LMFDB - Embedded newform 252.4.b.g.55.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.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:	$14.8684813214$
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} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} + \cdots + 52705588025 $ x^16 - 4x^15 + 358x^14 - 2828x^13 + 52557x^12 - 549972x^11 + 4434734x^10 - 37785264x^9 + 272741368x^8 - 1739202044x^7 + 9778426658x^6 - 39463975388x^5 + 101978126949x^4 - 176540053420x^3 + 219245087130x^2 - 139977817400*x + 52705588025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.7
Root			$4.06402 - 1.75957i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.g.55.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79845 + 2.18302i) q^{2} +(-1.53113 - 7.85211i) q^{4} -17.7710i q^{5} +(-5.15121 - 17.7895i) q^{7} +(19.8950 + 10.7792i) q^{8} +O(q^{10})$	\(q+(-1.79845 + 2.18302i) q^{2} +(-1.53113 - 7.85211i) q^{4} -17.7710i q^{5} +(-5.15121 - 17.7895i) q^{7} +(19.8950 + 10.7792i) q^{8} +(38.7945 + 31.9604i) q^{10} +10.7792i q^{11} -72.4083i q^{13} +(48.0989 + 20.7483i) q^{14} +(-59.3113 + 24.0452i) q^{16} +62.7518i q^{17} -98.1938 q^{19} +(-139.540 + 27.2097i) q^{20} +(-23.5311 - 19.3858i) q^{22} +160.312i q^{23} -190.809 q^{25} +(158.069 + 130.223i) q^{26} +(-131.798 + 67.6859i) q^{28} -90.1466 q^{29} +201.859 q^{31} +(54.1775 - 172.722i) q^{32} +(-136.988 - 112.856i) q^{34} +(-316.137 + 91.5424i) q^{35} -139.685 q^{37} +(176.597 - 214.359i) q^{38} +(191.557 - 353.554i) q^{40} -297.094i q^{41} +22.8078i q^{43} +(84.6393 - 16.5043i) q^{44} +(-349.963 - 288.313i) q^{46} +484.046 q^{47} +(-289.930 + 183.275i) q^{49} +(343.162 - 416.540i) q^{50} +(-568.558 + 110.866i) q^{52} -502.433 q^{53} +191.557 q^{55} +(89.2726 - 409.446i) q^{56} +(162.125 - 196.792i) q^{58} -148.228 q^{59} +438.958i q^{61} +(-363.035 + 440.663i) q^{62} +(279.619 + 428.903i) q^{64} -1286.77 q^{65} -667.659i q^{67} +(492.734 - 96.0811i) q^{68} +(368.719 - 854.767i) q^{70} +174.191i q^{71} -1167.55i q^{73} +(251.217 - 304.934i) q^{74} +(150.347 + 771.028i) q^{76} +(191.756 - 55.5258i) q^{77} +680.430i q^{79} +(427.308 + 1054.02i) q^{80} +(648.562 + 534.310i) q^{82} -780.502 q^{83} +1115.16 q^{85} +(-49.7899 - 41.0188i) q^{86} +(-116.191 + 214.451i) q^{88} +27.2097i q^{89} +(-1288.10 + 372.990i) q^{91} +(1258.78 - 245.458i) q^{92} +(-870.535 + 1056.68i) q^{94} +1745.00i q^{95} +212.717i q^{97} +(121.334 - 962.533i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 40 q^{4}+O(q^{10}) $ 16 * q + 40 * q^4	$ 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88}+O(q^{100}) $ 16 * q + 40 * q^4 - 304 * q^16 - 312 * q^22 - 1376 * q^25 - 816 * q^28 - 816 * q^37 - 2568 * q^46 - 640 * q^49 + 2336 * q^58 + 1120 * q^64 - 424 * q^70 + 5072 * q^85 - 3536 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.79845	+	2.18302i	−0.635849	+	0.771813i
$2$	−1.79845	+	2.18302i	−0.635849	+	0.771813i
$3$		0			0
$3$		0			0
$4$	−1.53113	−	7.85211i	−0.191391	−	0.981514i
$5$		−	17.7710i		−	1.58949i	−0.606944	−	0.794744i	$-0.707605\pi$
$5$		−	17.7710i		−	1.58949i	0.606944	−	0.794744i	$-0.292395\pi$
$6$		0			0
$7$	−5.15121	−	17.7895i	−0.278139	−	0.960541i
$7$	−5.15121	−	17.7895i	−0.278139	−	0.960541i
$8$	19.8950	+	10.7792i	0.879241	+	0.476377i
$9$		0			0
$10$	38.7945	+	31.9604i	1.22679	+	1.01068i
$11$			10.7792i			0.295459i	0.989028	+	0.147729i	$0.0471964\pi$
$11$			10.7792i			0.295459i	−0.989028	+	0.147729i	$0.952804\pi$
$12$		0			0
$13$		−	72.4083i		−	1.54480i	−0.635135	−	0.772402i	$-0.719055\pi$
$13$		−	72.4083i		−	1.54480i	0.635135	−	0.772402i	$-0.280945\pi$
$14$	48.0989	+	20.7483i	0.918213	+	0.396088i
$15$		0			0
$16$	−59.3113	+	24.0452i	−0.926739	+	0.375706i
$17$			62.7518i			0.895267i	0.894217	+	0.447634i	$0.147733\pi$
$17$			62.7518i			0.895267i	−0.894217	+	0.447634i	$0.852267\pi$
$18$		0			0
$19$	−98.1938			−1.18564			−0.592821	−	0.805334i	$-0.701986\pi$
$19$	−98.1938			−1.18564			−0.592821	+	0.805334i	$0.701986\pi$
$20$	−139.540	+	27.2097i	−1.56011	+	0.304214i
$21$		0			0
$22$	−23.5311	−	19.3858i	−0.228039	−	0.187867i
$23$			160.312i			1.45336i	0.686976	+	0.726680i	$0.258938\pi$
$23$			160.312i			1.45336i	−0.686976	+	0.726680i	$0.741062\pi$
$24$		0			0
$25$	−190.809			−1.52647
$26$	158.069	+	130.223i	1.19230	+	0.982262i
$27$		0			0
$28$	−131.798	+	67.6859i	−0.889551	+	0.456837i
$29$	−90.1466			−0.577235			−0.288617	−	0.957445i	$-0.593196\pi$
$29$	−90.1466			−0.577235			−0.288617	+	0.957445i	$0.593196\pi$
$30$		0			0
$31$	201.859			1.16952			0.584759	−	0.811207i	$-0.301189\pi$
$31$	201.859			1.16952			0.584759	+	0.811207i	$0.301189\pi$
$32$	54.1775	−	172.722i	0.299291	−	0.954162i
$33$		0			0
$34$	−136.988	−	112.856i	−0.690979	−	0.569255i
$35$	−316.137	+	91.5424i	−1.52677	+	0.442099i
$36$		0			0
$37$	−139.685			−0.620650			−0.310325	−	0.950631i	$-0.600438\pi$
$37$	−139.685			−0.620650			−0.310325	+	0.950631i	$0.600438\pi$
$38$	176.597	−	214.359i	0.753890	−	0.915094i
$39$		0			0
$40$	191.557	−	353.554i	0.757196	−	1.39754i
$41$		−	297.094i		−	1.13167i	−0.824520	−	0.565833i	$-0.808555\pi$
$41$		−	297.094i		−	1.13167i	0.824520	−	0.565833i	$-0.191445\pi$
$42$		0			0
$43$			22.8078i			0.0808875i	0.999182	+	0.0404437i	$0.0128772\pi$
$43$			22.8078i			0.0808875i	−0.999182	+	0.0404437i	$0.987123\pi$
$44$	84.6393	−	16.5043i	0.289997	−	0.0565481i
$45$		0			0
$46$	−349.963	−	288.313i	−1.12172	−	0.924118i
$47$	484.046			1.50224			0.751122	−	0.660164i	$-0.229513\pi$
$47$	484.046			1.50224			0.751122	+	0.660164i	$0.229513\pi$
$48$		0			0
$49$	−289.930	+	183.275i	−0.845277	+	0.534328i
$50$	343.162	−	416.540i	0.970608	−	1.17815i
$51$		0			0
$52$	−568.558	+	110.866i	−1.51625	+	0.295662i
$53$	−502.433			−1.30216			−0.651081	−	0.759009i	$-0.725684\pi$
$53$	−502.433			−1.30216			−0.651081	+	0.759009i	$0.725684\pi$
$54$		0			0
$55$	191.557			0.469628
$56$	89.2726	−	409.446i	0.213028	−	0.977046i
$57$		0			0
$58$	162.125	−	196.792i	0.367034	−	0.445517i
$59$	−148.228			−0.327078			−0.163539	−	0.986537i	$-0.552291\pi$
$59$	−148.228			−0.327078			−0.163539	+	0.986537i	$0.552291\pi$
$60$		0			0
$61$			438.958i			0.921357i	0.887567	+	0.460678i	$0.152394\pi$
$61$			438.958i			0.921357i	−0.887567	+	0.460678i	$0.847606\pi$
$62$	−363.035	+	440.663i	−0.743637	+	0.902649i
$63$		0			0
$64$	279.619	+	428.903i	0.546130	+	0.837700i
$65$	−1286.77			−2.45545
$66$		0			0
$67$		−	667.659i		−	1.21743i	−0.793391	−	0.608713i	$-0.791686\pi$
$67$		−	667.659i		−	1.21743i	0.793391	−	0.608713i	$-0.208314\pi$
$68$	492.734	−	96.0811i	0.878717	−	0.171346i
$69$		0			0
$70$	368.719	−	854.767i	0.629577	−	1.45949i
$71$			174.191i			0.291165i	0.989346	+	0.145582i	$0.0465056\pi$
