LMFDB - Embedded newform 189.3.l.a.118.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(118,189)]

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([2, 3]))

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

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

chi := DirichletCharacter("189.118");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.l (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			118.4
Character	$\chi$	$=$	189.118
Dual form			189.3.l.a.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30753 - 2.26471i) q^{2} +(-1.41927 + 2.45825i) q^{4} +(3.19140 + 1.84256i) q^{5} +(6.42567 + 2.77682i) q^{7} -3.03728 q^{8} +O(q^{10})$	\(q+(-1.30753 - 2.26471i) q^{2} +(-1.41927 + 2.45825i) q^{4} +(3.19140 + 1.84256i) q^{5} +(6.42567 + 2.77682i) q^{7} -3.03728 q^{8} -9.63680i q^{10} +(6.63066 + 11.4846i) q^{11} +(16.2463 + 9.37981i) q^{13} +(-2.11307 - 18.1831i) q^{14} +(9.64842 + 16.7116i) q^{16} -8.23398i q^{17} -22.6432i q^{19} +(-9.05893 + 5.23018i) q^{20} +(17.3396 - 30.0330i) q^{22} +(-0.369057 + 0.639226i) q^{23} +(-5.70996 - 9.88995i) q^{25} -49.0575i q^{26} +(-15.9459 + 11.8548i) q^{28} +(6.13829 + 10.6318i) q^{29} +(-28.6323 - 16.5308i) q^{31} +(19.1566 - 33.1803i) q^{32} +(-18.6476 + 10.7662i) q^{34} +(15.3905 + 20.7016i) q^{35} -9.96860 q^{37} +(-51.2802 + 29.6066i) q^{38} +(-9.69320 - 5.59637i) q^{40} +(23.3769 + 13.4966i) q^{41} +(10.1549 + 17.5888i) q^{43} -37.6428 q^{44} +1.93021 q^{46} +(69.3523 - 40.0406i) q^{47} +(33.5785 + 35.6859i) q^{49} +(-14.9319 + 25.8628i) q^{50} +(-46.1158 + 26.6250i) q^{52} -39.0420 q^{53} +48.8695i q^{55} +(-19.5166 - 8.43400i) q^{56} +(16.0520 - 27.8029i) q^{58} +(40.3543 + 23.2986i) q^{59} +(34.7549 - 20.0658i) q^{61} +86.4583i q^{62} -23.0042 q^{64} +(34.5657 + 59.8695i) q^{65} +(-54.5167 + 94.4257i) q^{67} +(20.2412 + 11.6862i) q^{68} +(26.7597 - 61.9229i) q^{70} -83.8258 q^{71} +37.3200i q^{73} +(13.0342 + 22.5760i) q^{74} +(55.6625 + 32.1368i) q^{76} +(10.7157 + 92.2086i) q^{77} +(-49.4165 - 85.5918i) q^{79} +71.1111i q^{80} -70.5890i q^{82} +(-124.459 + 71.8564i) q^{83} +(15.1716 - 26.2779i) q^{85} +(26.5557 - 45.9958i) q^{86} +(-20.1392 - 34.8821i) q^{88} -133.114i q^{89} +(78.3474 + 105.385i) q^{91} +(-1.04758 - 1.81447i) q^{92} +(-181.360 - 104.708i) q^{94} +(41.7213 - 72.2635i) q^{95} +(-58.0415 + 33.5103i) q^{97} +(36.9132 - 122.706i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8	$ 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8} - 4 q^{11} - 34 q^{14} - 42 q^{16} + 14 q^{22} - 4 q^{23} + 28 q^{25} + 20 q^{28} + 38 q^{29} + 168 q^{32} + 264 q^{35} + 36 q^{37} - 66 q^{43} - 108 q^{44} - 40 q^{46} - 38 q^{49} - 196 q^{50} - 520 q^{53} - 332 q^{56} - 34 q^{58} + 72 q^{64} + 102 q^{65} + 68 q^{67} + 102 q^{70} + 332 q^{71} + 616 q^{74} - 334 q^{77} + 146 q^{79} + 78 q^{85} + 340 q^{86} - 74 q^{88} - 384 q^{91} - 606 q^{92} + 360 q^{95} + 1076 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8 - 4 * q^11 - 34 * q^14 - 42 * q^16 + 14 * q^22 - 4 * q^23 + 28 * q^25 + 20 * q^28 + 38 * q^29 + 168 * q^32 + 264 * q^35 + 36 * q^37 - 66 * q^43 - 108 * q^44 - 40 * q^46 - 38 * q^49 - 196 * q^50 - 520 * q^53 - 332 * q^56 - 34 * q^58 + 72 * q^64 + 102 * q^65 + 68 * q^67 + 102 * q^70 + 332 * q^71 + 616 * q^74 - 334 * q^77 + 146 * q^79 + 78 * q^85 + 340 * q^86 - 74 * q^88 - 384 * q^91 - 606 * q^92 + 360 * q^95 + 1076 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.30753	−	2.26471i	−0.653765	−	1.13235i	−0.982202	−	0.187828i	$-0.939855\pi$
$2$	−1.30753	−	2.26471i	−0.653765	−	1.13235i	0.328437	−	0.944526i	$-0.393478\pi$
$3$		0			0
$3$		0			0
$4$	−1.41927	+	2.45825i	−0.354818	+	0.614562i
$5$	3.19140	+	1.84256i	0.638281	+	0.368512i	0.783952	−	0.620822i	$-0.213201\pi$
$5$	3.19140	+	1.84256i	0.638281	+	0.368512i	−0.145671	+	0.989333i	$0.546534\pi$
$6$		0			0
$7$	6.42567	+	2.77682i	0.917953	+	0.396689i
$7$	6.42567	+	2.77682i	0.917953	+	0.396689i
$8$	−3.03728			−0.379661
$9$		0			0
$10$		−	9.63680i		−	0.963680i
$11$	6.63066	+	11.4846i	0.602787	+	1.04406i	0.992397	+	0.123078i	$0.0392765\pi$
$11$	6.63066	+	11.4846i	0.602787	+	1.04406i	−0.389610	+	0.920980i	$0.627390\pi$
$12$		0			0
$13$	16.2463	+	9.37981i	1.24972	+	0.721524i	0.971053	−	0.238865i	$-0.0767755\pi$
$13$	16.2463	+	9.37981i	1.24972	+	0.721524i	0.278663	+	0.960389i	$0.410109\pi$
$14$	−2.11307	−	18.1831i	−0.150934	−	1.29879i
$15$		0			0
$16$	9.64842	+	16.7116i	0.603027	+	1.04447i
$17$		−	8.23398i		−	0.484352i	−0.970232	−	0.242176i	$-0.922139\pi$
$17$		−	8.23398i		−	0.484352i	0.970232	−	0.242176i	$-0.0778611\pi$
$18$		0			0
$19$		−	22.6432i		−	1.19175i	−0.803079	−	0.595873i	$-0.796806\pi$
$19$		−	22.6432i		−	1.19175i	0.803079	−	0.595873i	$-0.203194\pi$
$20$	−9.05893	+	5.23018i	−0.452947	+	0.261509i
$21$		0			0
$22$	17.3396	−	30.0330i	0.788162	−	1.36514i
$23$	−0.369057	+	0.639226i	−0.0160460	+	0.0277924i	−0.873937	−	0.486039i	$-0.838441\pi$
$23$	−0.369057	+	0.639226i	−0.0160460	+	0.0277924i	0.857891	+	0.513832i	$0.171774\pi$
$24$		0			0
$25$	−5.70996	−	9.88995i	−0.228399	−	0.395598i
$26$		−	49.0575i		−	1.88683i
$27$		0			0
$28$	−15.9459	+	11.8548i	−0.569496	+	0.423387i
$29$	6.13829	+	10.6318i	0.211665	+	0.366615i	0.952236	−	0.305364i	$-0.0987781\pi$
$29$	6.13829	+	10.6318i	0.211665	+	0.366615i	−0.740571	+	0.671978i	$0.765445\pi$
$30$		0			0
$31$	−28.6323	−	16.5308i	−0.923621	−	0.533253i	−0.0388326	−	0.999246i	$-0.512364\pi$
$31$	−28.6323	−	16.5308i	−0.923621	−	0.533253i	−0.884788	+	0.465993i	$0.845697\pi$
$32$	19.1566	−	33.1803i	0.598645	−	1.03688i
$33$		0			0
$34$	−18.6476	+	10.7662i	−0.548458	+	0.316652i
$35$	15.3905	+	20.7016i	0.439727	+	0.591475i
$36$		0			0
$37$	−9.96860			−0.269422			−0.134711	−	0.990885i	$-0.543011\pi$
$37$	−9.96860			−0.269422			−0.134711	+	0.990885i	$0.543011\pi$
$38$	−51.2802	+	29.6066i	−1.34948	+	0.779122i
$39$		0			0
$40$	−9.69320	−	5.59637i	−0.242330	−	0.139909i
$41$	23.3769	+	13.4966i	0.570167	+	0.329186i	0.757216	−	0.653164i	$-0.226559\pi$
$41$	23.3769	+	13.4966i	0.570167	+	0.329186i	−0.187049	+	0.982351i	$0.559892\pi$
$42$		0			0
$43$	10.1549	+	17.5888i	0.236160	+	0.409042i	0.959609	−	0.281336i	$-0.0907776\pi$
$43$	10.1549	+	17.5888i	0.236160	+	0.409042i	−0.723449	+	0.690378i	$0.757444\pi$
$44$	−37.6428			−0.855518
$45$		0			0
$46$	1.93021			0.0419612
$47$	69.3523	−	40.0406i	1.47558	−	0.851927i	0.475959	−	0.879467i	$-0.342101\pi$
$47$	69.3523	−	40.0406i	1.47558	−	0.851927i	0.999621	+	0.0275406i	$0.00876755\pi$
$48$		0			0
$49$	33.5785	+	35.6859i	0.685276	+	0.728283i
$50$	−14.9319	+	25.8628i	−0.298638	+	0.517256i
$51$		0			0
$52$	−46.1158	+	26.6250i	−0.886842	+	0.512019i
$53$	−39.0420			−0.736641			−0.368320	−	0.929699i	$-0.620067\pi$
$53$	−39.0420			−0.736641			−0.368320	+	0.929699i	$0.620067\pi$
$54$		0			0
$55$			48.8695i			0.888536i
$56$	−19.5166	−	8.43400i	−0.348511	−	0.150607i
$57$		0			0
$58$	16.0520	−	27.8029i	0.276758	−	0.479360i
$59$	40.3543	+	23.2986i	0.683971	+	0.394891i	0.801350	−	0.598196i	$-0.204116\pi$
$59$	40.3543	+	23.2986i	0.683971	+	0.394891i	−0.117378	+	0.993087i	$0.537449\pi$
$60$		0			0
$61$	34.7549	−	20.0658i	0.569753	−	0.328947i	−0.187298	−	0.982303i	$-0.559973\pi$
$61$	34.7549	−	20.0658i	0.569753	−	0.328947i	0.757051	+	0.653356i	$0.226640\pi$
$62$			86.4583i			1.39449i
$63$		0			0
$64$	−23.0042			−0.359440
$65$	34.5657	+	59.8695i	0.531779	+	0.921069i
$66$		0			0
