LMFDB - Embedded newform 966.2.i.h.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (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:	$7.71354883526$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.h.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.41421 q^{13} +(1.00000 - 2.44949i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.292893 - 0.507306i) q^{19} -1.00000 q^{20} +(1.62132 + 2.09077i) q^{21} -3.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.707107 - 1.22474i) q^{26} +1.00000 q^{27} +(1.62132 + 2.09077i) q^{28} -9.24264 q^{29} +(0.500000 - 0.866025i) q^{30} +(3.32843 + 5.76500i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +1.41421 q^{34} +(-1.00000 + 2.44949i) q^{35} +1.00000 q^{36} +(-2.53553 + 4.39167i) q^{37} +(0.292893 + 0.507306i) q^{38} +(0.707107 + 1.22474i) q^{39} +(0.500000 - 0.866025i) q^{40} +10.2426 q^{41} +(-2.62132 + 0.358719i) q^{42} +3.65685 q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.65685 + 11.5300i) q^{47} +1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} -4.00000 q^{50} +(-0.707107 + 1.22474i) q^{51} +(0.707107 + 1.22474i) q^{52} +(3.91421 + 6.77962i) q^{53} +(-0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(-2.62132 + 0.358719i) q^{56} -0.585786 q^{57} +(4.62132 - 8.00436i) q^{58} +(4.62132 + 8.00436i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.00000 - 5.19615i) q^{61} -6.65685 q^{62} +(1.00000 - 2.44949i) q^{63} +1.00000 q^{64} +(-0.707107 + 1.22474i) q^{65} +(1.50000 + 2.59808i) q^{66} +(7.82843 + 13.5592i) q^{67} +(-0.707107 + 1.22474i) q^{68} -1.00000 q^{69} +(-1.62132 - 2.09077i) q^{70} -13.8995 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.82843 + 4.89898i) q^{73} +(-2.53553 - 4.39167i) q^{74} +(2.00000 - 3.46410i) q^{75} -0.585786 q^{76} +(-4.86396 - 6.27231i) q^{77} -1.41421 q^{78} +(-1.20711 + 2.09077i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.12132 + 8.87039i) q^{82} -10.3137 q^{83} +(1.00000 - 2.44949i) q^{84} -1.41421 q^{85} +(-1.82843 + 3.16693i) q^{86} +(4.62132 + 8.00436i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.36396 - 9.29065i) q^{89} -1.00000 q^{90} +(3.70711 - 0.507306i) q^{91} -1.00000 q^{92} +(3.32843 - 5.76500i) q^{93} +(-6.65685 - 11.5300i) q^{94} +(-0.292893 - 0.507306i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.41421 q^{97} +(-1.74264 + 6.77962i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} + 4 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{19} - 4 q^{20} - 2 q^{21} - 12 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} - 2 q^{28} - 20 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{32} + 6 q^{33} - 4 q^{35} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 2 q^{40} + 24 q^{41} - 2 q^{42} - 8 q^{43} + 6 q^{44} + 2 q^{45} + 2 q^{46} - 4 q^{47} + 4 q^{48} + 10 q^{49} - 16 q^{50} + 10 q^{53} - 2 q^{54} + 12 q^{55} - 2 q^{56} - 8 q^{57} + 10 q^{58} + 10 q^{59} + 2 q^{60} + 12 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 6 q^{66} + 20 q^{67} - 4 q^{69} + 2 q^{70} - 16 q^{71} - 2 q^{72} + 4 q^{74} + 8 q^{75} - 8 q^{76} + 6 q^{77} - 2 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{86} + 10 q^{87} + 6 q^{88} - 4 q^{89} - 4 q^{90} + 12 q^{91} - 4 q^{92} + 2 q^{93} - 4 q^{94} - 4 q^{95} - 2 q^{96} - 20 q^{97} + 10 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 + 4 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 + 4 * q^19 - 4 * q^20 - 2 * q^21 - 12 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 - 2 * q^28 - 20 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^32 + 6 * q^33 - 4 * q^35 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 2 * q^40 + 24 * q^41 - 2 * q^42 - 8 * q^43 + 6 * q^44 + 2 * q^45 + 2 * q^46 - 4 * q^47 + 4 * q^48 + 10 * q^49 - 16 * q^50 + 10 * q^53 - 2 * q^54 + 12 * q^55 - 2 * q^56 - 8 * q^57 + 10 * q^58 + 10 * q^59 + 2 * q^60 + 12 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 6 * q^66 + 20 * q^67 - 4 * q^69 + 2 * q^70 - 16 * q^71 - 2 * q^72 + 4 * q^74 + 8 * q^75 - 8 * q^76 + 6 * q^77 - 2 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^86 + 10 * q^87 + 6 * q^88 - 4 * q^89 - 4 * q^90 + 12 * q^91 - 4 * q^92 + 2 * q^93 - 4 * q^94 - 4 * q^95 - 2 * q^96 - 20 * q^97 + 10 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	1.00000			0.408248
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.41421			−0.392232			−0.196116	−	0.980581i	$-0.562833\pi$
$13$	−1.41421			−0.392232			−0.196116	+	0.980581i	$0.562833\pi$
$14$	1.00000	−	2.44949i	0.267261	−	0.654654i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.707107	−	1.22474i	−0.171499	−	0.297044i	0.767445	−	0.641114i	$-0.221528\pi$
$17$	−0.707107	−	1.22474i	−0.171499	−	0.297044i	−0.938944	+	0.344070i	$0.888194\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	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	$0.145262\pi$
$20$	−1.00000			−0.223607
$21$	1.62132	+	2.09077i	0.353801	+	0.456243i
$22$	−3.00000			−0.639602
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	0.707107	−	1.22474i	0.138675	−	0.240192i
$27$	1.00000			0.192450
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	−9.24264			−1.71632			−0.858158	−	0.513386i	$-0.828391\pi$
$29$	−9.24264			−1.71632			−0.858158	+	0.513386i	$0.828391\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	3.32843	+	5.76500i	0.597803	+	1.03543i	0.993145	+	0.116891i	$0.0372929\pi$
$31$	3.32843	+	5.76500i	0.597803	+	1.03543i	−0.395342	+	0.918534i	$0.629374\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	1.41421			0.242536
$35$	−1.00000	+	2.44949i	−0.169031	+	0.414039i
$36$	1.00000			0.166667
$37$	−2.53553	+	4.39167i	−0.416839	+	0.721987i	−0.995620	−	0.0934968i	$-0.970196\pi$
$37$	−2.53553	+	4.39167i	−0.416839	+	0.721987i	0.578780	+	0.815483i	$0.303529\pi$
$38$	0.292893	+	0.507306i	0.0475136	+	0.0822959i
$39$	0.707107	+	1.22474i	0.113228	+	0.196116i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	10.2426			1.59963			0.799816	−	0.600245i	$-0.204930\pi$
$41$	10.2426			1.59963			0.799816	+	0.600245i	$0.204930\pi$
$42$	−2.62132	+	0.358719i	−0.404479	+	0.0553516i
$43$	3.65685			0.557665			0.278833	−	0.960340i	$-0.410053\pi$
$43$	3.65685			0.557665			0.278833	+	0.960340i	$0.410053\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−6.65685	+	11.5300i	−0.971002	+	1.68182i	−0.278459	+	0.960448i	$0.589824\pi$
$47$	−6.65685	+	11.5300i	−0.971002	+	1.68182i	−0.692543	+	0.721377i	$0.743510\pi$
$48$	1.00000			0.144338
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	−4.00000			−0.565685
$51$	−0.707107	+	1.22474i	−0.0990148	+	0.171499i
$52$	0.707107	+	1.22474i	0.0980581	+	0.169842i
$53$	3.91421	+	6.77962i	0.537659	+	0.931252i	0.999030	+	0.0440447i	$0.0140244\pi$
$53$	3.91421	+	6.77962i	0.537659	+	0.931252i	−0.461371	+	0.887207i	$0.652642\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	3.00000			0.404520
$56$	−2.62132	+	0.358719i	−0.350289	+	0.0479359i
$57$	−0.585786			−0.0775893
$58$	4.62132	−	8.00436i	0.606809	−	1.05102i
$59$	4.62132	+	8.00436i	0.601645	+	1.04208i	0.992572	+	0.121658i	$0.0388210\pi$
$59$	4.62132	+	8.00436i	0.601645	+	1.04208i	−0.390927	+	0.920421i	$0.627846\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−6.65685			−0.845421
$63$	1.00000	−	2.44949i	0.125988	−	0.308607i
$64$	1.00000			0.125000
$65$	−0.707107	+	1.22474i	−0.0877058	+	0.151911i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	7.82843	+	13.5592i	0.956395	+	1.65652i	0.731144	+	0.682223i	$0.238987\pi$
$67$	7.82843	+	13.5592i	0.956395	+	1.65652i	0.225251	+	0.974301i	$0.427680\pi$
$68$	−0.707107	+	1.22474i	−0.0857493	+	0.148522i
$69$	−1.00000			−0.120386
$70$	−1.62132	−	2.09077i	−0.193785	−	0.249895i
$71$	−13.8995			−1.64957			−0.824783	−	0.565449i	$-0.808703\pi$
$71$	−13.8995			−1.64957			−0.824783	+	0.565449i	$0.808703\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	2.82843	+	4.89898i	0.331042	+	0.573382i	0.982717	−	0.185117i	$-0.0592664\pi$
$73$	2.82843	+	4.89898i	0.331042	+	0.573382i	−0.651674	+	0.758499i	$0.725933\pi$
$74$	−2.53553	−	4.39167i	−0.294750	−	0.510522i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$	−0.585786			−0.0671943
$77$	−4.86396	−	6.27231i	−0.554300	−	0.714796i
$78$	−1.41421			−0.160128
$79$	−1.20711	+	2.09077i	−0.135810	+	0.235230i	−0.925907	−	0.377752i	$-0.876697\pi$
$79$	−1.20711	+	2.09077i	−0.135810	+	0.235230i	0.790097	+	0.612982i	$0.210030\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.12132	+	8.87039i	−0.565555	+	0.979570i
