LMFDB - Embedded newform 966.2.i.k.277.2

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29428272.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 $ x^6 - 6x^4 - 4x^3 - 42*x^2 + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$2.63435 - 0.245357i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.k.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.10469 - 2.40409i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.10469 - 2.40409i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.02966 + 3.51547i) q^{11} +(0.500000 + 0.866025i) q^{12} -6.26870 q^{13} +(1.52966 - 2.15874i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.92497 + 3.33415i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.60469 - 2.77940i) q^{19} +1.00000 q^{20} +(-2.63435 - 0.245357i) q^{21} -4.05932 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-3.13435 - 5.42885i) q^{26} -1.00000 q^{27} +(2.63435 + 0.245357i) q^{28} -1.26870 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-3.23904 + 5.61018i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.02966 + 3.51547i) q^{33} -3.84994 q^{34} +(-1.52966 + 2.15874i) q^{35} +1.00000 q^{36} +(5.45463 + 9.44770i) q^{37} +(1.60469 - 2.77940i) q^{38} +(-3.13435 + 5.42885i) q^{39} +(0.500000 + 0.866025i) q^{40} -4.79062 q^{41} +(-1.10469 - 2.40409i) q^{42} -8.11864 q^{43} +(-2.02966 - 3.51547i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-2.73904 - 4.74416i) q^{47} -1.00000 q^{48} +(-4.55932 + 5.31155i) q^{49} +4.00000 q^{50} +(1.92497 + 3.33415i) q^{51} +(3.13435 - 5.42885i) q^{52} +(4.55932 - 7.89697i) q^{53} +(-0.500000 - 0.866025i) q^{54} +4.05932 q^{55} +(1.10469 + 2.40409i) q^{56} -3.20938 q^{57} +(-0.634350 - 1.09873i) q^{58} +(3.42497 - 5.93222i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} -6.47808 q^{62} +(-1.52966 + 2.15874i) q^{63} +1.00000 q^{64} +(3.13435 + 5.42885i) q^{65} +(-2.02966 + 3.51547i) q^{66} +(6.73904 - 11.6724i) q^{67} +(-1.92497 - 3.33415i) q^{68} +1.00000 q^{69} +(-2.63435 - 0.245357i) q^{70} +12.3873 q^{71} +(0.500000 + 0.866025i) q^{72} +(-4.52966 + 7.84560i) q^{73} +(-5.45463 + 9.44770i) q^{74} +(-2.00000 - 3.46410i) q^{75} +3.20938 q^{76} +(10.6937 + 0.995981i) q^{77} -6.26870 q^{78} +(-4.69367 - 8.12968i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.39531 - 4.14880i) q^{82} +0.0593201 q^{83} +(1.52966 - 2.15874i) q^{84} +3.84994 q^{85} +(-4.05932 - 7.03095i) q^{86} +(-0.634350 + 1.09873i) q^{87} +(2.02966 - 3.51547i) q^{88} +(-5.45463 - 9.44770i) q^{89} -1.00000 q^{90} +(6.92497 + 15.0705i) q^{91} -1.00000 q^{92} +(3.23904 + 5.61018i) q^{93} +(2.73904 - 4.74416i) q^{94} +(-1.60469 + 2.77940i) q^{95} +(-0.500000 - 0.866025i) q^{96} -15.8061 q^{97} +(-6.87960 - 1.29271i) q^{98} +4.05932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{23} - 3 q^{24} + 12 q^{25} - 3 q^{26} - 6 q^{27} + 24 q^{29} - 3 q^{30} + 3 q^{32} - 6 q^{34} + 3 q^{35} + 6 q^{36} + 12 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 36 q^{41} - 3 q^{42} - 3 q^{45} - 3 q^{46} + 3 q^{47} - 6 q^{48} - 3 q^{49} + 24 q^{50} + 3 q^{51} + 3 q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 3 q^{60} - 30 q^{61} + 3 q^{63} + 6 q^{64} + 3 q^{65} + 21 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} + 3 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} + 12 q^{76} + 24 q^{77} - 6 q^{78} + 12 q^{79} - 3 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} - 3 q^{84} + 6 q^{85} + 12 q^{87} - 12 q^{89} - 6 q^{90} + 33 q^{91} - 6 q^{92} - 3 q^{94} - 6 q^{95} - 3 q^{96} - 12 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 - 3 * q^16 - 3 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^23 - 3 * q^24 + 12 * q^25 - 3 * q^26 - 6 * q^27 + 24 * q^29 - 3 * q^30 + 3 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 12 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 36 * q^41 - 3 * q^42 - 3 * q^45 - 3 * q^46 + 3 * q^47 - 6 * q^48 - 3 * q^49 + 24 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 3 * q^54 + 3 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 3 * q^60 - 30 * q^61 + 3 * q^63 + 6 * q^64 + 3 * q^65 + 21 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 + 3 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 + 12 * q^76 + 24 * q^77 - 6 * q^78 + 12 * q^79 - 3 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 - 3 * q^84 + 6 * q^85 + 12 * q^87 - 12 * q^89 - 6 * q^90 + 33 * q^91 - 6 * q^92 - 3 * q^94 - 6 * q^95 - 3 * q^96 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	1.00000			0.408248
$7$	−1.10469	−	2.40409i	−0.417534	−	0.908662i
$7$	−1.10469	−	2.40409i	−0.417534	−	0.908662i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.02966	+	3.51547i	−0.611966	+	1.05996i	0.378943	+	0.925420i	$0.376288\pi$
$11$	−2.02966	+	3.51547i	−0.611966	+	1.05996i	−0.990909	+	0.134535i	$0.957046\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−6.26870			−1.73862			−0.869312	−	0.494263i	$-0.835438\pi$
$13$	−6.26870			−1.73862			−0.869312	+	0.494263i	$0.835438\pi$
$14$	1.52966	−	2.15874i	0.408819	−	0.576946i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.92497	+	3.33415i	−0.466874	+	0.808649i	−0.999284	−	0.0378374i	$-0.987953\pi$
$17$	−1.92497	+	3.33415i	−0.466874	+	0.808649i	0.532410	+	0.846487i	$0.321286\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.60469	−	2.77940i	−0.368141	−	0.637639i	0.621134	−	0.783705i	$-0.286672\pi$
$19$	−1.60469	−	2.77940i	−0.368141	−	0.637639i	−0.989275	+	0.146065i	$0.953339\pi$
$20$	1.00000			0.223607
$21$	−2.63435	−	0.245357i	−0.574862	−	0.0535412i
$22$	−4.05932			−0.865450
$23$	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
$26$	−3.13435	−	5.42885i	−0.614697	−	1.06469i
$27$	−1.00000			−0.192450
$28$	2.63435	+	0.245357i	0.497845	+	0.0463680i
$29$	−1.26870			−0.235592			−0.117796	−	0.993038i	$-0.537583\pi$
$29$	−1.26870			−0.235592			−0.117796	+	0.993038i	$0.537583\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−3.23904	+	5.61018i	−0.581749	+	1.00762i	0.413523	+	0.910493i	$0.364298\pi$
$31$	−3.23904	+	5.61018i	−0.581749	+	1.00762i	−0.995272	+	0.0971249i	$0.969035\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.02966	+	3.51547i	0.353318	+	0.611966i
$34$	−3.84994			−0.660259
$35$	−1.52966	+	2.15874i	−0.258560	+	0.364893i
$36$	1.00000			0.166667
$37$	5.45463	+	9.44770i	0.896736	+	1.55319i	0.831642	+	0.555313i	$0.187401\pi$
$37$	5.45463	+	9.44770i	0.896736	+	1.55319i	0.0650940	+	0.997879i	$0.479265\pi$
$38$	1.60469	−	2.77940i	0.260315	−	0.450879i
$39$	−3.13435	+	5.42885i	−0.501898	+	0.869312i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−4.79062			−0.748169			−0.374085	−	0.927395i	$-0.622043\pi$
$41$	−4.79062			−0.748169			−0.374085	+	0.927395i	$0.622043\pi$
$42$	−1.10469	−	2.40409i	−0.170457	−	0.370960i
$43$	−8.11864			−1.23808			−0.619041	−	0.785359i	$-0.712478\pi$
$43$	−8.11864			−1.23808			−0.619041	+	0.785359i	$0.712478\pi$
$44$	−2.02966	−	3.51547i	−0.305983	−	0.529978i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−2.73904	−	4.74416i	−0.399530	−	0.692006i	0.594138	−	0.804363i	$-0.297493\pi$
$47$	−2.73904	−	4.74416i	−0.399530	−	0.692006i	−0.993668	+	0.112357i	$0.964160\pi$
$48$	−1.00000			−0.144338
$49$	−4.55932	+	5.31155i	−0.651331	+	0.758793i
$50$	4.00000			0.565685
$51$	1.92497	+	3.33415i	0.269550	+	0.466874i
$52$	3.13435	−	5.42885i	0.434656	−	0.752847i
$53$	4.55932	−	7.89697i	0.626271	−	1.08473i	−0.362023	−	0.932169i	$-0.617914\pi$
$53$	4.55932	−	7.89697i	0.626271	−	1.08473i	0.988294	−	0.152564i	$-0.0487529\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	4.05932			0.547359
$56$	1.10469	+	2.40409i	0.147620	+	0.321260i
$57$	−3.20938			−0.425093
$58$	−0.634350	−	1.09873i	−0.0832942	−	0.144270i
$59$	3.42497	−	5.93222i	0.445893	−	0.772310i	−0.552221	−	0.833698i	$-0.686219\pi$
$59$	3.42497	−	5.93222i	0.445893	−	0.772310i	0.998114	+	0.0613883i	$0.0195528\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−6.47808			−0.822717
$63$	−1.52966	+	2.15874i	−0.192719	+	0.271975i
$64$	1.00000			0.125000
$65$	3.13435	+	5.42885i	0.388768	+	0.673366i
$66$	−2.02966	+	3.51547i	−0.249834	+	0.432725i
$67$	6.73904	−	11.6724i	0.823305	−	1.42601i	−0.0799032	−	0.996803i	$-0.525461\pi$
$67$	6.73904	−	11.6724i	0.823305	−	1.42601i	0.903208	−	0.429203i	$-0.141206\pi$
$68$	−1.92497	−	3.33415i	−0.233437	−	0.404325i
$69$	1.00000			0.120386
$70$	−2.63435	−	0.245357i	−0.314865	−	0.0293257i
$71$	12.3873			1.47011			0.735053	−	0.678009i	$-0.237157\pi$
$71$	12.3873			1.47011			0.735053	+	0.678009i	$0.237157\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−4.52966	+	7.84560i	−0.530157	+	0.918258i	0.469224	+	0.883079i	$0.344534\pi$
