LMFDB - Embedded newform 117.3.n.a.38.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.17
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.641309 - 1.11078i) q^{2} +(2.61442 + 1.47132i) q^{3} +(1.17745 + 2.03940i) q^{4} +(0.763734 + 1.32283i) q^{5} +(3.31097 - 1.96048i) q^{6} +(-5.50560 - 3.17866i) q^{7} +8.15090 q^{8} +(4.67043 + 7.69331i) q^{9} +1.95916 q^{10} +(-4.76900 + 8.26015i) q^{11} +(0.0777368 + 7.06425i) q^{12} +(2.64085 - 12.7289i) q^{13} +(-7.06158 + 4.07700i) q^{14} +(0.0504229 + 4.58213i) q^{15} +(0.517455 - 0.896258i) q^{16} -5.91142i q^{17} +(11.5408 - 0.254026i) q^{18} -28.1819i q^{19} +(-1.79851 + 3.11511i) q^{20} +(-9.71714 - 16.4109i) q^{21} +(6.11681 + 10.5946i) q^{22} +(2.58138 - 1.49036i) q^{23} +(21.3099 + 11.9926i) q^{24} +(11.3334 - 19.6301i) q^{25} +(-12.4454 - 11.0966i) q^{26} +(0.891147 + 26.9853i) q^{27} -14.9708i q^{28} +(-23.3655 - 13.4901i) q^{29} +(5.12207 + 2.88255i) q^{30} +(-40.4659 + 23.3630i) q^{31} +(15.6381 + 27.0860i) q^{32} +(-24.6215 + 14.5788i) q^{33} +(-6.56629 - 3.79105i) q^{34} -9.71060i q^{35} +(-10.1905 + 18.5833i) q^{36} +16.0478i q^{37} +(-31.3039 - 18.0733i) q^{38} +(25.6327 - 29.3933i) q^{39} +(6.22512 + 10.7822i) q^{40} +(0.217120 + 0.376063i) q^{41} +(-24.4605 + 0.269170i) q^{42} +(24.2584 - 42.0167i) q^{43} -22.4610 q^{44} +(-6.60995 + 12.0538i) q^{45} -3.82312i q^{46} +(-41.9845 + 72.7193i) q^{47} +(2.67153 - 1.58186i) q^{48} +(-4.29226 - 7.43442i) q^{49} +(-14.5364 - 25.1779i) q^{50} +(8.69760 - 15.4550i) q^{51} +(29.0688 - 9.60190i) q^{52} +67.8592i q^{53} +(30.5462 + 16.3160i) q^{54} -14.5690 q^{55} +(-44.8756 - 25.9089i) q^{56} +(41.4646 - 73.6795i) q^{57} +(-29.9689 + 17.3026i) q^{58} +(-26.9800 - 46.7307i) q^{59} +(-9.28541 + 5.49804i) q^{60} +(-1.50215 + 2.60180i) q^{61} +59.9315i q^{62} +(-1.25908 - 57.2020i) q^{63} +44.2550 q^{64} +(18.8551 - 6.22814i) q^{65} +(0.403841 + 36.6986i) q^{66} +(18.4220 - 10.6359i) q^{67} +(12.0557 - 6.96038i) q^{68} +(8.94161 - 0.0983958i) q^{69} +(-10.7863 - 6.22749i) q^{70} +105.408 q^{71} +(38.0682 + 62.7074i) q^{72} -15.3294i q^{73} +(17.8256 + 10.2916i) q^{74} +(58.5125 - 34.6462i) q^{75} +(57.4741 - 33.1827i) q^{76} +(52.5124 - 30.3181i) q^{77} +(-16.2110 - 47.3224i) q^{78} +(-37.8643 + 65.5828i) q^{79} +1.58079 q^{80} +(-37.3742 + 71.8622i) q^{81} +0.556964 q^{82} +(19.0458 - 32.9882i) q^{83} +(22.0269 - 39.1400i) q^{84} +(7.81979 - 4.51476i) q^{85} +(-31.1142 - 53.8914i) q^{86} +(-41.2390 - 69.6468i) q^{87} +(-38.8716 + 67.3277i) q^{88} +73.4436 q^{89} +(9.15011 + 15.0724i) q^{90} +(-55.0004 + 61.6861i) q^{91} +(6.07887 + 3.50964i) q^{92} +(-140.169 + 1.54246i) q^{93} +(53.8500 + 93.2710i) q^{94} +(37.2798 - 21.5235i) q^{95} +(1.03245 + 93.8229i) q^{96} +(53.3827 + 30.8205i) q^{97} -11.0107 q^{98} +(-85.8213 + 1.88903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.641309	−	1.11078i	0.320654	−	0.555390i	−0.659969	−	0.751293i	$-0.729431\pi$
$2$	0.641309	−	1.11078i	0.320654	−	0.555390i	0.980623	+	0.195903i	$0.0627639\pi$
$3$	2.61442	+	1.47132i	0.871475	+	0.490440i
$3$	2.61442	+	1.47132i	0.871475	+	0.490440i
$4$	1.17745	+	2.03940i	0.294362	+	0.509849i
$5$	0.763734	+	1.32283i	0.152747	+	0.264565i	0.932236	−	0.361850i	$-0.117855\pi$
$5$	0.763734	+	1.32283i	0.152747	+	0.264565i	−0.779489	+	0.626415i	$0.784521\pi$
$6$	3.31097	−	1.96048i	0.551828	−	0.326746i
$7$	−5.50560	−	3.17866i	−0.786514	−	0.454094i	0.0522199	−	0.998636i	$-0.483370\pi$
$7$	−5.50560	−	3.17866i	−0.786514	−	0.454094i	−0.838734	+	0.544542i	$0.816704\pi$
$8$	8.15090			1.01886
$9$	4.67043	+	7.69331i	0.518937	+	0.854813i
$10$	1.95916			0.195916
$11$	−4.76900	+	8.26015i	−0.433546	+	0.750923i	−0.997176	−	0.0751042i	$-0.976071\pi$
$11$	−4.76900	+	8.26015i	−0.433546	+	0.750923i	0.563630	+	0.826027i	$0.309404\pi$
$12$	0.0777368	+	7.06425i	0.00647807	+	0.588688i
$13$	2.64085	−	12.7289i	0.203142	−	0.979149i
$13$	2.64085	−	12.7289i	0.203142	−	0.979149i
$14$	−7.06158	+	4.07700i	−0.504398	+	0.291214i
$15$	0.0504229	+	4.58213i	0.00336153	+	0.305475i
$16$	0.517455	−	0.896258i	0.0323409	−	0.0560161i
$17$		−	5.91142i		−	0.347731i	−0.984769	−	0.173865i	$-0.944374\pi$
$17$		−	5.91142i		−	0.347731i	0.984769	−	0.173865i	$-0.0556258\pi$
$18$	11.5408	−	0.254026i	0.641153	−	0.0141125i
$19$		−	28.1819i		−	1.48326i	−0.670810	−	0.741629i	$-0.734053\pi$
$19$		−	28.1819i		−	1.48326i	0.670810	−	0.741629i	$-0.265947\pi$
$20$	−1.79851	+	3.11511i	−0.0899256	+	0.155756i
$21$	−9.71714	−	16.4109i	−0.462721	−	0.781470i
$22$	6.11681	+	10.5946i	0.278037	+	0.481574i
$23$	2.58138	−	1.49036i	0.112234	−	0.0647982i	−0.442832	−	0.896604i	$-0.646026\pi$
$23$	2.58138	−	1.49036i	0.112234	−	0.0647982i	0.555066	+	0.831806i	$0.312693\pi$
$24$	21.3099	+	11.9926i	0.887912	+	0.499691i
$25$	11.3334	−	19.6301i	0.453337	−	0.785202i
$26$	−12.4454	−	11.0966i	−0.478671	−	0.426792i
$27$	0.891147	+	26.9853i	0.0330054	+	0.999455i
$28$		−	14.9708i		−	0.534671i
$29$	−23.3655	−	13.4901i	−0.805706	−	0.465174i	0.0397567	−	0.999209i	$-0.487342\pi$
$29$	−23.3655	−	13.4901i	−0.805706	−	0.465174i	−0.845462	+	0.534035i	$0.820675\pi$
$30$	5.12207	+	2.88255i	0.170736	+	0.0960850i
$31$	−40.4659	+	23.3630i	−1.30535	+	0.753645i	−0.981316	−	0.192401i	$-0.938373\pi$
$31$	−40.4659	+	23.3630i	−1.30535	+	0.753645i	−0.324034	+	0.946045i	$0.605039\pi$
$32$	15.6381	+	27.0860i	0.488690	+	0.846437i
$33$	−24.6215	+	14.5788i	−0.746107	+	0.441782i
$34$	−6.56629	−	3.79105i	−0.193126	−	0.111501i
$35$		−	9.71060i		−	0.277446i
$36$	−10.1905	+	18.5833i	−0.283071	+	0.516203i
$37$			16.0478i			0.433725i	0.976202	+	0.216863i	$0.0695824\pi$
$37$			16.0478i			0.433725i	−0.976202	+	0.216863i	$0.930418\pi$
$38$	−31.3039	−	18.0733i	−0.823786	−	0.475613i
$39$	25.6327	−	29.3933i	0.657248	−	0.753675i
$40$	6.22512	+	10.7822i	0.155628	+	0.269556i
$41$	0.217120	+	0.376063i	0.00529561	+	0.00917227i	0.868661	−	0.495407i	$-0.164981\pi$
$41$	0.217120	+	0.376063i	0.00529561	+	0.00917227i	−0.863365	+	0.504579i	$0.831648\pi$
$42$	−24.4605	+	0.269170i	−0.582394	+	0.00640881i
$43$	24.2584	−	42.0167i	0.564148	−	0.977134i	−0.432980	−	0.901404i	$-0.642538\pi$
$43$	24.2584	−	42.0167i	0.564148	−	0.977134i	0.997128	−	0.0757301i	$-0.0241287\pi$
$44$	−22.4610			−0.510477
$45$	−6.60995	+	12.0538i	−0.146888	+	0.267863i
$46$		−	3.82312i		−	0.0831113i
$47$	−41.9845	+	72.7193i	−0.893287	+	1.54722i	−0.0573761	+	0.998353i	$0.518273\pi$
$47$	−41.9845	+	72.7193i	−0.893287	+	1.54722i	−0.835911	+	0.548866i	$0.815060\pi$
$48$	2.67153	−	1.58186i	0.0556569	−	0.0329553i
$49$	−4.29226	−	7.43442i	−0.0875972	−	0.151723i
$50$	−14.5364	−	25.1779i	−0.290729	−	0.503557i
$51$	8.69760	−	15.4550i	0.170541	−	0.303039i
$52$	29.0688	−	9.60190i	0.559016	−	0.184652i
$53$			67.8592i			1.28036i	0.768224	+	0.640181i	$0.221141\pi$
$53$			67.8592i			1.28036i	−0.768224	+	0.640181i	$0.778859\pi$
$54$	30.5462	+	16.3160i	0.565670	+	0.302149i
