LMFDB - Embedded newform 189.4.s.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(17,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	189.17
Dual form			189.4.s.a.89.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52419 - 1.45734i) q^{2} +(0.247680 + 0.428994i) q^{4} -17.2113 q^{5} +(17.7231 + 5.37495i) q^{7} +21.8736i q^{8} +O(q^{10})$	\(q+(-2.52419 - 1.45734i) q^{2} +(0.247680 + 0.428994i) q^{4} -17.2113 q^{5} +(17.7231 + 5.37495i) q^{7} +21.8736i q^{8} +(43.4446 + 25.0828i) q^{10} +35.6923i q^{11} +(-8.99430 - 5.19286i) q^{13} +(-36.9034 - 39.3960i) q^{14} +(33.8587 - 58.6451i) q^{16} +(64.1402 - 111.094i) q^{17} +(-84.7576 + 48.9348i) q^{19} +(-4.26290 - 7.38356i) q^{20} +(52.0158 - 90.0941i) q^{22} -25.5640i q^{23} +171.230 q^{25} +(15.1355 + 26.2155i) q^{26} +(2.08385 + 8.93439i) q^{28} +(14.1366 - 8.16176i) q^{29} +(160.589 - 92.7160i) q^{31} +(-19.3867 + 11.1929i) q^{32} +(-323.804 + 186.948i) q^{34} +(-305.039 - 92.5101i) q^{35} +(-0.462855 - 0.801688i) q^{37} +285.259 q^{38} -376.474i q^{40} +(231.546 - 401.049i) q^{41} +(-43.2469 - 74.9058i) q^{43} +(-15.3118 + 8.84027i) q^{44} +(-37.2555 + 64.5283i) q^{46} +(143.746 - 248.976i) q^{47} +(285.220 + 190.522i) q^{49} +(-432.217 - 249.541i) q^{50} -5.14467i q^{52} +(334.811 + 193.303i) q^{53} -614.313i q^{55} +(-117.570 + 387.669i) q^{56} -47.5778 q^{58} +(45.2274 + 78.3362i) q^{59} +(120.761 + 69.7214i) q^{61} -540.475 q^{62} -476.492 q^{64} +(154.804 + 89.3761i) q^{65} +(-151.612 - 262.599i) q^{67} +63.5449 q^{68} +(635.157 + 678.059i) q^{70} +351.969i q^{71} +(761.691 + 439.763i) q^{73} +2.69815i q^{74} +(-41.9855 - 24.2403i) q^{76} +(-191.844 + 632.580i) q^{77} +(7.12361 - 12.3385i) q^{79} +(-582.755 + 1009.36i) q^{80} +(-1168.93 + 674.881i) q^{82} +(125.688 + 217.699i) q^{83} +(-1103.94 + 1912.08i) q^{85} +252.102i q^{86} -780.720 q^{88} +(505.658 + 875.825i) q^{89} +(-131.496 - 140.378i) q^{91} +(10.9668 - 6.33169i) q^{92} +(-725.684 + 418.974i) q^{94} +(1458.79 - 842.234i) q^{95} +(1125.76 - 649.959i) q^{97} +(-442.293 - 896.575i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	$ 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) $ 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.52419	−	1.45734i	−0.892435	−	0.515248i	−0.0176967	−	0.999843i	$-0.505633\pi$
$2$	−2.52419	−	1.45734i	−0.892435	−	0.515248i	−0.874738	+	0.484596i	$0.838967\pi$
$3$		0			0
$3$		0			0
$4$	0.247680	+	0.428994i	0.0309600	+	0.0536243i
$5$	−17.2113			−1.53943			−0.769715	−	0.638388i	$-0.779602\pi$
$5$	−17.2113			−1.53943			−0.769715	+	0.638388i	$0.779602\pi$
$6$		0			0
$7$	17.7231	+	5.37495i	0.956960	+	0.290220i
$7$	17.7231	+	5.37495i	0.956960	+	0.290220i
$8$			21.8736i			0.966687i
$9$		0			0
$10$	43.4446	+	25.0828i	1.37384	+	0.793187i
$11$			35.6923i			0.978331i	0.872191	+	0.489165i	$0.162699\pi$
$11$			35.6923i			0.978331i	−0.872191	+	0.489165i	$0.837301\pi$
$12$		0			0
$13$	−8.99430	−	5.19286i	−0.191890	−	0.110788i	0.400977	−	0.916088i	$-0.368671\pi$
$13$	−8.99430	−	5.19286i	−0.191890	−	0.110788i	−0.592867	+	0.805300i	$0.702004\pi$
$14$	−36.9034	−	39.3960i	−0.704489	−	0.752074i
$15$		0			0
$16$	33.8587	−	58.6451i	0.529043	−	0.916329i
$17$	64.1402	−	111.094i	0.915075	−	1.58496i	0.108285	−	0.994120i	$-0.465464\pi$
$17$	64.1402	−	111.094i	0.915075	−	1.58496i	0.806791	−	0.590837i	$-0.201202\pi$
$18$		0			0
$19$	−84.7576	+	48.9348i	−1.02341	+	0.590864i	−0.915089	−	0.403253i	$-0.867880\pi$
$19$	−84.7576	+	48.9348i	−1.02341	+	0.590864i	−0.108317	+	0.994116i	$0.534546\pi$
$20$	−4.26290	−	7.38356i	−0.0476607	−	0.0825508i
$21$		0			0
$22$	52.0158	−	90.0941i	0.504082	−	0.873096i
$23$		−	25.5640i		−	0.231759i	−0.993263	−	0.115880i	$-0.963031\pi$
$23$		−	25.5640i		−	0.231759i	0.993263	−	0.115880i	$-0.0369687\pi$
$24$		0			0
$25$	171.230			1.36984
$26$	15.1355	+	26.2155i	0.114166	+	0.197742i
$27$		0			0
$28$	2.08385	+	8.93439i	0.0140646	+	0.0603015i
$29$	14.1366	−	8.16176i	0.0905206	−	0.0522621i	−0.454056	−	0.890973i	$-0.650024\pi$
$29$	14.1366	−	8.16176i	0.0905206	−	0.0522621i	0.544577	+	0.838711i	$0.316690\pi$
$30$		0			0
$31$	160.589	−	92.7160i	0.930406	−	0.537170i	0.0434664	−	0.999055i	$-0.486160\pi$
$31$	160.589	−	92.7160i	0.930406	−	0.537170i	0.886940	+	0.461884i	$0.152827\pi$
$32$	−19.3867	+	11.1929i	−0.107097	+	0.0618327i
$33$		0			0
$34$	−323.804	+	186.948i	−1.63329	+	0.942981i
$35$	−305.039	−	92.5101i	−1.47317	−	0.446773i
$36$		0			0
$37$	−0.462855	−	0.801688i	−0.00205656	−	0.00356207i	0.864995	−	0.501780i	$-0.167321\pi$
$37$	−0.462855	−	0.801688i	−0.00205656	−	0.00356207i	−0.867052	+	0.498218i	$0.833988\pi$
$38$	285.259			1.21776
$39$		0			0
$40$		−	376.474i		−	1.48815i
$41$	231.546	−	401.049i	0.881984	−	1.52764i	0.0328523	−	0.999460i	$-0.489541\pi$
$41$	231.546	−	401.049i	0.881984	−	1.52764i	0.849132	−	0.528181i	$-0.177126\pi$
$42$		0			0
$43$	−43.2469	−	74.9058i	−0.153374	−	0.265652i	0.779092	−	0.626910i	$-0.215681\pi$
$43$	−43.2469	−	74.9058i	−0.153374	−	0.265652i	−0.932466	+	0.361258i	$0.882347\pi$
$44$	−15.3118	+	8.84027i	−0.0524623	+	0.0302891i
$45$		0			0
$46$	−37.2555	+	64.5283i	−0.119413	+	0.206830i
$47$	143.746	−	248.976i	0.446118	−	0.772698i	−0.552012	−	0.833836i	$-0.686140\pi$
$47$	143.746	−	248.976i	0.446118	−	0.772698i	0.998129	+	0.0611380i	$0.0194730\pi$
$48$		0			0
$49$	285.220	+	190.522i	0.831545	+	0.555458i
$50$	−432.217	−	249.541i	−1.22250	−	0.705808i
$51$		0			0
$52$		−	5.14467i		−	0.0137200i
$53$	334.811	+	193.303i	0.867732	+	0.500985i	0.866594	−	0.499014i	$-0.166304\pi$
$53$	334.811	+	193.303i	0.867732	+	0.500985i	0.00113806	+	0.999999i	$0.499638\pi$
$54$		0			0
$55$		−	614.313i		−	1.50607i
$56$	−117.570	+	387.669i	−0.280552	+	0.925081i
$57$		0			0
$58$	−47.5778			−0.107712
$59$	45.2274	+	78.3362i	0.0997985	+	0.172856i	0.911601	−	0.411076i	$-0.134847\pi$
$59$	45.2274	+	78.3362i	0.0997985	+	0.172856i	−0.811803	+	0.583932i	$0.801514\pi$
$60$		0			0
$61$	120.761	+	69.7214i	0.253473	+	0.146343i	0.621354	−	0.783530i	$-0.286583\pi$
$61$	120.761	+	69.7214i	0.253473	+	0.146343i	−0.367880	+	0.929873i	$0.619916\pi$
$62$	−540.475			−1.10710
$63$		0			0
$64$	−476.492			−0.930649
$65$	154.804	+	89.3761i	0.295401	+	0.170550i
$66$		0			0
$67$	−151.612	−	262.599i	−0.276452	−	0.478830i	0.694048	−	0.719929i	$-0.255826\pi$
$67$	−151.612	−	262.599i	−0.276452	−	0.478830i	−0.970501	+	0.241099i	$0.922492\pi$
$68$	63.5449			0.113323
$69$		0			0
$70$	635.157	+	678.059i	1.08451	+	1.15776i
$71$			351.969i			0.588325i	0.955755	+	0.294163i	$0.0950407\pi$
$71$			351.969i			0.588325i	−0.955755	+	0.294163i	$0.904959\pi$
$72$		0			0
$73$	761.691	+	439.763i	1.22122	+	0.705073i	0.965179	−	0.261592i	$-0.0842475\pi$
$73$	761.691	+	439.763i	1.22122	+	0.705073i	0.256044	+	0.966665i	$0.417581\pi$
$74$			2.69815i			0.00423856i
$75$		0			0
$76$	−41.9855	−	24.2403i	−0.0633693	−	0.0365863i
$77$	−191.844	+	632.580i	−0.283931	+	0.936223i
$78$		0			0
$79$	7.12361	−	12.3385i	0.0101452	−	0.0175720i	−0.860908	−	0.508760i	$-0.830104\pi$
$79$	7.12361	−	12.3385i	0.0101452	−	0.0175720i	0.871053	+	0.491188i	$0.163437\pi$
$80$	−582.755	+	1009.36i	−0.814424	+	1.41062i
$81$		0			0