$83$	−10.3137			−1.13208			−0.566038	−	0.824379i	$-0.691525\pi$
$83$	−10.3137			−1.13208			−0.566038	+	0.824379i	$0.691525\pi$
$84$	1.00000	−	2.44949i	0.109109	−	0.267261i
$85$	−1.41421			−0.153393
$86$	−1.82843	+	3.16693i	−0.197164	+	0.341499i
$87$	4.62132	+	8.00436i	0.495458	+	0.858158i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	5.36396	−	9.29065i	0.568579	−	0.984807i	−0.428128	−	0.903718i	$-0.640827\pi$
$89$	5.36396	−	9.29065i	0.568579	−	0.984807i	0.996707	−	0.0810892i	$-0.0258399\pi$
$90$	−1.00000			−0.105409
$91$	3.70711	−	0.507306i	0.388610	−	0.0531801i
$92$	−1.00000			−0.104257
$93$	3.32843	−	5.76500i	0.345142	−	0.597803i
$94$	−6.65685	−	11.5300i	−0.686602	−	1.18923i
$95$	−0.292893	−	0.507306i	−0.0300502	−	0.0520485i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−6.41421			−0.651265			−0.325632	−	0.945496i	$-0.605577\pi$
$97$	−6.41421			−0.651265			−0.325632	+	0.945496i	$0.605577\pi$
$98$	−1.74264	+	6.77962i	−0.176033	+	0.684845i
$99$	−3.00000			−0.301511
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	−6.24264	−	10.8126i	−0.621166	−	1.07589i	−0.989269	−	0.146106i	$-0.953326\pi$
$101$	−6.24264	−	10.8126i	−0.621166	−	1.07589i	0.368103	−	0.929785i	$-0.380007\pi$
$102$	−0.707107	−	1.22474i	−0.0700140	−	0.121268i
$103$	1.17157	−	2.02922i	0.115439	−	0.199945i	−0.802516	−	0.596630i	$-0.796506\pi$
$103$	1.17157	−	2.02922i	0.115439	−	0.199945i	0.917955	+	0.396685i	$0.129839\pi$
$104$	−1.41421			−0.138675
$105$	2.62132	−	0.358719i	0.255815	−	0.0350074i
$106$	−7.82843			−0.760364
$107$	−4.74264	+	8.21449i	−0.458488	+	0.794125i	−0.998881	−	0.0472876i	$-0.984942\pi$
$107$	−4.74264	+	8.21449i	−0.458488	+	0.794125i	0.540393	+	0.841413i	$0.318276\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	8.65685	+	14.9941i	0.829176	+	1.43618i	0.898685	+	0.438594i	$0.144523\pi$
$109$	8.65685	+	14.9941i	0.829176	+	1.43618i	−0.0695090	+	0.997581i	$0.522143\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$	5.07107			0.481324
$112$	1.00000	−	2.44949i	0.0944911	−	0.231455i
$113$	−14.5858			−1.37212			−0.686058	−	0.727547i	$-0.740660\pi$
$113$	−14.5858			−1.37212			−0.686058	+	0.727547i	$0.740660\pi$
$114$	0.292893	−	0.507306i	0.0274320	−	0.0475136i
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$	4.62132	+	8.00436i	0.429079	+	0.743186i
$117$	0.707107	−	1.22474i	0.0653720	−	0.113228i
$118$	−9.24264			−0.850854
$119$	2.29289	+	2.95680i	0.210189	+	0.271049i
$120$	−1.00000			−0.0912871
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	3.00000	+	5.19615i	0.271607	+	0.470438i
$123$	−5.12132	−	8.87039i	−0.461774	−	0.799816i
$124$	3.32843	−	5.76500i	0.298902	−	0.517713i
$125$	9.00000			0.804984
$126$	1.62132	+	2.09077i	0.144439	+	0.186261i
$127$	−0.171573			−0.0152246			−0.00761232	−	0.999971i	$-0.502423\pi$
$127$	−0.171573			−0.0152246			−0.00761232	+	0.999971i	$0.502423\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.82843	−	3.16693i	−0.160984	−	0.278833i
$130$	−0.707107	−	1.22474i	−0.0620174	−	0.107417i
$131$	−3.62132	+	6.27231i	−0.316396	+	0.548014i	−0.979733	−	0.200306i	$-0.935806\pi$
$131$	−3.62132	+	6.27231i	−0.316396	+	0.548014i	0.663337	+	0.748321i	$0.269140\pi$
$132$	−3.00000			−0.261116
$133$	−0.585786	+	1.43488i	−0.0507941	+	0.124420i
$134$	−15.6569			−1.35255
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−0.707107	−	1.22474i	−0.0606339	−	0.105021i
$137$	−7.48528	−	12.9649i	−0.639511	−	1.10767i	−0.985540	−	0.169441i	$-0.945804\pi$
$137$	−7.48528	−	12.9649i	−0.639511	−	1.10767i	0.346030	−	0.938224i	$-0.387530\pi$
$138$	0.500000	−	0.866025i	0.0425628	−	0.0737210i
$139$	17.3137			1.46853			0.734265	−	0.678863i	$-0.237527\pi$
$139$	17.3137			1.46853			0.734265	+	0.678863i	$0.237527\pi$
$140$	2.62132	−	0.358719i	0.221542	−	0.0303173i
$141$	13.3137			1.12122
$142$	6.94975	−	12.0373i	0.583210	−	1.01015i
$143$	−2.12132	−	3.67423i	−0.177394	−	0.307255i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.62132	+	8.00436i	−0.383780	+	0.664726i
$146$	−5.65685			−0.468165
$147$	−5.00000	−	4.89898i	−0.412393	−	0.404061i
$148$	5.07107			0.416839
$149$	−1.17157	+	2.02922i	−0.0959790	+	0.166240i	−0.910017	−	0.414571i	$-0.863931\pi$
$149$	−1.17157	+	2.02922i	−0.0959790	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	6.32843	+	10.9612i	0.515000	+	0.892006i	0.999848	+	0.0174081i	$0.00554145\pi$
$151$	6.32843	+	10.9612i	0.515000	+	0.892006i	−0.484848	+	0.874598i	$0.661125\pi$
$152$	0.292893	−	0.507306i	0.0237568	−	0.0411479i
$153$	1.41421			0.114332
$154$	7.86396	−	1.07616i	0.633696	−	0.0867193i
$155$	6.65685			0.534691
$156$	0.707107	−	1.22474i	0.0566139	−	0.0980581i
$157$	−7.94975	−	13.7694i	−0.634459	−	1.09892i	−0.986629	−	0.162979i	$-0.947890\pi$
$157$	−7.94975	−	13.7694i	−0.634459	−	1.09892i	0.352171	−	0.935936i	$-0.385444\pi$
$158$	−1.20711	−	2.09077i	−0.0960323	−	0.166333i
$159$	3.91421	−	6.77962i	0.310417	−	0.537659i
$160$	−1.00000			−0.0790569
$161$	−1.00000	+	2.44949i	−0.0788110	+	0.193047i
$162$	1.00000			0.0785674
$163$	−0.707107	+	1.22474i	−0.0553849	+	0.0959294i	−0.892389	−	0.451268i	$-0.850972\pi$
$163$	−0.707107	+	1.22474i	−0.0553849	+	0.0959294i	0.837004	+	0.547197i	$0.184305\pi$
$164$	−5.12132	−	8.87039i	−0.399908	−	0.692661i
$165$	−1.50000	−	2.59808i	−0.116775	−	0.202260i
$166$	5.15685	−	8.93193i	0.400250	−	0.693252i
$167$	1.51472			0.117212			0.0586062	−	0.998281i	$-0.481334\pi$
$167$	1.51472			0.117212			0.0586062	+	0.998281i	$0.481334\pi$
$168$	1.62132	+	2.09077i	0.125088	+	0.161306i
$169$	−11.0000			−0.846154
$170$	0.707107	−	1.22474i	0.0542326	−	0.0939336i
$171$	0.292893	+	0.507306i	0.0223981	+	0.0387947i
$172$	−1.82843	−	3.16693i	−0.139416	−	0.241476i
$173$	0.414214	−	0.717439i	0.0314921	−	0.0545459i	−0.849850	−	0.527025i	$-0.823307\pi$
$173$	0.414214	−	0.717439i	0.0314921	−	0.0545459i	0.881342	+	0.472479i	$0.156641\pi$
$174$	−9.24264			−0.700683
$175$	−6.48528	−	8.36308i	−0.490241	−	0.632190i
$176$	−3.00000			−0.226134
$177$	4.62132	−	8.00436i	0.347360	−	0.601645i
$178$	5.36396	+	9.29065i	0.402046	+	0.696364i
$179$	−8.00000	−	13.8564i	−0.597948	−	1.03568i	−0.993124	−	0.117071i	$-0.962650\pi$
$179$	−8.00000	−	13.8564i	−0.597948	−	1.03568i	0.395175	−	0.918606i	$-0.370684\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	4.48528			0.333388			0.166694	−	0.986009i	$-0.446691\pi$
$181$	4.48528			0.333388			0.166694	+	0.986009i	$0.446691\pi$
$182$	−1.41421	+	3.46410i	−0.104828	+	0.256776i
$183$	−6.00000			−0.443533
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	2.53553	+	4.39167i	0.186416	+	0.322882i
$186$	3.32843	+	5.76500i	0.244052	+	0.422711i
$187$	2.12132	−	3.67423i	0.155126	−	0.268687i
$188$	13.3137			0.971002
$189$	−2.62132	+	0.358719i	−0.190673	+	0.0260930i
$190$	0.585786			0.0424974
$191$	0.707107	−	1.22474i	0.0511645	−	0.0886194i	−0.839309	−	0.543655i	$-0.817040\pi$
$191$	0.707107	−	1.22474i	0.0511645	−	0.0886194i	0.890473	+	0.455035i	$0.150373\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.8137	−	22.1940i	−0.922351	−	1.59756i	−0.795767	−	0.605603i	$-0.792932\pi$
$193$	−12.8137	−	22.1940i	−0.922351	−	1.59756i	−0.126584	−	0.991956i	$-0.540401\pi$
$194$	3.20711	−	5.55487i	0.230257	−	0.398817i
$195$	1.41421			0.101274
$196$	−5.00000	−	4.89898i	−0.357143	−	0.349927i
$197$	−8.82843			−0.628999			−0.314500	−	0.949258i	$-0.601837\pi$
$197$	−8.82843			−0.628999			−0.314500	+	0.949258i	$0.601837\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	8.65685	+	14.9941i	0.613668	+	1.06290i	0.990617	+	0.136670i	$0.0436400\pi$
$199$	8.65685	+	14.9941i	0.613668	+	1.06290i	−0.376948	+	0.926234i	$0.623027\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	7.82843	−	13.5592i	0.552175	−	0.956395i
$202$	12.4853			0.878461
$203$	24.2279	−	3.31552i	1.70047	−	0.232704i
$204$	1.41421			0.0990148
$205$	5.12132	−	8.87039i	0.357689	−	0.619535i
$206$	1.17157	+	2.02922i	0.0816274	+	0.141383i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	0.707107	−	1.22474i	0.0490290	−	0.0849208i
$209$	1.75736			0.121559
$210$	−1.00000	+	2.44949i	−0.0690066	+	0.169031i
$211$	−0.828427			−0.0570313			−0.0285156	−	0.999593i	$-0.509078\pi$
$211$	−0.828427			−0.0570313			−0.0285156	+	0.999593i	$0.509078\pi$
$212$	3.91421	−	6.77962i	0.268829	−	0.465626i
$213$	6.94975	+	12.0373i	0.476189	+	0.824783i
$214$	−4.74264	−	8.21449i	−0.324200	−	0.561531i
$215$	1.82843	−	3.16693i	0.124698	−	0.215983i
$216$	1.00000			0.0680414
