LMFDB - Embedded newform 420.2.l.d.239.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.7
Root			$-1.19503 - 0.756243i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.d.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19503 - 0.756243i) q^{2} +(0.356193 - 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-0.856193 - 2.29498i) q^{6} -1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} +(-2.74625 - 1.20752i) q^{9} +O(q^{10})$	\(q+(1.19503 - 0.756243i) q^{2} +(0.356193 - 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-0.856193 - 2.29498i) q^{6} -1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} +(-2.74625 - 1.20752i) q^{9} +(2.70752 + 1.63382i) q^{10} +0.712386 q^{11} +(-2.75874 - 2.09508i) q^{12} -6.41503i q^{13} +(-1.19503 + 0.756243i) q^{14} +(3.74625 - 0.982644i) q^{15} +(-2.53387 - 3.09508i) q^{16} +5.49251 q^{17} +(-4.19503 + 0.633817i) q^{18} +0.975028i q^{19} +(4.47113 - 0.0950798i) q^{20} +(-0.356193 + 1.69503i) q^{21} +(0.851323 - 0.538737i) q^{22} +5.80509i q^{23} +(-4.88117 - 0.417406i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(-4.85132 - 7.66616i) q^{26} +(-3.02497 + 4.22487i) q^{27} +(-0.856193 + 1.80747i) q^{28} +6.41503i q^{29} +(3.73377 - 4.00737i) q^{30} -0.244852i q^{31} +(-5.36868 - 1.78249i) q^{32} +(0.253747 - 1.20752i) q^{33} +(6.56371 - 4.15367i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(-4.53387 + 3.92989i) q^{36} +5.42477i q^{37} +(0.737358 + 1.16519i) q^{38} +(-10.8737 - 2.28499i) q^{39} +(5.27122 - 3.49488i) q^{40} +1.42477i q^{41} +(0.856193 + 2.29498i) q^{42} +8.20489 q^{43} +(0.609940 - 1.28761i) q^{44} +(-0.331221 - 6.70002i) q^{45} +(4.39006 + 6.93726i) q^{46} +3.39006i q^{47} +(-6.14880 + 3.19253i) q^{48} +1.00000 q^{49} +(-0.560118 + 7.04885i) q^{50} +(1.95639 - 9.30996i) q^{51} +(-11.5950 - 5.49251i) q^{52} +4.84954 q^{53} +(-0.419902 + 7.33646i) q^{54} +(0.712386 + 1.42477i) q^{55} +(0.343707 + 2.80747i) q^{56} +(1.65270 + 0.347298i) q^{57} +(4.85132 + 7.66616i) q^{58} -7.47472 q^{59} +(1.43142 - 7.61256i) q^{60} -1.26982 q^{61} +(-0.185168 - 0.292606i) q^{62} +(2.74625 + 1.20752i) q^{63} +(-7.76373 + 1.92989i) q^{64} +(12.8301 - 6.41503i) q^{65} +(-0.609940 - 1.63491i) q^{66} -13.0350 q^{67} +(4.70265 - 9.92752i) q^{68} +(9.83980 + 2.06773i) q^{69} +(-2.70752 - 1.63382i) q^{70} +8.00000 q^{71} +(-2.44615 + 8.12504i) q^{72} -8.00000i q^{73} +(4.10245 + 6.48277i) q^{74} +(5.71154 + 6.50986i) q^{75} +(1.76233 + 0.834812i) q^{76} -0.712386 q^{77} +(-14.7224 + 5.49251i) q^{78} +15.0002i q^{79} +(3.65629 - 8.16281i) q^{80} +(6.08381 + 6.63229i) q^{81} +(1.07747 + 1.70265i) q^{82} -7.96004i q^{83} +(2.75874 + 2.09508i) q^{84} +(5.49251 + 10.9850i) q^{85} +(9.80509 - 6.20489i) q^{86} +(10.8737 + 2.28499i) q^{87} +(-0.244852 - 2.00000i) q^{88} +6.25484i q^{89} +(-5.46266 - 7.75624i) q^{90} +6.41503i q^{91} +(10.4925 + 4.97028i) q^{92} +(-0.415032 - 0.0872147i) q^{93} +(2.56371 + 4.05122i) q^{94} +(-1.95006 + 0.975028i) q^{95} +(-4.93367 + 8.46516i) q^{96} -18.0946i q^{97} +(1.19503 - 0.756243i) q^{98} +(-1.95639 - 0.860218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{4} + 8 q^{5} - 2 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 2 * q^4 + 8 * q^5 - 2 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{3} + 2 q^{4} + 8 q^{5} - 2 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9} + 4 q^{10} - 4 q^{11} + 10 q^{12} + 6 q^{15} - 6 q^{16} - 4 q^{17} - 24 q^{18} - 6 q^{20} + 2 q^{21} - 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} - 8 q^{27} - 2 q^{28} + 14 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} - 20 q^{38} - 18 q^{39} + 2 q^{40} + 2 q^{42} + 8 q^{43} + 24 q^{44} - 14 q^{45} + 16 q^{46} + 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} - 16 q^{52} + 24 q^{54} - 4 q^{55} + 6 q^{56} + 20 q^{57} + 26 q^{58} - 8 q^{59} + 26 q^{60} - 16 q^{61} - 40 q^{62} - 2 q^{63} + 26 q^{64} + 32 q^{65} - 24 q^{66} + 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} + 6 q^{72} + 4 q^{74} + 22 q^{75} - 28 q^{76} + 4 q^{77} + 4 q^{78} + 26 q^{80} + 2 q^{81} - 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} + 18 q^{87} - 24 q^{88} - 4 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^4 + 8 * q^5 - 2 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9 + 4 * q^10 - 4 * q^11 + 10 * q^12 + 6 * q^15 - 6 * q^16 - 4 * q^17 - 24 * q^18 - 6 * q^20 + 2 * q^21 - 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 - 8 * q^27 - 2 * q^28 + 14 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 - 20 * q^38 - 18 * q^39 + 2 * q^40 + 2 * q^42 + 8 * q^43 + 24 * q^44 - 14 * q^45 + 16 * q^46 + 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 - 16 * q^52 + 24 * q^54 - 4 * q^55 + 6 * q^56 + 20 * q^57 + 26 * q^58 - 8 * q^59 + 26 * q^60 - 16 * q^61 - 40 * q^62 - 2 * q^63 + 26 * q^64 + 32 * q^65 - 24 * q^66 + 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 + 6 * q^72 + 4 * q^74 + 22 * q^75 - 28 * q^76 + 4 * q^77 + 4 * q^78 + 26 * q^80 + 2 * q^81 - 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 + 18 * q^87 - 24 * q^88 - 4 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.19503	−	0.756243i	0.845014	−	0.534745i
$2$	1.19503	−	0.756243i	0.845014	−	0.534745i
$3$	0.356193	−	1.69503i	0.205648	−	0.978626i
$3$	0.356193	−	1.69503i	0.205648	−	0.978626i
$4$	0.856193	−	1.80747i	0.428097	−	0.903733i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	−0.856193	−	2.29498i	−0.349539	−	0.936922i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.343707	−	2.80747i	−0.121519	−	0.992589i
$9$	−2.74625	−	1.20752i	−0.915418	−	0.402505i
$10$	2.70752	+	1.63382i	0.856192	+	0.516658i
$11$	0.712386			0.214793			0.107396	−	0.994216i	$-0.465749\pi$
$11$	0.712386			0.214793			0.107396	+	0.994216i	$0.465749\pi$
$12$	−2.75874	−	2.09508i	−0.796379	−	0.604797i
$13$		−	6.41503i		−	1.77921i	−0.456731	−	0.889605i	$-0.650980\pi$
$13$		−	6.41503i		−	1.77921i	0.456731	−	0.889605i	$-0.349020\pi$
$14$	−1.19503	+	0.756243i	−0.319385	+	0.202114i
$15$	3.74625	−	0.982644i	0.967278	−	0.253718i
$16$	−2.53387	−	3.09508i	−0.633467	−	0.773770i
$17$	5.49251			1.33213			0.666064	−	0.745894i	$-0.267978\pi$
$17$	5.49251			1.33213			0.666064	+	0.745894i	$0.267978\pi$
$18$	−4.19503	+	0.633817i	−0.988778	+	0.149392i
$19$			0.975028i			0.223687i	0.993726	+	0.111843i	$0.0356755\pi$
$19$			0.975028i			0.223687i	−0.993726	+	0.111843i	$0.964325\pi$
$20$	4.47113	−	0.0950798i	0.999774	−	0.0212605i
$21$	−0.356193	+	1.69503i	−0.0777277	+	0.369886i
$22$	0.851323	−	0.538737i	0.181503	−	0.114859i
$23$			5.80509i			1.21045i	0.796056	+	0.605223i	$0.206916\pi$
$23$			5.80509i			1.21045i	−0.796056	+	0.605223i	$0.793084\pi$
$24$	−4.88117	−	0.417406i	−0.996364	−	0.0852027i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	−4.85132	−	7.66616i	−0.951423	−	1.50346i
$27$	−3.02497	+	4.22487i	−0.582156	+	0.813077i
$28$	−0.856193	+	1.80747i	−0.161805	+	0.341579i
$29$			6.41503i			1.19124i	0.803266	+	0.595621i	$0.203094\pi$
$29$			6.41503i			1.19124i	−0.803266	+	0.595621i	$0.796906\pi$
$30$	3.73377	−	4.00737i	0.681689	−	0.731642i
$31$		−	0.244852i		−	0.0439768i	−0.999758	−	0.0219884i	$-0.993000\pi$
$31$		−	0.244852i		−	0.0439768i	0.999758	−	0.0219884i	$-0.00699968\pi$
$32$	−5.36868	−	1.78249i	−0.949057	−	0.315103i
$33$	0.253747	−	1.20752i	0.0441717	−	0.210202i
$34$	6.56371	−	4.15367i	1.12567	−	0.712348i
$35$	−1.00000	−	2.00000i	−0.169031	−	0.338062i
$36$	−4.53387	+	3.92989i	−0.755644	+	0.654982i
$37$			5.42477i			0.891827i	0.895076	+	0.445914i	$0.147121\pi$
$37$			5.42477i			0.891827i	−0.895076	+	0.445914i	$0.852879\pi$
$38$	0.737358	+	1.16519i	0.119615	+	0.189018i
$39$	−10.8737	−	2.28499i	−1.74118	−	0.365891i
$40$	5.27122	−	3.49488i	0.833454	−	0.552589i
$41$			1.42477i			0.222512i	0.993792	+	0.111256i	$0.0354874\pi$
$41$			1.42477i			0.222512i	−0.993792	+	0.111256i	$0.964513\pi$
$42$	0.856193	+	2.29498i	0.132113	+	0.354123i
$43$	8.20489			1.25123			0.625617	−	0.780130i	$-0.284847\pi$
$43$	8.20489			1.25123			0.625617	+	0.780130i	$0.284847\pi$
$44$	0.609940	−	1.28761i	0.0919519	−	0.194115i
$45$	−0.331221	−	6.70002i	−0.0493755	−	0.998780i
$46$	4.39006	+	6.93726i	0.647279	+	1.02284i
$47$			3.39006i			0.494491i	0.968953	+	0.247246i	$0.0795254\pi$
$47$			3.39006i			0.494491i	−0.968953	+	0.247246i	$0.920475\pi$
$48$	−6.14880	+	3.19253i	−0.887503	+	0.460803i
$49$	1.00000			0.142857
$50$	−0.560118	+	7.04885i	−0.0792126	+	0.996858i
$51$	1.95639	−	9.30996i	0.273950	−	1.30366i
$52$	−11.5950	−	5.49251i	−1.60793	−	0.761674i
$53$	4.84954			0.666136			0.333068	−	0.942903i	$-0.391916\pi$
$53$	4.84954			0.666136			0.333068	+	0.942903i	$0.391916\pi$
$54$	−0.419902	+	7.33646i	−0.0571414	+	0.998366i
$55$	0.712386	+	1.42477i	0.0960581	+	0.192116i
$56$	0.343707	+	2.80747i	0.0459298	+	0.375163i