$55$	−14.5690			−0.264891
$56$	−44.8756	−	25.9089i	−0.801349	−	0.462659i
$57$	41.4646	−	73.6795i	0.727450	−	1.29262i
$58$	−29.9689	+	17.3026i	−0.516706	+	0.298320i
$59$	−26.9800	−	46.7307i	−0.457288	−	0.792046i	0.541529	−	0.840682i	$-0.317846\pi$
$59$	−26.9800	−	46.7307i	−0.457288	−	0.792046i	−0.998817	+	0.0486363i	$0.984512\pi$
$60$	−9.28541	+	5.49804i	−0.154757	+	0.0916340i
$61$	−1.50215	+	2.60180i	−0.0246254	+	0.0426525i	−0.878075	−	0.478522i	$-0.841173\pi$
$61$	−1.50215	+	2.60180i	−0.0246254	+	0.0426525i	0.853450	+	0.521175i	$0.174506\pi$
$62$			59.9315i			0.966638i
$63$	−1.25908	−	57.2020i	−0.0199854	−	0.907968i
$64$	44.2550			0.691485
$65$	18.8551	−	6.22814i	0.290078	−	0.0958175i
$66$	0.403841	+	36.6986i	0.00611880	+	0.556040i
$67$	18.4220	−	10.6359i	0.274955	−	0.158745i	−0.356183	−	0.934416i	$-0.615922\pi$
$67$	18.4220	−	10.6359i	0.274955	−	0.158745i	0.631137	+	0.775671i	$0.282589\pi$
$68$	12.0557	−	6.96038i	0.177290	−	0.102359i
$69$	8.94161	−	0.0983958i	0.129589	−	0.00142603i
$70$	−10.7863	−	6.22749i	−0.154090	−	0.0889642i
$71$	105.408			1.48462			0.742310	−	0.670057i	$-0.233730\pi$
$71$	105.408			1.48462			0.742310	+	0.670057i	$0.233730\pi$
$72$	38.0682	+	62.7074i	0.528725	+	0.870936i
$73$		−	15.3294i		−	0.209992i	−0.994473	−	0.104996i	$-0.966517\pi$
$73$		−	15.3294i		−	0.209992i	0.994473	−	0.104996i	$-0.0334830\pi$
$74$	17.8256	+	10.2916i	0.240886	+	0.139076i
$75$	58.5125	−	34.6462i	0.780167	−	0.461949i
$76$	57.4741	−	33.1827i	0.756238	−	0.436614i
$77$	52.5124	−	30.3181i	0.681979	−	0.393741i
$78$	−16.2110	−	47.3224i	−0.207834	−	0.606698i
$79$	−37.8643	+	65.5828i	−0.479294	+	0.830162i	−0.999718	−	0.0237459i	$-0.992441\pi$
$79$	−37.8643	+	65.5828i	−0.479294	+	0.830162i	0.520424	+	0.853908i	$0.325774\pi$
$80$	1.58079			0.0197599
$81$	−37.3742	+	71.8622i	−0.461410	+	0.887187i
$82$	0.556964			0.00679224
$83$	19.0458	−	32.9882i	0.229467	−	0.397449i	−0.728183	−	0.685383i	$-0.759635\pi$
$83$	19.0458	−	32.9882i	0.229467	−	0.397449i	0.957650	+	0.287934i	$0.0929683\pi$
$84$	22.0269	−	39.1400i	0.262224	−	0.465953i
$85$	7.81979	−	4.51476i	0.0919975	−	0.0531148i
$86$	−31.1142	−	53.8914i	−0.361793	−	0.626644i
$87$	−41.2390	−	69.6468i	−0.474012	−	0.800538i
$88$	−38.8716	+	67.3277i	−0.441723	+	0.765087i
$89$	73.4436			0.825209			0.412604	−	0.910910i	$-0.364619\pi$
$89$	73.4436			0.825209			0.412604	+	0.910910i	$0.364619\pi$
$90$	9.15011	+	15.0724i	0.101668	+	0.167471i
$91$	−55.0004	+	61.6861i	−0.604400	+	0.677869i
$92$	6.07887	+	3.50964i	0.0660747	+	0.0381482i
$93$	−140.169	+	1.54246i	−1.50720	+	0.0165856i
$94$	53.8500	+	93.2710i	0.572873	+	0.992244i
$95$	37.2798	−	21.5235i	0.392419	−	0.226563i
$96$	1.03245	+	93.8229i	0.0107547	+	0.977322i
$97$	53.3827	+	30.8205i	0.550337	+	0.317737i	0.749258	−	0.662278i	$-0.230410\pi$
$97$	53.3827	+	30.8205i	0.550337	+	0.317737i	−0.198921	+	0.980016i	$0.563744\pi$
$98$	−11.0107			−0.112354
$99$	−85.8213	+	1.88903i	−0.866881	+	0.0190811i
$100$	53.3780			0.533780
$101$	26.3652	+	15.2219i	0.261041	+	0.150712i	0.624809	−	0.780777i	$-0.285177\pi$
$101$	26.3652	+	15.2219i	0.261041	+	0.150712i	−0.363768	+	0.931490i	$0.618510\pi$
$102$	−11.5892	−	19.5725i	−0.113620	−	0.191887i
$103$	−49.7692	−	86.2028i	−0.483196	−	0.836920i	0.516618	−	0.856216i	$-0.327191\pi$
$103$	−49.7692	−	86.2028i	−0.483196	−	0.836920i	−0.999814	+	0.0192959i	$0.993858\pi$
$104$	21.5253	−	103.752i	0.206974	−	0.997618i
$105$	14.2874	−	25.3876i	0.136071	−	0.241787i
$106$	75.3766	+	43.5187i	0.711100	+	0.410554i
$107$			147.476i			1.37828i	0.724628	+	0.689140i	$0.242011\pi$
$107$			147.476i			1.37828i	−0.724628	+	0.689140i	$0.757989\pi$
$108$	−53.9844	+	33.5911i	−0.499856	+	0.311029i
$109$			51.9537i			0.476639i	0.971187	+	0.238320i	$0.0765966\pi$
$109$			51.9537i			0.476639i	−0.971187	+	0.238320i	$0.923403\pi$
$110$	−9.34323	+	16.1829i	−0.0849384	+	0.147118i
$111$	−23.6115	+	41.9558i	−0.212716	+	0.377981i
$112$	−5.69780	+	3.28962i	−0.0508732	+	0.0293716i
$113$	129.729	−	74.8990i	1.14804	−	0.662823i	0.199633	−	0.979871i	$-0.436025\pi$
$113$	129.729	−	74.8990i	1.14804	−	0.662823i	0.948409	+	0.317048i	$0.102692\pi$
$114$	−55.2500	−	93.3093i	−0.484649	−	0.818503i
$115$	3.94297	+	2.27648i	0.0342867	+	0.0197955i
$116$		−	63.5353i		−	0.547718i
$117$	110.262	−	39.1327i	0.942407	−	0.334468i
$118$	−69.2100			−0.586526
$119$	−18.7904	+	32.5459i	−0.157902	+	0.273495i
$120$	0.410992	+	37.3484i	0.00342493	+	0.311237i
$121$	15.0132	+	26.0037i	0.124076	+	0.214906i
$122$	1.92668	+	3.33711i	0.0157925	+	0.0273534i
$123$	0.0143346	+	1.30264i	0.000116541	+	0.0105906i
$124$	−95.2928	−	55.0173i	−0.768490	−	0.443688i
$125$	72.8096			0.582477
$126$	−64.3462	−	35.2856i	−0.510685	−	0.280044i
$127$	−199.708			−1.57250			−0.786252	−	0.617906i	$-0.787981\pi$
$127$	−199.708			−1.57250			−0.786252	+	0.617906i	$0.787981\pi$
$128$	−34.1712	+	59.1863i	−0.266963	+	0.462393i
$129$	125.242	−	74.1577i	0.970867	−	0.574866i
$130$	5.17384	−	24.9380i	0.0397988	−	0.191831i
$131$	−98.4809	+	56.8580i	−0.751763	+	0.434030i	−0.826330	−	0.563186i	$-0.809576\pi$
$131$	−98.4809	+	56.8580i	−0.751763	+	0.434030i	0.0745678	+	0.997216i	$0.476242\pi$
$132$	−58.7225	−	33.0473i	−0.444868	−	0.250358i
$133$	−89.5806	+	155.158i	−0.673539	+	1.16660i
$134$		−	27.2836i		−	0.203609i
$135$	−35.0163	+	21.7884i	−0.259380	+	0.161396i
$136$		−	48.1834i		−	0.354290i
$137$	50.6445	−	87.7189i	0.369668	−	0.640284i	−0.619845	−	0.784724i	$-0.712805\pi$
$137$	50.6445	−	87.7189i	0.369668	−	0.640284i	0.989514	+	0.144440i	$0.0461380\pi$
$138$	5.62504	−	9.99526i	0.0407612	−	0.0724294i
$139$	−13.9512	−	24.1642i	−0.100368	−	0.173843i	0.811468	−	0.584397i	$-0.198669\pi$
$139$	−13.9512	−	24.1642i	−0.100368	−	0.173843i	−0.911836	+	0.410554i	$0.865335\pi$
$140$	19.8038	−	11.4337i	0.141455	−	0.0816694i
$141$	−216.759	+	128.346i	−1.53730	+	0.910258i
$142$	67.5991	−	117.085i	0.476050	−	0.824542i
$143$	92.5488	+	82.5182i	0.647194	+	0.577050i
$144$	9.31193	−	0.204966i	0.0646662	−	0.00142338i
$145$		−	41.2113i		−	0.284216i
$146$	−17.0276	−	9.83089i	−0.116627	−	0.0673349i
$147$	−0.283382	−	25.7520i	−0.00192777	−	0.175184i
$148$	−32.7279	+	18.8955i	−0.221134	+	0.127672i
$149$	−135.912	−	235.407i	−0.912162	−	1.57991i	−0.811004	−	0.585040i	$-0.801079\pi$
$149$	−135.912	−	235.407i	−0.912162	−	1.57991i	−0.101157	−	0.994870i	$-0.532255\pi$
$150$	−0.959718	−	87.2134i	−0.00639812	−	0.581422i
$151$	72.5363	+	41.8788i	0.480373	+	0.277343i	0.720572	−	0.693380i	$-0.243879\pi$
$151$	72.5363	+	41.8788i	0.480373	+	0.277343i	−0.240199	+	0.970724i	$0.577213\pi$
$152$		−	229.708i		−	1.51124i
$153$	45.4784	−	27.6089i	0.297245	−	0.180450i
$154$		−	77.7729i		−	0.505019i
$155$	−61.8103	−	35.6862i	−0.398776	−	0.230234i
$156$	90.1257	+	17.6661i	0.577729	+	0.113244i
$157$	−30.2181	−	52.3394i	−0.192472	−	0.333372i	0.753597	−	0.657337i	$-0.228317\pi$
$157$	−30.2181	−	52.3394i	−0.192472	−	0.333372i	−0.946069	+	0.323965i	$0.894984\pi$
