LMFDB - Embedded newform 189.3.j.b.44.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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, 2]))

N = Newforms(chi, 3, names="a")

//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);

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

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			44.5
Character	$\chi$	$=$	189.44
Dual form			189.3.j.b.116.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29088i q^{2} +2.33363 q^{4} +(-4.18841 + 2.41818i) q^{5} +(6.74202 + 1.88284i) q^{7} -8.17595i q^{8} +O(q^{10})$	\(q-1.29088i q^{2} +2.33363 q^{4} +(-4.18841 + 2.41818i) q^{5} +(6.74202 + 1.88284i) q^{7} -8.17595i q^{8} +(3.12158 + 5.40673i) q^{10} +(11.8481 + 6.84049i) q^{11} +(8.59380 - 14.8849i) q^{13} +(2.43053 - 8.70314i) q^{14} -1.21966 q^{16} +(7.11684 - 4.10891i) q^{17} +(-6.93167 + 12.0060i) q^{19} +(-9.77419 + 5.64313i) q^{20} +(8.83026 - 15.2945i) q^{22} +(16.0497 - 9.26631i) q^{23} +(-0.804824 + 1.39400i) q^{25} +(-19.2146 - 11.0936i) q^{26} +(15.7334 + 4.39386i) q^{28} +(18.1723 - 10.4918i) q^{29} -51.5552 q^{31} -31.1294i q^{32} +(-5.30411 - 9.18698i) q^{34} +(-32.7914 + 8.41730i) q^{35} +(13.8496 - 23.9882i) q^{37} +(15.4983 + 8.94795i) q^{38} +(19.7709 + 34.2442i) q^{40} +(-18.4583 - 10.6569i) q^{41} +(18.1984 + 31.5205i) q^{43} +(27.6490 + 15.9632i) q^{44} +(-11.9617 - 20.7183i) q^{46} +59.3810i q^{47} +(41.9098 + 25.3884i) q^{49} +(1.79948 + 1.03893i) q^{50} +(20.0547 - 34.7358i) q^{52} +(-81.0775 + 46.8101i) q^{53} -66.1662 q^{55} +(15.3940 - 55.1225i) q^{56} +(-13.5436 - 23.4583i) q^{58} +1.67629i q^{59} -65.4713 q^{61} +66.5516i q^{62} -45.0629 q^{64} +83.1254i q^{65} -55.2191 q^{67} +(16.6081 - 9.58867i) q^{68} +(10.8657 + 42.3298i) q^{70} -14.2603i q^{71} +(32.6549 + 56.5599i) q^{73} +(-30.9659 - 17.8782i) q^{74} +(-16.1759 + 28.0176i) q^{76} +(67.0005 + 68.4269i) q^{77} -6.70408 q^{79} +(5.10843 - 2.94935i) q^{80} +(-13.7568 + 23.8274i) q^{82} +(-11.6006 + 6.69762i) q^{83} +(-19.8721 + 34.4196i) q^{85} +(40.6892 - 23.4919i) q^{86} +(55.9276 - 96.8694i) q^{88} +(-13.7259 - 7.92464i) q^{89} +(85.9656 - 84.1736i) q^{91} +(37.4541 - 21.6241i) q^{92} +76.6538 q^{94} -67.0481i q^{95} +(-40.7574 - 70.5938i) q^{97} +(32.7733 - 54.1005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) $ 22 * q - 24 * q^4 - 12 * q^5	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.29088i		−	0.645440i	−0.946494	−	0.322720i	$-0.895403\pi$
$2$		−	1.29088i		−	0.645440i	0.946494	−	0.322720i	$-0.104597\pi$
$3$		0			0
$3$		0			0
$4$	2.33363			0.583407
$5$	−4.18841	+	2.41818i	−0.837682	+	0.483636i	−0.856476	−	0.516188i	$-0.827351\pi$
$5$	−4.18841	+	2.41818i	−0.837682	+	0.483636i	0.0187939	+	0.999823i	$0.494017\pi$
$6$		0			0
$7$	6.74202	+	1.88284i	0.963146	+	0.268978i
$7$	6.74202	+	1.88284i	0.963146	+	0.268978i
$8$		−	8.17595i		−	1.02199i
$9$		0			0
$10$	3.12158	+	5.40673i	0.312158	+	0.540673i
$11$	11.8481	+	6.84049i	1.07710	+	0.621863i	0.930112	−	0.367275i	$-0.119709\pi$
$11$	11.8481	+	6.84049i	1.07710	+	0.621863i	0.146986	+	0.989139i	$0.453043\pi$
$12$		0			0
$13$	8.59380	−	14.8849i	0.661062	−	1.14499i	−0.319275	−	0.947662i	$-0.603439\pi$
$13$	8.59380	−	14.8849i	0.661062	−	1.14499i	0.980337	−	0.197330i	$-0.0632272\pi$
$14$	2.43053	−	8.70314i	0.173609	−	0.621653i
$15$		0			0
$16$	−1.21966			−0.0762287
$17$	7.11684	−	4.10891i	0.418638	−	0.241700i	−0.275857	−	0.961199i	$-0.588962\pi$
$17$	7.11684	−	4.10891i	0.418638	−	0.241700i	0.694494	+	0.719498i	$0.255628\pi$
$18$		0			0
$19$	−6.93167	+	12.0060i	−0.364825	+	0.631895i	−0.988748	−	0.149591i	$-0.952204\pi$
$19$	−6.93167	+	12.0060i	−0.364825	+	0.631895i	0.623923	+	0.781486i	$0.285538\pi$
$20$	−9.77419	+	5.64313i	−0.488710	+	0.282157i
$21$		0			0
$22$	8.83026	−	15.2945i	0.401375	−	0.695202i
$23$	16.0497	−	9.26631i	0.697814	−	0.402883i	−0.108719	−	0.994073i	$-0.534675\pi$
$23$	16.0497	−	9.26631i	0.697814	−	0.402883i	0.806533	+	0.591190i	$0.201341\pi$
$24$		0			0
$25$	−0.804824	+	1.39400i	−0.0321930	+	0.0557598i
$26$	−19.2146	−	11.0936i	−0.739024	−	0.426676i
$27$		0			0
$28$	15.7334	+	4.39386i	0.561907	+	0.156924i
$29$	18.1723	−	10.4918i	0.626631	−	0.361786i	−0.152815	−	0.988255i	$-0.548834\pi$
$29$	18.1723	−	10.4918i	0.626631	−	0.361786i	0.779446	+	0.626469i	$0.215501\pi$
$30$		0			0
$31$	−51.5552			−1.66307			−0.831536	−	0.555471i	$-0.812538\pi$
$31$	−51.5552			−1.66307			−0.831536	+	0.555471i	$0.812538\pi$
$32$		−	31.1294i		−	0.972793i
$33$		0			0
$34$	−5.30411	−	9.18698i	−0.156003	−	0.270205i
$35$	−32.7914	+	8.41730i	−0.936897	+	0.240494i
$36$		0			0
$37$	13.8496	−	23.9882i	0.374314	−	0.648331i	−0.615910	−	0.787816i	$-0.711212\pi$
$37$	13.8496	−	23.9882i	0.374314	−	0.648331i	0.990224	+	0.139486i	$0.0445449\pi$
$38$	15.4983	+	8.94795i	0.407850	+	0.235472i
$39$		0			0
$40$	19.7709	+	34.2442i	0.494273	+	0.856106i
$41$	−18.4583	−	10.6569i	−0.450202	−	0.259924i	0.257714	−	0.966221i	$-0.417031\pi$
$41$	−18.4583	−	10.6569i	−0.450202	−	0.259924i	−0.707915	+	0.706297i	$0.750364\pi$
$42$		0			0
$43$	18.1984	+	31.5205i	0.423218	+	0.733035i	0.996252	−	0.0864962i	$-0.0275670\pi$
$43$	18.1984	+	31.5205i	0.423218	+	0.733035i	−0.573034	+	0.819532i	$0.694234\pi$
$44$	27.6490	+	15.9632i	0.628387	+	0.362799i
$45$		0			0
$46$	−11.9617	−	20.7183i	−0.260037	−	0.450397i
$47$			59.3810i			1.26343i	0.775202	+	0.631713i	$0.217648\pi$
$47$			59.3810i			1.26343i	−0.775202	+	0.631713i	$0.782352\pi$
$48$		0			0
$49$	41.9098	+	25.3884i	0.855302	+	0.518130i
$50$	1.79948	+	1.03893i	0.0359896	+	0.0207786i
$51$		0			0
$52$	20.0547	−	34.7358i	0.385668	−	0.667997i
$53$	−81.0775	+	46.8101i	−1.52976	+	0.883210i	−0.530393	+	0.847752i	$0.677956\pi$
$53$	−81.0775	+	46.8101i	−1.52976	+	0.883210i	−0.999371	+	0.0354576i	$0.988711\pi$
$54$		0			0
$55$	−66.1662			−1.20302
$56$	15.3940	−	55.1225i	0.274894	−	0.984330i
$57$		0			0
$58$	−13.5436	−	23.4583i	−0.233511	−	0.404453i
$59$			1.67629i			0.0284116i	0.999899	+	0.0142058i	$0.00452200\pi$
$59$			1.67629i			0.0284116i	−0.999899	+	0.0142058i	$0.995478\pi$
$60$		0			0
$61$	−65.4713			−1.07330			−0.536650	−	0.843805i	$-0.680311\pi$
$61$	−65.4713			−1.07330			−0.536650	+	0.843805i	$0.680311\pi$
$62$			66.5516i			1.07341i
$63$		0			0
$64$	−45.0629			−0.704108
$65$			83.1254i			1.27885i
$66$		0			0
$67$	−55.2191			−0.824166			−0.412083	−	0.911146i	$-0.635199\pi$
$67$	−55.2191			−0.824166			−0.412083	+	0.911146i	$0.635199\pi$
$68$	16.6081	−	9.58867i	0.244236	−	0.141010i
$69$		0			0
$70$	10.8657	+	42.3298i	0.155225	+	0.604711i
$71$		−	14.2603i		−	0.200849i	−0.994945	−	0.100425i	$-0.967980\pi$
$71$		−	14.2603i		−	0.200849i	0.994945	−	0.100425i	$-0.0320202\pi$
$72$		0			0
$73$	32.6549	+	56.5599i	0.447327	+	0.774794i	0.998211	−	0.0597882i	$-0.0190425\pi$
$73$	32.6549	+	56.5599i	0.447327	+	0.774794i	−0.550884	+	0.834582i	$0.685709\pi$
$74$	−30.9659	−	17.8782i	−0.418459	−	0.241597i
$75$		0			0
$76$	−16.1759	+	28.0176i	−0.212841	+	0.368652i
$77$	67.0005	+	68.4269i	0.870136	+	0.888661i
$78$		0			0
$79$	−6.70408			−0.0848617			−0.0424309	−	0.999099i	$-0.513510\pi$
$79$	−6.70408			−0.0848617			−0.0424309	+	0.999099i	$0.513510\pi$
