LMFDB - Embedded newform 420.2.n.b.71.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(71,420)]

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, 0, 0]))

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

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

chi := DirichletCharacter("420.71");

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.n (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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0797590 + 1.41196i) q^{2} +(-1.52443 + 0.822258i) q^{3} +(-1.98728 - 0.225233i) q^{4} -1.00000i q^{5} +(-1.03941 - 2.21802i) q^{6} -1.00000i q^{7} +(0.476524 - 2.78800i) q^{8} +(1.64778 - 2.50695i) q^{9} +O(q^{10})$	\(q+(-0.0797590 + 1.41196i) q^{2} +(-1.52443 + 0.822258i) q^{3} +(-1.98728 - 0.225233i) q^{4} -1.00000i q^{5} +(-1.03941 - 2.21802i) q^{6} -1.00000i q^{7} +(0.476524 - 2.78800i) q^{8} +(1.64778 - 2.50695i) q^{9} +(1.41196 + 0.0797590i) q^{10} -2.48966 q^{11} +(3.21467 - 1.29070i) q^{12} +5.62558 q^{13} +(1.41196 + 0.0797590i) q^{14} +(0.822258 + 1.52443i) q^{15} +(3.89854 + 0.895203i) q^{16} +0.700377i q^{17} +(3.40830 + 2.52656i) q^{18} -4.84194i q^{19} +(-0.225233 + 1.98728i) q^{20} +(0.822258 + 1.52443i) q^{21} +(0.198573 - 3.51530i) q^{22} +3.16686 q^{23} +(1.56602 + 4.64194i) q^{24} -1.00000 q^{25} +(-0.448691 + 7.94311i) q^{26} +(-0.450572 + 5.17658i) q^{27} +(-0.225233 + 1.98728i) q^{28} -5.02241i q^{29} +(-2.21802 + 1.03941i) q^{30} +4.00937i q^{31} +(-1.57494 + 5.43319i) q^{32} +(3.79531 - 2.04714i) q^{33} +(-0.988906 - 0.0558614i) q^{34} -1.00000 q^{35} +(-3.83925 + 4.61087i) q^{36} +3.83971 q^{37} +(6.83664 + 0.386188i) q^{38} +(-8.57582 + 4.62568i) q^{39} +(-2.78800 - 0.476524i) q^{40} +0.589774i q^{41} +(-2.21802 + 1.03941i) q^{42} -10.9284i q^{43} +(4.94764 + 0.560754i) q^{44} +(-2.50695 - 1.64778i) q^{45} +(-0.252586 + 4.47149i) q^{46} +13.3036 q^{47} +(-6.67914 + 1.84093i) q^{48} -1.00000 q^{49} +(0.0797590 - 1.41196i) q^{50} +(-0.575891 - 1.06768i) q^{51} +(-11.1796 - 1.26707i) q^{52} -8.21289i q^{53} +(-7.27320 - 1.04907i) q^{54} +2.48966i q^{55} +(-2.78800 - 0.476524i) q^{56} +(3.98132 + 7.38121i) q^{57} +(7.09146 + 0.400583i) q^{58} +8.14703 q^{59} +(-1.29070 - 3.21467i) q^{60} -15.3108 q^{61} +(-5.66108 - 0.319783i) q^{62} +(-2.50695 - 1.64778i) q^{63} +(-7.54585 - 2.65710i) q^{64} -5.62558i q^{65} +(2.58778 + 5.52212i) q^{66} -2.48284i q^{67} +(0.157748 - 1.39184i) q^{68} +(-4.82766 + 2.60398i) q^{69} +(0.0797590 - 1.41196i) q^{70} +1.15305 q^{71} +(-6.20417 - 5.78864i) q^{72} +6.50644 q^{73} +(-0.306251 + 5.42152i) q^{74} +(1.52443 - 0.822258i) q^{75} +(-1.09057 + 9.62228i) q^{76} +2.48966i q^{77} +(-5.84729 - 12.4777i) q^{78} -16.5324i q^{79} +(0.895203 - 3.89854i) q^{80} +(-3.56962 - 8.26183i) q^{81} +(-0.832739 - 0.0470398i) q^{82} -3.32162 q^{83} +(-1.29070 - 3.21467i) q^{84} +0.700377 q^{85} +(15.4305 + 0.871636i) q^{86} +(4.12972 + 7.65633i) q^{87} +(-1.18638 + 6.94115i) q^{88} +1.26927i q^{89} +(2.52656 - 3.40830i) q^{90} -5.62558i q^{91} +(-6.29343 - 0.713283i) q^{92} +(-3.29674 - 6.11201i) q^{93} +(-1.06108 + 18.7842i) q^{94} -4.84194 q^{95} +(-2.06660 - 9.57753i) q^{96} +8.03979 q^{97} +(0.0797590 - 1.41196i) q^{98} +(-4.10241 + 6.24145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * 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 $

$2$	−0.0797590	+	1.41196i	−0.0563981	+	0.998408i
$2$	−0.0797590	+	1.41196i	−0.0563981	+	0.998408i
$3$	−1.52443	+	0.822258i	−0.880131	+	0.474731i
$3$	−1.52443	+	0.822258i	−0.880131	+	0.474731i
$4$	−1.98728	−	0.225233i	−0.993639	−	0.112617i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.03941	−	2.21802i	−0.424338	−	0.905504i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.476524	−	2.78800i	0.168477	−	0.985706i
$9$	1.64778	−	2.50695i	0.549261	−	0.835651i
$10$	1.41196	+	0.0797590i	0.446502	+	0.0252220i
$11$	−2.48966			−0.750660			−0.375330	−	0.926891i	$-0.622471\pi$
$11$	−2.48966			−0.750660			−0.375330	+	0.926891i	$0.622471\pi$
$12$	3.21467	−	1.29070i	0.927995	−	0.372593i
$13$	5.62558			1.56026			0.780128	−	0.625620i	$-0.215154\pi$
$13$	5.62558			1.56026			0.780128	+	0.625620i	$0.215154\pi$
$14$	1.41196	+	0.0797590i	0.377363	+	0.0213165i
$15$	0.822258	+	1.52443i	0.212306	+	0.393607i
$16$	3.89854	+	0.895203i	0.974635	+	0.223801i
$17$			0.700377i			0.169866i	0.996387	+	0.0849332i	$0.0270677\pi$
$17$			0.700377i			0.169866i	−0.996387	+	0.0849332i	$0.972932\pi$
$18$	3.40830	+	2.52656i	0.803343	+	0.595516i
$19$		−	4.84194i		−	1.11082i	−0.831578	−	0.555409i	$-0.812562\pi$
$19$		−	4.84194i		−	1.11082i	0.831578	−	0.555409i	$-0.187438\pi$
$20$	−0.225233	+	1.98728i	−0.0503637	+	0.444369i
$21$	0.822258	+	1.52443i	0.179431	+	0.332658i
$22$	0.198573	−	3.51530i	0.0423358	−	0.749465i
$23$	3.16686			0.660336			0.330168	−	0.943922i	$-0.392895\pi$
$23$	3.16686			0.660336			0.330168	+	0.943922i	$0.392895\pi$
$24$	1.56602	+	4.64194i	0.319663	+	0.947531i
$25$	−1.00000			−0.200000
$26$	−0.448691	+	7.94311i	−0.0879955	+	1.55777i
$27$	−0.450572	+	5.17658i	−0.0867125	+	0.996233i
$28$	−0.225233	+	1.98728i	−0.0425651	+	0.375560i
$29$		−	5.02241i		−	0.932639i	−0.884616	−	0.466320i	$-0.845580\pi$
$29$		−	5.02241i		−	0.932639i	0.884616	−	0.466320i	$-0.154420\pi$
$30$	−2.21802	+	1.03941i	−0.404954	+	0.189770i
$31$			4.00937i			0.720104i	0.932932	+	0.360052i	$0.117241\pi$
$31$			4.00937i			0.720104i	−0.932932	+	0.360052i	$0.882759\pi$
$32$	−1.57494	+	5.43319i	−0.278412	+	0.960462i
$33$	3.79531	−	2.04714i	0.660679	−	0.356361i
$34$	−0.988906	−	0.0558614i	−0.169596	−	0.00958014i
$35$	−1.00000			−0.169031
$36$	−3.83925	+	4.61087i	−0.639875	+	0.768479i
$37$	3.83971			0.631244			0.315622	−	0.948885i	$-0.397787\pi$
$37$	3.83971			0.631244			0.315622	+	0.948885i	$0.397787\pi$
$38$	6.83664	+	0.386188i	1.10905	+	0.0626480i
$39$	−8.57582	+	4.62568i	−1.37323	+	0.740702i
$40$	−2.78800	−	0.476524i	−0.440821	−	0.0753451i
$41$			0.589774i			0.0921072i	0.998939	+	0.0460536i	$0.0146645\pi$
$41$			0.589774i			0.0921072i	−0.998939	+	0.0460536i	$0.985335\pi$
$42$	−2.21802	+	1.03941i	−0.342248	+	0.160385i
$43$		−	10.9284i		−	1.66656i	−0.552850	−	0.833281i	$-0.686460\pi$
$43$		−	10.9284i		−	1.66656i	0.552850	−	0.833281i	$-0.313540\pi$
$44$	4.94764	+	0.560754i	0.745884	+	0.0845368i
$45$	−2.50695	−	1.64778i	−0.373714	−	0.245637i
$46$	−0.252586	+	4.47149i	−0.0372417	+	0.659285i
$47$	13.3036			1.94053			0.970264	−	0.242050i	$-0.0778199\pi$
$47$	13.3036			1.94053			0.970264	+	0.242050i	$0.0778199\pi$
$48$	−6.67914	+	1.84093i	−0.964052	+	0.265715i
$49$	−1.00000			−0.142857
$50$	0.0797590	−	1.41196i	0.0112796	−	0.199682i
$51$	−0.575891	−	1.06768i	−0.0806408	−	0.149505i
$52$	−11.1796	−	1.26707i	−1.55033	−	0.175711i
$53$		−	8.21289i		−	1.12813i	−0.825731	−	0.564064i	$-0.809237\pi$
$53$		−	8.21289i		−	1.12813i	0.825731	−	0.564064i	$-0.190763\pi$
$54$	−7.27320	−	1.04907i	−0.989757	−	0.142760i
$55$			2.48966i			0.335705i
$56$	−2.78800	−	0.476524i	−0.372562	−	0.0636783i
$57$	3.98132	+	7.38121i	0.527339	+	0.977665i
$58$	7.09146	+	0.400583i	0.931155	+	0.0525991i
$59$	8.14703			1.06065			0.530327	−	0.847793i	$-0.322069\pi$
$59$	8.14703			1.06065			0.530327	+	0.847793i	$0.322069\pi$
$60$	−1.29070	−	3.21467i	−0.166629	−	0.415012i
$61$	−15.3108			−1.96034			−0.980171	−	0.198153i	$-0.936506\pi$
$61$	−15.3108			−1.96034			−0.980171	+	0.198153i	$0.936506\pi$
$62$	−5.66108	−	0.319783i	−0.718958	−	0.0406125i
$63$	−2.50695	−	1.64778i	−0.315846	−	0.207601i
$64$	−7.54585	−	2.65710i	−0.943231	−	0.332137i
$65$		−	5.62558i		−	0.697768i
$66$	2.58778	+	5.52212i	0.318533	+	0.679725i
$67$		−	2.48284i		−	0.303328i	−0.988432	−	0.151664i	$-0.951537\pi$
$67$		−	2.48284i		−	0.303328i	0.988432	−	0.151664i	$-0.0484631\pi$
$68$	0.157748	−	1.39184i	0.0191298	−	0.168786i
$69$	−4.82766	+	2.60398i	−0.581183	+	0.313482i
$70$	0.0797590	−	1.41196i	0.00953302	−	0.168762i
$71$	1.15305			0.136842			0.0684211	−	0.997657i	$-0.478204\pi$
$71$	1.15305			0.136842			0.0684211	+	0.997657i	$0.478204\pi$
$72$	−6.20417	−	5.78864i	−0.731168	−	0.682198i
$73$	6.50644			0.761521			0.380760	−	0.924674i	$-0.375662\pi$
$73$	6.50644			0.761521			0.380760	+	0.924674i	$0.375662\pi$
