LMFDB - Embedded newform 135.3.i.a.71.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(71,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			71.8
Root			$-3.73655i$ of defining polynomial
Character	$\chi$	$=$	135.71
Dual form			135.3.i.a.116.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	0.630528	−	0.776167i	$-0.282839\pi$
$2$	3.23594	−	1.86827i	1.61797	−	0.934136i	0.987444	−	0.157969i	$-0.0504947\pi$
$3$		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	0.999765	+	0.0216804i	$0.00690163\pi$
$7$	3.63061	+	6.28840i	0.518658	+	0.898342i	−0.481107	+	0.876662i	$0.659765\pi$
$8$		−	22.2764i		−	2.78455i
$9$		0			0
$10$	−8.35517			−0.835517
$11$	−6.50668	+	3.75663i	−0.591516	+	0.341512i	−0.765697	−	0.643202i	$-0.777606\pi$
$11$	−6.50668	+	3.75663i	−0.591516	+	0.341512i	0.174181	+	0.984714i	$0.444272\pi$
$12$		0			0
$13$	−1.46668	+	2.54036i	−0.112821	+	0.195412i	−0.916907	−	0.399102i	$-0.869322\pi$
$13$	−1.46668	+	2.54036i	−0.112821	+	0.195412i	0.804085	+	0.594514i	$0.202655\pi$
$14$	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	$0.0178072\pi$
$17$			1.90107i			0.111828i	−0.998436	+	0.0559139i	$0.982193\pi$
$18$		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	0.985731	−	0.168326i	$-0.0538360\pi$
$23$	30.6549	+	17.6986i	1.33282	+	0.769506i	0.347091	+	0.937831i	$0.387169\pi$
$24$		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	−0.234747	−	0.972057i	$-0.575426\pi$
$29$	14.2015	−	8.19922i	0.489705	−	0.282732i	0.724452	+	0.689325i	$0.242093\pi$
$30$		0			0
$31$	−13.3206	+	23.0720i	−0.429697	+	0.744257i	−0.996846	−	0.0793581i	$-0.974713\pi$
$31$	−13.3206	+	23.0720i	−0.429697	+	0.744257i	0.567149	+	0.823615i	$0.308046\pi$
$32$	−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	0.307664	−	0.951495i	$-0.400453\pi$
$41$	−14.8634	−	8.58140i	−0.362522	−	0.209302i	−0.670187	+	0.742193i	$0.733786\pi$
$42$		0			0
$43$	−20.5554	−	35.6031i	−0.478033	−	0.827978i	0.521650	−	0.853160i	$-0.325317\pi$
$43$	−20.5554	−	35.6031i	−0.478033	−	0.827978i	−0.999683	+	0.0251818i	$0.991984\pi$
$44$			74.8454i			1.70103i
$45$		0			0
$46$	132.263			2.87529
$47$	−36.4950	+	21.0704i	−0.776490	+	0.448307i	−0.835185	−	0.549969i	$-0.814639\pi$
$47$	−36.4950	+	21.0704i	−0.776490	+	0.448307i	0.0586949	+	0.998276i	$0.481306\pi$
$48$		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	$-0.603236\pi$
$53$		−	100.474i		−	1.89573i	0.318671	−	0.947865i	$-0.396764\pi$
$54$		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	0.534509	−	0.845163i	$-0.320497\pi$
$59$	4.12003	+	2.37870i	0.0698310	+	0.0403169i	−0.464678	+	0.885480i	$0.653830\pi$
$60$		0			0
$61$	38.4629	+	66.6197i	0.630539	+	1.09213i	0.987442	+	0.157985i	$0.0504996\pi$
$61$	38.4629	+	66.6197i	0.630539	+	1.09213i	−0.356902	+	0.934142i	$0.616167\pi$
$62$			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	−0.362694	−	0.931908i	$-0.618143\pi$
$67$	41.9225	−	72.6119i	0.625709	−	1.08376i	0.988403	−	0.151852i	$-0.0485237\pi$
$68$	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	$0.0520429\pi$
$71$			23.1134i			0.325540i	−0.986664	+	0.162770i	$0.947957\pi$
$72$		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	−0.999938	−	0.0111586i	$-0.996448\pi$
$79$	−40.2610	−	69.7340i	−0.509633	−	0.882709i	0.490305	−	0.871551i	$-0.336885\pi$
$80$			97.0225i			1.21278i
$81$		0			0
