LMFDB - Embedded newform 336.4.bc.c.17.3

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			17.3
Root			$2.99268 + 0.209499i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.c.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.362863 - 5.18347i) q^{3} +(7.41560 + 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(-26.7367 - 3.76177i) q^{9} +O(q^{10})$	\(q+(0.362863 - 5.18347i) q^{3} +(7.41560 + 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(-26.7367 - 3.76177i) q^{9} +(0.589052 + 0.340089i) q^{11} +52.4373i q^{13} +(69.2683 - 33.7779i) q^{15} +(-51.6784 + 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(48.0530 - 83.3781i) q^{21} +(-3.63771 + 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(-29.2008 + 137.224i) q^{27} -53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(1.97659 - 2.92992i) q^{33} +(19.3922 + 273.992i) q^{35} +(25.2855 + 43.7957i) q^{37} +(271.807 + 19.0276i) q^{39} +318.804 q^{41} -168.515 q^{43} +(-149.951 - 371.307i) q^{45} +(313.988 + 543.844i) q^{47} +(211.629 + 269.930i) q^{49} +(445.218 + 300.353i) q^{51} +(625.481 + 361.121i) q^{53} +10.0879i q^{55} +(228.115 + 467.795i) q^{57} +(263.093 - 455.691i) q^{59} +(205.162 - 118.450i) q^{61} +(-414.751 - 279.336i) q^{63} +(-673.515 + 388.854i) q^{65} +(149.359 - 258.697i) q^{67} +(9.56651 + 19.6181i) q^{69} -379.893i q^{71} +(-559.469 - 323.010i) q^{73} +(409.068 + 275.966i) q^{75} +(7.05302 + 10.4375i) q^{77} +(211.386 + 366.132i) q^{79} +(700.698 + 201.155i) q^{81} +391.295 q^{83} -1532.91 q^{85} +(-277.506 - 19.4265i) q^{87} +(-316.431 - 548.075i) q^{89} +(-424.987 + 873.226i) q^{91} +(-791.747 + 1173.62i) q^{93} +(-1286.48 - 742.752i) q^{95} +1432.13i q^{97} +(-14.4699 - 11.3087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.362863	−	5.18347i	0.0698330	−	0.997559i
$3$	0.362863	−	5.18347i	0.0698330	−	0.997559i
$4$		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
$7$	16.6528	+	8.10467i	0.899164	+	0.437611i
$7$	16.6528	+	8.10467i	0.899164	+	0.437611i
$8$		0			0
$9$	−26.7367	−	3.76177i	−0.990247	−	0.139325i
$10$		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	$0.188955\pi$
$13$			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	$0.430559\pi$
$17$	−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
$21$	48.0530	−	83.3781i	0.499334	−	0.866410i
$22$		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	$-0.945169\pi$
$29$		−	53.5367i		−	0.342811i	0.985201	−	0.171406i	$-0.0548308\pi$
$30$		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
$33$	1.97659	−	2.92992i	0.0104266	−	0.0154556i
$34$		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
$39$	271.807	+	19.0276i	1.11600	+	0.0781243i
$40$		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	$-0.596592\pi$
$43$	−168.515			−0.597634			−0.298817	+	0.954310i	$0.596592\pi$
$44$		0			0
$45$	−149.951	−	371.307i	−0.496743	−	1.23003i
$46$		0			0
$47$	313.988	+	543.844i	0.974467	+	1.68783i	0.681684	+	0.731647i	$0.261248\pi$
$47$	313.988	+	543.844i	0.974467	+	1.68783i	0.292782	+	0.956179i	$0.405419\pi$
$48$		0			0
$49$	211.629	+	269.930i	0.616993	+	0.786969i
$50$		0			0
$51$	445.218	+	300.353i	1.22241	+	0.824663i
$52$		0			0
$53$	625.481	+	361.121i	1.62106	+	0.935922i	0.986636	+	0.162939i	$0.0520974\pi$
$53$	625.481	+	361.121i	1.62106	+	0.935922i	0.634427	+	0.772982i	$0.281236\pi$
