LMFDB - Embedded newform 189.4.g.a.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(100,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$, degree $2$, not 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43564 - 4.21866i) q^{2} +(-7.86471 + 13.6221i) q^{4} +6.21080 q^{5} +(-4.64741 - 17.9277i) q^{7} +37.6522 q^{8} +O(q^{10})$	\(q+(-2.43564 - 4.21866i) q^{2} +(-7.86471 + 13.6221i) q^{4} +6.21080 q^{5} +(-4.64741 - 17.9277i) q^{7} +37.6522 q^{8} +(-15.1273 - 26.2012i) q^{10} -55.5320 q^{11} +(-6.74110 - 11.6759i) q^{13} +(-64.3113 + 63.2712i) q^{14} +(-28.7896 - 49.8651i) q^{16} +(43.1841 + 74.7970i) q^{17} +(-42.1062 + 72.9300i) q^{19} +(-48.8461 + 84.6039i) q^{20} +(135.256 + 234.270i) q^{22} -10.5364 q^{23} -86.4260 q^{25} +(-32.8378 + 56.8767i) q^{26} +(280.763 + 77.6886i) q^{28} +(-76.2157 + 132.009i) q^{29} +(127.033 - 220.027i) q^{31} +(10.3664 - 17.9551i) q^{32} +(210.362 - 364.358i) q^{34} +(-28.8641 - 111.345i) q^{35} +(-172.072 + 298.038i) q^{37} +410.222 q^{38} +233.850 q^{40} +(57.9241 + 100.328i) q^{41} +(46.7504 - 80.9741i) q^{43} +(436.743 - 756.461i) q^{44} +(25.6629 + 44.4494i) q^{46} +(159.921 + 276.991i) q^{47} +(-299.803 + 166.635i) q^{49} +(210.503 + 364.602i) q^{50} +212.067 q^{52} +(136.535 + 236.486i) q^{53} -344.898 q^{55} +(-174.985 - 675.016i) q^{56} +742.536 q^{58} +(175.149 - 303.367i) q^{59} +(145.565 + 252.126i) q^{61} -1237.63 q^{62} -561.629 q^{64} +(-41.8676 - 72.5168i) q^{65} +(-416.690 + 721.729i) q^{67} -1358.52 q^{68} +(-399.424 + 392.965i) q^{70} -771.625 q^{71} +(-140.112 - 242.682i) q^{73} +1676.42 q^{74} +(-662.305 - 1147.15i) q^{76} +(258.080 + 995.559i) q^{77} +(-172.942 - 299.545i) q^{79} +(-178.806 - 309.702i) q^{80} +(282.165 - 488.724i) q^{82} +(62.9091 - 108.962i) q^{83} +(268.207 + 464.549i) q^{85} -455.469 q^{86} -2090.90 q^{88} +(163.146 - 282.578i) q^{89} +(-177.994 + 175.115i) q^{91} +(82.8657 - 143.528i) q^{92} +(779.019 - 1349.30i) q^{94} +(-261.513 + 452.953i) q^{95} +(124.352 - 215.384i) q^{97} +(1433.19 + 858.904i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.43564	−	4.21866i	−0.861130	−	1.49152i	−0.870840	−	0.491567i	$-0.836424\pi$
$2$	−2.43564	−	4.21866i	−0.861130	−	1.49152i	0.00970988	−	0.999953i	$-0.496909\pi$
$3$		0			0
$3$		0			0
$4$	−7.86471	+	13.6221i	−0.983089	+	1.70276i
$5$	6.21080			0.555511			0.277755	−	0.960652i	$-0.410410\pi$
$5$	6.21080			0.555511			0.277755	+	0.960652i	$0.410410\pi$
$6$		0			0
$7$	−4.64741	−	17.9277i	−0.250937	−	0.968004i
$7$	−4.64741	−	17.9277i	−0.250937	−	0.968004i
$8$	37.6522			1.66401
$9$		0			0
$10$	−15.1273	−	26.2012i	−0.478367	−	0.828555i
$11$	−55.5320			−1.52214			−0.761069	−	0.648671i	$-0.775325\pi$
$11$	−55.5320			−1.52214			−0.761069	+	0.648671i	$0.775325\pi$
$12$		0			0
$13$	−6.74110	−	11.6759i	−0.143819	−	0.249101i	0.785113	−	0.619353i	$-0.212605\pi$
$13$	−6.74110	−	11.6759i	−0.143819	−	0.249101i	−0.928932	+	0.370251i	$0.879272\pi$
$14$	−64.3113	+	63.2712i	−1.22771	+	1.20785i
$15$		0			0
$16$	−28.7896	−	49.8651i	−0.449838	−	0.779141i
$17$	43.1841	+	74.7970i	0.616099	+	1.06711i	0.990191	+	0.139723i	$0.0446211\pi$
$17$	43.1841	+	74.7970i	0.616099	+	1.06711i	−0.374092	+	0.927392i	$0.622046\pi$
$18$		0			0
$19$	−42.1062	+	72.9300i	−0.508411	+	0.880594i	0.491541	+	0.870854i	$0.336434\pi$
$19$	−42.1062	+	72.9300i	−0.508411	+	0.880594i	−0.999953	+	0.00973986i	$0.996900\pi$
$20$	−48.8461	+	84.6039i	−0.546116	+	0.945901i
$21$		0			0
$22$	135.256	+	234.270i	1.31076	+	2.27030i
$23$	−10.5364			−0.0955213			−0.0477607	−	0.998859i	$-0.515208\pi$
$23$	−10.5364			−0.0955213			−0.0477607	+	0.998859i	$0.515208\pi$
$24$		0			0
$25$	−86.4260			−0.691408
$26$	−32.8378	+	56.8767i	−0.247693	+	0.429017i
$27$		0			0
$28$	280.763	+	77.6886i	1.89497	+	0.524349i
$29$	−76.2157	+	132.009i	−0.488031	+	0.845294i	−0.999905	−	0.0137662i	$-0.995618\pi$
$29$	−76.2157	+	132.009i	−0.488031	+	0.845294i	0.511874	+	0.859060i	$0.328951\pi$
$30$		0			0
$31$	127.033	−	220.027i	0.735992	−	1.27478i	−0.218295	−	0.975883i	$-0.570049\pi$
$31$	127.033	−	220.027i	0.735992	−	1.27478i	0.954287	−	0.298893i	$-0.0966173\pi$
$32$	10.3664	−	17.9551i	0.0572668	−	0.0991891i
$33$		0			0
$34$	210.362	−	364.358i	1.06108	−	1.83785i
$35$	−28.8641	−	111.345i	−0.139398	−	0.537736i
$36$		0			0
$37$	−172.072	+	298.038i	−0.764554	+	1.32425i	0.175928	+	0.984403i	$0.443707\pi$
$37$	−172.072	+	298.038i	−0.764554	+	1.32425i	−0.940482	+	0.339843i	$0.889626\pi$
$38$	410.222			1.75123
$39$		0			0
$40$	233.850			0.924374
$41$	57.9241	+	100.328i	0.220640	+	0.382159i	0.955002	−	0.296598i	$-0.0958521\pi$
$41$	57.9241	+	100.328i	0.220640	+	0.382159i	−0.734363	+	0.678757i	$0.762519\pi$
$42$		0			0
$43$	46.7504	−	80.9741i	0.165799	−	0.287173i	−0.771139	−	0.636666i	$-0.780313\pi$
$43$	46.7504	−	80.9741i	0.165799	−	0.287173i	0.936939	+	0.349493i	$0.113646\pi$
$44$	436.743	−	756.461i	1.49640	−	2.59184i
$45$		0			0
$46$	25.6629	+	44.4494i	0.0822562	+	0.142472i
$47$	159.921	+	276.991i	0.496316	+	0.859644i	0.999991	−	0.00424920i	$-0.00135257\pi$
$47$	159.921	+	276.991i	0.496316	+	0.859644i	−0.503675	+	0.863893i	$0.668019\pi$
$48$		0			0
$49$	−299.803	+	166.635i	−0.874062	+	0.485815i
$50$	210.503	+	364.602i	0.595392	+	1.03125i
$51$		0			0
$52$	212.067			0.565546
$53$	136.535	+	236.486i	0.353859	+	0.612902i	0.986922	−	0.161199i	$-0.0515359\pi$
$53$	136.535	+	236.486i	0.353859	+	0.612902i	−0.633063	+	0.774100i	$0.718203\pi$
$54$		0			0
$55$	−344.898			−0.845564
$56$	−174.985	−	675.016i	−0.417560	−	1.61076i
$57$		0			0
$58$	742.536			1.68103
$59$	175.149	−	303.367i	0.386482	−	0.669406i	−0.605492	−	0.795852i	$-0.707023\pi$
$59$	175.149	−	303.367i	0.386482	−	0.669406i	0.991974	+	0.126445i	$0.0403568\pi$
$60$		0			0
$61$	145.565	+	252.126i	0.305536	+	0.529205i	0.977381	−	0.211488i	$-0.0678309\pi$
$61$	145.565	+	252.126i	0.305536	+	0.529205i	−0.671844	+	0.740692i	$0.734498\pi$
$62$	−1237.63			−2.53514
$63$		0			0
$64$	−561.629			−1.09693
$65$	−41.8676	−	72.5168i	−0.0798928	−	0.138378i
$66$		0			0
$67$	−416.690	+	721.729i	−0.759804	+	1.31602i	0.183147	+	0.983086i	$0.441372\pi$
$67$	−416.690	+	721.729i	−0.759804	+	1.31602i	−0.942951	+	0.332933i	$0.891962\pi$
$68$	−1358.52			−2.42272
$69$		0			0
$70$	−399.424	+	392.965i	−0.682005	+	0.670975i
$71$	−771.625			−1.28979			−0.644895	−	0.764271i	$-0.723099\pi$
$71$	−771.625			−1.28979			−0.644895	+	0.764271i	$0.723099\pi$
$72$		0			0
$73$	−140.112	−	242.682i	−0.224643	−	0.389093i	0.731569	−	0.681767i	$-0.238788\pi$
$73$	−140.112	−	242.682i	−0.224643	−	0.389093i	−0.956212	+	0.292674i	$0.905455\pi$
$74$	1676.42			2.63352
$75$		0			0
$76$	−662.305	−	1147.15i	−0.999627	−	1.73140i
$77$	258.080	+	995.559i	0.381960	+	1.47344i
$78$		0			0
$79$	−172.942	−	299.545i	−0.246298	−	0.426600i	0.716198	−	0.697897i	$-0.245881\pi$
$79$	−172.942	−	299.545i	−0.246298	−	0.426600i	−0.962496	+	0.271297i	$0.912547\pi$
$80$	−178.806	−	309.702i	−0.249889	−	0.432821i
$81$		0			0