$80$	5.10843	−	2.94935i	0.0638554	−	0.0368669i
$81$		0			0
$82$	−13.7568	+	23.8274i	−0.167765	+	0.290578i
$83$	−11.6006	+	6.69762i	−0.139767	+	0.0806943i	−0.568253	−	0.822854i	$-0.692380\pi$
$83$	−11.6006	+	6.69762i	−0.139767	+	0.0806943i	0.428486	+	0.903548i	$0.359047\pi$
$84$		0			0
$85$	−19.8721	+	34.4196i	−0.233790	+	0.404936i
$86$	40.6892	−	23.4919i	0.473130	−	0.273162i
$87$		0			0
$88$	55.9276	−	96.8694i	0.635541	−	1.10079i
$89$	−13.7259	−	7.92464i	−0.154223	−	0.0890410i	0.420902	−	0.907106i	$-0.361714\pi$
$89$	−13.7259	−	7.92464i	−0.154223	−	0.0890410i	−0.575126	+	0.818065i	$0.695047\pi$
$90$		0			0
$91$	85.9656	−	84.1736i	0.944677	−	0.924984i
$92$	37.4541	−	21.6241i	0.407110	−	0.235045i
$93$		0			0
$94$	76.6538			0.815466
$95$		−	67.0481i		−	0.705769i
$96$		0			0
$97$	−40.7574	−	70.5938i	−0.420179	−	0.727771i	0.575778	−	0.817606i	$-0.304699\pi$
$97$	−40.7574	−	70.5938i	−0.420179	−	0.727771i	−0.995957	+	0.0898349i	$0.971366\pi$
$98$	32.7733	−	54.1005i	0.334422	−	0.552046i
$99$		0			0
$100$	−1.87816	+	3.25307i	−0.0187816	+	0.0325307i
$101$	−12.8955	−	7.44522i	−0.127678	−	0.0737150i	0.434801	−	0.900527i	$-0.356819\pi$
$101$	−12.8955	−	7.44522i	−0.127678	−	0.0737150i	−0.562479	+	0.826812i	$0.690152\pi$
$102$		0			0
$103$	−38.9876	−	67.5286i	−0.378521	−	0.655617i	0.612327	−	0.790605i	$-0.290234\pi$
$103$	−38.9876	−	67.5286i	−0.378521	−	0.655617i	−0.990847	+	0.134988i	$0.956900\pi$
$104$	−121.698	−	70.2625i	−1.17018	−	0.675601i
$105$		0			0
$106$	60.4262	+	104.661i	0.570059	+	0.987371i
$107$	−73.0945	−	42.2012i	−0.683127	−	0.394403i	0.117905	−	0.993025i	$-0.462382\pi$
$107$	−73.0945	−	42.2012i	−0.683127	−	0.394403i	−0.801032	+	0.598622i	$0.795715\pi$
$108$		0			0
$109$	−18.7753	−	32.5198i	−0.172251	−	0.298347i	0.766956	−	0.641700i	$-0.221771\pi$
$109$	−18.7753	−	32.5198i	−0.172251	−	0.298347i	−0.939206	+	0.343353i	$0.888437\pi$
$110$			85.4126i			0.776478i
$111$		0			0
$112$	−8.22297	−	2.29643i	−0.0734194	−	0.0205038i
$113$	9.59066	+	5.53717i	0.0848731	+	0.0490015i	0.541836	−	0.840484i	$-0.317729\pi$
$113$	9.59066	+	5.53717i	0.0848731	+	0.0490015i	−0.456963	+	0.889486i	$0.651063\pi$
$114$		0			0
$115$	−44.8152	+	77.6222i	−0.389697	+	0.674975i
$116$	42.4074	−	24.4839i	0.365581	−	0.211068i
$117$		0			0
$118$	2.16388			0.0183380
$119$	55.7183	−	14.3025i	0.468221	−	0.120189i
$120$		0			0
$121$	33.0847	+	57.3045i	0.273428	+	0.473590i
$122$			84.5156i			0.692751i
$123$		0			0
$124$	−120.311			−0.970248
$125$		−	128.694i		−	1.02955i
$126$		0			0
$127$	240.533			1.89396			0.946982	−	0.321287i	$-0.104116\pi$
$127$	240.533			1.89396			0.946982	+	0.321287i	$0.104116\pi$
$128$		−	66.3467i		−	0.518334i
$129$		0			0
$130$	107.305			0.825422
$131$	21.6755	−	12.5144i	0.165462	−	0.0955294i	−0.414982	−	0.909829i	$-0.636212\pi$
$131$	21.6755	−	12.5144i	0.165462	−	0.0955294i	0.580444	+	0.814300i	$0.302879\pi$
$132$		0			0
$133$	−69.3389	+	67.8935i	−0.521345	+	0.510478i
$134$			71.2813i			0.531950i
$135$		0			0
$136$	−33.5942	−	58.1869i	−0.247017	−	0.427845i
$137$	−221.699	−	127.998i	−1.61824	−	0.934293i	−0.987375	−	0.158403i	$-0.949366\pi$
$137$	−221.699	−	127.998i	−1.61824	−	0.934293i	−0.630868	−	0.775890i	$-0.717301\pi$
$138$		0			0
$139$	25.1689	−	43.5938i	0.181071	−	0.313625i	−0.761174	−	0.648547i	$-0.775377\pi$
$139$	25.1689	−	43.5938i	0.181071	−	0.313625i	0.942246	+	0.334923i	$0.108710\pi$
$140$	−76.5230	+	19.6429i	−0.546593	+	0.140306i
$141$		0			0
$142$	−18.4083			−0.129636
$143$	203.640	−	117.572i	1.42406	−	0.822180i
$144$		0			0
$145$	−50.7420	+	87.8877i	−0.349945	+	0.606122i
$146$	73.0121	−	42.1536i	0.500083	−	0.288723i
$147$		0			0
$148$	32.3199	−	55.9797i	0.218377	−	0.378241i
$149$	−114.335	+	66.0114i	−0.767350	+	0.443030i	−0.831929	−	0.554883i	$-0.812763\pi$
$149$	−114.335	+	66.0114i	−0.767350	+	0.443030i	0.0645783	+	0.997913i	$0.479430\pi$
$150$		0			0
$151$	144.042	−	249.488i	0.953922	−	1.65224i	0.217105	−	0.976148i	$-0.430338\pi$
$151$	144.042	−	249.488i	0.953922	−	1.65224i	0.736816	−	0.676093i	$-0.236328\pi$
$152$	98.1605	+	56.6730i	0.645793	+	0.372849i
$153$		0			0
$154$	88.3309	−	86.4896i	0.573577	−	0.561621i
$155$	215.934	−	124.670i	1.39312	−	0.804321i
$156$		0			0
$157$	8.53375			0.0543551			0.0271775	−	0.999631i	$-0.491348\pi$
$157$	8.53375			0.0543551			0.0271775	+	0.999631i	$0.491348\pi$
$158$			8.65416i			0.0547731i
$159$		0			0
$160$	75.2764	+	130.383i	0.470478	+	0.814891i
$161$	125.655	−	32.2546i	0.780463	−	0.200339i
$162$		0			0
$163$	−96.2204	+	166.659i	−0.590309	+	1.02245i	0.403881	+	0.914811i	$0.367661\pi$
$163$	−96.2204	+	166.659i	−0.590309	+	1.02245i	−0.994191	+	0.107634i	$0.965672\pi$
$164$	−43.0748	−	24.8692i	−0.262651	−	0.151642i
$165$		0			0
$166$	8.64583	+	14.9750i	0.0520833	+	0.0902109i
$167$	125.010	+	72.1747i	0.748564	+	0.432184i	0.825175	−	0.564877i	$-0.191077\pi$
$167$	125.010	+	72.1747i	0.748564	+	0.432184i	−0.0766107	+	0.997061i	$0.524410\pi$
$168$		0			0
$169$	−63.2069	−	109.477i	−0.374005	−	0.647796i
$170$	44.4315	+	25.6526i	0.261362	+	0.150897i
$171$		0			0
$172$	42.4683	+	73.5572i	0.246909	+	0.427658i
$173$			306.768i			1.77322i	0.462513	+	0.886612i	$0.346948\pi$
$173$			306.768i			1.77322i	−0.462513	+	0.886612i	$0.653052\pi$
$174$		0			0
$175$	−8.05082	+	7.88300i	−0.0460047	+	0.0450457i
$176$	−14.4506	−	8.34307i	−0.0821058	−	0.0474038i
$177$		0			0
$178$	−10.2298	+	17.7185i	−0.0574706	+	0.0995420i
$179$	−180.597	+	104.268i	−1.00892	+	0.582502i	−0.910876	−	0.412680i	$-0.864593\pi$
$179$	−180.597	+	104.268i	−1.00892	+	0.582502i	−0.0980467	+	0.995182i	$0.531259\pi$
$180$		0			0
$181$	−132.399			−0.731485			−0.365742	−	0.930716i	$-0.619185\pi$
$181$	−132.399			−0.731485			−0.365742	+	0.930716i	$0.619185\pi$
$182$	−108.658	−	110.971i	−0.597022	−	0.609732i
$183$		0			0
$184$	−75.7609	−	131.222i	−0.411744	−	0.713162i
$185$			133.963i			0.724126i
$186$		0			0
$187$	112.428			0.601219
$188$			138.573i			0.737092i
$189$		0			0
$190$	−86.5510			−0.455531
$191$		−	106.630i		−	0.558271i	−0.960252	−	0.279136i	$-0.909952\pi$
$191$		−	106.630i		−	0.558271i	0.960252	−	0.279136i	$-0.0900479\pi$
$192$		0			0
$193$	−127.692			−0.661618			−0.330809	−	0.943698i	$-0.607322\pi$
$193$	−127.692			−0.661618			−0.330809	+	0.943698i	$0.607322\pi$
$194$	−91.1282	+	52.6129i	−0.469733	+	0.271200i
$195$		0			0
$196$	97.8019	+	59.2470i	0.498989	+	0.302281i
$197$		−	0.117739i		−	0.000597658i	−1.00000		0.000298829i	$-0.999905\pi$
$197$		−	0.117739i		−	0.000597658i	1.00000		0.000298829i	$-9.51202e-5\pi$
$198$		0			0
$199$	53.3999	+	92.4913i	0.268341	+	0.464780i	0.968434	−	0.249272i	$-0.0801913\pi$
$199$	53.3999	+	92.4913i	0.268341	+	0.464780i	−0.700093	+	0.714052i	$0.746858\pi$
$200$	11.3972	+	6.58020i	0.0569862	+	0.0329010i
$201$		0			0
$202$	−9.61088	+	16.6465i	−0.0475786	+	0.0824086i
$203$	142.273	−	36.5202i	0.700850	−	0.179903i
$204$		0			0
$205$	103.081			0.502834
$206$	−87.1713	+	50.3283i	−0.423161	+	0.244312i
$207$		0			0
$208$	−10.4815	+	18.1545i	−0.0503919	+	0.0872813i
$209$	−164.254	+	94.8321i	−0.785904	+	0.453742i
$210$		0			0
$211$	−35.3849	+	61.2884i	−0.167701	+	0.290466i	−0.937611	−	0.347686i	$-0.886968\pi$