$82$	−64.1296			−0.782068
$83$	17.1034	−	9.87463i	0.206065	−	0.118971i	−0.393417	−	0.919360i	$-0.628707\pi$
$83$	17.1034	−	9.87463i	0.206065	−	0.118971i	0.599481	+	0.800389i	$0.295374\pi$
$84$		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	$-0.947806\pi$
$89$		−	29.0566i		−	0.326478i	0.986587	−	0.163239i	$-0.0521942\pi$
$90$		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	0.999965	−	0.00834602i	$-0.00265665\pi$
$97$	47.7972	+	82.7872i	0.492755	+	0.853476i	−0.507210	+	0.861822i	$0.669323\pi$
$98$			13.9196i			0.142036i
$99$		0			0
$100$	49.8088			0.498088
$101$	−117.817	+	68.0219i	−1.16651	+	0.673484i	−0.952855	−	0.303426i	$-0.901870\pi$
$101$	−117.817	+	68.0219i	−1.16651	+	0.673484i	−0.213653	+	0.976910i	$0.568536\pi$
$102$		0			0
$103$	85.9401	−	148.853i	0.834370	−	1.44517i	−0.0601721	−	0.998188i	$-0.519165\pi$
$103$	85.9401	−	148.853i	0.834370	−	1.44517i	0.894542	−	0.446983i	$-0.147502\pi$
$104$	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	$-0.847572\pi$
$107$		−	98.6056i		−	0.921548i	0.887518	−	0.460774i	$-0.152428\pi$
$108$		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	0.489486	−	0.872011i	$-0.337184\pi$
$113$	−2.36782	−	1.36706i	−0.0209542	−	0.0120979i	−0.510440	+	0.859913i	$0.670518\pi$
$114$		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	0.999049	+	0.0435937i	$0.0138807\pi$
$131$	201.259	+	116.197i	1.53633	+	0.886999i	0.537278	+	0.843405i	$0.319453\pi$
$132$		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	−0.942759	−	0.333475i	$-0.891779\pi$
$137$	−154.172	+	89.0111i	−1.12534	+	0.649716i	−0.182582	+	0.983191i	$0.558445\pi$
$138$		0			0
$139$	−16.0343	+	27.7722i	−0.115355	+	0.199800i	−0.917922	−	0.396762i	$-0.870134\pi$
$139$	−16.0343	+	27.7722i	−0.115355	+	0.199800i	0.802567	+	0.596562i	$0.203467\pi$
$140$	−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	0.205058	−	0.978750i	$-0.434262\pi$
$149$	−80.4653	−	46.4567i	−0.540036	−	0.311790i	−0.745093	+	0.666960i	$0.767595\pi$
$150$		0			0
$151$	113.614	+	196.785i	0.752408	+	1.30321i	0.946653	+	0.322256i	$0.104441\pi$
$151$	113.614	+	196.785i	0.752408	+	1.30321i	−0.194245	+	0.980953i	$0.562226\pi$
$152$			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	−0.863491	−	0.504365i	$-0.831727\pi$
$157$	0.792406	−	1.37249i	0.00504717	−	0.00874196i	0.868538	+	0.495623i	$0.165060\pi$
$158$	−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	0.475814	−	0.879546i	$-0.342154\pi$
$167$	−8.01405	−	4.62692i	−0.0479884	−	0.0277061i	−0.523802	+	0.851840i	$0.675487\pi$
$168$		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	−0.0834771	−	0.996510i	$-0.526603\pi$
$173$	127.637	−	73.6913i	0.737787	−	0.425962i	0.821264	+	0.570548i	$0.193269\pi$
$174$		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	$0.147504\pi$
$179$			160.022i			0.893977i	−0.894540	+	0.446988i	$0.852496\pi$
$180$		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	0.326716	−	0.945122i	$-0.394058\pi$
$191$	249.938	−	144.302i	1.30857	−	0.755506i	0.981858	+	0.189617i	$0.0607245\pi$
$192$		0			0
$193$	47.3339	−	81.9847i	0.245253	−	0.424791i	−0.716949	−	0.697125i	$-0.754462\pi$
$193$	47.3339	−	81.9847i	0.245253	−	0.424791i	0.962203	+	0.272334i	$0.0877955\pi$
$194$	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	$0.106822\pi$
$197$			129.755i			0.658657i	−0.944215	+	0.329329i	$0.893178\pi$
