LMFDB - Embedded newform 336.4.bc.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (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:	$19.8246417619$
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:	$\Z[a_1, \ldots, a_{13}]$
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			17.1
Root			$-1.67777 - 2.48698i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.c.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.30758 + 2.90598i) q^{3} +(-7.41560 - 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(10.1105 - 25.0355i) q^{9} +O(q^{10})$	\(q+(-4.30758 + 2.90598i) q^{3} +(-7.41560 - 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(10.1105 - 25.0355i) q^{9} +(-0.589052 - 0.340089i) q^{11} +52.4373i q^{13} +(69.2683 + 33.7779i) q^{15} +(51.6784 - 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(-95.2852 + 13.4811i) q^{21} +(3.63771 - 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(29.2008 + 137.224i) q^{27} +53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(3.52568 - 0.246811i) q^{33} +(-19.3922 - 273.992i) q^{35} +(25.2855 + 43.7957i) q^{37} +(-152.382 - 225.878i) q^{39} -318.804 q^{41} -168.515 q^{43} +(-396.537 + 55.7917i) q^{45} +(-313.988 - 543.844i) q^{47} +(211.629 + 269.930i) q^{49} +(37.5043 + 535.747i) q^{51} +(-625.481 - 361.121i) q^{53} +10.0879i q^{55} +(228.115 - 467.795i) q^{57} +(-263.093 + 455.691i) q^{59} +(205.162 - 118.450i) q^{61} +(371.273 - 334.968i) q^{63} +(673.515 - 388.854i) q^{65} +(149.359 - 258.697i) q^{67} +(-9.56651 + 19.6181i) q^{69} +379.893i q^{71} +(-559.469 - 323.010i) q^{73} +(-34.4592 - 492.246i) q^{75} +(-7.05302 - 10.4375i) q^{77} +(211.386 + 366.132i) q^{79} +(-524.554 - 506.245i) q^{81} -391.295 q^{83} -1532.91 q^{85} +(-155.577 - 230.614i) q^{87} +(316.431 + 548.075i) q^{89} +(-424.987 + 873.226i) q^{91} +(1412.26 - 98.8635i) q^{93} +(1286.48 + 742.752i) q^{95} +1432.13i q^{97} +(-14.4699 + 11.3087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 42 q^{7} - 84 q^{9}+O(q^{10}) $ 12 * q + 42 * q^7 - 84 * q^9	$ 12 q + 42 q^{7} - 84 q^{9} - 132 q^{15} - 204 q^{19} - 378 q^{21} - 444 q^{25} - 1458 q^{31} - 108 q^{33} + 240 q^{37} + 432 q^{39} - 342 q^{45} - 1218 q^{49} + 300 q^{51} + 180 q^{57} + 2148 q^{61} - 1596 q^{63} - 1980 q^{67} - 3084 q^{73} + 3384 q^{75} + 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} - 3780 q^{91} + 882 q^{93} - 9216 q^{99}+O(q^{100}) $ 12 * q + 42 * q^7 - 84 * q^9 - 132 * q^15 - 204 * q^19 - 378 * q^21 - 444 * q^25 - 1458 * q^31 - 108 * q^33 + 240 * q^37 + 432 * q^39 - 342 * q^45 - 1218 * q^49 + 300 * q^51 + 180 * q^57 + 2148 * q^61 - 1596 * q^63 - 1980 * q^67 - 3084 * q^73 + 3384 * q^75 + 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 - 3780 * q^91 + 882 * q^93 - 9216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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	$-0.935834\pi$
$5$	−7.41560	−	12.8442i	−0.663272	−	1.14882i	0.316479	−	0.948600i	$-0.397499\pi$
$6$		0			0
$7$	16.6528	+	8.10467i	0.899164	+	0.437611i
$7$	16.6528	+	8.10467i	0.899164	+	0.437611i
$8$		0			0
$9$	10.1105	−	25.0355i	0.374464	−	0.927241i
$10$		0			0
$11$	−0.589052	−	0.340089i	−0.0161460	−	0.00932189i	0.491905	−	0.870649i	$-0.336301\pi$
$11$	−0.589052	−	0.340089i	−0.0161460	−	0.00932189i	−0.508051	+	0.861327i	$0.669634\pi$
$12$		0			0
$13$			52.4373i			1.11873i	0.828921	+	0.559365i	$0.188955\pi$
$13$			52.4373i			1.11873i	−0.828921	+	0.559365i	$0.811045\pi$
$14$		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	$-0.569441\pi$
$17$	51.6784	−	89.5096i	0.737286	−	1.27702i	0.953713	−	0.300717i	$-0.0972261\pi$
$18$		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