$57$	1.65270	+	0.347298i	0.218906	+	0.0460008i
$58$	4.85132	+	7.66616i	0.637010	+	1.00662i
$59$	−7.47472			−0.973125			−0.486563	−	0.873646i	$-0.661749\pi$
$59$	−7.47472			−0.973125			−0.486563	+	0.873646i	$0.661749\pi$
$60$	1.43142	−	7.61256i	0.184796	−	0.982777i
$61$	−1.26982			−0.162584			−0.0812922	−	0.996690i	$-0.525905\pi$
$61$	−1.26982			−0.162584			−0.0812922	+	0.996690i	$0.525905\pi$
$62$	−0.185168	−	0.292606i	−0.0235163	−	0.0371610i
$63$	2.74625	+	1.20752i	0.345995	+	0.152133i
$64$	−7.76373	+	1.92989i	−0.970466	+	0.241237i
$65$	12.8301	−	6.41503i	1.59137	−	0.795687i
$66$	−0.609940	−	1.63491i	−0.0750784	−	0.201244i
$67$	−13.0350			−1.59247			−0.796237	−	0.604985i	$-0.793179\pi$
$67$	−13.0350			−1.59247			−0.796237	+	0.604985i	$0.793179\pi$
$68$	4.70265	−	9.92752i	0.570280	−	1.20389i
$69$	9.83980	+	2.06773i	1.18457	+	0.248926i
$70$	−2.70752	−	1.63382i	−0.323610	−	0.195278i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−2.44615	+	8.12504i	−0.288282	+	0.957546i
$73$		−	8.00000i		−	0.936329i	−0.883641	−	0.468165i	$-0.844915\pi$
$73$		−	8.00000i		−	0.936329i	0.883641	−	0.468165i	$-0.155085\pi$
$74$	4.10245	+	6.48277i	0.476900	+	0.753606i
$75$	5.71154	+	6.50986i	0.659512	+	0.751694i
$76$	1.76233	+	0.834812i	0.202153	+	0.0957595i
$77$	−0.712386			−0.0811839
$78$	−14.7224	+	5.49251i	−1.66698	+	0.621904i
$79$			15.0002i			1.68766i	0.536611	+	0.843830i	$0.319704\pi$
$79$			15.0002i			1.68766i	−0.536611	+	0.843830i	$0.680296\pi$
$80$	3.65629	−	8.16281i	0.408786	−	0.912630i
$81$	6.08381	+	6.63229i	0.675979	+	0.736921i
$82$	1.07747	+	1.70265i	0.118987	+	0.188026i
$83$		−	7.96004i		−	0.873728i	−0.899528	−	0.436864i	$-0.856089\pi$
$83$		−	7.96004i		−	0.873728i	0.899528	−	0.436864i	$-0.143911\pi$
$84$	2.75874	+	2.09508i	0.301003	+	0.228592i
$85$	5.49251	+	10.9850i	0.595746	+	1.19149i
$86$	9.80509	−	6.20489i	1.05731	−	0.669091i
$87$	10.8737	+	2.28499i	1.16578	+	0.244977i
$88$	−0.244852	−	2.00000i	−0.0261013	−	0.213201i
$89$			6.25484i			0.663011i	0.943453	+	0.331506i	$0.107557\pi$
$89$			6.25484i			0.663011i	−0.943453	+	0.331506i	$0.892443\pi$
$90$	−5.46266	−	7.75624i	−0.575815	−	0.817580i
$91$			6.41503i			0.672478i
$92$	10.4925	+	4.97028i	1.09392	+	0.518187i
$93$	−0.415032	−	0.0872147i	−0.0430368	−	0.00904374i
$94$	2.56371	+	4.05122i	0.264426	+	0.417852i
$95$	−1.95006	+	0.975028i	−0.200072	+	0.100036i
$96$	−4.93367	+	8.46516i	−0.503540	+	0.863972i
$97$		−	18.0946i		−	1.83723i	−0.395151	−	0.918616i	$-0.629308\pi$
$97$		−	18.0946i		−	1.83723i	0.395151	−	0.918616i	$-0.370692\pi$
$98$	1.19503	−	0.756243i	0.120716	−	0.0763921i
$99$	−1.95639	−	0.860218i	−0.196625	−	0.0864551i
$100$	4.66128	+	8.84717i	0.466128	+	0.884717i
$101$		−	4.69460i		−	0.467130i	−0.972341	−	0.233565i	$-0.924961\pi$
$101$		−	4.69460i		−	0.467130i	0.972341	−	0.233565i	$-0.0750391\pi$
$102$	−4.70265	−	12.6052i	−0.465631	−	1.24810i
$103$	−2.66244			−0.262338			−0.131169	−	0.991360i	$-0.541873\pi$
$103$	−2.66244			−0.262338			−0.131169	+	0.991360i	$0.541873\pi$
$104$	−18.0100	+	2.20489i	−1.76602	+	0.216207i
$105$	−3.74625	+	0.982644i	−0.365597	+	0.0958962i
$106$	5.79535	−	3.66743i	0.562894	−	0.356213i
$107$		−	15.2299i		−	1.47233i	−0.676804	−	0.736163i	$-0.736636\pi$
$107$		−	15.2299i		−	1.47233i	0.676804	−	0.736163i	$-0.263364\pi$
$108$	5.04635	+	9.08484i	0.485586	+	0.874189i
$109$	−1.49251			−0.142956			−0.0714781	−	0.997442i	$-0.522772\pi$
$109$	−1.49251			−0.142956			−0.0714781	+	0.997442i	$0.522772\pi$
$110$	1.92880	+	1.16391i	0.183904	+	0.110974i
$111$	9.19515	+	1.93227i	0.872765	+	0.183403i
$112$	2.53387	+	3.09508i	0.239428	+	0.292458i
$113$	−8.25484			−0.776550			−0.388275	−	0.921544i	$-0.626929\pi$
$113$	−8.25484			−0.776550			−0.388275	+	0.921544i	$0.626929\pi$
$114$	2.23767	−	0.834812i	0.209577	−	0.0781873i
$115$	−11.6102	+	5.80509i	−1.08266	+	0.541328i
$116$	11.5950	+	5.49251i	1.07656	+	0.509966i
$117$	−7.74625	+	17.6173i	−0.716141	+	1.62872i
$118$	−8.93251	+	5.65270i	−0.822304	+	0.520373i
$119$	−5.49251			−0.503497
$120$	−4.04635	−	10.1797i	−0.369380	−	0.929279i
$121$	−10.4925			−0.953864
$122$	−1.51748	+	0.960296i	−0.137386	+	0.0869411i
$123$	2.41503	+	0.507494i	0.217756	+	0.0457592i
$124$	−0.442562	−	0.209641i	−0.0397432	−	0.0188263i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	4.19503	−	0.633817i	0.373723	−	0.0564649i
$127$	−9.42477			−0.836313			−0.418157	−	0.908375i	$-0.637324\pi$
$127$	−9.42477			−0.836313			−0.418157	+	0.908375i	$0.637324\pi$
$128$	−7.81842	+	8.17755i	−0.691058	+	0.722800i
$129$	2.92253	−	13.9075i	0.257314	−	1.22449i
$130$	10.4810	−	17.3688i	0.919243	−	1.52334i
$131$	17.6297			1.54031			0.770155	−	0.637856i	$-0.220179\pi$
$131$	17.6297			1.54031			0.770155	+	0.637856i	$0.220179\pi$
$132$	−1.96529	−	1.49251i	−0.171056	−	0.129906i
$133$		−	0.975028i		−	0.0845457i
$134$	−15.5772	+	9.85759i	−1.34566	+	0.851566i
$135$	−11.4747	−	1.82507i	−0.987586	−	0.157077i
$136$	−1.88781	−	15.4200i	−0.161879	−	1.32226i
$137$	−2.73018			−0.233255			−0.116627	−	0.993176i	$-0.537208\pi$
$137$	−2.73018			−0.233255			−0.116627	+	0.993176i	$0.537208\pi$
$138$	13.3226	−	4.97028i	1.13409	−	0.423098i
$139$		−	0.449744i		−	0.0381468i	−0.999818	−	0.0190734i	$-0.993928\pi$
$139$		−	0.449744i		−	0.0381468i	0.999818	−	0.0190734i	$-0.00607162\pi$
$140$	−4.47113	+	0.0950798i	−0.377879	+	0.00803571i
$141$	5.74625	+	1.20752i	0.483922	+	0.101691i
$142$	9.56024	−	6.04994i	0.802277	−	0.507700i
$143$		−	4.56998i		−	0.382161i
$144$	3.22128	+	11.5596i	0.268440	+	0.963296i
$145$	−12.8301	+	6.41503i	−1.06548	+	0.532739i
$146$	−6.04994	−	9.56024i	−0.500697	−	0.791211i
$147$	0.356193	−	1.69503i	0.0293783	−	0.139804i
$148$	9.80509	+	4.64465i	0.805974	+	0.381788i
$149$			1.15046i			0.0942490i	0.998889	+	0.0471245i	$0.0150057\pi$
$149$			1.15046i			0.0942490i	−0.998889	+	0.0471245i	$0.984994\pi$
$150$	11.7485	+	3.46017i	0.959261	+	0.282522i
$151$		−	1.40954i		−	0.114707i	−0.998354	−	0.0573534i	$-0.981734\pi$
$151$		−	1.40954i		−	0.114707i	0.998354	−	0.0573534i	$-0.0182662\pi$
$152$	2.73736	−	0.335124i	0.222029	−	0.0271822i
$153$	−15.0838	−	6.63229i	−1.21945	−	0.536189i
$154$	−0.851323	+	0.538737i	−0.0686015	+	0.0434127i
$155$	0.489704	−	0.244852i	0.0393340	−	0.0196670i
$156$	−13.4400	+	17.6974i	−1.07606	+	1.41693i
$157$			1.15046i			0.0918163i	0.998946	+	0.0459082i	$0.0146182\pi$
$157$			1.15046i			0.0918163i	−0.998946	+	0.0459082i	$0.985382\pi$
$158$	11.3438	+	17.9257i	0.902467	+	1.42610i
$159$	1.72737	−	8.22012i	0.136990	−	0.651898i
$160$	−1.80369	−	12.5199i	−0.142594	−	0.989781i
$161$		−	5.80509i		−	0.457505i
$162$	12.2860	+	3.32494i	0.965276	+	0.261232i
$163$	15.4747			1.21207			0.606037	−	0.795437i	$-0.292758\pi$
$163$	15.4747			1.21207			0.606037	+	0.795437i	$0.292758\pi$
$164$	2.57523	+	1.21988i	0.201091	+	0.0952566i
$165$	2.66878	−	0.700022i	0.207764	−	0.0544966i
$166$	−6.01972	−	9.51249i	−0.467221	−	0.738312i
$167$			14.9698i			1.15840i	0.815187	+	0.579198i	$0.196634\pi$
$167$			14.9698i			1.15840i	−0.815187	+	0.579198i	$0.803366\pi$
$168$	4.88117	+	0.417406i	0.376590	+	0.0322036i
$169$	−28.1526			−2.16559
$170$	14.8710	+	8.97375i	1.14056	+	0.688255i
$171$	1.17736	−	2.67767i	0.0900351	−	0.204767i
$172$	7.02497	−	14.8301i	0.535649	−	1.13078i
$173$	9.49251			0.721702			0.360851	−	0.932624i	$-0.382486\pi$
$173$	9.49251			0.721702			0.360851	+	0.932624i	$0.382486\pi$
$174$	14.7224	−	5.49251i	1.11610	−	0.416386i
$175$	3.00000	−	4.00000i	0.226779	−	0.302372i
$176$	−1.80509	−	2.20489i	−0.136064	−	0.166200i
$177$	−2.66244	+	12.6699i	−0.200121	+	0.952326i
$178$	4.73018	+	7.47472i	0.354542	+	0.560254i
$179$	3.61018			0.269838			0.134919	−	0.990857i	$-0.456923\pi$
$179$	3.61018			0.269838			0.134919	+	0.990857i	$0.456923\pi$
$180$	−12.3937	−	5.13784i	−0.923768	−	0.382952i
$181$	11.5602			0.859266			0.429633	−	0.903004i	$-0.358643\pi$
$181$	11.5602			0.859266			0.429633	+	0.903004i	$0.358643\pi$
$182$	4.85132	+	7.66616i	0.359604	+	0.568253i
$183$	−0.452303	+	2.15239i	−0.0334352	+	0.159109i
$184$	16.2976	−	1.99525i	1.20147	−	0.147092i
$185$	−10.8495	+	5.42477i	−0.797674	+	0.398837i
$186$	−0.561931	+	0.209641i	−0.0412028	+	0.0153716i
$187$	3.91279			0.286131
$188$	6.12742	+	2.90255i	0.446888	+	0.211690i
$189$	3.02497	−	4.22487i	0.220034	−	0.307314i
$190$	−1.59302	+	2.63990i	−0.115570	+	0.191519i
$191$	−26.8978			−1.94626			−0.973128	−	0.230264i	$-0.926041\pi$
$191$	−26.8978			−1.94626			−0.973128	+	0.230264i	$0.926041\pi$
$192$	0.505838	+	13.8472i	0.0365057	+	0.999333i
$193$		−	10.1549i		−	0.730969i	−0.930817	−	0.365485i	$-0.880903\pi$
$193$		−	10.1549i		−	0.730969i	0.930817	−	0.365485i	$-0.119097\pi$
$194$	−13.6839	−	21.6236i	−0.982450	−	1.55249i
$195$	−6.30369	−	24.0323i	−0.451417	−	1.72099i
$196$	0.856193	−	1.80747i	0.0611566	−	0.129105i