$198$		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	−0.990320	−	0.138806i	$-0.955673\pi$
$211$	−79.1144	+	137.030i	−0.374950	+	0.649432i	0.615370	+	0.788239i	$0.289007\pi$
$212$	−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	0.999082	−	0.0428406i	$-0.0136407\pi$
$223$	103.124	+	178.616i	0.462440	+	0.800969i	−0.536642	+	0.843810i	$0.680307\pi$
$224$		−	530.230i		−	2.36710i
$225$		0			0
$226$	−10.2162			−0.0452044
$227$	127.562	−	73.6481i	0.561948	−	0.324441i	−0.191979	−	0.981399i	$-0.561490\pi$
$227$	127.562	−	73.6481i	0.561948	−	0.324441i	0.753927	+	0.656958i	$0.228157\pi$
$228$		0			0
$229$	13.5751	−	23.5127i	0.0592798	−	0.102676i	−0.834863	−	0.550458i	$-0.814453\pi$
$229$	13.5751	−	23.5127i	0.0592798	−	0.102676i	0.894142	+	0.447783i	$0.147786\pi$
$230$	−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	$-0.972917\pi$
$233$		−	39.6011i		−	0.169962i	0.996383	−	0.0849808i	$-0.0270829\pi$
$234$		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	0.380641	−	0.924723i	$-0.375703\pi$
$239$	−54.9394	−	31.7193i	−0.229872	−	0.132717i	−0.610513	+	0.792006i	$0.709037\pi$
$240$		0			0
$241$	69.1161	+	119.713i	0.286789	+	0.496733i	0.973041	−	0.230630i	$-0.0740789\pi$
$241$	69.1161	+	119.713i	0.286789	+	0.496733i	−0.686253	+	0.727363i	$0.740746\pi$
$242$			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	$0.121145\pi$
$251$			186.477i			0.742936i	−0.928446	+	0.371468i	$0.878855\pi$
$252$		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	0.0532790	−	0.998580i	$-0.483033\pi$
$257$	−201.713	−	116.459i	−0.784877	−	0.453149i	−0.838156	+	0.545431i	$0.816366\pi$
$258$		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	−0.482124	−	0.876103i	$-0.660135\pi$
$263$	9.34728	−	5.39665i	0.0355410	−	0.0205196i	0.517665	+	0.855583i	$0.326801\pi$
$264$		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	$0.0346566\pi$
$269$			58.4601i			0.217324i	−0.994079	+	0.108662i	$0.965343\pi$
$270$		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	0.515618	−	0.856819i	$-0.327562\pi$
$277$	−134.128	−	232.317i	−0.484218	−	0.838690i	−0.999836	+	0.0181286i	$0.994229\pi$
$278$			119.826i			0.431028i
$279$		0			0
$280$	−361.693			−1.29176
$281$	−159.428	+	92.0461i	−0.567361	+	0.327566i	−0.756095	−	0.654462i	$-0.772895\pi$
$281$	−159.428	+	92.0461i	−0.567361	+	0.327566i	0.188734	+	0.982028i	$0.439562\pi$
$282$		0			0
$283$	231.303	−	400.628i	0.817324	−	1.41565i	−0.0903234	−	0.995912i	$-0.528790\pi$
$283$	231.303	−	400.628i	0.817324	−	1.41565i	0.907647	−	0.419734i	$-0.137877\pi$
$284$	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	0.0122351	−	0.999925i	$-0.496105\pi$
$293$	−248.349	−	143.384i	−0.847608	−	0.489367i	−0.859843	+	0.510559i	$0.829439\pi$
$294$		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	−0.444421	−	0.895818i	$-0.646591\pi$
$311$	−448.597	−	258.997i	−1.44243	−	0.832789i	−0.998012	+	0.0630292i	$0.979924\pi$
$312$		0			0
$313$	247.615	+	428.882i	0.791102	+	1.37023i	0.925285	+	0.379272i	$0.123826\pi$
$313$	247.615	+	428.882i	0.791102	+	1.37023i	−0.134183	+	0.990957i	$0.542841\pi$
$314$		−	5.92172i		−	0.0188590i
$315$		0			0
$316$	−802.141			−2.53842
$317$	189.840	−	109.604i	0.598864	−	0.345754i	−0.169731	−	0.985491i	$-0.554290\pi$
$317$	189.840	−	109.604i	0.598864	−	0.345754i	0.768595	+	0.639736i	$0.220956\pi$
