LMFDB - Embedded newform 420.2.l.f.239.8

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

$q$-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} +(-0.317456 + 3.14630i) q^{10} -0.712386 q^{11} +(-3.36868 + 0.807466i) 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} +(-2.36868 - 3.51985i) q^{18} -0.975028i q^{19} +(-2.75874 + 3.51985i) 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} +(-5.22000 - 1.65879i) 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} +(-5.95864 + 2.12005i) q^{40} +1.42477i q^{41} +(-1.70752 + 1.75624i) 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} +(-4.34371 - 5.39743i) q^{48} +1.00000 q^{49} +(-6.61006 + 2.51139i) 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} +(-4.98361 - 5.92989i) 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} +(-0.317456 + 3.14630i) q^{70} -8.00000 q^{71} +(4.33397 - 7.29498i) 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} +(11.2664 + 10.9538i) q^{78} -15.0002i q^{79} +(-8.72403 - 1.97265i) 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} +(4.67103 - 8.25721i) 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} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 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} + 10 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} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 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 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * 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 + 10 * 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 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * 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
$10$	−0.317456	+	3.14630i	−0.100388	+	0.994948i
$11$	−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
$15$	−3.74625	+	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	$0.267978\pi$
$18$	−2.36868	−	3.51985i	−0.558303	−	0.829637i
$19$		−	0.975028i		−	0.223687i	−0.993726	−	0.111843i	$-0.964325\pi$
$19$		−	0.975028i		−	0.223687i	0.993726	−	0.111843i	$-0.0356755\pi$
$20$	−2.75874	+	3.51985i	−0.616873	+	0.787063i
$21$	−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	$0.203094\pi$
$29$			6.41503i			1.19124i	−0.803266	+	0.595621i	$0.796906\pi$
$30$	−5.22000	−	1.65879i	−0.953038	−	0.302852i
$31$			0.244852i			0.0439768i	0.999758	+	0.0219884i	$0.00699968\pi$
$31$			0.244852i			0.0439768i	−0.999758	+	0.0219884i	$0.993000\pi$
$32$	−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
$40$	−5.95864	+	2.12005i	−0.942144	+	0.335210i
$41$			1.42477i			0.222512i	0.993792	+	0.111256i	$0.0354874\pi$
$41$			1.42477i			0.222512i	−0.993792	+	0.111256i	$0.964513\pi$
$42$	−1.70752	+	1.75624i	−0.263475	+	0.270994i
$43$	−8.20489			−1.25123			−0.625617	−	0.780130i	$-0.715153\pi$
$43$	−8.20489			−1.25123			−0.625617	+	0.780130i	$0.715153\pi$
$44$	−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	$-0.920475\pi$
$47$		−	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
$50$	−6.61006	+	2.51139i	−0.934804	+	0.355164i
$51$	−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	$0.391916\pi$
$54$	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	$0.338251\pi$
$60$	−4.98361	−	5.92989i	−0.643381	−	0.765546i
$61$	−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	$-0.206821\pi$
$67$	13.0350			1.59247			0.796237	+	0.604985i	$0.206821\pi$
$68$	4.70265	+	9.92752i	0.570280	+	1.20389i
$69$	9.83980	+	2.06773i	1.18457	+	0.248926i
$70$	−0.317456	+	3.14630i	−0.0379433	+	0.376055i
$71$	−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
$75$	−5.71154	−	6.50986i	−0.659512	−	0.751694i
$76$	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	$-0.680296\pi$
$79$		−	15.0002i		−	1.68766i	0.536611	−	0.843830i	$-0.319704\pi$
$80$	−8.72403	−	1.97265i	−0.975376	−	0.220549i
$81$	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	$0.107557\pi$
$89$			6.25484i			0.663011i	−0.943453	+	0.331506i	$0.892443\pi$