$67$	−54.5167	+	94.4257i	−0.813682	+	1.40934i	0.0965884	+	0.995324i	$0.469207\pi$
$67$	−54.5167	+	94.4257i	−0.813682	+	1.40934i	−0.910270	+	0.414014i	$0.864126\pi$
$68$	20.2412	+	11.6862i	0.297664	+	0.171857i
$69$		0			0
$70$	26.7597	−	61.9229i	0.382281	−	0.884613i
$71$	−83.8258			−1.18064			−0.590322	−	0.807168i	$-0.700999\pi$
$71$	−83.8258			−1.18064			−0.590322	+	0.807168i	$0.700999\pi$
$72$		0			0
$73$			37.3200i			0.511233i	0.966778	+	0.255617i	$0.0822785\pi$
$73$			37.3200i			0.511233i	−0.966778	+	0.255617i	$0.917722\pi$
$74$	13.0342	+	22.5760i	0.176138	+	0.305081i
$75$		0			0
$76$	55.6625	+	32.1368i	0.732402	+	0.422852i
$77$	10.7157	+	92.2086i	0.139164	+	1.19751i
$78$		0			0
$79$	−49.4165	−	85.5918i	−0.625525	−	1.08344i	−0.988439	−	0.151618i	$-0.951552\pi$
$79$	−49.4165	−	85.5918i	−0.625525	−	1.08344i	0.362914	−	0.931823i	$-0.381782\pi$
$80$			71.1111i			0.888889i
$81$		0			0
$82$		−	70.5890i		−	0.860842i
$83$	−124.459	+	71.8564i	−1.49951	+	0.865740i	−1.00000		0.000570370i	$-0.999818\pi$
$83$	−124.459	+	71.8564i	−1.49951	+	0.865740i	−0.499506	+	0.866310i	$0.666485\pi$
$84$		0			0
$85$	15.1716	−	26.2779i	0.178489	−	0.309152i
$86$	26.5557	−	45.9958i	0.308787	−	0.534834i
$87$		0			0
$88$	−20.1392	−	34.8821i	−0.228854	−	0.396388i
$89$		−	133.114i		−	1.49566i	−0.663887	−	0.747832i	$-0.731095\pi$
$89$		−	133.114i		−	1.49566i	0.663887	−	0.747832i	$-0.268905\pi$
$90$		0			0
$91$	78.3474	+	105.385i	0.860960	+	1.15807i
$92$	−1.04758	−	1.81447i	−0.0113868	−	0.0197225i
$93$		0			0
$94$	−181.360	−	104.708i	−1.92937	−	1.11392i
$95$	41.7213	−	72.2635i	0.439172	−	0.760668i
$96$		0			0
$97$	−58.0415	+	33.5103i	−0.598366	+	0.345467i	−0.768399	−	0.639972i	$-0.778946\pi$
$97$	−58.0415	+	33.5103i	−0.598366	+	0.345467i	0.170032	+	0.985438i	$0.445613\pi$
$98$	36.9132	−	122.706i	0.376665	−	1.25210i
$99$		0			0
$100$	32.4159			0.324159
$101$	−18.6008	+	10.7392i	−0.184166	+	0.106328i	−0.589249	−	0.807952i	$-0.700576\pi$
$101$	−18.6008	+	10.7392i	−0.184166	+	0.106328i	0.405082	+	0.914280i	$0.367243\pi$
$102$		0			0
$103$	−12.9916	−	7.50068i	−0.126132	−	0.0728222i	0.435607	−	0.900137i	$-0.356534\pi$
$103$	−12.9916	−	7.50068i	−0.126132	−	0.0728222i	−0.561738	+	0.827315i	$0.689867\pi$
$104$	−49.3446	−	28.4891i	−0.474468	−	0.273934i
$105$		0			0
$106$	51.0485	+	88.4187i	0.481590	+	0.834138i
$107$	51.7878			0.483998			0.241999	−	0.970276i	$-0.422197\pi$
$107$	51.7878			0.483998			0.241999	+	0.970276i	$0.422197\pi$
$108$		0			0
$109$	141.473			1.29792			0.648960	−	0.760823i	$-0.275204\pi$
$109$	141.473			1.29792			0.648960	+	0.760823i	$0.275204\pi$
$110$	110.675	−	63.8983i	1.00614	−	0.580894i
$111$		0			0
$112$	15.5926	+	134.175i	0.139220	+	1.19799i
$113$	53.4919	−	92.6507i	0.473380	−	0.819918i	−0.526156	−	0.850388i	$-0.676367\pi$
$113$	53.4919	−	92.6507i	0.473380	−	0.819918i	0.999536	+	0.0304701i	$0.00970045\pi$
$114$		0			0
$115$	−2.35562	+	1.36002i	−0.0204837	+	0.0118263i
$116$	−34.8476			−0.300410
$117$		0			0
$118$		−	121.854i		−	1.03266i
$119$	22.8643	−	52.9088i	0.192137	−	0.444612i
$120$		0			0
$121$	−27.4312	+	47.5123i	−0.226704	+	0.392663i
$122$	−90.8862	−	52.4732i	−0.744969	−	0.430108i
$123$		0			0
$124$	81.2738	−	46.9235i	0.655434	−	0.378415i
$125$		−	134.212i		−	1.07369i
$126$		0			0
$127$	−179.059			−1.40991			−0.704956	−	0.709251i	$-0.749033\pi$
$127$	−179.059			−1.40991			−0.704956	+	0.709251i	$0.749033\pi$
$128$	−46.5479	−	80.6234i	−0.363656	−	0.629870i
$129$		0			0
$130$	90.3913	−	156.562i	0.695318	−	1.20433i
$131$	−101.017	−	58.3219i	−0.771119	−	0.445206i	0.0621549	−	0.998067i	$-0.480203\pi$
$131$	−101.017	−	58.3219i	−0.771119	−	0.445206i	−0.833274	+	0.552861i	$0.813536\pi$
$132$		0			0
$133$	62.8760	−	145.498i	0.472752	−	1.09397i
$134$	285.129			2.12783
$135$		0			0
$136$			25.0089i			0.183889i
$137$	35.8160	+	62.0351i	0.261430	+	0.452811i	0.966622	−	0.256206i	$-0.0824724\pi$
$137$	35.8160	+	62.0351i	0.261430	+	0.452811i	−0.705192	+	0.709017i	$0.749139\pi$
$138$		0			0
$139$	−188.775	−	108.989i	−1.35809	−	0.784094i	−0.368724	−	0.929539i	$-0.620205\pi$
$139$	−188.775	−	108.989i	−1.35809	−	0.784094i	−0.989366	+	0.145445i	$0.953539\pi$
$140$	−72.7330	+	8.45237i	−0.519521	+	0.0603741i
$141$		0			0
$142$	109.605	+	189.841i	0.771864	+	1.33691i
$143$			248.777i			1.73970i
$144$		0			0
$145$			45.2406i			0.312004i
$146$	84.5190	−	48.7971i	0.578897	−	0.334226i
$147$		0			0
$148$	14.1481	−	24.5053i	0.0955955	−	0.165576i
$149$	13.2091	−	22.8789i	0.0886520	−	0.153550i	−0.818290	−	0.574806i	$-0.805077\pi$
$149$	13.2091	−	22.8789i	0.0886520	−	0.153550i	0.906942	+	0.421256i	$0.138411\pi$
$150$		0			0
$151$	−41.6516	−	72.1427i	−0.275838	−	0.477766i	0.694508	−	0.719485i	$-0.255622\pi$
$151$	−41.6516	−	72.1427i	−0.275838	−	0.477766i	−0.970346	+	0.241719i	$0.922289\pi$
$152$			68.7737i			0.452459i
$153$		0			0
$154$	194.815	−	144.833i	1.26503	−	0.940477i
$155$	−60.9180	−	105.513i	−0.393020	−	0.680730i
$156$		0			0
$157$	128.067	+	73.9397i	0.815715	+	0.470953i	0.848937	−	0.528495i	$-0.177243\pi$
$157$	128.067	+	73.9397i	0.815715	+	0.470953i	−0.0332215	+	0.999448i	$0.510577\pi$
$158$	−129.227	+	223.828i	−0.817893	+	1.41663i
$159$		0			0
$160$	122.273	−	70.5944i	0.764207	−	0.441215i
$161$	−4.14646	+	3.08265i	−0.0257544	+	0.0191469i
$162$		0			0
$163$	−80.9615			−0.496696			−0.248348	−	0.968671i	$-0.579888\pi$
$163$	−80.9615			−0.496696			−0.248348	+	0.968671i	$0.579888\pi$
$164$	−66.3562	+	38.3108i	−0.404611	+	0.233602i
$165$		0			0
$166$	325.468	+	187.909i	1.96065	+	1.13198i
$167$	1.93139	+	1.11509i	0.0115652	+	0.00667716i	0.505771	−	0.862668i	$-0.331208\pi$
$167$	1.93139	+	1.11509i	0.0115652	+	0.00667716i	−0.494206	+	0.869345i	$0.664541\pi$
$168$		0			0
$169$	91.4615	+	158.416i	0.541192	+	0.937373i
$170$	−79.3492			−0.466760
$171$		0			0
$172$	−57.6502			−0.335175
$173$	−146.304	+	84.4688i	−0.845690	+	0.488259i	−0.859194	−	0.511650i	$-0.829035\pi$
$173$	−146.304	+	84.4688i	−0.845690	+	0.488259i	0.0135045	+	0.999909i	$0.495701\pi$
$174$		0			0
$175$	−9.22774	−	79.4051i	−0.0527299	−	0.453743i
$176$	−127.951	+	221.617i	−0.726993	+	1.25919i
$177$		0			0
$178$	−301.465	+	174.051i	−1.69362	+	0.977814i
$179$	−74.8944			−0.418405			−0.209202	−	0.977872i	$-0.567087\pi$
$179$	−74.8944			−0.418405			−0.209202	+	0.977872i	$0.567087\pi$
$180$		0			0
$181$			1.66857i			0.00921864i	0.999989	+	0.00460932i	$0.00146720\pi$
$181$			1.66857i			0.00921864i	−0.999989	+	0.00460932i	$0.998533\pi$
$182$	136.224	−	315.228i	0.748483	−	1.73202i
$183$		0			0
$184$	1.12093	−	1.94151i	0.00609202	−	0.0105517i
$185$	−31.8138	−	18.3677i	−0.171967	−	0.0992849i
$186$		0			0
$187$	94.5642	−	54.5967i	0.505691	−	0.291961i
$188$			227.314i			1.20911i
$189$		0			0
$190$	−218.208			−1.14846
$191$	60.4724	+	104.741i	0.316609	+	0.548383i	0.979778	−	0.200086i	$-0.0641223\pi$
$191$	60.4724	+	104.741i	0.316609	+	0.548383i	−0.663169	+	0.748470i	$0.730789\pi$
$192$		0			0
$193$	−101.401	+	175.631i	−0.525393	+	0.910007i	0.474170	+	0.880433i	$0.342748\pi$
$193$	−101.401	+	175.631i	−0.525393	+	0.910007i	−0.999563	+	0.0295736i	$0.990585\pi$
$194$	151.782	+	87.6315i	0.782382	+	0.451709i
$195$		0			0
$196$	−135.382	+	31.8965i	−0.690724	+	0.162737i
$197$	213.013			1.08129			0.540643	−	0.841252i	$-0.318181\pi$
$197$	213.013			1.08129			0.540643	+	0.841252i	$0.318181\pi$
$198$		0			0
$199$		−	200.308i		−	1.00657i	−0.864119	−	0.503287i	$-0.832124\pi$
