LMFDB - Embedded newform 115.3.k.a.108.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(2,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.k (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			108.20
Character	$\chi$	$=$	115.108
Dual form			115.3.k.a.82.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212094 + 2.96546i) q^{2} +(-1.22528 - 0.266542i) q^{3} +(-4.78967 + 0.688650i) q^{4} +(2.28653 + 4.44655i) q^{5} +(0.530547 - 3.69003i) q^{6} +(-2.50296 + 4.58383i) q^{7} +(-0.530168 - 2.43714i) q^{8} +(-6.75643 - 3.08556i) q^{9} +(-12.7011 + 7.72369i) q^{10} +(-0.453365 - 0.523211i) q^{11} +(6.05222 + 0.432863i) q^{12} +(-7.30032 - 13.3695i) q^{13} +(-14.1240 - 6.45021i) q^{14} +(-1.61643 - 6.05770i) q^{15} +(-11.4568 + 3.36403i) q^{16} +(17.6342 + 23.5566i) q^{17} +(7.71710 - 20.6903i) q^{18} +(16.4235 - 2.36134i) q^{19} +(-14.0138 - 19.7229i) q^{20} +(4.28860 - 4.94930i) q^{21} +(1.45540 - 1.45540i) q^{22} +(19.3820 + 12.3830i) q^{23} +3.12748i q^{24} +(-14.5436 + 20.3343i) q^{25} +(38.0985 - 24.4844i) q^{26} +(16.4905 + 12.3446i) q^{27} +(8.83169 - 23.6787i) q^{28} +(-17.1941 - 2.47213i) q^{29} +(17.6210 - 6.07826i) q^{30} +(9.23156 + 5.93276i) q^{31} +(-15.8923 - 42.6088i) q^{32} +(0.416039 + 0.761919i) q^{33} +(-66.1160 + 57.2898i) q^{34} +(-26.1053 - 0.648479i) q^{35} +(34.4859 + 10.1260i) q^{36} +(15.1203 + 40.5391i) q^{37} +(10.4858 + 48.2023i) q^{38} +(5.38136 + 18.3272i) q^{39} +(9.62463 - 7.93001i) q^{40} +(-0.718415 - 1.57311i) q^{41} +(15.5865 + 11.6679i) q^{42} +(34.6512 + 7.53792i) q^{43} +(2.53178 + 2.19380i) q^{44} +(-1.72868 - 37.0980i) q^{45} +(-32.6104 + 60.1029i) q^{46} +(63.6541 - 63.6541i) q^{47} +(14.9345 - 1.06813i) q^{48} +(11.7447 + 18.2752i) q^{49} +(-63.3851 - 38.8156i) q^{50} +(-15.3280 - 33.5636i) q^{51} +(44.1731 + 59.0083i) q^{52} +(-3.43406 - 1.87514i) q^{53} +(-33.1099 + 51.5200i) q^{54} +(1.28985 - 3.21225i) q^{55} +(12.4984 + 3.66987i) q^{56} +(-20.7527 - 1.48426i) q^{57} +(3.68426 - 51.5126i) q^{58} +(9.70051 - 33.0369i) q^{59} +(11.9138 + 27.9012i) q^{60} +(-7.28236 - 4.68009i) q^{61} +(-15.6354 + 28.6341i) q^{62} +(31.0547 - 23.2473i) q^{63} +(79.5381 - 36.3239i) q^{64} +(42.7559 - 63.0311i) q^{65} +(-2.17120 + 1.39534i) q^{66} +(-4.84584 - 67.7537i) q^{67} +(-100.684 - 100.684i) q^{68} +(-20.4477 - 20.3387i) q^{69} +(-3.61373 - 77.5516i) q^{70} +(-29.2788 + 33.7896i) q^{71} +(-3.93790 + 18.1022i) q^{72} +(-51.7453 + 69.1237i) q^{73} +(-117.010 + 53.4367i) q^{74} +(23.2398 - 21.0387i) q^{75} +(-77.0369 + 22.6201i) q^{76} +(3.53306 - 0.768570i) q^{77} +(-53.2072 + 19.8453i) q^{78} +(28.5413 - 97.2029i) q^{79} +(-41.1547 - 43.2515i) q^{80} +(26.8617 + 31.0001i) q^{81} +(4.51262 - 2.46408i) q^{82} +(-1.80438 + 0.672999i) q^{83} +(-17.1326 + 26.6589i) q^{84} +(-64.4243 + 132.274i) q^{85} +(-15.0041 + 104.356i) q^{86} +(20.4085 + 7.61200i) q^{87} +(-1.03478 + 1.38230i) q^{88} +(-57.0723 - 88.8062i) q^{89} +(109.646 - 12.9946i) q^{90} +79.5561 q^{91} +(-101.361 - 45.9629i) q^{92} +(-9.72987 - 9.72987i) q^{93} +(202.264 + 175.263i) q^{94} +(48.0525 + 67.6285i) q^{95} +(8.11536 + 56.4435i) q^{96} +(-155.869 - 58.1361i) q^{97} +(-51.7033 + 38.7046i) q^{98} +(1.44873 + 4.93392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) $ 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.212094	+	2.96546i	0.106047	+	1.48273i	0.720324	+	0.693638i	$0.243993\pi$
$2$	0.212094	+	2.96546i	0.106047	+	1.48273i	−0.614277	+	0.789091i	$0.710552\pi$
$3$	−1.22528	−	0.266542i	−0.408425	−	0.0888475i	0.00365887	−	0.999993i	$-0.498835\pi$
$3$	−1.22528	−	0.266542i	−0.408425	−	0.0888475i	−0.412084	+	0.911146i	$0.635199\pi$
$4$	−4.78967	+	0.688650i	−1.19742	+	0.172163i
$5$	2.28653	+	4.44655i	0.457306	+	0.889310i
$5$	2.28653	+	4.44655i	0.457306	+	0.889310i
$6$	0.530547	−	3.69003i	0.0884245	−	0.615006i
$7$	−2.50296	+	4.58383i	−0.357565	+	0.654832i	−0.993104	−	0.117237i	$-0.962596\pi$
$7$	−2.50296	+	4.58383i	−0.357565	+	0.654832i	0.635539	+	0.772069i	$0.280778\pi$
$8$	−0.530168	−	2.43714i	−0.0662710	−	0.304643i
$9$	−6.75643	−	3.08556i	−0.750715	−	0.342840i
$10$	−12.7011	+	7.72369i	−1.27011	+	0.772369i
$11$	−0.453365	−	0.523211i	−0.0412150	−	0.0475646i	0.734768	−	0.678319i	$-0.237291\pi$
$11$	−0.453365	−	0.523211i	−0.0412150	−	0.0475646i	−0.775983	+	0.630754i	$0.782746\pi$
$12$	6.05222	+	0.432863i	0.504351	+	0.0360719i
$13$	−7.30032	−	13.3695i	−0.561563	−	1.02843i	−0.992052	−	0.125830i	$-0.959840\pi$
$13$	−7.30032	−	13.3695i	−0.561563	−	1.02843i	0.430488	−	0.902596i	$-0.358341\pi$
$14$	−14.1240	−	6.45021i	−1.00886	−	0.460730i
$15$	−1.61643	−	6.05770i	−0.107762	−	0.403847i
$16$	−11.4568	+	3.36403i	−0.716053	+	0.210252i
$17$	17.6342	+	23.5566i	1.03731	+	1.38568i	0.919700	+	0.392622i	$0.128432\pi$
$17$	17.6342	+	23.5566i	1.03731	+	1.38568i	0.117609	+	0.993060i	$0.462477\pi$
$18$	7.71710	−	20.6903i	0.428728	−	1.14946i
$19$	16.4235	−	2.36134i	0.864394	−	0.124281i	0.304165	−	0.952619i	$-0.401623\pi$
$19$	16.4235	−	2.36134i	0.864394	−	0.124281i	0.560228	+	0.828338i	$0.310713\pi$
$20$	−14.0138	−	19.7229i	−0.700691	−	0.986144i
$21$	4.28860	−	4.94930i	0.204219	−	0.235681i
$22$	1.45540	−	1.45540i	0.0661547	−	0.0661547i
$23$	19.3820	+	12.3830i	0.842696	+	0.538390i
$23$	19.3820	+	12.3830i	0.842696	+	0.538390i
$24$			3.12748i			0.130312i
$25$	−14.5436	+	20.3343i	−0.581743	+	0.813372i
$26$	38.0985	−	24.4844i	1.46533	−	0.941708i
$27$	16.4905	+	12.3446i	0.610758	+	0.457208i
$28$	8.83169	−	23.6787i	0.315417	−	0.845667i
$29$	−17.1941	−	2.47213i	−0.592899	−	0.0852460i	−0.160667	−	0.987009i	$-0.551365\pi$
$29$	−17.1941	−	2.47213i	−0.592899	−	0.0852460i	−0.432232	+	0.901763i	$0.642274\pi$
$30$	17.6210	−	6.07826i	0.587367	−	0.202609i
$31$	9.23156	+	5.93276i	0.297792	+	0.191379i	0.681001	−	0.732282i	$-0.261545\pi$
$31$	9.23156	+	5.93276i	0.297792	+	0.191379i	−0.383209	+	0.923662i	$0.625181\pi$
$32$	−15.8923	−	42.6088i	−0.496634	−	1.33153i
$33$	0.416039	+	0.761919i	0.0126072	+	0.0230884i
$34$	−66.1160	+	57.2898i	−1.94459	+	1.68499i
$35$	−26.1053	−	0.648479i	−0.745865	−	0.0185280i
$36$	34.4859	+	10.1260i	0.957943	+	0.281277i
$37$	15.1203	+	40.5391i	0.408657	+	1.09565i	0.964435	+	0.264321i	$0.0851479\pi$
$37$	15.1203	+	40.5391i	0.408657	+	1.09565i	−0.555778	+	0.831331i	$0.687579\pi$
$38$	10.4858	+	48.2023i	0.275941	+	1.26848i
$39$	5.38136	+	18.3272i	0.137984	+	0.469929i
$40$	9.62463	−	7.93001i	0.240616	−	0.198250i
$41$	−0.718415	−	1.57311i	−0.0175223	−	0.0383685i	0.900669	−	0.434507i	$-0.143077\pi$
$41$	−0.718415	−	1.57311i	−0.0175223	−	0.0383685i	−0.918191	+	0.396138i	$0.870350\pi$
$42$	15.5865	+	11.6679i	0.371108	+	0.277808i
$43$	34.6512	+	7.53792i	0.805843	+	0.175300i	0.596574	−	0.802558i	$-0.296528\pi$
$43$	34.6512	+	7.53792i	0.805843	+	0.175300i	0.209269	+	0.977858i	$0.432892\pi$
$44$	2.53178	+	2.19380i	0.0575404	+	0.0498590i
$45$	−1.72868	−	37.0980i	−0.0384152	−	0.824400i
$46$	−32.6104	+	60.1029i	−0.708921	+	1.30658i
$47$	63.6541	−	63.6541i	1.35434	−	1.35434i	0.473605	−	0.880737i	$-0.342952\pi$
$47$	63.6541	−	63.6541i	1.35434	−	1.35434i	0.880737	−	0.473605i	$-0.157048\pi$
$48$	14.9345	−	1.06813i	0.311134	−	0.0222528i
$49$	11.7447	+	18.2752i	0.239689	+	0.372963i
$50$	−63.3851	−	38.8156i	−1.26770	−	0.776312i
$51$	−15.3280	−	33.5636i	−0.300549	−	0.658110i
$52$	44.1731	+	59.0083i	0.849482	+	1.13478i
$53$	−3.43406	−	1.87514i	−0.0647937	−	0.0353800i	0.446526	−	0.894771i	$-0.352661\pi$
$53$	−3.43406	−	1.87514i	−0.0647937	−	0.0353800i	−0.511319	+	0.859391i	$0.670843\pi$
$54$	−33.1099	+	51.5200i	−0.613146	+	0.954074i
$55$	1.28985	−	3.21225i	0.0234518	−	0.0584045i
$56$	12.4984	+	3.66987i	0.223186	+	0.0655333i
$57$	−20.7527	−	1.48426i	−0.364082	−	0.0260397i
$58$	3.68426	−	51.5126i	0.0635216	−	0.888149i
$59$	9.70051	−	33.0369i	0.164415	−	0.559947i	−0.835529	−	0.549446i	$-0.814839\pi$
$59$	9.70051	−	33.0369i	0.164415	−	0.559947i	0.999945	−	0.0105018i	$-0.00334289\pi$
$60$	11.9138	+	27.9012i	0.198564	+	0.465020i
$61$	−7.28236	−	4.68009i	−0.119383	−	0.0767227i	0.479587	−	0.877495i	$-0.340787\pi$
$61$	−7.28236	−	4.68009i	−0.119383	−	0.0767227i	−0.598970	+	0.800772i	$0.704423\pi$
$62$	−15.6354	+	28.6341i	−0.252184	+	0.461840i
$63$	31.0547	−	23.2473i	0.492932	−	0.369004i
$64$	79.5381	−	36.3239i	1.24278	−	0.567560i
$65$	42.7559	−	63.0311i	0.657784	−	0.969709i
$66$	−2.17120	+	1.39534i	−0.0328969	+	0.0211416i
$67$	−4.84584	−	67.7537i	−0.0723260	−	1.01125i	−0.895962	−	0.444131i	$-0.853513\pi$
$67$	−4.84584	−	67.7537i	−0.0723260	−	1.01125i	0.823636	−	0.567119i	$-0.191942\pi$
$68$	−100.684	−	100.684i	−1.48065	−	1.48065i
$69$	−20.4477	−	20.3387i	−0.296344	−	0.294763i
$70$	−3.61373	−	77.5516i	−0.0516247	−	1.10788i
$71$	−29.2788	+	33.7896i	−0.412378	+	0.475910i	−0.923500	−	0.383599i	$-0.874685\pi$
$71$	−29.2788	+	33.7896i	−0.412378	+	0.475910i	0.511122	+	0.859508i	$0.329230\pi$
$72$	−3.93790	+	18.1022i	−0.0546931	+	0.251420i
$73$	−51.7453	+	69.1237i	−0.708840	+	0.946899i	−0.999952	−	0.00978959i	$-0.996884\pi$
$73$	−51.7453	+	69.1237i	−0.708840	+	0.946899i	0.291112	+	0.956689i	$0.405975\pi$
$74$	−117.010	+	53.4367i	−1.58122	+	0.722118i
$75$	23.2398	−	21.0387i	0.309865	−	0.280515i
$76$	−77.0369	+	22.6201i	−1.01364	+	0.297632i
$77$	3.53306	−	0.768570i	0.0458839	−	0.00998143i
$78$	−53.2072	+	19.8453i	−0.682144	+	0.254427i