$318$		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	0.928796	−	0.370592i	$-0.120845\pi$
$331$	47.4838	+	82.2443i	0.143455	+	0.248472i	−0.785340	+	0.619064i	$0.787512\pi$
$332$		−	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	−0.174411	−	0.984673i	$-0.555802\pi$
$337$	257.989	−	446.850i	0.765547	−	1.32597i	0.939957	−	0.341293i	$-0.110865\pi$
$338$	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	0.632561	−	0.774510i	$-0.282004\pi$
$347$	96.4994	+	55.7140i	0.278096	+	0.160559i	−0.354465	+	0.935069i	$0.615337\pi$
$348$		0			0
$349$	−310.131	−	537.162i	−0.888627	−	1.53915i	−0.841499	−	0.540258i	$-0.818327\pi$
$349$	−310.131	−	537.162i	−0.888627	−	1.53915i	−0.0471279	−	0.998889i	$-0.515007\pi$
$350$			135.659i			0.387598i
$351$		0			0
$352$	548.635			1.55862
$353$	−488.067	+	281.786i	−1.38263	+	0.798260i	−0.992470	−	0.122488i	$-0.960913\pi$
$353$	−488.067	+	281.786i	−1.38263	+	0.798260i	−0.390157	+	0.920748i	$0.627579\pi$
$354$		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	$-0.803766\pi$
$359$		−	415.128i		−	1.15635i	0.815915	−	0.578173i	$-0.196234\pi$
$360$		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	−0.876252	−	0.481853i	$-0.839964\pi$
$367$	−313.940	−	543.761i	−0.855423	−	1.48164i	0.0208286	−	0.999783i	$-0.493370\pi$
$368$		−	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	0.475568	+	0.879679i	$0.342243\pi$
$373$	−195.467	+	338.559i	−0.524040	+	0.907665i	−0.999608	+	0.0279857i	$0.991091\pi$
$374$	−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	0.620136	−	0.784494i	$-0.287077\pi$
$383$	96.0614	+	55.4610i	0.250813	+	0.144807i	−0.369324	+	0.929301i	$0.620411\pi$
$384$		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	−0.377604	−	0.925967i	$-0.623252\pi$
$389$	91.6114	−	52.8918i	0.235505	−	0.135969i	0.613109	+	0.789998i	$0.289919\pi$
$390$		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	0.659985	−	0.751279i	$-0.270563\pi$
$401$	136.080	+	78.5658i	0.339352	+	0.195925i	−0.320634	+	0.947203i	$0.603896\pi$
$402$		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	0.0541134	+	0.998535i	$0.482767\pi$
$409$	−342.619	+	593.434i	−0.837700	+	1.45094i	−0.891813	+	0.452404i	$0.850567\pi$
$410$	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	0.552373	−	0.833597i	$-0.313722\pi$
$419$	44.6836	+	25.7981i	0.106643	+	0.0615706i	−0.445730	+	0.895168i	$0.647056\pi$
$420$		0			0
$421$	−7.37620	−	12.7760i	−0.0175207	−	0.0303467i	0.857132	−	0.515097i	$-0.172244\pi$
$421$	−7.37620	−	12.7760i	−0.0175207	−	0.0303467i	−0.874653	+	0.484750i	$0.838911\pi$
$422$			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	$-0.985711\pi$
$431$		−	38.6810i		−	0.0897472i	0.998993	−	0.0448736i	$-0.0142885\pi$
$432$		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	0.686583	−	0.727051i	$-0.259110\pi$
$439$	−125.709	−	217.735i	−0.286353	−	0.495978i	−0.972936	+	0.231073i	$0.925776\pi$
$440$		−	374.248i		−	0.850563i
$441$		0			0
$442$	−20.8369			−0.0471423
$443$	−632.952	+	365.435i	−1.42878	+	0.824909i	−0.997025	−	0.0770796i	$-0.975440\pi$
$443$	−632.952	+	365.435i	−1.42878	+	0.824909i	−0.431760	+	0.901989i	$0.642107\pi$
$444$		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	$-0.966362\pi$
$449$		−	94.7211i		−	0.210960i	0.994421	−	0.105480i	$-0.0336379\pi$
$450$		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	0.998178	−	0.0603323i	$-0.0192160\pi$
