LMFDB - Embedded newform 588.4.k.c.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

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, 5]))

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

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

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (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:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} + \cdots + 531441 $ x^12 - 14x^10 - 32x^9 + 70x^8 + 224x^7 - 50x^6 + 2016x^5 + 5670x^4 - 23328x^3 - 91854*x^2 + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{7} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.1
Root			$2.99268 + 0.209499i$ of defining polynomial
Character	$\chi$	$=$	588.521
Dual form			588.4.k.c.509.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +O(q^{10})$	\(q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +(0.589052 + 0.340089i) q^{11} -52.4373i q^{13} +(-69.2683 - 33.7779i) q^{15} +(-51.6784 + 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(-3.63771 + 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(29.2008 + 137.224i) q^{27} +53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(-3.52568 + 0.246811i) q^{33} +(25.2855 + 43.7957i) q^{37} +(152.382 + 225.878i) q^{39} +318.804 q^{41} +168.515 q^{43} +(396.537 - 55.7917i) q^{45} +(-313.988 - 543.844i) q^{47} +(-37.5043 - 535.747i) q^{51} +(-625.481 - 361.121i) q^{53} +10.0879i q^{55} +(228.115 - 467.795i) q^{57} +(-263.093 + 455.691i) q^{59} +(-205.162 + 118.450i) q^{61} +(673.515 - 388.854i) q^{65} +(-149.359 + 258.697i) q^{67} +(9.56651 - 19.6181i) q^{69} -379.893i q^{71} +(559.469 + 323.010i) q^{73} +(-34.4592 - 492.246i) q^{75} +(-211.386 - 366.132i) q^{79} +(-524.554 - 506.245i) q^{81} -391.295 q^{83} -1532.91 q^{85} +(-155.577 - 230.614i) q^{87} +(-316.431 - 548.075i) q^{89} +(1412.26 - 98.8635i) q^{93} +(-1286.48 - 742.752i) q^{95} -1432.13i q^{97} +(14.4699 - 11.3087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 84 q^{9}+O(q^{10}) $ 12 * q - 84 * q^9	$ 12 q - 84 q^{9} + 132 q^{15} - 204 q^{19} - 444 q^{25} - 1458 q^{31} + 108 q^{33} + 240 q^{37} - 432 q^{39} + 342 q^{45} - 300 q^{51} + 180 q^{57} - 2148 q^{61} + 1980 q^{67} + 3084 q^{73} + 3384 q^{75} - 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} + 882 q^{93} + 9216 q^{99}+O(q^{100}) $ 12 * q - 84 * q^9 + 132 * q^15 - 204 * q^19 - 444 * q^25 - 1458 * q^31 + 108 * q^33 + 240 * q^37 - 432 * q^39 + 342 * q^45 - 300 * q^51 + 180 * q^57 - 2148 * q^61 + 1980 * q^67 + 3084 * q^73 + 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 + 882 * q^93 + 9216 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−4.30758	+	2.90598i	−0.828995	+	0.559256i
$3$	−4.30758	+	2.90598i	−0.828995	+	0.559256i
$4$		0			0
$5$	7.41560	+	12.8442i	0.663272	+	1.14882i	0.979751	+	0.200221i	$0.0641660\pi$
$5$	7.41560	+	12.8442i	0.663272	+	1.14882i	−0.316479	+	0.948600i	$0.602501\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	10.1105	−	25.0355i	0.374464	−	0.927241i
$10$		0			0
$11$	0.589052	+	0.340089i	0.0161460	+	0.00932189i	0.508051	−	0.861327i	$-0.330366\pi$
$11$	0.589052	+	0.340089i	0.0161460	+	0.00932189i	−0.491905	+	0.870649i	$0.663699\pi$
$12$		0			0
$13$		−	52.4373i		−	1.11873i	−0.828921	−	0.559365i	$-0.811045\pi$
$13$		−	52.4373i		−	1.11873i	0.828921	−	0.559365i	$-0.188955\pi$
$14$		0			0
$15$	−69.2683	−	33.7779i	−1.19233	−	0.581427i
$16$		0			0
$17$	−51.6784	+	89.5096i	−0.737286	+	1.27702i	0.216428	+	0.976299i	$0.430559\pi$
$17$	−51.6784	+	89.5096i	−0.737286	+	1.27702i	−0.953713	+	0.300717i	$0.902774\pi$
$18$		0			0
$19$	−86.7417	+	50.0804i	−1.04736	+	0.604696i	−0.921910	−	0.387404i	$-0.873372\pi$
$19$	−86.7417	+	50.0804i	−1.04736	+	0.604696i	−0.125454	+	0.992099i	$0.540039\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.63771	+	2.10024i	−0.0329790	+	0.0190404i	−0.516399	−	0.856348i	$-0.672728\pi$
$23$	−3.63771	+	2.10024i	−0.0329790	+	0.0190404i	0.483420	+	0.875389i	$0.339394\pi$
$24$		0			0
$25$	−47.4824	+	82.2418i	−0.379859	+	0.657935i
$26$		0			0
$27$	29.2008	+	137.224i	0.208137	+	0.978100i
$28$		0			0
$29$			53.5367i			0.342811i	0.985201	+	0.171406i	$0.0548308\pi$
$29$			53.5367i			0.342811i	−0.985201	+	0.171406i	$0.945169\pi$
$30$		0			0
$31$	−235.952	−	136.227i	−1.36704	−	0.789261i	−0.376492	−	0.926420i	$-0.622870\pi$
$31$	−235.952	−	136.227i	−1.36704	−	0.789261i	−0.990549	+	0.137158i	$0.956203\pi$
$32$		0			0
$33$	−3.52568	+	0.246811i	−0.0185983	+	0.00130195i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	25.2855	+	43.7957i	0.112349	+	0.194594i	0.916717	−	0.399538i	$-0.130829\pi$
$37$	25.2855	+	43.7957i	0.112349	+	0.194594i	−0.804368	+	0.594131i	$0.797496\pi$
$38$		0			0
$39$	152.382	+	225.878i	0.625657	+	0.927421i
$40$		0			0
$41$	318.804			1.21436			0.607181	−	0.794563i	$-0.292300\pi$
$41$	318.804			1.21436			0.607181	+	0.794563i	$0.292300\pi$
$42$		0			0
$43$	168.515			0.597634			0.298817	−	0.954310i	$-0.403408\pi$
$43$	168.515			0.597634			0.298817	+	0.954310i	$0.403408\pi$
$44$		0			0
$45$	396.537	−	55.7917i	1.31361	−	0.184821i
$46$		0			0
$47$	−313.988	−	543.844i	−0.974467	−	1.68783i	−0.681684	−	0.731647i	$-0.738752\pi$
$47$	−313.988	−	543.844i	−0.974467	−	1.68783i	−0.292782	−	0.956179i	$-0.594581\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−37.5043	−	535.747i	−0.102974	−	1.47097i
$52$		0			0
$53$	−625.481	−	361.121i	−1.62106	−	0.935922i	−0.986636	−	0.162939i	$-0.947903\pi$
$53$	−625.481	−	361.121i	−1.62106	−	0.935922i	−0.634427	−	0.772982i	$-0.718764\pi$
$54$		0			0
$55$			10.0879i			0.0247318i
$56$		0			0
$57$	228.115	−	467.795i	0.530079	−	1.08703i
$58$		0			0
$59$	−263.093	+	455.691i	−0.580539	+	1.00552i	0.414876	+	0.909878i	$0.363825\pi$
$59$	−263.093	+	455.691i	−0.580539	+	1.00552i	−0.995415	+	0.0956456i	$0.969508\pi$
$60$		0			0
$61$	−205.162	+	118.450i	−0.430627	+	0.248623i	−0.699614	−	0.714521i	$-0.746645\pi$
$61$	−205.162	+	118.450i	−0.430627	+	0.248623i	0.268987	+	0.963144i	$0.413311\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	673.515	−	388.854i	1.28522	−	0.742022i
$66$		0			0
$67$	−149.359	+	258.697i	−0.272344	+	0.471714i	−0.969462	−	0.245243i	$-0.921132\pi$
$67$	−149.359	+	258.697i	−0.272344	+	0.471714i	0.697117	+	0.716957i	$0.254466\pi$
$68$		0			0
$69$	9.56651	−	19.6181i	0.0166909	−	0.0342281i
$70$		0			0
$71$		−	379.893i		−	0.634999i	−0.948258	−	0.317500i	$-0.897157\pi$