$199$		−	200.308i		−	1.00657i	0.864119	−	0.503287i	$-0.167876\pi$
$200$	17.3428	+	30.0386i	0.0867139	+	0.150193i
$201$		0			0
$202$	48.6422	+	28.0836i	0.240803	+	0.139028i
$203$	9.91994	+	85.3616i	0.0488667	+	0.420500i
$204$		0			0
$205$	49.7366	+	86.1464i	0.242618	+	0.420226i
$206$			39.2295i			0.190434i
$207$		0			0
$208$			362.001i			1.74039i
$209$	260.048	−	150.139i	1.24425	−	0.718369i
$210$		0			0
$211$	142.883	−	247.481i	0.677173	−	1.17290i	−0.298656	−	0.954361i	$-0.596538\pi$
$211$	142.883	−	247.481i	0.677173	−	1.17290i	0.975829	−	0.218537i	$-0.0701284\pi$
$212$	55.4111	−	95.9749i	0.261373	−	0.452712i
$213$		0			0
$214$	−67.7141	−	117.284i	−0.316421	−	0.548058i
$215$			74.8439i			0.348111i
$216$		0			0
$217$	−138.078	−	185.728i	−0.636306	−	0.855891i
$218$	−184.981	−	320.396i	−0.848535	−	1.46970i
$219$		0			0
$220$	−120.133	−	69.3590i	−0.546061	−	0.315268i
$221$	77.2331	−	133.772i	0.349471	−	0.605302i
$222$		0			0
$223$	−326.190	+	188.326i	−1.46273	+	0.844510i	−0.999137	−	0.0415367i	$-0.986775\pi$
$223$	−326.190	+	188.326i	−1.46273	+	0.844510i	−0.463597	+	0.886046i	$0.653441\pi$
$224$	215.230	−	160.011i	0.960848	−	0.714335i
$225$		0			0
$226$	−279.769			−1.23792
$227$	−191.360	+	110.482i	−0.842997	+	0.486704i	−0.858282	−	0.513179i	$-0.828468\pi$
$227$	−191.360	+	110.482i	−0.842997	+	0.486704i	0.0152850	+	0.999883i	$0.495134\pi$
$228$		0			0
$229$	24.9109	+	14.3823i	0.108781	+	0.0628049i	0.553404	−	0.832913i	$-0.313329\pi$
$229$	24.9109	+	14.3823i	0.108781	+	0.0628049i	−0.444622	+	0.895718i	$0.646662\pi$
$230$	6.16009	+	3.55653i	0.0267830	+	0.0154632i
$231$		0			0
$232$	−18.6437	−	32.2919i	−0.0803609	−	0.139189i
$233$	−405.664			−1.74105			−0.870524	−	0.492126i	$-0.836220\pi$
$233$	−405.664			−1.74105			−0.870524	+	0.492126i	$0.836220\pi$
$234$		0			0
$235$	295.108			1.25578
$236$	−114.547	+	66.1340i	−0.485370	+	0.280229i
$237$		0			0
$238$	−149.719	+	17.3990i	−0.629071	+	0.0731049i
$239$	−66.2069	+	114.674i	−0.277016	+	0.479807i	−0.970642	−	0.240529i	$-0.922679\pi$
$239$	−66.2069	+	114.674i	−0.277016	+	0.479807i	0.693625	+	0.720336i	$0.256012\pi$
$240$		0			0
$241$	71.7575	−	41.4292i	0.297749	−	0.171905i	−0.343682	−	0.939086i	$-0.611674\pi$
$241$	71.7575	−	41.4292i	0.297749	−	0.171905i	0.641431	+	0.767181i	$0.278341\pi$
$242$	143.469			0.592846
$243$		0			0
$244$			113.915i			0.466865i
$245$	41.4093	+	175.758i	0.169018	+	0.717381i
$246$		0			0
$247$	212.388	−	367.868i	0.859872	−	1.48934i
$248$	86.9643	+	50.2089i	0.350662	+	0.202455i
$249$		0			0
$250$	−303.950	+	175.486i	−1.21580	+	0.701943i
$251$		−	182.888i		−	0.728636i	−0.931275	−	0.364318i	$-0.881302\pi$
$251$		−	182.888i		−	0.728636i	0.931275	−	0.364318i	$-0.118698\pi$
$252$		0			0
$253$	−9.78837			−0.0386892
$254$	234.125	+	405.516i	0.921752	+	1.59652i
$255$		0			0
$256$	−167.734	+	290.524i	−0.655211	+	1.13486i
$257$	−41.1681	−	23.7684i	−0.160187	−	0.0924842i	0.417763	−	0.908556i	$-0.362814\pi$
$257$	−41.1681	−	23.7684i	−0.160187	−	0.0924842i	−0.577951	+	0.816072i	$0.696147\pi$
$258$		0			0
$259$	−64.0549	−	27.6810i	−0.247316	−	0.106876i
$260$	−196.232			−0.754739
$261$		0			0
$262$			305.031i			1.16424i
$263$	−204.796	−	354.717i	−0.778693	−	1.34874i	−0.932696	−	0.360665i	$-0.882550\pi$
$263$	−204.796	−	354.717i	−0.778693	−	1.34874i	0.154003	−	0.988070i	$-0.450783\pi$
$264$		0			0
$265$	−124.599	−	71.9371i	−0.470184	−	0.271461i
$266$	−411.722	+	47.8466i	−1.54783	+	0.179874i
$267$		0			0
$268$	−154.748	−	268.031i	−0.577418	−	1.00012i
$269$		−	154.435i		−	0.574108i	−0.957914	−	0.287054i	$-0.907324\pi$
$269$		−	154.435i		−	0.574108i	0.957914	−	0.287054i	$-0.0926759\pi$
$270$		0			0
$271$		−	62.1999i		−	0.229520i	−0.993393	−	0.114760i	$-0.963390\pi$
$271$		−	62.1999i		−	0.229520i	0.993393	−	0.114760i	$-0.0366099\pi$
$272$	137.603	−	79.4449i	0.505892	−	0.292077i
$273$		0			0
$274$	93.6609	−	162.226i	0.341828	−	0.592064i
$275$	75.7216	−	131.154i	0.275351	−	0.476922i
$276$		0			0
$277$	2.87637	+	4.98202i	0.0103840	+	0.0179856i	0.871171	−	0.490980i	$-0.163361\pi$
$277$	2.87637	+	4.98202i	0.0103840	+	0.0179856i	−0.860787	+	0.508966i	$0.830028\pi$
$278$			570.026i			2.05045i
$279$		0			0
$280$	−46.7452	−	62.8767i	−0.166947	−	0.224560i
$281$	126.093	+	218.400i	0.448731	+	0.777225i	0.998304	−	0.0582207i	$-0.0185427\pi$
$281$	126.093	+	218.400i	0.448731	+	0.777225i	−0.549573	+	0.835446i	$0.685209\pi$
$282$		0			0
$283$	117.523	+	67.8520i	0.415276	+	0.239760i	0.693054	−	0.720886i	$-0.256265\pi$
$283$	117.523	+	67.8520i	0.415276	+	0.239760i	−0.277778	+	0.960645i	$0.589598\pi$
$284$	118.971	−	206.065i	0.418914	−	0.725580i
$285$		0			0
$286$	563.408	−	325.284i	1.96996	−	1.13736i
$287$	112.734	+	151.638i	0.392802	+	0.528356i
$288$		0			0
$289$	221.202			0.765404
$290$	102.457	−	59.1534i	0.353299	−	0.203977i
$291$		0			0
$292$	−91.7419	−	52.9672i	−0.314185	−	0.181395i
$293$	−72.9007	−	42.0892i	−0.248808	−	0.143649i	0.370410	−	0.928868i	$-0.379217\pi$
$293$	−72.9007	−	42.0892i	−0.248808	−	0.143649i	−0.619218	+	0.785219i	$0.712550\pi$
$294$		0			0
$295$	85.8579	+	148.710i	0.291044	+	0.504103i
$296$	30.2775			0.102289
$297$		0			0
$298$	−69.0854			−0.231830
$299$	−11.9916	+	6.92337i	−0.0401058	+	0.0231551i
$300$		0			0
$301$	16.4111	+	141.218i	0.0545219	+	0.469163i
$302$	−108.921	+	188.658i	−0.360667	+	0.624694i
$303$		0			0
$304$	378.403	−	218.471i	1.24475	−	0.718654i
$305$	147.889			0.484883
$306$		0			0
$307$		−	155.490i		−	0.506483i	−0.967403	−	0.253242i	$-0.918503\pi$
$307$		−	155.490i		−	0.506483i	0.967403	−	0.253242i	$-0.0814968\pi$
$308$	−241.880	−	104.527i	−0.785325	−	0.339374i
$309$		0			0
$310$	−159.304	+	275.923i	−0.513885	+	0.890075i
$311$	168.154	+	97.0835i	0.540687	+	0.312166i	0.745357	−	0.666665i	$-0.232279\pi$
$311$	168.154	+	97.0835i	0.540687	+	0.312166i	−0.204670	+	0.978831i	$0.565612\pi$
$312$		0			0
$313$	300.308	−	173.383i	0.959450	−	0.553939i	0.0634463	−	0.997985i	$-0.479791\pi$
$313$	300.308	−	173.383i	0.959450	−	0.553939i	0.896004	+	0.444047i	$0.146458\pi$
$314$		−	386.713i		−	1.23157i
$315$		0			0
$316$	280.541			0.887789
$317$	34.5304	+	59.8083i	0.108929	+	0.188670i	0.915336	−	0.402690i	$-0.131925\pi$
$317$	34.5304	+	59.8083i	0.108929	+	0.188670i	−0.806408	+	0.591360i	$0.798591\pi$
$318$		0			0
$319$	−81.4018	+	140.992i	−0.255178	+	0.441981i
$320$	−73.4156	−	42.3865i	−0.229424	−	0.132458i
$321$		0			0
$322$	12.4029	+	5.35986i	0.0385184	+	0.0166455i
$323$	−186.443			−0.577224
$324$		0			0
$325$		−	214.233i		−	0.659180i
$326$	105.860	+	183.354i	0.324723	+	0.562436i
$327$		0			0
$328$	−71.0022	−	40.9931i	−0.216470	−	0.124979i
$329$	556.820	−	64.7086i	1.69246	−	0.196683i
$330$		0			0
$331$	125.821	+	217.928i	0.380123	+	0.658393i	0.991080	−	0.133272i	$-0.0425483\pi$
$331$	125.821	+	217.928i	0.380123	+	0.658393i	−0.610956	+	0.791664i	$0.709215\pi$
$332$		−	407.935i		−	1.22872i
$333$		0			0
$334$		−	5.83203i		−	0.0174612i
$335$	−347.970	+	200.900i	−1.03872	+	0.599702i
$336$		0			0
$337$	−140.785	+	243.846i	−0.417759	+	0.723580i	−0.995714	−	0.0924890i	$-0.970518\pi$
$337$	−140.785	+	243.846i	−0.417759	+	0.723580i	0.577955	+	0.816069i	$0.303851\pi$
$338$	239.177	−	414.267i	0.707625	−	1.22564i
$339$		0			0
$340$	43.0652	+	74.5910i	0.126662	+	0.219385i
$341$		−	438.441i		−	1.28575i
$342$		0			0
$343$	116.671	+	322.547i	0.340150	+	0.940371i
$344$	−30.8433	−	53.4222i	−0.0896608	−	0.155297i
$345$		0			0
$346$	382.595	+	220.891i	1.10576	+	0.638414i
