LMFDB - Embedded newform 189.4.o.a.62.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

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([1, 3]))

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

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.5
Character	$\chi$	$=$	189.62
Dual form			189.4.o.a.125.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(-13.5435 - 12.6323i) q^{7} +21.0785i q^{8} +O(q^{10})$	\(q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(-13.5435 - 12.6323i) q^{7} +21.0785i q^{8} +46.6969i q^{10} +(-46.4700 - 26.8295i) q^{11} +(29.1434 - 16.8260i) q^{13} +(16.1997 + 53.0078i) q^{14} +(35.3701 - 61.2628i) q^{16} +43.5488 q^{17} -32.2524i q^{19} +(7.46605 - 12.9316i) q^{20} +(80.2960 + 139.077i) q^{22} +(-129.309 + 74.6565i) q^{23} +(-59.2260 + 102.582i) q^{25} -100.714 q^{26} +(3.98894 - 17.2693i) q^{28} +(127.390 + 73.5487i) q^{29} +(61.1678 - 35.3153i) q^{31} +(-37.3130 + 21.5427i) q^{32} +(-112.873 - 65.1670i) q^{34} +(-65.0355 + 281.557i) q^{35} +40.3540 q^{37} +(-48.2629 + 83.5938i) q^{38} +(284.824 - 164.443i) q^{40} +(179.454 + 310.824i) q^{41} +(-253.886 + 439.743i) q^{43} -51.3519i q^{44} +446.867 q^{46} +(228.160 - 395.185i) q^{47} +(23.8504 + 342.170i) q^{49} +(307.011 - 177.253i) q^{50} +(27.8904 + 16.1025i) q^{52} +213.420i q^{53} +837.238i q^{55} +(266.269 - 285.475i) q^{56} +(-220.118 - 381.256i) q^{58} +(-159.593 - 276.424i) q^{59} +(-303.662 - 175.319i) q^{61} -211.385 q^{62} -436.974 q^{64} +(-454.723 - 262.535i) q^{65} +(-289.258 - 501.009i) q^{67} +(20.8382 + 36.0928i) q^{68} +(589.889 - 632.437i) q^{70} -787.243i q^{71} -146.373i q^{73} +(-104.592 - 60.3863i) q^{74} +(26.7305 - 15.4329i) q^{76} +(290.447 + 950.387i) q^{77} +(-193.095 + 334.451i) q^{79} -1103.76 q^{80} -1074.15i q^{82} +(-98.9043 + 171.307i) q^{83} +(-339.745 - 588.455i) q^{85} +(1316.07 - 759.835i) q^{86} +(565.524 - 979.517i) q^{88} -596.020 q^{89} +(-607.253 - 140.267i) q^{91} +(-123.749 - 71.4466i) q^{92} +(-1182.72 + 682.844i) q^{94} +(-435.812 + 251.616i) q^{95} +(-631.485 - 364.588i) q^{97} +(450.210 - 922.547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.59186	−	1.49641i	−0.916362	−	0.529062i	−0.0338893	−	0.999426i	$-0.510789\pi$
$2$	−2.59186	−	1.49641i	−0.916362	−	0.529062i	−0.882473	+	0.470364i	$0.844123\pi$
$3$		0			0
$3$		0			0
$4$	0.478502	+	0.828790i	0.0598128	+	0.103599i
$5$	−7.80147	−	13.5125i	−0.697785	−	1.20860i	−0.969233	−	0.246146i	$-0.920836\pi$
$5$	−7.80147	−	13.5125i	−0.697785	−	1.20860i	0.271448	−	0.962453i	$-0.412498\pi$
$6$		0			0
$7$	−13.5435	−	12.6323i	−0.731278	−	0.682080i
$7$	−13.5435	−	12.6323i	−0.731278	−	0.682080i
$8$			21.0785i			0.931545i
$9$		0			0
$10$			46.6969i			1.47669i
$11$	−46.4700	−	26.8295i	−1.27375	−	0.735400i	−0.298058	−	0.954548i	$-0.596339\pi$
$11$	−46.4700	−	26.8295i	−1.27375	−	0.735400i	−0.975692	+	0.219148i	$0.929672\pi$
$12$		0			0
$13$	29.1434	−	16.8260i	0.621764	−	0.358976i	−0.155791	−	0.987790i	$-0.549793\pi$
$13$	29.1434	−	16.8260i	0.621764	−	0.358976i	0.777555	+	0.628814i	$0.216459\pi$
$14$	16.1997	+	53.0078i	0.309253	+	1.01192i
$15$		0			0
$16$	35.3701	−	61.2628i	0.552658	−	0.957231i
$17$	43.5488			0.621302			0.310651	−	0.950524i	$-0.399453\pi$
$17$	43.5488			0.621302			0.310651	+	0.950524i	$0.399453\pi$
$18$		0			0
$19$		−	32.2524i		−	0.389432i	−0.980860	−	0.194716i	$-0.937621\pi$
$19$		−	32.2524i		−	0.389432i	0.980860	−	0.194716i	$-0.0623785\pi$
$20$	7.46605	−	12.9316i	0.0834729	−	0.144579i
$21$		0			0
$22$	80.2960	+	139.077i	0.778144	+	1.34778i
$23$	−129.309	+	74.6565i	−1.17229	+	0.676824i	−0.954219	−	0.299108i	$-0.903311\pi$
$23$	−129.309	+	74.6565i	−1.17229	+	0.676824i	−0.218074	+	0.975932i	$0.569977\pi$
$24$		0			0
$25$	−59.2260	+	102.582i	−0.473808	+	0.820659i
$26$	−100.714			−0.759681
$27$		0			0
$28$	3.98894	−	17.2693i	0.0269228	−	0.116557i
$29$	127.390	+	73.5487i	0.815715	+	0.470953i	0.848937	−	0.528495i	$-0.177243\pi$
$29$	127.390	+	73.5487i	0.815715	+	0.470953i	−0.0332217	+	0.999448i	$0.510577\pi$
$30$		0			0
$31$	61.1678	−	35.3153i	0.354389	−	0.204607i	−0.312228	−	0.950007i	$-0.601075\pi$
$31$	61.1678	−	35.3153i	0.354389	−	0.204607i	0.666617	+	0.745401i	$0.267742\pi$
$32$	−37.3130	+	21.5427i	−0.206127	+	0.119008i
$33$		0			0
$34$	−112.873	−	65.1670i	−0.569338	−	0.328707i
$35$	−65.0355	+	281.557i	−0.314086	+	1.35977i
$36$		0			0
$37$	40.3540			0.179302			0.0896509	−	0.995973i	$-0.471425\pi$
$37$	40.3540			0.179302			0.0896509	+	0.995973i	$0.471425\pi$
$38$	−48.2629	+	83.5938i	−0.206034	+	0.356861i
$39$		0			0
$40$	284.824	−	164.443i	1.12586	−	0.650018i
$41$	179.454	+	310.824i	0.683562	+	1.18396i	0.973886	+	0.227036i	$0.0729036\pi$
$41$	179.454	+	310.824i	0.683562	+	1.18396i	−0.290324	+	0.956928i	$0.593763\pi$
$42$		0			0
$43$	−253.886	+	439.743i	−0.900400	+	1.55954i	−0.0734235	+	0.997301i	$0.523392\pi$
$43$	−253.886	+	439.743i	−0.900400	+	1.55954i	−0.826976	+	0.562237i	$0.809941\pi$
$44$		−	51.3519i		−	0.175945i
$45$		0			0
$46$	446.867			1.43233
$47$	228.160	−	395.185i	0.708098	−	1.22646i	−0.257464	−	0.966288i	$-0.582887\pi$
$47$	228.160	−	395.185i	0.708098	−	1.22646i	0.965562	−	0.260174i	$-0.0837800\pi$
$48$		0			0
$49$	23.8504	+	342.170i	0.0695348	+	0.997580i
$50$	307.011	−	177.253i	0.868359	−	0.501347i
$51$		0			0
$52$	27.8904	+	16.1025i	0.0743789	+	0.0429427i
$53$			213.420i			0.553123i	0.960996	+	0.276561i	$0.0891949\pi$
$53$			213.420i			0.553123i	−0.960996	+	0.276561i	$0.910805\pi$
$54$		0			0
$55$			837.238i			2.05260i
$56$	266.269	−	285.475i	0.635388	−	0.681218i
$57$		0			0
$58$	−220.118	−	381.256i	−0.498327	−	0.863127i
$59$	−159.593	−	276.424i	−0.352157	−	0.609954i	0.634470	−	0.772947i	$-0.281218\pi$
$59$	−159.593	−	276.424i	−0.352157	−	0.609954i	−0.986627	+	0.162993i	$0.947885\pi$
$60$		0			0
$61$	−303.662	−	175.319i	−0.637375	−	0.367989i	0.146227	−	0.989251i	$-0.453287\pi$
$61$	−303.662	−	175.319i	−0.637375	−	0.367989i	−0.783603	+	0.621262i	$0.786620\pi$
$62$	−211.385			−0.432998
$63$		0			0
$64$	−436.974			−0.853466
$65$	−454.723	−	262.535i	−0.867715	−	0.500976i
$66$		0			0
$67$	−289.258	−	501.009i	−0.527440	−	0.913553i	−0.999489	−	0.0319801i	$-0.989819\pi$
$67$	−289.258	−	501.009i	−0.527440	−	0.913553i	0.472049	−	0.881572i	$-0.343515\pi$
$68$	20.8382	+	36.0928i	0.0371618	+	0.0643662i
$69$		0			0
$70$	589.889	−	632.437i	1.00722	−	1.07987i
$71$		−	787.243i		−	1.31589i	−0.753064	−	0.657947i	$-0.771425\pi$
$71$		−	787.243i		−	1.31589i	0.753064	−	0.657947i	$-0.228575\pi$
$72$		0			0
$73$		−	146.373i		−	0.234681i	−0.993092	−	0.117340i	$-0.962563\pi$
$73$		−	146.373i		−	0.234681i	0.993092	−	0.117340i	$-0.0374368\pi$
$74$	−104.592	−	60.3863i	−0.164305	−	0.0948617i
$75$		0			0
$76$	26.7305	−	15.4329i	0.0403447	−	0.0232930i
$77$	290.447	+	950.387i	0.429864	+	1.40658i
$78$		0			0
$79$	−193.095	+	334.451i	−0.274999	+	0.476312i	−0.970135	−	0.242566i	$-0.922011\pi$
$79$	−193.095	+	334.451i	−0.274999	+	0.476312i	0.695136	+	0.718878i	$0.255344\pi$
$80$	−1103.76			−1.54254
$81$		0			0
$82$		−	1074.15i		−	1.44659i
