LMFDB - Embedded newform 168.2.v.a.107.4

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			107.4
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32990 + 0.481016i) q^{2} +(1.28463 - 1.16178i) q^{3} +(1.53725 - 1.27940i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 + 2.16297i) q^{6} +(2.42742 + 1.05244i) q^{7} +(-1.42896 + 2.44091i) q^{8} +(0.300539 - 2.98491i) q^{9} +O(q^{10})$	\(q+(-1.32990 + 0.481016i) q^{2} +(1.28463 - 1.16178i) q^{3} +(1.53725 - 1.27940i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 + 2.16297i) q^{6} +(2.42742 + 1.05244i) q^{7} +(-1.42896 + 2.44091i) q^{8} +(0.300539 - 2.98491i) q^{9} +(0.321101 - 1.79988i) q^{10} +(1.60004 - 0.923782i) q^{11} +(0.488406 - 3.42950i) q^{12} -2.25432i q^{13} +(-3.73446 - 0.232013i) q^{14} +(0.470342 + 2.18925i) q^{15} +(0.726254 - 3.93352i) q^{16} +(3.89580 - 2.24924i) q^{17} +(1.03610 + 4.11418i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(0.438742 + 2.54811i) q^{20} +(4.34104 - 1.46812i) q^{21} +(-1.68353 + 1.99818i) q^{22} +(0.519880 - 0.900459i) q^{23} +(1.00011 + 4.79581i) q^{24} +(1.66433 + 2.88270i) q^{25} +(1.08436 + 2.99801i) q^{26} +(-3.08172 - 4.18366i) q^{27} +(5.07804 - 1.48778i) q^{28} -1.32085 q^{29} +(-1.67857 - 2.68523i) q^{30} +(-3.69700 + 2.13446i) q^{31} +(0.926243 + 5.58051i) q^{32} +(0.982223 - 3.04561i) q^{33} +(-4.09909 + 4.86521i) q^{34} +(-2.74740 + 2.03744i) q^{35} +(-3.35690 - 4.97305i) q^{36} +(-8.18394 - 4.72500i) q^{37} +(1.39513 - 7.82020i) q^{38} +(-2.61902 - 2.89596i) q^{39} +(-1.80916 - 3.17768i) q^{40} +1.39634i q^{41} +(-5.06694 + 4.04056i) q^{42} -6.02578 q^{43} +(1.27776 - 3.46717i) q^{44} +(3.14763 + 2.26593i) q^{45} +(-0.258251 + 1.44759i) q^{46} +(-5.90249 + 10.2234i) q^{47} +(-3.63691 - 5.89685i) q^{48} +(4.78472 + 5.10944i) q^{49} +(-3.60001 - 3.03313i) q^{50} +(2.39154 - 7.41551i) q^{51} +(-2.88418 - 3.46544i) q^{52} +(-6.02901 - 10.4425i) q^{53} +(6.11078 + 4.08147i) q^{54} +2.38854i q^{55} +(-6.03762 + 4.42122i) q^{56} +(2.04356 + 9.51192i) q^{57} +(1.75660 - 0.635353i) q^{58} +(-9.57732 + 5.52947i) q^{59} +(3.52396 + 2.76365i) q^{60} +(7.65220 + 4.41800i) q^{61} +(3.88991 - 4.61693i) q^{62} +(3.87098 - 6.92932i) q^{63} +(-3.91612 - 6.97596i) q^{64} +(2.52393 + 1.45719i) q^{65} +(0.158732 + 4.52281i) q^{66} +(3.05545 + 5.29219i) q^{67} +(3.11112 - 8.44195i) q^{68} +(-0.378281 - 1.76074i) q^{69} +(2.67372 - 4.03113i) q^{70} +14.0121 q^{71} +(6.85644 + 4.99892i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(13.1566 + 2.34715i) q^{74} +(5.48711 + 1.76962i) q^{75} +(1.90626 + 11.0711i) q^{76} +(4.85619 - 0.558456i) q^{77} +(4.87602 + 2.59153i) q^{78} +(2.37061 + 1.36867i) q^{79} +(3.93451 + 3.35575i) q^{80} +(-8.81935 - 1.79416i) q^{81} +(-0.671663 - 1.85699i) q^{82} +4.74366i q^{83} +(4.79492 - 7.81081i) q^{84} +5.81566i q^{85} +(8.01366 - 2.89850i) q^{86} +(-1.69681 + 1.53454i) q^{87} +(-0.0315236 + 5.22561i) q^{88} +(-8.31219 - 4.79904i) q^{89} +(-5.27598 - 1.49939i) q^{90} +(2.37254 - 5.47217i) q^{91} +(-0.352866 - 2.04936i) q^{92} +(-2.26949 + 7.03709i) q^{93} +(2.93207 - 16.4353i) q^{94} +(-3.63085 - 6.28882i) q^{95} +(7.67320 + 6.09279i) q^{96} -8.73466 q^{97} +(-8.82091 - 4.49350i) q^{98} +(-2.27653 - 5.05360i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.32990	+	0.481016i	−0.940378	+	0.340130i
$2$	−1.32990	+	0.481016i	−0.940378	+	0.340130i
$3$	1.28463	−	1.16178i	0.741680	−	0.670753i
$3$	1.28463	−	1.16178i	0.741680	−	0.670753i
$4$	1.53725	−	1.27940i	0.768623	−	0.639702i
$5$	−0.646402	+	1.11960i	−0.289080	+	0.500700i	−0.973590	−	0.228302i	$-0.926683\pi$
$5$	−0.646402	+	1.11960i	−0.289080	+	0.500700i	0.684511	+	0.729003i	$0.260016\pi$
$6$	−1.14959	+	2.16297i	−0.469317	+	0.883030i
$7$	2.42742	+	1.05244i	0.917478	+	0.397786i
$7$	2.42742	+	1.05244i	0.917478	+	0.397786i
$8$	−1.42896	+	2.44091i	−0.505215	+	0.862993i
$9$	0.300539	−	2.98491i	0.100180	−	0.994969i
$10$	0.321101	−	1.79988i	0.101541	−	0.569173i
$11$	1.60004	−	0.923782i	0.482430	−	0.278531i	−0.238999	−	0.971020i	$-0.576819\pi$
$11$	1.60004	−	0.923782i	0.482430	−	0.278531i	0.721428	+	0.692489i	$0.243486\pi$
$12$	0.488406	−	3.42950i	0.140991	−	0.990011i
$13$		−	2.25432i		−	0.625235i	−0.949879	−	0.312617i	$-0.898794\pi$
$13$		−	2.25432i		−	0.625235i	0.949879	−	0.312617i	$-0.101206\pi$
$14$	−3.73446	−	0.232013i	−0.998076	−	0.0620081i
$15$	0.470342	+	2.18925i	0.121442	+	0.565261i
$16$	0.726254	−	3.93352i	0.181564	−	0.983379i
$17$	3.89580	−	2.24924i	0.944871	−	0.545522i	0.0533874	−	0.998574i	$-0.482998\pi$
$17$	3.89580	−	2.24924i	0.944871	−	0.545522i	0.891484	+	0.453052i	$0.149665\pi$
$18$	1.03610	+	4.11418i	0.244212	+	0.969722i
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	0.340142	+	0.940374i	$0.389525\pi$
$19$	−2.80851	+	4.86448i	−0.644317	+	1.11599i	−0.984459	+	0.175615i	$0.943809\pi$
$20$	0.438742	+	2.54811i	0.0981056	+	0.569775i
$21$	4.34104	−	1.46812i	0.947292	−	0.320371i
$22$	−1.68353	+	1.99818i	−0.358930	+	0.426013i
$23$	0.519880	−	0.900459i	0.108402	−	0.187759i	−0.806721	−	0.590933i	$-0.798760\pi$
$23$	0.519880	−	0.900459i	0.108402	−	0.187759i	0.915123	+	0.403174i	$0.132093\pi$
$24$	1.00011	+	4.79581i	0.204148	+	0.978940i
$25$	1.66433	+	2.88270i	0.332866	+	0.576541i
$26$	1.08436	+	2.99801i	0.212661	+	0.587957i
$27$	−3.08172	−	4.18366i	−0.593078	−	0.805145i
$28$	5.07804	−	1.48778i	0.959660	−	0.281164i
$29$	−1.32085			−0.245277			−0.122638	−	0.992451i	$-0.539135\pi$
$29$	−1.32085			−0.245277			−0.122638	+	0.992451i	$0.539135\pi$
$30$	−1.67857	−	2.68523i	−0.306463	−	0.490253i
$31$	−3.69700	+	2.13446i	−0.664000	+	0.383361i	−0.793800	−	0.608179i	$-0.791900\pi$
$31$	−3.69700	+	2.13446i	−0.664000	+	0.383361i	0.129799	+	0.991540i	$0.458567\pi$
$32$	0.926243	+	5.58051i	0.163738	+	0.986504i
$33$	0.982223	−	3.04561i	0.170983	−	0.530172i
$34$	−4.09909	+	4.86521i	−0.702988	+	0.834376i
$35$	−2.74740	+	2.03744i	−0.464396	+	0.344390i
$36$	−3.35690	−	4.97305i	−0.559483	−	0.828842i
$37$	−8.18394	−	4.72500i	−1.34543	−	0.776786i	−0.357834	−	0.933785i	$-0.616484\pi$
$37$	−8.18394	−	4.72500i	−1.34543	−	0.776786i	−0.987599	+	0.157000i	$0.949818\pi$
$38$	1.39513	−	7.82020i	0.226320	−	1.26860i
$39$	−2.61902	−	2.89596i	−0.419378	−	0.463724i
$40$	−1.80916	−	3.17768i	−0.286054	−	0.502435i
$41$			1.39634i			0.218072i	0.994038	+	0.109036i	$0.0347764\pi$
$41$			1.39634i			0.218072i	−0.994038	+	0.109036i	$0.965224\pi$
$42$	−5.06694	+	4.04056i	−0.781845	+	0.623472i
$43$	−6.02578			−0.918922			−0.459461	−	0.888198i	$-0.651957\pi$
$43$	−6.02578			−0.918922			−0.459461	+	0.888198i	$0.651957\pi$
$44$	1.27776	−	3.46717i	0.192630	−	0.522696i
$45$	3.14763	+	2.26593i	0.469222	+	0.337785i
$46$	−0.258251	+	1.44759i	−0.0380770	+	0.213435i
$47$	−5.90249	+	10.2234i	−0.860966	+	1.49124i	0.0100312	+	0.999950i	$0.496807\pi$
$47$	−5.90249	+	10.2234i	−0.860966	+	1.49124i	−0.870997	+	0.491288i	$0.836526\pi$
$48$	−3.63691	−	5.89685i	−0.524943	−	0.851138i
$49$	4.78472	+	5.10944i	0.683532	+	0.729921i
$50$	−3.60001	−	3.03313i	−0.509119	−	0.428949i
$51$	2.39154	−	7.41551i	0.334882	−	1.03838i
$52$	−2.88418	−	3.46544i	−0.399964	−	0.480570i
$53$	−6.02901	−	10.4425i	−0.828148	−	1.43439i	−0.899489	−	0.436943i	$-0.856061\pi$
