LMFDB - Embedded newform 675.3.j.b.476.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,3,Mod(251,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 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("675.251"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,16,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.3924178443$
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:	$ 2^{2}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			476.1
Root			$3.73655i$ of defining polynomial
Character	$\chi$	$=$	675.476
Dual form			675.3.j.b.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23594 + 1.86827i) q^{2} +(4.98088 - 8.62715i) q^{4} +(-3.63061 - 6.28840i) q^{7} +22.2764i q^{8} +(-6.50668 + 3.75663i) q^{11} +(1.46668 - 2.54036i) q^{13} +(23.4969 + 13.5659i) q^{14} +(-21.6949 - 37.5766i) q^{16} -1.90107i q^{17} -7.38378 q^{19} +(14.0368 - 24.3125i) q^{22} +(-30.6549 - 17.6986i) q^{23} +10.9606i q^{26} -72.3346 q^{28} +(14.2015 - 8.19922i) q^{29} +(-13.3206 + 23.0720i) q^{31} +(63.2391 + 36.5111i) q^{32} +(3.55172 + 6.15176i) q^{34} +44.6613 q^{37} +(23.8935 - 13.7949i) q^{38} +(-14.8634 - 8.58140i) q^{41} +(20.5554 + 35.6031i) q^{43} +74.8454i q^{44} +132.263 q^{46} +(36.4950 - 21.0704i) q^{47} +(-1.86263 + 3.22616i) q^{49} +(-14.6107 - 25.3065i) q^{52} +100.474i q^{53} +(140.083 - 80.8770i) q^{56} +(-30.6367 + 53.0644i) q^{58} +(4.12003 + 2.37870i) q^{59} +(38.4629 + 66.6197i) q^{61} -99.5461i q^{62} -99.2915 q^{64} +(-41.9225 + 72.6119i) q^{67} +(-16.4008 - 9.46903i) q^{68} +23.1134i q^{71} +103.753 q^{73} +(-144.521 + 83.4395i) q^{74} +(-36.7778 + 63.7010i) q^{76} +(47.2464 + 27.2777i) q^{77} +(-40.2610 - 69.7340i) q^{79} +64.1296 q^{82} +(-17.1034 + 9.87463i) q^{83} +(-133.032 - 76.8063i) q^{86} +(-83.6843 - 144.945i) q^{88} -29.0566i q^{89} -21.2997 q^{91} +(-305.377 + 176.310i) q^{92} +(-78.7306 + 136.365i) q^{94} +(-47.7972 - 82.7872i) q^{97} -13.9196i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{28} + 54 q^{29} + 32 q^{31} + 216 q^{32} + 54 q^{34} - 44 q^{37} + 252 q^{38} - 144 q^{41}+ \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 - 32 * q^28 + 54 * q^29 + 32 * q^31 + 216 * q^32 + 54 * q^34 - 44 * q^37 + 252 * q^38 - 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 - 14 * q^67 - 288 * q^68 + 268 * q^73 - 540 * q^74 - 106 * q^76 + 702 * q^77 - 40 * q^79 + 204 * q^82 + 522 * q^83 - 54 * q^86 - 144 * q^88 + 136 * q^91 - 1332 * q^92 - 150 * q^94 + 142 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	$0.717161\pi$
$2$	−3.23594	+	1.86827i	−1.61797	+	0.934136i	−0.987444	+	0.157969i	$0.949505\pi$
$3$		0			0
$3$		0			0
$4$	4.98088	−	8.62715i	1.24522	−	2.15679i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.63061	−	6.28840i	−0.518658	−	0.898342i	−0.999765	−	0.0216804i	$-0.993098\pi$
$7$	−3.63061	−	6.28840i	−0.518658	−	0.898342i	0.481107	−	0.876662i	$-0.340235\pi$
$8$			22.2764i			2.78455i
$9$		0			0
$10$		0			0
$11$	−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	−0.804085	−	0.594514i	$-0.797345\pi$
$13$	1.46668	−	2.54036i	0.112821	−	0.195412i	0.916907	+	0.399102i	$0.130678\pi$
$14$	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	$0.562247\pi$
$20$		0			0
$21$		0			0
$22$	14.0368	−	24.3125i	0.638037	−	1.10511i
$23$	−30.6549	−	17.6986i	−1.33282	−	0.769506i	−0.347091	−	0.937831i	$-0.612831\pi$