$83$	−98.9043	+	171.307i	−0.130797	+	0.226547i	−0.923984	−	0.382431i	$-0.875087\pi$
$83$	−98.9043	+	171.307i	−0.130797	+	0.226547i	0.793187	+	0.608978i	$0.208420\pi$
$84$		0			0
$85$	−339.745	−	588.455i	−0.433535	−	0.750905i
$86$	1316.07	−	759.835i	1.65018	−	0.952734i
$87$		0			0
$88$	565.524	−	979.517i	0.685058	−	1.18656i
$89$	−596.020			−0.709865			−0.354932	−	0.934892i	$-0.615496\pi$
$89$	−596.020			−0.709865			−0.354932	+	0.934892i	$0.615496\pi$
$90$		0			0
$91$	−607.253	−	140.267i	−0.699532	−	0.161582i
$92$	−123.749	−	71.4466i	−0.140236	−	0.0809654i
$93$		0			0
$94$	−1182.72	+	682.844i	−1.29775	+	0.749255i
$95$	−435.812	+	251.616i	−0.470667	+	0.271740i
$96$		0			0
$97$	−631.485	−	364.588i	−0.661006	−	0.381632i	0.131654	−	0.991296i	$-0.457971\pi$
$97$	−631.485	−	364.588i	−0.661006	−	0.381632i	−0.792660	+	0.609664i	$0.791304\pi$
$98$	450.210	−	922.547i	0.464062	−	0.950932i
$99$		0			0
$100$	−113.359			−0.113359
$101$	−286.723	+	496.619i	−0.282476	+	0.489262i	−0.971994	−	0.235006i	$-0.924489\pi$
$101$	−286.723	+	496.619i	−0.282476	+	0.489262i	0.689518	+	0.724268i	$0.257822\pi$
$102$		0			0
$103$	1420.04	−	819.860i	1.35845	−	0.784303i	0.369038	−	0.929414i	$-0.379687\pi$
$103$	1420.04	−	819.860i	1.35845	−	0.784303i	0.989415	+	0.145111i	$0.0463539\pi$
$104$	354.665	+	614.298i	0.334402	+	0.579201i
$105$		0			0
$106$	319.365	−	553.156i	0.292636	−	0.506861i
$107$			377.596i			0.341155i	0.985344	+	0.170577i	$0.0545633\pi$
$107$			377.596i			0.341155i	−0.985344	+	0.170577i	$0.945437\pi$
$108$		0			0
$109$	−1166.06			−1.02467			−0.512334	−	0.858787i	$-0.671219\pi$
$109$	−1166.06			−1.02467			−0.512334	+	0.858787i	$0.671219\pi$
$110$	1252.85	−	2170.01i	1.08595	−	1.88093i
$111$		0			0
$112$	−1252.92	+	382.905i	−1.05705	+	0.323045i
$113$	279.069	−	161.121i	0.232324	−	0.134132i	−0.379320	−	0.925266i	$-0.623842\pi$
$113$	279.069	−	161.121i	0.232324	−	0.134132i	0.611644	+	0.791133i	$0.290509\pi$
$114$		0			0
$115$	2017.60	+	1164.86i	1.63602	+	0.944555i
$116$			140.773i			0.112676i
$117$		0			0
$118$			955.269i			0.745252i
$119$	−589.802	−	550.121i	−0.454345	−	0.423778i
$120$		0			0
$121$	774.144	+	1340.86i	0.581626	+	1.00741i
$122$	524.700	+	908.806i	0.389378	+	0.674422i
$123$		0			0
$124$	58.5379	+	33.7969i	0.0423940	+	0.0244762i
$125$	−102.169			−0.0731064
$126$		0			0
$127$	1356.31			0.947663			0.473832	−	0.880615i	$-0.342871\pi$
$127$	1356.31			0.947663			0.473832	+	0.880615i	$0.342871\pi$
$128$	1431.08	+	826.236i	0.988211	+	0.570544i
$129$		0			0
$130$	785.720	+	1360.91i	0.530094	+	0.918150i
$131$	−978.999	−	1695.68i	−0.652943	−	1.13093i	−0.982405	−	0.186762i	$-0.940201\pi$
$131$	−978.999	−	1695.68i	−0.652943	−	1.13093i	0.329462	−	0.944169i	$-0.393133\pi$
$132$		0			0
$133$	−407.422	+	436.809i	−0.265624	+	0.284783i
$134$			1731.40i			1.11619i
$135$		0			0
$136$			917.942i			0.578771i
$137$	859.395	+	496.172i	0.535935	+	0.309422i	0.743430	−	0.668814i	$-0.233198\pi$
$137$	859.395	+	496.172i	0.535935	+	0.309422i	−0.207495	+	0.978236i	$0.566531\pi$
$138$		0			0
$139$	−722.161	+	416.940i	−0.440668	+	0.254420i	−0.703881	−	0.710318i	$-0.748551\pi$
$139$	−722.161	+	416.940i	−0.440668	+	0.254420i	0.263213	+	0.964738i	$0.415218\pi$
$140$	−264.471	+	80.8249i	−0.159657	+	0.0487925i
$141$		0			0
$142$	−1178.04	+	2040.43i	−0.696190	+	1.20584i
$143$	−1805.73			−1.05596
$144$		0			0
$145$		−	2295.15i		−	1.31450i
$146$	−219.035	+	379.379i	−0.124161	+	0.215052i
$147$		0			0
$148$	19.3095	+	33.4450i	0.0107245	+	0.0185754i
$149$	−1324.03	+	764.428i	−0.727978	+	0.420298i	−0.817682	−	0.575670i	$-0.804741\pi$
$149$	−1324.03	+	764.428i	−0.727978	+	0.420298i	0.0897042	+	0.995968i	$0.471408\pi$
$150$		0			0
$151$	−373.571	+	647.044i	−0.201330	+	0.348713i	−0.948957	−	0.315405i	$-0.897860\pi$
$151$	−373.571	+	647.044i	−0.201330	+	0.348713i	0.747627	+	0.664118i	$0.231193\pi$
$152$	679.831			0.362774
$153$		0			0
$154$	669.373	−	2897.90i	0.350257	−	1.51636i
$155$	−954.398	−	551.022i	−0.494575	−	0.285543i
$156$		0			0
$157$	−1193.21	+	688.900i	−0.606551	+	0.350192i	−0.771614	−	0.636091i	$-0.780550\pi$
$157$	−1193.21	+	688.900i	−0.606551	+	0.350192i	0.165064	+	0.986283i	$0.447217\pi$
$158$	1000.95	−	577.901i	0.503997	−	0.290983i
$159$		0			0
$160$	582.193	+	336.129i	0.287665	+	0.166083i
$161$	2694.37	+	622.360i	1.31892	+	0.304651i
$162$		0			0
$163$	1900.28			0.913139			0.456569	−	0.889688i	$-0.349078\pi$
$163$	1900.28			0.913139			0.456569	+	0.889688i	$0.349078\pi$
$164$	−171.739	+	297.460i	−0.0817715	+	0.141632i
$165$		0			0
$166$	512.693	−	296.003i	0.239715	−	0.138399i
$167$	836.404	+	1448.69i	0.387562	+	0.671277i	0.992121	−	0.125283i	$-0.0399839\pi$
$167$	836.404	+	1448.69i	0.387562	+	0.671277i	−0.604559	+	0.796560i	$0.706651\pi$
$168$		0			0
$169$	−532.274	+	921.925i	−0.242273	+	0.419629i
$170$			2033.59i			0.917468i
$171$		0			0
$172$	−485.939			−0.215422
$173$	−496.398	+	859.787i	−0.218153	+	0.377852i	−0.954243	−	0.299031i	$-0.903336\pi$
$173$	−496.398	+	859.787i	−0.218153	+	0.377852i	0.736090	+	0.676883i	$0.236670\pi$
$174$		0			0
$175$	2097.97	−	641.160i	0.906240	−	0.276955i
$176$	−3287.30	+	1897.92i	−1.40790	+	0.812849i
$177$		0			0
$178$	1544.80	+	891.891i	0.650493	+	0.375562i
$179$		−	145.772i		−	0.0608687i	−0.999537	−	0.0304343i	$-0.990311\pi$
$179$		−	145.772i		−	0.0608687i	0.999537	−	0.0304343i	$-0.00968905\pi$
$180$		0			0
$181$			2253.56i			0.925448i	0.886502	+	0.462724i	$0.153128\pi$
$181$			2253.56i			0.925448i	−0.886502	+	0.462724i	$0.846872\pi$
$182$	1364.02	+	1272.25i	0.555538	+	0.518163i
$183$		0			0
$184$	−1573.64	−	2725.63i	−0.630492	−	1.09204i
$185$	−314.821	−	545.286i	−0.125114	−	0.216704i
$186$		0			0
$187$	−2023.72	−	1168.39i	−0.791384	−	0.456906i
$188$	436.701			0.169413
$189$		0			0
$190$	1506.09			0.575069
$191$	−3201.45	−	1848.36i	−1.21282	−	0.700222i	−0.249448	−	0.968388i	$-0.580249\pi$
$191$	−3201.45	−	1848.36i	−1.21282	−	0.700222i	−0.963373	+	0.268166i	$0.913583\pi$
$192$		0			0
$193$	2194.75	+	3801.42i	0.818559	+	1.41779i	0.906744	+	0.421681i	$0.138560\pi$
$193$	2194.75	+	3801.42i	0.818559	+	1.41779i	−0.0881856	+	0.996104i	$0.528107\pi$
$194$	1091.15	+	1889.92i	0.403814	+	0.699426i
$195$		0			0
$196$	−272.174	+	183.496i	−0.0991890	+	0.0668717i
$197$		−	2110.35i		−	0.763229i	−0.924322	−	0.381615i	$-0.875368\pi$
$197$		−	2110.35i		−	0.763229i	0.924322	−	0.381615i	$-0.124632\pi$
$198$		0			0
$199$			3443.20i			1.22654i	0.789873	+	0.613271i	$0.210146\pi$
$199$			3443.20i			1.22654i	−0.789873	+	0.613271i	$0.789854\pi$
$200$	−2162.28	−	1248.39i	−0.764481	−	0.441373i
$201$		0			0
$202$	1486.29	−	858.113i	0.517700	−	0.298894i
$203$	−796.213	−	2605.33i	−0.275287	−	0.900780i
$204$		0			0
$205$	2800.02	−	4849.77i	0.953959	−	1.65231i
$206$	−4907.40			−1.65978
$207$		0			0
$208$		−	2380.54i		−	0.793562i
$209$	−865.316	+	1498.77i	−0.286388	+	0.496039i
$210$		0			0
$211$	−1865.08	−	3230.41i	−0.608518	−	1.05398i	−0.991485	−	0.130223i	$-0.958431\pi$
$211$	−1865.08	−	3230.41i	−0.608518	−	1.05398i	0.382966	−	0.923762i	$-0.374903\pi$
$212$	−176.881	+	102.122i	−0.0573028	+	0.0330838i
