LMFDB - Embedded newform 168.2.v.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(11,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("168.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32999 + 0.480762i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(1.53774 - 1.27882i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 - 2.41702i) q^{6} +(-2.46429 + 0.962962i) q^{7} +(-1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +O(q^{10})$	\(q+(-1.32999 + 0.480762i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(1.53774 - 1.27882i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 - 2.41702i) q^{6} +(-2.46429 + 0.962962i) q^{7} +(-1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +(4.02451 + 3.39209i) q^{10} +(-2.26958 - 1.31034i) q^{11} +(1.69067 + 3.02352i) q^{12} -3.57182i q^{13} +(2.81451 - 2.46546i) q^{14} +(6.07784 - 2.14810i) q^{15} +(0.729261 - 3.93296i) q^{16} +(0.186192 + 0.107498i) q^{17} +(4.24172 + 0.0885645i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(-6.98334 - 2.57661i) q^{20} +(-0.859391 - 4.50127i) q^{21} +(3.64848 + 0.651612i) q^{22} +(2.33586 + 4.04583i) q^{23} +(-3.70216 - 3.20843i) q^{24} +(-4.42574 + 7.66560i) q^{25} +(1.71720 + 4.75048i) q^{26} +(2.72309 - 4.42547i) q^{27} +(-2.55797 + 4.63215i) q^{28} -2.57415 q^{29} +(-7.05072 + 5.77894i) q^{30} +(-4.26196 - 2.46064i) q^{31} +(0.920911 + 5.58139i) q^{32} +(2.95006 - 3.44980i) q^{33} +(-0.299314 - 0.0534570i) q^{34} +(7.68949 + 6.15077i) q^{35} +(-5.68401 + 1.92147i) q^{36} +(-7.31104 + 4.22103i) q^{37} +(2.46769 + 2.07991i) q^{38} +(6.08229 + 1.13113i) q^{39} +(10.5265 + 0.0695365i) q^{40} +0.909442i q^{41} +(3.30702 + 5.57347i) q^{42} +3.73541 q^{43} +(-5.16570 + 0.887414i) q^{44} +(1.73317 + 11.0299i) q^{45} +(-5.05175 - 4.25791i) q^{46} +(0.586728 + 1.01624i) q^{47} +(6.46632 + 2.48732i) q^{48} +(5.14541 - 4.74603i) q^{49} +(2.20085 - 12.3229i) q^{50} +(-0.242017 + 0.283015i) q^{51} +(-4.56770 - 5.49252i) q^{52} +(1.06171 - 1.83894i) q^{53} +(-1.49408 + 7.19498i) q^{54} +9.75355i q^{55} +(1.17511 - 7.39048i) q^{56} +(3.72672 - 1.31714i) q^{57} +(3.42359 - 1.23755i) q^{58} +(-6.79199 - 3.92136i) q^{59} +(6.59908 - 11.0756i) q^{60} +(0.301301 - 0.173956i) q^{61} +(6.85134 + 1.22364i) q^{62} +(7.93716 - 0.0379510i) q^{63} +(-3.90812 - 6.98044i) q^{64} +(-11.5125 + 6.64673i) q^{65} +(-2.26500 + 6.00647i) q^{66} +(-4.98736 + 8.63836i) q^{67} +(0.423784 - 0.0728018i) q^{68} +(-7.62919 + 2.69640i) q^{69} +(-13.1840 - 4.48364i) q^{70} -10.0808 q^{71} +(6.63590 - 5.28818i) q^{72} +(4.45173 - 7.71062i) q^{73} +(7.69428 - 9.12879i) q^{74} +(-11.6519 - 9.96394i) q^{75} +(-4.28194 - 1.57989i) q^{76} +(6.85470 + 1.04354i) q^{77} +(-8.63318 + 1.41975i) q^{78} +(9.70950 - 5.60578i) q^{79} +(-14.0335 + 4.96826i) q^{80} +(6.67358 + 6.03849i) q^{81} +(-0.437225 - 1.20955i) q^{82} -1.73937i q^{83} +(-7.07781 - 5.82276i) q^{84} -0.800163i q^{85} +(-4.96805 + 1.79584i) q^{86} +(0.815185 - 4.38341i) q^{87} +(6.44368 - 3.66372i) q^{88} +(15.4694 - 8.93127i) q^{89} +(-7.60786 - 13.8364i) q^{90} +(3.43953 + 8.80199i) q^{91} +(8.76581 + 3.23428i) q^{92} +(5.53980 - 6.47826i) q^{93} +(-1.26891 - 1.06951i) q^{94} +(-4.24662 + 7.35536i) q^{95} +(-9.79593 - 0.199344i) q^{96} -8.88553 q^{97} +(-4.56162 + 8.78588i) q^{98} +(4.94029 + 6.11600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36} + 14 q^{40} - 8 q^{42} - 16 q^{43} - 12 q^{46} + 64 q^{48} - 16 q^{49} - 34 q^{51} - 8 q^{52} + 32 q^{54} + 4 q^{57} - 18 q^{58} + 40 q^{60} + 4 q^{64} - 20 q^{66} - 36 q^{67} - 42 q^{70} + 22 q^{72} + 4 q^{73} + 104 q^{76} + 28 q^{78} - 10 q^{81} + 52 q^{82} + 4 q^{84} + 46 q^{88} + 140 q^{90} + 72 q^{91} - 46 q^{96} - 32 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.32999	+	0.480762i	−0.940443	+	0.339950i
$2$	−1.32999	+	0.480762i	−0.940443	+	0.339950i
$3$	−0.316681	+	1.70285i	−0.182836	+	0.983143i
$3$	−0.316681	+	1.70285i	−0.182836	+	0.983143i
$4$	1.53774	−	1.27882i	0.768868	−	0.639408i
$5$	−1.86088	−	3.22314i	−0.832210	−	1.44143i	−0.896282	−	0.443485i	$-0.853742\pi$
$5$	−1.86088	−	3.22314i	−0.832210	−	1.44143i	0.0640716	−	0.997945i	$-0.479591\pi$
$6$	−0.397486	−	2.41702i	−0.162273	−	0.986746i
$7$	−2.46429	+	0.962962i	−0.931412	+	0.363965i
$7$	−2.46429	+	0.962962i	−0.931412	+	0.363965i
$8$	−1.43036	+	2.44009i	−0.505710	+	0.862704i
$9$	−2.79943	−	1.07852i	−0.933142	−	0.359508i
$10$	4.02451	+	3.39209i	1.27266	+	1.07267i
$11$	−2.26958	−	1.31034i	−0.684304	−	0.395083i	0.117171	−	0.993112i	$-0.462618\pi$
$11$	−2.26958	−	1.31034i	−0.684304	−	0.395083i	−0.801475	+	0.598029i	$0.795951\pi$
$12$	1.69067	+	3.02352i	0.488053	+	0.872814i
$13$		−	3.57182i		−	0.990645i	−0.868709	−	0.495323i	$-0.835050\pi$
$13$		−	3.57182i		−	0.990645i	0.868709	−	0.495323i	$-0.164950\pi$
$14$	2.81451	−	2.46546i	0.752211	−	0.658923i
$15$	6.07784	−	2.14810i	1.56929	−	0.554637i
$16$	0.729261	−	3.93296i	0.182315	−	0.983240i
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	0.522409	−	0.852695i	$-0.325033\pi$
$17$	0.186192	+	0.107498i	0.0451582	+	0.0260721i	−0.477251	+	0.878767i	$0.658367\pi$
$18$	4.24172	+	0.0885645i	0.999782	+	0.0208749i
$19$	−1.14103	−	1.97631i	−0.261769	−	0.453398i	0.704943	−	0.709264i	$-0.250973\pi$
$19$	−1.14103	−	1.97631i	−0.261769	−	0.453398i	−0.966712	+	0.255866i	$0.917639\pi$
$20$	−6.98334	−	2.57661i	−1.56152	−	0.576148i
$21$	−0.859391	−	4.50127i	−0.187535	−	0.982258i
$22$	3.64848	+	0.651612i	0.777858	+	0.138924i
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	0.999889	−	0.0148767i	$-0.00473557\pi$
$23$	2.33586	+	4.04583i	0.487061	+	0.843615i	−0.512828	+	0.858491i	$0.671402\pi$
$24$	−3.70216	−	3.20843i	−0.755700	−	0.654918i
$25$	−4.42574	+	7.66560i	−0.885148	+	1.53312i
$26$	1.71720	+	4.75048i	0.336770	+	0.931646i
$27$	2.72309	−	4.42547i	0.524060	−	0.851682i
$28$	−2.55797	+	4.63215i	−0.483411	+	0.875394i
$29$	−2.57415			−0.478008			−0.239004	−	0.971019i	$-0.576821\pi$
$29$	−2.57415			−0.478008			−0.239004	+	0.971019i	$0.576821\pi$
$30$	−7.05072	+	5.77894i	−1.28728	+	1.05509i
$31$	−4.26196	−	2.46064i	−0.765471	−	0.441945i	0.0657857	−	0.997834i	$-0.479045\pi$
$31$	−4.26196	−	2.46064i	−0.765471	−	0.441945i	−0.831257	+	0.555889i	$0.812378\pi$
$32$	0.920911	+	5.58139i	0.162796	+	0.986660i
$33$	2.95006	−	3.44980i	0.513539	−	0.600534i
$34$	−0.299314	−	0.0534570i	−0.0513319	−	0.00916779i
$35$	7.68949	+	6.15077i	1.29976	+	1.03967i
$36$	−5.68401	+	1.92147i	−0.947335	+	0.320244i
$37$	−7.31104	+	4.22103i	−1.20193	+	0.693933i	−0.960983	−	0.276606i	$-0.910790\pi$
$37$	−7.31104	+	4.22103i	−1.20193	+	0.693933i	−0.240944	+	0.970539i	$0.577457\pi$
$38$	2.46769	+	2.07991i	0.400312	+	0.337406i
$39$	6.08229	+	1.13113i	0.973946	+	0.181125i
$40$	10.5265	+	0.0695365i	1.66438	+	0.0109947i
$41$			0.909442i			0.142031i	0.997475	+	0.0710155i	$0.0226240\pi$
$41$			0.909442i			0.142031i	−0.997475	+	0.0710155i	$0.977376\pi$
$42$	3.30702	+	5.57347i	0.510284	+	0.860006i
$43$	3.73541			0.569644			0.284822	−	0.958580i	$-0.408065\pi$
$43$	3.73541			0.569644			0.284822	+	0.958580i	$0.408065\pi$
$44$	−5.16570	+	0.887414i	−0.778759	+	0.133783i
$45$	1.73317	+	11.0299i	0.258365	+	1.64425i
$46$	−5.05175	−	4.25791i	−0.744840	−	0.627795i
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	0.905640	−	0.424048i	$-0.139391\pi$
