LMFDB - Embedded newform 406.2.e.a.233.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [406,2,Mod(233,406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(406, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("406.233");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 406 = 2 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	406.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.24192632206$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			233.5
Root			$-1.80582 - 0.194943i$ of defining polynomial
Character	$\chi$	$=$	406.233
Dual form			406.2.e.a.291.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.22122 + 2.11522i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07173 + 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 - 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 + 2.56824i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.22122 + 2.11522i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07173 + 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 - 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 + 2.56824i) q^{9} +(-2.07173 - 3.58835i) q^{10} +(2.35349 + 4.07636i) q^{11} +(1.22122 - 2.11522i) q^{12} -1.91061 q^{13} +(2.44070 + 1.02127i) q^{14} -10.1202 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.38357 - 2.39642i) q^{17} +(-1.48277 - 2.56824i) q^{18} +(-2.02020 + 3.49909i) q^{19} +4.14347 q^{20} +(5.14085 - 3.91542i) q^{21} -4.70697 q^{22} +(1.08634 - 1.88160i) q^{23} +(1.22122 + 2.11522i) q^{24} +(-6.08417 - 10.5381i) q^{25} +(0.955306 - 1.65464i) q^{26} +0.0841506 q^{27} +(-2.10480 + 1.60307i) q^{28} -1.00000 q^{29} +(5.06010 - 8.76435i) q^{30} +(0.484522 + 0.839217i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.74826 + 9.95629i) q^{33} +2.76714 q^{34} +(10.1130 + 4.23160i) q^{35} +2.96555 q^{36} +(0.736701 - 1.27600i) q^{37} +(-2.02020 - 3.49909i) q^{38} +(-2.33328 - 4.04137i) q^{39} +(-2.07173 + 3.58835i) q^{40} +10.4741 q^{41} +(0.820425 + 6.40982i) q^{42} +7.84520 q^{43} +(2.35349 - 4.07636i) q^{44} +(-6.14382 - 10.6414i) q^{45} +(1.08634 + 1.88160i) q^{46} +(-5.86469 + 10.1579i) q^{47} -2.44245 q^{48} +(-6.77434 + 1.76305i) q^{49} +12.1683 q^{50} +(3.37930 - 5.85312i) q^{51} +(0.955306 + 1.65464i) q^{52} +(1.39041 + 2.40826i) q^{53} +(-0.0420753 + 0.0728765i) q^{54} -19.5032 q^{55} +(-0.335903 - 2.62434i) q^{56} -9.86847 q^{57} +(0.500000 - 0.866025i) q^{58} +(-1.70836 - 2.95897i) q^{59} +(5.06010 + 8.76435i) q^{60} +(-5.70959 + 9.88930i) q^{61} -0.969044 q^{62} +(7.23800 + 3.02862i) q^{63} +1.00000 q^{64} +(3.95828 - 6.85594i) q^{65} +(-5.74826 - 9.95629i) q^{66} +(1.13788 + 1.97086i) q^{67} +(-1.38357 + 2.39642i) q^{68} +5.30667 q^{69} +(-8.72115 + 6.64228i) q^{70} -6.24653 q^{71} +(-1.48277 + 2.56824i) q^{72} +(6.76148 + 11.7112i) q^{73} +(0.736701 + 1.27600i) q^{74} +(14.8603 - 25.7387i) q^{75} +4.04040 q^{76} +(9.90721 - 7.54561i) q^{77} +4.66657 q^{78} +(2.23146 - 3.86501i) q^{79} +(-2.07173 - 3.58835i) q^{80} +(4.55109 + 7.88271i) q^{81} +(-5.23706 + 9.07085i) q^{82} -6.06003 q^{83} +(-5.96128 - 2.49440i) q^{84} +11.4656 q^{85} +(-3.92260 + 6.79415i) q^{86} +(-1.22122 - 2.11522i) q^{87} +(2.35349 + 4.07636i) q^{88} +(-6.63308 + 11.4888i) q^{89} +12.2876 q^{90} +(0.641780 + 5.01410i) q^{91} -2.17268 q^{92} +(-1.18342 + 2.04974i) q^{93} +(-5.86469 - 10.1579i) q^{94} +(-8.37064 - 14.4984i) q^{95} +(1.22122 - 2.11522i) q^{96} +16.8452 q^{97} +(1.86032 - 6.74827i) q^{98} -13.9587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/406\mathbb{Z}\right)^\times$.

$n$	$59$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.22122	+	2.11522i	0.705074	+	1.22122i	0.966665	+	0.256045i	$0.0824194\pi$
$3$	1.22122	+	2.11522i	0.705074	+	1.22122i	−0.261591	+	0.965179i	$0.584247\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.07173	+	3.58835i	−0.926508	+	1.60476i	−0.137390	+	0.990517i	$0.543871\pi$
$5$	−2.07173	+	3.58835i	−0.926508	+	1.60476i	−0.789118	+	0.614241i	$0.789462\pi$
$6$	−2.44245			−0.997125
$7$	−0.335903	−	2.62434i	−0.126959	−	0.991908i
$7$	−0.335903	−	2.62434i	−0.126959	−	0.991908i
$8$	1.00000			0.353553
$9$	−1.48277	+	2.56824i	−0.494258	+	0.856080i
$10$	−2.07173	−	3.58835i	−0.655140	−	1.13474i
$11$	2.35349	+	4.07636i	0.709603	+	1.22907i	0.965005	+	0.262233i	$0.0844589\pi$
$11$	2.35349	+	4.07636i	0.709603	+	1.22907i	−0.255402	+	0.966835i	$0.582208\pi$
$12$	1.22122	−	2.11522i	0.352537	−	0.610612i
$13$	−1.91061			−0.529908			−0.264954	−	0.964261i	$-0.585357\pi$
$13$	−1.91061			−0.529908			−0.264954	+	0.964261i	$0.585357\pi$
$14$	2.44070	+	1.02127i	0.652304	+	0.272946i
$15$	−10.1202			−2.61302
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.38357	−	2.39642i	−0.335565	−	0.581216i	0.648028	−	0.761617i	$-0.275594\pi$
$17$	−1.38357	−	2.39642i	−0.335565	−	0.581216i	−0.983593	+	0.180400i	$0.942261\pi$
$18$	−1.48277	−	2.56824i	−0.349493	−	0.605340i
$19$	−2.02020	+	3.49909i	−0.463466	+	0.802747i	−0.999131	−	0.0416840i	$-0.986728\pi$
$19$	−2.02020	+	3.49909i	−0.463466	+	0.802747i	0.535665	+	0.844431i	$0.320061\pi$
$20$	4.14347			0.926508
$21$	5.14085	−	3.91542i	1.12183	−	0.854414i
$22$	−4.70697			−1.00353
$23$	1.08634	−	1.88160i	0.226518	−	0.392341i	−0.730256	−	0.683174i	$-0.760599\pi$
$23$	1.08634	−	1.88160i	0.226518	−	0.392341i	0.956774	+	0.290833i	$0.0939324\pi$
$24$	1.22122	+	2.11522i	0.249281	+	0.431768i
$25$	−6.08417	−	10.5381i	−1.21683	−	2.10762i
$26$	0.955306	−	1.65464i	0.187351	−	0.324501i
$27$	0.0841506			0.0161948
$28$	−2.10480	+	1.60307i	−0.397769	+	0.302952i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	5.06010	−	8.76435i	0.923844	−	1.60014i
$31$	0.484522	+	0.839217i	0.0870227	+	0.150728i	0.906251	−	0.422739i	$-0.138931\pi$
$31$	0.484522	+	0.839217i	0.0870227	+	0.150728i	−0.819229	+	0.573467i	$0.805598\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−5.74826	+	9.95629i	−1.00064	+	1.73317i
$34$	2.76714			0.474561
$35$	10.1130	+	4.23160i	1.70940	+	0.715271i
$36$	2.96555			0.494258
$37$	0.736701	−	1.27600i	0.121113	−	0.209774i	−0.799094	−	0.601206i	$-0.794687\pi$
$37$	0.736701	−	1.27600i	0.121113	−	0.209774i	0.920207	+	0.391432i	$0.128020\pi$
$38$	−2.02020	−	3.49909i	−0.327720	−	0.567628i
$39$	−2.33328	−	4.04137i	−0.373625	−	0.647137i
$40$	−2.07173	+	3.58835i	−0.327570	+	0.567368i
$41$	10.4741			1.63578			0.817891	−	0.575373i	$-0.195143\pi$
$41$	10.4741			1.63578			0.817891	+	0.575373i	$0.195143\pi$
$42$	0.820425	+	6.40982i	0.126594	+	0.989056i
$43$	7.84520			1.19638			0.598191	−	0.801353i	$-0.295886\pi$
$43$	7.84520			1.19638			0.598191	+	0.801353i	$0.295886\pi$
$44$	2.35349	−	4.07636i	0.354801	−	0.614534i
$45$	−6.14382	−	10.6414i	−0.915867	−	1.58633i
$46$	1.08634	+	1.88160i	0.160172	+	0.277427i
$47$	−5.86469	+	10.1579i	−0.855453	+	1.48169i	0.0207706	+	0.999784i	$0.493388\pi$
$47$	−5.86469	+	10.1579i	−0.855453	+	1.48169i	−0.876224	+	0.481904i	$0.839945\pi$
$48$	−2.44245			−0.352537
$49$	−6.77434	+	1.76305i	−0.967763	+	0.251864i
$50$	12.1683			1.72086
$51$	3.37930	−	5.85312i	0.473197	−	0.819601i
$52$	0.955306	+	1.65464i	0.132477	+	0.229457i
$53$	1.39041	+	2.40826i	0.190988	+	0.330800i	0.945578	−	0.325396i	$-0.105498\pi$
$53$	1.39041	+	2.40826i	0.190988	+	0.330800i	−0.754590	+	0.656196i	$0.772164\pi$
$54$	−0.0420753	+	0.0728765i	−0.00572572	+	0.00991724i
$55$	−19.5032			−2.62981
$56$	−0.335903	−	2.62434i	−0.0448869	−	0.350692i
$57$	−9.86847			−1.30711
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	−1.70836	−	2.95897i	−0.222410	−	0.385226i	0.733129	−	0.680089i	$-0.238059\pi$
$59$	−1.70836	−	2.95897i	−0.222410	−	0.385226i	−0.955539	+	0.294864i	$0.904726\pi$
$60$	5.06010	+	8.76435i	0.653256	+	1.13147i
$61$	−5.70959	+	9.88930i	−0.731038	+	1.26620i	0.225402	+	0.974266i	$0.427631\pi$
$61$	−5.70959	+	9.88930i	−0.731038	+	1.26620i	−0.956440	+	0.291929i	$0.905703\pi$
$62$	−0.969044			−0.123069
$63$	7.23800	+	3.02862i	0.911903	+	0.381571i
$64$	1.00000			0.125000
$65$	3.95828	−	6.85594i	0.490964	−	0.850375i
$66$	−5.74826	−	9.95629i	−0.707562	−	1.22553i
$67$	1.13788	+	1.97086i	0.139014	+	0.240779i	0.927124	−	0.374756i	$-0.122273\pi$
$67$	1.13788	+	1.97086i	0.139014	+	0.240779i	−0.788110	+	0.615535i	$0.788940\pi$
$68$	−1.38357	+	2.39642i	−0.167783	+	0.290608i
$69$	5.30667			0.638848
$70$	−8.72115	+	6.64228i	−1.04238	+	0.793904i
$71$	−6.24653			−0.741327			−0.370664	−	0.928767i	$-0.620870\pi$
$71$	−6.24653			−0.741327			−0.370664	+	0.928767i	$0.620870\pi$
$72$	−1.48277	+	2.56824i	−0.174747	+	0.302670i
$73$	6.76148	+	11.7112i	0.791371	+	1.37070i	0.925118	+	0.379680i	$0.123966\pi$
