LMFDB - Embedded newform 117.3.n.a.38.2

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			38.2
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.77860 + 3.08062i) q^{2} +(2.89850 - 0.773763i) q^{3} +(-4.32683 - 7.49428i) q^{4} +(-4.26663 - 7.39002i) q^{5} +(-2.77159 + 10.3054i) q^{6} +(7.99720 + 4.61719i) q^{7} +16.5540 q^{8} +(7.80258 - 4.48550i) q^{9} +30.3545 q^{10} +(1.10564 - 1.91503i) q^{11} +(-18.3401 - 18.3742i) q^{12} +(12.8550 - 1.93598i) q^{13} +(-28.4476 + 16.4242i) q^{14} +(-18.0849 - 18.1186i) q^{15} +(-12.1356 + 21.0194i) q^{16} +4.52923i q^{17} +(-0.0595170 + 32.0147i) q^{18} -20.6555i q^{19} +(-36.9219 + 63.9507i) q^{20} +(26.7525 + 7.19497i) q^{21} +(3.93299 + 6.81214i) q^{22} +(14.0417 - 8.10700i) q^{23} +(47.9816 - 12.8088i) q^{24} +(-23.9082 + 41.4103i) q^{25} +(-16.8999 + 43.0449i) q^{26} +(19.1450 - 19.0386i) q^{27} -79.9111i q^{28} +(-28.3224 - 16.3520i) q^{29} +(87.9824 - 23.4872i) q^{30} +(-31.8459 + 18.3862i) q^{31} +(-10.0606 - 17.4255i) q^{32} +(1.72292 - 6.40622i) q^{33} +(-13.9529 - 8.05569i) q^{34} -78.7993i q^{35} +(-67.3760 - 39.0668i) q^{36} +3.67771i q^{37} +(63.6317 + 36.7378i) q^{38} +(35.7623 - 15.5582i) q^{39} +(-70.6296 - 122.334i) q^{40} +(22.5628 + 39.0799i) q^{41} +(-69.7469 + 69.6174i) q^{42} +(11.1768 - 19.3588i) q^{43} -19.1357 q^{44} +(-66.4387 - 38.5232i) q^{45} +57.6764i q^{46} +(7.92578 - 13.7278i) q^{47} +(-18.9108 + 70.3147i) q^{48} +(18.1368 + 31.4139i) q^{49} +(-85.0463 - 147.305i) q^{50} +(3.50455 + 13.1280i) q^{51} +(-70.1303 - 87.9627i) q^{52} +79.1568i q^{53} +(24.5993 + 92.8407i) q^{54} -18.8695 q^{55} +(132.385 + 76.4328i) q^{56} +(-15.9824 - 59.8698i) q^{57} +(100.748 - 58.1671i) q^{58} +(15.2856 + 26.4755i) q^{59} +(-57.5355 + 213.930i) q^{60} +(-0.328289 + 0.568613i) q^{61} -130.807i q^{62} +(83.1092 + 0.154504i) q^{63} -25.5091 q^{64} +(-69.1546 - 86.7389i) q^{65} +(16.6708 + 16.7018i) q^{66} +(-8.00214 + 4.62004i) q^{67} +(33.9434 - 19.5972i) q^{68} +(34.4271 - 34.3631i) q^{69} +(242.751 + 140.152i) q^{70} -21.4350 q^{71} +(129.164 - 74.2528i) q^{72} +59.7788i q^{73} +(-11.3296 - 6.54116i) q^{74} +(-37.2562 + 138.527i) q^{75} +(-154.798 + 89.3726i) q^{76} +(17.6841 - 10.2099i) q^{77} +(-15.6779 + 137.842i) q^{78} +(-64.5091 + 111.733i) q^{79} +207.112 q^{80} +(40.7605 - 69.9970i) q^{81} -160.521 q^{82} +(-48.6117 + 84.1979i) q^{83} +(-61.8323 - 231.622i) q^{84} +(33.4711 - 19.3246i) q^{85} +(39.7581 + 68.8630i) q^{86} +(-94.7450 - 25.4813i) q^{87} +(18.3028 - 31.7013i) q^{88} +46.5189 q^{89} +(236.843 - 136.155i) q^{90} +(111.743 + 43.8717i) q^{91} +(-121.512 - 70.1552i) q^{92} +(-78.0787 + 77.9337i) q^{93} +(28.1936 + 48.8327i) q^{94} +(-152.644 + 88.1291i) q^{95} +(-42.6439 - 42.7233i) q^{96} +(9.25813 + 5.34518i) q^{97} -129.033 q^{98} +(0.0369980 - 19.9015i) 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 $

$2$	−1.77860	+	3.08062i	−0.889299	+	1.54031i	−0.0485941	+	0.998819i	$0.515474\pi$
$2$	−1.77860	+	3.08062i	−0.889299	+	1.54031i	−0.840705	+	0.541493i	$0.817859\pi$
$3$	2.89850	−	0.773763i	0.966166	−	0.257921i
$3$	2.89850	−	0.773763i	0.966166	−	0.257921i
$4$	−4.32683	−	7.49428i	−1.08171	−	1.87357i
$5$	−4.26663	−	7.39002i	−0.853326	−	1.47800i	−0.878190	−	0.478313i	$-0.841249\pi$
$5$	−4.26663	−	7.39002i	−0.853326	−	1.47800i	0.0248639	−	0.999691i	$-0.492085\pi$
$6$	−2.77159	+	10.3054i	−0.461932	+	1.71757i
$7$	7.99720	+	4.61719i	1.14246	+	0.659598i	0.947038	−	0.321122i	$-0.104060\pi$
$7$	7.99720	+	4.61719i	1.14246	+	0.659598i	0.195420	+	0.980720i	$0.437393\pi$
$8$	16.5540			2.06925
$9$	7.80258	−	4.48550i	0.866953	−	0.498389i
$10$	30.3545			3.03545
$11$	1.10564	−	1.91503i	0.100513	−	0.174094i	−0.811383	−	0.584515i	$-0.801285\pi$
$11$	1.10564	−	1.91503i	0.100513	−	0.174094i	0.911896	+	0.410421i	$0.134618\pi$
$12$	−18.3401	−	18.3742i	−1.52834	−	1.53119i
$13$	12.8550	−	1.93598i	0.988849	−	0.148921i
$13$	12.8550	−	1.93598i	0.988849	−	0.148921i
$14$	−28.4476	+	16.4242i	−2.03197	+	1.17316i
$15$	−18.0849	−	18.1186i	−1.20566	−	1.20791i
$16$	−12.1356	+	21.0194i	−0.758472	+	1.31371i
$17$			4.52923i			0.266425i	0.991087	+	0.133213i	$0.0425293\pi$
$17$			4.52923i			0.266425i	−0.991087	+	0.133213i	$0.957471\pi$
$18$	−0.0595170	+	32.0147i	−0.00330650	+	1.77860i
$19$		−	20.6555i		−	1.08713i	−0.839367	−	0.543565i	$-0.817074\pi$
$19$		−	20.6555i		−	1.08713i	0.839367	−	0.543565i	$-0.182926\pi$
$20$	−36.9219	+	63.9507i	−1.84610	+	3.19753i
$21$	26.7525	+	7.19497i	1.27393	+	0.342617i
$22$	3.93299	+	6.81214i	0.178772	+	0.309643i
$23$	14.0417	−	8.10700i	0.610511	−	0.352478i	−0.162655	−	0.986683i	$-0.552006\pi$
$23$	14.0417	−	8.10700i	0.610511	−	0.352478i	0.773165	+	0.634205i	$0.218672\pi$
$24$	47.9816	−	12.8088i	1.99923	−	0.533702i
$25$	−23.9082	+	41.4103i	−0.956330	+	1.65641i
$26$	−16.8999	+	43.0449i	−0.649998	+	1.65557i
$27$	19.1450	−	19.0386i	0.709076	−	0.705132i
$28$		−	79.9111i		−	2.85397i
$29$	−28.3224	−	16.3520i	−0.976635	−	0.563860i	−0.0753824	−	0.997155i	$-0.524018\pi$
$29$	−28.3224	−	16.3520i	−0.976635	−	0.563860i	−0.901252	+	0.433294i	$0.857351\pi$
$30$	87.9824	−	23.4872i	2.93275	−	0.782906i
$31$	−31.8459	+	18.3862i	−1.02729	+	0.593105i	−0.916206	−	0.400707i	$-0.868765\pi$
$31$	−31.8459	+	18.3862i	−1.02729	+	0.593105i	−0.111081	+	0.993811i	$0.535431\pi$
$32$	−10.0606	−	17.4255i	−0.314395	−	0.544547i
$33$	1.72292	−	6.40622i	0.0522098	−	0.194128i
$34$	−13.9529	−	8.05569i	−0.410378	−	0.236932i
$35$		−	78.7993i		−	2.25141i
$36$	−67.3760	−	39.0668i	−1.87156	−	1.08519i
$37$			3.67771i			0.0993974i	0.998764	+	0.0496987i	$0.0158261\pi$
$37$			3.67771i			0.0993974i	−0.998764	+	0.0496987i	$0.984174\pi$
$38$	63.6317	+	36.7378i	1.67452	+	0.966783i
$39$	35.7623	−	15.5582i	0.916982	−	0.398928i
$40$	−70.6296	−	122.334i	−1.76574	−	3.05835i
$41$	22.5628	+	39.0799i	0.550312	+	0.953168i	0.998252	+	0.0591047i	$0.0188246\pi$
$41$	22.5628	+	39.0799i	0.550312	+	0.953168i	−0.447940	+	0.894064i	$0.647842\pi$
$42$	−69.7469	+	69.6174i	−1.66064	+	1.65756i
$43$	11.1768	−	19.3588i	0.259926	−	0.450204i	−0.706296	−	0.707917i	$-0.749635\pi$
$43$	11.1768	−	19.3588i	0.259926	−	0.450204i	0.966222	+	0.257712i	$0.0829686\pi$
$44$	−19.1357			−0.434902
$45$	−66.4387	−	38.5232i	−1.47641	−	0.856072i
$46$			57.6764i			1.25384i
$47$	7.92578	−	13.7278i	0.168634	−	0.292082i	−0.769306	−	0.638880i	$-0.779398\pi$
$47$	7.92578	−	13.7278i	0.168634	−	0.292082i	0.937940	+	0.346798i	$0.112731\pi$
$48$	−18.9108	+	70.3147i	−0.393976	+	1.46489i
$49$	18.1368	+	31.4139i	0.370139	+	0.641100i
$50$	−85.0463	−	147.305i	−1.70093	−	2.94609i
$51$	3.50455	+	13.1280i	0.0687167	+	0.257411i
$52$	−70.1303	−	87.9627i	−1.34866	−	1.69159i
$53$			79.1568i			1.49352i	0.665091	+	0.746762i	$0.268393\pi$
$53$			79.1568i			1.49352i	−0.665091	+	0.746762i	$0.731607\pi$
$54$	24.5993	+	92.8407i	0.455543	+	1.71927i
