LMFDB - Embedded newform 189.3.j.b.44.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,3,Mod(44,189)] 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("189.44"); 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([5, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.j (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			44.1
Character	$\chi$	$=$	189.44
Dual form			189.3.j.b.116.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.69072i q^{2} -9.62138 q^{4} +(-5.05096 + 2.91617i) q^{5} +(3.74467 + 5.91417i) q^{7} +20.7469i q^{8} +(10.7628 + 18.6416i) q^{10} +(-2.91374 - 1.68225i) q^{11} +(0.158134 - 0.273895i) q^{13} +(21.8275 - 13.8205i) q^{14} +38.0855 q^{16} +(2.99912 - 1.73154i) q^{17} +(-12.0337 + 20.8430i) q^{19} +(48.5972 - 28.0576i) q^{20} +(-6.20870 + 10.7538i) q^{22} +(-29.4672 + 17.0129i) q^{23} +(4.50810 - 7.80826i) q^{25} +(-1.01087 - 0.583626i) q^{26} +(-36.0289 - 56.9025i) q^{28} +(-31.6161 + 18.2536i) q^{29} +24.1833 q^{31} -57.5750i q^{32} +(-6.39064 - 11.0689i) q^{34} +(-36.1609 - 18.9521i) q^{35} +(4.23403 - 7.33356i) q^{37} +(76.9256 + 44.4130i) q^{38} +(-60.5016 - 104.792i) q^{40} +(39.9308 + 23.0541i) q^{41} +(-26.4994 - 45.8984i) q^{43} +(28.0342 + 16.1855i) q^{44} +(62.7897 + 108.755i) q^{46} -19.9421i q^{47} +(-20.9549 + 44.2933i) q^{49} +(-28.8181 - 16.6381i) q^{50} +(-1.52146 + 2.63525i) q^{52} +(-29.2909 + 16.9111i) q^{53} +19.6229 q^{55} +(-122.701 + 77.6905i) q^{56} +(67.3688 + 116.686i) q^{58} -36.4493i q^{59} +12.0428 q^{61} -89.2535i q^{62} -60.1511 q^{64} +1.84458i q^{65} -34.9256 q^{67} +(-28.8557 + 16.6599i) q^{68} +(-69.9469 + 133.460i) q^{70} +85.7413i q^{71} +(-35.3783 - 61.2770i) q^{73} +(-27.0661 - 15.6266i) q^{74} +(115.781 - 200.539i) q^{76} +(-0.961895 - 23.5318i) q^{77} -101.406 q^{79} +(-192.368 + 111.064i) q^{80} +(85.0860 - 147.373i) q^{82} +(-26.0171 + 15.0210i) q^{83} +(-10.0990 + 17.4919i) q^{85} +(-169.398 + 97.8019i) q^{86} +(34.9015 - 60.4511i) q^{88} +(-46.5438 - 26.8721i) q^{89} +(2.21202 - 0.0904195i) q^{91} +(283.515 - 163.688i) q^{92} -73.6006 q^{94} -140.369i q^{95} +(-3.60974 - 6.25225i) q^{97} +(163.474 + 77.3384i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31}+ \cdots + 483 q^{98}+O(q^{100}) $ 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	3.69072i		−	1.84536i	−0.385569	−	0.922679i	$-0.625995\pi$
$2$		−	3.69072i		−	1.84536i	0.385569	−	0.922679i	$-0.374005\pi$
$3$		0			0
$3$		0			0
$4$	−9.62138			−2.40535
$5$	−5.05096	+	2.91617i	−1.01019	+	0.583234i	−0.911248	−	0.411859i	$-0.864880\pi$
$5$	−5.05096	+	2.91617i	−1.01019	+	0.583234i	−0.0989435	+	0.995093i	$0.531546\pi$
$6$		0			0
$7$	3.74467	+	5.91417i	0.534953	+	0.844882i
$7$	3.74467	+	5.91417i	0.534953	+	0.844882i
$8$			20.7469i			2.59337i
$9$		0			0
$10$	10.7628	+	18.6416i	1.07628	+	1.86416i
$11$	−2.91374	−	1.68225i	−0.264885	−	0.152932i	0.361676	−	0.932304i	$-0.382205\pi$
$11$	−2.91374	−	1.68225i	−0.264885	−	0.152932i	−0.626561	+	0.779372i	$0.715538\pi$
$12$		0			0
$13$	0.158134	−	0.273895i	0.0121641	−	0.0210689i	−0.859879	−	0.510497i	$-0.829461\pi$
$13$	0.158134	−	0.273895i	0.0121641	−	0.0210689i	0.872043	+	0.489429i	$0.162795\pi$
$14$	21.8275	−	13.8205i	1.55911	−	0.987180i
$15$		0			0
$16$	38.0855			2.38034
$17$	2.99912	−	1.73154i	0.176419	−	0.101856i	−0.409190	−	0.912449i	$-0.634189\pi$
$17$	2.99912	−	1.73154i	0.176419	−	0.101856i	0.585609	+	0.810594i	$0.300855\pi$
$18$		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
$23$	−29.4672	+	17.0129i	−1.28118	+	0.739691i	−0.977064	−	0.212944i	$-0.931695\pi$
$23$	−29.4672	+	17.0129i	−1.28118	+	0.739691i	−0.304117	+	0.952635i	$0.598362\pi$
$24$		0			0
$25$	4.50810	−	7.80826i	0.180324	−	0.312331i
$26$	−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	−0.933633	−	0.358231i	$-0.883380\pi$
$29$	−31.6161	+	18.2536i	−1.09021	+	0.629434i	−0.156579	+	0.987665i	$0.550047\pi$
$30$		0			0
$31$	24.1833			0.780105			0.390052	−	0.920793i	$-0.372457\pi$
$31$	24.1833			0.780105			0.390052	+	0.920793i	$0.372457\pi$
$32$		−	57.5750i		−	1.79922i
$33$		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	$0.130161\pi$
$38$	76.9256	+	44.4130i	2.02436	+	1.16876i
$39$		0			0
$40$	−60.5016	−	104.792i	−1.51254	−	2.61980i
$41$	39.9308	+	23.0541i	0.973922	+	0.562294i	0.900430	−	0.435002i	$-0.143252\pi$
$41$	39.9308	+	23.0541i	0.973922	+	0.562294i	0.0734924	+	0.997296i	$0.476586\pi$
$42$		0			0
$43$	−26.4994	−	45.8984i	−0.616266	−	1.06740i	−0.990161	−	0.139933i	$-0.955311\pi$
$43$	−26.4994	−	45.8984i	−0.616266	−	1.06740i	0.373895	−	0.927471i	$-0.378022\pi$
$44$	28.0342	+	16.1855i	0.637141	+	0.367853i
$45$		0			0
$46$	62.7897	+	108.755i	1.36499	+	2.36424i
$47$		−	19.9421i		−	0.424300i	−0.977237	−	0.212150i	$-0.931954\pi$
$47$		−	19.9421i		−	0.424300i	0.977237	−	0.212150i	$-0.0680465\pi$
$48$		0			0
$49$	−20.9549	+	44.2933i	−0.427650	+	0.903944i
$50$	−28.8181	−	16.6381i	−0.576362	−	0.332763i
$51$		0			0
$52$	−1.52146	+	2.63525i	−0.0292589	+	0.0506779i
$53$	−29.2909	+	16.9111i	−0.552659	+	0.319078i	−0.750194	−	0.661218i	$-0.770040\pi$
$53$	−29.2909	+	16.9111i	−0.552659	+	0.319078i	0.197535	+	0.980296i	$0.436706\pi$
$54$		0			0
$55$	19.6229			0.356780
$56$	−122.701	+	77.6905i	−2.19109	+	1.38733i
$57$		0			0
$58$	67.3688	+	116.686i	1.16153	+	2.01183i
$59$		−	36.4493i		−	0.617785i	−0.951097	−	0.308892i	$-0.900042\pi$
$59$		−	36.4493i		−	0.617785i	0.951097	−	0.308892i	$-0.0999583\pi$
$60$		0			0
$61$	12.0428			0.197422			0.0987111	−	0.995116i	$-0.468528\pi$
$61$	12.0428			0.197422			0.0987111	+	0.995116i	$0.468528\pi$
$62$		−	89.2535i		−	1.43957i
$63$		0			0
$64$	−60.1511			−0.939861
$65$			1.84458i			0.0283781i
$66$		0			0
$67$	−34.9256			−0.521278			−0.260639	−	0.965436i	$-0.583933\pi$
$67$	−34.9256			−0.521278			−0.260639	+	0.965436i	$0.583933\pi$
$68$	−28.8557	+	16.6599i	−0.424349	+	0.244998i
$69$		0			0
$70$	−69.9469	+	133.460i	−0.999241	+	1.90657i
$71$			85.7413i			1.20762i	0.797127	+	0.603812i	$0.206352\pi$
$71$			85.7413i			1.20762i	−0.797127	+	0.603812i	$0.793648\pi$
