LMFDB - Embedded newform 588.3.p.e.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,3,Mod(557,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("588.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.2
Root			$-1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	588.557
Dual form			588.3.p.e.569.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.93649 - 0.614017i) q^{3} +(-5.80948 + 3.35410i) q^{5} +(8.24597 - 3.60611i) q^{9} +O(q^{10})$	\(q+(2.93649 - 0.614017i) q^{3} +(-5.80948 + 3.35410i) q^{5} +(8.24597 - 3.60611i) q^{9} +(5.80948 + 3.35410i) q^{11} -14.0000 q^{13} +(-15.0000 + 13.4164i) q^{15} +(23.2379 + 13.4164i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-11.6190 + 6.70820i) q^{23} +(10.0000 - 17.3205i) q^{25} +(22.0000 - 15.6525i) q^{27} +46.9574i q^{29} +(-15.5000 + 26.8468i) q^{31} +(19.1190 + 6.28218i) q^{33} +(14.0000 + 24.2487i) q^{37} +(-41.1109 + 8.59624i) q^{39} +67.0820i q^{41} -52.0000 q^{43} +(-35.8095 + 48.6074i) q^{45} +(34.8569 - 20.1246i) q^{47} +(76.4758 + 25.1287i) q^{51} +(-5.80948 - 3.35410i) q^{53} -45.0000 q^{55} +(16.0000 + 17.8885i) q^{57} +(17.4284 + 10.0623i) q^{59} +(7.00000 + 12.1244i) q^{61} +(81.3327 - 46.9574i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-30.0000 + 26.8328i) q^{69} -40.2492i q^{71} +(49.0000 - 84.8705i) q^{73} +(18.7298 - 57.0017i) q^{75} +(-50.5000 - 87.4686i) q^{79} +(54.9919 - 59.4717i) q^{81} -87.2067i q^{83} -180.000 q^{85} +(28.8327 + 137.890i) q^{87} +(58.0948 - 33.5410i) q^{89} +(-29.0312 + 88.3526i) q^{93} +(-46.4758 - 26.8328i) q^{95} +13.0000 q^{97} +(60.0000 + 6.70820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 2 * q^9	$ 4 q + 4 q^{3} + 2 q^{9} - 56 q^{13} - 60 q^{15} + 16 q^{19} + 40 q^{25} + 88 q^{27} - 62 q^{31} + 30 q^{33} + 56 q^{37} - 56 q^{39} - 208 q^{43} - 120 q^{45} + 120 q^{51} - 180 q^{55} + 64 q^{57} + 28 q^{61} + 8 q^{67} - 120 q^{69} + 196 q^{73} - 80 q^{75} - 202 q^{79} + 158 q^{81} - 720 q^{85} - 210 q^{87} + 124 q^{93} + 52 q^{97} + 240 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 2 * q^9 - 56 * q^13 - 60 * q^15 + 16 * q^19 + 40 * q^25 + 88 * q^27 - 62 * q^31 + 30 * q^33 + 56 * q^37 - 56 * q^39 - 208 * q^43 - 120 * q^45 + 120 * q^51 - 180 * q^55 + 64 * q^57 + 28 * q^61 + 8 * q^67 - 120 * q^69 + 196 * q^73 - 80 * q^75 - 202 * q^79 + 158 * q^81 - 720 * q^85 - 210 * q^87 + 124 * q^93 + 52 * q^97 + 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	2.93649	−	0.614017i	0.978831	−	0.204672i
$3$	2.93649	−	0.614017i	0.978831	−	0.204672i
$4$		0			0
$5$	−5.80948	+	3.35410i	−1.16190	+	0.670820i	−0.951757	−	0.306851i	$-0.900725\pi$
$5$	−5.80948	+	3.35410i	−1.16190	+	0.670820i	−0.210138	+	0.977672i	$0.567391\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	8.24597	−	3.60611i	0.916219	−	0.400679i
$10$		0			0
$11$	5.80948	+	3.35410i	0.528134	+	0.304918i	0.740256	−	0.672325i	$-0.234704\pi$
$11$	5.80948	+	3.35410i	0.528134	+	0.304918i	−0.212122	+	0.977243i	$0.568037\pi$
$12$		0			0
$13$	−14.0000			−1.07692			−0.538462	−	0.842650i	$-0.680994\pi$
$13$	−14.0000			−1.07692			−0.538462	+	0.842650i	$0.680994\pi$
$14$		0			0
$15$	−15.0000	+	13.4164i	−1.00000	+	0.894427i
$16$		0			0
$17$	23.2379	+	13.4164i	1.36694	+	0.789200i	0.990535	−	0.137257i	$-0.0438286\pi$
$17$	23.2379	+	13.4164i	1.36694	+	0.789200i	0.376400	+	0.926457i	$0.377162\pi$
$18$		0			0
$19$	4.00000	+	6.92820i	0.210526	+	0.364642i	0.951879	−	0.306473i	$-0.0991489\pi$
$19$	4.00000	+	6.92820i	0.210526	+	0.364642i	−0.741353	+	0.671115i	$0.765816\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−11.6190	+	6.70820i	−0.505172	+	0.291661i	−0.730847	−	0.682542i	$-0.760875\pi$
$23$	−11.6190	+	6.70820i	−0.505172	+	0.291661i	0.225675	+	0.974203i	$0.427541\pi$
$24$		0			0
$25$	10.0000	−	17.3205i	0.400000	−	0.692820i
$26$		0			0
$27$	22.0000	−	15.6525i	0.814815	−	0.579721i
$28$		0			0
$29$			46.9574i			1.61922i	0.586967	+	0.809611i	$0.300322\pi$
$29$			46.9574i			1.61922i	−0.586967	+	0.809611i	$0.699678\pi$
$30$		0			0
$31$	−15.5000	+	26.8468i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$31$	−15.5000	+	26.8468i	−0.500000	+	0.866025i	−1.00000			$\pi$
$32$		0			0
$33$	19.1190	+	6.28218i	0.579362	+	0.190369i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	14.0000	+	24.2487i	0.378378	+	0.655371i	0.990826	−	0.135140i	$-0.0431485\pi$
$37$	14.0000	+	24.2487i	0.378378	+	0.655371i	−0.612448	+	0.790511i	$0.709815\pi$
$38$		0			0
$39$	−41.1109	+	8.59624i	−1.05413	+	0.220416i
$40$		0			0
$41$			67.0820i			1.63615i	0.575113	+	0.818074i	$0.304958\pi$
$41$			67.0820i			1.63615i	−0.575113	+	0.818074i	$0.695042\pi$
$42$		0			0
$43$	−52.0000			−1.20930			−0.604651	−	0.796490i	$-0.706687\pi$
$43$	−52.0000			−1.20930			−0.604651	+	0.796490i	$0.706687\pi$
$44$		0			0
$45$	−35.8095	+	48.6074i	−0.795766	+	1.08016i
$46$		0			0
$47$	34.8569	−	20.1246i	0.741635	−	0.428183i	−0.0810284	−	0.996712i	$-0.525820\pi$
$47$	34.8569	−	20.1246i	0.741635	−	0.428183i	0.822664	+	0.568529i	$0.192487\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	76.4758	+	25.1287i	1.49953	+	0.492720i
$52$		0			0
$53$	−5.80948	−	3.35410i	−0.109613	−	0.0632849i	0.444191	−	0.895932i	$-0.353491\pi$
$53$	−5.80948	−	3.35410i	−0.109613	−	0.0632849i	−0.553804	+	0.832647i	$0.686824\pi$
$54$		0			0
$55$	−45.0000			−0.818182
$56$		0			0
$57$	16.0000	+	17.8885i	0.280702	+	0.313834i
$58$		0			0
$59$	17.4284	+	10.0623i	0.295397	+	0.170548i	0.640373	−	0.768064i	$-0.278780\pi$
$59$	17.4284	+	10.0623i	0.295397	+	0.170548i	−0.344976	+	0.938611i	$0.612113\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.114754	+	0.198760i	0.917681	−	0.397317i	$-0.130059\pi$
$61$	7.00000	+	12.1244i	0.114754	+	0.198760i	−0.802927	+	0.596077i	$0.796725\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	81.3327	−	46.9574i	1.25127	−	0.722422i
$66$		0			0
$67$	2.00000	−	3.46410i	0.0298507	−	0.0517030i	−0.850714	−	0.525629i	$-0.823830\pi$
$67$	2.00000	−	3.46410i	0.0298507	−	0.0517030i	0.880565	+	0.473926i	$0.157163\pi$
$68$		0			0
$69$	−30.0000	+	26.8328i	−0.434783	+	0.388881i
$70$		0			0
$71$		−	40.2492i		−	0.566890i	−0.958988	−	0.283445i	$-0.908523\pi$
$71$		−	40.2492i		−	0.566890i	0.958988	−	0.283445i	$-0.0914774\pi$
$72$		0			0
$73$	49.0000	−	84.8705i	0.671233	−	1.16261i	−0.306322	−	0.951928i	$-0.599098\pi$
$73$	49.0000	−	84.8705i	0.671233	−	1.16261i	0.977555	−	0.210681i	$-0.0675683\pi$
