LMFDB - Embedded newform 154.2.e.e.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(23,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("154.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.e (of order $3$, 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:	$1.22969619113$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			23.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	154.23
Dual form			154.2.e.e.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -2.41421 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -2.41421 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +(0.292893 + 0.507306i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.20711 - 2.09077i) q^{12} -3.82843 q^{13} +(-2.62132 + 0.358719i) q^{14} +1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.82843 - 3.16693i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(0.292893 - 0.507306i) q^{19} -0.585786 q^{20} +(-2.41421 + 5.91359i) q^{21} +1.00000 q^{22} +(3.12132 - 5.40629i) q^{23} +(1.20711 + 2.09077i) q^{24} +(2.32843 + 4.03295i) q^{25} +(1.91421 - 3.31552i) q^{26} +0.414214 q^{27} +(1.00000 - 2.44949i) q^{28} +2.65685 q^{29} +(-0.707107 + 1.22474i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.20711 - 2.09077i) q^{33} +3.65685 q^{34} +(1.53553 - 0.210133i) q^{35} +2.82843 q^{36} +(4.70711 - 8.15295i) q^{37} +(0.292893 + 0.507306i) q^{38} +(-4.62132 - 8.00436i) q^{39} +(0.292893 - 0.507306i) q^{40} -5.41421 q^{41} +(-3.91421 - 5.04757i) q^{42} -5.65685 q^{43} +(-0.500000 + 0.866025i) q^{44} +(0.828427 + 1.43488i) q^{45} +(3.12132 + 5.40629i) q^{46} +(5.24264 - 9.08052i) q^{47} -2.41421 q^{48} +(-1.74264 + 6.77962i) q^{49} -4.65685 q^{50} +(4.41421 - 7.64564i) q^{51} +(1.91421 + 3.31552i) q^{52} +(-3.94975 - 6.84116i) q^{53} +(-0.207107 + 0.358719i) q^{54} -0.585786 q^{55} +(1.62132 + 2.09077i) q^{56} +1.41421 q^{57} +(-1.32843 + 2.30090i) q^{58} +(2.79289 + 4.83743i) q^{59} +(-0.707107 - 1.22474i) q^{60} +(-5.91421 + 10.2437i) q^{61} -4.00000 q^{62} +(-7.41421 + 1.01461i) q^{63} +1.00000 q^{64} +(-1.12132 + 1.94218i) q^{65} +(1.20711 + 2.09077i) q^{66} +(-1.37868 - 2.38794i) q^{67} +(-1.82843 + 3.16693i) q^{68} +15.0711 q^{69} +(-0.585786 + 1.43488i) q^{70} -11.0711 q^{71} +(-1.41421 + 2.44949i) q^{72} +(4.70711 + 8.15295i) q^{73} +(4.70711 + 8.15295i) q^{74} +(-5.62132 + 9.73641i) q^{75} -0.585786 q^{76} +(1.00000 - 2.44949i) q^{77} +9.24264 q^{78} +(6.62132 - 11.4685i) q^{79} +(0.292893 + 0.507306i) q^{80} +(4.74264 + 8.21449i) q^{81} +(2.70711 - 4.68885i) q^{82} -12.1421 q^{83} +(6.32843 - 0.866025i) q^{84} -2.14214 q^{85} +(2.82843 - 4.89898i) q^{86} +(3.20711 + 5.55487i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-6.24264 + 10.8126i) q^{89} -1.65685 q^{90} +(-6.20711 - 8.00436i) q^{91} -6.24264 q^{92} +(-4.82843 + 8.36308i) q^{93} +(5.24264 + 9.08052i) q^{94} +(-0.171573 - 0.297173i) q^{95} +(1.20711 - 2.09077i) q^{96} -3.82843 q^{97} +(-5.00000 - 4.89898i) q^{98} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 4 q^{27} + 4 q^{28} - 12 q^{29} + 8 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} - 8 q^{35} + 16 q^{37} + 4 q^{38} - 10 q^{39} + 4 q^{40} - 16 q^{41} - 10 q^{42} - 2 q^{44} - 8 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} + 12 q^{51} + 2 q^{52} + 4 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} + 6 q^{58} + 14 q^{59} - 18 q^{61} - 16 q^{62} - 24 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} - 14 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 16 q^{71} + 16 q^{73} + 16 q^{74} - 14 q^{75} - 8 q^{76} + 4 q^{77} + 20 q^{78} + 18 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{82} + 8 q^{83} + 14 q^{84} + 48 q^{85} + 10 q^{87} - 2 q^{88} - 8 q^{89} + 16 q^{90} - 22 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} - 12 q^{95} + 2 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 4 * q^27 + 4 * q^28 - 12 * q^29 + 8 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 - 8 * q^35 + 16 * q^37 + 4 * q^38 - 10 * q^39 + 4 * q^40 - 16 * q^41 - 10 * q^42 - 2 * q^44 - 8 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 + 12 * q^51 + 2 * q^52 + 4 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 + 6 * q^58 + 14 * q^59 - 18 * q^61 - 16 * q^62 - 24 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 - 14 * q^67 + 4 * q^68 + 32 * q^69 - 8 * q^70 - 16 * q^71 + 16 * q^73 + 16 * q^74 - 14 * q^75 - 8 * q^76 + 4 * q^77 + 20 * q^78 + 18 * q^79 + 4 * q^80 + 2 * q^81 + 8 * q^82 + 8 * q^83 + 14 * q^84 + 48 * q^85 + 10 * q^87 - 2 * q^88 - 8 * q^89 + 16 * q^90 - 22 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 - 12 * q^95 + 2 * q^96 - 4 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	0.969528	+	0.244981i	$0.0787816\pi$
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	−0.272605	+	0.962126i	$0.587885\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	−0.793071	−	0.609129i	$-0.791519\pi$
$5$	0.292893	−	0.507306i	0.130986	−	0.226874i	0.924057	+	0.382255i	$0.124852\pi$
$6$	−2.41421			−0.985599
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	1.00000			0.353553
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$	0.292893	+	0.507306i	0.0926210	+	0.160424i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.20711	−	2.09077i	0.348462	−	0.603553i
$13$	−3.82843			−1.06181			−0.530907	−	0.847430i	$-0.678149\pi$
$13$	−3.82843			−1.06181			−0.530907	+	0.847430i	$0.678149\pi$
$14$	−2.62132	+	0.358719i	−0.700577	+	0.0958718i
$15$	1.41421			0.365148
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	0.554485	−	0.832194i	$-0.312915\pi$
$17$	−1.82843	−	3.16693i	−0.443459	−	0.768093i	−0.997943	+	0.0641009i	$0.979582\pi$
$18$	−1.41421	−	2.44949i	−0.333333	−	0.577350i
$19$	0.292893	−	0.507306i	0.0671943	−	0.116384i	−0.830471	−	0.557062i	$-0.811929\pi$
$19$	0.292893	−	0.507306i	0.0671943	−	0.116384i	0.897665	+	0.440678i	$0.145262\pi$
$20$	−0.585786			−0.130986
$21$	−2.41421	+	5.91359i	−0.526825	+	1.29045i
$22$	1.00000			0.213201
$23$	3.12132	−	5.40629i	0.650840	−	1.12729i	−0.332079	−	0.943252i	$-0.607750\pi$
$23$	3.12132	−	5.40629i	0.650840	−	1.12729i	0.982919	−	0.184037i	$-0.0589166\pi$
$24$	1.20711	+	2.09077i	0.246400	+	0.426777i
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$	1.91421	−	3.31552i	0.375408	−	0.650226i
$27$	0.414214			0.0797154
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	2.65685			0.493365			0.246683	−	0.969096i	$-0.420659\pi$
$29$	2.65685			0.493365			0.246683	+	0.969096i	$0.420659\pi$
$30$	−0.707107	+	1.22474i	−0.129099	+	0.223607i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.20711	−	2.09077i	0.210130	−	0.363956i
$34$	3.65685			0.627145
$35$	1.53553	−	0.210133i	0.259553	−	0.0355190i
$36$	2.82843			0.471405
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	−0.161599	−	0.986857i	$-0.551665\pi$
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	0.935442	−	0.353480i	$-0.115002\pi$
$38$	0.292893	+	0.507306i	0.0475136	+	0.0822959i