$79$	28.5413	−	97.2029i	0.361283	−	1.23042i	−0.555664	−	0.831407i	$-0.687536\pi$
$79$	28.5413	−	97.2029i	0.361283	−	1.23042i	0.916947	−	0.399009i	$-0.130646\pi$
$80$	−41.1547	−	43.2515i	−0.514434	−	0.540643i
$81$	26.8617	+	31.0001i	0.331626	+	0.382717i
$82$	4.51262	−	2.46408i	0.0550319	−	0.0300497i
$83$	−1.80438	+	0.672999i	−0.0217395	+	0.00810842i	−0.360310	−	0.932832i	$-0.617329\pi$
$83$	−1.80438	+	0.672999i	−0.0217395	+	0.00810842i	0.338571	+	0.940941i	$0.390057\pi$
$84$	−17.1326	+	26.6589i	−0.203960	+	0.317367i
$85$	−64.4243	+	132.274i	−0.757933	+	1.55617i
$86$	−15.0041	+	104.356i	−0.174466	+	1.21344i
$87$	20.4085	+	7.61200i	0.234581	+	0.0874942i
$88$	−1.03478	+	1.38230i	−0.0117589	+	0.0157080i
$89$	−57.0723	−	88.8062i	−0.641262	−	0.997822i	−0.997975	−	0.0636086i	$-0.979739\pi$
$89$	−57.0723	−	88.8062i	−0.641262	−	0.997822i	0.356713	−	0.934214i	$-0.383897\pi$
$90$	109.646	−	12.9946i	1.21829	−	0.144384i
$91$	79.5561			0.874242
$92$	−101.361	−	45.9629i	−1.10175	−	0.499597i
$93$	−9.72987	−	9.72987i	−0.104622	−	0.104622i
$94$	202.264	+	175.263i	2.15175	+	1.86450i
$95$	48.0525	+	67.6285i	0.505816	+	0.711879i
$96$	8.11536	+	56.4435i	0.0845350	+	0.587954i
$97$	−155.869	−	58.1361i	−1.60690	−	0.599341i	−0.623663	−	0.781693i	$-0.714356\pi$
$97$	−155.869	−	58.1361i	−1.60690	−	0.599341i	−0.983233	+	0.182352i	$0.941629\pi$
$98$	−51.7033	+	38.7046i	−0.527585	+	0.394945i
$99$	1.44873	+	4.93392i	0.0146336	+	0.0498376i
$100$	55.6557	−	107.410i	0.556557	−	1.07410i
$101$	7.82266	−	17.1292i	0.0774520	−	0.169596i	−0.866945	−	0.498404i	$-0.833920\pi$
$101$	7.82266	−	17.1292i	0.0774520	−	0.169596i	0.944397	+	0.328808i	$0.106647\pi$
$102$	96.2804	−	52.5731i	0.943926	−	0.515423i
$103$	−9.15340	+	127.981i	−0.0888680	+	1.24254i	0.735910	+	0.677080i	$0.236755\pi$
$103$	−9.15340	+	127.981i	−0.0888680	+	1.24254i	−0.824778	+	0.565457i	$0.808700\pi$
$104$	−28.7131	+	24.8800i	−0.276087	+	0.239231i
$105$	31.8133	+	7.75273i	0.302984	+	0.0738355i
$106$	4.83231	−	10.5813i	0.0455878	−	0.0998234i
$107$	−81.5418	+	17.7383i	−0.762073	+	0.165779i	−0.576774	−	0.816904i	$-0.695689\pi$
$107$	−81.5418	+	17.7383i	−0.762073	+	0.165779i	−0.185298	+	0.982682i	$0.559325\pi$
$108$	−87.4850	−	47.7704i	−0.810047	−	0.442319i
$109$	53.4650	+	7.68711i	0.490505	+	0.0705240i	0.383130	−	0.923695i	$-0.374846\pi$
$109$	53.4650	+	7.68711i	0.490505	+	0.0705240i	0.107375	+	0.994219i	$0.465755\pi$
$110$	9.79935	+	3.14370i	0.0890850	+	0.0285791i
$111$	−7.72115	−	53.7018i	−0.0695599	−	0.483800i
$112$	13.2559	−	60.9362i	0.118356	−	0.544073i
$113$	8.22096	−	0.587974i	0.0727518	−	0.00520331i	−0.0349158	−	0.999390i	$-0.511116\pi$
$113$	8.22096	−	0.587974i	0.0727518	−	0.00520331i	0.107668	+	0.994187i	$0.465662\pi$
$114$		−	61.8560i		−	0.542596i
$115$	−10.7440	+	114.497i	−0.0934258	+	0.995626i
$116$	84.0564			0.724624
$117$	8.07162	+	112.856i	0.0689882	+	0.964581i
$118$	100.027	+	21.7595i	0.847686	+	0.184403i
$119$	−152.117	+	21.8711i	−1.27829	+	0.183791i
$120$	−13.9065	+	7.15108i	−0.115887	+	0.0595923i
$121$	17.1519	−	119.294i	0.141751	−	0.985901i
$122$	12.3341	−	22.5881i	0.101099	−	0.185149i
$123$	0.460956	+	2.11898i	0.00374761	+	0.0172275i
$124$	−48.3017	−	22.0586i	−0.389530	−	0.177892i
$125$	−123.672	−	18.1738i	−0.989374	−	0.145390i
$126$	75.5253	+	87.1609i	0.599407	+	0.691753i
$127$	−38.3282	−	2.74128i	−0.301797	−	0.0215849i	−0.0803802	−	0.996764i	$-0.525613\pi$
$127$	−38.3282	−	2.74128i	−0.301797	−	0.0215849i	−0.221416	+	0.975179i	$0.571068\pi$
$128$	37.4088	+	68.5091i	0.292256	+	0.535228i
$129$	−40.4481	−	18.4720i	−0.313552	−	0.143194i
$130$	195.984	+	113.422i	1.50757	+	0.872480i
$131$	74.2117	−	21.7905i	0.566502	−	0.166340i	0.0140744	−	0.999901i	$-0.495520\pi$
$131$	74.2117	−	21.7905i	0.566502	−	0.166340i	0.552427	+	0.833561i	$0.313702\pi$
$132$	−2.51738	−	3.36283i	−0.0190711	−	0.0254760i
$133$	−30.2833	+	81.1927i	−0.227694	+	0.610471i
$134$	199.893	−	28.7403i	1.49174	−	0.214480i
$135$	−17.1850	+	101.552i	−0.127296	+	0.752237i
$136$	48.0617	−	55.4661i	0.353395	−	0.407839i
$137$	154.377	−	154.377i	1.12684	−	1.12684i	0.136151	−	0.990688i	$-0.456527\pi$
$137$	154.377	−	154.377i	1.12684	−	1.12684i	0.990688	−	0.136151i	$-0.0434733\pi$
$138$	55.9766	−	64.9505i	0.405628	−	0.470656i
$139$		−	39.6770i		−	0.285446i	−0.989763	−	0.142723i	$-0.954414\pi$
$139$		−	39.6770i		−	0.285446i	0.989763	−	0.142723i	$-0.0455858\pi$
$140$	125.482	−	14.8714i	0.896302	−	0.106224i
$141$	−94.9603	+	61.0273i	−0.673477	+	0.432818i
$142$	−106.411	−	79.6586i	−0.749376	−	0.560976i
$143$	−3.68538	+	9.88089i	−0.0257719	+	0.0690972i
$144$	87.7874	+	12.6219i	0.609634	+	0.0876522i
$145$	−28.3223	−	82.1069i	−0.195326	−	0.566254i
$146$	−215.958	−	138.788i	−1.47917	−	0.950602i
$147$	−9.51944	−	25.5226i	−0.0647581	−	0.173623i
$148$	−100.339	−	183.756i	−0.677963	−	1.24160i
$149$	117.372	−	101.703i	0.787730	−	0.682572i	−0.165033	−	0.986288i	$-0.552773\pi$
$149$	117.372	−	101.703i	0.787730	−	0.682572i	0.952762	+	0.303716i	$0.0982276\pi$
$150$	67.3183	+	64.4546i	0.448788	+	0.429697i
$151$	54.1768	+	15.9077i	0.358787	+	0.105349i	0.456158	−	0.889899i	$-0.349225\pi$
$151$	54.1768	+	15.9077i	0.358787	+	0.105349i	−0.0973712	+	0.995248i	$0.531043\pi$
$152$	−14.4621	−	38.7744i	−0.0951455	−	0.255095i
$153$	−46.4593	−	213.570i	−0.303656	−	1.39588i
$154$	3.02850	+	10.3141i	0.0196656	+	0.0669749i
$155$	−5.27210	+	54.6140i	−0.0340135	+	0.352348i
$156$	−38.3960	−	84.0754i	−0.246128	−	0.538945i
$157$	102.052	+	76.3952i	0.650013	+	0.486594i	0.872675	−	0.488302i	$-0.162384\pi$
$157$	102.052	+	76.3952i	0.650013	+	0.486594i	−0.222662	+	0.974896i	$0.571475\pi$
$158$	294.304	+	64.0220i	1.86269	+	0.405203i
$159$	3.70787	+	3.21289i	0.0233199	+	0.0202068i
$160$	153.124	−	168.092i	0.957026	−	1.05058i
$161$	−105.274	+	57.8497i	−0.653874	+	0.359315i
$162$	−86.2322	+	86.2322i	−0.532297	+	0.532297i
$163$	286.842	−	20.5153i	1.75977	−	0.125861i	0.846282	−	0.532735i	$-0.178836\pi$
$163$	286.842	−	20.5153i	1.75977	−	0.125861i	0.913484	+	0.406874i	$0.133381\pi$
$164$	4.52429	+	7.03994i	0.0275871	+	0.0429264i
$165$	−2.43662	+	3.59209i	−0.0147674	+	0.0217702i
$166$	−2.37845	−	5.20807i	−0.0143280	−	0.0313739i
$167$	135.906	+	181.549i	0.813808	+	1.08712i	0.994619	+	0.103603i	$0.0330370\pi$
$167$	135.906	+	181.549i	0.813808	+	1.08712i	−0.180811	+	0.983518i	$0.557872\pi$
$168$	−14.3358	−	7.82796i	−0.0853323	−	0.0465950i
$169$	−34.0817	+	53.0322i	−0.201667	+	0.313800i
$170$	−405.918	−	162.993i	−2.38775	−	0.958783i
$171$	−118.250	−	34.7214i	−0.691521	−	0.203049i
$172$	−171.159	−	12.2415i	−0.995110	−	0.0711717i
$173$	−20.2971	+	283.790i	−0.117324	+	1.64041i	0.508946	+	0.860799i	$0.330035\pi$
$173$	−20.2971	+	283.790i	−0.117324	+	1.64041i	−0.626270	+	0.779606i	$0.715419\pi$
$174$	−18.2445	+	62.1351i	−0.104854	+	0.357099i
$175$	−56.8070	−	117.561i	−0.324611	−	0.671778i
$176$	6.95423	+	4.46921i	0.0395127	+	0.0253933i
$177$	−20.6915	+	37.8937i	−0.116901	+	0.214089i
$178$	251.246	−	188.081i	1.41150	−	1.05663i
$179$	−43.9619	+	20.0767i	−0.245597	+	0.112161i	−0.534411	−	0.845225i	$-0.679466\pi$
$179$	−43.9619	+	20.0767i	−0.245597	+	0.112161i	0.288814	+	0.957385i	$0.406739\pi$
$180$	33.8274	+	176.497i	0.187930	+	0.980538i
$181$	−175.624	+	112.867i	−0.970300	+	0.623574i	−0.926830	−	0.375480i	$-0.877478\pi$
$181$	−175.624	+	112.867i	−0.970300	+	0.623574i	−0.0434702	+	0.999055i	$0.513841\pi$
$182$	16.8733	+	235.920i	0.0927107	+	1.29626i
$183$	7.67545	+	7.67545i	0.0419424	+	0.0419424i
$184$	19.9033	−	53.8017i	0.108170	−	0.292401i
$185$	−145.686	+	159.927i	−0.787493	+	0.864471i
$186$	26.7899	−	30.9172i	0.144032	−	0.166221i
$187$	4.33032	−	19.9062i	0.0231568	−	0.106450i
$188$	−261.047	+	348.717i	−1.38855	+	1.85488i
$189$	−97.8605	+	44.6914i	−0.517781	+	0.236462i
$190$	−190.358	+	156.841i	−1.00188	+	0.825481i
$191$	271.735	−	79.7885i	1.42269	−	0.417741i	0.522280	−	0.852774i	$-0.325081\pi$
$191$	271.735	−	79.7885i	1.42269	−	0.417741i	0.900414	+	0.435033i	$0.143263\pi$
$192$	−107.138	+	23.3064i	−0.558010	+	0.121388i
$193$	−281.583	+	105.025i	−1.45898	+	0.544171i	−0.948795	−	0.315894i	$-0.897696\pi$
$193$	−281.583	+	105.025i	−1.45898	+	0.544171i	−0.510185	+	0.860065i	$0.670423\pi$
$194$	139.341	−	474.553i	0.718254	−	2.44615i
$195$	−69.1882	+	65.8342i	−0.354812	+	0.337611i
$196$	−68.8386	−	79.4440i	−0.351218	−	0.405327i
$197$	−1.85719	+	1.01410i	−0.00942738	+	0.00514774i	−0.483956	−	0.875092i	$-0.660800\pi$
$197$	−1.85719	+	1.01410i	−0.00942738	+	0.00514774i	0.474528	+	0.880240i	$0.342619\pi$
$198$	−14.3241	+	5.34260i	−0.0723438	+	0.0269829i
$199$	−75.6622	+	117.733i	−0.380212	+	0.591622i	−0.977636	−	0.210304i	$-0.932555\pi$
$199$	−75.6622	+	117.733i	−0.380212	+	0.591622i	0.597424	+	0.801926i	$0.296191\pi$
$200$	57.2681	+	24.6642i	0.286341	+	0.123321i
$201$	−12.1217	+	84.3086i	−0.0603072	+	0.419446i
$202$	52.4551	+	19.5648i	0.259679	+	0.0968552i
$203$	54.3679	−	72.6270i	0.267822	−	0.357768i
$204$	96.5295	+	150.203i	0.473184	+	0.736288i
$205$	5.35223	−	6.79143i	0.0261084	−	0.0331289i
$206$	−381.464			−1.85177
$207$	−92.7448	−	143.469i	−0.448043	−	0.693087i
$208$	128.614	+	128.614i	0.618338	+	0.618338i
$209$	−8.68131	−	7.52240i	−0.0415374	−	0.0359923i
$210$	−16.2430	+	95.9853i	−0.0773475	+	0.457073i