$197$	−8.15495			−0.581016			−0.290508	−	0.956873i	$-0.593824\pi$
$197$	−8.15495			−0.581016			−0.290508	+	0.956873i	$0.593824\pi$
$198$	−2.98848	+	0.451522i	−0.212382	+	0.0320883i
$199$		−	7.96004i		−	0.564272i	−0.959374	−	0.282136i	$-0.908957\pi$
$199$		−	7.96004i		−	0.564272i	0.959374	−	0.282136i	$-0.0910430\pi$
$200$	12.2610	+	7.04757i	0.866983	+	0.498338i
$201$	−4.64296	+	22.0946i	−0.327489	+	1.55844i
$202$	−3.55026	−	5.61018i	−0.249795	−	0.394731i
$203$		−	6.41503i		−	0.450247i
$204$	−15.1524	−	11.5072i	−1.06088	−	0.805668i
$205$	−2.84954	+	1.42477i	−0.199021	+	0.0995104i
$206$	−3.18170	+	2.01345i	−0.221679	+	0.140284i
$207$	7.00974	−	15.9423i	0.487211	−	1.10806i
$208$	−19.8550	+	16.2548i	−1.37670	+	1.12707i
$209$			0.694597i			0.0480462i
$210$	−3.73377	+	4.00737i	−0.257654	+	0.276535i
$211$			14.9698i			1.03056i	0.857021	+	0.515281i	$0.172312\pi$
$211$			14.9698i			1.03056i	−0.857021	+	0.515281i	$0.827688\pi$
$212$	4.15215	−	8.76539i	0.285171	−	0.602009i
$213$	2.84954	−	13.5602i	0.195248	−	0.929132i
$214$	−11.5175	−	18.2001i	−0.787319	−	1.24414i
$215$	8.20489	+	16.4098i	0.559569	+	1.11914i
$216$	12.9009	+	7.04039i	0.877794	+	0.479038i
$217$			0.244852i			0.0166217i
$218$	−1.78359	+	1.12870i	−0.120800	+	0.0764450i
$219$	−13.5602	−	2.84954i	−0.916316	−	0.192554i
$220$	3.18517	−	0.0677336i	0.214744	−	0.00456660i
$221$		−	35.2346i		−	2.37014i
$222$	12.4497	−	4.64465i	0.835572	−	0.311729i
$223$	2.62686			0.175908			0.0879539	−	0.996125i	$-0.471967\pi$
$223$	2.62686			0.175908			0.0879539	+	0.996125i	$0.471967\pi$
$224$	5.36868	+	1.78249i	0.358710	+	0.119098i
$225$	13.0688	−	7.36246i	0.871255	−	0.490831i
$226$	−9.86478	+	6.24266i	−0.656195	+	0.415256i
$227$		−	3.39006i		−	0.225006i	−0.993651	−	0.112503i	$-0.964113\pi$
$227$		−	3.39006i		−	0.225006i	0.993651	−	0.112503i	$-0.0358868\pi$
$228$	2.04276	−	2.68985i	0.135285	−	0.178140i
$229$	24.5647			1.62328			0.811642	−	0.584156i	$-0.198574\pi$
$229$	24.5647			1.62328			0.811642	+	0.584156i	$0.198574\pi$
$230$	−9.48446	+	15.7174i	−0.625387	+	1.03637i
$231$	−0.253747	+	1.20752i	−0.0166953	+	0.0794487i
$232$	18.0100	−	2.20489i	1.18241	−	0.144758i
$233$	−21.0849			−1.38132			−0.690659	−	0.723181i	$-0.742679\pi$
$233$	−21.0849			−1.38132			−0.690659	+	0.723181i	$0.742679\pi$
$234$	4.06596	+	26.9113i	0.265800	+	1.75924i
$235$	−6.78012	+	3.39006i	−0.442286	+	0.221143i
$236$	−6.39980	+	13.5103i	−0.416592	+	0.879445i
$237$	25.4259	+	5.34298i	1.65159	+	0.347064i
$238$	−6.56371	+	4.15367i	−0.425462	+	0.269242i
$239$	12.3581			0.799382			0.399691	−	0.916650i	$-0.369117\pi$
$239$	12.3581			0.799382			0.399691	+	0.916650i	$0.369117\pi$
$240$	−12.5339	−	9.10506i	−0.809058	−	0.587729i
$241$	−14.9655			−0.964015			−0.482007	−	0.876167i	$-0.660092\pi$
$241$	−14.9655			−0.964015			−0.482007	+	0.876167i	$0.660092\pi$
$242$	−12.5389	+	7.93488i	−0.806028	+	0.510074i
$243$	13.4089	−	7.94987i	0.860184	−	0.509984i
$244$	−1.08721	+	2.29516i	−0.0696018	+	0.146933i
$245$	1.00000	+	2.00000i	0.0638877	+	0.127775i
$246$	3.26982	−	1.21988i	0.208476	−	0.0777767i
$247$	6.25484			0.397986
$248$	−0.687414	+	0.0841574i	−0.0436508	+	0.00534400i
$249$	−13.4925	−	2.83531i	−0.855053	−	0.179681i
$250$	−14.6578	+	5.92861i	−0.927042	+	0.374958i
$251$	−7.47472			−0.471800			−0.235900	−	0.971777i	$-0.575804\pi$
$251$	−7.47472			−0.471800			−0.235900	+	0.971777i	$0.575804\pi$
$252$	4.53387	−	3.92989i	0.285607	−	0.247560i
$253$			4.13547i			0.259995i
$254$	−11.2629	+	7.12742i	−0.706696	+	0.447214i
$255$	20.5763	−	5.39718i	1.28854	−	0.337984i
$256$	−3.15904	+	15.6850i	−0.197440	+	0.980315i
$257$	−22.5097			−1.40411			−0.702057	−	0.712120i	$-0.747735\pi$
$257$	−22.5097			−1.40411			−0.702057	+	0.712120i	$0.747735\pi$
$258$	−7.02497	−	18.8301i	−0.437356	−	1.17231i
$259$		−	5.42477i		−	0.337079i
$260$	−0.609940	−	28.6824i	−0.0378269	−	1.77881i
$261$	7.74625	−	17.6173i	0.479481	−	1.09048i
$262$	21.0680	−	13.3323i	1.30158	−	0.823673i
$263$		−	9.17992i		−	0.566058i	−0.959111	−	0.283029i	$-0.908661\pi$
$263$		−	9.17992i		−	0.566058i	0.959111	−	0.283029i	$-0.0913393\pi$
$264$	−3.47727	−	0.297354i	−0.214011	−	0.0183009i
$265$	4.84954	+	9.69909i	0.297905	+	0.595810i
$266$	−0.737358	−	1.16519i	−0.0452103	−	0.0714422i
$267$	10.6021	+	2.22793i	0.648840	+	0.136347i
$268$	−11.1604	+	23.5602i	−0.681732	+	1.43917i
$269$			19.6796i			1.19989i	0.800042	+	0.599943i	$0.204810\pi$
$269$			19.6796i			1.19989i	−0.800042	+	0.599943i	$0.795190\pi$
$270$	−15.0928	+	6.49666i	−0.918520	+	0.395374i
$271$		−	29.3459i		−	1.78263i	−0.453381	−	0.891317i	$-0.649782\pi$
$271$		−	29.3459i		−	1.78263i	0.453381	−	0.891317i	$-0.350218\pi$
$272$	−13.9173	−	16.9997i	−0.843859	−	1.03076i
$273$	10.8737	+	2.28499i	0.658105	+	0.138294i
$274$	−3.26264	+	2.06468i	−0.197103	+	0.124732i
$275$	−2.13716	+	2.84954i	−0.128876	+	0.171834i
$276$	12.1621	−	16.0147i	0.732074	−	0.963974i
$277$		−	6.11937i		−	0.367677i	−0.982956	−	0.183839i	$-0.941148\pi$
$277$		−	6.11937i		−	0.367677i	0.982956	−	0.183839i	$-0.0588524\pi$
$278$	−0.340116	−	0.537458i	−0.0203988	−	0.0322346i
$279$	−0.295663	+	0.672426i	−0.0177009	+	0.0402571i
$280$	−5.27122	+	3.49488i	−0.315016	+	0.208859i
$281$			0.434513i			0.0259209i	0.999916	+	0.0129604i	$0.00412555\pi$
$281$			0.434513i			0.0259209i	−0.999916	+	0.0129604i	$0.995874\pi$
$282$	7.78012	−	2.90255i	0.463299	−	0.172844i
$283$	−1.72737			−0.102682			−0.0513409	−	0.998681i	$-0.516349\pi$
$283$	−1.72737			−0.102682			−0.0513409	+	0.998681i	$0.516349\pi$
$284$	6.84954	−	14.4597i	0.406446	−	0.858027i
$285$	0.958105	+	3.65270i	0.0567533	+	0.216367i
$286$	−3.45602	−	5.46126i	−0.204358	−	0.322931i
$287$		−	1.42477i		−	0.0841017i
$288$	12.5914	+	11.3779i	0.741953	+	0.670452i
$289$	13.1676			0.774566
$290$	−10.4810	+	17.3688i	−0.615465	+	1.01993i
$291$	−30.6710	−	6.44519i	−1.79796	−	0.377823i
$292$	−14.4597	−	6.84954i	−0.846192	−	0.400839i
$293$	−23.1526			−1.35259			−0.676296	−	0.736630i	$-0.736416\pi$
$293$	−23.1526			−1.35259			−0.676296	+	0.736630i	$0.736416\pi$
$294$	−0.856193	−	2.29498i	−0.0499342	−	0.133846i
$295$	−7.47472	−	14.9494i	−0.435195	−	0.870390i
$296$	15.2299	−	1.86453i	0.885218	−	0.108374i
$297$	−2.15495	+	3.00974i	−0.125043	+	0.174643i
$298$	0.870024	+	1.37483i	0.0503991	+	0.0796417i
$299$	37.2398			2.15364
$300$	16.6565	−	4.74972i	0.961666	−	0.274225i
$301$	−8.20489			−0.472922
$302$	−1.06596	−	1.68444i	−0.0613388	−	0.0969288i
$303$	−7.95748	−	1.67218i	−0.457145	−	0.0960644i
$304$	3.01779	−	2.47059i	0.173082	−	0.141698i
$305$	−1.26982	−	2.53965i	−0.0727099	−	0.145420i
$306$	−23.0412	+	3.48124i	−1.31718	+	0.199009i
$307$	9.99831			0.570634			0.285317	−	0.958433i	$-0.407901\pi$
$307$	9.99831			0.570634			0.285317	+	0.958433i	$0.407901\pi$
$308$	−0.609940	+	1.28761i	−0.0347546	+	0.0733686i
$309$	−0.948344	+	4.51292i	−0.0539494	+	0.256731i
$310$	0.400044	−	0.662941i	0.0227210	−	0.0376525i
$311$	−26.5647			−1.50635			−0.753174	−	0.657821i	$-0.771478\pi$
$311$	−26.5647			−1.50635			−0.753174	+	0.657821i	$0.771478\pi$
$312$	−2.67767	+	31.3128i	−0.151593	+	1.77274i
$313$		−	15.5655i		−	0.879813i	−0.898043	−	0.439907i	$-0.855012\pi$
$313$		−	15.5655i		−	0.879813i	0.898043	−	0.439907i	$-0.144988\pi$
$314$	0.870024	+	1.37483i	0.0490983	+	0.0775861i
$315$	0.331221	+	6.70002i	0.0186622	+	0.377503i
$316$	27.1124	+	12.8431i	1.52519	+	0.722481i
$317$	8.98501			0.504649			0.252324	−	0.967643i	$-0.418805\pi$
$317$	8.98501			0.504649			0.252324	+	0.967643i	$0.418805\pi$
$318$	−4.15215	−	11.1296i	−0.232841	−	0.624117i
$319$			4.56998i			0.255870i
$320$	−11.6235	−	13.5976i	−0.649774	−	0.760127i
$321$	−25.8151	−	5.42477i	−1.44086	−	0.302781i
$322$	−4.39006	−	6.93726i	−0.244648	−	0.386598i
$323$			5.35535i			0.297979i
$324$	17.1966	−	5.31776i	0.955364	−	0.295431i
$325$	25.6601	+	19.2451i	1.42337	+	1.06753i
$326$	18.4927	−	11.7026i	1.02422	−	0.648150i
$327$	−0.531620	+	2.52984i	−0.0293987	+	0.139901i
$328$	4.00000	−	0.489704i	0.220863	−	0.0270394i
$329$		−	3.39006i		−	0.186900i
$330$	2.65988	−	2.85479i	0.146422	−	0.157151i
$331$			3.65014i			0.200630i	0.994956	+	0.100315i	$0.0319851\pi$
$331$			3.65014i			0.200630i	−0.994956	+	0.100315i	$0.968015\pi$
$332$	−14.3875	−	6.81533i	−0.789617	−	0.374040i
$333$	6.55050	−	14.8978i	0.358965	−	0.816394i
$334$	11.3208	+	17.8893i	0.619446	+	0.978861i
$335$	−13.0350	−	26.0699i	−0.712176	−	1.42435i
$336$	6.14880	−	3.19253i	0.335444	−	0.174167i
$337$			25.1400i			1.36946i	0.728796	+	0.684730i	$0.240080\pi$
$337$			25.1400i			1.36946i	−0.728796	+	0.684730i	$0.759920\pi$
$338$	−33.6432	+	21.2902i	−1.82995	+	1.15804i
$339$	−2.94032	+	13.9922i	−0.159696	+	0.759952i
$340$	24.5577	−	0.522227i	1.33183	−	0.0283217i
$341$		−	0.174429i		−	0.00944588i
$342$	−0.617989	−	4.09027i	−0.0334170	−	0.221177i
$343$	−1.00000			−0.0539949
$344$	−2.82008	−	23.0350i	−0.152049	−	1.24196i