$213$		0			0
$214$	565.039	−	978.676i	0.180492	−	0.312621i
$215$	7922.73			2.51314
$216$		0			0
$217$	−1274.54	−	294.399i	−0.398715	−	0.0920973i
$218$	3022.28	+	1744.91i	0.938966	+	0.542112i
$219$		0			0
$220$	−693.895	+	400.620i	−0.212647	+	0.122772i
$221$	1269.16	−	732.751i	0.386303	−	0.223032i
$222$		0			0
$223$	−2359.66	−	1362.35i	−0.708585	−	0.409101i	0.101952	−	0.994789i	$-0.467491\pi$
$223$	−2359.66	−	1362.35i	−0.708585	−	0.409101i	−0.810537	+	0.585688i	$0.800824\pi$
$224$	777.481	+	179.587i	0.231909	+	0.0535675i
$225$		0			0
$226$	−964.411			−0.283857
$227$	−2832.72	+	4906.41i	−0.828256	+	1.43458i	0.0711495	+	0.997466i	$0.477333\pi$
$227$	−2832.72	+	4906.41i	−0.828256	+	1.43458i	−0.899405	+	0.437116i	$0.856000\pi$
$228$		0			0
$229$	−366.827	+	211.787i	−0.105854	+	0.0611149i	−0.551992	−	0.833849i	$-0.686132\pi$
$229$	−366.827	+	211.787i	−0.105854	+	0.0611149i	0.446138	+	0.894964i	$0.352799\pi$
$230$	−3486.22	−	6038.32i	−0.999456	−	1.73111i
$231$		0			0
$232$	−1550.29	+	2685.18i	−0.438714	+	0.759875i
$233$		−	234.803i		−	0.0660192i	−0.999455	−	0.0330096i	$-0.989491\pi$
$233$		−	234.803i		−	0.0660192i	0.999455	−	0.0330096i	$-0.0105092\pi$
$234$		0			0
$235$	−7119.95			−1.97640
$236$	152.731	−	264.539i	0.0421270	−	0.0729661i
$237$		0			0
$238$	705.476	+	2308.43i	0.192140	+	0.628710i
$239$	−1575.90	+	909.844i	−0.426511	+	0.246246i	−0.697859	−	0.716235i	$-0.745864\pi$
$239$	−1575.90	+	909.844i	−0.426511	+	0.246246i	0.271348	+	0.962481i	$0.412531\pi$
$240$		0			0
$241$	−2358.44	−	1361.65i	−0.630377	−	0.363948i	0.150521	−	0.988607i	$-0.451905\pi$
$241$	−2358.44	−	1361.65i	−0.630377	−	0.363948i	−0.780898	+	0.624659i	$0.785238\pi$
$242$		−	4633.75i		−	1.23086i
$243$		0			0
$244$		−	335.562i		−	0.0880417i
$245$	4437.52	−	2991.71i	1.15715	−	0.780136i
$246$		0			0
$247$	−542.678	−	939.946i	−0.139797	−	0.242135i
$248$	744.391	+	1289.32i	0.190600	+	0.330129i
$249$		0			0
$250$	264.809	+	152.887i	0.0669919	+	0.0386778i
$251$	−4214.66			−1.05987			−0.529934	−	0.848039i	$-0.677783\pi$
$251$	−4214.66			−1.05987			−0.529934	+	0.848039i	$0.677783\pi$
$252$		0			0
$253$	8011.98			1.99094
$254$	−3515.38	−	2029.60i	−0.868403	−	0.501372i
$255$		0			0
$256$	−724.881	−	1255.53i	−0.176973	−	0.306526i
$257$	−1388.99	−	2405.80i	−0.337132	−	0.583929i	0.646760	−	0.762693i	$-0.276123\pi$
$257$	−1388.99	−	2405.80i	−0.337132	−	0.583929i	−0.983892	+	0.178764i	$0.942790\pi$
$258$		0			0
$259$	−546.533	−	509.764i	−0.131119	−	0.122298i
$260$		−	502.494i		−	0.119859i
$261$		0			0
$262$			5859.95i			1.38179i
$263$	2737.40	+	1580.44i	0.641808	+	0.370548i	0.785311	−	0.619102i	$-0.212503\pi$
$263$	2737.40	+	1580.44i	0.641808	+	0.370548i	−0.143503	+	0.989650i	$0.545837\pi$
$264$		0			0
$265$	2883.85	−	1664.99i	0.668504	−	0.385961i
$266$	1709.63	−	522.478i	0.394075	−	0.120433i
$267$		0			0
$268$	276.821	−	479.468i	0.0630953	−	0.109284i
$269$	4337.32			0.983088			0.491544	−	0.870853i	$-0.336433\pi$
$269$	4337.32			0.983088			0.491544	+	0.870853i	$0.336433\pi$
$270$		0			0
$271$			8399.64i			1.88281i	0.337276	+	0.941406i	$0.390495\pi$
$271$			8399.64i			1.88281i	−0.337276	+	0.941406i	$0.609505\pi$
$272$	1540.33	−	2667.92i	0.343368	−	0.594730i
$273$		0			0
$274$	−1484.96	−	2572.02i	−0.327407	−	0.567085i
$275$	5504.47	−	3178.01i	1.20702	−	0.696876i
$276$		0			0
$277$	1826.45	−	3163.50i	0.396176	−	0.686197i	−0.597075	−	0.802186i	$-0.703670\pi$
$277$	1826.45	−	3163.50i	0.396176	−	0.686197i	0.993250	+	0.115989i	$0.0370038\pi$
$278$	2495.66			0.538415
$279$		0			0
$280$	−5934.79	−	1370.85i	−1.26668	−	0.292585i
$281$	7198.88	+	4156.27i	1.52829	+	0.882358i	0.999434	+	0.0336451i	$0.0107116\pi$
$281$	7198.88	+	4156.27i	1.52829	+	0.882358i	0.528854	+	0.848713i	$0.322622\pi$
$282$		0			0
$283$	−1294.63	+	747.458i	−0.271937	+	0.157003i	−0.629767	−	0.776784i	$-0.716850\pi$
$283$	−1294.63	+	747.458i	−0.271937	+	0.157003i	0.357831	+	0.933786i	$0.383516\pi$
$284$	652.459	−	376.697i	0.136325	−	0.0787073i
$285$		0			0
$286$	4680.20	+	2702.12i	0.967644	+	0.558669i
$287$	1495.99	−	6476.55i	0.307684	−	1.33205i
$288$		0			0
$289$	−3016.50			−0.613983
$290$	−3434.49	+	5948.72i	−0.695450	+	1.20455i
$291$		0			0
$292$	121.313	−	70.0399i	0.0243126	−	0.0140369i
$293$	−139.838	−	242.207i	−0.0278820	−	0.0482931i	0.851748	−	0.523952i	$-0.175543\pi$
$293$	−139.838	−	242.207i	−0.0278820	−	0.0482931i	−0.879630	+	0.475659i	$0.842210\pi$
$294$		0			0
$295$	−2490.12	+	4313.02i	−0.491460	+	0.851233i
$296$			850.601i			0.167028i
$297$		0			0
$298$	4575.60			0.889455
$299$	−2512.33	+	4351.49i	−0.485926	+	0.841649i
$300$		0			0
$301$	8993.45	−	2748.48i	1.72217	−	0.526311i
$302$	1936.49	−	1118.03i	0.368982	−	0.213032i
$303$		0			0
$304$	−1975.87	−	1140.77i	−0.372777	−	0.215223i
$305$			5470.99i			1.02711i
$306$		0			0
$307$		−	10727.5i		−	1.99430i	−0.0754451	−	0.997150i	$-0.524038\pi$
$307$		−	10727.5i		−	1.99430i	0.0754451	−	0.997150i	$-0.475962\pi$
$308$	−648.692	+	695.482i	−0.120009	+	0.128665i
$309$		0			0
$310$	1649.11	+	2856.35i	0.302140	+	0.523321i
$311$	−4776.34	−	8272.87i	−0.870873	−	1.50840i	−0.861095	−	0.508445i	$-0.830221\pi$
$311$	−4776.34	−	8272.87i	−0.870873	−	1.50840i	−0.00977881	−	0.999952i	$-0.503113\pi$
$312$		0			0
$313$	−3195.36	−	1844.84i	−0.577037	−	0.333153i	0.182918	−	0.983128i	$-0.441446\pi$
$313$	−3195.36	−	1844.84i	−0.577037	−	0.333153i	−0.759955	+	0.649976i	$0.774779\pi$
$314$	4123.51			0.741093
$315$		0			0
$316$	−369.586			−0.0657938
$317$	652.484	+	376.712i	0.115606	+	0.0667453i	0.556688	−	0.830722i	$-0.312072\pi$
$317$	652.484	+	376.712i	0.115606	+	0.0667453i	−0.441082	+	0.897467i	$0.645405\pi$
$318$		0			0
$319$	−3946.55	−	6835.62i	−0.692678	−	1.19975i
$320$	3409.04	+	5904.64i	0.595536	+	1.03150i
$321$		0			0
$322$	−6052.13	−	5644.96i	−1.04743	−	0.976961i
$323$		−	1404.55i		−	0.241955i
$324$		0			0
$325$			3986.14i			0.680342i
$326$	−4925.27	−	2843.61i	−0.836766	−	0.483107i
$327$		0			0
$328$	−6551.69	+	3782.62i	−1.10292	+	0.636769i
$329$	−8082.18	+	2469.99i	−1.35436	+	0.413905i
$330$		0			0
$331$	−3119.34	+	5402.86i	−0.517989	+	0.897184i	0.481792	+	0.876285i	$0.339986\pi$
$331$	−3119.34	+	5402.86i	−0.517989	+	0.897184i	−0.999782	+	0.0208983i	$0.993347\pi$
$332$	−189.304			−0.0312933
$333$		0			0
$334$		−	5006.42i		−	0.820177i
$335$	−4513.27	+	7817.22i	−0.736079	+	1.27493i
$336$		0			0
$337$	−3929.76	−	6806.55i	−0.635216	−	1.10023i	−0.986469	−	0.163946i	$-0.947578\pi$
$337$	−3929.76	−	6806.55i	−0.635216	−	1.10023i	0.351254	−	0.936280i	$-0.385756\pi$
$338$	2759.16	−	1593.00i	0.444020	−	0.256355i
$339$		0			0
$340$	325.137	−	563.155i	0.0518619	−	0.0898275i
$341$	−3789.96			−0.601871
$342$		0			0
$343$	3999.37	−	4935.45i	0.629579	−	0.776936i
$344$	−9269.10	−	5351.52i	−1.45278	−	0.838763i
$345$		0			0
$346$	2573.19	−	1485.63i	0.399814	−	0.230833i
$347$	−1142.47	+	659.607i	−0.176747	+	0.102045i	−0.585763	−	0.810482i	$-0.699205\pi$
$347$	−1142.47	+	659.607i	−0.176747	+	0.102045i	0.409016	+	0.912527i	$0.365872\pi$
$348$		0			0
$349$	4291.07	+	2477.45i	0.658153	+	0.379985i	0.791573	−	0.611075i	$-0.209262\pi$