$23$	−30.6549	−	17.6986i	−1.33282	−	0.769506i	−0.985731	+	0.168326i	$0.946164\pi$
$24$		0			0
$25$		0			0
$26$			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
$35$		0			0
$36$		0			0
$37$	44.6613			1.20706			0.603531	−	0.797340i	$-0.293760\pi$
$37$	44.6613			1.20706			0.603531	+	0.797340i	$0.293760\pi$
$38$	23.8935	−	13.7949i	0.628776	−	0.363024i
$39$		0			0
$40$		0			0
$41$	−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	0.999683	−	0.0251818i	$-0.00801646\pi$
$43$	20.5554	+	35.6031i	0.478033	+	0.827978i	−0.521650	+	0.853160i	$0.674683\pi$
$44$			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	$-0.518694\pi$
$47$	36.4950	−	21.0704i	0.776490	−	0.448307i	0.835185	+	0.549969i	$0.185361\pi$
$48$		0			0
$49$	−1.86263	+	3.22616i	−0.0380128	+	0.0658401i
$50$		0			0
$51$		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
$55$		0			0
$56$	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
$65$		0			0
$66$		0			0
$67$	−41.9225	+	72.6119i	−0.625709	+	1.08376i	0.362694	+	0.931908i	$0.381857\pi$
$67$	−41.9225	+	72.6119i	−0.625709	+	1.08376i	−0.988403	+	0.151852i	$0.951476\pi$
$68$	−16.4008	−	9.46903i	−0.241189	−	0.139250i
$69$		0			0
$70$		0			0
$71$			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	$-0.248407\pi$
$73$	103.753			1.42127			0.710637	+	0.703559i	$0.248407\pi$
$74$	−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	$-0.336885\pi$
$80$		0			0
$81$		0			0
$82$	64.1296			0.782068
$83$	−17.1034	+	9.87463i	−0.206065	+	0.118971i	−0.599481	−	0.800389i	$-0.704626\pi$
$83$	−17.1034	+	9.87463i	−0.206065	+	0.118971i	0.393417	+	0.919360i	$0.371293\pi$
$84$		0			0
$85$		0			0
$86$	−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
$95$		0			0
$96$		0			0
$97$	−47.7972	−	82.7872i	−0.492755	−	0.853476i	0.507210	−	0.861822i	$-0.330677\pi$
$97$	−47.7972	−	82.7872i	−0.492755	−	0.853476i	−0.999965	+	0.00834602i	$0.997343\pi$
$98$		−	13.9196i		−	0.142036i
$99$		0			0
$100$		0			0
$101$	−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	$0.480835\pi$
$103$	−85.9401	+	148.853i	−0.834370	+	1.44517i	−0.894542	+	0.446983i	$0.852498\pi$
$104$	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	$0.496165\pi$
$110$		0			0
$111$		0			0
$112$	−157.531	+	272.852i	−1.40653	+	2.43618i
$113$	2.36782	+	1.36706i	0.0209542	+	0.0120979i	0.510440	−	0.859913i	$-0.329482\pi$
$113$	2.36782	+	1.36706i	0.0209542	+	0.0120979i	−0.489486	+	0.872011i	$0.662816\pi$
$114$		0			0
$115$		0			0
$116$		−	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
$125$		0			0
$126$		0			0
$127$	−193.060			−1.52015			−0.760077	−	0.649833i	$-0.774839\pi$
$127$	−193.060			−1.52015			−0.760077	+	0.649833i	$0.774839\pi$
$128$	68.3455	−	39.4593i	0.533950	−	0.308276i
$129$		0			0
$130$		0			0
$131$	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	0.182582	−	0.983191i	$-0.441555\pi$
$137$	154.172	−	89.0111i	1.12534	−	0.649716i	0.942759	+	0.333475i	$0.108221\pi$
$138$		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	$0.203467\pi$
$140$		0			0
$141$		0			0
$142$	−43.1820	−	74.7935i	−0.304099	−	0.526715i
$143$			22.0390i			0.154119i
$144$		0			0
$145$		0			0
$146$	−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
$155$		0			0
$156$		0			0
$157$	−0.792406	+	1.37249i	−0.00504717	+	0.00874196i	−0.868538	−	0.495623i	$-0.834940\pi$
$157$	−0.792406	+	1.37249i	−0.00504717	+	0.00874196i	0.863491	+	0.504365i	$0.168273\pi$
