LMFDB - Embedded newform 420.2.n.b.71.9

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			71.9
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637711 - 1.26227i) q^{2} +(1.30156 - 1.14278i) q^{3} +(-1.18665 + 1.60993i) q^{4} +1.00000i q^{5} +(-2.27252 - 0.914147i) q^{6} +1.00000i q^{7} +(2.78890 + 0.471201i) q^{8} +(0.388091 - 2.97479i) q^{9} +O(q^{10})$	\(q+(-0.637711 - 1.26227i) q^{2} +(1.30156 - 1.14278i) q^{3} +(-1.18665 + 1.60993i) q^{4} +1.00000i q^{5} +(-2.27252 - 0.914147i) q^{6} +1.00000i q^{7} +(2.78890 + 0.471201i) q^{8} +(0.388091 - 2.97479i) q^{9} +(1.26227 - 0.637711i) q^{10} +5.64400 q^{11} +(0.295310 + 3.45149i) q^{12} -1.61019 q^{13} +(1.26227 - 0.637711i) q^{14} +(1.14278 + 1.30156i) q^{15} +(-1.18373 - 3.82084i) q^{16} -7.50301i q^{17} +(-4.00248 + 1.40718i) q^{18} -1.37110i q^{19} +(-1.60993 - 1.18665i) q^{20} +(1.14278 + 1.30156i) q^{21} +(-3.59924 - 7.12425i) q^{22} +7.52677 q^{23} +(4.16839 - 2.57382i) q^{24} -1.00000 q^{25} +(1.02683 + 2.03249i) q^{26} +(-2.89442 - 4.31536i) q^{27} +(-1.60993 - 1.18665i) q^{28} +4.39407i q^{29} +(0.914147 - 2.27252i) q^{30} +3.82849i q^{31} +(-4.06805 + 3.93078i) q^{32} +(7.34598 - 6.44987i) q^{33} +(-9.47082 + 4.78476i) q^{34} -1.00000 q^{35} +(4.32867 + 4.15483i) q^{36} -4.24761 q^{37} +(-1.73070 + 0.874368i) q^{38} +(-2.09574 + 1.84009i) q^{39} +(-0.471201 + 2.78890i) q^{40} +6.37874i q^{41} +(0.914147 - 2.27252i) q^{42} +1.27656i q^{43} +(-6.69744 + 9.08643i) q^{44} +(2.97479 + 0.388091i) q^{45} +(-4.79991 - 9.50081i) q^{46} -0.846593 q^{47} +(-5.90708 - 3.62028i) q^{48} -1.00000 q^{49} +(0.637711 + 1.26227i) q^{50} +(-8.57432 - 9.76558i) q^{51} +(1.91072 - 2.59228i) q^{52} -10.1584i q^{53} +(-3.60134 + 6.40549i) q^{54} +5.64400i q^{55} +(-0.471201 + 2.78890i) q^{56} +(-1.56687 - 1.78457i) q^{57} +(5.54650 - 2.80215i) q^{58} -5.48196 q^{59} +(-3.45149 + 0.295310i) q^{60} +6.86368 q^{61} +(4.83259 - 2.44147i) q^{62} +(2.97479 + 0.388091i) q^{63} +(7.55594 + 2.62827i) q^{64} -1.61019i q^{65} +(-12.8261 - 5.15945i) q^{66} +8.93621i q^{67} +(12.0793 + 8.90344i) q^{68} +(9.79651 - 8.60147i) q^{69} +(0.637711 + 1.26227i) q^{70} -11.3023 q^{71} +(2.48407 - 8.11353i) q^{72} +4.97379 q^{73} +(2.70875 + 5.36163i) q^{74} +(-1.30156 + 1.14278i) q^{75} +(2.20738 + 1.62702i) q^{76} +5.64400i q^{77} +(3.65917 + 1.47195i) q^{78} +6.47755i q^{79} +(3.82084 - 1.18373i) q^{80} +(-8.69877 - 2.30898i) q^{81} +(8.05169 - 4.06780i) q^{82} -1.90366 q^{83} +(-3.45149 + 0.295310i) q^{84} +7.50301 q^{85} +(1.61137 - 0.814078i) q^{86} +(5.02147 + 5.71912i) q^{87} +(15.7406 + 2.65946i) q^{88} -6.71482i q^{89} +(-1.40718 - 4.00248i) q^{90} -1.61019i q^{91} +(-8.93163 + 12.1176i) q^{92} +(4.37514 + 4.98300i) q^{93} +(0.539882 + 1.06863i) q^{94} +1.37110 q^{95} +(-0.802757 + 9.76502i) q^{96} -18.6630 q^{97} +(0.637711 + 1.26227i) q^{98} +(2.19039 - 16.7897i) 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 $

$2$	−0.637711	−	1.26227i	−0.450930	−	0.892559i
$2$	−0.637711	−	1.26227i	−0.450930	−	0.892559i
$3$	1.30156	−	1.14278i	0.751453	−	0.659786i
$3$	1.30156	−	1.14278i	0.751453	−	0.659786i
$4$	−1.18665	+	1.60993i	−0.593324	+	0.804964i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.27252	−	0.914147i	−0.927751	−	0.373199i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.78890	+	0.471201i	0.986025	+	0.166595i
$9$	0.388091	−	2.97479i	0.129364	−	0.991597i
$10$	1.26227	−	0.637711i	0.399165	−	0.201662i
$11$	5.64400			1.70173			0.850865	−	0.525385i	$-0.176079\pi$
$11$	5.64400			1.70173			0.850865	+	0.525385i	$0.176079\pi$
$12$	0.295310	+	3.45149i	0.0852487	+	0.996360i
$13$	−1.61019			−0.446585			−0.223293	−	0.974751i	$-0.571681\pi$
$13$	−1.61019			−0.446585			−0.223293	+	0.974751i	$0.571681\pi$
$14$	1.26227	−	0.637711i	0.337356	−	0.170436i
$15$	1.14278	+	1.30156i	0.295065	+	0.336060i
$16$	−1.18373	−	3.82084i	−0.295933	−	0.955209i
$17$		−	7.50301i		−	1.81975i	−0.414885	−	0.909874i	$-0.636178\pi$
$17$		−	7.50301i		−	1.81975i	0.414885	−	0.909874i	$-0.363822\pi$
$18$	−4.00248	+	1.40718i	−0.943393	+	0.331676i
$19$		−	1.37110i		−	0.314553i	−0.987555	−	0.157276i	$-0.949729\pi$
$19$		−	1.37110i		−	0.314553i	0.987555	−	0.157276i	$-0.0502713\pi$
$20$	−1.60993	−	1.18665i	−0.359991	−	0.265343i
$21$	1.14278	+	1.30156i	0.249376	+	0.284023i
$22$	−3.59924	−	7.12425i	−0.767361	−	1.51889i
$23$	7.52677			1.56944			0.784720	−	0.619850i	$-0.212807\pi$
$23$	7.52677			1.56944			0.784720	+	0.619850i	$0.212807\pi$
$24$	4.16839	−	2.57382i	0.850869	−	0.525378i
$25$	−1.00000			−0.200000
$26$	1.02683	+	2.03249i	0.201379	+	0.398604i
$27$	−2.89442	−	4.31536i	−0.557032	−	0.830491i
$28$	−1.60993	−	1.18665i	−0.304248	−	0.224255i
$29$			4.39407i			0.815958i	0.912991	+	0.407979i	$0.133766\pi$
$29$			4.39407i			0.815958i	−0.912991	+	0.407979i	$0.866234\pi$
$30$	0.914147	−	2.27252i	0.166900	−	0.414903i
$31$			3.82849i			0.687618i	0.939040	+	0.343809i	$0.111717\pi$
$31$			3.82849i			0.687618i	−0.939040	+	0.343809i	$0.888283\pi$
$32$	−4.06805	+	3.93078i	−0.719136	+	0.694870i
$33$	7.34598	−	6.44987i	1.27877	−	1.12278i
$34$	−9.47082	+	4.78476i	−1.62423	+	0.820579i
$35$	−1.00000			−0.169031
$36$	4.32867	+	4.15483i	0.721445	+	0.692472i
$37$	−4.24761			−0.698304			−0.349152	−	0.937066i	$-0.613530\pi$
$37$	−4.24761			−0.698304			−0.349152	+	0.937066i	$0.613530\pi$
$38$	−1.73070	+	0.874368i	−0.280757	+	0.141841i
$39$	−2.09574	+	1.84009i	−0.335588	+	0.294651i
$40$	−0.471201	+	2.78890i	−0.0745035	+	0.440964i
$41$			6.37874i			0.996192i	0.867122	+	0.498096i	$0.165967\pi$
$41$			6.37874i			0.996192i	−0.867122	+	0.498096i	$0.834033\pi$
$42$	0.914147	−	2.27252i	0.141056	−	0.350657i
$43$			1.27656i			0.194674i	0.995251	+	0.0973370i	$0.0310325\pi$
$43$			1.27656i			0.194674i	−0.995251	+	0.0973370i	$0.968968\pi$
$44$	−6.69744	+	9.08643i	−1.00968	+	1.36983i
$45$	2.97479	+	0.388091i	0.443456	+	0.0578532i
$46$	−4.79991	−	9.50081i	−0.707708	−	1.40082i
$47$	−0.846593			−0.123488			−0.0617441	−	0.998092i	$-0.519666\pi$
$47$	−0.846593			−0.123488			−0.0617441	+	0.998092i	$0.519666\pi$
$48$	−5.90708	−	3.62028i	−0.852613	−	0.522542i
$49$	−1.00000			−0.142857
$50$	0.637711	+	1.26227i	0.0901860	+	0.178512i
$51$	−8.57432	−	9.76558i	−1.20064	−	1.36746i
$52$	1.91072	−	2.59228i	0.264970	−	0.359485i
$53$		−	10.1584i		−	1.39537i	−0.716406	−	0.697684i	$-0.754214\pi$
$53$		−	10.1584i		−	1.39537i	0.716406	−	0.697684i	$-0.245786\pi$
$54$	−3.60134	+	6.40549i	−0.490080	+	0.871677i
$55$			5.64400i			0.761037i
$56$	−0.471201	+	2.78890i	−0.0629669	+	0.372683i
$57$	−1.56687	−	1.78457i	−0.207538	−	0.236372i
$58$	5.54650	−	2.80215i	0.728291	−	0.367940i
$59$	−5.48196			−0.713690			−0.356845	−	0.934164i	$-0.616148\pi$
$59$	−5.48196			−0.713690			−0.356845	+	0.934164i	$0.616148\pi$
$60$	−3.45149	+	0.295310i	−0.445586	+	0.0381244i
$61$	6.86368			0.878804			0.439402	−	0.898290i	$-0.355190\pi$
$61$	6.86368			0.878804			0.439402	+	0.898290i	$0.355190\pi$
$62$	4.83259	−	2.44147i	0.613740	−	0.310068i
$63$	2.97479	+	0.388091i	0.374789	+	0.0488949i
$64$	7.55594	+	2.62827i	0.944492	+	0.328533i
$65$		−	1.61019i		−	0.199719i
$66$	−12.8261	−	5.15945i	−1.57878	−	0.635084i
$67$			8.93621i			1.09173i	0.837873	+	0.545866i	$0.183799\pi$
$67$			8.93621i			1.09173i	−0.837873	+	0.545866i	$0.816201\pi$
$68$	12.0793	+	8.90344i	1.46483	+	1.07970i
$69$	9.79651	−	8.60147i	1.17936	−	1.03550i
$70$	0.637711	+	1.26227i	0.0762211	+	0.150870i
$71$	−11.3023			−1.34134			−0.670668	−	0.741757i	$-0.733993\pi$
$71$	−11.3023			−1.34134			−0.670668	+	0.741757i	$0.733993\pi$
$72$	2.48407	−	8.11353i	0.292751	−	0.956189i
$73$	4.97379			0.582139			0.291069	−	0.956702i	$-0.405989\pi$
$73$	4.97379			0.582139			0.291069	+	0.956702i	$0.405989\pi$
$74$	2.70875	+	5.36163i	0.314886	+	0.623277i
$75$	−1.30156	+	1.14278i	−0.150291	+	0.131957i
$76$	2.20738	+	1.62702i	0.253203	+	0.186632i
$77$			5.64400i			0.643193i
$78$	3.65917	+	1.47195i	0.414320	+	0.166665i
$79$			6.47755i			0.728781i	0.931246	+	0.364390i	$0.118723\pi$
$79$			6.47755i			0.728781i	−0.931246	+	0.364390i	$0.881277\pi$