$39$	−4.62132	−	8.00436i	−0.740003	−	1.28172i
$40$	0.292893	−	0.507306i	0.0463105	−	0.0802121i
$41$	−5.41421			−0.845558			−0.422779	−	0.906233i	$-0.638945\pi$
$41$	−5.41421			−0.845558			−0.422779	+	0.906233i	$0.638945\pi$
$42$	−3.91421	−	5.04757i	−0.603976	−	0.778856i
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	0.828427	+	1.43488i	0.123495	+	0.213899i
$46$	3.12132	+	5.40629i	0.460214	+	0.797113i
$47$	5.24264	−	9.08052i	0.764718	−	1.32453i	−0.175678	−	0.984448i	$-0.556212\pi$
$47$	5.24264	−	9.08052i	0.764718	−	1.32453i	0.940396	−	0.340082i	$-0.110455\pi$
$48$	−2.41421			−0.348462
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−4.65685			−0.658579
$51$	4.41421	−	7.64564i	0.618114	−	1.07060i
$52$	1.91421	+	3.31552i	0.265454	+	0.459779i
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	−0.998757	−	0.0498379i	$-0.984130\pi$
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	0.456218	−	0.889868i	$-0.349204\pi$
$54$	−0.207107	+	0.358719i	−0.0281837	+	0.0488155i
$55$	−0.585786			−0.0789874
$56$	1.62132	+	2.09077i	0.216658	+	0.279391i
$57$	1.41421			0.187317
$58$	−1.32843	+	2.30090i	−0.174431	+	0.302123i
$59$	2.79289	+	4.83743i	0.363604	+	0.629780i	0.988551	−	0.150887i	$-0.0482129\pi$
$59$	2.79289	+	4.83743i	0.363604	+	0.629780i	−0.624947	+	0.780667i	$0.714880\pi$
$60$	−0.707107	−	1.22474i	−0.0912871	−	0.158114i
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	0.187017	+	0.982357i	$0.440118\pi$
$61$	−5.91421	+	10.2437i	−0.757237	+	1.31157i	−0.944254	+	0.329217i	$0.893215\pi$
$62$	−4.00000			−0.508001
$63$	−7.41421	+	1.01461i	−0.934103	+	0.127829i
$64$	1.00000			0.125000
$65$	−1.12132	+	1.94218i	−0.139083	+	0.240898i
$66$	1.20711	+	2.09077i	0.148585	+	0.257356i
$67$	−1.37868	−	2.38794i	−0.168433	−	0.291734i	0.769436	−	0.638723i	$-0.220537\pi$
$67$	−1.37868	−	2.38794i	−0.168433	−	0.291734i	−0.937869	+	0.346990i	$0.887204\pi$
$68$	−1.82843	+	3.16693i	−0.221729	+	0.384047i
$69$	15.0711			1.81434
$70$	−0.585786	+	1.43488i	−0.0700149	+	0.171501i
$71$	−11.0711			−1.31389			−0.656947	−	0.753937i	$-0.728152\pi$
$71$	−11.0711			−1.31389			−0.656947	+	0.753937i	$0.728152\pi$
$72$	−1.41421	+	2.44949i	−0.166667	+	0.288675i
$73$	4.70711	+	8.15295i	0.550925	+	0.954230i	0.998208	+	0.0598379i	$0.0190584\pi$
$73$	4.70711	+	8.15295i	0.550925	+	0.954230i	−0.447283	+	0.894393i	$0.647608\pi$
$74$	4.70711	+	8.15295i	0.547190	+	0.947761i
$75$	−5.62132	+	9.73641i	−0.649094	+	1.12426i
$76$	−0.585786			−0.0671943
$77$	1.00000	−	2.44949i	0.113961	−	0.279145i
$78$	9.24264			1.04652
$79$	6.62132	−	11.4685i	0.744957	−	1.29030i	−0.205258	−	0.978708i	$-0.565803\pi$
$79$	6.62132	−	11.4685i	0.744957	−	1.29030i	0.950215	−	0.311595i	$-0.100863\pi$
$80$	0.292893	+	0.507306i	0.0327465	+	0.0567185i
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	2.70711	−	4.68885i	0.298950	−	0.517796i
$83$	−12.1421			−1.33277			−0.666386	−	0.745607i	$-0.732160\pi$
$83$	−12.1421			−1.33277			−0.666386	+	0.745607i	$0.732160\pi$
$84$	6.32843	−	0.866025i	0.690488	−	0.0944911i
$85$	−2.14214			−0.232347
$86$	2.82843	−	4.89898i	0.304997	−	0.528271i
$87$	3.20711	+	5.55487i	0.343838	+	0.595545i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−6.24264	+	10.8126i	−0.661719	+	1.14613i	0.318445	+	0.947941i	$0.396839\pi$
$89$	−6.24264	+	10.8126i	−0.661719	+	1.14613i	−0.980164	+	0.198189i	$0.936494\pi$
$90$	−1.65685			−0.174648
$91$	−6.20711	−	8.00436i	−0.650682	−	0.839085i
$92$	−6.24264			−0.650840
$93$	−4.82843	+	8.36308i	−0.500685	+	0.867211i
$94$	5.24264	+	9.08052i	0.540737	+	0.936584i
$95$	−0.171573	−	0.297173i	−0.0176030	−	0.0304893i
$96$	1.20711	−	2.09077i	0.123200	−	0.213388i
$97$	−3.82843			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$97$	−3.82843			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$98$	−5.00000	−	4.89898i	−0.505076	−	0.494872i
$99$	2.82843			0.284268
$100$	2.32843	−	4.03295i	0.232843	−	0.403295i
$101$	−3.08579	−	5.34474i	−0.307047	−	0.531821i	0.670668	−	0.741758i	$-0.266008\pi$
$101$	−3.08579	−	5.34474i	−0.307047	−	0.531821i	−0.977715	+	0.209936i	$0.932674\pi$
$102$	4.41421	+	7.64564i	0.437072	+	0.757031i
$103$	−6.70711	+	11.6170i	−0.660871	+	1.14466i	0.319516	+	0.947581i	$0.396480\pi$
$103$	−6.70711	+	11.6170i	−0.660871	+	1.14466i	−0.980387	+	0.197081i	$0.936854\pi$
$104$	−3.82843			−0.375408
$105$	2.29289	+	2.95680i	0.223763	+	0.288554i
$106$	7.89949			0.767267
$107$	1.53553	−	2.65962i	0.148446	−	0.257115i	−0.782207	−	0.623018i	$-0.785906\pi$
$107$	1.53553	−	2.65962i	0.148446	−	0.257115i	0.930653	+	0.365903i	$0.119240\pi$
$108$	−0.207107	−	0.358719i	−0.0199289	−	0.0345178i
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	−0.926272	−	0.376854i	$-0.877006\pi$
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	0.136771	−	0.990603i	$-0.456328\pi$
$110$	0.292893	−	0.507306i	0.0279263	−	0.0483697i
$111$	22.7279			2.15724
$112$	−2.62132	+	0.358719i	−0.247691	+	0.0338958i
$113$	−8.17157			−0.768717			−0.384358	−	0.923184i	$-0.625577\pi$
$113$	−8.17157			−0.768717			−0.384358	+	0.923184i	$0.625577\pi$
$114$	−0.707107	+	1.22474i	−0.0662266	+	0.114708i
$115$	−1.82843	−	3.16693i	−0.170502	−	0.295318i
$116$	−1.32843	−	2.30090i	−0.123341	−	0.213634i
$117$	5.41421	−	9.37769i	0.500544	−	0.866968i
$118$	−5.58579			−0.514213
$119$	3.65685	−	8.95743i	0.335223	−	0.821126i
$120$	1.41421			0.129099
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−5.91421	−	10.2437i	−0.535448	−	0.927423i
$123$	−6.53553	−	11.3199i	−0.589289	−	1.02068i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	5.65685			0.505964
$126$	2.82843	−	6.92820i	0.251976	−	0.617213i
$127$	15.7279			1.39563			0.697814	−	0.716279i	$-0.254156\pi$
$127$	15.7279			1.39563			0.697814	+	0.716279i	$0.254156\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.82843	−	11.8272i	−0.601209	−	1.04133i
$130$	−1.12132	−	1.94218i	−0.0983463	−	0.170341i
$131$	0.292893	−	0.507306i	0.0255902	−	0.0443235i	−0.852947	−	0.521998i	$-0.825187\pi$
$131$	0.292893	−	0.507306i	0.0255902	−	0.0443235i	0.878537	+	0.477674i	$0.158520\pi$
$132$	−2.41421			−0.210130
$133$	1.53553	−	0.210133i	0.133148	−	0.0182208i
$134$	2.75736			0.238200
$135$	0.121320	−	0.210133i	0.0104416	−	0.0180854i
$136$	−1.82843	−	3.16693i	−0.156786	−	0.271562i
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	0.964277	+	0.264897i	$0.0853378\pi$
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	−0.252731	+	0.967537i	$0.581329\pi$
$138$	−7.53553	+	13.0519i	−0.641467	+	1.11105i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−0.949747	−	1.22474i	−0.0802683	−	0.103510i
$141$	25.3137			2.13180
$142$	5.53553	−	9.58783i	0.464532	−	0.804592i
$143$	1.91421	+	3.31552i	0.160075	+	0.277257i
$144$	−1.41421	−	2.44949i	−0.117851	−	0.204124i
$145$	0.778175	−	1.34784i	0.0646239	−	0.111932i
$146$	−9.41421			−0.779126
$147$	−16.2782	+	4.54026i	−1.34260	+	0.374474i
$148$	−9.41421			−0.773844
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	0.236436	+	0.971647i	$0.424021\pi$