$82$	282.165	−	488.724i	0.379999	−	0.658177i
$83$	62.9091	−	108.962i	0.0831948	−	0.144098i	−0.821426	−	0.570315i	$-0.806821\pi$
$83$	62.9091	−	108.962i	0.0831948	−	0.144098i	0.904621	+	0.426218i	$0.140154\pi$
$84$		0			0
$85$	268.207	+	464.549i	0.342249	+	0.592793i
$86$	−455.469			−0.571099
$87$		0			0
$88$	−2090.90			−2.53285
$89$	163.146	−	282.578i	0.194309	−	0.336552i	−0.752365	−	0.658746i	$-0.771087\pi$
$89$	163.146	−	282.578i	0.194309	−	0.336552i	0.946674	+	0.322194i	$0.104420\pi$
$90$		0			0
$91$	−177.994	+	175.115i	−0.205042	+	0.201726i
$92$	82.8657	−	143.528i	0.0939059	−	0.162650i
$93$		0			0
$94$	779.019	−	1349.30i	0.854784	−	1.48053i
$95$	−261.513	+	452.953i	−0.282428	+	0.489179i
$96$		0			0
$97$	124.352	−	215.384i	0.130165	−	0.225453i	−0.793575	−	0.608472i	$-0.791783\pi$
$97$	124.352	−	215.384i	0.130165	−	0.225453i	0.923740	+	0.383020i	$0.125116\pi$
$98$	1433.19	+	858.904i	1.47728	+	0.885331i
$99$		0			0
$100$	679.715	−	1177.30i	0.679715	−	1.17730i
$101$	−1956.74			−1.92775			−0.963877	−	0.266349i	$-0.914183\pi$
$101$	−1956.74			−1.92775			−0.963877	+	0.266349i	$0.914183\pi$
$102$		0			0
$103$	−1895.80			−1.81358			−0.906790	−	0.421583i	$-0.861475\pi$
$103$	−1895.80			−1.81358			−0.906790	+	0.421583i	$0.861475\pi$
$104$	−253.817	−	439.624i	−0.239315	−	0.414507i
$105$		0			0
$106$	665.101	−	1151.99i	0.609437	−	1.05558i
$107$	518.000	−	897.202i	0.468009	−	0.810615i	−0.531323	−	0.847169i	$-0.678305\pi$
$107$	518.000	−	897.202i	0.468009	−	0.810615i	0.999332	+	0.0365546i	$0.0116383\pi$
$108$		0			0
$109$	−21.1870	−	36.6969i	−0.0186178	−	0.0322470i	0.856566	−	0.516037i	$-0.172593\pi$
$109$	−21.1870	−	36.6969i	−0.0186178	−	0.0322470i	−0.875184	+	0.483790i	$0.839260\pi$
$110$	840.048	+	1455.01i	0.728140	+	1.26118i
$111$		0			0
$112$	−760.167	+	747.874i	−0.641331	+	0.630959i
$113$	−1063.25	−	1841.60i	−0.885149	−	1.53312i	−0.845543	−	0.533908i	$-0.820723\pi$
$113$	−1063.25	−	1841.60i	−0.885149	−	1.53312i	−0.0396063	−	0.999215i	$-0.512610\pi$
$114$		0			0
$115$	−65.4394			−0.0530631
$116$	−1198.83	−	2076.43i	−0.959555	−	1.66200i
$117$		0			0
$118$	−1706.40			−1.33124
$119$	1140.24	−	1121.80i	0.878369	−	0.864164i
$120$		0			0
$121$	1752.80			1.31691
$122$	709.090	−	1228.18i	0.526213	−	0.911428i
$123$		0			0
$124$	1998.15	+	3460.90i	1.44709	+	2.50643i
$125$	−1313.12			−0.939595
$126$		0			0
$127$	1147.33			0.801646			0.400823	−	0.916156i	$-0.368724\pi$
$127$	1147.33			0.801646			0.400823	+	0.916156i	$0.368724\pi$
$128$	1285.00	+	2225.68i	0.887334	+	1.53691i
$129$		0			0
$130$	−203.949	+	353.250i	−0.137596	+	0.238324i
$131$	−142.943			−0.0953359			−0.0476679	−	0.998863i	$-0.515179\pi$
$131$	−142.943			−0.0953359			−0.0476679	+	0.998863i	$0.515179\pi$
$132$		0			0
$133$	1503.15	+	415.930i	0.979997	+	0.271171i
$134$	4059.64			2.61716
$135$		0			0
$136$	1625.97	+	2816.27i	1.02519	+	1.77569i
$137$	−1364.58			−0.850976			−0.425488	−	0.904964i	$-0.639898\pi$
$137$	−1364.58			−0.850976			−0.425488	+	0.904964i	$0.639898\pi$
$138$		0			0
$139$	549.346	+	951.496i	0.335215	+	0.580610i	0.983526	−	0.180766i	$-0.0578576\pi$
$139$	549.346	+	951.496i	0.335215	+	0.580610i	−0.648311	+	0.761376i	$0.724524\pi$
$140$	1743.76	+	482.508i	1.05268	+	0.291281i
$141$		0			0
$142$	1879.40	+	3255.22i	1.11068	+	1.92375i
$143$	374.346	+	648.387i	0.218912	+	0.379167i
$144$		0			0
$145$	−473.360	+	819.883i	−0.271106	+	0.469570i
$146$	−682.527	+	1182.17i	−0.386893	+	0.670118i
$147$		0			0
$148$	−2706.59	−	4687.96i	−1.50325	−	2.60370i
$149$	597.956			0.328768			0.164384	−	0.986396i	$-0.447436\pi$
$149$	597.956			0.328768			0.164384	+	0.986396i	$0.447436\pi$
$150$		0			0
$151$	−1269.70			−0.684283			−0.342141	−	0.939648i	$-0.611152\pi$
$151$	−1269.70			−0.684283			−0.342141	+	0.939648i	$0.611152\pi$
$152$	−1585.39	+	2745.97i	−0.846000	+	1.46532i
$153$		0			0
$154$	3571.33	−	3513.58i	1.86874	−	1.83852i
$155$	788.975	−	1366.54i	0.408851	−	0.708151i
$156$		0			0
$157$	−1282.59	+	2221.50i	−0.651984	+	1.12927i	0.330657	+	0.943751i	$0.392730\pi$
$157$	−1282.59	+	2221.50i	−0.651984	+	1.12927i	−0.982641	+	0.185518i	$0.940604\pi$
$158$	−842.451	+	1459.17i	−0.424189	+	0.734717i
$159$		0			0
$160$	64.3836	−	111.516i	0.0318123	−	0.0551006i
$161$	48.9670	+	188.893i	0.0239698	+	0.0924650i
$162$		0			0
$163$	1074.23	−	1860.62i	0.516196	−	0.894078i	−0.483627	−	0.875274i	$-0.660681\pi$
$163$	1074.23	−	1860.62i	0.516196	−	0.894078i	0.999823	−	0.0188039i	$-0.00598583\pi$
$164$	−1822.23			−0.867634
$165$		0			0
$166$	−612.896			−0.286566
$167$	700.461	+	1213.23i	0.324570	+	0.562173i	0.981425	−	0.191845i	$-0.0614469\pi$
$167$	700.461	+	1213.23i	0.324570	+	0.562173i	−0.656855	+	0.754017i	$0.728114\pi$
$168$		0			0
$169$	1007.62	−	1745.24i	0.458632	−	0.794374i
$170$	1306.52	−	2262.95i	0.589442	−	1.02094i
$171$		0			0
$172$	735.357	+	1273.68i	0.325991	+	0.564633i
$173$	−668.642	−	1158.12i	−0.293849	−	0.508962i	0.680867	−	0.732407i	$-0.261603\pi$
$173$	−668.642	−	1158.12i	−0.293849	−	0.508962i	−0.974717	+	0.223445i	$0.928270\pi$
$174$		0			0
$175$	401.657	+	1549.42i	0.173500	+	0.669285i
$176$	1598.74	+	2769.11i	0.684715	+	1.18596i
$177$		0			0
$178$	−1589.46			−0.669300
$179$	−512.284	−	887.302i	−0.213910	−	0.370503i	0.739025	−	0.673678i	$-0.235287\pi$
$179$	−512.284	−	887.302i	−0.213910	−	0.370503i	−0.952935	+	0.303175i	$0.901953\pi$
$180$		0			0
$181$	−892.316			−0.366438			−0.183219	−	0.983072i	$-0.558652\pi$
$181$	−892.316			−0.366438			−0.183219	+	0.983072i	$0.558652\pi$
$182$	1172.28	+	324.376i	0.477445	+	0.132112i
$183$		0			0
$184$	−396.718			−0.158948
$185$	−1068.71	+	1851.05i	−0.424718	+	0.735633i
$186$		0			0
$187$	−2398.10	−	4153.63i	−0.937787	−	1.62430i
$188$	−5030.92			−1.95169
$189$		0			0
$190$	2547.81			0.972828
$191$	−399.396	−	691.774i	−0.151305	−	0.262068i	0.780402	−	0.625278i	$-0.215014\pi$
$191$	−399.396	−	691.774i	−0.151305	−	0.262068i	−0.931707	+	0.363210i	$0.881681\pi$
$192$		0			0
$193$	348.814	−	604.163i	0.130094	−	0.225330i	−0.793619	−	0.608416i	$-0.791805\pi$
$193$	348.814	−	604.163i	0.130094	−	0.225330i	0.923713	+	0.383086i	$0.125139\pi$
$194$	−1211.51			−0.448356
$195$		0			0
$196$	87.9562	−	5394.47i	0.0320540	−	1.96592i
$197$	−84.5351			−0.0305730			−0.0152865	−	0.999883i	$-0.504866\pi$
$197$	−84.5351			−0.0305730			−0.0152865	+	0.999883i	$0.504866\pi$
$198$		0			0
$199$	−1291.09	−	2236.23i	−0.459914	−	0.796595i	0.539042	−	0.842279i	$-0.318786\pi$
$199$	−1291.09	−	2236.23i	−0.459914	−	0.796595i	−0.998956	+	0.0456844i	$0.985453\pi$
$200$	−3254.13			−1.15051
$201$		0			0
$202$	4765.92	+	8254.82i	1.66005	+	2.87528i
$203$	2720.83	+	752.868i	0.940712	+	0.260300i
$204$		0			0
$205$	359.755	+	623.114i	0.122568	+	0.212294i
$206$	4617.49	+	7997.73i	1.56173	+	2.70499i
$207$		0			0
$208$	−388.147	+	672.290i	−0.129390	+	0.224110i
$209$	2338.24	−	4049.95i	0.773872	−	1.34039i
$210$		0			0
$211$	−456.706	−	791.037i	−0.149009	−	0.258091i	0.781852	−	0.623464i	$-0.214275\pi$