$21$	−95.2852	+	13.4811i	−0.990139	+	0.140086i
$22$		0			0
$23$	3.63771	−	2.10024i	0.0329790	−	0.0190404i	−0.483420	−	0.875389i	$-0.660606\pi$
$23$	3.63771	−	2.10024i	0.0329790	−	0.0190404i	0.516399	+	0.856348i	$0.327272\pi$
$24$		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
$35$	−19.3922	−	273.992i	−0.0936537	−	1.32323i
$36$		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	$-0.707700\pi$
$41$	−318.804			−1.21436			−0.607181	+	0.794563i	$0.707700\pi$
$42$		0			0
$43$	−168.515			−0.597634			−0.298817	−	0.954310i	$-0.596592\pi$
$43$	−168.515			−0.597634			−0.298817	+	0.954310i	$0.596592\pi$
$44$		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
$49$	211.629	+	269.930i	0.616993	+	0.786969i
$50$		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	−0.268987	−	0.963144i	$-0.586689\pi$
$61$	205.162	−	118.450i	0.430627	−	0.248623i	0.699614	+	0.714521i	$0.253355\pi$
$62$		0			0
$63$	371.273	−	334.968i	0.742476	−	0.669873i
$64$		0			0
$65$	673.515	−	388.854i	1.28522	−	0.742022i
$66$		0			0
$67$	149.359	−	258.697i	0.272344	−	0.471714i	−0.697117	−	0.716957i	$-0.745534\pi$
$67$	149.359	−	258.697i	0.272344	−	0.471714i	0.969462	+	0.245243i	$0.0788677\pi$
$68$		0			0
$69$	−9.56651	+	19.6181i	−0.0166909	+	0.0342281i
$70$		0			0
$71$			379.893i			0.634999i	0.948258	+	0.317500i	$0.102843\pi$
$71$			379.893i			0.634999i	−0.948258	+	0.317500i	$0.897157\pi$
$72$		0			0
$73$	−559.469	−	323.010i	−0.896999	−	0.517882i	−0.0207735	−	0.999784i	$-0.506613\pi$
$73$	−559.469	−	323.010i	−0.896999	−	0.517882i	−0.876225	+	0.481902i	$0.839946\pi$
$74$		0			0
$75$	−34.4592	−	492.246i	−0.0530533	−	0.757863i
$76$		0			0
$77$	−7.05302	−	10.4375i	−0.0104385	−	0.0154476i
$78$		0			0
$79$	211.386	+	366.132i	0.301048	+	0.521431i	0.976374	−	0.216089i	$-0.0693301\pi$
$79$	211.386	+	366.132i	0.301048	+	0.521431i	−0.675325	+	0.737520i	$0.735997\pi$
$80$		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	0.990605	−	0.136752i	$-0.0436663\pi$
$89$	316.431	+	548.075i	0.376872	+	0.652762i	−0.613733	+	0.789513i	$0.710333\pi$
$90$		0			0
$91$	−424.987	+	873.226i	−0.489569	+	1.00592i
$92$		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	$0.269725\pi$
$97$			1432.13i			1.49908i	−0.661959	+	0.749540i	$0.730275\pi$
$98$		0			0
$99$	−14.4699	+	11.3087i	−0.0146897	+	0.0114805i
$100$		0			0
$101$	−445.537	+	771.692i	−0.438936	+	0.760260i	−0.997608	−	0.0691294i	$-0.977978\pi$
$101$	−445.537	+	771.692i	−0.438936	+	0.760260i	0.558672	+	0.829389i	$0.311311\pi$
$102$		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
$105$	879.750	+	1123.89i	0.817665	+	1.04458i
$106$		0			0
$107$	−585.738	+	338.176i	−0.529209	+	0.305539i	−0.740694	−	0.671842i	$-0.765503\pi$
$107$	−585.738	+	338.176i	−0.529209	+	0.305539i	0.211485	+	0.977381i	$0.432170\pi$
$108$		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
$119$	1586.03	−	1071.75i	1.22178	−	0.825603i
$120$		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	$-0.399882\pi$
$127$	885.551			0.618740			0.309370	+	0.950942i	$0.399882\pi$
$128$		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
$133$	−1850.37	+	130.963i	−1.20637	+	0.0853828i
$134$		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
$147$	−1696.02	−	547.758i	−0.951601	−	0.307336i
$148$		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	−0.812404	−	0.583095i	$-0.801842\pi$
$151$	183.275	−	317.442i	0.0987731	−	0.171080i	0.911177	+	0.412015i	$0.135175\pi$
$152$		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	0.591230	−	0.806503i	$-0.298643\pi$
$157$	370.608	+	213.970i	0.188393	+	0.108769i	−0.402837	+	0.915272i	$0.631976\pi$
$158$		0			0
$159$	3743.72	−	262.075i	1.86727	−	0.130716i