$71$		−	379.893i		−	0.634999i	0.948258	−	0.317500i	$-0.102843\pi$
$72$		0			0
$73$	559.469	+	323.010i	0.896999	+	0.517882i	0.876225	−	0.481902i	$-0.160054\pi$
$73$	559.469	+	323.010i	0.896999	+	0.517882i	0.0207735	+	0.999784i	$0.493387\pi$
$74$		0			0
$75$	−34.4592	−	492.246i	−0.0530533	−	0.757863i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−211.386	−	366.132i	−0.301048	−	0.521431i	0.675325	−	0.737520i	$-0.264003\pi$
$79$	−211.386	−	366.132i	−0.301048	−	0.521431i	−0.976374	+	0.216089i	$0.930670\pi$
$80$		0			0
$81$	−524.554	−	506.245i	−0.719553	−	0.694438i
$82$		0			0
$83$	−391.295			−0.517472			−0.258736	−	0.965948i	$-0.583306\pi$
$83$	−391.295			−0.517472			−0.258736	+	0.965948i	$0.583306\pi$
$84$		0			0
$85$	−1532.91			−1.95608
$86$		0			0
$87$	−155.577	−	230.614i	−0.191719	−	0.284189i
$88$		0			0
$89$	−316.431	−	548.075i	−0.376872	−	0.652762i	0.613733	−	0.789513i	$-0.289667\pi$
$89$	−316.431	−	548.075i	−0.376872	−	0.652762i	−0.990605	+	0.136752i	$0.956334\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1412.26	−	98.8635i	1.57467	−	0.110233i
$94$		0			0
$95$	−1286.48	−	742.752i	−1.38937	−	0.802155i
$96$		0			0
$97$		−	1432.13i		−	1.49908i	−0.661959	−	0.749540i	$-0.730275\pi$
$97$		−	1432.13i		−	1.49908i	0.661959	−	0.749540i	$-0.269725\pi$
$98$		0			0
$99$	14.4699	−	11.3087i	0.0146897	−	0.0114805i
$100$		0			0
$101$	445.537	−	771.692i	0.438936	−	0.760260i	−0.558672	−	0.829389i	$-0.688689\pi$
$101$	445.537	−	771.692i	0.438936	−	0.760260i	0.997608	+	0.0691294i	$0.0220221\pi$
$102$		0			0
$103$	−1067.48	+	616.313i	−1.02119	+	0.589583i	−0.914448	−	0.404704i	$-0.867375\pi$
$103$	−1067.48	+	616.313i	−1.02119	+	0.589583i	−0.106740	+	0.994287i	$0.534041\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	585.738	−	338.176i	0.529209	−	0.305539i	−0.211485	−	0.977381i	$-0.567830\pi$
$107$	585.738	−	338.176i	0.529209	−	0.305539i	0.740694	+	0.671842i	$0.234497\pi$
$108$		0			0
$109$	497.209	−	861.191i	0.436917	−	0.756762i	−0.560533	−	0.828132i	$-0.689404\pi$
$109$	497.209	−	861.191i	0.436917	−	0.756762i	0.997450	+	0.0713697i	$0.0227370\pi$
$110$		0			0
$111$	−236.189	−	115.175i	−0.201964	−	0.0984854i
$112$		0			0
$113$			707.915i			0.589337i	0.955600	+	0.294668i	$0.0952091\pi$
$113$			707.915i			0.589337i	−0.955600	+	0.294668i	$0.904791\pi$
$114$		0			0
$115$	−53.9517	−	31.1490i	−0.0437480	−	0.0252579i
$116$		0			0
$117$	−1312.80	−	530.169i	−1.03733	−	0.418925i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−665.269	−	1152.28i	−0.499826	−	0.865724i
$122$		0			0
$123$	−1373.28	+	926.440i	−1.00670	+	0.679140i
$124$		0			0
$125$	445.460			0.318745
$126$		0			0
$127$	−885.551			−0.618740			−0.309370	−	0.950942i	$-0.600118\pi$
$127$	−885.551			−0.618740			−0.309370	+	0.950942i	$0.600118\pi$
$128$		0			0
$129$	−725.891	+	489.701i	−0.495435	+	0.334231i
$130$		0			0
$131$	−844.911	−	1463.43i	−0.563513	−	0.976034i	−0.997186	−	0.0749634i	$-0.976116\pi$
$131$	−844.911	−	1463.43i	−0.563513	−	0.976034i	0.433673	−	0.901070i	$-0.357217\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1545.99	+	1392.66i	−0.985610	+	0.887858i
$136$		0			0
$137$	1670.17	+	964.276i	1.04155	+	0.601340i	0.920273	−	0.391278i	$-0.127967\pi$
$137$	1670.17	+	964.276i	1.04155	+	0.601340i	0.121280	+	0.992618i	$0.461300\pi$
$138$		0			0
$139$		−	402.721i		−	0.245744i	−0.992423	−	0.122872i	$-0.960790\pi$
$139$		−	402.721i		−	0.245744i	0.992423	−	0.122872i	$-0.0392104\pi$
$140$		0			0
$141$	2932.93	+	1430.21i	1.75176	+	0.854222i
$142$		0			0
$143$	17.8334	−	30.8883i	0.0104287	−	0.0180630i
$144$		0			0
$145$	−687.637	+	397.007i	−0.393828	+	0.227377i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1392.62	−	804.032i	0.765692	−	0.442073i	−0.0656434	−	0.997843i	$-0.520910\pi$
$149$	1392.62	−	804.032i	0.765692	−	0.442073i	0.831336	+	0.555770i	$0.187577\pi$
$150$		0			0
$151$	−183.275	+	317.442i	−0.0987731	+	0.171080i	−0.911177	−	0.412015i	$-0.864825\pi$
$151$	−183.275	+	317.442i	−0.0987731	+	0.171080i	0.812404	+	0.583095i	$0.198158\pi$
$152$		0			0
$153$	1718.42	+	2198.79i	0.908015	+	1.16184i
$154$		0			0
$155$		−	4040.82i		−	2.09398i
$156$		0			0
$157$	−370.608	−	213.970i	−0.188393	−	0.108769i	0.402837	−	0.915272i	$-0.368024\pi$
$157$	−370.608	−	213.970i	−0.188393	−	0.108769i	−0.591230	+	0.806503i	$0.701357\pi$
$158$		0			0
$159$	3743.72	−	262.075i	1.86727	−	0.130716i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	116.502	+	201.787i	0.0559823	+	0.0969643i	0.892658	−	0.450734i	$-0.148838\pi$
$163$	116.502	+	201.787i	0.0559823	+	0.0969643i	−0.836676	+	0.547698i	$0.815504\pi$
$164$		0			0
$165$	−29.3152	−	43.4543i	−0.0138314	−	0.0205025i
$166$		0			0
$167$	1013.86			0.469791			0.234896	−	0.972021i	$-0.424525\pi$
$167$	1013.86			0.469791			0.234896	+	0.972021i	$0.424525\pi$
$168$		0			0
$169$	−552.672			−0.251558
$170$		0			0
$171$	376.782	+	2677.96i	0.168498	+	1.19760i
$172$		0			0
$173$	1657.13	+	2870.23i	0.728262	+	1.26139i	0.957617	+	0.288044i	$0.0930048\pi$
$173$	1657.13	+	2870.23i	0.728262	+	1.26139i	−0.229356	+	0.973343i	$0.573662\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−190.933	−	2727.47i	−0.0810816	−	1.15824i
$178$		0			0
$179$	1196.04	+	690.531i	0.499418	+	0.288339i	0.728473	−	0.685074i	$-0.240230\pi$
$179$	1196.04	+	690.531i	0.499418	+	0.288339i	−0.229055	+	0.973413i	$0.573564\pi$
$180$		0			0
$181$			1558.38i			0.639963i	0.947424	+	0.319981i	$0.103677\pi$
$181$			1558.38i			0.639963i	−0.947424	+	0.319981i	$0.896323\pi$
$182$		0			0
$183$	539.537	−	1106.43i	0.217944	−	0.446938i
$184$		0			0
$185$	−375.014	+	649.543i	−0.149035	+	0.258137i
$186$		0			0
$187$	−60.8825	+	35.1505i	−0.0238084	+	0.0137458i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1884.48	+	1088.00i	−0.713905	+	0.412173i	−0.812505	−	0.582954i	$-0.801897\pi$
$191$	−1884.48	+	1088.00i	−0.713905	+	0.412173i	0.0986002	+	0.995127i	$0.468564\pi$
$192$		0			0
$193$	−1749.63	+	3030.45i	−0.652546	+	1.13024i	0.329957	+	0.943996i	$0.392966\pi$
$193$	−1749.63	+	3030.45i	−0.652546	+	1.13024i	−0.982503	+	0.186247i	$0.940368\pi$
$194$		0			0
$195$	−1771.22	+	3632.25i	−0.650460	+	1.33390i
$196$		0			0
$197$			1297.91i			0.469401i	0.972068	+	0.234700i	$0.0754109\pi$
$197$			1297.91i			0.469401i	−0.972068	+	0.234700i	$0.924589\pi$
$198$		0			0
$199$	−3062.79	−	1768.30i	−1.09103	−	0.629908i	−0.157182	−	0.987570i	$-0.550241\pi$