$158$	260.564	+	150.437i	1.64914	+	0.952133i
$159$		0			0
$160$		0			0
$161$			257.027i			1.59644i
$162$		0			0
$163$	41.6801			0.255706			0.127853	−	0.991793i	$-0.459191\pi$
$163$	41.6801			0.255706			0.127853	+	0.991793i	$0.459191\pi$
$164$	−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	$-0.324513\pi$
$167$	8.01405	+	4.62692i	0.0479884	+	0.0277061i	−0.475814	+	0.879546i	$0.657846\pi$
$168$		0			0
$169$	80.1977	+	138.907i	0.474543	+	0.821932i
$170$		0			0
$171$		0			0
$172$	409.537			2.38103
$173$	−127.637	+	73.6913i	−0.737787	+	0.425962i	−0.821264	−	0.570548i	$-0.806731\pi$
$173$	−127.637	+	73.6913i	−0.737787	+	0.425962i	0.0834771	+	0.996510i	$0.473397\pi$
$174$		0			0
$175$		0			0
$176$	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
$185$		0			0
$186$		0			0
$187$	7.14163	+	12.3697i	0.0381905	+	0.0661480i
$188$		−	419.797i		−	2.23296i
$189$		0			0
$190$		0			0
$191$	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	−0.962203	−	0.272334i	$-0.912205\pi$
$193$	−47.3339	+	81.9847i	−0.245253	+	0.424791i	0.716949	+	0.697125i	$0.245538\pi$
$194$	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	$0.388630\pi$
$200$		0			0
$201$		0			0
$202$	254.167	−	440.230i	1.25825	−	2.17936i
$203$	−103.120	−	59.5363i	−0.507980	−	0.293282i
$204$		0			0
$205$		0			0
$206$		−	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
$215$		0			0
$216$		0			0
$217$	193.448			0.891463
$218$	−8.49925	+	4.90704i	−0.0389874	+	0.0225094i
$219$		0			0
$220$		0			0
$221$	−4.82941	−	2.78826i	−0.0218525	−	0.0126166i
$222$		0			0
$223$	−103.124	−	178.616i	−0.462440	−	0.800969i	0.536642	−	0.843810i	$-0.319693\pi$
$223$	−103.124	−	178.616i	−0.462440	−	0.800969i	−0.999082	+	0.0428406i	$0.986359\pi$
$224$		−	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	$-0.771843\pi$
$227$	−127.562	+	73.6481i	−0.561948	+	0.324441i	0.191979	+	0.981399i	$0.438510\pi$
$228$		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	$0.147786\pi$
$230$		0			0
$231$		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
$235$		0			0
$236$	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
$245$		0			0
$246$		0			0
$247$	−10.8296	+	18.7575i	−0.0438446	+	0.0759411i
$248$	−513.961	−	296.735i	−2.07242	−	1.19651i
$249$		0			0
$250$		0			0
$251$			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	0.838156	−	0.545431i	$-0.183634\pi$
$257$	201.713	+	116.459i	0.784877	+	0.453149i	−0.0532790	+	0.998580i	$0.516967\pi$
$258$		0			0
$259$	−162.148	−	280.848i	−0.626053	−	1.08435i
$260$		0			0
$261$		0			0
$262$	−868.350			−3.31431
$263$	−9.34728	+	5.39665i	−0.0355410	+	0.0205196i	−0.517665	−	0.855583i	$-0.673199\pi$
$263$	−9.34728	+	5.39665i	−0.0355410	+	0.0205196i	0.482124	+	0.876103i	$0.339865\pi$
$264$		0			0
$265$		0			0
$266$	−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
$275$		0			0
$276$		0			0
$277$	134.128	+	232.317i	0.484218	+	0.838690i	0.999836	−	0.0181286i	$-0.00577084\pi$
$277$	134.128	+	232.317i	0.484218	+	0.838690i	−0.515618	+	0.856819i	$0.672438\pi$
$278$		−	119.826i		−	0.431028i
$279$		0			0
$280$		0			0
$281$	−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	$0.471210\pi$
$283$	−231.303	+	400.628i	−0.817324	+	1.41565i	−0.907647	+	0.419734i	$0.862123\pi$
$284$	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
$290$		0			0
$291$		0			0
$292$	516.782	−	895.093i	1.76980	−	3.06539i