$457$	204.206	+	353.695i	0.446840	+	0.773949i	−0.551339	+	0.834282i	$0.685883\pi$
$458$		−	101.448i		−	0.221502i
$459$		0			0
$460$	−788.481			−1.71409
$461$	511.735	−	295.450i	1.11005	−	0.640890i	0.171211	−	0.985234i	$-0.445232\pi$
$461$	511.735	−	295.450i	1.11005	−	0.640890i	0.938843	+	0.344344i	$0.111899\pi$
$462$		0			0
$463$	−400.967	+	694.496i	−0.866020	+	1.49999i	1.04649e−5		1.00000i	$0.499997\pi$
$463$	−400.967	+	694.496i	−0.866020	+	1.49999i	−0.866031	+	0.499991i	$0.833337\pi$
$464$	−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	$-0.992964\pi$
$467$		−	20.6432i		−	0.0442039i	0.999756	−	0.0221019i	$-0.00703584\pi$
$468$		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	−0.880087	−	0.474812i	$-0.842516\pi$
$479$	−435.378	+	251.366i	−0.908931	+	0.524771i	−0.0288439	+	0.999584i	$0.509183\pi$
$480$		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	0.861078	−	0.508473i	$-0.169790\pi$
$491$	417.972	+	241.316i	0.851267	+	0.491479i	−0.00981129	+	0.999952i	$0.503123\pi$
$492$		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	−0.847951	−	0.530074i	$-0.822164\pi$
$499$	17.5059	−	30.3212i	0.0350820	−	0.0607638i	0.883033	+	0.469310i	$0.155497\pi$
$500$	−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	$0.0672673\pi$
$503$			211.016i			0.419514i	−0.977754	+	0.209757i	$0.932733\pi$
$504$		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	0.997759	−	0.0669144i	$-0.0213154\pi$
$509$	732.292	+	422.789i	1.43869	+	0.830627i	0.440930	+	0.897542i	$0.354649\pi$
$510$		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	$0.0805758\pi$
$521$			260.960i			0.500883i	−0.968132	+	0.250442i	$0.919424\pi$
$522$		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	0.997901	+	0.0647606i	$0.0206284\pi$
$547$	303.604	+	525.858i	0.555035	+	0.961348i	−0.442866	+	0.896588i	$0.646038\pi$
$548$			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	$-0.788540\pi$
$557$		−	686.808i		−	1.23305i	0.787336	−	0.616524i	$-0.211460\pi$
$558$		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	0.673975	−	0.738754i	$-0.264586\pi$
$563$	208.976	+	120.652i	0.371182	+	0.214302i	−0.302792	+	0.953057i	$0.597919\pi$
$564$		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	0.216796	−	0.976217i	$-0.430439\pi$
$569$	666.084	−	384.564i	1.17062	−	0.675859i	0.953827	+	0.300358i	$0.0971061\pi$
$570$		0			0
$571$	−48.7253	+	84.3947i	−0.0853333	+	0.147802i	−0.905533	−	0.424275i	$-0.860529\pi$
$571$	−48.7253	+	84.3947i	−0.0853333	+	0.147802i	0.820200	+	0.572077i	$0.193862\pi$
$572$	−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	−0.803603	−	0.595165i	$-0.797087\pi$
$587$	−405.017	+	233.836i	−0.689977	+	0.398358i	0.113626	+	0.993524i	$0.463753\pi$
$588$		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	$0.0688160\pi$
$593$			254.411i			0.429023i	−0.976721	+	0.214512i	$0.931184\pi$
$594$		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	0.176439	−	0.984312i	$-0.443542\pi$
$599$	−352.081	−	203.274i	−0.587780	−	0.339355i	−0.764219	+	0.644956i	$0.776876\pi$
$600$		0			0
$601$	−249.967	−	432.956i	−0.415919	−	0.720393i	0.579605	−	0.814897i	$-0.303207\pi$
$601$	−249.967	−	432.956i	−0.415919	−	0.720393i	−0.995524	+	0.0945042i	$0.969873\pi$
$602$		−	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	−0.889651	−	0.456642i	$-0.849052\pi$