$199$	−3062.79	−	1768.30i	−1.09103	−	0.629908i	−0.933851	+	0.357661i	$0.883574\pi$
$200$		0			0
$201$	−108.393	−	1548.39i	−0.0380372	−	0.543359i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2364.13	+	4094.79i	0.805452	+	1.39508i
$206$		0			0
$207$	15.8012	+	112.307i	0.00530561	+	0.0377094i
$208$		0			0
$209$	−68.1271			−0.0225476
$210$		0			0
$211$	−2131.02			−0.695286			−0.347643	−	0.937627i	$-0.613018\pi$
$211$	−2131.02			−0.695286			−0.347643	+	0.937627i	$0.613018\pi$
$212$		0			0
$213$	1103.96	+	1636.42i	0.355128	+	0.526411i
$214$		0			0
$215$	1249.64	+	2164.44i	0.396394	+	0.686574i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3348.62	+	234.416i	−1.03324	+	0.0723306i
$220$		0			0
$221$	4693.64	+	2709.88i	1.42864	+	0.824824i
$222$		0			0
$223$		−	6147.95i		−	1.84617i	−0.384590	−	0.923087i	$-0.625657\pi$
$223$		−	6147.95i		−	1.84617i	0.384590	−	0.923087i	$-0.374343\pi$
$224$		0			0
$225$	1578.89	+	2020.25i	0.467821	+	0.598594i
$226$		0			0
$227$	1484.97	−	2572.05i	0.434190	−	0.752039i	−0.563039	−	0.826430i	$-0.690368\pi$
$227$	1484.97	−	2572.05i	0.434190	−	0.752039i	0.997229	+	0.0743914i	$0.0237014\pi$
$228$		0			0
$229$	−2479.18	+	1431.35i	−0.715409	+	0.413042i	−0.813061	−	0.582179i	$-0.802200\pi$
$229$	−2479.18	+	1431.35i	−0.715409	+	0.413042i	0.0976515	+	0.995221i	$0.468867\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5177.16	+	2989.03i	−1.45565	+	0.840421i	−0.998793	−	0.0491180i	$-0.984359\pi$
$233$	−5177.16	+	2989.03i	−1.45565	+	0.840421i	−0.456859	+	0.889539i	$0.651026\pi$
$234$		0			0
$235$	4656.83	−	8065.86i	1.29267	−	2.23897i
$236$		0			0
$237$	1974.54	+	962.858i	0.541181	+	0.263900i
$238$		0			0
$239$			5571.82i			1.50800i	0.656876	+	0.753998i	$0.271877\pi$
$239$			5571.82i			1.50800i	−0.656876	+	0.753998i	$0.728123\pi$
$240$		0			0
$241$	−3591.11	−	2073.33i	−0.959851	−	0.554170i	−0.0637236	−	0.997968i	$-0.520298\pi$
$241$	−3591.11	−	2073.33i	−0.959851	−	0.554170i	−0.896127	+	0.443798i	$0.853631\pi$
$242$		0			0
$243$	3730.70	+	656.348i	0.984874	+	0.173271i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2626.08	+	4548.50i	0.676492	+	1.17172i
$248$		0			0
$249$	1685.54	−	1137.10i	0.428982	−	0.289400i
$250$		0			0
$251$	−7611.35			−1.91404			−0.957021	−	0.290020i	$-0.906338\pi$
$251$	−7611.35			−1.91404			−0.957021	+	0.290020i	$0.906338\pi$
$252$		0			0
$253$	−2.85707			−0.000709970
$254$		0			0
$255$	6603.12	−	4454.60i	1.62158	−	1.09395i
$256$		0			0
$257$	1174.76	+	2034.74i	0.285134	+	0.493867i	0.972642	−	0.232310i	$-0.0746284\pi$
$257$	1174.76	+	2034.74i	0.285134	+	0.493867i	−0.687507	+	0.726177i	$0.741295\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1340.32	+	541.285i	0.317869	+	0.128371i
$262$		0			0
$263$	−4441.42	−	2564.25i	−1.04133	−	0.601211i	−0.121119	−	0.992638i	$-0.538648\pi$
$263$	−4441.42	−	2564.25i	−1.04133	−	0.601211i	−0.920209	+	0.391426i	$0.871982\pi$
$264$		0			0
$265$		−	10711.7i		−	2.48308i
$266$		0			0
$267$	2955.75	+	1441.33i	0.677486	+	0.330368i
$268$		0			0
$269$	−20.2532	+	35.0795i	−0.00459055	+	0.00795107i	−0.868312	−	0.496019i	$-0.834795\pi$
$269$	−20.2532	+	35.0795i	−0.00459055	+	0.00795107i	0.863721	+	0.503970i	$0.168128\pi$
$270$		0			0
$271$	−2807.84	+	1621.11i	−0.629389	+	0.363378i	−0.780515	−	0.625137i	$-0.785043\pi$
$271$	−2807.84	+	1621.11i	−0.629389	+	0.363378i	0.151127	+	0.988514i	$0.451710\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−55.9391	+	32.2965i	−0.0122664	+	0.00708200i
$276$		0			0
$277$	1107.85	−	1918.85i	0.240304	−	0.416219i	−0.720497	−	0.693458i	$-0.756086\pi$
$277$	1107.85	−	1918.85i	0.240304	−	0.416219i	0.960801	+	0.277239i	$0.0894195\pi$
$278$		0			0
$279$	−5796.12	+	4529.86i	−1.24374	+	0.972027i
$280$		0			0
$281$			5882.33i			1.24879i	0.781108	+	0.624395i	$0.214655\pi$
$281$			5882.33i			1.24879i	−0.781108	+	0.624395i	$0.785345\pi$
$282$		0			0
$283$	1323.79	+	764.290i	0.278060	+	0.160538i	0.632545	−	0.774524i	$-0.282010\pi$
$283$	1323.79	+	764.290i	0.278060	+	0.160538i	−0.354485	+	0.935062i	$0.615344\pi$
$284$		0			0
$285$	7700.06	−	539.034i	1.60039	−	0.112034i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2884.82	−	4996.65i	−0.587180	−	1.01703i
$290$		0			0
$291$	4161.74	+	6169.02i	0.838370	+	1.24273i
$292$		0			0
$293$	6038.37			1.20398			0.601989	−	0.798505i	$-0.294375\pi$
$293$	6038.37			1.20398			0.601989	+	0.798505i	$0.294375\pi$
$294$		0			0
$295$	−7803.98			−1.54022
$296$		0			0
$297$	−29.4675	+	90.7627i	−0.00575716	+	0.0177326i
$298$		0			0
$299$	110.131	+	190.752i	0.0213011	+	0.0368946i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	323.337	+	4618.85i	0.0613044	+	0.875729i
$304$		0			0
$305$	−3042.79	−	1756.76i	−0.571246	−	0.329809i
$306$		0			0
$307$			7231.98i			1.34447i	0.740340	+	0.672233i	$0.234665\pi$
$307$			7231.98i			1.34447i	−0.740340	+	0.672233i	$0.765335\pi$
$308$		0			0
$309$	2807.29	−	5756.91i	0.516831	−	1.05987i
$310$		0			0
$311$	−859.000	+	1487.83i	−0.156622	+	0.271277i	−0.933648	−	0.358191i	$-0.883394\pi$
$311$	−859.000	+	1487.83i	−0.156622	+	0.271277i	0.777027	+	0.629468i	$0.216727\pi$
$312$		0			0
$313$	4787.88	−	2764.28i	0.864622	−	0.499190i	−0.000935213	−	1.00000i	$-0.500298\pi$
$313$	4787.88	−	2764.28i	0.864622	−	0.499190i	0.865557	+	0.500810i	$0.166964\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1541.66	+	890.076i	−0.273149	+	0.157702i	−0.630318	−	0.776337i	$-0.717075\pi$
$317$	−1541.66	+	890.076i	−0.273149	+	0.157702i	0.357169	+	0.934040i	$0.383742\pi$
$318$		0			0
$319$	−18.2073	+	31.5359i	−0.00319565	+	0.00553502i
$320$		0			0
$321$	−1540.38	+	3158.86i	−0.267837	+	0.549254i
$322$		0			0
$323$		−	10352.3i		−	1.78333i
$324$		0			0
$325$	4312.54	+	2489.85i	0.736052	+	0.424960i
$326$		0			0
$327$	360.837	+	5154.53i	0.0610224	+	0.871701i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3219.65	+	5576.59i	0.534646	+	0.926034i	0.999180	+	0.0404789i	$0.0128884\pi$
$331$	3219.65	+	5576.59i	0.534646	+	0.926034i	−0.464534	+	0.885555i	$0.653778\pi$
$332$		0			0
$333$	1352.10	−	190.236i	0.222506	−	0.0313060i
$334$		0			0
$335$	−4430.34			−0.722553
$336$		0			0
$337$	2095.32			0.338692			0.169346	−	0.985557i	$-0.445834\pi$
$337$	2095.32			0.338692			0.169346	+	0.985557i	$0.445834\pi$
$338$		0			0
$339$	−2057.19	−	3049.40i	−0.329590	−	0.488557i
$340$		0			0
$341$	−92.6587	−	160.490i	−0.0147148	−	0.0254868i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	322.920	−	22.6057i	0.0503925	−	0.00352767i
