LMFDB - Embedded newform 189.3.n.b.170.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,3,Mod(170,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.170"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			170.11
Character	$\chi$	$=$	189.170
Dual form			189.3.n.b.179.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.19625 - 1.84536i) q^{2} +(4.81069 - 8.33236i) q^{4} +5.83234i q^{5} +(3.24949 - 6.20007i) q^{7} -20.7469i q^{8} +(10.7628 + 18.6416i) q^{10} -3.36449i q^{11} +(0.158134 + 0.273895i) q^{13} +(-1.05516 - 25.8135i) q^{14} +(-19.0428 - 32.9830i) q^{16} +(-2.99912 + 1.73154i) q^{17} +(-12.0337 + 20.8430i) q^{19} +(48.5972 + 28.0576i) q^{20} +(-6.20870 - 10.7538i) q^{22} +34.0258i q^{23} -9.01621 q^{25} +(1.01087 + 0.583626i) q^{26} +(-36.0289 - 56.9025i) q^{28} +(-31.6161 - 18.2536i) q^{29} +(-12.0916 + 20.9433i) q^{31} +(-49.8615 - 28.7875i) q^{32} +(-6.39064 + 11.0689i) q^{34} +(36.1609 + 18.9521i) q^{35} +(4.23403 - 7.33356i) q^{37} +88.8260i q^{38} +121.003 q^{40} +(39.9308 - 23.0541i) q^{41} +(-26.4994 + 45.8984i) q^{43} +(-28.0342 - 16.1855i) q^{44} +(62.7897 + 108.755i) q^{46} +(17.2703 - 9.97104i) q^{47} +(-27.8817 - 40.2941i) q^{49} +(-28.8181 + 16.6381i) q^{50} +3.04293 q^{52} +(29.2909 - 16.9111i) q^{53} +19.6229 q^{55} +(-128.632 - 67.4169i) q^{56} -134.738 q^{58} +(-31.5660 - 18.2246i) q^{59} +(-6.02138 - 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(-1.59745 + 0.922289i) q^{65} +(17.4628 - 30.2465i) q^{67} +33.3197i q^{68} +(150.553 - 6.15405i) q^{70} -85.7413i q^{71} +(-35.3783 - 61.2770i) q^{73} -31.2532i q^{74} +(115.781 + 200.539i) q^{76} +(-20.8601 - 10.9329i) q^{77} +(50.7030 + 87.8201i) q^{79} +(192.368 - 111.064i) q^{80} +(85.0860 - 147.373i) q^{82} +(-26.0171 - 15.0210i) q^{83} +(-10.0990 - 17.4919i) q^{85} +195.604i q^{86} -69.8030 q^{88} +(46.5438 + 26.8721i) q^{89} +(2.21202 - 0.0904195i) q^{91} +(283.515 + 163.688i) q^{92} +(36.8003 - 63.7400i) q^{94} +(-121.563 - 70.1847i) q^{95} +(-3.60974 + 6.25225i) q^{97} +(-163.474 - 77.3384i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7} + 25 q^{10} - 18 q^{13} + 90 q^{14} + 12 q^{16} - 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 114 q^{25} + 3 q^{26} + 34 q^{28} + 63 q^{29} - 29 q^{31} - 246 q^{32}+ \cdots - 483 q^{98}+O(q^{100}) $ 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7 + 25 * q^10 - 18 * q^13 + 90 * q^14 + 12 * q^16 - 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 114 * q^25 + 3 * q^26 + 34 * q^28 + 63 * q^29 - 29 * q^31 - 246 * q^32 - 99 * q^34 + 27 * q^35 - 20 * q^37 + 210 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 75 * q^46 - 261 * q^47 - 131 * q^49 - 63 * q^50 + 92 * q^52 + 63 * q^53 - 100 * q^55 - 153 * q^56 - 80 * q^58 + 102 * q^59 + 78 * q^61 + 106 * q^64 + 225 * q^65 - 132 * q^67 + 179 * q^70 + q^73 + 233 * q^76 + 447 * q^77 + 140 * q^79 - 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 816 * q^88 + 720 * q^89 - 70 * q^91 + 1239 * q^92 + 261 * q^94 - 642 * q^95 + 178 * q^97 - 483 * q^98

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.19625	−	1.84536i	1.59813	−	0.922679i	0.606279	−	0.795252i	$-0.292661\pi$
$2$	3.19625	−	1.84536i	1.59813	−	0.922679i	0.991848	−	0.127427i	$-0.0406718\pi$
$3$		0			0
$3$		0			0
$4$	4.81069	−	8.33236i	1.20267	−	2.08309i
$5$			5.83234i			1.16647i	0.812304	+	0.583234i	$0.198213\pi$
$5$			5.83234i			1.16647i	−0.812304	+	0.583234i	$0.801787\pi$
$6$		0			0
$7$	3.24949	−	6.20007i	0.464212	−	0.885724i
$7$	3.24949	−	6.20007i	0.464212	−	0.885724i
$8$		−	20.7469i		−	2.59337i
$9$		0			0
$10$	10.7628	+	18.6416i	1.07628	+	1.86416i
$11$		−	3.36449i		−	0.305863i	−0.988237	−	0.152932i	$-0.951129\pi$
$11$		−	3.36449i		−	0.305863i	0.988237	−	0.152932i	$-0.0488714\pi$
$12$		0			0
$13$	0.158134	+	0.273895i	0.0121641	+	0.0210689i	0.872043	−	0.489429i	$-0.162795\pi$
$13$	0.158134	+	0.273895i	0.0121641	+	0.0210689i	−0.859879	+	0.510497i	$0.829461\pi$
$14$	−1.05516	−	25.8135i	−0.0753686	−	1.84382i
$15$		0			0
$16$	−19.0428	−	32.9830i	−1.19017	−	2.06144i
$17$	−2.99912	+	1.73154i	−0.176419	+	0.101856i	−0.585609	−	0.810594i	$-0.699145\pi$
$17$	−2.99912	+	1.73154i	−0.176419	+	0.101856i	0.409190	+	0.912449i	$0.365811\pi$
$18$		0			0
$19$	−12.0337	+	20.8430i	−0.633353	+	1.09700i	0.353508	+	0.935431i	$0.384989\pi$
$19$	−12.0337	+	20.8430i	−0.633353	+	1.09700i	−0.986861	+	0.161569i	$0.948345\pi$
$20$	48.5972	+	28.0576i	2.42986	+	1.40288i
$21$		0			0
$22$	−6.20870	−	10.7538i	−0.282214	−	0.488808i
$23$			34.0258i			1.47938i	0.672947	+	0.739691i	$0.265028\pi$
$23$			34.0258i			1.47938i	−0.672947	+	0.739691i	$0.734972\pi$
$24$		0			0
$25$	−9.01621			−0.360648
$26$	1.01087	+	0.583626i	0.0388796	+	0.0224472i
$27$		0			0
$28$	−36.0289	−	56.9025i	−1.28675	−	2.03223i
$29$	−31.6161	−	18.2536i	−1.09021	−	0.629434i	−0.156579	−	0.987665i	$-0.550047\pi$
$29$	−31.6161	−	18.2536i	−1.09021	−	0.629434i	−0.933633	+	0.358231i	$0.883380\pi$
$30$		0			0
$31$	−12.0916	+	20.9433i	−0.390052	+	0.675591i	−0.992456	−	0.122601i	$-0.960876\pi$
$31$	−12.0916	+	20.9433i	−0.390052	+	0.675591i	0.602404	+	0.798192i	$0.294210\pi$
$32$	−49.8615	−	28.7875i	−1.55817	−	0.899610i
$33$		0			0
$34$	−6.39064	+	11.0689i	−0.187960	+	0.325556i
$35$	36.1609	+	18.9521i	1.03317	+	0.541489i
$36$		0			0
$37$	4.23403	−	7.33356i	0.114433	−	0.198204i	−0.803120	−	0.595818i	$-0.796828\pi$
$37$	4.23403	−	7.33356i	0.114433	−	0.198204i	0.917553	+	0.397613i	$0.130161\pi$
$38$			88.8260i			2.33753i
$39$		0			0
$40$	121.003			3.02508
$41$	39.9308	−	23.0541i	0.973922	−	0.562294i	0.0734924	−	0.997296i	$-0.476586\pi$
$41$	39.9308	−	23.0541i	0.973922	−	0.562294i	0.900430	+	0.435002i	$0.143252\pi$
$42$		0			0
$43$	−26.4994	+	45.8984i	−0.616266	+	1.06740i	0.373895	+	0.927471i	$0.378022\pi$
$43$	−26.4994	+	45.8984i	−0.616266	+	1.06740i	−0.990161	+	0.139933i	$0.955311\pi$
$44$	−28.0342	−	16.1855i	−0.637141	−	0.367853i
$45$		0			0
$46$	62.7897	+	108.755i	1.36499	+	2.36424i
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	−0.304891	−	0.952387i	$-0.598620\pi$
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	0.672346	+	0.740237i	$0.265287\pi$
$48$		0			0
$49$	−27.8817	−	40.2941i	−0.569014	−	0.822328i
$50$	−28.8181	+	16.6381i	−0.576362	+	0.332763i
$51$		0			0
$52$	3.04293			0.0585179
$53$	29.2909	−	16.9111i	0.552659	−	0.319078i	−0.197535	−	0.980296i	$-0.563294\pi$
$53$	29.2909	−	16.9111i	0.552659	−	0.319078i	0.750194	+	0.661218i	$0.229960\pi$
$54$		0			0
$55$	19.6229			0.356780
$56$	−128.632	−	67.4169i	−2.29701	−	1.20387i
$57$		0			0
$58$	−134.738			−2.32306
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	0.208040	−	0.978120i	$-0.433292\pi$
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	−0.743057	+	0.669228i	$0.766625\pi$
$60$		0			0
$61$	−6.02138	−	10.4293i	−0.0987111	−	0.170973i	0.812440	−	0.583044i	$-0.198139\pi$
$61$	−6.02138	−	10.4293i	−0.0987111	−	0.170973i	−0.911151	+	0.412072i	$0.864805\pi$
$62$			89.2535i			1.43957i
$63$		0			0
$64$	−60.1511			−0.939861
$65$	−1.59745	+	0.922289i	−0.0245762	+	0.0141891i
$66$		0			0
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	−0.705773	−	0.708438i	$-0.749400\pi$
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	0.966412	+	0.256998i	$0.0827334\pi$
$68$			33.3197i			0.489996i
$69$		0			0
$70$	150.553	−	6.15405i	2.15076	−	0.0879151i