$53$	−6.02901	−	10.4425i	−0.828148	−	1.43439i	0.0713414	−	0.997452i	$-0.477272\pi$
$54$	6.11078	+	4.08147i	0.831571	+	0.555418i
$55$			2.38854i			0.322070i
$56$	−6.03762	+	4.42122i	−0.806811	+	0.590810i
$57$	2.04356	+	9.51192i	0.270676	+	1.25988i
$58$	1.75660	−	0.635353i	0.230653	−	0.0834259i
$59$	−9.57732	+	5.52947i	−1.24686	+	0.719875i	−0.970482	−	0.241174i	$-0.922468\pi$
$59$	−9.57732	+	5.52947i	−1.24686	+	0.719875i	−0.276378	+	0.961049i	$0.589134\pi$
$60$	3.52396	+	2.76365i	0.454941	+	0.356786i
$61$	7.65220	+	4.41800i	0.979764	+	0.565667i	0.902199	−	0.431320i	$-0.141952\pi$
$61$	7.65220	+	4.41800i	0.979764	+	0.565667i	0.0775652	+	0.996987i	$0.475285\pi$
$62$	3.88991	−	4.61693i	0.494019	−	0.586351i
$63$	3.87098	−	6.92932i	0.487698	−	0.873012i
$64$	−3.91612	−	6.97596i	−0.489515	−	0.871995i
$65$	2.52393	+	1.45719i	0.313055	+	0.180743i
$66$	0.158732	+	4.52281i	0.0195386	+	0.556719i
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	0.990068	−	0.140587i	$-0.0448989\pi$
$67$	3.05545	+	5.29219i	0.373283	+	0.646544i	−0.616786	+	0.787131i	$0.711566\pi$
$68$	3.11112	−	8.44195i	0.377279	−	1.02374i
$69$	−0.378281	−	1.76074i	−0.0455397	−	0.211968i
$70$	2.67372	−	4.03113i	0.319571	−	0.481812i
$71$	14.0121			1.66293			0.831464	−	0.555578i	$-0.187503\pi$
$71$	14.0121			1.66293			0.831464	+	0.555578i	$0.187503\pi$
$72$	6.85644	+	4.99892i	0.808040	+	0.589128i
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	−0.999879	−	0.0155626i	$-0.995046\pi$
$73$	−4.38664	−	7.59788i	−0.513417	−	0.889264i	0.486462	−	0.873702i	$-0.338287\pi$
$74$	13.1566	+	2.34715i	1.52942	+	0.272851i
$75$	5.48711	+	1.76962i	0.633597	+	0.204338i
$76$	1.90626	+	11.0711i	0.218663	+	1.26995i
$77$	4.85619	−	0.558456i	0.553414	−	0.0636420i
$78$	4.87602	+	2.59153i	0.552101	+	0.293433i
$79$	2.37061	+	1.36867i	0.266714	+	0.153987i	0.627393	−	0.778702i	$-0.284122\pi$
$79$	2.37061	+	1.36867i	0.266714	+	0.153987i	−0.360679	+	0.932690i	$0.617455\pi$
$80$	3.93451	+	3.35575i	0.439892	+	0.375184i
$81$	−8.81935	−	1.79416i	−0.979928	−	0.199352i
$82$	−0.671663	−	1.85699i	−0.0741728	−	0.205070i
$83$			4.74366i			0.520685i	0.965516	+	0.260342i	$0.0838354\pi$
$83$			4.74366i			0.520685i	−0.965516	+	0.260342i	$0.916165\pi$
$84$	4.79492	−	7.81081i	0.523169	−	0.852229i
$85$			5.81566i			0.630797i
$86$	8.01366	−	2.89850i	0.864135	−	0.312553i
$87$	−1.69681	+	1.53454i	−0.181917	+	0.164520i
$88$	−0.0315236	+	5.22561i	−0.00336043	+	0.557051i
$89$	−8.31219	−	4.79904i	−0.881090	−	0.508697i	−0.0100723	−	0.999949i	$-0.503206\pi$
$89$	−8.31219	−	4.79904i	−0.881090	−	0.508697i	−0.871018	+	0.491252i	$0.836539\pi$
$90$	−5.27598	−	1.49939i	−0.556137	−	0.158050i
$91$	2.37254	−	5.47217i	0.248710	−	0.573639i
$92$	−0.352866	−	2.04936i	−0.0367888	−	0.213661i
$93$	−2.26949	+	7.03709i	−0.235336	+	0.729712i
$94$	2.93207	−	16.4353i	0.302420	−	1.69517i
$95$	−3.63085	−	6.28882i	−0.372517	−	0.645219i
$96$	7.67320	+	6.09279i	0.783142	+	0.621843i
$97$	−8.73466			−0.886871			−0.443435	−	0.896306i	$-0.646240\pi$
$97$	−8.73466			−0.886871			−0.443435	+	0.896306i	$0.646240\pi$
$98$	−8.82091	−	4.49350i	−0.891046	−	0.453912i
$99$	−2.27653	−	5.05360i	−0.228800	−	0.507906i
$100$	6.24663	+	2.30208i	0.624663	+	0.230208i
$101$	3.42033	+	5.92419i	0.340336	+	0.589479i	0.984495	−	0.175413i	$-0.0561259\pi$
$101$	3.42033	+	5.92419i	0.340336	+	0.589479i	−0.644159	+	0.764891i	$0.722793\pi$
$102$	0.386485	+	11.0122i	0.0382677	+	1.09037i
$103$	−3.88733	−	2.24435i	−0.383030	−	0.221143i	0.296106	−	0.955155i	$-0.404312\pi$
$103$	−3.88733	−	2.24435i	−0.383030	−	0.221143i	−0.679136	+	0.734013i	$0.737645\pi$
$104$	5.50259	+	3.22134i	0.539574	+	0.315878i
$105$	−1.16234	+	5.80923i	−0.113433	+	0.566922i
$106$	13.0410	+	10.9875i	1.26665	+	1.06720i
$107$	6.27888	+	3.62511i	0.607002	+	0.350453i	0.771791	−	0.635876i	$-0.219361\pi$
$107$	6.27888	+	3.62511i	0.607002	+	0.350453i	−0.164789	+	0.986329i	$0.552694\pi$
$108$	−10.0900	−	2.48855i	−0.970906	−	0.239461i
$109$	10.6680	−	6.15916i	1.02181	−	0.589941i	0.107180	−	0.994240i	$-0.465818\pi$
$109$	10.6680	−	6.15916i	1.02181	−	0.589941i	0.914627	+	0.404299i	$0.132484\pi$
$110$	−1.14893	−	3.17651i	−0.109546	−	0.302868i
$111$	−16.0027	+	3.43806i	−1.51891	+	0.326326i
$112$	5.90273	−	8.78395i	0.557756	−	0.830005i
$113$		−	7.27566i		−	0.684437i	−0.939620	−	0.342218i	$-0.888822\pi$
$113$		−	7.27566i		−	0.684437i	0.939620	−	0.342218i	$-0.111178\pi$
$114$	−7.29311	−	11.6669i	−0.683063	−	1.09270i
$115$	0.672102	+	1.16412i	0.0626739	+	0.108554i
$116$	−2.03048	+	1.68991i	−0.188525	+	0.156904i
$117$	−6.72893	−	0.677511i	−0.622089	−	0.0626359i
$118$	10.0771	−	11.9605i	0.927669	−	1.10105i
$119$	11.8240	−	1.35974i	1.08390	−	0.124647i
$120$	−6.01586	−	1.98029i	−0.549171	−	0.180775i
$121$	−3.79325	+	6.57011i	−0.344841	+	0.597282i
$122$	−12.3018	−	2.19465i	−1.11375	−	0.198694i
$123$	1.62224	+	1.79378i	0.146272	+	0.161740i
$124$	−2.95236	+	8.01115i	−0.265130	+	0.719422i
$125$	−10.7673			−0.963058
$126$	−1.81489	+	11.0773i	−0.161683	+	0.986843i
$127$		−	21.7722i		−	1.93197i	−0.258595	−	0.965986i	$-0.583260\pi$
$127$		−	21.7722i		−	1.93197i	0.258595	−	0.965986i	$-0.416740\pi$
$128$	8.56359	+	7.39358i	0.756921	+	0.653506i
$129$	−7.74088	+	7.00062i	−0.681547	+	0.616370i
$130$	−4.05750	−	0.723863i	−0.355866	−	0.0634870i
$131$	−4.65916	−	2.68997i	−0.407073	−	0.235024i	0.282458	−	0.959280i	$-0.408850\pi$
$131$	−4.65916	−	2.68997i	−0.407073	−	0.235024i	−0.689531	+	0.724256i	$0.742183\pi$
$132$	−2.38664	−	5.93851i	−0.207730	−	0.516881i
$133$	−11.9370	+	8.85234i	−1.03507	+	0.767595i
$134$	−6.60906	−	5.56835i	−0.570936	−	0.481032i
$135$	6.67605	−	0.745974i	0.574583	−	0.0642033i
$136$	−0.0767544	+	12.7234i	−0.00658163	+	1.09102i
$137$	11.3713	−	6.56523i	0.971517	−	0.560905i	0.0718185	−	0.997418i	$-0.477120\pi$
$137$	11.3713	−	6.56523i	0.971517	−	0.560905i	0.899698	+	0.436512i	$0.143786\pi$
$138$	1.35002	+	2.15964i	0.114921	+	0.183841i
$139$	12.9760			1.10061			0.550307	−	0.834963i	$-0.314511\pi$
$139$	12.9760			1.10061			0.550307	+	0.834963i	$0.314511\pi$
$140$	−1.61673	+	6.64708i	−0.136639	+	0.561781i
$141$	4.29484	+	19.9907i	0.361691	+	1.68352i
$142$	−18.6346	+	6.74004i	−1.56378	+	0.565612i
$143$	−2.08250	−	3.60699i	−0.174147	−	0.301632i
$144$	−11.5229	−	3.34998i	−0.960243	−	0.279165i
$145$	0.853802	−	1.47883i	0.0709044	−	0.122810i
$146$	9.48848	+	7.99434i	0.785272	+	0.661617i
$147$	12.0826	+	1.00495i	0.996559	+	0.0828866i
$148$	−18.6259	+	3.20707i	−1.53104	+	0.263620i
$149$	3.42033	−	5.92419i	0.280205	−	0.485328i	−0.691230	−	0.722634i	$-0.742931\pi$
$149$	3.42033	−	5.92419i	0.280205	−	0.485328i	0.971435	+	0.237306i	$0.0762644\pi$
$150$	−8.14850	+	0.285980i	−0.665322	+	0.0233502i
$151$	3.16245	−	1.82584i	0.257356	−	0.148585i	−0.365772	−	0.930705i	$-0.619195\pi$
$151$	3.16245	−	1.82584i	0.257356	−	0.148585i	0.623128	+	0.782120i	$0.285862\pi$
$152$	−7.86052	−	13.8065i	−0.637573	−	1.11986i
$153$	−5.54294	−	12.3046i	−0.448120	−	0.994768i
$154$	−6.18960	+	3.07860i	−0.498772	+	0.248080i
$155$		−	5.51888i		−	0.443287i
$156$	−7.73117	−	1.10102i	−0.618989	−	0.0881524i