$160$		0			0
$161$	77.5997	−	5.49223i	0.0379858	−	0.00268850i
$162$		0			0
$163$	−116.502	−	201.787i	−0.0559823	−	0.0969643i	0.836676	−	0.547698i	$-0.184496\pi$
$163$	−116.502	−	201.787i	−0.0559823	−	0.0969643i	−0.892658	+	0.450734i	$0.851162\pi$
$164$		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	$-0.906995\pi$
$173$	−1657.13	−	2870.23i	−0.728262	−	1.26139i	0.229356	−	0.973343i	$-0.426338\pi$
$174$		0			0
$175$	−1457.26	+	984.725i	−0.629475	+	0.425361i
$176$		0			0
$177$	−190.933	−	2727.47i	−0.0810816	−	1.15824i
$178$		0			0
$179$	−1196.04	−	690.531i	−0.499418	−	0.288339i	0.229055	−	0.973413i	$-0.426436\pi$
$179$	−1196.04	−	690.531i	−0.499418	−	0.288339i	−0.728473	+	0.685074i	$0.759770\pi$
$180$		0			0
$181$		−	1558.38i		−	0.639963i	−0.947424	−	0.319981i	$-0.896323\pi$
$181$		−	1558.38i		−	0.639963i	0.947424	−	0.319981i	$-0.103677\pi$
$182$		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
$189$	−625.879	+	2521.81i	−0.240878	+	0.970555i
$190$		0			0
$191$	1884.48	−	1088.00i	0.713905	−	0.412173i	−0.0986002	−	0.995127i	$-0.531436\pi$
$191$	1884.48	−	1088.00i	0.713905	−	0.412173i	0.812505	+	0.582954i	$0.198103\pi$
$192$		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
$203$	−433.898	+	891.534i	−0.150018	+	0.308244i
$204$		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	$-0.386982\pi$
$211$	2131.02			0.695286			0.347643	+	0.937627i	$0.386982\pi$
$212$		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
$217$	−2825.18	−	4180.87i	−0.883805	−	1.30791i
$218$		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	−0.0976515	−	0.995221i	$-0.531133\pi$
$229$	2479.18	−	1431.35i	0.715409	−	0.413042i	0.813061	+	0.582179i	$0.197800\pi$
$230$		0			0
$231$	60.7126	+	24.4644i	0.0172926	+	0.00696814i
$232$		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	$-0.728123\pi$
$239$		−	5571.82i		−	1.50800i	0.656876	−	0.753998i	$-0.271877\pi$
$240$		0			0
$241$	3591.11	+	2073.33i	0.959851	+	0.554170i	0.896127	−	0.443798i	$-0.146369\pi$
$241$	3591.11	+	2073.33i	0.959851	+	0.554170i	0.0637236	+	0.997968i	$0.479702\pi$
$242$		0			0
$243$	3730.70	+	656.348i	0.984874	+	0.173271i
$244$		0			0
$245$	1897.68	−	4719.90i	0.494852	−	1.23079i
$246$		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	0.687507	−	0.726177i	$-0.258705\pi$
$257$	−1174.76	−	2034.74i	−0.285134	−	0.493867i	−0.972642	+	0.232310i	$0.925372\pi$
$258$		0			0
$259$	66.1228	+	934.249i	0.0158636	+	0.224137i
$260$		0			0
$261$	1340.32	+	541.285i	0.317869	+	0.128371i
$262$		0			0
$263$	4441.42	+	2564.25i	1.04133	+	0.601211i	0.920209	−	0.391426i	$-0.128018\pi$
$263$	4441.42	+	2564.25i	1.04133	+	0.601211i	0.121119	+	0.992638i	$0.461352\pi$
$264$		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	−0.863721	−	0.503970i	$-0.831872\pi$
$269$	20.2532	−	35.0795i	0.00459055	−	0.00795107i	0.868312	+	0.496019i	$0.165205\pi$
$270$		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
$273$	−706.911	−	4996.50i	−0.156719	−	1.10770i
$274$		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
$287$	−5308.97	−	2583.80i	−1.09191	−	0.531419i
$288$		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	$-0.705625\pi$
$293$	−6038.37			−1.20398			−0.601989	+	0.798505i	$0.705625\pi$
$294$		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
$301$	−2806.23	−	1365.76i	−0.537371	−	0.261531i
$302$		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	−0.865557	−	0.500810i	$-0.833036\pi$
$313$	−4787.88	+	2764.28i	−0.864622	+	0.499190i	0.000935213		1.00000i	$0.499702\pi$
$314$		0			0
$315$	−7055.61	−	2284.72i	−1.26203	−	0.408664i
$316$		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
$329$	−821.097	−	11601.3i	−0.137594	−	1.94407i