$211$	−35.3849	+	61.2884i	−0.167701	+	0.290466i	0.769910	+	0.638152i	$0.220301\pi$
$212$	−189.205	+	109.237i	−0.892475	+	0.515271i
$213$		0			0
$214$	−54.4766	+	94.3563i	−0.254564	+	0.440917i
$215$	−152.445	−	88.0139i	−0.709044	−	0.409367i
$216$		0			0
$217$	−347.586	−	97.0704i	−1.60178	−	0.447329i
$218$	−41.9791	+	24.2367i	−0.192565	+	0.111177i
$219$		0			0
$220$	−154.407			−0.701851
$221$		−	141.245i		−	0.639116i
$222$		0			0
$223$	118.725	+	205.638i	0.532399	+	0.922142i	0.999284	+	0.0378245i	$0.0120428\pi$
$223$	118.725	+	205.638i	0.532399	+	0.922142i	−0.466885	+	0.884318i	$0.654624\pi$
$224$	58.6118	−	209.875i	0.261660	−	0.936942i
$225$		0			0
$226$	7.14782	−	12.3804i	0.0316275	−	0.0547805i
$227$	−274.812	−	158.663i	−1.21063	−	0.698956i	−0.247731	−	0.968829i	$-0.579685\pi$
$227$	−274.812	−	158.663i	−1.21063	−	0.698956i	−0.962896	+	0.269873i	$0.913018\pi$
$228$		0			0
$229$	38.3306	+	66.3906i	0.167383	+	0.289915i	0.937499	−	0.347988i	$-0.113135\pi$
$229$	38.3306	+	66.3906i	0.167383	+	0.289915i	−0.770116	+	0.637904i	$0.779802\pi$
$230$	100.201	+	57.8510i	0.435656	+	0.251526i
$231$		0			0
$232$	−85.7803	−	148.576i	−0.369743	−	0.640413i
$233$	285.287	+	164.710i	1.22441	+	0.706912i	0.965854	−	0.259085i	$-0.0834211\pi$
$233$	285.287	+	164.710i	1.22441	+	0.706912i	0.258553	+	0.965997i	$0.416754\pi$
$234$		0			0
$235$	−143.594	−	248.712i	−0.611038	−	1.05835i
$236$			3.91183i			0.0165755i
$237$		0			0
$238$	−18.4628	−	71.9257i	−0.0775746	−	0.302209i
$239$	−50.1733	−	28.9676i	−0.209930	−	0.121203i	0.391349	−	0.920242i	$-0.372009\pi$
$239$	−50.1733	−	28.9676i	−0.209930	−	0.121203i	−0.601279	+	0.799039i	$0.705342\pi$
$240$		0			0
$241$	−39.9081	+	69.1229i	−0.165594	+	0.286817i	−0.936866	−	0.349689i	$-0.886287\pi$
$241$	−39.9081	+	69.1229i	−0.165594	+	0.286817i	0.771272	+	0.636506i	$0.219621\pi$
$242$	73.9732	−	42.7084i	0.305674	−	0.176481i
$243$		0			0
$244$	−152.786			−0.626171
$245$	−236.929	−	4.99147i	−0.967057	−	0.0203733i
$246$		0			0
$247$	119.139	+	206.354i	0.482343	+	0.835443i
$248$			421.513i			1.69965i
$249$		0			0
$250$	−166.128			−0.664513
$251$			186.751i			0.744029i	0.928227	+	0.372014i	$0.121333\pi$
$251$			186.751i			0.744029i	−0.928227	+	0.372014i	$0.878667\pi$
$252$		0			0
$253$	253.545			1.00215
$254$		−	310.500i		−	1.22244i
$255$		0			0
$256$	−265.897			−1.03866
$257$	313.154	−	180.800i	1.21850	−	0.703500i	0.253902	−	0.967230i	$-0.418286\pi$
$257$	313.154	−	180.800i	1.21850	−	0.703500i	0.964597	+	0.263730i	$0.0849527\pi$
$258$		0			0
$259$	138.541	−	135.653i	0.534906	−	0.523755i
$260$			193.984i			0.746092i
$261$		0			0
$262$	−16.1545	−	27.9805i	−0.0616585	−	0.106796i
$263$	331.834	+	191.585i	1.26173	+	0.728458i	0.973409	−	0.229076i	$-0.0735705\pi$
$263$	331.834	+	191.585i	1.26173	+	0.728458i	0.288319	+	0.957535i	$0.406904\pi$
$264$		0			0
$265$	226.390	−	392.120i	0.854303	−	1.47970i
$266$	87.6424	+	89.5082i	0.329483	+	0.336497i
$267$		0			0
$268$	−128.861			−0.480825
$269$	70.7645	−	40.8559i	0.263065	−	0.151881i	−0.362667	−	0.931919i	$-0.618134\pi$
$269$	70.7645	−	40.8559i	0.263065	−	0.151881i	0.625732	+	0.780038i	$0.284800\pi$
$270$		0			0
$271$	187.954	−	325.546i	0.693558	−	1.20128i	−0.277107	−	0.960839i	$-0.589376\pi$
$271$	187.954	−	325.546i	0.693558	−	1.20128i	0.970665	−	0.240438i	$-0.0772910\pi$
$272$	−8.68012	+	5.01147i	−0.0319122	+	0.0184245i
$273$		0			0
$274$	−165.230	+	286.187i	−0.603030	+	1.04448i
$275$	−19.0712	+	11.0108i	−0.0693500	+	0.0400392i
$276$		0			0
$277$	−55.5534	+	96.2213i	−0.200554	+	0.347369i	−0.948707	−	0.316157i	$-0.897607\pi$
$277$	−55.5534	+	96.2213i	−0.200554	+	0.347369i	0.748153	+	0.663526i	$0.230941\pi$
$278$	−56.2744	−	32.4900i	−0.202426	−	0.116871i
$279$		0			0
$280$	68.8195	+	268.101i	0.245784	+	0.957504i
$281$	−88.6512	+	51.1828i	−0.315485	+	0.182145i	−0.649378	−	0.760466i	$-0.724971\pi$
$281$	−88.6512	+	51.1828i	−0.315485	+	0.182145i	0.333893	+	0.942611i	$0.391637\pi$
$282$		0			0
$283$	114.057			0.403027			0.201513	−	0.979486i	$-0.435414\pi$
$283$	114.057			0.403027			0.201513	+	0.979486i	$0.435414\pi$
$284$		−	33.2783i		−	0.117177i
$285$		0			0
$286$	−151.771	−	262.875i	−0.530668	−	0.919143i
$287$	−104.381	−	106.603i	−0.363696	−	0.371439i
$288$		0			0
$289$	−110.734	+	191.796i	−0.383162	+	0.663656i
$290$	113.453	+	65.5018i	0.391216	+	0.225868i
$291$		0			0
$292$	76.2044	+	131.990i	0.260974	+	0.452020i
$293$	−98.3627	−	56.7897i	−0.335709	−	0.193822i	0.322664	−	0.946514i	$-0.395422\pi$
$293$	−98.3627	−	56.7897i	−0.335709	−	0.193822i	−0.658373	+	0.752692i	$0.728755\pi$
$294$		0			0
$295$	−4.05356	−	7.02097i	−0.0137409	−	0.0237999i
$296$	−196.127	−	113.234i	−0.662590	−	0.382547i
$297$		0			0
$298$	85.2129	+	147.593i	0.285949	+	0.495278i
$299$		−	318.531i		−	1.06532i
$300$		0			0
$301$	63.3457	+	246.777i	0.210451	+	0.819857i
$302$	−322.060	−	185.941i	−1.06642	−	0.615699i
$303$		0			0
$304$	8.45427	−	14.6432i	0.0278101	−	0.0481685i
$305$	274.221	−	158.321i	0.899084	−	0.519087i
$306$		0			0
$307$	375.302			1.22248			0.611241	−	0.791445i	$-0.290671\pi$
$307$	375.302			1.22248			0.611241	+	0.791445i	$0.290671\pi$
$308$	156.354	+	159.683i	0.507644	+	0.518451i
$309$		0			0
$310$	−160.934	−	278.745i	−0.519141	−	0.899178i
$311$		−	551.374i		−	1.77291i	−0.462819	−	0.886453i	$-0.653162\pi$
$311$		−	551.374i		−	1.77291i	0.462819	−	0.886453i	$-0.346838\pi$
$312$		0			0
$313$	−188.882			−0.603456			−0.301728	−	0.953394i	$-0.597564\pi$
$313$	−188.882			−0.603456			−0.301728	+	0.953394i	$0.597564\pi$
$314$		−	11.0160i		−	0.0350829i
$315$		0			0
$316$	−15.6448			−0.0495089
$317$			461.451i			1.45568i	0.685746	+	0.727841i	$0.259476\pi$
$317$			461.451i			1.45568i	−0.685746	+	0.727841i	$0.740524\pi$
$318$		0			0
$319$	287.076			0.899925
$320$	188.742	−	108.970i	0.589819	−	0.340532i
$321$		0			0
$322$	−41.6368	−	162.205i	−0.129307	−	0.503742i
$323$			113.926i			0.352713i
$324$		0			0
$325$	13.8330	+	23.9594i	0.0425631	+	0.0737214i
$326$	215.136	+	124.209i	0.659927	+	0.381009i
$327$		0			0
$328$	−87.1302	+	150.914i	−0.265641	+	0.460104i
$329$	−111.805	+	400.348i	−0.339834	+	1.21686i
$330$		0			0
$331$	146.396			0.442284			0.221142	−	0.975242i	$-0.429022\pi$
$331$	146.396			0.442284			0.221142	+	0.975242i	$0.429022\pi$
$332$	−27.0716	+	15.6298i	−0.0815408	+	0.0470776i
$333$		0			0
$334$	93.1689	−	161.373i	0.278949	−	0.483153i
$335$	231.280	−	133.530i	0.690389	−	0.398596i
$336$		0			0
$337$	122.785	−	212.670i	0.364348	−	0.631070i	−0.624323	−	0.781166i	$-0.714625\pi$
$337$	122.785	−	212.670i	0.364348	−	0.631070i	0.988671	+	0.150097i	$0.0479585\pi$
$338$	−141.322	+	81.5925i	−0.418113	+	0.241398i
$339$		0			0
$340$	−46.3742	+	80.3225i	−0.136395	+	0.236243i
$341$	−610.830	−	352.663i	−1.79129	−	1.03420i
$342$		0			0
$343$	234.755	+	250.079i	0.684416	+	0.729092i
$344$	257.710	−	148.789i	0.749158	−	0.432527i
$345$		0			0
$346$	396.000			1.14451
$347$			22.5905i			0.0651023i	0.999470	+	0.0325511i	$0.0103632\pi$
$347$			22.5905i			0.0651023i	−0.999470	+	0.0325511i	$0.989637\pi$
$348$		0			0
$349$	167.280	+	289.738i	0.479313	+	0.830195i	0.999719	−	0.0237246i	$-0.00755249\pi$
$349$	167.280	+	289.738i	0.479313	+	0.830195i	−0.520405	+	0.853919i	$0.674219\pi$