$82$	−1168.93	+	674.881i	−1.57423	+	0.908880i
$83$	125.688	+	217.699i	0.166218	+	0.287898i	0.937087	−	0.349095i	$-0.113511\pi$
$83$	125.688	+	217.699i	0.166218	+	0.287898i	−0.770869	+	0.636994i	$0.780178\pi$
$84$		0			0
$85$	−1103.94	+	1912.08i	−1.40869	+	2.43993i
$86$			252.102i			0.316102i
$87$		0			0
$88$	−780.720			−0.945739
$89$	505.658	+	875.825i	0.602243	+	1.04312i	0.992481	+	0.122401i	$0.0390595\pi$
$89$	505.658	+	875.825i	0.602243	+	1.04312i	−0.390238	+	0.920714i	$0.627607\pi$
$90$		0			0
$91$	−131.496	−	140.378i	−0.151478	−	0.161710i
$92$	10.9668	−	6.33169i	0.0124279	−	0.00717527i
$93$		0			0
$94$	−725.684	+	418.974i	−0.796262	+	0.459722i
$95$	1458.79	−	842.234i	1.57546	−	0.909593i
$96$		0			0
$97$	1125.76	−	649.959i	1.17839	−	0.680344i	0.222748	−	0.974876i	$-0.428497\pi$
$97$	1125.76	−	649.959i	1.17839	−	0.680344i	0.955642	+	0.294532i	$0.0951638\pi$
$98$	−442.293	−	896.575i	−0.455901	−	0.924161i
$99$		0			0
$100$	42.4103	+	73.4568i	0.0424103	+	0.0734568i
$101$	852.814			0.840180			0.420090	−	0.907482i	$-0.361998\pi$
$101$	852.814			0.840180			0.420090	+	0.907482i	$0.361998\pi$
$102$		0			0
$103$		−	42.6846i		−	0.0408334i	−0.999792	−	0.0204167i	$-0.993501\pi$
$103$		−	42.6846i		−	0.0408334i	0.999792	−	0.0204167i	$-0.00649929\pi$
$104$	113.587	−	196.738i	0.107097	−	0.185498i
$105$		0			0
$106$	−563.417	−	975.866i	−0.516263	−	0.894193i
$107$	−718.939	+	415.080i	−0.649556	+	0.375021i	−0.788286	−	0.615309i	$-0.789031\pi$
$107$	−718.939	+	415.080i	−0.649556	+	0.375021i	0.138730	+	0.990330i	$0.455698\pi$
$108$		0			0
$109$	689.418	−	1194.11i	0.605819	−	1.04931i	−0.386103	−	0.922456i	$-0.626179\pi$
$109$	689.418	−	1194.11i	0.605819	−	1.04931i	0.991921	−	0.126853i	$-0.0404877\pi$
$110$	−895.262	+	1550.64i	−0.775999	+	1.34407i
$111$		0			0
$112$	915.298	−	857.386i	0.772210	−	0.723352i
$113$	−1325.63	−	765.354i	−1.10358	−	0.637155i	−0.166424	−	0.986054i	$-0.553222\pi$
$113$	−1325.63	−	765.354i	−1.10358	−	0.637155i	−0.937160	+	0.348900i	$0.886555\pi$
$114$		0			0
$115$			439.991i			0.356777i
$116$	7.00269	+	4.04301i	0.00560503	+	0.00323607i
$117$		0			0
$118$		−	263.647i		−	0.205684i
$119$	1733.89	−	1624.19i	1.33568	−	1.25117i
$120$		0			0
$121$	57.0592			0.0428694
$122$	−203.216	−	351.980i	−0.150806	−	0.261203i
$123$		0			0
$124$	79.5492	+	45.9278i	0.0576107	+	0.0332616i
$125$	−795.686			−0.569347
$126$		0			0
$127$	106.298			0.0742710			0.0371355	−	0.999310i	$-0.488177\pi$
$127$	106.298			0.0742710			0.0371355	+	0.999310i	$0.488177\pi$
$128$	1357.85	+	783.955i	0.937641	+	0.541347i
$129$		0			0
$130$	−260.503	−	451.204i	−0.175751	−	0.304409i
$131$	27.2836			0.0181968			0.00909841	−	0.999959i	$-0.497104\pi$
$131$	27.2836			0.0181968			0.00909841	+	0.999959i	$0.497104\pi$
$132$		0			0
$133$	−1765.19	+	411.711i	−1.15084	+	0.268420i
$134$			883.799i			0.569766i
$135$		0			0
$136$	2430.03	+	1402.98i	1.53216	+	0.884591i
$137$		−	86.9719i		−	0.0542373i	−0.999632	−	0.0271186i	$-0.991367\pi$
$137$		−	86.9719i		−	0.0542373i	0.999632	−	0.0271186i	$-0.00863319\pi$
$138$		0			0
$139$	−248.393	−	143.410i	−0.151572	−	0.0875099i	0.422296	−	0.906458i	$-0.361224\pi$
$139$	−248.393	−	143.410i	−0.151572	−	0.0875099i	−0.573868	+	0.818948i	$0.694558\pi$
$140$	−35.8658	−	153.773i	−0.0216515	−	0.0928299i
$141$		0			0
$142$	512.939	−	888.437i	0.303133	−	0.525042i
$143$	185.345	−	321.027i	0.108387	−	0.187732i
$144$		0			0
$145$	−243.310	+	140.475i	−0.139350	+	0.0804538i
$146$	−1281.77	−	2220.09i	−0.726574	−	1.25846i
$147$		0			0
$148$	0.229280	−	0.397124i	0.000127342	−	0.000220563i
$149$		−	2020.90i		−	1.11113i	−0.831473	−	0.555566i	$-0.812502\pi$
$149$		−	2020.90i		−	1.11113i	0.831473	−	0.555566i	$-0.187498\pi$
$150$		0			0
$151$	−1919.05			−1.03424			−0.517120	−	0.855913i	$-0.672996\pi$
$151$	−1919.05			−1.03424			−0.517120	+	0.855913i	$0.672996\pi$
$152$	−1070.38	−	1853.95i	−0.571180	−	0.989313i
$153$		0			0
$154$	1406.14	−	1317.17i	0.735777	−	0.689223i
$155$	−2763.95	+	1595.77i	−1.43230	+	0.826936i
$156$		0			0
$157$	784.058	−	452.676i	0.398565	−	0.230111i	−0.287300	−	0.957841i	$-0.592758\pi$
$157$	784.058	−	452.676i	0.398565	−	0.230111i	0.685864	+	0.727729i	$0.259424\pi$
$158$	−35.9626	+	20.7630i	−0.0181078	+	0.0104545i
$159$		0			0
$160$	333.671	−	192.645i	0.164869	−	0.0951871i
$161$	137.405	−	453.075i	0.0672612	−	0.221784i
$162$		0			0
$163$	1124.59	+	1947.85i	0.540397	+	0.935995i	0.998881	+	0.0472926i	$0.0150593\pi$
$163$	1124.59	+	1947.85i	0.540397	+	0.935995i	−0.458484	+	0.888703i	$0.651607\pi$
$164$	229.397			0.109225
$165$		0			0
$166$		−	732.683i		−	0.342574i
$167$	−1097.47	+	1900.88i	−0.508534	+	0.880807i	0.491417	+	0.870924i	$0.336479\pi$
$167$	−1097.47	+	1900.88i	−0.508534	+	0.880807i	−0.999951	+	0.00988229i	$0.996854\pi$
$168$		0			0
$169$	−1044.57	−	1809.25i	−0.475452	−	0.823507i
$170$	5573.10	−	3217.63i	2.51434	−	1.45165i
$171$		0			0
$172$	21.4228	−	37.1053i	0.00949692	−	0.0164491i
$173$	1351.18	−	2340.32i	0.593807	−	1.02850i	−0.399908	−	0.916555i	$-0.630958\pi$
$173$	1351.18	−	2340.32i	0.593807	−	1.02850i	0.993714	−	0.111948i	$-0.0357089\pi$
$174$		0			0
$175$	3034.74	+	920.354i	1.31088	+	0.397556i
$176$	2093.18	+	1208.50i	0.896473	+	0.517579i
$177$		0			0
$178$		−	2947.66i		−	1.24122i
$179$	−351.098	−	202.707i	−0.146605	−	0.0846425i	0.424903	−	0.905239i	$-0.360308\pi$
$179$	−351.098	−	202.707i	−0.146605	−	0.0846425i	−0.571508	+	0.820596i	$0.693641\pi$
$180$		0			0
$181$		−	3023.81i		−	1.24176i	−0.783907	−	0.620878i	$-0.786776\pi$
$181$		−	3023.81i		−	1.24176i	0.783907	−	0.620878i	$-0.213224\pi$
$182$	127.342	+	545.974i	0.0518639	+	0.222364i
$183$		0			0
$184$	559.178			0.224039
$185$	7.96635	+	13.7981i	0.00316593	+	0.00548356i
$186$		0			0
$187$	3965.20	+	2289.31i	1.55061	+	0.895246i
$188$	142.412			0.0552472
$189$		0			0
$190$	−4909.68			−1.87466
$191$	890.669	+	514.228i	0.337416	+	0.194807i	0.659129	−	0.752030i	$-0.270925\pi$
$191$	890.669	+	514.228i	0.337416	+	0.194807i	−0.321713	+	0.946837i	$0.604258\pi$
$192$		0			0
$193$	2051.01	+	3552.46i	0.764948	+	1.32493i	0.940274	+	0.340419i	$0.110569\pi$
$193$	2051.01	+	3552.46i	0.764948	+	1.32493i	−0.175326	+	0.984510i	$0.556098\pi$
$194$	−3788.85			−1.40218
$195$		0			0
$196$	−11.0896	+	169.546i	−0.00404140	+	0.0617879i
$197$			805.333i			0.291257i	0.989339	+	0.145628i	$0.0465204\pi$
$197$			805.333i			0.291257i	−0.989339	+	0.145628i	$0.953480\pi$
$198$		0			0
$199$	−1923.11	−	1110.31i	−0.685054	−	0.395516i	0.116702	−	0.993167i	$-0.462768\pi$
$199$	−1923.11	−	1110.31i	−0.685054	−	0.395516i	−0.801757	+	0.597651i	$0.796101\pi$
$200$			3745.43i			1.32421i
$201$		0			0
$202$	−2152.66	−	1242.84i	−0.749806	−	0.432901i
$203$	294.414	−	68.6687i	0.101792	−	0.0237418i
$204$		0			0
$205$	−3985.21	+	6902.59i	−1.35775	+	2.35170i
$206$	−62.2060	+	107.744i	−0.0210393	+	0.0364411i
$207$		0			0
$208$	−609.072	+	351.648i	−0.203036	+	0.117223i
$209$	−1746.60	−	3025.19i	−0.578060	−	1.00123i
$210$		0			0
$211$	1123.34	−	1945.68i	0.366511	−	0.634816i	−0.622506	−	0.782615i	$-0.713885\pi$
$211$	1123.34	−	1945.68i	0.366511	−	0.634816i	0.989017	+	0.147799i	$0.0472188\pi$
$212$			191.509i			0.0620420i
$213$		0			0