$157$	2.34584	−	1.35437i	0.187219	−	0.108091i	−0.403461	−	0.914997i	$-0.632193\pi$
$157$	2.34584	−	1.35437i	0.187219	−	0.108091i	0.590680	+	0.806906i	$0.298860\pi$
$158$	−3.81101	−	0.679889i	−0.303188	−	0.0540891i
$159$	−19.8770	−	6.41042i	−1.57635	−	0.508379i
$160$	−6.84666	−	2.57023i	−0.541276	−	0.203194i
$161$	2.20965	−	1.63865i	0.174145	−	0.129143i
$162$	12.5918	−	1.85620i	0.989309	−	0.145837i
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	−0.639471	−	0.768815i	$-0.720847\pi$
$163$	4.41842	−	7.65293i	0.346078	−	0.599424i	0.985549	+	0.169391i	$0.0541801\pi$
$164$	1.78648	+	2.14652i	0.139501	+	0.167615i
$165$	2.77495	+	3.06838i	0.216030	+	0.238873i
$166$	−2.28178	−	6.30858i	−0.177100	−	0.489641i
$167$	11.8815			0.919417			0.459709	−	0.888070i	$-0.347954\pi$
$167$	11.8815			0.919417			0.459709	+	0.888070i	$0.347954\pi$
$168$	−2.61962	+	12.6940i	−0.202108	+	0.979363i
$169$	7.91806			0.609081
$170$	−2.79743	−	7.73422i	−0.214553	−	0.593188i
$171$	13.6760	+	9.84512i	1.04583	+	0.752875i
$172$	−9.26310	+	7.70940i	−0.706305	+	0.587836i
$173$	−3.12500	+	5.41265i	−0.237589	+	0.411516i	−0.960022	−	0.279925i	$-0.909691\pi$
$173$	−3.12500	+	5.41265i	−0.237589	+	0.411516i	0.722433	+	0.691441i	$0.243024\pi$
$174$	1.51844	−	2.85697i	0.115112	−	0.216586i
$175$	1.00614	+	8.74915i	0.0760571	+	0.661373i
$176$	−2.47168	−	6.96468i	−0.186310	−	0.524982i
$177$	−5.87927	+	18.2300i	−0.441913	+	1.37025i
$178$	13.3628	+	2.38393i	1.00158	+	0.178683i
$179$	1.43978	−	0.831255i	0.107614	−	0.0621309i	−0.445227	−	0.895418i	$-0.646877\pi$
$179$	1.43978	−	0.831255i	0.107614	−	0.0621309i	0.552841	+	0.833287i	$0.313544\pi$
$180$	7.73773	−	0.543797i	0.576737	−	0.0405322i
$181$			4.46877i			0.332161i	0.986112	+	0.166081i	$0.0531112\pi$
$181$			4.46877i			0.332161i	−0.986112	+	0.166081i	$0.946889\pi$
$182$	−0.523031	+	8.41865i	−0.0387696	+	0.624032i
$183$	14.9630	−	3.21468i	1.10609	−	0.237636i
$184$	1.45505	+	2.55571i	0.107268	+	0.188409i
$185$	10.5802	−	6.10850i	0.777874	−	0.449106i
$186$	−0.366762	−	10.4503i	−0.0268923	−	0.766250i
$187$	4.15562	−	7.19775i	0.303889	−	0.526352i
$188$	4.00628	+	23.2676i	0.292188	+	1.69696i
$189$	−3.07756	−	13.3988i	−0.223860	−	0.974621i
$190$	7.85368	+	6.61698i	0.569766	+	0.480046i
$191$	−11.2771	+	19.5325i	−0.815982	+	1.41332i	0.0926380	+	0.995700i	$0.470470\pi$
$191$	−11.2771	+	19.5325i	−0.815982	+	1.41332i	−0.908620	+	0.417623i	$0.862863\pi$
$192$	−13.1353	−	4.41184i	−0.947957	−	0.318397i
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	0.742427	−	0.669927i	$-0.233675\pi$
$193$	−2.90298	−	5.02810i	−0.208961	−	0.361931i	−0.951387	+	0.307997i	$0.900341\pi$
$194$	11.6162	−	4.20152i	0.833994	−	0.301651i
$195$	4.93525	−	1.06030i	0.353421	−	0.0759297i
$196$	13.8923	+	1.73289i	0.992310	+	0.123778i
$197$	3.15873			0.225050			0.112525	−	0.993649i	$-0.464106\pi$
$197$	3.15873			0.225050			0.112525	+	0.993649i	$0.464106\pi$
$198$	5.45841	+	5.62571i	0.387912	+	0.399802i
$199$	−12.2352	+	7.06397i	−0.867327	+	0.500751i	−0.866459	−	0.499248i	$-0.833610\pi$
$199$	−12.2352	+	7.06397i	−0.867327	+	0.500751i	−0.000867851		1.00000i	$0.500276\pi$
$200$	−9.41470	−	0.0567945i	−0.665720	−	0.00401598i
$201$	10.0735	+	3.24874i	0.710528	+	0.229149i
$202$	−7.39832	−	6.23332i	−0.520544	−	0.438575i
$203$	−3.20627	−	1.39013i	−0.225036	−	0.0975677i
$204$	−5.81104	−	14.4592i	−0.406854	−	1.01235i
$205$	−1.56334	−	0.902597i	−0.109189	−	0.0630401i
$206$	6.24932	+	1.11488i	0.435411	+	0.0776777i
$207$	−2.53154	−	1.82242i	−0.175954	−	0.126667i
$208$	−8.86739	−	1.63721i	−0.614843	−	0.113520i
$209$			10.3778i			0.717848i
$210$	−1.24854	−	8.28477i	−0.0861574	−	0.571703i
$211$	1.95410			0.134526			0.0672629	−	0.997735i	$-0.478573\pi$
$211$	1.95410			0.134526			0.0672629	+	0.997735i	$0.478573\pi$
$212$	−22.6283	−	8.33924i	−1.55412	−	0.572741i
$213$	18.0003	−	16.2789i	1.23336	−	1.11541i
$214$	−10.0940	−	1.80078i	−0.690011	−	0.123099i
$215$	3.89507	−	6.74646i	0.265642	−	0.460105i
$216$	14.6156	−	1.54392i	0.994467	−	0.105051i
$217$	−11.2206	+	1.29035i	−0.761702	+	0.0875948i
$218$	−11.2246	+	13.3225i	−0.760229	+	0.902315i
$219$	−14.4623	−	4.66415i	−0.977269	−	0.315174i
$220$	3.05590	+	3.67177i	0.206029	+	0.247551i
$221$	−5.07051	−	8.78238i	−0.341079	−	0.590766i
$222$	19.6282	−	12.2698i	1.31736	−	0.823498i
$223$		−	3.59985i		−	0.241064i	−0.992709	−	0.120532i	$-0.961540\pi$
$223$		−	3.59985i		−	0.241064i	0.992709	−	0.120532i	$-0.0384600\pi$
$224$	−3.62479	+	14.5210i	−0.242192	+	0.970228i
$225$	9.10480	−	4.10151i	0.606987	−	0.273434i
$226$	3.49971	+	9.67588i	0.232797	+	0.643630i
$227$	5.05015	−	2.91571i	0.335190	−	0.193522i	−0.322953	−	0.946415i	$-0.604675\pi$
$227$	5.05015	−	2.91571i	0.335190	−	0.193522i	0.658143	+	0.752893i	$0.271342\pi$
$228$	15.3110	+	12.0076i	1.01400	+	0.795225i
$229$	11.2803	+	6.51269i	0.745424	+	0.430371i	0.824038	−	0.566535i	$-0.191716\pi$
$229$	11.2803	+	6.51269i	0.745424	+	0.430371i	−0.0786144	+	0.996905i	$0.525050\pi$
$230$	−1.45378	−	1.22486i	−0.0958597	−	0.0807649i
$231$	5.58960	−	6.35923i	0.367768	−	0.418406i
$232$	1.88745	−	3.22409i	0.123917	−	0.211672i
$233$	−13.6565	−	7.88458i	−0.894667	−	0.516536i	−0.0192009	−	0.999816i	$-0.506112\pi$
$233$	−13.6565	−	7.88458i	−0.894667	−	0.516536i	−0.875466	+	0.483279i	$0.839446\pi$
$234$	9.27467	−	2.33570i	0.606304	−	0.152690i
$235$	−7.63075	−	13.2169i	−0.497775	−	0.862172i
$236$	−7.64828	+	20.7534i	−0.497861	+	1.35093i
$237$	4.63544	−	0.995889i	0.301104	−	0.0646899i
$238$	−15.0706	+	7.49583i	−0.976880	+	0.485882i
$239$	−22.7458			−1.47130			−0.735651	−	0.677361i	$-0.763124\pi$
$239$	−22.7458			−1.47130			−0.735651	+	0.677361i	$0.763124\pi$
$240$	8.95302	−	0.260151i	0.577915	−	0.0167927i
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	0.558282	−	0.829651i	$-0.311461\pi$
$241$	−6.82067	−	11.8137i	−0.439358	−	0.760990i	−0.997640	+	0.0686608i	$0.978127\pi$
$242$	1.88430	−	10.5622i	0.121128	−	0.678962i
$243$	−13.4140	+	7.94130i	−0.860509	+	0.509435i
$244$	17.4157	−	2.99870i	1.11493	−	0.191972i
$245$	−8.81339	+	2.05422i	−0.563067	+	0.131240i
$246$	−3.02025	−	1.60522i	−0.192564	−	0.102345i
$247$	10.9661	+	6.33127i	0.697755	+	0.402849i
$248$	0.0728375	−	12.0741i	0.00462519	−	0.766708i
$249$	5.51109	+	6.09384i	0.349251	+	0.386182i
$250$	14.3194	−	5.17926i	0.905639	−	0.327565i
$251$			5.33090i			0.336484i	0.985746	+	0.168242i	$0.0538089\pi$
$251$			5.33090i			0.336484i	−0.985746	+	0.168242i	$0.946191\pi$
$252$	−2.91474	−	15.6046i	−0.183611	−	0.982999i
$253$		−	1.92102i		−	0.120774i
$254$	10.4728	+	28.9548i	0.657121	+	1.81678i
$255$	6.75651	+	7.47096i	0.423109	+	0.467850i
$256$	−14.9451	−	5.71347i	−0.934069	−	0.357092i
$257$	7.26678	+	4.19547i	0.453289	+	0.261707i	0.709218	−	0.704989i	$-0.249048\pi$
$257$	7.26678	+	4.19547i	0.453289	+	0.261707i	−0.255929	+	0.966696i	$0.582381\pi$
$258$	6.92716	−	13.0336i	0.431266	−	0.811436i
$259$	−14.8931	−	20.0827i	−0.925410	−	1.24788i
$260$	5.74425	−	0.989063i	0.356243	−	0.0613391i
$261$	−0.396969	+	3.94263i	−0.0245717	+	0.244043i
$262$	7.49012	+	1.33625i	0.462741	+	0.0825536i
$263$	1.58410	+	2.74375i	0.0976800	+	0.169187i	0.910724	−	0.413016i	$-0.135525\pi$
$263$	1.58410	+	2.74375i	0.0976800	+	0.169187i	−0.813044	+	0.582202i	$0.802191\pi$