$330$		0			0
$331$	−3219.65	−	5576.59i	−0.534646	−	0.926034i	−0.999180	−	0.0404789i	$-0.987112\pi$
$331$	−3219.65	−	5576.59i	−0.534646	−	0.926034i	0.464534	−	0.885555i	$-0.346222\pi$
$332$		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
$343$	1336.50	+	6210.26i	0.210392	+	0.977617i
$344$		0			0
$345$	322.920	−	22.6057i	0.0503925	−	0.00352767i
$346$		0			0
$347$	−2115.84	−	1221.58i	−0.327332	−	0.188985i	0.327324	−	0.944912i	$-0.393853\pi$
$347$	−2115.84	−	1221.58i	−0.327332	−	0.188985i	−0.654656	+	0.755927i	$0.727186\pi$
$348$		0			0
$349$		−	1583.72i		−	0.242907i	−0.992597	−	0.121453i	$-0.961244\pi$
$349$		−	1583.72i		−	0.242907i	0.992597	−	0.121453i	$-0.0387555\pi$
$350$		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	$-0.625310\pi$
$353$	4032.35	−	6984.23i	0.607989	−	1.05307i	0.991571	−	0.129561i	$-0.0413568\pi$
$354$		0			0
$355$	4879.42	−	2817.13i	0.729500	−	0.421177i
$356$		0			0
$357$	−3717.50	+	9225.62i	−0.551123	+	1.36771i
$358$		0			0
$359$	5312.56	−	3067.21i	0.781020	−	0.450922i	−0.0557719	−	0.998444i	$-0.517762\pi$
$359$	5312.56	−	3067.21i	0.781020	−	0.450922i	0.836792	+	0.547522i	$0.184429\pi$
$360$		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
$371$	−7489.21	−	11083.0i	−1.04803	−	1.55094i
$372$		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	$-0.430340\pi$
$379$	3203.69			0.434201			0.217101	+	0.976149i	$0.430340\pi$
$380$		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
$385$	−81.7588	+	167.991i	−0.0108229	+	0.0222379i
$386$		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	$-0.188660\pi$
$397$	13668.1	−	7891.30i	1.72792	−	0.997614i	0.898478	−	0.439018i	$-0.144673\pi$
$398$		0			0
$399$	7590.06	−	5941.28i	0.952327	−	0.745454i
$400$		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	0.997868	−	0.0652706i	$-0.0207911\pi$
$409$	11913.3	+	6878.12i	1.44028	+	0.831543i	0.442408	+	0.896814i	$0.354124\pi$
$410$		0			0
$411$	−9996.58	+	699.800i	−1.19974	+	0.0839868i
$412$		0			0
$413$	−8074.45	+	5456.22i	−0.962028	+	0.650080i
$414$		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
$427$	4376.51	−	309.753i	0.496005	−	0.0351054i
$428$		0			0
$429$	12.9421	+	184.877i	0.00145653	+	0.0208064i
$430$		0			0
$431$	−76.0396	−	43.9015i	−0.00849814	−	0.00490641i	0.495745	−	0.868468i	$-0.334895\pi$
$431$	−76.0396	−	43.9015i	−0.00849814	−	0.00490641i	−0.504243	+	0.863562i	$0.668228\pi$
$432$		0			0
$433$			1782.09i			0.197787i	0.995098	+	0.0988936i	$0.0315303\pi$
$433$			1782.09i			0.197787i	−0.995098	+	0.0988936i	$0.968470\pi$
$434$		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
$441$	8897.52	−	2569.09i	0.960752	−	0.277410i
$442$		0			0
$443$	4831.09	−	2789.23i	0.518131	−	0.299143i	−0.218039	−	0.975940i	$-0.569966\pi$
$443$	4831.09	−	2789.23i	0.518131	−	0.299143i	0.736170	+	0.676797i	$0.236633\pi$
$444$		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
$455$	14367.4	−	1016.87i	1.48034	−	0.104773i
$456$		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	$-0.456203\pi$
$461$	2715.21			0.274317			0.137159	+	0.990549i	$0.456203\pi$
$462$		0			0
$463$	11587.7			1.16313			0.581563	−	0.813502i	$-0.302442\pi$
$463$	11587.7			1.16313			0.581563	+	0.813502i	$0.302442\pi$
$464$		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
$469$	4583.88	−	3097.51i	0.451309	−	0.304968i
$470$		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
$483$	−318.307	+	249.162i	−0.0299865	+	0.0234726i
$484$		0			0
$485$	18394.6	−	10620.1i	1.72217	−	0.994297i
$486$		0			0
$487$	521.790	−	903.766i	0.0485514	−	0.0840935i	−0.840728	−	0.541457i	$-0.817873\pi$
$487$	521.790	−	903.766i	0.0485514	−	0.0840935i	0.889280	+	0.457364i	$0.151206\pi$