$73$	6.76148	+	11.7112i	0.791371	+	1.37070i	−0.133747	+	0.991016i	$0.542701\pi$
$74$	0.736701	+	1.27600i	0.0856398	+	0.148332i
$75$	14.8603	−	25.7387i	1.71591	−	2.97205i
$76$	4.04040			0.463466
$77$	9.90721	−	7.54561i	1.12903	−	0.859902i
$78$	4.66657			0.528385
$79$	2.23146	−	3.86501i	0.251059	−	0.434847i	−0.712758	−	0.701410i	$-0.752554\pi$
$79$	2.23146	−	3.86501i	0.251059	−	0.434847i	0.963818	+	0.266562i	$0.0858877\pi$
$80$	−2.07173	−	3.58835i	−0.231627	−	0.401190i
$81$	4.55109	+	7.88271i	0.505676	+	0.875857i
$82$	−5.23706	+	9.07085i	−0.578336	+	1.00171i
$83$	−6.06003			−0.665175			−0.332587	−	0.943072i	$-0.607922\pi$
$83$	−6.06003			−0.665175			−0.332587	+	0.943072i	$0.607922\pi$
$84$	−5.96128	−	2.49440i	−0.650428	−	0.272161i
$85$	11.4656			1.24362
$86$	−3.92260	+	6.79415i	−0.422985	+	0.732632i
$87$	−1.22122	−	2.11522i	−0.130929	−	0.226775i
$88$	2.35349	+	4.07636i	0.250882	+	0.434541i
$89$	−6.63308	+	11.4888i	−0.703105	+	1.21781i	0.264266	+	0.964450i	$0.414870\pi$
$89$	−6.63308	+	11.4888i	−0.703105	+	1.21781i	−0.967371	+	0.253364i	$0.918463\pi$
$90$	12.2876			1.29523
$91$	0.641780	+	5.01410i	0.0672768	+	0.525620i
$92$	−2.17268			−0.226518
$93$	−1.18342	+	2.04974i	−0.122715	+	0.212548i
$94$	−5.86469	−	10.1579i	−0.604897	−	1.04771i
$95$	−8.37064	−	14.4984i	−0.858810	−	1.48750i
$96$	1.22122	−	2.11522i	0.124641	−	0.215884i
$97$	16.8452			1.71037			0.855186	−	0.518322i	$-0.173443\pi$
$97$	16.8452			1.71037			0.855186	+	0.518322i	$0.173443\pi$
$98$	1.86032	−	6.74827i	0.187921	−	0.681679i
$99$	−13.9587			−1.40291
$100$	−6.08417	+	10.5381i	−0.608417	+	1.05381i
$101$	6.21303	+	10.7613i	0.618219	+	1.07079i	0.989811	+	0.142391i	$0.0454790\pi$
$101$	6.21303	+	10.7613i	0.618219	+	1.07079i	−0.371591	+	0.928396i	$0.621188\pi$
$102$	3.37930	+	5.85312i	0.334601	+	0.579545i
$103$	8.08592	−	14.0052i	0.796729	−	1.37998i	−0.125007	−	0.992156i	$-0.539895\pi$
$103$	8.08592	−	14.0052i	0.796729	−	1.37998i	0.921736	−	0.387819i	$-0.126771\pi$
$104$	−1.91061			−0.187351
$105$	3.39941	+	26.5589i	0.331748	+	2.59188i
$106$	−2.78082			−0.270097
$107$	−5.31229	+	9.20116i	−0.513558	+	0.889509i	0.486318	+	0.873782i	$0.338340\pi$
$107$	−5.31229	+	9.20116i	−0.513558	+	0.889509i	−0.999876	+	0.0157273i	$0.994994\pi$
$108$	−0.0420753	−	0.0728765i	−0.00404870	−	0.00701255i
$109$	−3.04942	−	5.28175i	−0.292081	−	0.505900i	0.682220	−	0.731147i	$-0.261014\pi$
$109$	−3.04942	−	5.28175i	−0.292081	−	0.505900i	−0.974302	+	0.225247i	$0.927681\pi$
$110$	9.75159	−	16.8903i	0.929778	−	1.61042i
$111$	3.59871			0.341574
$112$	2.44070	+	1.02127i	0.230624	+	0.0965010i
$113$	14.5875			1.37228			0.686139	−	0.727471i	$-0.259304\pi$
$113$	14.5875			1.37228			0.686139	+	0.727471i	$0.259304\pi$
$114$	4.93423	−	8.54635i	0.462133	−	0.800439i
$115$	4.50123	+	7.79635i	0.419741	+	0.727014i
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	2.83300	−	4.90691i	0.261911	−	0.453644i
$118$	3.41673			0.314535
$119$	−5.82427	+	4.43593i	−0.533910	+	0.406641i
$120$	−10.1202			−0.923844
$121$	−5.57779	+	9.66102i	−0.507072	+	0.878274i
$122$	−5.70959	−	9.88930i	−0.516922	−	0.895335i
$123$	12.7912	+	22.1551i	1.15335	+	1.99766i
$124$	0.484522	−	0.839217i	0.0435114	−	0.0753639i
$125$	29.7018			2.65661
$126$	−6.24187	+	4.75398i	−0.556070	+	0.423518i
$127$	5.46381			0.484835			0.242418	−	0.970172i	$-0.422060\pi$
$127$	5.46381			0.484835			0.242418	+	0.970172i	$0.422060\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	9.58075	+	16.5943i	0.843538	+	1.46105i
$130$	3.95828	+	6.85594i	0.347164	+	0.601306i
$131$	6.70909	−	11.6205i	0.586176	−	1.01529i	−0.408552	−	0.912735i	$-0.633966\pi$
$131$	6.70909	−	11.6205i	0.586176	−	1.01529i	0.994728	−	0.102551i	$-0.0327005\pi$
$132$	11.4965			1.00064
$133$	9.86140	+	4.12634i	0.855092	+	0.357799i
$134$	−2.27575			−0.196595
$135$	−0.174338	+	0.301962i	−0.0150046	+	0.0259887i
$136$	−1.38357	−	2.39642i	−0.118640	−	0.205491i
$137$	−8.55161	−	14.8118i	−0.730613	−	1.26546i	−0.956621	−	0.291334i	$-0.905901\pi$
$137$	−8.55161	−	14.8118i	−0.730613	−	1.26546i	0.226008	−	0.974125i	$-0.427432\pi$
$138$	−2.65333	+	4.59571i	−0.225867	+	0.391213i
$139$	−3.90711			−0.331397			−0.165699	−	0.986176i	$-0.552988\pi$
$139$	−3.90711			−0.331397			−0.165699	+	0.986176i	$0.552988\pi$
$140$	−1.39180	−	10.8739i	−0.117629	−	0.919010i
$141$	−28.6484			−2.41263
$142$	3.12327	−	5.40966i	0.262099	−	0.453968i
$143$	−4.49660	−	7.78834i	−0.376024	−	0.651293i
$144$	−1.48277	−	2.56824i	−0.123564	−	0.214020i
$145$	2.07173	−	3.58835i	0.172048	−	0.297996i
$146$	−13.5230			−1.11917
$147$	−12.0022	−	12.1761i	−0.989926	−	1.00427i
$148$	−1.47340			−0.121113
$149$	3.74913	−	6.49369i	0.307141	−	0.531984i	−0.670595	−	0.741824i	$-0.733961\pi$
$149$	3.74913	−	6.49369i	0.307141	−	0.531984i	0.977736	+	0.209840i	$0.0672943\pi$
$150$	14.8603	+	25.7387i	1.21333	+	2.10156i
$151$	−4.70909	−	8.15638i	−0.383220	−	0.663757i	0.608300	−	0.793707i	$-0.291852\pi$
$151$	−4.70909	−	8.15638i	−0.383220	−	0.663757i	−0.991521	+	0.129950i	$0.958518\pi$
$152$	−2.02020	+	3.49909i	−0.163860	+	0.283814i
$153$	8.20609			0.663423
$154$	1.58109	+	12.3527i	0.127408	+	0.995409i
$155$	−4.01520			−0.322509
$156$	−2.33328	+	4.04137i	−0.186812	+	0.323568i
$157$	−8.91431	−	15.4400i	−0.711439	−	1.23225i	−0.964317	−	0.264751i	$-0.914710\pi$
$157$	−8.91431	−	15.4400i	−0.711439	−	1.23225i	0.252878	−	0.967498i	$-0.418623\pi$
$158$	2.23146	+	3.86501i	0.177526	+	0.307484i
$159$	−3.39600	+	5.88205i	−0.269321	+	0.466477i
$160$	4.14347			0.327570
$161$	−5.30287	−	2.21890i	−0.417925	−	0.174874i
$162$	−9.10217			−0.715134
$163$	5.43945	−	9.42141i	0.426051	−	0.737942i	−0.570467	−	0.821320i	$-0.693238\pi$
$163$	5.43945	−	9.42141i	0.426051	−	0.737942i	0.996518	+	0.0833788i	$0.0265711\pi$
$164$	−5.23706	−	9.07085i	−0.408945	−	0.708314i
$165$	−23.8178	−	41.2536i	−1.85421	−	3.21159i
$166$	3.03002	−	5.24814i	0.235175	−	0.407335i
$167$	16.0326			1.24064			0.620318	−	0.784350i	$-0.287003\pi$
$167$	16.0326			1.24064			0.620318	+	0.784350i	$0.287003\pi$
$168$	5.14085	−	3.91542i	0.396625	−	0.302081i
$169$	−9.34956			−0.719197
$170$	−5.73279	+	9.92948i	−0.439685	+	0.761556i
$171$	−5.99100	−	10.3767i	−0.458143	−	0.793528i
$172$	−3.92260	−	6.79415i	−0.299096	−	0.518049i
$173$	3.09439	−	5.35964i	0.235262	−	0.407486i	−0.724087	−	0.689709i	$-0.757739\pi$
$173$	3.09439	−	5.35964i	0.235262	−	0.407486i	0.959349	+	0.282223i	$0.0910719\pi$
$174$	2.44245			0.185161
$175$	−25.6118	+	19.5067i	−1.93607	+	1.47457i
$176$	−4.70697			−0.354801
$177$	4.17259	−	7.22714i	0.313631	−	0.543225i
$178$	−6.63308	−	11.4888i	−0.497170	−	0.861124i
$179$	−0.602699	−	1.04391i	−0.0450479	−	0.0780252i	0.842622	−	0.538505i	$-0.181011\pi$
$179$	−0.602699	−	1.04391i	−0.0450479	−	0.0780252i	−0.887670	+	0.460480i	$0.847677\pi$
$180$	−6.14382	+	10.6414i	−0.457934	+	0.793164i
$181$	6.95105			0.516668			0.258334	−	0.966056i	$-0.416827\pi$
$181$	6.95105			0.516668			0.258334	+	0.966056i	$0.416827\pi$
$182$	−4.66323	−	1.95125i	−0.345661	−	0.144636i
$183$	−27.8907			−2.06174
$184$	1.08634	−	1.88160i	0.0800862	−	0.138713i
$185$	3.05250	+	5.28708i	0.224424	+	0.388714i
$186$	−1.18342	−	2.04974i	−0.0867725	−	0.150294i
$187$	6.51243	−	11.2799i	0.476236	−	0.824865i
$188$	11.7294			0.855453
$189$	−0.0282664	−	0.220840i	−0.00205608	−	0.0160637i
$190$	16.7413			1.21454
$191$	3.40424	−	5.89631i	0.246322	−	0.426642i	−0.716181	−	0.697915i	$-0.754111\pi$
$191$	3.40424	−	5.89631i	0.246322	−	0.426642i	0.962502	+	0.271273i	$0.0874446\pi$
$192$	1.22122	+	2.11522i	0.0881342	+	0.152653i
$193$	1.94832	+	3.37459i	0.140243	+	0.242908i	0.927588	−	0.373604i	$-0.121878\pi$
$193$	1.94832	+	3.37459i	0.140243	+	0.242908i	−0.787345	+	0.616513i	$0.788545\pi$
$194$	−8.42260	+	14.5884i	−0.604708	+	1.04738i
$195$	19.3358			1.38466
$196$	4.91401	+	4.98523i	0.351001	+	0.356088i
$197$	15.5624			1.10877			0.554386	−	0.832260i	$-0.312953\pi$
$197$	15.5624			1.10877			0.554386	+	0.832260i	$0.312953\pi$
$198$	6.97937	−	12.0886i	0.496002	−	0.859101i
$199$	−12.2868	−	21.2813i	−0.870986	−	1.50859i	−0.860978	−	0.508642i	$-0.830148\pi$
$199$	−12.2868	−	21.2813i	−0.870986	−	1.50859i	−0.0100081	−	0.999950i	$-0.503186\pi$
$200$	−6.08417	−	10.5381i	−0.430216	−	0.745155i
$201$	−2.77920	+	4.81372i	−0.196030	+	0.339533i
$202$	−12.4261			−0.874294
$203$	0.335903	+	2.62434i	0.0235758	+	0.184193i
$204$	−6.75860			−0.473197
$205$	−21.6996	+	37.5848i	−1.51556	+	2.62504i
$206$	8.08592	+	14.0052i	0.563372	+	0.975790i
$207$	3.22160	+	5.57997i	0.223917	+	0.387835i
$208$	0.955306	−	1.65464i	0.0662386	−	0.114729i
$209$	−19.0181			−1.31551