$349$	4291.07	+	2477.45i	0.658153	+	0.379985i	−0.133420	+	0.991060i	$0.542596\pi$
$350$	−6397.10	−	1477.64i	−0.976970	−	0.225666i
$351$		0			0
$352$	2311.92			0.350073
$353$	2690.76	−	4660.53i	0.405707	−	0.702706i	−0.588696	−	0.808354i	$-0.700359\pi$
$353$	2690.76	−	4660.53i	0.405707	−	0.702706i	0.994404	+	0.105648i	$0.0336918\pi$
$354$		0			0
$355$	−10637.7	+	6141.65i	−1.59039	+	0.918211i
$356$	−285.197	−	493.975i	−0.0424590	−	0.0735411i
$357$		0			0
$358$	−218.135	+	377.820i	−0.0322033	+	0.0557777i
$359$			3814.03i			0.560715i	0.959896	+	0.280357i	$0.0904530\pi$
$359$			3814.03i			0.560715i	−0.959896	+	0.280357i	$0.909547\pi$
$360$		0			0
$361$	5818.78			0.848343
$362$	3372.26	−	5840.93i	0.489619	−	0.848046i
$363$		0			0
$364$	−174.321	−	570.403i	−0.0251013	−	0.0821353i
$365$	−1977.88	+	1141.93i	−0.283635	+	0.163757i
$366$		0			0
$367$	10883.1	+	6283.37i	1.54794	+	0.893704i	0.998299	+	0.0583038i	$0.0185692\pi$
$367$	10883.1	+	6283.37i	1.54794	+	0.893704i	0.549642	+	0.835400i	$0.314764\pi$
$368$			10562.4i			1.49621i
$369$		0			0
$370$			1884.41i			0.264772i
$371$	2695.99	−	2890.45i	0.377274	−	0.404486i
$372$		0			0
$373$	2338.60	+	4050.58i	0.324633	+	0.562281i	0.981438	−	0.191779i	$-0.0614258\pi$
$373$	2338.60	+	4050.58i	0.324633	+	0.562281i	−0.656805	+	0.754061i	$0.728092\pi$
$374$	3496.80	+	6056.63i	0.483463	+	0.837382i
$375$		0			0
$376$	8329.90	+	4809.27i	1.14250	+	0.659625i
$377$	4950.11			0.676243
$378$		0			0
$379$	−4851.71			−0.657561			−0.328780	−	0.944406i	$-0.606638\pi$
$379$	−4851.71			−0.657561			−0.328780	+	0.944406i	$0.606638\pi$
$380$	−417.074	−	240.798i	−0.0563038	−	0.0325070i
$381$		0			0
$382$	5531.81	+	9581.38i	0.740922	+	1.28331i
$383$	2456.18	+	4254.22i	0.327689	+	0.567573i	0.982053	−	0.188606i	$-0.0603970\pi$
$383$	2456.18	+	4254.22i	0.327689	+	0.567573i	−0.654364	+	0.756180i	$0.727064\pi$
$384$		0			0
$385$	10576.2	−	11339.1i	1.40004	−	1.50102i
$386$		−	13137.0i		−	1.73227i
$387$		0			0
$388$		−	697.825i		−	0.0913059i
$389$	4621.95	+	2668.48i	0.602421	+	0.347808i	0.769994	−	0.638052i	$-0.220259\pi$
$389$	4621.95	+	2668.48i	0.602421	+	0.347808i	−0.167572	+	0.985860i	$0.553593\pi$
$390$		0			0
$391$	−5631.24	+	3251.20i	−0.728349	+	0.420512i
$392$	−7212.41	+	502.731i	−0.929290	+	0.0647748i
$393$		0			0
$394$	−3157.95	+	5469.74i	−0.403795	+	0.699394i
$395$	6025.71			0.767561
$396$		0			0
$397$		−	1308.17i		−	0.165378i	−0.996575	−	0.0826889i	$-0.973649\pi$
$397$		−	1308.17i		−	0.165378i	0.996575	−	0.0826889i	$-0.0263508\pi$
$398$	5152.44	−	8924.29i	0.648916	−	1.12396i
$399$		0			0
$400$	4189.66	+	7256.70i	0.523707	+	0.907087i
$401$	1742.21	−	1005.86i	0.216962	−	0.125263i	−0.387581	−	0.921836i	$-0.626689\pi$
$401$	1742.21	−	1005.86i	0.216962	−	0.125263i	0.604543	+	0.796573i	$0.293356\pi$
$402$		0			0
$403$	1188.43	−	2058.42i	0.146898	−	0.254434i
$404$	−548.791			−0.0675826
$405$		0			0
$406$	−1834.98	+	7944.12i	−0.224306	+	0.971084i
$407$	−1875.25	−	1082.68i	−0.228386	−	0.131858i
$408$		0			0
$409$	−61.5250	+	35.5215i	−0.00743818	+	0.00429444i	−0.503714	−	0.863870i	$-0.668034\pi$
$409$	−61.5250	+	35.5215i	−0.00743818	+	0.00429444i	0.496276	+	0.868165i	$0.334700\pi$
$410$	−14514.5	+	8379.96i	−1.74834	+	1.00941i
$411$		0			0
$412$	1358.98	+	784.610i	0.162506	+	0.0938227i
$413$	−1330.42	+	5759.76i	−0.158512	+	0.686245i
$414$		0			0
$415$	3086.40			0.365073
$416$	−724.953	+	1255.66i	−0.0854417	+	0.147989i
$417$		0			0
$418$	4485.56	−	2589.74i	0.524871	−	0.303034i
$419$	−1825.15	−	3161.25i	−0.212803	−	0.368585i	0.739788	−	0.672840i	$-0.234926\pi$
$419$	−1825.15	−	3161.25i	−0.212803	−	0.368585i	−0.952591	+	0.304255i	$0.901592\pi$
$420$		0			0
$421$	−2970.12	+	5144.40i	−0.343836	+	0.595541i	−0.985142	−	0.171744i	$-0.945060\pi$
$421$	−2970.12	+	5144.40i	−0.343836	+	0.595541i	0.641306	+	0.767285i	$0.278393\pi$
$422$			11163.7i			1.28778i
$423$		0			0
$424$	−4498.57			−0.515259
$425$	−2579.22	+	4467.34i	−0.294378	+	0.509877i
$426$		0			0
$427$	1897.95	+	6210.37i	0.215101	+	0.703843i
$428$	−312.948	+	180.680i	−0.0353432	+	0.0204054i
$429$		0			0
$430$	−20534.6	−	11855.7i	−2.30295	−	1.32961i
$431$		−	7508.08i		−	0.839098i	−0.907733	−	0.419549i	$-0.862188\pi$
$431$		−	7508.08i		−	0.839098i	0.907733	−	0.419549i	$-0.137812\pi$
$432$		0			0
$433$		−	6880.95i		−	0.763689i	−0.924227	−	0.381845i	$-0.875289\pi$
$433$		−	6880.95i		−	0.763689i	0.924227	−	0.381845i	$-0.124711\pi$
$434$	2862.88	+	2670.27i	0.316642	+	0.295339i
$435$		0			0
$436$	−557.964	−	966.423i	−0.0612882	−	0.106154i
$437$	2407.85	+	4170.52i	0.263577	+	0.456529i
$438$		0			0
$439$	−4495.14	−	2595.27i	−0.488705	−	0.282154i	0.235332	−	0.971915i	$-0.424382\pi$
$439$	−4495.14	−	2595.27i	−0.488705	−	0.282154i	−0.724037	+	0.689761i	$0.757715\pi$
$440$	−17647.7			−1.91209
$441$		0			0
$442$	−4385.99			−0.471992
$443$	878.510	+	507.208i	0.0942196	+	0.0543977i	0.546369	−	0.837544i	$-0.316009\pi$
$443$	878.510	+	507.208i	0.0942196	+	0.0543977i	−0.452150	+	0.891942i	$0.649343\pi$
$444$		0			0
$445$	4649.83	+	8053.74i	0.495333	+	0.857942i
$446$	4077.27	+	7062.04i	0.432880	+	0.749770i
$447$		0			0
$448$	5918.14	+	5519.99i	0.624121	+	0.582132i
$449$			6361.05i			0.668589i	0.942469	+	0.334295i	$0.108498\pi$
$449$			6361.05i			0.668589i	−0.942469	+	0.334295i	$0.891502\pi$
$450$		0			0
$451$		−	19258.7i		−	2.01077i
$452$	267.070	+	154.193i	0.0277919	+	0.0160456i
$453$		0			0
$454$	14684.0	−	8477.83i	1.51796	−	0.876397i
$455$	2842.11	+	9299.82i	0.292836	+	0.958203i
$456$		0			0
$457$	−2808.03	+	4863.65i	−0.287427	+	0.497838i	−0.973195	−	0.229982i	$-0.926133\pi$
$457$	−2808.03	+	4863.65i	−0.287427	+	0.497838i	0.685768	+	0.727820i	$0.259467\pi$
$458$	1267.69			0.129334
$459$		0			0
$460$			2229.55i			0.225986i
$461$	2311.52	−	4003.68i	0.233532	−	0.404490i	−0.725313	−	0.688420i	$-0.758305\pi$
$461$	2311.52	−	4003.68i	0.233532	−	0.404490i	0.958845	+	0.283929i	$0.0916382\pi$
$462$		0			0
$463$	2180.04	+	3775.94i	0.218823	+	0.379012i	0.954448	−	0.298376i	$-0.0964450\pi$
$463$	2180.04	+	3775.94i	0.218823	+	0.379012i	−0.735626	+	0.677388i	$0.763112\pi$
$464$	9011.59	−	5202.85i	0.901622	−	0.520552i
$465$		0			0
$466$	−351.363	+	608.578i	−0.0349283	+	0.0604975i
$467$	−10923.9			−1.08243			−0.541216	−	0.840884i	$-0.682036\pi$
$467$	−10923.9			−1.08243			−0.541216	+	0.840884i	$0.682036\pi$
$468$		0			0
$469$	−2411.34	+	10439.4i	−0.237410	+	1.02782i
$470$	18453.9	+	10654.4i	1.81110	+	1.04564i
$471$		0			0
$472$	5826.58	−	3363.98i	0.568200	−	0.328050i
$473$	23596.1	−	13623.2i	2.29377	−	1.32431i
$474$		0			0
$475$	3308.53	+	1910.18i	0.319591	+	0.184516i
$476$	173.714	−	752.056i	0.0167272	−	0.0724169i
$477$		0			0
$478$	5446.01			0.521118
$479$	4797.57	−	8309.64i	0.457634	−	0.792645i	−0.541202	−	0.840893i	$-0.682030\pi$
$479$	4797.57	−	8309.64i	0.457634	−	0.792645i	0.998835	+	0.0482479i	$0.0153637\pi$
$480$		0			0
$481$	1176.06	−	678.996i	0.111483	−	0.0643649i
$482$	4075.18	+	7058.41i	0.385102	+	0.667016i
$483$		0			0
$484$	−740.859	+	1283.21i	−0.0695773	+	0.120511i
$485$			11377.3i			1.06519i