$217$	−10.7929	−	13.9180i	−0.732669	−	0.944812i
$218$	−17.3137			−1.17263
$219$	2.82843	−	4.89898i	0.191127	−	0.331042i
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$	−2.53553	+	4.39167i	−0.170174	+	0.294750i
$223$	−15.8284			−1.05995			−0.529975	−	0.848013i	$-0.677799\pi$
$223$	−15.8284			−1.05995			−0.529975	+	0.848013i	$0.677799\pi$
$224$	1.62132	+	2.09077i	0.108329	+	0.139695i
$225$	−4.00000			−0.266667
$226$	7.29289	−	12.6317i	0.485116	−	0.840246i
$227$	1.08579	+	1.88064i	0.0720662	+	0.124822i	0.899807	−	0.436289i	$-0.143707\pi$
$227$	1.08579	+	1.88064i	0.0720662	+	0.124822i	−0.827741	+	0.561111i	$0.810374\pi$
$228$	0.292893	+	0.507306i	0.0193973	+	0.0335972i
$229$	1.36396	−	2.36245i	0.0901331	−	0.156115i	−0.817434	−	0.576022i	$-0.804604\pi$
$229$	1.36396	−	2.36245i	0.0901331	−	0.156115i	0.907567	+	0.419907i	$0.137937\pi$
$230$	1.00000			0.0659380
$231$	−3.00000	+	7.34847i	−0.197386	+	0.483494i
$232$	−9.24264			−0.606809
$233$	13.6066	−	23.5673i	0.891398	−	1.54395i	0.0531980	−	0.998584i	$-0.483059\pi$
$233$	13.6066	−	23.5673i	0.891398	−	1.54395i	0.838200	−	0.545363i	$-0.183608\pi$
$234$	0.707107	+	1.22474i	0.0462250	+	0.0800641i
$235$	6.65685	+	11.5300i	0.434245	+	0.752135i
$236$	4.62132	−	8.00436i	0.300822	−	0.521040i
$237$	2.41421			0.156820
$238$	−3.70711	+	0.507306i	−0.240296	+	0.0328838i
$239$	−0.686292			−0.0443925			−0.0221963	−	0.999754i	$-0.507066\pi$
$239$	−0.686292			−0.0443925			−0.0221963	+	0.999754i	$0.507066\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	12.0355	+	20.8462i	0.775277	+	1.34282i	0.934639	+	0.355599i	$0.115723\pi$
$241$	12.0355	+	20.8462i	0.775277	+	1.34282i	−0.159362	+	0.987220i	$0.550944\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.00000			−0.384111
$245$	1.74264	−	6.77962i	0.111333	−	0.433134i
$246$	10.2426			0.653047
$247$	−0.414214	+	0.717439i	−0.0263558	+	0.0456495i
$248$	3.32843	+	5.76500i	0.211355	+	0.366078i
$249$	5.15685	+	8.93193i	0.326802	+	0.566038i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	20.1716			1.27322			0.636609	−	0.771187i	$-0.280336\pi$
$251$	20.1716			1.27322			0.636609	+	0.771187i	$0.280336\pi$
$252$	−2.62132	+	0.358719i	−0.165128	+	0.0225972i
$253$	3.00000			0.188608
$254$	0.0857864	−	0.148586i	0.00538272	−	0.00932314i
$255$	0.707107	+	1.22474i	0.0442807	+	0.0766965i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.707107	+	1.22474i	−0.0441081	+	0.0763975i	−0.887237	−	0.461315i	$-0.847378\pi$
$257$	−0.707107	+	1.22474i	−0.0441081	+	0.0763975i	0.843129	+	0.537712i	$0.180711\pi$
$258$	3.65685			0.227666
$259$	5.07107	−	12.4215i	0.315101	−	0.771836i
$260$	1.41421			0.0877058
$261$	4.62132	−	8.00436i	0.286053	−	0.495458i
$262$	−3.62132	−	6.27231i	−0.223726	−	0.387505i
$263$	11.4853	+	19.8931i	0.708213	+	1.22666i	0.965519	+	0.260331i	$0.0838316\pi$
$263$	11.4853	+	19.8931i	0.708213	+	1.22666i	−0.257307	+	0.966330i	$0.582835\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	7.82843			0.480896
$266$	−0.949747	−	1.22474i	−0.0582328	−	0.0750939i
$267$	−10.7279			−0.656538
$268$	7.82843	−	13.5592i	0.478197	−	0.828262i
$269$	−2.20711	−	3.82282i	−0.134570	−	0.233082i	0.790863	−	0.611993i	$-0.209632\pi$
$269$	−2.20711	−	3.82282i	−0.134570	−	0.233082i	−0.925433	+	0.378911i	$0.876299\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	1.41421			0.0857493
$273$	−2.29289	−	2.95680i	−0.138772	−	0.178953i
$274$	14.9706			0.904405
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	−1.41421	−	2.44949i	−0.0849719	−	0.147176i	0.820407	−	0.571779i	$-0.193747\pi$
$277$	−1.41421	−	2.44949i	−0.0849719	−	0.147176i	−0.905379	+	0.424604i	$0.860413\pi$
$278$	−8.65685	+	14.9941i	−0.519204	+	0.899287i
$279$	−6.65685			−0.398535
$280$	−1.00000	+	2.44949i	−0.0597614	+	0.146385i
$281$	−1.27208			−0.0758858			−0.0379429	−	0.999280i	$-0.512081\pi$
$281$	−1.27208			−0.0758858			−0.0379429	+	0.999280i	$0.512081\pi$
$282$	−6.65685	+	11.5300i	−0.396410	+	0.686602i
$283$	−2.07107	−	3.58719i	−0.123112	−	0.213237i	0.797881	−	0.602815i	$-0.205954\pi$
$283$	−2.07107	−	3.58719i	−0.123112	−	0.213237i	−0.920993	+	0.389578i	$0.872621\pi$
$284$	6.94975	+	12.0373i	0.412392	+	0.714283i
$285$	−0.292893	+	0.507306i	−0.0173495	+	0.0300502i
$286$	4.24264			0.250873
$287$	−26.8492	+	3.67423i	−1.58486	+	0.216883i
$288$	1.00000			0.0589256
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	−4.62132	−	8.00436i	−0.271373	−	0.470032i
$291$	3.20711	+	5.55487i	0.188004	+	0.325632i
$292$	2.82843	−	4.89898i	0.165521	−	0.286691i
$293$	23.6274			1.38033			0.690164	−	0.723653i	$-0.257538\pi$
$293$	23.6274			1.38033			0.690164	+	0.723653i	$0.257538\pi$
$294$	6.74264	−	1.88064i	0.393239	−	0.109681i
$295$	9.24264			0.538127
$296$	−2.53553	+	4.39167i	−0.147375	+	0.255261i
$297$	1.50000	+	2.59808i	0.0870388	+	0.150756i
$298$	−1.17157	−	2.02922i	−0.0678674	−	0.117550i
$299$	−0.707107	+	1.22474i	−0.0408930	+	0.0708288i
$300$	−4.00000			−0.230940
$301$	−9.58579	+	1.31178i	−0.552516	+	0.0756100i
$302$	−12.6569			−0.728320
$303$	−6.24264	+	10.8126i	−0.358630	+	0.621166i
$304$	0.292893	+	0.507306i	0.0167986	+	0.0290960i
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	−0.707107	+	1.22474i	−0.0404226	+	0.0700140i
$307$	6.10051			0.348174			0.174087	−	0.984730i	$-0.444303\pi$
$307$	6.10051			0.348174			0.174087	+	0.984730i	$0.444303\pi$
$308$	−3.00000	+	7.34847i	−0.170941	+	0.418718i
$309$	−2.34315			−0.133297
$310$	−3.32843	+	5.76500i	−0.189042	+	0.327430i
$311$	−0.292893	−	0.507306i	−0.0166085	−	0.0287667i	0.857602	−	0.514314i	$-0.171954\pi$
$311$	−0.292893	−	0.507306i	−0.0166085	−	0.0287667i	−0.874210	+	0.485548i	$0.838620\pi$
$312$	0.707107	+	1.22474i	0.0400320	+	0.0693375i
$313$	−12.6213	+	21.8608i	−0.713399	+	1.23564i	0.250175	+	0.968201i	$0.419512\pi$
$313$	−12.6213	+	21.8608i	−0.713399	+	1.23564i	−0.963574	+	0.267443i	$0.913821\pi$
$314$	15.8995			0.897260
$315$	−1.62132	−	2.09077i	−0.0913511	−	0.117802i
$316$	2.41421			0.135810
$317$	−12.0355	+	20.8462i	−0.675983	+	1.17084i	0.300198	+	0.953877i	$0.402947\pi$
$317$	−12.0355	+	20.8462i	−0.675983	+	1.17084i	−0.976181	+	0.216960i	$0.930386\pi$
$318$	3.91421	+	6.77962i	0.219498	+	0.380182i
$319$	−13.8640	−	24.0131i	−0.776233	−	1.34447i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	9.48528			0.529417
$322$	−1.62132	−	2.09077i	−0.0903527	−	0.116514i
$323$	−0.828427			−0.0460949
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.82843	−	4.89898i	−0.156893	−	0.271746i
$326$	−0.707107	−	1.22474i	−0.0391630	−	0.0678323i
$327$	8.65685	−	14.9941i	0.478725	−	0.829176i
$328$	10.2426			0.565555
$329$	13.3137	−	32.6118i	0.734009	−	1.79795i
$330$	3.00000			0.165145
$331$	−3.05025	+	5.28319i	−0.167657	+	0.290391i	−0.937596	−	0.347727i	$-0.886953\pi$
$331$	−3.05025	+	5.28319i	−0.167657	+	0.290391i	0.769939	+	0.638118i	$0.220287\pi$
$332$	5.15685	+	8.93193i	0.283019	+	0.490204i
$333$	−2.53553	−	4.39167i	−0.138946	−	0.240662i
$334$	−0.757359	+	1.31178i	−0.0414409	+	0.0717777i
$335$	15.6569			0.855425
$336$	−2.62132	+	0.358719i	−0.143005	+	0.0195698i
$337$	−28.0711			−1.52913			−0.764564	−	0.644548i	$-0.777046\pi$
$337$	−28.0711			−1.52913			−0.764564	+	0.644548i	$0.777046\pi$
$338$	5.50000	−	9.52628i	0.299161	−	0.518161i
$339$	7.29289	+	12.6317i	0.396096	+	0.686058i
$340$	0.707107	+	1.22474i	0.0383482	+	0.0664211i
$341$	−9.98528	+	17.2950i	−0.540733	+	0.936578i
$342$	−0.585786			−0.0316757
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	3.65685			0.197164
$345$	−0.500000	+	0.866025i	−0.0269191	+	0.0466252i
$346$	0.414214	+	0.717439i	0.0222683	+	0.0385698i
$347$	−15.3137	−	26.5241i	−0.822083	−	1.42389i	−0.904128	−	0.427261i	$-0.859479\pi$
$347$	−15.3137	−	26.5241i	−0.822083	−	1.42389i	0.0820455	−	0.996629i	$-0.473855\pi$
$348$	4.62132	−	8.00436i	0.247729	−	0.429079i
$349$	−22.0416			−1.17986			−0.589931	−	0.807454i	$-0.700845\pi$
$349$	−22.0416			−1.17986			−0.589931	+	0.807454i	$0.700845\pi$
$350$	10.4853	−	1.43488i	0.560462	−	0.0766974i
$351$	−1.41421			−0.0754851
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−1.36396	−	2.36245i	−0.0725963	−	0.125741i	0.827442	−	0.561551i	$-0.189795\pi$
$353$	−1.36396	−	2.36245i	−0.0725963	−	0.125741i	−0.900038	+	0.435810i	$0.856462\pi$
$354$	4.62132	+	8.00436i	0.245620	+	0.425427i
$355$	−6.94975	+	12.0373i	−0.368854	+	0.638874i
$356$	−10.7279			−0.568579
$357$	1.41421	−	3.46410i	0.0748481	−	0.183340i
$358$	16.0000			0.845626