$47$	0.586728	+	1.01624i	0.0855831	+	0.148234i	−0.820056	+	0.572283i	$0.806058\pi$
$48$	6.46632	+	2.48732i	0.933332	+	0.359014i
$49$	5.14541	−	4.74603i	0.735058	−	0.678004i
$50$	2.20085	−	12.3229i	0.311247	−	1.74272i
$51$	−0.242017	+	0.283015i	−0.0338891	+	0.0396301i
$52$	−4.56770	−	5.49252i	−0.633426	−	0.761675i
$53$	1.06171	−	1.83894i	0.145837	−	0.252598i	−0.783848	−	0.620953i	$-0.786746\pi$
$53$	1.06171	−	1.83894i	0.145837	−	0.252598i	0.929685	+	0.368355i	$0.120079\pi$
$54$	−1.49408	+	7.19498i	−0.203319	+	0.979113i
$55$			9.75355i			1.31517i
$56$	1.17511	−	7.39048i	0.157030	−	0.987594i
$57$	3.72672	−	1.31714i	0.493616	−	0.174459i
$58$	3.42359	−	1.23755i	0.449539	−	0.162499i
$59$	−6.79199	−	3.92136i	−0.884242	−	0.510517i	−0.0121872	−	0.999926i	$-0.503879\pi$
$59$	−6.79199	−	3.92136i	−0.884242	−	0.510517i	−0.872055	+	0.489408i	$0.837213\pi$
$60$	6.59908	−	11.0756i	0.851938	−	1.42986i
$61$	0.301301	−	0.173956i	0.0385776	−	0.0222728i	−0.480587	−	0.876947i	$-0.659576\pi$
$61$	0.301301	−	0.173956i	0.0385776	−	0.0222728i	0.519165	+	0.854674i	$0.326243\pi$
$62$	6.85134	+	1.22364i	0.870121	+	0.155402i
$63$	7.93716	−	0.0379510i	0.999989	−	0.00478137i
$64$	−3.90812	−	6.98044i	−0.488515	−	0.872555i
$65$	−11.5125	+	6.64673i	−1.42795	+	0.824425i
$66$	−2.26500	+	6.00647i	−0.278803	+	0.739346i
$67$	−4.98736	+	8.63836i	−0.609303	+	1.05534i	0.382053	+	0.924140i	$0.375217\pi$
$67$	−4.98736	+	8.63836i	−0.609303	+	1.05534i	−0.991356	+	0.131203i	$0.958116\pi$
$68$	0.423784	−	0.0728018i	0.0513914	−	0.00882851i
$69$	−7.62919	+	2.69640i	−0.918446	+	0.324608i
$70$	−13.1840	−	4.48364i	−1.57579	−	0.535897i
$71$	−10.0808			−1.19637			−0.598183	−	0.801359i	$-0.704111\pi$
$71$	−10.0808			−1.19637			−0.598183	+	0.801359i	$0.704111\pi$
$72$	6.63590	−	5.28818i	0.782048	−	0.623219i
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	−0.478665	−	0.877998i	$-0.658879\pi$
$73$	4.45173	−	7.71062i	0.521036	−	0.902460i	0.999701	−	0.0244626i	$-0.00778746\pi$
$74$	7.69428	−	9.12879i	0.894442	−	1.06120i
$75$	−11.6519	−	9.96394i	−1.34544	−	1.15054i
$76$	−4.28194	−	1.57989i	−0.491172	−	0.181226i
$77$	6.85470	+	1.04354i	0.781166	+	0.118922i
$78$	−8.63318	+	1.41975i	−0.977515	+	0.160755i
$79$	9.70950	−	5.60578i	1.09240	−	0.630700i	0.158189	−	0.987409i	$-0.449434\pi$
$79$	9.70950	−	5.60578i	1.09240	−	0.630700i	0.934216	+	0.356709i	$0.116101\pi$
$80$	−14.0335	+	4.96826i	−1.56900	+	0.555468i
$81$	6.67358	+	6.03849i	0.741508	+	0.670944i
$82$	−0.437225	−	1.20955i	−0.0482835	−	0.133572i
$83$		−	1.73937i		−	0.190921i	−0.995433	−	0.0954603i	$-0.969568\pi$
$83$		−	1.73937i		−	0.190921i	0.995433	−	0.0954603i	$-0.0304323\pi$
$84$	−7.07781	−	5.82276i	−0.772253	−	0.635315i
$85$		−	0.800163i		−	0.0867898i
$86$	−4.96805	+	1.79584i	−0.535718	+	0.193651i
$87$	0.815185	−	4.38341i	0.0873970	−	0.469950i
$88$	6.44368	−	3.66372i	0.686899	−	0.390554i
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.658837	−	0.752286i	$-0.271049\pi$
$89$	15.4694	−	8.93127i	1.63975	−	0.946712i	0.980917	−	0.194426i	$-0.0622845\pi$
$90$	−7.60786	−	13.8364i	−0.801939	−	1.45849i
$91$	3.43953	+	8.80199i	0.360560	+	0.922699i
$92$	8.76581	+	3.23428i	0.913899	+	0.337197i
$93$	5.53980	−	6.47826i	0.574451	−	0.671764i
$94$	−1.26891	−	1.06951i	−0.130878	−	0.110312i
$95$	−4.24662	+	7.35536i	−0.435694	+	0.754644i
$96$	−9.79593	−	0.199344i	−0.999793	−	0.0203454i
$97$	−8.88553			−0.902189			−0.451094	−	0.892476i	$-0.648966\pi$
$97$	−8.88553			−0.902189			−0.451094	+	0.892476i	$0.648966\pi$
$98$	−4.56162	+	8.78588i	−0.460793	+	0.887507i
$99$	4.94029	+	6.11600i	0.496518	+	0.614681i
$100$	2.99728	+	17.4474i	0.299728	+	1.74474i
$101$	7.38721	−	12.7950i	0.735055	−	1.27315i	−0.219644	−	0.975580i	$-0.570490\pi$
$101$	7.38721	−	12.7950i	0.735055	−	1.27315i	0.954699	−	0.297573i	$-0.0961770\pi$
$102$	0.185816	−	0.492759i	0.0183986	−	0.0487905i
$103$	−6.50151	+	3.75365i	−0.640613	+	0.369858i	−0.784851	−	0.619685i	$-0.787260\pi$
$103$	−6.50151	+	3.75365i	−0.640613	+	0.369858i	0.144238	+	0.989543i	$0.453927\pi$
$104$	8.71558	+	5.10900i	0.854633	+	0.500979i
$105$	−12.9090	+	11.1463i	−1.25979	+	1.08776i
$106$	−0.527972	+	2.95620i	−0.0512812	+	0.287131i
$107$	10.9396	−	6.31597i	1.05757	−	0.610588i	0.132810	−	0.991141i	$-0.457600\pi$
$107$	10.9396	−	6.31597i	1.05757	−	0.610588i	0.924759	+	0.380554i	$0.124267\pi$
$108$	−1.47196	−	10.2875i	−0.141639	−	0.989918i
$109$	11.2275	+	6.48219i	1.07540	+	0.620881i	0.929651	−	0.368441i	$-0.120108\pi$
$109$	11.2275	+	6.48219i	1.07540	+	0.620881i	0.145747	+	0.989322i	$0.453442\pi$
$110$	−4.68914	−	12.9721i	−0.447092	−	1.23684i
$111$	−4.87253	−	13.7864i	−0.462480	−	1.30854i
$112$	1.99018	+	10.3942i	0.188055	+	0.982159i
$113$		−	7.10498i		−	0.668380i	−0.942506	−	0.334190i	$-0.891537\pi$
$113$		−	7.10498i		−	0.668380i	0.942506	−	0.334190i	$-0.108463\pi$
$114$	−4.32326	+	3.54344i	−0.404910	+	0.331874i
$115$	8.69351	−	15.0576i	0.810674	−	1.40413i
$116$	−3.95836	+	3.29187i	−0.367525	+	0.305642i
$117$	−3.85229	+	9.99905i	−0.356145	+	0.924413i
$118$	10.9185	+	1.95003i	1.00513	+	0.179514i
$119$	−0.562347	−	0.0856100i	−0.0515502	−	0.00784786i
$120$	−3.45195	+	17.9031i	−0.315118	+	1.63432i
$121$	−2.06600	−	3.57842i	−0.187819	−	0.325311i
$122$	−0.317095	+	0.376214i	−0.0287084	+	0.0340608i
$123$	−1.54865	−	0.288003i	−0.139637	−	0.0259684i
$124$	−9.70048	+	1.66644i	−0.871129	+	0.149651i
$125$	14.3343			1.28210
$126$	−10.5381	+	3.86636i	−0.938807	+	0.344443i
$127$		−	2.53093i		−	0.224584i	−0.993675	−	0.112292i	$-0.964181\pi$
$127$		−	2.53093i		−	0.224584i	0.993675	−	0.112292i	$-0.0358192\pi$
$128$	8.55369	+	7.40503i	0.756046	+	0.654518i
$129$	−1.18293	+	6.36086i	−0.104151	+	0.560042i
$130$	12.1159	−	14.3748i	1.06264	−	1.26076i
$131$	−5.04824	+	2.91460i	−0.441067	+	0.254650i	−0.704050	−	0.710150i	$-0.748627\pi$
$131$	−5.04824	+	2.91460i	−0.441067	+	0.254650i	0.262983	+	0.964800i	$0.415294\pi$
$132$	0.124742	−	9.07746i	0.0108574	−	0.790092i
$133$	4.71493	+	3.77144i	0.408836	+	0.327025i
$134$	2.48013	−	13.8866i	0.214251	−	1.19962i
$135$	−19.3312	−	0.541642i	−1.66377	−	0.0466171i
$136$	−0.528627	+	0.300565i	−0.0453294	+	0.0257732i
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	0.109582	−	0.993978i	$-0.465049\pi$
$137$	−8.15158	−	4.70632i	−0.696437	−	0.402088i	−0.806019	+	0.591890i	$0.798382\pi$
$138$	8.85040	−	7.25400i	0.753396	−	0.617501i
$139$	−7.53929			−0.639474			−0.319737	−	0.947506i	$-0.603595\pi$
$139$	−7.53929			−0.639474			−0.319737	+	0.947506i	$0.603595\pi$
$140$	19.6901	−	0.375182i	1.66412	−	0.0317086i
$141$	−1.91632	+	0.677288i	−0.161383	+	0.0570379i
$142$	13.4073	−	4.84645i	1.12512	−	0.406705i
$143$	−4.68031	+	8.10654i	−0.391387	+	0.677903i
$144$	−6.28330	+	10.2235i	−0.523608	+	0.851959i
$145$	4.79018	+	8.29684i	0.397803	+	0.689015i
$146$	−2.21377	+	12.3953i	−0.183213	+	1.02584i
$147$	6.45234	+	10.2649i	0.532180	+	0.846631i
$148$	−5.84452	+	15.8403i	−0.480417	+	1.30206i
$149$	7.38721	+	12.7950i	0.605184	+	1.04821i	0.992022	+	0.126062i	$0.0402338\pi$
$149$	7.38721	+	12.7950i	0.605184	+	1.04821i	−0.386838	+	0.922148i	$0.626433\pi$
$150$	20.2871	+	7.65014i	1.65644	+	0.624632i
$151$	−3.18729	−	1.84018i	−0.259378	−	0.149752i	0.364673	−	0.931136i	$-0.381181\pi$
$151$	−3.18729	−	1.84018i	−0.259378	−	0.149752i	−0.624051	+	0.781384i	$0.714514\pi$