$74$	−0.306251	+	5.42152i	−0.0356010	+	0.630239i
$75$	1.52443	−	0.822258i	0.176026	−	0.0949462i
$76$	−1.09057	+	9.62228i	−0.125097	+	1.10375i
$77$			2.48966i			0.283723i
$78$	−5.84729	−	12.4777i	−0.662075	−	1.41282i
$79$		−	16.5324i		−	1.86004i	−0.367514	−	0.930018i	$-0.619791\pi$
$79$		−	16.5324i		−	1.86004i	0.367514	−	0.930018i	$-0.380209\pi$
$80$	0.895203	−	3.89854i	0.100087	−	0.435870i
$81$	−3.56962	−	8.26183i	−0.396624	−	0.917981i
$82$	−0.832739	−	0.0470398i	−0.0919606	−	0.00519468i
$83$	−3.32162			−0.364595			−0.182297	−	0.983243i	$-0.558353\pi$
$83$	−3.32162			−0.364595			−0.182297	+	0.983243i	$0.558353\pi$
$84$	−1.29070	−	3.21467i	−0.140827	−	0.350749i
$85$	0.700377			0.0759665
$86$	15.4305	+	0.871636i	1.66391	+	0.0939909i
$87$	4.12972	+	7.65633i	0.442753	+	0.820845i
$88$	−1.18638	+	6.94115i	−0.126469	+	0.739929i
$89$			1.26927i			0.134543i	0.997735	+	0.0672714i	$0.0214293\pi$
$89$			1.26927i			0.134543i	−0.997735	+	0.0672714i	$0.978571\pi$
$90$	2.52656	−	3.40830i	0.266323	−	0.359266i
$91$		−	5.62558i		−	0.589721i
$92$	−6.29343	−	0.713283i	−0.656136	−	0.0743649i
$93$	−3.29674	−	6.11201i	−0.341855	−	0.633786i
$94$	−1.06108	+	18.7842i	−0.109442	+	1.93744i
$95$	−4.84194			−0.496773
$96$	−2.06660	−	9.57753i	−0.210922	−	0.977503i
$97$	8.03979			0.816317			0.408159	−	0.912911i	$-0.366171\pi$
$97$	8.03979			0.816317			0.408159	+	0.912911i	$0.366171\pi$
$98$	0.0797590	−	1.41196i	0.00805688	−	0.142630i
$99$	−4.10241	+	6.24145i	−0.412308	+	0.627289i
$100$	1.98728	+	0.225233i	0.198728	+	0.0225233i
$101$			1.92108i			0.191155i	0.995422	+	0.0955773i	$0.0304697\pi$
$101$			1.92108i			0.191155i	−0.995422	+	0.0955773i	$0.969530\pi$
$102$	1.55345	−	0.727979i	0.153815	−	0.0720807i
$103$			14.0901i			1.38834i	0.719810	+	0.694171i	$0.244229\pi$
$103$			14.0901i			1.38834i	−0.719810	+	0.694171i	$0.755771\pi$
$104$	2.68073	−	15.6841i	0.262867	−	1.53795i
$105$	1.52443	−	0.822258i	0.148769	−	0.0802442i
$106$	11.5963	+	0.655052i	1.12633	+	0.0636243i
$107$	−13.0959			−1.26603			−0.633017	−	0.774138i	$-0.718183\pi$
$107$	−13.0959			−1.26603			−0.633017	+	0.774138i	$0.718183\pi$
$108$	2.06135	−	10.1858i	0.198353	−	0.980131i
$109$	−10.1922			−0.976234			−0.488117	−	0.872778i	$-0.662316\pi$
$109$	−10.1922			−0.976234			−0.488117	+	0.872778i	$0.662316\pi$
$110$	−3.51530	−	0.198573i	−0.335171	−	0.0189331i
$111$	−5.85337	+	3.15723i	−0.555577	+	0.299671i
$112$	0.895203	−	3.89854i	0.0845887	−	0.368377i
$113$		−	5.15324i		−	0.484776i	−0.970179	−	0.242388i	$-0.922069\pi$
$113$		−	5.15324i		−	0.484776i	0.970179	−	0.242388i	$-0.0779308\pi$
$114$	−10.7395	+	5.03276i	−1.00585	+	0.471361i
$115$		−	3.16686i		−	0.295311i
$116$	−1.13122	+	9.98093i	−0.105031	+	0.926706i
$117$	9.26974	−	14.1031i	0.856988	−	1.30383i
$118$	−0.649799	+	11.5033i	−0.0598189	+	1.05896i
$119$	0.700377			0.0642034
$120$	4.64194	−	1.56602i	0.423749	−	0.142958i
$121$	−4.80161			−0.436510
$122$	1.22117	−	21.6182i	0.110560	−	1.95722i
$123$	−0.484946	−	0.899070i	−0.0437261	−	0.0810664i
$124$	0.903044	−	7.96772i	0.0810957	−	0.715523i
$125$			1.00000i			0.0894427i
$126$	2.52656	−	3.40830i	0.225084	−	0.303635i
$127$			6.60247i			0.585875i	0.956132	+	0.292937i	$0.0946327\pi$
$127$			6.60247i			0.585875i	−0.956132	+	0.292937i	$0.905367\pi$
$128$	4.35357	−	10.4425i	0.384805	−	0.922998i
$129$	8.98594	+	16.6596i	0.791168	+	1.46679i
$130$	7.94311	+	0.448691i	0.696657	+	0.0393528i
$131$	18.5612			1.62170			0.810851	−	0.585253i	$-0.199005\pi$
$131$	18.5612			1.62170			0.810851	+	0.585253i	$0.199005\pi$
$132$	−8.00342	+	3.21340i	−0.696608	+	0.279691i
$133$	−4.84194			−0.419849
$134$	3.50568	+	0.198029i	0.302845	+	0.0171071i
$135$	5.17658	+	0.450572i	0.445529	+	0.0387790i
$136$	1.95265	+	0.333747i	0.167438	+	0.0286185i
$137$			12.5912i			1.07574i	0.843027	+	0.537871i	$0.180771\pi$
$137$			12.5912i			1.07574i	−0.843027	+	0.537871i	$0.819229\pi$
$138$	−3.29167	−	7.02417i	−0.280206	−	0.597937i
$139$			4.14637i			0.351691i	0.984418	+	0.175845i	$0.0562659\pi$
$139$			4.14637i			0.351691i	−0.984418	+	0.175845i	$0.943734\pi$
$140$	1.98728	+	0.225233i	0.167956	+	0.0190357i
$141$	−20.2804	+	10.9390i	−1.70792	+	0.921228i
$142$	−0.0919663	+	1.62807i	−0.00771764	+	0.136624i
$143$	−14.0058			−1.17122
$144$	8.66818	−	8.29835i	0.722348	−	0.691529i
$145$	−5.02241			−0.417089
$146$	−0.518947	+	9.18685i	−0.0429484	+	0.760309i
$147$	1.52443	−	0.822258i	0.125733	−	0.0678187i
$148$	−7.63056	−	0.864830i	−0.627228	−	0.0710886i
$149$			11.7266i			0.960681i	0.877082	+	0.480340i	$0.159487\pi$
$149$			11.7266i			0.960681i	−0.877082	+	0.480340i	$0.840513\pi$
$150$	1.03941	+	2.21802i	0.0848675	+	0.181101i
$151$		−	1.55545i		−	0.126581i	−0.997995	−	0.0632905i	$-0.979841\pi$
$151$		−	1.55545i		−	0.126581i	0.997995	−	0.0632905i	$-0.0201595\pi$
$152$	−13.4993	−	2.30730i	−1.09494	−	0.187147i
$153$	1.75581	+	1.15407i	0.141949	+	0.0933010i
$154$	−3.51530	−	0.198573i	−0.283271	−	0.0160014i
$155$	4.00937			0.322040
$156$	18.0844	−	7.26095i	1.44791	−	0.581341i
$157$	−4.71613			−0.376388			−0.188194	−	0.982132i	$-0.560263\pi$
$157$	−4.71613			−0.376388			−0.188194	+	0.982132i	$0.560263\pi$
$158$	23.3431	+	1.31860i	1.85708	+	0.104903i
$159$	6.75312	+	12.5200i	0.535557	+	0.992900i
$160$	5.43319	+	1.57494i	0.429532	+	0.124510i
$161$		−	3.16686i		−	0.249584i
$162$	11.9501	−	4.38121i	0.938889	−	0.344221i
$163$			1.95261i			0.152940i	0.997072	+	0.0764702i	$0.0243650\pi$
$163$			1.95261i			0.152940i	−0.997072	+	0.0764702i	$0.975635\pi$
$164$	0.132837	−	1.17204i	0.0103728	−	0.0915213i
$165$	−2.04714	−	3.79531i	−0.159370	−	0.295465i
$166$	0.264929	−	4.69000i	0.0205625	−	0.364014i
$167$	−12.4091			−0.960243			−0.480122	−	0.877202i	$-0.659408\pi$
$167$	−12.4091			−0.960243			−0.480122	+	0.877202i	$0.659408\pi$
$168$	4.64194	−	1.56602i	0.358133	−	0.120821i
$169$	18.6472			1.43440
$170$	−0.0558614	+	0.988906i	−0.00428437	+	0.0758456i
$171$	−12.1385	−	7.97847i	−0.928255	−	0.610129i
$172$	−2.46144	+	21.7177i	−0.187683	+	1.65596i
$173$			6.14122i			0.466908i	0.972368	+	0.233454i	$0.0750029\pi$
$173$			6.14122i			0.466908i	−0.972368	+	0.233454i	$0.924997\pi$
$174$	−11.1398	+	5.22035i	−0.844508	+	0.395754i
$175$			1.00000i			0.0755929i
$176$	−9.70603	−	2.22875i	−0.731619	−	0.167998i
$177$	−12.4196	+	6.69896i	−0.933514	+	0.503525i
$178$	−1.79217	−	0.101236i	−0.134329	−	0.00758796i
$179$	−16.2094			−1.21155			−0.605775	−	0.795636i	$-0.707137\pi$
$179$	−16.2094			−1.21155			−0.605775	+	0.795636i	$0.707137\pi$
$180$	4.61087	+	3.83925i	0.343674	+	0.286161i
$181$	−14.6267			−1.08719			−0.543597	−	0.839346i	$-0.682938\pi$
$181$	−14.6267			−1.08719			−0.543597	+	0.839346i	$0.682938\pi$
$182$	7.94311	+	0.448691i	0.588783	+	0.0332592i
$183$	23.3402	−	12.5894i	1.72536	−	0.930635i
$184$	1.50909	−	8.82920i	0.111251	−	0.650897i
$185$		−	3.83971i		−	0.282301i
$186$	8.89287	−	4.16738i	0.652057	−	0.305567i
$187$		−	1.74370i		−	0.127512i
$188$	−26.4379	−	2.99641i	−1.92818	−	0.218536i
$189$	5.17658	+	0.450572i	0.376541	+	0.0327743i
$190$	0.386188	−	6.83664i	0.0280170	−	0.495982i
$191$	7.82825			0.566432			0.283216	−	0.959056i	$-0.408599\pi$
$191$	7.82825			0.566432			0.283216	+	0.959056i	$0.408599\pi$
$192$	13.6879	−	2.15407i	0.987843	−	0.155457i
$193$	3.94011			0.283615			0.141808	−	0.989894i	$-0.454709\pi$
$193$	3.94011			0.283615			0.141808	+	0.989894i	$0.454709\pi$
$194$	−0.641246	+	11.3519i	−0.0460388	+	0.815018i
$195$	4.62568	+	8.57582i	0.331252	+	0.614127i
$196$	1.98728	+	0.225233i	0.141948	+	0.0160881i
$197$			13.2325i			0.942779i	0.881925	+	0.471389i	$0.156247\pi$
$197$			13.2325i			0.942779i	−0.881925	+	0.471389i	$0.843753\pi$
$198$	−8.48549	−	6.29027i	−0.603038	−	0.447030i
$199$		−	13.5986i		−	0.963981i	−0.876177	−	0.481990i	$-0.839914\pi$
$199$		−	13.5986i		−	0.963981i	0.876177	−	0.481990i	$-0.160086\pi$
$200$	−0.476524	+	2.78800i	−0.0336954	+	0.197141i
$201$	2.04154	+	3.78493i	0.143999	+	0.266968i
$202$	−2.71249	−	0.153223i	−0.190850	−	0.0107808i
$203$	−5.02241			−0.352504
$204$	0.903977	+	2.25148i	0.0632911	+	0.157635i
$205$	0.589774			0.0411916
$206$	−19.8948	−	1.12382i	−1.38613	−	0.0782999i
$207$	5.21830	−	7.93917i	0.362697	−	0.551811i