$72$		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	$0.994381\pi$
$74$	−27.0661	−	15.6266i	−0.365758	−	0.211170i
$75$		0			0
$76$	115.781	−	200.539i	1.52343	−	2.63866i
$77$	−0.961895	−	23.5318i	−0.0124921	−	0.305608i
$78$		0			0
$79$	−101.406			−1.28362			−0.641810	−	0.766864i	$-0.721816\pi$
$79$	−101.406			−1.28362			−0.641810	+	0.766864i	$0.721816\pi$
$80$	−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	−0.648473	−	0.761237i	$-0.724592\pi$
$83$	−26.0171	+	15.0210i	−0.313459	+	0.180976i	0.335014	+	0.942213i	$0.391259\pi$
$84$		0			0
$85$	−10.0990	+	17.4919i	−0.118811	+	0.205787i
$86$	−169.398	+	97.8019i	−1.96974	+	1.13723i
$87$		0			0
$88$	34.9015	−	60.4511i	0.396608	−	0.686945i
$89$	−46.5438	−	26.8721i	−0.522964	−	0.301933i	0.215183	−	0.976574i	$-0.430965\pi$
$89$	−46.5438	−	26.8721i	−0.522964	−	0.301933i	−0.738146	+	0.674641i	$0.764299\pi$
$90$		0			0
$91$	2.21202	−	0.0904195i	0.0243079	−	0.000993620i
$92$	283.515	−	163.688i	3.08169	−	1.77921i
$93$		0			0
$94$	−73.6006			−0.782985
$95$		−	140.369i		−	1.47757i
$96$		0			0
$97$	−3.60974	−	6.25225i	−0.0372138	−	0.0644561i	0.846819	−	0.531882i	$-0.178515\pi$
$97$	−3.60974	−	6.25225i	−0.0372138	−	0.0644561i	−0.884032	+	0.467426i	$0.845182\pi$
$98$	163.474	+	77.3384i	1.66810	+	0.789167i
$99$		0			0
$100$	−43.3742	+	75.1263i	−0.433742	+	0.751263i
$101$	52.3908	+	30.2479i	0.518721	+	0.299484i	0.736411	−	0.676534i	$-0.236519\pi$
$101$	52.3908	+	30.2479i	0.518721	+	0.299484i	−0.217690	+	0.976018i	$0.569852\pi$
$102$		0			0
$103$	81.6220	+	141.373i	0.792447	+	1.37256i	0.924448	+	0.381308i	$0.124526\pi$
$103$	81.6220	+	141.373i	0.792447	+	1.37256i	−0.132001	+	0.991250i	$0.542140\pi$
$104$	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	0.881752	−	0.471714i	$-0.156364\pi$
$107$	97.8099	+	56.4706i	0.914111	+	0.527762i	0.0323597	+	0.999476i	$0.489698\pi$
$108$		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	$-0.361512\pi$
$110$		−	72.4225i		−	0.658386i
$111$		0			0
$112$	142.618	+	225.244i	1.27337	+	2.01111i
$113$	29.6935	+	17.1435i	0.262774	+	0.151713i	0.625599	−	0.780144i	$-0.284854\pi$
$113$	29.6935	+	17.1435i	0.262774	+	0.151713i	−0.362825	+	0.931857i	$0.618188\pi$
$114$		0			0
$115$	99.2250	−	171.863i	0.862826	−	1.49446i
$116$	304.191	−	175.625i	2.62234	−	1.51401i
$117$		0			0
$118$	−134.524			−1.14003
$119$	21.4714	+	11.2533i	0.180432	+	0.0945652i
$120$		0			0
$121$	−54.8401	−	94.9858i	−0.453224	−	0.785007i
$122$		−	44.4464i		−	0.364315i
$123$		0			0
$124$	−232.676			−1.87642
$125$		−	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	$0.174011\pi$
$128$		−	8.29948i		−	0.0648397i
$129$		0			0
$130$	6.80781			0.0523678
$131$	107.699	−	62.1798i	0.822126	−	0.474655i	−0.0290229	−	0.999579i	$-0.509240\pi$
$131$	107.699	−	62.1798i	0.822126	−	0.474655i	0.851149	+	0.524924i	$0.175906\pi$
$132$		0			0
$133$	−168.331	+	6.88077i	−1.26565	+	0.0517351i
$134$			128.901i			0.961944i
$135$		0			0
$136$	35.9242	+	62.2226i	0.264149	+	0.457519i
$137$	5.77715	+	3.33544i	0.0421690	+	0.0243463i	0.520936	−	0.853596i	$-0.325583\pi$
$137$	5.77715	+	3.33544i	0.0421690	+	0.0243463i	−0.478767	+	0.877942i	$0.658916\pi$
$138$		0			0
$139$	−8.80202	+	15.2455i	−0.0633239	+	0.109680i	−0.895949	−	0.444156i	$-0.853503\pi$
$139$	−8.80202	+	15.2455i	−0.0633239	+	0.109680i	0.832625	+	0.553837i	$0.186837\pi$
$140$	347.918	+	182.346i	2.48513	+	1.30247i
$141$		0			0
$142$	316.447			2.22850
$143$	−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
$149$	25.7165	−	14.8474i	0.172594	−	0.0996472i	−0.411214	−	0.911539i	$-0.634895\pi$
$149$	25.7165	−	14.8474i	0.172594	−	0.0996472i	0.583808	+	0.811891i	$0.301562\pi$
$150$		0			0
$151$	34.9796	−	60.5864i	0.231653	−	0.401234i	−0.726642	−	0.687016i	$-0.758920\pi$
$151$	34.9796	−	60.5864i	0.231653	−	0.401234i	0.958295	+	0.285782i	$0.0922534\pi$
$152$	−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
$157$	−196.639			−1.25248			−0.626239	−	0.779631i	$-0.715407\pi$
$157$	−196.639			−1.25248			−0.626239	+	0.779631i	$0.715407\pi$
$158$			374.261i			2.36874i
$159$		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	$0.175732\pi$
$164$	−384.190	−	221.812i	−2.34262	−	1.35251i
$165$		0			0
$166$	55.4382	+	96.0219i	0.333965	+	0.578445i
$167$	91.5268	+	52.8430i	0.548065	+	0.316425i	0.748341	−	0.663314i	$-0.230851\pi$
$167$	91.5268	+	52.8430i	0.548065	+	0.316425i	−0.200276	+	0.979739i	$0.564184\pi$
$168$		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
$173$			192.578i			1.11317i	0.830791	+	0.556585i	$0.187889\pi$
$173$			192.578i			1.11317i	−0.830791	+	0.556585i	$0.812111\pi$
$174$		0			0
$175$	63.0608	−	2.57770i	0.360347	−	0.0147297i
$176$	−110.971	−	64.0692i	−0.630518	−	0.364030i
$177$		0			0
$178$	−99.1771	+	171.780i	−0.557175	+	0.965055i
$179$	46.3963	−	26.7869i	0.259197	−	0.149648i	−0.364771	−	0.931097i	$-0.618853\pi$
$179$	46.3963	−	26.7869i	0.259197	−	0.149648i	0.623968	+	0.781450i	$0.285519\pi$
$180$		0			0
$181$	−113.509			−0.627124			−0.313562	−	0.949568i	$-0.601522\pi$
$181$	−113.509			−0.627124			−0.313562	+	0.949568i	$0.601522\pi$
$182$	−0.333713	−	8.16395i	−0.00183359	−	0.0448569i
$183$		0			0
$184$	−352.965	−	611.354i	−1.91829	−	3.32257i
$185$			49.3886i			0.266966i
$186$		0			0
$187$	−11.6515			−0.0623077
$188$			191.870i			1.02059i
$189$		0			0
$190$	−518.064			−2.72665
$191$		−	172.586i		−	0.903593i	−0.892121	−	0.451797i	$-0.850783\pi$
$191$		−	172.586i		−	0.903593i	0.892121	−	0.451797i	$-0.149217\pi$
$192$		0			0
$193$	190.324			0.986135			0.493068	−	0.869991i	$-0.335876\pi$
$193$	190.324			0.986135			0.493068	+	0.869991i	$0.335876\pi$
$194$	−23.0753	+	13.3225i	−0.118945	+	0.0686727i
$195$		0			0
$196$	201.615	−	426.163i	1.02865	−	2.17430i
$197$			98.0156i			0.497541i	0.968562	+	0.248770i	$0.0800265\pi$
$197$			98.0156i			0.497541i	−0.968562	+	0.248770i	$0.919974\pi$
$198$		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	$0.610622\pi$
$200$	161.998	+	93.5293i	0.809988	+	0.467647i
$201$		0			0
$202$	111.636	−	193.360i	0.552655	−	0.957226i
$203$	−226.347	−	118.630i	−1.11501	−	0.584382i
$204$		0			0
