LMFDB - Embedded newform 420.2.l.c.239.2

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			239.2
Root			$-1.19503 - 0.756243i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.c.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19503 + 0.756243i) q^{2} +(0.356193 + 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.70752 - 1.75624i) q^{6} -1.00000 q^{7} +(0.343707 + 2.80747i) q^{8} +(-2.74625 + 1.20752i) q^{9} +O(q^{10})$	\(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} +(-1.70752 - 1.75624i) 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} +(3.36868 + 0.807466i) q^{12} -6.41503i q^{13} +(1.19503 - 0.756243i) q^{14} +(3.03387 - 2.40742i) q^{15} +(-2.53387 - 3.09508i) q^{16} -5.49251 q^{17} +(2.36868 - 3.51985i) 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} +(-4.63631 + 1.58259i) 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} +(-1.80497 + 5.17127i) 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} +(-0.168779 + 5.99763i) 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} +(1.70752 + 1.75624i) q^{42} +8.20489 q^{43} +(-0.609940 + 1.28761i) q^{44} +(5.16128 + 4.28499i) q^{45} +(4.39006 + 6.93726i) q^{46} -3.39006i q^{47} +(4.34371 - 5.39743i) 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} +(6.80996 + 2.76123i) 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} +(-1.75375 - 7.54482i) 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} +(1.21641 + 1.25112i) 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} +(-4.33397 - 7.29498i) q^{72} -8.00000i q^{73} +(-4.10245 - 6.48277i) q^{74} +(-7.84870 - 3.66032i) q^{75} +(1.76233 + 0.834812i) q^{76} +0.712386 q^{77} +(-11.2664 + 10.9538i) 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} +(-3.36868 - 0.807466i) 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} +(-9.40838 - 1.21751i) 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} +(-1.10909 + 9.73498i) 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} + 4 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 + 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q - 2 q^{3} + 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{10} + 4 q^{11} + 14 q^{12} + 10 q^{15} - 6 q^{16} + 4 q^{17} + 6 q^{18} + 6 q^{20} + 2 q^{21} - 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} - 8 q^{27} - 2 q^{28} - 24 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} + 20 q^{38} + 18 q^{39} + 2 q^{40} - 4 q^{42} + 8 q^{43} - 24 q^{44} - 18 q^{45} + 16 q^{46} + 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} - 16 q^{52} + 8 q^{54} - 4 q^{55} - 6 q^{56} - 20 q^{57} + 26 q^{58} + 8 q^{59} - 38 q^{60} - 16 q^{61} + 40 q^{62} - 2 q^{63} + 26 q^{64} - 32 q^{65} - 6 q^{66} + 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} - 22 q^{72} - 4 q^{74} - 10 q^{75} - 28 q^{76} - 4 q^{77} - 42 q^{78} - 26 q^{80} + 2 q^{81} - 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} + 18 q^{87} - 24 q^{88} - 6 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^10 + 4 * q^11 + 14 * q^12 + 10 * q^15 - 6 * q^16 + 4 * q^17 + 6 * q^18 + 6 * q^20 + 2 * q^21 - 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 - 8 * q^27 - 2 * q^28 - 24 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 + 20 * q^38 + 18 * q^39 + 2 * q^40 - 4 * q^42 + 8 * q^43 - 24 * q^44 - 18 * q^45 + 16 * q^46 + 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 - 16 * q^52 + 8 * q^54 - 4 * q^55 - 6 * q^56 - 20 * q^57 + 26 * q^58 + 8 * q^59 - 38 * q^60 - 16 * q^61 + 40 * q^62 - 2 * q^63 + 26 * q^64 - 32 * q^65 - 6 * q^66 + 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 - 22 * q^72 - 4 * q^74 - 10 * q^75 - 28 * q^76 - 4 * q^77 - 42 * q^78 - 26 * q^80 + 2 * q^81 - 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 + 18 * q^87 - 24 * q^88 - 6 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * 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
$6$	−1.70752	−	1.75624i	−0.697090	−	0.716983i
$7$	−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	$-0.534251\pi$
$11$	−0.712386			−0.214793			−0.107396	+	0.994216i	$0.534251\pi$
$12$	3.36868	+	0.807466i	0.972454	+	0.233095i
$13$		−	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
$15$	3.03387	−	2.40742i	0.783341	−	0.621592i
$16$	−2.53387	−	3.09508i	−0.633467	−	0.773770i
$17$	−5.49251			−1.33213			−0.666064	−	0.745894i	$-0.732022\pi$
$17$	−5.49251			−1.33213			−0.666064	+	0.745894i	$0.732022\pi$
$18$	2.36868	−	3.51985i	0.558303	−	0.829637i
$19$			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	$-0.793084\pi$
$23$		−	5.80509i		−	1.21045i	0.796056	−	0.605223i	$-0.206916\pi$
$24$	−4.63631	+	1.58259i	−0.946383	+	0.323046i
$25$	−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	$-0.796906\pi$