$54$		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	$-0.636175\pi$
$59$	263.093	−	455.691i	0.580539	−	1.00552i	0.995415	−	0.0956456i	$-0.0304916\pi$
$60$		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
$63$	−414.751	−	279.336i	−0.829424	−	0.558619i
$64$		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	$-0.897157\pi$
$71$		−	379.893i		−	0.634999i	0.948258	−	0.317500i	$-0.102843\pi$
$72$		0			0
$73$	−559.469	−	323.010i	−0.896999	−	0.517882i	−0.0207735	−	0.999784i	$-0.506613\pi$
$73$	−559.469	−	323.010i	−0.896999	−	0.517882i	−0.876225	+	0.481902i	$0.839946\pi$
$74$		0			0
$75$	409.068	+	275.966i	0.629802	+	0.424877i
$76$		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
$81$	700.698	+	201.155i	0.961177	+	0.275932i
$82$		0			0
$83$	391.295			0.517472			0.258736	−	0.965948i	$-0.416694\pi$
$83$	391.295			0.517472			0.258736	+	0.965948i	$0.416694\pi$
$84$		0			0
$85$	−1532.91			−1.95608
$86$		0			0
$87$	−277.506	−	19.4265i	−0.341974	−	0.0239395i
$88$		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
$91$	−424.987	+	873.226i	−0.489569	+	1.00592i
$92$		0			0
$93$	−791.747	+	1173.62i	−0.882799	+	1.30859i
$94$		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	−0.558672	−	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
$105$	1427.27	−	1.09716i	1.32654	−	0.00101973i
$106$		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	$-0.904791\pi$
$113$		−	707.915i		−	0.589337i	0.955600	−	0.294668i	$-0.0952091\pi$
$114$		0			0
$115$	−53.9517	−	31.1490i	−0.0437480	−	0.0252579i
$116$		0			0
$117$	197.257	−	1402.00i	0.155867	−	1.10782i
$118$		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
$123$	115.682	−	1652.51i	0.0848026	−	1.21140i
$124$		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
$129$	−61.1477	+	873.490i	−0.0417345	+	0.596175i
$130$		0			0
$131$	844.911	+	1463.43i	0.563513	+	0.976034i	0.997186	+	0.0749634i	$0.0238840\pi$
$131$	844.911	+	1463.43i	0.563513	+	0.976034i	−0.433673	+	0.901070i	$0.642783\pi$
$132$		0			0
$133$	−1850.37	+	130.963i	−1.20637	+	0.0853828i
$134$		0			0
$135$	−1979.07	+	642.535i	−1.26171	+	0.409634i
$136$		0			0
$137$	−1670.17	−	964.276i	−1.04155	−	0.601340i	−0.121280	−	0.992618i	$-0.538700\pi$
$137$	−1670.17	−	964.276i	−1.04155	−	0.601340i	−0.920273	+	0.391278i	$0.872033\pi$
$138$		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
$147$	1475.97	−	999.022i	0.828134	−	0.560530i
$148$		0			0
$149$	−1392.62	+	804.032i	−0.765692	+	0.442073i	−0.831336	−	0.555770i	$-0.812423\pi$
$149$	−1392.62	+	804.032i	−0.765692	+	0.442073i	0.0656434	+	0.997843i	$0.479090\pi$
$150$		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
$159$	2098.82	−	3111.12i	1.04684	−	1.55175i
$160$		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
$165$	52.2901	+	3.66051i	0.0246714	+	0.00172709i
$166$		0			0
$167$	−1013.86			−0.469791			−0.234896	−	0.972021i	$-0.575475\pi$
$167$	−1013.86			−0.469791			−0.234896	+	0.972021i	$0.575475\pi$
$168$		0			0
$169$	−552.672			−0.251558
$170$		0			0
$171$	2507.57	−	1012.68i	1.12140	−	0.452874i
$172$		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
$175$	−1457.26	+	984.725i	−0.629475	+	0.425361i
$176$		0			0
$177$	−2266.59	−	1529.09i	−0.962528	−	0.649341i
$178$		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	$-0.896323\pi$