$208$	21.9316	+	5.03604i	1.52068	+	0.349186i
$209$			12.0548i			0.833846i
$210$	1.03941	+	2.21802i	0.0717261	+	0.153058i
$211$			9.10785i			0.627010i	0.949587	+	0.313505i	$0.101503\pi$
$211$			9.10785i			0.627010i	−0.949587	+	0.313505i	$0.898497\pi$
$212$	−1.84982	+	16.3213i	−0.127046	+	1.12095i
$213$	−1.75775	+	0.948107i	−0.120439	+	0.0649632i
$214$	1.04452	−	18.4910i	0.0714019	−	1.26402i
$215$	−10.9284			−0.745309
$216$	14.2176	+	3.72296i	0.967384	+	0.253315i
$217$	4.00937			0.272174
$218$	0.812918	−	14.3910i	0.0550578	−	0.974680i
$219$	−9.91862	+	5.34997i	−0.670238	+	0.361517i
$220$	0.560754	−	4.94764i	0.0378060	−	0.333570i
$221$			3.94003i			0.265035i
$222$	−3.99103	−	8.51656i	−0.267860	−	0.571594i
$223$			14.8716i			0.995876i	0.867213	+	0.497938i	$0.165909\pi$
$223$			14.8716i			0.995876i	−0.867213	+	0.497938i	$0.834091\pi$
$224$	5.43319	+	1.57494i	0.363020	+	0.105230i
$225$	−1.64778	+	2.50695i	−0.109852	+	0.167130i
$226$	7.27619	+	0.411018i	0.484005	+	0.0273405i
$227$	−8.82098			−0.585469			−0.292734	−	0.956194i	$-0.594565\pi$
$227$	−8.82098			−0.585469			−0.292734	+	0.956194i	$0.594565\pi$
$228$	−6.24950	−	15.5652i	−0.413883	−	1.03083i
$229$	19.2604			1.27276			0.636382	−	0.771374i	$-0.280430\pi$
$229$	19.2604			1.27276			0.636382	+	0.771374i	$0.280430\pi$
$230$	4.47149	+	0.252586i	0.294841	+	0.0166550i
$231$	−2.04714	−	3.79531i	−0.134692	−	0.249713i
$232$	−14.0025	−	2.39330i	−0.919308	−	0.157128i
$233$			24.2301i			1.58736i	0.608333	+	0.793682i	$0.291839\pi$
$233$			24.2301i			1.58736i	−0.608333	+	0.793682i	$0.708161\pi$
$234$	19.1737	+	14.2134i	1.25342	+	0.929158i
$235$		−	13.3036i		−	0.867830i
$236$	−16.1904	−	1.83498i	−1.05391	−	0.119447i
$237$	13.5939	+	25.2025i	0.883017	+	1.63708i
$238$	−0.0558614	+	0.988906i	−0.00362095	+	0.0641013i
$239$	24.9846			1.61612			0.808059	−	0.589102i	$-0.200518\pi$
$239$	24.9846			1.61612			0.808059	+	0.589102i	$0.200518\pi$
$240$	1.84093	+	6.67914i	0.118832	+	0.431137i
$241$	−4.59672			−0.296101			−0.148050	−	0.988980i	$-0.547300\pi$
$241$	−4.59672			−0.296101			−0.148050	+	0.988980i	$0.547300\pi$
$242$	0.382972	−	6.77969i	0.0246183	−	0.435815i
$243$	12.2350	+	9.65944i	0.784875	+	0.619654i
$244$	30.4267	+	3.44850i	1.94787	+	0.220767i
$245$			1.00000i			0.0638877i
$246$	1.30813	−	0.613017i	0.0834035	−	0.0390846i
$247$		−	27.2387i		−	1.73316i
$248$	11.1781	+	1.91056i	0.709810	+	0.121321i
$249$	5.06358	−	2.73123i	0.320891	−	0.173084i
$250$	−1.41196	−	0.0797590i	−0.0893004	−	0.00504440i
$251$	22.8144			1.44003			0.720017	−	0.693957i	$-0.244134\pi$
$251$	22.8144			1.44003			0.720017	+	0.693957i	$0.244134\pi$
$252$	4.61087	+	3.83925i	0.290458	+	0.241850i
$253$	−7.88440			−0.495688
$254$	−9.32244	−	0.526607i	−0.584942	−	0.0330422i
$255$	−1.06768	+	0.575891i	−0.0668605	+	0.0360637i
$256$	14.3972	+	6.97997i	0.899827	+	0.436248i
$257$			17.1031i			1.06686i	0.845843	+	0.533431i	$0.179098\pi$
$257$			17.1031i			1.06686i	−0.845843	+	0.533431i	$0.820902\pi$
$258$	−24.2394	+	11.3591i	−1.50908	+	0.707184i
$259$		−	3.83971i		−	0.238588i
$260$	−1.26707	+	11.1796i	−0.0785803	+	0.693329i
$261$	−12.5910	−	8.27585i	−0.779360	−	0.512262i
$262$	−1.48042	+	26.2078i	−0.0914610	+	1.61912i
$263$	−10.8795			−0.670859			−0.335429	−	0.942065i	$-0.608881\pi$
$263$	−10.8795			−0.670859			−0.335429	+	0.942065i	$0.608881\pi$
$264$	−3.89886	−	11.5568i	−0.239958	−	0.711273i
$265$	−8.21289			−0.504514
$266$	0.386188	−	6.83664i	0.0236787	−	0.419181i
$267$	−1.04367	−	1.93492i	−0.0638716	−	0.118415i
$268$	−0.559219	+	4.93410i	−0.0341598	+	0.301398i
$269$		−	10.8641i		−	0.662397i	−0.943561	−	0.331199i	$-0.892547\pi$
$269$		−	10.8641i		−	0.662397i	0.943561	−	0.331199i	$-0.107453\pi$
$270$	−1.04907	+	7.27320i	−0.0638443	+	0.442633i
$271$		−	2.13227i		−	0.129526i	−0.997901	−	0.0647630i	$-0.979371\pi$
$271$		−	2.13227i		−	0.129526i	0.997901	−	0.0647630i	$-0.0206291\pi$
$272$	−0.626979	+	2.73045i	−0.0380162	+	0.165558i
$273$	4.62568	+	8.57582i	0.279959	+	0.519032i
$274$	−17.7784	−	1.00426i	−1.07403	−	0.0606698i
$275$	2.48966			0.150132
$276$	10.1804	−	4.08747i	0.612789	−	0.246037i
$277$	19.4532			1.16883			0.584414	−	0.811456i	$-0.301325\pi$
$277$	19.4532			1.16883			0.584414	+	0.811456i	$0.301325\pi$
$278$	−5.85453	−	0.330711i	−0.351131	−	0.0198347i
$279$	10.0513	+	6.60657i	0.601755	+	0.395525i
$280$	−0.476524	+	2.78800i	−0.0284778	+	0.166615i
$281$		−	24.7357i		−	1.47561i	−0.675015	−	0.737804i	$-0.735863\pi$
$281$		−	24.7357i		−	1.47561i	0.675015	−	0.737804i	$-0.264137\pi$
$282$	−13.8279	−	29.5077i	−0.823439	−	1.75716i
$283$		−	11.3820i		−	0.676591i	−0.941040	−	0.338296i	$-0.890150\pi$
$283$		−	11.3820i		−	0.676591i	0.941040	−	0.338296i	$-0.109850\pi$
$284$	−2.29144	−	0.259706i	−0.135972	−	0.0154107i
$285$	7.38121	−	3.98132i	0.437225	−	0.235833i
$286$	1.11709	−	19.7756i	0.0660547	−	1.16936i
$287$	0.589774			0.0348133
$288$	11.0256	+	12.9010i	0.649690	+	0.760200i
$289$	16.5095			0.971145
$290$	0.400583	−	7.09146i	0.0235230	−	0.416425i
$291$	−12.2561	+	6.61078i	−0.718466	+	0.387531i
$292$	−12.9301	−	1.46547i	−0.756676	−	0.0857600i
$293$		−	26.4963i		−	1.54793i	−0.633228	−	0.773966i	$-0.718270\pi$
$293$		−	26.4963i		−	1.54793i	0.633228	−	0.773966i	$-0.281730\pi$
$294$	1.03941	+	2.21802i	0.0606197	+	0.129358i
$295$		−	8.14703i		−	0.474338i
$296$	1.82971	−	10.7051i	0.106350	−	0.622220i
$297$	1.12177	−	12.8879i	0.0650916	−	0.747832i
$298$	−16.5575	−	0.935302i	−0.959151	−	0.0541806i
$299$	17.8154			1.03029
$300$	−3.21467	+	1.29070i	−0.185599	+	0.0745187i
$301$	−10.9284			−0.629901
$302$	2.19624	+	0.124061i	0.126380	+	0.00713894i
$303$	−1.57962	−	2.92856i	−0.0907470	−	0.168241i
$304$	4.33452	−	18.8765i	0.248602	−	1.08264i
$305$			15.3108i			0.876692i
$306$	−1.76954	+	2.38709i	−0.101158	+	0.136461i
$307$			7.59310i			0.433361i	0.976243	+	0.216680i	$0.0695230\pi$
$307$			7.59310i			0.433361i	−0.976243	+	0.216680i	$0.930477\pi$
$308$	0.560754	−	4.94764i	0.0319519	−	0.281918i
$309$	−11.5857	−	21.4795i	−0.659089	−	1.22192i
$310$	−0.319783	+	5.66108i	−0.0181625	+	0.321528i
$311$	−21.6538			−1.22787			−0.613936	−	0.789356i	$-0.710415\pi$
$311$	−21.6538			−1.22787			−0.613936	+	0.789356i	$0.710415\pi$
$312$	8.80980	+	26.1136i	0.498757	+	1.47839i
$313$	−16.7533			−0.946951			−0.473476	−	0.880807i	$-0.657001\pi$
$313$	−16.7533			−0.946951			−0.473476	+	0.880807i	$0.657001\pi$
$314$	0.376154	−	6.65900i	0.0212276	−	0.375789i
$315$	−1.64778	+	2.50695i	−0.0928421	+	0.141251i
$316$	−3.72364	+	32.8544i	−0.209471	+	1.84820i
$317$		−	17.3233i		−	0.972971i	−0.873689	−	0.486486i	$-0.838279\pi$
$317$		−	17.3233i		−	0.972971i	0.873689	−	0.486486i	$-0.161721\pi$
$318$	−18.2164	+	8.53657i	−1.02152	+	0.478707i
$319$			12.5041i			0.700095i
$320$	−2.65710	+	7.54585i	−0.148536	+	0.421826i
$321$	19.9639	−	10.7682i	1.11427	−	0.601025i
$322$	4.47149	+	0.252586i	0.249186	+	0.0140761i
$323$	3.39118			0.188690
$324$	5.23298	+	17.2225i	0.290721	+	0.956808i
$325$	−5.62558			−0.312051
$326$	−2.75702	−	0.155738i	−0.152697	−	0.00862555i
$327$	15.5373	−	8.38060i	0.859214	−	0.463448i
$328$	1.64429	+	0.281042i	0.0907906	+	0.0155179i
$329$		−	13.3036i		−	0.733450i
$330$	5.52212	−	2.58778i	0.303982	−	0.142452i
$331$			7.93550i			0.436175i	0.975929	+	0.218087i	$0.0699818\pi$
$331$			7.93550i			0.436175i	−0.975929	+	0.218087i	$0.930018\pi$
$332$	6.60097	+	0.748139i	0.362275	+	0.0410595i
$333$	6.32700	−	9.62596i	0.346718	−	0.527499i
$334$	0.989736	−	17.5212i	0.0541559	−	0.958715i
$335$	−2.48284			−0.135652
$336$	1.84093	+	6.67914i	0.100431	+	0.364377i
$337$	25.2958			1.37795			0.688976	−	0.724784i	$-0.258060\pi$
$337$	25.2958			1.37795			0.688976	+	0.724784i	$0.258060\pi$
$338$	−1.48728	+	26.3291i	−0.0808974	+	1.43212i
$339$	4.23730	+	7.85577i	0.230138	+	0.426667i
$340$	−1.39184	−	0.157748i	−0.0754833	−	0.00855510i
$341$		−	9.98195i		−	0.540553i
$342$	12.2335	−	16.5028i	0.661510	−	0.892368i
$343$			1.00000i			0.0539949i
$344$	−30.4683	−	5.20764i	−1.64274	−	0.280777i
$345$	2.60398	+	4.82766i	0.140193	+	0.259913i
$346$	−8.67117	−	0.489817i	−0.466165	−	0.0263328i
$347$	16.5514			0.888524			0.444262	−	0.895897i	$-0.353466\pi$