$29$		−	6.41503i		−	1.19124i	0.803266	−	0.595621i	$-0.203094\pi$
$30$	−1.80497	+	5.17127i	−0.329541	+	0.944141i
$31$		−	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
$36$	−0.168779	+	5.99763i	−0.0281298	+	0.999604i
$37$			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	$-0.964513\pi$
$41$		−	1.42477i		−	0.222512i	0.993792	−	0.111256i	$-0.0354874\pi$
$42$	1.70752	+	1.75624i	0.263475	+	0.270994i
$43$	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
$45$	5.16128	+	4.28499i	0.769399	+	0.638769i
$46$	4.39006	+	6.93726i	0.647279	+	1.02284i
$47$		−	3.39006i		−	0.494491i	−0.968953	−	0.247246i	$-0.920475\pi$
$47$		−	3.39006i		−	0.494491i	0.968953	−	0.247246i	$-0.0795254\pi$
$48$	4.34371	−	5.39743i	0.626960	−	0.779051i
$49$	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	$-0.608084\pi$
$53$	−4.84954			−0.666136			−0.333068	+	0.942903i	$0.608084\pi$
$54$	6.80996	+	2.76123i	0.926718	+	0.375756i
$55$	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	$-0.338251\pi$
$59$	7.47472			0.973125			0.486563	+	0.873646i	$0.338251\pi$
$60$	−1.75375	−	7.54482i	−0.226408	−	0.974033i
$61$	−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
$66$	1.21641	+	1.25112i	0.149730	+	0.154003i
$67$	−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	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−4.33397	−	7.29498i	−0.510763	−	0.859722i
$73$		−	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
$75$	−7.84870	−	3.66032i	−0.906290	−	0.422657i
$76$	1.76233	+	0.834812i	0.202153	+	0.0957595i
$77$	0.712386			0.0811839
$78$	−11.2664	+	10.9538i	−1.27566	+	1.24027i
$79$			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	$0.143911\pi$
$83$			7.96004i			0.873728i	−0.899528	+	0.436864i	$0.856089\pi$
$84$	−3.36868	−	0.807466i	−0.367553	−	0.0881018i
$85$	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	$-0.892443\pi$
$89$		−	6.25484i		−	0.663011i	0.943453	−	0.331506i	$-0.107557\pi$
$90$	−9.40838	−	1.21751i	−0.991731	−	0.128336i
$91$			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
$96$	−1.10909	+	9.73498i	−0.113196	+	0.993573i
$97$		−	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	$0.0750391\pi$
$101$			4.69460i			0.467130i	−0.972341	+	0.233565i	$0.924961\pi$
$102$	9.37854	+	9.64618i	0.928614	+	0.955114i
$103$	−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
$105$	−3.03387	+	2.40742i	−0.296075	+	0.234940i
$106$	5.79535	−	3.66743i	0.562894	−	0.356213i
$107$			15.2299i			1.47233i	0.676804	+	0.736163i	$0.263364\pi$
$107$			15.2299i			1.47233i	−0.676804	+	0.736163i	$0.736636\pi$
$108$	−10.2263	+	1.85023i	−0.984024	+	0.178038i
$109$	−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	$-0.373071\pi$
$113$	8.25484			0.776550			0.388275	+	0.921544i	$0.373071\pi$
$114$	1.71239	−	1.66488i	0.160380	−	0.155930i
$115$	−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
$120$	7.80150	+	7.69003i	0.712176	+	0.702001i
$121$	−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
$126$	−2.36868	+	3.51985i	−0.211019	+	0.313573i
$127$	−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	$-0.779821\pi$
$131$	−17.6297			−1.54031			−0.770155	+	0.637856i	$0.779821\pi$
$132$	−2.39980	−	0.575228i	−0.208876	−	0.0500671i
$133$		−	0.975028i		−	0.0845457i
$134$	15.5772	−	9.85759i	1.34566	−	0.851566i
$135$	−5.42477	+	10.2748i	−0.466890	+	0.884315i
$136$	−1.88781	−	15.4200i	−0.161879	−	1.32226i
$137$	2.73018			0.233255			0.116627	−	0.993176i	$-0.462792\pi$
$137$	2.73018			0.233255			0.116627	+	0.993176i	$0.462792\pi$
$138$	−10.1952	+	9.91229i	−0.867869	+	0.843790i
$139$		−	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
$144$	10.6960	+	5.44019i	0.891333	+	0.453349i
$145$	−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	$-0.984994\pi$
$149$		−	1.15046i		−	0.0942490i	0.998889	−	0.0471245i	$-0.0150057\pi$
$150$	12.1475	−	1.56133i	0.991841	−	0.127482i
$151$		−	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
$156$	5.17992	−	21.6102i	0.414726	−	1.73020i
$157$			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
$162$	−2.25471	+	12.5266i	−0.177147	+	0.984184i
$163$	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
$165$	−2.16128	+	1.71501i	−0.168256	+	0.133513i
$166$	−6.01972	−	9.51249i	−0.467221	−	0.738312i
$167$		−	14.9698i		−	1.15840i	−0.815187	−	0.579198i	$-0.803366\pi$
$167$		−	14.9698i		−	1.15840i	0.815187	−	0.579198i	$-0.196634\pi$
$168$	4.63631	−	1.58259i	0.357699	−	0.122100i
$169$	−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	$-0.617514\pi$
$173$	−9.49251			−0.721702			−0.360851	+	0.932624i	$0.617514\pi$
$174$	−11.2664	+	10.9538i	−0.854100	+	0.830403i
$175$	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	$-0.543077\pi$
