LMFDB - Embedded newform 168.2.v.a.11.1

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			11.1
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40790 + 0.133456i) q^{2} +(-1.71959 - 0.207430i) q^{3} +(1.96438 - 0.375786i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(-2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(2.91395 + 0.713387i) q^{9} +O(q^{10})$	\(q+(-1.40790 + 0.133456i) q^{2} +(-1.71959 - 0.207430i) q^{3} +(1.96438 - 0.375786i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(-2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(2.91395 + 0.713387i) q^{9} +(-1.13438 - 1.59535i) q^{10} +(3.82316 + 2.20731i) q^{11} +(-3.45587 + 0.238725i) q^{12} +6.43609i q^{13} +(3.15733 + 2.00781i) q^{14} +(-0.941460 - 2.20490i) q^{15} +(3.71757 - 1.47637i) q^{16} +(2.52866 + 1.45992i) q^{17} +(-4.19776 - 0.615496i) q^{18} +(1.58928 + 2.75271i) q^{19} +(1.81001 + 2.09470i) q^{20} +(3.25469 + 3.22599i) q^{21} +(-5.67722 - 2.59745i) q^{22} +(1.84696 + 3.19902i) q^{23} +(4.83366 - 0.797307i) q^{24} +(1.54201 - 2.67084i) q^{25} +(-0.858934 - 9.06138i) q^{26} +(-4.86280 - 1.83117i) q^{27} +(-4.71316 - 2.40544i) q^{28} -6.67884 q^{29} +(1.61974 + 2.97864i) q^{30} +(-2.17580 - 1.25620i) q^{31} +(-5.03695 + 2.57472i) q^{32} +(-6.11640 - 4.58869i) q^{33} +(-3.75494 - 1.71796i) q^{34} +(0.501330 - 3.62774i) q^{35} +(5.99217 + 0.306343i) q^{36} +(5.00149 - 2.88761i) q^{37} +(-2.60492 - 3.66345i) q^{38} +(1.33504 - 11.0674i) q^{39} +(-2.82786 - 2.70758i) q^{40} -0.497427i q^{41} +(-5.01281 - 4.10752i) q^{42} +0.865898 q^{43} +(8.33962 + 2.89929i) q^{44} +(1.16156 + 3.98680i) q^{45} +(-3.02726 - 4.25743i) q^{46} +(1.59001 + 2.75398i) q^{47} +(-6.69892 + 1.76761i) q^{48} +(1.72472 + 6.78420i) q^{49} +(-1.81456 + 3.96608i) q^{50} +(-4.04541 - 3.03498i) q^{51} +(2.41859 + 12.6429i) q^{52} +(4.12906 - 7.15175i) q^{53} +(7.09073 + 1.92914i) q^{54} +6.11065i q^{55} +(6.95669 + 2.75762i) q^{56} +(-2.16191 - 5.06319i) q^{57} +(9.40316 - 0.891331i) q^{58} +(-6.62279 - 3.82367i) q^{59} +(-2.67795 - 3.97747i) q^{60} +(-2.99321 + 1.72813i) q^{61} +(3.23096 + 1.47823i) q^{62} +(-4.92754 - 6.22248i) q^{63} +(6.74792 - 4.29716i) q^{64} +(-7.71521 + 4.45438i) q^{65} +(9.22368 + 5.64416i) q^{66} +(-3.36806 + 5.83364i) q^{67} +(5.51586 + 1.91760i) q^{68} +(-2.51243 - 5.88411i) q^{69} +(-0.221680 + 5.17441i) q^{70} +1.90437 q^{71} +(-8.47728 + 0.368391i) q^{72} +(3.23515 - 5.60345i) q^{73} +(-6.65624 + 4.73295i) q^{74} +(-3.20563 + 4.27288i) q^{75} +(4.15638 + 4.81014i) q^{76} +(-4.40032 - 10.8194i) q^{77} +(-0.402592 + 15.7600i) q^{78} +(-1.65073 + 0.953048i) q^{79} +(4.34270 + 3.43462i) q^{80} +(7.98216 + 4.15754i) q^{81} +(0.0663845 + 0.700328i) q^{82} +7.00064i q^{83} +(7.60572 + 5.11400i) q^{84} +4.04161i q^{85} +(-1.21910 + 0.115559i) q^{86} +(11.4848 + 1.38539i) q^{87} +(-12.1283 - 2.96895i) q^{88} +(-8.22776 + 4.75030i) q^{89} +(-2.16742 - 5.45801i) q^{90} +(10.4527 - 13.4426i) q^{91} +(4.83027 + 5.59004i) q^{92} +(3.48090 + 2.61147i) q^{93} +(-2.60612 - 3.66514i) q^{94} +(-2.19986 + 3.81027i) q^{95} +(9.19553 - 3.38264i) q^{96} +1.19214 q^{97} +(-3.33362 - 9.32132i) q^{98} +(9.56583 + 9.15936i) 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 $

$2$	−1.40790	+	0.133456i	−0.995537	+	0.0943676i
$2$	−1.40790	+	0.133456i	−0.995537	+	0.0943676i
$3$	−1.71959	−	0.207430i	−0.992803	−	0.119760i
$3$	−1.71959	−	0.207430i	−0.992803	−	0.119760i
$4$	1.96438	−	0.375786i	0.982190	−	0.187893i
$5$	0.692094	+	1.19874i	0.309514	+	0.536094i	0.978256	−	0.207401i	$-0.0665004\pi$
$5$	0.692094	+	1.19874i	0.309514	+	0.536094i	−0.668742	+	0.743494i	$0.733167\pi$
$6$	2.44869	+	0.0625523i	0.999674	+	0.0255369i
$7$	−2.08863	−	1.62408i	−0.789426	−	0.613845i
$7$	−2.08863	−	1.62408i	−0.789426	−	0.613845i
$8$	−2.71550	+	0.791228i	−0.960075	+	0.279741i
$9$	2.91395	+	0.713387i	0.971315	+	0.237796i
$10$	−1.13438	−	1.59535i	−0.358723	−	0.504493i
$11$	3.82316	+	2.20731i	1.15273	+	0.665528i	0.949550	−	0.313614i	$-0.101540\pi$
$11$	3.82316	+	2.20731i	1.15273	+	0.665528i	0.203177	+	0.979142i	$0.434873\pi$
$12$	−3.45587	+	0.238725i	−0.997623	+	0.0689139i
$13$			6.43609i			1.78505i	0.450999	+	0.892525i	$0.351068\pi$
$13$			6.43609i			1.78505i	−0.450999	+	0.892525i	$0.648932\pi$
$14$	3.15733	+	2.00781i	0.843831	+	0.536610i
$15$	−0.941460	−	2.20490i	−0.243084	−	0.569303i
$16$	3.71757	−	1.47637i	0.929392	−	0.369093i
$17$	2.52866	+	1.45992i	0.613289	+	0.354083i	0.774252	−	0.632878i	$-0.218126\pi$
$17$	2.52866	+	1.45992i	0.613289	+	0.354083i	−0.160962	+	0.986961i	$0.551460\pi$
$18$	−4.19776	−	0.615496i	−0.989421	−	0.145074i
$19$	1.58928	+	2.75271i	0.364606	+	0.631515i	0.988713	−	0.149823i	$-0.0478705\pi$
$19$	1.58928	+	2.75271i	0.364606	+	0.631515i	−0.624107	+	0.781339i	$0.714537\pi$
$20$	1.81001	+	2.09470i	0.404730	+	0.468390i
$21$	3.25469	+	3.22599i	0.710231	+	0.703969i
$22$	−5.67722	−	2.59745i	−1.21039	−	0.553777i
$23$	1.84696	+	3.19902i	0.385117	+	0.667043i	0.991785	−	0.127912i	$-0.0408277\pi$
$23$	1.84696	+	3.19902i	0.385117	+	0.667043i	−0.606668	+	0.794955i	$0.707494\pi$
$24$	4.83366	−	0.797307i	0.986667	−	0.162750i
$25$	1.54201	−	2.67084i	0.308402	−	0.534169i
$26$	−0.858934	−	9.06138i	−0.168451	−	1.77708i
$27$	−4.86280	−	1.83117i	−0.935846	−	0.352409i
$28$	−4.71316	−	2.40544i	−0.890704	−	0.454585i
$29$	−6.67884			−1.24023			−0.620115	−	0.784511i	$-0.712914\pi$
$29$	−6.67884			−1.24023			−0.620115	+	0.784511i	$0.712914\pi$
$30$	1.61974	+	2.97864i	0.295723	+	0.543823i
$31$	−2.17580	−	1.25620i	−0.390786	−	0.225620i	0.291715	−	0.956505i	$-0.405774\pi$
$31$	−2.17580	−	1.25620i	−0.390786	−	0.225620i	−0.682500	+	0.730885i	$0.739107\pi$
$32$	−5.03695	+	2.57472i	−0.890415	+	0.455150i
$33$	−6.11640	−	4.58869i	−1.06473	−	0.798788i
$34$	−3.75494	−	1.71796i	−0.643966	−	0.294628i
$35$	0.501330	−	3.62774i	0.0847402	−	0.613200i
$36$	5.99217	+	0.306343i	0.998696	+	0.0510571i
$37$	5.00149	−	2.88761i	0.822240	−	0.474720i	−0.0289485	−	0.999581i	$-0.509216\pi$
$37$	5.00149	−	2.88761i	0.822240	−	0.474720i	0.851188	+	0.524861i	$0.175883\pi$
$38$	−2.60492	−	3.66345i	−0.422573	−	0.594290i
$39$	1.33504	−	11.0674i	0.213777	−	1.77220i
$40$	−2.82786	−	2.70758i	−0.447124	−	0.428107i
$41$		−	0.497427i		−	0.0776850i	−0.999245	−	0.0388425i	$-0.987633\pi$
$41$		−	0.497427i		−	0.0776850i	0.999245	−	0.0388425i	$-0.0123671\pi$
$42$	−5.01281	−	4.10752i	−0.773493	−	0.633805i
$43$	0.865898			0.132048			0.0660241	−	0.997818i	$-0.478969\pi$
$43$	0.865898			0.132048			0.0660241	+	0.997818i	$0.478969\pi$
$44$	8.33962	+	2.89929i	1.25724	+	0.437085i
$45$	1.16156	+	3.98680i	0.173155	+	0.594317i
$46$	−3.02726	−	4.25743i	−0.446346	−	0.627723i
$47$	1.59001	+	2.75398i	0.231927	+	0.401710i	0.958375	−	0.285512i	$-0.0921635\pi$
$47$	1.59001	+	2.75398i	0.231927	+	0.401710i	−0.726448	+	0.687221i	$0.758830\pi$
$48$	−6.69892	+	1.76761i	−0.966906	+	0.255133i
$49$	1.72472	+	6.78420i	0.246388	+	0.969171i
$50$	−1.81456	+	3.96608i	−0.256618	+	0.560888i
$51$	−4.04541	−	3.03498i	−0.566471	−	0.424982i
$52$	2.41859	+	12.6429i	0.335398	+	1.75326i
$53$	4.12906	−	7.15175i	0.567171	−	0.982368i	−0.429673	−	0.902984i	$-0.641371\pi$