$347$	−105.071	+	181.988i	−0.302798	+	0.524462i	−0.976769	−	0.214296i	$-0.931254\pi$
$347$	−105.071	+	181.988i	−0.302798	+	0.524462i	0.673971	+	0.738758i	$0.264587\pi$
$348$		0			0
$349$	−64.0467	+	36.9774i	−0.183515	+	0.105952i	−0.588943	−	0.808175i	$-0.700456\pi$
$349$	−64.0467	+	36.9774i	−0.183515	+	0.105952i	0.405428	+	0.914127i	$0.367122\pi$
$350$	−167.764	+	124.723i	−0.479325	+	0.356351i
$351$		0			0
$352$	508.085			1.44342
$353$	281.010	−	162.241i	0.796061	−	0.459606i	−0.0460309	−	0.998940i	$-0.514657\pi$
$353$	281.010	−	162.241i	0.796061	−	0.459606i	0.842092	+	0.539334i	$0.181324\pi$
$354$		0			0
$355$	−267.522	−	154.454i	−0.753583	−	0.435081i
$356$	327.228	+	188.925i	0.919179	+	0.530688i
$357$		0			0
$358$	97.9267	+	169.614i	0.273538	+	0.473782i
$359$	−261.171			−0.727495			−0.363748	−	0.931498i	$-0.618503\pi$
$359$	−261.171			−0.727495			−0.363748	+	0.931498i	$0.618503\pi$
$360$		0			0
$361$	−151.713			−0.420257
$362$	3.77883	−	2.18171i	0.0104388	−	0.00602683i
$363$		0			0
$364$	−370.258	+	43.0280i	−1.01719	+	0.118209i
$365$	−68.7643	+	119.103i	−0.188395	+	0.326310i
$366$		0			0
$367$	97.1508	−	56.0900i	0.264716	−	0.152834i	−0.361768	−	0.932268i	$-0.617827\pi$
$367$	97.1508	−	56.0900i	0.264716	−	0.152834i	0.626484	+	0.779434i	$0.284493\pi$
$368$	−14.2433			−0.0387046
$369$		0			0
$370$			96.0654i			0.259636i
$371$	−250.871	−	108.413i	−0.676202	−	0.292217i
$372$		0			0
$373$	7.84680	−	13.5911i	0.0210370	−	0.0364371i	−0.855315	−	0.518108i	$-0.826637\pi$
$373$	7.84680	−	13.5911i	0.0210370	−	0.0364371i	0.876352	+	0.481671i	$0.159970\pi$
$374$	−247.291	−	142.774i	−0.661206	−	0.381748i
$375$		0			0
$376$	−210.643	+	121.615i	−0.560220	+	0.323443i
$377$			230.304i			0.610885i
$378$		0			0
$379$	197.268			0.520496			0.260248	−	0.965542i	$-0.416196\pi$
$379$	197.268			0.520496			0.260248	+	0.965542i	$0.416196\pi$
$380$	118.428	+	205.123i	0.311652	+	0.539797i
$381$		0			0
$382$	158.139	−	273.905i	0.413976	−	0.717028i
$383$	−474.698	−	274.067i	−1.23942	−	0.715580i	−0.270446	−	0.962735i	$-0.587171\pi$
$383$	−474.698	−	274.067i	−1.23942	−	0.715580i	−0.968976	+	0.247155i	$0.920504\pi$
$384$		0			0
$385$	−135.702	+	314.019i	−0.352472	+	0.815634i
$386$	530.339			1.37393
$387$		0			0
$388$		−	190.241i		−	0.490311i
$389$	152.755	+	264.579i	0.392686	+	0.680152i	0.992803	−	0.119760i	$-0.0382127\pi$
$389$	152.755	+	264.579i	0.392686	+	0.680152i	−0.600117	+	0.799912i	$0.704879\pi$
$390$		0			0
$391$	5.26337	+	3.03881i	0.0134613	+	0.00777189i
$392$	−101.988	−	108.388i	−0.260172	−	0.276500i
$393$		0			0
$394$	−278.522	−	482.413i	−0.706907	−	1.22440i
$395$		−	364.211i		−	0.922052i
$396$		0			0
$397$		−	472.112i		−	1.18920i	−0.804022	−	0.594599i	$-0.797311\pi$
$397$		−	472.112i		−	1.18920i	0.804022	−	0.594599i	$-0.202689\pi$
$398$	−453.640	+	261.909i	−1.13980	+	0.658063i
$399$		0			0
$400$	110.184	−	190.845i	0.275461	−	0.477112i
$401$	347.256	−	601.466i	0.865976	−	1.49991i	−9.86522e−5	−	1.00000i	$-0.500031\pi$
$401$	347.256	−	601.466i	0.865976	−	1.49991i	0.866075	−	0.499915i	$-0.166635\pi$
$402$		0			0
$403$	−310.112	−	537.130i	−0.769509	−	1.33283i
$404$		−	60.9671i		−	0.150909i
$405$		0			0
$406$	180.348	−	134.079i	0.444208	−	0.330243i
$407$	−66.0983	−	114.486i	−0.162404	−	0.281292i
$408$		0			0
$409$	256.107	+	147.864i	0.626180	+	0.361525i	0.779271	−	0.626687i	$-0.215590\pi$
$409$	256.107	+	147.864i	0.626180	+	0.361525i	−0.153091	+	0.988212i	$0.548923\pi$
$410$	130.064	−	225.278i	0.317230	−	0.549459i
$411$		0			0
$412$	36.8771	−	21.2910i	0.0895075	−	0.0516772i
$413$	194.608	+	261.766i	0.471205	+	0.633815i
$414$		0			0
$415$	−529.598			−1.27614
$416$	622.449	−	359.371i	1.49627	−	0.863873i
$417$		0			0
$418$	−680.042	−	392.623i	−1.62690	−	0.939289i
$419$	−191.051	−	110.304i	−0.455970	−	0.263254i	0.254378	−	0.967105i	$-0.418129\pi$
$419$	−191.051	−	110.304i	−0.455970	−	0.263254i	−0.710348	+	0.703850i	$0.751463\pi$
$420$		0			0
$421$	−355.146	−	615.130i	−0.843576	−	1.46112i	−0.886852	−	0.462054i	$-0.847113\pi$
$421$	−355.146	−	615.130i	−0.843576	−	1.46112i	0.0432759	−	0.999063i	$-0.486221\pi$
$422$	−747.298			−1.77085
$423$		0			0
$424$	118.582			0.279673
$425$	−81.4336	+	47.0157i	−0.191608	+	0.110625i
$426$		0			0
$427$	279.043	−	32.4278i	0.653496	−	0.0759434i
$428$	−73.5009	+	127.307i	−0.171731	+	0.297447i
$429$		0			0
$430$	169.500	−	97.8607i	0.394185	−	0.227583i
$431$	−72.6197			−0.168491			−0.0842456	−	0.996445i	$-0.526848\pi$
$431$	−72.6197			−0.168491			−0.0842456	+	0.996445i	$0.526848\pi$
$432$		0			0
$433$			572.654i			1.32253i	0.750154	+	0.661264i	$0.229980\pi$
$433$			572.654i			1.32253i	−0.750154	+	0.661264i	$0.770020\pi$
$434$	−240.079	+	555.553i	−0.553178	+	1.28008i
$435$		0			0
$436$	−200.789	+	347.776i	−0.460525	+	0.797652i
$437$	14.4741	+	8.35663i	0.0331215	+	0.0191227i
$438$		0			0
$439$	−386.765	+	223.299i	−0.881013	+	0.508653i	−0.870992	−	0.491297i	$-0.836523\pi$
$439$	−386.765	+	223.299i	−0.881013	+	0.508653i	−0.0100205	+	0.999950i	$0.503190\pi$
$440$		−	148.430i		−	0.337342i
$441$		0			0
$442$	−403.939			−0.913888
$443$	301.249	+	521.778i	0.680020	+	1.17783i	0.974974	+	0.222317i	$0.0713621\pi$
$443$	301.249	+	521.778i	0.680020	+	1.17783i	−0.294955	+	0.955511i	$0.595305\pi$
$444$		0			0
$445$	245.271	−	424.821i	0.551170	−	0.954654i
$446$	853.006	+	492.483i	1.91257	+	1.10422i
$447$		0			0
$448$	−147.817	−	63.8785i	−0.329949	−	0.142586i
$449$	59.7471			0.133067			0.0665335	−	0.997784i	$-0.478806\pi$
$449$	59.7471			0.133067			0.0665335	+	0.997784i	$0.478806\pi$
$450$		0			0
$451$			357.966i			0.793717i
$452$	151.839	+	262.993i	0.335927	+	0.581843i
$453$		0			0
$454$	500.419	+	288.917i	1.10224	+	0.636381i
$455$	55.8608	+	480.684i	0.122771	+	1.05645i
$456$		0			0
$457$	355.662	+	616.024i	0.778253	+	1.34797i	0.932948	+	0.360012i	$0.117227\pi$
$457$	355.662	+	616.024i	0.778253	+	1.34797i	−0.154695	+	0.987962i	$0.549439\pi$
$458$		−	75.2213i		−	0.164239i
$459$		0			0
$460$		−	7.72094i		−	0.0167847i
$461$	1.39410	−	0.804886i	0.00302409	−	0.00174596i	−0.498487	−	0.866897i	$-0.666111\pi$
$461$	1.39410	−	0.804886i	0.00302409	−	0.00174596i	0.501511	+	0.865151i	$0.332778\pi$
$462$		0			0
$463$	21.4251	−	37.1094i	0.0462745	−	0.0801499i	−0.841960	−	0.539539i	$-0.818598\pi$
$463$	21.4251	−	37.1094i	0.0462745	−	0.0801499i	0.888235	+	0.459389i	$0.151932\pi$
$464$	−118.450	+	205.161i	−0.255279	+	0.442157i
$465$		0			0
$466$	530.418	+	918.711i	1.13824	+	1.97148i
$467$		−	231.151i		−	0.494969i	−0.968892	−	0.247485i	$-0.920396\pi$
$467$		−	231.151i		−	0.494969i	0.968892	−	0.247485i	$-0.0796040\pi$
$468$		0			0
$469$	−612.510	+	455.365i	−1.30599	+	0.970928i
$470$	−385.863	−	668.334i	−0.820985	−	1.42199i
$471$		0			0
$472$	−122.568	−	70.7644i	−0.259677	−	0.149925i
$473$	−134.667	+	233.251i	−0.284709	+	0.493130i
$474$		0			0
$475$	−223.940	+	129.292i	−0.471452	+	0.272193i
$476$	97.6125	+	131.298i	0.205068	+	0.275836i
$477$		0			0
$478$	346.270			0.724415
$479$	213.744	−	123.405i	0.446229	−	0.257631i	−0.260007	−	0.965607i	$-0.583725\pi$
$479$	213.744	−	123.405i	0.446229	−	0.257631i	0.706236	+	0.707976i	$0.250392\pi$
$480$		0			0
$481$	−161.953	−	93.5035i	−0.336700	−	0.194394i
$482$	−187.650	−	108.340i	−0.389316	−	0.224771i
$483$		0			0
$484$	−77.8647	−	134.866i	−0.160877	−	0.278648i
$485$	−246.979			−0.509234
$486$		0			0
$487$	−618.473			−1.26996			−0.634982	−	0.772527i	$-0.718993\pi$