$347$	16.5514			0.888524			0.444262	+	0.895897i	$0.353466\pi$
$348$	−6.48244	−	16.1454i	−0.347495	−	0.865484i
$349$	−33.7073			−1.80431			−0.902154	−	0.431414i	$-0.858015\pi$
$349$	−33.7073			−1.80431			−0.902154	+	0.431414i	$0.858015\pi$
$350$	−1.41196	−	0.0797590i	−0.0754726	−	0.00426330i
$351$	−2.53473	+	29.1213i	−0.135294	+	1.55438i
$352$	3.92105	−	13.5268i	0.208993	−	0.720980i
$353$			7.71123i			0.410427i	0.978717	+	0.205214i	$0.0657889\pi$
$353$			7.71123i			0.410427i	−0.978717	+	0.205214i	$0.934211\pi$
$354$	−8.46811	−	18.0703i	−0.450075	−	0.960426i
$355$		−	1.15305i		−	0.0611977i
$356$	0.285883	−	2.52240i	0.0151518	−	0.133687i
$357$	−1.06768	+	0.575891i	−0.0565074	+	0.0304794i
$358$	1.29285	−	22.8871i	0.0683292	−	1.20962i
$359$	−32.3042			−1.70495			−0.852476	−	0.522766i	$-0.824900\pi$
$359$	−32.3042			−1.70495			−0.852476	+	0.522766i	$0.824900\pi$
$360$	−5.78864	+	6.20417i	−0.305088	+	0.326988i
$361$	−4.44438			−0.233915
$362$	1.16661	−	20.6524i	0.0613157	−	1.08546i
$363$	7.31973	−	3.94816i	0.384186	−	0.207225i
$364$	−1.26707	+	11.1796i	−0.0664125	+	0.585970i
$365$		−	6.50644i		−	0.340562i
$366$	15.9142	+	33.9596i	0.831847	+	1.77510i
$367$			16.5959i			0.866300i	0.901322	+	0.433150i	$0.142598\pi$
$367$			16.5959i			0.866300i	−0.901322	+	0.433150i	$0.857402\pi$
$368$	12.3461	+	2.83498i	0.643587	+	0.147784i
$369$	1.47854	+	0.971820i	0.0769695	+	0.0505909i
$370$	5.42152	+	0.306251i	0.281851	+	0.0159212i
$371$	−8.21289			−0.426392
$372$	5.17490	+	12.8888i	0.268306	+	0.668252i
$373$	−14.4281			−0.747058			−0.373529	−	0.927619i	$-0.621852\pi$
$373$	−14.4281			−0.747058			−0.373529	+	0.927619i	$0.621852\pi$
$374$	2.46204	+	0.139076i	0.127309	+	0.00719143i
$375$	−0.822258	−	1.52443i	−0.0424612	−	0.0787213i
$376$	6.33948	−	37.0904i	0.326934	−	1.91279i
$377$		−	28.2540i		−	1.45516i
$378$	−1.04907	+	7.27320i	−0.0539583	+	0.374093i
$379$		−	20.1383i		−	1.03443i	−0.855854	−	0.517217i	$-0.826968\pi$
$379$		−	20.1383i		−	1.03443i	0.855854	−	0.517217i	$-0.173032\pi$
$380$	9.62228	+	1.09057i	0.493612	+	0.0559449i
$381$	−5.42894	−	10.0650i	−0.278133	−	0.515646i
$382$	−0.624373	+	11.0532i	−0.0319457	+	0.565530i
$383$	−0.227107			−0.0116046			−0.00580232	−	0.999983i	$-0.501847\pi$
$383$	−0.227107			−0.0116046			−0.00580232	+	0.999983i	$0.501847\pi$
$384$	1.94973	+	19.4987i	0.0994969	+	0.995038i
$385$	2.48966			0.126885
$386$	−0.314259	+	5.56328i	−0.0159954	+	0.283164i
$387$	−27.3969	−	18.0076i	−1.39266	−	0.915377i
$388$	−15.9773	−	1.81083i	−0.811124	−	0.0919310i
$389$			22.3680i			1.13410i	0.823682	+	0.567052i	$0.191916\pi$
$389$			22.3680i			1.13410i	−0.823682	+	0.567052i	$0.808084\pi$
$390$	−12.4777	+	5.84729i	−0.631832	+	0.296089i
$391$			2.21800i			0.112169i
$392$	−0.476524	+	2.78800i	−0.0240681	+	0.140815i
$393$	−28.2953	+	15.2621i	−1.42731	+	0.769872i
$394$	−18.6838	−	1.05541i	−0.941278	−	0.0531710i
$395$	−16.5324			−0.831833
$396$	9.55842	−	11.4795i	0.480329	−	0.576866i
$397$	−23.0801			−1.15836			−0.579179	−	0.815201i	$-0.696627\pi$
$397$	−23.0801			−1.15836			−0.579179	+	0.815201i	$0.696627\pi$
$398$	19.2007	+	1.08461i	0.962446	+	0.0543667i
$399$	7.38121	−	3.98132i	0.369523	−	0.199316i
$400$	−3.89854	−	0.895203i	−0.194927	−	0.0447601i
$401$			3.84416i			0.191968i	0.995383	+	0.0959841i	$0.0305998\pi$
$401$			3.84416i			0.191968i	−0.995383	+	0.0959841i	$0.969400\pi$
$402$	−5.50700	+	2.58069i	−0.274664	+	0.128713i
$403$			22.5550i			1.12355i
$404$	0.432692	−	3.81772i	0.0215272	−	0.189939i
$405$	−8.26183	+	3.56962i	−0.410534	+	0.177376i
$406$	0.400583	−	7.09146i	0.0198806	−	0.351943i
$407$	−9.55955			−0.473849
$408$	−3.25110	+	1.09681i	−0.160954	+	0.0543000i
$409$	−0.589890			−0.0291682			−0.0145841	−	0.999894i	$-0.504642\pi$
$409$	−0.589890			−0.0291682			−0.0145841	+	0.999894i	$0.504642\pi$
$410$	−0.0470398	+	0.832739i	−0.00232313	+	0.0411260i
$411$	−10.3532	−	19.1945i	−0.510688	−	0.946794i
$412$	3.17357	−	28.0010i	0.156351	−	1.37951i
$413$		−	8.14703i		−	0.400889i
$414$	10.7936	+	8.00127i	0.530477	+	0.393241i
$415$			3.32162i			0.163052i
$416$	−8.85994	+	30.5649i	−0.434394	+	1.49857i
$417$	−3.40939	−	6.32086i	−0.166959	−	0.309534i
$418$	−17.0209	−	0.961476i	−0.832519	−	0.0470273i
$419$	15.2074			0.742931			0.371465	−	0.928447i	$-0.378855\pi$
$419$	15.2074			0.742931			0.371465	+	0.928447i	$0.378855\pi$
$420$	−3.21467	+	1.29070i	−0.156860	+	0.0629798i
$421$	26.2807			1.28084			0.640422	−	0.768024i	$-0.278760\pi$
$421$	26.2807			1.28084			0.640422	+	0.768024i	$0.278760\pi$
$422$	−12.8599	−	0.726433i	−0.626012	−	0.0353622i
$423$	21.9214	−	33.3515i	1.06586	−	1.62160i
$424$	−22.8975	−	3.91365i	−1.11200	−	0.190063i
$425$		−	0.700377i		−	0.0339733i
$426$	−1.19850	−	2.55750i	−0.0580673	−	0.123911i
$427$			15.3108i			0.740940i
$428$	26.0253	+	2.94965i	1.25798	+	0.142577i
$429$	21.3508	−	11.5164i	1.03083	−	0.556015i
$430$	0.871636	−	15.4305i	0.0420340	−	0.744123i
$431$	−14.0101			−0.674843			−0.337421	−	0.941354i	$-0.609555\pi$
$431$	−14.0101			−0.674843			−0.337421	+	0.941354i	$0.609555\pi$
$432$	−6.39066	+	19.7778i	−0.307471	+	0.951558i
$433$	34.4031			1.65331			0.826653	−	0.562712i	$-0.190242\pi$
$433$	34.4031			1.65331			0.826653	+	0.562712i	$0.190242\pi$
$434$	−0.319783	+	5.66108i	−0.0153501	+	0.271740i
$435$	7.65633	−	4.12972i	0.367093	−	0.198005i
$436$	20.2547	+	2.29562i	0.970024	+	0.109940i
$437$		−	15.3338i		−	0.733513i
$438$	−6.76286	−	14.4314i	−0.323142	−	0.689560i
$439$			29.7280i			1.41884i	0.704787	+	0.709419i	$0.251043\pi$
$439$			29.7280i			1.41884i	−0.704787	+	0.709419i	$0.748957\pi$
$440$	6.94115	+	1.18638i	0.330907	+	0.0565586i
$441$	−1.64778	+	2.50695i	−0.0784659	+	0.119379i
$442$	−5.56317	−	0.314253i	−0.264613	−	0.0149475i
$443$	−32.1666			−1.52828			−0.764140	−	0.645050i	$-0.776836\pi$
$443$	−32.1666			−1.52828			−0.764140	+	0.645050i	$0.776836\pi$
$444$	12.3434	−	4.95591i	0.585791	−	0.235197i
$445$	1.26927			0.0601694
$446$	−20.9981	−	1.18614i	−0.994291	−	0.0561655i
$447$	−9.64229	−	17.8764i	−0.456065	−	0.845525i
$448$	−2.65710	+	7.54585i	−0.125536	+	0.356508i
$449$			8.77878i			0.414296i	0.978310	+	0.207148i	$0.0664182\pi$
$449$			8.77878i			0.414296i	−0.978310	+	0.207148i	$0.933582\pi$
$450$	−3.40830	−	2.52656i	−0.160669	−	0.119103i
$451$		−	1.46833i		−	0.0691412i
$452$	−1.16068	+	10.2409i	−0.0545939	+	0.481693i
$453$	1.27898	+	2.37118i	0.0600919	+	0.111408i
$454$	0.703552	−	12.4549i	0.0330194	−	0.584537i
$455$	−5.62558			−0.263731
$456$	22.4760	−	7.58259i	1.05253	−	0.355087i
$457$	7.81135			0.365399			0.182700	−	0.983169i	$-0.441516\pi$
$457$	7.81135			0.365399			0.182700	+	0.983169i	$0.441516\pi$
$458$	−1.53619	+	27.1950i	−0.0717815	+	1.27074i
$459$	−3.62556	−	0.315570i	−0.169227	−	0.0147295i
$460$	−0.713283	+	6.29343i	−0.0332570	+	0.293433i
$461$		−	33.3103i		−	1.55142i	−0.631091	−	0.775708i	$-0.717393\pi$
$461$		−	33.3103i		−	1.55142i	0.631091	−	0.775708i	$-0.282607\pi$
$462$	5.52212	−	2.58778i	0.256912	−	0.120394i
$463$			16.1098i			0.748688i	0.927290	+	0.374344i	$0.122132\pi$
$463$			16.1098i			0.748688i	−0.927290	+	0.374344i	$0.877868\pi$
$464$	4.49608	−	19.5801i	0.208725	−	0.908983i
$465$	−6.11201	+	3.29674i	−0.283438	+	0.152882i
$466$	−34.2119	−	1.93257i	−1.58484	−	0.0895244i
$467$	37.8821			1.75298			0.876488	−	0.481423i	$-0.159880\pi$
$467$	37.8821			1.75298			0.876488	+	0.481423i	$0.159880\pi$
$468$	−21.5980	+	25.9388i	−0.998369	+	1.19902i
$469$	−2.48284			−0.114647
$470$	18.7842	+	1.06108i	0.866449	+	0.0489440i
$471$	7.18942	−	3.87788i	0.331271	−	0.178683i
$472$	3.88226	−	22.7139i	0.178695	−	1.04549i
$473$			27.2079i			1.25102i
$474$	−36.6692	+	17.1839i	−1.68427	+	0.789283i
$475$			4.84194i			0.222163i
$476$	−1.39184	−	0.157748i	−0.0637950	−	0.00723038i
$477$	−20.5893	−	13.5331i	−0.942721	−	0.619637i
$478$	−1.99274	+	35.2773i	−0.0911460	+	1.61354i
$479$	−7.73631			−0.353481			−0.176741	−	0.984257i	$-0.556555\pi$
$479$	−7.73631			−0.353481			−0.176741	+	0.984257i	$0.556555\pi$
$480$	−9.57753	+	2.06660i	−0.437153	+	0.0943271i
$481$	21.6006			0.984902
$482$	0.366630	−	6.49039i	0.0166995	−	0.295629i
$483$	2.60398	+	4.82766i	0.118485	+	0.219666i
$484$	9.54213	+	1.08148i	0.433733	+	0.0491583i