$90$	4.67103	−	8.25721i	0.492369	−	0.870386i
$91$		−	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
$100$	−9.79844	−	1.99763i	−0.979844	−	0.199763i
$101$		−	4.69460i		−	0.467130i	−0.972341	−	0.233565i	$-0.924961\pi$
$101$		−	4.69460i		−	0.467130i	0.972341	−	0.233565i	$-0.0750391\pi$
$102$	−9.37854	+	9.64618i	−0.928614	+	0.955114i
$103$	2.66244			0.262338			0.131169	−	0.991360i	$-0.458127\pi$
$103$	2.66244			0.262338			0.131169	+	0.991360i	$0.458127\pi$
$104$	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	$0.263364\pi$
$107$			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	$0.522772\pi$
$110$	0.226151	−	2.24138i	0.0215627	−	0.213707i
$111$	−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	$0.626929\pi$
$114$	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
$120$	−1.47113	−	10.8552i	−0.134295	−	0.990941i
$121$	−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	$-0.362676\pi$
$127$	9.42477			0.836313			0.418157	+	0.908375i	$0.362676\pi$
$128$	−7.81842	−	8.17755i	−0.691058	−	0.722800i
$129$	2.92253	−	13.9075i	0.257314	−	1.22449i
$130$	20.1836	+	2.03649i	1.77022	+	0.178612i
$131$	−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
$135$	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	$0.537208\pi$
$138$	10.1952	+	9.91229i	0.867869	+	0.843790i
$139$			0.449744i			0.0381468i	0.999818	+	0.0190734i	$0.00607162\pi$
$139$			0.449744i			0.0381468i	−0.999818	+	0.0190734i	$0.993928\pi$
$140$	−2.75874	+	3.51985i	−0.233156	+	0.297482i
$141$	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	$0.0150057\pi$
$149$			1.15046i			0.0942490i	−0.998889	+	0.0471245i	$0.984994\pi$
$150$	−1.90242	−	12.0988i	−0.155332	−	0.987862i
$151$			1.40954i			0.114707i	0.998354	+	0.0573534i	$0.0182662\pi$
$151$			1.40954i			0.114707i	−0.998354	+	0.0573534i	$0.981734\pi$
$152$	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
$160$	−8.93367	−	8.95486i	−0.706268	−	0.707944i
$161$		−	5.80509i		−	0.457505i
$162$	2.25471	+	12.5266i	0.177147	+	0.984184i
$163$	−15.4747			−1.21207			−0.606037	−	0.795437i	$-0.707242\pi$
$163$	−15.4747			−1.21207			−0.606037	+	0.795437i	$0.707242\pi$
$164$	−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	$-0.803366\pi$
$167$		−	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
$170$	−1.74363	+	17.2811i	−0.133730	+	1.32540i
$171$	−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	$0.382486\pi$
$174$	−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	$0.543077\pi$
$180$	11.8265	−	6.33518i	0.881493	−	0.472197i
$181$	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
$190$	3.06773	+	0.309529i	0.222557	+	0.0224556i
$191$	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
$195$	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	$0.593824\pi$
$198$	1.68741	+	2.50749i	0.119919	+	0.178200i
$199$			7.96004i			0.564272i	0.959374	+	0.282136i	$0.0910430\pi$
$199$			7.96004i			0.564272i	−0.959374	+	0.282136i	$0.908957\pi$
$200$	−10.1987	−	9.79723i	−0.721160	−	0.692769i
$201$	−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
$210$	−5.22000	−	1.65879i	−0.360214	−	0.114467i
$211$		−	14.9698i		−	1.03056i	−0.857021	−	0.515281i	$-0.827688\pi$
$211$		−	14.9698i		−	1.03056i	0.857021	−	0.515281i	$-0.172312\pi$
$212$	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
$220$	1.96529	−	2.50749i	0.132500	−	0.169055i
$221$		−	35.2346i		−	2.37014i
$222$	−9.52722	−	9.26289i	−0.639425	−	0.621684i
$223$	−2.62686			−0.175908			−0.0879539	−	0.996125i	$-0.528033\pi$
$223$	−2.62686			−0.175908			−0.0879539	+	0.996125i	$0.528033\pi$
$224$	−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	$0.0358868\pi$
$227$			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	$0.198574\pi$
$230$	18.2646	+	1.84286i	1.20433	+	0.121515i
$231$	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	$0.742679\pi$
$234$	−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	$0.630883\pi$
$240$	6.45115	−	14.0848i	0.416420	−	0.909173i