$181$		−	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
$189$	−1598.43	+	2048.49i	−0.615176	+	0.788389i
$190$		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	$-0.924589\pi$
$197$		−	1297.91i		−	0.469401i	0.972068	−	0.234700i	$-0.0754109\pi$
$198$		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
$201$	−1286.75	−	868.067i	−0.451544	−	0.304621i
$202$		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
$207$	105.161	−	42.4690i	0.0353101	−	0.0142599i
$208$		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
$213$	−1969.16	−	137.849i	−0.633449	−	0.0443439i
$214$		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
$219$	−1877.32	+	2782.78i	−0.579258	+	0.858644i
$220$		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	−0.997229	−	0.0743914i	$-0.976299\pi$
$227$	−1484.97	+	2572.05i	−0.434190	+	0.752039i	0.563039	+	0.826430i	$0.309632\pi$
$228$		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
$231$	56.6617	−	32.7717i	0.0161388	−	0.00933429i
$232$		0			0
$233$	5177.16	−	2989.03i	1.45565	−	0.840421i	0.456859	−	0.889539i	$-0.348974\pi$
$233$	5177.16	−	2989.03i	1.45565	−	0.840421i	0.998793	+	0.0491180i	$0.0156410\pi$
$234$		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	0.896127	−	0.443798i	$-0.146369\pi$
$241$	3591.11	+	2073.33i	0.959851	+	0.554170i	0.0637236	+	0.997968i	$0.479702\pi$
$242$		0			0
$243$	1296.94	−	3559.05i	0.342380	−	0.939561i
$244$		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
$249$	141.986	−	2028.27i	0.0361366	−	0.516209i
$250$		0			0
$251$	7611.35			1.91404			0.957021	−	0.290020i	$-0.0936619\pi$
$251$	7611.35			1.91404			0.957021	+	0.290020i	$0.0936619\pi$
$252$		0			0
$253$	−2.85707			−0.000709970
$254$		0			0
$255$	−556.235	+	7945.77i	−0.136599	+	1.95131i
$256$		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
$259$	66.1228	+	934.249i	0.0158636	+	0.224137i
$260$		0			0
$261$	−201.393	+	1431.39i	−0.0477622	+	0.339468i
$262$		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
$273$	4372.13	+	2519.77i	0.969279	+	0.558620i
$274$		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	$-0.785345\pi$
$281$		−	5882.33i		−	1.24879i	0.781108	−	0.624395i	$-0.214655\pi$
$282$		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
$285$	−4316.85	+	6398.93i	−0.897221	+	1.32996i
$286$		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
$291$	7423.40	+	519.667i	1.49542	+	0.104685i
$292$		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
$297$	−63.8690	+	70.9009i	−0.0124783	+	0.0138522i
$298$		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
$303$	−3838.37	−	2589.44i	−0.727751	−	0.490956i
$304$		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	−0.777027	−	0.629468i	$-0.783273\pi$
$311$	859.000	−	1487.83i	0.156622	−	0.271277i	0.933648	+	0.358191i	$0.116606\pi$
$312$		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
$315$	512.215	−	7398.59i	0.0916192	−	1.32338i
$316$		0			0
$317$	1541.66	−	890.076i	0.273149	−	0.157702i	−0.357169	−	0.934040i	$-0.616258\pi$
$317$	1541.66	−	890.076i	0.273149	−	0.157702i	0.630318	+	0.776337i	$0.282925\pi$
$318$		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
$327$	−4283.53	−	2889.76i	−0.724404	−	0.488697i
$328$		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
$333$	−511.299	−	1266.07i	−0.0841412	−	0.208349i