$74$		0			0
$75$	18.7298	−	57.0017i	0.249731	−	0.760023i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−50.5000	−	87.4686i	−0.639241	−	1.10720i	−0.985600	−	0.169095i	$-0.945916\pi$
$79$	−50.5000	−	87.4686i	−0.639241	−	1.10720i	0.346359	−	0.938102i	$-0.387418\pi$
$80$		0			0
$81$	54.9919	−	59.4717i	0.678913	−	0.734219i
$82$		0			0
$83$		−	87.2067i		−	1.05068i	−0.850892	−	0.525341i	$-0.823938\pi$
$83$		−	87.2067i		−	1.05068i	0.850892	−	0.525341i	$-0.176062\pi$
$84$		0			0
$85$	−180.000			−2.11765
$86$		0			0
$87$	28.8327	+	137.890i	0.331410	+	1.58494i
$88$		0			0
$89$	58.0948	−	33.5410i	0.652750	−	0.376865i	−0.136759	−	0.990604i	$-0.543669\pi$
$89$	58.0948	−	33.5410i	0.652750	−	0.376865i	0.789509	+	0.613739i	$0.210335\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−29.0312	+	88.3526i	−0.312164	+	0.950028i
$94$		0			0
$95$	−46.4758	−	26.8328i	−0.489219	−	0.282451i
$96$		0			0
$97$	13.0000			0.134021			0.0670103	−	0.997752i	$-0.478654\pi$
$97$	13.0000			0.134021			0.0670103	+	0.997752i	$0.478654\pi$
$98$		0			0
$99$	60.0000	+	6.70820i	0.606061	+	0.0677596i
$100$		0			0
$101$	11.6190	+	6.70820i	0.115039	+	0.0664179i	0.556416	−	0.830904i	$-0.312176\pi$
$101$	11.6190	+	6.70820i	0.115039	+	0.0664179i	−0.441376	+	0.897322i	$0.645510\pi$
$102$		0			0
$103$	79.0000	+	136.832i	0.766990	+	1.32847i	0.939188	+	0.343404i	$0.111580\pi$
$103$	79.0000	+	136.832i	0.766990	+	1.32847i	−0.172198	+	0.985062i	$0.555087\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.80948	+	3.35410i	−0.0542942	+	0.0313467i	−0.526901	−	0.849926i	$-0.676646\pi$
$107$	−5.80948	+	3.35410i	−0.0542942	+	0.0313467i	0.472607	+	0.881273i	$0.343313\pi$
$108$		0			0
$109$	−4.00000	+	6.92820i	−0.0366972	+	0.0635615i	−0.883791	−	0.467882i	$-0.845017\pi$
$109$	−4.00000	+	6.92820i	−0.0366972	+	0.0635615i	0.847093	+	0.531444i	$0.178350\pi$
$110$		0			0
$111$	56.0000	+	62.6099i	0.504505	+	0.564053i
$112$		0			0
$113$			174.413i			1.54348i	0.635938	+	0.771740i	$0.280613\pi$
$113$			174.413i			1.54348i	−0.635938	+	0.771740i	$0.719387\pi$
$114$		0			0
$115$	45.0000	−	77.9423i	0.391304	−	0.677759i
$116$		0			0
$117$	−115.444	+	50.4855i	−0.986697	+	0.431500i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−38.0000	−	65.8179i	−0.314050	−	0.543950i
$122$		0			0
$123$	41.1895	+	196.986i	0.334874	+	1.60151i
$124$		0			0
$125$		−	33.5410i		−	0.268328i
$126$		0			0
$127$	197.000			1.55118			0.775591	−	0.631236i	$-0.217452\pi$
$127$	197.000			1.55118			0.775591	+	0.631236i	$0.217452\pi$
$128$		0			0
$129$	−152.698	+	31.9289i	−1.18370	+	0.247511i
$130$		0			0
$131$	−145.237	+	83.8525i	−1.10868	+	0.640096i	−0.938487	−	0.345315i	$-0.887772\pi$
$131$	−145.237	+	83.8525i	−1.10868	+	0.640096i	−0.170192	+	0.985411i	$0.554439\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−75.3085	+	164.723i	−0.557840	+	1.22017i
$136$		0			0
$137$	−46.4758	−	26.8328i	−0.339239	−	0.195860i	0.320696	−	0.947182i	$-0.396083\pi$
$137$	−46.4758	−	26.8328i	−0.339239	−	0.195860i	−0.659936	+	0.751322i	$0.729416\pi$
$138$		0			0
$139$	−86.0000			−0.618705			−0.309353	−	0.950947i	$-0.600112\pi$
$139$	−86.0000			−0.618705			−0.309353	+	0.950947i	$0.600112\pi$
$140$		0			0
$141$	90.0000	−	80.4984i	0.638298	−	0.570911i
$142$		0			0
$143$	−81.3327	−	46.9574i	−0.568760	−	0.328374i
$144$		0			0
$145$	−157.500	−	272.798i	−1.08621	−	1.88137i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.6190	+	6.70820i	−0.0779795	+	0.0450215i	−0.538483	−	0.842637i	$-0.681002\pi$
$149$	−11.6190	+	6.70820i	−0.0779795	+	0.0450215i	0.460503	+	0.887658i	$0.347669\pi$
$150$		0			0
$151$	60.5000	−	104.789i	0.400662	−	0.693967i	−0.593144	−	0.805097i	$-0.702113\pi$
$151$	60.5000	−	104.789i	0.400662	−	0.693967i	0.993806	+	0.111129i	$0.0354467\pi$
$152$		0			0
$153$	240.000	+	26.8328i	1.56863	+	0.175378i
$154$		0			0
$155$		−	207.954i		−	1.34164i
$156$		0			0
$157$	76.0000	−	131.636i	0.484076	−	0.838445i	−0.515756	−	0.856735i	$-0.672489\pi$
$157$	76.0000	−	131.636i	0.484076	−	0.838445i	0.999833	+	0.0182904i	$0.00582233\pi$
$158$		0			0
$159$	−19.1190	−	6.28218i	−0.120245	−	0.0395105i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−19.0000	−	32.9090i	−0.116564	−	0.201895i	0.801840	−	0.597539i	$-0.203855\pi$
$163$	−19.0000	−	32.9090i	−0.116564	−	0.201895i	−0.918404	+	0.395644i	$0.870521\pi$
$164$		0			0
$165$	−132.142	+	27.6308i	−0.800861	+	0.167459i
$166$		0			0
$167$		−	53.6656i		−	0.321351i	−0.987007	−	0.160676i	$-0.948633\pi$
$167$		−	53.6656i		−	0.321351i	0.987007	−	0.160676i	$-0.0513673\pi$
$168$		0			0
$169$	27.0000			0.159763
$170$		0			0
$171$	57.9677	+	42.7053i	0.338993	+	0.249739i
$172$		0			0
$173$	−104.571	+	60.3738i	−0.604454	+	0.348982i	−0.770792	−	0.637087i	$-0.780139\pi$
$173$	−104.571	+	60.3738i	−0.604454	+	0.348982i	0.166338	+	0.986069i	$0.446806\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	57.3569	+	18.8465i	0.324050	+	0.106478i
$178$		0			0
$179$	290.474	+	167.705i	1.62276	+	0.936900i	0.986178	+	0.165690i	$0.0529850\pi$
$179$	290.474	+	167.705i	1.62276	+	0.936900i	0.636580	+	0.771210i	$0.280348\pi$
$180$		0			0
$181$	−314.000			−1.73481			−0.867403	−	0.497606i	$-0.834213\pi$
$181$	−314.000			−1.73481			−0.867403	+	0.497606i	$0.834213\pi$
$182$		0			0
$183$	28.0000	+	31.3050i	0.153005	+	0.171065i
$184$		0			0
$185$	−162.665	−	93.9149i	−0.879272	−	0.507648i
$186$		0			0
$187$	90.0000	+	155.885i	0.481283	+	0.833607i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−209.141	+	120.748i	−1.09498	+	0.632187i	−0.934898	−	0.354917i	$-0.884509\pi$
$191$	−209.141	+	120.748i	−1.09498	+	0.632187i	−0.160082	+	0.987104i	$0.551176\pi$
$192$		0			0
$193$	78.5000	−	135.966i	0.406736	−	0.704487i	−0.587786	−	0.809016i	$-0.700000\pi$
$193$	78.5000	−	135.966i	0.406736	−	0.704487i	0.994522	+	0.104529i	$0.0333336\pi$
$194$		0			0
$195$	210.000	−	187.830i	1.07692	−	0.963229i
$196$		0			0
$197$		−	281.745i		−	1.43018i	−0.699035	−	0.715088i	$-0.746387\pi$
$197$		−	281.745i		−	1.43018i	0.699035	−	0.715088i	$-0.253613\pi$
$198$		0			0
$199$	163.000	−	282.324i	0.819095	−	1.41871i	−0.0872540	−	0.996186i	$-0.527809\pi$
$199$	163.000	−	282.324i	0.819095	−	1.41871i	0.906349	−	0.422529i	$-0.138857\pi$
$200$		0			0
$201$	3.74597	−	11.4003i	0.0186367	−	0.0567181i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−225.000	−	389.711i	−1.09756	−	1.90103i
$206$		0			0