$607$	−29.9627	+	51.8970i	−0.0493620	+	0.0854975i	0.840289	+	0.542139i	$0.182385\pi$
$608$	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	0.736436	−	0.676507i	$-0.236507\pi$
$617$	320.088	+	184.803i	0.518782	+	0.299519i	−0.217654	+	0.976026i	$0.569841\pi$
$618$		0			0
$619$	−598.225	−	1036.16i	−0.966438	−	1.67392i	−0.705701	−	0.708510i	$-0.749368\pi$
$619$	−598.225	−	1036.16i	−0.966438	−	1.67392i	−0.260738	−	0.965410i	$-0.583966\pi$
$620$		−	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	−0.977964	−	0.208774i	$-0.933053\pi$
$641$	−824.417	+	475.977i	−1.28614	+	0.742554i	−0.308178	+	0.951329i	$0.599719\pi$
$642$		0			0
$643$	35.7759	−	61.9656i	0.0556390	−	0.0963696i	−0.836864	−	0.547410i	$-0.815614\pi$
$643$	35.7759	−	61.9656i	0.0556390	−	0.0963696i	0.892503	+	0.451041i	$0.148947\pi$
$644$	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	$0.244925\pi$
$647$			900.292i			1.39149i	−0.718290	+	0.695744i	$0.755075\pi$
$648$		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	0.660817	−	0.750547i	$-0.270210\pi$
$653$	222.825	+	128.648i	0.341233	+	0.197011i	−0.319584	+	0.947558i	$0.603543\pi$
$654$		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	−0.816697	−	0.577067i	$-0.804197\pi$
$659$	−477.967	+	275.954i	−0.725291	+	0.418747i	0.0914057	+	0.995814i	$0.470864\pi$
$660$		0			0
$661$	523.413	−	906.578i	0.791851	−	1.37153i	−0.132969	−	0.991120i	$-0.542451\pi$
$661$	523.413	−	906.578i	0.791851	−	1.37153i	0.924820	−	0.380405i	$-0.124216\pi$
$662$	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	0.764091	−	0.645108i	$-0.223188\pi$
$673$	−118.875	−	205.898i	−0.176635	−	0.305940i	−0.940726	+	0.339168i	$0.889854\pi$
$674$		−	1927.98i		−	2.86050i
$675$		0			0
$676$	1597.82			2.36364
$677$	145.591	−	84.0570i	0.215053	−	0.124161i	−0.388605	−	0.921405i	$-0.627043\pi$
$677$	145.591	−	84.0570i	0.215053	−	0.124161i	0.603658	+	0.797244i	$0.293709\pi$
$678$		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	$-0.740111\pi$
$683$		−	995.446i		−	1.45746i	0.684800	−	0.728731i	$-0.259889\pi$
$684$		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	0.997053	−	0.0767211i	$-0.0244451\pi$
$691$	298.570	+	517.138i	0.432084	+	0.748391i	−0.564969	+	0.825112i	$0.691112\pi$
$692$		−	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	$-0.904647\pi$
$701$		−	413.729i		−	0.590199i	0.955467	−	0.295099i	$-0.0953528\pi$
$702$		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	0.999129	−	0.0417311i	$-0.0132873\pi$
$709$	328.568	+	569.096i	0.463424	+	0.802674i	−0.535705	+	0.844405i	$0.679954\pi$
$710$		−	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	$0.0482690\pi$
$719$			217.226i			0.302122i	−0.988524	+	0.151061i	$0.951731\pi$
$720$		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	0.577057	−	0.816704i	$-0.304201\pi$
$727$	−304.437	−	527.300i	−0.418757	−	0.725309i	−0.995815	+	0.0913946i	$0.970868\pi$
$728$			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	−0.391957	−	0.919984i	$-0.628202\pi$
$733$	440.351	−	762.709i	0.600751	−	1.04053i	0.992708	−	0.120548i	$-0.0384650\pi$
$734$	−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	0.978179	−	0.207765i	$-0.0666191\pi$
$743$	956.492	+	552.231i	1.28734	+	0.743245i	0.309159	+	0.951010i	$0.399952\pi$
$744$		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	−0.997669	−	0.0682453i	$-0.978260\pi$