$488$		0			0
$489$	1088.23	+	530.662i	0.100637	+	0.0490744i
$490$		0			0
$491$			13213.2i			1.21446i	0.794525	+	0.607232i	$0.207720\pi$
$491$			13213.2i			1.21446i	−0.794525	+	0.607232i	$0.792280\pi$
$492$		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
$497$	−3078.90	+	6326.26i	−0.277883	+	0.570969i
$498$		0			0
$499$	−874.489	−	1514.66i	−0.0784519	−	0.135883i	0.824130	−	0.566400i	$-0.191664\pi$
$499$	−874.489	−	1514.66i	−0.0784519	−	0.135883i	−0.902582	+	0.430518i	$0.858331\pi$
$500$		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	$0.0979256\pi$
$509$	8483.69	+	14694.2i	0.738768	+	1.27958i	−0.214282	+	0.976772i	$0.568741\pi$
$510$		0			0
$511$	−6698.82	−	9913.31i	−0.579918	−	0.858198i
$512$		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	−0.940814	−	0.338922i	$-0.889938\pi$
$521$	−2103.60	+	3643.55i	−0.176892	+	0.306385i	0.763923	+	0.645308i	$0.223271\pi$
$522$		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
$525$	3415.66	−	8476.54i	0.283946	−	0.704660i
$526$		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
$539$	−32.8598	−	230.975i	−0.00262592	−	0.0184579i
$540$		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	$-0.685204\pi$
$547$	−14061.3			−1.09912			−0.549558	+	0.835456i	$0.685204\pi$
$548$		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
$553$	552.786	+	7810.32i	0.0425079	+	0.600594i
$554$		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
$567$	−4632.32	−	12681.7i	−0.343103	−	0.939298i
$568$		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	−0.877169	−	0.480182i	$-0.840571\pi$
$571$	−310.198	+	537.278i	−0.0227345	+	0.0393772i	0.854434	+	0.519559i	$0.173904\pi$
$572$		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	0.172294	−	0.985046i	$-0.444882\pi$
$577$	−8241.62	−	4758.30i	−0.594633	−	0.343312i	−0.766927	+	0.641734i	$0.778215\pi$
$578$		0			0
$579$	−1269.75	−	18138.3i	−0.0911385	−	1.30191i
$580$		0			0
$581$	−6516.14	−	3171.32i	−0.465293	−	0.226452i
$582$		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	0.984076	−	0.177750i	$-0.0568818\pi$
$593$	4882.36	+	8456.49i	0.338102	+	0.585610i	−0.645974	+	0.763360i	$0.723549\pi$
$594$		0			0
$595$	−25527.1	−	12423.7i	−1.75884	−	0.856004i
$596$		0			0
$597$	18331.9	−	1283.30i	1.25674	−	0.0879768i
$598$		0			0
$599$	−12740.2	−	7355.53i	−0.869029	−	0.501734i	−0.00200376	−	0.999998i	$-0.500638\pi$
$599$	−12740.2	−	7355.53i	−0.869029	−	0.501734i	−0.867026	+	0.498264i	$0.833971\pi$
$600$		0			0
$601$		−	14047.5i		−	0.953425i	−0.879059	−	0.476713i	$-0.841828\pi$
$601$		−	14047.5i		−	0.953425i	0.879059	−	0.476713i	$-0.158172\pi$
$602$		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
$609$	−721.732	−	5101.26i	−0.0480231	−	0.339431i
$610$		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
$623$	827.484	+	11691.5i	0.0532142	+	0.751863i
$624$		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	$-0.376940\pi$
$631$	11952.7			0.754091			0.377046	+	0.926195i	$0.376940\pi$
$632$		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
$637$	−14154.4	+	11097.2i	−0.880406	+	0.690249i
$638$		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
$651$	24319.2	+	9799.53i	1.46413	+	0.589975i
$652$		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	$-0.959087\pi$
$659$		−	4336.79i		−	0.256354i	0.991751	−	0.128177i	$-0.0409125\pi$
$660$		0			0
$661$	16220.2	+	9364.73i	0.954451	+	0.551053i	0.894461	−	0.447146i	$-0.147560\pi$
$661$	16220.2	+	9364.73i	0.954451	+	0.551053i	0.0599904	+	0.998199i	$0.480893\pi$
$662$		0			0
$663$	−28093.1	+	1966.63i	−1.64562	+	0.115200i
$664$		0			0
$665$	15403.7	+	22795.4i	0.898243	+	1.32927i