$487$	−618.473			−1.26996			−0.634982	+	0.772527i	$0.718993\pi$
$488$	−105.561	+	60.9454i	−0.216313	+	0.124888i
$489$		0			0
$490$	343.898	−	323.590i	0.701832	−	0.660387i
$491$	160.661	−	278.274i	0.327212	−	0.566749i	−0.654745	−	0.755850i	$-0.727224\pi$
$491$	160.661	−	278.274i	0.327212	−	0.566749i	0.981958	+	0.189101i	$0.0605574\pi$
$492$		0			0
$493$	87.5422	−	50.5425i	0.177570	−	0.102520i
$494$	−1110.82			−2.24862
$495$		0			0
$496$		−	637.986i		−	1.28626i
$497$	−538.637	−	232.769i	−1.08378	−	0.468349i
$498$		0			0
$499$	−80.4854	+	139.405i	−0.161293	+	0.279368i	−0.935333	−	0.353769i	$-0.884900\pi$
$499$	−80.4854	+	139.405i	−0.161293	+	0.279368i	0.774039	+	0.633137i	$0.218233\pi$
$500$	329.926	+	190.483i	0.659851	+	0.380965i
$501$		0			0
$502$	−414.187	+	239.131i	−0.825074	+	0.476357i
$503$			941.248i			1.87127i	0.352971	+	0.935634i	$0.385171\pi$
$503$			941.248i			1.87127i	−0.352971	+	0.935634i	$0.614829\pi$
$504$		0			0
$505$	−79.1501			−0.156733
$506$	12.7986	+	22.1678i	0.0252937	+	0.0438099i
$507$		0			0
$508$	254.133	−	440.171i	0.500262	−	0.866479i
$509$	410.539	+	237.025i	0.806560	+	0.465667i	0.845760	−	0.533564i	$-0.179148\pi$
$509$	410.539	+	237.025i	0.806560	+	0.465667i	−0.0392001	+	0.999231i	$0.512481\pi$
$510$		0			0
$511$	−103.631	+	239.806i	−0.202800	+	0.469288i
$512$	504.886			0.986105
$513$		0			0
$514$			124.312i			0.241852i
$515$	−27.6409	−	47.8754i	−0.0536716	−	0.0929620i
$516$		0			0
$517$	919.702	+	530.990i	1.77892	+	1.02706i
$518$	21.0643	+	181.260i	0.0406647	+	0.349922i
$519$		0			0
$520$	−104.986	−	181.841i	−0.201896	−	0.349694i
$521$		−	179.082i		−	0.343728i	−0.985121	−	0.171864i	$-0.945021\pi$
$521$		−	179.082i		−	0.343728i	0.985121	−	0.171864i	$-0.0549790\pi$
$522$		0			0
$523$		−	742.307i		−	1.41932i	−0.704542	−	0.709662i	$-0.748848\pi$
$523$		−	742.307i		−	1.41932i	0.704542	−	0.709662i	$-0.251152\pi$
$524$	286.740	−	165.549i	0.547213	−	0.315934i
$525$		0			0
$526$	−535.554	+	927.607i	−1.01816	+	1.76351i
$527$	−136.115	+	235.757i	−0.258282	+	0.447357i
$528$		0			0
$529$	264.228	+	457.656i	0.499485	+	0.865133i
$530$			376.240i			0.709886i
$531$		0			0
$532$	268.431	+	361.065i	0.504570	+	0.678694i
$533$	253.192	+	438.541i	0.475031	+	0.822778i
$534$		0			0
$535$	165.276	+	95.4220i	0.308927	+	0.178359i
$536$	165.583	−	286.798i	0.308923	−	0.535070i
$537$		0			0
$538$	−349.751	+	201.929i	−0.650094	+	0.375332i
$539$	−187.192	+	622.258i	−0.347294	+	1.15447i
$540$		0			0
$541$	−546.499			−1.01016			−0.505082	−	0.863071i	$-0.668538\pi$
$541$	−546.499			−1.01016			−0.505082	+	0.863071i	$0.668538\pi$
$542$	−140.865	+	81.3283i	−0.259898	+	0.150052i
$543$		0			0
$544$	−273.206	−	157.735i	−0.502216	−	0.289955i
$545$	451.498	+	260.673i	0.828437	+	0.478298i
$546$		0			0
$547$	192.148	+	332.810i	0.351276	+	0.608429i	0.986473	−	0.163922i	$-0.0524144\pi$
$547$	192.148	+	332.810i	0.351276	+	0.608429i	−0.635197	+	0.772350i	$0.719081\pi$
$548$	−203.330			−0.371041
$549$		0			0
$550$	−396.033			−0.720060
$551$	240.738	−	138.990i	0.436911	−	0.252251i
$552$		0			0
$553$	−79.8608	−	687.206i	−0.144414	−	1.24269i
$554$	7.52189	−	13.0283i	0.0135774	−	0.0235168i
$555$		0			0
$556$	535.845	−	309.370i	0.963749	−	0.556421i
$557$	314.249			0.564182			0.282091	−	0.959388i	$-0.408972\pi$
$557$	314.249			0.564182			0.282091	+	0.959388i	$0.408972\pi$
$558$		0			0
$559$			381.004i			0.681581i
$560$	−197.463	+	456.937i	−0.352612	+	0.815958i
$561$		0			0
$562$	329.742	−	571.130i	0.586730	−	1.01625i
$563$	98.8474	+	57.0696i	0.175573	+	0.101367i	0.585211	−	0.810881i	$-0.301012\pi$
$563$	98.8474	+	57.0696i	0.175573	+	0.101367i	−0.409638	+	0.912248i	$0.634345\pi$
$564$		0			0
$565$	341.429	−	197.124i	0.604299	−	0.348892i
$566$		−	354.874i		−	0.626986i
$567$		0			0
$568$	254.603			0.448244
$569$	−178.041	−	308.376i	−0.312901	−	0.541961i	0.666088	−	0.745873i	$-0.267968\pi$
$569$	−178.041	−	308.376i	−0.312901	−	0.541961i	−0.978989	+	0.203912i	$0.934634\pi$
$570$		0			0
$571$	−170.256	+	294.892i	−0.298171	+	0.516448i	−0.975718	−	0.219032i	$-0.929710\pi$
$571$	−170.256	+	294.892i	−0.298171	+	0.516448i	0.677546	+	0.735480i	$0.263043\pi$
$572$	−611.556	−	353.082i	−1.06915	−	0.617276i
$573$		0			0
$574$	196.013	−	453.582i	0.341486	−	0.790212i
$575$	8.42921			0.0146595
$576$		0			0
$577$		−	390.835i		−	0.677356i	−0.940902	−	0.338678i	$-0.890020\pi$
$577$		−	390.835i		−	0.677356i	0.940902	−	0.338678i	$-0.109980\pi$
$578$	−289.228	−	500.957i	−0.500394	−	0.866708i
$579$		0			0
$580$	−111.213	−	64.2086i	−0.191746	−	0.110705i
$581$	−999.265	+	116.126i	−1.71991	+	0.199872i
$582$		0			0
$583$	−258.874	−	448.383i	−0.444037	−	0.769095i
$584$		−	113.352i		−	0.194095i
$585$		0			0
$586$			220.132i			0.375652i
$587$	878.394	−	507.141i	1.49641	−	0.863954i	0.496421	−	0.868082i	$-0.334647\pi$
$587$	878.394	−	507.141i	1.49641	−	0.863954i	0.999991	+	0.00412823i	$0.00131406\pi$
$588$		0			0
$589$	−374.311	+	648.325i	−0.635502	+	1.10072i
$590$	224.524	−	388.886i	0.380549	−	0.659130i
$591$		0			0
$592$	−96.1812	−	166.591i	−0.162468	−	0.281403i
$593$		−	769.152i		−	1.29705i	−0.761193	−	0.648526i	$-0.775386\pi$
$593$		−	769.152i		−	1.29705i	0.761193	−	0.648526i	$-0.224614\pi$
$594$		0			0
$595$	170.457	−	126.725i	0.286482	−	0.212983i
$596$	37.4947	+	64.9427i	0.0629106	+	0.108964i
$597$		0			0
$598$	31.3588	+	18.1050i	0.0524395	+	0.0302760i
$599$	−263.413	+	456.244i	−0.439754	+	0.761677i	−0.997670	−	0.0682206i	$-0.978268\pi$
$599$	−263.413	+	456.244i	−0.439754	+	0.761677i	0.557916	+	0.829897i	$0.311601\pi$
$600$		0			0
$601$	35.7573	−	20.6445i	0.0594963	−	0.0343502i	−0.469957	−	0.882689i	$-0.655731\pi$
$601$	35.7573	−	20.6445i	0.0594963	−	0.0343502i	0.529453	+	0.848339i	$0.322397\pi$
$602$	298.360	−	221.813i	0.495615	−	0.368461i
$603$		0			0
$604$	236.460			0.391489
$605$	−175.088	+	101.087i	−0.289402	+	0.167086i
$606$		0			0
$607$	388.261	+	224.163i	0.639640	+	0.369296i	0.784476	−	0.620159i	$-0.212932\pi$
$607$	388.261	+	224.163i	0.639640	+	0.369296i	−0.144836	+	0.989456i	$0.546265\pi$
$608$	−751.307	−	433.767i	−1.23570	−	0.713433i
$609$		0			0
$610$	−193.370	−	334.926i	−0.317000	−	0.549059i
$611$	1502.29			2.45874
$612$		0			0
$613$	1000.80			1.63262			0.816309	−	0.577615i	$-0.196016\pi$
$613$	1000.80			1.63262			0.816309	+	0.577615i	$0.196016\pi$
$614$	−352.140	+	203.308i	−0.573518	+	0.331121i
$615$		0			0
$616$	−32.5465	−	280.064i	−0.0528352	−	0.454649i
$617$	88.6179	−	153.491i	0.143627	−	0.248769i	−0.785233	−	0.619201i	$-0.787457\pi$
$617$	88.6179	−	153.491i	0.143627	−	0.248769i	0.928860	+	0.370431i	$0.120790\pi$
$618$		0			0
$619$	290.267	−	167.586i	0.468928	−	0.270736i	−0.246863	−	0.969050i	$-0.579400\pi$
$619$	290.267	−	167.586i	0.468928	−	0.270736i	0.715791	+	0.698315i	$0.246066\pi$
$620$	345.837			0.557801
$621$		0			0
$622$		−	507.759i		−	0.816332i
$623$	369.634	−	855.348i	0.593313	−	1.37295i
$624$		0			0
$625$	104.544	−	181.075i	0.167270	−	0.289720i
$626$	−785.323	−	453.407i	−1.25451	−	0.724292i
$627$		0			0
$628$	−363.524	+	209.881i	−0.578860	+	0.334205i
$629$			82.0812i			0.130495i
$630$		0			0
$631$	1077.15			1.70705			0.853524	−	0.521053i	$-0.174461\pi$
$631$	1077.15			1.70705			0.853524	+	0.521053i	$0.174461\pi$
$632$	150.092	+	259.967i	0.237487	+	0.411340i
$633$		0			0
$634$	90.2990	−	156.402i	0.142427	−	0.246691i
$635$	−571.449	−	329.926i	−0.899920	−	0.519569i
$636$		0			0
$637$	210.800	+	894.724i	0.330927	+	1.40459i