$345$	5.70434	+	21.7473i	0.307111	+	1.17084i
$346$	11.3438	−	7.17864i	0.609848	−	0.385926i
$347$			15.1144i			0.811382i	0.914010	+	0.405691i	$0.132969\pi$
$347$			15.1144i			0.811382i	−0.914010	+	0.405691i	$0.867031\pi$
$348$	13.4400	−	17.6974i	0.720460	−	0.948680i
$349$	8.39030			0.449123			0.224561	−	0.974460i	$-0.427905\pi$
$349$	8.39030			0.449123			0.224561	+	0.974460i	$0.427905\pi$
$350$	0.560118	−	7.04885i	0.0299396	−	0.376777i
$351$	27.1027	+	19.4053i	1.44663	+	1.03578i
$352$	−3.82457	−	1.26982i	−0.203850	−	0.0676819i
$353$	19.0172			1.01218			0.506091	−	0.862480i	$-0.331090\pi$
$353$	19.0172			1.01218			0.506091	+	0.862480i	$0.331090\pi$
$354$	6.39980	+	17.1543i	0.340146	+	0.911742i
$355$	8.00000	+	16.0000i	0.424596	+	0.849192i
$356$	11.3054	+	5.35535i	0.599185	+	0.283833i
$357$	−1.95639	+	9.30996i	−0.103543	+	0.492735i
$358$	4.31428	−	2.73018i	0.228017	−	0.144294i
$359$	17.6601			0.932066			0.466033	−	0.884767i	$-0.345683\pi$
$359$	17.6601			0.932066			0.466033	+	0.884767i	$0.345683\pi$
$360$	−18.6962	+	3.23274i	−0.985378	+	0.170380i
$361$	18.0493			0.949964
$362$	13.8148	−	8.74235i	0.726091	−	0.459488i
$363$	−3.73736	+	17.7851i	−0.196160	+	0.933476i
$364$	11.5950	+	5.49251i	0.607741	+	0.287886i
$365$	16.0000	−	8.00000i	0.837478	−	0.418739i
$366$	1.08721	+	2.91422i	0.0568296	+	0.152329i
$367$	−27.2720			−1.42359			−0.711793	−	0.702389i	$-0.752117\pi$
$367$	−27.2720			−1.42359			−0.711793	+	0.702389i	$0.752117\pi$
$368$	17.9672	−	14.7093i	0.936606	−	0.766777i
$369$	1.72044	−	3.91279i	0.0895623	−	0.203691i
$370$	−8.86308	+	14.6877i	−0.460770	+	0.763575i
$371$	−4.84954			−0.251776
$372$	−0.512985	+	0.675483i	−0.0265970	+	0.0350222i
$373$		−	5.10438i		−	0.264295i	−0.991230	−	0.132147i	$-0.957813\pi$
$373$		−	5.10438i		−	0.264295i	0.991230	−	0.132147i	$-0.0421872\pi$
$374$	4.67590	−	2.95902i	0.241785	−	0.153007i
$375$	−7.30818	+	17.9329i	−0.377393	+	0.926053i
$376$	9.51748	−	1.16519i	0.490826	−	0.0600900i
$377$	41.1526			2.11947
$378$	0.419902	−	7.33646i	0.0215974	−	0.377347i
$379$		−	16.3109i		−	0.837834i	−0.908024	−	0.418917i	$-0.862410\pi$
$379$		−	16.3109i		−	0.837834i	0.908024	−	0.418917i	$-0.137590\pi$
$380$	0.0927055	+	4.35947i	0.00475569	+	0.223636i
$381$	−3.35704	+	15.9753i	−0.171986	+	0.818438i
$382$	−32.1437	+	20.3413i	−1.64461	+	1.04075i
$383$			25.3492i			1.29529i	0.761944	+	0.647643i	$0.224245\pi$
$383$			25.3492i			1.29529i	−0.761944	+	0.647643i	$0.775755\pi$
$384$	11.0763	+	16.1652i	0.565236	+	0.824929i
$385$	−0.712386	−	1.42477i	−0.0363066	−	0.0726131i
$386$	−7.67961	−	12.1355i	−0.390882	−	0.617679i
$387$	−22.5327	−	9.90754i	−1.14540	−	0.503628i
$388$	−32.7054	−	15.4925i	−1.66037	−	0.786513i
$389$		−	12.1141i		−	0.614210i	−0.951676	−	0.307105i	$-0.900640\pi$
$389$		−	12.1141i		−	0.614210i	0.951676	−	0.307105i	$-0.0993603\pi$
$390$	−25.7074	−	23.9522i	−1.30174	−	1.21287i
$391$			31.8845i			1.61247i
$392$	−0.343707	−	2.80747i	−0.0173598	−	0.141798i
$393$	6.27956	−	29.8828i	0.316762	−	1.50739i
$394$	−9.74541	+	6.16712i	−0.490967	+	0.310695i
$395$	−30.0005	+	15.0002i	−1.50949	+	0.754744i
$396$	−3.22986	+	2.79960i	−0.162307	+	0.140685i
$397$		−	17.5355i		−	0.880082i	−0.897978	−	0.440041i	$-0.854964\pi$
$397$		−	17.5355i		−	0.880082i	0.897978	−	0.440041i	$-0.145036\pi$
$398$	−6.01972	−	9.51249i	−0.301742	−	0.476818i
$399$	−1.65270	−	0.347298i	−0.0827386	−	0.0173867i
$400$	19.9819	−	0.850228i	0.999096	−	0.0425114i
$401$			16.7054i			0.834230i	0.908854	+	0.417115i	$0.136959\pi$
$401$			16.7054i			0.834230i	−0.908854	+	0.417115i	$0.863041\pi$
$402$	11.1604	+	29.9150i	0.556632	+	1.49202i
$403$	−1.57073			−0.0782439
$404$	−8.48532	−	4.01948i	−0.422161	−	0.199977i
$405$	−7.18077	+	18.7999i	−0.356815	+	0.934175i
$406$	−4.85132	−	7.66616i	−0.240767	−	0.380465i
$407$			3.86453i			0.191558i
$408$	−26.8098	−	2.29261i	−1.32728	−	0.113501i
$409$	−23.8346			−1.17854			−0.589271	−	0.807935i	$-0.700585\pi$
$409$	−23.8346			−1.17854			−0.589271	+	0.807935i	$0.700585\pi$
$410$	−2.32782	+	3.85759i	−0.114963	+	0.190513i
$411$	−0.972470	+	4.62773i	−0.0479684	+	0.228269i
$412$	−2.27956	+	4.81227i	−0.112306	+	0.237084i
$413$	7.47472			0.367807
$414$	−3.67937	−	24.3525i	−0.180831	−	1.19686i
$415$	15.9201	−	7.96004i	0.781486	−	0.390743i
$416$	−11.4348	+	34.4402i	−0.560635	+	1.68857i
$417$	−0.762330	−	0.160196i	−0.0373315	−	0.00784482i
$418$	0.525284	+	0.830064i	0.0256925	+	0.0405997i
$419$	20.6252			1.00761			0.503803	−	0.863819i	$-0.331934\pi$
$419$	20.6252			1.00761			0.503803	+	0.863819i	$0.331934\pi$
$420$	−1.43142	+	7.61256i	−0.0698462	+	0.371455i
$421$	2.64296			0.128810			0.0644050	−	0.997924i	$-0.479485\pi$
$421$	2.64296			0.128810			0.0644050	+	0.997924i	$0.479485\pi$
$422$	11.3208	+	17.8893i	0.551088	+	0.870839i
$423$	4.09355	−	9.30996i	0.199035	−	0.452666i
$424$	−1.66682	−	13.6149i	−0.0809481	−	0.661200i
$425$	−16.4775	+	21.9700i	−0.799277	+	1.06570i
$426$	−6.84954	−	18.3598i	−0.331862	−	0.889537i
$427$	1.26982			0.0614511
$428$	−27.5275	−	13.0397i	−1.33059	−	0.630298i
$429$	−7.74625	−	1.62780i	−0.373993	−	0.0785907i
$430$	22.2149	+	13.4053i	1.07130	+	0.646461i
$431$	6.93676			0.334132			0.167066	−	0.985946i	$-0.446571\pi$
$431$	6.93676			0.334132			0.167066	+	0.985946i	$0.446571\pi$
$432$	20.7412	−	1.34273i	0.997911	−	0.0646023i
$433$			14.5396i			0.698731i	0.936987	+	0.349365i	$0.113603\pi$
$433$			14.5396i			0.698731i	−0.936987	+	0.349365i	$0.886397\pi$
$434$	0.185168	+	0.292606i	0.00888834	+	0.0140455i
$435$	6.30369	+	24.0323i	0.302239	+	1.15226i
$436$	−1.27787	+	2.69765i	−0.0611990	+	0.129194i
$437$	−5.66013			−0.270761
$438$	−18.3598	+	6.84954i	−0.877267	+	0.327284i
$439$			24.8595i			1.18648i	0.805025	+	0.593240i	$0.202152\pi$
$439$			24.8595i			1.18648i	−0.805025	+	0.593240i	$0.797848\pi$
$440$	3.75515	−	2.48970i	0.179020	−	0.118692i
$441$	−2.74625	−	1.20752i	−0.130774	−	0.0575008i
$442$	−26.6459	−	42.1064i	−1.26742	−	2.00280i
$443$			7.43476i			0.353236i	0.984279	+	0.176618i	$0.0565157\pi$
$443$			7.43476i			0.353236i	−0.984279	+	0.176618i	$0.943484\pi$
$444$	11.3653	−	14.9655i	0.539375	−	0.710233i
$445$	−12.5097	+	6.25484i	−0.593015	+	0.296508i
$446$	3.13918	−	1.98655i	0.148644	−	0.0940657i
$447$	1.95006	+	0.409784i	0.0922345	+	0.0193821i
$448$	7.76373	−	1.92989i	0.366802	−	0.0911788i
$449$			6.97416i			0.329131i	0.986366	+	0.164566i	$0.0526222\pi$
$449$			6.97416i			0.329131i	−0.986366	+	0.164566i	$0.947378\pi$
$450$	10.0498	−	18.6816i	0.473753	−	0.880658i
$451$			1.01499i			0.0477939i
$452$	−7.06773	+	14.9203i	−0.332438	+	0.701794i
$453$	−2.38921	−	0.502069i	−0.112255	−	0.0235892i
$454$	−2.56371	−	4.05122i	−0.120321	−	0.190133i
$455$	−12.8301	+	6.41503i	−0.601483	+	0.300741i
$456$	0.406983	−	4.75927i	0.0190587	−	0.222873i
$457$		−	31.2559i		−	1.46209i	−0.682328	−	0.731046i	$-0.739033\pi$
$457$		−	31.2559i		−	1.46209i	0.682328	−	0.731046i	$-0.260967\pi$
$458$	29.3556	−	18.5769i	1.37170	−	0.868042i
$459$	−16.6147	+	23.2051i	−0.775507	+	1.08312i
$460$	0.551947	+	25.9553i	0.0257347	+	1.21017i
$461$			19.1594i			0.892344i	0.894947	+	0.446172i	$0.147213\pi$
$461$			19.1594i			0.892344i	−0.894947	+	0.446172i	$0.852787\pi$
$462$	0.609940	+	1.63491i	0.0283770	+	0.0760630i
$463$	−23.9150			−1.11142			−0.555711	−	0.831375i	$-0.687554\pi$
$463$	−23.9150			−1.11142			−0.555711	+	0.831375i	$0.687554\pi$
$464$	19.8550	−	16.2548i	0.921747	−	0.754612i
$465$	−0.240602	−	0.917278i	−0.0111577	−	0.0425378i
$466$	−25.1971	+	15.9453i	−1.16723	+	0.738652i
$467$		−	6.23960i		−	0.288734i	−0.989524	−	0.144367i	$-0.953885\pi$
$467$		−	6.23960i		−	0.288734i	0.989524	−	0.144367i	$-0.0461147\pi$
$468$	25.2104	+	29.0849i	1.16535	+	1.34445i
$469$	13.0350			0.601898
$470$	−5.53874	+	9.17864i	−0.255483	+	0.423379i
$471$	1.95006	+	0.409784i	0.0898538	+	0.0188819i
$472$	2.56911	+	20.9850i	0.118253	+	0.965913i
$473$	5.84505			0.268756
$474$	34.4253	−	12.8431i	1.58120	−	0.589903i
$475$	−3.90011	−	2.92508i	−0.178949	−	0.134212i
$476$	−4.70265	+	9.92752i	−0.215545	+	0.455027i
$477$	−13.3181	−	5.85590i	−0.609793	−	0.268123i
$478$	14.7684	−	9.34576i	0.675489	−	0.427465i
$479$	9.13996			0.417615			0.208808	−	0.977957i	$-0.433042\pi$
$479$	9.13996			0.417615			0.208808	+	0.977957i	$0.433042\pi$
$480$	−21.8640	−	1.40217i	−0.997950	−	0.0640002i
$481$	34.8001			1.58675
$482$	−17.8843	+	11.3176i	−0.814606	+	0.515502i
$483$	−9.83980	−	2.06773i	−0.447727	−	0.0940851i
$484$	−8.98361	+	18.9648i	−0.408346	+	0.862039i
$485$	36.1893	−	18.0946i	1.64327	−	0.821635i
$486$	10.0121	−	19.6407i	0.454156	−	0.890922i
$487$	34.1055			1.54547			0.772734	−	0.634730i	$-0.218889\pi$
$487$	34.1055			1.54547			0.772734	+	0.634730i	$0.218889\pi$
$488$	0.436448	+	3.56499i	0.0197571	+	0.161379i
$489$	5.51199	−	26.2301i	0.249261	−	1.18617i
$490$	2.70752	+	1.63382i	0.122313	+	0.0738083i