$666$		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	$-0.841668\pi$
$677$	−15019.2	−	26014.1i	−0.852638	−	1.47681i	0.0261815	−	0.999657i	$-0.491665\pi$
$678$		0			0
$679$	−11606.9	+	23848.9i	−0.656014	+	1.34792i
$680$		0			0
$681$	1077.68	+	15394.6i	0.0606415	+	0.866259i
$682$		0			0
$683$	−3348.00	−	1932.97i	−0.187566	−	0.108291i	0.403277	−	0.915078i	$-0.367871\pi$
$683$	−3348.00	−	1932.97i	−0.187566	−	0.108291i	−0.590843	+	0.806787i	$0.701205\pi$
$684$		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
$693$	−332.618	+	71.0474i	−0.0182325	+	0.00389447i
$694$		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
$707$	−13673.7	+	9239.87i	−0.727374	+	0.491515i
$708$		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
$721$	−22771.6	+	1611.69i	−1.17622	+	0.0832489i
$722$		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	−0.870015	−	0.493024i	$-0.835891\pi$
$733$	−17425.1	+	10060.4i	−0.878052	+	0.506943i	−0.00803608	+	0.999968i	$0.502558\pi$
$734$		0			0
$735$	5541.50	+	25846.0i	0.278097	+	1.29707i
$736$		0			0
$737$	−175.960	+	101.590i	−0.00879453	+	0.00507752i
$738$		0			0
$739$	−4889.49	+	8468.84i	−0.243387	+	0.421558i	−0.961677	−	0.274186i	$-0.911592\pi$
$739$	−4889.49	+	8468.84i	−0.243387	+	0.421558i	0.718290	+	0.695744i	$0.244925\pi$
$740$		0			0
$741$	24529.9	+	11961.7i	1.21610	+	0.593015i
$742$		0			0
$743$		−	35045.8i		−	1.73043i	−0.501404	−	0.865213i	$-0.667183\pi$
$743$		−	35045.8i		−	1.73043i	0.501404	−	0.865213i	$-0.332817\pi$
$744$		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
$749$	−12495.0	+	884.348i	−0.609554	+	0.0431420i
$750$		0			0
$751$	10043.6	+	17396.0i	0.488011	+	0.845260i	0.999905	−	0.0137887i	$-0.00438922\pi$
$751$	10043.6	+	17396.0i	0.488011	+	0.845260i	−0.511894	+	0.859049i	$0.671056\pi$
$752$		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	$-0.993644\pi$
$761$	−10857.5	−	18805.7i	−0.517191	−	0.895801i	0.482610	−	0.875836i	$-0.339689\pi$
$762$		0			0
$763$	15259.6	−	10311.5i	0.724028	−	0.489254i
$764$		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	$-0.877942\pi$
$769$		−	15956.6i		−	0.748257i	0.927377	−	0.374128i	$-0.122058\pi$
$770$		0			0
$771$	10973.3	+	5351.00i	0.512573	+	0.249950i
$772$		0			0
$773$	3910.77	−	6773.65i	0.181967	−	0.315176i	−0.760583	−	0.649240i	$-0.775087\pi$
$773$	3910.77	−	6773.65i	0.181967	−	0.315176i	0.942550	+	0.334064i	$0.108420\pi$
$774$		0			0
$775$	22407.1	−	12936.8i	1.03857	−	0.599616i
$776$		0			0
$777$	−2999.74	−	3832.20i	−0.138501	−	0.176936i
$778$		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
$791$	−5737.42	+	11788.7i	−0.257900	+	0.529910i
$792$		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	$-0.619139\pi$
$797$	−16452.6			−0.731217			−0.365609	+	0.930769i	$0.619139\pi$
$798$		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
$805$	−645.992	−	955.978i	−0.0282835	−	0.0418557i
$806$		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
$819$	17564.8	+	19468.6i	0.749407	+	0.830631i
$820$		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	−0.982966	−	0.183786i	$-0.941165\pi$
$823$	−7846.13	+	13589.9i	−0.332319	+	0.575594i	0.650647	+	0.759381i	$0.274498\pi$
$824$		0			0
$825$	−147.109	+	301.678i	−0.00620811	+	0.0127310i
$826$		0			0
$827$		−	17201.9i		−	0.723301i	−0.932314	−	0.361650i	$-0.882213\pi$
$827$		−	17201.9i		−	0.723301i	0.932314	−	0.361650i	$-0.117787\pi$
$828$		0			0
$829$	16605.1	+	9586.94i	0.695679	+	0.401650i	0.805736	−	0.592275i	$-0.201770\pi$
$829$	16605.1	+	9586.94i	0.695679	+	0.401650i	−0.110057	+	0.993925i	$0.535103\pi$
$830$		0			0
$831$	803.995	+	11485.0i	0.0335623	+	0.479435i
$832$		0			0
$833$	35098.0	−	4993.23i	1.45987	−	0.207689i