$80$	3.82084	−	1.18373i	0.427182	−	0.132345i
$81$	−8.69877	−	2.30898i	−0.966530	−	0.256553i
$82$	8.05169	−	4.06780i	0.889161	−	0.449213i
$83$	−1.90366			−0.208953			−0.104477	−	0.994527i	$-0.533317\pi$
$83$	−1.90366			−0.208953			−0.104477	+	0.994527i	$0.533317\pi$
$84$	−3.45149	+	0.295310i	−0.376589	+	0.0322210i
$85$	7.50301			0.813816
$86$	1.61137	−	0.814078i	0.173758	−	0.0877843i
$87$	5.02147	+	5.71912i	0.538358	+	0.613154i
$88$	15.7406	+	2.65946i	1.67795	+	0.283499i
$89$		−	6.71482i		−	0.711769i	−0.934530	−	0.355885i	$-0.884180\pi$
$89$		−	6.71482i		−	0.711769i	0.934530	−	0.355885i	$-0.115820\pi$
$90$	−1.40718	−	4.00248i	−0.148330	−	0.421898i
$91$		−	1.61019i		−	0.168793i
$92$	−8.93163	+	12.1176i	−0.931187	+	1.26334i
$93$	4.37514	+	4.98300i	0.453681	+	0.516713i
$94$	0.539882	+	1.06863i	0.0556845	+	0.110221i
$95$	1.37110			0.140672
$96$	−0.802757	+	9.76502i	−0.0819310	+	0.996638i
$97$	−18.6630			−1.89495			−0.947473	−	0.319837i	$-0.896372\pi$
$97$	−18.6630			−1.89495			−0.947473	+	0.319837i	$0.896372\pi$
$98$	0.637711	+	1.26227i	0.0644186	+	0.127508i
$99$	2.19039	−	16.7897i	0.220142	−	1.68743i
$100$	1.18665	−	1.60993i	0.118665	−	0.160993i
$101$			13.8901i			1.38211i	0.722801	+	0.691056i	$0.242854\pi$
$101$			13.8901i			1.38211i	−0.722801	+	0.691056i	$0.757146\pi$
$102$	−6.85886	+	17.0507i	−0.679128	+	1.68827i
$103$		−	7.55760i		−	0.744673i	−0.928098	−	0.372336i	$-0.878557\pi$
$103$		−	7.55760i		−	0.744673i	0.928098	−	0.372336i	$-0.121443\pi$
$104$	−4.49065	−	0.758721i	−0.440344	−	0.0743988i
$105$	−1.30156	+	1.14278i	−0.127019	+	0.111524i
$106$	−12.8227	+	6.47814i	−1.24545	+	0.629213i
$107$	17.5622			1.69780			0.848902	−	0.528550i	$-0.177264\pi$
$107$	17.5622			1.69780			0.848902	+	0.528550i	$0.177264\pi$
$108$	10.3821	+	0.461008i	0.999016	+	0.0443605i
$109$	−11.4817			−1.09974			−0.549872	−	0.835249i	$-0.685324\pi$
$109$	−11.4817			−1.09974			−0.549872	+	0.835249i	$0.685324\pi$
$110$	7.12425	−	3.59924i	0.679270	−	0.343174i
$111$	−5.52850	+	4.85410i	−0.524742	+	0.460731i
$112$	3.82084	−	1.18373i	0.361035	−	0.111852i
$113$			14.1781i			1.33376i	0.745165	+	0.666880i	$0.232371\pi$
$113$			14.1781i			1.33376i	−0.745165	+	0.666880i	$0.767629\pi$
$114$	−1.25339	+	3.11586i	−0.117391	+	0.291827i
$115$			7.52677i			0.701875i
$116$	−7.07413	−	5.21421i	−0.656816	−	0.484128i
$117$	−0.624899	+	4.78997i	−0.0577719	+	0.442832i
$118$	3.49591	+	6.91971i	0.321824	+	0.637011i
$119$	7.50301			0.687800
$120$	2.57382	+	4.16839i	0.234956	+	0.380520i
$121$	20.8547			1.89588
$122$	−4.37705	−	8.66382i	−0.396279	−	0.784385i
$123$	7.28952	+	8.30228i	0.657274	+	0.748592i
$124$	−6.16360	−	4.54308i	−0.553507	−	0.407980i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.40718	−	4.00248i	−0.125362	−	0.356569i
$127$			3.55316i			0.315292i	0.987496	+	0.157646i	$0.0503905\pi$
$127$			3.55316i			0.315292i	−0.987496	+	0.157646i	$0.949609\pi$
$128$	−1.50093	−	11.2137i	−0.132664	−	0.991161i
$129$	1.45883	+	1.66152i	0.128443	+	0.146288i
$130$	−2.03249	+	1.02683i	−0.178261	+	0.0900592i
$131$	−2.30148			−0.201081			−0.100540	−	0.994933i	$-0.532057\pi$
$131$	−2.30148			−0.201081			−0.100540	+	0.994933i	$0.532057\pi$
$132$	1.66673	+	19.4802i	0.145070	+	1.69553i
$133$	1.37110			0.118890
$134$	11.2799	−	5.69872i	0.974435	−	0.492295i
$135$	4.31536	−	2.89442i	0.371407	−	0.249112i
$136$	3.53543	−	20.9252i	0.303161	−	1.79432i
$137$		−	5.21419i		−	0.445478i	−0.974878	−	0.222739i	$-0.928500\pi$
$137$		−	5.21419i		−	0.445478i	0.974878	−	0.222739i	$-0.0714998\pi$
$138$	−17.1047	−	6.88058i	−1.45605	−	0.585714i
$139$			5.32412i			0.451586i	0.974175	+	0.225793i	$0.0724972\pi$
$139$			5.32412i			0.451586i	−0.974175	+	0.225793i	$0.927503\pi$
$140$	1.18665	−	1.60993i	0.100290	−	0.136064i
$141$	−1.10189	+	0.967472i	−0.0927956	+	0.0814758i
$142$	7.20761	+	14.2666i	0.604849	+	1.19722i
$143$	−9.08788			−0.759967
$144$	−11.8256	+	2.03852i	−0.985465	+	0.169877i
$145$	−4.39407			−0.364907
$146$	−3.17185	−	6.27827i	−0.262504	−	0.519593i
$147$	−1.30156	+	1.14278i	−0.107350	+	0.0942552i
$148$	5.04043	−	6.83835i	0.414320	−	0.562109i
$149$			17.4146i			1.42666i	0.700826	+	0.713332i	$0.252815\pi$
$149$			17.4146i			1.42666i	−0.700826	+	0.713332i	$0.747185\pi$
$150$	2.27252	+	0.914147i	0.185550	+	0.0746398i
$151$			3.99634i			0.325218i	0.986691	+	0.162609i	$0.0519909\pi$
$151$			3.99634i			0.325218i	−0.986691	+	0.162609i	$0.948009\pi$
$152$	0.646066	−	3.82387i	0.0524029	−	0.310157i
$153$	−22.3199	−	2.91185i	−1.80446	−	0.235409i
$154$	7.12425	−	3.59924i	0.574088	−	0.290035i
$155$	−3.82849			−0.307512
$156$	−0.475504	−	5.55754i	−0.0380708	−	0.444959i
$157$	−0.796159			−0.0635404			−0.0317702	−	0.999495i	$-0.510114\pi$
$157$	−0.796159			−0.0635404			−0.0317702	+	0.999495i	$0.510114\pi$
$158$	8.17641	−	4.13080i	0.650480	−	0.328629i
$159$	−11.6089	−	13.2218i	−0.920644	−	1.04855i
$160$	−3.93078	−	4.06805i	−0.310755	−	0.321607i
$161$			7.52677i			0.593193i
$162$	2.63275	+	12.4527i	0.206848	+	0.978373i
$163$			15.8094i			1.23829i	0.785276	+	0.619146i	$0.212521\pi$
$163$			15.8094i			1.23829i	−0.785276	+	0.619146i	$0.787479\pi$
$164$	−10.2693	−	7.56932i	−0.801898	−	0.591065i
$165$	6.44987	+	7.34598i	0.502122	+	0.571883i
$166$	1.21398	+	2.40293i	0.0942233	+	0.186503i
$167$	−17.6227			−1.36369			−0.681845	−	0.731497i	$-0.738822\pi$
$167$	−17.6227			−1.36369			−0.681845	+	0.731497i	$0.738822\pi$
$168$	2.57382	+	4.16839i	0.198574	+	0.321598i
$169$	−10.4073			−0.800562
$170$	−4.78476	−	9.47082i	−0.366974	−	0.726379i
$171$	−4.07875	−	0.532113i	−0.311910	−	0.0406917i
$172$	−2.05517	−	1.51483i	−0.156705	−	0.115505i
$173$		−	13.9973i		−	1.06419i	−0.846684	−	0.532096i	$-0.821405\pi$
$173$		−	13.9973i		−	1.06419i	0.846684	−	0.532096i	$-0.178595\pi$
$174$	4.01682	−	9.98559i	0.304515	−	0.757006i
$175$		−	1.00000i		−	0.0755929i
$176$	−6.68098	−	21.5648i	−0.503597	−	1.62551i
$177$	−7.13507	+	6.26469i	−0.536305	+	0.470883i
$178$	−8.47591	+	4.28212i	−0.635296	+	0.320958i
$179$	11.0438			0.825450			0.412725	−	0.910856i	$-0.364577\pi$
$179$	11.0438			0.825450			0.412725	+	0.910856i	$0.364577\pi$
$180$	−4.15483	+	4.32867i	−0.309683	+	0.322640i
$181$	−1.73431			−0.128910			−0.0644550	−	0.997921i	$-0.520531\pi$
$181$	−1.73431			−0.128910			−0.0644550	+	0.997921i	$0.520531\pi$
$182$	−2.03249	+	1.02683i	−0.150658	+	0.0761140i
$183$	8.93346	−	7.84370i	0.660380	−	0.579823i
$184$	20.9914	+	3.54662i	1.54751	+	0.261461i
$185$		−	4.24761i		−	0.312291i
$186$	3.49981	−	8.70032i	0.256618	−	0.637938i
$187$		−	42.3470i		−	3.09672i
$188$	1.00461	−	1.36295i	0.0732686	−	0.0994035i
$189$	4.31536	−	2.89442i	0.313896	−	0.210538i
$190$	−0.874368	−	1.73070i	−0.0634333	−	0.125558i
$191$	0.197305			0.0142765			0.00713825	−	0.999975i	$-0.497728\pi$
$191$	0.197305			0.0142765			0.00713825	+	0.999975i	$0.497728\pi$
$192$	12.8380	−	5.21397i	0.926504	−	0.376286i
$193$	−4.45052			−0.320356			−0.160178	−	0.987088i	$-0.551207\pi$
$193$	−4.45052			−0.320356			−0.160178	+	0.987088i	$0.551207\pi$
$194$	11.9016	+	23.5578i	0.854488	+	1.69135i
$195$	−1.84009	−	2.09574i	−0.131772	−	0.150079i
$196$	1.18665	−	1.60993i	0.0847606	−	0.114995i
$197$		−	12.0984i		−	0.861978i	−0.902357	−	0.430989i	$-0.858165\pi$
$197$		−	12.0984i		−	0.861978i	0.902357	−	0.430989i	$-0.141835\pi$
$198$	−22.5900	+	7.94214i	−1.60540	+	0.564423i
$199$		−	5.15325i		−	0.365304i	−0.983178	−	0.182652i	$-0.941532\pi$
$199$		−	5.15325i		−	0.365304i	0.983178	−	0.182652i	$-0.0584681\pi$
$200$	−2.78890	−	0.471201i	−0.197205	−	0.0333190i
$201$	10.2122	+	11.6310i	0.720310	+	0.820385i
$202$	17.5330	−	8.85785i	1.23362	−	0.623236i
$203$	−4.39407			−0.308403
$204$	25.8966	−	2.21571i	1.81312	−	0.155131i
$205$	−6.37874			−0.445511
$206$	−9.53973	+	4.81957i	−0.664665	+	0.335795i
$207$	2.92107	−	22.3906i	0.203029	−	1.55625i
$208$	1.90603	+	6.15225i	0.132159	+	0.426582i
$209$		−	7.73851i		−	0.535284i
$210$	2.27252	+	0.914147i	0.156819	+	0.0630821i
$211$		−	5.63197i		−	0.387721i	−0.981029	−	0.193861i	$-0.937899\pi$
$211$		−	5.63197i		−	0.387721i	0.981029	−	0.193861i	$-0.0621009\pi$