$71$			174.191i			0.291165i	−0.989346	+	0.145582i	$0.953494\pi$
$72$		0			0
$73$		−	1167.55i		−	1.87193i	−0.352088	−	0.935967i	$-0.614528\pi$
$73$		−	1167.55i		−	1.87193i	0.352088	−	0.935967i	$-0.385472\pi$
$74$	251.217	−	304.934i	0.394640	−	0.479026i
$75$		0			0
$76$	150.347	+	771.028i	0.226921	+	1.16372i
$77$	191.756	−	55.5258i	0.283800	−	0.0821787i
$78$		0			0
$79$			680.430i			0.969042i	0.874780	+	0.484521i	$0.161006\pi$
$79$			680.430i			0.969042i	−0.874780	+	0.484521i	$0.838994\pi$
$80$	427.308	+	1054.02i	0.597181	+	1.47304i
$81$		0			0
$82$	648.562	+	534.310i	0.873435	+	0.719569i
$83$	−780.502			−1.03218			−0.516091	−	0.856534i	$-0.672614\pi$
$83$	−780.502			−1.03218			−0.516091	+	0.856534i	$0.672614\pi$
$84$		0			0
$85$	1115.16			1.42302
$86$	−49.7899	−	41.0188i	−0.0624300	−	0.0514323i
$87$		0			0
$88$	−116.191	+	214.451i	−0.140750	+	0.259779i
$89$			27.2097i			0.0324070i	0.999869	+	0.0162035i	$0.00515796\pi$
$89$			27.2097i			0.0324070i	−0.999869	+	0.0162035i	$0.994842\pi$
$90$		0			0
$91$	−1288.10	+	372.990i	−1.48385	+	0.429671i
$92$	1258.78	−	245.458i	1.42649	−	0.278160i
$93$		0			0
$94$	−870.535	+	1056.68i	−0.955201	+	1.15945i
$95$			1745.00i			1.88456i
$96$		0			0
$97$			212.717i			0.222661i	0.993783	+	0.111331i	$0.0355112\pi$
$97$			212.717i			0.222661i	−0.993783	+	0.111331i	$0.964489\pi$
$98$	121.334	−	962.533i	0.125067	−	0.992148i
$99$		0			0
$100$	292.154	+	1498.26i	0.292154	+	1.49826i
$101$		−	896.296i		−	0.883018i	−0.897257	−	0.441509i	$-0.854443\pi$
$101$		−	896.296i		−	0.883018i	0.897257	−	0.441509i	$-0.145557\pi$
$102$		0			0
$103$	−1319.65			−1.26242			−0.631210	−	0.775612i	$-0.717441\pi$
$103$	−1319.65			−1.26242			−0.631210	+	0.775612i	$0.717441\pi$
$104$	780.502	−	1440.56i	0.735908	−	1.35825i
$105$		0			0
$106$	903.603	−	1096.82i	0.827978	−	1.00503i
$107$			1490.63i			1.34677i	0.739292	+	0.673385i	$0.235160\pi$
$107$			1490.63i			1.34677i	−0.739292	+	0.673385i	$0.764840\pi$
$108$		0			0
$109$	555.346			0.488005			0.244002	−	0.969775i	$-0.421539\pi$
$109$	555.346			0.488005			0.244002	+	0.969775i	$0.421539\pi$
$110$	−344.506	+	418.172i	−0.298613	+	0.362465i
$111$		0			0
$112$	733.276	+	931.254i	0.618644	+	0.785672i
$113$	−75.1011			−0.0625214			−0.0312607	−	0.999511i	$-0.509952\pi$
$113$	−75.1011			−0.0625214			−0.0312607	+	0.999511i	$0.509952\pi$
$114$		0			0
$115$	2848.90			2.31010
$116$	138.026	+	707.841i	0.110478	+	0.566564i
$117$		0			0
$118$	266.580	−	323.583i	0.207972	−	0.252443i
$119$	1116.32	−	323.248i	0.859941	−	0.249009i
$120$		0			0
$121$	1214.81			0.912704
$122$	−958.252	−	789.445i	−0.711115	−	0.585844i
$123$		0			0
$124$	−309.073	−	1585.02i	−0.223835	−	1.14790i
$125$			1169.50i			0.836826i
$126$		0			0
$127$		−	14.4669i		−	0.0101081i	−0.999987	−	0.00505404i	$-0.998391\pi$
$127$		−	14.4669i		−	0.0101081i	0.999987	−	0.00505404i	$-0.00160876\pi$
$128$	−1439.18	−	160.949i	−0.993805	−	0.111141i
$129$		0			0
$130$	2314.19	−	2809.04i	1.56129	−	1.89515i
$131$	−2380.87			−1.58792			−0.793960	−	0.607970i	$-0.791984\pi$
$131$	−2380.87			−1.58792			−0.793960	+	0.607970i	$0.791984\pi$
$132$		0			0
$133$	505.817	+	1746.81i	0.329774	+	1.13886i
$134$	1457.51	+	1200.75i	0.939625	+	0.774099i
$135$		0			0
$136$	−676.413	+	1248.44i	−0.426485	+	0.787156i
$137$	176.710			0.110200			0.0550999	−	0.998481i	$-0.482452\pi$
$137$	176.710			0.110200			0.0550999	+	0.998481i	$0.482452\pi$
$138$		0			0
$139$	370.887			0.226318			0.113159	−	0.993577i	$-0.463903\pi$
$139$	370.887			0.226318			0.113159	+	0.993577i	$0.463903\pi$
$140$	1202.85	+	2342.18i	0.726137	+	1.41393i
$141$		0			0
$142$	−380.263	−	313.275i	−0.224725	−	0.185137i
$143$	780.502			0.456425
$144$		0			0
$145$			1602.00i			0.917508i
$146$	2548.78	+	2099.78i	1.44478	+	1.19027i
$147$		0			0
$148$	213.875	+	1096.82i	0.118787	+	0.609176i
$149$	−2274.32			−1.25047			−0.625234	−	0.780437i	$-0.714997\pi$
$149$	−2274.32			−1.25047			−0.625234	+	0.780437i	$0.714997\pi$
$150$		0			0
$151$		−	2222.44i		−	1.19774i	−0.800845	−	0.598872i	$-0.795616\pi$
$151$		−	2222.44i		−	1.19774i	0.800845	−	0.598872i	$-0.204384\pi$
$152$	−1953.56	−	1058.45i	−1.04247	−	0.564812i
$153$		0			0
$154$	−223.650	+	518.467i	−0.117027	+	0.271294i
$155$		−	3587.25i		−	1.85893i
$156$		0			0
$157$		−	158.340i		−	0.0804901i	−0.999190	−	0.0402450i	$-0.987186\pi$
$157$		−	158.340i		−	0.0804901i	0.999190	−	0.0402450i	$-0.0128139\pi$
$158$	−1485.39	−	1223.72i	−0.747919	−	0.616165i
$159$		0			0
$160$	−3069.44	−	962.791i	−1.51663	−	0.475720i
$161$	2851.86	−	825.799i	1.39601	−	0.404237i
$162$		0			0
$163$			1468.12i			0.705470i	0.935723	+	0.352735i	$0.114748\pi$
$163$			1468.12i			0.705470i	−0.935723	+	0.352735i	$0.885252\pi$
$164$	−2332.82	+	454.890i	−1.11075	+	0.216591i
$165$		0			0
$166$	1403.70	−	1703.85i	0.656313	−	0.796652i
$167$	2529.10			1.17190			0.585950	−	0.810347i	$-0.300721\pi$
$167$	2529.10			1.17190			0.585950	+	0.810347i	$0.300721\pi$
$168$		0			0
$169$	−3045.96			−1.38642
$170$	−2005.57	+	2434.42i	−0.904825	+	1.09830i
$171$		0			0
$172$	179.090	−	34.9217i	0.0793922	−	0.0154811i
$173$		−	834.063i		−	0.366547i	−0.983062	−	0.183273i	$-0.941331\pi$
$173$		−	834.063i		−	0.366547i	0.983062	−	0.183273i	$-0.0586694\pi$
$174$		0			0
$175$	982.900	+	3394.40i	0.424573	+	1.46624i
$176$	−259.187	−	639.327i	−0.111006	−	0.273813i
$177$		0			0
$178$	−59.3993	−	48.9354i	−0.0250122	−	0.0206060i
$179$		−	2094.57i		−	0.874611i	−0.899313	−	0.437305i	$-0.855933\pi$
$179$		−	2094.57i		−	0.874611i	0.899313	−	0.437305i	$-0.144067\pi$
$180$		0			0
$181$		−	2968.74i		−	1.21914i	−0.792732	−	0.609571i	$-0.791342\pi$
$181$		−	2968.74i		−	1.21914i	0.792732	−	0.609571i	$-0.208658\pi$
$182$	1502.35	−	3482.76i	0.611877	−	1.41846i
$183$		0			0
$184$	−1728.03	+	3189.39i	−0.692347	+	1.27785i
$185$			2482.34i			0.986516i
$186$		0			0
$187$	−676.413			−0.264514
$188$	−741.138	−	3800.79i	−0.287516	−	1.47447i
$189$		0			0
$190$	−3809.37	−	3138.31i	−1.45453	−	1.19830i
$191$		−	2411.20i		−	0.913446i	−0.889609	−	0.456723i	$-0.849023\pi$
$191$		−	2411.20i		−	0.913446i	0.889609	−	0.456723i	$-0.150977\pi$
$192$		0			0
$193$	2435.71			0.908426			0.454213	−	0.890893i	$-0.349921\pi$
$193$	2435.71			0.908426			0.454213	+	0.890893i	$0.349921\pi$
$194$	−464.365	−	382.561i	−0.171853	−	0.141579i
$195$		0			0
$196$	1883.01	+	1995.95i	0.686229	+	0.727385i
$197$	2087.70			0.755039			0.377520	−	0.926002i	$-0.376777\pi$
$197$	2087.70			0.755039			0.377520	+	0.926002i	$0.376777\pi$
$198$		0			0
$199$	−3388.82			−1.20717			−0.603585	−	0.797299i	$-0.706262\pi$
$199$	−3388.82			−1.20717			−0.603585	+	0.797299i	$0.706262\pi$