$834$		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
$847$	−1739.71	−	24580.4i	−0.0705753	−	0.997158i
$848$		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	$-0.668953\pi$
$853$		−	42970.3i		−	1.72482i	0.506207	−	0.862412i	$-0.331047\pi$
$854$		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	$0.426929\pi$
$857$	−18302.7	+	31701.2i	−0.729532	+	1.26359i	−0.957081	+	0.289820i	$0.906404\pi$
$858$		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
$861$	30377.3	−	4297.82i	1.20239	−	0.170115i
$862$		0			0
$863$	11425.0	−	6596.25i	0.450652	−	0.260184i	−0.257453	−	0.966291i	$-0.582883\pi$
$863$	11425.0	−	6596.25i	0.450652	−	0.260184i	0.708106	+	0.706106i	$0.249550\pi$
$864$		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
$875$	−7418.13	−	3610.30i	−0.286604	−	0.139486i
$876$		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	$-0.357389\pi$
$881$	22655.3			0.866376			0.433188	+	0.901304i	$0.357389\pi$
$882$		0			0
$883$	−32700.9			−1.24629			−0.623145	−	0.782107i	$-0.714145\pi$
$883$	−32700.9			−1.24629			−0.623145	+	0.782107i	$0.714145\pi$
$884$		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
$889$	14746.9	+	7177.10i	0.556349	+	0.270768i
$890$		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
$903$	16056.9	−	2271.76i	0.591741	−	0.0837202i
$904$		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	$0.470418\pi$
$907$	−22286.5	+	38601.3i	−0.815888	+	1.41316i	−0.908688	+	0.417475i	$0.862915\pi$
$908$		0			0
$909$	14815.1	+	18956.5i	0.540578	+	0.691690i
$910$		0			0
$911$		−	581.992i		−	0.0211660i	−0.999944	−	0.0105830i	$-0.996631\pi$
$911$		−	581.992i		−	0.0211660i	0.999944	−	0.0105830i	$-0.00336874\pi$
$912$		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
$917$	−2209.49	−	31217.9i	−0.0795679	−	1.12421i
$918$		0			0
$919$	−20983.4	−	36344.4i	−0.753188	−	1.30456i	−0.946270	−	0.323377i	$-0.895182\pi$
$919$	−20983.4	−	36344.4i	−0.753188	−	1.30456i	0.193082	−	0.981183i	$-0.438152\pi$
$920$		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	0.865406	−	0.501071i	$-0.167060\pi$
$929$	−35.0320	−	60.6772i	−0.00123720	−	0.00214290i	−0.866643	+	0.498928i	$0.833727\pi$
$930$		0			0
$931$	−31875.2	−	12815.8i	−1.12209	−	0.451149i
$932$		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	$0.154266\pi$
$937$			26725.4i			0.931783i	−0.884842	+	0.465892i	$0.845734\pi$
$938$		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	$0.403246\pi$
$941$	−19532.8	+	33831.7i	−0.676673	+	1.17203i	−0.975977	+	0.217875i	$0.930088\pi$
$942$		0			0
$943$	−1159.72	+	669.564i	−0.0400484	+	0.0231220i
$944$		0			0
$945$	37032.0	−	10661.9i	1.27476	−	0.367016i
$946$		0			0
$947$	−25718.0	+	14848.3i	−0.882495	+	0.509509i	−0.871480	−	0.490430i	$-0.836840\pi$
$947$	−25718.0	+	14848.3i	−0.882495	+	0.509509i	−0.0110151	+	0.999939i	$0.503506\pi$
$948$		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
$959$	19997.9	+	29594.1i	0.673373	+	0.996499i
$960$		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	$-0.443226\pi$
$967$	10669.9			0.354831			0.177416	+	0.984136i	$0.443226\pi$
$968$		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
$973$	3263.92	−	6706.42i	0.107540	−	0.220964i
$974$		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
$987$	37250.0	+	47587.4i	1.20130	+	1.53467i
$988$		0			0
$989$	−613.008	+	353.921i	−0.0197093	+	0.0113792i
$990$		0			0
$991$	14449.0	−	25026.5i	0.463157	−	0.802212i	−0.535959	−	0.844244i	$-0.680050\pi$
$991$	14449.0	−	25026.5i	0.463157	−	0.802212i	0.999116	+	0.0420324i	$0.0133833\pi$
$992$		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	0.353051	−	0.935604i	$-0.385144\pi$
$997$	−8836.00	−	5101.46i	−0.280681	−	0.162051i	−0.633732	+	0.773553i	$0.718478\pi$