$179$	−3.61018			−0.269838			−0.134919	+	0.990857i	$0.543077\pi$
$180$	12.1640	−	5.66007i	0.906653	−	0.421877i
$181$	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
$186$	−0.430020	+	0.418089i	−0.0315306	+	0.0306558i
$187$	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	$-0.0739590\pi$
$191$	26.8978			1.94626			0.973128	+	0.230264i	$0.0739590\pi$
$192$	−6.03661	−	12.4723i	−0.435655	−	0.900114i
$193$		−	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
$195$	−15.4437	−	19.4624i	−1.10594	−	1.39373i
$196$	0.856193	−	1.80747i	0.0611566	−	0.129105i
$197$	8.15495			0.581016			0.290508	−	0.956873i	$-0.406176\pi$
$197$	8.15495			0.581016			0.290508	+	0.956873i	$0.406176\pi$
$198$	−1.68741	+	2.50749i	−0.119919	+	0.178200i
$199$		−	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
$204$	−18.5025	−	4.43501i	−1.29543	−	0.310513i
$205$	−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
$210$	1.80497	−	5.17127i	0.124555	−	0.356852i
$211$			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
$216$	10.8215	−	9.94462i	0.736308	−	0.676646i
$217$			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
$222$	9.52722	−	9.26289i	0.639425	−	0.621684i
$223$	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
$225$	3.40870	−	14.6076i	0.227246	−	0.973837i
$226$	−9.86478	+	6.24266i	−0.656195	+	0.415256i
$227$			3.39006i			0.225006i	0.993651	+	0.112503i	$0.0358868\pi$
$227$			3.39006i			0.225006i	−0.993651	+	0.112503i	$0.964113\pi$
$228$	−0.787302	+	3.28456i	−0.0521403	+	0.217525i
$229$	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	$-0.257321\pi$
$233$	21.0849			1.38132			0.690659	+	0.723181i	$0.257321\pi$
$234$	−22.5800	−	15.1952i	−1.47610	−	0.993338i
$235$	−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	$-0.630883\pi$
$239$	−12.3581			−0.799382			−0.399691	+	0.916650i	$0.630883\pi$
$240$	−15.1386	−	3.28999i	−0.977190	−	0.212368i
$241$	−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
$246$	−2.50225	+	2.43282i	−0.159537	+	0.155111i
$247$	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	$-0.424196\pi$
$251$	7.47472			0.471800			0.235900	+	0.971777i	$0.424196\pi$
$252$	0.168779	−	5.99763i	0.0106321	−	0.377815i
$253$			4.13547i			0.259995i
$254$	11.2629	−	7.12742i	0.706696	−	0.447214i
$255$	−16.6635	+	13.2227i	−1.04351	+	0.828041i
$256$	−3.15904	+	15.6850i	−0.197440	+	0.980315i
$257$	22.5097			1.40411			0.702057	−	0.712120i	$-0.252265\pi$
$257$	22.5097			1.40411			0.702057	+	0.712120i	$0.252265\pi$
$258$	−14.0100	−	14.4098i	−0.872223	−	0.897114i
$259$		−	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	$0.0913393\pi$
$263$			9.17992i			0.566058i	−0.959111	+	0.283029i	$0.908661\pi$
$264$	3.30285	−	1.12742i	0.203276	−	0.0693878i
$265$	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	$-0.795190\pi$
$269$		−	19.6796i		−	1.19989i	0.800042	−	0.599943i	$-0.204810\pi$
$270$	−1.28749	−	16.3812i	−0.0783543	−	0.996926i
$271$		−	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
$276$	4.68741	−	19.5555i	0.282149	−	1.17710i
$277$		−	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	$-0.995874\pi$
$281$		−	0.434513i		−	0.0259209i	0.999916	−	0.0129604i	$-0.00412555\pi$
$282$	−5.95377	+	5.78858i	−0.354542	+	0.344705i
$283$	−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
$285$	2.34730	+	2.95811i	0.139042	+	0.175223i
$286$	−3.45602	−	5.46126i	−0.204358	−	0.322931i
$287$			1.42477i			0.0841017i
$288$	−16.8961	+	1.58759i	−0.995615	+	0.0935494i
$289$	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	$-0.263584\pi$
$293$	23.1526			1.35259			0.676296	+	0.736630i	$0.263584\pi$
$294$	−1.70752	−	1.75624i	−0.0995844	−	0.102426i
$295$	−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
$300$	−13.3359	+	11.0523i	−0.769949	+	0.638106i
$301$	−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
$306$	−13.0100	+	19.3328i	−0.743731	+	1.10518i
$307$	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	$-0.228522\pi$
$311$	26.5647			1.50635			0.753174	+	0.657821i	$0.228522\pi$
$312$	10.1524	+	29.7421i	0.574766	+	1.68381i
$313$		−	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
$315$	−5.16128	−	4.28499i	−0.290805	−	0.241432i
$316$	27.1124	+	12.8431i	1.52519	+	0.722481i
$317$	−8.98501			−0.504649			−0.252324	−	0.967643i	$-0.581195\pi$
$317$	−8.98501			−0.504649			−0.252324	+	0.967643i	$0.581195\pi$
$318$	8.28067	+	8.51698i	0.464357	+	0.477608i
$319$			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
$324$	−6.77872	−	16.6748i	−0.376595	−	0.926378i
$325$	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
$330$	1.28584	−	3.68394i	0.0707829	−	0.202794i
$331$			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
$336$	−4.34371	+	5.39743i	−0.236969	+	0.294454i