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	−0.959689	+	0.281064i	$0.909313\pi$
$150$	−5.62132	−	9.73641i	−0.458979	−	0.794975i
$151$	7.86396	+	13.6208i	0.639960	+	1.10844i	0.985441	+	0.170018i	$0.0543825\pi$
$151$	7.86396	+	13.6208i	0.639960	+	1.10844i	−0.345481	+	0.938426i	$0.612284\pi$
$152$	0.292893	−	0.507306i	0.0237568	−	0.0411479i
$153$	10.3431			0.836194
$154$	1.62132	+	2.09077i	0.130650	+	0.168479i
$155$	2.34315			0.188206
$156$	−4.62132	+	8.00436i	−0.370002	+	0.640862i
$157$	−8.82843	−	15.2913i	−0.704585	−	1.22038i	−0.966841	−	0.255379i	$-0.917800\pi$
$157$	−8.82843	−	15.2913i	−0.704585	−	1.22038i	0.262256	−	0.964998i	$-0.415534\pi$
$158$	6.62132	+	11.4685i	0.526764	+	0.912382i
$159$	9.53553	−	16.5160i	0.756217	−	1.30981i
$160$	−0.585786			−0.0463105
$161$	16.3640	−	2.23936i	1.28966	−	0.176486i
$162$	−9.48528			−0.745234
$163$	−4.86396	+	8.42463i	−0.380975	+	0.659868i	−0.991202	−	0.132359i	$-0.957745\pi$
$163$	−4.86396	+	8.42463i	−0.380975	+	0.659868i	0.610227	+	0.792227i	$0.291078\pi$
$164$	2.70711	+	4.68885i	0.211390	+	0.366137i
$165$	−0.707107	−	1.22474i	−0.0550482	−	0.0953463i
$166$	6.07107	−	10.5154i	0.471206	−	0.816153i
$167$	13.7279			1.06230			0.531149	−	0.847278i	$-0.321760\pi$
$167$	13.7279			1.06230			0.531149	+	0.847278i	$0.321760\pi$
$168$	−2.41421	+	5.91359i	−0.186261	+	0.456243i
$169$	1.65685			0.127450
$170$	1.07107	−	1.85514i	0.0821472	−	0.142283i
$171$	0.828427	+	1.43488i	0.0633514	+	0.109728i
$172$	2.82843	+	4.89898i	0.215666	+	0.373544i
$173$	4.91421	−	8.51167i	0.373621	−	0.647130i	−0.616499	−	0.787356i	$-0.711449\pi$
$173$	4.91421	−	8.51167i	0.373621	−	0.647130i	0.990120	+	0.140226i	$0.0447828\pi$
$174$	−6.41421			−0.486260
$175$	−4.65685	+	11.4069i	−0.352025	+	0.862282i
$176$	1.00000			0.0753778
$177$	−6.74264	+	11.6786i	−0.506808	+	0.877817i
$178$	−6.24264	−	10.8126i	−0.467906	−	0.810436i
$179$	−0.449747	−	0.778985i	−0.0336157	−	0.0582241i	0.848728	−	0.528829i	$-0.177369\pi$
$179$	−0.449747	−	0.778985i	−0.0336157	−	0.0582241i	−0.882344	+	0.470605i	$0.844036\pi$
$180$	0.828427	−	1.43488i	0.0617473	−	0.106949i
$181$	−7.65685			−0.569129			−0.284565	−	0.958657i	$-0.591849\pi$
$181$	−7.65685			−0.569129			−0.284565	+	0.958657i	$0.591849\pi$
$182$	10.0355	−	1.37333i	0.743883	−	0.101798i
$183$	−28.5563			−2.11095
$184$	3.12132	−	5.40629i	0.230107	−	0.398557i
$185$	−2.75736	−	4.77589i	−0.202725	−	0.351130i
$186$	−4.82843	−	8.36308i	−0.354037	−	0.613211i
$187$	−1.82843	+	3.16693i	−0.133708	+	0.231589i
$188$	−10.4853			−0.764718
$189$	0.671573	+	0.866025i	0.0488497	+	0.0629941i
$190$	0.343146			0.0248944
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	−0.706639	−	0.707575i	$-0.749789\pi$
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	0.966097	+	0.258180i	$0.0831226\pi$
$192$	1.20711	+	2.09077i	0.0871154	+	0.150888i
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	−0.927081	−	0.374862i	$-0.877690\pi$
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	0.138901	−	0.990306i	$-0.455643\pi$
$194$	1.91421	−	3.31552i	0.137433	−	0.238040i
$195$	−5.41421			−0.387720
$196$	6.74264	−	1.88064i	0.481617	−	0.134331i
$197$	−0.514719			−0.0366722			−0.0183361	−	0.999832i	$-0.505837\pi$
$197$	−0.514719			−0.0366722			−0.0183361	+	0.999832i	$0.505837\pi$
$198$	−1.41421	+	2.44949i	−0.100504	+	0.174078i
$199$	−0.0502525	−	0.0870399i	−0.00356231	−	0.00617010i	0.864239	−	0.503082i	$-0.167801\pi$
$199$	−0.0502525	−	0.0870399i	−0.00356231	−	0.00617010i	−0.867801	+	0.496912i	$0.834467\pi$
$200$	2.32843	+	4.03295i	0.164645	+	0.285173i
$201$	3.32843	−	5.76500i	0.234769	−	0.406632i
$202$	6.17157			0.434230
$203$	4.30761	+	5.55487i	0.302335	+	0.389876i
$204$	−8.82843			−0.618114
$205$	−1.58579	+	2.74666i	−0.110756	+	0.191835i
$206$	−6.70711	−	11.6170i	−0.467306	−	0.809398i
$207$	8.82843	+	15.2913i	0.613618	+	1.06282i
$208$	1.91421	−	3.31552i	0.132727	−	0.229890i
$209$	−0.585786			−0.0405197
$210$	−3.70711	+	0.507306i	−0.255815	+	0.0350074i
$211$	7.41421			0.510416			0.255208	−	0.966886i	$-0.417856\pi$
$211$	7.41421			0.510416			0.255208	+	0.966886i	$0.417856\pi$
$212$	−3.94975	+	6.84116i	−0.271270	+	0.469853i
$213$	−13.3640	−	23.1471i	−0.915684	−	1.58601i
$214$	1.53553	+	2.65962i	0.104967	+	0.181808i
$215$	−1.65685	+	2.86976i	−0.112997	+	0.195716i
$216$	0.414214			0.0281837
$217$	−4.00000	+	9.79796i	−0.271538	+	0.665129i
$218$	16.4853			1.11652
$219$	−11.3640	+	19.6830i	−0.767905	+	1.33005i
$220$	0.292893	+	0.507306i	0.0197469	+	0.0342026i
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$	−11.3640	+	19.6830i	−0.762699	+	1.32103i
$223$	8.58579			0.574947			0.287473	−	0.957789i	$-0.407185\pi$
$223$	8.58579			0.574947			0.287473	+	0.957789i	$0.407185\pi$
$224$	1.00000	−	2.44949i	0.0668153	−	0.163663i
$225$	−13.1716			−0.878105
$226$	4.08579	−	7.07679i	0.271782	−	0.470741i
$227$	14.4142	+	24.9662i	0.956705	+	1.65706i	0.730417	+	0.683001i	$0.239326\pi$
$227$	14.4142	+	24.9662i	0.956705	+	1.65706i	0.226288	+	0.974061i	$0.427341\pi$
$228$	−0.707107	−	1.22474i	−0.0468293	−	0.0811107i
$229$	−11.6569	+	20.1903i	−0.770307	+	1.33421i	0.167088	+	0.985942i	$0.446564\pi$
$229$	−11.6569	+	20.1903i	−0.770307	+	1.33421i	−0.937395	+	0.348268i	$0.886770\pi$
$230$	3.65685			0.241126
$231$	6.32843	−	0.866025i	0.416380	−	0.0569803i
$232$	2.65685			0.174431
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	−0.888258	−	0.459345i	$-0.848084\pi$
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	0.841934	+	0.539581i	$0.181417\pi$
$234$	5.41421	+	9.37769i	0.353938	+	0.613039i
$235$	−3.07107	−	5.31925i	−0.200334	−	0.346989i
$236$	2.79289	−	4.83743i	0.181802	−	0.314890i
$237$	31.9706			2.07671
$238$	5.92893	+	7.64564i	0.384316	+	0.495593i
$239$	20.2132			1.30748			0.653742	−	0.756718i	$-0.273198\pi$
$239$	20.2132			1.30748			0.653742	+	0.756718i	$0.273198\pi$
$240$	−0.707107	+	1.22474i	−0.0456435	+	0.0790569i
$241$	−6.12132	−	10.6024i	−0.394309	−	0.682963i	0.598704	−	0.800971i	$-0.295683\pi$
$241$	−6.12132	−	10.6024i	−0.394309	−	0.682963i	−0.993013	+	0.118007i	$0.962349\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$	11.8284			0.757237
$245$	2.92893	+	2.86976i	0.187123	+	0.183342i
$246$	13.0711			0.833381
$247$	−1.12132	+	1.94218i	−0.0713479	+	0.123578i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−14.6569	−	25.3864i	−0.928840	−	1.60880i
$250$	−2.82843	+	4.89898i	−0.178885	+	0.309839i
$251$	−26.1421			−1.65008			−0.825038	−	0.565077i	$-0.808847\pi$
$251$	−26.1421			−1.65008			−0.825038	+	0.565077i	$0.808847\pi$
$252$	4.58579	+	5.91359i	0.288877	+	0.372521i
$253$	−6.24264			−0.392471
$254$	−7.86396	+	13.6208i	−0.493429	+	0.854644i
$255$	−2.58579	−	4.47871i	−0.161928	−	0.280468i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.5711	−	21.7737i	0.784162	−	1.35821i	−0.145337	−	0.989382i	$-0.546427\pi$
$257$	12.5711	−	21.7737i	0.784162	−	1.35821i	0.929499	−	0.368826i	$-0.120240\pi$
$258$	13.6569			0.850239
$259$	24.6777	−	3.37706i	1.53340	−	0.209840i