$346$		0			0
$347$	2115.84	+	1221.58i	0.327332	+	0.188985i	0.654656	−	0.755927i	$-0.272814\pi$
$347$	2115.84	+	1221.58i	0.327332	+	0.188985i	−0.327324	+	0.944912i	$0.606147\pi$
$348$		0			0
$349$			1583.72i			0.242907i	0.992597	+	0.121453i	$0.0387555\pi$
$349$			1583.72i			0.242907i	−0.992597	+	0.121453i	$0.961244\pi$
$350$		0			0
$351$	7195.64	−	1531.21i	1.09423	−	0.232849i
$352$		0			0
$353$	−4032.35	+	6984.23i	−0.607989	+	1.05307i	0.383583	+	0.923507i	$0.374690\pi$
$353$	−4032.35	+	6984.23i	−0.607989	+	1.05307i	−0.991571	+	0.129561i	$0.958643\pi$
$354$		0			0
$355$	4879.42	−	2817.13i	0.729500	−	0.421177i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5312.56	+	3067.21i	−0.781020	+	0.450922i	−0.836792	−	0.547522i	$-0.815571\pi$
$359$	−5312.56	+	3067.21i	−0.781020	+	0.450922i	0.0557719	+	0.998444i	$0.482238\pi$
$360$		0			0
$361$	1586.58	−	2748.04i	0.231314	−	0.400648i
$362$		0			0
$363$	6214.20	+	3030.28i	0.898515	+	0.438150i
$364$		0			0
$365$			9581.25i			1.37399i
$366$		0			0
$367$	3351.77	+	1935.14i	0.476733	+	0.275242i	0.719054	−	0.694954i	$-0.244575\pi$
$367$	3351.77	+	1935.14i	0.476733	+	0.275242i	−0.242321	+	0.970196i	$0.577909\pi$
$368$		0			0
$369$	3223.28	−	7981.43i	0.454736	−	1.12601i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−3644.06	−	6311.70i	−0.505851	−	0.876160i	−0.999977	−	0.00676929i	$-0.997845\pi$
$373$	−3644.06	−	6311.70i	−0.505851	−	0.876160i	0.494126	−	0.869390i	$-0.335488\pi$
$374$		0			0
$375$	−1918.85	+	1294.50i	−0.264238	+	0.178260i
$376$		0			0
$377$	2807.32			0.383513
$378$		0			0
$379$	−3203.69			−0.434201			−0.217101	−	0.976149i	$-0.569660\pi$
$379$	−3203.69			−0.434201			−0.217101	+	0.976149i	$0.569660\pi$
$380$		0			0
$381$	3814.59	−	2573.40i	0.512932	−	0.346034i
$382$		0			0
$383$	2096.49	+	3631.22i	0.279701	+	0.484456i	0.971310	−	0.237816i	$-0.0764314\pi$
$383$	2096.49	+	3631.22i	0.279701	+	0.484456i	−0.691610	+	0.722272i	$0.743098\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1703.77	−	4218.85i	0.223793	−	0.554151i
$388$		0			0
$389$	5025.75	+	2901.62i	0.655053	+	0.378195i	0.790390	−	0.612605i	$-0.209878\pi$
$389$	5025.75	+	2901.62i	0.655053	+	0.378195i	−0.135336	+	0.990800i	$0.543212\pi$
$390$		0			0
$391$		−	434.147i		−	0.0561529i
$392$		0			0
$393$	7892.22	+	3848.55i	1.01300	+	0.493978i
$394$		0			0
$395$	3135.11	−	5430.18i	0.399354	−	0.691701i
$396$		0			0
$397$	−13668.1	+	7891.30i	−1.72792	+	0.997614i	−0.829440	+	0.558596i	$0.811340\pi$
$397$	−13668.1	+	7891.30i	−1.72792	+	0.997614i	−0.898478	+	0.439018i	$0.855327\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6782.69	−	3915.99i	0.844667	−	0.487669i	−0.0141808	−	0.999899i	$-0.504514\pi$
$401$	6782.69	−	3915.99i	0.844667	−	0.487669i	0.858848	+	0.512231i	$0.171181\pi$
$402$		0			0
$403$	−7143.38	+	12372.7i	−0.882971	+	1.52935i
$404$		0			0
$405$	2612.43	−	10491.6i	0.320525	−	1.28724i
$406$		0			0
$407$			34.3972i			0.00418921i
$408$		0			0
$409$	−11913.3	−	6878.12i	−1.44028	−	0.831543i	−0.442408	−	0.896814i	$-0.645876\pi$
$409$	−11913.3	−	6878.12i	−1.44028	−	0.831543i	−0.997868	+	0.0652706i	$0.979209\pi$
$410$		0			0
$411$	−9996.58	+	699.800i	−1.19974	+	0.0839868i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2901.69	−	5025.87i	−0.343225	−	0.594483i
$416$		0			0
$417$	1170.30	+	1734.76i	0.137434	+	0.203720i
$418$		0			0
$419$	9478.94			1.10519			0.552597	−	0.833448i	$-0.313637\pi$
$419$	9478.94			1.10519			0.552597	+	0.833448i	$0.313637\pi$
$420$		0			0
$421$	−7360.46			−0.852082			−0.426041	−	0.904704i	$-0.640092\pi$
$421$	−7360.46			−0.852082			−0.426041	+	0.904704i	$0.640092\pi$
$422$		0			0
$423$	−16790.0	+	2362.31i	−1.92992	+	0.271535i
$424$		0			0
$425$	−4907.62	−	8500.26i	−0.560129	−	0.970172i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	12.9421	+	184.877i	0.00145653	+	0.0208064i
$430$		0			0
$431$	76.0396	+	43.9015i	0.00849814	+	0.00490641i	0.504243	−	0.863562i	$-0.331772\pi$
$431$	76.0396	+	43.9015i	0.00849814	+	0.00490641i	−0.495745	+	0.868468i	$0.665105\pi$
$432$		0			0
$433$		−	1782.09i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$433$		−	1782.09i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315303\pi$
$434$		0			0
$435$	1808.36	−	3708.40i	0.199320	−	0.408745i
$436$		0			0
$437$	210.361	−	364.356i	0.0230273	−	0.0398845i
$438$		0			0
$439$	−8035.74	+	4639.44i	−0.873634	+	0.504393i	−0.868554	−	0.495595i	$-0.834950\pi$
$439$	−8035.74	+	4639.44i	−0.873634	+	0.504393i	−0.00507951	+	0.999987i	$0.501617\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4831.09	+	2789.23i	−0.518131	+	0.299143i	−0.736170	−	0.676797i	$-0.763367\pi$
$443$	−4831.09	+	2789.23i	−0.518131	+	0.299143i	0.218039	+	0.975940i	$0.430034\pi$
$444$		0			0
$445$	4693.05	−	8128.61i	0.499937	−	0.865917i
$446$		0			0
$447$	−3662.34	+	7510.37i	−0.387523	+	0.794694i
$448$		0			0
$449$		−	5410.98i		−	0.568730i	−0.958716	−	0.284365i	$-0.908217\pi$
$449$		−	5410.98i		−	0.568730i	0.958716	−	0.284365i	$-0.0917827\pi$
$450$		0			0
$451$	187.792	+	108.422i	0.0196071	+	0.0113201i
$452$		0			0
$453$	−133.008	−	1900.00i	−0.0137952	−	0.197064i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3971.67	+	6879.13i	0.406536	+	0.704140i	0.994499	−	0.104747i	$-0.0334034\pi$
$457$	3971.67	+	6879.13i	0.406536	+	0.704140i	−0.587963	+	0.808888i	$0.700070\pi$
$458$		0			0
$459$	−13791.9	−	4477.75i	−1.40251	−	0.455345i
$460$		0			0
$461$	−2715.21			−0.274317			−0.137159	−	0.990549i	$-0.543797\pi$
$461$	−2715.21			−0.274317			−0.137159	+	0.990549i	$0.543797\pi$
$462$		0			0
$463$	−11587.7			−1.16313			−0.581563	−	0.813502i	$-0.697558\pi$
$463$	−11587.7			−1.16313			−0.581563	+	0.813502i	$0.697558\pi$
$464$		0			0
$465$	11742.6	+	17406.2i	1.17107	+	1.73590i
$466$		0			0
$467$	1879.76	+	3255.83i	0.186263	+	0.322617i	0.944001	−	0.329942i	$-0.107029\pi$
$467$	1879.76	+	3255.83i	0.186263	+	0.322617i	−0.757738	+	0.652558i	$0.773696\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2218.22	−	155.284i	0.217006	−	0.0151913i
$472$		0			0
$473$	99.2639	+	57.3100i	0.00964938	+	0.00557107i
$474$		0			0
$475$		−	9511.73i		−	0.918796i
$476$		0			0
$477$	−15364.8	+	12008.1i	−1.47486	+	1.15265i
$478$		0			0
$479$	−2666.10	+	4617.82i	−0.254316	+	0.440488i	−0.964709	−	0.263317i	$-0.915184\pi$
$479$	−2666.10	+	4617.82i	−0.254316	+	0.440488i	0.710394	+	0.703804i	$0.248517\pi$
$480$		0			0