$200$	−3796.14	−	2056.77i	−1.34214	−	0.727177i
$201$		0			0
$202$	1956.63	+	1611.95i	0.681525	+	0.561466i
$203$	464.365	+	1603.66i	0.160552	+	0.554457i
$204$		0			0
$205$	−5279.67			−1.79877
$206$	2373.33	−	2880.83i	0.802709	−	0.974352i
$207$		0			0
$208$	1741.07	+	4294.63i	0.580392	+	1.43163i
$209$		−	1058.45i		−	0.350308i
$210$		0			0
$211$		−	4614.70i		−	1.50564i	−0.658228	−	0.752818i	$-0.728694\pi$
$211$		−	4614.70i		−	1.50564i	0.658228	−	0.752818i	$-0.271306\pi$
$212$	769.290	+	3945.16i	0.249222	+	1.27809i
$213$		0			0
$214$	−3254.06	−	2680.82i	−1.03945	−	0.856343i
$215$	405.319			0.128570
$216$		0			0
$217$	−1039.82	−	3590.97i	−0.325289	−	1.12337i
$218$	−998.765	+	1212.33i	−0.310298	+	0.376649i
$219$		0			0
$220$	−293.298	−	1504.13i	−0.0898826	−	0.460946i
$221$	4543.75			1.38301
$222$		0			0
$223$	−294.922			−0.0885625			−0.0442812	−	0.999019i	$-0.514100\pi$
$223$	−294.922			−0.0885625			−0.0442812	+	0.999019i	$0.514100\pi$
$224$	−3351.71	−	74.0629i	−0.999756	−	0.0220917i
$225$		0			0
$226$	135.066	−	163.947i	0.0397542	−	0.0482548i
$227$	−2272.00			−0.664310			−0.332155	−	0.943225i	$-0.607776\pi$
$227$	−2272.00			−0.664310			−0.332155	+	0.943225i	$0.607776\pi$
$228$		0			0
$229$		−	3054.67i		−	0.881478i	−0.897635	−	0.440739i	$-0.854717\pi$
$229$		−	3054.67i		−	0.881478i	0.897635	−	0.440739i	$-0.145283\pi$
$230$	−5123.62	+	6219.20i	−1.46888	+	1.78297i
$231$		0			0
$232$	−1793.46	−	971.706i	−0.507529	−	0.274981i
$233$	3277.16			0.921433			0.460717	−	0.887547i	$-0.347592\pi$
$233$	3277.16			0.921433			0.460717	+	0.887547i	$0.347592\pi$
$234$		0			0
$235$		−	8602.00i		−	2.38780i
$236$	226.955	+	1163.90i	0.0625997	+	0.321031i
$237$		0			0
$238$	−1302.00	+	3018.29i	−0.354604	+	0.822046i
$239$		−	5776.27i		−	1.56333i	−0.623698	−	0.781665i	$-0.714371\pi$
$239$		−	5776.27i		−	1.56333i	0.623698	−	0.781665i	$-0.285629\pi$
$240$		0			0
$241$		−	321.470i		−	0.0859240i	−0.999077	−	0.0429620i	$-0.986321\pi$
$241$		−	321.470i		−	0.0859240i	0.999077	−	0.0429620i	$-0.0136794\pi$
$242$	−2184.78	+	2651.95i	−0.580342	+	0.704437i
$243$		0			0
$244$	3446.74	−	672.101i	0.904324	−	0.176339i
$245$	3256.98	+	5152.35i	0.849309	+	1.34356i
$246$		0			0
$247$			7110.04i			1.83158i
$248$	4015.99	+	2175.88i	1.02829	+	0.557131i
$249$		0			0
$250$	−2553.04	−	2103.29i	−0.645873	−	0.532095i
$251$	1818.09			0.457200			0.228600	−	0.973520i	$-0.426585\pi$
$251$	1818.09			0.457200			0.228600	+	0.973520i	$0.426585\pi$
$252$		0			0
$253$	−1728.03			−0.429408
$254$	31.5814	+	26.0180i	0.00780155	+	0.00642722i
$255$		0			0
$256$	2939.66	−	2852.30i	0.717690	−	0.696363i
$257$			2438.33i			0.591824i	0.955215	+	0.295912i	$0.0956236\pi$
$257$			2438.33i			0.591824i	−0.955215	+	0.295912i	$0.904376\pi$
$258$		0			0
$259$	719.546	+	2484.92i	0.172627	+	0.596159i
$260$	1970.21	+	10103.9i	0.469951	+	2.41006i
$261$		0			0
$262$	4281.88	−	5197.48i	1.00968	−	1.22558i
$263$			4083.47i			0.957406i	0.877977	+	0.478703i	$0.158893\pi$
$263$			4083.47i			0.957406i	−0.877977	+	0.478703i	$0.841107\pi$
$264$		0			0
$265$			8928.76i			2.06977i
$266$	−4723.01	−	2037.36i	−1.08867	−	0.469618i
$267$		0			0
$268$	−5242.53	+	1022.27i	−1.19492	+	0.233004i
$269$		−	2121.53i		−	0.480862i	−0.970666	−	0.240431i	$-0.922711\pi$
$269$		−	2121.53i		−	0.480862i	0.970666	−	0.240431i	$-0.0772888\pi$
$270$		0			0
$271$	6897.68			1.54614			0.773070	−	0.634321i	$-0.218720\pi$
$271$	6897.68			1.54614			0.773070	+	0.634321i	$0.218720\pi$
$272$	−1508.88	−	3721.89i	−0.336357	−	0.829679i
$273$		0			0
$274$	−317.805	+	385.762i	−0.0700705	+	0.0850537i
$275$		−	2056.77i		−	0.451010i
$276$		0			0
$277$	−1456.63			−0.315957			−0.157979	−	0.987443i	$-0.550498\pi$
$277$	−1456.63			−0.315957			−0.157979	+	0.987443i	$0.550498\pi$
$278$	−667.024	+	809.654i	−0.143904	+	0.174676i
$279$		0			0
$280$	−7276.28	−	1586.47i	−1.55300	−	0.338605i
$281$	−6013.55			−1.27665			−0.638325	−	0.769767i	$-0.720372\pi$
$281$	−6013.55			−1.27665			−0.638325	+	0.769767i	$0.720372\pi$
$282$		0			0
$283$	−2485.71			−0.522121			−0.261060	−	0.965322i	$-0.584072\pi$
$283$	−2485.71			−0.522121			−0.261060	+	0.965322i	$0.584072\pi$
$284$	1367.77	−	266.709i	0.285782	−	0.0557264i
$285$		0			0
$286$	−1403.70	+	1703.85i	−0.290218	+	0.352275i
$287$	−5285.15	+	1530.40i	−1.08701	+	0.314761i
$288$		0			0
$289$	975.214			0.198497
$290$	−3497.19	−	2881.12i	−0.708145	−	0.583397i
$291$		0			0
$292$	−9167.72	+	1787.67i	−1.83733	+	0.358272i
$293$		−	2245.72i		−	0.447769i	−0.974616	−	0.223884i	$-0.928126\pi$
$293$		−	2245.72i		−	0.447769i	0.974616	−	0.223884i	$-0.0718738\pi$
$294$		0			0
$295$			2634.15i			0.519886i
$296$	−2779.02	−	1505.69i	−0.545701	−	0.295663i
$297$		0			0
$298$	4090.27	−	4964.89i	0.795110	−	0.965128i
$299$	11607.9			2.24516
$300$		0			0
$301$	405.739	−	117.488i	0.0776957	−	0.0224980i
$302$	4851.62	+	3996.95i	0.924435	+	0.761585i
$303$		0			0
$304$	5824.00	−	2361.09i	1.09878	−	0.445453i
$305$	7800.73			1.46449
$306$		0			0
$307$	−839.287			−0.156028			−0.0780141	−	0.996952i	$-0.524858\pi$
$307$	−839.287			−0.156028			−0.0780141	+	0.996952i	$0.524858\pi$
$308$	−729.598	−	1420.67i	−0.134976	−	0.262825i
$309$		0			0
$310$	7831.03	+	6451.50i	1.43475	+	1.18200i
$311$	1155.68			0.210717			0.105358	−	0.994434i	$-0.466401\pi$
$311$	1155.68			0.210717			0.105358	+	0.994434i	$0.466401\pi$
$312$		0			0
$313$		−	4244.76i		−	0.766543i	−0.923636	−	0.383272i	$-0.874797\pi$
$313$		−	4244.76i		−	0.766543i	0.923636	−	0.383272i	$-0.125203\pi$
$314$	345.660	+	284.768i	0.0621233	+	0.0511796i
$315$		0			0
$316$	5342.81	−	1041.83i	0.951128	−	0.185466i
$317$	3876.67			0.686863			0.343431	−	0.939178i	$-0.388411\pi$
$317$	3876.67			0.686863			0.343431	+	0.939178i	$0.388411\pi$
$318$		0			0
$319$		−	971.706i		−	0.170549i
$320$	7622.04	−	4969.11i	1.33152	−	0.868068i
$321$		0			0
$322$	−3326.20	+	7710.82i	−0.575658	+	1.33449i
$323$		−	6161.83i		−	1.06147i
$324$		0			0
$325$			13816.2i			2.35810i
$326$	−3204.92	−	2640.34i	−0.544491	−	0.448573i
$327$		0			0
$328$	3202.43	−	5910.68i	0.539100	−	0.995008i
$329$	−2493.43	−	8610.93i	−0.417833	−	1.44297i
$330$		0			0
$331$		−	475.573i		−	0.0789724i	−0.999220	−	0.0394862i	$-0.987428\pi$
$331$		−	475.573i		−	0.0789724i	0.999220	−	0.0394862i	$-0.0125721\pi$
$332$	1195.05	+	6128.58i	0.197551	+	1.01310i
$333$		0			0
$334$	−4548.46	+	5521.06i	−0.745152	+	0.904488i
$335$	−11865.0			−1.93508
$336$		0			0
$337$	10012.6			1.61847			0.809233	−	0.587488i	$-0.199883\pi$
$337$	10012.6			1.61847			0.809233	+	0.587488i	$0.199883\pi$
$338$	5478.01	−	6649.38i	0.881552	−	1.07005i
$339$		0			0
$340$	−1707.46	−	8756.39i	−0.272353	−	1.39671i
$341$			2175.88i			0.345544i