$210$	−24.7004	−	10.3355i	−1.70449	−	0.713215i
$211$	8.65646			0.595935			0.297968	−	0.954576i	$-0.403691\pi$
$211$	8.65646			0.595935			0.297968	+	0.954576i	$0.403691\pi$
$212$	1.39041	−	2.40826i	0.0954938	−	0.165400i
$213$	−7.62841	−	13.2128i	−0.522690	−	0.905326i
$214$	−5.31229	−	9.20116i	−0.363141	−	0.628978i
$215$	−16.2532	+	28.1513i	−1.10846	+	1.91990i
$216$	0.0841506			0.00572572
$217$	2.03964	−	1.55345i	0.138460	−	0.105455i
$218$	6.09884			0.413065
$219$	−16.5146	+	28.6040i	−1.11595	+	1.93288i
$220$	9.75159	+	16.8903i	0.657452	+	1.13874i
$221$	2.64347	+	4.57862i	0.177819	+	0.307991i
$222$	−1.79935	+	3.11657i	−0.120765	+	0.209171i
$223$	−10.9191			−0.731194			−0.365597	−	0.930773i	$-0.619135\pi$
$223$	−10.9191			−0.731194			−0.365597	+	0.930773i	$0.619135\pi$
$224$	−2.10480	+	1.60307i	−0.140633	+	0.107110i
$225$	36.0858			2.40572
$226$	−7.29376	+	12.6332i	−0.485173	+	0.840345i
$227$	5.24754	+	9.08901i	0.348292	+	0.603259i	0.985946	−	0.167064i	$-0.0534286\pi$
$227$	5.24754	+	9.08901i	0.348292	+	0.603259i	−0.637655	+	0.770322i	$0.720095\pi$
$228$	4.93423	+	8.54635i	0.326778	+	0.565996i
$229$	3.75763	−	6.50840i	0.248311	−	0.430087i	−0.714746	−	0.699384i	$-0.753458\pi$
$229$	3.75763	−	6.50840i	0.248311	−	0.430087i	0.963057	+	0.269297i	$0.0867912\pi$
$230$	−9.00245			−0.593604
$231$	28.0596	+	11.7411i	1.84618	+	0.772505i
$232$	−1.00000			−0.0656532
$233$	−2.57131	+	4.45364i	−0.168452	+	0.291767i	−0.937876	−	0.346971i	$-0.887210\pi$
$233$	−2.57131	+	4.45364i	−0.168452	+	0.291767i	0.769424	+	0.638739i	$0.220543\pi$
$234$	2.83300	+	4.90691i	0.185199	+	0.320775i
$235$	−24.3002	−	42.0891i	−1.58517	−	2.74559i
$236$	−1.70836	+	2.95897i	−0.111205	+	0.192613i
$237$	10.9005			0.708061
$238$	−0.929492	−	7.26193i	−0.0602500	−	0.470721i
$239$	0.749673			0.0484923			0.0242462	−	0.999706i	$-0.492281\pi$
$239$	0.749673			0.0484923			0.0242462	+	0.999706i	$0.492281\pi$
$240$	5.06010	−	8.76435i	0.326628	−	0.565737i
$241$	4.50979	+	7.81119i	0.290501	+	0.503163i	0.973928	−	0.226856i	$-0.0728446\pi$
$241$	4.50979	+	7.81119i	0.290501	+	0.503163i	−0.683427	+	0.730019i	$0.739511\pi$
$242$	−5.57779	−	9.66102i	−0.358554	−	0.621034i
$243$	−10.9896	+	19.0345i	−0.704981	+	1.22106i
$244$	11.4192			0.731038
$245$	7.70820	−	27.9613i	0.492459	−	1.78638i
$246$	−25.5825			−1.63108
$247$	3.85982	−	6.68541i	0.245595	−	0.425382i
$248$	0.484522	+	0.839217i	0.0307672	+	0.0532903i
$249$	−7.40065	−	12.8183i	−0.468997	−	0.812327i
$250$	−14.8509	+	25.7225i	−0.939252	+	1.62683i
$251$	−29.1169			−1.83784			−0.918921	−	0.394441i	$-0.870938\pi$
$251$	−29.1169			−1.83784			−0.918921	+	0.394441i	$0.870938\pi$
$252$	−0.996136	−	7.78261i	−0.0627507	−	0.490258i
$253$	10.2268			0.642951
$254$	−2.73191	+	4.73180i	−0.171415	+	0.296900i
$255$	14.0020	+	24.2522i	0.876841	+	1.51873i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.6138	−	20.1156i	0.724447	−	1.25478i	−0.234754	−	0.972055i	$-0.575428\pi$
$257$	11.6138	−	20.1156i	0.724447	−	1.25478i	0.959201	−	0.282725i	$-0.0912383\pi$
$258$	−19.1615			−1.19294
$259$	−3.59613	−	1.50474i	−0.223453	−	0.0935001i
$260$	−7.91656			−0.490964
$261$	1.48277	−	2.56824i	0.0917814	−	0.158970i
$262$	6.70909	+	11.6205i	0.414489	+	0.717916i
$263$	10.2517	+	17.7564i	0.632145	+	1.09491i	0.987112	+	0.160028i	$0.0511585\pi$
$263$	10.2517	+	17.7564i	0.632145	+	1.09491i	−0.354968	+	0.934879i	$0.615508\pi$
$264$	−5.74826	+	9.95629i	−0.353781	+	0.612767i
$265$	−11.5222			−0.707806
$266$	−8.50422	+	6.47705i	−0.521427	+	0.397134i
$267$	−32.4019			−1.98296
$268$	1.13788	−	1.97086i	0.0695068	−	0.120389i
$269$	5.69760	+	9.86853i	0.347389	+	0.601695i	0.985785	−	0.168013i	$-0.0537351\pi$
$269$	5.69760	+	9.86853i	0.347389	+	0.601695i	−0.638396	+	0.769708i	$0.720402\pi$
$270$	−0.174338	−	0.301962i	−0.0106098	−	0.0183768i
$271$	−8.98753	+	15.5669i	−0.545954	+	0.945620i	0.452592	+	0.891717i	$0.350499\pi$
$271$	−8.98753	+	15.5669i	−0.545954	+	0.945620i	−0.998546	+	0.0539021i	$0.982834\pi$
$272$	2.76714			0.167783
$273$	−9.82217	+	7.48084i	−0.594465	+	0.452761i
$274$	17.1032			1.03324
$275$	28.6380	−	49.6025i	1.72694	−	2.99114i
$276$	−2.65333	−	4.59571i	−0.159712	−	0.276629i
$277$	1.04016	+	1.80161i	0.0624971	+	0.108248i	0.895581	−	0.444898i	$-0.146760\pi$
$277$	1.04016	+	1.80161i	0.0624971	+	0.108248i	−0.833084	+	0.553147i	$0.813427\pi$
$278$	1.95356	−	3.38366i	0.117167	−	0.202938i
$279$	−2.87375			−0.172047
$280$	10.1130	+	4.23160i	0.604365	+	0.252887i
$281$	7.35741			0.438906			0.219453	−	0.975623i	$-0.429573\pi$
$281$	7.35741			0.438906			0.219453	+	0.975623i	$0.429573\pi$
$282$	14.3242	−	24.8102i	0.852994	−	1.47743i
$283$	3.04027	+	5.26590i	0.180725	+	0.313025i	0.942128	−	0.335254i	$-0.108822\pi$
$283$	3.04027	+	5.26590i	0.180725	+	0.313025i	−0.761403	+	0.648279i	$0.775489\pi$
$284$	3.12327	+	5.40966i	0.185332	+	0.321004i
$285$	20.4448	−	35.4115i	1.21105	−	2.09760i
$286$	8.99320			0.531779
$287$	−3.51829	−	27.4877i	−0.207678	−	1.62255i
$288$	2.96555			0.174747
$289$	4.67146	−	8.09120i	0.274792	−	0.475953i
$290$	2.07173	+	3.58835i	0.121656	+	0.210715i
$291$	20.5718	+	35.6313i	1.20594	+	2.08875i
$292$	6.76148	−	11.7112i	0.395686	−	0.685348i
$293$	13.7159			0.801291			0.400646	−	0.916233i	$-0.368786\pi$
$293$	13.7159			0.801291			0.400646	+	0.916233i	$0.368786\pi$
$294$	16.5460	−	4.30615i	0.964980	−	0.251140i
$295$	14.1571			0.824259
$296$	0.736701	−	1.27600i	0.0428199	−	0.0741662i
$297$	0.198047	+	0.343028i	0.0114919	+	0.0199045i
$298$	3.74913	+	6.49369i	0.217181	+	0.376169i
$299$	−2.07558	+	3.59501i	−0.120034	+	0.207905i
$300$	−29.7205			−1.71591
$301$	−2.63523	−	20.5885i	−0.151892	−	1.18670i
$302$	9.41817			0.541955
$303$	−15.1750	+	26.2839i	−0.871780	+	1.50997i
$304$	−2.02020	−	3.49909i	−0.115867	−	0.200687i
$305$	−23.6575	−	40.9760i	−1.35463	−	2.34628i
$306$	−4.10305	+	7.10668i	−0.234556	+	0.406262i
$307$	7.64494			0.436320			0.218160	−	0.975913i	$-0.429995\pi$
$307$	7.64494			0.436320			0.218160	+	0.975913i	$0.429995\pi$
$308$	−11.4883	−	4.80709i	−0.654606	−	0.273909i
$309$	39.4988			2.24701
$310$	2.00760	−	3.47727i	0.114024	−	0.197496i
$311$	−12.2126	−	21.1528i	−0.692512	−	1.19947i	−0.971012	−	0.239030i	$-0.923171\pi$
$311$	−12.2126	−	21.1528i	−0.692512	−	1.19947i	0.278500	−	0.960436i	$-0.410163\pi$
$312$	−2.33328	−	4.04137i	−0.132096	−	0.228797i
$313$	9.13225	−	15.8175i	0.516185	−	0.894059i	−0.483638	−	0.875268i	$-0.660685\pi$
$313$	9.13225	−	15.8175i	0.516185	−	0.894059i	0.999823	−	0.0187912i	$-0.00598179\pi$
$314$	17.8286			1.00613
$315$	−25.8630	+	19.6980i	−1.45721	+	1.10986i
$316$	−4.46293			−0.251059
$317$	5.21086	−	9.02547i	0.292671	−	0.506921i	−0.681770	−	0.731567i	$-0.738789\pi$
$317$	5.21086	−	9.02547i	0.292671	−	0.506921i	0.974440	+	0.224646i	$0.0721227\pi$
$318$	−3.39600	−	5.88205i	−0.190438	−	0.329849i
$319$	−2.35349	−	4.07636i	−0.131770	−	0.228232i
$320$	−2.07173	+	3.58835i	−0.115813	+	0.200595i
$321$	−25.9500			−1.44839
$322$	4.57306	−	3.48297i	0.254846	−	0.194098i
$323$	11.1804			0.622093
$324$	4.55109	−	7.88271i	0.252838	−	0.437929i
$325$	11.6245	+	20.1342i	0.644810	+	1.11684i
$326$	5.43945	+	9.42141i	0.301263	+	0.521804i
$327$	7.44804	−	12.9004i	0.411878	−	0.713393i
$328$	10.4741			0.578336
$329$	28.6279	+	11.9789i	1.57831	+	0.660417i
$330$	47.6355			2.62225
$331$	−2.34176	+	4.05604i	−0.128715	+	0.222940i	−0.923179	−	0.384371i	$-0.874418\pi$
$331$	−2.34176	+	4.05604i	−0.128715	+	0.222940i	0.794464	+	0.607311i	$0.207752\pi$
$332$	3.03002	+	5.24814i	0.166294	+	0.288029i
$333$	2.18472	+	3.78405i	0.119722	+	0.207365i
$334$	−8.01628	+	13.8846i	−0.438631	+	0.759731i
$335$	−9.42950			−0.515189
$336$	0.820425	+	6.40982i	0.0447579	+	0.349684i
$337$	−25.3719			−1.38210			−0.691048	−	0.722809i	$-0.742851\pi$
$337$	−25.3719			−1.38210			−0.691048	+	0.722809i	$0.742851\pi$
$338$	4.67478	−	8.09696i	0.254275	−	0.440416i
$339$	17.8146	+	30.8558i	0.967557	+	1.67586i
$340$	−5.73279	−	9.92948i	−0.310904	−	0.538501i
$341$	−2.28063	+	3.95017i	−0.123503	+	0.213914i
$342$	11.9820			0.647913
$343$	6.90236	+	17.1860i	0.372692	+	0.927955i
$344$	7.84520			0.422985
$345$	−10.9940	+	19.0422i	−0.591897	+	1.02520i
$346$	3.09439	+	5.35964i	0.166355	+	0.288136i
$347$	0.965287	+	1.67193i	0.0518193	+	0.0897537i	0.890772	−	0.454451i	$-0.150165\pi$
$347$	0.965287	+	1.67193i	0.0518193	+	0.0897537i	−0.838952	+	0.544205i	$0.816831\pi$
$348$	−1.22122	+	2.11522i	−0.0654644	+	0.113388i
$349$	1.95782			0.104800			0.0523998	−	0.998626i	$-0.483313\pi$
$349$	1.95782			0.104800			0.0523998	+	0.998626i	$0.483313\pi$
$350$	−4.08738	−	31.9339i	−0.218480	−	1.70694i