$212$	16.3543	+	12.0545i	1.12322	+	0.827905i
$213$	−14.7106	+	12.9161i	−1.00795	+	0.884996i
$214$	−11.1996	−	22.1683i	−0.765591	−	1.51539i
$215$	−1.27656			−0.0870608
$216$	−6.03885	−	13.3990i	−0.410892	−	0.911684i
$217$	−3.82849			−0.259895
$218$	7.32199	+	14.4930i	0.495908	+	0.981587i
$219$	6.47367	−	5.68397i	0.437450	−	0.384087i
$220$	−9.08643	−	6.69744i	−0.612607	−	0.451541i
$221$			12.0812i			0.812672i
$222$	9.65278	+	3.88294i	0.647852	+	0.260606i
$223$			3.09304i			0.207125i	0.994623	+	0.103563i	$0.0330242\pi$
$223$			3.09304i			0.207125i	−0.994623	+	0.103563i	$0.966976\pi$
$224$	−3.93078	−	4.06805i	−0.262636	−	0.271808i
$225$	−0.388091	+	2.97479i	−0.0258727	+	0.198319i
$226$	17.8965	−	9.04152i	1.19046	−	0.601433i
$227$	8.40329			0.557746			0.278873	−	0.960328i	$-0.410039\pi$
$227$	8.40329			0.557746			0.278873	+	0.960328i	$0.410039\pi$
$228$	4.73235	−	0.404901i	0.313408	−	0.0268152i
$229$	−12.9422			−0.855244			−0.427622	−	0.903958i	$-0.640649\pi$
$229$	−12.9422			−0.855244			−0.427622	+	0.903958i	$0.640649\pi$
$230$	9.50081	−	4.79991i	0.626465	−	0.316497i
$231$	6.44987	+	7.34598i	0.424370	+	0.483330i
$232$	−2.07049	+	12.2546i	−0.135934	+	0.804555i
$233$		−	9.92492i		−	0.650203i	−0.945679	−	0.325101i	$-0.894602\pi$
$233$		−	9.92492i		−	0.650203i	0.945679	−	0.325101i	$-0.105398\pi$
$234$	6.44473	−	2.26582i	0.421305	−	0.148122i
$235$		−	0.846593i		−	0.0552256i
$236$	6.50516	−	8.82555i	0.423450	−	0.574494i
$237$	7.40243	+	8.43088i	0.480840	+	0.547645i
$238$	−4.78476	−	9.47082i	−0.310150	−	0.613902i
$239$	5.73282			0.370825			0.185413	−	0.982661i	$-0.440638\pi$
$239$	5.73282			0.370825			0.185413	+	0.982661i	$0.440638\pi$
$240$	3.62028	−	5.90708i	0.233688	−	0.381300i
$241$	−26.9631			−1.73684			−0.868422	−	0.495826i	$-0.834865\pi$
$241$	−26.9631			−1.73684			−0.868422	+	0.495826i	$0.834865\pi$
$242$	−13.2993	−	26.3243i	−0.854911	−	1.69219i
$243$	−13.9606	+	6.93555i	−0.895573	+	0.444916i
$244$	−8.14478	+	11.0500i	−0.521416	+	0.707406i
$245$		−	1.00000i		−	0.0638877i
$246$	5.83111	−	14.4958i	0.371778	−	0.924219i
$247$			2.20773i			0.140475i
$248$	−1.80399	+	10.6773i	−0.114554	+	0.678009i
$249$	−2.47771	+	2.17547i	−0.157019	+	0.137865i
$250$	−1.26227	+	0.637711i	−0.0798329	+	0.0403324i
$251$	−15.7543			−0.994406			−0.497203	−	0.867634i	$-0.665639\pi$
$251$	−15.7543			−0.994406			−0.497203	+	0.867634i	$0.665639\pi$
$252$	−4.15483	+	4.32867i	−0.261730	+	0.272681i
$253$	42.4811			2.67076
$254$	4.48505	−	2.26589i	0.281417	−	0.142175i
$255$	9.76558	−	8.57432i	0.611544	−	0.536945i
$256$	−13.1976	+	9.04568i	−0.824848	+	0.565355i
$257$		−	19.8316i		−	1.23706i	−0.785762	−	0.618529i	$-0.787729\pi$
$257$		−	19.8316i		−	1.23706i	0.785762	−	0.618529i	$-0.212271\pi$
$258$	1.16697	−	2.90101i	0.0726521	−	0.180609i
$259$		−	4.24761i		−	0.263934i
$260$	2.59228	+	1.91072i	0.160766	+	0.118498i
$261$	13.0714	+	1.70530i	0.809101	+	0.105555i
$262$	1.46768	+	2.90508i	0.0906734	+	0.179477i
$263$	−5.67244			−0.349778			−0.174889	−	0.984588i	$-0.555957\pi$
$263$	−5.67244			−0.349778			−0.174889	+	0.984588i	$0.555957\pi$
$264$	23.5264	−	14.5266i	1.44795	−	0.894051i
$265$	10.1584			0.624027
$266$	−0.874368	−	1.73070i	−0.0536110	−	0.106116i
$267$	−7.67358	−	8.73970i	−0.469616	−	0.534861i
$268$	−14.3866	−	10.6041i	−0.878804	−	0.647751i
$269$			5.37729i			0.327859i	0.986472	+	0.163930i	$0.0524170\pi$
$269$			5.37729i			0.327859i	−0.986472	+	0.163930i	$0.947583\pi$
$270$	−6.40549	−	3.60134i	−0.389826	−	0.219171i
$271$			13.7741i			0.836720i	0.908281	+	0.418360i	$0.137395\pi$
$271$			13.7741i			0.836720i	−0.908281	+	0.418360i	$0.862605\pi$
$272$	−28.6678	+	8.88155i	−1.73824	+	0.538523i
$273$	−1.84009	−	2.09574i	−0.111368	−	0.126840i
$274$	−6.58172	+	3.32515i	−0.397616	+	0.200880i
$275$	−5.64400			−0.340346
$276$	2.22273	+	25.9786i	0.133793	+	1.56373i
$277$	−3.27242			−0.196620			−0.0983102	−	0.995156i	$-0.531344\pi$
$277$	−3.27242			−0.196620			−0.0983102	+	0.995156i	$0.531344\pi$
$278$	6.72047	−	3.39525i	0.403067	−	0.203633i
$279$	11.3890	+	1.48580i	0.681840	+	0.0889528i
$280$	−2.78890	−	0.471201i	−0.166669	−	0.0281597i
$281$		−	11.8151i		−	0.704829i	−0.935844	−	0.352415i	$-0.885361\pi$
$281$		−	11.8151i		−	0.704829i	0.935844	−	0.352415i	$-0.114639\pi$
$282$	1.92390	+	0.773910i	0.114566	+	0.0460857i
$283$		−	10.5546i		−	0.627408i	−0.949521	−	0.313704i	$-0.898430\pi$
$283$		−	10.5546i		−	0.627408i	0.949521	−	0.313704i	$-0.101570\pi$
$284$	13.4119	−	18.1959i	0.795848	−	1.07973i
$285$	1.78457	−	1.56687i	0.105709	−	0.0928136i
$286$	5.79545	+	11.4714i	0.342692	+	0.678316i
$287$	−6.37874			−0.376525
$288$	10.1145	+	13.6271i	0.596001	+	0.802984i
$289$	−39.2952			−2.31148
$290$	2.80215	+	5.54650i	0.164548	+	0.325701i
$291$	−24.2910	+	21.3278i	−1.42396	+	1.25026i
$292$	−5.90215	+	8.00745i	−0.345397	+	0.468600i
$293$		−	7.35644i		−	0.429768i	−0.976640	−	0.214884i	$-0.931063\pi$
$293$		−	7.35644i		−	0.429768i	0.976640	−	0.214884i	$-0.0689373\pi$
$294$	2.27252	+	0.914147i	0.132536	+	0.0533141i
$295$		−	5.48196i		−	0.319172i
$296$	−11.8462	−	2.00148i	−0.688545	−	0.116334i
$297$	−16.3361	−	24.3559i	−0.947917	−	1.41327i
$298$	21.9820	−	11.1055i	1.27338	−	0.643325i
$299$	−12.1195			−0.700889
$300$	−0.295310	−	3.45149i	−0.0170497	−	0.199272i
$301$	−1.27656			−0.0735798
$302$	5.04446	−	2.54851i	0.290276	−	0.146650i
$303$	15.8733	+	18.0787i	0.911899	+	1.03859i
$304$	−5.23876	+	1.62302i	−0.300463	+	0.0930864i
$305$			6.86368i			0.393013i
$306$	10.5581	+	30.0306i	0.603567	+	1.71674i
$307$			16.7203i			0.954277i	0.878828	+	0.477139i	$0.158326\pi$
$307$			16.7203i			0.954277i	−0.878828	+	0.477139i	$0.841674\pi$
$308$	−9.08643	−	6.69744i	−0.517747	−	0.381622i
$309$	−8.63671	−	9.83664i	−0.491325	−	0.559587i
$310$	2.44147	+	4.83259i	0.138666	+	0.274473i
$311$	27.1499			1.53953			0.769765	−	0.638328i	$-0.220373\pi$
$311$	27.1499			1.53953			0.769765	+	0.638328i	$0.220373\pi$
$312$	−6.71188	+	4.14432i	−0.379985	+	0.234626i
$313$	−13.2877			−0.751062			−0.375531	−	0.926810i	$-0.622540\pi$
$313$	−13.2877			−0.751062			−0.375531	+	0.926810i	$0.622540\pi$
$314$	0.507720	+	1.00497i	0.0286523	+	0.0567136i
$315$	−0.388091	+	2.97479i	−0.0218665	+	0.167611i
$316$	−10.4284	−	7.68657i	−0.586642	−	0.432403i
$317$			13.5847i			0.762994i	0.924370	+	0.381497i	$0.124591\pi$
$317$			13.5847i			0.762994i	−0.924370	+	0.381497i	$0.875409\pi$
$318$	−9.28630	+	23.0852i	−0.520750	+	1.29455i
$319$			24.8001i			1.38854i
$320$	−2.62827	+	7.55594i	−0.146925	+	0.422390i
$321$	22.8582	−	20.0698i	1.27582	−	1.12019i
$322$	9.50081	−	4.79991i	0.529460	−	0.267488i
$323$	−10.2874			−0.572406
$324$	14.0397	−	11.2644i	0.779982	−	0.625802i
$325$	1.61019			0.0893170
$326$	19.9558	−	10.0819i	1.10525	−	0.558383i
$327$	−14.9440	+	13.1211i	−0.826407	+	0.725597i
$328$	−3.00567	+	17.7897i	−0.165960	+	0.982271i
$329$		−	0.846593i		−	0.0466742i
$330$	5.15945	−	12.8261i	0.284018	−	0.706053i
$331$			19.8508i			1.09110i	0.838078	+	0.545550i	$0.183679\pi$
$331$			19.8508i			1.09110i	−0.838078	+	0.545550i	$0.816321\pi$
$332$	2.25897	−	3.06475i	0.123977	−	0.168200i
$333$	−1.64846	+	12.6358i	−0.0903352	+	0.692436i
$334$	11.2382	+	22.2447i	0.614928	+	1.21717i
$335$	−8.93621			−0.488237
$336$	3.62028	−	5.90708i	0.197502	−	0.322258i
$337$	7.49420			0.408235			0.204118	−	0.978946i	$-0.434568\pi$
$337$	7.49420			0.408235			0.204118	+	0.978946i	$0.434568\pi$
$338$	6.63686	+	13.1368i	0.360997	+	0.714549i
$339$	16.2025	+	18.4535i	0.879997	+	1.00226i
$340$	−8.90344	+	12.0793i	−0.482857	+	0.655092i
$341$			21.6080i			1.17014i
$342$	1.92939	+	5.48781i	0.104330	+	0.296747i
$343$		−	1.00000i		−	0.0539949i
$344$	−0.601518	+	3.56021i	−0.0324317	+	0.191953i
$345$	8.60147	+	9.79651i	0.463088	+	0.527426i
$346$	−17.6683	+	8.92621i	−0.949855	+	0.479876i
$347$	29.4334			1.58007			0.790034	−	0.613064i	$-0.210063\pi$
$347$	29.4334			1.58007			0.790034	+	0.613064i	$0.210063\pi$
$348$	−15.1661	+	1.29761i	−0.812987	+	0.0695593i
$349$	26.2559			1.40545			0.702723	−	0.711464i	$-0.251967\pi$
$349$	26.2559			1.40545			0.702723	+	0.711464i	$0.251967\pi$