$73$	−4.52966	+	7.84560i	−0.530157	+	0.918258i	−0.999381	+	0.0351792i	$0.988800\pi$
$74$	−5.45463	+	9.44770i	−0.634088	+	1.09827i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	3.20938			0.368141
$77$	10.6937	+	0.995981i	1.21866	+	0.113503i
$78$	−6.26870			−0.709791
$79$	−4.69367	−	8.12968i	−0.528079	−	0.914660i	−0.999464	−	0.0327324i	$-0.989579\pi$
$79$	−4.69367	−	8.12968i	−0.528079	−	0.914660i	0.471385	−	0.881928i	$-0.343754\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.39531	−	4.14880i	−0.264518	−	0.458158i
$83$	0.0593201			0.00651123			0.00325562	−	0.999995i	$-0.498964\pi$
$83$	0.0593201			0.00651123			0.00325562	+	0.999995i	$0.498964\pi$
$84$	1.52966	−	2.15874i	0.166900	−	0.235537i
$85$	3.84994			0.417585
$86$	−4.05932	−	7.03095i	−0.437728	−	0.758167i
$87$	−0.634350	+	1.09873i	−0.0680095	+	0.117796i
$88$	2.02966	−	3.51547i	0.216362	−	0.374751i
$89$	−5.45463	−	9.44770i	−0.578190	−	1.00145i	−0.995687	−	0.0927757i	$-0.970426\pi$
$89$	−5.45463	−	9.44770i	−0.578190	−	1.00145i	0.417497	−	0.908678i	$-0.362907\pi$
$90$	−1.00000			−0.105409
$91$	6.92497	+	15.0705i	0.725934	+	1.57982i
$92$	−1.00000			−0.104257
$93$	3.23904	+	5.61018i	0.335873	+	0.581749i
$94$	2.73904	−	4.74416i	0.282510	−	0.489322i
$95$	−1.60469	+	2.77940i	−0.164638	+	0.285161i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−15.8061			−1.60487			−0.802433	−	0.596742i	$-0.796462\pi$
$97$	−15.8061			−1.60487			−0.802433	+	0.596742i	$0.796462\pi$
$98$	−6.87960	−	1.29271i	−0.694945	−	0.130583i
$99$	4.05932			0.407977
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	7.05932	−	12.2271i	0.702429	−	1.21664i	−0.265183	−	0.964198i	$-0.585432\pi$
$101$	7.05932	−	12.2271i	0.702429	−	1.21664i	0.967612	−	0.252444i	$-0.0812343\pi$
$102$	−1.92497	+	3.33415i	−0.190600	+	0.330130i
$103$	−0.260960	−	0.451996i	−0.0257132	−	0.0445365i	0.852882	−	0.522103i	$-0.174852\pi$
$103$	−0.260960	−	0.451996i	−0.0257132	−	0.0445365i	−0.878596	+	0.477566i	$0.841519\pi$
$104$	6.26870			0.614697
$105$	1.10469	+	2.40409i	0.107807	+	0.234615i
$106$	9.11864			0.885681
$107$	7.02966	+	12.1757i	0.679583	+	1.17707i	0.975107	+	0.221737i	$0.0711725\pi$
$107$	7.02966	+	12.1757i	0.679583	+	1.17707i	−0.295524	+	0.955335i	$0.595494\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	6.05932	−	10.4951i	0.580378	−	1.00524i	−0.415057	−	0.909795i	$-0.636238\pi$
$109$	6.05932	−	10.4951i	0.580378	−	1.00524i	0.995434	−	0.0954480i	$-0.0304284\pi$
$110$	2.02966	+	3.51547i	0.193520	+	0.335187i
$111$	10.9093			1.03546
$112$	−1.52966	+	2.15874i	−0.144539	+	0.203981i
$113$	−5.43118			−0.510922			−0.255461	−	0.966819i	$-0.582227\pi$
$113$	−5.43118			−0.510922			−0.255461	+	0.966819i	$0.582227\pi$
$114$	−1.60469	−	2.77940i	−0.150293	−	0.260315i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	0.634350	−	1.09873i	0.0588979	−	0.102014i
$117$	3.13435	+	5.42885i	0.289771	+	0.501898i
$118$	6.84994			0.630588
$119$	10.1421	+	0.944608i	0.929724	+	0.0865921i
$120$	1.00000			0.0912871
$121$	−2.73904	−	4.74416i	−0.249004	−	0.431287i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$	−2.39531	+	4.14880i	−0.215978	+	0.374085i
$124$	−3.23904	−	5.61018i	−0.290874	−	0.503809i
$125$	−9.00000			−0.804984
$126$	−2.63435	−	0.245357i	−0.234687	−	0.0218581i
$127$	−16.0593			−1.42503			−0.712517	−	0.701655i	$-0.752445\pi$
$127$	−16.0593			−1.42503			−0.712517	+	0.701655i	$0.752445\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.05932	+	7.03095i	−0.357403	+	0.619041i
$130$	−3.13435	+	5.42885i	−0.274901	+	0.476142i
$131$	9.43271	+	16.3379i	0.824140	+	1.42745i	0.902575	+	0.430533i	$0.141674\pi$
$131$	9.43271	+	16.3379i	0.824140	+	1.42745i	−0.0784353	+	0.996919i	$0.524992\pi$
$132$	−4.05932			−0.353318
$133$	−4.90926	+	6.92820i	−0.425687	+	0.600751i
$134$	13.4781			1.16433
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	1.92497	−	3.33415i	0.165065	−	0.285901i
$137$	−7.79836	+	13.5072i	−0.666259	+	1.15399i	0.312683	+	0.949857i	$0.398772\pi$
$137$	−7.79836	+	13.5072i	−0.666259	+	1.15399i	−0.978942	+	0.204137i	$0.934561\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	6.83752			0.579951			0.289975	−	0.957034i	$-0.406353\pi$
$139$	6.83752			0.579951			0.289975	+	0.957034i	$0.406353\pi$
$140$	−1.10469	−	2.40409i	−0.0933633	−	0.203183i
$141$	−5.47808			−0.461338
$142$	6.19367	+	10.7278i	0.519761	+	0.900253i
$143$	12.7233	−	22.0375i	1.06398	−	1.84286i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.634350	+	1.09873i	0.0526799	+	0.0912443i
$146$	−9.05932			−0.749755
$147$	2.32028	+	6.60426i	0.191373	+	0.544710i
$148$	−10.9093			−0.896736
$149$	−1.58898	−	2.75219i	−0.130174	−	0.225469i	0.793569	−	0.608480i	$-0.208220\pi$
$149$	−1.58898	−	2.75219i	−0.130174	−	0.225469i	−0.923744	+	0.383011i	$0.874887\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−5.02966	+	8.71163i	−0.409308	+	0.708942i	−0.994812	−	0.101727i	$-0.967563\pi$
$151$	−5.02966	+	8.71163i	−0.409308	+	0.708942i	0.585504	+	0.810669i	$0.300896\pi$
$152$	1.60469	+	2.77940i	0.130158	+	0.225439i
$153$	3.84994			0.311249
$154$	4.48429	+	9.75898i	0.361354	+	0.786401i
$155$	6.47808			0.520332
$156$	−3.13435	−	5.42885i	−0.250949	−	0.434656i
$157$	−1.03587	+	1.79418i	−0.0826714	+	0.143191i	−0.904397	−	0.426693i	$-0.859679\pi$
$157$	−1.03587	+	1.79418i	−0.0826714	+	0.143191i	0.821725	+	0.569884i	$0.193012\pi$
$158$	4.69367	−	8.12968i	0.373408	−	0.646762i
$159$	−4.55932	−	7.89697i	−0.361578	−	0.626271i
$160$	−1.00000			−0.0790569
$161$	1.52966	−	2.15874i	0.120554	−	0.170132i
$162$	−1.00000			−0.0785674
$163$	−2.03587	−	3.52623i	−0.159462	−	0.276196i	0.775213	−	0.631700i	$-0.217643\pi$
$163$	−2.03587	−	3.52623i	−0.159462	−	0.276196i	−0.934675	+	0.355504i	$0.884309\pi$
$164$	2.39531	−	4.14880i	0.187042	−	0.323967i
$165$	2.02966	−	3.51547i	0.158009	−	0.273679i
$166$	0.0296601	+	0.0513728i	0.00230207	+	0.00398730i
$167$	18.0155			1.39408			0.697040	−	0.717032i	$-0.254500\pi$
$167$	18.0155			1.39408			0.697040	+	0.717032i	$0.254500\pi$
$168$	2.63435	+	0.245357i	0.203245	+	0.0189297i
$169$	26.2966			2.02282
$170$	1.92497	+	3.33415i	0.147638	+	0.255717i
$171$	−1.60469	+	2.77940i	−0.122714	+	0.212546i
$172$	4.05932	−	7.03095i	0.309520	−	0.536105i
$173$	7.26870	+	12.5898i	0.552629	+	0.957182i	0.998084	+	0.0618771i	$0.0197087\pi$
$173$	7.26870	+	12.5898i	0.552629	+	0.957182i	−0.445455	+	0.895304i	$0.646958\pi$
$174$	−1.26870			−0.0961799
$175$	−10.5374	−	0.981426i	−0.796553	−	0.0741889i
$176$	4.05932			0.305983
$177$	−3.42497	−	5.93222i	−0.257437	−	0.445893i
$178$	5.45463	−	9.44770i	0.408842	−	0.708135i
$179$	6.37960	−	11.0498i	0.476834	−	0.825900i	−0.522814	−	0.852447i	$-0.675118\pi$
$179$	6.37960	−	11.0498i	0.476834	−	0.825900i	0.999648	+	0.0265467i	$0.00845105\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−12.5374			−0.931898			−0.465949	−	0.884812i	$-0.654287\pi$
$181$	−12.5374			−0.931898			−0.465949	+	0.884812i	$0.654287\pi$
$182$	−9.58898	+	13.5325i	−0.710783	+	1.00309i
$183$	−10.0000			−0.739221
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	5.45463	−	9.44770i	0.401032	−	0.694608i
$186$	−3.23904	+	5.61018i	−0.237498	+	0.411358i
$187$	−7.81407	−	13.5344i	−0.571421	−	0.989731i
$188$	5.47808			0.399530
$189$	1.10469	+	2.40409i	0.0803544	+	0.174872i
$190$	−3.20938			−0.232833
$191$	−2.03587	−	3.52623i	−0.147310	−	0.255149i	0.782922	−	0.622120i	$-0.213728\pi$
$191$	−2.03587	−	3.52623i	−0.147310	−	0.255149i	−0.930233	+	0.366971i	$0.880395\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−11.8873	+	20.5895i	−0.855669	+	1.48206i	0.0203531	+	0.999793i	$0.493521\pi$
$193$	−11.8873	+	20.5895i	−0.855669	+	1.48206i	−0.876023	+	0.482270i	$0.839812\pi$
$194$	−7.90305	−	13.6885i	−0.567406	−	0.982776i
$195$	6.26870			0.448911
$196$	−2.32028	−	6.60426i	−0.165734	−	0.471733i
$197$	0.418760			0.0298354			0.0149177	−	0.999889i	$-0.495251\pi$
$197$	0.418760			0.0298354			0.0149177	+	0.999889i	$0.495251\pi$
$198$	2.02966	+	3.51547i	0.144242	+	0.249834i
$199$	2.84994	−	4.93624i	0.202027	−	0.349921i	−0.747154	−	0.664650i	$-0.768580\pi$
$199$	2.84994	−	4.93624i	0.202027	−	0.349921i	0.949181	+	0.314730i	$0.101914\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$	−6.73904	−	11.6724i	−0.475335	−	0.823305i
$202$	14.1186			0.993384
$203$	1.40152	+	3.05007i	0.0983674	+	0.214073i
$204$	−3.84994			−0.269550
$205$	2.39531	+	4.14880i	0.167296	+	0.289765i
$206$	0.260960	−	0.451996i	0.0181819	−	0.0314921i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	3.13435	+	5.42885i	0.217328	+	0.376423i