$152$	6.45448	+	0.0426373i	0.523527	+	0.00345834i
$153$	−0.405292	−	0.501745i	−0.0327659	−	0.0405637i
$154$	−9.61837	+	1.90759i	−0.775070	+	0.153718i
$155$			18.3158i			1.47116i
$156$	10.7995	−	6.03876i	0.864649	−	0.483487i
$157$	−18.5989	−	10.7381i	−1.48436	−	0.856993i	−0.484514	−	0.874784i	$-0.661003\pi$
$157$	−18.5989	−	10.7381i	−1.48436	−	0.856993i	−0.999842	+	0.0177905i	$0.994337\pi$
$158$	−10.2185	+	12.1236i	−0.812938	+	0.964501i
$159$	2.79522	+	2.39030i	0.221676	+	0.189563i
$160$	16.2759	−	13.3545i	1.28672	−	1.05577i
$161$	−9.65222	−	7.72074i	−0.760701	−	0.608480i
$162$	−11.7789	−	4.82272i	−0.925434	−	0.378909i
$163$	−0.756294	−	1.30994i	−0.0592375	−	0.102602i	0.834886	−	0.550423i	$-0.185534\pi$
$163$	−0.756294	−	1.30994i	−0.0592375	−	0.102602i	−0.894123	+	0.447821i	$0.852200\pi$
$164$	1.16301	+	1.39848i	0.0908158	+	0.109203i
$165$	−16.6089	−	3.08877i	−1.29300	−	0.240460i
$166$	0.836223	+	2.31334i	0.0649035	+	0.179550i
$167$	−7.21687			−0.558459			−0.279229	−	0.960224i	$-0.590079\pi$
$167$	−7.21687			−0.558459			−0.279229	+	0.960224i	$0.590079\pi$
$168$	12.2128	+	4.34146i	0.942236	+	0.334951i
$169$	0.242090			0.0186223
$170$	0.384688	+	1.06421i	0.0295042	+	0.0816209i
$171$	1.06272	+	6.76317i	0.0812680	+	0.517193i
$172$	5.74407	−	4.77690i	0.437981	−	0.364235i
$173$	−1.33696	−	2.31567i	−0.101647	−	0.176057i	0.810716	−	0.585439i	$-0.199078\pi$
$173$	−1.33696	−	2.31567i	−0.101647	−	0.176057i	−0.912363	+	0.409382i	$0.865744\pi$
$174$	1.02319	+	6.22179i	0.0775678	+	0.471672i
$175$	3.52460	−	23.1521i	0.266435	−	1.75013i
$176$	−6.80864	+	7.97059i	−0.513221	+	0.600806i
$177$	8.82840	−	10.3240i	0.663583	−	0.775996i
$178$	−16.2803	+	19.3156i	−1.22026	+	1.44776i
$179$	−7.29346	−	4.21088i	−0.545139	−	0.314736i	0.202020	−	0.979381i	$-0.435249\pi$
$179$	−7.29346	−	4.21088i	−0.545139	−	0.314736i	−0.747159	+	0.664645i	$0.768583\pi$
$180$	16.7704	+	14.7447i	1.24999	+	1.09901i
$181$			6.12284i			0.455107i	0.973766	+	0.227553i	$0.0730726\pi$
$181$			6.12284i			0.455107i	−0.973766	+	0.227553i	$0.926927\pi$
$182$	−8.80619	−	10.0529i	−0.652759	−	0.745174i
$183$	0.200806	+	0.568160i	0.0148440	+	0.0419996i
$184$	−13.2133	−	0.0872854i	−0.974101	−	0.00643477i
$185$	27.2099	+	15.7096i	2.00051	+	1.15500i
$186$	−4.25337	+	11.2793i	−0.311872	+	0.827041i
$187$	−0.281718	−	0.487951i	−0.0206013	−	0.0356825i
$188$	2.20182	+	0.812396i	0.160584	+	0.0592500i
$189$	−2.44892	+	13.5279i	−0.178133	+	0.984006i
$190$	2.11177	−	11.8242i	0.153204	−	0.857815i
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	−0.998454	−	0.0555887i	$-0.982296\pi$
$191$	−7.56478	−	13.1026i	−0.547368	−	0.948069i	0.451086	−	0.892481i	$-0.351037\pi$
$192$	13.1243	−	4.44439i	0.947165	−	0.320746i
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	−0.915812	−	0.401607i	$-0.868452\pi$
$193$	−1.52962	+	2.64937i	−0.110104	+	0.190706i	0.805708	+	0.592313i	$0.201785\pi$
$194$	11.8176	−	4.27183i	0.848457	−	0.306699i
$195$	−7.67263	−	21.7089i	−0.549448	−	1.55461i
$196$	1.84299	−	13.8782i	0.131642	−	0.991297i
$197$	14.5736			1.03833			0.519163	−	0.854675i	$-0.326244\pi$
$197$	14.5736			1.03833			0.519163	+	0.854675i	$0.326244\pi$
$198$	−9.51086	−	5.75911i	−0.675908	−	0.409282i
$199$	15.0386	+	8.68255i	1.06606	+	0.615490i	0.927102	−	0.374809i	$-0.122292\pi$
$199$	15.0386	+	8.68255i	1.06606	+	0.615490i	0.138957	+	0.990298i	$0.455625\pi$
$200$	−12.3744	−	21.7638i	−0.875001	−	1.53893i
$201$	−13.1305	−	11.2283i	−0.926151	−	0.791987i
$202$	−3.67354	+	20.5687i	−0.258469	+	1.44721i
$203$	6.34345	−	2.47881i	0.445223	−	0.173978i
$204$	−0.0102336	+	0.744698i	−0.000716494	+	0.0521393i
$205$	2.93126	−	1.69236i	0.204728	−	0.118200i
$206$	6.84232	−	8.11799i	0.476727	−	0.565607i
$207$	−2.17555	−	13.8453i	−0.151211	−	0.962314i
$208$	−14.0478	−	2.60479i	−0.974042	−	0.180610i
$209$			5.98054i			0.413683i
$210$	11.8101	−	21.0305i	0.814974	−	1.45124i
$211$	−21.2686			−1.46419			−0.732097	−	0.681201i	$-0.761458\pi$
$211$	−21.2686			−1.46419			−0.732097	+	0.681201i	$0.761458\pi$
$212$	−0.719032	−	4.18554i	−0.0493833	−	0.287464i
$213$	3.19239	−	17.1661i	0.218739	−	1.17620i
$214$	−11.5130	+	13.6595i	−0.787015	+	0.933744i
$215$	−6.95114	−	12.0397i	−0.474064	−	0.821103i
$216$	6.90355	+	12.9746i	0.469727	+	0.882812i
$217$	12.8722	+	1.95963i	0.873822	+	0.133028i
$218$	−18.0488	−	3.22349i	−1.22242	−	0.218322i
$219$	11.7203	+	10.0225i	0.791984	+	0.677255i
$220$	12.4730	+	14.9984i	0.840929	+	1.01119i
$221$	0.383964	−	0.665045i	0.0258282	−	0.0447357i
$222$	13.1084	+	15.9932i	0.879776	+	1.07339i
$223$		−	6.68788i		−	0.447854i	−0.974606	−	0.223927i	$-0.928112\pi$
$223$		−	6.68788i		−	0.447854i	0.974606	−	0.223927i	$-0.0718877\pi$
$224$	−7.64405	−	12.8673i	−0.510740	−	0.859735i
$225$	20.6571	−	16.6860i	1.37714	−	1.11240i
$226$	3.41580	+	9.44953i	0.227216	+	0.628574i
$227$	−20.7637	−	11.9879i	−1.37813	−	0.795666i	−0.386199	−	0.922415i	$-0.626212\pi$
$227$	−20.7637	−	11.9879i	−1.37813	−	0.795666i	−0.991935	+	0.126749i	$0.959546\pi$
$228$	4.04633	−	6.79120i	0.267975	−	0.449758i
$229$	14.3077	−	8.26054i	0.945478	−	0.545872i	0.0538045	−	0.998551i	$-0.482865\pi$
$229$	14.3077	−	8.26054i	0.945478	−	0.545872i	0.891673	+	0.452680i	$0.149532\pi$
$230$	−4.32314	+	24.2060i	−0.285059	+	1.59609i
$231$	−3.94775	+	11.3421i	−0.259743	+	0.746255i
$232$	3.68197	−	6.28117i	0.241733	−	0.412379i
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.870086	−	0.492901i	$-0.835937\pi$
$233$	−13.4061	+	7.74002i	−0.878264	+	0.507066i	−0.00817827	+	0.999967i	$0.502603\pi$
$234$	0.316337	−	15.1507i	0.0206796	−	0.990429i
$235$	2.18366	−	3.78221i	0.142446	−	0.246724i
$236$	−15.4590	+	2.65569i	−1.00629	+	0.172871i
$237$	6.47102	+	18.3091i	0.420338	+	1.18930i
$238$	0.789072	−	0.156495i	0.0511480	−	0.0101440i
$239$	20.5460			1.32901			0.664505	−	0.747284i	$-0.268642\pi$
$239$	20.5460			1.32901			0.664505	+	0.747284i	$0.268642\pi$
$240$	−4.01606	−	25.4704i	−0.259236	−	1.64411i
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	−0.993383	−	0.114848i	$-0.963362\pi$
$241$	−6.16667	+	10.6810i	−0.397230	+	0.688023i	0.596153	+	0.802871i	$0.296695\pi$
$242$	4.46813	+	3.76600i	0.287222	+	0.242088i
$243$	−12.3961	+	9.45185i	−0.795208	+	0.606337i
$244$	0.240863	−	0.652807i	0.0154197	−	0.0417917i
$245$	−24.8721	−	7.75258i	−1.58902	−	0.495294i
$246$	2.19814	−	0.361491i	0.140149	−	0.0230478i
$247$	−7.05904	+	4.07554i	−0.449156	+	0.259320i
$248$	12.1004	−	6.87997i	0.768374	−	0.436879i
$249$	2.96189	+	0.550825i	0.187702	+	0.0349071i
$250$	−19.0644	+	6.89137i	−1.20574	+	0.435848i
$251$			21.2978i			1.34430i	0.740413	+	0.672152i	$0.234630\pi$
$251$			21.2978i			1.34430i	−0.740413	+	0.672152i	$0.765370\pi$
$252$	12.1567	−	10.2085i	0.765802	−	0.643077i
$253$		−	12.2431i		−	0.769719i
$254$	1.21678	+	3.36611i	0.0763473	+	0.211208i
$255$	1.36256	+	0.253396i	0.0853269	+	0.0158683i
$256$	−14.9364	−	5.73631i	−0.933522	−	0.358519i
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	−0.852226	−	0.523173i	$-0.824748\pi$
$257$	−13.2299	+	7.63828i	−0.825258	+	0.476463i	0.0269684	+	0.999636i	$0.491415\pi$
$258$	−1.48477	−	9.02857i	−0.0924379	−	0.562094i
$259$	13.9518	−	17.4421i	0.866922	−	1.08380i
$260$	−9.20319	+	24.9432i	−0.570758	+	1.54691i
$261$	7.20615	+	2.77628i	0.446049	+	0.171848i
$262$	5.31287	−	6.30339i	0.328230	−	0.389425i
