.04329	+	0.409057i
$89$	90.7241			1.01937			0.509686	−	0.860360i	$-0.329762\pi$
$89$	90.7241			1.01937			0.509686	+	0.860360i	$0.329762\pi$
$90$		0			0
$91$	146.061			1.60506
$92$	−3.67444	+	14.4440i	−0.0399396	+	0.157000i
$93$		0			0
$94$	6.34589	−	50.6851i	0.0675095	−	0.539203i
$95$		−	98.4742i		−	1.03657i
$96$		0			0
$97$	−22.8060			−0.235114			−0.117557	−	0.993066i	$-0.537506\pi$
$97$	−22.8060			−0.235114			−0.117557	+	0.993066i	$0.537506\pi$
$98$	25.4932	+	3.19181i	0.260135	+	0.0325695i
$99$		0			0
$100$	−181.529	−	46.1795i	−1.81529	−	0.461795i
$101$			115.573i			1.14429i	0.820154	+	0.572143i	$0.193888\pi$
$101$			115.573i			1.14429i	−0.820154	+	0.572143i	$0.806112\pi$
$102$		0			0
$103$			21.8449i			0.212086i	0.994362	+	0.106043i	$0.0338181\pi$
$103$			21.8449i			0.212086i	−0.994362	+	0.106043i	$0.966182\pi$
$104$	−54.2365	+	138.329i	−0.521505	+	1.33009i
$105$		0			0
$106$	11.3883	−	90.9594i	0.107437	−	0.858108i
$107$	−115.958			−1.08372			−0.541858	−	0.840470i	$-0.682279\pi$
$107$	−115.958			−1.08372			−0.541858	+	0.840470i	$0.682279\pi$
$108$		0			0
$109$		−	132.440i		−	1.21505i	−0.794301	−	0.607524i	$-0.792163\pi$
$109$		−	132.440i		−	1.21505i	0.794301	−	0.607524i	$-0.207837\pi$
$110$	−25.9574	+	207.324i	−0.235977	+	1.88476i
$111$		0			0
$112$	−60.1280	+	110.532i	−0.536857	+	0.986889i
$113$	−82.4136			−0.729324			−0.364662	−	0.931140i	$-0.618815\pi$
$113$	−82.4136			−0.729324			−0.364662	+	0.931140i	$0.618815\pi$
$114$		0			0
$115$	−31.5784			−0.274595
$116$	34.3077	−	134.861i	0.295756	−	1.16260i
$117$		0			0
$118$	−73.5148	−	9.20422i	−0.623007	−	0.0780019i
$119$		−	20.6842i		−	0.173817i
$120$		0			0
$121$	30.9507			0.255791
$122$	7.12167	−	56.8813i	0.0583743	−	0.466240i
$123$		0			0
$124$	−29.7131	+	116.801i	−0.239622	+	0.941940i
$125$		−	184.992i		−	1.47993i
$126$		0			0
$127$			220.170i			1.73362i	0.498640	+	0.866809i	$0.333833\pi$
$127$			220.170i			1.73362i	−0.498640	+	0.866809i	$0.666167\pi$
$128$	−82.3539	−	97.9890i	−0.643389	−	0.765539i
$129$		0			0
$130$	−312.374	−	39.1099i	−2.40288	−	0.300845i
$131$	76.3612			0.582910			0.291455	−	0.956585i	$-0.405861\pi$
$131$	76.3612			0.582910			0.291455	+	0.956585i	$0.405861\pi$
$132$		0			0
$133$		−	91.3762i		−	0.687039i
$134$	−5.56425	−	0.696657i	−0.0415243	−	0.00519893i
$135$		0			0
$136$	19.5894	+	7.68067i	0.144040	+	0.0564755i
$137$	81.9252			0.597994			0.298997	−	0.954254i	$-0.403348\pi$
$137$	81.9252			0.597994			0.298997	+	0.954254i	$0.403348\pi$
$138$		0			0
$139$	37.6437			0.270818			0.135409	−	0.990790i	$-0.456765\pi$
$139$	37.6437			0.270818			0.135409	+	0.990790i	$0.456765\pi$
$140$	−258.372	−	65.7278i	−1.84551	−	0.469484i
$141$		0			0
$142$	0.441642	−	3.52743i	0.00311015	−	0.0248410i
$143$			228.943i			1.60100i
$144$		0			0
$145$	294.843			2.03340
$146$	−83.8253	−	10.4951i	−0.574146	−	0.0718843i
$147$		0			0
$148$	−55.7595	+	219.187i	−0.376754	+	1.48100i
$149$			233.905i			1.56983i	0.619602	+	0.784916i	$0.287294\pi$
$149$			233.905i			1.56983i	−0.619602	+	0.784916i	$0.712706\pi$
$150$		0			0
$151$		−	66.6977i		−	0.441706i	−0.975307	−	0.220853i	$-0.929116\pi$
$151$		−	66.6977i		−	0.441706i	0.975307	−	0.220853i	$-0.0708842\pi$
$152$	86.5396	+	33.9307i	0.569340	+	0.223228i
$153$		0			0
$154$	−24.0864	+	192.380i	−0.156405	+	1.24922i
$155$	−255.357			−1.64746
$156$		0			0
$157$			123.638i			0.787501i	0.919217	+	0.393750i	$0.128823\pi$
$157$			123.638i			0.787501i	−0.919217	+	0.393750i	$0.871177\pi$
$158$	9.46515	−	75.5989i	0.0599060	−	0.478474i
$159$		0			0
$160$	158.190	−	220.289i	0.988686	−	1.37681i
$161$	−29.3022			−0.182001
$162$		0			0
$163$	153.360			0.940862			0.470431	−	0.882437i	$-0.344099\pi$
$163$	153.360			0.940862			0.470431	+	0.882437i	$0.344099\pi$
$164$	183.069	+	46.5714i	1.11628	+	0.283972i
$165$		0			0
$166$	261.877	+	32.7875i	1.57757	+	0.197515i
$167$			255.949i			1.53263i	0.642465	+	0.766315i	$0.277912\pi$
$167$			255.949i			1.53263i	−0.642465	+	0.766315i	$0.722088\pi$
$168$		0			0
$169$	−175.948			−1.04111
$170$	−5.53852	+	44.2366i	−0.0325795	+	0.260215i
$171$		0			0
$172$	−290.119	−	73.8040i	−1.68674	−	0.429093i
$173$		−	182.166i		−	1.05298i	−0.850181	−	0.526490i	$-0.823508\pi$
$173$		−	182.166i		−	1.05298i	0.850181	−	0.526490i	$-0.176492\pi$
$174$		0			0
$175$		−	368.263i		−	2.10436i
$176$	−173.253	−	94.2479i	−0.984394	−	0.535499i
$177$		0			0
$178$	−180.043	−	22.5417i	−1.01148	−	0.126639i
$179$	164.310			0.917935			0.458967	−	0.888453i	$-0.348220\pi$
$179$	164.310			0.917935			0.458967	+	0.888453i	$0.348220\pi$
$180$		0			0
$181$		−	169.284i		−	0.935272i	−0.883921	−	0.467636i	$-0.845106\pi$
$181$		−	169.284i		−	0.935272i	0.883921	−	0.467636i	$-0.154894\pi$
$182$	−289.858	−	36.2909i	−1.59263	−	0.199400i
$183$		0			0
$184$	10.8808	−	27.7512i	0.0591346	−	0.150822i
$185$	−479.201			−2.59028
$186$		0			0
$187$	32.4216			0.173378
$188$	−25.1869	+	99.0082i	−0.133973	+	0.526639i
$189$		0			0
$190$	−24.4674	+	195.423i	−0.128776	+	1.02854i
$191$		−	138.568i		−	0.725489i	−0.931889	−	0.362744i	$-0.881840\pi$
$191$		−	138.568i		−	0.725489i	0.931889	−	0.362744i	$-0.118160\pi$
$192$		0			0
$193$	267.191			1.38441			0.692203	−	0.721702i	$-0.256640\pi$
$193$	267.191			1.38441			0.692203	+	0.721702i	$0.256640\pi$
$194$	45.2587	+	5.66649i	0.233292	+	0.0292087i
$195$		0			0
$196$	−49.7984	−	12.6683i	−0.254074	−	0.0646343i
$197$			136.746i			0.694143i	0.937839	+	0.347071i	$0.112824\pi$
$197$			136.746i			0.694143i	−0.937839	+	0.347071i	$0.887176\pi$
$198$		0			0
$199$		−	69.1304i		−	0.347389i	−0.984800	−	0.173695i	$-0.944429\pi$
$199$		−	69.1304i		−	0.347389i	0.984800	−	0.173695i	$-0.0555705\pi$