$205$	−268.918			−1.31180
$206$	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	0.368955	+	0.929447i	$0.379716\pi$
$211$	−130.914	+	226.750i	−0.620447	+	1.07465i	−0.989402	+	0.145199i	$0.953618\pi$
$212$	281.819	−	162.708i	1.32934	−	0.767493i
$213$		0			0
$214$	208.417	−	360.989i	0.973911	−	1.68686i
$215$	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
$220$	−188.799			−0.858179
$221$		−	1.09526i		−	0.00495593i
$222$		0			0
$223$	179.709	+	311.266i	0.805872	+	1.39581i	0.915701	+	0.401860i	$0.131636\pi$
$223$	179.709	+	311.266i	0.805872	+	1.39581i	−0.109829	+	0.993950i	$0.535030\pi$
$224$	340.509	−	215.600i	1.52013	−	0.962499i
$225$		0			0
$226$	63.2719	−	109.590i	0.279964	−	0.484912i
$227$	353.118	+	203.873i	1.55559	+	0.898118i	0.997670	+	0.0682208i	$0.0217322\pi$
$227$	353.118	+	203.873i	1.55559	+	0.898118i	0.557916	+	0.829897i	$0.311601\pi$
$228$		0			0
$229$	−38.7964	−	67.1973i	−0.169417	−	0.293438i	0.768798	−	0.639491i	$-0.220855\pi$
$229$	−38.7964	−	67.1973i	−0.169417	−	0.293438i	−0.938215	+	0.346053i	$0.887522\pi$
$230$	−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	$-0.904640\pi$
$233$	−393.484	−	227.178i	−1.68877	−	0.975013i	−0.733312	−	0.679892i	$-0.762027\pi$
$234$		0			0
$235$	58.1545	+	100.727i	0.247466	+	0.428624i
$236$			350.693i			1.48599i
$237$		0			0
$238$	41.5326	−	79.2448i	0.174507	−	0.332961i
$239$	44.0684	+	25.4429i	0.184387	+	0.106456i	0.589352	−	0.807876i	$-0.299383\pi$
$239$	44.0684	+	25.4429i	0.184387	+	0.106456i	−0.404965	+	0.914332i	$0.632716\pi$
$240$		0			0
$241$	95.7821	−	165.900i	0.397436	−	0.688380i	−0.595973	−	0.803005i	$-0.703233\pi$
$241$	95.7821	−	165.900i	0.397436	−	0.688380i	0.993409	+	0.114625i	$0.0365666\pi$
$242$	−350.566	+	202.399i	−1.44862	+	0.836360i
$243$		0			0
$244$	−115.868			−0.474869
$245$	−23.3247	−	284.831i	−0.0952029	−	1.16258i
$246$		0			0
$247$	3.80587	+	6.59196i	0.0154084	+	0.0266881i
$248$			501.728i			2.02310i
$249$		0			0
$250$	−344.059			−1.37624
$251$		−	262.216i		−	1.04469i	−0.852735	−	0.522343i	$-0.825058\pi$
$251$		−	262.216i		−	1.04469i	0.852735	−	0.522343i	$-0.174942\pi$
$252$		0			0
$253$	114.480			0.452488
$254$		−	800.818i		−	3.15283i
$255$		0			0
$256$	−271.236			−1.05951
$257$	−122.518	+	70.7359i	−0.476724	+	0.275237i	−0.719050	−	0.694958i	$-0.755423\pi$
$257$	−122.518	+	70.7359i	−0.476724	+	0.275237i	0.242326	+	0.970195i	$0.422090\pi$
$258$		0			0
$259$	59.2270	−	2.42098i	0.228676	−	0.00934743i
$260$		−	17.7474i		−	0.0682592i
$261$		0			0
$262$	−229.488	−	397.485i	−0.875908	−	1.51712i
$263$	382.349	+	220.750i	1.45380	+	0.839352i	0.998694	−	0.0510853i	$-0.0162680\pi$
$263$	382.349	+	220.750i	1.45380	+	0.839352i	0.455106	+	0.890437i	$0.349601\pi$
$264$		0			0
$265$	98.6315	−	170.835i	0.372194	−	0.644659i
$266$	25.3950	+	621.263i	0.0954699	+	2.33558i
$267$		0			0
$268$	336.033			1.25385
$269$	−88.6239	+	51.1670i	−0.329457	+	0.190212i	−0.655600	−	0.755108i	$-0.727584\pi$
$269$	−88.6239	+	51.1670i	−0.329457	+	0.190212i	0.326143	+	0.945320i	$0.394251\pi$
$270$		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
$275$	−26.2709	+	15.1675i	−0.0955304	+	0.0551545i
$276$		0			0
$277$	−102.207	+	177.028i	−0.368979	+	0.639091i	−0.989406	−	0.145173i	$-0.953626\pi$
$277$	−102.207	+	177.028i	−0.368979	+	0.639091i	0.620427	+	0.784264i	$0.286959\pi$
$278$	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	−0.481933	−	0.876208i	$-0.660065\pi$
$281$	10.0933	−	5.82736i	0.0359191	−	0.0207379i	0.517852	+	0.855470i	$0.326732\pi$
$282$		0			0
$283$	346.245			1.22348			0.611740	−	0.791059i	$-0.290470\pi$
$283$	346.245			1.22348			0.611740	+	0.791059i	$0.290470\pi$
$284$		−	824.950i		−	2.90475i
$285$		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
$290$	−680.554	−	392.918i	−2.34674	−	1.35489i
$291$		0			0
$292$	340.388	+	589.569i	1.16571	+	2.01907i
$293$	81.5708	+	47.0949i	0.278399	+	0.160734i	0.632698	−	0.774398i	$-0.281947\pi$
$293$	81.5708	+	47.0949i	0.278399	+	0.160734i	−0.354300	+	0.935132i	$0.615281\pi$
$294$		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
$299$			10.7612i			0.0359908i
$300$		0			0
$301$	172.219	−	328.596i	0.572156	−	1.09168i
$302$	−223.607	−	129.100i	−0.740421	−	0.427482i
$303$		0			0
$304$	−458.310	+	793.816i	−1.50760	+	2.61124i
$305$	−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	$0.806253\pi$
$308$	9.25476	+	226.409i	0.0300479	+	0.735093i
$309$		0			0
$310$	260.278	+	450.816i	0.839608	+	1.45424i
$311$			275.966i			0.887350i	0.896188	+	0.443675i	$0.146325\pi$
$311$			275.966i			0.887350i	−0.896188	+	0.443675i	$0.853675\pi$
$312$		0			0
$313$	381.083			1.21752			0.608759	−	0.793355i	$-0.291668\pi$
$313$	381.083			1.21752			0.608759	+	0.793355i	$0.291668\pi$
$314$			725.739i			2.31127i
$315$		0			0
$316$	975.665			3.08755
$317$			609.376i			1.92232i	0.275990	+	0.961160i	$0.410994\pi$
$317$			609.376i			1.92232i	−0.275990	+	0.961160i	$0.589006\pi$
$318$		0			0
$319$	122.828			0.385041
$320$	303.821	−	175.411i	0.949440	−	0.548159i
$321$		0			0
$322$	−408.069	+	778.601i	−1.26729	+	2.41802i
$323$			83.3476i			0.258042i
$324$		0			0
$325$	−1.42577	−	2.46950i	−0.00438697	−	0.00759846i
$326$	29.6724	+	17.1313i	0.0910195	+	0.0525501i
$327$		0			0
$328$	−478.301	+	828.442i	−1.45824	+	2.52574i
$329$	117.941	−	74.6766i	0.358483	−	0.226980i
$330$		0			0
$331$	−510.883			−1.54345			−0.771727	−	0.635954i	$-0.780607\pi$
$331$	−510.883			−1.54345			−0.771727	+	0.635954i	$0.780607\pi$
$332$	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	−0.953750	−	0.300600i	$-0.902813\pi$
$337$	−72.9765	+	126.399i	−0.216547	+	0.375071i	0.737203	+	0.675672i	$0.236146\pi$
$338$	539.847	−	311.681i	1.59718	−	0.922133i
$339$		0			0
$340$	97.1659	−	168.296i	0.285782	−	0.494989i
$341$	−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
$346$	710.752			2.05420
$347$		−	275.853i		−	0.794967i	−0.917609	−	0.397483i	$-0.869884\pi$
$347$		−	275.853i		−	0.794967i	0.917609	−	0.397483i	$-0.130116\pi$
$348$		0			0
$349$	119.986	+	207.822i	0.343800	+	0.595480i	0.985135	−	0.171782i	$-0.0549523\pi$