$485$		−	8.03979i		−	0.365068i
$486$	−14.6146	+	16.5049i	−0.662933	+	0.748679i
$487$		−	40.4558i		−	1.83323i	−0.399773	−	0.916614i	$-0.630911\pi$
$487$		−	40.4558i		−	1.83323i	0.399773	−	0.916614i	$-0.369089\pi$
$488$	−7.29595	+	42.6864i	−0.330272	+	1.93232i
$489$	−1.60555	−	2.97662i	−0.0726055	−	0.134608i
$490$	−1.41196	−	0.0797590i	−0.0637860	−	0.00360314i
$491$	16.2068			0.731401			0.365700	−	0.930733i	$-0.380830\pi$
$491$	16.2068			0.731401			0.365700	+	0.930733i	$0.380830\pi$
$492$	0.761222	+	1.89593i	0.0343185	+	0.0854750i
$493$	3.51758			0.158424
$494$	38.4601	+	2.17253i	1.73040	+	0.0977470i
$495$	6.24145	+	4.10241i	0.280532	+	0.184390i
$496$	−3.58920	+	15.6307i	−0.161160	+	0.701838i
$497$		−	1.15305i		−	0.0517215i
$498$	3.45252	+	7.36742i	0.154711	+	0.330142i
$499$			34.4548i			1.54241i	0.636587	+	0.771205i	$0.280346\pi$
$499$			34.4548i			1.54241i	−0.636587	+	0.771205i	$0.719654\pi$
$500$	0.225233	−	1.98728i	0.0100727	−	0.0888737i
$501$	18.9168	−	10.2035i	0.845140	−	0.455857i
$502$	−1.81966	+	32.2131i	−0.0812152	+	1.43774i
$503$	−19.0907			−0.851213			−0.425607	−	0.904908i	$-0.639939\pi$
$503$	−19.0907			−0.851213			−0.425607	+	0.904908i	$0.639939\pi$
$504$	−5.78864	+	6.20417i	−0.257846	+	0.276355i
$505$	1.92108			0.0854870
$506$	0.628852	−	11.1325i	0.0279559	−	0.494899i
$507$	−28.4264	+	15.3328i	−1.26246	+	0.680954i
$508$	1.48710	−	13.1209i	0.0659793	−	0.582148i
$509$		−	14.0542i		−	0.622942i	−0.950256	−	0.311471i	$-0.899178\pi$
$509$		−	14.0542i		−	0.622942i	0.950256	−	0.311471i	$-0.100822\pi$
$510$	−0.727979	−	1.55345i	−0.0322355	−	0.0687880i
$511$		−	6.50644i		−	0.287828i
$512$	−11.0038	+	19.7716i	−0.486302	+	0.873791i
$513$	25.0647	+	2.18164i	1.10663	+	0.0963218i
$514$	−24.1490	−	1.36413i	−1.06516	−	0.0601691i
$515$	14.0901			0.620886
$516$	−14.1053	−	35.1311i	−0.620950	−	1.54656i
$517$	−33.1214			−1.45668
$518$	5.42152	+	0.306251i	0.238208	+	0.0134559i
$519$	−5.04967	−	9.36187i	−0.221656	−	0.410940i
$520$	−15.6841	−	2.68073i	−0.687794	−	0.117558i
$521$		−	1.54713i		−	0.0677808i	−0.999426	−	0.0338904i	$-0.989210\pi$
$521$		−	1.54713i		−	0.0677808i	0.999426	−	0.0338904i	$-0.0107897\pi$
$522$	12.6894	−	17.1179i	0.555402	−	0.749229i
$523$			20.2125i			0.883833i	0.897056	+	0.441916i	$0.145701\pi$
$523$			20.2125i			0.883833i	−0.897056	+	0.441916i	$0.854299\pi$
$524$	−36.8863	−	4.18061i	−1.61139	−	0.182631i
$525$	−0.822258	−	1.52443i	−0.0358863	−	0.0665316i
$526$	0.867738	−	15.3614i	0.0378352	−	0.669791i
$527$	−2.80807			−0.122321
$528$	16.6288	−	4.58328i	0.723675	−	0.199462i
$529$	−12.9710			−0.563956
$530$	0.655052	−	11.5963i	0.0284537	−	0.503711i
$531$	13.4245	−	20.4242i	0.582576	−	0.886336i
$532$	9.62228	+	1.09057i	0.417179	+	0.0472821i
$533$			3.31782i			0.143711i
$534$	2.81528	−	1.31930i	0.121829	−	0.0570916i
$535$			13.0959i			0.566187i
$536$	−6.92216	−	1.18314i	−0.298992	−	0.0511037i
$537$	24.7102	−	13.3283i	1.06632	−	0.575161i
$538$	15.3397	+	0.866511i	0.661343	+	0.0373580i
$539$	2.48966			0.107237
$540$	−10.1858	−	2.06135i	−0.438328	−	0.0887064i
$541$	3.86114			0.166003			0.0830016	−	0.996549i	$-0.473549\pi$
$541$	3.86114			0.166003			0.0830016	+	0.996549i	$0.473549\pi$
$542$	3.01068	+	0.170067i	0.129320	+	0.00730502i
$543$	22.2974	−	12.0269i	0.956873	−	0.516125i
$544$	−3.80528	−	1.10305i	−0.163150	−	0.0472928i
$545$			10.1922i			0.436585i
$546$	−12.4777	+	5.84729i	−0.533995	+	0.250241i
$547$			42.2903i			1.80820i	0.427320	+	0.904101i	$0.359458\pi$
$547$			42.2903i			1.80820i	−0.427320	+	0.904101i	$0.640542\pi$
$548$	2.83597	−	25.0223i	0.121147	−	1.06890i
$549$	−25.2288	+	38.3834i	−1.07674	+	1.63816i
$550$	−0.198573	+	3.51530i	−0.00846716	+	0.149893i
$551$	−24.3182			−1.03599
$552$	4.95938	+	14.7004i	0.211085	+	0.625689i
$553$	−16.5324			−0.703028
$554$	−1.55156	+	27.4671i	−0.0659197	+	1.16697i
$555$	3.15723	+	5.85337i	0.134017	+	0.248462i
$556$	0.933902	−	8.23999i	0.0396063	−	0.349454i
$557$		−	6.09323i		−	0.258178i	−0.991633	−	0.129089i	$-0.958795\pi$
$557$		−	6.09323i		−	0.258178i	0.991633	−	0.129089i	$-0.0412054\pi$
$558$	−10.1299	+	13.6651i	−0.428833	+	0.578491i
$559$		−	61.4785i		−	2.60026i
$560$	−3.89854	−	0.895203i	−0.164743	−	0.0378292i
$561$	1.43377	+	2.65815i	0.0605338	+	0.112227i
$562$	34.9259	+	1.97289i	1.47326	+	0.0832215i
$563$	28.8511			1.21593			0.607964	−	0.793965i	$-0.291987\pi$
$563$	28.8511			1.21593			0.607964	+	0.793965i	$0.291987\pi$
$564$	42.7666	−	17.1710i	1.80080	−	0.723028i
$565$	−5.15324			−0.216799
$566$	16.0710	+	0.907819i	0.675515	+	0.0381585i
$567$	−8.26183	+	3.56962i	−0.346964	+	0.149910i
$568$	0.549458	−	3.21471i	0.0230547	−	0.134886i
$569$		−	24.6996i		−	1.03546i	−0.855544	−	0.517730i	$-0.826777\pi$
$569$		−	24.6996i		−	1.03546i	0.855544	−	0.517730i	$-0.173223\pi$
$570$	5.03276	+	10.7395i	0.210799	+	0.449830i
$571$		−	0.342957i		−	0.0143523i	−0.999974	−	0.00717614i	$-0.997716\pi$
$571$		−	0.342957i		−	0.0143523i	0.999974	−	0.00717614i	$-0.00228426\pi$
$572$	27.8333	+	3.15457i	1.16377	+	0.131899i
$573$	−11.9336	+	6.43684i	−0.498534	+	0.268903i
$574$	−0.0470398	+	0.832739i	−0.00196340	+	0.0347579i
$575$	−3.16686			−0.132067
$576$	−19.0951	+	14.5388i	−0.795631	+	0.605782i
$577$	33.5331			1.39600			0.698000	−	0.716097i	$-0.254073\pi$
$577$	33.5331			1.39600			0.698000	+	0.716097i	$0.254073\pi$
$578$	−1.31678	+	23.3108i	−0.0547708	+	0.969600i
$579$	−6.00642	+	3.23978i	−0.249618	+	0.134641i
$580$	9.98093	+	1.13122i	0.414436	+	0.0469712i
$581$			3.32162i			0.137804i
$582$	−8.35664	−	17.8324i	−0.346394	−	0.739179i
$583$			20.4473i			0.846840i
$584$	3.10048	−	18.1399i	0.128299	−	0.750635i
$585$	−14.1031	−	9.26974i	−0.583090	−	0.383257i
$586$	37.4118	+	2.11332i	1.54547	+	0.0873004i
$587$	7.34601			0.303202			0.151601	−	0.988442i	$-0.451557\pi$
$587$	7.34601			0.303202			0.151601	+	0.988442i	$0.451557\pi$
$588$	−3.21467	+	1.29070i	−0.132571	+	0.0532276i
$589$	19.4131			0.799904
$590$	11.5033	+	0.649799i	0.473584	+	0.0267518i
$591$	−10.8806	−	20.1721i	−0.447566	−	0.829769i
$592$	14.9692	+	3.43731i	0.615232	+	0.141273i
$593$			23.3538i			0.959024i	0.877535	+	0.479512i	$0.159186\pi$
$593$			23.3538i			0.959024i	−0.877535	+	0.479512i	$0.840814\pi$
$594$	18.1078	+	2.61182i	0.742971	+	0.107164i
$595$		−	0.700377i		−	0.0287127i
$596$	2.64122	−	23.3040i	0.108189	−	0.954569i
$597$	11.1816	+	20.7302i	0.457631	+	0.848429i
$598$	−1.42094	+	25.1547i	−0.0581067	+	1.02865i
$599$	16.4787			0.673300			0.336650	−	0.941630i	$-0.390706\pi$
$599$	16.4787			0.673300			0.336650	+	0.941630i	$0.390706\pi$
$600$	−1.56602	−	4.64194i	−0.0639326	−	0.189506i
$601$	12.2358			0.499111			0.249555	−	0.968361i	$-0.419716\pi$
$601$	12.2358			0.499111			0.249555	+	0.968361i	$0.419716\pi$
$602$	0.871636	−	15.4305i	0.0355252	−	0.628898i
$603$	−6.22437	−	4.09119i	−0.253476	−	0.166606i
$604$	−0.350340	+	3.09112i	−0.0142551	+	0.125776i
$605$			4.80161i			0.195213i
$606$	4.26100	−	1.99679i	0.173091	−	0.0811141i
$607$			16.9237i			0.686912i	0.939169	+	0.343456i	$0.111598\pi$
$607$			16.9237i			0.686912i	−0.939169	+	0.343456i	$0.888402\pi$
$608$	26.3072	+	7.62575i	1.06690	+	0.309265i
$609$	7.65633	−	4.12972i	0.310250	−	0.167345i
$610$	−21.6182	−	1.22117i	−0.875296	−	0.0494438i
$611$	74.8404			3.02772
$612$	−3.22935	−	2.68892i	−0.130539	−	0.108693i
$613$	32.8271			1.32587			0.662937	−	0.748675i	$-0.269310\pi$
$613$	32.8271			1.32587			0.662937	+	0.748675i	$0.269310\pi$
$614$	−10.7212	−	0.605618i	−0.432671	−	0.0244407i
$615$	−0.899070	+	0.484946i	−0.0362540	+	0.0195549i
$616$	6.94115	+	1.18638i	0.279667	+	0.0478007i
$617$		−	21.3327i		−	0.858823i	−0.903109	−	0.429412i	$-0.858721\pi$
$617$		−	21.3327i		−	0.858823i	0.903109	−	0.429412i	$-0.141279\pi$
$618$	31.2523	−	14.6454i	1.25715	−	0.589126i
$619$		−	1.22334i		−	0.0491703i	−0.999698	−	0.0245851i	$-0.992174\pi$
$619$		−	1.22334i		−	0.0491703i	0.999698	−	0.0245851i	$-0.00782648\pi$
$620$	−7.96772	−	0.903044i	−0.319992	−	0.0362671i
$621$	−1.42690	+	16.3935i	−0.0572594	+	0.657849i
$622$	1.72708	−	30.5743i	0.0692497	−	1.22592i
$623$	1.26927			0.0508524
$624$	−37.5741	+	10.3563i	−1.50417	+	0.414584i
$625$	1.00000			0.0400000