$351$	−0.160779			−0.00858175
$352$	2.35349	−	4.07636i	0.125441	−	0.217271i
$353$	8.16649	+	14.1448i	0.434658	+	0.752850i	0.997268	−	0.0738726i	$-0.0235358\pi$
$353$	8.16649	+	14.1448i	0.434658	+	0.752850i	−0.562609	+	0.826723i	$0.690202\pi$
$354$	4.17259	+	7.22714i	0.221771	+	0.384118i
$355$	12.9412	−	22.4147i	0.686845	−	1.18965i
$356$	13.2662			0.703105
$357$	−16.4957	−	6.90236i	−0.873045	−	0.365312i
$358$	1.20540			0.0637073
$359$	5.89004	−	10.2019i	0.310865	−	0.538433i	−0.667685	−	0.744444i	$-0.732715\pi$
$359$	5.89004	−	10.2019i	0.310865	−	0.538433i	0.978550	+	0.206010i	$0.0660481\pi$
$360$	−6.14382	−	10.6414i	−0.323808	−	0.560852i
$361$	1.33757	+	2.31674i	0.0703985	+	0.121934i
$362$	−3.47553	+	6.01979i	−0.182670	+	0.316393i
$363$	−27.2469			−1.43009
$364$	4.02145	−	3.06285i	0.210781	−	0.160537i
$365$	−56.0320			−2.93285
$366$	13.9454	−	24.1541i	0.728936	−	1.26255i
$367$	−17.8219	−	30.8684i	−0.930295	−	1.61132i	−0.782816	−	0.622253i	$-0.786218\pi$
$367$	−17.8219	−	30.8684i	−0.930295	−	1.61132i	−0.147478	−	0.989065i	$-0.547116\pi$
$368$	1.08634	+	1.88160i	0.0566295	+	0.0980852i
$369$	−15.5307	+	26.9000i	−0.808498	+	1.40036i
$370$	−6.10500			−0.317384
$371$	5.85306	−	4.45785i	0.303876	−	0.231440i
$372$	2.36684			0.122715
$373$	−8.87414	+	15.3705i	−0.459486	+	0.795852i	−0.998934	−	0.0461665i	$-0.985300\pi$
$373$	−8.87414	+	15.3705i	−0.459486	+	0.795852i	0.539448	+	0.842019i	$0.318633\pi$
$374$	6.51243	+	11.2799i	0.336750	+	0.583268i
$375$	36.2725	+	62.8258i	1.87310	+	3.24431i
$376$	−5.86469	+	10.1579i	−0.302448	+	0.523856i
$377$	1.91061			0.0984015
$378$	0.205386	+	0.0859405i	0.0105639	+	0.00442030i
$379$	−15.2263			−0.782124			−0.391062	−	0.920364i	$-0.627892\pi$
$379$	−15.2263			−0.782124			−0.391062	+	0.920364i	$0.627892\pi$
$380$	−8.37064	+	14.4984i	−0.429405	+	0.743751i
$381$	6.67254	+	11.5572i	0.341844	+	0.592092i
$382$	3.40424	+	5.89631i	0.174176	+	0.301681i
$383$	7.90588	−	13.6934i	0.403971	−	0.699699i	−0.590230	−	0.807235i	$-0.700963\pi$
$383$	7.90588	−	13.6934i	0.403971	−	0.699699i	0.994201	+	0.107536i	$0.0342962\pi$
$384$	−2.44245			−0.124641
$385$	6.55118	+	51.1830i	0.333879	+	2.60853i
$386$	−3.89664			−0.198334
$387$	−11.6327	+	20.1484i	−0.591321	+	1.02420i
$388$	−8.42260	−	14.5884i	−0.427593	−	0.740612i
$389$	10.8586	+	18.8076i	0.550552	+	0.953584i	0.998235	+	0.0593917i	$0.0189161\pi$
$389$	10.8586	+	18.8076i	0.550552	+	0.953584i	−0.447683	+	0.894193i	$0.647751\pi$
$390$	−9.66789	+	16.7453i	−0.489553	+	0.847930i
$391$	−6.01213			−0.304047
$392$	−6.77434	+	1.76305i	−0.342156	+	0.0890474i
$393$	32.7732			1.65319
$394$	−7.78118	+	13.4774i	−0.392010	+	0.678981i
$395$	9.24600	+	16.0145i	0.465217	+	0.805779i
$396$	6.97937	+	12.0886i	0.350727	+	0.607476i
$397$	−0.630167	+	1.09148i	−0.0316272	+	0.0547798i	−0.881406	−	0.472360i	$-0.843402\pi$
$397$	−0.630167	+	1.09148i	−0.0316272	+	0.0547798i	0.849779	+	0.527140i	$0.176736\pi$
$398$	24.5735			1.23176
$399$	3.31485	+	25.8982i	0.165950	+	1.29653i
$400$	12.1683			0.608417
$401$	0.955905	−	1.65568i	0.0477356	−	0.0826806i	−0.841170	−	0.540770i	$-0.818133\pi$
$401$	0.955905	−	1.65568i	0.0477356	−	0.0826806i	0.888906	+	0.458090i	$0.151466\pi$
$402$	−2.77920	−	4.81372i	−0.138614	−	0.240086i
$403$	−0.925734	−	1.60342i	−0.0461141	−	0.0798719i
$404$	6.21303	−	10.7613i	0.309110	−	0.535394i
$405$	−37.7146			−1.87405
$406$	−2.44070	−	1.02127i	−0.121130	−	0.0506848i
$407$	6.93526			0.343768
$408$	3.37930	−	5.85312i	0.167300	−	0.289773i
$409$	1.50907	+	2.61379i	0.0746189	+	0.129244i	0.900921	−	0.433984i	$-0.142893\pi$
$409$	1.50907	+	2.61379i	0.0746189	+	0.129244i	−0.826302	+	0.563228i	$0.809559\pi$
$410$	−21.6996	−	37.5848i	−1.07167	−	1.85618i
$411$	20.8869	−	36.1771i	1.03027	−	1.78448i
$412$	−16.1718			−0.796729
$413$	−7.19151	+	5.47726i	−0.353871	+	0.269518i
$414$	−6.44320			−0.316666
$415$	12.5548	−	21.7455i	0.616290	−	1.06744i
$416$	0.955306	+	1.65464i	0.0468377	+	0.0811253i
$417$	−4.77146	−	8.26441i	−0.233659	−	0.404710i
$418$	9.50903	−	16.4701i	0.465102	−	0.805580i
$419$	4.64504			0.226925			0.113463	−	0.993542i	$-0.463806\pi$
$419$	4.64504			0.226925			0.113463	+	0.993542i	$0.463806\pi$
$420$	21.3010	−	16.2234i	1.03938	−	0.791621i
$421$	−26.6202			−1.29739			−0.648695	−	0.761048i	$-0.724685\pi$
$421$	−26.6202			−1.29739			−0.648695	+	0.761048i	$0.724685\pi$
$422$	−4.32823	+	7.49671i	−0.210695	+	0.364934i
$423$	−17.3920	−	30.1239i	−0.845629	−	1.46467i
$424$	1.39041	+	2.40826i	0.0675243	+	0.116956i
$425$	−16.8358	+	29.1604i	−0.816654	+	1.41449i
$426$	15.2568			0.739196
$427$	27.8708	+	11.6621i	1.34876	+	0.564367i
$428$	10.6246			0.513558
$429$	10.9827	−	19.0226i	0.530250	−	0.918420i
$430$	−16.2532	−	28.1513i	−0.783798	−	1.35758i
$431$	4.81935	+	8.34735i	0.232140	+	0.402078i	0.958438	−	0.285302i	$-0.0920940\pi$
$431$	4.81935	+	8.34735i	0.232140	+	0.402078i	−0.726298	+	0.687380i	$0.758761\pi$
$432$	−0.0420753	+	0.0728765i	−0.00202435	+	0.00350627i
$433$	−3.16466			−0.152084			−0.0760420	−	0.997105i	$-0.524228\pi$
$433$	−3.16466			−0.152084			−0.0760420	+	0.997105i	$0.524228\pi$
$434$	0.325505	+	2.54310i	0.0156247	+	0.122073i
$435$	10.1202			0.485227
$436$	−3.04942	+	5.28175i	−0.146041	+	0.252950i
$437$	4.38926	+	7.60242i	0.209967	+	0.363673i
$438$	−16.5146	−	28.6040i	−0.789096	−	1.36675i
$439$	−6.94499	+	12.0291i	−0.331467	+	0.574117i	−0.982800	−	0.184675i	$-0.940877\pi$
$439$	−6.94499	+	12.0291i	−0.331467	+	0.574117i	0.651333	+	0.758792i	$0.274210\pi$
$440$	−19.5032			−0.929778
$441$	5.51688	−	20.0123i	0.262709	−	0.952968i
$442$	−5.28694			−0.251474
$443$	−10.1854	+	17.6416i	−0.483923	+	0.838179i	−0.999829	−	0.0184661i	$-0.994122\pi$
$443$	−10.1854	+	17.6416i	−0.483923	+	0.838179i	0.515907	+	0.856645i	$0.327455\pi$
$444$	−1.79935	−	3.11657i	−0.0853936	−	0.147906i
$445$	−27.4840	−	47.6036i	−1.30286	−	2.25663i
$446$	5.45953	−	9.45618i	0.258516	−	0.447763i
$447$	18.3141			0.866228
$448$	−0.335903	−	2.62434i	−0.0158699	−	0.123988i
$449$	33.1442			1.56417			0.782086	−	0.623170i	$-0.214156\pi$
$449$	33.1442			1.56417			0.782086	+	0.623170i	$0.214156\pi$
$450$	−18.0429	+	31.2512i	−0.850550	+	1.47320i
$451$	24.6507	+	42.6962i	1.16076	+	2.01049i
$452$	−7.29376	−	12.6332i	−0.343069	−	0.594214i
$453$	11.5017	−	19.9215i	0.540397	−	0.935995i
$454$	−10.4951			−0.492559
$455$	−19.3219	−	8.08495i	−0.905826	−	0.379028i
$456$	−9.86847			−0.462133
$457$	9.10435	−	15.7692i	0.425883	−	0.737652i	−0.570619	−	0.821215i	$-0.693297\pi$
$457$	9.10435	−	15.7692i	0.425883	−	0.737652i	0.996502	+	0.0835631i	$0.0266300\pi$
$458$	3.75763	+	6.50840i	0.175582	+	0.304117i
$459$	−0.116428	−	0.201660i	−0.00543441	−	0.00941267i
$460$	4.50123	−	7.79635i	0.209871	−	0.363507i
$461$	−3.52484			−0.164168			−0.0820841	−	0.996625i	$-0.526158\pi$
$461$	−3.52484			−0.164168			−0.0820841	+	0.996625i	$0.526158\pi$
$462$	−24.1978	+	18.4298i	−1.12579	+	0.857430i
$463$	10.7653			0.500304			0.250152	−	0.968207i	$-0.419519\pi$
$463$	10.7653			0.500304			0.250152	+	0.968207i	$0.419519\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$	−4.90346	−	8.49305i	−0.227393	−	0.393856i
$466$	−2.57131	−	4.45364i	−0.119114	−	0.206311i
$467$	−6.00994	+	10.4095i	−0.278107	+	0.481695i	−0.970914	−	0.239427i	$-0.923040\pi$
$467$	−6.00994	+	10.4095i	−0.278107	+	0.481695i	0.692807	+	0.721123i	$0.256374\pi$
$468$	−5.66601			−0.261911
$469$	4.78999	−	3.64819i	0.221181	−	0.168458i
$470$	48.6003			2.24177
$471$	21.7727	−	37.7115i	1.00323	−	1.73765i
$472$	−1.70836	−	2.95897i	−0.0786338	−	0.136198i
$473$	18.4636	+	31.9798i	0.848956	+	1.47043i
$474$	−5.45023	+	9.44008i	−0.250337	+	0.433597i
$475$	49.1650			2.25584
$476$	6.75376	+	2.82600i	0.309558	+	0.129530i
$477$	−8.24666			−0.377588
$478$	−0.374837	+	0.649236i	−0.0171446	+	0.0296954i
$479$	−4.14601	−	7.18110i	−0.189436	−	0.328113i	0.755626	−	0.655003i	$-0.227333\pi$
$479$	−4.14601	−	7.18110i	−0.189436	−	0.328113i	−0.945062	+	0.326890i	$0.893999\pi$
$480$	5.06010	+	8.76435i	0.230961	+	0.400036i
$481$	−1.40755	+	2.43795i	−0.0641788	+	0.111161i
$482$	−9.01959			−0.410831
$483$	−1.78253	−	13.9265i	−0.0811077	−	0.633678i
$484$	11.1556			0.507072
$485$	−34.8988	+	60.4465i	−1.58467	+	2.74473i
$486$	−10.9896	−	19.0345i	−0.498497	−	0.863421i
$487$	−3.94673	−	6.83593i	−0.178843	−	0.309766i	0.762641	−	0.646822i	$-0.223902\pi$
$487$	−3.94673	−	6.83593i	−0.178843	−	0.309766i	−0.941485	+	0.337056i	$0.890569\pi$
$488$	−5.70959	+	9.88930i	−0.258461	+	0.447668i
$489$	26.5711			1.20159
$490$	20.3611	+	20.6561i	0.919819	+	0.933149i
$491$	−37.7250			−1.70250			−0.851252	−	0.524757i	$-0.824156\pi$