$359$	−1.00000	+	1.73205i	−0.0527780	+	0.0914141i	−0.891207	−	0.453596i	$-0.850141\pi$
$359$	−1.00000	+	1.73205i	−0.0527780	+	0.0914141i	0.838429	+	0.545010i	$0.183474\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	9.32843	+	16.1573i	0.490970	+	0.850385i
$362$	−2.24264	+	3.88437i	−0.117871	+	0.204158i
$363$	−2.00000			−0.104973
$364$	−2.29289	−	2.95680i	−0.120180	−	0.154978i
$365$	5.65685			0.296093
$366$	3.00000	−	5.19615i	0.156813	−	0.271607i
$367$	−12.3492	−	21.3895i	−0.644625	−	1.11652i	−0.984388	−	0.176012i	$-0.943680\pi$
$367$	−12.3492	−	21.3895i	−0.644625	−	1.11652i	0.339763	−	0.940511i	$-0.389653\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−5.12132	+	8.87039i	−0.266605	+	0.461774i
$370$	−5.07107			−0.263632
$371$	−12.6924	−	16.3674i	−0.658956	−	0.849755i
$372$	−6.65685			−0.345142
$373$	12.8284	−	22.2195i	0.664231	−	1.15048i	−0.315262	−	0.949005i	$-0.602093\pi$
$373$	12.8284	−	22.2195i	0.664231	−	1.15048i	0.979493	−	0.201477i	$-0.0645741\pi$
$374$	2.12132	+	3.67423i	0.109691	+	0.189990i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−6.65685	+	11.5300i	−0.343301	+	0.594615i
$377$	13.0711			0.673194
$378$	1.00000	−	2.44949i	0.0514344	−	0.125988i
$379$	−4.97056			−0.255321			−0.127660	−	0.991818i	$-0.540747\pi$
$379$	−4.97056			−0.255321			−0.127660	+	0.991818i	$0.540747\pi$
$380$	−0.292893	+	0.507306i	−0.0150251	+	0.0260242i
$381$	0.0857864	+	0.148586i	0.00439497	+	0.00761232i
$382$	0.707107	+	1.22474i	0.0361787	+	0.0626634i
$383$	13.3640	−	23.1471i	0.682867	−	1.18276i	−0.291236	−	0.956651i	$-0.594066\pi$
$383$	13.3640	−	23.1471i	0.682867	−	1.18276i	0.974102	−	0.226108i	$-0.0726003\pi$
$384$	1.00000			0.0510310
$385$	−7.86396	+	1.07616i	−0.400785	+	0.0548461i
$386$	25.6274			1.30440
$387$	−1.82843	+	3.16693i	−0.0929442	+	0.160984i
$388$	3.20711	+	5.55487i	0.162816	+	0.282006i
$389$	3.41421	+	5.91359i	0.173107	+	0.299831i	0.939505	−	0.342536i	$-0.111286\pi$
$389$	3.41421	+	5.91359i	0.173107	+	0.299831i	−0.766397	+	0.642367i	$0.777953\pi$
$390$	−0.707107	+	1.22474i	−0.0358057	+	0.0620174i
$391$	−1.41421			−0.0715199
$392$	6.74264	−	1.88064i	0.340555	−	0.0949865i
$393$	7.24264			0.365343
$394$	4.41421	−	7.64564i	0.222385	−	0.385182i
$395$	1.20711	+	2.09077i	0.0607361	+	0.105198i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−15.7782	+	27.3286i	−0.791884	+	1.37158i	0.132915	+	0.991127i	$0.457566\pi$
$397$	−15.7782	+	27.3286i	−0.791884	+	1.37158i	−0.924799	+	0.380456i	$0.875767\pi$
$398$	−17.3137			−0.867858
$399$	1.53553	−	0.210133i	0.0768728	−	0.0105198i
$400$	−4.00000			−0.200000
$401$	−8.24264	+	14.2767i	−0.411618	+	0.712943i	−0.995067	−	0.0992068i	$-0.968369\pi$
$401$	−8.24264	+	14.2767i	−0.411618	+	0.712943i	0.583449	+	0.812150i	$0.301703\pi$
$402$	7.82843	+	13.5592i	0.390446	+	0.676273i
$403$	−4.70711	−	8.15295i	−0.234478	−	0.406127i
$404$	−6.24264	+	10.8126i	−0.310583	+	0.537946i
$405$	−1.00000			−0.0496904
$406$	−9.24264	+	22.6398i	−0.458705	+	1.12359i
$407$	−15.2132			−0.754090
$408$	−0.707107	+	1.22474i	−0.0350070	+	0.0606339i
$409$	12.3284	+	21.3535i	0.609601	+	1.05586i	0.991306	+	0.131576i	$0.0420039\pi$
$409$	12.3284	+	21.3535i	0.609601	+	1.05586i	−0.381705	+	0.924284i	$0.624663\pi$
$410$	5.12132	+	8.87039i	0.252924	+	0.438077i
$411$	−7.48528	+	12.9649i	−0.369222	+	0.639511i
$412$	−2.34315			−0.115439
$413$	−14.9853	−	19.3242i	−0.737377	−	0.950884i
$414$	−1.00000			−0.0491473
$415$	−5.15685	+	8.93193i	−0.253140	+	0.438451i
$416$	0.707107	+	1.22474i	0.0346688	+	0.0600481i
$417$	−8.65685	−	14.9941i	−0.423928	−	0.734265i
$418$	−0.878680	+	1.52192i	−0.0429776	+	0.0744394i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$	−1.62132	−	2.09077i	−0.0791123	−	0.102019i
$421$	−19.4558			−0.948220			−0.474110	−	0.880466i	$-0.657230\pi$
$421$	−19.4558			−0.948220			−0.474110	+	0.880466i	$0.657230\pi$
$422$	0.414214	−	0.717439i	0.0201636	−	0.0349244i
$423$	−6.65685	−	11.5300i	−0.323667	−	0.560608i
$424$	3.91421	+	6.77962i	0.190091	+	0.329247i
$425$	2.82843	−	4.89898i	0.137199	−	0.237635i
$426$	−13.8995			−0.673433
$427$	−6.00000	+	14.6969i	−0.290360	+	0.711235i
$428$	9.48528			0.458488
$429$	−2.12132	+	3.67423i	−0.102418	+	0.177394i
$430$	1.82843	+	3.16693i	0.0881746	+	0.152723i
$431$	−8.82843	−	15.2913i	−0.425250	−	0.736555i	0.571193	−	0.820816i	$-0.306481\pi$
$431$	−8.82843	−	15.2913i	−0.425250	−	0.736555i	−0.996444	+	0.0842603i	$0.973147\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$	17.4497	−	2.38794i	0.837615	−	0.114625i
$435$	9.24264			0.443151
$436$	8.65685	−	14.9941i	0.414588	−	0.718088i
$437$	−0.292893	−	0.507306i	−0.0140110	−	0.0242677i
$438$	2.82843	+	4.89898i	0.135147	+	0.234082i
$439$	8.57107	−	14.8455i	0.409075	−	0.708538i	−0.585712	−	0.810520i	$-0.699185\pi$
$439$	8.57107	−	14.8455i	0.409075	−	0.708538i	0.994786	+	0.101981i	$0.0325182\pi$
$440$	3.00000			0.143019
$441$	−1.74264	+	6.77962i	−0.0829829	+	0.322839i
$442$	−2.00000			−0.0951303
$443$	−17.8640	+	30.9413i	−0.848742	+	1.47006i	0.0335887	+	0.999436i	$0.489306\pi$
$443$	−17.8640	+	30.9413i	−0.848742	+	1.47006i	−0.882331	+	0.470629i	$0.844027\pi$
$444$	−2.53553	−	4.39167i	−0.120331	−	0.208420i
$445$	−5.36396	−	9.29065i	−0.254276	−	0.440419i
$446$	7.91421	−	13.7078i	0.374749	−	0.649084i
$447$	2.34315			0.110827
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	−10.2426			−0.483380			−0.241690	−	0.970354i	$-0.577702\pi$
$449$	−10.2426			−0.483380			−0.241690	+	0.970354i	$0.577702\pi$
$450$	2.00000	−	3.46410i	0.0942809	−	0.163299i
$451$	15.3640	+	26.6112i	0.723461	+	1.25307i
$452$	7.29289	+	12.6317i	0.343029	+	0.594143i
$453$	6.32843	−	10.9612i	0.297335	−	0.515000i
$454$	−2.17157			−0.101917
$455$	1.41421	−	3.46410i	0.0662994	−	0.162400i
$456$	−0.585786			−0.0274320
$457$	11.1066	−	19.2372i	0.519545	−	0.899878i	−0.480197	−	0.877161i	$-0.659435\pi$
$457$	11.1066	−	19.2372i	0.519545	−	0.899878i	0.999742	−	0.0227175i	$-0.00723183\pi$
$458$	1.36396	+	2.36245i	0.0637337	+	0.110390i
$459$	−0.707107	−	1.22474i	−0.0330049	−	0.0571662i
$460$	−0.500000	+	0.866025i	−0.0233126	+	0.0403786i
$461$	−2.97056			−0.138353			−0.0691765	−	0.997604i	$-0.522037\pi$
$461$	−2.97056			−0.138353			−0.0691765	+	0.997604i	$0.522037\pi$
$462$	−4.86396	−	6.27231i	−0.226292	−	0.291814i
$463$	25.7990			1.19898			0.599490	−	0.800382i	$-0.295370\pi$
$463$	25.7990			1.19898			0.599490	+	0.800382i	$0.295370\pi$
$464$	4.62132	−	8.00436i	0.214539	−	0.371593i
$465$	−3.32843	−	5.76500i	−0.154352	−	0.267346i
$466$	13.6066	+	23.5673i	0.630314	+	1.09174i
$467$	−11.5858	+	20.0672i	−0.536126	+	0.928598i	0.462982	+	0.886368i	$0.346780\pi$
$467$	−11.5858	+	20.0672i	−0.536126	+	0.928598i	−0.999108	+	0.0422301i	$0.986554\pi$
$468$	−1.41421			−0.0653720
$469$	−25.3848	−	32.7349i	−1.17216	−	1.51156i
$470$	−13.3137			−0.614116
$471$	−7.94975	+	13.7694i	−0.366305	+	0.634459i
$472$	4.62132	+	8.00436i	0.212714	+	0.368431i
$473$	5.48528	+	9.50079i	0.252214	+	0.436847i
$474$	−1.20711	+	2.09077i	−0.0554443	+	0.0960323i
$475$	2.34315			0.107511
$476$	1.41421	−	3.46410i	0.0648204	−	0.158777i
$477$	−7.82843			−0.358439
$478$	0.343146	−	0.594346i	0.0156951	−	0.0271847i
$479$	17.2635	+	29.9012i	0.788787	+	1.36622i	0.926710	+	0.375777i	$0.122624\pi$
$479$	17.2635	+	29.9012i	0.788787	+	1.36622i	−0.137923	+	0.990443i	$0.544043\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	3.58579	−	6.21076i	0.163498	−	0.283186i
$482$	−24.0711			−1.09641
$483$	2.62132	−	0.358719i	0.119274	−	0.0163223i
$484$	−2.00000			−0.0909091
$485$	−3.20711	+	5.55487i	−0.145627	+	0.252234i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	6.25736	+	10.8381i	0.283548	+	0.491120i	0.972256	−	0.233919i	$-0.0751551\pi$
$487$	6.25736	+	10.8381i	0.283548	+	0.491120i	−0.688708	+	0.725039i	$0.741822\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$	1.41421			0.0639529
$490$	5.00000	+	4.89898i	0.225877	+	0.221313i
$491$	−28.8995			−1.30422			−0.652108	−	0.758126i	$-0.726115\pi$
$491$	−28.8995			−1.30422			−0.652108	+	0.758126i	$0.726115\pi$
$492$	−5.12132	+	8.87039i	−0.230887	+	0.399908i
$493$	6.53553	+	11.3199i	0.294346	+	0.509822i
$494$	−0.414214	−	0.717439i	−0.0186363	−	0.0322791i
$495$	−1.50000	+	2.59808i	−0.0674200	+	0.116775i
$496$	−6.65685			−0.298902
$497$	36.4350	−	4.98602i	1.63433	−	0.223654i
$498$	−10.3137			−0.462168
$499$	−12.8995	+	22.3426i	−0.577461	+	1.00019i	0.418309	+	0.908305i	$0.362623\pi$