$211$	−456.706	−	791.037i	−0.149009	−	0.258091i	−0.930861	+	0.365372i	$0.880942\pi$
$212$	−4295.23			−1.39150
$213$		0			0
$214$	−5046.65			−1.61206
$215$	290.357	−	502.914i	0.0921033	−	0.159528i
$216$		0			0
$217$	−4534.95	−	1254.85i	−1.41867	−	0.392555i
$218$	−103.208	+	178.761i	−0.0320647	+	0.0555378i
$219$		0			0
$220$	2712.52	−	4698.22i	0.831264	−	1.43979i
$221$	582.216	−	1008.43i	0.177213	−	0.306942i
$222$		0			0
$223$	484.137	−	838.550i	0.145382	−	0.251809i	−0.784133	−	0.620592i	$-0.786892\pi$
$223$	484.137	−	838.550i	0.145382	−	0.251809i	0.929515	+	0.368783i	$0.120226\pi$
$224$	−370.071	−	102.401i	−0.110386	−	0.0305443i
$225$		0			0
$226$	−5179.38	+	8970.95i	−1.52446	+	2.64044i
$227$	−3313.50			−0.968830			−0.484415	−	0.874838i	$-0.660967\pi$
$227$	−3313.50			−0.968830			−0.484415	+	0.874838i	$0.660967\pi$
$228$		0			0
$229$	3589.91			1.03593			0.517964	−	0.855402i	$-0.326690\pi$
$229$	3589.91			1.03593			0.517964	+	0.855402i	$0.326690\pi$
$230$	159.387	+	276.066i	0.0456942	+	0.0791447i
$231$		0			0
$232$	−2869.69	+	4970.44i	−0.812087	+	1.40658i
$233$	−2516.03	+	4357.90i	−0.707428	+	1.22530i	0.258379	+	0.966044i	$0.416812\pi$
$233$	−2516.03	+	4357.90i	−0.707428	+	1.22530i	−0.965808	+	0.259259i	$0.916522\pi$
$234$		0			0
$235$	993.235	+	1720.33i	0.275709	+	0.477541i
$236$	2754.99	+	4771.78i	0.759892	+	1.31617i
$237$		0			0
$238$	−7509.72	−	2077.98i	−2.04531	−	0.565948i
$239$	322.817	+	559.135i	0.0873694	+	0.151328i	0.906398	−	0.422424i	$-0.138821\pi$
$239$	322.817	+	559.135i	0.0873694	+	0.151328i	−0.819029	+	0.573752i	$0.805487\pi$
$240$		0			0
$241$	3195.72			0.854168			0.427084	−	0.904212i	$-0.359541\pi$
$241$	3195.72			0.854168			0.427084	+	0.904212i	$0.359541\pi$
$242$	−4269.20	−	7394.47i	−1.13403	−	1.96419i
$243$		0			0
$244$	−4579.31			−1.20148
$245$	−1862.02	+	1034.93i	−0.485550	+	0.269875i
$246$		0			0
$247$	1135.37			0.292476
$248$	4783.06	−	8284.50i	1.22470	−	2.12124i
$249$		0			0
$250$	3198.30	+	5539.62i	0.809113	+	1.40142i
$251$	3686.56			0.927066			0.463533	−	0.886080i	$-0.346582\pi$
$251$	3686.56			0.927066			0.463533	+	0.886080i	$0.346582\pi$
$252$		0			0
$253$	585.107			0.145397
$254$	−2794.48	−	4840.19i	−0.690321	−	1.19567i
$255$		0			0
$256$	4013.07	−	6950.84i	0.979753	−	1.69698i
$257$	−1591.76			−0.386347			−0.193174	−	0.981165i	$-0.561878\pi$
$257$	−1591.76			−0.386347			−0.193174	+	0.981165i	$0.561878\pi$
$258$		0			0
$259$	6142.81	+	1699.75i	1.47373	+	0.407789i
$260$	1317.11			0.314167
$261$		0			0
$262$	348.158	+	603.028i	0.0820966	+	0.142195i
$263$	3911.27			0.917032			0.458516	−	0.888686i	$-0.348381\pi$
$263$	3911.27			0.917032			0.458516	+	0.888686i	$0.348381\pi$
$264$		0			0
$265$	847.991	+	1468.76i	0.196572	+	0.340473i
$266$	−1906.47	−	7354.33i	−0.439448	−	1.69520i
$267$		0			0
$268$	−6554.30	−	11352.4i	−1.49391	−	2.58753i
$269$	191.371	+	331.465i	0.0433759	+	0.0751292i	0.886898	−	0.461965i	$-0.152855\pi$
$269$	191.371	+	331.465i	0.0433759	+	0.0751292i	−0.843522	+	0.537094i	$0.819522\pi$
$270$		0			0
$271$	403.244	−	698.439i	0.0903887	−	0.156558i	−0.817286	−	0.576232i	$-0.804522\pi$
$271$	403.244	−	698.439i	0.0903887	−	0.156558i	0.907675	+	0.419674i	$0.137856\pi$
$272$	2486.50	−	4306.75i	0.554289	−	0.960056i
$273$		0			0
$274$	3323.62	+	5756.69i	0.732801	+	1.26925i
$275$	4799.41			1.05242
$276$		0			0
$277$	−1333.55			−0.289261			−0.144630	−	0.989486i	$-0.546199\pi$
$277$	−1333.55			−0.289261			−0.144630	+	0.989486i	$0.546199\pi$
$278$	2676.02	−	4635.01i	0.577328	−	0.999961i
$279$		0			0
$280$	−1086.80	−	4192.39i	−0.231959	−	0.894797i
$281$	−1518.16	+	2629.53i	−0.322299	+	0.558238i	−0.980962	−	0.194200i	$-0.937789\pi$
$281$	−1518.16	+	2629.53i	−0.322299	+	0.558238i	0.658663	+	0.752438i	$0.271122\pi$
$282$		0			0
$283$	−1269.07	+	2198.09i	−0.266566	+	0.461706i	−0.967973	−	0.251055i	$-0.919222\pi$
$283$	−1269.07	+	2198.09i	−0.266566	+	0.461706i	0.701406	+	0.712761i	$0.252556\pi$
$284$	6068.61	−	10511.1i	1.26798	−	2.19620i
$285$		0			0
$286$	1823.55	−	3158.48i	0.377023	−	0.653024i
$287$	1529.44	−	1504.71i	0.314565	−	0.309478i
$288$		0			0
$289$	−1273.23	+	2205.30i	−0.259155	+	0.448870i
$290$	4611.74			0.933830
$291$		0			0
$292$	4407.77			0.883375
$293$	−1537.15	−	2662.43i	−0.306489	−	0.530855i	0.671102	−	0.741365i	$-0.265821\pi$
$293$	−1537.15	−	2662.43i	−0.306489	−	0.530855i	−0.977592	+	0.210510i	$0.932488\pi$
$294$		0			0
$295$	1087.81	−	1884.15i	0.214695	−	0.371862i
$296$	−6478.89	+	11221.8i	−1.27222	+	2.20355i
$297$		0			0
$298$	−1456.41	−	2522.57i	−0.283112	−	0.490365i
$299$	71.0269	+	123.022i	0.0137378	+	0.0237945i
$300$		0			0
$301$	−1668.95	−	461.807i	−0.319590	−	0.0884322i
$302$	3092.54	+	5356.43i	0.589256	+	1.02062i
$303$		0			0
$304$	4848.88			0.914810
$305$	904.076	+	1565.91i	0.169729	+	0.293979i
$306$		0			0
$307$	−8776.30			−1.63156			−0.815781	−	0.578360i	$-0.803693\pi$
$307$	−8776.30			−1.63156			−0.815781	+	0.578360i	$0.803693\pi$
$308$	−15591.3	−	4314.20i	−2.88441	−	0.798131i
$309$		0			0
$310$	−7686.64			−1.40830
$311$	1212.47	−	2100.06i	0.221070	−	0.382905i	−0.734063	−	0.679081i	$-0.762378\pi$
$311$	1212.47	−	2100.06i	0.221070	−	0.382905i	0.955133	+	0.296177i	$0.0957117\pi$
$312$		0			0
$313$	3254.62	+	5637.17i	0.587738	+	1.01799i	0.994528	+	0.104471i	$0.0333149\pi$
$313$	3254.62	+	5637.17i	0.587738	+	1.01799i	−0.406790	+	0.913522i	$0.633352\pi$
$314$	12495.7			2.24577
$315$		0			0
$316$	5440.56			0.968531
$317$	4869.93	+	8434.97i	0.862847	+	1.49450i	0.869169	+	0.494516i	$0.164655\pi$
$317$	4869.93	+	8434.97i	0.862847	+	1.49450i	−0.00632133	+	0.999980i	$0.502012\pi$
$318$		0			0
$319$	4232.41	−	7330.74i	0.742850	−	1.28665i
$320$	−3488.16			−0.609357
$321$		0			0
$322$	677.609	−	666.651i	0.117272	−	0.115376i
$323$	−7273.26			−1.25293
$324$		0			0
$325$	582.606	+	1009.10i	0.0994375	+	0.172231i
$326$	−10465.7			−1.77805
$327$		0			0
$328$	2180.97	+	3777.55i	0.367146	+	0.635916i
$329$	4222.58	−	4154.30i	0.707594	−	0.696151i
$330$		0			0
$331$	−3675.00	−	6365.29i	−0.610261	−	1.05700i	−0.991196	−	0.132401i	$-0.957731\pi$
$331$	−3675.00	−	6365.29i	−0.610261	−	1.05700i	0.380935	−	0.924602i	$-0.375602\pi$
$332$	989.524	+	1713.91i	0.163576	+	0.283322i
$333$		0			0
$334$	3412.14	−	5910.00i	0.558994	−	0.968207i
$335$	−2587.98	+	4482.51i	−0.422079	+	0.731062i
$336$		0			0
$337$	−2340.00	−	4053.01i	−0.378244	−	0.655137i	0.612563	−	0.790422i	$-0.290139\pi$
$337$	−2340.00	−	4053.01i	−0.378244	−	0.655137i	−0.990807	+	0.135284i	$0.956805\pi$
$338$	−9816.76			−1.57977
$339$		0			0
$340$	−8437.49			−1.34585
$341$	−7054.38	+	12218.5i	−1.12028	+	1.94039i
$342$		0			0
$343$	4380.68	+	4600.35i	0.689605	+	0.724186i
$344$	1760.26	−	3048.85i	0.275891	−	0.477858i
$345$		0			0
$346$	−3257.14	+	5641.54i	−0.506084	+	0.876564i
$347$	−3801.18	+	6583.84i	−0.588064	+	1.01856i	0.406422	+	0.913686i	$0.366776\pi$
$347$	−3801.18	+	6583.84i	−0.588064	+	1.01856i	−0.994486	+	0.104871i	$0.966557\pi$
$348$		0			0