$481$	2296.53	−	1325.90i	0.217698	−	0.125688i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	18394.6	−	10620.1i	1.72217	−	0.994297i
$486$		0			0
$487$	−521.790	+	903.766i	−0.0485514	+	0.0840935i	−0.889280	−	0.457364i	$-0.848794\pi$
$487$	−521.790	+	903.766i	−0.0485514	+	0.0840935i	0.840728	+	0.541457i	$0.182127\pi$
$488$		0			0
$489$	−1088.23	−	530.662i	−0.100637	−	0.0490744i
$490$		0			0
$491$		−	13213.2i		−	1.21446i	−0.794525	−	0.607232i	$-0.792280\pi$
$491$		−	13213.2i		−	1.21446i	0.794525	−	0.607232i	$-0.207720\pi$
$492$		0			0
$493$	−4792.05	−	2766.69i	−0.437775	−	0.252750i
$494$		0			0
$495$	252.555	+	101.994i	0.0229323	+	0.00926117i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	874.489	+	1514.66i	0.0784519	+	0.135883i	0.902582	−	0.430518i	$-0.141669\pi$
$499$	874.489	+	1514.66i	0.0784519	+	0.135883i	−0.824130	+	0.566400i	$0.808336\pi$
$500$		0			0
$501$	−4367.30	+	2946.27i	−0.389454	+	0.262734i
$502$		0			0
$503$	−12215.5			−1.08283			−0.541414	−	0.840756i	$-0.682111\pi$
$503$	−12215.5			−1.08283			−0.541414	+	0.840756i	$0.682111\pi$
$504$		0			0
$505$	13215.7			1.16454
$506$		0			0
$507$	2380.68	−	1606.05i	0.208540	−	0.140685i
$508$		0			0
$509$	−8483.69	−	14694.2i	−0.738768	−	1.27958i	−0.953050	−	0.302812i	$-0.902074\pi$
$509$	−8483.69	−	14694.2i	−0.738768	−	1.27958i	0.214282	−	0.976772i	$-0.431259\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−9405.13	−	10440.6i	−0.809448	−	0.898567i
$514$		0			0
$515$	−15832.1	−	9140.66i	−1.35465	−	0.782108i
$516$		0			0
$517$		−	427.136i		−	0.0363355i
$518$		0			0
$519$	−15479.1	−	7548.18i	−1.30916	−	0.638397i
$520$		0			0
$521$	2103.60	−	3643.55i	0.176892	−	0.306385i	−0.763923	−	0.645308i	$-0.776729\pi$
$521$	2103.60	−	3643.55i	0.176892	−	0.306385i	0.940814	+	0.338922i	$0.110062\pi$
$522$		0			0
$523$	5104.44	−	2947.05i	0.426772	−	0.246397i	−0.271199	−	0.962523i	$-0.587420\pi$
$523$	5104.44	−	2947.05i	0.426772	−	0.246397i	0.697970	+	0.716127i	$0.254087\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24387.3	−	14080.0i	2.01580	−	1.16382i
$528$		0			0
$529$	−6074.68	+	10521.7i	−0.499275	+	0.864770i
$530$		0			0
$531$	8748.44	+	11194.0i	0.714972	+	0.914833i
$532$		0			0
$533$		−	16717.2i		−	1.35854i
$534$		0			0
$535$	8687.20	+	5015.56i	0.702019	+	0.405311i
$536$		0			0
$537$	−7158.69	+	501.136i	−0.575271	+	0.0402712i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8059.86	−	13960.1i	−0.640518	−	1.10941i	−0.985317	−	0.170734i	$-0.945386\pi$
$541$	−8059.86	−	13960.1i	−0.640518	−	1.10941i	0.344799	−	0.938677i	$-0.387947\pi$
$542$		0			0
$543$	−4528.61	−	6712.84i	−0.357903	−	0.530526i
$544$		0			0
$545$	14748.4			1.15918
$546$		0			0
$547$	14061.3			1.09912			0.549558	−	0.835456i	$-0.314796\pi$
$547$	14061.3			1.09912			0.549558	+	0.835456i	$0.314796\pi$
$548$		0			0
$549$	891.165	+	6333.92i	0.0692787	+	0.492396i
$550$		0			0
$551$	−2681.14	−	4643.87i	−0.207296	−	0.359048i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−272.157	−	3887.74i	−0.0208152	−	0.297343i
$556$		0			0
$557$	−7010.50	−	4047.52i	−0.533294	−	0.307897i	0.209063	−	0.977902i	$-0.432959\pi$
$557$	−7010.50	−	4047.52i	−0.533294	−	0.307897i	−0.742357	+	0.670005i	$0.766292\pi$
$558$		0			0
$559$		−	8836.46i		−	0.668591i
$560$		0			0
$561$	160.110	−	328.337i	0.0120496	−	0.0247102i
$562$		0			0
$563$	5149.34	−	8918.92i	0.385469	−	0.667651i	−0.606366	−	0.795186i	$-0.707373\pi$
$563$	5149.34	−	8918.92i	0.385469	−	0.667651i	0.991834	+	0.127535i	$0.0407065\pi$
$564$		0			0
$565$	−9092.60	+	5249.62i	−0.677042	+	0.390890i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2507.30	−	1447.59i	0.184730	−	0.106654i	−0.404783	−	0.914413i	$-0.632653\pi$
$569$	2507.30	−	1447.59i	0.184730	−	0.106654i	0.589513	+	0.807759i	$0.299320\pi$
$570$		0			0
$571$	310.198	−	537.278i	0.0227345	−	0.0393772i	−0.854434	−	0.519559i	$-0.826096\pi$
$571$	310.198	−	537.278i	0.0227345	−	0.0393772i	0.877169	+	0.480182i	$0.159429\pi$
$572$		0			0
$573$	4955.82	−	10162.9i	0.361313	−	0.740946i
$574$		0			0
$575$		−	398.897i		−	0.0289307i
$576$		0			0
$577$	8241.62	+	4758.30i	0.594633	+	0.343312i	0.766927	−	0.641734i	$-0.221785\pi$
$577$	8241.62	+	4758.30i	0.594633	+	0.343312i	−0.172294	+	0.985046i	$0.555118\pi$
$578$		0			0
$579$	−1269.75	−	18138.3i	−0.0911385	−	1.30191i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−245.627	−	425.438i	−0.0174491	−	0.0302227i
$584$		0			0
$585$	−2925.56	−	20793.3i	−0.206764	−	1.46957i
$586$		0			0
$587$	−1093.47			−0.0768861			−0.0384431	−	0.999261i	$-0.512240\pi$
$587$	−1093.47			−0.0768861			−0.0384431	+	0.999261i	$0.512240\pi$
$588$		0			0
$589$	27289.2			1.90905
$590$		0			0
$591$	−3771.69	−	5590.83i	−0.262515	−	0.389131i
$592$		0			0
$593$	−4882.36	−	8456.49i	−0.338102	−	0.585610i	0.645974	−	0.763360i	$-0.276451\pi$
$593$	−4882.36	−	8456.49i	−0.338102	−	0.585610i	−0.984076	+	0.177750i	$0.943118\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18331.9	−	1283.30i	1.25674	−	0.0879768i
$598$		0			0
$599$	12740.2	+	7355.53i	0.869029	+	0.501734i	0.867026	−	0.498264i	$-0.166029\pi$
$599$	12740.2	+	7355.53i	0.869029	+	0.501734i	0.00200376	+	0.999998i	$0.499362\pi$
$600$		0			0
$601$			14047.5i			0.953425i	0.879059	+	0.476713i	$0.158172\pi$
$601$			14047.5i			0.953425i	−0.879059	+	0.476713i	$0.841828\pi$
$602$		0			0
$603$	4966.51	+	6354.83i	0.335409	+	0.429169i
$604$		0			0
$605$	9866.74	−	17089.7i	0.663041	−	1.14842i
$606$		0			0
$607$	14931.5	−	8620.73i	0.998439	−	0.576449i	0.0906530	−	0.995883i	$-0.471105\pi$
$607$	14931.5	−	8620.73i	0.998439	−	0.576449i	0.907786	+	0.419434i	$0.137771\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28517.7	+	16464.7i	−1.88822	+	1.09017i
$612$		0			0
$613$	−3608.26	+	6249.69i	−0.237742	+	0.411782i	−0.960066	−	0.279773i	$-0.909741\pi$
$613$	−3608.26	+	6249.69i	−0.237742	+	0.411782i	0.722324	+	0.691555i	$0.243074\pi$
$614$		0			0
$615$	−22083.0	−	10768.5i	−1.44793	−	0.706063i
$616$		0			0
$617$			25662.2i			1.67443i	0.546877	+	0.837213i	$0.315817\pi$
$617$			25662.2i			1.67443i	−0.546877	+	0.837213i	$0.684183\pi$
$618$		0			0
$619$	10818.3	+	6245.96i	0.702464	+	0.405568i	0.808265	−	0.588820i	$-0.200407\pi$
$619$	10818.3	+	6245.96i	0.702464	+	0.405568i	−0.105800	+	0.994387i	$0.533740\pi$
$620$		0			0
$621$	−394.426	−	437.852i	−0.0254876	−	0.0282937i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9238.65	+	16001.8i	0.591273	+	1.02412i
$626$		0			0