$71$		−	85.7413i		−	1.20762i	−0.797127	−	0.603812i	$-0.793648\pi$
$71$		−	85.7413i		−	1.20762i	0.797127	−	0.603812i	$-0.206352\pi$
$72$		0			0
$73$	−35.3783	−	61.2770i	−0.484634	−	0.839411i	0.515210	−	0.857064i	$-0.327714\pi$
$73$	−35.3783	−	61.2770i	−0.484634	−	0.839411i	−0.999844	+	0.0176532i	$0.994381\pi$
$74$		−	31.2532i		−	0.422341i
$75$		0			0
$76$	115.781	+	200.539i	1.52343	+	2.63866i
$77$	−20.8601	−	10.9329i	−0.270910	−	0.141985i
$78$		0			0
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	0.985029	+	0.172392i	$0.0551494\pi$
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	−0.343219	+	0.939255i	$0.611517\pi$
$80$	192.368	−	111.064i	2.40460	−	1.38830i
$81$		0			0
$82$	85.0860	−	147.373i	1.03763	−	1.79723i
$83$	−26.0171	−	15.0210i	−0.313459	−	0.180976i	0.335014	−	0.942213i	$-0.391259\pi$
$83$	−26.0171	−	15.0210i	−0.313459	−	0.180976i	−0.648473	+	0.761237i	$0.724592\pi$
$84$		0			0
$85$	−10.0990	−	17.4919i	−0.118811	−	0.205787i
$86$			195.604i			2.27446i
$87$		0			0
$88$	−69.8030			−0.793215
$89$	46.5438	+	26.8721i	0.522964	+	0.301933i	0.738146	−	0.674641i	$-0.235701\pi$
$89$	46.5438	+	26.8721i	0.522964	+	0.301933i	−0.215183	+	0.976574i	$0.569035\pi$
$90$		0			0
$91$	2.21202	−	0.0904195i	0.0243079	−	0.000993620i
$92$	283.515	+	163.688i	3.08169	+	1.77921i
$93$		0			0
$94$	36.8003	−	63.7400i	0.391492	−	0.678085i
$95$	−121.563	−	70.1847i	−1.27962	−	0.738786i
$96$		0			0
$97$	−3.60974	+	6.25225i	−0.0372138	+	0.0644561i	−0.884032	−	0.467426i	$-0.845182\pi$
$97$	−3.60974	+	6.25225i	−0.0372138	+	0.0644561i	0.846819	+	0.531882i	$0.178515\pi$
$98$	−163.474	−	77.3384i	−1.66810	−	0.789167i
$99$		0			0
$100$	−43.3742	+	75.1263i	−0.433742	+	0.751263i
$101$			60.4957i			0.598967i	0.954101	+	0.299484i	$0.0968144\pi$
$101$			60.4957i			0.598967i	−0.954101	+	0.299484i	$0.903186\pi$
$102$		0			0
$103$	−163.244			−1.58489			−0.792447	−	0.609941i	$-0.791193\pi$
$103$	−163.244			−1.58489			−0.792447	+	0.609941i	$0.791193\pi$
$104$	5.68249	−	3.28079i	0.0546393	−	0.0315460i
$105$		0			0
$106$	62.4142	−	108.105i	0.588813	−	1.01985i
$107$	−97.8099	−	56.4706i	−0.914111	−	0.527762i	−0.0323597	−	0.999476i	$-0.510302\pi$
$107$	−97.8099	−	56.4706i	−0.914111	−	0.527762i	−0.881752	+	0.471714i	$0.843636\pi$
$108$		0			0
$109$	−62.6322	−	108.482i	−0.574607	−	0.995248i	−0.996084	−	0.0884094i	$-0.971822\pi$
$109$	−62.6322	−	108.482i	−0.574607	−	0.995248i	0.421477	−	0.906839i	$-0.361512\pi$
$110$	62.7197	−	36.2112i	0.570179	−	0.329193i
$111$		0			0
$112$	−266.376	+	10.8885i	−2.37836	+	0.0972186i
$113$	29.6935	−	17.1435i	0.262774	−	0.151713i	−0.362825	−	0.931857i	$-0.618188\pi$
$113$	29.6935	−	17.1435i	0.262774	−	0.151713i	0.625599	+	0.780144i	$0.284854\pi$
$114$		0			0
$115$	−198.450			−1.72565
$116$	−304.191	+	175.625i	−2.62234	+	1.51401i
$117$		0			0
$118$	−134.524			−1.14003
$119$	0.990082	+	24.2214i	0.00832002	+	0.203541i
$120$		0			0
$121$	109.680			0.906448
$122$	−38.4917	−	22.2232i	−0.315506	−	0.182157i
$123$		0			0
$124$	116.338	+	201.504i	0.938211	+	1.62503i
$125$			93.2229i			0.745784i
$126$		0			0
$127$	216.982			1.70852			0.854259	−	0.519847i	$-0.174011\pi$
$127$	216.982			1.70852			0.854259	+	0.519847i	$0.174011\pi$
$128$	7.18756	−	4.14974i	0.0561528	−	0.0324199i
$129$		0			0
$130$	−3.40391	+	5.89574i	−0.0261839	+	0.0453519i
$131$		−	124.360i		−	0.949310i	−0.880172	−	0.474655i	$-0.842573\pi$
$131$		−	124.360i		−	0.949310i	0.880172	−	0.474655i	$-0.157427\pi$
$132$		0			0
$133$	90.1246	+	142.339i	0.677629	+	1.07022i
$134$		−	128.901i		−	0.961944i
$135$		0			0
$136$	35.9242	+	62.2226i	0.264149	+	0.457519i
$137$			6.67088i			0.0486925i	0.999704	+	0.0243463i	$0.00775042\pi$
$137$			6.67088i			0.0486925i	−0.999704	+	0.0243463i	$0.992250\pi$
$138$		0			0
$139$	−8.80202	−	15.2455i	−0.0633239	−	0.109680i	0.832625	−	0.553837i	$-0.186837\pi$
$139$	−8.80202	−	15.2455i	−0.0633239	−	0.109680i	−0.895949	+	0.444156i	$0.853503\pi$
$140$	331.875	−	210.133i	2.37054	−	1.50095i
$141$		0			0
$142$	−158.223	−	274.051i	−1.11425	−	1.92994i
$143$	0.921520	−	0.532040i	0.00644419	−	0.00372056i
$144$		0			0
$145$	106.461	−	184.396i	0.734215	−	1.27170i
$146$	−226.156	−	130.571i	−1.54901	−	0.894323i
$147$		0			0
$148$	−40.7373	−	70.5590i	−0.275252	−	0.476750i
$149$		−	29.6949i		−	0.199294i	−0.995023	−	0.0996472i	$-0.968229\pi$
$149$		−	29.6949i		−	0.199294i	0.995023	−	0.0996472i	$-0.0317714\pi$
$150$		0			0
$151$	−69.9591			−0.463306			−0.231653	−	0.972799i	$-0.574413\pi$
$151$	−69.9591			−0.463306			−0.231653	+	0.972799i	$0.574413\pi$
$152$	432.428	+	249.663i	2.84492	+	1.64252i
$153$		0			0
$154$	−86.8492	+	3.55008i	−0.563956	+	0.0230525i
$155$	−122.149	−	70.5225i	−0.788055	−	0.454984i
$156$		0			0
$157$	98.3195	−	170.294i	0.626239	−	1.08468i	−0.362061	−	0.932155i	$-0.617927\pi$
$157$	98.3195	−	170.294i	0.626239	−	1.08468i	0.988300	−	0.152523i	$-0.0487400\pi$
$158$	324.119	+	187.130i	2.05139	+	1.18437i
$159$		0			0
$160$	167.899	−	290.809i	1.04937	−	1.81756i
$161$	210.962	+	110.566i	1.31032	+	0.686747i
$162$		0			0
$163$	−4.64174	+	8.03973i	−0.0284769	+	0.0493235i	−0.879913	−	0.475135i	$-0.842399\pi$
$163$	−4.64174	+	8.03973i	−0.0284769	+	0.0493235i	0.851436	+	0.524459i	$0.175732\pi$
$164$		−	443.624i		−	2.70502i
$165$		0			0
$166$	−110.876			−0.667931
$167$	91.5268	−	52.8430i	0.548065	−	0.316425i	−0.200276	−	0.979739i	$-0.564184\pi$
$167$	91.5268	−	52.8430i	0.548065	−	0.316425i	0.748341	+	0.663314i	$0.230851\pi$
$168$		0			0
$169$	84.4500	−	146.272i	0.499704	−	0.865513i
$170$	−64.5577	−	37.2724i	−0.379751	−	0.219249i
$171$		0			0
$172$	254.961	+	441.606i	1.48233	+	2.56748i
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.897412	−	0.441194i	$-0.854555\pi$
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.0666210	+	0.997778i	$0.521222\pi$
$174$		0			0
$175$	−29.2980	+	55.9011i	−0.167417	+	0.319435i
$176$	−110.971	+	64.0692i	−0.630518	+	0.364030i
$177$		0			0
$178$	198.354			1.11435
$179$	−46.3963	+	26.7869i	−0.259197	+	0.149648i	−0.623968	−	0.781450i	$-0.714481\pi$
$179$	−46.3963	+	26.7869i	−0.259197	+	0.149648i	0.364771	+	0.931097i	$0.381147\pi$
$180$		0			0
$181$	−113.509			−0.627124			−0.313562	−	0.949568i	$-0.601522\pi$
$181$	−113.509			−0.627124			−0.313562	+	0.949568i	$0.601522\pi$
$182$	6.90333	−	4.37098i	0.0379304	−	0.0240164i
$183$		0			0
$184$	705.930			3.83658
$185$	42.7718	+	24.6943i	0.231199	+	0.133483i
$186$		0			0
$187$	5.82577	+	10.0905i	0.0311539	+	0.0539601i
$188$		−	191.870i		−	1.02059i
$189$		0			0
$190$	−518.064			−2.72665
$191$	149.464	−	86.2931i	0.782535	−	0.451797i	−0.0547932	−	0.998498i	$-0.517450\pi$
$191$	149.464	−	86.2931i	0.782535	−	0.451797i	0.837328	+	0.546701i	$0.184117\pi$
$192$		0			0
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	−0.999968	−	0.00798645i	$-0.997458\pi$
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	0.506901	+	0.862005i	$0.330791\pi$
$194$			26.6450i			0.137345i
$195$		0			0
$196$	−469.875	+	38.4779i	−2.39732	+	0.196316i
$197$		−	98.0156i		−	0.497541i	−0.968562	−	0.248770i	$-0.919974\pi$
$197$		−	98.0156i		−	0.497541i	0.968562	−	0.248770i	$-0.0800265\pi$
$198$		0			0
$199$	128.149	+	221.961i	0.643965	+	1.11538i	0.984540	+	0.175162i	$0.0560451\pi$
$199$	128.149	+	221.961i	0.643965	+	1.11538i	−0.340575	+	0.940217i	$0.610622\pi$
$200$			187.059i			0.935293i