$53$	4.12906	−	7.15175i	0.567171	−	0.982368i	0.996844	−	0.0793841i	$-0.0252954\pi$
$54$	7.09073	+	1.92914i	0.964926	+	0.262522i
$55$			6.11065i			0.823960i
$56$	6.95669	+	2.75762i	0.929627	+	0.368502i
$57$	−2.16191	−	5.06319i	−0.286351	−	0.670635i
$58$	9.40316	−	0.891331i	1.23470	−	0.117038i
$59$	−6.62279	−	3.82367i	−0.862214	−	0.497799i	0.00253919	−	0.999997i	$-0.499192\pi$
$59$	−6.62279	−	3.82367i	−0.862214	−	0.497799i	−0.864753	+	0.502197i	$0.832525\pi$
$60$	−2.67795	−	3.97747i	−0.345722	−	0.513489i
$61$	−2.99321	+	1.72813i	−0.383241	+	0.221265i	−0.679228	−	0.733928i	$-0.737685\pi$
$61$	−2.99321	+	1.72813i	−0.383241	+	0.221265i	0.295986	+	0.955192i	$0.404352\pi$
$62$	3.23096	+	1.47823i	0.410333	+	0.187736i
$63$	−4.92754	−	6.22248i	−0.620812	−	0.783959i
$64$	6.74792	−	4.29716i	0.843490	−	0.537146i
$65$	−7.71521	+	4.45438i	−0.956954	+	0.552497i
$66$	9.22368	+	5.64416i	1.13536	+	0.694748i
$67$	−3.36806	+	5.83364i	−0.411473	+	0.712693i	−0.995051	−	0.0993644i	$-0.968319\pi$
$67$	−3.36806	+	5.83364i	−0.411473	+	0.712693i	0.583578	+	0.812057i	$0.301652\pi$
$68$	5.51586	+	1.91760i	0.668896	+	0.232544i
$69$	−2.51243	−	5.88411i	−0.302461	−	0.708363i
$70$	−0.221680	+	5.17441i	−0.0264958	+	0.618460i
$71$	1.90437			0.226007			0.113004	−	0.993595i	$-0.463953\pi$
$71$	1.90437			0.226007			0.113004	+	0.993595i	$0.463953\pi$
$72$	−8.47728	+	0.368391i	−0.999057	+	0.0434152i
$73$	3.23515	−	5.60345i	0.378646	−	0.655834i	−0.612219	−	0.790688i	$-0.709723\pi$
$73$	3.23515	−	5.60345i	0.378646	−	0.655834i	0.990866	+	0.134854i	$0.0430564\pi$
$74$	−6.65624	+	4.73295i	−0.773772	+	0.550195i
$75$	−3.20563	+	4.27288i	−0.370155	+	0.493390i
$76$	4.15638	+	4.81014i	0.476769	+	0.551761i
$77$	−4.40032	−	10.8194i	−0.501463	−	1.23298i
$78$	−0.402592	+	15.7600i	−0.0455846	+	1.78447i
$79$	−1.65073	+	0.953048i	−0.185721	+	0.107226i	−0.589978	−	0.807419i	$-0.700864\pi$
$79$	−1.65073	+	0.953048i	−0.185721	+	0.107226i	0.404257	+	0.914646i	$0.367530\pi$
$80$	4.34270	+	3.43462i	0.485528	+	0.384002i
$81$	7.98216	+	4.15754i	0.886906	+	0.461949i
$82$	0.0663845	+	0.700328i	0.00733094	+	0.0773383i
$83$			7.00064i			0.768420i	0.923246	+	0.384210i	$0.125526\pi$
$83$			7.00064i			0.768420i	−0.923246	+	0.384210i	$0.874474\pi$
$84$	7.60572	+	5.11400i	0.829852	+	0.557983i
$85$			4.04161i			0.438374i
$86$	−1.21910	+	0.115559i	−0.131459	+	0.0124611i
$87$	11.4848	+	1.38539i	1.23130	+	0.148530i
$88$	−12.1283	−	2.96895i	−1.29288	−	0.316491i
$89$	−8.22776	+	4.75030i	−0.872141	+	0.503531i	−0.868059	−	0.496461i	$-0.834633\pi$
$89$	−8.22776	+	4.75030i	−0.872141	+	0.503531i	−0.00408165	+	0.999992i	$0.501299\pi$
$90$	−2.16742	−	5.45801i	−0.228466	−	0.575325i
$91$	10.4527	−	13.4426i	1.09574	−	1.40916i
$92$	4.83027	+	5.59004i	0.503591	+	0.582801i
$93$	3.48090	+	2.61147i	0.360953	+	0.270797i
$94$	−2.60612	−	3.66514i	−0.268801	−	0.378031i
$95$	−2.19986	+	3.81027i	−0.225701	+	0.390926i
$96$	9.19553	−	3.38264i	0.938515	−	0.345239i
$97$	1.19214			0.121044			0.0605218	−	0.998167i	$-0.480724\pi$
$97$	1.19214			0.121044			0.0605218	+	0.998167i	$0.480724\pi$
$98$	−3.33362	−	9.32132i	−0.336747	−	0.941595i
$99$	9.56583	+	9.15936i	0.961402	+	0.920551i
$100$	2.02543	−	5.82601i	0.202543	−	0.582601i
$101$	1.03566	−	1.79382i	0.103052	−	0.178491i	−0.809889	−	0.586584i	$-0.800473\pi$
$101$	1.03566	−	1.79382i	0.103052	−	0.178491i	0.912941	+	0.408092i	$0.133806\pi$
$102$	6.10058	+	3.73307i	0.604047	+	0.369629i
$103$	4.80043	−	2.77153i	0.473000	−	0.273087i	−0.244495	−	0.969651i	$-0.578622\pi$
$103$	4.80043	−	2.77153i	0.473000	−	0.273087i	0.717495	+	0.696564i	$0.245289\pi$
$104$	−5.09241	−	17.4772i	−0.499352	−	1.71378i
$105$	−1.61458	+	6.13422i	−0.157567	+	0.598638i
$106$	−4.85888	+	10.6200i	−0.471936	+	1.03151i
$107$	5.17522	−	2.98792i	0.500308	−	0.288853i	−0.228533	−	0.973536i	$-0.573393\pi$
$107$	5.17522	−	2.98792i	0.500308	−	0.288853i	0.728841	+	0.684683i	$0.240060\pi$
$108$	−10.2405	−	1.76974i	−0.985393	−	0.170293i
$109$	−1.43595	−	0.829048i	−0.137539	−	0.0794084i	0.429651	−	0.902995i	$-0.358636\pi$
$109$	−1.43595	−	0.829048i	−0.137539	−	0.0794084i	−0.567191	+	0.823586i	$0.691970\pi$
$110$	−0.815503	−	8.60320i	−0.0777551	−	0.820283i
$111$	−9.19946	+	3.92803i	−0.873174	+	0.372832i
$112$	−10.1624	−	2.95405i	−0.960253	−	0.279131i
$113$		−	16.4545i		−	1.54791i	−0.633241	−	0.773955i	$-0.718276\pi$
$113$		−	16.4545i		−	1.54791i	0.633241	−	0.773955i	$-0.281724\pi$
$114$	3.71946	+	6.83995i	0.348360	+	0.640620i
$115$	−2.55654	+	4.42805i	−0.238398	+	0.412918i
$116$	−13.1198	+	2.50982i	−1.21814	+	0.233030i
$117$	−4.59142	+	18.7544i	−0.424477	+	1.73385i
$118$	9.83453	+	4.49950i	0.905342	+	0.414213i
$119$	−2.91039	−	7.15597i	−0.266795	−	0.655987i
$120$	4.30112	+	5.24250i	0.392636	+	0.478573i
$121$	4.24439	+	7.35150i	0.385854	+	0.668318i
$122$	3.98352	−	2.83250i	0.360651	−	0.256443i
$123$	−0.103181	+	0.855367i	−0.00930353	+	0.0771259i
$124$	−4.74616	−	1.65002i	−0.426218	−	0.148176i
$125$	11.1898			1.00085
$126$	7.76793	+	8.10304i	0.692022	+	0.721876i
$127$		−	2.31360i		−	0.205299i	−0.994718	−	0.102649i	$-0.967268\pi$
$127$		−	2.31360i		−	0.205299i	0.994718	−	0.102649i	$-0.0327319\pi$
$128$	−8.92693	+	6.95054i	−0.789036	+	0.614347i
$129$	−1.48898	−	0.179613i	−0.131098	−	0.0158141i
$130$	10.2678	−	7.30097i	0.900545	−	0.640337i
$131$	4.11383	−	2.37512i	0.359427	−	0.207515i	−0.309402	−	0.950931i	$-0.600129\pi$
$131$	4.11383	−	2.37512i	0.359427	−	0.207515i	0.668830	+	0.743416i	$0.266796\pi$
$132$	−13.7393	−	6.71547i	−1.19585	−	0.584506i
$133$	1.15122	−	8.33050i	0.0998234	−	0.722346i
$134$	3.96336	−	8.66269i	0.342382	−	0.748342i
$135$	−1.17042	−	7.09658i	−0.100733	−	0.610777i
$136$	−8.02171	−	1.96368i	−0.687856	−	0.168384i
$137$	0.290760	+	0.167870i	0.0248413	+	0.0143421i	0.512369	−	0.858765i	$-0.328768\pi$
$137$	0.290760	+	0.167870i	0.0248413	+	0.0143421i	−0.487528	+	0.873107i	$0.662101\pi$
$138$	4.32252	+	7.94895i	0.367957	+	0.676660i
$139$	−9.35410			−0.793405			−0.396702	−	0.917947i	$-0.629845\pi$
$139$	−9.35410			−0.793405			−0.396702	+	0.917947i	$0.629845\pi$
$140$	−0.378453	−	7.31465i	−0.0319851	−	0.618201i
$141$	−2.16290	−	5.06553i	−0.182149	−	0.426594i
$142$	−2.68117	+	0.254150i	−0.224999	+	0.0213278i
$143$	−14.2064	+	24.6062i	−1.18800	+	2.05768i
$144$	11.8860	−	1.65000i	0.990502	−	0.137500i
$145$	−4.62239	−	8.00621i	−0.383868	−	0.664880i
$146$	−3.80697	+	8.32086i	−0.315067	+	0.688639i
$147$	−1.55855	−	12.0238i	−0.128547	−	0.991703i
$148$	8.73970	−	7.55185i	0.718399	−	0.620758i
$149$	1.03566	+	1.79382i	0.0848446	+	0.146955i	0.905325	−	0.424720i	$-0.139627\pi$
$149$	1.03566	+	1.79382i	0.0848446	+	0.146955i	−0.820480	+	0.571675i	$0.806294\pi$
$150$	3.94298	−	6.44361i	0.321943	−	0.526119i
$151$	20.2661	+	11.7007i	1.64923	+	0.952186i	0.977377	+	0.211506i	$0.0678369\pi$
$151$	20.2661	+	11.7007i	1.64923	+	0.952186i	0.671858	+	0.740680i	$0.265496\pi$
$152$	−6.49372	−	6.21752i	−0.526710	−	0.504307i
$153$	6.32688	+	6.05804i	0.511498	+	0.489763i
$154$	7.63913	+	14.6454i	0.615578	+	1.18016i
$155$		−	3.47763i		−	0.279330i
$156$	−1.53645	−	22.2423i	−0.123015	−	1.78081i
$157$	−19.3264	−	11.1581i	−1.54241	−	0.890511i	−0.998686	−	0.0512477i	$-0.983680\pi$
