LMFDB - Embedded newform 135.3.i.a.116.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(71,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("135.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.i (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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.8
Root			$3.73655i$ of defining polynomial
Character	$\chi$	$=$	135.116
Dual form			135.3.i.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.23594 + 1.86827i) q^{2} +(4.98088 + 8.62715i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.63061 - 6.28840i) q^{7} +22.2764i q^{8} +O(q^{10})$	\(q+(3.23594 + 1.86827i) q^{2} +(4.98088 + 8.62715i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.63061 - 6.28840i) q^{7} +22.2764i q^{8} -8.35517 q^{10} +(-6.50668 - 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} +(23.4969 - 13.5659i) q^{14} +(-21.6949 + 37.5766i) q^{16} -1.90107i q^{17} -7.38378 q^{19} +(-19.2909 - 11.1376i) q^{20} +(-14.0368 - 24.3125i) q^{22} +(30.6549 - 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} -10.9606i q^{26} +72.3346 q^{28} +(14.2015 + 8.19922i) q^{29} +(-13.3206 - 23.0720i) q^{31} +(-63.2391 + 36.5111i) q^{32} +(3.55172 - 6.15176i) q^{34} +16.2366i q^{35} -44.6613 q^{37} +(-23.8935 - 13.7949i) q^{38} +(-24.9058 - 43.1381i) q^{40} +(-14.8634 + 8.58140i) q^{41} +(-20.5554 + 35.6031i) q^{43} -74.8454i q^{44} +132.263 q^{46} +(-36.4950 - 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +(16.1797 - 9.34136i) q^{50} +(14.6107 - 25.3065i) q^{52} +100.474i q^{53} +16.8002 q^{55} +(140.083 + 80.8770i) q^{56} +(30.6367 + 53.0644i) q^{58} +(4.12003 - 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} -99.5461i q^{62} -99.2915 q^{64} +(5.68041 + 3.27959i) q^{65} +(41.9225 + 72.6119i) q^{67} +(16.4008 - 9.46903i) q^{68} +(-30.3343 + 52.5406i) q^{70} -23.1134i q^{71} -103.753 q^{73} +(-144.521 - 83.4395i) q^{74} +(-36.7778 - 63.7010i) q^{76} +(-47.2464 + 27.2777i) q^{77} +(-40.2610 + 69.7340i) q^{79} -97.0225i q^{80} -64.1296 q^{82} +(17.1034 + 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +(-133.032 + 76.8063i) q^{86} +(83.6843 - 144.945i) q^{88} +29.0566i q^{89} -21.2997 q^{91} +(305.377 + 176.310i) q^{92} +(-78.7306 - 136.365i) q^{94} +(14.2986 - 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} -13.9196i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 16 * q^4 + 2 * q^7	$ 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.23594	+	1.86827i	1.61797	+	0.934136i	0.987444	+	0.157969i	$0.0504947\pi$
$2$	3.23594	+	1.86827i	1.61797	+	0.934136i	0.630528	+	0.776167i	$0.282839\pi$
$3$		0			0
$3$		0			0
$4$	4.98088	+	8.62715i	1.24522	+	2.15679i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	3.63061	−	6.28840i	0.518658	−	0.898342i	−0.481107	−	0.876662i	$-0.659765\pi$
$7$	3.63061	−	6.28840i	0.518658	−	0.898342i	0.999765	−	0.0216804i	$-0.00690163\pi$
$8$			22.2764i			2.78455i
$9$		0			0
$10$	−8.35517			−0.835517
$11$	−6.50668	−	3.75663i	−0.591516	−	0.341512i	0.174181	−	0.984714i	$-0.444272\pi$
$11$	−6.50668	−	3.75663i	−0.591516	−	0.341512i	−0.765697	+	0.643202i	$0.777606\pi$
$12$		0			0
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	0.804085	−	0.594514i	$-0.202655\pi$
$13$	−1.46668	−	2.54036i	−0.112821	−	0.195412i	−0.916907	+	0.399102i	$0.869322\pi$
$14$	23.4969	−	13.5659i	1.67835	−	0.968995i
$15$		0			0
$16$	−21.6949	+	37.5766i	−1.35593	+	2.34854i
$17$		−	1.90107i		−	0.111828i	−0.998436	−	0.0559139i	$-0.982193\pi$
$17$		−	1.90107i		−	0.111828i	0.998436	−	0.0559139i	$-0.0178072\pi$
$18$		0			0
$19$	−7.38378			−0.388620			−0.194310	−	0.980940i	$-0.562247\pi$
$19$	−7.38378			−0.388620			−0.194310	+	0.980940i	$0.562247\pi$
$20$	−19.2909	−	11.1376i	−0.964544	−	0.556880i
$21$		0			0
$22$	−14.0368	−	24.3125i	−0.638037	−	1.10511i
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.347091	−	0.937831i	$-0.387169\pi$
$23$	30.6549	−	17.6986i	1.33282	−	0.769506i	0.985731	+	0.168326i	$0.0538360\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		−	10.9606i		−	0.421562i
$27$		0			0
$28$	72.3346			2.58338
$29$	14.2015	+	8.19922i	0.489705	+	0.282732i	0.724452	−	0.689325i	$-0.242093\pi$
$29$	14.2015	+	8.19922i	0.489705	+	0.282732i	−0.234747	+	0.972057i	$0.575426\pi$
$30$		0			0
$31$	−13.3206	−	23.0720i	−0.429697	−	0.744257i	0.567149	−	0.823615i	$-0.308046\pi$
$31$	−13.3206	−	23.0720i	−0.429697	−	0.744257i	−0.996846	+	0.0793581i	$0.974713\pi$
$32$	−63.2391	+	36.5111i	−1.97622	+	1.14097i
$33$		0			0
$34$	3.55172	−	6.15176i	0.104462	−	0.180934i
$35$			16.2366i			0.463902i
$36$		0			0
$37$	−44.6613			−1.20706			−0.603531	−	0.797340i	$-0.706240\pi$
$37$	−44.6613			−1.20706			−0.603531	+	0.797340i	$0.706240\pi$
$38$	−23.8935	−	13.7949i	−0.628776	−	0.363024i
$39$		0			0
$40$	−24.9058	−	43.1381i	−0.622645	−	1.07845i
$41$	−14.8634	+	8.58140i	−0.362522	+	0.209302i	−0.670187	−	0.742193i	$-0.733786\pi$
$41$	−14.8634	+	8.58140i	−0.362522	+	0.209302i	0.307664	+	0.951495i	$0.400453\pi$
$42$		0			0
$43$	−20.5554	+	35.6031i	−0.478033	+	0.827978i	−0.999683	−	0.0251818i	$-0.991984\pi$
$43$	−20.5554	+	35.6031i	−0.478033	+	0.827978i	0.521650	+	0.853160i	$0.325317\pi$
$44$		−	74.8454i		−	1.70103i
$45$		0			0
$46$	132.263			2.87529
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	0.0586949	−	0.998276i	$-0.481306\pi$
$47$	−36.4950	−	21.0704i	−0.776490	−	0.448307i	−0.835185	+	0.549969i	$0.814639\pi$
$48$		0			0
$49$	−1.86263	−	3.22616i	−0.0380128	−	0.0658401i
$50$	16.1797	−	9.34136i	0.323594	−	0.186827i
$51$		0			0
$52$	14.6107	−	25.3065i	0.280975	−	0.486663i
$53$			100.474i			1.89573i	0.318671	+	0.947865i	$0.396764\pi$
$53$			100.474i			1.89573i	−0.318671	+	0.947865i	$0.603236\pi$
$54$		0			0
$55$	16.8002			0.305458
$56$	140.083	+	80.8770i	2.50148	+	1.44423i
$57$		0			0
$58$	30.6367	+	53.0644i	0.528220	+	0.914903i
$59$	4.12003	−	2.37870i	0.0698310	−	0.0403169i	−0.464678	−	0.885480i	$-0.653830\pi$
$59$	4.12003	−	2.37870i	0.0698310	−	0.0403169i	0.534509	+	0.845163i	$0.320497\pi$
$60$		0			0
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	−0.356902	−	0.934142i	$-0.616167\pi$
$61$	38.4629	−	66.6197i	0.630539	−	1.09213i	0.987442	−	0.157985i	$-0.0504996\pi$
$62$		−	99.5461i		−	1.60558i
$63$		0			0
$64$	−99.2915			−1.55143
$65$	5.68041	+	3.27959i	0.0873910	+	0.0504552i
$66$		0			0
$67$	41.9225	+	72.6119i	0.625709	+	1.08376i	0.988403	+	0.151852i	$0.0485237\pi$
$67$	41.9225	+	72.6119i	0.625709	+	1.08376i	−0.362694	+	0.931908i	$0.618143\pi$
$68$	16.4008	−	9.46903i	0.241189	−	0.139250i
$69$		0			0
$70$	−30.3343	+	52.5406i	−0.433348	+	0.750580i
$71$		−	23.1134i		−	0.325540i	−0.986664	−	0.162770i	$-0.947957\pi$
$71$		−	23.1134i		−	0.325540i	0.986664	−	0.162770i	$-0.0520429\pi$
$72$		0			0
$73$	−103.753			−1.42127			−0.710637	−	0.703559i	$-0.751593\pi$
$73$	−103.753			−1.42127			−0.710637	+	0.703559i	$0.751593\pi$
$74$	−144.521	−	83.4395i	−1.95299	−	1.12756i
$75$		0			0
$76$	−36.7778	−	63.7010i	−0.483918	−	0.838171i
$77$	−47.2464	+	27.2777i	−0.613589	+	0.354256i
$78$		0			0
$79$	−40.2610	+	69.7340i	−0.509633	+	0.882709i	0.490305	+	0.871551i	$0.336885\pi$