$200$	348.771	+	136.747i	1.74385	+	0.683735i
$201$		0			0
$202$	28.7158	−	229.355i	0.142157	−	1.13542i
$203$	273.590			1.34774
$204$		0			0
$205$			400.238i			1.95238i
$206$	5.42767	−	43.3513i	0.0263479	−	0.210443i
$207$		0			0
$208$	142.003	−	261.040i	0.682706	−	1.25500i
$209$	143.228			0.685302
$210$		0			0
$211$	159.974			0.758173			0.379086	−	0.925361i	$-0.376238\pi$
$211$	159.974			0.758173			0.379086	+	0.925361i	$0.376238\pi$
$212$	−45.2004	+	177.680i	−0.213209	+	0.838113i
$213$		0			0
$214$	230.119	+	28.8114i	1.07532	+	0.134633i
$215$		−	634.277i		−	2.95012i
$216$		0			0
$217$	−236.951			−1.09194
$218$	−32.9067	+	262.829i	−0.150948	+	1.20564i
$219$		0			0
$220$	103.025	−	404.986i	0.468297	−	1.84085i
$221$			48.8495i			0.221038i
$222$		0			0
$223$			1.22659i			0.00550039i	0.999996	+	0.00275020i	$0.000875416\pi$
$223$			1.22659i			0.00550039i	−0.999996	+	0.00275020i	$0.999125\pi$
$224$	146.788	−	204.411i	0.655301	−	0.912549i
$225$		0			0
$226$	163.550	+	20.4769i	0.723674	+	0.0906055i
$227$	65.5679			0.288845			0.144423	−	0.989516i	$-0.453868\pi$
$227$	65.5679			0.288845			0.144423	+	0.989516i	$0.453868\pi$
$228$		0			0
$229$			212.338i			0.927241i	0.886034	+	0.463620i	$0.153450\pi$
$229$			212.338i			0.927241i	−0.886034	+	0.463620i	$0.846550\pi$
$230$	62.6675	+	7.84611i	0.272467	+	0.0341135i
$231$		0			0
$232$	−101.592	+	259.109i	−0.437897	+	1.11685i
$233$	272.478			1.16943			0.584716	−	0.811238i	$-0.301206\pi$
$233$	272.478			1.16943			0.584716	+	0.811238i	$0.301206\pi$
$234$		0			0
$235$	−216.458			−0.921098
$236$	143.604	+	36.5317i	0.608490	+	0.154795i
$237$		0			0
$238$	−5.13930	+	41.0480i	−0.0215937	+	0.172471i
$239$		−	275.545i		−	1.15291i	−0.817129	−	0.576454i	$-0.804436\pi$
$239$		−	275.545i		−	1.15291i	0.817129	−	0.576454i	$-0.195564\pi$
$240$		0			0
$241$	101.757			0.422228			0.211114	−	0.977461i	$-0.432291\pi$
$241$	101.757			0.422228			0.211114	+	0.977461i	$0.432291\pi$
$242$	−61.4218	−	7.69014i	−0.253809	−	0.0317775i
$243$		0			0
$244$	−28.2660	+	111.112i	−0.115844	+	0.455376i
$245$		−	108.872i		−	0.444377i
$246$		0			0
$247$			215.801i			0.873688i
$248$	87.9867	−	224.409i	0.354785	−	0.904874i
$249$		0			0
$250$	−45.9639	+	367.117i	−0.183855	+	1.46847i
$251$	307.152			1.22371			0.611857	−	0.790968i	$-0.290423\pi$
$251$	307.152			1.22371			0.611857	+	0.790968i	$0.290423\pi$
$252$		0			0
$253$		−	45.9299i		−	0.181541i
$254$	54.7043	−	436.928i	0.215371	−	1.72019i
$255$		0			0
$256$	139.085	+	214.922i	0.543301	+	0.839538i
$257$	−489.046			−1.90290			−0.951452	−	0.307798i	$-0.900408\pi$
$257$	−489.046			−1.90290			−0.951452	+	0.307798i	$0.900408\pi$
$258$		0			0
$259$	−444.660			−1.71684
$260$	610.191	+	155.228i	2.34689	+	0.597030i
$261$		0			0
$262$	−151.539	−	18.9730i	−0.578394	−	0.0724162i
$263$			497.353i			1.89108i	0.325510	+	0.945539i	$0.394464\pi$
$263$			497.353i			1.89108i	−0.325510	+	0.945539i	$0.605536\pi$
$264$		0			0
$265$	−388.455			−1.46587
$266$	−22.7038	+	181.337i	−0.0853525	+	0.681717i
$267$		0			0
$268$	10.8692	+	2.76504i	0.0405567	+	0.0103173i
$269$			184.199i			0.684753i	0.939563	+	0.342377i	$0.111232\pi$
$269$			184.199i			0.684753i	−0.939563	+	0.342377i	$0.888768\pi$
$270$		0			0
$271$		−	72.4970i		−	0.267517i	−0.991014	−	0.133758i	$-0.957295\pi$
$271$		−	72.4970i		−	0.267517i	0.991014	−	0.133758i	$-0.0427046\pi$
$272$	−36.9670	−	20.1096i	−0.135908	−	0.0739324i
$273$		0			0
$274$	−162.581	−	20.3555i	−0.593362	−	0.0742902i
$275$	577.236			2.09904
$276$		0			0
$277$		−	407.050i		−	1.46950i	−0.678340	−	0.734748i	$-0.737300\pi$
$277$		−	407.050i		−	1.46950i	0.678340	−	0.734748i	$-0.262700\pi$
$278$	−74.7042	−	9.35313i	−0.268720	−	0.0336443i
$279$		0			0
$280$	496.410	+	194.633i	1.77289	+	0.695120i
$281$	−90.6558			−0.322618			−0.161309	−	0.986904i	$-0.551572\pi$
$281$	−90.6558			−0.322618			−0.161309	+	0.986904i	$0.551572\pi$
$282$		0			0
$283$	−344.581			−1.21760			−0.608801	−	0.793323i	$-0.708349\pi$
$283$	−344.581			−1.21760			−0.608801	+	0.793323i	$0.708349\pi$
$284$	−1.75288	+	6.89047i	−0.00617212	+	0.0242622i
$285$		0			0
$286$	56.8843	−	454.339i	0.198896	−	1.58860i
$287$			371.388i			1.29404i
$288$		0			0
$289$	−282.082			−0.976063
$290$	−585.117	−	73.2580i	−2.01765	−	0.252614i
$291$		0			0
$292$	163.744	+	41.6552i	0.560768	+	0.142655i
$293$		−	300.663i		−	1.02615i	−0.858342	−	0.513077i	$-0.828505\pi$
$293$		−	300.663i		−	1.02615i	0.858342	−	0.513077i	$-0.171495\pi$
$294$		0			0
$295$			313.956i			1.06426i
$296$	165.115	−	421.124i	0.557822	−	1.42272i
$297$		0			0
$298$	58.1171	−	464.186i	0.195024	−	1.55767i
$299$	69.2023			0.231446
$300$		0			0
$301$		−	588.558i		−	1.95534i
$302$	−16.5720	+	132.362i	−0.0548742	+	0.438284i
$303$		0			0
$304$	−163.308	−	88.8377i	−0.537197	−	0.292229i
$305$	−242.920			−0.796458
$306$		0			0
$307$	−108.717			−0.354126			−0.177063	−	0.984200i	$-0.556660\pi$
$307$	−108.717			−0.354126			−0.177063	+	0.984200i	$0.556660\pi$
$308$	95.5993	−	375.795i	0.310387	−	1.22011i
$309$		0			0
$310$	506.757	+	63.4471i	1.63470	+	0.204668i
$311$		−	5.16140i		−	0.0165962i	−0.999966	−	0.00829808i	$-0.997359\pi$
$311$		−	5.16140i		−	0.0165962i	0.999966	−	0.00829808i	$-0.00264139\pi$
$312$		0			0
$313$	−106.502			−0.340261			−0.170130	−	0.985422i	$-0.554419\pi$
$313$	−106.502			−0.340261			−0.170130	+	0.985422i	$0.554419\pi$
$314$	30.7196	−	245.360i	0.0978330	−	0.781400i
$315$		0			0
$316$	−37.5673	+	147.675i	−0.118884	+	0.467325i
$317$			280.570i			0.885080i	0.896749	+	0.442540i	$0.145923\pi$
$317$			280.570i			0.885080i	−0.896749	+	0.442540i	$0.854077\pi$
$318$		0			0
$319$			428.841i			1.34433i