$342$		0			0
$343$	4753.85	+	4213.61i	0.748349	+	0.663305i
$344$	−245.850	+	453.761i	−0.0385329	+	0.0711196i
$345$		0			0
$346$	1820.77	+	1500.02i	0.282906	+	0.233069i
$347$			10771.5i			1.66642i	0.552959	+	0.833209i	$0.313499\pi$
$347$			10771.5i			1.66642i	−0.552959	+	0.833209i	$0.686501\pi$
$348$		0			0
$349$		−	9281.78i		−	1.42362i	−0.702373	−	0.711809i	$-0.747876\pi$
$349$		−	9281.78i		−	1.42362i	0.702373	−	0.711809i	$-0.252124\pi$
$350$	−9177.72	−	3958.98i	−1.40163	−	0.604618i
$351$		0			0
$352$	1861.80	+	583.989i	0.281915	+	0.0884282i
$353$			4527.91i			0.682709i	0.939935	+	0.341355i	$0.110886\pi$
$353$			4527.91i			0.682709i	−0.939935	+	0.341355i	$0.889114\pi$
$354$		0			0
$355$	3095.56			0.462803
$356$	213.654	−	41.6616i	0.0318079	−	0.00620242i
$357$		0			0
$358$	4572.48	+	3766.98i	0.675036	+	0.556121i
$359$		−	9834.05i		−	1.44574i	−0.690983	−	0.722871i	$-0.742822\pi$
$359$		−	9834.05i		−	1.44574i	0.690983	−	0.722871i	$-0.257178\pi$
$360$		0			0
$361$	2783.02			0.405747
$362$	6480.81	+	5339.14i	0.940950	+	0.775190i
$363$		0			0
$364$	4901.02	+	9543.24i	0.705723	+	1.37418i
$365$	−20748.5			−2.97542
$366$		0			0
$367$	−11847.0			−1.68504			−0.842518	−	0.538669i	$-0.818927\pi$
$367$	−11847.0			−1.68504			−0.842518	+	0.538669i	$0.818927\pi$
$368$	−3854.72	−	9508.29i	−0.546036	−	1.34689i
$369$		0			0
$370$	−5419.00	−	4464.38i	−0.761406	−	0.627276i
$371$	2588.14	+	8938.02i	0.362182	+	1.25078i
$372$		0			0
$373$	10310.6			1.43127			0.715634	−	0.698475i	$-0.246138\pi$
$373$	10310.6			1.43127			0.715634	+	0.698475i	$0.246138\pi$
$374$	1216.50	−	1476.62i	0.168191	−	0.204156i
$375$		0			0
$376$	9630.08	+	5217.62i	1.32083	+	0.715634i
$377$			6527.36i			0.891714i
$378$		0			0
$379$		−	3861.94i		−	0.523416i	−0.965147	−	0.261708i	$-0.915714\pi$
$379$		−	3861.94i		−	0.523416i	0.965147	−	0.261708i	$-0.0842857\pi$
$380$	13702.0	−	2671.83i	1.84973	−	0.360689i
$381$		0			0
$382$	5263.69	+	4336.43i	0.705010	+	0.580814i
$383$	−9178.43			−1.22453			−0.612266	−	0.790652i	$-0.709742\pi$
$383$	−9178.43			−1.22453			−0.612266	+	0.790652i	$0.709742\pi$
$384$		0			0
$385$	−986.751	−	3407.70i	−0.130622	−	0.451097i
$386$	−4380.51	+	5317.19i	−0.577622	+	0.701135i
$387$		0			0
$388$	1670.28	−	325.697i	0.218545	−	0.0426153i
$389$	−314.387			−0.0409770			−0.0204885	−	0.999790i	$-0.506522\pi$
$389$	−314.387			−0.0409770			−0.0204885	+	0.999790i	$0.506522\pi$
$390$		0			0
$391$	−10059.8			−1.30115
$392$	−7743.69	+	521.035i	−0.997744	+	0.0671333i
$393$		0			0
$394$	−3754.64	+	4557.49i	−0.480091	+	0.582749i
$395$	12091.9			1.54028
$396$		0			0
$397$		−	2126.89i		−	0.268880i	−0.990922	−	0.134440i	$-0.957076\pi$
$397$		−	2126.89i		−	0.268880i	0.990922	−	0.134440i	$-0.0429236\pi$
$398$	6094.63	−	7397.85i	0.767579	−	0.931710i
$399$		0			0
$400$	11317.1	−	4588.05i	1.41464	−	0.573506i
$401$	−6506.32			−0.810249			−0.405125	−	0.914261i	$-0.632772\pi$
$401$	−6506.32			−0.810249			−0.405125	+	0.914261i	$0.632772\pi$
$402$		0			0
$403$		−	14616.3i		−	1.80667i
$404$	−7037.82	+	1372.34i	−0.866694	+	0.169002i
$405$		0			0
$406$	−4335.96	−	1870.39i	−0.530024	−	0.228635i
$407$		−	1505.69i		−	0.183376i
$408$		0			0
$409$		−	3280.91i		−	0.396652i	−0.980136	−	0.198326i	$-0.936450\pi$
$409$		−	3280.91i		−	0.396652i	0.980136	−	0.198326i	$-0.0635505\pi$
$410$	9495.24	−	11525.6i	1.14375	−	1.38832i
$411$		0			0
$412$	2020.56	+	10362.1i	0.241616	+	1.23908i
$413$	763.552	+	2636.89i	0.0909732	+	0.314171i
$414$		0			0
$415$			13870.3i			1.64064i
$416$	−12506.5	−	3922.90i	−1.47399	−	0.462346i
$417$		0			0
$418$	2310.61	+	1903.57i	0.270372	+	0.222743i
$419$	1313.14			0.153105			0.0765526	−	0.997066i	$-0.475609\pi$
$419$	1313.14			0.153105			0.0765526	+	0.997066i	$0.475609\pi$
$420$		0			0
$421$	7669.52			0.887861			0.443931	−	0.896061i	$-0.353584\pi$
$421$	7669.52			0.887861			0.443931	+	0.896061i	$0.353584\pi$
$422$	10074.0	+	8299.33i	1.16207	+	0.957358i
$423$		0			0
$424$	−9995.89	−	5415.82i	−1.14491	−	0.620319i
$425$		−	11973.6i		−	1.36660i
$426$		0			0
$427$	7808.82	−	2261.16i	0.885001	−	0.256266i
$428$	11704.6	−	2282.34i	1.32187	−	0.257760i
$429$		0			0
$430$	−728.947	+	884.817i	−0.0817510	+	0.0992318i
$431$			2360.49i			0.263807i	0.991263	+	0.131903i	$0.0421088\pi$
$431$			2360.49i			0.263807i	−0.991263	+	0.131903i	$0.957891\pi$
$432$		0			0
$433$			4914.75i			0.545468i	0.962089	+	0.272734i	$0.0879279\pi$
$433$			4914.75i			0.545468i	−0.962089	+	0.272734i	$0.912072\pi$
$434$	9709.22	+	4188.25i	1.07387	+	0.463231i
$435$		0			0
$436$	−850.307	−	4360.64i	−0.0933998	−	0.478984i
$437$		−	15741.6i		−	1.72316i
$438$		0			0
$439$	−3334.78			−0.362552			−0.181276	−	0.983432i	$-0.558023\pi$
$439$	−3334.78			−0.362552			−0.181276	+	0.983432i	$0.558023\pi$
$440$	3811.02	+	2064.83i	0.412916	+	0.223720i
$441$		0			0
$442$	−8171.72	+	9919.08i	−0.879387	+	1.06743i
$443$			3590.57i			0.385086i	0.981288	+	0.192543i	$0.0616736\pi$
$443$			3590.57i			0.385086i	−0.981288	+	0.192543i	$0.938326\pi$
$444$		0			0
$445$	483.545			0.0515106
$446$	530.403	−	643.820i	0.0563124	−	0.0683537i
$447$		0			0
$448$	6189.57	−	7183.64i	0.652745	−	0.757578i
$449$	−15166.2			−1.59407			−0.797037	−	0.603931i	$-0.793600\pi$
$449$	−15166.2			−1.59407			−0.797037	+	0.603931i	$0.793600\pi$
$450$		0			0
$451$	3202.43			0.334361
$452$	114.990	+	589.702i	0.0119660	+	0.0613656i
$453$		0			0
$454$	4086.10	−	4959.83i	0.422401	−	0.512723i
$455$	6628.42	+	22890.9i	0.682957	+	2.35856i
$456$		0			0
$457$	−15092.8			−1.54489			−0.772443	−	0.635084i	$-0.780965\pi$
$457$	−15092.8			−1.54489			−0.772443	+	0.635084i	$0.780965\pi$
$458$	6668.40	+	5493.68i	0.680336	+	0.560487i
$459$		0			0
$460$	−4362.04	−	22369.9i	−0.442133	−	2.26740i
$461$		−	1332.96i		−	0.134669i	−0.997730	−	0.0673344i	$-0.978551\pi$
$461$		−	1332.96i		−	0.134669i	0.997730	−	0.0673344i	$-0.0214494\pi$
$462$		0			0
$463$			10483.5i			1.05229i	0.850394	+	0.526146i	$0.176363\pi$
$463$			10483.5i			1.05229i	−0.850394	+	0.526146i	$0.823637\pi$
$464$	5346.71	−	2167.59i	0.534946	−	0.216871i
$465$		0			0
$466$	−5893.82	+	7154.10i	−0.585893	+	0.711174i
$467$	−15964.3			−1.58188			−0.790942	−	0.611891i	$-0.790409\pi$
$467$	−15964.3			−1.58188			−0.790942	+	0.611891i	$0.790409\pi$
$468$		0			0
$469$	−11877.3	+	3439.25i	−1.16939	+	0.338614i
$470$	18778.3	+	15470.3i	1.84293	+	1.51828i
$471$		0			0
$472$	−2948.98	−	1597.77i	−0.287580	−	0.155812i
$473$	−245.850			−0.0238989
$474$		0			0
$475$	18736.3			1.80985
$476$	−4247.41	−	8270.54i	−0.408991	−	0.796385i
$477$		0			0
$478$	12609.7	+	10388.4i	1.20660	+	0.994043i
$479$	−19452.3			−1.85553			−0.927763	−	0.373170i	$-0.878271\pi$