$157$	−19.3264	−	11.1581i	−1.54241	−	0.890511i	−0.543725	−	0.839264i	$-0.682986\pi$
$158$	2.19687	−	1.56210i	0.174774	−	0.124274i
$159$	−8.58377	+	11.4416i	−0.680737	+	0.907374i
$160$	−6.57246	−	4.25605i	−0.519599	−	0.336470i
$161$	1.33787	−	9.68118i	0.105439	−	0.762983i
$162$	−11.7929	−	4.78815i	−0.926542	−	0.376192i
$163$	−8.50029	−	14.7229i	−0.665794	−	1.15319i	−0.979069	−	0.203526i	$-0.934760\pi$
$163$	−8.50029	−	14.7229i	−0.665794	−	1.15319i	0.313276	−	0.949662i	$-0.398574\pi$
$164$	−0.186926	−	0.977134i	−0.0145965	−	0.0763014i
$165$	1.26753	−	10.5078i	0.0986772	−	0.818030i
$166$	−0.934277	−	9.85621i	−0.0725139	−	0.764991i
$167$	23.9142			1.85054			0.925269	−	0.379311i	$-0.123839\pi$
$167$	23.9142			1.85054			0.925269	+	0.379311i	$0.123839\pi$
$168$	−11.3906	−	6.18499i	−0.878804	−	0.477182i
$169$	−28.4232			−2.18640
$170$	−0.539377	−	5.69019i	−0.0413683	−	0.436418i
$171$	2.66732	+	9.15502i	0.203975	+	0.700102i
$172$	1.70095	−	0.325392i	0.129696	−	0.0248109i
$173$	−4.38442	−	7.59404i	−0.333341	−	0.577364i	0.649824	−	0.760085i	$-0.274843\pi$
$173$	−4.38442	−	7.59404i	−0.333341	−	0.577364i	−0.983165	+	0.182721i	$0.941509\pi$
$174$	−16.3544	−	0.417777i	−1.23983	−	0.0316716i
$175$	−7.55835	+	3.07404i	−0.571358	+	0.232375i
$176$	17.4717	+	2.56140i	1.31698	+	0.193073i
$177$	10.5953	+	7.94889i	0.796392	+	0.597475i
$178$	10.9499	−	7.78600i	0.820732	−	0.583585i
$179$	5.26665	+	3.04070i	0.393648	+	0.227273i	0.683740	−	0.729726i	$-0.260352\pi$
$179$	5.26665	+	3.04070i	0.393648	+	0.227273i	−0.290092	+	0.956999i	$0.593686\pi$
$180$	3.77992	+	7.39509i	0.281739	+	0.551197i
$181$		−	11.5816i		−	0.860857i	−0.902625	−	0.430429i	$-0.858362\pi$
$181$		−	11.5816i		−	0.860857i	0.902625	−	0.430429i	$-0.141638\pi$
$182$	−12.9224	+	20.3208i	−0.957874	+	1.50628i
$183$	5.50555	−	2.35079i	0.406982	−	0.173775i
$184$	−7.54658	−	7.22560i	−0.556341	−	0.532678i
$185$	6.92300	+	3.99700i	0.508989	+	0.293865i
$186$	−5.24929	−	3.21215i	−0.384897	−	0.235526i
$187$	6.44498	+	11.1630i	0.471304	+	0.816322i
$188$	4.15830	+	4.81236i	0.303275	+	0.350978i
$189$	7.18260	+	11.7222i	0.522457	+	0.852665i
$190$	2.58869	−	5.65807i	0.187803	−	0.410480i
$191$	0.757053	+	1.31125i	0.0547784	+	0.0948790i	0.892114	−	0.451810i	$-0.149221\pi$
$191$	0.757053	+	1.31125i	0.0547784	+	0.0948790i	−0.837336	+	0.546689i	$0.815888\pi$
$192$	−12.4950	+	5.98962i	−0.901747	+	0.432264i
$193$	−7.97806	+	13.8184i	−0.574273	+	0.994670i	0.421847	+	0.906667i	$0.361382\pi$
$193$	−7.97806	+	13.8184i	−0.574273	+	0.994670i	−0.996120	+	0.0880034i	$0.971951\pi$
$194$	−1.67842	+	0.159098i	−0.120504	+	0.0114226i
$195$	14.1909	−	6.05931i	1.01623	−	0.433917i
$196$	5.93740	+	12.6786i	0.424100	+	0.905615i
$197$	0.963016			0.0686121			0.0343060	−	0.999411i	$-0.489078\pi$
$197$	0.963016			0.0686121			0.0343060	+	0.999411i	$0.489078\pi$
$198$	−14.6901	−	11.6189i	−1.04398	−	0.825717i
$199$	−1.72593	−	0.996469i	−0.122348	−	0.0706378i	0.437577	−	0.899181i	$-0.355837\pi$
$199$	−1.72593	−	0.996469i	−0.122348	−	0.0706378i	−0.559925	+	0.828543i	$0.689170\pi$
$200$	−2.07409	+	8.47276i	−0.146660	+	0.599115i
$201$	7.00173	−	9.33281i	0.493864	−	0.658286i
$202$	−1.21871	+	2.66373i	−0.0857484	+	0.187420i
$203$	13.9496	+	10.8470i	0.979070	+	0.761309i
$204$	−9.08722	−	4.44164i	−0.636232	−	0.310977i
$205$	0.596286	−	0.344266i	0.0416464	−	0.0240446i
$206$	−6.38866	+	4.54269i	−0.445119	+	0.316504i
$207$	3.09979	+	10.6394i	0.215450	+	0.739488i
$208$	9.50206	+	23.9266i	0.658849	+	1.65901i
$209$			14.0321i			0.970620i
$210$	1.45452	−	8.85186i	0.100372	−	0.610836i
$211$	21.4567			1.47714			0.738569	−	0.674178i	$-0.235502\pi$
$211$	21.4567			1.47714			0.738569	+	0.674178i	$0.235502\pi$
$212$	5.42352	−	15.6004i	0.372489	−	1.07144i
$213$	−3.27473	−	0.395024i	−0.224381	−	0.0270666i
$214$	−6.88746	+	4.89736i	−0.470817	+	0.334777i
$215$	0.599283	+	1.03799i	0.0408707	+	0.0707902i
$216$	14.6538	+	1.12496i	0.997066	+	0.0765440i
$217$	2.50427	+	6.15741i	0.170001	+	0.417992i
$218$	2.13232	+	0.975582i	0.144419	+	0.0660747i
$219$	−6.72544	+	8.96454i	−0.454463	+	0.605768i
$220$	2.29630	+	12.0036i	0.154816	+	0.809285i
$221$	−9.39617	+	16.2747i	−0.632055	+	1.09475i
$222$	12.4277	−	6.75801i	0.834094	−	0.453568i
$223$		−	12.1938i		−	0.816559i	−0.912857	−	0.408279i	$-0.866129\pi$
$223$		−	12.1938i		−	0.816559i	0.912857	−	0.408279i	$-0.133871\pi$
$224$	14.7019	+	2.80279i	0.982309	+	0.187269i
$225$	6.39868	−	6.68264i	0.426579	−	0.445509i
$226$	2.19595	+	23.1663i	0.146073	+	1.54100i
$227$	−13.5954	−	7.84932i	−0.902360	−	0.520978i	−0.0243951	−	0.999702i	$-0.507766\pi$
$227$	−13.5954	−	7.84932i	−0.902360	−	0.520978i	−0.877965	+	0.478724i	$0.841099\pi$
$228$	−6.14948	−	9.13360i	−0.407259	−	0.604888i
$229$	10.4894	−	6.05608i	0.693161	−	0.400197i	−0.111634	−	0.993749i	$-0.535608\pi$
$229$	10.4894	−	6.05608i	0.693161	−	0.400197i	0.804795	+	0.593553i	$0.202275\pi$
$230$	3.00840	−	6.57545i	0.198368	−	0.433572i
$231$	5.32246	+	19.5176i	0.350192	+	1.28416i
$232$	18.1364	−	5.28449i	1.19071	−	0.346944i
$233$	−5.05877	+	2.92068i	−0.331411	+	0.191340i	−0.656468	−	0.754354i	$-0.727950\pi$
$233$	−5.05877	+	2.92068i	−0.331411	+	0.191340i	0.325056	+	0.945695i	$0.394617\pi$
$234$	3.96138	−	27.0171i	0.258964	−	1.76616i
$235$	−2.20088	+	3.81203i	−0.143569	+	0.248670i
$236$	−14.4466	−	5.02239i	−0.940390	−	0.326929i
$237$	3.03626	−	1.29644i	0.197226	−	0.0842126i
$238$	5.05255	+	9.68650i	0.327508	+	0.627883i
$239$	−22.6171			−1.46298			−0.731490	−	0.681852i	$-0.761175\pi$
$239$	−22.6171			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$240$	−6.75519	−	6.80693i	−0.436046	−	0.439385i
$241$	12.7459	−	22.0766i	0.821038	−	1.42208i	−0.0838714	−	0.996477i	$-0.526729\pi$
$241$	12.7459	−	22.0766i	0.821038	−	1.42208i	0.904910	−	0.425604i	$-0.139938\pi$
$242$	−6.95679	−	9.78376i	−0.447200	−	0.628924i
$243$	−12.8636	−	8.80499i	−0.825200	−	0.564840i
$244$	−5.23039	+	4.51951i	−0.334842	+	0.289332i
$245$	−6.93884	+	6.76279i	−0.443306	+	0.432059i
$246$	0.0311152	−	1.21804i	0.00198383	−	0.0776596i
$247$	−17.7167	+	10.2287i	−1.12729	+	0.650839i
$248$	6.90234	+	1.68966i	0.438299	+	0.107293i
$249$	1.45214	−	12.0382i	0.0920258	−	0.762889i
$250$	−15.7542	+	1.49335i	−0.996381	+	0.0944475i
$251$			1.11008i			0.0700675i	0.999386	+	0.0350338i	$0.0111539\pi$
$251$			1.11008i			0.0700675i	−0.999386	+	0.0350338i	$0.988846\pi$
$252$	−12.0179	−	10.3716i	−0.757056	−	0.653350i
$253$			16.3072i			1.02522i
$254$	0.308763	+	3.25732i	0.0193735	+	0.204382i
$255$	0.838351	−	6.94989i	0.0524996	−	0.435219i
$256$	11.6407	−	10.9770i	0.727541	−	0.686064i
$257$	12.0906	−	6.98049i	0.754188	−	0.435431i	−0.0730169	−	0.997331i	$-0.523263\pi$
$257$	12.0906	−	6.98049i	0.754188	−	0.435431i	0.827205	+	0.561900i	$0.189929\pi$
$258$	2.12032	+	0.0541639i	0.132005	+	0.00337210i
$259$	−15.1360	−	2.09169i	−0.940503	−	0.129971i
$260$	−13.4817	+	11.6494i	−0.836099	+	0.722462i
$261$	−19.4618	−	4.76460i	−1.20465	−	0.294921i
$262$	−5.47490	+	3.89296i	−0.338241	+	0.240508i
$263$	7.08483	−	12.2713i	0.436870	−	0.756680i	−0.560577	−	0.828103i	$-0.689420\pi$
$263$	7.08483	−	12.2713i	0.436870	−	0.756680i	0.997446	+	0.0714223i	$0.0227538\pi$