$209$	13.0279			0.901159
$210$	−1.52966	+	2.15874i	−0.105557	+	0.148967i
$211$	−4.41876			−0.304200			−0.152100	−	0.988365i	$-0.548604\pi$
$211$	−4.41876			−0.304200			−0.152100	+	0.988365i	$0.548604\pi$
$212$	4.55932	+	7.89697i	0.313135	+	0.542366i
$213$	6.19367	−	10.7278i	0.424383	−	0.735053i
$214$	−7.02966	+	12.1757i	−0.480538	+	0.832316i
$215$	4.05932	+	7.03095i	0.276843	+	0.479507i
$216$	1.00000			0.0680414
$217$	17.0655	+	1.58944i	1.15848	+	0.107898i
$218$	12.1186			0.820778
$219$	4.52966	+	7.84560i	0.306086	+	0.530157i
$220$	−2.02966	+	3.51547i	−0.136840	+	0.237013i
$221$	12.0671	−	20.9008i	0.811718	−	1.40594i
$222$	5.45463	+	9.44770i	0.366091	+	0.634088i
$223$	11.7592			0.787454			0.393727	−	0.919227i	$-0.371185\pi$
$223$	11.7592			0.787454			0.393727	+	0.919227i	$0.371185\pi$
$224$	−2.63435	−	0.245357i	−0.176015	−	0.0163936i
$225$	−4.00000			−0.266667
$226$	−2.71559	−	4.70354i	−0.180638	−	0.312875i
$227$	−6.87960	+	11.9158i	−0.456615	+	0.790881i	−0.998779	−	0.0493919i	$-0.984272\pi$
$227$	−6.87960	+	11.9158i	−0.456615	+	0.790881i	0.542164	+	0.840272i	$0.317605\pi$
$228$	1.60469	−	2.77940i	0.106273	−	0.184071i
$229$	−10.8141	−	18.7305i	−0.714614	−	1.23775i	−0.963108	−	0.269114i	$-0.913269\pi$
$229$	−10.8141	−	18.7305i	−0.714614	−	1.23775i	0.248494	−	0.968633i	$-0.420064\pi$
$230$	1.00000			0.0659380
$231$	6.20938	−	8.76300i	0.408547	−	0.576563i
$232$	1.26870			0.0832942
$233$	13.3046	+	23.0442i	0.871611	+	1.50968i	0.860329	+	0.509739i	$0.170258\pi$
$233$	13.3046	+	23.0442i	0.871611	+	1.50968i	0.0112822	+	0.999936i	$0.496409\pi$
$234$	−3.13435	+	5.42885i	−0.204899	+	0.354895i
$235$	−2.73904	+	4.74416i	−0.178675	+	0.309475i
$236$	3.42497	+	5.93222i	0.222947	+	0.386155i
$237$	−9.38734			−0.609773
$238$	4.25299	+	9.25561i	0.275680	+	0.599952i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−14.1124	+	24.4434i	−0.909062	+	1.57454i	−0.0936910	+	0.995601i	$0.529867\pi$
$241$	−14.1124	+	24.4434i	−0.909062	+	1.57454i	−0.815371	+	0.578939i	$0.803467\pi$
$242$	2.73904	−	4.74416i	0.176072	−	0.304966i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	10.0000			0.640184
$245$	6.87960	+	1.29271i	0.439522	+	0.0825882i
$246$	−4.79062			−0.305439
$247$	10.0593	+	17.4233i	0.640059	+	1.10862i
$248$	3.23904	−	5.61018i	0.205679	−	0.356247i
$249$	0.0296601	−	0.0513728i	0.00187963	−	0.00325562i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−8.29660			−0.523677			−0.261838	−	0.965112i	$-0.584329\pi$
$251$	−8.29660			−0.523677			−0.261838	+	0.965112i	$0.584329\pi$
$252$	−1.10469	−	2.40409i	−0.0695889	−	0.151444i
$253$	−4.05932			−0.255207
$254$	−8.02966	−	13.9078i	−0.503826	−	0.872652i
$255$	1.92497	−	3.33415i	0.120546	−	0.208792i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.51395	−	16.4786i	−0.593464	−	1.02791i	−0.993762	−	0.111525i	$-0.964427\pi$
$257$	−9.51395	−	16.4786i	−0.593464	−	1.02791i	0.400298	−	0.916385i	$-0.368907\pi$
$258$	−8.11864			−0.505444
$259$	16.6875	−	23.5502i	1.03691	−	1.46334i
$260$	−6.26870			−0.388768
$261$	0.634350	+	1.09873i	0.0392653	+	0.0680095i
$262$	−9.43271	+	16.3379i	−0.582755	+	1.00936i
$263$	−0.0593201	+	0.102746i	−0.00365784	+	0.00633556i	−0.867849	−	0.496829i	$-0.834498\pi$
$263$	−0.0593201	+	0.102746i	−0.00365784	+	0.00633556i	0.864191	+	0.503164i	$0.167831\pi$
$264$	−2.02966	−	3.51547i	−0.124917	−	0.216362i
$265$	−9.11864			−0.560154
$266$	−8.45463	−	0.787443i	−0.518387	−	0.0482812i
$267$	−10.9093			−0.667636
$268$	6.73904	+	11.6724i	0.411652	+	0.713003i
$269$	−1.48429	+	2.57087i	−0.0904988	+	0.156748i	−0.907721	−	0.419574i	$-0.862179\pi$
$269$	−1.48429	+	2.57087i	−0.0904988	+	0.156748i	0.817222	+	0.576323i	$0.195513\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	6.44842	+	11.1690i	0.391714	+	0.678468i	0.992676	−	0.120810i	$-0.0385491\pi$
$271$	6.44842	+	11.1690i	0.391714	+	0.678468i	−0.600962	+	0.799278i	$0.705216\pi$
$272$	3.84994			0.233437
$273$	16.5140	+	1.53807i	0.999470	+	0.0930880i
$274$	−15.5967			−0.942232
$275$	8.11864	+	14.0619i	0.489572	+	0.847964i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	−5.58898	+	9.68040i	−0.335809	+	0.581639i	−0.983640	−	0.180146i	$-0.942343\pi$
$277$	−5.58898	+	9.68040i	−0.335809	+	0.581639i	0.647831	+	0.761784i	$0.275676\pi$
$278$	3.41876	+	5.92147i	0.205044	+	0.355146i
$279$	6.47808			0.387833
$280$	1.52966	−	2.15874i	0.0914147	−	0.129009i
$281$	−31.4621			−1.87687			−0.938437	−	0.345450i	$-0.887726\pi$
$281$	−31.4621			−1.87687			−0.938437	+	0.345450i	$0.887726\pi$
$282$	−2.73904	−	4.74416i	−0.163107	−	0.282510i
$283$	5.00774	−	8.67366i	0.297679	−	0.515596i	−0.677925	−	0.735131i	$-0.737121\pi$
$283$	5.00774	−	8.67366i	0.297679	−	0.515596i	0.975605	+	0.219535i	$0.0704541\pi$
$284$	−6.19367	+	10.7278i	−0.367527	+	0.636575i
$285$	1.60469	+	2.77940i	0.0950536	+	0.164638i
$286$	25.4467			1.50469
$287$	5.29215	+	11.5171i	0.312386	+	0.679833i
$288$	−1.00000			−0.0589256
$289$	1.08898	+	1.88617i	0.0640577	+	0.110951i
$290$	−0.634350	+	1.09873i	−0.0372503	+	0.0645194i
$291$	−7.90305	+	13.6885i	−0.463285	+	0.802433i
$292$	−4.52966	−	7.84560i	−0.265078	−	0.459129i
$293$	3.83752			0.224190			0.112095	−	0.993697i	$-0.464244\pi$
$293$	3.83752			0.224190			0.112095	+	0.993697i	$0.464244\pi$
$294$	−4.55932	+	5.31155i	−0.265905	+	0.309776i
$295$	−6.84994			−0.398819
$296$	−5.45463	−	9.44770i	−0.317044	−	0.549136i
$297$	2.02966	−	3.51547i	0.117773	−	0.203989i
$298$	1.58898	−	2.75219i	0.0920472	−	0.159430i
$299$	−3.13435	−	5.42885i	−0.181264	−	0.313959i
$300$	4.00000			0.230940
$301$	8.96858	+	19.5180i	0.516940	+	1.12500i
$302$	−10.0593			−0.578849
$303$	−7.05932	−	12.2271i	−0.405547	−	0.702429i
$304$	−1.60469	+	2.77940i	−0.0920353	+	0.159410i
$305$	−5.00000	+	8.66025i	−0.286299	+	0.495885i
$306$	1.92497	+	3.33415i	0.110043	+	0.190600i
$307$	13.9841			0.798112			0.399056	−	0.916926i	$-0.369338\pi$
$307$	13.9841			0.798112			0.399056	+	0.916926i	$0.369338\pi$
$308$	−6.20938	+	8.76300i	−0.353812	+	0.499318i
$309$	−0.521920			−0.0296910
$310$	3.23904	+	5.61018i	0.183965	+	0.318637i
$311$	13.1937	−	22.8521i	0.748144	−	1.29582i	−0.200567	−	0.979680i	$-0.564278\pi$
$311$	13.1937	−	22.8521i	0.748144	−	1.29582i	0.948711	−	0.316144i	$-0.102388\pi$
$312$	3.13435	−	5.42885i	0.177448	−	0.307348i
$313$	−4.57503	−	7.92418i	−0.258596	−	0.447901i	0.707270	−	0.706943i	$-0.249926\pi$
$313$	−4.57503	−	7.92418i	−0.258596	−	0.447901i	−0.965866	+	0.259042i	$0.916593\pi$
$314$	−2.07174			−0.116915
$315$	2.63435	+	0.245357i	0.148429	+	0.0138243i
$316$	9.38734			0.528079
$317$	−10.1124	−	17.5152i	−0.567971	−	0.983754i	−0.996767	−	0.0803526i	$-0.974395\pi$
$317$	−10.1124	−	17.5152i	−0.567971	−	0.983754i	0.428796	−	0.903401i	$-0.358938\pi$
$318$	4.55932	−	7.89697i	0.255674	−	0.442840i
$319$	2.57503	−	4.46008i	0.144174	−	0.249717i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	14.0593			0.784715
$322$	2.63435	+	0.245357i	0.146807	+	0.0136732i
$323$	12.3559			0.687502
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−12.5374	+	21.7154i	−0.695450	+	1.20455i
$326$	2.03587	−	3.52623i	0.112756	−	0.195300i
$327$	−6.05932	−	10.4951i	−0.335081	−	0.580378i
$328$	4.79062			0.264518
$329$	−8.37960	+	11.8257i	−0.461982	+	0.651973i
$330$	4.05932			0.223458
$331$	10.3046	+	17.8480i	0.566390	+	0.981017i	0.996919	+	0.0784400i	$0.0249939\pi$
$331$	10.3046	+	17.8480i	0.566390	+	0.981017i	−0.430528	+	0.902577i	$0.641673\pi$
$332$	−0.0296601	+	0.0513728i	−0.00162781	+	0.00281945i
$333$	5.45463	−	9.44770i	0.298912	−	0.517731i
$334$	9.00774	+	15.6019i	0.492882	+	0.853696i
$335$	−13.4781			−0.736386
$336$	1.10469	+	2.40409i	0.0602658	+	0.131154i
$337$	−26.2249			−1.42856			−0.714280	−	0.699860i	$-0.753245\pi$
$337$	−26.2249			−1.42856			−0.714280	+	0.699860i	$0.753245\pi$
$338$	13.1483	+	22.7735i	0.715173	+	1.23872i
$339$	−2.71559	+	4.70354i	−0.147491	+	0.255461i
$340$	−1.92497	+	3.33415i	−0.104396	+	0.180819i
$341$	−13.1483	−	22.7735i	−0.712020	−	1.23326i
$342$	−3.20938			−0.173543
$343$	17.8061	+	5.09341i	0.961439	+	0.275018i
$344$	8.11864			0.437728
$345$	−0.500000	−	0.866025i	−0.0269191	−	0.0466252i
$346$	−7.26870	+	12.5898i	−0.390768	+	0.676830i
$347$	−12.7984	+	22.1674i	−0.687052	+	1.19001i	0.285735	+	0.958309i	$0.407762\pi$
$347$	−12.7984	+	22.1674i	−0.687052	+	1.19001i	−0.972787	+	0.231700i	$0.925571\pi$
$348$	−0.634350	−	1.09873i	−0.0340047	−	0.0588979i
$349$	1.61266			0.0863237			0.0431618	−	0.999068i	$-0.486257\pi$
$349$	1.61266			0.0863237			0.0431618	+	0.999068i	$0.486257\pi$
$350$	−4.41876	−	9.61637i	−0.236193	−	0.514017i
$351$	6.26870			0.334598
$352$	2.02966	+	3.51547i	0.108181	+	0.187375i