$158$	48.5654	+	84.1177i	0.307376	+	0.532390i
$159$	−99.8426	+	177.413i	−0.627941	+	1.11580i
$160$	−23.8867	+	41.3730i	−0.149292	+	0.258581i
$161$	−18.9494			−0.117698
$162$	55.8546	+	87.6003i	0.344781	+	0.540743i
$163$			304.325i			1.86703i	0.358543	+	0.933513i	$0.383274\pi$
$163$			304.325i			1.86703i	−0.358543	+	0.933513i	$0.616726\pi$
$164$	−0.511294	+	0.885588i	−0.00311765	+	0.00539993i
$165$	−38.0896	−	21.4357i	−0.230846	−	0.129913i
$166$	−24.4284	−	42.3113i	−0.147159	−	0.254887i
$167$	124.037	+	214.839i	0.742739	+	1.28646i	0.951244	+	0.308440i	$0.0998068\pi$
$167$	124.037	+	214.839i	0.742739	+	1.28646i	−0.208505	+	0.978021i	$0.566860\pi$
$168$	−79.2034	−	133.763i	−0.471449	−	0.796210i
$169$	−155.052	−	67.2305i	−0.917466	−	0.397814i
$170$		−	11.5814i		−	0.0681259i
$171$	216.812	−	131.622i	1.26791	−	0.769717i
$172$	114.252			0.664254
$173$	1.94606	+	1.12356i	0.0112489	+	0.00649456i	0.505614	−	0.862760i	$-0.331266\pi$
$173$	1.94606	+	1.12356i	0.0112489	+	0.00649456i	−0.494365	+	0.869254i	$0.664599\pi$
$174$	−103.809	+	1.14234i	−0.596605	+	0.00656519i
$175$	−124.795	+	72.0501i	−0.713111	+	0.411715i
$176$	4.93549	+	8.54851i	0.0280425	+	0.0485711i
$177$	−1.78126	−	161.870i	−0.0100636	−	0.914521i
$178$	47.1000	−	81.5796i	0.264607	−	0.458312i
$179$			352.455i			1.96902i	0.175316	+	0.984512i	$0.443905\pi$
$179$			352.455i			1.96902i	−0.175316	+	0.984512i	$0.556095\pi$
$180$	−32.3654	+	0.712400i	−0.179808	+	0.00395778i
$181$	65.7252			0.363123			0.181561	−	0.983380i	$-0.441885\pi$
$181$	65.7252			0.363123			0.181561	+	0.983380i	$0.441885\pi$
$182$	33.2473	+	100.653i	0.182678	+	0.553039i
$183$	−7.75534	+	4.59206i	−0.0423789	+	0.0250932i
$184$	21.0405	−	12.1478i	0.114351	−	0.0660205i
$185$	−21.2285	+	12.2563i	−0.114749	+	0.0662501i
$186$	−88.1785	+	156.686i	−0.474078	+	0.842400i
$187$	48.8293	+	28.1916i	0.261119	+	0.150757i
$188$	−197.738			−1.05180
$189$	80.8707	−	151.403i	0.427887	−	0.801073i
$190$		−	55.2128i		−	0.290594i
$191$	−216.394	−	124.935i	−1.13295	−	0.654110i	−0.188276	−	0.982116i	$-0.560290\pi$
$191$	−216.394	−	124.935i	−1.13295	−	0.654110i	−0.944675	+	0.328007i	$0.893623\pi$
$192$	115.701	+	65.1133i	0.602611	+	0.339132i
$193$	192.811	−	111.320i	0.999022	−	0.576785i	0.0910629	−	0.995845i	$-0.470974\pi$
$193$	192.811	−	111.320i	0.999022	−	0.576785i	0.907959	+	0.419060i	$0.137640\pi$
$194$	68.4695	−	39.5309i	0.352936	−	0.203768i
$195$	58.4588	+	11.4589i	0.299789	+	0.0587635i
$196$	10.1078	−	17.5073i	0.0515705	−	0.0893227i
$197$	−130.336			−0.661604			−0.330802	−	0.943700i	$-0.607319\pi$
$197$	−130.336			−0.661604			−0.330802	+	0.943700i	$0.607319\pi$
$198$	−52.9396	+	96.5399i	−0.267372	+	0.487575i
$199$	237.077			1.19134			0.595670	−	0.803229i	$-0.296887\pi$
$199$	237.077			1.19134			0.595670	+	0.803229i	$0.296887\pi$
$200$	92.3775	−	160.003i	0.461888	−	0.800013i
$201$	63.8117	−	0.702200i	0.317471	−	0.00349353i
$202$	33.8164	−	19.5239i	0.167408	−	0.0966531i
$203$	85.7606	+	148.542i	0.422466	+	0.731732i
$204$	41.7598	−	0.459535i	0.204705	−	0.00225262i
$205$	−0.331644	+	0.574424i	−0.00161778	+	0.00280207i
$206$	−127.670			−0.619756
$207$	23.5219	+	12.8987i	0.113633	+	0.0623127i
$208$	−10.0419	−	8.95354i	−0.0482783	−	0.0430458i
$209$	232.787	+	134.400i	1.11381	+	0.643060i
$210$	−19.0374	−	32.1515i	−0.0906543	−	0.153102i
$211$	95.3287	+	165.114i	0.451795	+	0.782532i	0.998498	−	0.0547951i	$-0.0174506\pi$
$211$	95.3287	+	165.114i	0.451795	+	0.782532i	−0.546703	+	0.837327i	$0.684117\pi$
$212$	−138.392	+	79.9005i	−0.652791	+	0.376889i
$213$	275.581	+	155.089i	1.29381	+	0.728118i
$214$	163.813	+	94.5776i	0.765482	+	0.441951i
$215$	74.1078			0.344688
$216$	7.26364	+	219.954i	0.0336280	+	1.01831i
$217$	297.052			1.36890
$218$	57.7091	+	33.3183i	0.264720	+	0.152836i
$219$	22.5545	−	40.0776i	0.102989	−	0.183003i
$220$	−17.1542	−	29.7120i	−0.0779737	−	0.135054i
$221$	−75.2461	−	15.6112i	−0.340480	−	0.0706389i
$222$	31.4614	+	53.1338i	0.141718	+	0.239342i
$223$	−107.197	−	61.8903i	−0.480705	−	0.277535i	0.240006	−	0.970772i	$-0.422851\pi$
$223$	−107.197	−	61.8903i	−0.480705	−	0.277535i	−0.720710	+	0.693237i	$0.756184\pi$
$224$		−	198.833i		−	0.887646i
$225$	203.952	−	4.48923i	0.906454	−	0.0199521i
$226$		−	192.133i		−	0.850148i
$227$	−83.2671	+	144.223i	−0.366815	+	0.635343i	−0.989066	−	0.147476i	$-0.952885\pi$
$227$	−83.2671	+	144.223i	−0.366815	+	0.635343i	0.622250	+	0.782818i	$0.286219\pi$
$228$	199.084	−	2.19077i	0.873176	−	0.00960864i
$229$	231.335	−	133.561i	1.01020	−	0.583237i	0.0989474	−	0.995093i	$-0.468452\pi$
$229$	231.335	−	133.561i	1.01020	−	0.583237i	0.911249	+	0.411855i	$0.135119\pi$
$230$	5.05733	−	2.91985i	0.0219884	−	0.0126950i
$231$	181.897	−	2.00164i	0.787434	−	0.00866513i
$232$	−190.449	−	109.956i	−0.820903	−	0.473948i
$233$			1.80691i			0.00775499i	0.999992	+	0.00387750i	$0.00123425\pi$
$233$			1.80691i			0.00775499i	−0.999992	+	0.00387750i	$0.998766\pi$
$234$	27.2440	−	147.572i	0.116427	−	0.630652i
$235$	−128.260			−0.545787
$236$	63.5350	−	110.046i	0.269216	−	0.466296i
$237$	−195.487	+	115.751i	−0.824838	+	0.488400i
$238$	24.1009	+	41.7440i	0.101264	+	0.175395i
$239$	−146.044	−	252.956i	−0.611063	−	1.05839i	−0.991062	−	0.133405i	$-0.957409\pi$
$239$	−146.044	−	252.956i	−0.611063	−	1.05839i	0.379998	−	0.924987i	$-0.375925\pi$
$240$	4.13286	+	2.32585i	0.0172203	+	0.00969105i
$241$	−244.389	−	141.098i	−1.01406	−	0.585469i	−0.101684	−	0.994817i	$-0.532423\pi$
$241$	−244.389	−	141.098i	−1.01406	−	0.585469i	−0.912378	+	0.409348i	$0.865756\pi$
$242$	38.5125			0.159142
$243$	−203.444	+	132.889i	−0.837219	+	0.546867i
$244$	−7.07480			−0.0289951
$245$	6.55629	−	11.3558i	0.0267604	−	0.0463503i
$246$	1.45614	+	0.819473i	0.00591927	+	0.00333119i
$247$	−358.726	−	74.4242i	−1.45233	−	0.301313i
$248$	−329.833	+	190.429i	−1.32997	+	0.767860i
$249$	98.3300	−	58.2228i	0.394900	−	0.233827i
$250$	46.6934	−	80.8754i	0.186774	−	0.323502i
$251$		−	156.171i		−	0.622195i	−0.950378	−	0.311098i	$-0.899303\pi$
$251$		−	156.171i		−	0.622195i	0.950378	−	0.311098i	$-0.100697\pi$
$252$	115.175	−	69.9201i	0.457044	−	0.277461i
$253$			28.4301i			0.112372i
$254$	−128.074	+	221.832i	−0.504230	+	0.873353i
$255$	27.0869	−	0.298071i	0.106223	−	0.00116891i
$256$	132.339	+	229.217i	0.516948	+	0.895380i
$257$	−119.335	+	68.8983i	−0.464340	+	0.268087i	−0.713867	−	0.700281i	$-0.753058\pi$
$257$	−119.335	+	68.8983i	−0.464340	+	0.268087i	0.249528	+	0.968368i	$0.419725\pi$
$258$	−2.05421	−	186.674i	−0.00796205	−	0.723543i
$259$	51.0106	−	88.3529i	0.196952	−	0.341131i
$260$	34.9025	+	31.1197i	0.134240	+	0.119691i
$261$	−5.34348	−	242.762i	−0.0204731	−	0.930123i
$262$			145.854i			0.556695i
$263$	−348.259	−	201.068i	−1.32418	−	0.764516i	−0.339787	−	0.940502i	$-0.610355\pi$
$263$	−348.259	−	201.068i	−1.32418	−	0.764516i	−0.984393	+	0.175987i	$0.943688\pi$
$264$	−200.688	+	118.830i	−0.760180	+	0.450115i