$260$	2.24264			0.139083
$261$	−3.75736	+	6.50794i	−0.232575	+	0.402831i
$262$	0.292893	+	0.507306i	0.0180950	+	0.0313415i
$263$	8.52082	+	14.7585i	0.525416	+	0.910047i	0.999562	+	0.0296008i	$0.00942362\pi$
$263$	8.52082	+	14.7585i	0.525416	+	0.910047i	−0.474146	+	0.880446i	$0.657243\pi$
$264$	1.20711	−	2.09077i	0.0742923	−	0.128678i
$265$	−4.62742			−0.284260
$266$	−0.585786	+	1.43488i	−0.0359169	+	0.0879780i
$267$	−30.1421			−1.84467
$268$	−1.37868	+	2.38794i	−0.0842163	+	0.145867i
$269$	−1.17157	−	2.02922i	−0.0714321	−	0.123724i	0.828097	−	0.560585i	$-0.189424\pi$
$269$	−1.17157	−	2.02922i	−0.0714321	−	0.123724i	−0.899529	+	0.436861i	$0.856090\pi$
$270$	0.121320	+	0.210133i	0.00738332	+	0.0127883i
$271$	−2.27817	+	3.94591i	−0.138389	+	0.239697i	−0.926887	−	0.375340i	$-0.877526\pi$
$271$	−2.27817	+	3.94591i	−0.138389	+	0.239697i	0.788498	+	0.615038i	$0.210859\pi$
$272$	3.65685			0.221729
$273$	9.24264	−	22.6398i	0.559390	−	1.37022i
$274$	−16.6569			−1.00628
$275$	2.32843	−	4.03295i	0.140409	−	0.243196i
$276$	−7.53553	−	13.0519i	−0.453586	−	0.785634i
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	0.837253	−	0.546816i	$-0.184160\pi$
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	−0.892183	+	0.451675i	$0.850827\pi$
$278$		0			0
$279$	−11.3137			−0.677334
$280$	1.53553	−	0.210133i	0.0917657	−	0.0125578i
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$	−12.6569	+	21.9223i	−0.753705	+	1.30545i
$283$	11.7071	+	20.2773i	0.695915	+	1.20536i	0.969871	+	0.243618i	$0.0783344\pi$
$283$	11.7071	+	20.2773i	0.695915	+	1.20536i	−0.273956	+	0.961742i	$0.588332\pi$
$284$	5.53553	+	9.58783i	0.328474	+	0.568933i
$285$	0.414214	−	0.717439i	0.0245359	−	0.0424974i
$286$	−3.82843			−0.226380
$287$	−8.77817	−	11.3199i	−0.518159	−	0.668191i
$288$	2.82843			0.166667
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	0.778175	+	1.34784i	0.0456960	+	0.0791478i
$291$	−4.62132	−	8.00436i	−0.270907	−	0.469224i
$292$	4.70711	−	8.15295i	0.275463	−	0.477115i
$293$	−10.8284			−0.632603			−0.316302	−	0.948659i	$-0.602441\pi$
$293$	−10.8284			−0.632603			−0.316302	+	0.948659i	$0.602441\pi$
$294$	4.20711	−	16.3674i	0.245363	−	0.954569i
$295$	3.27208			0.190508
$296$	4.70711	−	8.15295i	0.273595	−	0.473880i
$297$	−0.207107	−	0.358719i	−0.0120176	−	0.0208150i
$298$	−8.82843	−	15.2913i	−0.511417	−	0.885800i
$299$	−11.9497	+	20.6976i	−0.691072	+	1.19697i
$300$	11.2426			0.649094
$301$	−9.17157	−	11.8272i	−0.528641	−	0.681707i
$302$	−15.7279			−0.905040
$303$	7.44975	−	12.9033i	0.427977	−	0.741278i
$304$	0.292893	+	0.507306i	0.0167986	+	0.0290960i
$305$	3.46447	+	6.00063i	0.198375	+	0.343595i
$306$	−5.17157	+	8.95743i	−0.295639	+	0.512062i
$307$	9.89949			0.564994			0.282497	−	0.959268i	$-0.408837\pi$
$307$	9.89949			0.564994			0.282497	+	0.959268i	$0.408837\pi$
$308$	−2.62132	+	0.358719i	−0.149364	+	0.0204399i
$309$	−32.3848			−1.84231
$310$	−1.17157	+	2.02922i	−0.0665409	+	0.115252i
$311$	−8.36396	−	14.4868i	−0.474277	−	0.821471i	0.525289	−	0.850924i	$-0.323957\pi$
$311$	−8.36396	−	14.4868i	−0.474277	−	0.821471i	−0.999566	+	0.0294522i	$0.990624\pi$
$312$	−4.62132	−	8.00436i	−0.261631	−	0.453158i
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	−0.411227	−	0.911533i	$-0.634900\pi$
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	0.995024	−	0.0996335i	$-0.0317670\pi$
$314$	17.6569			0.996434
$315$	−1.65685	+	4.05845i	−0.0933532	+	0.228668i
$316$	−13.2426			−0.744957
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	−0.961832	−	0.273642i	$-0.911772\pi$
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	0.717896	+	0.696150i	$0.245105\pi$
$318$	9.53553	+	16.5160i	0.534726	+	0.926173i
$319$	−1.32843	−	2.30090i	−0.0743776	−	0.128826i
$320$	0.292893	−	0.507306i	0.0163732	−	0.0283593i
$321$	7.41421			0.413821
$322$	−6.24264	+	15.2913i	−0.347889	+	0.852150i
$323$	−2.14214			−0.119192
$324$	4.74264	−	8.21449i	0.263480	−	0.456361i
$325$	−8.91421	−	15.4399i	−0.494472	−	0.856450i
$326$	−4.86396	−	8.42463i	−0.269390	−	0.466597i
$327$	19.8995	−	34.4669i	1.10044	−	1.90603i
$328$	−5.41421			−0.298950
$329$	27.4853	−	3.76127i	1.51531	−	0.207366i
$330$	1.41421			0.0778499
$331$	12.0355	−	20.8462i	0.661533	−	1.14581i	−0.318680	−	0.947862i	$-0.603240\pi$
$331$	12.0355	−	20.8462i	0.661533	−	1.14581i	0.980213	−	0.197946i	$-0.0634271\pi$
$332$	6.07107	+	10.5154i	0.333193	+	0.577107i
$333$	13.3137	+	23.0600i	0.729587	+	1.26368i
$334$	−6.86396	+	11.8887i	−0.375579	+	0.650522i
$335$	−1.61522			−0.0882491
$336$	−3.91421	−	5.04757i	−0.213538	−	0.275367i
$337$	−28.2426			−1.53847			−0.769237	−	0.638963i	$-0.779364\pi$
$337$	−28.2426			−1.53847			−0.769237	+	0.638963i	$0.779364\pi$
$338$	−0.828427	+	1.43488i	−0.0450605	+	0.0780471i
$339$	−9.86396	−	17.0849i	−0.535737	−	0.927923i
$340$	1.07107	+	1.85514i	0.0580868	+	0.100609i
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$	−1.65685			−0.0895924
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−5.65685			−0.304997
$345$	4.41421	−	7.64564i	0.237653	−	0.411628i
$346$	4.91421	+	8.51167i	0.264190	+	0.457590i
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	0.531885	−	0.846816i	$-0.321484\pi$
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	−0.999307	+	0.0372179i	$0.988150\pi$
$348$	3.20711	−	5.55487i	0.171919	−	0.297772i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−7.55025	−	9.73641i	−0.403578	−	0.520433i
$351$	−1.58579			−0.0846430
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	1.34315	+	2.32640i	0.0714884	+	0.123822i	0.899554	−	0.436810i	$-0.143892\pi$
$353$	1.34315	+	2.32640i	0.0714884	+	0.123822i	−0.828065	+	0.560632i	$0.810558\pi$
$354$	−6.74264	−	11.6786i	−0.358367	−	0.620710i
$355$	−3.24264	+	5.61642i	−0.172101	+	0.298089i
$356$	12.4853			0.661719
$357$	23.1421	−	3.16693i	1.22481	−	0.167612i
$358$	0.899495			0.0475398
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	0.492165	+	0.870502i	$0.336206\pi$
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	−0.999959	+	0.00902308i	$0.997128\pi$
$360$	0.828427	+	1.43488i	0.0436619	+	0.0756247i
$361$	9.32843	+	16.1573i	0.490970	+	0.850385i
$362$	3.82843	−	6.63103i	0.201218	−	0.348519i
$363$	−2.41421			−0.126713
$364$	−3.82843	+	9.37769i	−0.200664	+	0.491525i
$365$	5.51472			0.288654
$366$	14.2782	−	24.7305i	0.746332	−	1.29269i
$367$	5.36396	+	9.29065i	0.279996	+	0.484968i	0.971384	−	0.237516i	$-0.0763334\pi$
$367$	5.36396	+	9.29065i	0.279996	+	0.484968i	−0.691387	+	0.722485i	$0.743000\pi$
$368$	3.12132	+	5.40629i	0.162710	+	0.281822i
$369$	7.65685	−	13.2621i	0.398600	−	0.690395i
$370$	5.51472			0.286697
$371$	7.89949	−	19.3497i	0.410121	−	1.00459i
$372$	9.65685			0.500685
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	−0.482786	−	0.875738i	$-0.660375\pi$
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	0.999805	−	0.0197638i	$-0.00629142\pi$
$374$	−1.82843	−	3.16693i	−0.0945457	−	0.163758i
$375$	6.82843	+	11.8272i	0.352618	+	0.610753i