$207$	−71.6190	+	97.2148i	−0.345985	+	0.469637i
$208$		0			0
$209$			53.6656i			0.256773i
$210$		0			0
$211$	134.000			0.635071			0.317536	−	0.948246i	$-0.397145\pi$
$211$	134.000			0.635071			0.317536	+	0.948246i	$0.397145\pi$
$212$		0			0
$213$	−24.7137	−	118.192i	−0.116027	−	0.554890i
$214$		0			0
$215$	302.093	−	174.413i	1.40508	−	0.811225i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	91.7762	−	279.308i	0.419069	−	1.27538i
$220$		0			0
$221$	−325.331	−	187.830i	−1.47208	−	0.849908i
$222$		0			0
$223$	247.000			1.10762			0.553812	−	0.832642i	$-0.313173\pi$
$223$	247.000			1.10762			0.553812	+	0.832642i	$0.313173\pi$
$224$		0			0
$225$	20.0000	−	178.885i	0.0888889	−	0.795046i
$226$		0			0
$227$	29.0474	+	16.7705i	0.127962	+	0.0738789i	0.562615	−	0.826719i	$-0.309796\pi$
$227$	29.0474	+	16.7705i	0.127962	+	0.0738789i	−0.434653	+	0.900598i	$0.643129\pi$
$228$		0			0
$229$	−11.0000	−	19.0526i	−0.0480349	−	0.0831989i	0.841008	−	0.541022i	$-0.181963\pi$
$229$	−11.0000	−	19.0526i	−0.0480349	−	0.0831989i	−0.889043	+	0.457823i	$0.848629\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−92.9516	+	53.6656i	−0.398934	+	0.230325i	−0.686024	−	0.727579i	$-0.740645\pi$
$233$	−92.9516	+	53.6656i	−0.398934	+	0.230325i	0.287090	+	0.957904i	$0.407312\pi$
$234$		0			0
$235$	−135.000	+	233.827i	−0.574468	+	0.995008i
$236$		0			0
$237$	−202.000	−	225.843i	−0.852321	−	0.952923i
$238$		0			0
$239$		−	147.580i		−	0.617492i	−0.951145	−	0.308746i	$-0.900091\pi$
$239$		−	147.580i		−	0.617492i	0.951145	−	0.308746i	$-0.0999092\pi$
$240$		0			0
$241$	29.5000	−	51.0955i	0.122407	−	0.212015i	−0.798310	−	0.602247i	$-0.794272\pi$
$241$	29.5000	−	51.0955i	0.122407	−	0.212015i	0.920716	+	0.390233i	$0.127605\pi$
$242$		0			0
$243$	124.967	−	208.404i	0.514266	−	0.857631i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−56.0000	−	96.9948i	−0.226721	−	0.392692i
$248$		0			0
$249$	−53.5464	−	256.082i	−0.215046	−	1.02844i
$250$		0			0
$251$			60.3738i			0.240533i	0.992742	+	0.120267i	$0.0383749\pi$
$251$			60.3738i			0.240533i	−0.992742	+	0.120267i	$0.961625\pi$
$252$		0			0
$253$	−90.0000			−0.355731
$254$		0			0
$255$	−528.569	+	110.523i	−2.07282	+	0.433424i
$256$		0			0
$257$	−336.950	+	194.538i	−1.31109	+	0.756957i	−0.982276	−	0.187439i	$-0.939981\pi$
$257$	−336.950	+	194.538i	−1.31109	+	0.756957i	−0.328811	+	0.944396i	$0.606648\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	169.334	+	387.209i	0.648788	+	1.48356i
$262$		0			0
$263$	371.806	+	214.663i	1.41371	+	0.816207i	0.995736	−	0.0922504i	$-0.0294060\pi$
$263$	371.806	+	214.663i	1.41371	+	0.816207i	0.417977	+	0.908458i	$0.362739\pi$
$264$		0			0
$265$	45.0000			0.169811
$266$		0			0
$267$	150.000	−	134.164i	0.561798	−	0.502487i
$268$		0			0
$269$	40.6663	+	23.4787i	0.151176	+	0.0872815i	0.573680	−	0.819080i	$-0.305515\pi$
$269$	40.6663	+	23.4787i	0.151176	+	0.0872815i	−0.422504	+	0.906361i	$0.638849\pi$
$270$		0			0
$271$	−21.5000	−	37.2391i	−0.0793358	−	0.137414i	0.823628	−	0.567131i	$-0.191947\pi$
$271$	−21.5000	−	37.2391i	−0.0793358	−	0.137414i	−0.902964	+	0.429717i	$0.858613\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	116.190	−	67.0820i	0.422507	−	0.243935i
$276$		0			0
$277$	62.0000	−	107.387i	0.223827	−	0.387679i	−0.732140	−	0.681154i	$-0.761478\pi$
$277$	62.0000	−	107.387i	0.223827	−	0.387679i	0.955967	+	0.293475i	$0.0948117\pi$
$278$		0			0
$279$	−31.0000	+	277.272i	−0.111111	+	0.993808i
$280$		0			0
$281$			107.331i			0.381962i	0.981594	+	0.190981i	$0.0611669\pi$
$281$			107.331i			0.381962i	−0.981594	+	0.190981i	$0.938833\pi$
$282$		0			0
$283$	52.0000	−	90.0666i	0.183746	−	0.318257i	−0.759408	−	0.650615i	$-0.774511\pi$
$283$	52.0000	−	90.0666i	0.183746	−	0.318257i	0.943153	+	0.332359i	$0.107844\pi$
$284$		0			0
$285$	−152.952	−	50.2574i	−0.536672	−	0.176342i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	215.500	+	373.257i	0.745675	+	1.29155i
$290$		0			0
$291$	38.1744	−	7.98222i	0.131183	−	0.0274303i
$292$		0			0
$293$			207.954i			0.709742i	0.934915	+	0.354871i	$0.115475\pi$
$293$			207.954i			0.709742i	−0.934915	+	0.354871i	$0.884525\pi$
$294$		0			0
$295$	−135.000			−0.457627
$296$		0			0
$297$	180.308	−	17.1424i	0.607099	−	0.0577186i
$298$		0			0
$299$	162.665	−	93.9149i	0.544031	−	0.314097i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	38.2379	+	12.5644i	0.126198	+	0.0414665i
$304$		0			0
$305$	−81.3327	−	46.9574i	−0.266664	−	0.153959i
$306$		0			0
$307$	−62.0000			−0.201954			−0.100977	−	0.994889i	$-0.532197\pi$
$307$	−62.0000			−0.201954			−0.100977	+	0.994889i	$0.532197\pi$
$308$		0			0
$309$	316.000	+	353.299i	1.02265	+	1.14336i
$310$		0			0
$311$	−34.8569	−	20.1246i	−0.112080	−	0.0647094i	0.442912	−	0.896565i	$-0.353945\pi$
$311$	−34.8569	−	20.1246i	−0.112080	−	0.0647094i	−0.554992	+	0.831856i	$0.687279\pi$
$312$		0			0
$313$	−3.50000	−	6.06218i	−0.0111821	−	0.0193680i	0.860380	−	0.509653i	$-0.170226\pi$
$313$	−3.50000	−	6.06218i	−0.0111821	−	0.0193680i	−0.871562	+	0.490285i	$0.836893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−261.426	+	150.935i	−0.824689	+	0.476134i	−0.852031	−	0.523492i	$-0.824629\pi$
$317$	−261.426	+	150.935i	−0.824689	+	0.476134i	0.0273418	+	0.999626i	$0.491296\pi$
$318$		0			0
$319$	−157.500	+	272.798i	−0.493730	+	0.855166i
$320$		0			0
$321$	−15.0000	+	13.4164i	−0.0467290	+	0.0417957i
$322$		0			0
$323$			214.663i			0.664590i
$324$		0			0
$325$	−140.000	+	242.487i	−0.430769	+	0.746114i
$326$		0			0
$327$	−7.49193	+	22.8007i	−0.0229111	+	0.0697268i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	0.877857	−	0.478923i	$-0.158973\pi$
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	−0.853688	+	0.520785i	$0.825639\pi$
$332$		0			0
$333$	202.887	+	149.469i	0.609270	+	0.448854i
$334$		0			0
$335$			26.8328i			0.0800980i
$336$		0			0
$337$	−373.000			−1.10682			−0.553412	−	0.832907i	$-0.686675\pi$
$337$	−373.000			−1.10682			−0.553412	+	0.832907i	$0.686675\pi$
$338$		0			0
$339$	107.093	+	512.163i	0.315908	+	1.51081i
$340$		0			0
$341$	−180.094	+	103.977i	−0.528134	+	0.304918i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	84.2843	−	256.508i	0.244302	−	0.743500i
$346$		0			0
$347$	−383.425	−	221.371i	−1.10497	−	0.637956i	−0.167450	−	0.985881i	$-0.553553\pi$
$347$	−383.425	−	221.371i	−1.10497	−	0.637956i	−0.937523	+	0.347925i	$0.886887\pi$
$348$		0			0