$55$	−18.8695			−0.343081
$56$	132.385	+	76.4328i	2.36403	+	1.36487i
$57$	−15.9824	−	59.8698i	−0.280394	−	1.05035i
$58$	100.748	−	58.1671i	1.73704	−	1.00288i
$59$	15.2856	+	26.4755i	0.259079	+	0.448737i	0.965995	−	0.258559i	$-0.0832478\pi$
$59$	15.2856	+	26.4755i	0.259079	+	0.448737i	−0.706917	+	0.707297i	$0.749914\pi$
$60$	−57.5355	+	213.930i	−0.958924	+	3.56549i
$61$	−0.328289	+	0.568613i	−0.00538178	+	0.00932152i	−0.868704	−	0.495332i	$-0.835046\pi$
$61$	−0.328289	+	0.568613i	−0.00538178	+	0.00932152i	0.863322	+	0.504654i	$0.168380\pi$
$62$		−	130.807i		−	2.10979i
$63$	83.1092	+	0.154504i	1.31919	+	0.00245245i
$64$	−25.5091			−0.398580
$65$	−69.1546	−	86.7389i	−1.06392	−	1.33444i
$66$	16.6708	+	16.7018i	0.252587	+	0.253057i
$67$	−8.00214	+	4.62004i	−0.119435	+	0.0689558i	−0.558527	−	0.829486i	$-0.688633\pi$
$67$	−8.00214	+	4.62004i	−0.119435	+	0.0689558i	0.439092	+	0.898442i	$0.355300\pi$
$68$	33.9434	−	19.5972i	0.499167	−	0.288194i
$69$	34.4271	−	34.3631i	0.498943	−	0.498016i
$70$	242.751	+	140.152i	3.46787	+	2.00218i
$71$	−21.4350			−0.301901			−0.150951	−	0.988541i	$-0.548233\pi$
$71$	−21.4350			−0.301901			−0.150951	+	0.988541i	$0.548233\pi$
$72$	129.164	−	74.2528i	1.79394	−	1.03129i
$73$			59.7788i			0.818887i	0.912335	+	0.409444i	$0.134277\pi$
$73$			59.7788i			0.818887i	−0.912335	+	0.409444i	$0.865723\pi$
$74$	−11.3296	−	6.54116i	−0.153103	−	0.0883941i
$75$	−37.2562	+	138.527i	−0.496750	+	1.84703i
$76$	−154.798	+	89.3726i	−2.03681	+	1.17595i
$77$	17.6841	−	10.2099i	0.229664	−	0.132596i
$78$	−15.6779	+	137.842i	−0.200999	+	1.76720i
$79$	−64.5091	+	111.733i	−0.816571	+	1.41434i	0.0916236	+	0.995794i	$0.470794\pi$
$79$	−64.5091	+	111.733i	−0.816571	+	1.41434i	−0.908194	+	0.418549i	$0.862539\pi$
$80$	207.112			2.58889
$81$	40.7605	−	69.9970i	0.503217	−	0.864160i
$82$	−160.521			−1.95757
$83$	−48.6117	+	84.1979i	−0.585683	+	1.01443i	0.409107	+	0.912486i	$0.365840\pi$
$83$	−48.6117	+	84.1979i	−0.585683	+	1.01443i	−0.994790	+	0.101946i	$0.967493\pi$
$84$	−61.8323	−	231.622i	−0.736098	−	2.75741i
$85$	33.4711	−	19.3246i	0.393778	−	0.227348i
$86$	39.7581	+	68.8630i	0.462303	+	0.800733i
$87$	−94.7450	−	25.4813i	−1.08902	−	0.292888i
$88$	18.3028	−	31.7013i	0.207986	−	0.360243i
$89$	46.5189			0.522684			0.261342	−	0.965246i	$-0.415835\pi$
$89$	46.5189			0.522684			0.261342	+	0.965246i	$0.415835\pi$
$90$	236.843	−	136.155i	2.63159	−	1.51283i
$91$	111.743	+	43.8717i	1.22795	+	0.482107i
$92$	−121.512	−	70.1552i	−1.32079	−	0.762557i
$93$	−78.0787	+	77.9337i	−0.839556	+	0.837997i
$94$	28.1936	+	48.8327i	0.299931	+	0.519496i
$95$	−152.644	+	88.1291i	−1.60678	+	0.927675i
$96$	−42.6439	−	42.7233i	−0.444208	−	0.445034i
$97$	9.25813	+	5.34518i	0.0954446	+	0.0551050i	0.546963	−	0.837157i	$-0.315784\pi$
$97$	9.25813	+	5.34518i	0.0954446	+	0.0551050i	−0.451518	+	0.892262i	$0.649117\pi$
$98$	−129.033			−1.31666
$99$	0.0369980	−	19.9015i	0.000373717	−	0.201026i
$100$	413.787			4.13787
$101$	1.37535	+	0.794060i	0.0136173	+	0.00786198i	0.506793	−	0.862068i	$-0.330831\pi$
$101$	1.37535	+	0.794060i	0.0136173	+	0.00786198i	−0.493176	+	0.869930i	$0.664164\pi$
$102$	−46.6755	−	12.5532i	−0.457603	−	0.123070i
$103$	−55.9144	−	96.8465i	−0.542858	−	0.940258i	−0.998738	−	0.0502166i	$-0.984009\pi$
$103$	−55.9144	−	96.8465i	−0.542858	−	0.940258i	0.455880	−	0.890041i	$-0.349325\pi$
$104$	212.802	−	32.0481i	2.04617	−	0.308155i
$105$	−60.9720	−	228.400i	−0.580686	−	2.17523i
$106$	−243.852	−	140.788i	−2.30049	−	1.32819i
$107$		−	37.5159i		−	0.350616i	−0.984514	−	0.175308i	$-0.943908\pi$
$107$		−	37.5159i		−	0.350616i	0.984514	−	0.175308i	$-0.0560921\pi$
$108$	−225.518	−	61.1018i	−2.08813	−	0.565758i
$109$		−	157.644i		−	1.44628i	−0.690702	−	0.723139i	$-0.742699\pi$
$109$		−	157.644i		−	1.44628i	0.690702	−	0.723139i	$-0.257301\pi$
$110$	33.5612	−	58.1298i	0.305102	−	0.528452i
$111$	2.84567	+	10.6598i	0.0256367	+	0.0960344i
$112$	−194.101	+	112.064i	−1.73304	+	1.00057i
$113$	−16.4737	+	9.51108i	−0.145785	+	0.0841689i	−0.571118	−	0.820868i	$-0.693490\pi$
$113$	−16.4737	+	9.51108i	−0.145785	+	0.0841689i	0.425333	+	0.905037i	$0.360157\pi$
$114$	212.863	+	57.2485i	1.86722	+	0.502180i
$115$	−119.822	−	69.1791i	−1.04193	−	0.601558i
$116$			283.008i			2.43973i
$117$	91.6186	−	72.7669i	0.783065	−	0.621939i
$118$	−108.748			−0.921594
$119$	−20.9123	+	36.2212i	−0.175734	+	0.304380i
$120$	−299.377	−	299.935i	−2.49481	−	2.49945i
$121$	58.0551	+	100.554i	0.479794	+	0.831028i
$122$	−1.16779	−	2.02267i	−0.00957203	−	0.0165793i
$123$	95.6368	+	95.8148i	0.777535	+	0.778982i
$124$	275.583	+	159.108i	2.22245	+	1.28313i
$125$	194.699			1.55759
$126$	−148.294	+	255.753i	−1.17694	+	2.02979i
$127$	−123.075			−0.969091			−0.484545	−	0.874766i	$-0.661015\pi$
$127$	−123.075			−0.969091			−0.484545	+	0.874766i	$0.661015\pi$
$128$	85.6130	−	148.286i	0.668852	−	1.15849i
$129$	17.4168	−	64.7596i	0.135014	−	0.502012i
$130$	390.208	−	58.7656i	3.00160	−	0.452043i
$131$	208.821	−	120.563i	1.59405	−	0.920327i	0.601452	−	0.798909i	$-0.294589\pi$
$131$	208.821	−	120.563i	1.59405	−	0.920327i	0.992601	−	0.121418i	$-0.0387441\pi$
$132$	−55.4648	+	14.8065i	−0.420188	+	0.112171i
$133$	95.3701	−	165.186i	0.717068	−	1.24200i
$134$		−	32.8688i		−	0.245289i
$135$	−222.380	−	60.2517i	−1.64726	−	0.446309i
$136$			74.9768i			0.551300i
$137$	−79.8067	+	138.229i	−0.582531	+	1.00897i	0.412648	+	0.910891i	$0.364604\pi$
$137$	−79.8067	+	138.229i	−0.582531	+	1.00897i	−0.995178	+	0.0980819i	$0.968729\pi$
$138$	44.6279	+	167.175i	0.323391	+	1.21141i
$139$	121.640	+	210.687i	0.875109	+	1.51573i	0.856647	+	0.515903i	$0.172543\pi$
$139$	121.640	+	210.687i	0.875109	+	1.51573i	0.0184615	+	0.999830i	$0.494123\pi$
$140$	−590.544	+	340.951i	−4.21817	+	2.43536i
$141$	12.3507	−	45.9228i	0.0875939	−	0.325694i
$142$	38.1242	−	66.0331i	0.268480	−	0.465022i
$143$	10.5056	−	26.7583i	0.0734660	−	0.187121i
$144$	−0.406091	+	218.440i	−0.00282007	+	1.51694i
$145$			279.071i			1.92463i
$146$	−184.156	−	106.322i	−1.26134	−	0.728236i
$147$	76.8765	+	77.0196i	0.522969	+	0.523943i
$148$	27.5618	−	15.9128i	0.186228	−	0.107519i
$149$	−45.2052	−	78.2977i	−0.303390	−	0.525488i	0.673511	−	0.739177i	$-0.264785\pi$
$149$	−45.2052	−	78.2977i	−0.303390	−	0.525488i	−0.976902	+	0.213689i	$0.931452\pi$
$150$	−360.485	−	361.156i	−2.40324	−	2.40771i
$151$	−100.794	−	58.1934i	−0.667509	−	0.385387i	0.127623	−	0.991823i	$-0.459265\pi$
$151$	−100.794	−	58.1934i	−0.667509	−	0.385387i	−0.795132	+	0.606436i	$0.792599\pi$
$152$		−	341.930i		−	2.24954i
$153$	20.3159	+	35.3397i	0.132784	+	0.230978i
$154$			72.6374i			0.471672i
$155$	271.749	+	156.895i	1.75322	+	1.01222i
$156$	−271.335	−	200.695i	−1.73933	−	1.28651i
$157$	81.3376	+	140.881i	0.518074	+	0.897330i	0.999780	+	0.0209969i	$0.00668401\pi$