$241$	−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
$250$	−11.6328	−	10.7087i	−0.735726	−	0.677280i
$251$	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
$255$	−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	$0.747735\pi$
$258$	14.0100	−	14.4098i	0.872223	−	0.897114i
$259$			5.42477i			0.337079i
$260$	22.5800	+	17.6974i	1.40035	+	1.09755i
$261$	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	$0.204810\pi$
$269$			19.6796i			1.19989i	−0.800042	+	0.599943i	$0.795190\pi$
$270$	12.3324	+	10.8587i	0.750528	+	0.660839i
$271$			29.3459i			1.78263i	0.453381	+	0.891317i	$0.350218\pi$
$271$			29.3459i			1.78263i	−0.453381	+	0.891317i	$0.649782\pi$
$272$	−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
$280$	−5.95864	+	2.12005i	−0.356097	+	0.126697i
$281$			0.434513i			0.0259209i	0.999916	+	0.0129604i	$0.00412555\pi$
$281$			0.434513i			0.0259209i	−0.999916	+	0.0129604i	$0.995874\pi$
$282$	5.95377	+	5.78858i	0.354542	+	0.344705i
$283$	1.72737			0.102682			0.0513409	−	0.998681i	$-0.483651\pi$
$283$	1.72737			0.102682			0.0513409	+	0.998681i	$0.483651\pi$
$284$	−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
$288$	16.8961	+	1.58759i	0.995615	+	0.0935494i
$289$	13.1676			0.774566
$290$	−20.1836	−	2.03649i	−1.18522	−	0.119587i
$291$	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	$0.736416\pi$
$294$	−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
$300$	6.87617	−	15.8971i	0.396996	−	0.917820i
$301$	−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	$-0.592099\pi$
$307$	−9.99831			−0.570634			−0.285317	+	0.958433i	$0.592099\pi$
$308$	−0.609940	−	1.28761i	−0.0347546	−	0.0733686i
$309$	−0.948344	+	4.51292i	−0.0539494	+	0.256731i
$310$	−0.770379	−	0.0777298i	−0.0437546	−	0.00441476i
$311$	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
$315$	−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	$0.418805\pi$
$318$	−8.28067	+	8.51698i	−0.464357	+	0.477608i
$319$		−	4.56998i		−	0.255870i
$320$	−3.90395	−	17.4574i	−0.218237	−	0.975896i
$321$	−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
$330$	3.71866	+	1.18170i	0.204705	+	0.0650503i
$331$		−	3.65014i		−	0.200630i	−0.994956	−	0.100315i	$-0.968015\pi$
$331$		−	3.65014i		−	0.200630i	0.994956	−	0.100315i	$-0.0319851\pi$
$332$	−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
$340$	−15.1524	+	19.3328i	−0.821754	+	1.04847i
$341$		−	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
$345$	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	$-0.867031\pi$
$347$		−	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	$0.427905\pi$
$350$	−6.61006	+	2.51139i	−0.353323	+	0.134239i
$351$	−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	$0.331090\pi$
$354$	−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	$0.654317\pi$
$360$	18.9239	+	1.37295i	0.997379	+	0.0723610i
$361$	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	$-0.247883\pi$
$367$	27.2720			1.42359			0.711793	+	0.702389i	$0.247883\pi$
$368$	17.9672	+	14.7093i	0.936606	+	0.766777i
$369$	1.72044	−	3.91279i	0.0895623	−	0.203691i
$370$	−17.0680	−	1.72213i	−0.887322	−	0.0895291i
$371$	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
$375$	7.30818	−	17.9329i	0.377393	−	0.926053i
$376$	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	$0.137590\pi$
$379$			16.3109i			0.837834i	−0.908024	+	0.418917i	$0.862410\pi$
$380$	3.43195	+	2.68985i	0.176056	+	0.137986i
$381$	−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	$-0.900640\pi$
$389$		−	12.1141i		−	0.614210i	0.951676	−	0.307105i	$-0.0993603\pi$
$390$	−10.6412	+	33.4865i	−0.538837	+	1.69565i
$391$		−	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
$400$	−4.77872	−	19.4207i	−0.238936	−	0.971035i
$401$			16.7054i			0.834230i	0.908854	+	0.417115i	$0.136959\pi$
$401$			16.7054i			0.834230i	−0.908854	+	0.417115i	$0.863041\pi$
$402$	−22.2574	+	22.8925i	−1.11010	+	1.14178i
$403$	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