$320$	−368.663	+	397.861i	−1.15207	+	1.24332i
$321$		0			0
$322$	58.1504	+	7.28056i	0.180591	+	0.0226104i
$323$	30.5605			0.0946145
$324$		0			0
$325$			869.718i			2.67606i
$326$	−304.345	−	38.1046i	−0.933573	−	0.116885i
$327$		0			0
$328$	−351.731	−	137.907i	−1.07235	−	0.420449i
$329$	−200.856			−0.610504
$330$		0			0
$331$	552.160			1.66816			0.834078	−	0.551646i	$-0.186000\pi$
$331$	552.160			1.66816			0.834078	+	0.551646i	$0.186000\pi$
$332$	−511.549	−	130.134i	−1.54081	−	0.391970i
$333$		0			0
$334$	63.5944	−	507.933i	0.190402	−	1.52076i
$335$			23.7629i			0.0709341i
$336$		0			0
$337$	−80.7501			−0.239615			−0.119807	−	0.992797i	$-0.538228\pi$
$337$	−80.7501			−0.239615			−0.119807	+	0.992797i	$0.538228\pi$
$338$	349.169	+	43.7167i	1.03304	+	0.129339i
$339$		0			0
$340$	21.9825	−	86.4117i	0.0646543	−	0.254152i
$341$		−	371.409i		−	1.08918i
$342$		0			0
$343$			284.322i			0.828928i
$344$	557.405	+	218.549i	1.62036	+	0.635316i
$345$		0			0
$346$	−45.2617	+	361.509i	−0.130814	+	1.04482i
$347$	148.005			0.426529			0.213264	−	0.976995i	$-0.431590\pi$
$347$	148.005			0.426529			0.213264	+	0.976995i	$0.431590\pi$
$348$		0			0
$349$		−	247.698i		−	0.709737i	−0.934916	−	0.354868i	$-0.884526\pi$
$349$		−	247.698i		−	0.709737i	0.934916	−	0.354868i	$-0.115474\pi$
$350$	−91.5004	+	730.821i	−0.261430	+	2.08806i
$351$		0			0
$352$	320.405	+	230.083i	0.910242	+	0.653644i
$353$	145.977			0.413533			0.206767	−	0.978390i	$-0.433706\pi$
$353$	145.977			0.413533			0.206767	+	0.978390i	$0.433706\pi$
$354$		0			0
$355$	−15.0644			−0.0424349
$356$	351.695	+	89.4684i	0.987907	+	0.251316i
$357$		0			0
$358$	−326.075	−	40.8253i	−0.910824	−	0.114037i
$359$		−	60.3086i		−	0.167991i	−0.996466	−	0.0839953i	$-0.973232\pi$
$359$		−	60.3086i		−	0.167991i	0.996466	−	0.0839953i	$-0.0267681\pi$
$360$		0			0
$361$	−225.994			−0.626021
$362$	−42.0612	+	335.946i	−0.116191	+	0.928027i
$363$		0			0
$364$	566.208	+	144.039i	1.55552	+	0.395711i
$365$			357.988i			0.980789i
$366$		0			0
$367$		−	444.553i		−	1.21131i	−0.795726	−	0.605657i	$-0.792910\pi$
$367$		−	444.553i		−	1.21131i	0.795726	−	0.605657i	$-0.207090\pi$
$368$	−28.4882	+	52.3690i	−0.0774135	+	0.142307i
$369$		0			0
$370$	950.978	+	119.065i	2.57021	+	0.321796i
$371$	−360.455			−0.971577
$372$		0			0
$373$		−	179.393i		−	0.480945i	−0.970656	−	0.240473i	$-0.922698\pi$
$373$		−	179.393i		−	0.480945i	0.970656	−	0.240473i	$-0.0773024\pi$
$374$	−64.3409	−	8.05563i	−0.172035	−	0.0215391i
$375$		0			0
$376$	74.5836	−	190.224i	0.198361	−	0.505916i
$377$	−646.132			−1.71388
$378$		0			0
$379$	−364.395			−0.961465			−0.480733	−	0.876867i	$-0.659629\pi$
$379$	−364.395			−0.961465			−0.480733	+	0.876867i	$0.659629\pi$
$380$	97.1113	−	381.738i	0.255556	−	1.00457i
$381$		0			0
$382$	−34.4293	+	274.990i	−0.0901291	+	0.719868i
$383$		−	644.001i		−	1.68146i	−0.541451	−	0.840732i	$-0.682125\pi$
$383$		−	644.001i		−	1.68146i	0.541451	−	0.840732i	$-0.317875\pi$
$384$		0			0
$385$	821.587			2.13399
$386$	−530.241	−	66.3874i	−1.37368	−	0.171988i
$387$		0			0
$388$	−88.4082	−	22.4904i	−0.227856	−	0.0579648i
$389$		−	100.621i		−	0.258666i	−0.991601	−	0.129333i	$-0.958716\pi$
$389$		−	100.621i		−	0.258666i	0.991601	−	0.129333i	$-0.0412836\pi$
$390$		0			0
$391$		−	9.80003i		−	0.0250640i
$392$	95.6777	+	37.5135i	0.244076	+	0.0956978i
$393$		0			0
$394$	33.9766	−	271.374i	0.0862350	−	0.688766i
$395$	−322.856			−0.817357
$396$		0			0
$397$		−	126.733i		−	0.319226i	−0.987180	−	0.159613i	$-0.948975\pi$
$397$		−	126.733i		−	0.319226i	0.987180	−	0.159613i	$-0.0510246\pi$
$398$	−17.1765	+	137.190i	−0.0431569	+	0.344698i
$399$		0			0
$400$	−658.161	−	358.032i	−1.64540	−	0.895081i
$401$	−244.592			−0.609955			−0.304977	−	0.952360i	$-0.598649\pi$
$401$	−244.592			−0.609955			−0.304977	+	0.952360i	$0.598649\pi$
$402$		0			0
$403$	559.601			1.38859
$404$	−113.973	+	448.022i	−0.282112	+	1.10897i
$405$		0			0
$406$	−542.942	−	67.9775i	−1.33730	−	0.167432i
$407$		−	696.985i		−	1.71249i
$408$		0			0
$409$	−480.788			−1.17552			−0.587760	−	0.809035i	$-0.699990\pi$
$409$	−480.788			−1.17552			−0.587760	+	0.809035i	$0.699990\pi$
$410$	99.4448	−	794.274i	0.242548	−	1.93725i
$411$		0			0
$412$	−21.5425	+	84.6823i	−0.0522876	+	0.205539i
$413$			291.326i			0.705389i
$414$		0			0
$415$		−	1118.38i		−	2.69490i
$416$	−346.664	+	482.753i	−0.833328	+	1.16046i
$417$		0			0
$418$	−284.237	−	35.5871i	−0.679993	−	0.0851366i
$419$	−41.5892			−0.0992582			−0.0496291	−	0.998768i	$-0.515804\pi$
$419$	−41.5892			−0.0992582			−0.0496291	+	0.998768i	$0.515804\pi$
$420$		0			0
$421$			284.119i			0.674868i	0.941349	+	0.337434i	$0.109559\pi$
$421$			284.119i			0.674868i	−0.941349	+	0.337434i	$0.890441\pi$
$422$	−317.470	−	39.7480i	−0.752300	−	0.0941896i
$423$		0			0
$424$	133.848	−	341.376i	0.315678	−	0.805133i
$425$	123.164			0.289799
$426$		0			0
$427$	−225.410			−0.527893
$428$	−449.513	−	114.353i	−1.05026	−	0.267179i
$429$		0			0
$430$	−157.595	+	1258.73i	−0.366501	+	2.92727i
$431$			772.342i			1.79198i	0.444078	+	0.895988i	$0.353531\pi$
$431$			772.342i			1.79198i	−0.444078	+	0.895988i	$0.646469\pi$
$432$		0			0
$433$	527.772			1.21887			0.609437	−	0.792835i	$-0.291396\pi$
$433$	527.772			1.21887			0.609437	+	0.792835i	$0.291396\pi$
$434$	470.230	+	58.8738i	1.08348	+	0.135654i
$435$		0			0
$436$	130.607	−	513.409i	0.299558	−	1.17754i
$437$		−	43.2933i		−	0.0990694i
$438$		0			0
$439$		−	159.012i		−	0.362214i	−0.983463	−	0.181107i	$-0.942032\pi$
$439$		−	159.012i		−	0.362214i	0.983463	−	0.181107i	$-0.0579681\pi$
$440$	−305.079	+	778.100i	−0.693362	+	1.76841i
$441$		0			0
$442$	12.1374	−	96.9421i	0.0274601	−	0.219326i