$350$	−1.26227	+	0.637711i	−0.0674711	+	0.0340871i
$351$	4.66055	+	6.94853i	0.248762	+	0.370885i
$352$	−22.9600	+	22.1853i	−1.22377	+	1.18248i
$353$			19.2513i			1.02464i	0.858793	+	0.512322i	$0.171215\pi$
$353$			19.2513i			1.02464i	−0.858793	+	0.512322i	$0.828785\pi$
$354$	12.4578	+	5.01132i	0.662127	+	0.266348i
$355$		−	11.3023i		−	0.599864i
$356$	10.8104	+	7.96813i	0.572948	+	0.422310i
$357$	9.76558	−	8.57432i	0.516849	−	0.453801i
$358$	−7.04273	−	13.9402i	−0.372220	−	0.736763i
$359$	−3.84879			−0.203131			−0.101566	−	0.994829i	$-0.532385\pi$
$359$	−3.84879			−0.203131			−0.101566	+	0.994829i	$0.532385\pi$
$360$	8.11353	+	2.48407i	0.427621	+	0.130922i
$361$	17.1201			0.901057
$362$	1.10599	+	2.18916i	0.0581294	+	0.115060i
$363$	27.1436	−	23.8324i	1.42467	−	1.25088i
$364$	2.59228	+	1.91072i	0.135872	+	0.100149i
$365$			4.97379i			0.260340i
$366$	−15.5978	−	6.27442i	−0.815312	−	0.327969i
$367$		−	9.05402i		−	0.472616i	−0.971678	−	0.236308i	$-0.924063\pi$
$367$		−	9.05402i		−	0.472616i	0.971678	−	0.236308i	$-0.0759375\pi$
$368$	−8.90967	−	28.7586i	−0.464449	−	1.49914i
$369$	18.9754	+	2.47553i	0.987821	+	0.128871i
$370$	−5.36163	+	2.70875i	−0.278738	+	0.140821i
$371$	10.1584			0.527399
$372$	−13.2140	+	1.13059i	−0.685115	+	0.0586185i
$373$	−6.90250			−0.357398			−0.178699	−	0.983904i	$-0.557189\pi$
$373$	−6.90250			−0.357398			−0.178699	+	0.983904i	$0.557189\pi$
$374$	−53.4533	+	27.0052i	−2.76400	+	1.39640i
$375$	−1.14278	−	1.30156i	−0.0590131	−	0.0672120i
$376$	−2.36106	−	0.398916i	−0.121763	−	0.0205725i
$377$		−	7.07526i		−	0.364394i
$378$	−6.40549	−	3.60134i	−0.329463	−	0.185233i
$379$			10.7959i			0.554547i	0.960791	+	0.277274i	$0.0894309\pi$
$379$			10.7959i			0.554547i	−0.960791	+	0.277274i	$0.910569\pi$
$380$	−1.62702	+	2.20738i	−0.0834642	+	0.113236i
$381$	4.06050	+	4.62464i	0.208026	+	0.236927i
$382$	−0.125824	−	0.249052i	−0.00643770	−	0.0127426i
$383$	−27.3393			−1.39697			−0.698485	−	0.715624i	$-0.746142\pi$
$383$	−27.3393			−1.39697			−0.698485	+	0.715624i	$0.746142\pi$
$384$	−14.7684	−	12.8800i	−0.753646	−	0.657281i
$385$	−5.64400			−0.287645
$386$	2.83815	+	5.61776i	0.144458	+	0.285936i
$387$	3.79751	+	0.495423i	0.193038	+	0.0251837i
$388$	22.1465	−	30.0461i	1.12432	−	1.52536i
$389$		−	23.4407i		−	1.18849i	−0.804284	−	0.594245i	$-0.797451\pi$
$389$		−	23.4407i		−	1.18849i	0.804284	−	0.594245i	$-0.202549\pi$
$390$	−1.47195	+	3.65917i	−0.0745349	+	0.185289i
$391$		−	56.4735i		−	2.85599i
$392$	−2.78890	−	0.471201i	−0.140861	−	0.0237993i
$393$	−2.99550	+	2.63009i	−0.151103	+	0.132670i
$394$	−15.2715	+	7.71532i	−0.769367	+	0.388692i
$395$	−6.47755			−0.325921
$396$	24.4310	+	23.4499i	1.22770	+	1.17840i
$397$	34.2375			1.71833			0.859164	−	0.511700i	$-0.170984\pi$
$397$	34.2375			1.71833			0.859164	+	0.511700i	$0.170984\pi$
$398$	−6.50478	+	3.28628i	−0.326055	+	0.164726i
$399$	1.78457	−	1.56687i	0.0893401	−	0.0784418i
$400$	1.18373	+	3.82084i	0.0591865	+	0.191042i
$401$		−	17.5199i		−	0.874901i	−0.899242	−	0.437451i	$-0.855882\pi$
$401$		−	17.5199i		−	0.874901i	0.899242	−	0.437451i	$-0.144118\pi$
$402$	8.16901	−	20.3077i	0.407433	−	1.01286i
$403$		−	6.16458i		−	0.307080i
$404$	−22.3620	−	16.4826i	−1.11255	−	0.820041i
$405$	2.30898	−	8.69877i	0.114734	−	0.432245i
$406$	2.80215	+	5.54650i	0.139068	+	0.275268i
$407$	−23.9735			−1.18832
$408$	−19.3114	−	31.2755i	−0.956055	−	1.54837i
$409$	21.7658			1.07625			0.538124	−	0.842866i	$-0.319133\pi$
$409$	21.7658			1.07625			0.538124	+	0.842866i	$0.319133\pi$
$410$	4.06780	+	8.05169i	0.200894	+	0.397645i
$411$	−5.95869	−	6.78656i	−0.293921	−	0.334756i
$412$	12.1672	+	8.96822i	0.599435	+	0.441832i
$413$		−	5.48196i		−	0.269749i
$414$	−30.1257	+	10.5915i	−1.48060	+	0.520546i
$415$		−	1.90366i		−	0.0934468i
$416$	6.55031	−	6.32928i	0.321155	−	0.310318i
$417$	6.08431	+	6.92963i	0.297950	+	0.339345i
$418$	−9.76808	+	4.93493i	−0.477772	+	0.241375i
$419$	24.9087			1.21687			0.608435	−	0.793604i	$-0.291798\pi$
$419$	24.9087			1.21687			0.608435	+	0.793604i	$0.291798\pi$
$420$	−0.295310	−	3.45149i	−0.0144097	−	0.168416i
$421$	31.9855			1.55888			0.779438	−	0.626479i	$-0.215505\pi$
$421$	31.9855			1.55888			0.779438	+	0.626479i	$0.215505\pi$
$422$	−7.10907	+	3.59157i	−0.346064	+	0.174835i
$423$	−0.328555	+	2.51844i	−0.0159749	+	0.122451i
$424$	4.78666	−	28.3308i	0.232461	−	1.37587i
$425$			7.50301i			0.363949i
$426$	25.6847	+	10.3320i	1.24443	+	0.500586i
$427$			6.86368i			0.332157i
$428$	−20.8402	+	28.2739i	−1.00735	+	1.36667i
$429$	−11.8284	+	10.3855i	−0.571080	+	0.501416i
$430$	0.814078	+	1.61137i	0.0392583	+	0.0777069i
$431$	38.8415			1.87093			0.935463	−	0.353423i	$-0.114982\pi$
$431$	38.8415			1.87093			0.935463	+	0.353423i	$0.114982\pi$
$432$	−13.0621	+	16.1673i	−0.628449	+	0.777851i
$433$	−33.0897			−1.59019			−0.795095	−	0.606484i	$-0.792579\pi$
$433$	−33.0897			−1.59019			−0.795095	+	0.606484i	$0.792579\pi$
$434$	2.44147	+	4.83259i	0.117195	+	0.231972i
$435$	−5.71912	+	5.02147i	−0.274211	+	0.240761i
$436$	13.6247	−	18.4847i	0.652505	−	0.885254i
$437$		−	10.3200i		−	0.493672i
$438$	−11.3030	−	4.54678i	−0.540080	−	0.217254i
$439$			6.51638i			0.311010i	0.987835	+	0.155505i	$0.0497004\pi$
$439$			6.51638i			0.311010i	−0.987835	+	0.155505i	$0.950300\pi$
$440$	−2.65946	+	15.7406i	−0.126785	+	0.750401i
$441$	−0.388091	+	2.97479i	−0.0184805	+	0.141657i
$442$	15.2498	−	7.70434i	0.725358	−	0.366458i
$443$	−23.9687			−1.13879			−0.569394	−	0.822065i	$-0.692822\pi$
$443$	−23.9687			−1.13879			−0.569394	+	0.822065i	$0.692822\pi$
$444$	−1.25436	−	14.6606i	−0.0595294	−	0.695762i
$445$	6.71482			0.318313
$446$	3.90425	−	1.97247i	0.184872	−	0.0933991i
$447$	19.9012	+	22.6661i	0.941293	+	1.07207i
$448$	−2.62827	+	7.55594i	−0.124174	+	0.356985i
$449$		−	26.3914i		−	1.24549i	−0.782427	−	0.622743i	$-0.786018\pi$
$449$		−	26.3914i		−	1.24549i	0.782427	−	0.622743i	$-0.213982\pi$
$450$	4.00248	−	1.40718i	0.188679	−	0.0663352i
$451$			36.0016i			1.69525i
$452$	−22.8257	−	16.8244i	−1.07363	−	0.791352i
$453$	4.56696	+	5.20146i	0.214574	+	0.244386i
$454$	−5.35887	−	10.6072i	−0.251504	−	0.497821i
$455$	1.61019			0.0754866
$456$	−3.52897	−	5.71529i	−0.165259	−	0.267643i
$457$	4.98415			0.233149			0.116574	−	0.993182i	$-0.462809\pi$
$457$	4.98415			0.233149			0.116574	+	0.993182i	$0.462809\pi$
$458$	8.25338	+	16.3365i	0.385655	+	0.763356i
$459$	−32.3782	+	21.7169i	−1.51128	+	1.01366i
$460$	−12.1176	−	8.93163i	−0.564984	−	0.416439i
$461$			5.47805i			0.255138i	0.991830	+	0.127569i	$0.0407174\pi$
$461$			5.47805i			0.255138i	−0.991830	+	0.127569i	$0.959283\pi$
$462$	5.15945	−	12.8261i	0.240039	−	0.596723i
$463$		−	8.52800i		−	0.396330i	−0.980169	−	0.198165i	$-0.936502\pi$
$463$		−	8.52800i		−	0.396330i	0.980169	−	0.198165i	$-0.0634981\pi$
$464$	16.7890	−	5.20139i	0.779410	−	0.241469i
$465$	−4.98300	+	4.37514i	−0.231081	+	0.202892i
$466$	−12.5279	+	6.32923i	−0.580345	+	0.293196i
$467$	20.0495			0.927782			0.463891	−	0.885892i	$-0.346453\pi$
$467$	20.0495			0.927782			0.463891	+	0.885892i	$0.346453\pi$
$468$	−6.96996	−	6.69005i	−0.322187	−	0.309248i
$469$	−8.93621			−0.412636
$470$	−1.06863	+	0.539882i	−0.0492921	+	0.0249029i
$471$	−1.03624	+	0.909838i	−0.0477476	+	0.0419231i
$472$	−15.2886	−	2.58311i	−0.703716	−	0.118897i
$473$			7.20492i			0.331282i
$474$	5.92143	−	14.7203i	0.271980	−	0.676127i
$475$			1.37110i			0.0629105i
$476$	−8.90344	+	12.0793i	−0.408088	+	0.553654i
$477$	−30.2192	−	3.94240i	−1.38364	−	0.180510i
$478$	−3.65588	−	7.23636i	−0.167216	−	0.330983i
$479$	−15.9625			−0.729346			−0.364673	−	0.931136i	$-0.618819\pi$
$479$	−15.9625			−0.729346			−0.364673	+	0.931136i	$0.618819\pi$
$480$	−9.76502	−	0.802757i	−0.445710	−	0.0366407i
$481$	6.83945			0.311852
$482$	17.1947	+	34.0347i	0.783195	+	1.55024i
$483$	8.60147	+	9.79651i	0.391380	+	0.445757i
$484$	−24.7472	+	33.5746i	−1.12487	+	1.52612i
$485$		−	18.6630i		−	0.847445i
$486$	17.6574	+	13.1992i	0.800954	+	0.598726i
$487$		−	31.1973i		−	1.41369i	−0.707370	−	0.706843i	$-0.750119\pi$