$638$	425.741			0.667306
$639$		0			0
$640$		−	343.069i		−	0.536045i
$641$	102.765	+	177.995i	0.160320	+	0.277683i	0.934984	−	0.354691i	$-0.115414\pi$
$641$	102.765	+	177.995i	0.160320	+	0.277683i	−0.774663	+	0.632374i	$0.782081\pi$
$642$		0			0
$643$	−413.913	−	238.973i	−0.643721	−	0.371653i	0.142325	−	0.989820i	$-0.454542\pi$
$643$	−413.913	−	238.973i	−0.643721	−	0.371653i	−0.786047	+	0.618167i	$0.787875\pi$
$644$	−1.69298	−	14.5681i	−0.00262885	−	0.0226213i
$645$		0			0
$646$	243.780	+	422.240i	0.377369	+	0.653622i
$647$		−	308.180i		−	0.476322i	−0.971226	−	0.238161i	$-0.923455\pi$
$647$		−	308.180i		−	0.476322i	0.971226	−	0.238161i	$-0.0765446\pi$
$648$		0			0
$649$			617.939i			0.952141i
$650$	−485.176	+	280.117i	−0.746425	+	0.430949i
$651$		0			0
$652$	114.906	−	199.023i	0.176237	−	0.305251i
$653$	−350.775	+	607.559i	−0.537174	+	0.930413i	0.461881	+	0.886942i	$0.347175\pi$
$653$	−350.775	+	607.559i	−0.537174	+	0.930413i	−0.999055	+	0.0434705i	$0.986159\pi$
$654$		0			0
$655$	−214.923	−	372.258i	−0.328127	−	0.568332i
$656$			520.885i			0.794032i
$657$		0			0
$658$	−874.606	−	1176.43i	−1.32919	−	1.78788i
$659$	−362.623	−	628.082i	−0.550263	−	0.953084i	−0.998255	−	0.0590463i	$-0.981194\pi$
$659$	−362.623	−	628.082i	−0.550263	−	0.953084i	0.447992	−	0.894038i	$-0.352139\pi$
$660$		0			0
$661$	−716.938	−	413.924i	−1.08463	−	0.626210i	−0.152486	−	0.988306i	$-0.548728\pi$
$661$	−716.938	−	413.924i	−1.08463	−	0.626210i	−0.932141	+	0.362096i	$0.882061\pi$
$662$	329.029	−	569.895i	0.497023	−	0.860868i
$663$		0			0
$664$	378.017	−	218.248i	0.569303	−	0.328687i
$665$	468.750	−	348.489i	0.704888	−	0.524043i
$666$		0			0
$667$	−9.06152			−0.0135855
$668$	−5.48232	+	3.16522i	−0.00820706	+	0.00473835i
$669$		0			0
$670$	909.961	+	525.366i	1.35815	+	0.784129i
$671$	460.896	+	266.098i	0.686879	+	0.396570i
$672$		0			0
$673$	−582.601	−	1009.10i	−0.865678	−	1.49940i	−0.866372	−	0.499399i	$-0.833554\pi$
$673$	−582.601	−	1009.10i	−0.865678	−	1.49940i	0.000694329	−	1.00000i	$-0.499779\pi$
$674$	736.321			1.09247
$675$		0			0
$676$	−519.235			−0.768099
$677$	255.760	−	147.663i	0.377785	−	0.218114i	−0.299069	−	0.954231i	$-0.596676\pi$
$677$	255.760	−	147.663i	0.377785	−	0.218114i	0.676854	+	0.736117i	$0.263343\pi$
$678$		0			0
$679$	−466.008	+	54.1552i	−0.686315	+	0.0797573i
$680$	−46.0804	+	79.8136i	−0.0677653	+	0.117373i
$681$		0			0
$682$	−992.942	+	573.275i	−1.45593	+	0.840580i
$683$	637.558			0.933467			0.466734	−	0.884398i	$-0.345431\pi$
$683$	637.558			0.933467			0.466734	+	0.884398i	$0.345431\pi$
$684$		0			0
$685$			263.972i			0.385361i
$686$	577.925	−	685.967i	0.842456	−	0.999952i
$687$		0			0
$688$	−195.957	+	339.408i	−0.284822	+	0.493326i
$689$	−634.287	−	366.206i	−0.920591	−	0.531504i
$690$		0			0
$691$	635.956	−	367.169i	0.920342	−	0.531360i	0.0365976	−	0.999330i	$-0.488348\pi$
$691$	635.956	−	367.169i	0.920342	−	0.531360i	0.883744	+	0.467971i	$0.155015\pi$
$692$		−	479.537i		−	0.692972i
$693$		0			0
$694$	549.534			0.791835
$695$	−401.637	−	695.656i	−0.577895	−	1.00094i
$696$		0			0
$697$	111.131	−	192.484i	0.159442	−	0.276161i
$698$	167.486	+	96.6981i	0.239951	+	0.138536i
$699$		0			0
$700$	208.294	+	90.0132i	0.297563	+	0.128590i
$701$	−1045.20			−1.49101			−0.745507	−	0.666498i	$-0.767792\pi$
$701$	−1045.20			−1.49101			−0.745507	+	0.666498i	$0.767792\pi$
$702$		0			0
$703$			225.721i			0.321082i
$704$	−152.533	−	264.195i	−0.216666	−	0.375276i
$705$		0			0
$706$	−734.857	−	424.270i	−1.04087	−	0.600949i
$707$	−149.343	+	17.3553i	−0.211235	+	0.0245478i
$708$		0			0
$709$	−25.0780	−	43.4364i	−0.0353710	−	0.0612644i	0.847798	−	0.530319i	$-0.177928\pi$
$709$	−25.0780	−	43.4364i	−0.0353710	−	0.0612644i	−0.883169	+	0.469055i	$0.844595\pi$
$710$			807.812i			1.13776i
$711$		0			0
$712$			404.306i			0.567845i
$713$	21.1339	−	12.2017i	0.0296408	−	0.0171131i
$714$		0			0
$715$	−458.386	+	793.948i	−0.641100	+	1.11042i
$716$	106.295	−	184.109i	0.148457	−	0.257136i
$717$		0			0
$718$	341.489	+	591.476i	0.475611	+	0.823782i
$719$			1315.02i			1.82896i	0.404629	+	0.914481i	$0.367401\pi$
$719$			1315.02i			1.82896i	−0.404629	+	0.914481i	$0.632599\pi$
$720$		0			0
$721$	−62.6515	−	84.2722i	−0.0868953	−	0.116882i
$722$	198.369	+	343.585i	0.274750	+	0.475880i
$723$		0			0
$724$	−4.10177	−	2.36816i	−0.00566543	−	0.00327094i
$725$	70.0988	−	121.415i	0.0966880	−	0.167468i
$726$		0			0
$727$	701.577	−	405.056i	0.965030	−	0.557160i	0.0673125	−	0.997732i	$-0.478558\pi$
$727$	701.577	−	405.056i	0.965030	−	0.557160i	0.897717	+	0.440572i	$0.145224\pi$
$728$	−237.963	−	320.083i	−0.326873	−	0.439675i
$729$		0			0
$730$	359.646			0.492665
$731$	144.826	−	83.6152i	0.198120	−	0.114385i
$732$		0			0
$733$	−87.1731	−	50.3294i	−0.118926	−	0.0686622i	0.439357	−	0.898313i	$-0.355206\pi$
$733$	−87.1731	−	50.3294i	−0.118926	−	0.0686622i	−0.558283	+	0.829650i	$0.688540\pi$
$734$	−254.055	−	146.679i	−0.346124	−	0.199835i
$735$		0			0
$736$	14.1398	+	24.4909i	0.0192117	+	0.0332756i
$737$	−1445.93			−1.96191
$738$		0			0
$739$	422.292			0.571437			0.285719	−	0.958314i	$-0.407768\pi$
$739$	422.292			0.571437			0.285719	+	0.958314i	$0.407768\pi$
$740$	90.3048	−	52.1375i	0.122034	−	0.0704561i
$741$		0			0
$742$	82.4984	+	709.902i	0.111184	+	0.956741i
$743$	−405.350	+	702.087i	−0.545559	+	0.944936i	0.453013	+	0.891504i	$0.350349\pi$
$743$	−405.350	+	702.087i	−0.545559	+	0.944936i	−0.998572	+	0.0534316i	$0.982984\pi$
$744$		0			0
$745$	84.3114	−	48.6772i	0.113170	−	0.0653386i
$746$	−41.0397			−0.0550130
$747$		0			0
$748$			309.950i			0.414372i
$749$	332.772	+	143.805i	0.444288	+	0.191997i
$750$		0			0
$751$	−199.187	+	345.003i	−0.265230	+	0.459391i	−0.967624	−	0.252397i	$-0.918781\pi$
$751$	−199.187	+	345.003i	−0.265230	+	0.459391i	0.702394	+	0.711788i	$0.252114\pi$
$752$	1338.28	+	772.656i	1.77963	+	1.02747i
$753$		0			0
$754$	521.571	−	301.129i	0.691739	−	0.399376i
$755$		−	306.982i		−	0.406599i
$756$		0			0
$757$	730.998			0.965652			0.482826	−	0.875716i	$-0.339610\pi$
$757$	730.998			0.965652			0.482826	+	0.875716i	$0.339610\pi$
$758$	−257.934	−	446.754i	−0.340282	−	0.589385i
$759$		0			0
$760$	−126.720	+	219.485i	−0.166736	+	0.288796i
$761$	−79.2466	−	45.7530i	−0.104135	−	0.0601222i	0.447028	−	0.894520i	$-0.352482\pi$
$761$	−79.2466	−	45.7530i	−0.104135	−	0.0601222i	−0.551163	+	0.834398i	$0.685816\pi$
$762$		0			0
$763$	909.061	+	392.846i	1.19143	+	0.514870i
$764$	−343.307			−0.449354
$765$		0			0
$766$			1433.40i			1.87129i
$767$	437.072	+	757.031i	0.569846	+	0.987003i
$768$		0			0
$769$	−391.783	−	226.196i	−0.509470	−	0.294143i	0.223146	−	0.974785i	$-0.428367\pi$
$769$	−391.783	−	226.196i	−0.509470	−	0.294143i	−0.732616	+	0.680642i	$0.761701\pi$
$770$	888.596	−	103.265i	1.15402	−	0.134110i
$771$		0			0
$772$	−287.830	−	498.537i	−0.372837	−	0.645773i
$773$			1138.79i			1.47321i	0.676321	+	0.736607i	$0.263573\pi$
$773$			1138.79i			1.47321i	−0.676321	+	0.736607i	$0.736427\pi$
$774$		0			0
$775$			377.562i			0.487177i
$776$	176.289	−	101.780i	0.227176	−	0.131160i
$777$		0			0
$778$	399.463	−	691.890i	0.513449	−	0.889319i
$779$	305.606	−	529.326i	0.392306	−	0.679494i
$780$		0			0
$781$	−555.820	−	962.709i	−0.711677	−	1.23266i
$782$		−	15.8933i		−	0.0203240i
$783$		0			0
$784$	−272.387	+	905.462i	−0.347432	+	1.15493i
$785$	272.476	+	471.943i	0.347103	+	0.601201i
$786$		0			0
$787$	252.358	+	145.699i	0.320659	+	0.185132i	0.651686	−	0.758489i	$-0.274062\pi$