$353$	13.3046	−	23.0442i	0.708131	−	1.22652i	−0.257419	−	0.966300i	$-0.582872\pi$
$353$	13.3046	−	23.0442i	0.708131	−	1.22652i	0.965550	−	0.260219i	$-0.0837947\pi$
$354$	3.42497	−	5.93222i	0.182035	−	0.315294i
$355$	−6.19367	−	10.7278i	−0.328726	−	0.569370i
$356$	10.9093			0.578190
$357$	5.88910	−	8.31100i	0.311684	−	0.439865i
$358$	12.7592			0.674345
$359$	9.41876	+	16.3138i	0.497103	+	0.861008i	0.999994	−	0.00334179i	$-0.00106373\pi$
$359$	9.41876	+	16.3138i	0.497103	+	0.861008i	−0.502891	+	0.864350i	$0.667730\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	4.34994	−	7.53432i	0.228944	−	0.396543i
$362$	−6.26870	−	10.8577i	−0.329476	−	0.570668i
$363$	−5.47808			−0.287525
$364$	−16.5140	−	1.53807i	−0.865566	−	0.0806166i
$365$	9.05932			0.474186
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−0.373390	+	0.646731i	−0.0194908	+	0.0337591i	−0.875606	−	0.483025i	$-0.839538\pi$
$367$	−0.373390	+	0.646731i	−0.0194908	+	0.0337591i	0.856115	+	0.516785i	$0.172871\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	2.39531	+	4.14880i	0.124695	+	0.215978i
$370$	10.9093			0.567145
$371$	−24.0217	−	2.23732i	−1.24714	−	0.116156i
$372$	−6.47808			−0.335873
$373$	−9.47808	−	16.4165i	−0.490756	−	0.850015i	0.509187	−	0.860656i	$-0.329946\pi$
$373$	−9.47808	−	16.4165i	−0.490756	−	0.850015i	−0.999943	+	0.0106409i	$0.996613\pi$
$374$	7.81407	−	13.5344i	0.404056	−	0.699845i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	2.73904	+	4.74416i	0.141255	+	0.244661i
$377$	7.95310			0.409606
$378$	−1.52966	+	2.15874i	−0.0786772	+	0.111033i
$379$	11.7154			0.601778			0.300889	−	0.953659i	$-0.402717\pi$
$379$	11.7154			0.601778			0.300889	+	0.953659i	$0.402717\pi$
$380$	−1.60469	−	2.77940i	−0.0823189	−	0.142580i
$381$	−8.02966	+	13.9078i	−0.411372	+	0.712517i
$382$	2.03587	−	3.52623i	0.104164	−	0.180418i
$383$	13.0828	+	22.6600i	0.668498	+	1.15787i	0.978324	+	0.207080i	$0.0663959\pi$
$383$	13.0828	+	22.6600i	0.668498	+	1.15787i	−0.309826	+	0.950793i	$0.600271\pi$
$384$	1.00000			0.0510310
$385$	−4.48429	−	9.75898i	−0.228541	−	0.497364i
$386$	−23.7747			−1.21010
$387$	4.05932	+	7.03095i	0.206347	+	0.357403i
$388$	7.90305	−	13.6885i	0.401217	−	0.694928i
$389$	13.8968	−	24.0700i	0.704598	−	1.22040i	−0.262239	−	0.965003i	$-0.584461\pi$
$389$	13.8968	−	24.0700i	0.704598	−	1.22040i	0.966837	−	0.255396i	$-0.0822059\pi$
$390$	3.13435	+	5.42885i	0.158714	+	0.274901i
$391$	−3.84994			−0.194700
$392$	4.55932	−	5.31155i	0.230280	−	0.268274i
$393$	18.8654			0.951635
$394$	0.209380	+	0.362657i	0.0105484	+	0.0182704i
$395$	−4.69367	+	8.12968i	−0.236164	+	0.409048i
$396$	−2.02966	+	3.51547i	−0.101994	+	0.176659i
$397$	−1.92497	−	3.33415i	−0.0966115	−	0.167336i	0.813669	−	0.581329i	$-0.197467\pi$
$397$	−1.92497	−	3.33415i	−0.0966115	−	0.167336i	−0.910280	+	0.413993i	$0.864134\pi$
$398$	5.69988			0.285709
$399$	3.54537	+	7.71565i	0.177490	+	0.386265i
$400$	−4.00000			−0.200000
$401$	−3.58898	−	6.21630i	−0.179225	−	0.310427i	0.762390	−	0.647118i	$-0.224026\pi$
$401$	−3.58898	−	6.21630i	−0.179225	−	0.310427i	−0.941615	+	0.336691i	$0.890692\pi$
$402$	6.73904	−	11.6724i	0.336113	−	0.582164i
$403$	20.3046	−	35.1685i	1.01144	−	1.75187i
$404$	7.05932	+	12.2271i	0.351214	+	0.608321i
$405$	1.00000			0.0496904
$406$	−1.94068	+	2.73879i	−0.0963143	+	0.135924i
$407$	−44.2842			−2.19509
$408$	−1.92497	−	3.33415i	−0.0953002	−	0.165065i
$409$	8.18746	−	14.1811i	0.404844	−	0.701210i	−0.589459	−	0.807798i	$-0.700659\pi$
$409$	8.18746	−	14.1811i	0.404844	−	0.701210i	0.994303	+	0.106588i	$0.0339925\pi$
$410$	−2.39531	+	4.14880i	−0.118296	+	0.204895i
$411$	7.79836	+	13.5072i	0.384665	+	0.666259i
$412$	0.521920			0.0257132
$413$	−18.0451	−	1.68068i	−0.887943	−	0.0827008i
$414$	1.00000			0.0491473
$415$	−0.0296601	−	0.0513728i	−0.00145596	−	0.00252179i
$416$	−3.13435	+	5.42885i	−0.153674	+	0.266171i
$417$	3.41876	−	5.92147i	0.167417	−	0.289975i
$418$	6.51395	+	11.2825i	0.318608	+	0.551845i
$419$	−25.9372			−1.26711			−0.633557	−	0.773696i	$-0.718406\pi$
$419$	−25.9372			−1.26711			−0.633557	+	0.773696i	$0.718406\pi$
$420$	−2.63435	−	0.245357i	−0.128543	−	0.0119722i
$421$	3.13764			0.152919			0.0764596	−	0.997073i	$-0.475638\pi$
$421$	3.13764			0.152919			0.0764596	+	0.997073i	$0.475638\pi$
$422$	−2.20938	−	3.82676i	−0.107551	−	0.186284i
$423$	−2.73904	+	4.74416i	−0.133177	+	0.230669i
$424$	−4.55932	+	7.89697i	−0.221420	+	0.383511i
$425$	7.69988	+	13.3366i	0.373499	+	0.646919i
$426$	12.3873			0.600169
$427$	−15.2966	+	21.5874i	−0.740254	+	1.04469i
$428$	−14.0593			−0.679583
$429$	−12.7233	−	22.0375i	−0.614288	−	1.06398i
$430$	−4.05932	+	7.03095i	−0.195758	+	0.339062i
$431$	8.53740	−	14.7872i	0.411232	−	0.712275i	−0.583793	−	0.811903i	$-0.698432\pi$
$431$	8.53740	−	14.7872i	0.411232	−	0.712275i	0.995025	+	0.0996279i	$0.0317652\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−34.4746			−1.65674			−0.828371	−	0.560180i	$-0.810732\pi$
$433$	−34.4746			−1.65674			−0.828371	+	0.560180i	$0.810732\pi$
$434$	7.15627	+	15.5739i	0.343512	+	0.747571i
$435$	1.26870			0.0608295
$436$	6.05932	+	10.4951i	0.290189	+	0.502622i
$437$	1.60469	−	2.77940i	0.0767627	−	0.132957i
$438$	−4.52966	+	7.84560i	−0.216436	+	0.374877i
$439$	−1.29836	−	2.24883i	−0.0619673	−	0.107331i	0.833377	−	0.552704i	$-0.186404\pi$
$439$	−1.29836	−	2.24883i	−0.0619673	−	0.107331i	−0.895345	+	0.445374i	$0.853071\pi$
$440$	−4.05932			−0.193520
$441$	6.87960	+	1.29271i	0.327600	+	0.0615576i
$442$	24.1341			1.14794
$443$	−2.01395	−	3.48826i	−0.0956857	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$443$	−2.01395	−	3.48826i	−0.0956857	−	0.165732i	−0.909895	+	0.414840i	$0.863838\pi$
$444$	−5.45463	+	9.44770i	−0.258865	+	0.448368i
$445$	−5.45463	+	9.44770i	−0.258574	+	0.447864i
$446$	5.87960	+	10.1838i	0.278407	+	0.482215i
$447$	−3.17796			−0.150312
$448$	−1.10469	−	2.40409i	−0.0521917	−	0.113583i
$449$	−22.1655			−1.04606			−0.523028	−	0.852315i	$-0.675198\pi$
$449$	−22.1655			−1.04606			−0.523028	+	0.852315i	$0.675198\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	9.72333	−	16.8413i	0.457854	−	0.793026i
$452$	2.71559	−	4.70354i	0.127731	−	0.221236i
$453$	5.02966	+	8.71163i	0.236314	+	0.409308i
$454$	−13.7592			−0.645751
$455$	9.58898	−	13.5325i	0.449538	−	0.634412i
$456$	3.20938			0.150293
$457$	−16.3811	−	28.3729i	−0.766277	−	1.32723i	−0.939569	−	0.342360i	$-0.888774\pi$
$457$	−16.3811	−	28.3729i	−0.766277	−	1.32723i	0.173292	−	0.984871i	$-0.444560\pi$
$458$	10.8141	−	18.7305i	0.505308	−	0.875220i
$459$	1.92497	−	3.33415i	0.0898499	−	0.155625i
$460$	0.500000	+	0.866025i	0.0233126	+	0.0403786i
$461$	−10.2373			−0.476798			−0.238399	−	0.971167i	$-0.576623\pi$
$461$	−10.2373			−0.476798			−0.238399	+	0.971167i	$0.576623\pi$
$462$	10.6937	+	0.995981i	0.497515	+	0.0463372i
$463$	−0.118640			−0.00551368			−0.00275684	−	0.999996i	$-0.500878\pi$
$463$	−0.118640			−0.00551368			−0.00275684	+	0.999996i	$0.500878\pi$
$464$	0.634350	+	1.09873i	0.0294490	+	0.0510071i
$465$	3.23904	−	5.61018i	0.150207	−	0.260166i
$466$	−13.3046	+	23.0442i	−0.616322	+	1.06750i
$467$	4.05932	+	7.03095i	0.187843	+	0.325354i	0.944531	−	0.328423i	$-0.106517\pi$
$467$	4.05932	+	7.03095i	0.187843	+	0.325354i	−0.756688	+	0.653776i	$0.773184\pi$
$468$	−6.26870			−0.289771
$469$	−35.5060	−	3.30694i	−1.63951	−	0.152700i
$470$	−5.47808			−0.252685
$471$	1.03587	+	1.79418i	0.0477304	+	0.0826714i
$472$	−3.42497	+	5.93222i	−0.157647	+	0.273053i
$473$	16.4781	−	28.5409i	0.757663	−	1.31231i
$474$	−4.69367	−	8.12968i	−0.215587	−	0.373408i
$475$	−12.8375			−0.589026
$476$	−5.88910	+	8.31100i	−0.269926	+	0.380934i
$477$	−9.11864			−0.417514
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	2.27667	−	3.94331i	0.104024	−	0.180174i	−0.809315	−	0.587375i	$-0.800162\pi$
$479$	2.27667	−	3.94331i	0.104024	−	0.180174i	0.913339	+	0.407200i	$0.133495\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	−34.1934	−	59.2248i	−1.55909	−	2.70042i
$482$	−28.2249			−1.28561
$483$	−1.10469	−	2.40409i	−0.0502651	−	0.109390i
$484$	5.47808			0.249004
$485$	7.90305	+	13.6885i	0.358859	+	0.621562i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	10.6578	−	18.4599i	0.482951	−	0.836496i	−0.516857	−	0.856072i	$-0.672898\pi$
$487$	10.6578	−	18.4599i	0.482951	−	0.836496i	0.999808	+	0.0195758i	$0.00623158\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	−4.07174			−0.184130
$490$	2.32028	+	6.60426i	0.104820	+	0.298350i
$491$	2.09074			0.0943538			0.0471769	−	0.998887i	$-0.484978\pi$
$491$	2.09074			0.0943538			0.0471769	+	0.998887i	$0.484978\pi$