$293$	248.349	+	143.384i	0.847608	+	0.489367i	0.859843	−	0.510559i	$-0.170561\pi$
$293$	248.349	+	143.384i	0.847608	+	0.489367i	−0.0122351	+	0.999925i	$0.503895\pi$
$294$		0			0
$295$		0			0
$296$			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
$305$		0			0
$306$		0			0
$307$	236.738			0.771133			0.385567	−	0.922680i	$-0.374006\pi$
$307$	236.738			0.771133			0.385567	+	0.922680i	$0.374006\pi$
$308$	470.658	−	271.734i	1.52811	−	0.882254i
$309$		0			0
$310$		0			0
$311$	−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	$-0.876174\pi$
$313$	−247.615	−	428.882i	−0.791102	−	1.37023i	0.134183	−	0.990957i	$-0.457159\pi$
$314$		−	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	$-0.779044\pi$
$317$	−189.840	+	109.604i	−0.598864	+	0.345754i	0.169731	+	0.985491i	$0.445710\pi$
$318$		0			0
$319$	−61.6029	+	106.699i	−0.193112	+	0.334481i
$320$		0			0
$321$		0			0
$322$	−480.197	−	831.725i	−1.49129	−	2.58300i
$323$			14.0371i			0.0434586i
$324$		0			0
$325$		0			0
$326$	−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
$335$		0			0
$336$		0			0
$337$	−257.989	+	446.850i	−0.765547	+	1.32597i	0.174411	+	0.984673i	$0.444198\pi$
$337$	−257.989	+	446.850i	−0.765547	+	1.32597i	−0.939957	+	0.341293i	$0.889135\pi$
$338$	−519.031	−	299.662i	−1.53559	−	0.886575i
$339$		0			0
$340$		0			0
$341$		−	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	$-0.384663\pi$
$347$	−96.4994	−	55.7140i	−0.278096	−	0.160559i	−0.632561	+	0.774510i	$0.717996\pi$
$348$		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	$-0.515007\pi$
$350$		0			0
$351$		0			0
$352$	−548.635			−1.55862
$353$	488.067	−	281.786i	1.38263	−	0.798260i	0.390157	−	0.920748i	$-0.372421\pi$
$353$	488.067	−	281.786i	1.38263	−	0.798260i	0.992470	+	0.122488i	$0.0390873\pi$
$354$		0			0
$355$		0			0
$356$	−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
$365$		0			0
$366$		0			0
$367$	313.940	+	543.761i	0.855423	+	1.48164i	0.876252	+	0.481853i	$0.160036\pi$
$367$	313.940	+	543.761i	0.855423	+	1.48164i	−0.0208286	+	0.999783i	$0.506630\pi$
$368$			1535.88i			4.17358i
$369$		0			0
$370$		0			0
$371$	631.819	−	364.781i	1.70302	−	0.983237i
$372$		0			0
$373$	195.467	−	338.559i	0.524040	−	0.907665i	−0.475568	−	0.879679i	$-0.657757\pi$
$373$	195.467	−	338.559i	0.524040	−	0.907665i	0.999608	−	0.0279857i	$-0.00890929\pi$
$374$	−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	$0.477960\pi$
$380$		0			0
$381$		0			0
$382$	−539.189	+	933.904i	−1.41149	+	2.44477i
$383$	−96.0614	−	55.4610i	−0.250813	−	0.144807i	0.369324	−	0.929301i	$-0.379589\pi$
$383$	−96.0614	−	55.4610i	−0.250813	−	0.144807i	−0.620136	+	0.784494i	$0.712923\pi$
$384$		0			0
$385$		0			0
$386$		−	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
$395$		0			0
$396$		0			0
$397$	−99.8892			−0.251610			−0.125805	−	0.992055i	$-0.540151\pi$
$397$	−99.8892			−0.251610			−0.125805	+	0.992055i	$0.540151\pi$
$398$	−441.475	+	254.885i	−1.10923	+	0.640416i
$399$		0			0
$400$		0			0
$401$	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	$0.850567\pi$
$410$		0			0
$411$		0			0
$412$	856.116	+	1482.84i	2.07795	+	3.59912i
$413$		−	34.5445i		−	0.0836428i
$414$		0			0
$415$		0			0
$416$	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
$425$		0			0
$426$		0			0
$427$	279.287	−	483.740i	0.654069	−	1.13288i
$428$	850.685	+	491.143i	1.98758	+	1.14753i
$429$		0			0
$430$		0			0