$349$	292.000			0.836676			0.418338	−	0.908291i	$-0.362613\pi$
$349$	292.000			0.836676			0.418338	+	0.908291i	$0.362613\pi$
$350$		0			0
$351$	−308.000	+	219.135i	−0.877493	+	0.624315i
$352$		0			0
$353$	185.903	+	107.331i	0.526638	+	0.304055i	0.739646	−	0.672996i	$-0.234993\pi$
$353$	185.903	+	107.331i	0.526638	+	0.304055i	−0.213008	+	0.977050i	$0.568326\pi$
$354$		0			0
$355$	135.000	+	233.827i	0.380282	+	0.658667i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	185.903	−	107.331i	0.517836	−	0.298973i	−0.218213	−	0.975901i	$-0.570023\pi$
$359$	185.903	−	107.331i	0.517836	−	0.298973i	0.736049	+	0.676928i	$0.236689\pi$
$360$		0			0
$361$	148.500	−	257.210i	0.411357	−	0.712492i
$362$		0			0
$363$	−152.000	−	169.941i	−0.418733	−	0.468157i
$364$		0			0
$365$			657.404i			1.80111i
$366$		0			0
$367$	−111.500	+	193.124i	−0.303815	+	0.526223i	−0.976997	−	0.213254i	$-0.931594\pi$
$367$	−111.500	+	193.124i	−0.303815	+	0.526223i	0.673182	+	0.739477i	$0.264927\pi$
$368$		0			0
$369$	241.905	+	553.156i	0.655570	+	1.49907i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−97.0000	−	168.009i	−0.260054	−	0.450426i	0.706202	−	0.708010i	$-0.250407\pi$
$373$	−97.0000	−	168.009i	−0.260054	−	0.450426i	−0.966256	+	0.257584i	$0.917074\pi$
$374$		0			0
$375$	−20.5948	−	98.4929i	−0.0549193	−	0.262648i
$376$		0			0
$377$		−	657.404i		−	1.74378i
$378$		0			0
$379$	−82.0000			−0.216359			−0.108179	−	0.994131i	$-0.534502\pi$
$379$	−82.0000			−0.216359			−0.108179	+	0.994131i	$0.534502\pi$
$380$		0			0
$381$	578.489	−	120.961i	1.51834	−	0.317484i
$382$		0			0
$383$	81.3327	−	46.9574i	0.212357	−	0.122604i	−0.390049	−	0.920794i	$-0.627542\pi$
$383$	81.3327	−	46.9574i	0.212357	−	0.122604i	0.602406	+	0.798190i	$0.294209\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−428.790	+	187.518i	−1.10799	+	0.484542i
$388$		0			0
$389$	336.950	+	194.538i	0.866194	+	0.500097i	0.866082	−	0.499903i	$-0.166631\pi$
$389$	336.950	+	194.538i	0.866194	+	0.500097i	0.000112547		1.00000i	$0.499964\pi$
$390$		0			0
$391$	−360.000			−0.920716
$392$		0			0
$393$	−375.000	+	335.410i	−0.954198	+	0.853461i
$394$		0			0
$395$	586.757	+	338.764i	1.48546	+	0.857631i
$396$		0			0
$397$	76.0000	+	131.636i	0.191436	+	0.331576i	0.945726	−	0.324964i	$-0.105352\pi$
$397$	76.0000	+	131.636i	0.191436	+	0.331576i	−0.754291	+	0.656541i	$0.772019\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	650.661	−	375.659i	1.62260	−	0.936807i	0.636374	−	0.771380i	$-0.280433\pi$
$401$	650.661	−	375.659i	1.62260	−	0.936807i	0.986222	−	0.165426i	$-0.0528999\pi$
$402$		0			0
$403$	217.000	−	375.855i	0.538462	−	0.932643i
$404$		0			0
$405$	−120.000	+	529.948i	−0.296296	+	1.30851i
$406$		0			0
$407$			187.830i			0.461498i
$408$		0			0
$409$	−123.500	+	213.908i	−0.301956	+	0.523003i	−0.976579	−	0.215159i	$-0.930973\pi$
$409$	−123.500	+	213.908i	−0.301956	+	0.523003i	0.674623	+	0.738162i	$0.264306\pi$
$410$		0			0
$411$	−152.952	−	50.2574i	−0.372145	−	0.122281i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	292.500	+	506.625i	0.704819	+	1.22078i
$416$		0			0
$417$	−252.538	+	52.8054i	−0.605607	+	0.126632i
$418$		0			0
$419$			228.079i			0.544341i	0.962249	+	0.272171i	$0.0877415\pi$
$419$			228.079i			0.544341i	−0.962249	+	0.272171i	$0.912259\pi$
$420$		0			0
$421$	−106.000			−0.251781			−0.125891	−	0.992044i	$-0.540179\pi$
$421$	−106.000			−0.251781			−0.125891	+	0.992044i	$0.540179\pi$
$422$		0			0
$423$	214.857	−	291.645i	0.507936	−	0.689467i
$424$		0			0
$425$	464.758	−	268.328i	1.09355	−	0.631360i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−267.665	−	87.9505i	−0.623928	−	0.205013i
$430$		0			0
$431$	−58.0948	−	33.5410i	−0.134791	−	0.0778214i	0.431088	−	0.902310i	$-0.358130\pi$
$431$	−58.0948	−	33.5410i	−0.134791	−	0.0778214i	−0.565879	+	0.824488i	$0.691463\pi$
$432$		0			0
$433$	−278.000			−0.642032			−0.321016	−	0.947074i	$-0.604024\pi$
$433$	−278.000			−0.642032			−0.321016	+	0.947074i	$0.604024\pi$
$434$		0			0
$435$	−630.000	−	704.361i	−1.44828	−	1.61922i
$436$		0			0
$437$	−92.9516	−	53.6656i	−0.212704	−	0.122805i
$438$		0			0
$439$	−114.500	−	198.320i	−0.260820	−	0.451754i	0.705640	−	0.708571i	$-0.250660\pi$
$439$	−114.500	−	198.320i	−0.260820	−	0.451754i	−0.966460	+	0.256817i	$0.917326\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	644.852	−	372.305i	1.45565	−	0.840418i	0.456855	−	0.889541i	$-0.348976\pi$
$443$	644.852	−	372.305i	1.45565	−	0.840418i	0.998793	+	0.0491231i	$0.0156427\pi$
$444$		0			0
$445$	−225.000	+	389.711i	−0.505618	+	0.875756i
$446$		0			0
$447$	−30.0000	+	26.8328i	−0.0671141	+	0.0600287i
$448$		0			0
$449$		−	201.246i		−	0.448210i	−0.974565	−	0.224105i	$-0.928054\pi$
$449$		−	201.246i		−	0.448210i	0.974565	−	0.224105i	$-0.0719458\pi$
$450$		0			0
$451$	−225.000	+	389.711i	−0.498891	+	0.864105i
$452$		0			0
$453$	113.315	−	344.860i	0.250145	−	0.761281i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	291.500	+	504.893i	0.637856	+	1.10480i	0.985902	+	0.167321i	$0.0535117\pi$
$457$	291.500	+	504.893i	0.637856	+	1.10480i	−0.348047	+	0.937477i	$0.613155\pi$
$458$		0			0
$459$	721.234	−	68.5697i	1.57132	−	0.149389i
$460$		0			0
$461$			415.909i			0.902188i	0.892476	+	0.451094i	$0.148966\pi$
$461$			415.909i			0.902188i	−0.892476	+	0.451094i	$0.851034\pi$
$462$		0			0
$463$	698.000			1.50756			0.753780	−	0.657127i	$-0.228229\pi$
$463$	698.000			1.50756			0.753780	+	0.657127i	$0.228229\pi$
$464$		0			0
$465$	−127.687	−	610.656i	−0.274597	−	1.31324i
$466$		0			0
$467$	58.0948	−	33.5410i	0.124400	−	0.0718223i	−0.436509	−	0.899700i	$-0.643785\pi$
$467$	58.0948	−	33.5410i	0.124400	−	0.0718223i	0.560909	+	0.827878i	$0.310452\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	142.347	−	433.213i	0.302222	−	0.919773i
$472$		0			0
$473$	−302.093	−	174.413i	−0.638674	−	0.368738i
$474$		0			0
$475$	160.000			0.336842
$476$		0			0
$477$	−60.0000	−	6.70820i	−0.125786	−	0.0140633i
$478$		0			0
$479$	−232.379	−	134.164i	−0.485134	−	0.280092i	0.237420	−	0.971407i	$-0.423698\pi$
$479$	−232.379	−	134.164i	−0.485134	−	0.280092i	−0.722553	+	0.691315i	$0.757032\pi$
$480$		0			0
$481$	−196.000	−	339.482i	−0.407484	−	0.705784i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−75.5232	+	43.6033i	−0.155718	+	0.0899038i
$486$		0			0
$487$	−53.5000	+	92.6647i	−0.109856	+	0.190277i	−0.915712	−	0.401835i	$-0.868372\pi$