$79$	−40.2610	+	69.7340i	−0.509633	+	0.882709i	−0.999938	+	0.0111586i	$0.996448\pi$
$80$		−	97.0225i		−	1.21278i
$81$		0			0
$82$	−64.1296			−0.782068
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	0.599481	−	0.800389i	$-0.295374\pi$
$83$	17.1034	+	9.87463i	0.206065	+	0.118971i	−0.393417	+	0.919360i	$0.628707\pi$
$84$		0			0
$85$	2.12546	+	3.68141i	0.0250055	+	0.0433107i
$86$	−133.032	+	76.8063i	−1.54689	+	0.893097i
$87$		0			0
$88$	83.6843	−	144.945i	0.950958	−	1.64711i
$89$			29.0566i			0.326478i	0.986587	+	0.163239i	$0.0521942\pi$
$89$			29.0566i			0.326478i	−0.986587	+	0.163239i	$0.947806\pi$
$90$		0			0
$91$	−21.2997			−0.234063
$92$	305.377	+	176.310i	3.31932	+	1.91641i
$93$		0			0
$94$	−78.7306	−	136.365i	−0.837559	−	1.45070i
$95$	14.2986	−	8.25532i	0.150512	−	0.0868981i
$96$		0			0
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	−0.507210	−	0.861822i	$-0.669323\pi$
$97$	47.7972	−	82.7872i	0.492755	−	0.853476i	0.999965	+	0.00834602i	$0.00265665\pi$
$98$		−	13.9196i		−	0.142036i
$99$		0			0
$100$	49.8088			0.498088
$101$	−117.817	−	68.0219i	−1.16651	−	0.673484i	−0.213653	−	0.976910i	$-0.568536\pi$
$101$	−117.817	−	68.0219i	−1.16651	−	0.673484i	−0.952855	+	0.303426i	$0.901870\pi$
$102$		0			0
$103$	85.9401	+	148.853i	0.834370	+	1.44517i	0.894542	+	0.446983i	$0.147502\pi$
$103$	85.9401	+	148.853i	0.834370	+	1.44517i	−0.0601721	+	0.998188i	$0.519165\pi$
$104$	56.5901	−	32.6723i	0.544135	−	0.314157i
$105$		0			0
$106$	−187.712	+	325.127i	−1.77087	+	3.06724i
$107$			98.6056i			0.921548i	0.887518	+	0.460774i	$0.152428\pi$
$107$			98.6056i			0.921548i	−0.887518	+	0.460774i	$0.847572\pi$
$108$		0			0
$109$	2.62651			0.0240965			0.0120482	−	0.999927i	$-0.496165\pi$
$109$	2.62651			0.0240965			0.0120482	+	0.999927i	$0.496165\pi$
$110$	54.3644	+	31.3873i	0.494222	+	0.285339i
$111$		0			0
$112$	157.531	+	272.852i	1.40653	+	2.43618i
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	−0.510440	−	0.859913i	$-0.670518\pi$
$113$	−2.36782	+	1.36706i	−0.0209542	+	0.0120979i	0.489486	+	0.872011i	$0.337184\pi$
$114$		0			0
$115$	−39.5753	+	68.5465i	−0.344133	+	0.596056i
$116$			163.357i			1.40825i
$117$		0			0
$118$	17.7762			0.150646
$119$	−11.9547	−	6.90205i	−0.100460	−	0.0580004i
$120$		0			0
$121$	−32.2754	−	55.9027i	−0.266739	−	0.462006i
$122$	248.928	−	143.718i	2.04039	−	1.17802i
$123$		0			0
$124$	132.697	−	229.838i	1.07014	−	1.85353i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	193.060			1.52015			0.760077	−	0.649833i	$-0.225161\pi$
$127$	193.060			1.52015			0.760077	+	0.649833i	$0.225161\pi$
$128$	−68.3455	−	39.4593i	−0.533950	−	0.308276i
$129$		0			0
$130$	12.2543	+	21.2251i	0.0942641	+	0.163270i
$131$	201.259	−	116.197i	1.53633	−	0.886999i	0.537278	−	0.843405i	$-0.319453\pi$
$131$	201.259	−	116.197i	1.53633	−	0.886999i	0.999049	−	0.0435937i	$-0.0138807\pi$
$132$		0			0
$133$	−26.8076	+	46.4322i	−0.201561	+	0.349114i
$134$			313.291i			2.33799i
$135$		0			0
$136$	42.3491			0.311390
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.182582	−	0.983191i	$-0.558445\pi$
$137$	−154.172	−	89.0111i	−1.12534	−	0.649716i	−0.942759	+	0.333475i	$0.891779\pi$
$138$		0			0
$139$	−16.0343	−	27.7722i	−0.115355	−	0.199800i	0.802567	−	0.596562i	$-0.203467\pi$
$139$	−16.0343	−	27.7722i	−0.115355	−	0.199800i	−0.917922	+	0.396762i	$0.870134\pi$
$140$	−140.075	+	80.8725i	−1.00054	+	0.577661i
$141$		0			0
$142$	43.1820	−	74.7935i	0.304099	−	0.526715i
$143$			22.0390i			0.154119i
$144$		0			0
$145$	−36.6680			−0.252883
$146$	−335.739	−	193.839i	−2.29958	−	1.32766i
$147$		0			0
$148$	−222.453	−	385.299i	−1.50306	−	2.60337i
$149$	−80.4653	+	46.4567i	−0.540036	+	0.311790i	−0.745093	−	0.666960i	$-0.767595\pi$
$149$	−80.4653	+	46.4567i	−0.540036	+	0.311790i	0.205058	+	0.978750i	$0.434262\pi$
$150$		0			0
$151$	113.614	−	196.785i	0.752408	−	1.30321i	−0.194245	−	0.980953i	$-0.562226\pi$
$151$	113.614	−	196.785i	0.752408	−	1.30321i	0.946653	−	0.322256i	$-0.104441\pi$
$152$		−	164.484i		−	1.08213i
$153$		0			0
$154$	−203.849			−1.32369
$155$	51.5905	+	29.7858i	0.332842	+	0.192166i
$156$		0			0
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	0.868538	−	0.495623i	$-0.165060\pi$
$157$	0.792406	+	1.37249i	0.00504717	+	0.00874196i	−0.863491	+	0.504365i	$0.831727\pi$
$158$	−260.564	+	150.437i	−1.64914	+	0.952133i
$159$		0			0
$160$	81.6413	−	141.407i	0.510258	−	0.883793i
$161$		−	257.027i		−	1.59644i
$162$		0			0
$163$	−41.6801			−0.255706			−0.127853	−	0.991793i	$-0.540809\pi$
$163$	−41.6801			−0.255706			−0.127853	+	0.991793i	$0.540809\pi$
$164$	−148.066	−	85.4859i	−0.902841	−	0.521256i
$165$		0			0
$166$	36.8970	+	63.9075i	0.222271	+	0.384985i
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	−0.523802	−	0.851840i	$-0.675487\pi$
$167$	−8.01405	+	4.62692i	−0.0479884	+	0.0277061i	0.475814	+	0.879546i	$0.342154\pi$
$168$		0			0
$169$	80.1977	−	138.907i	0.474543	−	0.821932i
$170$			15.8838i			0.0934340i
$171$		0			0
$172$	−409.537			−2.38103
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	0.821264	−	0.570548i	$-0.193269\pi$
$173$	127.637	+	73.6913i	0.737787	+	0.425962i	−0.0834771	+	0.996510i	$0.526603\pi$
$174$		0			0
$175$	−18.1530	−	31.4420i	−0.103732	−	0.179668i
$176$	282.323	−	162.999i	1.60411	−	0.926133i
$177$		0			0
$178$	−54.2856	+	94.0254i	−0.304975	+	0.528233i
$179$		−	160.022i		−	0.893977i	−0.894540	−	0.446988i	$-0.852496\pi$
$179$		−	160.022i		−	0.893977i	0.894540	−	0.446988i	$-0.147504\pi$
$180$		0			0
$181$	−30.3346			−0.167595			−0.0837973	−	0.996483i	$-0.526705\pi$
$181$	−30.3346			−0.167595			−0.0837973	+	0.996483i	$0.526705\pi$
$182$	−68.9246	−	39.7937i	−0.378707	−	0.218646i
$183$		0			0
$184$	394.262	+	682.882i	2.14273	+	3.71132i
$185$	86.4862	−	49.9328i	0.467493	−	0.269907i
$186$		0			0
$187$	−7.14163	+	12.3697i	−0.0381905	+	0.0661480i
$188$		−	419.797i		−	2.23296i
$189$		0			0
$190$	61.6928			0.324699
$191$	249.938	+	144.302i	1.30857	+	0.755506i	0.981858	−	0.189617i	$-0.0607245\pi$
$191$	249.938	+	144.302i	1.30857	+	0.755506i	0.326716	+	0.945122i	$0.394058\pi$
$192$		0			0
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	0.962203	−	0.272334i	$-0.0877955\pi$
$193$	47.3339	+	81.9847i	0.245253	+	0.424791i	−0.716949	+	0.697125i	$0.754462\pi$
$194$	309.338	−	178.596i	1.59453	−	0.920600i
$195$		0			0
$196$	18.5551	−	32.1383i	0.0946686	−	0.163971i
$197$		−	129.755i		−	0.658657i	−0.944215	−	0.329329i	$-0.893178\pi$
$197$		−	129.755i		−	0.658657i	0.944215	−	0.329329i	$-0.106822\pi$
$198$		0			0
$199$	136.428			0.685570			0.342785	−	0.939414i	$-0.388630\pi$
$199$	136.428			0.685570			0.342785	+	0.939414i	$0.388630\pi$
$200$	96.4597	+	55.6911i	0.482299	+	0.278455i
$201$		0			0
$202$	−254.167	−	440.230i	−1.25825	−	2.17936i
$203$	103.120	−	59.5363i	0.507980	−	0.293282i
$204$		0			0
$205$	19.1886	−	33.2356i	0.0936029	−	0.162125i
$206$			642.238i			3.11766i
$207$		0			0
$208$	127.278			0.611911
$209$	48.0439	+	27.7382i	0.229875	+	0.132718i
$210$		0			0
$211$	−79.1144	−	137.030i	−0.374950	−	0.649432i	0.615370	−	0.788239i	$-0.289007\pi$
$211$	−79.1144	−	137.030i	−0.374950	−	0.649432i	−0.990320	+	0.138806i	$0.955673\pi$