$211$	−49.0630	−	341.241i	−0.232526	−	1.61725i	−0.687112	−	0.726552i	$-0.741122\pi$
$211$	−49.0630	−	341.241i	−0.232526	−	1.61725i	0.454586	−	0.890703i	$-0.349787\pi$
$212$	17.7393	+	6.61643i	0.0836761	+	0.0312096i
$213$	44.8810	−	33.5975i	0.210709	−	0.157735i
$214$	−69.8967	−	238.046i	−0.326620	−	1.11237i
$215$	45.7133	+	171.314i	0.212620	+	0.796810i
$216$	21.3429	−	46.7343i	0.0988095	−	0.216363i
$217$	−50.3009	+	27.4664i	−0.231802	+	0.126573i
$218$	−11.4562	+	160.179i	−0.0525514	+	0.734765i
$219$	81.8266	−	70.9032i	0.373638	−	0.323759i
$220$	−3.96585	+	16.2738i	−0.0180266	+	0.0739720i
$221$	186.205	−	407.733i	0.842558	−	1.84494i
$222$	157.613	−	34.2866i	0.709968	−	0.154444i
$223$	−254.077	−	138.736i	−1.13936	−	0.622136i	−0.205102	−	0.978741i	$-0.565753\pi$
$223$	−254.077	−	138.736i	−1.13936	−	0.622136i	−0.934256	+	0.356604i	$0.883934\pi$
$224$	235.089	+	33.8007i	1.04951	+	0.150896i
$225$	161.005	−	92.5123i	0.715580	−	0.411166i
$226$	3.48723	+	24.2542i	0.0154302	+	0.107319i
$227$	−66.0974	+	303.845i	−0.291178	+	1.33852i	0.566384	+	0.824142i	$0.308342\pi$
$227$	−66.0974	+	303.845i	−0.291178	+	1.33852i	−0.857561	+	0.514381i	$0.828022\pi$
$228$	100.421	−	7.18222i	0.440441	−	0.0315010i
$229$		−	97.7615i		−	0.426906i	−0.976953	−	0.213453i	$-0.931529\pi$
$229$		−	97.7615i		−	0.426906i	0.976953	−	0.213453i	$-0.0684710\pi$
$230$	−341.815	−	7.57668i	−1.48615	−	0.0329421i
$231$	−4.53383			−0.0196270
$232$	3.09080	+	43.2150i	0.0133224	+	0.186272i
$233$	−171.749	−	37.3618i	−0.737122	−	0.160351i	−0.171696	−	0.985150i	$-0.554925\pi$
$233$	−171.749	−	37.3618i	−0.737122	−	0.160351i	−0.565426	+	0.824799i	$0.691288\pi$
$234$	−332.958	+	47.8721i	−1.42290	+	0.204582i
$235$	428.588	+	137.494i	1.82378	+	0.585081i
$236$	−23.7113	+	164.916i	−0.100472	+	0.698797i
$237$	−60.8797	+	111.493i	−0.256876	+	0.470434i
$238$	−97.1210	−	446.458i	−0.408071	−	1.87587i
$239$	274.715	+	125.458i	1.14943	+	0.524929i	0.896714	−	0.442611i	$-0.145948\pi$
$239$	274.715	+	125.458i	1.14943	+	0.524929i	0.252720	+	0.967539i	$0.418675\pi$
$240$	38.8976	+	63.9645i	0.162073	+	0.266519i
$241$	180.186	+	207.946i	0.747662	+	0.862847i	0.994339	−	0.106250i	$-0.0338844\pi$
$241$	180.186	+	207.946i	0.747662	+	0.862847i	−0.246678	+	0.969098i	$0.579339\pi$
$242$	357.399	+	25.5617i	1.47686	+	0.105627i
$243$	−113.499	−	207.858i	−0.467075	−	0.855384i
$244$	38.1030	+	17.4011i	0.156160	+	0.0713158i
$245$	−54.4068	+	94.0103i	−0.222069	+	0.383715i
$246$	−6.18598	+	1.81637i	−0.0251463	+	0.00738361i
$247$	−151.467	−	202.336i	−0.613226	−	0.819174i
$248$	9.56471	−	25.6440i	0.0385674	−	0.103403i
$249$	2.39024	−	0.343665i	0.00959938	−	0.00138018i
$250$	27.6635	−	370.598i	0.110654	−	1.48239i
$251$	171.198	−	197.573i	0.682064	−	0.787143i	−0.304149	−	0.952624i	$-0.598372\pi$
$251$	171.198	−	197.573i	0.682064	−	0.787143i	0.986213	+	0.165481i	$0.0529177\pi$
$252$	−132.733	+	132.733i	−0.526717	+	0.526717i
$253$	−2.30822	−	15.7549i	−0.00912339	−	0.0622723i
$254$		−	114.242i		−	0.449771i
$255$	114.194	−	144.901i	0.447821	−	0.568238i
$256$	99.0098	−	63.6297i	0.386757	−	0.248554i
$257$	−52.8473	−	39.5610i	−0.205632	−	0.153934i	0.491499	−	0.870878i	$-0.336449\pi$
$257$	−52.8473	−	39.5610i	−0.205632	−	0.153934i	−0.697130	+	0.716944i	$0.745540\pi$
$258$	46.1993	−	123.865i	0.179067	−	0.480097i
$259$	−223.670	−	32.1589i	−0.863590	−	0.124165i
$260$	−161.380	+	331.342i	−0.620694	+	1.27439i
$261$	108.543	+	69.7562i	0.415872	+	0.267265i
$262$	80.3587	+	215.450i	0.306713	+	0.822329i
$263$	37.9772	+	69.5500i	0.144400	+	0.264449i	0.939862	−	0.341555i	$-0.110954\pi$
$263$	37.9772	+	69.5500i	0.144400	+	0.264449i	−0.795462	+	0.606004i	$0.792772\pi$
$264$	1.63633	−	1.41789i	0.00619823	−	0.00537080i
$265$	0.485821	−	19.5573i	0.00183329	−	0.0738011i
$266$	−247.196	−	72.5834i	−0.929309	−	0.272870i
$267$	46.2586	+	124.024i	0.173253	+	0.464510i
$268$	69.8686	+	321.181i	0.260704	+	1.19844i
$269$	−114.946	−	391.470i	−0.427309	−	1.45528i	−0.839088	−	0.543996i	$-0.816911\pi$
$269$	−114.946	−	391.470i	−0.427309	−	1.45528i	0.411779	−	0.911284i	$-0.364907\pi$
$270$	−304.793	−	29.4228i	−1.12886	−	0.108973i
$271$	−45.9671	−	100.654i	−0.169620	−	0.371417i	0.805663	−	0.592374i	$-0.201809\pi$
$271$	−45.9671	−	100.654i	−0.169620	−	0.371417i	−0.975284	+	0.220957i	$0.929082\pi$
$272$	−281.278	−	210.562i	−1.03411	−	0.774126i
$273$	−97.4781	−	21.2051i	−0.357063	−	0.0776742i
$274$	490.541	+	425.056i	1.79029	+	1.55130i
$275$	17.2327	−	1.60950i	0.0626643	−	0.00585274i
$276$	111.944	+	83.3342i	0.405594	+	0.301935i
$277$	203.892	−	203.892i	0.736074	−	0.736074i	−0.235742	−	0.971816i	$-0.575752\pi$
$277$	203.892	−	203.892i	0.736074	−	0.736074i	0.971816	+	0.235742i	$0.0757520\pi$
$278$	117.660	−	8.41523i	0.423239	−	0.0302706i
$279$	−44.0665	−	68.5688i	−0.157944	−	0.245766i
$280$	12.2597	+	63.9661i	0.0437848	+	0.228450i
$281$	−30.1779	−	66.0804i	−0.107395	−	0.235162i	0.848303	−	0.529511i	$-0.177624\pi$
$281$	−30.1779	−	66.0804i	−0.107395	−	0.235162i	−0.955698	+	0.294349i	$0.904897\pi$
$282$	−201.114	−	268.657i	−0.713171	−	0.952685i
$283$	−3.62936	−	1.98178i	−0.0128246	−	0.00700276i	0.472824	−	0.881157i	$-0.343235\pi$
$283$	−3.62936	−	1.98178i	−0.0128246	−	0.00700276i	−0.485648	+	0.874154i	$0.661416\pi$
$284$	116.967	−	182.004i	0.411855	−	0.640858i
$285$	−40.8517	−	95.6716i	−0.143339	−	0.335690i
$286$	−30.0830	−	8.83317i	−0.105185	−	0.0308852i
$287$	9.00902	+	0.644338i	0.0313903	+	0.00224508i
$288$	−24.0970	+	336.920i	−0.0836702	+	1.16986i
$289$	−162.526	+	553.512i	−0.562373	+	1.91527i
$290$	237.478	−	101.403i	0.818888	−	0.349665i
$291$	175.487	+	112.778i	0.603047	+	0.387555i
$292$	200.241	−	366.714i	0.685756	−	1.25587i
$293$	230.686	−	172.690i	0.787326	−	0.589385i	−0.128152	−	0.991755i	$-0.540904\pi$
$293$	230.686	−	172.690i	0.787326	−	0.589385i	0.915477	+	0.402370i	$0.131813\pi$
$294$	73.6672	−	33.6427i	0.250569	−	0.114431i
$295$	169.081	−	32.4060i	0.573155	−	0.109851i
$296$	90.7833	−	58.3429i	0.306700	−	0.197104i
$297$	−1.01736	−	14.2246i	−0.00342547	−	0.0478943i
$298$	326.490	+	326.490i	1.09560	+	1.09560i
$299$	24.0597	−	349.528i	0.0804673	−	1.16899i
$300$	−96.8229	+	116.772i	−0.322743	+	0.389241i
$301$	−121.283	+	139.968i	−0.402934	+	0.465010i
$302$	−35.6832	+	164.033i	−0.118156	+	0.543155i
$303$	−14.1506	+	18.9030i	−0.0467016	+	0.0623860i
$304$	−180.218	+	82.3027i	−0.592821	+	0.270732i
$305$	4.15892	−	43.0825i	0.0136358	−	0.141254i
$306$	623.479	−	183.070i	2.03751	−	0.598268i
$307$	−11.8810	+	2.58455i	−0.0387003	+	0.00841873i	−0.231874	−	0.972746i	$-0.574486\pi$
$307$	−11.8810	+	2.58455i	−0.0387003	+	0.00841873i	0.193173	+	0.981165i	$0.438122\pi$
$308$	−16.3929	+	6.11424i	−0.0532237	+	0.0198514i
$309$	45.3279	−	154.373i	0.146692	−	0.499587i
$310$	−163.074	−	4.05090i	−0.526044	−	0.0130674i
$311$	−163.945	−	189.203i	−0.527156	−	0.608370i	0.428252	−	0.903659i	$-0.359130\pi$
$311$	−163.945	−	189.203i	−0.527156	−	0.608370i	−0.955408	+	0.295289i	$0.904584\pi$
$312$	41.8130	−	22.8316i	0.134016	−	0.0731783i
$313$	−299.406	+	111.672i	−0.956567	+	0.356781i	−0.778787	−	0.627289i	$-0.784164\pi$
$313$	−299.406	+	111.672i	−0.956567	+	0.356781i	−0.177781	+	0.984070i	$0.556892\pi$
$314$	−204.902	+	318.834i	−0.652554	+	1.01539i
$315$	174.378	+	84.9308i	0.553580	+	0.269622i
$316$	−69.7648	+	485.225i	−0.220775	+	1.53552i
$317$	518.143	+	193.257i	1.63452	+	0.609644i	0.988165	−	0.153394i	$-0.0490203\pi$
$317$	518.143	+	193.257i	1.63452	+	0.609644i	0.646354	+	0.763038i	$0.276293\pi$
$318$	−8.74127	+	11.6770i	−0.0274883	+	0.0367200i
$319$	6.50174	+	10.1169i	0.0203816	+	0.0317144i
$320$	343.382	+	270.615i	1.07307	+	0.845671i
$321$	104.639			0.325979
$322$	−193.879	−	299.915i	−0.602108	−	0.931413i
$323$	345.241	+	345.241i	1.06886	+	1.06886i
$324$	−150.007	−	129.982i	−0.462984	−	0.401178i
$325$	378.033	+	45.9940i	1.16318	+	0.141520i
$326$	121.675	+	846.266i	0.373235	+	2.59591i
$327$	−63.4605	−	23.6695i	−0.194069	−	0.0723839i
$328$	−3.45301	+	2.58489i	−0.0105275	+	0.00788077i
$329$	132.456	+	451.103i	0.402601	+	1.37113i
$330$	−11.1690	−	6.46384i	−0.0338454	−	0.0195874i
$331$	−225.242	+	493.211i	−0.680489	+	1.49006i	0.181635	+	0.983366i	$0.441861\pi$
$331$	−225.242	+	493.211i	−0.680489	+	1.49006i	−0.862124	+	0.506697i	$0.830866\pi$
$332$	8.17892	−	4.46603i	0.0246353	−	0.0134519i
$333$	22.9265	−	320.555i	0.0688484	−	0.962626i
$334$	−509.551	+	441.529i	−1.52560	+	1.32194i
$335$	290.190	−	176.468i	0.866239	−	0.526770i
$336$	−32.4842	+	71.1304i	−0.0966791	+	0.211698i
$337$	−356.124	+	77.4701i	−1.05675	+	0.229882i	−0.707183	−	0.707030i	$-0.750034\pi$
$337$	−356.124	+	77.4701i	−1.05675	+	0.229882i	−0.349565	+	0.936912i	$0.613671\pi$
$338$	−164.493	−	89.8201i	−0.486666	−	0.265740i
$339$	−10.2297	−	1.47080i	−0.0301760	−	0.00433865i
$340$	217.480	−	677.916i	0.639648	−	1.99387i
$341$	−1.08118	−	7.51976i	−0.00317061	−	0.0220521i
$342$	77.8847	−	358.030i	0.227733	−	1.04687i
$343$	−368.425	+	26.3503i	−1.07413	+	0.0768231i
$344$		−	88.4464i		−	0.257112i
$345$	43.6826	−	137.427i	0.126616	−	0.398338i
$346$	−845.872			−2.44472
$347$	−30.3034	−	423.697i	−0.0873297	−	1.22103i	−0.832451	−	0.554099i	$-0.813063\pi$
$347$	−30.3034	−	423.697i	−0.0873297	−	1.22103i	0.745121	−	0.666929i	$-0.232392\pi$
$348$	−102.992	−	22.4046i	−0.295955	−	0.0643810i