$787$	252.358	+	145.699i	0.320659	+	0.185132i	−0.331028	+	0.943621i	$0.607395\pi$
$788$	−302.324	+	523.640i	−0.383660	+	0.664518i
$789$		0			0
$790$	−824.831	+	476.217i	−1.04409	+	0.602806i
$791$	600.996	−	446.806i	0.759793	−	0.564862i
$792$		0			0
$793$	752.852			0.949372
$794$	−1069.20	+	617.300i	−1.34659	+	0.777457i
$795$		0			0
$796$	492.407	+	284.292i	0.618602	+	0.357150i
$797$	833.171	+	481.032i	1.04538	+	0.603553i	0.921354	−	0.388725i	$-0.127085\pi$
$797$	833.171	+	481.032i	1.04538	+	0.603553i	0.124031	+	0.992278i	$0.460418\pi$
$798$		0			0
$799$	−329.693	−	571.045i	−0.412632	−	0.714700i
$800$	−437.535			−0.546919
$801$		0			0
$802$	−1816.19			−2.26458
$803$	−428.607	+	247.456i	−0.533757	+	0.308165i
$804$		0			0
$805$	−18.9130	+	2.19790i	−0.0234944	+	0.00273030i
$806$	−810.962	+	1404.63i	−1.00616	+	1.74271i
$807$		0			0
$808$	56.4959	−	32.6179i	0.0699206	−	0.0403687i
$809$	−681.749			−0.842706			−0.421353	−	0.906897i	$-0.638445\pi$
$809$	−681.749			−0.842706			−0.421353	+	0.906897i	$0.638445\pi$
$810$		0			0
$811$		−	1531.25i		−	1.88810i	−0.329801	−	0.944050i	$-0.606982\pi$
$811$		−	1531.25i		−	1.88810i	0.329801	−	0.944050i	$-0.393018\pi$
$812$	−223.919	−	96.7655i	−0.275762	−	0.119169i
$813$		0			0
$814$	−172.851	+	299.387i	−0.212348	+	0.367797i
$815$	−258.381	−	149.176i	−0.317032	−	0.183038i
$816$		0			0
$817$	398.266	−	229.939i	0.487474	−	0.281443i
$818$		−	773.345i		−	0.945410i
$819$		0			0
$820$	−282.359			−0.344340
$821$	46.3290	+	80.2441i	0.0564299	+	0.0977395i	0.892860	−	0.450334i	$-0.148695\pi$
$821$	46.3290	+	80.2441i	0.0564299	+	0.0977395i	−0.836430	+	0.548073i	$0.815362\pi$
$822$		0			0
$823$	−253.184	+	438.528i	−0.307636	+	0.532841i	−0.977845	−	0.209332i	$-0.932871\pi$
$823$	−253.184	+	438.528i	−0.307636	+	0.532841i	0.670209	+	0.742172i	$0.266204\pi$
$824$	39.4591	+	22.7817i	0.0478872	+	0.0276477i
$825$		0			0
$826$	338.368	−	782.996i	0.409646	−	0.947937i
$827$	909.882			1.10022			0.550110	−	0.835092i	$-0.314586\pi$
$827$	909.882			1.10022			0.550110	+	0.835092i	$0.314586\pi$
$828$		0			0
$829$		−	162.129i		−	0.195572i	−0.995207	−	0.0977862i	$-0.968824\pi$
$829$		−	162.129i		−	0.195572i	0.995207	−	0.0977862i	$-0.0311761\pi$
$830$	692.466	+	1199.39i	0.834296	+	1.44504i
$831$		0			0
$832$	−373.733	−	215.775i	−0.449198	−	0.259345i
$833$	293.837	−	276.485i	0.352745	−	0.331915i
$834$		0			0
$835$	4.10922	+	7.11738i	0.00492122	+	0.00852380i
$836$			852.352i			1.01956i
$837$		0			0
$838$			576.901i			0.688426i
$839$	−640.732	+	369.927i	−0.763686	+	0.440914i	−0.830617	−	0.556843i	$-0.812012\pi$
$839$	−640.732	+	369.927i	−0.763686	+	0.440914i	0.0669319	+	0.997758i	$0.478679\pi$
$840$		0			0
$841$	345.143	−	597.805i	0.410396	−	0.710826i
$842$	−928.727	+	1608.60i	−1.10300	+	1.91045i
$843$		0			0
$844$	405.581	+	702.486i	0.480546	+	0.832330i
$845$			674.092i			0.797743i
$846$		0			0
$847$	−308.197	+	229.127i	−0.363869	+	0.270516i
$848$	−376.693	−	652.452i	−0.444214	−	0.769401i
$849$		0			0
$850$	212.954	+	122.949i	0.250534	+	0.144646i
$851$	3.67898	−	6.37219i	0.00432313	−	0.00748788i
$852$		0			0
$853$	−824.037	+	475.758i	−0.966045	+	0.557747i	−0.898028	−	0.439938i	$-0.855001\pi$
$853$	−824.037	+	475.758i	−0.966045	+	0.557747i	−0.0680170	+	0.997684i	$0.521667\pi$
$854$	−438.296	−	589.550i	−0.513228	−	0.690340i
$855$		0			0
$856$	−157.294			−0.183755
$857$	−1109.18	+	640.387i	−1.29426	+	0.747243i	−0.979407	−	0.201896i	$-0.935290\pi$
$857$	−1109.18	+	640.387i	−1.29426	+	0.747243i	−0.314856	+	0.949139i	$0.601956\pi$
$858$		0			0
$859$	656.241	+	378.881i	0.763959	+	0.441072i	0.830715	−	0.556697i	$-0.187932\pi$
$859$	656.241	+	378.881i	0.763959	+	0.441072i	−0.0667562	+	0.997769i	$0.521265\pi$
$860$	−183.985	−	106.224i	−0.213936	−	0.123516i
$861$		0			0
$862$	94.9525	+	164.462i	0.110154	+	0.190792i
$863$	1321.75			1.53158			0.765790	−	0.643091i	$-0.222348\pi$
$863$	1321.75			1.53158			0.765790	+	0.643091i	$0.222348\pi$
$864$		0			0
$865$	−622.555			−0.719716
$866$	1296.90	−	748.763i	1.49757	−	0.864622i
$867$		0			0
$868$	652.537	−	75.8319i	0.751771	−	0.0873640i
$869$	655.327	−	1135.06i	0.754117	−	1.30617i
$870$		0			0
$871$	−1771.39	+	1022.71i	−2.03374	+	1.17418i
$872$	−429.694			−0.492769
$873$		0			0
$874$		−	43.7062i		−	0.0500071i
$875$	372.682	−	862.400i	0.425922	−	0.985600i
$876$		0			0
$877$	241.743	−	418.711i	0.275648	−	0.477436i	−0.694651	−	0.719347i	$-0.744441\pi$
$877$	241.743	−	418.711i	0.275648	−	0.477436i	0.970298	+	0.241911i	$0.0777743\pi$
$878$	1011.41	+	583.939i	1.15195	+	0.665079i
$879$		0			0
$880$	−816.685	+	471.513i	−0.928051	+	0.535811i
$881$			379.667i			0.430950i	0.976509	+	0.215475i	$0.0691299\pi$
$881$			379.667i			0.430950i	−0.976509	+	0.215475i	$0.930870\pi$
$882$		0			0
$883$	−754.801			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$883$	−754.801			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$884$	219.229	+	379.716i	0.247997	+	0.429543i
$885$		0			0
$886$	787.784	−	1364.48i	0.889146	−	1.54005i
$887$	−181.405	−	104.734i	−0.204516	−	0.118077i	0.394244	−	0.919006i	$-0.371006\pi$
$887$	−181.405	−	104.734i	−0.204516	−	0.118077i	−0.598760	+	0.800929i	$0.704340\pi$
$888$		0			0
$889$	−1150.57	−	497.214i	−1.29423	−	0.559296i
$890$	−1282.79			−1.44134
$891$		0			0
$892$		−	1069.14i		−	1.19859i
$893$	−906.645	−	1570.35i	−1.01528	−	1.75852i
$894$		0			0
$895$	−239.018	−	137.997i	−0.267060	−	0.154187i
$896$	−75.2250	−	647.315i	−0.0839565	−	0.722449i
$897$		0			0
$898$	−78.1211	−	135.310i	−0.0869945	−	0.150679i
$899$		−	405.884i		−	0.451484i
$900$		0			0
$901$			321.471i			0.356793i
$902$	810.689	−	468.052i	0.898768	−	0.518904i
$903$		0			0
$904$	−162.470	+	281.407i	−0.179724	+	0.311291i
$905$	−3.07444	+	5.32509i	−0.00339718	+	0.00588408i
$906$		0			0
$907$	464.373	+	804.318i	0.511988	+	0.886790i	0.999903	+	0.0138986i	$0.00442420\pi$
$907$	464.373	+	804.318i	0.511988	+	0.886790i	−0.487915	+	0.872891i	$0.662242\pi$
$908$		−	627.215i		−	0.690765i
$909$		0			0
$910$	1015.57	−	755.018i	1.11601	−	0.829690i
$911$	157.855	+	273.414i	0.173277	+	0.300125i	0.939564	−	0.342374i	$-0.111231\pi$
$911$	157.855	+	273.414i	0.173277	+	0.300125i	−0.766287	+	0.642499i	$0.777898\pi$
$912$		0			0
$913$	−1650.49	−	952.911i	−1.80777	−	1.04371i
$914$	930.077	−	1610.94i	1.01759	−	1.76252i
$915$		0			0
$916$	−70.7107	+	40.8248i	−0.0771951	+	0.0445686i
$917$	−487.150	−	655.262i	−0.531243	−	0.714572i
$918$		0			0
$919$	−374.838			−0.407876			−0.203938	−	0.978984i	$-0.565374\pi$
$919$	−374.838			−0.407876			−0.203938	+	0.978984i	$0.565374\pi$
$920$	7.15469	−	4.13076i	0.00777684	−	0.00448996i
$921$		0			0
$922$	−3.64566	−	2.10483i	−0.00395408	−	0.00228289i
$923$	−1361.86	−	786.270i	−1.47547	−	0.851863i
$924$		0			0
$925$	56.9203	+	98.5889i	0.0615355	+	0.106583i
$926$	−112.056			−0.121011
$927$		0			0
$928$	470.356			0.506849
$929$	−838.196	+	483.932i	−0.902256	+	0.520918i	−0.877931	−	0.478787i	$-0.841077\pi$
$929$	−838.196	+	483.932i	−0.902256	+	0.520918i	−0.0243244	+	0.999704i	$0.507743\pi$
$930$		0			0
$931$	808.041	−	760.324i	0.867928	−	0.816675i
$932$	575.747	−	997.223i	0.617754	−	1.06998i
$933$		0			0
$934$	−523.489	+	302.236i	−0.560481	+	0.323594i
$935$	402.390			0.430364
$936$		0			0
$937$			184.891i			0.197322i	0.995121	+	0.0986610i	$0.0314559\pi$
$937$			184.891i			0.197322i	−0.995121	+	0.0986610i	$0.968544\pi$