$491$	−29.2576			−1.32038			−0.660189	−	0.751099i	$-0.729524\pi$
$491$	−29.2576			−1.32038			−0.660189	+	0.751099i	$0.729524\pi$
$492$	2.98501	−	3.93058i	0.134575	−	0.177204i
$493$			35.2346i			1.58689i
$494$	7.47472	−	4.73018i	0.336303	−	0.212821i
$495$	−0.235957	−	4.77300i	−0.0106055	−	0.214531i
$496$	−0.757837	+	0.620423i	−0.0340279	+	0.0278578i
$497$	−8.00000			−0.358849
$498$	−18.2681	+	6.81533i	−0.818615	+	0.305402i
$499$		−	7.32063i		−	0.327717i	−0.986484	−	0.163858i	$-0.947606\pi$
$499$		−	7.32063i		−	0.327717i	0.986484	−	0.163858i	$-0.0523940\pi$
$500$	−13.0331	+	18.1697i	−0.582856	+	0.812575i
$501$	25.3742	+	5.33213i	1.13364	+	0.238222i
$502$	−8.93251	+	5.65270i	−0.398677	+	0.252292i
$503$			23.7609i			1.05945i	0.848171	+	0.529723i	$0.177704\pi$
$503$			23.7609i			1.05945i	−0.848171	+	0.529723i	$0.822296\pi$
$504$	2.44615	−	8.12504i	0.108960	−	0.361918i
$505$	9.38919	−	4.69460i	0.417814	−	0.208907i
$506$	3.12742	+	4.94201i	0.139031	+	0.219699i
$507$	−10.0278	+	47.7196i	−0.445349	+	2.11930i
$508$	−8.06942	+	17.0350i	−0.358023	+	0.755804i
$509$			16.8301i			0.745979i	0.927835	+	0.372990i	$0.121667\pi$
$509$			16.8301i			0.745979i	−0.927835	+	0.372990i	$0.878333\pi$
$510$	20.5077	−	22.0105i	0.908098	−	0.974641i
$511$			8.00000i			0.353899i
$512$	8.08656	+	21.1331i	0.357379	+	0.933960i
$513$	−4.11937	−	2.94943i	−0.181875	−	0.130221i
$514$	−26.8997	+	17.0228i	−1.18650	+	0.750843i
$515$	−2.66244	−	5.32488i	−0.117321	−	0.234642i
$516$	−22.6352	−	17.1899i	−0.996457	−	0.756743i
$517$			2.41503i			0.106213i
$518$	−4.10245	−	6.48277i	−0.180251	−	0.284836i
$519$	3.38117	−	16.0901i	0.148417	−	0.706276i
$520$	−22.4198	−	33.8151i	−0.983172	−	1.48289i
$521$		−	0.555747i		−	0.0243477i	−0.999926	−	0.0121738i	$-0.996125\pi$
$521$		−	0.555747i		−	0.0243477i	0.999926	−	0.0121738i	$-0.00387515\pi$
$522$	−4.06596	−	26.9113i	−0.177962	−	1.17787i
$523$	30.7307			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$523$	30.7307			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$524$	15.0944	−	31.8650i	0.659402	−	1.39203i
$525$	−5.71154	−	6.50986i	−0.249272	−	0.284114i
$526$	−6.94225	−	10.9703i	−0.302696	−	0.478327i
$527$		−	1.34485i		−	0.0585827i
$528$	−4.38032	+	2.27432i	−0.190629	+	0.0989769i
$529$	−10.6991			−0.465178
$530$	13.1302	+	7.92327i	0.570340	+	0.344165i
$531$	20.5275	+	9.02584i	0.890816	+	0.391688i
$532$	−1.76233	−	0.834812i	−0.0764067	−	0.0361937i
$533$	9.13996			0.395896
$534$	14.3547	−	5.35535i	0.621190	−	0.231749i
$535$	30.4597	−	15.2299i	1.31689	−	0.658444i
$536$	4.48021	+	36.5952i	0.193515	+	1.58067i
$537$	1.28592	−	6.11937i	0.0554916	−	0.264070i
$538$	14.8826	+	23.5177i	0.641633	+	1.01392i
$539$	0.712386			0.0306846
$540$	−13.1233	+	19.1775i	−0.564738	+	0.825270i
$541$	12.0322			0.517303			0.258651	−	0.965971i	$-0.416722\pi$
$541$	12.0322			0.517303			0.258651	+	0.965971i	$0.416722\pi$
$542$	−22.1926	−	35.0692i	−0.953254	−	1.50635i
$543$	4.11768	−	19.5950i	0.176706	−	0.840900i
$544$	−29.4875	−	9.79036i	−1.26427	−	0.419758i
$545$	−1.49251	−	2.98501i	−0.0639319	−	0.127864i
$546$	14.7224	−	5.49251i	0.630059	−	0.235058i
$547$	−3.89500			−0.166538			−0.0832690	−	0.996527i	$-0.526536\pi$
$547$	−3.89500			−0.166538			−0.0832690	+	0.996527i	$0.526536\pi$
$548$	−2.33756	+	4.93470i	−0.0998555	+	0.210800i
$549$	3.48726	+	1.53333i	0.148833	+	0.0654411i
$550$	−0.399020	+	5.02150i	−0.0170143	+	0.214118i
$551$	−6.25484			−0.266465
$552$	2.42308	−	28.3356i	0.103133	−	1.20604i
$553$		−	15.0002i		−	0.637875i
$554$	−4.62773	−	7.31283i	−0.196613	−	0.310692i
$555$	5.33062	+	20.3226i	0.226272	+	0.862645i
$556$	−0.812898	−	0.385068i	−0.0344745	−	0.0163305i
$557$	36.1055			1.52984			0.764919	−	0.644126i	$-0.222779\pi$
$557$	36.1055			1.52984			0.764919	+	0.644126i	$0.222779\pi$
$558$	0.155191	+	1.02716i	0.00656978	+	0.0434832i
$559$		−	52.6346i		−	2.22621i
$560$	−3.65629	+	8.16281i	−0.154507	+	0.344942i
$561$	1.39371	−	6.63229i	0.0588424	−	0.280015i
$562$	0.328597	+	0.519256i	0.0138610	+	0.0219035i
$563$		−	29.3103i		−	1.23528i	−0.786461	−	0.617640i	$-0.788089\pi$
$563$		−	29.3103i		−	1.23528i	0.786461	−	0.617640i	$-0.211911\pi$
$564$	7.10245	−	9.35229i	0.299067	−	0.393802i
$565$	−8.25484	−	16.5097i	−0.347284	−	0.694567i
$566$	−2.06426	+	1.30631i	−0.0867675	+	0.0549085i
$567$	−6.08381	−	6.63229i	−0.255496	−	0.278530i
$568$	−2.74966	−	22.4597i	−0.115373	−	0.942389i
$569$		−	32.2709i		−	1.35287i	−0.736503	−	0.676434i	$-0.763524\pi$
$569$		−	32.2709i		−	1.35287i	0.736503	−	0.676434i	$-0.236476\pi$
$570$	3.90729	+	3.64053i	0.163659	+	0.152485i
$571$		−	40.8595i		−	1.70992i	−0.518696	−	0.854959i	$-0.673582\pi$
$571$		−	40.8595i		−	1.70992i	0.518696	−	0.854959i	$-0.326418\pi$
$572$	−8.26008	−	3.91279i	−0.345371	−	0.163602i
$573$	−9.58081	+	45.5926i	−0.400244	+	1.90466i
$574$	−1.07747	−	1.70265i	−0.0449729	−	0.0710671i
$575$	−23.2204	−	17.4153i	−0.968356	−	0.726267i
$576$	23.6515	+	4.07486i	0.985481	+	0.169786i
$577$		−	8.43451i		−	0.351133i	−0.984468	−	0.175567i	$-0.943824\pi$
$577$		−	8.43451i		−	0.351133i	0.984468	−	0.175567i	$-0.0561758\pi$
$578$	15.7357	−	9.95792i	0.654519	−	0.414195i
$579$	−17.2129	−	3.61712i	−0.715345	−	0.150322i
$580$	0.609940	+	28.6824i	0.0253264	+	1.19097i
$581$			7.96004i			0.330238i
$582$	−41.5268	+	15.4925i	−1.72134	+	0.642185i
$583$	3.45475			0.143081
$584$	−22.4597	+	2.74966i	−0.929390	+	0.113782i
$585$	−42.9809	+	2.12479i	−1.77704	+	0.0878494i
$586$	−27.6681	+	17.5090i	−1.14296	+	0.723291i
$587$			3.57022i			0.147359i	0.997282	+	0.0736794i	$0.0234742\pi$
$587$			3.57022i			0.147359i	−0.997282	+	0.0736794i	$0.976526\pi$
$588$	−2.75874	−	2.09508i	−0.113768	−	0.0863996i
$589$	0.238738			0.00983702
$590$	−20.2379	−	12.2123i	−0.833182	−	0.502773i
$591$	−2.90474	+	13.8229i	−0.119485	+	0.568597i
$592$	16.7901	−	13.7457i	0.690069	−	0.564943i
$593$	32.9872			1.35462			0.677311	−	0.735697i	$-0.263145\pi$
$593$	32.9872			1.35462			0.677311	+	0.735697i	$0.263145\pi$
$594$	−0.299132	+	5.22639i	−0.0122736	+	0.214442i
$595$	−5.49251	−	10.9850i	−0.225171	−	0.450342i
$596$	2.07941	+	0.985012i	0.0851759	+	0.0403477i
$597$	−13.4925	−	2.83531i	−0.552212	−	0.116042i
$598$	44.5027	−	28.1624i	1.81985	−	1.15165i
$599$	26.2926			1.07429			0.537143	−	0.843491i	$-0.319504\pi$
$599$	26.2926			1.07429			0.537143	+	0.843491i	$0.319504\pi$
$600$	16.3131	−	18.2724i	0.665980	−	0.745969i
$601$	−43.1548			−1.76032			−0.880161	−	0.474676i	$-0.842565\pi$
$601$	−43.1548			−1.76032			−0.880161	+	0.474676i	$0.842565\pi$
$602$	−9.80509	+	6.20489i	−0.399626	+	0.252893i
$603$	35.7973	+	15.7399i	1.45778	+	0.640979i
$604$	−2.54770	−	1.20684i	−0.103664	−	0.0491056i
$605$	−10.4925	−	20.9850i	−0.426581	−	0.853162i
$606$	−10.7740	+	4.01948i	−0.437664	+	0.163280i
$607$	−28.3581			−1.15102			−0.575511	−	0.817794i	$-0.695197\pi$
$607$	−28.3581			−1.15102			−0.575511	+	0.817794i	$0.695197\pi$
$608$	1.73798	−	5.23461i	0.0704845	−	0.212292i
$609$	−10.8737	−	2.28499i	−0.440623	−	0.0925925i
$610$	−3.43807	−	2.07466i	−0.139203	−	0.0840005i
$611$	21.7473			0.879803
$612$	−24.9023	+	21.5850i	−1.00662	+	0.872520i
$613$			23.2593i			0.939435i	0.882817	+	0.469718i	$0.155644\pi$
$613$			23.2593i			0.939435i	−0.882817	+	0.469718i	$0.844356\pi$
$614$	11.9483	−	7.56115i	0.482193	−	0.305143i
$615$	1.40004	+	5.33756i	0.0564552	+	0.215231i
$616$	0.244852	+	2.00000i	0.00986538	+	0.0805823i
$617$	−12.4398			−0.500806			−0.250403	−	0.968142i	$-0.580563\pi$
$617$	−12.4398			−0.500806			−0.250403	+	0.968142i	$0.580563\pi$
$618$	2.27956	+	6.11025i	0.0916975	+	0.245790i
$619$		−	22.2948i		−	0.896104i	−0.894008	−	0.448052i	$-0.852118\pi$
$619$		−	22.2948i		−	0.896104i	0.894008	−	0.448052i	$-0.147882\pi$
$620$	−0.0232805	−	1.09476i	−0.000934968	−	0.0439668i
$621$	−24.5258	−	17.5602i	−0.984185	−	0.704668i
$622$	−31.7457	+	20.0894i	−1.27288	+	0.805511i
$623$		−	6.25484i		−	0.250595i
$624$	20.4802	+	39.4447i	0.819864	+	1.57905i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−11.7713	−	18.6012i	−0.470475	−	0.743454i
$627$	1.17736	+	0.247410i	0.0470193	+	0.00988062i
$628$	2.07941	+	0.985012i	0.0829774	+	0.0393063i
$629$			29.7956i			1.18803i
$630$	5.46266	+	7.75624i	0.217638	+	0.309016i
$631$		−	41.0397i		−	1.63376i	−0.576805	−	0.816882i	$-0.695701\pi$
$631$		−	41.0397i		−	1.63376i	0.576805	−	0.816882i	$-0.304299\pi$
$632$	42.1127	−	5.15569i	1.67515	−	0.205082i
$633$	25.3742	+	5.33213i	1.00853	+	0.211933i
$634$	10.7374	−	6.79485i	0.426435	−	0.269858i
$635$	−9.42477	−	18.8495i	−0.374011	−	0.748021i
$636$	−13.3786	−	10.1602i	−0.530497	−	0.402877i
$637$		−	6.41503i		−	0.254173i
$638$	3.45602	+	5.46126i	0.136825	+	0.216213i
$639$	−21.9700	−	9.66013i	−0.869121	−	0.382149i
$640$	−24.1735	−	7.45930i	−0.955542	−	0.294855i
$641$			32.4707i			1.28252i	0.767325	+	0.641258i	$0.221587\pi$