$349$	−5989.27	+	10373.7i	−0.918619	+	1.59109i	−0.117105	+	0.993120i	$0.537361\pi$
$349$	−5989.27	+	10373.7i	−0.918619	+	1.59109i	−0.801515	+	0.597975i	$0.795972\pi$
$350$	5558.17	−	5468.28i	0.848847	−	0.835120i
$351$		0			0
$352$	−575.667	+	997.084i	−0.0871681	+	0.150979i
$353$	6559.32			0.989001			0.494500	−	0.869177i	$-0.335351\pi$
$353$	6559.32			0.989001			0.494500	+	0.869177i	$0.335351\pi$
$354$		0			0
$355$	−4792.41			−0.716492
$356$	2566.19	+	4444.78i	0.382045	+	0.661721i
$357$		0			0
$358$	−2495.48	+	4322.30i	−0.368409	+	0.638103i
$359$	−132.469	+	229.443i	−0.0194747	+	0.0337313i	−0.875599	−	0.483040i	$-0.839533\pi$
$359$	−132.469	+	229.443i	−0.0194747	+	0.0337313i	0.856124	+	0.516771i	$0.172866\pi$
$360$		0			0
$361$	−116.356	−	201.535i	−0.0169640	−	0.0293825i
$362$	2173.36	+	3764.37i	0.315551	+	0.546550i
$363$		0			0
$364$	−985.563	−	3801.87i	−0.141916	−	0.547451i
$365$	−870.210	−	1507.25i	−0.124791	−	0.216145i
$366$		0			0
$367$	−6000.06			−0.853408			−0.426704	−	0.904391i	$-0.640325\pi$
$367$	−6000.06			−0.853408			−0.426704	+	0.904391i	$0.640325\pi$
$368$	303.339	+	525.398i	0.0429691	+	0.0744246i
$369$		0			0
$370$	10411.9			1.46295
$371$	3605.10	−	3546.80i	0.504495	−	0.496336i
$372$		0			0
$373$	918.939			0.127563			0.0637813	−	0.997964i	$-0.479684\pi$
$373$	918.939			0.127563			0.0637813	+	0.997964i	$0.479684\pi$
$374$	−11681.8	+	20233.5i	−1.61511	+	2.79746i
$375$		0			0
$376$	6021.36	+	10429.3i	0.825873	+	1.43045i
$377$	2055.11			0.280752
$378$		0			0
$379$	6188.59			0.838751			0.419375	−	0.907813i	$-0.362249\pi$
$379$	6188.59			0.838751			0.419375	+	0.907813i	$0.362249\pi$
$380$	−4113.44	−	7124.69i	−0.555303	−	0.961813i
$381$		0			0
$382$	−1945.57	+	3369.83i	−0.260587	+	0.451349i
$383$	4141.94			0.552594			0.276297	−	0.961072i	$-0.410893\pi$
$383$	4141.94			0.552594			0.276297	+	0.961072i	$0.410893\pi$
$384$		0			0
$385$	1602.88	+	6183.22i	0.212183	+	0.818509i
$386$	−3398.34			−0.448112
$387$		0			0
$388$	1955.98	+	3387.86i	0.255928	+	0.443280i
$389$	−995.534			−0.129757			−0.0648786	−	0.997893i	$-0.520666\pi$
$389$	−995.534			−0.129757			−0.0648786	+	0.997893i	$0.520666\pi$
$390$		0			0
$391$	−455.005	−	788.091i	−0.0588506	−	0.101932i
$392$	−11288.2	+	6274.16i	−1.45444	+	0.808400i
$393$		0			0
$394$	205.897	+	356.625i	0.0263273	+	0.0456002i
$395$	−1074.11	−	1860.41i	−0.136821	−	0.236981i
$396$		0			0
$397$	4285.78	−	7423.18i	0.541806	−	0.938435i	−0.456994	−	0.889470i	$-0.651074\pi$
$397$	4285.78	−	7423.18i	0.541806	−	0.938435i	0.998800	−	0.0489659i	$-0.0155926\pi$
$398$	−6289.26	+	10893.3i	−0.792091	+	1.37194i
$399$		0			0
$400$	2488.17	+	4309.64i	0.311021	+	0.538705i
$401$	14097.1			1.75555			0.877775	−	0.479073i	$-0.159027\pi$
$401$	14097.1			1.75555			0.877775	+	0.479073i	$0.159027\pi$
$402$		0			0
$403$	−3425.36			−0.423398
$404$	15389.2	−	26654.9i	1.89515	−	3.28250i
$405$		0			0
$406$	−3450.87	−	13312.0i	−0.421832	−	1.62724i
$407$	9555.51	−	16550.6i	1.16376	−	2.01569i
$408$		0			0
$409$	−2429.12	+	4207.35i	−0.293673	+	0.508656i	−0.974675	−	0.223625i	$-0.928211\pi$
$409$	−2429.12	+	4207.35i	−0.293673	+	0.508656i	0.681003	+	0.732281i	$0.261544\pi$
$410$	1752.47	−	3035.37i	0.211093	−	0.365625i
$411$		0			0
$412$	14909.9	−	25824.7i	1.78291	−	3.08809i
$413$	−6252.65	−	1730.14i	−0.744970	−	0.206137i
$414$		0			0
$415$	390.716	−	676.739i	0.0462156	−	0.0800478i
$416$	−279.524			−0.0329442
$417$		0			0
$418$	−22780.4			−2.66562
$419$	3476.72	+	6021.85i	0.405367	+	0.702116i	0.994364	−	0.106019i	$-0.0338104\pi$
$419$	3476.72	+	6021.85i	0.405367	+	0.702116i	−0.588997	+	0.808135i	$0.700477\pi$
$420$		0			0
$421$	4777.73	−	8275.27i	0.553094	−	0.957986i	−0.444956	−	0.895553i	$-0.646781\pi$
$421$	4777.73	−	8275.27i	0.553094	−	0.957986i	0.998049	−	0.0624335i	$-0.0198861\pi$
$422$	−2224.74	+	3853.37i	−0.256632	+	0.444500i
$423$		0			0
$424$	5140.84	+	8904.20i	0.588824	+	1.01987i
$425$	−3732.23	−	6464.41i	−0.425976	−	0.737811i
$426$		0			0
$427$	3843.54	−	3781.38i	0.435602	−	0.428557i
$428$	8147.83	+	14112.5i	0.920188	+	1.59381i
$429$		0			0
$430$	−2828.83			−0.317252
$431$	1817.99	+	3148.84i	0.203177	+	0.351913i	0.949550	−	0.313615i	$-0.101540\pi$
$431$	1817.99	+	3148.84i	0.203177	+	0.351913i	−0.746373	+	0.665527i	$0.768207\pi$
$432$		0			0
$433$	2102.96			0.233399			0.116700	−	0.993167i	$-0.462768\pi$
$433$	2102.96			0.233399			0.116700	+	0.993167i	$0.462768\pi$
$434$	5751.75	+	22187.7i	0.636159	+	2.45402i
$435$		0			0
$436$	666.517			0.0732119
$437$	443.647	−	768.419i	0.0485641	−	0.0841155i
$438$		0			0
$439$	2023.15	+	3504.19i	0.219953	+	0.380970i	0.954793	−	0.297270i	$-0.0960762\pi$
$439$	2023.15	+	3504.19i	0.219953	+	0.380970i	−0.734840	+	0.678240i	$0.762743\pi$
$440$	−12986.2			−1.40702
$441$		0			0
$442$	−5672.28			−0.610414
$443$	−1906.77	−	3302.62i	−0.204499	−	0.354203i	0.745474	−	0.666535i	$-0.232223\pi$
$443$	−1906.77	−	3302.62i	−0.204499	−	0.354203i	−0.949973	+	0.312332i	$0.898890\pi$
$444$		0			0
$445$	1013.27	−	1755.03i	0.107940	−	0.186958i
$446$	−4716.74			−0.500771
$447$		0			0
$448$	2610.12	+	10068.7i	0.275260	+	1.06183i
$449$	−2025.85			−0.212931			−0.106465	−	0.994316i	$-0.533953\pi$
$449$	−2025.85			−0.212931			−0.106465	+	0.994316i	$0.533953\pi$
$450$		0			0
$451$	−3216.64	−	5571.39i	−0.335844	−	0.581699i
$452$	33448.5			3.48072
$453$		0			0
$454$	8070.49	+	13978.5i	0.834288	+	1.44503i
$455$	−1105.48	+	1087.60i	−0.113903	+	0.112061i
$456$		0			0
$457$	9393.37	+	16269.8i	0.961495	+	1.66536i	0.718751	+	0.695268i	$0.244714\pi$
$457$	9393.37	+	16269.8i	0.961495	+	1.66536i	0.242744	+	0.970090i	$0.421952\pi$
$458$	−8743.73	−	15144.6i	−0.892069	−	1.54511i
$459$		0			0
$460$	514.662	−	891.420i	0.0521657	−	0.0903537i
$461$	−2012.59	+	3485.90i	−0.203331	+	0.352179i	−0.949600	−	0.313466i	$-0.898510\pi$
$461$	−2012.59	+	3485.90i	−0.203331	+	0.352179i	0.746269	+	0.665645i	$0.231843\pi$
$462$		0			0
$463$	−6347.17	−	10993.6i	−0.637101	−	1.10349i	−0.986066	−	0.166356i	$-0.946800\pi$
$463$	−6347.17	−	10993.6i	−0.637101	−	1.10349i	0.348965	−	0.937136i	$-0.386533\pi$
$464$	8776.87			0.878138
$465$		0			0
$466$	24512.6			2.43675
$467$	1929.44	−	3341.89i	0.191186	−	0.331144i	−0.754457	−	0.656349i	$-0.772100\pi$
$467$	1929.44	−	3341.89i	0.191186	−	0.331144i	0.945644	+	0.325205i	$0.105433\pi$
$468$		0			0
$469$	14875.5	+	4116.12i	1.46457	+	0.405255i
$470$	4838.33	−	8380.23i	0.474842	−	0.822450i
$471$		0			0
$472$	6594.74	−	11422.4i	0.643109	−	1.11390i
$473$	−2596.14	+	4496.65i	−0.252370	+	0.437117i
$474$		0			0
$475$	3639.07	−	6303.05i	0.351520	−	0.608850i
$476$	6313.60	+	24355.1i	0.607949	+	2.34520i
$477$		0			0
$478$	1572.53	−	2723.71i	0.150473	−	0.260627i
$479$	−9491.81			−0.905411			−0.452706	−	0.891660i	$-0.649541\pi$
$479$	−9491.81			−0.905411			−0.452706	+	0.891660i	$0.649541\pi$
$480$		0			0
$481$	4639.82			0.439829
$482$	−7783.63	−	13481.6i	−0.735549	−	1.27401i
$483$		0			0
$484$	−13785.3	+	23876.8i	−1.29463	+	2.24237i