$264$	6.03050	+	6.74958i	0.371152	+	0.415408i
$265$	15.5886			0.957603
$266$	11.6169	−	17.5146i	0.712277	−	1.07389i
$267$	−16.2535	+	3.49194i	−0.994698	+	0.213703i
$268$	11.4678	+	4.22625i	0.700509	+	0.258160i
$269$	7.81827	+	13.5416i	0.476689	+	0.825649i	0.999643	−	0.0267117i	$-0.00850361\pi$
$269$	7.81827	+	13.5416i	0.476689	+	0.825649i	−0.522955	+	0.852361i	$0.675170\pi$
$270$	−8.51963	+	4.20336i	−0.518488	+	0.255808i
$271$	12.4371	+	7.18058i	0.755502	+	0.436189i	0.827678	−	0.561203i	$-0.189661\pi$
$271$	12.4371	+	7.18058i	0.755502	+	0.436189i	−0.0721766	+	0.997392i	$0.522995\pi$
$272$	−6.01809	−	16.9577i	−0.364901	−	1.02821i
$273$	−3.30962	−	9.78607i	−0.200307	−	0.592280i
$274$	−11.9647	+	14.2009i	−0.722813	+	0.857905i
$275$	5.32598	+	3.07496i	0.321169	+	0.185427i
$276$	−2.83421	−	2.22272i	−0.170599	−	0.133792i
$277$	−3.23202	+	1.86601i	−0.194193	+	0.112117i	−0.593944	−	0.804506i	$-0.702430\pi$
$277$	−3.23202	+	1.86601i	−0.194193	+	0.112117i	0.399751	+	0.916624i	$0.369097\pi$
$278$	−17.2568	+	6.24169i	−1.03499	+	0.374351i
$279$	5.26008	+	11.6767i	0.314913	+	0.699065i
$280$	−1.04727	−	9.61760i	−0.0625862	−	0.574762i
$281$			18.8375i			1.12375i	0.827223	+	0.561874i	$0.189920\pi$
$281$			18.8375i			1.12375i	−0.827223	+	0.561874i	$0.810080\pi$
$282$	−15.3275	−	24.5196i	−0.912741	−	1.46012i
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	0.985352	+	0.170534i	$0.0545492\pi$
$283$	10.7726	+	18.6586i	0.640362	+	1.10914i	−0.344989	+	0.938607i	$0.612117\pi$
$284$	21.5400	−	17.9271i	1.27817	−	1.06378i
$285$	−11.9705	−	3.86055i	−0.709072	−	0.228679i
$286$	4.50453	+	3.79521i	0.266358	+	0.224415i
$287$	−1.46957	+	3.38951i	−0.0867460	+	0.200076i
$288$	16.9357	−	1.08759i	0.997944	−	0.0640868i
$289$	1.61820	−	2.80280i	0.0951880	−	0.164870i
$290$	−0.424127	+	2.37738i	−0.0249056	+	0.139605i
$291$	−11.2208	+	10.1477i	−0.657775	+	0.594871i
$292$	−16.4641	−	6.06754i	−0.963488	−	0.355076i
$293$	4.13814			0.241753			0.120876	−	0.992668i	$-0.461430\pi$
$293$	4.13814			0.241753			0.120876	+	0.992668i	$0.461430\pi$
$294$	−16.5520	+	4.47547i	−0.965335	+	0.261015i
$295$		−	14.2970i		−	0.832405i
$296$	23.2279	−	13.2244i	1.35009	−	0.768655i
$297$	−8.79566	−	3.84717i	−0.510376	−	0.223235i
$298$	−1.69905	+	9.52379i	−0.0984236	+	0.551698i
$299$	−2.02992	−	1.17197i	−0.117393	−	0.0677770i
$300$	10.6991	−	4.29989i	0.617713	−	0.248254i
$301$	−14.6271	−	6.34179i	−0.843091	−	0.365535i
$302$	−3.32747	+	3.94937i	−0.191474	+	0.227260i
$303$	11.2765	+	3.63671i	0.647815	+	0.208924i
$304$	17.0948	+	14.5802i	0.980456	+	0.836230i
$305$	−9.89279	+	5.71160i	−0.566459	+	0.327046i
$306$	13.2903	+	13.6976i	0.759753	+	0.783040i
$307$	−4.63154			−0.264336			−0.132168	−	0.991227i	$-0.542194\pi$
$307$	−4.63154			−0.264336			−0.132168	+	0.991227i	$0.542194\pi$
$308$	6.75067	−	7.07151i	0.384655	−	0.402937i
$309$	−7.60122	+	1.63306i	−0.432418	+	0.0929017i
$310$	2.65467	+	7.33954i	0.150775	+	0.416858i
$311$	−7.04878	−	12.2088i	−0.399700	−	0.692300i	0.593989	−	0.804473i	$-0.297552\pi$
$311$	−7.04878	−	12.2088i	−0.399700	−	0.692300i	−0.993689	+	0.112173i	$0.964219\pi$
$312$	10.8113	−	2.25458i	0.612067	−	0.127640i
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	−0.599780	−	0.800165i	$-0.704745\pi$
$313$	6.95418	−	12.0450i	0.393074	−	0.680824i	0.992853	+	0.119342i	$0.0380784\pi$
$314$	−2.46825	+	2.92956i	−0.139292	+	0.165325i
$315$	5.25586	+	8.81308i	0.296134	+	0.496561i
$316$	5.39529	−	0.928978i	0.303509	−	0.0522591i
$317$	8.34364	−	14.4516i	0.468625	−	0.811683i	−0.530731	−	0.847540i	$-0.678083\pi$
$317$	8.34364	−	14.4516i	0.468625	−	0.811683i	0.999357	+	0.0358569i	$0.0114161\pi$
$318$	29.5178	−	1.03596i	1.65528	−	0.0580936i
$319$	−2.11342	+	1.22018i	−0.118329	+	0.0683171i
$320$	10.3417	+	0.124777i	0.578117	+	0.00697527i
$321$	12.2776	−	2.63775i	0.685269	−	0.147225i
$322$	−2.15039	+	3.24211i	−0.119836	+	0.180675i
$323$			25.2681i			1.40595i
$324$	−15.8530	+	8.52544i	−0.880721	+	0.473635i
$325$	6.49853	−	3.75193i	0.360473	−	0.208119i
$326$	−2.19486	+	12.3029i	−0.121562	+	0.681397i
$327$	6.54881	−	20.3061i	0.362150	−	1.12293i
$328$	−3.40835	−	1.99532i	−0.188195	−	0.110173i
$329$	−25.0874	+	18.6045i	−1.38311	+	1.02570i
$330$	−5.16634	−	2.74583i	−0.284398	−	0.151153i
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	−0.967567	−	0.252615i	$-0.918709\pi$
$331$	−4.82148	+	8.35105i	−0.265012	+	0.459015i	0.702554	+	0.711630i	$0.252043\pi$
$332$	6.06906	+	7.29218i	0.333083	+	0.400210i
$333$	−16.5633	+	23.0083i	−0.907663	+	1.26085i
$334$	−15.8011	+	5.71519i	−0.864600	+	0.312721i
$335$	−7.90019			−0.431633
$336$	−2.62220	−	18.1418i	−0.143053	−	0.989715i
$337$	29.4886			1.60635			0.803173	−	0.595746i	$-0.203144\pi$
$337$	29.4886			1.60635			0.803173	+	0.595746i	$0.203144\pi$
$338$	−10.5302	+	3.80872i	−0.572767	+	0.207167i
$339$	−8.45271	−	9.34652i	−0.459088	−	0.507633i
$340$	7.44057	+	8.94010i	0.403522	+	0.484845i
$341$	−3.94356	+	6.83044i	−0.213556	+	0.369889i
$342$	−22.9233	−	6.51462i	−1.23955	−	0.352270i
$343$	6.23712	+	17.4384i	0.336773	+	0.941586i
$344$	8.61062	−	14.7084i	0.464253	−	0.793024i
$345$	2.21585	+	0.714621i	0.119297	+	0.0384739i
$346$	1.55235	−	8.70144i	0.0834547	−	0.467792i
$347$	10.8911	−	6.28800i	0.584667	−	0.337558i	−0.178319	−	0.983973i	$-0.557066\pi$
$347$	10.8911	−	6.28800i	0.584667	−	0.337558i	0.762986	+	0.646415i	$0.223733\pi$
$348$	−0.645114	+	4.52987i	−0.0345817	+	0.242826i
$349$		−	34.5012i		−	1.84681i	−0.383830	−	0.923404i	$-0.625395\pi$
$349$		−	34.5012i		−	1.84681i	0.383830	−	0.923404i	$-0.374605\pi$
$350$	−5.54654	−	11.1515i	−0.296475	−	0.596072i
$351$	−9.43129	+	6.94718i	−0.503405	+	0.370813i
$352$	6.63720	+	8.07338i	0.353764	+	0.430312i
$353$	−9.10737	+	5.25815i	−0.484737	+	0.279863i	−0.722388	−	0.691488i	$-0.756956\pi$
$353$	−9.10737	+	5.25815i	−0.484737	+	0.279863i	0.237652	+	0.971350i	$0.423622\pi$
$354$	−0.950121	−	27.0721i	−0.0504984	−	1.43886i
$355$	−9.05743	+	15.6879i	−0.480719	+	0.832629i
$356$	−18.9178	+	3.25733i	−1.00264	+	0.172638i
$357$	13.6097	−	15.4836i	0.720300	−	0.819478i
$358$	−1.51491	+	1.79804i	−0.0800652	+	0.0950293i
$359$	8.02903	−	13.9067i	0.423756	−	0.733967i	−0.572547	−	0.819872i	$-0.694045\pi$
$359$	8.02903	−	13.9067i	0.423756	−	0.733967i	0.996303	+	0.0859047i	$0.0273780\pi$
$360$	−10.0288	+	4.44517i	−0.528564	+	0.234281i
$361$	−6.27547	−	10.8694i	−0.330288	−	0.572075i
$362$	−2.14955	−	5.94300i	−0.112978	−	0.312357i
$363$	2.76009	+	12.8471i	0.144867	+	0.674296i
$364$	−3.35393	−	11.4475i	−0.175794	−	0.600013i
$365$	11.3421			0.593673
$366$	−18.3529	+	11.4726i	−0.959321	+	0.599684i
$367$	−20.8250	+	12.0233i	−1.08706	+	0.627613i	−0.932791	−	0.360417i	$-0.882634\pi$
$367$	−20.8250	+	12.0233i	−1.08706	+	0.627613i	−0.154266	+	0.988029i	$0.549301\pi$
$368$	−3.16440	−	2.69892i	−0.164956	−	0.140691i
$369$	4.16795	+	0.419655i	0.216975	+	0.0218464i
$370$	−11.1323	+	13.2129i	−0.578742	+	0.686907i
$371$	−3.64473	−	31.6936i	−0.189225	−	1.64545i
$372$	5.51450	+	13.7213i	0.285913	+	0.711418i
$373$	−12.5120	−	7.22381i	−0.647847	−	0.374035i	0.139784	−	0.990182i	$-0.455359\pi$
$373$	−12.5120	−	7.22381i	−0.647847	−	0.374035i	−0.787631	+	0.616147i	$0.788693\pi$