$349$	119.986	+	207.822i	0.343800	+	0.595480i	−0.641335	+	0.767261i	$0.721619\pi$
$350$	−9.51354	−	232.739i	−0.0271815	−	0.664970i
$351$		0			0
$352$	−96.8555	+	167.759i	−0.275158	+	0.476587i
$353$	−469.244	−	270.918i	−1.32930	−	0.767474i	−0.344112	−	0.938929i	$-0.611820\pi$
$353$	−469.244	−	270.918i	−1.32930	−	0.767474i	−0.985192	+	0.171455i	$0.945153\pi$
$354$		0			0
$355$	−250.036	−	433.076i	−0.704328	−	1.21993i
$356$	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	−0.139754	−	0.990186i	$-0.544631\pi$
$359$	−383.110	−	221.189i	−1.06716	−	0.616124i	−0.927404	+	0.374062i	$0.877965\pi$
$360$		0			0
$361$	−109.120	−	189.002i	−0.302273	−	0.523551i
$362$			418.931i			1.15727i
$363$		0			0
$364$	−21.2827	+	0.869960i	−0.0584690	+	0.00239000i
$365$	357.388	+	206.338i	0.979146	+	0.565310i
$366$		0			0
$367$	153.095	−	265.167i	0.417151	−	0.722527i	−0.578500	−	0.815682i	$-0.696362\pi$
$367$	153.095	−	265.167i	0.417151	−	0.722527i	0.995652	+	0.0931549i	$0.0296952\pi$
$368$	−1122.27	+	647.944i	−3.04965	+	1.76072i
$369$		0			0
$370$	182.279			0.492647
$371$	−209.700	−	109.905i	−0.565230	−	0.296240i
$372$		0			0
$373$	−109.315	−	189.339i	−0.293069	−	0.507610i	0.681465	−	0.731851i	$-0.261343\pi$
$373$	−109.315	−	189.339i	−0.293069	−	0.507610i	−0.974534	+	0.224241i	$0.928010\pi$
$374$			43.0025i			0.114980i
$375$		0			0
$376$	413.737			1.10036
$377$			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	$0.391010\pi$
$380$			1350.55i			3.55407i
$381$		0			0
$382$	−636.967			−1.66745
$383$	491.482	−	283.757i	1.28324	−	0.740881i	0.305803	−	0.952095i	$-0.401075\pi$
$383$	491.482	−	283.757i	1.28324	−	0.740881i	0.977440	+	0.211214i	$0.0677417\pi$
$384$		0			0
$385$	73.4813	+	116.053i	0.190860	+	0.301437i
$386$		−	702.432i		−	1.81977i
$387$		0			0
$388$	34.7307	+	60.1553i	0.0895120	+	0.155039i
$389$	−251.771	−	145.360i	−0.647226	−	0.373676i	0.140166	−	0.990128i	$-0.455236\pi$
$389$	−251.771	−	145.360i	−0.647226	−	0.373676i	−0.787393	+	0.616452i	$0.788570\pi$
$390$		0			0
$391$	−58.9171	+	102.047i	−0.150683	+	0.260991i
$392$	−918.950	−	434.749i	−2.34426	−	1.10905i
$393$		0			0
$394$	361.748			0.918141
$395$	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
$401$	−398.361	+	229.994i	−0.993418	+	0.573550i	−0.906294	−	0.422647i	$-0.861101\pi$
$401$	−398.361	+	229.994i	−0.993418	+	0.573550i	−0.0871241	+	0.996197i	$0.527768\pi$
$402$		0			0
$403$	3.82418	−	6.62368i	0.00948929	−	0.0164359i
$404$	−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
$409$	−583.840			−1.42748			−0.713741	−	0.700410i	$-0.753001\pi$
$409$	−583.840			−1.42748			−0.713741	+	0.700410i	$0.753001\pi$
$410$			992.501i			2.42073i
$411$		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
$416$	−15.7695	−	9.10455i	−0.0379076	−	0.0218859i
$417$		0			0
$418$	−149.427	−	258.816i	−0.357482	−	0.619176i
$419$	−125.878	−	72.6756i	−0.300424	−	0.173450i	0.342209	−	0.939624i	$-0.388825\pi$
$419$	−125.878	−	72.6756i	−0.300424	−	0.173450i	−0.642634	+	0.766174i	$0.722158\pi$
$420$		0			0
$421$	23.2429	+	40.2578i	0.0552087	+	0.0956243i	0.892309	−	0.451425i	$-0.149084\pi$
$421$	23.2429	+	40.2578i	0.0552087	+	0.0956243i	−0.837100	+	0.547050i	$0.815751\pi$
$422$	836.871	+	483.168i	1.98311	+	1.14495i
$423$		0			0
$424$	−350.854	−	607.697i	−0.827486	−	1.43325i
$425$		−	31.2239i		−	0.0734680i
$426$		0			0
$427$	45.0962	+	71.2229i	0.105612	+	0.166798i
$428$	−941.067	−	543.325i	−2.19875	−	1.26945i
$429$		0			0
$430$	570.414	−	987.986i	1.32654	−	2.29764i
$431$	217.312	−	125.465i	0.504204	−	0.291103i	−0.226244	−	0.974071i	$-0.572645\pi$
$431$	217.312	−	125.465i	0.504204	−	0.291103i	0.730448	+	0.682968i	$0.239311\pi$
$432$		0			0
$433$	158.357			0.365720			0.182860	−	0.983139i	$-0.441464\pi$
$433$	158.357			0.365720			0.182860	+	0.983139i	$0.441464\pi$
$434$	527.861	−	334.225i	1.21627	−	0.770104i
$435$		0			0
$436$	602.608	+	1043.75i	1.38213	+	2.39392i
$437$		−	818.913i		−	1.87394i
$438$		0			0
$439$	334.767			0.762568			0.381284	−	0.924458i	$-0.375482\pi$
$439$	334.767			0.762568			0.381284	+	0.924458i	$0.375482\pi$
$440$			407.115i			0.925261i
$441$		0			0
$442$	−4.04230			−0.00914547
$443$			21.4373i			0.0483912i	0.999707	+	0.0241956i	$0.00770245\pi$
$443$			21.4373i			0.0483912i	−0.999707	+	0.0241956i	$0.992298\pi$
$444$		0			0
$445$	313.454			0.704391
$446$	1148.79	−	663.256i	2.57577	−	1.48712i
$447$		0			0
$448$	−225.246	−	355.744i	−0.502782	−	0.794072i
$449$			113.632i			0.253078i	0.991962	+	0.126539i	$0.0403868\pi$
$449$			113.632i			0.253078i	−0.991962	+	0.126539i	$0.959613\pi$
$450$		0			0
$451$	−77.5653	−	134.347i	−0.171985	−	0.297887i
$452$	−285.692	−	164.945i	−0.632063	−	0.364922i
$453$		0			0
$454$	752.437	−	1303.26i	1.65735	−	2.87061i
$455$	−10.9092	+	6.90734i	−0.0239762	+	0.0151810i
$456$		0			0
$457$	111.500			0.243982			0.121991	−	0.992531i	$-0.461072\pi$
$457$	111.500			0.243982			0.121991	+	0.992531i	$0.461072\pi$
$458$	−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	−0.335779	−	0.941941i	$-0.608999\pi$
$461$	143.867	−	83.0619i	0.312077	−	0.180178i	0.647855	+	0.761763i	$0.275666\pi$
$462$		0			0
$463$	121.635	−	210.678i	0.262711	−	0.455028i	−0.704251	−	0.709951i	$-0.748717\pi$
$463$	121.635	−	210.678i	0.262711	−	0.455028i	0.966961	+	0.254923i	$0.0820502\pi$
$464$	−1204.12	+	695.197i	−2.59508	+	1.49827i
$465$		0			0
$466$	−838.450	+	1452.24i	−1.79925	+	3.11639i
$467$	300.050	+	173.234i	0.642505	+	0.370950i	0.785579	−	0.618762i	$-0.212365\pi$
$467$	300.050	+	173.234i	0.642505	+	0.370950i	−0.143074	+	0.989712i	$0.545699\pi$
$468$		0			0
$469$	−130.785	−	206.556i	−0.278859	−	0.440418i
$470$	371.753	−	214.632i	0.790964	−	0.456663i
$471$		0			0
$472$	756.211			1.60214
$473$			178.314i			0.376986i
$474$		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
$479$	482.865	+	278.782i	1.00807	+	0.582009i	0.910626	−	0.413232i	$-0.135600\pi$
$479$	482.865	+	278.782i	1.00807	+	0.582009i	0.0974437	+	0.995241i	$0.468933\pi$
$480$		0			0
$481$	−1.33909	−	2.31936i	−0.00278396	−	0.00482196i