$491$	−37.7250			−1.70250			−0.851252	+	0.524757i	$0.824156\pi$
$492$	12.7912	−	22.1551i	0.576673	−	0.998828i
$493$	1.38357	+	2.39642i	0.0623129	+	0.107929i
$494$	3.85982	+	6.68541i	0.173662	+	0.300791i
$495$	28.9188	−	50.0888i	1.29980	−	2.25133i
$496$	−0.969044			−0.0435114
$497$	2.09823	+	16.3930i	0.0941184	+	0.735328i
$498$	14.8013			0.663262
$499$	4.23971	−	7.34340i	0.189796	−	0.328736i	−0.755386	−	0.655280i	$-0.772551\pi$
$499$	4.23971	−	7.34340i	0.189796	−	0.328736i	0.945182	+	0.326544i	$0.105884\pi$
$500$	−14.8509	−	25.7225i	−0.664152	−	1.15034i
$501$	19.5793	+	33.9124i	0.874740	+	1.51509i
$502$	14.5584	−	25.2160i	0.649775	−	1.12544i
$503$	−25.2796			−1.12716			−0.563581	−	0.826061i	$-0.690577\pi$
$503$	−25.2796			−1.12716			−0.563581	+	0.826061i	$0.690577\pi$
$504$	7.23800	+	3.02862i	0.322406	+	0.134906i
$505$	−51.4870			−2.29114
$506$	−5.11338	+	8.85664i	−0.227318	+	0.393726i
$507$	−11.4179	−	19.7764i	−0.507087	−	0.878300i
$508$	−2.73191	−	4.73180i	−0.121209	−	0.209940i
$509$	−2.48482	+	4.30383i	−0.110138	+	0.190764i	−0.915826	−	0.401576i	$-0.868462\pi$
$509$	−2.48482	+	4.30383i	−0.110138	+	0.190764i	0.805688	+	0.592340i	$0.201796\pi$
$510$	−28.0041			−1.24004
$511$	28.4631	−	21.6783i	1.25913	−	0.958990i
$512$	1.00000			0.0441942
$513$	−0.170001	+	0.294451i	−0.00750573	+	0.0130003i
$514$	11.6138	+	20.1156i	0.512262	+	0.887263i
$515$	33.5037	+	58.0302i	1.47635	+	2.55712i
$516$	9.58075	−	16.5943i	0.421769	−	0.730525i
$517$	−55.2099			−2.42813
$518$	3.10121	−	2.36197i	0.136259	−	0.103779i
$519$	15.1158			0.663508
$520$	3.95828	−	6.85594i	0.173582	−	0.300653i
$521$	−13.4814	−	23.3505i	−0.590631	−	1.02300i	−0.994148	−	0.108030i	$-0.965546\pi$
$521$	−13.4814	−	23.3505i	−0.590631	−	1.02300i	0.403517	−	0.914972i	$-0.367788\pi$
$522$	1.48277	+	2.56824i	0.0648992	+	0.112409i
$523$	5.24494	−	9.08451i	0.229345	−	0.397238i	−0.728269	−	0.685291i	$-0.759675\pi$
$523$	5.24494	−	9.08451i	0.229345	−	0.397238i	0.957614	+	0.288054i	$0.0930082\pi$
$524$	−13.4182			−0.586176
$525$	−72.5388	−	30.3527i	−3.16585	−	1.32470i
$526$	−20.5033			−0.893988
$527$	1.34074	−	2.32223i	0.0584036	−	0.101158i
$528$	−5.74826	−	9.95629i	−0.250161	−	0.433292i
$529$	9.13972	+	15.8305i	0.397379	+	0.688281i
$530$	5.76112	−	9.97856i	0.250247	−	0.433441i
$531$	10.1325			0.439712
$532$	−1.35718	−	10.6034i	−0.0588414	−	0.459716i
$533$	−20.0120			−0.866815
$534$	16.2009	−	28.0609i	0.701084	−	1.21431i
$535$	−22.0113	−	38.1247i	−0.951632	−	1.64827i
$536$	1.13788	+	1.97086i	0.0491487	+	0.0851281i
$537$	1.47206	−	2.54968i	0.0635241	−	0.110027i
$538$	−11.3952			−0.491282
$539$	−23.1301	−	23.4653i	−0.996285	−	1.01072i
$540$	0.348675			0.0150046
$541$	22.2847	−	38.5982i	0.958093	−	1.65947i	0.230968	−	0.972961i	$-0.425811\pi$
$541$	22.2847	−	38.5982i	0.958093	−	1.65947i	0.727125	−	0.686505i	$-0.240856\pi$
$542$	−8.98753	−	15.5669i	−0.386048	−	0.668654i
$543$	8.48879	+	14.7030i	0.364289	+	0.630967i
$544$	−1.38357	+	2.39642i	−0.0593201	+	0.102746i
$545$	25.2703			1.08246
$546$	−1.56751	−	12.2467i	−0.0670834	−	0.524109i
$547$	34.8005			1.48796			0.743980	−	0.668202i	$-0.232936\pi$
$547$	34.8005			1.48796			0.743980	+	0.668202i	$0.232936\pi$
$548$	−8.55161	+	14.8118i	−0.365307	+	0.632730i
$549$	−16.9321	−	29.3272i	−0.722643	−	1.25165i
$550$	28.6380	+	49.6025i	1.22113	+	2.11506i
$551$	2.02020	−	3.49909i	0.0860635	−	0.149066i
$552$	5.30667			0.225867
$553$	−10.8927	−	4.55786i	−0.463203	−	0.193820i
$554$	−2.08032			−0.0883843
$555$	−7.45557	+	12.9134i	−0.316471	+	0.548144i
$556$	1.95356	+	3.38366i	0.0828493	+	0.143499i
$557$	16.8832	+	29.2426i	0.715365	+	1.23905i	0.962818	+	0.270149i	$0.0870731\pi$
$557$	16.8832	+	29.2426i	0.715365	+	1.23905i	−0.247453	+	0.968900i	$0.579594\pi$
$558$	1.43687	−	2.48874i	0.0608277	−	0.105357i
$559$	−14.9891			−0.633973
$560$	−8.72115	+	6.64228i	−0.368536	+	0.280687i
$561$	31.8125			1.34313
$562$	−3.67871	+	6.37170i	−0.155177	+	0.268774i
$563$	−20.6204	−	35.7156i	−0.869047	−	1.50523i	−0.862972	−	0.505252i	$-0.831400\pi$
$563$	−20.6204	−	35.7156i	−0.869047	−	1.50523i	−0.00607459	−	0.999982i	$-0.501934\pi$
$564$	14.3242	+	24.8102i	0.603158	+	1.04470i
$565$	−30.2215	+	52.3451i	−1.27143	+	2.20217i
$566$	−6.08053			−0.255584
$567$	19.1582	−	14.5914i	0.804569	−	0.612783i
$568$	−6.24653			−0.262099
$569$	12.9593	−	22.4461i	0.543281	−	0.940990i	−0.455432	−	0.890270i	$-0.650515\pi$
$569$	12.9593	−	22.4461i	0.543281	−	0.940990i	0.998713	−	0.0507193i	$-0.0161514\pi$
$570$	20.4448	+	35.4115i	0.856340	+	1.48323i
$571$	−7.94763	−	13.7657i	−0.332598	−	0.576077i	0.650422	−	0.759573i	$-0.274592\pi$
$571$	−7.94763	−	13.7657i	−0.332598	−	0.576077i	−0.983020	+	0.183496i	$0.941259\pi$
$572$	−4.49660	+	7.78834i	−0.188012	+	0.325647i
$573$	16.6293			0.694700
$574$	25.5642	+	10.6969i	1.06703	+	0.446480i
$575$	−26.4380			−1.10254
$576$	−1.48277	+	2.56824i	−0.0617822	+	0.107010i
$577$	5.13613	+	8.89603i	0.213820	+	0.370347i	0.952907	−	0.303263i	$-0.0980761\pi$
$577$	5.13613	+	8.89603i	0.213820	+	0.370347i	−0.739087	+	0.673610i	$0.764743\pi$
$578$	4.67146	+	8.09120i	0.194307	+	0.336550i
$579$	−4.75867	+	8.24225i	−0.197763	+	0.342536i
$580$	−4.14347			−0.172048
$581$	2.03558	+	15.9036i	0.0844502	+	0.659792i
$582$	−41.1435			−1.70545
$583$	−6.54462	+	11.3356i	−0.271051	+	0.469473i
$584$	6.76148	+	11.7112i	0.279792	+	0.484614i
$585$	11.7385	+	20.3316i	0.485326	+	0.840609i
$586$	−6.85795	+	11.8783i	−0.283299	+	0.490689i
$587$	−23.9902			−0.990183			−0.495091	−	0.868841i	$-0.664865\pi$
$587$	−23.9902			−0.990183			−0.495091	+	0.868841i	$0.664865\pi$
$588$	−4.54374	+	16.4823i	−0.187381	+	0.679719i
$589$	−3.91533			−0.161328
$590$	−7.07855	+	12.2604i	−0.291419	+	0.504753i
$591$	19.0051	+	32.9178i	0.781766	+	1.35406i
$592$	0.736701	+	1.27600i	0.0302782	+	0.0524434i
$593$	7.76833	−	13.4551i	0.319007	−	0.552536i	−0.661274	−	0.750144i	$-0.729984\pi$
$593$	7.76833	−	13.4551i	0.319007	−	0.552536i	0.980281	+	0.197608i	$0.0633173\pi$
$594$	−0.396094			−0.0162519
$595$	−3.85132	−	30.0896i	−0.157889	−	1.23355i
$596$	−7.49827			−0.307141
$597$	30.0098	−	51.9785i	1.22822	−	2.12734i
$598$	−2.07558	−	3.59501i	−0.0848767	−	0.147011i
$599$	10.4154	+	18.0400i	0.425561	+	0.737094i	0.996473	−	0.0839180i	$-0.0267434\pi$
$599$	10.4154	+	18.0400i	0.425561	+	0.737094i	−0.570911	+	0.821012i	$0.693410\pi$
$600$	14.8603	−	25.7387i	0.606667	−	1.05078i
$601$	17.7149			0.722606			0.361303	−	0.932448i	$-0.382332\pi$
$601$	17.7149			0.722606			0.361303	+	0.932448i	$0.382332\pi$
$602$	19.1478	+	8.01207i	0.780405	+	0.326548i
$603$	−6.74884			−0.274834
$604$	−4.70909	+	8.15638i	−0.191610	+	0.331878i
$605$	−23.1114	−	40.0301i	−0.939612	−	1.62746i
$606$	−15.1750	−	26.2839i	−0.616442	−	1.06771i
$607$	1.22259	−	2.11758i	0.0496233	−	0.0859501i	−0.840147	−	0.542359i	$-0.817531\pi$
$607$	1.22259	−	2.11758i	0.0496233	−	0.0859501i	0.889770	+	0.456409i	$0.150865\pi$
$608$	4.04040			0.163860
$609$	−5.14085	+	3.91542i	−0.208318	+	0.158661i
$610$	47.3150			1.91573
$611$	11.2052	−	19.4079i	0.453312	−	0.785159i
$612$	−4.10305	−	7.10668i	−0.165856	−	0.287271i
$613$	0.903050	+	1.56413i	0.0364739	+	0.0631746i	0.883686	−	0.468080i	$-0.155054\pi$
$613$	0.903050	+	1.56413i	0.0364739	+	0.0631746i	−0.847212	+	0.531255i	$0.821721\pi$
$614$	−3.82247	+	6.62071i	−0.154262	+	0.267190i
$615$	−106.000			−4.27434
$616$	9.90721	−	7.54561i	0.399173	−	0.304021i
$617$	−15.0917			−0.607567			−0.303784	−	0.952741i	$-0.598250\pi$
$617$	−15.0917			−0.607567			−0.303784	+	0.952741i	$0.598250\pi$
$618$	−19.7494	+	34.2070i	−0.794438	+	1.37601i
$619$	22.2955	+	38.6170i	0.896133	+	1.55215i	0.832396	+	0.554181i	$0.186968\pi$
$619$	22.2955	+	38.6170i	0.896133	+	1.55215i	0.0637362	+	0.997967i	$0.479698\pi$
$620$	2.00760	+	3.47727i	0.0806272	+	0.139650i
$621$	0.0914163	−	0.158338i	0.00366841	−	0.00635387i
$622$	24.4252			0.979360
$623$	32.3787	+	13.5483i	1.29723	+	0.542803i
$624$	4.66657			0.186812
$625$	−31.1133	+	53.8899i	−1.24453	+	2.15560i
$626$	9.13225	+	15.8175i	0.364998	+	0.632195i
$627$	−23.2253	−	40.2274i	−0.927529	−	1.60653i
$628$	−8.91431	+	15.4400i	−0.355720	+	0.616125i
$629$	−4.07712			−0.162565
$630$	−4.12746	−	32.2470i	−0.164442	−	1.28475i
$631$	−14.3265			−0.570328			−0.285164	−	0.958479i	$-0.592048\pi$
$631$	−14.3265			−0.570328			−0.285164	+	0.958479i	$0.592048\pi$
$632$	2.23146	−	3.86501i	0.0887629	−	0.153742i
$633$	10.5715	+	18.3103i	0.420178	+	0.727770i
$634$	5.21086	+	9.02547i	0.206950	+	0.358447i
$635$	−11.3196	+	19.6061i	−0.449203	+	0.778043i
$636$	6.79201			0.269321
$637$	12.9431	−	3.36850i	0.512826	−	0.133465i