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	−0.873628	−	0.486594i	$-0.838239\pi$
$263$	−0.249921	+	0.432876i	−0.0154108	+	0.0266923i	0.858217	+	0.513287i	$0.171572\pi$
$264$	4.19820	+	12.1329i	0.258381	+	0.746728i
$265$	−7.90287			−0.485470
$266$	−8.08396	−	2.74921i	−0.495660	−	0.168565i
$267$	10.3098	+	29.1705i	0.630948	+	1.78521i
$268$	3.37763	+	19.6614i	0.206322	+	1.20101i
$269$	−10.9207	+	18.9153i	−0.665849	+	1.15328i	0.313205	+	0.949685i	$0.398597\pi$
$269$	−10.9207	+	18.9153i	−0.665849	+	1.15328i	−0.979054	+	0.203599i	$0.934736\pi$
$270$	25.9707	−	8.57335i	1.58053	−	0.521757i
$271$	13.6308	−	7.86975i	0.828013	−	0.478053i	−0.0251590	−	0.999683i	$-0.508009\pi$
$271$	13.6308	−	7.86975i	0.828013	−	0.478053i	0.853172	+	0.521630i	$0.174676\pi$
$272$	0.558568	−	0.653892i	0.0338681	−	0.0396480i
$273$	−16.0777	+	3.06959i	−0.973069	+	0.185780i
$274$	13.1041	+	2.34037i	0.791649	+	0.141387i
$275$	20.0891	−	11.5985i	1.21142	−	0.699414i
$276$	−8.28348	+	13.9027i	−0.498607	+	0.836842i
$277$	10.8672	+	6.27417i	0.652945	+	0.376978i	0.789584	−	0.613643i	$-0.210297\pi$
$277$	10.8672	+	6.27417i	0.652945	+	0.376978i	−0.136639	+	0.990621i	$0.543630\pi$
$278$	10.0272	−	3.62461i	0.601389	−	0.217389i
$279$	9.27718	+	11.4850i	0.555411	+	0.687590i
$280$	−26.0072	+	9.96525i	−1.55423	+	0.595538i
$281$		−	22.7512i		−	1.35722i	−0.734498	−	0.678610i	$-0.762582\pi$
$281$		−	22.7512i		−	1.35722i	0.734498	−	0.678610i	$-0.237418\pi$
$282$	2.22307	−	1.82208i	0.132382	−	0.108503i
$283$	0.440379	−	0.762759i	0.0261778	−	0.0453413i	−0.852640	−	0.522499i	$-0.825000\pi$
$283$	0.440379	−	0.762759i	0.0261778	−	0.0453413i	0.878818	+	0.477158i	$0.158333\pi$
$284$	−15.5015	+	12.8914i	−0.919848	+	0.764966i
$285$	−11.1803	−	9.56068i	−0.662263	−	0.566326i
$286$	2.32744	−	13.0317i	0.137624	−	0.770581i
$287$	−0.875758	−	2.24113i	−0.0516944	−	0.132289i
$288$	3.44164	−	16.6179i	0.202800	−	0.979220i
$289$	−8.47689	−	14.6824i	−0.498640	−	0.863671i
$290$	−10.3597	−	8.73176i	−0.608342	−	0.512747i
$291$	2.81388	−	15.1308i	0.164952	−	0.886981i
$292$	−3.01488	−	17.5498i	−0.176433	−	1.02703i
$293$	−22.1280			−1.29273			−0.646366	−	0.763028i	$-0.723712\pi$
$293$	−22.1280			−1.29273			−0.646366	+	0.763028i	$0.723712\pi$
$294$	−13.5165	−	10.5501i	−0.788298	−	0.615294i
$295$			29.1887i			1.69943i
$296$	0.157729	−	23.8772i	0.00916784	−	1.38784i
$297$	−11.9792	+	6.47577i	−0.695101	+	0.375762i
$298$	−15.9763	−	13.4657i	−0.925480	−	0.780049i
$299$	14.4510	−	8.34329i	0.835723	−	0.482505i
$300$	−30.6595	−	0.421321i	−1.77013	−	0.0243250i
$301$	−9.20511	+	3.59705i	−0.530574	+	0.207331i
$302$	5.12375	+	0.915093i	0.294839	+	0.0526577i
$303$	19.4487	+	16.6313i	1.11730	+	0.955442i
$304$	−8.60487	+	3.04636i	−0.493523	+	0.174721i
$305$	−1.12137	−	0.647422i	−0.0642094	−	0.0370713i
$306$	0.780253	+	0.472466i	0.0446041	+	0.0270091i
$307$	9.96754			0.568878			0.284439	−	0.958694i	$-0.408193\pi$
$307$	9.96754			0.568878			0.284439	+	0.958694i	$0.408193\pi$
$308$	11.8752	−	7.16121i	0.676653	−	0.408048i
$309$	−4.33301	−	12.2598i	−0.246496	−	0.697438i
$310$	−8.80556	−	24.3598i	−0.500122	−	1.38355i
$311$	−5.87187	+	10.1704i	−0.332963	+	0.576709i	−0.983091	−	0.183115i	$-0.941382\pi$
$311$	−5.87187	+	10.1704i	−0.332963	+	0.576709i	0.650128	+	0.759825i	$0.274715\pi$
$312$	−11.4599	+	13.2234i	−0.648792	+	0.748630i
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	0.856154	−	0.516721i	$-0.172848\pi$
$313$	−0.343520	−	0.594993i	−0.0194169	−	0.0336310i	−0.875571	+	0.483090i	$0.839514\pi$
$314$	29.8988	+	5.33988i	1.68729	+	0.301347i
$315$	−14.8924	−	25.5119i	−0.839093	−	1.43743i
$316$	7.76188	−	21.0369i	0.436640	−	1.18342i
$317$	−16.4535	−	28.4983i	−0.924120	−	1.60062i	−0.792970	−	0.609261i	$-0.791466\pi$
$317$	−16.4535	−	28.4983i	−0.924120	−	1.60062i	−0.131150	−	0.991363i	$-0.541867\pi$
$318$	−4.86678	−	1.83523i	−0.272915	−	0.102915i
$319$	5.84224	+	3.37302i	0.327103	+	0.188853i
$320$	−15.2264	+	25.5862i	−0.851180	+	1.43031i
$321$	7.29082	+	20.6287i	0.406934	+	1.15138i
$322$	16.5492	+	5.62807i	0.922249	+	0.313640i
$323$		−	0.490632i		−	0.0272995i
$324$	17.9843	+	0.751331i	0.999128	+	0.0417406i
$325$	27.3802	+	15.8079i	1.51878	+	0.876867i
$326$	1.63563	+	1.37861i	0.0905893	+	0.0763540i
$327$	−14.5938	+	17.0660i	−0.807037	+	0.943751i
$328$	−2.21913	−	1.30083i	−0.122531	−	0.0718265i
$329$	−2.42447	−	1.93932i	−0.133665	−	0.106918i
$330$	23.5746	−	3.87690i	1.29774	−	0.213416i
$331$	−0.833276	−	1.44328i	−0.0458010	−	0.0793297i	0.842216	−	0.539140i	$-0.181251\pi$
$331$	−0.833276	−	1.44328i	−0.0458010	−	0.0793297i	−0.888017	+	0.459810i	$0.847917\pi$
$332$	−2.22433	−	2.67469i	−0.122076	−	0.146793i
$333$	25.0192	−	3.93134i	1.37104	−	0.215436i
$334$	9.59836	−	3.46960i	0.525199	−	0.189848i
$335$	37.1235			2.02827
$336$	−18.3300	+	0.0973507i	−0.999986	+	0.00531091i
$337$	9.04814			0.492884			0.246442	−	0.969158i	$-0.420739\pi$
$337$	9.04814			0.492884			0.246442	+	0.969158i	$0.420739\pi$
$338$	−0.321976	+	0.116388i	−0.0175132	+	0.00633065i
$339$	12.0987	+	2.25001i	0.657113	+	0.122204i
$340$	−1.02326	−	1.23044i	−0.0554941	−	0.0667299i
$341$	6.44858	+	11.1693i	0.349210	+	0.604849i
$342$	−4.66488	−	8.48402i	−0.252248	−	0.458763i
$343$	−8.10952	+	16.6504i	−0.437873	+	0.899037i
$344$	−5.34299	+	9.11475i	−0.288075	+	0.491434i
$345$	22.8878	+	19.5722i	1.23224	+	1.05373i
$346$	2.89142	+	2.43706i	0.155444	+	0.131017i
$347$	4.59168	+	2.65101i	0.246494	+	0.142313i	0.618158	−	0.786054i	$-0.287879\pi$
$347$	4.59168	+	2.65101i	0.246494	+	0.142313i	−0.371664	+	0.928367i	$0.621213\pi$
$348$	−4.35203	−	7.78299i	−0.233293	−	0.417212i
$349$		−	10.7938i		−	0.577779i	−0.957362	−	0.288890i	$-0.906714\pi$
$349$		−	10.7938i		−	0.577779i	0.957362	−	0.288890i	$-0.0932861\pi$
$350$	6.44295	+	32.4864i	0.344390	+	1.73647i
$351$	−15.8070	−	9.72640i	−0.843714	−	0.519157i
$352$	5.22345	−	13.8741i	0.278411	−	0.739493i
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.981732	−	0.190268i	$-0.0609357\pi$
$353$	24.5717	+	14.1865i	1.30782	+	0.755071i	0.326089	+	0.945339i	$0.394269\pi$
$354$	−6.77829	+	17.9751i	−0.360262	+	0.955365i
$355$	18.7591	+	32.4917i	0.995628	+	1.72448i
$356$	12.3664	−	33.5164i	0.655418	−	1.77637i
$357$	0.323866	−	0.930483i	0.0171408	−	0.0492464i
$358$	11.7247	+	2.09400i	0.619667	+	0.110671i
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	0.867570	−	0.497315i	$-0.165681\pi$
$359$	0.0586851	+	0.101646i	0.00309728	+	0.00536465i	−0.864473	+	0.502680i	$0.832347\pi$
$360$	−29.3931	−	11.5477i	−1.54915	−	0.608619i
$361$	6.89612	−	11.9444i	0.362954	−	0.628654i
$362$	−2.94363	−	8.14330i	−0.154714	−	0.428002i
$363$	6.74780	−	2.38489i	0.354168	−	0.125174i
$364$	16.5452	+	9.13661i	0.867204	+	0.478888i
$365$	−33.1365			−1.73444
$366$	−0.540219	−	0.659106i	−0.0282377	−	0.0344520i
$367$	−7.31080	−	4.22089i	−0.381621	−	0.220329i	0.296902	−	0.954908i	$-0.404046\pi$
$367$	−7.31080	−	4.22089i	−0.381621	−	0.220329i	−0.678523	+	0.734579i	$0.737380\pi$
$368$	17.6156	−	6.23639i	0.918274	−	0.325094i
$369$	0.980855	−	2.54592i	0.0510613	−	0.132535i
$370$	−43.7414	−	7.81215i	−2.27401	−	0.406134i
$371$	−0.845534	+	5.55406i	−0.0438980	+	0.288353i
$372$	0.234248	−	17.0462i	0.0121452	−	0.883806i
$373$	−0.0783826	+	0.0452542i	−0.00405850	+	0.00234318i	−0.502028	−	0.864851i	$-0.667413\pi$