$482$	−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	$0.961611\pi$
$488$			249.850i			0.511988i
$489$		0			0
$490$	−1051.23	+	86.0849i	−2.14537	+	0.175683i
$491$	−448.359	−	258.860i	−0.913155	−	0.527210i	−0.0317099	−	0.999497i	$-0.510095\pi$
$491$	−448.359	−	258.860i	−0.913155	−	0.527210i	−0.881445	+	0.472287i	$0.843429\pi$
$492$		0			0
$493$	−63.2138	+	109.489i	−0.128223	+	0.222088i
$494$	24.3290	−	14.0464i	0.0492491	−	0.0284340i
$495$		0			0
$496$	921.031			1.85692
$497$	−507.089	+	321.073i	−1.02030	+	0.646022i
$498$		0			0
$499$	31.1288	+	53.9167i	0.0623824	+	0.108049i	0.895530	−	0.445001i	$-0.146797\pi$
$499$	31.1288	+	53.9167i	0.0623824	+	0.108049i	−0.833147	+	0.553051i	$0.813463\pi$
$500$			896.934i			1.79387i
$501$		0			0
$502$	−967.766			−1.92782
$503$			608.089i			1.20892i	0.796634	+	0.604462i	$0.206612\pi$
$503$			608.089i			1.20892i	−0.796634	+	0.604462i	$0.793388\pi$
$504$		0			0
$505$	−352.832			−0.698677
$506$		−	422.511i		−	0.835003i
$507$		0			0
$508$	−2087.67			−4.10958
$509$	−335.722	+	193.829i	−0.659572	+	0.380804i	−0.792114	−	0.610373i	$-0.791019\pi$
$509$	−335.722	+	193.829i	−0.659572	+	0.380804i	0.132542	+	0.991177i	$0.457686\pi$
$510$		0			0
$511$	229.922	−	438.695i	0.449946	−	0.858504i
$512$			967.855i			1.89034i
$513$		0			0
$514$	261.066	+	452.180i	0.507911	+	0.879727i
$515$	−824.538	−	476.047i	−1.60105	−	0.924364i
$516$		0			0
$517$	−33.5475	+	58.1060i	−0.0648888	+	0.112391i
$518$	−8.93516	−	218.590i	−0.0172494	−	0.421988i
$519$		0			0
$520$	−38.2693			−0.0735949
$521$	−457.542	+	264.162i	−0.878200	+	0.507029i	−0.870064	−	0.492938i	$-0.835923\pi$
$521$	−457.542	+	264.162i	−0.878200	+	0.507029i	−0.00813547	+	0.999967i	$0.502590\pi$
$522$		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
$527$	72.5285	−	41.8744i	0.137625	−	0.0794580i
$528$		0			0
$529$	314.377	−	544.516i	0.594285	−	1.02933i
$530$	−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
$535$	−658.711			−1.23124
$536$		−	724.600i		−	1.35186i
$537$		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	$0.145744\pi$
$542$	1025.38	+	592.002i	1.89184	+	1.09225i
$543$		0			0
$544$	−99.6937	−	172.675i	−0.183261	−	0.317417i
$545$	632.705	+	365.292i	1.16093	+	0.670261i
$546$		0			0
$547$	−180.236	−	312.177i	−0.329498	−	0.570708i	0.652914	−	0.757432i	$-0.273546\pi$
$547$	−180.236	−	312.177i	−0.329498	−	0.570708i	−0.982412	+	0.186724i	$0.940213\pi$
$548$	−55.5842	−	32.0915i	−0.101431	−	0.0585612i
$549$		0			0
$550$	55.9789	+	96.9583i	0.101780	+	0.176288i
$551$		−	878.634i		−	1.59462i
$552$		0			0
$553$	−379.732	−	599.732i	−0.686676	−	1.08451i
$554$	653.361	+	377.218i	1.17935	+	0.680899i
$555$		0			0
$556$	84.6876	−	146.683i	0.152316	−	0.263819i
$557$	−133.574	+	77.1188i	−0.239809	+	0.138454i	−0.615089	−	0.788458i	$-0.710880\pi$
$557$	−133.574	+	77.1188i	−0.239809	+	0.138454i	0.375280	+	0.926912i	$0.377547\pi$
$558$		0			0
$559$	−16.7618			−0.0299853
$560$	−1377.21	−	721.801i	−2.45930	−	1.28893i
$561$		0			0
$562$	−21.5071	−	37.2514i	−0.0382689	−	0.0662837i
$563$			792.263i			1.40722i	0.710588	+	0.703608i	$0.248429\pi$
$563$			792.263i			1.40722i	−0.710588	+	0.703608i	$0.751571\pi$
$564$		0			0
$565$	−199.974			−0.353936
$566$		−	1277.89i		−	2.25776i
$567$		0			0
$568$	−1778.87			−3.13181
$569$			257.560i			0.452654i	0.974051	+	0.226327i	$0.0726717\pi$
$569$			257.560i			0.452654i	−0.974051	+	0.226327i	$0.927328\pi$
$570$		0			0
$571$	673.354			1.17925			0.589627	−	0.807675i	$-0.299275\pi$
$571$	673.354			1.17925			0.589627	+	0.807675i	$0.299275\pi$
$572$	8.86630	−	5.11896i	0.0155005	−	0.00894923i
$573$		0			0
$574$	1190.21	−	48.6515i	2.07354	−	0.0847586i
$575$			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	$0.569824\pi$
$578$	885.385	+	511.177i	1.53181	+	0.884389i
$579$		0			0
$580$	−1024.30	+	1774.15i	−1.76604	+	3.05887i
$581$	−186.262	−	97.6211i	−0.320589	−	0.168023i
$582$		0			0
$583$	113.795			0.195188
$584$	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	−0.646243	−	0.763132i	$-0.723661\pi$
$587$	−181.073	+	104.543i	−0.308472	+	0.178097i	0.337770	+	0.941229i	$0.390327\pi$
$588$		0			0
$589$	−291.014	+	504.051i	−0.494082	+	0.855775i
$590$	679.475	−	392.295i	1.15165	−	0.664907i
$591$		0			0
$592$	161.255	−	279.302i	0.272391	−	0.471794i
$593$	−123.884	−	71.5246i	−0.208911	−	0.120615i	0.391894	−	0.920010i	$-0.371820\pi$
$593$	−123.884	−	71.5246i	−0.208911	−	0.120615i	−0.600805	+	0.799395i	$0.705153\pi$
$594$		0			0
$595$	−141.267	+	5.77450i	−0.237424	+	0.00970504i
$596$	−247.428	+	142.853i	−0.415148	+	0.239686i
$597$		0			0
$598$	39.7167			0.0664158
$599$		−	655.280i		−	1.09396i	−0.837147	−	0.546978i	$-0.815778\pi$
$599$		−	655.280i		−	1.09396i	0.837147	−	0.546978i	$-0.184222\pi$
$600$		0			0
$601$	−403.102	−	698.192i	−0.670718	−	1.16172i	−0.977701	−	0.210003i	$-0.932653\pi$
$601$	−403.102	−	698.192i	−0.670718	−	1.16172i	0.306983	−	0.951715i	$-0.400681\pi$
$602$	−1212.76	−	635.612i	−2.01455	−	1.05583i
$603$		0			0
$604$	−336.552	+	582.925i	−0.557205	+	0.965107i
$605$	553.990	+	319.846i	0.915685	+	0.528671i
$606$		0			0
$607$	593.332	+	1027.68i	0.977483	+	1.69305i	0.671486	+	0.741017i	$0.265656\pi$
$607$	593.332	+	1027.68i	0.977483	+	1.69305i	0.305996	+	0.952033i	$0.401010\pi$
$608$	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	$0.925687\pi$
$614$			1859.12i			3.02789i
$615$		0			0
$616$	488.213	−	19.9564i	0.792554	−	0.0323967i
$617$	161.583	+	93.2899i	0.261885	+	0.151199i	0.625194	−	0.780469i	$-0.285020\pi$
$617$	161.583	+	93.2899i	0.261885	+	0.151199i	−0.363309	+	0.931669i	$0.618353\pi$
$618$		0			0
$619$	−271.539	+	470.319i	−0.438673	+	0.759804i	−0.997587	−	0.0694215i	$-0.977885\pi$
$619$	−271.539	+	470.319i	−0.438673	+	0.759804i	0.558915	+	0.829225i	$0.311218\pi$
$620$	1175.24	−	678.524i	1.89555	−	1.09439i
$621$		0			0
$622$	1018.51			1.63748
$623$	−15.3652	−	375.895i	−0.0246633	−	0.603363i
$624$		0			0
$625$	384.557	+	666.072i	0.615291	+	1.06571i
$626$		−	1406.47i		−	2.24676i
$627$		0			0
$628$	1891.94			3.01264
$629$		−	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	$0.545965\pi$