$751$	−330.239	+	571.990i	−0.439732	+	0.761638i	0.557936	+	0.829884i	$0.311593\pi$
$752$	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	−0.0437722	−	0.999042i	$-0.513938\pi$
$761$	−708.380	−	408.983i	−0.930854	−	0.537429i	−0.887081	+	0.461613i	$0.847271\pi$
$762$		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	−0.332222	−	0.943201i	$-0.607798\pi$
$769$	500.408	−	866.732i	0.650725	−	1.12709i	0.982947	−	0.183888i	$-0.0588684\pi$
$770$	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	$-0.812121\pi$
$773$		−	860.440i		−	1.11312i	0.830808	−	0.556559i	$-0.187879\pi$
$774$		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	0.405439	+	0.914122i	$0.367119\pi$
$787$	−463.491	+	802.789i	−0.588933	+	1.02006i	−0.994372	+	0.105940i	$0.966215\pi$
$788$	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	0.918533	−	0.395345i	$-0.129375\pi$
$797$	825.230	+	476.447i	1.03542	+	0.597800i	0.116888	+	0.993145i	$0.462708\pi$
$798$		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	$0.343031\pi$
$809$			1425.22i			1.76171i	−0.473387	+	0.880855i	$0.656969\pi$
$810$		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	−0.460835	−	0.887486i	$-0.652450\pi$
$821$	63.4905	−	36.6562i	0.0773331	−	0.0446483i	0.538168	+	0.842838i	$0.319117\pi$
$822$		0			0
$823$	−316.027	+	547.374i	−0.383994	+	0.665096i	−0.991629	−	0.129120i	$-0.958785\pi$
$823$	−316.027	+	547.374i	−0.383994	+	0.665096i	0.607635	+	0.794216i	$0.292118\pi$
$824$	−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	$-0.956340\pi$
$827$		−	226.153i		−	0.273462i	0.990608	−	0.136731i	$-0.0436597\pi$
$828$		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	−0.772750	−	0.634710i	$-0.781119\pi$
$839$	−511.329	+	295.216i	−0.609450	+	0.351866i	0.163300	+	0.986576i	$0.447786\pi$
$840$		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	−0.910538	−	0.413424i	$-0.864333\pi$
$853$	−693.749	−	1201.61i	−0.813305	−	1.40869i	0.0972332	−	0.995262i	$-0.469001\pi$
$854$			2087.14i			2.44396i
$855$		0			0
$856$	−2196.58			−2.56610
$857$	683.058	−	394.363i	0.797033	−	0.460167i	−0.0453994	−	0.998969i	$-0.514456\pi$
$857$	683.058	−	394.363i	0.797033	−	0.460167i	0.842433	+	0.538801i	$0.181123\pi$
$858$		0			0
$859$	−413.601	+	716.378i	−0.481491	+	0.833968i	−0.999774	−	0.0212416i	$-0.993238\pi$
$859$	−413.601	+	716.378i	−0.481491	+	0.833968i	0.518283	+	0.855209i	$0.326571\pi$
$860$	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	$-0.782504\pi$
$863$		−	1089.70i		−	1.26268i	0.775504	−	0.631342i	$-0.217496\pi$
$864$		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	−0.961814	−	0.273705i	$-0.911751\pi$
$877$	−213.875	+	370.443i	−0.243872	+	0.422398i	0.717942	+	0.696103i	$0.245084\pi$
$878$	−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	$0.217832\pi$
$881$			1113.87i			1.26432i	−0.774837	+	0.632161i	$0.782168\pi$
$882$		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	0.861087	−	0.508457i	$-0.169784\pi$
$887$	755.098	+	435.956i	0.851294	+	0.491495i	−0.00979311	+	0.999952i	$0.503117\pi$
$888$		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	0.784085	+	0.620653i	$0.213133\pi$
$907$	843.097	+	1460.29i	0.929544	+	1.61002i	0.145459	+	0.989364i	$0.453534\pi$
$908$		−	1467.33i		−	1.61600i
$909$		0			0
$910$	177.963			0.195563