$479$	−19452.3			−1.85553			−0.927763	+	0.373170i	$0.878271\pi$
$480$		0			0
$481$			10114.3i			0.958782i
$482$	701.774	+	578.148i	0.0663172	+	0.0546347i
$483$		0			0
$484$	−1860.03	−	9538.82i	−0.174683	−	0.895832i
$485$	3780.20			0.353917
$486$		0			0
$487$			8465.85i			0.787729i	0.919168	+	0.393865i	$0.128862\pi$
$487$			8465.85i			0.787729i	−0.919168	+	0.393865i	$0.871138\pi$
$488$	−4731.60	+	8733.04i	−0.438913	+	0.810095i
$489$		0			0
$490$	−17105.2	−	2156.23i	−1.57701	−	0.198793i
$491$		−	7175.25i		−	0.659500i	−0.944068	−	0.329750i	$-0.893035\pi$
$491$		−	7175.25i		−	0.659500i	0.944068	−	0.329750i	$-0.106965\pi$
$492$		0			0
$493$		−	5656.86i		−	0.516779i
$494$	−15521.3	−	12787.1i	−1.41364	−	1.16461i
$495$		0			0
$496$	−11972.5	+	4853.75i	−1.08384	+	0.439395i
$497$	3098.77	−	897.297i	0.279676	−	0.0809844i
$498$		0			0
$499$		−	17503.9i		−	1.57030i	−0.619303	−	0.785152i	$-0.712585\pi$
$499$		−	17503.9i		−	1.57030i	0.619303	−	0.785152i	$-0.287415\pi$
$500$	9183.04	−	1790.65i	0.821356	−	0.160161i
$501$		0			0
$502$	−3269.76	+	3968.93i	−0.290710	+	0.352873i
$503$	16033.8			1.42130			0.710648	−	0.703548i	$-0.248402\pi$
$503$	16033.8			1.42130			0.710648	+	0.703548i	$0.248402\pi$
$504$		0			0
$505$	−15928.1			−1.40355
$506$	3107.78	−	3772.31i	0.273039	−	0.331423i
$507$		0			0
$508$	−113.595	+	22.1506i	−0.00992123	+	0.00193460i
$509$			12929.7i			1.12593i	0.826480	+	0.562965i	$0.190340\pi$
$509$			12929.7i			1.12593i	−0.826480	+	0.562965i	$0.809660\pi$
$510$		0			0
$511$	−20770.1	+	6014.29i	−1.79807	+	0.520659i
$512$	939.786	+	11547.1i	0.0811193	+	0.996704i
$513$		0			0
$514$	−5322.92	−	4385.22i	−0.456778	−	0.376311i
$515$			23451.6i			2.00660i
$516$		0			0
$517$			5217.62i			0.443851i
$518$	−6718.69	−	2898.23i	−0.569889	−	0.245832i
$519$		0			0
$520$	−25600.2	−	13870.3i	−2.15893	−	1.16972i
$521$			19765.0i			1.66204i	0.556245	+	0.831018i	$0.312241\pi$
$521$			19765.0i			1.66204i	−0.556245	+	0.831018i	$0.687759\pi$
$522$		0			0
$523$	−5646.25			−0.472071			−0.236036	−	0.971744i	$-0.575848\pi$
$523$	−5646.25			−0.472071			−0.236036	+	0.971744i	$0.575848\pi$
$524$	3645.42	+	18694.8i	0.303914	+	1.55856i
$525$		0			0
$526$	−8914.29	−	7343.94i	−0.738939	−	0.608766i
$527$			12667.0i			1.04703i
$528$		0			0
$529$	−13532.8			−1.11226
$530$	−19491.6	−	16058.0i	−1.59748	−	1.31606i
$531$		0			0
$532$	12941.7	−	6646.33i	1.05469	−	0.541645i
$533$	−21512.1			−1.74820
$534$		0			0
$535$	26490.0			2.14068
$536$	7196.81	−	13283.0i	0.579953	−	1.07041i
$537$		0			0
$538$	4631.33	+	3815.47i	0.371136	+	0.305756i
$539$	−1975.55	−	3125.21i	−0.157872	−	0.249744i
$540$		0			0
$541$	6642.27			0.527862			0.263931	−	0.964542i	$-0.414981\pi$
$541$	6642.27			0.527862			0.263931	+	0.964542i	$0.414981\pi$
$542$	−12405.2	+	15057.7i	−0.983112	+	1.19333i
$543$		0			0
$544$	10838.6	+	3399.74i	0.854230	+	0.267946i
$545$		−	9869.08i		−	0.775678i
$546$		0			0
$547$		−	15445.0i		−	1.20728i	−0.797257	−	0.603640i	$-0.793717\pi$
$547$		−	15445.0i		−	1.20728i	0.797257	−	0.603640i	$-0.206283\pi$
$548$	−270.566	−	1387.55i	−0.0210913	−	0.108163i
$549$		0			0
$550$	4489.96	+	3699.00i	0.348095	+	0.286774i
$551$	8851.84			0.684394
$552$		0			0
$553$	12104.5	−	3505.04i	0.930804	−	0.269529i
$554$	2619.67	−	3179.84i	0.200901	−	0.243860i
$555$		0			0
$556$	−567.876	−	2912.25i	−0.0433153	−	0.222135i
$557$	20224.1			1.53846			0.769231	−	0.638971i	$-0.220639\pi$
$557$	20224.1			1.53846			0.769231	+	0.638971i	$0.220639\pi$
$558$		0			0
$559$	1651.48			0.124955
$560$	16549.3	−	13031.1i	1.24882	−	0.983327i
$561$		0			0
$562$	10815.1	−	13127.7i	0.811757	−	0.985335i
$563$	−12972.1			−0.971061			−0.485531	−	0.874220i	$-0.661374\pi$
$563$	−12972.1			−0.971061			−0.485531	+	0.874220i	$0.661374\pi$
$564$		0			0
$565$			1334.62i			0.0993771i
$566$	4470.44	−	5426.35i	0.331990	−	0.402980i
$567$		0			0
$568$	−1877.64	+	3465.53i	−0.138704	+	0.256004i
$569$	1451.30			0.106928			0.0534638	−	0.998570i	$-0.482974\pi$
$569$	1451.30			0.106928			0.0534638	+	0.998570i	$0.482974\pi$
$570$		0			0
$571$			8530.19i			0.625179i	0.949888	+	0.312590i	$0.101196\pi$
$571$			8530.19i			0.625179i	−0.949888	+	0.312590i	$0.898804\pi$
$572$	−1195.05	−	6128.58i	−0.0873557	−	0.447988i
$573$		0			0
$574$	6164.21	−	14289.9i	0.448239	−	1.03911i
$575$		−	30589.0i		−	2.21852i
$576$		0			0
$577$		−	21396.2i		−	1.54374i	−0.635782	−	0.771869i	$-0.719322\pi$
$577$		−	21396.2i		−	1.54374i	0.635782	−	0.771869i	$-0.280678\pi$
$578$	−1753.88	+	2128.91i	−0.126214	+	0.153202i
$579$		0			0
$580$	12579.1	−	2452.87i	0.900547	−	0.175603i
$581$	4020.53	+	13884.7i	0.287091	+	0.991454i
$582$		0			0
$583$		−	5415.82i		−	0.384735i
$584$	12585.2	−	23228.3i	0.891746	−	1.64588i
$585$		0			0
$586$	4902.44	+	4038.82i	0.345594	+	0.284714i
$587$	7212.11			0.507113			0.253557	−	0.967321i	$-0.418400\pi$
$587$	7212.11			0.507113			0.253557	+	0.967321i	$0.418400\pi$
$588$		0			0
$589$	−19821.3			−1.38663
$590$	−5750.41	−	4737.41i	−0.401255	−	0.330569i
$591$		0			0
$592$	8284.89	−	3358.75i	0.575180	−	0.233182i
$593$		−	18362.2i		−	1.27158i	−0.771863	−	0.635789i	$-0.780675\pi$
$593$		−	18362.2i		−	1.27158i	0.771863	−	0.635789i	$-0.219325\pi$
$594$		0			0
$595$	−5744.45	−	19838.2i	−0.395797	−	1.36687i
$596$	3482.28	+	17858.2i	0.239329	+	1.22735i
$597$		0			0
$598$	−20876.2	+	25340.2i	−1.42758	+	1.73284i
$599$			2402.54i			0.163881i	0.996637	+	0.0819407i	$0.0261118\pi$
$599$			2402.54i			0.163881i	−0.996637	+	0.0819407i	$0.973888\pi$
$600$		0			0
$601$		−	15264.1i		−	1.03600i	−0.855382	−	0.517998i	$-0.826677\pi$
$601$		−	15264.1i		−	1.03600i	0.855382	−	0.517998i	$-0.173323\pi$
$602$	−473.225	+	1097.03i	−0.0320385	+	0.0742719i
$603$		0			0
$604$	−17450.8	+	3402.84i	−1.17560	+	0.229238i
$605$		−	21588.4i		−	1.45073i
$606$		0			0
$607$	−18675.5			−1.24879			−0.624395	−	0.781109i	$-0.714654\pi$
$607$	−18675.5			−1.24879			−0.624395	+	0.781109i	$0.714654\pi$
$608$	−5319.90	+	16960.2i	−0.354853	+	1.13129i
$609$		0			0
$610$	−14029.2	+	17029.1i	−0.931193	+	1.13031i
$611$		−	35049.0i		−	2.32067i
$612$		0			0
$613$	6537.07			0.430718			0.215359	−	0.976535i	$-0.430908\pi$
$613$	6537.07			0.430718			0.215359	+	0.976535i	$0.430908\pi$
$614$	1509.42	−	1832.18i	0.0992104	−	0.120425i
$615$		0			0
$616$	4413.50	+	962.285i	0.288677	+	0.0629409i
$617$	−3529.67			−0.230307			−0.115153	−	0.993348i	$-0.536736\pi$
$617$	−3529.67			−0.230307			−0.115153	+	0.993348i	$0.536736\pi$
$618$		0			0
$619$	557.614			0.0362074			0.0181037	−	0.999836i	$-0.494237\pi$
$619$	557.614			0.0362074			0.0181037	+	0.999836i	$0.494237\pi$
$620$	−28167.5	+	5492.54i	−1.82457	+	0.355783i
$621$		0			0