$264$	20.2398	+	7.62113i	1.24567	+	0.469048i
$265$	11.4308			0.702189
$266$	−0.509050	+	11.8822i	−0.0312119	+	0.728543i
$267$	15.1337	−	6.46186i	0.926166	−	0.395459i
$268$	−4.42394	+	12.7252i	−0.270235	+	0.777312i
$269$	9.11023	−	15.7794i	0.555461	−	0.962086i	−0.442407	−	0.896814i	$-0.645875\pi$
$269$	9.11023	−	15.7794i	0.555461	−	0.962086i	0.997868	−	0.0652716i	$-0.0207914\pi$
$270$	2.59491	+	9.83510i	0.157921	+	0.598545i
$271$	21.9278	−	12.6600i	1.33202	−	0.769041i	0.346410	−	0.938083i	$-0.387401\pi$
$271$	21.9278	−	12.6600i	1.33202	−	0.769041i	0.985609	+	0.169042i	$0.0540673\pi$
$272$	11.5558	+	1.69412i	0.700676	+	0.102721i
$273$	−20.7628	+	20.9474i	−1.25662	+	1.26780i
$274$	−0.431765	−	0.197542i	−0.0260839	−	0.0119339i
$275$	11.7907	−	6.80738i	0.711008	−	0.410500i
$276$	−7.14652	−	10.6145i	−0.430170	−	0.638917i
$277$	16.2822	+	9.40051i	0.978300	+	0.564822i	0.901756	−	0.432245i	$-0.142278\pi$
$277$	16.2822	+	9.40051i	0.978300	+	0.564822i	0.0765434	+	0.997066i	$0.475612\pi$
$278$	13.1697	−	1.24836i	0.789864	−	0.0748717i
$279$	−5.44401	−	5.21269i	−0.325924	−	0.312075i
$280$	1.50901	+	10.2478i	0.0901805	+	0.612424i
$281$			25.4910i			1.52067i	0.649533	+	0.760333i	$0.274964\pi$
$281$			25.4910i			1.52067i	−0.649533	+	0.760333i	$0.725036\pi$
$282$	3.72118	+	6.84311i	0.221593	+	0.407502i
$283$	−6.01848	+	10.4243i	−0.357761	+	0.619661i	−0.987586	−	0.157076i	$-0.949793\pi$
$283$	−6.01848	+	10.4243i	−0.357761	+	0.619661i	0.629825	+	0.776737i	$0.283126\pi$
$284$	3.74091	−	0.715636i	0.221982	−	0.0424652i
$285$	4.57321	−	6.09577i	0.270894	−	0.361082i
$286$	16.7174	−	36.5391i	0.988520	−	2.16060i
$287$	−0.807861	+	1.03894i	−0.0476865	+	0.0613266i
$288$	−16.5142	+	3.90930i	−0.973106	+	0.230358i
$289$	−4.23726	−	7.33916i	−0.249251	−	0.431715i
$290$	7.57635	+	10.6551i	0.444898	+	0.625688i
$291$	−2.04999	−	0.247286i	−0.120173	−	0.0144962i
$292$	4.24937	−	12.2230i	0.248676	−	0.715298i
$293$	−3.90464			−0.228111			−0.114056	−	0.993474i	$-0.536384\pi$
$293$	−3.90464			−0.228111			−0.114056	+	0.993474i	$0.536384\pi$
$294$	3.79893	+	16.7203i	0.221558	+	0.975147i
$295$		−	10.5854i		−	0.616303i
$296$	−11.2968	+	11.7986i	−0.656613	+	0.685782i
$297$	−14.5493	−	17.7345i	−0.844238	−	1.02906i
$298$	−1.69750	−	2.38730i	−0.0983338	−	0.138293i
$299$	−20.5892	+	11.8872i	−1.19070	+	0.687453i
$300$	−4.69139	+	9.59819i	−0.270858	+	0.554152i
$301$	−1.80854	−	1.40629i	−0.104242	−	0.0810571i
$302$	−30.0943	−	13.7688i	−1.73173	−	0.792303i
$303$	−2.15300	+	2.86979i	−0.123686	+	0.164865i
$304$	9.97228	+	7.88703i	0.571950	+	0.452352i
$305$	−4.14317	−	2.39206i	−0.237237	−	0.136969i
$306$	−9.71611	−	7.68477i	−0.555433	−	0.439309i
$307$	−11.0339			−0.629740			−0.314870	−	0.949135i	$-0.601961\pi$
$307$	−11.0339			−0.629740			−0.314870	+	0.949135i	$0.601961\pi$
$308$	−12.7097	−	19.5998i	−0.724200	−	1.11680i
$309$	−8.82964	+	3.77013i	−0.502301	+	0.214475i
$310$	0.464111	+	4.89617i	0.0263597	+	0.278084i
$311$	15.6553	−	27.1158i	0.887732	−	1.53760i	0.0451815	−	0.998979i	$-0.485613\pi$
$311$	15.6553	−	27.1158i	0.887732	−	1.53760i	0.842550	−	0.538618i	$-0.181053\pi$
$312$	5.13154	+	31.1099i	0.290516	+	1.76125i
$313$	6.53063	+	11.3114i	0.369133	+	0.639357i	0.989430	−	0.145010i	$-0.0463213\pi$
$313$	6.53063	+	11.3114i	0.369133	+	0.639357i	−0.620297	+	0.784367i	$0.712988\pi$
$314$	28.6987	+	13.1303i	1.61956	+	0.740984i
$315$	4.04883	−	10.2134i	0.228126	−	0.575460i
$316$	−2.88451	+	2.49247i	−0.162267	+	0.140212i
$317$	12.2315	+	21.1856i	0.686990	+	1.18990i	0.972807	+	0.231618i	$0.0744018\pi$
$317$	12.2315	+	21.1856i	0.686990	+	1.18990i	−0.285817	+	0.958284i	$0.592265\pi$
$318$	10.5582	−	17.2541i	0.592072	−	0.967564i
$319$	−25.5343	−	14.7422i	−1.42965	−	0.825407i
$320$	9.82138	+	5.11497i	0.549032	+	0.285935i
$321$	−9.51902	+	4.06448i	−0.531300	+	0.226857i
$322$	−0.591585	+	13.8087i	−0.0329678	+	0.769529i
$323$			9.28088i			0.516402i
$324$	17.2423	+	5.16740i	0.957907	+	0.287078i
$325$	17.1898	+	9.92452i	0.953517	+	0.550513i
$326$	13.9324	+	19.5940i	0.771646	+	1.08521i
$327$	2.29727	+	1.72348i	0.127039	+	0.0953085i
$328$	0.393578	+	1.35076i	0.0217317	+	0.0745834i
$329$	1.15175	−	8.33435i	0.0634981	−	0.459488i
$330$	−0.382236	+	14.9631i	−0.0210414	+	0.823691i
$331$	−7.26267	−	12.5793i	−0.399192	−	0.691422i	0.594434	−	0.804144i	$-0.297376\pi$
$331$	−7.26267	−	12.5793i	−0.399192	−	0.691422i	−0.993626	+	0.112723i	$0.964043\pi$
$332$	2.63074	+	13.7519i	0.144381	+	0.754734i
$333$	16.6341	−	4.84634i	0.911540	−	0.265578i
$334$	−33.6689	+	3.19150i	−1.84228	+	0.174631i
$335$	−9.32404			−0.509427
$336$	16.8623	+	7.18772i	0.919913	+	0.392122i
$337$	−18.7954			−1.02385			−0.511924	−	0.859030i	$-0.671067\pi$
$337$	−18.7954			−1.02385			−0.511924	+	0.859030i	$0.671067\pi$
$338$	40.0171	−	3.79324i	2.17664	−	0.206325i
$339$	−3.41316	+	28.2949i	−0.185377	+	1.53677i
$340$	1.51878	+	7.93925i	0.0823674	+	0.430566i
$341$	−5.54563	−	9.60532i	−0.300313	−	0.520157i
$342$	−4.97712	−	12.5334i	−0.269132	−	0.677729i
$343$	7.41581	−	16.9707i	0.400416	−	0.916334i
$344$	−2.35135	+	0.685122i	−0.126776	+	0.0369393i
$345$	5.31469	−	7.08411i	0.286133	−	0.381396i
$346$	7.18630	+	10.1065i	0.386338	+	0.543331i
$347$	−20.7411	−	11.9749i	−1.11344	−	0.642846i	−0.173723	−	0.984795i	$-0.555580\pi$
$347$	−20.7411	−	11.9749i	−1.11344	−	0.642846i	−0.939719	+	0.341949i	$0.888913\pi$
$348$	23.0812	−	1.59441i	1.23728	−	0.0854691i
$349$		−	3.59423i		−	0.192395i	−0.995362	−	0.0961974i	$-0.969332\pi$
$349$		−	3.59423i		−	0.192395i	0.995362	−	0.0961974i	$-0.0306680\pi$
$350$	10.2312	−	5.33665i	0.546879	−	0.285256i
$351$	11.7856	−	31.2974i	0.629067	−	1.67053i
$352$	−24.9403	−	1.27450i	−1.32932	−	0.0679310i
$353$	22.4603	+	12.9675i	1.19544	+	0.690189i	0.959536	−	0.281587i	$-0.0908607\pi$
$353$	22.4603	+	12.9675i	1.19544	+	0.690189i	0.235907	+	0.971776i	$0.424194\pi$
$354$	−15.9780	−	9.77726i	−0.849220	−	0.519655i
$355$	1.31800	+	2.28285i	0.0699524	+	0.121161i
$356$	−14.3773	+	12.4233i	−0.761998	+	0.658432i
$357$	3.52030	+	12.9090i	0.186314	+	0.683217i
$358$	−7.82073	−	3.57815i	−0.413338	−	0.189111i
$359$	−14.1756	−	24.5529i	−0.748162	−	1.29585i	−0.948703	−	0.316169i	$-0.897603\pi$
$359$	−14.1756	−	24.5529i	−0.748162	−	1.29585i	0.200541	−	0.979685i	$-0.435730\pi$
$360$	−6.30868	−	9.90711i	−0.332497	−	0.522151i
$361$	4.44838	−	7.70483i	0.234126	−	0.405517i
$362$	1.54564	+	16.3058i	0.0812370	+	0.857016i
$363$	−5.77367	−	13.5219i	−0.303039	−	0.709718i
$364$	15.4816	−	30.3343i	0.811456	−	1.58995i
$365$	8.95612			0.468785
$366$	−7.43755	+	4.04443i	−0.388767	+	0.211406i
$367$	3.10999	+	1.79556i	0.162340	+	0.0937272i	0.578969	−	0.815349i	$-0.303455\pi$
$367$	3.10999	+	1.79556i	0.162340	+	0.0937272i	−0.416629	+	0.909077i	$0.636789\pi$
$368$	11.5891	+	9.16580i	0.604126	+	0.477800i
$369$	0.354858	−	1.44947i	0.0184731	−	0.0754566i
$370$	−10.2803	−	4.70347i	−0.534449	−	0.244522i
$371$	−20.2391	+	8.23139i	−1.05076	+	0.427353i
$372$	7.81917	+	3.82184i	0.405405	+	0.198153i
$373$	−13.4339	+	7.75604i	−0.695579	+	0.401593i	−0.805699	−	0.592326i	$-0.798210\pi$
$373$	−13.4339	+	7.75604i	−0.695579	+	0.401593i	0.110120	+	0.993918i	$0.464877\pi$