$214$	2419.65			0.772915
$215$	744.337	+	1289.23i	0.236109	+	0.408952i
$216$		0			0
$217$	3344.48	−	780.062i	1.04626	−	0.244028i
$218$	−3480.44	+	2009.43i	−1.08131	+	0.624293i
$219$		0			0
$220$	263.536	−	152.153i	0.0807619	−	0.0466279i
$221$	−1153.79	+	666.142i	−0.351188	+	0.202758i
$222$		0			0
$223$	3632.93	−	2097.48i	1.09094	−	0.629854i	0.157112	−	0.987581i	$-0.449782\pi$
$223$	3632.93	−	2097.48i	1.09094	−	0.629854i	0.933826	+	0.357727i	$0.116448\pi$
$224$	−403.755	+	94.1712i	−0.120433	+	0.0280896i
$225$		0			0
$226$	2230.76	+	3863.79i	0.656585	+	1.13724i
$227$	2341.01			0.684487			0.342243	−	0.939611i	$-0.388813\pi$
$227$	2341.01			0.684487			0.342243	+	0.939611i	$0.388813\pi$
$228$		0			0
$229$		−	3060.73i		−	0.883225i	−0.897206	−	0.441613i	$-0.854407\pi$
$229$		−	3060.73i		−	0.883225i	0.897206	−	0.441613i	$-0.145593\pi$
$230$	641.217	−	1110.62i	0.183829	−	0.318400i
$231$		0			0
$232$	178.527	+	309.218i	0.0505211	+	0.0875051i
$233$	−2201.24	+	1270.89i	−0.618920	+	0.357333i	−0.776448	−	0.630181i	$-0.782981\pi$
$233$	−2201.24	+	1270.89i	−0.618920	+	0.357333i	0.157529	+	0.987514i	$0.449647\pi$
$234$		0			0
$235$	−2474.06	+	4285.20i	−0.686766	+	1.18951i
$236$	−22.4039	+	38.8046i	−0.00617952	+	0.0107032i
$237$		0			0
$238$	−6743.66	+	1572.88i	−1.83667	+	0.428381i
$239$	1543.33	+	891.040i	0.417697	+	0.241157i	0.694091	−	0.719887i	$-0.255806\pi$
$239$	1543.33	+	891.040i	0.417697	+	0.241157i	−0.276395	+	0.961044i	$0.589140\pi$
$240$		0			0
$241$		−	1610.36i		−	0.430426i	−0.976567	−	0.215213i	$-0.930955\pi$
$241$		−	1610.36i		−	0.430426i	0.976567	−	0.215213i	$-0.0690445\pi$
$242$	−144.028	−	83.1547i	−0.0382582	−	0.0220884i
$243$		0			0
$244$			69.0743i			0.0181231i
$245$	−4909.02	−	3279.14i	−1.28010	−	0.855088i
$246$		0			0
$247$	1016.45			0.261842
$248$	2028.03	+	3512.66i	0.519276	+	0.899412i
$249$		0			0
$250$	2008.46	+	1159.59i	0.508105	+	0.293355i
$251$	603.105			0.151664			0.0758320	−	0.997121i	$-0.475839\pi$
$251$	603.105			0.151664			0.0758320	+	0.997121i	$0.475839\pi$
$252$		0			0
$253$	912.439			0.226737
$254$	−268.316	−	154.912i	−0.0662820	−	0.0382679i
$255$		0			0
$256$	−379.008	−	656.461i	−0.0925312	−	0.160269i
$257$	1336.18			0.324313			0.162157	−	0.986765i	$-0.448155\pi$
$257$	1336.18			0.324313			0.162157	+	0.986765i	$0.448155\pi$
$258$		0			0
$259$	−3.89421	−	16.6962i	−0.000934264	−	0.00400562i
$260$			88.5467i			0.0211209i
$261$		0			0
$262$	−68.8690	−	39.7615i	−0.0162395	−	0.00937587i
$263$			5754.61i			1.34922i	0.738175	+	0.674609i	$0.235688\pi$
$263$			5754.61i			1.34922i	−0.738175	+	0.674609i	$0.764312\pi$
$264$		0			0
$265$	−5762.54	−	3327.01i	−1.33581	−	0.771231i
$266$	5055.68	+	1533.25i	1.16535	+	0.353420i
$267$		0			0
$268$	75.1023	−	130.081i	0.0171179	−	0.0296491i
$269$	926.438	−	1604.64i	0.209985	−	0.363704i	−0.741725	−	0.670705i	$-0.765992\pi$
$269$	926.438	−	1604.64i	0.209985	−	0.363704i	0.951709	+	0.307000i	$0.0993252\pi$
$270$		0			0
$271$	−6459.12	+	3729.17i	−1.44784	+	0.835908i	−0.998352	−	0.0573809i	$-0.981725\pi$
$271$	−6459.12	+	3729.17i	−1.44784	+	0.835908i	−0.449483	+	0.893289i	$0.648392\pi$
$272$	−4343.41	−	7523.01i	−0.968228	−	1.67702i
$273$		0			0
$274$	−126.748	+	219.533i	−0.0279456	+	0.0484032i
$275$			6111.61i			1.34016i
$276$		0			0
$277$	1370.01			0.297169			0.148585	−	0.988900i	$-0.452528\pi$
$277$	1370.01			0.297169			0.148585	+	0.988900i	$0.452528\pi$
$278$	417.994	+	723.987i	0.0901785	+	0.156194i
$279$		0			0
$280$	2023.53	−	6672.31i	0.431890	−	1.42410i
$281$	3574.32	−	2063.63i	0.758811	−	0.438100i	−0.0700574	−	0.997543i	$-0.522318\pi$
$281$	3574.32	−	2063.63i	0.758811	−	0.438100i	0.828869	+	0.559443i	$0.188985\pi$
$282$		0			0
$283$	−1647.02	+	950.906i	−0.345954	+	0.199737i	−0.662902	−	0.748706i	$-0.730675\pi$
$283$	−1647.02	+	950.906i	−0.345954	+	0.199737i	0.316948	+	0.948443i	$0.397342\pi$
$284$	−150.993	+	87.1758i	−0.0315485	+	0.0182145i
$285$		0			0
$286$	−935.692	+	540.222i	−0.193457	+	0.111692i
$287$	6259.33	−	5863.30i	1.28738	−	1.20592i
$288$		0			0
$289$	−5771.43	−	9996.41i	−1.17473	−	2.03469i
$290$	818.878			0.165814
$291$		0			0
$292$			435.681i			0.0873162i
$293$	−3959.77	+	6858.52i	−0.789530	+	1.36751i	0.136726	+	0.990609i	$0.456342\pi$
$293$	−3959.77	+	6858.52i	−0.789530	+	1.36751i	−0.926255	+	0.376896i	$0.876991\pi$
$294$		0			0
$295$	−778.425	−	1348.27i	−0.153633	−	0.266100i
$296$	17.5358	−	10.1243i	0.00344341	−	0.00198805i
$297$		0			0
$298$	−2945.14	+	5101.13i	−0.572508	+	0.991612i
$299$	−132.750	+	229.930i	−0.0256761	+	0.0444723i
$300$		0			0
$301$	−363.856	−	1560.02i	−0.0696754	−	0.298730i
$302$	4844.05	+	2796.71i	0.922993	+	0.532890i
$303$		0			0
$304$			6627.48i			1.25037i
$305$	−2078.46	−	1200.00i	−0.390204	−	0.225284i
$306$		0			0
$307$			1709.99i			0.317896i	0.987287	+	0.158948i	$0.0508102\pi$
$307$			1709.99i			0.317896i	−0.987287	+	0.158948i	$0.949190\pi$
$308$	−318.889	+	74.3772i	−0.0589948	+	0.0137599i
$309$		0			0
$310$	9302.30			1.70431
$311$	−5182.89	−	8977.03i	−0.944999	−	1.63679i	−0.755753	−	0.654856i	$-0.772729\pi$
$311$	−5182.89	−	8977.03i	−0.944999	−	1.63679i	−0.189245	−	0.981930i	$-0.560604\pi$
$312$		0			0
$313$	−7088.96	−	4092.81i	−1.28016	−	0.739103i	−0.303286	−	0.952899i	$-0.598084\pi$
$313$	−7088.96	−	4092.81i	−1.28016	−	0.739103i	−0.976878	+	0.213796i	$0.931417\pi$
$314$	−2638.81			−0.474257
$315$		0			0
$316$	7.05750			0.00125638
$317$	−3116.43	−	1799.27i	−0.552165	−	0.318792i	0.197830	−	0.980236i	$-0.436611\pi$
$317$	−3116.43	−	1799.27i	−0.552165	−	0.318792i	−0.749995	+	0.661444i	$0.769944\pi$
$318$		0			0
$319$	291.312	+	504.567i	0.0511296	+	0.0885591i
$320$	8201.07			1.43267
$321$		0			0
$322$	−1007.12	+	943.399i	−0.174300	+	0.163272i
$323$			12554.7i			2.16274i
$324$		0			0
$325$	−1540.10	−	889.176i	−0.262859	−	0.151762i
$326$		−	6555.64i		−	1.11375i
$327$		0			0
$328$	8772.39	+	5064.74i	1.47675	+	0.852602i
$329$	3885.86	−	3640.00i	0.651169	−	0.609969i
$330$		0			0
$331$	−3992.83	+	6915.79i	−0.663039	+	1.14842i	0.316773	+	0.948501i	$0.397401\pi$
$331$	−3992.83	+	6915.79i	−0.663039	+	1.14842i	−0.979813	+	0.199917i	$0.935933\pi$
$332$	−62.2610	+	107.839i	−0.0102922	+	0.0178266i
$333$		0			0
$334$	5540.46	−	3198.79i	0.907667	−	0.524042i
$335$	2609.44	+	4519.68i	0.425579	+	0.737125i
$336$		0			0
$337$	−4758.03	+	8241.15i	−0.769100	+	1.33212i	0.168952	+	0.985624i	$0.445962\pi$
$337$	−4758.03	+	8241.15i	−0.769100	+	1.33212i	−0.938052	+	0.346495i	$0.887372\pi$
$338$			6089.17i			0.979902i
$339$		0			0
$340$	−1093.69			−0.174453
$341$	3309.25	+	5731.78i	0.525530	+	0.910245i
$342$		0			0
$343$	4030.95	+	4909.69i	0.634550	+	0.772882i
$344$	1638.46	−	945.966i	0.256802	−	0.148265i
$345$		0			0
$346$	−6821.28	+	3938.27i	−1.05987	+	0.611915i
$347$	−6785.01	+	3917.33i	−1.04968	+	0.606032i	−0.922559	−	0.385855i	$-0.873906\pi$
$347$	−6785.01	+	3917.33i	−1.04968	+	0.606032i	−0.127119	+	0.991887i	$0.540573\pi$
$348$		0			0
$349$	5127.39	−	2960.30i	0.786427	−	0.454044i	−0.0522759	−	0.998633i	$-0.516648\pi$
$349$	5127.39	−	2960.30i	0.786427	−	0.454044i	0.838703	+	0.544589i	$0.183314\pi$
$350$	−6318.98	−	6745.80i	−0.965040	−	1.03022i
$351$		0			0