$350$	10.1760	+	10.3926i	0.0290743	+	0.0296933i
$351$		0			0
$352$	212.940	−	368.824i	0.604944	−	1.04779i
$353$	329.152	+	190.036i	0.932443	+	0.538346i	0.887583	−	0.460647i	$-0.152383\pi$
$353$	329.152	+	190.036i	0.932443	+	0.538346i	0.0448593	+	0.998993i	$0.485716\pi$
$354$		0			0
$355$	34.4840	+	59.7280i	0.0971380	+	0.168248i
$356$	−32.0311	−	18.4932i	−0.0899751	−	0.0519471i
$357$		0			0
$358$	134.597	+	233.129i	0.375970	+	0.651199i
$359$	−1.25505	−	0.724605i	−0.00349597	−	0.00201840i	0.498251	−	0.867033i	$-0.333976\pi$
$359$	−1.25505	−	0.724605i	−0.00349597	−	0.00201840i	−0.501747	+	0.865014i	$0.667309\pi$
$360$		0			0
$361$	84.4039	+	146.192i	0.233806	+	0.404964i
$362$			170.911i			0.472130i
$363$		0			0
$364$	200.612	−	196.430i	0.551131	−	0.539643i
$365$	−273.544	−	157.931i	−0.749436	−	0.432687i
$366$		0			0
$367$	215.427	−	373.131i	0.586995	−	1.01671i	−0.407628	−	0.913148i	$-0.633644\pi$
$367$	215.427	−	373.131i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$368$	−19.5752	+	11.3017i	−0.0531934	+	0.0307112i
$369$		0			0
$370$	172.931			0.467380
$371$	−634.763	+	162.939i	−1.71095	+	0.439188i
$372$		0			0
$373$	−17.9931	−	31.1650i	−0.0482390	−	0.0835524i	0.840898	−	0.541194i	$-0.182028\pi$
$373$	−17.9931	−	31.1650i	−0.0482390	−	0.0835524i	−0.889137	+	0.457642i	$0.848694\pi$
$374$		−	145.131i		−	0.388050i
$375$		0			0
$376$	485.497			1.29121
$377$		−	360.657i		−	0.956650i
$378$		0			0
$379$	−694.643			−1.83283			−0.916415	−	0.400229i	$-0.868931\pi$
$379$	−694.643			−1.83283			−0.916415	+	0.400229i	$0.868931\pi$
$380$		−	156.465i		−	0.411751i
$381$		0			0
$382$	−137.646			−0.360331
$383$	298.698	−	172.453i	0.779890	−	0.450270i	−0.0565010	−	0.998403i	$-0.517994\pi$
$383$	298.698	−	172.453i	0.779890	−	0.450270i	0.836391	+	0.548133i	$0.184661\pi$
$384$		0			0
$385$	−446.094	−	124.581i	−1.15869	−	0.323586i
$386$			164.835i			0.427035i
$387$		0			0
$388$	−95.1126	−	164.740i	−0.245136	−	0.424587i
$389$	382.336	+	220.742i	0.982870	+	0.567460i	0.903135	−	0.429356i	$-0.141259\pi$
$389$	382.336	+	220.742i	0.982870	+	0.567460i	0.0797346	+	0.996816i	$0.474593\pi$
$390$		0			0
$391$	76.1488	−	131.894i	0.194754	−	0.337324i
$392$	207.574	−	342.653i	0.529526	−	0.874114i
$393$		0			0
$394$	−0.151986			−0.000385752
$395$	28.0794	−	16.2117i	0.0710871	−	0.0410422i
$396$		0			0
$397$	43.5787	−	75.4806i	0.109770	−	0.190127i	−0.805907	−	0.592042i	$-0.798322\pi$
$397$	43.5787	−	75.4806i	0.109770	−	0.190127i	0.915677	+	0.401915i	$0.131655\pi$
$398$	119.395	−	68.9328i	0.299988	−	0.173198i
$399$		0			0
$400$	0.981611	−	1.70020i	0.00245403	−	0.00425050i
$401$	570.263	−	329.241i	1.42210	−	0.821051i	0.425623	−	0.904900i	$-0.360055\pi$
$401$	570.263	−	329.241i	1.42210	−	0.821051i	0.996478	+	0.0838495i	$0.0267215\pi$
$402$		0			0
$403$	−443.055	+	767.394i	−1.09939	+	1.90420i
$404$	−30.0933	−	17.3744i	−0.0744884	−	0.0430059i
$405$		0			0
$406$	−47.1433	−	183.657i	−0.116116	−	0.452356i
$407$	328.183	−	189.476i	0.806346	−	0.465544i
$408$		0			0
$409$	−617.037			−1.50865			−0.754324	−	0.656502i	$-0.772035\pi$
$409$	−617.037			−1.50865			−0.754324	+	0.656502i	$0.772035\pi$
$410$		−	133.065i		−	0.324549i
$411$		0			0
$412$	−90.9827	−	157.587i	−0.220832	−	0.382492i
$413$	−3.15618	+	11.3016i	−0.00764209	+	0.0273645i
$414$		0			0
$415$	32.3921	−	56.1048i	0.0780533	−	0.135192i
$416$	−463.358	−	267.520i	−1.11384	−	0.643076i
$417$		0			0
$418$	122.417	+	212.032i	0.292863	+	0.507254i
$419$	−186.805	−	107.852i	−0.445835	−	0.257403i	0.260235	−	0.965545i	$-0.416200\pi$
$419$	−186.805	−	107.852i	−0.445835	−	0.257403i	−0.706069	+	0.708143i	$0.749533\pi$
$420$		0			0
$421$	−277.485	−	480.618i	−0.659110	−	1.14161i	−0.980847	−	0.194782i	$-0.937600\pi$
$421$	−277.485	−	480.618i	−0.659110	−	1.14161i	0.321737	−	0.946829i	$-0.395733\pi$
$422$	79.1160	+	45.6776i	0.187479	+	0.108241i
$423$		0			0
$424$	382.717	+	662.886i	0.902635	+	1.56341i
$425$			13.2278i			0.0311242i
$426$		0			0
$427$	−441.409	−	123.272i	−1.03375	−	0.288694i
$428$	−170.576	−	98.4818i	−0.398541	−	0.230098i
$429$		0			0
$430$	−113.615	+	196.788i	−0.264222	+	0.457645i
$431$	−702.016	+	405.309i	−1.62881	+	0.940392i	−0.644357	+	0.764725i	$0.722875\pi$
$431$	−702.016	+	405.309i	−1.62881	+	0.940392i	−0.984450	+	0.175667i	$0.943792\pi$
$432$		0			0
$433$	−352.669			−0.814477			−0.407239	−	0.913322i	$-0.633508\pi$
$433$	−352.669			−0.814477			−0.407239	+	0.913322i	$0.633508\pi$
$434$	−125.306	+	448.692i	−0.288724	+	1.03385i
$435$		0			0
$436$	−43.8146	−	75.8891i	−0.100492	−	0.174058i
$437$			256.924i			0.587927i
$438$		0			0
$439$	390.249			0.888950			0.444475	−	0.895791i	$-0.353390\pi$
$439$	390.249			0.888950			0.444475	+	0.895791i	$0.353390\pi$
$440$			540.971i			1.22948i
$441$		0			0
$442$	−182.330			−0.412511
$443$		−	183.549i		−	0.414331i	−0.978306	−	0.207165i	$-0.933576\pi$
$443$		−	183.549i		−	0.414331i	0.978306	−	0.207165i	$-0.0664238\pi$
$444$		0			0
$445$	76.6528			0.172254
$446$	265.454	−	153.260i	0.595188	−	0.343632i
$447$		0			0
$448$	−303.815	−	84.8465i	−0.678159	−	0.189389i
$449$			653.190i			1.45477i	0.686231	+	0.727383i	$0.259264\pi$
$449$			653.190i			1.45477i	−0.686231	+	0.727383i	$0.740736\pi$
$450$		0			0
$451$	−145.797	−	252.527i	−0.323275	−	0.559928i
$452$	22.3810	+	12.9217i	0.0495156	+	0.0285878i
$453$		0			0
$454$	−204.815	+	354.750i	−0.451134	+	0.781387i
$455$	−156.512	+	560.433i	−0.343983	+	1.23172i
$456$		0			0
$457$	145.728			0.318880			0.159440	−	0.987208i	$-0.449031\pi$
$457$	145.728			0.318880			0.159440	+	0.987208i	$0.449031\pi$
$458$	85.7023	−	49.4802i	0.187123	−	0.108035i
$459$		0			0
$460$	−104.582	+	181.141i	−0.227352	+	0.393786i
$461$	6.30986	−	3.64300i	0.0136873	−	0.00790238i	−0.493141	−	0.869950i	$-0.664151\pi$
$461$	6.30986	−	3.64300i	0.0136873	−	0.00790238i	0.506828	+	0.862047i	$0.330818\pi$
$462$		0			0
$463$	−22.2343	+	38.5110i	−0.0480223	+	0.0831771i	−0.889037	−	0.457835i	$-0.848625\pi$
$463$	−22.2343	+	38.5110i	−0.0480223	+	0.0831771i	0.841015	+	0.541012i	$0.181959\pi$
$464$	−22.1640	+	12.7964i	−0.0477673	+	0.0275784i
$465$		0			0
$466$	212.621	−	368.271i	0.456269	−	0.790281i
$467$	−174.902	−	100.980i	−0.374523	−	0.216231i	0.300909	−	0.953653i	$-0.402710\pi$
$467$	−174.902	−	100.980i	−0.374523	−	0.216231i	−0.675433	+	0.737422i	$0.736043\pi$
$468$		0			0
$469$	−372.289	−	103.969i	−0.793793	−	0.221682i
$470$	−321.057	+	185.363i	−0.683101	+	0.394388i
$471$		0			0
$472$	13.7052			0.0290365
$473$			497.944i			1.05274i
$474$		0			0
$475$	−11.1575	−	19.3254i	−0.0234896	−	0.0406851i
$476$	130.026	−	33.3766i	0.273164	−	0.0701190i
$477$		0			0
$478$	−37.3936	+	64.7677i	−0.0782294	+	0.135497i
$479$	−165.224	−	95.3922i	−0.344935	−	0.199149i	0.317517	−	0.948253i	$-0.397151\pi$
$479$	−165.224	−	95.3922i	−0.344935	−	0.199149i	−0.662452	+	0.749104i	$0.730484\pi$
$480$		0			0
$481$	−238.042	−	412.300i	−0.494889	−	0.857173i
$482$	89.2294	+	51.5166i	0.185123	+	0.106881i
$483$		0			0
$484$	77.2075	+	133.727i	0.159520	+	0.276296i
$485$	341.417	+	197.117i	0.703953	+	0.406427i
$486$		0			0
$487$	−60.9902	−	105.638i	−0.125236	−	0.216916i	0.796589	−	0.604521i	$-0.206636\pi$