$485$	772.324	−	1337.70i	0.0723081	−	0.125241i
$486$		0			0
$487$	7850.24	+	13597.0i	0.730448	+	1.26517i	0.956692	+	0.291102i	$0.0940220\pi$
$487$	7850.24	+	13597.0i	0.730448	+	1.26517i	−0.226244	+	0.974071i	$0.572645\pi$
$488$	5480.85	+	9493.11i	0.508415	+	0.880600i
$489$		0			0
$490$	8901.23	+	5334.48i	0.820646	+	0.491811i
$491$	−5964.99	−	10331.7i	−0.548261	−	0.949616i	−0.998394	−	0.0566544i	$-0.981957\pi$
$491$	−5964.99	−	10331.7i	−0.548261	−	0.949616i	0.450133	−	0.892962i	$-0.351377\pi$
$492$		0			0
$493$	−13165.2			−1.20270
$494$	−2765.35	−	4789.72i	−0.251860	−	0.436234i
$495$		0			0
$496$	−14628.9			−1.32431
$497$	3586.06	+	13833.4i	0.323655	+	1.24852i
$498$		0			0
$499$	18196.3			1.63242			0.816209	−	0.577757i	$-0.196072\pi$
$499$	18196.3			1.63242			0.816209	+	0.577757i	$0.196072\pi$
$500$	10327.3	−	17887.5i	0.923705	−	1.59990i
$501$		0			0
$502$	−8979.14	−	15552.3i	−0.798324	−	1.38274i
$503$	−1851.20			−0.164097			−0.0820487	−	0.996628i	$-0.526146\pi$
$503$	−1851.20			−0.164097			−0.0820487	+	0.996628i	$0.526146\pi$
$504$		0			0
$505$	−12152.9			−1.07089
$506$	−1425.11	−	2468.37i	−0.125205	−	0.216862i
$507$		0			0
$508$	−9023.41	+	15629.0i	−0.788088	+	1.36501i
$509$	−21592.6			−1.88030			−0.940151	−	0.340757i	$-0.889317\pi$
$509$	−21592.6			−1.88030			−0.940151	+	0.340757i	$0.889317\pi$
$510$		0			0
$511$	−3699.56	+	3639.73i	−0.320272	+	0.315092i
$512$	−18537.6			−1.60011
$513$		0			0
$514$	3876.96	+	6715.09i	0.332695	+	0.576245i
$515$	−11774.4			−1.00746
$516$		0			0
$517$	−8880.71	−	15381.8i	−0.755461	−	1.30850i
$518$	−7791.04	−	30054.4i	−0.660846	−	2.54926i
$519$		0			0
$520$	−1576.41	−	2730.42i	−0.132942	−	0.230263i
$521$	647.296	+	1121.15i	0.0544310	+	0.0942772i	0.891957	−	0.452120i	$-0.149332\pi$
$521$	647.296	+	1121.15i	0.0544310	+	0.0942772i	−0.837526	+	0.546397i	$0.815999\pi$
$522$		0			0
$523$	5051.51	−	8749.48i	0.422347	−	0.731526i	−0.573822	−	0.818980i	$-0.694540\pi$
$523$	5051.51	−	8749.48i	0.422347	−	0.731526i	0.996169	+	0.0874543i	$0.0278732\pi$
$524$	1124.21	−	1947.18i	0.0937236	−	0.162334i
$525$		0			0
$526$	−9526.47	−	16500.3i	−0.789684	−	1.36777i
$527$	21943.2			1.81377
$528$		0			0
$529$	−12056.0			−0.990876
$530$	4130.81	−	7154.77i	0.338549	−	0.586383i
$531$		0			0
$532$	−17487.7	+	17204.9i	−1.42516	+	1.40211i
$533$	780.945	−	1352.64i	0.0634643	−	0.109923i
$534$		0			0
$535$	3217.19	−	5572.34i	0.259984	−	0.450305i
$536$	−15689.3	+	27174.7i	−1.26432	+	2.18986i
$537$		0			0
$538$	932.224	−	1614.66i	0.0747045	−	0.129392i
$539$	16648.7	−	9253.55i	1.33044	−	0.739478i
$540$		0			0
$541$	284.987	−	493.612i	0.0226480	−	0.0392275i	−0.854479	−	0.519485i	$-0.826124\pi$
$541$	284.987	−	493.612i	0.0226480	−	0.0392275i	0.877127	+	0.480258i	$0.159457\pi$
$542$	−3928.63			−0.311346
$543$		0			0
$544$	1790.65			0.141128
$545$	−131.588	−	227.917i	−0.0103424	−	0.0179136i
$546$		0			0
$547$	7263.43	−	12580.6i	0.567755	−	0.983380i	−0.429033	−	0.903289i	$-0.641145\pi$
$547$	7263.43	−	12580.6i	0.567755	−	0.983380i	0.996788	−	0.0800915i	$-0.0255212\pi$
$548$	10732.0	−	18588.4i	0.836585	−	1.44901i
$549$		0			0
$550$	−11689.6	−	20247.1i	−0.906269	−	1.56970i
$551$	−6418.30	−	11116.8i	−0.496241	−	0.859514i
$552$		0			0
$553$	−4566.41	+	4492.56i	−0.351146	+	0.345467i
$554$	3248.05	+	5625.79i	0.249091	+	0.431438i
$555$		0			0
$556$	−17281.8			−1.31819
$557$	8262.96	+	14311.9i	0.628569	+	1.08871i	0.987839	+	0.155480i	$0.0496924\pi$
$557$	8262.96	+	14311.9i	0.628569	+	1.08871i	−0.359270	+	0.933234i	$0.616974\pi$
$558$		0			0
$559$	−1260.60			−0.0953803
$560$	−4721.24	+	4644.89i	−0.356266	+	0.350505i
$561$		0			0
$562$	14790.8			1.11016
$563$	−10369.6	+	17960.7i	−0.776249	+	1.34450i	0.157841	+	0.987465i	$0.449547\pi$
$563$	−10369.6	+	17960.7i	−0.776249	+	1.34450i	−0.934090	+	0.357038i	$0.883787\pi$
$564$		0			0
$565$	−6603.61	−	11437.8i	−0.491710	−	0.851666i
$566$	12364.0			0.918193
$567$		0			0
$568$	−29053.4			−2.14622
$569$	−7379.18	−	12781.1i	−0.543675	−	0.941673i	−0.998689	−	0.0511888i	$-0.983699\pi$
$569$	−7379.18	−	12781.1i	−0.543675	−	0.941673i	0.455014	−	0.890484i	$-0.349634\pi$
$570$		0			0
$571$	−4762.17	+	8248.33i	−0.349021	+	0.604522i	−0.986076	−	0.166297i	$-0.946819\pi$
$571$	−4762.17	+	8248.33i	−0.349021	+	0.604522i	0.637055	+	0.770818i	$0.280152\pi$
$572$	−11776.5			−0.860840
$573$		0			0
$574$	−10073.0	−	2787.26i	−0.732474	−	0.202680i
$575$	910.619			0.0660442
$576$		0			0
$577$	−3301.32	−	5718.06i	−0.238190	−	0.412558i	0.722005	−	0.691888i	$-0.243221\pi$
$577$	−3301.32	−	5718.06i	−0.238190	−	0.412558i	−0.960195	+	0.279330i	$0.909888\pi$
$578$	12404.5			0.892664
$579$		0			0
$580$	−7445.67	−	12896.3i	−0.533043	−	0.923257i
$581$	−2245.80	−	621.424i	−0.160364	−	0.0443735i
$582$		0			0
$583$	−7582.06	−	13132.5i	−0.538622	−	0.932921i
$584$	−5275.54	−	9137.50i	−0.373807	−	0.647453i
$585$		0			0
$586$	−7487.90	+	12969.4i	−0.527854	+	0.914270i
$587$	9789.93	−	16956.7i	0.688371	−	1.19229i	−0.283994	−	0.958826i	$-0.591659\pi$
$587$	9789.93	−	16956.7i	0.688371	−	1.19229i	0.972365	−	0.233467i	$-0.0750072\pi$
$588$		0			0
$589$	10697.7	+	18529.0i	0.748373	+	1.29622i
$590$	−10598.1			−0.739520
$591$		0			0
$592$	19815.6			1.37570
$593$	207.262	−	358.988i	0.0143528	−	0.0248598i	−0.858760	−	0.512378i	$-0.828765\pi$
$593$	207.262	−	358.988i	0.0143528	−	0.0248598i	0.873113	+	0.487519i	$0.162098\pi$
$594$		0			0
$595$	7081.81	−	6967.29i	0.487943	−	0.480052i
$596$	−4702.75	+	8145.40i	−0.323208	+	0.559813i
$597$		0			0
$598$	345.992	−	599.276i	0.0236600	−	0.0409803i
$599$	1890.06	−	3273.67i	0.128924	−	0.223303i	−0.794336	−	0.607479i	$-0.792181\pi$
$599$	1890.06	−	3273.67i	0.128924	−	0.223303i	0.923260	+	0.384176i	$0.125514\pi$
$600$		0			0
$601$	−9461.13	+	16387.2i	−0.642143	+	1.11222i	0.342811	+	0.939404i	$0.388621\pi$
$601$	−9461.13	+	16387.2i	−0.642143	+	1.11222i	−0.984954	+	0.172819i	$0.944712\pi$
$602$	2116.75	+	8165.51i	0.143310	+	0.552826i
$603$		0			0
$604$	9985.82	−	17295.9i	0.672711	−	1.16517i
$605$	10886.3			0.731555
$606$		0			0
$607$	−28176.5			−1.88410			−0.942050	−	0.335472i	$-0.891104\pi$
$607$	−28176.5			−1.88410			−0.942050	+	0.335472i	$0.891104\pi$
$608$	872.979	+	1512.04i	0.0582302	+	0.100858i
$609$		0			0
$610$	4404.01	−	7627.97i	0.292317	−	0.506308i
$611$	2156.08	−	3734.44i	0.142759	−	0.247266i
$612$		0			0
$613$	3008.42	+	5210.73i	0.198220	+	0.343327i	0.947951	−	0.318415i	$-0.103151\pi$
$613$	3008.42	+	5210.73i	0.198220	+	0.343327i	−0.749731	+	0.661742i	$0.769817\pi$
$614$	21375.9	+	37024.2i	1.40499	+	2.43351i
$615$		0			0
$616$	9717.27	+	37485.0i	0.635585	+	2.45181i
$617$	−3597.75	−	6231.49i	−0.234749	−	0.406597i	0.724451	−	0.689327i	$-0.242093\pi$
$617$	−3597.75	−	6231.49i	−0.234749	−	0.406597i	−0.959200	+	0.282729i	$0.908760\pi$
$618$		0			0
$619$	9165.92			0.595169			0.297584	−	0.954696i	$-0.403819\pi$
$619$	9165.92			0.595169			0.297584	+	0.954696i	$0.403819\pi$
$620$	12410.1	+	21494.9i	0.803874	+	1.39235i