$334$		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
$339$	−3669.45	−	256.876i	−0.587898	−	0.0411551i
$340$		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
$345$	−181.037	+	268.354i	−0.0282513	+	0.0418774i
$346$		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	$-0.961244\pi$
$349$		−	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	$0.374690\pi$
$353$	−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
$357$	4979.84	+	8610.05i	0.738267	+	1.27645i
$358$		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
$369$	−8523.76	−	1199.27i	−1.20252	−	0.169191i
$370$		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
$375$	161.641	−	2309.03i	0.0222589	−	0.317967i
$376$		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
$381$	321.334	−	4590.23i	0.0432085	−	0.617229i
$382$		0			0
$383$	−2096.49	−	3631.22i	−0.279701	−	0.484456i	0.691610	−	0.722272i	$-0.256902\pi$
$383$	−2096.49	−	3631.22i	−0.279701	−	0.484456i	−0.971310	+	0.237816i	$0.923569\pi$
$384$		0			0
$385$	−81.7588	+	167.991i	−0.0108229	+	0.0222379i
$386$		0			0
$387$	4505.52	+	633.914i	0.591805	+	0.0832653i
$388$		0			0
$389$	−5025.75	−	2901.62i	−0.655053	−	0.378195i	0.135336	−	0.990800i	$-0.456788\pi$
$389$	−5025.75	−	2901.62i	−0.655053	−	0.378195i	−0.790390	+	0.612605i	$0.790122\pi$
$390$		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
$399$	7.40953	+	9638.87i	0.000929675	+	1.20939i
$400$		0			0
$401$	−6782.69	+	3915.99i	−0.844667	+	0.487669i	−0.858848	−	0.512231i	$-0.828819\pi$
$401$	−6782.69	+	3915.99i	−0.844667	+	0.487669i	0.0141808	+	0.999899i	$0.495486\pi$
$402$		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
$411$	−5604.34	+	8307.39i	−0.672607	+	0.997016i
$412$		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
$417$	−2087.49	−	146.133i	−0.245144	−	0.0171610i
$418$		0			0
$419$	−9478.94			−1.10519			−0.552597	−	0.833448i	$-0.686363\pi$
$419$	−9478.94			−1.10519			−0.552597	+	0.833448i	$0.686363\pi$
$420$		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
$423$	−6349.19	−	15721.7i	−0.729806	−	1.80713i
$424$		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
$429$	153.637	+	103.647i	0.0172906	+	0.0116646i
$430$		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	$0.0315303\pi$
$433$			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
$441$	−4642.83	−	8013.13i	−0.501331	−	0.865256i
$442$		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	$0.0917827\pi$
$449$			5410.98i			0.568730i	−0.958716	+	0.284365i	$0.908217\pi$
$450$		0			0
$451$	187.792	+	108.422i	0.0196071	+	0.0113201i
$452$		0			0
$453$	−1578.95	−	1065.19i	−0.163765	−	0.110479i
$454$		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
$459$	−10773.8	−	9705.25i	−1.09559	−	0.986933i
$460$		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	$-0.302442\pi$
$463$	11587.7			1.16313			0.581563	+	0.813502i	$0.302442\pi$
$464$		0			0
$465$	−20945.5	−	1466.26i	−2.08887	−	0.146229i
$466$		0			0
$467$	−1879.76	−	3255.83i	−0.186263	−	0.322617i	0.757738	−	0.652558i	$-0.226304\pi$
$467$	−1879.76	−	3255.83i	−0.186263	−	0.322617i	−0.944001	+	0.329942i	$0.892971\pi$
$468$		0			0
$469$	4583.88	−	3097.51i	0.451309	−	0.304968i
$470$		0			0
$471$	1243.59	−	1843.39i	0.121659	−	0.180337i
$472$		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	−0.710394	−	0.703804i	$-0.751483\pi$