$157$	81.3376	+	140.881i	0.518074	+	0.897330i	−0.481706	+	0.876333i	$0.659983\pi$
$158$	−229.472	−	397.456i	−1.45235	−	2.51555i
$159$	61.2486	+	229.436i	0.385211	+	1.44299i
$160$	−85.8499	+	148.696i	−0.536562	+	0.929353i
$161$	149.726			0.929976
$162$	143.138	+	250.064i	0.883566	+	1.54361i
$163$			104.242i			0.639521i	0.947498	+	0.319761i	$0.103603\pi$
$163$			104.242i			0.639521i	−0.947498	+	0.319761i	$0.896397\pi$
$164$	195.251	−	338.184i	1.19055	−	2.06210i
$165$	−54.6931	+	14.6005i	−0.331474	+	0.0884879i
$166$	−172.921	−	299.509i	−1.04170	−	1.80427i
$167$	45.9089	+	79.5165i	0.274903	+	0.476147i	0.970111	−	0.242663i	$-0.0780208\pi$
$167$	45.9089	+	79.5165i	0.274903	+	0.476147i	−0.695207	+	0.718809i	$0.744687\pi$
$168$	442.860	+	119.105i	2.63607	+	0.708960i
$169$	161.504	−	49.7741i	0.955645	−	0.294521i
$170$			137.482i			0.808721i
$171$	−92.6501	−	161.166i	−0.541813	−	0.942490i
$172$	−193.440			−1.12465
$173$	9.99415	+	5.77012i	0.0577696	+	0.0333533i	0.528607	−	0.848867i	$-0.322715\pi$
$173$	9.99415	+	5.77012i	0.0577696	+	0.0333533i	−0.470837	+	0.882220i	$0.656048\pi$
$174$	247.011	−	246.553i	1.41961	−	1.41697i
$175$	−382.398	+	220.778i	−2.18513	+	1.26159i
$176$	26.8352	+	46.4799i	0.152473	+	0.264090i
$177$	64.7912	+	64.9117i	0.366052	+	0.366733i
$178$	−82.7385	+	143.307i	−0.464823	+	0.805097i
$179$		−	178.709i		−	0.998373i	−0.866495	−	0.499186i	$-0.833632\pi$
$179$		−	178.709i		−	0.998373i	0.866495	−	0.499186i	$-0.166368\pi$
$180$	−1.23551	+	664.594i	−0.00686397	+	3.69219i
$181$	−112.019			−0.618889			−0.309444	−	0.950918i	$-0.600143\pi$
$181$	−112.019			−0.618889			−0.309444	+	0.950918i	$0.600143\pi$
$182$	−333.898	+	266.208i	−1.83461	+	1.46268i
$183$	−0.511573	+	1.90214i	−0.00279548	+	0.0103942i
$184$	232.446	−	134.203i	1.26330	−	0.729364i
$185$	27.1783	−	15.6914i	0.146910	−	0.0848184i
$186$	−101.214	−	379.144i	−0.544159	−	2.03841i
$187$	8.67362	+	5.00772i	0.0463830	+	0.0267792i
$188$	−137.174			−0.729648
$189$	241.011	−	63.8590i	1.27519	−	0.337878i
$190$		−	626.986i		−	3.29992i
$191$	228.202	+	131.752i	1.19477	+	0.689803i	0.959385	−	0.282098i	$-0.0910305\pi$
$191$	228.202	+	131.752i	1.19477	+	0.689803i	0.235388	+	0.971901i	$0.424364\pi$
$192$	−73.9382	+	19.7380i	−0.385095	+	0.102802i
$193$	210.880	−	121.751i	1.09264	−	0.630836i	0.158362	−	0.987381i	$-0.449379\pi$
$193$	210.880	−	121.751i	1.09264	−	0.630836i	0.934278	+	0.356545i	$0.116045\pi$
$194$	−32.9330	+	19.0139i	−0.169758	+	0.0980097i
$195$	−267.560	−	197.903i	−1.37210	−	1.01489i
$196$	156.950	−	271.845i	0.800765	−	1.38697i
$197$	81.2828			0.412603			0.206302	−	0.978488i	$-0.433857\pi$
$197$	81.2828			0.412603			0.206302	+	0.978488i	$0.433857\pi$
$198$	61.2434	+	35.5108i	0.309310	+	0.179348i
$199$	−29.2384			−0.146926			−0.0734632	−	0.997298i	$-0.523405\pi$
$199$	−29.2384			−0.146926			−0.0734632	+	0.997298i	$0.523405\pi$
$200$	−395.776	+	685.504i	−1.97888	+	3.42752i
$201$	−19.6194	+	19.5829i	−0.0976088	+	0.0974275i
$202$	−4.89240	+	2.82463i	−0.0242198	+	0.0139833i
$203$	−151.000	−	261.540i	−0.743843	−	1.28837i
$204$	83.2211	−	83.0666i	0.407947	−	0.407189i
$205$	192.534	−	333.479i	0.939191	−	1.62673i
$206$	397.797			1.93105
$207$	73.1978	−	126.240i	0.353613	−	0.609854i
$208$	−115.310	+	293.699i	−0.554375	+	1.41202i
$209$	−39.5558	−	22.8376i	−0.189262	−	0.109271i
$210$	812.058	+	218.399i	3.86694	+	1.04000i
$211$	−51.2914	−	88.8394i	−0.243087	−	0.421040i	0.718505	−	0.695522i	$-0.244827\pi$
$211$	−51.2914	−	88.8394i	−0.243087	−	0.421040i	−0.961592	+	0.274482i	$0.911493\pi$
$212$	593.223	−	342.498i	2.79822	−	1.61555i
$213$	−62.1292	+	16.5856i	−0.291687	+	0.0778667i
$214$	115.572	+	66.7258i	0.540058	+	0.311803i
$215$	−190.749			−0.887205
$216$	316.926	−	315.164i	1.46725	−	1.45909i
$217$	−339.571			−1.56484
$218$	485.643	+	280.386i	2.22772	+	1.28617i
$219$	46.2546	+	173.269i	0.211208	+	0.791181i
$220$	81.6450	+	141.413i	0.371113	+	0.642787i
$221$	8.76849	+	58.2235i	0.0396764	+	0.263455i
$222$	−37.9002	−	10.1931i	−0.170722	−	0.0459149i
$223$	−211.597	−	122.165i	−0.948864	−	0.547827i	−0.0561363	−	0.998423i	$-0.517878\pi$
$223$	−211.597	−	122.165i	−0.948864	−	0.547827i	−0.892728	+	0.450596i	$0.851211\pi$
$224$		−	185.807i		−	0.829497i
$225$	−0.800039	+	430.348i	−0.00355573	+	1.91266i
$226$		−	67.6656i		−	0.299405i
$227$	−148.741	+	257.628i	−0.655249	+	1.13492i	0.326583	+	0.945169i	$0.394103\pi$
$227$	−148.741	+	257.628i	−0.655249	+	1.13492i	−0.981831	+	0.189756i	$0.939230\pi$
$228$	−379.528	+	378.823i	−1.66460	+	1.66150i
$229$	−363.823	+	210.053i	−1.58875	+	0.917264i	−0.595233	+	0.803553i	$0.702940\pi$
$229$	−363.823	+	210.053i	−1.58875	+	0.917264i	−0.993514	+	0.113711i	$0.963726\pi$
$230$	426.230	−	246.084i	1.85317	−	1.06993i
$231$	43.3573	−	43.2768i	0.187694	−	0.187345i
$232$	−468.848	−	270.690i	−2.02090	−	1.16677i
$233$		−	244.853i		−	1.05087i	−0.850833	−	0.525436i	$-0.823902\pi$
$233$		−	244.853i		−	1.05087i	0.850833	−	0.525436i	$-0.176098\pi$
$234$	61.2147	+	411.666i	0.261601	+	1.75926i
$235$	−135.265			−0.575597
$236$	132.277	−	229.110i	0.560494	−	0.970804i
$237$	−100.525	+	373.773i	−0.424154	+	1.57710i
$238$	−74.3892	−	128.846i	−0.312560	−	0.541369i
$239$	148.612	+	257.404i	0.621809	+	1.07700i	0.989149	+	0.146918i	$0.0469353\pi$
$239$	148.612	+	257.404i	0.621809	+	1.07700i	−0.367340	+	0.930087i	$0.619731\pi$
$240$	600.313	−	160.255i	2.50130	−	0.667731i
$241$	9.79779	+	5.65676i	0.0406547	+	0.0234720i	0.520190	−	0.854051i	$-0.325861\pi$
$241$	9.79779	+	5.65676i	0.0406547	+	0.0234720i	−0.479535	+	0.877523i	$0.659195\pi$
$242$	−413.027			−1.70672
$243$	63.9832	−	234.425i	0.263305	−	0.964713i
$244$	5.68180			0.0232860
$245$	154.766	−	268.063i	0.631699	−	1.09413i
$246$	−465.269	+	124.205i	−1.89134	+	0.504898i
$247$	−39.9885	−	265.527i	−0.161897	−	1.07501i
$248$	−527.176	+	304.365i	−2.12571	+	1.22728i
$249$	−75.7516	+	281.661i	−0.304223	+	1.13117i
$250$	−346.291	+	599.794i	−1.38516	+	2.39918i
$251$			200.026i			0.796918i	0.917186	+	0.398459i	$0.130455\pi$
$251$			200.026i			0.796918i	−0.917186	+	0.398459i	$0.869545\pi$
$252$	−358.441	−	623.513i	−1.42239	−	2.47426i
$253$		−	35.8538i		−	0.141715i
$254$	218.900	−	379.146i	0.861812	−	1.49270i
$255$	82.0633	−	81.9109i	0.321817	−	0.321219i
$256$	253.524	+	439.117i	0.990329	+	1.71530i
$257$	−91.5222	+	52.8404i	−0.356117	+	0.205604i	−0.667376	−	0.744721i	$-0.732583\pi$
$257$	−91.5222	+	52.8404i	−0.356117	+	0.205604i	0.311259	+	0.950325i	$0.399249\pi$
$258$	168.522	+	168.836i	0.653188	+	0.654403i
$259$	−16.9807	+	29.4114i	−0.0655624	+	0.113557i
$260$	−350.826	+	893.568i	−1.34933	+	3.43680i
$261$	−294.335	−	0.547183i	−1.12772	−	0.00209649i
$262$			857.732i			3.27378i
$263$	−169.963	−	98.1280i	−0.646246	−	0.373110i	0.140771	−	0.990042i	$-0.455042\pi$
$263$	−169.963	−	98.1280i	−0.646246	−	0.373110i	−0.787016	+	0.616932i	$0.788375\pi$