$408$	−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	$0.700585\pi$
$410$	−4.48277	−	0.452303i	−0.221388	−	0.0223376i
$411$	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	$0.668066\pi$
$420$	−4.98361	−	5.92989i	−0.243175	−	0.289349i
$421$	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
$430$	2.60469	−	25.8151i	0.125609	−	1.24491i
$431$	−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
$435$	−6.30369	−	24.0323i	−0.302239	−	1.15226i
$436$	−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	$-0.797848\pi$
$439$		−	24.8595i		−	1.18648i	0.805025	−	0.593240i	$-0.202152\pi$
$440$	4.24485	−	1.51030i	0.202365	−	0.0720005i
$441$	−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	$0.0526222\pi$
$449$			6.97416i			0.329131i	−0.986366	+	0.164566i	$0.947378\pi$
$450$	21.1854	+	1.08484i	0.998692	+	0.0511399i
$451$		−	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
$460$	20.4331	+	16.0147i	0.952697	+	0.746691i
$461$			19.1594i			0.892344i	0.894947	+	0.446172i	$0.147213\pi$
$461$			19.1594i			0.892344i	−0.894947	+	0.446172i	$0.852787\pi$
$462$	1.21641	−	1.25112i	0.0565925	−	0.0582075i
$463$	23.9150			1.11142			0.555711	−	0.831375i	$-0.312446\pi$
$463$	23.9150			1.11142			0.555711	+	0.831375i	$0.312446\pi$
$464$	−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	$0.0461147\pi$
$467$			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
$470$	10.6662	+	1.07619i	0.491993	+	0.0496412i
$471$	−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	$0.566958\pi$
$480$	18.3609	−	11.9532i	0.838055	−	0.545585i
$481$	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	$-0.781111\pi$
$487$	−34.1055			−1.54547			−0.772734	+	0.634730i	$0.781111\pi$
$488$	0.436448	−	3.56499i	0.0197571	−	0.161379i
$489$	5.51199	−	26.2301i	0.249261	−	1.18617i
$490$	−0.317456	+	3.14630i	−0.0143412	+	0.142135i
$491$	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
$495$	0.235957	+	4.77300i	0.0106055	+	0.214531i
$496$	−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	$0.0523940\pi$
$499$			7.32063i			0.327717i	−0.986484	+	0.163858i	$0.947606\pi$
$500$	−5.80319	−	21.5945i	−0.259527	−	0.965736i
$501$	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	$0.121667\pi$
$509$			16.8301i			0.745979i	−0.927835	+	0.372990i	$0.878333\pi$
$510$	−28.6709	−	9.11091i	−1.26957	−	0.403438i
$511$		−	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
$520$	13.6002	+	38.2249i	0.596408	+	1.67627i
$521$		−	0.555747i		−	0.0243477i	−0.999926	−	0.0121738i	$-0.996125\pi$
$521$		−	0.555747i		−	0.0243477i	0.999926	−	0.0121738i	$-0.00387515\pi$
$522$	22.5800	−	15.1952i	0.988298	−	0.665074i
$523$	−30.7307			−1.34376			−0.671879	−	0.740661i	$-0.734513\pi$
$523$	−30.7307			−1.34376			−0.671879	+	0.740661i	$0.734513\pi$
$524$	−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
$528$	3.09440	+	3.84505i	0.134666	+	0.167334i
$529$	−10.6991			−0.465178
$530$	−1.53952	+	15.2581i	−0.0668724	+	0.662771i
$531$	−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
$540$	6.52582	+	22.3028i	0.280826	+	0.959759i
$541$	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	$-0.473464\pi$
$547$	3.89500			0.166538			0.0832690	+	0.996527i	$0.473464\pi$
$548$	−2.33756	−	4.93470i	−0.0998555	−	0.210800i
$549$	3.48726	+	1.53333i	0.148833	+	0.0654411i
$550$	4.70892	−	1.78908i	0.200789	−	0.0762866i
$551$	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
$555$	−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	$0.222779\pi$
$558$	0.861844	−	0.579976i	0.0364847	−	0.0245524i
$559$			52.6346i			2.22621i
$560$	−8.72403	−	1.97265i	−0.368657	−	0.0833598i
$561$	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	$-0.763524\pi$
$569$		−	32.2709i		−	1.35287i	0.736503	−	0.676434i	$-0.236476\pi$
$570$	−1.61737	+	5.08965i	−0.0677440	+	0.213182i
$571$			40.8595i			1.70992i	0.518696	+	0.854959i	$0.326418\pi$
$571$			40.8595i			1.70992i	−0.518696	+	0.854959i	$0.673582\pi$
$572$	−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