$479$	2666.10	−	4617.82i	0.254316	−	0.440488i	0.964709	+	0.263317i	$0.0848164\pi$
$480$		0			0
$481$	−2296.53	+	1325.90i	−0.217698	+	0.125688i
$482$		0			0
$483$	0.310736	+	404.228i	2.92732e−5	+	0.0380808i
$484$		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	$-0.792280\pi$
$491$		−	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
$495$	37.9483	−	269.716i	0.00344575	−	0.0244906i
$496$		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
$501$	−367.893	+	5255.33i	−0.0328069	+	0.468644i
$502$		0			0
$503$	12215.5			1.08283			0.541414	−	0.840756i	$-0.317889\pi$
$503$	12215.5			1.08283			0.541414	+	0.840756i	$0.317889\pi$
$504$		0			0
$505$	13215.7			1.16454
$506$		0			0
$507$	−200.544	+	2864.76i	−0.0175670	+	0.250943i
$508$		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
$511$	−6698.82	−	9913.31i	−0.579918	−	0.858198i
$512$		0			0
$513$	−4339.28	−	13365.4i	−0.373458	−	1.15029i
$514$		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
$525$	4575.50	+	7910.95i	0.380364	+	0.657643i
$526$		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
$537$	4013.34	−	5949.04i	0.322511	−	0.478064i
$538$		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
$543$	−8077.79	−	565.477i	−0.638400	−	0.0446905i
$544$		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
$549$	−5930.92	+	2395.19i	−0.461066	+	0.186201i
$550$		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
$555$	3230.81	+	2179.57i	0.247099	+	0.166698i
$556$		0			0
$557$	7010.50	+	4047.52i	0.533294	+	0.307897i	0.742357	−	0.670005i	$-0.233708\pi$
$557$	7010.50	+	4047.52i	0.533294	+	0.307897i	−0.209063	+	0.977902i	$0.567041\pi$
$558$		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	−0.991834	−	0.127535i	$-0.959294\pi$
$563$	−5149.34	+	8918.92i	−0.385469	+	0.667651i	0.606366	+	0.795186i	$0.292627\pi$
$564$		0			0
$565$	9092.60	−	5249.62i	0.677042	−	0.390890i
$566$		0			0
$567$	10038.3	+	9028.71i	0.743505	+	0.668730i
$568$		0			0
$569$	−2507.30	+	1447.59i	−0.184730	+	0.106654i	−0.589513	−	0.807759i	$-0.700680\pi$
$569$	−2507.30	+	1447.59i	−0.184730	+	0.106654i	0.404783	+	0.914413i	$0.367347\pi$
$570$		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
$579$	15073.4	+	10168.8i	1.08191	+	0.729881i
$580$		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
$585$	19470.3	−	7863.05i	1.37607	−	0.555722i
$586$		0			0
$587$	1093.47			0.0768861			0.0384431	−	0.999261i	$-0.487760\pi$
$587$	1093.47			0.0768861			0.0384431	+	0.999261i	$0.487760\pi$
$588$		0			0
$589$	27289.2			1.90905
$590$		0			0
$591$	−6727.65	−	470.962i	−0.468255	−	0.0327796i
$592$		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
$595$	−25527.1	−	12423.7i	−1.75884	−	0.856004i
$596$		0			0
$597$	−10277.3	+	15234.2i	−0.704561	+	1.04438i
$598$		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	$-0.841828\pi$
$601$		−	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
$609$	−4463.79	−	2572.60i	−0.297015	−	0.171177i
$610$		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	$-0.684183\pi$
$617$		−	25662.2i		−	1.67443i	0.546877	−	0.837213i	$-0.315817\pi$
$618$		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
$621$	−181.978	−	560.509i	−0.0117593	−	0.0362197i
$622$		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
$627$	−24.7208	+	353.135i	−0.00157457	+	0.0224926i