$492$	−2.39531	−	4.14880i	−0.107989	−	0.187042i
$493$	2.44221	−	4.23003i	0.109992	−	0.190511i
$494$	−10.0593	+	17.4233i	−0.452590	+	0.783909i
$495$	−2.02966	−	3.51547i	−0.0912264	−	0.158009i
$496$	6.47808			0.290874
$497$	−13.6842	−	29.7803i	−0.613819	−	1.33583i
$498$	0.0593201			0.00265820
$499$	3.56882	+	6.18138i	0.159762	+	0.276716i	0.934783	−	0.355220i	$-0.115594\pi$
$499$	3.56882	+	6.18138i	0.159762	+	0.276716i	−0.775021	+	0.631936i	$0.782261\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	9.00774	−	15.6019i	0.402436	−	0.697040i
$502$	−4.14830	−	7.18507i	−0.185148	−	0.320685i
$503$	11.9372			0.532252			0.266126	−	0.963938i	$-0.414256\pi$
$503$	11.9372			0.532252			0.266126	+	0.963938i	$0.414256\pi$
$504$	1.52966	−	2.15874i	0.0681365	−	0.0961577i
$505$	−14.1186			−0.628271
$506$	−2.02966	−	3.51547i	−0.0902294	−	0.156282i
$507$	13.1483	−	22.7735i	0.583937	−	1.01141i
$508$	8.02966	−	13.9078i	0.356259	−	0.617058i
$509$	−0.784410	−	1.35864i	−0.0347684	−	0.0602206i	0.848118	−	0.529808i	$-0.177736\pi$
$509$	−0.784410	−	1.35864i	−0.0347684	−	0.0602206i	−0.882886	+	0.469587i	$0.844403\pi$
$510$	3.84994			0.170478
$511$	23.8654	+	2.22276i	1.05574	+	0.0983293i
$512$	−1.00000			−0.0441942
$513$	1.60469	+	2.77940i	0.0708488	+	0.122714i
$514$	9.51395	−	16.4786i	0.419642	−	0.726842i
$515$	−0.260960	+	0.451996i	−0.0114993	+	0.0199173i
$516$	−4.05932	−	7.03095i	−0.178702	−	0.309520i
$517$	22.2373			0.977994
$518$	28.7388	+	2.67666i	1.26271	+	0.117606i
$519$	14.5374			0.638121
$520$	−3.13435	−	5.42885i	−0.137450	−	0.238071i
$521$	−3.37960	+	5.85364i	−0.148063	+	0.256453i	−0.930512	−	0.366263i	$-0.880637\pi$
$521$	−3.37960	+	5.85364i	−0.148063	+	0.256453i	0.782449	+	0.622715i	$0.213970\pi$
$522$	−0.634350	+	1.09873i	−0.0277647	+	0.0480900i
$523$	−3.85768	−	6.68170i	−0.168685	−	0.292170i	0.769273	−	0.638920i	$-0.220619\pi$
$523$	−3.85768	−	6.68170i	−0.168685	−	0.292170i	−0.937958	+	0.346750i	$0.887285\pi$
$524$	−18.8654			−0.824140
$525$	−6.11864	+	8.63494i	−0.267039	+	0.376860i
$526$	−0.118640			−0.00517296
$527$	−12.4701	−	21.5989i	−0.543207	−	0.940861i
$528$	2.02966	−	3.51547i	0.0883296	−	0.152991i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−4.55932	−	7.89697i	−0.198044	−	0.343023i
$531$	−6.84994			−0.297262
$532$	−3.54537	−	7.71565i	−0.153711	−	0.334516i
$533$	30.0310			1.30079
$534$	−5.45463	−	9.44770i	−0.236045	−	0.408842i
$535$	7.02966	−	12.1757i	0.303919	−	0.526403i
$536$	−6.73904	+	11.6724i	−0.291082	+	0.504169i
$537$	−6.37960	−	11.0498i	−0.275300	−	0.476834i
$538$	−2.96858			−0.127985
$539$	−9.41876	−	26.8088i	−0.405695	−	1.15474i
$540$	−1.00000			−0.0430331
$541$	0.924970	+	1.60210i	0.0397676	+	0.0688795i	0.885224	−	0.465165i	$-0.154005\pi$
$541$	0.924970	+	1.60210i	0.0397676	+	0.0688795i	−0.845457	+	0.534044i	$0.820672\pi$
$542$	−6.44842	+	11.1690i	−0.276983	+	0.479749i
$543$	−6.26870	+	10.8577i	−0.269016	+	0.465949i
$544$	1.92497	+	3.33415i	0.0825324	+	0.142950i
$545$	−12.1186			−0.519106
$546$	6.92497	+	15.0705i	0.296361	+	0.644959i
$547$	−37.6839			−1.61125			−0.805624	−	0.592427i	$-0.798170\pi$
$547$	−37.6839			−1.61125			−0.805624	+	0.592427i	$0.798170\pi$
$548$	−7.79836	−	13.5072i	−0.333129	−	0.576997i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	−8.11864	+	14.0619i	−0.346180	+	0.599601i
$551$	2.03587	+	3.52623i	0.0867310	+	0.150222i
$552$	−1.00000			−0.0425628
$553$	−14.3594	+	20.2648i	−0.610625	+	0.861746i
$554$	−11.1780			−0.474906
$555$	−5.45463	−	9.44770i	−0.231536	−	0.401032i
$556$	−3.41876	+	5.92147i	−0.144988	+	0.251126i
$557$	−10.9982	+	19.0495i	−0.466010	+	0.807154i	−0.999247	−	0.0388128i	$-0.987642\pi$
$557$	−10.9982	+	19.0495i	−0.466010	+	0.807154i	0.533236	+	0.845966i	$0.320976\pi$
$558$	3.23904	+	5.61018i	0.137119	+	0.237498i
$559$	50.8933			2.15256
$560$	2.63435	+	0.245357i	0.111322	+	0.0103682i
$561$	−15.6281			−0.659821
$562$	−15.7311	−	27.2470i	−0.663575	−	1.14935i
$563$	17.9389	−	31.0711i	0.756035	−	1.30949i	−0.188823	−	0.982011i	$-0.560467\pi$
$563$	17.9389	−	31.0711i	0.756035	−	1.30949i	0.944858	−	0.327480i	$-0.106200\pi$
$564$	2.73904	−	4.74416i	0.115334	−	0.199765i
$565$	2.71559	+	4.70354i	0.114246	+	0.197879i
$566$	10.0155			0.420982
$567$	2.63435	+	0.245357i	0.110632	+	0.0103040i
$568$	−12.3873			−0.519761
$569$	10.5297	+	18.2379i	0.441426	+	0.764573i	0.997796	−	0.0663624i	$-0.0211393\pi$
$569$	10.5297	+	18.2379i	0.441426	+	0.764573i	−0.556369	+	0.830935i	$0.687806\pi$
$570$	−1.60469	+	2.77940i	−0.0672131	+	0.116416i
$571$	17.0312	−	29.4989i	0.712733	−	1.23449i	−0.251094	−	0.967963i	$-0.580790\pi$
$571$	17.0312	−	29.4989i	0.712733	−	1.23449i	0.963827	−	0.266527i	$-0.0858763\pi$
$572$	12.7233	+	22.0375i	0.531989	+	0.921432i
$573$	−4.07174			−0.170099
$574$	−7.32802	+	10.3417i	−0.305866	+	0.431654i
$575$	4.00000			0.166812
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−17.3577	+	30.0644i	−0.722610	+	1.25160i	0.237341	+	0.971426i	$0.423724\pi$
$577$	−17.3577	+	30.0644i	−0.722610	+	1.25160i	−0.959950	+	0.280170i	$0.909609\pi$
$578$	−1.08898	+	1.88617i	−0.0452956	+	0.0784543i
$579$	11.8873	+	20.5895i	0.494021	+	0.855669i
$580$	−1.26870			−0.0526799
$581$	−0.0655304	−	0.142611i	−0.00271866	−	0.00591651i
$582$	−15.8061			−0.655184
$583$	18.5077	+	32.0563i	0.766512	+	1.32764i
$584$	4.52966	−	7.84560i	0.187439	−	0.324653i
$585$	3.13435	−	5.42885i	0.129589	−	0.224455i
$586$	1.91876	+	3.32339i	0.0792632	+	0.137288i
$587$	−41.5843			−1.71637			−0.858184	−	0.513342i	$-0.828407\pi$
$587$	−41.5843			−1.71637			−0.858184	+	0.513342i	$0.828407\pi$
$588$	−6.87960	−	1.29271i	−0.283710	−	0.0533105i
$589$	20.7906			0.856663
$590$	−3.42497	−	5.93222i	−0.141004	−	0.244226i
$591$	0.209380	−	0.362657i	0.00861274	−	0.0149177i
$592$	5.45463	−	9.44770i	0.224184	−	0.388298i
$593$	12.6406	+	21.8941i	0.519086	+	0.899083i	0.999754	+	0.0221802i	$0.00706075\pi$
$593$	12.6406	+	21.8941i	0.519086	+	0.899083i	−0.480668	+	0.876902i	$0.659606\pi$
$594$	4.05932			0.166556
$595$	−4.25299	−	9.25561i	−0.174356	−	0.379443i
$596$	3.17796			0.130174
$597$	−2.84994	−	4.93624i	−0.116640	−	0.202027i
$598$	3.13435	−	5.42885i	0.128173	−	0.222002i
$599$	−10.7625	+	18.6412i	−0.439743	+	0.761658i	−0.997669	−	0.0682328i	$-0.978264\pi$
$599$	−10.7625	+	18.6412i	−0.439743	+	0.761658i	0.557926	+	0.829891i	$0.311597\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	4.17796			0.170423			0.0852113	−	0.996363i	$-0.472843\pi$
$601$	4.17796			0.170423			0.0852113	+	0.996363i	$0.472843\pi$
$602$	−12.4188	+	17.5260i	−0.506151	+	0.714306i
$603$	−13.4781			−0.548870
$604$	−5.02966	−	8.71163i	−0.204654	−	0.354471i
$605$	−2.73904	+	4.74416i	−0.111358	+	0.192877i
$606$	7.05932	−	12.2271i	0.286765	−	0.496692i
$607$	10.6264	+	18.4054i	0.431311	+	0.747053i	0.996987	−	0.0775749i	$-0.0247177\pi$
$607$	10.6264	+	18.4054i	0.431311	+	0.747053i	−0.565675	+	0.824628i	$0.691384\pi$
$608$	−3.20938			−0.130158
$609$	3.34220	+	0.311284i	0.135433	+	0.0126139i
$610$	−10.0000			−0.404888
$611$	17.1702	+	29.7397i	0.694633	+	1.20314i
$612$	−1.92497	+	3.33415i	−0.0778123	+	0.134775i
$613$	−1.17796	+	2.04029i	−0.0475774	+	0.0824064i	−0.888833	−	0.458231i	$-0.848483\pi$
$613$	−1.17796	+	2.04029i	−0.0475774	+	0.0824064i	0.841256	+	0.540637i	$0.181817\pi$
$614$	6.99203	+	12.1106i	0.282175	+	0.488742i
$615$	4.79062			0.193176
$616$	−10.6937	−	0.995981i	−0.430860	−	0.0401292i
$617$	−12.8778			−0.518442			−0.259221	−	0.965818i	$-0.583466\pi$
$617$	−12.8778			−0.518442			−0.259221	+	0.965818i	$0.583466\pi$
$618$	−0.260960	−	0.451996i	−0.0104974	−	0.0181819i
$619$	5.97187	−	10.3436i	0.240030	−	0.415744i	−0.720693	−	0.693255i	$-0.756176\pi$
$619$	5.97187	−	10.3436i	0.240030	−	0.415744i	0.960722	+	0.277511i	$0.0895095\pi$
$620$	−3.23904	+	5.61018i	−0.130083	+	0.225310i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	26.3873			1.05804
$623$	−16.6875	+	23.5502i	−0.668569	+	0.943519i
$624$	6.26870			0.250949
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	4.57503	−	7.92418i	0.182855	−	0.316714i
$627$	6.51395	−	11.2825i	0.260142	−	0.450579i
$628$	−1.03587	−	1.79418i	−0.0413357	−	0.0715956i
$629$	−42.0000			−1.67465
$630$	1.10469	+	2.40409i	0.0440119	+	0.0957813i
$631$	10.9841			0.437269			0.218634	−	0.975807i	$-0.429840\pi$
$631$	10.9841			0.437269			0.218634	+	0.975807i	$0.429840\pi$
$632$	4.69367	+	8.12968i	0.186704	+	0.323381i
$633$	−2.20938	+	3.82676i	−0.0878150	+	0.152100i
$634$	10.1124	−	17.5152i	0.401616	−	0.695619i
$635$	8.02966	+	13.9078i	0.318647	+	0.551913i
$636$	9.11864			0.361578
$637$	28.5810	−	33.2965i	1.13242	−	1.31926i
$638$	5.15006			0.203893