$373$	−0.0783826	+	0.0452542i	−0.00405850	+	0.00234318i	0.497969	+	0.867195i	$0.334079\pi$
$374$	0.609270	+	0.513529i	0.0315046	+	0.0265539i
$375$	−4.53939	+	24.4092i	−0.234413	+	1.26048i
$376$	−3.31896	−	0.0219246i	−0.171162	−	0.00113067i
$377$			9.19441i			0.473536i
$378$	−3.24664	−	19.1692i	−0.166989	−	0.985959i
$379$	−19.7881			−1.01645			−0.508224	−	0.861225i	$-0.669698\pi$
$379$	−19.7881			−1.01645			−0.508224	+	0.861225i	$0.669698\pi$
$380$	2.87597	+	16.7412i	0.147534	+	0.858808i
$381$	4.30981	+	0.801498i	0.220798	+	0.0410620i
$382$	16.3603	+	13.7894i	0.837065	+	0.705528i
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	0.985880	+	0.167456i	$0.0535551\pi$
$383$	12.4851	+	21.6249i	0.637961	+	1.10498i	−0.347919	+	0.937525i	$0.613112\pi$
$384$	−15.3185	+	12.2207i	−0.781718	+	0.623633i
$385$	−9.39230	−	24.0355i	−0.478676	−	1.22496i
$386$	0.760653	−	4.25902i	0.0387162	−	0.216778i
$387$	−10.4570	−	4.02872i	−0.531559	−	0.204792i
$388$	−13.6636	+	11.3630i	−0.693664	+	0.576867i
$389$	−15.0483	+	26.0644i	−0.762979	+	1.32152i	0.178329	+	0.983971i	$0.442931\pi$
$389$	−15.0483	+	26.0644i	−0.762979	+	1.32152i	−0.941308	+	0.337548i	$0.890403\pi$
$390$	20.6413	+	25.1839i	1.04522	+	1.27524i
$391$			1.00440i			0.0507948i
$392$	4.22095	+	19.3438i	0.213190	+	0.977011i
$393$	−3.36446	−	9.51942i	−0.169715	−	0.480191i
$394$	−19.3827	+	7.00644i	−0.976487	+	0.352979i
$395$	−36.1364	−	20.8634i	−1.81822	−	1.04975i
$396$	15.4181	+	3.08708i	0.774788	+	0.155131i
$397$	−4.91661	+	2.83861i	−0.246758	+	0.142466i	−0.618279	−	0.785959i	$-0.712170\pi$
$397$	−4.91661	+	2.83861i	−0.246758	+	0.142466i	0.371521	+	0.928425i	$0.378836\pi$
$398$	−24.1754	−	4.31769i	−1.21180	−	0.216426i
$399$	−7.91534	+	6.83449i	−0.396263	+	0.342153i
$400$	26.9210	+	22.9965i	1.34605	+	1.14982i
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	−0.522244	−	0.852796i	$-0.674905\pi$
$401$	−0.897563	+	0.518208i	−0.0448222	+	0.0258781i	0.477421	+	0.878674i	$0.341572\pi$
$402$	22.8615	+	8.62094i	1.14023	+	0.429973i
$403$	−8.78898	+	15.2230i	−0.437810	+	0.758310i
$404$	−5.00290	−	29.1222i	−0.248904	−	1.44889i
$405$	7.04417	−	32.7467i	0.350028	−	1.62720i
$406$	−7.24499	+	6.34648i	−0.359563	+	0.314970i
$407$	22.1240			1.09664
$408$	−0.344412	−	0.995359i	−0.0170509	−	0.0492776i
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	−0.816947	−	0.576712i	$-0.804335\pi$
$409$	1.83983	−	3.18669i	0.0909739	−	0.157571i	0.907921	+	0.419141i	$0.137669\pi$
$410$	−3.08491	+	3.66006i	−0.152353	+	0.180757i
$411$	10.5956	−	12.3906i	0.522644	−	0.611181i
$412$	−5.19738	+	14.0864i	−0.256056	+	0.693985i
$413$	20.5135	+	3.12292i	1.00940	+	0.153669i
$414$	9.54975	+	17.3682i	0.469345	+	0.853598i
$415$	−5.60623	+	3.23676i	−0.275199	+	0.158886i
$416$	19.9357	−	3.28933i	0.977430	−	0.161273i
$417$	2.38755	−	12.8383i	0.116919	−	0.628695i
$418$	−2.87522	−	7.95404i	−0.140631	−	0.389045i
$419$			9.81445i			0.479467i	0.970839	+	0.239734i	$0.0770601\pi$
$419$			9.81445i			0.479467i	−0.970839	+	0.239734i	$0.922940\pi$
$420$	−5.59660	+	33.6482i	−0.273086	+	1.64186i
$421$			33.0188i			1.60924i	0.593790	+	0.804620i	$0.297631\pi$
$421$			33.0188i			1.60924i	−0.593790	+	0.804620i	$0.702369\pi$
$422$	28.2870	−	10.2252i	1.37699	−	0.497753i
$423$	−0.546461	−	3.47770i	−0.0265698	−	0.169091i
$424$	2.96855	+	5.22103i	0.144166	+	0.253556i
$425$	−1.64807	+	0.951516i	−0.0799433	+	0.0461553i
$426$	4.00696	+	24.3654i	0.194138	+	1.18051i
$427$	−0.574978	+	0.718819i	−0.0278252	+	0.0347861i
$428$	8.74522	−	23.7020i	0.422716	−	1.14568i
$429$	−12.3221	−	10.5371i	−0.594916	−	0.508735i
$430$	15.0332	+	12.6708i	0.724964	+	0.611042i
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	−0.710628	−	0.703568i	$-0.751589\pi$
$431$	5.27304	−	9.13317i	0.253993	−	0.439929i	0.964622	+	0.263638i	$0.0849226\pi$
$432$	−15.4193	−	13.9371i	−0.741864	−	0.670551i
$433$	13.7135			0.659026			0.329513	−	0.944151i	$-0.393115\pi$
$433$	13.7135			0.659026			0.329513	+	0.944151i	$0.393115\pi$
$434$	−18.0620	+	3.58219i	−0.867003	+	0.171950i
$435$	−15.6453	+	5.52953i	−0.750133	+	0.265121i
$436$	25.5544	−	4.38999i	1.22384	−	0.210242i
$437$	5.33056	−	9.23280i	0.254995	−	0.441665i
$438$	−20.4063	−	7.69507i	−0.975049	−	0.367685i
$439$	8.62149	−	4.97762i	0.411481	−	0.237569i	−0.279945	−	0.960016i	$-0.590316\pi$
$439$	8.62149	−	4.97762i	0.411481	−	0.237569i	0.691426	+	0.722447i	$0.256983\pi$
$440$	−23.7996	−	13.9511i	−1.13460	−	0.665094i
$441$	−19.5229	+	7.73671i	−0.929662	+	0.368415i
$442$	−0.190939	+	1.06910i	−0.00908203	+	0.0508517i
$443$	−0.202164	+	0.116720i	−0.00960512	+	0.00554552i	−0.504795	−	0.863239i	$-0.668432\pi$
$443$	−0.202164	+	0.116720i	−0.00960512	+	0.00554552i	0.495190	+	0.868785i	$0.335099\pi$
$444$	−25.1229	−	14.9687i	−1.19228	−	0.710383i
$445$	−57.5734	−	33.2400i	−2.72924	−	1.57573i
$446$	3.21528	+	8.89480i	0.152248	+	0.421181i
$447$	−24.1275	+	8.52740i	−1.14119	+	0.403332i
$448$	16.3526	+	13.4384i	0.772589	+	0.634906i
$449$			5.83932i			0.275575i	0.990462	+	0.137787i	$0.0439990\pi$
$449$			5.83932i			0.275575i	−0.990462	+	0.137787i	$0.956001\pi$
$450$	−19.4516	+	32.1234i	−0.916958	+	1.51431i
$451$	1.19168	−	2.06405i	0.0561141	−	0.0971924i
$452$	−9.08596	−	10.9256i	−0.427367	−	0.513896i
$453$	4.14292	−	4.84475i	0.194651	−	0.227626i
$454$	33.3788	+	5.96139i	1.56654	+	0.279782i
$455$	21.9695	−	27.4655i	1.02994	−	1.28760i
$456$	−2.11661	+	10.9775i	−0.0991196	+	0.514070i
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	0.995730	−	0.0923098i	$-0.0294250\pi$
$457$	8.93416	+	15.4744i	0.417923	+	0.723863i	−0.577808	+	0.816173i	$0.696092\pi$
$458$	−15.0577	+	17.8650i	−0.703599	+	0.834777i
$459$	0.982747	−	0.531260i	0.0458707	−	0.0247971i
$460$	−5.88758	−	34.2720i	−0.274510	−	1.59794i
$461$	0.400330			0.0186452			0.00932262	−	0.999957i	$-0.497032\pi$
$461$	0.400330			0.0186452			0.00932262	+	0.999957i	$0.497032\pi$
$462$	−0.202388	−	16.9828i	−0.00941595	−	0.790110i
$463$		−	29.4293i		−	1.36769i	−0.729626	−	0.683847i	$-0.760306\pi$
$463$		−	29.4293i		−	1.36769i	0.729626	−	0.683847i	$-0.239694\pi$
$464$	−1.87723	+	10.1240i	−0.0871481	+	0.469997i
$465$	−31.1892	−	5.80028i	−1.44637	−	0.268982i
$466$	14.1089	−	16.7393i	0.653580	−	0.775433i
$467$	−6.75074	+	3.89754i	−0.312387	+	0.180357i	−0.647994	−	0.761645i	$-0.724392\pi$
$467$	−6.75074	+	3.89754i	−0.312387	+	0.180357i	0.335607	+	0.942002i	$0.391059\pi$
$468$	6.86314	+	20.3023i	0.317249	+	0.938473i
$469$	3.97187	−	26.0900i	0.183404	−	1.20472i
$470$	−1.08590	+	6.08011i	−0.0500887	+	0.280455i
$471$	24.1753	−	28.2707i	1.11394	−	1.30265i
$472$	19.2835	−	10.9641i	0.887595	−	0.504665i
$473$	−8.47781	−	4.89466i	−0.389810	−	0.225057i
$474$	−17.4087	−	21.2399i	−0.799609	−	0.975580i
$475$	20.1995			0.926818
$476$	−0.974220	+	0.587492i	−0.0446533	+	0.0269277i
$477$	−4.95553	+	4.00290i	−0.226898	+	0.183280i
$478$	−27.3259	+	9.87774i	−1.24986	+	0.451797i
$479$	19.3422	−	33.5016i	0.883765	−	1.53073i	0.0366434	−	0.999328i	$-0.488333\pi$
$479$	19.3422	−	33.5016i	0.883765	−	1.53073i	0.847122	−	0.531398i	$-0.178333\pi$
$480$	17.5865	+	31.9446i	0.802711	+	1.45806i
$481$	15.0768	+	26.1137i	0.687441	+	1.19068i
$482$	3.06658	−	17.1703i	0.139679	−	0.782085i
$483$	16.2040	−	13.9913i	0.737306	−	0.636627i
$484$	−7.75311	−	2.86063i	−0.352414	−	0.130029i