$638$	4.70697			0.186351
$639$	9.26219	−	16.0426i	0.366407	−	0.634635i
$640$	−2.07173	−	3.58835i	−0.0818925	−	0.141842i
$641$	8.71772	+	15.0995i	0.344329	+	0.596395i	0.985232	−	0.171227i	$-0.0547731\pi$
$641$	8.71772	+	15.0995i	0.344329	+	0.596395i	−0.640903	+	0.767622i	$0.721440\pi$
$642$	12.9750	−	22.4733i	0.512082	−	0.886952i
$643$	−6.99067			−0.275685			−0.137843	−	0.990454i	$-0.544017\pi$
$643$	−6.99067			−0.275685			−0.137843	+	0.990454i	$0.544017\pi$
$644$	0.729811	+	5.70187i	0.0287586	+	0.224685i
$645$	−79.3950			−3.12618
$646$	−5.59019	+	9.68249i	−0.219943	+	0.380952i
$647$	8.11703	+	14.0591i	0.319113	+	0.552721i	0.980303	−	0.197498i	$-0.0632816\pi$
$647$	8.11703	+	14.0591i	0.319113	+	0.552721i	−0.661190	+	0.750219i	$0.729948\pi$
$648$	4.55109	+	7.88271i	0.178784	+	0.309662i
$649$	8.04122	−	13.9278i	0.315646	−	0.546714i
$650$	−23.2490			−0.911899
$651$	5.77674	+	2.41718i	0.226408	+	0.0947369i
$652$	−10.8789			−0.426051
$653$	−11.2601	+	19.5030i	−0.440641	+	0.763212i	−0.997737	−	0.0672359i	$-0.978582\pi$
$653$	−11.2601	+	19.5030i	−0.440641	+	0.763212i	0.557097	+	0.830448i	$0.311915\pi$
$654$	7.44804	+	12.9004i	0.291241	+	0.504445i
$655$	27.7989	+	48.1491i	1.08619	+	1.88134i
$656$	−5.23706	+	9.07085i	−0.204473	+	0.354157i
$657$	−40.1030			−1.56457
$658$	−24.6880	+	18.8030i	−0.962437	+	0.733019i
$659$	−6.71682			−0.261650			−0.130825	−	0.991405i	$-0.541763\pi$
$659$	−6.71682			−0.261650			−0.130825	+	0.991405i	$0.541763\pi$
$660$	−23.8178	+	41.2536i	−0.927105	+	1.60579i
$661$	17.6804	+	30.6234i	0.687689	+	1.19111i	0.972584	+	0.232553i	$0.0747079\pi$
$661$	17.6804	+	30.6234i	0.687689	+	1.19111i	−0.284895	+	0.958559i	$0.591959\pi$
$662$	−2.34176	−	4.05604i	−0.0910149	−	0.157643i
$663$	−6.45653	+	11.1830i	−0.250751	+	0.434313i
$664$	−6.06003			−0.235175
$665$	−35.2370	+	26.8375i	−1.36643	+	1.04071i
$666$	−4.36944			−0.169313
$667$	−1.08634	+	1.88160i	−0.0420633	+	0.0728559i
$668$	−8.01628	−	13.8846i	−0.310159	−	0.537211i
$669$	−13.3346	−	23.0962i	−0.515546	−	0.892951i
$670$	4.71475	−	8.16619i	0.182147	−	0.315487i
$671$	−53.7498			−2.07499
$672$	−5.96128	−	2.49440i	−0.229961	−	0.0962235i
$673$	−23.1388			−0.891935			−0.445967	−	0.895049i	$-0.647140\pi$
$673$	−23.1388			−0.891935			−0.445967	+	0.895049i	$0.647140\pi$
$674$	12.6860	−	21.9727i	0.488645	−	0.846358i
$675$	−0.511986	−	0.886786i	−0.0197064	−	0.0341324i
$676$	4.67478	+	8.09696i	0.179799	+	0.311421i
$677$	−11.3672	+	19.6886i	−0.436878	+	0.756694i	−0.997447	−	0.0714135i	$-0.977249\pi$
$677$	−11.3672	+	19.6886i	−0.436878	+	0.756694i	0.560569	+	0.828108i	$0.310582\pi$
$678$	−35.6292			−1.36833
$679$	−5.65835	−	44.2076i	−0.217148	−	1.69653i
$680$	11.4656			0.439685
$681$	−12.8168	+	22.1994i	−0.491142	+	0.850684i
$682$	−2.28063	−	3.95017i	−0.0873299	−	0.151260i
$683$	−10.1464	−	17.5741i	−0.388242	−	0.672454i	0.603972	−	0.797006i	$-0.293584\pi$
$683$	−10.1464	−	17.5741i	−0.388242	−	0.672454i	−0.992213	+	0.124552i	$0.960251\pi$
$684$	−5.99100	+	10.3767i	−0.229072	+	0.396764i
$685$	70.8667			2.70768
$686$	−18.3347	−	2.61536i	−0.700021	−	0.0998550i
$687$	18.3556			0.700310
$688$	−3.92260	+	6.79415i	−0.149548	+	0.259024i
$689$	−2.65654	−	4.60125i	−0.101206	−	0.175294i
$690$	−10.9940	−	19.0422i	−0.418535	−	0.724923i
$691$	−1.00590	+	1.74227i	−0.0382662	+	0.0662790i	−0.884524	−	0.466494i	$-0.845517\pi$
$691$	−1.00590	+	1.74227i	−0.0382662	+	0.0662790i	0.846258	+	0.532773i	$0.178850\pi$
$692$	−6.18878			−0.235262
$693$	4.68878	+	36.6325i	0.178112	+	1.39155i
$694$	−1.93057			−0.0732836
$695$	8.09450	−	14.0201i	0.307042	−	0.531812i
$696$	−1.22122	−	2.11522i	−0.0462904	−	0.0801772i
$697$	−14.4917	−	25.1003i	−0.548912	−	0.950743i
$698$	−0.978909	+	1.69552i	−0.0370523	+	0.0641764i
$699$	−12.5606			−0.475084
$700$	29.6992	+	12.4272i	1.12253	+	0.469702i
$701$	−3.02432			−0.114227			−0.0571136	−	0.998368i	$-0.518190\pi$
$701$	−3.02432			−0.114227			−0.0571136	+	0.998368i	$0.518190\pi$
$702$	0.0803895	−	0.139239i	0.00303411	−	0.00525523i
$703$	2.97657	+	5.15557i	0.112263	+	0.194446i
$704$	2.35349	+	4.07636i	0.0887003	+	0.153633i
$705$	59.3519	−	102.800i	2.23532	−	3.87169i
$706$	−16.3330			−0.614700
$707$	26.1543	−	19.9199i	0.983634	−	0.749163i
$708$	−8.34518			−0.313631
$709$	22.7334	−	39.3755i	0.853772	−	1.47878i	−0.0240072	−	0.999712i	$-0.507642\pi$
$709$	22.7334	−	39.3755i	0.853772	−	1.47878i	0.877779	−	0.479065i	$-0.159024\pi$
$710$	12.9412	+	22.4147i	0.485673	+	0.841210i
$711$	6.61751	+	11.4619i	0.248176	+	0.429853i
$712$	−6.63308	+	11.4888i	−0.248585	+	0.430562i
$713$	2.10543			0.0788489
$714$	14.2255	−	10.8345i	0.532375	−	0.405472i
$715$	37.2630			1.39356
$716$	−0.602699	+	1.04391i	−0.0225239	+	0.0390126i
$717$	0.915519	+	1.58572i	0.0341907	+	0.0592200i
$718$	5.89004	+	10.2019i	0.219814	+	0.380730i
$719$	−15.0720	+	26.1055i	−0.562092	+	0.973572i	0.435221	+	0.900323i	$0.356670\pi$
$719$	−15.0720	+	26.1055i	−0.562092	+	0.973572i	−0.997314	+	0.0732489i	$0.976663\pi$
$720$	12.2876			0.457934
$721$	−39.4706	−	16.5158i	−1.46996	−	0.615081i
$722$	−2.67514			−0.0995585
$723$	−11.0149	+	19.0784i	−0.409650	+	0.709534i
$724$	−3.47553	−	6.01979i	−0.129167	−	0.223724i
$725$	6.08417	+	10.5381i	0.225960	+	0.391375i
$726$	13.6235	−	23.5965i	0.505614	−	0.875749i
$727$	45.6599			1.69343			0.846717	−	0.532044i	$-0.178576\pi$
$727$	45.6599			1.69343			0.846717	+	0.532044i	$0.178576\pi$
$728$	0.641780	+	5.01410i	0.0237860	+	0.185835i
$729$	−26.3763			−0.976901
$730$	28.0160	−	48.5251i	1.03692	−	1.79599i
$731$	−10.8544	−	18.8004i	−0.401465	−	0.695357i
$732$	13.9454	+	24.1541i	0.515436	+	0.892761i
$733$	13.6729	−	23.6822i	0.505020	−	0.874721i	−0.494963	−	0.868914i	$-0.664818\pi$
$733$	13.6729	−	23.6822i	0.505020	−	0.874721i	0.999983	−	0.00580686i	$-0.00184839\pi$
$734$	35.6438			1.31564
$735$	68.5577	−	17.8424i	2.52879	−	0.658127i
$736$	−2.17268			−0.0800862
$737$	−5.35595	+	9.27677i	−0.197289	+	0.341714i
$738$	−15.5307	−	26.9000i	−0.571694	−	0.990204i
$739$	−24.9583	−	43.2291i	−0.918106	−	1.59021i	−0.802289	−	0.596936i	$-0.796385\pi$
$739$	−24.9583	−	43.2291i	−0.918106	−	1.59021i	−0.115817	−	0.993271i	$-0.536949\pi$
$740$	3.05250	−	5.28708i	0.112212	−	0.194357i
$741$	18.8548			0.692649
$742$	0.934086	+	7.29783i	0.0342914	+	0.267912i
$743$	28.6655			1.05164			0.525818	−	0.850597i	$-0.323759\pi$
$743$	28.6655			1.05164			0.525818	+	0.850597i	$0.323759\pi$
$744$	−1.18342	+	2.04974i	−0.0433863	+	0.0751472i
$745$	15.5344	+	26.9064i	0.569137	+	0.985774i
$746$	−8.87414	−	15.3705i	−0.324905	−	0.562753i
$747$	8.98565	−	15.5636i	0.328768	−	0.569443i
$748$	−13.0249			−0.476236
$749$	25.9314	+	10.8506i	0.947512	+	0.396471i
$750$	−72.5450			−2.64897
$751$	9.51580	−	16.4818i	0.347236	−	0.601431i	−0.638521	−	0.769604i	$-0.720453\pi$
$751$	9.51580	−	16.4818i	0.347236	−	0.601431i	0.985757	+	0.168173i	$0.0537868\pi$
$752$	−5.86469	−	10.1579i	−0.213863	−	0.370422i
$753$	−35.5582	−	61.5887i	−1.29581	−	2.24442i
$754$	−0.955306	+	1.65464i	−0.0347902	+	0.0602584i
$755$	39.0239			1.42023
$756$	−0.177120	+	0.134899i	−0.00644178	+	0.00490624i
$757$	−9.39694			−0.341538			−0.170769	−	0.985311i	$-0.554625\pi$
$757$	−9.39694			−0.341538			−0.170769	+	0.985311i	$0.554625\pi$
$758$	7.61317	−	13.1864i	0.276523	−	0.478951i
$759$	12.4892	+	21.6319i	0.453328	+	0.785187i
$760$	−8.37064	−	14.4984i	−0.303635	−	0.525911i
$761$	5.37464	−	9.30916i	0.194831	−	0.337457i	−0.752014	−	0.659147i	$-0.770918\pi$
$761$	5.37464	−	9.30916i	0.194831	−	0.337457i	0.946845	+	0.321690i	$0.104251\pi$
$762$	−13.3451			−0.483441
$763$	−12.8368	+	9.77687i	−0.464723	+	0.353946i
$764$	−6.80847			−0.246322
$765$	−17.0008	+	29.4463i	−0.614667	+	1.06463i
$766$	7.90588	+	13.6934i	0.285651	+	0.494762i
$767$	3.26402	+	5.65345i	0.117857	+	0.204134i
$768$	1.22122	−	2.11522i	0.0440671	−	0.0763265i
$769$	39.3774			1.41998			0.709992	−	0.704209i	$-0.248698\pi$
$769$	39.3774			1.41998			0.709992	+	0.704209i	$0.248698\pi$
$770$	−47.6014	−	19.9180i	−1.71544	−	0.717796i
$771$	56.7321			2.04316
$772$	1.94832	−	3.37459i	0.0701216	−	0.121454i
$773$	9.52357	+	16.4953i	0.342539	+	0.593295i	0.984903	−	0.173104i	$-0.0553798\pi$
$773$	9.52357	+	16.4953i	0.342539	+	0.593295i	−0.642365	+	0.766399i	$0.722046\pi$
$774$	−11.6327	−	20.1484i	−0.418127	−	0.724218i
$775$	5.89583	−	10.2119i	0.211784	−	0.366821i
$776$	16.8452			0.604708
$777$	−1.20882	−	9.44424i	−0.0433660	−	0.338810i
$778$	−21.7172			−0.778598
$779$	−21.1598	+	36.6499i	−0.758129	+	1.31312i
$780$	−9.66789	−	16.7453i	−0.346166	−	0.599577i
$781$	−14.7011	−	25.4631i	−0.526048	−	0.911142i