$639$	−6.19367	−	10.7278i	−0.245018	−	0.424383i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−13.7311	+	23.7829i	−0.542345	+	0.939369i	0.456424	+	0.889762i	$0.349130\pi$
$641$	−13.7311	+	23.7829i	−0.542345	+	0.939369i	−0.998769	+	0.0496062i	$0.984203\pi$
$642$	7.02966	+	12.1757i	0.277439	+	0.480538i
$643$	−3.32802			−0.131244			−0.0656222	−	0.997845i	$-0.520903\pi$
$643$	−3.32802			−0.131244			−0.0656222	+	0.997845i	$0.520903\pi$
$644$	1.10469	+	2.40409i	0.0435309	+	0.0947345i
$645$	8.11864			0.319671
$646$	6.17796	+	10.7005i	0.243069	+	0.421007i
$647$	−15.9247	+	27.5825i	−0.626066	+	1.08438i	0.362268	+	0.932074i	$0.382003\pi$
$647$	−15.9247	+	27.5825i	−0.626066	+	1.08438i	−0.988334	+	0.152304i	$0.951331\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	13.9031	+	24.0808i	0.545742	+	0.945254i
$650$	−25.0748			−0.983515
$651$	9.90926	−	13.9845i	0.388375	−	0.548094i
$652$	4.07174			0.159462
$653$	1.14385	+	1.98121i	0.0447623	+	0.0775306i	0.887539	−	0.460734i	$-0.152414\pi$
$653$	1.14385	+	1.98121i	0.0447623	+	0.0775306i	−0.842776	+	0.538264i	$0.819080\pi$
$654$	6.05932	−	10.4951i	0.236938	−	0.410389i
$655$	9.43271	−	16.3379i	0.368566	−	0.638376i
$656$	2.39531	+	4.14880i	0.0935211	+	0.161983i
$657$	9.05932			0.353438
$658$	−14.4312	−	1.34408i	−0.562586	−	0.0523978i
$659$	−8.18148			−0.318705			−0.159353	−	0.987222i	$-0.550941\pi$
$659$	−8.18148			−0.318705			−0.159353	+	0.987222i	$0.550941\pi$
$660$	2.02966	+	3.51547i	0.0790044	+	0.136840i
$661$	13.3404	−	23.1063i	0.518883	−	0.898732i	−0.480876	−	0.876788i	$-0.659681\pi$
$661$	13.3404	−	23.1063i	0.518883	−	0.898732i	0.999759	−	0.0219432i	$-0.00698531\pi$
$662$	−10.3046	+	17.8480i	−0.400499	+	0.693684i
$663$	−12.0671	−	20.9008i	−0.468646	−	0.811718i
$664$	−0.0593201			−0.00230207
$665$	8.45463	+	0.787443i	0.327856	+	0.0305357i
$666$	10.9093			0.422725
$667$	−0.634350	−	1.09873i	−0.0245621	−	0.0425429i
$668$	−9.00774	+	15.6019i	−0.348520	+	0.603654i
$669$	5.87960	−	10.1838i	0.227318	−	0.393727i
$670$	−6.73904	−	11.6724i	−0.260352	−	0.450943i
$671$	40.5932			1.56708
$672$	−1.52966	+	2.15874i	−0.0590079	+	0.0832750i
$673$	−48.6525			−1.87542			−0.937708	−	0.347423i	$-0.887057\pi$
$673$	−48.6525			−1.87542			−0.937708	+	0.347423i	$0.887057\pi$
$674$	−13.1124	−	22.7114i	−0.505072	−	0.874810i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	−13.1483	+	22.7735i	−0.505704	+	0.875905i
$677$	−0.618640	−	1.07152i	−0.0237763	−	0.0411817i	0.853892	−	0.520450i	$-0.174236\pi$
$677$	−0.618640	−	1.07152i	−0.0237763	−	0.0411817i	−0.877669	+	0.479268i	$0.840902\pi$
$678$	−5.43118			−0.208583
$679$	17.4608	+	37.9993i	0.670086	+	1.45828i
$680$	−3.84994			−0.147638
$681$	6.87960	+	11.9158i	0.263627	+	0.456615i
$682$	13.1483	−	22.7735i	0.503474	−	0.872043i
$683$	−2.67351	+	4.63065i	−0.102299	+	0.177187i	−0.912631	−	0.408783i	$-0.865953\pi$
$683$	−2.67351	+	4.63065i	−0.102299	+	0.177187i	0.810332	+	0.585970i	$0.199287\pi$
$684$	−1.60469	−	2.77940i	−0.0613569	−	0.106273i
$685$	15.5967			0.595920
$686$	4.49203	+	17.9672i	0.171507	+	0.685992i
$687$	−21.6281			−0.825165
$688$	4.05932	+	7.03095i	0.154760	+	0.268052i
$689$	−28.5810	+	49.5038i	−1.08885	+	1.88594i
$690$	0.500000	−	0.866025i	0.0190347	−	0.0329690i
$691$	−1.76717	−	3.06083i	−0.0672263	−	0.116439i	0.830453	−	0.557089i	$-0.188082\pi$
$691$	−1.76717	−	3.06083i	−0.0672263	−	0.116439i	−0.897679	+	0.440649i	$0.854748\pi$
$692$	−14.5374			−0.552629
$693$	−4.48429	−	9.75898i	−0.170344	−	0.370713i
$694$	−25.5967			−0.971638
$695$	−3.41876	−	5.92147i	−0.129681	−	0.224614i
$696$	0.634350	−	1.09873i	0.0240450	−	0.0416471i
$697$	9.22180	−	15.9726i	0.349301	−	0.605006i
$698$	0.806330	+	1.39660i	0.0305200	+	0.0528622i
$699$	26.6091			1.00645
$700$	6.11864	−	8.63494i	0.231263	−	0.326370i
$701$	−32.6999			−1.23506			−0.617529	−	0.786548i	$-0.711866\pi$
$701$	−32.6999			−1.23506			−0.617529	+	0.786548i	$0.711866\pi$
$702$	3.13435	+	5.42885i	0.118298	+	0.204899i
$703$	17.5060	−	30.3212i	0.660251	−	1.14359i
$704$	−2.02966	+	3.51547i	−0.0764957	+	0.132494i
$705$	2.73904	+	4.74416i	0.103158	+	0.178675i
$706$	26.6091			1.00145
$707$	−37.1934	−	3.46410i	−1.39880	−	0.130281i
$708$	6.84994			0.257437
$709$	−21.1107	−	36.5648i	−0.792828	−	1.37322i	−0.924209	−	0.381886i	$-0.875275\pi$
$709$	−21.1107	−	36.5648i	−0.792828	−	1.37322i	0.131381	−	0.991332i	$-0.458059\pi$
$710$	6.19367	−	10.7278i	0.232444	−	0.402605i
$711$	−4.69367	+	8.12968i	−0.176026	+	0.304887i
$712$	5.45463	+	9.44770i	0.204421	+	0.354067i
$713$	−6.47808			−0.242606
$714$	10.1421	+	0.944608i	0.379558	+	0.0353511i
$715$	−25.4467			−0.951651
$716$	6.37960	+	11.0498i	0.238417	+	0.412950i
$717$	−8.00000	+	13.8564i	−0.298765	+	0.517477i
$718$	−9.41876	+	16.3138i	−0.351505	+	0.608825i
$719$	−11.6483	−	20.1754i	−0.434408	−	0.752417i	0.562839	−	0.826567i	$-0.309709\pi$
$719$	−11.6483	−	20.1754i	−0.434408	−	0.752417i	−0.997247	+	0.0741494i	$0.976376\pi$
$720$	1.00000			0.0372678
$721$	−0.798360	+	1.12669i	−0.0297325	+	0.0419600i
$722$	8.69988			0.323776
$723$	14.1124	+	24.4434i	0.524847	+	0.909062i
$724$	6.26870	−	10.8577i	0.232974	−	0.403524i
$725$	−2.53740	+	4.39491i	−0.0942367	+	0.163223i
$726$	−2.73904	−	4.74416i	−0.101655	−	0.176072i
$727$	−32.5498			−1.20721			−0.603603	−	0.797285i	$-0.706269\pi$
$727$	−32.5498			−1.20721			−0.603603	+	0.797285i	$0.706269\pi$
$728$	−6.92497	−	15.0705i	−0.256656	−	0.558551i
$729$	1.00000			0.0370370
$730$	4.52966	+	7.84560i	0.167650	+	0.290379i
$731$	15.6281	−	27.0687i	0.578028	−	1.00117i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	−4.38289	−	7.59139i	−0.161886	−	0.280394i	0.773659	−	0.633602i	$-0.218424\pi$
$733$	−4.38289	−	7.59139i	−0.161886	−	0.280394i	−0.935545	+	0.353208i	$0.885091\pi$
$734$	−0.746780			−0.0275642
$735$	4.55932	−	5.31155i	0.168173	−	0.195920i
$736$	1.00000			0.0368605
$737$	27.3559	+	47.3818i	1.00767	+	1.74533i
$738$	−2.39531	+	4.14880i	−0.0881726	+	0.152719i
$739$	12.5498	−	21.7369i	0.461653	−	0.799606i	−0.537391	−	0.843333i	$-0.680590\pi$
$739$	12.5498	−	21.7369i	0.461653	−	0.799606i	0.999043	+	0.0437275i	$0.0139233\pi$
$740$	5.45463	+	9.44770i	0.200516	+	0.347304i
$741$	20.1186			0.739077
$742$	−10.0733	−	21.9221i	−0.369801	−	0.804784i
$743$	18.3090			0.671693			0.335846	−	0.941917i	$-0.390978\pi$
$743$	18.3090			0.671693			0.335846	+	0.941917i	$0.390978\pi$
$744$	−3.23904	−	5.61018i	−0.118749	−	0.205679i
$745$	−1.58898	+	2.75219i	−0.0582157	+	0.100833i
$746$	9.47808	−	16.4165i	0.347017	−	0.601051i
$747$	−0.0296601	−	0.0513728i	−0.00108521	−	0.00187963i
$748$	15.6281			0.571421
$749$	21.5060	−	30.3504i	0.785811	−	1.10898i
$750$	−9.00000			−0.328634
$751$	14.0217	+	24.2863i	0.511659	+	0.886219i	0.999909	+	0.0135151i	$0.00430212\pi$
$751$	14.0217	+	24.2863i	0.511659	+	0.886219i	−0.488250	+	0.872704i	$0.662365\pi$
$752$	−2.73904	+	4.74416i	−0.0998825	+	0.173002i
$753$	−4.14830	+	7.18507i	−0.151172	+	0.261838i
$754$	3.97655	+	6.88759i	0.144817	+	0.250831i
$755$	10.0593			0.366096
$756$	−2.63435	−	0.245357i	−0.0958104	−	0.00892353i
$757$	21.7468			0.790400			0.395200	−	0.918595i	$-0.370675\pi$
$757$	21.7468			0.790400			0.395200	+	0.918595i	$0.370675\pi$
$758$	5.85768	+	10.1458i	0.212761	+	0.368512i
$759$	−2.02966	+	3.51547i	−0.0736720	+	0.127604i
$760$	1.60469	−	2.77940i	0.0582082	−	0.100820i
$761$	19.9606	+	34.5728i	0.723572	+	1.25326i	0.959559	+	0.281507i	$0.0908342\pi$
$761$	19.9606	+	34.5728i	0.723572	+	1.25326i	−0.235988	+	0.971756i	$0.575833\pi$
$762$	−16.0593			−0.581768
$763$	−31.9247	−	2.97339i	−1.15575	−	0.107644i
$764$	4.07174			0.147310
$765$	−1.92497	−	3.33415i	−0.0695974	−	0.120546i
$766$	−13.0828	+	22.6600i	−0.472700	+	0.818740i
$767$	−21.4701	+	37.1873i	−0.775241	+	1.34276i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−29.3245			−1.05747			−0.528734	−	0.848787i	$-0.677333\pi$
$769$	−29.3245			−1.05747			−0.528734	+	0.848787i	$0.677333\pi$
$770$	6.20938	−	8.76300i	0.223771	−	0.315797i
$771$	−19.0279			−0.685273
$772$	−11.8873	−	20.5895i	−0.427835	−	0.741032i
$773$	−2.67972	+	4.64141i	−0.0963828	+	0.166940i	−0.910185	−	0.414202i	$-0.864061\pi$
$773$	−2.67972	+	4.64141i	−0.0963828	+	0.166940i	0.813802	+	0.581142i	$0.197394\pi$
$774$	−4.05932	+	7.03095i	−0.145909	+	0.252722i
$775$	12.9562	+	22.4407i	0.465399	+	0.806095i
$776$	15.8061			0.567406
$777$	−12.0514	−	26.2269i	−0.432340	−	0.940884i
$778$	27.7937			0.996452
$779$	7.68746	+	13.3151i	0.275432	+	0.477062i
$780$	−3.13435	+	5.42885i	−0.112228	+	0.194384i
$781$	−25.1421	+	43.5474i	−0.899655	+	1.55825i
$782$	−1.92497	−	3.33415i	−0.0688368	−	0.119229i