$487$	−60.9902	−	105.638i	−0.125236	−	0.216916i	−0.921825	+	0.387605i	$0.873302\pi$
$488$			535.291i			1.09691i
$489$		0			0
$490$	−6.44339	+	305.847i	−0.0131498	+	0.624177i
$491$	121.061	+	69.8948i	0.246561	+	0.142352i	0.618189	−	0.786030i	$-0.287867\pi$
$491$	121.061	+	69.8948i	0.246561	+	0.142352i	−0.371628	+	0.928382i	$0.621200\pi$
$492$		0			0
$493$	86.2196	−	149.337i	0.174888	−	0.302914i
$494$	266.379	−	153.794i	0.539228	−	0.311324i
$495$		0			0
$496$	62.8798			0.126774
$497$	26.8499	−	96.1434i	0.0540240	−	0.193447i
$498$		0			0
$499$	113.725	+	196.977i	0.227906	+	0.394744i	0.957187	−	0.289469i	$-0.0934789\pi$
$499$	113.725	+	196.977i	0.227906	+	0.394744i	−0.729282	+	0.684214i	$0.760146\pi$
$500$		−	300.324i		−	0.600647i
$501$		0			0
$502$	241.073			0.480226
$503$		−	911.427i		−	1.81198i	−0.423298	−	0.905991i	$-0.639128\pi$
$503$		−	911.427i		−	1.81198i	0.423298	−	0.905991i	$-0.360872\pi$
$504$		0			0
$505$	72.0155			0.142605
$506$		−	327.296i		−	0.646829i
$507$		0			0
$508$	561.316			1.10495
$509$	63.1748	−	36.4740i	0.124116	−	0.0716581i	−0.436657	−	0.899628i	$-0.643838\pi$
$509$	63.1748	−	36.4740i	0.124116	−	0.0716581i	0.560772	+	0.827970i	$0.310504\pi$
$510$		0			0
$511$	113.667	+	442.813i	0.222439	+	0.866561i
$512$			77.8547i			0.152060i
$513$		0			0
$514$	−233.391	−	404.244i	−0.454067	−	0.786467i
$515$	326.592	+	188.558i	0.634160	+	0.366132i
$516$		0			0
$517$	−406.196	+	703.552i	−0.785678	+	1.36083i
$518$	−175.111	−	178.839i	−0.338053	−	0.345249i
$519$		0			0
$520$	679.629			1.30698
$521$	−317.781	+	183.471i	−0.609944	+	0.352152i	−0.772944	−	0.634475i	$-0.781216\pi$
$521$	−317.781	+	183.471i	−0.609944	+	0.352152i	0.162999	+	0.986626i	$0.447883\pi$
$522$		0			0
$523$	−52.6461	+	91.1858i	−0.100662	+	0.174351i	−0.911958	−	0.410285i	$-0.865429\pi$
$523$	−52.6461	+	91.1858i	−0.100662	+	0.174351i	0.811296	+	0.584636i	$0.198763\pi$
$524$	50.5826	−	29.2039i	0.0965316	−	0.0557326i
$525$		0			0
$526$	247.313	−	428.358i	0.470176	−	0.814369i
$527$	−366.910	+	211.836i	−0.696224	+	0.401965i
$528$		0			0
$529$	−92.7710	+	160.684i	−0.175371	+	0.303751i
$530$	−506.179	−	292.243i	−0.955056	−	0.551402i
$531$		0			0
$532$	−161.811	+	158.438i	−0.304157	+	0.297816i
$533$	−317.254	+	183.166i	−0.595222	+	0.343652i
$534$		0			0
$535$	408.200			0.762990
$536$			451.469i			0.842293i
$537$		0			0
$538$	−52.7400	−	91.3484i	−0.0980298	−	0.169793i
$539$	322.882	+	587.487i	0.599039	+	1.08996i
$540$		0			0
$541$	65.3800	−	113.242i	0.120850	−	0.209319i	−0.799253	−	0.600995i	$-0.794771\pi$
$541$	65.3800	−	113.242i	0.120850	−	0.209319i	0.920103	+	0.391676i	$0.128105\pi$
$542$	−420.241	−	242.626i	−0.775352	−	0.447650i
$543$		0			0
$544$	−127.908	−	221.543i	−0.235125	−	0.407248i
$545$	157.277	+	90.8041i	0.288582	+	0.166613i
$546$		0			0
$547$	36.9358	+	63.9746i	0.0675242	+	0.116955i	0.897811	−	0.440381i	$-0.145157\pi$
$547$	36.9358	+	63.9746i	0.0675242	+	0.116955i	−0.830287	+	0.557337i	$0.811823\pi$
$548$	−517.364	−	298.700i	−0.944094	−	0.545073i
$549$		0			0
$550$	14.2136	+	24.6187i	0.0258429	+	0.0447612i
$551$			290.902i			0.527953i
$552$		0			0
$553$	−45.1990	−	12.6227i	−0.0817343	−	0.0228259i
$554$	124.210	+	71.7127i	0.224206	+	0.129445i
$555$		0			0
$556$	58.7349	−	101.732i	0.105638	−	0.182971i
$557$	−220.844	+	127.504i	−0.396488	+	0.228912i	−0.684968	−	0.728574i	$-0.740184\pi$
$557$	−220.844	+	127.504i	−0.396488	+	0.228912i	0.288480	+	0.957486i	$0.406850\pi$
$558$		0			0
$559$	625.573			1.11909
$560$	39.9943	−	10.2662i	0.0714185	−	0.0183326i
$561$		0			0
$562$	66.0708	+	114.438i	0.117564	+	0.203626i
$563$			274.865i			0.488214i	0.969748	+	0.244107i	$0.0784948\pi$
$563$			274.865i			0.488214i	−0.969748	+	0.244107i	$0.921505\pi$
$564$		0			0
$565$	−53.5594			−0.0947955
$566$		−	147.233i		−	0.260130i
$567$		0			0
$568$	−116.592			−0.205267
$569$		−	262.635i		−	0.461573i	−0.973004	−	0.230786i	$-0.925870\pi$
$569$		−	262.635i		−	0.461573i	0.973004	−	0.230786i	$-0.0741299\pi$
$570$		0			0
$571$	−431.424			−0.755558			−0.377779	−	0.925896i	$-0.623312\pi$
$571$	−431.424			−0.755558			−0.377779	+	0.925896i	$0.623312\pi$
$572$	475.221	−	274.369i	0.830805	−	0.479666i
$573$		0			0
$574$	−137.612	+	134.743i	−0.239742	+	0.234744i
$575$			29.8310i			0.0518800i
$576$		0			0
$577$	389.031	+	673.821i	0.674230	+	1.16780i	0.976693	+	0.214640i	$0.0688578\pi$
$577$	389.031	+	673.821i	0.674230	+	1.16780i	−0.302463	+	0.953161i	$0.597809\pi$
$578$	247.586	+	142.944i	0.428350	+	0.247308i
$579$		0			0
$580$	−118.413	+	205.097i	−0.204160	+	0.353616i
$581$	−90.8223	+	23.3134i	−0.156321	+	0.0401263i
$582$		0			0
$583$	−1280.82			−2.19694
$584$	462.432	−	266.985i	0.791835	−	0.457166i
$585$		0			0
$586$	−73.3087	+	126.974i	−0.125100	+	0.216680i
$587$	743.197	−	429.085i	1.26609	−	0.730980i	0.291847	−	0.956465i	$-0.405730\pi$
$587$	743.197	−	429.085i	1.26609	−	0.730980i	0.974247	+	0.225485i	$0.0723968\pi$
$588$		0			0
$589$	357.364	−	618.972i	0.606729	−	1.05089i
$590$	−9.06323	+	5.23266i	−0.0153614	+	0.00886891i
$591$		0			0
$592$	−16.8918	+	29.2575i	−0.0285335	+	0.0494214i
$593$	362.591	+	209.342i	0.611452	+	0.353022i	0.773534	−	0.633755i	$-0.218487\pi$
$593$	362.591	+	209.342i	0.611452	+	0.353022i	−0.162081	+	0.986777i	$0.551821\pi$
$594$		0			0
$595$	−198.785	+	194.641i	−0.334093	+	0.327128i
$596$	−266.816	+	154.046i	−0.447678	+	0.258467i
$597$		0			0
$598$	−411.186			−0.687601
$599$		−	672.773i		−	1.12316i	−0.827423	−	0.561580i	$-0.810194\pi$
$599$		−	672.773i		−	1.12316i	0.827423	−	0.561580i	$-0.189806\pi$
$600$		0			0
$601$	66.6761	+	115.486i	0.110942	+	0.192157i	0.916150	−	0.400835i	$-0.131280\pi$
$601$	66.6761	+	115.486i	0.110942	+	0.192157i	−0.805208	+	0.592992i	$0.797947\pi$
$602$	318.559	−	81.7717i	0.529168	−	0.135833i
$603$		0			0
$604$	336.141	−	582.213i	0.556525	−	0.963929i
$605$	−277.145	−	160.010i	−0.458091	−	0.264479i
$606$		0			0
$607$	−389.657	−	674.907i	−0.641940	−	1.11187i	−0.984999	−	0.172559i	$-0.944797\pi$
$607$	−389.657	−	674.907i	−0.641940	−	1.11187i	0.343059	−	0.939314i	$-0.388537\pi$
$608$	373.739	+	215.779i	0.614703	+	0.354899i
$609$		0			0
$610$	−204.374	−	353.986i	−0.335039	−	0.580305i
$611$	883.881	+	510.309i	1.44661	+	0.835203i
$612$		0			0
$613$	38.9459	+	67.4563i	0.0635333	+	0.110043i	0.896042	−	0.443968i	$-0.146430\pi$
$613$	38.9459	+	67.4563i	0.0635333	+	0.110043i	−0.832509	+	0.554011i	$0.813096\pi$
$614$		−	484.469i		−	0.789038i
$615$		0			0
$616$	559.455	−	547.793i	0.908206	−	0.889274i
$617$	−956.905	−	552.470i	−1.55090	−	0.895413i	−0.998069	−	0.0621194i	$-0.980214\pi$
$617$	−956.905	−	552.470i	−1.55090	−	0.895413i	−0.552831	−	0.833293i	$-0.686453\pi$
$618$		0			0
$619$	157.655	−	273.066i	0.254693	−	0.441141i	−0.710119	−	0.704082i	$-0.751359\pi$
$619$	157.655	−	273.066i	0.254693	−	0.441141i	0.964812	+	0.262940i	$0.0846923\pi$
$620$	503.910	−	290.933i	0.812759	−	0.469247i
$621$		0			0
$622$	−711.757			−1.14430
$623$	−77.6194	−	79.2719i	−0.124590	−	0.127242i
$624$		0			0
$625$	291.084	+	504.172i	0.465734	+	0.806675i
$626$			243.824i			0.389495i
$627$		0			0
$628$	19.9146			0.0317111
$629$		−	227.627i		−	0.361887i
$630$		0			0