$374$	−2.06431	+	11.5712i	−0.106743	+	0.598332i
$375$	−13.8320	+	12.5092i	−0.714281	+	0.645975i
$376$	−16.5200	−	29.0163i	−0.851955	−	1.49640i
$377$			2.97762i			0.153355i
$378$	10.5379	+	16.3387i	0.542011	+	0.840371i
$379$	−29.8048			−1.53097			−0.765485	−	0.643453i	$-0.777501\pi$
$379$	−29.8048			−1.53097			−0.765485	+	0.643453i	$0.777501\pi$
$380$	−13.6274	−	5.02214i	−0.699073	−	0.257630i
$381$	−25.2945	−	27.9692i	−1.29588	−	1.43291i
$382$	5.60191	−	31.4007i	0.286619	−	1.60660i
$383$	5.62806	−	9.74809i	0.287581	−	0.498104i	−0.685651	−	0.727930i	$-0.740482\pi$
$383$	5.62806	−	9.74809i	0.287581	−	0.498104i	0.973232	+	0.229826i	$0.0738158\pi$
$384$	19.5907	−	0.450993i	0.999735	−	0.0230146i
$385$	−2.51380	+	5.79798i	−0.128115	+	0.295492i
$386$	6.27926	+	5.29048i	0.319606	+	0.269278i
$387$	−1.81098	+	17.9864i	−0.0920574	+	0.914300i
$388$	−13.4273	+	11.1752i	−0.681669	+	0.567333i
$389$	13.4807	+	23.3492i	0.683498	+	1.18385i	0.973906	+	0.226950i	$0.0728755\pi$
$389$	13.4807	+	23.3492i	0.683498	+	1.18385i	−0.290408	+	0.956903i	$0.593791\pi$
$390$	−6.05335	+	3.78403i	−0.306523	+	0.191612i
$391$		−	4.67735i		−	0.236544i
$392$	−19.3089	+	4.37788i	−0.975247	+	0.221117i
$393$	−9.11045	+	1.95731i	−0.459561	+	0.0987331i
$394$	−4.20078	+	1.51940i	−0.211632	+	0.0765463i
$395$	−3.06473	+	1.76942i	−0.154203	+	0.0890293i
$396$	−9.96518	−	4.85603i	−0.500769	−	0.244024i
$397$	6.75185	+	3.89818i	0.338866	+	0.195644i	0.659770	−	0.751467i	$-0.270654\pi$
$397$	6.75185	+	3.89818i	0.338866	+	0.195644i	−0.320905	+	0.947111i	$0.603987\pi$
$398$	12.8736	−	15.2796i	0.645295	−	0.765900i
$399$	−5.05018	+	25.2402i	−0.252825	+	1.26359i
$400$	12.5479	−	4.45309i	0.627395	−	0.222655i
$401$	−2.98430	−	1.72299i	−0.149029	−	0.0860420i	0.423631	−	0.905835i	$-0.360755\pi$
$401$	−2.98430	−	1.72299i	−0.149029	−	0.0860420i	−0.572660	+	0.819793i	$0.694089\pi$
$402$	−14.9594	+	0.525014i	−0.746106	+	0.0261853i
$403$	4.81175	+	8.33420i	0.239691	+	0.415156i
$404$	12.8373	+	4.73095i	0.638681	+	0.235374i
$405$	7.70959	−	8.71440i	0.383093	−	0.433022i
$406$	4.93267	+	0.306456i	0.244805	+	0.0152091i
$407$	−17.4595			−0.865435
$408$	14.6832	+	16.4340i	0.726926	+	0.813606i
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	0.999833	−	0.0182590i	$-0.00581236\pi$
$409$	9.79039	+	16.9575i	0.484104	+	0.838492i	−0.515729	+	0.856752i	$0.672479\pi$
$410$	2.51325	+	0.448366i	0.124121	+	0.0221432i
$411$	6.98056	−	21.6448i	0.344326	−	1.06766i
$412$	−8.84722	+	1.52334i	−0.435871	+	0.0750497i
$413$	−29.0676	+	3.34274i	−1.43032	+	0.164485i
$414$	4.24330	+	1.20591i	0.208547	+	0.0592674i
$415$	−5.31101	−	3.06631i	−0.260707	−	0.150519i
$416$	12.5802	−	2.08805i	0.616797	−	0.102375i
$417$	16.6694	−	15.0753i	0.816303	−	0.738240i
$418$	−4.99190	−	13.8014i	−0.244162	−	0.675049i
$419$		−	27.6189i		−	1.34927i	−0.738150	−	0.674637i	$-0.764300\pi$
$419$		−	27.6189i		−	1.34927i	0.738150	−	0.674637i	$-0.235700\pi$
$420$	5.64554	+	10.4173i	0.275474	+	0.508313i
$421$			9.36226i			0.456289i	0.973627	+	0.228144i	$0.0732658\pi$
$421$			9.36226i			0.456289i	−0.973627	+	0.228144i	$0.926734\pi$
$422$	−2.59875	+	0.939954i	−0.126505	+	0.0457563i
$423$	28.7420	+	20.6909i	1.39748	+	1.00603i
$424$	34.1046	+	0.205737i	1.65627	+	0.00999147i
$425$	12.9678	+	7.48697i	0.629031	+	0.363171i
$426$	−16.1081	+	30.3078i	−0.780441	+	1.46842i
$427$	13.9254	+	18.7779i	0.673897	+	0.908724i
$428$	14.2902	−	2.46053i	0.690741	−	0.118934i
$429$	−6.86576	−	2.21424i	−0.331482	−	0.106905i
$430$	−1.93488	+	10.8457i	−0.0933083	+	0.523025i
$431$	4.22951	+	7.32573i	0.203729	+	0.352868i	0.949727	−	0.313080i	$-0.101361\pi$
$431$	4.22951	+	7.32573i	0.203729	+	0.352868i	−0.745998	+	0.665948i	$0.768027\pi$
$432$	−18.6946	+	9.08361i	−0.899444	+	0.437035i
$433$	−10.9191			−0.524737			−0.262369	−	0.964968i	$-0.584504\pi$
$433$	−10.9191			−0.524737			−0.262369	+	0.964968i	$0.584504\pi$
$434$	14.3015	−	7.11331i	0.686494	−	0.341450i
$435$	−0.621254	−	2.89168i	−0.0297868	−	0.138645i
$436$	8.51927	−	23.1168i	0.407999	−	1.10709i
$437$	2.92018	+	5.05790i	0.139691	+	0.241952i
$438$	21.4768	−	0.753750i	1.02620	−	0.0360156i
$439$	20.2600	+	11.6971i	0.966959	+	0.558274i	0.898308	−	0.439367i	$-0.144797\pi$
$439$	20.2600	+	11.6971i	0.966959	+	0.558274i	0.0686510	+	0.997641i	$0.478131\pi$
$440$	−5.83021	−	3.41313i	−0.277944	−	0.162715i
$441$	16.6892	−	12.7464i	0.794725	−	0.606970i
$442$	10.9677	+	9.24065i	0.521681	+	0.439533i
$443$	5.31199	+	3.06688i	0.252380	+	0.145712i	0.620854	−	0.783926i	$-0.286786\pi$
$443$	5.31199	+	3.06688i	0.252380	+	0.145712i	−0.368473	+	0.929638i	$0.620119\pi$
$444$	−20.2015	+	25.7591i	−0.958720	+	1.22247i
$445$	10.7460	−	6.20422i	0.509410	−	0.294108i
$446$	1.73159	+	4.78743i	0.0819931	+	0.226691i
$447$	−2.48874	−	11.5840i	−0.117713	−	0.547907i
$448$	−2.16426	−	21.0551i	−0.102252	−	0.994759i
$449$		−	35.8658i		−	1.69261i	−0.532696	−	0.846307i	$-0.678821\pi$
$449$		−	35.8658i		−	1.69261i	0.532696	−	0.846307i	$-0.321179\pi$
$450$	−10.1356	+	9.83414i	−0.477794	+	0.463586i
$451$	1.28992	+	2.23420i	0.0607397	+	0.105204i
$452$	−9.30851	−	11.1845i	−0.437835	−	0.526074i
$453$	1.94135	−	6.01959i	0.0912124	−	0.282825i
$454$	−5.31368	+	6.30679i	−0.249383	+	0.295992i
$455$	4.59303	+	6.19352i	0.215324	+	0.290357i
$456$	−26.1380	−	8.60404i	−1.22402	−	0.402921i
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	−0.899382	−	0.437163i	$-0.855983\pi$
$457$	−1.51987	+	2.63249i	−0.0710964	+	0.123143i	0.828286	+	0.560306i	$0.189316\pi$
$458$	−18.1343	−	3.23519i	−0.847362	−	0.151170i
$459$	−21.4159	−	9.36717i	−0.999606	−	0.437222i
$460$	2.52256	+	0.929643i	0.117615	+	0.0433448i
$461$	30.7564			1.43247			0.716233	−	0.697861i	$-0.245865\pi$
$461$	30.7564			1.43247			0.716233	+	0.697861i	$0.245865\pi$
$462$	−4.37469	+	11.1458i	−0.203529	+	0.518550i
$463$		−	9.54146i		−	0.443429i	−0.975112	−	0.221715i	$-0.928835\pi$
$463$		−	9.54146i		−	0.443429i	0.975112	−	0.221715i	$-0.0711653\pi$
$464$	−0.959276	+	5.19560i	−0.0445333	+	0.241200i
$465$	−6.41172	−	7.08971i	−0.297336	−	0.328777i
$466$	21.9543	+	3.91668i	1.01702	+	0.181437i
$467$	4.36437	+	2.51977i	0.201959	+	0.116601i	0.597569	−	0.801818i	$-0.296133\pi$
$467$	4.36437	+	2.51977i	0.201959	+	0.116601i	−0.395610	+	0.918419i	$0.629467\pi$
$468$	−11.2108	+	7.56751i	−0.518221	+	0.349808i
$469$	1.84712	+	16.0621i	0.0852920	+	0.741677i
$470$	16.5056	+	13.9065i	0.761348	+	0.641460i
$471$	1.44005	−	4.46522i	0.0663542	−	0.205746i
$472$	0.188690	−	31.2788i	0.00868518	−	1.43972i
$473$	−9.64147	+	5.56650i	−0.443315	+	0.255948i
$474$	−5.68562	+	3.55415i	−0.261149	+	0.163248i
$475$	−18.6972			−0.857884
$476$	16.4367	−	17.2179i	0.753374	−	0.789179i
$477$	−32.9820	+	14.8576i	−1.51014	+	0.680285i
$478$	30.2495	−	10.9411i	1.38358	−	0.500434i
$479$	−13.6307	−	23.6091i	−0.622804	−	1.07873i	−0.988961	−	0.148175i	$-0.952660\pi$
$479$	−13.6307	−	23.6091i	−0.622804	−	1.07873i	0.366157	−	0.930553i	$-0.380673\pi$
$480$	−11.7815	+	4.65252i	−0.537747	+	0.212358i
$481$	−10.6516	+	18.4492i	−0.485673	+	0.841211i
$482$	14.7534	+	12.4302i	0.671998	+	0.566180i
$483$	0.934833	−	4.67217i	0.0425364	−	0.212591i