$783$	1.26870			0.0453396
$784$	6.87960	+	1.29271i	0.245700	+	0.0461682i
$785$	2.07174			0.0739436
$786$	9.43271	+	16.3379i	0.336454	+	0.582755i
$787$	−13.9484	+	24.1594i	−0.497207	+	0.861189i	−0.999995	−	0.00322154i	$-0.998975\pi$
$787$	−13.9484	+	24.1594i	−0.497207	+	0.861189i	0.502787	+	0.864410i	$0.332308\pi$
$788$	−0.209380	+	0.362657i	−0.00745885	+	0.0129191i
$789$	0.0593201	+	0.102746i	0.00211185	+	0.00365784i
$790$	−9.38734			−0.333987
$791$	5.99977	+	13.0571i	0.213327	+	0.464256i
$792$	−4.05932			−0.144242
$793$	31.3435	+	54.2885i	1.11304	+	1.92784i
$794$	1.92497	−	3.33415i	0.0683146	−	0.118324i
$795$	−4.55932	+	7.89697i	−0.161702	+	0.280077i
$796$	2.84994	+	4.93624i	0.101013	+	0.174960i
$797$	13.6560			0.483722			0.241861	−	0.970311i	$-0.422242\pi$
$797$	13.6560			0.483722			0.241861	+	0.970311i	$0.422242\pi$
$798$	−4.90926	+	6.92820i	−0.173786	+	0.245256i
$799$	21.0903			0.746120
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	−5.45463	+	9.44770i	−0.192730	+	0.333818i
$802$	3.58898	−	6.21630i	0.126731	−	0.219505i
$803$	−18.3873	−	31.8478i	−0.648875	−	1.12388i
$804$	13.4781			0.475335
$805$	−2.63435	−	0.245357i	−0.0928486	−	0.00864768i
$806$	40.6091			1.43040
$807$	1.48429	+	2.57087i	0.0522495	+	0.0904988i
$808$	−7.05932	+	12.2271i	−0.248346	+	0.430148i
$809$	8.36389	−	14.4867i	0.294059	−	0.509325i	−0.680707	−	0.732556i	$-0.738327\pi$
$809$	8.36389	−	14.4867i	0.294059	−	0.509325i	0.974765	+	0.223231i	$0.0716605\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−17.3998			−0.610988			−0.305494	−	0.952194i	$-0.598822\pi$
$811$	−17.3998			−0.610988			−0.305494	+	0.952194i	$0.598822\pi$
$812$	−3.34220	−	0.311284i	−0.117288	−	0.0109239i
$813$	12.8968			0.452312
$814$	−22.1421	−	38.3512i	−0.776080	−	1.34421i
$815$	−2.03587	+	3.52623i	−0.0713134	+	0.123518i
$816$	1.92497	−	3.33415i	0.0673874	−	0.116718i
$817$	13.0279	+	22.5650i	0.455789	+	0.789449i
$818$	16.3749			0.572536
$819$	9.58898	−	13.5325i	0.335066	−	0.472863i
$820$	−4.79062			−0.167296
$821$	14.3656	+	24.8820i	0.501365	+	0.868389i	0.999999	+	0.00157647i	$0.000501806\pi$
$821$	14.3656	+	24.8820i	0.501365	+	0.868389i	−0.498634	+	0.866813i	$0.666165\pi$
$822$	−7.79836	+	13.5072i	−0.271999	+	0.471116i
$823$	16.0155	−	27.7396i	0.558265	−	0.966943i	−0.439377	−	0.898303i	$-0.644801\pi$
$823$	16.0155	−	27.7396i	0.558265	−	0.966943i	0.997642	−	0.0686398i	$-0.0218659\pi$
$824$	0.260960	+	0.451996i	0.00909097	+	0.0157460i
$825$	16.2373			0.565310
$826$	−7.56706	−	16.4679i	−0.263292	−	0.572991i
$827$	26.3214			0.915286			0.457643	−	0.889136i	$-0.348694\pi$
$827$	26.3214			0.915286			0.457643	+	0.889136i	$0.348694\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	10.7669	−	18.6489i	0.373951	−	0.647703i	−0.616218	−	0.787575i	$-0.711336\pi$
$829$	10.7669	−	18.6489i	0.373951	−	0.647703i	0.990169	+	0.139873i	$0.0446694\pi$
$830$	0.0296601	−	0.0513728i	0.00102952	−	0.00178317i
$831$	5.58898	+	9.68040i	0.193880	+	0.335809i
$832$	−6.26870			−0.217328
$833$	−8.93294	−	25.4260i	−0.309508	−	0.880959i
$834$	6.83752			0.236764
$835$	−9.00774	−	15.6019i	−0.311726	−	0.539925i
$836$	−6.51395	+	11.2825i	−0.225290	+	0.390213i
$837$	3.23904	−	5.61018i	0.111958	−	0.193916i
$838$	−12.9686	−	22.4622i	−0.447992	−	0.775945i
$839$	6.25322			0.215885			0.107943	−	0.994157i	$-0.465574\pi$
$839$	6.25322			0.215885			0.107943	+	0.994157i	$0.465574\pi$
$840$	−1.10469	−	2.40409i	−0.0381154	−	0.0829491i
$841$	−27.3904			−0.944497
$842$	1.56882	+	2.71728i	0.0540651	+	0.0936435i
$843$	−15.7311	+	27.2470i	−0.541807	+	0.938437i
$844$	2.20938	−	3.82676i	0.0760500	−	0.131722i
$845$	−13.1483	−	22.7735i	−0.452315	−	0.783433i
$846$	−5.47808			−0.188340
$847$	−8.37960	+	11.8257i	−0.287926	+	0.406337i
$848$	−9.11864			−0.313135
$849$	−5.00774	−	8.67366i	−0.171865	−	0.297679i
$850$	−7.69988	+	13.3366i	−0.264104	+	0.457441i
$851$	−5.45463	+	9.44770i	−0.186982	+	0.323863i
$852$	6.19367	+	10.7278i	0.212192	+	0.367527i
$853$	4.65604			0.159420			0.0797099	−	0.996818i	$-0.474601\pi$
$853$	4.65604			0.159420			0.0797099	+	0.996818i	$0.474601\pi$
$854$	−26.3435	−	2.45357i	−0.901456	−	0.0839593i
$855$	3.20938			0.109758
$856$	−7.02966	−	12.1757i	−0.240269	−	0.416158i
$857$	22.8420	−	39.5635i	0.780267	−	1.35146i	−0.151519	−	0.988454i	$-0.548417\pi$
$857$	22.8420	−	39.5635i	0.780267	−	1.35146i	0.931786	−	0.363008i	$-0.118250\pi$
$858$	12.7233	−	22.0375i	0.434367	−	0.752346i
$859$	−21.0045	−	36.3808i	−0.716663	−	1.24130i	−0.962315	−	0.271938i	$-0.912335\pi$
$859$	−21.0045	−	36.3808i	−0.716663	−	1.24130i	0.245652	−	0.969358i	$-0.420998\pi$
$860$	−8.11864			−0.276843
$861$	12.6202	+	1.17541i	0.430094	+	0.0400579i
$862$	17.0748			0.581570
$863$	25.1029	+	43.4796i	0.854514	+	1.48006i	0.877095	+	0.480316i	$0.159478\pi$
$863$	25.1029	+	43.4796i	0.854514	+	1.48006i	−0.0225817	+	0.999745i	$0.507189\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	7.26870	−	12.5898i	0.247143	−	0.428065i
$866$	−17.2373	−	29.8558i	−0.585747	−	1.01454i
$867$	2.17796			0.0739674
$868$	−9.90926	+	13.9845i	−0.336342	+	0.474664i
$869$	38.1062			1.29266
$870$	0.634350	+	1.09873i	0.0215065	+	0.0372503i
$871$	−42.2450	+	73.1705i	−1.43142	+	2.47929i
$872$	−6.05932	+	10.4951i	−0.205194	+	0.355407i
$873$	7.90305	+	13.6885i	0.267478	+	0.463285i
$874$	3.20938			0.108559
$875$	9.94221	+	21.6368i	0.336108	+	0.731458i
$876$	−9.05932			−0.306086
$877$	4.22509	+	7.31807i	0.142671	+	0.247114i	0.928502	−	0.371328i	$-0.121098\pi$
$877$	4.22509	+	7.31807i	0.142671	+	0.247114i	−0.785831	+	0.618442i	$0.787764\pi$
$878$	1.29836	−	2.24883i	0.0438175	−	0.0758942i
$879$	1.91876	−	3.32339i	0.0647182	−	0.112095i
$880$	−2.02966	−	3.51547i	−0.0684198	−	0.118507i
$881$	1.17796			0.0396865			0.0198432	−	0.999803i	$-0.493683\pi$
$881$	1.17796			0.0396865			0.0198432	+	0.999803i	$0.493683\pi$
$882$	2.32028	+	6.60426i	0.0781279	+	0.222377i
$883$	27.5653			0.927646			0.463823	−	0.885928i	$-0.346477\pi$
$883$	27.5653			0.927646			0.463823	+	0.885928i	$0.346477\pi$
$884$	12.0671	+	20.9008i	0.405859	+	0.702969i
$885$	−3.42497	+	5.93222i	−0.115129	+	0.199409i
$886$	2.01395	−	3.48826i	0.0676600	−	0.117191i
$887$	−24.1186	−	41.7747i	−0.809825	−	1.40266i	−0.912985	−	0.407993i	$-0.866229\pi$
$887$	−24.1186	−	41.7747i	−0.809825	−	1.40266i	0.103160	−	0.994665i	$-0.467104\pi$
$888$	−10.9093			−0.366091
$889$	17.7406	+	38.6081i	0.595000	+	1.29487i
$890$	−10.9093			−0.365679
$891$	−2.02966	−	3.51547i	−0.0679962	−	0.117773i
$892$	−5.87960	+	10.1838i	−0.196864	+	0.340978i
$893$	−8.79062	+	15.2258i	−0.294167	+	0.509512i
$894$	−1.58898	−	2.75219i	−0.0531434	−	0.0920472i
$895$	−12.7592			−0.426493
$896$	1.52966	−	2.15874i	0.0511024	−	0.0721183i
$897$	−6.26870			−0.209306
$898$	−11.0828	−	19.1959i	−0.369837	−	0.640576i
$899$	4.10937	−	7.11764i	0.137055	−	0.237387i
$900$	2.00000	−	3.46410i	0.0666667	−	0.115470i
$901$	17.5531	+	30.4029i	0.584779	+	1.01287i
$902$	19.4467			0.647503
$903$	21.3873	+	1.99196i	0.711726	+	0.0662883i
$904$	5.43118			0.180638
$905$	6.26870	+	10.8577i	0.208379	+	0.360922i
$906$	−5.02966	+	8.71163i	−0.167099	+	0.289424i
$907$	12.1344	−	21.0173i	0.402914	−	0.697868i	−0.591162	−	0.806553i	$-0.701331\pi$
$907$	12.1344	−	21.0173i	0.402914	−	0.697868i	0.994076	+	0.108685i	$0.0346639\pi$
$908$	−6.87960	−	11.9158i	−0.228308	−	0.395440i
$909$	−14.1186			−0.468286
$910$	16.5140	+	1.53807i	0.547432	+	0.0509864i
$911$	−6.68088			−0.221347			−0.110674	−	0.993857i	$-0.535301\pi$
$911$	−6.68088			−0.221347			−0.110674	+	0.993857i	$0.535301\pi$
$912$	1.60469	+	2.77940i	0.0531366	+	0.0920353i
$913$	−0.120400	+	0.208538i	−0.00398465	+	0.00690162i
$914$	16.3811	−	28.3729i	0.541840	−	0.938494i
$915$	5.00000	+	8.66025i	0.165295	+	0.286299i
$916$	21.6281			0.714614
$917$	28.8577	−	40.7255i	0.952965	−	1.34487i
$918$	3.84994			0.127067
$919$	−2.14232	−	3.71061i	−0.0706686	−	0.122402i	0.828526	−	0.559951i	$-0.189180\pi$
$919$	−2.14232	−	3.71061i	−0.0706686	−	0.122402i	−0.899195	+	0.437549i	$0.855847\pi$
$920$	−0.500000	+	0.866025i	−0.0164845	+	0.0285520i
$921$	6.99203	−	12.1106i	0.230395	−	0.399056i
$922$	−5.11864	−	8.86575i	−0.168573	−	0.291978i
$923$	−77.6525			−2.55596
$924$	4.48429	+	9.75898i	0.147522	+	0.321047i
$925$	43.6370			1.43478
$926$	−0.0593201	−	0.102746i	−0.00194938	−	0.00337643i
$927$	−0.260960	+	0.451996i	−0.00857105	+	0.0148455i
$928$	−0.634350	+	1.09873i	−0.0208236	+	0.0360675i
$929$	1.59227	+	2.75789i	0.0522407	+	0.0904835i	0.890963	−	0.454076i	$-0.150030\pi$
$929$	1.59227	+	2.75789i	0.0522407	+	0.0904835i	−0.838723	+	0.544559i	$0.816697\pi$
$930$	6.47808			0.212425