$431$		−	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	$-0.283496\pi$
$433$	544.647			1.25784			0.628922	+	0.777468i	$0.283496\pi$
$434$	−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	$0.925776\pi$
$440$		0			0
$441$		0			0
$442$	20.8369			0.0471423
$443$	632.952	−	365.435i	1.42878	−	0.824909i	0.431760	−	0.901989i	$-0.357893\pi$
$443$	632.952	−	365.435i	1.42878	−	0.824909i	0.997025	+	0.0770796i	$0.0245596\pi$
$444$		0			0
$445$		0			0
$446$	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
$455$		0			0
$456$		0			0
$457$	−204.206	−	353.695i	−0.446840	−	0.773949i	0.551339	−	0.834282i	$-0.314117\pi$
$457$	−204.206	−	353.695i	−0.446840	−	0.773949i	−0.998178	+	0.0603323i	$0.980784\pi$
$458$			101.448i			0.221502i
$459$		0			0
$460$		0			0
$461$	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	$-0.500003\pi$
$463$	400.967	−	694.496i	0.866020	−	1.49999i	0.866031	−	0.499991i	$-0.166663\pi$
$464$	−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
$470$		0			0
$471$		0			0
$472$	−52.9889	+	91.7795i	−0.112265	+	0.194448i
$473$	−267.495	−	154.438i	−0.565529	−	0.326508i
$474$		0			0
$475$		0			0
$476$			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
$485$		0			0
$486$		0			0
$487$	−80.4336			−0.165161			−0.0825807	−	0.996584i	$-0.526316\pi$
$487$	−80.4336			−0.165161			−0.0825807	+	0.996584i	$0.526316\pi$
$488$	−1484.05	+	856.816i	−3.04108	+	1.75577i
$489$		0			0
$490$		0			0
$491$	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	$0.155497\pi$
$500$		0			0
$501$		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
$505$		0			0
$506$	−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
$515$		0			0
$516$		0			0
$517$	−158.308	+	274.197i	−0.306204	+	0.530361i
$518$	1049.40	+	605.872i	2.02587	+	1.16964i
$519$		0			0
$520$		0			0
$521$			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	$-0.677431\pi$
$523$	−553.330			−1.05799			−0.528996	+	0.848624i	$0.677431\pi$
$524$	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
$530$		0			0
$531$		0			0
$532$	534.103			1.00395
$533$	−43.5996	+	25.1723i	−0.0818005	+	0.0472275i
$534$		0			0
$535$		0			0
$536$	−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
$545$		0			0
$546$		0			0
$547$	−303.604	−	525.858i	−0.555035	−	0.961348i	−0.997901	−	0.0647606i	$-0.979372\pi$
$547$	−303.604	−	525.858i	−0.555035	−	0.961348i	0.442866	−	0.896588i	$-0.353962\pi$
$548$		−	1773.42i		−	3.23616i
$549$		0			0
$550$		0			0
$551$	−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
$560$		0			0
$561$		0			0
$562$	343.934	−	595.712i	0.611983	−	1.05999i
$563$	−208.976	−	120.652i	−0.371182	−	0.214302i	0.302792	−	0.953057i	$-0.402081\pi$
$563$	−208.976	−	120.652i	−0.371182	−	0.214302i	−0.673975	+	0.738754i	$0.735414\pi$
$564$		0			0
$565$		0			0
$566$		−	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
$575$		0			0
$576$		0			0
$577$	−277.283			−0.480560			−0.240280	−	0.970704i	$-0.577239\pi$
$577$	−277.283			−0.480560			−0.240280	+	0.970704i	$0.577239\pi$
$578$	−923.493	+	533.179i	−1.59774	+	0.922454i
$579$		0			0
$580$		0			0
$581$	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	$-0.536247\pi$
$587$	405.017	−	233.836i	0.689977	−	0.398358i	0.803603	+	0.595165i	$0.202913\pi$
$588$		0			0
$589$	98.3565	−	170.358i	0.166989	−	0.289233i
$590$		0			0
$591$		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