$337$			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
$342$	3.43195	+	2.30953i	0.185579	+	0.124885i
$343$	−1.00000			−0.0539949
$344$	2.82008	+	23.0350i	0.152049	+	1.24196i
$345$	−13.9753	−	17.6119i	−0.752403	−	0.948191i
$346$	11.3438	−	7.17864i	0.609848	−	0.385926i
$347$		−	15.1144i		−	0.811382i	−0.914010	−	0.405691i	$-0.867031\pi$
$347$		−	15.1144i		−	0.811382i	0.914010	−	0.405691i	$-0.132969\pi$
$348$	5.17992	−	21.6102i	0.277673	−	1.15843i
$349$	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	$-0.668910\pi$
$353$	−19.0172			−1.01218			−0.506091	+	0.862480i	$0.668910\pi$
$354$	−12.7632	−	13.1274i	−0.678356	−	0.697714i
$355$	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	$-0.654317\pi$
$359$	−17.6601			−0.932066			−0.466033	+	0.884767i	$0.654317\pi$
$360$	−10.2560	+	15.9629i	−0.540538	+	0.841319i
$361$	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
$366$	2.16824	+	2.23012i	0.113336	+	0.116570i
$367$	−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
$372$	0.197710	−	0.824828i	0.0102508	−	0.0427654i
$373$		−	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
$375$	0.528064	+	19.3577i	0.0272691	+	0.999628i
$376$	9.51748	−	1.16519i	0.490826	−	0.0600900i
$377$	−41.1526			−2.11947
$378$	−6.80996	−	2.76123i	−0.350267	−	0.142023i
$379$		−	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	$-0.775755\pi$
$383$		−	25.3492i		−	1.29529i	0.761944	−	0.647643i	$-0.224245\pi$
$384$	16.6461	+	10.3397i	0.849465	+	0.527644i
$385$	−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	$0.0993603\pi$
$389$			12.1141i			0.614210i	−0.951676	+	0.307105i	$0.900640\pi$
$390$	33.1739	+	11.5789i	1.67983	+	0.586322i
$391$			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
$396$	0.120236	−	4.27263i	0.00604207	−	0.214708i
$397$		−	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	$-0.863041\pi$
$401$		−	16.7054i		−	0.834230i	0.908854	−	0.417115i	$-0.136959\pi$
$402$	22.2574	+	22.8925i	1.11010	+	1.14178i
$403$	−1.57073			−0.0782439
$404$	8.48532	+	4.01948i	0.422161	+	0.199977i
$405$	−19.3484	−	5.53533i	−0.961429	−	0.275053i
$406$	−4.85132	−	7.66616i	−0.240767	−	0.380465i
$407$		−	3.86453i		−	0.191558i
$408$	25.4650	−	8.69241i	1.26070	−	0.430338i
$409$	−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
$414$	−20.4331	−	13.7504i	−1.00423	−	0.675795i
$415$	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	$-0.668066\pi$
$419$	−20.6252			−1.00761			−0.503803	+	0.863819i	$0.668066\pi$
$420$	1.75375	+	7.54482i	0.0855741	+	0.368150i
$421$	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
$426$	13.6601	+	14.0499i	0.661835	+	0.680722i
$427$	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	$-0.553429\pi$
$431$	−6.93676			−0.334132			−0.167066	+	0.985946i	$0.553429\pi$
$432$	−5.41144	+	20.0678i	−0.260358	+	0.965512i
$433$			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
$435$	−15.4437	−	19.4624i	−0.740466	−	0.933148i
$436$	−1.27787	+	2.69765i	−0.0611990	+	0.129194i
$437$	5.66013			0.270761
$438$	−14.0499	+	13.6601i	−0.671332	+	0.652706i
$439$			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	$-0.943484\pi$
$443$		−	7.43476i		−	0.353236i	0.984279	−	0.176618i	$-0.0565157\pi$
$444$	−4.38032	+	18.2743i	−0.207881	+	0.867261i
$445$	−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	$-0.947378\pi$
$449$		−	6.97416i		−	0.329131i	0.986366	−	0.164566i	$-0.0526222\pi$
$450$	6.97337	+	20.0343i	0.328728	+	0.944425i
$451$			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
$456$	−1.54307	−	4.52054i	−0.0722610	−	0.211693i
$457$		−	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	$-0.852787\pi$
$461$		−	19.1594i		−	0.892344i	0.894947	−	0.446172i	$-0.147213\pi$
$462$	−1.21641	−	1.25112i	−0.0565925	−	0.0582075i
$463$	−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
$465$	−0.589461	−	0.742849i	−0.0273356	−	0.0344488i
$466$	−25.1971	+	15.9453i	−1.16723	+	0.738652i
$467$			6.23960i			0.288734i	0.989524	+	0.144367i	$0.0461147\pi$
$467$			6.23960i			0.288734i	−0.989524	+	0.144367i	$0.953885\pi$
$468$	38.4750	+	1.08272i	1.77851	+	0.0500488i
$469$	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
$474$	26.3441	−	25.6132i	1.21002	−	1.17645i
$475$	−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	$-0.566958\pi$
$479$	−9.13996			−0.417615			−0.208808	+	0.977957i	$0.566958\pi$
$480$	20.5791	−	7.51679i	0.939301	−	0.343093i
$481$	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
$486$	−22.0361	+	0.640088i	−0.999578	+	0.0290350i
$487$	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	$-0.270476\pi$
$491$	29.2576			1.32038			0.660189	+	0.751099i	$0.270476\pi$
$492$	1.15046	−	4.79960i	0.0518665	−	0.216383i
$493$			35.2346i			1.58689i