$627$	293.463	−	197.976i	0.0186919	−	0.0126099i
$628$		0			0
$629$	−5226.85			−0.331332
$630$		0			0
$631$	−11952.7			−0.754091			−0.377046	−	0.926195i	$-0.623060\pi$
$631$	−11952.7			−0.754091			−0.377046	+	0.926195i	$0.623060\pi$
$632$		0			0
$633$	9179.54	−	6192.70i	0.576388	−	0.388843i
$634$		0			0
$635$	−6566.90	−	11374.2i	−0.410393	−	0.710821i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−9510.81	−	3840.92i	−0.588798	−	0.237785i
$640$		0			0
$641$	−12156.4	−	7018.51i	−0.749063	−	0.432472i	0.0762922	−	0.997086i	$-0.475692\pi$
$641$	−12156.4	−	7018.51i	−0.749063	−	0.432472i	−0.825355	+	0.564614i	$0.809025\pi$
$642$		0			0
$643$			12089.9i			0.741493i	0.928734	+	0.370747i	$0.120898\pi$
$643$			12089.9i			0.741493i	−0.928734	+	0.370747i	$0.879102\pi$
$644$		0			0
$645$	−11672.7	−	5692.06i	−0.712579	−	0.347480i
$646$		0			0
$647$	−2411.27	+	4176.44i	−0.146517	+	0.253775i	−0.929938	−	0.367716i	$-0.880140\pi$
$647$	−2411.27	+	4176.44i	−0.146517	+	0.253775i	0.783421	+	0.621492i	$0.213473\pi$
$648$		0			0
$649$	−309.951	+	178.950i	−0.0187467	+	0.0108234i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2592.48	−	1496.77i	0.155362	−	0.0896983i	−0.420303	−	0.907384i	$-0.638076\pi$
$653$	2592.48	−	1496.77i	0.155362	−	0.0896983i	0.575666	+	0.817685i	$0.304743\pi$
$654$		0			0
$655$	12531.1	−	21704.4i	0.747525	−	1.29475i
$656$		0			0
$657$	13743.2	−	10740.8i	0.816096	−	0.637806i
$658$		0			0
$659$			4336.79i			0.256354i	0.991751	+	0.128177i	$0.0409125\pi$
$659$			4336.79i			0.256354i	−0.991751	+	0.128177i	$0.959087\pi$
$660$		0			0
$661$	−16220.2	−	9364.73i	−0.954451	−	0.551053i	−0.0599904	−	0.998199i	$-0.519107\pi$
$661$	−16220.2	−	9364.73i	−0.954451	−	0.551053i	−0.894461	+	0.447146i	$0.852440\pi$
$662$		0			0
$663$	−28093.1	+	1966.63i	−1.64562	+	0.115200i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−112.440	−	194.751i	−0.00652726	−	0.0113056i
$668$		0			0
$669$	17865.8	+	26482.8i	1.03249	+	1.53047i
$670$		0			0
$671$	−161.134			−0.00927053
$672$		0			0
$673$	−19919.4			−1.14092			−0.570459	−	0.821326i	$-0.693235\pi$
$673$	−19919.4			−1.14092			−0.570459	+	0.821326i	$0.693235\pi$
$674$		0			0
$675$	−12672.0	−	4114.17i	−0.722588	−	0.234599i
$676$		0			0
$677$	15019.2	+	26014.1i	0.852638	+	1.47681i	0.878819	+	0.477155i	$0.158332\pi$
$677$	15019.2	+	26014.1i	0.852638	+	1.47681i	−0.0261815	+	0.999657i	$0.508335\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1077.68	+	15394.6i	0.0606415	+	0.866259i
$682$		0			0
$683$	3348.00	+	1932.97i	0.187566	+	0.108291i	0.590843	−	0.806787i	$-0.298795\pi$
$683$	3348.00	+	1932.97i	0.187566	+	0.108291i	−0.403277	+	0.915078i	$0.632129\pi$
$684$		0			0
$685$			28602.7i			1.59541i
$686$		0			0
$687$	6519.78	−	13370.1i	0.362074	−	0.742507i
$688$		0			0
$689$	−18936.2	+	32798.5i	−1.04704	+	1.81353i
$690$		0			0
$691$	5762.10	−	3326.75i	0.317222	−	0.183148i	−0.332931	−	0.942951i	$-0.608038\pi$
$691$	5762.10	−	3326.75i	0.317222	−	0.183148i	0.650154	+	0.759803i	$0.274704\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5172.64	−	2986.42i	0.282315	−	0.162995i
$696$		0			0
$697$	−16475.3	+	28536.1i	−0.895332	+	1.55076i
$698$		0			0
$699$	13615.0	−	27920.2i	0.736717	−	1.51079i
$700$		0			0
$701$		−	21100.3i		−	1.13687i	−0.822728	−	0.568435i	$-0.807549\pi$
$701$		−	21100.3i		−	1.13687i	0.822728	−	0.568435i	$-0.192451\pi$
$702$		0			0
$703$	−4386.61	−	2532.61i	−0.235340	−	0.135874i
$704$		0			0
$705$	3379.58	+	48277.0i	0.180542	+	2.57903i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−11715.1	−	20291.1i	−0.620548	−	1.07482i	−0.989384	−	0.145326i	$-0.953577\pi$
$709$	−11715.1	−	20291.1i	−0.620548	−	1.07482i	0.368836	−	0.929494i	$-0.379756\pi$
$710$		0			0
$711$	−11303.5	+	1590.38i	−0.596224	+	0.0838871i
$712$		0			0
$713$	1144.44			0.0601114
$714$		0			0
$715$	528.981			0.0276682
$716$		0			0
$717$	−16191.6	−	24001.1i	−0.843357	−	1.25012i
$718$		0			0
$719$	4247.60	+	7357.06i	0.220318	+	0.381603i	0.954905	−	0.296913i	$-0.0959571\pi$
$719$	4247.60	+	7357.06i	0.220318	+	0.381603i	−0.734586	+	0.678515i	$0.762624\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	21494.1	−	1504.67i	1.10563	−	0.0773987i
$724$		0			0
$725$	−4402.96	−	2542.05i	−0.225547	−	0.130220i
$726$		0			0
$727$			2662.18i			0.135811i	0.997692	+	0.0679057i	$0.0216317\pi$
$727$			2662.18i			0.135811i	−0.997692	+	0.0679057i	$0.978368\pi$
$728$		0			0
$729$	−17977.6	+	8014.07i	−0.913358	+	0.407157i
$730$		0			0
$731$	−8708.57	+	15083.7i	−0.440627	+	0.763188i
$732$		0			0
$733$	17425.1	−	10060.4i	0.878052	−	0.506943i	0.00803608	−	0.999968i	$-0.497442\pi$
$733$	17425.1	−	10060.4i	0.878052	−	0.506943i	0.870015	+	0.493024i	$0.164109\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−175.960	+	101.590i	−0.00879453	+	0.00507752i
$738$		0			0
$739$	4889.49	−	8468.84i	0.243387	−	0.421558i	−0.718290	−	0.695744i	$-0.755075\pi$
$739$	4889.49	−	8468.84i	0.243387	−	0.421558i	0.961677	+	0.274186i	$0.0884083\pi$
$740$		0			0
$741$	−24529.9	−	11961.7i	−1.21610	−	0.593015i
$742$		0			0
$743$			35045.8i			1.73043i	0.501404	+	0.865213i	$0.332817\pi$
$743$			35045.8i			1.73043i	−0.501404	+	0.865213i	$0.667183\pi$
$744$		0			0
$745$	20654.3	+	11924.8i	1.01572	+	0.586429i
$746$		0			0
$747$	−3956.20	+	9796.27i	−0.193775	+	0.479822i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10043.6	−	17396.0i	−0.488011	−	0.845260i	0.511894	−	0.859049i	$-0.328944\pi$
$751$	−10043.6	−	17396.0i	−0.488011	−	0.845260i	−0.999905	+	0.0137887i	$0.995611\pi$
$752$		0			0
$753$	32786.5	−	22118.5i	1.58673	−	1.07044i
$754$		0			0
$755$	−5436.39			−0.262054
$756$		0			0
$757$	−2813.68			−0.135092			−0.0675462	−	0.997716i	$-0.521517\pi$
$757$	−2813.68			−0.135092			−0.0675462	+	0.997716i	$0.521517\pi$
$758$		0			0
$759$	12.3071	−	8.30259i	0.000588561	−	0.000397055i
$760$		0			0
$761$	10857.5	+	18805.7i	0.517191	+	0.895801i	0.999801	+	0.0199656i	$0.00635567\pi$
$761$	10857.5	+	18805.7i	0.517191	+	0.895801i	−0.482610	+	0.875836i	$0.660311\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−15498.5	+	38377.1i	−0.732483	+	1.81376i
$766$		0			0
$767$	23895.2	+	13795.9i	1.12491	+	0.649467i
$768$		0			0
$769$			15956.6i			0.748257i	0.927377	+	0.374128i	$0.122058\pi$
$769$			15956.6i			0.748257i	−0.927377	+	0.374128i	$0.877942\pi$
$770$		0			0
$771$	−10973.3	−	5351.00i	−0.512573	−	0.249950i
$772$		0			0
$773$	−3910.77	+	6773.65i	−0.181967	+	0.315176i	−0.942550	−	0.334064i	$-0.891580\pi$