$374$	−10.5637	−	14.8563i	−0.546235	−	0.768203i
$375$	−19.2418	−	2.32110i	−0.993644	−	0.119861i
$376$	−6.49672	−	6.22039i	−0.335043	−	0.320792i
$377$		−	42.9856i		−	2.21387i
$378$	−11.6768	−	15.5452i	−0.600590	−	0.799557i
$379$	−14.5848			−0.749171			−0.374586	−	0.927192i	$-0.622215\pi$
$379$	−14.5848			−0.749171			−0.374586	+	0.927192i	$0.622215\pi$
$380$	−2.88951	+	8.31149i	−0.148229	+	0.426371i
$381$	−0.479910	+	3.97843i	−0.0245865	+	0.203821i
$382$	−1.24085	−	1.74509i	−0.0634875	−	0.0892863i
$383$	−5.47353	−	9.48043i	−0.279684	−	0.484427i	0.691622	−	0.722260i	$-0.256896\pi$
$383$	−5.47353	−	9.48043i	−0.279684	−	0.484427i	−0.971306	+	0.237832i	$0.923563\pi$
$384$	16.7924	−	10.1003i	0.856932	−	0.515430i
$385$	9.92420	−	12.7629i	0.505784	−	0.650456i
$386$	9.38818	−	20.5197i	0.477846	−	1.04442i
$387$	2.52318	+	0.617720i	0.128260	+	0.0314005i
$388$	2.34182	−	0.447990i	0.118888	−	0.0227433i
$389$	−9.51835	+	16.4863i	−0.482600	+	0.835887i	−0.999800	−	0.0199769i	$-0.993641\pi$
$389$	−9.51835	+	16.4863i	−0.482600	+	0.835887i	0.517201	+	0.855864i	$0.326974\pi$
$390$	−19.1708	+	10.4248i	−0.970751	+	0.527880i
$391$			10.7856i			0.545453i
$392$	−10.0513	−	17.0579i	−0.507668	−	0.861553i
$393$	−7.56676	+	3.23089i	−0.381692	+	0.162977i
$394$	−1.35583	+	0.128520i	−0.0683059	+	0.00647475i
$395$	−2.28492	−	1.31920i	−0.114967	−	0.0663760i
$396$	22.2329	+	14.3978i	1.11724	+	0.723514i
$397$	6.49649	−	3.75075i	0.326050	−	0.188245i	−0.328036	−	0.944665i	$-0.606387\pi$
$397$	6.49649	−	3.75075i	0.326050	−	0.188245i	0.654086	+	0.756420i	$0.273053\pi$
$398$	2.56293	+	1.17259i	0.128468	+	0.0587768i
$399$	−3.70762	+	14.0862i	−0.185613	+	0.705193i
$400$	1.78938	−	12.2056i	0.0894690	−	0.610281i
$401$	−24.3528	+	14.0601i	−1.21612	+	0.702128i	−0.964086	−	0.265591i	$-0.914433\pi$
$401$	−24.3528	+	14.0601i	−1.21612	+	0.702128i	−0.252035	+	0.967718i	$0.581100\pi$
$402$	−8.61223	+	14.0741i	−0.429539	+	0.701953i
$403$	8.08501	−	14.0036i	0.402743	−	0.697571i
$404$	1.36034	−	3.91292i	0.0676794	−	0.194675i
$405$	0.540584	+	12.4460i	0.0268618	+	0.618445i
$406$	−21.0873	−	13.4098i	−1.04654	−	0.665519i
$407$	25.4954			1.26376
$408$	13.3867	+	5.04065i	0.662739	+	0.249549i
$409$	6.57782	−	11.3931i	0.325252	−	0.563353i	−0.656311	−	0.754490i	$-0.727884\pi$
$409$	6.57782	−	11.3931i	0.325252	−	0.563353i	0.981563	+	0.191137i	$0.0612175\pi$
$410$	−0.793568	+	0.564271i	−0.0391915	+	0.0278673i
$411$	−0.465165	−	0.348980i	−0.0229449	−	0.0172139i
$412$	8.38836	−	7.24827i	0.413265	−	0.357096i
$413$	7.62258	+	18.7422i	0.375083	+	0.922242i
$414$	−5.78409	−	14.5655i	−0.284273	−	0.715856i
$415$	−8.39196	+	4.84510i	−0.411945	+	0.237837i
$416$	−16.5711	−	32.4182i	−0.812466	−	1.58943i
$417$	16.0852	+	1.94032i	0.787694	+	0.0950179i
$418$	−1.87267	−	19.7558i	−0.0915951	−	0.966289i
$419$			4.42222i			0.216040i	0.994149	+	0.108020i	$0.0344510\pi$
$419$			4.42222i			0.216040i	−0.994149	+	0.108020i	$0.965549\pi$
$420$	−0.866496	+	12.6567i	−0.0422807	+	0.617582i
$421$			22.2013i			1.08203i	0.841014	+	0.541014i	$0.181959\pi$
$421$			22.2013i			1.08203i	−0.841014	+	0.541014i	$0.818041\pi$
$422$	−30.2089	+	2.86352i	−1.47055	+	0.139394i
$423$	2.66856	+	9.15925i	0.129750	+	0.445338i
$424$	−5.55382	+	22.6876i	−0.269718	+	1.10181i
$425$	7.79844	−	4.50243i	0.378280	−	0.218400i
$426$	4.66322	+	0.119123i	0.225934	+	0.00577153i
$427$	9.05832	+	1.25180i	0.438363	+	0.0605788i
$428$	9.04328	−	7.81418i	0.437124	−	0.377713i
$429$	29.5332	−	39.3656i	1.42588	−	1.90059i
$430$	−0.982257	−	1.38141i	−0.0473686	−	0.0666174i
$431$	−8.76759	+	15.1859i	−0.422320	+	0.731479i	−0.996166	−	0.0874837i	$-0.972117\pi$
$431$	−8.76759	+	15.1859i	−0.422320	+	0.731479i	0.573846	+	0.818963i	$0.305451\pi$
$432$	−20.7813	+	0.371801i	−0.999840	+	0.0178883i
$433$	0.852347			0.0409612			0.0204806	−	0.999790i	$-0.493480\pi$
$433$	0.852347			0.0409612			0.0204806	+	0.999790i	$0.493480\pi$
$434$	−4.34750	−	8.33483i	−0.208687	−	0.400085i
$435$	6.28786	+	14.7262i	0.301480	+	0.706066i
$436$	−3.13230	−	1.08895i	−0.150010	−	0.0521514i
$437$	−5.87066	+	10.1683i	−0.280832	+	0.486415i
$438$	8.27240	−	13.5187i	0.395271	−	0.645951i
$439$	−14.5943	+	8.42604i	−0.696549	+	0.402153i	−0.806061	−	0.591833i	$-0.798405\pi$
$439$	−14.5943	+	8.42604i	−0.696549	+	0.402153i	0.109512	+	0.993986i	$0.465071\pi$
$440$	−4.83492	−	16.5935i	−0.230496	−	0.791064i
$441$	0.185972	+	20.9992i	0.00885582	+	0.999961i
$442$	11.0569	−	24.1671i	0.525925	−	1.14951i
$443$	24.9578	−	14.4094i	1.18578	−	0.684611i	0.228436	−	0.973559i	$-0.426639\pi$
$443$	24.9578	−	14.4094i	1.18578	−	0.684611i	0.957345	+	0.288948i	$0.0933055\pi$
$444$	−16.5951	+	11.1732i	−0.787570	+	0.530255i
$445$	−11.3888	−	6.57531i	−0.539879	−	0.311699i
$446$	1.62734	+	17.1677i	0.0770567	+	0.812915i
$447$	−1.40881	−	3.29945i	−0.0666347	−	0.156058i
$448$	−21.0728	−	1.98400i	−0.995597	−	0.0937352i
$449$			1.27217i			0.0600373i	0.999549	+	0.0300186i	$0.00955666\pi$
$449$			1.27217i			0.0600373i	−0.999549	+	0.0300186i	$0.990443\pi$
$450$	−8.11688	+	10.2624i	−0.382634	+	0.483776i
$451$	1.09797	−	1.90174i	0.0517015	−	0.0895496i
$452$	−6.18337	−	32.3229i	−0.290841	−	1.52034i
$453$	−32.4223	−	24.3241i	−1.52333	−	1.14285i
$454$	20.1886	+	9.23669i	0.947497	+	0.433499i
$455$	23.3485	+	3.22660i	1.09459	+	0.151265i
$456$	9.87680	+	12.0385i	0.462523	+	0.563756i
$457$	7.46471	+	12.9293i	0.349185	+	0.604805i	0.986105	−	0.166124i	$-0.0531253\pi$
$457$	7.46471	+	12.9293i	0.349185	+	0.604805i	−0.636920	+	0.770930i	$0.719792\pi$
$458$	−13.9599	+	9.92624i	−0.652302	+	0.463823i
$459$	−9.62299	−	11.7297i	−0.449163	−	0.547495i
$460$	−3.35801	+	9.65908i	−0.156568	+	0.450357i
$461$	−27.1371			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$461$	−27.1371			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$462$	−10.0982	−	26.7685i	−0.469813	−	1.24539i
$463$			24.3062i			1.12960i	0.825227	+	0.564801i	$0.191047\pi$
$463$			24.3062i			1.12960i	−0.825227	+	0.564801i	$0.808953\pi$
$464$	−24.8291	+	9.86046i	−1.15266	+	0.457760i
$465$	−0.721366	+	5.98009i	−0.0334525	+	0.277320i
$466$	6.73248	−	4.78716i	0.311876	−	0.221761i
$467$	22.2686	−	12.8568i	1.03047	−	0.594940i	0.113349	−	0.993555i	$-0.463842\pi$
$467$	22.2686	−	12.8568i	1.03047	−	0.594940i	0.917118	+	0.398615i	$0.130509\pi$
$468$	−1.97165	+	38.5661i	−0.0911395	+	1.78272i
$469$	16.5089	−	6.71430i	0.762311	−	0.310038i
$470$	2.58988	−	5.66069i	0.119462	−	0.261108i
$471$	30.9188	+	23.1961i	1.42466	+	1.06882i
$472$	21.0096	+	5.14305i	0.967045	+	0.236728i
$473$	3.31047	+	1.91130i	0.152216	+	0.0878817i
$474$	−4.10174	+	2.23046i	−0.188399	+	0.102449i
$475$	9.80275			0.449781
$476$	−8.40622	−	12.9634i	−0.385298	−	0.594175i
$477$	17.1338	−	17.8942i	0.784504	−	0.819319i
$478$	31.8427	−	3.01839i	1.45645	−	0.138058i
$479$	4.48448	−	7.76735i	0.204901	−	0.354899i	−0.745200	−	0.666841i	$-0.767646\pi$
$479$	4.48448	−	7.76735i	0.204901	−	0.354899i	0.950101	+	0.311942i	$0.100979\pi$
$480$	10.4191	+	8.68197i	0.475564	+	0.396276i
$481$	18.5849	+	32.1900i	0.847399	+	1.46774i
$482$	−14.9988	+	32.7828i	−0.683176	+	1.49321i
$483$	−4.30875	+	16.3701i	−0.196055	+	0.744865i
$484$	11.1002	+	12.8462i	0.504554	+	0.583916i