$628$		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
$633$	773.267	−	11046.1i	0.0485539	−	0.693588i
$634$		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
$639$	−1429.07	+	10157.1i	−0.0884713	+	0.628806i
$640$		0			0
$641$	12156.4	+	7018.51i	0.749063	+	0.432472i	0.825355	−	0.564614i	$-0.190975\pi$
$641$	12156.4	+	7018.51i	0.749063	+	0.432472i	−0.0762922	+	0.997086i	$0.524308\pi$
$642$		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	−0.783421	−	0.621492i	$-0.786527\pi$
$647$	2411.27	−	4176.44i	0.146517	−	0.253775i	0.929938	+	0.367716i	$0.119860\pi$
$648$		0			0
$649$	309.951	−	178.950i	0.0187467	−	0.0108234i
$650$		0			0
$651$	−22696.6	+	13127.1i	−1.36643	+	0.790312i
$652$		0			0
$653$	−2592.48	+	1496.77i	−0.155362	+	0.0896983i	−0.575666	−	0.817685i	$-0.695257\pi$
$653$	−2592.48	+	1496.77i	−0.155362	+	0.0896983i	0.420303	+	0.907384i	$0.361924\pi$
$654$		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	0.894461	−	0.447146i	$-0.147560\pi$
$661$	16220.2	+	9364.73i	0.954451	+	0.551053i	0.0599904	+	0.998199i	$0.480893\pi$
$662$		0			0
$663$	−15749.7	+	23346.0i	−0.922576	+	1.36755i
$664$		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
$669$	−31867.7	−	2230.86i	−1.84167	−	0.128924i
$670$		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
$675$	−9899.00	−	8917.22i	−0.564463	−	0.508480i
$676$		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
$679$	−11606.9	+	23848.9i	−0.656014	+	1.34792i
$680$		0			0
$681$	12793.3	+	8630.60i	0.719882	+	0.485647i
$682$		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
$693$	−149.311	−	305.596i	−0.00818449	−	0.0167513i
$694$		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	$0.192451\pi$
$701$			21100.3i			1.13687i	−0.822728	+	0.568435i	$0.807549\pi$
$702$		0			0
$703$	−4386.61	−	2532.61i	−0.235340	−	0.135874i
$704$		0			0
$705$	40119.3	+	27065.3i	2.14324	+	1.44587i
$706$		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
$711$	−4274.46	−	10584.3i	−0.225464	−	0.558289i
$712$		0			0
$713$	1144.44			0.0601114
$714$		0			0
$715$	−528.981			−0.0276682
$716$		0			0
$717$	28881.4	+	2021.81i	1.50432	+	0.105308i
$718$		0			0
$719$	−4247.60	−	7357.06i	−0.220318	−	0.381603i	0.734586	−	0.678515i	$-0.237376\pi$
$719$	−4247.60	−	7357.06i	−0.220318	−	0.381603i	−0.954905	+	0.296913i	$0.904043\pi$
$720$		0			0
$721$	−22771.6	+	1611.69i	−1.17622	+	0.0832489i
$722$		0			0
$723$	12050.1	−	17862.1i	0.619846	−	0.918808i
$724$		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
$735$	23776.8	+	11549.3i	1.19323	+	0.579593i
$736$		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	$0.332817\pi$
$743$			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
$747$	−10461.9	−	1471.96i	−0.512425	−	0.0720969i
$748$		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
$753$	2761.88	−	39453.2i	0.133663	−	1.90937i
$754$		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
$759$	−1.03672	+	14.8095i	−4.95793e−5	+	0.000708237i
$760$		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
$763$	15259.6	−	10311.5i	0.724028	−	0.489254i
$764$		0			0
$765$	40984.8	+	5766.45i	1.93700	+	0.272531i
$766$		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	−0.942550	−	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
$777$	4866.64	−	3.74105i	0.224697	−	0.000172728i