$264$	28.5212	−	106.048i	0.108035	−	0.401698i
$265$	584.970	−	337.733i	2.20743	−	1.27446i
$266$	339.250	+	587.599i	1.27538	+	2.20902i
$267$	134.835	−	35.9946i	0.505000	−	0.134811i
$268$	69.2477	+	39.9802i	0.258387	+	0.149180i
$269$			33.6839i			0.125219i	0.998038	+	0.0626095i	$0.0199423\pi$
$269$			33.6839i			0.125219i	−0.998038	+	0.0626095i	$0.980058\pi$
$270$	581.138	−	577.906i	2.15236	−	2.14039i
$271$		−	326.125i		−	1.20341i	−0.798717	−	0.601707i	$-0.794488\pi$
$271$		−	326.125i		−	1.20341i	0.798717	−	0.601707i	$-0.205512\pi$
$272$	−95.2017	−	54.9647i	−0.350006	−	0.202076i
$273$	357.833	+	40.6994i	1.31075	+	0.149082i
$274$	−283.888	−	491.709i	−1.03609	−	1.79456i
$275$	52.8680	+	91.5700i	0.192247	+	0.332982i
$276$	−406.487	−	109.323i	−1.47278	−	0.396097i
$277$	101.171	−	175.233i	0.365237	−	0.632609i	−0.623577	−	0.781762i	$-0.714321\pi$
$277$	101.171	−	175.233i	0.365237	−	0.632609i	0.988814	+	0.149153i	$0.0476545\pi$
$278$	−865.396			−3.11293
$279$	−166.009	+	286.305i	−0.595013	+	1.02618i
$280$		−	1304.44i		−	4.65872i
$281$	183.407	−	317.669i	0.652692	−	1.13050i	−0.329775	−	0.944060i	$-0.606973\pi$
$281$	183.407	−	317.669i	0.652692	−	1.13050i	0.982467	−	0.186436i	$-0.0596938\pi$
$282$	119.504	+	119.726i	0.423773	+	0.424561i
$283$	70.2215	+	121.627i	0.248133	+	0.429778i	0.963008	−	0.269474i	$-0.0868498\pi$
$283$	70.2215	+	121.627i	0.248133	+	0.429778i	−0.714875	+	0.699252i	$0.753516\pi$
$284$	92.7454	+	160.640i	0.326568	+	0.565633i
$285$	−374.248	+	373.553i	−1.31315	+	1.31071i
$286$	63.7469	+	79.9561i	0.222891	+	0.279567i
$287$			416.707i			1.45194i
$288$	−156.661	−	90.8371i	−0.543962	−	0.315406i
$289$	268.486			0.929017
$290$	−859.712	−	496.355i	−2.96452	−	1.71157i
$291$	30.9706	+	8.32940i	0.106428	+	0.0286234i
$292$	447.999	−	258.652i	1.53424	−	0.885796i
$293$	−210.517	−	364.625i	−0.718487	−	1.24446i	−0.961599	−	0.274457i	$-0.911502\pi$
$293$	−210.517	−	364.625i	−0.718487	−	1.24446i	0.243113	−	0.969998i	$-0.421832\pi$
$294$	−374.001	+	99.8407i	−1.27211	+	0.339594i
$295$	130.436	−	225.922i	0.442157	−	0.765838i
$296$			60.8806i			0.205678i
$297$	−15.2918	−	57.7132i	−0.0514877	−	0.194321i
$298$	321.607			1.07922
$299$	164.812	−	131.400i	0.551211	−	0.439466i
$300$	1199.36	−	320.173i	3.99787	−	1.06724i
$301$	178.766	−	103.211i	0.593908	−	0.342893i
$302$	358.544	−	207.005i	1.18723	−	0.685448i
$303$	4.60087	+	1.23738i	0.0151844	+	0.00408377i
$304$	434.165	+	250.665i	1.42817	+	0.824557i
$305$	5.60275			0.0183697
$306$	−145.002	−	0.269567i	−0.473863	−	0.000880936i
$307$			34.4745i			0.112295i	0.998422	+	0.0561474i	$0.0178817\pi$
$307$			34.4745i			0.112295i	−0.998422	+	0.0561474i	$0.982118\pi$
$308$	−153.032	−	88.3531i	−0.496858	−	0.286861i
$309$	−237.004	−	237.445i	−0.767003	−	0.768430i
$310$	−966.666	+	558.105i	−3.11828	+	1.80034i
$311$	−516.874	+	298.418i	−1.66198	+	0.959542i	−0.690205	+	0.723614i	$0.742480\pi$
$311$	−516.874	+	298.418i	−1.66198	+	0.959542i	−0.971770	+	0.235928i	$0.924187\pi$
$312$	592.008	−	257.550i	1.89746	−	0.825479i
$313$	11.0811	−	19.1931i	0.0354030	−	0.0613198i	−0.847781	−	0.530346i	$-0.822062\pi$
$313$	11.0811	−	19.1931i	0.0354030	−	0.0613198i	0.883184	+	0.469027i	$0.155395\pi$
$314$	−578.667			−1.84289
$315$	−353.454	−	614.838i	−1.12208	−	1.95187i
$316$	1116.48			3.53316
$317$	114.400	−	198.146i	0.360882	−	0.625066i	−0.627224	−	0.778839i	$-0.715809\pi$
$317$	114.400	−	198.146i	0.360882	−	0.625066i	0.988106	+	0.153773i	$0.0491425\pi$
$318$	−815.742	−	219.390i	−2.56523	−	0.689906i
$319$	−62.6290	+	36.1589i	−0.196329	+	0.113351i
$320$	108.838	+	188.513i	0.340119	+	0.589103i
$321$	−29.0284	−	108.740i	−0.0904313	−	0.338753i
$322$	−266.303	+	461.250i	−0.827027	+	1.43245i
$323$	93.5533			0.289639
$324$	−700.941	−	2.60618i	−2.16340	−	0.00804377i
$325$	−227.172	+	578.617i	−0.698991	+	1.78036i
$326$	−321.130	−	185.405i	−0.985062	−	0.568726i
$327$	−121.979	−	456.932i	−0.373026	−	1.39734i
$328$	373.504	+	646.927i	1.13873	+	1.97234i
$329$	126.768	−	73.1896i	0.385313	−	0.222461i
$330$	52.2985	−	194.457i	0.158480	−	0.589265i
$331$	−112.933	−	65.2017i	−0.341186	−	0.196984i	0.319610	−	0.947549i	$-0.396448\pi$
$331$	−112.933	−	65.2017i	−0.341186	−	0.196984i	−0.660796	+	0.750565i	$0.729781\pi$
$332$	841.337			2.53415
$333$	16.4964	+	28.6956i	0.0495386	+	0.0861730i
$334$	−326.614			−0.977885
$335$	68.2843	+	39.4240i	0.203834	+	0.117683i
$336$	−475.890	+	475.006i	−1.41634	+	1.41371i
$337$	279.875	+	484.758i	0.830490	+	1.43845i	0.897650	+	0.440708i	$0.145273\pi$
$337$	279.875	+	484.758i	0.830490	+	1.43845i	−0.0671604	+	0.997742i	$0.521394\pi$
$338$	−133.915	+	586.061i	−0.396200	+	1.73391i
$339$	−40.3896	+	40.3146i	−0.119143	+	0.118922i
$340$	−289.647	−	167.228i	−0.851904	−	0.491847i
$341$			81.3145i			0.238459i
$342$	661.279	+	1.22935i	1.93356	+	0.00359459i
$343$		−	117.520i		−	0.342623i
$344$	185.020	−	320.465i	0.537850	−	0.931583i
$345$	−400.832	−	107.802i	−1.16183	−	0.312469i
$346$	−35.5512	+	20.5255i	−0.102749	+	0.0593222i
$347$	9.75535	−	5.63225i	0.0281134	−	0.0162313i	−0.485877	−	0.874027i	$-0.661500\pi$
$347$	9.75535	−	5.63225i	0.0281134	−	0.0162313i	0.513991	+	0.857796i	$0.328167\pi$
$348$	218.981	+	820.299i	0.629257	+	2.35718i
$349$	180.138	+	104.003i	0.516154	+	0.298002i	0.735360	−	0.677677i	$-0.237013\pi$
$349$	180.138	+	104.003i	0.516154	+	0.298002i	−0.219206	+	0.975679i	$0.570347\pi$
$350$		−	1570.70i		−	4.48771i
$351$	209.252	−	281.806i	0.596160	−	0.802866i
$352$	−44.4939			−0.126403
$353$	−199.769	+	346.010i	−0.565918	+	0.980199i	0.431045	+	0.902330i	$0.358145\pi$
$353$	−199.769	+	346.010i	−0.565918	+	0.980199i	−0.996964	+	0.0778688i	$0.975188\pi$
$354$	−315.206	+	84.1453i	−0.890413	+	0.237698i
$355$	91.4551	+	158.405i	0.257620	+	0.446211i
$356$	−201.279	−	348.626i	−0.565391	−	0.979286i
$357$	−32.5877	+	121.168i	−0.0912820	+	0.339407i
$358$	550.534	+	317.851i	1.53781	+	0.887852i
$359$	−53.7452			−0.149708			−0.0748540	−	0.997195i	$-0.523849\pi$
$359$	−53.7452			−0.149708			−0.0748540	+	0.997195i	$0.523849\pi$
$360$	−1099.82	−	637.712i	−3.05506	−	1.77142i
$361$	−65.6477			−0.181850
$362$	199.237	−	345.088i	0.550377	−	0.953281i
$363$	246.078	+	246.536i	0.677901	+	0.679162i
$364$	−154.706	−	1027.26i	−0.425016	−	2.82214i
$365$	441.766	−	255.054i	1.21032	−	0.698778i
$366$	−4.94990	−	4.95911i	−0.0135243	−	0.0135495i
$367$	−106.321	+	184.153i	−0.289703	+	0.501780i	−0.973739	−	0.227669i	$-0.926890\pi$
$367$	−106.321	+	184.153i	−0.289703	+	0.501780i	0.684036	+	0.729448i	$0.260223\pi$
$368$			393.532i			1.06938i
$369$	351.341	+	203.719i	0.952144	+	0.552083i
$370$			111.635i			0.301716i
$371$	−365.482	+	633.033i	−0.985126	+	1.70629i
$372$	921.890	+	247.938i	2.47820	+	0.666501i
$373$	−350.464	−	607.021i	−0.939580	−	1.62740i	−0.766255	−	0.642537i	$-0.777882\pi$
$373$	−350.464	−	607.021i	−0.939580	−	1.62740i	−0.173325	−	0.984865i	$-0.555451\pi$