$352$	−399.501	−	691.956i	−0.0604928	−	0.104777i
$353$	−4592.76			−0.692487			−0.346244	−	0.938145i	$-0.612543\pi$
$353$	−4592.76			−0.692487			−0.346244	+	0.938145i	$0.612543\pi$
$354$		0			0
$355$		−	6057.87i		−	0.905685i
$356$	−250.483	+	433.849i	−0.0372909	+	0.0645897i
$357$		0			0
$358$	590.825	+	1023.34i	0.0872237	+	0.151076i
$359$	10030.3	−	5790.97i	1.47459	−	0.851353i	0.474997	−	0.879987i	$-0.342449\pi$
$359$	10030.3	−	5790.97i	1.47459	−	0.851353i	0.999590	+	0.0286338i	$0.00911568\pi$
$360$		0			0
$361$	1359.73	−	2355.12i	0.198240	−	0.343362i
$362$	−4406.72	+	7632.66i	−0.639812	+	1.10819i
$363$		0			0
$364$	27.6523	−	91.1797i	0.00398180	−	0.0131294i
$365$	−13109.7	−	7568.91i	−1.87999	−	1.08541i
$366$		0			0
$367$		−	4647.15i		−	0.660979i	−0.943810	−	0.330490i	$-0.892786\pi$
$367$		−	4647.15i		−	0.660979i	0.943810	−	0.330490i	$-0.107214\pi$
$368$	−1499.20	−	865.565i	−0.212368	−	0.122611i
$369$		0			0
$370$		−	46.4387i		−	0.00652496i
$371$	4894.91	+	5225.53i	0.684989	+	0.731256i
$372$		0			0
$373$	13272.9			1.84247			0.921237	−	0.389001i	$-0.127180\pi$
$373$	13272.9			1.84247			0.921237	+	0.389001i	$0.127180\pi$
$374$	−6672.61	−	11557.3i	−0.922547	−	1.59790i
$375$		0			0
$376$	5446.00	+	3144.25i	0.746957	+	0.431256i
$377$	−169.532			−0.0231600
$378$		0			0
$379$	11820.6			1.60207			0.801033	−	0.598620i	$-0.204284\pi$
$379$	11820.6			1.60207			0.801033	+	0.598620i	$0.204284\pi$
$380$	722.626	+	417.209i	0.0975525	+	0.0563220i
$381$		0			0
$382$	−1498.81	−	2596.02i	−0.200748	−	0.347706i
$383$	−4630.60			−0.617787			−0.308894	−	0.951097i	$-0.599959\pi$
$383$	−4630.60			−0.617787			−0.308894	+	0.951097i	$0.599959\pi$
$384$		0			0
$385$	3301.90	−	10887.6i	0.437092	−	1.44125i
$386$		−	11956.1i		−	1.57655i
$387$		0			0
$388$	557.657	+	321.964i	0.0729659	+	0.0421269i
$389$			8332.61i			1.08607i	0.839711	+	0.543034i	$0.182724\pi$
$389$			8332.61i			1.08607i	−0.839711	+	0.543034i	$0.817276\pi$
$390$		0			0
$391$	−2840.01	−	1639.68i	−0.367329	−	0.212077i
$392$	−4167.41	+	6238.79i	−0.536954	+	0.803843i
$393$		0			0
$394$	1173.64	−	2032.81i	0.150069	−	0.259928i
$395$	−122.607	+	212.361i	−0.0156178	+	0.0270508i
$396$		0			0
$397$	5613.15	−	3240.75i	0.709611	−	0.409694i	−0.101306	−	0.994855i	$-0.532302\pi$
$397$	5613.15	−	3240.75i	0.709611	−	0.409694i	0.810917	+	0.585161i	$0.198969\pi$
$398$	3236.20	+	5605.26i	0.407577	+	0.705945i
$399$		0			0
$400$	5797.65	−	10041.8i	0.724706	−	1.25523i
$401$			1709.94i			0.212944i	0.994316	+	0.106472i	$0.0339554\pi$
$401$			1709.94i			0.212944i	−0.994316	+	0.106472i	$0.966045\pi$
$402$		0			0
$403$	−1925.85			−0.238048
$404$	211.225	+	365.852i	0.0260120	+	0.0450540i
$405$		0			0
$406$	−843.229	−	255.728i	−0.103076	−	0.0312601i
$407$	28.6141	−	16.5203i	0.00348488	−	0.00201200i
$408$		0			0
$409$	−5376.61	+	3104.19i	−0.650016	+	0.375287i	−0.788462	−	0.615083i	$-0.789122\pi$
$409$	−5376.61	+	3104.19i	−0.650016	+	0.375287i	0.138447	+	0.990370i	$0.455789\pi$
$410$	20118.8	−	11615.6i	2.42341	−	1.39916i
$411$		0			0
$412$	18.3114	−	10.5721i	0.00218966	−	0.00126420i
$413$	380.519	+	1631.46i	0.0453369	+	0.194380i
$414$		0			0
$415$	−2163.27	−	3746.89i	−0.255881	−	0.443199i
$416$	232.493			0.0274012
$417$		0			0
$418$			10181.5i			1.19138i
$419$	5926.05	−	10264.2i	0.690946	−	1.19675i	−0.280582	−	0.959830i	$-0.590527\pi$
$419$	5926.05	−	10264.2i	0.690946	−	1.19675i	0.971528	−	0.236924i	$-0.0761393\pi$
$420$		0			0
$421$	−218.101	−	377.763i	−0.0252485	−	0.0437317i	0.853125	−	0.521706i	$-0.174704\pi$
$421$	−218.101	−	377.763i	−0.0252485	−	0.0437317i	−0.878374	+	0.477975i	$0.841371\pi$
$422$	−5671.04	+	3274.17i	−0.654175	+	0.377688i
$423$		0			0
$424$	−4228.24	+	7323.52i	−0.484296	+	0.838825i
$425$	10982.7	−	19022.7i	1.25351	−	2.17114i
$426$		0			0
$427$	1765.52	+	1884.77i	0.200092	+	0.213607i
$428$	−356.133	−	205.614i	−0.0402205	−	0.0232213i
$429$		0			0
$430$		−	4339.01i		−	0.486617i
$431$	−10890.9	−	6287.86i	−1.21716	−	0.702728i	−0.252850	−	0.967505i	$-0.581368\pi$
$431$	−10890.9	−	6287.86i	−1.21716	−	0.702728i	−0.964309	+	0.264778i	$0.914701\pi$
$432$		0			0
$433$			15488.3i			1.71898i	0.511149	+	0.859492i	$0.329220\pi$
$433$			15488.3i			1.71898i	−0.511149	+	0.859492i	$0.670780\pi$
$434$	−9578.92	−	2905.02i	−1.05945	−	0.321303i
$435$		0			0
$436$	683.020			0.0750246
$437$	1250.97	+	2166.74i	0.136938	+	0.237184i
$438$		0			0
$439$	−10844.1	−	6260.84i	−1.17895	−	0.680669i	−0.223181	−	0.974777i	$-0.571644\pi$
$439$	−10844.1	−	6260.84i	−1.17895	−	0.680669i	−0.955772	+	0.294108i	$0.904977\pi$
$440$	13437.2			1.45590
$441$		0			0
$442$	3883.18			0.417883
$443$	−705.907	−	407.556i	−0.0757080	−	0.0437100i	0.461668	−	0.887053i	$-0.347251\pi$
$443$	−705.907	−	407.556i	−0.0757080	−	0.0437100i	−0.537376	+	0.843343i	$0.680584\pi$
$444$		0			0
$445$	−8703.05	−	15074.1i	−0.927111	−	1.60580i
$446$	−12226.9			−1.29812
$447$		0			0
$448$	−8444.95	−	2561.12i	−0.890594	−	0.270093i
$449$			5276.20i			0.554565i	0.960788	+	0.277282i	$0.0894337\pi$
$449$			5276.20i			0.554565i	−0.960788	+	0.277282i	$0.910566\pi$
$450$		0			0
$451$	14314.4	+	8264.40i	1.49454	+	0.862872i
$452$		−	758.251i		−	0.0789052i
$453$		0			0
$454$	−5909.15	−	3411.65i	−0.610860	−	0.352680i
$455$	2263.22	+	2416.09i	0.233190	+	0.248941i
$456$		0			0
$457$	4560.82	−	7899.58i	0.466841	−	0.808592i	−0.532442	−	0.846467i	$-0.678725\pi$
$457$	4560.82	−	7899.58i	0.466841	−	0.808592i	0.999283	+	0.0378745i	$0.0120587\pi$
$458$	−4460.52	+	7725.85i	−0.455080	+	0.788221i
$459$		0			0
$460$	−188.754	+	108.977i	−0.0191319	+	0.0110458i
$461$	420.112	+	727.655i	0.0424437	+	0.0735147i	0.886467	−	0.462792i	$-0.153152\pi$
$461$	420.112	+	727.655i	0.0424437	+	0.0735147i	−0.844023	+	0.536307i	$0.819819\pi$
$462$		0			0
$463$	−1889.21	+	3272.21i	−0.189631	+	0.328450i	−0.945127	−	0.326703i	$-0.894062\pi$
$463$	−1889.21	+	3272.21i	−0.189631	+	0.328450i	0.755496	+	0.655153i	$0.227396\pi$
$464$		−	1105.39i		−	0.110596i
$465$		0			0
$466$	7408.47			0.736461
$467$	−3197.40	−	5538.05i	−0.316826	−	0.548759i	0.662998	−	0.748621i	$-0.269284\pi$
$467$	−3197.40	−	5538.05i	−0.316826	−	0.548759i	−0.979824	+	0.199862i	$0.935951\pi$
$468$		0			0
$469$	−1275.58	−	5468.99i	−0.125588	−	0.538453i
$470$	12490.0	−	7211.10i	1.22579	−	0.707709i
$471$		0			0
$472$	−1713.50	+	989.288i	−0.167098	+	0.0964739i
$473$	2673.56	−	1543.58i	0.259895	−	0.150051i
$474$		0			0
$475$	−14513.1	+	8379.12i	−1.40191	+	0.809390i
$476$	1126.22	+	341.551i	0.108445	+	0.0328886i
$477$		0			0
$478$	−2597.10	−	4498.30i	−0.248511	−	0.430434i
$479$	17221.8			1.64276			0.821382	−	0.570379i	$-0.193203\pi$
$479$	17221.8			1.64276			0.821382	+	0.570379i	$0.193203\pi$
$480$		0			0
$481$			9.61416i			0.000911368i
$482$	−2346.85	+	4064.86i	−0.221776	+	0.384127i
$483$		0			0
$484$	14.1324	+	24.4781i	0.00132724	+	0.00229884i
$485$	−19375.9	+	11186.7i	−1.81405	+	1.04734i
$486$		0			0
$487$	1435.74	−	2486.77i	0.133592	−	0.231389i	−0.791466	−	0.611213i	$-0.790682\pi$
$487$	1435.74	−	2486.77i	0.133592	−	0.231389i	0.925059	+	0.379824i	$0.124015\pi$
$488$	−1525.06	+	2641.48i	−0.141468	+	0.245029i
$489$		0			0
$490$	7612.45	+	15431.3i	0.701828	+	1.42268i