$778$		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
$789$	−14903.3	+	22091.5i	−0.672463	+	0.996802i
$790$		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
$795$	55523.9	+	3886.89i	2.47702	+	0.173401i
$796$		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
$801$	6398.58	+	15844.0i	0.282250	+	0.698903i
$802$		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
$807$	174.485	+	117.711i	0.00761109	+	0.00513459i
$808$		0			0
$809$	8105.17	+	4679.52i	0.352240	+	0.203366i	0.665672	−	0.746245i	$-0.268145\pi$
$809$	8105.17	+	4679.52i	0.352240	+	0.203366i	−0.313431	+	0.949611i	$0.601479\pi$
$810$		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
$819$	14647.6	−	21748.4i	0.624944	−	0.927902i
$820$		0			0
$821$	23251.5	−	13424.3i	0.988407	−	0.570657i	0.0836095	−	0.996499i	$-0.473355\pi$
$821$	23251.5	−	13424.3i	0.988407	−	0.570657i	0.904798	+	0.425841i	$0.140022\pi$
$822$		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	$0.117787\pi$
$827$			17201.9i			0.723301i	−0.932314	+	0.361650i	$0.882213\pi$
$828$		0			0
$829$	16605.1	+	9586.94i	0.695679	+	0.401650i	0.805736	−	0.592275i	$-0.201770\pi$
$829$	16605.1	+	9586.94i	0.695679	+	0.401650i	−0.110057	+	0.993925i	$0.535103\pi$
$830$		0			0
$831$	−9544.31	−	6438.78i	−0.398422	−	0.268783i
$832$		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
$837$	25583.6	−	28400.3i	1.05651	−	1.17283i
$838$		0			0
$839$	−10848.7			−0.446410			−0.223205	−	0.974771i	$-0.571652\pi$
$839$	−10848.7			−0.446410			−0.223205	+	0.974771i	$0.571652\pi$
$840$		0			0
$841$	21522.8			0.882481
$842$		0			0
$843$	−30490.8	−	2134.48i	−1.24574	−	0.0872068i
$844$		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
$849$	4442.02	−	6584.48i	0.179564	−	0.266171i
$850$		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	$-0.573071\pi$
$857$	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
$861$	15319.5	−	26581.3i	0.606373	−	1.05214i
$862$		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
$873$	5387.35	−	38290.4i	0.208859	−	1.48446i
$874$		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
$879$	2191.10	−	31299.7i	0.0840773	−	1.20104i
$880$		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	$-0.714145\pi$
$883$	−32700.9			−1.24629			−0.623145	+	0.782107i	$0.714145\pi$
$884$		0			0
$885$	2831.77	−	40451.7i	0.107558	−	1.53646i
$886$		0			0
$887$	−12678.9	−	21960.5i	−0.479950	−	0.831299i	0.519785	−	0.854297i	$-0.326012\pi$
$887$	−12678.9	−	21960.5i	−0.479950	−	0.831299i	−0.999735	+	0.0229985i	$0.992679\pi$
$888$		0			0
$889$	14746.9	+	7177.10i	0.556349	+	0.270768i
$890$		0			0
$891$	344.337	+	356.790i	0.0129469	+	0.0134152i
$892$		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
$903$	−8097.63	+	14050.4i	−0.298419	+	0.517796i
$904$		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	$0.00336874\pi$
$911$			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
$915$	10210.2	−	15134.8i	0.368895	−	0.546819i
$916$		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
$921$	37486.7	+	2624.22i	1.34118	+	0.0938880i
$922$		0			0
$923$	19920.5			0.710393
$924$		0			0
$925$	−4802.45			−0.170707
$926$		0			0
$927$	30859.4	−	12462.5i	1.09337	−	0.441556i
$928$		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
$931$	−31875.2	−	12815.8i	−1.12209	−	0.451149i
$932$		0			0