$212$	−866.802	+	500.448i	−4.08869	+	2.36060i
$213$		0			0
$214$	−184.222	+	319.082i	−0.860851	+	1.49104i
$215$		−	91.9267i		−	0.427566i
$216$		0			0
$217$	−193.448			−0.891463
$218$	8.49925	+	4.90704i	0.0389874	+	0.0225094i
$219$		0			0
$220$	83.6797	+	144.937i	0.380362	+	0.658807i
$221$	−4.82941	+	2.78826i	−0.0218525	+	0.0126166i
$222$		0			0
$223$	103.124	−	178.616i	0.462440	−	0.800969i	−0.536642	−	0.843810i	$-0.680307\pi$
$223$	103.124	−	178.616i	0.462440	−	0.800969i	0.999082	+	0.0428406i	$0.0136407\pi$
$224$			530.230i			2.36710i
$225$		0			0
$226$	−10.2162			−0.0452044
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	0.753927	−	0.656958i	$-0.228157\pi$
$227$	127.562	+	73.6481i	0.561948	+	0.324441i	−0.191979	+	0.981399i	$0.561490\pi$
$228$		0			0
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	0.894142	−	0.447783i	$-0.147786\pi$
$229$	13.5751	+	23.5127i	0.0592798	+	0.102676i	−0.834863	+	0.550458i	$0.814453\pi$
$230$	−256.127	+	147.875i	−1.11360	+	0.642935i
$231$		0			0
$232$	−182.649	+	316.358i	−0.787281	+	1.36361i
$233$			39.6011i			0.169962i	0.996383	+	0.0849808i	$0.0270829\pi$
$233$			39.6011i			0.169962i	−0.996383	+	0.0849808i	$0.972917\pi$
$234$		0			0
$235$	94.2298			0.400978
$236$	41.0428	+	23.6960i	0.173910	+	0.100407i
$237$		0			0
$238$	−25.7898	−	44.6693i	−0.108361	−	0.187686i
$239$	−54.9394	+	31.7193i	−0.229872	+	0.132717i	−0.610513	−	0.792006i	$-0.709037\pi$
$239$	−54.9394	+	31.7193i	−0.229872	+	0.132717i	0.380641	+	0.924723i	$0.375703\pi$
$240$		0			0
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	−0.686253	−	0.727363i	$-0.740746\pi$
$241$	69.1161	−	119.713i	0.286789	−	0.496733i	0.973041	+	0.230630i	$0.0740789\pi$
$242$		−	241.197i		−	0.996683i
$243$		0			0
$244$	766.317			3.14064
$245$	7.21392	+	4.16496i	0.0294446	+	0.0169998i
$246$		0			0
$247$	10.8296	+	18.7575i	0.0438446	+	0.0759411i
$248$	513.961	−	296.735i	2.07242	−	1.19651i
$249$		0			0
$250$	−20.8879	+	36.1789i	−0.0835517	+	0.144716i
$251$		−	186.477i		−	0.742936i	−0.928446	−	0.371468i	$-0.878855\pi$
$251$		−	186.477i		−	0.742936i	0.928446	−	0.371468i	$-0.121145\pi$
$252$		0			0
$253$	−265.949			−1.05118
$254$	624.730	+	360.688i	2.45957	+	1.42003i
$255$		0			0
$256$	51.1416	+	88.5798i	0.199772	+	0.346015i
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	−0.838156	−	0.545431i	$-0.816366\pi$
$257$	−201.713	+	116.459i	−0.784877	+	0.453149i	0.0532790	+	0.998580i	$0.483033\pi$
$258$		0			0
$259$	−162.148	+	280.848i	−0.626053	+	1.08435i
$260$			65.3410i			0.251312i
$261$		0			0
$262$	868.350			3.31431
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	0.517665	−	0.855583i	$-0.326801\pi$
$263$	9.34728	+	5.39665i	0.0355410	+	0.0205196i	−0.482124	+	0.876103i	$0.660135\pi$
$264$		0			0
$265$	−112.333	−	194.567i	−0.423898	−	0.734213i
$266$	−173.496	+	100.168i	−0.652240	+	0.376571i
$267$		0			0
$268$	−417.622	+	723.343i	−1.55829	+	2.69904i
$269$		−	58.4601i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$269$		−	58.4601i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$270$		0			0
$271$	−65.5995			−0.242065			−0.121032	−	0.992649i	$-0.538620\pi$
$271$	−65.5995			−0.242065			−0.121032	+	0.992649i	$0.538620\pi$
$272$	71.4360	+	41.2436i	0.262632	+	0.151631i
$273$		0			0
$274$	−332.594	−	576.069i	−1.21385	−	2.10244i
$275$	−32.5334	+	18.7832i	−0.118303	+	0.0683024i
$276$		0			0
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	−0.999836	−	0.0181286i	$-0.994229\pi$
$277$	−134.128	+	232.317i	−0.484218	+	0.838690i	0.515618	+	0.856819i	$0.327562\pi$
$278$		−	119.826i		−	0.431028i
$279$		0			0
$280$	−361.693			−1.29176
$281$	−159.428	−	92.0461i	−0.567361	−	0.327566i	0.188734	−	0.982028i	$-0.439562\pi$
$281$	−159.428	−	92.0461i	−0.567361	−	0.327566i	−0.756095	+	0.654462i	$0.772895\pi$
$282$		0			0
$283$	231.303	+	400.628i	0.817324	+	1.41565i	0.907647	+	0.419734i	$0.137877\pi$
$283$	231.303	+	400.628i	0.817324	+	1.41565i	−0.0903234	+	0.995912i	$0.528790\pi$
$284$	199.402	−	115.125i	0.702121	−	0.405370i
$285$		0			0
$286$	−41.1750	+	71.3171i	−0.143968	+	0.249361i
$287$			124.623i			0.434226i
$288$		0			0
$289$	285.386			0.987495
$290$	−118.656	−	68.5058i	−0.409157	−	0.236227i
$291$		0			0
$292$	−516.782	−	895.093i	−1.76980	−	3.06539i
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	−0.859843	−	0.510559i	$-0.829439\pi$
$293$	−248.349	+	143.384i	−0.847608	+	0.489367i	0.0122351	+	0.999925i	$0.496105\pi$
$294$		0			0
$295$	−5.31893	+	9.21266i	−0.0180303	+	0.0312294i
$296$		−	994.894i		−	3.36113i
$297$		0			0
$298$	−347.175			−1.16502
$299$	−89.9217	−	51.9163i	−0.300741	−	0.173633i
$300$		0			0
$301$	149.257	+	258.521i	0.495872	+	0.858875i
$302$	735.294	−	424.522i	2.43475	−	1.40570i
$303$		0			0
$304$	160.190	−	277.458i	0.526942	−	0.912690i
$305$			172.011i			0.563972i
$306$		0			0
$307$	−236.738			−0.771133			−0.385567	−	0.922680i	$-0.625994\pi$
$307$	−236.738			−0.771133			−0.385567	+	0.922680i	$0.625994\pi$
$308$	−470.658	−	271.734i	−1.52811	−	0.882254i
$309$		0			0
$310$	111.296	+	192.770i	0.359019	+	0.621839i
$311$	−448.597	+	258.997i	−1.44243	+	0.832789i	−0.998012	−	0.0630292i	$-0.979924\pi$
$311$	−448.597	+	258.997i	−1.44243	+	0.832789i	−0.444421	+	0.895818i	$0.646591\pi$
$312$		0			0
$313$	247.615	−	428.882i	0.791102	−	1.37023i	−0.134183	−	0.990957i	$-0.542841\pi$
$313$	247.615	−	428.882i	0.791102	−	1.37023i	0.925285	−	0.379272i	$-0.123826\pi$
$314$			5.92172i			0.0188590i
$315$		0			0
$316$	−802.141			−2.53842
$317$	189.840	+	109.604i	0.598864	+	0.345754i	0.768595	−	0.639736i	$-0.220956\pi$
$317$	189.840	+	109.604i	0.598864	+	0.345754i	−0.169731	+	0.985491i	$0.554290\pi$
$318$		0			0
$319$	−61.6029	−	106.699i	−0.193112	−	0.334481i
$320$	192.277	−	111.011i	0.600866	−	0.346910i
$321$		0			0
$322$	480.197	−	831.725i	1.49129	−	2.58300i
$323$			14.0371i			0.0434586i
$324$		0			0
$325$	−14.6668			−0.0451285
$326$	−134.874	−	77.8697i	−0.413725	−	0.238864i
$327$		0			0
$328$	−191.163	−	331.104i	−0.582813	−	1.00946i
$329$	−264.998	+	152.997i	−0.805466	+	0.465036i
$330$		0			0
$331$	47.4838	−	82.2443i	0.143455	−	0.248472i	−0.785340	−	0.619064i	$-0.787512\pi$
$331$	47.4838	−	82.2443i	0.143455	−	0.248472i	0.928796	+	0.370592i	$0.120845\pi$
$332$			196.738i			0.592583i
$333$		0			0
$334$	−34.5774			−0.103525
$335$	−162.365	−	93.7416i	−0.484672	−	0.279826i
$336$		0			0
$337$	257.989	+	446.850i	0.765547	+	1.32597i	0.939957	+	0.341293i	$0.110865\pi$
$337$	257.989	+	446.850i	0.765547	+	1.32597i	−0.174411	+	0.984673i	$0.555802\pi$
$338$	519.031	−	299.662i	1.53559	−	0.886575i
$339$		0			0
$340$	−21.1734	+	36.6734i	−0.0622747	+	0.107863i
$341$			200.162i			0.586986i
$342$		0			0
$343$	328.750			0.958454
$344$	−793.109	−	457.902i	−2.30555	−	1.33111i
$345$		0			0
$346$	275.351	+	476.922i	0.795812	+	1.37839i
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	−0.354465	−	0.935069i	$-0.615337\pi$
$347$	96.4994	−	55.7140i	0.278096	−	0.160559i	0.632561	+	0.774510i	$0.282004\pi$
$348$		0			0
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.0471279	+	0.998889i	$0.515007\pi$