$376$	5.24264	−	9.08052i	0.270369	−	0.468292i
$377$	−10.1716			−0.523863
$378$	−1.08579	+	0.148586i	−0.0558468	+	0.00764246i
$379$	27.8701			1.43159			0.715794	−	0.698311i	$-0.246065\pi$
$379$	27.8701			1.43159			0.715794	+	0.698311i	$0.246065\pi$
$380$	−0.171573	+	0.297173i	−0.00880150	+	0.0152447i
$381$	18.9853	+	32.8835i	0.972645	+	1.68467i
$382$	3.58579	+	6.21076i	0.183465	+	0.317770i
$383$	3.19239	−	5.52938i	0.163123	−	0.282538i	−0.772864	−	0.634572i	$-0.781176\pi$
$383$	3.19239	−	5.52938i	0.163123	−	0.282538i	0.935987	+	0.352034i	$0.114510\pi$
$384$	−2.41421			−0.123200
$385$	−0.949747	−	1.22474i	−0.0484036	−	0.0624188i
$386$	21.8995			1.11465
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	1.91421	+	3.31552i	0.0971795	+	0.168320i
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	0.995913	+	0.0903199i	$0.0287889\pi$
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	−0.419737	+	0.907646i	$0.637878\pi$
$390$	2.70711	−	4.68885i	0.137080	−	0.237429i
$391$	−22.8284			−1.15448
$392$	−1.74264	+	6.77962i	−0.0880166	+	0.342422i
$393$	1.41421			0.0713376
$394$	0.257359	−	0.445759i	0.0129656	−	0.0224570i
$395$	−3.87868	−	6.71807i	−0.195158	−	0.338023i
$396$	−1.41421	−	2.44949i	−0.0710669	−	0.123091i
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	0.100505			0.00503786
$399$	2.29289	+	2.95680i	0.114788	+	0.148025i
$400$	−4.65685			−0.232843
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	−0.998816	−	0.0486549i	$-0.984507\pi$
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	0.541544	+	0.840672i	$0.317840\pi$
$402$	3.32843	+	5.76500i	0.166007	+	0.287532i
$403$	−7.65685	−	13.2621i	−0.381415	−	0.660630i
$404$	−3.08579	+	5.34474i	−0.153524	+	0.265911i
$405$	5.55635			0.276097
$406$	−6.96447	+	0.953065i	−0.345641	+	0.0472998i
$407$	−9.41421			−0.466645
$408$	4.41421	−	7.64564i	0.218536	−	0.378516i
$409$	−1.36396	−	2.36245i	−0.0674435	−	0.116816i	0.830332	−	0.557269i	$-0.188151\pi$
$409$	−1.36396	−	2.36245i	−0.0674435	−	0.116816i	−0.897775	+	0.440454i	$0.854818\pi$
$410$	−1.58579	−	2.74666i	−0.0783164	−	0.135648i
$411$	−20.1066	+	34.8257i	−0.991786	+	1.71782i
$412$	13.4142			0.660871
$413$	−5.58579	+	13.6823i	−0.274859	+	0.673263i
$414$	−17.6569			−0.867787
$415$	−3.55635	+	6.15978i	−0.174574	+	0.302372i
$416$	1.91421	+	3.31552i	0.0938520	+	0.162557i
$417$		0			0
$418$	0.292893	−	0.507306i	0.0143259	−	0.0248131i
$419$	−26.1421			−1.27713			−0.638563	−	0.769569i	$-0.720471\pi$
$419$	−26.1421			−1.27713			−0.638563	+	0.769569i	$0.720471\pi$
$420$	1.41421	−	3.46410i	0.0690066	−	0.169031i
$421$	0.686292			0.0334478			0.0167239	−	0.999860i	$-0.494676\pi$
$421$	0.686292			0.0334478			0.0167239	+	0.999860i	$0.494676\pi$
$422$	−3.70711	+	6.42090i	−0.180459	+	0.312564i
$423$	14.8284	+	25.6836i	0.720983	+	1.24878i
$424$	−3.94975	−	6.84116i	−0.191817	−	0.332236i
$425$	8.51472	−	14.7479i	0.413025	−	0.715379i
$426$	26.7279			1.29497
$427$	−31.0061	+	4.24309i	−1.50049	+	0.205337i
$428$	−3.07107			−0.148446
$429$	−4.62132	+	8.00436i	−0.223119	+	0.386454i
$430$	−1.65685	−	2.86976i	−0.0799006	−	0.138392i
$431$	8.79289	+	15.2297i	0.423539	+	0.733591i	0.996283	−	0.0861437i	$-0.0274544\pi$
$431$	8.79289	+	15.2297i	0.423539	+	0.733591i	−0.572744	+	0.819734i	$0.694121\pi$
$432$	−0.207107	+	0.358719i	−0.00996443	+	0.0172589i
$433$	26.1421			1.25631			0.628155	−	0.778088i	$-0.283810\pi$
$433$	26.1421			1.25631			0.628155	+	0.778088i	$0.283810\pi$
$434$	−6.48528	−	8.36308i	−0.311303	−	0.401441i
$435$	3.75736			0.180152
$436$	−8.24264	+	14.2767i	−0.394751	+	0.683729i
$437$	−1.82843	−	3.16693i	−0.0874655	−	0.151495i
$438$	−11.3640	−	19.6830i	−0.542991	−	0.940488i
$439$	13.6924	−	23.7159i	0.653502	−	1.13190i	−0.328765	−	0.944412i	$-0.606632\pi$
$439$	13.6924	−	23.7159i	0.653502	−	1.13190i	0.982267	−	0.187487i	$-0.0600342\pi$
$440$	−0.585786			−0.0279263
$441$	−14.1421	−	13.8564i	−0.673435	−	0.659829i
$442$	−14.0000			−0.665912
$443$	−6.31371	+	10.9357i	−0.299973	+	0.519569i	−0.976130	−	0.217189i	$-0.930311\pi$
$443$	−6.31371	+	10.9357i	−0.299973	+	0.519569i	0.676156	+	0.736758i	$0.263644\pi$
$444$	−11.3640	−	19.6830i	−0.539310	−	0.934112i
$445$	3.65685	+	6.33386i	0.173352	+	0.300254i
$446$	−4.29289	+	7.43551i	−0.203274	+	0.352082i
$447$	−42.6274			−2.01621
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$	22.3431			1.05444			0.527219	−	0.849729i	$-0.323235\pi$
$449$	22.3431			1.05444			0.527219	+	0.849729i	$0.323235\pi$
$450$	6.58579	−	11.4069i	0.310457	−	0.537727i
$451$	2.70711	+	4.68885i	0.127473	+	0.220789i
$452$	4.08579	+	7.07679i	0.192179	+	0.332864i
$453$	−18.9853	+	32.8835i	−0.892006	+	1.54500i
$454$	−28.8284			−1.35299
$455$	−5.87868	+	0.804479i	−0.275597	+	0.0377146i
$456$	1.41421			0.0662266
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	−0.696895	−	0.717173i	$-0.745436\pi$
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	0.969538	+	0.244943i	$0.0787691\pi$
$458$	−11.6569	−	20.1903i	−0.544689	−	0.943429i
$459$	−0.757359	−	1.31178i	−0.0353505	−	0.0612289i
$460$	−1.82843	+	3.16693i	−0.0852509	+	0.147659i
$461$	−8.31371			−0.387208			−0.193604	−	0.981080i	$-0.562018\pi$
$461$	−8.31371			−0.387208			−0.193604	+	0.981080i	$0.562018\pi$
$462$	−2.41421	+	5.91359i	−0.112319	+	0.275125i
$463$	12.8284			0.596188			0.298094	−	0.954537i	$-0.403649\pi$
$463$	12.8284			0.596188			0.298094	+	0.954537i	$0.403649\pi$
$464$	−1.32843	+	2.30090i	−0.0616707	+	0.106817i
$465$	2.82843	+	4.89898i	0.131165	+	0.227185i
$466$	−0.707107	−	1.22474i	−0.0327561	−	0.0567352i
$467$	17.0000	−	29.4449i	0.786666	−	1.36255i	−0.141332	−	0.989962i	$-0.545139\pi$
$467$	17.0000	−	29.4449i	0.786666	−	1.36255i	0.927999	−	0.372584i	$-0.121528\pi$
$468$	−10.8284			−0.500544
$469$	2.75736	−	6.75412i	0.127323	−	0.311876i
$470$	6.14214			0.283316
$471$	21.3137	−	36.9164i	0.982084	−	1.70102i
$472$	2.79289	+	4.83743i	0.128553	+	0.222661i
$473$	2.82843	+	4.89898i	0.130051	+	0.225255i
$474$	−15.9853	+	27.6873i	−0.734228	+	1.27172i
$475$	2.72792			0.125166
$476$	−9.58579	+	1.31178i	−0.439364	+	0.0601256i
$477$	22.3431			1.02302
$478$	−10.1066	+	17.5051i	−0.462265	+	0.800667i
$479$	5.96447	+	10.3308i	0.272523	+	0.472024i	0.969507	−	0.245062i	$-0.0788084\pi$
$479$	5.96447	+	10.3308i	0.272523	+	0.472024i	−0.696984	+	0.717087i	$0.745475\pi$
$480$	−0.707107	−	1.22474i	−0.0322749	−	0.0559017i
$481$	−18.0208	+	31.2130i	−0.821678	+	1.42319i
$482$	12.2426			0.557637
$483$	24.4350	+	31.5101i	1.11183	+	1.43376i
$484$	1.00000			0.0454545
$485$	−1.12132	+	1.94218i	−0.0509165	+	0.0881900i
$486$	−10.8284	−	18.7554i	−0.491187	−	0.850762i
$487$	4.82843	+	8.36308i	0.218797	+	0.378967i	0.954440	−	0.298402i	$-0.0964534\pi$
$487$	4.82843	+	8.36308i	0.218797	+	0.378967i	−0.735644	+	0.677369i	$0.763120\pi$
$488$	−5.91421	+	10.2437i	−0.267724	+	0.463711i
$489$	−23.4853			−1.06204
$490$	−3.94975	+	1.10165i	−0.178431	+	0.0497676i
$491$	19.1716			0.865201			0.432600	−	0.901586i	$-0.357596\pi$
$491$	19.1716			0.865201			0.432600	+	0.901586i	$0.357596\pi$