$485$	0.825074	+	1.42907i	0.0374647	+	0.0648908i
$486$	19.2858	+	10.6798i	0.874820	+	0.484447i
$487$	5.02256	+	2.89978i	0.227594	+	0.131401i	0.609462	−	0.792816i	$-0.291386\pi$
$487$	5.02256	+	2.89978i	0.227594	+	0.131401i	−0.381868	+	0.924217i	$0.624719\pi$
$488$	6.76073	−	7.06106i	0.306044	−	0.319639i
$489$	11.5630	+	27.0805i	0.522896	+	1.22462i
$490$	8.86667	−	10.4474i	0.400555	−	0.471965i
$491$		−	13.5893i		−	0.613275i	−0.951826	−	0.306637i	$-0.900796\pi$
$491$		−	13.5893i		−	0.613275i	0.951826	−	0.306637i	$-0.0992039\pi$
$492$	0.118748	+	1.71904i	0.00535357	+	0.0775003i
$493$	−16.8885	−	9.75058i	−0.760620	−	0.439144i
$494$	23.5783	−	16.7655i	1.06084	−	0.754314i
$495$	−4.35926	+	17.8061i	−0.195934	+	0.800325i
$496$	−9.94331	−	1.45772i	−0.446468	−	0.0654535i
$497$	−3.97752	−	3.09286i	−0.178416	−	0.138734i
$498$	−0.437906	+	17.1424i	−0.0196230	+	0.768169i
$499$	18.6144	+	32.2411i	0.833294	+	1.44331i	0.895412	+	0.445239i	$0.146881\pi$
$499$	18.6144	+	32.2411i	0.833294	+	1.44331i	−0.0621178	+	0.998069i	$0.519785\pi$
$500$	21.9810	−	4.20497i	0.983021	−	0.188052i
$501$	−41.1225	−	4.96053i	−1.83722	−	0.221620i
$502$	−0.148147	−	1.56288i	−0.00661210	−	0.0697548i
$503$	−24.5224			−1.09340			−0.546699	−	0.837329i	$-0.684116\pi$
$503$	−24.5224			−1.09340			−0.546699	+	0.837329i	$0.684116\pi$
$504$	18.3042	+	12.9984i	0.815332	+	0.578993i
$505$	2.86710			0.127584
$506$	−2.17629	−	22.9589i	−0.0967480	−	1.02065i
$507$	48.8761	+	5.89582i	2.17066	+	0.261843i
$508$	−0.869418	−	4.54478i	−0.0385742	−	0.201642i
$509$	21.4381	+	37.1319i	0.950226	+	1.64584i	0.744932	+	0.667140i	$0.232482\pi$
$509$	21.4381	+	37.1319i	0.950226	+	1.64584i	0.205294	+	0.978700i	$0.434185\pi$
$510$	−0.252812	+	9.89665i	−0.0111947	+	0.438231i
$511$	−15.8575	+	6.44936i	−0.701494	+	0.285303i
$512$	−14.9240	+	17.0081i	−0.659552	+	0.751659i
$513$	−2.68766	−	16.2961i	−0.118663	−	0.719492i
$514$	−16.0907	+	11.4414i	−0.709732	+	0.504659i
$515$	6.64470	+	3.83632i	0.292800	+	0.169048i
$516$	−2.99243	+	0.206711i	−0.131734	+	0.00909995i
$517$			14.0386i			0.617416i
$518$	21.5891	+	0.924909i	0.948571	+	0.0406382i
$519$	5.96415	+	13.9681i	0.261797	+	0.613129i
$520$	17.4262	−	18.2004i	0.764191	−	0.798139i
$521$	−1.58214	−	0.913450i	−0.0693149	−	0.0400190i	0.464942	−	0.885341i	$-0.346075\pi$
$521$	−1.58214	−	0.913450i	−0.0693149	−	0.0400190i	−0.534257	+	0.845322i	$0.679409\pi$
$522$	28.0362	+	4.11080i	1.22711	+	0.179925i
$523$	12.7145	+	22.0222i	0.555966	+	0.962962i	0.997828	+	0.0658788i	$0.0209851\pi$
$523$	12.7145	+	22.0222i	0.555966	+	0.962962i	−0.441861	+	0.897083i	$0.645682\pi$
$524$	7.18859	−	6.21156i	0.314035	−	0.271353i
$525$	13.6349	−	3.71824i	0.595075	−	0.162277i
$526$	−8.33708	+	18.2223i	−0.363514	+	0.794530i
$527$	−3.66790	−	6.35300i	−0.159776	−	0.276741i
$528$	−29.5127	−	8.02869i	−1.28438	−	0.349404i
$529$	4.67750	−	8.10166i	0.203369	−	0.352246i
$530$	−16.0935	+	1.52551i	−0.699055	+	0.0662639i
$531$	−16.5707	−	15.8666i	−0.719107	−	0.688551i
$532$	−0.869054	−	16.7969i	−0.0376783	−	0.728237i
$533$	3.20148			0.138671
$534$	−20.4444	+	11.1173i	−0.884715	+	0.481095i
$535$	7.16348	+	4.13584i	0.309704	+	0.178808i
$536$	4.53022	−	18.5062i	0.195676	−	0.799345i
$537$	−8.42572	−	6.32121i	−0.363597	−	0.272780i
$538$	−10.7205	+	23.4317i	−0.462192	+	1.01021i
$539$	−8.38092	+	29.7441i	−0.360992	+	1.28117i
$540$	−4.96593	−	13.5006i	−0.213700	−	0.580971i
$541$	−16.3531	+	9.44148i	−0.703076	+	0.405921i	−0.808492	−	0.588507i	$-0.799716\pi$
$541$	−16.3531	+	9.44148i	−0.703076	+	0.405921i	0.105416	+	0.994428i	$0.466382\pi$
$542$	−29.1826	+	20.7505i	−1.25350	+	0.891309i
$543$	−2.40238	+	19.9156i	−0.103096	+	0.854662i
$544$	−16.4956	−	0.842959i	−0.707243	−	0.0361416i
$545$		−	2.29512i		−	0.0983119i
$546$	26.4364	−	32.2629i	1.13137	−	1.38072i
$547$	13.0624			0.558509			0.279254	−	0.960217i	$-0.409913\pi$
$547$	13.0624			0.558509			0.279254	+	0.960217i	$0.409913\pi$
$548$	0.634247	+	0.220498i	0.0270937	+	0.00941919i
$549$	−9.95488	+	2.90036i	−0.424864	+	0.123784i
$550$	−15.6917	+	11.1577i	−0.669097	+	0.475765i
$551$	−10.6145	−	18.3849i	−0.452195	−	0.783224i
$552$	11.4782	+	13.9904i	0.488544	+	0.595472i
$553$	4.99558	+	0.690356i	0.212434	+	0.0293569i
$554$	−24.1782	−	11.0620i	−1.02723	−	0.469981i
$555$	−11.0756	−	8.30921i	−0.470133	−	0.352706i
$556$	−18.3750	+	3.51514i	−0.779274	+	0.149075i
$557$	15.9928	−	27.7003i	0.677635	−	1.17370i	−0.298056	−	0.954549i	$-0.596338\pi$
$557$	15.9928	−	27.7003i	0.677635	−	1.17370i	0.975691	−	0.219151i	$-0.0703286\pi$
$558$	8.36030	+	6.61242i	0.353920	+	0.279926i
$559$			5.57299i			0.235712i
$560$	−3.49217	−	14.2265i	−0.147571	−	0.601181i
$561$	−8.76714	−	20.5327i	−0.370149	−	0.866890i
$562$	−3.40193	−	35.8889i	−0.143502	−	1.51388i
$563$	−31.2546	−	18.0449i	−1.31723	−	0.760501i	−0.333944	−	0.942593i	$-0.608380\pi$
$563$	−31.2546	−	18.0449i	−1.31723	−	0.760501i	−0.983281	+	0.182092i	$0.941713\pi$
$564$	−6.15232	−	9.13782i	−0.259059	−	0.384772i
$565$	19.7247	−	11.3881i	0.829825	−	0.479100i
$566$	7.08224	−	15.4796i	0.297689	−	0.650656i
$567$	−9.91956	−	21.6472i	−0.416582	−	0.909098i
$568$	−5.17133	+	1.50679i	−0.216984	+	0.0632236i
$569$	23.5336	−	13.5871i	0.986579	−	0.569601i	0.0823288	−	0.996605i	$-0.473764\pi$
$569$	23.5336	−	13.5871i	0.986579	−	0.569601i	0.904250	+	0.427004i	$0.140431\pi$
$570$	−5.62512	+	9.19257i	−0.235610	+	0.385034i
$571$	−7.45448	+	12.9115i	−0.311960	+	0.540331i	−0.978787	−	0.204882i	$-0.934319\pi$
$571$	−7.45448	+	12.9115i	−0.311960	+	0.540331i	0.666826	+	0.745213i	$0.267652\pi$
$572$	−18.6601	+	53.6745i	−0.780218	+	2.24424i
$573$	−1.02982	−	2.41185i	−0.0430215	−	0.100756i
$574$	0.998738	−	1.57054i	0.0416865	−	0.0655530i
$575$	11.3921			0.475084
$576$	22.7286	−	7.70783i	0.947025	−	0.321159i
$577$	−19.1659	+	33.1963i	−0.797886	+	1.38198i	0.123104	+	0.992394i	$0.460715\pi$
$577$	−19.1659	+	33.1963i	−0.797886	+	1.38198i	−0.920990	+	0.389585i	$0.872618\pi$
$578$	6.94511	+	9.76733i	0.288878	+	0.406267i
$579$	16.5853	−	22.1070i	0.689262	−	0.918737i
$580$	−12.0887	−	13.9902i	−0.501958	−	0.580912i
$581$	11.3696	−	14.6217i	0.471691	−	0.606611i
$582$	2.91919	+	0.0745713i	0.121004	+	0.00309108i
$583$	31.5722	−	18.2282i	1.30759	−	0.754935i
$584$	−4.35146	+	17.7759i	−0.180065	+	0.735573i
$585$	−25.6594	+	7.47588i	−1.06089	+	0.309090i
$586$	5.49735	−	0.521097i	0.227093	−	0.0215263i
$587$			0.964880i			0.0398249i	0.999802	+	0.0199124i	$0.00633874\pi$
$587$			0.964880i			0.0398249i	−0.999802	+	0.0199124i	$0.993661\pi$
$588$	−7.57995	−	23.0335i	−0.312592	−	0.949888i
$589$		−	7.98581i		−	0.329050i
$590$	1.41268	+	14.9031i	0.0581591	+	0.613553i
$591$	−1.65599	−	0.199758i	−0.0681182	−	0.00821696i
$592$	14.3302	−	18.1190i	0.588967	−	0.744684i
$593$	14.9519	−	8.63251i	0.614003	−	0.354495i	−0.160528	−	0.987031i	$-0.551320\pi$
$593$	14.9519	−	8.63251i	0.614003	−	0.354495i	0.774530	+	0.632537i	$0.217986\pi$
$594$	22.8508	+	23.0268i	0.937581	+	0.944802i
$595$	6.56390	−	8.44141i	0.269094	−	0.346064i
$596$	2.70852	+	3.13455i	0.110945	+	0.128396i
$597$	2.76119	+	2.07152i	0.113008	+	0.0847818i
$598$	27.4012	−	19.4837i	1.12052	−	0.796749i