$631$	−154.111			−0.244234			−0.122117	−	0.992516i	$-0.538968\pi$
$631$	−154.111			−0.244234			−0.122117	+	0.992516i	$0.538968\pi$
$632$			54.8122i			0.0867282i
$633$		0			0
$634$	595.678			0.939555
$635$	−1007.45	+	581.653i	−1.58654	+	0.915988i
$636$		0			0
$637$	738.068	−	405.641i	1.15866	−	0.636798i
$638$		−	370.581i		−	0.580847i
$639$		0			0
$640$	160.438	+	277.887i	0.250685	+	0.434199i
$641$	−559.206	−	322.858i	−0.872396	−	0.503678i	−0.00425219	−	0.999991i	$-0.501354\pi$
$641$	−559.206	−	322.858i	−0.872396	−	0.503678i	−0.868144	+	0.496313i	$0.834687\pi$
$642$		0			0
$643$	153.144	−	265.252i	0.238170	−	0.412523i	−0.722019	−	0.691873i	$-0.756786\pi$
$643$	153.144	−	265.252i	0.238170	−	0.412523i	0.960189	+	0.279350i	$0.0901190\pi$
$644$	293.231	−	75.2702i	0.455328	−	0.116879i
$645$		0			0
$646$	147.065			0.227655
$647$	483.124	−	278.932i	0.746715	−	0.431116i	−0.0777910	−	0.996970i	$-0.524787\pi$
$647$	483.124	−	278.932i	0.746715	−	0.431116i	0.824506	+	0.565854i	$0.191453\pi$
$648$		0			0
$649$	−11.4666	+	19.8608i	−0.0176681	+	0.0306021i
$650$	30.9288	−	17.8567i	0.0475827	−	0.0274719i
$651$		0			0
$652$	−224.543	+	388.920i	−0.344391	+	0.596502i
$653$	129.378	−	74.6964i	0.198129	−	0.114390i	−0.397654	−	0.917536i	$-0.630175\pi$
$653$	129.378	−	74.6964i	0.198129	−	0.114390i	0.595782	+	0.803146i	$0.296842\pi$
$654$		0			0
$655$	−60.5239	+	104.830i	−0.0924029	+	0.160046i
$656$	22.5128	+	12.9978i	0.0343183	+	0.0198137i
$657$		0			0
$658$	516.802	+	144.327i	0.785413	+	0.219342i
$659$	462.734	−	267.160i	0.702176	−	0.405401i	−0.105981	−	0.994368i	$-0.533798\pi$
$659$	462.734	−	267.160i	0.702176	−	0.405401i	0.808157	+	0.588967i	$0.200465\pi$
$660$		0			0
$661$	189.050			0.286006			0.143003	−	0.989722i	$-0.454324\pi$
$661$	189.050			0.286006			0.143003	+	0.989722i	$0.454324\pi$
$662$		−	188.980i		−	0.285468i
$663$		0			0
$664$	54.7595	+	94.8462i	0.0824691	+	0.142841i
$665$	126.241	−	452.040i	0.189836	−	0.679759i
$666$		0			0
$667$	194.440	−	336.780i	0.291515	−	0.504918i
$668$	291.727	+	168.429i	0.436718	+	0.252139i
$669$		0			0
$670$	−172.371	−	298.555i	−0.257270	−	0.445605i
$671$	−775.710	−	447.856i	−1.15605	−	0.667446i
$672$		0			0
$673$	429.674	+	744.217i	0.638446	+	1.10582i	0.985774	+	0.168077i	$0.0537557\pi$
$673$	429.674	+	744.217i	0.638446	+	1.10582i	−0.347328	+	0.937744i	$0.612911\pi$
$674$	−274.532	−	158.501i	−0.407318	−	0.235165i
$675$		0			0
$676$	−147.501	−	255.480i	−0.218197	−	0.377929i
$677$		−	1056.40i		−	1.56041i	−0.625525	−	0.780204i	$-0.715115\pi$
$677$		−	1056.40i		−	1.56041i	0.625525	−	0.780204i	$-0.284885\pi$
$678$		0			0
$679$	−141.870	−	552.685i	−0.208940	−	0.813969i
$680$	281.413	+	162.474i	0.413842	+	0.238932i
$681$		0			0
$682$	−455.246	+	788.509i	−0.667516	+	1.15617i
$683$	−70.7663	+	40.8570i	−0.103611	+	0.0598199i	−0.550910	−	0.834565i	$-0.685719\pi$
$683$	−70.7663	+	40.8570i	−0.103611	+	0.0598199i	0.447299	+	0.894384i	$0.352386\pi$
$684$		0			0
$685$	1238.09			1.80743
$686$	322.821	−	303.040i	0.470585	−	0.441749i
$687$		0			0
$688$	−22.1958	−	38.4443i	−0.0322614	−	0.0558783i
$689$			1609.11i			2.33542i
$690$		0			0
$691$	359.205			0.519834			0.259917	−	0.965631i	$-0.416305\pi$
$691$	359.205			0.519834			0.259917	+	0.965631i	$0.416305\pi$
$692$			715.882i			1.03451i
$693$		0			0
$694$	29.1616			0.0420196
$695$			243.452i			0.350290i
$696$		0			0
$697$	−175.153			−0.251295
$698$	374.017	−	215.939i	0.535841	−	0.309368i
$699$		0			0
$700$	−18.7876	+	18.3960i	−0.0268395	+	0.0262800i
$701$		−	894.651i		−	1.27625i	−0.769933	−	0.638125i	$-0.779710\pi$
$701$		−	894.651i		−	1.27625i	0.769933	−	0.638125i	$-0.220290\pi$
$702$		0			0
$703$	192.002	+	332.557i	0.273118	+	0.473054i
$704$	−533.909	−	308.253i	−0.758394	−	0.437859i
$705$		0			0
$706$	245.314	−	424.896i	0.347470	−	0.601836i
$707$	−72.9236	−	74.4761i	−0.103145	−	0.105341i
$708$		0			0
$709$	−260.550			−0.367490			−0.183745	−	0.982974i	$-0.558822\pi$
$709$	−260.550			−0.367490			−0.183745	+	0.982974i	$0.558822\pi$
$710$	77.1017	−	44.5147i	0.108594	−	0.0626967i
$711$		0			0
$712$	−64.7915	+	112.222i	−0.0909993	+	0.157615i
$713$	−827.447	+	477.727i	−1.16051	+	0.670023i
$714$		0			0
$715$	−568.619	+	984.877i	−0.795271	+	1.37745i
$716$	−421.447	+	243.322i	−0.588613	+	0.339836i
$717$		0			0
$718$	−0.935378	+	1.62012i	−0.00130275	+	0.00225644i
$719$	775.636	+	447.814i	1.07877	+	0.622829i	0.930565	−	0.366128i	$-0.119317\pi$
$719$	775.636	+	447.814i	1.07877	+	0.622829i	0.148206	+	0.988956i	$0.452650\pi$
$720$		0			0
$721$	−135.710	−	528.687i	−0.188224	−	0.733269i
$722$	188.716	−	108.955i	0.261380	−	0.150908i
$723$		0			0
$724$	−308.970			−0.426754
$725$			33.7762i			0.0465878i
$726$		0			0
$727$	−409.883	−	709.938i	−0.563800	−	0.976531i	−0.997160	−	0.0753098i	$-0.976005\pi$
$727$	−409.883	−	709.938i	−0.563800	−	0.976531i	0.433360	−	0.901221i	$-0.357328\pi$
$728$	−688.199	−	702.851i	−0.945329	−	0.965454i
$729$		0			0
$730$	−203.870	+	353.113i	−0.279274	+	0.483716i
$731$	259.030	+	149.551i	0.354350	+	0.204584i
$732$		0			0
$733$	574.169	+	994.489i	0.783313	+	1.35674i	0.930001	+	0.367556i	$0.119805\pi$
$733$	574.169	+	994.489i	0.783313	+	1.35674i	−0.146688	+	0.989183i	$0.546861\pi$
$734$	−481.667	−	278.091i	−0.656223	−	0.378870i
$735$		0			0
$736$	−288.455	−	499.618i	−0.391922	−	0.678829i
$737$	−654.241	−	377.726i	−0.887708	−	0.512519i
$738$		0			0
$739$	−322.085	−	557.868i	−0.435839	−	0.754895i	0.561525	−	0.827460i	$-0.310215\pi$
$739$	−322.085	−	557.868i	−0.435839	−	0.754895i	−0.997364	+	0.0725646i	$0.976882\pi$
$740$			312.621i			0.422461i
$741$		0			0
$742$	210.334	+	819.402i	0.283469	+	1.10432i
$743$	599.923	+	346.366i	0.807434	+	0.466172i	0.846064	−	0.533082i	$-0.178966\pi$
$743$	599.923	+	346.366i	0.807434	+	0.466172i	−0.0386303	+	0.999254i	$0.512299\pi$
$744$		0			0
$745$	319.255	−	552.966i	0.428530	−	0.742236i
$746$	−40.2303	+	23.2270i	−0.0539280	+	0.0311354i
$747$		0			0
$748$	262.365			0.350755
$749$	−413.347	−	422.147i	−0.551865	−	0.563614i
$750$		0			0
$751$	434.397	+	752.398i	0.578425	+	1.00186i	0.995660	+	0.0930628i	$0.0296657\pi$
$751$	434.397	+	752.398i	0.578425	+	1.00186i	−0.417235	+	0.908798i	$0.637001\pi$
$752$		−	72.4246i		−	0.0963093i
$753$		0			0
$754$	−465.565			−0.617460
$755$			1393.28i			1.84540i
$756$		0			0
$757$	878.499			1.16050			0.580250	−	0.814438i	$-0.302955\pi$
$757$	878.499			1.16050			0.580250	+	0.814438i	$0.302955\pi$
$758$			896.700i			1.18298i
$759$		0			0
$760$	−548.182			−0.721292
$761$	42.5983	−	24.5941i	0.0559768	−	0.0323182i	−0.471750	−	0.881732i	$-0.656378\pi$
$761$	42.5983	−	24.5941i	0.0559768	−	0.0323182i	0.527727	+	0.849414i	$0.323044\pi$
$762$		0			0
$763$	−65.3539	−	254.600i	−0.0856539	−	0.333683i
$764$		−	248.834i		−	0.325700i
$765$		0			0
$766$	−222.617	−	385.583i	−0.290622	−	0.503372i
$767$	24.9513	+	14.4057i	0.0325311	+	0.0187818i
$768$		0			0
$769$	231.085	−	400.251i	0.300501	−	0.520482i	−0.675749	−	0.737132i	$-0.736180\pi$
$769$	231.085	−	400.251i	0.300501	−	0.520482i	0.976249	+	0.216650i	$0.0695130\pi$
$770$	−160.819	+	575.854i	−0.208855	+	0.747862i
$771$		0			0
$772$	−297.986			−0.385993
$773$	469.184	−	270.883i	0.606965	−	0.350431i	−0.164812	−	0.986325i	$-0.552702\pi$