$201$		0			0
$202$	111.636	+	193.360i	0.552655	+	0.957226i
$203$	−215.910	+	136.707i	−1.06359	+	0.673436i
$204$		0			0
$205$	134.459	+	232.890i	0.655898	+	1.13605i
$206$	−521.769	+	301.244i	−2.53286	+	1.46235i
$207$		0			0
$208$	6.02260	−	10.4314i	0.0289548	−	0.0501512i
$209$	70.1262	+	40.4874i	0.335532	+	0.193719i
$210$		0			0
$211$	−130.914	−	226.750i	−0.620447	−	1.07465i	−0.989402	−	0.145199i	$-0.953618\pi$
$211$	−130.914	−	226.750i	−0.620447	−	1.07465i	0.368955	−	0.929447i	$-0.379716\pi$
$212$		−	325.417i		−	1.53499i
$213$		0			0
$214$	−416.834			−1.94782
$215$	−267.695	−	154.554i	−1.24509	−	0.718854i
$216$		0			0
$217$	90.5584	+	143.024i	0.417320	+	0.659096i
$218$	−400.377	−	231.157i	−1.83659	−	1.06036i
$219$		0			0
$220$	94.3997	−	163.505i	0.429089	−	0.743205i
$221$	−0.948524	−	0.547631i	−0.00429196	−	0.00247797i
$222$		0			0
$223$	179.709	−	311.266i	0.805872	−	1.39581i	−0.109829	−	0.993950i	$-0.535030\pi$
$223$	179.709	−	311.266i	0.805872	−	1.39581i	0.915701	−	0.401860i	$-0.131636\pi$
$224$	−340.509	+	215.600i	−1.52013	+	0.962499i
$225$		0			0
$226$	63.2719	−	109.590i	0.279964	−	0.484912i
$227$			407.746i			1.79624i	0.439754	+	0.898118i	$0.355066\pi$
$227$			407.746i			1.79624i	−0.439754	+	0.898118i	$0.644934\pi$
$228$		0			0
$229$	77.5928			0.338833			0.169417	−	0.985545i	$-0.445812\pi$
$229$	77.5928			0.338833			0.169417	+	0.985545i	$0.445812\pi$
$230$	−634.296	+	366.211i	−2.75781	+	1.59222i
$231$		0			0
$232$	−378.706	+	655.938i	−1.63235	+	2.82732i
$233$	393.484	+	227.178i	1.68877	+	0.975013i	0.955460	+	0.295121i	$0.0953599\pi$
$233$	393.484	+	227.178i	1.68877	+	0.975013i	0.733312	+	0.679892i	$0.237973\pi$
$234$		0			0
$235$	58.1545	+	100.727i	0.247466	+	0.428624i
$236$	−303.709	+	175.346i	−1.28690	+	0.742993i
$237$		0			0
$238$	47.8617	+	75.5907i	0.201100	+	0.317608i
$239$	44.0684	−	25.4429i	0.184387	−	0.106456i	−0.404965	−	0.914332i	$-0.632716\pi$
$239$	44.0684	−	25.4429i	0.184387	−	0.106456i	0.589352	+	0.807876i	$0.299383\pi$
$240$		0			0
$241$	−191.564			−0.794873			−0.397436	−	0.917630i	$-0.630100\pi$
$241$	−191.564			−0.794873			−0.397436	+	0.917630i	$0.630100\pi$
$242$	350.566	−	202.399i	1.44862	−	0.836360i
$243$		0			0
$244$	−115.868			−0.474869
$245$	235.009	−	162.615i	0.959220	−	0.663736i
$246$		0			0
$247$	−7.61174			−0.0308167
$248$	434.509	+	250.864i	1.75205	+	1.01155i
$249$		0			0
$250$	172.030	+	297.964i	0.688119	+	1.19186i
$251$			262.216i			1.04469i	0.852735	+	0.522343i	$0.174942\pi$
$251$			262.216i			1.04469i	−0.852735	+	0.522343i	$0.825058\pi$
$252$		0			0
$253$	114.480			0.452488
$254$	693.529	−	400.409i	2.73043	−	1.57641i
$255$		0			0
$256$	135.618	−	234.897i	0.529757	−	0.917566i
$257$			141.472i			0.550474i	0.961376	+	0.275237i	$0.0887563\pi$
$257$			141.472i			0.550474i	−0.961376	+	0.275237i	$0.911244\pi$
$258$		0			0
$259$	−31.7101	−	50.0816i	−0.122433	−	0.193365i
$260$			17.7474i			0.0682592i
$261$		0			0
$262$	−229.488	−	397.485i	−0.875908	−	1.51712i
$263$			441.499i			1.67870i	0.543588	+	0.839352i	$0.317065\pi$
$263$			441.499i			1.67870i	−0.543588	+	0.839352i	$0.682935\pi$
$264$		0			0
$265$	98.6315	+	170.835i	0.372194	+	0.644659i
$266$	550.727	+	288.639i	2.07040	+	1.08511i
$267$		0			0
$268$	−168.016	−	291.013i	−0.626927	−	1.08587i
$269$	88.6239	−	51.1670i	0.329457	−	0.190212i	−0.326143	−	0.945320i	$-0.605749\pi$
$269$	88.6239	−	51.1670i	0.329457	−	0.190212i	0.655600	+	0.755108i	$0.272416\pi$
$270$		0			0
$271$	−160.403	+	277.826i	−0.591893	+	1.02519i	0.402084	+	0.915603i	$0.368286\pi$
$271$	−160.403	+	277.826i	−0.591893	+	1.02519i	−0.993977	+	0.109586i	$0.965047\pi$
$272$	114.223	+	65.9467i	0.419938	+	0.242451i
$273$		0			0
$274$	12.3102	+	21.3218i	0.0449276	+	0.0778168i
$275$			30.3350i			0.110309i
$276$		0			0
$277$	204.414			0.737958			0.368979	−	0.929438i	$-0.379707\pi$
$277$	204.414			0.737958			0.368979	+	0.929438i	$0.379707\pi$
$278$	−56.2670	−	32.4857i	−0.202399	−	0.116855i
$279$		0			0
$280$	393.198	−	750.228i	1.40428	−	2.67939i
$281$	10.0933	+	5.82736i	0.0359191	+	0.0207379i	0.517852	−	0.855470i	$-0.326732\pi$
$281$	10.0933	+	5.82736i	0.0359191	+	0.0207379i	−0.481933	+	0.876208i	$0.660065\pi$
$282$		0			0
$283$	−173.123	+	299.857i	−0.611740	+	1.05957i	0.379207	+	0.925312i	$0.376197\pi$
$283$	−173.123	+	299.857i	−0.611740	+	1.05957i	−0.990947	+	0.134254i	$0.957136\pi$
$284$	−714.428	−	412.475i	−2.51559	−	1.45238i
$285$		0			0
$286$	1.96361	−	3.40107i	0.00686576	−	0.0118918i
$287$	−13.1821	−	322.488i	−0.0459307	−	1.12365i
$288$		0			0
$289$	−138.504	+	239.895i	−0.479251	+	0.830087i
$290$		−	785.836i		−	2.70978i
$291$		0			0
$292$	−680.776			−2.33142
$293$	81.5708	−	47.0949i	0.278399	−	0.160734i	−0.354300	−	0.935132i	$-0.615281\pi$
$293$	81.5708	−	47.0949i	0.278399	−	0.160734i	0.632698	+	0.774398i	$0.281947\pi$
$294$		0			0
$295$	106.292	−	184.104i	0.360313	−	0.624081i
$296$	−152.149	−	87.8432i	−0.514016	−	0.296768i
$297$		0			0
$298$	−54.7976	−	94.9123i	−0.183885	−	0.318498i
$299$	−9.31950	+	5.38062i	−0.0311689	+	0.0179954i
$300$		0			0
$301$	198.463	+	313.444i	0.659347	+	1.04134i
$302$	−223.607	+	129.100i	−0.740421	+	0.427482i
$303$		0			0
$304$	916.620			3.01520
$305$	60.8274	−	35.1187i	0.199434	−	0.115143i
$306$		0			0
$307$	−503.730			−1.64081			−0.820407	−	0.571781i	$-0.806253\pi$
$307$	−503.730			−1.64081			−0.820407	+	0.571781i	$0.806253\pi$
$308$	−191.448	+	121.219i	−0.621585	+	0.393569i
$309$		0			0
$310$	−520.557			−1.67922
$311$	238.993	+	137.983i	0.768467	+	0.443675i	0.832328	−	0.554284i	$-0.187008\pi$
$311$	238.993	+	137.983i	0.768467	+	0.443675i	−0.0638603	+	0.997959i	$0.520341\pi$
$312$		0			0
$313$	−190.541	−	330.028i	−0.608759	−	1.05440i	−0.991445	−	0.130523i	$-0.958334\pi$
$313$	−190.541	−	330.028i	−0.608759	−	1.05440i	0.382687	−	0.923878i	$-0.374999\pi$
$314$		−	725.739i		−	2.31127i
$315$		0			0
$316$	975.665			3.08755
$317$	−527.735	+	304.688i	−1.66478	+	0.961160i	−0.694394	+	0.719595i	$0.744328\pi$
$317$	−527.735	+	304.688i	−1.66478	+	0.961160i	−0.970384	+	0.241566i	$0.922339\pi$
$318$		0			0
$319$	−61.4141	+	106.372i	−0.192521	+	0.333456i
$320$		−	350.822i		−	1.09632i
$321$		0			0
$322$	878.323	−	35.9026i	2.72771	−	0.111499i
$323$		−	83.3476i		−	0.258042i
$324$		0			0
$325$	−1.42577	−	2.46950i	−0.00438697	−	0.00759846i
$326$			34.2627i			0.105100i
$327$		0			0
$328$	−478.301	−	828.442i	−1.45824	−	2.52574i
$329$	−5.70136	−	139.478i	−0.0173294	−	0.423946i
$330$		0			0
$331$	255.442	+	442.438i	0.771727	+	1.33667i	0.936616	+	0.350358i	$0.113940\pi$
$331$	255.442	+	442.438i	0.771727	+	1.33667i	−0.164889	+	0.986312i	$0.552727\pi$
$332$	−250.321	+	144.523i	−0.753979	+	0.435310i
$333$		0			0
$334$	195.029	−	337.799i	0.583918	−	1.01138i
$335$	176.408	+	101.849i	0.526590	+	0.304027i
$336$		0			0
$337$	−72.9765	−	126.399i	−0.216547	−	0.375071i	0.737203	−	0.675672i	$-0.236146\pi$
$337$	−72.9765	−	126.399i	−0.216547	−	0.375071i	−0.953750	+	0.300600i	$0.902813\pi$
$338$		−	623.362i		−	1.84427i
$339$		0			0
$340$	−194.332			−0.571564
$341$	70.4637	+	40.6822i	0.206638	+	0.119303i
$342$		0			0
$343$	−340.427	+	41.9332i	−0.992499	+	0.122254i
$344$	952.250	+	549.782i	2.76817	+	1.59820i
$345$		0			0
$346$	−355.376	+	615.529i	−1.02710	+	1.77899i
$347$	−238.896	−	137.927i	−0.688461	−	0.397483i	0.114574	−	0.993415i	$-0.463450\pi$