$485$	16.5349	+	28.6393i	0.750811	+	1.30044i
$486$	11.9425	−	18.5304i	0.541724	−	0.840556i
$487$	−8.63096	−	4.98308i	−0.391106	−	0.225805i	0.291533	−	0.956561i	$-0.405835\pi$
$487$	−8.63096	−	4.98308i	−0.391106	−	0.225805i	−0.682639	+	0.730756i	$0.739168\pi$
$488$	−0.00650031	+	0.984023i	−0.000294255	+	0.0445446i
$489$	2.47014	−	0.873026i	0.111704	−	0.0394796i
$490$	36.8067	−	1.64672i	1.66276	−	0.0743911i
$491$		−	15.5075i		−	0.699845i	−0.936779	−	0.349923i	$-0.886208\pi$
$491$		−	15.5075i		−	0.699845i	0.936779	−	0.349923i	$-0.113792\pi$
$492$	−2.74971	+	1.53756i	−0.123967	+	0.0693187i
$493$	−0.479286	−	0.276716i	−0.0215860	−	0.0124627i
$494$	7.42908	−	8.81414i	0.334250	−	0.396567i
$495$	10.5194	−	27.3044i	0.472813	−	1.22724i
$496$	−12.7857	+	14.9677i	−0.574095	+	0.672068i
$497$	24.8419	−	9.70739i	1.11431	−	0.435436i
$498$	−4.20410	+	0.691375i	−0.188390	+	0.0309813i
$499$	−0.275544	−	0.477256i	−0.0123350	−	0.0213649i	0.859792	−	0.510644i	$-0.170593\pi$
$499$	−0.275544	−	0.477256i	−0.0123350	−	0.0213649i	−0.872127	+	0.489279i	$0.837260\pi$
$500$	22.0423	−	18.3309i	0.985762	−	0.819782i
$501$	2.28545	−	12.2893i	0.102106	−	0.549045i
$502$	−10.2392	−	28.3258i	−0.456997	−	1.26424i
$503$	−32.2097			−1.43616			−0.718079	−	0.695962i	$-0.754978\pi$
$503$	−32.2097			−1.43616			−0.718079	+	0.695962i	$0.754978\pi$
$504$	−11.2604	+	19.4217i	−0.501579	+	0.865112i
$505$	−54.9868			−2.44688
$506$	5.88603	+	16.2832i	0.261666	+	0.723877i
$507$	−0.0766652	+	0.412243i	−0.00340482	+	0.0183084i
$508$	−3.23660	−	3.89190i	−0.143601	−	0.172675i
$509$	0.906135	+	1.56947i	0.0401637	+	0.0695656i	0.885408	−	0.464814i	$-0.153879\pi$
$509$	0.906135	+	1.56947i	0.0401637	+	0.0695656i	−0.845245	+	0.534379i	$0.820545\pi$
$510$	−1.93401	+	0.318054i	−0.0856395	+	0.0140836i
$511$	−3.54530	+	23.2880i	−0.156835	+	1.03020i
$512$	22.6230	+	0.448384i	0.999804	+	0.0198160i
$513$	−11.8532	−	0.332116i	−0.523333	−	0.0146633i
$514$	13.9234	−	16.5193i	0.614135	−	0.728633i
$515$	24.1970	+	13.9702i	1.06625	+	0.615599i
$516$	6.31532	+	11.2941i	0.278017	+	0.497194i
$517$		−	3.07526i		−	0.135250i
$518$	−10.1702	+	29.9052i	−0.446854	+	1.31396i
$519$	4.36664	−	1.54331i	0.191674	−	0.0677438i
$520$	0.248372	−	37.5987i	0.0108918	−	1.64881i
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	0.638657	−	0.769491i	$-0.279490\pi$
$521$	6.65560	+	3.84261i	0.291587	+	0.168348i	−0.347070	+	0.937839i	$0.612823\pi$
$522$	−10.9188	−	0.227978i	−0.477904	−	0.00997835i
$523$	−4.33611	−	7.51035i	−0.189605	−	0.328405i	0.755514	−	0.655133i	$-0.227387\pi$
$523$	−4.33611	−	7.51035i	−0.189605	−	0.328405i	−0.945118	+	0.326728i	$0.894054\pi$
$524$	−4.03562	+	10.9377i	−0.176297	+	0.477814i
$525$	38.3084	+	13.3337i	1.67192	+	0.581930i
$526$	0.124281	−	0.695872i	0.00541893	−	0.0303415i
$527$	−0.529029	−	0.916305i	−0.0230449	−	0.0399149i
$528$	−11.4166	−	14.1183i	−0.496843	−	0.614418i
$529$	0.587489	−	1.01756i	0.0255430	−	0.0442417i
$530$	10.5107	−	3.79940i	0.456557	−	0.165035i
$531$	14.7844	+	18.3029i	0.641588	+	0.794277i
$532$	12.0733	−	0.230048i	0.523444	−	0.00997385i
$533$	3.24837			0.140702
$534$	−27.7360	−	33.8399i	−1.20025	−	1.46439i
$535$	−40.7145	−	23.5065i	−1.76024	−	1.01627i
$536$	−13.9447	−	24.5256i	−0.602318	−	1.05935i
$537$	9.48022	−	11.0862i	0.409102	−	0.478405i
$538$	5.43070	−	30.4074i	0.234134	−	1.31095i
$539$	−17.8968	+	4.02924i	−0.770871	+	0.173551i
$540$	−30.4190	+	23.8882i	−1.30902	+	1.02798i
$541$	−10.0751	+	5.81687i	−0.433163	+	0.250087i	−0.700693	−	0.713463i	$-0.747126\pi$
$541$	−10.0751	+	5.81687i	−0.433163	+	0.250087i	0.267530	+	0.963549i	$0.413792\pi$
$542$	−14.3453	+	17.0199i	−0.616185	+	0.731065i
$543$	−10.4263	−	1.93899i	−0.447435	−	0.0832098i
$544$	−0.428522	+	1.13821i	−0.0183727	+	0.0488002i
$545$		−	48.2503i		−	2.06681i
$546$	19.9075	−	11.8121i	0.851960	−	0.505511i
$547$	−27.7574			−1.18682			−0.593410	−	0.804900i	$-0.702219\pi$
$547$	−27.7574			−1.18682			−0.593410	+	0.804900i	$0.702219\pi$
$548$	−18.5535	+	3.18730i	−0.792566	+	0.136155i
$549$	−1.03109	+	0.162017i	−0.0440056	+	0.00691473i
$550$	−21.1422	+	25.0839i	−0.901506	+	1.06958i
$551$	2.93717	+	5.08733i	0.125128	+	0.216728i
$552$	4.33305	−	22.4728i	0.184427	−	0.956504i
$553$	−18.5288	+	23.1641i	−0.787926	+	0.985039i
$554$	−17.4696	−	3.12004i	−0.742212	−	0.132558i
$555$	−35.3681	+	41.3596i	−1.50129	+	1.75562i
$556$	−11.5934	+	9.64136i	−0.491671	+	0.408885i
$557$	7.71096	−	13.3558i	0.326724	−	0.565902i	−0.655136	−	0.755511i	$-0.727389\pi$
$557$	7.71096	−	13.3558i	0.326724	−	0.565902i	0.981860	+	0.189609i	$0.0607220\pi$
$558$	−17.8601	−	10.8148i	−0.756079	−	0.457828i
$559$		−	13.3422i		−	0.564315i
$560$	29.7984	−	25.7570i	1.25921	−	1.08843i
$561$	0.920124	−	0.325201i	0.0388476	−	0.0137300i
$562$	10.9379	+	30.2588i	0.461388	+	1.27639i
$563$	11.5626	+	6.67567i	0.487305	+	0.281346i	0.723456	−	0.690371i	$-0.242553\pi$
$563$	11.5626	+	6.67567i	0.487305	+	0.281346i	−0.236151	+	0.971716i	$0.575886\pi$
$564$	−2.08067	+	3.49211i	−0.0876119	+	0.147044i
$565$	−22.9003	+	13.2215i	−0.963423	+	0.556233i
$566$	−0.218993	+	1.22618i	−0.00920497	+	0.0515401i
$567$	−22.2604	−	8.45417i	−0.934850	−	0.355042i
$568$	14.4192	−	24.5980i	0.605014	−	1.03211i
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.677034	+	0.735951i	$0.736735\pi$
$569$	−39.4279	+	22.7637i	−1.65290	+	0.954305i	−0.975870	+	0.218353i	$0.929931\pi$
$570$	19.4661	+	7.34053i	0.815344	+	0.307461i
$571$	20.3243	−	35.2028i	0.850546	−	1.47319i	−0.0301698	−	0.999545i	$-0.509605\pi$
$571$	20.3243	−	35.2028i	0.850546	−	1.47319i	0.880716	−	0.473645i	$-0.157062\pi$
$572$	3.16969	+	18.4510i	0.132531	+	0.771473i
$573$	24.7074	−	8.73238i	1.03217	−	0.364800i
$574$	2.24220	+	2.55964i	0.0935875	+	0.106837i
$575$	−41.3517			−1.72448
$576$	3.41193	+	23.7562i	0.142164	+	0.989843i
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	−0.986971	−	0.160899i	$-0.948561\pi$
$577$	−8.50680	+	14.7342i	−0.354143	+	0.613393i	0.632828	+	0.774292i	$0.281894\pi$
$578$	18.3329	+	15.4520i	0.762548	+	0.642720i
$579$	−4.02710	−	3.44372i	−0.167360	−	0.143116i
$580$	17.9762	+	6.63259i	0.746420	+	0.275403i
$581$	1.67495	+	4.28630i	0.0694885	+	0.177826i
$582$	3.53187	+	21.4765i	0.146401	+	0.890231i
$583$	−4.81928	+	2.78241i	−0.199594	+	0.115236i
$584$	12.4471	+	21.8916i	0.515063	+	0.905882i
$585$	39.3970	−	6.19056i	1.62886	−	0.255948i
$586$	29.4300	−	10.6383i	1.21574	−	0.439464i
$587$		−	28.5925i		−	1.18014i	−0.807352	−	0.590070i	$-0.799100\pi$
$587$		−	28.5925i		−	1.18014i	0.807352	−	0.590070i	$-0.200900\pi$
$588$	23.0489	+	7.53329i	0.950519	+	0.310668i
$589$			11.2306i			0.462750i
$590$	−14.0328	−	38.8206i	−0.577722	−	1.59822i
$591$	−4.61518	+	24.8167i	−0.189843	+	1.02082i
$592$	11.2695	+	31.8322i	0.463173	+	1.30830i
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	−0.589532	−	0.807745i	$-0.700688\pi$
$593$	−4.49943	+	2.59775i	−0.184770	+	0.106677i	0.404762	+	0.914422i	$0.367354\pi$
$594$	12.8188	−	14.3718i	0.525963	−	0.589683i
$595$	0.770526	+	1.97183i	0.0315885	+	0.0808371i
$596$	27.7221	+	10.2285i	1.13554	+	0.418975i
$597$	−19.5476	+	22.8590i	−0.800029	+	0.935556i
$598$	−15.2085	+	18.0440i	−0.621922	+	0.737872i
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.141519	−	0.989936i	$-0.454801\pi$
$599$	22.7140	−	39.3418i	0.928069	−	1.60746i	0.786550	−	0.617527i	$-0.211865\pi$