$782$	3.00607	−	5.20666i	0.107497	−	0.186190i
$783$	−0.0841506			−0.00300730
$784$	1.86032	−	6.74827i	0.0664402	−	0.241010i
$785$	73.8723			2.63662
$786$	−16.3866	+	28.3824i	−0.584490	+	1.01237i
$787$	−13.2223	−	22.9017i	−0.471325	−	0.816358i	0.528137	−	0.849159i	$-0.322891\pi$
$787$	−13.2223	−	22.9017i	−0.471325	−	0.816358i	−0.999462	+	0.0328007i	$0.989557\pi$
$788$	−7.78118	−	13.4774i	−0.277193	−	0.480112i
$789$	−25.0391	+	43.3691i	−0.891417	+	1.54398i
$790$	−18.4920			−0.657916
$791$	−4.89999	−	38.2826i	−0.174224	−	1.36117i
$792$	−13.9587			−0.496002
$793$	10.9088	−	18.8946i	0.387383	−	0.670968i
$794$	−0.630167	−	1.09148i	−0.0223638	−	0.0387352i
$795$	−14.0712	−	24.3721i	−0.499055	−	0.864389i
$796$	−12.2868	+	21.2813i	−0.435493	+	0.754296i
$797$	−42.8772			−1.51879			−0.759395	−	0.650630i	$-0.774505\pi$
$797$	−42.8772			−1.51879			−0.759395	+	0.650630i	$0.774505\pi$
$798$	−24.0860	−	10.0784i	−0.852634	−	0.356771i
$799$	32.4569			1.14824
$800$	−6.08417	+	10.5381i	−0.215108	+	0.372578i
$801$	−19.6707	−	34.0707i	−0.695030	−	1.20383i
$802$	0.955905	+	1.65568i	0.0337542	+	0.0584640i
$803$	−31.8261	+	55.1244i	−1.12312	+	1.94530i
$804$	5.55840			0.196030
$805$	18.9483	−	14.4316i	0.667840	−	0.508646i
$806$	1.85147			0.0652152
$807$	−13.9161	+	24.1034i	−0.489869	+	0.848479i
$808$	6.21303	+	10.7613i	0.218574	+	0.378580i
$809$	0.861958	+	1.49295i	0.0303048	+	0.0524895i	0.880780	−	0.473526i	$-0.157019\pi$
$809$	0.861958	+	1.49295i	0.0303048	+	0.0524895i	−0.850475	+	0.526015i	$0.823686\pi$
$810$	18.8573	−	32.6618i	0.662577	−	1.14762i
$811$	7.23311			0.253989			0.126995	−	0.991903i	$-0.459467\pi$
$811$	7.23311			0.253989			0.126995	+	0.991903i	$0.459467\pi$
$812$	2.10480	−	1.60307i	0.0738638	−	0.0562568i
$813$	−43.9031			−1.53975
$814$	−3.46763	+	6.00611i	−0.121540	+	0.210514i
$815$	22.5382	+	39.0373i	0.789479	+	1.36742i
$816$	3.37930	+	5.85312i	0.118299	+	0.204900i
$817$	−15.8489	+	27.4511i	−0.554482	+	0.960392i
$818$	−3.01815			−0.105527
$819$	−13.8290	−	5.78653i	−0.483225	−	0.202198i
$820$	43.3992			1.51556
$821$	−15.3520	+	26.5905i	−0.535789	+	0.928014i	0.463335	+	0.886183i	$0.346653\pi$
$821$	−15.3520	+	26.5905i	−0.535789	+	0.928014i	−0.999125	+	0.0418313i	$0.986681\pi$
$822$	20.8869	+	36.1771i	0.728513	+	1.26182i
$823$	4.79289	+	8.30153i	0.167070	+	0.289373i	0.937388	−	0.348286i	$-0.113236\pi$
$823$	4.79289	+	8.30153i	0.167070	+	0.289373i	−0.770319	+	0.637659i	$0.779903\pi$
$824$	8.08592	−	14.0052i	0.281686	−	0.487895i
$825$	139.894			4.87047
$826$	−1.14769	−	8.96666i	−0.0399332	−	0.311990i
$827$	−6.26986			−0.218025			−0.109012	−	0.994040i	$-0.534769\pi$
$827$	−6.26986			−0.218025			−0.109012	+	0.994040i	$0.534769\pi$
$828$	3.22160	−	5.57997i	0.111958	−	0.193917i
$829$	−5.64488	−	9.77723i	−0.196055	−	0.339577i	0.751191	−	0.660085i	$-0.229480\pi$
$829$	−5.64488	−	9.77723i	−0.196055	−	0.339577i	−0.947246	+	0.320508i	$0.896146\pi$
$830$	12.5548	+	21.7455i	0.435783	+	0.754798i
$831$	−2.54053	+	4.40034i	−0.0881302	+	0.152646i
$832$	−1.91061			−0.0662386
$833$	13.5978	+	13.7948i	0.471135	+	0.477963i
$834$	9.54292			0.330444
$835$	−33.2152	+	57.5304i	−1.14946	+	1.99092i
$836$	9.50903	+	16.4701i	0.328877	+	0.569631i
$837$	0.0407728	+	0.0706206i	0.00140931	+	0.00244100i
$838$	−2.32252	+	4.02272i	−0.0802302	+	0.138963i
$839$	−44.0101			−1.51940			−0.759698	−	0.650276i	$-0.774653\pi$
$839$	−44.0101			−1.51940			−0.759698	+	0.650276i	$0.774653\pi$
$840$	3.39941	+	26.5589i	0.117291	+	0.916368i
$841$	1.00000			0.0344828
$842$	13.3101	−	23.0538i	0.458697	−	0.794486i
$843$	8.98504	+	15.5625i	0.309461	+	0.536003i
$844$	−4.32823	−	7.49671i	−0.148984	−	0.258048i
$845$	19.3698	−	33.5495i	0.666342	−	1.15414i
$846$	34.7840			1.19590
$847$	27.2274	+	11.3929i	0.935545	+	0.391463i
$848$	−2.78082			−0.0954938
$849$	−7.42569	+	12.8617i	−0.254849	+	0.441411i
$850$	−16.8358	−	29.1604i	−0.577462	−	1.00019i
$851$	−1.60062	−	2.77235i	−0.0548685	−	0.0950351i
$852$	−7.62841	+	13.2128i	−0.261345	+	0.452663i
$853$	10.9272			0.374141			0.187070	−	0.982347i	$-0.440101\pi$
$853$	10.9272			0.374141			0.187070	+	0.982347i	$0.440101\pi$
$854$	−24.0350	+	18.3058i	−0.822462	+	0.626410i
$855$	49.6471			1.69789
$856$	−5.31229	+	9.20116i	−0.181570	+	0.314489i
$857$	−14.6377	−	25.3533i	−0.500015	−	0.866052i	−1.00000		1.75014e-5i	$-0.999994\pi$
$857$	−14.6377	−	25.3533i	−0.500015	−	0.866052i	0.499985	−	0.866034i	$-0.333339\pi$
$858$	10.9827	+	19.0226i	0.374943	+	0.649421i
$859$	21.6611	−	37.5181i	0.739067	−	1.28010i	−0.213849	−	0.976867i	$-0.568600\pi$
$859$	21.6611	−	37.5181i	0.739067	−	1.28010i	0.952916	−	0.303235i	$-0.0980666\pi$
$860$	32.5064			1.10846
$861$	53.8459	−	41.0105i	1.83506	−	1.39763i
$862$	−9.63869			−0.328295
$863$	21.9190	−	37.9649i	0.746133	−	1.29234i	−0.203531	−	0.979069i	$-0.565242\pi$
$863$	21.9190	−	37.9649i	0.746133	−	1.29234i	0.949664	−	0.313271i	$-0.101425\pi$
$864$	−0.0420753	−	0.0728765i	−0.00143143	−	0.00247931i
$865$	12.8215	+	22.2075i	0.435944	+	0.755077i
$866$	1.58233	−	2.74068i	0.0537698	−	0.0931320i
$867$	22.8196			0.774994
$868$	−2.36514	−	0.989656i	−0.0802782	−	0.0335911i
$869$	21.0069			0.712609
$870$	−5.06010	+	8.76435i	−0.171553	+	0.297139i
$871$	−2.17404	−	3.76555i	−0.0736645	−	0.127591i
$872$	−3.04942	−	5.28175i	−0.103266	−	0.178862i
$873$	−24.9776	+	43.2625i	−0.845364	+	1.46421i
$874$	−8.77852			−0.296938
$875$	−9.97691	−	77.9476i	−0.337281	−	2.63511i
$876$	33.0291			1.11595
$877$	−14.7536	+	25.5540i	−0.498194	+	0.862898i	−0.999998	−	0.00208396i	$-0.999337\pi$
$877$	−14.7536	+	25.5540i	−0.498194	+	0.862898i	0.501804	+	0.864982i	$0.332670\pi$
$878$	−6.94499	−	12.0291i	−0.234382	−	0.405962i
$879$	16.7502	+	29.0122i	0.564969	+	0.978556i
$880$	9.75159	−	16.8903i	0.328726	−	0.569370i
$881$	−13.1060			−0.441554			−0.220777	−	0.975324i	$-0.570859\pi$
$881$	−13.1060			−0.441554			−0.220777	+	0.975324i	$0.570859\pi$
$882$	14.5727	+	14.7839i	0.490690	+	0.497800i
$883$	−7.44435			−0.250522			−0.125261	−	0.992124i	$-0.539977\pi$
$883$	−7.44435			−0.250522			−0.125261	+	0.992124i	$0.539977\pi$
$884$	2.64347	−	4.57862i	0.0889095	−	0.153996i
$885$	17.2890	+	29.9454i	0.581163	+	1.00660i
$886$	−10.1854	−	17.6416i	−0.342185	−	0.592682i
$887$	−19.3417	+	33.5008i	−0.649430	+	1.12485i	0.333830	+	0.942633i	$0.391659\pi$
$887$	−19.3417	+	33.5008i	−0.649430	+	1.12485i	−0.983259	+	0.182212i	$0.941674\pi$
$888$	3.59871			0.120765
$889$	−1.83531	−	14.3389i	−0.0615544	−	0.480912i
$890$	54.9679			1.84253
$891$	−21.4218	+	37.1037i	−0.717658	+	1.24302i
$892$	5.45953	+	9.45618i	0.182798	+	0.316616i
$893$	−23.6957	−	41.0422i	−0.792947	−	1.37342i
$894$	−9.15706	+	15.8605i	−0.306258	+	0.530454i
$895$	4.99453			0.166949
$896$	2.44070	+	1.02127i	0.0815380	+	0.0341182i
$897$	−10.1390			−0.338531
$898$	−16.5721	+	28.7037i	−0.553018	+	0.957856i
$899$	−0.484522	−	0.839217i	−0.0161597	−	0.0279895i
$900$	−18.0429	−	31.2512i	−0.601429	−	1.04171i
$901$	3.84747	−	6.66401i	0.128178	−	0.222010i
$902$	−49.3014			−1.64156
$903$	40.3310	−	30.7172i	1.34213	−	1.02221i
$904$	14.5875			0.485173
$905$	−14.4007	+	24.9428i	−0.478697	+	0.829127i
$906$	11.5017	+	19.9215i	0.382118	+	0.661848i
$907$	−1.21313	−	2.10120i	−0.0402812	−	0.0697691i	0.845182	−	0.534479i	$-0.179492\pi$
$907$	−1.21313	−	2.10120i	−0.0402812	−	0.0697691i	−0.885463	+	0.464710i	$0.846159\pi$
$908$	5.24754	−	9.08901i	0.174146	−	0.301629i
$909$	−36.8500			−1.22224
$910$	16.6627	−	12.6908i	0.552364	−	0.420696i
$911$	−1.86661			−0.0618435			−0.0309218	−	0.999522i	$-0.509844\pi$
$911$	−1.86661			−0.0618435			−0.0309218	+	0.999522i	$0.509844\pi$
$912$	4.93423	−	8.54635i	0.163389	−	0.282998i
$913$	−14.2622	−	24.7028i	−0.472010	−	0.817545i
$914$	9.10435	+	15.7692i	0.301145	+	0.521599i
$915$	57.7822	−	100.082i	1.91022	−	3.30860i
$916$	−7.51525			−0.248311
$917$	−32.7497	−	13.7036i	−1.08149	−	0.452532i
$918$	0.232857			0.00768542
$919$	−13.7029	+	23.7340i	−0.452015	+	0.782914i	−0.998511	−	0.0545482i	$-0.982628\pi$
$919$	−13.7029	+	23.7340i	−0.452015	+	0.782914i	0.546496	+	0.837462i	$0.315961\pi$
$920$	4.50123	+	7.79635i	0.148401	+	0.257038i
$921$	9.33618	+	16.1707i	0.307638	+	0.532844i
$922$	1.76242	−	3.05260i	0.0580422	−	0.100532i
$923$	11.9347			0.392836
$924$	−3.86172	−	30.1708i	−0.127041	−	0.992547i
$925$	−17.9289			−0.589497
$926$	−5.38263	+	9.32299i	−0.176884	+	0.306372i
$927$	23.9792	+	41.5331i	0.787579	+	1.36413i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−21.9798	+	38.0701i	−0.721133	+	1.24904i	0.239413	+	0.970918i	$0.423045\pi$
$929$	−21.9798	+	38.0701i	−0.721133	+	1.24904i	−0.960546	+	0.278121i	$0.910288\pi$