$374$	−30.8538	+	17.8134i	−0.0824967	+	0.0476295i
$375$	564.334	−	150.651i	1.50489	−	0.401736i
$376$	131.203	−	227.250i	0.348944	−	0.604389i
$377$	−395.743	−	155.373i	−1.04972	−	0.412131i
$378$	−231.937	+	856.045i	−0.613590	+	2.26467i
$379$		−	310.349i		−	0.818863i	−0.912341	−	0.409431i	$-0.865727\pi$
$379$		−	310.349i		−	0.818863i	0.912341	−	0.409431i	$-0.134273\pi$
$380$	1320.93	+	762.639i	3.47613	+	2.00694i
$381$	−356.731	+	95.2305i	−0.936302	+	0.249949i
$382$	−811.759	+	468.669i	−2.12502	+	1.22688i
$383$	86.8368	+	150.406i	0.226728	+	0.392704i	0.956836	−	0.290627i	$-0.0938639\pi$
$383$	86.8368	+	150.406i	0.226728	+	0.392704i	−0.730109	+	0.683331i	$0.760531\pi$
$384$	133.411	−	496.051i	0.347424	−	1.29180i
$385$	−150.903	−	87.1239i	−0.391956	−	0.226296i
$386$			866.188i			2.24401i
$387$	0.374008	−	201.182i	0.000966429	−	0.519850i
$388$		−	92.5107i		−	0.238430i
$389$	34.6432	+	20.0013i	0.0890572	+	0.0514172i	0.543867	−	0.839171i	$-0.316960\pi$
$389$	34.6432	+	20.0013i	0.0890572	+	0.0514172i	−0.454810	+	0.890588i	$0.650293\pi$
$390$	1085.55	−	472.260i	2.78345	−	1.21092i
$391$	36.7185	+	63.5983i	0.0939092	+	0.162656i
$392$	300.237	+	520.025i	0.765909	+	1.32659i
$393$	511.980	−	511.029i	1.30275	−	1.30033i
$394$	−144.569	+	250.402i	−0.366928	+	0.635537i
$395$	1100.95			2.78720
$396$	−149.308	+	85.8333i	−0.377040	+	0.216751i
$397$		−	210.037i		−	0.529061i	−0.964377	−	0.264530i	$-0.914783\pi$
$397$		−	210.037i		−	0.529061i	0.964377	−	0.264530i	$-0.0852169\pi$
$398$	52.0033	−	90.0724i	0.130662	−	0.226312i
$399$	148.615	−	552.585i	0.372469	−	1.38492i
$400$	−580.279	−	1005.07i	−1.45070	−	2.51268i
$401$	−282.348	−	489.041i	−0.704110	−	1.21955i	−0.967012	−	0.254732i	$-0.918013\pi$
$401$	−282.348	−	489.041i	−0.704110	−	1.21955i	0.262901	−	0.964823i	$-0.415321\pi$
$402$	−25.4326	−	95.2701i	−0.0632653	−	0.236990i
$403$	−373.785	+	298.009i	−0.927506	+	0.739476i
$404$		−	13.7430i		−	0.0340174i
$405$	−691.189	−	2.56992i	−1.70664	−	0.00634549i
$406$	1074.27			2.64599
$407$	7.04292	+	4.06623i	0.0173045	+	0.00999074i
$408$	58.0143	+	217.320i	0.142192	+	0.532647i
$409$	45.2077	−	26.1007i	0.110532	−	0.0638159i	−0.443715	−	0.896168i	$-0.646340\pi$
$409$	45.2077	−	26.1007i	0.110532	−	0.0638159i	0.554247	+	0.832352i	$0.313006\pi$
$410$	684.882	+	1186.25i	1.67044	+	2.89329i
$411$	−124.363	+	462.409i	−0.302586	+	1.12508i
$412$	−483.864	+	838.076i	−1.17443	+	2.03417i
$413$			282.307i			0.683551i
$414$	258.708	+	450.025i	0.624898	+	1.08702i
$415$	829.632			1.99911
$416$	−163.065	−	204.529i	−0.391984	−	0.491655i
$417$	515.595	+	516.555i	1.23644	+	1.23874i
$418$	140.708	−	81.2377i	0.336622	−	0.194349i
$419$	−5.61635	+	3.24260i	−0.0134042	+	0.00773890i	−0.506687	−	0.862130i	$-0.669130\pi$
$419$	−5.61635	+	3.24260i	−0.0134042	+	0.00773890i	0.493283	+	0.869869i	$0.335797\pi$
$420$	−1447.88	+	1445.19i	−3.44732	+	3.44092i
$421$	−200.295	−	115.640i	−0.475760	−	0.274680i	0.242888	−	0.970054i	$-0.421905\pi$
$421$	−200.295	−	115.640i	−0.475760	−	0.274680i	−0.718648	+	0.695374i	$0.755239\pi$
$422$	364.907			0.864710
$423$	0.265219	−	142.664i	0.000626996	−	0.337267i
$424$			1310.36i			3.09047i
$425$	−187.557	−	108.286i	−0.441310	−	0.254791i
$426$	59.4090	−	220.896i	0.139458	−	0.518535i
$427$	−5.25078	+	3.03154i	−0.0122969	+	0.00709963i
$428$	−281.155	+	162.325i	−0.656904	+	0.379264i
$429$	9.74597	−	85.6877i	0.0227179	−	0.199738i
$430$	339.266	−	587.626i	0.788991	−	1.36657i
$431$	−68.5059			−0.158947			−0.0794733	−	0.996837i	$-0.525324\pi$
$431$	−68.5059			−0.158947			−0.0794733	+	0.996837i	$0.525324\pi$
$432$	167.843	+	633.461i	0.388527	+	1.46634i
$433$	−266.248			−0.614892			−0.307446	−	0.951566i	$-0.599474\pi$
$433$	−266.248			−0.614892			−0.307446	+	0.951566i	$0.599474\pi$
$434$	603.960	−	1046.09i	1.39161	−	2.41035i
$435$	215.935	+	808.886i	0.496402	+	1.85951i
$436$	−1181.43	+	682.100i	−2.70970	+	1.56445i
$437$	−167.454	−	290.039i	−0.383190	−	0.663704i
$438$	−616.044	−	165.682i	−1.40649	−	0.378270i
$439$	−159.639	+	276.503i	−0.363642	+	0.629847i	−0.988557	−	0.150846i	$-0.951800\pi$
$439$	−159.639	+	276.503i	−0.363642	+	0.629847i	0.624915	+	0.780693i	$0.285134\pi$
$440$	−312.365			−0.709920
$441$	282.421	+	163.757i	0.640411	+	0.371331i
$442$	−194.960	−	76.5437i	−0.441086	−	0.173176i
$443$	−410.290	−	236.881i	−0.926162	−	0.534720i	−0.0405663	−	0.999177i	$-0.512916\pi$
$443$	−410.290	−	236.881i	−0.926162	−	0.534720i	−0.885596	+	0.464457i	$0.846250\pi$
$444$	67.5750	−	67.4495i	0.152196	−	0.151913i
$445$	−198.479	−	343.776i	−0.446020	−	0.772529i
$446$	752.691	−	434.567i	1.68765	−	0.974364i
$447$	−191.611	−	191.967i	−0.428660	−	0.429457i
$448$	−204.002	−	117.780i	−0.455361	−	0.262903i
$449$	−695.860			−1.54980			−0.774900	−	0.632084i	$-0.782200\pi$
$449$	−695.860			−1.54980			−0.774900	+	0.632084i	$0.782200\pi$
$450$	−1324.32	−	767.880i	−2.94292	−	1.70640i
$451$	99.7856			0.221254
$452$	142.557	+	82.3056i	0.315393	+	0.182092i
$453$	−337.179	−	90.6828i	−0.744324	−	0.200183i
$454$	−529.103	−	916.433i	−1.16542	−	2.01857i
$455$	−152.554	−	1012.97i	−0.335283	−	2.22630i
$456$	−264.573	−	991.082i	−0.580203	−	2.17343i
$457$	733.743	+	423.627i	1.60556	+	0.926973i	0.990346	+	0.138617i	$0.0442657\pi$
$457$	733.743	+	423.627i	1.60556	+	0.926973i	0.615219	+	0.788356i	$0.289068\pi$
$458$		−	1494.40i		−	3.26289i
$459$	86.2301	+	86.7124i	0.187865	+	0.188916i
$460$			1197.30i			2.60284i
$461$	111.907	−	193.829i	0.242749	−	0.420454i	−0.718747	−	0.695271i	$-0.755284\pi$
$461$	111.907	−	193.829i	0.242749	−	0.420454i	0.961496	+	0.274818i	$0.0886175\pi$
$462$	56.2042	+	210.539i	0.121654	+	0.455713i
$463$	529.309	−	305.596i	1.14322	−	0.660036i	0.195990	−	0.980606i	$-0.437208\pi$
$463$	529.309	−	305.596i	1.14322	−	0.660036i	0.947225	+	0.320570i	$0.103875\pi$
$464$	687.416	−	396.880i	1.48150	−	0.855345i
$465$	909.064	+	244.489i	1.95498	+	0.525783i
$466$	754.300	+	435.496i	1.61867	+	0.934540i
$467$		−	490.321i		−	1.04994i	−0.851121	−	0.524969i	$-0.824077\pi$
$467$		−	490.321i		−	1.04994i	0.851121	−	0.524969i	$-0.175923\pi$
$468$	−941.754	−	371.766i	−2.01229	−	0.794372i
$469$	−85.3263			−0.181932
$470$	240.583	−	416.702i	0.511878	−	0.886599i
$471$	344.765	+	345.407i	0.731985	+	0.733347i
$472$	253.038	+	438.275i	0.536097	+	0.928548i
$473$	−24.7151	−	42.8078i	−0.0522518	−	0.0905028i
$474$	−972.660	−	974.470i	−2.05203	−	2.05584i
$475$	855.348	+	493.836i	1.80073	+	1.03965i
$476$	361.936			0.760369
$477$	355.058	+	617.627i	0.744356	+	1.29482i
$478$	−1057.29			−2.21190
$479$	−198.146	+	343.199i	−0.413666	+	0.716490i	−0.995287	−	0.0969695i	$-0.969085\pi$
$479$	−198.146	+	343.199i	−0.413666	+	0.716490i	0.581622	+	0.813459i	$0.302418\pi$
$480$	−133.780	+	497.424i	−0.278708	+	1.03630i
$481$	7.11995	+	47.2770i	0.0148024	+	0.0982891i