$487$	−53.5000	+	92.6647i	−0.109856	+	0.190277i	0.805856	+	0.592112i	$0.201706\pi$
$488$		0			0
$489$	−76.0000	−	84.9706i	−0.155419	−	0.173764i
$490$		0			0
$491$			476.282i			0.970025i	0.874507	+	0.485013i	$0.161185\pi$
$491$			476.282i			0.970025i	−0.874507	+	0.485013i	$0.838815\pi$
$492$		0			0
$493$	−630.000	+	1091.19i	−1.27789	+	2.21337i
$494$		0			0
$495$	−371.069	+	162.275i	−0.749633	+	0.327828i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	371.000	+	642.591i	0.743487	+	1.28776i	0.950898	+	0.309503i	$0.100163\pi$
$499$	371.000	+	642.591i	0.743487	+	1.28776i	−0.207411	+	0.978254i	$0.566504\pi$
$500$		0			0
$501$	−32.9516	−	157.589i	−0.0657717	−	0.314548i
$502$		0			0
$503$			80.4984i			0.160037i	0.996793	+	0.0800183i	$0.0254979\pi$
$503$			80.4984i			0.160037i	−0.996793	+	0.0800183i	$0.974502\pi$
$504$		0			0
$505$	−90.0000			−0.178218
$506$		0			0
$507$	79.2853	−	16.5785i	0.156381	−	0.0326991i
$508$		0			0
$509$	447.330	−	258.266i	0.878840	−	0.507399i	0.00856426	−	0.999963i	$-0.497274\pi$
$509$	447.330	−	258.266i	0.878840	−	0.507399i	0.870276	+	0.492565i	$0.163941\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	196.444	+	89.8106i	0.382931	+	0.175069i
$514$		0			0
$515$	−917.897	−	529.948i	−1.78232	−	1.02903i
$516$		0			0
$517$	270.000			0.522244
$518$		0			0
$519$	−270.000	+	241.495i	−0.520231	+	0.465309i
$520$		0			0
$521$	−534.472	−	308.577i	−1.02586	−	0.592279i	−0.110062	−	0.993925i	$-0.535105\pi$
$521$	−534.472	−	308.577i	−1.02586	−	0.592279i	−0.915795	+	0.401646i	$0.868438\pi$
$522$		0			0
$523$	409.000	+	708.409i	0.782027	+	1.35451i	0.930759	+	0.365633i	$0.119147\pi$
$523$	409.000	+	708.409i	0.782027	+	1.35451i	−0.148732	+	0.988877i	$0.547519\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−720.375	+	415.909i	−1.36694	+	0.789200i
$528$		0			0
$529$	−174.500	+	302.243i	−0.329868	+	0.571348i
$530$		0			0
$531$	180.000	+	20.1246i	0.338983	+	0.0378995i
$532$		0			0
$533$		−	939.149i		−	1.76200i
$534$		0			0
$535$	22.5000	−	38.9711i	0.0420561	−	0.0728433i
$536$		0			0
$537$	955.948	+	314.109i	1.78016	+	0.584933i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−346.000	−	599.290i	−0.639556	−	1.10774i	−0.985530	−	0.169500i	$-0.945785\pi$
$541$	−346.000	−	599.290i	−0.639556	−	1.10774i	0.345974	−	0.938244i	$-0.387549\pi$
$542$		0			0
$543$	−922.058	+	192.801i	−1.69808	+	0.355067i
$544$		0			0
$545$		−	53.6656i		−	0.0984690i
$546$		0			0
$547$	536.000			0.979890			0.489945	−	0.871753i	$-0.337017\pi$
$547$	536.000			0.979890			0.489945	+	0.871753i	$0.337017\pi$
$548$		0			0
$549$	101.444	+	74.7343i	0.184779	+	0.136128i
$550$		0			0
$551$	−325.331	+	187.830i	−0.590437	+	0.340889i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−535.331	−	175.901i	−0.964560	−	0.316939i
$556$		0			0
$557$	865.612	+	499.761i	1.55406	+	0.897237i	0.997805	+	0.0662264i	$0.0210959\pi$
$557$	865.612	+	499.761i	1.55406	+	0.897237i	0.556256	+	0.831011i	$0.312237\pi$
$558$		0			0
$559$	728.000			1.30233
$560$		0			0
$561$	360.000	+	402.492i	0.641711	+	0.717455i
$562$		0			0
$563$	−87.1421	−	50.3115i	−0.154782	−	0.0893633i	0.420609	−	0.907242i	$-0.361817\pi$
$563$	−87.1421	−	50.3115i	−0.154782	−	0.0893633i	−0.575390	+	0.817879i	$0.695150\pi$
$564$		0			0
$565$	−585.000	−	1013.25i	−1.03540	−	1.79336i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−209.141	+	120.748i	−0.367559	+	0.212210i	−0.672392	−	0.740196i	$-0.734733\pi$
$569$	−209.141	+	120.748i	−0.367559	+	0.212210i	0.304832	+	0.952406i	$0.401400\pi$
$570$		0			0
$571$	119.000	−	206.114i	0.208406	−	0.360970i	−0.742806	−	0.669506i	$-0.766506\pi$
$571$	119.000	−	206.114i	0.208406	−	0.360970i	0.951213	+	0.308536i	$0.0998390\pi$
$572$		0			0
$573$	−540.000	+	482.991i	−0.942408	+	0.842916i
$574$		0			0
$575$			268.328i			0.466658i
$576$		0			0
$577$	−36.5000	+	63.2199i	−0.0632582	+	0.109566i	−0.895920	−	0.444215i	$-0.853483\pi$
$577$	−36.5000	+	63.2199i	−0.0632582	+	0.109566i	0.832662	+	0.553782i	$0.186816\pi$
$578$		0			0
$579$	147.029	−	447.463i	0.253936	−	0.772821i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−22.5000	−	38.9711i	−0.0385935	−	0.0668459i
$584$		0			0
$585$	501.333	−	680.504i	0.856979	−	1.16325i
$586$		0			0
$587$		−	771.443i		−	1.31421i	−0.753797	−	0.657107i	$-0.771780\pi$
$587$		−	771.443i		−	1.31421i	0.753797	−	0.657107i	$-0.228220\pi$
$588$		0			0
$589$	−248.000			−0.421053
$590$		0			0
$591$	−172.996	−	827.341i	−0.292717	−	1.39990i
$592$		0			0
$593$	−81.3327	+	46.9574i	−0.137155	+	0.0791862i	−0.567007	−	0.823713i	$-0.691899\pi$
$593$	−81.3327	+	46.9574i	−0.137155	+	0.0791862i	0.429853	+	0.902899i	$0.358566\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	305.296	−	929.128i	0.511384	−	1.55633i
$598$		0			0
$599$	697.137	+	402.492i	1.16383	+	0.671940i	0.952220	−	0.305413i	$-0.0987945\pi$
$599$	697.137	+	402.492i	1.16383	+	0.671940i	0.211615	+	0.977353i	$0.432128\pi$
$600$		0			0
$601$	943.000			1.56905			0.784526	−	0.620096i	$-0.212906\pi$
$601$	943.000			1.56905			0.784526	+	0.620096i	$0.212906\pi$
$602$		0			0
$603$	4.00000	−	35.7771i	0.00663350	−	0.0593318i
$604$		0			0
$605$	441.520	+	254.912i	0.729785	+	0.421342i
$606$		0			0
$607$	218.500	+	378.453i	0.359967	+	0.623481i	0.987955	−	0.154742i	$-0.0494546\pi$
$607$	218.500	+	378.453i	0.359967	+	0.623481i	−0.627988	+	0.778223i	$0.716121\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−487.996	+	281.745i	−0.798684	+	0.461120i
$612$		0			0
$613$	−307.000	+	531.740i	−0.500816	+	0.867438i	0.499184	+	0.866496i	$0.333633\pi$
$613$	−307.000	+	531.740i	−0.500816	+	0.867438i	−1.00000		0.000942100i	$0.999700\pi$
$614$		0			0
$615$	−900.000	−	1006.23i	−1.46341	−	1.63615i
$616$		0			0
$617$		−	952.565i		−	1.54387i	−0.635704	−	0.771933i	$-0.719290\pi$
$617$		−	952.565i		−	1.54387i	0.635704	−	0.771933i	$-0.280710\pi$
$618$		0			0
$619$	523.000	−	905.863i	0.844911	−	1.46343i	−0.0407872	−	0.999168i	$-0.512987\pi$
$619$	523.000	−	905.863i	0.844911	−	1.46343i	0.885698	−	0.464261i	$-0.153680\pi$
$620$		0			0
$621$	−150.617	+	329.446i	−0.242539	+	0.530509i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	362.500	+	627.868i	0.580000	+	1.00459i
$626$		0			0
$627$	32.9516	+	157.589i	0.0525544	+	0.251338i
$628$		0			0
$629$			751.319i			1.19447i
$630$		0			0
$631$	−601.000			−0.952456			−0.476228	−	0.879322i	$-0.657996\pi$
$631$	−601.000			−0.952456			−0.476228	+	0.879322i	$0.657996\pi$