$486$		0			0
$487$	−8240.46			−0.766758			−0.383379	−	0.923591i	$-0.625240\pi$
$487$	−8240.46			−0.766758			−0.383379	+	0.923591i	$0.625240\pi$
$488$	3695.46	−	6400.72i	0.342798	−	0.593744i
$489$		0			0
$490$	−15978.3	+	1113.74i	−1.47311	+	0.102681i
$491$	−1742.44	+	1006.00i	−0.160153	+	0.0924645i	−0.577935	−	0.816083i	$-0.696141\pi$
$491$	−1742.44	+	1006.00i	−0.160153	+	0.0924645i	0.417781	+	0.908548i	$0.362808\pi$
$492$		0			0
$493$	5547.68	+	3202.96i	0.506806	+	0.292604i
$494$			3248.28i			0.295844i
$495$		0			0
$496$		−	4996.42i		−	0.452310i
$497$	−9944.68	+	10662.0i	−0.897545	+	0.962285i
$498$		0			0
$499$	−7186.51	−	12447.4i	−0.644714	−	1.11668i	−0.984367	−	0.176127i	$-0.943643\pi$
$499$	−7186.51	−	12447.4i	−0.644714	−	1.11668i	0.339653	−	0.940551i	$-0.389690\pi$
$500$	−48.8883	−	84.6769i	−0.00437270	−	0.00757374i
$501$		0			0
$502$	10923.8	+	6306.87i	0.971222	+	0.560735i
$503$	12261.8			1.08693			0.543467	−	0.839430i	$-0.317111\pi$
$503$	12261.8			1.08693			0.543467	+	0.839430i	$0.317111\pi$
$504$		0			0
$505$	8947.46			0.788429
$506$	−20766.0	−	11989.2i	−1.82443	−	1.05333i
$507$		0			0
$508$	648.998	+	1124.10i	0.0566824	+	0.0981768i
$509$	−10985.2	−	19026.9i	−0.956602	−	1.65688i	−0.730658	−	0.682744i	$-0.760787\pi$
$509$	−10985.2	−	19026.9i	−0.956602	−	1.65688i	−0.225945	−	0.974140i	$-0.572547\pi$
$510$		0			0
$511$	−1849.03	+	1982.40i	−0.160071	+	0.171617i
$512$		−	8880.88i		−	0.766569i
$513$		0			0
$514$			8314.01i			0.713454i
$515$	−22156.8	−	12792.2i	−1.89582	−	1.09455i
$516$		0			0
$517$	−21205.3	+	12242.9i	−1.80388	+	1.04147i
$518$	653.722	+	2139.08i	0.0554496	+	0.181440i
$519$		0			0
$520$	5533.82	−	9584.87i	0.466681	−	0.808316i
$521$	−9869.79			−0.829949			−0.414974	−	0.909833i	$-0.636209\pi$
$521$	−9869.79			−0.829949			−0.414974	+	0.909833i	$0.636209\pi$
$522$		0			0
$523$			4243.21i			0.354766i	0.984142	+	0.177383i	$0.0567632\pi$
$523$			4243.21i			0.354766i	−0.984142	+	0.177383i	$0.943237\pi$
$524$	936.906	−	1622.77i	0.0781087	−	0.135288i
$525$		0			0
$526$	−4729.98	−	8192.57i	−0.392086	−	0.679112i
$527$	2663.79	−	1537.94i	0.220183	−	0.127123i
$528$		0			0
$529$	5063.67	−	8770.54i	0.416181	−	0.720846i
$530$	−9966.06			−0.816788
$531$		0			0
$532$	−556.976	−	128.653i	−0.0453909	−	0.0104846i
$533$	10459.8	+	6038.99i	0.850029	+	0.490765i
$534$		0			0
$535$	5102.28	−	2945.80i	0.412319	−	0.238053i
$536$	10560.5	−	6097.11i	0.851015	−	0.491334i
$537$		0			0
$538$	−11241.7	−	6490.41i	−0.900865	−	0.520115i
$539$	8071.91	−	16540.5i	0.645050	−	1.32180i
$540$		0			0
$541$	3649.63			0.290037			0.145018	−	0.989429i	$-0.453676\pi$
$541$	3649.63			0.290037			0.145018	+	0.989429i	$0.453676\pi$
$542$	12569.3	−	21770.7i	0.996124	−	1.72534i
$543$		0			0
$544$	−1624.94	+	938.158i	−0.128067	+	0.0739397i
$545$	9097.02	+	15756.5i	0.714997	+	1.23841i
$546$		0			0
$547$	758.912	−	1314.47i	0.0593212	−	0.102747i	−0.834840	−	0.550493i	$-0.814440\pi$
$547$	758.912	−	1314.47i	0.0593212	−	0.102747i	0.894161	+	0.447746i	$0.147773\pi$
$548$			949.678i			0.0740296i
$549$		0			0
$550$	−19022.4			−1.47476
$551$	2372.12	−	4108.64i	0.183404	−	0.317666i
$552$		0			0
$553$	6840.06	−	2090.39i	0.525984	−	0.160745i
$554$	−9467.81	+	5466.24i	−0.726081	+	0.419203i
$555$		0			0
$556$	−691.111	−	399.013i	−0.0527152	−	0.0304351i
$557$		−	3101.35i		−	0.235922i	−0.993018	−	0.117961i	$-0.962364\pi$
$557$		−	3101.35i		−	0.235922i	0.993018	−	0.117961i	$-0.0376357\pi$
$558$		0			0
$559$			17087.5i			1.29289i
$560$	14948.7	+	13943.0i	1.12803	+	1.05214i
$561$		0			0
$562$	−12439.0	−	21545.0i	−0.933643	−	1.61712i
$563$	−488.465	−	846.047i	−0.0365655	−	0.0633333i	0.847164	−	0.531332i	$-0.178308\pi$
$563$	−488.465	−	846.047i	−0.0365655	−	0.0633333i	−0.883729	+	0.467999i	$0.844975\pi$
$564$		0			0
$565$	−4354.30	−	2513.96i	−0.324224	−	0.187191i
$566$	4474.02			0.332256
$567$		0			0
$568$	16593.9			1.22581
$569$	−14997.0	−	8658.53i	−1.10493	−	0.637934i	−0.167421	−	0.985885i	$-0.553544\pi$
$569$	−14997.0	−	8658.53i	−1.10493	−	0.637934i	−0.937513	+	0.347952i	$0.886877\pi$
$570$		0			0
$571$	−9602.72	−	16632.4i	−0.703785	−	1.21899i	−0.967128	−	0.254289i	$-0.918158\pi$
$571$	−9602.72	−	16632.4i	−0.703785	−	1.21899i	0.263343	−	0.964702i	$-0.415175\pi$
$572$	−864.045	−	1496.57i	−0.0631601	−	0.109396i
$573$		0			0
$574$	−13569.0	+	14547.7i	−0.986688	+	1.05786i
$575$		−	17686.4i		−	1.28274i
$576$		0			0
$577$		−	19299.1i		−	1.39243i	−0.717832	−	0.696216i	$-0.754866\pi$
$577$		−	19299.1i		−	1.39243i	0.717832	−	0.696216i	$-0.245134\pi$
$578$	7818.36	+	4513.93i	0.562631	+	0.324835i
$579$		0			0
$580$	1902.20	−	1098.24i	0.136180	−	0.0786237i
$581$	3503.51	−	1070.70i	0.250172	−	0.0764549i
$582$		0			0
$583$	5725.95	−	9917.64i	0.406766	−	0.704540i
$584$	3085.32			0.218616
$585$		0			0
$586$			837.023i			0.0590053i
$587$	−4690.62	+	8124.39i	−0.329817	+	0.571260i	−0.982475	−	0.186392i	$-0.940320\pi$
$587$	−4690.62	+	8124.39i	−0.329817	+	0.571260i	0.652658	+	0.757652i	$0.273654\pi$
$588$		0			0
$589$	−1139.00	−	1972.81i	−0.0796804	−	0.138011i
$590$	12908.1	−	7452.51i	0.900710	−	0.520025i
$591$		0			0
$592$	1427.33	−	2472.20i	0.0990925	−	0.171633i
$593$	−21351.5			−1.47859			−0.739294	−	0.673383i	$-0.764841\pi$
$593$	−21351.5			−1.47859			−0.739294	+	0.673383i	$0.764841\pi$
$594$		0			0
$595$	−2832.22	+	12261.5i	−0.195142	+	0.844826i
$596$	−1267.10	−	731.562i	−0.0870847	−	0.0502784i
$597$		0			0
$598$	13023.2	−	7518.98i	0.890569	−	0.514170i
$599$	−15576.0	+	8992.82i	−1.06247	+	0.613417i	−0.926114	−	0.377243i	$-0.876872\pi$
$599$	−15576.0	+	8992.82i	−1.06247	+	0.613417i	−0.136355	+	0.990660i	$0.543539\pi$
$600$		0			0
$601$	−14051.1	−	8112.39i	−0.953669	−	0.550601i	−0.0594502	−	0.998231i	$-0.518935\pi$
$601$	−14051.1	−	8112.39i	−0.953669	−	0.550601i	−0.894219	+	0.447630i	$0.852268\pi$
$602$	−27422.6	−	6334.22i	−1.85658	−	0.428843i
$603$		0			0
$604$	−715.019			−0.0481684
$605$	12078.9	−	20921.3i	0.811699	−	1.40590i
$606$		0			0
$607$	9689.02	−	5593.96i	0.647883	−	0.374055i	−0.139762	−	0.990185i	$-0.544634\pi$
$607$	9689.02	−	5593.96i	0.647883	−	0.374055i	0.787645	+	0.616130i	$0.211300\pi$
$608$	694.803	+	1203.43i	0.0463454	+	0.0802726i
$609$		0			0
$610$	8186.86	−	14180.1i	0.543404	−	0.941203i
$611$		−	15356.1i		−	1.01676i
$612$		0			0
$613$	26379.5			1.73810			0.869052	−	0.494720i	$-0.164729\pi$
$613$	26379.5			1.73810			0.869052	+	0.494720i	$0.164729\pi$
$614$	−16052.7	+	27804.2i	−1.05511	+	1.82750i
$615$		0			0
$616$	−20032.7	+	6122.18i	−1.31029	+	0.400438i
$617$	−18989.8	+	10963.8i	−1.23906	+	0.715371i	−0.968902	−	0.247445i	$-0.920409\pi$
$617$	−18989.8	+	10963.8i	−1.23906	+	0.715371i	−0.270157	+	0.962816i	$0.587076\pi$
$618$		0			0
$619$	−15019.6	−	8671.59i	−0.975267	−	0.563071i	−0.0744291	−	0.997226i	$-0.523713\pi$
$619$	−15019.6	−	8671.59i	−0.975267	−	0.563071i	−0.900838	+	0.434156i	$0.857047\pi$
$620$		−	1054.66i		−	0.0683165i
$621$		0			0
$622$			28589.5i			1.84298i
$623$	8072.17	+	7529.09i	0.519108	+	0.484184i
$624$		0			0
$625$	8200.32	+	14203.4i	0.524820	+	0.909015i