$580$	−22.5800	−	17.6974i	−0.937582	−	0.734844i
$581$			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
$585$	−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	$-0.976526\pi$
$587$		−	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
$590$	−2.37289	+	23.5177i	−0.0976905	+	0.968209i
$591$	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	$0.263145\pi$
$594$	−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	$0.680496\pi$
$600$	20.2393	−	13.7975i	0.826267	−	0.563279i
$601$	−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	$-0.304803\pi$
$607$	28.3581			1.15102			0.575511	+	0.817794i	$0.304803\pi$
$608$	1.73798	+	5.23461i	0.0704845	+	0.212292i
$609$	−10.8737	−	2.28499i	−0.440623	−	0.0925925i
$610$	0.403113	−	3.99525i	0.0163216	−	0.161763i
$611$	−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
$615$	−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	$0.580563\pi$
$618$	−4.54616	+	4.67590i	−0.182873	+	0.188092i
$619$			22.2948i			0.896104i	0.894008	+	0.448052i	$0.147882\pi$
$619$			22.2948i			0.896104i	−0.894008	+	0.448052i	$0.852118\pi$
$620$	−0.861844	−	0.675483i	−0.0346125	−	0.0271281i
$621$	−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
$630$	4.67103	−	8.25721i	0.186098	−	0.328975i
$631$			41.0397i			1.63376i	0.576805	+	0.816882i	$0.304299\pi$
$631$			41.0397i			1.63376i	−0.576805	+	0.816882i	$0.695701\pi$
$632$	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
$640$	8.53667	−	23.8144i	0.337441	−	0.941347i
$641$			32.4707i			1.28252i	0.767325	+	0.641258i	$0.221587\pi$
$641$			32.4707i			1.28252i	−0.767325	+	0.641258i	$0.778413\pi$
$642$	−26.7473	−	26.0052i	−1.05563	−	1.02634i
$643$	−23.5230			−0.927655			−0.463828	−	0.885925i	$-0.653524\pi$
$643$	−23.5230			−0.927655			−0.463828	+	0.885925i	$0.653524\pi$
$644$	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	$0.286069\pi$
$647$			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
$650$	16.1107	+	42.4038i	0.631912	+	1.66321i
$651$	−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	$0.825874\pi$
$654$	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	$0.540076\pi$
$660$	3.55026	+	4.22437i	0.138194	+	0.164434i
$661$	−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
$670$	−4.13803	+	41.0119i	−0.159866	+	1.58443i
$671$	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
$675$	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	$0.547851\pi$
$678$	14.0953	−	14.4975i	0.541325	−	0.556773i
$679$		−	18.0946i		−	0.694409i
$680$	−32.7279	+	11.6444i	−1.25506	+	0.446542i
$681$	−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
$690$	−9.62942	+	30.3026i	−0.366586	+	1.15360i
$691$			28.0295i			1.06629i	0.846024	+	0.533146i	$0.178990\pi$
$691$			28.0295i			1.06629i	−0.846024	+	0.533146i	$0.821010\pi$
$692$	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
$700$	−9.79844	−	1.99763i	−0.370346	−	0.0755032i
$701$			23.2346i			0.877559i	0.898595	+	0.438779i	$0.144589\pi$
$701$			23.2346i			0.877559i	−0.898595	+	0.438779i	$0.855411\pi$
$702$	−17.7134	−	43.6861i	−0.668550	−	1.64883i
$703$	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
$708$	−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	$0.319171\pi$
$710$	2.53965	−	25.1704i	0.0953113	−	0.944629i
$711$	−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	$0.587089\pi$
$720$	21.5764	+	15.9518i	0.804104	+	0.594489i
$721$	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	$-0.606202\pi$
$727$	−17.6601			−0.654978			−0.327489	+	0.944855i	$0.606202\pi$
$728$	18.0100	+	2.20489i	0.667494	+	0.0817187i
$729$	−8.69909	−	25.5602i	−0.322188	−	0.946676i
$730$	25.1704	+	2.53965i	0.931599	+	0.0939966i
$731$	−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
$735$	−3.74625	+	0.982644i	−0.138183	+	0.0362454i
$736$	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	$0.00269664\pi$
$739$			0.460595i			0.0169433i	−0.999964	+	0.00847163i	$0.997303\pi$
$740$	−19.0944	−	14.9655i	−0.701924	−	0.550144i