$626$	1.33623	−	23.6550i	0.0534063	−	0.945444i
$627$	−9.91213	−	18.3767i	−0.395852	−	0.733893i
$628$	9.37226	+	1.06223i	0.373994	+	0.0423876i
$629$			2.68924i			0.107227i
$630$	−3.40830	−	2.52656i	−0.135790	−	0.100661i
$631$			25.9260i			1.03210i	0.856560	+	0.516048i	$0.172597\pi$
$631$			25.9260i			1.03210i	−0.856560	+	0.516048i	$0.827403\pi$
$632$	−46.0922	−	7.87808i	−1.83345	−	0.313373i
$633$	−7.48900	−	13.8843i	−0.297661	−	0.551851i
$634$	24.4598	+	1.38169i	0.971422	+	0.0548738i
$635$	6.60247			0.262011
$636$	−10.6004	−	26.4017i	−0.420333	−	1.04690i
$637$	−5.62558			−0.222894
$638$	−17.6553	−	0.997314i	−0.698980	−	0.0394840i
$639$	1.89998	−	2.89065i	0.0751621	−	0.114352i
$640$	−10.4425	−	4.35357i	−0.412777	−	0.172090i
$641$			29.4751i			1.16420i	0.813119	+	0.582098i	$0.197768\pi$
$641$			29.4751i			1.16420i	−0.813119	+	0.582098i	$0.802232\pi$
$642$	13.6121	+	29.0471i	0.537225	+	1.14640i
$643$		−	30.0809i		−	1.18628i	−0.805101	−	0.593138i	$-0.797889\pi$
$643$		−	30.0809i		−	1.18628i	0.805101	−	0.593138i	$-0.202111\pi$
$644$	−0.713283	+	6.29343i	−0.0281073	+	0.247996i
$645$	16.6596	−	8.98594i	0.655969	−	0.353821i
$646$	−0.270477	+	4.78822i	−0.0106418	+	0.188390i
$647$	43.5494			1.71210			0.856051	−	0.516891i	$-0.172911\pi$
$647$	43.5494			1.71210			0.856051	+	0.516891i	$0.172911\pi$
$648$	−24.7350	+	6.01512i	−0.971681	+	0.236296i
$649$	−20.2833			−0.796190
$650$	0.448691	−	7.94311i	0.0175991	−	0.311555i
$651$	−6.11201	+	3.29674i	−0.239548	+	0.129209i
$652$	0.439794	−	3.88038i	0.0172236	−	0.151967i
$653$			8.38910i			0.328291i	0.986436	+	0.164145i	$0.0524866\pi$
$653$			8.38910i			0.328291i	−0.986436	+	0.164145i	$0.947513\pi$
$654$	10.5939	+	22.6065i	0.414253	+	0.883984i
$655$		−	18.5612i		−	0.725247i
$656$	−0.527967	+	2.29926i	−0.0206137	+	0.0897709i
$657$	10.7212	−	16.3113i	0.418274	−	0.636365i
$658$	18.7842	+	1.06108i	0.732283	+	0.0413652i
$659$	−31.7645			−1.23737			−0.618685	−	0.785639i	$-0.712334\pi$
$659$	−31.7645			−1.23737			−0.618685	+	0.785639i	$0.712334\pi$
$660$	3.21340	+	8.00342i	0.125082	+	0.311533i
$661$	12.8485			0.499749			0.249874	−	0.968278i	$-0.419611\pi$
$661$	12.8485			0.499749			0.249874	+	0.968278i	$0.419611\pi$
$662$	−11.2046	−	0.632928i	−0.435481	−	0.0245994i
$663$	−3.23972	−	6.00630i	−0.125820	−	0.233266i
$664$	−1.58283	+	9.26065i	−0.0614258	+	0.359383i
$665$			4.84194i			0.187762i
$666$	13.0869	+	9.70125i	0.507105	+	0.375916i
$667$		−	15.9053i		−	0.615855i
$668$	24.6603	+	2.79494i	0.954135	+	0.108139i
$669$	−12.2283	−	22.6707i	−0.472773	−	0.876501i
$670$	0.198029	−	3.50568i	0.00765053	−	0.135436i
$671$	38.1185			1.47155
$672$	−9.57753	+	2.06660i	−0.369461	+	0.0797210i
$673$	12.3146			0.474693			0.237346	−	0.971425i	$-0.423722\pi$
$673$	12.3146			0.474693			0.237346	+	0.971425i	$0.423722\pi$
$674$	−2.01757	+	35.7168i	−0.0777139	+	1.37576i
$675$	0.450572	−	5.17658i	0.0173425	−	0.199247i
$676$	−37.0571	−	4.19997i	−1.42527	−	0.161537i
$677$			30.6935i			1.17965i	0.807531	+	0.589824i	$0.200803\pi$
$677$			30.6935i			1.17965i	−0.807531	+	0.589824i	$0.799197\pi$
$678$	−11.4300	+	5.35634i	−0.438967	+	0.205709i
$679$		−	8.03979i		−	0.308539i
$680$	0.333747	−	1.95265i	0.0127986	−	0.0748806i
$681$	13.4470	−	7.25312i	0.515289	−	0.277940i
$682$	14.0941	+	0.796150i	0.539692	+	0.0304862i
$683$	−35.2969			−1.35060			−0.675299	−	0.737544i	$-0.735985\pi$
$683$	−35.2969			−1.35060			−0.675299	+	0.737544i	$0.735985\pi$
$684$	22.3256	+	18.5894i	0.853639	+	0.710785i
$685$	12.5912			0.481086
$686$	−1.41196	−	0.0797590i	−0.0539090	−	0.00304521i
$687$	−29.3612	+	15.8370i	−1.12020	+	0.604220i
$688$	9.78311	−	42.6047i	0.372977	−	1.62429i
$689$		−	46.2023i		−	1.76017i
$690$	−7.02417	+	3.29167i	−0.267406	+	0.125312i
$691$		−	11.3873i		−	0.433195i	−0.976261	−	0.216598i	$-0.930504\pi$
$691$		−	11.3873i		−	0.433195i	0.976261	−	0.216598i	$-0.0694959\pi$
$692$	1.38321	−	12.2043i	0.0525817	−	0.463938i
$693$	6.24145	+	4.10241i	0.237093	+	0.155838i
$694$	−1.32012	+	23.3699i	−0.0501111	+	0.887110i
$695$	4.14637			0.157281
$696$	23.3137	−	7.86522i	0.883705	−	0.298130i
$697$	−0.413064			−0.0156459
$698$	2.68846	−	47.5934i	0.101760	−	1.80144i
$699$	−19.9234	−	36.9371i	−0.753571	−	1.39709i
$700$	0.225233	−	1.98728i	0.00851302	−	0.0751120i
$701$			28.3012i			1.06892i	0.845193	+	0.534461i	$0.179485\pi$
$701$			28.3012i			1.06892i	−0.845193	+	0.534461i	$0.820515\pi$
$702$	−40.9160	−	5.90163i	−1.54427	−	0.222742i
$703$		−	18.5916i		−	0.701196i
$704$	18.7866	+	6.61526i	0.708046	+	0.249322i
$705$	10.9390	+	20.2804i	0.411986	+	0.763804i
$706$	−10.8880	−	0.615040i	−0.409774	−	0.0231473i
$707$	1.92108			0.0722497
$708$	26.1900	−	10.5154i	0.984280	−	0.395192i
$709$	−14.1810			−0.532580			−0.266290	−	0.963893i	$-0.585798\pi$
$709$	−14.1810			−0.532580			−0.266290	+	0.963893i	$0.585798\pi$
$710$	1.62807	+	0.0919663i	0.0611003	+	0.00345144i
$711$	−41.4458	−	27.2418i	−1.55434	−	1.02165i
$712$	3.53873	+	0.604840i	0.132620	+	0.0226674i
$713$			12.6971i			0.475511i
$714$	−0.727979	−	1.55345i	−0.0272439	−	0.0581365i
$715$			14.0058i			0.523786i
$716$	32.2127	+	3.65091i	1.20384	+	0.136441i
$717$	−38.0873	+	20.5438i	−1.42239	+	0.767221i
$718$	2.57655	−	45.6124i	0.0961561	−	1.70224i
$719$	−24.5685			−0.916250			−0.458125	−	0.888888i	$-0.651479\pi$
$719$	−24.5685			−0.916250			−0.458125	+	0.888888i	$0.651479\pi$
$720$	−8.29835	−	8.66818i	−0.309261	−	0.323044i
$721$	14.0901			0.524744
$722$	0.354480	−	6.27531i	0.0131924	−	0.233543i
$723$	7.00738	−	3.77969i	0.260607	−	0.140568i
$724$	29.0673	+	3.29442i	1.08028	+	0.122436i
$725$			5.02241i			0.186528i
$726$	4.99084	+	10.6501i	0.185228	+	0.395262i
$727$			31.9507i			1.18499i	0.805576	+	0.592493i	$0.201856\pi$
$727$			31.9507i			1.18499i	−0.805576	+	0.592493i	$0.798144\pi$
$728$	−15.6841	−	2.68073i	−0.581292	−	0.0993544i
$729$	−26.5940	−	4.66484i	−0.984962	−	0.172772i
$730$	9.18685	+	0.518947i	0.340020	+	0.0192071i
$731$	7.65398			0.283093
$732$	−49.2190	+	19.7616i	−1.81919	+	0.730411i
$733$	4.07842			0.150640			0.0753200	−	0.997159i	$-0.476002\pi$
$733$	4.07842			0.150640			0.0753200	+	0.997159i	$0.476002\pi$
$734$	−23.4328	−	1.32367i	−0.864921	−	0.0488577i
$735$	−0.822258	−	1.52443i	−0.0303294	−	0.0562295i
$736$	−4.98761	+	17.2062i	−0.183846	+	0.634228i
$737$			6.18143i			0.227696i
$738$	−1.49010	+	2.01013i	−0.0548513	+	0.0739937i
$739$			42.4999i			1.56338i	0.623664	+	0.781692i	$0.285643\pi$
$739$			42.4999i			1.56338i	−0.623664	+	0.781692i	$0.714357\pi$
$740$	−0.864830	+	7.63056i	−0.0317918	+	0.280505i
$741$	22.3973	+	41.5236i	0.822784	+	1.52541i
$742$	0.655052	−	11.5963i	0.0240477	−	0.425714i
$743$	−22.4080			−0.822069			−0.411035	−	0.911620i	$-0.634832\pi$
$743$	−22.4080			−0.822069			−0.411035	+	0.911620i	$0.634832\pi$
$744$	−18.6112	+	6.27876i	−0.682321	+	0.230191i
$745$	11.7266			0.429629
$746$	1.15077	−	20.3719i	0.0421327	−	0.745869i
$747$	−5.47330	+	8.32713i	−0.200258	+	0.304674i
$748$	−0.392739	+	3.46521i	−0.0143600	+	0.126701i
$749$			13.0959i			0.478516i
$750$	2.21802	−	1.03941i	0.0809907	−	0.0379539i
$751$			43.0144i			1.56962i	0.619737	+	0.784809i	$0.287239\pi$
$751$			43.0144i			1.56962i	−0.619737	+	0.784809i	$0.712761\pi$
$752$	51.8646	+	11.9094i	1.89131	+	0.434291i
$753$	−34.7790	+	18.7593i	−1.26742	+	0.683628i
$754$	39.8936	+	2.25351i	1.45284	+	0.0820681i
$755$	−1.55545			−0.0566088
$756$	−10.1858	−	2.06135i	−0.370455	−	0.0749706i
$757$	−15.8394			−0.575694			−0.287847	−	0.957676i	$-0.592939\pi$
$757$	−15.8394			−0.575694			−0.287847	+	0.957676i	$0.592939\pi$
$758$	28.4345	+	1.60621i	1.03279	+	0.0583401i
$759$	12.0192	−	6.48301i	0.436270	−	0.235318i
$760$	−2.30730	+	13.4993i	−0.0836947	+	0.489672i
$761$		−	19.4133i		−	0.703733i	−0.936050	−	0.351866i	$-0.885547\pi$
$761$		−	19.4133i		−	0.703733i	0.936050	−	0.351866i	$-0.114453\pi$
$762$	14.6444	−	6.86268i	0.530512	−	0.248609i
$763$			10.1922i			0.368982i
$764$	−15.5569	−	1.76318i	−0.562829	−	0.0637897i
$765$	1.15407	−	1.75581i	0.0417255	−	0.0634815i
$766$	0.0181138	−	0.320667i	0.000654480	−	0.0115862i
$767$	45.8318			1.65489
$768$	−27.6869	+	1.19775i	−0.999066	+	0.0432202i
$769$	−29.2264			−1.05393			−0.526966	−	0.849887i	$-0.676670\pi$