$938$	1832.14	+	791.752i	1.95325	+	0.844085i
$939$		0			0
$940$	−418.838	+	725.449i	−0.445573	+	0.771754i
$941$	−1091.52	−	630.188i	−1.15995	−	0.669700i	−0.208661	−	0.977988i	$-0.566911\pi$
$941$	−1091.52	−	630.188i	−1.15995	−	0.669700i	−0.951293	+	0.308288i	$0.900244\pi$
$942$		0			0
$943$	−17.2548	+	9.96206i	−0.0182978	+	0.0105642i
$944$			899.178i			0.952519i
$945$		0			0
$946$	704.326			0.744531
$947$	−229.847	−	398.107i	−0.242711	−	0.420387i	0.718775	−	0.695243i	$-0.244703\pi$
$947$	−229.847	−	398.107i	−0.242711	−	0.420387i	−0.961485	+	0.274856i	$0.911370\pi$
$948$		0			0
$949$	−350.055	+	606.312i	−0.368867	+	0.638896i
$950$	585.616	+	338.105i	0.616438	+	0.355900i
$951$		0			0
$952$	−69.4453	+	160.699i	−0.0729468	+	0.168802i
$953$	278.059			0.291772			0.145886	−	0.989301i	$-0.453397\pi$
$953$	278.059			0.291772			0.145886	+	0.989301i	$0.453397\pi$
$954$		0			0
$955$			445.695i			0.466697i
$956$	−187.931	−	325.506i	−0.196581	−	0.340488i
$957$		0			0
$958$	−558.953	−	322.712i	−0.583459	−	0.336860i
$959$	57.8814	+	498.072i	0.0603560	+	0.519366i
$960$		0			0
$961$	66.0373	+	114.380i	0.0687173	+	0.119022i
$962$			489.035i			0.508352i
$963$		0			0
$964$			235.197i			0.243980i
$965$	−647.222	+	373.674i	−0.670696	+	0.387227i
$966$		0			0
$967$	239.574	−	414.955i	0.247750	−	0.429116i	−0.715151	−	0.698970i	$-0.753642\pi$
$967$	239.574	−	414.955i	0.247750	−	0.429116i	0.962901	+	0.269854i	$0.0869755\pi$
$968$	83.3164	−	144.308i	0.0860707	−	0.149079i
$969$		0			0
$970$	322.932	+	559.335i	0.332920	+	0.576634i
$971$		−	1621.52i		−	1.66995i	−0.550291	−	0.834973i	$-0.685483\pi$
$971$		−	1621.52i		−	1.66995i	0.550291	−	0.834973i	$-0.314517\pi$
$972$		0			0
$973$	−910.361	−	1224.52i	−0.935623	−	1.25850i
$974$	808.672	+	1400.66i	0.830258	+	1.43805i
$975$		0			0
$976$	670.660	+	387.206i	0.687152	+	0.396727i
$977$	−211.767	+	366.791i	−0.216752	+	0.375425i	−0.953813	−	0.300401i	$-0.902880\pi$
$977$	−211.767	+	366.791i	−0.216752	+	0.375425i	0.737061	+	0.675826i	$0.236213\pi$
$978$		0			0
$979$	1528.77	−	882.634i	1.56156	−	0.901567i
$980$	−490.829	−	147.654i	−0.500846	−	0.150668i
$981$		0			0
$982$	−840.278			−0.855680
$983$	1363.91	−	787.455i	1.38750	−	0.801073i	0.394466	−	0.918910i	$-0.370929\pi$
$983$	1363.91	−	787.455i	1.38750	−	0.801073i	0.993033	+	0.117837i	$0.0375961\pi$
$984$		0			0
$985$	679.812	+	392.490i	0.690164	+	0.398467i
$986$	−228.928	−	132.172i	−0.232179	−	0.134048i
$987$		0			0
$988$	602.874	+	1044.21i	0.610196	+	1.05689i
$989$	−14.9910			−0.0151577
$990$		0			0
$991$	640.630			0.646448			0.323224	−	0.946322i	$-0.395233\pi$
$991$	640.630			0.646448			0.323224	+	0.946322i	$0.395233\pi$
$992$	−1097.00	+	633.351i	−1.10584	+	0.638458i
$993$		0			0
$994$	177.130	+	1524.21i	0.178199	+	1.53341i
$995$	369.079	−	639.264i	0.370934	−	0.642477i
$996$		0			0
$997$	−264.891	+	152.935i	−0.265688	+	0.153395i	−0.626926	−	0.779078i	$-0.715687\pi$
$997$	−264.891	+	152.935i	−0.265688	+	0.153395i	0.361239	+	0.932473i	$0.382354\pi$
$998$	420.948			0.421792
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.l.a.118.4		28
3.2	odd	2		63.3.l.a.13.11	✓	28
7.6	odd	2	inner	189.3.l.a.118.3		28
9.2	odd	6		63.3.l.a.34.12	yes	28
9.4	even	3		567.3.d.g.244.11		14
9.5	odd	6		567.3.d.h.244.4		14
9.7	even	3	inner	189.3.l.a.181.3		28
21.2	odd	6		441.3.k.a.31.11		28
21.5	even	6		441.3.k.a.31.12		28
21.11	odd	6		441.3.t.b.166.4		28
21.17	even	6		441.3.t.b.166.3		28
21.20	even	2		63.3.l.a.13.12	yes	28
63.2	odd	6		441.3.t.b.178.3		28
63.11	odd	6		441.3.k.a.313.12		28
63.13	odd	6		567.3.d.g.244.12		14
63.20	even	6		63.3.l.a.34.11	yes	28
63.34	odd	6	inner	189.3.l.a.181.4		28
63.38	even	6		441.3.k.a.313.11		28
63.41	even	6		567.3.d.h.244.3		14
63.47	even	6		441.3.t.b.178.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.11	✓	28	3.2	odd	2
63.3.l.a.13.12	yes	28	21.20	even	2
63.3.l.a.34.11	yes	28	63.20	even	6
63.3.l.a.34.12	yes	28	9.2	odd	6
189.3.l.a.118.3		28	7.6	odd	2	inner
189.3.l.a.118.4		28	1.1	even	1	trivial
189.3.l.a.181.3		28	9.7	even	3	inner
189.3.l.a.181.4		28	63.34	odd	6	inner
441.3.k.a.31.11		28	21.2	odd	6
441.3.k.a.31.12		28	21.5	even	6
441.3.k.a.313.11		28	63.38	even	6
441.3.k.a.313.12		28	63.11	odd	6
441.3.t.b.166.3		28	21.17	even	6
441.3.t.b.166.4		28	21.11	odd	6
441.3.t.b.178.3		28	63.2	odd	6
441.3.t.b.178.4		28	63.47	even	6
567.3.d.g.244.11		14	9.4	even	3
567.3.d.g.244.12		14	63.13	odd	6
567.3.d.h.244.3		14	63.41	even	6
567.3.d.h.244.4		14	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30753 - 2.26471i) q^{2} +(-1.41927 + 2.45825i) q^{4} +(3.19140 + 1.84256i) q^{5} +(6.42567 + 2.77682i) q^{7} -3.03728 q^{8} +O(q^{10})\)	\(q+(-1.30753 - 2.26471i) q^{2} +(-1.41927 + 2.45825i) q^{4} +(3.19140 + 1.84256i) q^{5} +(6.42567 + 2.77682i) q^{7} -3.03728 q^{8} -9.63680i q^{10} +(6.63066 + 11.4846i) q^{11} +(16.2463 + 9.37981i) q^{13} +(-2.11307 - 18.1831i) q^{14} +(9.64842 + 16.7116i) q^{16} -8.23398i q^{17} -22.6432i q^{19} +(-9.05893 + 5.23018i) q^{20} +(17.3396 - 30.0330i) q^{22} +(-0.369057 + 0.639226i) q^{23} +(-5.70996 - 9.88995i) q^{25} -49.0575i q^{26} +(-15.9459 + 11.8548i) q^{28} +(6.13829 + 10.6318i) q^{29} +(-28.6323 - 16.5308i) q^{31} +(19.1566 - 33.1803i) q^{32} +(-18.6476 + 10.7662i) q^{34} +(15.3905 + 20.7016i) q^{35} -9.96860 q^{37} +(-51.2802 + 29.6066i) q^{38} +(-9.69320 - 5.59637i) q^{40} +(23.3769 + 13.4966i) q^{41} +(10.1549 + 17.5888i) q^{43} -37.6428 q^{44} +1.93021 q^{46} +(69.3523 - 40.0406i) q^{47} +(33.5785 + 35.6859i) q^{49} +(-14.9319 + 25.8628i) q^{50} +(-46.1158 + 26.6250i) q^{52} -39.0420 q^{53} +48.8695i q^{55} +(-19.5166 - 8.43400i) q^{56} +(16.0520 - 27.8029i) q^{58} +(40.3543 + 23.2986i) q^{59} +(34.7549 - 20.0658i) q^{61} +86.4583i q^{62} -23.0042 q^{64} +(34.5657 + 59.8695i) q^{65} +(-54.5167 + 94.4257i) q^{67} +(20.2412 + 11.6862i) q^{68} +(26.7597 - 61.9229i) q^{70} -83.8258 q^{71} +37.3200i q^{73} +(13.0342 + 22.5760i) q^{74} +(55.6625 + 32.1368i) q^{76} +(10.7157 + 92.2086i) q^{77} +(-49.4165 - 85.5918i) q^{79} +71.1111i q^{80} -70.5890i q^{82} +(-124.459 + 71.8564i) q^{83} +(15.1716 - 26.2779i) q^{85} +(26.5557 - 45.9958i) q^{86} +(-20.1392 - 34.8821i) q^{88} -133.114i q^{89} +(78.3474 + 105.385i) q^{91} +(-1.04758 - 1.81447i) q^{92} +(-181.360 - 104.708i) q^{94} +(41.7213 - 72.2635i) q^{95} +(-58.0415 + 33.5103i) q^{97} +(36.9132 - 122.706i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8	\( 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8} - 4 q^{11} - 34 q^{14} - 42 q^{16} + 14 q^{22} - 4 q^{23} + 28 q^{25} + 20 q^{28} + 38 q^{29} + 168 q^{32} + 264 q^{35} + 36 q^{37} - 66 q^{43} - 108 q^{44} - 40 q^{46} - 38 q^{49} - 196 q^{50} - 520 q^{53} - 332 q^{56} - 34 q^{58} + 72 q^{64} + 102 q^{65} + 68 q^{67} + 102 q^{70} + 332 q^{71} + 616 q^{74} - 334 q^{77} + 146 q^{79} + 78 q^{85} + 340 q^{86} - 74 q^{88} - 384 q^{91} - 606 q^{92} + 360 q^{95} + 1076 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8 - 4 * q^11 - 34 * q^14 - 42 * q^16 + 14 * q^22 - 4 * q^23 + 28 * q^25 + 20 * q^28 + 38 * q^29 + 168 * q^32 + 264 * q^35 + 36 * q^37 - 66 * q^43 - 108 * q^44 - 40 * q^46 - 38 * q^49 - 196 * q^50 - 520 * q^53 - 332 * q^56 - 34 * q^58 + 72 * q^64 + 102 * q^65 + 68 * q^67 + 102 * q^70 + 332 * q^71 + 616 * q^74 - 334 * q^77 + 146 * q^79 + 78 * q^85 + 340 * q^86 - 74 * q^88 - 384 * q^91 - 606 * q^92 + 360 * q^95 + 1076 * q^98

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