$621$		0			0
$622$	−11812.6			−0.761480
$623$	−5824.17	−	1611.58i	−0.374543	−	0.103638i
$624$		0			0
$625$	2647.71			0.169453
$626$	15854.2	−	27460.3i	1.01224	−	1.75325i
$627$		0			0
$628$	−20174.3	−	34942.9i	−1.28192	−	2.22034i
$629$	−29723.1			−1.88416
$630$		0			0
$631$	19395.9			1.22368			0.611838	−	0.790983i	$-0.290431\pi$
$631$	19395.9			1.22368			0.611838	+	0.790983i	$0.290431\pi$
$632$	−6511.66	−	11278.5i	−0.409842	−	0.709866i
$633$		0			0
$634$	23722.8	−	41089.1i	1.48605	−	2.57391i
$635$	7125.83			0.445323
$636$		0			0
$637$	3966.61	+	2377.18i	0.246724	+	0.147861i
$638$	−41234.5			−2.55876
$639$		0			0
$640$	7980.85	+	13823.2i	0.492923	+	0.853768i
$641$	−7779.25			−0.479348			−0.239674	−	0.970853i	$-0.577041\pi$
$641$	−7779.25			−0.479348			−0.239674	+	0.970853i	$0.577041\pi$
$642$		0			0
$643$	1786.80	+	3094.83i	0.109587	+	0.189810i	0.915603	−	0.402083i	$-0.131714\pi$
$643$	1786.80	+	3094.83i	0.109587	+	0.189810i	−0.806016	+	0.591894i	$0.798380\pi$
$644$	−2958.23	−	818.558i	−0.181010	−	0.0500865i
$645$		0			0
$646$	17715.1	+	30683.4i	1.07893	+	1.86876i
$647$	−8518.34	−	14754.2i	−0.517605	−	0.896518i	−0.999791	−	0.0204493i	$-0.993490\pi$
$647$	−8518.34	−	14754.2i	−0.517605	−	0.896518i	0.482186	−	0.876069i	$-0.339843\pi$
$648$		0			0
$649$	−9726.36	+	16846.6i	−0.588279	+	1.01893i
$650$	2838.04	−	4915.63i	0.171257	−	0.296626i
$651$		0			0
$652$	16897.0	+	29266.4i	1.01493	+	1.75792i
$653$	−4227.77			−0.253362			−0.126681	−	0.991944i	$-0.540432\pi$
$653$	−4227.77			−0.253362			−0.126681	+	0.991944i	$0.540432\pi$
$654$		0			0
$655$	−887.791			−0.0529601
$656$	3335.23	−	5776.78i	0.198504	−	0.343819i
$657$		0			0
$658$	−27810.3	−	7695.25i	−1.64765	−	0.455915i
$659$	−9443.52	+	16356.6i	−0.558220	+	0.966866i	0.439425	+	0.898279i	$0.355182\pi$
$659$	−9443.52	+	16356.6i	−0.558220	+	0.966866i	−0.997645	+	0.0685865i	$0.978151\pi$
$660$		0			0
$661$	779.007	−	1349.28i	0.0458394	−	0.0793962i	−0.842195	−	0.539172i	$-0.818737\pi$
$661$	779.007	−	1349.28i	0.0458394	−	0.0793962i	0.888035	+	0.459776i	$0.152070\pi$
$662$	−17902.0	+	31007.1i	−1.05103	+	1.82043i
$663$		0			0
$664$	2368.67	−	4102.65i	0.138437	−	0.239780i
$665$	9335.76	+	2583.26i	0.544399	+	0.150638i
$666$		0			0
$667$	803.038	−	1390.90i	0.0466173	−	0.0807436i
$668$	−22035.7			−1.27633
$669$		0			0
$670$	25213.6			1.45386
$671$	−8083.53	−	14001.1i	−0.465069	−	0.805523i
$672$		0			0
$673$	−4809.90	+	8330.98i	−0.275495	+	0.477171i	−0.970260	−	0.242066i	$-0.922175\pi$
$673$	−4809.90	+	8330.98i	−0.275495	+	0.477171i	0.694765	+	0.719237i	$0.255508\pi$
$674$	−11398.8	+	19743.3i	−0.651434	+	1.12832i
$675$		0			0
$676$	15849.2	+	27451.6i	0.901752	+	1.56188i
$677$	6825.65	+	11822.4i	0.387491	+	0.671153i	0.992111	−	0.125360i	$-0.0400086\pi$
$677$	6825.65	+	11822.4i	0.387491	+	0.671153i	−0.604621	+	0.796514i	$0.706675\pi$
$678$		0			0
$679$	−4439.24	−	1228.36i	−0.250902	−	0.0694260i
$680$	10098.6	+	17491.3i	0.569505	+	0.986412i
$681$		0			0
$682$	68727.8			3.85883
$683$	−1545.24	−	2676.43i	−0.0865694	−	0.149943i	0.819489	−	0.573094i	$-0.194257\pi$
$683$	−1545.24	−	2676.43i	−0.0865694	−	0.149943i	−0.906059	+	0.423152i	$0.860924\pi$
$684$		0			0
$685$	−8475.12			−0.472726
$686$	8737.55	−	29685.4i	0.486299	−	1.65218i
$687$		0			0
$688$	−5383.71			−0.298331
$689$	1840.79	−	3188.34i	0.101783	−	0.176294i
$690$		0			0
$691$	−529.152	−	916.518i	−0.0291315	−	0.0504573i	0.851092	−	0.525016i	$-0.175941\pi$
$691$	−529.152	−	916.518i	−0.0291315	−	0.0504573i	−0.880224	+	0.474559i	$0.842607\pi$
$692$	21034.7			1.15552
$693$		0			0
$694$	37033.3			2.02560
$695$	3411.88	+	5909.55i	0.186216	+	0.322535i
$696$		0			0
$697$	−5002.80	+	8665.11i	−0.271872	+	0.470896i
$698$	58350.8			3.16420
$699$		0			0
$700$	−24265.2	−	6714.31i	−1.31020	−	0.362539i
$701$	−3542.05			−0.190844			−0.0954219	−	0.995437i	$-0.530420\pi$
$701$	−3542.05			−0.190844			−0.0954219	+	0.995437i	$0.530420\pi$
$702$		0			0
$703$	−14490.6	−	25098.4i	−0.777415	−	1.34652i
$704$	31188.4			1.66968
$705$		0			0
$706$	−15976.2	−	27671.5i	−0.851658	−	1.47511i
$707$	9093.78	+	35079.8i	0.483744	+	1.86607i
$708$		0			0
$709$	−10434.4	−	18073.0i	−0.552712	−	0.957326i	−0.998078	−	0.0619768i	$-0.980260\pi$
$709$	−10434.4	−	18073.0i	−0.552712	−	0.957326i	0.445365	−	0.895349i	$-0.353074\pi$
$710$	11672.6	+	20217.5i	0.616992	+	1.06866i
$711$		0			0
$712$	6142.81	−	10639.7i	0.323331	−	0.560026i
$713$	−1338.47	+	2318.29i	−0.0703029	+	0.121768i
$714$		0			0
$715$	2324.99	+	4027.00i	0.121608	+	0.210631i
$716$	16115.9			0.841170
$717$		0			0
$718$	1290.59			0.0670811
$719$	4711.93	−	8161.31i	0.244403	−	0.423318i	−0.717561	−	0.696496i	$-0.754742\pi$
$719$	4711.93	−	8161.31i	0.244403	−	0.423318i	0.961963	+	0.273178i	$0.0880748\pi$
$720$		0			0
$721$	8810.56	+	33987.3i	0.455094	+	1.75555i
$722$	−566.803	+	981.732i	−0.0292164	+	0.0506043i
$723$		0			0
$724$	7017.80	−	12155.2i	0.360241	−	0.623956i
$725$	6587.01	−	11409.0i	0.337428	−	0.584443i
$726$		0			0
$727$	−5340.37	+	9249.79i	−0.272439	+	0.471879i	−0.969486	−	0.245147i	$-0.921164\pi$
$727$	−5340.37	+	9249.79i	−0.272439	+	0.471879i	0.697047	+	0.717026i	$0.254497\pi$
$728$	−6701.85	+	6593.46i	−0.341191	+	0.335673i
$729$		0			0
$730$	−4239.04	+	7342.23i	−0.214923	+	0.372258i
$731$	8075.50			0.408595
$732$		0			0
$733$	27511.4			1.38630			0.693149	−	0.720794i	$-0.256223\pi$
$733$	27511.4			1.38630			0.693149	+	0.720794i	$0.256223\pi$
$734$	14614.0	+	25312.2i	0.734895	+	1.27288i
$735$		0			0
$736$	−109.225	+	189.182i	−0.00547020	+	0.00947467i
$737$	23139.6	−	40079.0i	1.15653	−	2.00316i
$738$		0			0
$739$	10392.7	+	18000.7i	0.517322	+	0.896028i	0.999798	+	0.0201186i	$0.00640440\pi$
$739$	10392.7	+	18000.7i	0.517322	+	0.896028i	−0.482476	+	0.875909i	$0.660262\pi$
$740$	−16810.1	−	29116.0i	−0.835070	−	1.44638i
$741$		0			0
$742$	−23743.5	−	6569.95i	−1.17473	−	0.325055i
$743$	−2159.74	−	3740.79i	−0.106640	−	0.184705i	0.807767	−	0.589502i	$-0.200676\pi$
$743$	−2159.74	−	3740.79i	−0.106640	−	0.184705i	−0.914407	+	0.404796i	$0.867342\pi$
$744$		0			0
$745$	3713.78			0.182634
$746$	−2238.21	−	3876.69i	−0.109848	−	0.190262i
$747$		0			0
$748$	75441.3			3.68771
$749$	−18492.1	−	5116.87i	−0.902118	−	0.249621i
$750$		0			0
$751$	−9065.68			−0.440495			−0.220247	−	0.975444i	$-0.570686\pi$
$751$	−9065.68			−0.440495			−0.220247	+	0.975444i	$0.570686\pi$
$752$	9208.11	−	15948.9i	0.446523	−	0.773400i
$753$		0			0
$754$	−5005.51	−	8669.80i	−0.241764	−	0.418747i
$755$	−7885.85			−0.380126
$756$		0			0
$757$	−21632.0			−1.03861			−0.519305	−	0.854589i	$-0.673809\pi$
$757$	−21632.0			−1.03861			−0.519305	+	0.854589i	$0.673809\pi$
$758$	−15073.2	−	26107.5i	−0.722273	−	1.25101i
$759$		0			0
$760$	−9846.53	+	17054.7i	−0.469962	+	0.813998i
$761$	−19069.3			−0.908361			−0.454181	−	0.890910i	$-0.650068\pi$
$761$	−19069.3			−0.908361			−0.454181	+	0.890910i	$0.650068\pi$
$762$		0			0
$763$	−559.426	+	550.379i	−0.0265433	+	0.0261141i