$626$	5521.30	+	9563.17i	0.352517	+	0.610577i
$627$		0			0
$628$	−1141.91	−	659.280i	−0.0725590	−	0.0418919i
$629$	1757.37			0.111401
$630$		0			0
$631$	−30543.8			−1.92699			−0.963495	−	0.267727i	$-0.913727\pi$
$631$	−30543.8			−1.92699			−0.963495	+	0.267727i	$0.913727\pi$
$632$	−7049.71	−	4070.15i	−0.443706	−	0.256174i
$633$		0			0
$634$	−1127.43	−	1952.77i	−0.0706248	−	0.122326i
$635$	−10581.2	−	18327.2i	−0.661265	−	1.14534i
$636$		0			0
$637$	6452.42	+	9570.69i	0.401341	+	0.595298i
$638$			23622.7i			1.46588i
$639$		0			0
$640$		−	25783.4i		−	1.59247i
$641$	513.438	+	296.433i	0.0316374	+	0.0182659i	0.515735	−	0.856748i	$-0.327519\pi$
$641$	513.438	+	296.433i	0.0316374	+	0.0182659i	−0.484098	+	0.875014i	$0.660852\pi$
$642$		0			0
$643$	27553.5	−	15908.0i	1.68990	−	0.975661i	0.735307	−	0.677735i	$-0.237038\pi$
$643$	27553.5	−	15908.0i	1.68990	−	0.975661i	0.954589	−	0.297927i	$-0.0962951\pi$
$644$	773.457	+	2530.87i	0.0473268	+	0.154861i
$645$		0			0
$646$	−2101.79	+	3640.41i	−0.128009	+	0.221718i
$647$	14337.8			0.871218			0.435609	−	0.900136i	$-0.356533\pi$
$647$	14337.8			0.871218			0.435609	+	0.900136i	$0.356533\pi$
$648$		0			0
$649$			17127.2i			1.03591i
$650$	5964.90	−	10331.5i	0.359943	−	0.623439i
$651$		0			0
$652$	909.290	+	1574.94i	0.0546174	+	0.0946001i
$653$	−1310.50	+	756.617i	−0.0785356	+	0.0453426i	−0.538754	−	0.842463i	$-0.681105\pi$
$653$	−1310.50	+	756.617i	−0.0785356	+	0.0453426i	0.460218	+	0.887806i	$0.347771\pi$
$654$		0			0
$655$	−15275.3	+	26457.5i	−0.911228	+	1.57829i
$656$	25389.3			1.51110
$657$		0			0
$658$	24644.0	+	5692.40i	1.46007	+	0.337254i
$659$	−2743.47	−	1583.94i	−0.162171	−	0.0936293i	0.416718	−	0.909036i	$-0.363180\pi$
$659$	−2743.47	−	1583.94i	−0.162171	−	0.0936293i	−0.578889	+	0.815406i	$0.696514\pi$
$660$		0			0
$661$	−4954.29	+	2860.36i	−0.291527	+	0.168313i	−0.638630	−	0.769514i	$-0.720499\pi$
$661$	−4954.29	+	2860.36i	−0.291527	+	0.168313i	0.347103	+	0.937827i	$0.387165\pi$
$662$	16169.8	−	9335.64i	0.949331	−	0.548097i
$663$		0			0
$664$	−3610.89	−	2084.75i	−0.211039	−	0.121843i
$665$	9080.90	+	2097.55i	0.529537	+	0.122315i
$666$		0			0
$667$	−21963.5			−1.27501
$668$	−800.442	+	1386.41i	−0.0463623	+	0.0803019i
$669$		0			0
$670$	23395.6	−	13507.4i	1.34903	−	0.778863i
$671$	9407.45	+	16294.2i	0.541238	+	0.937451i
$672$		0			0
$673$	3370.28	−	5837.50i	0.193038	−	0.334352i	−0.753217	−	0.657772i	$-0.771499\pi$
$673$	3370.28	−	5837.50i	0.193038	−	0.334352i	0.946256	+	0.323420i	$0.104833\pi$
$674$			23522.2i			1.34427i
$675$		0			0
$676$	−1018.78			−0.0579641
$677$	2209.63	−	3827.20i	0.125440	−	0.217269i	−0.796465	−	0.604685i	$-0.793299\pi$
$677$	2209.63	−	3827.20i	0.125440	−	0.217269i	0.921905	+	0.387416i	$0.126632\pi$
$678$		0			0
$679$	3946.91	+	12914.9i	0.223076	+	0.729938i
$680$	12403.7	−	7161.30i	0.699502	−	0.403858i
$681$		0			0
$682$	9823.06	+	5671.35i	0.551532	+	0.318427i
$683$			25188.7i			1.41115i	0.708633	+	0.705577i	$0.249312\pi$
$683$			25188.7i			1.41115i	−0.708633	+	0.705577i	$0.750688\pi$
$684$		0			0
$685$		−	15483.5i		−	0.863640i
$686$	−17751.3	+	6807.29i	−0.987970	+	0.378868i
$687$		0			0
$688$	17959.9	+	31107.5i	0.995225	+	1.72378i
$689$	3591.00	+	6219.79i	0.198558	+	0.343912i
$690$		0			0
$691$	21.1593	+	12.2163i	0.00116489	+	0.000672548i	0.500582	−	0.865689i	$-0.333119\pi$
$691$	21.1593	+	12.2163i	0.00116489	+	0.000672548i	−0.499417	+	0.866361i	$0.666453\pi$
$692$	−950.111			−0.0521933
$693$		0			0
$694$	3948.18			0.215952
$695$	11267.8	+	6505.49i	0.614983	+	0.355061i
$696$		0			0
$697$	7815.02	+	13536.0i	0.424699	+	0.735600i
$698$	−7414.57	−	12842.4i	−0.402071	−	0.696408i
$699$		0			0
$700$	1535.27	+	1431.98i	0.0828970	+	0.0773199i
$701$			5989.84i			0.322729i	0.986895	+	0.161365i	$0.0515895\pi$
$701$			5989.84i			0.322729i	−0.986895	+	0.161365i	$0.948411\pi$
$702$		0			0
$703$		−	1301.52i		−	0.0698259i
$704$	20306.2	+	11723.8i	1.08710	+	0.627639i
$705$		0			0
$706$	−13948.2	+	8052.98i	−0.743550	+	0.429289i
$707$	10156.7	−	3103.97i	0.540284	−	0.165116i
$708$		0			0
$709$	−2214.14	+	3835.00i	−0.117283	+	0.203140i	−0.918690	−	0.394979i	$-0.870752\pi$
$709$	−2214.14	+	3835.00i	−0.117283	+	0.203140i	0.801407	+	0.598119i	$0.204085\pi$
$710$	36761.8			1.94316
$711$		0			0
$712$		−	12563.2i		−	0.661271i
$713$	−5273.02	+	9133.15i	−0.276965	+	0.479718i
$714$		0			0
$715$	14087.3	+	24400.0i	0.736835	+	1.27624i
$716$	120.814	−	69.7521i	0.00630592	−	0.00364073i
$717$		0			0
$718$	5707.36	−	9885.44i	0.296653	−	0.513818i
$719$	−28053.6			−1.45511			−0.727554	−	0.686050i	$-0.759343\pi$
$719$	−28053.6			−1.45511			−0.727554	+	0.686050i	$0.759343\pi$
$720$		0			0
$721$	−29589.0	−	6834.61i	−1.52836	−	0.353030i
$722$	−15081.5	−	8707.30i	−0.777389	−	0.448826i
$723$		0			0
$724$	−1867.73	+	1078.34i	−0.0958753	+	0.0553536i
$725$	−15089.6	+	8711.98i	−0.772984	+	0.446282i
$726$		0			0
$727$	13620.1	+	7863.54i	0.694828	+	0.401159i	0.805418	−	0.592707i	$-0.201941\pi$
$727$	13620.1	+	7863.54i	0.694828	+	0.401159i	−0.110590	+	0.993866i	$0.535274\pi$
$728$	2956.60	−	12800.0i	0.150521	−	0.651646i
$729$		0			0
$730$	6835.18			0.346550
$731$	−11056.4	+	19150.3i	−0.559420	+	0.968945i
$732$		0			0
$733$	−28543.9	+	16479.8i	−1.43833	+	0.830418i	−0.997734	−	0.0672892i	$-0.978565\pi$
$733$	−28543.9	+	16479.8i	−1.43833	+	0.830418i	−0.440593	+	0.897707i	$0.645232\pi$
$734$	−18805.0	−	32571.3i	−0.945649	−	1.63791i
$735$		0			0
$736$	3216.60	−	5571.32i	0.161094	−	0.279024i
$737$			31042.6i			1.55152i
$738$		0			0
$739$	18483.4			0.920056			0.460028	−	0.887905i	$-0.347839\pi$
$739$	18483.4			0.920056			0.460028	+	0.887905i	$0.347839\pi$
$740$	301.285	−	521.841i	0.0149668	−	0.0259233i
$741$		0			0
$742$	−11312.9	+	3457.33i	−0.559718	+	0.171055i
$743$	−27952.9	+	16138.6i	−1.38020	+	0.796861i	−0.992183	−	0.124790i	$-0.960174\pi$
$743$	−27952.9	+	16138.6i	−1.38020	+	0.796861i	−0.388020	+	0.921651i	$0.626841\pi$
$744$		0			0
$745$	20658.8	+	11927.3i	1.01594	+	0.586555i
$746$		−	13998.0i		−	0.687004i
$747$		0			0
$748$		−	2236.31i		−	0.109315i
$749$	4769.90	−	5113.95i	0.232695	−	0.249479i
$750$		0			0
$751$	12875.3	+	22300.7i	0.625601	+	1.08357i	0.988424	+	0.151715i	$0.0484796\pi$
$751$	12875.3	+	22300.7i	0.625601	+	1.08357i	−0.362823	+	0.931858i	$0.618187\pi$
$752$	−16140.1	−	27955.5i	−0.782672	−	1.35563i
$753$		0			0
$754$	−12830.0	−	7407.41i	−0.619683	−	0.357774i
$755$	11657.6			0.561939
$756$		0			0
$757$	14678.2			0.704741			0.352371	−	0.935861i	$-0.385376\pi$
$757$	14678.2			0.704741			0.352371	+	0.935861i	$0.385376\pi$
$758$	12575.0	+	7260.16i	0.602564	+	0.347890i
$759$		0			0
$760$	−5303.68	−	9186.25i	−0.253138	−	0.438448i
$761$	15248.7	+	26411.6i	0.726369	+	1.25811i	0.958408	+	0.285401i	$0.0921268\pi$
$761$	15248.7	+	26411.6i	0.726369	+	1.25811i	−0.232039	+	0.972706i	$0.574540\pi$
$762$		0			0
$763$	15792.5	+	14730.1i	0.749316	+	0.698905i
$764$		−	3537.77i		−	0.167529i
$765$		0			0
$766$		−	14701.8i		−	0.693470i
$767$	−9302.19	−	5370.62i	−0.437917	−	0.252832i
$768$		0			0
$769$	30619.6	−	17678.2i	1.43585	−	0.828989i	0.438294	−	0.898832i	$-0.355583\pi$