$347$	−238.896	−	137.927i	−0.688461	−	0.397483i	−0.803035	+	0.595931i	$0.796783\pi$
$348$		0			0
$349$	119.986	−	207.822i	0.343800	−	0.595480i	−0.641335	−	0.767261i	$-0.721619\pi$
$349$	119.986	−	207.822i	0.343800	−	0.595480i	0.985135	+	0.171782i	$0.0549523\pi$
$350$	9.51354	+	232.739i	0.0271815	+	0.664970i
$351$		0			0
$352$	−96.8555	+	167.759i	−0.275158	+	0.476587i
$353$		−	541.837i		−	1.53495i	−0.641080	−	0.767474i	$-0.721513\pi$
$353$		−	541.837i		−	1.53495i	0.641080	−	0.767474i	$-0.278487\pi$
$354$		0			0
$355$	500.073			1.40866
$356$	447.815	−	258.546i	1.25791	−	0.726254i
$357$		0			0
$358$	−98.8629	+	171.236i	−0.276153	+	0.478312i
$359$	383.110	+	221.189i	1.06716	+	0.616124i	0.927404	−	0.374062i	$-0.122035\pi$
$359$	383.110	+	221.189i	1.06716	+	0.616124i	0.139754	+	0.990186i	$0.455369\pi$
$360$		0			0
$361$	−109.120	−	189.002i	−0.302273	−	0.523551i
$362$	−362.805	+	209.466i	−1.00222	+	0.578634i
$363$		0			0
$364$	9.88796	−	18.8664i	0.0271647	−	0.0518307i
$365$	357.388	−	206.338i	0.979146	−	0.565310i
$366$		0			0
$367$	−306.189			−0.834303			−0.417151	−	0.908837i	$-0.636971\pi$
$367$	−306.189			−0.834303			−0.417151	+	0.908837i	$0.636971\pi$
$368$	1122.27	−	647.944i	3.04965	−	1.76072i
$369$		0			0
$370$	182.279			0.492647
$371$	−9.66964	−	236.558i	−0.0260637	−	0.637623i
$372$		0			0
$373$	218.629			0.586138			0.293069	−	0.956091i	$-0.405323\pi$
$373$	218.629			0.586138			0.293069	+	0.956091i	$0.405323\pi$
$374$	37.2413	+	21.5013i	0.0995756	+	0.0574900i
$375$		0			0
$376$	−206.869	−	358.307i	−0.550182	−	0.952944i
$377$		−	11.5460i		−	0.0306261i
$378$		0			0
$379$	254.498			0.671500			0.335750	−	0.941951i	$-0.391010\pi$
$379$	254.498			0.671500			0.335750	+	0.941951i	$0.391010\pi$
$380$	−1169.61	+	675.274i	−3.07792	+	1.77704i
$381$		0			0
$382$	318.483	−	551.630i	0.833726	−	1.44406i
$383$		−	567.515i		−	1.48176i	−0.671637	−	0.740881i	$-0.734408\pi$
$383$		−	567.515i		−	1.48176i	0.671637	−	0.740881i	$-0.265592\pi$
$384$		0			0
$385$	63.7643	−	121.663i	0.165622	−	0.316008i
$386$			702.432i			1.81977i
$387$		0			0
$388$	34.7307	+	60.1553i	0.0895120	+	0.155039i
$389$		−	290.720i		−	0.747352i	−0.927559	−	0.373676i	$-0.878097\pi$
$389$		−	290.720i		−	0.747352i	0.927559	−	0.373676i	$-0.121903\pi$
$390$		0			0
$391$	−58.9171	−	102.047i	−0.150683	−	0.260991i
$392$	−835.978	+	578.459i	−2.13260	+	1.47566i
$393$		0			0
$394$	−180.874	−	313.283i	−0.459071	−	0.795134i
$395$	−512.197	+	295.717i	−1.29670	+	0.748651i
$396$		0			0
$397$	229.543	−	397.580i	0.578194	−	1.00146i	−0.417493	−	0.908680i	$-0.637091\pi$
$397$	229.543	−	397.580i	0.578194	−	1.00146i	0.995687	−	0.0927809i	$-0.0295756\pi$
$398$	819.194	+	472.962i	2.05828	+	1.18835i
$399$		0			0
$400$	171.693	+	297.382i	0.429234	+	0.743454i
$401$			459.987i			1.14710i	0.819170	+	0.573550i	$0.194434\pi$
$401$			459.987i			1.14710i	−0.819170	+	0.573550i	$0.805566\pi$
$402$		0			0
$403$	−7.64837			−0.0189786
$404$	504.072	+	291.026i	1.24770	+	0.720362i
$405$		0			0
$406$	−437.828	+	835.382i	−1.07839	+	2.05759i
$407$	−24.6737	−	14.2454i	−0.0606234	−	0.0350009i
$408$		0			0
$409$	291.920	−	505.621i	0.713741	−	1.23624i	−0.249702	−	0.968323i	$-0.580333\pi$
$409$	291.920	−	505.621i	0.713741	−	1.23624i	0.963443	−	0.267913i	$-0.0863340\pi$
$410$	859.531	+	496.251i	2.09642	+	1.21037i
$411$		0			0
$412$	−785.317	+	1360.21i	−1.90611	+	3.30148i
$413$	−215.567	+	136.491i	−0.521955	+	0.330486i
$414$		0			0
$415$	87.6076	−	151.741i	0.211103	−	0.365641i
$416$		−	18.2091i		−	0.0437719i
$417$		0			0
$418$	298.855			0.714963
$419$	−125.878	+	72.6756i	−0.300424	+	0.173450i	−0.642634	−	0.766174i	$-0.722158\pi$
$419$	−125.878	+	72.6756i	−0.300424	+	0.173450i	0.342209	+	0.939624i	$0.388825\pi$
$420$		0			0
$421$	23.2429	−	40.2578i	0.0552087	−	0.0956243i	−0.837100	−	0.547050i	$-0.815751\pi$
$421$	23.2429	−	40.2578i	0.0552087	−	0.0956243i	0.892309	+	0.451425i	$0.149084\pi$
$422$	−836.871	−	483.168i	−1.98311	−	1.14495i
$423$		0			0
$424$	−350.854	−	607.697i	−0.827486	−	1.43325i
$425$	27.0407	−	15.6120i	0.0636252	−	0.0367340i
$426$		0			0
$427$	−84.2290	+	3.44297i	−0.197258	+	0.00806317i
$428$	−941.067	+	543.325i	−2.19875	+	1.26945i
$429$		0			0
$430$	−1140.83			−2.65309
$431$	−217.312	+	125.465i	−0.504204	+	0.291103i	−0.730448	−	0.682968i	$-0.760689\pi$
$431$	−217.312	+	125.465i	−0.504204	+	0.291103i	0.226244	+	0.974071i	$0.427355\pi$
$432$		0			0
$433$	158.357			0.365720			0.182860	−	0.983139i	$-0.441464\pi$
$433$	158.357			0.365720			0.182860	+	0.983139i	$0.441464\pi$
$434$	553.378	+	290.028i	1.27506	+	0.668267i
$435$		0			0
$436$	−1205.22			−2.76426
$437$	−709.199	−	409.456i	−1.62288	−	0.936971i
$438$		0			0
$439$	−167.384	−	289.917i	−0.381284	−	0.660403i	0.609962	−	0.792431i	$-0.291185\pi$
$439$	−167.384	−	289.917i	−0.381284	−	0.660403i	−0.991246	+	0.132027i	$0.957851\pi$
$440$		−	407.115i		−	0.925261i
$441$		0			0
$442$	−4.04230			−0.00914547
$443$	−18.5652	+	10.7187i	−0.0419080	+	0.0241956i	−0.520808	−	0.853674i	$-0.674369\pi$
$443$	−18.5652	+	10.7187i	−0.0419080	+	0.0241956i	0.478900	+	0.877870i	$0.341036\pi$
$444$		0			0
$445$	−156.727	+	271.459i	−0.352196	+	0.610021i
$446$		−	1326.51i		−	2.97424i
$447$		0			0
$448$	−195.460	+	372.941i	−0.436295	+	0.832458i
$449$		−	113.632i		−	0.253078i	−0.991962	−	0.126539i	$-0.959613\pi$
$449$		−	113.632i		−	0.253078i	0.991962	−	0.126539i	$-0.0403868\pi$
$450$		0			0
$451$	−77.5653	−	134.347i	−0.171985	−	0.297887i
$452$		−	329.889i		−	0.729843i
$453$		0			0
$454$	752.437	+	1303.26i	1.65735	+	2.87061i
$455$	0.527357	+	12.9013i	0.00115903	+	0.0283545i
$456$		0			0
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	0.798562	−	0.601913i	$-0.205595\pi$
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	−0.920553	+	0.390618i	$0.872261\pi$
$458$	248.006	−	143.186i	0.541498	−	0.312634i
$459$		0			0
$460$	−954.681	+	1653.56i	−2.07539	+	3.59469i
$461$	143.867	+	83.0619i	0.312077	+	0.180178i	0.647855	−	0.761763i	$-0.275666\pi$
$461$	143.867	+	83.0619i	0.312077	+	0.180178i	−0.335779	+	0.941941i	$0.608999\pi$
$462$		0			0
$463$	121.635	+	210.678i	0.262711	+	0.455028i	0.966961	−	0.254923i	$-0.0820502\pi$
$463$	121.635	+	210.678i	0.262711	+	0.455028i	−0.704251	+	0.709951i	$0.748717\pi$
$464$			1390.39i			2.99654i
$465$		0			0
$466$	1676.90			3.59850
$467$	−300.050	−	173.234i	−0.642505	−	0.370950i	0.143074	−	0.989712i	$-0.454301\pi$
$467$	−300.050	−	173.234i	−0.642505	−	0.370950i	−0.785579	+	0.618762i	$0.787635\pi$
$468$		0			0
$469$	−130.785	−	206.556i	−0.278859	−	0.440418i
$470$	371.753	+	214.632i	0.790964	+	0.456663i
$471$		0			0
$472$	−378.106	+	654.898i	−0.801071	+	1.38750i
$473$	154.425	+	89.1572i	0.326479	+	0.188493i
$474$		0			0
$475$	108.498	−	187.925i	0.228418	−	0.395631i
$476$	206.584	+	108.272i	0.434001	+	0.227462i
$477$		0			0
$478$	93.9026	−	162.644i	0.196449	−	0.340260i
$479$			557.565i			1.16402i	0.813182	+	0.582009i	$0.197733\pi$
$479$			557.565i			1.16402i	−0.813182	+	0.582009i	$0.802267\pi$
$480$		0			0
$481$	2.67817			0.00556792
$482$	−612.288	+	353.505i	−1.27031	+	0.733412i
$483$		0			0
$484$	527.638	−	913.895i	1.09016	−	1.88821i
$485$	−36.4652	−	21.0532i	−0.0751860	−	0.0434087i
$486$		0			0
$487$	−190.990	−	330.804i	−0.392176	−	0.679269i	0.600560	−	0.799580i	$-0.294944\pi$
$487$	−190.990	−	330.804i	−0.392176	−	0.679269i	−0.992736	+	0.120310i	$0.961611\pi$