$773$	469.184	−	270.883i	0.606965	−	0.350431i	0.771777	+	0.635894i	$0.219368\pi$
$774$		0			0
$775$	41.4929	−	71.8678i	0.0535392	−	0.0927326i
$776$	−577.172	+	333.230i	−0.743778	+	0.429421i
$777$		0			0
$778$	284.951	−	493.550i	0.366261	−	0.634384i
$779$	255.893	−	147.740i	0.328489	−	0.189653i
$780$		0			0
$781$	97.5476	−	168.957i	0.124901	−	0.216335i
$782$	−170.259	−	98.2990i	−0.217722	−	0.125702i
$783$		0			0
$784$	−51.1157	−	30.9651i	−0.0651985	−	0.0394964i
$785$	−35.7428	+	20.6361i	−0.0455322	+	0.0262881i
$786$		0			0
$787$	532.234			0.676282			0.338141	−	0.941095i	$-0.390202\pi$
$787$	532.234			0.676282			0.338141	+	0.941095i	$0.390202\pi$
$788$		−	0.274758i		−	0.000348678i
$789$		0			0
$790$	−20.9273	−	36.2471i	−0.0264902	−	0.0458825i
$791$	54.2348	+	55.3894i	0.0685649	+	0.0700246i
$792$		0			0
$793$	−562.648	+	974.534i	−0.709518	+	1.22892i
$794$	−97.4364	−	56.2549i	−0.122716	−	0.0708500i
$795$		0			0
$796$	124.615	+	215.840i	0.156552	+	0.271156i
$797$	1209.31	+	698.198i	1.51733	+	0.876032i	0.999792	+	0.0203733i	$0.00648547\pi$
$797$	1209.31	+	698.198i	1.51733	+	0.876032i	0.517540	+	0.855659i	$0.326848\pi$
$798$		0			0
$799$	243.991	+	422.605i	0.305371	+	0.528918i
$800$	43.3942	+	25.0537i	0.0542428	+	0.0313171i
$801$		0			0
$802$	−425.011	−	736.141i	−0.529939	−	0.917881i
$803$			893.503i			1.11271i
$804$		0			0
$805$	−448.296	+	438.951i	−0.556889	+	0.545280i
$806$	990.614	+	571.931i	1.22905	+	0.709592i
$807$		0			0
$808$	−60.8718	+	105.433i	−0.0753363	+	0.130486i
$809$	587.272	−	339.062i	0.725924	−	0.419112i	−0.0910054	−	0.995850i	$-0.529008\pi$
$809$	587.272	−	339.062i	0.725924	−	0.419112i	0.816929	+	0.576738i	$0.195675\pi$
$810$		0			0
$811$	−877.972			−1.08258			−0.541290	−	0.840836i	$-0.682064\pi$
$811$	−877.972			−1.08258			−0.541290	+	0.840836i	$0.682064\pi$
$812$	332.011	−	85.2247i	0.408881	−	0.104957i
$813$		0			0
$814$	−244.591	−	423.645i	−0.300481	−	0.520448i
$815$		−	930.713i		−	1.14198i
$816$		0			0
$817$	−504.581			−0.617602
$818$			796.521i			0.973742i
$819$		0			0
$820$	240.553			0.293357
$821$		−	401.621i		−	0.489185i	−0.969626	−	0.244592i	$-0.921346\pi$
$821$		−	401.621i		−	0.489185i	0.969626	−	0.244592i	$-0.0786541\pi$
$822$		0			0
$823$	−121.760			−0.147946			−0.0739730	−	0.997260i	$-0.523568\pi$
$823$	−121.760			−0.147946			−0.0739730	+	0.997260i	$0.523568\pi$
$824$	−552.110	+	318.761i	−0.670037	+	0.386846i
$825$		0			0
$826$	14.5890	+	4.07426i	0.0176622	+	0.00493251i
$827$			1365.90i			1.65163i	0.563941	+	0.825815i	$0.309285\pi$
$827$			1365.90i			1.65163i	−0.563941	+	0.825815i	$0.690715\pi$
$828$		0			0
$829$	−452.116	−	783.089i	−0.545376	−	0.944618i	−0.998583	−	0.0532133i	$-0.983054\pi$
$829$	−452.116	−	783.089i	−0.545376	−	0.944618i	0.453208	−	0.891405i	$-0.350280\pi$
$830$	−72.4245	−	41.8143i	−0.0872584	−	0.0503787i
$831$		0			0
$832$	−387.262	+	670.757i	−0.465459	+	0.806199i
$833$	402.584	+	8.48138i	0.483294	+	0.0101817i
$834$		0			0
$835$	−698.125			−0.836078
$836$	−383.308	+	221.303i	−0.458502	+	0.264716i
$837$		0			0
$838$	−139.224	+	241.142i	−0.166138	+	0.287759i
$839$	−115.048	+	66.4230i	−0.137125	+	0.0791692i	−0.566993	−	0.823723i	$-0.691893\pi$
$839$	−115.048	+	66.4230i	−0.137125	+	0.0791692i	0.429868	+	0.902892i	$0.358560\pi$
$840$		0			0
$841$	−200.345	+	347.008i	−0.238222	+	0.412613i
$842$	−620.421	+	358.200i	−0.736841	+	0.425416i
$843$		0			0
$844$	−82.5752	+	143.024i	−0.0978379	+	0.169460i
$845$	529.472	+	305.691i	0.626594	+	0.361764i
$846$		0			0
$847$	115.163	+	448.641i	0.135965	+	0.529683i
$848$	98.8869	−	57.0924i	0.116612	−	0.0673259i
$849$		0			0
$850$	17.0755			0.0200888
$851$		−	513.339i		−	0.603219i
$852$		0			0
$853$	−324.186	−	561.507i	−0.380054	−	0.658273i	0.611016	−	0.791619i	$-0.290761\pi$
$853$	−324.186	−	561.507i	−0.380054	−	0.658273i	−0.991070	+	0.133346i	$0.957428\pi$
$854$	−159.130	+	569.806i	−0.186335	+	0.667221i
$855$		0			0
$856$	−345.035	+	597.618i	−0.403078	+	0.698151i
$857$	−352.871	−	203.730i	−0.411752	−	0.237725i	0.279790	−	0.960061i	$-0.409735\pi$
$857$	−352.871	−	203.730i	−0.411752	−	0.237725i	−0.691542	+	0.722336i	$0.743068\pi$
$858$		0			0
$859$	168.262	+	291.438i	0.195881	+	0.339276i	0.947189	−	0.320676i	$-0.103910\pi$
$859$	168.262	+	291.438i	0.195881	+	0.339276i	−0.751308	+	0.659952i	$0.770577\pi$
$860$	−355.749	−	205.392i	−0.413662	−	0.238828i
$861$		0			0
$862$	523.205	+	906.218i	0.606966	+	1.05130i
$863$	−604.222	−	348.847i	−0.700141	−	0.404227i	0.107259	−	0.994231i	$-0.465793\pi$
$863$	−604.222	−	348.847i	−0.700141	−	0.404227i	−0.807400	+	0.590005i	$0.799126\pi$
$864$		0			0
$865$	−741.820	−	1284.87i	−0.857595	−	1.48540i
$866$			455.253i			0.525696i
$867$		0			0
$868$	−811.138	−	226.526i	−0.934491	−	0.260975i
$869$	−79.4304	−	45.8592i	−0.0914044	−	0.0527724i
$870$		0			0
$871$	−474.542	+	821.931i	−0.544825	+	0.943664i
$872$	−265.880	+	153.506i	−0.304909	+	0.176039i
$873$		0			0
$874$	331.658			0.379471
$875$	242.310	−	867.657i	0.276926	−	0.991607i
$876$		0			0
$877$	−806.130	−	1396.26i	−0.919190	−	1.59208i	−0.800648	−	0.599135i	$-0.795511\pi$
$877$	−806.130	−	1396.26i	−0.919190	−	1.59208i	−0.118542	−	0.992949i	$-0.537822\pi$
$878$		−	503.765i		−	0.573764i
$879$		0			0
$880$	80.7001			0.0917047
$881$		−	667.659i		−	0.757842i	−0.925429	−	0.378921i	$-0.876295\pi$
$881$		−	667.659i		−	0.757842i	0.925429	−	0.378921i	$-0.123705\pi$
$882$		0			0
$883$	−779.788			−0.883112			−0.441556	−	0.897234i	$-0.645573\pi$
$883$	−779.788			−0.883112			−0.441556	+	0.897234i	$0.645573\pi$
$884$		−	329.612i		−	0.372865i
$885$		0			0
$886$	−236.939			−0.267426
$887$	−494.078	+	285.256i	−0.557021	+	0.321596i	−0.751949	−	0.659221i	$-0.770886\pi$
$887$	−494.078	+	285.256i	−0.557021	+	0.321596i	0.194928	+	0.980818i	$0.437553\pi$
$888$		0			0
$889$	1621.68	+	452.887i	1.82416	+	0.509434i
$890$		−	98.9496i		−	0.111179i
$891$		0			0
$892$	277.060	+	479.882i	0.310606	+	0.537985i
$893$	−712.929	−	411.610i	−0.798353	−	0.460929i
$894$		0			0
$895$	504.276	−	873.432i	0.563437	−	0.975902i
$896$	124.921	−	447.311i	0.139420	−	0.499231i
$897$		0			0
$898$	843.190			0.938964
$899$	−936.877	+	540.906i	−1.04213	+	0.601675i
$900$		0			0
$901$	−384.677	+	666.280i	−0.426944	+	0.739489i
$902$	−325.983	+	188.206i	−0.361400	+	0.208654i
$903$		0			0
$904$	45.2716	−	78.4128i	0.0500792	−	0.0867398i
$905$	554.540	−	320.164i	0.612751	−	0.353772i
$906$		0			0
$907$	716.503	−	1241.02i	0.789970	−	1.36827i	−0.136015	−	0.990707i	$-0.543429\pi$
$907$	716.503	−	1241.02i	0.789970	−	1.36827i	0.925985	−	0.377561i	$-0.123237\pi$
$908$	−641.310	−	370.261i	−0.706289	−	0.407776i
$909$		0			0
$910$	723.452	+	202.038i	0.795003	+	0.222020i
$911$	866.010	−	499.991i	0.950615	−	0.548838i	0.0573431	−	0.998355i	$-0.481737\pi$
$911$	866.010	−	499.991i	0.950615	−	0.548838i	0.893272	+	0.449517i	$0.148404\pi$
$912$		0			0
$913$	−183.260			−0.200723
$914$		−	188.118i		−	0.205818i
$915$		0			0
$916$	89.4495	+	154.931i	0.0976522	+	0.169139i
$917$	169.699	−	43.5605i	0.185059	−	0.0475033i
$918$		0			0
$919$	−100.551	+	174.159i	−0.109413	+	0.189509i	−0.915533	−	0.402244i	$-0.868230\pi$