$349$	−310.131	+	537.162i	−0.888627	+	1.53915i	−0.841499	+	0.540258i	$0.818327\pi$
$350$		−	135.659i		−	0.387598i
$351$		0			0
$352$	548.635			1.55862
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.390157	−	0.920748i	$-0.627579\pi$
$353$	−488.067	−	281.786i	−1.38263	−	0.798260i	−0.992470	+	0.122488i	$0.960913\pi$
$354$		0			0
$355$	25.8415	+	44.7588i	0.0727930	+	0.126081i
$356$	−250.675	+	144.727i	−0.704144	+	0.406538i
$357$		0			0
$358$	298.964	−	517.822i	0.835096	−	1.44643i
$359$			415.128i			1.15635i	0.815915	+	0.578173i	$0.196234\pi$
$359$			415.128i			1.15635i	−0.815915	+	0.578173i	$0.803766\pi$
$360$		0			0
$361$	−306.480			−0.848974
$362$	−98.1611	−	56.6733i	−0.271163	−	0.156556i
$363$		0			0
$364$	−106.091	−	183.756i	−0.291460	−	0.504823i
$365$	200.917	−	115.999i	0.550457	−	0.317807i
$366$		0			0
$367$	−313.940	+	543.761i	−0.855423	+	1.48164i	0.0208286	+	0.999783i	$0.493370\pi$
$367$	−313.940	+	543.761i	−0.855423	+	1.48164i	−0.876252	+	0.481853i	$0.839964\pi$
$368$			1535.88i			4.17358i
$369$		0			0
$370$	373.153			1.00852
$371$	631.819	+	364.781i	1.70302	+	0.983237i
$372$		0			0
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	−0.999608	−	0.0279857i	$-0.991091\pi$
$373$	−195.467	−	338.559i	−0.524040	−	0.907665i	0.475568	−	0.879679i	$-0.342243\pi$
$374$	−46.2198	+	26.6850i	−0.123582	+	0.0713503i
$375$		0			0
$376$	469.373	−	812.979i	1.24833	−	2.16218i
$377$		−	48.1024i		−	0.127593i
$378$		0			0
$379$	52.4430			0.138372			0.0691860	−	0.997604i	$-0.477960\pi$
$379$	52.4430			0.138372			0.0691860	+	0.997604i	$0.477960\pi$
$380$	142.440	+	82.2376i	0.374841	+	0.216415i
$381$		0			0
$382$	539.189	+	933.904i	1.41149	+	2.44477i
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	−0.369324	−	0.929301i	$-0.620411\pi$
$383$	96.0614	−	55.4610i	0.250813	−	0.144807i	0.620136	+	0.784494i	$0.287077\pi$
$384$		0			0
$385$	60.9948	−	105.646i	0.158428	−	0.274405i
$386$			353.731i			0.916400i
$387$		0			0
$388$	952.290			2.45435
$389$	91.6114	+	52.8918i	0.235505	+	0.135969i	0.613109	−	0.789998i	$-0.289919\pi$
$389$	91.6114	+	52.8918i	0.235505	+	0.135969i	−0.377604	+	0.925967i	$0.623252\pi$
$390$		0			0
$391$	−33.6464	−	58.2773i	−0.0860521	−	0.149047i
$392$	71.8674	−	41.4926i	0.183335	−	0.105849i
$393$		0			0
$394$	242.419	−	419.881i	0.615276	−	1.06569i
$395$		−	180.053i		−	0.455829i
$396$		0			0
$397$	99.8892			0.251610			0.125805	−	0.992055i	$-0.459849\pi$
$397$	99.8892			0.251610			0.125805	+	0.992055i	$0.459849\pi$
$398$	441.475	+	254.885i	1.10923	+	0.640416i
$399$		0			0
$400$	108.474	+	187.883i	0.271186	+	0.469708i
$401$	136.080	−	78.5658i	0.339352	−	0.195925i	−0.320634	−	0.947203i	$-0.603896\pi$
$401$	136.080	−	78.5658i	0.339352	−	0.195925i	0.659985	+	0.751279i	$0.270563\pi$
$402$		0			0
$403$	−39.0740	+	67.6782i	−0.0969579	+	0.167936i
$404$		−	1355.24i		−	3.35455i
$405$		0			0
$406$	444.920			1.09586
$407$	290.597	+	167.776i	0.713996	+	0.412226i
$408$		0			0
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	−0.891813	−	0.452404i	$-0.850567\pi$
$409$	−342.619	−	593.434i	−0.837700	−	1.45094i	0.0541134	−	0.998535i	$-0.482767\pi$
$410$	124.186	−	71.6990i	0.302894	−	0.174876i
$411$		0			0
$412$	−856.116	+	1482.84i	−2.07795	+	3.59912i
$413$		−	34.5445i		−	0.0836428i
$414$		0			0
$415$	−44.1607			−0.106411
$416$	185.502	+	107.100i	0.445919	+	0.257452i
$417$		0			0
$418$	103.645	+	179.518i	0.247954	+	0.429469i
$419$	44.6836	−	25.7981i	0.106643	−	0.0615706i	−0.445730	−	0.895168i	$-0.647056\pi$
$419$	44.6836	−	25.7981i	0.106643	−	0.0615706i	0.552373	+	0.833597i	$0.313722\pi$
$420$		0			0
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	−0.874653	−	0.484750i	$-0.838911\pi$
$421$	−7.37620	+	12.7760i	−0.0175207	+	0.0303467i	0.857132	+	0.515097i	$0.172244\pi$
$422$		−	591.229i		−	1.40102i
$423$		0			0
$424$	−2238.20			−5.27876
$425$	−8.23189	−	4.75268i	−0.0193691	−	0.0111828i
$426$		0			0
$427$	−279.287	−	483.740i	−0.654069	−	1.13288i
$428$	−850.685	+	491.143i	−1.98758	+	1.14753i
$429$		0			0
$430$	171.744	−	297.470i	0.399405	−	0.691790i
$431$			38.6810i			0.0897472i	0.998993	+	0.0448736i	$0.0142885\pi$
$431$			38.6810i			0.0897472i	−0.998993	+	0.0448736i	$0.985711\pi$
$432$		0			0
$433$	−544.647			−1.25784			−0.628922	−	0.777468i	$-0.716504\pi$
$433$	−544.647			−1.25784			−0.628922	+	0.777468i	$0.716504\pi$
$434$	−625.985	−	361.413i	−1.44236	−	0.832748i
$435$		0			0
$436$	13.0824	+	22.6593i	0.0300054	+	0.0519709i
$437$	−226.349	+	130.683i	−0.517962	+	0.299045i
$438$		0			0
$439$	−125.709	+	217.735i	−0.286353	+	0.495978i	−0.972936	−	0.231073i	$-0.925776\pi$
$439$	−125.709	+	217.735i	−0.286353	+	0.495978i	0.686583	+	0.727051i	$0.259110\pi$
$440$			374.248i			0.850563i
$441$		0			0
$442$	−20.8369			−0.0471423
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.431760	−	0.901989i	$-0.642107\pi$
$443$	−632.952	−	365.435i	−1.42878	−	0.824909i	−0.997025	+	0.0770796i	$0.975440\pi$
$444$		0			0
$445$	−32.4862	−	56.2678i	−0.0730028	−	0.126445i
$446$	667.407	−	385.328i	1.49643	−	0.863964i
$447$		0			0
$448$	−360.489	+	624.385i	−0.804662	+	1.39372i
$449$			94.7211i			0.210960i	0.994421	+	0.105480i	$0.0336379\pi$
$449$			94.7211i			0.210960i	−0.994421	+	0.105480i	$0.966362\pi$
$450$		0			0
$451$	128.949			0.285917
$452$	−23.5877	−	13.6184i	−0.0521852	−	0.0301291i
$453$		0			0
$454$	275.190	+	476.642i	0.606144	+	1.04987i
$455$	41.2467	−	23.8138i	0.0906521	−	0.0523380i
$456$		0			0
$457$	204.206	−	353.695i	0.446840	−	0.773949i	−0.551339	−	0.834282i	$-0.685883\pi$
$457$	204.206	−	353.695i	0.446840	−	0.773949i	0.998178	+	0.0603323i	$0.0192160\pi$
$458$			101.448i			0.221502i
$459$		0			0
$460$	−788.481			−1.71409
$461$	511.735	+	295.450i	1.11005	+	0.640890i	0.938843	−	0.344344i	$-0.111899\pi$
$461$	511.735	+	295.450i	1.11005	+	0.640890i	0.171211	+	0.985234i	$0.445232\pi$
$462$		0			0
$463$	−400.967	−	694.496i	−0.866020	−	1.49999i	−0.866031	−	0.499991i	$-0.833337\pi$
$463$	−400.967	−	694.496i	−0.866020	−	1.49999i	1.04649e−5	−	1.00000i	$-0.499997\pi$
$464$	−616.198	+	355.762i	−1.32801	+	0.766729i
$465$		0			0
$466$	−73.9856	+	128.147i	−0.158767	+	0.274993i
$467$			20.6432i			0.0442039i	0.999756	+	0.0221019i	$0.00703584\pi$
$467$			20.6432i			0.0442039i	−0.999756	+	0.0221019i	$0.992964\pi$
$468$		0			0
$469$	608.817			1.29812
$470$	304.922	+	176.047i	0.648771	+	0.374568i
$471$		0			0
$472$	52.9889	+	91.7795i	0.112265	+	0.194448i
$473$	267.495	−	154.438i	0.565529	−	0.326508i
$474$		0			0
$475$	−18.4595	+	31.9727i	−0.0388620	+	0.0673110i
$476$		−	137.513i		−	0.288893i
$477$		0			0
$478$	−237.041			−0.495902
$479$	−435.378	−	251.366i	−0.908931	−	0.524771i	−0.0288439	−	0.999584i	$-0.509183\pi$
$479$	−435.378	−	251.366i	−0.908931	−	0.524771i	−0.880087	+	0.474812i	$0.842516\pi$
$480$		0			0
$481$	65.5037	+	113.456i	0.136182	+	0.235875i
$482$	447.312	−	258.255i	0.928032	−	0.535800i
$483$		0			0
$484$	321.521	−	556.890i	0.664299	−	1.15060i
$485$			213.756i			0.440733i
$486$		0			0
$487$	80.4336			0.165161			0.0825807	−	0.996584i	$-0.473684\pi$
$487$	80.4336			0.165161			0.0825807	+	0.996584i	$0.473684\pi$