$487$		−	31.1973i		−	1.41369i	0.707370	−	0.706843i	$-0.249881\pi$
$488$	19.1421	+	3.23418i	0.866524	+	0.146404i
$489$	18.0668	+	20.5769i	0.817008	+	0.930518i
$490$	−1.26227	+	0.637711i	−0.0570235	+	0.0288089i
$491$	12.1719			0.549311			0.274655	−	0.961543i	$-0.411436\pi$
$491$	12.1719			0.549311			0.274655	+	0.961543i	$0.411436\pi$
$492$	−22.0162	+	1.88371i	−0.992566	+	0.0849240i
$493$	32.9687			1.48484
$494$	2.78675	−	1.40789i	0.125382	−	0.0633442i
$495$	16.7897	+	2.19039i	0.754642	+	0.0984505i
$496$	14.6280	−	4.53191i	0.656819	−	0.203489i
$497$		−	11.3023i		−	0.506978i
$498$	4.32609	+	1.74022i	0.193857	+	0.0779812i
$499$		−	15.5693i		−	0.696978i	−0.937313	−	0.348489i	$-0.886695\pi$
$499$		−	15.5693i		−	0.696978i	0.937313	−	0.348489i	$-0.113305\pi$
$500$	1.60993	+	1.18665i	0.0719981	+	0.0530685i
$501$	−22.9370	+	20.1390i	−1.02475	+	0.899744i
$502$	10.0467	+	19.8862i	0.448407	+	0.887566i
$503$	−39.7268			−1.77133			−0.885664	−	0.464326i	$-0.846297\pi$
$503$	−39.7268			−1.77133			−0.885664	+	0.464326i	$0.846297\pi$
$504$	8.11353	+	2.48407i	0.361405	+	0.110649i
$505$	−13.8901			−0.618100
$506$	−27.0907	−	53.6226i	−1.20433	−	2.38381i
$507$	−13.5457	+	11.8933i	−0.601585	+	0.528200i
$508$	−5.72033	−	4.21635i	−0.253799	−	0.187071i
$509$		−	0.230794i		−	0.0102298i	−0.999987	−	0.00511488i	$-0.998372\pi$
$509$		−	0.230794i		−	0.0102298i	0.999987	−	0.00511488i	$-0.00162812\pi$
$510$	−17.0507	−	6.85886i	−0.755019	−	0.303715i
$511$			4.97379i			0.220028i
$512$	19.8343	+	10.8903i	0.876561	+	0.481290i
$513$	−5.91680	+	3.96855i	−0.261233	+	0.175216i
$514$	−25.0328	+	12.6468i	−1.10415	+	0.557827i
$515$	7.55760			0.333028
$516$	−4.40604	+	0.376982i	−0.193965	+	0.0165957i
$517$	−4.77817			−0.210144
$518$	−5.36163	+	2.70875i	−0.235577	+	0.119016i
$519$	−15.9958	−	18.2182i	−0.702140	−	0.799691i
$520$	0.758721	−	4.49065i	0.0332721	−	0.196928i
$521$		−	7.79231i		−	0.341387i	−0.985324	−	0.170694i	$-0.945399\pi$
$521$		−	7.79231i		−	0.341387i	0.985324	−	0.170694i	$-0.0546009\pi$
$522$	−6.18325	−	17.5872i	−0.270634	−	0.769769i
$523$		−	7.38460i		−	0.322906i	−0.986880	−	0.161453i	$-0.948382\pi$
$523$		−	7.38460i		−	0.322906i	0.986880	−	0.161453i	$-0.0516180\pi$
$524$	2.73104	−	3.70521i	0.119306	−	0.161863i
$525$	−1.14278	−	1.30156i	−0.0498752	−	0.0568045i
$526$	3.61738	+	7.16015i	0.157725	+	0.312197i
$527$	28.7252			1.25129
$528$	−33.3395	−	20.4329i	−1.45092	−	0.889226i
$529$	33.6523			1.46314
$530$	−6.47814	−	12.8227i	−0.281393	−	0.556981i
$531$	−2.12750	+	16.3077i	−0.0923256	+	0.707693i
$532$	−1.62702	+	2.20738i	−0.0705402	+	0.0957019i
$533$		−	10.2710i		−	0.444884i
$534$	−6.13833	+	15.2595i	−0.265632	+	0.660345i
$535$			17.5622i			0.759281i
$536$	−4.21075	+	24.9222i	−0.181877	+	1.07648i
$537$	14.3741	−	12.6206i	0.620287	−	0.544621i
$538$	6.78759	−	3.42916i	0.292634	−	0.147842i
$539$	−5.64400			−0.243104
$540$	−0.461008	+	10.3821i	−0.0198386	+	0.446773i
$541$	1.84582			0.0793582			0.0396791	−	0.999212i	$-0.487366\pi$
$541$	1.84582			0.0793582			0.0396791	+	0.999212i	$0.487366\pi$
$542$	17.3867	−	8.78393i	0.746822	−	0.377302i
$543$	−2.25729	+	1.98194i	−0.0968698	+	0.0850530i
$544$	29.4927	+	30.5226i	1.26449	+	1.30865i
$545$		−	11.4817i		−	0.491821i
$546$	−1.47195	+	3.65917i	−0.0629935	+	0.156598i
$547$			24.2245i			1.03576i	0.855452	+	0.517882i	$0.173279\pi$
$547$			24.2245i			1.03576i	−0.855452	+	0.517882i	$0.826721\pi$
$548$	8.39447	+	6.18741i	0.358594	+	0.264313i
$549$	2.66373	−	20.4180i	0.113685	−	0.871420i
$550$	3.59924	+	7.12425i	0.153472	+	0.303779i
$551$	6.02472			0.256662
$552$	31.3745	−	19.3725i	1.33539	−	0.824549i
$553$	−6.47755			−0.275453
$554$	2.08686	+	4.13067i	0.0886620	+	0.175495i
$555$	−4.85410	−	5.52850i	−0.206045	−	0.234672i
$556$	−8.57144	−	6.31785i	−0.363510	−	0.267937i
$557$			41.4429i			1.75599i	0.478666	+	0.877997i	$0.341120\pi$
$557$			41.4429i			1.75599i	−0.478666	+	0.877997i	$0.658880\pi$
$558$	−5.38739	−	15.3235i	−0.228066	−	0.648694i
$559$		−	2.05550i		−	0.0869385i
$560$	1.18373	+	3.82084i	0.0500218	+	0.161460i
$561$	−48.3934	−	55.1169i	−2.04317	−	2.32704i
$562$	−14.9138	+	7.53462i	−0.629102	+	0.317829i
$563$	37.7575			1.59129			0.795644	−	0.605764i	$-0.207132\pi$
$563$	37.7575			1.59129			0.795644	+	0.605764i	$0.207132\pi$
$564$	−0.250007	−	2.92201i	−0.0105272	−	0.123039i
$565$	−14.1781			−0.596476
$566$	−13.3228	+	6.73081i	−0.559999	+	0.282917i
$567$	2.30898	−	8.69877i	0.0969681	−	0.365314i
$568$	−31.5210	−	5.32566i	−1.32259	−	0.223460i
$569$		−	7.64737i		−	0.320594i	−0.987069	−	0.160297i	$-0.948755\pi$
$569$		−	7.64737i		−	0.320594i	0.987069	−	0.160297i	$-0.0512453\pi$
$570$	−3.11586	−	1.25339i	−0.130509	−	0.0524987i
$571$		−	8.53962i		−	0.357372i	−0.983906	−	0.178686i	$-0.942815\pi$
$571$		−	8.53962i		−	0.357372i	0.983906	−	0.178686i	$-0.0571846\pi$
$572$	10.7841	−	14.6308i	0.450907	−	0.611746i
$573$	0.256804	−	0.225477i	0.0107281	−	0.00941944i
$574$	4.06780	+	8.05169i	0.169787	+	0.336071i
$575$	−7.52677			−0.313888
$576$	10.7509	−	21.4573i	0.447956	−	0.894056i
$577$	3.35139			0.139520			0.0697600	−	0.997564i	$-0.477777\pi$
$577$	3.35139			0.139520			0.0697600	+	0.997564i	$0.477777\pi$
$578$	25.0590	+	49.6011i	1.04232	+	2.06313i
$579$	−5.79260	+	5.08599i	−0.240732	+	0.211366i
$580$	5.21421	−	7.07413i	0.216508	−	0.293737i
$581$		−	1.90366i		−	0.0789769i
$582$	42.4121	+	17.0608i	1.75804	+	0.707192i
$583$		−	57.3341i		−	2.37454i
$584$	13.8714	+	2.34366i	0.574004	+	0.0969813i
$585$	−4.78997	−	0.624899i	−0.198041	−	0.0258364i
$586$	−9.28580	+	4.69128i	−0.383593	+	0.193795i
$587$	19.8065			0.817502			0.408751	−	0.912646i	$-0.365964\pi$
$587$	19.8065			0.817502			0.408751	+	0.912646i	$0.365964\pi$
$588$	−0.295310	−	3.45149i	−0.0121784	−	0.142337i
$589$	5.24926			0.216292
$590$	−6.91971	+	3.49591i	−0.284880	+	0.143924i
$591$	−13.8259	−	15.7468i	−0.568722	−	0.647736i
$592$	5.02803	+	16.2294i	0.206651	+	0.667026i
$593$		−	20.8867i		−	0.857715i	−0.903372	−	0.428858i	$-0.858916\pi$
$593$		−	20.8867i		−	0.857715i	0.903372	−	0.428858i	$-0.141084\pi$
$594$	−20.3260	+	36.1526i	−0.833984	+	1.48336i
$595$			7.50301i			0.307593i
$596$	−28.0363	−	20.6651i	−1.14841	−	0.846474i
$597$	−5.88904	−	6.70723i	−0.241023	−	0.274509i
$598$	7.72874	+	15.2981i	0.316052	+	0.625585i
$599$	−10.6095			−0.433491			−0.216746	−	0.976228i	$-0.569544\pi$
$599$	−10.6095			−0.433491			−0.216746	+	0.976228i	$0.569544\pi$
$600$	−4.16839	+	2.57382i	−0.170174	+	0.105076i
$601$	1.32334			0.0539803			0.0269902	−	0.999636i	$-0.491408\pi$
$601$	1.32334			0.0539803			0.0269902	+	0.999636i	$0.491408\pi$
$602$	0.814078	+	1.61137i	0.0331794	+	0.0656744i
$603$	26.5834	+	3.46806i	1.08256	+	0.141231i
$604$	−6.43382	−	4.74226i	−0.261789	−	0.192960i
$605$			20.8547i			0.847865i
$606$	12.6976	−	31.5654i	0.515803	−	1.28226i
$607$			4.42087i			0.179438i	0.995967	+	0.0897189i	$0.0285969\pi$
$607$			4.42087i			0.179438i	−0.995967	+	0.0897189i	$0.971403\pi$
$608$	5.38950	+	5.57771i	0.218573	+	0.226206i
$609$	−5.71912	+	5.02147i	−0.231750	+	0.203480i
$610$	8.66382	−	4.37705i	0.350788	−	0.177221i
$611$	1.36317			0.0551480
$612$	31.1737	−	32.4781i	1.26012	−	1.31285i
$613$	−13.4458			−0.543072			−0.271536	−	0.962428i	$-0.587532\pi$
$613$	−13.4458			−0.543072			−0.271536	+	0.962428i	$0.587532\pi$
$614$	21.1055	−	10.6627i	0.851749	−	0.430312i
$615$	−8.30228	+	7.28952i	−0.334780	+	0.293942i
$616$	−2.65946	+	15.7406i	−0.107153	+	0.634205i
$617$			36.0695i			1.45210i	0.687640	+	0.726052i	$0.258647\pi$
$617$			36.0695i			1.45210i	−0.687640	+	0.726052i	$0.741353\pi$
$618$	−6.90876	+	17.1748i	−0.277911	+	0.690871i
$619$		−	26.0493i		−	1.04701i	−0.852022	−	0.523506i	$-0.824624\pi$
$619$		−	26.0493i		−	1.04701i	0.852022	−	0.523506i	$-0.175376\pi$
$620$	4.54308	−	6.16360i	0.182454	−	0.247536i
$621$	−21.7856	−	32.4807i	−0.874228	−	1.30341i
$622$	−17.3138	−	34.2705i	−0.694220	−	1.37412i
$623$	6.71482			0.269023
$624$	9.51149	+	5.82932i	0.380764	+	0.233360i
$625$	1.00000			0.0400000
$626$	8.47369	+	16.7726i	0.338677	+	0.670368i
$627$	−8.84344	−	10.0721i	−0.353173	−	0.402241i