$764$	12564.5			0.594985
$765$		0			0
$766$	−10088.3	−	17473.4i	−0.475855	−	0.824205i
$767$	−4722.78			−0.222333
$768$		0			0
$769$	−13418.5	−	23241.4i	−0.629235	−	1.08987i	−0.987706	−	0.156326i	$-0.950035\pi$
$769$	−13418.5	−	23241.4i	−0.629235	−	1.08987i	0.358471	−	0.933541i	$-0.383298\pi$
$770$	22180.8	−	21822.1i	1.03811	−	1.02132i
$771$		0			0
$772$	5486.64	+	9503.14i	0.255788	+	0.443038i
$773$	12766.9	+	22113.0i	0.594043	+	1.02891i	0.993681	+	0.112239i	$0.0358023\pi$
$773$	12766.9	+	22113.0i	0.594043	+	1.02891i	−0.399639	+	0.916673i	$0.630864\pi$
$774$		0			0
$775$	−10978.9	+	19016.1i	−0.508871	+	0.881390i
$776$	4682.12	−	8109.67i	0.216596	−	0.375155i
$777$		0			0
$778$	2424.76	+	4199.82i	0.111738	+	0.193536i
$779$	−9755.85			−0.448703
$780$		0			0
$781$	42849.9			1.96324
$782$	−2216.46	+	3839.02i	−0.101356	+	0.175554i
$783$		0			0
$784$	16940.5	+	10152.4i	0.771704	+	0.462480i
$785$	−7965.87	+	13797.3i	−0.362184	+	0.627321i
$786$		0			0
$787$	−15118.3	+	26185.6i	−0.684763	+	1.18604i	0.288748	+	0.957405i	$0.406761\pi$
$787$	−15118.3	+	26185.6i	−0.684763	+	1.18604i	−0.973511	+	0.228639i	$0.926572\pi$
$788$	664.844	−	1151.54i	0.0300559	−	0.0520584i
$789$		0			0
$790$	−5232.29	+	9062.60i	−0.235641	+	0.408143i
$791$	−28074.2	+	27620.2i	−1.26195	+	1.24154i
$792$		0			0
$793$	1962.54	−	3399.22i	0.0878837	−	0.152219i
$794$	−41754.5			−1.86626
$795$		0			0
$796$	40616.2			1.80854
$797$	813.308	+	1408.69i	0.0361466	+	0.0626078i	0.883533	−	0.468369i	$-0.155158\pi$
$797$	813.308	+	1408.69i	0.0361466	+	0.0626078i	−0.847386	+	0.530977i	$0.821825\pi$
$798$		0			0
$799$	−13812.1	+	23923.2i	−0.611559	+	1.05925i
$800$	−895.927	+	1551.79i	−0.0395948	+	0.0685801i
$801$		0			0
$802$	−34335.5	−	59470.8i	−1.51176	−	2.61844i
$803$	7780.72	+	13476.6i	0.341937	+	0.592253i
$804$		0			0
$805$	304.124	+	1173.18i	0.0133155	+	0.0513653i
$806$	8342.95	+	14450.4i	0.364600	+	0.631507i
$807$		0			0
$808$	−73675.6			−3.20780
$809$	−450.273	−	779.895i	−0.0195683	−	0.0338933i	0.856075	−	0.516851i	$-0.172896\pi$
$809$	−450.273	−	779.895i	−0.0195683	−	0.0338933i	−0.875644	+	0.482958i	$0.839563\pi$
$810$		0			0
$811$	33501.8			1.45056			0.725282	−	0.688452i	$-0.241709\pi$
$811$	33501.8			1.45056			0.725282	+	0.688452i	$0.241709\pi$
$812$	−31654.1	+	31142.2i	−1.36803	+	1.34591i
$813$		0			0
$814$	−93095.2			−4.00858
$815$	6671.81	−	11555.9i	0.286752	−	0.496670i
$816$		0			0
$817$	3936.96	+	6819.02i	0.168589	+	0.292004i
$818$	23665.8			1.01156
$819$		0			0
$820$	−11317.5			−0.481980
$821$	17082.4	+	29587.5i	0.726162	+	1.25775i	0.958494	+	0.285113i	$0.0920311\pi$
$821$	17082.4	+	29587.5i	0.726162	+	1.25775i	−0.232332	+	0.972637i	$0.574636\pi$
$822$		0			0
$823$	−3918.87	+	6787.69i	−0.165982	+	0.287490i	−0.937004	−	0.349320i	$-0.886413\pi$
$823$	−3918.87	+	6787.69i	−0.165982	+	0.287490i	0.771021	+	0.636809i	$0.219746\pi$
$824$	−71381.0			−3.01781
$825$		0			0
$826$	7930.34	+	30591.8i	0.334058	+	1.28865i
$827$	4205.91			0.176849			0.0884244	−	0.996083i	$-0.471817\pi$
$827$	4205.91			0.176849			0.0884244	+	0.996083i	$0.471817\pi$
$828$		0			0
$829$	−8247.65	−	14285.3i	−0.345540	−	0.598493i	0.639912	−	0.768448i	$-0.278971\pi$
$829$	−8247.65	−	14285.3i	−0.345540	−	0.598493i	−0.985452	+	0.169956i	$0.945638\pi$
$830$	−3806.57			−0.159191
$831$		0			0
$832$	3786.00	+	6557.54i	0.157759	+	0.273247i
$833$	−25410.5	−	15228.4i	−1.05693	−	0.633414i
$834$		0			0
$835$	4350.42	+	7535.14i	0.180302	+	0.312293i
$836$	36779.1	+	63703.3i	1.52157	+	2.63544i
$837$		0			0
$838$	16936.1	−	29334.2i	0.698147	−	1.20923i
$839$	9452.55	−	16372.3i	0.388961	−	0.673700i	−0.603349	−	0.797477i	$-0.706167\pi$
$839$	9452.55	−	16372.3i	0.388961	−	0.673700i	0.992310	+	0.123777i	$0.0395007\pi$
$840$		0			0
$841$	576.848	+	999.130i	0.0236520	+	0.0409664i
$842$	−46547.4			−1.90514
$843$		0			0
$844$	14367.4			0.585956
$845$	6258.09	−	10839.3i	0.254775	−	0.441283i
$846$		0			0
$847$	−8145.99	−	31423.7i	−0.330460	−	1.27477i
$848$	7861.58	−	13616.7i	0.318358	−	0.551412i
$849$		0			0
$850$	−18180.7	+	31490.0i	−0.733640	+	1.27070i
$851$	1813.02	−	3140.24i	0.0730312	−	0.126494i
$852$		0			0
$853$	−4724.30	+	8182.73i	−0.189633	+	0.328454i	−0.945128	−	0.326700i	$-0.894063\pi$
$853$	−4724.30	+	8182.73i	−0.189633	+	0.328454i	0.755495	+	0.655155i	$0.227396\pi$
$854$	−25313.8	−	7004.48i	−1.01431	−	0.280665i
$855$		0			0
$856$	19503.8	−	33781.6i	0.778770	−	1.34887i
$857$	−33032.0			−1.31663			−0.658315	−	0.752743i	$-0.728730\pi$
$857$	−33032.0			−1.31663			−0.658315	+	0.752743i	$0.728730\pi$
$858$		0			0
$859$	−41136.7			−1.63395			−0.816977	−	0.576670i	$-0.804352\pi$
$859$	−41136.7			−1.63395			−0.816977	+	0.576670i	$0.804352\pi$
$860$	4567.15	+	7910.54i	0.181091	+	0.313660i
$861$		0			0
$862$	8855.93	−	15338.9i	0.349923	−	0.606085i
$863$	−9828.49	+	17023.4i	−0.387677	+	0.671477i	−0.992137	−	0.125159i	$-0.960056\pi$
$863$	−9828.49	+	17023.4i	−0.387677	+	0.671477i	0.604459	+	0.796636i	$0.293389\pi$
$864$		0			0
$865$	−4152.80	−	7192.86i	−0.163236	−	0.282733i
$866$	−5122.07	−	8871.68i	−0.200987	−	0.348120i
$867$		0			0
$868$	52759.6	−	51906.4i	2.06311	−	2.02975i
$869$	9603.83	+	16634.3i	0.374900	+	0.649345i
$870$		0			0
$871$	11235.8			0.437096
$872$	−797.736	−	1381.72i	−0.0309802	−	0.0536593i
$873$		0			0
$874$	−4322.26			−0.167280
$875$	6102.63	+	23541.3i	0.235779	+	0.909531i
$876$		0			0
$877$	36070.4			1.38884			0.694420	−	0.719570i	$-0.255661\pi$
$877$	36070.4			1.38884			0.694420	+	0.719570i	$0.255661\pi$
$878$	9855.32	−	17069.9i	0.378817	−	0.656130i
$879$		0			0
$880$	9929.47	+	17198.3i	0.380366	+	0.658814i
$881$	−7267.41			−0.277918			−0.138959	−	0.990298i	$-0.544376\pi$
$881$	−7267.41			−0.277918			−0.138959	+	0.990298i	$0.544376\pi$
$882$		0			0
$883$	−48964.7			−1.86613			−0.933065	−	0.359708i	$-0.882876\pi$
$883$	−48964.7			−1.86613			−0.933065	+	0.359708i	$0.882876\pi$
$884$	9157.92	+	15862.0i	0.348432	+	0.603502i
$885$		0			0
$886$	−9288.40	+	16088.0i	−0.352201	+	0.610030i
$887$	18431.3			0.697704			0.348852	−	0.937178i	$-0.386572\pi$
$887$	18431.3			0.697704			0.348852	+	0.937178i	$0.386572\pi$
$888$		0			0
$889$	−5332.11	−	20568.9i	−0.201162	−	0.775996i
$890$	−9871.83			−0.371803
$891$		0			0
$892$	7615.19	+	13189.9i	0.285847	+	0.495102i
$893$	−26934.6			−1.00933
$894$		0			0
$895$	−3181.69	−	5510.85i	−0.118829	−	0.205818i
$896$	33929.3	−	33380.6i	1.26507	−	1.24461i
$897$		0			0
$898$	4934.25	+	8546.37i	0.183361	+	0.317590i
$899$	19363.8	+	33539.0i	0.718374	+	1.24426i
$900$		0			0
$901$	−11792.3	+	20424.8i	−0.436024	+	0.755216i
$902$	−15669.2	+	27139.8i	−0.578411	+	1.00184i
$903$		0			0
$904$	−40033.6	−	69340.2i	−1.47289	−	2.55113i
$905$	−5541.99			−0.203560
$906$		0			0
$907$	−21799.1			−0.798046			−0.399023	−	0.916941i	$-0.630651\pi$
$907$	−21799.1			−0.798046			−0.399023	+	0.916941i	$0.630651\pi$
$908$	26059.7	−	45136.7i	0.952446	−	1.64968i
$909$		0			0
$910$	7280.78	+	2014.63i	0.265226	+	0.0733895i