$349$	312.380	−	44.9135i	0.895072	−	0.128692i	0.320599	−	0.947215i	$-0.396116\pi$
$349$	312.380	−	44.9135i	0.895072	−	0.128692i	0.574473	+	0.818523i	$0.305207\pi$
$350$	336.574	−	193.393i	0.961641	−	0.552550i
$351$	44.6561	−	310.590i	0.127225	−	0.884871i
$352$	−15.0884	+	27.6324i	−0.0428648	+	0.0785011i
$353$	14.1036	+	64.8333i	0.0399536	+	0.183664i	0.992799	−	0.119793i	$-0.0382230\pi$
$353$	14.1036	+	64.8333i	0.0399536	+	0.183664i	−0.952845	+	0.303456i	$0.901859\pi$
$354$	−116.761	−	53.3228i	−0.329833	−	0.150629i
$355$	−217.194	−	52.9289i	−0.611814	−	0.149096i
$356$	334.514	+	386.049i	0.939645	+	1.08441i
$357$	192.215	+	13.7475i	0.538417	+	0.0385084i
$358$	−68.8607	−	126.109i	−0.192348	−	0.352260i
$359$	241.224	+	110.163i	0.671933	+	0.306862i	0.722009	−	0.691884i	$-0.243219\pi$
$359$	241.224	+	110.163i	0.671933	+	0.306862i	−0.0500755	+	0.998745i	$0.515946\pi$
$360$	−89.4966	+	23.8812i	−0.248602	+	0.0663367i
$361$	−82.2223	+	24.1426i	−0.227763	+	0.0668771i
$362$	−371.951	−	496.868i	−1.02749	−	1.37256i
$363$	−52.8127	+	141.596i	−0.145489	+	0.390072i
$364$	−381.047	+	54.7863i	−1.04683	+	0.150512i
$365$	−425.679	−	72.0349i	−1.16624	−	0.197356i
$366$	−21.1333	+	24.3891i	−0.0577413	+	0.0666370i
$367$	−287.060	+	287.060i	−0.782179	+	0.782179i	−0.980198	−	0.198019i	$-0.936549\pi$
$367$	−287.060	+	287.060i	−0.782179	+	0.782179i	0.198019	+	0.980198i	$0.436549\pi$
$368$	−263.713	−	76.6681i	−0.716613	−	0.208337i
$369$			12.8453i			0.0348112i
$370$	−505.156	−	398.107i	−1.36529	−	1.07596i
$371$	17.1906	−	11.0478i	0.0463359	−	0.0297783i
$372$	53.3033	+	39.9024i	0.143288	+	0.107264i
$373$	147.478	−	395.404i	0.395383	−	1.06006i	−0.574928	−	0.818204i	$-0.694970\pi$
$373$	147.478	−	395.404i	0.395383	−	1.06006i	0.970311	−	0.241859i	$-0.0777573\pi$
$374$	59.9493	+	8.61941i	0.160292	+	0.0230466i
$375$	146.688	+	55.2316i	0.391168	+	0.147284i
$376$	−188.881	−	121.387i	−0.502344	−	0.322837i
$377$	92.4710	+	247.924i	0.245281	+	0.657624i
$378$	−153.286	−	280.722i	−0.405519	−	0.742652i
$379$	35.4445	−	30.7129i	0.0935212	−	0.0810366i	−0.606845	−	0.794820i	$-0.707565\pi$
$379$	35.4445	−	30.7129i	0.0935212	−	0.0810366i	0.700367	+	0.713783i	$0.253020\pi$
$380$	−276.728	−	290.827i	−0.728232	−	0.765333i
$381$	46.2319	+	13.5749i	0.121344	+	0.0356297i
$382$	294.243	+	788.895i	0.770269	+	2.06517i
$383$	−99.5403	−	457.579i	−0.259896	−	1.19472i	−0.903236	−	0.429143i	$-0.858816\pi$
$383$	−99.5403	−	457.579i	−0.259896	−	1.19472i	0.643340	−	0.765580i	$-0.277548\pi$
$384$	−27.5755	−	93.9136i	−0.0718112	−	0.244567i
$385$	11.4959	+	13.9526i	0.0298596	+	0.0362404i
$386$	−371.169	−	812.747i	−0.961578	−	2.10556i
$387$	−210.860	−	157.848i	−0.544858	−	0.407876i
$388$	786.596	+	171.114i	2.02731	+	0.441014i
$389$	107.692	+	93.3155i	0.276843	+	0.239886i	0.782204	−	0.623022i	$-0.214095\pi$
$389$	107.692	+	93.3155i	0.276843	+	0.239886i	−0.505361	+	0.862908i	$0.668641\pi$
$390$	−209.903	−	191.212i	−0.538212	−	0.490287i
$391$	50.0865	+	674.938i	0.128098	+	1.72619i
$392$	38.3125	−	38.3125i	0.0977360	−	0.0977360i
$393$	−96.7379	+	6.91883i	−0.246152	+	0.0176052i
$394$	−3.40118	−	5.29235i	−0.00863245	−	0.0134323i
$395$	497.478	−	95.3467i	1.25944	−	0.241384i
$396$	−10.3367	−	22.6342i	−0.0261028	−	0.0571571i
$397$	−18.1031	−	24.1830i	−0.0455999	−	0.0609143i	0.777162	−	0.629301i	$-0.216659\pi$
$397$	−18.1031	−	24.1830i	−0.0455999	−	0.0609143i	−0.822762	+	0.568387i	$0.807568\pi$
$398$	−365.179	−	199.403i	−0.917535	−	0.501012i
$399$	58.7467	−	91.4116i	0.147235	−	0.229102i
$400$	98.2183	−	281.892i	0.245546	−	0.704731i
$401$	461.932	+	135.635i	1.15195	+	0.338243i	0.801299	−	0.598264i	$-0.204143\pi$
$401$	461.932	+	135.635i	1.15195	+	0.338243i	0.350650	+	0.936507i	$0.385961\pi$
$402$	−252.584	−	18.0652i	−0.628320	−	0.0449383i
$403$	11.9250	−	166.733i	0.0295905	−	0.413729i
$404$	−25.6719	+	87.4304i	−0.0635443	+	0.216412i
$405$	−76.4232	+	190.324i	−0.188699	+	0.469937i
$406$	226.903	+	145.822i	0.558875	+	0.359167i
$407$	14.3555	−	26.2901i	0.0352715	−	0.0645949i
$408$	−73.6728	+	55.1508i	−0.180571	+	0.135174i
$409$	−565.090	+	258.068i	−1.38164	+	0.630973i	−0.961074	−	0.276291i	$-0.910895\pi$
$409$	−565.090	+	258.068i	−1.38164	+	0.630973i	−0.420563	+	0.907263i	$0.638167\pi$
$410$	21.2749	+	14.4314i	0.0518899	+	0.0351985i
$411$	−230.302	+	148.006i	−0.560346	+	0.360113i
$412$	−44.2926	−	619.291i	−0.107506	−	1.50313i
$413$	127.155	+	127.155i	0.307882	+	0.307882i
$414$	405.781	−	305.460i	0.980147	−	0.737825i
$415$	−7.11829	−	6.48443i	−0.0171525	−	0.0156251i
$416$	−453.642	+	523.531i	−1.09049	+	1.25849i
$417$	−10.5756	+	48.6152i	−0.0253611	+	0.116583i
$418$	20.4661	−	27.3395i	0.0489619	−	0.0654055i
$419$	377.504	−	172.400i	0.900964	−	0.411456i	0.0895863	−	0.995979i	$-0.471446\pi$
$419$	377.504	−	172.400i	0.900964	−	0.411456i	0.811377	+	0.584523i	$0.198718\pi$
$420$	−157.714	−	15.2247i	−0.375510	−	0.0362494i
$421$	−231.191	+	67.8839i	−0.549148	+	0.161245i	−0.544525	−	0.838745i	$-0.683290\pi$
$421$	−231.191	+	67.8839i	−0.549148	+	0.161245i	−0.00462364	+	0.999989i	$0.501472\pi$
$422$	1001.53	−	217.869i	2.37329	−	0.516278i
$423$	−626.483	+	233.666i	−1.48105	+	0.552402i
$424$	−2.74935	+	9.36344i	−0.00648433	+	0.0220836i
$425$	−735.472	+	15.9830i	−1.73052	+	0.0376071i
$426$	109.151	+	125.967i	0.256223	+	0.295697i
$427$	39.6801	−	21.6670i	0.0929277	−	0.0507424i
$428$	378.342	−	141.114i	0.883978	−	0.329707i
$429$	7.14929	−	11.1245i	0.0166650	−	0.0259312i
$430$	−498.329	+	171.896i	−1.15890	+	0.399757i
$431$	−26.2558	+	182.613i	−0.0609184	+	0.423697i	0.936426	+	0.350865i	$0.114113\pi$
$431$	−26.2558	+	182.613i	−0.0609184	+	0.423697i	−0.997344	+	0.0728312i	$0.976797\pi$
$432$	−230.457	−	85.9559i	−0.533464	−	0.198972i
$433$	443.066	−	591.867i	1.02325	−	1.36690i	0.0947745	−	0.995499i	$-0.469787\pi$
$433$	443.066	−	591.867i	1.02325	−	1.36690i	0.928473	−	0.371400i	$-0.121122\pi$
$434$	−92.1189	−	143.340i	−0.212256	−	0.330276i
$435$	12.8176	+	108.153i	0.0294658	+	0.248627i
$436$	−261.374			−0.599481
$437$	347.560	+	157.604i	0.795332	+	0.360650i
$438$	227.615	+	227.615i	0.519670	+	0.519670i
$439$	181.701	+	157.444i	0.413896	+	0.358643i	0.836779	−	0.547541i	$-0.184436\pi$
$439$	181.701	+	157.444i	0.413896	+	0.358643i	−0.422882	+	0.906185i	$0.638982\pi$
$440$	−8.51254	−	1.44052i	−0.0193467	−	0.00327391i
$441$	−22.9634	−	159.714i	−0.0520713	−	0.362164i
$442$	1248.61	+	465.706i	2.82490	+	1.05363i
$443$	−495.320	+	370.792i	−1.11810	+	0.837002i	−0.987993	−	0.154497i	$-0.950624\pi$
$443$	−495.320	+	370.792i	−1.11810	+	0.837002i	−0.130111	+	0.991499i	$0.541533\pi$
$444$	73.9635	+	251.897i	0.166585	+	0.567335i
$445$	264.384	−	456.832i	0.594121	−	1.02659i
$446$	357.529	−	782.879i	0.801634	−	1.75533i
$447$	−170.921	+	93.3299i	−0.382373	+	0.208792i
$448$	−32.5784	+	455.506i	−0.0727197	+	1.01675i
$449$	−509.573	+	441.548i	−1.13491	+	0.983403i	−0.999972	−	0.00745161i	$-0.997628\pi$
$449$	−509.573	+	441.548i	−1.13491	+	0.983403i	−0.134935	+	0.990854i	$0.543083\pi$
$450$	308.490	+	457.834i	0.685533	+	1.01741i
$451$	−0.497364	+	1.08908i	−0.00110280	+	0.00241480i
$452$	−38.9707	+	8.47757i	−0.0862185	+	0.0187557i
$453$	−62.1414	−	33.9318i	−0.137177	−	0.0749046i
$454$	−915.058	−	131.565i	−2.01555	−	0.289792i
$455$	181.907	+	353.750i	0.399796	+	0.777472i
$456$	7.38505	+	51.3641i	0.0161953	+	0.112641i
$457$	−39.2987	+	180.653i	−0.0859928	+	0.395303i	−0.999945	−	0.0105201i	$-0.996651\pi$
$457$	−39.2987	+	180.653i	−0.0859928	+	0.395303i	0.913952	+	0.405823i	$0.133015\pi$
$458$	289.908	−	20.7346i	0.632986	−	0.0452721i
$459$			606.147i			1.32058i
$460$	−27.3884	−	555.802i	−0.0595400	−	1.20826i
$461$	607.237			1.31722			0.658608	−	0.752486i	$-0.271146\pi$
$461$	607.237			1.31722			0.658608	+	0.752486i	$0.271146\pi$
$462$	−0.961597	−	13.4449i	−0.00208138	−	0.0291015i
$463$	124.187	+	27.0152i	0.268222	+	0.0583481i	0.344665	−	0.938726i	$-0.387993\pi$
$463$	124.187	+	27.0152i	0.268222	+	0.0583481i	−0.0764429	+	0.997074i	$0.524356\pi$
$464$	205.306	−	29.5186i	0.442470	−	0.0636176i
$465$	21.0167	−	65.5119i	0.0451972	−	0.140886i
$466$	74.3678	−	517.240i	0.159588	−	1.10996i
$467$	−179.887	+	329.439i	−0.385198	+	0.705437i	−0.996284	−	0.0861267i	$-0.972551\pi$
$467$	−179.887	+	329.439i	−0.385198	+	0.705437i	0.611086	+	0.791564i	$0.290733\pi$
$468$	−116.379	−	534.984i	−0.248673	−	1.14313i
$469$	322.700	+	147.372i	0.688060	+	0.314226i
$470$	−316.832	+	1300.12i	−0.674111	+	2.76621i
$471$	−104.679	−	120.806i	−0.222249	−	0.256489i
$472$	−85.6585	−	6.12642i	−0.181480	−	0.0129797i
$473$	−11.7657	−	21.5473i	−0.0248747	−	0.0455546i
$474$	−343.539	−	156.889i	−0.724767	−	0.330990i
$475$	−190.840	+	368.302i	−0.401768	+	0.775374i
$476$	713.529	−	209.511i	1.49901	−	0.440149i
$477$	17.4162	+	23.2653i	0.0365119	+	0.0487742i
$478$	−313.775	+	841.264i	−0.656433	+	1.75997i
$479$	−806.678	+	115.983i	−1.68409	+	0.242135i	−0.916851	−	0.399229i	$-0.869278\pi$
$479$	−806.678	+	115.983i	−1.68409	+	0.242135i	−0.767237	+	0.641364i	$0.778369\pi$
$480$	−232.423	+	165.145i	−0.484214	+	0.344052i
$481$	431.607	−	498.101i	0.897311	−	1.03555i
$482$	−578.439	+	578.439i	−1.20008	+	1.20008i
$483$	144.409	−	42.8219i	0.298983	−	0.0886582i
$484$			583.190i			1.20494i
$485$	−97.8937	−	826.009i	−0.201843	−	1.70311i
$486$	592.323	−	380.663i	1.21877	−	0.783257i