$443$	174.235			0.393307			0.196654	−	0.980473i	$-0.436993\pi$
$443$	174.235			0.393307			0.196654	+	0.980473i	$0.436993\pi$
$444$		0			0
$445$			768.898i			1.72786i
$446$	0.304764	−	2.43417i	0.000683327	−	0.00545778i
$447$		0			0
$448$	−342.090	+	369.183i	−0.763593	+	0.824070i
$449$	360.384			0.802638			0.401319	−	0.915938i	$-0.368552\pi$
$449$	360.384			0.802638			0.401319	+	0.915938i	$0.368552\pi$
$450$		0			0
$451$	−582.135			−1.29076
$452$	−319.479	−	81.2729i	−0.706811	−	0.179807i
$453$		0			0
$454$	−130.120	−	16.2913i	−0.286608	−	0.0358839i
$455$			1237.88i			2.72062i
$456$		0			0
$457$	−46.8499			−0.102516			−0.0512581	−	0.998685i	$-0.516323\pi$
$457$	−46.8499			−0.102516			−0.0512581	+	0.998685i	$0.516323\pi$
$458$	52.7585	−	421.386i	0.115193	−	0.920057i
$459$		0			0
$460$	−122.415	−	31.1413i	−0.266119	−	0.0676985i
$461$			332.749i			0.721797i	0.932605	+	0.360899i	$0.117530\pi$
$461$			332.749i			0.721797i	−0.932605	+	0.360899i	$0.882470\pi$
$462$		0			0
$463$			302.025i			0.652322i	0.945314	+	0.326161i	$0.105755\pi$
$463$			302.025i			0.652322i	−0.945314	+	0.326161i	$0.894245\pi$
$464$	265.990	−	488.962i	0.573254	−	1.05380i
$465$		0			0
$466$	−540.734	−	67.7011i	−1.16037	−	0.145281i
$467$	−789.857			−1.69134			−0.845671	−	0.533704i	$-0.820800\pi$
$467$	−789.857			−1.69134			−0.845671	+	0.533704i	$0.820800\pi$
$468$		0			0
$469$			22.0501i			0.0470152i
$470$	429.562	+	53.7822i	0.913963	+	0.114430i
$471$		0			0
$472$	−275.906	−	108.178i	−0.584546	−	0.229190i
$473$	922.538			1.95040
$474$		0			0
$475$	544.100			1.14547
$476$	20.3980	−	80.1831i	0.0428529	−	0.168452i
$477$		0			0
$478$	−68.4632	+	546.821i	−0.143228	+	1.14398i
$479$		−	239.162i		−	0.499295i	−0.968337	−	0.249647i	$-0.919685\pi$
$479$		−	239.162i		−	0.499295i	0.968337	−	0.249647i	$-0.0803147\pi$
$480$		0			0
$481$	1050.14			2.18325
$482$	−201.937	−	25.2830i	−0.418957	−	0.0524544i
$483$		0			0
$484$	119.981	+	30.5223i	0.247895	+	0.0630626i
$485$		−	193.284i		−	0.398523i
$486$		0			0
$487$			280.377i			0.575722i	0.957672	+	0.287861i	$0.0929441\pi$
$487$			280.377i			0.575722i	−0.957672	+	0.287861i	$0.907056\pi$
$488$	83.7014	−	213.479i	0.171519	−	0.437457i
$489$		0			0
$490$	−27.0510	+	216.058i	−0.0552060	+	0.440935i
$491$	498.602			1.01548			0.507742	−	0.861509i	$-0.330480\pi$
$491$	498.602			1.01548			0.507742	+	0.861509i	$0.330480\pi$
$492$		0			0
$493$			91.5015i			0.185601i
$494$	53.6189	−	428.258i	0.108540	−	0.866920i
$495$		0			0
$496$	−230.368	+	423.479i	−0.464451	+	0.853788i
$497$	−13.9785			−0.0281258
$498$		0			0
$499$	445.305			0.892394			0.446197	−	0.894935i	$-0.352778\pi$
$499$	445.305			0.892394			0.446197	+	0.894935i	$0.352778\pi$
$500$	182.431	−	717.126i	0.364862	−	1.43425i
$501$		0			0
$502$	−609.545	−	76.3164i	−1.21423	−	0.152025i
$503$		−	677.433i		−	1.34678i	−0.739285	−	0.673392i	$-0.764837\pi$
$503$		−	677.433i		−	1.34678i	0.739285	−	0.673392i	$-0.235163\pi$
$504$		0			0
$505$	−979.494			−1.93959
$506$	−11.4120	+	91.1482i	−0.0225533	+	0.180135i
$507$		0			0
$508$	−217.122	+	853.494i	−0.427406	+	1.68011i
$509$			87.0341i			0.170990i	0.996339	+	0.0854952i	$0.0272472\pi$
$509$			87.0341i			0.170990i	−0.996339	+	0.0854952i	$0.972753\pi$
$510$		0			0
$511$			332.184i			0.650067i
$512$	−222.615	−	461.071i	−0.434794	−	0.900530i
$513$		0			0
$514$	970.515	+	121.511i	1.88816	+	0.236402i
$515$	−185.138			−0.359491
$516$		0			0
$517$		−	314.832i		−	0.608960i
$518$	882.431	+	110.482i	1.70354	+	0.213286i
$519$		0			0
$520$	−1172.36	−	459.661i	−2.25454	−	0.883964i
$521$	−2.63017			−0.00504831			−0.00252415	−	0.999997i	$-0.500803\pi$
$521$	−2.63017			−0.00504831			−0.00252415	+	0.999997i	$0.500803\pi$
$522$		0			0
$523$	793.046			1.51634			0.758170	−	0.652057i	$-0.226094\pi$
$523$	793.046			1.51634			0.758170	+	0.652057i	$0.226094\pi$
$524$	296.016	+	75.3043i	0.564917	+	0.143710i
$525$		0			0
$526$	123.575	−	987.001i	0.234933	−	1.87643i
$527$		−	79.2474i		−	0.150375i
$528$		0			0
$529$	515.117			0.973756
$530$	770.892	+	96.5173i	1.45451	+	0.182108i
$531$		0			0
$532$	90.1115	−	354.223i	0.169383	−	0.665832i
$533$		−	877.099i		−	1.64559i
$534$		0			0
$535$		−	982.754i		−	1.83692i
$536$	−20.8830	−	8.18785i	−0.0389608	−	0.0152758i
$537$		0			0
$538$	45.7668	−	365.543i	0.0850685	−	0.679449i
$539$	158.352			0.293789
$540$		0			0
$541$		−	376.176i		−	0.695334i	−0.937618	−	0.347667i	$-0.886974\pi$
$541$		−	376.176i		−	0.695334i	0.937618	−	0.347667i	$-0.113026\pi$
$542$	−18.0129	+	143.871i	−0.0332342	+	0.265444i
$543$		0			0
$544$	68.3646	+	49.0926i	0.125670	+	0.0902438i
$545$	1122.45			2.05954
$546$		0			0
$547$	45.9657			0.0840323			0.0420161	−	0.999117i	$-0.486622\pi$
$547$	45.9657			0.0840323			0.0420161	+	0.999117i	$0.486622\pi$
$548$	317.586	+	80.7913i	0.579536	+	0.147429i
$549$		0			0
$550$	−1145.53	−	143.423i	−2.08278	−	0.260769i
$551$			404.223i			0.733618i
$552$		0			0
$553$	−299.584			−0.541744
$554$	−101.138	+	807.794i	−0.182559	+	1.45811i
$555$		0			0
$556$	145.927	+	37.1227i	0.262459	+	0.0667674i
$557$			174.170i			0.312693i	0.987702	+	0.156346i	$0.0499716\pi$
$557$			174.170i			0.312693i	−0.987702	+	0.156346i	$0.950028\pi$
$558$		0			0
$559$			1389.98i			2.48655i
$560$	−936.768	−	509.592i	−1.67280	−	0.909985i
$561$		0			0
$562$	179.907	+	22.5248i	0.320119	+	0.0400796i
$563$	−749.092			−1.33054			−0.665268	−	0.746604i	$-0.731683\pi$
$563$	−749.092			−1.33054			−0.665268	+	0.746604i	$0.731683\pi$
$564$		0			0
$565$		−	698.465i		−	1.23622i
$566$	683.823	+	85.6162i	1.20817	+	0.151265i
$567$		0			0
$568$	5.19064	−	13.2386i	0.00913845	−	0.0233075i