$491$	4900.34	+	2829.21i	0.450406	+	0.260042i	0.708002	−	0.706211i	$-0.249597\pi$
$491$	4900.34	+	2829.21i	0.450406	+	0.260042i	−0.257596	+	0.966253i	$0.582930\pi$
$492$		0			0
$493$		−	2093.99i		−	0.191295i
$494$	−2565.70	−	1481.31i	−0.233677	−	0.134913i
$495$		0			0
$496$		−	12557.0i		−	1.13674i
$497$	−1891.82	+	6238.01i	−0.170744	+	0.563004i
$498$		0			0
$499$	−18601.4			−1.66876			−0.834380	−	0.551190i	$-0.814174\pi$
$499$	−18601.4			−1.66876			−0.834380	+	0.551190i	$0.814174\pi$
$500$	−197.075	−	341.345i	−0.0176270	−	0.0305308i
$501$		0			0
$502$	−1522.35	−	878.930i	−0.135350	−	0.0781445i
$503$	14649.8			1.29862			0.649308	−	0.760526i	$-0.275059\pi$
$503$	14649.8			1.29862			0.649308	+	0.760526i	$0.275059\pi$
$504$		0			0
$505$	−14678.1			−1.29340
$506$	−2303.17	−	1329.73i	−0.202348	−	0.116826i
$507$		0			0
$508$	26.3279	+	45.6012i	0.00229943	+	0.00398273i
$509$	2629.20			0.228953			0.114477	−	0.993426i	$-0.463481\pi$
$509$	2629.20			0.228953			0.114477	+	0.993426i	$0.463481\pi$
$510$		0			0
$511$	11135.9	+	11888.0i	0.964035	+	1.02915i
$512$		−	10333.9i		−	0.891989i
$513$		0			0
$514$	−3372.76	−	1947.27i	−0.289428	−	0.167102i
$515$			734.659i			0.0628601i
$516$		0			0
$517$	8886.51	+	5130.63i	0.755954	+	0.436450i
$518$	−14.5024	+	47.8196i	−0.00123011	+	0.00405613i
$519$		0			0
$520$	−1954.98	+	3386.13i	−0.164868	+	0.285560i
$521$	−8915.56	+	15442.2i	−0.749708	+	1.29853i	0.198255	+	0.980151i	$0.436473\pi$
$521$	−8915.56	+	15442.2i	−0.749708	+	1.29853i	−0.947963	+	0.318382i	$0.896861\pi$
$522$		0			0
$523$	−18929.9	+	10929.2i	−1.58269	+	0.913766i	−0.588224	+	0.808698i	$0.700173\pi$
$523$	−18929.9	+	10929.2i	−1.58269	+	0.913766i	−0.994465	+	0.105068i	$0.966494\pi$
$524$	6.75761	+	11.7045i	0.000563373	+	0.000975791i
$525$		0			0
$526$	8386.42	−	14525.7i	0.695181	−	1.20409i
$527$		−	23787.3i		−	1.96621i
$528$		0			0
$529$	11513.5			0.946288
$530$	9697.16	+	16796.0i	0.794750	+	1.37655i
$531$		0			0
$532$	−613.824	−	655.285i	−0.0500238	−	0.0534026i
$533$	−4165.18	+	2404.77i	−0.338488	+	0.195426i
$534$		0			0
$535$	12373.9	−	7144.08i	0.999945	−	0.577319i
$536$	5744.00	−	3316.30i	0.462878	−	0.267243i
$537$		0			0
$538$	−4677.01	+	2700.27i	−0.374796	+	0.216388i
$539$	−6800.17	+	10180.2i	−0.543421	+	0.813526i
$540$		0			0
$541$	−5561.14	−	9632.17i	−0.441944	−	0.765470i	0.555889	−	0.831256i	$-0.312378\pi$
$541$	−5561.14	−	9632.17i	−0.441944	−	0.765470i	−0.997834	+	0.0657862i	$0.979044\pi$
$542$	21738.7			1.72280
$543$		0			0
$544$			2871.66i			0.226326i
$545$	−11865.8	+	20552.2i	−0.932615	+	1.61534i
$546$		0			0
$547$	7533.25	+	13048.0i	0.588845	+	1.01991i	0.994384	+	0.105832i	$0.0337506\pi$
$547$	7533.25	+	13048.0i	0.588845	+	1.01991i	−0.405539	+	0.914078i	$0.632916\pi$
$548$	37.3104	−	21.5412i	0.00290843	−	0.00167919i
$549$		0			0
$550$	8906.69	−	15426.8i	0.690514	−	1.19600i
$551$	−798.788	+	1383.54i	−0.0617596	+	0.106971i
$552$		0			0
$553$	192.571	−	180.387i	0.0148083	−	0.0138713i
$554$	−3458.16	−	1996.57i	−0.265204	−	0.153116i
$555$		0			0
$556$		−	142.079i		−	0.0108372i
$557$	−6994.00	−	4037.99i	−0.532038	−	0.307172i	0.209808	−	0.977743i	$-0.432716\pi$
$557$	−6994.00	−	4037.99i	−0.532038	−	0.307172i	−0.741846	+	0.670570i	$0.766049\pi$
$558$		0			0
$559$			898.300i			0.0679679i
$560$	−15753.5	+	14756.8i	−1.18876	+	1.11355i
$561$		0			0
$562$	−12029.7			−0.902920
$563$	−4491.15	−	7778.89i	−0.336198	−	0.582311i	0.647517	−	0.762051i	$-0.275808\pi$
$563$	−4491.15	−	7778.89i	−0.336198	−	0.582311i	−0.983714	+	0.179740i	$0.942474\pi$
$564$		0			0
$565$	22815.9	+	13172.8i	1.69889	+	0.980855i
$566$	5543.18			0.411656
$567$		0			0
$568$	−7698.85			−0.568726
$569$	−9591.95	−	5537.92i	−0.706706	−	0.408017i	0.103134	−	0.994667i	$-0.467113\pi$
$569$	−9591.95	−	5537.92i	−0.706706	−	0.408017i	−0.809840	+	0.586651i	$0.800446\pi$
$570$		0			0
$571$	11164.3	+	19337.1i	0.818233	+	1.41722i	0.906983	+	0.421167i	$0.138380\pi$
$571$	11164.3	+	19337.1i	0.818233	+	1.41722i	−0.0887498	+	0.996054i	$0.528287\pi$
$572$	183.625			0.0134226
$573$		0			0
$574$	−24344.5	+	5678.09i	−1.77025	+	0.412890i
$575$		−	4377.33i		−	0.317474i
$576$		0			0
$577$	2753.56	+	1589.77i	0.198669	+	0.114702i	0.596035	−	0.802959i	$-0.296742\pi$
$577$	2753.56	+	1589.77i	0.198669	+	0.114702i	−0.397365	+	0.917660i	$0.630075\pi$
$578$			33643.7i			2.42110i
$579$		0			0
$580$	−120.526	−	69.5856i	−0.00862855	−	0.00498170i
$581$	1057.47	+	4533.87i	0.0755102	+	0.323747i
$582$		0			0
$583$	−6899.43	+	11950.2i	−0.490129	+	0.848929i
$584$	−9619.21	+	16661.0i	−0.681585	+	1.18054i
$585$		0			0
$586$	19990.4	−	11541.5i	1.40921	−	0.813606i
$587$	−9230.28	−	15987.3i	−0.649019	−	1.12413i	−0.983357	−	0.181681i	$-0.941846\pi$
$587$	−9230.28	−	15987.3i	−0.649019	−	1.12413i	0.334338	−	0.942453i	$-0.391487\pi$
$588$		0			0
$589$	−9074.08	+	15716.8i	−0.634789	+	1.09949i
$590$			4537.72i			0.316636i
$591$		0			0
$592$	−62.6867			−0.00435204
$593$	−4842.31	−	8387.12i	−0.335328	−	0.580806i	0.648220	−	0.761453i	$-0.275514\pi$
$593$	−4842.31	−	8387.12i	−0.335328	−	0.580806i	−0.983548	+	0.180648i	$0.942181\pi$
$594$		0			0
$595$	−29842.6	+	27954.4i	−2.05618	+	1.92608i
$596$	866.954	−	500.536i	0.0595836	−	0.0344006i
$597$		0			0
$598$	670.174	−	386.925i	0.0458285	−	0.0264591i
$599$	3303.93	−	1907.53i	0.225367	−	0.130116i	−0.383066	−	0.923721i	$-0.625132\pi$
$599$	3303.93	−	1907.53i	0.225367	−	0.130116i	0.608433	+	0.793605i	$0.291798\pi$
$600$		0			0
$601$	7609.28	−	4393.22i	0.516454	−	0.298175i	−0.219029	−	0.975718i	$-0.570289\pi$
$601$	7609.28	−	4393.22i	0.516454	−	0.298175i	0.735483	+	0.677544i	$0.236955\pi$
$602$	−1355.03	+	4468.03i	−0.0917392	+	0.302497i
$603$		0			0
$604$	−475.311	−	823.263i	−0.0320201	−	0.0554604i
$605$	−982.066			−0.0659944
$606$		0			0
$607$		−	11742.5i		−	0.785194i	−0.919711	−	0.392597i	$-0.871577\pi$
$607$		−	11742.5i		−	0.785194i	0.919711	−	0.392597i	$-0.128423\pi$
$608$	1095.45	−	1897.37i	0.0730694	−	0.126560i
$609$		0			0
$610$	3497.61	+	6058.04i	0.232154	+	0.402103i
$611$	−2585.79	+	1492.91i	−0.171211	+	0.0988487i
$612$		0			0
$613$	9443.86	−	16357.2i	0.622241	−	1.07775i	−0.366826	−	0.930289i	$-0.619556\pi$
$613$	9443.86	−	16357.2i	0.622241	−	1.07775i	0.989067	−	0.147464i	$-0.0471110\pi$
$614$	2492.03	−	4316.33i	0.163795	−	0.283702i
$615$		0			0
$616$	−13836.8	−	4196.33i	−0.905035	−	0.274472i
$617$	10726.8	+	6193.11i	0.699909	+	0.404093i	0.807314	−	0.590123i	$-0.200921\pi$
$617$	10726.8	+	6193.11i	0.699909	+	0.404093i	−0.107404	+	0.994215i	$0.534254\pi$
$618$		0			0
$619$		−	2663.48i		−	0.172947i	−0.996254	−	0.0864735i	$-0.972440\pi$
$619$		−	2663.48i		−	0.172947i	0.996254	−	0.0864735i	$-0.0275598\pi$
$620$	−1369.15	−	790.479i	−0.0886877	−	0.0512038i
$621$		0			0
$622$			30212.9i			1.94763i
$623$	4254.33	+	18240.3i	0.273590	+	1.17300i
$624$		0			0
$625$	−7708.96			−0.493374
$626$	11929.2	+	20662.0i	0.761642	+	1.31920i
$627$		0			0
$628$	388.391	+	224.238i	0.0246791	+	0.0142485i
$629$	−118.750			−0.00752764
$630$		0			0
$631$	20380.6			1.28580			0.642898	−	0.765952i	$-0.277732\pi$
$631$	20380.6			1.28580			0.642898	+	0.765952i	$0.277732\pi$