$632$		0			0
$633$	393.490	−	82.2783i	0.621627	−	0.129981i
$634$		0			0
$635$	−1144.47	+	660.758i	−1.80231	+	1.04056i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−145.143	−	331.894i	−0.227141	−	0.519396i
$640$		0			0
$641$	58.0948	+	33.5410i	0.0906314	+	0.0523261i	0.544631	−	0.838676i	$-0.316670\pi$
$641$	58.0948	+	33.5410i	0.0906314	+	0.0523261i	−0.453999	+	0.891002i	$0.650003\pi$
$642$		0			0
$643$	−788.000			−1.22551			−0.612753	−	0.790275i	$-0.709938\pi$
$643$	−788.000			−1.22551			−0.612753	+	0.790275i	$0.709938\pi$
$644$		0			0
$645$	780.000	−	697.653i	1.20930	−	1.08163i
$646$		0			0
$647$	476.377	+	275.036i	0.736286	+	0.425095i	0.820717	−	0.571334i	$-0.193574\pi$
$647$	476.377	+	275.036i	0.736286	+	0.425095i	−0.0844315	+	0.996429i	$0.526907\pi$
$648$		0			0
$649$	67.5000	+	116.913i	0.104006	+	0.180144i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−656.471	+	379.014i	−1.00531	+	0.580419i	−0.909817	−	0.415011i	$-0.863778\pi$
$653$	−656.471	+	379.014i	−1.00531	+	0.580419i	−0.0954984	+	0.995430i	$0.530444\pi$
$654$		0			0
$655$	562.500	−	974.279i	0.858779	−	1.48745i
$656$		0			0
$657$	98.0000	−	876.539i	0.149163	−	1.33415i
$658$		0			0
$659$			228.079i			0.346099i	0.984913	+	0.173049i	$0.0553620\pi$
$659$			228.079i			0.346099i	−0.984913	+	0.173049i	$0.944638\pi$
$660$		0			0
$661$	142.000	−	245.951i	0.214826	−	0.372090i	−0.738393	−	0.674371i	$-0.764415\pi$
$661$	142.000	−	245.951i	0.214826	−	0.372090i	0.953219	+	0.302281i	$0.0977482\pi$
$662$		0			0
$663$	−1070.66	−	351.802i	−1.61487	−	0.530621i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−315.000	−	545.596i	−0.472264	−	0.817985i
$668$		0			0
$669$	725.313	−	151.662i	1.08418	−	0.226700i
$670$		0			0
$671$			93.9149i			0.139963i
$672$		0			0
$673$	1163.00			1.72808			0.864042	−	0.503420i	$-0.167925\pi$
$673$	1163.00			1.72808			0.864042	+	0.503420i	$0.167925\pi$
$674$		0			0
$675$	−51.1088	−	537.576i	−0.0757168	−	0.796409i
$676$		0			0
$677$	−400.854	+	231.433i	−0.592103	+	0.341851i	−0.765929	−	0.642926i	$-0.777720\pi$
$677$	−400.854	+	231.433i	−0.592103	+	0.341851i	0.173826	+	0.984776i	$0.444387\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	95.5948	+	31.4109i	0.140374	+	0.0461246i
$682$		0			0
$683$	−40.6663	−	23.4787i	−0.0595407	−	0.0343759i	0.469934	−	0.882701i	$-0.344278\pi$
$683$	−40.6663	−	23.4787i	−0.0595407	−	0.0343759i	−0.529475	+	0.848326i	$0.677611\pi$
$684$		0			0
$685$	360.000			0.525547
$686$		0			0
$687$	−44.0000	−	49.1935i	−0.0640466	−	0.0716063i
$688$		0			0
$689$	81.3327	+	46.9574i	0.118044	+	0.0681530i
$690$		0			0
$691$	−503.000	−	871.222i	−0.727931	−	1.26081i	−0.957756	−	0.287581i	$-0.907149\pi$
$691$	−503.000	−	871.222i	−0.727931	−	1.26081i	0.229826	−	0.973232i	$-0.426184\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	499.615	−	288.453i	0.718870	−	0.415040i
$696$		0			0
$697$	−900.000	+	1558.85i	−1.29125	+	2.23651i
$698$		0			0
$699$	−240.000	+	214.663i	−0.343348	+	0.307099i
$700$		0			0
$701$			342.118i			0.488043i	0.969770	+	0.244022i	$0.0784668\pi$
$701$			342.118i			0.488043i	−0.969770	+	0.244022i	$0.921533\pi$
$702$		0			0
$703$	−112.000	+	193.990i	−0.159317	+	0.275946i
$704$		0			0
$705$	−252.853	+	769.523i	−0.358656	+	1.09152i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−223.000	−	386.247i	−0.314528	−	0.544778i	0.664809	−	0.747013i	$-0.268513\pi$
$709$	−223.000	−	386.247i	−0.314528	−	0.544778i	−0.979337	+	0.202235i	$0.935179\pi$
$710$		0			0
$711$	−731.843	−	539.154i	−1.02931	−	0.758304i
$712$		0			0
$713$		−	415.909i		−	0.583322i
$714$		0			0
$715$	630.000			0.881119
$716$		0			0
$717$	−90.6169	−	433.369i	−0.126383	−	0.604420i
$718$		0			0
$719$	−151.046	+	87.2067i	−0.210078	+	0.121289i	−0.601348	−	0.798987i	$-0.705369\pi$
$719$	−151.046	+	87.2067i	−0.210078	+	0.121289i	0.391269	+	0.920276i	$0.372036\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	55.2530	−	168.155i	0.0764219	−	0.232580i
$724$		0			0
$725$	813.327	+	469.574i	1.12183	+	0.647689i
$726$		0			0
$727$	889.000			1.22283			0.611417	−	0.791309i	$-0.290600\pi$
$727$	889.000			1.22283			0.611417	+	0.791309i	$0.290600\pi$
$728$		0			0
$729$	239.000	−	688.709i	0.327846	−	0.944731i
$730$		0			0
$731$	−1208.37	−	697.653i	−1.65304	−	0.954382i
$732$		0			0
$733$	124.000	+	214.774i	0.169168	+	0.293007i	0.938128	−	0.346290i	$-0.112559\pi$
$733$	124.000	+	214.774i	0.169168	+	0.293007i	−0.768960	+	0.639297i	$0.779225\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.2379	−	13.4164i	0.0315304	−	0.0182041i
$738$		0			0
$739$	−283.000	+	490.170i	−0.382950	+	0.663289i	−0.991482	−	0.130240i	$-0.958425\pi$
$739$	−283.000	+	490.170i	−0.382950	+	0.663289i	0.608533	+	0.793529i	$0.291758\pi$
$740$		0			0
$741$	−224.000	−	250.440i	−0.302294	−	0.337975i
$742$		0			0
$743$		−	1234.31i		−	1.66125i	−0.556831	−	0.830626i	$-0.687983\pi$
$743$		−	1234.31i		−	1.66125i	0.556831	−	0.830626i	$-0.312017\pi$
$744$		0			0
$745$	45.0000	−	77.9423i	0.0604027	−	0.104621i
$746$		0			0
$747$	−314.477	−	719.103i	−0.420986	−	0.962655i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	285.500	+	494.501i	0.380160	+	0.658456i	0.991085	−	0.133232i	$-0.0425357\pi$
$751$	285.500	+	494.501i	0.380160	+	0.658456i	−0.610925	+	0.791688i	$0.709202\pi$
$752$		0			0
$753$	37.0706	+	177.287i	0.0492305	+	0.235441i
$754$		0			0
$755$			811.693i			1.07509i
$756$		0			0
$757$	542.000			0.715984			0.357992	−	0.933725i	$-0.383461\pi$
$757$	542.000			0.715984			0.357992	+	0.933725i	$0.383461\pi$
$758$		0			0
$759$	−264.284	+	55.2615i	−0.348201	+	0.0728083i
$760$		0			0
$761$	569.329	−	328.702i	0.748132	−	0.431934i	−0.0768865	−	0.997040i	$-0.524498\pi$
$761$	569.329	−	328.702i	0.748132	−	0.431934i	0.825019	+	0.565106i	$0.191165\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1484.27	+	649.100i	−1.94023	+	0.848497i
$766$		0			0
$767$	−243.998	−	140.872i	−0.318120	−	0.183667i
$768$		0			0
$769$	229.000			0.297789			0.148895	−	0.988853i	$-0.452428\pi$
$769$	229.000			0.297789			0.148895	+	0.988853i	$0.452428\pi$
$770$		0			0
$771$	−870.000	+	778.152i	−1.12840	+	1.00928i
$772$		0			0
$773$	−429.901	−	248.204i	−0.556146	−	0.321091i	0.195451	−	0.980713i	$-0.437383\pi$
$773$	−429.901	−	248.204i	−0.556146	−	0.321091i	−0.751597	+	0.659622i	$0.770716\pi$
$774$		0			0