$494$	−7.47472	+	4.73018i	−0.336303	+	0.212821i
$495$	−3.67683	−	3.05257i	−0.165261	−	0.137203i
$496$	−0.757837	+	0.620423i	−0.0340279	+	0.0278578i
$497$	8.00000			0.358849
$498$	13.9798	−	13.5919i	0.626448	−	0.609067i
$499$		−	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	$-0.822296\pi$
$503$		−	23.7609i		−	1.05945i	0.848171	−	0.529723i	$-0.177704\pi$
$504$	4.33397	+	7.29498i	0.193050	+	0.324944i
$505$	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	$-0.878333\pi$
$509$		−	16.8301i		−	0.745979i	0.927835	−	0.372990i	$-0.121667\pi$
$510$	9.91381	−	28.4033i	0.438991	−	1.25772i
$511$			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
$516$	27.6396	+	6.62517i	1.21677	+	0.291657i
$517$			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	$0.00387515\pi$
$521$			0.555747i			0.0243477i	−0.999926	+	0.0121738i	$0.996125\pi$
$522$	−22.5800	−	15.1952i	−0.988298	−	0.665074i
$523$	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
$525$	7.84870	+	3.66032i	0.342545	+	0.159749i
$526$	−6.94225	−	10.9703i	−0.302696	−	0.478327i
$527$			1.34485i			0.0585827i
$528$	−3.09440	+	3.84505i	−0.134666	+	0.167334i
$529$	−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
$534$	−10.9850	+	10.6802i	−0.475368	+	0.462179i
$535$	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
$540$	13.9267	+	18.6023i	0.599311	+	0.800516i
$541$	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
$546$	11.2664	−	10.9538i	0.482155	−	0.468778i
$547$	−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
$552$	9.18710	+	26.9142i	0.391029	+	1.14555i
$553$		−	15.0002i		−	0.637875i
$554$	4.62773	+	7.31283i	0.196613	+	0.310692i
$555$	13.0597	+	16.4580i	0.554353	+	0.698605i
$556$	−0.812898	−	0.385068i	−0.0344745	−	0.0163305i
$557$	−36.1055			−1.52984			−0.764919	−	0.644126i	$-0.777221\pi$
$557$	−36.1055			−1.52984			−0.764919	+	0.644126i	$0.777221\pi$
$558$	−0.861844	−	0.579976i	−0.0364847	−	0.0245524i
$559$		−	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	$0.211911\pi$
$563$			29.3103i			1.23528i	−0.786461	+	0.617640i	$0.788089\pi$
$564$	2.73736	−	11.4200i	0.115264	−	0.480870i
$565$	−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	$0.236476\pi$
$569$			32.2709i			1.35287i	−0.736503	+	0.676434i	$0.763524\pi$
$570$	−5.04214	−	1.75990i	−0.211192	−	0.0737140i
$571$		−	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
$576$	18.9908	−	14.6748i	0.791283	−	0.611450i
$577$		−	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
$582$	−31.7786	+	30.8969i	−1.31726	+	1.28072i
$583$	3.45475			0.143081
$584$	22.4597	−	2.74966i	0.929390	−	0.113782i
$585$	27.4883	−	33.1098i	1.13650	−	1.36892i
$586$	−27.6681	+	17.5090i	−1.14296	+	0.723291i
$587$		−	3.57022i		−	0.147359i	−0.997282	−	0.0736794i	$-0.976526\pi$
$587$		−	3.57022i		−	0.147359i	0.997282	−	0.0736794i	$-0.0234742\pi$
$588$	3.36868	+	0.807466i	0.138922	+	0.0332993i
$589$	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	$-0.736855\pi$
$593$	−32.9872			−1.35462			−0.677311	+	0.735697i	$0.736855\pi$
$594$	−4.85132	−	1.96707i	−0.199052	−	0.0807097i
$595$	−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	$-0.680496\pi$
$599$	−26.2926			−1.07429			−0.537143	+	0.843491i	$0.680496\pi$
$600$	7.57856	−	23.2930i	0.309394	−	0.950934i
$601$	−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
$606$	8.24485	−	8.01610i	0.334924	−	0.325632i
$607$	−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
$612$	0.927019	−	32.9420i	0.0374725	−	1.33160i
$613$			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
$615$	−3.43002	−	4.32257i	−0.138312	−	0.174303i
$616$	0.244852	+	2.00000i	0.00986538	+	0.0805823i
$617$	12.4398			0.500806			0.250403	−	0.968142i	$-0.419437\pi$
$617$	12.4398			0.500806			0.250403	+	0.968142i	$0.419437\pi$
$618$	4.54616	+	4.67590i	0.182873	+	0.188092i
$619$		−	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
$624$	−34.6247	−	27.8650i	−1.38610	−	1.11549i
$625$	−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
$630$	9.40838	+	1.21751i	0.374839	+	0.0485066i
$631$		−	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
$636$	−16.3366	−	3.91584i	−0.647787	−	0.155273i
$637$		−	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	$-0.778413\pi$
$641$		−	32.4707i		−	1.28252i	0.767325	−	0.641258i	$-0.221587\pi$
$642$	26.7473	−	26.0052i	1.05563	−	1.02634i
$643$	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
$645$	24.8925	−	19.7526i	0.980143	−	0.777757i
$646$	4.04994	+	6.39980i	0.159343	+	0.251797i
$647$			39.8090i			1.56505i	0.622618	+	0.782526i	$0.286069\pi$
$647$			39.8090i			1.56505i	−0.622618	+	0.782526i	$0.713931\pi$
$648$	20.7110	+	14.8005i	0.813604	+	0.581420i
$649$	−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	$-0.174126\pi$