$622$	−2078.44	+	2522.88i	−0.133984	+	0.162634i
$623$	484.046	−	140.163i	0.0311283	−	0.00901367i
$624$		0			0
$625$	−3067.96			−0.196349
$626$	9266.38	+	7634.00i	0.591628	+	0.487406i
$627$		0			0
$628$	−1243.31	+	242.440i	−0.0790021	+	0.0154051i
$629$		−	8765.47i		−	0.555647i
$630$		0			0
$631$			14053.9i			0.886650i	0.896361	+	0.443325i	$0.146201\pi$
$631$			14053.9i			0.886650i	−0.896361	+	0.443325i	$0.853799\pi$
$632$	−7334.47	+	13537.1i	−0.461629	+	0.852022i
$633$		0			0
$634$	−6972.01	+	8462.83i	−0.436741	+	0.530130i
$635$	−257.091			−0.0160667
$636$		0			0
$637$	13270.6	+	20993.3i	0.825432	+	1.30579i
$638$	2121.25	+	1747.57i	0.131632	+	0.108443i
$639$		0			0
$640$	−2860.23	+	25575.8i	−0.176657	+	1.57964i
$641$	8223.99			0.506752			0.253376	−	0.967368i	$-0.418459\pi$
$641$	8223.99			0.506752			0.253376	+	0.967368i	$0.418459\pi$
$642$		0			0
$643$	−26162.2			−1.60457			−0.802283	−	0.596944i	$-0.796381\pi$
$643$	−26162.2			−1.60457			−0.802283	+	0.596944i	$0.796381\pi$
$644$	−10850.8	−	21128.7i	−0.663948	−	1.29284i
$645$		0			0
$646$	13451.4	+	11081.8i	0.819254	+	0.674933i
$647$	28473.2			1.73014			0.865068	−	0.501654i	$-0.167275\pi$
$647$	28473.2			1.73014			0.865068	+	0.501654i	$0.167275\pi$
$648$		0			0
$649$		−	1597.77i		−	0.0966379i
$650$	−30160.9	−	24847.7i	−1.82001	−	1.49940i
$651$		0			0
$652$	11527.8	−	2247.87i	0.692429	−	0.135021i
$653$	−30403.4			−1.82202			−0.911009	−	0.412386i	$-0.864696\pi$
$653$	−30403.4			−1.82202			−0.911009	+	0.412386i	$0.864696\pi$
$654$		0			0
$655$			42310.5i			2.52398i
$656$	7143.69	+	17621.0i	0.425174	+	1.04876i
$657$		0			0
$658$	23282.1	+	10043.2i	1.37938	+	0.595020i
$659$		−	24719.1i		−	1.46118i	−0.682814	−	0.730592i	$-0.739244\pi$
$659$		−	24719.1i		−	1.46118i	0.682814	−	0.730592i	$-0.260756\pi$
$660$		0			0
$661$		−	16458.4i		−	0.968467i	−0.874939	−	0.484233i	$-0.839099\pi$
$661$		−	16458.4i		−	0.968467i	0.874939	−	0.484233i	$-0.160901\pi$
$662$	1038.18	+	855.296i	0.0609519	+	0.0502145i
$663$		0			0
$664$	−15528.0	−	8413.16i	−0.907538	−	0.491708i
$665$	31042.7	−	8988.89i	1.81020	−	0.524172i
$666$		0			0
$667$		−	14451.6i		−	0.838930i
$668$	−3872.37	−	19858.7i	−0.224291	−	1.15024i
$669$		0			0
$670$	21338.6	−	25901.5i	1.23042	−	1.49352i
$671$	−4731.60			−0.272223
$672$		0			0
$673$	13350.6			0.764676			0.382338	−	0.924023i	$-0.375119\pi$
$673$	13350.6			0.764676			0.382338	+	0.924023i	$0.375119\pi$
$674$	−18007.3	+	21857.8i	−1.02910	+	1.24915i
$675$		0			0
$676$	4663.75	+	23917.2i	0.265348	+	1.36079i
$677$			28935.9i			1.64269i	0.570435	+	0.821343i	$0.306775\pi$
$677$			28935.9i			1.64269i	−0.570435	+	0.821343i	$0.693225\pi$
$678$		0			0
$679$	3784.12	−	1095.75i	0.213875	−	0.0619308i
$680$	22186.1	+	12020.5i	1.25118	+	0.677892i
$681$		0			0
$682$	−4749.98	−	3913.22i	−0.266695	−	0.219714i
$683$			5796.62i			0.324746i	0.986729	+	0.162373i	$0.0519148\pi$
$683$			5796.62i			0.324746i	−0.986729	+	0.162373i	$0.948085\pi$
$684$		0			0
$685$		−	3140.32i		−	0.175161i
$686$	−17748.0	+	2799.75i	−0.987785	+	0.155824i
$687$		0			0
$688$	−548.419	−	1352.76i	−0.0303899	−	0.0749616i
$689$			36380.3i			2.01158i
$690$		0			0
$691$	19975.6			1.09972			0.549861	−	0.835256i	$-0.314681\pi$
$691$	19975.6			1.09972			0.549861	+	0.835256i	$0.314681\pi$
$692$	−6549.15	+	1277.06i	−0.359771	+	0.0701538i
$693$		0			0
$694$	−23514.5	−	19372.1i	−1.28616	−	1.05959i
$695$		−	6591.05i		−	0.359731i
$696$		0			0
$697$	18643.2			1.01314
$698$	20262.3	+	16692.9i	1.09877	+	0.905206i
$699$		0			0
$700$	25148.2	−	12915.1i	1.35788	−	0.697350i
$701$	35866.0			1.93244			0.966219	−	0.257723i	$-0.0829721\pi$
$701$	35866.0			1.93244			0.966219	+	0.257723i	$0.0829721\pi$
$702$		0			0
$703$	13716.2			0.735868
$704$	−4623.22	+	3014.06i	−0.247506	+	0.161359i
$705$		0			0
$706$	−9884.51	−	8143.24i	−0.526924	−	0.434100i
$707$	−15944.6	+	4617.01i	−0.848174	+	0.245602i
$708$		0			0
$709$	−1806.89			−0.0957109			−0.0478555	−	0.998854i	$-0.515239\pi$
$709$	−1806.89			−0.0957109			−0.0478555	+	0.998854i	$0.515239\pi$
$710$	−5567.22	+	6757.66i	−0.294273	+	0.357198i
$711$		0			0
$712$	−293.298	+	541.336i	−0.0154380	+	0.0284936i
$713$			32360.4i			1.69973i
$714$		0			0
$715$		−	13870.3i		−	0.725483i
$716$	−16446.8	+	3207.05i	−0.858443	+	0.167393i
$717$		0			0
$718$	21467.9	+	17686.1i	1.11584	+	0.919274i
$719$	23227.5			1.20478			0.602391	−	0.798201i	$-0.294215\pi$
$719$	23227.5			1.20478			0.602391	+	0.798201i	$0.294215\pi$
$720$		0			0
$721$	6797.81	+	23475.9i	0.351129	+	1.21261i
$722$	−5005.13	+	6075.37i	−0.257994	+	0.313161i
$723$		0			0
$724$	−23310.9	+	4545.52i	−1.19660	+	0.233333i
$725$	17200.8			0.881134
$726$		0			0
$727$	27835.1			1.42001			0.710006	−	0.704196i	$-0.248692\pi$
$727$	27835.1			1.42001			0.710006	+	0.704196i	$0.248692\pi$
$728$	−29647.3	−	6464.07i	−1.50934	−	0.329086i
$729$		0			0
$730$	37315.3	−	45294.4i	1.89192	−	2.29647i
$731$	−1431.23			−0.0724159
$732$		0			0
$733$			26967.4i			1.35889i	0.733727	+	0.679444i	$0.237779\pi$
$733$			26967.4i			1.35889i	−0.733727	+	0.679444i	$0.762221\pi$
$734$	21306.3	−	25862.2i	1.07143	−	1.30053i
$735$		0			0
$736$	27689.3	+	8685.29i	1.38674	+	0.434978i
$737$	7196.81			0.359699
$738$		0			0
$739$		−	4459.65i		−	0.221990i	−0.993821	−	0.110995i	$-0.964596\pi$
$739$		−	4459.65i		−	0.221990i	0.993821	−	0.110995i	$-0.0354038\pi$
$740$	19491.6	−	3800.79i	0.968279	−	0.188810i
$741$		0			0
$742$	−24166.5	−	10424.7i	−1.19566	−	0.515770i
$743$		−	9276.26i		−	0.458026i	−0.973423	−	0.229013i	$-0.926450\pi$
$743$		−	9276.26i		−	0.458026i	0.973423	−	0.229013i	$-0.0735498\pi$
$744$		0			0
$745$			40417.1i			1.98761i
$746$	−18543.1	+	22508.2i	−0.910071	+	1.10467i
$747$		0			0
$748$	1035.67	+	5311.27i	0.0506257	+	0.259625i
$749$	26517.5	−	7678.54i	1.29363	−	0.374590i
$750$		0			0
$751$			6411.40i			0.311525i	0.987795	+	0.155763i	$0.0497835\pi$
$751$			6411.40i			0.311525i	−0.987795	+	0.155763i	$0.950217\pi$
$752$	−28709.4	+	11639.0i	−1.39219	+	0.564402i
$753$		0			0
$754$	−14249.3	−	11739.2i	−0.688237	−	0.566996i
$755$	−39495.0			−1.90380
$756$		0			0
$757$	18447.3			0.885705			0.442853	−	0.896594i	$-0.353967\pi$
$757$	18447.3			0.885705			0.442853	+	0.896594i	$0.353967\pi$
$758$	8430.68	+	6945.52i	0.403979	+	0.332814i
$759$		0			0
$760$	−18809.7	+	34716.8i	−0.897763	+	1.65699i
$761$		−	31940.7i		−	1.52149i	−0.649054	−	0.760743i	$-0.724835\pi$
$761$		−	31940.7i		−	1.52149i	0.649054	−	0.760743i	$-0.275165\pi$
$762$		0			0
$763$	−2860.71	−	9879.31i	−0.135733	−	0.468749i
$764$	−18933.0	+	3691.86i	−0.896560	+	0.174825i
$765$		0			0
$766$	16507.0	−	20036.7i	0.778618	−	0.945110i
$767$			10732.9i			0.505270i
$768$		0			0