$499$	−12.8995	+	22.3426i	−0.577461	+	1.00019i	−0.995769	+	0.0918864i	$0.970710\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$	−0.757359	−	1.31178i	−0.0338363	−	0.0586062i
$502$	−10.0858	+	17.4691i	−0.450151	+	0.779684i
$503$	−1.17157			−0.0522379			−0.0261189	−	0.999659i	$-0.508315\pi$
$503$	−1.17157			−0.0522379			−0.0261189	+	0.999659i	$0.508315\pi$
$504$	1.00000	−	2.44949i	0.0445435	−	0.109109i
$505$	−12.4853			−0.555588
$506$	−1.50000	+	2.59808i	−0.0666831	+	0.115499i
$507$	5.50000	+	9.52628i	0.244264	+	0.423077i
$508$	0.0857864	+	0.148586i	0.00380616	+	0.00659246i
$509$	−8.13604	+	14.0920i	−0.360624	+	0.624618i	−0.988064	−	0.154047i	$-0.950769\pi$
$509$	−8.13604	+	14.0920i	−0.360624	+	0.624618i	0.627440	+	0.778665i	$0.284103\pi$
$510$	−1.41421			−0.0626224
$511$	−9.17157	−	11.8272i	−0.405726	−	0.523204i
$512$	1.00000			0.0441942
$513$	0.292893	−	0.507306i	0.0129316	−	0.0223981i
$514$	−0.707107	−	1.22474i	−0.0311891	−	0.0540212i
$515$	−1.17157	−	2.02922i	−0.0516257	−	0.0894183i
$516$	−1.82843	+	3.16693i	−0.0804920	+	0.139416i
$517$	−39.9411			−1.75661
$518$	8.22183	+	10.6024i	0.361246	+	0.465844i
$519$	−0.828427			−0.0363639
$520$	−0.707107	+	1.22474i	−0.0310087	+	0.0537086i
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	−0.996611	−	0.0822547i	$-0.973788\pi$
$521$	−13.0000	−	22.5167i	−0.569540	−	0.986473i	0.427071	−	0.904218i	$-0.359545\pi$
$522$	4.62132	+	8.00436i	0.202270	+	0.350341i
$523$	−20.1421	+	34.8872i	−0.880754	+	1.52551i	−0.0302500	+	0.999542i	$0.509630\pi$
$523$	−20.1421	+	34.8872i	−0.880754	+	1.52551i	−0.850504	+	0.525968i	$0.823703\pi$
$524$	7.24264			0.316396
$525$	−4.00000	+	9.79796i	−0.174574	+	0.427618i
$526$	−22.9706			−1.00156
$527$	4.70711	−	8.15295i	0.205045	−	0.355148i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−3.91421	+	6.77962i	−0.170023	+	0.294488i
$531$	−9.24264			−0.401096
$532$	1.53553	−	0.210133i	0.0665738	−	0.00911042i
$533$	−14.4853			−0.627427
$534$	5.36396	−	9.29065i	0.232121	−	0.402046i
$535$	4.74264	+	8.21449i	0.205042	+	0.355144i
$536$	7.82843	+	13.5592i	0.338137	+	0.585670i
$537$	−8.00000	+	13.8564i	−0.345225	+	0.597948i
$538$	4.41421			0.190310
$539$	15.0000	+	14.6969i	0.646096	+	0.633042i
$540$	−1.00000			−0.0430331
$541$	−9.84924	+	17.0594i	−0.423452	+	0.733440i	−0.996274	−	0.0862391i	$-0.972515\pi$
$541$	−9.84924	+	17.0594i	−0.423452	+	0.733440i	0.572822	+	0.819679i	$0.305848\pi$
$542$	3.50000	+	6.06218i	0.150338	+	0.260393i
$543$	−2.24264	−	3.88437i	−0.0962409	−	0.166694i
$544$	−0.707107	+	1.22474i	−0.0303170	+	0.0525105i
$545$	17.3137			0.741638
$546$	3.70711	−	0.507306i	0.158650	−	0.0217107i
$547$	15.7574			0.673736			0.336868	−	0.941552i	$-0.390632\pi$
$547$	15.7574			0.673736			0.336868	+	0.941552i	$0.390632\pi$
$548$	−7.48528	+	12.9649i	−0.319755	+	0.553833i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−2.70711	+	4.68885i	−0.115327	+	0.199752i
$552$	−1.00000			−0.0425628
$553$	2.41421	−	5.91359i	0.102663	−	0.251471i
$554$	2.82843			0.120168
$555$	2.53553	−	4.39167i	0.107627	−	0.186416i
$556$	−8.65685	−	14.9941i	−0.367132	−	0.635892i
$557$	8.84315	+	15.3168i	0.374696	+	0.648993i	0.990282	−	0.139077i	$-0.0444137\pi$
$557$	8.84315	+	15.3168i	0.374696	+	0.648993i	−0.615585	+	0.788070i	$0.711080\pi$
$558$	3.32843	−	5.76500i	0.140904	−	0.244052i
$559$	−5.17157			−0.218734
$560$	−1.62132	−	2.09077i	−0.0685133	−	0.0883512i
$561$	−4.24264			−0.179124
$562$	0.636039	−	1.10165i	0.0268297	−	0.0464704i
$563$	−7.57107	−	13.1135i	−0.319082	−	0.552667i	0.661214	−	0.750197i	$-0.270041\pi$
$563$	−7.57107	−	13.1135i	−0.319082	−	0.552667i	−0.980297	+	0.197530i	$0.936708\pi$
$564$	−6.65685	−	11.5300i	−0.280304	−	0.485501i
$565$	−7.29289	+	12.6317i	−0.306814	+	0.531418i
$566$	4.14214			0.174107
$567$	1.62132	+	2.09077i	0.0680891	+	0.0878041i
$568$	−13.8995			−0.583210
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	−0.247049	−	0.969003i	$-0.579461\pi$
$569$	17.0711	−	29.5680i	0.715656	−	1.23955i	0.962706	−	0.270550i	$-0.0872057\pi$
$570$	−0.292893	−	0.507306i	−0.0122679	−	0.0212487i
$571$	12.2635	+	21.2409i	0.513210	+	0.888905i	0.999883	+	0.0153210i	$0.00487701\pi$
$571$	12.2635	+	21.2409i	0.513210	+	0.888905i	−0.486673	+	0.873584i	$0.661790\pi$
$572$	−2.12132	+	3.67423i	−0.0886969	+	0.153627i
$573$	−1.41421			−0.0590796
$574$	10.2426	−	25.0892i	0.427520	−	1.04720i
$575$	4.00000			0.166812
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−18.8137	−	32.5863i	−0.783225	−	1.35659i	−0.930054	−	0.367423i	$-0.880240\pi$
$577$	−18.8137	−	32.5863i	−0.783225	−	1.35659i	0.146829	−	0.989162i	$-0.453093\pi$
$578$	7.50000	+	12.9904i	0.311959	+	0.540329i
$579$	−12.8137	+	22.1940i	−0.532520	+	0.922351i
$580$	9.24264			0.383780
$581$	27.0355	−	3.69973i	1.12162	−	0.153491i
$582$	−6.41421			−0.265878
$583$	−11.7426	+	20.3389i	−0.486330	+	0.842349i
$584$	2.82843	+	4.89898i	0.117041	+	0.202721i
$585$	−0.707107	−	1.22474i	−0.0292353	−	0.0506370i
$586$	−11.8137	+	20.4619i	−0.488020	+	0.845275i
$587$	0.414214			0.0170964			0.00854821	−	0.999963i	$-0.497279\pi$
$587$	0.414214			0.0170964			0.00854821	+	0.999963i	$0.497279\pi$
$588$	−1.74264	+	6.77962i	−0.0718653	+	0.279587i
$589$	3.89949			0.160676
$590$	−4.62132	+	8.00436i	−0.190257	+	0.329534i
$591$	4.41421	+	7.64564i	0.181576	+	0.314500i
$592$	−2.53553	−	4.39167i	−0.104210	−	0.180497i
$593$	12.4853	−	21.6251i	0.512709	−	0.888038i	−0.487182	−	0.873300i	$-0.661975\pi$
$593$	12.4853	−	21.6251i	0.512709	−	0.888038i	0.999891	−	0.0147379i	$-0.00469138\pi$
$594$	−3.00000			−0.123091
$595$	3.70711	−	0.507306i	0.151977	−	0.0207975i
$596$	2.34315			0.0959790
$597$	8.65685	−	14.9941i	0.354301	−	0.613668i
$598$	−0.707107	−	1.22474i	−0.0289157	−	0.0500835i
$599$	7.53553	+	13.0519i	0.307894	+	0.533287i	0.977901	−	0.209067i	$-0.0670426\pi$
$599$	7.53553	+	13.0519i	0.307894	+	0.533287i	−0.670008	+	0.742354i	$0.733709\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	26.9411			1.09895			0.549476	−	0.835510i	$-0.314827\pi$
$601$	26.9411			1.09895			0.549476	+	0.835510i	$0.314827\pi$
$602$	3.65685	−	8.95743i	0.149042	−	0.365077i
$603$	−15.6569			−0.637596
$604$	6.32843	−	10.9612i	0.257500	−	0.446003i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	−6.24264	−	10.8126i	−0.253590	−	0.439231i
$607$	18.6421	−	32.2891i	0.756661	−	1.31058i	−0.187883	−	0.982191i	$-0.560163\pi$
$607$	18.6421	−	32.2891i	0.756661	−	1.31058i	0.944544	−	0.328384i	$-0.106504\pi$
$608$	−0.585786			−0.0237568
$609$	−14.9853	−	19.3242i	−0.607234	−	0.783058i
$610$	6.00000			0.242933
$611$	9.41421	−	16.3059i	0.380858	−	0.659666i
$612$	−0.707107	−	1.22474i	−0.0285831	−	0.0495074i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−3.05025	+	5.28319i	−0.123098	+	0.213212i
$615$	−10.2426			−0.413023
$616$	−4.86396	−	6.27231i	−0.195975	−	0.252719i
$617$	35.9411			1.44694			0.723468	−	0.690358i	$-0.242547\pi$
$617$	35.9411			1.44694			0.723468	+	0.690358i	$0.242547\pi$
$618$	1.17157	−	2.02922i	0.0471276	−	0.0816274i
$619$	4.94975	+	8.57321i	0.198947	+	0.344587i	0.948187	−	0.317712i	$-0.102914\pi$
$619$	4.94975	+	8.57321i	0.198947	+	0.344587i	−0.749240	+	0.662298i	$0.769581\pi$
$620$	−3.32843	−	5.76500i	−0.133673	−	0.231528i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	0.585786			0.0234879
$623$	−10.7279	+	26.2779i	−0.429805	+	1.05280i
$624$	−1.41421			−0.0566139
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−12.6213	−	21.8608i	−0.504449	−	0.873732i
$627$	−0.878680	−	1.52192i	−0.0350911	−	0.0607795i
$628$	−7.94975	+	13.7694i	−0.317229	+	0.549458i
$629$	7.17157			0.285949
$630$	2.62132	−	0.358719i	0.104436	−	0.0142917i
$631$	−0.414214			−0.0164896			−0.00824479	−	0.999966i	$-0.502624\pi$
$631$	−0.414214			−0.0164896			−0.00824479	+	0.999966i	$0.502624\pi$
$632$	−1.20711	+	2.09077i	−0.0480161	+	0.0831664i
$633$	0.414214	+	0.717439i	0.0164635	+	0.0285156i
$634$	−12.0355	−	20.8462i	−0.477992	−	0.827907i
$635$	−0.0857864	+	0.148586i	−0.00340433	+	0.00589647i
$636$	−7.82843			−0.310417
$637$	−9.53553	+	2.65962i	−0.377812	+	0.105378i
$638$	27.7279			1.09776
$639$	6.94975	−	12.0373i	0.274928	−	0.476189i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	9.84924	+	17.0594i	0.389022	+	0.673805i	0.992318	−	0.123712i	$-0.0394798\pi$
$641$	9.84924	+	17.0594i	0.389022	+	0.673805i	−0.603297	+	0.797517i	$0.706146\pi$
$642$	−4.74264	+	8.21449i	−0.187177	+	0.324200i
$643$	−13.4142			−0.529005			−0.264502	−	0.964385i	$-0.585208\pi$
$643$	−13.4142			−0.529005			−0.264502	+	0.964385i	$0.585208\pi$
$644$	2.62132	−	0.358719i	0.103294	−	0.0141355i