$482$	−34.8527	+	20.1222i	−0.0723085	+	0.0417473i
$483$	433.981	−	115.853i	0.898512	−	0.239861i
$484$	502.389	−	870.163i	1.03799	−	1.79786i
$485$		−	91.2237i		−	0.188090i
$486$	608.375	+	614.056i	1.25180	+	1.26349i
$487$		−	535.852i		−	1.10031i	−0.835062	−	0.550156i	$-0.814568\pi$
$487$		−	535.852i		−	1.10031i	0.835062	−	0.550156i	$-0.185432\pi$
$488$	−5.43448	+	9.41280i	−0.0111362	+	0.0192885i
$489$	80.6586	+	302.145i	0.164946	+	0.617884i
$490$	550.534	+	953.553i	1.12354	+	1.94603i
$491$	−673.912	+	389.083i	−1.37253	+	0.792431i	−0.991246	−	0.132027i	$-0.957851\pi$
$491$	−673.912	+	389.083i	−1.37253	+	0.792431i	−0.381284	+	0.924458i	$0.624518\pi$
$492$	304.259	−	1131.30i	0.618413	−	2.29940i
$493$	74.0618	−	128.279i	0.150227	−	0.260200i
$494$	889.111	+	349.076i	1.79982	+	0.706631i
$495$	−147.231	+	84.6391i	−0.297436	+	0.170988i
$496$		−	892.509i		−	1.79941i
$497$	−171.420	−	98.9693i	−0.344909	−	0.199133i
$498$	−732.961	−	734.325i	−1.47181	−	1.47455i
$499$	487.876	−	281.675i	0.977708	−	0.564480i	0.0761305	−	0.997098i	$-0.475743\pi$
$499$	487.876	−	281.675i	0.977708	−	0.564480i	0.901577	+	0.432618i	$0.142410\pi$
$500$	−842.428	−	1459.13i	−1.68486	−	2.91826i
$501$	194.594	+	194.956i	0.388410	+	0.389133i
$502$	−616.206	−	355.767i	−1.22750	−	0.708698i
$503$		−	866.676i		−	1.72301i	−0.507746	−	0.861507i	$-0.669521\pi$
$503$		−	866.676i		−	1.72301i	0.507746	−	0.861507i	$-0.330479\pi$
$504$	1375.79	+	2.55766i	2.72974	+	0.00507472i
$505$		−	13.5518i		−	0.0268353i
$506$	110.452	+	63.7696i	0.218285	+	0.126027i
$507$	429.606	−	269.236i	0.847348	−	0.531037i
$508$	532.522	+	922.355i	1.04827	+	1.81566i
$509$	−41.4465	−	71.7874i	−0.0814272	−	0.141036i	0.822436	−	0.568858i	$-0.192614\pi$
$509$	−41.4465	−	71.7874i	−0.0814272	−	0.141036i	−0.903863	+	0.427822i	$0.859281\pi$
$510$	106.379	+	398.493i	0.208586	+	0.781358i
$511$	−276.010	+	478.063i	−0.540137	+	0.935544i
$512$	−1118.77			−2.18509
$513$	−393.250	−	395.450i	−0.766570	−	0.770857i
$514$		−	375.927i		−	0.731376i
$515$	−477.132	+	826.416i	−0.926469	+	1.60469i
$516$	−560.686	+	149.677i	−1.08660	+	0.290072i
$517$	−17.5262	−	30.3562i	−0.0338997	−	0.0587161i
$518$	−60.4035	−	104.622i	−0.116609	−	0.201973i
$519$	33.4327	+	8.99159i	0.0644176	+	0.0173248i
$520$	−1144.78	−	1435.87i	−2.20150	−	2.76129i
$521$		−	104.870i		−	0.201287i	−0.994923	−	0.100643i	$-0.967910\pi$
$521$		−	104.870i		−	0.201287i	0.994923	−	0.100643i	$-0.0320901\pi$
$522$	525.189	−	905.761i	1.00611	−	1.73517i
$523$	−171.381			−0.327688			−0.163844	−	0.986486i	$-0.552389\pi$
$523$	−171.381			−0.327688			−0.163844	+	0.986486i	$0.552389\pi$
$524$	−1807.06	−	1043.31i	−3.44860	−	1.99105i
$525$	−937.550	+	935.809i	−1.78581	+	1.78249i
$526$	604.591	−	349.061i	1.14941	−	0.663613i
$527$	−83.2756	−	144.238i	−0.158018	−	0.273696i
$528$	113.746	+	113.958i	0.215428	+	0.215829i
$529$	−133.053	+	230.455i	−0.251518	+	0.435642i
$530$			2402.76i			4.53351i
$531$	238.023	+	138.013i	0.448255	+	0.259912i
$532$	−1650.60			−3.10263
$533$	365.703	+	458.693i	0.686123	+	0.860587i
$534$	−128.931	+	479.396i	−0.241445	+	0.897745i
$535$	−277.243	+	160.066i	−0.518212	+	0.299190i
$536$	−132.467	+	76.4799i	−0.247140	+	0.142686i
$537$	−138.278	−	517.987i	−0.257501	−	0.964594i
$538$	−103.767	−	59.9101i	−0.192876	−	0.111357i
$539$	80.2115			0.148815
$540$	510.657	+	1927.28i	0.945661	+	3.56904i
$541$			654.979i			1.21068i	0.795966	+	0.605341i	$0.206963\pi$
$541$			654.979i			1.21068i	−0.795966	+	0.605341i	$0.793037\pi$
$542$	1004.67	+	580.045i	1.85363	+	1.07019i
$543$	−324.686	+	86.6761i	−0.597949	+	0.159624i
$544$	78.9242	−	45.5669i	0.145081	−	0.0837627i
$545$	−1164.99	+	672.610i	−2.13760	+	1.23415i
$546$	−761.822	+	1029.96i	−1.39528	+	1.88638i
$547$	14.2036	−	24.6014i	0.0259664	−	0.0449751i	−0.852750	−	0.522319i	$-0.825067\pi$
$547$	14.2036	−	24.6014i	0.0259664	−	0.0449751i	0.878717	+	0.477344i	$0.158400\pi$
$548$	1381.24			2.52051
$549$	−0.0109855	+	5.90919i	−2.00100e−5	+	0.0107635i
$550$	−376.124			−0.683861
$551$	−337.757	+	585.012i	−0.612989	+	1.06173i
$552$	569.904	−	568.846i	1.03244	−	1.03052i
$553$	−1031.78	+	595.701i	−1.86580	+	1.07722i
$554$	359.884	+	623.338i	0.649610	+	1.12516i
$555$	66.6348	−	66.5111i	0.120063	−	0.119840i
$556$	1052.63	−	1823.21i	1.89322	−	3.27916i
$557$	−94.4151			−0.169506			−0.0847532	−	0.996402i	$-0.527010\pi$
$557$	−94.4151			−0.169506			−0.0847532	+	0.996402i	$0.527010\pi$
$558$	−586.735	−	1020.63i	−1.05150	−	1.82909i
$559$	106.200	−	270.496i	0.189982	−	0.483893i
$560$	1656.31	+	956.273i	2.95770	+	1.70763i
$561$	29.0152	+	7.80353i	0.0517206	+	0.0139100i
$562$	652.413	+	1130.01i	1.16088	+	2.01070i
$563$	824.506	−	476.029i	1.46449	−	0.845522i	0.465273	−	0.885167i	$-0.345956\pi$
$563$	824.506	−	476.029i	1.46449	−	0.845522i	0.999214	+	0.0396457i	$0.0126229\pi$
$564$	−397.598	+	106.140i	−0.704961	+	0.188192i
$565$	140.574	+	81.1605i	0.248804	+	0.143647i
$566$	−499.584			−0.882656
$567$	649.159	−	371.581i	1.14490	−	0.655346i
$568$	−354.834			−0.624708
$569$	−815.701	−	470.945i	−1.43357	−	0.827671i	−0.436178	−	0.899861i	$-0.643668\pi$
$569$	−815.701	−	470.945i	−1.43357	−	0.827671i	−0.997391	+	0.0721892i	$0.977001\pi$
$570$	−485.138	−	1817.32i	−0.851120	−	3.18827i
$571$	−103.595	−	179.432i	−0.181427	−	0.314241i	0.760940	−	0.648823i	$-0.224738\pi$
$571$	−103.595	−	179.432i	−0.181427	−	0.314241i	−0.942367	+	0.334582i	$0.891405\pi$
$572$	−245.990	+	37.0463i	−0.430053	+	0.0647662i
$573$	763.388	+	205.310i	1.33226	+	0.358307i
$574$	−1283.72	−	741.154i	−2.23644	−	1.29121i
$575$			775.297i			1.34834i
$576$	−199.037	+	114.421i	−0.345551	+	0.198648i
$577$		−	424.521i		−	0.735738i	−0.929878	−	0.367869i	$-0.880087\pi$
$577$		−	424.521i		−	0.735738i	0.929878	−	0.367869i	$-0.119913\pi$
$578$	−477.529	+	827.104i	−0.826175	+	1.43098i
$579$	517.027	−	516.067i	0.892966	−	0.891308i
$580$	2091.44	−	1207.49i	3.60592	−	2.08188i
$581$	−777.515	+	448.899i	−1.33824	+	0.772631i
$582$	−80.7440	+	80.5940i	−0.138735	+	0.138478i
$583$	151.588	+	87.5192i	0.260013	+	0.150119i
$584$			989.576i			1.69448i
$585$	−928.652	−	366.594i	−1.58744	−	0.626656i
$586$	1497.70			2.55580
$587$	−113.586	+	196.736i	−0.193502	+	0.335156i	−0.946408	−	0.322972i	$-0.895318\pi$
$587$	−113.586	+	196.736i	−0.193502	+	0.335156i	0.752906	+	0.658128i	$0.228651\pi$
$588$	244.575	−	909.385i	0.415944	−	1.54657i
$589$	379.776	+	657.792i	0.644781	+	1.11679i
$590$	463.988	+	803.650i	0.786420	+	1.36212i
$591$	235.598	−	62.8936i	0.398643	−	0.106419i
$592$	−77.3031	−	44.6310i	−0.130580	−	0.0753902i
$593$	948.620			1.59970			0.799848	−	0.600202i	$-0.204913\pi$
$593$	948.620			1.59970			0.799848	+	0.600202i	$0.204913\pi$
$594$	204.991	+	55.5402i	0.345102	+	0.0935021i
$595$	356.900			0.599832
$596$	−391.190	+	677.561i	−0.656359	+	1.13685i
$597$	−84.7473	+	22.6236i	−0.141955	+	0.0378954i