$484$	2.57465	+	14.9530i	0.117030	+	0.679681i
$485$	5.64610	−	9.77933i	0.256376	−	0.444057i
$486$	14.0193	−	17.0135i	0.635930	−	0.771746i
$487$	0.905513	−	0.522798i	0.0410327	−	0.0236902i	−0.479343	−	0.877627i	$-0.659125\pi$
$487$	0.905513	−	0.522798i	0.0410327	−	0.0236902i	0.520376	+	0.853937i	$0.325792\pi$
$488$	−21.7187	+	12.3652i	−0.983159	+	0.559746i
$489$	−3.21499	−	14.9644i	−0.145387	−	0.676714i
$490$	10.7328	−	6.97129i	0.484857	−	0.314931i
$491$		−	29.3101i		−	1.32275i	−0.750057	−	0.661373i	$-0.769974\pi$
$491$		−	29.3101i		−	1.32275i	0.750057	−	0.661373i	$-0.230026\pi$
$492$	4.78875	+	0.681982i	0.215894	+	0.0307461i
$493$	−5.14579	+	2.97092i	−0.231755	+	0.133804i
$494$	−17.6292	−	3.14507i	−0.793175	−	0.141503i
$495$	7.12956	+	0.717849i	0.320450	+	0.0322649i
$496$	5.71098	+	16.0924i	0.256431	+	0.722569i
$497$	34.0132	+	14.7469i	1.52570	+	0.661490i
$498$	−10.2604	−	5.45325i	−0.459780	−	0.244366i
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	−0.341133	−	0.940015i	$-0.610811\pi$
$499$	14.3749	−	24.8981i	0.643510	−	1.11459i	0.984643	−	0.174578i	$-0.0558560\pi$
$500$	−16.5520	+	13.7757i	−0.740229	+	0.616070i
$501$	15.2633	−	13.8037i	0.681914	−	0.616702i
$502$	−2.56425	−	7.08955i	−0.114448	−	0.316422i
$503$	19.8016			0.882910			0.441455	−	0.897283i	$-0.354462\pi$
$503$	19.8016			0.882910			0.441455	+	0.897283i	$0.354462\pi$
$504$	11.3824	+	19.3505i	0.507011	+	0.861939i
$505$	−8.84363			−0.393536
$506$	0.924044	+	2.55476i	0.0410788	+	0.113573i
$507$	10.1718	−	9.19903i	0.451744	−	0.408543i
$508$	−27.8554	−	33.4693i	−1.23589	−	1.48496i
$509$	14.1795	−	24.5596i	0.628494	−	1.08858i	−0.359360	−	0.933199i	$-0.617005\pi$
$509$	14.1795	−	24.5596i	0.628494	−	1.08858i	0.987854	−	0.155385i	$-0.0496618\pi$
$510$	−12.5791	−	6.68561i	−0.557012	−	0.296044i
$511$	−2.65186	−	23.0599i	−0.117312	−	1.02011i
$512$	22.6237	+	0.409474i	0.999836	+	0.0180964i
$513$	29.0064	−	3.24114i	1.28066	−	0.143100i
$514$	−11.6821	−	2.08411i	−0.515277	−	0.0919260i
$515$	5.02555	−	2.90151i	0.221452	−	0.127856i
$516$	−2.94303	+	20.6654i	−0.129560	+	0.909743i
$517$			21.8104i			0.959222i
$518$	29.4663	+	19.5441i	1.29468	+	0.858719i
$519$	2.27385	+	10.5838i	0.0998108	+	0.464577i
$520$	−7.16349	+	4.07843i	−0.314140	+	0.178851i
$521$	27.4943	−	15.8738i	1.20455	−	0.695445i	0.242984	−	0.970030i	$-0.421874\pi$
$521$	27.4943	−	15.8738i	1.20455	−	0.695445i	0.961563	+	0.274585i	$0.0885404\pi$
$522$	−1.36854	−	5.43424i	−0.0598995	−	0.237850i
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	−0.789858	−	0.613290i	$-0.789846\pi$
$523$	3.11470	−	5.39482i	0.136196	−	0.235899i	0.926054	+	0.377392i	$0.123179\pi$
$524$	−10.6038	+	1.82580i	−0.463231	+	0.0797606i
$525$	11.4571	+	10.0705i	0.500028	+	0.439512i
$526$	−3.42648	−	2.88692i	−0.149402	−	0.125876i
$527$	−9.60185	+	16.6309i	−0.418263	+	0.724453i
$528$	−11.2666	−	6.07547i	−0.490316	−	0.264401i
$529$	10.9594	+	18.9823i	0.476498	+	0.825318i
$530$	−20.7313	+	7.49839i	−0.900509	+	0.325709i
$531$	13.6266	+	30.2492i	0.591344	+	1.31270i
$532$	−7.02445	+	28.8805i	−0.304548	+	1.25213i
$533$	3.14780			0.136346
$534$	19.9358	−	12.4621i	0.862705	−	0.539288i
$535$	−8.11735	+	4.68656i	−0.350944	+	0.202618i
$536$	−17.2839	−	0.104266i	−0.746551	−	0.00450359i
$537$	0.883842	−	2.74056i	0.0381406	−	0.118264i
$538$	−16.9112	−	14.2483i	−0.729096	−	0.614286i
$539$	12.3758	+	3.75526i	0.533061	+	0.161751i
$540$	9.30834	−	9.68811i	0.400567	−	0.416910i
$541$	1.99979	+	1.15458i	0.0859776	+	0.0496392i	0.542372	−	0.840138i	$-0.317526\pi$
$541$	1.99979	+	1.15458i	0.0859776	+	0.0496392i	−0.456395	+	0.889777i	$0.650860\pi$
$542$	−19.9941	−	3.56696i	−0.858819	−	0.153214i
$543$	5.19172	+	5.74071i	0.222798	+	0.246357i
$544$	16.1604	+	19.6572i	0.692871	+	0.842796i
$545$			15.9252i			0.682159i
$546$	9.10871	+	11.4225i	0.389817	+	0.488837i
$547$	32.5136			1.39018			0.695090	−	0.718922i	$-0.255364\pi$
$547$	32.5136			1.39018			0.695090	+	0.718922i	$0.255364\pi$
$548$	9.08093	−	24.6409i	0.387918	−	1.05261i
$549$	15.4871	−	21.5133i	0.660974	−	0.918167i
$550$	−8.56211	−	1.52749i	−0.365089	−	0.0651323i
$551$	3.70963	−	6.42528i	0.158036	−	0.273726i
$552$	4.83837	+	1.59268i	0.205935	+	0.0677891i
$553$	4.31401	+	5.81727i	0.183450	+	0.247375i
$554$	3.40067	−	4.03624i	0.144480	−	0.171484i
$555$	6.49494	−	20.1390i	0.275695	−	0.854854i
$556$	19.9474	−	16.6016i	0.845957	−	0.704064i
$557$	16.5711	+	28.7020i	0.702140	+	1.21614i	0.967714	+	0.252052i	$0.0811053\pi$
$557$	16.5711	+	28.7020i	0.702140	+	1.21614i	−0.265574	+	0.964091i	$0.585561\pi$
$558$	−12.6120	−	12.9986i	−0.533910	−	0.550274i
$559$			13.5840i			0.574542i
$560$	6.01898	+	12.2867i	0.254348	+	0.519206i
$561$	−3.02376	−	14.0743i	−0.127663	−	0.594219i
$562$	−9.06112	−	25.0519i	−0.382220	−	1.05675i
$563$	−13.6362	+	7.87286i	−0.574697	+	0.331801i	−0.759023	−	0.651064i	$-0.774323\pi$
$563$	−13.6362	+	7.87286i	−0.574697	+	0.331801i	0.184326	+	0.982865i	$0.440990\pi$
$564$	32.1783	+	25.2357i	1.35495	+	1.06262i
$565$	8.14583	+	4.70300i	0.342698	+	0.197857i
$566$	−23.3015	−	19.6323i	−0.979435	−	0.825205i
$567$	−19.5200	−	13.6371i	−0.819763	−	0.572703i
$568$	−20.0228	+	34.2023i	−0.840137	+	1.43510i
$569$	−20.1971	−	11.6608i	−0.846706	−	0.488846i	0.0128319	−	0.999918i	$-0.495915\pi$
$569$	−20.1971	−	11.6608i	−0.846706	−	0.488846i	−0.859538	+	0.511072i	$0.829249\pi$
$570$	17.7765	−	0.623885i	0.744577	−	0.0261317i
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	0.999996	+	0.00267009i	$0.000849917\pi$
$571$	12.0030	+	20.7898i	0.502311	+	0.870027i	−0.497686	+	0.867357i	$0.665817\pi$
$572$	−7.81611	−	2.88048i	−0.326808	−	0.120439i
$573$	8.20558	+	38.1935i	0.342793	+	1.59556i
$574$	0.323969	−	5.21458i	0.0135222	−	0.217652i
$575$	3.46101			0.144334
$576$	−21.9995	+	9.59272i	−0.916648	+	0.399697i
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	0.804523	−	0.593921i	$-0.202421\pi$
$577$	−2.69246	−	4.66349i	−0.112089	−	0.194143i	−0.916612	+	0.399777i	$0.869087\pi$
$578$	−0.803841	+	4.50581i	−0.0334354	+	0.187417i
$579$	−9.57079	−	3.08663i	−0.397749	−	0.128276i
$580$	−0.579514	−	3.36568i	−0.0240630	−	0.139752i
$581$	−4.99244	+	11.5149i	−0.207121	+	0.477717i
$582$	10.0413	−	18.8928i	0.416223	−	0.783133i
$583$	−19.2933	−	11.1390i	−0.799046	−	0.461329i
$584$	24.8141	+	0.149692i	1.02682	+	0.00619430i
$585$	5.10813	−	7.09576i	0.211195	−	0.293374i
$586$	−5.50330	+	1.99051i	−0.227339	+	0.0822274i
$587$		−	20.8871i		−	0.862104i	−0.902327	−	0.431052i	$-0.858143\pi$
$587$		−	20.8871i		−	0.862104i	0.902327	−	0.431052i	$-0.141857\pi$
$588$	19.8597	−	13.9137i	0.819001	−	0.573792i
$589$		−	23.9786i		−	0.988023i
$590$	6.87710	+	19.0135i	0.283126	+	0.782775i
$591$	4.05780	−	3.66975i	0.166915	−	0.150953i
$592$	−24.5295	+	28.7601i	−1.00816	+	1.18203i
$593$	−31.7953	−	18.3570i	−1.30567	−	0.753832i	−0.324303	−	0.945953i	$-0.605130\pi$
$593$	−31.7953	−	18.3570i	−1.30567	−	0.753832i	−0.981371	+	0.192122i	$0.938463\pi$
$594$	13.5479	+	0.885479i	0.555876	+	0.0363317i
$595$	−6.12065	+	14.1170i	−0.250922	+	0.578742i
$596$	−2.32153	−	13.4829i	−0.0950937	−	0.552282i
$597$	−7.51085	+	23.2891i	−0.307399	+	0.953160i
$598$	3.26332	+	0.582180i	0.133447	+	0.0238071i