$595$		0			0
$596$	−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
$605$		0			0
$606$		0			0
$607$	29.9627	−	51.8970i	0.0493620	−	0.0854975i	−0.840289	−	0.542139i	$-0.817615\pi$
$607$	29.9627	−	51.8970i	0.0493620	−	0.0854975i	0.889651	+	0.456642i	$0.150948\pi$
$608$	−466.944	−	269.590i	−0.767999	−	0.443405i
$609$		0			0
$610$		0			0
$611$		−	123.614i		−	0.202314i
$612$		0			0
$613$	373.866			0.609896			0.304948	−	0.952369i	$-0.401361\pi$
$613$	373.866			0.609896			0.304948	+	0.952369i	$0.401361\pi$
$614$	−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	$-0.430159\pi$
$617$	−320.088	−	184.803i	−0.518782	−	0.299519i	−0.736436	+	0.676507i	$0.763493\pi$
$618$		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	$-0.583966\pi$
$620$		0			0
$621$		0			0
$622$	1935.51			3.11175
$623$	−182.719	+	105.493i	−0.293289	+	0.169331i
$624$		0			0
$625$		0			0
$626$	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
$635$		0			0
$636$		0			0
$637$	5.46374	+	9.46347i	0.00857730	+	0.0148563i
$638$		−	460.364i		−	0.721573i
$639$		0			0
$640$		0			0
$641$	−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	−0.892503	−	0.451041i	$-0.851053\pi$
$643$	−35.7759	+	61.9656i	−0.0556390	+	0.0963696i	0.836864	+	0.547410i	$0.184386\pi$
$644$	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
$650$		0			0
$651$		0			0
$652$	207.604	−	359.580i	0.318410	−	0.551503i
$653$	−222.825	−	128.648i	−0.341233	−	0.197011i	0.319584	−	0.947558i	$-0.396457\pi$
$653$	−222.825	−	128.648i	−0.341233	−	0.197011i	−0.660817	+	0.750547i	$0.729790\pi$
$654$		0			0
$655$		0			0
$656$			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
$665$		0			0
$666$		0			0
$667$	−580.460			−0.870254
$668$	79.8342	−	46.0923i	0.119512	−	0.0690004i
$669$		0			0
$670$		0			0
$671$	−500.531	−	288.982i	−0.745948	−	0.430673i
$672$		0			0
$673$	118.875	+	205.898i	0.176635	+	0.305940i	0.940726	−	0.339168i	$-0.110146\pi$
$673$	118.875	+	205.898i	0.176635	+	0.305940i	−0.764091	+	0.645108i	$0.776812\pi$
$674$		−	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	$-0.706291\pi$
$677$	−145.591	+	84.0570i	−0.215053	+	0.124161i	0.388605	+	0.921405i	$0.372957\pi$
$678$		0			0
$679$	−347.066	+	601.136i	−0.511143	+	0.885325i
$680$		0			0
$681$		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
$685$		0			0
$686$	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
$695$		0			0
$696$		0			0
$697$	−16.3139	+	28.2564i	−0.0234058	+	0.0405401i
$698$	2007.13	+	1158.82i	2.87555	+	1.66020i
$699$		0			0
$700$		0			0
$701$		−	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	$0.679954\pi$
$710$		0			0
$711$		0			0
$712$	647.277			0.909096
$713$	816.684	−	471.513i	1.14542	−	0.661308i
$714$		0			0
$715$		0			0
$716$	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
$725$		0			0
$726$		0			0
$727$	304.437	+	527.300i	0.418757	+	0.725309i	0.995815	−	0.0913946i	$-0.0291325\pi$
$727$	304.437	+	527.300i	0.418757	+	0.725309i	−0.577057	+	0.816704i	$0.695799\pi$
$728$		−	474.481i		−	0.651760i
$729$		0			0
$730$		0			0
$731$	67.6840	−	39.0774i	0.0925910	−	0.0534574i
$732$		0			0
$733$	−440.351	+	762.709i	−0.600751	+	1.04053i	0.391957	+	0.919984i	$0.371798\pi$
$733$	−440.351	+	762.709i	−0.600751	+	1.04053i	−0.992708	+	0.120548i	$0.961535\pi$
$734$	−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	$0.713086\pi$
$740$		0			0
$741$		0			0