$492$	−6.53553	+	11.3199i	−0.294645	+	0.510339i
$493$	−4.85786	−	8.41407i	−0.218787	−	0.378951i
$494$	−1.12132	−	1.94218i	−0.0504506	−	0.0873830i
$495$	0.828427	−	1.43488i	0.0372350	−	0.0644930i
$496$	−4.00000			−0.179605
$497$	−17.9497	−	23.1471i	−0.805156	−	1.03829i
$498$	29.3137			1.31358
$499$	−11.0711	+	19.1757i	−0.495609	+	0.858420i	−0.999987	−	0.00506282i	$-0.998388\pi$
$499$	−11.0711	+	19.1757i	−0.495609	+	0.858420i	0.504378	+	0.863483i	$0.331722\pi$
$500$	−2.82843	−	4.89898i	−0.126491	−	0.219089i
$501$	16.5711	+	28.7019i	0.740341	+	1.28231i
$502$	13.0711	−	22.6398i	0.583390	−	1.01046i
$503$	4.21320			0.187857			0.0939287	−	0.995579i	$-0.470057\pi$
$503$	4.21320			0.187857			0.0939287	+	0.995579i	$0.470057\pi$
$504$	−7.41421	+	1.01461i	−0.330255	+	0.0451944i
$505$	−3.61522			−0.160875
$506$	3.12132	−	5.40629i	0.138760	−	0.240339i
$507$	2.00000	+	3.46410i	0.0888231	+	0.153846i
$508$	−7.86396	−	13.6208i	−0.348907	−	0.604324i
$509$	−4.65685	+	8.06591i	−0.206411	+	0.357515i	−0.950582	−	0.310475i	$-0.899512\pi$
$509$	−4.65685	+	8.06591i	−0.206411	+	0.357515i	0.744170	+	0.667990i	$0.232845\pi$
$510$	5.17157			0.229001
$511$	−9.41421	+	23.0600i	−0.416460	+	1.02012i
$512$	1.00000			0.0441942
$513$	0.121320	−	0.210133i	0.00535642	−	0.00927760i
$514$	12.5711	+	21.7737i	0.554486	+	0.960398i
$515$	3.92893	+	6.80511i	0.173129	+	0.299869i
$516$	−6.82843	+	11.8272i	−0.300605	+	0.520663i
$517$	−10.4853			−0.461142
$518$	−9.41421	+	23.0600i	−0.413637	+	1.01320i
$519$	23.7279			1.04154
$520$	−1.12132	+	1.94218i	−0.0491731	+	0.0851704i
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	0.989563	+	0.144103i	$0.0460297\pi$
$521$	14.1421	+	24.4949i	0.619578	+	1.07314i	−0.369984	+	0.929038i	$0.620637\pi$
$522$	−3.75736	−	6.50794i	−0.164455	−	0.284845i
$523$	6.36396	−	11.0227i	0.278277	−	0.481989i	−0.692680	−	0.721245i	$-0.743570\pi$
$523$	6.36396	−	11.0227i	0.278277	−	0.481989i	0.970957	+	0.239256i	$0.0769035\pi$
$524$	−0.585786			−0.0255902
$525$	−29.4706	+	4.03295i	−1.28620	+	0.176013i
$526$	−17.0416			−0.743050
$527$	7.31371	−	12.6677i	0.318590	−	0.551814i
$528$	1.20711	+	2.09077i	0.0525326	+	0.0909891i
$529$	−7.98528	−	13.8309i	−0.347186	−	0.601344i
$530$	2.31371	−	4.00746i	0.100501	−	0.174073i
$531$	−15.7990			−0.685618
$532$	−0.949747	−	1.22474i	−0.0411768	−	0.0530994i
$533$	20.7279			0.897826
$534$	15.0711	−	26.1039i	0.652189	−	1.12962i
$535$	−0.899495	−	1.55797i	−0.0388886	−	0.0673570i
$536$	−1.37868	−	2.38794i	−0.0595499	−	0.103143i
$537$	1.08579	−	1.88064i	0.0468551	−	0.0811555i
$538$	2.34315			0.101020
$539$	6.74264	−	1.88064i	0.290426	−	0.0810048i
$540$	−0.242641			−0.0104416
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	−0.694086	−	0.719892i	$-0.744191\pi$
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	0.970488	+	0.241151i	$0.0775248\pi$
$542$	−2.27817	−	3.94591i	−0.0978560	−	0.169492i
$543$	−9.24264	−	16.0087i	−0.396640	−	0.687000i
$544$	−1.82843	+	3.16693i	−0.0783932	+	0.135781i
$545$	−9.65685			−0.413654
$546$	14.9853	+	19.3242i	0.641311	+	0.827001i
$547$	34.8701			1.49094			0.745468	−	0.666541i	$-0.232226\pi$
$547$	34.8701			1.49094			0.745468	+	0.666541i	$0.232226\pi$
$548$	8.32843	−	14.4253i	0.355773	−	0.616217i
$549$	−16.7279	−	28.9736i	−0.713930	−	1.23656i
$550$	2.32843	+	4.03295i	0.0992845	+	0.171966i
$551$	0.778175	−	1.34784i	0.0331514	−	0.0574198i
$552$	15.0711			0.641467
$553$	34.7132	−	4.75039i	1.47616	−	0.202007i
$554$	1.82843			0.0776824
$555$	6.65685	−	11.5300i	0.282568	−	0.489422i
$556$		0			0
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	0.775378	−	0.631498i	$-0.217560\pi$
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	−0.934582	+	0.355748i	$0.884226\pi$
$558$	5.65685	−	9.79796i	0.239474	−	0.414781i
$559$	21.6569			0.915987
$560$	−0.585786	+	1.43488i	−0.0247540	+	0.0606347i
$561$	−8.82843			−0.372736
$562$	−4.36396	+	7.55860i	−0.184083	+	0.318840i
$563$	−4.53553	−	7.85578i	−0.191150	−	0.331081i	0.754482	−	0.656321i	$-0.227888\pi$
$563$	−4.53553	−	7.85578i	−0.191150	−	0.331081i	−0.945632	+	0.325240i	$0.894555\pi$
$564$	−12.6569	−	21.9223i	−0.532950	−	0.923096i
$565$	−2.39340	+	4.14549i	−0.100691	+	0.174402i
$566$	−23.4142			−0.984173
$567$	−9.48528	+	23.2341i	−0.398344	+	0.975740i
$568$	−11.0711			−0.464532
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$570$	0.414214	+	0.717439i	0.0173495	+	0.0300502i
$571$	−13.1924	−	22.8499i	−0.552084	−	0.956238i	−0.998124	−	0.0612248i	$-0.980499\pi$
$571$	−13.1924	−	22.8499i	−0.552084	−	0.956238i	0.446040	−	0.895013i	$-0.352834\pi$
$572$	1.91421	−	3.31552i	0.0800373	−	0.138629i
$573$	17.3137			0.723291
$574$	14.1924	−	1.94218i	0.592379	−	0.0810652i
$575$	29.0711			1.21235
$576$	−1.41421	+	2.44949i	−0.0589256	+	0.102062i
$577$	4.84315	+	8.38857i	0.201623	+	0.349221i	0.949051	−	0.315121i	$-0.102045\pi$
$577$	4.84315	+	8.38857i	0.201623	+	0.349221i	−0.747429	+	0.664342i	$0.768712\pi$
$578$	1.81371	+	3.14144i	0.0754403	+	0.130666i
$579$	26.4350	−	45.7868i	1.09860	−	1.90284i
$580$	−1.55635			−0.0646239
$581$	−19.6863	−	25.3864i	−0.816725	−	1.05321i
$582$	9.24264			0.383120
$583$	−3.94975	+	6.84116i	−0.163582	+	0.283332i
$584$	4.70711	+	8.15295i	0.194781	+	0.337371i
$585$	−3.17157	−	5.49333i	−0.131128	−	0.227121i
$586$	5.41421	−	9.37769i	0.223659	−	0.387389i
$587$	−25.1005			−1.03601			−0.518004	−	0.855378i	$-0.673325\pi$
$587$	−25.1005			−1.03601			−0.518004	+	0.855378i	$0.673325\pi$
$588$	12.0711	+	11.8272i	0.497802	+	0.487745i
$589$	2.34315			0.0965476
$590$	−1.63604	+	2.83370i	−0.0673547	+	0.116662i
$591$	−0.621320	−	1.07616i	−0.0255577	−	0.0442672i
$592$	4.70711	+	8.15295i	0.193461	+	0.335084i
$593$	−11.8492	+	20.5235i	−0.486590	+	0.842799i	−0.999881	−	0.0154159i	$-0.995093\pi$
$593$	−11.8492	+	20.5235i	−0.486590	+	0.842799i	0.513291	+	0.858215i	$0.328426\pi$
$594$	0.414214			0.0169954
$595$	−3.47309	−	4.47871i	−0.142383	−	0.183609i
$596$	17.6569			0.723253
$597$	0.121320	−	0.210133i	0.00496531	−	0.00860017i
$598$	−11.9497	−	20.6976i	−0.488662	−	0.846387i
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.861114	−	0.508412i	$-0.830233\pi$
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.00974040	−	0.999953i	$-0.503101\pi$
$600$	−5.62132	+	9.73641i	−0.229489	+	0.397487i
$601$	31.9411			1.30291			0.651453	−	0.758689i	$-0.274160\pi$
$601$	31.9411			1.30291			0.651453	+	0.758689i	$0.274160\pi$
$602$	14.8284	−	2.02922i	0.604362	−	0.0827050i
$603$	7.79899			0.317599
$604$	7.86396	−	13.6208i	0.319980	−	0.554222i
$605$	0.292893	+	0.507306i	0.0119078	+	0.0206249i
$606$	7.44975	+	12.9033i	0.302625	+	0.524162i
$607$	21.4853	−	37.2136i	0.872061	−	1.51045i	0.0121994	−	0.999926i	$-0.496117\pi$
$607$	21.4853	−	37.2136i	0.872061	−	1.51045i	0.859861	−	0.510528i	$-0.170550\pi$
$608$	−0.585786			−0.0237568
$609$	−6.41421	+	15.7116i	−0.259917	+	0.636664i
$610$	−6.92893			−0.280544
$611$	−20.0711	+	34.7641i	−0.811988	+	1.40641i
$612$	−5.17157	−	8.95743i	−0.209048	−	0.362083i