$645$	−3.65685			−0.143988
$646$	0.414214	−	0.717439i	0.0162970	−	0.0282273i
$647$	−2.41421	−	4.18154i	−0.0949125	−	0.164393i	0.814660	−	0.579939i	$-0.196924\pi$
$647$	−2.41421	−	4.18154i	−0.0949125	−	0.164393i	−0.909572	+	0.415546i	$0.863590\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−13.8640	+	24.0131i	−0.544208	+	0.942596i
$650$	5.65685			0.221880
$651$	−6.65685	+	16.3059i	−0.260903	+	0.639078i
$652$	1.41421			0.0553849
$653$	−10.1360	+	17.5561i	−0.396654	+	0.687025i	−0.993311	−	0.115472i	$-0.963162\pi$
$653$	−10.1360	+	17.5561i	−0.396654	+	0.687025i	0.596657	+	0.802496i	$0.296495\pi$
$654$	8.65685	+	14.9941i	0.338510	+	0.586316i
$655$	3.62132	+	6.27231i	0.141497	+	0.245079i
$656$	−5.12132	+	8.87039i	−0.199954	+	0.346330i
$657$	−5.65685			−0.220695
$658$	21.5858	+	27.8359i	0.841502	+	1.08516i
$659$	23.9411			0.932614			0.466307	−	0.884623i	$-0.345584\pi$
$659$	23.9411			0.932614			0.466307	+	0.884623i	$0.345584\pi$
$660$	−1.50000	+	2.59808i	−0.0583874	+	0.101130i
$661$	11.4853	+	19.8931i	0.446726	+	0.773752i	0.998171	−	0.0604597i	$-0.0192567\pi$
$661$	11.4853	+	19.8931i	0.446726	+	0.773752i	−0.551445	+	0.834211i	$0.685923\pi$
$662$	−3.05025	−	5.28319i	−0.118551	−	0.205337i
$663$	1.00000	−	1.73205i	0.0388368	−	0.0672673i
$664$	−10.3137			−0.400250
$665$	0.949747	+	1.22474i	0.0368296	+	0.0474936i
$666$	5.07107			0.196500
$667$	−4.62132	+	8.00436i	−0.178938	+	0.309930i
$668$	−0.757359	−	1.31178i	−0.0293031	−	0.0507545i
$669$	7.91421	+	13.7078i	0.305981	+	0.529975i
$670$	−7.82843	+	13.5592i	−0.302439	+	0.523839i
$671$	18.0000			0.694882
$672$	1.00000	−	2.44949i	0.0385758	−	0.0944911i
$673$	43.9706			1.69494			0.847470	−	0.530843i	$-0.178125\pi$
$673$	43.9706			1.69494			0.847470	+	0.530843i	$0.178125\pi$
$674$	14.0355	−	24.3103i	0.540629	−	0.936396i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	5.50000	+	9.52628i	0.211538	+	0.366395i
$677$	15.6716	−	27.1440i	0.602307	−	1.04323i	−0.390163	−	0.920746i	$-0.627581\pi$
$677$	15.6716	−	27.1440i	0.602307	−	1.04323i	0.992471	−	0.122481i	$-0.0390852\pi$
$678$	−14.5858			−0.560164
$679$	16.8137	−	2.30090i	0.645251	−	0.0883006i
$680$	−1.41421			−0.0542326
$681$	1.08579	−	1.88064i	0.0416074	−	0.0720662i
$682$	−9.98528	−	17.2950i	−0.382356	−	0.662260i
$683$	−20.5208	−	35.5431i	−0.785207	−	1.36002i	−0.928875	−	0.370393i	$-0.879223\pi$
$683$	−20.5208	−	35.5431i	−0.785207	−	1.36002i	0.143668	−	0.989626i	$-0.454110\pi$
$684$	0.292893	−	0.507306i	0.0111991	−	0.0193973i
$685$	−14.9706			−0.571996
$686$	2.13604	−	18.3967i	0.0815543	−	0.702388i
$687$	−2.72792			−0.104077
$688$	−1.82843	+	3.16693i	−0.0697081	+	0.120738i
$689$	−5.53553	−	9.58783i	−0.210887	−	0.365267i
$690$	−0.500000	−	0.866025i	−0.0190347	−	0.0329690i
$691$	24.7071	−	42.7940i	0.939903	−	1.62796i	0.174253	−	0.984701i	$-0.444249\pi$
$691$	24.7071	−	42.7940i	0.939903	−	1.62796i	0.765649	−	0.643258i	$-0.222418\pi$
$692$	−0.828427			−0.0314921
$693$	7.86396	−	1.07616i	0.298727	−	0.0408799i
$694$	30.6274			1.16260
$695$	8.65685	−	14.9941i	0.328373	−	0.568759i
$696$	4.62132	+	8.00436i	0.175171	+	0.303405i
$697$	−7.24264	−	12.5446i	−0.274335	−	0.475161i
$698$	11.0208	−	19.0886i	0.417144	−	0.722515i
$699$	−27.2132			−1.02930
$700$	−4.00000	+	9.79796i	−0.151186	+	0.370328i
$701$	17.4853			0.660410			0.330205	−	0.943909i	$-0.392882\pi$
$701$	17.4853			0.660410			0.330205	+	0.943909i	$0.392882\pi$
$702$	0.707107	−	1.22474i	0.0266880	−	0.0462250i
$703$	1.48528	+	2.57258i	0.0560184	+	0.0970268i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	6.65685	−	11.5300i	0.250712	−	0.434245i
$706$	2.72792			0.102667
$707$	20.2426	+	26.1039i	0.761303	+	0.981737i
$708$	−9.24264			−0.347360
$709$	4.70711	−	8.15295i	0.176779	−	0.306190i	−0.763996	−	0.645220i	$-0.776766\pi$
$709$	4.70711	−	8.15295i	0.176779	−	0.306190i	0.940776	+	0.339030i	$0.110099\pi$
$710$	−6.94975	−	12.0373i	−0.260819	−	0.451752i
$711$	−1.20711	−	2.09077i	−0.0452700	−	0.0784100i
$712$	5.36396	−	9.29065i	0.201023	−	0.348182i
$713$	6.65685			0.249301
$714$	2.29289	+	2.95680i	0.0858094	+	0.110655i
$715$	−4.24264			−0.158666
$716$	−8.00000	+	13.8564i	−0.298974	+	0.517838i
$717$	0.343146	+	0.594346i	0.0128150	+	0.0221963i
$718$	−1.00000	−	1.73205i	−0.0373197	−	0.0646396i
$719$	−14.0711	+	24.3718i	−0.524762	+	0.908915i	0.474822	+	0.880082i	$0.342512\pi$
$719$	−14.0711	+	24.3718i	−0.524762	+	0.908915i	−0.999584	+	0.0288331i	$0.990821\pi$
$720$	−1.00000			−0.0372678
$721$	−2.34315	+	5.73951i	−0.0872633	+	0.213751i
$722$	−18.6569			−0.694336
$723$	12.0355	−	20.8462i	0.447606	−	0.775277i
$724$	−2.24264	−	3.88437i	−0.0833471	−	0.144361i
$725$	−18.4853	−	32.0174i	−0.686526	−	1.18910i
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−36.5563			−1.35580			−0.677900	−	0.735154i	$-0.737110\pi$
$727$	−36.5563			−1.35580			−0.677900	+	0.735154i	$0.737110\pi$
$728$	3.70711	−	0.507306i	0.137395	−	0.0188020i
$729$	1.00000			0.0370370
$730$	−2.82843	+	4.89898i	−0.104685	+	0.181319i
$731$	−2.58579	−	4.47871i	−0.0956388	−	0.165651i
$732$	3.00000	+	5.19615i	0.110883	+	0.192055i
$733$	7.77817	−	13.4722i	0.287293	−	0.497607i	−0.685869	−	0.727725i	$-0.740578\pi$
$733$	7.77817	−	13.4722i	0.287293	−	0.497607i	0.973163	+	0.230118i	$0.0739112\pi$
$734$	24.6985			0.911638
$735$	−6.74264	+	1.88064i	−0.248706	+	0.0693684i
$736$	−1.00000			−0.0368605
$737$	−23.4853	+	40.6777i	−0.865091	+	1.49838i
$738$	−5.12132	−	8.87039i	−0.188518	−	0.326523i
$739$	−7.58579	−	13.1390i	−0.279048	−	0.483325i	0.692101	−	0.721801i	$-0.256685\pi$
$739$	−7.58579	−	13.1390i	−0.279048	−	0.483325i	−0.971148	+	0.238476i	$0.923352\pi$
$740$	2.53553	−	4.39167i	0.0932081	−	0.161441i
$741$	0.828427			0.0304330
$742$	20.5208	−	2.80821i	0.753343	−	0.103093i
$743$	2.24264			0.0822745			0.0411373	−	0.999154i	$-0.486902\pi$
$743$	2.24264			0.0822745			0.0411373	+	0.999154i	$0.486902\pi$
$744$	3.32843	−	5.76500i	0.122026	−	0.211355i
$745$	1.17157	+	2.02922i	0.0429231	+	0.0743450i
$746$	12.8284	+	22.2195i	0.469682	+	0.813513i
$747$	5.15685	−	8.93193i	0.188679	−	0.326802i
$748$	−4.24264			−0.155126
$749$	9.48528	−	23.2341i	0.346585	−	0.848956i
$750$	9.00000			0.328634
$751$	14.7635	−	25.5711i	0.538726	−	0.933101i	−0.460247	−	0.887791i	$-0.652239\pi$
$751$	14.7635	−	25.5711i	0.538726	−	0.933101i	0.998973	−	0.0453101i	$-0.0144276\pi$
$752$	−6.65685	−	11.5300i	−0.242750	−	0.420456i
$753$	−10.0858	−	17.4691i	−0.367546	−	0.636609i
$754$	−6.53553	+	11.3199i	−0.238010	+	0.412246i
$755$	12.6569			0.460630
$756$	1.62132	+	2.09077i	0.0589669	+	0.0760406i
$757$	24.9289			0.906057			0.453029	−	0.891496i	$-0.350343\pi$
$757$	24.9289			0.906057			0.453029	+	0.891496i	$0.350343\pi$
$758$	2.48528	−	4.30463i	0.0902695	−	0.156351i
$759$	−1.50000	−	2.59808i	−0.0544466	−	0.0943042i
$760$	−0.292893	−	0.507306i	−0.0106244	−	0.0184019i
$761$	−3.70711	+	6.42090i	−0.134383	+	0.232757i	−0.925361	−	0.379086i	$-0.876238\pi$
$761$	−3.70711	+	6.42090i	−0.134383	+	0.232757i	0.790979	+	0.611843i	$0.209572\pi$
$762$	−0.171573			−0.00621543
$763$	−28.0711	−	36.1990i	−1.01624	−	1.31049i
$764$	−1.41421			−0.0511645
$765$	0.707107	−	1.22474i	0.0255655	−	0.0442807i
$766$	13.3640	+	23.1471i	0.482860	+	0.836337i
$767$	−6.53553	−	11.3199i	−0.235984	−	0.408737i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	40.0122			1.44288			0.721438	−	0.692479i	$-0.243481\pi$
$769$	40.0122			1.44288			0.721438	+	0.692479i	$0.243481\pi$
$770$	3.00000	−	7.34847i	0.108112	−	0.264820i
$771$	1.41421			0.0509317
$772$	−12.8137	+	22.1940i	−0.461175	+	0.798779i
$773$	−8.58579	−	14.8710i	−0.308809	−	0.534873i	0.669293	−	0.742999i	$-0.266597\pi$
$773$	−8.58579	−	14.8710i	−0.308809	−	0.534873i	−0.978102	+	0.208125i	$0.933264\pi$
$774$	−1.82843	−	3.16693i	−0.0657215	−	0.113833i
$775$	−13.3137	+	23.0600i	−0.478243	+	0.828340i
$776$	−6.41421			−0.230257
$777$	−13.2929	+	1.81909i	−0.476880	+	0.0652595i
$778$	−6.82843			−0.244811
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$	−0.707107	−	1.22474i	−0.0253185	−	0.0438529i
$781$	−20.8492	−	36.1119i	−0.746045	−	1.29219i
$782$	0.707107	−	1.22474i	0.0252861	−	0.0437968i
$783$	−9.24264			−0.330305
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$	−15.8995			−0.567477
$786$	−3.62132	+	6.27231i	−0.129168	+	0.223726i
$787$	13.7279	+	23.7775i	0.489348	+	0.847575i	0.999925	−	0.0122570i	$-0.00390162\pi$
$787$	13.7279	+	23.7775i	0.489348	+	0.847575i	−0.510577	+	0.859832i	$0.670568\pi$