$769$	−29.2264			−1.05393			−0.526966	+	0.849887i	$0.676670\pi$
$770$	−0.198573	+	3.51530i	−0.00715606	+	0.126683i
$771$	−14.0632	−	26.0725i	−0.506473	−	0.938979i
$772$	−7.83008	−	0.887444i	−0.281811	−	0.0319398i
$773$		−	2.35932i		−	0.0848588i	−0.999099	−	0.0424294i	$-0.986490\pi$
$773$		−	2.35932i		−	0.0848588i	0.999099	−	0.0424294i	$-0.0135097\pi$
$774$	27.6112	−	37.2471i	0.992464	−	1.33882i
$775$		−	4.00937i		−	0.144021i
$776$	3.83116	−	22.4149i	0.137531	−	0.804648i
$777$	3.15723	+	5.85337i	0.113265	+	0.209988i
$778$	−31.5828	−	1.78405i	−1.13230	−	0.0639614i
$779$	2.85565			0.102314
$780$	−7.26095	−	18.0844i	−0.259984	−	0.647525i
$781$	−2.87071			−0.102722
$782$	−3.13173	−	0.176905i	−0.111990	−	0.00632612i
$783$	25.9989	+	2.26296i	0.929126	+	0.0808715i
$784$	−3.89854	−	0.895203i	−0.139234	−	0.0319715i
$785$			4.71613i			0.168326i
$786$	−19.2927	−	41.1692i	−0.688149	−	1.46846i
$787$			36.0526i			1.28514i	0.766228	+	0.642569i	$0.222131\pi$
$787$			36.0526i			1.28514i	−0.766228	+	0.642569i	$0.777869\pi$
$788$	2.98041	−	26.2967i	0.106173	−	0.936781i
$789$	16.5851	−	8.94575i	0.590443	−	0.318477i
$790$	1.31860	−	23.3431i	0.0469139	−	0.830509i
$791$	−5.15324			−0.183228
$792$	15.4462	+	14.4117i	0.548858	+	0.512098i
$793$	−86.1320			−3.05864
$794$	1.84085	−	32.5882i	0.0653292	−	1.15651i
$795$	12.5200	−	6.75312i	0.444039	−	0.239508i
$796$	−3.06286	+	27.0242i	−0.108560	+	0.957848i
$797$			34.6794i			1.22841i	0.789147	+	0.614204i	$0.210523\pi$
$797$			34.6794i			1.22841i	−0.789147	+	0.614204i	$0.789477\pi$
$798$	5.03276	+	10.7395i	0.178158	+	0.380175i
$799$			9.31752i			0.329630i
$800$	1.57494	−	5.43319i	0.0556824	−	0.192092i
$801$	3.18201	+	2.09149i	0.112431	+	0.0738992i
$802$	−5.42781	−	0.306606i	−0.191663	−	0.0108267i
$803$	−16.1988			−0.571643
$804$	−3.20461	−	7.98152i	−0.113018	−	0.281486i
$805$	−3.16686			−0.111617
$806$	−31.8469	−	1.79897i	−1.12176	−	0.0633659i
$807$	8.93311	+	16.5616i	0.314460	+	0.582996i
$808$	5.35597	+	0.915442i	0.188422	+	0.0322051i
$809$			18.2187i			0.640537i	0.947327	+	0.320268i	$0.103773\pi$
$809$			18.2187i			0.640537i	−0.947327	+	0.320268i	$0.896227\pi$
$810$	−4.38121	−	11.9501i	−0.153940	−	0.419884i
$811$		−	11.6690i		−	0.409754i	−0.978788	−	0.204877i	$-0.934321\pi$
$811$		−	11.6690i		−	0.409754i	0.978788	−	0.204877i	$-0.0656795\pi$
$812$	9.98093	+	1.13122i	0.350262	+	0.0396979i
$813$	1.75327	+	3.25049i	0.0614899	+	0.114000i
$814$	0.762460	−	13.4977i	0.0267242	−	0.473095i
$815$	1.95261			0.0683970
$816$	−1.28935	−	4.67792i	−0.0451361	−	0.163760i
$817$	−52.9145			−1.85124
$818$	0.0470490	−	0.832902i	0.00164503	−	0.0291217i
$819$	−14.1031	−	9.26974i	−0.492801	−	0.323911i
$820$	−1.17204	−	0.132837i	−0.0409296	−	0.00463886i
$821$			38.8538i			1.35601i	0.735059	+	0.678004i	$0.237155\pi$
$821$			38.8538i			1.35601i	−0.735059	+	0.678004i	$0.762845\pi$
$822$	27.9276	−	13.0875i	0.974088	−	0.456478i
$823$		−	18.0289i		−	0.628450i	−0.949349	−	0.314225i	$-0.898255\pi$
$823$		−	18.0289i		−	0.628450i	0.949349	−	0.314225i	$-0.101745\pi$
$824$	39.2833	+	6.71430i	1.36850	+	0.233904i
$825$	−3.79531	+	2.04714i	−0.132136	+	0.0712723i
$826$	11.5033	+	0.649799i	0.400251	+	0.0226094i
$827$	3.14692			0.109429			0.0547146	−	0.998502i	$-0.482575\pi$
$827$	3.14692			0.109429			0.0547146	+	0.998502i	$0.482575\pi$
$828$	−12.1584	+	14.6020i	−0.422533	+	0.507455i
$829$	−4.84530			−0.168284			−0.0841421	−	0.996454i	$-0.526815\pi$
$829$	−4.84530			−0.168284			−0.0841421	+	0.996454i	$0.526815\pi$
$830$	−4.69000	−	0.264929i	−0.162792	−	0.00919581i
$831$	−29.6550	+	15.9955i	−1.02872	+	0.554878i
$832$	−42.4498	−	14.9477i	−1.47168	−	0.518219i
$833$		−	0.700377i		−	0.0242666i
$834$	9.19675	−	4.30979i	0.318458	−	0.149236i
$835$			12.4091i			0.429434i
$836$	2.71514	−	23.9562i	0.0939050	−	0.828541i
$837$	−20.7548	−	1.80651i	−0.717391	−	0.0624420i
$838$	−1.21293	+	21.4723i	−0.0418999	+	0.741748i
$839$	−12.2531			−0.423024			−0.211512	−	0.977375i	$-0.567839\pi$
$839$	−12.2531			−0.423024			−0.211512	+	0.977375i	$0.567839\pi$
$840$	−1.56602	−	4.64194i	−0.0540329	−	0.160162i
$841$	3.77535			0.130184
$842$	−2.09612	+	37.1074i	−0.0722372	+	1.27880i
$843$	20.3391	+	37.7079i	0.700516	+	1.29873i
$844$	2.05139	−	18.0998i	0.0706118	−	0.623021i
$845$		−	18.6472i		−	0.641483i
$846$	45.3426	+	33.6123i	1.55891	+	1.15562i
$847$			4.80161i			0.164985i
$848$	7.35220	−	32.0183i	0.252476	−	1.09951i
$849$	9.35897	+	17.3511i	0.321199	+	0.595489i
$850$	0.988906	+	0.0558614i	0.0339192	+	0.00191603i
$851$	12.1598			0.416833
$852$	3.70668	−	1.48825i	0.126989	−	0.0509865i
$853$	18.9278			0.648074			0.324037	−	0.946044i	$-0.394960\pi$
$853$	18.9278			0.648074			0.324037	+	0.946044i	$0.394960\pi$
$854$	−21.6182	−	1.22117i	−0.739760	−	0.0417876i
$855$	−7.97847	+	12.1385i	−0.272858	+	0.415128i
$856$	−6.24054	+	36.5115i	−0.213297	+	1.24794i
$857$		−	3.92204i		−	0.133974i	−0.997754	−	0.0669872i	$-0.978661\pi$
$857$		−	3.92204i		−	0.133974i	0.997754	−	0.0669872i	$-0.0213387\pi$
$858$	14.5577	+	31.0651i	0.496993	+	1.06055i
$859$			0.612982i			0.0209147i	0.999945	+	0.0104573i	$0.00332873\pi$
$859$			0.612982i			0.0209147i	−0.999945	+	0.0104573i	$0.996671\pi$
$860$	21.7177	+	2.46144i	0.740568	+	0.0839342i
$861$	−0.899070	+	0.484946i	−0.0306402	+	0.0165269i
$862$	1.11743	−	19.7817i	0.0380599	−	0.673769i
$863$	−44.6858			−1.52112			−0.760562	−	0.649265i	$-0.775076\pi$
$863$	−44.6858			−1.52112			−0.760562	+	0.649265i	$0.775076\pi$
$864$	−27.4157	−	10.6008i	−0.932702	−	0.360647i
$865$	6.14122			0.208808
$866$	−2.74395	+	48.5758i	−0.0932434	+	1.65067i
$867$	−25.1676	+	13.5750i	−0.854735	+	0.461033i
$868$	−7.96772	−	0.903044i	−0.270442	−	0.0306513i
$869$			41.1599i			1.39625i
$870$	5.22035	+	11.1398i	0.176986	+	0.377676i
$871$		−	13.9674i		−	0.473269i
$872$	−4.85682	+	28.4158i	−0.164473	+	0.962279i
$873$	13.2478	−	20.1554i	0.448371	−	0.682156i
$874$	21.6507	+	1.22301i	0.732346	+	0.0413688i
$875$	1.00000			0.0338062
$876$	20.9160	−	8.39787i	0.706687	−	0.283738i
$877$	−37.3591			−1.26153			−0.630764	−	0.775975i	$-0.717258\pi$
$877$	−37.3591			−1.26153			−0.630764	+	0.775975i	$0.717258\pi$
$878$	−41.9748	−	2.37107i	−1.41658	−	0.0800198i
$879$	21.7868	+	40.3918i	0.734851	+	1.36238i
$880$	−2.22875	+	9.70603i	−0.0751310	+	0.327190i
$881$		−	8.91131i		−	0.300230i	−0.988669	−	0.150115i	$-0.952036\pi$
$881$		−	8.91131i		−	0.300230i	0.988669	−	0.150115i	$-0.0479643\pi$
$882$	−3.40830	−	2.52656i	−0.114763	−	0.0850737i
$883$		−	51.5725i		−	1.73555i	−0.496956	−	0.867776i	$-0.665549\pi$
$883$		−	51.5725i		−	1.73555i	0.496956	−	0.867776i	$-0.334451\pi$
$884$	0.887426	−	7.82993i	0.0298474	−	0.263349i
$885$	6.69896	+	12.4196i	0.225183	+	0.417480i
$886$	2.56557	−	45.4180i	0.0861922	−	1.52585i
$887$	0.361532			0.0121391			0.00606954	−	0.999982i	$-0.498068\pi$
$887$	0.361532			0.0121391			0.00606954	+	0.999982i	$0.498068\pi$
$888$	6.01307	+	17.8237i	0.201785	+	0.598123i
$889$	6.60247			0.221440
$890$	−0.101236	+	1.79217i	−0.00339344	+	0.0600736i
$891$	8.88713	+	20.5691i	0.297730	+	0.689091i
$892$	3.34958	−	29.5540i	0.112152	−	0.989541i
$893$		−	64.4152i		−	2.15557i
$894$	26.0099	−	12.1888i	0.869900	−	0.407653i
$895$			16.2094i			0.541822i
$896$	−10.4425	−	4.35357i	−0.348860	−	0.145443i
$897$	−27.1584	+	14.6489i	−0.906794	+	0.489112i
$898$	−12.3953	−	0.700187i	−0.413637	−	0.0233655i
$899$	20.1367			0.671597
$900$	3.83925	−	4.61087i	0.127975	−	0.153696i
$901$	5.75212			0.191631
$902$	2.07323	+	0.117113i	0.0690311	+	0.00389943i
$903$	16.6596	−	8.98594i	0.554395	−	0.299033i
$904$	−14.3672	−	2.45565i	−0.477847	−	0.0816736i
$905$			14.6267i			0.486208i
$906$	−3.45003	+	1.61676i	−0.114620	+	0.0537131i
$907$		−	18.9446i		−	0.629046i	−0.949250	−	0.314523i	$-0.898155\pi$
$907$		−	18.9446i		−	0.629046i	0.949250	−	0.314523i	$-0.101845\pi$
$908$	17.5297	+	1.98678i	0.581744	+	0.0659336i
$909$	4.81606	+	3.16552i	0.159739	+	0.104994i
$910$	0.448691	−	7.94311i	0.0148740	−	0.263312i
$911$	−2.96658			−0.0982872			−0.0491436	−	0.998792i	$-0.515649\pi$
$911$	−2.96658			−0.0982872			−0.0491436	+	0.998792i	$0.515649\pi$
$912$	8.91368	+	32.3400i	0.295161	+	1.07089i
$913$	8.26968			0.273687