$653$	43.6496			1.70814			0.854071	+	0.520156i	$0.174126\pi$
$654$	2.54848	+	2.62120i	0.0996534	+	0.102497i
$655$	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	$-0.540076\pi$
$659$	−6.44705			−0.251142			−0.125571	+	0.992085i	$0.540076\pi$
$660$	1.24935	+	5.37483i	0.0486307	+	0.209215i
$661$	−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
$666$	19.0944	+	12.8495i	0.739893	+	0.497910i
$667$	−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
$672$	1.10909	−	9.73498i	0.0427842	−	0.375535i
$673$			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
$675$	25.9744	+	0.574729i	0.999755	+	0.0221213i
$676$	−24.1041	+	50.8849i	−0.927080	+	1.95711i
$677$	7.79342			0.299525			0.149763	−	0.988722i	$-0.452149\pi$
$677$	7.79342			0.299525			0.149763	+	0.988722i	$0.452149\pi$
$678$	−14.0953	−	14.4975i	−0.541325	−	0.556773i
$679$			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	$0.179125\pi$
$683$			27.8855i			1.06701i	−0.845797	+	0.533504i	$0.820875\pi$
$684$	−5.84785	−	0.164564i	−0.223598	−	0.00629227i
$685$	−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
$690$	30.0197	+	10.4780i	1.14283	+	0.398891i
$691$		−	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
$696$	10.1524	+	29.7421i	0.384825	+	1.12737i
$697$			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	$-0.855411\pi$
$701$		−	23.2346i		−	0.877559i	0.898595	−	0.438779i	$-0.144589\pi$
$702$	17.7134	−	43.6861i	0.668550	−	1.64883i
$703$	−5.28931			−0.199490
$704$	5.53077	−	1.37483i	0.208449	−	0.0518158i
$705$	−8.16128	−	10.2850i	−0.307372	−	0.387355i
$706$	22.7261	−	14.3816i	0.855307	−	0.541259i
$707$		−	4.69460i		−	0.176558i
$708$	25.1799	+	6.03558i	0.946319	+	0.226831i
$709$	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
$714$	−9.37854	−	9.64618i	−0.350983	−	0.360999i
$715$	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	$-0.587089\pi$
$719$	−14.4902			−0.540393			−0.270196	+	0.962805i	$0.587089\pi$
$720$	0.184378	−	26.8322i	0.00687137	−	0.999976i
$721$	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
$726$	17.9161	+	18.4274i	0.664930	+	0.683905i
$727$	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
$732$	−4.27763	−	1.02534i	−0.158106	−	0.0378977i
$733$		−	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
$735$	3.03387	−	2.40742i	0.111906	−	0.0887989i
$736$	10.3475	−	31.1657i	0.381415	−	1.14878i
$737$	9.28592			0.342051
$738$	−5.01499	−	3.37483i	−0.184604	−	0.124229i
$739$		−	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	$-0.896908\pi$
$743$		−	17.3492i		−	0.636482i	0.948010	−	0.318241i	$-0.103092\pi$
$744$	0.387502	+	1.13521i	0.0142065	+	0.0416189i
$745$	−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
$750$	−15.2702	−	22.7337i	−0.557588	−	0.830118i
$751$		−	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
$756$	10.2263	−	1.85023i	0.371926	−	0.0672921i
$757$			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	$0.144761\pi$
$761$			24.2354i			0.878531i	−0.898357	+	0.439265i	$0.855239\pi$
$762$	16.0929	+	16.5522i	0.582986	+	0.599623i
$763$	1.49251			0.0540323
$764$	23.0297	−	48.6169i	0.833186	−	1.75890i
$765$	−28.3484	−	23.5353i	−1.02494	−	0.850922i
$766$	19.1702	+	30.2931i	0.692647	+	1.09453i
$767$		−	47.9505i		−	1.73139i
$768$	−27.7118	+	0.232238i	−0.999965	+	0.00838018i
$769$	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	$-0.539270\pi$
$773$	−6.84274			−0.246116			−0.123058	+	0.992399i	$0.539270\pi$
$774$	19.4348	−	28.8800i	0.698568	−	1.03807i
$775$	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
$780$	−48.4003	+	11.2503i	−1.73301	+	0.402827i
$781$	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
$786$	30.1029	+	30.9620i	1.07374	+	1.10438i
$787$	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
$792$	3.08746	+	5.19684i	0.109708	+	0.184662i
$793$			8.14596i			0.289272i
$794$	13.2611	+	20.9555i	0.470619	+	0.743681i
$795$	−14.7129	+	11.6749i	−0.521812	+	0.414065i
$796$	−14.3875	−	6.81533i	−0.509951	−	0.241563i
$797$	24.7874			0.878015			0.439008	−	0.898483i	$-0.355330\pi$
$797$	24.7874			0.878015			0.439008	+	0.898483i	$0.355330\pi$
$798$	−1.71239	+	1.66488i	−0.0606178	+	0.0589360i
$799$			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
$804$	−43.9106	−	10.5253i	−1.54861	−	0.371198i
$805$	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	$-0.787379\pi$
$809$		−	35.2346i		−	1.23878i	0.785082	−	0.619391i	$-0.212621\pi$
$810$	27.3080	−	8.01719i	0.959504	−	0.281695i
$811$			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
$816$	−23.8578	+	29.6454i	−0.835191	+	1.03780i
$817$			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	$0.0795088\pi$
$821$			14.1658i			0.494390i	−0.968966	+	0.247195i	$0.920491\pi$