$599$	12.0639	+	20.8953i	0.492918	+	0.853760i	0.999967	−	0.00815783i	$-0.00259675\pi$
$599$	12.0639	+	20.8953i	0.492918	+	0.853760i	−0.507048	+	0.861918i	$0.669263\pi$
$600$	−12.1604	+	10.8648i	−0.496445	+	0.443555i
$601$	−30.7421			−1.25399			−0.626997	−	0.779021i	$-0.715716\pi$
$601$	−30.7421			−1.25399			−0.626997	+	0.779021i	$0.715716\pi$
$602$	22.5030	+	1.39806i	0.917154	+	0.0569806i
$603$	16.7150	−	7.52972i	0.680687	−	0.306634i
$604$	2.52548	−	6.85281i	0.102760	−	0.278837i
$605$	−4.90393	−	8.49385i	−0.199373	−	0.345324i
$606$	−16.7458	+	0.587711i	−0.680253	+	0.0238741i
$607$	−3.75552	−	2.16825i	−0.152432	−	0.0880066i	0.421844	−	0.906668i	$-0.361383\pi$
$607$	−3.75552	−	2.16825i	−0.152432	−	0.0880066i	−0.574276	+	0.818662i	$0.694716\pi$
$608$	−29.7477	−	11.1672i	−1.20643	−	0.452891i
$609$	−5.73388	+	1.93918i	−0.232349	+	0.0785795i
$610$	10.4090	−	12.3544i	0.421448	−	0.500216i
$611$	23.0468	+	13.3061i	0.932373	+	0.538306i
$612$	−24.2634	−	11.8236i	−0.980791	−	0.477939i
$613$	−26.2945	+	15.1812i	−1.06203	+	0.613161i	−0.925992	−	0.377543i	$-0.876769\pi$
$613$	−26.2945	+	15.1812i	−1.06203	+	0.613161i	−0.136034	+	0.990704i	$0.543436\pi$
$614$	6.15947	−	2.22785i	0.248576	−	0.0899086i
$615$	−3.05693	+	0.656759i	−0.123268	+	0.0264831i
$616$	−5.57618	+	12.6516i	−0.224671	+	0.509746i
$617$			11.5709i			0.465827i	0.972497	+	0.232913i	$0.0748259\pi$
$617$			11.5709i			0.465827i	−0.972497	+	0.232913i	$0.925174\pi$
$618$	9.32330	−	5.82811i	0.375038	−	0.234441i
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	0.639127	−	0.769101i	$-0.279296\pi$
$619$	−8.62076	−	14.9316i	−0.346497	−	0.600151i	−0.985625	+	0.168950i	$0.945962\pi$
$620$	−7.06087	−	8.48388i	−0.283571	−	0.340721i
$621$	−5.36934	+	0.599963i	−0.215464	+	0.0240757i
$622$	15.2468	+	12.8459i	0.611341	+	0.515074i
$623$	−15.1264	−	20.3974i	−0.606028	−	0.817204i
$624$	−13.2934	+	8.19875i	−0.532161	+	0.328213i
$625$	−1.36164	+	2.35843i	−0.0544656	+	0.0943372i
$626$	−3.45450	+	19.3637i	−0.138070	+	0.773928i
$627$	12.0567	+	13.3316i	0.481499	+	0.532414i
$628$	1.87335	−	5.08329i	0.0747548	−	0.202845i
$629$	−42.5107			−1.69501
$630$	−11.2290	−	9.19232i	−0.447373	−	0.366231i
$631$		−	4.91146i		−	0.195522i	−0.995210	−	0.0977611i	$-0.968832\pi$
$631$		−	4.91146i		−	0.195522i	0.995210	−	0.0977611i	$-0.0311681\pi$
$632$	−6.72832	+	3.83067i	−0.267638	+	0.152376i
$633$	2.51029	−	2.27023i	0.0997752	−	0.0902336i
$634$	−4.14471	+	23.2326i	−0.164608	+	0.922683i
$635$	24.3762	+	14.0736i	0.967339	+	0.558493i
$636$	−38.7573	+	15.5763i	−1.53683	+	0.617639i
$637$	11.5183	−	10.7863i	0.456372	−	0.427368i
$638$	2.22370	−	2.63930i	0.0880370	−	0.104491i
$639$	4.21118	−	41.8248i	0.166592	−	1.65456i
$640$	−13.8134	+	4.80857i	−0.546021	+	0.190075i
$641$	−34.7916	+	20.0870i	−1.37419	+	0.793387i	−0.991452	−	0.130471i	$-0.958351\pi$
$641$	−34.7916	+	20.0870i	−1.37419	+	0.793387i	−0.382735	+	0.923858i	$0.625018\pi$
$642$	−15.0591	+	9.41366i	−0.594337	+	0.371527i
$643$	12.5997			0.496884			0.248442	−	0.968647i	$-0.420081\pi$
$643$	12.5997			0.496884			0.248442	+	0.968647i	$0.420081\pi$
$644$	1.30029	−	5.34603i	0.0512385	−	0.210663i
$645$	−2.83418	−	13.1919i	−0.111596	−	0.519431i
$646$	−12.1544	−	33.6039i	−0.478207	−	1.32213i
$647$	−9.55483	−	16.5495i	−0.375639	−	0.650626i	0.614783	−	0.788696i	$-0.289243\pi$
$647$	−9.55483	−	16.5495i	−0.375639	−	0.650626i	−0.990422	+	0.138070i	$0.955910\pi$
$648$	16.9819	−	18.9635i	0.667114	−	0.744956i
$649$	−10.2160	+	17.6947i	−0.401015	+	0.694578i
$650$	−6.83763	+	8.11557i	−0.268194	+	0.318319i
$651$	−12.9152	+	14.6934i	−0.506185	+	0.575881i
$652$	−2.99898	−	17.4174i	−0.117449	−	0.682118i
$653$	−4.01546	+	6.95497i	−0.157137	+	0.272169i	−0.933835	−	0.357704i	$-0.883560\pi$
$653$	−4.01546	+	6.95497i	−0.157137	+	0.272169i	0.776698	+	0.629873i	$0.216893\pi$
$654$	1.05832	+	30.1550i	0.0413836	+	1.17916i
$655$	6.02338	−	3.47760i	0.235353	−	0.135881i
$656$	5.49253	+	1.01410i	0.214447	+	0.0395939i
$657$	−23.9973	+	10.8102i	−0.936225	+	0.421748i
$658$	24.4145	−	36.8094i	0.951778	−	1.43498i
$659$			5.21061i			0.202977i	0.994837	+	0.101488i	$0.0323604\pi$
$659$			5.21061i			0.202977i	−0.994837	+	0.101488i	$0.967640\pi$
$660$	8.19148	+	1.16658i	0.318853	+	0.0454089i
$661$	−33.5498	+	19.3700i	−1.30494	+	0.753406i	−0.981246	−	0.192757i	$-0.938257\pi$
$661$	−33.5498	+	19.3700i	−1.30494	+	0.753406i	−0.323690	+	0.946163i	$0.604924\pi$
$662$	2.39508	−	13.4252i	0.0930873	−	0.521787i
$663$	−16.7169	−	5.39128i	−0.649230	−	0.209380i
$664$	−11.5789	−	6.77852i	−0.449347	−	0.263058i
$665$	−2.19497	−	19.0869i	−0.0851171	−	0.740157i
$666$	10.9601	−	38.5658i	0.424695	−	1.49440i
$667$	−0.686686	+	1.18937i	−0.0265886	+	0.0460528i
$668$	18.2648	−	15.2012i	0.706685	−	0.588153i
$669$	−4.18223	−	4.62447i	−0.161694	−	0.178792i
$670$	10.5064	−	3.80012i	0.405899	−	0.146811i
$671$	16.3251			0.630223
$672$	12.2137	+	22.8654i	0.471155	+	0.882050i
$673$	−33.1783			−1.27893			−0.639465	−	0.768821i	$-0.720844\pi$
$673$	−33.1783			−1.27893			−0.639465	+	0.768821i	$0.720844\pi$
$674$	−39.2168	+	14.1845i	−1.51057	+	0.546366i
$675$	6.93124	−	15.8467i	0.266784	−	0.609939i
$676$	12.1720	−	10.1304i	0.468154	−	0.389630i
$677$	15.7573	−	27.2925i	0.605602	−	1.04893i	−0.386354	−	0.922351i	$-0.626266\pi$
$677$	15.7573	−	27.2925i	0.605602	−	1.04893i	0.991956	−	0.126583i	$-0.0404011\pi$
$678$	15.7371	+	8.36401i	0.604378	+	0.321218i
$679$	−21.2027	−	9.19274i	−0.813684	−	0.352785i
$680$	−14.1955	−	8.31037i	−0.544373	−	0.318688i
$681$	3.10016	−	9.61276i	0.118798	−	0.368362i
$682$	1.95897	−	10.9807i	0.0750127	−	0.420472i
$683$	−19.4038	+	11.2028i	−0.742465	+	0.428663i	−0.822965	−	0.568092i	$-0.807682\pi$
$683$	−19.4038	+	11.2028i	−0.742465	+	0.428663i	0.0804996	+	0.996755i	$0.474348\pi$
$684$	33.6192	−	2.36271i	1.28546	−	0.0903405i
$685$			16.9751i			0.648585i
$686$	−16.6829	−	20.1911i	−0.636956	−	0.770901i
$687$	22.0573	−	4.73884i	0.841539	−	0.180798i
$688$	−4.37625	+	23.7025i	−0.166843	+	0.903649i
$689$	−23.5408	+	13.5913i	−0.896833	+	0.517787i
$690$	−3.29059	+	0.115487i	−0.125271	+	0.00439650i
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	−0.970288	−	0.241953i	$-0.922212\pi$
$691$	−7.24483	+	12.5484i	−0.275606	+	0.477364i	0.694682	+	0.719317i	$0.255545\pi$
$692$	2.12108	+	12.3187i	0.0806312	+	0.468287i
$693$	−0.207464	−	14.6631i	−0.00788090	−	0.557006i
$694$	−11.4594	+	13.6012i	−0.434995	+	0.516294i
$695$	−8.38773	+	14.5280i	−0.318165	+	0.551077i
$696$	−1.32101	−	6.33456i	−0.0500726	−	0.240111i
$697$	3.14071	+	5.43987i	0.118963	+	0.206050i
$698$	16.5956	+	45.8830i	0.628155	+	1.73670i
$699$	−26.7037	+	5.73708i	−1.01003	+	0.216996i
$700$	12.7404	+	12.1623i	0.481541	+	0.459693i
$701$	−21.9950			−0.830738			−0.415369	−	0.909653i	$-0.636348\pi$
$701$	−21.9950			−0.830738			−0.415369	+	0.909653i	$0.636348\pi$
$702$	9.20092	−	13.7756i	0.347267	−	0.519927i
$703$	45.9694	−	26.5404i	1.73377	−	1.00099i
$704$	−12.7102	−	7.54415i	−0.479034	−	0.284331i
$705$	−25.1577	−	8.11349i	−0.947495	−	0.305572i
$706$	9.58261	−	11.3736i	0.360646	−	0.428050i
$707$	2.06770	+	17.9802i	0.0777639	+	0.676215i
$708$	14.2857	+	35.5460i	0.536888	+	1.33590i