$769$	30619.6	−	17678.2i	1.43585	−	0.828989i	0.997558	+	0.0698425i	$0.0222497\pi$
$770$	−44380.1	+	13563.0i	−2.07708	+	0.634774i
$771$		0			0
$772$	−2100.39	+	3637.98i	−0.0979205	+	0.169603i
$773$	−4097.47			−0.190654			−0.0953272	−	0.995446i	$-0.530390\pi$
$773$	−4097.47			−0.190654			−0.0953272	+	0.995446i	$0.530390\pi$
$774$		0			0
$775$			8366.32i			0.387777i
$776$	7684.95	−	13310.7i	0.355507	−	0.615757i
$777$		0			0
$778$	−7986.30	−	13832.7i	−0.368024	−	0.637436i
$779$	10024.8	−	5787.84i	0.461074	−	0.266201i
$780$		0			0
$781$	−21121.3	+	36583.2i	−0.967709	+	1.67612i
$782$	19460.6			0.889908
$783$		0			0
$784$	21805.9	+	10641.4i	0.993343	+	0.484759i
$785$	18617.6	+	10748.9i	0.846484	+	0.488718i
$786$		0			0
$787$	−29205.4	+	16861.7i	−1.32282	+	0.763730i	−0.984178	−	0.177185i	$-0.943301\pi$
$787$	−29205.4	+	16861.7i	−1.32282	+	0.763730i	−0.338642	+	0.940915i	$0.609968\pi$
$788$	1749.04	−	1009.81i	0.0790696	−	0.0456509i
$789$		0			0
$790$	−15617.8	−	9016.95i	−0.703363	−	0.406087i
$791$	−5814.88	−	1343.15i	−0.261382	−	0.0603754i
$792$		0			0
$793$	−11799.7			−0.528396
$794$	−1957.56	+	3390.59i	−0.0874950	+	0.151546i
$795$		0			0
$796$	−2853.69	+	1647.58i	−0.127068	+	0.0733628i
$797$	−7132.81	−	12354.4i	−0.317010	−	0.549077i	0.662853	−	0.748750i	$-0.269346\pi$
$797$	−7132.81	−	12354.4i	−0.317010	−	0.549077i	−0.979863	+	0.199672i	$0.936012\pi$
$798$		0			0
$799$	9936.12	−	17209.9i	0.439943	−	0.762004i
$800$		−	5103.54i		−	0.225547i
$801$		0			0
$802$	−6020.75			−0.265087
$803$	−3927.12	+	6801.97i	−0.172584	+	0.298925i
$804$		0			0
$805$	−12610.4	−	41263.1i	−0.552122	−	1.80663i
$806$	−6160.48	+	3556.75i	−0.269223	+	0.155436i
$807$		0			0
$808$	−10468.0	−	6043.68i	−0.455770	−	0.263139i
$809$		−	13916.9i		−	0.604812i	−0.953179	−	0.302406i	$-0.902210\pi$
$809$		−	13916.9i		−	0.604812i	0.953179	−	0.302406i	$-0.0977898\pi$
$810$		0			0
$811$			7296.14i			0.315909i	0.987446	+	0.157954i	$0.0504899\pi$
$811$			7296.14i			0.315909i	−0.987446	+	0.157954i	$0.949510\pi$
$812$	1778.28	−	1906.55i	0.0768541	−	0.0823975i
$813$		0			0
$814$	3240.27	+	5612.31i	0.139523	+	0.241660i
$815$	−14825.0	−	25677.7i	−0.637175	−	1.10362i
$816$		0			0
$817$	14182.8	+	8188.42i	0.607334	+	0.350645i
$818$	212.619			0.00908809
$819$		0			0
$820$	5359.26			0.228236
$821$	−30269.4	−	17476.0i	−1.28673	−	0.742897i	−0.308664	−	0.951171i	$-0.599882\pi$
$821$	−30269.4	−	17476.0i	−1.28673	−	0.742897i	−0.978070	+	0.208274i	$0.933215\pi$
$822$		0			0
$823$	−11765.3	−	20378.1i	−0.498314	−	0.863105i	0.501684	−	0.865051i	$-0.332714\pi$
$823$	−11765.3	−	20378.1i	−0.498314	−	0.863105i	−0.999998	+	0.00194598i	$0.999381\pi$
$824$	17281.4	+	29932.2i	0.730614	+	1.26546i
$825$		0			0
$826$	12067.2	−	12937.7i	0.508321	−	0.544986i
$827$		−	40158.9i		−	1.68859i	−0.535880	−	0.844294i	$-0.680020\pi$
$827$		−	40158.9i		−	1.68859i	0.535880	−	0.844294i	$-0.319980\pi$
$828$		0			0
$829$		−	10739.4i		−	0.449934i	−0.974366	−	0.224967i	$-0.927773\pi$
$829$		−	10739.4i		−	0.449934i	0.974366	−	0.224967i	$-0.0722275\pi$
$830$	−7999.52	−	4618.52i	−0.334539	−	0.193146i
$831$		0			0
$832$	−12734.9	+	7352.52i	−0.530654	+	0.306373i
$833$	1038.66	+	14901.1i	0.0432022	+	0.619799i
$834$		0			0
$835$	13050.4	−	22603.9i	0.540870	−	0.936814i
$836$	−1656.22			−0.0685187
$837$		0			0
$838$			10924.7i			0.450343i
$839$	−9285.04	+	16082.2i	−0.382068	+	0.661762i	−0.991358	−	0.131186i	$-0.958121\pi$
$839$	−9285.04	+	16082.2i	−0.382068	+	0.661762i	0.609289	+	0.792948i	$0.291455\pi$
$840$		0			0
$841$	−1375.69	−	2382.76i	−0.0564062	−	0.0976983i
$842$	15396.3	−	8889.05i	0.630156	−	0.363821i
$843$		0			0
$844$	1784.89	−	3091.52i	0.0727944	−	0.126084i
$845$	16610.1			0.676218
$846$		0			0
$847$	6453.50	−	27939.0i	0.261801	−	1.13341i
$848$	13074.7	+	7548.69i	0.529466	+	0.305688i
$849$		0			0
$850$	13370.0	−	7719.16i	0.539513	−	0.311488i
$851$	−5218.13	+	3012.69i	−0.210194	+	0.121356i
$852$		0			0
$853$	−4663.07	−	2692.22i	−0.187175	−	0.108066i	0.403484	−	0.914987i	$-0.367799\pi$
$853$	−4663.07	−	2692.22i	−0.187175	−	0.108066i	−0.590659	+	0.806921i	$0.701132\pi$
$854$	4374.06	−	18936.5i	0.175266	−	0.758776i
$855$		0			0
$856$	−7959.13			−0.317801
$857$	−5528.79	+	9576.15i	−0.220373	+	0.381698i	−0.954921	−	0.296859i	$-0.904061\pi$
$857$	−5528.79	+	9576.15i	−0.220373	+	0.381698i	0.734548	+	0.678557i	$0.237394\pi$
$858$		0			0
$859$	−14136.9	+	8161.94i	−0.561519	+	0.324193i	−0.753755	−	0.657156i	$-0.771759\pi$
$859$	−14136.9	+	8161.94i	−0.561519	+	0.324193i	0.192236	+	0.981349i	$0.438426\pi$
$860$	3791.04	+	6566.28i	0.150318	+	0.260358i
$861$		0			0
$862$	−11235.2	+	19459.9i	−0.443935	+	0.768917i
$863$			37617.5i			1.48379i	0.670515	+	0.741896i	$0.266073\pi$
$863$			37617.5i			1.48379i	−0.670515	+	0.741896i	$0.733927\pi$
$864$		0			0
$865$	15490.5			0.608895
$866$	−10296.7	+	17834.5i	−0.404039	+	0.699816i
$867$		0			0
$868$	−365.874	−	1197.19i	−0.0143071	−	0.0468150i
$869$	17946.3	−	10361.3i	0.700560	−	0.404468i
$870$		0			0
$871$	−16859.9	−	9734.08i	−0.655886	−	0.378676i
$872$		−	24578.8i		−	0.954523i
$873$		0			0
$874$		−	14412.6i		−	0.557794i
$875$	1383.73	+	1290.63i	0.0534611	+	0.0498644i
$876$		0			0
$877$	−21070.2	−	36494.6i	−0.811275	−	1.40517i	−0.911972	−	0.410253i	$-0.865440\pi$
$877$	−21070.2	−	36494.6i	−0.811275	−	1.40517i	0.100696	−	0.994917i	$-0.467893\pi$
$878$	7767.19	+	13453.2i	0.298553	+	0.517110i
$879$		0			0
$880$	51291.6	+	29613.2i	1.96482	+	1.13439i
$881$	17255.0			0.659861			0.329930	−	0.944005i	$-0.392975\pi$
$881$	17255.0			0.659861			0.329930	+	0.944005i	$0.392975\pi$
$882$		0			0
$883$	−26461.1			−1.00848			−0.504240	−	0.863564i	$-0.668227\pi$
$883$	−26461.1			−1.00848			−0.504240	+	0.863564i	$0.668227\pi$
$884$	1214.59	+	701.246i	0.0462118	+	0.0266804i
$885$		0			0
$886$	−1517.98	−	2629.23i	−0.0575595	−	0.0996959i
$887$	−9683.24	−	16771.9i	−0.366552	−	0.634886i	0.622472	−	0.782642i	$-0.286128\pi$
$887$	−9683.24	−	16771.9i	−0.366552	−	0.634886i	−0.989024	+	0.147756i	$0.952795\pi$
$888$		0			0
$889$	−18369.2	−	17133.3i	−0.693005	−	0.646382i
$890$		−	27832.3i		−	1.04825i
$891$		0			0
$892$		−	2607.55i		−	0.0978780i
$893$	−12745.7	−	7358.72i	−0.477624	−	0.275756i
$894$		0			0
$895$	−1969.75	+	1137.23i	−0.0735658	+	0.0424732i
$896$	−8944.55	−	29267.9i	−0.333500	−	1.09126i
$897$		0			0
$898$	9518.76	−	16487.0i	0.353725	−	0.612670i
$899$	10389.6			0.385441
$900$		0			0
$901$			9294.19i			0.343656i
$902$	−28818.9	+	49915.9i	−1.06382	+	1.84259i
$903$		0			0
$904$	3396.17	+	5882.34i	0.124950	+	0.216420i
$905$	30451.4	−	17581.1i	1.11850	−	0.645764i
$906$		0			0
$907$	569.688	−	986.728i	0.0208558	−	0.0361232i	−0.855409	−	0.517953i	$-0.826694\pi$
$907$	569.688	−	986.728i	0.0208558	−	0.0361232i	0.876265	+	0.481830i	$0.160028\pi$
$908$	−5421.85			−0.198161
$909$		0			0
$910$	6550.01	−	28356.8i	0.238605	−	1.03299i
$911$	7531.25	+	4348.17i	0.273898	+	0.158135i	0.630658	−	0.776061i	$-0.282785\pi$
$911$	7531.25	+	4348.17i	0.273898	+	0.158135i	−0.356760	+	0.934196i	$0.616118\pi$
$912$		0			0