$488$	1484.05	+	856.816i	3.04108	+	1.75577i
$489$		0			0
$490$	15.5626	+	26.9551i	0.0317603	+	0.0550105i
$491$	417.972	−	241.316i	0.851267	−	0.491479i	−0.00981129	−	0.999952i	$-0.503123\pi$
$491$	417.972	−	241.316i	0.851267	−	0.491479i	0.861078	+	0.508473i	$0.169790\pi$
$492$		0			0
$493$	15.5873	−	26.9980i	0.0316173	−	0.0547627i
$494$			80.9307i			0.163827i
$495$		0			0
$496$	1155.96			2.33056
$497$	−145.346	−	83.9155i	−0.292447	−	0.168844i
$498$		0			0
$499$	17.5059	+	30.3212i	0.0350820	+	0.0607638i	0.883033	−	0.469310i	$-0.155497\pi$
$499$	17.5059	+	30.3212i	0.0350820	+	0.0607638i	−0.847951	+	0.530074i	$0.822164\pi$
$500$	−96.4544	+	55.6880i	−0.192909	+	0.111376i
$501$		0			0
$502$	348.390	−	603.429i	0.694004	−	1.20205i
$503$		−	211.016i		−	0.419514i	−0.977754	−	0.209757i	$-0.932733\pi$
$503$		−	211.016i		−	0.419514i	0.977754	−	0.209757i	$-0.0672673\pi$
$504$		0			0
$505$	304.203			0.602382
$506$	−860.595	−	496.865i	−1.70078	−	0.981947i
$507$		0			0
$508$	961.608	+	1665.55i	1.89293	+	3.27865i
$509$	732.292	−	422.789i	1.43869	−	0.830627i	0.440930	−	0.897542i	$-0.354649\pi$
$509$	732.292	−	422.789i	1.43869	−	0.830627i	0.997759	+	0.0669144i	$0.0213154\pi$
$510$		0			0
$511$	−376.687	+	652.440i	−0.737156	+	1.27679i
$512$			697.860i			1.36301i
$513$		0			0
$514$	−870.311			−1.69321
$515$	−332.845	−	192.168i	−0.646300	−	0.373142i
$516$		0			0
$517$	158.308	+	274.197i	0.306204	+	0.530361i
$518$	−1049.40	+	605.872i	−2.02587	+	1.16964i
$519$		0			0
$520$	−73.0575	+	126.539i	−0.140495	+	0.243345i
$521$		−	260.960i		−	0.500883i	−0.968132	−	0.250442i	$-0.919424\pi$
$521$		−	260.960i		−	0.500883i	0.968132	−	0.250442i	$-0.0805758\pi$
$522$		0			0
$523$	553.330			1.05799			0.528996	−	0.848624i	$-0.322569\pi$
$523$	553.330			1.05799			0.528996	+	0.848624i	$0.322569\pi$
$524$	2004.89	+	1157.53i	3.82613	+	2.20902i
$525$		0			0
$526$	20.1648	+	34.9265i	0.0383362	+	0.0664003i
$527$	−43.8615	+	25.3234i	−0.0832286	+	0.0480521i
$528$		0			0
$529$	361.983	−	626.973i	0.684278	−	1.18520i
$530$		−	839.475i		−	1.58392i
$531$		0			0
$532$	−534.103			−1.00395
$533$	43.5996	+	25.1723i	0.0818005	+	0.0472275i
$534$		0			0
$535$	−110.244	−	190.949i	−0.206064	−	0.356914i
$536$	−1617.53	+	933.884i	−3.01779	+	1.74232i
$537$		0			0
$538$	109.219	−	189.174i	0.203010	−	0.351624i
$539$			27.9888i			0.0519273i
$540$		0			0
$541$	−795.168			−1.46981			−0.734906	−	0.678169i	$-0.762774\pi$
$541$	−795.168			−1.46981			−0.734906	+	0.678169i	$0.762774\pi$
$542$	−212.276	−	122.558i	−0.391654	−	0.226121i
$543$		0			0
$544$	69.4102	+	120.222i	0.127592	+	0.220996i
$545$	−5.08622	+	2.93653i	−0.00933252	+	0.00538813i
$546$		0			0
$547$	303.604	−	525.858i	0.555035	−	0.961348i	−0.442866	−	0.896588i	$-0.646038\pi$
$547$	303.604	−	525.858i	0.555035	−	0.961348i	0.997901	−	0.0647606i	$-0.0206284\pi$
$548$		−	1773.42i		−	3.23616i
$549$		0			0
$550$	−140.368			−0.255215
$551$	−104.861	−	60.5412i	−0.190309	−	0.109875i
$552$		0			0
$553$	292.344	+	506.354i	0.528650	+	0.915649i
$554$	−868.064	+	501.177i	−1.56690	+	0.904651i
$555$		0			0
$556$	159.730	−	276.661i	0.287284	−	0.497591i
$557$			686.808i			1.23305i	0.787336	+	0.616524i	$0.211460\pi$
$557$			686.808i			1.23305i	−0.787336	+	0.616524i	$0.788540\pi$
$558$		0			0
$559$	120.593			0.215729
$560$	−610.116	−	352.251i	−1.08949	−	0.629019i
$561$		0			0
$562$	−343.934	−	595.712i	−0.611983	−	1.05999i
$563$	208.976	−	120.652i	0.371182	−	0.214302i	−0.302792	−	0.953057i	$-0.597919\pi$
$563$	208.976	−	120.652i	0.371182	−	0.214302i	0.673975	+	0.738754i	$0.264586\pi$
$564$		0			0
$565$	3.05685	−	5.29461i	0.00541035	−	0.00937099i
$566$			1728.55i			3.05397i
$567$		0			0
$568$	514.883			0.906484
$569$	666.084	+	384.564i	1.17062	+	0.675859i	0.953827	−	0.300358i	$-0.0971061\pi$
$569$	666.084	+	384.564i	1.17062	+	0.675859i	0.216796	+	0.976217i	$0.430439\pi$
$570$		0			0
$571$	−48.7253	−	84.3947i	−0.0853333	−	0.147802i	0.820200	−	0.572077i	$-0.193862\pi$
$571$	−48.7253	−	84.3947i	−0.0853333	−	0.147802i	−0.905533	+	0.424275i	$0.860529\pi$
$572$	−190.134	+	109.774i	−0.332402	+	0.191913i
$573$		0			0
$574$	−232.829	+	403.272i	−0.405626	+	0.702565i
$575$		−	176.986i		−	0.307802i
$576$		0			0
$577$	277.283			0.480560			0.240280	−	0.970704i	$-0.422761\pi$
$577$	277.283			0.480560			0.240280	+	0.970704i	$0.422761\pi$
$578$	923.493	+	533.179i	1.59774	+	0.922454i
$579$		0			0
$580$	−182.639	−	316.340i	−0.314895	−	0.545414i
$581$	124.191	−	71.7018i	0.213754	−	0.123411i
$582$		0			0
$583$	377.443	−	653.750i	0.647415	−	1.12136i
$584$		−	2311.25i		−	3.95761i
$585$		0			0
$586$	−1071.52			−1.82854
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	0.113626	−	0.993524i	$-0.463753\pi$
$587$	−405.017	−	233.836i	−0.689977	−	0.398358i	−0.803603	+	0.595165i	$0.797087\pi$
$588$		0			0
$589$	98.3565	+	170.358i	0.166989	+	0.289233i
$590$	−34.4235	+	19.8744i	−0.0583449	+	0.0336855i
$591$		0			0
$592$	968.922	−	1678.22i	1.63669	−	2.83483i
$593$		−	254.411i		−	0.429023i	−0.976721	−	0.214512i	$-0.931184\pi$
$593$		−	254.411i		−	0.429023i	0.976721	−	0.214512i	$-0.0688160\pi$
$594$		0			0
$595$	30.8669			0.0518772
$596$	−801.577	−	462.791i	−1.34493	−	0.776495i
$597$		0			0
$598$	−193.988	−	335.997i	−0.324394	−	0.561867i
$599$	−352.081	+	203.274i	−0.587780	+	0.339355i	−0.764219	−	0.644956i	$-0.776876\pi$
$599$	−352.081	+	203.274i	−0.587780	+	0.339355i	0.176439	+	0.984312i	$0.443542\pi$
$600$		0			0
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	−0.995524	−	0.0945042i	$-0.969873\pi$
$601$	−249.967	+	432.956i	−0.415919	+	0.720393i	0.579605	+	0.814897i	$0.303207\pi$
$602$			1115.41i			1.85285i
$603$		0			0
$604$	2263.59			3.74766
$605$	125.002	+	72.1701i	0.206615	+	0.119289i
$606$		0			0
$607$	−29.9627	−	51.8970i	−0.0493620	−	0.0854975i	0.840289	−	0.542139i	$-0.182385\pi$
$607$	−29.9627	−	51.8970i	−0.0493620	−	0.0854975i	−0.889651	+	0.456642i	$0.849052\pi$
$608$	466.944	−	269.590i	0.767999	−	0.443405i
$609$		0			0
$610$	−321.364	+	556.619i	−0.526826	+	0.912490i
$611$			123.614i			0.202314i
$612$		0			0
$613$	−373.866			−0.609896			−0.304948	−	0.952369i	$-0.598639\pi$
$613$	−373.866			−0.609896			−0.304948	+	0.952369i	$0.598639\pi$
$614$	−766.071	−	442.291i	−1.24767	−	0.720344i
$615$		0			0
$616$	−607.650	−	1052.48i	−0.986444	−	1.70857i
$617$	320.088	−	184.803i	0.518782	−	0.299519i	−0.217654	−	0.976026i	$-0.569841\pi$
$617$	320.088	−	184.803i	0.518782	−	0.299519i	0.736436	+	0.676507i	$0.236507\pi$
$618$		0			0
$619$	−598.225	+	1036.16i	−0.966438	+	1.67392i	−0.260738	+	0.965410i	$0.583966\pi$
$619$	−598.225	+	1036.16i	−0.966438	+	1.67392i	−0.705701	+	0.708510i	$0.749368\pi$
$620$			593.438i			0.957158i
$621$		0			0
$622$	−1935.51			−3.11175
$623$	182.719	+	105.493i	0.293289	+	0.169331i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	1602.54	−	925.224i	2.55996	−	1.47799i
$627$		0			0
$628$	−7.89377	+	13.6724i	−0.0125697	+	0.0217713i
$629$			84.9044i			0.134983i
$630$		0			0
$631$	628.525			0.996078			0.498039	−	0.867155i	$-0.334054\pi$
$631$	628.525			0.996078			0.498039	+	0.867155i	$0.334054\pi$
$632$	−1553.43	−	896.870i	−2.45795	−	1.41910i
$633$		0			0