$598$	111.660	+	741.433i	0.186723	+	1.23985i
$599$	−111.846	+	64.5744i	−0.186721	+	0.107804i	−0.590447	−	0.807077i	$-0.701048\pi$
$599$	−111.846	+	64.5744i	−0.186721	+	0.107804i	0.403725	+	0.914880i	$0.367715\pi$
$600$	−616.738	+	2293.17i	−1.02790	+	3.82195i
$601$	−540.338	+	935.893i	−0.899065	+	1.55723i	−0.0703728	+	0.997521i	$0.522419\pi$
$601$	−540.338	+	935.893i	−0.899065	+	1.55723i	−0.828692	+	0.559705i	$0.810914\pi$
$602$			734.282i			1.21974i
$603$	−41.7142	+	71.9418i	−0.0691777	+	0.119307i
$604$			1007.17i			1.66750i
$605$	495.399	−	858.056i	0.818842	−	1.41828i
$606$	−11.9950	+	11.9727i	−0.0197937	+	0.0197570i
$607$	−227.695	−	394.379i	−0.375115	−	0.649718i	0.615229	−	0.788348i	$-0.289063\pi$
$607$	−227.695	−	394.379i	−0.375115	−	0.649718i	−0.990344	+	0.138630i	$0.955730\pi$
$608$	−359.932	+	207.807i	−0.591993	+	0.341788i
$609$	−640.043	−	641.234i	−1.05097	−	1.05293i
$610$	−9.96504	+	17.2600i	−0.0163361	+	0.0282950i
$611$	75.3094	−	191.816i	0.123256	−	0.313938i
$612$	176.942	−	305.162i	0.289122	−	0.498630i
$613$			456.722i			0.745061i	0.928020	+	0.372530i	$0.121510\pi$
$613$			456.722i			0.745061i	−0.928020	+	0.372530i	$0.878490\pi$
$614$	−106.203	−	61.3163i	−0.172969	−	0.0998637i
$615$	300.026	−	1115.56i	0.487847	−	1.81392i
$616$	292.742	−	169.015i	0.475231	−	0.274375i
$617$	223.694	+	387.449i	0.362551	+	0.627957i	0.988380	−	0.152004i	$-0.0485726\pi$
$617$	223.694	+	387.449i	0.362551	+	0.627957i	−0.625829	+	0.779960i	$0.715239\pi$
$618$	1153.01	−	307.801i	1.86572	−	0.498059i
$619$	302.016	+	174.369i	0.487909	+	0.281694i	0.723707	−	0.690108i	$-0.242437\pi$
$619$	302.016	+	174.369i	0.487909	+	0.281694i	−0.235798	+	0.971802i	$0.575770\pi$
$620$		−	2715.42i		−	4.37971i
$621$	114.484	−	422.544i	0.184354	−	0.680425i
$622$		−	2123.06i		−	3.41328i
$623$	372.021	+	214.787i	0.597145	+	0.344762i
$624$	−106.972	+	940.509i	−0.171429	+	1.50723i
$625$	−233.002	−	403.571i	−0.372803	−	0.645714i
$626$	39.4178	+	68.2736i	0.0629677	+	0.109063i
$627$	−132.323	−	35.5878i	−0.211042	−	0.0567588i
$628$	703.867	−	1219.13i	1.12081	−	1.94130i
$629$	−16.6572			−0.0264820
$630$	2522.74	+	4.68990i	4.00435	+	0.00744429i
$631$			264.639i			0.419396i	0.977766	+	0.209698i	$0.0672481\pi$
$631$			264.639i			0.419396i	−0.977766	+	0.209698i	$0.932752\pi$
$632$	−1067.88	+	1849.62i	−1.68969	+	2.92662i
$633$	−217.409	−	217.813i	−0.343458	−	0.344097i
$634$	406.942	+	704.844i	0.641864	+	1.11174i
$635$	525.113	+	909.523i	0.826950	+	1.43232i
$636$	1454.44	−	1451.74i	2.28686	−	2.28262i
$637$	293.966	+	368.715i	0.461486	+	0.578830i
$638$		−	257.248i		−	0.403211i
$639$	−167.248	+	96.1467i	−0.261734	+	0.150464i
$640$	−1461.12			−2.28299
$641$	798.001	+	460.726i	1.24493	+	0.718761i	0.970094	−	0.242730i	$-0.0780429\pi$
$641$	798.001	+	460.726i	1.24493	+	0.718761i	0.274837	+	0.961491i	$0.411376\pi$
$642$	386.616	+	103.979i	0.602206	+	0.161961i
$643$	−456.685	+	263.667i	−0.710241	+	0.410058i	−0.811150	−	0.584838i	$-0.801158\pi$
$643$	−456.685	+	263.667i	−0.710241	+	0.410058i	0.100909	+	0.994896i	$0.467825\pi$
$644$	−647.839	−	1122.09i	−1.00596	−	1.74238i
$645$	−552.886	+	147.595i	−0.857187	+	0.228829i
$646$	−166.394	+	288.203i	−0.257576	+	0.446134i
$647$		−	854.869i		−	1.32128i	−0.750702	−	0.660641i	$-0.770285\pi$
$647$		−	854.869i		−	1.32128i	0.750702	−	0.660641i	$-0.229715\pi$
$648$	674.748	−	1158.73i	1.04128	−	1.78816i
$649$	67.6019			0.104163
$650$	−1378.45	−	1728.96i	−2.12070	−	2.65994i
$651$	−984.246	+	262.748i	−1.51190	+	0.403606i
$652$	781.219	−	451.037i	1.19819	−	0.691775i
$653$	504.015	−	290.993i	0.771845	−	0.445625i	−0.0616871	−	0.998096i	$-0.519648\pi$
$653$	504.015	−	290.993i	0.771845	−	0.445625i	0.833533	+	0.552470i	$0.186315\pi$
$654$	1624.59	+	436.926i	2.48408	+	0.668082i
$655$	−1781.92	−	1028.79i	−2.72049	−	1.57068i
$656$	−1095.25			−1.66959
$657$	268.138	+	466.429i	0.408125	+	0.709937i
$658$			520.700i			0.791337i
$659$	−282.573	−	163.144i	−0.428791	−	0.247563i	0.270040	−	0.962849i	$-0.412963\pi$
$659$	−282.573	−	163.144i	−0.428791	−	0.247563i	−0.698832	+	0.715286i	$0.746296\pi$
$660$	346.068	+	346.712i	0.524346	+	0.525321i
$661$	820.918	−	473.957i	1.24193	−	0.717030i	0.272445	−	0.962171i	$-0.412168\pi$
$661$	820.918	−	473.957i	1.24193	−	0.717030i	0.969487	+	0.245141i	$0.0788342\pi$
$662$	401.724	−	231.935i	0.606833	−	0.350355i
$663$	70.4666	+	161.976i	0.106284	+	0.244307i
$664$	−804.716	+	1393.81i	−1.21192	+	2.09911i
$665$	−1627.64			−2.44757
$666$	−117.741	−	0.218886i	−0.176788	−	0.000328658i
$667$	−530.261			−0.794995
$668$	397.279	−	688.108i	0.594730	−	1.03010i
$669$	−707.840	−	190.370i	−1.05806	−	0.284560i
$670$	−242.901	+	140.239i	−0.362539	+	0.209312i
$671$	0.725941	+	1.25737i	0.00108188	+	0.00187387i
$672$	−143.771	−	538.562i	−0.213945	−	0.801431i
$673$	568.119	−	984.011i	0.844159	−	1.46213i	−0.0421905	−	0.999110i	$-0.513434\pi$
$673$	568.119	−	984.011i	0.844159	−	1.46213i	0.886350	−	0.463017i	$-0.153233\pi$
$674$	−1991.14			−2.95422
$675$	330.668	+	1247.98i	0.489879	+	1.84886i
$676$	−1071.82	−	994.993i	−1.58553	−	1.47188i
$677$	158.811	+	91.6894i	0.234580	+	0.135435i	0.612683	−	0.790329i	$-0.290090\pi$
$677$	158.811	+	91.6894i	0.234580	+	0.135435i	−0.378103	+	0.925764i	$0.623424\pi$
$678$	−52.3571	−	196.129i	−0.0772229	−	0.289275i
$679$	49.3594	+	85.4930i	0.0726943	+	0.125910i
$680$	554.080	−	319.898i	0.814823	−	0.470438i
$681$	−231.784	+	861.824i	−0.340358	+	1.26553i
$682$	−250.499	−	144.626i	−0.367301	−	0.212061i
$683$	35.1239			0.0514259			0.0257130	−	0.999669i	$-0.491814\pi$
$683$	35.1239			0.0514259			0.0257130	+	0.999669i	$0.491814\pi$
$684$	−806.942	+	1391.68i	−1.17974	+	2.03462i
$685$	1362.02			1.98835
$686$	362.034	+	209.020i	0.527746	+	0.304694i
$687$	−892.009	+	890.352i	−1.29841	+	1.29600i
$688$	271.273	+	469.859i	0.394293	+	0.682935i
$689$	153.246	+	1017.56i	0.222418	+	1.47687i
$690$	1045.02	−	1043.07i	1.51452	−	1.51170i
$691$	−255.283	−	147.388i	−0.369440	−	0.213296i	0.303774	−	0.952744i	$-0.401753\pi$
$691$	−255.283	−	147.388i	−0.369440	−	0.213296i	−0.673214	+	0.739448i	$0.735087\pi$
$692$		−	99.8653i		−	0.144314i
$693$	92.1850	−	158.986i	0.133023	−	0.229417i
$694$			40.0701i			0.0577378i
$695$	1037.99	−	1797.84i	1.49351	−	2.58683i
$696$	−1568.41	−	421.816i	−2.25346	−	0.606057i
$697$	−177.002	+	102.192i	−0.253948	+	0.146617i
$698$	−640.785	+	369.958i	−0.918031	+	0.530025i
$699$	−189.458	−	709.706i	−0.271042	−	1.01532i
$700$	3309.14	+	1910.53i	4.72734	+	2.72933i
$701$			1218.80i			1.73866i	0.494235	+	0.869328i	$0.335448\pi$
$701$			1218.80i			1.73866i	−0.494235	+	0.869328i	$0.664552\pi$
$702$	495.962	+	1145.85i	0.706499	+	1.63226i
$703$	75.9647			0.108058
$704$	−28.2040	+	48.8508i	−0.0400625	+	0.0693903i
$705$	−392.066	+	104.663i	−0.556123	+	0.148459i
$706$	−710.618	−	1230.83i	−1.00654	−	1.74338i