$628$	0.944761	−	1.28176i	0.0377001	−	0.0511477i
$629$			31.8699i			1.27074i
$630$	4.00248	−	1.40718i	0.159463	−	0.0560635i
$631$			7.04647i			0.280516i	0.990115	+	0.140258i	$0.0447931\pi$
$631$			7.04647i			0.280516i	−0.990115	+	0.140258i	$0.955207\pi$
$632$	−3.05223	+	18.0652i	−0.121411	+	0.718597i
$633$	−6.43613	−	7.33033i	−0.255813	−	0.291354i
$634$	17.1476	−	8.66313i	0.681017	−	0.344057i
$635$	−3.55316			−0.141003
$636$	35.0617	−	2.99988i	1.39029	−	0.118953i
$637$	1.61019			0.0637979
$638$	31.3044	−	15.8153i	1.23935	−	0.626134i
$639$	−4.38632	+	33.6220i	−0.173520	+	1.33007i
$640$	11.2137	−	1.50093i	0.443261	−	0.0593293i
$641$		−	27.8101i		−	1.09843i	−0.835680	−	0.549216i	$-0.814926\pi$
$641$		−	27.8101i		−	1.09843i	0.835680	−	0.549216i	$-0.185074\pi$
$642$	−39.9105	−	16.0545i	−1.57514	−	0.633619i
$643$		−	35.3461i		−	1.39391i	−0.717114	−	0.696956i	$-0.754537\pi$
$643$		−	35.3461i		−	1.39391i	0.717114	−	0.696956i	$-0.245463\pi$
$644$	−12.1176	−	8.93163i	−0.477499	−	0.351956i
$645$	−1.66152	+	1.45883i	−0.0654221	+	0.0574415i
$646$	6.56039	+	12.9855i	0.258115	+	0.510907i
$647$	−36.9247			−1.45166			−0.725829	−	0.687875i	$-0.758544\pi$
$647$	−36.9247			−1.45166			−0.725829	+	0.687875i	$0.758544\pi$
$648$	−23.1720	−	10.5384i	−0.910283	−	0.413987i
$649$	−30.9402			−1.21451
$650$	−1.02683	−	2.03249i	−0.0402757	−	0.0797207i
$651$	−4.98300	+	4.37514i	−0.195299	+	0.171475i
$652$	−25.4521	−	18.7603i	−0.996779	−	0.734708i
$653$			7.80266i			0.305342i	0.988277	+	0.152671i	$0.0487874\pi$
$653$			7.80266i			0.305342i	−0.988277	+	0.152671i	$0.951213\pi$
$654$	26.0923	+	10.4959i	1.02029	+	0.410424i
$655$		−	2.30148i		−	0.0899261i
$656$	24.3721	−	7.55071i	0.951572	−	0.294806i
$657$	1.93029	−	14.7960i	0.0753076	−	0.577247i
$658$	−1.06863	+	0.539882i	−0.0416595	+	0.0210468i
$659$	37.0951			1.44502			0.722509	−	0.691361i	$-0.242989\pi$
$659$	37.0951			1.44502			0.722509	+	0.691361i	$0.242989\pi$
$660$	−19.4802	+	1.66673i	−0.758266	+	0.0648774i
$661$	9.20519			0.358041			0.179020	−	0.983845i	$-0.442707\pi$
$661$	9.20519			0.358041			0.179020	+	0.983845i	$0.442707\pi$
$662$	25.0571	−	12.6591i	0.973871	−	0.492009i
$663$	13.8062	+	15.7244i	0.536190	+	0.610685i
$664$	−5.30911	−	0.897005i	−0.206033	−	0.0348105i
$665$			1.37110i			0.0531691i
$666$	17.0010	−	5.97717i	0.658775	−	0.231611i
$667$			33.0731i			1.28060i
$668$	20.9120	−	28.3713i	0.809110	−	1.09772i
$669$	3.53468	+	4.02576i	0.136659	+	0.155645i
$670$	5.69872	+	11.2799i	0.220161	+	0.435781i
$671$	38.7386			1.49549
$672$	−9.76502	−	0.802757i	−0.376694	−	0.0309670i
$673$	12.5907			0.485334			0.242667	−	0.970110i	$-0.421978\pi$
$673$	12.5907			0.485334			0.242667	+	0.970110i	$0.421978\pi$
$674$	−4.77914	−	9.45970i	−0.184085	−	0.364374i
$675$	2.89442	+	4.31536i	0.111406	+	0.166098i
$676$	12.3498	−	16.7550i	0.474993	−	0.644423i
$677$			2.99651i			0.115165i	0.998341	+	0.0575827i	$0.0183393\pi$
$677$			2.99651i			0.115165i	−0.998341	+	0.0575827i	$0.981661\pi$
$678$	12.9608	−	32.2199i	0.497758	−	1.23740i
$679$		−	18.6630i		−	0.716222i
$680$	20.9252	+	3.53543i	0.802443	+	0.135578i
$681$	10.9373	−	9.60314i	0.419120	−	0.367993i
$682$	27.2751	−	13.7797i	1.04442	−	0.527651i
$683$	−22.5880			−0.864307			−0.432154	−	0.901800i	$-0.642246\pi$
$683$	−22.5880			−0.864307			−0.432154	+	0.901800i	$0.642246\pi$
$684$	5.69670	−	5.93505i	0.217819	−	0.226932i
$685$	5.21419			0.199224
$686$	−1.26227	+	0.637711i	−0.0481937	+	0.0243479i
$687$	−16.8450	+	14.7901i	−0.642676	+	0.564278i
$688$	4.87753	−	1.51111i	0.185954	−	0.0576104i
$689$			16.3569i			0.623150i
$690$	6.88058	−	17.1047i	0.261939	−	0.651166i
$691$		−	31.7749i		−	1.20877i	−0.796692	−	0.604386i	$-0.793418\pi$
$691$		−	31.7749i		−	1.20877i	0.796692	−	0.604386i	$-0.206582\pi$
$692$	22.5346	+	16.6098i	0.856636	+	0.631411i
$693$	16.7897	+	2.19039i	0.637789	+	0.0832059i
$694$	−18.7700	−	37.1529i	−0.712500	−	1.41030i
$695$	−5.32412			−0.201955
$696$	11.3095	+	18.3162i	0.428686	+	0.694273i
$697$	47.8598			1.81282
$698$	−16.7437	−	33.1420i	−0.633758	−	1.25444i
$699$	−11.3420	−	12.9178i	−0.428995	−	0.488597i
$700$	1.60993	+	1.18665i	0.0608495	+	0.0448511i
$701$			13.8310i			0.522390i	0.965286	+	0.261195i	$0.0841166\pi$
$701$			13.8310i			0.522390i	−0.965286	+	0.261195i	$0.915883\pi$
$702$	5.79883	−	10.3140i	0.218863	−	0.389278i
$703$			5.82392i			0.219653i
$704$	42.6457	+	14.8339i	1.60727	+	0.559075i
$705$	−0.967472	−	1.10189i	−0.0364371	−	0.0414995i
$706$	24.3004	−	12.2768i	0.914556	−	0.462043i
$707$	−13.8901			−0.522390
$708$	−1.61888	−	18.9209i	−0.0608411	−	0.711092i
$709$	6.25095			0.234760			0.117380	−	0.993087i	$-0.462551\pi$
$709$	6.25095			0.234760			0.117380	+	0.993087i	$0.462551\pi$
$710$	−14.2666	+	7.20761i	−0.535414	+	0.270497i
$711$	19.2694	+	2.51388i	0.722657	+	0.0942778i
$712$	3.16403	−	18.7270i	0.118577	−	0.701823i
$713$			28.8162i			1.07918i
$714$	−17.0507	−	6.85886i	−0.638107	−	0.256686i
$715$		−	9.08788i		−	0.339868i
$716$	−13.1051	+	17.7797i	−0.489759	+	0.664457i
$717$	7.46158	−	6.55137i	0.278658	−	0.244665i
$718$	2.45442	+	4.85821i	0.0915980	+	0.181307i
$719$	−37.9713			−1.41609			−0.708045	−	0.706168i	$-0.750422\pi$
$719$	−37.9713			−1.41609			−0.708045	+	0.706168i	$0.750422\pi$
$720$	−2.03852	−	11.8256i	−0.0759712	−	0.440713i
$721$	7.55760			0.281460
$722$	−10.9177	−	21.6101i	−0.406313	−	0.804246i
$723$	−35.0939	+	30.8129i	−1.30516	+	1.14595i
$724$	2.05801	−	2.79211i	0.0764854	−	0.103768i
$725$		−	4.39407i		−	0.163192i
$726$	−47.3927	−	19.0643i	−1.75891	−	0.707542i
$727$		−	11.1370i		−	0.413047i	−0.978442	−	0.206523i	$-0.933785\pi$
$727$		−	11.1370i		−	0.413047i	0.978442	−	0.206523i	$-0.0662150\pi$
$728$	0.758721	−	4.49065i	0.0281201	−	0.166434i
$729$	−10.2447	+	24.9809i	−0.379432	+	0.925220i
$730$	6.27827	−	3.17185i	0.232369	−	0.117395i
$731$	9.57806			0.354257
$732$	2.02691	+	23.6899i	0.0749169	+	0.875605i
$733$	−7.08138			−0.261557			−0.130778	−	0.991412i	$-0.541748\pi$
$733$	−7.08138			−0.261557			−0.130778	+	0.991412i	$0.541748\pi$
$734$	−11.4286	+	5.77385i	−0.421838	+	0.213117i
$735$	−1.14278	−	1.30156i	−0.0421522	−	0.0480086i
$736$	−30.6192	+	29.5861i	−1.12864	+	1.09056i
$737$			50.4360i			1.85783i
$738$	−8.97606	−	25.5308i	−0.330413	−	0.939801i
$739$			26.4674i			0.973620i	0.873508	+	0.486810i	$0.161840\pi$
$739$			26.4674i			0.973620i	−0.873508	+	0.486810i	$0.838160\pi$
$740$	6.83835	+	5.04043i	0.251383	+	0.185290i
$741$	2.52296	+	2.87348i	0.0926832	+	0.105560i
$742$	−6.47814	−	12.8227i	−0.237820	−	0.470735i
$743$	−22.6733			−0.831801			−0.415900	−	0.909410i	$-0.636534\pi$
$743$	−22.6733			−0.831801			−0.415900	+	0.909410i	$0.636534\pi$
$744$	9.85384	+	15.9587i	0.361259	+	0.585073i
$745$	−17.4146			−0.638023
$746$	4.40181	+	8.71282i	0.161162	+	0.318999i
$747$	−0.738792	+	5.66298i	−0.0270310	+	0.207198i
$748$	68.1756	+	50.2510i	2.49275	+	1.83736i
$749$			17.5622i			0.641710i
$750$	−0.914147	+	2.27252i	−0.0333799	+	0.0829806i
$751$		−	27.4574i		−	1.00193i	−0.865467	−	0.500967i	$-0.832978\pi$
$751$		−	27.4574i		−	1.00193i	0.865467	−	0.500967i	$-0.167022\pi$
$752$	1.00214	+	3.23469i	0.0365442	+	0.117957i
$753$	−20.5051	+	18.0038i	−0.747249	+	0.656095i
$754$	−8.93089	+	4.51197i	−0.325244	+	0.164316i
$755$	−3.99634			−0.145442
$756$	−0.461008	+	10.3821i	−0.0167667	+	0.377592i
$757$	−40.8860			−1.48603			−0.743013	−	0.669276i	$-0.766604\pi$
$757$	−40.8860			−1.48603			−0.743013	+	0.669276i	$0.766604\pi$
$758$	13.6273	−	6.88466i	0.494967	−	0.250062i
$759$	55.2915	−	48.5467i	2.00695	−	1.76213i
$760$	3.82387	+	0.646066i	0.138706	+	0.0234353i
$761$			22.5747i			0.818334i	0.912460	+	0.409167i	$0.134181\pi$
$761$			22.5747i			0.818334i	−0.912460	+	0.409167i	$0.865819\pi$
$762$	3.24811	−	8.07462i	0.117667	−	0.292513i
$763$		−	11.4817i		−	0.415664i
$764$	−0.234132	+	0.317647i	−0.00847060	+	0.0114921i
$765$	2.91185	−	22.3199i	0.105278	−	0.806977i
$766$	17.4346	+	34.5095i	0.629936	+	1.24688i
$767$	8.82697			0.318723
$768$	−6.84010	+	26.8554i	−0.246821	+	0.969061i
$769$	−14.9174			−0.537935			−0.268967	−	0.963149i	$-0.586682\pi$