$742$	−1363.02	+	2360.82i	−1.83695	+	3.18170i
$743$	−956.492	−	552.231i	−1.28734	−	0.743245i	−0.309159	−	0.951010i	$-0.600048\pi$
$743$	−956.492	−	552.231i	−1.28734	−	0.743245i	−0.978179	+	0.207765i	$0.933381\pi$
$744$		0			0
$745$		0			0
$746$			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
$755$		0			0
$756$		0			0
$757$	353.728			0.467276			0.233638	−	0.972324i	$-0.424937\pi$
$757$	353.728			0.467276			0.233638	+	0.972324i	$0.424937\pi$
$758$	−169.702	+	97.9778i	−0.223882	+	0.129258i
$759$		0			0
$760$		0			0
$761$	−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	$-0.0588684\pi$
$770$		0			0
$771$		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
$775$		0			0
$776$	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
$785$		0			0
$786$		0			0
$787$	463.491	−	802.789i	0.588933	−	1.02006i	−0.405439	−	0.914122i	$-0.632881\pi$
$787$	463.491	−	802.789i	0.588933	−	1.02006i	0.994372	−	0.105940i	$-0.0337853\pi$
$788$	−1119.42	−	646.297i	−1.42058	−	0.820174i
$789$		0			0
$790$		0			0
$791$		−	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	$-0.537292\pi$
$797$	−825.230	−	476.447i	−1.03542	−	0.597800i	−0.918533	+	0.395345i	$0.870625\pi$
$798$		0			0
$799$	−40.0564	−	69.3797i	−0.0501332	−	0.0868332i
$800$		0			0
$801$		0			0
$802$	−587.129			−0.732082
$803$	−675.087	+	389.762i	−0.840707	+	0.485382i
$804$		0			0
$805$		0			0
$806$	−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
$815$		0			0
$816$		0			0
$817$	−151.777	−	262.885i	−0.185773	−	0.321769i
$818$		−	2560.42i		−	3.13010i
$819$		0			0
$820$		0			0
$821$	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	−0.607635	−	0.794216i	$-0.707882\pi$
$823$	316.027	−	547.374i	0.383994	−	0.665096i	0.991629	+	0.129120i	$0.0412151\pi$
$824$	−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	$0.602030\pi$
$830$		0			0
$831$		0			0
$832$	−145.629	+	252.236i	−0.175034	+	0.303168i
$833$	6.13317	+	3.54099i	0.00736275	+	0.00425089i
$834$		0			0
$835$		0			0
$836$		−	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
$845$		0			0
$846$		0			0
$847$	468.718			0.553386
$848$	3775.47	−	2179.77i	4.45220	−	2.57048i
$849$		0			0
$850$		0			0
$851$	−1369.09	−	790.444i	−1.60880	−	0.928841i
$852$		0			0
$853$	693.749	+	1201.61i	0.813305	+	1.40869i	0.910538	+	0.413424i	$0.135667\pi$
$853$	693.749	+	1201.61i	0.813305	+	1.40869i	−0.0972332	+	0.995262i	$0.530999\pi$
$854$			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	$-0.818877\pi$
$857$	−683.058	+	394.363i	−0.797033	+	0.460167i	0.0453994	+	0.998969i	$0.485544\pi$
$858$		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	$0.326571\pi$
$860$		0			0
$861$		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
$865$		0			0
$866$	−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
$875$		0			0
$876$		0			0
$877$	213.875	−	370.443i	0.243872	−	0.422398i	−0.717942	−	0.696103i	$-0.754916\pi$
$877$	213.875	−	370.443i	0.243872	−	0.422398i	0.961814	+	0.273705i	$0.0882491\pi$
$878$	813.575	+	469.718i	0.926623	+	0.534986i
$879$		0			0
$880$		0			0
$881$			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	$-0.425683\pi$
$883$	408.581			0.462719			0.231359	+	0.972868i	$0.425683\pi$
$884$	−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	$-0.496883\pi$
$887$	−755.098	−	435.956i	−0.851294	−	0.491495i	−0.861087	+	0.508457i	$0.830216\pi$
$888$		0			0
$889$	700.924	+	1214.04i	0.788441	+	1.36562i