$709$	17.2122	+	9.93745i	0.646416	+	0.373209i	0.787082	−	0.616849i	$-0.211591\pi$
$709$	17.2122	+	9.93745i	0.646416	+	0.373209i	−0.140666	+	0.990057i	$0.544924\pi$
$710$	4.49929	−	25.2201i	0.168855	−	0.946493i
$711$	4.79782	−	6.66471i	0.179932	−	0.249946i
$712$	23.5919	−	13.4317i	0.884143	−	0.503373i
$713$			4.43866i			0.166229i
$714$	−10.6516	+	27.1380i	−0.398626	+	1.01561i
$715$	5.38452			0.201370
$716$	1.14978	−	3.11990i	0.0429693	−	0.116596i
$717$	−29.2199	+	26.4256i	−1.09124	+	0.986881i
$718$	−3.98843	+	22.3565i	−0.148847	+	0.834339i
$719$	4.05138	−	7.01719i	0.151091	−	0.261697i	−0.780538	−	0.625108i	$-0.785055\pi$
$719$	4.05138	−	7.01719i	0.151091	−	0.261697i	0.931629	+	0.363411i	$0.118388\pi$
$720$	11.1991	−	10.7356i	0.417365	−	0.400093i
$721$	−7.07413	−	9.53918i	−0.263454	−	0.355258i
$722$	13.5741	+	11.4366i	0.505175	+	0.425626i
$723$	−22.4870	−	7.25216i	−0.836300	−	0.269711i
$724$	5.71736	+	6.86960i	0.212484	+	0.255307i
$725$	−2.19834	−	3.80763i	−0.0816442	−	0.141412i
$726$	−9.85028	−	15.7576i	−0.365578	−	0.584820i
$727$			1.56460i			0.0580278i	0.999579	+	0.0290139i	$0.00923671\pi$
$727$			1.56460i			0.0580278i	−0.999579	+	0.0290139i	$0.990763\pi$
$728$	9.96682	+	13.6107i	0.369395	+	0.504446i
$729$	−8.00598	+	25.7857i	−0.296518	+	0.955027i
$730$	−15.0838	+	5.45574i	−0.558278	+	0.201926i
$731$	−23.4752	+	13.5534i	−0.868263	+	0.501292i
$732$	18.8889	−	24.0854i	0.698154	−	0.890223i
$733$	10.2679	+	5.92818i	0.379254	+	0.218962i	0.677493	−	0.735529i	$-0.263066\pi$
$733$	10.2679	+	5.92818i	0.379254	+	0.218962i	−0.298240	+	0.954491i	$0.596400\pi$
$734$	21.9117	−	26.0069i	0.808775	−	0.959934i
$735$	−8.93537	+	12.8781i	−0.329586	+	0.475017i
$736$	5.50655	+	2.06715i	0.202974	+	0.0761962i
$737$	9.77767	+	5.64514i	0.360165	+	0.207941i
$738$	−5.74480	+	1.44675i	−0.211469	+	0.0532558i
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	0.709511	−	0.704694i	$-0.248916\pi$
$739$	−6.94639	−	12.0315i	−0.255527	−	0.442586i	−0.965039	+	0.262108i	$0.915582\pi$
$740$	8.44919	−	22.9266i	0.310598	−	0.842800i
$741$	21.4429	−	4.60684i	0.787724	−	0.169236i
$742$	20.0923	+	40.3961i	0.737610	+	1.48299i
$743$	−25.3287			−0.929221			−0.464611	−	0.885515i	$-0.653806\pi$
$743$	−25.3287			−0.929221			−0.464611	+	0.885515i	$0.653806\pi$
$744$	−13.9339	−	15.5954i	−0.510841	−	0.571754i
$745$	4.42182	+	7.65881i	0.162003	+	0.280597i
$746$	20.1144	+	3.58844i	0.736442	+	0.131382i
$747$	14.1594	+	1.42566i	0.518065	+	0.0521621i
$748$	−2.82061	−	16.3814i	−0.103132	−	0.598965i
$749$	11.4262	+	15.4078i	0.417506	+	0.562990i
$750$	12.3780	−	23.2894i	0.451980	−	0.850409i
$751$	−10.4902	−	6.05653i	−0.382793	−	0.221006i	0.296240	−	0.955114i	$-0.404267\pi$
$751$	−10.4902	−	6.05653i	−0.382793	−	0.221006i	−0.679033	+	0.734108i	$0.737601\pi$
$752$	35.9272	+	30.6423i	1.31013	+	1.11741i
$753$	6.19333	+	6.84823i	0.225698	+	0.249563i
$754$	−1.43229	−	3.95993i	−0.0521608	−	0.144212i
$755$			4.72090i			0.171811i
$756$	−21.8735	−	16.6599i	−0.795531	−	0.605913i
$757$		−	21.6528i		−	0.786983i	−0.919328	−	0.393491i	$-0.871267\pi$
$757$		−	21.6528i		−	0.786983i	0.919328	−	0.393491i	$-0.128733\pi$
$758$	39.6373	−	14.3366i	1.43969	−	0.520729i
$759$	−2.23180	−	2.46780i	−0.0810094	−	0.0895755i
$760$	20.5388	+	0.123901i	0.745021	+	0.00449436i
$761$	33.4532	+	19.3142i	1.21268	+	0.700141i	0.963342	−	0.268276i	$-0.0864539\pi$
$761$	33.4532	+	19.3142i	1.21268	+	0.700141i	0.249337	+	0.968417i	$0.419787\pi$
$762$	47.0927	+	25.0291i	1.70599	+	0.906707i
$763$	32.3778	−	3.72341i	1.17216	−	0.134797i
$764$	7.65428	+	44.4542i	0.276922	+	1.60830i
$765$	17.3592	+	1.74783i	0.627623	+	0.0631931i
$766$	−2.79575	+	15.6711i	−0.101014	+	0.566221i
$767$	12.4652	+	21.5903i	0.450091	+	0.779580i
$768$	−25.8367	+	10.0232i	−0.932301	+	0.361682i
$769$	32.8604			1.18498			0.592489	−	0.805579i	$-0.298145\pi$
$769$	32.8604			1.18498			0.592489	+	0.805579i	$0.298145\pi$
$770$	0.554172	−	8.91989i	0.0199710

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)

\(f(q)\)	\(=\)	\(q+(-1.32990 + 0.481016i) q^{2} +(1.28463 - 1.16178i) q^{3} +(1.53725 - 1.27940i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 + 2.16297i) q^{6} +(2.42742 + 1.05244i) q^{7} +(-1.42896 + 2.44091i) q^{8} +(0.300539 - 2.98491i) q^{9} +O(q^{10})\)	\(q+(-1.32990 + 0.481016i) q^{2} +(1.28463 - 1.16178i) q^{3} +(1.53725 - 1.27940i) q^{4} +(-0.646402 + 1.11960i) q^{5} +(-1.14959 + 2.16297i) q^{6} +(2.42742 + 1.05244i) q^{7} +(-1.42896 + 2.44091i) q^{8} +(0.300539 - 2.98491i) q^{9} +(0.321101 - 1.79988i) q^{10} +(1.60004 - 0.923782i) q^{11} +(0.488406 - 3.42950i) q^{12} -2.25432i q^{13} +(-3.73446 - 0.232013i) q^{14} +(0.470342 + 2.18925i) q^{15} +(0.726254 - 3.93352i) q^{16} +(3.89580 - 2.24924i) q^{17} +(1.03610 + 4.11418i) q^{18} +(-2.80851 + 4.86448i) q^{19} +(0.438742 + 2.54811i) q^{20} +(4.34104 - 1.46812i) q^{21} +(-1.68353 + 1.99818i) q^{22} +(0.519880 - 0.900459i) q^{23} +(1.00011 + 4.79581i) q^{24} +(1.66433 + 2.88270i) q^{25} +(1.08436 + 2.99801i) q^{26} +(-3.08172 - 4.18366i) q^{27} +(5.07804 - 1.48778i) q^{28} -1.32085 q^{29} +(-1.67857 - 2.68523i) q^{30} +(-3.69700 + 2.13446i) q^{31} +(0.926243 + 5.58051i) q^{32} +(0.982223 - 3.04561i) q^{33} +(-4.09909 + 4.86521i) q^{34} +(-2.74740 + 2.03744i) q^{35} +(-3.35690 - 4.97305i) q^{36} +(-8.18394 - 4.72500i) q^{37} +(1.39513 - 7.82020i) q^{38} +(-2.61902 - 2.89596i) q^{39} +(-1.80916 - 3.17768i) q^{40} +1.39634i q^{41} +(-5.06694 + 4.04056i) q^{42} -6.02578 q^{43} +(1.27776 - 3.46717i) q^{44} +(3.14763 + 2.26593i) q^{45} +(-0.258251 + 1.44759i) q^{46} +(-5.90249 + 10.2234i) q^{47} +(-3.63691 - 5.89685i) q^{48} +(4.78472 + 5.10944i) q^{49} +(-3.60001 - 3.03313i) q^{50} +(2.39154 - 7.41551i) q^{51} +(-2.88418 - 3.46544i) q^{52} +(-6.02901 - 10.4425i) q^{53} +(6.11078 + 4.08147i) q^{54} +2.38854i q^{55} +(-6.03762 + 4.42122i) q^{56} +(2.04356 + 9.51192i) q^{57} +(1.75660 - 0.635353i) q^{58} +(-9.57732 + 5.52947i) q^{59} +(3.52396 + 2.76365i) q^{60} +(7.65220 + 4.41800i) q^{61} +(3.88991 - 4.61693i) q^{62} +(3.87098 - 6.92932i) q^{63} +(-3.91612 - 6.97596i) q^{64} +(2.52393 + 1.45719i) q^{65} +(0.158732 + 4.52281i) q^{66} +(3.05545 + 5.29219i) q^{67} +(3.11112 - 8.44195i) q^{68} +(-0.378281 - 1.76074i) q^{69} +(2.67372 - 4.03113i) q^{70} +14.0121 q^{71} +(6.85644 + 4.99892i) q^{72} +(-4.38664 - 7.59788i) q^{73} +(13.1566 + 2.34715i) q^{74} +(5.48711 + 1.76962i) q^{75} +(1.90626 + 11.0711i) q^{76} +(4.85619 - 0.558456i) q^{77} +(4.87602 + 2.59153i) q^{78} +(2.37061 + 1.36867i) q^{79} +(3.93451 + 3.35575i) q^{80} +(-8.81935 - 1.79416i) q^{81} +(-0.671663 - 1.85699i) q^{82} +4.74366i q^{83} +(4.79492 - 7.81081i) q^{84} +5.81566i q^{85} +(8.01366 - 2.89850i) q^{86} +(-1.69681 + 1.53454i) q^{87} +(-0.0315236 + 5.22561i) q^{88} +(-8.31219 - 4.79904i) q^{89} +(-5.27598 - 1.49939i) q^{90} +(2.37254 - 5.47217i) q^{91} +(-0.352866 - 2.04936i) q^{92} +(-2.26949 + 7.03709i) q^{93} +(2.93207 - 16.4353i) q^{94} +(-3.63085 - 6.28882i) q^{95} +(7.67320 + 6.09279i) q^{96} -8.73466 q^{97} +(-8.82091 - 4.49350i) q^{98} +(-2.27653 - 5.05360i) 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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