$641$			32.4707i			1.28252i	−0.767325	+	0.641258i	$0.778413\pi$
$642$	−34.9522	+	13.0397i	−1.37945	+	0.514636i
$643$	23.5230			0.927655			0.463828	−	0.885925i	$-0.346476\pi$
$643$	23.5230			0.927655			0.463828	+	0.885925i	$0.346476\pi$
$644$	−10.4925	−	4.97028i	−0.413463	−	0.195856i
$645$	30.7376	−	8.06249i	1.21029	−	0.317460i
$646$	4.04994	+	6.39980i	0.159343	+	0.251797i
$647$		−	39.8090i		−	1.56505i	−0.622618	−	0.782526i	$-0.713931\pi$
$647$		−	39.8090i		−	1.56505i	0.622618	−	0.782526i	$-0.286069\pi$
$648$	16.5289	−	19.3597i	0.649316	−	0.760519i
$649$	−5.32488			−0.209020
$650$	45.2186	+	3.59317i	1.77362	+	0.140936i
$651$	0.415032	+	0.0872147i	0.0162664	+	0.00341821i
$652$	13.2493	−	27.9700i	0.518884	−	1.09539i
$653$	−43.6496			−1.70814			−0.854071	−	0.520156i	$-0.825874\pi$
$653$	−43.6496			−1.70814			−0.854071	+	0.520156i	$0.825874\pi$
$654$	1.27787	+	3.42527i	0.0499688	+	0.133939i
$655$	17.6297	+	35.2593i	0.688848	+	1.37770i
$656$	4.40978	−	3.61018i	0.172173	−	0.140954i
$657$	−9.66013	+	21.9700i	−0.376877	+	0.857132i
$658$	−2.56371	−	4.05122i	−0.0999438	−	0.157933i
$659$	6.44705			0.251142			0.125571	−	0.992085i	$-0.459924\pi$
$659$	6.44705			0.251142			0.125571	+	0.992085i	$0.459924\pi$
$660$	1.01972	−	5.42308i	0.0396927	−	0.211093i
$661$	−6.27432			−0.244043			−0.122021	−	0.992527i	$-0.538938\pi$
$661$	−6.27432			−0.244043			−0.122021	+	0.992527i	$0.538938\pi$
$662$	2.76040	+	4.36203i	0.107286	+	0.169535i
$663$	−59.7237	−	12.5503i	−2.31948	−	0.487414i
$664$	−22.3475	+	2.73592i	−0.867253	+	0.106174i
$665$	1.95006	−	0.975028i	0.0756199	−	0.0378100i
$666$	−3.43831	−	22.7571i	−0.133232	−	0.881819i
$667$	−37.2398			−1.44193
$668$	27.0574	+	12.8170i	1.04688	+	0.495905i
$669$	0.935670	−	4.45261i	0.0361751	−	0.172148i
$670$	−35.2924	−	21.2967i	−1.36346	−	0.822764i
$671$	−0.904605			−0.0349219
$672$	4.93367	−	8.46516i	0.190320	−	0.326551i
$673$			44.0860i			1.69939i	0.527274	+	0.849695i	$0.323214\pi$
$673$			44.0860i			1.69939i	−0.527274	+	0.849695i	$0.676786\pi$
$674$	19.0119	+	30.0430i	0.732312	+	1.15721i
$675$	−7.82457	−	24.7745i	−0.301168	−	0.953571i
$676$	−24.1041	+	50.8849i	−0.927080	+	1.95711i
$677$	−7.79342			−0.299525			−0.149763	−	0.988722i	$-0.547851\pi$
$677$	−7.79342			−0.299525			−0.149763	+	0.988722i	$0.547851\pi$
$678$	7.06773	+	18.9447i	0.271435	+	0.727566i
$679$			18.0946i			0.694409i
$680$	28.9522	−	19.1957i	1.11027	−	0.736120i
$681$	−5.74625	−	1.20752i	−0.220197	−	0.0462721i
$682$	−0.131911	−	0.208448i	−0.00505113	−	0.00798190i
$683$		−	27.8855i		−	1.06701i	−0.845797	−	0.533504i	$-0.820875\pi$
$683$		−	27.8855i		−	1.06701i	0.845797	−	0.533504i	$-0.179125\pi$
$684$	−3.83176	−	4.42065i	−0.146511	−	0.169028i
$685$	−2.73018	−	5.46035i	−0.104315	−	0.208629i
$686$	−1.19503	+	0.756243i	−0.0456265	+	0.0288735i
$687$	8.74979	−	41.6380i	0.333825	−	1.58859i
$688$	−20.7901	−	25.3948i	−0.792615	−	0.968168i
$689$		−	31.1100i		−	1.18520i
$690$	23.2631	+	21.6749i	0.885612	+	0.825148i
$691$		−	28.0295i		−	1.06629i	−0.846024	−	0.533146i	$-0.821010\pi$
$691$		−	28.0295i		−	1.06629i	0.846024	−	0.533146i	$-0.178990\pi$
$692$	8.12742	−	17.1574i	0.308958	−	0.652226i
$693$	1.95639	+	0.860218i	0.0743172	+	0.0326770i
$694$	11.4301	+	18.0621i	0.433882	+	0.685629i
$695$	0.899489	−	0.449744i	0.0341195	−	0.0170598i
$696$	2.67767	−	31.3128i	0.101497	−	1.18691i
$697$			7.82557i			0.296415i
$698$	10.0267	−	6.34511i	0.379515	−	0.240166i
$699$	−7.51030	+	35.7395i	−0.284065	+	1.35179i
$700$	−4.66128	−	8.84717i	−0.176180	−	0.334392i
$701$			23.2346i			0.877559i	0.898595	+	0.438779i	$0.144589\pi$
$701$			23.2346i			0.877559i	−0.898595	+	0.438779i	$0.855411\pi$
$702$	47.0636	+	2.69369i	1.77630	+	0.101667i
$703$	−5.28931			−0.199490
$704$	−5.53077	+	1.37483i	−0.208449	+	0.0518158i
$705$	3.33122	+	12.7000i	0.125461	+	0.478310i
$706$	22.7261	−	14.3816i	0.855307	−	0.541259i
$707$			4.69460i			0.176558i
$708$	20.6208	+	15.6601i	0.774977	+	0.588544i
$709$	28.6519			1.07605			0.538023	−	0.842930i	$-0.319171\pi$
$709$	28.6519			1.07605			0.538023	+	0.842930i	$0.319171\pi$
$710$	21.6601	+	13.0705i	0.812890	+	0.490528i
$711$	18.1130	−	41.1945i	0.679292	−	1.54491i
$712$	17.5602	−	2.14983i	0.658098	−	0.0805683i
$713$	1.42139			0.0532315
$714$	4.70265	+	12.6052i	0.175992	+	0.471737i
$715$	9.13996	−	4.56998i	0.341815	−	0.170908i
$716$	3.09101	−	6.52528i	0.115517	−	0.243861i
$717$	4.40189	−	20.9474i	0.164391	−	0.782296i
$718$	21.1044	−	13.3553i	0.787608	−	0.498417i
$719$	14.4902			0.540393			0.270196	−	0.962805i	$-0.412911\pi$
$719$	14.4902			0.540393			0.270196	+	0.962805i	$0.412911\pi$
$720$	−19.8978	+	18.0021i	−0.741548	+	0.670899i
$721$	2.66244			0.0991545
$722$	21.5695	−	13.6497i	0.802733	−	0.507988i
$723$	−5.33062	+	25.3670i	−0.198248	+	0.943410i
$724$	9.89780	−	20.8947i	0.367849	−	0.776547i
$725$	−25.6601	−	19.2451i	−0.952993	−	0.714745i
$726$	8.98361	+	24.0801i	0.333413	+	0.893696i
$727$	17.6601			0.654978			0.327489	−	0.944855i	$-0.393798\pi$
$727$	17.6601			0.654978			0.327489	+	0.944855i	$0.393798\pi$
$728$	18.0100	−	2.20489i	0.667494	−	0.0817187i
$729$	−8.69909	−	25.5602i	−0.322188	−	0.946676i
$730$	13.0705	−	21.6601i	0.483762	−	0.801677i
$731$	45.0654			1.66680
$732$	3.50311	+	2.66038i	0.129479	+	0.0983306i
$733$		−	12.7054i		−	0.469286i	−0.972082	−	0.234643i	$-0.924608\pi$
$733$		−	12.7054i		−	0.469286i	0.972082	−	0.234643i	$-0.0753922\pi$
$734$	−32.5909	+	20.6243i	−1.20295	+	0.761255i
$735$	3.74625	−	0.982644i	0.138183	−	0.0362454i
$736$	10.3475	−	31.1657i	0.381415	−	1.14878i
$737$	−9.28592			−0.342051
$738$	−0.903045	−	5.97696i	−0.0332415	−	0.220015i
$739$		−	0.460595i		−	0.0169433i	−0.999964	−	0.00847163i	$-0.997303\pi$
$739$		−	0.460595i		−	0.0169433i	0.999964	−	0.00847163i	$-0.00269664\pi$
$740$	0.515786	+	24.2548i	0.0189607	+	0.891626i
$741$	2.22793	−	10.6021i	0.0818450	−	0.389479i
$742$	−5.79535	+	3.66743i	−0.212754	+	0.134636i
$743$			17.3492i			0.636482i	0.948010	+	0.318241i	$0.103092\pi$
$743$			17.3492i			0.636482i	−0.948010	+	0.318241i	$0.896908\pi$
$744$	−0.102203	+	1.19516i	−0.00374694	+	0.0438168i
$745$	−2.30091	+	1.15046i	−0.0842988	+	0.0421494i
$746$	−3.86015	−	6.09989i	−0.141330	−	0.223333i
$747$	−9.61187	+	21.8603i	−0.351680	+	0.799826i
$748$	3.35010	−	7.07223i	0.122492	−	0.258586i
$749$			15.2299i			0.556487i
$750$	4.82816	+	26.9572i	0.176300	+	0.984337i
$751$		−	21.1890i		−	0.773199i	−0.922248	−	0.386599i	$-0.873650\pi$
$751$		−	21.1890i		−	0.773199i	0.922248	−	0.386599i	$-0.126350\pi$
$752$	10.4925	−	8.58996i	0.382622	−	0.313244i
$753$	−2.66244	+	12.6699i	−0.0970248	+	0.461716i
$754$	49.1786	−	31.1214i	1.79098	−	1.13337i
$755$	2.81908	−	1.40954i	0.102597	−	0.0512984i
$756$	−5.04635	−	9.08484i	−0.183534	−	0.330412i
$757$			11.2204i			0.407811i	0.978991	+	0.203906i	$0.0653636\pi$
$757$			11.2204i			0.407811i	−0.978991	+	0.203906i	$0.934636\pi$
$758$	−12.3350	−	19.4920i	−0.448027	−	0.707982i
$759$	7.00974	+	1.47302i	0.254437	+	0.0534674i
$760$	3.40761	+	5.13959i	0.123607	+	0.186433i
$761$		−	24.2354i		−	0.878531i	−0.898357	−	0.439265i	$-0.855239\pi$
$761$		−	24.2354i		−	0.878531i	0.898357	−	0.439265i	$-0.144761\pi$
$762$	8.06942	+	21.6297i	0.292324	+	0.783560i
$763$	1.49251			0.0540323
$764$	−23.0297	+	48.6169i	−0.833186	+	1.75890i
$765$	−1.81923	−	36.7999i	−0.0657745	−	1.33050i
$766$	19.1702	+	30.2931i	0.692647	+	1.09453i
$767$			47.9505i			1.73139i
$768$	25.4614	+	10.9416i	0.918759	+	0.394820i
$769$	8.43638			0.304224			0.152112	−	0.988363i	$-0.451393\pi$
$769$	8.43638			0.304224			0.152112	+	0.988363i	$0.451393\pi$
$770$	−1.92880	−	1.16391i	−0.0695090	−	0.0419444i
$771$	−8.01779	+	38.1546i	−0.288754	+	1.37410i
$772$	−18.3547	−	8.69460i	−0.660601	−	0.312925i
$773$	6.84274			0.246116			0.123058	−	0.992399i	$-0.460730\pi$
$773$	6.84274			0.246116			0.123058	+	0.992399i	$0.460730\pi$
$774$	−34.4198	+	5.20040i	−1.23719	+	0.186924i
$775$	0.979409	+	0.734557i	0.0351814	+	0.0263861i
$776$	−50.8001	+	6.21926i	−1.82362	+	0.223258i
$777$	−9.19515	−	1.93227i	−0.329874	−	0.0693197i
$778$	−9.16122	−	14.4767i	−0.328446	−	0.519016i
$779$	−1.38919			−0.0497730
$780$	−48.8348	−	9.18261i	−1.74857	−	0.328790i
$781$	5.69909			0.203929
$782$	24.1124	+	38.1029i	0.862259	+	1.36256i
$783$	−27.1027	−	19.4053i	−0.968571	−	0.693489i
$784$	−2.53387	−	3.09508i	−0.0904952	−	0.110539i
$785$	−2.30091	+	1.15046i	−0.0821230	+	0.0410615i
$786$	−15.0944	−	40.4597i	−0.538399	−	1.44315i
$787$	33.0866			1.17941			0.589705	−	0.807619i	$-0.299244\pi$
$787$	33.0866			1.17941			0.589705	+	0.807619i	$0.299244\pi$
$788$	−6.98221	+	14.7398i	−0.248731	+	0.525083i
$789$	−15.5602	−	3.26982i	−0.553959	−	0.116409i
$790$	−24.5077	+	40.6134i	−0.871943	+	1.44496i
$791$	8.25484			0.293508
$792$	−1.74261	+	5.78817i	−0.0619208	+	0.205674i
$793$			8.14596i			0.289272i