$599$	−6.22127	+	10.7756i	−0.254194	+	0.440277i	−0.964676	−	0.263438i	$-0.915144\pi$
$599$	−6.22127	+	10.7756i	−0.254194	+	0.440277i	0.710482	+	0.703715i	$0.248477\pi$
$600$	5.32408	−	14.1394i	0.217355	−	0.577239i
$601$	−27.7052			−1.13012			−0.565059	−	0.825051i	$-0.691147\pi$
$601$	−27.7052			−1.13012			−0.565059	+	0.825051i	$0.691147\pi$
$602$	2.73392	+	1.73856i	0.111426	+	0.0708583i
$603$	−13.9760	+	14.5962i	−0.569146	+	0.594403i
$604$	44.2073	+	15.3688i	1.79877	+	0.625348i
$605$	−5.87504	+	10.1759i	−0.238854	+	0.413708i
$606$	2.64822	−	4.32772i	0.107577	−	0.175802i
$607$	5.43950	−	3.14050i	0.220783	−	0.127469i	−0.385530	−	0.922695i	$-0.625981\pi$
$607$	5.43950	−	3.14050i	0.220783	−	0.127469i	0.606313	+	0.795226i	$0.292648\pi$
$608$	−15.0926	−	9.77331i	−0.612085	−	0.396360i
$609$	−21.7375	−	21.5459i	−0.880850	−	0.873083i
$610$	6.15241	+	2.81486i	0.249104	+	0.113970i
$611$	−17.7249	+	10.2335i	−0.717072	+	0.414002i
$612$	14.7049	+	9.52273i	0.594411	+	0.384934i
$613$	−17.0190	−	9.82590i	−0.687389	−	0.396864i	0.115244	−	0.993337i	$-0.463235\pi$
$613$	−17.0190	−	9.82590i	−0.687389	−	0.396864i	−0.802633	+	0.596473i	$0.796568\pi$
$614$	15.5347	−	1.47255i	0.626930	−	0.0594271i
$615$	−1.09678	+	0.468307i	−0.0442263	+	0.0188840i
$616$	20.5097	+	25.8984i	0.826358	+	1.04348i
$617$			32.2579i			1.29865i	0.760509	+	0.649327i	$0.224949\pi$
$617$			32.2579i			1.29865i	−0.760509	+	0.649327i	$0.775051\pi$
$618$	11.9281	−	6.48634i	0.479820	−	0.260919i
$619$	13.3846	−	23.1828i	0.537973	−	0.931797i	−0.461040	−	0.887379i	$-0.652524\pi$
$619$	13.3846	−	23.1828i	0.537973	−	0.931797i	0.999013	−	0.0444173i	$-0.0141431\pi$
$620$	−1.30685	−	6.83139i	−0.0524842	−	0.274355i
$621$	−3.12343	−	18.9383i	−0.125339	−	0.759968i
$622$	−18.4224	+	40.2657i	−0.738671	+	1.61451i
$623$	24.8996	+	3.44096i	0.997581	+	0.137859i
$624$	−11.3765	−	43.1148i	−0.455424	−	1.72597i
$625$	0.0343418	+	0.0594818i	0.00137367	+	0.00237927i
$626$	−10.7041	−	15.0538i	−0.427820	−	0.601670i
$627$	2.91068	−	24.1294i	0.116241	−	0.963635i
$628$	−42.1573	−	14.6561i	−1.68226	−	0.584843i
$629$	16.8627			0.672361
$630$	−4.33732	+	14.9198i	−0.172803	+	0.594419i
$631$			29.4363i			1.17184i	0.810369	+	0.585920i	$0.199267\pi$
$631$			29.4363i			1.17184i	−0.810369	+	0.585920i	$0.800733\pi$
$632$	3.72848	−	3.89411i	0.148311	−	0.154899i
$633$	−36.8966	−	4.45076i	−1.46651	−	0.176902i
$634$	−20.0481	−	28.1949i	−0.796213	−	1.11976i
$635$	2.77341	−	1.60123i	0.110059	−	0.0635428i
$636$	−12.5622	+	25.7012i	−0.498123	+	1.01912i
$637$	−43.6637	+	11.1004i	−1.73002	+	0.439815i
$638$	37.9173	+	17.3479i	1.50116	+	0.686811i
$639$	5.54924	+	1.35855i	0.219524	+	0.0537436i
$640$	−14.5102	−	5.89066i	−0.573565	−	0.232849i
$641$	−34.2214	−	19.7578i	−1.35167	−	0.780384i	−0.363183	−	0.931718i	$-0.618310\pi$
$641$	−34.2214	−	19.7578i	−1.35167	−	0.780384i	−0.988483	+	0.151334i	$0.951643\pi$
$642$	12.8594	−	6.99276i	0.507521	−	0.275982i
$643$	17.3857			0.685626			0.342813	−	0.939404i	$-0.388620\pi$
$643$	17.3857			0.685626			0.342813	+	0.939404i	$0.388620\pi$
$644$	−1.00996	−	19.5203i	−0.0397979	−	0.769206i
$645$	−0.815208	−	1.90922i	−0.0320988	−	0.0751754i
$646$	−1.23859	−	13.0666i	−0.0487316	−	0.514098i
$647$	−23.6414	+	40.9480i	−0.929438	+	1.60983i	−0.145174	+	0.989406i	$0.546374\pi$
$647$	−23.6414	+	40.9480i	−0.929438	+	1.60983i	−0.784264	+	0.620427i	$0.786959\pi$
$648$	−24.9651	−	4.97411i	−0.980723	−	0.195402i
$649$	−16.8800	−	29.2370i	−0.662598	−	1.14765i
$650$	−25.5260	−	11.6787i	−1.00121	−	0.458075i
$651$	−3.02907	−	11.1077i	−0.118718	−	0.435343i
$652$	−22.2305	−	25.7271i	−0.870612	−	1.00755i
$653$	−14.1939	−	24.5845i	−0.555449	−	0.962067i	−0.997868	−	0.0652581i	$-0.979213\pi$
$653$	−14.1939	−	24.5845i	−0.555449	−	0.962067i	0.442419	−	0.896808i	$-0.354120\pi$
$654$	−3.46434	−	2.11990i	−0.135467	−	0.0828948i
$655$	5.69432	+	3.28762i	0.222495	+	0.128458i
$656$	−0.734387	−	1.84922i	−0.0286730	−	0.0721998i
$657$	13.4245	−	14.0202i	0.523739	−	0.546981i
$658$	−0.509285	+	11.8877i	−0.0198540	+	0.463429i
$659$		−	3.58703i		−	0.139731i	−0.997556	−	0.0698654i	$-0.977743\pi$
$659$		−	3.58703i		−	0.139731i	0.997556	−	0.0698654i	$-0.0222570\pi$
$660$	−1.45876	−	21.1176i	−0.0567823	−	0.822001i
$661$	−1.09189	−	0.630403i	−0.0424696	−	0.0245198i	0.478615	−	0.878025i	$-0.341139\pi$
$661$	−1.09189	−	0.630403i	−0.0424696	−	0.0245198i	−0.521084	+	0.853505i	$0.674472\pi$
$662$	11.9039	+	16.7412i	0.462659	+	0.650665i
$663$	19.5334	−	26.0366i	0.758613	−	1.01118i
$664$	−5.53910	−	19.0103i	−0.214959	−	0.737741i
$665$	10.7829	−	4.38548i	0.418142	−	0.170062i
$666$	−22.7723	+	9.04309i	−0.882411	+	0.350413i
$667$	−12.3355	−	21.3658i	−0.477634	−	0.827286i
$668$	46.9766	−	8.98663i	1.81758	−	0.347703i
$669$	−2.52936	+	20.9683i	−0.0977909	+	0.810682i
$670$	13.1273	−	1.24435i	0.507154	−	0.0480734i
$671$	−15.2581			−0.589031
$672$	−24.6997	−	7.86923i	−0.952812	−	0.303562i
$673$	34.9662			1.34785			0.673925	−	0.738800i	$-0.264607\pi$
$673$	34.9662			1.34785			0.673925	+	0.738800i	$0.264607\pi$
$674$	26.4620	−	2.50835i	1.01928	−	0.0966182i
$675$	−12.3893	+	10.1641i	−0.476863	+	0.391216i
$676$	−55.8339	+	10.6810i	−2.14746	+	0.410809i
$677$	−2.84885	−	4.93435i	−0.109490	−	0.189642i	0.806074	−	0.591815i	$-0.201588\pi$
$677$	−2.84885	−	4.93435i	−0.109490	−	0.189642i	−0.915564	+	0.402173i	$0.868255\pi$
$678$	1.02927	−	40.2920i	0.0395288	−	1.54741i
$679$	−2.48994	−	1.93614i	−0.0955551	−	0.0743021i
$680$	−3.19783	−	10.9750i	−0.122631	−	0.420872i
$681$	21.7503	+	16.3177i	0.833474	+	0.625295i
$682$	9.08960	+	12.7833i	0.348059	+	0.489496i
$683$	19.9548	+	11.5209i	0.763551	+	0.440836i	0.830569	−	0.556915i	$-0.188015\pi$
$683$	19.9548	+	11.5209i	0.763551	+	0.440836i	−0.0670183	+	0.997752i	$0.521349\pi$
$684$	8.67996	+	16.9816i	0.331887	+	0.649307i
$685$			0.464729i			0.0177564i
$686$	−8.17589	+	24.8828i	−0.312157	+	0.950031i
$687$	−19.2937	+	8.23812i	−0.736100	+	0.314304i
$688$	3.21904	−	1.27839i	0.122725	−	0.0487380i
$689$	46.0293	+	26.5750i	1.75358	+	1.01243i
$690$	−6.53715	+	10.6830i	−0.248865	+	0.406695i
$691$	−18.0614	−	31.2833i	−0.687090	−	1.19007i	−0.972775	−	0.231751i	$-0.925555\pi$
$691$	−18.0614	−	31.2833i	−0.687090	−	1.19007i	0.285686	−	0.958323i	$-0.407779\pi$
$692$	−11.4664	−	13.2700i	−0.435887	−	0.504448i
$693$	−5.10389	−	34.6662i	−0.193881	−	1.31686i
$694$	30.7996	+	14.0915i	1.16914	+	0.534904i
$695$	−6.47392	−	11.2132i	−0.245570	−	0.425339i
$696$	−32.2833	+	5.32509i	−1.22369	+	0.201847i
$697$	0.726203	−	1.25782i	0.0275069	−	0.0476434i
$698$	0.479672	+	5.06033i	0.0181558	+	0.191536i
$699$	9.30483	−	3.97302i	0.351941	−	0.150274i
$700$	−13.6923	+	8.87890i	−0.517520	+	0.335591i
$701$	29.8672			1.12807			0.564035	−	0.825751i	$-0.309248\pi$
$701$	29.8672			1.12807			0.564035	+	0.825751i	$0.309248\pi$
$702$	−12.4161	+	45.6365i	−0.468615	+	1.72244i
$703$	15.8975	+	9.17844i	0.599586	+	0.346171i
$704$	35.2835	−	1.53406i	1.32980	−	0.0578169i
$705$	4.57533	−	6.09858i	0.172317	−	0.229686i
$706$	−33.3525	−	15.2595i	−1.25524	−	0.574298i
$707$	−5.07641	+	2.06461i	−0.190918	+	0.0776478i
$708$	23.8003	+	11.6331i	0.894469	+	0.437197i
$709$	42.5302	−	24.5548i	1.59725	−	0.922175i	0.605240	−	0.796043i	$-0.293077\pi$