$773$	−3910.77	+	6773.65i	−0.181967	+	0.315176i	0.760583	+	0.649240i	$0.224913\pi$
$774$		0			0
$775$	22407.1	−	12936.8i	1.03857	−	0.599616i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27653.6	+	15965.8i	−1.27188	+	0.734320i
$780$		0			0
$781$	129.197	−	223.776i	0.00591939	−	0.0102527i
$782$		0			0
$783$	−7346.50	+	1563.31i	−0.335304	+	0.0713516i
$784$		0			0
$785$		−	6346.88i		−	0.288573i
$786$		0			0
$787$	21587.3	+	12463.4i	0.977767	+	0.564514i	0.901595	−	0.432581i	$-0.142397\pi$
$787$	21587.3	+	12463.4i	0.977767	+	0.564514i	0.0761716	+	0.997095i	$0.475730\pi$
$788$		0			0
$789$	26583.4	−	1860.94i	1.19949	−	0.0839688i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6211.21	+	10758.1i	0.278142	+	0.481756i
$794$		0			0
$795$	31128.1	+	46141.7i	1.38868	+	2.05846i
$796$		0			0
$797$	16452.6			0.731217			0.365609	−	0.930769i	$-0.380861\pi$
$797$	16452.6			0.731217			0.365609	+	0.930769i	$0.380861\pi$
$798$		0			0
$799$	64905.7			2.87384
$800$		0			0
$801$	−16920.6	+	2380.68i	−0.746393	+	0.105015i
$802$		0			0
$803$	219.704	+	380.539i	0.00965528	+	0.0167234i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.6983	−	209.963i	−0.000641144	−	0.00915869i
$808$		0			0
$809$	−8105.17	−	4679.52i	−0.352240	−	0.203366i	0.313431	−	0.949611i	$-0.398521\pi$
$809$	−8105.17	−	4679.52i	−0.352240	−	0.203366i	−0.665672	+	0.746245i	$0.731855\pi$
$810$		0			0
$811$		−	6805.42i		−	0.294662i	−0.989087	−	0.147331i	$-0.952932\pi$
$811$		−	6805.42i		−	0.294662i	0.989087	−	0.147331i	$-0.0470682\pi$
$812$		0			0
$813$	7384.10	−	15142.6i	0.318539	−	0.653228i
$814$		0			0
$815$	−1727.86	+	2992.74i	−0.0742630	+	0.128627i
$816$		0			0
$817$	−14617.3	+	8439.27i	−0.625940	+	0.361387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23251.5	+	13424.3i	−0.988407	+	0.570657i	−0.904798	−	0.425841i	$-0.859978\pi$
$821$	−23251.5	+	13424.3i	−0.988407	+	0.570657i	−0.0836095	+	0.996499i	$0.526645\pi$
$822$		0			0
$823$	7846.13	−	13589.9i	0.332319	−	0.575594i	−0.650647	−	0.759381i	$-0.725502\pi$
$823$	7846.13	−	13589.9i	0.332319	−	0.575594i	0.982966	+	0.183786i	$0.0588355\pi$
$824$		0			0
$825$	147.109	−	301.678i	0.00620811	−	0.0127310i
$826$		0			0
$827$			17201.9i			0.723301i	0.932314	+	0.361650i	$0.117787\pi$
$827$			17201.9i			0.723301i	−0.932314	+	0.361650i	$0.882213\pi$
$828$		0			0
$829$	−16605.1	−	9586.94i	−0.695679	−	0.401650i	0.110057	−	0.993925i	$-0.464897\pi$
$829$	−16605.1	−	9586.94i	−0.695679	−	0.401650i	−0.805736	+	0.592275i	$0.798230\pi$
$830$		0			0
$831$	803.995	+	11485.0i	0.0335623	+	0.479435i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	7518.41	+	13022.3i	0.311599	+	0.539706i
$836$		0			0
$837$	11803.6	−	36356.1i	0.487445	−	1.50138i
$838$		0			0
$839$	10848.7			0.446410			0.223205	−	0.974771i	$-0.428348\pi$
$839$	10848.7			0.446410			0.223205	+	0.974771i	$0.428348\pi$
$840$		0			0
$841$	21522.8			0.882481
$842$		0			0
$843$	−17093.9	−	25338.6i	−0.698394	−	1.03524i
$844$		0			0
$845$	−4098.40	−	7098.63i	−0.166851	−	0.288994i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7923.34	+	554.665i	−0.320292	+	0.0224217i
$850$		0			0
$851$	−183.963	−	106.211i	−0.00741029	−	0.00427833i
$852$		0			0
$853$			42970.3i			1.72482i	0.506207	+	0.862412i	$0.331047\pi$
$853$			42970.3i			1.72482i	−0.506207	+	0.862412i	$0.668953\pi$
$854$		0			0
$855$	−31602.2	+	24698.2i	−1.26406	+	0.987906i
$856$		0			0
$857$	18302.7	−	31701.2i	0.729532	−	1.26359i	−0.227549	−	0.973767i	$-0.573071\pi$
$857$	18302.7	−	31701.2i	0.729532	−	1.26359i	0.957081	−	0.289820i	$-0.0935955\pi$
$858$		0			0
$859$	8607.79	−	4969.71i	0.341902	−	0.197397i	−0.319211	−	0.947684i	$-0.603418\pi$
$859$	8607.79	−	4969.71i	0.341902	−	0.197397i	0.661113	+	0.750286i	$0.270084\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11425.0	+	6596.25i	−0.450652	+	0.260184i	−0.708106	−	0.706106i	$-0.750450\pi$
$863$	−11425.0	+	6596.25i	−0.450652	+	0.260184i	0.257453	+	0.966291i	$0.417117\pi$
$864$		0			0
$865$	−24577.2	+	42569.0i	−0.966071	+	1.67328i
$866$		0			0
$867$	26946.7	+	13140.2i	1.05555	+	0.514725i
$868$		0			0
$869$		−	287.561i		−	0.0112254i
$870$		0			0
$871$	13565.4	+	7831.97i	0.527721	+	0.304680i
$872$		0			0
$873$	−35854.1	−	14479.6i	−1.39001	−	0.561352i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4666.37	−	8082.39i	−0.179672	−	0.311201i	0.762096	−	0.647464i	$-0.224170\pi$
$877$	−4666.37	−	8082.39i	−0.179672	−	0.311201i	−0.941768	+	0.336263i	$0.890837\pi$
$878$		0			0
$879$	−26010.8	+	17547.4i	−0.998091	+	0.673332i
$880$		0			0
$881$	−22655.3			−0.866376			−0.433188	−	0.901304i	$-0.642611\pi$
$881$	−22655.3			−0.866376			−0.433188	+	0.901304i	$0.642611\pi$
$882$		0			0
$883$	32700.9			1.24629			0.623145	−	0.782107i	$-0.285855\pi$
$883$	32700.9			1.24629			0.623145	+	0.782107i	$0.285855\pi$
$884$		0			0
$885$	33616.3	−	22678.2i	1.27684	−	0.861379i
$886$		0			0
$887$	12678.9	+	21960.5i	0.479950	+	0.831299i	0.999735	−	0.0229985i	$-0.00732131\pi$
$887$	12678.9	+	21960.5i	0.479950	+	0.831299i	−0.519785	+	0.854297i	$0.673988\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−136.821	−	476.600i	−0.00514442	−	0.0179200i
$892$		0			0
$893$	54471.8	+	31449.3i	2.04124	+	1.17851i
$894$		0			0
$895$			20482.8i			0.764989i
$896$		0			0
$897$	−1028.72	−	501.642i	−0.0382920	−	0.0186726i
$898$		0			0
$899$	7293.15	−	12632.1i	0.270568	−	0.468637i
$900$		0			0
$901$	64647.7	−	37324.4i	2.39037	−	1.38008i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−20016.1	+	11556.3i	−0.735202	+	0.424469i
$906$		0			0
$907$	22286.5	−	38601.3i	0.815888	−	1.41316i	−0.0928000	−	0.995685i	$-0.529582\pi$
$907$	22286.5	−	38601.3i	0.815888	−	1.41316i	0.908688	−	0.417475i	$-0.137085\pi$
$908$		0			0
$909$	−14815.1	−	18956.5i	−0.540578	−	0.691690i
$910$		0			0
$911$			581.992i			0.0211660i	0.999944	+	0.0105830i	$0.00336874\pi$
$911$			581.992i			0.0211660i	−0.999944	+	0.0105830i	$0.996631\pi$
$912$		0			0
$913$	−230.493	−	133.075i	−0.00835510	−	0.00482382i
$914$		0			0
$915$	18212.2	−	1274.92i	0.658007	−	0.0460631i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	20983.4	+	36344.4i	0.753188	+	1.30456i	0.946270	+	0.323377i	$0.104818\pi$
$919$	20983.4	+	36344.4i	0.753188	+	1.30456i	−0.193082	+	0.981183i	$0.561848\pi$
$920$		0			0
$921$	−21016.0	−	31152.3i	−0.751901	−	1.11455i
$922$		0			0
$923$	−19920.5			−0.710393
$924$		0			0
$925$	−4802.45			−0.170707