$822$	−4.66182	−	4.79485i	−0.162600	−	0.167240i
$823$	−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
$825$	5.59130	+	2.60756i	0.194664	+	0.0907836i
$826$	8.93251	−	5.65270i	0.310802	−	0.196683i
$827$			16.0989i			0.559813i	0.960027	+	0.279907i	$0.0903035\pi$
$827$			16.0989i			0.559813i	−0.960027	+	0.279907i	$0.909696\pi$
$828$	34.8168	+	0.979777i	1.20997	+	0.0340496i
$829$	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
$834$	−0.789860	+	0.767946i	−0.0273506	+	0.0265918i
$835$	−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	$-0.237095\pi$
$839$	42.5901			1.47037			0.735186	+	0.677865i	$0.237095\pi$
$840$	−7.80150	−	7.69003i	−0.269177	−	0.265331i
$841$	−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
$846$	−11.9325	−	8.02996i	−0.410248	−	0.276076i
$847$	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
$852$	−26.9494	−	6.45973i	−0.923272	−	0.221307i
$853$		−	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
$855$	−4.17799	+	5.03240i	−0.142884	+	0.172104i
$856$	−42.7573	+	5.23461i	−1.46142	+	0.178915i
$857$	7.35023			0.251079			0.125540	−	0.992089i	$-0.459934\pi$
$857$	7.35023			0.251079			0.125540	+	0.992089i	$0.459934\pi$
$858$	8.02600	−	7.80331i	0.274003	−	0.266401i
$859$			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	$-0.901023\pi$
$863$		−	17.9761i		−	0.611915i	0.952045	−	0.305957i	$-0.0989765\pi$
$864$	−8.70929	−	28.0740i	−0.296296	−	0.955096i
$865$	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
$870$	33.1739	+	11.5789i	1.12470	+	0.392563i
$871$			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
$876$	6.45973	−	26.9494i	0.218254	−	0.910537i
$877$		−	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	$-0.925148\pi$
$881$		−	13.8312i		−	0.465984i	0.972479	−	0.232992i	$-0.0748516\pi$
$882$	2.36868	−	3.51985i	0.0797576	−	0.118520i
$883$	−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
$885$	22.6773	−	17.9948i	0.762289	−	0.604887i
$886$	5.62248	+	8.88476i	0.188891	+	0.298489i
$887$			12.4108i			0.416713i	0.978053	+	0.208357i	$0.0668115\pi$
$887$			12.4108i			0.416713i	−0.978053	+	0.208357i	$0.933189\pi$
$888$	−8.58521	−	25.1509i	−0.288101	−	0.844010i
$889$	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
$894$	−2.02048	+	1.96442i	−0.0675749	+	0.0657001i
$895$	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
$900$	−23.4842	−	18.6680i	−0.782806	−	0.622266i
$901$	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
$906$	−2.47550	+	2.40681i	−0.0822429	+	0.0799610i
$907$	−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	$-0.635227\pi$
$911$	−24.8805			−0.824328			−0.412164	+	0.911110i	$0.635227\pi$
$912$	5.26264	+	4.23524i	0.174263	+	0.140243i
$913$		−	5.67062i		−	0.187670i
$914$	23.6371	+	37.3518i	0.781845	+	1.23549i
$915$	−3.85248	+	3.05700i	−0.127359	+	0.101061i
$916$	21.0322	−	44.3999i	0.694922	−	1.46701i
$917$	17.6297			0.582183
$918$	−37.4038	−	15.1661i	−1.23451	−	0.500556i
$919$			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
$924$	2.39980	+	0.575228i	0.0789476	+	0.0189236i
$925$	−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	$0.176462\pi$
$929$			32.0894i			1.05282i	−0.850231	+	0.526409i	$0.823538\pi$
$930$	1.26620	+	0.441951i	0.0415203	+	0.0144921i
$931$			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
$936$	−46.7975	+	27.8025i	−1.52963	+	0.908754i
$937$		−	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	$0.0722489\pi$
$941$			13.8061i			0.450066i	−0.974351	+	0.225033i	$0.927751\pi$
$942$	2.02048	−	1.96442i	0.0658308	−	0.0640043i
$943$	−8.27093			−0.269339
$944$	−18.9399	−	23.1348i	−0.616442	−	0.752975i
$945$	5.42477	−	10.2748i	0.176468	−	0.334240i
$946$	6.98501	−	4.42028i	0.227102	−	0.143716i
$947$			39.4652i			1.28245i	0.767354	+	0.641224i	$0.221573\pi$
$947$			39.4652i			1.28245i	−0.767354	+	0.641224i	$0.778427\pi$
$948$	−12.1122	+	50.5310i	−0.393386	+	1.64117i
$949$	−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	$-0.533862\pi$
$953$	−6.55575			−0.212361			−0.106181	+	0.994347i	$0.533862\pi$
$954$	−11.4870	+	17.0697i	−0.371906	+	0.552651i
$955$	−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
$960$	−18.9081	+	24.5456i	−0.610255	+	0.792205i
$961$	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
$966$	10.1952	−	9.91229i	0.328024	−	0.318923i
$967$	−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	$-0.453453\pi$
$971$	9.08103			0.291424			0.145712	+	0.989327i	$0.453453\pi$
$972$	25.8498	−	17.4296i	0.829131	−	0.559054i
$973$			0.449744i			0.0144181i
$974$	−40.7571	+	25.7920i	−1.30594	+	0.826430i
$975$	−23.4811	+	50.3497i	−0.751996	+	1.61248i
$976$	3.21757	+	3.93021i	0.102992	+	0.125803i
$977$	8.70020			0.278344			0.139172	−	0.990268i	$-0.455556\pi$