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	−0.995694	−	0.0926971i	$-0.970451\pi$
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	0.417569	−	0.908645i	$-0.362882\pi$
$614$	−4.94975	+	8.57321i	−0.199756	+	0.345987i
$615$	−7.65685			−0.308754
$616$	1.00000	−	2.44949i	0.0402911	−	0.0986928i
$617$	−41.9706			−1.68967			−0.844836	−	0.535026i	$-0.820302\pi$
$617$	−41.9706			−1.68967			−0.844836	+	0.535026i	$0.820302\pi$
$618$	16.1924	−	28.0460i	0.651353	−	1.12818i
$619$	10.9706	+	19.0016i	0.440944	+	0.763738i	0.997760	−	0.0668984i	$-0.0213104\pi$
$619$	10.9706	+	19.0016i	0.440944	+	0.763738i	−0.556816	+	0.830636i	$0.687977\pi$
$620$	−1.17157	−	2.02922i	−0.0470515	−	0.0814956i
$621$	1.29289	−	2.23936i	0.0518820	−	0.0898623i
$622$	16.7279			0.670729
$623$	−32.7279	+	4.47871i	−1.31122	+	0.179436i
$624$	9.24264			0.370002
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	10.3284	+	17.8894i	0.412807	+	0.715003i
$627$	−0.707107	−	1.22474i	−0.0282391	−	0.0489116i
$628$	−8.82843	+	15.2913i	−0.352293	+	0.610189i
$629$	−34.4264			−1.37267
$630$	−2.68629	−	3.46410i	−0.107024	−	0.138013i
$631$	23.2721			0.926447			0.463223	−	0.886242i	$-0.346693\pi$
$631$	23.2721			0.926447			0.463223	+	0.886242i	$0.346693\pi$
$632$	6.62132	−	11.4685i	0.263382	−	0.456191i
$633$	8.94975	+	15.5014i	0.355721	+	0.616126i
$634$	−4.34315	−	7.52255i	−0.172488	−	0.298759i
$635$	4.60660	−	7.97887i	0.182807	−	0.316632i
$636$	−19.0711			−0.756217
$637$	6.67157	−	25.9553i	0.264337	−	1.02839i
$638$	2.65685			0.105186
$639$	15.6569	−	27.1185i	0.619376	−	1.07279i
$640$	0.292893	+	0.507306i	0.0115776	+	0.0200530i
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	0.674708	−	0.738085i	$-0.264270\pi$
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	−0.976554	+	0.215272i	$0.930936\pi$
$642$	−3.70711	+	6.42090i	−0.146308	+	0.253413i
$643$	1.58579			0.0625373			0.0312687	−	0.999511i	$-0.490045\pi$
$643$	1.58579			0.0625373			0.0312687	+	0.999511i	$0.490045\pi$
$644$	−10.1213	−	13.0519i	−0.398836	−	0.514318i
$645$	−8.00000			−0.315000
$646$	1.07107	−	1.85514i	0.0421406	−	0.0729897i
$647$	−15.0919	−	26.1399i	−0.593323	−	1.02767i	−0.993781	−	0.111351i	$-0.964482\pi$
$647$	−15.0919	−	26.1399i	−0.593323	−	1.02767i	0.400458	−	0.916315i	$-0.368851\pi$
$648$	4.74264	+	8.21449i	0.186309	+	0.322696i
$649$	2.79289	−	4.83743i	0.109631	−	0.189886i
$650$	17.8284			0.699288
$651$	−25.3137	+	3.46410i	−0.992122	+	0.135769i
$652$	9.72792			0.380975
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	−0.628189	−	0.778061i	$-0.716204\pi$
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	0.987915	+	0.154997i	$0.0495369\pi$
$654$	19.8995	+	34.4669i	0.778132	+	1.34776i
$655$	−0.171573	−	0.297173i	−0.00670391	−	0.0116115i
$656$	2.70711	−	4.68885i	0.105695	−	0.183069i
$657$	−26.6274			−1.03883
$658$	−10.4853	+	25.6836i	−0.408759	+	1.00125i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−0.707107	+	1.22474i	−0.0275241	+	0.0476731i
$661$	−9.48528	−	16.4290i	−0.368935	−	0.639014i	0.620465	−	0.784234i	$-0.286944\pi$
$661$	−9.48528	−	16.4290i	−0.368935	−	0.639014i	−0.989399	+	0.145221i	$0.953611\pi$
$662$	12.0355	+	20.8462i	0.467774	+	0.810209i
$663$	−16.8995	+	29.2708i	−0.656322	+	1.13678i
$664$	−12.1421			−0.471206
$665$	0.343146	−	0.840532i	0.0133066	−	0.0325944i
$666$	−26.6274			−1.03179
$667$	8.29289	−	14.3637i	0.321102	−	0.556165i
$668$	−6.86396	−	11.8887i	−0.265575	−	0.459989i
$669$	10.3640	+	17.9509i	0.400694	+	0.694022i
$670$	0.807612	−	1.39882i	0.0312008	−	0.0540413i
$671$	11.8284			0.456631
$672$	6.32843	−	0.866025i	0.244124	−	0.0334077i
$673$	5.55635			0.214182			0.107091	−	0.994249i	$-0.465846\pi$
$673$	5.55635			0.214182			0.107091	+	0.994249i	$0.465846\pi$
$674$	14.1213	−	24.4588i	0.543933	−	0.942119i
$675$	0.964466	+	1.67050i	0.0371223	+	0.0642977i
$676$	−0.828427	−	1.43488i	−0.0318626	−	0.0551876i
$677$	17.6569	−	30.5826i	0.678608	−	1.17538i	−0.296792	−	0.954942i	$-0.595917\pi$
$677$	17.6569	−	30.5826i	0.678608	−	1.17538i	0.975400	−	0.220441i	$-0.0707498\pi$
$678$	19.7279			0.757646
$679$	−6.20711	−	8.00436i	−0.238207	−	0.307179i
$680$	−2.14214			−0.0821472
$681$	−34.7990	+	60.2736i	−1.33350	+	2.30969i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	−6.79289	−	11.7656i	−0.259923	−	0.450200i	0.706298	−	0.707914i	$-0.250364\pi$
$683$	−6.79289	−	11.7656i	−0.259923	−	0.450200i	−0.966221	+	0.257715i	$0.917030\pi$
$684$	0.828427	−	1.43488i	0.0316757	−	0.0548639i
$685$	9.75736			0.372810
$686$	2.13604	−	18.3967i	0.0815543	−	0.702388i
$687$	−56.2843			−2.14738
$688$	2.82843	−	4.89898i	0.107833	−	0.186772i
$689$	15.1213	+	26.1909i	0.576076	+	0.997794i
$690$	4.41421	+	7.64564i	0.168046	+	0.291065i
$691$	−14.0355	+	24.3103i	−0.533937	+	0.924806i	0.465277	+	0.885165i	$0.345955\pi$
$691$	−14.0355	+	24.3103i	−0.533937	+	0.924806i	−0.999214	+	0.0396407i	$0.987379\pi$
$692$	−9.82843			−0.373621
$693$	4.58579	+	5.91359i	0.174200	+	0.224639i
$694$	17.4142			0.661035
$695$		0			0
$696$	3.20711	+	5.55487i	0.121565	+	0.210557i
$697$	9.89949	+	17.1464i	0.374970	+	0.649467i
$698$		0			0
$699$	−3.41421			−0.129137
$700$	12.2071	−	1.67050i	0.461385	−	0.0631391i
$701$	−26.1127			−0.986263			−0.493132	−	0.869955i	$-0.664148\pi$
$701$	−26.1127			−0.986263			−0.493132	+	0.869955i	$0.664148\pi$
$702$	0.792893	−	1.37333i	0.0299258	−	0.0518331i
$703$	−2.75736	−	4.77589i	−0.103996	−	0.180126i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	7.41421	−	12.8418i	0.279235	−	0.483650i
$706$	−2.68629			−0.101100
$707$	6.17157	−	15.1172i	0.232106	−	0.568541i
$708$	13.4853			0.506808
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	−0.730537	−	0.682873i	$-0.760730\pi$
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	0.956654	+	0.291228i	$0.0940637\pi$
$710$	−3.24264	−	5.61642i	−0.121694	−	0.210780i
$711$	18.7279	+	32.4377i	0.702352	+	1.21651i
$712$	−6.24264	+	10.8126i	−0.233953	+	0.405218i
$713$	24.9706			0.935155
$714$	−8.82843	+	21.6251i	−0.330396	+	0.809301i
$715$	2.24264			0.0838700
$716$	−0.449747	+	0.778985i	−0.0168079	+	0.0291121i
$717$	24.3995	+	42.2612i	0.911216	+	1.57827i
$718$	−9.62132	−	16.6646i	−0.359064	−	0.621918i
$719$	0.757359	−	1.31178i	0.0282447	−	0.0489213i	−0.851558	−	0.524261i	$-0.824342\pi$
$719$	0.757359	−	1.31178i	0.0282447	−	0.0489213i	0.879802	+	0.475340i	$0.157675\pi$
$720$	−1.65685			−0.0617473
$721$	−35.1630	+	4.81194i	−1.30954	+	0.179206i
$722$	−18.6569			−0.694336
$723$	14.7782	−	25.5965i	0.549606	−	0.951946i
$724$	3.82843	+	6.63103i	0.142282	+	0.246440i
$725$	6.18629	+	10.7150i	0.229753	+	0.397944i
$726$	1.20711	−	2.09077i	0.0447999	−	0.0775958i
$727$	36.4264			1.35098			0.675490	−	0.737369i	$-0.263932\pi$
$727$	36.4264			1.35098			0.675490	+	0.737369i	$0.263932\pi$
$728$	−6.20711	−	8.00436i	−0.230051	−	0.296661i
$729$	−23.8284			−0.882534
$730$	−2.75736	+	4.77589i	−0.102054	+	0.176763i
$731$	10.3431	+	17.9149i	0.382555	+	0.662605i
$732$	14.2782	+	24.7305i	0.527737	+	0.914066i