$775$	310.000	+	536.936i	0.400000	+	0.692820i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−464.758	+	268.328i	−0.596608	+	0.344452i
$780$		0			0
$781$	135.000	−	233.827i	0.172855	−	0.299394i
$782$		0			0
$783$	735.000	+	1033.06i	0.938697	+	1.31937i
$784$		0			0
$785$			1019.65i			1.29891i
$786$		0			0
$787$	−509.000	+	881.614i	−0.646760	+	1.12022i	0.337132	+	0.941457i	$0.390543\pi$
$787$	−509.000	+	881.614i	−0.646760	+	1.12022i	−0.983892	+	0.178764i	$0.942790\pi$
$788$		0			0
$789$	1223.61	+	402.059i	1.55084	+	0.509581i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−98.0000	−	169.741i	−0.123581	−	0.214049i
$794$		0			0
$795$	132.142	−	27.6308i	0.166217	−	0.0347557i
$796$		0			0
$797$		−	878.775i		−	1.10260i	−0.834306	−	0.551302i	$-0.814131\pi$
$797$		−	878.775i		−	1.10260i	0.834306	−	0.551302i	$-0.185869\pi$
$798$		0			0
$799$	1080.00			1.35169
$800$		0			0
$801$	358.095	−	486.074i	0.447060	−	0.606834i
$802$		0			0
$803$	569.329	−	328.702i	0.709002	−	0.409342i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	133.833	+	43.9752i	0.165840	+	0.0544922i
$808$		0			0
$809$	−1208.37	−	697.653i	−1.49366	−	0.862365i	−0.493686	−	0.869640i	$-0.664351\pi$
$809$	−1208.37	−	697.653i	−1.49366	−	0.862365i	−0.999974	+	0.00727516i	$0.997684\pi$
$810$		0			0
$811$	−164.000			−0.202219			−0.101110	−	0.994875i	$-0.532239\pi$
$811$	−164.000			−0.202219			−0.101110	+	0.994875i	$0.532239\pi$
$812$		0			0
$813$	−86.0000	−	96.1509i	−0.105781	−	0.118267i
$814$		0			0
$815$	220.760	+	127.456i	0.270871	+	0.156388i
$816$		0			0
$817$	−208.000	−	360.267i	−0.254590	−	0.440963i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−784.279	+	452.804i	−0.955273	+	0.551527i	−0.894715	−	0.446638i	$-0.852621\pi$
$821$	−784.279	+	452.804i	−0.955273	+	0.551527i	−0.0605580	+	0.998165i	$0.519288\pi$
$822$		0			0
$823$	581.000	−	1006.32i	0.705954	−	1.22275i	−0.260392	−	0.965503i	$-0.583852\pi$
$823$	581.000	−	1006.32i	0.705954	−	1.22275i	0.966346	−	0.257245i	$-0.0828147\pi$
$824$		0			0
$825$	300.000	−	268.328i	0.363636	−	0.325246i
$826$		0			0
$827$		−	945.857i		−	1.14372i	−0.820351	−	0.571860i	$-0.806222\pi$
$827$		−	945.857i		−	1.14372i	0.820351	−	0.571860i	$-0.193778\pi$
$828$		0			0
$829$	−212.000	+	367.195i	−0.255730	+	0.442937i	−0.965093	−	0.261906i	$-0.915649\pi$
$829$	−212.000	+	367.195i	−0.255730	+	0.442937i	0.709364	+	0.704843i	$0.248982\pi$
$830$		0			0
$831$	116.125	−	353.411i	0.139741	−	0.425283i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	180.000	+	311.769i	0.215569	+	0.373376i
$836$		0			0
$837$	79.2187	+	833.243i	0.0946460	+	0.995511i
$838$		0			0
$839$		−	268.328i		−	0.319819i	−0.987132	−	0.159910i	$-0.948880\pi$
$839$		−	268.328i		−	0.319819i	0.987132	−	0.159910i	$-0.0511202\pi$
$840$		0			0
$841$	−1364.00			−1.62188
$842$		0			0
$843$	65.9032	+	315.177i	0.0781770	+	0.373876i
$844$		0			0
$845$	−156.856	+	90.5608i	−0.185628	+	0.107172i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	97.3951	−	296.409i	0.114717	−	0.349127i
$850$		0			0
$851$	−325.331	−	187.830i	−0.382292	−	0.220716i
$852$		0			0
$853$	−128.000			−0.150059			−0.0750293	−	0.997181i	$-0.523905\pi$
$853$	−128.000			−0.150059			−0.0750293	+	0.997181i	$0.523905\pi$
$854$		0			0
$855$	−480.000	−	53.6656i	−0.561404	−	0.0627668i
$856$		0			0
$857$	−336.950	−	194.538i	−0.393173	−	0.226999i	0.290361	−	0.956917i	$-0.406225\pi$
$857$	−336.950	−	194.538i	−0.393173	−	0.226999i	−0.683534	+	0.729918i	$0.739558\pi$
$858$		0			0
$859$	−176.000	−	304.841i	−0.204889	−	0.354879i	0.745208	−	0.666832i	$-0.232350\pi$
$859$	−176.000	−	304.841i	−0.204889	−	0.354879i	−0.950097	+	0.311953i	$0.899017\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	639.042	−	368.951i	0.740489	−	0.427522i	−0.0817579	−	0.996652i	$-0.526053\pi$
$863$	639.042	−	368.951i	0.740489	−	0.427522i	0.822247	+	0.569131i	$0.192720\pi$
$864$		0			0
$865$	405.000	−	701.481i	0.468208	−	0.810960i
$866$		0			0
$867$	862.000	+	963.745i	0.994233	+	1.11159i
$868$		0			0
$869$		−	677.529i		−	0.779665i
$870$		0			0
$871$	−28.0000	+	48.4974i	−0.0321470	+	0.0556802i
$872$		0			0
$873$	107.198	−	46.8794i	0.122792	−	0.0536992i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	104.000	+	180.133i	0.118586	+	0.205397i	0.919208	−	0.393773i	$-0.128831\pi$
$877$	104.000	+	180.133i	0.118586	+	0.205397i	−0.800621	+	0.599170i	$0.795497\pi$
$878$		0			0
$879$	127.687	+	610.656i	0.145264	+	0.694717i
$880$		0			0
$881$		−	1207.48i		−	1.37058i	−0.728273	−	0.685288i	$-0.759677\pi$
$881$		−	1207.48i		−	1.37058i	0.728273	−	0.685288i	$-0.240323\pi$
$882$		0			0
$883$	−406.000			−0.459796			−0.229898	−	0.973215i	$-0.573839\pi$
$883$	−406.000			−0.459796			−0.229898	+	0.973215i	$0.573839\pi$
$884$		0			0
$885$	−396.426	+	82.8923i	−0.447939	+	0.0936636i
$886$		0			0
$887$	1336.18	−	771.443i	1.50640	−	0.869722i	0.506430	−	0.862281i	$-0.330965\pi$
$887$	1336.18	−	771.443i	1.50640	−	0.869722i	0.999972	−	0.00744123i	$-0.00236864\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	518.949	−	161.051i	0.582434	−	0.180753i
$892$		0			0
$893$	278.855	+	160.997i	0.312267	+	0.180288i
$894$		0			0
$895$	−2250.00			−2.51397
$896$		0			0
$897$	420.000	−	375.659i	0.468227	−	0.418795i
$898$		0			0
$899$	−1260.66	−	727.840i	−1.40229	−	0.809611i
$900$		0			0
$901$	−90.0000	−	155.885i	−0.0998890	−	0.173013i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1824.18	−	1053.19i	2.01566	−	1.16374i
$906$		0			0
$907$	89.0000	−	154.153i	0.0981257	−	0.169959i	−0.812783	−	0.582566i	$-0.802049\pi$
$907$	89.0000	−	154.153i	0.0981257	−	0.169959i	0.910909	+	0.412608i	$0.135382\pi$
$908$		0			0
$909$	120.000	+	13.4164i	0.132013	+	0.0147595i
$910$		0			0
$911$			147.580i			0.161998i	0.996714	+	0.0809992i	$0.0258111\pi$
$911$			147.580i			0.161998i	−0.996714	+	0.0809992i	$0.974189\pi$
$912$		0			0
$913$	292.500	−	506.625i	0.320372	−	0.554901i
$914$		0			0
$915$	−267.665	−	87.9505i	−0.292530	−	0.0961207i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−283.000	−	490.170i	−0.307943	−	0.533374i	0.669969	−	0.742389i	$-0.266307\pi$
$919$	−283.000	−	490.170i	−0.307943	−	0.533374i	−0.977912	+	0.209016i	$0.932974\pi$
$920$		0			0
$921$	−182.062	+	38.0690i	−0.197679	+	0.0413345i
$922$		0			0
$923$			563.489i			0.610497i
$924$		0			0
$925$	560.000			0.605405
$926$		0			0
$927$	1144.86	+	843.429i	1.23502	+	0.909848i
$928$		0			0
$929$	−278.855	+	160.997i	−0.300167	+	0.173301i	−0.642518	−	0.766271i	$-0.722110\pi$