$977$	8.70020			0.278344			0.139172	+	0.990268i	$0.455556\pi$
$978$	−26.4233	−	27.1774i	−0.844925	−	0.869036i
$979$			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	$-0.765764\pi$
$983$		−	42.0903i		−	1.34247i	0.741244	−	0.671235i	$-0.234236\pi$
$984$	2.25484	+	6.60569i	0.0718815	+	0.210582i
$985$	−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
$990$	6.70240	+	0.867334i	0.213016	+	0.0275657i
$991$		−	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
$996$	−6.42746	+	26.8148i	−0.203662	+	0.849660i
$997$			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.c.239.2	yes	8
3.2	odd	2		420.2.l.d.239.7	yes	8
4.3	odd	2		420.2.l.e.239.1	yes	8
5.4	even	2		420.2.l.f.239.7	yes	8
12.11	even	2		420.2.l.f.239.8	yes	8
15.14	odd	2		420.2.l.e.239.2	yes	8
20.19	odd	2		420.2.l.d.239.8	yes	8
60.59	even	2	inner	420.2.l.c.239.1	✓	8

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

\(f(q)\)	\(=\)	\(q+(-1.19503 + 0.756243i) q^{2} +(0.356193 + 1.69503i) q^{3} +(0.856193 - 1.80747i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.70752 - 1.75624i) q^{6} -1.00000 q^{7} +(0.343707 + 2.80747i) q^{8} +(-2.74625 + 1.20752i) q^{9} +O(q^{10})\)	\(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} +(-1.70752 - 1.75624i) 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} +(3.36868 + 0.807466i) q^{12} -6.41503i q^{13} +(1.19503 - 0.756243i) q^{14} +(3.03387 - 2.40742i) q^{15} +(-2.53387 - 3.09508i) q^{16} -5.49251 q^{17} +(2.36868 - 3.51985i) 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} +(-4.63631 + 1.58259i) 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} +(-1.80497 + 5.17127i) 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} +(-0.168779 + 5.99763i) 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} +(1.70752 + 1.75624i) q^{42} +8.20489 q^{43} +(-0.609940 + 1.28761i) q^{44} +(5.16128 + 4.28499i) q^{45} +(4.39006 + 6.93726i) q^{46} -3.39006i q^{47} +(4.34371 - 5.39743i) 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} +(6.80996 + 2.76123i) 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} +(-1.75375 - 7.54482i) 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} +(1.21641 + 1.25112i) 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} +(-4.33397 - 7.29498i) q^{72} -8.00000i q^{73} +(-4.10245 - 6.48277i) q^{74} +(-7.84870 - 3.66032i) q^{75} +(1.76233 + 0.834812i) q^{76} +0.712386 q^{77} +(-11.2664 + 10.9538i) 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} +(-3.36868 - 0.807466i) 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} +(-9.40838 - 1.21751i) 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} +(-1.10909 + 9.73498i) q^{96} -18.0946i q^{97} +(-1.19503 + 0.756243i) q^{98} +(1.95639 - 0.860218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q - 2 q^{3} + 2 q^{4} - 8 q^{5} + 4 q^{6} - 8 q^{7} + 6 q^{8} + 2 q^{9} + 4 q^{10} + 4 q^{11} + 14 q^{12} + 10 q^{15} - 6 q^{16} + 4 q^{17} + 6 q^{18} + 6 q^{20} + 2 q^{21} - 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} - 8 q^{27} - 2 q^{28} - 24 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} + 20 q^{38} + 18 q^{39} + 2 q^{40} - 4 q^{42} + 8 q^{43} - 24 q^{44} - 18 q^{45} + 16 q^{46} + 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} - 16 q^{52} + 8 q^{54} - 4 q^{55} - 6 q^{56} - 20 q^{57} + 26 q^{58} + 8 q^{59} - 38 q^{60} - 16 q^{61} + 40 q^{62} - 2 q^{63} + 26 q^{64} - 32 q^{65} - 6 q^{66} + 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} - 22 q^{72} - 4 q^{74} - 10 q^{75} - 28 q^{76} - 4 q^{77} - 42 q^{78} - 26 q^{80} + 2 q^{81} - 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} + 18 q^{87} - 24 q^{88} - 6 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^4 - 8 * q^5 + 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9 + 4 * q^10 + 4 * q^11 + 14 * q^12 + 10 * q^15 - 6 * q^16 + 4 * q^17 + 6 * q^18 + 6 * q^20 + 2 * q^21 - 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 - 8 * q^27 - 2 * q^28 - 24 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 + 20 * q^38 + 18 * q^39 + 2 * q^40 - 4 * q^42 + 8 * q^43 - 24 * q^44 - 18 * q^45 + 16 * q^46 + 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 - 16 * q^52 + 8 * q^54 - 4 * q^55 - 6 * q^56 - 20 * q^57 + 26 * q^58 + 8 * q^59 - 38 * q^60 - 16 * q^61 + 40 * q^62 - 2 * q^63 + 26 * q^64 - 32 * q^65 - 6 * q^66 + 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 - 22 * q^72 - 4 * q^74 - 10 * q^75 - 28 * q^76 - 4 * q^77 - 42 * q^78 - 26 * q^80 + 2 * q^81 - 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 + 18 * q^87 - 24 * q^88 - 6 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * q^96 + 14 * q^99

Introduction

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