$600$	40.9793	−	14.1796i	1.67297	−	0.578879i
$601$	45.5994			1.86004			0.930019	−	0.367511i	$-0.119790\pi$
$601$	45.5994			1.86004			0.930019	+	0.367511i	$0.119790\pi$
$602$	10.5134	−	9.20951i	0.428493	−	0.375352i
$603$	23.2784	−	18.8035i	0.947970	−	0.765736i
$604$	−7.25447	+	1.24624i	−0.295180	+	0.0507089i
$605$	−7.68917	+	13.3180i	−0.312609	+	0.541455i
$606$	−33.8622	−	12.7692i	−1.37556	−	0.518714i
$607$	−18.3382	+	10.5876i	−0.744324	+	0.429736i	−0.823639	−	0.567114i	$-0.808060\pi$
$607$	−18.3382	+	10.5876i	−0.744324	+	0.429736i	0.0793155	+	0.996850i	$0.474727\pi$
$608$	9.97980	−	8.18852i	0.404734	−	0.332088i
$609$	2.21220	+	11.5870i	0.0896430	+	0.469527i
$610$	1.80266	+	0.321952i	0.0729877	+	0.0130355i
$611$	3.62984	−	2.09569i	0.146848	−	0.0847825i
$612$	−1.26487	−	0.253258i	−0.0511294	−	0.0102373i
$613$	22.2592	+	12.8513i	0.899039	+	0.519060i	0.876888	−	0.480694i	$-0.159615\pi$
$613$	22.2592	+	12.8513i	0.899039	+	0.519060i	0.0221508	+	0.999755i	$0.492949\pi$
$614$	−13.2567	+	4.79202i	−0.534997	+	0.193390i
$615$	1.95357	+	5.52744i	0.0787756	+	0.222888i
$616$	−12.3511	+	15.2335i	−0.497638	+	0.613775i
$617$			16.9888i			0.683941i	0.939711	+	0.341971i	$0.111094\pi$
$617$			16.9888i			0.683941i	−0.939711	+	0.341971i	$0.888906\pi$
$618$	11.6569	+	14.2223i	0.468910	+	0.572104i
$619$	−11.6456	+	20.1708i	−0.468076	+	0.810732i	−0.999334	−	0.0364781i	$-0.988386\pi$
$619$	−11.6456	+	20.1708i	−0.468076	+	0.810732i	0.531258	+	0.847210i	$0.321719\pi$
$620$	23.4226	+	28.1649i	0.940674	+	1.13113i
$621$	24.2655	+	0.679895i	0.973740	+	0.0272832i
$622$	2.91998	−	16.3495i	0.117081	−	0.655554i
$623$	−29.5206	+	36.9056i	−1.18272	+	1.47859i
$624$	8.88426	−	23.0965i	0.355655	−	0.924601i
$625$	−4.54562	−	7.87325i	−0.181825	−	0.314930i
$626$	0.742927	+	0.626183i	0.0296933	+	0.0250273i
$627$	−10.1840	−	1.89392i	−0.406709	−	0.0756360i
$628$	−42.3323	+	7.27225i	−1.68924	+	0.290194i
$629$	−1.81501			−0.0723691
$630$	32.0719	+	26.7709i	1.27778	+	1.06658i
$631$			15.0554i			0.599347i	0.954042	+	0.299674i	$0.0968778\pi$
$631$			15.0554i			0.599347i	−0.954042	+	0.299674i	$0.903122\pi$
$632$	−0.209474	+	31.7104i	−0.00833244	+	1.26137i
$633$	6.73537	−	36.2174i	0.267707	−	1.43951i
$634$	35.5838	+	29.9922i	1.41321	+	1.19114i
$635$	−8.15754	+	4.70976i	−0.323722	+	0.186901i
$636$	7.35507	+	0.101073i	0.291647	+	0.00400780i
$637$	−16.9520	−	18.3785i	−0.671661	−	0.728182i
$638$	−9.39173	−	1.67735i	−0.371822	−	0.0664068i
$639$	28.2204	+	10.8723i	1.11638	+	0.430103i
$640$	7.95004	−	41.3496i	0.314253	−	1.63448i
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.879062	−	0.476707i	$-0.158170\pi$
$641$	22.9318	+	13.2397i	0.905752	+	0.522936i	0.0266904	+	0.999644i	$0.491503\pi$
$642$	−19.6142	−	23.9307i	−0.774110	−	0.944470i
$643$	−29.9973			−1.18298			−0.591490	−	0.806312i	$-0.701460\pi$
$643$	−29.9973			−1.18298			−0.591490	+	0.806312i	$0.701460\pi$
$644$	−24.7160	+	0.470946i	−0.973945	+	0.0185579i
$645$	22.7032	−	8.02403i	0.893937	−	0.315946i
$646$	0.235877	+	0.652534i	0.00928047	+	0.0256736i
$647$	−9.22707	+	15.9817i	−0.362753	+	0.628307i	−0.988413	−	0.151789i	$-0.951497\pi$
$647$	−9.22707	+	15.9817i	−0.362753	+	0.628307i	0.625659	+	0.780096i	$0.284830\pi$
$648$	−24.2801	+	7.64692i	−0.953814	+	0.300399i
$649$	10.2766	+	17.7997i	0.403394	+	0.698698i
$650$	−44.0152	−	7.86103i	−1.72642	−	0.308335i
$651$	−7.41334	+	21.2989i	−0.290552	+	0.834770i
$652$	−2.83815	−	1.04718i	−0.111151	−	0.0410107i
$653$	8.95898	+	15.5174i	0.350592	+	0.607243i	0.986353	−	0.164643i	$-0.0526470\pi$
$653$	8.95898	+	15.5174i	0.350592	+	0.607243i	−0.635761	+	0.771886i	$0.719314\pi$
$654$	11.2048	−	29.7137i	0.438144	−	1.16190i
$655$	18.7883	+	10.8474i	0.734121	+	0.423845i
$656$	3.57680	+	0.663221i	0.139651	+	0.0258944i
$657$	−20.7784	+	16.7840i	−0.810642	+	0.654807i
$658$	4.15686	+	1.41367i	0.162051	+	0.0551108i
$659$		−	30.7250i		−	1.19687i	−0.801170	−	0.598437i	$-0.795789\pi$
$659$		−	30.7250i		−	1.19687i	0.801170	−	0.598437i	$-0.204211\pi$
$660$	−29.4900	+	16.4900i	−1.14790	+	0.641872i
$661$	13.0311	+	7.52352i	0.506852	+	0.292631i	0.731539	−	0.681800i	$-0.238803\pi$
$661$	13.0311	+	7.52352i	0.506852	+	0.292631i	−0.224687	+	0.974431i	$0.572136\pi$
$662$	1.80212	+	1.51893i	0.0700414	+	0.0590350i
$663$	1.01088	+	0.864441i	0.0392593	+	0.0335721i
$664$	4.24423	+	2.48793i	0.164708	+	0.0965504i
$665$	3.38195	−	22.2151i	0.131147	−	0.861463i
$666$	−31.3852	+	17.2569i	−1.21615	+	0.668692i
$667$	−6.01287	−	10.4146i	−0.232819	−	0.403254i
$668$	−11.0976	+	9.22905i	−0.429381	+	0.357083i
$669$	11.3885	+	2.11793i	0.440304	+	0.0818837i
$670$	−49.3738	+	17.8476i	−1.90747	+	0.689511i
$671$	−0.911768			−0.0351984
$672$	24.3319	−	8.94187i	0.938625	−	0.344940i
$673$	20.6079			0.794376			0.397188	−	0.917737i	$-0.369986\pi$
$673$	20.6079			0.794376			0.397188	+	0.917737i	$0.369986\pi$
$674$	−12.0339	+	4.35000i	−0.463529	+	0.167556i
$675$	21.8722	+	40.4601i	0.841861	+	1.55731i
$676$	0.372270	−	0.309588i	0.0143181	−	0.0119072i
$677$	−5.13682	−	8.89723i	−0.197424	−	0.341948i	0.750268	−	0.661133i	$-0.229924\pi$
$677$	−5.13682	−	8.89723i	−0.197424	−	0.341948i	−0.947692	+	0.319185i	$0.896591\pi$
$678$	−17.1729	+	2.82413i	−0.659521	+	0.108460i
$679$	21.8965	−	8.55642i	0.840310	−	0.328365i
$680$	1.95247	+	1.14452i	0.0748739	+	0.0438905i
$681$	26.9891	−	31.5612i	1.03423	−	1.20943i
$682$	−13.9463	−	11.7547i	−0.534031	−	0.450113i
$683$	30.7725	+	17.7665i	1.17748	+	0.679817i	0.955430	−	0.295218i	$-0.0953924\pi$
$683$	30.7725	+	17.7665i	1.17748	+	0.679817i	0.222048	+	0.975036i	$0.428726\pi$
$684$	10.2830	+	9.04095i	0.393181	+	0.345689i
$685$			35.0316i			1.33849i
$686$	2.78068	−	26.0436i	0.106167	−	0.994348i
$687$	9.53553	+	26.9798i	0.363803	+	1.02935i
$688$	2.72409	−	14.6912i	0.103855	−	0.560097i
$689$	−6.56837	−	3.79225i	−0.250235	−	0.144473i
$690$	−39.8502	−	15.0272i	−1.51707	−	0.572077i
$691$	17.0490	+	29.5298i	0.648576	+	1.12337i	0.983463	+	0.181109i	$0.0579685\pi$
$691$	17.0490	+	29.5298i	0.648576	+	1.12337i	−0.334887	+	0.942258i	$0.608698\pi$
$692$	−5.01720	−	1.85118i	−0.190725	−	0.0703711i
$693$	−18.0638	−	10.3143i	−0.686185	−	0.391807i
$694$	−7.38138	−	1.31830i	−0.280193	−	0.0500420i
$695$	14.0297	+	24.3002i	0.532177	+	0.921758i
$696$	9.52991	+	8.25899i	0.361230	+	0.313056i
$697$	−0.0977632	+	0.169331i	−0.00370305	+	0.00641386i
$698$	5.18926	+	14.3556i	0.196416	+	0.543369i
$699$	−8.93467	−	25.2798i	−0.337940	−	0.956169i
$700$	−24.1873	−	40.1090i	−0.914194	−	1.51598i
$701$	42.6496			1.61085			0.805426	−	0.592696i	$-0.201937\pi$
$701$	42.6496			1.61085			0.805426	+	0.592696i	$0.201937\pi$
$702$	25.6992	+	5.33660i	0.969953	+	0.201417i
$703$	16.6842	+	9.63261i	0.629255	+	0.363301i
$704$	−0.276978	+	20.9637i	−0.0104390	+	0.790097i
$705$	5.74903	+	4.91621i	0.216521	+	0.185155i
$706$	−39.5004	−	7.05471i	−1.48662	−	0.265507i
$707$	−5.88308	+	38.6442i	−0.221256	+	1.45336i
$708$	0.373305	−	27.1654i	0.0140297	−	1.02094i
$709$	24.7114	−	14.2671i	0.928054	−	0.535812i	0.0418586	−	0.999124i	$-0.486672\pi$
$709$	24.7114	−	14.2671i	0.928054	−	0.535812i	0.886196	+	0.463311i	$0.153339\pi$
$710$	−40.5701	−	34.1949i	−1.52257	−	1.28331i
$711$	−33.2270	+	5.22106i	−1.24611	+	0.195805i
$712$	−0.333739	+	50.5218i	−0.0125074	+	1.89338i
$713$		−	22.9909i		−	0.861017i