$632$		−	2103.86i		−	3.32890i
$633$		0			0
$634$	2249.03			3.54737
$635$	−1095.97	+	632.756i	−1.72593	+	0.996466i
$636$		0			0
$637$	8.81806	+	12.7437i	0.0138431	+	0.0200058i
$638$		−	453.324i		−	0.710539i
$639$		0			0
$640$	24.2027	+	41.9203i	0.0378167	+	0.0655005i
$641$	286.732	+	165.545i	0.447320	+	0.258260i	0.706698	−	0.707516i	$-0.250184\pi$
$641$	286.732	+	165.545i	0.447320	+	0.258260i	−0.259378	+	0.965776i	$0.583517\pi$
$642$		0			0
$643$	457.251	−	791.983i	0.711122	−	1.23170i	−0.253314	−	0.967384i	$-0.581521\pi$
$643$	457.251	−	791.983i	0.711122	−	1.23170i	0.964436	−	0.264315i	$-0.0851459\pi$
$644$	2029.75	+	1063.80i	3.15178	+	1.65186i
$645$		0			0
$646$	307.612			0.476180
$647$	−364.736	+	210.580i	−0.563733	+	0.325472i	−0.754643	−	0.656136i	$-0.772190\pi$
$647$	−364.736	+	210.580i	−0.563733	+	0.325472i	0.190909	+	0.981608i	$0.438856\pi$
$648$		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
$653$	245.370	−	141.664i	0.375758	−	0.216944i	−0.300213	−	0.953872i	$-0.597058\pi$
$653$	245.370	−	141.664i	0.375758	−	0.216944i	0.675971	+	0.736928i	$0.263724\pi$
$654$		0			0
$655$	−362.654	+	628.135i	−0.553670	+	0.958984i
$656$	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	−0.572586	−	0.819845i	$-0.694060\pi$
$659$	−98.1069	+	56.6421i	−0.148872	+	0.0859515i	0.423713	+	0.905796i	$0.360726\pi$
$660$		0			0
$661$	−1068.00			−1.61574			−0.807869	−	0.589362i	$-0.799379\pi$
$661$	−1068.00			−1.61574			−0.807869	+	0.589362i	$0.799379\pi$
$662$			1885.52i			2.84822i
$663$		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
$668$	−880.615	−	508.423i	−1.31829	−	0.761112i
$669$		0			0
$670$	−375.896	−	651.071i	−0.561039	−	0.971748i
$671$	−35.0894	−	20.2589i	−0.0522943	−	0.0301921i
$672$		0			0
$673$	−438.286	−	759.133i	−0.651242	−	1.12798i	−0.982822	−	0.184557i	$-0.940915\pi$
$673$	−438.286	−	759.133i	−0.651242	−	1.12798i	0.331580	−	0.943427i	$-0.392418\pi$
$674$	466.503	+	269.335i	0.692140	+	0.399607i
$675$		0			0
$676$	−812.526	−	1407.34i	−1.20196	−	2.08186i
$677$		−	1188.95i		−	1.75621i	−0.478469	−	0.878104i	$-0.658808\pi$
$677$		−	1188.95i		−	1.75621i	0.478469	−	0.878104i	$-0.341192\pi$
$678$		0			0
$679$	23.4596	−	44.7612i	0.0345502	−	0.0659223i
$680$	−362.903	−	209.522i	−0.533681	−	0.308121i
$681$		0			0
$682$	−150.146	+	260.061i	−0.220156	+	0.381322i
$683$	−604.484	+	348.999i	−0.885043	+	0.510980i	−0.872318	−	0.488939i	$-0.837384\pi$
$683$	−604.484	+	348.999i	−0.885043	+	0.510980i	−0.0127252	+	0.999919i	$0.504051\pi$
$684$		0			0
$685$	−38.9068			−0.0567983
$686$	154.764	+	1256.42i	0.225603	+	1.83152i
$687$		0			0
$688$	−1009.24	−	1748.06i	−1.46692	−	2.54079i
$689$			10.6969i			0.0155252i
$690$		0			0
$691$	−1013.22			−1.46630			−0.733151	−	0.680066i	$-0.761951\pi$
$691$	−1013.22			−1.46630			−0.733151	+	0.680066i	$0.761951\pi$
$692$		−	1852.87i		−	2.67756i
$693$		0			0
$694$	−1018.10			−1.46700
$695$		−	102.673i		−	0.147731i
$696$		0			0
$697$	159.676			0.229091
$698$	767.013	−	442.835i	1.09887	−	0.634435i
$699$		0			0
$700$	−606.732	+	24.8010i	−0.866760	+	0.0354300i
$701$		−	910.897i		−	1.29942i	−0.760180	−	0.649712i	$-0.774889\pi$
$701$		−	910.897i		−	1.29942i	0.760180	−	0.649712i	$-0.225111\pi$
$702$		0			0
$703$	101.902	+	176.500i	0.144953	+	0.251067i
$704$	175.265	+	101.189i	0.248955	+	0.143734i
$705$		0			0
$706$	−999.883	+	1731.85i	−1.41626	+	2.45304i
$707$	17.2955	+	423.117i	0.0244632	+	0.598468i
$708$		0			0
$709$	−938.350			−1.32348			−0.661742	−	0.749732i	$-0.730183\pi$
$709$	−938.350			−1.32348			−0.661742	+	0.749732i	$0.730183\pi$
$710$	−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
$716$	−446.397	+	257.727i	−0.623459	+	0.359954i
$717$		0			0
$718$	−816.344	+	1413.95i	−1.13697	+	1.96929i
$719$	268.462	+	154.996i	0.373382	+	0.215572i	0.674935	−	0.737877i	$-0.264172\pi$
$719$	268.462	+	154.996i	0.373382	+	0.215572i	−0.301553	+	0.953449i	$0.597505\pi$
$720$		0			0
$721$	−530.459	+	1012.12i	−0.735727	+	1.40378i
$722$	−697.553	+	402.732i	−0.966140	+	0.557801i
$723$		0			0
$724$	1092.12			1.50845
$725$			329.156i			0.454009i
$726$		0			0
$727$	712.724	+	1234.47i	0.980363	+	1.69804i	0.660963	+	0.750418i	$0.270148\pi$
$727$	712.724	+	1234.47i	0.980363	+	1.69804i	0.319400	+	0.947620i	$0.396519\pi$
$728$	1.87593	+	45.8927i	0.00257682	+	0.0630394i
$729$		0			0
$730$	761.536	−	1319.02i	1.04320	−	1.80687i
$731$	−158.950	−	91.7699i	−0.217442	−	0.125540i
$732$		0			0
$733$	470.224	+	814.451i	0.641506	+	1.11112i	0.985097	+	0.172001i	$0.0550232\pi$
$733$	470.224	+	814.451i	0.641506	+	1.11112i	−0.343591	+	0.939119i	$0.611643\pi$
$734$	−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	$0.603301\pi$
$740$		−	475.187i		−	0.642145i
$741$		0			0
$742$	−405.628	+	773.944i	−0.546669	+	1.04305i
$743$	−626.132	−	361.497i	−0.842707	−	0.486537i	0.0154762	−	0.999880i	$-0.495074\pi$
$743$	−626.132	−	361.497i	−0.842707	−	0.486537i	−0.858184	+	0.513343i	$0.828407\pi$
$744$		0			0
$745$	−86.5953	+	149.987i	−0.116235	+	0.201325i
$746$	−698.795	+	403.449i	−0.936722	+	0.540817i
$747$		0			0
$748$	112.104			0.149872
$749$	32.2894	+	789.929i	0.0431100	+	1.05464i
$750$		0			0
$751$	115.796	+	200.565i	0.154189	+	0.267064i	0.932764	−	0.360489i	$-0.117390\pi$
$751$	115.796	+	200.565i	0.154189	+	0.267064i	−0.778574	+	0.627553i	$0.784057\pi$
$752$		−	759.504i		−	1.00998i
$753$		0			0
$754$	42.6131			0.0565160
$755$			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	$0.244592\pi$
$758$		−	939.282i		−	1.23916i
$759$		0			0
$760$	2912.24			3.83189
$761$	117.838	−	68.0337i	0.154846	−	0.0894004i	−0.420575	−	0.907258i	$-0.638172\pi$
$761$	117.838	−	68.0337i	0.154846	−	0.0894004i	0.575421	+	0.817857i	$0.304838\pi$
$762$		0			0
$763$	407.045	−	776.647i	0.533479	−	1.01789i
$764$			1660.52i			2.17345i
$765$		0			0
$766$	−1047.27	−	1813.92i	−1.36719	−	2.36804i
$767$	−9.98330	−	5.76386i	−0.0130160	−	0.00751481i
$768$		0			0
$769$	−402.392	+	696.964i	−0.523267	+	0.906325i	0.476367	+	0.879247i	$0.341954\pi$
$769$	−402.392	+	696.964i	−0.523267	+	0.906325i	−0.999633	+	0.0270779i	$0.991380\pi$