$707$	7.33264	+	12.7005i	0.0103715	+	0.0179639i
$708$	206.127	−	766.425i	0.291140	−	1.08252i
$709$	1030.36	+	594.876i	1.45325	+	0.839035i	0.998664	−	0.0516675i	$-0.0164536\pi$
$709$	1030.36	+	594.876i	1.45325	+	0.839035i	0.454587	+	0.890702i	$0.349787\pi$
$710$	−650.648			−0.916405
$711$	−2.15866	+	1161.16i	−0.00303609	+	1.63314i
$712$	770.072			1.08156
$713$	−298.115	+	516.350i	−0.418113	+	0.724193i
$714$	−315.313	−	315.900i	−0.441615	−	0.442437i
$715$	−242.568	+	36.5309i	−0.339256	+	0.0510921i
$716$	−1339.29	+	773.242i	−1.87052	+	1.07995i
$717$	629.922	+	631.094i	0.878553	+	0.880188i
$718$	95.5911	−	165.569i	0.133135	−	0.230597i
$719$			218.688i			0.304155i	0.988369	+	0.152078i	$0.0485964\pi$
$719$			218.688i			0.304155i	−0.988369	+	0.152078i	$0.951404\pi$
$720$	1616.00	−	929.000i	2.24445	−	1.29028i
$721$		−	1032.67i		−	1.43227i
$722$	116.761	−	202.236i	0.161719	−	0.280105i
$723$	32.7759	+	8.81493i	0.0453331	+	0.0121922i
$724$	484.686	+	839.501i	0.669456	+	1.15953i
$725$	1354.28	−	781.893i	1.86797	−	1.07847i
$726$	−1197.16	+	319.585i	−1.64898	+	0.440200i
$727$	−343.657	+	595.231i	−0.472705	+	0.818750i	−0.999512	−	0.0312355i	$-0.990056\pi$
$727$	−343.657	+	595.231i	−0.472705	+	0.818750i	0.526807	+	0.849985i	$0.323389\pi$
$728$	1849.79	+	726.251i	2.54092	+	0.997597i
$729$	4.06572	−	728.989i	0.00557712	−	0.999984i
$730$			1814.55i			2.48569i
$731$	87.6805	+	50.6223i	0.119946	+	0.0692508i
$732$	16.4687	−	4.39636i	0.0224982	−	0.00600596i
$733$	−579.462	+	334.552i	−0.790535	+	0.456415i	−0.840151	−	0.542353i	$-0.817534\pi$
$733$	−579.462	+	334.552i	−0.790535	+	0.456415i	0.0496161	+	0.998768i	$0.484200\pi$
$734$	−378.204	−	655.069i	−0.515265	−	0.892464i
$735$	241.172	−	896.733i	0.328126	−	1.22004i
$736$	−282.538	−	163.123i	−0.383882	−	0.221635i
$737$			20.4325i			0.0277238i
$738$	−1252.48	+	720.016i	−1.69712	+	0.975631i
$739$			1086.56i			1.47032i	0.677895	+	0.735159i	$0.262892\pi$
$739$			1086.56i			1.47032i	−0.677895	+	0.735159i	$0.737108\pi$
$740$	−235.192	−	135.788i	−0.317827	−	0.183497i
$741$	−321.361	−	738.687i	−0.433686	−	0.996878i
$742$	−1300.09	−	2251.82i	−1.75214	−	3.03480i
$743$	−206.370	−	357.443i	−0.277752	−	0.481081i	0.693074	−	0.720867i	$-0.256256\pi$
$743$	−206.370	−	357.443i	−0.277752	−	0.481081i	−0.970826	+	0.239786i	$0.922923\pi$
$744$	−1292.51	+	1290.11i	−1.73725	+	1.73402i
$745$	−385.747	+	668.134i	−0.517782	+	0.896824i
$746$	2493.34			3.34227
$747$	−1.62669	+	875.009i	−0.00217763	+	1.17136i
$748$		−	86.6701i		−	0.115869i
$749$	173.218	−	300.022i	0.231266	−	0.400564i
$750$	−539.626	+	2006.45i	−0.719501	+	2.67527i
$751$	−706.938	−	1224.45i	−0.941328	−	1.63043i	−0.762941	−	0.646468i	$-0.776245\pi$
$751$	−706.938	−	1224.45i	−0.941328	−	1.63043i	−0.178387	−	0.983960i	$-0.557088\pi$
$752$	192.367	+	333.190i	0.255808	+	0.443072i
$753$	154.773	+	579.776i	0.205542	+	0.769955i
$754$	1182.51	−	942.787i	1.56832	−	1.25038i
$755$			993.158i			1.31544i
$756$	−1521.39	−	1529.90i	−2.01242	−	2.02368i
$757$	775.327			1.02421			0.512105	−	0.858923i	$-0.328866\pi$
$757$	775.327			1.02421			0.512105	+	0.858923i	$0.328866\pi$
$758$	956.068	+	551.986i	1.26130	+	0.728214i
$759$	−27.7424	−	103.922i	−0.0365512	−	0.136920i
$760$	−2526.87	+	1458.89i	−3.32482	+	1.91959i
$761$	−573.511	−	993.351i	−0.753629	−	1.30532i	−0.946053	−	0.324011i	$-0.894968\pi$
$761$	−573.511	−	993.351i	−0.753629	−	1.30532i	0.192425	−	0.981312i	$-0.438365\pi$
$762$	341.112	−	1268.33i	0.447654	−	1.66448i
$763$	727.873	−	1260.71i	0.953962	−	1.65231i
$764$		−	2280.28i		−	2.98466i
$765$	174.481	−	300.916i	0.228079	−	0.393354i
$766$	−617.791			−0.806516
$767$	247.753	+	310.751i	0.323016	+	0.405151i
$768$	1074.61	+	1076.61i	1.39923	+	1.40184i
$769$	1110.74	−	641.287i	1.44440	−	0.833923i	0.446258	−	0.894904i	$-0.352756\pi$
$769$	1110.74	−	641.287i	1.44440	−	0.833923i	0.998139	+	0.0609811i	$0.0194229\pi$
$770$	536.792	−	309.917i	0.697132	−	0.402490i
$771$	−224.391	+	223.974i	−0.291039	+	0.290498i
$772$

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+(-1.77860 + 3.08062i) q^{2} +(2.89850 - 0.773763i) q^{3} +(-4.32683 - 7.49428i) q^{4} +(-4.26663 - 7.39002i) q^{5} +(-2.77159 + 10.3054i) q^{6} +(7.99720 + 4.61719i) q^{7} +16.5540 q^{8} +(7.80258 - 4.48550i) q^{9} +30.3545 q^{10} +(1.10564 - 1.91503i) q^{11} +(-18.3401 - 18.3742i) q^{12} +(12.8550 - 1.93598i) q^{13} +(-28.4476 + 16.4242i) q^{14} +(-18.0849 - 18.1186i) q^{15} +(-12.1356 + 21.0194i) q^{16} +4.52923i q^{17} +(-0.0595170 + 32.0147i) q^{18} -20.6555i q^{19} +(-36.9219 + 63.9507i) q^{20} +(26.7525 + 7.19497i) q^{21} +(3.93299 + 6.81214i) q^{22} +(14.0417 - 8.10700i) q^{23} +(47.9816 - 12.8088i) q^{24} +(-23.9082 + 41.4103i) q^{25} +(-16.8999 + 43.0449i) q^{26} +(19.1450 - 19.0386i) q^{27} -79.9111i q^{28} +(-28.3224 - 16.3520i) q^{29} +(87.9824 - 23.4872i) q^{30} +(-31.8459 + 18.3862i) q^{31} +(-10.0606 - 17.4255i) q^{32} +(1.72292 - 6.40622i) q^{33} +(-13.9529 - 8.05569i) q^{34} -78.7993i q^{35} +(-67.3760 - 39.0668i) q^{36} +3.67771i q^{37} +(63.6317 + 36.7378i) q^{38} +(35.7623 - 15.5582i) q^{39} +(-70.6296 - 122.334i) q^{40} +(22.5628 + 39.0799i) q^{41} +(-69.7469 + 69.6174i) q^{42} +(11.1768 - 19.3588i) q^{43} -19.1357 q^{44} +(-66.4387 - 38.5232i) q^{45} +57.6764i q^{46} +(7.92578 - 13.7278i) q^{47} +(-18.9108 + 70.3147i) q^{48} +(18.1368 + 31.4139i) q^{49} +(-85.0463 - 147.305i) q^{50} +(3.50455 + 13.1280i) q^{51} +(-70.1303 - 87.9627i) q^{52} +79.1568i q^{53} +(24.5993 + 92.8407i) q^{54} -18.8695 q^{55} +(132.385 + 76.4328i) q^{56} +(-15.9824 - 59.8698i) q^{57} +(100.748 - 58.1671i) q^{58} +(15.2856 + 26.4755i) q^{59} +(-57.5355 + 213.930i) q^{60} +(-0.328289 + 0.568613i) q^{61} -130.807i q^{62} +(83.1092 + 0.154504i) q^{63} -25.5091 q^{64} +(-69.1546 - 86.7389i) q^{65} +(16.6708 + 16.7018i) q^{66} +(-8.00214 + 4.62004i) q^{67} +(33.9434 - 19.5972i) q^{68} +(34.4271 - 34.3631i) q^{69} +(242.751 + 140.152i) q^{70} -21.4350 q^{71} +(129.164 - 74.2528i) q^{72} +59.7788i q^{73} +(-11.3296 - 6.54116i) q^{74} +(-37.2562 + 138.527i) q^{75} +(-154.798 + 89.3726i) q^{76} +(17.6841 - 10.2099i) q^{77} +(-15.6779 + 137.842i) q^{78} +(-64.5091 + 111.733i) q^{79} +207.112 q^{80} +(40.7605 - 69.9970i) q^{81} -160.521 q^{82} +(-48.6117 + 84.1979i) q^{83} +(-61.8323 - 231.622i) q^{84} +(33.4711 - 19.3246i) q^{85} +(39.7581 + 68.8630i) q^{86} +(-94.7450 - 25.4813i) q^{87} +(18.3028 - 31.7013i) q^{88} +46.5189 q^{89} +(236.843 - 136.155i) q^{90} +(111.743 + 43.8717i) q^{91} +(-121.512 - 70.1552i) q^{92} +(-78.0787 + 77.9337i) q^{93} +(28.1936 + 48.8327i) q^{94} +(-152.644 + 88.1291i) q^{95} +(-42.6439 - 42.7233i) q^{96} +(9.25813 + 5.34518i) q^{97} -129.033 q^{98} +(0.0369980 - 19.9015i) 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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