$569$	782.222			1.37473			0.687365	−	0.726312i	$-0.258767\pi$
$569$	782.222			1.37473			0.687365	+	0.726312i	$0.258767\pi$
$570$		0			0
$571$	314.675			0.551095			0.275547	−	0.961287i	$-0.411141\pi$
$571$	314.675			0.551095			0.275547	+	0.961287i	$0.411141\pi$
$572$	−225.774	+	887.505i	−0.394711	+	1.55158i
$573$		0			0
$574$	92.2769	−	737.023i	0.160761	−	1.28401i
$575$		−	174.480i		−	0.303444i
$576$		0			0
$577$	712.215			1.23434			0.617170	−	0.786829i	$-0.288279\pi$
$577$	712.215			1.23434			0.617170	+	0.786829i	$0.288279\pi$
$578$	559.794	+	70.0874i	0.968502	+	0.121259i
$579$		0			0
$580$	1142.97	+	290.762i	1.97063	+	0.501313i
$581$		−	1037.77i		−	1.78618i
$582$		0			0
$583$		−	564.997i		−	0.969121i
$584$	−314.602	−	123.350i	−0.538701	−	0.211215i
$585$		0			0
$586$	−74.7042	+	596.668i	−0.127482	+	1.01821i
$587$	−413.505			−0.704437			−0.352219	−	0.935918i	$-0.614573\pi$
$587$	−413.505			−0.704437			−0.352219	+	0.935918i	$0.614573\pi$
$588$		0			0
$589$		−	350.089i		−	0.594379i
$590$	78.0068	−	623.047i	0.132215	−	1.05601i
$591$		0			0
$592$	−432.307	+	794.698i	−0.730248	+	1.34240i
$593$	520.704			0.878085			0.439042	−	0.898466i	$-0.355318\pi$
$593$	520.704			0.878085			0.439042	+	0.898466i	$0.355318\pi$
$594$		0			0
$595$	175.301			0.294624
$596$	−230.668	+	906.740i	−0.387026	+	1.52138i
$597$		0			0
$598$	−137.332	−	17.1943i	−0.229653	−	0.0287531i
$599$		−	761.157i		−	1.27071i	−0.772219	−	0.635357i	$-0.780853\pi$
$599$		−	761.157i		−	1.27071i	0.772219	−	0.635357i	$-0.219147\pi$
$600$		0			0
$601$	118.405			0.197014			0.0985070	−	0.995136i	$-0.468593\pi$
$601$	118.405			0.197014			0.0985070	+	0.995136i	$0.468593\pi$
$602$	−146.236	+	1168.00i	−0.242917	+	1.94019i
$603$		0			0
$604$	65.7745	−	258.555i	0.108898	−	0.428072i
$605$			262.311i			0.433571i
$606$		0			0
$607$		−	210.770i		−	0.347232i	−0.984813	−	0.173616i	$-0.944455\pi$
$607$		−	210.770i		−	0.347232i	0.984813	−	0.173616i	$-0.0555451\pi$
$608$	302.013	+	216.875i	0.496731	+	0.356703i
$609$		0			0
$610$	482.076	+	60.3570i	0.790288	+	0.0989459i
$611$	474.356			0.776360
$612$		0			0
$613$		−	1193.70i		−	1.94730i	−0.228039	−	0.973652i	$-0.573231\pi$
$613$		−	1193.70i		−	1.94730i	0.228039	−	0.973652i	$-0.426769\pi$
$614$	215.749	+	27.0123i	0.351383	+	0.0439939i
$615$		0			0
$616$	−283.089	+	722.014i	−0.459560	+	1.17210i
$617$	−244.741			−0.396663			−0.198331	−	0.980135i	$-0.563552\pi$
$617$	−244.741			−0.396663			−0.198331	+	0.980135i	$0.563552\pi$
$618$		0			0
$619$	−981.731			−1.58600			−0.792998	−	0.609225i	$-0.791481\pi$
$619$	−981.731			−1.58600			−0.792998	+	0.609225i	$0.791481\pi$
$620$	−989.898	−	251.822i	−1.59661	−	0.406165i
$621$		0			0
$622$	−1.28243	+	10.2428i	−0.00206178	+	0.0164676i
$623$			713.475i			1.14523i
$624$		0			0
$625$	397.135			0.635416
$626$	211.353	+	26.4619i	0.337625	+	0.0422714i
$627$		0			0
$628$	−121.926	+	479.285i	−0.194150	+	0.763193i
$629$		−	148.715i		−	0.236431i
$630$		0			0
$631$			775.932i			1.22969i	0.788650	+	0.614843i	$0.210781\pi$
$631$			775.932i			1.22969i	−0.788650	+	0.614843i	$0.789219\pi$
$632$	111.245	−	283.727i	0.176020	−	0.448936i
$633$		0			0
$634$	69.7118	−	556.794i	0.109956	−	0.878224i
$635$	−1865.96			−2.93852
$636$		0			0
$637$			238.588i			0.374550i
$638$	106.552	−	851.037i	0.167009	−	1.33391i
$639$		0			0
$640$	830.468	−	697.959i	1.29761	−	1.09056i
$641$	−954.825			−1.48959			−0.744794	−	0.667295i	$-0.767452\pi$
$641$	−954.825			−1.48959			−0.744794	+	0.667295i	$0.767452\pi$
$642$		0			0
$643$	527.110			0.819767			0.409883	−	0.912138i	$-0.365569\pi$
$643$	527.110			0.819767			0.409883	+	0.912138i	$0.365569\pi$
$644$	−113.591	−	28.8966i	−0.176383	−	0.0448706i
$645$		0			0
$646$	−60.6475	−	7.59320i	−0.0938816	−	0.0117542i
$647$			351.365i			0.543068i	0.962429	+	0.271534i	$0.0875310\pi$
$647$			351.365i			0.543068i	−0.962429	+	0.271534i	$0.912469\pi$
$648$		0			0
$649$	−456.640			−0.703605
$650$	216.094	−	1725.96i	0.332453	−	2.65533i
$651$		0			0
$652$	594.507	+	151.238i	0.911820	+	0.231960i
$653$			146.581i			0.224473i	0.993682	+	0.112236i	$0.0358014\pi$
$653$			146.581i			0.224473i	−0.993682	+	0.112236i	$0.964199\pi$
$654$		0			0
$655$			647.170i			0.988046i
$656$	663.747	+	361.071i	1.01181	+	0.550413i
$657$		0			0
$658$	398.600	+	49.9055i	0.605774	+	0.0758443i
$659$	1093.14			1.65878			0.829389	−	0.558671i	$-0.188689\pi$
$659$	1093.14			1.65878			0.829389	+	0.558671i	$0.188689\pi$
$660$		0			0
$661$			842.784i			1.27501i	0.770445	+	0.637507i	$0.220034\pi$
$661$			842.784i			1.27501i	−0.770445	+	0.637507i	$0.779966\pi$
$662$	−1095.76	−	137.192i	−1.65523	−	0.207239i
$663$		0			0
$664$	982.839	+	385.354i	1.48018	+	0.580352i
$665$	774.424			1.16455
$666$		0			0
$667$	129.625			0.194340
$668$	−252.407	+	992.195i	−0.377854	+	1.48532i
$669$		0			0
$670$	5.90425	−	47.1577i	0.00881231	−	0.0703846i
$671$		−	353.320i		−	0.526558i
$672$		0			0
$673$	−289.359			−0.429954			−0.214977	−	0.976619i	$-0.568968\pi$
$673$	−289.359			−0.429954			−0.214977	+	0.976619i	$0.568968\pi$
$674$	160.249	+	20.0636i	0.237758	+	0.0297679i
$675$		0			0
$676$	−682.066	−	173.512i	−1.00897	−	0.256675i
$677$			964.734i			1.42501i	0.701665	+	0.712507i	$0.252440\pi$
$677$			964.734i			1.42501i	−0.701665	+	0.712507i	$0.747560\pi$
$678$		0			0
$679$		−	179.352i		−	0.264141i
$680$	−65.0946	+	166.023i	−0.0957273	+	0.244151i
$681$		0			0
$682$	−92.2821	+	737.064i	−0.135311	+	1.08074i
$683$	−893.843			−1.30870			−0.654351	−	0.756191i	$-0.727058\pi$
$683$	−893.843			−1.30870			−0.654351	+	0.756191i	$0.727058\pi$
$684$		0			0
$685$			694.326i			1.01361i
$686$	70.6440	−	564.240i	0.102980	−	0.822507i
$687$		0			0