$265$	−89.7659	+	51.8264i	−0.338739	+	0.195571i
$266$	114.898	+	199.009i	0.431946	+	0.748153i
$267$	192.013	+	108.059i	0.719149	+	0.404716i
$268$	43.3817	+	25.0465i	0.161872	+	0.0934569i
$269$		−	449.323i		−	1.67035i	−0.549986	−	0.835174i	$-0.685367\pi$
$269$		−	449.323i		−	1.67035i	0.549986	−	0.835174i	$-0.314633\pi$
$270$	1.74590	+	52.8684i	0.00646628	+	0.195809i
$271$		−	2.53296i		−	0.00934670i	−0.999989	−	0.00467335i	$-0.998512\pi$
$271$		−	2.53296i		−	0.00934670i	0.999989	−	0.00467335i	$-0.00148758\pi$
$272$	−5.29816	−	3.05889i	−0.0194785	−	0.0112459i
$273$	−234.554	+	80.3502i	−0.859174	+	0.294323i
$274$	−64.9576	−	112.510i	−0.237071	−	0.410620i
$275$	108.098	+	187.232i	0.393084	+	0.680842i
$276$	10.7289	+	18.1196i	0.0388730	+	0.0656509i
$277$	33.6096	−	58.2134i	0.121334	−	0.210157i	−0.798960	−	0.601384i	$-0.794616\pi$
$277$	33.6096	−	58.2134i	0.121334	−	0.210157i	0.920294	+	0.391227i	$0.127949\pi$
$278$	−35.7881			−0.128734
$279$	−368.732	−	202.202i	−1.32162	−	0.724737i
$280$		−	79.1501i		−	0.282679i
$281$	−85.9968	+	148.951i	−0.306039	+	0.530074i	−0.977492	−	0.210972i	$-0.932337\pi$
$281$	−85.9968	+	148.951i	−0.306039	+	0.530074i	0.671453	+	0.741047i	$0.265670\pi$
$282$	3.55526	+	323.081i	0.0126073	+	1.14568i
$283$	−179.573	−	311.030i	−0.634534	−	1.09904i	−0.986614	−	0.163075i	$-0.947859\pi$
$283$	−179.573	−	311.030i	−0.634534	−	1.09904i	0.352080	−	0.935970i	$-0.385475\pi$
$284$	124.112	+	214.969i	0.437015	+	0.756932i
$285$	129.133	−	1.42101i	0.453099	−	0.00498601i
$286$	151.012	−	49.8816i	0.528013	−	0.174411i
$287$		−	2.76060i		−	0.00961882i
$288$	−135.344	+	246.812i	−0.469946	+	0.856986i
$289$	254.055			0.879083
$290$	−45.7766	−	26.4291i	−0.157850	−	0.0911350i
$291$	94.2181	+	159.121i	0.323773	+	0.546807i
$292$	31.2628	−	18.0496i	0.107064	−	0.0618136i
$293$	−41.9881	−	72.7256i	−0.143304	−	0.248210i	0.785435	−	0.618944i	$-0.212439\pi$
$293$	−41.9881	−	72.7256i	−0.143304	−	0.248210i	−0.928739	+	0.370734i	$0.879106\pi$
$294$	−28.7865	−	16.2002i	−0.0979134	−	0.0551028i
$295$	41.2111	−	71.3797i	0.139699	−	0.241965i
$296$			130.804i			0.441906i
$297$	−227.153	−	121.332i	−0.764823	−	0.408525i
$298$	−348.646			−1.16995
$299$	−12.1537	−	36.7940i	−0.0406477	−	0.123057i
$300$	139.553	+	78.5361i	0.465176	+	0.261787i
$301$	−267.114	+	154.218i	−0.887421	+	0.512353i
$302$	93.0363	−	53.7145i	0.308067	−	0.177863i
$303$	46.5334	+	78.5882i	0.153576	+	0.259367i
$304$	−25.2583	−	14.5829i	−0.0830864	−	0.0479699i
$305$	−4.58897			−0.0150458
$306$	−1.50165	−	68.2223i	−0.00490736	−	0.222949i
$307$		−	355.975i		−	1.15953i	−0.814785	−	0.579764i	$-0.803145\pi$
$307$		−	355.975i		−	1.15953i	0.814785	−	0.579764i	$-0.196855\pi$
$308$	123.661	+	71.3958i	0.401497	+	0.231804i
$309$	−3.28584	−	298.597i	−0.0106338	−	0.966334i
$310$	−79.2790	+	45.7718i	−0.255739	+	0.147651i
$311$	−29.6195	+	17.1008i	−0.0952397	+	0.0549866i	−0.546863	−	0.837222i	$-0.684178\pi$
$311$	−29.6195	+	17.1008i	−0.0952397	+	0.0549866i	0.451624	+	0.892209i	$0.350845\pi$
$312$	208.929	−	239.582i	0.669645	−	0.767890i
$313$	−72.6374	+	125.812i	−0.232068	+	0.401954i	−0.958417	−	0.285373i	$-0.907883\pi$
$313$	−72.6374	+	125.812i	−0.232068	+	0.401954i	0.726348	+	0.687327i	$0.241216\pi$
$314$	−77.5166			−0.246868
$315$	74.7067	−	45.3527i	0.237164	−	0.143977i
$316$	−178.333			−0.564344
$317$	−35.8311	+	62.0613i	−0.113032	+	0.195777i	−0.916991	−	0.398907i	$-0.869390\pi$
$317$	−35.8311	+	62.0613i	−0.113032	+	0.195777i	0.803959	+	0.594684i	$0.202723\pi$
$318$	133.036	+	224.679i	0.418353	+	0.706539i
$319$	222.860	−	128.668i	0.698620	−	0.403349i
$320$	33.7991	+	58.5417i	0.105622	+	0.182943i
$321$	−216.984	+	385.565i	−0.675964	+	1.20114i
$322$	−12.1524	+	21.0486i	−0.0377404	+	0.0653682i
$323$	−166.595			−0.515775
$324$	−190.562	+	8.39303i	−0.588153	+	0.0259044i
$325$	−219.940	−	196.102i	−0.676738	−	0.603392i
$326$	338.038	+	195.166i	1.03693	+	0.598670i
$327$	−76.4405	+	135.829i	−0.233763	+	0.415379i
$328$	1.76972	+	3.06525i	0.00539550	+	0.00934527i
$329$	462.299	−	266.909i	1.40517	−	0.811272i
$330$	−48.2375	+	28.5622i	−0.146174	+	0.0865521i
$331$	−358.154	−	206.781i	−1.08204	−	0.624715i	−0.150592	−	0.988596i	$-0.548118\pi$
$331$	−358.154	−	206.781i	−1.08204	−	0.624715i	−0.931445	+	0.363881i	$0.881451\pi$
$332$	89.7015			0.270185
$333$	−123.461	+	74.9503i	−0.370754	+	0.225076i
$334$	318.185			0.952649
$335$	28.1390	+	16.2460i	0.0839969	+	0.0484956i
$336$	−19.7365	+	0.217186i	−0.0587397	+	0.000646387i
$337$	86.6599	+	150.099i	0.257151	+	0.445398i	0.965478	−	0.260486i	$-0.0838829\pi$
$337$	86.6599	+	150.099i	0.257151	+	0.445398i	−0.708327	+	0.705885i	$0.750550\pi$
$338$	−174.114	+	129.113i	−0.515131	+	0.381991i
$339$	449.367	−	4.94494i	1.32556	−	0.0145868i
$340$	18.4148	+	10.6318i	0.0541611	+	0.0312699i
$341$		−	445.673i		−	1.30696i
$342$	−7.15893	−	325.241i	−0.0209325	−	0.950996i
$343$			366.083i			1.06730i
$344$	197.728	−	342.474i	0.574789	−	0.995564i
$345$	6.95918	+	11.7531i	0.0201715	+	0.0340668i
$346$	2.49605	−	1.44110i	0.00721402	−	0.00416502i
$347$	−370.144	+	213.703i	−1.06670	+	0.615859i	−0.927278	−	0.374375i	$-0.877857\pi$
$347$	−370.144	+	213.703i	−1.06670	+	0.615859i	−0.139421	+	0.990233i	$0.544524\pi$
$348$	93.4808	−	166.108i	0.268623	−	0.477322i
$349$	392.043	+	226.346i	1.12333	+	0.648557i	0.942250	−	0.334911i	$-0.108706\pi$
$349$	392.043	+	226.346i	1.12333	+	0.648557i	0.181084	+	0.983468i	$0.442039\pi$
$350$			184.826i			0.528073i
$351$	345.848	+	59.9208i	0.985321	+	0.170715i
$352$	−298.312			−0.847479
$353$	96.4367	−	167.033i	0.273192	−	0.473182i	−0.696486	−	0.717571i	$-0.745254\pi$
$353$	96.4367	−	167.033i	0.273192	−	0.473182i	0.969677	+	0.244389i	$0.0785873\pi$
$354$	−180.944	−	101.830i	−0.511142	−	0.287656i
$355$	80.5037	+	139.437i	0.226771	+	0.392779i
$356$	86.4759	+	149.781i	0.242910	+	0.420732i
$357$	−97.0116	+	57.4421i	−0.271741	+	0.160902i
$358$	391.500	+	226.033i	1.09358	+	0.631376i
$359$	18.1458			0.0505454			0.0252727	−	0.999681i	$-0.491955\pi$
$359$	18.1458			0.0505454			0.0252727	+	0.999681i	$0.491955\pi$
$360$	−53.8770	+	98.2494i	−0.149658	+	0.272915i
$361$	−433.220			−1.20005
$362$	42.1502	−	73.0062i	0.116437	−	0.201675i
$363$	0.991196	+	90.0739i	0.00273057	+	0.248138i
$364$	−190.562	−	39.5357i	−0.523523	−	0.108614i
$365$	20.2782	−	11.7076i	0.0555566	−	0.0320756i
$366$	0.127203	+	11.5594i	0.000347548	+	0.0315831i
$367$	223.747	−	387.541i	0.609665	−	1.05597i	−0.381631	−	0.924315i	$-0.624637\pi$
$367$	223.747	−	387.541i	0.609665	−	1.05597i	0.991296	−	0.131655i	$-0.0420292\pi$
$368$		−	3.08477i		−	0.00838254i
$369$	−1.87913	+	3.42675i	−0.00509249	+	0.00928658i
$370$			31.4402i			0.0849736i
$371$	215.701	−	373.605i	0.581405	−	1.00702i
$372$	−168.188	−	284.045i	−0.452117	−	0.763562i
$373$	355.982	+	616.580i	0.954376	+	1.65303i	0.735789	+	0.677211i	$0.236812\pi$