$769$			4067.55i			0.190740i	0.995442	+	0.0953702i	$0.0304035\pi$
$769$			4067.55i			0.190740i	−0.995442	+	0.0953702i	$0.969597\pi$
$770$	9213.69	+	3974.49i	0.431218	+	0.186014i
$771$		0			0
$772$	−3729.38	−	19125.5i	−0.173865	−	0.891632i
$773$		−	21053.6i		−	0.979620i	−0.871829	−	0.489810i	$-0.837066\pi$
$773$		−	21053.6i		−	0.979620i	0.871829	−	0.489810i	$-0.162934\pi$
$774$		0			0
$775$	−38516.7			−1.78524
$776$	−2292.91	+	4231.99i	−0.106071	+	0.195773i
$777$		0			0
$778$	565.410	−	686.312i	0.0260552	−	0.0316266i
$779$			29172.8i			1.34175i
$780$		0			0
$781$	−1877.64			−0.0860272
$782$	18092.2	−	21960.8i	0.827333	−	1.00424i
$783$		0			0
$784$	12789.2	−	17841.7i	0.582601	−	0.812759i
$785$	−2813.87			−0.127938
$786$		0			0
$787$	15197.8			0.688367			0.344183	−	0.938902i	$-0.388156\pi$
$787$	15197.8			0.688367			0.344183	+	0.938902i	$0.388156\pi$
$788$	−3196.54	−	16392.9i	−0.144508	−	0.741082i
$789$		0			0
$790$	−21746.8	+	26396.9i	−0.979387	+	1.18881i
$791$	386.862	+	1336.01i	0.0173897	+	0.0600544i
$792$		0			0
$793$	31784.2			1.42331
$794$	4643.03	+	3825.11i	0.207525	+	0.170967i
$795$		0			0
$796$	5188.72	+	26609.4i	0.231042	+	1.18485i
$797$		−	3899.94i		−	0.173329i	−0.996238	−	0.0866644i	$-0.972379\pi$
$797$		−	3899.94i		−	0.173329i	0.996238	−	0.0866644i	$-0.0276208\pi$
$798$		0			0
$799$			30374.8i			1.34491i
$800$	−10337.6	+	32956.9i	−0.456861	+	1.45650i
$801$		0			0
$802$	11701.3	−	14203.4i	0.515196	−	0.625361i
$803$	12585.2			0.553079
$804$		0			0
$805$	−14675.3	−	50680.4i	−0.642530	−	2.21895i
$806$	31907.6	+	26286.7i	1.39441	+	1.14877i
$807$		0			0
$808$	9661.33	−	17831.8i	0.420649	−	0.776386i
$809$	21045.2			0.914600			0.457300	−	0.889313i	$-0.348817\pi$
$809$	21045.2			0.914600			0.457300	+	0.889313i	$0.348817\pi$
$810$		0			0
$811$	16381.3			0.709279			0.354640	−	0.935003i	$-0.384604\pi$
$811$	16381.3			0.709279			0.354640	+	0.935003i	$0.384604\pi$
$812$	11881.1	−	6101.65i	0.513479	−	0.263702i
$813$		0			0
$814$	3286.94	+	2707.91i	0.141532	+	0.116600i
$815$	26089.9			1.12134
$816$		0			0
$817$		−	2239.59i		−	0.0959036i
$818$	7162.29	+	5900.57i	0.306141	+	0.252211i
$819$		0			0
$820$	8083.85	+	41456.6i	0.344269	+	1.76552i
$821$	11681.1			0.496556			0.248278	−	0.968689i	$-0.420135\pi$
$821$	11681.1			0.496556			0.248278	+	0.968689i	$0.420135\pi$
$822$		0			0
$823$			33978.6i			1.43915i	0.694416	+	0.719574i	$0.255663\pi$
$823$			33978.6i			1.43915i	−0.694416	+	0.719574i	$0.744337\pi$
$824$	−26254.4	−	14224.8i	−1.10997	−	0.601388i
$825$		0			0
$826$	−7129.58	−	3075.47i	−0.300327	−	0.129551i
$827$		−	40342.5i		−	1.69631i	−0.529750	−	0.848154i	$-0.677714\pi$
$827$		−	40342.5i		−	1.69631i	0.529750	−	0.848154i	$-0.322286\pi$
$828$		0			0
$829$		−	23175.7i		−	0.970960i	−0.874248	−	0.485480i	$-0.838645\pi$
$829$		−	23175.7i		−	0.970960i	0.874248	−	0.485480i	$-0.161355\pi$
$830$	−30279.1	−	24945.1i	−1.26627	−	1.04320i
$831$		0			0
$832$	31056.1	−	20246.7i	1.29408	−	0.843664i
$833$	−11500.8	−	18193.6i	−0.478367	−	0.756749i
$834$		0			0
$835$		−	44944.6i		−	1.86272i
$836$	−8311.05	+	1620.62i	−0.343832	+	0.0670458i
$837$		0			0
$838$	−2361.62	+	2866.61i	−0.0973519	+	0.118169i
$839$	−3793.64			−0.156104			−0.0780519	−	0.996949i	$-0.524870\pi$
$839$	−3793.64			−0.156104			−0.0780519	+	0.996949i	$0.524870\pi$
$840$		0			0
$841$	−16262.6			−0.666800
$842$	−13793.3	+	16742.7i	−0.564546	+	0.685263i
$843$		0			0
$844$	−36235.2	+	7065.71i	−1.47780	+	0.288165i
$845$			54129.8i			2.20369i
$846$		0			0
$847$	−6257.74	−	21610.8i	−0.253859	−	0.876690i
$848$	29800.0	−	12081.1i	1.20676	−	0.489230i
$849$		0			0
$850$	26138.6	+	21534.0i	1.05476	+	0.868954i
$851$		−	22393.1i		−	0.902028i
$852$		0			0
$853$			18804.2i			0.754798i	0.926051	+	0.377399i	$0.123181\pi$
$853$			18804.2i			0.754798i	−0.926051	+	0.377399i	$0.876819\pi$
$854$	−9107.64	+	21113.4i	−0.364938	+	0.846001i
$855$		0			0
$856$	−16067.7	+	29656.0i	−0.641570	+	1.18414i
$857$			950.192i			0.0378739i	0.999821	+	0.0189370i	$0.00602818\pi$
$857$			950.192i			0.0378739i	−0.999821	+	0.0189370i	$0.993972\pi$
$858$		0			0
$859$	12509.1			0.496862			0.248431	−	0.968650i	$-0.420085\pi$
$859$	12509.1			0.496862			0.248431	+	0.968650i	$0.420085\pi$
$860$	−620.595	−	3182.61i	−0.0246071	−	0.126193i
$861$		0			0
$862$	−5152.98	−	4245.23i	−0.203609	−	0.167741i
$863$			7301.04i			0.287984i	0.989579	+	0.143992i	$0.0459940\pi$
$863$			7301.04i			0.287984i	−0.989579	+	0.143992i	$0.954006\pi$
$864$		0			0
$865$	−14822.2			−0.582622
$866$	−10729.0	−	8838.94i	−0.420999	−	0.346835i
$867$		0			0
$868$	−26604.6	+	13663.0i	−1.04034	+	0.534278i
$869$	−7334.47			−0.286312
$870$		0			0
$871$	−48344.0			−1.88068
$872$	11048.6	+	5986.18i	0.429074	+	0.232474i
$873$		0			0
$874$	34364.2	+	28310.5i	1.32996	+	1.09567i
$875$	20804.8	−	6024.34i	0.803805	−	0.232754i
$876$		0			0
$877$	−15791.2			−0.608017			−0.304009	−	0.952669i	$-0.598325\pi$
$877$	−15791.2			−0.608017			−0.304009	+	0.952669i	$0.598325\pi$
$878$	5997.45	−	7279.88i	0.230528	−	0.279822i
$879$		0			0
$880$	−11361.5	+	4606.02i	−0.435223	+	0.176442i
$881$			5782.40i			0.221128i	0.993869	+	0.110564i	$0.0352657\pi$
$881$			5782.40i			0.221128i	−0.993869	+	0.110564i	$0.964734\pi$
$882$		0			0
$883$			16075.8i			0.612675i	0.951923	+	0.306338i	$0.0991037\pi$
$883$			16075.8i			0.612675i	−0.951923	+	0.306338i	$0.900896\pi$
$884$	−6957.06	−	35678.0i	−0.264696	−	1.35745i
$885$		0			0
$886$	−7838.28	−	6457.48i	−0.297215	−	0.244857i
$887$	−6165.28			−0.233382			−0.116691	−	0.993168i	$-0.537229\pi$
$887$	−6165.28			−0.233382			−0.116691	+	0.993168i	$0.537229\pi$
$888$		0			0
$889$	−257.358	+	74.5219i	−0.00970923	+	0.00281146i
$890$	−869.633	+	1055.59i	−0.0327530	+	0.0397566i
$891$		0			0
$892$	451.564	+	2315.76i	0.0169501	+	0.0869253i
$893$	−47530.3			−1.78112
$894$		0			0
$895$	−37222.6			−1.39018
$896$	4550.35	+	26431.4i	0.169661	+	0.985502i
$897$		0			0
$898$	27275.8	−	33108.2i	1.01359	−	1.23033i
$899$	−18196.9			−0.675086
$900$		0			0
$901$		−	31528.6i		−	1.16578i
$902$	−5759.42	+	6990.96i	−0.212603	+	0.258064i
$903$		0			0
$904$	−1494.13	−	809.528i	−0.0549714	−	0.0297838i
$905$	−52757.5			−1.93781
$906$		0			0
$907$			24380.1i			0.892534i	0.894900	+	0.446267i	$0.147247\pi$
$907$			24380.1i			0.892534i	−0.894900	+	0.446267i	$0.852753\pi$
$908$	3478.73	+	17840.0i	0.127143	+	0.652029i
$909$		0			0
$910$	−61892.2	−	26698.3i	−2.25462	−	0.972572i
$911$		−	9713.23i		−	0.353253i	−0.984278	−	0.176627i	$-0.943482\pi$
$911$		−	9713.23i		−	0.353253i	0.984278	−	0.176627i	$-0.0565185\pi$
$912$		0			0
$913$		−	8413.16i		−	0.304967i
$914$	27143.7	−	32947.9i	0.982314	−	1.19236i
$915$		0			0