$794$	−13.2611	−	20.9555i	−0.470619	−	0.743681i
$795$	18.1676	−	4.76537i	0.644339	−	0.169010i
$796$	−14.3875	−	6.81533i	−0.509951	−	0.241563i
$797$	−24.7874			−0.878015			−0.439008	−	0.898483i	$-0.644670\pi$
$797$	−24.7874			−0.878015			−0.439008	+	0.898483i	$0.644670\pi$
$798$	−2.23767	+	0.834812i	−0.0792127	+	0.0295520i
$799$			18.6199i			0.658726i
$800$	23.2360	−	16.1272i	0.821517	−	0.570184i
$801$	7.55281	−	17.1774i	0.266866	−	0.606932i
$802$	12.6334	+	19.9635i	0.446100	+	0.704936i
$803$		−	5.69909i		−	0.201117i
$804$	35.9600	+	27.3093i	1.26821	+	0.963124i
$805$	11.6102	−	5.80509i	0.409205	−	0.204603i
$806$	−1.87707	+	1.18786i	−0.0661171	+	0.0418405i
$807$	33.3575	+	7.00974i	1.17424	+	0.246755i
$808$	−13.1799	+	1.61357i	−0.463668	+	0.0567651i
$809$			35.2346i			1.23878i	0.785082	+	0.619391i	$0.212621\pi$
$809$			35.2346i			1.23878i	−0.785082	+	0.619391i	$0.787379\pi$
$810$	5.63607	+	27.8969i	0.198031	+	0.980196i
$811$			33.7590i			1.18544i	0.805409	+	0.592720i	$0.201946\pi$
$811$			33.7590i			1.18544i	−0.805409	+	0.592720i	$0.798054\pi$
$812$	−11.5950	−	5.49251i	−0.406903	−	0.192749i
$813$	−49.7421	−	10.4528i	−1.74453	−	0.366595i
$814$	2.92253	+	4.61823i	0.102434	+	0.161869i
$815$	15.4747	+	30.9494i	0.542056	+	1.08411i
$816$	−33.7723	+	17.5350i	−1.18227	+	0.613848i
$817$			8.00000i			0.279885i
$818$	−28.4830	+	18.0247i	−0.995885	+	0.630219i
$819$	7.74625	−	17.6173i	0.270676	−	0.615598i
$820$	0.135467	+	6.37034i	0.00473072	+	0.222462i
$821$		−	14.1658i		−	0.494390i	−0.968966	−	0.247195i	$-0.920491\pi$
$821$		−	14.1658i		−	0.494390i	0.968966	−	0.247195i	$-0.0795088\pi$
$822$	2.33756	+	6.26570i	0.0815317	+	0.218541i
$823$	−24.2282			−0.844543			−0.422272	−	0.906469i	$-0.638767\pi$
$823$	−24.2282			−0.844543			−0.422272	+	0.906469i	$0.638767\pi$
$824$	0.915100	+	7.47472i	0.0318790	+	0.260394i
$825$	4.06882	+	4.63754i	0.141658	+	0.161458i
$826$	8.93251	−	5.65270i	0.310802	−	0.196683i
$827$		−	16.0989i		−	0.559813i	−0.960027	−	0.279907i	$-0.909696\pi$
$827$		−	16.0989i		−	0.559813i	0.960027	−	0.279907i	$-0.0903035\pi$
$828$	−22.8134	−	26.3195i	−0.792820	−	0.914666i
$829$	3.98390			0.138367			0.0691833	−	0.997604i	$-0.477961\pi$
$829$	3.98390			0.138367			0.0691833	+	0.997604i	$0.477961\pi$
$830$	13.0052	−	21.5519i	0.451419	−	0.748079i
$831$	−10.3725	−	2.17968i	−0.359819	−	0.0756122i
$832$	12.3803	+	49.8046i	0.429210	+	1.72666i
$833$	5.49251			0.190304
$834$	−1.03215	+	0.385068i	−0.0357406	+	0.0133338i
$835$	−29.9396	+	14.9698i	−1.03610	+	0.518051i
$836$	1.25546	+	0.594709i	0.0434210	+	0.0205684i
$837$	1.03447	+	0.740671i	0.0357565	+	0.0256013i
$838$	24.6477	−	15.5976i	0.851441	−	0.538812i
$839$	−42.5901			−1.47037			−0.735186	−	0.677865i	$-0.762905\pi$
$839$	−42.5901			−1.47037			−0.735186	+	0.677865i	$0.762905\pi$
$840$	4.04635	+	10.1797i	0.139612	+	0.351234i
$841$	−12.1526			−0.419056
$842$	3.15842	−	1.99872i	0.108846	−	0.0688805i
$843$	0.736512	+	0.154771i	0.0253668	+	0.00533058i
$844$	27.0574	+	12.8170i	0.931353	+	0.441180i
$845$	−28.1526	−	56.3053i	−0.968480	−	1.93696i
$846$	−2.14868	−	14.2214i	−0.0738730	−	0.488942i
$847$	10.4925			0.360527
$848$	−12.2881	−	15.0097i	−0.421975	−	0.515436i
$849$	−0.615279	+	2.92795i	−0.0211163	+	0.100487i
$850$	−3.07645	+	38.7158i	−0.105521	+	1.32794i
$851$	−31.4913			−1.07951
$852$	−22.0699	−	16.7606i	−0.756103	−	0.574210i
$853$		−	5.46035i		−	0.186959i	−0.995621	−	0.0934794i	$-0.970201\pi$
$853$		−	5.46035i		−	0.186959i	0.995621	−	0.0934794i	$-0.0297989\pi$
$854$	1.51748	−	0.960296i	0.0519270	−	0.0328606i
$855$	6.53271	−	0.322950i	0.223414	−	0.0110447i
$856$	−42.7573	+	5.23461i	−1.46142	+	0.178915i
$857$	−7.35023			−0.251079			−0.125540	−	0.992089i	$-0.540066\pi$
$857$	−7.35023			−0.251079			−0.125540	+	0.992089i	$0.540066\pi$
$858$	−10.4880	+	3.91279i	−0.358055	+	0.133580i
$859$			27.1909i			0.927742i	0.885903	+	0.463871i	$0.153540\pi$
$859$			27.1909i			0.927742i	−0.885903	+	0.463871i	$0.846460\pi$
$860$	36.6851	−	0.780120i	1.25095	−	0.0266019i
$861$	−2.41503	−	0.507494i	−0.0823041	−	0.0172954i
$862$	8.28964	−	5.24588i	0.282346	−	0.178675i
$863$			17.9761i			0.611915i	0.952045	+	0.305957i	$0.0989765\pi$
$863$			17.9761i			0.611915i	−0.952045	+	0.305957i	$0.901023\pi$
$864$	23.7709	−	17.2900i	0.808703	−	0.588217i
$865$	9.49251	+	18.9850i	0.322755	+	0.645510i
$866$	10.9955	+	17.3753i	0.373643	+	0.590437i
$867$	4.69022	−	22.3195i	0.159288	−	0.758010i
$868$	0.442562	+	0.209641i	0.0150215	+	0.00711567i
$869$			10.6860i			0.362497i
$870$	25.7074	+	23.9522i	0.871562	+	0.812057i
$871$			83.6197i			2.83334i
$872$	0.512985	+	4.19016i	0.0173719	+	0.141897i
$873$	−21.8496	+	49.6925i	−0.739496	+	1.68183i
$874$	−6.76402	+	4.28043i	−0.228796	+	0.144788i
$875$	11.0000	+	2.00000i	0.371868	+	0.0676123i
$876$	−16.7606	+	22.0699i	−0.566290	+	0.745673i
$877$		−	0.594709i		−	0.0200819i	−0.999950	−	0.0100409i	$-0.996804\pi$
$877$		−	0.594709i		−	0.0200819i	0.999950	−	0.0100409i	$-0.00319619\pi$
$878$	18.7998	+	29.7079i	0.634464	+	1.00259i
$879$	−8.24681	+	39.2444i	−0.278158	+	1.32368i
$880$	2.60469	−	5.81508i	0.0878042	−	0.196026i
$881$			13.8312i			0.465984i	0.972479	+	0.232992i	$0.0748516\pi$
$881$			13.8312i			0.465984i	−0.972479	+	0.232992i	$0.925148\pi$
$882$	−4.19503	+	0.633817i	−0.141254	+	0.0213417i
$883$	−35.2542			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$883$	−35.2542			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$884$	−63.6853	−	30.1676i	−2.14197	−	1.01465i
$885$	−28.0022	+	7.34498i	−0.941283	+	0.246899i
$886$	5.62248	+	8.88476i	0.188891	+	0.298489i
$887$		−	12.4108i		−	0.416713i	−0.978053	−	0.208357i	$-0.933189\pi$
$887$		−	12.4108i		−	0.416713i	0.978053	−	0.208357i	$-0.0668115\pi$
$888$	2.26433	−	26.4792i	0.0759861	−	0.888584i
$889$	9.42477			0.316097
$890$	−10.2193	+	16.9351i	−0.342550	+	0.567665i
$891$	4.33402	+	4.72475i	0.145195	+	0.158285i
$892$	2.24910	−	4.74797i	0.0753055	−	0.158974i
$893$	−3.30540			−0.110611
$894$	2.64027	−	0.985012i	0.0883039	−	0.0329437i
$895$	3.61018	+	7.22037i	0.120675	+	0.241350i
$896$	7.81842	−	8.17755i	0.261195	−	0.273193i
$897$	13.2646	−	63.1227i	0.442891	−	2.10760i
$898$	5.27416	+	8.33433i	0.176001	+	0.278120i
$899$	1.57073			0.0523869
$900$	−2.11797	−	29.9251i	−0.0705989	−	0.997505i
$901$	26.6362			0.887379
$902$	0.767578	+	1.21294i	0.0255575	+	0.0403865i
$903$	−2.92253	+	13.9075i	−0.0972556	+	0.462814i
$904$	2.83725	+	23.1752i	0.0943654	+	0.770795i
$905$	11.5602	+	23.1205i	0.384275	+	0.768551i
$906$	−3.23487	+	1.20684i	−0.107471	+	0.0400945i
$907$	−11.0900			−0.368238			−0.184119	−	0.982904i	$-0.558943\pi$
$907$	−11.0900			−0.368238			−0.184119	+	0.982904i	$0.558943\pi$
$908$	−6.12742	−	2.90255i	−0.203346	−	0.0963244i
$909$	−5.66880	+	12.8925i	−0.188022	+	0.427619i
$910$	−10.4810	+	17.3688i	−0.347441	+	0.575770i
$911$	24.8805			0.824328			0.412164	−	0.911110i	$-0.364773\pi$
$911$	24.8805			0.824328			0.412164	+	0.911110i	$0.364773\pi$
$912$	−3.11281	−	5.99525i	−0.103075	−	0.198523i
$913$		−	5.67062i		−	0.187670i
$914$	−23.6371	−	37.3518i	−0.781845	−	1.23549i
$915$	−4.75708	+	1.24778i	−0.157264	+	0.0412505i
$916$	21.0322	−	44.3999i	0.694922	−	1.46701i
$917$	−17.6297			−0.582183
$918$	−2.30631	+	40.2956i	−0.0761197	+	1.32995i
$919$			15.4595i			0.509961i	0.966946	+	0.254981i	$0.0820691\pi$
$919$			15.4595i			0.509961i	−0.966946	+	0.254981i	$0.917931\pi$
$920$	20.2881	+	30.5999i	0.668879	+	1.00885i
$921$	3.56133	−	16.9474i	0.117350	−	0.558437i
$922$	14.4892	+	22.8961i	0.477176	+	0.754043i
$923$		−	51.3203i		−	1.68923i
$924$	1.96529	+	1.49251i	0.0646532	+	0.0490998i
$925$	−21.6991	−	16.2743i	−0.713462	−	0.535096i
$926$	−28.5791	+	18.0855i	−0.939167	+	0.594327i
$927$	7.31174	+	3.21494i	0.240149	+	0.105593i
$928$	11.4348	−	34.4402i	0.375364	−	1.13056i
$929$		−	32.0894i		−	1.05282i	−0.850231	−	0.526409i	$-0.823538\pi$
$929$		−	32.0894i		−	1.05282i	0.850231	−	0.526409i	$-0.176462\pi$
$930$	−0.981212	−	0.914221i	−0.0321752	−	0.0299785i
$931$			0.975028i			0.0319553i
$932$	−18.0527	+	38.1102i	−0.591337	+	1.24834i
$933$	−9.46217	+	45.0280i	−0.309778	+	1.47415i
$934$	−4.71866	−	7.45651i	−0.154399	−	0.243985i
$935$	3.91279	+	7.82557i	0.127962	+	0.255924i
$936$	52.1224	+	15.6922i	1.70367	+	0.512914i
$937$		−	8.75490i		−	0.286010i	−0.989722	−	0.143005i	$-0.954323\pi$
$937$		−	8.75490i		−	0.286010i	0.989722	−	0.143005i	$-0.0456765\pi$
$938$	15.5772	−	9.85759i	0.508612	−	0.321862i
$939$	−26.3840	−	5.54432i	−0.861008	−	0.180932i
$940$	0.322326	+	15.1574i	0.0105131	+	0.494379i
$941$		−	13.8061i		−	0.450066i	−0.974351	−	0.225033i	$-0.927751\pi$
$941$		−	13.8061i		−	0.450066i	0.974351	−	0.225033i	$-0.0722489\pi$
$942$	2.64027	−	0.985012i	0.0860247	−	0.0320934i
$943$	−8.27093			−0.269339
$944$	18.9399	+	23.1348i	0.616442	+	0.752975i