$769$	−14.9174			−0.537935			−0.268967	+	0.963149i	$0.586682\pi$
$770$	3.59924	+	7.12425i	0.129708	+	0.256740i
$771$	−22.6632	−	25.8119i	−0.816195	−	0.929592i
$772$	5.28121	−	7.16502i	0.190075	−	0.257875i
$773$		−	51.7299i		−	1.86060i	−0.366805	−	0.930298i	$-0.619548\pi$
$773$		−	51.7299i		−	1.86060i	0.366805	−	0.930298i	$-0.380452\pi$
$774$	−1.79636	−	5.10941i	−0.0645687	−	0.183654i
$775$		−	3.82849i		−	0.137524i
$776$	−52.0494	−	8.79405i	−1.86846	−	0.315688i
$777$	−4.85410	−	5.52850i	−0.174140	−	0.198334i
$778$	−29.5884	+	14.9484i	−1.06080	+	0.535926i
$779$	8.74591			0.313355
$780$	5.55754	−	0.475504i	0.198992	−	0.0170258i
$781$	−63.7902			−2.28259
$782$	−71.2847	+	36.0138i	−2.54914	+	1.28785i
$783$	18.9620	−	12.7183i	0.677646	−	0.454514i
$784$	1.18373	+	3.82084i	0.0422761	+	0.136458i
$785$		−	0.796159i		−	0.0284161i
$786$	5.23014	+	2.10389i	0.186553	+	0.0750432i
$787$			3.52895i			0.125794i	0.998020	+	0.0628968i	$0.0200339\pi$
$787$			3.52895i			0.125794i	−0.998020	+	0.0628968i	$0.979966\pi$
$788$	19.4776	+	14.3566i	0.693861	+	0.511433i
$789$	−7.38300	+	6.48238i	−0.262842	+	0.230779i
$790$	4.13080	+	8.17641i	0.146967	+	0.290904i
$791$	−14.1781			−0.504114
$792$	14.0201	−	45.7928i	0.498183	−	1.62717i
$793$	−11.0518			−0.392461
$794$	−21.8336	−	43.2169i	−0.774846	−	1.53371i
$795$	13.2218	−	11.6089i	0.468927	−	0.411725i
$796$	8.29635	+	6.11509i	0.294056	+	0.216744i
$797$			38.1364i			1.35086i	0.737424	+	0.675431i	$0.236042\pi$
$797$			38.1364i			1.35086i	−0.737424	+	0.675431i	$0.763958\pi$
$798$	−3.11586	−	1.25339i	−0.110300	−	0.0443695i
$799$			6.35199i			0.224717i
$800$	4.06805	−	3.93078i	0.143827	−	0.138974i
$801$	−19.9752	−	2.60596i	−0.705788	−	0.0920771i
$802$	−22.1148	+	11.1726i	−0.780901	+	0.394519i
$803$	28.0721			0.990643
$804$	−30.8433	+	2.63895i	−1.08776	+	0.0930687i
$805$	−7.52677			−0.265284
$806$	−7.78137	+	3.93123i	−0.274087	+	0.138471i
$807$	6.14508	+	6.99884i	0.216317	+	0.246371i
$808$	−6.54502	+	38.7380i	−0.230253	+	1.36280i
$809$		−	1.51683i		−	0.0533288i	−0.999644	−	0.0266644i	$-0.991511\pi$
$809$		−	1.51683i		−	0.0533288i	0.999644	−	0.0266644i	$-0.00848855\pi$
$810$	−12.4527	+	2.63275i	−0.437542	+	0.0925054i
$811$		−	1.44010i		−	0.0505686i	−0.999680	−	0.0252843i	$-0.991951\pi$
$811$		−	1.44010i		−	0.0505686i	0.999680	−	0.0252843i	$-0.00804910\pi$
$812$	5.21421	−	7.07413i	0.182983	−	0.248253i
$813$	15.7409	+	17.9278i	0.552056	+	0.628756i
$814$	15.2882	+	30.2611i	0.535851	+	1.06065i
$815$	−15.8094			−0.553781
$816$	−27.1630	+	44.3209i	−0.950895	+	1.55154i
$817$	1.75030			0.0612352
$818$	−13.8803	−	27.4743i	−0.485313	−	0.960615i
$819$	−4.78997	−	0.624899i	−0.167375	−	0.0218357i
$820$	7.56932	−	10.2693i	0.264332	−	0.358620i
$821$		−	42.7409i		−	1.49167i	−0.666132	−	0.745834i	$-0.732051\pi$
$821$		−	42.7409i		−	1.49167i	0.666132	−	0.745834i	$-0.267949\pi$
$822$	−4.76654	+	11.8493i	−0.166252	+	0.413293i
$823$			37.0701i			1.29218i	0.763261	+	0.646090i	$0.223597\pi$
$823$			37.0701i			1.29218i	−0.763261	+	0.646090i	$0.776403\pi$
$824$	3.56115	−	21.0774i	0.124059	−	0.734266i
$825$	−7.34598	+	6.44987i	−0.255754	+	0.224556i
$826$	−6.91971	+	3.49591i	−0.240767	+	0.121638i
$827$	38.1185			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$827$	38.1185			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$828$	32.5809	+	31.2725i	1.13226	+	1.08679i
$829$	39.6263			1.37628			0.688140	−	0.725578i	$-0.258428\pi$
$829$	39.6263			1.37628			0.688140	+	0.725578i	$0.258428\pi$
$830$	−2.40293	+	1.21398i	−0.0834068	+	0.0421380i
$831$	−4.25923	+	3.73966i	−0.147751	+	0.129727i
$832$	−12.1665	−	4.23200i	−0.421796	−	0.146718i
$833$			7.50301i			0.259964i
$834$	4.86702	−	12.0991i	0.168531	−	0.418959i
$835$		−	17.6227i		−	0.609860i
$836$	12.4584	+	9.18289i	0.430884	+	0.317597i
$837$	16.5213	−	11.0813i	0.571061	−	0.383025i
$838$	−15.8846	−	31.4415i	−0.548723	−	1.08613i
$839$	7.30233			0.252105			0.126052	−	0.992024i	$-0.459769\pi$
$839$	7.30233			0.252105			0.126052	+	0.992024i	$0.459769\pi$
$840$	−4.16839	+	2.57382i	−0.143823	+	0.0888051i
$841$	9.69218			0.334213
$842$	−20.3975	−	40.3743i	−0.702944	−	1.39139i
$843$	−13.5021	−	15.3780i	−0.465037	−	0.529646i
$844$	9.06707	+	6.68317i	0.312101	+	0.230044i
$845$		−	10.4073i		−	0.358022i
$846$	3.38847	−	1.19131i	0.116498	−	0.0409581i
$847$			20.8547i			0.716577i
$848$	−38.8137	+	12.0248i	−1.33287	+	0.412935i
$849$	−12.0617	−	13.7374i	−0.413955	−	0.471468i
$850$	9.47082	−	4.78476i	0.324847	−	0.164116i
$851$	−31.9708			−1.09595
$852$	−3.33768	−	39.0098i	−0.114347	−	1.33645i
$853$	40.0413			1.37099			0.685494	−	0.728079i	$-0.259586\pi$
$853$	40.0413			1.37099			0.685494	+	0.728079i	$0.259586\pi$
$854$	8.66382	−	4.37705i	0.296470	−	0.149779i
$855$	0.532113	−	4.07875i	0.0181979	−	0.139490i
$856$	48.9793	+	8.27535i	1.67408	+	0.282846i
$857$			29.9523i			1.02315i	0.859238	+	0.511575i	$0.170938\pi$
$857$			29.9523i			1.02315i	−0.859238	+	0.511575i	$0.829062\pi$
$858$	20.6524	+	8.30766i	0.705060	+	0.283619i
$859$			3.90809i			0.133342i	0.997775	+	0.0666712i	$0.0212379\pi$
$859$			3.90809i			0.133342i	−0.997775	+	0.0666712i	$0.978762\pi$
$860$	1.51483	−	2.05517i	0.0516553	−	0.0700808i
$861$	−8.30228	+	7.28952i	−0.282941	+	0.248426i
$862$	−24.7696	−	49.0284i	−0.843657	−	1.66991i
$863$	3.15695			0.107464			0.0537320	−	0.998555i	$-0.482888\pi$
$863$	3.15695			0.107464			0.0537320	+	0.998555i	$0.482888\pi$
$864$	28.7374	+	6.17775i	0.977665	+	0.210171i
$865$	13.9973			0.475921
$866$	21.1017	+	41.7682i	0.717065	+	1.41934i
$867$	−51.1448	+	44.9059i	−1.73697	+	1.52508i
$868$	4.54308	−	6.16360i	0.154202	−	0.209206i
$869$			36.5593i			1.24019i
$870$	9.98559	+	4.01682i	0.338543	+	0.136183i
$871$		−	14.3890i		−	0.487551i
$872$	−32.0212	−	5.41018i	−1.08438	−	0.183212i
$873$	−7.24296	+	55.5187i	−0.245137	+	1.87902i
$874$	−13.0266	+	6.58117i	−0.440631	+	0.222611i
$875$	1.00000			0.0338062
$876$	1.46881	+	17.1670i	0.0496265	+	0.580020i
$877$	−44.2616			−1.49461			−0.747305	−	0.664482i	$-0.768652\pi$
$877$	−44.2616			−1.49461			−0.747305	+	0.664482i	$0.768652\pi$
$878$	8.22542	−	4.15557i	0.277595	−	0.140244i
$879$	−8.40681	−	9.57481i	−0.283555	−	0.322950i
$880$	21.5648	−	6.68098i	0.726949	−	0.225216i
$881$			18.5472i			0.624869i	0.949939	+	0.312435i	$0.101145\pi$
$881$			18.5472i			0.624869i	−0.949939	+	0.312435i	$0.898855\pi$
$882$	4.00248	−	1.40718i	0.134770	−	0.0473823i
$883$			16.9885i			0.571709i	0.958273	+	0.285854i	$0.0922774\pi$
$883$			16.9885i			0.571709i	−0.958273	+	0.285854i	$0.907723\pi$
$884$	−19.4499	−	14.3362i	−0.654171	−	0.482178i
$885$	−6.26469	−	7.13507i	−0.210585	−	0.239843i
$886$	15.2851	+	30.2550i	0.513513	+	1.01644i
$887$	5.98747			0.201040			0.100520	−	0.994935i	$-0.467949\pi$
$887$	5.98747			0.201040			0.100520	+	0.994935i	$0.467949\pi$
$888$	−17.7057	+	10.9326i	−0.594165	+	0.366873i
$889$	−3.55316			−0.119169
$890$	−4.28212	−	8.47591i	−0.143537	−	0.284113i
$891$	−49.0959	−	13.0319i	−1.64477	−	0.436585i
$892$	−4.97957	−	3.67035i	−0.166728	−	0.122893i
$893$			1.16077i			0.0388435i
$894$	15.9196	−	39.5751i	0.532429	−	1.32359i
$895$			11.0438i			0.369152i
$896$	11.2137	−	1.50093i	0.374624	−	0.0501424i
$897$	−15.7742	+	13.8500i	−0.526685	+	0.462437i
$898$	−33.3130	+	16.8301i	−1.11167	+	0.561627i
$899$	−16.8227			−0.561067
$900$	−4.32867	−	4.15483i	−0.144289	−	0.138494i
$901$	−76.2188			−2.53922
$902$	45.4437	−	22.9586i	1.51311	−	0.764439i
$903$	−1.66152	+	1.45883i	−0.0552918	+	0.0485470i
$904$	−6.68073	+	39.5412i	−0.222198	+	1.31512i
$905$		−	1.73431i		−	0.0576503i
$906$	3.65325	−	9.08176i	0.121371	−	0.301721i
$907$		−	39.4692i		−	1.31055i	−0.755388	−	0.655277i	$-0.772552\pi$
$907$		−	39.4692i		−	1.31055i	0.755388	−	0.655277i	$-0.227448\pi$
$908$	−9.97175	+	13.5287i	−0.330924	+	0.448965i
$909$	41.3200	+	5.39061i	1.37050	+	0.178795i
$910$	−1.02683	−	2.03249i	−0.0340392	−	0.0673763i
$911$	−29.7901			−0.986990			−0.493495	−	0.869749i	$-0.664281\pi$
$911$	−29.7901			−0.986990			−0.493495	+	0.869749i	$0.664281\pi$
$912$	−4.96378	+	8.09922i	−0.164367	+	0.268192i
$913$	−10.7442			−0.355582