$911$	23078.1	−	39972.4i	0.839309	−	1.45373i	−0.0511643	−	0.998690i	$-0.516293\pi$
$911$	23078.1	−	39972.4i	0.839309	−	1.45373i	0.890473	−	0.455036i	$-0.150373\pi$
$912$		0			0
$913$	−3493.47	+	6050.86i	−0.126634	+	0.219337i
$914$	45757.8	−	79254.8i	1.65594	−	2.86818i
$915$		0			0
$916$	−28233.6	+	48902.0i	−1.01841	+	1.76394i
$917$	664.316	+	2562.64i	0.0239233	+	0.0922855i
$918$		0			0
$919$	−9991.72	+	17306.2i	−0.358647	+	0.621194i	−0.987735	−	0.156140i	$-0.950095\pi$
$919$	−9991.72	+	17306.2i	−0.358647	+	0.621194i	0.629088	+	0.777334i	$0.283428\pi$
$920$	−2463.94			−0.0882974
$921$		0			0
$922$	19607.8			0.700376
$923$	5201.60	+	9009.44i	0.185496	+	0.321288i
$924$		0			0
$925$	14871.5	−	25758.2i	0.528619	−	0.915594i
$926$	−30918.9	+	53553.0i	−1.09725	+	1.90050i
$927$		0			0
$928$	1580.16	+	2736.93i	0.0558960	+	0.0968146i
$929$	9345.46	+	16186.8i	0.330048	+	0.571660i	0.982521	−	0.186152i	$-0.0596017\pi$
$929$	9345.46	+	16186.8i	0.330048	+	0.571660i	−0.652473	+	0.757812i	$0.726268\pi$
$930$		0			0
$931$	470.901	−	28881.0i	0.0165770	−	1.01669i
$932$	−39575.7	−	68547.2i	−1.39093	−	2.40916i
$933$		0			0
$934$	−18797.7			−0.658544
$935$	−14894.1	−	25797.3i	−0.520951	−	0.902313i
$936$		0			0
$937$	40532.5			1.41317			0.706584	−	0.707630i	$-0.250235\pi$
$937$	40532.5			1.41317			0.706584	+	0.707630i	$0.250235\pi$
$938$	−18866.8	−	72779.8i	−0.656741	−	2.53342i
$939$		0			0
$940$	−31246.0			−1.08418
$941$	22537.8	−	39036.6i	0.780777	−	1.35235i	−0.150713	−	0.988578i	$-0.548157\pi$
$941$	22537.8	−	39036.6i	0.780777	−	1.35235i	0.931490	−	0.363768i	$-0.118510\pi$
$942$		0			0
$943$	−610.312	−	1057.09i	−0.0210758	−	0.0365044i
$944$	−20169.9			−0.695416
$945$		0			0
$946$	25293.1			0.869292
$947$	18177.0	+	31483.6i	0.623732	+	1.08034i	0.988785	+	0.149349i	$0.0477177\pi$
$947$	18177.0	+	31483.6i	0.623732	+	1.08034i	−0.365052	+	0.930987i	$0.618949\pi$
$948$		0			0
$949$	−1889.02	+	3271.88i	−0.0646157	+	0.111918i
$950$	−35453.9			−1.21082
$951$		0			0
$952$	42932.6	−	42238.3i	1.46161	−	1.43797i
$953$	41151.2			1.39876			0.699379	−	0.714751i	$-0.253460\pi$
$953$	41151.2			1.39876			0.699379	+	0.714751i	$0.253460\pi$
$954$		0			0
$955$	−2480.57	−	4296.47i	−0.0840515	−	0.145582i
$956$	−10155.4			−0.343567
$957$		0			0
$958$	23118.7	+	40042.7i	0.779676	+	1.35044i
$959$	6341.75	+	24463.7i	0.213541	+	0.823748i
$960$		0			0
$961$	−17379.1	−	30101.5i	−0.583369	−	1.01042i
$962$	−11300.9	−	19573.8i	−0.378750	−	0.656013i
$963$		0			0
$964$	−25133.4	+	43532.3i	−0.839723	+	1.45444i
$965$	2166.41	−	3752.34i	0.0722687	−	0.125173i
$966$		0			0
$967$	18935.0	+	32796.4i	0.629688	+	1.09065i	0.987614	+	0.156902i	$0.0501506\pi$
$967$	18935.0	+	32796.4i	0.629688	+	1.09065i	−0.357926	+	0.933750i	$0.616516\pi$
$968$	65996.8			2.19134
$969$		0			0
$970$	−7524.42			−0.249067
$971$	24532.9	−	42492.3i	0.810813	−	1.40437i	−0.101483	−	0.994837i	$-0.532359\pi$
$971$	24532.9	−	42492.3i	0.810813	−	1.40437i	0.912296	−	0.409532i	$-0.134308\pi$
$972$		0			0
$973$	14505.1	−	14270.5i	0.477915	−	0.470186i
$974$	38240.7	−	66234.9i	1.25802	−	2.17896i
$975$		0			0
$976$	8381.53	−	14517.2i	0.274883	−	0.476112i
$977$	−18714.8	+	32414.9i	−0.612834	+	1.06146i	0.377927	+	0.925835i	$0.376637\pi$
$977$	−18714.8	+	32414.9i	−0.612834	+	1.06146i	−0.990760	+	0.135624i	$0.956696\pi$
$978$		0			0
$979$	−9059.83	+	15692.1i	−0.295765	+	0.512279i
$980$	546.278	−	33504.0i	0.0178063	−	1.09209i
$981$		0			0
$982$	−29057.2	+	50328.5i	−0.944248	+	1.63549i
$983$	42468.8			1.37797			0.688985	−	0.724775i	$-0.258056\pi$
$983$	42468.8			1.37797			0.688985	+	0.724775i	$0.258056\pi$
$984$		0			0
$985$	−525.030			−0.0169836
$986$	32065.7	+	55539.5i	1.03568	+	1.79385i
$987$		0			0
$988$	−8929.33	+	15466.0i	−0.287530	+	0.498017i
$989$	−492.581	+	853.176i	−0.0158374	+	0.0274311i
$990$		0			0
$991$	−23124.4	−	40052.7i	−0.741243	−	1.28387i	−0.951930	−	0.306316i	$-0.900904\pi$
$991$	−23124.4	−	40052.7i	−0.741243	−	1.28387i	0.210687	−	0.977554i	$-0.432430\pi$
$992$	−2633.75	−	4561.78i	−0.0842959	−	0.146005i
$993$		0			0
$994$	49624.2	−	48821.7i	1.58348	−	1.55788i
$995$	−8018.69	−	13888.8i	−0.255487	−	0.442517i
$996$		0			0
$997$	20653.2			0.656063			0.328031	−	0.944667i	$-0.393615\pi$
$997$	20653.2			0.656063			0.328031	+	0.944667i	$0.393615\pi$
$998$	−44319.6	−	76763.8i	−1.40572	−	2.43478i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.3		44
3.2	odd	2		63.4.g.a.16.20	yes	44
7.4	even	3		189.4.h.a.46.20		44
9.4	even	3		189.4.h.a.37.20		44
9.5	odd	6		63.4.h.a.58.3	yes	44
21.11	odd	6		63.4.h.a.25.3	yes	44
63.4	even	3	inner	189.4.g.a.172.3		44
63.32	odd	6		63.4.g.a.4.20	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.20	✓	44	63.32	odd	6
63.4.g.a.16.20	yes	44	3.2	odd	2
63.4.h.a.25.3	yes	44	21.11	odd	6
63.4.h.a.58.3	yes	44	9.5	odd	6
189.4.g.a.100.3		44	1.1	even	1	trivial
189.4.g.a.172.3		44	63.4	even	3	inner
189.4.h.a.37.20		44	9.4	even	3
189.4.h.a.46.20		44	7.4	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.43564 - 4.21866i) q^{2} +(-7.86471 + 13.6221i) q^{4} +6.21080 q^{5} +(-4.64741 - 17.9277i) q^{7} +37.6522 q^{8} +O(q^{10})\)	\(q+(-2.43564 - 4.21866i) q^{2} +(-7.86471 + 13.6221i) q^{4} +6.21080 q^{5} +(-4.64741 - 17.9277i) q^{7} +37.6522 q^{8} +(-15.1273 - 26.2012i) q^{10} -55.5320 q^{11} +(-6.74110 - 11.6759i) q^{13} +(-64.3113 + 63.2712i) q^{14} +(-28.7896 - 49.8651i) q^{16} +(43.1841 + 74.7970i) q^{17} +(-42.1062 + 72.9300i) q^{19} +(-48.8461 + 84.6039i) q^{20} +(135.256 + 234.270i) q^{22} -10.5364 q^{23} -86.4260 q^{25} +(-32.8378 + 56.8767i) q^{26} +(280.763 + 77.6886i) q^{28} +(-76.2157 + 132.009i) q^{29} +(127.033 - 220.027i) q^{31} +(10.3664 - 17.9551i) q^{32} +(210.362 - 364.358i) q^{34} +(-28.8641 - 111.345i) q^{35} +(-172.072 + 298.038i) q^{37} +410.222 q^{38} +233.850 q^{40} +(57.9241 + 100.328i) q^{41} +(46.7504 - 80.9741i) q^{43} +(436.743 - 756.461i) q^{44} +(25.6629 + 44.4494i) q^{46} +(159.921 + 276.991i) q^{47} +(-299.803 + 166.635i) q^{49} +(210.503 + 364.602i) q^{50} +212.067 q^{52} +(136.535 + 236.486i) q^{53} -344.898 q^{55} +(-174.985 - 675.016i) q^{56} +742.536 q^{58} +(175.149 - 303.367i) q^{59} +(145.565 + 252.126i) q^{61} -1237.63 q^{62} -561.629 q^{64} +(-41.8676 - 72.5168i) q^{65} +(-416.690 + 721.729i) q^{67} -1358.52 q^{68} +(-399.424 + 392.965i) q^{70} -771.625 q^{71} +(-140.112 - 242.682i) q^{73} +1676.42 q^{74} +(-662.305 - 1147.15i) q^{76} +(258.080 + 995.559i) q^{77} +(-172.942 - 299.545i) q^{79} +(-178.806 - 309.702i) q^{80} +(282.165 - 488.724i) q^{82} +(62.9091 - 108.962i) q^{83} +(268.207 + 464.549i) q^{85} -455.469 q^{86} -2090.90 q^{88} +(163.146 - 282.578i) q^{89} +(-177.994 + 175.115i) q^{91} +(82.8657 - 143.528i) q^{92} +(779.019 - 1349.30i) q^{94} +(-261.513 + 452.953i) q^{95} +(124.352 - 215.384i) q^{97} +(1433.19 + 858.904i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

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