$926$		0			0
$927$	4636.86	+	32956.3i	0.164287	+	1.16767i
$928$		0			0
$929$	35.0320	+	60.6772i	0.00123720	+	0.00214290i	0.866643	−	0.498928i	$-0.166273\pi$
$929$	35.0320	+	60.6772i	0.00123720	+	0.00214290i	−0.865406	+	0.501071i	$0.832940\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−623.398	−	8905.20i	−0.0218748	−	0.312479i
$934$		0			0
$935$	−902.961	−	521.325i	−0.0315829	−	0.0182344i
$936$		0			0
$937$		−	26725.4i		−	0.931783i	−0.884842	−	0.465892i	$-0.845734\pi$
$937$		−	26725.4i		−	0.931783i	0.884842	−	0.465892i	$-0.154266\pi$
$938$		0			0
$939$	−12591.2	+	25820.9i	−0.437592	+	0.897371i
$940$		0			0
$941$	19532.8	−	33831.7i	0.676673	−	1.17203i	−0.299303	−	0.954158i	$-0.596754\pi$
$941$	19532.8	−	33831.7i	0.676673	−	1.17203i	0.975977	−	0.217875i	$-0.0699124\pi$
$942$		0			0
$943$	−1159.72	+	669.564i	−0.0400484	+	0.0231220i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25718.0	−	14848.3i	0.882495	−	0.509509i	0.0110151	−	0.999939i	$-0.496494\pi$
$947$	25718.0	−	14848.3i	0.882495	−	0.509509i	0.871480	+	0.490430i	$0.163160\pi$
$948$		0			0
$949$	16937.8	−	29337.1i	0.579371	−	1.00350i
$950$		0			0
$951$	4054.27	−	8314.11i	0.138243	−	0.283495i
$952$		0			0
$953$			29039.6i			0.987079i	0.869723	+	0.493539i	$0.164297\pi$
$953$			29039.6i			0.987079i	−0.869723	+	0.493539i	$0.835703\pi$
$954$		0			0
$955$	−27949.0	−	16136.4i	−0.947026	−	0.546766i
$956$		0			0
$957$	−13.2135	−	188.754i	−0.000446323	−	0.00637569i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	22220.1	+	38486.4i	0.745867	+	1.29188i
$962$		0			0
$963$	−2544.28	−	18083.4i	−0.0851385	−	0.605118i
$964$		0			0
$965$	−51898.3			−1.73126
$966$		0			0
$967$	−10669.9			−0.354831			−0.177416	−	0.984136i	$-0.556774\pi$
$967$	−10669.9			−0.354831			−0.177416	+	0.984136i	$0.556774\pi$
$968$		0			0
$969$	30083.6	+	44593.3i	0.997341	+	1.47837i
$970$		0			0
$971$	20680.1	+	35819.0i	0.683478	+	1.18382i	0.973913	+	0.226923i	$0.0728667\pi$
$971$	20680.1	+	35819.0i	0.683478	+	1.18382i	−0.290435	+	0.956895i	$0.593800\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−25812.1	+	1806.95i	−0.847844	+	0.0593524i
$976$		0			0
$977$	−31547.9	−	18214.2i	−1.03307	−	0.596443i	−0.115207	−	0.993342i	$-0.536753\pi$
$977$	−31547.9	−	18214.2i	−1.03307	−	0.596443i	−0.917862	+	0.396899i	$0.870086\pi$
$978$		0			0
$979$		−	430.459i		−	0.0140526i
$980$		0			0
$981$	−16533.3	−	21155.0i	−0.538092	−	0.688508i
$982$		0			0
$983$	362.416	−	627.723i	0.0117592	−	0.0203675i	−0.860086	−	0.510149i	$-0.829590\pi$
$983$	362.416	−	627.723i	0.0117592	−	0.0203675i	0.871845	+	0.489782i	$0.162924\pi$
$984$		0			0
$985$	−16670.6	+	9624.75i	−0.539257	+	0.311340i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−613.008	+	353.921i	−0.0197093	+	0.0113792i
$990$		0			0
$991$	−14449.0	+	25026.5i	−0.463157	+	0.802212i	−0.999116	−	0.0420324i	$-0.986617\pi$
$991$	−14449.0	+	25026.5i	−0.463157	+	0.802212i	0.535959	+	0.844244i	$0.319950\pi$
$992$		0			0
$993$	−30074.4	−	14665.4i	−0.961109	−	0.468673i
$994$		0			0
$995$		−	52452.2i		−	1.67120i
$996$		0			0
$997$	8836.00	+	5101.46i	0.280681	+	0.162051i	0.633732	−	0.773553i	$-0.281522\pi$
$997$	8836.00	+	5101.46i	0.280681	+	0.162051i	−0.353051	+	0.935604i	$0.614856\pi$
$998$		0			0
$999$	−5271.45	+	4748.63i	−0.166948	+	0.150390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.c.521.1		12
3.2	odd	2	inner	588.4.k.c.521.3		12
7.2	even	3		84.4.k.c.5.4	✓	12
7.3	odd	6		588.4.f.c.293.3		12
7.4	even	3		588.4.f.c.293.10		12
7.5	odd	6	inner	588.4.k.c.509.3		12
7.6	odd	2		84.4.k.c.17.6	yes	12
21.2	odd	6		84.4.k.c.5.6	yes	12
21.5	even	6	inner	588.4.k.c.509.1		12
21.11	odd	6		588.4.f.c.293.4		12
21.17	even	6		588.4.f.c.293.9		12
21.20	even	2		84.4.k.c.17.4	yes	12
28.23	odd	6		336.4.bc.c.257.3		12
28.27	even	2		336.4.bc.c.17.1		12
84.23	even	6		336.4.bc.c.257.1		12
84.83	odd	2		336.4.bc.c.17.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.c.5.4	✓	12	7.2	even	3
84.4.k.c.5.6	yes	12	21.2	odd	6
84.4.k.c.17.4	yes	12	21.20	even	2
84.4.k.c.17.6	yes	12	7.6	odd	2
336.4.bc.c.17.1		12	28.27	even	2
336.4.bc.c.17.3		12	84.83	odd	2
336.4.bc.c.257.1		12	84.23	even	6
336.4.bc.c.257.3		12	28.23	odd	6
588.4.f.c.293.3		12	7.3	odd	6
588.4.f.c.293.4		12	21.11	odd	6
588.4.f.c.293.9		12	21.17	even	6
588.4.f.c.293.10		12	7.4	even	3
588.4.k.c.509.1		12	21.5	even	6	inner
588.4.k.c.509.3		12	7.5	odd	6	inner
588.4.k.c.521.1		12	1.1	even	1	trivial
588.4.k.c.521.3		12	3.2	odd	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +O(q^{10})\)	\(q+(-4.30758 + 2.90598i) q^{3} +(7.41560 + 12.8442i) q^{5} +(10.1105 - 25.0355i) q^{9} +(0.589052 + 0.340089i) q^{11} -52.4373i q^{13} +(-69.2683 - 33.7779i) q^{15} +(-51.6784 + 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(-3.63771 + 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(29.2008 + 137.224i) q^{27} +53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(-3.52568 + 0.246811i) q^{33} +(25.2855 + 43.7957i) q^{37} +(152.382 + 225.878i) q^{39} +318.804 q^{41} +168.515 q^{43} +(396.537 - 55.7917i) q^{45} +(-313.988 - 543.844i) q^{47} +(-37.5043 - 535.747i) q^{51} +(-625.481 - 361.121i) q^{53} +10.0879i q^{55} +(228.115 - 467.795i) q^{57} +(-263.093 + 455.691i) q^{59} +(-205.162 + 118.450i) q^{61} +(673.515 - 388.854i) q^{65} +(-149.359 + 258.697i) q^{67} +(9.56651 - 19.6181i) q^{69} -379.893i q^{71} +(559.469 + 323.010i) q^{73} +(-34.4592 - 492.246i) q^{75} +(-211.386 - 366.132i) q^{79} +(-524.554 - 506.245i) q^{81} -391.295 q^{83} -1532.91 q^{85} +(-155.577 - 230.614i) q^{87} +(-316.431 - 548.075i) q^{89} +(1412.26 - 98.8635i) q^{93} +(-1286.48 - 742.752i) q^{95} -1432.13i q^{97} +(14.4699 - 11.3087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 84 q^{9}+O(q^{10}) \) 12 * q - 84 * q^9	\( 12 q - 84 q^{9} + 132 q^{15} - 204 q^{19} - 444 q^{25} - 1458 q^{31} + 108 q^{33} + 240 q^{37} - 432 q^{39} + 342 q^{45} - 300 q^{51} + 180 q^{57} - 2148 q^{61} + 1980 q^{67} + 3084 q^{73} + 3384 q^{75} - 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} + 882 q^{93} + 9216 q^{99}+O(q^{100}) \) 12 * q - 84 * q^9 + 132 * q^15 - 204 * q^19 - 444 * q^25 - 1458 * q^31 + 108 * q^33 + 240 * q^37 - 432 * q^39 + 342 * q^45 - 300 * q^51 + 180 * q^57 - 2148 * q^61 + 1980 * q^67 + 3084 * q^73 + 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 + 882 * q^93 + 9216 * q^99

Introduction

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