$914$	−3.17845	−	6.29134i	−0.105134	−	0.208099i
$915$	7.84370	+	8.93346i	0.259305	+	0.295331i
$916$	15.3578	−	20.8360i	0.507437	−	0.688440i
$917$		−	2.30148i		−	0.0760014i
$918$	48.0605	+	27.0209i	1.58623	+	0.891823i
$919$		−	1.20183i		−	0.0396447i	−0.999804	−	0.0198223i	$-0.993690\pi$
$919$		−	1.20183i		−	0.0396447i	0.999804	−	0.0198223i	$-0.00631006\pi$
$920$	−3.54662	+	20.9914i	−0.116929	+	0.692067i
$921$	19.1077	+	21.7624i	0.629619	+	0.717095i
$922$	6.91477	−	3.49341i	0.227726	−	0.115049i
$923$	18.1988			0.599021
$924$	−19.4802	+	1.66673i	−0.640852	+	0.0548314i
$925$	4.24761			0.139661
$926$	−10.7646	+	5.43840i	−0.353748	+	0.178717i
$927$	−22.4823	−	2.93304i	−0.738416	−	0.0963337i
$928$	−17.2721	−	17.8753i	−0.566984	−	0.586784i
$929$		−	52.6765i		−	1.72826i	−0.503268	−	0.864131i	$-0.667869\pi$
$929$		−	52.6765i		−	1.72826i	0.503268	−	0.864131i	$-0.332131\pi$
$930$	8.70032	+	3.49981i	0.285295	+	0.114763i
$931$			1.37110i			0.0449361i
$932$	15.9784	+	11.7774i	0.523390	+	0.385781i
$933$	35.3371	−	31.0265i	1.15688	−	1.01576i
$934$	−12.7858	−	25.3079i	−0.418365	−	0.828101i
$935$	42.3470			1.38489
$936$	−3.99982	+	13.0643i	−0.130738	+	0.427020i
$937$	−10.6682			−0.348513			−0.174257	−	0.984700i	$-0.555752\pi$
$937$	−10.6682			−0.348513			−0.174257	+	0.984700i	$0.555752\pi$
$938$	5.69872	+	11.2799i	0.186070	+	0.368302i
$939$	−17.2946	+	15.1849i	−0.564388	+	0.495541i
$940$	1.36295	+	1.00461i	0.0444546	+	0.0327667i
$941$			8.36206i			0.272595i	0.990668	+	0.136298i	$0.0435203\pi$
$941$			8.36206i			0.272595i	−0.990668	+	0.136298i	$0.956480\pi$
$942$	1.80929	+	0.727807i	0.0589497	+	0.0237132i
$943$			48.0113i			1.56346i
$944$	6.48916	+	20.9457i	0.211204	+	0.681723i
$945$	2.89442	+	4.31536i	0.0941555	+	0.140379i
$946$	9.09455	−	4.59466i	0.295689	−	0.149385i
$947$	−14.7027			−0.477774			−0.238887	−	0.971047i	$-0.576783\pi$
$947$	−14.7027			−0.477774			−0.238887	+	0.971047i	$0.576783\pi$
$948$	−22.3572	+	1.91288i	−0.726128	+	0.0621276i
$949$	−8.00873			−0.259974
$950$	1.73070	−	0.874368i	0.0561514	−	0.0283682i
$951$	15.5244	+	17.6813i	0.503413	+	0.573354i
$952$	20.9252	+	3.53543i	0.678188	+	0.114584i
$953$		−	13.8304i		−	0.448012i	−0.974588	−	0.224006i	$-0.928086\pi$
$953$		−	13.8304i		−	0.448012i	0.974588	−	0.224006i	$-0.0719135\pi$
$954$	14.2948	+	40.6589i	0.462810	+	1.31638i
$955$			0.197305i			0.00638465i
$956$	−6.80284	+	9.22942i	−0.220020	+	0.298501i
$957$	28.3412	+	32.2787i	0.916140	+	1.04342i
$958$	10.1795	+	20.1490i	0.328884	+	0.650984i
$959$	5.21419			0.168375
$960$	5.21397	+	12.8380i	0.168280	+	0.414345i
$961$	16.3426			0.527182
$962$	−4.36159	−	8.63322i	−0.140623	−	0.278346i
$963$	6.81575	−	52.2440i	0.219634	−	1.68354i
$964$	31.9957	−	43.4086i	1.03051	−	1.39810i
$965$		−	4.45052i		−	0.143267i
$966$	6.88058	−	17.1047i	0.221379	−	0.550335i
$967$			47.2859i			1.52061i	0.649566	+	0.760305i	$0.274951\pi$
$967$			47.2859i			1.52061i	−0.649566	+	0.760305i	$0.725049\pi$
$968$	58.1618	+	9.82677i	1.86939	+	0.315844i
$969$	−13.3896	+	11.7563i	−0.430137	+	0.377666i
$970$	−23.5578	+	11.9016i	−0.756395	+	0.382139i
$971$	43.3157			1.39007			0.695034	−	0.718977i	$-0.255389\pi$
$971$	43.3157			1.39007			0.695034	+	0.718977i	$0.255389\pi$
$972$	5.40059	−	30.7056i	0.173224	−	0.984882i
$973$	−5.32412			−0.170683
$974$	−39.3794	+	19.8949i	−1.26180	+	0.637474i
$975$	2.09574	−	1.84009i	0.0671175	−	0.0589301i
$976$	−8.12475	−	26.2250i	−0.260067	−	0.839442i
$977$		−	13.1574i		−	0.420942i	−0.977600	−	0.210471i	$-0.932500\pi$
$977$		−	13.1574i		−	0.420942i	0.977600	−	0.210471i	$-0.0674997\pi$
$978$	14.4522	−	35.9272i	0.462129	−	1.14883i
$979$		−	37.8984i		−	1.21124i
$980$	1.60993	+	1.18665i	0.0514272	+	0.0379061i
$981$	−4.45594	+	34.1556i	−0.142267	+	1.09050i
$982$	−7.76217	−	15.3642i	−0.247701	−	0.490292i
$983$	−9.02748			−0.287932			−0.143966	−	0.989583i	$-0.545986\pi$
$983$	−9.02748			−0.287932			−0.143966	+	0.989583i	$0.545986\pi$
$984$	16.4177	+	26.5891i	0.523377	+	0.847629i
$985$	12.0984			0.385488
$986$	−21.0245	−	41.6154i	−0.669558	−	1.32531i
$987$	−0.967472	−	1.10189i	−0.0307950	−	0.0350734i
$988$	−3.55428	−	2.61980i	−0.113077	−	0.0833469i
$989$			9.60839i			0.305529i
$990$	−7.94214	−	22.5900i	−0.252418	−	0.717957i
$991$		−	21.8477i		−	0.694014i	−0.937863	−	0.347007i	$-0.887198\pi$
$991$		−	21.8477i		−	0.694014i	0.937863	−	0.347007i	$-0.112802\pi$
$992$	−15.0490	−	15.5745i	−0.477805	−	0.494490i
$993$	22.6852	+	25.8369i	0.719893	+	0.819910i
$994$	−14.2666	+	7.20761i	−0.452508	+	0.228611i
$995$	5.15325			0.163369
$996$	−0.562169	−	6.57045i	−0.0178130	−	0.208193i
$997$	33.6089			1.06441			0.532203	−	0.846617i	$-0.321364\pi$
$997$	33.6089			1.06441			0.532203	+	0.846617i	$0.321364\pi$
$998$	−19.6527	+	9.92872i	−0.622094	+	0.314288i
$999$	12.2944	+	18.3300i	0.388977	+	0.579935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.9	yes	24
3.2	odd	2		420.2.n.a.71.16	yes	24
4.3	odd	2		420.2.n.a.71.15	✓	24
12.11	even	2	inner	420.2.n.b.71.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.15	✓	24	4.3	odd	2
420.2.n.a.71.16	yes	24	3.2	odd	2
420.2.n.b.71.9	yes	24	1.1	even	1	trivial
420.2.n.b.71.10	yes	24	12.11	even	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.637711 - 1.26227i) q^{2} +(1.30156 - 1.14278i) q^{3} +(-1.18665 + 1.60993i) q^{4} +1.00000i q^{5} +(-2.27252 - 0.914147i) q^{6} +1.00000i q^{7} +(2.78890 + 0.471201i) q^{8} +(0.388091 - 2.97479i) q^{9} +O(q^{10})\)	\(q+(-0.637711 - 1.26227i) q^{2} +(1.30156 - 1.14278i) q^{3} +(-1.18665 + 1.60993i) q^{4} +1.00000i q^{5} +(-2.27252 - 0.914147i) q^{6} +1.00000i q^{7} +(2.78890 + 0.471201i) q^{8} +(0.388091 - 2.97479i) q^{9} +(1.26227 - 0.637711i) q^{10} +5.64400 q^{11} +(0.295310 + 3.45149i) q^{12} -1.61019 q^{13} +(1.26227 - 0.637711i) q^{14} +(1.14278 + 1.30156i) q^{15} +(-1.18373 - 3.82084i) q^{16} -7.50301i q^{17} +(-4.00248 + 1.40718i) q^{18} -1.37110i q^{19} +(-1.60993 - 1.18665i) q^{20} +(1.14278 + 1.30156i) q^{21} +(-3.59924 - 7.12425i) q^{22} +7.52677 q^{23} +(4.16839 - 2.57382i) q^{24} -1.00000 q^{25} +(1.02683 + 2.03249i) q^{26} +(-2.89442 - 4.31536i) q^{27} +(-1.60993 - 1.18665i) q^{28} +4.39407i q^{29} +(0.914147 - 2.27252i) q^{30} +3.82849i q^{31} +(-4.06805 + 3.93078i) q^{32} +(7.34598 - 6.44987i) q^{33} +(-9.47082 + 4.78476i) q^{34} -1.00000 q^{35} +(4.32867 + 4.15483i) q^{36} -4.24761 q^{37} +(-1.73070 + 0.874368i) q^{38} +(-2.09574 + 1.84009i) q^{39} +(-0.471201 + 2.78890i) q^{40} +6.37874i q^{41} +(0.914147 - 2.27252i) q^{42} +1.27656i q^{43} +(-6.69744 + 9.08643i) q^{44} +(2.97479 + 0.388091i) q^{45} +(-4.79991 - 9.50081i) q^{46} -0.846593 q^{47} +(-5.90708 - 3.62028i) q^{48} -1.00000 q^{49} +(0.637711 + 1.26227i) q^{50} +(-8.57432 - 9.76558i) q^{51} +(1.91072 - 2.59228i) q^{52} -10.1584i q^{53} +(-3.60134 + 6.40549i) q^{54} +5.64400i q^{55} +(-0.471201 + 2.78890i) q^{56} +(-1.56687 - 1.78457i) q^{57} +(5.54650 - 2.80215i) q^{58} -5.48196 q^{59} +(-3.45149 + 0.295310i) q^{60} +6.86368 q^{61} +(4.83259 - 2.44147i) q^{62} +(2.97479 + 0.388091i) q^{63} +(7.55594 + 2.62827i) q^{64} -1.61019i q^{65} +(-12.8261 - 5.15945i) q^{66} +8.93621i q^{67} +(12.0793 + 8.90344i) q^{68} +(9.79651 - 8.60147i) q^{69} +(0.637711 + 1.26227i) q^{70} -11.3023 q^{71} +(2.48407 - 8.11353i) q^{72} +4.97379 q^{73} +(2.70875 + 5.36163i) q^{74} +(-1.30156 + 1.14278i) q^{75} +(2.20738 + 1.62702i) q^{76} +5.64400i q^{77} +(3.65917 + 1.47195i) q^{78} +6.47755i q^{79} +(3.82084 - 1.18373i) q^{80} +(-8.69877 - 2.30898i) q^{81} +(8.05169 - 4.06780i) q^{82} -1.90366 q^{83} +(-3.45149 + 0.295310i) q^{84} +7.50301 q^{85} +(1.61137 - 0.814078i) q^{86} +(5.02147 + 5.71912i) q^{87} +(15.7406 + 2.65946i) q^{88} -6.71482i q^{89} +(-1.40718 - 4.00248i) q^{90} -1.61019i q^{91} +(-8.93163 + 12.1176i) q^{92} +(4.37514 + 4.98300i) q^{93} +(0.539882 + 1.06863i) q^{94} +1.37110 q^{95} +(-0.802757 + 9.76502i) q^{96} -18.6630 q^{97} +(0.637711 + 1.26227i) q^{98} +(2.19039 - 16.7897i) 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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