$788$	4.41421	+	7.64564i	0.157250	+	0.272365i
$789$	11.4853	−	19.8931i	0.408887	−	0.708213i
$790$	−2.41421			−0.0858939
$791$	38.2340	−	5.23221i	1.35945	−	0.186036i
$792$	−3.00000			−0.106600
$793$	−4.24264	+	7.34847i	−0.150661	+	0.260952i
$794$	−15.7782	−	27.3286i	−0.559946	−	0.969856i
$795$	−3.91421	−	6.77962i	−0.138823	−	0.240448i
$796$	8.65685	−	14.9941i	0.306834	−	0.531452i
$797$	29.9706			1.06161			0.530806	−	0.847493i	$-0.321889\pi$
$797$	29.9706			1.06161			0.530806	+	0.847493i	$0.321889\pi$
$798$	−0.585786	+	1.43488i	−0.0207366	+	0.0507941i
$799$	18.8284			0.666102
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	5.36396	+	9.29065i	0.189526	+	0.328269i
$802$	−8.24264	−	14.2767i	−0.291058	−	0.504127i
$803$	−8.48528	+	14.6969i	−0.299439	+	0.518644i
$804$	−15.6569			−0.552175
$805$	1.62132	+	2.09077i	0.0571440	+	0.0736900i
$806$	9.41421			0.331602
$807$	−2.20711	+	3.82282i	−0.0776938	+	0.134570i
$808$	−6.24264	−	10.8126i	−0.219615	−	0.380385i
$809$	7.26346	+	12.5807i	0.255370	+	0.442313i	0.964996	−	0.262265i	$-0.0844695\pi$
$809$	7.26346	+	12.5807i	0.255370	+	0.442313i	−0.709626	+	0.704578i	$0.751136\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	14.2843			0.501589			0.250794	−	0.968040i	$-0.419308\pi$
$811$	14.2843			0.501589			0.250794	+	0.968040i	$0.419308\pi$
$812$	−14.9853	−	19.3242i	−0.525880	−	0.678148i
$813$	−7.00000			−0.245501
$814$	7.60660	−	13.1750i	0.266611	−	0.461784i
$815$	0.707107	+	1.22474i	0.0247689	+	0.0429009i
$816$	−0.707107	−	1.22474i	−0.0247537	−	0.0428746i
$817$	1.07107	−	1.85514i	0.0374719	−	0.0649033i
$818$	−24.6569			−0.862107
$819$	−1.41421	+	3.46410i	−0.0494166	+	0.121046i
$820$	−10.2426			−0.357689
$821$	−11.6213	+	20.1287i	−0.405587	+	0.702497i	−0.994390	−	0.105780i	$-0.966266\pi$
$821$	−11.6213	+	20.1287i	−0.405587	+	0.702497i	0.588803	+	0.808277i	$0.299599\pi$
$822$	−7.48528	−	12.9649i	−0.261079	−	0.452202i
$823$	−0.686292	−	1.18869i	−0.0239226	−	0.0414352i	0.853816	−	0.520575i	$-0.174282\pi$
$823$	−0.686292	−	1.18869i	−0.0239226	−	0.0414352i	−0.877739	+	0.479139i	$0.840949\pi$
$824$	1.17157	−	2.02922i	0.0408137	−	0.0706914i
$825$	12.0000			0.417786
$826$	24.2279	−	3.31552i	0.842997	−	0.115362i
$827$	−18.7990			−0.653705			−0.326852	−	0.945075i	$-0.605988\pi$
$827$	−18.7990			−0.653705			−0.326852	+	0.945075i	$0.605988\pi$
$828$	0.500000	−	0.866025i	0.0173762	−	0.0300965i
$829$	22.2426	+	38.5254i	0.772519	+	1.33804i	0.936178	+	0.351525i	$0.114337\pi$
$829$	22.2426	+	38.5254i	0.772519	+	1.33804i	−0.163660	+	0.986517i	$0.552330\pi$
$830$	−5.15685	−	8.93193i	−0.178997	−	0.310032i
$831$	−1.41421	+	2.44949i	−0.0490585	+	0.0849719i
$832$	−1.41421			−0.0490290
$833$	−7.07107	−	6.92820i	−0.244998	−	0.240048i
$834$	17.3137			0.599525
$835$	0.757359	−	1.31178i	0.0262095	−	0.0453962i
$836$	−0.878680	−	1.52192i	−0.0303898	−	0.0526366i
$837$	3.32843	+	5.76500i	0.115047	+	0.199268i
$838$	3.00000	−	5.19615i	0.103633	−	0.179498i
$839$	41.6985			1.43959			0.719796	−	0.694186i	$-0.244235\pi$
$839$	41.6985			1.43959			0.719796	+	0.694186i	$0.244235\pi$
$840$	2.62132	−	0.358719i	0.0904441	−	0.0123770i
$841$	56.4264			1.94574
$842$	9.72792	−	16.8493i	0.335246	−	0.580664i
$843$	0.636039	+	1.10165i	0.0219063	+	0.0379429i
$844$	0.414214	+	0.717439i	0.0142578	+	0.0246953i
$845$	−5.50000	+	9.52628i	−0.189206	+	0.327714i
$846$	13.3137			0.457735
$847$	−2.00000	+	4.89898i	−0.0687208	+	0.168331i
$848$	−7.82843			−0.268829
$849$	−2.07107	+	3.58719i	−0.0710789	+	0.123112i
$850$	2.82843	+	4.89898i	0.0970143	+	0.168034i
$851$	2.53553	+	4.39167i	0.0869170	+	0.150545i
$852$	6.94975	−	12.0373i	0.238094	−	0.412392i
$853$	0.142136			0.00486663			0.00243332	−	0.999997i	$-0.499225\pi$
$853$	0.142136			0.00486663			0.00243332	+	0.999997i	$0.499225\pi$
$854$	−9.72792	−	12.5446i	−0.332883	−	0.429268i
$855$	0.585786			0.0200335
$856$	−4.74264	+	8.21449i	−0.162100	+	0.280766i
$857$	13.4350	+	23.2702i	0.458932	+	0.794893i	0.998905	−	0.0467891i	$-0.0148989\pi$
$857$	13.4350	+	23.2702i	0.458932	+	0.794893i	−0.539973	+	0.841682i	$0.681566\pi$
$858$	−2.12132	−	3.67423i	−0.0724207	−	0.125436i
$859$	−8.29289	+	14.3637i	−0.282950	+	0.490084i	−0.972110	−	0.234526i	$-0.924646\pi$
$859$	−8.29289	+	14.3637i	−0.282950	+	0.490084i	0.689160	+	0.724609i	$0.257980\pi$
$860$	−3.65685			−0.124698
$861$	16.6066	+	21.4150i	0.565951	+	0.729822i
$862$	17.6569			0.601395
$863$	7.43503	−	12.8778i	0.253091	−	0.438367i	−0.711284	−	0.702905i	$-0.751886\pi$
$863$	7.43503	−	12.8778i	0.253091	−	0.438367i	0.964375	+	0.264538i	$0.0852194\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−0.414214	−	0.717439i	−0.0140837	−	0.0243937i
$866$	−15.0000	+	25.9808i	−0.509721	+	0.882862i
$867$	−15.0000			−0.509427
$868$	−6.65685	+	16.3059i	−0.225948	+	0.553458i
$869$	−7.24264			−0.245690
$870$	−4.62132	+	8.00436i	−0.156677	+	0.271373i
$871$	−11.0711	−	19.1757i	−0.375129	−	0.649742i
$872$	8.65685	+	14.9941i	0.293158	+	0.507765i
$873$	3.20711	−	5.55487i	0.108544	−	0.188004i
$874$	0.585786			0.0198145
$875$	−23.5919	+	3.22848i	−0.797551	+	0.109142i
$876$	−5.65685			−0.191127
$877$	−9.05025	+	15.6755i	−0.305605	+	0.529324i	−0.977396	−	0.211417i	$-0.932192\pi$
$877$	−9.05025	+	15.6755i	−0.305605	+	0.529324i	0.671791	+	0.740741i	$0.265525\pi$
$878$	8.57107	+	14.8455i	0.289260	+	0.501012i
$879$	−11.8137	−	20.4619i	−0.398466	−	0.690164i
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−20.1421			−0.678606			−0.339303	−	0.940677i	$-0.610191\pi$
$881$	−20.1421			−0.678606			−0.339303	+	0.940677i	$0.610191\pi$
$882$	−5.00000	−	4.89898i	−0.168359	−	0.164957i
$883$	−5.69848			−0.191769			−0.0958846	−	0.995392i	$-0.530568\pi$
$883$	−5.69848			−0.191769			−0.0958846	+	0.995392i	$0.530568\pi$
$884$	1.00000	−	1.73205i	0.0336336	−	0.0582552i
$885$	−4.62132	−	8.00436i	−0.155344	−	0.269064i
$886$	−17.8640	−	30.9413i	−0.600152	−	1.03949i
$887$	17.1716	−	29.7420i	0.576565	−	0.998640i	−0.419305	−	0.907846i	$-0.637726\pi$
$887$	17.1716	−	29.7420i	0.576565	−	0.998640i	0.995870	−	0.0907943i	$-0.0289406\pi$
$888$	5.07107			0.170174
$889$	0.449747	−	0.0615465i	0.0150840	−	0.00206420i
$890$	10.7279			0.359601
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	7.91421	+	13.7078i	0.264987	+	0.458972i
$893$	3.89949	+	6.75412i	0.130492	+	0.226018i
$894$	−1.17157	+	2.02922i	−0.0391833	+	0.0678674i
$895$	−16.0000			−0.534821
$896$	1.00000	−	2.44949i	0.0334077	−	0.0818317i
$897$	1.41421			0.0472192
$898$	5.12132	−	8.87039i	0.170901	−	0.296009i
$899$	−30.7635	−	53.2839i	−1.02602	−	1.77712i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	5.53553	−	9.58783i	0.184415	−	0.319417i
$902$	−30.7279			−1.02313
$903$	5.92893	+	7.64564i	0.197303	+	0.254431i
$904$	−14.5858			−0.485116
$905$	2.24264	−	3.88437i	0.0745479	−	0.129121i
$906$	6.32843	+	10.9612i	0.210248	+	0.364160i
$907$	5.46447	+	9.46473i	0.181445	+	0.314271i	0.942373	−	0.334565i	$-0.108589\pi$
$907$	5.46447	+	9.46473i	0.181445	+	0.314271i	−0.760928	+	0.648836i	$0.775256\pi$
$908$	1.08579	−	1.88064i	0.0360331	−	0.0624111i
$909$	12.4853			0.414111
$910$	2.29289	+	2.95680i	0.0760087	+	0.0980168i
$911$	−15.6569			−0.518735			−0.259367	−	0.965779i	$-0.583514\pi$
$911$	−15.6569			−0.518735			−0.259367	+	0.965779i	$0.583514\pi$
$912$	0.292893	−	0.507306i	0.00969866	−	0.0167986i
$913$	−15.4706	−	26.7958i	−0.512001	−	0.886812i
$914$	11.1066	+	19.2372i	0.367374	+	0.636310i
$915$	−3.00000	+	5.19615i	−0.0991769	+	0.171780i
$916$	−2.72792			−0.0901331
$917$	7.24264	−	17.7408i	0.239173	−	0.585852i
$918$	1.41421			0.0466760
$919$	10.1421	−	17.5667i	0.334558	−	0.579472i	−0.648842	−	0.760923i	$-0.724746\pi$
$919$	10.1421	−	17.5667i	0.334558	−	0.579472i	0.983400	+	0.181452i	$0.0580796\pi$
$920$	−0.500000	−	0.866025i	−0.0164845	−	0.0285520i
$921$	−3.05025	−	5.28319i	−0.100509	−	0.174087i
$922$	1.48528	−	2.57258i	0.0489151	−	0.0847235i
$923$	19.6569			0.647013
$924$	7.86396	−	1.07616i	0.258705	−	0.0354030i
$925$	−20.2843			−0.666943
$926$	−12.8995	+	22.3426i	−0.423904	+	0.734223i
$927$	1.17157	+	2.02922i	0.0384795	+	0.0666485i
$928$	4.62132	+	8.00436i	0.151702	+	0.262756i
$929$	12.3640	−	21.4150i	0.405648	−	0.702604i	−0.588748	−	0.808316i	$-0.700379\pi$
$929$	12.3640	−	21.4150i	0.405648	−	0.702604i	0.994397	+	0.105713i	$0.0337124\pi$
$930$	6.65685			0.218287
$931$	1.02082	−	3.97141i	0.0334559	−	0.130158i
$932$	−27.2132			−0.891398
$933$	−0.292893	+	0.507306i	−0.00958889	+	0.0166085i
$934$	−11.5858	−	20.0672i	−0.379099	−	0.656618i