$919$	−100.551	+	174.159i	−0.109413	+	0.189509i	0.806120	+	0.591753i	$0.201564\pi$
$920$	634.635	+	366.407i	0.689821	+	0.398268i
$921$		0			0
$922$	−4.70267	−	8.14527i	−0.00510051	−	0.00883434i
$923$	−212.263	−	122.550i	−0.229971	−	0.132774i
$924$		0			0
$925$	22.2930	+	38.6126i	0.0241005	+	0.0417434i
$926$	49.7130	+	28.7018i	0.0536858	+	0.0309955i
$927$		0			0
$928$	−326.603	−	565.693i	−0.351943	−	0.609583i
$929$		−	663.006i		−	0.713677i	−0.934166	−	0.356838i	$-0.883855\pi$
$929$		−	663.006i		−	0.713677i	0.934166	−	0.356838i	$-0.116145\pi$
$930$		0			0
$931$	−595.318	+	327.185i	−0.639439	+	0.351434i
$932$	665.754	+	384.373i	0.714328	+	0.412417i
$933$		0			0
$934$	−130.353	+	225.778i	−0.139564	+	0.241732i
$935$	−470.894	+	271.871i	−0.503630	+	0.290771i
$936$		0			0
$937$	251.201			0.268091			0.134045	−	0.990975i	$-0.457203\pi$
$937$	251.201			0.268091			0.134045	+	0.990975i	$0.457203\pi$
$938$	−134.212	+	480.580i	−0.143083	+	0.512346i
$939$		0			0
$940$	−335.095	−	580.402i	−0.356484	−	0.617449i
$941$		−	689.265i		−	0.732482i	−0.930520	−	0.366241i	$-0.880645\pi$
$941$		−	689.265i		−	0.732482i	0.930520	−	0.366241i	$-0.119355\pi$
$942$		0			0
$943$	−395.000			−0.418876
$944$		−	2.04450i		−	0.00216578i
$945$		0			0
$946$	642.786			0.679477
$947$			1593.32i			1.68250i	0.540650	+	0.841248i	$0.318178\pi$
$947$			1593.32i			1.68250i	−0.540650	+	0.841248i	$0.681822\pi$
$948$		0			0
$949$	1122.52			1.18284
$950$	−24.9468	+	14.4031i	−0.0262598	+	0.0151611i
$951$		0			0
$952$	−116.936	−	455.551i	−0.122832	−	0.478519i
$953$		−	820.886i		−	0.861370i	−0.902502	−	0.430685i	$-0.858272\pi$
$953$		−	820.886i		−	0.861370i	0.902502	−	0.430685i	$-0.141728\pi$
$954$		0			0
$955$	257.850	+	446.609i	0.270000	+	0.467654i
$956$	−117.086	−	67.5995i	−0.122475	−	0.0707108i
$957$		0			0
$958$	−123.140	+	213.284i	−0.128538	+	0.222635i
$959$	−1253.70	−	1280.39i	−1.30730	−	1.33513i
$960$		0			0
$961$	1696.94			1.76581
$962$	−532.230	+	307.283i	−0.553254	+	0.319421i
$963$		0			0
$964$	−93.1308	+	161.307i	−0.0966087	+	0.167331i
$965$	534.828	−	308.783i	0.554225	−	0.319982i
$966$		0			0
$967$	194.448	−	336.793i	0.201083	−	0.348287i	−0.747794	−	0.663930i	$-0.768887\pi$
$967$	194.448	−	336.793i	0.201083	−	0.348287i	0.948878	+	0.315644i	$0.102220\pi$
$968$	468.519	−	270.499i	0.484007	−	0.279441i
$969$		0			0
$970$	254.455	−	440.728i	0.262324	−	0.454359i
$971$	503.065	+	290.445i	0.518090	+	0.299119i	0.736153	−	0.676815i	$-0.236641\pi$
$971$	503.065	+	290.445i	0.518090	+	0.299119i	−0.218063	+	0.975935i	$0.569974\pi$
$972$		0			0
$973$	251.770	−	246.522i	0.258756	−	0.253362i
$974$	−136.366	+	78.7310i	−0.140006	+	0.0808326i
$975$		0			0
$976$	79.8527			0.0818163
$977$		−	191.559i		−	0.196069i	−0.995183	−	0.0980343i	$-0.968745\pi$
$977$		−	191.559i		−	0.196069i	0.995183	−	0.0980343i	$-0.0312555\pi$
$978$		0			0
$979$	−108.417	−	187.784i	−0.110743	−	0.191812i
$980$	−552.904	−	11.6482i	−0.564188	−	0.0118860i
$981$		0			0
$982$	90.2258	−	156.276i	0.0918797	−	0.159140i
$983$	1140.95	+	658.727i	1.16068	+	0.670119i	0.951467	−	0.307751i	$-0.0995765\pi$
$983$	1140.95	+	658.727i	1.16068	+	0.670119i	0.209213	+	0.977870i	$0.432910\pi$
$984$		0			0
$985$	0.284713	+	0.493137i	0.000289049	+	0.000500647i
$986$	−192.776	−	111.299i	−0.195513	−	0.112879i
$987$		0			0
$988$	278.026	+	481.555i	0.281403	+	0.487403i
$989$	584.158	+	337.264i	0.590655	+	0.341015i
$990$		0			0
$991$	711.008	+	1231.50i	0.717465	+	1.24269i	0.962001	+	0.273046i	$0.0880310\pi$
$991$	711.008	+	1231.50i	0.717465	+	1.24269i	−0.244536	+	0.969640i	$0.578636\pi$
$992$			1604.88i			1.61782i
$993$		0			0
$994$	−124.110	−	34.6601i	−0.124859	−	0.0348693i
$995$	−447.321	−	258.261i	−0.449569	−	0.259559i
$996$		0			0
$997$	−589.218	+	1020.55i	−0.590991	+	1.02363i	0.403109	+	0.915152i	$0.367930\pi$
$997$	−589.218	+	1020.55i	−0.590991	+	1.02363i	−0.994099	+	0.108474i	$0.965404\pi$
$998$	254.274	−	146.805i	0.254784	−	0.147099i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.b.44.5		22
3.2	odd	2		63.3.j.b.23.7	yes	22
7.4	even	3		189.3.n.b.179.7		22
9.2	odd	6		189.3.n.b.170.7		22
9.7	even	3		63.3.n.b.2.5	yes	22
21.2	odd	6		441.3.r.g.50.7		22
21.5	even	6		441.3.r.f.50.7		22
21.11	odd	6		63.3.n.b.32.5	yes	22
21.17	even	6		441.3.n.f.410.5		22
21.20	even	2		441.3.j.f.275.7		22
63.11	odd	6	inner	189.3.j.b.116.7		22
63.16	even	3		441.3.r.g.344.7		22
63.25	even	3		63.3.j.b.11.5	✓	22
63.34	odd	6		441.3.n.f.128.5		22
63.52	odd	6		441.3.j.f.263.5		22
63.61	odd	6		441.3.r.f.344.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.5	✓	22	63.25	even	3
63.3.j.b.23.7	yes	22	3.2	odd	2
63.3.n.b.2.5	yes	22	9.7	even	3
63.3.n.b.32.5	yes	22	21.11	odd	6
189.3.j.b.44.5		22	1.1	even	1	trivial
189.3.j.b.116.7		22	63.11	odd	6	inner
189.3.n.b.170.7		22	9.2	odd	6
189.3.n.b.179.7		22	7.4	even	3
441.3.j.f.263.5		22	63.52	odd	6
441.3.j.f.275.7		22	21.20	even	2
441.3.n.f.128.5		22	63.34	odd	6
441.3.n.f.410.5		22	21.17	even	6
441.3.r.f.50.7		22	21.5	even	6
441.3.r.f.344.7		22	63.61	odd	6
441.3.r.g.50.7		22	21.2	odd	6
441.3.r.g.344.7		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.29088i q^{2} +2.33363 q^{4} +(-4.18841 + 2.41818i) q^{5} +(6.74202 + 1.88284i) q^{7} -8.17595i q^{8} +O(q^{10})\)	\(q-1.29088i q^{2} +2.33363 q^{4} +(-4.18841 + 2.41818i) q^{5} +(6.74202 + 1.88284i) q^{7} -8.17595i q^{8} +(3.12158 + 5.40673i) q^{10} +(11.8481 + 6.84049i) q^{11} +(8.59380 - 14.8849i) q^{13} +(2.43053 - 8.70314i) q^{14} -1.21966 q^{16} +(7.11684 - 4.10891i) q^{17} +(-6.93167 + 12.0060i) q^{19} +(-9.77419 + 5.64313i) q^{20} +(8.83026 - 15.2945i) q^{22} +(16.0497 - 9.26631i) q^{23} +(-0.804824 + 1.39400i) q^{25} +(-19.2146 - 11.0936i) q^{26} +(15.7334 + 4.39386i) q^{28} +(18.1723 - 10.4918i) q^{29} -51.5552 q^{31} -31.1294i q^{32} +(-5.30411 - 9.18698i) q^{34} +(-32.7914 + 8.41730i) q^{35} +(13.8496 - 23.9882i) q^{37} +(15.4983 + 8.94795i) q^{38} +(19.7709 + 34.2442i) q^{40} +(-18.4583 - 10.6569i) q^{41} +(18.1984 + 31.5205i) q^{43} +(27.6490 + 15.9632i) q^{44} +(-11.9617 - 20.7183i) q^{46} +59.3810i q^{47} +(41.9098 + 25.3884i) q^{49} +(1.79948 + 1.03893i) q^{50} +(20.0547 - 34.7358i) q^{52} +(-81.0775 + 46.8101i) q^{53} -66.1662 q^{55} +(15.3940 - 55.1225i) q^{56} +(-13.5436 - 23.4583i) q^{58} +1.67629i q^{59} -65.4713 q^{61} +66.5516i q^{62} -45.0629 q^{64} +83.1254i q^{65} -55.2191 q^{67} +(16.6081 - 9.58867i) q^{68} +(10.8657 + 42.3298i) q^{70} -14.2603i q^{71} +(32.6549 + 56.5599i) q^{73} +(-30.9659 - 17.8782i) q^{74} +(-16.1759 + 28.0176i) q^{76} +(67.0005 + 68.4269i) q^{77} -6.70408 q^{79} +(5.10843 - 2.94935i) q^{80} +(-13.7568 + 23.8274i) q^{82} +(-11.6006 + 6.69762i) q^{83} +(-19.8721 + 34.4196i) q^{85} +(40.6892 - 23.4919i) q^{86} +(55.9276 - 96.8694i) q^{88} +(-13.7259 - 7.92464i) q^{89} +(85.9656 - 84.1736i) q^{91} +(37.4541 - 21.6241i) q^{92} +76.6538 q^{94} -67.0481i q^{95} +(-40.7574 - 70.5938i) q^{97} +(32.7733 - 54.1005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) 22 * q - 24 * q^4 - 12 * q^5	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) 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

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