$487$	−46.4396	−	34.7642i	−0.0953585	−	0.0713845i	0.550535	−	0.834812i	$-0.314424\pi$
$487$	−46.4396	−	34.7642i	−0.0953585	−	0.0713845i	−0.645893	+	0.763428i	$0.723515\pi$
$488$	−7.54517	+	20.2294i	−0.0154614	+	0.0414536i
$489$	−356.928	−	51.3186i	−0.729915	−	0.104946i
$490$	−290.323	−	141.402i	−0.592496	−	0.288576i
$491$	672.276	+	432.045i	1.36920	+	0.879930i	0.998802	−	0.0489444i	$-0.0155857\pi$
$491$	672.276	+	432.045i	1.36920	+	0.879930i	0.370396	+	0.928874i	$0.379222\pi$
$492$	−3.66706	−	9.83178i	−0.00745338	−	0.0199833i
$493$	−244.969	−	448.628i	−0.496896	−	0.909996i
$494$	567.893	−	492.082i	1.14958	−	0.996118i
$495$	−18.6264	+	17.7234i	−0.0376290	+	0.0358049i
$496$	−125.723	−	36.9155i	−0.253473	−	0.0744264i
$497$	−81.6018	−	218.783i	−0.164189	−	0.440207i
$498$	1.52608	+	7.01528i	0.00306442	+	0.0140869i
$499$	−194.592	−	662.721i	−0.389965	−	1.32810i	−0.887562	−	0.460689i	$-0.847602\pi$
$499$	−194.592	−	662.721i	−0.389965	−	1.32810i	0.497597	−	0.867408i	$-0.334216\pi$
$500$	604.862	+	1.87965i	1.20972	+	0.00375930i
$501$	−118.132	−	258.672i	−0.235792	−	0.516312i
$502$	622.204	+	465.776i	1.23945	+	0.927841i
$503$	567.140	+	123.374i	1.12752	+	0.245276i	0.737378	−	0.675481i	$-0.236064\pi$
$503$	567.140	+	123.374i	1.12752	+	0.245276i	0.390137	+	0.920757i	$0.372427\pi$
$504$	−73.1211	−	63.3598i	−0.145082	−	0.125714i
$505$	94.0527	−	4.38264i	0.186243	−	0.00867849i
$506$	46.2309	−	10.1864i	0.0913654	−	0.0201313i
$507$	55.8948	−	55.8948i	0.110246	−	0.110246i
$508$	185.467	−	13.2649i	0.365092	−	0.0261119i
$509$	−233.298	−	363.019i	−0.458346	−	0.713201i	0.532761	−	0.846266i	$-0.321154\pi$
$509$	−233.298	−	363.019i	−0.458346	−	0.713201i	−0.991107	+	0.133065i	$0.957518\pi$
$510$	453.917	+	307.906i	0.890033	+	0.603737i
$511$	−187.334	−	410.205i	−0.366603	−	0.802750i
$512$	396.802	+	530.066i	0.775004	+	1.03528i
$513$	299.981	+	163.802i	0.584758	+	0.319302i
$514$	106.108	−	165.107i	0.206436	−	0.321220i
$515$	−590.004	+	251.932i	−1.14564	+	0.489188i
$516$	206.454	+	60.6204i	0.400105	+	0.117481i
$517$	−62.1631	−	4.44599i	−0.120238	−	0.00859959i
$518$	47.9268	−	670.104i	0.0925227	−	1.29364i
$519$	100.512	−	342.311i	0.193664	−	0.659559i
$520$	−176.284	−	70.7852i	−0.339007	−	0.136125i
$521$	−234.470	−	150.685i	−0.450038	−	0.289222i	0.295922	−	0.955212i	$-0.404373\pi$
$521$	−234.470	−	150.685i	−0.450038	−	0.289222i	−0.745961	+	0.665990i	$0.768009\pi$
$522$	−183.838	+	336.674i	−0.352179	+	0.644969i
$523$	−243.066	+	181.957i	−0.464754	+	0.347910i	−0.805852	−	0.592117i	$-0.798292\pi$
$523$	−243.066	+	181.957i	−0.464754	+	0.347910i	0.341098	+	0.940028i	$0.389201\pi$
$524$	−340.443	+	155.475i	−0.649701	+	0.296709i
$525$	38.2691	+	159.186i	0.0728936	+	0.303212i
$526$	−198.193	+	127.371i	−0.376793	+	0.242150i
$527$	23.0359	+	322.084i	0.0437114	+	0.611165i
$528$	−7.32962	−	7.32962i	−0.0138819	−	0.0138819i
$529$	222.324	+	480.013i	0.420273	+	0.907398i
$530$	58.0994	−	2.70730i	0.109621	−	0.00510811i
$531$	−167.478	+	193.280i	−0.315401	+	0.363993i
$532$	89.1336	−	409.741i	0.167544	−	0.770189i
$533$	−15.7871	+	21.0891i	−0.0296193	+	0.0395668i
$534$	−357.977	+	163.483i	−0.670370	+	0.306148i
$535$	−265.322	−	322.020i	−0.495929	−	0.601907i
$536$	−162.556	+	47.7308i	−0.303277	+	0.0890501i
$537$	59.2167	−	12.8818i	0.110273	−	0.0239885i
$538$	1136.51	−	423.896i	2.11247	−	0.787911i
$539$	4.23712	−	14.4303i	0.00786108	−	0.0267724i
$540$	12.3766	−	498.235i	0.0229196	−	0.922657i
$541$	129.899	+	149.911i	0.240109	+	0.277101i	0.862995	−	0.505212i	$-0.168586\pi$
$541$	129.899	+	149.911i	0.240109	+	0.277101i	−0.622886	+	0.782312i	$0.714040\pi$
$542$	288.736	−	157.662i	0.532723	−	0.290889i
$543$	245.272	−	91.4817i	0.451698	−	0.168475i
$544$	723.471	−	1125.74i	1.32991	−	2.06938i
$545$	88.0682	+	255.312i	0.161593	+	0.468462i
$546$	42.2082	−	293.565i	0.0773044	−	0.537664i
$547$	456.513	+	170.270i	0.834575	+	0.311281i	0.730180	−	0.683255i	$-0.239436\pi$
$547$	456.513	+	170.270i	0.834575	+	0.311281i	0.104396	+	0.994536i	$0.466709\pi$
$548$	−633.103	+	845.726i	−1.15530	+	1.54330i
$549$	34.7621	+	54.0908i	0.0633189	+	0.0985261i
$550$	8.42786	+	50.7614i	0.0153234	+	0.0922935i
$551$	−288.224			−0.523093
$552$	−38.7275	+	60.6169i	−0.0701585	+	0.109813i
$553$	374.123	+	374.123i	0.676534	+	0.676534i
$554$	647.879	+	561.390i	1.16946	+	1.01334i
$555$	221.133	−	157.123i	0.398438	−	0.283105i
$556$	27.3236	+	190.040i	0.0491431	+	0.341798i
$557$	−138.980	−	51.8368i	−0.249515	−	0.0930643i	0.221595	−	0.975139i	$-0.428874\pi$
$557$	−138.980	−	51.8368i	−0.249515	−	0.0930643i	−0.471110	+	0.882075i	$0.656146\pi$
$558$	193.992	−	145.220i	0.347655	−	0.260252i
$559$	−152.187	−	518.301i	−0.272248	−	0.927193i
$560$	301.266	−	80.3895i	0.537975	−	0.143553i
$561$	−10.6117	+	23.2363i	−0.0189156	+	0.0414195i
$562$	189.558	−	103.507i	0.337292	−	0.184175i
$563$	68.1729	−	953.182i	0.121089	−	1.69304i	−0.467010	−	0.884252i	$-0.654669\pi$
$563$	68.1729	−	953.182i	0.121089	−	1.69304i	0.588099	−	0.808789i	$-0.299876\pi$
$564$	412.802	−	357.695i	0.731918	−	0.634211i
$565$	21.4119	+	35.2105i	0.0378972	+	0.0623194i
$566$	5.10712	−	11.1830i	0.00902319	−	0.0197580i
$567$	−209.333	+	45.5375i	−0.369193	+	0.0803131i
$568$	97.8727	+	53.4425i	0.172311	+	0.0940890i
$569$	134.913	+	19.3975i	0.237105	+	0.0340905i	0.259843	−	0.965651i	$-0.416329\pi$
$569$	134.913	+	19.3975i	0.237105	+	0.0340905i	−0.0227379	+	0.999741i	$0.507238\pi$
$570$	275.046	−	141.435i	0.482536	−	0.248132i
$571$	−147.661	−	1027.01i	−0.258601	−	1.79861i	−0.542817	−	0.839851i	$-0.682642\pi$
$571$	−147.661	−	1027.01i	−0.258601	−	1.79861i	0.284216	−	0.958760i	$-0.408267\pi$
$572$	10.8473	−	49.8641i	0.0189638	−	0.0871751i
$573$	−354.217	+	25.3341i	−0.618180	+	0.0442131i
$574$			26.8525i			0.0467814i
$575$	−533.683	+	214.027i	−0.928144	+	0.372221i
$576$	−649.473			−1.12756
$577$	−58.4521	−	817.267i	−0.101303	−	1.41641i	−0.753047	−	0.657967i	$-0.771416\pi$
$577$	−58.4521	−	817.267i	−0.101303	−	1.41641i	0.651743	−	0.758440i	$-0.274038\pi$
$578$	−1675.89	−	364.567i	−2.89946	−	0.630739i
$579$	373.010	−	53.6308i	0.644232	−	0.0926266i
$580$	192.197	+	373.761i	0.331374	+	0.644415i
$581$	1.43138	−	9.95545i	0.00246364	−	0.0171350i
$582$	−297.220	+	544.318i	−0.510687	+	0.935254i
$583$	0.575790	+	2.64686i	0.000987633	+	0.00454007i
$584$	195.898	+	89.4635i	0.335442	+	0.153191i
$585$	−483.364	+	293.939i	−0.826263	+	0.502460i
$586$	561.031	+	647.464i	0.957391	+	1.10489i
$587$	−941.899	−	67.3660i	−1.60460	−	0.114763i	−0.759913	−	0.650025i	$-0.774758\pi$
$587$	−941.899	−	67.3660i	−1.60460	−	0.114763i	−0.844686	+	0.535262i	$0.820213\pi$
$588$	63.1711	+	115.689i	0.107434	+	0.196750i
$589$	165.624	+	75.6377i	0.281194	+	0.128417i
$590$	131.960	+	494.528i	0.223660	+	0.838184i
$591$	2.54588	−	0.747537i	0.00430774	−	0.00126487i
$592$	−309.606	−	413.585i	−0.522983	−	0.698624i
$593$	−266.993	+	715.835i	−0.450241	+	1.20714i	0.491522	+	0.870865i	$0.336441\pi$
$593$	−266.993	+	715.835i	−0.450241	+	1.20714i	−0.941763	+	0.336277i	$0.890832\pi$
$594$	41.9667	−	6.03390i	0.0706510	−	0.0101581i
$595$	−445.071	−	626.387i	−0.748019	−	1.05275i
$596$	−492.134	+	567.953i	−0.825728	+	0.952940i
$597$	124.088	−	124.088i	0.207852	−	0.207852i
$598$	1041.61	−	2.78466i	1.74183	−	0.00465662i
$599$		−	234.762i		−	0.391923i	−0.980612	−	0.195962i	$-0.937217\pi$
$599$		−	234.762i		−	0.391923i	0.980612	−	0.195962i	$-0.0627828\pi$
$600$	−63.5952	−	45.4848i	−0.105992	−	0.0758080i
$601$	230.705	−	148.265i	0.383868	−	0.246697i	−0.334448	−	0.942414i	$-0.608550\pi$
$601$	230.705	−	148.265i	0.383868	−	0.246697i	0.718316	+	0.695717i	$0.244913\pi$
$602$	−440.793	−	329.973i	−0.732214	−	0.548129i
$603$	−176.318	+	472.726i	−0.292401	+	0.783956i
$604$	−270.444	−	38.8839i	−0.447754	−	0.0643774i
$605$	569.665	−	196.502i	0.941595	−	0.324797i
$606$	−59.0572	−	37.9537i	−0.0974540	−	0.0626299i
$607$	35.9596	+	96.4115i	0.0592415	+	0.158833i	0.963199	−	0.268790i	$-0.0866238\pi$
$607$	35.9596	+	96.4115i	0.0592415	+	0.158833i	−0.903957	+	0.427623i	$0.859351\pi$
$608$	−361.620	−	662.258i	−0.594770	−	1.08924i
$609$	−85.9738	+	74.4967i	−0.141172	+	0.122326i
$610$	128.641	+	3.19557i	0.210888	+	0.00523864i
$611$	−1315.72	−	386.331i	−2.15339	−	0.632293i
$612$	369.600	+	990.936i	0.603921	+	1.61918i
$613$	9.71353	+	44.6524i	0.0158459	+	0.0728424i	0.984391	−	0.175996i	$-0.0563147\pi$
$613$	9.71353	+	44.6524i	0.0158459	+	0.0728424i	−0.968545	+	0.248839i	$0.919951\pi$
$614$	−10.1843	−	34.6844i	−0.0165867	−	0.0564892i
$615$	−8.36816	+	6.89477i	−0.0136068	+	0.0112110i
$616$	−3.74623	−	8.20310i	−0.00608154	−	0.0133167i
$617$	−175.779	−	131.586i	−0.284892	−	0.213268i	0.447268	−	0.894400i	$-0.352397\pi$
$617$	−175.779	−	131.586i	−0.284892	−	0.213268i	−0.732160	+	0.681132i	$0.761488\pi$
$618$	467.399	+	101.676i	0.756309	+	0.164525i
$619$	−100.148	−	86.7786i	−0.161790	−	0.140192i	0.570204	−	0.821503i	$-0.306864\pi$
$619$	−100.148	−	86.7786i	−0.161790	−	0.140192i	−0.731993	+	0.681312i	$0.761410\pi$
$620$	−12.3583	−	265.214i	−0.0199328	−	0.427764i
$621$	166.756	+	443.464i	0.268527	+	0.714113i
$622$	526.302	−	526.302i	0.846145	−	0.846145i
$623$	549.922	−	39.3312i	0.882699	−	0.0631319i
$624$	−123.307	−	191.869i	−0.197607	−	0.307483i
$625$	−201.969	−	591.467i	−0.323150	−	0.946348i