$632$	269.887	+	155.819i	0.0169866	+	0.00980720i
$633$		0			0
$634$	5244.30	+	9083.40i	0.328514	+	0.569003i
$635$	−1829.53			−0.114335
$636$		0			0
$637$	−1576.00	−	3194.72i	−0.0980272	−	0.198712i
$638$		−	1698.16i		−	0.105378i
$639$		0			0
$640$	−23370.4	−	13492.9i	−1.44343	−	0.833366i
$641$		−	20778.8i		−	1.28036i	−0.768224	−	0.640181i	$-0.778859\pi$
$641$		−	20778.8i		−	1.28036i	0.768224	−	0.640181i	$-0.221141\pi$
$642$		0			0
$643$	−6344.01	−	3662.72i	−0.389088	−	0.224640i	0.292677	−	0.956211i	$-0.405454\pi$
$643$	−6344.01	−	3662.72i	−0.389088	−	0.224640i	−0.681765	+	0.731572i	$0.738787\pi$
$644$	228.399	−	53.2714i	0.0139754	−	0.00325961i
$645$		0			0
$646$	18296.5	−	31690.5i	1.11435	−	1.93010i
$647$	−5424.13	+	9394.87i	−0.329590	+	0.570866i	−0.982430	−	0.186629i	$-0.940244\pi$
$647$	−5424.13	+	9394.87i	−0.329590	+	0.570866i	0.652841	+	0.757495i	$0.273577\pi$
$648$		0			0
$649$	−2796.00	+	1614.27i	−0.169110	+	0.0976359i
$650$	2591.66	+	4488.89i	0.156390	+	0.270875i
$651$		0			0
$652$	−557.077	+	964.885i	−0.0334614	+	0.0579568i
$653$		−	11896.6i		−	0.712941i	−0.934307	−	0.356470i	$-0.883980\pi$
$653$		−	11896.6i		−	0.712941i	0.934307	−	0.356470i	$-0.116020\pi$
$654$		0			0
$655$	−469.588			−0.0280127
$656$	−15679.7	−	27158.0i	−0.933215	−	1.61638i
$657$		0			0
$658$	−15113.4	+	3525.02i	−0.895411	+	0.208844i
$659$	24001.0	−	13857.0i	1.41874	−	0.819108i	0.422549	−	0.906340i	$-0.361135\pi$
$659$	24001.0	−	13857.0i	1.41874	−	0.819108i	0.996188	+	0.0872319i	$0.0278021\pi$
$660$		0			0
$661$	24782.6	−	14308.3i	1.45829	−	0.841947i	0.459367	−	0.888246i	$-0.348076\pi$
$661$	24782.6	−	14308.3i	1.45829	−	0.841947i	0.998928	+	0.0462996i	$0.0147429\pi$
$662$	20157.3	−	11637.8i	1.18344	−	0.683259i
$663$		0			0
$664$	−4761.86	+	2749.26i	−0.278307	+	0.160681i
$665$	30381.3	−	7086.10i	1.77164	−	0.413214i
$666$		0			0
$667$	−208.647	−	361.388i	−0.0121122	−	0.0209790i
$668$	−1087.29			−0.0629768
$669$		0			0
$670$		−	15211.4i		−	0.877114i
$671$	−2488.52	+	4310.24i	−0.143172	+	0.247981i
$672$		0			0
$673$	−3408.12	−	5903.03i	−0.195205	−	0.338106i	0.751762	−	0.659434i	$-0.229204\pi$
$673$	−3408.12	−	5903.03i	−0.195205	−	0.338106i	−0.946968	+	0.321328i	$0.895871\pi$
$674$	24020.3	−	13868.1i	1.37274	−	0.792553i
$675$		0			0
$676$	517.437	−	896.227i	0.0294400	−	0.0509915i
$677$	2806.77	−	4861.47i	0.159340	−	0.275984i	−0.775291	−	0.631604i	$-0.782397\pi$
$677$	2806.77	−	4861.47i	0.159340	−	0.275984i	0.934631	+	0.355620i	$0.115730\pi$
$678$		0			0
$679$	23445.5	−	5468.41i	1.32512	−	0.309069i
$680$	−41824.1	−	24147.1i	−2.35865	−	1.36177i
$681$		0			0
$682$		−	19290.8i		−	1.08311i
$683$	8374.35	+	4834.94i	0.469159	+	0.270869i	0.715888	−	0.698215i	$-0.246022\pi$
$683$	8374.35	+	4834.94i	0.469159	+	0.270869i	−0.246728	+	0.969085i	$0.579356\pi$
$684$		0			0
$685$			1496.90i			0.0834945i
$686$	−3019.77	−	18267.4i	−0.168069	−	1.01670i
$687$		0			0
$688$	−5857.14			−0.324566
$689$	−2007.59	−	3477.25i	−0.111006	−	0.192268i
$690$		0			0
$691$	3737.34	+	2157.76i	0.205753	+	0.118792i	0.599336	−	0.800497i	$-0.295431\pi$
$691$	3737.34	+	2157.76i	0.205753	+	0.118792i	−0.393583	+	0.919289i	$0.628765\pi$
$692$	1338.64			0.0735370
$693$		0			0
$694$	22835.5			1.24903
$695$	4275.18	+	2468.28i	0.233334	+	0.134715i
$696$		0			0
$697$	−29702.8	−	51446.7i	−1.61416	−	2.79581i
$698$	−17256.7			−0.935780
$699$		0			0
$700$	356.818	+	1529.84i	0.0192663	+	0.0826035i
$701$		−	22520.8i		−	1.21341i	−0.794929	−	0.606703i	$-0.792492\pi$
$701$		−	22520.8i		−	1.21341i	0.794929	−	0.606703i	$-0.207508\pi$
$702$		0			0
$703$	78.4608	+	45.2994i	0.00420940	+	0.00243030i
$704$		−	17007.1i		−	0.910483i
$705$		0			0
$706$	11593.0	+	6693.21i	0.618000	+	0.356802i
$707$	15114.6	+	4583.83i	0.804019	+	0.243837i
$708$		0			0
$709$	1407.50	−	2437.87i	0.0745556	−	0.129134i	−0.826337	−	0.563175i	$-0.809579\pi$
$709$	1407.50	−	2437.87i	0.0745556	−	0.129134i	0.900893	+	0.434041i	$0.142913\pi$
$710$	−8828.37	+	15291.2i	−0.466652	+	0.808265i
$711$		0			0
$712$	−19157.5	+	11060.6i	−1.00837	+	0.582180i
$713$	−2370.19	−	4105.29i	−0.124494	−	0.215630i
$714$		0			0
$715$	−3190.04	+	5525.31i	−0.166854	+	0.289000i
$716$		−	200.826i		−	0.0104821i
$717$		0			0
$718$	−33757.7			−1.75463
$719$	5377.34	+	9313.82i	0.278916	+	0.483097i	0.971116	−	0.238609i	$-0.0766914\pi$
$719$	5377.34	+	9313.82i	0.278916	+	0.483097i	−0.692199	+	0.721706i	$0.743358\pi$
$720$		0			0
$721$	229.428	−	756.505i	0.0118507	−	0.0390759i
$722$	−6864.42	+	3963.17i	−0.353833	+	0.204285i
$723$		0			0
$724$	1297.20	−	748.936i	0.0665883	−	0.0384447i
$725$	2420.61	−	1397.54i	0.123999	−	0.0715908i
$726$		0			0
$727$	5477.81	−	3162.62i	0.279451	−	0.161341i	−0.353724	−	0.935350i	$-0.615085\pi$
$727$	5477.81	−	3162.62i	0.279451	−	0.161341i	0.633175	+	0.774009i	$0.281751\pi$
$728$	3070.57	−	2876.29i	0.156323	−	0.146432i
$729$		0			0
$730$	22060.9	+	38210.7i	1.11851	+	1.93732i
$731$	−11095.4			−0.561395
$732$		0			0
$733$			14798.7i			0.745706i	0.927890	+	0.372853i	$0.121620\pi$
$733$			14798.7i			0.745706i	−0.927890	+	0.372853i	$0.878380\pi$
$734$	−6772.48	+	11730.3i	−0.340568	+	0.589881i
$735$		0			0
$736$	286.136	+	495.602i	0.0143303	+	0.0248208i
$737$	9372.77	−	5411.37i	0.468454	−	0.270462i
$738$		0			0
$739$	12825.4	−	22214.3i	0.638418	−	1.10577i	−0.347362	−	0.937731i	$-0.612923\pi$
$739$	12825.4	−	22214.3i	0.638418	−	1.10577i	0.985780	−	0.168041i	$-0.0537441\pi$
$740$	−3.94621	+	6.83503i	−0.000196034	+	0.000339542i
$741$		0			0
$742$	−4740.28	−	20323.8i	−0.234530	−	1.00554i
$743$	30440.0	+	17574.5i	1.50301	+	0.867761i	0.999994	+	0.00348188i	$0.00110832\pi$
$743$	30440.0	+	17574.5i	1.50301	+	0.867761i	0.503012	+	0.864279i	$0.332225\pi$
$744$		0			0
$745$			34782.4i			1.71051i
$746$	−33503.2	−	19343.1i	−1.64429	−	0.949331i
$747$		0			0
$748$			2268.07i			0.110867i
$749$	−14972.9	+	3492.26i	−0.730438	+	0.170366i
$750$		0			0
$751$	−15906.4			−0.772881			−0.386440	−	0.922314i	$-0.626295\pi$
$751$	−15906.4			−0.772881			−0.386440	+	0.922314i	$0.626295\pi$
$752$	−9734.13	−	16860.0i	−0.472031	−	0.817581i
$753$		0			0
$754$	427.929	+	247.065i	0.0206688	+	0.0119331i
$755$	33029.5			1.59214
$756$		0			0
$757$	8886.22			0.426651			0.213326	−	0.976981i	$-0.431570\pi$
$757$	8886.22			0.426651			0.213326	+	0.976981i	$0.431570\pi$
$758$	−29837.4	−	17226.6i	−1.42974	−	0.825461i
$759$		0			0
$760$	18422.7	+	31909.1i	0.879292	+	1.52298i
$761$	−6896.64			−0.328519			−0.164259	−	0.986417i	$-0.552523\pi$
$761$	−6896.64			−0.328519			−0.164259	+	0.986417i	$0.552523\pi$
$762$		0			0
$763$	18636.9	−	17457.7i	0.884275	−	0.828326i
$764$			509.456i			0.0241249i
$765$		0			0
$766$	11688.5	+	6748.35i	0.551335	+	0.318313i
$767$		−	939.440i		−	0.0442258i
$768$		0			0
$769$	23996.6	+	13854.4i	1.12528	+	0.649680i	0.942743	−	0.333519i	$-0.108236\pi$
$769$	23996.6	+	13854.4i	1.12528	+	0.649680i	0.182536	+	0.983199i	$0.441569\pi$
$770$	−24201.5	+	22670.2i	−1.13268	+	1.06101i
$771$		0			0
$772$	−1015.99	+	1759.74i	−0.0473656	+	0.0820396i
$773$	17922.3	−	31042.4i	0.833921	−	1.44439i	−0.0609846	−	0.998139i	$-0.519424\pi$
$773$	17922.3	−	31042.4i	0.833921	−	1.44439i	0.894906	−	0.446255i	$-0.147243\pi$