$488$	−216.377	+	124.925i	−0.443395	+	0.255994i
$489$		0			0
$490$	451.064	−	953.436i	0.920539	−	1.94579i
$491$	−448.359	+	258.860i	−0.913155	+	0.527210i	−0.881445	−	0.472287i	$-0.843429\pi$
$491$	−448.359	+	258.860i	−0.913155	+	0.527210i	−0.0317099	+	0.999497i	$0.510095\pi$
$492$		0			0
$493$	126.428			0.256445
$494$	−24.3290	+	14.0464i	−0.0492491	+	0.0284340i
$495$		0			0
$496$	921.031			1.85692
$497$	−531.602	−	278.615i	−1.06962	−	0.560594i
$498$		0			0
$499$	−62.2576			−0.124765			−0.0623824	−	0.998052i	$-0.519870\pi$
$499$	−62.2576			−0.124765			−0.0623824	+	0.998052i	$0.519870\pi$
$500$	776.767	+	448.467i	1.55353	+	0.896934i
$501$		0			0
$502$	483.883	+	838.110i	0.963911	+	1.66954i
$503$		−	608.089i		−	1.20892i	−0.796634	−	0.604462i	$-0.793388\pi$
$503$		−	608.089i		−	1.20892i	0.796634	−	0.604462i	$-0.206612\pi$
$504$		0			0
$505$	−352.832			−0.698677
$506$	365.906	−	211.256i	0.723134	−	0.417501i
$507$		0			0
$508$	1043.83	−	1807.97i	2.05479	−	3.55900i
$509$			387.658i			0.761608i	0.924656	+	0.380804i	$0.124353\pi$
$509$			387.658i			0.761608i	−0.924656	+	0.380804i	$0.875647\pi$
$510$		0			0
$511$	−494.883	+	20.2290i	−0.968459	+	0.0395871i
$512$		−	967.855i		−	1.89034i
$513$		0			0
$514$	261.066	+	452.180i	0.507911	+	0.879727i
$515$		−	952.095i		−	1.84873i
$516$		0			0
$517$	−33.5475	−	58.1060i	−0.0648888	−	0.112391i
$518$	−193.772	−	101.557i	−0.374077	−	0.196056i
$519$		0			0
$520$	19.1347	+	33.1422i	0.0367974	+	0.0637351i
$521$	457.542	−	264.162i	0.878200	−	0.507029i	0.00813547	−	0.999967i	$-0.497410\pi$
$521$	457.542	−	264.162i	0.878200	−	0.507029i	0.870064	+	0.492938i	$0.164077\pi$
$522$		0			0
$523$	−179.837	+	311.487i	−0.343856	+	0.595577i	−0.985145	−	0.171723i	$-0.945067\pi$
$523$	−179.837	+	311.487i	−0.343856	+	0.595577i	0.641289	+	0.767300i	$0.278400\pi$
$524$	−1036.21	−	598.256i	−1.97750	−	1.14171i
$525$		0			0
$526$	814.724	+	1411.14i	1.54890	+	2.68278i
$527$		−	83.7487i		−	0.158916i
$528$		0			0
$529$	−628.753			−1.18857
$530$	630.502	+	364.021i	1.18963	+	0.686832i
$531$		0			0
$532$	1619.58	−	66.2026i	3.04433	−	0.124441i
$533$	12.6288	+	7.29124i	0.0236938	+	0.0136796i
$534$		0			0
$535$	329.356	−	570.461i	0.615618	−	1.06628i
$536$	−627.522	−	362.300i	−1.17075	−	0.675932i
$537$		0			0
$538$	188.843	−	327.086i	0.351009	−	0.607966i
$539$	−135.569	+	93.8077i	−0.251520	+	0.174040i
$540$		0			0
$541$	35.5347	−	61.5479i	0.0656834	−	0.113767i	−0.831314	−	0.555804i	$-0.812411\pi$
$541$	35.5347	−	61.5479i	0.0656834	−	0.113767i	0.896997	+	0.442037i	$0.145744\pi$
$542$			1184.00i			2.18451i
$543$		0			0
$544$	199.387			0.366521
$545$	632.705	−	365.292i	1.16093	−	0.670261i
$546$		0			0
$547$	−180.236	+	312.177i	−0.329498	+	0.570708i	−0.982412	−	0.186724i	$-0.940213\pi$
$547$	−180.236	+	312.177i	−0.329498	+	0.570708i	0.652914	+	0.757432i	$0.273546\pi$
$548$	55.5842	+	32.0915i	0.101431	+	0.0585612i
$549$		0			0
$550$	55.9789	+	96.9583i	0.101780	+	0.176288i
$551$	760.919	−	439.317i	1.38098	−	0.797308i
$552$		0			0
$553$	709.249	−	28.9915i	1.28255	−	0.0524259i
$554$	653.361	−	377.218i	1.17935	−	0.680899i
$555$		0			0
$556$	−169.375			−0.304632
$557$	133.574	−	77.1188i	0.239809	−	0.138454i	−0.375280	−	0.926912i	$-0.622453\pi$
$557$	133.574	−	77.1188i	0.239809	−	0.138454i	0.615089	+	0.788458i	$0.289120\pi$
$558$		0			0
$559$	−16.7618			−0.0299853
$560$	−63.5054	−	1553.60i	−0.113402	−	2.77428i
$561$		0			0
$562$	43.0142			0.0765378
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.964637	−	0.263583i	$-0.0849044\pi$
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.254049	+	0.967191i	$0.418238\pi$
$564$		0			0
$565$	99.9870	+	173.183i	0.176968	+	0.306518i
$566$			1277.89i			2.25776i
$567$		0			0
$568$	−1778.87			−3.13181
$569$	−223.053	+	128.780i	−0.392009	+	0.226327i	−0.683030	−	0.730390i	$-0.739338\pi$
$569$	−223.053	+	128.780i	−0.392009	+	0.226327i	0.291021	+	0.956717i	$0.406005\pi$
$570$		0			0
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	0.404654	+	0.914470i	$0.367392\pi$
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	−0.994281	+	0.106794i	$0.965941\pi$
$572$		−	10.2379i		−	0.0178985i
$573$		0			0
$574$	−637.238	−	1006.43i	−1.11017	−	1.75336i
$575$		−	306.783i		−	0.533536i
$576$		0			0
$577$	424.944	+	736.025i	0.736472	+	1.27561i	0.954075	+	0.299569i	$0.0968428\pi$
$577$	424.944	+	736.025i	0.736472	+	1.27561i	−0.217603	+	0.976037i	$0.569824\pi$
$578$			1022.35i			1.76878i
$579$		0			0
$580$	−1024.30	−	1774.15i	−1.76604	−	3.05887i
$581$	−177.674	+	112.497i	−0.305806	+	0.193627i
$582$		0			0
$583$	−56.8974	−	98.5492i	−0.0975942	−	0.169038i
$584$	−1271.31	+	733.991i	−2.17690	+	1.25683i
$585$		0			0
$586$	173.814	−	301.055i	0.296611	−	0.513745i
$587$	−181.073	−	104.543i	−0.308472	−	0.178097i	0.337770	−	0.941229i	$-0.390327\pi$
$587$	−181.073	−	104.543i	−0.308472	−	0.178097i	−0.646243	+	0.763132i	$0.723661\pi$
$588$		0			0
$589$	−291.014	−	504.051i	−0.494082	−	0.855775i
$590$		−	784.590i		−	1.32981i
$591$		0			0
$592$	−322.511			−0.544781
$593$	123.884	+	71.5246i	0.208911	+	0.120615i	0.600805	−	0.799395i	$-0.294847\pi$
$593$	123.884	+	71.5246i	0.208911	+	0.120615i	−0.391894	+	0.920010i	$0.628180\pi$
$594$		0			0
$595$	−141.267	+	5.77450i	−0.237424	+	0.00970504i
$596$	−247.428	−	142.853i	−0.415148	−	0.239686i
$597$		0			0
$598$	−19.8583	+	34.3956i	−0.0332079	+	0.0575178i
$599$	−567.489	−	327.640i	−0.947394	−	0.546978i	−0.0551235	−	0.998480i	$-0.517555\pi$
$599$	−567.489	−	327.640i	−0.947394	−	0.546978i	−0.892270	+	0.451501i	$0.850889\pi$
$600$		0			0
$601$	−403.102	+	698.192i	−0.670718	+	1.16172i	0.306983	+	0.951715i	$0.400681\pi$
$601$	−403.102	+	698.192i	−0.670718	+	1.16172i	−0.977701	+	0.210003i	$0.932653\pi$
$602$	1212.76	+	635.612i	2.01455	+	1.05583i
$603$		0			0
$604$	−336.552	+	582.925i	−0.557205	+	0.965107i
$605$			639.692i			1.05734i
$606$		0			0
$607$	−1186.66			−1.95497			−0.977483	−	0.211016i	$-0.932323\pi$
$607$	−1186.66			−1.95497			−0.977483	+	0.211016i	$0.932323\pi$
$608$	1200.04	−	692.841i	1.97374	−	1.13954i
$609$		0			0
$610$	129.613	−	224.497i	0.212481	−	0.368028i
$611$	5.46205	+	3.15351i	0.00893952	+	0.00516123i
$612$		0			0
$613$	−175.369	−	303.748i	−0.286083	−	0.495510i	0.686788	−	0.726858i	$-0.259020\pi$
$613$	−175.369	−	303.748i	−0.286083	−	0.495510i	−0.972871	+	0.231347i	$0.925687\pi$
$614$	−1610.05	+	929.562i	−2.62223	+	1.51394i
$615$		0			0
$616$	−226.824	+	432.783i	−0.368220	+	0.702570i
$617$	161.583	−	93.2899i	0.261885	−	0.151199i	−0.363309	−	0.931669i	$-0.618353\pi$
$617$	161.583	−	93.2899i	0.261885	−	0.151199i	0.625194	+	0.780469i	$0.285020\pi$
$618$		0			0
$619$	543.077			0.877346			0.438673	−	0.898647i	$-0.355449\pi$
$619$	543.077			0.877346			0.438673	+	0.898647i	$0.355449\pi$
$620$	−1175.24	+	678.524i	−1.89555	+	1.09439i
$621$		0			0
$622$	1018.51			1.63748
$623$	317.852	−	201.254i	0.510196	−	0.323040i
$624$		0			0
$625$	−769.113			−1.23058
$626$	−1218.04	−	703.235i	−1.94575	−	1.12338i
$627$		0			0
$628$	−945.970	−	1638.47i	−1.50632	−	2.60903i
$629$			29.3257i			0.0466227i
$630$		0			0
$631$	−181.605			−0.287805			−0.143902	−	0.989592i	$-0.545965\pi$
$631$	−181.605			−0.287805			−0.143902	+	0.989592i	$0.545965\pi$
$632$	1822.00	−	1051.93i	2.88291	−	1.66445i
$633$		0			0