$373$	355.982	+	616.580i	0.954376	+	1.65303i	0.218588	+	0.975817i	$0.429855\pi$
$374$	62.6293	−	36.1590i	0.167458	−	0.0966819i
$375$	190.355	+	107.126i	0.507614	+	0.285670i
$376$	−342.211	+	592.727i	−0.910136	+	1.57640i
$377$	−233.419	+	261.792i	−0.619148	+	0.694409i
$378$	−116.312	−	186.925i	−0.307704	−	0.494512i
$379$		−	633.425i		−	1.67131i	−0.549257	−	0.835653i	$-0.685089\pi$
$379$		−	633.425i		−	1.67131i	0.549257	−	0.835653i	$-0.314911\pi$
$380$	87.7899	+	50.6855i	0.231026	+	0.133383i
$381$	−522.122	−	293.835i	−1.37040	−	0.771220i
$382$	−277.550	+	160.244i	−0.726571	+	0.419486i
$383$	48.4518	+	83.9210i	0.126506	+	0.219115i	0.922321	−	0.386425i	$-0.126290\pi$
$383$	48.4518	+	83.9210i	0.126506	+	0.219115i	−0.795815	+	0.605540i	$0.792957\pi$
$384$	−176.420	+	104.461i	−0.459428	+	0.272035i
$385$	80.2111	+	46.3099i	0.208340	+	0.120285i
$386$		−	285.561i		−	0.739795i
$387$	436.545	−	9.60887i	1.12802	−	0.0248291i
$388$			145.158i			0.374118i
$389$	534.942	+	308.849i	1.37517	+	0.793956i	0.991574	−	0.129543i	$-0.0413512\pi$
$389$	534.942	+	308.849i	1.37517	+	0.793956i	0.383599	+	0.923500i	$0.374685\pi$
$390$	50.2184	−	57.5861i	0.128765	−	0.147657i
$391$	−8.81015	−	15.2596i	−0.0225323	−	0.0390272i
$392$	−34.9858	−	60.5971i	−0.0892494	−	0.154585i
$393$	−341.127	+	3.75385i	−0.868008	+	0.00955178i
$394$	−83.5856	+	144.774i	−0.212146	+	0.367448i
$395$	−115.673			−0.292843
$396$	−104.902	−	172.799i	−0.264905	−	0.436362i
$397$			207.827i			0.523493i	0.965137	+	0.261747i	$0.0842985\pi$
$397$			207.827i			0.523493i	−0.965137	+	0.261747i	$0.915702\pi$
$398$	152.039	−	263.340i	0.382008	−	0.661658i
$399$	−462.489	+	273.848i	−1.15912	+	0.686335i
$400$	−11.7291	−	20.3153i	−0.0293227	−	0.0507883i
$401$	−226.908	−	393.017i	−0.565856	−	0.980091i	−0.996969	−	0.0777935i	$-0.975213\pi$
$401$	−226.908	−	393.017i	−0.565856	−	0.980091i	0.431114	−	0.902298i	$-0.358121\pi$
$402$	40.1430	−	71.3310i	0.0998582	−	0.177440i
$403$	190.522	+	576.786i	0.472758	+	1.43123i
$404$			71.6921i			0.177456i
$405$	−123.605	+	5.44402i	−0.305198	+	0.0134420i
$406$	219.996			0.541862
$407$	−132.558	−	76.5321i	−0.325694	−	0.188040i
$408$	70.8932	−	125.972i	0.173758	−	0.308755i
$409$	494.383	−	285.432i	1.20876	−	0.697878i	0.246272	−	0.969201i	$-0.420794\pi$
$409$	494.383	−	285.432i	1.20876	−	0.697878i	0.962488	+	0.271323i	$0.0874612\pi$
$410$	0.425372	+	0.736767i	0.00103749	+	0.00179699i
$411$	261.469	−	154.820i	0.636178	−	0.376691i
$412$	117.201	−	202.998i	0.284469	−	0.492714i
$413$			343.041i			0.830607i
$414$	29.4125	−	17.8556i	0.0710446	−	0.0431295i
$415$	58.1836			0.140201
$416$	386.074	−	127.526i	0.928062	−	0.306554i
$417$	−0.921079	−	83.7021i	−0.00220882	−	0.200724i
$418$	298.577	−	172.383i	0.714298	−	0.412400i
$419$	620.074	−	358.000i	1.47989	−	0.854416i	0.480151	−	0.877186i	$-0.340582\pi$
$419$	620.074	−	358.000i	1.47989	−	0.854416i	0.999741	+	0.0227704i	$0.00724866\pi$
$420$	68.5981	−	0.754871i	0.163329	−	0.00179731i
$421$	148.999	+	86.0245i	0.353916	+	0.204334i	0.666409	−	0.745586i	$-0.267831\pi$
$421$	148.999	+	86.0245i	0.353916	+	0.204334i	−0.312492	+	0.949920i	$0.601164\pi$
$422$	244.541			0.579480
$423$	−755.538	+	16.6303i	−1.78614	+	0.0393150i
$424$			553.113i			1.30451i
$425$	−116.042	−	66.9966i	−0.273039	−	0.157639i
$426$	349.002	−	206.650i	0.819254	−	0.485094i
$427$	16.5405	−	9.54964i	0.0387364	−	0.0223645i
$428$	−300.762	+	173.645i	−0.702715	+	0.405713i
$429$	120.551	+	351.907i	0.281005	+	0.820295i
$430$	47.5260	−	82.3174i	0.110526	−	0.191436i
$431$	285.388			0.662153			0.331076	−	0.943604i	$-0.392588\pi$
$431$	285.388			0.662153			0.331076	+	0.943604i	$0.392588\pi$
$432$	24.6469	+	13.1650i	0.0570530	+	0.0304745i
$433$	159.813			0.369082			0.184541	−	0.982825i	$-0.440920\pi$
$433$	159.813			0.369082			0.184541	+	0.982825i	$0.440920\pi$
$434$	190.502	−	329.959i	0.438944	−	0.760274i
$435$	60.6350	−	107.744i	0.139391	−	0.247687i
$436$	−105.954	+	61.1727i	−0.243014	+	0.140304i
$437$	−42.0012	−	72.7482i	−0.0961125	−	0.166472i
$438$	−30.0530	−	50.7552i	−0.0686141	−	0.115879i
$439$	93.6335	−	162.178i	0.213288	−	0.369426i	−0.739454	−	0.673208i	$-0.764916\pi$
$439$	93.6335	−	162.178i	0.213288	−	0.369426i	0.952742	+	0.303782i	$0.0982494\pi$
$440$	−118.750			−0.269887
$441$	37.1486	−	67.7436i	0.0842372	−	0.153614i
$442$	−65.5966	+	73.5703i	−0.148409	+	0.166449i
$443$	541.940	+	312.889i	1.22334	+	0.706296i	0.965629	−	0.259926i	$-0.0836981\pi$
$443$	541.940	+	312.889i	1.22334	+	0.706296i	0.257712	+	0.966222i	$0.417031\pi$
$444$	−113.366	+	1.24751i	−0.255329	+	0.00280970i
$445$	56.0914	+	97.1531i	0.126048	+	0.218322i
$446$	−137.493	+	79.3815i	−0.308280	+	0.177986i
$447$	−8.97312	−	815.423i	−0.0200741	−	1.82421i
$448$	−243.650	−	140.672i	−0.543862	−	0.313999i
$449$	−437.533			−0.974460			−0.487230	−	0.873274i	$-0.661993\pi$
$449$	−437.533			−0.974460			−0.487230	+	0.873274i	$0.661993\pi$
$450$	125.810	−	229.425i	0.279577	−	0.509833i
$451$	−4.14178			−0.00918356
$452$	305.497	+	176.379i	0.675879	+	0.390219i
$453$	128.023	+	216.213i	0.282612	+	0.477292i
$454$	106.800	+	184.983i	0.235242	+	0.407451i
$455$	−123.606	−	25.6443i	−0.271661	−	0.0563610i
$456$	337.974	−	600.554i	0.741171	−	1.31700i
$457$	518.150	+	299.154i	1.13381	+	0.654604i	0.944890	−	0.327388i	$-0.106169\pi$
$457$	518.150	+	299.154i	1.13381	+	0.654604i	0.188918	+	0.981993i	$0.439502\pi$
$458$		−	342.616i		−	0.748070i
$459$	159.521	−	5.26794i	0.347541	−	0.0114770i
$460$			10.7217i			0.0233081i
$461$	−146.252	+	253.316i	−0.317250	+	0.549493i	−0.979913	−	0.199425i	$-0.936093\pi$
$461$	−146.252	+	253.316i	−0.317250	+	0.549493i	0.662663	+	0.748917i	$0.269426\pi$
$462$	114.429	−	203.331i	0.247682	−	0.440111i
$463$	−675.611	+	390.064i	−1.45920	+	0.842471i	−0.998972	−	0.0453276i	$-0.985567\pi$
$463$	−675.611	+	390.064i	−1.45920	+	0.842471i	−0.460231	+	0.887799i	$0.652233\pi$
$464$	−24.1811	+	13.9610i	−0.0521145	+	0.0300883i
$465$	−109.093	−	184.242i	−0.234608	−	0.396219i
$466$	2.00708	+	1.15879i	0.00430704	+	0.00248667i
$467$			441.322i			0.945015i	0.881327	+	0.472508i	$0.156651\pi$
$467$			441.322i			0.945015i	−0.881327	+	0.472508i	$0.843349\pi$
$468$	209.634	+	178.791i	0.447937	+	0.382031i
$469$	−135.232			−0.288341
$470$	−82.2542	+	142.468i	−0.175009	+	0.303124i
$471$	−1.99505	−	181.298i	−0.00423577	−	0.384921i
$472$	−219.911	−	380.897i	−0.465913	−	0.806986i
$473$	231.377	+	400.756i	0.489168	+	0.847264i
$474$	3.20636	+	291.375i	0.00676447	+	0.614714i
$475$	−553.212	−	319.397i	−1.16466	−	0.672416i
$476$	−88.4987			−0.185922
$477$	−522.062	+	316.931i	−1.09447	+	0.664426i
$478$	−374.637			−0.783760
$479$	−220.584	+	382.062i	−0.460509	+	0.797625i	−0.998986	−	0.0450152i	$-0.985666\pi$
$479$	−220.584	+	382.062i	−0.460509	+	0.797625i	0.538477	+	0.842640i	$0.319000\pi$
$480$	−123.323	+	73.0215i	−0.256923	+	0.152128i
$481$	204.272	+	42.3799i	0.424682	+	0.0881080i
$482$	−313.458	+	180.975i	−0.650327	+	0.375466i