$741$	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
$750$	22.2952	−	15.9036i	0.814104	−	0.580719i
$751$			21.1890i			0.773199i	0.922248	+	0.386599i	$0.126350\pi$
$751$			21.1890i			0.773199i	−0.922248	+	0.386599i	$0.873650\pi$
$752$	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
$760$	2.06711	+	5.80984i	0.0749820	+	0.210745i
$761$		−	24.2354i		−	0.878531i	−0.898357	−	0.439265i	$-0.855239\pi$
$761$		−	24.2354i		−	0.878531i	0.898357	−	0.439265i	$-0.144761\pi$
$762$	−16.0929	+	16.5522i	−0.582986	+	0.599623i
$763$	−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
$768$	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	$0.451393\pi$
$770$	0.226151	−	2.24138i	0.00814993	−	0.0807738i
$771$	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	$0.460730\pi$
$774$	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
$780$	−38.0404	+	31.9700i	−1.36207	+	1.14471i
$781$	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	$-0.700756\pi$
$787$	−33.0866			−1.17941			−0.589705	+	0.807619i	$0.700756\pi$
$788$	−6.98221	−	14.7398i	−0.248731	−	0.525083i
$789$	−15.5602	−	3.26982i	−0.553959	−	0.116409i
$790$	47.1953	+	4.76192i	1.67913	+	0.169421i
$791$	−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
$795$	−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	$0.644670\pi$
$798$	1.71239	+	1.66488i	0.0606178	+	0.0589360i
$799$		−	18.6199i		−	0.658726i
$800$	8.97606	−	26.8222i	0.317352	−	0.948308i
$801$	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	$0.212621\pi$
$809$			35.2346i			1.23878i	−0.785082	+	0.619391i	$0.787379\pi$
$810$	−22.7985	+	17.0361i	−0.801059	+	0.598586i
$811$		−	33.7590i		−	1.18544i	−0.805409	−	0.592720i	$-0.798054\pi$
$811$		−	33.7590i		−	1.18544i	0.805409	−	0.592720i	$-0.201946\pi$
$812$	−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
$820$	−5.01499	−	3.93058i	−0.175131	−	0.137262i
$821$		−	14.1658i		−	0.494390i	−0.968966	−	0.247195i	$-0.920491\pi$
$821$		−	14.1658i		−	0.494390i	0.968966	−	0.247195i	$-0.0795088\pi$
$822$	4.66182	−	4.79485i	0.162600	−	0.167240i
$823$	24.2282			0.844543			0.422272	−	0.906469i	$-0.361233\pi$
$823$	24.2282			0.844543			0.422272	+	0.906469i	$0.361233\pi$
$824$	−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	$0.0903035\pi$
$827$			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	$0.477961\pi$
$830$	−25.0447	−	2.52696i	−0.869314	−	0.0877122i
$831$	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	$0.237095\pi$
$840$	−1.47113	−	10.8552i	−0.0507586	−	0.374541i
$841$	−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
$850$	−36.3058	+	13.7938i	−1.24528	+	0.473124i
$851$	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
$855$	−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	$0.540066\pi$
$858$	−8.02600	−	7.80331i	−0.274003	−	0.266401i
$859$		−	27.1909i		−	0.927742i	−0.885903	−	0.463871i	$-0.846460\pi$
$859$		−	27.1909i		−	0.927742i	0.885903	−	0.463871i	$-0.153540\pi$
$860$	22.6352	−	28.8800i	0.771852	−	0.984800i
$861$	−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
$870$	10.6412	−	33.4865i	0.360770	−	1.13530i
$871$		−	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
$880$	6.21488	+	1.40529i	0.209503	+	0.0473724i
$881$			13.8312i			0.465984i	0.972479	+	0.232992i	$0.0748516\pi$
$881$			13.8312i			0.465984i	−0.972479	+	0.232992i	$0.925148\pi$
$882$	−2.36868	−	3.51985i	−0.0797576	−	0.118520i
$883$	35.2542			1.18640			0.593199	−	0.805056i	$-0.297865\pi$
$883$	35.2542			1.18640			0.593199	+	0.805056i	$0.297865\pi$
$884$	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	$0.0668115\pi$
$887$			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
$890$	−19.6796	−	1.98564i	−0.659662	−	0.0665587i
$891$	−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
$900$	24.4968	+	17.3178i	0.816561	+	0.577259i
$901$	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	$-0.441057\pi$
$907$	11.0900			0.368238			0.184119	+	0.982904i	$0.441057\pi$