$634$	−1124.52	+	1947.72i	−1.77369	+	3.07211i
$635$			1265.51i			1.99293i
$636$		0			0
$637$	6.62733	−	14.0085i	0.0104040	−	0.0219914i
$638$			453.324i			0.710539i
$639$		0			0
$640$	24.2027	+	41.9203i	0.0378167	+	0.0655005i
$641$			331.090i			0.516521i	0.966075	+	0.258260i	$0.0831492\pi$
$641$			331.090i			0.516521i	−0.966075	+	0.258260i	$0.916851\pi$
$642$		0			0
$643$	457.251	+	791.983i	0.711122	+	1.23170i	0.964436	+	0.264315i	$0.0851459\pi$
$643$	457.251	+	791.983i	0.711122	+	1.23170i	−0.253314	+	0.967384i	$0.581521\pi$
$644$	1936.15	−	1225.91i	3.00645	−	1.90359i
$645$		0			0
$646$	−153.806	−	266.400i	−0.238090	−	0.412384i
$647$	364.736	−	210.580i	0.563733	−	0.325472i	−0.190909	−	0.981608i	$-0.561144\pi$
$647$	364.736	−	210.580i	0.563733	−	0.325472i	0.754643	+	0.656136i	$0.227810\pi$
$648$		0			0
$649$	−61.3167	+	106.204i	−0.0944788	+	0.163642i
$650$	−9.11422	−	5.26209i	−0.0140219	−	0.00809553i
$651$		0			0
$652$	44.6600	+	77.3533i	0.0684969	+	0.118640i
$653$		−	283.329i		−	0.433888i	−0.976184	−	0.216944i	$-0.930391\pi$
$653$		−	283.329i		−	0.433888i	0.976184	−	0.216944i	$-0.0696089\pi$
$654$		0			0
$655$	725.307			1.10734
$656$	−1520.78	−	878.026i	−2.31827	−	1.33845i
$657$		0			0
$658$	−275.610	−	435.286i	−0.418860	−	0.661529i
$659$	−98.1069	−	56.6421i	−0.148872	−	0.0859515i	0.423713	−	0.905796i	$-0.360726\pi$
$659$	−98.1069	−	56.6421i	−0.148872	−	0.0859515i	−0.572586	+	0.819845i	$0.694060\pi$
$660$		0			0
$661$	534.002	−	924.918i	0.807869	−	1.39927i	−0.106468	−	0.994316i	$-0.533954\pi$
$661$	534.002	−	924.918i	0.807869	−	1.39927i	0.914337	−	0.404954i	$-0.132713\pi$
$662$	1632.91	+	942.762i	2.46664	+	1.42411i
$663$		0			0
$664$	−311.640	+	539.776i	−0.469337	+	0.812915i
$665$	−830.169	+	525.638i	−1.24837	+	0.790432i
$666$		0			0
$667$	621.092	−	1075.76i	0.931173	−	1.61284i
$668$		−	1016.85i		−	1.52222i
$669$		0			0
$670$	751.792			1.12208
$671$	−35.0894	+	20.2589i	−0.0522943	+	0.0301921i
$672$		0			0
$673$	−438.286	+	759.133i	−0.651242	+	1.12798i	0.331580	+	0.943427i	$0.392418\pi$
$673$	−438.286	+	759.133i	−0.651242	+	1.12798i	−0.982822	+	0.184557i	$0.940915\pi$
$674$	−466.503	−	269.335i	−0.692140	−	0.399607i
$675$		0			0
$676$	−812.526	−	1407.34i	−1.20196	−	2.08186i
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.521226	−	0.853419i	$-0.325475\pi$
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.999695	−	0.0246857i	$-0.00785851\pi$
$678$		0			0
$679$	27.0346	+	42.6972i	0.0398153	+	0.0628825i
$680$	−362.903	+	209.522i	−0.533681	+	0.308121i
$681$		0			0
$682$	300.293			0.440312
$683$	604.484	−	348.999i	0.885043	−	0.510980i	0.0127252	−	0.999919i	$-0.495949\pi$
$683$	604.484	−	348.999i	0.885043	−	0.510980i	0.872318	+	0.488939i	$0.162616\pi$
$684$		0			0
$685$	−38.9068			−0.0567983
$686$	−1010.71	+	762.239i	−1.47334	+	1.11114i
$687$		0			0
$688$	2018.49			2.93385
$689$	9.26376	+	5.34844i	0.0134452	+	0.00776261i
$690$		0			0
$691$	506.608	+	877.470i	0.733151	+	1.26986i	0.955530	+	0.294895i	$0.0952846\pi$
$691$	506.608	+	877.470i	0.733151	+	1.26986i	−0.222378	+	0.974960i	$0.571382\pi$
$692$			1852.87i			2.67756i
$693$		0			0
$694$	−1018.10			−1.46700
$695$	88.9172	−	51.3364i	0.127938	−	0.0738653i
$696$		0			0
$697$	−79.8382	+	138.284i	−0.114546	+	0.198399i
$698$		−	885.671i		−	1.26887i
$699$		0			0
$700$	324.844	+	513.045i	0.464063	+	0.732921i
$701$			910.897i			1.29942i	0.760180	+	0.649712i	$0.225111\pi$
$701$			910.897i			1.29942i	−0.760180	+	0.649712i	$0.774889\pi$
$702$		0			0
$703$	101.902	+	176.500i	0.144953	+	0.251067i
$704$			202.378i			0.287469i
$705$		0			0
$706$	−999.883	−	1731.85i	−1.41626	−	2.45304i
$707$	375.077	+	196.580i	0.530520	+	0.278048i
$708$		0			0
$709$	469.175	+	812.635i	0.661742	+	1.14617i	0.980158	+	0.198219i	$0.0635159\pi$
$709$	469.175	+	812.635i	0.661742	+	1.14617i	−0.318416	+	0.947951i	$0.603151\pi$
$710$	1598.36	−	922.813i	2.25121	−	1.29974i
$711$		0			0
$712$	557.513	−	965.640i	0.783024	−	1.35624i
$713$	−712.612	−	411.427i	−0.999456	−	0.577036i
$714$		0			0
$715$	3.10304	+	5.37462i	0.00433991	+	0.00751695i
$716$			515.454i			0.719908i
$717$		0			0
$718$	1632.69			2.27394
$719$	−268.462	−	154.996i	−0.373382	−	0.215572i	0.301553	−	0.953449i	$-0.402495\pi$
$719$	−268.462	−	154.996i	−0.373382	−	0.215572i	−0.674935	+	0.737877i	$0.735828\pi$
$720$		0			0
$721$	−530.459	+	1012.12i	−0.735727	+	1.40378i
$722$	−697.553	−	402.732i	−0.966140	−	0.557801i
$723$		0			0
$724$	−546.059	+	945.802i	−0.754225	+	1.30636i
$725$	285.058	+	164.578i	0.393183	+	0.227004i
$726$		0			0
$727$	712.724	−	1234.47i	0.980363	−	1.69804i	0.319400	−	0.947620i	$-0.396519\pi$
$727$	712.724	−	1234.47i	0.980363	−	1.69804i	0.660963	−	0.750418i	$-0.270148\pi$
$728$	−1.87593	−	45.8927i	−0.00257682	−	0.0630394i
$729$		0			0
$730$	761.536	−	1319.02i	1.04320	−	1.80687i
$731$		−	183.540i		−	0.251080i
$732$		0			0
$733$	−940.447			−1.28301			−0.641506	−	0.767118i	$-0.721690\pi$
$733$	−940.447			−1.28301			−0.641506	+	0.767118i	$0.721690\pi$
$734$	−978.658	+	565.028i	−1.33332	+	0.769793i
$735$		0			0
$736$	979.518	−	1696.57i	1.33087	−	2.30513i
$737$	−101.764	−	58.7535i	−0.138079	−	0.0797199i
$738$		0			0
$739$	488.765	+	846.566i	0.661387	+	1.14556i	0.980251	+	0.197756i	$0.0633654\pi$
$739$	488.765	+	846.566i	0.661387	+	1.14556i	−0.318864	+	0.947801i	$0.603301\pi$
$740$	411.524	−	237.594i	0.556114	−	0.321072i
$741$		0			0
$742$	−467.441	−	738.256i	−0.629975	−	0.994955i
$743$	−626.132	+	361.497i	−0.842707	+	0.486537i	−0.858184	−	0.513343i	$-0.828407\pi$
$743$	−626.132	+	361.497i	−0.842707	+	0.486537i	0.0154762	+	0.999880i	$0.495074\pi$
$744$		0			0
$745$	173.191			0.232471
$746$	698.795	−	403.449i	0.936722	−	0.540817i
$747$		0			0
$748$	112.104			0.149872
$749$	−667.953	+	422.928i	−0.891794	+	0.564657i
$750$		0			0
$751$	−231.592			−0.308379			−0.154189	−	0.988041i	$-0.549277\pi$
$751$	−231.592			−0.308379			−0.154189	+	0.988041i	$0.549277\pi$
$752$	−657.750	−	379.752i	−0.874668	−	0.504990i
$753$		0			0
$754$	−21.3065	−	36.9040i	−0.0282580	−	0.0489443i
$755$		−	408.026i		−	0.540431i
$756$		0			0
$757$	1088.59			1.43804			0.719018	−	0.694992i	$-0.244592\pi$
$757$	1088.59			1.43804			0.719018	+	0.694992i	$0.244592\pi$
$758$	813.442	−	469.641i	1.07314	−	0.619579i
$759$		0			0
$760$	−1456.12	+	2522.07i	−1.91594	+	3.31851i
$761$		−	136.067i		−	0.178801i	−0.995996	−	0.0894004i	$-0.971505\pi$
$761$		−	136.067i		−	0.178801i	0.995996	−	0.0894004i	$-0.0284951\pi$
$762$		0			0
$763$	−876.119	+	35.8125i	−1.14825	+	0.0469365i
$764$		−	1660.52i		−	2.17345i
$765$		0			0
$766$	−1047.27	−	1813.92i	−1.36719	−	2.36804i
$767$		−	11.5277i		−	0.0150296i
$768$		0			0
$769$	−402.392	−	696.964i	−0.523267	−	0.906325i	−0.999633	−	0.0270779i	$-0.991380\pi$
$769$	−402.392	−	696.964i	−0.523267	−	0.906325i	0.476367	−	0.879247i	$-0.341954\pi$
$770$	−20.7053	−	506.534i	−0.0268900	−	0.657837i
$771$		0			0
$772$	915.591	+	1585.85i	1.18600	+	2.05421i
$773$	−299.560	+	172.951i	−0.387529	+	0.223740i	−0.681089	−	0.732201i	$-0.738493\pi$
$773$	−299.560	+	172.951i	−0.387529	+	0.223740i	0.293560	+	0.955941i	$0.405160\pi$
$774$		0			0
$775$	109.021	−	188.829i	0.140672	−	0.243651i
$776$	129.715	+	74.8910i	0.167158	+	0.0965090i
$777$		0			0
$778$	−536.483	−	929.215i	−0.689566	−	1.19436i
$779$			1109.70i			1.42452i
$780$		0			0
$781$	−288.476			−0.369368