$688$	−1051.87	−	572.207i	−1.52888	−	0.831696i
$689$	851.278			1.23553
$690$		0			0
$691$	−536.144			−0.775895			−0.387948	−	0.921681i	$-0.626816\pi$
$691$	−536.144			−0.775895			−0.387948	+	0.921681i	$0.626816\pi$
$692$	179.644	−	706.171i	0.259602	−	1.02048i
$693$		0			0
$694$	−293.718	−	36.7741i	−0.423224	−	0.0529886i
$695$			319.035i			0.459043i
$696$		0			0
$697$	−124.210			−0.178206
$698$	−61.5442	+	491.558i	−0.0881722	+	0.704239i
$699$		0			0
$700$	363.166	−	1427.58i	0.518809	−	2.03941i
$701$			215.436i			0.307326i	0.988123	+	0.153663i	$0.0491071\pi$
$701$			215.436i			0.307326i	−0.988123	+	0.153663i	$0.950893\pi$
$702$		0			0
$703$		−	656.975i		−	0.934531i
$704$	−578.678	−	536.210i	−0.821986	−	0.761662i
$705$		0			0
$706$	−289.693	−	36.2702i	−0.410330	−	0.0513742i
$707$	−908.892			−1.28556
$708$		0			0
$709$			987.806i			1.39324i	0.717441	+	0.696619i	$0.245313\pi$
$709$			987.806i			1.39324i	−0.717441	+	0.696619i	$0.754687\pi$
$710$	29.8953	+	3.74296i	0.0421061	+	0.00527178i
$711$		0			0
$712$	−675.711	−	264.934i	−0.949032	−	0.372099i
$713$	−112.265			−0.157455
$714$		0			0
$715$	−1940.32			−2.71374
$716$	636.954	+	162.036i	0.889600	+	0.226307i
$717$		0			0
$718$	−14.9846	+	119.683i	−0.0208699	+	0.166689i
$719$			40.4042i			0.0561950i	0.999605	+	0.0280975i	$0.00894488\pi$
$719$			40.4042i			0.0561950i	−0.999605	+	0.0280975i	$0.991055\pi$
$720$		0			0
$721$	−171.793			−0.238271
$722$	448.486	+	56.1514i	0.621172	+	0.0777721i
$723$		0			0
$724$	166.941	−	656.236i	0.230582	−	0.906403i
$725$			1629.10i			2.24703i
$726$		0			0
$727$		−	163.660i		−	0.225117i	−0.993645	−	0.112559i	$-0.964095\pi$
$727$		−	163.660i		−	0.225117i	0.993645	−	0.112559i	$-0.0359046\pi$
$728$	−1087.85	−	426.529i	−1.49431	−	0.585891i
$729$		0			0
$730$	88.9473	−	710.429i	0.121846	−	0.973191i
$731$	196.841			0.269277
$732$		0			0
$733$			629.486i			0.858781i	0.903119	+	0.429390i	$0.141272\pi$
$733$			629.486i			0.858781i	−0.903119	+	0.429390i	$0.858728\pi$
$734$	−110.456	+	882.217i	−0.150484	+	1.20193i
$735$		0			0
$736$	69.5468	−	96.8483i	0.0944929	−	0.131587i
$737$	−34.5625			−0.0468963
$738$		0			0
$739$	−526.754			−0.712793			−0.356397	−	0.934335i	$-0.615995\pi$
$739$	−526.754			−0.712793			−0.356397	+	0.934335i	$0.615995\pi$
$740$	−1857.64	−	472.569i	−2.51032	−	0.638606i
$741$		0			0
$742$	715.326	+	89.5604i	0.964051	+	0.120701i
$743$			354.791i			0.477511i	0.971080	+	0.238755i	$0.0767394\pi$
$743$			354.791i			0.477511i	−0.971080	+	0.238755i	$0.923261\pi$
$744$		0			0
$745$	−1982.37			−2.66090
$746$	−44.5727	+	356.006i	−0.0597489	+	0.477219i
$747$		0			0
$748$	125.683	+	31.9729i	0.168026	+	0.0427445i
$749$		−	911.917i		−	1.21751i
$750$		0			0
$751$		−	134.214i		−	0.178714i	−0.996000	−	0.0893568i	$-0.971519\pi$
$751$		−	134.214i		−	0.178714i	0.996000	−	0.0893568i	$-0.0284811\pi$
$752$	−195.276	+	358.970i	−0.259675	+	0.477354i
$753$		0			0
$754$	1282.25	+	160.541i	1.70060	+	0.212919i
$755$	565.270			0.748703
$756$		0			0
$757$		−	233.323i		−	0.308221i	−0.988054	−	0.154110i	$-0.950749\pi$
$757$		−	233.323i		−	0.308221i	0.988054	−	0.154110i	$-0.0492512\pi$
$758$	723.145	+	90.5394i	0.954017	+	0.119445i
$759$		0			0
$760$	−287.566	+	733.434i	−0.378377	+	0.965044i
$761$	−208.640			−0.274165			−0.137083	−	0.990560i	$-0.543773\pi$
$761$	−208.640			−0.274165			−0.137083	+	0.990560i	$0.543773\pi$
$762$		0			0
$763$	1041.54			1.36506
$764$	136.650	−	537.164i	0.178862	−	0.703095i
$765$		0			0
$766$	−160.011	+	1278.02i	−0.208892	+	1.66844i
$767$		−	688.017i		−	0.897023i
$768$		0			0
$769$	−1089.77			−1.41713			−0.708565	−	0.705645i	$-0.750657\pi$
$769$	−1089.77			−1.41713			−0.708565	+	0.705645i	$0.750657\pi$
$770$	−1630.44	−	204.135i	−2.11746	−	0.265111i
$771$		0			0
$772$	1035.77	+	263.492i	1.34167	+	0.341311i
$773$			470.993i			0.609306i	0.952463	+	0.304653i	$0.0985405\pi$
$773$			470.993i			0.609306i	−0.952463	+	0.304653i	$0.901460\pi$
$774$		0			0
$775$		−	1410.92i		−	1.82055i
$776$	169.859	+	66.5986i	0.218890	+	0.0858229i
$777$		0			0
$778$	−25.0007	+	199.683i	−0.0321346	+	0.256662i
$779$	−548.718			−0.704387
$780$		0			0
$781$		−	21.9107i		−	0.0280547i
$782$	−2.43496	+	19.4482i	−0.00311376	+	0.0248699i
$783$		0			0
$784$	−180.552	−	98.2183i	−0.230296	−	0.125279i
$785$	−1047.84			−1.33483
$786$		0			0
$787$	606.203			0.770271			0.385135	−	0.922860i	$-0.374155\pi$
$787$	606.203			0.770271			0.385135	+	0.922860i	$0.374155\pi$
$788$	−134.853	+	530.101i	−0.171134	+	0.672717i
$789$		0			0
$790$	640.710	+	80.2183i	0.811025	+	0.101542i
$791$		−	648.119i		−	0.819367i
$792$		0			0
$793$	532.346			0.671306
$794$	−31.4886	+	251.502i	−0.0396581	+	0.316753i
$795$		0			0
$796$	68.1736	−	267.986i	0.0856452	−	0.336666i
$797$		−	1312.55i		−	1.64686i	−0.567415	−	0.823432i	$-0.692056\pi$
$797$		−	1312.55i		−	1.64686i	0.567415	−	0.823432i	$-0.307944\pi$
$798$		0			0
$799$		−	67.1756i		−	0.0840746i
$800$	1217.17	+	874.047i	1.52146	+	1.09256i
$801$		0			0
$802$	485.394	+	60.7724i	0.605230	+	0.0757761i
$803$	−520.684			−0.648423
$804$		0			0
$805$		−	248.340i		−	0.308496i
$806$	−1110.53	−	139.041i	−1.37783	−	0.172507i
$807$		0			0
$808$	337.498	−	860.784i	0.417696	−	1.06533i
$809$	−1250.49			−1.54572			−0.772862	−	0.634575i	$-0.781175\pi$
$809$	−1250.49			−1.54572			−0.772862	+	0.634575i	$0.781175\pi$
$810$		0			0
$811$	−358.157			−0.441624			−0.220812	−	0.975316i	$-0.570871\pi$
$811$	−358.157			−0.441624			−0.220812	+	0.975316i	$0.570871\pi$
$812$	1060.58	+	269.804i	1.30613	+	0.332271i
$813$		0			0
$814$	−173.176	+	1383.17i	−0.212747	+	1.69923i
$815$			1299.75i			1.59478i
$816$		0			0
$817$	869.581			1.06436