$890$		0			0
$891$		0			0
$892$	−2054.60			−2.30336
$893$	−269.471	+	155.579i	−0.301760	+	0.174221i
$894$		0			0
$895$		0			0
$896$	−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
$905$		0			0
$906$		0			0
$907$	−843.097	−	1460.29i	−0.929544	−	1.61002i	−0.784085	−	0.620653i	$-0.786867\pi$
$907$	−843.097	−	1460.29i	−0.929544	−	1.61002i	−0.145459	−	0.989364i	$-0.546466\pi$
$908$			1467.33i			1.61600i
$909$		0			0
$910$		0			0
$911$	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	$0.531612\pi$
$920$		0			0
$921$		0			0
$922$	−1103.96	+	1912.12i	−1.19736	+	2.07388i
$923$	58.7162	+	33.8998i	0.0636145	+	0.0367279i
$924$		0			0
$925$		0			0
$926$			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
$935$		0			0
$936$		0			0
$937$	276.582			0.295178			0.147589	−	0.989049i	$-0.452849\pi$
$937$	276.582			0.295178			0.147589	+	0.989049i	$0.452849\pi$
$938$	−1970.10	+	1137.44i	−2.10032	+	1.21262i
$939$		0			0
$940$		0			0
$941$	−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	−0.904577	−	0.426310i	$-0.859813\pi$
$947$	−935.323	+	540.009i	−0.987670	+	0.570232i	−0.0830930	+	0.996542i	$0.526480\pi$
$948$		0			0
$949$	152.172	−	263.570i	0.160350	−	0.277734i
$950$		0			0
$951$		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
$955$		0			0
$956$	−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
$965$		0			0
$966$		0			0
$967$	−298.854	+	517.631i	−0.309053	+	0.535296i	−0.978155	−	0.207875i	$-0.933345\pi$
$967$	−298.854	+	517.631i	−0.309053	+	0.535296i	0.669102	+	0.743170i	$0.266679\pi$
$968$	−1245.31	−	718.981i	−1.28648	−	0.742749i
$969$		0			0
$970$		0			0
$971$			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	0.642058	−	0.766656i	$-0.278081\pi$
$977$	292.262	+	168.738i	0.299142	+	0.172710i	−0.342915	+	0.939366i	$0.611414\pi$
$978$		0			0
$979$	109.155	+	189.062i	0.111496	+	0.193117i
$980$		0			0
$981$		0			0
$982$	−1803.38			−1.83643
$983$	−274.504	+	158.485i	−0.279252	+	0.161226i	−0.633085	−	0.774083i	$-0.718211\pi$
$983$	−274.504	+	158.485i	−0.279252	+	0.161226i	0.353833	+	0.935309i	$0.384878\pi$
$984$		0			0
$985$		0			0
$986$	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
$995$		0			0
$996$		0			0
$997$	293.035	+	507.551i	0.293917	+	0.509078i	0.974732	−	0.223376i	$-0.0717079\pi$
$997$	293.035	+	507.551i	0.293917	+	0.509078i	−0.680816	+	0.732455i	$0.738375\pi$
$998$			130.823i			0.131086i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	45.34	even	6
45.3.i.a.41.1	yes	16	15.14	odd	2
135.3.i.a.71.8		16	5.4	even	2
135.3.i.a.116.8		16	45.29	odd	6
225.3.i.b.74.1		32	45.7	odd	12
225.3.i.b.74.16		32	45.43	odd	12
225.3.i.b.149.1		32	15.8	even	4
225.3.i.b.149.16		32	15.2	even	4
225.3.j.b.101.8		16	9.7	even	3
225.3.j.b.176.8		16	3.2	odd	2
405.3.c.a.161.1		16	45.14	odd	6
405.3.c.a.161.16		16	45.4	even	6
675.3.i.c.224.1		32	45.38	even	12
675.3.i.c.224.16		32	45.2	even	12
675.3.i.c.449.1		32	5.2	odd	4
675.3.i.c.449.16		32	5.3	odd	4
675.3.j.b.251.1		16	9.2	odd	6	inner
675.3.j.b.476.1		16	1.1	even	1	trivial
720.3.bs.c.401.2		16	60.59	even	2
720.3.bs.c.641.2		16	180.79	odd	6
2160.3.bs.c.881.1		16	20.19	odd	2
2160.3.bs.c.1601.1		16	180.119	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.j (of order \(6\), degree \(2\), not minimal)

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

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