$908$	−6.12742	+	2.90255i	−0.203346	+	0.0963244i
$909$	−5.66880	+	12.8925i	−0.188022	+	0.427619i
$910$	20.1836	+	2.03649i	0.669081	+	0.0675090i
$911$	−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
$915$	4.75708	−	1.24778i	0.157264	−	0.0412505i
$916$	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	$-0.917931\pi$
$919$		−	15.4595i		−	0.509961i	0.966946	−	0.254981i	$-0.0820691\pi$
$920$	12.3071	+	34.5904i	0.405753	+	1.14041i
$921$	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	$-0.823538\pi$
$929$		−	32.0894i		−	1.05282i	0.850231	−	0.526409i	$-0.176462\pi$
$930$	0.406158	−	1.27813i	0.0133184	−	0.0419115i
$931$		−	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
$940$	11.9325	+	9.35229i	0.389196	+	0.305038i
$941$		−	13.8061i		−	0.450066i	−0.974351	−	0.225033i	$-0.927751\pi$
$941$		−	13.8061i		−	0.450066i	0.974351	−	0.225033i	$-0.0722489\pi$
$942$	−2.02048	−	1.96442i	−0.0658308	−	0.0640043i
$943$	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	$0.221573\pi$
$947$			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
$950$	2.44868	+	6.44500i	0.0794456	+	0.209103i
$951$	−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	$0.466138\pi$
$954$	−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
$960$	30.9813	−	0.399118i	0.999917	−	0.0128815i
$961$	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	$-0.335021\pi$
$967$	30.8106			0.990802			0.495401	+	0.868665i	$0.335021\pi$
$968$	3.60635	−	29.4574i	0.115912	−	0.946795i
$969$	9.07747	+	1.90754i	0.291610	+	0.0612789i
$970$	56.9312	+	5.74425i	1.82795	+	0.184437i
$971$	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
$975$	−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	$0.544444\pi$
$978$	26.4233	−	27.1774i	0.844925	−	0.869036i
$979$		−	4.45586i		−	0.142410i
$980$	−2.75874	+	3.51985i	−0.0881247	+	0.112438i
$981$	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
$990$	−3.32757	+	5.88232i	−0.105757	+	0.186952i
$991$			34.6707i			1.10135i	0.834719	+	0.550676i	$0.185630\pi$
$991$			34.6707i			1.10135i	−0.834719	+	0.550676i	$0.814370\pi$
$992$	−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.f.239.8	yes	8
3.2	odd	2		420.2.l.e.239.1	yes	8
4.3	odd	2		420.2.l.d.239.7	yes	8
5.4	even	2		420.2.l.c.239.1	✓	8
12.11	even	2		420.2.l.c.239.2	yes	8
15.14	odd	2		420.2.l.d.239.8	yes	8
20.19	odd	2		420.2.l.e.239.2	yes	8
60.59	even	2	inner	420.2.l.f.239.7	yes	8

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

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} +(-0.317456 + 3.14630i) q^{10} -0.712386 q^{11} +(-3.36868 + 0.807466i) 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} +(-2.36868 - 3.51985i) q^{18} -0.975028i q^{19} +(-2.75874 + 3.51985i) 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} +(-5.22000 - 1.65879i) 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} +(-5.95864 + 2.12005i) q^{40} +1.42477i q^{41} +(-1.70752 + 1.75624i) 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} +(-4.34371 - 5.39743i) q^{48} +1.00000 q^{49} +(-6.61006 + 2.51139i) 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} +(-4.98361 - 5.92989i) 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} +(-0.317456 + 3.14630i) q^{70} -8.00000 q^{71} +(4.33397 - 7.29498i) 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} +(11.2664 + 10.9538i) q^{78} -15.0002i q^{79} +(-8.72403 - 1.97265i) 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} +(4.67103 - 8.25721i) 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	\( 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) \) 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 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * 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 + 10 * 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 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * 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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