$483$	−49.5417	−	27.8806i	−0.102571	−	0.0577238i
$484$	−35.3546	+	61.2359i	−0.0730466	+	0.126520i
$485$			94.1547i			0.194133i
$486$	17.1395	+	311.204i	0.0352664	+	0.640338i
$487$			331.192i			0.680066i	0.940414	+	0.340033i	$0.110438\pi$
$487$			331.192i			0.680066i	−0.940414	+	0.340033i	$0.889562\pi$
$488$	−12.2439	+	21.2070i	−0.0250899	+	0.0434570i
$489$	−447.760	+	795.635i	−0.915665	+	1.62707i
$490$	−8.40922	−	14.5652i	−0.0171617	−	0.0297249i
$491$	−262.207	+	151.385i	−0.534026	+	0.308320i	−0.742654	−	0.669675i	$-0.766433\pi$
$491$	−262.207	+	151.385i	−0.534026	+	0.308320i	0.208628	+	0.977995i	$0.433100\pi$
$492$	−2.63972	+	1.56302i	−0.00536529	+	0.00317688i
$493$	−79.7454	+	138.123i	−0.161755	+	0.280169i
$494$	−312.723	+	350.736i	−0.633042	+	0.709992i
$495$	−68.0435	−	112.084i	−0.137462	−	0.226432i
$496$			48.3572i			0.0974943i
$497$	−580.334	−	335.056i	−1.16767	−	0.674157i
$498$	−1.61280	−	146.562i	−0.00323856	−	0.294301i
$499$	329.683	−	190.343i	0.660688	−	0.381448i	−0.131851	−	0.991270i	$-0.542092\pi$
$499$	329.683	−	190.343i	0.660688	−	0.381448i	0.792539	+	0.609821i	$0.208759\pi$
$500$	85.7294	+	148.488i	0.171459	+	0.296975i
$501$	8.18913	+	744.179i	0.0163456	+	1.48539i
$502$	−173.471	−	100.154i	−0.345561	−	0.199510i
$503$		−	766.223i		−	1.52331i	−0.647985	−	0.761654i	$-0.724388\pi$
$503$		−	766.223i		−	1.52331i	0.647985	−	0.761654i	$-0.275612\pi$
$504$	−10.2627	−	466.247i	−0.0203624	−	0.925094i
$505$			46.5021i			0.0920833i
$506$	31.5796	+	18.2325i	0.0624102	+	0.0360326i
$507$	−306.454	−	403.900i	−0.604445	−	0.796647i
$508$	−235.146	−	407.284i	−0.462885	−	0.801740i
$509$	−239.507	−	414.839i	−0.470545	−	0.815008i	0.528887	−	0.848692i	$-0.322609\pi$
$509$	−239.507	−	414.839i	−0.470545	−	0.815008i	−0.999433	+	0.0336839i	$0.989276\pi$
$510$	17.0400	−	30.2787i	0.0334117	−	0.0593700i
$511$	−48.7270	+	84.3976i	−0.0953561	+	0.165162i
$512$	66.1098			0.129121
$513$	760.497	−	25.1142i	1.48245	−	0.0489556i
$514$			176.740i			0.343853i
$515$	76.0209	−	131.672i	0.147613	−	0.255674i
$516$	298.703	+	168.101i	0.578881	+	0.325777i
$517$	−400.448	−	693.597i	−0.774561	−	1.34158i
$518$	−65.4270	−	113.323i	−0.126307	−	0.218770i
$519$	3.43471	+	5.80074i	0.00661795	+	0.0111768i
$520$	153.686	−	50.7649i	0.295550	−	0.0976248i
$521$		−	794.176i		−	1.52433i	−0.647382	−	0.762165i	$-0.724136\pi$
$521$		−	794.176i		−	1.52433i	0.647382	−	0.762165i	$-0.275864\pi$
$522$	−273.082	−	149.750i	−0.523146	−	0.286878i
$523$	788.966			1.50854			0.754270	−	0.656564i	$-0.227991\pi$
$523$	788.966			1.50854			0.754270	+	0.656564i	$0.227991\pi$
$524$	−231.912	−	133.894i	−0.442580	−	0.255524i
$525$	−432.275	+	4.75686i	−0.823380	+	0.00906068i
$526$	−446.683	+	257.893i	−0.849208	+	0.490291i
$527$	138.108	+	239.211i	0.262065	+	0.453911i
$528$	0.325848	+	29.6111i	0.000617137	+	0.0560817i
$529$	−260.058	+	450.433i	−0.491602	+	0.851480i
$530$			132.947i			0.250843i
$531$	233.506	−	425.818i	0.439748	−	0.801917i
$532$	−421.906			−0.793056
$533$	5.36026	−	1.77058i	0.0100568	−	0.00332192i
$534$	243.169	−	143.984i	0.455373	−	0.269634i
$535$	−195.085	+	112.632i	−0.364645	+	0.210528i
$536$	150.155	−	86.6923i	0.280141	−	0.161739i
$537$	−518.575	+	921.468i	−0.965689	+	1.71596i
$538$	−499.099	−	288.155i	−0.927694	−	0.535604i
$539$	81.8792			0.151910
$540$	−85.6650	−	45.7573i	−0.158639	−	0.0847358i
$541$		−	151.515i		−	0.280064i	−0.990147	−	0.140032i	$-0.955279\pi$
$541$		−	151.515i		−	0.280064i	0.990147	−	0.140032i	$-0.0447206\pi$
$542$	−2.81356	−	1.62441i	−0.00519106	−	0.00299706i
$543$	171.834	+	96.7029i	0.316452	+	0.178090i
$544$	160.117	−	92.4434i	0.294332	−	0.169933i
$545$	−68.7257	+	39.6788i	−0.126102	+	0.0728051i
$546$	−61.1704	+	312.067i	−0.112034	+	0.571552i
$547$	288.796	−	500.209i	0.527963	−	0.914458i	−0.471506	−	0.881863i	$-0.656289\pi$
$547$	288.796	−	500.209i	0.527963	−	0.914458i	0.999469	−	0.0325954i	$-0.0103773\pi$
$548$	238.525			0.435264
$549$	−27.0321	+	0.595009i	−0.0492389	+	0.00108381i
$550$	277.297			0.504177
$551$	−380.175	+	658.483i	−0.689974	+	1.19507i
$552$	72.8822	−	0.802014i	0.132033	−	0.00145292i
$553$	416.931	−	240.715i	0.753944	−	0.435290i
$554$	−43.1082	−	74.6656i	−0.0778126	−	0.134775i
$555$	−73.5332	+	0.809178i	−0.132492	+	0.00145798i
$556$	32.8536	−	56.9040i	0.0590891	−	0.102345i
$557$	977.285			1.75455			0.877275	−	0.479988i	$-0.159359\pi$
$557$	977.285			1.75455			0.877275	+	0.479988i	$0.159359\pi$
$558$	−461.072	+	279.906i	−0.826294	+	0.501624i
$559$	−470.766	−	419.743i	−0.842157	−	0.750883i
$560$	−8.70320	−	5.02480i	−0.0155414	−	0.00897285i
$561$	86.1815	+	145.548i	0.153621	+	0.259444i
$562$	110.301	+	191.047i	0.196265	+	0.339941i
$563$	394.123	−	227.547i	0.700041	−	0.404169i	−0.107322	−	0.994224i	$-0.534227\pi$
$563$	394.123	−	227.547i	0.700041	−	0.404169i	0.807363	+	0.590055i	$0.200894\pi$
$564$	−516.971	−	290.936i	−0.916615	−	0.515844i
$565$	198.157	+	114.406i	0.350720	+	0.202488i
$566$	−460.647			−0.813864
$567$	434.193	−	276.844i	0.765772	−	0.488262i
$568$	859.170			1.51262
$569$	−389.346	−	224.789i	−0.684263	−	0.395060i	0.117196	−	0.993109i	$-0.462609\pi$
$569$	−389.346	−	224.789i	−0.684263	−	0.395060i	−0.801459	+	0.598049i	$0.795943\pi$
$570$	81.2357	−	144.350i	0.142519	−	0.253245i
$571$	−146.524	−	253.787i	−0.256610	−	0.444461i	0.708722	−	0.705488i	$-0.249272\pi$
$571$	−146.524	−	253.787i	−0.256610	−	0.444461i	−0.965331	+	0.261027i	$0.915939\pi$
$572$	−59.3161	+	285.904i	−0.103700	+	0.499833i
$573$	−381.925	−	645.017i	−0.666536	−	1.12568i
$574$	−3.06642	−	1.77040i	−0.00534219	−	0.00308432i
$575$		−	67.5635i		−	0.117502i
$576$	206.690	+	340.468i	0.358837	+	0.591090i
$577$		−	528.656i		−	0.916215i	−0.888897	−	0.458108i	$-0.848527\pi$
$577$		−	528.656i		−	0.916215i	0.888897	−	0.458108i	$-0.151473\pi$
$578$	162.928	−	282.199i	0.281882	−	0.488234i
$579$	667.877	−	7.34949i	1.15350	−	0.0126934i
$580$	84.0461	−	48.5241i	0.144907	−	0.0836622i
$581$	−209.717	+	121.080i	−0.360958	+	0.208399i
$582$	237.171	−	2.60989i	0.407510	−	0.00448435i
$583$	−560.527	−	323.621i	−0.961453	−	0.555095i
$584$		−	124.948i		−	0.213953i
$585$	135.976	+	115.970i	0.232438	+	0.198239i
$586$	−107.709			−0.183804
$587$	−334.347	+	579.106i	−0.569586	+	0.986552i	0.427020	+	0.904242i	$0.359563\pi$
$587$	−334.347	+	579.106i	−0.569586	+	0.986552i	−0.996607	+	0.0823105i	$0.973770\pi$
$588$	52.1849	−	30.8995i	0.0887498	−	0.0525502i
$589$	658.413	+	1140.41i	1.11785	+	1.93617i
$590$	−52.8581	−	91.5528i	−0.0895899	−	0.155174i
$591$	−340.753	−	191.766i	−0.576571	−	0.324477i
$592$	14.3830	+	8.30403i	0.0242956	+	0.0140271i
$593$	−705.106			−1.18905			−0.594525	−	0.804077i	$-0.702660\pi$
$593$	−705.106			−1.18905			−0.594525	+	0.804077i	$0.702660\pi$
$594$	−280.448	+	174.505i	−0.472134	+	0.293780i
$595$	−57.4035			−0.0964764
$596$	320.058	−	554.357i	0.537011	−	0.930130i
$597$	619.819	+	348.816i	1.03822	+	0.584281i