$626$	−394.662	−	864.189i	−0.630451	−	1.38049i
$627$	8.63196	+	11.5309i	0.0137671	+	0.0183907i
$628$	−541.405	−	295.629i	−0.862110	−	0.470748i
$629$	−688.329	+	1071.06i	−1.09432	+	1.70280i
$630$	−214.874	+	535.123i	−0.341070	+	0.849401i
$631$	−1.05882	−	0.310898i	−0.00167800	−	0.000492707i	0.280893	−	0.959739i	$-0.409369\pi$
$631$	−1.05882	−	0.310898i	−0.00167800	−	0.000492707i	−0.282571	+	0.959246i	$0.591187\pi$
$632$	−252.029	−	18.0255i	−0.398780	−	0.0285213i
$633$	−30.8394	+	431.191i	−0.0487194	+	0.681187i
$634$	−463.201	+	1577.52i	−0.730601	+	2.48820i
$635$	−75.4492	−	176.696i	−0.118818	−	0.278261i
$636$	−19.9720	−	12.8352i	−0.0314026	−	0.0201812i
$637$	158.590	−	290.437i	0.248965	−	0.455945i
$638$	−28.6223	+	21.4264i	−0.0448625	+	0.0335837i
$639$	302.080	−	137.955i	0.472739	−	0.215893i
$640$	−219.093	+	322.988i	−0.342333	+	0.504669i
$641$	−155.659	+	100.036i	−0.242838	+	0.156062i	−0.656399	−	0.754414i	$-0.727921\pi$
$641$	−155.659	+	100.036i	−0.242838	+	0.156062i	0.413561	+	0.910476i	$0.364285\pi$
$642$	22.1933	+	310.303i	0.0345690	+	0.483338i
$643$	491.081	+	491.081i	0.763734	+	0.763734i	0.976995	−	0.213261i	$-0.0684085\pi$
$643$	491.081	+	491.081i	0.763734	+	0.763734i	−0.213261	+	0.976995i	$0.568409\pi$
$644$	464.388	−	349.578i	0.721099	−	0.542822i
$645$	−10.3490	−	222.091i	−0.0160449	−	0.344328i
$646$	−950.573	+	1097.02i	−1.47148	+	1.69817i
$647$	−135.136	+	621.210i	−0.208866	+	0.960140i	0.746654	+	0.665213i	$0.231659\pi$
$647$	−135.136	+	621.210i	−0.208866	+	0.960140i	−0.955520	+	0.294927i	$0.904705\pi$
$648$	61.3103	−	81.9010i	0.0946147	−	0.126390i
$649$	−21.6831	+	9.90236i	−0.0334101	+	0.0152579i
$650$	−56.2147	+	1130.80i	−0.0864842	+	1.73969i
$651$	68.9535	−	20.2466i	0.105919	−	0.0311007i
$652$	−1359.75	+	295.795i	−2.08551	+	0.453674i
$653$	819.580	−	305.688i	1.25510	−	0.468128i	0.368052	−	0.929805i	$-0.380025\pi$
$653$	819.580	−	305.688i	1.25510	−	0.468128i	0.887048	+	0.461677i	$0.152752\pi$
$654$	56.7314	−	193.209i	0.0867453	−	0.295427i
$655$	266.580	+	280.161i	0.406992	+	0.427727i
$656$	13.5228	+	15.6061i	0.0206140	+	0.0237898i
$657$	562.899	−	307.366i	0.856772	−	0.467833i
$658$	−1309.63	+	488.468i	−1.99032	+	0.742352i
$659$	61.1420	−	95.1388i	0.0927800	−	0.144368i	−0.791761	−	0.610831i	$-0.790835\pi$
$659$	61.1420	−	95.1388i	0.0927800	−	0.144368i	0.884541	+	0.466463i	$0.154472\pi$
$660$	9.19692	−	18.8829i	0.0139347	−	0.0286104i
$661$	−185.899	+	1292.96i	−0.281240	+	1.95606i	0.0116949	+	0.999932i	$0.496277\pi$
$661$	−185.899	+	1292.96i	−0.281240	+	1.95606i	−0.292934	+	0.956133i	$0.594632\pi$
$662$	−1510.37	−	563.338i	−2.28152	−	0.850964i
$663$	−336.831	+	449.953i	−0.508040	+	0.678662i
$664$	2.59682	+	4.04073i	0.00391087	+	0.00608543i
$665$	−430.271	+	50.9932i	−0.647024	+	0.0766814i
$666$	955.453			1.43461
$667$	−302.643	−	260.829i	−0.453738	−	0.391047i
$668$	−775.968	−	775.968i	−1.16163	−	1.16163i
$669$	274.335	+	237.713i	0.410067	+	0.355325i
$670$	584.856	+	823.118i	0.872919	+	1.22853i
$671$	0.852892	+	5.93200i	0.00127108	+	0.00884053i
$672$	−279.040	−	104.076i	−0.415238	−	0.154876i
$673$	665.646	−	498.296i	0.989072	−	0.740410i	0.0232806	−	0.999729i	$-0.492589\pi$
$673$	665.646	−	498.296i	0.989072	−	0.740410i	0.965792	+	0.259319i	$0.0834980\pi$
$674$	−305.266	−	1039.64i	−0.452917	−	1.54249i
$675$	−490.850	+	155.788i	−0.727185	+	0.230796i
$676$	126.720	−	277.477i	0.187455	−	0.410469i
$677$	415.131	−	226.679i	0.613192	−	0.334828i	−0.142461	−	0.989800i	$-0.545501\pi$
$677$	415.131	−	226.679i	0.613192	−	0.334828i	0.755653	+	0.654972i	$0.227320\pi$
$678$	2.19196	−	30.6476i	0.00323297	−	0.0452029i
$679$	656.619	−	568.964i	0.967039	−	0.837944i
$680$	356.527	+	86.8837i	0.524304	+	0.127770i
$681$	161.975	−	354.676i	0.237849	−	0.520816i
$682$	22.0702	−	4.80108i	0.0323610	−	0.00703971i
$683$	175.143	+	95.6354i	0.256432	+	0.140023i	0.602324	−	0.798252i	$-0.294242\pi$
$683$	175.143	+	95.6354i	0.256432	+	0.140023i	−0.345891	+	0.938275i	$0.612423\pi$
$684$	590.290	+	84.8709i	0.862997	+	0.124080i
$685$	1039.43	+	333.457i	1.51742	+	0.486799i
$686$	−156.281	−	1086.96i	−0.227816	−	1.58449i
$687$	−26.0576	+	119.785i	−0.0379295	+	0.174359i
$688$	−422.352	+	30.2072i	−0.613884	+	0.0439058i
$689$			59.6010i			0.0865036i
$690$	416.798	+	100.392i	0.604055	+	0.145495i
$691$	−1013.08			−1.46610			−0.733050	−	0.680174i	$-0.761904\pi$
$691$	−1013.08			−1.46610			−0.733050	+	0.680174i	$0.761904\pi$
$692$	−98.2159	−	1373.24i	−0.141931	−	1.98445i
$693$	−26.2424	−	5.70868i	−0.0378678	−	0.00823763i
$694$	1250.03	−	179.727i	1.80119	−	0.258973i
$695$	176.426	−	90.7225i	0.253850	−	0.130536i
$696$	7.73156	−	53.7742i	0.0111086	−	0.0772617i
$697$	24.3884	−	44.6640i	0.0349905	−	0.0640804i
$698$	199.443	+	916.824i	0.285735	+	1.31350i
$699$	200.482	+	91.5570i	0.286812	+	0.130983i
$700$	353.045	+	523.959i	0.504350	+	0.748513i
$701$	327.196	+	377.605i	0.466756	+	0.538666i	0.939507	−	0.342531i	$-0.111284\pi$
$701$	327.196	+	377.605i	0.466756	+	0.538666i	−0.472750	+	0.881197i	$0.656739\pi$
$702$	930.512	+	66.5516i	1.32552	+	0.0948028i
$703$	344.055	+	630.089i	0.489409	+	0.896286i
$704$	−55.0648	−	25.1473i	−0.0782171	−	0.0357206i
$705$	−488.490	−	282.705i	−0.692894	−	0.401000i
$706$	−189.269	+	55.5744i	−0.268087	+	0.0787173i
$707$	58.9376	+	78.7314i	0.0833630	+	0.111360i
$708$	73.0100	−	195.748i	0.103122	−	0.276480i
$709$	826.271	−	118.800i	1.16540	−	0.167560i	0.467660	−	0.883908i	$-0.345097\pi$
$709$	826.271	−	118.800i	1.16540	−	0.167560i	0.697743	+	0.716349i	$0.254188\pi$
$710$	110.893	−	655.305i	0.156187	−	0.922965i
$711$	−492.763	+	568.679i	−0.693056	+	0.799829i
$712$	−186.175	+	186.175i	−0.261482	+	0.261482i
$713$	105.461	+	229.303i	0.147911	+	0.321603i
$714$			572.921i			0.802410i
$715$	−52.3626	+	6.20571i	−0.0732344	+	0.00867931i
$716$	196.737	−	126.435i	0.274773	−	0.176586i
$717$	−303.161	−	226.944i	−0.422819	−	0.316518i
$718$	−275.523	+	738.705i	−0.383736	+	1.02884i
$719$	284.376	+	40.8871i	0.395516	+	0.0568666i	0.337203	−	0.941432i	$-0.390519\pi$
$719$	284.376	+	40.8871i	0.395516	+	0.0568666i	0.0583123	+	0.998298i	$0.481428\pi$
$720$	144.604	+	419.211i	0.200839	+	0.582238i
$721$	−563.733	−	362.289i	−0.781877	−	0.502482i
$722$	−89.0328	−	238.706i	−0.123314	−	0.330618i
$723$	−165.352	−	302.819i	−0.228702	−	0.418836i
$724$	763.457	−	661.539i	1.05450	−	0.913728i
$725$	300.333	−	313.676i	0.414252	−	0.432657i
$726$	−431.099	−	126.582i	−0.593800	−	0.174355i
$727$	−408.799	−	1096.03i	−0.562310	−	1.50761i	−0.837618	−	0.546256i	$-0.816053\pi$
$727$	−408.799	−	1096.03i	−0.562310	−	1.50761i	0.275308	−	0.961356i	$-0.411220\pi$
$728$	−42.1781	−	193.889i	−0.0579369	−	0.266332i
$729$	−20.3426	−	69.2805i	−0.0279048	−	0.0950349i
$730$	123.333	−	1277.61i	0.168949	−	1.75015i
$731$	433.481	+	949.191i	0.592997	+	1.29848i
$732$	−42.0486	−	31.4772i	−0.0574434	−	0.0430016i
$733$	−555.394	−	120.819i	−0.757700	−	0.164827i	−0.182911	−	0.983129i	$-0.558552\pi$
$733$	−555.394	−	120.819i	−0.757700	−	0.164827i	−0.574789	+	0.818302i	$0.694916\pi$
$734$	−912.147	−	790.380i	−1.24271	−	1.07681i
$735$	91.7210	−	100.687i	0.124791	−	0.136989i
$736$	219.600	−	1022.64i	0.298369	−	1.38945i
$737$	−33.2526	+	33.2526i	−0.0451188	+	0.0451188i
$738$	−38.0923	+	2.72441i	−0.0516155	+	0.00369161i
$739$	−116.686	−	181.567i	−0.157897	−	0.245693i	0.753287	−	0.657692i	$-0.228467\pi$
$739$	−116.686	−	181.567i	−0.157897	−	0.245693i	−0.911184	+	0.411999i	$0.864831\pi$
$740$	587.655	−	866.324i	0.794128	−	1.17071i
$741$	131.657	+	288.289i	0.177675	+	0.389055i
$742$	36.4077	+	48.6349i	0.0490669	+	0.0655457i
$743$	−561.210	−	306.444i	−0.755329	−	0.412441i	0.0549469	−	0.998489i	$-0.482501\pi$
$743$	−561.210	−	306.444i	−0.755329	−	0.412441i	−0.810276	+	0.586048i	$0.800683\pi$
$744$	−18.5546	+	28.8715i	−0.0249390	+	0.0388058i
$745$	720.602	+	289.352i	0.967251	+	0.388392i
$746$	1203.83	+	353.477i	1.61372	+	0.473830i
$747$	14.2677	+	1.02045i	0.0191001	+	0.00136606i
$748$	−7.03242	+	98.3260i	−0.00940162	+	0.131452i
$749$	122.786	−	418.171i	0.163934	−	0.558306i
$750$	−132.675	+	446.711i	−0.176901	+	0.595615i
$751$	−684.046	−	439.610i	−0.910847	−	0.585366i	−0.000858873	−	1.00000i	$-0.500273\pi$
$751$	−684.046	−	439.610i	−0.910847	−	0.585366i	−0.909988	+	0.414634i	$0.863910\pi$
$752$	−515.141	+	943.410i	−0.685028	+	1.25453i
$753$	−262.426	+	196.450i	−0.348508	+	0.260890i
$754$	−715.597	+	326.802i	−0.949067	+	0.433424i
$755$	53.1422	+	277.273i	0.0703870	+	0.367249i
$756$	437.943	−	281.449i	0.579289	−	0.372287i
$757$	−58.9472	−	824.190i	−0.0778695	−	1.08876i	−0.874735	−	0.484601i	$-0.838965\pi$
$757$	−58.9472	−	824.190i	−0.0778695	−	1.08876i	0.796866	−	0.604157i	$-0.206490\pi$
$758$	98.5953	+	98.5953i	0.130073	+	0.130073i
$759$	−1.37114	+	19.9193i	−0.00180651	+	0.0262441i
$760$	139.344	−	152.965i	0.183348	−	0.201270i
$761$	53.9647	−	62.2786i	0.0709129	−	0.0818378i	−0.719185	−	0.694819i	$-0.755484\pi$
$761$	53.9647	−	62.2786i	0.0709129	−	0.0818378i	0.790097	+	0.612981i	$0.210030\pi$
$762$	−30.4503	+	139.978i	−0.0399610	+	0.183698i
$763$	−169.057	+	225.834i	−0.221569	+	0.295981i
$764$	−1246.57	+	569.291i	−1.63164	+	0.745145i
$765$	843.419	−	694.918i	1.10251	−	0.908389i
$766$	1335.82	−	392.232i	1.74389	−	0.512052i
$767$	−512.505	+	111.489i	−0.668195	+	0.145357i