$929$	−278.855	+	160.997i	−0.300167	+	0.173301i	0.342351	+	0.939572i	$0.388777\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−114.714	−	37.6931i	−0.122951	−	0.0403999i
$934$		0			0
$935$	−1045.71	−	603.738i	−1.11840	−	0.645709i
$936$		0			0
$937$	−197.000			−0.210245			−0.105123	−	0.994459i	$-0.533524\pi$
$937$	−197.000			−0.210245			−0.105123	+	0.994459i	$0.533524\pi$
$938$		0			0
$939$	−14.0000	−	15.6525i	−0.0149095	−	0.0166693i
$940$		0			0
$941$	1341.99	+	774.798i	1.42613	+	0.823377i	0.996813	−	0.0797768i	$-0.0254207\pi$
$941$	1341.99	+	774.798i	1.42613	+	0.823377i	0.429318	+	0.903154i	$0.358754\pi$
$942$		0			0
$943$	−450.000	−	779.423i	−0.477200	−	0.826535i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	871.421	−	503.115i	0.920191	−	0.531273i	0.0364953	−	0.999334i	$-0.488381\pi$
$947$	871.421	−	503.115i	0.920191	−	0.531273i	0.883696	+	0.468061i	$0.155047\pi$
$948$		0			0
$949$	−686.000	+	1188.19i	−0.722866	+	1.25204i
$950$		0			0
$951$	−675.000	+	603.738i	−0.709779	+	0.634846i
$952$		0			0
$953$			643.988i			0.675748i	0.941191	+	0.337874i	$0.109708\pi$
$953$			643.988i			0.675748i	−0.941191	+	0.337874i	$0.890292\pi$
$954$		0			0
$955$	810.000	−	1402.96i	0.848168	−	1.46907i
$956$		0			0
$957$	−294.995	+	897.777i	−0.308250	+	0.938116i
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	−35.8095	+	48.6074i	−0.0371853	+	0.0504750i
$964$		0			0
$965$			1053.19i			1.09139i
$966$		0			0
$967$	−733.000			−0.758014			−0.379007	−	0.925394i	$-0.623734\pi$
$967$	−733.000			−0.758014			−0.379007	+	0.925394i	$0.623734\pi$
$968$		0			0
$969$	131.806	+	630.355i	0.136023	+	0.650521i
$970$		0			0
$971$	−1109.61	+	640.633i	−1.14275	+	0.659767i	−0.947110	−	0.320909i	$-0.896012\pi$
$971$	−1109.61	+	640.633i	−1.14275	+	0.659767i	−0.195639	+	0.980676i	$0.562678\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−262.218	+	798.024i	−0.268941	+	0.818486i
$976$		0			0
$977$	975.992	+	563.489i	0.998968	+	0.576754i	0.907943	−	0.419094i	$-0.137652\pi$
$977$	975.992	+	563.489i	0.998968	+	0.576754i	0.0910253	+	0.995849i	$0.470986\pi$
$978$		0			0
$979$	450.000			0.459653
$980$		0			0
$981$	−8.00000	+	71.5542i	−0.00815494	+	0.0729400i
$982$		0			0
$983$	1196.75	+	690.945i	1.21745	+	0.702894i	0.964371	−	0.264552i	$-0.0852241\pi$
$983$	1196.75	+	690.945i	1.21745	+	0.702894i	0.253077	+	0.967446i	$0.418557\pi$
$984$		0			0
$985$	945.000	+	1636.79i	0.959391	+	1.66171i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	604.185	−	348.827i	0.610905	−	0.352706i
$990$		0			0
$991$	405.500	−	702.347i	0.409183	−	0.708725i	−0.585616	−	0.810589i	$-0.699147\pi$
$991$	405.500	−	702.347i	0.409183	−	0.708725i	0.994798	+	0.101864i	$0.0324806\pi$
$992$		0			0
$993$	32.0000	+	35.7771i	0.0322256	+	0.0360293i
$994$		0			0
$995$			2186.87i			2.19786i
$996$		0			0
$997$	−404.000	+	699.749i	−0.405216	+	0.701854i	−0.994347	−	0.106184i	$-0.966137\pi$
$997$	−404.000	+	699.749i	−0.405216	+	0.701854i	0.589131	+	0.808038i	$0.299470\pi$
$998$		0			0
$999$	687.552	+	314.337i	0.688241	+	0.314652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.p.e.557.2		4
3.2	odd	2	inner	588.3.p.e.557.1		4
7.2	even	3	inner	588.3.p.e.569.1		4
7.3	odd	6		588.3.c.g.197.2		2
7.4	even	3		588.3.c.d.197.1		2
7.5	odd	6		84.3.p.b.65.2	yes	4
7.6	odd	2		84.3.p.b.53.1	✓	4
21.2	odd	6	inner	588.3.p.e.569.2		4
21.5	even	6		84.3.p.b.65.1	yes	4
21.11	odd	6		588.3.c.d.197.2		2
21.17	even	6		588.3.c.g.197.1		2
21.20	even	2		84.3.p.b.53.2	yes	4
28.19	even	6		336.3.bn.e.65.1		4
28.27	even	2		336.3.bn.e.305.2		4
84.47	odd	6		336.3.bn.e.65.2		4
84.83	odd	2		336.3.bn.e.305.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.p.b.53.1	✓	4	7.6	odd	2
84.3.p.b.53.2	yes	4	21.20	even	2
84.3.p.b.65.1	yes	4	21.5	even	6
84.3.p.b.65.2	yes	4	7.5	odd	6
336.3.bn.e.65.1		4	28.19	even	6
336.3.bn.e.65.2		4	84.47	odd	6
336.3.bn.e.305.1		4	84.83	odd	2
336.3.bn.e.305.2		4	28.27	even	2
588.3.c.d.197.1		2	7.4	even	3
588.3.c.d.197.2		2	21.11	odd	6
588.3.c.g.197.1		2	21.17	even	6
588.3.c.g.197.2		2	7.3	odd	6
588.3.p.e.557.1		4	3.2	odd	2	inner
588.3.p.e.557.2		4	1.1	even	1	trivial
588.3.p.e.569.1		4	7.2	even	3	inner
588.3.p.e.569.2		4	21.2	odd	6	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.93649 - 0.614017i) q^{3} +(-5.80948 + 3.35410i) q^{5} +(8.24597 - 3.60611i) q^{9} +O(q^{10})\)	\(q+(2.93649 - 0.614017i) q^{3} +(-5.80948 + 3.35410i) q^{5} +(8.24597 - 3.60611i) q^{9} +(5.80948 + 3.35410i) q^{11} -14.0000 q^{13} +(-15.0000 + 13.4164i) q^{15} +(23.2379 + 13.4164i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-11.6190 + 6.70820i) q^{23} +(10.0000 - 17.3205i) q^{25} +(22.0000 - 15.6525i) q^{27} +46.9574i q^{29} +(-15.5000 + 26.8468i) q^{31} +(19.1190 + 6.28218i) q^{33} +(14.0000 + 24.2487i) q^{37} +(-41.1109 + 8.59624i) q^{39} +67.0820i q^{41} -52.0000 q^{43} +(-35.8095 + 48.6074i) q^{45} +(34.8569 - 20.1246i) q^{47} +(76.4758 + 25.1287i) q^{51} +(-5.80948 - 3.35410i) q^{53} -45.0000 q^{55} +(16.0000 + 17.8885i) q^{57} +(17.4284 + 10.0623i) q^{59} +(7.00000 + 12.1244i) q^{61} +(81.3327 - 46.9574i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-30.0000 + 26.8328i) q^{69} -40.2492i q^{71} +(49.0000 - 84.8705i) q^{73} +(18.7298 - 57.0017i) q^{75} +(-50.5000 - 87.4686i) q^{79} +(54.9919 - 59.4717i) q^{81} -87.2067i q^{83} -180.000 q^{85} +(28.8327 + 137.890i) q^{87} +(58.0948 - 33.5410i) q^{89} +(-29.0312 + 88.3526i) q^{93} +(-46.4758 - 26.8328i) q^{95} +13.0000 q^{97} +(60.0000 + 6.70820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 2 * q^9	\( 4 q + 4 q^{3} + 2 q^{9} - 56 q^{13} - 60 q^{15} + 16 q^{19} + 40 q^{25} + 88 q^{27} - 62 q^{31} + 30 q^{33} + 56 q^{37} - 56 q^{39} - 208 q^{43} - 120 q^{45} + 120 q^{51} - 180 q^{55} + 64 q^{57} + 28 q^{61} + 8 q^{67} - 120 q^{69} + 196 q^{73} - 80 q^{75} - 202 q^{79} + 158 q^{81} - 720 q^{85} - 210 q^{87} + 124 q^{93} + 52 q^{97} + 240 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 2 * q^9 - 56 * q^13 - 60 * q^15 + 16 * q^19 + 40 * q^25 + 88 * q^27 - 62 * q^31 + 30 * q^33 + 56 * q^37 - 56 * q^39 - 208 * q^43 - 120 * q^45 + 120 * q^51 - 180 * q^55 + 64 * q^57 + 28 * q^61 + 8 * q^67 - 120 * q^69 + 196 * q^73 - 80 * q^75 - 202 * q^79 + 158 * q^81 - 720 * q^85 - 210 * q^87 + 124 * q^93 + 52 * q^97 + 240 * q^99

Introduction

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