$935$	−2.12132	−	3.67423i	−0.0693746	−	0.120160i
$936$	0.707107	−	1.22474i	0.0231125	−	0.0400320i
$937$	−29.1838			−0.953392			−0.476696	−	0.879068i	$-0.658166\pi$
$937$	−29.1838			−0.953392			−0.476696	+	0.879068i	$0.658166\pi$
$938$	41.0416	−	5.61642i	1.34006	−	0.183383i
$939$	25.2426			0.823762
$940$	6.65685	−	11.5300i	0.217123	−	0.376067i
$941$	−9.25736	−	16.0342i	−0.301781	−	0.522701i	0.674758	−	0.738039i	$-0.264248\pi$
$941$	−9.25736	−	16.0342i	−0.301781	−	0.522701i	−0.976540	+	0.215338i	$0.930915\pi$
$942$	−7.94975	−	13.7694i	−0.259017	−	0.448630i
$943$	5.12132	−	8.87039i	0.166773	−	0.288860i
$944$	−9.24264			−0.300822
$945$	−1.00000	+	2.44949i	−0.0325300	+	0.0796819i
$946$	−10.9706			−0.356684
$947$	−25.1421	+	43.5475i	−0.817010	+	1.41510i	0.0908662	+	0.995863i	$0.471036\pi$
$947$	−25.1421	+	43.5475i	−0.817010	+	1.41510i	−0.907876	+	0.419239i	$0.862297\pi$
$948$	−1.20711	−	2.09077i	−0.0392050	−	0.0679051i
$949$	−4.00000	−	6.92820i	−0.129845	−	0.224899i
$950$	−1.17157	+	2.02922i	−0.0380108	+	0.0658367i
$951$	24.0711			0.780558
$952$	2.29289	+	2.95680i	0.0743131	+	0.0958303i
$953$	1.79899			0.0582750			0.0291375	−	0.999575i	$-0.490724\pi$
$953$	1.79899			0.0582750			0.0291375	+	0.999575i	$0.490724\pi$
$954$	3.91421	−	6.77962i	0.126727	−	0.219498i
$955$	−0.707107	−	1.22474i	−0.0228814	−	0.0396318i
$956$	0.343146	+	0.594346i	0.0110981	+	0.0192225i
$957$	−13.8640	+	24.0131i	−0.448158	+	0.776233i
$958$	−34.5269			−1.11551
$959$	24.2721	+	31.3000i	0.783786	+	1.01073i
$960$	−1.00000			−0.0322749
$961$	−6.65685	+	11.5300i	−0.214737	+	0.371936i
$962$	3.58579	+	6.21076i	0.115610	+	0.200243i
$963$	−4.74264	−	8.21449i	−0.152829	−	0.264708i
$964$	12.0355	−	20.8462i	0.387638	−	0.671409i
$965$	−25.6274			−0.824976
$966$	−1.00000	+	2.44949i	−0.0321745	+	0.0788110i
$967$	−2.02944			−0.0652623			−0.0326312	−	0.999467i	$-0.510389\pi$
$967$	−2.02944			−0.0652623			−0.0326312	+	0.999467i	$0.510389\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	0.414214	+	0.717439i	0.0133065	+	0.0230475i
$970$	−3.20711	−	5.55487i	−0.102974	−	0.178356i
$971$	14.9853	−	25.9553i	0.480901	−	0.832944i	−0.518859	−	0.854860i	$-0.673643\pi$
$971$	14.9853	−	25.9553i	0.480901	−	0.832944i	0.999760	+	0.0219155i	$0.00697647\pi$
$972$	1.00000			0.0320750
$973$	−45.3848	+	6.21076i	−1.45497	+	0.199108i
$974$	−12.5147			−0.400997
$975$	−2.82843	+	4.89898i	−0.0905822	+	0.156893i
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	−0.514719	−	0.891519i	−0.0164673	−	0.0285222i	0.857674	−	0.514193i	$-0.171909\pi$
$977$	−0.514719	−	0.891519i	−0.0164673	−	0.0285222i	−0.874142	+	0.485671i	$0.838575\pi$
$978$	−0.707107	+	1.22474i	−0.0226108	+	0.0391630i
$979$	32.1838			1.02860
$980$	−6.74264	+	1.88064i	−0.215386	+	0.0600748i
$981$	−17.3137			−0.552784
$982$	14.4497	−	25.0277i	0.461110	−	0.798666i
$983$	−4.70711	−	8.15295i	−0.150133	−	0.260039i	0.781143	−	0.624352i	$-0.214637\pi$
$983$	−4.70711	−	8.15295i	−0.150133	−	0.260039i	−0.931276	+	0.364314i	$0.881304\pi$
$984$	−5.12132	−	8.87039i	−0.163262	−	0.282778i
$985$	−4.41421	+	7.64564i	−0.140649	+	0.243610i
$986$	−13.0711			−0.416268
$987$	−34.8995	+	4.77589i	−1.11086	+	0.152018i
$988$	0.828427			0.0263558
$989$	1.82843	−	3.16693i	0.0581406	−	0.100702i
$990$	−1.50000	−	2.59808i	−0.0476731	−	0.0825723i
$991$	−18.8848	−	32.7094i	−0.599895	−	1.03905i	−0.992836	−	0.119485i	$-0.961876\pi$
$991$	−18.8848	−	32.7094i	−0.599895	−	1.03905i	0.392941	−	0.919564i	$-0.371458\pi$
$992$	3.32843	−	5.76500i	0.105678	−	0.183039i
$993$	6.10051			0.193594
$994$	−13.8995	+	34.0467i	−0.440865	+	1.07989i
$995$	17.3137			0.548881
$996$	5.15685	−	8.93193i	0.163401	−	0.283019i
$997$	−4.43503	−	7.68170i	−0.140459	−	0.243282i	0.787211	−	0.616684i	$-0.211524\pi$
$997$	−4.43503	−	7.68170i	−0.140459	−	0.243282i	−0.927669	+	0.373402i	$0.878191\pi$
$998$	−12.8995	−	22.3426i	−0.408326	−	0.707242i
$999$	−2.53553	+	4.39167i	−0.0802207	+	0.138946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.h.415.1	yes	4
7.2	even	3		6762.2.a.cc.1.1		2
7.4	even	3	inner	966.2.i.h.277.1	✓	4
7.5	odd	6		6762.2.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.h.277.1	✓	4	7.4	even	3	inner
966.2.i.h.415.1	yes	4	1.1	even	1	trivial
6762.2.a.ca.1.2		2	7.5	odd	6
6762.2.a.cc.1.1		2	7.2	even	3

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.41421 q^{13} +(1.00000 - 2.44949i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.292893 - 0.507306i) q^{19} -1.00000 q^{20} +(1.62132 + 2.09077i) q^{21} -3.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.707107 - 1.22474i) q^{26} +1.00000 q^{27} +(1.62132 + 2.09077i) q^{28} -9.24264 q^{29} +(0.500000 - 0.866025i) q^{30} +(3.32843 + 5.76500i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +1.41421 q^{34} +(-1.00000 + 2.44949i) q^{35} +1.00000 q^{36} +(-2.53553 + 4.39167i) q^{37} +(0.292893 + 0.507306i) q^{38} +(0.707107 + 1.22474i) q^{39} +(0.500000 - 0.866025i) q^{40} +10.2426 q^{41} +(-2.62132 + 0.358719i) q^{42} +3.65685 q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-6.65685 + 11.5300i) q^{47} +1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} -4.00000 q^{50} +(-0.707107 + 1.22474i) q^{51} +(0.707107 + 1.22474i) q^{52} +(3.91421 + 6.77962i) q^{53} +(-0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(-2.62132 + 0.358719i) q^{56} -0.585786 q^{57} +(4.62132 - 8.00436i) q^{58} +(4.62132 + 8.00436i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.00000 - 5.19615i) q^{61} -6.65685 q^{62} +(1.00000 - 2.44949i) q^{63} +1.00000 q^{64} +(-0.707107 + 1.22474i) q^{65} +(1.50000 + 2.59808i) q^{66} +(7.82843 + 13.5592i) q^{67} +(-0.707107 + 1.22474i) q^{68} -1.00000 q^{69} +(-1.62132 - 2.09077i) q^{70} -13.8995 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.82843 + 4.89898i) q^{73} +(-2.53553 - 4.39167i) q^{74} +(2.00000 - 3.46410i) q^{75} -0.585786 q^{76} +(-4.86396 - 6.27231i) q^{77} -1.41421 q^{78} +(-1.20711 + 2.09077i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.12132 + 8.87039i) q^{82} -10.3137 q^{83} +(1.00000 - 2.44949i) q^{84} -1.41421 q^{85} +(-1.82843 + 3.16693i) q^{86} +(4.62132 + 8.00436i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.36396 - 9.29065i) q^{89} -1.00000 q^{90} +(3.70711 - 0.507306i) q^{91} -1.00000 q^{92} +(3.32843 - 5.76500i) q^{93} +(-6.65685 - 11.5300i) q^{94} +(-0.292893 - 0.507306i) q^{95} +(-0.500000 + 0.866025i) q^{96} -6.41421 q^{97} +(-1.74264 + 6.77962i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{10} + 6 q^{11} - 2 q^{12} + 4 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} + 4 q^{19} - 4 q^{20} - 2 q^{21} - 12 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} - 2 q^{28} - 20 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{32} + 6 q^{33} - 4 q^{35} + 4 q^{36} + 4 q^{37} + 4 q^{38} + 2 q^{40} + 24 q^{41} - 2 q^{42} - 8 q^{43} + 6 q^{44} + 2 q^{45} + 2 q^{46} - 4 q^{47} + 4 q^{48} + 10 q^{49} - 16 q^{50} + 10 q^{53} - 2 q^{54} + 12 q^{55} - 2 q^{56} - 8 q^{57} + 10 q^{58} + 10 q^{59} + 2 q^{60} + 12 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 6 q^{66} + 20 q^{67} - 4 q^{69} + 2 q^{70} - 16 q^{71} - 2 q^{72} + 4 q^{74} + 8 q^{75} - 8 q^{76} + 6 q^{77} - 2 q^{79} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{86} + 10 q^{87} + 6 q^{88} - 4 q^{89} - 4 q^{90} + 12 q^{91} - 4 q^{92} + 2 q^{93} - 4 q^{94} - 4 q^{95} - 2 q^{96} - 20 q^{97} + 10 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^10 + 6 * q^11 - 2 * q^12 + 4 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 + 4 * q^19 - 4 * q^20 - 2 * q^21 - 12 * q^22 + 2 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^27 - 2 * q^28 - 20 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^32 + 6 * q^33 - 4 * q^35 + 4 * q^36 + 4 * q^37 + 4 * q^38 + 2 * q^40 + 24 * q^41 - 2 * q^42 - 8 * q^43 + 6 * q^44 + 2 * q^45 + 2 * q^46 - 4 * q^47 + 4 * q^48 + 10 * q^49 - 16 * q^50 + 10 * q^53 - 2 * q^54 + 12 * q^55 - 2 * q^56 - 8 * q^57 + 10 * q^58 + 10 * q^59 + 2 * q^60 + 12 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 6 * q^66 + 20 * q^67 - 4 * q^69 + 2 * q^70 - 16 * q^71 - 2 * q^72 + 4 * q^74 + 8 * q^75 - 8 * q^76 + 6 * q^77 - 2 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^86 + 10 * q^87 + 6 * q^88 - 4 * q^89 - 4 * q^90 + 12 * q^91 - 4 * q^92 + 2 * q^93 - 4 * q^94 - 4 * q^95 - 2 * q^96 - 20 * q^97 + 10 * q^98 - 12 * q^99

Introduction

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