$945$	11.4747	+	1.82507i	0.373273	+	0.0593696i
$946$	6.98501	−	4.42028i	0.227102	−	0.143716i
$947$		−	39.4652i		−	1.28245i	−0.767354	−	0.641224i	$-0.778427\pi$
$947$		−	39.4652i		−	1.28245i	0.767354	−	0.641224i	$-0.221573\pi$
$948$	31.4267	−	41.3818i	1.02069	−	1.34402i
$949$	−51.3203			−1.66593
$950$	−6.87283	−	0.546131i	−0.222984	−	0.0177188i
$951$	3.20040	−	15.2299i	0.103780	−	0.493862i
$952$	1.88781	+	15.4200i	0.0611844	+	0.499766i
$953$	6.55575			0.212361			0.106181	−	0.994347i	$-0.466138\pi$
$953$	6.55575			0.212361			0.106181	+	0.994347i	$0.466138\pi$
$954$	−20.3440	+	3.07372i	−0.658661	+	0.0995155i
$955$	−26.8978	−	53.7956i	−0.870392	−	1.74078i
$956$	10.5810	−	22.3369i	0.342213	−	0.722428i
$957$	7.74625	+	1.62780i	0.250401	+	0.0526191i
$958$	10.9225	−	6.91203i	0.352891	−	0.223318i
$959$	2.73018			0.0881620
$960$	−27.1885	+	14.8588i	−0.877505	+	0.479567i
$961$	30.9400			0.998066
$962$	41.5871	−	26.3173i	1.34082	−	0.848505i
$963$	−18.3903	+	41.8251i	−0.592619	+	1.34779i
$964$	−12.8134	+	27.0497i	−0.412691	+	0.871212i
$965$	20.3099	−	10.1549i	0.653799	−	0.326899i
$966$	−13.3226	+	4.97028i	−0.428647	+	0.159916i
$967$	−30.8106			−0.990802			−0.495401	−	0.868665i	$-0.664979\pi$
$967$	−30.8106			−0.990802			−0.495401	+	0.868665i	$0.664979\pi$
$968$	3.60635	+	29.4574i	0.115912	+	0.946795i
$969$	9.07747	+	1.90754i	0.291610	+	0.0612789i
$970$	29.5633	−	48.9915i	0.949221	−	1.57302i
$971$	−9.08103			−0.291424			−0.145712	−	0.989327i	$-0.546547\pi$
$971$	−9.08103			−0.291424			−0.145712	+	0.989327i	$0.546547\pi$
$972$	−2.88847	−	31.0428i	−0.0926478	−	0.995699i
$973$			0.449744i			0.0144181i
$974$	40.7571	−	25.7920i	1.30594	−	0.826430i
$975$	41.7610	−	36.6397i	1.33742	−	1.17341i
$976$	3.21757	+	3.93021i	0.102992	+	0.125803i
$977$	−8.70020			−0.278344			−0.139172	−	0.990268i	$-0.544444\pi$
$977$	−8.70020			−0.278344			−0.139172	+	0.990268i	$0.544444\pi$
$978$	−13.2493	−	35.5142i	−0.423667	−	1.13562i
$979$			4.45586i			0.142410i
$980$	4.47113	−	0.0950798i	0.142825	−	0.00303721i
$981$	4.09880	+	1.80222i	0.130865	+	0.0575406i
$982$	−34.9638	+	22.1259i	−1.11574	+	0.706065i
$983$			42.0903i			1.34247i	0.741244	+	0.671235i	$0.234236\pi$
$983$			42.0903i			1.34247i	−0.741244	+	0.671235i	$0.765764\pi$
$984$	0.594709	−	6.95455i	0.0189586	−	0.221703i
$985$	−8.15495	−	16.3099i	−0.259838	−	0.519677i
$986$	26.6459	+	42.1064i	0.848579	+	1.34094i
$987$	−5.74625	−	1.20752i	−0.182905	−	0.0384357i
$988$	5.35535	−	11.3054i	0.170376	−	0.359673i
$989$			47.6302i			1.51455i
$990$	−3.89153	−	5.52544i	−0.123681	−	0.175610i
$991$		−	34.6707i		−	1.10135i	−0.834719	−	0.550676i	$-0.814370\pi$
$991$		−	34.6707i		−	1.10135i	0.834719	−	0.550676i	$-0.185630\pi$
$992$	−0.436448	+	1.31453i	−0.0138572	+	0.0417365i
$993$	6.18710	+	1.30016i	0.196342	+	0.0412592i
$994$	−9.56024	+	6.04994i	−0.303232	+	0.191893i
$995$	15.9201	−	7.96004i	0.504700	−	0.252350i
$996$	−16.6769	+	21.9597i	−0.528428	+	0.695819i
$997$			40.6950i			1.28882i	0.764679	+	0.644411i	$0.222897\pi$
$997$			40.6950i			1.28882i	−0.764679	+	0.644411i	$0.777103\pi$
$998$	−5.53618	−	8.74838i	−0.175245	−	0.276925i
$999$	−22.9190	−	16.4098i	−0.725124	−	0.519183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.d.239.7	yes	8
3.2	odd	2		420.2.l.c.239.2	yes	8
4.3	odd	2		420.2.l.f.239.8	yes	8
5.4	even	2		420.2.l.e.239.2	yes	8
12.11	even	2		420.2.l.e.239.1	yes	8
15.14	odd	2		420.2.l.f.239.7	yes	8
20.19	odd	2		420.2.l.c.239.1	✓	8
60.59	even	2	inner	420.2.l.d.239.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.c.239.1	✓	8	20.19	odd	2
420.2.l.c.239.2	yes	8	3.2	odd	2
420.2.l.d.239.7	yes	8	1.1	even	1	trivial
420.2.l.d.239.8	yes	8	60.59	even	2	inner
420.2.l.e.239.1	yes	8	12.11	even	2
420.2.l.e.239.2	yes	8	5.4	even	2
420.2.l.f.239.7	yes	8	15.14	odd	2
420.2.l.f.239.8	yes	8	4.3	odd	2

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19503 - 0.756243i) q^{2} +(0.356193 - 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-0.856193 - 2.29498i) q^{6} -1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} +(-2.74625 - 1.20752i) q^{9} +O(q^{10})\)	\(q+(1.19503 - 0.756243i) q^{2} +(0.356193 - 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-0.856193 - 2.29498i) q^{6} -1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} +(-2.74625 - 1.20752i) q^{9} +(2.70752 + 1.63382i) q^{10} +0.712386 q^{11} +(-2.75874 - 2.09508i) q^{12} -6.41503i q^{13} +(-1.19503 + 0.756243i) q^{14} +(3.74625 - 0.982644i) q^{15} +(-2.53387 - 3.09508i) q^{16} +5.49251 q^{17} +(-4.19503 + 0.633817i) q^{18} +0.975028i q^{19} +(4.47113 - 0.0950798i) q^{20} +(-0.356193 + 1.69503i) q^{21} +(0.851323 - 0.538737i) q^{22} +5.80509i q^{23} +(-4.88117 - 0.417406i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(-4.85132 - 7.66616i) q^{26} +(-3.02497 + 4.22487i) q^{27} +(-0.856193 + 1.80747i) q^{28} +6.41503i q^{29} +(3.73377 - 4.00737i) q^{30} -0.244852i q^{31} +(-5.36868 - 1.78249i) q^{32} +(0.253747 - 1.20752i) q^{33} +(6.56371 - 4.15367i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(-4.53387 + 3.92989i) q^{36} +5.42477i q^{37} +(0.737358 + 1.16519i) q^{38} +(-10.8737 - 2.28499i) q^{39} +(5.27122 - 3.49488i) q^{40} +1.42477i q^{41} +(0.856193 + 2.29498i) q^{42} +8.20489 q^{43} +(0.609940 - 1.28761i) q^{44} +(-0.331221 - 6.70002i) q^{45} +(4.39006 + 6.93726i) q^{46} +3.39006i q^{47} +(-6.14880 + 3.19253i) q^{48} +1.00000 q^{49} +(-0.560118 + 7.04885i) q^{50} +(1.95639 - 9.30996i) q^{51} +(-11.5950 - 5.49251i) q^{52} +4.84954 q^{53} +(-0.419902 + 7.33646i) q^{54} +(0.712386 + 1.42477i) q^{55} +(0.343707 + 2.80747i) q^{56} +(1.65270 + 0.347298i) q^{57} +(4.85132 + 7.66616i) q^{58} -7.47472 q^{59} +(1.43142 - 7.61256i) q^{60} -1.26982 q^{61} +(-0.185168 - 0.292606i) q^{62} +(2.74625 + 1.20752i) q^{63} +(-7.76373 + 1.92989i) q^{64} +(12.8301 - 6.41503i) q^{65} +(-0.609940 - 1.63491i) q^{66} -13.0350 q^{67} +(4.70265 - 9.92752i) q^{68} +(9.83980 + 2.06773i) q^{69} +(-2.70752 - 1.63382i) q^{70} +8.00000 q^{71} +(-2.44615 + 8.12504i) q^{72} -8.00000i q^{73} +(4.10245 + 6.48277i) q^{74} +(5.71154 + 6.50986i) q^{75} +(1.76233 + 0.834812i) q^{76} -0.712386 q^{77} +(-14.7224 + 5.49251i) q^{78} +15.0002i q^{79} +(3.65629 - 8.16281i) q^{80} +(6.08381 + 6.63229i) q^{81} +(1.07747 + 1.70265i) q^{82} -7.96004i q^{83} +(2.75874 + 2.09508i) q^{84} +(5.49251 + 10.9850i) q^{85} +(9.80509 - 6.20489i) q^{86} +(10.8737 + 2.28499i) q^{87} +(-0.244852 - 2.00000i) q^{88} +6.25484i q^{89} +(-5.46266 - 7.75624i) q^{90} +6.41503i q^{91} +(10.4925 + 4.97028i) q^{92} +(-0.415032 - 0.0872147i) q^{93} +(2.56371 + 4.05122i) q^{94} +(-1.95006 + 0.975028i) q^{95} +(-4.93367 + 8.46516i) q^{96} -18.0946i q^{97} +(1.19503 - 0.756243i) q^{98} +(-1.95639 - 0.860218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{4} + 8 q^{5} - 2 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 2 * q^4 + 8 * q^5 - 2 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{3} + 2 q^{4} + 8 q^{5} - 2 q^{6} - 8 q^{7} - 6 q^{8} + 2 q^{9} + 4 q^{10} - 4 q^{11} + 10 q^{12} + 6 q^{15} - 6 q^{16} - 4 q^{17} - 24 q^{18} - 6 q^{20} + 2 q^{21} - 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} - 8 q^{27} - 2 q^{28} + 14 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} - 20 q^{38} - 18 q^{39} + 2 q^{40} + 2 q^{42} + 8 q^{43} + 24 q^{44} - 14 q^{45} + 16 q^{46} + 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} - 16 q^{52} + 24 q^{54} - 4 q^{55} + 6 q^{56} + 20 q^{57} + 26 q^{58} - 8 q^{59} + 26 q^{60} - 16 q^{61} - 40 q^{62} - 2 q^{63} + 26 q^{64} + 32 q^{65} - 24 q^{66} + 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} + 6 q^{72} + 4 q^{74} + 22 q^{75} - 28 q^{76} + 4 q^{77} + 4 q^{78} + 26 q^{80} + 2 q^{81} - 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} + 18 q^{87} - 24 q^{88} - 4 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^4 + 8 * q^5 - 2 * q^6 - 8 * q^7 - 6 * q^8 + 2 * q^9 + 4 * q^10 - 4 * q^11 + 10 * q^12 + 6 * q^15 - 6 * q^16 - 4 * q^17 - 24 * q^18 - 6 * q^20 + 2 * q^21 - 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 - 8 * q^27 - 2 * q^28 + 14 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 - 20 * q^38 - 18 * q^39 + 2 * q^40 + 2 * q^42 + 8 * q^43 + 24 * q^44 - 14 * q^45 + 16 * q^46 + 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 - 16 * q^52 + 24 * q^54 - 4 * q^55 + 6 * q^56 + 20 * q^57 + 26 * q^58 - 8 * q^59 + 26 * q^60 - 16 * q^61 - 40 * q^62 - 2 * q^63 + 26 * q^64 + 32 * q^65 - 24 * q^66 + 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 + 6 * q^72 + 4 * q^74 + 22 * q^75 - 28 * q^76 + 4 * q^77 + 4 * q^78 + 26 * q^80 + 2 * q^81 - 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 + 18 * q^87 - 24 * q^88 - 4 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Introduction

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