$714$	0.0166035	+	1.39323i	0.000621372	+	0.0521405i
$715$	34.8380			1.30287
$716$	−16.6004	+	2.85177i	−0.620385	+	0.106576i
$717$	−6.50653	+	34.9869i	−0.242991	+	1.30661i
$718$	−0.126918	−	0.106974i	−0.00473653	−	0.00399223i
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.778837	−	0.627226i	$-0.784190\pi$
$719$	−25.0072	−	43.3138i	−0.932612	−	1.61533i	−0.153775	−	0.988106i	$-0.549143\pi$
$720$	44.6442	+	1.22723i	1.66379	+	0.0457361i
$721$	12.4070	−	15.5108i	0.462059	−	0.577651i
$722$	−3.42933	+	19.2013i	−0.127626	+	0.714600i
$723$	−16.2353	−	13.8834i	−0.603797	−	0.516329i
$724$	7.82998	+	9.41530i	0.290999	+	0.349917i
$725$	11.3925	−	19.7324i	0.423108	−	0.732844i
$726$	−7.82793	+	6.41596i	−0.290522	+	0.238118i
$727$		−	27.7338i		−	1.02859i	−0.857614	−	0.514295i	$-0.828054\pi$
$727$		−	27.7338i		−	1.02859i	0.857614	−	0.514295i	$-0.171946\pi$
$728$	−26.3975	−	4.19727i	−0.978355	−	0.155561i
$729$	−12.1695	−	24.1019i	−0.450723	−	0.892664i
$730$	44.0712	−	15.9308i	1.63115	−	0.589625i
$731$	0.695503	+	0.401549i	0.0257241	+	0.0148518i
$732$	1.03536	+	0.616886i	0.0382679	+	0.0228008i
$733$	24.4018	−	14.0884i	0.901300	−	0.520366i	0.0236782	−	0.999720i	$-0.492462\pi$
$733$	24.4018	−	14.0884i	0.901300	−	0.520366i	0.877622	+	0.479354i	$0.159129\pi$
$734$	11.7525	+	2.09898i	0.433794	+	0.0774748i
$735$	21.0780	−	39.8984i	0.777475	−	1.47168i
$736$	−20.4303	+	16.7632i	−0.753069	+	0.617900i
$737$	22.6384	−	13.0703i	0.833897	−	0.481450i
$738$	−0.0805443	+	3.85760i	−0.00296488	+	0.142000i
$739$	15.9133	−	27.5626i	0.585379	−	1.01391i	−0.409449	−	0.912333i	$-0.634279\pi$
$739$	15.9133	−	27.5626i	0.585379	−	1.01391i	0.994828	−	0.101573i	$-0.0323876\pi$
$740$	61.9314	−	10.6392i	2.27664	−	0.391104i
$741$	−4.70459	−	13.3112i	−0.172827	−	0.488998i
$742$	−1.54563	−	7.79334i	−0.0567420	−	0.286102i
$743$	−30.9943			−1.13707			−0.568535	−	0.822659i	$-0.692490\pi$
$743$	−30.9943			−1.13707			−0.568535	+	0.822659i	$0.692490\pi$
$744$	7.88364	+	22.7839i	0.289028	+	0.835299i
$745$	27.4934	−	47.6200i	1.00728	−	1.74466i
$746$	0.0824914	−	0.0978710i	0.00302023	−	0.00358331i
$747$	−1.87595	+	4.86924i	−0.0686375	+	0.178156i
$748$	−1.05721	−	0.390073i	−0.0386553	−	0.0142625i
$749$	−20.8762	+	26.0988i	−0.762800	+	0.953628i
$750$	−5.69767	−	34.6462i	−0.208049	−	1.26510i
$751$	−32.0364	+	18.4962i	−1.16902	+	0.674936i	−0.953450	−	0.301551i	$-0.902496\pi$
$751$	−32.0364	+	18.4962i	−1.16902	+	0.674936i	−0.215574	+	0.976488i	$0.569162\pi$
$752$	4.42472	−	1.56647i	0.161353	−	0.0571234i
$753$	−36.2670	−	6.74460i	−1.32164	−	0.245787i
$754$	−4.42032	−	12.2285i	−0.160979	−	0.445334i
$755$			13.6974i			0.498501i
$756$	13.5338	+	23.9340i	0.492221	+	0.870470i
$757$			2.01191i			0.0731242i	0.999331	+	0.0365621i	$0.0116407\pi$
$757$			2.01191i			0.0731242i	−0.999331	+	0.0365621i	$0.988359\pi$
$758$	26.3180	−	9.51339i	0.955912	−	0.345542i
$759$	20.8483	+	3.87716i	0.756744	+	0.140732i
$760$	−11.8736	−	20.8830i	−0.430700	−	0.757506i
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.978099	−	0.208140i	$-0.933259\pi$
$761$	−35.5006	+	20.4963i	−1.28689	+	0.742989i	−0.308795	+	0.951129i	$0.599926\pi$
$762$	−6.11732	+	1.00601i	−0.221607	+	0.0364439i
$763$	−33.9098	−	5.16233i	−1.22762	−	0.186889i
$764$	−28.3884	−	10.4743i	−1.02706	−	0.378948i
$765$	−0.862994	+	2.24000i	−0.0312016	+	0.0809873i
$766$	−27.0015	−	22.7585i	−0.975604	−	0.822297i
$767$	−14.0064	+	24.2598i	−0.505741	+	0.875970i
$768$	14.4982	−	23.6179i	0.523157	−	0.852236i
$769$	−46.8470			−1.68935			−0.844673	−	0.535282i	$-0.820205\pi$
$769$	−46.8470			−1.68935			−0.844673	+	0.535282i	$0.820205\pi$
$770$	24.0470	+	27.4515i

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32999 + 0.480762i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(1.53774 - 1.27882i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 - 2.41702i) q^{6} +(-2.46429 + 0.962962i) q^{7} +(-1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +O(q^{10})\)	\(q+(-1.32999 + 0.480762i) q^{2} +(-0.316681 + 1.70285i) q^{3} +(1.53774 - 1.27882i) q^{4} +(-1.86088 - 3.22314i) q^{5} +(-0.397486 - 2.41702i) q^{6} +(-2.46429 + 0.962962i) q^{7} +(-1.43036 + 2.44009i) q^{8} +(-2.79943 - 1.07852i) q^{9} +(4.02451 + 3.39209i) q^{10} +(-2.26958 - 1.31034i) q^{11} +(1.69067 + 3.02352i) q^{12} -3.57182i q^{13} +(2.81451 - 2.46546i) q^{14} +(6.07784 - 2.14810i) q^{15} +(0.729261 - 3.93296i) q^{16} +(0.186192 + 0.107498i) q^{17} +(4.24172 + 0.0885645i) q^{18} +(-1.14103 - 1.97631i) q^{19} +(-6.98334 - 2.57661i) q^{20} +(-0.859391 - 4.50127i) q^{21} +(3.64848 + 0.651612i) q^{22} +(2.33586 + 4.04583i) q^{23} +(-3.70216 - 3.20843i) q^{24} +(-4.42574 + 7.66560i) q^{25} +(1.71720 + 4.75048i) q^{26} +(2.72309 - 4.42547i) q^{27} +(-2.55797 + 4.63215i) q^{28} -2.57415 q^{29} +(-7.05072 + 5.77894i) q^{30} +(-4.26196 - 2.46064i) q^{31} +(0.920911 + 5.58139i) q^{32} +(2.95006 - 3.44980i) q^{33} +(-0.299314 - 0.0534570i) q^{34} +(7.68949 + 6.15077i) q^{35} +(-5.68401 + 1.92147i) q^{36} +(-7.31104 + 4.22103i) q^{37} +(2.46769 + 2.07991i) q^{38} +(6.08229 + 1.13113i) q^{39} +(10.5265 + 0.0695365i) q^{40} +0.909442i q^{41} +(3.30702 + 5.57347i) q^{42} +3.73541 q^{43} +(-5.16570 + 0.887414i) q^{44} +(1.73317 + 11.0299i) q^{45} +(-5.05175 - 4.25791i) q^{46} +(0.586728 + 1.01624i) q^{47} +(6.46632 + 2.48732i) q^{48} +(5.14541 - 4.74603i) q^{49} +(2.20085 - 12.3229i) q^{50} +(-0.242017 + 0.283015i) q^{51} +(-4.56770 - 5.49252i) q^{52} +(1.06171 - 1.83894i) q^{53} +(-1.49408 + 7.19498i) q^{54} +9.75355i q^{55} +(1.17511 - 7.39048i) q^{56} +(3.72672 - 1.31714i) q^{57} +(3.42359 - 1.23755i) q^{58} +(-6.79199 - 3.92136i) q^{59} +(6.59908 - 11.0756i) q^{60} +(0.301301 - 0.173956i) q^{61} +(6.85134 + 1.22364i) q^{62} +(7.93716 - 0.0379510i) q^{63} +(-3.90812 - 6.98044i) q^{64} +(-11.5125 + 6.64673i) q^{65} +(-2.26500 + 6.00647i) q^{66} +(-4.98736 + 8.63836i) q^{67} +(0.423784 - 0.0728018i) q^{68} +(-7.62919 + 2.69640i) q^{69} +(-13.1840 - 4.48364i) q^{70} -10.0808 q^{71} +(6.63590 - 5.28818i) q^{72} +(4.45173 - 7.71062i) q^{73} +(7.69428 - 9.12879i) q^{74} +(-11.6519 - 9.96394i) q^{75} +(-4.28194 - 1.57989i) q^{76} +(6.85470 + 1.04354i) q^{77} +(-8.63318 + 1.41975i) q^{78} +(9.70950 - 5.60578i) q^{79} +(-14.0335 + 4.96826i) q^{80} +(6.67358 + 6.03849i) q^{81} +(-0.437225 - 1.20955i) q^{82} -1.73937i q^{83} +(-7.07781 - 5.82276i) q^{84} -0.800163i q^{85} +(-4.96805 + 1.79584i) q^{86} +(0.815185 - 4.38341i) q^{87} +(6.44368 - 3.66372i) q^{88} +(15.4694 - 8.93127i) q^{89} +(-7.60786 - 13.8364i) q^{90} +(3.43953 + 8.80199i) q^{91} +(8.76581 + 3.23428i) q^{92} +(5.53980 - 6.47826i) q^{93} +(-1.26891 - 1.06951i) q^{94} +(-4.24662 + 7.35536i) q^{95} +(-9.79593 - 0.199344i) q^{96} -8.88553 q^{97} +(-4.56162 + 8.78588i) q^{98} +(4.94029 + 6.11600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36} + 14 q^{40} - 8 q^{42} - 16 q^{43} - 12 q^{46} + 64 q^{48} - 16 q^{49} - 34 q^{51} - 8 q^{52} + 32 q^{54} + 4 q^{57} - 18 q^{58} + 40 q^{60} + 4 q^{64} - 20 q^{66} - 36 q^{67} - 42 q^{70} + 22 q^{72} + 4 q^{73} + 104 q^{76} + 28 q^{78} - 10 q^{81} + 52 q^{82} + 4 q^{84} + 46 q^{88} + 140 q^{90} + 72 q^{91} - 46 q^{96} - 32 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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