$818$	954.126	+	119.459i	1.16641	+	0.146037i
$819$		0			0
$820$	−394.698	+	1551.53i	−0.481339	+	1.89211i
$821$		−	108.884i		−	0.132624i	−0.997799	−	0.0663120i	$-0.978877\pi$
$821$		−	108.884i		−	0.132624i	0.997799	−	0.0663120i	$-0.0211233\pi$
$822$		0			0
$823$			748.385i			0.909338i	0.890661	+	0.454669i	$0.150242\pi$
$823$			748.385i			0.909338i	−0.890661	+	0.454669i	$0.849758\pi$
$824$	63.7918	−	162.700i	0.0774172	−	0.197451i
$825$		0			0
$826$	72.3841	−	578.138i	0.0876321	−	0.699924i
$827$	947.300			1.14547			0.572733	−	0.819742i	$-0.305883\pi$
$827$	947.300			1.14547			0.572733	+	0.819742i	$0.305883\pi$
$828$		0			0
$829$			910.959i			1.09886i	0.835538	+	0.549432i	$0.185156\pi$
$829$			910.959i			1.09886i	−0.835538	+	0.549432i	$0.814844\pi$
$830$	−277.878	+	2219.44i	−0.334793	+	2.67402i
$831$		0			0
$832$	807.905	−	871.892i	0.971039	−	1.04795i
$833$	33.7875			0.0405612
$834$		0			0
$835$	−2169.20			−2.59785
$836$	555.228	+	141.246i	0.664148	+	0.168954i
$837$		0			0
$838$	82.5340	+	10.3334i	0.0984892	+	0.0123311i
$839$			231.400i			0.275805i	0.990446	+	0.137902i	$0.0440360\pi$
$839$			231.400i			0.275805i	−0.990446	+	0.137902i	$0.955964\pi$
$840$		0			0
$841$	−369.289			−0.439107
$842$	70.5936	−	563.836i	0.0838403	−	0.669639i
$843$		0			0
$844$	620.146	+	157.760i	0.734770	+	0.186920i
$845$		−	1491.18i		−	1.76471i
$846$		0			0
$847$			243.403i			0.287371i
$848$	−350.441	+	644.207i	−0.413256	+	0.759678i
$849$		0			0
$850$	−244.421	−	30.6020i	−0.287554	−	0.0360024i
$851$	−210.677			−0.247564
$852$		0			0
$853$			531.445i			0.623031i	0.950241	+	0.311515i	$0.100837\pi$
$853$			531.445i			0.623031i	−0.950241	+	0.311515i	$0.899163\pi$
$854$	447.328	+	56.0064i	0.523803	+	0.0655813i
$855$		0			0
$856$	863.649	+	338.622i	1.00894	+	0.395586i
$857$	−686.370			−0.800899			−0.400449	−	0.916319i	$-0.631146\pi$
$857$	−686.370			−0.800899			−0.400449	+	0.916319i	$0.631146\pi$
$858$		0			0
$859$	−130.522			−0.151946			−0.0759731	−	0.997110i	$-0.524206\pi$
$859$	−130.522			−0.151946			−0.0759731	+	0.997110i	$0.524206\pi$
$860$	625.498	−	2458.79i	0.727323	−	2.85906i
$861$		0			0
$862$	191.900	−	1532.72i	0.222621	−	1.77809i
$863$		−	233.883i		−	0.271012i	−0.990777	−	0.135506i	$-0.956734\pi$
$863$		−	233.883i		−	0.271012i	0.990777	−	0.135506i	$-0.0432660\pi$
$864$		0			0
$865$	1543.88			1.78483
$866$	−1047.37	−	131.133i	−1.20943	−	0.151423i
$867$		0			0
$868$	−918.546	−	233.671i	−1.05823	−	0.269206i
$869$		−	469.585i		−	0.540374i
$870$		0			0
$871$		−	52.0752i		−	0.0597878i
$872$	−386.755	+	986.412i	−0.443526	+	1.13121i
$873$		0			0
$874$	−10.7569	+	85.9159i	−0.0123076	+	0.0983019i
$875$	1454.82			1.66265
$876$		0			0
$877$		−	927.030i		−	1.05705i	−0.848919	−	0.528523i	$-0.822746\pi$
$877$		−	927.030i		−	1.05705i	0.848919	−	0.528523i	$-0.177254\pi$
$878$	−39.5089	+	315.560i	−0.0449987	+	0.359408i
$879$		0			0
$880$	798.762	−	1468.34i	0.907684	−	1.66857i
$881$	768.692			0.872522			0.436261	−	0.899820i	$-0.356302\pi$
$881$	768.692			0.872522			0.436261	+	0.899820i	$0.356302\pi$
$882$		0			0
$883$	977.326			1.10682			0.553412	−	0.832908i	$-0.313325\pi$
$883$	977.326			1.10682			0.553412	+	0.832908i	$0.313325\pi$
$884$	−48.1734	+	189.367i	−0.0544948	+	0.214216i
$885$		0			0
$886$	−345.771	−	43.2912i	−0.390260	−	0.0488614i
$887$			422.377i			0.476186i	0.971242	+	0.238093i	$0.0765223\pi$
$887$			422.377i			0.476186i	−0.971242	+	0.238093i	$0.923478\pi$
$888$		0			0
$889$	−1731.46			−1.94765
$890$	191.044	−	1525.88i	0.214656	−	1.71447i
$891$		0			0
$892$	−1.20961	+	4.75491i	−0.00135607	+	0.00533061i
$893$		−	296.760i		−	0.332318i
$894$		0			0
$895$			1392.55i			1.55592i
$896$	770.608	−	647.650i	0.860054	−	0.722823i
$897$		0			0
$898$	−715.185	−	89.5427i	−0.796420	−	0.0997135i
$899$	1048.20			1.16597
$900$		0			0
$901$		−	120.553i		−	0.133799i
$902$	1155.25	+	144.640i	1.28076	+	0.160355i
$903$		0			0
$904$	613.814	+	240.666i	0.678998	+	0.266223i
$905$	1434.70			1.58531
$906$		0			0
$907$	813.650			0.897078			0.448539	−	0.893763i	$-0.351945\pi$
$907$	813.650			0.897078			0.448539	+	0.893763i	$0.351945\pi$
$908$	254.176	+	64.6603i	0.279929	+	0.0712118i
$909$		0			0
$910$	307.569	−	2456.58i	0.337988	−	2.69954i
$911$		−	1306.03i		−	1.43362i	−0.697268	−	0.716810i	$-0.745601\pi$
$911$		−	1306.03i		−	1.43362i	0.697268	−	0.716810i	$-0.254399\pi$
$912$		0			0
$913$	1626.66			1.78166
$914$	92.9739	+	11.6405i	0.101722	+	0.0127358i
$915$		0			0
$916$	−209.399	+	823.135i	−0.228602	+	0.898619i
$917$			600.522i			0.654877i
$918$		0			0
$919$		−	519.032i		−	0.564779i	−0.959300	−	0.282390i	$-0.908873\pi$
$919$		−	519.032i		−	0.564779i	0.959300	−	0.282390i	$-0.0911271\pi$
$920$	235.195	+	92.2158i	0.255647	+	0.100235i
$921$		0			0
$922$	82.6762	−	660.342i	0.0896705	−	0.716206i
$923$	33.0128			0.0357668
$924$		0			0
$925$		−	2647.73i		−	2.86241i
$926$	75.0425	−	599.371i	0.0810395	−	0.647269i
$927$		0			0
$928$	−649.348	+	904.259i	−0.699728	+	0.974417i
$929$	−1008.36			−1.08542			−0.542712	−	0.839919i	$-0.682603\pi$
$929$	−1008.36			−1.08542			−0.542712	+	0.839919i	$0.682603\pi$
$930$		0			0
$931$	149.262			0.160324
$932$	1056.27	+	268.706i	1.13333	+	0.288312i
$933$		0			0
$934$	1567.48	+	196.252i	1.67824	+	0.210119i
$935$			274.777i			0.293879i
$936$		0			0
$937$	−120.784			−0.128905			−0.0644527	−	0.997921i	$-0.520530\pi$
$937$	−120.784			−0.128905			−0.0644527	+	0.997921i	$0.520530\pi$
$938$	5.47867	−	43.7586i	0.00584080	−	0.0466509i
$939$		0			0
$940$	−839.106	−	213.462i	−0.892666	−	0.227087i
$941$			793.971i			0.843753i	0.906653	+	0.421876i	$0.138628\pi$
$941$			793.971i			0.843753i	−0.906653	+	0.421876i	$0.861372\pi$