$774$		0			0
$775$	27497.7	−	15875.8i	1.27451	−	0.735839i
$776$	14217.0	+	24624.5i	0.657679	+	1.13913i
$777$		0			0
$778$	12143.5	−	21033.1i	0.559594	−	0.969245i
$779$			45322.5i			2.08453i
$780$		0			0
$781$	−12562.6			−0.575577
$782$	4779.14	+	8277.72i	0.218545	+	0.378530i
$783$		0			0
$784$	20830.4	−	10275.9i	0.948905	−	0.468108i
$785$	−13494.7	+	7791.17i	−0.613562	+	0.354240i
$786$		0			0
$787$	7049.71	−	4070.15i	0.319307	−	0.184352i	−0.331776	−	0.943358i	$-0.607648\pi$
$787$	7049.71	−	4070.15i	0.319307	−	0.184352i	0.651084	+	0.759006i	$0.274315\pi$
$788$	−345.483	+	199.465i	−0.0156184	+	0.00901730i
$789$		0			0
$790$	618.965	−	357.360i	0.0278757	−	0.0160940i
$791$	−19380.6	−	20689.7i	−0.871171	−	0.930014i
$792$		0			0
$793$	−724.107	−	1254.19i	−0.0324260	−	0.0561635i
$794$	−18891.5			−0.844376
$795$		0			0
$796$		−	1100.00i		−	0.0489807i
$797$	2028.87	−	3514.10i	0.0901708	−	0.156180i	−0.817412	−	0.576053i	$-0.804592\pi$
$797$	2028.87	−	3514.10i	0.0901708	−	0.156180i	0.907583	+	0.419873i	$0.137925\pi$
$798$		0			0
$799$	−18439.8	−	31938.7i	−0.816462	−	1.41415i
$800$	−3319.59	+	1916.57i	−0.146707	+	0.0847011i
$801$		0			0
$802$	2491.97	−	4316.21i	0.109719	−	0.190038i
$803$	−15696.1	+	27186.5i	−0.689794	+	1.19476i
$804$		0			0
$805$	−2364.93	+	7798.03i	−0.103544	+	0.341421i
$806$	4861.19	+	2806.61i	0.212442	+	0.122653i
$807$		0			0
$808$			18654.1i			0.812191i
$809$	−1680.09	−	970.002i	−0.0730148	−	0.0421551i	0.463048	−	0.886333i	$-0.346756\pi$
$809$	−1680.09	−	970.002i	−0.0730148	−	0.0421551i	−0.536063	+	0.844178i	$0.680089\pi$
$810$		0			0
$811$		−	35635.2i		−	1.54294i	−0.636268	−	0.771468i	$-0.719523\pi$
$811$		−	35635.2i		−	1.54294i	0.636268	−	0.771468i	$-0.280477\pi$
$812$	102.379	+	109.294i	0.00442462	+	0.00472348i
$813$		0			0
$814$	−96.3031			−0.00414671
$815$	−19355.7	−	33525.1i	−0.831903	−	1.44090i
$816$		0			0
$817$	7331.00	+	4232.55i	0.313928	+	0.181246i
$818$	18095.4			0.773462
$819$		0			0
$820$	−3948.23			−0.168144
$821$	−22330.0	−	12892.2i	−0.949234	−	0.548040i	−0.0563908	−	0.998409i	$-0.517959\pi$
$821$	−22330.0	−	12892.2i	−0.949234	−	0.548040i	−0.892843	+	0.450368i	$0.851293\pi$
$822$		0			0
$823$	18894.9	+	32726.9i	0.800284	+	1.38613i	0.919429	+	0.393255i	$0.128651\pi$
$823$	18894.9	+	32726.9i	0.800284	+	1.38613i	−0.119146	+	0.992877i	$0.538016\pi$
$824$	933.667			0.0394731
$825$		0			0
$826$	1417.09	−	4672.66i	0.0596935	−	0.196831i
$827$		−	9246.54i		−	0.388795i	−0.980923	−	0.194398i	$-0.937725\pi$
$827$		−	9246.54i		−	0.388795i	0.980923	−	0.194398i	$-0.0622752\pi$
$828$		0			0
$829$	−22476.1	−	12976.6i	−0.941649	−	0.543661i	−0.0511721	−	0.998690i	$-0.516296\pi$
$829$	−22476.1	−	12976.6i	−0.941649	−	0.543661i	−0.890477	+	0.455029i	$0.849629\pi$
$830$			12610.5i			0.527368i
$831$		0			0
$832$	4285.72	+	2474.36i	0.178582	+	0.103105i
$833$	39459.9	−	19466.1i	1.64130	−	0.809677i
$834$		0			0
$835$	18889.0	−	32716.7i	0.782852	−	1.35594i
$836$	865.193	−	1498.56i	0.0357935	−	0.0619961i
$837$		0			0
$838$	−29916.9	+	17272.5i	−1.23325	+	0.712017i
$839$	16562.3	+	28686.7i	0.681518	+	1.18042i	0.974517	+	0.224312i	$0.0720133\pi$
$839$	16562.3	+	28686.7i	0.681518	+	1.18042i	−0.292999	+	0.956113i	$0.594653\pi$
$840$		0			0
$841$	−12061.3	+	20890.7i	−0.494537	+	0.856564i
$842$			1271.39i			0.0520369i
$843$		0			0
$844$	1112.91			0.0453887
$845$	17978.4	+	31139.5i	0.731925	+	1.26773i
$846$		0			0
$847$	1011.27	+	306.690i	0.0410243	+	0.0124416i
$848$	22672.5	−	13090.0i	0.918135	−	0.530085i
$849$		0			0
$850$	−55445.0	+	32011.2i	−2.23735	+	1.29174i
$851$	−20.4944	+	11.8324i	−0.000825543	+	0.000476628i
$852$		0			0
$853$	−33036.5	+	19073.6i	−1.32608	+	0.765614i	−0.984691	−	0.174307i	$-0.944232\pi$
$853$	−33036.5	+	19073.6i	−1.32608	+	0.765614i	−0.341392	+	0.939921i	$0.610898\pi$
$854$	−1709.75	−	7330.46i	−0.0685086	−	0.293727i
$855$		0			0
$856$	−9079.30	−	15725.8i	−0.362528	−	0.627917i
$857$	29314.0			1.16843			0.584217	−	0.811598i	$-0.301402\pi$
$857$	29314.0			1.16843			0.584217	+	0.811598i	$0.301402\pi$
$858$		0			0
$859$			30802.0i			1.22346i	0.791067	+	0.611729i	$0.209526\pi$
$859$			30802.0i			1.22346i	−0.791067	+	0.611729i	$0.790474\pi$
$860$	−368.714	+	638.632i	−0.0146198	+	0.0253223i
$861$		0			0
$862$	18327.1	+	31743.5i	0.724157	+	1.25428i
$863$	−10009.9	+	5779.21i	−0.394832	+	0.227957i	−0.684252	−	0.729246i	$-0.739871\pi$
$863$	−10009.9	+	5779.21i	−0.394832	+	0.227957i	0.289419	+	0.957202i	$0.406538\pi$
$864$		0			0
$865$	−23255.7	+	40280.0i	−0.914123	+	1.58331i
$866$	22571.7	−	39095.4i	0.885702	−	1.53408i
$867$		0			0
$868$	1163.00	+	1241.56i	0.0454780	+	0.0485498i
$869$	440.388	+	254.258i	0.0171912	+	0.00992533i
$870$		0			0
$871$			3149.19i			0.122510i
$872$	26119.4	+	15080.1i	1.01435	+	0.585637i
$873$		0			0
$874$		−	7292.35i		−	0.282228i
$875$	−14102.1	−	4276.77i	−0.544842	−	0.165236i
$876$		0			0
$877$	−8118.17			−0.312578			−0.156289	−	0.987711i	$-0.549953\pi$
$877$	−8118.17			−0.312578			−0.156289	+	0.987711i	$0.549953\pi$
$878$	18248.3	+	31607.1i	0.701426	+	1.21490i
$879$		0			0
$880$	−36026.4	−	20799.9i	−1.38006	−	0.796776i
$881$	−20509.9			−0.784331			−0.392165	−	0.919895i	$-0.628274\pi$
$881$	−20509.9			−0.784331			−0.392165	+	0.919895i	$0.628274\pi$
$882$		0			0
$883$	−12792.6			−0.487549			−0.243774	−	0.969832i	$-0.578386\pi$
$883$	−12792.6			−0.487549			−0.243774	+	0.969832i	$0.578386\pi$
$884$	−571.542	−	329.980i	−0.0217455	−	0.0125548i
$885$		0			0
$886$	1187.89	+	2057.49i	0.0450430	+	0.0780167i
$887$	−1469.19			−0.0556150			−0.0278075	−	0.999613i	$-0.508853\pi$
$887$	−1469.19			−0.0556150			−0.0278075	+	0.999613i	$0.508853\pi$
$888$		0			0
$889$	1883.93	+	571.346i	0.0710743	+	0.0215549i
$890$			50733.2i			1.91077i
$891$		0			0
$892$	1799.61	+	1039.00i	0.0675509	+	0.0390005i
$893$			28136.7i			1.05438i
$894$		0			0
$895$	6042.87	+	3488.86i	0.225688	+	0.130301i
$896$	19851.7	+	21192.5i	0.740175	+	0.790170i
$897$		0			0
$898$	7689.22	−	13318.1i	0.285738	−	0.494913i
$899$	1513.45	−	2621.37i	0.0561473	−	0.0972500i
$900$		0			0
$901$	42949.7	−	24797.0i	1.58808	−	0.916879i
$902$	−24088.1	−	41721.8i	−0.889185	−	1.54011i
$903$		0			0
$904$	16741.1	−	28996.4i	0.615929	−	1.06682i
$905$			52043.8i			1.91160i
$906$		0			0
$907$	−9286.67			−0.339977			−0.169988	−	0.985446i	$-0.554373\pi$
$907$	−9286.67			−0.339977			−0.169988	+	0.985446i	$0.554373\pi$
$908$	579.822	+	1004.28i	0.0211917	+	0.0367051i
$909$		0			0
$910$	−2191.73	−	9396.95i	−0.0798409	−	0.342314i
$911$	−17555.0	+	10135.4i	−0.638444	+	0.368606i	−0.784015	−	0.620742i	$-0.786831\pi$
$911$	−17555.0	+	10135.4i	−0.638444	+	0.368606i	0.145571	+	0.989348i	$0.453498\pi$
$912$		0			0
$913$	−7770.17	+	4486.11i	−0.281659	+	0.162616i
$914$	−23024.7	+	13293.3i	−0.833250	+	0.481077i
$915$		0			0
$916$	1313.03	−	758.081i	0.0473623	−	0.0273446i
$917$	483.552	+	146.648i	0.0174136	+	0.00528108i
$918$		0			0
$919$	18209.8	+	31540.4i	0.653632	+	1.13212i	0.982235	+	0.187655i	$0.0600887\pi$
$919$	18209.8	+	31540.4i	0.653632	+	1.13212i	−0.328603	+	0.944468i	$0.606578\pi$
$920$	−9624.20			−0.344892
$921$		0			0
$922$		−	2448.98i		−	0.0874761i