$913$	9192.18	−	5307.10i	0.333205	−	0.192376i
$914$	14556.1	−	8403.95i	0.526775	−	0.304133i
$915$		0			0
$916$	−351.055	−	202.682i	−0.0126629	−	0.00731090i
$917$	−8161.24	+	35332.3i	−0.293902	+	1.27238i
$918$		0			0
$919$	−2297.46			−0.0824659			−0.0412330	−	0.999150i	$-0.513129\pi$
$919$	−2297.46			−0.0824659			−0.0412330	+	0.999150i	$0.513129\pi$
$920$	−24553.5	+	42527.8i	−0.879895	+	1.52402i
$921$		0			0
$922$	−11982.3	+	6917.99i	−0.428000	+	0.247106i
$923$	−13246.1	−	22942.9i	−0.472374	−	0.818176i
$924$		0			0
$925$	−2390.01	+	4139.61i	−0.0849545	+	0.147146i
$926$		−	13048.9i		−	0.463083i
$927$		0			0
$928$	−6337.74			−0.224188
$929$	24197.9	−	41911.9i	0.854581	−	1.48018i	−0.0224522	−	0.999748i	$-0.507147\pi$
$929$	24197.9	−	41911.9i	0.854581	−	1.48018i	0.877033	−	0.480430i	$-0.159519\pi$
$930$		0			0
$931$	11035.8	−	769.235i	0.388490	−	0.0270791i
$932$	194.603	−	112.354i	0.00683951	−	0.00394879i
$933$		0			0
$934$	28313.1	+	16346.6i	0.991900	+	0.572673i
$935$			36460.7i			1.27529i
$936$		0			0
$937$		−	23667.6i		−	0.825172i	−0.910919	−	0.412586i	$-0.864626\pi$
$937$		−	23667.6i		−	0.825172i	0.910919	−	0.412586i	$-0.135374\pi$
$938$	21871.5	−	23449.1i	0.761333	−	0.816247i
$939$		0			0
$940$	−3406.91	−	5900.94i	−0.118214	−	0.204753i
$941$	5099.48	+	8832.56i	0.176661	+	0.305987i	0.940735	−	0.339143i	$-0.110137\pi$
$941$	5099.48	+	8832.56i	0.176661	+	0.305987i	−0.764074	+	0.645129i	$0.776804\pi$
$942$		0			0
$943$	−46410.0	−	26794.9i	−1.60267	−	0.925303i
$944$	−22579.3			−0.778489
$945$		0			0
$946$	−81544.0			−2.80256
$947$	2943.58	+	1699.47i	0.101007	+	0.0583163i	0.549652	−	0.835393i	$-0.314760\pi$
$947$	2943.58	+	1699.47i	0.101007	+	0.0583163i	−0.448646	+	0.893710i	$0.648093\pi$
$948$		0			0
$949$	−2462.87	−	4265.82i	−0.0842447	−	0.145916i
$950$	−5716.84	−	9901.85i	−0.195241	−	0.338167i
$951$		0			0
$952$	11595.7	−	12432.1i	0.394768	−	0.423243i
$953$		−	27410.8i		−	0.931714i	−0.884860	−	0.465857i	$-0.845746\pi$
$953$		−	27410.8i		−	0.931714i	0.884860	−	0.465857i	$-0.154254\pi$
$954$		0			0
$955$			57679.7i			1.95442i
$956$	−1508.14	−	870.725i	−0.0510217	−	0.0294574i
$957$		0			0
$958$	−24869.3	+	14358.3i	−0.838716	+	0.484233i
$959$	−5371.39	−	17576.0i	−0.180867	−	0.591824i
$960$		0			0
$961$	−12401.2	+	21479.4i	−0.416272	+	0.721005i
$962$	−4064.23			−0.136212
$963$		0			0
$964$		−	2606.21i		−	0.0870750i
$965$	34244.6	−	59313.4i	1.14236	−	1.97862i
$966$		0			0
$967$	18511.5	+	32062.9i	0.615606	+	1.06626i	0.990278	+	0.139103i	$0.0444221\pi$
$967$	18511.5	+	32062.9i	0.615606	+	1.06626i	−0.374672	+	0.927158i	$0.622245\pi$
$968$	−28263.2	+	16317.8i	−0.938443	+	0.541810i
$969$		0			0
$970$	17025.1	−	29488.4i	0.563550	−	0.976098i
$971$	−17050.2			−0.563509			−0.281754	−	0.959487i	$-0.590916\pi$
$971$	−17050.2			−0.563509			−0.281754	+	0.959487i	$0.590916\pi$
$972$		0			0
$973$	15047.5	+	3475.74i	0.495786	+	0.114519i
$974$	21358.2	+	12331.1i	0.702628	+	0.405662i
$975$		0			0
$976$	−21481.1	+	12402.1i	−0.704501	+	0.406744i
$977$	14180.0	−	8186.83i	0.464338	−	0.268086i	−0.249528	−	0.968367i	$-0.580276\pi$
$977$	14180.0	−	8186.83i	0.464338	−	0.268086i	0.713867	+	0.700282i	$0.246942\pi$
$978$		0			0
$979$	27697.1	+	15990.9i	0.904190	+	0.522034i
$980$	4602.86	+	2246.23i	0.150034	+	0.0732176i
$981$		0			0
$982$	6021.56			0.195678
$983$	10769.1	−	18652.7i	0.349423	−	0.605218i	−0.636724	−	0.771092i	$-0.719711\pi$
$983$	10769.1	−	18652.7i	0.349423	−	0.605218i	0.986147	+	0.165874i	$0.0530444\pi$
$984$		0			0
$985$	−28516.2	+	16463.8i	−0.922438	+	0.532570i
$986$	−9585.89	−	16603.3i	−0.309612	−	0.536263i
$987$		0			0
$988$	519.345	−	899.533i	0.0167233	−	0.0289655i
$989$		−	75816.8i		−	2.43765i
$990$		0			0
$991$	39248.1			1.25808			0.629040	−	0.777373i	$-0.283448\pi$
$991$	39248.1			1.25808			0.629040	+	0.777373i	$0.283448\pi$
$992$	−1521.57	+	2635.44i	−0.0486995	+	0.0843500i
$993$		0			0
$994$	41730.0	−	12753.1i	1.33158	−	0.406944i
$995$	46526.3	−	26862.0i	1.48240	−	0.855862i
$996$		0			0
$997$	−3452.73	−	1993.43i	−0.109678	−	0.0633226i	0.444158	−	0.895949i	$-0.353503\pi$
$997$	−3452.73	−	1993.43i	−0.109678	−	0.0633226i	−0.553836	+	0.832626i	$0.686836\pi$
$998$			43015.9i			1.36437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.62.5		44
3.2	odd	2		63.4.o.a.20.18	yes	44
7.6	odd	2	inner	189.4.o.a.62.6		44
9.2	odd	6		567.4.c.c.566.7		44
9.4	even	3		63.4.o.a.41.17	yes	44
9.5	odd	6	inner	189.4.o.a.125.6		44
9.7	even	3		567.4.c.c.566.38		44
21.20	even	2		63.4.o.a.20.17	✓	44
63.13	odd	6		63.4.o.a.41.18	yes	44
63.20	even	6		567.4.c.c.566.37		44
63.34	odd	6		567.4.c.c.566.8		44
63.41	even	6	inner	189.4.o.a.125.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.17	✓	44	21.20	even	2
63.4.o.a.20.18	yes	44	3.2	odd	2
63.4.o.a.41.17	yes	44	9.4	even	3
63.4.o.a.41.18	yes	44	63.13	odd	6
189.4.o.a.62.5		44	1.1	even	1	trivial
189.4.o.a.62.6		44	7.6	odd	2	inner
189.4.o.a.125.5		44	63.41	even	6	inner
189.4.o.a.125.6		44	9.5	odd	6	inner
567.4.c.c.566.7		44	9.2	odd	6
567.4.c.c.566.8		44	63.34	odd	6
567.4.c.c.566.37		44	63.20	even	6
567.4.c.c.566.38		44	9.7	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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(-13.5435 - 12.6323i) q^{7} +21.0785i q^{8} +O(q^{10})\)	\(q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(-7.80147 - 13.5125i) q^{5} +(-13.5435 - 12.6323i) q^{7} +21.0785i q^{8} +46.6969i q^{10} +(-46.4700 - 26.8295i) q^{11} +(29.1434 - 16.8260i) q^{13} +(16.1997 + 53.0078i) q^{14} +(35.3701 - 61.2628i) q^{16} +43.5488 q^{17} -32.2524i q^{19} +(7.46605 - 12.9316i) q^{20} +(80.2960 + 139.077i) q^{22} +(-129.309 + 74.6565i) q^{23} +(-59.2260 + 102.582i) q^{25} -100.714 q^{26} +(3.98894 - 17.2693i) q^{28} +(127.390 + 73.5487i) q^{29} +(61.1678 - 35.3153i) q^{31} +(-37.3130 + 21.5427i) q^{32} +(-112.873 - 65.1670i) q^{34} +(-65.0355 + 281.557i) q^{35} +40.3540 q^{37} +(-48.2629 + 83.5938i) q^{38} +(284.824 - 164.443i) q^{40} +(179.454 + 310.824i) q^{41} +(-253.886 + 439.743i) q^{43} -51.3519i q^{44} +446.867 q^{46} +(228.160 - 395.185i) q^{47} +(23.8504 + 342.170i) q^{49} +(307.011 - 177.253i) q^{50} +(27.8904 + 16.1025i) q^{52} +213.420i q^{53} +837.238i q^{55} +(266.269 - 285.475i) q^{56} +(-220.118 - 381.256i) q^{58} +(-159.593 - 276.424i) q^{59} +(-303.662 - 175.319i) q^{61} -211.385 q^{62} -436.974 q^{64} +(-454.723 - 262.535i) q^{65} +(-289.258 - 501.009i) q^{67} +(20.8382 + 36.0928i) q^{68} +(589.889 - 632.437i) q^{70} -787.243i q^{71} -146.373i q^{73} +(-104.592 - 60.3863i) q^{74} +(26.7305 - 15.4329i) q^{76} +(290.447 + 950.387i) q^{77} +(-193.095 + 334.451i) q^{79} -1103.76 q^{80} -1074.15i q^{82} +(-98.9043 + 171.307i) q^{83} +(-339.745 - 588.455i) q^{85} +(1316.07 - 759.835i) q^{86} +(565.524 - 979.517i) q^{88} -596.020 q^{89} +(-607.253 - 140.267i) q^{91} +(-123.749 - 71.4466i) q^{92} +(-1182.72 + 682.844i) q^{94} +(-435.812 + 251.616i) q^{95} +(-631.485 - 364.588i) q^{97} +(450.210 - 922.547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

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