$770$	428.319	−	271.199i	0.556258	−	0.352206i
$771$		0			0
$772$	−1831.18			−2.37200
$773$	299.560	−	172.951i	0.387529	−	0.223740i	−0.293560	−	0.955941i	$-0.594840\pi$
$773$	299.560	−	172.951i	0.387529	−	0.223740i	0.681089	+	0.732201i	$0.261507\pi$
$774$		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
$779$	−961.031	+	554.852i	−1.23367	+	0.712262i
$780$		0			0
$781$	144.238	−	249.828i	0.184684	−	0.319882i
$782$	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
$787$	37.2833			0.0473739			0.0236870	−	0.999719i	$-0.492460\pi$
$787$	37.2833			0.0473739			0.0236870	+	0.999719i	$0.492460\pi$
$788$		−	943.045i		−	1.19676i
$789$		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
$794$	−1467.36	−	847.178i	−1.84805	−	1.06697i
$795$		0			0
$796$	−1232.97	−	2135.57i	−1.54896	−	2.68287i
$797$	1009.32	+	582.728i	1.26639	+	0.731152i	0.974304	−	0.225239i	$-0.0723162\pi$
$797$	1009.32	+	582.728i	1.26639	+	0.731152i	0.292089	+	0.956391i	$0.405650\pi$
$798$		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
$803$			238.060i			0.296463i
$804$		0			0
$805$	1387.99	−	56.7360i	1.72421	−	0.0704795i
$806$	−24.4461	−	14.1140i	−0.0303302	−	0.0175111i
$807$		0			0
$808$	−627.550	+	1086.95i	−0.776671	+	1.34523i
$809$	865.722	−	499.825i	1.07011	−	0.617830i	0.141901	−	0.989881i	$-0.454679\pi$
$809$	865.722	−	499.825i	1.07011	−	0.617830i	0.928212	+	0.372051i	$0.121345\pi$
$810$		0			0
$811$	634.194			0.781990			0.390995	−	0.920393i	$-0.372131\pi$
$811$	634.194			0.781990			0.390995	+	0.920393i	$0.372131\pi$
$812$	2177.77	+	1141.38i	2.68198	+	1.40564i
$813$		0			0
$814$	52.5757	+	91.0637i	0.0645893	+	0.111872i
$815$		−	54.1444i		−	0.0664349i
$816$		0			0
$817$	1275.55			1.56126
$818$			2154.79i			2.63422i
$819$		0			0
$820$	2587.37			3.15532
$821$			304.571i			0.370975i	0.982647	+	0.185488i	$0.0593864\pi$
$821$			304.571i			0.370975i	−0.982647	+	0.185488i	$0.940614\pi$
$822$		0			0
$823$	−850.775			−1.03375			−0.516874	−	0.856061i	$-0.672904\pi$
$823$	−850.775			−1.03375			−0.516874	+	0.856061i	$0.672904\pi$
$824$	−2933.07	+	1693.41i	−3.55955	+	2.05510i
$825$		0			0
$826$	−503.748	−	795.598i	−0.609865	−	0.963194i
$827$		−	0.427608i		−	0.000517059i	−1.00000		0.000258530i	$-0.999918\pi$
$827$		−	0.427608i		−	0.000517059i	1.00000		0.000258530i	$-8.22925e-5\pi$
$828$		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	$0.745972\pi$
$830$	−560.032	−	323.335i	−0.674738	−	0.389560i
$831$		0			0
$832$	−9.51191	+	16.4751i	−0.0114326	+	0.0198018i
$833$	13.8496	+	169.125i	0.0166262	+	0.203031i
$834$		0			0
$835$	−616.397			−0.738200
$836$	−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	−0.385048	−	0.922897i	$-0.625815\pi$
$839$	185.989	−	107.381i	0.221680	−	0.127987i	0.606728	+	0.794910i	$0.292482\pi$
$840$		0			0
$841$	245.887	−	425.889i	0.292374	−	0.506407i
$842$	148.580	−	85.7828i	0.176461	−	0.101880i
$843$		0			0
$844$	1259.58	−	2181.65i	1.49239	−	2.58490i
$845$	−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
$850$	−115.239			−0.135575
$851$			288.132i			0.338581i
$852$		0			0
$853$	192.842	+	334.012i	0.226075	+	0.391573i	0.956641	−	0.291269i	$-0.0940773\pi$
$853$	192.842	+	334.012i	0.226075	+	0.391573i	−0.730567	+	0.682841i	$0.760744\pi$
$854$	262.864	−	166.437i	0.307803	−	0.194891i
$855$		0			0
$856$	−1171.59	+	2029.26i	−1.36868	+	2.37063i
$857$	−1130.65	−	652.782i	−1.31931	−	0.761707i	−0.335696	−	0.941970i	$-0.608972\pi$
$857$	−1130.65	−	652.782i	−1.31931	−	0.761707i	−0.983618	+	0.180264i	$0.942305\pi$
$858$		0			0
$859$	−590.609	−	1022.96i	−0.687554	−	1.19088i	−0.972627	−	0.232372i	$-0.925351\pi$
$859$	−590.609	−	1022.96i	−0.687554	−	1.19088i	0.285073	−	0.958506i	$-0.407982\pi$
$860$	−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	0.879204	−	0.476445i	$-0.158075\pi$
$863$	782.044	+	451.514i	0.906193	+	0.523191i	0.0269886	+	0.999636i	$0.491408\pi$
$864$		0			0
$865$	−561.591	−	972.704i	−0.649238	−	1.12451i
$866$		−	584.450i		−	0.674884i
$867$		0			0
$868$	−871.297	−	1376.09i	−1.00380	−	1.58535i
$869$	295.470	+	170.590i	0.340012	+	0.196306i
$870$		0			0
$871$	−5.52291	+	9.56597i	−0.00634089	+	0.0109827i
$872$	2250.67	−	1299.43i	2.58104	−	1.49017i
$873$		0			0
$874$	−3022.37			−3.45809
$875$	551.336	−	349.089i	0.630099	−	0.398959i
$876$		0			0
$877$	277.106	+	479.961i	0.315970	+	0.547276i	0.979643	−	0.200747i	$-0.0643368\pi$
$877$	277.106	+	479.961i	0.315970	+	0.547276i	−0.663673	+	0.748023i	$0.731003\pi$
$878$		−	1235.53i		−	1.40721i
$879$		0			0
$880$	747.347			0.849258
$881$		−	750.603i		−	0.851990i	−0.904726	−	0.425995i	$-0.859924\pi$
$881$		−	750.603i		−	0.851990i	0.904726	−	0.425995i	$-0.140076\pi$
$882$		0			0
$883$	−1042.83			−1.18101			−0.590504	−	0.807035i	$-0.701071\pi$
$883$	−1042.83			−1.18101			−0.590504	+	0.807035i	$0.701071\pi$
$884$			10.5379i			0.0119207i
$885$		0			0
$886$	79.1190			0.0892991
$887$	−73.7419	+	42.5749i	−0.0831363	+	0.0479987i	−0.540992	−	0.841028i	$-0.681951\pi$
$887$	−73.7419	+	42.5749i	−0.0831363	+	0.0479987i	0.457856	+	0.889027i	$0.348618\pi$
$888$		0			0
$889$	812.526	+	1283.27i	0.913977	+	1.44350i
$890$		−	1156.87i		−	1.29985i
$891$		0			0
$892$	−1729.05	−	2994.81i	−1.93840	−	3.35741i
$893$	415.653	+	239.977i	0.465457	+	0.268732i
$894$		0			0
$895$	−156.230	+	270.599i	−0.174559	+	0.302345i
$896$	49.0846	−	31.0788i	0.0547819	−	0.0346862i
$897$		0			0
$898$	419.383			0.467019
$899$	−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
$905$	573.331	−	331.013i	0.633515	−	0.365760i
$906$		0			0
$907$	430.076	−	744.914i	0.474175	−	0.821294i	−0.525388	−	0.850863i	$-0.676080\pi$
$907$	430.076	−	744.914i	0.474175	−	0.821294i	0.999563	+	0.0295683i	$0.00941324\pi$
$908$	−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	0.466833	−	0.884345i	$-0.345395\pi$
$911$	1335.63	−	771.127i	1.46612	−	0.846462i	0.999282	+	0.0378830i	$0.0120614\pi$
$912$		0			0
$913$	101.076			0.110708
$914$		−	411.513i		−	0.450233i
$915$		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	$-0.198792\pi$
$920$	3565.62	+	2058.61i	3.87568	+	2.23762i