$598$	−48.6643	−	10.0963i	−0.0813784	−	0.0168834i
$599$	126.070	−	72.7864i	0.210467	−	0.121513i	−0.391061	−	0.920365i	$-0.627892\pi$
$599$	126.070	−	72.7864i	0.210467	−	0.121513i	0.601528	+	0.798851i	$0.294559\pi$
$600$	476.929	−	282.398i	0.794882	−	0.470663i
$601$	203.611	−	352.664i	0.338787	−	0.586796i	−0.645418	−	0.763829i	$-0.723317\pi$
$601$	203.611	−	352.664i	0.338787	−	0.586796i	0.984205	+	0.177034i	$0.0566502\pi$
$602$			395.606i			0.657153i
$603$	167.864	+	92.0516i	0.278381	+	0.152656i
$604$			197.240i			0.326557i
$605$	−22.9322	+	39.7198i	−0.0379045	+	0.0656526i
$606$	117.136	−	1.28900i	0.193294	−	0.00212706i
$607$	−2.73734	−	4.74122i	−0.00450963	−	0.00781091i	0.863762	−	0.503900i	$-0.168102\pi$
$607$	−2.73734	−	4.74122i	−0.00450963	−	0.00781091i	−0.868271	+	0.496089i	$0.834769\pi$
$608$	763.334	−	440.711i	1.25548	−	0.724854i
$609$	5.66204	+	514.532i	0.00929728	+	0.844880i
$610$	−2.94295	+	5.09734i	−0.00482450	+	0.00835629i
$611$	814.764	+	726.459i	1.33349	+	1.18897i
$612$	109.854	+	60.2406i	0.179500	+	0.0984324i
$613$			49.4537i			0.0806749i	0.999186	+	0.0403374i	$0.0128433\pi$
$613$			49.4537i			0.0806749i	−0.999186	+	0.0403374i	$0.987157\pi$
$614$	−395.410	−	228.290i	−0.643990	−	0.371808i
$615$	−1.71222	+	1.01383i	−0.00278410	+	0.00164851i
$616$	428.023	−	247.119i	0.694843	−	0.401168i
$617$	24.5895	+	42.5902i	0.0398533	+	0.0690279i	0.885264	−	0.465089i	$-0.153978\pi$
$617$	24.5895	+	42.5902i	0.0398533	+	0.0690279i	−0.845411	+	0.534117i	$0.820644\pi$
$618$	−333.783	−	187.843i	−0.540102	−	0.303953i
$619$	−73.8390	−	42.6310i	−0.119288	−	0.0688707i	0.439169	−	0.898404i	$-0.355273\pi$
$619$	−73.8390	−	42.6310i	−0.119288	−	0.0688707i	−0.558457	+	0.829534i	$0.688606\pi$
$620$		−	168.074i		−	0.271088i
$621$	42.5182	+	68.3311i	0.0684673	+	0.110034i
$622$			43.8677i			0.0705268i
$623$	−404.351	−	233.452i	−0.649038	−	0.374722i
$624$	−13.0802	−	38.1832i	−0.0209619	−	0.0611910i
$625$	−227.728	−	394.437i	−0.364365	−	0.631099i
$626$	93.1660	+	161.368i	0.148828	+	0.257777i
$627$	410.859	+	693.882i	0.655277	+	1.10667i
$628$	71.1605	−	123.254i	0.113313	−	0.196264i
$629$	94.8655			0.150820
$630$	−2.46674	−	112.068i	−0.00391546	−	0.177885i
$631$		−	520.845i		−	0.825428i	−0.910861	−	0.412714i	$-0.864581\pi$
$631$		−	520.845i		−	0.825428i	0.910861	−	0.412714i	$-0.135419\pi$
$632$	−308.628	+	534.559i	−0.488335	+	0.845821i
$633$	6.29375	+	571.938i	0.00994273	+	0.903535i
$634$	45.9576	+	79.6009i	0.0724883	+	0.125553i
$635$	−152.524	−	264.179i	−0.240195	−	0.416030i
$636$	−479.374	+	5.27515i	−0.753733	+	0.00829427i
$637$	−105.967	+	35.0028i	−0.166354	+	0.0549494i
$638$		−	330.064i		−	0.517342i
$639$	492.301	+	810.937i	0.770424	+	1.26907i
$640$	−104.391			−0.163111
$641$	−412.228	−	238.000i	−0.643101	−	0.371295i	0.142707	−	0.989765i	$-0.454419\pi$
$641$	−412.228	−	238.000i	−0.643101	−	0.371295i	−0.785808	+	0.618470i	$0.787753\pi$
$642$	289.123	+	488.288i	0.450348	+	0.760573i
$643$	835.538	−	482.398i	1.29944	−	0.750230i	0.319130	−	0.947711i	$-0.396609\pi$
$643$	835.538	−	482.398i	1.29944	−	0.750230i	0.980307	+	0.197480i	$0.0632759\pi$
$644$	−22.3119	−	38.6453i	−0.0346458	−	0.0600082i
$645$	193.749	+	109.036i	0.300386	+	0.169049i
$646$	−106.839	+	185.050i	−0.165385	+	0.286456i
$647$			1163.49i			1.79829i	0.437653	+	0.899144i	$0.355810\pi$
$647$			1163.49i			1.79829i	−0.437653	+	0.899144i	$0.644190\pi$
$648$	−304.633	+	585.741i	−0.470113	+	0.903921i
$649$	514.671			0.793021
$650$	−358.876	+	118.542i	−0.552117	+	0.182373i
$651$	776.619	+	437.059i	1.19296	+	0.671365i
$652$	−620.640	+	358.327i	−0.951902	+	0.549581i
$653$	430.864	−	248.759i	0.659822	−	0.380948i	−0.132387	−	0.991198i	$-0.542264\pi$
$653$	430.864	−	248.759i	0.659822	−	0.380948i	0.792209	+	0.610250i	$0.208931\pi$
$654$	101.854	+	172.017i	0.155740	+	0.263023i
$655$	−150.426	−	86.8488i	−0.229659	−	0.132594i
$656$	0.449399			0.000685060
$657$	117.934	−	71.5950i	0.179504	−	0.108973i
$658$		−	684.683i		−	1.04055i
$659$	−492.112	−	284.121i	−0.746756	−	0.431140i	0.0777643	−	0.996972i	$-0.475222\pi$
$659$	−492.112	−	284.121i	−0.746756	−	0.431140i	−0.824521	+	0.565832i	$0.808555\pi$
$660$	−1.13255	−	102.919i	−0.00171598	−	0.155938i
$661$	−489.391	+	282.550i	−0.740380	+	0.427459i	−0.822207	−	0.569188i	$-0.807258\pi$
$661$	−489.391	+	282.550i	−0.740380	+	0.427459i	0.0818275	+	0.996647i	$0.473924\pi$
$662$	−459.375	+	265.220i	−0.693920	+	0.400635i
$663$	−173.756	−	151.526i	−0.262076	−	0.228545i
$664$	155.240	−	268.884i	0.233795	−	0.404945i
$665$	−273.663			−0.411524
$666$	4.07656	+	185.204i	0.00612096	+	0.278084i
$667$	−80.4201			−0.120570
$668$	−292.095	+	505.923i	−0.437267	+	0.757369i
$669$	−189.198	−	319.529i	−0.282808	−	0.477622i
$670$	36.0915	−	20.8374i	0.0538679	−	0.0311007i
$671$	−14.3275	−	24.8160i	−0.0213525	−	0.0369836i
$672$	292.547	−	519.833i	0.435337	−	0.773561i
$673$	−174.406	+	302.079i	−0.259146	+	0.448855i	−0.966013	−	0.258492i	$-0.916775\pi$
$673$	−174.406	+	302.079i	−0.259146	+	0.448855i	0.706867	+	0.707346i	$0.250108\pi$
$674$	222.303			0.329826
$675$	539.823	+	288.342i	0.799737	+	0.427174i
$676$	−45.4555	−	395.372i	−0.0672419	−	0.584871i
$677$	19.5304	+	11.2759i	0.0288484	+	0.0166557i	0.514355	−	0.857577i	$-0.328031\pi$
$677$	19.5304	+	11.2759i	0.0288484	+	0.0166557i	−0.485506	+	0.874233i	$0.661365\pi$
$678$	282.690	−	502.318i	0.416947	−	0.740882i
$679$	−195.936	−	339.370i	−0.288565	−	0.499809i
$680$	63.7383	−	36.7993i	0.0937327	−	0.0541166i
$681$	−429.894	+	254.547i	−0.631268	+	0.373784i
$682$	−495.044	−	285.814i	−0.725871	−	0.419082i
$683$	827.260			1.21122			0.605608	−	0.795763i	$-0.292930\pi$
$683$	827.260			1.21122			0.605608	+	0.795763i	$0.292930\pi$
$684$	523.713	+	287.189i	0.765663	+	0.419867i
$685$	154.716			0.225863
$686$	406.637	+	234.772i	0.592766	+	0.342234i
$687$	801.319	−	8.81792i	1.16640	−	0.0128354i
$688$	−25.1052	−	43.4835i	−0.0364902	−	0.0632028i
$689$	863.775	+	179.206i	1.25367	+	0.260096i
$690$	17.5180	−	0.192773i	0.0253885	−	0.000279381i
$691$	177.380	+	102.410i	0.256700	+	0.148206i	0.622828	−	0.782358i	$-0.285983\pi$
$691$	177.380	+	102.410i	0.256700	+	0.148206i	−0.366128	+	0.930564i	$0.619317\pi$
$692$			5.29172i			0.00764700i
$693$	478.502	+	262.396i	0.690479	+	0.378638i
$694$			548.198i			0.789911i
$695$	21.3100	−	36.9100i	0.0306619	−	0.0531079i
$696$	−336.135	−	567.684i	−0.482953	−	0.815638i
$697$	2.22307	−	1.28349i	0.00318948	−	0.00184145i
$698$	502.842	−	290.316i	0.720404	−	0.415925i
$699$	−2.65855	+	4.72404i	−0.00380336	+	0.00675828i
$700$	−293.878	−	169.670i	−0.419825	−	0.242386i
$701$		−	181.050i		−	0.258274i	−0.991627	−	0.129137i	$-0.958779\pi$
$701$		−	181.050i		−	0.258274i	0.991627	−	0.129137i	$-0.0412208\pi$
$702$	288.354	−	345.732i	0.410760	−	0.492496i
$703$	452.258			0.643326
$704$	−211.052	+	365.553i	−0.299790	+	0.519252i
$705$	−335.326	−	188.712i	−0.475640	−	0.267676i