$911$	383.084	−	221.173i	0.420509	−	0.242781i	−0.274786	−	0.961505i	$-0.588607\pi$
$911$	383.084	−	221.173i	0.420509	−	0.242781i	0.695295	+	0.718724i	$0.255274\pi$
$912$		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	0.269463	−	0.963011i	$-0.413154\pi$
$929$	1150.27	−	664.111i	1.23819	−	0.714867i	0.968723	+	0.248144i	$0.0798205\pi$
$930$		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	−0.202196	−	0.979345i	$-0.564808\pi$
$941$	−1083.50	−	625.557i	−1.15143	−	0.664779i	−0.949236	+	0.314566i	$0.898141\pi$
$942$		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	0.0830930	−	0.996542i	$-0.473520\pi$
$947$	935.323	−	540.009i	0.987670	−	0.570232i	0.904577	+	0.426310i	$0.140187\pi$
$948$		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	$0.0551420\pi$
$953$			328.534i			0.344737i	−0.985033	+	0.172369i	$0.944858\pi$
$954$		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	−0.669102	−	0.743170i	$-0.733321\pi$
$967$	298.854	−	517.631i	0.309053	−	0.535296i	0.978155	+	0.207875i	$0.0666546\pi$
$968$	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	$0.119418\pi$
$971$			711.597i			0.732850i	−0.930448	+	0.366425i	$0.880582\pi$
$972$		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	0.342915	−	0.939366i	$-0.388586\pi$
$977$	−292.262	−	168.738i	−0.299142	−	0.172710i	−0.642058	+	0.766656i	$0.721919\pi$
$978$		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	−0.353833	−	0.935309i	$-0.615122\pi$
$983$	274.504	−	158.485i	0.279252	−	0.161226i	0.633085	+	0.774083i	$0.281789\pi$
$984$		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	0.680816	−	0.732455i	$-0.261625\pi$
$997$	−293.035	−	507.551i	−0.293917	−	0.509078i	−0.974732	+	0.223376i	$0.928292\pi$
$998$		−	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.71.8		16
3.2	odd	2		45.3.i.a.41.1	yes	16
4.3	odd	2		2160.3.bs.c.881.1		16
5.2	odd	4		675.3.i.c.449.16		32
5.3	odd	4		675.3.i.c.449.1		32
5.4	even	2		675.3.j.b.476.1		16
9.2	odd	6	inner	135.3.i.a.116.8		16
9.4	even	3		405.3.c.a.161.16		16
9.5	odd	6		405.3.c.a.161.1		16
9.7	even	3		45.3.i.a.11.1	✓	16
12.11	even	2		720.3.bs.c.401.2		16
15.2	even	4		225.3.i.b.149.1		32
15.8	even	4		225.3.i.b.149.16		32
15.14	odd	2		225.3.j.b.176.8		16
36.7	odd	6		720.3.bs.c.641.2		16
36.11	even	6		2160.3.bs.c.1601.1		16
45.2	even	12		675.3.i.c.224.1		32
45.7	odd	12		225.3.i.b.74.16		32
45.29	odd	6		675.3.j.b.251.1		16
45.34	even	6		225.3.j.b.101.8		16
45.38	even	12		675.3.i.c.224.16		32
45.43	odd	12		225.3.i.b.74.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	9.7	even	3
45.3.i.a.41.1	yes	16	3.2	odd	2
135.3.i.a.71.8		16	1.1	even	1	trivial
135.3.i.a.116.8		16	9.2	odd	6	inner
225.3.i.b.74.1		32	45.43	odd	12
225.3.i.b.74.16		32	45.7	odd	12
225.3.i.b.149.1		32	15.2	even	4
225.3.i.b.149.16		32	15.8	even	4
225.3.j.b.101.8		16	45.34	even	6
225.3.j.b.176.8		16	15.14	odd	2
405.3.c.a.161.1		16	9.5	odd	6
405.3.c.a.161.16		16	9.4	even	3
675.3.i.c.224.1		32	45.2	even	12
675.3.i.c.224.16		32	45.38	even	12
675.3.i.c.449.1		32	5.3	odd	4
675.3.i.c.449.16		32	5.2	odd	4
675.3.j.b.251.1		16	45.29	odd	6
675.3.j.b.476.1		16	5.4	even	2
720.3.bs.c.401.2		16	12.11	even	2
720.3.bs.c.641.2		16	36.7	odd	6
2160.3.bs.c.881.1		16	4.3	odd	2
2160.3.bs.c.1601.1		16	36.11	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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