$931$	22.0793	+	4.14880i	0.723618	+	0.135971i
$932$	−26.6091			−0.871611
$933$	−13.1937	−	22.8521i	−0.431941	−	0.748144i
$934$	−4.05932	+	7.03095i	−0.132825	+	0.230060i
$935$	−7.81407	+	13.5344i	−0.255547	+	0.442621i
$936$	−3.13435	−	5.42885i	−0.102449	−	0.177448i
$937$	25.8619			0.844871			0.422436	−	0.906393i	$-0.361175\pi$
$937$	25.8619			0.844871			0.422436	+	0.906393i	$0.361175\pi$
$938$	−14.8891	−	32.4025i	−0.486146	−	1.05798i
$939$	−9.15006			−0.298601
$940$	−2.73904	−	4.74416i	−0.0893376	−	0.154737i
$941$	−1.85170	+	3.20724i	−0.0603637	+	0.104553i	−0.894628	−	0.446812i	$-0.852559\pi$
$941$	−1.85170	+	3.20724i	−0.0603637	+	0.104553i	0.834264	+	0.551365i	$0.185893\pi$
$942$	−1.03587	+	1.79418i	−0.0337505	+	0.0584575i
$943$	−2.39531	−	4.14880i	−0.0780020	−	0.135103i
$944$	−6.84994			−0.222947
$945$	1.52966	−	2.15874i	0.0497598	−	0.0702237i
$946$	32.9562			1.07150
$947$	25.0077	+	43.3147i	0.812642	+	1.40754i	0.911009	+	0.412388i	$0.135305\pi$
$947$	25.0077	+	43.3147i	0.812642	+	1.40754i	−0.0983661	+	0.995150i	$0.531362\pi$
$948$	4.69367	−	8.12968i	0.152443	−	0.264040i
$949$	28.3951	−	49.1817i	0.921743	−	1.59651i
$950$	−6.41876	−	11.1176i	−0.208252	−	0.360703i
$951$	−20.2249			−0.655836
$952$	−10.1421	−	0.944608i	−0.328707	−	0.0306149i
$953$	24.4188			0.791001			0.395501	−	0.918466i	$-0.370571\pi$
$953$	24.4188			0.791001			0.395501	+	0.918466i	$0.370571\pi$
$954$	−4.55932	−	7.89697i	−0.147613	−	0.255674i
$955$	−2.03587	+	3.52623i	−0.0658792	+	0.114106i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$	−2.57503	−	4.46008i	−0.0832389	−	0.144174i
$958$	4.55334			0.147112
$959$	41.0872	+	3.82676i	1.32678	+	0.123572i
$960$	−1.00000			−0.0322749
$961$	−5.48276	−	9.49642i	−0.176863	−	0.306336i
$962$	34.1934	−	59.2248i	1.10244	−	1.90948i
$963$	7.02966	−	12.1757i	0.226528	−	0.392357i
$964$	−14.1124	−	24.4434i	−0.454531	−	0.787270i
$965$	23.7747			0.765334
$966$	1.52966	−	2.15874i	0.0492160	−	0.0694562i
$967$	−18.4152			−0.592194			−0.296097	−	0.955158i	$-0.595685\pi$
$967$	−18.4152			−0.592194			−0.296097	+	0.955158i	$0.595685\pi$
$968$	2.73904	+	4.74416i	0.0880361	+	0.152483i
$969$	6.17796	−	10.7005i	0.198465	−	0.343751i
$970$	−7.90305	+	13.6885i	−0.253752	+	0.439511i
$971$	8.97034	+	15.5371i	0.287872	+	0.498609i	0.973302	−	0.229530i	$-0.0737189\pi$
$971$	8.97034	+	15.5371i	0.287872	+	0.498609i	−0.685430	+	0.728139i	$0.740386\pi$
$972$	−1.00000			−0.0320750
$973$	−7.55334	−	16.4380i	−0.242149	−	0.526979i
$974$	21.3156			0.682996
$975$	12.5374	+	21.7154i	0.401518	+	0.695450i
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	−14.2171	+	24.6248i	−0.454846	+	0.787816i	−0.998679	−	0.0513769i	$-0.983639\pi$
$977$	−14.2171	+	24.6248i	−0.454846	+	0.787816i	0.543833	+	0.839193i	$0.316972\pi$
$978$	−2.03587	−	3.52623i	−0.0651000	−	0.112756i
$979$	44.2842			1.41533
$980$	−4.55932	+	5.31155i	−0.145642	+	0.169671i
$981$	−12.1186			−0.386918
$982$	1.04537	+	1.81063i	0.0333591	+	0.0577796i
$983$	−2.30457	+	3.99163i	−0.0735044	+	0.127313i	−0.900435	−	0.434991i	$-0.856752\pi$
$983$	−2.30457	+	3.99163i	−0.0735044	+	0.127313i	0.826931	+	0.562304i	$0.190085\pi$
$984$	2.39531	−	4.14880i	0.0763597	−	0.132259i
$985$	−0.209380	−	0.362657i	−0.00667140	−	0.0115552i
$986$	4.88442			0.155552
$987$	6.05158	+	13.1698i	0.192624	+	0.419200i
$988$	−20.1186			−0.640059
$989$	−4.05932	−	7.03095i	−0.129079	−	0.223571i
$990$	2.02966	−	3.51547i	0.0645068	−	0.111729i
$991$	20.9389	−	36.2673i	0.665147	−	1.15207i	−0.314099	−	0.949390i	$-0.601702\pi$
$991$	20.9389	−	36.2673i	0.665147	−	1.15207i	0.979246	−	0.202678i	$-0.0649643\pi$
$992$	3.23904	+	5.61018i	0.102840	+	0.178123i
$993$	20.6091			0.654011
$994$	18.9484	−	26.7410i	0.601007	−	0.848173i
$995$	−5.69988			−0.180698
$996$	0.0296601	+	0.0513728i	0.000939815	+	0.00162781i
$997$	−16.6640	+	28.8629i	−0.527754	+	0.914098i	0.471722	+	0.881747i	$0.343633\pi$
$997$	−16.6640	+	28.8629i	−0.527754	+	0.914098i	−0.999477	+	0.0323503i	$0.989701\pi$
$998$	−3.56882	+	6.18138i	−0.112969	+	0.195668i
$999$	−5.45463	−	9.44770i	−0.172577	−	0.298912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.k.277.2	✓	6
7.2	even	3	inner	966.2.i.k.415.2	yes	6
7.3	odd	6		6762.2.a.cf.1.3		3
7.4	even	3		6762.2.a.ce.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.2	✓	6	1.1	even	1	trivial
966.2.i.k.415.2	yes	6	7.2	even	3	inner
6762.2.a.ce.1.3		3	7.4	even	3
6762.2.a.cf.1.3		3	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-1.10469 - 2.40409i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-1.10469 - 2.40409i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.02966 + 3.51547i) q^{11} +(0.500000 + 0.866025i) q^{12} -6.26870 q^{13} +(1.52966 - 2.15874i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.92497 + 3.33415i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.60469 - 2.77940i) q^{19} +1.00000 q^{20} +(-2.63435 - 0.245357i) q^{21} -4.05932 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-3.13435 - 5.42885i) q^{26} -1.00000 q^{27} +(2.63435 + 0.245357i) q^{28} -1.26870 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-3.23904 + 5.61018i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.02966 + 3.51547i) q^{33} -3.84994 q^{34} +(-1.52966 + 2.15874i) q^{35} +1.00000 q^{36} +(5.45463 + 9.44770i) q^{37} +(1.60469 - 2.77940i) q^{38} +(-3.13435 + 5.42885i) q^{39} +(0.500000 + 0.866025i) q^{40} -4.79062 q^{41} +(-1.10469 - 2.40409i) q^{42} -8.11864 q^{43} +(-2.02966 - 3.51547i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-2.73904 - 4.74416i) q^{47} -1.00000 q^{48} +(-4.55932 + 5.31155i) q^{49} +4.00000 q^{50} +(1.92497 + 3.33415i) q^{51} +(3.13435 - 5.42885i) q^{52} +(4.55932 - 7.89697i) q^{53} +(-0.500000 - 0.866025i) q^{54} +4.05932 q^{55} +(1.10469 + 2.40409i) q^{56} -3.20938 q^{57} +(-0.634350 - 1.09873i) q^{58} +(3.42497 - 5.93222i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} -6.47808 q^{62} +(-1.52966 + 2.15874i) q^{63} +1.00000 q^{64} +(3.13435 + 5.42885i) q^{65} +(-2.02966 + 3.51547i) q^{66} +(6.73904 - 11.6724i) q^{67} +(-1.92497 - 3.33415i) q^{68} +1.00000 q^{69} +(-2.63435 - 0.245357i) q^{70} +12.3873 q^{71} +(0.500000 + 0.866025i) q^{72} +(-4.52966 + 7.84560i) q^{73} +(-5.45463 + 9.44770i) q^{74} +(-2.00000 - 3.46410i) q^{75} +3.20938 q^{76} +(10.6937 + 0.995981i) q^{77} -6.26870 q^{78} +(-4.69367 - 8.12968i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.39531 - 4.14880i) q^{82} +0.0593201 q^{83} +(1.52966 - 2.15874i) q^{84} +3.84994 q^{85} +(-4.05932 - 7.03095i) q^{86} +(-0.634350 + 1.09873i) q^{87} +(2.02966 - 3.51547i) q^{88} +(-5.45463 - 9.44770i) q^{89} -1.00000 q^{90} +(6.92497 + 15.0705i) q^{91} -1.00000 q^{92} +(3.23904 + 5.61018i) q^{93} +(2.73904 - 4.74416i) q^{94} +(-1.60469 + 2.77940i) q^{95} +(-0.500000 - 0.866025i) q^{96} -15.8061 q^{97} +(-6.87960 - 1.29271i) q^{98} +4.05932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{23} - 3 q^{24} + 12 q^{25} - 3 q^{26} - 6 q^{27} + 24 q^{29} - 3 q^{30} + 3 q^{32} - 6 q^{34} + 3 q^{35} + 6 q^{36} + 12 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 36 q^{41} - 3 q^{42} - 3 q^{45} - 3 q^{46} + 3 q^{47} - 6 q^{48} - 3 q^{49} + 24 q^{50} + 3 q^{51} + 3 q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 3 q^{60} - 30 q^{61} + 3 q^{63} + 6 q^{64} + 3 q^{65} + 21 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} + 3 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} + 12 q^{76} + 24 q^{77} - 6 q^{78} + 12 q^{79} - 3 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} - 3 q^{84} + 6 q^{85} + 12 q^{87} - 12 q^{89} - 6 q^{90} + 33 q^{91} - 6 q^{92} - 3 q^{94} - 6 q^{95} - 3 q^{96} - 12 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 - 3 * q^16 - 3 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^23 - 3 * q^24 + 12 * q^25 - 3 * q^26 - 6 * q^27 + 24 * q^29 - 3 * q^30 + 3 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 12 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 36 * q^41 - 3 * q^42 - 3 * q^45 - 3 * q^46 + 3 * q^47 - 6 * q^48 - 3 * q^49 + 24 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 3 * q^54 + 3 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 3 * q^60 - 30 * q^61 + 3 * q^63 + 6 * q^64 + 3 * q^65 + 21 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 + 3 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 + 12 * q^76 + 24 * q^77 - 6 * q^78 + 12 * q^79 - 3 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 - 3 * q^84 + 6 * q^85 + 12 * q^87 - 12 * q^89 - 6 * q^90 + 33 * q^91 - 6 * q^92 - 3 * q^94 - 6 * q^95 - 3 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more