$933$	−7400.43	−	4992.48i	−0.259677	−	0.175184i
$934$		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	$-0.596754\pi$
$941$	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
$945$	−38164.5	−	5339.72i	−1.31375	−	0.183811i
$946$		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	$-0.835703\pi$
$953$		−	29039.6i		−	0.987079i	0.869723	−	0.493539i	$-0.164297\pi$
$954$		0			0
$955$	−27949.0	−	16136.4i	−0.947026	−	0.546766i
$956$		0			0
$957$	−156.859	−	105.820i	−0.00529835	−	0.00357437i
$958$		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
$963$	−16932.8	+	6838.28i	−0.566617	+	0.228827i
$964$		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
$969$	−53660.8	−	3756.46i	−1.77898	−	0.124536i
$970$		0			0
$971$	−20680.1	−	35819.0i	−0.683478	−	1.18382i	−0.973913	−	0.226923i	$-0.927133\pi$
$971$	−20680.1	−	35819.0i	−0.683478	−	1.18382i	0.290435	−	0.956895i	$-0.406200\pi$
$972$		0			0
$973$	3263.92	−	6706.42i	0.107540	−	0.220964i
$974$		0			0
$975$	−14470.9	+	21450.4i	−0.475323	+	0.704578i
$976$		0			0
$977$	31547.9	+	18214.2i	1.03307	+	0.596443i	0.917862	−	0.396899i	$-0.129914\pi$
$977$	31547.9	+	18214.2i	1.03307	+	0.596443i	0.115207	+	0.993342i	$0.463247\pi$
$978$		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	−0.871845	−	0.489782i	$-0.837076\pi$
$983$	−362.416	+	627.723i	−0.0117592	+	0.0203675i	0.860086	+	0.510149i	$0.170410\pi$
$984$		0			0
$985$	16670.6	−	9624.75i	0.539257	−	0.311340i
$986$		0			0
$987$	60432.8	−	46.4555i	1.94893	−	0.00149817i
$988$		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
$999$	−6748.16	+	2190.89i	−0.213716	+	0.0693862i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.362863 - 5.18347i) q^{3} +(7.41560 + 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(-26.7367 - 3.76177i) q^{9} +O(q^{10})\)	\(q+(0.362863 - 5.18347i) q^{3} +(7.41560 + 12.8442i) q^{5} +(16.6528 + 8.10467i) q^{7} +(-26.7367 - 3.76177i) q^{9} +(0.589052 + 0.340089i) q^{11} +52.4373i q^{13} +(69.2683 - 33.7779i) q^{15} +(-51.6784 + 89.5096i) q^{17} +(-86.7417 + 50.0804i) q^{19} +(48.0530 - 83.3781i) q^{21} +(-3.63771 + 2.10024i) q^{23} +(-47.4824 + 82.2418i) q^{25} +(-29.2008 + 137.224i) q^{27} -53.5367i q^{29} +(-235.952 - 136.227i) q^{31} +(1.97659 - 2.92992i) q^{33} +(19.3922 + 273.992i) q^{35} +(25.2855 + 43.7957i) q^{37} +(271.807 + 19.0276i) q^{39} +318.804 q^{41} -168.515 q^{43} +(-149.951 - 371.307i) q^{45} +(313.988 + 543.844i) q^{47} +(211.629 + 269.930i) q^{49} +(445.218 + 300.353i) q^{51} +(625.481 + 361.121i) q^{53} +10.0879i q^{55} +(228.115 + 467.795i) q^{57} +(263.093 - 455.691i) q^{59} +(205.162 - 118.450i) q^{61} +(-414.751 - 279.336i) q^{63} +(-673.515 + 388.854i) q^{65} +(149.359 - 258.697i) q^{67} +(9.56651 + 19.6181i) q^{69} -379.893i q^{71} +(-559.469 - 323.010i) q^{73} +(409.068 + 275.966i) q^{75} +(7.05302 + 10.4375i) q^{77} +(211.386 + 366.132i) q^{79} +(700.698 + 201.155i) q^{81} +391.295 q^{83} -1532.91 q^{85} +(-277.506 - 19.4265i) q^{87} +(-316.431 - 548.075i) q^{89} +(-424.987 + 873.226i) q^{91} +(-791.747 + 1173.62i) q^{93} +(-1286.48 - 742.752i) q^{95} +1432.13i q^{97} +(-14.4699 - 11.3087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 42 q^{7} - 84 q^{9}+O(q^{10}) \) 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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