$768$	−138.274	+	51.5736i	−0.180045	+	0.0671532i
$769$	129.373	−	440.602i	0.168235	−	0.572955i	−0.831610	−	0.555359i	$-0.812581\pi$
$769$	129.373	−	440.602i	0.168235	−	0.572955i	0.999845	−	0.0175955i	$-0.00560110\pi$
$770$	−38.9375	+	37.0499i	−0.0505682	+	0.0481168i
$771$	54.2079	+	62.5592i	0.0703085	+	0.0811403i
$772$	1276.36	−	696.947i	1.65332	−	0.902781i
$773$	840.021	−	313.312i	1.08670	−	0.405319i	0.258651	−	0.965971i	$-0.416722\pi$
$773$	840.021	−	313.312i	1.08670	−	0.405319i	0.828052	+	0.560652i	$0.189449\pi$
$774$	423.369	−	658.775i	0.546989	−	0.851131i
$775$	−254.899	+	101.434i	−0.328901	+	0.130882i
$776$	−59.0493	+	410.697i	−0.0760944	+	0.529248i
$777$	265.485	+	99.0209i	0.341680	+	0.127440i
$778$	−253.882	+	339.147i	−0.326327	+	0.435922i
$779$	−15.5135	−	24.1395i	−0.0199147	−	0.0309878i
$780$	286.052	−	362.970i	0.366733	−	0.465347i
$781$	30.9531			0.0396326
$782$	−1990.88	+	291.680i	−2.54588	+	0.372992i
$783$	−253.021	−	253.021i	−0.323143	−	0.323143i
$784$	−196.036	−	169.866i	−0.250046	−	0.216666i
$785$	−106.350	+	628.459i	−0.135478	+	0.800585i
$786$	−41.0350	−	285.405i	−0.0522074	−	0.363110i
$787$	393.127	+	146.629i	0.499526	+	0.186314i	0.586582	−	0.809890i	$-0.300473\pi$
$787$	393.127	+	146.629i	0.499526	+	0.186314i	−0.0870558	+	0.996203i	$0.527746\pi$
$788$	8.19698	−	6.13618i	0.0104023	−	0.00778703i
$789$	−27.9945	−	95.3405i	−0.0354810	−	0.120837i
$790$	388.258	+	1455.03i	0.491466	+	1.84181i
$791$	−17.8815	+	39.1551i	−0.0226062	+	0.0495008i
$792$	11.2566	−	6.14657i	0.0142129	−	0.00776082i
$793$	−9.40707	+	131.528i	−0.0118626	+	0.165861i
$794$	67.8740	−	58.8132i	0.0854837	−	0.0740720i
$795$	−5.80811	+	23.8336i	−0.00730580	+	0.0299793i
$796$	281.320	−	616.006i	0.353417	−	0.773876i
$797$	803.015	−	174.685i	1.00755	−	0.219178i	0.321636	−	0.946863i	$-0.395767\pi$
$797$	803.015	−	174.685i	1.00755	−	0.219178i	0.685911	+	0.727685i	$0.259404\pi$
$798$	283.537	+	154.823i	0.355310	+	0.194014i
$799$	2621.97	+	376.982i	3.28156	+	0.471817i
$800$	1097.55	+	296.527i	1.37194	+	0.370658i
$801$	111.588	+	776.113i	0.139311	+	0.968930i
$802$	−304.248	+	1398.61i	−0.379362	+	1.74390i
$803$	59.6258	−	4.26452i	0.0742538	−	0.00531073i
$804$		−	412.158i		−	0.512634i
$805$	−497.943	−	335.830i	−0.618562	−	0.417180i
$806$	496.968			0.616586
$807$	36.4971	+	510.297i	0.0452257	+	0.632338i
$808$	−45.8937	−	9.98356i	−0.0567991	−	0.0123559i
$809$	−1331.75	+	191.477i	−1.64617	+	0.236684i	−0.902135	−	0.431454i	$-0.858001\pi$
$809$	−1331.75	+	191.477i	−1.64617	+	0.236684i	−0.744038	+	0.668138i	$0.767092\pi$
$810$	−580.608	−	186.263i	−0.716800	−	0.229955i
$811$	−10.1621	+	70.6790i	−0.0125303	+	0.0871505i	−0.995127	−	0.0986016i	$-0.968563\pi$
$811$	−10.1621	+	70.6790i	−0.0125303	+	0.0871505i	0.982597	+	0.185752i	$0.0594721\pi$
$812$	−210.390	+	385.300i	−0.259100	+	0.474507i
$813$	29.4939	+	135.581i	0.0362778	+	0.166766i
$814$	81.0070	+	36.9947i	0.0995172	+	0.0454480i
$815$	747.094	+	1228.55i	0.916680	+	1.50742i
$816$	288.519	+	332.969i	0.353578	+	0.408050i
$817$	586.893	+	41.9755i	0.718352	+	0.0513775i
$818$	−885.141	−	1621.01i	−1.08208	−	1.98168i
$819$	−537.515	−	245.475i	−0.656307	−	0.299725i
$820$	−20.9585	+	36.2145i	−0.0255591	+	0.0441640i
$821$	764.086	−	224.356i	0.930678	−	0.273272i	0.218957	−	0.975734i	$-0.429734\pi$
$821$	764.086	−	224.356i	0.930678	−	0.273272i	0.711720	+	0.702463i	$0.247916\pi$
$822$	−487.752	−	651.560i	−0.593372	−	0.792653i
$823$	−139.109	+	372.964i	−0.169026	+	0.453177i	−0.993651	−	0.112503i	$-0.964113\pi$
$823$	−139.109	+	372.964i	−0.169026	+	0.453177i	0.824625	+	0.565679i	$0.191386\pi$
$824$	316.761	−	45.5434i	0.384419	−	0.0552711i
$825$	−21.5438	−	2.62116i	−0.0261137	−	0.00317716i
$826$	−350.105	+	404.043i	−0.423856	+	0.489156i
$827$	307.923	−	307.923i	0.372338	−	0.372338i	−0.495990	−	0.868328i	$-0.665195\pi$
$827$	307.923	−	307.923i	0.372338	−	0.372338i	0.868328	+	0.495990i	$0.165195\pi$
$828$	543.017	+	623.300i	0.655818	+	0.752778i
$829$			343.283i			0.414092i	0.978331	+	0.207046i	$0.0663851\pi$
$829$			343.283i			0.414092i	−0.978331	+	0.207046i	$0.933615\pi$
$830$	17.7196	−	22.4843i	0.0213489	−	0.0270895i
$831$	−304.170	+	195.478i	−0.366029	+	0.235233i
$832$	−1066.29	−	798.213i	−1.28160	−	0.959390i
$833$	−223.391	+	598.935i	−0.268177	+	0.719010i
$834$	−146.409	−	21.0505i	−0.175551	−	0.0252404i
$835$	−496.514	+	1019.43i	−0.594628	+	1.22087i
$836$	46.7609	+	30.0514i	0.0559341	+	0.0359466i
$837$	78.9951	+	211.794i	0.0943789	+	0.253040i
$838$	591.312	+	1082.91i	0.705622	+	1.29225i
$839$	97.5822	−	84.5555i	0.116308	−	0.100781i	−0.594765	−	0.803899i	$-0.702755\pi$
$839$	97.5822	−	84.5555i	0.116308	−	0.100781i	0.711073	+	0.703118i	$0.248210\pi$
$840$	2.02811	−	81.6438i	0.00241441	−	0.0971950i
$841$	−517.409	−	151.925i	−0.615230	−	0.180648i
$842$	−250.341	−	671.191i	−0.297317	−	0.797139i
$843$	19.3630	+	89.0104i	0.0229692	+	0.105588i
$844$	469.991	+	1600.64i	0.556862	+	1.89650i
$845$	−313.739	−	30.2864i	−0.371289	−	0.0358419i
$846$	−825.800	−	1808.25i	−0.976123	−	2.13741i
$847$	503.892	+	377.209i	0.594914	+	0.445347i
$848$	45.6516	+	9.93090i	0.0538344	+	0.0117110i
$849$	3.91874	+	3.39561i	0.00461571	+	0.00399954i
$850$	−203.386	−	2177.62i	−0.239278	−	2.56191i
$851$	−208.933	+	972.964i	−0.245514	+	1.14332i
$852$	−191.828	+	191.828i	−0.225150	+	0.225150i
$853$	−46.3597	+	3.31571i	−0.0543490	+	0.00388712i	−0.0984872	−	0.995138i	$-0.531400\pi$
$853$	−46.3597	+	3.31571i	−0.0543490	+	0.00388712i	0.0441382	+	0.999025i	$0.485946\pi$
$854$	72.6685	+	113.074i	0.0850919	+	0.132406i
$855$	−115.992	−	605.196i	−0.135663	−	0.707832i
$856$	86.4616	+	189.325i	0.101007	+	0.221174i
$857$	301.978	+	403.396i	0.352367	+	0.470707i	0.941347	−	0.337441i	$-0.109561\pi$
$857$	301.978	+	403.396i	0.352367	+	0.470707i	−0.588980	+	0.808148i	$0.700470\pi$
$858$	34.5056	+	18.8415i	0.0402163	+	0.0219597i
$859$	−183.181	+	285.035i	−0.213249	+	0.331822i	−0.931356	−	0.364111i	$-0.881373\pi$
$859$	−183.181	+	285.035i	−0.213249	+	0.331822i	0.718106	+	0.695934i	$0.245009\pi$
$860$	−336.927	−	789.057i	−0.391776	−	0.917508i
$861$	−10.8668	−	3.19078i	−0.0126211	−	0.00370590i
$862$	−547.100	−	39.1294i	−0.634687	−	0.0453937i
$863$	23.1435	−	323.589i	0.0268175	−	0.374958i	−0.966266	−	0.257547i	$-0.917086\pi$
$863$	23.1435	−	323.589i	0.0268175	−	0.374958i	0.993083	−	0.117411i	$-0.0374596\pi$
$864$	263.919	−	898.824i	0.305461	−	1.04031i
$865$	−1308.30	+	558.642i	−1.51248	+	0.645829i
$866$	1849.13	+	1188.36i	2.13525	+	1.37224i
$867$	346.673	−	634.885i	0.399854	−	0.732278i
$868$	222.010	−	166.195i	0.255772	−	0.191468i
$869$	−63.7973	+	29.1352i	−0.0734146	+	0.0335273i
$870$	−318.004	+	60.9486i	−0.365521	+	0.0700558i
$871$	−870.460	+	559.411i	−0.999380	+	0.642263i
$872$	−9.61086	−	134.377i	−0.0110216	−	0.154102i
$873$	873.736	+	873.736i	1.00084	+	1.00084i
$874$	−393.652	+	1064.10i	−0.450403	+	1.21751i
$875$	392.851	−	521.402i	0.448972	−	0.595888i
$876$	−343.095	+	395.953i	−0.391661	+	0.452001i
$877$	−36.7090	+	168.749i	−0.0418575	+	0.192416i	−0.993328	−	0.115325i	$-0.963209\pi$
$877$	−36.7090	+	168.749i	−0.0418575	+	0.192416i	0.951470	+	0.307740i	$0.0995728\pi$
$878$	−428.357	+	572.218i	−0.487878	+	0.651729i
$879$	−328.683	+	150.105i	−0.373929	+	0.170768i
$880$	−3.97153	+	41.1413i	−0.00451310	+	0.0467515i
$881$	533.627	−	156.687i	0.605706	−	0.177851i	0.0355227	−	0.999369i	$-0.488690\pi$
$881$	533.627	−	156.687i	0.605706	−	0.177851i	0.570183	+	0.821518i	$0.306872\pi$
$882$	468.755	−	101.971i	0.531468	−	0.115614i
$883$	357.664	−	133.402i	0.405056	−	0.151078i	−0.138675	−	0.990338i	$-0.544284\pi$
$883$	357.664	−	133.402i	0.405056	−	0.151078i	0.543730	+	0.839260i	$0.317011\pi$
$884$	−611.076	+	2081.13i	−0.691263	+	2.35422i
$885$	−215.808	−	5.36086i	−0.243851	−	0.00605747i
$886$	−1204.62	−	1390.21i	−1.35962	−	1.56908i
$887$	1130.54	−	617.321i	1.27456	−	0.695965i	0.307756	−	0.951465i	$-0.400422\pi$
$887$	1130.54	−	617.321i	1.27456	−	0.695965i	0.966809	+	0.255501i	$0.0822403\pi$
$888$	−126.785	+	47.2885i	−0.142776	+	0.0532528i
$889$	108.499	−	168.828i	0.122047	−	0.189908i
$890$	1410.79	+	687.127i	1.58516	+	0.772053i
$891$	4.04142	−	28.1087i	0.00453582	−	0.0315473i
$892$	1312.48	+	489.531i	1.47139	+	0.548802i
$893$	895.113	−	1195.73i	1.00237	−	1.33900i
$894$	−313.017	−	487.064i	−0.350131	−	0.544814i
$895$	−189.792	−	149.573i	−0.212058	−	0.167120i
$896$	−407.667			−0.454985
$897$	−122.644	+	421.855i	−0.136727	+	0.470296i
$898$	−1417.47	−	1417.47i	−1.57847	−	1.57847i
$899$	−144.061	−	124.830i	−0.160246	−	0.138854i
$900$	−707.454	+	553.980i	−0.786060	+	0.615533i
$901$	−16.3852	−	113.962i	−0.0181856	−	0.126483i
$902$	−3.33509	−	1.24393i	−0.00369744	−	0.00137908i
$903$	185.913	−	139.172i	0.205883	−	0.154122i
$904$	−5.79146	−	19.7239i	−0.00640649	−	0.0218185i
$905$	−903.438	−	522.849i	−0.998274	−	0.577734i
$906$	87.4434	−	191.474i	0.0965159	−	0.211340i
$907$	−1447.98	+	790.655i	−1.59645	+	0.871725i	−0.598966	+	0.800774i	$0.704422\pi$
$907$	−1447.98	+	790.655i	−1.59645	+	0.871725i	−0.997480	+	0.0709509i	$0.977397\pi$
$908$	107.342	−	1500.83i	0.118218	−	1.65290i
$909$	−105.707	+	91.5952i	−0.116289	+	0.100765i
$910$	−1010.45	+	614.466i	−1.11038	+	0.675237i
$911$	358.396	−	784.779i	0.393410	−	0.861448i	−0.604486	−	0.796616i	$-0.706622\pi$