$914$	−0.623025	+	11.0293i	−0.0206078	+	0.364818i
$915$	−12.5894	−	23.3402i	−0.416193	−	0.771604i
$916$	−38.2758	−	4.33809i	−1.26467	−	0.143334i
$917$		−	18.5612i		−	0.612946i
$918$	0.734744	−	5.09398i	0.0242502	−	0.168126i
$919$		−	39.5168i		−	1.30354i	−0.758417	−	0.651770i	$-0.774027\pi$
$919$		−	39.5168i		−	1.30354i	0.758417	−	0.651770i	$-0.225973\pi$
$920$	−8.82920	−	1.50909i	−0.291090	−	0.0497531i
$921$	−6.24349	−	11.5752i	−0.205730	−	0.381414i
$922$	47.0329	+	2.65680i	1.54895	+	0.0874970i
$923$	6.48660			0.213509
$924$	3.21340	+	8.00342i	0.105713	+	0.263293i
$925$	−3.83971			−0.126249
$926$	−22.7465	−	1.28491i	−0.747496	−	0.0422246i
$927$	35.3233	+	23.2175i	1.16017	+	0.762563i
$928$	27.2877	+	7.90998i	0.895764	+	0.259658i
$929$			10.1614i			0.333384i	0.986009	+	0.166692i	$0.0533086\pi$
$929$			10.1614i			0.333384i	−0.986009	+	0.166692i	$0.946691\pi$
$930$	−4.16738	−	8.89287i	−0.136654	−	0.291609i
$931$			4.84194i			0.158688i
$932$	5.45742	−	48.1518i	0.178764	−	1.57727i
$933$	33.0097	−	17.8050i	1.08069	−	0.582909i
$934$	−3.02144	+	53.4882i	−0.0988646	+	1.75019i
$935$	−1.74370			−0.0570250
$936$	−34.9020	−	32.5645i	−1.14081	−	1.06440i
$937$	−50.9412			−1.66418			−0.832088	−	0.554643i	$-0.812855\pi$
$937$	−50.9412			−1.66418			−0.832088	+	0.554643i	$0.812855\pi$
$938$	0.198029	−	3.50568i	0.00646588	−	0.114465i
$939$	25.5392	−	13.7755i	0.833441	−	0.449547i
$940$	−2.99641	+	26.4379i	−0.0977322	+	0.862310i
$941$			52.6374i			1.71593i	0.513707	+	0.857966i	$0.328272\pi$
$941$			52.6374i			1.71593i	−0.513707	+	0.857966i	$0.671728\pi$
$942$	4.90199	+	10.4605i	0.159716	+	0.340821i
$943$			1.86773i			0.0608218i
$944$	31.7615	+	7.29324i	1.03375	+	0.237375i
$945$	0.450572	−	5.17658i	0.0146571	−	0.168394i
$946$	−38.4165	−	2.17007i	−1.24903	−	0.0705552i
$947$	−18.6248			−0.605226			−0.302613	−	0.953114i	$-0.597859\pi$
$947$	−18.6248			−0.605226			−0.302613	+	0.953114i	$0.597859\pi$
$948$	−21.3383	−	53.1461i	−0.693037	−	1.72610i
$949$	36.6025			1.18817
$950$	−6.83664	−	0.386188i	−0.221810	−	0.0125296i
$951$	14.2442	+	26.4081i	0.461899	+	0.856342i
$952$	0.333747	−	1.95265i	0.0108168	−	0.0632857i
$953$			1.56897i			0.0508238i	0.999677	+	0.0254119i	$0.00808973\pi$
$953$			1.56897i			0.0508238i	−0.999677	+	0.0254119i	$0.991910\pi$
$954$	20.7504	−	27.9920i	0.671818	−	0.906274i
$955$		−	7.82825i		−	0.253316i
$956$	−49.6512	−	5.62736i	−1.60584	−	0.182002i
$957$	−10.2816	−	19.0616i	−0.332356	−	0.616175i
$958$	0.617041	−	10.9234i	0.0199357	−	0.352919i
$959$	12.5912			0.406592
$960$	−2.15407	−	13.6879i	−0.0695224	−	0.441777i
$961$	14.9250			0.481451
$962$	−1.72284	+	30.4992i	−0.0555466	+	0.983334i
$963$	−21.5793	+	32.8309i	−0.695383	+	1.05796i
$964$	9.13495	+	1.03533i	0.294217	+	0.0333459i
$965$		−	3.94011i		−	0.126836i
$966$	−7.02417	+	3.29167i	−0.225999	+	0.105908i
$967$		−	28.9089i		−	0.929646i	−0.885404	−	0.464823i	$-0.846118\pi$
$967$		−	28.9089i		−	0.929646i	0.885404	−	0.464823i	$-0.153882\pi$
$968$	−2.28808	+	13.3869i	−0.0735418	+	0.430270i
$969$	−5.16963	+	2.78843i	−0.166072	+	0.0895772i
$970$	11.3519	+	0.641246i	0.364487	+	0.0205892i
$971$	−28.5884			−0.917447			−0.458723	−	0.888579i	$-0.651693\pi$
$971$	−28.5884			−0.917447			−0.458723	+	0.888579i	$0.651693\pi$
$972$	−22.1387	−	21.9517i	−0.710099	−	0.704102i
$973$	4.14637			0.132927
$974$	57.1221	+	3.22672i	1.83031	+	0.103391i
$975$	8.57582	−	4.62568i	0.274646	−	0.148140i
$976$	−59.6896	−	13.7062i	−1.91062	−	0.438726i
$977$		−	51.2091i		−	1.63833i	−0.573561	−	0.819163i	$-0.694438\pi$
$977$		−	51.2091i		−	1.63833i	0.573561	−	0.819163i	$-0.305562\pi$
$978$	4.33094	−	2.02957i	0.138488	−	0.0648983i
$979$		−	3.16006i		−	0.100996i
$980$	0.225233	−	1.98728i	0.00719482	−	0.0634812i
$981$	−16.7945	+	25.5513i	−0.536207	+	0.815791i
$982$	−1.29263	+	22.8833i	−0.0412496	+	0.730237i
$983$	13.8872			0.442934			0.221467	−	0.975168i	$-0.428916\pi$
$983$	13.8872			0.442934			0.221467	+	0.975168i	$0.428916\pi$
$984$	−2.73769	+	0.923600i	−0.0872745	+	0.0294433i
$985$	13.2325			0.421623
$986$	−0.280559	+	4.96670i	−0.00893482	+	0.158172i
$987$	10.9390	+	20.2804i	0.348192	+	0.645532i
$988$	−6.13508	+	54.1309i	−0.195183	+	1.72213i
$989$		−	34.6086i		−	1.10049i
$990$	−6.29027	+	8.48549i	−0.199918	+	0.269687i
$991$		−	4.67643i		−	0.148552i	−0.997238	−	0.0742758i	$-0.976335\pi$
$991$		−	4.67643i		−	0.148552i	0.997238	−	0.0742758i	$-0.0236645\pi$
$992$	−21.7837	−	6.31450i	−0.691632	−	0.200486i
$993$	−6.52503	−	12.0971i	−0.207066	−	0.383891i
$994$	1.62807	+	0.0919663i	0.0516392	+	0.00291700i
$995$	−13.5986			−0.431105
$996$	−10.6779	+	4.28721i	−0.338342	+	0.135846i
$997$	23.4680			0.743240			0.371620	−	0.928385i	$-0.378802\pi$
$997$	23.4680			0.743240			0.371620	+	0.928385i	$0.378802\pi$
$998$	−48.6489	−	2.74808i	−1.53995	−	0.0869890i
$999$	−1.73006	+	19.8765i	−0.0547367	+	0.628866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.12	yes	24
3.2	odd	2		420.2.n.a.71.13	✓	24
4.3	odd	2		420.2.n.a.71.14	yes	24
12.11	even	2	inner	420.2.n.b.71.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.13	✓	24	3.2	odd	2
420.2.n.a.71.14	yes	24	4.3	odd	2
420.2.n.b.71.11	yes	24	12.11	even	2	inner
420.2.n.b.71.12	yes	24	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.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0797590 + 1.41196i) q^{2} +(-1.52443 + 0.822258i) q^{3} +(-1.98728 - 0.225233i) q^{4} -1.00000i q^{5} +(-1.03941 - 2.21802i) q^{6} -1.00000i q^{7} +(0.476524 - 2.78800i) q^{8} +(1.64778 - 2.50695i) q^{9} +O(q^{10})\)	\(q+(-0.0797590 + 1.41196i) q^{2} +(-1.52443 + 0.822258i) q^{3} +(-1.98728 - 0.225233i) q^{4} -1.00000i q^{5} +(-1.03941 - 2.21802i) q^{6} -1.00000i q^{7} +(0.476524 - 2.78800i) q^{8} +(1.64778 - 2.50695i) q^{9} +(1.41196 + 0.0797590i) q^{10} -2.48966 q^{11} +(3.21467 - 1.29070i) q^{12} +5.62558 q^{13} +(1.41196 + 0.0797590i) q^{14} +(0.822258 + 1.52443i) q^{15} +(3.89854 + 0.895203i) q^{16} +0.700377i q^{17} +(3.40830 + 2.52656i) q^{18} -4.84194i q^{19} +(-0.225233 + 1.98728i) q^{20} +(0.822258 + 1.52443i) q^{21} +(0.198573 - 3.51530i) q^{22} +3.16686 q^{23} +(1.56602 + 4.64194i) q^{24} -1.00000 q^{25} +(-0.448691 + 7.94311i) q^{26} +(-0.450572 + 5.17658i) q^{27} +(-0.225233 + 1.98728i) q^{28} -5.02241i q^{29} +(-2.21802 + 1.03941i) q^{30} +4.00937i q^{31} +(-1.57494 + 5.43319i) q^{32} +(3.79531 - 2.04714i) q^{33} +(-0.988906 - 0.0558614i) q^{34} -1.00000 q^{35} +(-3.83925 + 4.61087i) q^{36} +3.83971 q^{37} +(6.83664 + 0.386188i) q^{38} +(-8.57582 + 4.62568i) q^{39} +(-2.78800 - 0.476524i) q^{40} +0.589774i q^{41} +(-2.21802 + 1.03941i) q^{42} -10.9284i q^{43} +(4.94764 + 0.560754i) q^{44} +(-2.50695 - 1.64778i) q^{45} +(-0.252586 + 4.47149i) q^{46} +13.3036 q^{47} +(-6.67914 + 1.84093i) q^{48} -1.00000 q^{49} +(0.0797590 - 1.41196i) q^{50} +(-0.575891 - 1.06768i) q^{51} +(-11.1796 - 1.26707i) q^{52} -8.21289i q^{53} +(-7.27320 - 1.04907i) q^{54} +2.48966i q^{55} +(-2.78800 - 0.476524i) q^{56} +(3.98132 + 7.38121i) q^{57} +(7.09146 + 0.400583i) q^{58} +8.14703 q^{59} +(-1.29070 - 3.21467i) q^{60} -15.3108 q^{61} +(-5.66108 - 0.319783i) q^{62} +(-2.50695 - 1.64778i) q^{63} +(-7.54585 - 2.65710i) q^{64} -5.62558i q^{65} +(2.58778 + 5.52212i) q^{66} -2.48284i q^{67} +(0.157748 - 1.39184i) q^{68} +(-4.82766 + 2.60398i) q^{69} +(0.0797590 - 1.41196i) q^{70} +1.15305 q^{71} +(-6.20417 - 5.78864i) q^{72} +6.50644 q^{73} +(-0.306251 + 5.42152i) q^{74} +(1.52443 - 0.822258i) q^{75} +(-1.09057 + 9.62228i) q^{76} +2.48966i q^{77} +(-5.84729 - 12.4777i) q^{78} -16.5324i q^{79} +(0.895203 - 3.89854i) q^{80} +(-3.56962 - 8.26183i) q^{81} +(-0.832739 - 0.0470398i) q^{82} -3.32162 q^{83} +(-1.29070 - 3.21467i) q^{84} +0.700377 q^{85} +(15.4305 + 0.871636i) q^{86} +(4.12972 + 7.65633i) q^{87} +(-1.18638 + 6.94115i) q^{88} +1.26927i q^{89} +(2.52656 - 3.40830i) q^{90} -5.62558i q^{91} +(-6.29343 - 0.713283i) q^{92} +(-3.29674 - 6.11201i) q^{93} +(-1.06108 + 18.7842i) q^{94} -4.84194 q^{95} +(-2.06660 - 9.57753i) q^{96} +8.03979 q^{97} +(0.0797590 - 1.41196i) q^{98} +(-4.10241 + 6.24145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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