$998$		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	336.4.bc.c.17.1		12
3.2	odd	2	inner	336.4.bc.c.17.3		12
4.3	odd	2		84.4.k.c.17.6	yes	12
7.5	odd	6	inner	336.4.bc.c.257.3		12
12.11	even	2		84.4.k.c.17.4	yes	12
21.5	even	6	inner	336.4.bc.c.257.1		12
28.3	even	6		588.4.f.c.293.10		12
28.11	odd	6		588.4.f.c.293.3		12
28.19	even	6		84.4.k.c.5.4	✓	12
28.23	odd	6		588.4.k.c.509.3		12
28.27	even	2		588.4.k.c.521.1		12
84.11	even	6		588.4.f.c.293.9		12
84.23	even	6		588.4.k.c.509.1		12
84.47	odd	6		84.4.k.c.5.6	yes	12
84.59	odd	6		588.4.f.c.293.4		12
84.83	odd	2		588.4.k.c.521.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.c.5.4	✓	12	28.19	even	6
84.4.k.c.5.6	yes	12	84.47	odd	6
84.4.k.c.17.4	yes	12	12.11	even	2
84.4.k.c.17.6	yes	12	4.3	odd	2
336.4.bc.c.17.1		12	1.1	even	1	trivial
336.4.bc.c.17.3		12	3.2	odd	2	inner
336.4.bc.c.257.1		12	21.5	even	6	inner
336.4.bc.c.257.3		12	7.5	odd	6	inner
588.4.f.c.293.3		12	28.11	odd	6
588.4.f.c.293.4		12	84.59	odd	6
588.4.f.c.293.9		12	84.11	even	6
588.4.f.c.293.10		12	28.3	even	6
588.4.k.c.509.1		12	84.23	even	6
588.4.k.c.509.3		12	28.23	odd	6
588.4.k.c.521.1		12	28.27	even	2
588.4.k.c.521.3		12	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.30758 + 2.90598i) q^{3} +(-7.41560 - 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(10.1105 - 25.0355i) q^{9} +O(q^{10})\)	\(q+(-4.30758 + 2.90598i) q^{3} +(-7.41560 - 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(10.1105 - 25.0355i) q^{9} +(-0.589052 - 0.340089i) q^{11} +52.4373i q^{13} +(69.2683 + 33.7779i) q^{15} +(51.6784 - 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(-95.2852 + 13.4811i) q^{21} +(3.63771 - 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(29.2008 + 137.224i) q^{27} +53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(3.52568 - 0.246811i) q^{33} +(-19.3922 - 273.992i) q^{35} +(25.2855 + 43.7957i) q^{37} +(-152.382 - 225.878i) q^{39} -318.804 q^{41} -168.515 q^{43} +(-396.537 + 55.7917i) q^{45} +(-313.988 - 543.844i) q^{47} +(211.629 + 269.930i) q^{49} +(37.5043 + 535.747i) q^{51} +(-625.481 - 361.121i) q^{53} +10.0879i q^{55} +(228.115 - 467.795i) q^{57} +(-263.093 + 455.691i) q^{59} +(205.162 - 118.450i) q^{61} +(371.273 - 334.968i) q^{63} +(673.515 - 388.854i) q^{65} +(149.359 - 258.697i) q^{67} +(-9.56651 + 19.6181i) q^{69} +379.893i q^{71} +(-559.469 - 323.010i) q^{73} +(-34.4592 - 492.246i) q^{75} +(-7.05302 - 10.4375i) q^{77} +(211.386 + 366.132i) q^{79} +(-524.554 - 506.245i) q^{81} -391.295 q^{83} -1532.91 q^{85} +(-155.577 - 230.614i) q^{87} +(316.431 + 548.075i) q^{89} +(-424.987 + 873.226i) q^{91} +(1412.26 - 98.8635i) q^{93} +(1286.48 + 742.752i) q^{95} +1432.13i q^{97} +(-14.4699 + 11.3087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 42 q^{7} - 84 q^{9}+O(q^{10}) \) 12 * q + 42 * q^7 - 84 * q^9	\( 12 q + 42 q^{7} - 84 q^{9} - 132 q^{15} - 204 q^{19} - 378 q^{21} - 444 q^{25} - 1458 q^{31} - 108 q^{33} + 240 q^{37} + 432 q^{39} - 342 q^{45} - 1218 q^{49} + 300 q^{51} + 180 q^{57} + 2148 q^{61} - 1596 q^{63} - 1980 q^{67} - 3084 q^{73} + 3384 q^{75} + 438 q^{79} + 1008 q^{81} - 6144 q^{85} + 2898 q^{87} - 3780 q^{91} + 882 q^{93} - 9216 q^{99}+O(q^{100}) \) 12 * q + 42 * q^7 - 84 * q^9 - 132 * q^15 - 204 * q^19 - 378 * q^21 - 444 * q^25 - 1458 * q^31 - 108 * q^33 + 240 * q^37 + 432 * q^39 - 342 * q^45 - 1218 * q^49 + 300 * q^51 + 180 * q^57 + 2148 * q^61 - 1596 * q^63 - 1980 * q^67 - 3084 * q^73 + 3384 * q^75 + 438 * q^79 + 1008 * q^81 - 6144 * q^85 + 2898 * q^87 - 3780 * q^91 + 882 * q^93 - 9216 * q^99

Introduction

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