$942$		0			0
$943$			175.961i			0.186597i
$944$	520.658	+	283.232i	0.551545	+	0.300034i
$945$		0			0
$946$	−1830.78	−	229.218i	−1.93529	−	0.242302i
$947$	1777.96			1.87747			0.938734	−	0.344643i	$-0.112000\pi$
$947$	1777.96			1.87747			0.938734	+	0.344643i	$0.112000\pi$
$948$		0			0
$949$		−	784.511i		−	0.826672i
$950$	−1079.77	−	135.190i	−1.13660	−	0.142305i
$951$		0			0
$952$	−60.4025	+	154.056i	−0.0634481	+	0.161823i
$953$	338.754			0.355461			0.177730	−	0.984079i	$-0.443124\pi$
$953$	338.754			0.355461			0.177730	+	0.984079i	$0.443124\pi$
$954$		0			0
$955$	1174.38			1.22972
$956$	271.731	−	1068.16i	0.284238	−	1.11732i
$957$		0			0
$958$	−59.4233	+	474.619i	−0.0620285	+	0.495427i
$959$			644.279i			0.671823i
$960$		0			0
$961$	53.1728			0.0553307
$962$	−2084.02	−	260.923i	−2.16634	−	0.271230i
$963$		0			0
$964$	394.464	+	100.349i	0.409195	+	0.104096i
$965$			2264.47i			2.34660i
$966$		0			0
$967$			1139.11i			1.17798i	0.808140	+	0.588991i	$0.200475\pi$
$967$			1139.11i			1.17798i	−0.808140	+	0.588991i	$0.799525\pi$
$968$	−230.520	−	90.3827i	−0.238140	−	0.0933706i
$969$		0			0
$970$	−48.0241	+	383.573i	−0.0495094	+	0.395436i
$971$	1443.81			1.48694			0.743468	−	0.668771i	$-0.233180\pi$
$971$	1443.81			1.48694			0.743468	+	0.668771i	$0.233180\pi$
$972$		0			0
$973$			296.039i			0.304254i
$974$	69.6637	−	556.409i	0.0715233	−	0.571262i
$975$		0			0
$976$	−219.148	+	402.854i	−0.224537	+	0.412760i
$977$	−323.495			−0.331110			−0.165555	−	0.986201i	$-0.552942\pi$
$977$	−323.495			−0.331110			−0.165555	+	0.986201i	$0.552942\pi$
$978$		0			0
$979$	−1118.34			−1.14233
$980$	107.366	−	422.048i	0.109557	−	0.430661i
$981$		0			0
$982$	−989.480	−	123.885i	−1.00762	−	0.126156i
$983$		−	1463.67i		−	1.48899i	−0.667630	−	0.744493i	$-0.732691\pi$
$983$		−	1463.67i		−	1.48899i	0.667630	−	0.744493i	$-0.267309\pi$
$984$		0			0
$985$	−1158.94			−1.17659
$986$	22.7349	−	181.585i	0.0230577	−	0.184164i
$987$		0			0
$988$	−212.814	+	836.559i	−0.215399	+	0.846720i
$989$		−	278.854i		−	0.281956i
$990$		0			0
$991$		−	521.147i		−	0.525880i	−0.964812	−	0.262940i	$-0.915308\pi$
$991$		−	521.147i		−	0.525880i	0.964812	−	0.262940i	$-0.0846921\pi$
$992$	562.386	−	783.158i	0.566921	−	0.789474i
$993$		0			0
$994$	27.7405	+	3.47317i	0.0279079	+	0.00349414i
$995$	585.888			0.588833
$996$		0			0
$997$			1431.25i			1.43555i	0.696274	+	0.717777i	$0.254840\pi$
$997$			1431.25i			1.43555i	−0.696274	+	0.717777i	$0.745160\pi$
$998$	−883.710	−	110.642i	−0.885481	−	0.110864i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.b.b.163.1	✓	16
3.2	odd	2	inner	216.3.b.b.163.16	yes	16
4.3	odd	2		864.3.b.b.271.15		16
8.3	odd	2	inner	216.3.b.b.163.2	yes	16
8.5	even	2		864.3.b.b.271.2		16
12.11	even	2		864.3.b.b.271.1		16
24.5	odd	2		864.3.b.b.271.16		16
24.11	even	2	inner	216.3.b.b.163.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.b.b.163.1	✓	16	1.1	even	1	trivial
216.3.b.b.163.2	yes	16	8.3	odd	2	inner
216.3.b.b.163.15	yes	16	24.11	even	2	inner
216.3.b.b.163.16	yes	16	3.2	odd	2	inner
864.3.b.b.271.1		16	12.11	even	2
864.3.b.b.271.2		16	8.5	even	2
864.3.b.b.271.15		16	4.3	odd	2
864.3.b.b.271.16		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98451 - 0.248465i) q^{2} +(3.87653 + 0.986159i) q^{4} +8.47512i q^{5} +7.86423i q^{7} +(-7.44797 - 2.92022i) q^{8} +O(q^{10})\)	\(q+(-1.98451 - 0.248465i) q^{2} +(3.87653 + 0.986159i) q^{4} +8.47512i q^{5} +7.86423i q^{7} +(-7.44797 - 2.92022i) q^{8} +(2.10577 - 16.8189i) q^{10} -12.3268 q^{11} -18.5728i q^{13} +(1.95398 - 15.6066i) q^{14} +(14.0550 + 7.64575i) q^{16} -2.63017 q^{17} -11.6192 q^{19} +(-8.35781 + 32.8541i) q^{20} +(24.4627 + 3.06278i) q^{22} +3.72601i q^{23} -46.8276 q^{25} +(-4.61467 + 36.8578i) q^{26} +(-7.75538 + 30.4859i) q^{28} -34.7892i q^{29} +30.1302i q^{31} +(-25.9925 - 18.6652i) q^{32} +(5.21958 + 0.653504i) q^{34} -66.6503 q^{35} +56.5421i q^{37} +(23.0584 + 2.88696i) q^{38} +(24.7492 - 63.1225i) q^{40} +47.2250 q^{41} -74.8399 q^{43} +(-47.7853 - 12.1562i) q^{44} +(0.925782 - 7.39429i) q^{46} +25.5404i q^{47} -12.8461 q^{49} +(92.9297 + 11.6350i) q^{50} +(18.3157 - 71.9979i) q^{52} +45.8348i q^{53} -104.471i q^{55} +(22.9653 - 58.5726i) q^{56} +(-8.64389 + 69.0394i) q^{58} +37.0444 q^{59} +28.6627i q^{61} +(7.48628 - 59.7935i) q^{62} +(46.9446 + 43.4994i) q^{64} +157.406 q^{65} +2.80385 q^{67} +(-10.1959 - 2.59376i) q^{68} +(132.268 + 16.5602i) q^{70} +1.77748i q^{71} +42.2399 q^{73} +(14.0487 - 112.208i) q^{74} +(-45.0423 - 11.4584i) q^{76} -96.9410i q^{77} +38.0946i q^{79} +(-64.7986 + 119.118i) q^{80} +(-93.7183 - 11.7337i) q^{82} -131.961 q^{83} -22.2910i q^{85} +(148.520 + 18.5951i) q^{86} +(91.8099 + 35.9970i) q^{88} +90.7241 q^{89} +146.061 q^{91} +(-3.67444 + 14.4440i) q^{92} +(6.34589 - 50.6851i) q^{94} -98.4742i q^{95} -22.8060 q^{97} +(25.4932 + 3.19181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} + 24 q^{10} + 16 q^{16} - 64 q^{19} + 80 q^{22} - 80 q^{25} - 12 q^{28} + 8 q^{34} - 72 q^{40} - 64 q^{43} - 192 q^{46} - 128 q^{49} + 84 q^{52} - 96 q^{58} + 376 q^{64} + 128 q^{67} + 192 q^{70} + 80 q^{73} + 308 q^{76} + 272 q^{82} - 136 q^{88} + 192 q^{91} + 336 q^{94} + 80 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 24 * q^10 + 16 * q^16 - 64 * q^19 + 80 * q^22 - 80 * q^25 - 12 * q^28 + 8 * q^34 - 72 * q^40 - 64 * q^43 - 192 * q^46 - 128 * q^49 + 84 * q^52 - 96 * q^58 + 376 * q^64 + 128 * q^67 + 192 * q^70 + 80 * q^73 + 308 * q^76 + 272 * q^82 - 136 * q^88 + 192 * q^91 + 336 * q^94 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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