$634$	409.541	+	709.345i	0.645963	+	1.11884i
$635$	−373.858	+	215.847i	−0.588753	+	0.339917i
$636$		0			0
$637$	−5.46374	+	9.46347i	−0.00857730	+	0.0148563i
$638$		−	460.364i		−	0.721573i
$639$		0			0
$640$	176.467			0.275730
$641$	−824.417	−	475.977i	−1.28614	−	0.742554i	−0.308178	−	0.951329i	$-0.599719\pi$
$641$	−824.417	−	475.977i	−1.28614	−	0.742554i	−0.977964	+	0.208774i	$0.933053\pi$
$642$		0			0
$643$	35.7759	+	61.9656i	0.0556390	+	0.0963696i	0.892503	−	0.451041i	$-0.148947\pi$
$643$	35.7759	+	61.9656i	0.0556390	+	0.0963696i	−0.836864	+	0.547410i	$0.815614\pi$
$644$	2217.41	−	1280.22i	3.44318	−	1.98792i
$645$		0			0
$646$	−26.2252	+	45.4233i	−0.0405962	+	0.0703147i
$647$		−	900.292i		−	1.39149i	−0.718290	−	0.695744i	$-0.755075\pi$
$647$		−	900.292i		−	1.39149i	0.718290	−	0.695744i	$-0.244925\pi$
$648$		0			0
$649$	−35.7436			−0.0550748
$650$	−47.4608	−	27.4015i	−0.0730166	−	0.0421562i
$651$		0			0
$652$	−207.604	−	359.580i	−0.318410	−	0.551503i
$653$	222.825	−	128.648i	0.341233	−	0.197011i	−0.319584	−	0.947558i	$-0.603543\pi$
$653$	222.825	−	128.648i	0.341233	−	0.197011i	0.660817	+	0.750547i	$0.270210\pi$
$654$		0			0
$655$	−259.824	+	450.029i	−0.396678	+	0.687066i
$656$		−	744.690i		−	1.13520i
$657$		0			0
$658$	−1143.36			−1.73763
$659$	−477.967	−	275.954i	−0.725291	−	0.418747i	0.0914057	−	0.995814i	$-0.470864\pi$
$659$	−477.967	−	275.954i	−0.725291	−	0.418747i	−0.816697	+	0.577067i	$0.804197\pi$
$660$		0			0
$661$	523.413	+	906.578i	0.791851	+	1.37153i	0.924820	+	0.380405i	$0.124216\pi$
$661$	523.413	+	906.578i	0.791851	+	1.37153i	−0.132969	+	0.991120i	$0.542451\pi$
$662$	307.309	−	177.425i	0.464214	−	0.268014i
$663$		0			0
$664$	−219.971	+	381.002i	−0.331282	+	0.573798i
$665$		−	119.887i		−	0.180282i
$666$		0			0
$667$	580.460			0.870254
$668$	−79.8342	−	46.0923i	−0.119512	−	0.0690004i
$669$		0			0
$670$	−350.270	−	606.685i	−0.522791	−	0.905500i
$671$	−500.531	+	288.982i	−0.745948	+	0.430673i
$672$		0			0
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	−0.940726	−	0.339168i	$-0.889854\pi$
$673$	−118.875	+	205.898i	−0.176635	+	0.305940i	0.764091	+	0.645108i	$0.223188\pi$
$674$			1927.98i			2.86050i
$675$		0			0
$676$	1597.82			2.36364
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	0.603658	−	0.797244i	$-0.293709\pi$
$677$	145.591	+	84.0570i	0.215053	+	0.124161i	−0.388605	+	0.921405i	$0.627043\pi$
$678$		0			0
$679$	−347.066	−	601.136i	−0.511143	−	0.885325i
$680$	−82.0087	+	47.3477i	−0.120601	+	0.0696290i
$681$		0			0
$682$	−373.958	+	647.714i	−0.548325	+	0.949727i
$683$			995.446i			1.45746i	0.684800	+	0.728731i	$0.259889\pi$
$683$			995.446i			1.45746i	−0.684800	+	0.728731i	$0.740111\pi$
$684$		0			0
$685$	398.070			0.581123
$686$	1063.82	+	614.194i	1.55075	+	0.895327i
$687$		0			0
$688$	−891.896	−	1544.81i	−1.29636	−	2.24536i
$689$	255.239	−	147.362i	0.370449	−	0.213879i
$690$		0			0
$691$	298.570	−	517.138i	0.432084	−	0.748391i	−0.564969	−	0.825112i	$-0.691112\pi$
$691$	298.570	−	517.138i	0.432084	−	0.748391i	0.997053	+	0.0767211i	$0.0244451\pi$
$692$			1468.19i			2.12167i
$693$		0			0
$694$	416.355			0.599936
$695$	62.1006	+	35.8538i	0.0893534	+	0.0515882i
$696$		0			0
$697$	16.3139	+	28.2564i	0.0234058	+	0.0405401i
$698$	−2007.13	+	1158.82i	−2.87555	+	1.66020i
$699$		0			0
$700$	180.836	−	313.218i	0.258338	−	0.447454i
$701$			413.729i			0.590199i	0.955467	+	0.295099i	$0.0953528\pi$
$701$			413.729i			0.590199i	−0.955467	+	0.295099i	$0.904647\pi$
$702$		0			0
$703$	329.769			0.469089
$704$	646.058	+	373.002i	0.917696	+	0.529832i
$705$		0			0
$706$	−1052.91	−	1823.69i	−1.49137	−	2.58312i
$707$	−855.497	+	493.921i	−1.21004	+	0.698616i
$708$		0			0
$709$	328.568	−	569.096i	0.463424	−	0.802674i	−0.535705	−	0.844405i	$-0.679954\pi$
$709$	328.568	−	569.096i	0.463424	−	0.802674i	0.999129	+	0.0417311i	$0.0132873\pi$
$710$			193.116i			0.271994i
$711$		0			0
$712$	−647.277			−0.909096
$713$	−816.684	−	471.513i	−1.14542	−	0.661308i
$714$		0			0
$715$	−24.6404	−	42.6784i	−0.0344621	−	0.0596901i
$716$	1380.53	−	797.051i	1.92812	−	1.11320i
$717$		0			0
$718$	−775.572	+	1343.33i	−1.08018	+	1.87093i
$719$		−	217.226i		−	0.302122i	−0.988524	−	0.151061i	$-0.951731\pi$
$719$		−	217.226i		−	0.302122i	0.988524	−	0.151061i	$-0.0482690\pi$
$720$		0			0
$721$	1248.06			1.73101
$722$	−991.751	−	572.588i	−1.37362	−	0.793058i
$723$		0			0
$724$	−151.093	−	261.701i	−0.208692	−	0.361466i
$725$	71.0073	−	40.9961i	0.0979411	−	0.0565463i
$726$		0			0
$727$	−304.437	+	527.300i	−0.418757	+	0.725309i	−0.995815	−	0.0913946i	$-0.970868\pi$
$727$	−304.437	+	527.300i	−0.418757	+	0.725309i	0.577057	+	0.816704i	$0.304201\pi$
$728$		−	474.481i		−	0.651760i
$729$		0			0
$730$	866.874			1.18750
$731$	67.6840	+	39.0774i	0.0925910	+	0.0534574i
$732$		0			0
$733$	440.351	+	762.709i	0.600751	+	1.04053i	0.992708	+	0.120548i	$0.0384650\pi$
$733$	440.351	+	762.709i	0.600751	+	1.04053i	−0.391957	+	0.919984i	$0.628202\pi$
$734$	−2031.79	+	1173.05i	−2.76810	+	1.59816i
$735$		0			0
$736$	−1292.39	+	2238.49i	−1.75597	+	3.04143i
$737$		−	629.950i		−	0.854749i
$738$		0			0
$739$	−917.157			−1.24108			−0.620540	−	0.784175i	$-0.713086\pi$
$739$	−917.157			−1.24108			−0.620540	+	0.784175i	$0.713086\pi$
$740$	861.556	+	497.419i	1.16426	+	0.672188i
$741$		0			0
$742$	1363.02	+	2360.82i	1.83695	+	3.18170i
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.309159	−	0.951010i	$-0.399952\pi$
$743$	956.492	−	552.231i	1.28734	−	0.743245i	0.978179	+	0.207765i	$0.0666191\pi$
$744$		0			0
$745$	103.880	−	179.926i	0.139437	−	0.241511i
$746$		−	1460.74i		−	1.95810i
$747$		0			0
$748$	−142.287			−0.190223
$749$	620.071	+	357.998i	0.827866	+	0.477968i
$750$		0			0
$751$	−330.239	−	571.990i	−0.439732	−	0.761638i	0.557936	−	0.829884i	$-0.311593\pi$
$751$	−330.239	−	571.990i	−0.439732	−	0.761638i	−0.997669	+	0.0682453i	$0.978260\pi$
$752$	1583.51	−	914.241i	2.10573	−	1.21575i
$753$		0			0
$754$	89.8684	−	155.657i	0.119189	−	0.206441i
$755$			508.096i			0.672974i
$756$		0			0
$757$	−353.728			−0.467276			−0.233638	−	0.972324i	$-0.575063\pi$
$757$	−353.728			−0.467276			−0.233638	+	0.972324i	$0.575063\pi$
$758$	169.702	+	97.9778i	0.223882	+	0.129258i
$759$		0			0
$760$	183.899	+	318.522i	0.241972	+	0.419108i
$761$	−708.380	+	408.983i	−0.930854	+	0.537429i	−0.887081	−	0.461613i	$-0.847271\pi$
$761$	−708.380	+	408.983i	−0.930854	+	0.537429i	−0.0437722	+	0.999042i	$0.513938\pi$
$762$		0			0
$763$	9.53584	−	16.5166i	0.0124978	−	0.0216469i
$764$			2875.00i			3.76309i
$765$		0			0
$766$	414.465			0.541078
$767$	−12.0855	−	6.97756i	−0.0157568	−	0.00909721i
$768$		0			0
$769$	500.408	+	866.732i	0.650725	+	1.12709i	0.982947	+	0.183888i	$0.0588684\pi$
$769$	500.408	+	866.732i	0.650725	+	1.12709i	−0.332222	+	0.943201i	$0.607798\pi$
$770$	394.751	−	227.910i	0.512664	−	0.295987i
$771$		0			0
$772$	−471.530	+	816.713i	−0.610790	+	1.05792i
$773$			860.440i			1.11312i	0.830808	+	0.556559i	$0.187879\pi$
$773$			860.440i			1.11312i	−0.830808	+	0.556559i	$0.812121\pi$
$774$		0			0
$775$	−133.206			−0.171879
$776$	1844.20	+	1064.75i	2.37655	+	1.37210i
$777$		0			0