$709$	42.5302	−	24.5548i	1.59725	−	0.922175i	0.992013	−	0.126132i	$-0.0402564\pi$
$710$	−2.16028	−	3.03814i	−0.0810740	−	0.114019i
$711$	−5.49002	+	1.59952i	−0.205892	+	0.0599868i
$712$	18.5839	−	19.4095i	0.696462	−	0.727401i
$713$		−	9.28059i		−	0.347561i
$714$	−6.67902	−	17.7048i	−0.249956	−	0.662586i
$715$	−39.3287			−1.47081
$716$	11.4883	+	3.99396i	0.429340	+	0.149261i
$717$	38.8921	+	4.69147i	1.45245	+	0.175206i
$718$	23.2347	+	32.6763i	0.867109	+	1.21947i
$719$	−8.31324	−	14.3990i	−0.310032	−	0.536991i	0.668337	−	0.743858i	$-0.267006\pi$
$719$	−8.31324	−	14.3990i	−0.310032	−	0.536991i	−0.978369	+	0.206868i	$0.933673\pi$
$720$	10.2042	+	13.1063i	0.380287	+	0.488444i
$721$	−14.5275	−	2.00760i	−0.541032	−	0.0747670i
$722$	−5.23464	+	11.4413i	−0.194813	+	0.425801i
$723$	−26.4971	+	35.3187i	−0.985437	+	1.31352i
$724$	−4.35222	−	22.7507i	−0.161749	−	0.845525i
$725$	−10.2989	+	17.8381i	−0.382490	+	0.662492i
$726$	9.93335	+	18.2671i	0.368661	+	0.677954i
$727$			6.37182i			0.236318i	0.992995	+	0.118159i	$0.0376992\pi$
$727$			6.37182i			0.236318i	−0.992995	+	0.118159i	$0.962301\pi$
$728$	−17.7483	+	44.7739i	−0.657795	+	1.65943i
$729$	20.2936	+	17.8092i	0.751616	+	0.659601i
$730$	−12.6093	+	1.19525i	−0.466693	+	0.0442381i
$731$	2.18956	+	1.26414i	0.0809837	+	0.0467560i
$732$	9.93159	−	6.68674i	0.367082	−	0.247149i
$733$	−33.2648	+	19.2054i	−1.22866	+	0.709369i	−0.966750	−	0.255723i	$-0.917686\pi$
$733$	−33.2648	+	19.2054i	−1.22866	+	0.709369i	−0.261912	+	0.965092i	$0.584353\pi$
$734$	−4.61819	−	2.11292i	−0.170461	−	0.0779893i
$735$	13.3347	−	10.1899i	0.491859	−	0.375859i
$736$	−17.5396	−	11.3579i	−0.646519	−	0.418658i
$737$	−25.7533	+	14.8687i	−0.948634	+	0.547694i
$738$	−0.306164	+	2.08808i	−0.0112701	+	0.0768631i
$739$	0.546366	−	0.946333i	0.0200984	−	0.0348114i	−0.855801	−	0.517305i	$-0.826935\pi$
$739$	0.546366	−	0.946333i	0.0200984	−	0.0348114i	0.875900	+	0.482493i	$0.160269\pi$
$740$	15.1014	+	5.25005i	0.555139	+	0.192996i
$741$	32.5871	−	13.9142i	1.19712	−	0.511151i
$742$	27.3962	−	14.2900i	1.00574	−	0.524603i
$743$	−26.5914			−0.975545			−0.487772	−	0.872971i	$-0.662190\pi$
$743$	−26.5914			−0.975545			−0.487772	+	0.872971i	$0.662190\pi$
$744$	−11.5187	−	4.33727i	−0.422295	−	0.159012i
$745$	−1.43355	+	2.48298i	−0.0525212	+	0.0909693i
$746$	17.8785	−	12.7126i	0.654578	−	0.465441i
$747$	−4.99416	+	20.3995i	−0.182727	+	0.746378i
$748$	16.8553	+	19.5065i	0.616291	+	0.713228i
$749$	−15.6617	−	2.16435i	−0.572267	−	0.0790835i
$750$	27.4004	+	0.699949i	1.00052	+	0.0255585i
$751$	24.4781	−	14.1324i	0.893217	−	0.515699i	0.0182235	−	0.999834i	$-0.494199\pi$
$751$	24.4781	−	14.1324i	0.893217	−	0.515699i	0.874993	+	0.484135i	$0.160866\pi$
$752$	9.97689	+	7.89068i	0.363820	+	0.287743i
$753$	0.230263	−	1.90887i	0.00839127	−	0.0695632i
$754$	5.73668	+	60.5195i	0.208918	+	2.20399i
$755$			32.3918i			1.17886i
$756$	18.5144	+	20.3277i	0.673362	+	0.739313i
$757$		−	26.8780i		−	0.976898i	−0.872592	−	0.488449i	$-0.837563\pi$
$757$		−	26.8780i		−	0.976898i	0.872592	−	0.488449i	$-0.162437\pi$
$758$	20.5340	−	1.94643i	0.745828	−	0.0706975i
$759$	3.38260	−	28.0416i	0.122781	−	1.01785i
$760$	2.95894	−	12.0874i	0.107332	−	0.438456i
$761$	−46.8523	+	27.0502i	−1.69840	+	0.980569i	−0.751111	+	0.660176i	$0.770482\pi$
$761$	−46.8523	+	27.0502i	−1.69840	+	0.980569i	−0.947285	+	0.320393i	$0.896185\pi$
$762$	0.144721	−	5.66529i	0.00524269	−	0.205232i
$763$	1.65273	+	4.06367i	0.0598327	+	0.147115i
$764$	1.97989	+	2.29131i	0.0716299	+	0.0828967i
$765$	−2.88323	+	11.7770i	−0.104243	+	0.425799i
$766$	8.97142	+	12.6170i	0.324150	+	0.455872i
$767$	24.6095	−	42.6248i	0.888596	−	1.53909i
$768$	−22.2941	+	16.4613i	−0.804467	+	0.593997i
$769$	−9.44304			−0.340525			−0.170262	−	0.985399i	$-0.554462\pi$
$769$	−9.44304			−0.340525			−0.170262	+	0.985399i	$0.554462\pi$
$770$	−12.2690	+	19.2933i

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)

\(f(q)\)	\(=\)	\(q+(-1.40790 + 0.133456i) q^{2} +(-1.71959 - 0.207430i) q^{3} +(1.96438 - 0.375786i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(-2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(2.91395 + 0.713387i) q^{9} +O(q^{10})\)	\(q+(-1.40790 + 0.133456i) q^{2} +(-1.71959 - 0.207430i) q^{3} +(1.96438 - 0.375786i) q^{4} +(0.692094 + 1.19874i) q^{5} +(2.44869 + 0.0625523i) q^{6} +(-2.08863 - 1.62408i) q^{7} +(-2.71550 + 0.791228i) q^{8} +(2.91395 + 0.713387i) q^{9} +(-1.13438 - 1.59535i) q^{10} +(3.82316 + 2.20731i) q^{11} +(-3.45587 + 0.238725i) q^{12} +6.43609i q^{13} +(3.15733 + 2.00781i) q^{14} +(-0.941460 - 2.20490i) q^{15} +(3.71757 - 1.47637i) q^{16} +(2.52866 + 1.45992i) q^{17} +(-4.19776 - 0.615496i) q^{18} +(1.58928 + 2.75271i) q^{19} +(1.81001 + 2.09470i) q^{20} +(3.25469 + 3.22599i) q^{21} +(-5.67722 - 2.59745i) q^{22} +(1.84696 + 3.19902i) q^{23} +(4.83366 - 0.797307i) q^{24} +(1.54201 - 2.67084i) q^{25} +(-0.858934 - 9.06138i) q^{26} +(-4.86280 - 1.83117i) q^{27} +(-4.71316 - 2.40544i) q^{28} -6.67884 q^{29} +(1.61974 + 2.97864i) q^{30} +(-2.17580 - 1.25620i) q^{31} +(-5.03695 + 2.57472i) q^{32} +(-6.11640 - 4.58869i) q^{33} +(-3.75494 - 1.71796i) q^{34} +(0.501330 - 3.62774i) q^{35} +(5.99217 + 0.306343i) q^{36} +(5.00149 - 2.88761i) q^{37} +(-2.60492 - 3.66345i) q^{38} +(1.33504 - 11.0674i) q^{39} +(-2.82786 - 2.70758i) q^{40} -0.497427i q^{41} +(-5.01281 - 4.10752i) q^{42} +0.865898 q^{43} +(8.33962 + 2.89929i) q^{44} +(1.16156 + 3.98680i) q^{45} +(-3.02726 - 4.25743i) q^{46} +(1.59001 + 2.75398i) q^{47} +(-6.69892 + 1.76761i) q^{48} +(1.72472 + 6.78420i) q^{49} +(-1.81456 + 3.96608i) q^{50} +(-4.04541 - 3.03498i) q^{51} +(2.41859 + 12.6429i) q^{52} +(4.12906 - 7.15175i) q^{53} +(7.09073 + 1.92914i) q^{54} +6.11065i q^{55} +(6.95669 + 2.75762i) q^{56} +(-2.16191 - 5.06319i) q^{57} +(9.40316 - 0.891331i) q^{58} +(-6.62279 - 3.82367i) q^{59} +(-2.67795 - 3.97747i) q^{60} +(-2.99321 + 1.72813i) q^{61} +(3.23096 + 1.47823i) q^{62} +(-4.92754 - 6.22248i) q^{63} +(6.74792 - 4.29716i) q^{64} +(-7.71521 + 4.45438i) q^{65} +(9.22368 + 5.64416i) q^{66} +(-3.36806 + 5.83364i) q^{67} +(5.51586 + 1.91760i) q^{68} +(-2.51243 - 5.88411i) q^{69} +(-0.221680 + 5.17441i) q^{70} +1.90437 q^{71} +(-8.47728 + 0.368391i) q^{72} +(3.23515 - 5.60345i) q^{73} +(-6.65624 + 4.73295i) q^{74} +(-3.20563 + 4.27288i) q^{75} +(4.15638 + 4.81014i) q^{76} +(-4.40032 - 10.8194i) q^{77} +(-0.402592 + 15.7600i) q^{78} +(-1.65073 + 0.953048i) q^{79} +(4.34270 + 3.43462i) q^{80} +(7.98216 + 4.15754i) q^{81} +(0.0663845 + 0.700328i) q^{82} +7.00064i q^{83} +(7.60572 + 5.11400i) q^{84} +4.04161i q^{85} +(-1.21910 + 0.115559i) q^{86} +(11.4848 + 1.38539i) q^{87} +(-12.1283 - 2.96895i) q^{88} +(-8.22776 + 4.75030i) q^{89} +(-2.16742 - 5.45801i) q^{90} +(10.4527 - 13.4426i) q^{91} +(4.83027 + 5.59004i) q^{92} +(3.48090 + 2.61147i) q^{93} +(-2.60612 - 3.66514i) q^{94} +(-2.19986 + 3.81027i) q^{95} +(9.19553 - 3.38264i) q^{96} +1.19214 q^{97} +(-3.33362 - 9.32132i) q^{98} +(9.56583 + 9.15936i) 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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