$921$		0			0
$922$	−306.558	−	530.974i	−0.332492	−	0.575894i
$923$	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
$929$			1466.71i			1.57880i	0.613879	+	0.789400i	$0.289608\pi$
$929$			1466.71i			1.57880i	−0.613879	+	0.789400i	$0.710392\pi$
$930$		0			0
$931$	−671.040	−	969.774i	−0.720773	−	1.04165i
$932$	3785.86	+	2185.77i	4.06208	+	2.34524i
$933$		0			0
$934$	639.357	−	1107.40i	0.684536	−	1.18565i
$935$	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	$0.445021\pi$
$938$	−762.340	+	482.690i	−0.812729	+	0.514595i
$939$		0			0
$940$	−559.527	−	969.129i	−0.595241	−	1.03099i
$941$		−	374.469i		−	0.397948i	−0.980005	−	0.198974i	$-0.936239\pi$
$941$		−	374.469i		−	0.397948i	0.980005	−	0.198974i	$-0.0637610\pi$
$942$		0			0
$943$	−1568.86			−1.66369
$944$		−	1388.19i		−	1.47054i
$945$		0			0
$946$	658.108			0.695674
$947$		−	164.942i		−	0.174173i	−0.996201	−	0.0870865i	$-0.972244\pi$
$947$		−	164.942i		−	0.174173i	0.996201	−	0.0870865i	$-0.0277556\pi$
$948$		0			0
$949$	−22.3780			−0.0235806
$950$	693.577	−	400.437i	0.730081	−	0.421513i
$951$		0			0
$952$	−233.471	+	445.465i	−0.245242	+	0.467926i
$953$		−	1354.42i		−	1.42122i	−0.703586	−	0.710610i	$-0.748419\pi$
$953$		−	1354.42i		−	1.42122i	0.703586	−	0.710610i	$-0.251581\pi$
$954$		0			0
$955$	503.291	+	871.726i	0.527006	+	0.912802i
$956$	−423.999	−	244.796i	−0.443514	−	0.256063i
$957$		0			0
$958$	1028.91	−	1782.12i	1.07402	−	1.86025i
$959$	1.90718	+	46.6572i	0.00198871	+	0.0486519i
$960$		0			0
$961$	−376.170			−0.391436
$962$	−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	−0.987413	−	0.158161i	$-0.949443\pi$
$967$	−344.963	+	597.493i	−0.356735	+	0.617883i	0.630678	+	0.776044i	$0.282777\pi$
$968$	1970.66	−	1137.76i	2.03581	−	1.17538i
$969$		0			0
$970$	77.7014	−	134.583i	0.0801046	−	0.138745i
$971$	665.293	+	384.107i	0.685163	+	0.395579i	0.801797	−	0.597596i	$-0.203877\pi$
$971$	665.293	+	384.107i	0.685163	+	0.395579i	−0.116634	+	0.993175i	$0.537211\pi$
$972$		0			0
$973$	−123.125	+	5.03292i	−0.126542	+	0.00517258i
$974$	−1220.90	+	704.889i	−1.25350	+	0.723706i
$975$		0			0
$976$	458.655			0.469933
$977$		−	1386.02i		−	1.41865i	−0.704880	−	0.709326i	$-0.748999\pi$
$977$		−	1386.02i		−	1.41865i	0.704880	−	0.709326i	$-0.251001\pi$
$978$		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
$983$	−454.966	−	262.675i	−0.462834	−	0.267217i	0.250401	−	0.968142i	$-0.419438\pi$
$983$	−454.966	−	262.675i	−0.462834	−	0.267217i	−0.713235	+	0.700925i	$0.752771\pi$
$984$		0			0
$985$	−285.830	−	495.072i	−0.290183	−	0.502611i
$986$	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	$0.763943\pi$
$992$		−	1392.35i		−	1.40358i
$993$		0			0
$994$	1184.99	+	1871.52i	1.19214	+	1.88282i
$995$	−1294.55	−	747.409i	−1.30106	−	0.751165i
$996$		0			0
$997$	598.383	−	1036.43i	0.600184	−	1.03955i	−0.392609	−	0.919705i	$-0.628427\pi$
$997$	598.383	−	1036.43i	0.600184	−	1.03955i	0.992793	−	0.119843i	$-0.0382392\pi$
$998$	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.j.b.44.1		22
3.2	odd	2		63.3.j.b.23.11	yes	22
7.4	even	3		189.3.n.b.179.11		22
9.2	odd	6		189.3.n.b.170.11		22
9.7	even	3		63.3.n.b.2.1	yes	22
21.2	odd	6		441.3.r.g.50.11		22
21.5	even	6		441.3.r.f.50.11		22
21.11	odd	6		63.3.n.b.32.1	yes	22
21.17	even	6		441.3.n.f.410.1		22
21.20	even	2		441.3.j.f.275.11		22
63.11	odd	6	inner	189.3.j.b.116.11		22
63.16	even	3		441.3.r.g.344.11		22
63.25	even	3		63.3.j.b.11.1	✓	22
63.34	odd	6		441.3.n.f.128.1		22
63.52	odd	6		441.3.j.f.263.1		22
63.61	odd	6		441.3.r.f.344.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.1	✓	22	63.25	even	3
63.3.j.b.23.11	yes	22	3.2	odd	2
63.3.n.b.2.1	yes	22	9.7	even	3
63.3.n.b.32.1	yes	22	21.11	odd	6
189.3.j.b.44.1		22	1.1	even	1	trivial
189.3.j.b.116.11		22	63.11	odd	6	inner
189.3.n.b.170.11		22	9.2	odd	6
189.3.n.b.179.11		22	7.4	even	3
441.3.j.f.263.1		22	63.52	odd	6
441.3.j.f.275.11		22	21.20	even	2
441.3.n.f.128.1		22	63.34	odd	6
441.3.n.f.410.1		22	21.17	even	6
441.3.r.f.50.11		22	21.5	even	6
441.3.r.f.344.11		22	63.61	odd	6
441.3.r.g.50.11		22	21.2	odd	6
441.3.r.g.344.11		22	63.16	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-3.69072i q^{2} -9.62138 q^{4} +(-5.05096 + 2.91617i) q^{5} +(3.74467 + 5.91417i) q^{7} +20.7469i q^{8} +(10.7628 + 18.6416i) q^{10} +(-2.91374 - 1.68225i) q^{11} +(0.158134 - 0.273895i) q^{13} +(21.8275 - 13.8205i) q^{14} +38.0855 q^{16} +(2.99912 - 1.73154i) q^{17} +(-12.0337 + 20.8430i) q^{19} +(48.5972 - 28.0576i) q^{20} +(-6.20870 + 10.7538i) q^{22} +(-29.4672 + 17.0129i) q^{23} +(4.50810 - 7.80826i) q^{25} +(-1.01087 - 0.583626i) q^{26} +(-36.0289 - 56.9025i) q^{28} +(-31.6161 + 18.2536i) q^{29} +24.1833 q^{31} -57.5750i q^{32} +(-6.39064 - 11.0689i) q^{34} +(-36.1609 - 18.9521i) q^{35} +(4.23403 - 7.33356i) q^{37} +(76.9256 + 44.4130i) q^{38} +(-60.5016 - 104.792i) q^{40} +(39.9308 + 23.0541i) q^{41} +(-26.4994 - 45.8984i) q^{43} +(28.0342 + 16.1855i) q^{44} +(62.7897 + 108.755i) q^{46} -19.9421i q^{47} +(-20.9549 + 44.2933i) q^{49} +(-28.8181 - 16.6381i) q^{50} +(-1.52146 + 2.63525i) q^{52} +(-29.2909 + 16.9111i) q^{53} +19.6229 q^{55} +(-122.701 + 77.6905i) q^{56} +(67.3688 + 116.686i) q^{58} -36.4493i q^{59} +12.0428 q^{61} -89.2535i q^{62} -60.1511 q^{64} +1.84458i q^{65} -34.9256 q^{67} +(-28.8557 + 16.6599i) q^{68} +(-69.9469 + 133.460i) q^{70} +85.7413i q^{71} +(-35.3783 - 61.2770i) q^{73} +(-27.0661 - 15.6266i) q^{74} +(115.781 - 200.539i) q^{76} +(-0.961895 - 23.5318i) q^{77} -101.406 q^{79} +(-192.368 + 111.064i) q^{80} +(85.0860 - 147.373i) q^{82} +(-26.0171 + 15.0210i) q^{83} +(-10.0990 + 17.4919i) q^{85} +(-169.398 + 97.8019i) q^{86} +(34.9015 - 60.4511i) q^{88} +(-46.5438 - 26.8721i) q^{89} +(2.21202 - 0.0904195i) q^{91} +(283.515 - 163.688i) q^{92} -73.6006 q^{94} -140.369i q^{95} +(-3.60974 - 6.25225i) q^{97} +(163.474 + 77.3384i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31}+ \cdots + 483 q^{98}+O(q^{100}) \) 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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