$916$	−23985.6	+	4677.10i	−0.865182	+	0.168707i
$917$	12264.4	+	42354.4i	0.441663	+	1.52526i
$918$		0			0
$919$		−	12841.3i		−	0.460931i	−0.973081	−	0.230465i	$-0.925975\pi$
$919$		−	12841.3i		−	0.460931i	0.973081	−	0.230465i	$-0.0740248\pi$
$920$	56678.8	+	30708.8i	2.03114	+	1.10048i
$921$		0			0
$922$	2909.88	+	2397.28i	0.103939	+	0.0856291i
$923$	12612.9			0.449792
$924$		0			0
$925$	26653.2			0.947406
$926$	−22885.7	−	18854.1i	−0.812173	−	0.669099i
$927$		0			0
$928$	−4883.92	+	15570.3i	−0.172761	+	0.550775i
$929$		−	21623.8i		−	0.763677i	−0.924229	−	0.381838i	$-0.875291\pi$
$929$		−	21623.8i		−	0.763677i	0.924229	−	0.381838i	$-0.124709\pi$
$930$		0			0
$931$	28469.3	−	17996.4i	1.00220	−	0.633522i
$932$	−5017.76	−	25732.6i	−0.176354	−	0.904399i
$933$		0			0
$934$	28711.1	−	34850.4i	1.00584	−	1.22092i
$935$			12020.5i			0.420443i
$936$		0			0
$937$		−	18396.5i		−	0.641395i	−0.947182	−	0.320697i	$-0.896083\pi$
$937$		−	18396.5i		−	0.641395i	0.947182	−	0.320697i	$-0.103917\pi$
$938$	13852.8	−	32113.7i	0.482207	−	1.11786i
$939$		0			0
$940$	−67543.9	+	13170.8i	−2.34366	+	0.457004i
$941$		−	43692.9i		−	1.51365i	−0.653615	−	0.756827i	$-0.726748\pi$
$941$		−	43692.9i		−	1.51365i	0.653615	−	0.756827i	$-0.273252\pi$
$942$		0			0
$943$	47627.7			1.64472
$944$	8791.56	−	3564.16i	0.303116	−	0.122885i
$945$		0			0
$946$	442.149	−	536.694i	0.0151961	−	0.0184455i
$947$			6009.34i			0.206206i	0.994671	+	0.103103i	$0.0328772\pi$
$947$			6009.34i			0.206206i	−0.994671	+	0.103103i	$0.967123\pi$
$948$		0			0
$949$	−84540.1			−2.89177
$950$	−33696.3	+	40901.6i	−1.15079	+	1.39687i
$951$		0			0
$952$	25693.5	+	5602.01i	0.874717	+	0.190717i
$953$	−7869.39			−0.267486			−0.133743	−	0.991016i	$-0.542700\pi$
$953$	−7869.39			−0.267486			−0.133743	+	0.991016i	$0.542700\pi$
$954$		0			0
$955$	−42849.5			−1.45191
$956$	−45355.9	+	8844.22i	−1.53443	+	0.299208i
$957$		0			0
$958$	34984.0	−	42464.6i	1.17983	−	1.43212i
$959$	−910.272	−	3143.58i	−0.0306509	−	0.105851i
$960$		0			0
$961$	10956.2			0.367770
$962$	−22079.8	−	18190.2i	−0.740000	−	0.609641i
$963$		0			0
$964$	−2524.21	+	492.211i	−0.0843356	+	0.0164451i
$965$		−	43285.0i		−	1.44393i
$966$		0			0
$967$		−	22172.9i		−	0.737365i	−0.929555	−	0.368682i	$-0.879809\pi$
$967$		−	22172.9i		−	0.737365i	0.929555	−	0.368682i	$-0.120191\pi$
$968$	24168.6	+	13094.6i	0.802487	+	0.434791i
$969$		0			0
$970$	−6798.51	+	8252.23i	−0.225038	+	0.273158i
$971$	−23116.1			−0.763988			−0.381994	−	0.924165i	$-0.624762\pi$
$971$	−23116.1			−0.763988			−0.381994	+	0.924165i	$0.624762\pi$
$972$		0			0
$973$	−1910.52	−	6597.89i	−0.0629481	−	0.217388i
$974$	−18481.1	−	15225.4i	−0.607980	−	0.500877i
$975$		0			0
$976$	−10554.8	−	26035.1i	−0.346159	−	0.853857i
$977$	6112.67			0.200166			0.100083	−	0.994979i	$-0.468089\pi$
$977$	6112.67			0.200166			0.100083	+	0.994979i	$0.468089\pi$
$978$		0			0
$979$	−293.298			−0.00957493
$980$	35470.0	−	33463.1i	1.15617	−	1.09075i
$981$		0			0
$982$	15663.7	+	12904.4i	0.509011	+	0.419343i
$983$	−42147.1			−1.36753			−0.683766	−	0.729702i	$-0.739659\pi$
$983$	−42147.1			−1.36753			−0.683766	+	0.729702i	$0.739659\pi$
$984$		0			0
$985$		−	37100.6i		−	1.20013i
$986$	12349.0	+	10173.6i	0.398857	+	0.328594i
$987$		0			0
$988$	55828.8	−	10886.4i	1.79772	−	0.350549i
$989$	−3656.36			−0.117559
$990$		0			0
$991$			3294.51i			0.105604i	0.998605	+	0.0528020i	$0.0168152\pi$
$991$			3294.51i			0.105604i	−0.998605	+	0.0528020i	$0.983185\pi$
$992$	10936.2	−	34865.5i	0.350026	−	1.11591i
$993$		0			0
$994$	−3614.18	+	8378.42i	−0.115327	+	0.267351i
$995$			60222.8i			1.91878i
$996$		0			0
$997$			54852.2i			1.74241i	0.490915	+	0.871207i	$0.336662\pi$
$997$			54852.2i			1.74241i	−0.490915	+	0.871207i	$0.663338\pi$
$998$	38211.3	+	31480.0i	1.21198	+	0.998477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.g.55.7	yes	16
3.2	odd	2	inner	252.4.b.g.55.10	yes	16
4.3	odd	2	inner	252.4.b.g.55.5	✓	16
7.6	odd	2	inner	252.4.b.g.55.8	yes	16
12.11	even	2	inner	252.4.b.g.55.12	yes	16
21.20	even	2	inner	252.4.b.g.55.9	yes	16
28.27	even	2	inner	252.4.b.g.55.6	yes	16
84.83	odd	2	inner	252.4.b.g.55.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.b.g.55.5	✓	16	4.3	odd	2	inner
252.4.b.g.55.6	yes	16	28.27	even	2	inner
252.4.b.g.55.7	yes	16	1.1	even	1	trivial
252.4.b.g.55.8	yes	16	7.6	odd	2	inner
252.4.b.g.55.9	yes	16	21.20	even	2	inner
252.4.b.g.55.10	yes	16	3.2	odd	2	inner
252.4.b.g.55.11	yes	16	84.83	odd	2	inner
252.4.b.g.55.12	yes	16	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79845 + 2.18302i) q^{2} +(-1.53113 - 7.85211i) q^{4} -17.7710i q^{5} +(-5.15121 - 17.7895i) q^{7} +(19.8950 + 10.7792i) q^{8} +O(q^{10})\)	\(q+(-1.79845 + 2.18302i) q^{2} +(-1.53113 - 7.85211i) q^{4} -17.7710i q^{5} +(-5.15121 - 17.7895i) q^{7} +(19.8950 + 10.7792i) q^{8} +(38.7945 + 31.9604i) q^{10} +10.7792i q^{11} -72.4083i q^{13} +(48.0989 + 20.7483i) q^{14} +(-59.3113 + 24.0452i) q^{16} +62.7518i q^{17} -98.1938 q^{19} +(-139.540 + 27.2097i) q^{20} +(-23.5311 - 19.3858i) q^{22} +160.312i q^{23} -190.809 q^{25} +(158.069 + 130.223i) q^{26} +(-131.798 + 67.6859i) q^{28} -90.1466 q^{29} +201.859 q^{31} +(54.1775 - 172.722i) q^{32} +(-136.988 - 112.856i) q^{34} +(-316.137 + 91.5424i) q^{35} -139.685 q^{37} +(176.597 - 214.359i) q^{38} +(191.557 - 353.554i) q^{40} -297.094i q^{41} +22.8078i q^{43} +(84.6393 - 16.5043i) q^{44} +(-349.963 - 288.313i) q^{46} +484.046 q^{47} +(-289.930 + 183.275i) q^{49} +(343.162 - 416.540i) q^{50} +(-568.558 + 110.866i) q^{52} -502.433 q^{53} +191.557 q^{55} +(89.2726 - 409.446i) q^{56} +(162.125 - 196.792i) q^{58} -148.228 q^{59} +438.958i q^{61} +(-363.035 + 440.663i) q^{62} +(279.619 + 428.903i) q^{64} -1286.77 q^{65} -667.659i q^{67} +(492.734 - 96.0811i) q^{68} +(368.719 - 854.767i) q^{70} +174.191i q^{71} -1167.55i q^{73} +(251.217 - 304.934i) q^{74} +(150.347 + 771.028i) q^{76} +(191.756 - 55.5258i) q^{77} +680.430i q^{79} +(427.308 + 1054.02i) q^{80} +(648.562 + 534.310i) q^{82} -780.502 q^{83} +1115.16 q^{85} +(-49.7899 - 41.0188i) q^{86} +(-116.191 + 214.451i) q^{88} +27.2097i q^{89} +(-1288.10 + 372.990i) q^{91} +(1258.78 - 245.458i) q^{92} +(-870.535 + 1056.68i) q^{94} +1745.00i q^{95} +212.717i q^{97} +(121.334 - 962.533i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 40 q^{4}+O(q^{10}) \) 16 * q + 40 * q^4	\( 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88}+O(q^{100}) \) 16 * q + 40 * q^4 - 304 * q^16 - 312 * q^22 - 1376 * q^25 - 816 * q^28 - 816 * q^37 - 2568 * q^46 - 640 * q^49 + 2336 * q^58 + 1120 * q^64 - 424 * q^70 + 5072 * q^85 - 3536 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more