$778$	197.633	+	342.310i	0.254027	+	0.439987i
$779$	109.748	−	63.3632i	0.140884	−	0.0813391i
$780$		0			0
$781$	−86.8283	+	150.391i	−0.111176	+	0.192562i
$782$		−	251.442i		−	0.321538i
$783$		0			0
$784$	161.638			0.206171
$785$	−3.06898	−	1.77187i	−0.00390952	−	0.00225716i
$786$		0			0
$787$	−463.491	−	802.789i	−0.588933	−	1.02006i	−0.994372	−	0.105940i	$-0.966215\pi$
$787$	−463.491	−	802.789i	−0.588933	−	1.02006i	0.405439	−	0.914122i	$-0.367119\pi$
$788$	1119.42	−	646.297i	1.42058	−	0.820174i
$789$		0			0
$790$	336.387	−	582.640i	0.425807	−	0.737519i
$791$			19.8531i			0.0250987i
$792$		0			0
$793$	−225.651			−0.284553
$794$	323.236	+	186.620i	0.407098	+	0.235038i
$795$		0			0
$796$	679.534	+	1176.99i	0.853686	+	1.47863i
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.116888	−	0.993145i	$-0.462708\pi$
$797$	825.230	−	476.447i	1.03542	−	0.597800i	0.918533	+	0.395345i	$0.129375\pi$
$798$		0			0
$799$	−40.0564	+	69.3797i	−0.0501332	+	0.0868332i
$800$			365.111i			0.456389i
$801$		0			0
$802$	587.129			0.732082
$803$	675.087	+	389.762i	0.840707	+	0.485382i
$804$		0			0
$805$	287.365	+	497.731i	0.356975	+	0.618299i
$806$	−252.883	+	146.002i	−0.313750	+	0.181144i
$807$		0			0
$808$	1515.28	−	2624.55i	1.87535	−	3.24820i
$809$		−	1425.22i		−	1.76171i	−0.473387	−	0.880855i	$-0.656969\pi$
$809$		−	1425.22i		−	1.76171i	0.473387	−	0.880855i	$-0.343031\pi$
$810$		0			0
$811$	−473.774			−0.584185			−0.292093	−	0.956390i	$-0.594352\pi$
$811$	−473.774			−0.584185			−0.292093	+	0.956390i	$0.594352\pi$
$812$	1027.26	+	593.087i	1.26509	+	0.730402i
$813$		0			0
$814$	626.903	+	1085.83i	0.770151	+	1.33394i
$815$	80.7131	−	46.5997i	0.0990345	−	0.0571776i
$816$		0			0
$817$	151.777	−	262.885i	0.185773	−	0.321769i
$818$		−	2560.42i		−	3.13010i
$819$		0			0
$820$	382.305			0.466225
$821$	63.4905	+	36.6562i	0.0773331	+	0.0446483i	0.538168	−	0.842838i	$-0.319117\pi$
$821$	63.4905	+	36.6562i	0.0773331	+	0.0446483i	−0.460835	+	0.887486i	$0.652450\pi$
$822$		0			0
$823$	−316.027	−	547.374i	−0.383994	−	0.665096i	0.607635	−	0.794216i	$-0.292118\pi$
$823$	−316.027	−	547.374i	−0.383994	−	0.665096i	−0.991629	+	0.129120i	$0.958785\pi$
$824$	−3315.90	+	1914.44i	−4.02416	+	2.32335i
$825$		0			0
$826$	64.5385	−	111.784i	0.0781338	−	0.135332i
$827$			226.153i			0.273462i	0.990608	+	0.136731i	$0.0436597\pi$
$827$			226.153i			0.273462i	−0.990608	+	0.136731i	$0.956340\pi$
$828$		0			0
$829$	−522.396			−0.630152			−0.315076	−	0.949067i	$-0.602030\pi$
$829$	−522.396			−0.630152			−0.315076	+	0.949067i	$0.602030\pi$
$830$	−142.901	−	82.5042i	−0.172170	−	0.0994026i
$831$		0			0
$832$	145.629	+	252.236i	0.175034	+	0.303168i
$833$	−6.13317	+	3.54099i	−0.00736275	+	0.00425089i
$834$		0			0
$835$	10.3461	−	17.9200i	0.0123905	−	0.0214610i
$836$			552.642i			0.661055i
$837$		0			0
$838$	192.792			0.230061
$839$	−511.329	−	295.216i	−0.609450	−	0.351866i	0.163300	−	0.986576i	$-0.447786\pi$
$839$	−511.329	−	295.216i	−0.609450	−	0.351866i	−0.772750	+	0.634710i	$0.781119\pi$
$840$		0			0
$841$	−286.046	−	495.446i	−0.340126	−	0.589115i
$842$	−47.7379	+	27.5615i	−0.0566959	+	0.0327334i
$843$		0			0
$844$	788.120	−	1365.06i	0.933791	−	1.61737i
$845$			358.655i			0.424444i
$846$		0			0
$847$	−468.718			−0.553386
$848$	−3775.47	−	2179.77i	−4.45220	−	2.57048i
$849$		0			0
$850$	−17.7586	−	30.7588i	−0.0208925	−	0.0361868i
$851$	−1369.09	+	790.444i	−1.60880	+	0.928841i
$852$		0			0
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	0.0972332	+	0.995262i	$0.469001\pi$
$853$	−693.749	+	1201.61i	−0.813305	+	1.40869i	−0.910538	+	0.413424i	$0.864333\pi$
$854$		−	2087.14i		−	2.44396i
$855$		0			0
$856$	−2196.58			−2.56610
$857$	683.058	+	394.363i	0.797033	+	0.460167i	0.842433	−	0.538801i	$-0.181123\pi$
$857$	683.058	+	394.363i	0.797033	+	0.460167i	−0.0453994	+	0.998969i	$0.514456\pi$
$858$		0			0
$859$	−413.601	−	716.378i	−0.481491	−	0.833968i	0.518283	−	0.855209i	$-0.326571\pi$
$859$	−413.601	−	716.378i	−0.481491	−	0.833968i	−0.999774	+	0.0212416i	$0.993238\pi$
$860$	793.065	−	457.876i	0.922169	−	0.532414i
$861$		0			0
$862$	−72.2667	+	125.170i	−0.0838361	+	0.145208i
$863$			1089.70i			1.26268i	0.775504	+	0.631342i	$0.217496\pi$
$863$			1089.70i			1.26268i	−0.775504	+	0.631342i	$0.782504\pi$
$864$		0			0
$865$	−329.558			−0.380992
$866$	−1762.45	−	1017.55i	−2.03516	−	1.17500i
$867$		0			0
$868$	−963.540	−	1668.90i	−1.11007	−	1.92270i
$869$	523.930	−	302.491i	0.602912	−	0.348091i
$870$		0			0
$871$	122.974	−	212.996i	0.141187	−	0.244542i
$872$			58.5093i			0.0670979i
$873$		0			0
$874$	−976.605			−1.11740
$875$	70.3064	+	40.5914i	0.0803502	+	0.0463902i
$876$		0			0
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	0.717942	−	0.696103i	$-0.245084\pi$
$877$	−213.875	−	370.443i	−0.243872	−	0.422398i	−0.961814	+	0.273705i	$0.911751\pi$
$878$	−813.575	+	469.718i	−0.926623	+	0.534986i
$879$		0			0
$880$	−364.478	+	631.294i	−0.414179	+	0.717379i
$881$		−	1113.87i		−	1.26432i	−0.774837	−	0.632161i	$-0.782168\pi$
$881$		−	1113.87i		−	1.26432i	0.774837	−	0.632161i	$-0.217832\pi$
$882$		0			0
$883$	−408.581			−0.462719			−0.231359	−	0.972868i	$-0.574317\pi$
$883$	−408.581			−0.462719			−0.231359	+	0.972868i	$0.574317\pi$
$884$	−48.1094	−	27.7760i	−0.0544224	−	0.0314208i
$885$		0			0
$886$	−1365.46	−	2365.05i	−1.54116	−	2.66936i
$887$	755.098	−	435.956i	0.851294	−	0.491495i	−0.00979311	−	0.999952i	$-0.503117\pi$
$887$	755.098	−	435.956i	0.851294	−	0.491495i	0.861087	+	0.508457i	$0.169784\pi$
$888$		0			0
$889$	700.924	−	1214.04i	0.788441	−	1.36562i
$890$		−	242.773i		−	0.272778i
$891$		0			0
$892$	2054.60			2.30336
$893$	269.471	+	155.579i	0.301760	+	0.174221i
$894$		0			0
$895$	178.910	+	309.881i	0.199899	+	0.346236i
$896$	−496.272	+	286.523i	−0.553875	+	0.319780i
$897$		0			0
$898$	−176.965	+	306.512i	−0.197066	+	0.341328i
$899$		−	436.874i		−	0.485956i
$900$		0			0
$901$	191.008			0.211995
$902$	417.270	+	240.911i	0.462606	+	0.267085i
$903$		0			0
$904$	−30.4533	−	52.7466i	−0.0336872	−	0.0583480i
$905$	58.7427	−	33.9151i	0.0649091	−	0.0374753i
$906$		0			0
$907$	843.097	−	1460.29i	0.929544	−	1.61002i	0.145459	−	0.989364i	$-0.453534\pi$
$907$	843.097	−	1460.29i	0.929544	−	1.61002i	0.784085	−	0.620653i	$-0.213133\pi$
$908$			1467.33i			1.61600i
$909$		0			0
$910$	177.963			0.195563
$911$	383.084	+	221.173i	0.420509	+	0.242781i	0.695295	−	0.718724i	$-0.255274\pi$
$911$	383.084	+	221.173i	0.420509	+	0.242781i	−0.274786	+	0.961505i	$0.588607\pi$
$912$		0			0
$913$	−74.1907	−	128.502i	−0.0812603	−	0.140747i
$914$	1321.60	−	763.024i	1.44595	−	0.834819i
$915$		0			0
$916$	−135.232	+	234.228i	−0.147633	+	0.255708i
$917$		−	1687.46i		−	1.84020i
$918$		0			0
$919$	−182.236			−0.198298			−0.0991489	−	0.995073i	$-0.531612\pi$
$919$	−182.236			−0.198298			−0.0991489	+	0.995073i	$0.531612\pi$
$920$	−1526.97	−	881.597i	−1.65975	−	0.958258i
$921$		0			0
$922$	1103.96	+	1912.12i	1.19736	+	2.07388i
$923$	−58.7162	+	33.8998i	−0.0636145	+	0.0367279i
$924$		0			0
$925$	−111.653	+	193.389i	−0.120706	+	0.209069i
$926$		−	2996.47i		−	3.23592i
$927$		0			0
$928$	−1197.45			−1.29035