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$	−10.7279			−0.395975
$735$	−2.46447	+	9.58783i	−0.0909032	+	0.353652i
$736$	−6.24264			−0.230107
$737$	−1.37868	+	2.38794i	−0.0507843	+	0.0879610i
$738$	7.65685	+	13.2621i	0.281853	+	0.488183i
$739$	26.2132	+	45.4026i	0.964268	+	1.67016i	0.711568	+	0.702617i	$0.247985\pi$
$739$	26.2132	+	45.4026i	0.964268	+	1.67016i	0.252700	+	0.967545i	$0.418681\pi$
$740$	−2.75736	+	4.77589i	−0.101363	+	0.175565i
$741$	−5.41421			−0.198896
$742$	12.8076	+	16.5160i	0.470182	+	0.606323i
$743$	−13.3137			−0.488433			−0.244216	−	0.969721i	$-0.578531\pi$
$743$	−13.3137			−0.488433			−0.244216	+	0.969721i	$0.578531\pi$
$744$	−4.82843	+	8.36308i	−0.177019	+	0.306605i
$745$	5.17157	+	8.95743i	0.189472	+	0.328175i
$746$	9.98528	+	17.2950i	0.365587	+	0.633215i
$747$	17.1716	−	29.7420i	0.628275	−	1.08820i
$748$	3.65685			0.133708
$749$	8.05025	−	1.10165i	0.294150	−	0.0402535i
$750$	−13.6569			−0.498678
$751$	−22.8284	+	39.5400i	−0.833021	+	1.44283i	0.0626103	+	0.998038i	$0.480057\pi$
$751$	−22.8284	+	39.5400i	−0.833021	+	1.44283i	−0.895631	+	0.444797i	$0.853276\pi$
$752$	5.24264	+	9.08052i	0.191179	+	0.331132i
$753$	−31.5563	−	54.6572i	−1.14998	−	1.99182i
$754$	5.08579	−	8.80884i	0.185213	−	0.320799i
$755$	9.21320			0.335303
$756$	0.414214	−	1.01461i	0.0150648	−	0.0369011i
$757$	8.34315			0.303237			0.151618	−	0.988439i	$-0.451552\pi$
$757$	8.34315			0.303237			0.151618	+	0.988439i	$0.451552\pi$
$758$	−13.9350	+	24.1362i	−0.506143	+	0.876665i
$759$	−7.53553	−	13.0519i	−0.273523	−	0.473755i
$760$	−0.171573	−	0.297173i	−0.00622360	−	0.0107796i
$761$	−15.4853	+	26.8213i	−0.561341	+	0.972271i	0.436039	+	0.899928i	$0.356381\pi$
$761$	−15.4853	+	26.8213i	−0.561341	+	0.972271i	−0.997380	+	0.0723433i	$0.976952\pi$
$762$	−37.9706			−1.37553
$763$	16.4853	−	40.3805i	0.596807	−	1.46187i
$764$	−7.17157			−0.259458
$765$	3.02944	−	5.24714i	0.109530	−	0.189711i
$766$	3.19239	+	5.52938i	0.115346	+	0.199785i
$767$	−10.6924	−	18.5198i	−0.386080	−	0.668710i
$768$	1.20711	−	2.09077i	0.0435577	−	0.0754442i
$769$	22.9706			0.828340			0.414170	−	0.910200i	$-0.364072\pi$
$769$	22.9706			0.828340			0.414170	+	0.910200i	$0.364072\pi$
$770$	1.53553	−	0.210133i	0.0553368	−	0.00757267i
$771$	60.6985			2.18600
$772$	−10.9497	+	18.9655i	−0.394090	+	0.682584i

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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -2.41421 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.20711 + 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.292893 - 0.507306i) q^{5} -2.41421 q^{6} +(1.62132 + 2.09077i) q^{7} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +(0.292893 + 0.507306i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.20711 - 2.09077i) q^{12} -3.82843 q^{13} +(-2.62132 + 0.358719i) q^{14} +1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.82843 - 3.16693i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(0.292893 - 0.507306i) q^{19} -0.585786 q^{20} +(-2.41421 + 5.91359i) q^{21} +1.00000 q^{22} +(3.12132 - 5.40629i) q^{23} +(1.20711 + 2.09077i) q^{24} +(2.32843 + 4.03295i) q^{25} +(1.91421 - 3.31552i) q^{26} +0.414214 q^{27} +(1.00000 - 2.44949i) q^{28} +2.65685 q^{29} +(-0.707107 + 1.22474i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.20711 - 2.09077i) q^{33} +3.65685 q^{34} +(1.53553 - 0.210133i) q^{35} +2.82843 q^{36} +(4.70711 - 8.15295i) q^{37} +(0.292893 + 0.507306i) q^{38} +(-4.62132 - 8.00436i) q^{39} +(0.292893 - 0.507306i) q^{40} -5.41421 q^{41} +(-3.91421 - 5.04757i) q^{42} -5.65685 q^{43} +(-0.500000 + 0.866025i) q^{44} +(0.828427 + 1.43488i) q^{45} +(3.12132 + 5.40629i) q^{46} +(5.24264 - 9.08052i) q^{47} -2.41421 q^{48} +(-1.74264 + 6.77962i) q^{49} -4.65685 q^{50} +(4.41421 - 7.64564i) q^{51} +(1.91421 + 3.31552i) q^{52} +(-3.94975 - 6.84116i) q^{53} +(-0.207107 + 0.358719i) q^{54} -0.585786 q^{55} +(1.62132 + 2.09077i) q^{56} +1.41421 q^{57} +(-1.32843 + 2.30090i) q^{58} +(2.79289 + 4.83743i) q^{59} +(-0.707107 - 1.22474i) q^{60} +(-5.91421 + 10.2437i) q^{61} -4.00000 q^{62} +(-7.41421 + 1.01461i) q^{63} +1.00000 q^{64} +(-1.12132 + 1.94218i) q^{65} +(1.20711 + 2.09077i) q^{66} +(-1.37868 - 2.38794i) q^{67} +(-1.82843 + 3.16693i) q^{68} +15.0711 q^{69} +(-0.585786 + 1.43488i) q^{70} -11.0711 q^{71} +(-1.41421 + 2.44949i) q^{72} +(4.70711 + 8.15295i) q^{73} +(4.70711 + 8.15295i) q^{74} +(-5.62132 + 9.73641i) q^{75} -0.585786 q^{76} +(1.00000 - 2.44949i) q^{77} +9.24264 q^{78} +(6.62132 - 11.4685i) q^{79} +(0.292893 + 0.507306i) q^{80} +(4.74264 + 8.21449i) q^{81} +(2.70711 - 4.68885i) q^{82} -12.1421 q^{83} +(6.32843 - 0.866025i) q^{84} -2.14214 q^{85} +(2.82843 - 4.89898i) q^{86} +(3.20711 + 5.55487i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-6.24264 + 10.8126i) q^{89} -1.65685 q^{90} +(-6.20711 - 8.00436i) q^{91} -6.24264 q^{92} +(-4.82843 + 8.36308i) q^{93} +(5.24264 + 9.08052i) q^{94} +(-0.171573 - 0.297173i) q^{95} +(1.20711 - 2.09077i) q^{96} -3.82843 q^{97} +(-5.00000 - 4.89898i) q^{98} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 2 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{19} - 8 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26} - 4 q^{27} + 4 q^{28} - 12 q^{29} + 8 q^{31} - 2 q^{32} + 2 q^{33} - 8 q^{34} - 8 q^{35} + 16 q^{37} + 4 q^{38} - 10 q^{39} + 4 q^{40} - 16 q^{41} - 10 q^{42} - 2 q^{44} - 8 q^{45} + 4 q^{46} + 4 q^{47} - 4 q^{48} + 10 q^{49} + 4 q^{50} + 12 q^{51} + 2 q^{52} + 4 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} + 6 q^{58} + 14 q^{59} - 18 q^{61} - 16 q^{62} - 24 q^{63} + 4 q^{64} + 4 q^{65} + 2 q^{66} - 14 q^{67} + 4 q^{68} + 32 q^{69} - 8 q^{70} - 16 q^{71} + 16 q^{73} + 16 q^{74} - 14 q^{75} - 8 q^{76} + 4 q^{77} + 20 q^{78} + 18 q^{79} + 4 q^{80} + 2 q^{81} + 8 q^{82} + 8 q^{83} + 14 q^{84} + 48 q^{85} + 10 q^{87} - 2 q^{88} - 8 q^{89} + 16 q^{90} - 22 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} - 12 q^{95} + 2 q^{96} - 4 q^{97} - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 - 2 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^19 - 8 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 4 * q^27 + 4 * q^28 - 12 * q^29 + 8 * q^31 - 2 * q^32 + 2 * q^33 - 8 * q^34 - 8 * q^35 + 16 * q^37 + 4 * q^38 - 10 * q^39 + 4 * q^40 - 16 * q^41 - 10 * q^42 - 2 * q^44 - 8 * q^45 + 4 * q^46 + 4 * q^47 - 4 * q^48 + 10 * q^49 + 4 * q^50 + 12 * q^51 + 2 * q^52 + 4 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 + 6 * q^58 + 14 * q^59 - 18 * q^61 - 16 * q^62 - 24 * q^63 + 4 * q^64 + 4 * q^65 + 2 * q^66 - 14 * q^67 + 4 * q^68 + 32 * q^69 - 8 * q^70 - 16 * q^71 + 16 * q^73 + 16 * q^74 - 14 * q^75 - 8 * q^76 + 4 * q^77 + 20 * q^78 + 18 * q^79 + 4 * q^80 + 2 * q^81 + 8 * q^82 + 8 * q^83 + 14 * q^84 + 48 * q^85 + 10 * q^87 - 2 * q^88 - 8 * q^89 + 16 * q^90 - 22 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 - 12 * q^95 + 2 * q^96 - 4 * q^97 - 20 * q^98

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