$782$	−376.628	−	217.446i	−0.481622	−	0.278064i
$783$		0			0
$784$	−798.076	+	1686.93i	−1.01795	+	2.15170i
$785$	993.215	+	573.433i	1.26524	+	0.730488i
$786$		0			0
$787$	−18.6416	+	32.2883i	−0.0236870	+	0.0410270i	−0.877626	−	0.479346i	$-0.840874\pi$
$787$	−18.6416	+	32.2883i	−0.0236870	+	0.0410270i	0.853939	+	0.520373i	$0.174207\pi$
$788$	−816.701	−	471.523i	−1.03642	−	0.598379i
$789$		0			0
$790$	−1091.41	+	1890.37i	−1.38153	+	2.39288i
$791$	−9.80253	−	239.809i	−0.0123926	−	0.303172i
$792$		0			0
$793$	1.90436	−	3.29846i	0.00240147	−	0.00415947i
$794$		−	1694.36i		−	2.13395i
$795$		0			0
$796$	2465.94			3.09792
$797$	1009.32	−	582.728i	1.26639	−	0.731152i	0.292089	−	0.956391i	$-0.405650\pi$
$797$	1009.32	−	582.728i	1.26639	−	0.731152i	0.974304	+	0.225239i	$0.0723162\pi$
$798$		0			0
$799$	−34.5306	+	59.8087i	−0.0432173	+	0.0748545i
$800$	449.561	+	259.554i	0.561951	+	0.324443i
$801$		0			0
$802$	848.841	+	1470.24i	1.05841	+	1.83321i
$803$	−206.166	+	119.030i	−0.256745	+	0.148232i
$804$		0			0
$805$	−644.860	+	1230.40i	−0.801069	+	1.52845i
$806$	−24.4461	+	14.1140i	−0.0303302	+	0.0175111i
$807$		0			0
$808$	1255.10			1.55334
$809$	−865.722	+	499.825i	−1.07011	+	0.617830i	−0.928212	−	0.372051i	$-0.878655\pi$
$809$	−865.722	+	499.825i	−1.07011	+	0.617830i	−0.141901	+	0.989881i	$0.545321\pi$
$810$		0			0
$811$	634.194			0.781990			0.390995	−	0.920393i	$-0.372131\pi$
$811$	634.194			0.781990			0.390995	+	0.920393i	$0.372131\pi$
$812$	100.421	+	2456.70i	0.123671	+	3.02549i
$813$		0			0
$814$	−105.151			−0.129179
$815$	−46.8905	−	27.0722i	−0.0575343	−	0.0332174i
$816$		0			0
$817$	−637.773	−	1104.66i	−0.780628	−	1.35209i
$818$		−	2154.79i		−	2.63422i
$819$		0			0
$820$	2587.37			3.15532
$821$	−263.766	+	152.285i	−0.321274	+	0.185488i	−0.651960	−	0.758253i	$-0.726053\pi$
$821$	−263.766	+	152.285i	−0.321274	+	0.185488i	0.330686	+	0.943741i	$0.392720\pi$
$822$		0			0
$823$	425.387	−	736.793i	0.516874	−	0.895252i	−0.482934	−	0.875657i	$-0.660429\pi$
$823$	425.387	−	736.793i	0.516874	−	0.895252i	0.999808	−	0.0195954i	$-0.00623780\pi$
$824$			3386.81i			4.11021i
$825$		0			0
$826$	−437.134	+	834.058i	−0.529218	+	1.00976i
$827$			0.427608i			0.000517059i	1.00000		0.000258530i	$8.22925e-5\pi$
$827$			0.427608i			0.000517059i	−1.00000		0.000258530i	$0.999918\pi$
$828$		0			0
$829$	224.677	+	389.151i	0.271021	+	0.469422i	0.969124	−	0.246575i	$-0.0793053\pi$
$829$	224.677	+	389.151i	0.271021	+	0.469422i	−0.698102	+	0.715998i	$0.745972\pi$
$830$		−	646.670i		−	0.779120i
$831$		0			0
$832$	−9.51191	−	16.4751i	−0.0114326	−	0.0198018i
$833$	153.392	+	72.5685i	0.184143	+	0.0871171i
$834$		0			0
$835$	308.199	+	533.816i	0.369100	+	0.639300i
$836$	674.711	−	389.544i	0.807070	−	0.465962i
$837$		0			0
$838$	−268.225	+	464.579i	−0.320078	+	0.554390i
$839$	185.989	+	107.381i	0.221680	+	0.127987i	0.606728	−	0.794910i	$-0.292482\pi$
$839$	185.989	+	107.381i	0.221680	+	0.127987i	−0.385048	+	0.922897i	$0.625815\pi$
$840$		0			0
$841$	245.887	+	425.889i	0.292374	+	0.506407i
$842$		−	171.566i		−	0.203760i
$843$		0			0
$844$	−2519.16			−2.98478
$845$	853.106	+	492.541i	1.00959	+	0.582889i
$846$		0			0
$847$	356.404	−	680.024i	0.420784	−	0.802862i
$848$	−1115.56	−	644.069i	−1.31552	−	0.759515i
$849$		0			0
$850$	57.6193	−	99.7996i	0.0677874	−	0.117411i
$851$	249.530	+	144.066i	0.293220	+	0.169291i
$852$		0			0
$853$	192.842	−	334.012i	0.226075	−	0.391573i	−0.730567	−	0.682841i	$-0.760744\pi$
$853$	192.842	−	334.012i	0.226075	−	0.391573i	0.956641	+	0.291269i	$0.0940773\pi$
$854$	−262.864	+	166.437i	−0.307803	+	0.194891i
$855$		0			0
$856$	−1171.59	+	2029.26i	−1.36868	+	2.37063i
$857$		−	1305.56i		−	1.52341i	−0.647922	−	0.761707i	$-0.724362\pi$
$857$		−	1305.56i		−	1.52341i	0.647922	−	0.761707i	$-0.275638\pi$
$858$		0			0
$859$	1181.22			1.37511			0.687554	−	0.726133i	$-0.258685\pi$
$859$	1181.22			1.37511			0.687554	+	0.726133i	$0.258685\pi$
$860$	−2575.60	+	1487.02i	−2.99488	+	1.72909i
$861$		0			0
$862$	−463.056	+	802.037i	−0.537188	+	0.930438i
$863$	−782.044	−	451.514i	−0.906193	−	0.523191i	−0.0269886	−	0.999636i	$-0.508592\pi$
$863$	−782.044	−	451.514i	−0.906193	−	0.523191i	−0.879204	+	0.476445i	$0.841925\pi$
$864$		0			0
$865$	−561.591	−	972.704i	−0.649238	−	1.12451i
$866$	506.148	−	292.225i	0.584467	−	0.337442i
$867$		0			0
$868$	1627.38	−	66.5212i	1.87486	−	0.0766373i
$869$	295.470	−	170.590i	0.340012	−	0.196306i
$870$		0			0
$871$	11.0458			0.0126818
$872$	−2250.67	+	1299.43i	−2.58104	+	1.49017i
$873$		0			0
$874$	−3022.37			−3.45809
$875$	577.989	+	302.927i	0.660558	+	0.346202i
$876$		0			0
$877$	−554.211			−0.631940			−0.315970	−	0.948769i	$-0.602330\pi$
$877$	−554.211			−0.631940			−0.315970	+	0.948769i	$0.602330\pi$
$878$	−1070.00	−	617.766i	−1.21868	−	0.703606i
$879$		0			0
$880$	−373.674	−	647.222i	−0.424629	−	0.735479i
$881$			750.603i			0.851990i	0.904726	+	0.425995i	$0.140076\pi$
$881$			750.603i			0.851990i	−0.904726	+	0.425995i	$0.859924\pi$
$882$		0			0
$883$	−1042.83			−1.18101			−0.590504	−	0.807035i	$-0.701071\pi$
$883$	−1042.83			−1.18101			−0.590504	+	0.807035i	$0.701071\pi$
$884$	−9.12611	+	5.26896i	−0.0103237	+	0.00596037i
$885$		0			0
$886$	−39.5595	+	68.5191i	−0.0446495	+	0.0773353i
$887$			85.1498i			0.0959975i	0.998847	+	0.0479987i	$0.0152843\pi$
$887$			85.1498i			0.0959975i	−0.998847	+	0.0479987i	$0.984716\pi$
$888$		0			0
$889$	705.080	−	1345.30i	0.793115	−	1.51328i
$890$			1156.87i			1.29985i
$891$		0			0
$892$	−1729.05	−	2994.81i	−1.93840	−	3.35741i
$893$			479.954i			0.537463i
$894$		0			0
$895$	−156.230	−	270.599i	−0.174559	−	0.302345i
$896$	−2.37279	−	58.0479i	−0.00264820	−	0.0647856i
$897$		0			0
$898$	−209.691	−	363.196i	−0.233509	−	0.404450i
$899$	764.581	−	441.431i	0.850479	−	0.491025i
$900$		0			0
$901$	−58.5647	+	101.437i	−0.0649997	+	0.112583i
$902$	−495.837	−	286.271i	−0.549708	−	0.317374i
$903$		0			0
$904$	−355.676	−	616.049i	−0.393447	−	0.681470i
$905$		−	662.026i		−	0.731520i
$906$		0			0
$907$	−860.153			−0.948349			−0.474175	−	0.880431i	$-0.657253\pi$
$907$	−860.153			−0.948349			−0.474175	+	0.880431i	$0.657253\pi$
$908$	3397.48	+	1961.54i	3.74172	+	2.16029i
$909$		0			0
$910$	25.4930	+	40.2626i	0.0280143	+	0.0442446i
$911$	1335.63	+	771.127i	1.46612	+	0.846462i	0.999282	−	0.0378830i	$-0.0120614\pi$
$911$	1335.63	+	771.127i	1.46612	+	0.846462i	0.466833	+	0.884345i	$0.345395\pi$
$912$		0			0
$913$	−50.5381	+	87.5345i	−0.0553539	+	0.0958757i
$914$	−356.381	−	205.757i	−0.389914	−	0.225117i
$915$		0			0
$916$	373.275	−	646.531i	0.407505	−	0.705820i
$917$	−771.038	−	404.105i	−0.840826	−	0.440681i
$918$		0			0
$919$	838.124	−	1451.67i	0.911995	−	1.57962i	0.100753	−	0.994911i	$-0.467875\pi$
$919$	838.124	−	1451.67i	0.911995	−	1.57962i	0.811242	−	0.584711i	$-0.198792\pi$
$920$			4117.23i			4.47525i
$921$		0			0
$922$	613.116			0.664985
$923$	23.4842	−	13.5586i	0.0254433	−	0.0146897i
$924$		0			0
$925$	−38.1749	+	66.1209i	−0.0412702	+	0.0714820i
$926$	777.553	+	448.920i	0.839690	+	0.484795i
$927$		0			0
$928$	1050.95	+	1820.30i	1.13249	+	1.96153i
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.990580	−	0.136935i	$-0.956275\pi$
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.376701	+	0.926335i	$0.622942\pi$
$930$		0			0
$931$	1175.37	−	96.2505i	1.26248	−	0.103384i