$911$	358.396	−	784.779i	0.393410	−	0.861448i	0.997896	−	0.0648321i	$-0.0206512\pi$
$912$	242.753	−	52.8078i	0.266177	−	0.0579033i
$913$	1.17016	+	0.638957i	0.00128167	+	0.000699844i
$914$	−544.055	−	78.2232i	−0.595246	−	0.0855834i
$915$	−16.5791	+	51.6794i	−0.0181193	+	0.0564802i
$916$	67.3235	+	468.245i	0.0734973	+	0.511185i
$917$	−85.8648	+	394.714i	−0.0936367	+	0.430441i
$918$	−1797.50	+	128.560i	−1.95807	+	0.140044i
$919$		−	1695.83i		−	1.84530i	−0.385636	−	0.922651i	$-0.626018\pi$
$919$		−	1695.83i		−	1.84530i	0.385636	−	0.922651i	$-0.373982\pi$
$920$	284.742	−	34.5181i	0.309502	−	0.0375196i
$921$	15.2464			0.0165541
$922$	128.791	+	1800.73i	0.139687	+	1.95307i
$923$	665.496	+	144.770i	0.721015	+	0.156847i
$924$	21.7155	−	3.12222i	0.0235017	−	0.00337903i
$925$	−1044.24	−	282.123i	−1.12891	−	0.304998i
$926$	−53.7731	+	374.000i	−0.0580703	+	0.403888i
$927$	456.738	−	836.453i	0.492706	−	0.902323i
$928$	167.918	+	771.908i	0.180946	+	0.831797i
$929$	−1258.52	−	574.748i	−1.35471	−	0.618674i	−0.400080	−	0.916480i	$-0.631018\pi$
$929$	−1258.52	−	574.748i	−1.35471	−	0.618674i	−0.954626	+	0.297807i	$0.903745\pi$
$930$	198.730	+	48.4295i	0.213689	+	0.0520747i
$931$	236.043	+	272.409i	0.253538	+	0.292598i
$932$	848.352	+	60.6753i	0.910249	+	0.0651023i
$933$	150.448	+	275.524i	0.161252	+	0.295310i
$934$	−1015.09	−	463.576i	−1.08682	−	0.496335i
$935$	98.4151	−	26.2610i	0.105257	−	0.0280867i
$936$	270.767	−	79.5043i	0.289281	−	0.0849405i
$937$	207.642	+	277.377i	0.221603	+	0.296027i	0.897540	−	0.440932i	$-0.145352\pi$
$937$	207.642	+	277.377i	0.221603	+	0.296027i	−0.675938	+	0.736959i	$0.736261\pi$
$938$	−368.583	+	988.210i	−0.392946	+	1.05353i
$939$	396.620	−	57.0253i	0.422385	−	0.0607298i
$940$	−2147.48	−	363.404i	−2.28455	−	0.386600i
$941$	−50.2834	+	58.0301i	−0.0534361	+	0.0616685i	−0.781838	−	0.623481i	$-0.785718\pi$
$941$	−50.2834	+	58.0301i	−0.0534361	+	0.0616685i	0.728402	+	0.685150i	$0.240263\pi$
$942$	336.044	−	336.044i	0.356735	−	0.356735i
$943$	5.55544	−	39.3861i	0.00589124	−	0.0417668i
$944$			411.132i			0.435521i
$945$	−422.483	−	332.953i	−0.447072	−	0.352332i
$946$	61.4023	−	39.4609i	0.0649073	−	0.0417134i
$947$	579.645	+	433.917i	0.612085	+	0.458201i	0.859799	−	0.510632i	$-0.170588\pi$
$947$	579.645	+	433.917i	0.612085	+	0.458201i	−0.247714	+	0.968833i	$0.579679\pi$
$948$	214.814	−	575.938i	0.226597	−	0.607530i
$949$	1301.91	+	187.186i	1.37188	+	0.197246i
$950$	−1132.66	−	487.813i	−1.19227	−	0.513487i
$951$	−583.356	−	374.900i	−0.613413	−	0.394217i
$952$	133.951	+	359.136i	0.140704	+	0.377243i
$953$	−301.850	−	552.796i	−0.316736	−	0.580059i	0.670006	−	0.742356i	$-0.266292\pi$
$953$	−301.850	−	552.796i	−0.316736	−	0.580059i	−0.986742	+	0.162297i	$0.948110\pi$
$954$	−65.2983	+	56.5813i	−0.0684469	+	0.0593096i
$955$	976.112	+	1025.84i	1.02211	+	1.07418i
$956$	−1402.19	−	411.720i	−1.46672	−	0.430669i
$957$	−5.26984	−	14.1290i	−0.00550663	−	0.0147638i
$958$	−515.033	−	2367.57i	−0.537613	−	2.47137i
$959$	321.238	+	1094.04i	0.334972	+	1.14081i
$960$	−348.607	−	423.103i	−0.363132	−	0.440733i
$961$	−349.190	−	764.619i	−0.363361	−	0.795649i
$962$	1568.64	+	1174.27i	1.63060	+	1.22065i
$963$	605.664	+	131.754i	0.628935	+	0.136816i
$964$	−1006.24	−	871.908i	−1.04381	−	0.904469i
$965$	−1110.85	−	1011.93i	−1.15114	−	1.04863i
$966$	157.615	+	419.155i	0.163162	+	0.433908i
$967$	695.076	−	695.076i	0.718796	−	0.718796i	−0.249562	−	0.968359i	$-0.580287\pi$
$967$	695.076	−	695.076i	0.718796	−	0.718796i	0.968359	+	0.249562i	$0.0802868\pi$
$968$	−299.830	+	21.4442i	−0.309741	+	0.0221531i
$969$	−330.994	−	515.036i	−0.341583	−	0.531513i
$970$	2428.73	−	465.491i	2.50385	−	0.479887i
$971$	−709.151	−	1552.83i	−0.730331	−	1.59920i	−0.798834	−	0.601551i	$-0.794550\pi$
$971$	−709.151	−	1552.83i	−0.730331	−	1.59920i	0.0685033	−	0.997651i	$-0.478178\pi$
$972$	686.766	+	917.412i	0.706549	+	0.943839i
$973$	181.872	+	99.3098i	0.186919	+	0.102066i
$974$	93.2423	−	145.088i	0.0957313	−	0.148961i
$975$	−450.936	−	157.117i	−0.462498	−	0.161146i
$976$	99.1769	+	29.1210i	0.101616	+	0.0298370i
$977$	−1266.29	−	90.5665i	−1.29610	−	0.0926986i	−0.593817	−	0.804600i	$-0.702380\pi$
$977$	−1266.29	−	90.5665i	−1.29610	−	0.0926986i	−0.702279	+	0.711902i	$0.747834\pi$
$978$	76.4807	−	1069.34i	0.0782012	−	1.09340i
$979$	−20.5898	+	70.1225i	−0.0210315	+	0.0716266i
$980$	195.850	−	487.745i	0.199847	−	0.497699i
$981$	−337.514	−	216.907i	−0.344051	−	0.221108i
$982$	−1138.63	+	2085.24i	−1.15950	+	2.12346i
$983$	−208.918	+	156.394i	−0.212531	+	0.159098i	−0.700240	−	0.713908i	$-0.746924\pi$
$983$	−208.918	+	156.394i	−0.212531	+	0.159098i	0.487709	+	0.873006i	$0.337833\pi$
$984$	4.91987	−	2.24683i	0.00499987	−	0.00228336i
$985$	−8.75579	−	5.93932i	−0.00888913	−	0.00602977i
$986$	1278.43	−	821.598i	1.29658	−	0.833263i
$987$	−42.0567	−	588.030i	−0.0426107	−	0.595775i
$988$	864.814	+	864.814i	0.875318	+	0.875318i
$989$	578.269	+	575.185i	0.584701	+	0.581583i
$990$	−56.5085	−	51.4767i	−0.0570793	−	0.0519967i
$991$	−107.950	+	124.581i	−0.108931	+	0.125713i	−0.807597	−	0.589735i	$-0.799232\pi$
$991$	−107.950	+	124.581i	−0.108931	+	0.125713i	0.698666	+	0.715448i	$0.253777\pi$
$992$	106.078	−	487.631i	0.106933	−	0.491564i
$993$	407.445	−	544.283i	0.410317	−	0.548119i
$994$	631.484	−	288.389i	0.635296	−	0.290130i
$995$	−696.508	−	67.2366i	−0.700008	−	0.0675745i
$996$	−11.2118	+	3.29209i	−0.0112568	+	0.00330531i
$997$	1548.00	−	336.747i	1.55266	−	0.337760i	0.647241	−	0.762285i	$-0.275923\pi$
$997$	1548.00	−	336.747i	1.55266	−	0.337760i	0.905416	+	0.424525i	$0.139559\pi$
$998$	1924.00	−	717.614i	1.92785	−	0.719052i
$999$	−251.099	+	855.164i	−0.251350	+	0.856020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.k.a.108.20	yes	440
5.2	odd	4	inner	115.3.k.a.62.3	yes	440
23.13	even	11	inner	115.3.k.a.13.3	✓	440
115.82	odd	44	inner	115.3.k.a.82.20	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.k.a.13.3	✓	440	23.13	even	11	inner
115.3.k.a.62.3	yes	440	5.2	odd	4	inner
115.3.k.a.82.20	yes	440	115.82	odd	44	inner
115.3.k.a.108.20	yes	440	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.k (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212094 + 2.96546i) q^{2} +(-1.22528 - 0.266542i) q^{3} +(-4.78967 + 0.688650i) q^{4} +(2.28653 + 4.44655i) q^{5} +(0.530547 - 3.69003i) q^{6} +(-2.50296 + 4.58383i) q^{7} +(-0.530168 - 2.43714i) q^{8} +(-6.75643 - 3.08556i) q^{9} +(-12.7011 + 7.72369i) q^{10} +(-0.453365 - 0.523211i) q^{11} +(6.05222 + 0.432863i) q^{12} +(-7.30032 - 13.3695i) q^{13} +(-14.1240 - 6.45021i) q^{14} +(-1.61643 - 6.05770i) q^{15} +(-11.4568 + 3.36403i) q^{16} +(17.6342 + 23.5566i) q^{17} +(7.71710 - 20.6903i) q^{18} +(16.4235 - 2.36134i) q^{19} +(-14.0138 - 19.7229i) q^{20} +(4.28860 - 4.94930i) q^{21} +(1.45540 - 1.45540i) q^{22} +(19.3820 + 12.3830i) q^{23} +3.12748i q^{24} +(-14.5436 + 20.3343i) q^{25} +(38.0985 - 24.4844i) q^{26} +(16.4905 + 12.3446i) q^{27} +(8.83169 - 23.6787i) q^{28} +(-17.1941 - 2.47213i) q^{29} +(17.6210 - 6.07826i) q^{30} +(9.23156 + 5.93276i) q^{31} +(-15.8923 - 42.6088i) q^{32} +(0.416039 + 0.761919i) q^{33} +(-66.1160 + 57.2898i) q^{34} +(-26.1053 - 0.648479i) q^{35} +(34.4859 + 10.1260i) q^{36} +(15.1203 + 40.5391i) q^{37} +(10.4858 + 48.2023i) q^{38} +(5.38136 + 18.3272i) q^{39} +(9.62463 - 7.93001i) q^{40} +(-0.718415 - 1.57311i) q^{41} +(15.5865 + 11.6679i) q^{42} +(34.6512 + 7.53792i) q^{43} +(2.53178 + 2.19380i) q^{44} +(-1.72868 - 37.0980i) q^{45} +(-32.6104 + 60.1029i) q^{46} +(63.6541 - 63.6541i) q^{47} +(14.9345 - 1.06813i) q^{48} +(11.7447 + 18.2752i) q^{49} +(-63.3851 - 38.8156i) q^{50} +(-15.3280 - 33.5636i) q^{51} +(44.1731 + 59.0083i) q^{52} +(-3.43406 - 1.87514i) q^{53} +(-33.1099 + 51.5200i) q^{54} +(1.28985 - 3.21225i) q^{55} +(12.4984 + 3.66987i) q^{56} +(-20.7527 - 1.48426i) q^{57} +(3.68426 - 51.5126i) q^{58} +(9.70051 - 33.0369i) q^{59} +(11.9138 + 27.9012i) q^{60} +(-7.28236 - 4.68009i) q^{61} +(-15.6354 + 28.6341i) q^{62} +(31.0547 - 23.2473i) q^{63} +(79.5381 - 36.3239i) q^{64} +(42.7559 - 63.0311i) q^{65} +(-2.17120 + 1.39534i) q^{66} +(-4.84584 - 67.7537i) q^{67} +(-100.684 - 100.684i) q^{68} +(-20.4477 - 20.3387i) q^{69} +(-3.61373 - 77.5516i) q^{70} +(-29.2788 + 33.7896i) q^{71} +(-3.93790 + 18.1022i) q^{72} +(-51.7453 + 69.1237i) q^{73} +(-117.010 + 53.4367i) q^{74} +(23.2398 - 21.0387i) q^{75} +(-77.0369 + 22.6201i) q^{76} +(3.53306 - 0.768570i) q^{77} +(-53.2072 + 19.8453i) q^{78} +(28.5413 - 97.2029i) q^{79} +(-41.1547 - 43.2515i) q^{80} +(26.8617 + 31.0001i) q^{81} +(4.51262 - 2.46408i) q^{82} +(-1.80438 + 0.672999i) q^{83} +(-17.1326 + 26.6589i) q^{84} +(-64.4243 + 132.274i) q^{85} +(-15.0041 + 104.356i) q^{86} +(20.4085 + 7.61200i) q^{87} +(-1.03478 + 1.38230i) q^{88} +(-57.0723 - 88.8062i) q^{89} +(109.646 - 12.9946i) q^{90} +79.5561 q^{91} +(-101.361 - 45.9629i) q^{92} +(-9.72987 - 9.72987i) q^{93} +(202.264 + 175.263i) q^{94} +(48.0525 + 67.6285i) q^{95} +(8.11536 + 56.4435i) q^{96} +(-155.869 - 58.1361i) q^{97} +(-51.7033 + 38.7046i) q^{98} +(1.44873 + 4.93392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) \) 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Introduction

L-functions

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