$706$	−123.691	−	214.240i	−0.175200	−	0.303456i
$707$	−96.7707	−	167.612i	−0.136875	−	0.237075i
$708$	328.020	−	194.226i	0.463305	−	0.274331i
$709$	−51.9677	−	30.0036i	−0.0732972	−	0.0423181i	0.462904	−	0.886409i	$-0.346808\pi$
$709$	−51.9677	−	30.0036i	−0.0732972	−	0.0423181i	−0.536201	+	0.844091i	$0.680141\pi$
$710$	206.511			0.290860
$711$	−681.392	+	14.9982i	−0.958357	+	0.0210946i
$712$	598.631			0.840774
$713$	−69.6385	+	120.617i	−0.0976697	+	0.169169i
$714$	1.59118	+	144.597i	0.00222854	+	0.202516i
$715$	−38.4746	+	185.448i	−0.0538106	+	0.259368i
$716$	−718.796	+	414.997i	−1.00391	+	0.579605i
$717$	−9.64205	−	876.212i	−0.0134478	−	1.22205i
$718$	11.6371	−	20.1560i	0.0162076	−	0.0280724i
$719$			437.875i			0.609005i	0.952511	+	0.304503i	$0.0984903\pi$
$719$			437.875i			0.609005i	−0.952511	+	0.304503i	$0.901510\pi$
$720$	7.38298	+	12.1615i	0.0102541	+	0.0168910i
$721$			632.797i			0.877666i
$722$	−277.828	+	481.211i	−0.384803	+	0.666498i
$723$	−431.336	−	728.465i	−0.596592	−	1.00756i
$724$	77.3879	+	134.040i	0.106889	+	0.185138i
$725$	−529.621	+	305.777i	−0.730512	+	0.421761i
$726$	100.688	+	56.6642i	0.138689	+	0.0780499i
$727$	347.346	−	601.621i	0.477780	−	0.827539i	−0.521896	−	0.853009i	$-0.674775\pi$
$727$	347.346	−	601.621i	0.477780	−	0.827539i	0.999676	+	0.0254704i	$0.00810836\pi$
$728$	−448.303	+	502.797i	−0.615800	+	0.690655i
$729$	−727.412	+	48.0957i	−0.997821	+	0.0659749i
$730$		−	30.0327i		−	0.0411407i
$731$	−248.379	−	143.402i	−0.339779	−	0.196172i
$732$	−18.4965	−	10.4093i	−0.0252685	−	0.0142204i
$733$	625.465	−	361.112i	0.853295	−	0.492650i	−0.00846655	−	0.999964i	$-0.502695\pi$
$733$	625.465	−	361.112i	0.853295	−	0.492650i	0.861761	+	0.507314i	$0.169362\pi$
$734$	−286.982	−	497.067i	−0.390983	−	0.677203i
$735$	33.8490	−	20.0426i	0.0460531	−	0.0272688i
$736$	80.7357	+	46.6128i	0.109695	+	0.0633326i
$737$			202.891i			0.275293i
$738$	2.60126	+	4.28490i	0.00352474	+	0.00580610i
$739$			480.571i			0.650298i	0.945663	+	0.325149i	$0.105415\pi$
$739$			480.571i			0.650298i	−0.945663	+	0.325149i	$0.894585\pi$
$740$	−49.9908	−	28.8622i	−0.0675552	−	0.0390030i
$741$	−828.359	−	722.377i	−1.11789	−	0.974868i
$742$	−276.662	−	479.193i	−0.372860	−	0.645812i
$743$	−657.788	−	1139.32i	−0.885314	−	1.53341i	−0.845353	−	0.534207i	$-0.820610\pi$
$743$	−657.788	−	1139.32i	−0.885314	−	1.53341i	−0.0399605	−	0.999201i	$-0.512723\pi$
$744$	−1142.51	+	12.5724i	−1.53563	+	0.0168984i
$745$	207.601	−	359.576i	0.278660	−	0.482653i
$746$	913.178			1.22410
$747$	342.741	−	7.54413i	0.458823	−	0.0100992i
$748$			132.776i			0.177508i
$749$	468.776	−	811.943i	0.625869	−	1.08404i
$750$	241.070	−	142.742i	0.321427	−	0.190322i
$751$	−12.7475	−	22.0793i	−0.0169740	−	0.0293999i	0.857414	−	0.514628i	$-0.172070\pi$
$751$	−12.7475	−	22.0793i	−0.0169740	−	0.0293999i	−0.874388	+	0.485228i	$0.838737\pi$
$752$	43.4501	+	75.2578i	0.0577794	+	0.100077i
$753$	229.778	−	408.297i	0.305150	−	0.542227i
$754$	141.100	+	427.166i	0.187135	+	0.566534i
$755$			127.937i			0.169453i
$756$	403.991	−	13.3412i	0.534380	−	0.0176471i
$757$	−226.199			−0.298810			−0.149405	−	0.988776i	$-0.547736\pi$
$757$	−226.199			−0.298810			−0.149405	+	0.988776i	$0.547736\pi$
$758$	−703.596	−	406.221i	−0.928226	−	0.535912i
$759$	−41.8298	+	74.3284i	−0.0551118	+	0.0979293i
$760$	303.864	−	175.436i	0.399820	−	0.230836i
$761$	112.781	+	195.343i	0.148202	+	0.256693i	0.930563	−	0.366132i	$-0.119318\pi$
$761$	112.781	+	195.343i	0.148202	+	0.256693i	−0.782361	+	0.622825i	$0.785985\pi$
$762$	−661.226	+	391.523i	−0.867751	+	0.513810i
$763$	165.143	−	286.036i	0.216439	−	0.374883i
$764$		−	588.417i		−	0.770179i
$765$	71.2552	+	39.0742i	0.0931441	+	0.0510774i
$766$	124.290			0.162259
$767$	−666.083	+	220.018i	−0.868426	+	0.286855i
$768$	8.73720	+	793.984i	0.0113766	+	1.03383i
$769$	−994.900	+	574.406i	−1.29376	+	0.746951i	−0.979318	−	0.202326i	$-0.935150\pi$
$769$	−994.900	+	574.406i	−1.29376	+	0.746951i	−0.314439	+	0.949278i	$0.601817\pi$
$770$	102.880	−	59.3979i	0.133611	−	0.0771401i
$771$	−413.365	+	4.54877i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.641309 - 1.11078i) q^{2} +(2.61442 + 1.47132i) q^{3} +(1.17745 + 2.03940i) q^{4} +(0.763734 + 1.32283i) q^{5} +(3.31097 - 1.96048i) q^{6} +(-5.50560 - 3.17866i) q^{7} +8.15090 q^{8} +(4.67043 + 7.69331i) q^{9} +1.95916 q^{10} +(-4.76900 + 8.26015i) q^{11} +(0.0777368 + 7.06425i) q^{12} +(2.64085 - 12.7289i) q^{13} +(-7.06158 + 4.07700i) q^{14} +(0.0504229 + 4.58213i) q^{15} +(0.517455 - 0.896258i) q^{16} -5.91142i q^{17} +(11.5408 - 0.254026i) q^{18} -28.1819i q^{19} +(-1.79851 + 3.11511i) q^{20} +(-9.71714 - 16.4109i) q^{21} +(6.11681 + 10.5946i) q^{22} +(2.58138 - 1.49036i) q^{23} +(21.3099 + 11.9926i) q^{24} +(11.3334 - 19.6301i) q^{25} +(-12.4454 - 11.0966i) q^{26} +(0.891147 + 26.9853i) q^{27} -14.9708i q^{28} +(-23.3655 - 13.4901i) q^{29} +(5.12207 + 2.88255i) q^{30} +(-40.4659 + 23.3630i) q^{31} +(15.6381 + 27.0860i) q^{32} +(-24.6215 + 14.5788i) q^{33} +(-6.56629 - 3.79105i) q^{34} -9.71060i q^{35} +(-10.1905 + 18.5833i) q^{36} +16.0478i q^{37} +(-31.3039 - 18.0733i) q^{38} +(25.6327 - 29.3933i) q^{39} +(6.22512 + 10.7822i) q^{40} +(0.217120 + 0.376063i) q^{41} +(-24.4605 + 0.269170i) q^{42} +(24.2584 - 42.0167i) q^{43} -22.4610 q^{44} +(-6.60995 + 12.0538i) q^{45} -3.82312i q^{46} +(-41.9845 + 72.7193i) q^{47} +(2.67153 - 1.58186i) q^{48} +(-4.29226 - 7.43442i) q^{49} +(-14.5364 - 25.1779i) q^{50} +(8.69760 - 15.4550i) q^{51} +(29.0688 - 9.60190i) q^{52} +67.8592i q^{53} +(30.5462 + 16.3160i) q^{54} -14.5690 q^{55} +(-44.8756 - 25.9089i) q^{56} +(41.4646 - 73.6795i) q^{57} +(-29.9689 + 17.3026i) q^{58} +(-26.9800 - 46.7307i) q^{59} +(-9.28541 + 5.49804i) q^{60} +(-1.50215 + 2.60180i) q^{61} +59.9315i q^{62} +(-1.25908 - 57.2020i) q^{63} +44.2550 q^{64} +(18.8551 - 6.22814i) q^{65} +(0.403841 + 36.6986i) q^{66} +(18.4220 - 10.6359i) q^{67} +(12.0557 - 6.96038i) q^{68} +(8.94161 - 0.0983958i) q^{69} +(-10.7863 - 6.22749i) q^{70} +105.408 q^{71} +(38.0682 + 62.7074i) q^{72} -15.3294i q^{73} +(17.8256 + 10.2916i) q^{74} +(58.5125 - 34.6462i) q^{75} +(57.4741 - 33.1827i) q^{76} +(52.5124 - 30.3181i) q^{77} +(-16.2110 - 47.3224i) q^{78} +(-37.8643 + 65.5828i) q^{79} +1.58079 q^{80} +(-37.3742 + 71.8622i) q^{81} +0.556964 q^{82} +(19.0458 - 32.9882i) q^{83} +(22.0269 - 39.1400i) q^{84} +(7.81979 - 4.51476i) q^{85} +(-31.1142 - 53.8914i) q^{86} +(-41.2390 - 69.6468i) q^{87} +(-38.8716 + 67.3277i) q^{88} +73.4436 q^{89} +(9.15011 + 15.0724i) q^{90} +(-55.0004 + 61.6861i) q^{91} +(6.07887 + 3.50964i) q^{92} +(-140.169 + 1.54246i) q^{93} +(53.8500 + 93.2710i) q^{94} +(37.2798 - 21.5235i) q^{95} +(1.03245 + 93.8229i) q^{96} +(53.3827 + 30.8205i) q^{97} -11.0107 q^{98} +(-85.8213 + 1.88903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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