$923$	1827.73	−	3165.72i	0.0651792	−	0.112894i
$924$		0			0
$925$	−79.2547	−	137.273i	−0.00281717	−	0.00487948i
$926$	9537.45	−	5506.45i	0.338467	−	0.195414i
$927$		0			0
$928$	−182.708	+	316.459i	−0.00646301	+	0.0111943i
$929$	10201.3	−	17669.2i	0.360275	−	0.624014i	−0.627731	−	0.778430i	$-0.716016\pi$
$929$	10201.3	−	17669.2i	0.360275	−	0.624014i	0.988006	+	0.154416i	$0.0493496\pi$
$930$		0			0
$931$	−33497.7	−	2191.00i	−1.17921	−	0.0771291i
$932$	−1090.41	−	629.547i	−0.0383235	−	0.0221261i
$933$		0			0
$934$			18638.8i			0.652976i
$935$	−68246.5	−	39402.1i	−2.38706	−	1.37817i
$936$		0			0
$937$			18280.7i			0.637357i	0.947863	+	0.318679i	$0.103239\pi$
$937$			18280.7i			0.637357i	−0.947863	+	0.318679i	$0.896761\pi$
$938$	−4750.37	+	15663.7i	−0.165357	+	0.545243i
$939$		0			0
$940$	−2451.10			−0.0850491
$941$	−20474.1	−	35462.2i	−0.709286	−	1.22852i	−0.965122	−	0.261799i	$-0.915684\pi$
$941$	−20474.1	−	35462.2i	−0.709286	−	1.22852i	0.255837	−	0.966720i	$-0.417649\pi$
$942$		0			0
$943$	−10252.4	−	5919.23i	−0.354045	−	0.204408i
$944$	6125.38			0.211191
$945$		0			0
$946$	−8998.08			−0.309253
$947$	29968.9	+	17302.6i	1.02836	+	0.593725i	0.916515	−	0.400001i	$-0.130990\pi$
$947$	29968.9	+	17302.6i	1.02836	+	0.593725i	0.111847	+	0.993725i	$0.464323\pi$
$948$		0			0
$949$	−4567.26	−	7910.72i	−0.156227	−	0.270593i
$950$	48844.9			1.66815
$951$		0			0
$952$	35526.8	+	37926.5i	1.20949	+	1.29118i
$953$			35792.0i			1.21660i	0.793709	+	0.608298i	$0.208147\pi$
$953$			35792.0i			1.21660i	−0.793709	+	0.608298i	$0.791853\pi$
$954$		0			0
$955$	−15329.6	−	8850.55i	−0.519429	−	0.299892i
$956$			882.771i			0.0298649i
$957$		0			0
$958$	−43471.0	−	25098.0i	−1.46606	−	0.846430i
$959$	467.469	−	1541.42i	0.0157407	−	0.0519029i
$960$		0			0
$961$	2297.01	−	3978.54i	0.0771041	−	0.133548i
$962$	14.0111	−	24.2679i	0.000469580	−	0.000813337i
$963$		0			0
$964$	690.836	−	398.854i	0.0230813	−	0.0133260i
$965$	−35300.7	−	61142.5i	−1.17758	−	2.03963i
$966$		0			0
$967$	−2517.30	+	4360.10i	−0.0837135	+	0.144996i	−0.904842	−	0.425747i	$-0.860011\pi$
$967$	−2517.30	+	4360.10i	−0.0837135	+	0.144996i	0.821129	+	0.570743i	$0.193345\pi$
$968$			1248.09i			0.0414413i
$969$		0			0
$970$	65211.1			2.15856
$971$	5636.92	+	9763.43i	0.186300	+	0.322681i	0.944014	−	0.329906i	$-0.107017\pi$
$971$	5636.92	+	9763.43i	0.186300	+	0.322681i	−0.757714	+	0.652587i	$0.773684\pi$
$972$		0			0
$973$	−3631.49	−	3876.78i	−0.119651	−	0.127733i
$974$	−7248.14	+	4184.72i	−0.238445	+	0.137666i
$975$		0			0
$976$	8177.63	−	4721.36i	0.268196	−	0.154843i
$977$	−28739.0	+	16592.5i	−0.941087	+	0.543337i	−0.890301	−	0.455373i	$-0.849506\pi$
$977$	−28739.0	+	16592.5i	−0.941087	+	0.543337i	−0.0507863	+	0.998710i	$0.516173\pi$
$978$		0			0
$979$	−31260.2	+	18048.1i	−1.02051	+	0.589193i
$980$	190.867	−	2918.12i	0.00622145	−	0.0951182i
$981$		0			0
$982$	−8246.25	−	14282.9i	−0.267972	−	0.464141i
$983$	−46854.4			−1.52027			−0.760134	−	0.649767i	$-0.774867\pi$
$983$	−46854.4			−1.52027			−0.760134	+	0.649767i	$0.774867\pi$
$984$		0			0
$985$		−	13860.9i		−	0.448369i
$986$	−3051.65	+	5285.62i	−0.0985643	+	0.170718i
$987$		0			0
$988$	251.753	+	436.050i	0.00810662	+	0.0140411i
$989$	−1914.89	+	1105.56i	−0.0615673	+	0.0355459i
$990$		0			0
$991$	−3756.98	+	6507.28i	−0.120428	+	0.208588i	−0.919937	−	0.392067i	$-0.871760\pi$
$991$	−3756.98	+	6507.28i	−0.120428	+	0.208588i	0.799508	+	0.600655i	$0.205093\pi$
$992$	−2075.52	+	3594.91i	−0.0664294	+	0.115059i
$993$		0			0
$994$	13866.2	−	12988.9i	0.442464	−	0.414469i
$995$	33099.3	+	19109.9i	1.05459	+	0.608869i
$996$		0			0
$997$		−	33471.9i		−	1.06325i	−0.846978	−	0.531627i	$-0.821581\pi$
$997$		−	33471.9i		−	1.06325i	0.846978	−	0.531627i	$-0.178419\pi$
$998$	46953.3	+	27108.5i	1.48926	+	0.859824i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.s.a.17.6		44
3.2	odd	2		63.4.s.a.59.17	yes	44
7.5	odd	6		189.4.i.a.152.17		44
9.2	odd	6		189.4.i.a.143.6		44
9.7	even	3		63.4.i.a.38.17	yes	44
21.5	even	6		63.4.i.a.5.6	✓	44
63.47	even	6	inner	189.4.s.a.89.6		44
63.61	odd	6		63.4.s.a.47.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.6	✓	44	21.5	even	6
63.4.i.a.38.17	yes	44	9.7	even	3
63.4.s.a.47.17	yes	44	63.61	odd	6
63.4.s.a.59.17	yes	44	3.2	odd	2
189.4.i.a.143.6		44	9.2	odd	6
189.4.i.a.152.17		44	7.5	odd	6
189.4.s.a.17.6		44	1.1	even	1	trivial
189.4.s.a.89.6		44	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.52419 - 1.45734i) q^{2} +(0.247680 + 0.428994i) q^{4} -17.2113 q^{5} +(17.7231 + 5.37495i) q^{7} +21.8736i q^{8} +O(q^{10})\)	\(q+(-2.52419 - 1.45734i) q^{2} +(0.247680 + 0.428994i) q^{4} -17.2113 q^{5} +(17.7231 + 5.37495i) q^{7} +21.8736i q^{8} +(43.4446 + 25.0828i) q^{10} +35.6923i q^{11} +(-8.99430 - 5.19286i) q^{13} +(-36.9034 - 39.3960i) q^{14} +(33.8587 - 58.6451i) q^{16} +(64.1402 - 111.094i) q^{17} +(-84.7576 + 48.9348i) q^{19} +(-4.26290 - 7.38356i) q^{20} +(52.0158 - 90.0941i) q^{22} -25.5640i q^{23} +171.230 q^{25} +(15.1355 + 26.2155i) q^{26} +(2.08385 + 8.93439i) q^{28} +(14.1366 - 8.16176i) q^{29} +(160.589 - 92.7160i) q^{31} +(-19.3867 + 11.1929i) q^{32} +(-323.804 + 186.948i) q^{34} +(-305.039 - 92.5101i) q^{35} +(-0.462855 - 0.801688i) q^{37} +285.259 q^{38} -376.474i q^{40} +(231.546 - 401.049i) q^{41} +(-43.2469 - 74.9058i) q^{43} +(-15.3118 + 8.84027i) q^{44} +(-37.2555 + 64.5283i) q^{46} +(143.746 - 248.976i) q^{47} +(285.220 + 190.522i) q^{49} +(-432.217 - 249.541i) q^{50} -5.14467i q^{52} +(334.811 + 193.303i) q^{53} -614.313i q^{55} +(-117.570 + 387.669i) q^{56} -47.5778 q^{58} +(45.2274 + 78.3362i) q^{59} +(120.761 + 69.7214i) q^{61} -540.475 q^{62} -476.492 q^{64} +(154.804 + 89.3761i) q^{65} +(-151.612 - 262.599i) q^{67} +63.5449 q^{68} +(635.157 + 678.059i) q^{70} +351.969i q^{71} +(761.691 + 439.763i) q^{73} +2.69815i q^{74} +(-41.9855 - 24.2403i) q^{76} +(-191.844 + 632.580i) q^{77} +(7.12361 - 12.3385i) q^{79} +(-582.755 + 1009.36i) q^{80} +(-1168.93 + 674.881i) q^{82} +(125.688 + 217.699i) q^{83} +(-1103.94 + 1912.08i) q^{85} +252.102i q^{86} -780.720 q^{88} +(505.658 + 875.825i) q^{89} +(-131.496 - 140.378i) q^{91} +(10.9668 - 6.33169i) q^{92} +(-725.684 + 418.974i) q^{94} +(1458.79 - 842.234i) q^{95} +(1125.76 - 649.959i) q^{97} +(-442.293 - 896.575i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7	\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) 44 * q + 3 * q^2 + 81 * q^4 + 6 * q^5 + 5 * q^7 - 6 * q^10 + 36 * q^13 - 129 * q^14 - 263 * q^16 - 72 * q^17 - 6 * q^19 + 24 * q^20 + 14 * q^22 + 698 * q^25 - 96 * q^26 - 156 * q^28 + 132 * q^29 + 177 * q^31 + 501 * q^32 - 24 * q^34 + 765 * q^35 + 82 * q^37 + 1746 * q^38 + 618 * q^41 + 82 * q^43 + 603 * q^44 + 266 * q^46 + 201 * q^47 + 515 * q^49 + 1845 * q^50 + 564 * q^53 - 3600 * q^56 - 538 * q^58 - 747 * q^59 - 1209 * q^61 - 2904 * q^62 - 1144 * q^64 + 831 * q^65 + 295 * q^67 - 7008 * q^68 - 390 * q^70 - 6 * q^73 + 144 * q^76 + 1203 * q^77 - 551 * q^79 - 4239 * q^80 + 18 * q^82 + 1830 * q^83 - 237 * q^85 + 1246 * q^88 + 4266 * q^89 - 1140 * q^91 - 7896 * q^92 - 3 * q^94 + 1053 * q^95 + 792 * q^97 + 5667 * q^98

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