$930$	9.80692			0.321582
$931$	7.51646	−	27.2657i	0.246342	−	0.893599i
$932$	5.14262			0.168452
$933$	29.8286	−	51.6646i	0.976544	−	1.69142i
$934$	−6.00994	−	10.4095i	−0.196651	−	0.340610i
$935$	26.9841	+	46.7378i	0.882473	+	1.52849i
$936$	2.83300	−	4.90691i	0.0925997	−	0.160387i
$937$	−29.9446			−0.978246			−0.489123	−	0.872215i	$-0.662683\pi$
$937$	−29.9446			−0.978246			−0.489123	+	0.872215i	$0.662683\pi$
$938$	0.764431	+	5.97235i	0.0249596	+	0.195004i
$939$	44.6101			1.45579
$940$	−24.3002	+	42.0891i	−0.792584	+	1.37280i
$941$	−10.7861	−	18.6821i	−0.351618	−	0.609020i	0.634915	−	0.772582i	$-0.281035\pi$
$941$	−10.7861	−	18.6821i	−0.351618	−	0.609020i	−0.986533	+	0.163562i	$0.947702\pi$
$942$	21.7727	+	37.7115i	0.709394	+	1.22871i
$943$	11.3785	−	19.7081i	0.370534	−	0.641784i
$944$	3.41673			0.111205
$945$	0.851011	+	0.356092i	0.0276834	+	0.0115837i
$946$	−36.9271			−1.20061
$947$	−2.19606	+	3.80369i	−0.0713624	+	0.123603i	−0.899499	−	0.436924i	$-0.856068\pi$
$947$	−2.19606	+	3.80369i	−0.0713624	+	0.123603i	0.828136	+	0.560527i	$0.189401\pi$
$948$	−5.45023	−	9.44008i	−0.177015	−	0.306600i
$949$	−12.9186	−	22.3756i	−0.419354	−	0.726343i
$950$	−24.5825	+	42.5781i	−0.797561	+	1.38142i
$951$	25.4545			0.825418
$952$	−5.82427	+	4.43593i	−0.188766	+	0.143769i
$953$	32.9052			1.06591			0.532953	−	0.846145i	$-0.321082\pi$
$953$	32.9052			1.06591			0.532953	+	0.846145i	$0.321082\pi$
$954$	4.12333	−	7.14181i	0.133498	−	0.231225i
$955$	14.1053	+	24.4312i	0.456438	+	0.790574i
$956$	−0.374837	−	0.649236i	−0.0121231	−	0.0209978i
$957$	5.74826	−	9.95629i	0.185815	−	0.321841i
$958$	8.29202			0.267903
$959$	−35.9988	+	27.4177i	−1.16246	+	0.885363i
$960$	−10.1202			−0.326628
$961$	15.0305	−	26.0335i	0.484854	−	0.839792i
$962$	−1.40755	−	2.43795i	−0.0453812	−	0.0786026i
$963$	−15.7538	−	27.2865i	−0.507660	−	0.879294i
$964$	4.50979	−	7.81119i	0.145251	−	0.251582i
$965$	−16.1456			−0.519745
$966$	12.9520	+	5.41954i	0.416723	+	0.174371i
$967$	4.50365			0.144827			0.0724137	−	0.997375i	$-0.476930\pi$
$967$	4.50365			0.144827			0.0724137	+	0.997375i	$0.476930\pi$
$968$	−5.57779	+	9.66102i	−0.179277	+	0.310517i
$969$	13.6537	+	23.6490i	0.438621	+	0.759714i
$970$	−34.8988	−	60.4465i	−1.12053	−	1.94082i
$971$	−15.2094	+	26.3435i	−0.488094	+	0.845403i	−0.999906	−	0.0136941i	$-0.995641\pi$
$971$	−15.2094	+	26.3435i	−0.488094	+	0.845403i	0.511813	+	0.859097i	$0.328974\pi$
$972$	21.9791			0.704981
$973$	1.31241	+	10.2536i	0.0420740	+	0.328715i
$974$	7.89345			0.252923
$975$	−28.3922	+	49.1767i	−0.909278	+	1.57491i
$976$	−5.70959	−	9.88930i	−0.182760	−	0.316549i
$977$	−18.7601	−	32.4935i	−0.600189	−	1.03956i	−0.992792	−	0.119850i	$-0.961759\pi$
$977$	−18.7601	−	32.4935i	−0.600189	−	1.03956i	0.392603	−	0.919708i	$-0.371575\pi$
$978$	−13.2856	+	23.0113i	−0.424826	+	0.735820i
$979$	−62.4434			−1.99570
$980$	−28.0693	+	7.30513i	−0.896640	+	0.233354i
$981$	18.0864			0.577454
$982$	18.8625	−	32.6708i	0.601926	−	1.04257i
$983$	−21.7439	−	37.6615i	−0.693523	−	1.20122i	−0.970676	−	0.240391i	$-0.922724\pi$
$983$	−21.7439	−	37.6615i	−0.693523	−	1.20122i	0.277153	−	0.960826i	$-0.410609\pi$
$984$	12.7912	+	22.1551i	0.407770	+	0.706278i
$985$	−32.2411	+	55.8432i	−1.02729	+	1.77931i
$986$	−2.76714			−0.0881238
$987$	9.62308	+	75.1832i	0.306306	+	2.39311i
$988$	−7.71964			−0.245595
$989$	8.52258	−	14.7615i	0.271002	−	0.469390i
$990$	28.9188	+	50.0888i	0.919100	+	1.59193i
$991$	27.7099	+	47.9949i	0.880233	+	1.52461i	0.851081	+	0.525034i	$0.175947\pi$
$991$	27.7099	+	47.9949i	0.880233	+	1.52461i	0.0291517	+	0.999575i	$0.490719\pi$
$992$	0.484522	−	0.839217i	0.0153836	−	0.0266452i
$993$	−11.4392			−0.363013
$994$	−15.2459	−	6.37940i	−0.483571	−	0.202342i
$995$	101.820			3.22790
$996$	−7.40065	+	12.8183i	−0.234499	+	0.406164i
$997$	11.9445	+	20.6884i	0.378285	+	0.655209i	0.990813	−	0.135240i	$-0.0431805\pi$
$997$	11.9445	+	20.6884i	0.378285	+	0.655209i	−0.612528	+	0.790449i	$0.709847\pi$
$998$	4.23971	+	7.34340i	0.134206	+	0.232451i
$999$	0.0619938	−	0.107376i	0.00196140	−	0.00339724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	406.2.e.a.233.5	✓	10
7.2	even	3		2842.2.a.z.1.1		5
7.4	even	3	inner	406.2.e.a.291.5	yes	10
7.5	odd	6		2842.2.a.x.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.5	✓	10	1.1	even	1	trivial
406.2.e.a.291.5	yes	10	7.4	even	3	inner
2842.2.a.x.1.5		5	7.5	odd	6
2842.2.a.z.1.1		5	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:	\( N \)	\(=\)	\( 406 = 2 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	406.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.22122 + 2.11522i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07173 + 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 - 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 + 2.56824i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.22122 + 2.11522i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07173 + 3.58835i) q^{5} -2.44245 q^{6} +(-0.335903 - 2.62434i) q^{7} +1.00000 q^{8} +(-1.48277 + 2.56824i) q^{9} +(-2.07173 - 3.58835i) q^{10} +(2.35349 + 4.07636i) q^{11} +(1.22122 - 2.11522i) q^{12} -1.91061 q^{13} +(2.44070 + 1.02127i) q^{14} -10.1202 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.38357 - 2.39642i) q^{17} +(-1.48277 - 2.56824i) q^{18} +(-2.02020 + 3.49909i) q^{19} +4.14347 q^{20} +(5.14085 - 3.91542i) q^{21} -4.70697 q^{22} +(1.08634 - 1.88160i) q^{23} +(1.22122 + 2.11522i) q^{24} +(-6.08417 - 10.5381i) q^{25} +(0.955306 - 1.65464i) q^{26} +0.0841506 q^{27} +(-2.10480 + 1.60307i) q^{28} -1.00000 q^{29} +(5.06010 - 8.76435i) q^{30} +(0.484522 + 0.839217i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-5.74826 + 9.95629i) q^{33} +2.76714 q^{34} +(10.1130 + 4.23160i) q^{35} +2.96555 q^{36} +(0.736701 - 1.27600i) q^{37} +(-2.02020 - 3.49909i) q^{38} +(-2.33328 - 4.04137i) q^{39} +(-2.07173 + 3.58835i) q^{40} +10.4741 q^{41} +(0.820425 + 6.40982i) q^{42} +7.84520 q^{43} +(2.35349 - 4.07636i) q^{44} +(-6.14382 - 10.6414i) q^{45} +(1.08634 + 1.88160i) q^{46} +(-5.86469 + 10.1579i) q^{47} -2.44245 q^{48} +(-6.77434 + 1.76305i) q^{49} +12.1683 q^{50} +(3.37930 - 5.85312i) q^{51} +(0.955306 + 1.65464i) q^{52} +(1.39041 + 2.40826i) q^{53} +(-0.0420753 + 0.0728765i) q^{54} -19.5032 q^{55} +(-0.335903 - 2.62434i) q^{56} -9.86847 q^{57} +(0.500000 - 0.866025i) q^{58} +(-1.70836 - 2.95897i) q^{59} +(5.06010 + 8.76435i) q^{60} +(-5.70959 + 9.88930i) q^{61} -0.969044 q^{62} +(7.23800 + 3.02862i) q^{63} +1.00000 q^{64} +(3.95828 - 6.85594i) q^{65} +(-5.74826 - 9.95629i) q^{66} +(1.13788 + 1.97086i) q^{67} +(-1.38357 + 2.39642i) q^{68} +5.30667 q^{69} +(-8.72115 + 6.64228i) q^{70} -6.24653 q^{71} +(-1.48277 + 2.56824i) q^{72} +(6.76148 + 11.7112i) q^{73} +(0.736701 + 1.27600i) q^{74} +(14.8603 - 25.7387i) q^{75} +4.04040 q^{76} +(9.90721 - 7.54561i) q^{77} +4.66657 q^{78} +(2.23146 - 3.86501i) q^{79} +(-2.07173 - 3.58835i) q^{80} +(4.55109 + 7.88271i) q^{81} +(-5.23706 + 9.07085i) q^{82} -6.06003 q^{83} +(-5.96128 - 2.49440i) q^{84} +11.4656 q^{85} +(-3.92260 + 6.79415i) q^{86} +(-1.22122 - 2.11522i) q^{87} +(2.35349 + 4.07636i) q^{88} +(-6.63308 + 11.4888i) q^{89} +12.2876 q^{90} +(0.641780 + 5.01410i) q^{91} -2.17268 q^{92} +(-1.18342 + 2.04974i) q^{93} +(-5.86469 - 10.1579i) q^{94} +(-8.37064 - 14.4984i) q^{95} +(1.22122 - 2.11522i) q^{96} +16.8452 q^{97} +(1.86032 - 6.74827i) q^{98} -13.9587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 3 * q^3 - 5 * q^4 - 7 * q^5 + 6 * q^6 - 3 * q^7 + 10 * q^8 - 8 * q^9 - 7 * q^10 - 3 * q^12 + 20 * q^13 + 3 * q^14 - 20 * q^15 - 5 * q^16 - 8 * q^17 - 8 * q^18 - 2 * q^19 + 14 * q^20 + 19 * q^21 - q^23 - 3 * q^24 - 12 * q^25 - 10 * q^26 + 30 * q^27 - 10 * q^29 + 10 * q^30 - 11 * q^31 - 5 * q^32 - 9 * q^33 + 16 * q^34 + 10 * q^35 + 16 * q^36 + 8 * q^37 - 2 * q^38 - 18 * q^39 - 7 * q^40 + 46 * q^41 - 8 * q^42 - 6 * q^43 - 4 * q^45 - q^46 - 16 * q^47 + 6 * q^48 - 11 * q^49 + 24 * q^50 - 7 * q^51 - 10 * q^52 - 7 * q^53 - 15 * q^54 + 12 * q^55 - 3 * q^56 - 68 * q^57 + 5 * q^58 + 9 * q^59 + 10 * q^60 - 15 * q^61 + 22 * q^62 - 3 * q^63 + 10 * q^64 - 5 * q^65 - 9 * q^66 + 4 * q^67 - 8 * q^68 + 28 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 8 * q^74 + 34 * q^75 + 4 * q^76 + 39 * q^77 + 36 * q^78 + 13 * q^79 - 7 * q^80 - 17 * q^81 - 23 * q^82 + 56 * q^83 - 11 * q^84 - 14 * q^85 + 3 * q^86 + 3 * q^87 - 17 * q^89 + 8 * q^90 + 6 * q^91 + 2 * q^92 - 17 * q^93 - 16 * q^94 + 9 * q^95 - 3 * q^96 + 84 * q^97 - 20 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more