$932$	3785.86	−	2185.77i	4.06208	−	2.34524i
$933$		0			0
$934$	−1278.71			−1.36907
$935$	−58.8514	+	33.9779i	−0.0629427	+	0.0363400i
$936$		0			0
$937$	322.074			0.343729			0.171864	−	0.985121i	$-0.445021\pi$
$937$	322.074			0.343729			0.171864	+	0.985121i	$0.445021\pi$
$938$	−799.192	−	418.861i	−0.852017	−	0.446547i
$939$		0			0
$940$	1119.05			1.19048
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	0.317686	−	0.948196i	$-0.397094\pi$
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	−0.662319	+	0.749222i	$0.730428\pi$
$942$		0			0
$943$	784.432	+	1358.68i	0.831847	+	1.44080i
$944$			1388.19i			1.47054i
$945$		0			0
$946$	658.108			0.695674
$947$	142.844	−	82.4709i	0.150838	−	0.0870865i	−0.422681	−	0.906278i	$-0.638911\pi$
$947$	142.844	−	82.4709i	0.150838	−	0.0870865i	0.573519	+	0.819192i	$0.305578\pi$
$948$		0			0
$949$	11.1890	−	19.3799i	0.0117903	−	0.0204214i
$950$		−	800.874i		−	0.843025i
$951$		0			0
$952$	502.520	−	20.5412i	0.527857	−	0.0215769i
$953$			1354.42i			1.42122i	0.703586	+	0.710610i	$0.251581\pi$
$953$			1354.42i			1.42122i	−0.703586	+	0.710610i	$0.748419\pi$
$954$		0			0
$955$	503.291	+	871.726i	0.527006	+	0.912802i
$956$		−	489.592i		−	0.512126i
$957$		0			0
$958$	1028.91	+	1782.12i	1.07402	+	1.86025i
$959$	41.3599	+	21.6769i	0.0431281	+	0.0226037i
$960$		0			0
$961$	188.085	+	325.773i	0.195718	+	0.338994i
$962$	8.56012	−	4.94218i	0.00889825	−	0.00513741i
$963$		0			0
$964$	−921.557	+	1596.18i	−0.955972	+	1.65579i
$965$	−961.319	−	555.018i	−0.996185	−	0.575148i
$966$		0			0
$967$	−344.963	−	597.493i	−0.356735	−	0.617883i	0.630678	−	0.776044i	$-0.282777\pi$
$967$	−344.963	−	597.493i	−0.356735	−	0.617883i	−0.987413	+	0.158161i	$0.949443\pi$
$968$		−	2275.53i		−	2.35075i
$969$		0			0
$970$	−155.403			−0.160209
$971$	−665.293	−	384.107i	−0.685163	−	0.395579i	0.116634	−	0.993175i	$-0.462789\pi$
$971$	−665.293	−	384.107i	−0.685163	−	0.395579i	−0.801797	+	0.597596i	$0.796123\pi$
$972$		0			0
$973$	−123.125	+	5.03292i	−0.126542	+	0.00517258i
$974$	−1220.90	−	704.889i	−1.25350	−	0.723706i
$975$		0			0
$976$	−229.327	+	397.207i	−0.234966	+	0.406974i
$977$	−1200.33	−	693.012i	−1.22859	−	0.709326i	−0.261854	−	0.965107i	$-0.584334\pi$
$977$	−1200.33	−	693.012i	−1.22859	−	0.709326i	−0.966735	+	0.255781i	$0.917667\pi$
$978$		0			0
$979$	90.4109	−	156.596i	0.0923502	−	0.159955i
$980$	−224.416	−	2740.47i	−0.228996	−	2.79640i
$981$		0			0
$982$	−955.379	+	1654.77i	−0.972891	+	1.68510i
$983$		−	525.350i		−	0.534435i	−0.963636	−	0.267217i	$-0.913896\pi$
$983$		−	525.350i		−	0.534435i	0.963636	−	0.267217i	$-0.0861042\pi$
$984$		0			0
$985$	571.660			0.580366
$986$	404.095	−	233.304i	0.409832	−	0.236617i
$987$		0			0
$988$	−36.6177	+	63.4238i	−0.0370625	+	0.0641941i
$989$	−1561.73	−	901.663i	−1.57910	−	0.911692i
$990$		0			0
$991$	214.326	+	371.223i	0.216272	+	0.374594i	0.953665	−	0.300869i	$-0.0972768\pi$
$991$	214.326	+	371.223i	0.216272	+	0.374594i	−0.737393	+	0.675464i	$0.763943\pi$
$992$	1205.81	−	696.176i	1.21554	−	0.701790i
$993$		0			0
$994$	−2213.28	+	90.4708i	−2.22664	+	0.0910169i
$995$	−1294.55	+	747.409i	−1.30106	+	0.751165i
$996$		0			0
$997$	−1196.77			−1.20037			−0.600184	−	0.799862i	$-0.704906\pi$
$997$	−1196.77			−1.20037			−0.600184	+	0.799862i	$0.704906\pi$
$998$	−198.991	+	114.888i	−0.199390	+	0.115118i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.n.b.170.11		22
3.2	odd	2		63.3.n.b.2.1	yes	22
7.4	even	3		189.3.j.b.116.11		22
9.4	even	3		63.3.j.b.23.11	yes	22
9.5	odd	6		189.3.j.b.44.1		22
21.2	odd	6		441.3.r.g.344.11		22
21.5	even	6		441.3.r.f.344.11		22
21.11	odd	6		63.3.j.b.11.1	✓	22
21.17	even	6		441.3.j.f.263.1		22
21.20	even	2		441.3.n.f.128.1		22
63.4	even	3		63.3.n.b.32.1	yes	22
63.13	odd	6		441.3.j.f.275.11		22
63.31	odd	6		441.3.n.f.410.1		22
63.32	odd	6	inner	189.3.n.b.179.11		22
63.40	odd	6		441.3.r.f.50.11		22
63.58	even	3		441.3.r.g.50.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.1	✓	22	21.11	odd	6
63.3.j.b.23.11	yes	22	9.4	even	3
63.3.n.b.2.1	yes	22	3.2	odd	2
63.3.n.b.32.1	yes	22	63.4	even	3
189.3.j.b.44.1		22	9.5	odd	6
189.3.j.b.116.11		22	7.4	even	3
189.3.n.b.170.11		22	1.1	even	1	trivial
189.3.n.b.179.11		22	63.32	odd	6	inner
441.3.j.f.263.1		22	21.17	even	6
441.3.j.f.275.11		22	63.13	odd	6
441.3.n.f.128.1		22	21.20	even	2
441.3.n.f.410.1		22	63.31	odd	6
441.3.r.f.50.11		22	63.40	odd	6
441.3.r.f.344.11		22	21.5	even	6
441.3.r.g.50.11		22	63.58	even	3
441.3.r.g.344.11		22	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.19625 - 1.84536i) q^{2} +(4.81069 - 8.33236i) q^{4} +5.83234i q^{5} +(3.24949 - 6.20007i) q^{7} -20.7469i q^{8} +(10.7628 + 18.6416i) q^{10} -3.36449i q^{11} +(0.158134 + 0.273895i) q^{13} +(-1.05516 - 25.8135i) q^{14} +(-19.0428 - 32.9830i) q^{16} +(-2.99912 + 1.73154i) q^{17} +(-12.0337 + 20.8430i) q^{19} +(48.5972 + 28.0576i) q^{20} +(-6.20870 - 10.7538i) q^{22} +34.0258i q^{23} -9.01621 q^{25} +(1.01087 + 0.583626i) q^{26} +(-36.0289 - 56.9025i) q^{28} +(-31.6161 - 18.2536i) q^{29} +(-12.0916 + 20.9433i) q^{31} +(-49.8615 - 28.7875i) q^{32} +(-6.39064 + 11.0689i) q^{34} +(36.1609 + 18.9521i) q^{35} +(4.23403 - 7.33356i) q^{37} +88.8260i q^{38} +121.003 q^{40} +(39.9308 - 23.0541i) q^{41} +(-26.4994 + 45.8984i) q^{43} +(-28.0342 - 16.1855i) q^{44} +(62.7897 + 108.755i) q^{46} +(17.2703 - 9.97104i) q^{47} +(-27.8817 - 40.2941i) q^{49} +(-28.8181 + 16.6381i) q^{50} +3.04293 q^{52} +(29.2909 - 16.9111i) q^{53} +19.6229 q^{55} +(-128.632 - 67.4169i) q^{56} -134.738 q^{58} +(-31.5660 - 18.2246i) q^{59} +(-6.02138 - 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(-1.59745 + 0.922289i) q^{65} +(17.4628 - 30.2465i) q^{67} +33.3197i q^{68} +(150.553 - 6.15405i) q^{70} -85.7413i q^{71} +(-35.3783 - 61.2770i) q^{73} -31.2532i q^{74} +(115.781 + 200.539i) q^{76} +(-20.8601 - 10.9329i) q^{77} +(50.7030 + 87.8201i) q^{79} +(192.368 - 111.064i) q^{80} +(85.0860 - 147.373i) q^{82} +(-26.0171 - 15.0210i) q^{83} +(-10.0990 - 17.4919i) q^{85} +195.604i q^{86} -69.8030 q^{88} +(46.5438 + 26.8721i) q^{89} +(2.21202 - 0.0904195i) q^{91} +(283.515 + 163.688i) q^{92} +(36.8003 - 63.7400i) q^{94} +(-121.563 - 70.1847i) q^{95} +(-3.60974 + 6.25225i) q^{97} +(-163.474 - 77.3384i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{2} + 12 q^{4} + 3 q^{7} + 25 q^{10} - 18 q^{13} + 90 q^{14} + 12 q^{16} - 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 114 q^{25} + 3 q^{26} + 34 q^{28} + 63 q^{29} - 29 q^{31} - 246 q^{32}+ \cdots - 483 q^{98}+O(q^{100}) \) 22 * q + 6 * q^2 + 12 * q^4 + 3 * q^7 + 25 * q^10 - 18 * q^13 + 90 * q^14 + 12 * q^16 - 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 114 * q^25 + 3 * q^26 + 34 * q^28 + 63 * q^29 - 29 * q^31 - 246 * q^32 - 99 * q^34 + 27 * q^35 - 20 * q^37 + 210 * q^40 + 51 * q^41 + 65 * q^43 - 54 * q^44 + 75 * q^46 - 261 * q^47 - 131 * q^49 - 63 * q^50 + 92 * q^52 + 63 * q^53 - 100 * q^55 - 153 * q^56 - 80 * q^58 + 102 * q^59 + 78 * q^61 + 106 * q^64 + 225 * q^65 - 132 * q^67 + 179 * q^70 + q^73 + 233 * q^76 + 447 * q^77 + 140 * q^79 - 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 816 * q^88 + 720 * q^89 - 70 * q^91 + 1239 * q^92 + 261 * q^94 - 642 * q^95 + 178 * q^97 - 483 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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