$929$	1150.27	+	664.111i	1.23819	+	0.714867i	0.968723	−	0.248144i	$-0.0798205\pi$
$929$	1150.27	+	664.111i	1.23819	+	0.714867i	0.269463	+	0.963011i	$0.413154\pi$
$930$		0			0
$931$	13.7532	+	23.8213i	0.0147725	+	0.0255868i
$932$	−341.644	+	197.248i	−0.366571	+	0.211640i
$933$		0			0
$934$	−38.5671	+	66.8003i	−0.0412924	+	0.0715206i
$935$		−	31.9383i		−	0.0341587i
$936$		0			0
$937$	−276.582			−0.295178			−0.147589	−	0.989049i	$-0.547151\pi$
$937$	−276.582			−0.295178			−0.147589	+	0.989049i	$0.547151\pi$
$938$	1970.10	+	1137.44i	2.10032	+	1.21262i
$939$		0			0
$940$	469.348	+	812.934i	0.499306	+	0.864823i
$941$	−1083.50	+	625.557i	−1.15143	+	0.664779i	−0.949236	−	0.314566i	$-0.898141\pi$
$941$	−1083.50	+	625.557i	−1.15143	+	0.664779i	−0.202196	+	0.979345i	$0.564808\pi$
$942$		0			0
$943$	−303.758	+	526.124i	−0.322119	+	0.557926i
$944$			206.422i			0.218668i
$945$		0			0
$946$	1154.13			1.22001
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.904577	−	0.426310i	$-0.140187\pi$
$947$	935.323	+	540.009i	0.987670	+	0.570232i	0.0830930	+	0.996542i	$0.473520\pi$
$948$		0			0
$949$	152.172	+	263.570i	0.160350	+	0.277734i
$950$	−119.468	+	68.9746i	−0.125755	+	0.0726048i
$951$		0			0
$952$	153.753	−	266.308i	0.161505	−	0.279735i
$953$		−	328.534i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$953$		−	328.534i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$954$		0			0
$955$	−645.336			−0.675745
$956$	−547.294	−	315.980i	−0.572483	−	0.330523i
$957$		0			0
$958$	−939.239	−	1626.81i	−0.980416	−	1.69813i
$959$	−1119.47	+	646.328i	−1.16733	+	0.673961i
$960$		0			0
$961$	125.623	−	217.585i	0.130721	−	0.226416i
$962$			489.515i			0.508851i
$963$		0			0
$964$	1377.04			1.42846
$965$	−183.323	−	105.842i	−0.189972	−	0.109681i
$966$		0			0
$967$	298.854	+	517.631i	0.309053	+	0.535296i	0.978155	−	0.207875i	$-0.0666546\pi$
$967$	298.854	+	517.631i	0.309053	+	0.535296i	−0.669102	+	0.743170i	$0.733321\pi$
$968$	1245.31	−	718.981i	1.28648	−	0.742749i
$969$		0			0
$970$	−399.354	+	691.701i	−0.411705	+	0.713094i
$971$		−	711.597i		−	0.732850i	−0.930448	−	0.366425i	$-0.880582\pi$
$971$		−	711.597i		−	0.732850i	0.930448	−	0.366425i	$-0.119418\pi$
$972$		0			0
$973$	−232.857			−0.239319
$974$	260.279	+	150.272i	0.267226	+	0.154283i
$975$		0			0
$976$	1668.90	+	2890.61i	1.70994	+	2.96169i
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	−0.642058	−	0.766656i	$-0.721919\pi$
$977$	−292.262	+	168.738i	−0.299142	+	0.172710i	0.342915	+	0.939366i	$0.388586\pi$
$978$		0			0
$979$	109.155	−	189.062i	0.111496	−	0.193117i
$980$			82.9807i			0.0846742i
$981$		0			0
$982$	1803.38			1.83643
$983$	274.504	+	158.485i	0.279252	+	0.161226i	0.633085	−	0.774083i	$-0.281789\pi$
$983$	274.504	+	158.485i	0.279252	+	0.161226i	−0.353833	+	0.935309i	$0.615122\pi$
$984$		0			0
$985$	145.071	+	251.270i	0.147280	+	0.255097i
$986$	100.879	−	58.2427i	0.102312	−	0.0590697i
$987$		0			0
$988$	−107.882	+	186.857i	−0.109193	+	0.189127i
$989$			1455.21i			1.47140i
$990$		0			0
$991$	685.922			0.692152			0.346076	−	0.938207i	$-0.387514\pi$
$991$	685.922			0.692152			0.346076	+	0.938207i	$0.387514\pi$
$992$	1684.76	+	972.700i	1.69835	+	0.980544i
$993$		0			0
$994$	−313.554	−	543.092i	−0.315447	−	0.546370i
$995$	−264.192	+	152.532i	−0.265520	+	0.153298i
$996$		0			0
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	−0.974732	−	0.223376i	$-0.928292\pi$
$997$	−293.035	+	507.551i	−0.293917	+	0.509078i	0.680816	+	0.732455i	$0.261625\pi$
$998$			130.823i			0.131086i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.116.8		16
3.2	odd	2		45.3.i.a.11.1	✓	16
4.3	odd	2		2160.3.bs.c.1601.1		16
5.2	odd	4		675.3.i.c.224.1		32
5.3	odd	4		675.3.i.c.224.16		32
5.4	even	2		675.3.j.b.251.1		16
9.2	odd	6		405.3.c.a.161.16		16
9.4	even	3		45.3.i.a.41.1	yes	16
9.5	odd	6	inner	135.3.i.a.71.8		16
9.7	even	3		405.3.c.a.161.1		16
12.11	even	2		720.3.bs.c.641.2		16
15.2	even	4		225.3.i.b.74.16		32
15.8	even	4		225.3.i.b.74.1		32
15.14	odd	2		225.3.j.b.101.8		16
36.23	even	6		2160.3.bs.c.881.1		16
36.31	odd	6		720.3.bs.c.401.2		16
45.4	even	6		225.3.j.b.176.8		16
45.13	odd	12		225.3.i.b.149.16		32
45.14	odd	6		675.3.j.b.476.1		16
45.22	odd	12		225.3.i.b.149.1		32
45.23	even	12		675.3.i.c.449.1		32
45.32	even	12		675.3.i.c.449.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	3.2	odd	2
45.3.i.a.41.1	yes	16	9.4	even	3
135.3.i.a.71.8		16	9.5	odd	6	inner
135.3.i.a.116.8		16	1.1	even	1	trivial
225.3.i.b.74.1		32	15.8	even	4
225.3.i.b.74.16		32	15.2	even	4
225.3.i.b.149.1		32	45.22	odd	12
225.3.i.b.149.16		32	45.13	odd	12
225.3.j.b.101.8		16	15.14	odd	2
225.3.j.b.176.8		16	45.4	even	6
405.3.c.a.161.1		16	9.7	even	3
405.3.c.a.161.16		16	9.2	odd	6
675.3.i.c.224.1		32	5.2	odd	4
675.3.i.c.224.16		32	5.3	odd	4
675.3.i.c.449.1		32	45.23	even	12
675.3.i.c.449.16		32	45.32	even	12
675.3.j.b.251.1		16	5.4	even	2
675.3.j.b.476.1		16	45.14	odd	6
720.3.bs.c.401.2		16	36.31	odd	6
720.3.bs.c.641.2		16	12.11	even	2
2160.3.bs.c.881.1		16	36.23	even	6
2160.3.bs.c.1601.1		16	4.3	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.23594 + 1.86827i) q^{2} +(4.98088 + 8.62715i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.63061 - 6.28840i) q^{7} +22.2764i q^{8} +O(q^{10})\)	\(q+(3.23594 + 1.86827i) q^{2} +(4.98088 + 8.62715i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(3.63061 - 6.28840i) q^{7} +22.2764i q^{8} -8.35517 q^{10} +(-6.50668 - 3.75663i) q^{11} +(-1.46668 - 2.54036i) q^{13} +(23.4969 - 13.5659i) q^{14} +(-21.6949 + 37.5766i) q^{16} -1.90107i q^{17} -7.38378 q^{19} +(-19.2909 - 11.1376i) q^{20} +(-14.0368 - 24.3125i) q^{22} +(30.6549 - 17.6986i) q^{23} +(2.50000 - 4.33013i) q^{25} -10.9606i q^{26} +72.3346 q^{28} +(14.2015 + 8.19922i) q^{29} +(-13.3206 - 23.0720i) q^{31} +(-63.2391 + 36.5111i) q^{32} +(3.55172 - 6.15176i) q^{34} +16.2366i q^{35} -44.6613 q^{37} +(-23.8935 - 13.7949i) q^{38} +(-24.9058 - 43.1381i) q^{40} +(-14.8634 + 8.58140i) q^{41} +(-20.5554 + 35.6031i) q^{43} -74.8454i q^{44} +132.263 q^{46} +(-36.4950 - 21.0704i) q^{47} +(-1.86263 - 3.22616i) q^{49} +(16.1797 - 9.34136i) q^{50} +(14.6107 - 25.3065i) q^{52} +100.474i q^{53} +16.8002 q^{55} +(140.083 + 80.8770i) q^{56} +(30.6367 + 53.0644i) q^{58} +(4.12003 - 2.37870i) q^{59} +(38.4629 - 66.6197i) q^{61} -99.5461i q^{62} -99.2915 q^{64} +(5.68041 + 3.27959i) q^{65} +(41.9225 + 72.6119i) q^{67} +(16.4008 - 9.46903i) q^{68} +(-30.3343 + 52.5406i) q^{70} -23.1134i q^{71} -103.753 q^{73} +(-144.521 - 83.4395i) q^{74} +(-36.7778 - 63.7010i) q^{76} +(-47.2464 + 27.2777i) q^{77} +(-40.2610 + 69.7340i) q^{79} -97.0225i q^{80} -64.1296 q^{82} +(17.1034 + 9.87463i) q^{83} +(2.12546 + 3.68141i) q^{85} +(-133.032 + 76.8063i) q^{86} +(83.6843 - 144.945i) q^{88} +29.0566i q^{89} -21.2997 q^{91} +(305.377 + 176.310i) q^{92} +(-78.7306 - 136.365i) q^{94} +(14.2986 - 8.25532i) q^{95} +(47.7972 - 82.7872i) q^{97} -13.9196i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 16 * q^4 + 2 * q^7	\( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

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